Answer:
The solution to the differential equation
y' = 1 + y²
is
y = tan x
Step-by-step explanation:
Given the differential equation
y' = 1 + y²
This can be written as
dy/dx = 1 + y²
Separate the variables
dy/(1 + y²) = dx
Integrate both sides
tan^(-1)y = x + c
y = tan(x+c)
Using the initial condition
y(0) = 0
0 = tan(0 + c)
tan c = 0
c = tan^(-1) 0 = 0
y = tan x
In this exercise we have to use our knowledge of differential equations to calculate the value of the first solution, so we have to:
[tex]y = tan x[/tex]
Then say the differential equation as:
[tex]y' = 1 + y^2[/tex]
then rewriting as:
[tex]dy/dx = 1 + y^2\\dy/(1 + y^2) = dx[/tex]
Integrate both sides, we have that:
[tex]tan^{(-1)}y = x + c\\y = tan(x+c)[/tex]
So we already have a preview of the solution, so we will have to apply the initial conditions and this results in:
[tex]y(0) = 0\\0 = tan(0 + c)\\tan c = 0\\c = tan^{(-1)} 0 = 0\\y = tan x[/tex]
See more about differential equations at brainly.com/question/2263981
26 POINTS!!! BRAINLIEST TOO.
Answer:
Therefore option A.) 0 is correct.
Step-by-step explanation:
The graph is attached.
The solution of the equations as seen from the intersection of the equations in the graph is (0,2).
Therefore x = 0 is the solution which gives y = 2 for both equations.
Therefore option A.) 0 is correct.
Haun and Wendy are 200 feet apart when they begin walking directly toward one another. Ian travels at a constant speed of 2.5 feet per second and Carolyn travels at a constant speed of 4.5 feet per second.
Let t represent the number of seconds that have elapsed since Ian and Carolyn started walking toward one another.
A) write an expression in terms of t that represent the number of feet Ian has traveled since he started walking toward Carolyn.
B) write an expression in terms of t that represents the number of feet Carolyn has traveled since she started walking toward ian.
C) write an expression in terms of t that represents the distance between Ian and Carolyn.
D) how many seconds after the two started walking will they reach each other?
Answer:
A) [tex]d_{I}=2.5t[/tex]
B)[tex]d_{C}=4.5t[/tex]
C) d=200-7t
D) t=28.57s
Step-by-step explanation:
A) in order to solve this part of the problem, we must remember that velocity is the ratio between a displacement and the time it takes for a body to go from one point to the other. So we can write it like this:
[tex]v=\frac{x}{t}[/tex]
when solvin for the distance x, we get the formula to be:
[tex]x=vt[/tex]
We can use this to write the expression they are asking us for, so we get:
[tex]d_{I}=2.5t[/tex]
B) the procedure for part b is the same as the procedure for par A with the difference that Carolyn's speed is different. So by using the same formula with Carolyn's speed we get:
[tex]d_{C}=4.5t[/tex]
C)
In order to find the distance between Ian and Carolyn, we subtract the distances found on the previous two questions from the 200ft, so we get:
[tex]d=200-d_{I}-d_{c}[/tex]
we can further substitute the d's with the equations we found on the previos two parts of the problem, so we get:
[tex]d=200-2.5t-4.5t[/tex]
which simplififfes to the following:
d=200-7t
D) we can figure the seconds out by substituing the distance for 0 and solving for t, so we get:
0=200-7t
which can be solved for t, lke this:
-7t=-200
[tex]t=\frac{-200}{-7}=28.57[/tex]
Six friends are going to the state fair. The cost of one admission is $9.50, and the cost for one ride on the Ferris wheel is $1.50. Write two equivalent expressions and then find the total cost.
Answer:
The two equivalent expression are [tex]T=6(9.5+1.5)[/tex] and [tex]T=6\times9.5+6\times1.5[/tex].
The Total cost at state fair will be $66.
Step-by-step explanation:
Given:
Number of friends = 6
Cost for admission for each at the fair = $9.50
Cost of each person ride on Ferris wheel = $1.50
We need to find the two equivalent expressions and then find the total cost.
Solution:
Let the Total Cost be denote by 'T'.
So we can say that;
Total Cost will be equal to Number of friends multiplied by sum of Cost for admission for each at the fair and Cost of each person ride on Ferris wheel.
framing in equation form we get;
[tex]T=6(9.5+1.5)[/tex]
Now Applying Distributive property we get;
[tex]T=6\times9.5+6\times1.5[/tex]
Hence The two equivalent expression are [tex]T=6(9.5+1.5)[/tex] and [tex]T=6\times9.5+6\times1.5[/tex].
On Solving the above equation we get;
[tex]T=57+9= \$66[/tex]
Hence The Total cost to state fair will be $66.
What is the best answer
Answer:
The answer to your question is letter A
Step-by-step explanation:
The first inequality is a circle with center (0,0) and radius 4, the inequality indicates that the solution must be greater than the radius (4) so the solutions are letters A and D.
The second inequality is the line, the solutions must be the numbers below the line, areas A and B.
The region where both inequalities cross is the solution letter A.
which inequality represents all values of x for which the quotient below is defined?
[tex]\sqrt{7x^2 divided by \sqrt{3x}
\\A. x \ \textgreater \ 1 \\B. x \ \textgreater \ -1\\C. x \ \textgreater \ 0\\D. x \geq 0[/tex]
Answer:
C. x>0
Step-by-step explanation:
The given quotient is
[tex] \frac{ \sqrt{7 {x}^{2} } }{ \sqrt{3x} } [/tex]
Recall that the expression in the denominator should not be equal to zero.
Also the expression under the radical should be greater than or equal to zero.
This means that we should have:
[tex] \frac{7 {x}^{2} }{3x} \: > \: 0[/tex]
This implies that:
[tex]x \: > \: 0[/tex]
Option C is correct
Find the x-intercepts of the parabola with
vertex (1,-13) and y-intercept (0.-11).
Write your answer in this form: (X1.),(X2,92).
If necessary, round to the nearest hundredth.
Enter the correct answer.
Answer:
[tex]x_1=3.55[/tex]
[tex]x_2=-1.55[/tex]
Step-by-step explanation:
we know that
If the vertex is (1,-13) and the y-intercept is (0.-11) (y-intercept above the vertex), we have a vertical parabola open upward
The equation of a vertical parabola written in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is a coefficient
(h,k) is the vertex
substitute the given value of the vertex
[tex]y=a(x-1)^2-13[/tex]
Find the value of a
Remember that we have the y-intercept
For x=0, y=-11
substitute
[tex]-11=a(0-1)^2-13[/tex]
[tex]a=13-11\\a=2[/tex]
so
[tex]y=2(x-1)^2-13[/tex]
Find the x-intercepts
For y=0
[tex]2(x-1)^2-13=0[/tex]
[tex]2(x-1)^2=13[/tex]
[tex](x-1)^2=6.5[/tex]
[tex]x-1=\pm\sqrt{6.5}[/tex]
[tex]x=1\pm\sqrt{6.5}[/tex]
[tex]x_1=1+\sqrt{6.5}=3.55[/tex]
[tex]x_2=1-\sqrt{6.5}=-1.55[/tex]
If a hurricane was headed your way, would you evacuate? The headline of a press release issued January 21, 2009 by the survey research company International Communications Research (icrsurvey) states, "Thirty- one Percent of People on High-Risk Coast Will Refuse Evacuation Order, Survey of Hurricane Preparedness Finds." This headline was based on a survey of 5046 adults who live within 20 miles of the coast in high hur- ricane risk counties of eight southern states. In selecting the sample, care was taken to ensure that the sample would be representative of the population of coastal resi- dents in these states.
Use this information to estimate the proportion of coastal residents who would evacuate using a 98% confidence interval.
Write a few sentences interpreting the interval and the confidence level assosiated with the interval.
Answer:
The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].
Step-by-step explanation:
The sample drawn is of size, n = 5046.
As the sample size is large, i.e. n > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean [tex]\hat p[/tex] and standard deviation [tex]\sqrt{\frac{\hat p (1-\hat p)}{n} }[/tex].
The mean is: [tex]\hat p=0.31[/tex]
The confidence level (CL) = 98%
The confidence interval for single proportion is:
[tex]CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }][/tex]
Here [tex]z_{(\alpha /2)}[/tex] = critical value and α = significance level.
Compute the value of α as follows:
[tex]\alpha =1-CL\\=1-0.98\\=0.02[/tex]
For α = 0.02 the critical value can be computed from the z table.
Then the value of [tex]z_{(\alpha /2)}[/tex] is ± 2.33.
The 98% confidence interval for population proportion is:
[tex]CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]\\=[0.31-2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} },\ 0.31+2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} } ]\\=[0.31-0.0152,\ 0.31+0.0152]\\=[0.2948,0.3252]\\\approx[0.30,\ 0.33][/tex]
Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.
Final answer:
The 98% confidence interval for the proportion of coastal residents who would evacuate is between approximately 67.49% and 70.51%. This reflects our confidence that the true proportion falls within this range, with only a 2% chance of being outside these bounds.
Explanation:
To estimate the proportion of coastal residents who would evacuate using a 98% confidence interval based on the available survey data, we look at the reported figure that 31% of the people will refuse to evacuate, which implies that 69% would evacuate. The sample size is 5046 adults. To calculate the 98% confidence interval for the true proportion, we use the formula for the confidence interval of a proportion:
Confidence interval = p ± Z*sqrt((p(1-p))/n)
where:
p is the sample proportion (0.69 in this case),
Z is the Z-score associated with the confidence level (2.326 for 98% confidence),
sqrt denotes the square root function,
n is the sample size.
Plugging the values into the formula, we get:
Confidence interval = 0.69 ± 2.326 * sqrt((0.69(1-0.69))/5046)
Performing these calculations:
Confidence interval = 0.69 ± 2.326 * sqrt(0.2141/5046)
Confidence interval = 0.69 ± 2.326 * sqrt(0.0000424451086)
Confidence interval = 0.69 ± 2.326 * 0.0065134
Confidence interval = 0.69 ± 0.015143
So the 98% confidence interval for the proportion of coastal residents who would evacuate is approximately 0.6749 to 0.7051, or 67.49% to 70.51%.
Interpreting this confidence interval at the 98% confidence level means that we can be 98% confident that the true proportion of all coastal residents in these high-risk areas who would evacuate falls between 67.49% and 70.51%. This does not mean that the true proportion is within this interval with 100% certainty, but rather that there's a 2% chance that the true proportion lies outside of this interval.
There was 1/4 watermelon in the refrigerator. Mom brought home 1/2 watermelon from the grocery store. What fractional part of the watermelon did the family have for supper
Answer:
The family would have [tex]\frac34[/tex] of the watermelon for supper.
Step-by-step explanation:
Given:
Amount of watermelon in refrigerator = [tex]\frac14[/tex]
Amount of water melon brought form grocery store =[tex]\frac12[/tex]
We need to find the fraction of water melon family have for supper.
Solution:
Now we can say that;
the fraction of water melon family have for supper is equal to sum of Amount of watermelon in refrigerator and Amount of water melon brought form grocery store.
framing in equation form we get;
the fraction of water melon family have for supper = [tex]\frac14+\frac12[/tex]
Now taking LCM to make the denominator common we get;
the fraction of water melon family have for supper = [tex]\frac{1\times1}{4\times1}+\frac{1\times2}{2\times2}=\frac{1}{4}+\frac24[/tex]
Now denominators are common so we will solve for numerator we get;
the fraction of water melon family have for supper = [tex]\frac{1+2}{4}=\frac34[/tex]
Hence the family would have [tex]\frac34[/tex] of the watermelon for supper.
What is the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang?
Answer:
17 cm is the side length of the smallest square plate.
Step-by-step explanation:
Length of the square = l
Length of the diagonal = d
Length of chopstick = s = 24 cm
If chopstick is to be fitted along a diagonal . then length of the diagonal will be:
d = s = 24 cm
Applying Pythagoras Theorem :
[tex]l^2+l^2=(24 cm)^2[/tex]
[tex]2l^2=576 cm[/tex]
[tex]l^2=\frac{576}{2} cm^2[/tex]
[tex]l=\sqrt{\frac{576}{2} cm^2}=16,97 cm \approx 17 cm[/tex]
17 cm is the side length of the smallest square plate.
Final answer:
To determine the size of the smallest square plate that a 24-cm chopstick can fit diagonally on without overhang, the Pythagorean theorem is used, yielding a side length of approximately 16.97 cm.
Explanation:
The question asks for the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang. To find this, we can use the Pythagorean theorem in the context of a square. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In the case of a square, the hypotenuse is the diagonal, and the other two sides are equal, each being the side length of the square.
Let's denote the side length of the square as s. The diagonal (d) is then given as d = 24 cm. According to the Pythagorean theorem applied to a square, this can be written as √(2*s²) = d, because the diagonal divides the square into two equal right-angled triangles. Solving for s, we get s = √(d² / 2). Substituting 24 cm for d gives:
s = √(24² / 2)
s = √(576 / 2)
s = √(288)
s = 16.97 cm (approximately)
Therefore, the side length of the smallest square plate on which a 24-cm chopstick can fit along a diagonal without any overhang is approximately 16.97 cm.
GEOMETRY HELP !!!!!!!!!What is the sequence of transformations that
maps A ABC to A A'B'C' ?
Select from the drop-down menus to correctly
identify each step.
Step 1: Choose ...
Reflect across the y-axis
Reflect across the line y = x.
Rotate 180 degrees about to origin.
Rotate 90 degrees clockwise about the origin.
Step 2: Choose...
Translate 1 units right.
Translate 2 units right.
Translate 4 units down.
Reflect across the x-axis.
The sequence of transformations is: reflect across the x-axis, rotate 180 degrees about the origin, and translate 4 units down.
Explanation:The sequence of transformations that maps triangle ABC to triangle A'B'C' is:
Reflect across the x-axisRotate 180 degrees about the originTranslate 4 units downLearn more about Sequences of Transformations here:https://brainly.com/question/27885960
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Danny has a coin collection. 20% of his collection are quarters. If Danny has 13 quarters, how many coins does he have in his collection altogether? A) 26 B) 39 C) 42 D) 65
Answer: Danny had 65 coins altogether in his collection.
Step-by-step explanation:
Let x represent the number of coins that Danny has in his collection.
20% of his collection are quarters. This means that the number of quarters that Danny has in his collection is
20/100 × x = 0.2 × x = 0.2x
If Danny has 13 quarters, it means that
0.2x = 13
Dividing the left hand side and the right hand side of the equation by 0.2, it becomes
0.2x/0.2 = 13/0.2
x = 65
Need some help doing this question, thanks!
Answer:
y = -5x + 6
Step-by-step explanation:
y = 1/5 x + 4/5
so that two lines are perpendicular, its slope must be opposite and reciprocal
y = m x + b
m: slope perpendicular -1/m
if our formula is y = 1/5 x + 4/5
m = 1/5
so the slope of our new formula will be
m' = -5/1
m' = -5
now if you tell us that you have to go through a certain point (1/1)
we just have to replace the values in the following formula and solve
y - y1 = m ( x - x1)
y - 1 = -5 ( x - 1)
y = -5x + 5 + 1
y = -5x + 6
Triangle ABE is similar to triangle ACD. Find y.
3.4
2.7
4.5
2.1
Answer:
Step-by-step explanation:
∆ ABE is similar to angle ACD. This means that the ratio of the length of each side of ∆ABE to the length of the corresponding side of ∆ ACD is constant. Therefore,
AB/AC = BE/CD = AE/AD
Therefore,
5/3 = (y + 3)/y
Cross multiplying, it becomes
5 × y = 3(y + 3)
5y = 3y + 9
5y - 3y = 9
2y = 9
Dividing the left hand side and the right hand side of the equation by 2, it becomes
2y/2 = 9/2
y = 4.5
Answer:
y = 4.5.
Step-by-step explanation:
Triangles ABE and ACD are similar, so their corresponding sides are in the same ratio.
AB/AC = AE / AD
Now AD = y + ED = y + 3, so:
3/5 = y / (y + 3)
5y = 3y + 9
2y = 9
y = 4.5.
An isosceles triangle in which the two equal sides, labeled x, are longer than side y. The isosceles triangle has a perimeter of 7.5 m. Which equation can be used to find the value of x if the shortest side, y, measures 2.1 m?
The equation to find the value of x in an isosceles triangle with a perimeter of 7.5 m and a side y measuring 2.1 m is 2x + 2.1 = 7.5. Solving for x, we find that x equals 2.7 meters.
To find the value of x for an isosceles triangle with a perimeter of 7.5 meters and the shortest side y measuring 2.1 meters, we can set up an equation. Since it's an isosceles triangle, the two equal sides are both x, and the perimeter is the sum of all sides: x + x + y = 7.5.
We can substitute y with 2.1 m to get 2x + 2.1 = 7.5. Solving for x, we subtract 2.1 from both sides to obtain 2x = 5.4, and then divide both sides by 2 to find x = 2.7 meters. This is the length of the two equal sides of the triangle.
A committee of 9 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the probability that the proposal wins by a vote of 7 to 2?
Answer:
The required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].
Step-by-step explanation:
Consider the provided information.
A committee of 9 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis,
The probability of yea or nay vote is equal, = [tex]\frac{1}{2}[/tex]
So, we can say that [tex]p=q=\frac{1}{2}[/tex]
Use the formula: [tex]P(x)=\binom{n}{x}p^xq^{n-x}[/tex]
Where n is the total number of trials, x is the number of successes, p is the probability of getting a success and q is the probability of failure.
We want proposal wins by a vote of 7 to 2, that means the value of x is 7.
Substitute the respective values in the above formula.
[tex]P(x)=\binom{9}{7}(\frac{1}{2})^7(\frac{1}{2})^{9-7}[/tex]
[tex]P(x)=\frac{9!}{7!2!}(\frac{1}{2})^7(\frac{1}{2})^{2}[/tex]
[tex]P(x)=\frac{8\times9}{2}\times(\frac{1}{2})^9[/tex]
[tex]P(x)=\frac{4\times9}{2^9}[/tex]
[tex]P(x)=\frac{9}{2^7}[/tex]
[tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex]
Hence, the required probability is [tex]P(x)=\frac{9}{128}[/tex] or [tex]P(x)=0.0703125[/tex].
Final answer:
The probability that a proposal wins by a 7 to 2 vote in a committee with 9 members is calculated using the binomial probability formula and is approximately 7.03%.
Explanation:
The question posed involves calculating the probability that a proposal wins by a vote of 7 to 2 in a committee with 9 members. We need to consider each vote as an independent 'yea' or 'nay' and find out the number of ways to get exactly 7 'yea' votes out of 9. This is a problem that can be solved using the binomial probability formula:
Binomial Probability Formula: P(X=k) = (n! / (k! * (n-k)!)) * p^k * (1-p)^(n-k), where 'n' is the total number of trials (or votes), 'k' is the number of successful outcomes need (yea votes), and 'p' is the probability of getting a yea vote. Since the voting is random, p = 0.5 assuming each member has an equal likely chance to vote yea or nay.
Plugging the values in, we get P(X=7) = (9! / (7! * 2!)) * 0.5^7 * 0.5^2. Calculating the factorials and powers of 0.5, the probability is:
P(X=7) = 36 * 0.5^9 = 36/512 = 0.0703125.
So, the probability that the proposal wins by a vote of 7 to 2 is approximately 7.03%.
John has finished compiling a list of the various members of the joint application development (JAD) group and the list is as follows: John is the JAD project leader, Tom is the representative from top management, Jennifer is a manager, Alen and Ian are users, Linda and Alex are systems analysts, and Clark is the recorder. There have been some rumblings within the firm that this development project is not necessary so John and others feel it is important to explain the reason for the project at the outset. Whose name goes next to this point on the agenda?
Answer:
d. His own
Step-by-step explanation:
John is the leader of the particular project team. He is in charge of delegating different tasks to his team members and also endure that everything is in order. He will also develop the necessary agenda and formulate the final report of the project. Therefore, the name that will be attached on the final tasks is his own.
Tom, the representative from top management, should be responsible for explaining the project's necessity, as his role allows him to address strategic concerns and ensure buy-in across the team.
Explanation:In the context of the Joint Application Development (JAD) group, explaining the reason for the project, especially given the internal skepticism about its necessity, is a pivotal responsibility that typically falls onto someone influential and with comprehensive knowledge of the project's goals and business impact. In this scenario, Tom, as the representative from top management, is the most suitable member to address this point on the agenda. Tom's position allows him to articulate the strategic importance of the project to the organization, reassuring the rest of the team and potentially quelling any concerns about its necessity. It is critical that this explanation is conveyed convincingly to ensure buy-in from all members of the team.
It is advantageous for team members to take on tasks that align with their strengths, as suggested in the reference material, but also to challenge themselves and learn by undertaking tasks outside their usual domain, with the support of their colleagues. This approach fosters a collaborative environment and harnesses the diverse skill sets of the team members, leading to a more efficient and innovative project outcome. To help manage this process, tools like the Honeycomb Map encourage the distribution of responsibilities and help with project visualization and tracking.
Newberg City Cafe recently introduced a new flavor of coffee. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equaled a total of 36,846 grams. The day before, 58 grande cups and 68 jumbo cups were served,which used a total of 59,460 grams. How much coffee is required to make each size?
Answer:
Grand coffee cup = 1469 gm
Jumbo coffee cup = 60 gm
Step-by-step explanation:
Let x be the grande coffee cup and y be the jumbo coffee cup.
Solution:
From the first statement. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equal a total of 36,846 grams.
So, the equation is.
[tex]23x+51y = 36846[/tex] ---------(1)
From the second statement. They served 58 grande cups and 68 jumbo cups of the new coffee tomorrow, which equal a total of 59460 grams.
[tex]58x+68y=59460[/tex] ----------(2)
Solve the equation 1 for x.
[tex]23x = 36846-51y[/tex]
[tex]x=\frac{36846}{23}-\frac{51}{23}y[/tex]
[tex]x=1602-\frac{51}{23}y[/tex] ---------(3)
Substitute [tex]x=1602-\frac{51}{23}y[/tex] in equation 2.
[tex]58(1602-\frac{51}{23}y)+68y=59460[/tex]
[tex]92916-\frac{51\times 58}{23}y+68y=59460[/tex]
[tex]-\frac{2958}{23}y+68y=59460-92916[/tex]
[tex]\frac{-2958+1564}{23}y=-33456[/tex]
[tex]\frac{-1394}{23}y=-33456[/tex]
Using cross multiplication.
[tex]y=\frac{-23\times 33456}{-1394}[/tex]
[tex]y = 55.99[/tex]
y ≅ 60 gram
Substitute y = 60 in equation 3.
[tex]x=1602-\frac{51}{23}\times 60[/tex]
[tex]x=1602-\frac{3060}{23}[/tex]
[tex]x=1602-133.04[/tex]
[tex]x = 1469[/tex] grams
Therefore, grand coffee cup = 1469 gm and jumbo coffee cup = 60 gm
Final answer:
The answer explains how to calculate the amount of coffee required to make each size (grande and jumbo cups) based on the given information. Answer is 722 grams
Explanation:
The coffee required to make each size:
To find the amount of coffee in a grande cup, use the information given:23 grande cups used 36,846 gramsEach grande cup's quantity = 36,846 grams ÷ 23 = 1,603 gramsCalculate the amount of coffee in a jumbo cup:51 jumbo cups used 36,846 gramsEach jumbo cup's quantity = 36,846 grams ÷ 51 = 722 gramsTo ascertain the amount of coffee needed for a jumbo cup, we look at the data indicating 51 jumbo cups utilizing the same 36,846 grams. Dividing this total by the number of jumbo cups, we find that each jumbo cup requires approximately 722 grams of coffee.
Thus, the calculation yields 722 grams of coffee for each jumbo cup, confirming the final answer.
Mr. C is such a mean teacher! The next time Mathias gets in trouble, Mr. C has designed a special detention for him. Mathias will have to go out into the hall and stand exactly meters away from the exit door and pause for a minute. Then he is allowed to walk exactly halfway to the door and pause for another minute. Then he can again walk exactly half the remaining distance to the door and pause again, and so on. Mr. C says that when Mathias reaches the door he can leave, unless he breaks the rules and goes more than halfway, even by a tiny amount. When can Mathias leave?
This is based on the mathematical concept of geometric series, where in theoretical terms Mathias would never reach the door because he keeps moving half the remaining distance each time. Although, in practical terms, there comes a point where the remaining distance becomes negligible.
Explanation:The situation you're describing is an example of a geometric series scenario in mathematics. In this case, where Mathias walks half the distance to the door each time, is often referred to as Zeno's paradox.
Zeno's paradox poses the question, how can one ever reach a destination if they are always traveling halfway there? Theoretically, Mathias is never able to fully reach the door, because no matter how small the remaining distance becomes, he is only allowed to cover half. Therefore, there will always technically be some distance remaining.
However, in practical terms, there would come a point where the distance remaining is so minuscule, it could be considered as Mathias having reached the door. For instance, if he started 10 meters away, after the first step he is 5 meters away, then 2.5 meters, then 1.25 meters, and so on. Eventually, this distance becomes negligible.
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Five hundred people attend a charity event, and each buys a raffle ticket. The 500 ticket stubs are put in a drum and thoroughly mixed. Next, 10 tickets are drawn. The 10 people whose tickets are drawn win a prize.This is which type of sample?
Answer:
The sample is a Simple Random sample.
explanation:
A simple random sample is the process where there is equal chance of selecting each member of a population to form a sample. in the example stated in the question there are equal chances of selecting every ticket among the five hundred ticket of the participant so as to form another set of ten tickets that win a prize.
PLEASE HELPPP!!! QUESTION AND ANSWERS IN PICTURE !!!
Samuel wants to eat at least 15 grams of protein each day. Let x represent the amount of protein he should eat each day to meet his goal. Which inequality represents this situation?
Answer:
X is greater than or equal to 15
Step-by-step explanation:
Final answer:
The inequality x >= 15 represents Samuel's goal of eating at least 15 grams of protein each day. Protein-rich foods like chicken breast and Greek yogurt are good sources of protein.
Explanation:
The inequality representing the situation is: x >= 15
To meet his goal of eating at least 15 grams of protein each day, Samuel should eat at least 15 grams of protein daily.
Examples of protein-rich foods include:
3 ounces of chicken breast: about 25 grams of protein
1 cup of Greek yogurt: approximately 20 grams of protein
A car is driving away from a crosswalk. The formula d = t2 + 2t expresses the car's distance from the crosswalk in feet, d, in terms of the number of seconds, t, since the car started moving. Suppose t varies from t=1to t=5. What is the car's average speed over this interval of time?
Average speed: 8 feet/second. Total distance traveled: 32 feet. Total time: 4 seconds (from[tex]\( t = 1 \)[/tex] to[tex]\( t = 5 \)).[/tex]
To find the average speed of the car over the interval from[tex]\( t = 1 \) to \( t = 5 \),[/tex] we need to find the total distance traveled by the car during this time interval and then divide it by the total time taken.
Given the formula [tex]\( d = t^2 + 2t \)[/tex] for the distance from the crosswalk in terms of time [tex]\( t \),[/tex] we'll find the distance at [tex]\( t = 1 \)[/tex] and[tex]\( t = 5 \),[/tex] and then subtract to find the total distance traveled:
1. At [tex]\( t = 1 \):[/tex]
[tex]\[ d_1 = (1)^2 + 2(1) = 1 + 2 = 3 \text{ feet} \][/tex]
2. At[tex]\( t = 5 \):[/tex]
[tex]\[ d_5 = (5)^2 + 2(5) = 25 + 10 = 35 \text{ feet} \][/tex]
Now, the total distance traveled is [tex]\( d_5 - d_1 = 35 - 3 = 32 \)[/tex] feet.
The total time taken is [tex]\( t = 5 - 1 = 4 \)[/tex] seconds.
To find the average speed, divide the total distance by the total time:
[tex]\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{32 \text{ feet}}{4 \text{ seconds}} = 8 \text{ feet/second} \][/tex]
So, the average speed of the car over the interval from [tex]\( t = 1 \) to \( t = 5 \) seconds is \( 8 \) feet per second.[/tex]
ary Egan needs to drain his 21 comma 000-gallon inground swimming pool to have it resurfaced. He uses two pumps to drain the pool. One drains 15 gallons of water a minute while the other drains 20 gallons of water a minute. If the pumps are turned on at the same time and remain on until the pool is drained, how long will it take for the pool to be drained?
Answer:
600 minutes = 10 hours
Step-by-step explanation:
Egan has to drain 21 000 ga of water out of the pool. Let the number of minutes it takes him to drain the pool be x minutes. The equation for determining x can be set up and solved as follows:
[tex]\frac{15 ga}{min}*xmin+\frac{20ga}{min}*xmin = 21000ga\\\\15x+20x=21000\\\\35x= 21000\\\\x = 600[/tex]
600 minutes = 10 hours
Please answer all three
Answer:
We conclude that the statement B is true. The solution is also attached below.
Step-by-step Explanation:
As the inequality graphed on the number line showing that solution must be < x (-∞, 3] U [5, ∞)
So, lets check the statements to know which statement has this solution.
Analyzing statement A)
[tex]x^2-3x+5>\:0[/tex]
[tex]\mathrm{Write}\:x^2-3x+5\:\mathrm{in\:the\:form:\:\:}x^2+2ax+a^2[/tex]
[tex]2a=-3\quad :\quad a=-\frac{3}{2}[/tex]
[tex]\mathrm{Add\:and\:subtract}\:\left(-\frac{3}{2}\right)^2\:[/tex]
[tex]x^2-3x+5+\left(-\frac{3}{2}\right)^2-\left(-\frac{3}{2}\right)^2[/tex]
[tex]\mathrm{Complete\:the\:square}[/tex]
[tex]\left(x-\frac{3}{2}\right)^2+5-\left(-\frac{3}{2}\right)^2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\left(x-\frac{3}{2}\right)^2+\frac{11}{4}[/tex]
So,
[tex]\left(x-\frac{3}{2}\right)^2>-\frac{11}{4}[/tex]
Thus,
[tex]x^2-3x+5>0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:\mathrm{True\:for\:all}\:x\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
Therefore, option A) is FALSE.
Analyzing statement B)
(x + 3) (x - 5) ≥ 0
[tex]x^2-2x-15\ge 0[/tex]
[tex]\left(x+3\right)\left(x-5\right)=0[/tex] [tex]\left(Factor\:left\:side\:of\:equation\right)[/tex]
[tex]x+3=0\:or\:x-5=0[/tex]
[tex]x=-3\:or\:x=5[/tex]
So
[tex]x\le \:-3\quad \mathrm{or}\quad \:x\ge \:5[/tex]
Thus,
[tex]\left(x+3\right)\left(x-5\right)\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-3\quad \mathrm{or}\quad \:x\ge \:5\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-3]\cup \:[5,\:\infty \:)\end{bmatrix}[/tex]
Therefore, the statement B is true.
Solution is also attached below.
Analyzing statement C)
[tex]x^2+2x-15\ge 0[/tex]
[tex]\mathrm{Factor}\:x^2+2x-15:\quad \left(x-3\right)\left(x+5\right)[/tex]
So,
[tex]x\le \:-5\quad \mathrm{or}\quad \:x\ge \:3[/tex]
[tex]x^2+2x-15\ge \:0\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:-5\quad \mathrm{or}\quad \:x\ge \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:-5]\cup \:[3,\:\infty \:)\end{bmatrix}[/tex]
Therefore, option C) is FALSE.
Analyzing statement D)
- 3 < x < 5
[tex]-3<x<5\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-3<x<5\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-3,\:5\right)\end{bmatrix}[/tex]
Therefore, option D) is FALSE.
Analyzing statement E)
None of the above
The statement E) is False also as the statement B represents the correct solution.
Therefore, from the discussion above, we conclude that the statement B is true. The solution is also attached below.
Question # 8Find the number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].
Answer:
Therefore, [tex]\frac{37}{36}[/tex] is the number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].
Step-by-step Explanation:
[tex]\mathrm{Convert\:mixed\:numbers\:to\:improper\:fraction:}\:a\frac{b}{c}=\frac{a\cdot \:c+b}{c}[/tex]
So,
[tex]2\frac{1}{6}=\frac{13}{6}[/tex]
[tex]5\frac{1}{4}=\frac{21}{4}[/tex]
As the length from [tex]\frac{21}{4}[/tex] to [tex]\frac{13}{6}[/tex] is
[tex]\frac{21}{4}-\frac{13}{6}=\frac{37}{12}[/tex]
Now Divide [tex]\frac{37}{12}[/tex] into 3 equal parts. So,
[tex]\frac{37}{12}\div \:3=\frac{37}{36}[/tex]
As we have to find number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex], it means it must have covered 2/3 of the way. As we have divided [tex]\frac{37}{12}[/tex] into 3 equal parts, which is [tex]\frac{37}{36}[/tex]
Therefore, [tex]\frac{37}{36}[/tex] is the number that is [tex]\frac{1}{3}[/tex] of the way from [tex]\:2\frac{1}{6}[/tex] to [tex]\:5\frac{1}{4}[/tex].
Question # 9Answer:
[tex]\left(2x+3\right)[/tex] is in the form [tex]dx+\:e[/tex].
Step-by-step Explanation:
Considering the expression
[tex]2x^2+11x+12[/tex]
Factor
[tex]2x^2+11x+12[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]
[tex]\left(2x^2+3x\right)+\left(8x+12\right)[/tex]
[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2+3x\mathrm{:\quad }x\left(2x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}4\mathrm{\:from\:}8x+12\mathrm{:\quad }4\left(2x+3\right)[/tex]
[tex]x\left(2x+3\right)+4\left(2x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}2x+3[/tex]
[tex]\left(2x+3\right)\left(x+4\right)[/tex]
Therefore, [tex]\left(2x+3\right)[/tex] is in the form [tex]dx+\:e[/tex].
Keywords: factor, ratio, solution
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Plsss help!! Work this travel problem based on the data provided in the table. Choose the correct answer.
What percentage increase occurs in the price of a round-trip economy ship fare from New York to London by electing to go in peak season economy air fare as opposed to a 30-day excursion fare?
41.1
52.1
34.3
Answer:
option 2
52.1
Step-by-step explanation:
Peak season economy air fare: $526.30
30-day excrusion ship fare: $345.95
To know the percentage with respect, we only have to put the most expensive value divided by the smallest value multiplied by one hundred, this will tell us what percentage you have with each other
526.30 / 345.95 * 100 =
1.5213 * 100 =
152.13
Now to know only the percentage that increased, we have to subtract 100 that would be the base value
152.13 - 100 = 52.13
52.1
Determine what type of observational study is described. Explain. Vitamin D is important for the metabolism of calcium and exposure to sunshine is an important source of vitamin D. A researcher wanted to determine whether osteoperosis was associated with a lack of exposure to sunshine. He selected a sample of 250 women with opteoperosis and an equal number of women without osteoperosis. The two groups were matched in other words they were similar in terms of age, diet, occupation, and exercise levels. Histories on exposure to sunshine over the previous twenty years were obtained for all women. The total number of hours that each woman had been exposed to sunshine in the previous twenty years was estimated. The amount of exposure to sunshine was compared for the two groups. a.cohort; Individuals are observed over a long period of time. b.cross-sectional; Information is collected at a specific point in time. c.retrospective; Individuals are asked to look back in time Question 15 4 pts
Answer:
thats too long to read but good luck!
Step-by-step explanation:
50 POINTS
A two-sided coin is flipped and a six-sided die is rolled. 'Die' is the singular version of the plural word 'dice.' How many ways can one coin flip and one die roll be done?
12 ways can one coin flip and one die roll be done.
What does a math probability mean?The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur.'Die' is the singular version of the plural word 'dice.'
when we flip coin we got
Heads: 1,2,3,4,5,6
Tails:1,2,3,4,5,6
so total flips are 12 ways.
or we can do in other way 6 × 2 = 12 ways
Therefore , 12 ways can one coin flip and one die roll be done.
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Mrs.Rodriquez is measuring fabric for costumes. She needs 58 feet of fabric. She has 10 1/3 yards of fabric. How many more yards of fabric does she need?
Answer:
9 yards
Step-by-step explanation:
Given data:
Needed fabric = 58feet
Available fabric = 10 1/3 yards
To convert yard to feet, the yards are multiplied by 3
10 1/3 yards = 31/3 * 3 = 31 feet.
More fabric needed = 58 - 31
More fabric needed = 27 feet
More fabric needed in yards = 27/3
More fabric needed in yards = 9
Answer:
9
Step-by-step explanation:
it's nine because 1 yard has three feet and um well like yeah
Racheal has a board that is 1 7/12 feet long and another board that is 2 11/12 feet long. Write an expression Racheal can use to find the total length I feet of the two boards
Racheal can use the expression [tex]\(4 \frac{1}{2}\)[/tex] feet to find the total length of the two boards.
To find the total length of the two boards, Racheal needs to add the lengths of the two boards together.
The length of the first board is [tex]\(1 \frac{7}{12}\)[/tex] feet, and the length of the second board is [tex]\(2 \frac{11}{12}\)[/tex] feet.
To add these lengths together, we first need to convert them to improper fractions:
[tex]\[ 1 \frac{7}{12} = \frac{12}{12} + \frac{7}{12} = \frac{19}{12} \][/tex]
[tex]\[ 2 \frac{11}{12} = \frac{24}{12} + \frac{11}{12} = \frac{35}{12} \][/tex]
Now, to find the total length, we add the lengths of the two boards:
[tex]\[ \text{Total length} = \frac{19}{12} + \frac{35}{12} \][/tex]
To add fractions, we need a common denominator, which in this case is [tex]\(12\)[/tex].
[tex]\[ \text{Total length} = \frac{19}{12} + \frac{35}{12} = \frac{19 + 35}{12} = \frac{54}{12} \][/tex]
Now, we simplify the fraction:
[tex]\[ \text{Total length} = \frac{54}{12} = 4 \frac{1}{2} \][/tex]
So, Racheal can use the expression [tex]\(4 \frac{1}{2}\)[/tex] feet to find the total length of the two boards.
Aliens have injected Ana with mathematical nanobots. These nanobots force Ana to think about math more and more. Initially, there were only five nanobots. The population of the nanobots doubles every hour. The population of the nanobots follows the equations p(t) = 5·2^t. After there are 106nanobots, Ana will cease thinking of anything other than math. How many hours will it take for math to take over Ana's brain?
Answer:
Math will take over Ana's brain at 4.4 hours
Step-by-step explanation:
Exponential Grow
The population of the nanobots follows the equation
[tex]p(t) = 5\cdot 2^t[/tex]
We must find the value of t such that the population of nanobots is 106 or more, that is
[tex]5\cdot 2^t\geq 106[/tex]
We'll solve the equation
[tex]5\cdot2^t= 106[/tex]
Dividing by 5
[tex]2^t= 106/5=21.2[/tex]
Taking logarithms
[tex]log(2^t)= log(21.2)[/tex]
By logarithms property
[tex]t\cdot log(2)= log(21.2)[/tex]
Solving for t
[tex]\displaystyle t=\frac{log21.2} {log2}[/tex]
[tex]t=4.4 \ hours[/tex]
Math will take over Ana's brain at 4.4 hours
It will take 5 hours for the nanobot population to reach 160, utilizing the equation p(t) = 5·[tex]2^t[/tex] and solving for t.
Explanation:The problem involves determining how long it will take for the population of nanobots, which doubles each hour, to reach a specific number. The equation given for the population of nanobots at any time t is p(t) = 5·[tex]2^t[/tex], where t is the time in hours. We are tasked with finding the value of t when the population reaches or exceeds 160 nanobots.
To solve this, we set the equation equal to 160 and solve for t:
p(t) = 5·[tex]2^t[/tex] = 160Dividing both sides by 5 gives:
[tex]2^t = 32[/tex]To find t, we need to determine the power of 2 that equals 32. This can be expressed as 2⁵ = 32. Therefore, t = 5. It will take 5 hours for the population of nanobots to reach 160, at which point Ana will think of nothing but math.