Answer:
a. No the particles will never collide.
b. The second particle is moving faster.
Step-by-step explanation:
We can tell they never collide based on the fact that they will never have the same two points. We can tell this because there is only one time in which they will have the same x value. To find this amount of time, set the two x values equal to each other and solve for t.
5t - 5 = 4t
-5 = -t
5 = t
So we know the x value will only be the same at 5 seconds. Now we can input that value and see if the y values are the same.
2t + 6 = t^2 - 2t - 1
2(5) + 6 = 5^2 - 2(5) - 1
10 + 6 = 25 - 10 - 1
16 = 14 (FALSE)
Therefore they do not collide.
For the second part of the question, we know that the second one is moving faster based on the fact that there is a squared value in the y formula. This shows that it is moving at an exponential rate, which always changes faster than a linear rate.
Particle A and particle B never collide.
The value of k where the particles collide is k = -4
The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Two particles:
Particle A:
x(t) = 5t - 5
y(t) = 2t - k
Particle B:
x(t) = 4t
y(t) = t² - 2t - 1
We see that,
The x(t) of particle A and x(t) of particle B are the same only at t = 5.
x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20
x(t) = 4t = 4 x 5 = 20
Now,
y(t) = 2t - k = 2 x 5 - k = 10 - k
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
(a) If k = -6.
x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20
x(t) = 4t = 4 x 5 = 20
y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 6 = 16
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
In order to collide both the x(t) of particles A and B must be the same.
Similarly, y(t) must be the same.
So,
Particle A and particle B never collide.
(b)
The value of k where the particles collide.
k = -4
y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 4 = 14
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
(c)
The time at which the particles collide.
t = 5 and k = -4
x(t) = 5t - 5 = 5 x 5 - 5 = 25 - 5 = 20
x(t) = 4t = 4 x 5 = 20
y(t) = 2t - k = 2 x 5 - k = 10 - k = 10 + 4 = 14
y(t) = t² - 2t - 1 = 25 - 10 - 1 = 25 - 11 = 14
The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.
Thus,
Particle A and particle B never collide.
The value of k where the particles collide is k = -4
The particle that is moving faster is Particle B since it has a square root in the y(t) = t² - 2t - 1.
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In a town’s study of its stray cats, a sample of stray cats had a mean weight of 7.3 lb. The study had a margin of error of 1.1 lb.
What is the interval estimate for the mean weight of the town’s stray cats in the form (lower limit, upper limit)?
Show your work:
Answer:
(6.2, 8.4)
Step-by-step explanation:
Mean weight of the cats = u = 7.3 lb
Margin of Error = E = 1.1 lb
The interval estimate is calculated by subtracting and adding the margin of error to the mean value as shown below:
( u - E, u + E)
Using the given values, we get:
(7.3 - 1.1, 7.3 + 1.1)
(6.2, 8.4)
Thus, the interval estimate for the mean weight of the town’s stray cats is (6.2, 8.4)
What is 32% of 82 ?????????????????????????/
Answer: 26.24
32% of 82
0.32 • 82 = 26.24
a normal distribution with a mean of 15 and standard deviation 0f 5.95% its area is within ?
Answer:
Step-by-step explanation:
B
The normal distribution describes how the values of a variable are distributed. Given a mean of 15 and standard deviation of 5.95, the area within which values lie could be found using the properties of a normal distribution, which state that ~68% of data falls within one standard deviation of the mean, ~95% within two standard deviations, and ~99.7% within three standard deviations.
Explanation:This question is related to the normal distribution in statistics. The normal distribution is a probability function that describes how the values of a variable are distributed. It is a symmetric distribution where most of the observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions. Extreme values in both tails of the distribution are similarly unlikely.
Given a normal distribution with a mean of 15 and a standard deviation of 5.95, we are asked to find the area within which the values lie. Using the properties of a normal distribution, we know that:
Approximately 68% of the data falls within one standard deviation of the mean (mean ± 1*standard deviation). Approximately 95% falls within two standard deviations (mean ± 2*standard deviation). Approximately 99.7% falls within three standard deviations (mean ± 3*standard deviation).
So, if we wanted to find the area within one standard deviation of the mean, for instance, we would calculate the values of (mean - standard deviation) and (mean + standard deviation), which would represent the range within which approximately 68% of the data lies.
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The sum of two numbers is 60. One number is four times as larger as the other. What are the numbers
The sum of two numbers is 60
The answer is
40 and 20
Consider the equation 5 + x = n. What must be true about any value of x if n is a negative number? Explain your answer. Include an example with numbers to support your explanation.
Answer:
x < 5
Step-by-step explanation:
Any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be LESS than 5 only.
Answer:
Step-by-step explanation:
In the space below, provide the larger of the two positive integers that add to 10 and have the largest possible product.
Answer:
5
Step-by-step explanation:
The integers 5 and 5 sum to 10 and have the largest possible product.
___
The two numbers will be x and (10-x). Their product is x(10-x), which describes a downward-opening parabola with zeros at x=0 and x=10. The maximum (vertex) of that parabola is halfway between the zeros, at x=5. Both integers have the same value: 5. Their product is 25.
If there is a requirement the integers be distinct, then 6 and 4 are the integers of choice. Their product is 24.
In the below system, solve for y in the first equation. x − 3y = −6 2x − 7y = 10
Answer:
[tex]y=\frac{1}{3}x+2[/tex]
Step-by-step explanation:
The given system of equation is;
[tex]x-3y=-6...(1)[/tex]
and
[tex]2x-7y=10...(2)[/tex]
To solve for y in the first equation; we add [tex]-x[/tex] to both sides.
[tex]-3y=-6-x[/tex]
We now divide through by -3;
This implies that;
[tex]y=\frac{1}{3}x+2[/tex]
Please people
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3^x.
A. h(x) = 0
B. h(x) = -3^2x
C. h(x) = 2(3^2x)
D. h(x) = 3^x (2 - 3^x)
Answer:
D
Step-by-step explanation:
Function composition substitutes more than just values or constants. It substitutes functions inside another function. Solve each expression by starting inner most and working to outermost. The expression f(x) ∘ g(x) means f(g(x)).
Let f(x) = x(2 - x) and g(x) = 3^x.
Begin by substituting g(x) in for x in f(x).
[tex]f(g(x)) = (3^x)(2-(3^x))[/tex]
The solution is D.
samantha purchased an automobile for 4,200. her state charged 4% tax for the car, $47 for the license plate, and $35 for the state safety and emission inspection. how much does samantha need to pay for the extra charges , not including the price of the car
The amount that need to be pay is $250.
The calculation is as follows;= 4% of 4,200 + $47 + $35
= $168 + $47 + $35
= $250
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Samantha needs to pay a total of $250 in extra charges, which includes $168 for the state tax, $47 for the license plate, and $35 for the state safety and emission inspection.
Explanation:Calculation of Extra Charges for Automobile PurchaseTo determine how much Samantha needs to pay in extra charges for her automobile purchase, we need to calculate each component separately and then sum them up. Firstly, we calculate the state tax by multiplying the purchase price by the tax percentage:
Tax = Purchase Price × Tax Rate
Tax = $4,200 × 0.04 = $168
Next, we add the fixed costs for the license plate and state safety and emission inspection:
Total Extra Charges = Tax + License Plate Fee + Inspection Fee
Total Extra Charges = $168 + $47 + $35 = $250
Therefore, Samantha needs to pay $250 in extra charges, not including the price of the car.
IF QR IS TANGENT TO O, FIND X.
[tex] \tan(60°) = \frac{x}{OR} \\ \Leftrightarrow x = OR \tan(60°) = OP \sqrt{3} = 12 \sqrt{3} [/tex]
A bag of flour weighs 15 pounds. A shopkeeper has one bag of flour. She sells 1.065 pounds of flour every day. How much flour is left after 8 days?
What's the sum of −62 and its opposite?
The sum of any negative number and its opposite is 0. So your answer is 0.
The sum of any negative number and its opposite is equal to 0.
The diameter of kitty's bicycle wheel is 24 inches what is the radius of the wheel
Diameter is the distance all the way across a circle (going through the center), and radius is the distance from the center to the edge. This means that the radius is always half of the diameter. If the diameter is 24, the radius is 24/2 = 12 inches.
Answer:
12
Step-by-step explanation:
it would be half of 24 which is half of the wheel
What is the solution set?
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[̲̅T̲̅][̲̅h̲̅][̲̅e̲̅]
[̲̅A̲̅][̲̅t̲̅][̲̅t̲̅][̲̅a̲̅][̲̅c̲̅][̲̅h̲̅][̲̅m̲̅][̲̅e̲̅][̲̅n̲̅][̲̅t̲̅] ❣
❣❣... ℏ✺℘ḙ !т ℏḙℓ℘ṧ ʏ✺ṳ...❣❣
Answer:
The possible solution that is obtained from the system of equation are:
(1,3) and (6,13)
Step-by-step explanation:
We are asked to find the solution set of the given system of equation as:
[tex]y=x^2-5x+7-----------(1)[/tex]
and [tex]y=2x+1--------(2)[/tex]
We know that the solution of the system of equations is the possible set of x and y-values that satisfy both the equations.
Or we may say the point of intersection of the graph that is obtained from both the equations.
We solve the system by substitution method as:
We put the value of y from equation (1) in equation (2) to obtain:
[tex]x^2-5x+7=2x+1[/tex]
which is further written by combining the like terms as:
[tex]x^2-5x-2x+7-1=0\\\\x^2-7x+6=0\\\\x^2-6x-x+6=0\\\\x(x-6)-1(x-6)\\\\(x-1)(x-6)=0[/tex]
Hence, we get the possible values of x as:
x=1 and x=6
Also the value of y when x=1 is:y=2×1+1=2+1 ( Putting the value of x in equation (2))
y=3
when x=6 we have the value of y as:y=2×6+1
y=13
Hence, the possible solutions are:
(1,3) and (6,13)
Identify the graph of the equation. What is the angle of rotation for the equation?
xy=-2.5
Answer:
It is B. hyperbola, 45 degrees.
SteIt is p-by-step explanation:
If we rotate the standard form x^2 - y^2 = 1 through 45 degrees we get xy = 1/2.
xy = -2.5 comes from x^2 - y^2 = -5 being rotated 45 degrees.
Answer:
The correct option is b
Step-by-step explanation:
The given equation is
[tex]xy=-2.5[/tex]
It can be written as
[tex]xy+2.5=0[/tex] .... (1)
The general forms of conic is
[tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] .... (2)
From (1) and (2), we get
[tex]A=0,B=1,C=0,D=0,E=0,E=2.5[/tex]
[tex]B^2-4AC=1-4(0)(0)=1>0[/tex]
Since the value of B²- 4AC > 0, then it is hyperbola.
The formula form angle of rotation is
[tex]\tan 2\theta=\frac{B}{A-C}[/tex]
[tex]\tan 2\theta=\frac{1}{0-0}[/tex]
[tex]\tan 2\theta=\infty[/tex]
[tex]\tan 2\theta=\tan (90^{\circ})[/tex]
[tex]2\theta=90^{\circ}[/tex]
[tex]\theta=45^{\circ}[/tex]
The angle of rotation is 45°. Therefore the correct option is b.
Determine the relationship between the quantities of the given graph.
D
The time worked is directly proportional to the wages. This means as the wages increase, the hours of work increases.
A company manufactures cell phones. In August, a random sample of 125 cell phones was inspected, and 3 phones were found to be defective. The company manufactured 8,000 cell phones in August. Based on the results from the sample, about how many cell phones are expected to be defective?
Answer:
192
Step-by-step explanation:
To find how many phones are expected to be defective, we need to represent the values in a fraction.
[tex]\dfrac{x}{8000}=\dfrac{3}{125}[/tex]
x = number of defective phones
Now we can solve this using algebra.
To get the value of x we need to multiply both sides by 8000 to leave x alone.
[tex]x=\dfrac{3}{125}(8000)[/tex]
[tex]x=0.024(8000)[/tex]
[tex]x=192[/tex]
So around 192 cell phones are expected to be defective out of 8000 phones.
Answer:
192
Step-by-step explanation:
The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) (The World Almanac, 2009): Critical Reading 502 Mathematics 515 Writing 494 Assume that the population standard deviation on each part of the test is = 100. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 502 on the Critical Reading part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places. What is the probability a sample of 90 test takers will provide a sample mean test score within 10 points of the population mean of 515 on the Mathematics part of the test (to 4 decimals)? Round z value in intermediate calculation to 2 decimals places.
Answer:
For the Critical Reading part: P = 0.6578
For the Math part: P = 0.6578
Step-by-step explanation:
See attached photo for solutions
The probability that a sample of 90 test takers will provide a sample mean test score within 10 points of the population means of 502 (Critical Reading) and 515 (Mathematics) on the SAT is approximately 68.26% for both.
Explanation:To calculate the probability for each section of the SAT, we use the formula for the z score: z = (X - μ) / (σ / sqrt(n)). In this case, X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
For the Critical Reading section, μ = 502, X is between 492 and 512 (502 ±10), σ = 100, and n = 90. When we input these values into the formula, we get a z value of -1 (for 492) and 1 (for 512) approximately. We then use a z-table to find the probability associated with these z-values. The probability for z = -1 is 0.1587 and for z = 1 is 0.8413. To find the probability that the sample mean lies within these z values, we subtract the lower probability from the higher one, which gives us 0.6826 or 68.26%.
The same steps are applied to the Mathematics section where μ = 515. The resulting probability also comes to around 68.26% that a sample mean test score will be within 10 points of the population mean.
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If you were to create a histogram from the data shown in this stem-and-leaf plot, how many data points would be contained in the bar from 95-105?
A) 3
B) 4
C) 5
D) 6
Answer:
the answer is A, 3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
Stem Leaf Plot : A special table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).
So, In the Given Stem leaf plot the numbers are :
100,101,90,93,94,94,95,81,86,87,89,70,72,76,69,56,58,49
Arrange in ascending order
49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101
Now we are supposed to find how many data points would be contained in the bar from 95-105
49,56,58,69,70,72,76,81,86,87,89,90,93,94,94,95,100,101
So, we can see there are 3 data points are contained in bar from 95 -105.
Hence 3 data points are contained in bar from 95 -105.
Wendy can ride her bike 0.7 miles in 6 minutes how many miles can she ride in 2.5 hours
Wendy can ride 17.5 miles in 2.5 hours
Answer:
17.5 miles
Step-by-step explanation:
[tex]\frac{miles}{min} = \frac{miles}{min} \\\\\\[/tex]
Convert hours to minutes
60 minutes = 1 hour
[tex]2.5*60=150[/tex]
2.5 hours = 150 minutes
[tex]\frac{0.7}{6} = \frac{x}{150} \\\\\\[/tex]
Cross multiply
[tex]0.7*150=6*x\\105=6x\\\frac{105}{6} =x\\17.5=x[/tex]
HELP URGENT 20 PTS!!!! Describe how to sketch a normal curve with a mean of 50 and a standard deviation of 2. Indicate how you would label the horizontal axis at 1, 2, and 3 standard deviations from the mean
Answer:
Step-by-step explanation:
Draw a generic normal curve. Subdivide the x-axis on each side of the center (mean) into four approx. = parts.
Label the mean with '50.'
1 std. dev. below the mean would be 50-2 = 48;
2 std. dev. would be 48-2= 46, and
3 std dev. would be 46 - 2 = 44
Do the same on the other side of the mean.
The 3 corresponding values will be 52, 54 and 56.
What is the simplest form of the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18
Please show all of your work.
Answer:
[tex]6\sqrt{2}[/tex]
Step-by-step explanation:
we have
[tex]3\sqrt{24} -2\sqrt{54}+2\sqrt{18}[/tex]
we know that
[tex]\sqrt{24}=\sqrt{2^{3}3}=2\sqrt{6}[/tex]
[tex]\sqrt{54}=\sqrt{3^{3}2}=3\sqrt{6}[/tex]
[tex]\sqrt{18}=\sqrt{3^{2}2}=3\sqrt{2}[/tex]
Substitute
[tex]3(2\sqrt{6}) -2(3\sqrt{6})+2(3\sqrt{2})[/tex]
[tex](6\sqrt{6}) -(6\sqrt{6})+(6\sqrt{2})[/tex]
[tex]6\sqrt{2}[/tex]
When simplifying the square roots in the expression 3sqrt(24) - 2sqrt(54) + 2sqrt(18), we find that the simplified solution is 6sqrt(2).
Explanation:To simplify the radical expression 3 sqrt 24 - 2 sqrt 54 + 2 sqrt 18, we first need to break down each square root into its simplest form. In order to do this, we look for perfect-square factors (numbers like 4, 9, 16, 25 that have an integer as a square root) within each number:
3sqrt(24) = 3sqrt(4*6) = 6sqrt(6)
2sqrt(54) = 2sqrt(9*6) = 6sqrt(6)
2sqrt(18) = 2sqrt(9*2) = 6sqrt(2)
Because the sqrt(6) terms are like terms we can combine those, and then include the sqrt(2) term:
6sqrt(6) - 6sqrt(6) + 6sqrt(2) = 6sqrt(2).
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Line A is represented by the equation given below: x + y = 3 What is most likely the equation for line B, so that the set of equations has infinitely many solutions? 3x + 3y = 3 3x + y = 3 x + y = 9 3x + 3y = 9
Answer:
3x + 3y = 9
Step-by-step explanation:
Multiplying the given equation by 3 gives you ...
3(x + y) = 3(3)
3x + 3y = 9 . . . . . . matches the last choice
This is an equation for the same line as the given equation, so the lines will have infinitely many points in common (infinitely many solutions).
Answer:
3x + 3y = 9
Step-by-step explanation:
You roll a die and flip three coins. The number of possible outcomes in the sample space is.
Answer:
48
Step-by-step explanation:
We assume that the die and coins are non-bias.
If you roll a die once, you have 6 possible outcomes (anything from 1-6).
If you flip 3 coins once, you have 2 possible outcomes for each coin (either heads or tails). Multiply those 3 possibilities (2x2x2), you get 8.
Multiply 8 with 6, and you get 48 possible outcomes in sample space.
*In the sample space shown below, do the same combinations to all roll die outcomes to get the whole sample space (i.e., 2TTT, 3TTT, 4TTT etc.).
A hot air balloon is flying above Groveburg. To the left side of the balloon, the balloonist measure the angle of depression to the Groveburg soccer fields to be 20° 15'. To the right side of the balloon, the balloonist measures the angle of depression to the high school football field to be 62° 30'. The distance between the two athletic complexes is 4 miles.
What is the distance from the balloon to the football field?
Answer:
The answer is 1.4 miles ⇒ answer (d)
Step-by-step explanation:
* Let the balloon is at the vertex A, and the soccer fields
at vertex B and the football field at vertex C
∴ m∠B = 20° 15' = 20.25°
∴ m∠C = 62° 30' = 62.5°
∴ m∠A = 180 - 20.25 - 62.5 = 97.25°
∵ BC = 4 miles
* By using the sin Rule:
∵ AC/sin(B) = BC/sin(A)
∴ AC = (BC)(sinB)/sin(A)
∴ AC = [4 × sin(20.25)] ÷ sin(97.25) = 1.395 ≅ 1.4 miles
∴ The distance from the balloon to the football filed = 1.4 miles
Answer:
1.4
Step-by-step explanation:
Simplify 13 2
the 2 is tiny so I think it's 13 to the power of 2
Answer: 169
Step-by-step explanation:
You just multiply 13 by 13
When simplifying 13 to the power of 2, you multiply 13 by itself, resulting in 13 x 13, which equals 169. This is known as squaring a number.
The question you've asked involves exponents, which is a way to express repeated multiplication of the same number. When you write 13 with a tiny 2 next to it, you're indicating that 13 should be multiplied by itself once, which is what squaring a number means. In other words, 13 to the power of 2 is 132, which is 13 × 13.
Let's simplify 132:
Multiply 13 by itself: 13 × 13.Calculate the product: 169.So, 132 equals 169. This process is using an integer power, which involves multiplying the base (in this case, 13) by itself as many times as indicated by the exponent (in this case, 2). This can apply to any number, where for example 53 (5 cubed) equals 5 × 5 × 5, which is 125.
The average annual costs for owning two different refrigerators for x years is given by the two functions: f(x) = 850 + 62x /x and g(x) = 1004 + 51x /xIn the long run, the cost of the refrigerator modeled by will be the cheapest, averaging $ per year.
Answer:
part 1: After one year, the cost of the refrigerator modeled by f(x) is cheaper.
part 2: 14 years
part 3: g(x)
part 4: 51
hope this helps :)
To find the cheapest refrigerator in the long run, calculate the limit of the cost per year as x approaches infinity for both given functions and compare the results. The cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.
Explanation:The average annual costs for owning two different refrigerators for x years can be calculated using the given functions: f(x) = 850 + (62x / x) and g(x) = 1004 + (51x / x). To determine which refrigerator will be cheaper in the long run, we need to find the limit of the cost per year as x approaches infinity for both functions. Taking the limit as x approaches infinity for f(x), we get 62. Therefore, the cost of the refrigerator modeled by f(x) will be the cheapest, averaging $62 per year.
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Type the correct answer in the box
Answer:
[tex]w=V/(lh)[/tex]
Step-by-step explanation:
Let
l------> the length of the base of the prism
w------> the width of the base of the prism
h------> the height of the prism
we know that
The volume of the prism is equal to
[tex]V=lwh[/tex]
Solve for w
That means-------> isolate the variable w
so
Divide both sides by (lh)
[tex]V/(lh)=lwh/(lh)[/tex]
Simplify
[tex]w=V/(lh)[/tex]
Can someone help me please I’m struggling so much. let me know if the things that I put already are right
your calculations for volume (pi x r^2 × h) and surface area (2 × pi × r (h+r)) are correct. However your ratio are incorrect. From the formulas the ratio of surface area to volume would be r×h:2(h+r)
Equivalent expression
Answer:
The answer is C. 9^-2
Step-by-step explanation:
Don’t know but not the first one