Answer:
The answer to your question is Positive
Step-by-step explanation:
Function
g(x) = x⁴ - 8x³ + x² + 42x
To know if the function is positive or negative in the interval (0, 3), look for two numbers between this interval and evaluate the function.
The numbers I chose were 1 and 2
- g(1) = (1)⁴ - 8(1)³ + (1)² + 42(1)
= 1 - 8 - 1 + 42
= + 36 positive
- g(2) = (2)⁴ - 8(2)³ + (2)² + 42(2)
= 16 - 64 + 4 + 84
= + 40
Conclusion
The function is positive in the interval (0, 3)
A student wants to know how his IQ of 160 stacks up with the population. Using your knowledge of IQ scores (mean=100, SD=15), how many standard deviations is his IQ score above the mean?
The standard deviation is his IQ score above the mean is found by the Z score whose value is 4.
What is the standard deviation?It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.
[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]
σ is the standard deviation
xi is each value from the data set
X is the mean of the data set
n is the number of observations in the data set.
It is given that,
Sample average, x = 160
mean, [tex]\mu[/tex] = 100
Standard deviation, [tex]\sigma =[/tex] 15
The Z-test value is found as,
[tex]\rm Z = \frac{x- \mu}{\sigma} \\\\ Z = \frac{160-100}{15} \\\\ Z = 4[/tex]
Thus, the standard deviation is his IQ score above the mean is found by the Z score whose value is 4.
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A student with an IQ score of 160 is 4 standard deviations above the mean IQ of 100 according to the given normal distribution, where one standard deviation equals 15 points.
To calculate how many standard deviations a score is above or below the mean, you can use the formula:
Z = (X - x) / SD
Where:
Z is the Z-score, which indicates the number of standard deviations a data point is from the mean.X is the data pointx is the mean of the distributionSD is the standard deviationApplying this to the student's IQ score:
Z = (160 - 100) / 15
Z = 60 / 15
Z = 4
Therefore, a student with an IQ score of 160 is 4 standard deviations above the mean IQ, which is considered exceptionally high.
What does the Principle of Superposition tell us about relative ages of the strata in the cross-sections you were looking at? Older rocks might be found on top of younger rocks-what could cause that? Why is an igneous intrusion younger than the rocks it’s found in?
Answer:
1. The Principle of superposition states that a strata of rock is younger than the one over which it is laid.
2. The intrusion of the younger rock by the principle of cross-cutting relationship
3. The intrusion igneous rock arrived after the rock it is found in had already been in place and is stable.
Step-by-step explanation:
In geology, the Principle of superposition states that, in its originally laid down state, a strata sequence consists of older rocks over which younger rocks are laid. That is, a stratum of rock is younger than the stratum upon which it rests.
The principle of cross cutting relationships in a geologic intrusion occurrence, the feature which intrudes or cut across another feature is always than the feature it cuts across.
The reason is that based on the geologic time frame, the rock 1 which ws cut across by rock 2 was already in the geologic zone in a more steady state than rock , therefore it is older than the cutting rock 2.
an equilateral triangle has an area of 25 √3 cm squared. what is the height
5 √ 3 c m
A t = √ 34 * s 2 = 25 √ 3
this makes the sides 10cm
At= 1/2 b * h
25 √ 3 = 12 ⋅ 10 ⋅ h = 5 √ 3 c m
Answer:
Height = 8.66 cm
Step-by-step explanation:
The formula for the area of an equilateral triangle is expressed as
A = S²√3/4,
where s represents the length of each side. The area of the given equilateral triangle is 25 √3 cm squared. Therefore
25 √3 = S²√3/4
Dividing both sides of the equation by √3, it becomes
25 √3/√3 = S²√3/4√3
25 = S²/4
Cross multiplying, it becomes
S² = 25 × 4 = 100
Taking square root of both sides of the equation, it becomes
√S² = √ 100
S = 10 cm
In an equilateral triangle, all the sides are equal. The height of the equilateral triangle divides it into two equal right angles triangle. The angles in each right angle triangle are 90, 60 and 30 degrees. To determine the height, h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
10² = h² + 5²
100 = h² + 25
h² = 100 - 25 = 75
h = √75
h = 8.66 cm
Eli made fancy blue costume decorations for each of the dancers in his year-end dance performance.He used 1/10 of a meter of ribbon for each decoration,which he got by cutting 1/5 of a meter of ribbon into equal pieces. How many decorations did Eli make?
Answer: There are 2 decorations that Eli makes.
Step-by-step explanation:
Since we have given that
Length of a meter of ribbon used = [tex]\dfrac{1}{10}=\dfrac{1}{10}\times 100=10[/tex]
Length of a meter cut into equal pieces = [tex]\dfrac{1}{5}=\dfrac{1}{5}\times 100=20[/tex]
So, Number of decorations that Eli make is given by
[tex]\dfrac{\text{Length of total ribbon}}{\text{Length of ribbon used}}\\\\=\dfrac{20}{10}\\\\=2[/tex]
Hence, there are 2 decorations that Eli makes.
Final answer:
Eli made 2 decorations from 1/5 meter of ribbon by using 1/10 meter of ribbon for each decoration.
Explanation:
Eli made fancy blue costume decorations for each dancer in his year-end dance performance.
Eli used 1/10 of a meter of ribbon for each decoration and initially cut a 1/5 meter ribbon into equal pieces.
To calculate the number of decorations Eli made, we need to divide the length of ribbon he cut (1/5 meter) by the length of ribbon used for each decoration (1/10 meter).
To solve this, we simply perform the division:
= 1/5 meter / 1/10 meter
= 2.
Therefore, Eli made 2 decorations from 1/5 meter of ribbon.
3 freshmen and 2 sophomores from a sorority will attend a conference. If the sorority has 12 freshmen and 9 sophomores, in how many different ways can the conference attendees be selected?
Answer:
7920
Step-by-step explanation:
12C3 × 9C2
= 220×36
= 7920
The number of different ways the conference attendees be selected is 7920 ways
What are Combinations?
The number of ways of selecting r objects from n unlike objects is:
ⁿCₓ = n! / ( ( n - x )! x! )
Given data ,
The number of fresher men in sorority = 12 fresher men
The number of sophomores in sorority = 9 sophomores
In the conference ,
The number of fresher men from sorority =3 fresher men
The number of sophomores from sorority = 2 sophomores
To calculate the number of different ways the conference attendees be selected is by using combination
So , the combination will become
Selecting 3 fresher men from 12 and selecting 2 sophomores from 9
And , the equation for combination is
ⁿCₓ = n! / ( ( n - x )! x! )
The combination is ¹²C₃ x ⁹P₂
¹²C₃ x ⁹P₂ = 12! / ( 9! 3! ) x 9! / ( 7! 2! )
= ( 12 x 11 x 10 ) / ( 3 x 2 ) x ( 9 x 8 ) / 2
= 1320 / 6 x 72 / 2
= 220 x 36
= 7920 ways
Hence , the number of different ways the conference attendees be selected is 7920 ways
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Factor the expression.
6n3 + 8n2 + 3n + 4
A. (2n2 + 1)(3n + 4)
B. (2n2 – 1)(3n + 4)
Answer:
The answer to your question is letter A
Step-by-step explanation:
Data
Factor 6n³ + 8n² + 3 n + 4
- To factor this expression, factor the common terms of the first two factors
6n³ + 8n² = 2n²(3n + 4)
- Factor 1 in the second two terms 1(3n + 4)
- Factor all the expression by like terms 2n²(3n + 4) + 1(3n + 4)
(3n + 4)(2n² + 1)
#10 FIND X, Y, AND Z!
WILL GIVE BRANLIEST
Answer:
25/6
Step-by-step explanation:
Because the line in the middle is an angle bisector, 5*10 = 12*x.
This means that 50 =12x, so 25/6 = x
Here are summary statistics for randomly selected weights of newborn girls: nequals177, x overbarequals28.9 hg, sequals6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hgless thanmuless than30.7 hg with only 20 sample values, x overbarequals29.4 hg, and sequals2.3 hg? What is the confidence interval for the population mean mu?
Answer:
(32.2,34.7)
Step-by-step explanation:
Solution :
Given that,
\bar x = 33.4 hg
s = 6.4 hg
n = 177
Degrees of freedom = df = n - 1 = 177 - 1 = 176
At 99% confidence level the t is ,
α = 1 - 99% = 1 - 0.99 = 0.01
α / 2 = 0.01 / 2 = 0.005
tα /2,df = t0.005,176 = 2.604
Margin of error = E = tα/2,df * (s /√n)
= 2.604* ( 6.4/ √177)
= 1.25
The 95% confidence interval estimate of the population mean is,
\bar x - E < \mu < \bar x + E = 33.4 - 1.25 < \mu < 33.4 + 1.25
32.15 < \mu < 34.65
32.2 < \mu < 34.7
(32.2,34.7)
Question:
Here are summary statistics for randomly selected weights of newborn girls: n = 177, x = 28.9 hg, s = 6.7 hg. Construct a confidence interval estimate of the mean. Use a 98% confidence level. Are these results very different from the confidence interval 28.1 hg < μ < 30.7 hg with only 20 sample values, x' =29.4 hg, and s = 2.3 hg? What is the confidence interval for the population mean μ?
Answer:
The confidence interval for the population mean μ is 27.73 ≤ μ ≤ 30.0714
Step-by-step explanation:
The equation to identify the confidence interval for the mean is given by
[tex]x'-z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} } \leq \mu\leq x'+z_{\frac{\alpha }{2}} \frac{s}{\sqrt{n} }[/tex]
Where
x' = Sample mean = 28.9
s = Standard deviation = 6.7
n = Sample size = 177
[tex]z_{\frac{\alpha }{2}}[/tex] = Critical value = 2.326
Therefore we have
[tex]28.9-2.326\frac{6.7}{\sqrt{177} } \leq \mu\leq 28.9+2.326 \frac{6.7}{\sqrt{177} }[/tex]
27.73 ≤ μ ≤ 30.0714
T test we have
t = [tex]\frac{x'-\mu}{\frac{s}{\sqrt{n} } }[/tex]
=[tex]\frac{29.4-28.9}{\frac{2.3}{\sqrt{16} } }[/tex] = 0.8696 which is < 1
df = 15 as sample size = 15
Upper tail statistics lies between 0.3 and 0.1
Can someone please actually help me with this?
Images Below
Answer:
65
62
Step-by-step explanation:
In inscribed quadrilaterals, opposite angles are supplementary.
First problem:
x + 148 = 180
x = 32
2x + 1 = 65
Second problem:
x + 20 + 3x = 180
x = 40
180 − (2x + 38) = 62
Write 3.45 as a reduced mixed number.
Answer:
3 [tex]\frac{9}{20}[/tex]
Step-by-step explanation:
3.45=3 45/100
reduce and divided by 5
3 45/100= 3 9/20
Answer:
Step-by-step explanation:
add me on fortnite
A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next. What is the probability that a customer must open three or more bottles before winning a prize
Answer:
The probability that the customer must open 3 or more bottles before finding a prize is 0.64
Step-by-step explanation:
In order for a customer to have to open at least 3 bottles before winning a prize, then the first two bottles shouldnt have a price. The probability that a bottle doesnt have a price is 1-0.2 = 0.8. Since the bottles are independent from each other, then the probability that 2 bottles dont have a prize is 0.8² = 0.64. Therefore, the probability that the customer must open 3 or more bottles before finding a prize is 0.64
Answer:
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
Step-by-step explanation:
We know that the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next.
Therefore, we get p=0.2 and q=1-p=1-0.2=0.8.
So we will calculate the probability that the buyer will not win the prize in the first and second bottles. We get:
[tex]P=0.8\cdot0.8=0.64[/tex]
We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.
Twenty people get into an elevator in a hotel with seven floors, and all of them get off at some point. How many different possibilities exist for how the people could get off the elevator?
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.
Explanation:To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.
Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:
P(20, 7) = 20! / (20 - 7)!
where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.
A boeing-747 is flying from New York City to Los Angeles. It leaves La Guardia Airport in NYC at 9:20am with an expectred arrival time at LA of 1:38pm. However, when it reaches Springfield (Illinois) which is 920 miles away from NYC, the piolets are informed that there is a storm in their path which they must avoid. In order to do so they turn 38 degrees to the right. Eventually they cleared to turn back left and return to their original flight path. They rejoin the path when they reach the four corners which is still 650 miles from LA at which point the piolets make one last turn 52 degrees to the right in order to head directly to los angeles. They arrive without futer incidents. How many minutes was the flight delayed
Answer:
I do not know sorry
Step-by-step explanation:
#7 HELP ! WILL GIVE BRANLIEST
Answer:
x = 8, y = 4√3, z = 8√3
Step-by-step explanation:
Assuming that y is the altitude of the triangle (perpendicular to the hypotenuse), the triangles are similar. So we can write proportions:
x / 4 = 16 / x
x² = 64
x = 8
4 / y = y / 12
y² = 48
y = 4√3
z / 12 = 16 / z
z² = 192
z = 8√3
Note: after finding one side, you can also use Pythagorean theorem to find the other two sides.
-2/x^2-4 + x-1/x^2-2x
1. Identify the type of problem
2. Think of how to do this problem
3. Do the Work
4. Answer
Answer:
I need help with this too
Step-by-step explanation:
Genevieve wants to verify that 1/5 * (5x - 20) - 1/2 * (4x - 8) equivalent to -x which procedure can Genevieve to determine if the two expressions are equivalent?
Answer with Step-by-step explanation:
We are given that
LHS
[tex]\frac{1}{5}(5x-20)-\frac{1}{2}(4x-8)[/tex]
Using distribution property
[tex]a\cdot (b+c)=a\cdot b+a\cdot c[/tex]
[tex]\frac{1}{5}(5x)-\frac{1}{5}(20)-\frac{1}{2}(4x)+\frac{1}{2}(8)[/tex]
After multiplication we get
[tex]x-4-2x+4[/tex]
Combine like terms
[tex](x-2x)+(4-4)[/tex]
Then, we get
[tex]-x+0=-x[/tex]
Hence,verified.
Answer:D
Step-by-step explanation: I took the unit test
Evaluate A ^ 2 for A = - 3 . -9 -6 6 9
Answer:
9
Step-by-step explanation:
We want to evaluate
[tex]A^2[/tex]
for A=-3.
This means, we need to substitute A=-2, into the given equation and simplify.
We substitute to get:
[tex] A^2 = {( - 3)}^{2} [/tex]
In this case the base is -3, so it multiplies itself twice.
[tex]A^2 = {( - 3)} \times - 3[/tex]
This gives us:
[tex]A^2 = 9[/tex]
A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of a material that costs 11 cents per square centimeter, while the sides are made of a material that costs 8 cents per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder.
Answer:
The answer to the question is
The total cost C of the material as a function of the radius r of the cylinder is
0.6912·r² + 800/r Dollars.
Step-by-step explanation:
To solve the question, we note that
The area of the top and bottom combined = 2·π·r²
The area of the sides = 2·π·r·h
and the volume = πr²h = 500 cm²
Therefore height = 500/(πr²)
Substituting the value of h into the area of the side we have
Area of the side = 2πr·500/(πr²) = 1000/r
Therefore total area of can = Area of top + Area of bottom + Area of side
Whereby the cost of the can = 0.11×Area of top +0.11×Area of bottom +0.8×Area of side
Which is equal to
0.11×2×π×r²+ 0.8×1000/r = 0.6912·r² + 800/r
The cost of the can is $(0.6912·r² + 800/r)
To express the cost of the cylinder's material as a function of its radius, we first find the expression for the cylinder's height using the volume formula. The total cost C is computed by calculating the expenses for the top, bottom, and sides of the cylinder using their respective costs and surface areas. These give the final expression for the cost C(r)= 22πr^2 + 8000/r.
Explanation:Given that the volume of the right circular cylinder is 500 cubic centimeters, we can first use the formula for the volume of a cylinder, which is V=πr2h, where r is the radius of the base and h is the height of the cylinder. This can be rearranged to solve for h, giving us h=V/(πr2).
Next, the total cost C is given by the cost of the materials for the top, bottom, and sides of the cylinder: C= 2(11πr2)+ (8 * 2π*r*h). Plugging the expression h= 500/(πr2) into the cost function gives us: C = 22πr2 + (16πr * 500/r2), which simplifies to: C = 22πr2 + 8000/r. So, the total cost of the material as a function of the radius r of the cylinder is C(r)= 22πr2 + 8000/r.
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How many solutions does the system have?
x+y=3
5x+5y=15
A. Exactly one solution
B. No solutions
C. Infinity many solutions
The system has infinitely many solutions because both equations represent the same line in the coordinate plane. So C. Infinity many solutions will be the answer.
To determine the number of solutions for this system of equations, let's analyze it:
[tex]\[\left\{\begin{array}{l}x + y = 3 \\5x + 5y = 15\end{array}\right.\][/tex]
We can simplify the second equation by dividing both sides by 5:
[tex]\[x + y = 3\][/tex]
This equation is identical to the first equation in the system. So, the two equations represent the same line in the coordinate plane.
When two equations represent the same line, they have infinitely many solutions, because every point on the line satisfies both equations.
Therefore, the correct answer is:
(C) Infinitely many solutions
Complete Question:
Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative. A researcher wishes to compare academic aptitudes of married lawyers and their spouses. She obtains a random sample of 517 such couples who take an academic aptitude test and determines each spouse's academic aptitude.
Answer:
a) Independent
b) Quantitative
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 517
Sample:
Married lawyers and their spouses.
Response variable:
Comparison of academic aptitudes of married lawyers and their spouses.
a) The given sampling is an example of independent sampling.
This is an independent sample because an individual of sample does not effect any other individual of the sample.
b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.
It is a quantitative measure because the scores can be expressed in numerical.
Answer:
The sampling is independent and the response variable is quantitative.
Explanation:
Given a random sample of [tex]517[/tex] couples
The researcher wishes to compare academic aptitudes of married lawyers and their spouses. Then, she obtains a random sample of [tex]517[/tex] such couples who take an academic aptitude test and determines each spouse's academic aptitudeAn individual of the sample will not affect any other individual of the sample.Therefore, the sampling is independent.Here, the response variable is the aptitude test.The scores of the academic test are represented in numerical form.Thus, the response variable is quantitative.Learn more about Random sample, refer:
https://brainly.com/question/16786843Rewrite the radical expression as an expression with a rational exponent. the fourth root of seven to the fifth power
Answer:
[tex]\sqrt[4]{7^5}[/tex]
Step-by-step explanation:
I apologize, I do not know how to explain this.
Answer:
7⁵/₄
Step-by-step explanation:
⁴√7⁵
The fourth root is equivalent to the power 1/4.
= 7^(1/4 * 5)
= 7^(5/4).
It is known that a certain function is an inverse proportion. Find the formula for this function if it is known that the function is equal to 12 when the independent variable is equal to 2.
Answer:
[tex]y=\frac{24}{x}[/tex]
Step-by-step explanation:
We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of variation.
Upon substituting [tex]y=12[/tex] and [tex]x=2[/tex] in above equation, we will get:
[tex]12=\frac{k}{2}[/tex]
Let us solve for constant of variation.
[tex]12\cdot 2=\frac{k}{2}\cdot 2[/tex]
[tex]24=k[/tex]
Now, we will substitute [tex]k=12[/tex] in inversely proportion equation as:
[tex]y=\frac{24}{x}[/tex]
Therefore, the formula for the given scenario would be [tex]y=\frac{24}{x}[/tex].
I don’t know how to find the surface area?
Answer:
Step-by-step explanation:
its just writing teh answwer out and then solving
Answer:
The surface area of a prism is the sum of the areas of the 6 faces. That will be
the 2 squares and the other 4 rectangles.
S=2*(b*h)+4(B*H)
b and h are base and height of the squares and B and H of the Rectangles.
b=2
h=2
B=5
H=2
so
S=2*(2*2)+4(2*5)=8+40=48
Joan is building a sandbox in the shape of a regular pentagon. The perimeter of the pentagon is 35y4 – 65x3 inches. What is the length of one side of the sandbox? 5y – 9 inches 5y4 – 9x3 inches 7y – 13 inches 7y4 – 13x3 inches
Answer:
Step-by-step explanation:
given that Joan is building a sandbox in the shape of a regular pentagon.
The perimeter of the pentagon is
[tex]35y^4 - 65x^3[/tex]inches.
Since regular pentagon we know that all sides are equal and there are totally five sides.
Perimeter of regular pentagon = 5*side
= 5a where a = length of side
Equate 5a to given perimeter to get
[tex]5a=35y^4 - 65x^3\\[/tex]
divide by 5
[tex]a=\frac{35y^4 - 65x^3}{5} \\=7y^4-13x^3[/tex]
Answer:
D. 7y^4 - 13x^3 inches
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. He made a total of $220.00 in interest. How much was invested at 3.25%?
A $4000
B $3000
C $5000
D $3500
Answer: A $4000
Step-by-step explanation:
Let x represent the amount which he invested at 3% interest.
Let y represent the amount which he invested at 3.25% interest.
Walt made an extra $7000 last year from a part-time job. He invested part of the money at 3% and the rest at 3.25%. This means that
x + y = 7000
The formula for determining simple interest is expressed as
I = PRT/100
Considering the account paying 3% interest,
P = $x
T = 1 year
R = 3℅
I = (x × 3 × 1)/100 = 0.03x
Considering the account paying 3.25% interest,
P = $y
T = 1 year
R = 3.25℅
I = (y × 3.25 × 1)/100 = 0.0325y
He made a total of $220.00 in interest., it means that
0.03x + 0.0325y = 220 - - - - - - - -- -1
Substituting x = 7000 - y into equation 1, it becomes
0.03(7000- y) + 0.0325y = 220
210 - 0.03y + 0.0325y = 220
- 0.03y + 0.0325y = 220 - 210
0.0025y = 10
y = 10/0.0025
y = 4000
A smart-phone is thrown upwards from the top of a 448-foot building with an initial velocity of 48 feet per second. The height h of the smart-phone after t seconds is given by the quadratic equation h = − 16 t 2 + 48 t + 448 h=-16t2+48t+448. When will the smart-phone hit the ground?
Answer:
The smart-phone hit the ground when t = 7 s
Step-by-step explanation:
The height "h" is defined as:
h=16t^2 + 48t + 448
And, when the smart-phone hits the ground, h = 0 ft . Then,
16t^2 + 48t + 448 = 0
And this is a quadratic equation, and we can solve it using the formula for ax^2 + bx + c = 0, which is
x=[tex]\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
So,
t = [tex]\frac{-48±\sqrt{48^{2} -4(-16)(448)} }{2(16)}[/tex]
t = [tex]\frac{-48±\sqrt{2304+28672} }{-32}[/tex]
And, we have two responses,
t_1 = [tex]\frac{-48+\sqrt{30976} }{-32}[/tex] and t_2 = [tex]\frac{-48-\sqrt{30976} }{-32}[/tex]
t_1 = - 4 s and t_2 = 7 s
As we know, the time is a quantity that cannot have a negative value, so, we take the result 2.
Final answer:
The smart-phone will hit the ground after approximately 3 seconds.
Explanation:
To find when the smart-phone will hit the ground, we need to determine the value of t that makes h equal to zero in the quadratic equation h = -16t^2 + 48t + 448. This equation represents the height h of the smart-phone after t seconds. To solve the equation, we can use the quadratic formula t = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values a = -16, b = 48, and c = 448, we can solve for t. The positive value of t will give us the time it takes for the smart-phone to hit the ground.
Step-by-step solution:
Substitute the values a = -16, b = 48, and c = 448 into the quadratic formula: t = (-48 ± sqrt(48^2 - 4*(-16)*448)) / (2*(-16))
Simplify the expression inside the square root: t = (-48 ± sqrt(2304 + 28672)) / (-32)
Simplify further: t = (-48 ± sqrt(30976)) / (-32)
Calculate the square root of 30976: t = (-48 ± 176) / (-32)
Determine the values of t: t = (-48 + 176) / (-32) = 3 or t = (-48 - 176) / (-32) = -5
Choose the positive value t = 3 since we are interested in the time it takes for the smart-phone to hit the ground
Therefore, the smart-phone will hit the ground after approximately 3 seconds.
ixl geometry help pls !
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{small}{large}\qquad \qquad \stackrel{sides}{\cfrac{3}{7}} ~~ = ~~ \stackrel{areas}{\sqrt{\cfrac{A_1}{98}}}\implies \left( \cfrac{3}{7} \right)^2 = \cfrac{A_1}{98}\implies \cfrac{3^2}{7^2}= \cfrac{A_1}{98} \\\\\\ \cfrac{9}{49}= \cfrac{A_1}{98}\implies 882 = 49A_1\implies \cfrac{882}{49}=A_1\implies 18=A_1[/tex]
Answer:
The answer to your question is 18 in²
Step-by-step explanation:
Data
Big rectangle Small rectangle
Area = 98 in² Area = ?
Height = 7 in Height = 3 in
Process
1.- Calculate the base of the big rectangle
Area = base x height
solve for base
base = Area / height
substitution
base = 98 / 7
base = 14 ni
2.- Use proportions to find the base of the small rectangle
x / 3 = 14 / 7
Simplify
x = (14)(3) / 7
result
x = 6 in
3.- Calculate the area of the small rectangle
Area = 6 x 3
= 18 in²
A fire engine starts pumping water at 9:20 am at the rate of 800 gallons per minute. Another fire engine, pumping at the rate of 1000 gallons per minute, starts at 9:30 am. At what time will the two engines have pumped the same number of gallon
Answer:
10:10 AM
Step-by-step explanation:
The first thing is to use an identical time variable for both cases, we will do it as follows:
Let t = number of minutes of pumping time of the first fire engine
Therefore, for the second fire truck it would be:
(t-10) = pumping time of the second fire engine, since it started 10 min after the first engine.
To find the value of t, we equalize the equations of the first engine and the second engine:
We know that the first one would be: 800 * t
And the second: 1000 * (t-10)
Thus
1000 * (t-10) = 800 * t
1000 * t - 10000 = 800t
1000 * t - 800 * t = 10000
200 * t = 10000
t = 10000/200
t = 50 minutes
In other words, 50 minutes after the first engine starts pumping, it equaled the second
To know the time they were matched it would be like this:
9:20 AM +: 50 = 10:10 AM
Therefore, at 10:10 AM both engines were matched.
To check the above we have to:
50 * 800 = 40000
40 * 1000 = 40000
Therefore, in that time, they were equalized.
Answer:
At 10:10 am
Step-by-step explanation:
Hi to answer this question we have to write a system of equations:
Fire engine 1: 800 mWhere m: pumping time of the engine
Fire engine 2: 1000 (m-10)Because it starts 10 minute later
So, putting together both equations:
800m = 1000(m-10)
800m = 1000m - 10000
10000 = 1000m-800m
10000= 200m
10000/200=m
50 =m (50 minutes after the first engine starts)
So, 9:20 am + 50 minutes : 10:10 am .
Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 15 of the 50 boxes on the shelf have the secret decoder ring. The other 35 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Answer:
3/35
Step-by-step explanation:
(15/50)×(14/49)
= 3/35 or 0.0857
Answer:
3/35.
Step-by-step explanation:
Probability (the first one selected has the decoder ring) = 15/50 = 3/10.
Probability (the second one selected has the decoder ring) = 14/49 = 2/7.
Therefore the probability that both have the ring =
3/10 * 2/7
= 6/70
= 3/35.
Note: The probabilities are multiplied because the 2 events are independent.
Dave owns 15 shares of ABC Mining stock. On Monday, the value of each share rose $2, but on Tuesday the value fell $5. What is the change in the value of Dave's shares?
Answer:
The change in the value of Dave's shares = $ 105
Step-by-step explanation:
Total number of shares = 15
Let initial value of a share = x
On Monday, the value of each share rose = $ 2
Now the value of each share = x + 2
Total value of 15 shares on Monday = 15 (x + 2) -------- (1)
On Tuesday the value of each share fell = $ 5
Now the value of each share = x - 5
Total value of 15 shares on Tuesday = 15 (x - 5) --------- (2)
The change in the value of Dave's shares = 15 (x + 2) - 15 (x - 5)
⇒ 15 x + 30 - 15 x + 75 = 105
⇒ Thus the change in the value of Dave's shares = $ 105