Answer:
90%
Step-by-step explanation:
72/80=0.9 so as a percentage that would be 90%
A travel agent is booking trips for tourists who travel from New York to Chicago. Tourists have three choices for how to travel from New York to Chicago. They can take an airplane for $350, a bus for $150, or a train for $225. Once they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. If each option is equally likely to occur, what is the probability that a tourist will spend more than $275 on these 2 legs of the trip?
Answer:
P = 1/2
Step-by-step explanation:
If the tourist spends more than 275$, they must not arrive in Chicago by bus.
( 150 + 60 < 275, 150 + 40 < 275)
The total options the tourist can make:
3 x 2 = 6
(1st leg: 3 possible options, 2nd leg: 2 possible options)
The number of options the tourist can make after excluding bus option:
2 x 2 = 4
(1st leg: 2 remaining possible options, 2nd leg: 2 possible options)
The number of options the tourist can make after excluding the bus option and spend more than 275$:
4 - 1 = 3
(excluding the case of selecting train and cab, because 225 + 40 < 275)
=> The probability that the tourist will spend more than 275$ on these 2 legs of the trip:
P = 3/6 = 1/2
Probability helps us to know the chances of an event occurring. The probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that Tourists have three choices for how to travel from New York to Chicago. They can take an aeroplane for $350, a bus for $150, or a train for $225. Also, when they arrive in Chicago, they can travel by van to their hotel for $60 or take a cab for $40. Therefore, the cost of different routes is,
Aeroplane($350) + Van($60) = $410Aeroplane($350) + Cab($40) = $390Bus($150) + Van($60) = $210Bus($150) + Cab($40) = $190Train($225) + Van($60) = $285Train($225) + Cab($40) = $265As it can be seen that there are 3 cases where a tourist will spend more than $275, while the total number of cases is 6. Therefore, the probability that a tourist will spend more than $275 on these 2 legs of the trip is,
Probability = 3/6 = 1/2 =0.5z
Hence, the probability that a tourist will spend more than $275 on these 2 legs of the trip is 0.5.
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Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor air pollution. An article presented information on various pulmonary characteristics in samples of children whose households in India used either biomass fuel or liquefied petroleum gas (LPG). For the 756 children in biomass households, the sample mean peak expiratory flow (a person's maximum speed of expiration) was 3.4 L/s, and the sample standard deviation was 1.2. For the 752 children whose households used liquefied petroleum gas, the sample mean PEF was 4.28 and the sample standard deviation was 1.19.
Required:
a. Calculate a confidence interval at the 95% confidence level for the population mean PEF for children in biomass households and then do likewise for children in LPG households. What is the simultaneous confidence level for the two
intervals?
b. Carry out a test of hypotheses at significance level 0.01 to decide whether true average PEF is lower for children in biomass households than it is for children in LPG households (the cited article included a P-value for this test).
c. FEVI, the forced expiratory volume in 1 second, is another measure of pulmonary function. The cited article reported that for the biomass households the sample mean FEY, was 2.3 L/S and the sample standard deviation was .5 L/s. If this information is used to compute a 95% Cl for population mean FEVI, would the simultaneous confidence level for this interval and the first interval calculated in (a) be the same as the simultaneous confidence level deter-mined there? Explain.
Answer:
A) 95% confidence interval for the population mean PEF for children in biomass households = (3.314, 3.486)
95% confidence interval for the population mean PEF for children in LPG households
= (4.195, 4.365)
Simultaneous confidence interval for both = (3.314, 4.365)
B) The result of the hypothesis test is significant, hence, the true average PEF is lower for children in biomass households than it is for children in LPG households.
C) 95% confidence interval for the population mean FEY for children in biomass households = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.365)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Step-by-step explanation:
A) Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Critical value will be obtained using the z-distribution. This is because although, there is no information provided for the population standard deviation, the sample sizes are large enough for the sample properties to approximate the population properties.
Finding the critical value from the z-tables,
z-critical value for 95% confidence level = 1.960 (from the z-tables)
For the children in the biomass households
Sample mean = 3.40
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.20
N = sample size = 756
σₓ = (1.20/√756) = 0.04364
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 3.40 ± (1.960 × 0.04364)
CI = 3.40 ± 0.08554
95% CI = (3.31446, 3.48554)
95% Confidence interval = (3.314, 3.486)
For the children in the LPG households
Sample mean = 4.28
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation of the sample = 1.19
N = sample size = 752
σₓ = (1.19/√752) = 0.043395
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 4.28 ± (1.960 × 0.043395)
CI = 4.28 ± 0.085054
95% CI = (4.1949, 4.3651)
95% Confidence interval = (4.195, 4.365)
Simultaneous confidence interval for both = (3.214, 4.375)
B) The null hypothesis usually goes against the claim we are trying to test and would be that the true average PEF for children in biomass households is not lower than that of children in LPG households.
The alternative hypothesis confirms the claim we are testing and is that the true average PEF is lower for children in biomass households than it is for children in LPG households.
Mathematically, if the true average PEF for children in biomass households is μ₁, the true average PEF for children in LPG households is μ₂ and the difference is μ = μ₁ - μ₂
The null hypothesis is
H₀: μ ≥ 0 or μ₁ ≥ μ₂
The alternative hypothesis is
Hₐ: μ < 0 or μ₁ < μ₂
Test statistic for 2 sample mean data is given as
Test statistic = (μ₂ - μ₁)/σ
σ = √[(s₂²/n₂) + (s₁²/n₁)]
μ₁ = 3.40
n₁ = 756
s₁ = 1.20
μ₂ = 4.28
n₂ = 752
s₂ = 1.19
σ = √[(1.20²/756) + (1.19²/752)] = 0.061546
z = (3.40 - 4.28) ÷ 0.061546 = -14.30
checking the tables for the p-value of this z-statistic
Significance level = 0.01
The hypothesis test uses a one-tailed condition because we're testing in only one direction.
p-value (for z = -14.30, at 0.01 significance level, with a one tailed condition) = 0.000000001
The interpretation of p-values is that
When the p-value > significance level, we fail to reject the null hypothesis and when the p-value < significance level, we reject the null hypothesis and accept the alternative hypothesis.
Significance level = 0.01
p-value = 0.000000001
0.000000001 < 0.01
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that true average PEF is lower for children in biomass households than it is for children in LPG households.
C) For FEY for biomass households,
Sample mean = 2.3 L/s
Standard error of the mean = σₓ = (σ/√N)
σ = standard deviation = 0.5
N = sample size = 756
σₓ = (0.5/√756) = 0.018185
95% Confidence Interval = (Sample mean) ± [(Critical value) × (standard Error of the mean)]
CI = 2.30 ± (1.960 × 0.018185)
CI = 2.30 ± 0.03564
95% CI = (2.264, 2.336)
Simultaneous confidence interval for both = (2.264, 4.365)
This simultaneous interval cannot be the same as that calculated in (a) above because the sample mean obtained for children in biomass households here (using FEY) is much lower than that obtained using PEF in (a).
Hope this Helps!!!
g In R simulate a sample of size 20 from a normal distribution with mean µ = 50 and standard deviation σ = 6. Hint: Use rnorm(20,50,6) to get one random sample of size 20. Determine the mean and standard deviation from this sample, compare these with the population mean and standard deviation.
Answer:
> a<-rnorm(20,50,6)
> a
[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905
[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501
Then we can find the mean and the standard deviation with the following formulas:
> mean(a)
[1] 50.72451
> sqrt(var(a))
[1] 7.470221
Step-by-step explanation:
For this case first we need to create the sample of size 20 for the following distribution:
[tex] X\sim N(\mu = 50, \sigma =6)[/tex]
And we can use the following code: rnorm(20,50,6) and we got this output:
> a<-rnorm(20,50,6)
> a
[1] 51.72213 53.09989 59.89221 32.44023 47.59386 33.59892 47.26718 55.61510 47.95505 48.19296 54.46905
[12] 45.78072 57.30045 57.91624 50.83297 52.61790 62.07713 53.75661 49.34651 53.01501
Then we can find the mean and the standard deviation with the following formulas:
> mean(a)
[1] 50.72451
> sqrt(var(a))
[1] 7.470221
Answer:
b
Step-by-step explanation:
meg mows 20% of a lawn in 10 minutes how much more time will she need to finish mowing the lawn
Answer: 40 mins
Step-by-step explanation:
10=20%
20=40%
30=60%
40=80%
50=100%
Will give brainliest answer
Answer: 49π square units
Step-by-step explanation:
Area of a circle = πr^2
Area = π x 7^2
Area = 49π
Answer:
9.8646 or I think 14 units 2
Estimate the volume of material in a cylindrical shell with height 32 in., radius 7 in. comma and shell thickness 0.5 in. Round to one decimal place. (Use 3.14 for pi.)
Answer:
703.36 in ^ 3
Step-by-step explanation:
We have the following information:
Height (h) = 32 in
Radius (r) = 7 in
Thickness (dr) = 0.5 in
Now the volume of a cylinder is:
V π (r ^ 2) * h
if we derive with respect to the radius we are left with:
dV / dr = 2 * π * r * h
then solved for dV, we would have:
dV = 2 * π * r * h * dr
we know all these values so we replace:
dV = 2 * π * 7 * 32 * 0.5
dV = 224 * π
if we say that π is approximately 3.14
V = 703.36
Therefore the estimate of the volume of that cylinder is 703.36 in ^ 3
HELP!!
Which Platonic solid has four faces that are equilateral triangles?
A. Hexahedron
B. Dodecahedron
C. Tetrahedron
D. Icosahedron
Answer:
C. Tetrahedron
Step-by-step explanation:
In figure
The Platonic solid that has four faces that are equilateral triangles is the Tetrahedron. The correct option is C.
What is Tetrahedron?A Tetrahedron is a three-dimensional shape made up of four equilateral triangles. It is one of the five Platonic solids, which are regular, convex polyhedra with identical vertices and faces.
Each vertex in a Tetrahedron is connected to the other three vertices by an edge, resulting in a pyramid-like structure.
The Tetrahedron is a unique shape with numerous applications in mathematics, engineering, and chemistry.
The Tetrahedron is a Platonic solid with four equilateral triangle faces. It has four faces, four vertices, and six edges in total. It is the most basic of the Platonic solids and the only one with no parallel faces.
Thus, the correct option is C.
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What is the greatest common factor of the polynomial below?
20x^3 - 14x
Answer:
the correct answer is 2x
Answer:
D. 2x
Step-by-step explanation:
20x² : 1, 2, 4, 5, 10, 20, x
14x : 1, 2, 7, 14, x
The greatest common factor of the polynomial is 2x.
2x(10x² - 7)
18 is divisible by both 2 and 3 it is also divisible by 2 into 36 similarly a number is divisible by both 4 and 6 can we say that the number must also be divided by 4 and 2 6 24 if not give an example to justify your answer
Answer:
no; 12
Step-by-step explanation:
A number divisible by 4 and 6 will be divisible by their least common multiple, 12. If it is an odd multiple of 12, it will not be divisible by 24.
Examples:
12÷4 = 3; 12÷6 = 2; 12 is not divisible by 24
24÷4 = 6; 24÷6 = 4; 24 is divisible by 24
36÷4 = 9; 36÷6 = 6; 36 is not divisible by 24
Find the slope-intercept form of the line with slope 6 that passes through the point (3,5).
Answer:
y=6x-13
Step-by-step explanation:
Since we are given a point and a slope, we can use the slope intercept formula.
[tex]y-y_{1} = m(x-x_{1} )[/tex]
where (x1, y1) is a point and m is the slope.
We know that the slope is 6 and the point is (3,5). Therefore,
x1= 3
y1= 5
m=6
Substitute these into the formula.
[tex]y-5 = 6(x-3 )[/tex]
Distribute the 6. Multiply each term inside the parentheses by the number outside the parentheses.
[tex]y-5= (6*x) + (6*-3)[/tex]
[tex]y-5=6x-18[/tex]
We want to find the slope-intercept form, or y=mx+b. Therefore, we must get y by itself.
5 is being subtracted from y. The inverse of subtraction is addition. Add 5 to both sides.
[tex]y-5+5=6x-18+5[/tex]
[tex]y= 6x-18+5[/tex]
[tex]y= 6x -13[/tex]
Not sure how to solve this
Answer:
-3/17
Step-by-step explanation:
(7,1) and (-10,4)
slope formula: m = (y₂ - y₁) / (x₂ - x₁)
plug in data: m = (4 - 1) / (-10 - 7)
solve: 3 / -17
simplify: -3/17 (written as a fraction)
The table shows three unique functions. (TABLE IN PIC) Which statements comparing the functions are true? Select three options. Only f(x) and h(x) have y-intercepts. Only f(x) and h(x) have x-intercepts. The minimum of h(x) is less than the other minimums. The range of h(x) has more values than the other ranges. The maximum of g(x) is greater than the other maximums.
Answer:
(A)Only f(x) and h(x) have y-intercepts.
(C)The minimum of h(x) is less than the other minimums.
(E)The maximum of g(x) is greater than the other maximums.
Step-by-step explanation:
From the table
f(0)=0 and h(0)=0, therefore, Only f(x) and h(x) have y-intercepts. (Option A)
Minimum of f(x)=-14Minimum of g(x)=1/49Minimum of h(x)=-28Therefore, the minimum of h(x) is less than the other minimums. (Option C).
Maximum of f(x)=14
Maximum of g(x)=49
Maximum of h(x)=0
Therefore, the maximum of g(x) is greater than the other maximums. (Option E)
Answer: It's B,C, and E
Step-by-step explanation:
Use implicit differentiation to find an equation of the tangent line to the curve at the given points. (x2 + y2)2 = 3x2y − y3;
(a) (0, −1),
(b) (−1/2, 1/2)
Answer:
a.[tex]y+1=0[/tex]
b.[tex]2x+4y=1[/tex]
Step-by-step explanation:
We are given that
[tex](x^2+y^2)^2=3x^2y-y^3[/tex]
a.(0,-1)
Differentiate w.r.t x
[tex]2(x^2+y^2)(2x+2yy')=6xy+3x^2y'-3y^2y'[/tex].....(1)
Substitute x=0 and y=-1 in equation (1)
[tex]2(0+1)(-2y')=-3y'[/tex]
[tex]-4y'+3y'=0[/tex]
[tex]-y'=0[/tex]
[tex]y'=0[/tex]
[tex]m=y'=0[/tex]
Point-slope form:
[tex]y-y_0=m(x-x_0)[/tex]
Using the formula
[tex]y+1=0[/tex]
This is required equation of tangent line to the given curve at point (0,-1).
b.(-1/2,1/2)
Substitute the value in equation (1)
[tex]2(1/4+1/4)(-1+y')=6(-1/2)(1/2)+3(1/4)y'-3(1/4)y'[/tex]
[tex]2(2/4)(-1+y')=-3/2+3/4y'-3/4y'[/tex]
[tex]-1+y'=-3/2[/tex]
[tex]y'=-3/2+1=\frac{-3+2}{2}=-\frac{1}{2}[/tex]
[tex]m=y'=-1/2[/tex]
Again using point-slope formula
[tex]y-1/2=-1/2(x+1/2)[/tex]
[tex]\frac{2y-1}{2}=-\frac{1}{4}(2x+1)[/tex]
[tex]2y-1=-\frac{1}{2}(2x+1)[/tex]
[tex]4y-2=-2x-1[/tex]
[tex]2x+4y=2-1[/tex]
[tex]2x+4y=1[/tex]
Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas's fastest-moving inventory item has a demand of 6,100 units per year. The cost of each unit is $101, and the inventory carrying cost is $8 per unit per year. The average ordering cost is $31 per order. It take about 5 days for an order to arrive, and the demand for 1 week is 120 units. (This is a corporate operation, and the are 250 working days per year.)A) What is the EOQ?B) What is the average inventory if the EOQ is used?C) What is the optimal number of orders per year?D) What is the optimal number of days in between any two orders?E) What is the annual cost of ordering and holding inventory?F) What is the total annual inventory cost, including cost of the 6,100 units?
Answer and Step-by-step explanation:
The computation is shown below:
a. The economic order quantity is
[tex]= \sqrt{\frac{2\times \text{Annual demand}\times \text{Ordering cost}}{\text{Carrying cost}}}[/tex]
[tex]= \sqrt{\frac{2\times \text{6,100}\times \text{\$31}}{\text{\$8}}}[/tex]
= 217 units
b. The average inventory used is
[tex]= \frac{economic\ order\ quantity}{2}[/tex]
[tex]= \frac{217}{2}[/tex]
= 108.5 units
c. The optimal order per year
[tex]= \frac{annual\ demand}{economic\ order\ quantity}[/tex]
[tex]= \frac{6,100}{217}[/tex]
= 28 orders
d. The optima number of days is
[tex]= \frac{working\ days}{optimal\ number\ of\ orders}[/tex]
[tex]= \frac{250}{28}[/tex]
= 8.9 days
e. The total annual inventory cost is
= Purchase cost + ordering cost + carrying cost
where,
Purchase cost is
[tex]= \$6,100 \times \$101[/tex]
= $616,100
Ordering cost = Number of orders × ordering cost per order
= 28 orders × $31
= $868
Carrying cost = average inventory × carrying cost per unit
= 108.50 units × $8
= $868
So, the total would be
= $616,100 + $868 + $868
= $617,836
HELP HELP PLEASE the height of the triangle is 16 cm, and fe=10 cm. What is the area of the triangle? A. 50 CM^2 B. 80 CM^2 C.160 CM^2 D.192 CM^2
Answer:
B. 80 cm^2
Step-by-step explanation:
A = bh/2
A = (FE)(16 cm)/2
A = (10 cm)(16 cm)/2
A = 80 cm^2
Steve Caples, a real estate appraiser in Lake Charles, Louisiana, has developed a regression model to help appraise residential housing in the Lake Charles Area. The model was developed using recently sold homes in a particular neighborhood. The price (y) of the house is based on the square footage (x) of the house. The model is:
Y=33,478+62.4X
The coefficient of correlation for the model is 0.63.
(a) Use the model to predict the selling price of a house that is 1,860 square feet.
(b) A house with 1,860 square feet recently sold for $165,000. Explain why this is not what the model predicted.
(c) If you were going to use multiple regression to develop an appraisal model, what other quanititative variables might be included in the model?
(d) What is the coefficient of determination for this model?
Answer:
Step-by-step explanation:
Hello!
Given the variables:
Y: Price of a house on sale
X: Square feet of a hose on sale
Y= 33.478 + 62.4X
r= 0.63
a)
To use the model to predict the price of a house with X= 1860 square feet you have to replace that value in the estimated equation:
^Y= 33478 + 62.4*1860= $149542
b)
The model predicts the estimated average value of Y given a certain value of X, that's why the value the house was sold for is different.
c)
Any variable that may vary the price of the house can be included in the model, for example:
X: Age of the house
X: Number of bedrooms
X: Type of neighborhood (residential area, industrial area, commercial area, etc...)
d)
Mathematically the coefficient of determination is equal to the square of the correlation coefficient:
R²= (r)²= 0.63²= 0.3969
This means that 39.69% of the variability of the house price is explained by the square footage of the house under the model: ^Y= 33.478 + 62.4X
I hope this helps!
Please help. I don’t understand this math problem . I’ll mark you as brainliest if correct
Answer:
[tex]f(x)=3\log_4{(2-x)}[/tex]
Step-by-step explanation:
You know that a log function has a vertical asymptote at x=0 and an x-intercept at (1, 0). It trends upward to the right.
The given graph has a vertical asymptote at x=2, indicating the transformation involves a right-shift of 2 units. It trends upward to the left of the vertical asymptote, suggesting a reflection is involved. At 1 unit left of the vertical asymptote, the graph crosses y=0, so there is no horizontal scaling involved.
At this point, you can write a version of the function f(x) that incorporates the reflection and translation:
f(x) = k·log(-(x -2)) = k·log(2-x)
To find the vertical scale factor k, we make use of the additional point that is given.
f(-2) = 3
k·log(2 -(-2)) = 3 . . . . substitute into our f(x) so far
k = 3/log(4) . . . . . . . . solve for k
Now, the function can be written as ...
[tex]f(x)=\dfrac{3}{\log{4}}\log{(2-x)}=3\dfrac{\log{(2-x)}}{\log{4}}[/tex]
Using the "change of base" formula for logarithms we can compact this to ...
[tex]\boxed{f(x)=3\log_4{(2-x)}}[/tex]
Can u pls tell the pythagroes thearom formula plsss
Answer:
a² + b² = c²
Step-by-step explanation:
The sum of the legs squared is equal to the hypotenuse squared.
a² + b² = c²
Where a and b are legs.
c is the hypotenuse.
Answer:
Trigonometry: Hypotenuse^2 = Opposite^2+ Adjacent^2General: a² + b² + c²Step-by-step explanation:
Pythagoras Theorem(used in trigonometry) :
[tex]Hypotenuse^2 = opp^2 + adj ^2 \: [/tex]
Pythagoras Theorem (General)
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Which data set is accurate and precise based on a correct value of 30?
Set 1: 30, 35, 32, 30, 29
Set 2: 15, 16, 12, 15, 14
Set 3: 19, 30, 78, 43, 30
Set 4: 30, 30, 67, 12, 90
Answer:
Set 1: 30, 35, 32, 30, 29
Step-by-step explanation:
Let's first clarify what is accurate and precise:
Precise is based on how close two or more measured values are to each other. While something is said to be accurate, when the standard value values are close, which in our case is 30.
Therefore, we analyze each set:
Set 1: 30, 35, 32, 30, 29
This set is precise and accurate, since 2 values are 30 and all their values are close to each other.
Set 2: 15, 16, 12, 15, 14
This set is precise, because all of its values are close but not accurate.
Set 3: 19, 30, 78, 43, 30
This set is somewhat accurate because there are 2 values of 30, but it is not precise because its values are separate.
Set 4: 30, 30, 67, 12, 90
It is the same case of Set 3.
Therefore the answer is Set 1.
Answer:
Set 1: 30, 35, 32, 30, 29
Step-by-step explanation:
Abox in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12
cubes measuring 6 inches on each side.
If the length and width of the base are doubled, how many cubes could the new box hold?
18
0 24
48
o 96
Answer:
48
Step-by-step explanation:
You are doubling 2 dimensions, so you just multiply the volume by 2 each time. Since you are doing it twice, you multiply the volume by 4. 12*4=48. You could also brute force it and just do 24*36*12/216(the volume of the 6 inch cube).
Given that, a box in the shape of a rectangular prism, with dimensions 12 inches by 18 inches by 12 inches, can hold exactly 12 cubes measuring 6 inches on each side.
We need to find that how many cubes it holds if the length and width of the base are doubled,
We know that,
Volume of a rectangular prism = length × width × height
Volume of the new rectangular prism, = 2length × 2width × height
= 4(length × width × height)
= 4(12·12·18)
= 4×2592
= 10,368
Volume of the cube = side³
= 6³ = 216
The number of cube that the new rectangular prism can hold = Volume of the rectangular prism / Volume of the cube
= 10,368 / 216
= 48
Hence, the new rectangular prism, can hold 48 cubes.
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Solve by completing the square. x2−12x=−27 Select each correct answer. −9 −3 3 9 15
Answer:
x=9,3
Step-by-step explanation:
x²-12x=-27
x²-12x+(12/2)²=-27+(12/2)²
x²-12x+6²=-27+36
(x-6)²=9
x-6=[tex] \frac{ + }{ - } \sqrt{9} [/tex]
x-6=+3 and x-6=-3
x=9 and 3
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h
Answer:
C
Step-by-step explanation:
We know that A is not true because we know that h(8) is 19, not 21. B is also not true because the value of h(x) can't be -1. D can't be true because x can't be 13, therefore the answer is C.
WILL GIVE BRAINLIEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter. plz help me
Answer:
P ≈ 317.08 m
Step-by-step explanation:
Circumference: C = πd
Step 1: Find circumference of both domes
C = π(50)
Since it's a dome, we divide by 2
50π/2 = 25π
Since we have 2 domes, we simply multiply by 2 again
25π(2) = 50π
Step 2: Find perimeter of track
50π + 80(2)
P = 50π + 160
P = 317.08 m
The tread life of a particular brand of tire is normally distributed with mean 60,000 miles and standard deviation 3800 miles. Suppose 35 tires are randomly selected for a quality assurance test. Find the probability that the mean tread life from this sample of 35 tires is greater than 59,000 miles. You may use your calculator, but show what you entered to find your answer. Round decimals to the nearest ten-thousandth (four decimal places).
Answer:
P [ x > 59000} = 0,6057
Step-by-step explanation:
We assume Normal Distribution
P [ x > 59000} = (x - μ₀ ) /σ/√n
P [ x > 59000} = (59000 - 60000)/ 3800
P [ x > 59000} = - 1000/3800/√35
P [ x > 59000} = - 1000*5,916 /3800
P [ x > 59000} = - 5916/3800
P [ x > 59000} = - 1,55
We look for p value for that z score n z-table and find
P [ x > 59000} = 0,6057
work out the following, giving your answer to the simplest form 5 3/5/2 2/3
Answer:
2 1/10
Step-by-step explanation:
We suppose you want the quotient of the mixed numbers 5 3/5 and 2 2/3.
(5 3/5)/(2 2/3) = (28/5)/(8/3) = (28/5)(3/8) = (4)(7)(3)/(5(4)(2)) = 21/10
= 2 1/10
Karri tests the charges of a random sample of 64 batteries from a large production run. The mean charge was 8.93 volts, and the process typically has a standard deviation of 0.2 volts. To see if the batch has a significantly different mean voltage from 9 volts, the value of the z-test statistic would be ___________.
Answer:
The Z-statistic value is
Z = -2.33
Step-by-step explanation:
Step(i):-
Random sample size 'n' = 64
mean of the sample 'x⁻ ' = 8.93 volts
standard deviation of the sample = 0.2 volts
mean of the Population"μ" = 9 volts
Step(ii):-
Z -statistic
[tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{8.93 -9}{\frac{0.2}{\sqrt{64} } } = -2.33[/tex]
Conclusion:-
The Z-statistic value is = -2.33
Here is a list of numbers 83,73,76,72,75,85,79,76 work out the median from the numbers from the list
Answer:
552.5
Step-by-step explanation:
Answer:
76Step-by-step explanation:
Median means the middle or central value.
Given data : 83 , 73 , 76 , 72 , 75 , 85 , 79 , 76
Arranging the data in ascending order:
72 , 73 , 75 , 76 , 76 , 79 , 83 , 85
N ( total number of items ) = 8
Here, as there are 8 terms , we cannot find the one central value within the set.
The median will be average of the two central terms, 76 and 76
Now, to find the median, we have to divide the sum of two central terms ( 76 and 76) by 2
Median :[tex] \frac{76 + 76}{2} [/tex]
Calculate the sum:
[tex] \frac{152}{2} [/tex]
Divide:
[tex]76[/tex]
Hope this helps..
Best regards!
On the "Compiled Information" tab, a VLOOKUP formula has been pre-entered into cell E3. This formula was written correctly, and it uses references to the numbers in cells E1 through G1 to determine the correct index_number parameter. Fill in cells F1 and G1 with the correct index numbers, then copy the formula in cell E3 down to all the rows in columns E, F, and G. What number did you enter into cell G1?
Answer:
3
Step-by-step explanation:
Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:
=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.
where true is approximate match and false is exact match.
which linear function is represented by the graph below?
A) f(x) = -2x + 1
B) f(x) = -1/2x + 1
C) f(x) = 1/2x + 1
D) f(x) = 2x + 1
Answer:
The answer is answer choice b.
Step-by-step explanation:
b/c its a negative line
Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ticket prices were set at $12, the average attendance was 30,000. When the ticket prices were on sale for $10, the average attendance was 35,000.
(a) Let D(x) represent the number of people that will buy tickets when they are priced at x dollars per ticket. If D(x) is a linear function, use the information above to find a formula for D(x). Show your work!
(b) The revenue generated by selling tickets for a baseball game at x dollars per ticket is given by R(x) = x-D(x). Write down a formula for R(x).
(c) Next, locate any critical values for R(x). Show your work!
(d) If the possible range of ticket prices (in dollars) is given by the interval [1,24], use the Closed Interval Method from Section 4.1 to determine the ticket price that will maximize revenue. Show your work!
Optimal ticket price:__________ Maximum Revenue:___________
Answer:
(a)[tex]D(x)=-2,500x+60,000[/tex]
(b)[tex]R(x)=60,000x-2500x^2[/tex]
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]
Therefore, we have:
[tex]y=-2500x+b[/tex]
At point (12,30000)
[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]
Therefore:
[tex]D(x)=-2,500x+60,000[/tex]
(b)Revenue
[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]
Therefore:
Optimal ticket price:$12Maximum Revenue:$360,000