Answers
Answer:
1350 square inches
Step-by-step explanation:
The area of the end trapezoid is ...
A = (1/2)(b1 +b2)h = (1/2)(12 +36)(5) = 120 . . . . . square inches
The perimeter of the end trapezoid is ...
P = 13 +12 +13 + 3×12 = 74 . . . . inches
so the total area of the rectangular surfaces (including the bottom) is ...
(74 in)(15 in) = 1110 in²
The total area of the ramp is this rectangular area plus the two trapezoidal ends:
total area = rectangle area + 2×trapezoid area
= 1110 in² +2×120 in²
total area = 1350 square inches
Related Questions
A package has dimensions 10x10x6 inches mrs James wants to gift a wrap it for her grandson what is the total surface area to be wrapped?
Answers
Answer:
440 square inches
Step-by-step explanation:
10x10x2=200
10x6x4=240
240+200=440
A rectangular field is 0.3 kilometers long and 0.15 kilometers wide. What is the area of the field in square meters?
Answers
Final answer:
To find the area of the rectangular field in square meters, convert the dimensions from kilometers to meters and then multiply them together, resulting in 45,000 square meters.
Explanation:
To calculate the area of a rectangular field that is 0.3 kilometers long and 0.15 kilometers wide, use the following steps:
Convert the dimensions from kilometers to meters. Since there are 1,000 meters in a kilometer, the length in meters is 0.3 km × 1,000 = 300 meters and the width is 0.15 km × 1,000 = 150 meters.Multiply the length and width in meters to get the field's area in square meters. So the area is 300 m × 150 m = 45,000 square meters.A manufacturing company is ready to introduce a new product with a national sales campaign. After extensive test marketing, the market research department estimates that sales (in millions of dollars) will increase at the monthly rate of S'(t) = 10 - 10e-0.2t for 0 ≤ t ≤ 24, t months after the national campaign has started. What will the total sales be five months after the beginning of the campaign if we assume zero sales at the beginning of the campaign? (Round the answer to the nearest million.)
Answers
Final answer:
The total sales five months after the beginning of the campaign is approximately 72 million dollars.
Explanation:
To find the total sales five months after the beginning of the campaign, we need to calculate the definite integral of the sales rate function from t=0 to t=5. The sales rate function can be expressed as S'(t) = 10 - 10e^(-0.2t).
First, let's find the antiderivative of the sales rate function. The antiderivative of 10 is 10t, and the antiderivative of -10e^(-0.2t) is 50e^(-0.2t). Therefore, the indefinite integral of S'(t) is S(t) = 10t - 50e^(-0.2t) + C, where C is the constant of integration.
Next, we evaluate the definite integral over the interval t=0 to t=5. Substituting the upper and lower limits into the antiderivative, we get S(5) - S(0) = (10(5) - 50e^(-0.2(5))) - (10(0) - 50e^(-0.2(0))) = (50 - 50e^(-1)) - (0 - 50e^0) = 50 - 50e^(-1) + 50 = 100 - 50e^(-1) million dollars.
Rounding the answer to the nearest million, the total sales five months after the beginning of the campaign is approximately 72 million dollars.
Jasmine has 3 and 3/8 pound of Turkey meat she is making 1/3 pound Turkey burgers does Jasmine have enough meat to make 12 Turkey burgers
Answers
Answer:
No
Step-by-step explanation:
To answer this you have to divide 3 and 3/8 by 1/3. The easiest way to do this without a calculator is to do this separately. First divide 3 by 1/3. When dividing fractions, the second number is flipped upside down and the two numbers are multiplied. From 3 pounds, Jasmine will be able to make nine 1/3 pound burgers.
3 ÷ 1/3 = 3 × 3/1 = 9
Next, divide 3/8 by 1/3. From 3/8 pounds, Jasmine will be able to make 1 1/8 burgers
3/8 ÷ 1/3 = 3/8 × 3/1 = 9/8 = 1 1/8
Add the two numbers together.
9 + 1 1/8 = 10 1/8
This is less than 12.
To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Jasmine has 3 and 3/8 pounds of turkey meat
Amount in pounds needed to make 1 burger = 1/3 pound
Number of burgers in 3 3/8 ⇒
(3 3/8)/(1/3) = 10 1/8
For making 12 Turkey burgers ⇒
Amount of meat required = 12 × 1/3 = 4 pounds
Hence "To make 12 Turkey burgers Jasmine needs 4 pounds thus 3 and 3/8 are not enough to make 12 Turkey burgers".
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I=$54, P=$900, t=18 months
Answers
Answer:
about $982.20
Step-by-step explanation:
Formula = P(1+I)^T
T =18/12 because its in months not years, so 1.5 years
1+I = 1 + 54/900 or 1.03
P = 900
Plug those in and you get about 982.20
Answer:
4%
Step-by-step explanation:
For the simple interest rate,
I=P(i)t
54=900(i)(18/12)
i=54/900*(12/18)=4% annually
Select the correct answer.
Which value of x makes the equation true?
x + 7 = -9
A. -16
B. -2
C. 2
D. 16
Answers
X + 7 = -9
Subtract -7 from both sideS
X = -16
Or
Then divide both by 1
X = -16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
The given equation is x+7=-9.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation can be solved as follows:
x+7=-9
Transpose 7 to RHS of the equation, we get
x=-9-7
=-16
The value of x makes the equation true is -16. Therefore, option A is the correct answer.
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The per capita electric power consumption level in a recent year in Ecuador is normally distributed, with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilowatt-hours. Random samples of size 35 are drawn from this population. Find (a) the mean and (b) the standard deviation of the sampling distribution of sample means. Round the answer from part (b) to the third decimal place.
Answers
Answer:
a) 471.5 kilo-watt hours.
b) 31.76 kilo-watt hours
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the population:
Mean 471.5 kilo-watt hours.
Standard deviation of 187.9 kilowatt-hours.
For the sample:
Sample size of 35, by the Central Limit Theorem:
a) Mean
471.5 kilo-watt hours.
b) Standard deviation
[tex]s = \frac{187.9}{\sqrt{35}} = 31.76[/tex]
31.76 kilo-watt hours
Final answer:
The mean of the sampling distribution of sample means is 471.5 kilo-watt hours, and the standard deviation (or standard error) of the sampling distribution, rounded to the third decimal place, is 31.749 kilo-watt hours.
Explanation:
The question concerns the concept of sampling distribution and its parameters, namely the mean and standard deviation, within the field of statistics. Given that the per capita electric power consumption level in Ecuador is normally distributed with a mean of 471.5 kilo-watt hours and a standard deviation of 187.9 kilo-watt hours, and considering samples of size 35, we are to find the mean and standard deviation of the sampling distribution of sample means.
(a) The mean of the sampling distribution of sample means is equal to the population mean. Therefore, the mean is:
471.5 kilo-watt hours
(b) The standard deviation of the sampling distribution of sample means, also known as the standard error (SE), is calculated using the following formula:
SE = σ / √n
where σ is the population standard deviation and n is the sample size. In this case:
SE = 187.9 / √35 ≈ 31.749 kilo-watt hours (rounded to the third decimal place)
Each student in a statistics class had a randomly assigned bag of candies and counted the number of each color (Blue, Red, Orange, Green, Brown, Yellow). The bags were all the same size. The investigators claimed to use a randomized block design, with Bag as the blocking factor. They counted the number of candies of each color in each bag. Their results are reproduced in the given ANOVA output. Complete parts (a) through (c).
Source Degrees Sum of Mean F-ratio P-value
of Freedom Squares Square
Bag 13 4.726 0.364 0.10 1.000
Color 6 350.679 70.136 18.72 <0.001
Error 65 243.488 3.746
Total 83 598.893
(a) Was this an observational or experimental study?
(b) What was the treatment? What factors were manipulated?
A. The factors were color and bag and the treatments were all possible combinations of those two factors.
B. The factors were bag and student and the treatments were all possible combinations of those two factors.
C. The factors were color and student and the treatments were all possible combinations of those two factors
D. There is no treatment. No factors were manipulated.
(c) What was the response variable?
Answers
Answer:
Step-by-step explanation:
Hello!
a)
An observational study is one where the investigator has no control or intervenes on it. He just defines the variable of interest and merely collects and documents the information. These types of studies are usually made as precursors to a more formal experimental study, to have an idea of what's to be expected from the population.
An experimental study or experiment is one where the investigator intervenes by defining the variable of interest and artificially manipulates the study factor. It is also one of its characteristics the randomization of cases or subjects in groups (two or more, depending on what is the hypothesis of study).
In this example, the investigators used a randomized block design with "Bag" as the blocking factor and assigned the bags randomly to the students of the statistic class.
The researchers manipulated all confounding factors in this experiment leaving only "the number of candies per color per bag" as the only random variable. This is an experimental study.
b)
This is an ANOVA with two factors, "Bag" and "Colour" and the treatments are all possible combinations between these two factors.
Correct Option A.
c) The response variable is the "number of candies per color per bag"
Colors: Blue, Red, Orange, Green, Brown and Yellow.
I hope you have a nice day!
Which exponential expressions are equivalent to the one below? Check all
that apply.
(5x9)^12
Answers
Answer:D
Step-by-step explanation:
(5x9)^12
5^12 x 9^12
Sketch the region of integration and evaluate the following integral. ModifyingBelow Integral from nothing to nothing Integral from nothing to nothing With Upper R StartFraction 1 Over 3 plus StartRoot x squared plus y squared EndRoot EndFraction dA , RequalsStartSet (r comma theta ): 0 less than or equals r less than or equals 2 comma StartFraction pi Over 2 EndFraction less than or equals theta less than or equals StartFraction 3 pi Over 2 EndFraction EndSet
Answers
Answer:
[tex]\frac{10\pi}{3}[/tex]
Step-by-step explanation:
According to the information of the problem we have to compute the following integral.
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA[/tex]
Where the region of integration is
[tex]R = \Big\{ (r,\theta) : 0 \leq r \leq 2 , \,\,\,\, \frac{\pi}{2} \leq \theta \leq \frac{3\pi}{2} \Big\}[/tex]
If you plot, that is just a circle between [tex]\pi/2[/tex] and [tex]3\pi/2[/tex], which is just half of the circle on the negative part of the plane.
When you switch coordinates
[tex]{\displaystyle \int\limits \int} \frac{1}{3} + \sqrt{x^2 + y^2} \, dA = {\displaystyle \int\limits_{0}^{2} \int\limits_{\pi/2}^{3\pi/2}} \bigg(\frac{1}{3} + r \bigg)r \, d\theta\, dr = \frac{10\pi}{3}[/tex]
Which of the following is the inverse of y = 12 Superscript x? y = log Subscript one-twelfth Baseline x y = log Subscript 12 Baseline StartFraction 1 Over x EndFraction y = log Subscript x Baseline 12 y = log Subscript 12 Baseline
Answers
The inverse of the function is logx/log12
The inverse of a functionGiven the function expressed as:
y = 12^x
To find the inverse, switch the variables to have:
x = 12^y
Take the log of both sides
logx = y log 12
y = logx/log12
Hence the inverse of the function is logx/log12
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A mountain climber starts a climb at an elevation of 453 feet above sea level. At his first rest stop he has climbed 162 feet, and by his second rest stop he has climbed another 207 feet. It's getting late in the day, so the climber starts his way down. If the climber descends 285 feet, how much does he need to ascend or descend to return to the original starting point?
A) ascend 84 feet
B) ascend 78 feet
Eliminate
C) descend 84 feet
D) descend 78 feet
Answers
Answer:
C) Descend 84 feet
Step-by-step explanation:
162+207=369
369-285=84ft above starting point, this means that he must descend 84 feet to reach the starting point.
Which equation represents an exponential function with an initial value of 500?
Answers
Answer:
the fourth one
Step-by-step explanation:
Answer:
Answer: f(x) = 500(2)^x
Step-by-step explanation:
Just took the test .
Which formula should be used to find the circumference of a circle?
C =πd
C=2πd
C=πr C=π/d
NEED HELP ASAP !
Answers
Answer:
C = πd or 2πr
Step-by-step explanation:
2r equals d
2r = d
The average speed of a baseball line drive is 83 miles per hour. Josiah practiced a new technique to improve his hitting speed. His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour. Part A: State the correct hypotheses Josiah is trying to prove the new technique is an improvement over the old technique. (4 points) Part B: Identify the correct test and check the appropriate conditions. (6 points)
Answers
Answer:
We conclude that the new technique is not an improvement over the old technique at 5% level of significance.
Step-by-step explanation:
We are given that the average speed of a baseball line drive is 83 miles per hour.
His coach recorded the speed of 42 random hits during practice and found that his average speed using the new technique was 84.2 miles per hour, with a standard deviation of 4.7 miles per hour.
Let [tex]\mu[/tex] = true average speed using the new technique.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 83 miles per hour {means that the new technique is not an improvement over the old technique}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 83 miles per hour {means that the new technique is an improvement over the old technique}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample average speed using the new technique = 84.2 mph
s = sample standard deviation = 4.7 mph
n = sample of hits = 42
So, the test statistics = [tex]\frac{84.2-83}{\frac{4.7}{\sqrt{42} } }[/tex] ~ [tex]t_4_1[/tex]
= 1.655
The value of t test statistics is 1.655.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of 1.6832 at 41 degree of freedom for right-tailed test.
Since our test statistic is less than the critical value of t as 1.655 < 1.6832, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the new technique is not an improvement over the old technique.
How is a net useful when finding the surface area or prisms and pyramids?
Answers
Answer:oh yeah I remember that
Step-by-step explanation:
That’s tuff
a. The number 86,362,575 rounded to the nearest hundred is
Answers
Answer:
86362600
Step-by-step explanation:
We want to round to the hundreds place
We look at the 7 in the tens place. Since it is 5 or greater we round up
86,362,575 round to 86362600
Answer:
86,362,600
Step-by-step explanation
You are in charge of buying office supplies for your business. Your workers use red and black pens. Red pens cost $5 per box and black pens cost $3 per box. You need at least 10 boxes of pens. You want no more than 7 boxes of black pens and no more than 6 boxes of red pens. You want to minimize the cost to your business.
The objective function for this situation is C = 5x + 3y. What (x, y) pair minimizes cost?
image
(6, 7)
(0, 7)
(3, 7)
(6, 4)
Answers
Answer:
C. (3, 7)
Step-by-step explanation:
plug all the numbers into all of the coordinates and (3, 7) is the lowest number :) pls rate 5 stars and thank me
The option of buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business, based on the objective function C = 5x + 3y and the given constraints of at least 10 boxes in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
Explanation:To minimize the cost of buying office supplies, particularly red and black pens, we need to use the given objective function C = 5x + 3y where x represents the number of boxes of red pens and y represents the number of boxes of black pens. We have the following constraints: at least 10 boxes of pens in total, no more than 7 boxes of black pens, and no more than 6 boxes of red pens.
By applying these constraints, we can determine the combinations of x and y that meet the criteria:
x + y ≥ 10 (at least 10 boxes of pens)x ≤ 6 (no more than 6 boxes of red pens)y ≤ 7 (no more than 7 boxes of black pens)Looking at the choices provided, (6, 4) meets all our constraints, and when plugged into the objective function:
C = 5(6) + 3(4) = 30 + 12 = $42
This results in the lowest cost when compared to the other presented options. Therefore, buying 6 boxes of red pens and 4 boxes of black pens minimizes the cost to the business.
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write a number with two decimal places, that is bigger than 4 wholes and 1/5 but smaller than 4.25
Answers
Answer :
11.45
step-by-step explantion :
4.25=17/4
when we add 41/5 and 17/4, we get
41×4+17×5/4×5
164+65/20
229/20
11.45 Ans
:
Product A requires 9 minutes of milling, 7 minutes for inspection, and 6 minutes of drilling per unit; product B requires 10 minutes of milling, 5 minutes for inspection, and 8 minutes of drilling per unit; product C requires 7 minutes of milling, 3 minutes for inspection, and 15 minutes of drilling. The department has 20 hours available during the next period for milling, 15 hours for inspection, and 24 hours for drilling. Product A contributes $2.0 per unit to profit, product B contributes $2.3 per unit, and product C contributes $4.0 per unit. a. How many constraints are there in the Linear Programming Formulation of this problem
Answers
Answer:
The Linear programming problem has 3 constraints :- Milling time, Inspection time, Drilling time constraints.
Step-by-step explanation:
Product A : 9 minutes milling, 7 minutes inspection, 6 minutes drilling Product B : 10 minutes milling, 5 minutes inspection, 8 minutes drilling Product C : 7 minutes milling, 3 minutes inspection, 15 minutes drilling
Total milling time available = 20 hours = (20 x 60) i.e 1200 minutes Total inspection time available = 15 hours = (15 x 60) i.e 900 minutes Total drilling time available = 24 hours = (24 x 60) i.e 1440 minutes
Let QA, QB, QC be quantities of product A, B, C respectively
Milling time constraint : 9QA + 10QB + 7QC = 1200 Inspection time constraint : 7QA + 5QB + 3QC = 900Drilling time constraint : 6QA + 8QB + 15QC = 1440Juan Pablo demora 7 minutos en dar una vuelta a la cancha de fútbol y Pedro demora 2 minutos más corriendo a la misma velocidad que Juan Pablo. ¿Cuánto tiempo demorará Pedro en dar 12 vueltas?
Answers
Answer: 108 minutes
Step-by-step explanation:
This translates to:
Juan Pablo takes 7 minutes to do a full lap on a football field, Pedro needs 2 more minutes ruuning at the same speed thanJuan Pablo.
How much time does Pedro need to do 12 laps?
The fact that Pedro runs at the same speed than Juan Pablo, and needs more time, may mean that the radius of the laps of Pedro are a little bit bigger than the ones of Juan Pablo (which means that the total distance that pedro runs is bigger)
If Juan Pablo does a lap in 7 minutes, then Pedro does a lap in 7 minutes + 2 minutes = 9 minutes.
Then to do 12 laps, he needs 12 times that amount of time, this is:
12*9 min = 108 minutes
A shipment to a warehouse consists of 500 PS4. The manager chooses a random sample of 50 PS4 and finds that 3 are defective. How many PS4 in the shipment are likely to be defective?
Answers
Answer:
30 PS4 in the shipment are likely to be defective
Step-by-step explanation:
We take the estimate from the sample and estimate to all the PS4 in store. This means that we can solve this question using a rule of 3.
From the sample of 50 PS4, 3 are defective. How many are expected to be defective out of 500?
50PS4 - 3 defective
500 PS4 - x defective
[tex]50x = 3*500[/tex]
[tex]x = \frac{1500}{50}[/tex]
[tex]x = 30[/tex]
30 PS4 in the shipment are likely to be defective
Answer:
don't take my word but I think 150
Step-by-step explanation:
Kelly walks 4/5 of a mile each day. How many miles does Kelly walk after three days?
Answers
Answer:
Kelly walks 4/5 of a mile each day.
After 3 days, Kelly walks a distance: D = 3 x 4/5 = 12/5 = 2.4 miles
Hope this helps!
:)
Kelly walks 4/5 of a mile each day, and after three days, she would have walked 2 and 2/5 miles.
Kelly walks 4/5 of a mile each day. To find out how many miles Kelly walks after three days, we simply multiply the daily distance by three.
Calculation:
4/5 mile/day * 3 days = 12/5 miles
To convert 12/5 miles into a mixed number, we divide 12 by 5. The quotient is 2 with a remainder of 2, so Kelly walks 2 and 2/5 miles after three days.
An environmental science teacher at a high school with a large population of students wanted to estimate the proportion of students at the school who regularly recycle plastic bottles. The teacher selected a random sample of students at the school to survey. Each selected student went into the teacher’s office, one at a time, and was asked to respond yes or no to the following question.
Do you regularly recycle plastic bottles?
Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816)
How many students were in the sample selected by the environmental science teacher?
Answers
Answer:
60 students
Step-by-step explanation:
The confidence interval of a proportion is given by:
[tex]p\pm z*\sqrt{\frac{p*(1-p)}{n} }[/tex]
Where 'p' is the proportion of students who responded 'yes', 'z' is the z-score for a 95% confidence interval (which is known to be 1.960), and 'n' is the number of students in the sample.
If the confidence interval is from 0.584 to 0.816, then:
[tex]p=\frac{0.584+0.816}{2}=0.7 \\0.816-0.584=2*(1.96*\sqrt{\frac{p*(1-p)}{n}}) \\0.116=1.96*\sqrt{\frac{0.7*(1-0.7)}{n}}\\n=16.8966^2*(0.7*0.3)\\n=60\ students[/tex]
60 students were in the sample.
Final answer:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher used a random sample and calculated a 95 percent confidence interval. Using the formula for the confidence interval for proportions, we can determine that the teacher selected approximately 223 students for the survey.
Explanation:
To estimate the proportion of students at the school who regularly recycle plastic bottles, the teacher selected a random sample of students and surveyed them one at a time, asking them if they regularly recycle plastic bottles. Based on the responses, a 95 percent confidence interval for the proportion of all students at the school who would respond yes to the question was calculated as (0.584, 0.816).
To find out how many students were in the sample selected by the teacher, we need to use the formula for the confidence interval for proportions:
n = (Z^2 * p * (1-p)) / (E^2)
Where:
n is the sample size,
Z is the Z-score corresponding to the desired level of confidence (in this case, 95 percent),
p is the estimated proportion of students who recycle plastic bottles (we can use the midpoint of the confidence interval, which is (0.584 + 0.816) / 2 = 0.7),
E is the margin of error (in this case, half the width of the confidence interval, which is (0.816 - 0.584) / 2 = 0.116).
Plugging in the values, we get:
n = (1.96^2 * 0.7 * (1-0.7)) / (0.116^2)
n = 2.992 / 0.013456
n ≈ 222.38
Since the sample size must be a whole number, we round up to the nearest whole number.
Therefore, the teacher selected approximately 223 students for the survey.
How many possible outcomes exist when Louisa spins the spinner below twice? A spinner with 8 equal sections labeled 1 through 8. 8 10 16 64
Answers
Answer:
64
Step-by-step explanation:
The spinner has 8 equal sections numbered from 1 to 8
Each time she spinns the spinner has 8 possible outcomes.
To know the number of possible results when spinning two times, you must multiply the possible results for the first spin (8 possible outcomes) by the possible results for the second spin (also 8 possible outcomes).
And because each spin has the same number of outcomes:
[tex]8*8=64[/tex]
the answer is that there are 64 possible outcomes
Answer:
64
Step-by-step explanation:
Labor statistics indicate that 77% of all U.S. cashiers and servers are women. A random sample of cashiers and servers in a particular metropolitan area found that 112 of 150 cashiers and 150 of 200 servers were women. At the 0.05 level of significance, is there sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population? What is the test statistic? Round to 2 decimal places.
Answers
Final Answer:
The test statistic for the difference in proportions between the metropolitan area and the U.S. population is approximately ( -0.11 ). Since this value does not exceed the critical value of [tex]\( \pm 1.96 \)[/tex] at the 0.05 significance level, there is insufficient evidence to conclude a significant difference. Therefore, we fail to reject the null hypothesis.
Step-by-step explanation:
To determine whether there is sufficient evidence to conclude that a difference exists between this metropolitan area and the larger U.S. population, we can perform a hypothesis test for the difference in proportions.
Let:
[tex]\( p_1 \)[/tex] be the proportion of women in the metropolitan area.
[tex]\( p_2 \)[/tex] be the proportion of women in the larger U.S. population.
The null hypothesis [tex](\( H_0 \))[/tex] is that there is no difference between the proportions, and the alternative hypothesis [tex](\( H_1 \))[/tex] is that there is a significant difference.
The formula for the test statistic for the difference in proportions ( z ) is given by:
[tex]\[ z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{p(1-p)\left(\frac{1}{n_1} + \frac{1}{n_2}\right)}} \][/tex]
Where:
[tex]\( \hat{p}_1 \)[/tex] and [tex]\( \hat{p}_2 \)[/tex] are the sample proportions of women in the metropolitan area and the U.S. population, respectively.
( p ) is the combined sample proportion.
[tex]\( n_1 \)[/tex] and [tex]\( n_2 \)[/tex] are the sample sizes for the metropolitan area and the U.S. population, respectively.
First, let's calculate [tex]\( \hat{p}_1 \)[/tex], [tex]\( \hat{p}_2 \)[/tex], ( p ), and then plug them into the formula to find the test statistic.
[tex]\[ \hat{p}_1 = \frac{112}{150} = 0.7467 \][/tex]
[tex]\[ \hat{p}_2 = \frac{150}{200} = 0.75 \][/tex]
[tex]\[ p = \frac{112 + 150}{150 + 200} = \frac{262}{350} = 0.7486 \][/tex]
Now, we can calculate the test statistic:
[tex]\[ z = \frac{(0.7467 - 0.75)}{\sqrt{0.7486(1-0.7486)\left(\frac{1}{150} + \frac{1}{200}\right)}} \][/tex]
Calculate the values and round the test statistic to two decimal places. If the absolute value of the test statistic is greater than the critical value for a two-tailed test at the 0.05 significance level, we reject the null hypothesis.
Note: The critical value for a two-tailed test at the 0.05 significance level is approximately [tex]\( \pm 1.96 \)[/tex].
If Zoe paints the visible outside faces of her shed, what is the total surface area that she paints? Alternative Text A. 48 ft2 B. 64 ft2 C. 96 ft2 D. 112 ft2
Answers
The total surface area that she paints will be 96 square feet. Thus, the correct option is C.
What is the area of the rectangle?Let W be the rectangle's width and L its length. The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be given as,
Area of the rectangle = L × W square units
Given that:
Length, L = 12 ft
Width, W = 8 ft
The area of the rectangle is given as,
A = 12 x 8
A = 96 square feet
Thus, the correct option is C.
More about the area of the rectangle link is given below.
https://brainly.com/question/20693059
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The missing diagram is given below.
Find the probability selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles when (a) you replace the first marble before drawing the second, and (b) you do not replace the first marble. Then, compare the probabilities. Round your answers to four decimal places.
Answers
Step-by-step explanation:
There are a total of 16 marbles, 8 of which are green.
(a) The probability the first marble is green is 8/16.
The marble is replaced, so there are still a total of 15 marbles, 8 of which are green. The probability the second marble is green is 8/16.
The probability of both events is (8/16) (8/16) = 1/4 = 0.2500.
(b) The probability the first marble is green is 8/16.
The marble is not replaced, so there are now a total of 15 marbles, 7 of which are green. The probability the second marble is green is 7/15.
The probability of both events is (8/16) (7/15) = 7/30 = 0.2333.
Final answer:
The probability of selecting a green marble, then another green marble from a bag of marbles is 0.25 when the first marble is replaced and 0.2333 when the first marble is not replaced.
Explanation:
To find the probability of selecting a green, then another green marble from a bag of 5 red, 8 green, and 3 blue marbles, we need to consider two scenarios: (a) replacing the first marble before drawing the second, and (b) not replacing the first marble.
a) If the first marble is replaced before drawing the second, the probability of selecting a green marble on the first draw is 8/16, and the probability of selecting a green marble on the second draw is also 8/16. We can multiply these probabilities together to get the overall probability: 8/16 × 8/16 = 16/64 = 0.25.
b) If the first marble is not replaced, the probability of selecting a green marble on the first draw is 8/16. However, since the first marble is not replaced, there are only 15 marbles left in the bag for the second draw, with 7 green marbles remaining. The probability of selecting a green marble on the second draw is 7/15. We can multiply these probabilities together to get the overall probability: 8/16 × 7/15 = 56/240 = 0.2333 (rounded to four decimal places).
Comparing the probabilities, we can see that the probability in scenario (a) when the first marble is replaced is higher than the probability in scenario (b) when the first marble is not replaced.
One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after 4 weeks in order to determine if there has been substantial improvement in the severity of the depression. Suppose volunteers were first divided by gender, and then half of the men were randomly assigned to the new drug and half of the women were assigned to the new drug. The remaining volunteers received the other drug. What is this an example of
Answers
Answer:
This is an example of placebo testing.
Step-by-step explanation:
This is an example of placebo testing in which, the two groups are given two substances that are said to have an effect on the condition that is being treated but one of them is the actual medicine that is being tested while the other one has no real effect over the medical condition. But the volunteers are not given information on which of the medicines is real and which is not, so that this does not affect the outcome of the experiment.
I hope this answer helps.
Which expressions are solutions to the equation (3/4)x = 15? Select all that apply.
Answers
The expressions that are solutions to the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C
as [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution and [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.
Let's solve the equation [tex]\( \frac{3}{4}x = 15 \)[/tex] and then check each expression to see if it is a solution:
1. Solve the equation:
[tex]\[ x = \frac{15}{\frac{3}{4}} \][/tex]
To divide by a fraction, we can multiply by its reciprocal:
[tex]\[ x = 15 \times \frac{4}{3} = 20 \][/tex]
Now, let's check each expression:
A. [tex]\( \frac{15}{\frac{3}{4}} = 20 \)[/tex] - This is a solution.
B. [tex]\( \frac{15}{\frac{4}{3}} \)[/tex] - This expression is equivalent to [tex]\( \frac{15 \times 3}{4} = \frac{45}{4} \)[/tex], not equal to 20.
C. [tex]\( \frac{4}{3} \times 15 = 20 \)[/tex] - This is a solution.
D. [tex]\( \frac{3}{4} \times 15 = 11.25 \)[/tex] - This is not equal to 20.
E. [tex]\( \frac{15}{\frac{3}{4}} \)[/tex] - This is equivalent to expression A, which is a solution.
Therefore, the expressions that are solutions to the equation[tex]\( \frac{3}{4}x = 15 \)[/tex] are A and C.
Complete Question: Which expressions are solutions to the equation 3/4 x=15 ? Select all that apply.
A. frac 15 3/4
B. frac 15 4/3
C. 4/3 · 15
D. 3/4 · 15
E. 15/ 3/4