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Answer:
a) $540 cost to paint
b) 72000 liters to fill
Step-by-step explanation:
Relevant formulas are ...
P = 2(L +W) . . . . perimeter of a rectangle of length L and width W
A = LW . . . . . . area of a rectangle of length L and width W
V = LWH . . . volume of a cuboid of length L, width W, and height H
__
a) The total painted area is the area of the pool walls plus the area of the pool bottom. The wall area is the product of pool perimeter and wall height. The bottom area is the product of pool length and width.
A = PH + LW = 2(L +W)H +LW
A = 2(8 m +6 m)(1.5 m) + (8 m)(6 m) = 42 m² +48 m² = 90 m²
At $6 per square meter, the cost of painting the pool is ...
($6 /m²)(90 m²) = $540 . . . . cost to paint the pool
__
b) The volume in liters is best figured using the dimensions in decimeters.
V = (80 dm)(60 dm)(15 dm) = 72000 dm³ = 72000 L
72000 liters will be needed to fill the pool.
A survey sampled men and women workers and asked if they expected to get a raise or promotion this year. Suppose the survey sampled 200 men and 200 women. If 98 of the men replied Yes and 72 of the women replied Yes, are the results statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year?
a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.
b. What is the sample proportion for men? For women?
c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?
Answer:
a)
The null hypothesis is: [tex]H_0: p_M - p_W = 0[/tex]
The alternative hypothesis is: [tex]H_1: p_M - p_W > 0[/tex]
b) For men is of 0.49 and for women is of 0.36.
c) The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.
Step-by-step explanation:
Before solving this question, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Men:
98 out of 200, so:
[tex]p_M = \frac{98}{200} = 0.49[/tex]
[tex]s_M = \sqrt{\frac{0.49*0.51}{200}} = 0.0353[/tex]
Women:
72 out of 200, so:
[tex]p_W = \frac{72}{200} = 0.36[/tex]
[tex]s_W = \sqrt{\frac{0.36*0.64}{200}} = 0.0339[/tex]
a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.
At the null hypothesis, we test if the proportion are similar, that is, if the subtraction of the proportions is 0, so:
[tex]H_0: p_M - p_W = 0[/tex]
At the alternative hypothesis, we test if the proportion of men is greater, that is, the subtraction is greater than 0, so:
[tex]H_1: p_M - p_W > 0[/tex]
b. What is the sample proportion for men? For women?
For men is of 0.49 and for women is of 0.36.
c. Use α= 0.01 level of significance. What is the p-value and what is your conclusion?
From the sample, we have that:
[tex]X = p_M - p_W = 0.49 - 0.36 = 0.13[/tex]
[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0353^2 + 0.0339^2} = 0.0489[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error, so:
[tex]z = \frac{0.13 - 0}{0.0489}[/tex]
[tex]z = 2.66[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference above 0.13, which is the p-value of z = 2.66.
Looking at the z-table, z = 2.66 has a p-value of 0.9961.
1 - 0.9961 = 0.0039.
The p-value of the test is 0.0039 < 0.01, which means that the results are statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year.
The length of a rectangle is 4 meters and the width is 4 meters. What is the perimeter of the rectangle? Do not include units in your answer.
Use the figure to find y.
Tanθ =sin /cos
tan θ = 5/2 / y
tan (30°) = 5/2 /y
[tex]y = \frac{5 \sqrt{3} }{2} [/tex]
y=4.33
PLEASE HELP ME PLEASE AND BE CORRECT
Answer:
12 cm²
Step-by-step explanation:
area = L *B
a = 6 * 2
a = 12cm²
HELP PLEASE BE CORRECT
Answer:
12
Step-by-step explanation:
Scale factor of 4
CD = 3
3 · 4 = 12
Length of C'D' is 12 units
Answer:
12 units
Step-by-step explanation:
The original segment CD = 3 units
Scale factor is 4.
3 x 4 = 12
Help me! Thanks! Show work too! Please!
Answer:
(2, 79) (12, 24)
24-79/12-2=-55/10
m=-0.55
24=-6,6+b
30.6=b
y=-0.55x+30.6
Step-by-step explanation:
you multiply
using the equation to represent your answer
A certain manufacturing process yields electrical fuses of which, in the long run
15% are defective. Find the probability that in a random sample of size n=10, fuses
selected from this process, there will be
(i) No defective fuse
(ii) At least one defective fuse
(iii) Exactly two defective fuses
(iv) At most one defective fuse
Answer:
i) 0.1969 = 19.69% probability that there will be no defective fuse.
ii) 0.8031 = 80.31% probability that there will be at least one defective fuse.
iii) 0.2759 = 27.59% probability that there will be exactly two defective fuses.
iv) 0.5443 = 54.43% probability that there will be at most one defective fuse.
Step-by-step explanation:
For each fuse, there are only two possible outcomes. Either it is defective, or it is not. The probability of a fuse being defective is independent of any other fuse, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
15% are defective.
This means that [tex]p = 0.15[/tex]
We also have:
[tex]n = 10[/tex]
(i) No defective fuse
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]
0.1969 = 19.69% probability that there will be no defective fuse.
(ii) At least one defective fuse
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
We already have P(X = 0) = 0.1969, so:
[tex]P(X \geq 1) = 1 - 0.1969 = 0.8031[/tex]
0.8031 = 80.31% probability that there will be at least one defective fuse.
(iii) Exactly two defective fuses
This is P(X = 2). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{10,2}.(0.15)^{2}.(0.85)^{8} = 0.2759[/tex]
0.2759 = 27.59% probability that there will be exactly two defective fuses.
(iv) At most one defective fuse
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.15)^{0}.(0.85)^{10} = 0.1969[/tex]
[tex]P(X = 1) = C_{10,1}.(0.15)^{1}.(0.85)^{9} = 0.3474[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1969 + 0.3474 = 0.5443[/tex]
0.5443 = 54.43% probability that there will be at most one defective fuse.
The diameter of the circle is 2”. What is the area of the circle
Answer:
[tex]\pi[/tex]
Step-by-step explanation:
1. 2/2 =1 1 is the radius
2. [tex]A = \pi r^2[/tex]
3. [tex]A=\pi 1^2[/tex]
4. [tex]A=\pi[/tex]
Complete the input-output table:
x 3x + 7
0
4
8
14
Step-by-step explanation:
When x = 0,
3x + 7
= 3 ( 0 ) + 7
= 0 + 7
= 7
When x = 4,
3x + 7
= 3 ( 4 ) + 7
= 12 + 7
= 19
When x = 8,
3x + 7
= 3 ( 8 ) + 7
= 24 + 7
= 31
When x = 14,
3x + 14
= 3 ( 14 ) + 14
= 14 ( 3 + 1 )
= 14 ( 4 )
= 56
URGENT!!!!!! 15 POINTDS
Answer:
Option C
Step-by-step explanation:
thankful that there are graphing tools. see screenshot
If f(x) = x
2−3x+1
x−1
find f(-1) and f(-3)
Answer:
f(-1) = 2-3(-1) +1
= 7
f(-3)= 2-3(-3)+1
= 12
f(-1) = -1-1
= -2
f(-3) = -3-1
= -4
Answer ASAP
Will give brainliest!
More information pleaseeeeeeee
A friend wants to buy a pool and has two places she wants to purchase the pool with the largest volume which pool should she buy a rectangular pool that is 20' x 15' in 54 inches deep or a cylindrical pool that has a 3.3 m radios and is 1.8 m deep
Answer:
20'×15 in 54 inches
Step-by-step explanation:
The Best as a pool should be rectangular in shape and 54inches deep for safety of life's
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
What is the volume of a cylinder?The volume of the cylinder is the product of the height, pie, and square of the radius.
The volume of the cylinder = [tex]\pi r^{2}[/tex]h
The volume of the cylindrical pool that has a 3.3 m radius and is 1.8 m deep is;
= [tex]\pi r^{2}[/tex]h
[tex]= 3.14 (3.3)^2 (1.8)\\\\= 61.55 m^3[/tex]
The volume of the rectangular pool that is 20' x 15' in 54 inches deep ;
V = 20 x 15 x 54
V = 16,200 cubic meter.
The volume of the rectangular pool that is 20' x 15' in 54 inches deep is largest.
Learn more about volume;
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a.
What is 46.7% of
4/5?
Answer:
0.3736
Step-by-step explanation:
46.7 percent of [tex]\frac{4}{5}[/tex] is 0.3736.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.What is a fraction?A number is stated as a quotient in mathematics when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.Solution -To find 46.7% of [tex]\frac{4}{5}[/tex].
So,
[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]
[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]
⇒ [tex]0.3736[/tex]
Therefore, 46.7% of [tex]\frac{4}{5}[/tex] is 0.3736.
Know more about percentages here:
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Triangles P Q R and S T U are shown. Angles P R Q and T S U are right angles. The length of P Q is 20, the length of Q R is 16, and the length of P R is 12. The length of S T is 30, the length of T U is 34, and the length of S U is 16.
Using the side lengths of △PQR and △STU, which angle has a sine ratio of Four-fifths?
∠P
∠Q
∠T
∠U
Answer:
[tex]\angle P[/tex]
Step-by-step explanation:
Given
[tex]\triangle PRQ = \triangle TSU = 90^o[/tex]
[tex]PQ = 20[/tex] [tex]QR = 16[/tex] [tex]PR = 12[/tex]
[tex]ST = 30[/tex] [tex]TU = 34[/tex] [tex]SU = 16[/tex]
See attachment
Required
Which sine of angle is equivalent to [tex]\frac{4}{5}[/tex]
Considering [tex]\triangle PQR[/tex]
We have:
[tex]\sin(P) = \frac{QR}{PQ}[/tex] --- i.e. opposite/hypotenuse
So, we have:
[tex]\sin(P) = \frac{16}{20}[/tex]
Divide by 4
[tex]\sin(P) = \frac{4}{5}[/tex]
Hence:
[tex]\angle P[/tex] is correct
Answer:
A or <P
Step-by-step explanation:
on edge 2021
Determine if the sequence below is arithmetic or
geometric and determine the common difference / ratio in
simplest form.
3, 8, 13, ..
(PLEASE HELPP)
9514 1404 393
Answer:
arithmetic; common difference of 5
Step-by-step explanation:
It usually works well to check differences first. Here, they are ...
8 -3 = 5
13 -8 = 5
These are the same value, so the sequence is arithmetic with a common difference of 5.
what's a divisor a dividend and a quotient
So for this problem, I almost got it however my rounding is off causing my answers to be wrong. Can someone please help me with the two that are wrong. Thank you for your help!
Answer:
it 94x26.2 i think it right if not sorry :/
Step-by-step explanation:
Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Express a simplified ratio
Answer:
5:12
Step-by-step explanation:
125:300 simplified = 5:12
I hope this helps
Counting numbers are to be formed using only the digits 1, 3, 7,5,4,8, and 2. Determine the number of different possibilities for two-digit numbers.
Answer:
11699 numbers and 42 two-digit numbers
graph a circle with General form.x^2 +y^2+8x-12y+24=0
Answer:
jhshejwjabsgsgshshsnsjs
Answer:
Step-by-step explanation:
Put the equation into center-radius form.
x² + y² + 8x - 12y + 24 = 0
x² + y² + 8x - 12y = -24
(x²+8x) + (y²-12y) = -24
(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24
(x+4)² + (y-6)² = 28
Center: (-4,6)
radius: √28
Which equation represents the parabola with focus (8, 4) and vertex (8, 2)
Answer:
Step-by-step explanation:
The focus lies above the vertex, so the parabola opens upwards.
which transformation of the red triangle on the graph maps it into the missing peice of the square?
A. a translation 16 units right
B. a reflection across the y-axis
C. a 90° counterclockwise rotation about the origin
D. a 90° clockwise rotation about the origin
E. a 180° rotation about the origin
Answer:
D
The missing piece (triangle) is facing right side up but the red triangle has its point facing left
TO get it facing up, turn it by 90 degrees clockwise
convert 2m 50cm 15mm in cm
Answer:
251.5 cm
Step-by-step explanation:
1 m = 100 cm
1 cm = 10 mm
2 m + 50 cm + 15 mm =
= 2 m * (100 cm)/m + 50 cm + 15 mm * (1 cm)/(10 mm)
= 200 cm + 50 cm + 1.5 cm
= 251.5 cm
Taree fourts of the 64 books were math books. determine the percent of the books that were math books.
Answer: 75% - these are books on mathematics.
Step-by-step explanation:
[tex]\dfrac{3}{4} \cdot 64 = 48\\[/tex]
64 - 100%
48 - x%
[tex]\dfrac{64}{100} =\dfrac{48}{x}\\\\x=\dfrac{48 \cdot 100}{64} \\\\x=75 \%[/tex]
What is the answer to this? Is it d?
Answer:
Step-by-step explanation:
yeah of course..your answer is true.. it's part d and there is no solution for that system...w and v both of them remove in solution of system and we don't have any unknown variable for solving.
9514 1404 393
Answer:
D. no solutions
Step-by-step explanation:
The first equation can be simplified to standard form:
0.5(8w +2v) = 3
4w +v = 3 . . . . . . . eliminate parentheses
__
The second equation can also be simplified to a comparable standard form:
8w = 2 -v +4w
4w +v = 2 . . . . . . add v -4w
__
Comparing these two equations, we find the variable expressions to be the same, but the constants to be different. If any set of variable values were to satisfy one of these equations, it could not satisfy the other equation. There are no solutions to the system.
According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Assume that blood pressure is normally distributed.
a.) State the random variable.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
f.) What blood pressure do 90% of all people in China have less than?
Answer:
a) Mean blood pressure for people in China, which has mean 128 and standard deviation 23.
b) 0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c) 0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.
d) 0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e) Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f) 90% of all people in China have a blood pressure of less than 157.44 mmHg.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg
This means that [tex]\mu = 128, \sigma = 23[/tex]
a.) State the random variable.
Mean blood pressure for people in China, which has mean 128 and standard deviation 23.
b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.
This is 1 subtracted by the p-value of Z when X = 135, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 128}{23}[/tex]
[tex]Z = 0.3[/tex]
[tex]Z = 0.3[/tex] has a p-value of 0.6179.
1 - 0.6179 = 0.3821
0.3821 = 38.21% probability that a person in China has blood pressure of 135 mmHg or more.
c.) Find the probability that a person in China has blood pressure of 141 mmHg or less.
This is the p-value of Z when X = 141, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{141 - 128}{23}[/tex]
[tex]Z = 0.565[/tex]
[tex]Z = 0.565[/tex] has a p-value of 0.7140.
0.714 = 71.4% probability that a person in China has blood pressure of 141 mmHg or less.
d.) Find the probability that a person in China has blood pressure between 120 and 125 mmHg.
This is the p-value of Z when X = 125 subtracted by the p-value of Z when X = 120, so:
X = 125
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{125 - 128}{23}[/tex]
[tex]Z = -0.13[/tex]
[tex]Z = -0.13[/tex] has a p-value of 0.4483.
X = 120
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{120 - 128}{23}[/tex]
[tex]Z = -0.35[/tex]
[tex]Z = -0.35[/tex] has a p-value of 0.3632.
0.4483 - 0.3632 = 0.0851
0.0851 = 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.
e.) Is it unusual for a person in China to have a blood pressure of 135 mmHg? Why or why not?
From item b, when X = 135, Z = 0.3.
Since |Z| = 0.3 < 2, it is not unusual for a person in China to have a blood pressure of 135 mmHg.
f.) What blood pressure do 90% of all people in China have less than?
The 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 128}{23}[/tex]
[tex]X - 128 = 1.28*23[/tex]
[tex]X = 157.44[/tex]
90% of all people in China have a blood pressure of less than 157.44 mmHg.
Find the value of x in each case and give an explanation plzzz, thank youu :)
Answer:
Step-by-step explanation:
the arrows from the picture tells us that TV is parallel to RS
since TS is a transversal that cuts the 2 parallel lines TV and RS than ∠S =x
(alternate interior angles)
sum of angles in a Δ is 180° so x+x+2x = 180°, 4x =180°, x= 45°
2x = 45*2 = 90°
Which number produces an irrational number when added to 0.4
Answer:
0.31311311131111....
Step-by-step explanation:
We need to tell a number which when adds to 0.4 makes it a Irrational Number . We know that ,
Rational number :- The number in the form of p/q where p and q are integers and q is not equal to zero is called a Rational number .
Irrational number :- Non terminating and non repeating decimals are called irrational number .
Recall the property that :-
Property :- Sum of a Rational Number and a Irrational number is Irrational .
So basically here we can add any Irrational number to 0.4 to make it Irrational . One Irrational number is ,
[tex] \rm\implies Irrational\ Number = 0.31311311131111... [/tex]
So when we add this to 0.4 , the result will be Irrational . That is ,
[tex] \rm\implies 0.4 + 0.31311311131111 ... = 0.731311311131111 .. [/tex]
what is the average speed for the interval t=1 hour to t=3 hours
Step-by-step explanation:
2 hours
3+1 / 2 = 4/2 = 2 hours speed average
