one month is what percentage of a year given that there are 7 days in a week, and 12 months in a year

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

Answer:

(-2,2) and (-3,-4)

Step-by-step explanation:

by graphing the line and parabola, you should get this graph

Answer: C

<BFE is 148 degrees

Step-by-step explanation:

We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?

1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same

2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.

3. Now, we have all the angles we need to find out <BFE.

4. <BFC+<CFD+<DFE=<BFE

5. Substitute to get

57+34+57=<BFE

91+57=<BFE

148=<BFE

6. Now we know that the answer is 148 degrees.

Answer:

135

Step-by-step explanation:

Given that :

Total score obtained by Peter, Jan and Maxim = 269

Let :

Peter's score = x

Jan's score = y

Maxim's score = z

x + y + z = 269

x > (y + z)

For x to be greater Than y + z ;

Then x > (269 / 2) ; x > 134.5

The least possible x score is 135

Hence, Peter's least possible score is 135.

If y (0) = -1/3, then

-1/3 = 1 / (1 + C e ⁻⁰)

Solve for C :

-1/3 = 1 / (1 + C )

-3 = 1 + C

C = -4

So the particular solution to the DE that satisfies the given initial condition is

[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]

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

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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.

Answer:

0.3736

Step-by-step explanation:

46.7 percent of  [tex]\frac{4}{5}[/tex] is 0.3736.

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.

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Tanθ =sin /cos

tan θ = 5/2 / y

tan (30°) = 5/2 /y

[tex]y = \frac{5 \sqrt{3} }{2} [/tex]

y=4.33

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

9514 1404 393

Answer:

  6 units

Step-by-step explanation:

The dilation factor is 2, so the length of A'B' will be 2 times the length of AB.

AB can be seen to be 3 units, so A'B' will be 2×3 = 6 units.

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]

Answer:

Step-by-step explanation:

The focus lies above the vertex, so the parabola opens upwards.

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

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

Answer:

Option C

Step-by-step explanation:

thankful that there are graphing tools. see screenshot

Answer:

8 minuets

Step-by-step explanation:

24min/3miles = 8

Answer:

8 minutes.

Step-by-step explanation:

If we divide 24 minutes by 3 miles, your answer will be 8 minutes.

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°

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.

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.

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

9514 1404 393

Answer:

  y = -9x +49

Step-by-step explanation:

The slope of line b is the same as the slope of line a. That can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -8)/(2 -1) = -9

The y-intercept can be found from the given point using the formula ...

  b = y - mx

  b = 13 -(-9)(4) = 13 +36 = 49

Then the slope-intercept equation of line b is ...

  y = -9x +49

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.

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.

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Answer:

Always. Always.

Step-by-step explanation:

All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.

Answer:

0.055 = 5.5% probability that exactly 5 employees were over 50.

Step-by-step explanation:

The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x successes is given by the following formula:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

In which:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

[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]

In this question:

Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]

7 over 50, which means that [tex]k = 7[/tex]

10 were dismissed, which means that [tex]n = 10[/tex]

What is the probability that exactly 5 employees were over 50?

This is P(X = 5). So

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]

0.055 = 5.5% probability that exactly 5 employees were over 50.