Which triangle is congruence postulate can be used to prove that

Answer:

Exact volume of the hexagonal prism = 240√3 cm³

Exact volume of the hexagonal pyramid = 80√3 cm³

Step by step explanation:

Volume of hexagonal prism = [(3√3)/2]×a²h

Where a = base edge

h = height

From the question,

a = 4cm, h = 10cm

V = [(3√3)/2]×(4)²×(10)

V = (3√3) × 160/2

V = 240√3 cm³

Exact volume of the hexagonal prism = 240√3 cm³

Volume of hexagonal pyramid = [(√3)/2]×a²h

a = 4cm, h = 10cm

V =  [(√3)/2]×(4)²×(10)

V = (√3) × 160/2

V = 80√3 cm³

Exact volume of the hexagonal pyramid = 80√3 cm³

Answer:

x = 24

Step-by-step explanation:

Of means multiply and is means equals

1/4 * x = 6

Multiply each side by 4

1/4*4 x = 6*4

x = 24

Answer:

[tex]10.71 yd[/tex]

Step-by-step explanation:

First let's find the radius of the quarter circle.

[tex]area =\frac{1}{4} \pi {r}^{2} \\ 7.065 = \frac{1}{4} *3.14 {r}^{2} \\ \frac{7.065}{3.14} = \frac{1}{4} * \frac{3.14 {r}^{2} }{3.14} \\ 9 = {r}^{2} \\ \sqrt{9} = r \\ 3 yd= r[/tex]

Now let's find the arc length of this quarter circle.

[tex] \frac{90}{360} \times 2\pi \: r \\ \frac{1}{4} \times 2 \times 3.14 \times 3 \\ = \frac{9.42}{4} \\ = 4.71yd \\ [/tex]

Now let's find the perimeter[tex]perimeter \\ = arc \: \: length + radius + radius \\ = 4.71 + 3 + 3 \\ = 10.71yd[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

The formula of an area of a quarter circle:

[tex]A=\dfrac{1}{4}\pi r^2[/tex]

We have the area of a quarter circle:

[tex]A=7.065\ yd^2[/tex]

Substitute to the formula and solve for r :

[tex]\dfrac{1}{4}\pi r^2=7.065[/tex]     multiply both sides by 4

[tex]4\cdot\dfrac{1}{4}\pi r^2=7.065\cdot4\\\\\pi r^2=28.26[/tex]

Use 3.14 for π

[tex]3.14r^2=28.26[/tex]            divide both sides by 3.14

[tex]\dfrac{3.14r^2}{3.14}=\dfrac{28.26}{3.14}\\\\r^2=9\to r=\sqrt9\\\\\boxed{r=3\ yd}[/tex]

The circumference of this figure consists of an arc (quarter of a cirumference of a circle) and two radiuses.

The formula of a circumference of a circle:

[tex]C=2\pi r[/tex]

The formula of a quarter of a cicrumference of a circle:

[tex]L=\dfrac{1}{4}\cdot2\pi r[/tex]

Substitute

[tex]L=\dfrac{1}{4}\cdot2\pi\cdot3=1.5\pi[/tex]

Use 3.14 for π

[tex]L=1.5(3.14)=4.71\ yd[/tex]

The perimeter of a quarter circle:

[tex]P=4.71+2(3)=4.71+6=10.71\ yd[/tex]

Answer:

Step-by-step explanation:

Let c represent the number of children that attended the concert.

Let a represent the number of adults that attended the concert.

At one of the concerts, each adult brought 4 children with them, and 10 children attended without an adult. This means that the number of children that attended is

c = 4a + 10

Tickets for a concert were $5 for each child and $8 for each adult. The total ticket sales were $1730. It means that

5c + 8a = 1730

Therefore, the systems of equations that can be solved to determine the number of children, c, and adults that attended the concert is

c = 4a + 10

5c + 8a = 1730

Answer:

c = 4a + 10

5c + 8a = 1730

Step-by-step explanation:

The answer is 12, 15, 30

Answer:x=1

Step-by-step explanation:

Given

[tex]F(x)=\dfrac{x^2+x-2}{x-1}[/tex]

F(x) will be discontinuous at x=1 because value of f(x) is undefined at that point.

F(x) is defined for all values of x except at x=1

Answer:

A symmetric bell shape

Step-by-step explanation:

A normal curve has a symmetrical bell shaped curve, this can be seen when a histogram is constructed with values that are normally distributed, the resulting shape is symmetrical and has a bell shape.

Answer:

  23,325 ft, about 4.42 miles

Step-by-step explanation:

The geometry of the situation can be modeled by a right triangle, where the side adjacent to the 2.7° angle of climb is the horizontal distance, and the side opposite is the vertical change in altitude. That change is ...

  5600 ft -4500 ft = 1100 ft

and the angle relation is ...

  tan(2.7°) = opposite/adjacent = (1100 ft)/(horizontal distance)

Multiplying this equation by (horizontal distance)/tan(2.7°) gives ...

   horizontal distance = (1100 ft)/tan(2.7°) ≈ 23,325 ft

Dividing this by 5280 ft/mi gives ...

  horizontal distance ≈ 4.42 mi

The airplane travels about 23,325 ft, or 4.42 miles, horizontally as it climbs.

Answer:

17.7

Step-by-step explanation:

62.3-7=55.3

55.3-19.9=35.4

35.4/2 = 17.7

brainliest pzz

Answer:

The value of s is 17.7mm.

Step-by-step explanation:

Given that perimeter of a shape happens when all sides are add up together. So for this question :

[tex]perimeter = 7 + 19.9 + s + s[/tex]

[tex]perimeter = 26.9 + 2s[/tex]

Let perimeter = 62.3mm,

[tex]62.3 = 26.9 + 2s[/tex]

[tex]2s = 62.3 - 26.9[/tex]

[tex]2s = 35.4[/tex]

[tex]s = 35.4 \div 2[/tex]

[tex]s = 17.7mm[/tex]

Answer:

850

Step-by-step explanation:

Current profit per year = $ 20

Number of subscribers = 3000

For each additional subscriber over 3000, the profit will increase by 1 cent or by $ 0.01. For example, for 3001 (3000 + 1) subscribers, the profit will be $ 20.01 per year. Similarly, for 3002 (3000 + 2) subscribers, the profit will be $20.02 per year and so on.

So, for x additional subscribers over 3000, the profit will increase by 0.01(x). i.e. for (3000 + x) subscribers, the profit will be $(20 + 0.01x)

Since, profit per each subscriber is $(20 + 0.01x), the profit for (3000 + x) subscribers will be:

Total profit = Number of subscribers x Profit per each subscriber

Total profit = (3000 + x)(20 + 0.01x)

We want to calculate how many subscribers will be needed to bring a profit of $109,725. So, we replace Total profit by $109,725. The equation now becomes:

Using quadratic formula, we can solve this equation as:

x = -5850 is not a possible solution as this would make the total number of subscribers to be negative. So we reject this value.

Therefore, the answer to this question is 850. 850 more subscribers are needed to being a total profit of $109,725

Answer:

620

Step-by-step explanation:

The formula to find the sum of the first n terms of an arithmetic sequence is n(a1 + aN)/2, where n is the number of terms,  aN is the last term and a1 is the first term. We do not know the last term, though, so we must find it. The equation for this is an=a1+(n−1)d, where d is the common difference and a1 is the first term, and n is the number of terms. Therefore, the last term, an is, -7+(19)4 = 69.

Finally, we plug it into the first formula, the formula to find the sum, and we get 20*(-7+69)/2, which gives us 620 as our final answer.

Answer:

Step-by-step explanation:

(a) Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent

(b) The required [tex]\lambda[/tex] = 1.7 * 10/5 = 3.4

(c) P(r ≥ 4 | r ≥ 2)

= P(r ≥ 4)/P(r ≥ 2)

= {1 - P(r < 4)}/{1 - P(r < 2)}

For Poisson distribution, P(X = x)

[tex]= \frac{e^{- \lambda} \lambda ^x}{x !}[/tex]

Thus, P(r < 4) = P(r = 0) + P(r = 1) + P(r = 2) + P(r = 3)

= 0.5584

and P(r < 2) = P(r = 0) + P(r = 1) = 0.1468

Thus, P(r ≥ 4 | r ≥ 2) = (1 - 0.5584)/(1 - 0.1468)

= 0.5177

(d) P(r < 6 | r ≥ 3)

= P(3 ≤ r < 6)/P(r ≥ 3)

P(3 ≤ r < 6) = P(r = 3) + P(r = 4) + P(r = 5) = 0.5308

P(r ≥ 3) = 1 - {P(r = 0) + P(r = 1) + P(r = 2)}

= 0.6603

Thus, P(r < 6 | r ≥ 3) = 0.5308/0.6603 = 0.8309

Answer:

Option A

Step-by-step explanation:

From the outlined data, the p value calculated was given as 0.005 which is way less than 0.05, thus we will reject the null hypothesis that there is no difference in drinking habit among students at two different universities. We can then conclude that the samples provide significant evidence that students at University 1 drink more than students at university 2.

Answer:

2

Step-by-step explanation:

g(1) = 1² + 1 = 2

Step-by-step explanation:

it is 2

Answer:

x=25[tex]\sqrt{2}[/tex]

Step-by-step explanation:

the hypotenuse is equal to a leg times the square root of 2. which means to find the leg with the hyp given. you take [tex]\frac{50}{\sqrt{2} }[/tex] which then translates to 50 root 2/2=x  therefore 25[tex]\sqrt{2}[/tex]

Answer:

a) Mean blood pressure for people in China.

b) 38.21% probability that a person in China has blood pressure of 135 mmHg or more.

c) 71.30% probability that a person in China has blood pressure of 141 mmHg or less.

d) 8.51% probability that a person in China has blood pressure between 120 and 125 mmHg.

e) Since Z when X = 135 is less than two standard deviations from the mean, it is not unusual for a person in China to have a blood pressure of 135 mmHg

f) 157.44mmHg

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

If X is two standard deviations from the mean or more, it is considered unusual.

In this question:

[tex]\mu = 128, \sigma = 23[/tex]

a.) State the random variable.

Mean blood pressure for people in China.

b.) Find the probability that a person in China has blood pressure of 135 mmHg or more.

This is 1 subtracted by the pvalue of Z when X = 135.

[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 pvalue of 0.6179

1 - 0.6179 = 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 pvalue of Z when X = 141.

[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 pvalue of 0.7140

71.30% 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 pvalue of Z when X = 125 subtracted by the pvalue 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 pvalue 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 pvalue of 0.3632

0.4483 - 0.3632 = 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 b), when X = 135, Z = 0.3

Since Z when X = 135 is less than two standard deviations from the mean, 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?

This is the 90th percentile, which is X when Z has a pvalue of 0.28. So X when Z = 1.28. Then

X = 120

[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]

So

157.44mmHg

Answer:

hello your question lacks the required options attached is a picture of the complete question

One would expect about 5% of tests to be significant just by chance if the null hypothesis is true, and for 60 tests, this is 0.05(60) = 3 tests. This could explain why these tests are statistically significant.

Step-by-step explanation:

What is misleading about this is the study's final report because this marketing study was carried out with a level of significance of 5% (0.05) which means that if we carry the same study with varying sample data we will mostly like arrive at a conclusion against our null conclusion 5% of the time and this is not good for the the study because it is a type 1  error and has to be eliminated and it cannot be eliminated totally .

hence  One would expect about 5% of tests to be significant just by chance if the null hypothesis is true, and for 60 tests, this is 0.05(60) = 3 tests. This could explain why these tests are statistically significant.

We are told that the marketing study conducts 60 tests and that 3 tests are statistically significant at the 0.05 level, in addition to this the study's final report emphasizes only the tests with significant results without mentioning the other 57 tests.

We can interpret it as follows:

By the 0.05 level, we mean that 5% of the tests are significant by chance when the null hypothesis is true.

Here 5% of the 60.

60 * 0.05 = 3

Therefore it only mentions 3 tests and does not mention the other 57 tests, which in itself is misleading because all 60 tests should be fully mentioned in the final report.

Answer:

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

Step-by-step explanation:

We have a sample of executives, of size n=160, and the proportion that prefer trucks is 26%.

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.26.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.26*0.74}{160}}\\\\\\ \sigma_p=\sqrt{0.0012}=0.0347[/tex]

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0347=0.068[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.26-0.068=0.192\\\\UL=p+z \cdot \sigma_p = 0.26+0.068=0.328[/tex]

The 95% confidence interval for the population proportion is (0.192, 0.328).

We can claim with 95% confidence that the proportion of executives that prefer trucks is between 19.2% and 32.8%.

Answer:

55.32% probability that a late package was delivered by express delivery service 2

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Late delivery.

Event B: Service 2 was used.

A certain company sends 35% of its overnight mail parcels via express delivery service 1 and the rest by express delivery service 2.

100 - 35 = 65%.

So [tex]P(B) = 0.65[/tex]

Service 2 has a record of 2.0% of packages being delivered late.

This means that [tex]P(A|B) = 0.02[/tex]

Probability of a late delivery.

35% from service 1. Of those, 3% are late.

65% from service 2. Of those, 2% are late.

So

[tex]P(A) = 0.35*0.03 + 0.65*0.02 = 0.0235[/tex]

What is the probability that a late package was delivered by express delivery service 2

[tex]P(B|A) = \frac{0.65*0.02}{0.0235} = 0.5532[/tex]

55.32% probability that a late package was delivered by express delivery service 2

Answer:

About 8.2 cm

Step-by-step explanation:

Assuming that a is one of the legs of this right triangle, then using the Pythagorean Theorem:

[tex]a=\sqrt{15.3^2-12.9^2}\approx 8.2[/tex]

Hope this helps!

Answer:

40m

Step-by-step explanation:

5.25 divided by 1.75=3

120 divided by 3=40

Answer:

  a) $115,840.97

  b) $306,000

  c) $190,159.03

Step-by-step explanation:

Loan payment calculations can be done using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

where A is the monthly payment, P is the principal value of the loan, r is the annual interest rate, and t is the loan duration in years.

The principal amount of the loan can be found by filling in the given values and solving for P.

  850 = P(0.08/12)/(1 -(1 +0.08/12)^(-12·30))

  P = 850(1 -1.0066667^-360)/0.0066667 ≈ 850×136.283494

  P = 115,840.97

You could afford a loan of $115,840.97.

The total amount paid is the sum of 360 payments of $850 each:

  360 × $850 = $306,000

You will pay $306,000 to the loan company.

The amount of interest is the difference between the amount paid and the amount borrowed:

  $306,000 -115,840.97 = $190,159.03

$190,159.03 of the amount paid is interest.

__

Additional comment

A variety of apps, calculators, and spreadsheets can do these calculations for you. The result from one of these calculators is attached. The PV is the Present Value of the series of 360 payments of $850 each. It is the loan amount.

Answer:

Approximately 28 times

Step-by-step explanation:

The tires are circular in shape.

We first need to find the circumference of the tire and then divide the length of the road by that circumference.

The circumference of a circle is given as:

C = πD

where D = diameter

The diameter of the tires is 1.7 m. Its circumference is therefore:

C = π * 1.7 = 5.34 m

Therefore, the number of times that the tire has to turn in traveling the length of the street is:

149 / 5.34 = 27.9 ≅ 28

Answer:

[tex]2^3 X5^2 X7[/tex]

Step-by-step explanation:

Given the number: 1400

A number is said to be prime when it can only be divided by 1 and itself.

We can express 1400 as a product of its prime numbers by gradually decomposing it into smaller units.

[tex]1400=14X100\\14=2X7\\100=10X10=2X5X2X5\\$Therefore:\\1400=2 X 7 X 2 X 5 X 5 X 5\\Reorganising\\1400=2 X 2 X 2 X 5 X 5 X 7\\Therefore, 1400 expressed as a product of its prime factors is:\\1400=2^3 X5^2 X7[/tex]

Answer:

no he should be fine it will be -10C when he gets back

Step-by-step explanation:

Answer:

The weather report says the temperature is 20°C and will drop 5°C per hour for the next 6 hours. Daryl plans to be gone for at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above –10°C, should Daryl move his plant to a warmer location before leaving?

An inequality to model the problem is  

✔ 20 - 5x > -10

.

The solution is  

✔ x < 6

.

Step-by-step explanation: no one could answer this write so here.

Answer:

Arc CR = 90 deg

=> angle CBR = 90 deg

=> angle CBV = 90 deg

=> 3x + 4 = 90

=> 3x = 86

=> x =~28.7 deg

=> Option A is correct

Hope this helps!

:)

Answer:

A: x = 28.7

Step-by-step explanation:

Since VR is the diameter and CB is bisecting it so arcVC= arcCR and

<CBV = <CBR

NOW

3x+4 = 90

3x = 90-4

3x = 86

Dividing both sides by 3

x ≈ 28.7

Answer:

  see below

Step-by-step explanation:

The probability a member is a girl is independent of the probability that a member plays sports if the fraction of members that are girls does not depend on whether the member plays sports or not.

That is, the fraction of members that are girls will be the same for sports players and non-sports players.

_____

Examples

(a) Suppose we have a membership that consists of ...

1 girl and 1 boy who play sports (as many girls as boys), and 1 girl who does not play sports.

We want to see if p(g) and p(s) are independent, so we compute p(g) and p(g|s).

  p(g) = 2/(2+1) = 2/3

  p(g|s) = p(g&s)/p(s) = (1/3)/(2/3) = 1/2 . . . . not independent

__

(b) Suppose we have a membership that consists of ...

1 girl and 1 boy who play sports, and 2 girls and 2 boys who don't play sports (girls are half the members who play, and half the members who don't play).

  p(g) = 3/6 = 1/2

  p(g|s) = p(g&s)/p(s) = (2/6)/(4/6) = 2/4 = 1/2 . . . . independent

__

(c) Suppose we have a membership that consists of ...

2 girls and 1 boy who play sports, and 2 boys and 1 girl who do not play sports (fraction of girl players = fraction of boy non-players)

  p(g) = 3/6 = 1/2

  p(g|s) = p(g&s)/p(s) = (2/6)/(3/6) = 2/3 . . . . not independent

__

(d) Suppose we have a membership that consists of ...

  1 girl and 1 boy who play sports, and 1 girl who does not play sports (as many girls play as do not)

  p(g) = 2/3

  p(g|s) = p(g&s)/p(s) = (1/6)/(2/6) = 1/2 . . . . not independent

__

These examples match our selection of the 2nd choice as being the one that demonstrates independence.

Answer:

-18root7

Step-by-step explanation:

-3root 84*3

-3root4*7*3*3

-3(2*3)root7

-18root7

Answer:

  15 litres

Step-by-step explanation:

  (1/2 litre/day)(30 days) = 15 litres

__

Multiply rate by time to get quantity.