the number 117 is divisible by nine and only if the sum of the digits in 117 are evenly divisible by 9, truth or false

Answer:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Step-by-step explanation:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Answer:

9x^4

Step-by-step explanation:

(3x)^2 * x^2

9x^2 * x^2

Add the exponents

9x^(2+2)

9x^4

Answer:

The answer is below

Step-by-step explanation:

What must be applied to know if the result is true or reliable is a  test statistic, since due to it we can calculate how true or rather what is the probability that this data will occur. There are many types of  test statistic, use the one that best fits the data.

The veracity of the medium where the information comes from is also important, whether they took a representative sample or not, among other parameters.

Answer:

c) H0: µ = 7 hours (null hypothesis)

H1: µ < 7 hours (alternative hypothesis and original claim)

Step-by-step explanation:

The hypothesis test is performed in order to see if a sample outcome gives evidence to reject a null hypothesis and support the researchers claim.

In this case, the claim is that the mean amount of sleep for adults is less than 7 hours.

For this claim, the alternative hypothesis will state the researcher's claim: the mean amount of sleep for adults is significantly less than 7 hours.

The null hypothesis will state the opposite: the mean amount of sleep for adults is not significantly less than 7 hours. In this case, it is the same to claim that the mean amount is 7 hours.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=7\\\\H_a:\mu< 7[/tex]

Answer: 95 degrees.

Step-by-step explanation:

A quadrilateral has a total combined angle measure of 360 degrees. If you do 360-(80+110+75) it would equal 95.

Answer:

Option C is the correct option

Solution,

The sum of the angles in the quadrilateral is 360°

Let the forth angle be X

X + 80° + 110° + 75° = 360°

Calculate the sum:

X + 265° = 360°

Subtract 265° on both sides

X + 265° - 265° = 360° - 265°

Calculate the difference

X = 95°

Hope this helps...

Good luck on your assignment...

Answer:

k = -10/9 and k = 10/9

Step-by-step explanation:

given y = cos(kt) and the differential equation 81y'' = -100y

y' = -ksin(kt)

y'' = -k²cos(kt)

Substituting the value of y and y'' in the differential equation we have;

81 (-k²cos(kt))= -100 (cos(kt))

-81k²cos(kt)) = -100cos(kt))

-81k² = -100

k² = 100/81

k = ±[tex]\sqrt{\frac{100}{81} }[/tex]

k = ±10/9

k = -10/9 and k = 10/9

Answer:

A ∪ B = {1,3,6,9,12,15,18,24}

Step-by-step explanation:

Let A = {3,6,9,12,15}

B = {1,6,12,18,24}

So,

A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}

A ∪ B = {1,3,6,9,12,15,18,24}

Answer:

{1,3,6,9,12,15,18,24}

Step-by-step explanation:

The union is joining of the elements of the sets

{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}

= {1,3,6,9,12,15,18,24}

Answer:

ADB = Major Arc

arc measure = 310

Step-by-step explanation:

major arc measure = 360 - 50 = 310

Answer:

8 is in the hundreds place as well as in the tens place.

Step-by-step explanation:

We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.

Answer:

13/20<--->65%

21/25<--->84%

3/4<--->75%

2/5<--->40%

3/5<--->60%

To find the matching pairs, divide the fraction and move the decimal point to your answer 2 places to the right to then get a percentage.

Ex:  1/2=   .50->5.0->50.->50%

The image did not show the rest of the answers, but I worked with what information I received from the current image, producing 5 sets of answers. If there are more than 5 sets, please send a second image with your question so we can help you with the rest.

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%

Fractions are written as a ratio of two integers. In order to convert fractions to percentage, we will simply multiply the fraction given  by 100.

For the fraction 13/20

13/20 * 100 = 13 * 5

13/20 = 65%

For the fraction 21/25

21/25 * 100 = 21 * 4

21/25 = 84%

For the fraction 3/4

3/4 * 100 = 3 * 25

3/4 = 75%

For the fraction 2/5

2/5 * 100 = 2 * 20

2/5 = 40%

For the fraction 3/5

3/5 * 100 = 3* 20

3/5 = 60%

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%
Learn more on percentages here: https://brainly.com/question/24304697

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Answer: The width of the garden is 6 Meters

Step-by-step explanation:

3x + x = 24

The length is 3x and the width is x

24 / 4 = 6

x= 6

The width of the garden is 6 Meters

Answer:

x = 6

Step-by-step explanation:

3x + x = 24

24 / 4 = 6

x = 6

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

Answer:

B.

Step-by-step explanation:

According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.

So in this case to find x, you would do the Sin(L)=x/y

Answer:

B.  Sin(L)=x/y  indeed!

Step-by-step explanation:

Answer:

8 and 4/9 i think... i am sorry if i am wrong

Step-by-step explanation:

Answer:

[tex]\$45[/tex]

Step-by-step explanation:

[tex]20+(2.5*20)=45[/tex]

Marking up means that the new value is added onto the original value.

As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%

Answer:

20*2.5 = $50 Gross margin $70 Selling price

Step-by-step explanation:

Answer:

4+10-284-4819+2948929

Answer:

Length=29.8 inches

Width=11.8 inches

Height=4.6 inches

Volume=1,617.54 cubic inches

Step-by-step explanation:

Let the side of congruent square cut =x inches

So the length of the rectangular box=(39-2x)

width = (21-2x)

height = x

The volume V=Length*Width*Height

= (39-2x)*(21-2x)*x

dV/dx= (39-2x)(21-4x)-2x(17-2x)=0

Simplify the equation above

819-156x-42x+8x^2-34x+4x^2=0

We have,

12x^2 -232 +819=0

Solve the quadratic equation using formula

a=12

b= -232

c=819

x= -b +or- √b^2-4ac/2a

= -(-232) +- √(-232)^2 - (4)(12)(819) / (2)(12)

= 232 +or- √53824 - 39312 / 24

= 232 +or- √14512 / 24

= 232 +or- 4√907 / 24

x= 232 / 24 + 4√907 / 24

=14.6861

Or

x=232 / 24 - 4√907 / 24

=4.64726

x=4.6 inches

Length=(39-2x)

={39-2(4.6)}

= 29.8 inches

Width=(21-2x)

={21-2(4.6)}

= 11.8 inches

Height=x= 4.6 inches

Volume=(39-2x)*(21-2x)*x

={39-2(4.6)}*{21-2(4.6)*4.6

=(39-9.2)*(21-9.2)*4.6

=29.8*11.8*4.6

=1,617.544

Approximately 1,617.54

Volume=1,617.54 cubic inches

Answer:

Solution,

[tex] \frac{ab}{bc} = tan \: 40 \\ ab = bc \times tan \: 40 \\ ab = 10 \times 0.84 \\ ab = 8.4 \: inches \: [/tex]

[tex] \frac{bc}{ac} = cos \: 40 \\ \frac{bc}{cos \: 40} = ac \\ ac = \frac{10}{cos \: 40} \\ ac = 13.05 \: inches[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

a. [tex]N(1)=2600[/tex]

b. [tex]N'(a) = 470/a[/tex]

c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)

d. lim a→[infinity] N′(a) = 0

Step-by-step explanation:

a.

the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:

[tex]N(1)=2600 + 470ln(1)[/tex]

[tex]N(1)=2600 + 470*0[/tex]

[tex]N(1)=2600[/tex]

b.

To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:

[tex]N'(a) = 2600' + (470ln(a))'[/tex]

[tex]N'(a) = 0 + 470*(1/a)[/tex]

[tex]N'(a) = 470/a[/tex]

c.

The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).

The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.

d.

When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.

Answer:

The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Step-by-step explanation:

The complete question is:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Solution:

As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.

So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]

The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.

The critical value of z for 98% confidence level is,

z = 2.33

Compute the 98% confidence interval as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]

Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Answer:

Step-by-step explanation:

Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]

To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;

[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]

As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;

[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]

Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]

Since the limit of the sequence gave a finite number , the sequence converges.

Note that the only case when the sequence diverges id when the limit of the sequence is infinite

Answer:

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

All outcoms of the dices:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

36 in all

Total outcomes:

In this question, we want all with no repetition.

There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.

Desired outcomes:

One landing on six:

(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

10 desired outcomes.

Probability:

10/30 = 0.3333

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Answer:D

Step-by-step explanation:

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

sin(B) = sin(A)

sin(B) = cos(90 – B)

cos(B) = sin(180 – B)

cos(B) = cos(A)

Assuming the angles are in degrees, the second relation is always true.

By definition of sine,

sin(B) = AC/AB

cos(90-B) = cos (A) = AC/AB

therefore the second relation is true, for arbitrary values of B.

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true?

Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

Answer:

a. 125.0714; 11.1835.

b. 109.4375; 10.4612.

Step-by-step explanation:

Given the following data;

70, 65, 71, 78, 89, 68, 50, 75.

Mean = 70.75

The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.

We would then find the square of this deviation;

[tex]=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2[/tex]

[tex]=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625[/tex]

= 875.5

Next is to find the population variance;

[tex]V = \frac{875.5}{8}[/tex]

Variance, V = 109.4375

The population standard deviation is the square root of the population variance;

[tex]Sd = \sqrt{109.4375}[/tex]

Standard deviation, Sd = 10.4612

To find the sample variance;

[tex]V = \frac{875.5}{8-1}[/tex]

[tex]V = \frac{875.5}{7}[/tex]

Variance, V = 125.0714

The sample variance is;

[tex]Sd = \sqrt{125.0714}[/tex]

Standard deviation, Sd = 11.1835

Therefore,

a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.

b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.

Answer:

C. 20.67

Step-by-step explanation:

I got it right on edge :)

Answer:

A

Step-by-step explanation:

Given the equality y > -½, it means the values of y is greater than -½.

The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .

Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.

Therefore, the graph that indicates the inequality y > ½ is A

Answer:

A

Step-by-step explanation:

Answer:

0.15 or 15%

Step-by-step explanation:

If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.

To calculate how much the price went up each day on average, we will create exponential equation.

x = price of the stock

y = average daily change

[tex]x*y^{4} =1.75x[/tex]  divide by x

[tex]y^{4} = 1.75[/tex]

We will calculate it using logarithms.

y = 1.15016, rounded to 1.15

We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%

Answer:

The height increase by

20/49π when pile is 14ft high

Step by step Explanation

Given:

rate of 20 ft3/min

To asolve this quest we will be using the volume of a cone then find the partial derivative

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION