Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE = CE and BE = DE
B.
С
E
A
D
Assemble the proof by dragging tiles to
the Statements and Reasons columns.

Answer:

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)

Step-by-step explanation:

Step(i):-

Given sample size 'n' =41

Mean of the sample(x⁻)  = 3.55

The estimated standard error

                                             [tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]

Given  estimated standard error ( S.E) = 3.478

Level of significance ∝=0.05

Step(ii):-

95% for the true average increase in total cholesterol under these circumstances

[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]

Degrees of freedom

ν= n-1 = 41-1 =40

t₀.₀₅ = 1.6839

95% for the true average increase in total cholesterol under these circumstances

[tex](x^{-} - t_{0.05} S.E ,x^{-} + t_{0.05} S.E)[/tex]

( 3.55 - 1.6839 ×3.478 ,3.55 + 1.6839 ×3.478 )

(3.55 - 5.856 , 3.55 + 5.856)

(-2.306 , 9.406)

Conclusion:-

95% for the true average increase in total cholesterol under these circumstances

(-2.306 , 9.406)

Answer:

Let x be her initial distance from the building, then tan 37 = 130/x

x = 130/tan 37 = 130/0.7536 = 172.5 feet

Let y be her distance from the building after moving forward, then

tan 40 = 130/y

y = 130/tan 40 = 130/0.8391 = 154.9

After moving forward, she is 172.5 - 154.9 = 17.6 ft closer.

Answer: B. 17.6 ft.

Step-by-step explanation: I just did it on the edge 2023 assignment. Check attached image.

Answer:

Bb

Step-by-step explanation:

Answer:

radius r of the zorb is ≅ 1.40 m

Step-by-step explanation:

GIven that;

the  radius r of a sphere with surface area A is given by;

[tex]r = \sqrt{\dfrac {A}{4 \pi }}[/tex]  which is read as : (r equals StartRoot StartFraction Upper A Over 4 pi EndFraction EndRoot .)

We are to calculate the radius of a zorb whose outside surface area is  24.63 sq  ( the missing part of the question)

Given that the outside surface area is : 24.63 sq

Let replace the value of the outside surface area which 24.63 sq for A in the equation given from above.

SO:  A = 24.63 sq

[tex]r = \sqrt{\dfrac {A}{4 \pi }}[/tex]

[tex]r = \sqrt{\dfrac {24.63}{4 \pi }}[/tex]

[tex]r = \sqrt{1.9599}[/tex]

r = 1.399

radius r of the zorb is ≅ 1.40 m

Answer:

Second option is the correct choice. See the explanation below.

Step-by-step explanation:

[tex]A=\frac{bh}{2}\\\\\mathrm{Switch\:sides}:\\\\\frac{bh}{2}=A\\\\\mathrm{Multiply\:both\:sides\:by\:}2\\\\\frac{2bh}{2}=2A\\\\hb=2A\\\\\mathrm{Divide\:both\:sides\:by\:}b;\\\\\frac{hb}{b}=\frac{2A}{b}\\\\h=\frac{2A}{b}[/tex]

Best Regards!

Answer:

[tex]h = \frac{2A}{b} [/tex]

Option B is the right option.

Solution,

[tex]a = \frac{bh}{2} \\ 2a = bh(cross \: multiplication) \\ 2a = b \times h \\ h = \frac{2A}{b} [/tex]

hope this helps...

Good luck on your assignment..

Answer: 3.9

Step-by-step explanation: Khan Academy

The length of BD if The angle ∠ DAC is equal to the angle ∠ BAD is 3.92.

Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.

Given:

The angle ∠ DAC = angle ∠ BAD

As we can see that the triangle BAD and triangle DAC are similar By SAS similarity,

AC / AB = CD / BD  (By the proportional theorem of similarity)

5.6 / 5.1 = 4.3 / BD

1.09 = 4.3 / BD

BD = 4.3 / 1.09

BD = 3.92

Thus, the length of BD is 3.92.

To know more about Triangles:

https://brainly.com/question/16886469

#SPJ2

Answer:

Option C is correct.

The sampling distribution with sample size n=100 will have less variability.

Step-by-step explanation:

Complete Question

Consider random samples selected from the population of all female college soccer players in the United States. Assume the mean height of female college soccer players in the United States is 66 inches and the standard deviation is 3.5 inches. Which do you expect to have less variability (spread): a sampling distribution with sample size n = 100 or a sample size of n = 20.

A. Both sampling distributions will have the same variability.

B.The sampling distribution with sample size n=20 will have less variability

C. The sampling distribution with sample size n =100 will have less variability

Solution

The central limit theorem allows us to say that as long as

- the sample is randomly selected from the population distribution with each variable independent of each other and with the sample having an adequate enough sample size.

- the random sample is normal or almost normal which is guaranteed if the population distribution that the random sample was extracted from is normal or approximately normal,

1) The mean of sampling distribution (μₓ) is approximately equal to the population mean (μ)

μₓ = μ = 66 inches

2) The standard deviation of the sampling distribution or the standard error of the sample mean is related to the population standard deviation through

σₓ = (σ/√N)

where σ = population standard deviation = 3.5 inches

N = Sample size

And the measure of variability for a sampling distribution is the magnitude of the standard deviation of the sampling distribution.

For sampling distribution with sample size n = 100

σₓ = (3.5/√100) = 0.35 inch

For sampling distribution with sample size n = 20

σₓ = (3.5/√20) = 0.7826 inch

The standard deviation of the sampling distribution with sample size n = 20 is more than double that of the sampling distribution with sample size n = 100, hence, it is evident that the bigger the sample size, the lesser the standard deviation of the sampling distribution and the lesser the variability that the sampling distribution shows.

Hope this Helps!!!

Answer:

The third options

Step-by-step explanation:

Counting we can see that 10 students went to two or less states, and 10 went to three or more

Answer:

(a)The total sales of ice-cream last month is 702 gallons.

(b)The total sales of broccoli last month is 510 pounds.

Step-by-step explanation:

Part A

Total Sales of gallons of ice cream this month = 597

Since it represents a decrease of 15% of last month's sales

Let the total sales of ice-cream last month =x

Then:

(100-15)% of x =597

85% of x=597

0.85x=597

x=597/0.85

x=702 (to the nearest integer)

The total sales of ice-cream last month is 702 gallons.

Part B

Total Sales of broccoli this month = 617 pounds

Since it represents an increase of 21% of last month's sales

Let the total sales of ice-cream last month =y

Then:

(100+21)% of y =617

121% of y=617

1.21y=617

y=617/1.21

y=510 (to the nearest integer)

The total sales of broccoli last month is 510 pounds.

Answer:

The 95% confidence interval for the average hourly wage of all information system managers is (39.14,42.36)

Step-by-step explanation:

In order to calculate the 95% confidence interval for the average hourly wage we would have to calculate first the margin of error as follows:

ME=t0.05/2,n-1s/√n

for n=75, t0.025,74=1.993

Therefore, ME=1.993*7/√75

ME=1.61

Therefore, the 95% confidence interval for the average hourly income of all syatem manager would be as follows:

(X-ME,X+ME)=(40.75-1.61,40.75+1.61)

=(39.14,42.36)

Answer:

Step-by-step explanation:

From the information given, the population is divided into sub groups. Each group would consist of citizens picking a particular choice as the most important problem facing the country. The choices are the different categories. In this case, the null hypothesis would state that the distribution of proportions for all categories is the same in each population. The alternative hypothesis would state that the distributions is different. Therefore, the correct test to use to determine if the distribution of​ "problem facing this country ​today" is different between the two different​ years is

A) Use a​ chi-square test of homogeneity.

Answer:

Step-by-step explanation:

Let the money earned during fundraising activities =x

Since the World Issues club has decided to donate 60% of all their fundraising activities this year to Stephen Lewis Foundation.

The amount of money the foundation will receive

=60% of x

= 0.6x

In the bake sale, the club raised $72.

Therefore, the amount the foundation will receive =0.6*72=$43.20

At the end of the year, the World Issues Club mailed a cheque to the foundation for $850.

Therefore:

0.6x=850

x=850/0.6

x=$1416.67

The total amount of money the club raised is $1416.67.

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{5}{6}-\frac{2}{3}=\frac{5}{6}-\frac{2*2}{3*2}\\\\=\frac{5}{6}-\frac{4}{6}\\\\=\frac{5-4}{6}\\\\=\frac{1}{6}[/tex]

Answer:

10 and 8

Step-by-step explanation:

10 and 8 are the factors in this equation because factors are the numbers that are mutiplied together to get the product (The answer to a mutiplication problem) Therefore the factors in this equation are 10 and 8 because those are the numbers that are mutiplied together to get the product.

Answer:

The 95% confidence interval is 2.5 < u <3.1.

Step-by-step explanation:

The provided sample mean is X = 2.8 and the sample standard deviation is s = 1.2, and the sample size is n = 64.

1. Null and Alternative Hypotheses:

The following null and alternative hypotheses need to be tested:

H0  u = 3

Ha: u < 3

This corresponds to a left-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

2. Rejection Region Based

on the information provided, the significance level is alpha = 0.05, and the critical value for a left-tailed test is t c = -1.669.

The rejection region for this left-tailed test is R = t : t < -1.669

3. Test Statistics

The t-statistic is computed as follows:

t = (X - uo)/[s/n^(1/2)] =

replacing

t = (2.8 - 3)/ [1.2/64 ^(1/2)]

t =-1.333  

4. Decision about the null hypothesis

Since it is observed that t = -1.333 > t c = -1.669, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.0936, and since p= 0.0936 => 0.05, it is concluded that the null hypothesis is not rejected.

5. Conclusion It is concluded that the null hypothesis H0 is not rejected. Therefore, there is not enough evidence to claim that the population mean u is less than 3, at the 0.05 significance level.

Confidence Interval

The 95% confidence interval is 2.5 < u <3.1.

Answer:

The numbers of doors that will have no blemishes will be about 6065 doors

Step-by-step explanation:

Let the number of counts by the  worker of each blemishes on the door be (X)

The distribution of blemishes followed the Poisson distribution with parameter  [tex]\lambda =0.5[/tex] / door

The probability mass function on of a poisson distribution Is:

[tex]P(X=x) = \dfrac{e^{- \lambda } \lambda ^x}{x!}[/tex]

[tex]P(X=x) = \dfrac{e^{- \ 0.5 }( 0.5)^ x}{x!}[/tex]

The probability that no blemishes occur is :

[tex]P(X=0) = \dfrac{e^{- \ 0.5 }( 0.5)^ 0}{0!}[/tex]

[tex]P(X=0) = 0.60653[/tex]

P(X=0) = 0.6065

Assume the number of paints on the door by q = 10000

Hence; the number of doors that have no blemishes  is = qp

=10,000(0.6065)

= 6065

Answer:

HJ > PK

Step-by-step explanation:

Notice that the side PL in one triangle has the same length as side GJ in the other, and side GH has the same size as side LK of the other triangle. Now what is different is the angle subtended between these sides in the case of the triangle on the lower left, the subtended angle is [tex]90^o[/tex] , which is larger angle than that subtended between equal sides on the other triangle ([tex]85^o[/tex])

Therefore, if the angle subtended by the equivalent sides in the triangle on the left is larger than the angle subtended on the right hand side triangle, then the sides associated with such angle aperture must keep the inequality. That is:

Since [tex]\angle\,G\,\,\,>\,\,\,\angle \,L[/tex], then   HJ > PK

Answer:

c. [1.771;4.245] feet

Step-by-step explanation:

Hello!

The variable of interest is

X: height of a student at UH

X~N(μ;σ²)

You have to estimate the population standard deviation using a 95% confidence interval.

The statistic to use for the interval is a student Chi-Square with n-1 degrees of freedom. First you have to calculate the CI for the population variance:

[tex][\frac{(n-1)S^2}{X^2_{n-1;1-\alpha /2}} ;\frac{(n-1)S^2}{X^2_{n-1;\alpha /2}} ][/tex]

[tex]X^2_{n-1;1-\alpha /2}= X^2_{11;0.975}= 21.920[/tex]

[tex]X^2_{n-1;\alpha /2}= X^2_{11;0.025}= 3.816[/tex]

n=12

S= 2.5

[tex][\frac{11*6.25}{21.920} ;\frac{11*6.25}{3.816}} ][/tex]

[3.136; 18.016] feet²

Then you calculate the square root of both limits to get the CI for the population standard deviation:

[√3.136; √18.016]

[1.771;4.245] feet

I hope this helps!

Step-by-step explanation:

1. 180 - (36 +36)= 108

2. angle ABC = 108 angle DBC = 108-72=36

3. angle DCB=angle DBC. This is because the base angles are equal

4 therefore triangle BDC is isoscles

Answer:

Because ΔABD is isosceles, ∠ABD ≅ ∠ADB = 72° because of Base Angles Theorem which states that the base angles of an isosceles triangle are congruent. Then, ∠BDC = 180° - ∠ADB = 108° because they are supplementary angles. Because ΔABC is isosceles, ∠BAC ≅ ∠BCA = 36° because of Base Angles Theorem, which means ∠CBD = 180° - 108° - 36° = 36° because of the sum of angles in a triangle. Therefore, ΔBCD is isosceles because of the Converse of Base Angles Theorem.

Answer:

d. 10 minutes and 1.33 minutes.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

[tex]M = \frac{a + b}{2}[/tex]

The variance of the uniform distribution is given by:

[tex]V = \frac{(b-a)^{2}}{12}[/tex]

The assembly time for a product is uniformly distributed between 8 and 12 minutes.

This means that [tex]a = 8, b = 12[/tex].

Mean:

[tex]M = \frac{8 + 12}{2} = 10[/tex]

Variance:

[tex]V = \frac{(12-8)^{2}}{12} = 1.33[/tex]

So the correct answer is:

d. 10 minutes and 1.33 minutes.

Answer:

91 2/3 pi cubic units

Step-by-step explanation:

The formula for the volume of cone is [tex]\dfrac{1}{3}\pi r^2 h[/tex]. Plugging in the given numbers, you get:

[tex]\dfrac{1}{3}\cdot \pi \cdot 5^2 \cdot 11= 91 \ 2/3 \pi[/tex]

Hope this helps!

Answer:

[tex]Volume=\frac{1}{3} \,275\,\pi[/tex] cubic units

Notice that this answer doesn't agree with any of the first three in the list provided via the screenshot

Step-by-step explanation:

Recall the formula for the volume of a cone:

[tex]Volume=\frac{1}{3} Base\,*\,Height[/tex]

In this case the Height is 11 units, and they also give us the radius of the circular base (5 units) from which we can find the circle's base area:

[tex]Area_{circle} = \pi\,R^2\\Area_{circle}=\pi\,(5)^2\\Area_{circle}=25 \pi[/tex]

therefore the total volume becomes:

[tex]Volume=\frac{1}{3} Base\,*\,Height\\Volume=\frac{1}{3} 25\,\pi\,*\,11\\\\Volume=\frac{1}{3} \,275\,\pi[/tex]

Answer:

210

Complete question found at brainly(ID): 18678557 is stated below.

There is more than one integer, greater than 1, which leaves a remainder of 1 when divided by each of the four smallest primes. What is the difference between the two smallest such integers?

Step-by-step explanation:

Prime numbers are numbers that can only be divided by itself and 1

The smallest of the prime numbers we have = 2, 3, 5, 7

Since the integers greater than 1 are said to be divided by the four smallest prime numbers, we would assume the number of integers are 4 in total.

Let the integers be T

From the question:

Integer/(prime number) = quotient + (remainder/prime number)

Integer/(prime number) = Q + R/P

Let the different quotients derived from all 4 prime number = w, x, y, z

For prime 2:

T/2 = w + 1/2

T/2 - 1/2 = w

(T-1)/2 = w

T = 2w + 1

T-1 = 2w

Following the above solution

For prime 3:

T = 3x + 1

T-1 = 3x

For prime 5:

T = 5y + 1

T-1 = 5y

For prime 7:

T = 7z + 1

T-1 = 7z

T-1= T-1 = T-1 = T-1

2w = 3x = 5y = 7z

T-1 = LCM of all the prime numbers

T- 1 = 2×3×5×7

T-1 = 210

T = 210+1 = 211

T = 211

The smallest of the integer greater than 1 that leaves a remainder of 1 = 1(T-1) + 1 = 211

The next after the smallest number: 2(T-1) +1= 2(210) + 1 = 421

The two smallest number = 1(T-1) + 1 and 2(T-1) +1 respectively

The difference between the two smallest such integers = 421-211 = 210

Answer:

$17.72 left

Step-by-step explanation:

144 inches = 4 yards

4(0.15) + 3.5(0.48) = 0.6 + 1.68 = $2.28 SPENT

20 - 2.28 = $17.72 left in change

Answer:

Question 1: 3 - 5 hours.

Question 2: 0 - 1 hour

Step-by-step explanation:

Question 1: As you can see in the diagram, the guy is moving really slowly and is almost stuck, therefore, it is 3 - 5  hours.

Question 2:  In hours 0 - 1, you can see that the graph is the closest to vertical as it gets.

Answer:

[tex]z=-\frac{20}{3}[/tex]

Step-by-step explanation:

[tex]\frac{3z}{10}-4=-6\\\\\frac{3z}{10}-4+4=-6+4\\\\\frac{3z}{10}=-2\\\\\frac{10\cdot \:3z}{10}=10\left(-2\right)\\\\3z=-20\\\\\frac{3z}{3}=\frac{-20}{3}\\\\z=-\frac{20}{3}[/tex]

Best Regards!

Answer:

Just replace the variables with the number

d5

c4 (uh oh)

a2

b-3

f-7

d-c = 5 - 4 = 1

1/3 - 4(ab+f)

2 x -3 = -6

-6 + -7 = -13

-13 x 4 = -52

1/3 - -52 = 1/3 + 52 =

52 1/3

Hope this helps

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Hope this helps.. if not im sorry :(

Answer:

50,063,860 different samples can be chosen

Step-by-step explanation:

The order in which the microchips are chosen is not important. So we use the combinations formula to solve this question.

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]

How many different samples can be chosen

We choose 6 microchips from a set of 60. So

[tex]C_{60,6} = \frac{60!}{6!(60-6)!} = 50063860[/tex]

50,063,860 different samples can be chosen

Answer:

The degrees of freedom are given by:

[tex] df = n_A +n_B -2 = 18 +15-2= 31[/tex]

And the 90% confidence interval for this case is:

[tex] -1.90 \leq \mu_A -\mu_B \leq 0.13[/tex]

And for this case since the confidence interval contains the value 0 we can conclude that:

A. We are 90% confident that, on average, there is no difference in operating hours between toothbrushes from Company A compared to those from Company B.

Step-by-step explanation:

We know the following info given:

[tex] \bar X_A= 119.7[/tex] sample mean for A

[tex] s_A = 1.74[/tex] sample deviation for A

[tex] n_A = 18[/tex] sample size from A

[tex] \bar X_B= 120.6[/tex] sample mean for B

[tex] s_B = 1.72[/tex] sample deviation for B

[tex] n_B = 15[/tex] sample size from B

The degrees of freedom are given by:

[tex] df = n_A +n_B -2 = 18 +15-2= 31[/tex]

And the 90% confidence interval for this case is:

[tex] -1.90 \leq \mu_A -\mu_B \leq 0.13[/tex]

And for this case since the confidence interval contains the value 0 we can conclude that:

A. We are 90% confident that, on average, there is no difference in operating hours between toothbrushes from Company A compared to those from Company B.