Find the value of x​

Answer:

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Step-by-step explanation:

Answer:

Common Examples of Negative Correlation. A student who has many absences has a decrease in grades. As weather gets colder, air conditioning costs decrease. If a train increases speed, the length of time to get to the final point decreases.

Answer:

Step-by-step explanation: Opposite sides of a parallelogram are equal.

Answer:

The opposite sides of the parallelogram have equal lengths.

Step-by-step explanation:

PLATO SAMPLE

Answer:

56

Step-by-step explanation:

Just took the quiz

Hope this helps!

Answer:

[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges

Step-by-step explanation:

Data given

[tex]\bar X_{1}=15[/tex] represent the mean for sample A

[tex]\bar X_{2}=20[/tex] represent the mean for sample B  

[tex]s_{1}=5[/tex] represent the sample standard deviation for A

[tex]s_{f}=4[/tex] represent the sample standard deviation for B  

[tex]n_{1}=500[/tex] sample size for the group A

[tex]n_{2}=400[/tex] sample size for the group B  

[tex]\alpha=0.01[/tex] Significance level provided

t would represent the statistic

System of hypothesis

The system of hypothesis is the true difference in the time students spent for online assignments between the two colleges, the system of hypothesis would be:  

Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]  

Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]  

Since we don't know the deviations the statistic is given by:

[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)  

The degrees of freedom are given by [tex]df=n_1 +n_2 -2=500+400-2=898[/tex]  

Replacing the info given we got:

[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]  

The p value would be given by:

[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]  

Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges

Answer:

116°

Step-by-step explanation:

Given that :

∠ ABD measures (4x + 10)

∠ ACD measures  (5x - 2)

Then

∠ABD = ∠ACD  ( rule : angle by same chord AD )

∠ABD =   (4x + 10)°

∠ACD =   (5x - 2)°

so we can as well say that :

(4x + 10)° = (5x - 2)°

4x - x = -10 -2

- x = - 12

x   = 12

∠ABD = (4x + 10)°

= ( 4 × 12 + 10)°

= 58°

∠ACD = (5x - 2)°

= ( 5 * 12 - 2)°

= 58°

∠AOD = 2∠ABD = 2∠ACD   ( since angle by arc AD at  center is  twice the  angle by same arc AC in other arc segment)

 ∠AOD =  2 × 58°

∠AOD = 116°

Measure of arc AD = 116°

Answer: player A = 11/16 and player B = 5/16

Step-by-step explanation:

If a coin was to be tossed to determine the winner possible outcomes using arithmetical triangle.

Player A needs 2 points = 11

Player B needs 3 points = 5

Total outcome of tossing a coin = 16

Player A = 11/16 = 0.6875

Player B = 5/16 = 0. 3125

Or

Using the fifth roll of the pascal triangle (2+3) outcome

( 1, 4, 6, 4, 1 )

Addition of the first 3 represent Player A chances of winning = ( 1+ 4 + 6 ) = 11

And the last two = ( 1 + 4 ) = 5 represents the chances of team B winning

Total number of outcome = ( 1 + 4 + 6 + 4 + 1 ) = 16

Answer:

C=2πr

Step-by-step explanation:

Final answer:

The possible model for the number of incorrect questions that agree is a binomial distribution. The teacher can use this model to calculate the probability of observing 8 or more agreed-upon answers.

Explanation:

The possible model for the number of incorrect questions that agree is a binomial distribution because there are a fixed number of trials (the number of questions) and each trial has two possible outcomes (agree or disagree).

The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4, so the probability of agreeing on a particular question is 1/4. Since there are 20 questions, the probability that they agree on exactly 8 questions is given by the binomial probability formula: P(x = 8) = C(20, 8) * (1/4)^8 * (3/4)^12.

The teacher can use this model to calculate the probability of observing 8 or more agreed-upon answers by summing the probabilities of all possible outcomes with 8 or more agreed-upon answers: P(x ≥ 8) = P(x = 8) + P(x = 9) + ... + P(x = 20).

Answer:

Step-by-step explanation:

Lines A B, C D, and D P intersect at point P. Angle A P C is 65 degrees, Angle C P E is blank, angle E P B is 90 degrees, and angle B P D is blank.

Determine the measures of the unknown angles in the figure.

m∠APD =  

✔ 115°

m∠CPE =  

✔ 25°

m∠BPD =  

✔ 65°

The measure of unknown angles

m∠APD = 115

m∠CPE = 25

m∠BPD = 65

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. They are also referred to as additional angles. Angles that share a vertex are said to be neighbouring. Hence, the linear angles have a common vertex in this instance as well.

Using Linear Pair

<APC + <CPE + <EPB = 180

65 + <CPE + 90 = 180

<CPE = 180 - 155

<CPE = 25

So, <APD = 90 + 25 = 115 degree

<CPE = 25 degree

<BPD = <APC = 65 degree (Vertically opposite angle)

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Answer:

13/15

Step-by-step explanation:

First, you find a common denominator. 10 x 3 and 6 x 5 both equal 30, so 30 can be used as a common denominator. You also have to multiply the numerator by the same number you multiplied in the denominator. Since we did 10 x 3, do 7 x 3, and with the other fraction we did 6 x 5, so do 1 x 5. You should get 21/30 + 5/30. Since they have the same denominator, you can add them. You'll get 26/30, which can still be simplified. 30 divided by 2 is 15, and 26 divided by 2 is 13. The final answer is 13/15.

Answer:

63.

Step-by-step explanation:

To solve this equation, we will first need to multiply both sides by 8 to get rid of the coefficient:

8×[tex]\frac{1}{8}[/tex](x-56)=[tex]\frac{7}{8}[/tex]×8

Now, this will get rid of the fractions, giving us:

x-56= 7

Next, simply add 56 to both sides:

x-56+56= 7+56

This results in:

x=63.

Answer:

The volume of the sphere is 972π mm³

Step-by-step explanation:

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius  = 9mm

π = pi

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * π * (9mm)³

V = π * ⁴⁄₃ *729mm³

V = π * 972mm³

V = 972π mm³

The volume of the sphere is 972π mm³

Answer:

its 6

just simplify the expression.

-Hops

Answer: 6

Divide

18÷9=2

Multiply

2×3=6

Answer:

The forumula for finding area of the circle is  \pi r^2.

Step-by-step explanation:

Let's find the radius of the mug:

r=\frac{d}{2}=\frac{8}{2}=4

Now, we can to express the area of each cookie in terms of pi:

Area= \pi *4^2=16\pi

Answer:

Step-by-step explanation:

Originally, there were 47 ducks.  After the dog jumped in, there were 29.  This means there were 18 ducks.

47 - 29 = 18

After the dog got out 5 groups of 3 ducks came.  This means that 15 ducks came back.

5 × 3 = 15

To find the total amount of ducks, add the ducks together.

18 + 15 = 33

To find the number of ducks remaining in the pond, subtract the 29 ducks scared away from the initial 47, then add the 15 ducks that returned in 5 groups of 3, resulting in 33 ducks now present in the pond.

The student has asked a question related to a basic arithmetic problem involving ducks in a pond. Initially, there were 47 ducks in the pond. A dog scares 29 ducks away. After the dog leaves, 5 groups of 3 ducks each return to the pond. To solve this, we perform two main steps:

The cost of the fabric per yard is approximately $6.39.

To find the cost of the fabric per yard, we need to first calculate the cost per foot and then convert it to yards.

Step 1: Calculate the cost per foot of fabric.

[tex]Cost per foot = Total cost / Total feet[/tex]

[tex]Cost per foot = $9.60 / 4.5 feet[/tex]

[tex]Cost per foot = $2.13[/tex]

Step 2: Convert the cost per foot to cost per yard.

Since there are 3 feet in a yard, we can find the cost per yard by multiplying the cost per foot by 3.

[tex]Cost per yard = Cost per foot * 3[/tex]

[tex]Cost per yard ≈ $2.13 * 3[/tex]

[tex]Cost per yard = $6.39[/tex]

Complete correct question:

Alvin makes pillows for his room he buys 4.5 feet of fabric for 9.60 what is the cost of the fabric per yard?

Answer:

4

Step-by-step explanation:

n/6+2

Let n = 12

12/6 +2

Division first

2 +2

4

Answer:

4

Step-by-step explanation:

plug in 12 for n and you get :: 12/6 + 2

PEMDAS says to divide first, 12/6 is 2. you add 2 next and you get 4

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Answer:

Number of students want to go to Theme Park = 75

Step-by-step explanation:

Note: The given question is incomplete. Complete question is as follow.

Given:

Number of sample student = 30

Place                 Number of students  want to go

Theme Park                          10

Theater                                  5

Sports Center                        8

Seaside                                  7

Find:

How many students want to go to Theme Park.

Computation:

⇒ Probability for  students want to go to Theme Park =  10 / 30

⇒ Probability for  students want to go to Theme Park =  1 / 3

⇒ Number of students want to go to Theme Park =  [1 / 3]225

⇒ Number of students want to go to Theme Park = 75

Final answer:

Using a sample proportion, if 12 out of 30 students chose the Theme Park, we estimate that 90 out of 225 students will want to go to the Theme Park.

Explanation:

To estimate how many of the 225 students will want to go to the Theme Park, we use the results from Sally's sample of 30 students. First, we need to know the number of students in the sample who chose the Theme Park. Suppose, for instance, that 12 out of the 30 sampled students chose the Theme Park. We can set up a proportion to find the estimated number of students out of 225 who would choose the same.

Here's the proportion based on the sample data:

Number of students who chose Theme Park in the sample / Total number of students in the sample = Estimated number of students who will choose Theme Park / Total number of students planning to go

In our example, this is 12/30 = x/225, where x is the estimated total.

We cross-multiply to solve for x:

12 × 225 = 30 × x

x = (12 × 225) / 30

x = 90

Thus, we estimate that 90 out of the 225 students will prefer to go to the Theme Park.

Answer:

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Step-by-step explanation:

Suppose we have a quadratic equation in the following format:

[tex]y = f(x) = ax^{2} + bx + c[/tex]

The vertex of the function is the point [tex](x_{v}, f(x_{v})[/tex], in which

[tex]x_{v} = -\frac{b}{2a}[/tex]

In this problem:

[tex]f(x) = x^{2} - x + 2[/tex]

This means that [tex]a = 1, b = -1, c = 2[/tex]

So

[tex]x_{v} = -\frac{-1}{2} = \frac{1}{2}[/tex]

[tex]f(x_{v}) = f(\frac{1}{2}) = (\frac{1}{2})^{2} - \frac{1}{2} + 2 = \frac{1}{4} - \frac{1}{2} + 2 = \frac{1 - 2 + 8}{4} = \frac{7}{4}[/tex]

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Answer: it will trave 56.89 meters before coming to rest.

Step-by-step explanation:

This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as

S = a/(1 - r)

where

S = sum of the distance travelled by the ball

a = initial distance or height of the ball

r = common ratio

From the information given,

a = 128/9

r = (32/3)/(128/9) = 0.75

Therefore,

S = (128/9)/(1 - 0.75) = 56.89 meters

The distance travelled is an illustration of the sum to infinity of a geometric sequence.

The ball will a travel 56.89 meters before coming to rest

The sequence is given as:

[tex]\mathbf{128/9, 32/3, 8, 6....}[/tex]

From the sequence above, we have:

[tex]\mathbf{a = 128/9}[/tex] --- the first term

[tex]\mathbf{r = 6/8 = 3/4}[/tex] -- the common ratio

The sum to infinity of a geometric progression is:

[tex]\mathbf{S_{\infty} = \frac{a}{1-r}}[/tex]

So, we have:

[tex]\mathbf{S_{\infty} = \frac{128/9}{1-3/4}}[/tex]

[tex]\mathbf{S_{\infty} = \frac{128/9}{1/4}}[/tex]

Divide

[tex]\mathbf{S_{\infty} = \frac{128}{9} \times 4}[/tex]

[tex]\mathbf{S_{\infty} = \frac{128\times 4}{9} }[/tex]

[tex]\mathbf{S_{\infty} = \frac{512}{9} }[/tex]

[tex]\mathbf{S_{\infty} = 56.89}[/tex]

Hence, the ball will a travel 56.89 meters before coming to rest

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Answer: 105

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

C

Answer:

They now should survey 800 people.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem:

Same level of confidence, so same z

Same proportion, so same [tex]\pi[/tex]

We have to change n

We want to reduce the margin of error by half.

M is inverse proportion to the square root of n. That is, as n increases, M decreases.

We want to decrese M by half. So we need to increase n by a factor of 2^2 = 4

The first survey had a sample of 200 people

Increasing by a factor of 4.

200*4 = 800

They now should survey 800 people.

Answer: y= -4x + 1

Step-by-step explanation:

(-1,5) (1,-3)

5-(-3)=8

-1-1=-2

8/-2=-4  negative 4 is the slope. Now find the y-intercept using the formula y=mx + b where b is the y intercept.

so we will plot the  y and x values plus the slope to find the y-intercept.

5=-4(-1) + b  solve for b

5=4 + b

b=1

so now will write the equation y = -4x +1

Answer:

x = 36

Step-by-step explanation:

Given;

(8/9)x = 32

Solving for x

Multiply through by 9

(8/9)×9 ×x = 32×9

8x = 32×9

Divide through by 8

8x/8 = 32×9/8

x = 36

Answer:

The correct option is option 2.

Step-by-step explanation:

In this case we need to test whether the previous data for the proportion of Americans who favored mandatory testing of students in public schools as a way to rate the school has decreased this year or not.

The hypothesis can be defined as follows:

H₀: The proportion supporting mandatory testing is not less than 74% this year, i.e. p ≥ 0.74.

Hₐ: The proportion supporting mandatory testing is less than 74% this year, i.e. p < 0.74.

It is provided that the p-value of the test is,

p-value = 0.015

The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.

The p-value of 0.015 or 1.5% implies that, if it is true that 74% of Americans still favor mandatory testing this year, then the probability that the poll results will show that 71% or less with the same opinion is 1.5%.

Thus, the correct option is option 2.

Answer:

29.3

Step-by-step explanation:

For Ice-cream Cone

height (h) = 7 cm

diameter (d) = 4 cm

radius (r) = diameter/2 = 4/2 cm

radius (r) = 2 cm

Volume Of A Cone

= π * r^2 * h/3

= 22/7 * 2 * 2 * 7/3

= 22 * 4 * 1/3 cm

= 88/3 cm

= 29.3 cm^3

Thus, the Volume of the cone would be 29.3 cm^3

Answer:

L = 2 m

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m

Step-by-step explanation:

Given;

Speed of sound v = 340 m/s

Frequency of sound f = 170 hz

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is;

Length L = v/f = speed/frequency

L = 340/170

L = 2 m

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m

Answer:

a) At least 842 adults must be surveyed.

b) At least 1068 adults must be surveyed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

a) 73% of adults used the Internet.

At least n adults must be surveyed.

n is found when [tex]M = 0.03, \pi = 0.73[/tex]

So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.73*0.27}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.73*0.27}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.73*0.27}}{0.03}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.73*0.27}}{0.03})^{2}[/tex]

[tex]n = 841.3[/tex]

Rounding up

At least 842 adults must be surveyed.

b. No known possible value of the proportion.

Same as above, the difference as the since we do not know the value of the proportion, we use [tex]\pi = 0.5[/tex], which is when the largest sample size is going to be needed.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.5*0.5}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.03}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.03})^{2}[/tex]

[tex]n = 1067.11[/tex]

Rounding up

At least 1068 adults must be surveyed.

To be 95% confident that the sample percentage of U.S. adults who use the Internet is in error by no more than 3 percentage points, a total of 1068 adults must be surveyed.

To estimate the current percentage of U.S. adults who use the Internet with a 95 percent confidence level and an error margin of no more than three percentage points, we must determine the sample size we need to survey. We'll follow the formula below for estimating the sample size:

n = (Z² * p(1-p)) / E^2

Where n is the sample size, Z is the z-score associated with our desired confidence level (for a 95% confidence level, Z is about 1.96), p is the estimated proportion of the population (based on the 2006 data, we'll use 0.73), and E is the margin of error (which we want to be 0.03).

Plug in the values:

n = (1.96² * 0.73 * 0.27) / 0.03² = 1067.14

Since we cannot survey a fraction of a person, we round up to the next whole number. Therefore, the manager would need to survey 1068 adults in order to be 95 percent confident that the sample percentage is in error by no more than three percentage points.

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Answer:

Substitute the slope and the coordinate of D into the equations and solve for b for each equation

Step-by-step explanation:

The equation for a line is y = mx+b

where m is the slope and b is the y intercept

We know m

We have a point (x,y)

We can substitute into the equation and solve for b

Answer:

First option

Step-by-step explanation:

In y = mx + b, m is the slope and b is the y-intercept

Plug in m, and coordinates of D and solve for b