What’s the correct answer for this question?

Answer:

Center is [tex](-12,9)[/tex]

Step-by-step explanation:

Given: Equation of a circle is [tex](x+12)^2+(y-9)^2=35[/tex]

To find: center of the circle

Solution:

A circle is a locus of all points which are at equidistant from the fixed point (center).

Equation of a circle is of form [tex](x-a)^2+(y-b)^2=r^2[/tex] where [tex](a,b)[/tex] represents center of the circle and r denotes radius of the circle.

Given equation is [tex](x+12)^2+(y-9)^2=35[/tex]

[tex]\left [ x-(-12) \right ]^2+(y-9)^2=35[/tex]

Compare this equation with [tex](x-a)^2+(y-b)^2=r^2[/tex]

Center is [tex](a,b)=(-12,9)[/tex]

Answer:

The raidus is 5.92

Step-by-step explanation:

Answer:

27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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.

In this question, we have that:

[tex]\mu = 211, \sigma = \sqrt{2.89} = 1.7, n = 86, s = \frac{1.7}{\sqrt{86}} = 0.1833[/tex]

What is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches.

Either greater than 211 + 0.2 = 211.2 or smaller than 211 - 0.2 = 210.8. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability of being less than 210.8:

This is the pvalue of Z when X = 210.8. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{210.8 - 211}{0.1833}[/tex]

[tex]Z = -1.09[/tex]

[tex]Z = -1.09[/tex] has a pvalue of 0.1379

Probability of differing from the population mean by greater than 0.2 inches :

2*0.1379 = 0.2758

27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches

Answer:

Probability is 86.24%

Step-by-step explanation:

We can solve this by using the Z-score formula.

Z = (X - μ)/σ

Where;

μ is mean = 211 inches

σ is standard deviation

Now, we are given variance as 2.89

Formula for standard deviation using variance is;

SD = √variance

SD = √2.89

SD = 1.7

To find the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches, we will find the p-value of z and subtract 1 from it.

Since we are told that the sample shafts would differ by 0.2 inches, thus;

X = 211 + 0.2 = 211.2

Since we are working with sample mean of 86, then we have;

Z = (X - μ)/s

s = σ/√86

s = 1.7/√86

s = 0.1833

So,

Z = (211.2 - 211)/0.1833

Z = 1.0911

From z-score calculator, the p-value is gotten to be 0.1376

Thus, probability that mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches is;

Probability = 1 - 0.1376 = 0.8624 = 86.24%

Answer:

X=8

Step-by-step explanation:

3x+ 6 = 5x -10

6+10=5X-3X

16=2X

X=8

Answer:

It should be 222

Step-by-step explanation:

Answer:

222

Step-by-step explanation:

3x^3+2x^2-2x+6

x=4

=3(4)^3+2(4)^2-2(4)+6

=192+32-8+6

=224-2

=222

Answer:

The probability that a customer purchases a black SUV is 0.05.

Step-by-step explanation:

The question is incomplete:

At a certain car dealership, the probability that a customer purchases an SUV is 0.20. Given that a customer purchases an SUV, the probability that it is black is 0.25.

The probability that a customer purchases a black SUV can be calculated as the multiplication of this 2 factors:

We know then:

[tex]P(SUV)=0.25\\\\P(B | SUV)=0.20[/tex]

We can now calculate the probability as:

[tex]P(B\,\&\,SUV)=P(B|SUV)\cdot P(SUV)=0.25\cdot0.20=0.05[/tex]

Answer:

Step-by-step explanation:

Volume of a triangular based prism = [tex]Base\ area * height[/tex]

Base area = Area of the triangle = 1/2 * base of the triangle * height of the triangle

Since the  triangular base has dimensions of 3" by 4" by 5", then it is a right angled triangle with base of 4in and height of 3in

Base Area = 1/2 * 3 * 4

Base Area = 6in²

Substituting the volume and the base area value in the formula to get the height of the prism we have;

210 = 6H

H = 210/6

H = 35in

Surface area of the triangular prism = bh + pH

b= base of the triangle  = 4in

h- height of the triangle  = 3in

p= perimeter of the triangle  = 3+4+5 = 12in

H= height of the prism = 35in

Surface area of the triangular prism = 4(3)+12(35)

Surface area of the triangular prism = 12+420in

Surface area of the triangular prism = 432in²

Answer:

Step-by-step explanation:

Given the cost of a car to be RS 1,000,000, if the car depreciates yearly by 5%, then the insurance premium paid which is the operating expenses eacg year will be calculated as thus;

In the first year;

insurance premium paid = 5% of RS 1,000,000

= 5/100 * 1,000,000

= RS50,000

cost of the car after the first year of usage = 1,000,000-50,000

= RS 950,000

In the second year;

Insurance premium paid in the second year = 5% of RS 950,000

= 5/100 * 950,000

= 5*9,500

= RS 47,500

cost of the car at the end of second year = 950,000-47,500 = RS 902,500

In the third year;

Insurance premium paid in the third year = 5% of RS 902,500

= 5/100 * 902,500

= 5*9,025

= RS 45,125

Answer:

Step-by-step explanation:

This is a hypothesis testing involving population proportion. The null hypothesis would be that fewer than or 50% of the people would favor spending money for a sewer system. Since she will vote to appropriate funds only if she can be reasonably sure that a majority of the people in her district favor the measure, then the alternative hypothesis which she should test is that more than 50% of the people would favor spending money for a sewer system.

Answer:

Check the answer. 1. ... 5 times a number plus 8 is equal to 3 times the number minus 4. 7 times a ... Twice a number is equal to 5 times the sum of the number and 6. The product ... If the equation is an identity, write the answer as “All real numbers.

Step-by-step explanation:

Answer:

(y-6)(y-6)

Step-by-step explanation:

y^2 - 12y + 36= y^2-2*6y+6^2= (y-6)^2= (y-6)(y-6)

Answer:

[tex](y-6)(y-6)[/tex]

Step-by-step explanation:

[tex]y^2 - 12y + 36[/tex]

[tex]y^2-6y-6y+36[/tex]

[tex]y(y-6)-6(y-6)[/tex]

[tex](y-6)(y-6)[/tex]

Answer: choice B

Step-by-step explanation:

50C40

=50C10

=50!/40!*10!

Answer:

Step-by-step explanation:

Since we are dealing with binomial probability in this scenario, then the outcome is either a success or a failure. A success in this case means that a chosen adult has a bachelor's degree. The probability of success, p would be 20/100 = 0.2

The number of adults sampled, n is 100

The number of success, x is 60

The probability that more than 60 adults have a bachelor's degree P(x >60) would be represented as

d. P(x<60)=binomcdf (100.0.20.60)

binompdf is used when we want to determine P(x = 60)

Answer:

20

Step-by-step explanation:

10 for each for their being in the tens place, and ten for the ones place.

Answer:

pHotOsPHerE

Step-by-step explanation:

Answer:

Photosphere

Step-by-step explanation:

Answer:

37044 different combinations of 4 movies can he rent if he wants at least one comedy

Step-by-step explanation:

The order in which the movies are selected 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 combinations of 4 movies can he rent if he wants at least one comedy

The easier way to solve this is subtract the total from the number of combinations with no comedies.

Total:

4 movies from a set of 14 + 19 = 33. So

[tex]C_{33,4} = \frac{33!}{4!(33-4)!} = 40920[/tex]

No comedies:

4 movies from a set of 19.

[tex]C_{19,4} = \frac{19!}{4!(19-4)!} = 3876[/tex]

At least one comedy:

40920 - 3876 = 37044

37044 different combinations of 4 movies can he rent if he wants at least one comedy

Answer:

Lance would need 3.125 gallons of water.

Step-by-step explanation:

Divide the value by 16

After converting the volume into gallons, Lance needs 3.125 gallons of water for the runners in a race.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Lance needs 50 cups of water for the runners in a race.

We know that;

⇒ 1 gallons = 16 cups

⇒ 1 cups = 1/16 gallons

Here, Lance needs 50 cups of water for the runners in a race.

Hence, We get;

⇒ 50 cups = 50 × 1/16 gallons

                 = 3.125 gallons

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ2

Answer:

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] s= 0.286[/tex]

And then the estimator for the standard error is given by:

[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]

Step-by-step explanation:

For this case we have the following dataset given:

20.05, 20.56, 20.72, and 20.43

We can assume that the distribution for the sample mean is given by:

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

And the standard error for this case would be:

[tex] SE= \frac{\sigma}{\sqrt{n}}[/tex]

And we can estimate the deviation with the sample deviation:

[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] s= 0.286[/tex]

And then the estimator for the standard error is given by:

[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]

Answer:

The probability that both are red is [tex]P(red\:and \:red)=\frac{45}{946}\approx0.04756\approx4.756\%[/tex].

Step-by-step explanation:

Probability is simply how likely something is to happen and its given by

Probability of an event = (# of ways it can happen) / (total number of outcomes)

Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.

                                     [tex]P(A\:and\: B)=P(A)\cdot P(A|B)[/tex]

At our first pull, there is an [tex]P(red)=\frac{10}{10+34}[/tex] chance that a red will be pulled.

At the second pull there is a [tex]P(red)=\frac{9}{9+34}[/tex] chance that the second marble will be red.

Therefore, the probability that both are red is

[tex]P(red\:and \:red)=\frac{10}{10+34}\cdot \frac{9}{9+34}=\frac{45}{946}\approx0.04756\approx4.756\%[/tex]

Answer:

A. G(x) = x - 9

Step-by-step explanation:

For the function F(x) to shift right, there needs to be a negative number being subtracted. In this case, only answer "A," fits. This is because 9 is being subtracted, making the function shift to the right 9 units.

Answer:

YG, YT, YU, BG, BT, BU, WG, WT and WU

Step-by-step explanation:

The sample space are all the posibles options that you can take, so the sample space in these case is:

YG, YT, YU, BG, BT, BU, WG, WT and WU

Where, for example, YG means that you choose Yellow for your game room and Green for your entertainment center and BU means that you chosse Yellow for your game room and Unfinished for your entertainment center.

Answer:

Answers are below

Step-by-step explanation:

10a) Find how many multiples of 3 there are       4/12 = 1/3

10b) Find how many factors of 12 there are         6/12 = 1/2

10c) Find how many prime numbers there are    5/12

10d)                                                                         3/12 = 1/4

10e) Find how many numbers are less than 12   11/12

Answer:

4 - 5

Step-by-step explanation:

square root of 20 is 4.472135955 therefore the two whole numbers it is between are 4 and 5.

Answer:

OK so we can see that when x increases y does too. The answer is C

Answer:

3. Vertical is the same as horizontal for linear equations because when moving the function up, it moves the whole line left along the x-axis too. When moving it down, it moves the equation right on the x-axis.

4. Alex is correct

5. g(x)=(2x-8)^2+5

6. This accomplishes these transformations because I made a graph about it

Step-by-step explanation:

Answer:

Step-by-step explanation:

ported that 22% of adults in France admitted to texting or e-mailing while driving. A random sample of 110 French adults was randomly selected. What is the probability that 26

Using a binomial distribution with mean = n*p = 110*0.22 = 24.2 and variance = n*p*(1-p) = 24.2*(1-0.22) = 18.876

Approximating it to a normal distribution,

[tex]P(x\geq 26)\\\\=P(Z\geq \frac{26-24.2}{\sqrt{18.876} } )\\\\=P(Z\geq 0.41)\\\\=0.3481[/tex]

Answer:

67 feet^2

Step-by-step explanation:

Surface Area = 2×(4×2.6 + 4×3.5 + 2.6×3.5) = 67 feet^2

Answer:

67 feet^2

Step-by-step explanation:

Surface Area = 2×(4×2.6 + 4×3.5 + 2.6×3.5) = 67 feet^2

Answer:

The maximum possible error of in measurement of the angle is  [tex]d\theta_1 =(14.36p)^o[/tex]

Step-by-step explanation:

From the question we are told that

    The angle of elevation  is  [tex]\theta_1 = 15 ^o = \frac{\pi}{12}[/tex]

     The height of the tree is  h

      The distance from the base is  D

h is mathematically represented as

            [tex]h = D tan \theta[/tex]       Note : this evaluated using SOHCAHTOA i,e

                                               [tex]tan\theta = \frac{h}{D}[/tex]

Generally for small angles the series approximation of  [tex]tan \theta \ is[/tex]

          [tex]tan \theta = \theta + \frac{\theta ^3 }{3}[/tex]

So given that [tex]\theta = 15 \ which \ is \ small[/tex]

       [tex]h = D (\theta + \frac{\theta^3}{3} )[/tex]

       [tex]dh = D (1 + \theta^2) d\theta[/tex]

=>        [tex]\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta[/tex]

Now from the question the relative error of height should be at  most

        [tex]\pm p[/tex]%

=>    [tex]\frac{dh}{h} = \pm p[/tex]

=>    [tex]\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p[/tex]

=>      [tex]d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p[/tex]

 So  for   [tex]\theta_1[/tex]

            [tex]d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p[/tex]

substituting values  

          [tex]d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p[/tex]

 =>       [tex]d\theta_1 = 0.25 p[/tex]

Converting to degree

           [tex]d\theta_1 = (0.25* 57.29) p[/tex]

            [tex]d\theta_1 =(14.36p)^o[/tex]

Answer:

=x^2+7x+10

Step-by-step explanation:

Simplify: xx+5x+2x+2.5: x+7x+10

Add similar elements: 5x+2x= 7x

=xx+7x+2.5

xx=x2

2.5=10

=x+7x+10

Answer: =x^2+7x+10

Hope this helps.