Use the area to find the radius. If you could include steps that’ll be very helpful :)

Answer:

The probability that either Alex or Bryan get an A is 0.9

Step-by-step explanation:

Before we proceed to answer, we shall be making some important notation;

Let A = event of Alex getting an A

Let B = event of Bryan getting an A

From the question, P(A) = 0.9, P(B) = 0.8 and P(A ∩ [tex]B^{c}[/tex] ) = 0.1

We are to calculate the probability that either Alex or Bryan get an A which can be represented as P(A ∪ B)

We can use the addition theorem here;

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)  .......................(i)

Also,

P(A) = P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)   .........................(ii)

We can insert ii into i and we have;

P(A ∪ B) =  P(A ∩ [tex]B^{c}[/tex] )  +   P(A ∩ B)  + P(B) - P(A ∩ B) =   P(A ∩ [tex]B^{c}[/tex] ) + P(B) = 0.1 + 0.8 = 0.9

Answer:

Step-by-step explanation:

To be able to draw a conclusion from the data given, lets find out the p value using the t score and this will be used to make a conclusion.

If the p value is less than 0.05 then, we will reject the null but if otherwise we will fail to reject the null.

Using a p value calculator with a t score of 2.83, significance level 0.05 and the test is a two tailed test, the p value is 0.004655 which is less than 0.05 and the result is significant.

This we will reject the null hypothesis H0:p∗=1/2 for this data set.

Answer:

[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-3.33)=0.000434[/tex]  

For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.

Step-by-step explanation:

Information given

[tex]\bar X=20[/tex] represent the sample mean  

[tex]\sigma=9[/tex] represent the population deviation

[tex]n=36[/tex] sample size  

[tex]\mu_o =25[/tex] represent the value to verify

[tex]\alpha=0.1[/tex] represent the significance level

tzwould represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test the hypothesis that the true mean is lower than 25  and the system of hypothesis are:  

Null hypothesis:[tex]\mu \geq 25[/tex]  

Alternative hypothesis:[tex]\mu < 25[/tex]  

The statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info given:

[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-3.33)=0.000434[/tex]  

For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.

Answer:Please include images of the graphs!

Step-by-step explanation:

Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.

Use the following equation to get the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:

(x₁ , y₁) & (x₂ , y₂)

In this equation, make sure that the slope (m) will equal 1/4 (given).

The full equation that you will use is:

1/4 =  (y₂ - y₁)/(x₂ - x₁)

Find the graph that will satisfy this equation.

The first differences are 8, 14, 20.

The second differences are 6.

Half of 6 is 3, so the first term of the sequence is 3n^2.

If you subtract 3n^2 from the sequence you get 0,-1,-2,-3 which has the nth term of -n + 1.

Therefore your final answer will be 3n^2 - n + 1

The length of the parametric curve (call it C ) is given by

[tex]\displaystyle\int_C\mathrm ds=\int_0^{8\pi}\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

We have

[tex]x=t-2\sin t\implies\dfrac{\mathrm dx}{\mathrm dt}=1-2\cos t[/tex]

[tex]y=1-2\cos t\implies\dfrac{\mathrm dy}{\mathrm dt}=2\sin t[/tex]

Now,

[tex]\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=5-4\cos t[/tex]

so that the arc length integral reduces to

[tex]\displaystyle\int_0^{8\pi}\sqrt{5-4\cos t}\,\mathrm dt[/tex]

which has an approximate value of 53.4596.

Answer:

Section 1:

a) 7:15 a.m - 19:15

b) 1:05 am - 01:05

c) 2:01 p.m - 14:01

d) 9:22 p.m - 21:22

e) 12:25 am- 24:25

Section 2:

a) 1155 hours - 11:55am

b) 1005 hours -10:05am

c) 1714 hours - 5:14pm

d) 0756 hours - 7:56am

e) 1345 hours- 1:45pm ​

Answer:

12:25 am= 00:25

Step-by-step explanation:

Answer:

The car's average 18 number of miles per gallon

Step-by-step explanation:

The car has different efficiencies depending if its used on highway or city streets.

The efficiency on a highway is:

[tex]E_h=\dfrac{350}{15}\;\text{miles/gal}=23.33\;\text{miles/gal}[/tex]

The efficiency for city driving is:

[tex]E_c=\dfrac{280}{18}\;\text{miles/gal}=15.56\;\text{miles/gal}[/tex]

We now that the car uses twice as many gallons for city driving as for highway driving. This means that, for every gallon consumed, 2/3 are for city driving and 1/3 are for highway driving.

Then, we can calculate how many miles makes the car on average as:

[tex]E=\dfrac{1}{3}E_h+\dfrac{2}{3}E_c\\\\\\E=\dfrac{1}{3}\cdot 23.33+\dfrac{2}{3}\cdot15.56=7.78+10.37=18.15\;\text{miles/gal}[/tex]

Answer:

y = -5(x) - 4

Step-by-step explanation:

Use the equation of a line and substitution.

Information given:

point 1: (-2,6)

x1 = -2 and y1 = 6

point 2: (0,4)

x2 = 0 and y2 = 4

Equation of a line: y = m(x) + b

m = slope

To find slope, you do the equation of a linear slope, which is:

m = [tex]\frac{rise}{run}[/tex]         in other words   m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]

plug in your values

[tex]\frac{6-(-4)}{-2-0}[/tex]

= -5

Great, we've found slope, now to find b

plug in the slope you found: y = -5(x) + b

Plug in and solve for each point given, aka (x,y) into the linear equation for both points.

FIRST POINT:

6 = -5(-2) + b

6 = 10 + b

6 - 10 = b

b = -4

SECOND POINT:

-4 = -5(0) + b

-4 = 0 + b

-4 - 0 = b

b = -4

We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.

Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.

Answer:

f(x)=-5x-4

Step-by-step explanation:

You are given two points (-2, 6) and (0, -4)

Find the slope: m=(-4-6)/[(0-(-2)]=-5

So you have y=-5x+b

next, find the y intercept b.

the y intercept is when x=0. in this case, the y intercept is -4

so the linear function is f(x)=-5x-4

Answer:

A) 0.026

B) 0.130

Step-by-step explanation:

Complete Question

A factory received a shipment of 10 generators and the vendor who sold the items knows there are 4 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment. Give answer as a decimal to three decimal places.

(A) If a sample of 4 generators is selected, find the probability that all in the sample are defective.

(B) If a sample of 4 generators is selected, find the probability that none in the sample is defective.

Solution

A) This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of generators to be picked = 4

x = Number of successes required = number of defective generators required = 4

p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40

q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60

P(X = 4) = ⁴C₄ (0.40)⁴ (0.6)⁴⁻⁴ = 0.0256 = 0.026 to 3 d.p.

B) n = total number of sample spaces = number of generators to be picked = 4

x = Number of successes required = number of defective generators required = 0

p = probability of success = probability that a randomly selected generator is defective = (4/10) = 0.40

q = probability of failure = probability that a randomly selected generator is NOT defective = 1 - p = 1 - 0.40 = 0.60

P(X = 0) = ⁴C₀ (0.40)⁰ (0.6)⁴⁻⁰ = 0.1296 = 0.130 to 3 d.p.

Hope this Helps!!!

Answer:

  4 cm

Step-by-step explanation:

The side of the square will be the average of the two sides of the rectangle with the same perimeter.

Formulas for the perimeters are ...

  P = 2(L+W)

  P = 4s

Equating these gives ...

  4s = 2(L+W)

  s = (L +W)/2 . . . . . divide by 4

For the given side lengths, ...

  s = (2 cm +6 cm)/2 = (8/2) cm = 4 cm

The length of one side of the square is 4 cm.

The gradient theorem applies here, because we can find a scalar function f for which ∇ f (or the gradient of f ) is equal to the underlying vector field:

[tex]\nabla f(x,y,z)=\langle2xy,x^2-z^2,-2yz\rangle[/tex]

We have

[tex]\dfrac{\partial f}{\partial x}=2xy\implies f(x,y,z)=x^2y+g(y,z)[/tex]

[tex]\dfrac{\partial f}{\partial y}=x^2-z^2=x^2+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=-z^2\implies g(y,z)=-yz^2+h(z)[/tex]

[tex]\dfrac{\partial f}{\partial z}=-2yz=-2yz+\dfrac{\mathrm dh}{\mathrm dz}\implies\dfrac{\mathrm dh}{\mathrm dz}=0\implies h(z)=C[/tex]

where C is an arbitrary constant.

So we found

[tex]f(x,y,z)=x^2y-yz^2+C[/tex]

and by the gradient theorem,

[tex]\displaystyle\int_{(0,0,0)}^{(1,2,3)}\nabla f\cdot\langle\mathrm dx,\mathrm dy,\mathrm dz\rangle=f(1,2,3)-f(0,0,0)=\boxed{-16}[/tex]

Hey there! :)

Answer:

Price per cup: $3.5

Price for 18 cups: $63.

Step-by-step explanation:

To find the cost of a single cup of ice cream, we can set up an equation where 'x' equals the price of a cup of ice cream.

30x = 105

Divide both sides by 30:

x = $3.5.

To find the cost of 18 cups, simply multiply this price by 18:

18 × 3.5 = $63 dollars. This is the price for 18 cups of ice cream.

Answer:

If a person is randomly selected from this group, the probability that they have both high blood pressure and high cholesterol is P=0.25.

Step-by-step explanation:

We can calculate the number of people from the sample that has both high blood pressure (HBP) and high cholesterol (HC) using this identity:

[tex]N(\text{HBP or HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP and HC})\\\\\\ N(\text{HBP and HC})=N(\text{HBP})+N(\text{HC})-N(\text{HBP or HC})\\\\\\ N(\text{HBP and HC})=15+25-30=10[/tex]

We can calculate the probability that a random person has both high blood pressure and high cholesterol as:

[tex]P(\text{HBP and HC})=\dfrac{10}{40}=0.25[/tex]

Answer:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Step-by-step explanation:

Information given

[tex]\bar X= 28.1[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma =4.7[/tex] represent the population standard deviation

n=40 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Answer:

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

Step-by-step explanation:

Simple interest for any amount p is given by

SI = p*r*t/100

where r is the annual rate rate of interest

t is the time

____________________________________________

Given

p= $500 (loan taken)

r = 8%

t = 1 year

SI = 500*8*1/100 = 40

Thus, $40 is the interest charged in a year.

Total money paid at the end of one year = loan taken  + interest charged

                                                                    = $500 + $40

                                                                    = $540

a. How much will she have to pay back at the end of the 1 year?

Answer: $540

b. How much interest does she have to pay?

Answer: $40

Answer:

a = 13

b = 0

Step-by-step explanation:

Conjugate of -3 + 2i is -3 - 2i

(-3 + 2i) (-3 - 2i)

We need to expand:

9 + 6i + -6i + -4i^2

-4i^2 =(-4)(-1) = 4

9 + 4 = 13

a = 13

b = 0

Answer:

Step-by-step explanation:

The given data is expressed as

1204, 1206, 1345, 1306, 1207, 1078, 1357, 1232, 1228, 1302, 1189, 1177, 1083, 1094, 1326, 1071, 1427, 1348, 1420, 1253, 1270

The number of items in the data, n is 21. The lowest value is 1071 while the highest value is 1427. The convenient starting point would be 1070.5 and the convenient ending point would be 1427.5

The number of class intervals is

√n = √21 = 4.5

Approximately 5

The width of each class interval is

(1427.5 - 1070.5)/5 = 72

The end of each class interval would be

1070.5 + 72 = 1142.5

1142.5 + 72 = 1214.5

1214.5 + 72 = 1286.5

1286.5 + 72 = 1358.5

1358.5 + 72 = 1430.5

The frequency for the fifth class, that is between 1358.5 to 1430.5 would be 2

Answer:

y = -2x + 5

slope = -2

y intercept = 5

Step-by-step explanation:

Slope intercept form of equation of line is given by y = mx + c

where m is the slope of line

c is the y intercept i.e point where given line intersect y axis.

________________________________________________

given equation 4x + 2y = 10

we have to re-write this equation in form y = mx + c

4x + 2y = 10

subtraction 4x from LHS and RHS

4x + 2y - 4x= 10 - 4x

2y = 10- 4x

we have to eliminate 2 from y for that we

divide  LHS and RHS by 2 we

2y /2 = 10/2- 4x/2

y = 5 - 2x

rearranging it in y = mx+c form

y = -2x + 5

thus, m = -2 , c = 5

Answer:

See below.

Step-by-step explanation:

The total is 20 friends. This means that we need to make each frequency into a fraction, then simplify to percentage.

1. 10/20 = 50%

2. 3/20 15%

3. 2/20 = 10%

4. 5/20 = 25%

Hope this helps! (Please consider giving brainliest)

Answer:

Bus: 50%

Walk: 15%

Bike: 10%

Car: 25%

Step-by-step explanation:

The total amount of friends is 20.

10 out of 20 is equal to 1/2, which is equal to 50%.

3 out of 20 is equal to 15%.

2 out of 20 is equal to 10%.

And 5 out of 20 is equal to 1/4, which is equal to 25%.

Please mark Brainliest if correct

Answer:

the answer you are looking for is D 778

Answer:

[tex]1<x<3[/tex]

Step-by-step explanation:

Let simplify each of these inequalities individually and then look at where they intersect afterwards

[tex]x+1<4\\\\x<3[/tex]

And

[tex]x-8>-7\\\\x>1[/tex]

This means that for these two inequalities to intersect, x must be greater than 1, but less than 3.

This can be represented by the following inequality [tex]1<x<3[/tex]

Answer:

The answer is D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

LCM = 75

Step-by-step explanation:

1: Multiply the factor by the greatest number

Description:

The least common  multiple for 75,5,3 is 75.

LCM= Least common Multiple

Please mark brainliest

Hope this helps.

Answer:

75

Step-by-step explanation:

Break each number into prime factors

75 = 25*3 = 5*5*3

5 = 5*1

3 = 3*1

Multiply by the greatest number of each factor

3 = 1 time

5 = =2 times

The least common multiple = 3 * 5*5 = 75

The angle of elevation of the sun when a 10-foot tree creates a shadow that is 15 feet long  is 33.69 degrees

To find the angle of elevation of the sun, we can use trigonometry and the concept of similar triangles.

Given that:

The tree's height is 10 feet.

The length of the shadow is 15 feet.

Let's assume that the tree's height is "h"  feet.

Length of its shadow is represented by "s" feet

The angle of elevation of the sun is the angle between the ground and the line from the top of the tree to the tip of its shadow.

The angle can be determined using the tangent function.

[tex]tan\theta[/tex] = [tex]\dfrac{h}{s}[/tex]

Now, substitute the given values:

[tex]tan\theta[/tex]= [tex]\dfrac{10}{15}[/tex]

[tex]tan\theta[/tex] = [tex]\dfrac{2}{3}[/tex]

The angle of elevation can be obtained by  taking the inverse tangent of 2/3

angle of elevation =[tex]\tan^-1\dfrac{2}{3}[/tex]

angle of elevation ≈ 33.66 degrees

So, the angle of elevation of the sun is approximately 33.69 degrees.

Learn more about angle of elevation here:

https://brainly.com/question/31006775

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Answer:

it is option A

Step-by-step explanation:

If the length of OB was ³/₄, then the length of OB' after dilation is; Option B: 3 units.

What this means is that it was enlarged by a scale factor of 4 with point O as the center of dilation.

Scale factor = new dilated length OB'/(³/₄)

new dilated length OB' = ³/₄ × 4

new dilated length OB' = 3 units

Read more on dilation at; https://brainly.com/question/8532602

Answer:

its 4 units trust just answered it

Step-by-step explanation:

Answer:

Step-by-step explanation:

There are no factors outside the parentheses that need to be distributed, so the parentheses can be simply dropped:

  6 -2x +15 -3x

The terms can be rearranged to put like terms next to each other:

  -2x -3x +6 +15

and the like terms can be combined.

  -5x +21 . . . . simplified expression

__

Put the value of x where x is, then do the arithmetic.

  -5(-0.2) +21 = 1 +21 = 22

Answer:

1. B

Step-by-step explanation:

1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A

2. The level of significance is 1% (99% confidence interval)

3. The null hypothesis: u = 0.8

Alternative hypothesis: u =/ 0.8

4. a. The Student's t, since we assume that x has a normal distribution with known σ

5. Using the formula t = (x - u) / σ√n

Where x = 1.22 u = 0.8 σ = 0.44 n = 9

t = (1.22-0.8) / 0.44√9

t = 0.42/(0.44x3)

t = 0.42/1.32

t = 0.318

P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.