The circle above has an area of 144 pi cm^2. What is the area of the blue sector? Use 3.14 for pi . A. 150.72 cm2 B. 25.12 cm2 C. 48 cm2 D. 113.04 cm2

Answer:

y=4

Step-by-step explanation:

if we draw a function we see that y=4 is paralel to the x axis

A line that is parallel to the x-axis will pass through the y-axis, horizontally.

The equation of line parallel to the x-axis is y = 4

A line that is parallel to the x-axis is represented with the following equation

y = n

Where n can be any real number.

In other words, the following equations are parallel to the x-axis

y = 2

y = 3

y = -2

y = 10

And so on....

Hence, the equation of line parallel to the x-axis is y = 4

Read more about parallel equations at:

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Answer: Three have a right angle. These are the green rectangle, the pinkish square, and the orange trapezoid.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The right answer is 5.

look at the attached picture

Hope it helps...

Good luck on your assignment

Answer:

x=5

Step-by-step explanation:

5x- 7 = 18

5x=18+7

5x=25

Therefore, 5 will cancel 25 five(5) times.

x= 5.

Answer:

x = 5

Step-by-step explanation:

Since AB is the bisector, so MO is equal to NO

MO = NO

5x-7 = 18

5x = 18+7

5x = 25

Dividing both sides by 5

x = 5

The question is incomplete. Here is the complete question.

Find the measurements (the lenght L and the width W) of an inscribed rectangle under the line y = -[tex]\frac{3}{4}[/tex]x + 3 with the 1st quadrant of the x & y coordinate system such that the area is maximum. Also, find that maximum area. To get full credit, you must draw the picture of the problem and label the length and the width in terms of x and y.

Answer: L = 1; W = 9/4; A = 2.25;

Step-by-step explanation: The rectangle is under a straight line. Area of a rectangle is given by A = L*W. To determine the maximum area:

A = x.y

A = x(-[tex]\frac{3}{4}.x + 3[/tex])

A = -[tex]\frac{3}{4}.x^{2} + 3x[/tex]

To maximize, we have to differentiate the equation:

[tex]\frac{dA}{dx}[/tex] = [tex]\frac{d}{dx}[/tex](-[tex]\frac{3}{4}.x^{2} + 3x[/tex])

[tex]\frac{dA}{dx}[/tex] = -3x + 3

The critical point is:

[tex]\frac{dA}{dx}[/tex] = 0

-3x + 3 = 0

x = 1

Substituing:

y = -[tex]\frac{3}{4}[/tex]x + 3

y = -[tex]\frac{3}{4}[/tex].1 + 3

y = 9/4

So, the measurements are x = L = 1 and y = W = 9/4

The maximum area is:

A = 1 . 9/4

A = 9/4

A = 2.25

Answer: 18.48

Step-by-step explanation:

To solve this problem, you would use the order of operations. You would solve the parenthesis first and then solve the rest.

(5.6-2.3)(5.4+0.2)

3.3(5.6)

18.48

Answer:

Step-by-step explanation:

18.48

Answer:

P(A∣D) = 0.667

Step-by-step explanation:

We are given;

P(A) = 3P(B)

P(D|A) = 0.03

P(D|B) = 0.045

Now, we want to find P(A∣D) which is the posterior probability that a computer comes from factory A when given that it is defective.

Using Bayes' Rule and Law of Total Probability, we will get;

P(A∣D) = [P(A) * P(D|A)]/[(P(A) * P(D|A)) + (P(B) * P(D|B))]

Plugging in the relevant values, we have;

P(A∣D) = [3P(B) * 0.03]/[(3P(B) * 0.03) + (P(B) * 0.045)]

P(A∣D) = [P(B)/P(B)] [0.09]/[0.09 + 0.045]

P(B) will cancel out to give;

P(A∣D) = 0.09/0.135

P(A∣D) = 0.667

Answer:

Step-by-step explanation:

The equation is not properly written. Here is the correct expression

[tex]\frac{59+74+62+x}{4} = 70[/tex]

Find the problem situation that matches according to the steps below:

Step 1: We will cross multiply

[tex]59+74+62+x = 4*70\\59+74+62+x = 280\\195+x = 280\\[/tex]

Step 2: Subtract 195 from both sides of the equation

[tex]195+x-195 = 280-195\\x = 280-195\\x = 85[/tex]

Answer:

False

Step-by-step explanation:

4 cos^4 (4x)-3 = 0

Substitute into the equation

4 cos^4 (4pi/24)-3 = 0

4 cos^4 (pi/6)-3 = 0

Take the cos pi/6

4 ( sqrt(3)/2) ^4 -3 =0

Take it to the 4th power

4 ( 9/16) -3 =0

9/4 -3 =0

9/4 - 12/4 = 0

-3/4 =0

False

Answer:

THE ANSWER IS TRUE.

Step-by-step explanation:

I did this on my homework.

Answer:

450 bacteria.

Step-by-step explanation:

To find this, we can set up an exponential equation as shown:

[tex]28800 = a (2)^{\frac{120}{20} }[/tex]

**'a' being the initial value

** '2' representing the culture doubling

Simplify the equation down:

[tex]28800 = a (2)^{6}[/tex]

[tex]28800 = 64a\\a = 450.[/tex]

Therefore, the initial amount of bacteria was 450.

Answer:

56.76% probability that it came from store A

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Defective.

Event B: Store A.

36% of the sales are from store A

This means that [tex]P(B) = 0.36[/tex]

7% of the DVD players sold at store A are defective.

This means that [tex]P(A|B) = 0.07[/tex]

Probability of a defective DVD:

36% come from store A, and of those, 7% are defective.

100 - 36 = 64% come from store B, and of those, 3% are defective. So

[tex]P(A) = 0.07*0.36 + 0.03*0.64 = 0.0444[/tex]

What is the probability that it came from store A

[tex]P(B|A) = \frac{0.36*0.07}{0.0444} = 0.5676[/tex]

56.76% probability that it came from store A

Answer & Step-by-step explanation:

We are given two equations...

a + b = 7

a - b = 3

We are asked to find 3a ÷ 3b. In order to find the value of a and b, we have to rearrange one of the equations so it will be easier to find the values of the variables. Let's rearrange the second equation.

a - b = 3 → a = 3 + b

Now that we have an equation that shows the value of a, we can use this equation and plug it into the first equation.

a + b = 7

a = 3 + b

(3 + b) + b = 7

3 + 2b = 7

2b = 4

b = 2

We have the value of b. Now, we have to find the value of a by plugging b into the second equation.

a - b = 3

b = 2

a - 2 = 3

a = 5

Now that we have the values of both variables, we can plug them into (3a÷3b)

3a ÷ 3b

3(5) ÷ 3(2)

15 ÷ 6

5/2 or 2.5

So, 3a ÷ 3b equals 5/2 or 2.5

Answer: 10

Step-by-step explanation: 4(2 x 10 + 6) -10

Answer:

[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]  

The p value for this case would be:

[tex]p_v =P(t_{18}>0.890)=0.193[/tex]  

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Step-by-step explanation:

Information given

[tex]\bar X_{1}=4[/tex] represent the mean for sample A

[tex]\bar X_{2}=3.5[/tex] represent the mean for sample B

[tex]s_{1}=1.5[/tex] represent the sample standard deviation for A

[tex]s_{2}=1[/tex] represent the sample standard deviation for B  

[tex]n_{1}=11[/tex] sample size for the group A

[tex]n_{2}=9[/tex] sample size for the group B  

[tex]\alpha=0.1[/tex] Significance level provided

t would represent the statistic

Hypothesis to test

We want to verify if the student who graduates from college A has taken more math classes, on the average, the system of hypothesis would be:  

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

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

The statistic is given by:

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

And the degrees of freedom are given by [tex]df=n_1 +n_2 -2=11+9-2=18[/tex]  

Replacing we got:

[tex]t=\frac{(4-3.5)-0}{\sqrt{\frac{1.5^2}{11}+\frac{1^2}{9}}}}=0.890[/tex]  

The p value for this case would be:

[tex]p_v =P(t_{18}>0.890)=0.193[/tex]  

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Answer:

55.95 ft²

Step-by-step explanation:

Circumference formula:  C = 2πr  =>  r = C / (2π)

Area formula:  A = πr²

Substituting C / (2π) for r in the above equation, we get:

               C                        47 ft

A = π( ----------- )²  =  π ( -------------- )²

              2π                       (2π)

or ...

          π(47 ft)²                   2209 ft²

A = ----------------------  =  --------------------  =  55.95 ft²

               4π²                   4(3.14159)²

Answer:

a) Null hypothesis:[tex]\mu \geq 3[/tex]  

Alternative hypothesis:[tex]\mu < 3[/tex]  

This hypothesis test is a left tailed test.

b) [tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]  

The p value for this case can be calculated with this probability:  

[tex]p_v =P(z<-2.784)=0.0027[/tex]  

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.

And we got the same results.  

Step-by-step explanation:

Information given

[tex]\bar X=2.8[/tex] represent the sample mean

[tex]s=2.6[/tex] represent the population standard deviation  

[tex]n=1310[/tex] sample size  

[tex]\mu_o =3[/tex] represent the value to test

[tex]\alpha=0.5[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic

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

Part a) System of hypothesis

We want to test if the true mean is less than 3, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 3[/tex]  

Alternative hypothesis:[tex]\mu < 3[/tex]  

This hypothesis test is a left tailed test.

Part b

The statistic is given by:

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

Replacing the info given we got:

[tex]t=\frac{2.8-3}{\frac{2.6}{\sqrt{1310}}}=-2.784[/tex]  

The p value for this case can be calculated with this probability:  

[tex]p_v =P(z<-2.784)=0.0027[/tex]  

We can conduct the test with the Ti84 using the following steps:

STAT>TESTS>T-test>Stats

We input the value [tex]\mu_o =3, \bar X= 2.8, s_x = 2.6, n=1310[/tex] and for the alternative we select [tex]< \mu_o[/tex]. Then press Calculate.

And we got the same results.  

Answer:

between 3 and 4

Step-by-step explanation:

type sqrt(10) into your calculator

The requried, square root 10 lies between integers 3 and  4.

Integers are a set of whole numbers and their negative counterparts. They include positive numbers, negative numbers, and zero.

Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on.

The integer squares nearest to 10 are 9 and 16, which are the perfect squares of 3 and 4, respectively.

Since [tex]$\sqrt{9}=3$[/tex] and [tex]$\sqrt{16}=4$[/tex], we know that [tex]$\sqrt{10}$[/tex]  is between these two integers, we can say that [tex]$3 < \sqrt{10} < 4$[/tex].

Learn more about integers here:

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Answer:

7.5 feet

Step-by-step explanation:

Scale of the Model =5 in: 25 ft.

If we divide both sides by 5

[tex]\dfrac{5 in.}{5} : \dfrac{25 ft.}{5}\\\\$1 inch: 5 feet[/tex]

If a window on the model is 1.5 inch wide, from the unit ratio derived above we then have that:

1 Inch X 1.5 : 5 feet X 1.5 feet

1.5 Inch : 7.5 feet

Therefore, if a window in the model is 1.5 in. wide, the actual window is  7.5 feet wide.

Answer:

180 ways

Step-by-step explanation:

U just multiply the number of sauce, noodle, vegetable, and meat

So 3 times 3 times 4 times 5

Correct me if this is wrong

Answer:

180

Step-by-step explanation:

you multiply 3X3X4X5 thus it equals 180

Answer:

[tex]1/16[/tex]

Step-by-step explanation:

[tex]\frac{4^{4} }{4^{6} }[/tex]

[tex]4^{4-6}[/tex]

[tex]4^{-2}[/tex]

[tex]\frac{1}{4^{2} }[/tex]

[tex]\frac{1}{16}[/tex]

Use the law of cosines to find the missing length, which we'll call [tex]d:[/tex]

[tex]d^2=100^2+120^2-2(100)(120)\cos 45^\circ[/tex]

[tex]d^2=24400-12000\sqrt{2}[/tex]

[tex]\boxed{d\approx 86\text{ cm}}.[/tex]

Answer:

D.

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

4x + 2x = 180

6x = 180  

x = 30

Hey there! I'm happy to help!

It appears that we are trying to figure out which triangles are similar, which means that their side lengths have the same ratio. In ΔABC, we see that two sides have a length of 10 and the shorter has a length of 5. This means that the ratio between the long sides and the short sides must be 2:1 to be similar to this triangle.

Let's look at ΔJKL. Our long side has to be double our short side. If we double 2.5, it will be 5, not six, so JKL is not similar with ABC.

Now, let's look at ΔDEF. We see that it's long sides are double the short sides because 6 is double three. This means that the triangles ABC and DEF are similar.

The answer is A) ΔABC ~ ΔDEF.

I hope that this helps! Have a wonderful day!

Answer:no the vertices of the image and pre image don’t correspond

Step-by-step explanation:

Just did it

No, the vertices of the image and pre-image do not correspond

Step-by-step explanation:

It’s correct

Answer:

Step-by-step explanation:

Consider a sample with data values of 10, 20, 12, 17, and 16. (a) Compute the mean and median. Mean = Median = (b) Consider a sample with data values 10, 20, 12, 17, 16, and 12.

Mean = Total of values/ Total number of observations

Total of values = 10+20+12+17+16 = 75

Total number of observations = 5

Mean = 75/5 = 15

Median:

Arrange in ascending order = 10, 12,16,17,20

Median = [n+1] / 2

N = number of observation = 5

Median = [5+1]/2 = 3rd observation

Median = 16

Answer:

[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]

And we can find this probability on this way:

[tex]P(z<-2.040)=0.0207[/tex]

Step-by-step explanation:

Let X the random variable that represent the lenghts of the pregnencies of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(222,15)[/tex]  

Where [tex]\mu=222[/tex] and [tex]\sigma=15[/tex]

We are interested on this probability

[tex]P(\bar X<216)[/tex]

The z score formula is given by:

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score we got:

[tex] z = \frac{216-222}{\frac{15}{\sqrt{26}}}= -2.040[/tex]

And we can find this probability on this way:

[tex]P(z<-2.040)=0.0207[/tex]

3x² + 2x - 4 = 0

Δ = b² - 4.a.c

Δ = 2² - 4 . 3 . -4

Δ = 4 - 4. 3 . -4

Δ = 52

x = (-b +- √Δ)/2a

x' = (-2 + √52)/2.3    

x'' = (-2 - √52)/2.3

x' = 0,8685170918213297    

x'' = -1,5351837584879966

2 Decimal places

x' = 0,87

x'' = -1,54

Answer: .8685

Step-by-step explanation: