If 8 Superscript y Baseline = 16 Superscript y + 2, what is the value of y? –8 –4 –2 –1

Answer:

( 2,1) is the center of dilation and 4 is the scale factor

Step-by-step explanation:

A' = k( x-a) +a, k( y-b)+b  where ( a,b) is the center of dilation and k is the scale factor

3,1 becomes 6,1

6,1 = k( 3-a) +a, k( 1-b)+b

6 = 3k -ka+a

1 = k -kb +b

4,1 becomes 10,1

10,1 = k( 4-a) +a, k( 1-b)+b

10 = 4k -ka+a

1 = k -kb +b

Using these two equations

6 = 3k -ka+a

10 = 4k -ka+a

Subtracting the top from the bottom

10 = 4k -ka+a

-6 = -3k +ka-a

------------------------

4 = k

Now solving for a

6 = 3k -ka+a

6 = 3(4) -4a+a

6 =12 -3a

Subtract 12

6-12 = -3a

-6 = -3a

Divide by -3

-6/-3 = -3a/-3

2 =a

Now finding b

1 = k -kb +b

1 = 4 - 4b+b

1 =4 -3b

Subtract 4

-3 = -3b

Divide by -3

1 = b

Answer:

Dilation factor: 4.  

Center of dilation: (2, 1).  

Step-by-step explanation:

The distance between the old vertices was 4 - 3 = 1. The distance between the new vertices is 10 - 6 = 4. 4 / 1 = 4. That means that the dilation factor is 4.  

Now that we have a dilation factor, we can use the formulas x1 = d(x-a) +a and y1 = d( y-b)+b to solve for the center of dilation.  

In this case, d = 4, x1 = 10, x = 4, y1 = 1, and y = 1.  

10 = 4(4 – a) + a

10 = 16 – 4a + a

10 = 16 – 3a

-3a + 16 = 10

-3a = -6

a = 2

1 = 4(1 – b) + b

1 = 4 – 4b + b

1 = 4 – 3b

-3b + 4 = 1

-3b = -3

b = 1

And so, your center of dilation will be (2, 1).  

Hope this helps!  

Answer:

18

Step-by-step explanation:

The pattern in this sequence is that you add 7 from the previous number to get the next number (-10 + 7 = -3, -3 + 7 = 4, etc). The next item will be 11 + 7 + 18. Hope this helps!

The next item in the sequence is 18.

You should be familiar with the following four main categories of sequences: arithmetic sequences, geometric sequences, quadratic sequences, and special sequences.

The sequence is  -10 ,-3, 4, 11,........

this sequence is following pattern ,you add 7 from the previous number to get the next number

First term =  -10 + 7 = -3,

Second term =-3 + 7 = 4, .

The next item will be 11 + 7 = 18.

Therefore, The next item in the sequence is 18.

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Answer:

(a) H₀: p = 0.11 vs. Hₐ: p > 0.11.

(b) A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

Step-by-step explanation:

A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus.

From past data, it is believed that 11% of all Americans are left-handed.

The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handed people than the general American population.

(a)

The hypothesis can be defined as follows:

H₀: The percentage of left-handed people in the college is 11%, i.e. p = 0.11.

Hₐ: The percentage of left-handed people in the college is more than 11%, i.e. p > 0.11.

(b)

A type I error occurs when we discard a true null hypothesis (H₀) and a type II error is made when we fail to discard a false null hypothesis (H₀).

In this case, a type I error would be committed if it is concluded that the percentage of left-handed people in the college is more than 11% when in fact it is 11%.

And, a type II error would be committed if it is concluded that the percentage of left-handed people in the college is 11% when in fact it is more than 11%.

Answer:

[tex] A.\angle 1\: \\\\D. \angle 3[/tex]

Step-by-step explanation:

[tex] \angle 1\: \&\: \angle 3[/tex] are remote interior angles of [tex] \angle 6[/tex]

Answer:

x = 22

Step-by-step explanation:

Since the the 2 bisectors are equal, that means the chords are also equal. Since bisector splits into 2 equal parts, 11 + 11 equals 22

Answer:  (a) [tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]

               (b) A = $1680.67

               (c) t = 9.99 years

               (d) A = $1689.85

Step-by-step explanation:

[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]   where

a) Given: P = 900, r = 7% = 0.07, n = quarterly = 4

[tex]\bold{A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}}[/tex]

b) Given: P = 900, r = 7% = 0.07, n = quarterly = 4, t = 9

[tex]A=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4(9)}\\\\\\A = 900\bigg(1+\dfrac{0.07}{4}\bigg)^{36}[/tex]

A = 1680.67

c) Given: A = 1800, P = 900, r = 7% = 0.07, n = quarterly = 4

[tex]1800=900\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\2=\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2=ln\bigg(1+\dfrac{0.07}{4}\bigg)^{4t}\\\\\\ln\ 2 = 4t\ ln\bigg(1+\dfrac{0.07}{4}\bigg)\\\\\\\dfrac{ln\ 2}{4\ ln\bigg(1+\dfrac{0.07}{4}\bigg)}=t\\\\\\\bold{t=9.99}[/tex]

d) [tex]A=Pe^{rt}[/tex]

Given: P = 900, r = 7% = 0.07, t = 9

[tex]A=900e^{0.07(9)}\\\\\\A=900e^{.63}\\\\\\\bold{A=1689.85}[/tex]

Measure of an arc = ( intercepted angle/ full circle) x circumference

4 ft =( intercepted angle/360) x (2 x 10 x pi)

4 = intercepted angle /360 x 62.8

Divide both sides by 62.8

4/62.8 = intercepted angle/360

Multiply both sides by 360

Intercepted angle = (4/62.8) x 360

Angle = 22.93 degrees

Answer:

22.9 degrees

Step-by-step explanation:

The degree measure (in radians) can be found using the following formula.

Θ=S/r

where S is the arc length and r is the radius.

We know the arc length is 4 feet and the radius is 10 feet. Substitute the values into the formula.

Θ= 4/10

Θ= 0.4

The measure is 0.4 radians.

Convert radians to degrees using the following formula.

Θ * 180/π

We know that Θ= 0.4 , so we can substitute it in.

0.4 * 180/π

0.4 * 57.2957795

22.9183118

Round to the nearest tenth. The 1 in the hundredth place tells us to leave the 9 in the tenth place.

22.9

The angle measure is about 22.9 degrees.

Answer:

D

Step-by-step explanation:

There isn't enough information to find a y-intercept.

Answer:

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

Step-by-step explanation:

Step(i):-

Given random sample of size 'n' =17

Given mean of the sample 'x⁻' = 56

Given standard deviation of sample 's' = 10

95% confidence intervals about the population mean is determined by

[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]

Degrees of freedom

ν = n-1 = 17-1 =16

t₀.₀₅ = 1.7459  (from t-table)

Step(ii):-

95% confidence intervals about the population mean is determined by

[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]

[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]

( 56 - 4.2344 , 56 + 4.2344)

(51.7656 , 60.2344)

Conclusion:-

95% confidence intervals about the population mean is

(51.7656 , 60.2344)

Answer: 7/8

Step-by-step explanation:

Let the boy is letter B and the girl is letter G.

So the possible outcomes are as follows below

BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG

SO the number of possible outcomes is 8

The number of outcomes where is at least 1 girl ( triples where is 1 girl, 2 girls or all 3 children are the girls) is 7

So the probability, that family with 3 kids has at least 1 girl is

P(number of girls >=1)=  7/8  

Answer:

24 cubic feet.

Step-by-step explanation:

What we need to do here, is to find the volume of the aquarium.

The Aquarium is a rectangular prism.

The volume of a rectangular prism is length*width*height (we just multiply the dimensions together)

2*4*3=8*3=24

The volume of the aquarium is 24 cubic feet, and therefore 24 cubic feet of water is required to fill the tank.

Answer:

Hello! :) The answer will be under “Explanation”

Step-by-step explanation:

The answer will be 24 cubic feet.

Work:

LxWxH

(Length,Width,Hight)

So you the question is asking about volume, we need to do the formula (length,width, and hight)

Now we have to multiply

2x4=8

8x3=24

So the answer will be 24 cubic feet.

Hope this helps! :)

Answer:

945 ways

Step-by-step explanation:

Total

Required Selection

2  Appetizers out of 7 can be selected in [tex]^7C_2[/tex] ways

8 main courses out of 9 can be selected in [tex]^9C_8[/tex] ways

4 desserts out of 5 can be selected in [tex]^5C_4[/tex] ways

Therefore, the number of ways this can be done

[tex]=^7C_2 \times ^9C_8 \times ^5C_4[/tex]

=945 ways

Answer:

53 in.

Step-by-step explanation:

to find the area u do 8 times 6 and 1/2 2(5)

triangle = 1/2bh

rectangle = bh

hope this helps

Answer:

16%

Step-by-step explanation:

Find the z-score.

z = (x − μ) / σ

z = (93 − 85) / 8

z = 1

This means 93 is one standard deviation above the mean.

According to the empirical rule, 68% of a normal distribution is between -1 and +1 standard deviations.  So 32% is either less than -1 or greater than +1 standard deviations.  Normal curves are symmetrical, so 16% is greater than +1 standard deviations.

Step-by-step explanation:

Using the trigonometric identity

sin(a - b) = sin a cos b - cos a sin b

So sin 79° cos 19° - cos 79° sin 19° can be written as

sin ( 79 - 19) = sin 60

And

[tex] \sin(60) = \frac{ \sqrt{3} }{2} [/tex]

Hope this helps you

Answer:

[tex]V(n) = 575000(0.7)^{n}[/tex]

Step-by-step explanation:

The value of the machine after n years is given by an exponential function in the following format:

[tex]V(n) = V(0)(1-r)^{n}[/tex]

In which V(0) is the initial value and r is the yearly rate of depreciation, as a decimal.

A company buys a machine for $575,000 that depreciates at a rate of 30% per year.

This means, respectively, that: [tex]V(0) = 575000, r = 0.3[/tex]. So

[tex]V(n) = V(0)(1-r)^{n}[/tex]

[tex]V(n) = 575000(1-0.3)^{n}[/tex]

[tex]V(n) = 575000(0.7)^{n}[/tex]

Answer:

The answer is

Step-by-step explanation:

Let n represent the number of children

Let c represent the number of candies

The above variation is written as

[tex]c = \frac{k}{n} [/tex]

when n = 12 c = 140

So we have

[tex]140 = \frac{k}{12} [/tex]

Cross multiply

That's

k = 1680

So the formula for the variation is

[tex]c = \frac{1680}{n} [/tex]

when n = 8

[tex]c = \frac{1680}{8} [/tex]

c = 210

Therefore there are 210 candies consumed when there are 8 children

Hope this helps you

Answer:

the square root is 6.48

Answer:

≈6.48

Step-by-step explanation:

[tex]\sqrt{42}=\\6.4807407...[/tex]

If you multiply it by itself, it will equal 42. (Or you can just use a calculator)

DE is secant on the circle below.

A secant line is a straight line that twice intersects a circle.

We have a diagram of circle.

As, Either a secant or a tangent will arise from the circle's junction.

A secant is a line that intersects a circle twice. The relationship between the circle and the line that intersects it is explained by this idea.

Again from the figure CA and CE intersect circle at B and D.

It can also represented that the AB and DE intersects at a point C.

So, the secant line that intersects the circle twice.

Learn more about Secant here:

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Answer:

84%

Step-by-step explanation:

The probability that the selected player is a football player, P(F)=19%

The probability that the selected player is a basketball player, P(B)=79%

The probability that the selected player play both football and basketball,

[tex]P(B \cap F)=14\%[/tex]

We want to determine the probability that a randomly chosen athlete is either a football player or a basketball player, [tex]P(B \cup F)[/tex]

In probability theory

[tex]P(B \cup F)=P(B)+P(F)-P(B \cap F)\\=79\%+19\%-14\%\\=84\%[/tex]

The probability that a randomly chosen athlete is either a football player or a basketball player is 84%.

Answer:

1). SUBTRACTION property of equality

2). MULTIPLICATION property of equality

Step-by-step explanation:

Step 2:

When we subtract the same number from both the sides of an equation it represents the subtraction property of equality.

[tex]\frac{x}{4}+5-(5)=23-(5)[/tex]

Here 5 has been subtracted from both the sides.

Therefore, SUBTRACTION property of equality was applied.

Step 4:

If the same number is multiplied to both the sides of an equation, multiplication property of equality is applied.

[tex]4\times \frac{x}{4}=4\times (18)[/tex]

Here 4 has been multiplied to both the sides.

Therefore, MULTIPLICATION property of equality was applied.

Answer:

A. Ryan conducted a survey where he asked about qualitative data.

Step-by-step explanation:

Surveys when carried out on people as the subjects are meant for the purpose of extracting some specific information from them. Observational studies involve close monitoring of the subject under evaluation. Quantitative data mainly deal with numbers and figures obtained from measurements or calculations. Qualitative data on the other hand is basically descriptive in nature and could sometimes be quite detailed.

Ryan's data collection would require a yes or no answer from the schools involved, and this information is descriptive or qualitative in nature. It also does not involve observation or close monitoring as he relies on the information provided by the school.

Answer: A

Step-by-step explanation:

Have a nice day

Answer:

B

Step-by-step explanation:

Trapezoids have only one pair of parallel lines.        

Answer: 342.32

Step-by-step explanation: sin(25) = h/a

Sin(25)= h/27

27*sin(25) = h

b*h = area

Answer:

y=4x-8

Step-by-step explanation:

First you must use the distributive property and get y-8=4x-16.

Then you have to add 8 on both sides so just y is left on the left side.

This will get you y=4x-8 in slope-intercept form.

Answer:

18 degrees

Step-by-step explanation:

The triangle is an iscoceles right triangle.

The angles in a triangle add up to 180.

90+2y (iscoceles) =180

2y=90

y=45

So the angles of the right triangle are 45. However, you have to take away 27 because you are solving for only a part of 45. 45-27=18

Answer:

D. 569.39 m^3

Step-by-step explanation:

First, we can split up the solid into two shapes: a cone and a cylinder.

Then we can find the volume of the cone

The formula is v= pi r^2 h/3

We know the radius is four and so is the height.

Plug it in and we get 67.02 m^3

Next is the cylinder

Formula is pi r^2 h

We know that the radius is 4 and the height is 10

Plus it in and we get 502.65 m^3

We add 67.02 and 502.65 together to get the total volume.

Answer is D. 569.39 m^3

Mine is a bit higher than D since I used a pi button instead of 3.14

Answer:

Make a point at (3pm, 45), (4.5 pm, 45), (5.5pm, 30), (6.5pm, 15), and (7.5pm, 0). Then connect the dots starting at (0,0) Then you have your graph :)

Step-by-step explanation: