write an equation of a line that is parellel to x=8 and that passes through the point -3,-2

Answer:

x = sqrt(15) - 1 or x = -1 - sqrt(15)

Step-by-step explanation:

Solve for x:

x^2 + 2 x + 7 = 21

Subtract 7 from both sides:

x^2 + 2 x = 14

Add 1 to both sides:

x^2 + 2 x + 1 = 15

Write the left hand side as a square:

(x + 1)^2 = 15

Take the square root of both sides:

x + 1 = sqrt(15) or x + 1 = -sqrt(15)

Subtract 1 from both sides:

x = sqrt(15) - 1 or x + 1 = -sqrt(15)

Subtract 1 from both sides:

Answer: x = sqrt(15) - 1 or x = -1 - sqrt(15)

Answer:

65.45 units^3

Step-by-step explanation:

5/2 (5 divided by 2) 2.5, to get the radius,

then using the volume equation you get 65.449846-bla bla, rounding: 65.45

-Hope this helps! ❤️

Answer:

x=4 and y=3

Step-by-step explanation:

put one of the equations in slope form and solve

Answer:x=4 y=3

Step-by-step explanation:

5x-4y=8.............(1)

2x+y=11................(11)

From (11) y=11-2x

Substitute y=11-2x in 5x-4y=8

5x-4y=8

5x-4(11-2x)=8

Open bracket

5x-44+8x=8

Collect like terms

5x+8x=8+44

13x=52

Divide both sides by 13

13x/13=52/13

x=4

Substitute x=4 in 2x+y=11

2(4)+y=11

8+y=11

Collect like terms

y=11-8

y=3

Answer:

The graph of g(x) = |x - h| + k is a translation of h units horizontally and k units vertically of the graph of f(x) = | x |.

Hope this helps.

Answer:

H units horizontally, k units vertically

Step-by-step explanation:

Answer:

1. The circumference of the circular base of the conical hat is 52.36 inches

2. The surface area of the cone that needs to be covered is  262 in.²

Step-by-step explanation:

Here we have that the given parameters are;

Diameter, D of circular = 20 in. = 2 × radius R, of the circle

R = 10 in.

Cut out section of cut out sector of circle = 60°

Therefore, circumference of the circular base = π×D×(360 - 60)/360 which gives;

The circumference of the circular base of the conical hat = π×20×(30)/36 = π·50/3 = 52.36 in.

Therefore, the radius of the formed cone = π·50/3/(2·π) = 25/3 = [tex]8\tfrac{1}{3}[/tex] = 8.33 in.

The formed cone satisfies the equation;

R² = h² + r²

Where:

h = Height of the cone

r = radius of the cone

∴ 10² = h² + 8.33²

∴ h² = 10² - 8.33² = 30.56 in.

The lateral surface area of the cone = π×r×l where l = R, we therefore have;

The lateral surface area of the cone = π×8.33×10 = [tex]\pi \cdot 8\tfrac{1}{3}[/tex] = 261.8 in.² = 262 in.².

The surface area of the cone that needs to be covered = The lateral surface area of the cone = 262 in.².

Answer:

4/5

Step-by-step explanation:

just divide by 10 since that's the largest number that both numbers can equally be divisible by

Answer:

4/5 because 40/50 simplified is 4/5 bc you knock off the zeros for question like that

Step-by-step explanation:

Answer:

the x intercept is 2

Step-by-step explanation:

I just went over this unit

Answer:

2

Step-by-step explanation:

Answer:

7 1\68

Step-by-step explanation:

all i did was look up a fraction calculator

calculator soup is the one i used :)

Answer:

  36,388.0 in³

Step-by-step explanation:

The volume of a sphere is usually expressed in terms of the radius as ...

  V = (4/3)πr³

Here, we want the volume of 1/2 of a sphere, given the diameter. So, our volume will be ...

  V = (1/2)(4/3)π(d/2)³ = (π/12)d³

For the given diameter, the hemisphere volume is ...

  V = (π/12)(51.8 in)³ ≈ 36,388.0 in³

Answer:

[tex]y^{-9}\neq \dfrac{1}{y^{-9}}[/tex]

Step-by-step explanation:

Tyler simplified the expression: [tex]x^{-3}y^{-9}[/tex]  as shown below:

[tex]x^{-3}y^{-9}=\dfrac{1}{x^3}X \dfrac{1}{y^{-9}}=\dfrac{1}{x^3y^{-9}}[/tex]

We notice that in Tyler's work:

[tex]y^{-9}= \dfrac{1}{y^{-9}}[/tex]

Whereas, the correct form would have been:

[tex]y^{-9}= \dfrac{1}{y^{9}}[/tex]

Making our solution:

[tex]x^{-3}y^{-9}=\dfrac{1}{x^3}X \dfrac{1}{y^{9}}=\dfrac{1}{x^3y^{9}}[/tex]

Answer:

The answer is 10/36 or if you want to simplify, 5/18

Step-by-step explanation:

To solve the area of a rectangle, you need to multiply the sides with each other, so 5/12 x 2/3 is 10/36 (unsimplified) . You multiply the numerators and then the denominators and simplify.

Answer: a) See below; b) 2/5([tex]h^{\frac{5}{2} }[/tex]) = - [tex]\frac{1}{200}[/tex].t + 0.215

Step-by-step explanation:

a) To determine the radius (x) of the volume of water remaining, use proportionality of similar triangles:

[tex]\frac{x}{2.5} = \frac{h}{4}[/tex]

x = 0.625h

Volume is

V = 1/3.π.(0.625h)².h

V = 1/3.π.0.391.h³

Using the chain rule to determine the rate of change of height in function of t:

[tex]\frac{dV}{dt} = \frac{dV}{dh} . \frac{dh}{dt}[/tex]

[tex]\frac{dh}{dt} = \frac{dV}{dt}/\frac{dV}{dh}[/tex]

[tex]\frac{dh}{dt} =[/tex] (π/512).[tex]\sqrt{h}[/tex] / 0.391.π.h²

[tex]\frac{dh}{dt} =[/tex] (π . [tex]\sqrt{h}[/tex]) / 512.0.391.π.h²

[tex]\frac{dh}{dt} =[/tex] [tex]\frac{h^{\frac{-3}{2} } }{200}[/tex]

[tex]h^{\frac{3}{2} }\frac{dh}{dt}=\frac{-1}{200}[/tex]

b) To find an equation:

[tex]h^{\frac{3}{2} }[/tex] dh = -(1/200) dt

∫ [tex]h^{\frac{3}{2} }[/tex] dh = -1/200 ∫dt

[tex]\frac{2.h^{\frac{5}{2} } }{5}[/tex] = [tex]\frac{-1.t}{200}[/tex] + c

It is known that it takes 43 minutes to empty the cone, so:

0 =  [tex]\frac{-1.43}{200}[/tex] + c

c = 0.215

The equation is:

[tex]\frac{2.\sqrt[5]{h^{2}} }{5}[/tex] = [tex]\frac{-t}{200}[/tex] + 0.215

c) The equation shows how height and time are inversely proportional to each other: as time goes up, height goes down. Mathematically, though, time cannot be negative. So, the model is suitable for modeling time and height but is not mathematically correct.

Answer:

Step-by-step explanation:

Hello!

A pilot study was conducted to test if three food rewards are equally appealing to the participants.

Of 60 participants surveyed:

16 preferred cupcakes (CC)

26 preferred candy bars (CB)

18 preferred dried apricots (DA)

If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3

1.

The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. [tex]X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex] Where k= number of categories of the variable.

For this example the statistical hypotheses are:

H₀: P(CC)=P(CB)=P(DA)= 1/3

H₁: At least one of the proportions isn't equal to the others.

2.

To calculate the expected frequencies for each category you have to use the formula: [tex]E_i= n* P_i[/tex] where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.

[tex]E_{CC}= n* P(CC)= 60*1/3= 20[/tex]

[tex]E_{CB}= n*P(CB)= 60*1/3= 20[/tex]

[tex]E_{DA}= n* P(DA)= 60* 1/3= 20[/tex]

3.

The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:

Assuming α: 0.05

[tex]X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378[/tex]

The rejection region is then X²₂ ≥ 7.378

4.

[tex]X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8[/tex]

I hope this helps!

Answer:

4

Step-by-step explanation:

The median is the middle number after ordered into numberical order. If there's two and the numbers are different, you add them and divide the total by 2.

Answer: 4

Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.

So let's write our data set from least to greatest.

So we have 1, 1, 2, 3, 4, 4, 4, 6, 6, 10.

Now, notice that there are two numbers that appear in the middle.

I have underlined them above.

When two numbers appear in the middle that are the same number (4 and 4), the median will be the same number too.

So the median of the given data set is 4.

Answer:

#3: x is approximately 0.37, -5.37, #4: x is approximately 4.19, -1.19

Step-by-step explanation:

You can solve using the quadratic equation or by solving with the perfect square

[tex]\frac{-b+/-\sqrt{b^{2}-4ac} }{2a}[/tex] = [tex]x^{2}+5x-2=0\\ \frac{-5+/-\sqrt{5^{2}-4(1)(-2) }}{2(1)}[/tex]

x is approximately 0.37, -5.37

Answer:

y = 3/2x+3

Step-by-step explanation:

The y intercept is 3.  That is where it crosses the y axis

The slope is

m= (y2-y1)/(x2-x1)  and we have points(0,3) and (-2,0)

   = (0-3)/(-2,0)

  =-3/-2

  =3/2

Using the slope intercept form of a line

y = mx +b where m is the slope and b is the y intercept

y = 3/2x+3

Answer: center (-7,-8) radius (2/3)

Step-by-step explanation:

Answer:

The average of the extracted scores that are extreme values (outliers) = 102

Step-by-step explanation:

With the logical assumption that the population size is large enough, for a normal distribution,

68% of the data lies within 1 standard deviation of the mean.

95% of the data lies between 2 standard deviations of the mean.

99.7% of the data lies within 3 standard deviations of the mean.

So, the outliers for a normal distribution are usually beyond 3 standard deviations of the mean.

The mean = 128.5

Standard deviation = 8.2

The range of scores within 3 standard deviations of the mean is obtainable thus

(Mean ± 3standard deviations)

3 × standard deviations = 3 × 8.2 = 24.6

(128.5 ± 24.6) = (103.9, 153.1)

The 3 extracted scores are 148, 102 and 152. The only extreme value of these 3 extracted scores is 102. The two other scores are within the range of 3 standard deviations of the mean.

Hence, the average of the extracted scores that are extreme values (outliers) = 102

Hope this Helps!!!

Answer:C

Took the test

Step-by-step explanation:

The  equations of an asymptote of the hyperbola are y = 3x - 5 and y = -3x - 5.

The standard form of a hyperbola is:

(x-h)²/a² - (y-k)²/b² = 1

The general equation of the asymptotes for a hyperbola centered at (h,k) with semi-axes a and b is given by:

(y - k) = ± (b/a)(x - h)

To find the equations of the asymptotes of the hyperbola with equation:

(x-2)²/2² - (y-1)²/6² = 1

Plugging in the values, we get:

(y - 1) = ± (6/2)(x - 2)

Simplifying:

y - 1 = ± 3(x - 2)

y = ± 3x - 5

Therefore, the equations of the asymptotes for the given hyperbola are y = 3x - 5 and y = -3x - 5.

To know more about hyperbola check:

https://brainly.com/question/15702563

#SPJ7

Answer:

1/8

Step-by-step explanation:

You would need to get the reciprocal of negative eight and then change the sign so you would get 1/8

Answer:

2(x+6)(x+6)

Step-by-step explanation:

splitting the middle term:

2x²+12x+12x+72

then2x(x+6)+12(x+6)

=(2x+12)(x+6)

=2(x+6)(x+6)(by takin common factor out)

plzz mark me brainliest

Answer:

i) The bottles of iced tea filled in a plant is the Population

ii) The Average of Population μ = 20 is called Parameter

iii) The sample size 'n' = 50

iv) The mean of the sample 'x⁻ = 19.6 ounces

Step-by-step explanation:-

Population:-

The total number of observations which we are concerned , whether this number be finite or infinite is called Population.

In Given data

The bottles of iced tea filled in a plant is the Population

Parameter:-

The statistical constants of the Population namely mean and variance are usually refereed to as Parameters.

The Average of Population μ = 20 is called Parameter

Sample:-

A sample is a subset of population

given data sample size n=50 bottles at random from the days of production

Statistics

The sample mean x⁻ and variance S² is called statistics

Given data

These bottles contained an average of 19.6 ounces of iced tea

x⁻ = 19.6 ounces

Answer:

135

Step-by-step explanation:

A P E X

Answer:

Option A

Step-by-step explanation:

Positive correlation describes a relationship between two variables where both variables move in the same direction. In this case, the response variable will increase as the explanatory variable increases.

Answer:

1 = 1000

0.43 L = _________ mL

0.43 * 1000 = 430 mL

430 mL is the answer.

Hope this helps

Answer:1236.4 ft^3

Step-by-step explanation:

height=h=7ft

Diameter=15ft

Radius=r=15/2=7.5ft

Volume of cylinder=π x r^2 x h

Volume of cylinder=3.14 x (7.5)^2 x 7

Volume of cylinder=3.14x7.5x7.5x7

Volume of cylinder=1236.375

Volume of cylinder=1236.4 ft^3

Answer:

112.5

Step-by-step explanation:

To find the area of a parallelogram, you can simply multiply the length of the base by the height. In this case, this is 15*7.5=112.5 square centimeters. Hope this helps!

Answer:

Step-by-step explanation: