Find the distance from point A(-1. 7) to the line y = 3x. Round your answer to the nearest tenth.​

By using the concept of rate of change, it is obtained that

Water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute

What is rate of change?

Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.

Here the concept of rate of change has been used

Let the radius of cone at any point be r m and height be h m

Volume of cone = [tex]\frac{1}{3}\pi\times r^2\times h[/tex]

Now,

By the concept of similarity,

[tex]\frac{r}{h} = \frac{4}{16}\\\\\frac{r}{h} = \frac{1}{4}\\\\r = \frac{1}{4}h[/tex]

Volume of cone (V) =

[tex]\frac{1}{3}\times \pi \times (\frac{1}{4} h)^2\timesh\\\\\frac{1}{48}\times \pi \times h^3\\[/tex]

[tex]\frac{dV}{dt} = \frac{1}{48} \times \pi \times 3h^2\times \frac{dh}{dt}\\\\\frac{dV}{dt} = \frac{1}{16} \times \pi \times h^2\times \frac{dh}{dt}\\\\[/tex]

Now,

[tex]\frac{dV}{dt} = -2,\ h = 12[/tex]

So,

[tex]-2 = \frac{1}{16}\times \pi \times (12)^2 \times \frac{dh}{dt}\\\\\frac{dh}{dt} = -\frac{2 \times 16}{\pi \times 12 \times 12}\\\\\frac{dh}{dt} =- \frac{2}{9\pi}[/tex]

So water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute

To learn more about rate of change, refer to the link-

brainly.com/question/24313700

#SPJ4

The 95% confidence interval for the average apple weight is (119.14, 125.86).

An apple typically weighs 120 grams with a 12-gram standard deviation, according to one manufacturer. The average weight of an apple was 122. 5 grams, according to statistics created from a sample of 49 apples that were randomly chosen from a shipment.

Let, n = 49

x = 122.5 

σ = 12

To calculate and interpret a 95% confidence interval for the average apple weight, use the formula;

⇒ (x ± 1.96*σ/√n)

⇒ (122.5 ± 1.96*12/√49)

⇒ (119.14, 125.86)

Consequently, the average apple weight has a 95% confidence interval of (119.14, 125.86).

To learn more about Confidence interval click here:

brainly.com/question/24131141

#SPJ4

The domain of the composite function is  - x - 3 ≥ 0 , x ≤ -3 .

The correct answer is (B).

Given,

In the question:

Over the set of real numbers.

F(x) = -x-3, G(v) = √y

G(F(x)) = √√-3-x

To find the domain of the composite function.

Now, According to the question:

Based on the given conditions:

The domain of F(x) = -x -3 is all real numbers.

The domain of

G(v) = √y is y ≥ 0

{The relationship of the domain of a composite function and the original functions}

So, - x - 3 ≥ 0 , x ≤ -3

Hence,  The domain of the composite function is  - x - 3 ≥ 0 , x ≤ -3 .

The correct answer is (B).

Learn more about Function at:

https://brainly.com/question/13461298

#SPJ1

There are 32 outfits that Evelyn can make.

This is basic combination.

Evelyn has 2 shirts each shirt can be worn with each of the 2 pair of pants.

So, there are 4 ways to wear them.

she  also has 8 pairs of shoes and each pair can be worn with each of the 4 outfits.

total number of outfits that she can make = 8*4

                                                                      =32 outfits

Evelyn can make 32 different outfits.

To learn more about combinations visit;

https://brainly.com/question/28065038

#SPJ4

A Paired t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.

T-test is a statistical statistics mainly use when population variance is unknown and sample size is small.

In Paired t-test , we compare means of two dependent samples . It gives hypothesis examination on difference between of mean.

It uses same items or people in both sample that's why they are also known as dependent t-test

Paired t-test also increases the statistical power of our analysis.

Formula of paired t-test :

[tex]t = \frac{m}{s/\sqrt{n} }[/tex]  with (n-1) degree

where , m is mean difference

s is standard deviation

n is sample size

To know more about Paired t-test here

https://brainly.com/question/28020847

#SPJ4

Answer:

7

Step-by-step explanation:

Answer:

x+6, y+2

Step-by-step explanation:

x goes left and right, y goes up and down. the little ' means that is the line after translation, so w and y are the originals, and w' and y' are after the translation. Add 6 to x(left and right) (negative sign means left and positive sign or no sign means right), so go 6 to the right, and add 2 to y, so go up two (negative sign means to go down, and positive or no sign means to go up)

Answer: $617.50

Step-by-step explanation:

9.5% of 6500 = 9.5*6500/100=9.5*65=617.5

So the interest is $617.5 or $617.50

Hope this helped. If you have any questions or clarifications please ask.

Thanks and please rate!

Answer:

Gretta will earn $617.50 interest

A = $7,117.50

Equation:

A = P(1 + rt)

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 9.5%/100 = 0.095 per year.

Solving our equation:

A = 6500(1 + (0.095 × 1)) = 7117.5

A = $7,117.50

The total amount accrued, principal plus interest, from simple interest on a principal of $6,500.00 at a rate of 9.5% per year for 1 years is $7,117.50.

As per the given ratio, the length of the actual counter is 120 feet.

Ratio:

Basically, the ratio refers an ordered pair of numbers a and b, written a / b where b does not equal 0. And a proportion is an equation in which two ratios are set equal to each other.

Given,

Gwen measured a kitchen and made a scale drawing. The scale she used was 11 inches : 5 feet.

Here we need to find the length of the actual counter if  a countertop in the kitchen is 22 inches long in the drawing.

While looking into the given question, we have identified the following things,

Scale drawing ratio = 11 inches : 5 feet

And the length of the drawing = 22 inches.

When we convert the inches into feet,

Then we get,

=> 11 inches = 11/12 feet.

So the actual length can be calculated as,

=>22 : 11/12 : 5

=> 22 x 12/11 x 5

=> 2 x 12 x 5

=> 120

Therefore, the length of the actual counter is 120 feet.

To know more about Ratio here.

https://brainly.com/question/13419413

#SPJ1

Using Rank theorem , the dimensions of col A and Null A add up to the number of colmns in A. It is true statement.

The rank of matrix A denoted as rank(A) is the dimension of the column space Col(A).

The nullity of matrix A written as nullity(A) is the dimension of the null space Nul(A)

Rank Theorem:

If A is a matrix with n columns, then

Rank (A) + nullity (A) = n

In other words we can say that

dim (Col(A) ) in column space + dim (Nul(A)) in empty space = total number of columns in A

The rank theorem is really important theorem.

It is gives a strong relationship between the Null space ( all possible vector x such that Ax = 0) and the column space (the set of vectors b matching Ax=b) explain the two main objectives. The more freedom we have for choosing x, the less freedom we have for choosing b, and vice versa.

To learn more about Rank theorem, refer:

https://brainly.com/question/12914662

#SPJA

In comparison to her classmates, Kay did better in quiz 2.

According to the question,

Kay scored 15 on Quiz 1 which had a mean of 12 and a standard deviation of 2.4

= Z-score = 15 - 12/ 2.4 = 1.25

She scored 14 on Quiz 2 which had a mean of 11 and a standard deviation of 2

= Z-score = 14 - 11/ 2 = 1.5

As we can see the Z-score of Quiz 2 is more than the Z-score of Quiz 1 hence Kay did better in Quiz 2.

To learn more about statistics, mean, median, and mode,

https://brainly.com/question/29342780

#SPJ4

Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.

Reason: E.g. P(a<x>b) = 0.95

confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.

A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.

Know more about Confidence intervals here: https://brainly.com/question/24131141

#SPJ4

The expression to represent the area of the rectangle is A = 6w⁷

The rectangle is a four-sided polygon with an internal angle of 90° at the corner of every side. The opposite sides of the rectangle are equal.

The formula for the area of the rectangle is given below

Area = Length × width

Here we have

Width of the rectangle = 3w² and

Length of the rectangle = 2w⁵

As we know the area of the rectangle = Length × width

Area of the rectangle, A = 3w² × 2w⁵

=> A = 6w²×w⁵

=> A = 6w²⁺⁵

=> A = 6w⁷

Therefore,

The expression to represent the area of the rectangle is A = 6 w⁷    

Learn more about the Rectangle at

https://brainly.com/question/2182040

#SPJ1

Answer:

Speed at which Carley was cycling at

= 72 miles ÷ 3 hours

= 24 miles/hour

Speed at which Catie was driving at

= 132 miles ÷ 2 hours

= 66 miles/hour

66 miles/hour - 24 miles/hour = 42 miles/hour

∴ The faster person, Catie, was travelling 42 miles/hour faster than Carley, the slower person.

Weak positive term describes the correlation  .

What does a weak positive indicate?

A weak positive graph is what?

Learn more about weak positive

brainly.com/question/17104826

#SPJ1

Answer:

I don't know if its right.

Ans:1.215

Answer:

The measure of angle 1=52

The measure of angle 2=58

The measure of angle 3=31

Step-by-step explanation:

The measure of angle 1 is 52 because the angle out of the triangle is 128. The measure of angle 1 plus 128 equals 180. Using this info you could do 180-128, which equals 52. The measure of angle 1 equals 52.

The measure of angle 2 is 58 because I already know 2 of the values of the triangle, in which Angle 2 is also in. One triangle adds up to 180. The values of the other 2 angles are 52 and 70. Using this information I can use the equation 52+70+x=180, which you then simplify to 122+x=180. X equals 58. The measure of angle 2 equals 58

The measure of angle 3 is 31 because the angle out of the triangle is 70. The missing angle plus 70 equals 180. Using this info I could do 180-70. The missing angle is 110. There is already one given angle, and I have figured out the other, using this info I can now finally find the measure of angle 3. I can find this out by using the equation 110+39+x=180. You would then simplify the equation to 149+x=180. X equals 31. The measure of angle 3 equals 31.

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{7}}} \implies \cfrac{ -4 }{ -4 } \implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{ 1}(x-\stackrel{x_1}{7}) \\\\\\ y-18=x-7\implies {\Large \begin{array}{llll} y=x+11 \end{array}}[/tex]

Answer:

a] 5 dogs

b] 16 dogs

Step-by-step explanation:

        The minimum number of dogs that could have a mass of more than 26 kg is 5. This is because dogs with a mass of 30 ≤ x ≤ 40 have a frequency of 5. The dogs in the 20 ≤ x ≤ 30 range could be more than 26 kg, but they could also be less than 26 kg, so these are not included in the minimum.

        The maximum number of dogs that could have a mass of 26 kg is 16 because both dogs in the 30 ≤ x ≤ 40 range (5) and 20 ≤ x ≤ 30 range (11) could weigh more than 26 kg. 11 + 5 = 16, giving us our answer for the maximum.

Answer:

Y= -7

X= 4.4

Step-by-step explanation:

Y= 2 - ( x-3)^2

When x= 0

Y= 2- ( 0-3)^2

Y will equals -7

When y = 0

(x-3)= √2

X = 4.4

Answer:

Step-by-step explanation:To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.

Answer:

the one that looks like a paper clip

Step-by-step explanation:

Answer:

Refer to photo for drawing

Step-by-step explanation:

1. Draw the x y plane

2. Identify -8, -1, 0 on x plane

3. Identify -4, -3, -2 on y plane

4. Mark the intersection point (-8,-4) with x

5. Mark the intersection point (-1,-3) with x

6. Mark the intersection point (0,-2) with x

7. Draw a straight line through the x mark

The values of the segments formed by the median lines in the triangles are;

1. KG = 22

2. [tex]\overline{JE}[/tex] = 19.5

3. FL = 11

9) CI = 4

10) XK = 4

14) x = 3

A median line of a triangle is a line drawn from a vertex of the triangle to the the middle of the of the opposite side, thereby bisecting the opposite side into two segments of the same length.

The median lines are; [tex]\overline{JE}[/tex], [tex]\overline{KF}[/tex], and [tex]\overline{LD}[/tex]

1. The length of [tex]\overline{GF}[/tex] = 11

The properties of a median line indicates;

[tex]\overline{GF}[/tex] = (1/3)·[tex]\overline{KF}[/tex]

Therefore;

11 = (1/3)·[tex]\overline{KF}[/tex]

[tex]\overline{KF}[/tex] = 3 × 11 = 33

[tex]\overline{KG}[/tex] = (2/3)×[tex]\overline{KF}[/tex]

Therefore;

[tex]\overline{KG}[/tex] = (2/3) × 33 = 22

[tex]\overline{KG}[/tex] = 22

2. [tex]\overline{JG}[/tex] = 13

[tex]\overline{JG}[/tex] = (2/3) × The median line [tex]\overline{JE}[/tex]

Therefore;

[tex]\overline{JG}[/tex] = (2/3) × [tex]\overline{JE}[/tex]

[tex]\overline{JE}[/tex] = (3/2) × [tex]\overline{JG}[/tex]

[tex]\overline{JE}[/tex] = (3/2) × 13 = 19.5

3. JL = 22

[tex]\overline{KF}[/tex] is a median line, therefore, the point F is the midpoint JL

JF = FL

JL = JF + FL by segment addition postulate

JL = FL + FL = 2·FL (substitution property of equality)

JL = 22 = 2·FL

FL = 22 ÷ 2 = 11

9) CS = 6

Where CS is a median line of the triangle ΔABC, then;

CI = (2/3) × CS

CI = (2/3) × 6 = 4

10) UX = 8

Where UX is a median of the triangle ΔTUX, we get;

XK = (1/3) × UK

UX = (2/3) × UK

UK = (3/2) × UX = (3/2) × 8 = 12

XK = (1/3) × 12 = 4XK = 4

14) KL = 7·x + 1

LE = 2·x + 5

The properties of median line indicates that, KL = (2/3)·KE

LE = (1/3)·KE

Therefore;

KL = 2 × LE

7·x + 1 = 2 × (2·x + 5) = 4·x + 10

7·x + 1 = 4·x + 10

7·x - 4·x = 10 - 1 = 9

3·x = 9

x = 9 ÷ 3 = 3

x = 3

Learn more about the median line of a triangle here:

https://brainly.com/question/2971205

#SPJ1

The exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

sin u=3/5, 0 < u < pi/2

tan u= 1/2, pi < u < 3pi/2

We need to find sin 2u, cos 2u, and tan 2u

sin2u=2sinucosu

tanu=sinu/cosu

1/2=3/5/cosu

cosu=3/5×2

cosu=6/5

So sin2u=2(3/5)(6/5)

sin2u=36/25

cos2u=1-2sin²u

=1-2(36/25)²

=1-2(1296/625)

=1-4.14

=-3.142

cos2u=-3.142

tan2u=sin2u/cos2u

Substitute the values of sin2u and cos2u

sin2u=36/25/(-3.142)

=1.44/-3.142

=-0.458

Hence, the exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

Answer:

Step-by-step explanation:

If the line is perpendicular to y = -2x + 5 then the new line has a slope of 1/2.

So solve for b: using y = mx + b

2 = 1/2(-4) + b

2 = -2 + b

4 = b

Put it all together

y = 1/2x + 4

Fatima paid $129.95 for pallet of grass cost and $ 76.20 for delivery. The total amount Fatima paid is $725.95.

Pallet Grass Cost: The quality and type of grass you want will impact the overall cost of sod. Most homeowners pay between $150 and $450 per pallet of sod for their yards or an average of $300. When it comes to square footage, sod costs between $0.35 and $0.85, or an average of $0.60 per square foot.

Given in the question:

Number of Pallets = 5

Cost of each pallet = $129.95

Total amount spend on Pallets

= Number of Pallets × Cost of each pallet

= 5 × $129.95  = $ 649.75

Also given;

Amount spend on Delivery = $76.20

Total Amount Paid by Fatima

= Total amount spend on Pallets + Amount spend on Delivery

=  $649.75 + $76.20

= $ 725.95

Hence Fatima paid a total amount of $725.95.

Learn more about Total amount:

https://brainly.com/question/11807738

#SPJ4