Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is
2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What
expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?

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.

Answer:

7

Step-by-step explanation:

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.

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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

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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

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    

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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.

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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.

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.

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

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Answer:

the one that looks like a paper clip

Step-by-step explanation:

Answer:

I don't know if its right.

Ans:1.215

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.

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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.

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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

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

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.

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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.

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

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The P∩V is {2,4,6,8}.

From the question, we have

P= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

V= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

P∩V = {2,4,6,8}

Intersection of Sets:

The set that contains all the elements that are shared by two given sets is the intersection of the two sets. The intersection of sets is represented by the symbol "∩". The intersection A∩ B (also written as A intersection B) lists all the elements that are shared by any two sets A and B that are present in both sets.

For instance, if Set A = 1, 2, 3, 4, and Set B = 3, 4, 6, then A ∩B = {3,4}.

Complete question:

Suppose P = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and V = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. what is P ∩ V ?

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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).

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[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]

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.

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Answer:

Step-by-step explanation:

First Selling price is $360, after mark down.

The second's selling price is $403, after both mark downs

Joanne should buy the first, because of the selling price after mark downs.

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).

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Weak positive term describes the correlation  .

What does a weak positive indicate?

A weak positive graph is what?

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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)

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

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