Please help out on question 1

The result of f times g is; -30x² + 28x - 6 while it's domain as required is the set of all real numbers.

As evident in the task content;

f(x) = -5x + 3 while g(x) = 6x - 2.

Hence, the result of f times g is; (-5x + 3) (6x - 2).

open parenthesis

f × g = -5x(6x) - 5x(-2) + 3(6x) + 3(-2)

= -30x² + 10x + 18x - 6

f × g = -30x² + 28x -6.

By observation, the function above is a quadratic function and hence, it's domain is the set of all real numbers.

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The linear correlation coefficient between the length of the right humerus and the length of the right tibia is 0.517.

To compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia, we will use the formula: r = (n∑xy - (∑x)(∑y)) / sqrt([(n∑x^2 - (∑x)^2)(n∑y^2 - (∑y)^2)])

Where r is the correlation coefficient, n is the number of observations, x is the length of the right humerus, and y is the length of the right tibia.

First, we will calculate the sum of x, y, xy, x^2, and y^2:

∑x = 24.8 + 24.59 + 24.59 + 24.29 + 23.81 + 24.87 + 25.90 + 26.11 + 26.63 + 26.31 + 26.84 = 278.74

∑y = 65.05 + 35.57 + 35.57 + 34.58 + 34.20 + 34.73 + 37.38 + 37.96 + 37.46 + 37.75 + 38.50 = 428.75

∑xy = (24.8)(65.05) + (24.59)(35.57) + (24.59)(35.57) + (24.29)(34.58) + (23.81)(34.20) + (24.87)(34.73) + (25.90)(37.38) + (26.11)(37.96) + (26.63)(37.46) + (26.31)(37.75) + (26.84)(38.50) = 10659.01

∑x^2 = (24.8)^2 + (24.59)^2 + (24.59)^2 + (24.29)^2 + (23.81)^2 + (24.87)^2 + (25.90)^2 + (26.11)^2 + (26.63)^2 + (26.31)^2 + (26.84)^2 = 7221.47

∑y^2 = (65.05)^2 + (35.57)^2 + (35.57)^2 + (34.58)^2 + (34.20)^2 + (34.73)^2 + (37.38)^2 + (37.96)^2 + (37.46)^2 + (37.75)^2 + (38.50)^2 = 15738.39

Now we can plug these values into the formula and calculate the correlation coefficient:

r = (11)(10659.01) - (278.74)(428.75) / sqrt([(11)(7221.47) - (278.74)^2][(11)(15738.39) - (428.75)^2])r = 117249.11 - 119475.235 / sqrt([79436.17 - 77691.79][173122.29 - 183744.56])r = -2226.125 / sqrt([1744.38][-10622.27])r = -2226.125 / sqrt(-18525838.35)r = -2226.125 / (-4304.18)r = 0.517

Therefore, the linear correlation coefficient between the length of the right humerus and the length of the right tibia is 0.517.

Note: The question is incomplete. The complete question probably is: Research performed at NASA and led by Emily Horton measured the lengths of the right humerus and right tibia in 11 rats that were sent to space on Spacelab Life Sciences 2.

Right Humerus (mm)      Right Tibia (mm)

24.8                                 65.05

24.59                               35.57

24.59                               35.57

24.29                               34.58

23.81                                34.20

24.87                               34.73

25.90                               37.38

26.11                                 37.96

26.63                               37.46

26.31                                37.75

26.84                              38.50

Compute the linear correlation coefficient between the length of the right humerus and the length of the right tibia.

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The farmer will make 14 baskets containing each of 5 apples and 7 peaches.

In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.

here, we have,

How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?

Given:

A farmer harvests 70 apples and 98 peaches.

They want to make baskets that have both apples and peaches to sell at the market.

Each basket should contain the same combinations of fruit.

They want to sell all the apples and peaches and as many baskets as possible.

Find:

How many baskets can the farm make having x apples and y peaches in the baskets?

Solution:

So, for solving this kind of question first we have to find the greatest common factor, we get;

70 = 2*5*7

98 = 2*7*7

the common factor are 2 and 7

the greatest common factor is 2*7=14

70 apples = 14*5

98 peaches = 14*7

So, the farmer will make 14 baskets each of 5 apples and 7 peaches.

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The remote interior angles of ∠4 are ∠1 and ∠2.

In a triangle, the remote interior angles are the two angles that are not adjacent to the exterior angle. In this case, ∠4 is the exterior angle, so the two angles that are not adjacent to it are ∠1 and ∠2. These are the remote interior angles of ∠4.

Here is a step-by-step explanation:

1. Identify the exterior angle. In this case, it is ∠4.
2. Find the two angles that are not adjacent to the exterior angle. These are ∠1 and ∠2.
3. These two angles are the remote interior angles of ∠4.

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There are 1.057 quarts in a liter, and there are 0.946 liters in a quart.

Therefore, 2 Quarts is 1.8927059 liters, which is equal to almost 2 liters.

Quart:

A quart is an English unit of volume equal to one quarter of a gallon. Currently, there are three types of quarts: Liquid Quart and Dry Quart of the US Conventional System, and Imperial Quart of the UK Imperial System. All of them are approximately equal to 1 liter. It is subdivided into 2 pints or (in the US) 4 cups. Historically, the exact size of a quart has varied over time and with the value of a gallon across different commodities.

Liter:

A liter or liter is a metric unit of volume. A liter is defined as the volume of a cube with sides measuring 10 centimeters. In the US, it is approximately 3.785 liters gallon.

According to the Question:

The conversion factor from quarts to liters is 0.94635295. To find how many liters are in quarts, multiply the conversion factor or use the volume converter above 2 quarts equals 1.8/10 of 93 liters.

To convert 2 quarts to equivalent liter values, multiply the amount in quarts by 0.94635295 (conversion factor). In this case, you should multiply 2 quarts by 0.94635295 to get the equivalent result in liters:

2 quarts x 0.94635295 = 1. 8927059 liters

Therefore,

2 quarts equals 1.8927059 liters.

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Answer:

4

Step-by-step explanation:

We know

f = 52

What is the value of f divided by 13

52 divided by 13 = 4

So, the value of f divided by 13 is 4.

Answer:

Circumference = 12.56 yd

Area = 12.56 yd²

Step-by-step explanation:

Equations we need to know:

Circumference of circle - 2πr

Area of circle - πr²

1) Circumference

2 x 3.14 x 2 = 12.56

2) Area

3.14 x 2² = 12.56

We have to make sure the we are using the radius and not the diameter otherwise our answer would be wrong

Hope this helps, have a lovely day! :)

Answer:

Area=12.56yd^2, Circumfrence=12.56yd

Step-by-step explanation:

the formula for the area of a circle is pi*r^2 and since pi is 3.14 and r is 2 so r^2 is 4 and 4*3.14 is 12.56 (r is the radius)

the formula for the circumference of a circle os 2*pi*r and r is 2 so its 2*3.14*2 multiplying all these terms again gives us 12.56 but be careful with the units as with the area comes yd^2 and with the circumference comes yd only

Based on the information in the graph, the angles of the parallelogram would be 68° and 112°, while the length of its sides would be 15 and 8.

To identify the length and angles of this figure we must carefully look at the lengths shown and the angles shown. Taking into account the shape of the parallelogram, we can infer that the values that correctly complete the dimensions of the figure are:

This is because the parallelogram has two equal sides and equal bases, so if the upper one measures 15, the lower one must measure the same. Additionally, if the side measures 8 the other side must measure 8. In the case of the angles it would be the same.

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The false statement regarding the trigonometric ratios is given as follows:

In △ABE, the sin(A) is the same as the tan(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.

The three trigonometric ratios are defined as follows:

For similar triangles, the ratios are equal, as the side lengths are proportional.

In a 45-45-90 triangle, the sine is equals to the cosine.

However, similar triangles have different values of sine and tangent, hence the first statement is false.

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The substitution v = y^1-n transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x) is shown below.

An equation is in the form  

dy/dx +P(x)y=Q(x)yⁿ,  where P and Q are functions of x alone or constants, is called Bernoulli's equation.

The substitution using [tex]v = y^{1-n}[/tex]

Differentiate both side with respect to 'x'

[tex]v^{'} = (1-n)y^{-n}y^{'}[/tex]

[tex]\frac{dy}{dx} = \frac{1}{1-n} y^{n}v^{'}[/tex]

we get, [tex]\frac{1}{1-n} y^{n}v^{'}[/tex] + P(x)y = Q(x)yⁿ

= [tex]v^{'} + (1-n)P(x)y^{1-n} = (1-n)Q(x)[/tex]

using [tex]v = y^{1-n}[/tex]

The given equation is well expressed as:

[tex]v^{'} + (1-n)P(x)v = (1-n)Q(x)[/tex]

or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)

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The remaining number of windows is given by the equation A = 11 windows

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of windows that needs to be washed = 30 windows

The number of windows that was washed before lunch = ( 2/5 ) of the total

Substituting the values in the equation , we get

The number of windows that was washed before lunch = ( 2/5 ) x 30

The number of windows that was washed before lunch = 2 x 6

The number of windows that was washed before lunch = 12 windows

So , the remaining number of windows = 30 - 12 = 18 windows

And ,

The number of windows that was washed after lunch = 7 windows

So , the remaining number of windows that needs to be washed A = remaining number of windows - number of windows that was washed after lunch

On simplifying the equation , we get

The remaining number of windows that needs to be washed A = 18 - 7

The remaining number of windows that needs to be washed A = 11 windows

Hence , the equation is A = 11 windows

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Answer:

[tex]y = 1[/tex]

Step-by-step explanation:

Rearranging the equation:

[tex]y = -8[/tex]

Three points to be considered:

1. Above is a horizontal line cutting through the y-axis at y value of [tex]-8[/tex].
2. A horizontal line has a slope (or gradient) of 0.
3. Parallel lines have the same slope (or gradient)

∴The straight line passing through (2, 1) will also have a zero slope. In addition, this is a horizontal line, which cuts the y-axis at y value of 1.
The equation of straight line:

y = 1

The probability that a student will enter a building that is not a multiple of 12 is 0.914

We can find the probability by finding the number of buildings that are not a multiple of 12 and dividing it by the total number of buildings (70).

The buildings that are multiples of 12 are:

12, 24, 36, 48, 60, and 70

So there are 6 buildings thar are multiple of 12.

So, the number of buildings that are not a multiple of 12 is

70 - 6 = 64

Therefore, the probability that a student will enter a building that is not a multiple of 12 is

= 64/70

= 0.914

= 91.4 %

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Answer:

your welcome

Step-by-step explanation:

A. she scored 89 %

B. 89 points

Which question are you seeking the answer to?

The length of the diagonal of the print would be = 36.7 in . That is option A (to the nearest tenth).

The print has the shape of a rectangle which is a type of a quadrilateral that has four sides with two sides parallel to each other.

The diagonal length of the print can be calculated by the use of the Pythagorean formula;

That is c² = a² + b²

C = hypothenuse = ?

a = 22 - 4 = 18in

b = 36 - 4 = 32 in

c² = 18² + 32²

c² = 324 + 1024

c² = 1348

C= √1348

C = 36.7 in ( nearest tenth)

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Answer:

[tex]\frac{2}{11}[/tex]

Step-by-step explanation:

[tex]\frac{6}{11} * \frac{1}{3}[/tex]

since 6 and 3 are opposite of each other in this multiplication problem, you can divide them by 3 since they are both divisible by 3

[tex]\frac{2}{11} * \frac{1}{1} = \frac{2}{11}[/tex]

According to the information, the surface area of the pyramids is as follows: 1.377 inches², 2.208 inches², 3.160 inches².

To find the surface area of the pyramids we must perform the following mathematical operations.

A. Find the surface area of the base:

B. We must find the surface area of the faces:

1.

2.

3.

To find the total area of the total surface of the figures we must perform the following procedure:

C. Add the area of the base to the area of the faces:

1.

2.

3.

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Answer: Let's call the total number of coins Karen and Bill have "t".

We can start by writing an expression for the number of coins Bill has:

2x - 9 = 9 + 2x

So the total number of coins Karen and Bill have is:

t = x + (2x - 9)

Simplifying the expression for t:

t = 3x - 9

So the total number of coins Karen and Bill have is equal to 3 times the number of coins Karen has minus 9.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Just divide the amount of the giftcard between the unit cost of the books.

[tex]\frac{gift-card-amount}{cost-of-books}=\frac{27}{3}=9[/tex]

Brad can buy 9 books with his gift card

Answer:

x = 33°

Step-by-step explanation:

         Vertically opposite angles are congruent.

          ∠AOB = ∠DOC

       4x - 6     = 2x + 60

Add 6 to both sides,

               4x  = 2x + 60 + 6

               4x = 2x + 66

Subtract 2x from both sides,

          4x - 2x = 66

                 2x = 66

Divide both sides by 2

                    x = 66 ÷ 2

                    [tex]\boxed{x = 33}[/tex]

∠AOB = 4x - 6

          = 4*33 -6

          = 132 -  6

∠AOB = 126°

∠DOC = 126°

Answer: 37164

Step-by-step explanation:

14% of 32,600 is 4564

-To find the new value of the car, you must add the 14% of the original value and the original value together

-4,564 + 32,600 = 37164

The area of the rectangular lawn Rachel mows is 100 square yards

The formula for calculating the area of a rectangle is expressed with the formula;

Area = lw

Where;

Now, substitute the values as given,

length = 12 yards

Width = 8 1/3 = 25/3 yards

Then,

Area = 12 × 25/3

Divide the factors

Area = 4(25)

Multiply the values

Area = 100 square yards

Hence, the value is 100 square yards

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Thus, a line graph would be more appropriate for this particular data set to observe the changes in the miles driven over a certain number of days.

Data refers to any collection of facts, figures, or information that can be processed, analyzed, and interpreted to gain insights and knowledge. It can be in various forms such as text, images, audio, video, or numerical values, and can be collected from various sources such as surveys, sensors, social media, or transactions.

Given by the question: -

The most appropriate graph to construct for the given data is a line graph because it would show how the miles driven change over time between each individual data point. A line graph is useful for showing trends or changes over time, and it allows us to see the progression of the miles driven during the trip. This graph would have days on the x-axis and miles driven on the y-axis, with a line connecting the data points. This would help to visualize any patterns or trends in how the miles driven change over time during the trip.

On the other hand, a scatter plot would show the relationship between the two variables, but it would not show the changes over time. While scatter plots are useful for showing relationships between variables, they do not show the order or progression of the data points over time.

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The distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).

The length along a line or line segment between two points on the line or line segment.

The distance formula is Distance=√(x₂-x₁)²+(y₂-y₁)²

Equation in terms of x for the distance between (x, y) and A(-1, 5) and  y = 3x. be any point on the line

Distance=√(x+1)²+(3x-5)²

b. We need to find coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1, 5).

√(x₁+1)²+(3x₁-5)² =√74

√(x₂+1)²+(3x₂-5)² =√74

Simplifying each equation and solving for x, we get:

x₁ = -4/3 or x₁ = -2

x₂ = 2/3 or  x₂  = -4

Simplifying each equation and solving for x, we get:

x₁ = -4/3 or x₁ = -2

x₂ = 2/3 or x₂ = -4

Substituting each value of x into y = 3x, we get the coordinates of B and C:

B: (-4/3, -4)

C: (2/3, 2)

The slope of y = 3x is 3,

Slope of any line perpendicular to it is -1/3.

Using the point-slope form of a line, we get the equation of the line passing through (-1, 5) with slope -1/3:

y-5=-1/3(x+1)

The point of intersection between y = 3x and the line y = (-1/3)x + (14/3), we can set the two equations equal to each other and solve for x:

3x = (-1/3)x + (14/3)

x = 14/10 = 7/5

y = 3(7/5) = 21/5

So the point of intersection is (7/5, 21/5).

To find the area of triangle ABC, we can use the distance formula between the points B and C:

d = √2/3 - (-4/3))² + (2 - (-4))²)

d=2√10

The base of the triangle is the distance between the x-coordinates of B and C, which is 2.

The area of the triangle is:1/2×b×h

=2√10

Hence, the distance is√(x+1)²+(3x-5)², coordinates are B: (-4/3, -4) and C: (2/3, 2), y = (-1/3)x + (14/3) is equation of the line that is perpendicular to y = 3x, point of intersection is (7/5, 21/5).

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A. 327 and C.751 have a remainder of 1 when divided by 2

Even Numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. They are  numbers that are a multiple of 2. Examples are: 2, 4, 6, 8, 10, and so on are even numbers.

How to determine this,

By dividing each words by 2

327 divided by 2 = 163 remainder 1

So, this is not an even number when divided by 2

400 divided by 2 = 200 remainder 0

This is an even number

751 divided by 2 = 375 remainder 1

This is not an even number

148 divided by 2 = 74 remainder 0

This is an even number

1356 divided by 2 = 678 remainder 0

So, this is an even number

Therefore, only 327 and 751 have a remainder of 1 when  divisible by 2.

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Answer:

Step-by-step explanation:

So here is what I did. If the picture is square then you would multiply Length times the Width to get 49 square inches. But if it’s not a square then you would still multiply Length by Width.

The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A

Addition of Fraction

Wood 1:

Length of each = 2 5/8 feet

Number of pieces = 6

Total = Length of each × Number of pieces

= 2 5/8 × 6

= 21/8 × 6

= 126 / 8

= 15 3/4 meters

Wood 2:

Length of each = 1 1/5 feet

Number of pieces = 3

Total = Length of each × Number of pieces

= 1 1/5 × 3

= 6/5 × 3

= 18/5

= 3 3/5 meters

Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters

= 126/8 + 18/5

= (630+144) / 40

= 774/40

= 19 14/40

= 19 7/20 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A

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The amount of simple interest  is (c) $90

From the question, we have the following parameters that can be used in our computation:

Principal = $600

Rate = 3%

TIme = 5 years

The simple interest is calclated as

Simple interest = PRT

Substitute the known values in the above equation, so, we have the following representation

Simple interest = 600 * 3% * 5

Evaluate

Simple interest = 90

Hence, the amount is $90

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