1. The total number of pancakes that can be made for a pancake breakfast fundraiser is directly related to the
amount of batter that is available. If 28 cups of batter make 112 pancakes, then which of the following is
closest to the number of pancakes that can be made with 45.4 cups of batter?

The simplified form of the given expression is x + a - 4

From the question, we are to simplify the given expression

From the given information, we have that

g(x) = x² - 4x,

Now,

We are to simplify

[tex]\frac{g(x)-g(a)}{x -a}[/tex]

First, we will determine g(a)

From the given function,

g(x) = x² - 4x

∴ g(a) = a² - 4a

Thus,

[tex]\frac{g(x)-g(a)}{x -a}[/tex] becomes

[tex]\frac{x^{2} -4x-(a^{2}-4a)}{x -a}[/tex]

[tex]\frac{x^{2} -4x-a^{2}+4a}{x -a}[/tex]

[tex]\frac{x^{2} -a^{2} -4x+4a }{x -a}[/tex]

Factoring

[tex]\frac{(x+a)(x-a)-4(x-a) }{x -a}[/tex]

Further factorization

[tex]\frac{(x-a)((x+a)-4) }{x -a}[/tex]

Dividing

((x +a) -4)

x + a - 4

Hence,

The simplification gives x + a - 4

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The equation of the line parallel to y = 4x - 2 and passes through (1, 8) is

y = 4x + 4

The equation of a line can be represented as follows:

y = mx + b

where

Therefore, the equation of a line is parallel to y = 4x - 2 and passes through (1, 8)

Parallel lines have the same slope.

Therefore,

y = 4x + b

let's find y-intercept using (1, 8)

8 = 4(1) + b

b = 8 - 4

b = 4

Therefore,

the equation of the line is y = 4x + 4

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Answer:

18 eggs are still good.

Step-by-step explanation:

If 40% was broken then 60% are still good.

30(.6) = 18

Answer: 18 eggs were not broken and considered good.

Step-by-step explanation:  30 x 40% is the amount of eggs that were broken.

30 x 60% would be the amount of eggs that were still good.

This is becuase the total percentage must add up to be 100% between good eggs and broken eggs.

30 x .60 = 18   So 18 eggs were good

30 x .40 = 12, so that was the number of eggs that were broken

You could have done this problem two ways.  Either calculate the broken eggs and subtract from the total.  30-12 = 18, or you could have just calculated the correct amount from figuring the percentage of eggs that were good from the beginning.  

Answer: 16 miles

Step-by-step explanation:.

The value of matrix 2M is  [tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]

A matrix is a collection of numbers that have been put in rows and columns to make a rectangular array. The entries of the matrix are the numbers, which are referred to as its elements. In addition to many areas of mathematics, matrices are widely used in the fields of engineering, physics, economics, and statistics. The representation of rotations and other picture changes has been accomplished using matrices, which have significant uses in computer graphics.

Multiplication of matrices, often known as matrix multiplication, is one of the operations that can be carried out on matrices in linear algebra. If the two matrices given, A and B, are compatible, then matrix A and matrix B can be multiplied. The binary operation of multiplying matrices produces a matrix from two input matrices.

M = [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]

2M = 2 [tex]\left[\begin{array}{ccc}3&5\\-4&0\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}6&10\\-8&0\\\end{array}\right][/tex]

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The graph of the function gives the type of function, (continuous or discrete function) the domain and the range as follows;

(A, 2A)

First graph;

Discrete function

Domain; {x| x = -8, -2, 3, 6}

Range; {y| y = 5, 4, -2, 7, }

Second graph

Continuous function

Domain; -4 < x < ∞

Range; 1 ≤ y < 9

(A3.A) 1. The slope of the graph is -1.5

2. The slope of the graph is 1.5

A function is an equation defining the relationship between input and output variables

(A, 2A)

A continuous function is one in which a continuous variation in the input values produces a continuous variation in the output. Therefore, a continuous function does not have discontinuity and it has a defined output within the interval in which it is contagious

A discrete function is one that have input values and output only at specified points, such that the function does not have inputs, and therefore, outputs at certain points.

The points in the scatter plot of the first graph are separate and not linked, such that the function is not contagious between any two x–values, which gives;

The function is a discrete function

The domain, which is the set of possible x–values is; {x| x = -8, -2, 3, 6}

The range is {y|y = 5, 4, -2, 7, }

The line joining the points on the second graph, indicates that the graph has values for all input or x–values

Therefore, the function of the graph is a continuous function

(A3. A) 1. Points on the graph are:

(0, 2), (2, -1)

The slope is given by the equation;

Slope = ∆y ÷ ∆x

Which gives;

2. The given function is; -3•x + 2•y = -6

To find the slope, the function is expressed in the slope and intercept form, y = m•x + c, as follows;

-3•x + 2•y = -6

2•y = 3•x - 6

Therefore;

2•y = 3•x - 6

y = (3•x - 6) = 1.5•x - 3

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1) A prime factorization of a particular number will always give the same prime factors.

2) All the factors in the list when multiplied will give the original number.

3) No, two different numbers cannot have the same prime factorization.

4) The prime factors of 40 are 2 and 5.

1) We anticipate finding factors in prime factorization that can add to themselves to get the original number. The original number can be obtained by multiplying the remaining components together as long as the first factor can divide the quantity without leaving a remnant.

Prime factorization of the number, 15 goes thus;

15/3=5

5/5=1

3*5=15

So, all the factors multiply to give the original number.

2) Numbers that split an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal halves.

3) The collection of prime numbers that can be multiplied together to produce a given number is known as the prime factorization of that number. Because the same set of numbers must provide the same result when multiplied together, two separate numbers cannot have the same prime factorization.

4) Any number can be represented as a sum of prime numbers using prime factorization. A number with exactly two elements, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 3 3. Here, the two main elements or prime factors of 18 are 2 and 3.

The prime factorization of 40 is :

40 = 2 × 2 × 2 × 5

Hence, the prime factors of 40 are 4 and 5.

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answer:

the third one

To solve the equation;

To solve for t, we shall take the following steps;

ANSWER:

The correct answer is option (b)

we can write an equation

where T is the total price, 55 the fixed charge, 0.5 the cost per minute and m the minutes used

if the total is 66 we must to replace T=66 and solve m

so

were charged 22 minutes on the bill

Answer:

1710

Step-by-step explanation:

simplify | 1×10^3 + 7×10^2 + 4×10 = 1710

Using the scale factor we calculate the length of the bridge to be 5.6 meters.

Scaling is a linear transformation that raises or decreases the size of objects by a constant scale factor in all directions.

The length of the bridge on the map is 80 cm .

Now the scale of the map is 1 : 7

Therefore the length of the bridge is 80 × 7 = 560 cm = 5.6 meters.

Hence the length of the bridge is 5.6 meters.

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Answer:

Yes

Step-by-step explanation:

Answer: Charts -> Stacked Totals -> Stacked Bar Totals

Step-by-step explanation:

after filling in in Macabacus the only add in feature that puts totals is stacked bar

Answer:4

Step-by-step explanation:

450 m² of metal are needed to cover the sides of the pyramid.

The correct answer is an option (A)

In this question, a monument is made in the form of a right pyramid with a regular hexagon as a base. each base side is 5 meters and the slant height is 30 meters.

If only the sides (and not the base) of the monument is to be covered by metal, we need to find the amount of metal needed to cover the sides of the pyramid.

Since the base of the pyramid is hexagon, there are 6 triangular sides of the pyramid.

We need to find the area of 6 triangular surfaces.

The base of the triangle b = 5 meters and the height of the triangle is the slant height of the pyramid.

h = 30 meters

So, area of the one triangular surface would be,

A1 = 1/2 × b × h

A1 = 1/2 × 5 × 30

A1 = 5 × 15

A1 = 75 square meters

And the area of the 6 triangular surfaces would be,

A = 6 × A1

A = 6 × 75

A = 450 square meters

Therefore, 450 m² of metal are needed to cover the sides of the pyramid.

The correct answer is an option (A)

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Answer:

[tex]y=-2x+6[/tex]

So, the slope is -2.

Step-by-step explanation:

Solve the literal equation for y and use the slope value formed.

[tex]10x+5y=30\\5y=-10x+30\\\frac{5y}{5}=\frac{-10}{5}x+\frac{30}{5}\\y=-2x+6[/tex]

So, according to [tex]y=mx+b[/tex], the slope is -2 where m is the slope.

Answer:

i swear your going to give a head ack i told you the answer

Step-by-step explanation:

Answer: 1 2/3 or 5/3

Step-by-step explanation: if you change 4 1/3 to a different denominator of 9, you will get 4 3/9. Then, you will do 4 3/9-2 7/9 which equals 1 2/3.

Answer:

$3,312.00

Step-by-step explanation:

If we add up her sales we get 207,000

We multiply that by .016 to get $3,312.00

step 1

Find out the scale factor

Remember that

If two figures are similar, then the ratio of their volumes is equal to the scale factor elevated to the cubic

so

Let

s ----> scale factor

s^3=11,000/8,019

s=1.11

step 2

Remember that

If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared

so

s^2=SA/1,134

s=1.11

1.11^2=SA/1,134

SA=(1.11)^2*(1,134)

SA=1,400 yd2

Answer:

Using a class size of 6.

Range = Highest value - Lowest value = 100 - 1 = 99

No. Of class = range/class size = 99/6 = 16.5 ~ 17/classes.

Upper-class limit of class (1) = Lower class limit of class (1) + class size - D

=> 1 + 6 - 1 = 7 - 1 = 6

.: UCL1 = 6

The table is shown below:

The length of the target is 4cm and the width of the target is 6cm.

A rectangle is an object that has four sides and four right angles. The sum of angles in a rectangle is 360 degrees.  The perimeter of a rectangle is the distance round the rectangle.

Perimeter = 2( length + width)

20 = 2(w - 2 + w)

20 = 2(2w - 2)

20 / 2 = 2w - 2

10 = 2w - 2

10 + 2 = 2w

12 = 2w

w = 12/2

w = 6

Length = 6 - 2 = 4

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The value is =[tex]\frac{-73}{22}[/tex]

The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category.

Given That : [tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex] and f(x)= -4

[tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex]

F(x)= -4

=[tex]\frac{-64-9}{18+4}[/tex]

=[tex]\frac{-73}{22}[/tex]

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To find the area of a rectangle, we can use the following formula

Therefore, to find the total area we have to multiply his length by his width.

Using the data given in the question, we know that the length is 21 yards and the width is 5 yards. Therefore we find that:

we conclude that the area of the rectangle is 105 yards^2.

Note that the units of the area are square units

The graph of the function H(x) = "x+5" and the graph of the function t(x) = "2x+5" are displayed in the picture that is attached below.

This is further explained below.

Generally, The set of ordered pairings that satisfy the condition [tex]"\displaystyle f(x)=y"[/tex] is the graph of the function f.

These pairings, which are Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane, are found under the usual scenario in which both x and f(x) are real values.

In conclusion, The Graph of the function H(x) =|x+5| and t(x)=|2x+5| is given in the image attached below.

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The P-value for a test to support the claim that less than 50% of the people is 0.2743.

The p-value is a figure that, when generated from a statistical test, indicates how likely it is that, if the null hypothesis were true, you would have discovered a certain collection of observations.

This will be illustrated thus:

Sample proportion = 47 / 100 = 0.47

Test statistics = {p} - p) / ✓ [ p( 1 - p) / n )

= ( 0.47 - 0.50) / ✓ 0.50 * 0.50 / 100)

= -0.6

p-value = P(Z < z)

= P(Z < -0.6)

This will be looked at on the distribution table. The value will be 0.2743.

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The probability that sunflower will be less than 136 cm tall is 0.9332.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

From the information, the biologist measures a large sample of sunflowers and creates a probability distribution and the distribution is normal in shape with a mean 112 cm and a standard deviation 16 cm.

It should be noted that the following can be deduced:

Mean = 112

Standard deviation = 16

Sunflower should be less than 136. This will be x < 136.

Therefore, the probability will be;

P(X < 136)

= P(Z < [(number - mean) / standard deviation)]

= P(Z < [136 - 112)/16]

= P(Z < 1.50)

= 0.9332

It should be noted that the probability is gotten by looking at the value of x in the z table.

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Answer:

Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.

Find gradient of the line first.

Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.

Gradient = (-3-0) ÷ (-2-5) = 3/7

Eqn is y = 3/7x + c

Substitute either one of the coordinates into the equation to find c.

0 = 3/7(5) + c

c = -15/7

Hence, the equation of the line is y = 3/7x - 15/7

Check the picture below.

so the base of that triangle is AB whilst the height of it is CD, so let's get them

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~2 - (-4)~~)^2 + (~~-8 - (-6)~~)^2} \implies AB=\sqrt{(2 +4)^2 + (-8 +6)^2} \\\\\\ AB=\sqrt{( 6 )^2 + ( -2 )^2} \implies AB=\sqrt{ 36 + 4 } \implies AB=\sqrt{ 40 }\implies \stackrel{base}{AB=2\sqrt{10}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CD=\sqrt{(~~-7 - (-6)~~)^2 + (~~-5 - (-2)~~)^2} \\\\\\ CD=\sqrt{(-7 +6)^2 + (-5 +2)^2} \\\\\\ CD=\sqrt{( -1 )^2 + ( -3 )^2} \implies CD=\sqrt{ 1 + 9 } \implies \stackrel{height}{CD=\sqrt{ 10 }} \\\\[-0.35em] ~\dotfill[/tex]

[tex]A=\cfrac{1}{2}(\stackrel{b}{2\sqrt{10}})(\stackrel{h}{\sqrt{10}})\implies A=\sqrt{10}\cdot \sqrt{10}\implies A=\sqrt{10^2}\implies {\Large \begin{array}{llll} A=10 \end{array}}[/tex]

Answer

The answer would be -45.

Step-by-step explanation:

I linked how I got this answer in the image. I hope this helps :)

The solution of the equation for the values of r is -2 and 2.

For the expression

2+ I5rI = 12

Subtract both side by 2

2 + I5rI -2 = 12 - 2

I5rI = 10

Open the modulus function as;

Solve for each term

-5r = 10

Divide both side by -5,

r = 2

Now,

5r = 10

Divide both side by 5,

r = 2

Therefore, the solution of the equation is for r = -2 and 2.

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