Please answer with if the slope is positive or negative and what the slope is.

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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Range and Domain. The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

What Separates a Function's Domain from its Range?

A function's domain and range are its constituent parts. In contrast to a function's range, which is the set of all potential outputs, a function's domain is the set of all possible inputs.

All real numbers fall under the expression's domain, with the exception of cases where it is undefined. No real number exists in this situation, rendering the statement undefinable.

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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

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; 4/35
2; -16g

sorry if wrong

Answer:

add -8 to -3 so thats 5 and your answer is 5=z

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: 16 miles

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

The answer would be -45.

Step-by-step explanation:

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

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:

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

Please mark me brainliest. please

Population of Arkansas is currently 3 million people. If it grew by just 5%, what would the new population be?

Answer : 3,150,000 people

Step-by-step explanation:

3,000,000 + 5% = 3,150,000

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 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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If a skier travels 4700 feet up a ski lift whose angle of inclination is 30°​, how high above his starting level is the​ skier is 2350 feet.

Given data:

Distance = 4700 feet

Angle of inclination = 30°​

Now let determine the height by  formulating an equation which will help us to find the height

4700 × sin 30°

Where:

Sin 30° = 0.5 or 1/2

Hence,

Height :

Height = 4700 feet × 0.5

Height = 2350 feet

So,

Height = 2350 feet above the starting level

Therefore we can conclude that the skier is 2350 feet above the starting level.

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Answer: 33

Step-by-step explanation:

(f+​g)(−6​)=

f(-6)+g(-6)=

-6-3 + (-6)^2-(-6)=

-(6+3) + 36+6=

-9+42=

42-9=33

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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In order to calculate the function (f/g)(x), we need to divide f(x) by g(x).

First, let's find the zeros of the function f(x), so we can write it in the factored form:

So the factored form is:

Now, calculating the composite function, we have:

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.  

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

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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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:

Given that,

Rectangular room is of the dimension 12 feet by 18 feet

To find the number of square feet of carpet needed.

Explanation:

Area of the rectangle is,

Area of the rectangular room is,

Area of the rectangular room is 270 square feet.

Therefore, 270 square feet of carpet are needed to cover the room.

we know that,

Using this conversion we get,

Answer:

1710

Step-by-step explanation:

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

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]

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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A merchant bought several pieces of silk for $70. He sold all but two of them at a profit of $4 per piece. His total profit was $18. How many pieces did he originally purchase?​

Let n be the number of pieces. He sold n - 2 pieces

Let p be the original price. His selling price = p + 4

Then n · p = 70.00

And (n - 2) · (p + 4) = 70.00+18.00 ---> np + 4n - 2p - 8 = 88.00

---> np + 4n - 2p = 96.00

---> 70.00 + 4n - 2p = 96.00

4n - 2p = 26.00

2n - p = 13.00

Trying some possibilities (7 & 1), (8 & 3), (9 & 5), and (10 & 7), finally gets us to the answer: n = 10 and p = 7.00.

therefore