What will happen to the object if the scale factor is greater than 1?

Answer:

To divide polynomials, we need to use polynomial long division. First, we divide the first term of the dividend by the first term of the divisor to get the first term of the quotient, which we write above the division bar. In this case, the first term of the dividend is 2x² and the first term of the divisor is x, so the first term of the quotient is 2x. We then multiply the divisor by the quotient and subtract it from the dividend to get the remainder.

Here's how the long division would look:

2x² + 15x + 20
===
x + 5

2x

_______

 15x - 10x

 15x + 20 - 10x - 20

 ___________

    5x - 20

After we perform the polynomial long division, we get the quotient 2x + 5 and the remainder -20. Therefore, the final result of the division is:

(2x² + 15x + 20) ÷ (x + 5) = 2x + 5 + (-20)/(x + 5)

Note that the remainder -20 is written as a fraction with the divisor x + 5 in the denominator. This is the correct way to write the remainder because it tells us that the remainder has a degree that is one less than the degree of the divisor. In this case, the degree of the divisor is 1, so the degree of the remainder is 0.

By using the slope intercept form of equation of line, it can be calculated that-

a) Equation of the graph

[tex]y = -\frac{5}{3}x +10[/tex]

b) Slope = [tex]-\frac{5}{3}[/tex]

It represents the ounces of ice cream reducing per minute when Katie has been eating the ice cream

c) y - intercept is 10.

It means Katie started eating with 10 ounces of ice cream

d) When y = 0, x = 6

It means Katie finished eating the ice cream in 6 minutes.

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex]  is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan\theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.

a) From the figure, it is clear that the graph passes through (6, 0) and (0, 10)

Slope = [tex]-\frac{10}{6}[/tex]

Slope = [tex]-\frac{5}{3}[/tex]

Equation of the graph

[tex]y - 0 = -\frac{5}{3}(x - 6)\\\\y = -\frac{5}{3}(x - 6)\\\\y = -\frac{5}{3}x +10[/tex]

b) Slope = [tex]-\frac{5}{3}[/tex]

It represents the ounces of ice cream reducing per minute when Katie has been eating the ice cream

c) y - intercept is 10.

It means Katie started eating with 10 ounces of ice cream

d) When y = 0, x = 6

It means Katie finished eating the ice cream in 6 minutes.

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Standard error of the mean is 1.375 and margin of error of the mean is 2.694.

Based on the provided information, mean µ = 67.8 and standard deviation σ = 11.5. The sample size n = 70

The standard error (SE) of a statistic refers to the standard deviation of its sampling distribution or an estimate of that standard deviation.

Standard error (SE) is given by:

SE = σ/√n = 11.5/√70 = 1.375

The margin of error (MOE) refers to a statistic demonstrating the amount of random sampling error in the results of a survey.

Margin of error (MOE) is the standard error multiplied by a Z value that correspondence to a confidence percentage. Assuming a 95% confidence the Z value is 1.96. Hence,

MOE = z * σ/√n = 1.96 x 1.374 = 2.694

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Triangle a is reflected in the x-axis to give b which is reflected in the line y=x. The coordinates of triangle C are  (-5,4) , (-2,2) and (-2,4)

Coordinates for Triangle A are (4,5), (2,2), and (4,2)

Triangle B is created by reflecting triangle A along the x-axis.

The x-axis coordinates stay the same after reflection in the x-axis, while the y-axis coordinates go negative with the same magnitude.

Consequently, triangle B's coordinates are (4, -5), (2, -2), and (4,-2)

The x and y coordinates of triangle B are now reversed as it is reflected by the line y = x to create triangle C.

Triangle C's coordinates are (-5,4), (-2,2), and (-2,4)

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Answer:

When the number 20 is increased by 20%, the result is 24. To find this, first multiply 20 by 20%, which is 0.20. Then, add this result to the original number 20 to find the final result, which is 20 + 0.20 = 24.

Step-by-step explanation:

The linear function in slope intercept form is y = -3x + 6

A linear function is a function represented by a straight line.

Slope intercept form of a linear function is y = mx + c where

To write the linear function in slope intercept form, we need to know its slope, which is given by

m = (y₂ - y₁)/x₂ - x₁) where

Substituting the values of the variables into the equation, we have

m = (y₂ - y₁)/x₂ - x₁)

m = (-6 - 0)/4 - 2)

m = -6/2

m = -3

Next we find the equation of the linear function in slope-point form which is

m = (y - y₁)/x - x₁) where

Substituting the the values of the variables into the equation, we have

m = (y - y₁)/x - x₁)

-3 = (y - 0)/x - 2)

-3 = y/(x - 2)

-3(x - 2) = y

-3x + 6 = y

y = -3x + 6 which is the slope-intercept form

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Any p-value less than 0.05 is a cause to reject the null hypothesis.

What is Null Hypothesis?

The statement "The null hypothesis is a claim about population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.

Explanation:
In this case, 0.015 is the only option for p-value that would lead to a rejection of the null hypothesis (if the level of significance for the test is 0.05).

Any p-value less than 0.05 is a cause to reject the null hypothesis.

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Answer:

y=10x+10

Step-by-step explanation:

Remember, y=mx+b, where m is the slope and b is the y-intercept.

In this case, the slope, or m, is 10 and the y-intercept, or b, is 10. We then substitute m=10 and b=10 in and get the equation y=10x+10.

Answer:

the hat is $47.50.

Step-by-step explanation:

To determine the regular price of the hat, you can use the formula for calculating the sale price of an item, which is:

regular price * (1 - discount percentage) = sale price

In this case, we can set up the equation as follows:

regular price * (1 - 0.20) = $38

Solving for the regular price, we get:

regular price = $38 / (1 - 0.20)

regular price = $38 / 0.80

regular price = $47.50

Therefore, the regular price of the hat is $47.50.

The standard deviation for the binomial distribution is 3.39

The standard deviation for the binomial distribution is given by,

σ = [tex]\sqrt{n * P(1-P}[/tex]

where n = Number of trials

P = probability of success of an individual trail

If n = 48 and P = 0.6

σ = [tex]\sqrt{48 *0.6(1-0.6})[/tex]

= [tex]\sqrt{48*0.24}[/tex]

=[tex]\sqrt{11.52}[/tex]

=3.39

Therefore, the standard deviation for the binomial distribution will be 3.36.

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Answer:B

Step-by-step explanation:hope this will solve your problem

Answer:B

Step-by-step explanation:

y=10x+235 is the equation of the least squares regression line.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We need to find the equation of the least squares regression line.

The value of the slope of the regression line can be find by using any two points from the table.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

(58, 335) and (70, 450)

Slope of line = 450-335/70-58

=115/12

=10

The equation of line is y=10x+b

335=10(10)+b

335=100+b

335-100=b

235=b

Hence, the equation of the least squares regression line is y=10x+235.

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When you dilate the figure by a scale factor less than 1 but greater than 0, then the size of the figure decreases

The dilation is the one form of the transformation of the figure, the change the size of the figure

The scale factor is the ratio between the original size of the figure and the new size of the figure.

When the dilate the figure by a scale factor greater than one then the size of the figure increases, but when  the scale factor is between 0 and 1 then the size of the figure decreases

Therefore, the size of the figure decreases after dilation

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Answer:

34

Step-by-step explanation:

First you arrange the data in an ascending order and the median is the middle value. if the number of values is an even number, then the median will be the average of the two middle numbers. In this case, the median is 34.

The solution is

a) The area of the sign is 3950 cm²

b) The total number of cans of paint is 3 cans of paint

What is the Area of a Rectangle?

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the total area of the sign be = S

Now , the area of the triangle be = T

Let the area of the rectangle be = R

The height of the triangle = 50 cm

The base of the triangle = 50 cm

So , the area of the triangle = ( 1 / 2 ) Height x Base

Area of Triangle T = ( 1/2 ) x 50 x 50

Area of Triangle T = 1250 cm²

Length of the rectangle = 90 cm

Width of the rectangle = 30 cm

Now , the area of rectangle R = Length x Width

Area of the rectangle R = 90 x 30

Area of the rectangle R = 2700 cm²

And , the area of the sign = Area of the rectangle R + Area of Triangle T

Substituting the values in the equation , we get

Area of the sign = 2700 cm² + 1250 cm²

Area of the sign = 3950 cm²

b)

Each can of paint covers = 1m²

So , Each can of paint covers = 10000 cm²

The number of signs = 6 signs

So , the total area of 6 signs = 6 x Area of the sign

The total area of 6 signs = 6 x 3950

The total area of 6 signs = 23700 cm²

And , the number of cans of paint for 6 signs = The total area of 6 signs / Area covered by each can

Substituting the values in the equation , we get

The number of cans of paint for 6 signs = 23700 / 10000

The number of cans of paint for 6 signs = 2.37 cans

The number of cans of paint for 6 signs ≈ 3 cans

Hence ,

a) The area of the sign is 3950 cm²

b) The total number of cans of paint is 3 cans of paint

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The value of cos(A - B) in simplest form is 651/203.

An acute angle is an angle that is less than 90 degrees, or less than a right angle. Acute angles are typically found in everyday life, such as the shape of a slice of pizza or the corner of a triangle. Acute angles are also found in shapes such as pentagons, hexagons, and octagons. Acute angles are important for engineering, architecture, and construction, as angles that are too wide or too small can affect the structural integrity of a building or other structure. Acute angles are also important in geometry, as they can be used to solve for the area, perimeter, and interior angles of a given shape.

We can use the formula for cos(A - B):
cos(A - B) = cos A cos B + sin A sin B
cos(A - B) = (21/29) * (24/7) + (21/29) * (7/24)
cos(A - B) = (504 + 147)/29 * 7
cos(A - B) = (651/203)
Therefore, the value of cos(A - B) in simplest form is 651/203.

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The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week

A relationship between two expressions or values that is not equal to one another is referred to as "inequality" in mathematics.

According to the given information

Let x be the more items that Julie will sell after First week

Number of items soled in First week = 6

So

The inequality formed will be

x + 6 > 20

Solving the inequality is

x > 20 - 6

x > 14

So

The inequality formed is x + 6 > 20 and Julie will sell more than 14 items after the first Week

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Answer:

Step-by-step explanation: Here is your answer 97



Answer:

Slope: 2.5, Y-Intercept: 10

Step-by-step explanation:

We can set up an equation, with

y = 2.5x + 10

The slope is 2.5, and the y-intercept is 10.

A; The distance between the starting point to Obstacle 2 is  13 meters

B; There are 10 meters around one lap of course.

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]  

Part A;

Starting point: (-12, 5); Obstacle 2: (0, 0)

(x₁, y₁) and (x₂, y₂)

Therefore,

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(0 - (-12))² + (0 - 5)²

d = √(12)² + (- 5)²

d = √144 + 25

d = √169

d = 13 meters

B. Starting point: (-12, 5); Obstacle 2: (0, 0);

Obstacle 1: (-12, 0)

(Starting Point + Obstacle 2)

Now,

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(0 - (-12))² + (0 - 5)²

d = √(12)² + (- 5)²

d = √144 + 25

d = √169

d = 13 meters

Therefore, (Starting Point + Obstacle 1)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-12 - (-12))² + (0 - 5)²

d = √(0)² + (-5)²

d = √25

d = 5 meters

(Obstacle 2 + Obstacle 1)

d = √(x₂ - x₁)² + (y₂ - y₁)²

d = √(-12 - 0)² + (0 - 0)²

d = √(-12)² + (0)²

d = √144

d = 12 meters

Total = 12m + 5m + 13m = 30

30 ÷ 3 = 10 meters

we can conclude that 10 meters around one lap of course.

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The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space.(a) A basis for the row space of A is {{1,2,3}, {2,3,4}}. The row rank of A is 2.(b) A basis for the column space of A is {{1,2}, {2,3}, {3,4}}.

(c) A basis for the null space of A is {{-1,1,0}, {1,-2,1}, {0,1,-1}}. The nullity of A is 3.

(d) A basis for the null space of At is {{1,-1,0}, {-1,1,1}, {0,-1,-1}}. The nullity of At is 3.The four fundamental subspaces of a matrix are the row space, column space, null space, and left null space. The row space is the set of all linear combinations of the rows of the matrix, and its dimension is the row rank. The column space is the set of all linear combinations of the columns of the matrix, and its dimension is the column rank. The null space is the set of all vectors that are solutions to the system of equations Ax = 0, and its dimension is the nullity. The left null space is the set of all vectors that are solutions to the system of equations A^T x = 0, and its dimension is the nullity.

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I’m not entirely sure but i believe it’s 1.05

Answer:

slope = -5/8

Step-by-step explanation:

Use the rise and the run from point C to point D to find the slope of the line.

C is at (7 , -2)

D is at (15 , -7)

slope = change in y / change in x

slope = (-2 - (-7)) / (7 - 15)

slope = (-2 + 7) / -8

slope = 5/-8

slope = -5/8

fff is a random variable in a game of luck

A random variable is a formula that gives each result in a sample space a numerical value.

There are two types of random variables: discrete and continuous. If a random variable only takes specified values inside an interval, it is said to be discrete. It is continuous if not.

We typically use capital letters, such X and Y, to designate the random variables

A random variable must be measured in order to be able to assign probabilities to a set of potential values. It is evident that the outcomes depend on a number of unpredictable physical elements.

According to the question,

In a game of luck, a turn consists of a player rolling 777 six-sided dice and counting how many of the dice show a 555. Let fff be the number of dice showing a 555 in a turn.

Here, fff is a Random variable.

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Answer:

22.9

Step-by-step explanation:

22.9

3x+7=20

 -7    -7

3x=13

/3  /3

x= 4.3

3(4.3)+10

12.9+10

22.9

(i think you put something in wrong. the answer usually shouldnt have a decimal)

Answer:

it is the linear graph

hope it helps

Let X be a random variable representing the time until the first sale of a book. Then X has a Poisson distribution with rate a*p per hour.

Let X be a random variable representing the time until the first sale of a book. This random variable is the sum of the times that customers take to arrive and purchase a book. Since customers arrive at a bookstore according to a Poisson process with rate a per hour, the time until the first customer arrives has an exponential distribution with rate a per hour. Moreover, each customer buys a book with probability p, independently of everything else. Thus, the time until the first sale of a book is the sum of the time until the first customer arrives and the time until the first successful purchase. This sum of two independent exponential random variables is a Poisson random variable with rate a*p per hour. Therefore, the distribution of the time until the first sale of a book is a Poisson distribution with rate a*p per hour.

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The length of the boundary of any closed figure is called its perimeter.

Perimeter is calculated only of 2-dimensional shape, or a 1-dimensional length. This means that shapes like cubes, cones, and cylinders don't have a perimeter.

The perimeter of any shape is calculated by adding up the length of all its sides. A side is referred to as any continuous uninterrupted length of the shape between two points.

A point to be noted is that the perimeter of a circle is calculated by its radius and a mathematical number called pi. This is denoted by π. All other curved sides are calculated in a similar manner as well.

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