What is the slope of the line that passes through the points (0, -10)(0,−10) and (-4, -11)(−4,−11)? Write your answer in simplest form.

Both the pairs of the points are linear.

Here i made the plot for the points and both the pairs of the points shows that the it follows a straight path which means it will be linear i nature.

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The probability of the next flip result in a trail is 0.5.

Given that,

If you flip a coin 100 times and receive 80 heads and 20 tails.

We have to find what is the probability that the upcoming flip will result in a tail based on these findings.

Probability refers to potential. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty.

One is the probability of every event in a sample space.

Next flip result is independent of the past results.

P(Next flip result is tail) = 1/2 = 0.5

Therefore, The probability of the next flip result in a trail is 0.5.

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The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k

The given function is f(x)=7x^2.

The given vertex = (3,5)

The equation of the parabola with the vertex of (h,k) is

y=a(x-h)^2+k

On comparing we get; a=7, h=3, k=5

Now putting the value

f(x)=7(x-3)^2+5

Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

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An artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.

What is a rectangle?

A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.

Here, we have

FH ≅ GH

FH = EG = 22in

If diagonals bisect each other then, an artist connects stained glass pieces with lead strips

1/2(EG) = JG

1/2 (22) = JG

11 = JG

Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.  

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The correct number of Standard deviation to generate a confidence interval is therefore 1.65.

Given that;

This shows that the percentage in a normal distribution that is at most 1.65 standard deviation above average is about 95%.

Percentage above 1.65 SD equals 100 - 95 = 5.

Now, because of the symmetric distribution,

Percentage above 1.65 SD = % below 1.65 SD is what we can see:

Below 1.65 SD + between 1.65 SD below and 1.65 above + above 1.65 SD + % above 1.65 SD = 100%

=> 5% + between -1.65 SD below and 1.65 above + 5% = 100%

=> % between -1.65 SD and 1.65 SD above mean = (100 - 5 - 5)% = 90%

The correct number of SDs to generate a confidence interval is therefore 1.65.

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The required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

t = time in months

H = total height

H= initial height+ rate of growth * time

H = 15 + 3t

So, the required equation for height H of the plant t months after Angel bought the plant is,

H = 15 + 3t

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Answer:

(- 8, 0 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

(0, - 8 ) → (- 8, 0 )

Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4

The first equation is

3t = 12

t = 12/3

t = 4

The solution is {4}

The second equation is

3m + 7 = 14

3m = 14 - 7

3m = 7

m = 7/3

The solution is not {4}

The third equation is

4(4c + 1) = 68

4c + 1 = 68/4

4c + 1 = 17

4c = 17-1

4c = 16

c = 16/4

c = 4

The solution is {4}

The fourth equation is

9 = 5p - 11

5p = 9 + 11

5p = 20

p = 20/5

p = 4

The solution is {4}

Hence, Based on the solution set S:{4}, the false equation is 3m + 7 = 14, because the solution of the equation is not 4

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The blanks are -2 and 0.5 respectively, by solving the expression (8 - 2x) *(-0.25x)

What does the term Algebraic Expression means?

In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.

Solution:

Given the expression, we need to solve it by using the properties of basic multiplication.

= (8 - 2x)*(-0.25x)

= (8*(-0.25x)) + (-2x * (-0.25x))

= -2x + 0.5[tex]x^{2}[/tex]

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The value of p that is statistically significant at a 5% level of significance refers to a p-value of 0.05 or less.

The fixed probability of incorrectly eliminating the null hypothesis when it is actually true is what is meant by the term "level of significance." The probability of type I error is defined as the degree of significance, which is decided by the researcher using the results of the error. The statistical significance is measured by the level of significance. It specifies whether or not the null hypothesis is thought to be true. The null hypothesis is anticipated to be shown as untrue or rejected if the result is statistically significant.

The symbol indicates the degree of significance (alpha). Therefore, the following definition applies to the level of significance:

Level of Significance = p (type I error) =

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a) product of function f(x) and g(x) is 2x² - 6x - 8 and b) product of function that is in part a and an (x) is 2x³ - 4x² - 14x - 8.

Here are the three functions given:

f(x) = x -4

g(x) = 2x + 2

c(x) = x + 1

a) The product of function f(x) and g(x)

f(x). g(x) = (x -4). ( 2x + 2)

= x( 2x + 2) - 4(2x + 2)

= 2x² + 2x - 8x - 8

= 2x² - 6x -8

b) product of function f(x). g(x) and a(x)

f(x). g(x) . a(x) =( 2x² - 6x - 8 ). ( x + 1)

= x( 2x² - 6x - 8) + 1(2x² -6x - 8)

= 2x³ - 6x² -8x + 2x² - 6x -8

= 2x³ -4x² - 14x - 8

Therefore we get a) 2x² - 6x - 8 and b) 2x³ - 4x² - 14x -8.

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The value for the number of red lights that Alice encounters are found.

X = no of red lights crossed by Alice.

X is Binomial distributed

In which  n=4, p=0.5, q = 0.5

Mean value is found by the formula,

Mean = np

Mean = 4×0.5

Mean = 2

And, variance = npq

Var = np(1-p)

Var = 4×0.5×0.5

Var = 1

PMF = ⁿCˣ0.5ˣ × 0.5 ⁽⁴⁻ˣ⁾

Thus, the value for  pmf, the mean, and the variance of the number of red lights that Alice encounters are found.

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If one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.

According to the question,

We have the following information:

A right triangle contains a 25° angle and length of one leg is 5 inches.

Now, the leg for which length is given can be opposite to given angle or adjacent to given angle. So, there are two possible for the length of hypotenuse (H).

Now, when it is opposite to the given angle:

Sin 25 = 5/H

H = Sin 25*5

H = 0.4226*5

H = 2.113 inches

Now, when it is adjacent to the given angle:

Cos 25 = 5/H

H = Cos 25*5

H = 0.9063*5

H = 4.5315 inches

Hence, if one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.

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Answer:

x-4<12 x<-4

-3x<12

-3x/-3=x

12/-3=-4

x-4+4=x

8+4=12

Answer: 0.0099

Step-by-step explanation:

The equation of the absolute value function graph is: y = |x - 3| + 5.

The equation of the absolute value function can be written in the vertex form as y = a|x – h| + k, where:

From the given graph, we have the following:

(h, k) = (3, 5) [the vertex]

Substitute the values into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (2, 6). To find the value of a, substitute (x, y) = (2, 6) into y = a|x - 3| + 5:

6 = a|2 - 3| + 5

6 = a|-1| + 5

6 = a + 5

6 - 5 = a

1 = a

a = 1

To write the equation of the graph, substitute a = 1 into y = a|x - 3| + 5:

y = 1|x - 3| + 5

y = |x - 3| + 5

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The length of the road in the simplest radial form is 10[tex]\sqrt{29}[/tex].

Here a rectangle of dimensions is 20m by 50m. So the length of 50m and the breadth is 20m

As the road is diagonal of the rectangle.

So we have to find the length of the diagonal of the rectangle.

Formula to find the diagonal of rectangle:

Diagonal = [tex]\sqrt{l^{2} + b^{2} }[/tex]

length (l) = 50m

Breadth(b) = 20m

Diagonal = [tex]\sqrt{50^{2} + 20^{2} }[/tex]

               = [tex]\sqrt{2500 + 400}[/tex]

               = √2900

              = 10√29

Therefore the length of the road is 10√29.

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Using the concepts of statistics, we got that 2004 is the sample size needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence.

The number of observations used to calculate estimates for the certain population is known as the sample size. The sample size was actually determined by drawing from the population. Sampling is a practice of choosing a portion of a population from which to draw conclusions about the characteristics of a entire population. A subset of the population is chosen for analysis based on the number of entities in it.

We have  Margin of error(E)=0.02,

Significance level([tex]\alpha[/tex])=0.01

Proportion(p)=0.13

Therefore, q is defined by =1-p

                =>  q =1-0.13

                =>q=0.87

So, the Z-score is 2.582

Now, we know that sample size(S) is given by

                =>S =[ [ [Z²×p×(1-p)] / e²] / [1+(Z²×p×(1-p)/e²)] ]

               =>S=[ [ ( 2.582)²×0.13×0.87/(0.02)²] / [1 + [(2.582)²×0.13×0.87] / (0.02)²]

               =>S= ([0.754/0.0004] / [1+(0.754/0.0004)])×1000

               =>S=([885.01] / [1+1885.01]) × 1000

                =>S=(0.200351)×1000

                =>S=2003.51=2004 (approx)

Hence, a federal report indicated that 13% of children under age 6 live in poverty in Massachusetts, an increase over previous years in that case size of  sample which is needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence is 2004.

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The transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.

So, the transformation from:

First, plot both graphs.

(Refer to the graph attached below)

Therefore, the transformation that occurs from the graph (y = x²) to the graph of [y = (x − 5)² + 7] is (D) a vertical shift up 7 units and a horizontal shift right 5.

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Answer:

[19+7] / [2 x 6 + 1]

Step-by-step explanation:

[19+7] / [2 x 6 + 1]

[26] / [13]

[2]

The angle that is same side exterior angle to ∠ABC is ∠EFH.

When parallel line are cut by a transversal line, angle relationships are formed such as corresponding angles, vertically opposite angles, alternate angles, same interior angles, etc.

AD and EG are parallel to each other.

CH is a transversal line to the parallel lines.

Therefore, let's find the angle that has the same relationship as same side exterior angles as angle ABC.

Two angles that are exterior to the parallel lines and on the same side of the transversal line are called same-side exterior angles.

Same side exterior angles are supplementary.

Therefore,

∠ABC and ∠EFH are same side exterior angles.

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The final answer of the given quadratic equation is 2x - 3y + 7= 0.

What is the quadratic equation?

Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.

We have,

                 2x = 3y - 7

Converting the given equation in the form of ax + by + c = 0, we get

                 2x - 3y + 7= 0

Hence, the final answer of the quadratic equation is 2x - 3y + 7= 0.

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Answer:

Lol

Step-by-step explanation:

k

Which one of the following is NOT equivalent to 3/4?

16/24 = 2/3

15/20 = 3/4

6/8 = 2/3

24/32 = 3/4

Answer: 16/24 and 24/32 are not equivalent to 3/4

Step-by-step explanation:

Equivalent fractions represent the same value, even though they look different.

Here, when we convert every fraction to its simplest form, we can verify if they are equal.

(16/24) ÷ (8/8) = 2/3

(15/20) ÷ (5/5) = 3/4

(6/8) ÷ (2/2) = 3/4

(24/32) ÷ (4/4) = 6/7

As the simplest forms of 16/24 and 24/32 are not 3/4, they are not equivalent fractions of 3/4.

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The length of the area is 8 feet.

What is the shape of outdoor space?

Step-by-step explanation:

Given :

Distance between the furthest corners(Length)= 4 feet

Width(breadth) = 2 feet

Area of rectangle = Length * Breadth

                              = 4 * 2

                              =8 feet

Hence, The length of the area is 8 feet.

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Answer:

-2

Step-by-step explanation:

2(2)*3-14

4*3-14

12-14

-2

The solution to the inequality 6 + t ≤ 13 is given as follows:

t ≤ 7.

An inequality is solved similarly to an equality, isolating the variable of which the solution we want to find.

The difference, of the inequality compared to an equality, is that the solution contains an infinity number of values, instead of a finite number of values. This is because the solution of an inequality is composed by a range of values in one of the infinity number sets.

For this problem, the inequality is given as follows:

6 + t ≤ 13

Hence the solution for variable t is found isolating it as follows:

t ≤ 13 - 6 (moving every term that is not the variable to the opposite side)

t ≤ 7.

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The number of months Ben can be a member of the fitness club is 7 months .

In the question ,

it is given that Ben wants to join a fitness club ,

initial membership fees for fitness club is = $49.50

monthly fees for fitness club = $17.50

let the number of months be [tex]=[/tex] x

the total fees that Ben paid = $172

So ,according to the question

the equation to represent the situation is  

49.50 + 17.50x = 172

17.50x = 172 - 49.50

17.50x = 122.5

x = 122.5/17.50

x = 7

Therefore , Ben can be a member of fitness club for 7 months .

The given question is incomplete , the complete question is

Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50 , Ben has $172 to spend on a membership at the fitness club . what is the number of months ben can be a member of the fitness club ?

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Answer:

f(1) = -2

Step-by-step explanation:

f(1) = -(1) - 1

f(1) = -1 - 1

f(1) = -2