Two points on a line are (10,55) and (15,82.5). what is the slope of the line

The function will be positive and increasing for all values of x.

The formula for an exponential function is f (x) = aˣ, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.

Given the function,

y = 7(5)ˣ

when x = 0, y = 7

x = -1, y = 1.4

x = 1, y = 35

an exponential function is,

y = abˣ

when a > 0 and b > 0 the function is an exponential growth function, for all values of x.

Hence the function will be positive and increasing.

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The function y = 7(5)ˣ is positive and increasing,

Exponential function, in mathematics, a relation of the form y = [tex]a^x[/tex], with the independent variable x ranging over the entire real number line as the exponent of a positive number a.

Given:

y = 7(5)ˣ

As, Exponential functions have the general form:  y = aˣ, where a>0

and a is called the base of the exponential function and x is any real number.

If the base a> 1 and has positive exponent(i.e. x>0) then the exponential function is increasing.

If the base 0 < a< 1 and has negative power then the function is decreasing.

Thus, the function y = 7(5)ˣ is increasing.

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Answer:

a. Congruent

Step-by-step explanation:

ABCD has the same dimensions of A'B'C'D', so that means that it is congruent, even though it's in a different place on the graph.

Answer: 15.40205

Step-by-step explanation:

The expression "cos 80° ÷ sin 10°" can be evaluated using the reciprocal identity of sine and cosine.

First, we convert 80° to its radian equivalent: 80° x (π/180°) = 4π/9 radians.

Next, we use the reciprocal identity of sine and cosine:

cos (θ) ÷ sin (θ) = cot (θ)

So,

cos 80° ÷ sin 10° = cot (10°).

The value of cot (10°) can be found using a calculator or a table of trigonometric values. The exact value is approximately 15.40205.

the test-taker made a score of 16 points on the test.

16 points

8 questions x 2 points per question = 16 points

The test consisted of 17 questions, each worth two points. By answering 8 of them correctly, the test-taker was able to earn 16 points. This score was acquired by multiplying the number of correct questions by the two points per question. Therefore, the test-taker made a score of 16 points on the test.

The test consisted of 17 multiple-choice questions, each worth two points. Each question contained four possible answers, one of which was the correct answer. By selecting the correct answer to 8 questions, the test-taker earned a total of 16 points. This score was calculated by multiplying the number of correct questions by the two points per question. Therefore, the test-taker achieved a score of 16 points on the test.

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The p-value of the test is 0.112

To determine whether the consumer group's belief is supported by the sample data, we can perform a one-sample t-test.

The null hypothesis is that the true average score improvement is equal to 50 points, while the alternative hypothesis is that it is less than 50 points.

Using the sample data, we can calculate the t-statistic as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (44 - 50) / (27 / √(31))

t = -1.24

The degrees of freedom for this test is 30 (sample size minus one).

Using a t-distribution table or calculator, we can find the p-value associated with this t-statistic and degrees of freedom, which is the probability of observing a t-statistic as extreme as -1.24 or more extreme, assuming that the null hypothesis is true.

The p-value is approximately 0.112.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is evidence that the true average score improvement is less than 50 points.

Therefore, the consumer group's belief is supported by the sample data.

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Answer:

I can if you post the question...

Step-by-step explanation:

The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.

The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.

The formula for population variance is given by:

σ² = (1/N) * ∑(X - μ)²,

where N is the total number of elements in the population, X is an individual value in the population, and μ is the mean of the population.

s²= (1/(n-1)) * ∑(X - m)²,

where n is the sample size and m is the mean of the sample.

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A possible vector function that represents the curve of intersection of the two surfaces is r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))

The cylinder x^2 + y^2 = 25 represents the set of points in 3D space where the distance from the origin to the point (x, y, z) is equal to 5. The surface z = xy represents the set of points in 3D space where the height of the point (x, y, z) is equal to its x-y coordinate.

The curve of intersection of the two surfaces is given by the set of points in 3D space that are simultaneously on the cylinder and on the surface z = xy. This means that for any point on the curve of intersection, the distance from the origin to the point must be equal to 5, and the height of the point must be equal to its x-y coordinate.

We can find a vector function that represents the curve of intersection by parameterising the points on the curve in terms of a scalar parameter t. For example, a possible parameterization of the curve of intersection is:

r(t) = (5 cos(t), 5 sin(t), 5 cos(t) sin(t))

where t is a scalar parameter that ranges over all values between 0 and 2π. The values of x, y, and z are given by 5 cos(t), 5 sin(t), and 5 cos(t) sin(t), respectively, and represent a point on the curve of intersection for each value of t.

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The probability of getting at least 1 red is 6/7

Probability is the likelihood of a desired event happening.

Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.

The probability that the first is blue and the second is blue

p(First blue, Second blue) = 3/7 × 2/6 = 1/7

Thus, the probability of getting at least 1 red, is the complement of getting both blue

That is, P(At least 1 red) = P'(both blue) = 1 - P(Both blue) = 1 - 1/7 = 6/7

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A statistic is an estimate or calculation based on a sample size of data, while a parameter is a numerical characteristic of an entire population.

A statistic is a value or set of values which are calculated from a sample of data. Statistic values are used to measure attributes of a population, such as the mean, median, or mode of a population. Statistic values are estimates and can be subject to sampling error. Parameters, on the other hand, are numerical characteristics of an entire population. Parameters are fixed values which describe the population as a whole. For example, thirty percent of all dog owners might be a statistic, as it is an estimate based on a sample of data. However, the total number of dog owners would be a parameter, as it describes the entire population of dog owners. Parameters are not subject to sampling error, and they cannot be calculated from a sample set of data.

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After dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

When two figures are congruent, it means they have the same shape and size, whereby, all pairs of corresponding angles and sides of both figures are congruent or equal in measure.

The image attached below shows a dilated figure.

Dilation is a transformation that enlarges a figure or reduces the figure.

After dilation, the new figure maintains the same shape of the original figure.

However, after dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.

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Answer: Yes, it is congruent.

Rt is same length as Tu

angle rst is equal to angle tvu

therefore the angle where they both meet would have to be the same aswell, so it is congruent

Step-by-step explanation:

Answe is attached in the above image.

Answer:

8 ounces per cup or 8/1

Step-by-step explanation:

64 ounces/8 cups = 8

We have the differential equation, [tex]y''+5y'+4y=2e^{-2x}[/tex]. The question asks to find the particular solution to the DE.

To find the particular solution look at the right-hand-side and make a “guess” of what the solution could be.

Since we have [tex]2e^{-2x}[/tex] we can guess that the particular solution could be in the form [tex]Ae^{-2x}[/tex], where [tex]A[/tex] is some unknown constant.

Now finding the value of the unknown constant, [tex]A[/tex]. Lets say [tex]g(x)=Ae^{-2x}[/tex], find [tex]g'(x)[/tex] and [tex]g''(x)[/tex].

[tex]g(x)=Ae^{-2x}[/tex]

=> [tex]g'(x)=-2Ae^{-2x}[/tex]

=> [tex]g''(x)=4Ae^{-2x}[/tex]

Now plug [tex]g(x)[/tex], [tex]g'(x)\\[/tex], and [tex]g''(x)[/tex] into the given differential equation.

=> [tex]y''+5y'+4y=2e^{-2x}[/tex]

=> [tex](4Ae^{-2x})+5(-2Ae^{-2x})+4(Ae^{-2x})=2e^{-2x}[/tex]

=> [tex]4Ae^{-2x}-10Ae^{-2x}+4Ae^{-2x}=2e^{-2x}[/tex]

=> [tex]8Ae^{-2x}-10Ae^{-2x}=2e^{-2x}[/tex]

=> [tex]-2Ae^{-2x}=2e^{-2x}[/tex]

Compare the coefficients,

=>[tex]-2A=2[/tex]

=>[tex]A=-1[/tex]

So we can say our "guess" to the particular solution of the given differential equation is, [tex]y_{p} =-e^{-2x}[/tex].

The simplification of the fractions gives 4 / (b - d).

Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.

Here, a is called the numerator and b is called the denominator.

Given expression is [tex]\frac{8a + 4b}{2ab+b^2-2ad-bd}[/tex].

We have to simplify each of the numerator and denominator in the expression [tex]\frac{8a + 4b}{2ab+b^2-2ad-bd}[/tex].

Take the common factor in each of the expressions in numerator and denominator.

8a + 4b = 4(2a + b)

2ab + b² - 2ad - bd = 2ab - 2ad + b² - bd

                               = 2a(b - d) + b(b - d)

                               = (b - d) (2a + b)

[tex]\frac{8a + 4b}{2ab+b^2-2ad-bd}[/tex] = [tex]\frac{4(2a+b)}{(b-d)(2a+b)}[/tex]

                     = [tex]\frac{4}{b-d}[/tex]

Hence the simplified expression is 4 / (b - d).

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The spherical coordinates of the given rectangular coordinates are (10, 0, 60).

The cartesian coordinate or rectangular coordinates describes the location of a point in space using an ordered triple where each coordinate represents a distance. The spherical coordinate system describes the location of a point in space using an ordered triple where coordinate describes one distance and two angles. In the spherical coordinate system, a point is represented by the ordered triple (ρ, θ, φ).

The equations which are used to convert from rectangular coordinates to spherical coordinates are:

ρ^2=x^2+y^2+z^2

tan⁡〖θ= y/x〗

φ=arccos⁡〖z/√(x^2+y^2+z^2 )〗

The given rectangular coordinates are (5√3, 0, 5). Hence,

ρ^2=〖(5√3)〗^2+0^2+5^2 ≈ 100

ρ ≈ √100 ≈ 10

tan⁡〖θ= 0/(5√3)=0〗

θ=  tan^(-1)⁡0=0

φ=arccos⁡〖5/√(〖(5√3)〗^2+0^2+5^2 )〗= arccos 5/10=arccos⁡0.5 ≈ 60

Note:  The question is incomplete. The complete question probably is: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*). (5√3, 0, 5)

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The value of a in the triangle is 17 degrees

An equilateral triangle is that type of triangle whose all sides and all angles are equal.  Recall theat the sum of angles of a triangle is 10 degrees.

This implies that

4a-8 +4a-8 +4a-8 = 180

12a -24 = 180

12a = 180+24

12a = 204

Making a the subject of the relation,

12a/12 = 204/12

Therefore the value of a= 17⁰

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The balance after 9 months with an APR of 9% and monthly payments of 250 is, $267.38

A quick and easy method of calculating the interest charge on a loan is called a Simple interest.

Given that;

The savings plan balance after 9 months with an APR of 9% and monthly payments of 250.

Now, Let the balance after 9 months with an APR of 9% and monthly payments of 250 is, x

Hence, We can formulate;

⇒ x = 250 (1 + 0.09/12)⁹

⇒ x = 250 × 1.0075⁹

⇒ x = 250 × 1.0695

⇒ x = $267.375

⇒ x = $267.38

Thus, The balance after 9 months with an APR of 9% and monthly payments of 250 is, $267.38

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[tex]17\frac{1}{2}[/tex] cups of flour we need to make three of each cake.

A fraction represents a part of a whole.

Given that the first recipe calls for 2 1/2 cups of flour and the second one calls for 3 1/3 cups of flour.

We need to make three of each cakes.

[tex]2\frac{1}{2}[/tex] cups x 3 = [tex]7\frac{1}{2}[/tex] cups of flour for the first recipe.

And for the second recipe [tex]3\frac{1}{3}[/tex] cups x 3 = 10 cups of flour.

So in total  [tex]7\frac{1}{2}[/tex]  cups + 10 cups = [tex]17\frac{1}{2}[/tex] cups of flour.

Hence,  [tex]17\frac{1}{2}[/tex] cups of flour we need to make three of each cake.

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Answer:154 LCM I hope this helps mark me brainlist

Step-by-step explanation:

The Least Common Multiple (LCM) of 22 and 77 is 154.

To get the Least Common Multiple (LCM) of 22 and 77 we need to factor each value first and then we choose all the factors which appear in any column and multiply them: 

22: 2 11

77: 7 11

______
LCM 2711

The Least Common Multiple (LCM) is: 
2 times 7 times 7=154

The Values for rectangle type wall and circle will be gallons of paint that are required to paint one side of a block wall =5.16 gallon, the gallons of sealer required to seal a floor=4.22 gallon and circumference of circle≈39 feet.

What exactly is a rectangle?

Rectangles are four-sided polygons with all internal angles equal to 90 degrees. At each corner or vertex, two sides meet at right angles. The rectangle differs from a square in that its opposite sides are equal in length.

For example, if one side of a rectangle is 20 cm long, the opposing side is similarly 20 cm long.

A rectangle has two diagonals that intersect. Both diagonals are the same length

P = 2 (Length + Width) is the perimeter.

Rectangle Area=Length*Breadth

Now,

1. Given Length of wall=172 feet and breadth =6 feet then area=172*6=1032

square feet and The paint being used will cover 200 square ft per gallon.

so, gallons of paint that are required to paint one side of a block wall

=1032/200=5.16 gallon

2. Length=250 feet, breadth=120 feet then perimeter=2*370=740 feet

paint used to seal 175 feet floor=1 gallon

then the gallons of sealer required to seal a floor 120' x250'=740/175=4.22 gallon

3. Incomplete question.

4.diameter=12feet 5inch=149 inch

circumference of circle=π*diameter=3.14*149≈39 feet

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Answer:

A: 4

Step-by-step explanation:

15 divided by 20 = 0.75

4 + 2 = 6

14 - 6 = 8

So, the smaller triangle base will be 6 and the bigger triangle base will be 8

6 divided by 8 = 0.75

So, A:4 is the correct answer.

The expression is equivalent to the given polynomial expression is

-7[tex]m^4[/tex]n + 18mn - 8m².

In particular, an expression must not contain any square roots of variables, any fractional or negative powers on the variables, and any variables in any fractions' denominators in order to qualify as a polynomial term.

These are trinomials, binomials, and monomials. A polynomial can be categorised into 4 categories based on its degree. The four are the cubic polynomial, linear polynomial, and polynomial of zero.

From all the options the equivalent polynomial expression as

-7[tex]m^4[/tex]n + 18mn - 8m²

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The Question attached here is incomplete, the complete question is

Which expression is equivalent to the given polynomial expression?

(9mn – 19m4n)19m4n) - (8m2 + 12m4n + 9mn)

A.-7mtn + 8m2

B.-7m4n + 18mn - 8m2

C.-31m 4n – 8m2

D.-31m 4n + 18mn

8m2

The smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0, a] is 2.

The intermediate value theorem states that if a function f is continuous on the closed interval [a, b] and if y is a value between f(a) and f(b), then there exists a point c in the interval [a, b] such that f(c) = y.

In this case, we want to find the smallest integer a such that f(x) has a zero on the interval [0, a]. Since f(0) = 7 and f(x) = -2x^3 + 8x^2 - 6x + 7, we need to find the smallest a such that f(a) < 0.

We can start by finding the values of x where f(x) changes sign. To do this, we can set f(x) equal to 0 and solve for x:

-2x^3 + 8x^2 - 6x + 7 = 0

This is a cubic equation and can be solved using various methods such as factoring, substitution, or the use of a numerical method. However, since we are looking for the smallest integer a, we can use an estimation method such as the Newton-Raphson method to approximate the smallest positive root of the equation.

A common initial guess for the smallest positive root of a cubic equation is x = 1. Using this as the initial guess, we can iterate using the following formula:

x_{n+1} = x_n - f(x_n)/f'(x_n)

where f'(x) is the derivative of f(x) and x_n is the nth estimate of the root.

After several iterations, the estimate for the smallest positive root of the equation can be found to be approximately 1.56. Therefore, the smallest integer a such that the intermediate value theorem guarantees that f(x) has a zero on the interval [0, a] is 2.

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Answer:

The rate at which the turtle is crawling can be found by dividing the distance traveled in miles by the time in hours.

So, the turtle can travel 3/20 of a mile in 5/6 of an hour, which means that the turtle is crawling at a rate of (3/20) / (5/6) miles per hour.

To simplify, we need to convert both the numerator and denominator to a common unit. If we multiply the numerator and denominator by 6, we get:

(3/20) * 6 / (5/6) * 6 = 3 / 5 miles per hour.

Therefore, the turtle is crawling at a rate of 3/5 miles per hour.

The measure of the smallest angle of the triangle would be = 33°

The total angle measurement of a triangle is a total of 180°.

That is ;

180° = 90 + (4x-7)° + (3x-15)°

180 = 90-7-15+4x+3x

180 = 90-22+7x

180 = 68+7x

180-68 = 7x

7x = 112

X= 112/7

X= 16

substitute X=16 into both angles (4x-7)° and (3x-15)° to know the smallest.

= 4(16)-7

= 64-7

= 57°

and;

= 3(16)-15

= 48-15

= 33°

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Answer:

Factor 3x+3

3x+3

=3(x+1)

Answer:

P=2[9x-3]

Step-by-step explanation:

perimeter of rectangle =2(L+W)=2L+2W

where P=perimeter of rectangle

L=length of rectangle =3x+3

W=width of rectangle =6x-6

P=2[(3x+3)+(6x-6)]

P=2[3x+3+6x-6]

P=2[9x-3]

Answer: 0.5 inches of rain per hour or 0.5/1

Step-by-step explanation:

divide 3/6 gets you 0.5