Find the equation of the line passing through the points (-3,8) and (3,-4). Write the
equation in slope-intercept form.

Answer:

\(=13a^{437}+12a\)

Step-by-step explanation:

\(\left(a^{413}a^{22}a+1\right)\cdot \:13a-2a+1\cdot \:a\)

\(\mathrm{Add\:similar\:elements:}\:-2a+1\cdot \:a=-a\)

\(=\left(a^{413}a^{22}a+1\right)\cdot \:13a-a\)

\(=\left(a^{436}+1\right)\cdot \:13a-a\)

\(=13a\left(a^{436}+1\right)-a\)

\(=13a^{437}+13a-a\)

\(\mathrm{Add\:similar\:elements:}\:13a-a=12a\)

\(=13a^{437}+12a\)

Answer:

x

Step-by-step explanation:

The formula of a line in its slope-intercept form is

y= mx + b

the slope is indicated by “m” that multiply the x

The probability that the sample of three apples contains two rotten apples is approximately 0.0286 or 2.86%.

To find the probability that the sample of three apples contains two rotten apples, we can use the hypergeometric distribution.

The number of ways to choose 3 apples from the basket of 15 apples is given by the combination formula:

C(15, 3) = 15! / (3! * 12!) = 455

The number of ways to choose 2 rotten apples from the 2 rotten apples in the basket is C(2, 2) = 1.

The number of ways to choose 1 good apple from the 13 good apples in the basket is C(13, 1) = 13.

So the number of ways to choose 2 rotten apples and 1 good apple from the basket is C(2, 2) * C(13, 1) = 13.

Therefore, the probability of selecting a sample of three apples that contains two rotten apples is:

P(2 rotten apples) = 13 / 455 = 0.0286 (rounded to four decimal places)

So the probability that the sample of three apples contains two rotten apples is approximately 0.0286 or 2.86%.

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Using the angle of elevation, the height of the tree is 71.57 feet.

The angles of elevation to a nearby tree from a point on the ground is measured to be 54 degrees.

The distance from the tree to the point on the ground is 52 feet.

The height of the tree can be found as follows:

The situation can be modelled to a right triangle.

Therefore, the height of the tree is the opposite side of the right triangle formed.

Hence,

tan ∅ = opposite / adjacent

where

∅ = angle of elevation

tan 54 = h / 52

cross multiply

h = 52 tan 54

h = 52 × 1.37638192047

h = 71.5718598645

Therefore,

height of the tree = 71.57 feet.

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Answer:

Area= 16

Perimeter= 16

Answer:

A = l*w

P = 2l + 2w

A = 4*4 = 16

A = area

l = length

l = 4

w = width

w = 4

The area is equal to 16.

P = 2*4 + 2*4 = 16

P = perimeter

2l = 2*length

2l = 2*4

2w = 2*width

2w = 2*4

The perimeter is equal to 16.

It can be concluded both are equal to each other.

Hope this helps

There is a 20 percent chance the relationship being studied is real.  Option D

If a study shows a result with a P value of 0.2, it means that there is a 20 percent chance that the observed relationship being studied is due to random chance or sampling variability.

In other words, the P value represents the probability of obtaining a result as extreme as, or more extreme than, the observed result if the null hypothesis were true.

The null hypothesis assumes that there is no real relationship or effect in the population being studied. The alternative hypothesis, on the other hand, suggests that there is a real relationship or effect. The P value helps determine the strength of evidence against the null hypothesis.

A P value of 0.2 means that if the null hypothesis were true (i.e., there is no real relationship), there would be a 20 percent chance of obtaining a result as extreme as, or more extreme than, the observed result by random chance alone.

This implies that the observed result is not statistically significant at conventional levels of significance (typically set at 0.05 or 0.01), which means there is not enough evidence to reject the null hypothesis.

Therefore, the correct answer is (D) There is a 20 percent chance the relationship being studied is real. It's important to note that the P value does not directly indicate the probability of the relationship being true or real, but rather the probability of obtaining the observed result under the assumption of no relationship. Option D

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Answer:

B

Step-by-step explanation:

You use PEDMAS to evaluate the perfect number so in the PEDMAS it says addition then to subtraction so, the addition goes first. And when you have both addition you go left to right :)

Answer:

The slope is 3. Thats what my friend said

Step-by-step explanation:

Answer:

Step-by-step explanation:

Not sure what your question is, but that is:

18 units are shaded (blue)

18/100 or 9/50 or 0.18 of the entire section is shaded.

Answer:

squared

Step-by-step explanation:

because shape

Answer:

1: 2x + y = 24

2: x - 3y = 54

Step-by-step explanation:

Answer:

\( y = - 3. \\ x = - 13.5\)

Step-by-step explanation:

\(equation 1: -x/3 - y/6 = -4 \: \: = - \frac{x}{3} - \frac{y}{6} = - 4 \\ \\

equation 2: -x/6 + y/2 = -9 \: \: = - \frac{x}{6} + \frac{y}{2} = - 9 \\ \\ - \frac{x}{3} - \frac{y}{6} = - 4 \\ - 6x - 3y = - 72 ...(eq3.) \\ \\ - \frac{x}{6} + \frac{y}{2} = - 9 \\ - 2x + 6y = - 9...(eq4.) \\ \\ \\ 2 \times - 6x - 3y = - 72 ...(eq3.) = > - 6y = -1 44 \\6 \times - 2x + 6y = - 9...(eq4.)= > - 36y = -54 \\ - 6y - ( - 36y) = - 144 - ( - 54) \\ 30y = - 90 \\ y = - \frac{90}{30} \\ y = - 3. \\ x = - 13.5

\)

Answer:

BC= 3

Step-by-step explanation:

Suppose a line BD is 10 and it has a point C somewhere on the  line. It is given that BC is  3times and CD is 7 times  or algebraically  if we take x as a variable then according to the given information

BC+ CD= BD

3x+ 7x= 10

10x= 10

x= 10/10

x= 1

3x would give 3 (1)= 3

Hence the Line BC = 3

and the line CD= 7

Step-by-step explanation:

a diameter is always twice the radius.

the only pairs I can see in the list, where one number is twice the other :

2.5 and 5

7.6 and 15.2

so,

2.5 is the radius of A

5 is the diameter of A

7.6 is the radius of B

15.2 is the diameter of B

15.7 is then the circumference of A (as the smaller of the remaining 2 numbers)

47.7 is the circumference of B

we can also check via the formula for circle circumference :

c = 2×pi×r

and yes, the rounded c for r=2.5 is 15.7, and for r=7.6 is 47.7

Answer:

LOOKS GREAT!!!

Step-by-step explanation:

HOPE YOU DO WELL!!!

Answer:

D

Step-by-step explanation:

7^2 is 49-8x2 what is 16-16you get 49-16-16 what equals 17  so ur answer is D

Using the Binomial probability distribution,

The probability that exactly two customers in the sample will default on their payments is 0.31..

We have given that,

4% of total customers a mortgage company default on their payments .

The probability of success i.e number of customers default on their payments (p) = 4%

= 0.04

The probability of failure (q) = 1-p = 1-0.04 = 0.06

Total number of customers in sample (n) = 20

we have to find out the probability that exactly two customers in the sample will default on their payments.

Using the Binomial probability distribution,

P(X=x)= ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾

the required probability is P(X= 2 )

Now, P(X= 2) = ²⁰C₂(0.04)²(0.06)¹⁸

=> P(X=2) = 190 × 0.0016 × 1.0155 = 0.31

Hence, the required probability is 0.31

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To find the volume of the solid generated by rotating the region bounded by the curves y = cos(x) and the x-axis on the interval [0, π/2] about the x-axis, we can use the method of cylindrical shells.

The volume V is given by the integral:

V = ∫[a,b] 2πx f(x) dx

In this case, the interval [a,b] is [0, π/2], and the function f(x) is cos(x).

V = ∫[0,π/2] 2πx cos(x) dx

To evaluate this integral, we can use integration by parts. Let's consider u = x and dv = 2π cos(x) dx. Then du = dx and v = 2π sin(x).

Using the formula for integration by parts, the integral becomes:

V = [2πx sin(x)]|[0,π/2] - ∫[0,π/2] 2π sin(x) dx

Evaluating the definite integral and plugging in the limits, we have:

V = [2π(π/2) sin(π/2)] - [-2π(0) sin(0)] - ∫[0,π/2] 2π sin(x) dx

V = π^2

Therefore, the volume of the solid is π^2 cubic units.

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The effective rate of interest his savings account has to earn is 1776%.

The amount of total deposits made by Peter in nine months would be:Amount of deposits in 9 months =\($1075 + $1075 + $1075 = $3225\)

Now, in order to reach a total of \($3300\)in nine months, the interest earned on the deposits should be:Interest earned in 9 months =\($3300 - $3225 = $75\)

effective rate of interest :ERI = (1 + R/n)^n - 1

Where, R = Rate of interest, n = number of times interest is compounded per year.

Now, since the deposits are being made every three months, there will be three deposits made in nine months. Therefore, the number of times interest will be compounded in one year would be 4. i.e., the deposits are made quarterly and there are four quarters in a year.

So, the formula for the amount after n years compounded quarterly would be given as:A = P(1 + (R/4)/100)^(4n)

\(3300 = 1075(1 + R/400)^(4(3/12))3300/1075 = (1 + R/400)^(4(3/12))\)

Taking logarithm of both sides:\(ln(3.07) = ln(1 + R/400)^(4/3)3ln(3.07) = 4/3 ln(1 + R/400)ln(3.07^(3/4)) = ln(1 + R/400)1.865 = ln(1 + R/400)\)

the antilogarithm of both sides\(:e^1.865 = 1 + R/4005.44 = 1 + R/400R/400 = 5.44 - 1R/400 = 4.44R = 4.44 × 400R = 1776\)

The effective rate of interest his savings account has to earn is 1776%.

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We find that the probability of a randomly generated sequence of 24 binary digits having exactly half of the digits as 0s is C(24, 12) / 2^24.

To find the probability that exactly half of the 24 binary digits are 0s in a randomly generated sequence, we can use the following steps:
Determine the total number of possible sequences.
Since there are 24 binary digits and each digit can be either 0 or 1, the total number of possible sequences is 2^24.
Calculate the number of sequences with exactly 12 0s.
In a sequence of 24 binary digits, we want to choose 12 positions for the 0s. This can be done using the combination formula, which is C(n, k) = n! / (k!(n-k)!), where n is the total number of digits and k is the number of 0s. In this case, n = 24 and k = 12. So, C(24, 12) = 24! / (12! * (24-12)!).
Compute the probability.
Divide the number of sequences with exactly 12 0s by the total number of possible sequences. Probability = C(24, 12) / 2^24.
By following these steps, we find that the probability of a randomly generated sequence of 24 binary digits having exactly half of the digits as 0s is C(24, 12) / 2^24.

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Place a point at -7, and another point at 7. These two points represent the solution to the given equation.

The given algebraic statement is \(|x| = 7.\) To find the values of x for which the statement is true, we need to solve the absolute value equation.

An absolute value of a number is its distance from 0 on the number line.

Therefore, |x| = 7 means that the distance of x from 0 is 7. There are two possible scenarios:

1. x is 7 units to the right of 0 (positive direction). In this case, x = 7.
2. x is 7 units to the left of 0 (negative direction). In this case, x = -7.

So, the values of x for which the statement is true are x = 7 and x = -7.

On a number line, the set of all points corresponding to the values of x would include only two points, at\(x = 7\)and \(x = -7\).

To visualize this, draw a number line with 0 in the center.

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An equation for water level in june for pensacola as a function of time (t) is f(t) = 5 cos pi/6 t + 7.

Which equation of cos show period amplitude ?

The equation given below show aplitude and period

\(y = A cos bx + c\)

where A = amplitude,

b = 2 pi/Period,

Period = 12 hrs,

c = midline,

x = t and y = f(t)

We have to find the amplitude

\(A = 1/2 (Xmax - Xmin)\)

\(12 - 2 / 2 = 10/2 = 5\)

\(b = 2 pi / 12 = pi/6\)

\(c = 1/2 (Xmax + Xmin)\)

\(12+2/2 = 7\)

Therefore, the an equation for water level in june for pensacola as a function of time (t)

\(f(t) = 5 cos pi/6 t + 7\)

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The carrot ate by Fluffy the bunny at the night will be equal to 2/4 or 1/2.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Carrot ate by bunny in the morning = 1/4

Then, carrot left after ate by bunny = 1- 1/4 = 3/4

Assume that the amount of carrot ate at the night be x.

Then, the carrot left = 1/4

So, the equation will be,

3/4 - x = 1/4

x = 3/4 - 1/4

x = 2/4 or,

x = 1/2.

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The independent variable for Scenario A is given as follows:

a. The employee benefits package.

In the case of a relation, we have that the independent and dependent variables are defined by the standard presented as follows:

In the context of this problem, we have that the input and the output of the relation are given as follows:

Hence the independent variable for Scenario A is given as follows:

a. The employee benefits package.

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Answer:

$13087.92

Step-by-step explanation:

formula: ab^x

a= starting  amount

a= 5072

b= 1+r

r=rate

r=9%=0.09

b=1+0.09 =1.09

x= 11 (years)

account after 11 years:

= 5072(1.09)^11

=13087.9227277

= 13087.92

Answer:

363 ft.

Step-by-step explanation:

To calculate the base side which is b we use the trigonometric identity called cosine.

\(cos \theta=\frac{base}{hypotenuse} \\\\cos25 = \frac{b}{400}\\\\b=400*cos 25\\b=400*0.906\\b=362.5\ ft\)

Since we the answer to the nearest whole number it would be b = 363 ft.

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

We have,

3.

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees.

= 25

We add up all the dots above the numbers between 98.5 and 98.7.

We will not include the dots above 98.5 and 98.7.

4.

The dot plot of the sample mean body temperature for 100 different random samples of size 10 from a population with a mean temperature of 98.6 degrees shows that the majority of the sample means are close to 98.6, and there are very few samples means that exceed 98.6, then it would be surprising to obtain a sample mean of 98.8 or greater from a different random sample.

Thus,

The number of samples that were greater than 98.5 degrees and less than 98.7 degrees is 25.

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Answer:

Step-by-step explanation:

To find the geodesic between the points (-3, 0, 9) and (3, 0, 9) on the surface defined by z = 16 - (x^2 + y^2), we can use the concept of geodesic equations.

A geodesic is a curve that locally minimizes the length between two points on a surface. The length of a curve on a surface can be expressed using the arc length formula:

ds^2 = dx^2 + dy^2 + dz^2

In this case, since the surface is defined by z = 16 - (x^2 + y^2), we can express the arc length in terms of x and y:

ds^2 = dx^2 + dy^2 + dz^2

= dx^2 + dy^2 + (dz/dx dx)^2 + (dz/dy dy)^2

To find the geodesic, we need to minimize the arc length, which is equivalent to minimizing the integral of ds:

L = ∫ √(dx^2 + dy^2 + (dz/dx dx)^2 + (dz/dy dy)^2)

To simplify the problem, we can notice that the surface defined by z = 16 - (x^2 + y^2) is rotationally symmetric about the z-axis. Therefore, the geodesic connecting the two points (-3, 0, 9) and (3, 0, 9) lies on the x-z plane.

We can parameterize the geodesic curve on the x-z plane as x = f(t) and z = g(t), where t is a parameter.

Now, we can rewrite the arc length integral in terms of t:

L = ∫ √(dx/dt)^2 + (dz/dt)^2 dt

Substituting the parameterization x = f(t) and z = g(t), we have:

L = ∫ √(df/dt)^2 + (dg/dt)^2 dt

To minimize L, we need to find the values of f(t) and g(t) that satisfy the Euler-Lagrange equations:

d/dt(dL/df') - dL/df = 0

d/dt(dL/dg') - dL/dg = 0

By solving these differential equations, we can determine the specific form of the geodesic between the two points (-3, 0, 9) and (3, 0, 9) on the surface.

Note that the solution to these equations is beyond the scope of a simple text-based response, as it involves solving a system of differential equations. It typically requires advanced mathematical techniques, such as variational calculus or numerical methods.

Therefore, to obtain the precise equation of the geodesic between the two given points on the surface z = 16 - (x^2 + y^2), it is recommended to use specialized software or consult advanced mathematical resources.

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