Provide a two-column proof: Given: Line segment PR is congruent to line segment LN
Q is the midpoint of line segment PR
M is the midpoint of line segment LN
Prove: PQ = LM

Roman has a certain amount of money. if he spends 15, then he has 14 of the original amount left. Roman had originally 20.

To find out how much money Roman had originally, you can follow these steps:
Step 1: Let the original amount of money be "x".
Step 2: According to the problem, if Roman spends $15, he has 1/4 of the original amount left.

So, after spending 15, he has (1/4)x left.
Step 3: Since he spent $15, we can write the equation as: x - 15 = (1/4)x.
Step 4: To solve for x, first multiply both sides of the equation by 4 to get rid of the fraction:

4(x - 15) = 4(1/4)x => 4x - 60 = x.
Step 5: Subtract "x" from both sides:

4x - x - 60 = 0 => 3x - 60 = 0.
Step 6: Add 60 to both sides:

3x = 60.
Step 7: Divide both sides by 3 to find the value of x:

x = 60 / 3 => x = 20.

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Answer:

It’s going to be B. 50+60+70=180 which is how many degrees are in a triangle.

To find the value of f(-2) given the differential equation dy/dx = e^(x-1) * e^y with the initial condition f(1) = 0, we can use separation of variables and solve the differential equation.

Starting with the given differential equation:

dy/dx = e^(x-1) * e^y

Separating variables by multiplying both sides by dx and e^(-y):

e^(-y) dy = e^(x-1) dx

Now, we can integrate both sides of the equation:

∫ e^(-y) dy = ∫ e^(x-1) dx

Integrating the left side with respect to y and the right side with respect to x:

e^(-y) = e^(x-1) + C

Applying the initial condition f(1) = 0, where x = 1 and f(1) = 0:

e^(-0) = e^(1-1) + C

1 = 1 + C

C = -2

Substituting the value of C back into the equation:

e^(-y) = e^(x-1) - 2

Now, we can find the value of f(-2) by substituting x = -2 into the equation:

e^(-y) = e^(-2-1) - 2

e^(-y) = e^(-3) - 2

To find the value of f(-2), we need to solve for y:

e^(-y) = 2 - e^(-3)

y = -ln(2 - e^(-3))

Therefore, the value of f(-2) is f(-2) = -ln(2 - e^(-3)).

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Step-by-step explanation:

600=150%

?= 100%

crossmultiplication

=400

600g=150%x

600 is therefore 150% of 400

There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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(a) The intersection point H of the line L₁ and the plane P is H(7/4, 3/2, 19/4).

(b) The parametric equations for the line L₂, which is contained in the plane P and perpendicular to the line passing through H(7/4, 3/2, 19/4) and R(1, 0, 2), are:

x = 7/4 + (17/4)t

y = 3/2 + (5/4)t

z = 19/4 - (9/4)t

(a) To find the intersection point H between the line L₁ and the plane P, we need to determine the direction vector of the line L₁ first. Since L₁ is perpendicular to the plane P, the normal vector of the plane P will be parallel to the line L₁.

The normal vector of the plane P can be obtained by taking the coefficients of x, y, and z in the plane equation: x - 2y + z = 3.

Therefore, the normal vector is N = (1, -2, 1).

Since L₁ is perpendicular to the plane P, its direction vector will be parallel to the normal vector N. Hence, the direction vector of L₁ is D = (1, -2, 1).

Now, we can express the line L₁ passing through point Q(2, 1, 5) parametrically as:

x = 2 + t

y = 1 - 2t

z = 5 + t

To find the intersection point H between the line L₁ and the plane P, we substitute the parametric equations of L₁ into the equation of the plane P:

(2 + t) - 2(1 - 2t) + (5 + t) = 3

Simplifying the equation:

2 + t - 2 + 4t + 5 + t = 3

8t + 5 = 3

t = -1/4

Substituting the value of t back into the parametric equations of L₁, we can find the coordinates of the intersection point H:

x = 2 + (-1/4) = 7/4

y = 1 - 2(-1/4) = 1 + 1/2 = 3/2

z = 5 + (-1/4) = 19/4

Therefore, the intersection point H of the line L₁ and the plane P is H(7/4, 3/2, 19/4).

(b) To find the parametric equation for the line L₂, which satisfies the given conditions, we need to find its direction vector.

(i) L₂ is contained in the plane P, so its direction vector will be perpendicular to the normal vector N of the plane P.

(ii) L₂ is perpendicular to the line passing through point H(7/4, 3/2, 19/4) and R(1, 0, 2). The direction vector of this line can be obtained by subtracting the coordinates of R from the coordinates of H:

D' = (7/4 - 1, 3/2 - 0, 19/4 - 2) = (3/4, 3/2, 11/4)

Since L₂ is perpendicular to this line, its direction vector will be orthogonal to D'. Thus, we can take the cross product of D' and N to obtain the direction vector of L₂:

D₂ = D' x N

D₂ = (3/4, 3/2, 11/4) x (1, -2, 1)

Using the cross product formula:

D₂ = ((3/2)(1) - (11/4)(-2), (11/4)(1) - (3/4)(1), (3/4)(-2) - (3/2)(1))

D₂ = (17/4, 5/4, -9/4)

Now we have the direction vector D₂ = (17/4, 5/4, -9/4).

To find the parametric equations for the line L₂, we can use the point H(7/4, 3/2, 19/4) on the line:

x = 7/4 + (17/4)t

y = 3/2 + (5/4)t

z = 19/4 - (9/4)t

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Answer:

y + 1/2 = 3(x - 2)

Step-by-step explanation:

We have to think about this question in point-slope form, which is a form that explicitly gives us the slope of the line and a single point that it passes through. Point-slope form looks like this: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point that the line goes through. We are given that the line goes through (2, -1/2) which means x1 = 2 and y1 = (-1/2). We are also given that the slope is 3. We can plug these quantities into the equation to solve:

y - (-1/2) = 3(x - 2) OR y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

The correct option is (3).

The slope of a line indicates its direction and steepness. Finding the slope of lines in a coordinate plane can help predict whether the lines are parallel, perpendicular, or have no relationship at all without actually using a compass.

As per the given data:

We have to find out the equation of the line that passes through (2, -1/2) and has a slope of 3.

As we know a point at the slope of the line, we can use the point slope form:

\(y - y_1 = m(x-x_1)\) , where m is the slope and \((x_1, y_1)\) is the point through which the line passes.

y - (-1/2) = 3(x - 2)

y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

Hence, The equation of the line is y + 1/2 = 3(x - 2).

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Answer:

x=12

Step-by-step explanation:

height of tree)/(shadow length of tree) = (height of pole)/(shadow length of pole)

x/26 = 6/13

13x = 26*6

13x = 156

x = 156/13

x = 12

(hope this helps can i plz have brainlist :D hehe)

The Null and Alternative hypothesis are

Hₒ: π= 0.79

Hₐ: π > 0.79

Statistic Z = -26.38

P-value = 0

Conclusion : The null hypothesis is

rejected .

Final Conclusion : which implies that population proportion is different from

π= 0.79.. This sample proportion can notbe product of chance.

There is enough evidence to support to the claim that selection of people is biased against allowing this ethnicity to sit on the grand jury.

We have problem of proportion and we have to apply hypothesis testing in it .

We claim that the selection is biased against allowing this ethnicity to sit on the grand jury. This means that proportion of people of enthic selected for jeury in a way below from proportion that eligible for jury .

Null and Alternative hypothesis are

Hₒ: π= 0.79

Hₐ : π> 0.79

The significance level is 0.01

The sample we will use is total of 876 people that were selected for grand jury duty (n= 876). 42% of them were entnicity for which we are testing , so sample proportion is p= 0.42

The standard error is

σₚ= s√ (π(1-π)/n)= √ 0.79 (1-0.79)/ 876 = √0.00019 = 0.0137~ 0.014

Then we can calculate Z – value

Z = (p-π+0.5/n)/ σₚ =( 0.42 – 0.79 + 0.5/876 )/ 0.014 = - 0.03964/0.014 = - 26.387

P-value for this test statistic is 0

P-value (z<-26.38)= 0

P-value = 0 < 0.01

As we see that P-value is less lower then significance level . This sample result is unpredictable. The null hypothesis is rejected which implies that population proportion is different from π= 0.79

This sample proportion can not be product of chance.

There is enough evidence to support to the claim that selection of people is biased against allowing this ethnicity to sit on the grand jury.

#Complete Question:

In a recent court case it was found that during a period of 11 years 876 people were selected for grand jury duty and 42% of them were from the same ethnicity. Among the people eligible for grand jury duty, 79.5% were of this ethnicity. Use a 0.01 significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution. Which of the following is the hypothesis test to be conducted?

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The derivate of f(y) is -9y^6 - 33y^4 + 84y^2.

To differentiate the given function f(y), we will use the product rule and the chain rule of differentiation. Let's break down the function into two parts:

f(y) = (1 y^2 - 9 y^4) * (y + 3y^3)

Using the product rule, we can differentiate each part separately:

f'(y) = (1 y^2 - 9 y^4)' * (y + 3y^3) + (1 y^2 - 9 y^4) * (y + 3y^3)'

The derivative of the first part is:

(1 y^2 - 9 y^4)' = 2y - 36y^3

Now we need to differentiate the second part using the chain rule. Let's call the inner function u:

u = y + 3y^3

Using the power rule, the derivative of u with respect to y is:

u' = 1 + 9y^2

Now we can substitute these values back into our original equation:

f'(y) = (2y - 36y^3) * (y + 3y^3) + (1 y^2 - 9 y^4) * (1 + 9y^2)

Simplifying further:

f'(y) = 2y^2 + 6y^4 - 36y^4 - 108y^6 + y^2 + 9y^4 - 9y^6 + 81y^2

Combining like terms:

f'(y) = -9y^6 - 33y^4 + 84y^2

Therefore, the derivative of f(y) is -9y^6 - 33y^4 + 84y^2.

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The number of hours it will take until the drill reaches its final depth of y feet would be (y * 24) / x.

To find the number of hours it will take for the drill to reach its final depth, we need to determine the drilling rate per hour.

Let's assume the drill can drill to a depth of x feet in one day (24 hours). Therefore, the drilling rate per hour would be:

Drilling rate per hour = Depth drilled in one day (feet) / Number of hours in one day

Now, we can calculate the drilling rate per hour:

Drilling rate per hour = x feet / 24 hours

To find the number of hours it will take to reach the final depth of y feet, we can set up the following proportion:

Drilling rate per hour = Depth drilled (feet) / Number of hours

We can rearrange this proportion to solve for the number of hours:

Number of hours = Depth drilled (feet) / Drilling rate per hour

Substituting the values we have:

Number of hours = y feet / (x feet / 24 hours)

Simplifying this expression:

Number of hours = (y * 24) / x

Therefore, the number of hours it will take until the drill reaches its final depth of y feet would be (y * 24) / x.

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The range of the picewise function is  R: [5, ∞)

Here we have a piecewise function. We can see that for x ≥ 2 we have a line with positive slope, so that part will go to ∞.

Now we need to analize the left part to find a minimum.

g(x) = x² + 5 for x < 2

The minimum there is when x = 0 (it minimizes the square part) we will get:

g(0) = 0² + 5 = 5

Then the range of the function is:

R: [5, ∞)

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In testing whether each individual independent variable (xs) in a multiple regression equation is statistically significant in explaining the dependent variable (y), one uses the t-test.

The t-test is a statistical test that helps determine the significance of each independent variable in a multiple regression model. It assesses whether the coefficient associated with each independent variable is significantly different from zero.

To perform the t-test, individual t-statistics are calculated for each independent variable. The t-statistic measures the ratio of the estimated coefficient of an independent variable to its standard error. It indicates how many standard deviations the estimated coefficient is away from zero.

The null hypothesis for each t-test states that the corresponding independent variable has no effect on the dependent variable, meaning its coefficient is equal to zero. The alternative hypothesis states that the independent variable does have a significant effect, implying that its coefficient is not equal to zero.

By comparing the calculated t-statistics with critical values from the t-distribution, one can determine whether to reject or fail to reject the null hypothesis for each independent variable. If the absolute value of the t-statistic is greater than the critical value, it indicates that the independent variable is statistically significant in explaining the dependent variable.

In summary, the t-test is utilized to assess the statistical significance of each individual independent variable in a multiple regression equation. It helps determine whether the coefficients associated with the independent variables are significantly different from zero, indicating their impact on the dependent variable.

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Answer:

700 hamburguesas....

The value of a = 11

What is complex numbers ?

Let  a + i b = (a,b)

       c + i d = (c , d)

the distance between two points = \(\sqrt{( a - c)^{2} + (b -d )^{2} }\)

put values in the formula -

\(\sqrt{(a- (-9))^{2} + (3 - 24 )^{2} }\) = 29

square both sides

\({(a + 9)^{2} + (21)^{2} } = 29^{2}\)

(a + 9)² = 841 - 441 ⇒ 400

(a + 9) = √400 = + 20

a =  +20 -9

So,  a = -29  or 11

Therefore, the value of a = 11

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Answer:

log (\(x^{6}\)\((x-8)^{5}\)

Step-by-step explanation:

Using the rules of logarithms

log \(x^{n}\) ⇔ nlog x

log x + log y = log(xy)

Given

6 log x + 5log(x - 8)

= log\(x^{6}\) + log\((x-8)^{5}\)

= log (\(x^{6}\)\((x-8)^{5}\) )

Answer:

d) on edge

Step-by-step explanation:

have a nice day :)

Answer:

(-3, 1.5)

Step-by-step explanation:

-8 +5 = -3

2 + -2 = 1.5

Answer:

A) 5/4

Step-by-step explanation:

The probability that the risk level is 0 irrespective of the applicant's marital status is 0.6.

The given information states that 60% of loan applicants were classified as low risk (risk level 0), and 40% were classified as high risk (risk level 1). Therefore, the probability of an applicant being classified as low risk is 0.6, and the probability of being classified as high risk is 0.4.

The question asks for the probability that an applicant is classified as low risk regardless of their marital status. This means that the probability is not affected by whether the applicant is married or not.

Since we know that the probability of an applicant being classified as low risk is 0.6, and this probability is not affected by their marital status, the answer to the question is simply 0.6.

In other words, regardless of whether an applicant is married or not, there is a 60% chance that they will be classified as low risk.

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Complete question is:

In a study, 60% of loan applicants were classified as low risk (risk level 0), while 40% were classified as high risk (risk level 1). And 40%of loan applicants were classified as low risk and married and 30% of loan applicants were classified as high risk and married. What is the probability that an applicant is classified as low risk (risk level 0) regardless of their marital status?

Answer: the answer is C $1932.12

Step-by-step explanation:

AP3X

The money you have to invested in total after 1 year $1932.12​, the correct option is D.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

APR= 7.5%

Invest=$2000

Now,

We can use the formula for the future value of an annuity to find the amount we need to invest each month to have a total of $2000 at the end of the year:

FV = PMT × [(1 + r/n)^(n*t) - 1]/(r/n)

where:

FV = future value = $2000

PMT = monthly payment (unknown)

r = annual interest rate = 7.5% = 0.075

n = number of times interest is compounded per year = 12 (compounded monthly)

t = time in years = 1

Substituting the given values into the formula, we have:

2000 = PMT × [(1 + 0.075/12)^(12*1) - 1]/(0.075/12)

Simplifying this equation, we get:

PMT = 2000 × (0.075/12) / [(1 + 0.075/12)^(12*1) - 1]

PMT ≈ $173.46

we need to invest approximately $173.46 each month for a year to have a total of $2000 at the end of the year. The total amount invested will be:

Total amount invested = 12 × $173.46 ≈ $1932.12

Therefore, by the given interest answer will be $1932.12

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To find a plane containing the point (-5, 6, -6) and the line defined by parametric equations x(t) = 7 - 5t, y(t) = 3 - 6t, and z(t) = -6 - 6t, we can use the point-normal form of the equation of a plane.

The equation of a plane in point-normal form is given by Ax + By + Cz + D = 0, where (A, B, C) is the normal vector to the plane, and (x, y, z) are the coordinates of a point on the plane. We can determine the normal vector by taking the cross product of two direction vectors in the plane.

The direction vector of the line can be obtained by taking the coefficients of t in the parametric equations, which gives us (-5, -6, -6). We can choose any two non-parallel direction vectors in the plane, for example, (1, 0, 0) and (0, 1, 0). Taking the cross product of these two vectors, we get the normal vector (0, 0, -1).

Now, we can substitute the values of the point (-5, 6, -6) and the normal vector (0, 0, -1) into the point-normal form equation. This gives us 0*(-5) + 0*6 + (-1)*(-6) + D = 0, which simplifies to D = -6. Thus, the equation of the plane containing the point (-5, 6, -6) and the given line is 0*x + 0*y - z - 6 = 0, or simply -z - 6 = 0.

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Answer:

the answer is 5

Step-by-step explanation:

are you doing test

Answer:

x = 64

Step-by-step explanation:

The interior angles of a triangle add up to 180 degrees, so the missing angle in the triangle on the right has an angle measurement of 180 - 47 - 81 = 52 degrees.

Since the angle and the rightmost angle in the triangle on the right are vertical angles. They are congruent.

Finally, since the triangle on the left is an isosceles triangle and the base angles, the angles on the top left and bottom left, are congruent and therefore their angle measures are both x degrees. So, 2x + 52 = 180 and x = 64.

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

The value of ∠A is 62° ⇒ c

The value of ∠B is 54°⇒ d

Step-by-step explanation:

In a triangle, the measure of an exterior angle at a vertex of the triangle equals the sum of the measures of the two opposite interior angles to this vertex.

In Δ ABC

∵ The measure of the exterior angle at the vertex C = 116°

∵ The opposite interior angles to vertex C are ∠A and ∠B

∵ m∠A = (3x - 13)°

∵ m∠B = (2x + 4)°

→ By using the rule above

∴ (3x - 13) + (2x + 4) = 116

→ Add the like terms in the left side

∵ (3x + 2x) + (-13 + 4) = 116

∴ 5x + -9 = 116

∴ 5x - 9 = 116

→ Add 9 to both sides

∵ 5x - 9 + 9 = 116 + 9

∴ 5x = 125

→ Divide both sides by 5

∴ x = 25

→ To find the measures of angle A and B substitute x in their

   measures by 25

∵ m∠A = 3(25) - 13 = 75 - 13

∴ m∠A = 62°

∴ The value of ∠A is 62°

∵ m∠B = 2(25) + 4 = 50 + 4

∴ m∠B = 54°

∴ The value of ∠B is 54°

Answer:

The answer is below

Step-by-step explanation:

The question is not complete, the correct question is:

The length of a rectangular room is 9 less than four times the width,  w , of the room. What expression represents the area of the room? How can the expression be rewritten as a polynomial in standard form

Answer: A rectangle is a polygon that has for sides in which the opposite sides are equal. All angles in a rectangle are equal and the diagonals bisect each other. The area of a rectangle is given by the formula:

Area = Length × Width

Given that The length is 9 less than four times the width and the width is w, hence, the length is given as:

Area = 4w² - 9w

A polynomial is in standard if its terms are arranged from highest degree to lowest degree.

The polynomial in standard form is: 4w² - 9w