8: Hector’s Math test grades for the final

quarter are 89, 93, 100, 98, and 95. He has one

more test to take this quarter. All tests count

equally. What is the minimum grade Hector must

make on the last test in order to obtain an

average of at least 93?

The measure of angles of intersecting lines are solved

Given data ,

When lines intersect, two angle relationships are formed:

Opposite angles are congruent

Adjacent angles are supplementary

a)

The total measure of angles = 90°

So , ( x + 16 )° + ( 3x + 2 )° = 90°

On simplifying , we get

4x + 18 = 90

Subtracting 18 on both sides , we get

4x = 72

Divide by 4 on both sides , we get

x = 18

Therefore , the angles are solved

b)

The angles on a straight line is supplementary = 180°

So , 3x° + 84° = 180°

Subtracting 84° on both sides , we get

3x = 96°

Divide by 3 on both sides , we get

x = 32

Therefore , the angles are solved

c)

The angles on a straight line is supplementary = 180°

So , ( 6x + 3)° + 87° = 180°

Subtracting 87° on both sides , we get

( 6x + 3)° = 93°

Subtracting 3 on both sides , we get

6x = 90

Divide by 6 on both sides , we get

x = 15

Therefore , the angles are solved

d)

The Opposite angles are congruent

So , 63° = 4x + 3

Subtracting 3 on both sides , we get

4x = 60

x = 15

Hence , the angles of intersecting lines are solved

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A)The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

B) The probability of at least two buses arriving in the next 2 hours is =0.865

C)  The probability of no buses arriving in the next 2 hours is =0.135

d) The probability that it will be between 30 and 90 minutes before the next bus arrives is ,0.185

a) Let \($X$\) be the number of buses that arrive in a 2-hour period. Since the time between arrivals of buses follows an exponential distribution with a mean of 60 minutes, the arrival rate λ is given by\($\lambda=1 / 60$\) 0 buses per minute.

Therefore, the number of buses that arrive in a 2-hour period is a Poisson distribution with parameter \(\mu=\lambda t=(1 / 60) \times 120=2$.\). Thus, X has a Poisson distribution with parameter μ = 2.

The probability of exactly four buses arriving in the next 2 hours is\($P(X=4)=e^{\wedge}(-2)\left(2^{\wedge} 4 / 4 !\right)=0.090$\) ≈ 0.090.

b) The probability of at least two buses arriving in the next 2 hours is

\($P(X \geq 2)=1-P(X=0)-P(X=1)=1-e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)-e^{\wedge}(-2)\left(2^{\wedge} 1 / 1 !\right)=0.865$.\)

c) The probability of no buses arriving in the next 2 hours is

\(P(X=0)=$ $e^{\wedge}(-2)\left(2^{\wedge} 0 / 0 !\right)=0.135$\)

d) Let Y be the time between the first and second bus arrivals. Then Y follows an exponential distribution with a mean of 60 minutes. We want to find the probability that \($30 \leq Y \leq 90$\).

This is equivalent to finding \(P(Y \leq$ $90)-P(Y \leq 30)$,\), which is equal to F(90) - F(30), where F is the cumulative distribution function of the exponential distribution with \($\lambda=1 / 60$\)

Therefore, the probability that it will be between 30 and 90 minutes before the next bus arrives is\(F(90)-F(30)=\left(1-e^{\wedge}(-90 / 60)\right)-(1$ $\left.e^{\wedge}(-30 / 60)\right)=e^{\wedge}(-1.5)-e^{\wedge}(-0.5)=0.185$\)

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The probability that the vehicle Bob chooses is new or is a car is \(\frac{31}{37}\)

To determine the probability that the vehicle Bob chooses is new or is a car at Bob's Auto Plaza, follow these steps:

1. Calculate the total number of vehicles:
  15 new cars + 7 used cars + 9 new trucks + 6 used trucks = 37 vehicles

2. Calculate the number of new vehicles:
  15 new cars + 9 new trucks = 24 new vehicles

3. Calculate the number of cars (both new and used):
  15 new cars + 7 used cars = 22 cars

4. Since we have already counted the new cars in both categories, we need to subtract the number of new cars once to avoid double counting:
  24 new vehicles + 22 cars - 15 new cars = 31 vehicles that are either new or cars

5. Finally, calculate the probability:
  Probability = (number of vehicles that are new or cars) / (total number of vehicles)
  \(Probability = \frac{31}{37}\)

So, the probability that the vehicle Bob chooses is new or is a car is \(\frac{31}{37}\)  .

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The transformations that make a rhombus onto itself are rotation by 180 degrees, reflection across its axes, and translation along parallel lines.

To make a rhombus onto itself, we need to apply a combination of transformations that preserve the shape and size of the rhombus. The transformations that achieve this are:

Translation:

A translation is a transformation that moves every point of an object by the same distance and direction. To maintain the rhombus shape, we can translate it along a straight line without rotating or distorting it.

Rotation:

A rotation is a transformation that rotates an object around a fixed point called the center of rotation. For a rhombus to map onto itself, the rotation angle must be a multiple of 180 degrees since opposite sides of a rhombus are parallel.

Reflection:

A reflection is a transformation that flips an object over a line, creating a mirror image. To preserve the rhombus shape, the reflection line should be a symmetry axis of the rhombus, passing through its opposite vertices.

By applying a combination of translations, rotations, and reflections along the proper axes, we can achieve the desired result of making a rhombus onto itself.

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the unit normal vector to the curve with vector equation \vec r \, (t) =<1^t,\ln(4/t^2), \, \ln(e/(t^4)) > r (t)=<1 t ,ln(4/t 2 ),ln(e/(t 4 ))> at the point where t=2t=2 is \vec n = <0,0,-1>

A unit normal vector is a normal vector with magnitude 1, and it points in the direction that is perpendicular to the tangent to the curve at a given point.

To determine the unit normal vector to a curve, it's important to find the tangent first and then find the normal. In this case, we're looking for the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2.

To find the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2, it is necessary to find the tangent to the curve and then find the normal. This is a crucial step in understanding the geometry of curves in 3D space.

To find the tangent to the curve, we'll differentiate the vector equation with respect to t and evaluate it at t = 2. The derivative of \vec r (t) is given by:

d\vec r/dt = <1, -2t^-3, -4e^-t^-4>

So the tangent to the curve at t = 2 is:

d\vec r/dt = <1, -2(2)^-3, -4e^-2^-4> = <1, 1.5, -1.648721>

Next, we'll find the normal to the tangent by taking the cross product of the tangent with a fixed vector, for example, the unit vector i = <1,0,0>. The cross product of two vectors results in a vector that is perpendicular to both of them.

The cross product of the tangent and the unit vector i is given by:

\vec T x \vec i = <1, 1.5, -1.648721> x <1,0,0> = <0,0,-1.5>

Since the magnitude of the normal is not 1, we'll normalize it by dividing it by its magnitude:

\vec n = \vec T x \vec i / ||\vec T x \vec i|| = <0,0,-1.5> / ||<0,0,-1.5>|| = <0,0,-1>

So the unit normal vector to the curve with the vector equation \vec r (t) =<1^t,\ln(4/t^2), \ln(e/(t^4)) > at the point where t = 2 is given by:

\vec n = <0,0,-1>

This is the unit normal vector that points in the direction that is perpendicular to the tangent to the curve at t = 2. The magnitude of 1 ensures that it's a unit vector and the direction points towards the normal direction.

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The formula for the given sequence is 1/(1x2)+1/(2x3)+1/(3x4)+...+1/(n(n+1)) = (n+1) [1/1! + (-1)^(n)/(n+1)!]

To find a formula for the given sequence, we can use the method of partial fractions. First, we can write each term as a fraction with a common denominator of (n+1):

1/(1x2) = (n+1)/(n+1)x1x2 = (n+1)/2!x(n+1)
1/(2x3) = (n+1)/(n+1)x2x3 = (n+1)/3!x(n+1)
1/(3x4) = (n+1)/(n+1)x3x4 = (n+1)/4!x(n+1)
...
1/(n(n+1)) = (n+1)/(n+1)xn(n+1) = (n+1)/(n+1)!x(n+1)

Then, we can add all the terms together:

1/(1x2)+1/(2x3)+1/(3x4)+...+1/(n(n+1)) = [(n+1)/2!x(n+1)] + [(n+1)/3!x(n+1)] + [(n+1)/4!x(n+1)] + ... + [(n+1)/(n+1)!x(n+1)]
= (n+1) [1/2! + 1/3! + 1/4! + ... + 1/(n+1)!]
= (n+1) [1/1! - 1/2! + 1/2! - 1/3! + 1/3! - ... + (-1)^(n)/(n+1)!]
= (n+1) [1/1! + (-1/2! + 1/2!) + (-1/3! + 1/3!) + ... + (-1)^(n)/(n+1)!]

We can simplify the terms in the brackets by noticing that every pair of adjacent terms cancels out, leaving only the first and last terms:

= (n+1) [1/1! + (-1)^(n)/(n+1)!]

Thus, the formula for the given sequence is:

1/(1x2)+1/(2x3)+1/(3x4)+...+1/(n(n+1)) = (n+1) [1/1! + (-1)^(n)/(n+1)!]

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Answer:

16

Step-by-step explanation:

If X is the centroid that means that EC is a median along with the other lines that intersect inside the triangle. Medians drawn from a triangle have a special rule; this rule is that all medians have a 2:1 ratio between the different sections of one median. For example, EC is one median with the two sections XC and EX. Therefore XC and EX have a 2:1, with the 2 representing the longer section closest to the vertex. This means that XC is double EX, so to find XC simply double EX measurement, which is 8. So XC must equal 16.

Answer:

A should be the right answer

Step-by-step explanation:

Because we are reffering to the domain the line only spans across 2 and 10. Thus making your inequality:

2<=x<=10

Answer:

c. Where the parabola changes direction

The number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

The number of calories that Darrell will burn in 1 minute while kayaking is obtained applying the proportions in the context of the problem.

For each input-output pair in the table, the constant of proportionality is of 4, hence the number of calories that Darrell will burn in 1 minute while kayaking is given as follows:

4 calories.

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Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

9514 1404 393

Answer:

Step-by-step explanation:

The ratios of side lengths in the given triangle are ...

  1 : √3 : 2 = shortest : middle length : longest

We can make the longest side match the given value if we multiply these numbers by 4√5

  y : x : 8√5 = 1(4√5) : √3(4√5) : 2(4√5) = 4√5 : 4√15 : 8√5

Then we have ...

  x = 4√15

  y = 4√5

Answer:

what do you mean

Step-by-step explanation:

The area of the region cut from the first quadrant by the cardioid is 3π/8 +1

A cardioid is a two-dimensional plane figure that has a heart-shaped curve. The equation of cardioid is r = a(1 ± sinθ) .

The area of the polar function can be calculated if the boundary condition that form the reason is given or can be found from the given information now we use the formula using the polar formula of the area as:

\(A = \int\limits^b_a {\frac{r^{2}}{2}} d\theta\)

The Area of the region cut from the first quadrant by cardioid,

\(A = \int\limits^\frac{\pi}{2}_0 {\frac{r^{2}}{2}} d\theta\)

Substituting r = 1 + sin ∅

\(A = \int\limits^\frac{\pi}{2}_0 {\frac{(1+ sin\theta)^{2}}{2}} d\theta\)

Opening square ,

\(A = \frac{1}{2}\int\limits^\frac{\pi}{2}_0 {1 +2sin\theta + sin^{2}\theta d\theta\)

=> \(A = [ \frac{1}{2} (\theta - 2cos\theta + \frac{1}{2} (\theta - \frac{1}{2}sin2\theta))]^\frac{1}{2}_{0}\)

=> 3π / 8 - (-1)

=> 3π/8 +1

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Answer:

It's the first option: -5, 1 and 4

On an annual basis, the first set of expenses (lottery tickets) is 52% of the second set of expenses (gasoline).

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To compute the annual cost of each expense, we can use the following formulas:

Annual cost of $18 a week on lottery tickets = $18 x 52 weeks = $936

Annual cost of $150 per month on gasoline = $150 x 12 months = $1800

To find the percentage of the first set of expenses (lottery tickets) relative to the second set of expenses (gasoline), we can divide the annual cost of the lottery tickets by the annual cost of gasoline and multiply by 100:

Percentage of lottery ticket expenses relative to gasoline expenses = ($936 / $1800) x 100% = 52%

Therefore, we can complete the sentence as follows: On an annual basis, the first set of expenses (lottery tickets) is 52% of the second set of expenses (gasoline).

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Therefore, it would be necessary to take the measurements in a manner that would guarantee that these requirements are met.

Two or more lines, dotted lines, or planes that remain the same distance apart and never cross, even if they are extended indefinitely in both directions, are referred to as parallel in mathematics. The sign "||" stands for parallel lines. There are many significant characteristics of parallel lines. The fact that a transversal line—a line that crosses two or more parallel lines—always forms equal angles is among the most significant.

given

If two lines are drawn, one from the highest spot on the roof to the surface and the other from the lowest point, they must be parallel to one another. Those lines must also be parallel to one another if we sketch one from the leftmost point on the roof to the surface and another from the rightmost point on the roof to the surface.

Therefore, it would be necessary to take the measurements in a manner that would guarantee that these requirements are met.

To ensure that the measurements are precise and that the roof is built at the right angle to be parallel to the road, this may require using a level or other instruments.

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The p-value is determined using the t-distribution with appropriate degrees of freedom. This allows us to assess the probability of observing a test statistic as extreme or more extreme than the calculated t-value.

The correct order of the steps to find the test statistic and evaluate a two-sample t-test with population variances equal but unknown is as follows:

Pull the sample variances.

Calculate the sample standard deviations.

Calculate the value of t.

Determine the p-value.

First, the sample variances are obtained by calculating the variance of each sample. This is done by finding the sum of squared differences between each observation and the sample mean, divided by the degrees of freedom.

Next, the sample standard deviations are calculated by taking the square root of the sample variances. This gives us a measure of the spread or variability within each sample.

The value of t is then computed using the formula: t = (mean1 - mean2) / (sqrt((s1^2 / n1) + (s2^2 / n2))), where mean1 and mean2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

The p-value helps in making a decision about the null hypothesis, such as rejecting or failing to reject it based on a predetermined significance level.

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The answer is C since the square root of 38 is about 6.1 and is the closest to the dot

The median price from the given data is 648,303.

To find the median price from the given data, we need to arrange the prices in ascending order and then locate the middle value. If there is an odd number of data points, the median will be the middle value. If there is an even number of data points, the median will be the average of the two middle values.

Let's arrange the data in ascending order:

181,386,243,922,355,008,406,791,542,820,648,303,782,200,845,053,924,494,1,089,774,1,175,704,1,274,928,1,308,954

There are a total of 13 data points, which is an odd number. So, the median price is the middle value.

The middle value is the 7th value:

Median Price = 648,303

Therefore, the median price from the given data is 648,303.

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Using a system of equations, it is found that the price of a student ticket is of $3.49.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The variables are given as follows:

Considering the revenues and the number of tickets sold, the equations are given as follows:

From the second equation:

90y = 935 - 100x

y = (935 - 100x)/90

y = 10.39 - 1.11x

Replacing in the first equation:

180x + 110y = 1345.

180x + 110(10.39 - 1.11x) = 1345

57.9x = 202.1.

x = 202.1/57.9

x = 3.49.

The price of a student ticket is of $3.49.

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Answer: 4th option (the one already selected)

Step-by-step explanation: as the X variable changes by 7 the Y variable changes by 1

Answer:

I think 334 is the answer

The LCM of 1250 and 525 is 26,250.

The HCF of 1250 and 525 is 5.

The factors of a number is the number that perfectly divides another number. For example, a factor of 30 is 3. A prime number is a number that is perfectly divisible by 1 and itself. An example of a prime number is 3. The highest common factor is the highest factor that is common to two or more numbers.

A multiple is the product of a number and another number. For example, the multiple of 3 is 15. This is because 3 multiplied by 5 is 15. The lowest common multiple is the smallest multiple that is common to two or more numbers.

Prime factors of 1250 = 2 x 5 x 5 x 5 x 5

Prime factors of 525 = 3 x 5 x 7

HCF = 5

LCM = 2 x 3 x  5 x 5 x 5 x 5 x 7 = 26,250

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Answer: x = 0.75

Step-by-step explanation:

3x+x - 3 =0

4x - 3=0

4x = 3

x = 0.75

How much tax will you pay? You will pay $25.20 worth of tax.

What is the total amount? The total amount is $340.20.

Answer:

Tax that will be paid: $25.20

Total Cost for tickets(including tax): $340.20

Step-by-step explanation:

I'm positive this is the answer.

(:

Answer:

drake saved up $150

Step-by-step explanation:

Answer:

125- 50=75, 75+75=150 so he saved $150

Answer:

x= 3126/125 or x=25.008 or as a mixed number form: x=25 and 1/125

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable.

x=25

Step-by-step explanation:

evaluate the power 125x=5^5

125=3125

divide both sides by 125

x=25

Answer:

Your other answers all look good - I think the word in the blank is producer, which means an organism that makes its own food. Green plants do so through photosynthesis.

Answer:

producer

Step-by-step explanation:

Because it makes sense