for a particular clothing store a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. suppose six customers are randomly selected and are mailed $10-off coupons. what is the probability that three of the customers redeem the coupon?

Therefore, the factored form of the expression is:(2x - 1)(8x + 5)

Factor pairs of80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

In question 8 This requirement is met by the pair -8 and 24.

In question9 16x² - 8x + 24x - 5

7. We can list all the pairs of numbers that multiply to -80 in order to identify all the factor pairs for this number. These are a few of the pairs:

80 and 1, 40 and 2, 20 and 5, 16 and 8, and 10

The biggest integer that divides each of two or more numbers without producing a remainder is known as the greatest common factor (GCF).

For instance, 6 is the highest number that divides both 12 and 18 without producing a residual, making it the GCF of 12 and 18.

The highest common factor (HCF) and greatest common divisor (GCD) are other names for the GCF (HCF).

8. We can seek for two values in the list from question 7 that add up to 16 in order to get the factor pair for -80 that adds to the sum of 16. This requirement is met by the pair -8 and 24.

9. Applying the answer to question 8, we can write 16x2 + 16x - 5 in its expanded form as:

16x² - 8x + 24x - 5

The terms can then be categorised as follows:

(16x² - 8x) + (24x - 5) (24x - 5)

When we take the biggest thing in common between each group, we get:8x(2x - 1) + 5(4x - 1) (4x - 1)

10. As a result, grouping can factor the enlarged form of 16x2 + 16x - 5 as follows:

8x(2x - 1) + 5(4x - 1) (4x - 1)

10. Using the enlarged form from answer 9, we may factor the formula 16x2 + 16x - 5 by grouping:

8x(2x - 1) + 5(4x - 1) (4x - 1)

We can factor it out because we can see that the common factor for both terms is (2x - 1):

(2x - 1)(8x + 5)

As a result, the expression's factored form is as follows:

(2x - 1)(8x + 5)

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Answer:

1. 16-x-x-x-x = 0

   x = 4

2. 18-y-y-y-y-y-y-y-y-y = 0

   y = 2

3. 27-x-x-x =0

   x = 9

4. 100-y-y-y-y-y-y-y-y-y-y = 0

   y = 10

The bisector of angle ∠ABC, divides the angle into two congruent angles.

ΔABD is congruent to ΔCBD, and by CPCTC, ∠ABD ≅ ∠CBD, therefore;

Reasons:

The two column proof is presented as follows;

Statement \({}\)                                         Reason

1. \(\overline{AB}\) ≅ \(\overline{BC}\) \({}\)                                       Given

D is the midpoint of \(\overline{AC}\)

2. \(\overline{AD}\) ≅ \(\overline{DC}\)   \({}\)                                    Definition of midpoint

3. \(\overline{BD}\) ≅ Reflexive property of congruency

4. ΔABD ≅ ΔCBD   \({}\)                           Side-Side-Side, Congruency Postulate

5. ∠ABD ≅ ∠CBD   \({}\)                         CPCTC

6. ∠ABD = ∠CBD     \({}\)                         Definition of congruency

7. ∠ABC = ∠ABD + ∠CBD    \({}\)             Angle addition postulate

8. \(\overline{BD}\) is bisects ∠ABC     \({}\)                 Definition of angle bisector

Reason 2.; The midpoint of the line \(\mathbf{\overline{AC}}\) is the middle of the line that is equidistant from the points A, and C, such that \(\overline{AD}\) = \(\mathbf{\overline{DC}}\), therefore;

\(\overline{AD}\) ≅ \(\overline{DC}\)  

Reason 3. \(\mathbf{\overline{BD}}\) is congruent to \(\overline{BD}\) (

Reasons 4; The Side-Side-Side, SSS, congruency postulate states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent

Reason 5; CPCTC is the acronym for Congruent Parts of Congruent Triangles are Congruent

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Answer: ima try

Step-by-step explanation: how i always do it is the second number (-2) you start for the mid point (0,0) if its -2 go down 2 if it 2 go up 2 if its 0 stay there then you go to the first number(2/3) from where you landed thats now the new start point then you go (x,y) in this equation its (2/3) so go up 2 right three but watch out for the negatives. so if it was -2/3 you would go down 2 then right 3

i hoped this helped its hard to explain but I tried

The probability of obtaining a sample mean between 4.1 and 4.11 in a random sample of size 511 is 0.

To calculate the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in a discrete uniform population with x = 2.4, we can use the properties of the sample mean and the given population.

In a discrete uniform population, all values are equally likely. Since the mean of the population is x = 2.4, it implies that each value in the population is 2.4.

The sample mean is calculated by summing all selected values and dividing by the sample size. In this case, the sample size is 511.

To find the probability, we need to calculate the cumulative distribution function (CDF) for the sample mean falling between 4.1 and 4.11.

Let's denote X as the value of each individual in the population. Since X is uniformly distributed, P(X = 2.4) = 1.

The sample mean, denoted as M, is given by M = (X1 + X2 + ... + X511) / 511.

To find the probability P(4.1 < M < 4.11), we need to calculate P(M < 4.11) - P(M < 4.1).

P(M < 4.11) = P((X1 + X2 + ... + X511) / 511 < 4.11)
           = P(X1 + X2 + ... + X511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(X1 + X2 + ... + X511 < 4.1 * 511)

Since each value of X is 2.4, we can rewrite the probabilities as:

P(M < 4.11) = P((2.4 + 2.4 + ... + 2.4) < 4.11 * 511)
           = P(2.4 * 511 < 4.11 * 511)

Similarly,
P(M < 4.1) = P(2.4 * 511 < 4.1 * 511)

Now, we can calculate the probabilities:

P(M < 4.11) = P(1224.4 < 2099.71) = 1 (since 1224.4 < 2099.71)
P(M < 4.1) = P(1224.4 < 2104.1) = 1 (since 1224.4 < 2104.1)

Finally, we can calculate the probability of the sample mean falling between 4.1 and 4.11:

P(4.1 < M < 4.11) = P(M < 4.11) - P(M < 4.1)
                 = 1 - 1
                 = 0

Therefore, the probability that a random sample of size 511, selected with replacement, will yield a sample mean between 4.1 and 4.11 in the given discrete uniform population is 0.

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Answer:

12

Step-by-step explanation:

(1/3) x  + 5 = 9

(1/3) x = 9 -5

(1/3) x = 4

Multiply both sides by 3

x = 12

Answer:

x = 12

Step-by-step explanation:

1/3x + 5 =9.

1/3x = 4,

x = 12

Answer:

Step-by-step explanation:

he height of the storage unit is equal to twice its radius (since the diameter is twice the radius), so the height is 2 x 8 = 16 feet.

The storage unit is in the shape of a cylinder, so we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height:

V = π(8^2)(16)

V = π(64)(16)

V = 3,218.69 cubic feet (rounded to two decimal places)

Therefore, the volume of the storage unit is approximately 3,218.69 cubic feet.

Answer:

The answer would be Y=10

Answer: Similar by SAS, and ABC ~ AVU

Step-by-step explanation:

AV = 77 - 66 = 11

AU = 42 - 36 = 6

6/36 = 1/6

11/66 = 1/6

Therefore, these two triangles ABC and AVU are similar by SAS similarity.

ABC ~AVU :>

The proportion of customers who require an oil change and wait for nine minutes or less is 0.07.

The information provided by the question can be used to calculate the percentage of customers who wait for nine minutes or less, and the percentage of customers who wait for nine minutes or less and require an oil change. This information can be used to find out the ratio between these two percentages, which is the percentage of customers who wait for nine minutes or less and require an oil change.

The proportion of customers who require an oil change and wait for nine minutes or less can be calculated using the following formula:

Proportion of customers who require an oil change and wait for nine minutes or less = (Number of customers who require an oil change and wait for nine minutes or less) / (Total number of customers who wait for nine minutes or less)

The number of customers who wait for nine minutes or less and require an oil change is 35. The total number of customers who wait for nine minutes or less is 500. Thus, the proportion of customers who require an oil change and wait for nine minutes or less is:

Proportion of customers who require an oil change and wait for nine minutes or less = 35/500 = 0.07 or 7%.

Thus, 7% of customers who wait for nine minutes or less require an oil change.

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Complete Question:

Using classes of 0-4, 5-9, and so on, show the proportion of customers needing an oil change who wait 9 minutes or less.

The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a 1-month period:

2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3

Answer:

2

Step-by-step explanation:

8:    2 2 2  

18:   2 9

GCF:    2

Hope it helps! Brainliest Please

Answer:

radius is 4 height is 10 volume is 167.55

Step-by-step explanation:

Expressed as fraction : \($\frac{116050}{59049}$\)

\(\begin{align*} S &= \frac{a(1-r^{n})}{1-r}= \frac{2}{3} \cdot \frac{1-\left(\frac{2}{3}\right)^{10}}{1-\frac{2}{3}}\\ & = \frac{2}{3}\cdot\frac{1-\frac{1024}{59049}}{\frac{1}{3}}=\frac{2}{3}\cdot\frac{3}{1}\cdot\frac{58025}{59049}=\frac{2\cdot58025}{59049}\\ & = \boxed{\frac{116050}{59049}}. \end{align*}\)\(S &= \frac{a(1-r^{n})}{1-r}= \frac{2}{3} \cdot \frac{1-\left(\frac{2}{3}\right)^{10}}{1-\frac{2}{3}}\\ & = \frac{2}{3}\cdot\frac{1-\frac{1024}{59049}}{\frac{1}{3}}=\frac{2}{3}\cdot\frac{3}{1}\cdot\frac{58025}{59049}=\frac{2\cdot58025}{59049}\\ & = {\frac{116050}{59049}}\)

The sum S is calculated using the formula for an infinite geometric series, which states that the sum of the series is equal to the first term divided by 1 minus the common ratio.

The first term in the series is \($\frac{2}{3}$\), and the common ratio is \($\frac{2}{3}$\), so the sum is equal to \($\frac{2}{3} \cdot \frac{1-(\frac{2}{3})^{10}}{1-\frac{2}{3}}$\)

This expression simplifies to \($\frac{2 \cdot 58025}{59049}$\), or \($\frac{116050}{59049}$\)

Complete question:

What is the value of sum \(\frac{2}{3}+\frac{2^2}{3^2}+\frac{2^3}{3^3}+ \ldots +\frac{2^{10}}{3^{10}}\)?

Express your answer as a common fraction

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Answer:

Step-by-step explanation:

finding the smallest possible distance from the line to the origin follows as

the normal vector=(-1,-2,1)

using direction vector we need to create the equation of the plane

-1(x-2)-2(y-3)+1(z+7)=0

we get;

-x+2-2y+6+z+7=0

-x-2y+z+13=0

x=2-t; y=2-3t; z=-7+t

on substituting;

-1(2-t)-2(3-2t)+1(-7+t)+13=0

-2+t-6+4t-7+t+13=0

we get;

t=1

so point is(1,1,-6)

distance from point to origin

d=\(\sqrt{(1^2+1^2+(-6)^2)}\)=\(\sqrt{38}\)

therefore

the answer is \(\sqrt{38}\)=6.16

Answer:

113.04 is our answer

Step-by-step explanation:

When finding Area the formula to do so is

radius x radius x pi

Sense we arent given radius we have to find out whats the radius but we must remember radius is just half of the diameter so since we are given diameter we will just do diameter divided by 2 so 12 ÷ 2 = 6 now that we have are radius we square it thats just a fancy way of saying multiply by itself so 6 x 6 = 36 now we multiply 36 with 3.14 So

3.14 x 36 = 113.04 So c is our answer!

Answer:

C

Step-by-step explanation:

The angle between the tangent and the radius at the point of contact = 90°

Then the angle between the radius and the chord = 90° - 65° = 25°

The triangle is isosceles ( 2 congruent radii ) the the 2 base angles are congruent, both 25° , so

x = 180° - (25 + 25)° ← sum of angles in a triangle

x = 180° - 50° = 130° → C

Answer:

C which is 130

Step-by-step explanation:

I usually don't like answering questions like this one. Sometimes as in your case, I'll do it, but you have to cut a bit of slack for me to do it. You have to assume that the nearly vertical arm of the 65 degree angle is a tangent, otherwise the question cannot be done.

All triangles have 180 degrees

25 + 25 + x = 180

50 + x = 180                        Subtract 70 from both sides

x  = 180 - 50

x = 130

Answer:

Step-by-step explanation:

Step-by-step explanation:

the second option.

you see that the steeper line has a slope of -3 (when x increases by 1 grid point, y decreases by 3 grid points, that makes the slope ratio of y/x = -3/1 = -3).

the slope is always the factor of x in an equation of

y = ax + b

the only equation provided in the answer options with slope -3 is

-y <= 3x + 4

because when we transform this into the general firm above, we need to multiply both sides by -1 (which flips the inequality symbol, by the way) :

y >= -3x - 4

there you have it. no other equation here can be transformed into this.

as a control we also look at the second equation :

-3x + 3y <= -9

3y <= 3x - 9

y <= x - 3

this has a slope of 1 (so, x and y both increase by the same amount), and the y-inteecept is -3 (the y value when x = 0). that also fits the graph.

so, it is all correct.

The radius of the circle is 21 mm

Remember that for a circle of radius R, the circumference is:

C = 2*pi*R

where pi = 3.14

Here the circumference of the circle is 131.88 mm

Replacing that value in the formula above, we will get the equation:

131.88mm = 2*3.14*R

Solving that for R we get:

R = 131.88mm/(2*3.14) = 21mm

That is the radius.

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To find the perimeter of triangle MNP, we need to find the lengths of MP, NP, and MN. Part A Answer: NP ≈ 23.04 inches;Part B Answer: The perimeter of MNP is ≈ 52.64 inches.

Since triangles LMN and MNP are similar, we have:\(NP / MN = MP / LN\).

Let x be the length of MP, which is also the length of LN. Then, we have:\(NP / x = x / 8\)

Simplifying, we get:\(NP = (x^2) / 8\)

We know that MP = x and MN = 16, so we just need to find NP in terms of x.

Using the equation above, we have:\(NP = (x^2) / 8\)

To find x, we can use the fact that the perimeter of triangle LMN is 43.2 inches. The perimeter of a triangle is the sum of the lengths of its sides, so we have:\(LM + MN + LN = 43.2\)

\(x + 16 + x = 43.2\)

\(2x + 16 = 43.2\)

\(2x = 27.2x = 13.6\)

\(NP = (13.6^2) / 8 \\=23.04 inches\)

The perimeter of triangle MNP is:

\(≈ 13.6 + 23.04 + 16\)=\(=52.64 inches\)

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Answer:

5-No

6-No

7-Yes

8-Yes

9-No

Step-by-step explanation:

5 has a repeating domain (10 is repeated in the x cord)

6 has a repeating domain (x cord) of -4 twice

7 has No repeating domains (x cord)

8 has no repeating domain

9 All of the domain repeats

We have the following equation

Since

So, we can rewrite our equation as

Then, the vertex form of our equation is:

The graph of this equation is:

The general vertex form of a quadratic equatio is:

By comparing this equation with our result, the vertex is:

From the general vertex form, we know that the axis of symmtry is given by

so, our axis of symmetry is x= -4.

The x-intercept ocurr at f(x)=0. Then, by subsituting this value into our function, we have

which leads to

which gives us two x-intercepts:

Answer:

answer C

Step-by-step explanation:

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc. The infinite line extension of a chord is a secant line, or just secant.

A diameter is also a chord.

The answer is C. 6 blocks.

Answer:

C. 6 blocks is correct. I took the test and got that right :)

Step-by-step explanation:

1) a) The symmetric equations for the line is (x - 4) / -1 = (y + 4) / 4 = (z - 8) / -3

b) XY-plane is (4/3, 20/3, 0), YZ-plane is (0, 12, -4) and XZ-plane is (3, 0, 5).

2) The equation of the plane is 16x + 4y + 8z - 42 = 0.

3) The equation of the plane is -2x - 9y - 5z = 0.

1) Symmetric Equations for the Line:

a) To find the symmetric equations for the line that passes through the point (4, -4, 8) and is parallel to the vector (-1, 4, -3), we can use the parametric form of the line and then convert it into symmetric form.

Parametric Equations:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

To convert these parametric equations into symmetric form, we eliminate the parameter 't' by setting up equations involving the ratios of differences of coordinates:

(x - 4) / -1 = (y + 4) / 4 = (z - 8) / -3

This gives us the symmetric equations for the line.

(b) Points of Intersection with Coordinate Planes:

To find the points in which the line intersects the coordinate planes, we substitute the appropriate values of coordinates into the equations of the line.

i) Intersection with XY-plane (z = 0):

Substituting z = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting z = 0, we have:

8 - 3t = 0

t = 8/3

Substituting t = 8/3 into the equations for x and y:

x = 4 - (8/3) = 4/3

y = -4 + 4(8/3) = 20/3

Therefore, the point of intersection with the XY-plane is (4/3, 20/3, 0).

ii) Intersection with YZ-plane (x = 0):

Substituting x = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting x = 0, we have:

4 - t = 0

t = 4

Substituting t = 4 into the equations for y and z:

y = -4 + 4(4) = 12

z = 8 - 3(4) = -4

Therefore, the point of intersection with the YZ-plane is (0, 12, -4).

iii) Intersection with XZ-plane (y = 0):

Substituting y = 0 into the parametric equations, we get:

x = 4 - t

y = -4 + 4t

z = 8 - 3t

Setting y = 0, we have:

-4 + 4t = 0

t = 1

Substituting t = 1 into the equations for x and z:

x = 4 - 1 = 3

z = 8 - 3(1) = 5

Therefore, the point of intersection with the XZ-plane is (3, 0, 5).

2) Equation for the Plane:

To find an equation for the plane consisting of all points equidistant from the points (-6, 4, 1) and (2, 6, 5), we can use the distance formula to set up an equation.

Let P(x, y, z) be a point on the plane.

The distance from P to (-6, 4, 1) should be equal to the distance from P to (2, 6, 5).

Using the distance formula, we have:

√[(x - (-6))² + (y - 4)² + (z - 1)²] = √[(x - 2)² + (y - 6)² + (z - 5)²]

Simplifying the equation gives:

(x + 6)² + (y - 4)² + (z - 1)² = (x - 2)² + (y - 6)² + (z - 5)²

Expanding and simplifying further:

x² + 12x + 36 + y² - 8y + 16 + z² - 2z + 1 = x² - 4x + 4 + y² - 12y + 36 + z² - 10z + 25

Rearranging the terms:

16x + 4y + 8z - 42 = 0

Therefore, the equation of the plane is 16x + 4y + 8z - 42 = 0.

3) Equation of the Plane:

To find the equation of the plane that passes through the point (-2, 1, 1) and contains the line of intersection of the planes x + y - z = 3 and 4x - y + 5z = 5, we can use the following steps:

Step 1: Find the direction vector of the line of intersection of the given planes.

To find the direction vector, we take the cross product of the normal vectors of the two planes.

The normal vector of the first plane, P1: (1, 1, -1)

The normal vector of the second plane, P2: (4, -1, 5)

The direction vector, D: P1 x P2

D = (1, 1, -1) x (4, -1, 5)

Using the cross product formula, we have:

D = ((1)(-1) - (-1)(1), (-1)(4) - (1)(5), (1)(-1) - (1)(4))

D = (-2, -9, -5)

So, the direction vector of the line of intersection is (-2, -9, -5).

Step 2: Use the point-direction form of the plane equation.

The equation of the plane passing through a given point (x0, y0, z0) with a direction vector (a, b, c) is given by:

a(x - x0) + b(y - y0) + c(z - z0) = 0

Substituting the values from the given information:

Point on the plane: (-2, 1, 1)

Direction vector: (-2, -9, -5)

The equation becomes:

(-2)(x - (-2)) + (-9)(y - 1) + (-5)(z - 1) = 0

(-2)(x + 2) - 9(y - 1) - 5(z - 1) = 0

-2x - 4 - 9y + 9 - 5z + 5 = 0

-2x - 9y - 5z = 0

Therefore, the equation of the plane is -2x - 9y - 5z = 0.

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Answer:

b = 10

Step-by-step explanation:

substitute x = 10 into the equation

b = \(\frac{2(10)^2(10-5)}{10(10)}\)

  = \(\frac{2(100)(5)}{100}\) ← cancel 100 on numerator/ denominator

 = 2(5)

 = 10