pls hurry; 10 pts The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. The second equation gives the cost of making x baseball caps. y = 8x y = -0.01 x2 + 4x + 3,200 The solution of the system is (400, 3,200). How would you interpret this solution?

Answer:

6 papers a day

Step-by-step explanation:

Answer:

Xmin: -10

Xmax: 10

Ymin: -10

Ymax: 10

Use the property of determinant det(AB) = det(A)det(B) and the fact that A and A' have the same transpose to show that det(AAT) = (det(A))^2, and then use the fact that AAT is similar to A'A to conclude that they have the same characteristic polynomial. Option C is the correct answer.

Start with det(AAT). Use the formula det(AB) = (det A)(det B) to write det(AAT) = (det A)(det A). Then use the formula AAT = EI.

We can show that A and A' have the same characteristic polynomial by showing that they have the same eigenvalues.

Let λ be an eigenvalue of A with corresponding eigenvector x. Then we have:

Ax = λx

Multiplying both sides by A' on the left, we get:

A'Ax = A'λx

Using the fact that A'A = AA' = I, we can simplify this expression to:

x = λA'x

This shows that λ is also an eigenvalue of A' with corresponding eigenvector A'x. Therefore, A and A' have the same set of eigenvalues, which means that they have the same characteristic polynomial.

To prove this using determinants, we start with det(AAT). Using the property det(AB) = (det A)(det B), we can write:

det(AAT) = det(A)det(AT)

Since det(AT) = det(A) (which can be shown using the fact that det(AT) = det(A) and the property det(AB) = det(A)det(B)), we can simplify this expression to:

det(AAT) = (det A)^2

Using the fact that AAT = EI, we can write:

det(AAT) = det(EI)

Since det(EI) = 1, we have:

(det A)^2 = 1

Taking the square root of both sides, we get:

det A = ±1

This means that A and A' have the same set of eigenvalues, which implies that they have the same characteristic polynomial.

So, the correct option is C.

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Answer:

Step-by-step explanation:

x + 8 < - 28

x < - 28 - 8

x < - 36

Option A is the correct answer

The length of the path described by the parametric equations

 is 3/2units.

We can find the length of the path described by the parametric equations x=cos³t and y=sin³t by using the arc length formula.

The arc length formula for a parametric curve given by:

x=f(t) and y=g(t) is given by:

L = ∫[a,b] √[f'(t)² + g'(t)²] dt

where f'(t) and g'(t) are the derivatives of f(t) and g(t), respectively.

In this case, we have:

x = cos³t, so x' = -3cos²t sin t

y = sin³t, so y' = 3sin²t cos t

Therefore,

f'(t)² + g'(t)² = (-3cos²t sin t)² + (3sin²t cos t)²

= 9(cos⁴t sin²t + sin⁴t cos²t)

= 9(cos²t sin²t)(cos²t + sin²t)

= 9(cos²t sin²t)

Thus, we have:

L = ∫[0,2π] √[f'(t)² + g'(t)²] dt

= ∫[0,2π] √[9(cos²t sin²t)] dt

= 3∫[0,2π] sin t cos t dt

Using the identity sin 2t = 2sin t cos t, we can rewrite the integral as:

L = 3/2 ∫[0,2π] sin 2t dt

Integrating, we get:

L = 3/2 [-1/2 cos 2t] from 0 to 2π

= 3/4 (cos 0 - cos 4π)

= 3/2

Therefore, the length of the path described by the parametric equations x=cos³t and y=sin³t is 3/2 units.

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Answer:

Junior PSAT

Training Packet

2016-17

Math Department  

Answer Key

Section 3: Math Test — No Calculator

QUESTION 1.

Choice C is correct. Subtracting 6 from each side of 5x + 6 = 10 yields 5x = 4.

Dividing both sides of 5x = 4 by 5 yields x =

_4

5

. Te value of x can now be

substituted into the expression 10x + 3, giving 10 ( _4

5 ) + 3 = 11.

Alternatively, the expression 10x + 3 can be rewritten as 2(5x + 6) − 9, and

10 can be substituted for 5x + 6, giving 2(10) − 9 = 11.

Choices A, B, and D are incorrect. Each of these choices leads to 5x + 6 ≠ 10,

contradicting the given equation, 5x + 6 = 10. For example, choice A is

incorrect because if the value of 10x + 3 were 4, then it would follow that

x = 0.1, and the value of 5x + 6 would be 6.5, not 10.

QUESTION 2.

Choice B is correct. Multiplying each side of x + y = 0 by 2 gives 2x + 2y = 0.

Ten, adding the corresponding sides of 2x + 2y = 0 and 3x − 2y = 10 gives

5x = 10. Dividing each side of 5x = 10 by 5 gives x = 2. Finally, substituting

2 for x in x + y = 0 gives 2 + y = 0, or y = −2. Terefore, the solution to the

given system of equations is (2, −2).

Alternatively, the equation x + y = 0 can be rewritten as x = −y, and substituting x for −y in 3x − 2y = 10 gives 5x = 10, or x = 2. Te value of y can then

be found in the same way as before.

Choices A, C, and D are incorrect because when the given values of x and

y are substituted into x + y = 0 and 3x − 2y = 10, either one or both of the

equations are not true. Tese answers may result from sign errors or other

computational errors.

QUESTION 3.

Choice A is correct. Te price of the job, in dollars, is calculated using

the expression 60 + 12nh, where 60 is a fxed price and 12nh depends on the

number of landscapers, n, working the job and the number of hours, h, the job

takes those n landscapers. Since nh is the total number of hours of work done

when n landscapers work h hours, the cost of the job increases by $12 for each

hour a landscaper works. Terefore, of the choices given, the best interpretation

of the number 12 is that the company charges $12 per hour for each landscaper.

Choice B is incorrect because the number of landscapers that will work each

job is represented by n in the equation, not by the number 12. Choice C is

incorrect because the price of the job increases by 12n dollars each hour,

which will not be equal to 12 dollars unless n = 1. Choice D is incorrect

because the total number of hours each landscaper works is equal to h. Te

number of hours each landscaper works in a day is not provided.

QUESTION 4.

Choice A is correct. If a polynomial expression is in the form (x)2

+ 2(x)(y) +

(y)2

, then it is equivalent to (x + y)2

. Because 9a4

+ 12a2

b2

+ 4b4

= (3a2

)2

+

2(3a2

)(2b2

) + (2b2

)2

, it can be rewritten as (3a2

+ 2b2

)2

.

Choice B is incorrect. Te expression (3a + 2b)4

is equivalent to the product

(3a + 2b)(3a + 2b)(3a + 2b)(3a + 2b). Tis product will contain the term

4(3a)3

(2b) = 216a3

b. However, the given polynomial, 9a4

+ 12a2

b2

+ 4b4

,

does not contain the term 216a3

b. Terefore, 9a4

+ 12a2

b2

+ 4b4 ≠ (3a + 2b)4

.

Choice C is incorrect. Te expression (9a2

+ 4b2

)2

is equivalent to the

product (9a2

+ 4b2

)(9a2

+ 4b2

). Tis product will contain the term (9a2

)

(9a2

Answer:

that looks hard

Step-by-step explanation:

b

Answer:

m∠CBD = 55°

Step-by-step explanation:

Angles BDA and BDC form a linear pair:

⇒ m∠BDA + m∠BDC = 180°

⇒ 80° + m∠BDC = 180°

⇒ m∠BDC = 100°

Interior angles of a triangle sum to 180°:

⇒ m∠CBD + m∠BDC + m∠DCB = 180°

⇒ m∠CBD + 100° + 25° = 180°

⇒ m∠CBD + 125° = 180°

⇒ m∠CBD = 55°

Answer:

361/50 or 7\(\frac{11}{50}\)

Step-by-step explanation:

7.22 = 722/100 = 361/50 = 7 11/50

The number 7.22 can be written using the fraction 722/100 which is equal to 361/50 when reduced to lowest terms.

It is also equal to 7 11/50 when written as a mixed number.

You can use the following approximate value(s) for this number:

7.22 =~ 7 2/9 (if you admit an error of = 0.030779%)

361/50 =~ 7 1/4 (if you admit an error of 0.415513%)

7.22 =~ 7 (if you admit an error of -3.047091%)

Answer:

1 farmer a makes 2.40 per acre    2 farmer b makes more per acre

Step-by-step explanation:

farmer A we know 3 one thirds is 1

to find one acre multiply .80 by 3

farmer A has $2.40 per acre

farmer B

.70 multiply by 4

$2.80

There are 10 different ways to choose 3 elements from a set of 5 elements. These 10 ways are: {A,B,C}, {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E}, {A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, and {C,D,E}.

The number of subsets of size r that can be chosen from a set of n elements is denoted by nCr, and can be calculated using the formula nCr. This formula is typically referred to as the "combination formula" or the "binomial coefficient formula."

To clarify, the symbol nCr represents the number of ways to choose r elements from a set of n elements without regard to order (i.e., choosing {1,2,3} is the same as choosing {2,3,1}). The formula nCr calculates this number by dividing the total number of possible combinations by the number of redundancies (i.e., arrangements that are considered equivalent due to the lack of order).

The formula for nCr is given by:

nCr = n! / (r! * (n-r)!)

where n! represents the factorial of n (i.e., n! = n * (n-1) * (n-2) * ... * 2 * 1), and r! and (n-r)! represent the factorials of r and n-r, respectively.

For example, suppose we have a set of 5 elements (A, B, C, D, and E) and we want to know how many ways there are to choose 3 elements from this set. Using the formula above, we can calculate nCr as follows:

nCr = 5! / (3! * (5-3)!) = 5! / (3! * 2!) = (5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (2 * 1)) = 10

Therefore, there are 10 different ways to choose 3 elements from a set of 5 elements. These 10 ways are: {A,B,C}, {A,B,D}, {A,B,E}, {A,C,D}, {A,C,E}, {A,D,E}, {B,C,D}, {B,C,E}, {B,D,E}, and {C,D,E}.

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Correct question is "consider the following theorem. theorem 9.5.1: the number of subsets of size r that can be chosen from a set of n elements is denoted nCr and is given by the formula nCr"

The final rankings of the top 20 NCAA college basketball teams are an example of an Ordinal level.              

We have to identify the level of measurement for the final rankings of the top 20 NCAA college basketball teams.

Level of measurement.

The numerical data are of two types discrete and continuous.

The categorical variable is of two types nominal and ordinal.

Nominal data is non-parametric data.

Ordinal data is also non-parametric data but order or ranking plays an important role.

Ordinal data is placed into some kind of order by their position.

Ordinal data are ordered data.

Thus, the final rankings of the top 20 NCAA college basketball teams are an example of ordinal data.

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Triangle ABC and Triangle EFG are similar triangles, meaning they have the same shape but potentially different sizes.  

To compare the two triangles ABC and EFG, we need to consider their side and angle measures:

Triangle ABC:

- Side AB measures 6 units.

- Angle A measures 45 degrees.

- Angle B measures 90 degrees.

- Side BC measures 8 units.

- Angle C measures 45 degrees.

Triangle EFG:

- Side EF measures 12 units.

- Angle E measures 45 degrees.

- Angle F measures 90 degrees.

- Side FG measures 16 units.

- Angle G measures 45 degrees.

By comparing the side and angle measures of the two triangles, we can see that they are proportional. The corresponding angles are congruent (45 degrees) and the corresponding sides are in proportion (6:12 and 8:16).

Therefore, the two triangles are similar, meaning they have the same shape but potentially different sizes. They have the same angles, which indicates their shapes are identical, but the lengths of their sides are different, indicating different sizes.

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Answer:

17

Step-by-step explanation:

by the Pythagorean theorem;

8x8 + 15x15 = 289

and the root of 289 is 17

The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.

To write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method

The digit 9 in the tenths place represents 9/10 or 0.9.

The digit 9 in the hundredths place represents 9/100 or 0.09.

The digit 9 in the thousandths place represents 9/1000 or 0.009.

Thus, the fractions are

0.9 = 9/10

0.09 = 9/100

0.009 = 9/1000

The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.

The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.

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The Construction of angle equal to 65 degree is shown below with attached figure.

Geometric constructions are precise drawings of geometrical shapes, angles, and lines. We will need a pencil, a ruler (or other straight edge), and compasses to do this. Perpendicular bisector and angle bisector are the fundamental constructs.

The steps to draw angle 65 and copy of Angle:

(i) Draw ∠AOB = 65° with the help of protractor.

(ii) Draw a ray O’X.

(iii) With O as center and any radius, draw an arc cutting OA and OB at C and D respectively.

(iv) With O’ as center and with the same radius, draw an arc, cutting O’X at P.

(v) With P as center and radius equal to CD, cut the arc through P at Q.

(vi) Join O’Q and produce it to Y. Then ∠YO’X is the required angle equal to ∠AOB.

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9514 1404 393

Answer:

  55, 91

Step-by-step explanation:

The 2nd through 8th numbers in the sequence are the 2-digit numbers ...

  19, 31, 43, 55, 67, 79, 91

Of these, the ones that are composite (not prime) are ...

  55 = 5·11

  91 = 7·13

True

In a symmetrically shaped distribution of scores, regardless of whether it has one mode or two modes, the mean value tends to be similar to the median value.

When a distribution is symmetric, it means that the data is evenly distributed around the central point, resulting in a bell-shaped curve. In such cases, the mean, median, and mode are typically close to each other.

The mean is the arithmetic average of all the scores in a distribution, while the median represents the middle value when the scores are arranged in ascending or descending order. In a symmetric distribution, the mean and median are located at the exact center of the distribution.

If the distribution has only one mode, it means that there is one prominent peak or high point in the data. In this case, the mean and median will coincide with the mode and will be similar.

If the distribution has two modes, it means that there are two prominent peaks in the data, but they are symmetrical around the center. Even though there are multiple modes, the mean and median will still be similar and tend to be located between the two modes.

In summary, in symmetrically shaped distributions, regardless of the presence of one or two modes, the mean and median values are expected to be close to each other.

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Answer:

A = (1, 10)

B = (4,10)

C = (4, 14)

D = (1, 16)

Step-by-step explanation:

Okay, so first, we move, or translate the quadrilateral PQRS down -8 spaces on the graph, turning old points:

P (1, -2) = (1, -10)     Q (4, -2) = (4, - 10)     S (1, -8) = (1, -16)     and R (4, -6) = (4, -14)

Now, we need to rotate this new box into -x, y. So our new points are:

(1, -10) = (-1, 10)     (4, -10) = (-4, 10)     (1, -16) = (-1, 16)     and (4,-14) = (-4, 14)

Now we're reflecting off the y-axis, making our x change. So for our final points:

A(1, 10)   B (4,10)    D(1, 16)    and C(4, 14)

Hope this helps! Please check my math and comment wether this worked or not! :)

Answer:

hi

Step-by-step explanation:

(a) the series ∑(k=1 to ∞) gk/k! converges.method to determine whether the series converges.

to determine the convergence of the series, we can apply the ratio test. let's calculate the ratio of consecutive terms:

lim(k→∞) |g(k+1)/((k+1)!) / (gk/k!)|= lim(k→∞) |g(k+1)/gk * k!/(k+1)!|

= lim(k→∞) |g(k+1)/gk * 1/(k+1)|= lim(k→∞) |g(k+1)/gk| * lim(k→∞) 1/(k+1)

= |l| * 0 (assuming l is the limit of g(k+1)/gk as k approaches infinity)

if |l| < 1, the series converges. otherwise, if |l| > 1, the series diverges. if |l| = 1, the ratio test is inconclusive.

based on the given information, it is not explicitly stated what gk represents, so we cannot determine the exact limit l. however, the fact that gk appears as a factor in the ratio suggests that it might have a significant impact on the convergence. (b) the series ∑(k=1 to ∞) k⁸⁰ * eᵏ diverges.

explanation: to determine the convergence of the series, we can apply the limit test. let's calculate the limit of the general term:

lim(k→∞) k⁸⁰ * eᵏ= ∞ * ∞ (since eᵏ approaches infinity faster than any power of k)

= ∞

since the limit of the general term is infinity, the series diverges.

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Answer:C

Step-by-step explanation:

Answer:

step by step

Step-by-step explanation:

the answer is 7

Answer:

If two individual forces are of equal magnitude and opposite direction, then the forces are said to be balanced. An object is said to be acted upon by an unbalanced force only when there is an individual force that is not being balanced by a force of equal magnitude and in the opposite direction.

The probability that the sum of the two is even and at least one of the dice shows 5 is 1/18.

There are a total of 36 possible outcomes when you roll two dice, since each die has 6 possible outcomes.

To find the number of outcomes where the sum of the dice is even, we can divide the 36 outcomes into two groups: outcomes where the sum is even, and outcomes where the sum is odd. There are 18 even sums (2, 4, 6, 8, 10, 12) and 18 odd sums (1, 3, 5, 7, 9, 11). So the probability that the sum of the dice is even is 18/36, or 1/2.

Now, we need to find the number of outcomes where at least one of the dice shows 5. There are 4 outcomes where the first die shows 5 (5,5; 5,1; 5,2; 5,3) and 4 outcomes where the second die shows 5 (1,5; 2,5; 3,5; 4,5). There are also 4 outcomes where both dice show 5. However, we have counted each of these outcomes twice (once as an outcome where the first die shows 5, and once as an outcome where the second die shows 5). So we need to subtract these 4 outcomes from our total. This leaves us with a total of 8 outcomes where at least one of the dice shows 5.

So the probability that at least one of the dice shows 5 is 8/36, or 2/9.

Finally, we want to find the probability that the sum of the dice is even and at least one of the dice shows 5. Since these two events are independent (the fact that the sum is even does not affect the probability that one of the dice shows 5, and vice versa), we can find the probability of both events occurring by multiplying the probabilities of the individual events.

So the probability that the sum of the dice is even and at least one of the dice shows 5 is (1/2) * (2/9) = 1/18.

Therefore the answer is: 1/18.

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Answer:

19

Step-by-step explanation:

Sorry if wrong :> Hope i helped! Have a awesome day!!! You're a great hooman ^_^ Please mark brainliest !!

The length of the diagonal of the rectangle is 25cm.

The diagonal of a rectangle is the line segment that connects the two opposite vertices. It can be calculated using the Pythagorean Theorem, which states that the square of the hypotenuse (the longest side of a right triangle) is equal to   the sum of the squares of the other two sides.

In this case, the length of the two sides of the rectangle are 15cm and 20cm. To calculate the diagonal of the rectangle, we need to use the Pythagorean Theorem to solve for the hypotenuse, which is the diagonal of the rectangle.

The formula is: a² + b² = c²

Using the sides of the rectangle, we get: 15² + 20² = c²

Simplifying the equation, we get: 225 + 400 = c²

Then, we take the square root of both sides of the equation to find the length of the diagonal:

√625 = c

The length of the diagonal of the rectangle is 25cm.

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Using the z-distribution, it is found that since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.

At the null hypothesis, it is tested if the mean length of jail time is still of 2.5 years, that is:

\(H_0: \mu = 2.5\)

At the alternative hypothesis, it is tested if it has increased, that is:

\(H_1: \mu > 2.5\)

We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

The parameters are:

For this problem, the values of the parameters are: \(\overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26\)

Hence, the value of the test statistic is:

\(z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}\)

\(z = 1.7\)

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, is of \(z^{\ast} = 1.645\)

Since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.

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Answer:

36 cups of flour

Step-by-step explanation:

if 3 cups of flour=8 ounces.what about 96 onces you cross multiply

The number of cups of flour will be use if he used 96 ounces of water is 36.

Given that, a baker is making bread dough. He uses 3 cups of flour for every 8 ounces of water.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the number of cups of flour will be use if he used 96 ounces of water is x.

3:8::x:96

⇒ 8×x=96×3

⇒ 8x=288

⇒ x=288/8

⇒ x=36

Therefore, the number of cups of flour will be use if he used 96 ounces of water is 36.

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bg is equal to 12 as well given that ky = 12, we can conclude that the length of xg is also 12, since the translation moves every point the same distance.

To find the length of bg, we need to understand how a translation works.

A translation is a transformation that moves every point of a figure the same distance in the same direction.

In this case, quadrilateral cky is mapped onto quadrilateral x bgo.

Given that ky = 12, we can conclude that the length of xg is also 12, since the translation moves every point the same distance.

Therefore, bg is equal to 12 as well.

In summary, bg has a length of 12 units.

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Answer and Step-by-step explanation:

We want to prove that 0.5555... = 5/9.

First, let's set 0.555... equal to x:

x = 0.555...

Now multiply this by 10:

10x = 5.555...

Now subtract the original from this new one:

   10x = 5.555...

-       x = 0.555...

______________

     9x = 5

Note that we could cancel all the recurring terms because they were the same for both 5.555... and 0.555... since the 5's go up to infinity.

We now have 9x = 5, so divide both sides by 9:

x = 5/9, as desired