Kate has a summer job as a swim instructor to earn her college tuition. She gets paid ​$4 per hour for the first 30 hours and ​$6 per hour for each hour in the week worked over 30 hours.​ Kate's goal is to earn at least ​$144 per week. How many hours of overtime per week will she need to achieve her​ goal?

Answer:

Some key features quadratic functions have are:

Step-by-step explanation:

Answer: You could say something like this ''I think the opposite function of a quadratic function would have an inverted parabolic curve that always opens upwards, since a quadratic function can open upwards or downwards. It would also have a single maximum or minimum point, depending on the coefficient of the quadratic term, since a quadratic function has a single vertex. Finally, the opposite function would have either no real roots or two real roots with opposite signs, depending on the discriminant, since a quadratic function can have either two distinct real roots or two complex roots.''

The vector equation for the given matrices is;b = 2(1,-2,0) + (-1)(0,1,2) + 6(5,-6,8)b = (2-0-30, -4-1+36, 0-2+48)b = (-28, 31, 46)

Yes, b is a linear combination of a1, a2, and a3. The reason behind this statement is explained below.What is a linear combination?A linear combination is a sum of a group of scalars, each multiplied by a single matrix or a single vector. These coefficients are scalar multiples of the vectors in the vector space.Linear Combination of MatricesIt is defined as a scalar multiplication and addition of matrices, with the combination of the coefficients from the given equation or formula. For example, if A and B are matrices with dimensions m×n and p×q, then the linear combination is given as;ax + by, where a and b are coefficients and x and y are the matrices. Let's discuss the given matrices: a1 = (1 -2 0), a2 = (0 1 2), and a3 = (5 -6 8), and b = (2 -1 6)Step-by-step explanationThe linear combination of the given matrices can be represented by the equation below;b = c1*a1 + c2*a2 + c3*a3, where c1, c2, and c3 are the coefficients that will be multiplied by the corresponding matrices.The vector equation for the given matrices is;b = 2(1,-2,0) + (-1)(0,1,2) + 6(5,-6,8)b = (2-0-30, -4-1+36, 0-2+48)b = (-28, 31, 46)Since we have arrived at the vector b using a linear combination of a1, a2, and a3, we can conclude that b is a linear combination of a1, a2, and a3.

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bbygirl where the question

Answer:

To three decimal places, The process capability index is 0.167

Step-by-step explanation:

We have to find the process capability index,

Upper specification = 16.5 ounces,

Lowe specification = 15.5 ounces

Mean = 16.0 ounces

Standard Deviation = S = 1 ounce

process capability index = (upper specification - lower specification)/6S

process capability index = (16.5 - 15.5)/6(1)

= 1/6

Process capability index = 1/6 = 0.16666667

To 3 decimal places, we get,

Process capability index = 0.167

Answer:

\(x^{-\frac{2}{7} }\)

Step-by-step explanation:

→ Add the powers together

\(x^{\frac{3}{7} {-\frac{5}{7} }\)

→ Simplify

\(x^{-\frac{2}{7} }\)

Simplified expression is [(5b + 3)(b - 5) / (3b + 5)], with a restriction on the variable b ≠ -5/3.

We first factor each term in the numerator and denominator. Then, we cancel out any common factors between the numerators and denominators of both fractions. Lastly, we'll state any restrictions on the variables.

1. Factor each term:
[(10b² + 42b + 36)/(6b² – 2b – 60)] : [(40b + 48)/(3b² – 13b + 10)]

(10b² + 42b + 36) = 2(5b² + 21b + 18) = 2(5b + 3)(b + 6)
(6b² - 2b - 60) = 2(3b² - b - 30) = 2(3b + 5)(b - 6)
(40b + 48) = 8(5b + 6)
(3b² - 13b + 10) = (3b - 2)(b - 5)

2. Substitute the factored terms back into the expression and cancel common factors:

[2(5b + 3)(b + 6) / 2(3b + 5)(b - 6)] : [8(5b + 6) / (3b - 2)(b - 5)]

Dividing by a fraction is equivalent to multiplying by its reciprocal, so:

[2(5b + 3)(b + 6) / 2(3b + 5)(b - 6)] * [(3b - 2)(b - 5) / 8(5b + 6)]

Now, cancel out common factors:

[(5b + 3)(b - 5) / (3b + 5)]

3. State any restrictions on the variables:

The restrictions on the variables are values of b that would cause the denominator to equal zero. In this case, those values are:

3b + 5 = 0
3b = -5
b = -5/3

So, the simplified expression is [(5b + 3)(b - 5) / (3b + 5)], with a restriction on the variable b ≠ -5/3.

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the gradient of the function at the given point (18, 13, -2) is ∇f(18,13,-2) = i tan(11) + j 324i + k 324i.

Given function is w = x tan(y + z).

Let's find the gradient of the function at the given point (18, 13, -2).

Gradient of the function is given by ; ∇f(x,y,z) = i ∂f/∂x + j ∂f/∂y + k ∂f/∂z

Where i, j, and k are unit vectors in the direction of x, y, and z-axes respectively.

To find the gradient of the function, w = x tan(y + z), differentiate it partially with respect to x, y, and z.

∂f/∂x = tan(y + z)∂f/∂y = x sec²(y + z)∂f/∂z = x sec²(y + z)

Gradient of the function ∇f(x,y,z) is,

∇f(x,y,z) = i ∂f/∂x + j ∂f/∂y + k ∂f/∂z∇f(x,y,z) = i tan(y + z) + j x sec²(y + z) + k x sec²(y + z)

At the point (18, 13, -2)

Gradient of the function ∇f(18,13,-2) is,

∇f(18,13,-2) = i tan(11) + j 324 + k 324∇f(18,13,-2) = i tan(11) + j 324i + k 324i

Therefore, the gradient of the function at the given point (18, 13, -2) is ∇f(18,13,-2) = i tan(11) + j 324i + k 324i.

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Answer: 8.40 dollars worth of intrest

Step-by-step explanation:

Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.  

A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.

Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.

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Answer:

$390.99 is the price sale!

Step-by-step explanation:

The complete question is

"Segment MP is a diameter of circle O. Circle O is shown. Line segment M P is a diameter. Line segment N O is a radius. Angle N O P is 150 degrees.

Which equation can be used to find mArc M N?

mArc M N + 150 = 180, mArc M N + 150 = 360, mArc M N – 150 = 180, mArc M N – 150 = 360"

The Equation m Arc(MN) + 150  = 180 is used to find mArc MN. Thus, the correct option is A.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

It is Given:

Segment MP is the diameter of circle O. Circle O is shown.

Line segment M P is a diameter.

Line segment N O is a radius.

∠NOP = 150°

We need to Find the Equation for m Arc MN

We already know the Diameter subtends 180° as it is the half of Circle 360°

∠NOP = 150°  

∴ m(Arc NP) = 150°

The measure of an arc is the measure of its central angle

Therefore,

m Arc Diameter = 180°

m Arc(MN) + m Arc(NP)  = 180

m Arc(MN) + 150  = 180

Therefore, the Equation m Arc(MN) + 150  = 180 is used to find mArc MN.

Thus, the correct option is A.

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Hey there!

Let's make an equation

=> 9h = 144

{ Make h the subject of formula}

=> 9h = 144

=> 9h/9 = 144/9

=> h = 144/9

=> h = 16

Transformation of the parent function it represents, linear translation down 3 units.

By modifying the value of x (for example, y(x) = x + 2) or by multiplying x by a constant (for example, y(x) = 3x), you can examine the graphs of linear functions. Do not forget that y(x) = x is the linear parent function. Its most fundamental and straightforward form is this.

The graph of y = f (x - h) is translated h units to the RIGHT of the graph of the parent function if h > 0, and it is translated h units to the LEFT if h 0.

as in f(x) = ( x – 3)

The graph of y=f(x-h) is a translation of |h| units to the LEFT of the graph of the parent function if h 0; otherwise, it is a straight line.

Example: f(x) = (x + 4).

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Problem

The difference of a number and 72 is 12. Find the number.​

Solution

Let x the number of intertest and we can write this:

x-72=12

And solving for x we got:

x= 72+12= 84

it’s on the bottom ~~~

A sample size of 60 is required to estimate a population mean with a 98% confidence interval, assuming that the population standard deviation is approximately .

To calculate the required sample size to estimate a population mean with a 98% confidence interval, based on previous evidence that the population standard deviation is approximately , and a margin of error of 1.5, the following formula can be used:

n = [Z-score * (Population Standard Deviation / Margin of Error)]²

where Z-score is the critical value for a 98% confidence level, which can be found using a Z-table or a calculator.

For a 98% confidence level, the Z-score is approximately 2.33.

Substituting the values, we get:

n = [2.33 * () / 1.5]²

n = [2.33 * ] / 1.5]²

n ≈ 59.3

Rounding up to the nearest whole number, the required sample size is approximately 60.

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Answer:

Prime Factors of 72: 2, 3

Step-by-step explanation:

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

Answer:

b=7

Step-by-step explanation:

7 squared is 49, so b equals 7. I hope that was what you were looking for, and that it helps.

Part a: Cost of mattress at that speciality store: $802.2

Part b: Cost of the mattress from distributor: $772.3

Part c: Christine would pay more if she gets it at the speciality store.

For the stated question-

Market value of the mattress = $429.0

Part a:

10% by distributor.

Cost after 10% = 10%$429.0 + $429.0

Cost after 10% = $471.9

70% by speciality store.

Cost after 70% = 10%$471.9 + $471.9

Cost after 70% = $802.2

Thus, Cost of mattress at that speciality store: $802.2.

Part b:

Cristina purchased from distributor who marked it at 80%.

80% of the marked value.

Final cost = 80% of $429.0 + $429.0

Final cost = $772.2

Thus,  Cost of the mattress from distributor: $772.3

Part c: Christine pays more if she gets it at the speciality store by paying $802.2.

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Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Answer:

Question 2:

We need to find the value of x when the amount of money in both accounts is the same. This means that we need to set the two equations equal to each other and solve for x:

10x + 25 = 5x + 50

5x = 25

x = 5

Therefore, after 5 weeks, both siblings will have the same amount of money. The answer is 5 weeks.

Question 3:

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). Therefore, the slope of the line passing through (-3, -1) and (3, 8) is (8 - (-1)) / (3 - (-3)) = 9/6 = 3/2. The answer is three halves.

Question 4:

The total number of trials is 200, so the probability of getting no heads is equal to the frequency of getting tails twice, which is 35/200 = 0.175 or 17.5%. The answer is 17.5%.

Question 5:

A proportional relationship is one in which y varies directly with x, that is, y = kx where k is a constant of proportionality. The equation y = -2 is a horizontal line, which means that y does not vary with x and there is no proportional relationship. The equation y = 3x + 1 does not have a constant ratio of y to x, so it does not represent a proportional relationship. The equation y = (3/2)x and y = (1/2)x - 3 both have a constant ratio of y to x, so they represent proportional relationships. The answer is y equals three halves times x or y equals one half times x minus 3.

Question 6:

A fair, 6-sided die has four outcomes greater than 4, namely 5 and 6 on each of two rolls. The probability of getting a number greater than 4 on one roll is 2/6 = 1/3. Since the rolls are independent, the probability of getting a number greater than 4 on 45 rolls is the same as the probability of getting a head on 45 coin flips, which is approximately 0.5 x 45 = 22.5 or 23. The answer is 23.

Question 7:

To rotate a point (x, y) 90 degrees counterclockwise about the origin, we swap the x and y coordinates and negate the new x coordinate. Therefore, to rotate triangle UVW, we apply the same transformation to each of its vertices:

U' = (1, -1)

V' = (4, 0)

W' = (1, 4)

The answer is U′(1, −1), V′(4, 0), W′(1, 4).

Question 8:

The scatter plot shows a decreasing linear association. As the number of cupcakes increases, the cost per cupcake decreases. The slope of the line of best fit would be negative. The answer is there is a strong, negative linear association.

Question 9:

To rotate polygon ABCD to A′B′C′D′, we need to apply a counterclockwise rotation about the origin. To determine the angle of rotation, we can look at the change in coordinates of a point that is not the origin. For example, the point A moves from (-7, 5) to (5, 7), which is a translation of (12, 2).

The confidence level for the interval i + 2.8101Vn is approximately 99%.

The confidence level for the interval + 1.44am is not specified as we do not have enough information about the sample size or the value of the population nstandard deviation (o).

To find the value of zo in the Cl formula (7.5) that results in a confidence level of 99.7%, we need to use the standard normal distribution table. From the table, we can find that the z-value corresponding to a cumulative area of 0.9985 is approximately 2.81. Therefore, zo = 2.81.

To find the value of zo in the Cl formula (7.5) that results in a confidence level of 75%, we again need to use the standard normal distribution table. From the table, we can find that the z-value corresponding to a cumulative area of 0.875 is approximately 1.15. Therefore, zo = 1.15.

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The value "234" for the attribute "number of cases" is a metric discrete value representing a count or quantity. The step not included in the K-Means algorithm is finding the correlation coefficient between centroids and data points. Data science is the methodology for extracting knowledge from data through discovery and hypothesis formulation, utilizing software, hardware, programming, and statistics.

The value "234" for the attribute "number of cases" in a dataset is a metric discrete value. It represents a count or a quantity that can only take on integer values and has a clear numerical meaning.

The step in the K-Means algorithm that is not included is "Find the correlation coefficient between the centroid and the data points." The K-Means algorithm does not involve calculating the correlation coefficient between centroids and data points. Instead, it focuses on iteratively assigning data points to the nearest centroid and updating the centroids based on the means of the data points within each cluster.

Data science is the methodology for the empirical synthesis of useful knowledge from data through a process of discovery or hypothesis formulation. It is a field of scientific research that utilizes computer software, hardware, programming methodologies, and statistical applications to extract insights, patterns, and valuable information from data.

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The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

Answer:

by using formula of median you can do it.

Answer:

put the numbers in order

20,20,23,39,60,64,82

Find the number in the middle

39 is in the middle because there is 3 numbers on each side so it is the median.

Divide by 3.

39 / 3 = 13

Hope this helps

Step-by-step explanation:

Answer:

185 R10 (185.21)

Step-by-step explanation:

The distance that Ellie ran each afternoon is 5.5 miles for a whole week.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the distance that Ellie ran each afternoon, since she ran 24 miles, hence:

3(2.5 + x) = 24

7.5 + 3x = 24

x = 5.5 miles

The distance that Ellie ran each afternoon is 5.5 miles for a whole week.

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Answer:

⇛65,472.

Step-by-step explanation:

Given expression is 2^2^2^2 - [(2^2)^3]

⇛ 2^2^4 - [2^(2×3)]

Since (a^m)^n = a^(mn)

⇛ 2^16 - [2^6]

Since (a^m)^n = a^(mn)

⇛ 2^(10+6) - (2^6)

⇛ (2^10 × 2^6)-(2^6)

Since a^m × a^n = a^(m+n)

⇛ 2^6[(2^10)-1]

⇛ 64×(1024-1)

⇛ 64×(1023)

⇛65,472

Answer ↓

The value of the given expression is 65472.

Read more:

simplified form of ( (2^-2) )^-3 x ( (2^-3) )^2....

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