Lindsey earns $15 per hour for the first 40 hours she works in a week and 50% more for every hour over 40. How many hours did Lindsey work in a week when she was paid $937.50 before taxes?


A. 15 hours
B. 30 hours
C. 40 hours
D. 45 hours
E. 55 hours​

The inflection point of f(t) is approximately t = 3.73.

(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.

Taking the derivative of f(t), we have:

f'(t) = -1.275t^2 + 9.516t + 6.741

To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:

-1.275t^2 + 9.516t + 6.741 = 0

Using the quadratic formula, we find two possible values for t:

t ≈ 0.94 and t ≈ 6.02

Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).

For t < 0.94, choose t = 0:

f'(0) = 6.741 > 0

For 0.94 < t < 6.02, choose t = 1:

f'(1) ≈ 14.982 > 0

For t > 6.02, choose t = 7:

f'(7) ≈ -5.325 < 0

From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).

(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.

Taking the second derivative of f(t), we have:

f''(t) = -2.55t + 9.516

Setting f''(t) = 0 and solving for t, we find:

-2.55t + 9.516 = 0

t ≈ 3.73

Therefore, The inflection point of f(t) is approximately t = 3.73.

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Answer:

just a guess I would say 70cm squared.

Answer:

\(\frac{27}{2} +9\sqrt{2}\); 26.22792

Step-by-step explanation:

Assuming you mean find the value of \(3x+\frac{1}{2}(3x)\) (please format your question correctly)...

The question has told you the x value or rather some numerical values. Just like for every other equation, replace x with its numerical value.

\(3(3+\sqrt{8})+\frac{1}{2}(3(3+\sqrt{8} ))\)

This question is best suited to use a calculator as doing this on paper is absolutely necessary.

Putting this in the calculator you should get: \(\frac{27}{2} +9\sqrt{2}\) or 26.22792

Answer: The equation of the line that passes through the point negative -5, 7 and has a slope of -2/5 is y = -0.4x + 5.

The correct option for the number of terms in the polynomial is option A. It can be obtained by converting all the given polynomial into Simplified form.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. Consider the example which only depeds on x is \(x^3-3x +5\).

What is simplified form of a polynomial?

A polynomial can be simplified by combining like terms and then writing the terms in descending order of the exponent.

Consider the given expression.

\(7+3g-8\)

The power of variable for 7 and -8 are same. Hence, write the expression as follows:

\(3g-1\)

Again write as follows:

\(3g-1g^0\)

Since there are two different power of g which are g and \(g^0\). Hence, there are two terms in the expression and the correct option is A.

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A rhombus has reflectional symmetry over either of its diagonals.

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Answer:

* Substation :

Subtract y from both sides of the equation.

x=6−y

x−y=4

Replace all occurrences of x with 6−y in each equation.

6−2y=4

x=6−y

Solve for y in the first equation.

y=1

x=6−y

Replace all occurrences of y with 1 in each equation.

x=5

y=1

The solution to the system is the complete set of ordered pairs that are valid solutions. (5,1)

The result can be shown in multiple forms. Point Form: (5,1)

Equation Form: x=5,y=1

* Elimination :

Multiply each equation by the value that makes the coefficients of x opposite.

       x+y=6

(−1)⋅(x−y)=(−1)(4)

Simplify.

 x+y=6

−x+y=−4

Add the two equations together to eliminate x from the system.

   (x+y=6) + (−x+y=−4) = (2y=2)

Divide each term by 2 and simplify.

y=1

Substitute the value found for y into one of the original equations, then solve for x.

x=5

The solution to the independent system of equations can be represented as a point.

(5,1)

The result can be shown in multiple forms. Point Form:(5,1)

Equation Form: x=5,y=1

Step-by-step explanation:

* Graph

The interval within which 95 percent of all possible sample estimates will fall by chance is defined as the sample mean +/- 1.96 standard errors.

C. The sample mean +/- 1.96 standard errors.

This is known as the confidence interval, and it is calculated by taking the sample mean and adding and subtracting 1.96 times the standard error of the sample.

This range provides a level of confidence that the true population parameter falls within this range, based on the sample data.

The Central Limit Theorem is a statistical concept that explains how sample means tend to follow a normal distribution, but it is not directly related to the calculation of confidence intervals.

The lower and upper confidence boundaries refer to the endpoints of the confidence interval.

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The interval within which 95 percent of all possible sample estimates will fall by chance. The correct answer is: C. The sample mean +/- 1.96 standard errors

The interval within which 95 percent of all possible sample estimates will fall by chance is defined as the "Upper and Lower Confidence Boundaries" or "Confidence Interval." This interval is calculated based on the sample mean and standard error, with the common formula being the sample mean +/- 1.96 standard errors for a 95% confidence interval.

This interval is often referred to as the 95% confidence interval. It is calculated by taking the sample mean and adding/subtracting 1.96 times the standard error. This range represents the boundary within which 95 percent of all possible sample estimates are expected to fall by chance.

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The x and y components of acceleration are:-  \(ax = (1/k)(c(dy^2/dt^2)),- ay = c(d^2y/dt^2)\)

To find the x-component of acceleration, we need to take the second derivative of the position function with respect to time:

2 = 4kx
2v = 4kx'  (taking the derivative with respect to time)
2a = 4kx''  (taking the derivative of v with respect to time)

So the x-component of acceleration is a_x = 2kx''.

To find the y-component of acceleration, we can use the given information about the velocity along the y-axis:

v_y = 1y ct

Taking the derivative with respect to time, we get:

a_y = c

So the y-component of acceleration is simply a_y = c.
To determine the x and y components of acceleration for the given path of a particle and the component of velocity along the y-axis, we'll use the given equations and find the second derivatives with respect to time.

The path of the particle is defined by \(y^2\) = 4kx. First, differentiate this equation with respect to time (t) to find the relation between the x and y components of velocity:

(1) 2y(dy/dt) = 4k(dx/dt)

The component of velocity along the y-axis is given as vy = dy/dt = cy. Substituting this into equation (1):

(2) 2y(cy) = 4k(dx/dt)

Now, solve for dx/dt (vx):

\(vx = (1/k)(cy^2/2)\)

Next, differentiate both vx and vy with respect to time to find the x and y components of acceleration:

\(ax = d^2x/dt^2 = (1/k)(c(dy^2/dt^2))\)
\(ay = d^2y/dt^2 = c(d^2y/dt^2)\)

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Answer:

£1092.96

Step-by-step explanation:

Amount of money Brian has after 2 years

= 2(5.2% × £990) + £990

= £102.96 + £990

= £1092.96

The slope of the line passing through (-1,1) and (2,-5) is -2.

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

To find the slope of the line passing through (-1,1) and (2,-5), we can use the formula:

m = (y2 - y1)/(x2 - x1)

where m is the slope of the line, (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given coordinates, we get:

m = (-5 - 1)/(2 - (-1))

m = (-6)/(3)

m = -2

Therefore, the slope of the line passing through (-1,1) and (2,-5) is -2.

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Answer: -12

Reason: After doing some multiplication, you know that 12 x 7 is 84. But, since it's a -7, you need a -12 for it to be a positive. So, the answer is -12. Also, 84 divided by a -7 is also -12, I just did it via multiplication.

I hope this helps, and Happy Holidays! :)

the answer is C 12

the factor of 84 is 12 and 7

hence

84=-7

84 is too large to cross over to divide -7

so we bring -7 across the equals to (=) sign

doing that

-7 will become +7

84/7=12

since the minus has disappeared because -7 crosses the sign (=) it now +

so our answer is a positive figure

12

happy holidays

the volume of the prism is 450 cubic units, obtained by multiplying the number of cubes along the length, width, and height.

The volume of a prism can be calculated by multiplying the length, width, and height of the prism.

In this case, the prism is packed with 15 cubes along the length, 6 cubes along the width, and 5 cubes along the height.

To find the volume, we multiply these three measurements together.

So, the volume of the prism is:

15 cubes * 6 cubes * 5 cubes = 450 cubes.

Therefore, the volume of the prism is 450 cubic units.

the volume of the prism is 450 cubic units, obtained by multiplying the number of cubes along the length, width, and height.

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Answer:-12x

Step-by-step explanation:

just trust me on this

Check the picture below.

a) Two vectors are proportional then compa b = compa a

b) Two vectors are parallel when proja b = proja a

A vector is a mathematical object with both magnitude and direction. In this problem, we have two vectors, a and b, which are assumed to be nonzero

(a) For two vectors a and b, the dot product (also known as the scalar product or inner product) is a scalar quantity that measures the extent to which the vectors are pointing in the same direction. The dot product of two vectors is defined as

=> compa b = ||a|| ||b|| cos(θ), where ||a|| and ||b|| are the magnitudes of the vectors and θ is the angle between them.

Hence,

=> compa b = compb a

if and only if the vectors are equal or parallel, meaning they have the same direction or are pointing in opposite directions.

(b) The projection of a vector onto another vector is the vector that points in the same direction as the second vector and has the same magnitude as the component of the first vector that lies in that direction. The projection of a vector a onto a vector b is given by

=> proja b = (compa b / compb b) b.

Since the dot product is commutative, it follows that

=> proja b = proj b

if and only if the vectors are equal.

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(a) To compute the eigenvalues and eigenvectors of A, we solve the characteristic equation:

det(A - λI) = 0

where I is the identity matrix and λ is the eigenvalue. Substituting the given matrix A and simplifying, we have:

|1-λ 1 4|

|2 3-λ 2|

|3 4 2-λ| = 0

Expanding along the first row, we get:

(1-λ)[(3-λ)(2-λ) - 4(4)] - (1)[(2)(2-λ) - 4(4)] + (4)[(2)(4) - (3)(3)] = 0

Simplifying and rearranging, we obtain:

λ^3 - 6λ^2 - 5λ + 60 = 0

We can factor this polynomial as (λ-5)(λ-4)(λ+3) = 0, so the eigenvalues of A are λ₁ = 5, λ₂ = 4, and λ₃ = -3.

To find the eigenvectors corresponding to each eigenvalue, we substitute back into the equation (A - λI)x = 0 and solve for x.

For λ₁ = 5, we have:

|1-5 1 4|   |-4 1 4|

|2 3-5 2| x =| 2-2|

|3 4 2-5|   | 3 4-3|

Reducing this to row echelon form, we get:

|1 0 -4/5|   | 4/5|

|0 1 -2/5| x =|-1/5|

|0 0 0   |   |  0 |

So the eigenvector corresponding to λ₁ is x₁ = (4/5, -1/5, 1).

Similarly, for λ₂ = 4, we have:

|-3 1 4|   | 1|

| 2 -1 2| x =|-1|

| 3 4 -2|   | 0|

Reducing to row echelon form, we get:

|1 0 -2|   |2/3|

|0 1 -2| x =|-1/3|

|0 0 0 |   |  0 |

So the eigenvector corresponding to λ₂ is x₂ = (2/3, 1/3, 1).

Finally, for λ₃ = -3, we have:

|4 1 4|   |-1|

|2 6 2| x =| 0|

|3 4 5|   |-1|

Reducing to row echelon form, we get:

|1 0 -2/5|   | 1/5|

|0 1 1/5 | x =|-1/5|

|0 0 0   |   |  0 |

So the eigenvector corresponding to λ₃ is x₃ = (2/5, -1/5, 1).

Next, we compute the eigenvalues and eigenvectors of I + A. Since I is the identity matrix, the characteristic equation is:

det(I + A - λI) = det(A + (I - I) - λI) = det(A + (1-λ)I) = 0

Substituting the given matrix A and simplifying, we have:

|2-λ 1 4|

|2 4-λ

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We draw a triangle QRS with vertices shown:

After dilation with a scale factor of r = 3/2, we multiply each coordinate by 3/2 and find the new coordinates Q', R', and S', respectively.

Shown below:

Drawing Q' R' S', we have the dilated triangle graph:

The total length of craft wire used by Samantha is 10x + 9

What is the scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Let's call the length of the smaller quadrilateral's 6-centimeter side "x".

Then the length of the corresponding side in the larger quadrilateral would be 6+3=9 centimeters, since the scale factor is 3.

To find the total length of craft wire used, we need to add up the lengths of all the sides in both quadrilaterals.

The smaller quadrilateral has four sides, each with a length of x.

The larger quadrilateral also has four sides, but only one of them has a different length (9 cm), while the other three sides are simply 3 times longer than the corresponding sides in the smaller quadrilateral.

So the total length of craft wire used by Samantha is:

4x + 9 + 3x + 3x + 3x

Simplifying this expression, we get:

10x + 9

Hence,  the total length of craft wire used by Samantha is:

10x + 9

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Answer:

The answer should be 75 if i did the math right

Answer:

Step-by-step explanation:

You have to add up all the numbers, then divide by how many numbers there are. In other words it is the sum divided by the count.

So in this case it would be:

46+56+64+64+72+76+77+82+94+96+99.

And the answer for the first step is: 826.

Next Step!

826 will have to be divided by 11.

Because there are 11 numbers that had to be added.

So 826÷11=75.

Answer: because it is out of 12

Step-by-step explanation:

With a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.

To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have electrical/environmental problems, we need to have a sample of data on this issue. Let's assume that we have a random sample of 100 homes, and 20 of them were found to have electrical/environmental problems.

To calculate the lower confidence bound, we can use the formula:

Lower bound = p - zα/2 * sqrt(p * (1-p) / n)

where:

p = proportion of homes in the sample that have electrical/environmental problems = 20/100 = 0.2

zα/2 = z-score for the given confidence level of 99% = 2.576 (obtained from a standard normal distribution table or calculator)

n = sample size = 100

Plugging in these values, we get:

Lower bound = 0.2 - 2.576 * sqrt(0.2 * 0.8 / 100) = 0.083

Therefore, with a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.

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This means we can be 99% confident that the true percentage of all homes with electrical/environmental problems is

at least 17.5%.

To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have

electrical/environmental problems, you would need a sample of homes and the number of homes in the sample that

have such problems. Using this information, you could calculate the sample proportion (p-hat) of homes with

electrical/environmental problems.

Then, using a formula or calculator, you could find the lower confidence bound by subtracting the margin of error (ME)

from the sample proportion.

The margin of error can be calculated using the sample proportion, sample size, and the chosen confidence level (in

this case, 99%).

For example, if the sample proportion is 0.25 and the sample size is 100, the margin of error would be 0.075 and the

lower confidence bound would be 0.175 (0.25 - 0.075).

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Answer:

Herman is wrong.  Latoya got the better deal.

Step-by-step explanation:

Latoya bought 8 pounds of potatoes for $18.

    ► 18 / 8 = $2.25 per pound

Herman bought 6 pounds of potatoes for $15.

    ► 15 / 6 = $2.50 per pound

Cheaper per pound is better!

Answer:

the answers provided are actually wrong the answer i got was 162

Answer:

162⁰

Step-by-step explanation:

1 line =180⁰

180-18

=162⁰

Answer:

64.3738

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

5 miles is = to 8km, so, since it takes 5 times to get to 40 using 8, it would be 8x8(km). 8x8=64. If using a speed calculator, it makes some wierd numbers, just round.

The baseball team can bring 11 players to the tournament based on their budget.

An equation is an expression that shows the relationship between two or more numbers and variables. An equation is a mathematical statement that represents the equality of two things.

It is made up of two expressions, one on each side of the equal to symbol. An equation, in other words, is a statement that the values of two mathematical expressions are equal.

Let x represent the number of players the team can bring to the tournament. They rented a bus for $856.50 and budgeted $24.75 per player for meals, hence:

24.75x + 856.5 = 1128.75

x = 11

The baseball team can bring 11 players to the tournament based on their budget.

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There are 66,960 number of ways to set up a batting order of 9 players from among the 12 players on the baseball team.

To determine the number of ways to set up a batting order of 9 players from among the 12 players on a baseball team, we can use the concept of permutations.

Since the order matters in a batting order, we can use the formula for permutations.

The number of permutations of selecting 9 players from a pool of 12 players is given by:

P(12, 9) = 12! / (12 - 9)!

Calculating this, we have:

P(12, 9) = 12! / 3!

= (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4) / (3 * 2 * 1)

= 12 * 11 * 10 * 3 * 7 * 2

= 66,960

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