Orlando skip the rope 125 times in 45 seconds write this as a unit rate

Answer:

Step-by-step explanation:

[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]

But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.

Therefore, the monthly payment for a student loan of $15,000 at a fixed APR of 12% for 20 years is $144.36.

Interest is the cost of borrowing money or the return on investing money. When you borrow money, you usually have to pay back more than you borrowed, and the additional amount you pay is the interest. The interest rate is expressed as a percentage of the borrowed amount, and it can vary depending on factors such as the borrower's credit score, the term of the loan, and the lender's policies.

Given by the question.

Assuming the loan has a fixed interest rate of 12% per annum, the amount of interest charged each year will be:

12% of $15,000 = $1,800

The total interest charged over 20 years will be:

$1,800 x 20 = $36,000

The total amount to be repaid (principal + interest) will be:

$15,000 + $36,000 = $51,000

If the loan is being repaid in equal monthly installments over the 20-year term, the monthly payment can be calculated using the following formula:

M = P * (r[tex](1+r)^{n}[/tex]) / ([tex](1+r)^{n}[/tex]- 1)

Where:

M = Monthly payment

P = Principal amount (in this case, $15,000)

r = Monthly interest rate (12% per annum / 12 months = 1% per month)

n = Total number of payments (20 years x 12 months per year = 240)

Plugging in the values:

M = $15,000 * (0.01[tex](1+0.01)^{240}[/tex]) / ([tex](1+0.01)^{240}[/tex] - 1)

M = $144.36

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Answer:

g(x)

=6x−4

=3x

2

−2x−10

Escribe (g∘f)(x) como una expresión en términos de x.

Step-by-step explanation:

Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).

Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:

f(x) = x^2 - 2x + 1

Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:

g(f(x)) = 6f(x) - 4

= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))

= 6x^2 - 12x + 2

Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.

If λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

[tex]v^T A^T = \lambda v^T[/tex]

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

[tex]\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right][/tex]

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

[tex]v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T[/tex]

Now, for transpose of A:

[tex]A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right][/tex]

The eigen vectors are:

[tex]u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T[/tex]

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of [tex]A^T[/tex]. Show with an example that the eigenvectors of A and [tex]A^T[/tex] are not the same.

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

we have 2 possible cases for the coin and 6 possible cases for the die.

so, we have 2×6 = 12 combined possible cases :

heads, 1

heads, 2

heads, 3

heads, 4

heads, 5

heads, 6

tails, 1

tails, 2

tails, 3

tails, 4

tails, 5

tails, 6

out of these 12 cases, which ones (how many) are desired ?

all first 6 plus (tails, 3) = 7 cases

so, the correct probability is

7/12

formally that is calculated :

1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12

the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.

The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.

An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.

Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.

For the given question.

geometric mean of a and b :

From the drawn diagram.

a = 4

b = 9

x = √ab

x = √9*4

x = 6

geometric mean: 6

Applying the altitude rule:

h² = x.y

6² = 9*4

36 = 36

Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.

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Step-by-step explanation:

We have:

x = a sin 2t

Differentiating with respect to t, we get:

dx/dt = 2a cos 2t

Next, we have:

y = a(cos 2t + log tan t)

Differentiating with respect to t, we get:

dy/dt = -2a sin 2t + (1/tan t)(1/ln 10)

Using the identity:

sin^2 t + cos^2 t = 1

We have:

sin 2t = 2sin t cos t

And:

cos 2t = cos^2 t - sin^2 t

cos 2t = 2cos^2 t - 1

Using these identities, we can rewrite dx/dt and dy/dt in terms of x and y:

dx/dt = 2a sqrt(1 - x^2/a^2)

dy/dt = -2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t)

Therefore, we have:

dx/dy = dx/dt ÷ dy/dt

Substituting the expressions for dx/dt and dy/dt, we get:

dx/dy = (2a sqrt(1 - x^2/a^2)) / (-2a sqrt(1 - x^2/a^2) + (1/ln 10)(y - a cos 2t))

Simplifying, we get:

dx/dy = (-2 sqrt(1 - x^2/a^2)) / (2 sqrt(1 - x^2/a^2) - (1/ln 10)(y - a cos 2t))

The answer of the given question based on the  transformation from its parent function the explanation part is given below and The equation of the function is y = -2(x+3)².

In mathematics,  function is  relation between  set of inputs and  set of possible outputs with  property that each input is related to exactly one output. It is  rule that assigns to each input value exactly one output value. Functions can be represented in various ways, like algebraic expressions, graphs, tables, and words. They are used to model relationships between variables, to describe how one quantity depends on another, and to make predictions about future values. Functions are  important concept in many fields of mathematics, as well as in science, engineering, economics, and other areas where quantitative analysis is used.

a. The graph appears to be a reflection of the parent function f(x) = x² over the x-axis followed by a vertical stretch by a factor of 2 and a horizontal shift to the left by 3 units.

b. The equation of the function is y = -2(x+3)².

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The correct options are:

The data contain a sample of multiple individuals.

The data are collected  are approximately at  the same point in time.

Cross-sectional data sets are a type of research design used in statistical analysis. They consist of a sample of multiple individuals or entities observed at a single point in time. One of the characteristics of cross-sectional data sets is that they do not involve any observation or measurement over time, making them different from longitudinal or time-series data sets.

One advantage of cross-sectional data sets is that they are relatively easy and inexpensive to collect. It can be assumed that the data were obtained through a random sampling of the underlying population, making them representative of the larger population. However, these data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.), as the timing of data collection can impact the results.

Overall, cross-sectional data sets can provide a snapshot of a population or phenomenon at a specific point in time, making them useful for a wide range of research questions in social, economic, and political sciences.

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Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

Answer:

Step-by-step explanation:

i think it B

Answer:

A≈1.83m²

Step-by-step explanation:

Using the formulas

A=πr2C=2πr

Solving forAA=C24π=4.824·π≈1.83346m²

Answer:

1.83 (approximate)

Step-by-step explanation:

First, we need to find the radius of the circle.

Using the formula:

[tex]C=2 \pi r[/tex]

We have to reorganize terms:

[tex]r=\frac{C}{2\pi}[/tex]

[tex]\frac{4.8}{2 \times \pi}[/tex]

r ≈ 0.76

Now we have the radius and the circumference in order to find the area.

Use the formulas:

[tex]A= \pi r^2[/tex]

[tex]C=2 \pi r[/tex]

A = C^2/4[tex]\pi[/tex]  = 4.8^2 / 4 * pi = 1.83

Answer:

They are similar

Step-by-step explanation:

It's because 27/18 = 12/8

27/18 = 1.5

12/8 = 1.5

Answer:

B is correct

Step-by-step explanation:

If it is spun twice then the probability of it landing on 2 and then an odd number is:

Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)

1/49 * 4

4/49

the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.

How to solve and what is graph?

The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.

In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.

A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.

Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.

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The midline equation of the function is y = 1.5.

The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.

Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.

Using the definition of the amplitude the midline is the given amplitude.

Hence, the midline equation of the function is y = 1.5.

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Answer:

3

Step-by-step explanation:

Khan Academy

The area to the right of x is 0.877.

In a normal distribution, the entire area under the curve is identical to 1. The area to the left of a specific value of x represents the possibility of observing a value largely lesser than or same tox.

However, we're capable to discover the area to the right of x with the aid of abating the left area from 1, If the place to the left of x is given.

In this case, the area to the left of x is 0.123. thus, the place to the right of x is

1-0.123 = 0.877

Thus, the area is 0.877 to the right of x.

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The value οf the given angle x = 39.8 degree

Trigοnοmetry uses six fundamental trigοnοmetric οperatiοns. Trigοnοmetric ratiοs describe these οperatiοns. The sine functiοn, cοsine functiοn, secant functiοn, cο-secant functiοn, tangent functiοn, and cο-tangent functiοn are the six fundamental trigοnοmetric functiοns.

The ratiο οf sides οf a right-angled triangle is the basis fοr trigοnοmetric functiοns and identities. Using trigοnοmetric fοrmulas, the sine, cοsine, tangent, secant, and cοtangent values are calculated fοr the perpendicular side, hypοtenuse, and base οf a right triangle.

In the figure tanx = p/h

[tex]x = tan^{-1(15/18)}[/tex]

x = 39.8

Hence the value οf the given angle x = 39.8 degree

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Parallelogram (Opposite sides have the same length). Parallelogram (Area is one-half the base times the height). Parallelogram (Opposite sides are parallel). Parallelogram (Angles can be right angles)

According to the parallelogram law, the sum of the squares of a parallelogram's four sides is equal to the sum of the squares of its two diagonals. It is essential for the parallelogram to have equal opposite sides in Euclidean geometry.

A parallelogram is a particular sort of polygon. It is a quadrilateral in which the opposite side pairs are parallel to one another. There are six crucial parallelogram characteristics to be aware of: Congruent sides are those when AB = DC.

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Neither anushka nor lukas are correct as both of their calculations are wrong.

Basic arithmetic operations like addition, subtraction, multiplication, and division are used to isolate the variable on one side of a linear equation and solve it. The objective is to make the equation as simple as possible until the variable can be identified and its value calculated. In order to solve a linear equation, you must first combine like terms to simplify the expressions on both sides of the problem.

Then, you can use inverse operations to get rid of constants and coefficients. The value of the variable can be ascertained by solving for it once it has been isolated. By looking at the coefficients and constants of the equation, it can be established if the equation has no solution or infinite solutions. In various disciplines, such as science, engineering, and finance, linear equations are used to represent connections between variables.

2/5b + 1 = -11

2/5b = -12

b= -12 x 5/2

b = -30

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The required answers are 80.8, 79,and g(42) > f(42).

Part A:

To determine the test average for the math class after completing test 2, we need to evaluate the function f(x) at x=2. That is,

[tex]$$f(2) = 0.9(2) + 79 = 80.8$$[/tex]

Therefore, the test average for the math class after completing test 2 is 80.8.

Part B:

To determine the test average for the science class after completing test 2, we need to find the equation of the linear function g(x) that passes through the given points (1,78) and (2,79). The slope of the line passing through these points is

[tex]$m=\frac{y_2-y_1}{x_2-x_1}=\frac{79-78}{2-1}=1$$[/tex]

We can use the point-slope form of a line to find the equation of the line passing through the point (1,78) with slope m=1. That is,

[tex]$$y-78 = 1(x-1)$$[/tex]

Simplifying, we get

y = x + 77

Therefore, the test average for the science class after completing test 2 is

g(2) = 2 + 77 = 79

Part C:

To determine which class had a higher average after completing test 42, we need to evaluate f(42) and g(42) and compare the results. We have

[tex]$$f(42) = 0.9(42) + 79 = 117.8$$[/tex]

To find (42), we need to extend the linear function g(x) beyond the given data points by assuming that the function is linear and continues with the same slope m=1. That is,

g(x) = x + 77

for all [tex]$x\geq 1$[/tex]. Therefore,

[tex]$$g(42) = 42 + 77 = 119$$[/tex]

Since g(42) > f(42), we conclude that the science class had a higher average after completing test 42.

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Answer: 66

Step-by-step explanation:

all 3 of them should equal to 180

so 79+35 is 114

180-114 will give us the answer which is 66

Answer:

159 proper subsets.

Step-by-step explanation:

Given a set {2, 4, 6, 8...100}, how many proper subsets are there?

First, find how many subsets there are in 2 - 10:

That's 16.

Then because there are 10 10s in 100, multiply by 10:

16 x 10 = 160

Finally, because it says proper subsets, subtract by 1:

160 - 1 = 159 proper subsets.

Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}

Answer:

Step-by-step explanation:

its 60

Answer:

................................

Because g(x) is continuous on the interval, we can see that the correct option is the last one (counting from the top)

Here we have the function g(x), and we know that it is continuous on the interval [1, 6], and that:

g(1) = 18

g(6) = 11

If it is continuous, then g(x) covers all the values between 18 and 11 in the given interval, this means that there must exist a value c in the given interval such that when we evaluat g(x) in that value c, we get the outcome 12, and we know this by the intermediate value theorem.

So the correct optionis the last one.

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Answer: -3/2

Step-by-step explanation:

FIrst rearrange the equation in y = mx + b form.

4x - 6y = -24

-6y = -4x - 24

y = 2/3x + 4

If the line is perpendicular, the slope must be the negative reciprocal of the current line.

The negative reciprocal of 2/3 is -3/2.

The horizontal line at $7.25 on the y-axis of the graph is the one with a slope that most accurately depicts the federal minimum wage of $7.25 per hour as of January 1, 2014.

Although it varies from state to state, the federally mandated minimum wage in the United States is $7.25 per hour. The District of Columbia had the highest minimum wage in the US as of January 1, 2023, at 16.50 dollars per hour.

The variable dearness allowance (VDA) component, which takes into account inflationary trends, such as an increase or fall in the Consumer Price Index (CPI), and, if applicable, the housing rent, are included in the computation of the monthly minimum salary.

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Answer:

To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:

∫[a,b] f(x) dx = F(b) - F(a)

where F(x) is the antiderivative of f(x).

First, we find the antiderivative of f(x):

F(x) = x^2 + (5/3)x + C

where C is the constant of integration.

Next, we evaluate F(5) and F(0):

F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C

F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C

Subtracting F(0) from F(5), we get:

∫[0,5] f(x) dx = F(5) - F(0)

= 25 + (25/3) + C - C

= 25 + (25/3)

= 100/3

Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.