The expression √52+√117 is equivalent to

F. 13

G. 5 √13

H. 6 √13

J. 13 √13

(a) The expression cos⁻¹(√2 / 2) evaluates to π/4 radians. (b) The expression cos⁻¹(0) evaluates to π/2 radians.

(a) To evaluate cos⁻¹(√2 / 2), we need to find the angle whose cosine is equal to √2 / 2. From the unit circle or trigonometric identities, we know that this corresponds to an angle of π/4 radians.

So, cos⁻¹(√2 / 2) = π/4

(b) To evaluate cos^⁻¹(0), we need to find the angle whose cosine is equal to 0. From the unit circle or trigonometric identities, we know that this corresponds to an angle of π/2 radians.

So, cos⁻¹(0) = π/2

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Addie measured her height on her 5th birthday, she was 44 4/5 inches tall. Each year, Addies grew 2/5 inch.  Addie height on her 12th birthday is 47 2/5 inches.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and understand mathematical relationships. In algebra, variables are used to represent unknown values, and equations are used to express relationships between these variables.

Algebra involves the use of mathematical operations such as addition, subtraction, multiplication, and division, as well as the use of exponents, logarithms, and other advanced mathematical concepts. Algebraic equations can be solved using various methods, such as substitution, elimination, and graphing.

Algebra has numerous practical applications in various fields, including science, engineering, economics, and finance. It is used to model and solve real-world problems, analyze data, and make predictions. Algebra is also an essential foundation for more advanced mathematical topics, such as calculus, linear algebra, and abstract algebra.

Addie was 44 4/5 inches tall on her 5th birthday. From her 5th to 12th birthday, she grew for 7 years, so her height increased by 7 * (2/5) = 2.8 inches.

Adding this to her height on her 5th birthday, we get:

44 4/5 + 2.8 = 47 2/5

Therefore, Addie was 47 2/5 inches tall on her 12th birthday.

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Answer:

im not sure the answer choices but heres what I found:" In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer. "-wikipidia

Step-by-step explanation:

For number 1 it's either 3 or 4 because it only goes up to like six and it needs to go up to 10 and the bottoms are 5 and 10 + 5 = 15

Answer:

Step-by-step explanation:

The slope of the line that passes through the given points (2, 12) and (6, 11) is -1/4.

The standard parametric equations for the line passing through points P and Q is \($\begin{cases} x = -6 + 2t \ y = 8 - 7t \ z = 1 + 2t \end{cases}$\) .

To find the standard parametric equations for the line passing through points P(-6, 8, 1) and Q(-4, 1, 3), we first need to find the direction vector of the line. This can be done by subtracting the coordinates of point P from the coordinates of point Q:

\($\vec{PQ} = \begin{pmatrix}-4 \ 1 \ 3\end{pmatrix} - \begin{pmatrix}-6 \ 8 \ 1\end{pmatrix} = \begin{pmatrix}2 \ -7 \ 2\end{pmatrix}$\)

Now we can write the parametric equations in the form:

\($\begin{cases} x = x_0 + at \ y = y_0 + bt \ z = z_0 + ct \end{cases}$\)

where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.

We can choose either point P or Q as the point on the line. Let's use point P. So we have:

\($\begin{cases} x = -6 + 2t \ y = 8 - 7t \ z = 1 + 2t \end{cases}$\)

These are the standard parametric equations for the line passing through points P and Q.

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Answer:

need more information to answer for you.

Step-by-step explanation:

Answer:

continuous random variable

The equation which can be used to represent each situation, in terms of x, is;

A = 80 + 2x

B = 45 + 3x

The interval of miles driven, x, for which Company A is cheaper than Company B is when x = 35 miles

Let

Company A:

A = 80 + 2x

Company B:

B = 45 + 3x

Company B > Company A:

45 + 3x > 80 + 2x

collect like terms

3x - 2x > 80 - 45

x > 35

In conclusion, the interval of miles driven, x, for which Company A is cheaper than Company B is 35 miles.

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Answer:

{5, 6, 7}

Step-by-step explanation:

The domain is the input values

The input values are the x values

{5, 6, 7}

Regression lines can be used to visually represent the relationship between the independent( x) and dependent( y) variables on a chart. This is point C

Point C represents the residual of the circled point in Graph 1.

The regression line is occasionally called the" best-fit line" because it's the line that stylish fits through the points. This is the line that minimizes the gap between factual results and anticipated results.

There are two charts:

In graph 1, one point is circled.

The five points labeled A, B, C, D and E can be set up in Graph 2.

Find which point on path 2 represents the remainder of the circled point on path 1

Point C represents the remainder of the circled point in Graph 1

Question

fiber diameter and fleece weight data were collected from a sample of 20 lamb. The data is presented in the graphs below. The plot is a scatterplot of pile weight versus fiber periphery, with the corresponding least places regression line indicated. Map 2 is a identified plot of residuals versus prognosticated values. Map 1 chief Weight 35 40 30 Fiber Periphery Map 2 Fiber Periphery Map 2 Remaining chief Weight 1. D 7 8 9 10 11 12 Anticipated chief Weight 13 14 15 A point is filled in the map and the points marked with ABC are displayed in the map 2 which represents the graph the rest of the circled point on the graph? Peille coat weight In Diagram 1, one point is circled. Five points, labeled A, B, C, D, and E, are linked in map

2 Which point on Chart 2 is the residual for the circled point on Chart 1?

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Answer:

Step-by-step explanation:

8. 7.5 Goes up by 2.5.

9. 7.3 Goes down by 2.1

10. 116/3

Answer:

8- 7.5

9-7.3

10-38 \(\frac{2}{3}\)

Step-by-step explanation:

The statement ''the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n.'' is false because the symbol "μ ˆ p" does not represent the proportion of a sample of size n.

In statistical notation, the symbol "μ ˆ p" typically represents the sample proportion, which is an estimate of the population proportion. The sample proportion is obtained by dividing the number of occurrences of a specific event in the sample by the sample size.

On the other hand, the population proportion, denoted by "p," represents the proportion of the entire population that exhibits a certain characteristic or has a specific attribute.

The symbol "μ ˆ p" could be a typographical error or a confusion between different symbols used in statistics. The correct symbol to represent the sample proportion is usually denoted as "p ˆ" or "p-hat." The symbol "μ" typically represents the population mean.

Therefore, it is incorrect to state that "μ ˆ p" represents the proportion of a sample of size n.

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Julia must sell 21 tacos to meet the requirement .

Given: Price of each taco = $ 3.75

Price of each burrito = $ 6

Total amount of money she needs to earn = $ 330

Also the number of burritos sold= 42.

So the total amount earned on selling these burritos= 42× 6 = $ 252

And as it is given that total money she needs to earn is $ 330 .

so required money= $ 330- $ 252

=$ 78

Thus the total number of tacos she needs to sell = 78/ price of 1 taco

= 78/ 3.75

= 20.8 ≈ 21

Thus Julia must sell 21 tacos to meet the requirement .

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(a) Since the sample size is large (n=105) and the population standard deviation is known, we can use a z-test.

The test statistic is calculated as:

z = (x - μ) / (σ / sqrt(n))

where x is the sample mean, μ is the hypothesized population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values given in the problem, we get:

z = (16 - 15.8) / (1.1 / sqrt(105)) ≈ 1.35

So the test statistic is z = 1.35.

(b) Since the sample size is small (n=20) and the population standard deviation is unknown, we can use a t-test.

The test statistic is calculated as:

t = (x - μ) / (s / sqrt(n))

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values given in the problem, we get:

t = (16 - 15.8) / (1.4 / sqrt(20)) ≈ 0.76

So the test statistic is t = 0.76.

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Note that the system of linear inequalities represents Jackson's workout are given as follow:

1) The system of equations are:

x ≤ 45

xy ≥ 400

6.9 ≤ y ≤ 10.4


2) Where  x: the number of minutes Jackson spends exercising on the stair stepper

y: the number of calories he burns per minute on the stair stepper

Let's define two variables:

We want to write a system of linear inequalities to represent Jackson's workout on the stair stepper.

First, we know that Jackson can exercise for at most 45 minutes, so we have the inequality:

x ≤ 45

Next, we know that the number of calories burned per minute on the stair stepper depends on the intensity of the workout. Since Jackson wants to burn at least 400 calories, we can write:

xy ≥ 400

Finally, we need to determine the range of values that y can take. We know that Jackson is either doing a light effort or a vigorous effort on the stair stepper.

According to the information given in the problem, the stair stepper can burn a maximum of 10.4 calories per minute with a vigorous effort. So we have:

6.9 ≤ y ≤ 10.4

Putting it all together, the system of linear inequalities to represent Jackson's workout on the stair stepper is:

x ≤ 45

xy ≥ 400

6.9 ≤ y ≤ 10.4

Note that we can simplify the second inequality to x ≥ 400/y, but we'll leave it in the current form for clarity.

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SOLUTION

We want to find the interquartile range of the box and whisker plot in the picture.

Interquartile range is calculated as

In the box and whisker plot

Hence the answer is 6

The objective is to develop and implement an adaptive cruise control system for vehicles using MATLAB, Arduino UNO, and ThingSpeak that automatically adjusts the speed to maintain a safe distance from vehicles ahead and uploads speed information to the cloud for connected vehicles and intelligent transport.

The system uses an Arduino UNO board, five buttons, a distance sensor, and a 4-digit 7-segment anode display. The buttons include Set_speed, Adaptive_speed, Cancel, Increase_speed, and Decrease_speed. The system has two modes, cruise control, and adaptive cruise control.

In cruise control, the speed is held constant and can be adjusted with the Increase_speed and Decrease_speed buttons. In adaptive cruise control, the speed automatically adjusts to maintain a safe distance from vehicles or objects in front and the display blinks to indicate this mode.

The system also communicates with the ThingSpeak platform to store speed data on the cloud for analysis and visualization in MATLAB.

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a) On the left side of the equation, Cara should be combining the terms that involve the variable "p." b) On the right side of the equation, Cara should be combining the terms that also involve the variable "p."

Cara is solving the equation 3 + 2p + 2 = 2p + 15 - p. To simplify the equation, she needs to combine like terms on both sides. Like terms are terms that have the same variable and exponent. On the left side, Cara has the terms "2p" and "2." Both of these terms involve the variable "p," so she needs to combine them. By adding them together, she will get the combined term "2p + 2."

On the right side, Cara has the terms "-p" and "15." Again, both of these terms involve the variable "p," so she needs to combine them. By adding them together, she will get the combined term "15 - p."

Once she has combined the terms on both sides of the equation, Cara can proceed with further simplifications or solving for the variable "p" based on the updated equation.

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The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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Answer:

X=90-22

X=68 is the answer

The tank starts with 41 gallons and ends with 1 gallon, the range of f is from 1 gallon to 41 gallons.

The range of f refers to the amount of water remaining in the tank after a certain period of time while draining at a constant rate.

Step 1: Identify the initial amount of water in the tank, which is 41 gallons.

Step 2: Determine the rate at which water is draining, which is 4 gallons per minute.

Step 3: Calculate the time it takes to completely drain the tank. Divide the initial amount of water by the draining rate: 41 gallons ÷ 4 gallons per minute = 10.25 minutes.

However, since the tank can't have a negative amount of water, the draining process stops after 10 minutes, with 1 gallon remaining in the tank.

Step 4: Identify the range of f, which is the range of water amounts in the tank during the draining process. Since the tank starts with 41 gallons and ends with 1 gallon, the range of f is from 1 gallon to 41 gallons.

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Answer:

It would end at 9:38

Step-by-step explanation:

but obviously it is not one of the answer choices, so I would go with 9:42

Answer:

1 one answer, 2 lot of answers, 3 no answer

Step-by-step explanation:

I have to go to bed sorry

Answer:

linear function, growth factor of 4

Step-by-step explanation:

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = (y2 - y1)/(x2 - x1) = (4 - 0)/(1 - 0) = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Answer:

Answer:

linear function,growth factor of 4

Step-by-step explanation:

Given:

The expression is

\(\dfrac{x-5}{3x^2-10x-25}\)

To find:

The restricted value of given expression.

Solution:

We have,

\(\dfrac{x-5}{3x^2-10x-25}\)

Equate the denominate equal to 0, to find the restricted value.

\(3x^2-10x-25=0\)

\(3x^2-15x+5x-25=0\)

\(3x(x-5)+5(x-5)=0\)

\((x-5)(3x+5)=0\)

Using zero product property, we get

\(x-5=0\text{ and }3x+5=0\)

\(x=5\text{ and }x=-\dfrac{5}{3}\)

Therefore, the restricted values are \(x=5\text{ and }x=-\dfrac{5}{3}\).

To find a power series solution to the differential equation (x² - 1)y'' + xy' - y = 0, we will assume a power series solution in the form y(x) = Σ(a_n * xⁿ), where a_n are coefficients.


1. Calculate the first derivative y'(x) = Σ(n * a_n * xⁿ⁻¹) and the second derivative y''(x) = Σ((n * (n-1)) * a_n * xⁿ⁻²).
2. Substitute y(x), y'(x), and y''(x) into the given differential equation.
3. Rearrange the equation and group the terms by the powers of x.
4. Set the coefficients of each power of x to zero, forming a recurrence relation for a_n.
5. Solve the recurrence relation to determine the coefficients a_n.
6. Substitute a_n back into the power series to obtain the solution y(x) = Σ(a_n * xⁿ).

By following these steps, we can find a power series solution to the given differential equation.

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As a result, the shaded region's area sector is **10.62 cm² cm.²

What is a sector?

A sector is a section of a circle in geometry that is bounded by two radii and an arc. It is a pie-shaped portion of a circle that touches the circle's center, has two straight edges (the two radius lines), and a curved edge created by the arc.

Arc Length = r is the formula for the arc length of a circle,

where is the radius of the circle and r is the radian measurement of the arc (or central angle).

The formula for arc length, L = r *, can be used to determine the value of zero. L is the length of the arc, r is the radius of the circle, and is the centre angle in radians. We can deduce from the facts provided that PQ equals 2 * OP.

Also obvious is that OR = 4 cm. We can claim that PQ = 2 * OR = 8cm because PQ is twice as long as OP. Now, we can calculate's value using the formula:

L = r * θ 8 = 4θ θ = 2

Consequently, = 2 radians.

We must know the length of arc RS in order to calculate the size of the shaded zone. PQ is twice RS, as we are aware. RS = PQ/2, which equals 4 cm. Now, we may apply the area of a formula.We may now apply the formula A = (1/2) * r² *, where A is the sector's area, r is the circle's radius, and is the centre angle in radians.

Sector PQR area equals (1/2) * OR2 * sector PQR area equals (1/2) * 16 * 2 sector PQR area equals (16)

Sector PSR area equals (1/2) * OR²2 * Sector PSR area equals (1/2) * 16 * π/3 Sector PSR area equals (8)/3

Sector PQR minus Sector PSR is equal to the area of the shaded region. Area of the shaded area is 16 - (8π)/3. Shaded area size: 10.62 cm²

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