(24x – 8y) – (7x – 20y).

From SOHCAHTOA.

Cos37 = x/25

x= 25cos37

x=21.5 = 22.

When rounded to the nearest integer... 20

Option A is legit

Answer:

The correct answer is B. 15

Step-by-step explanation:

Ap3x Approved

The desired fuel efficiency of a car two years from now would ideally be improved compared to the current fuel efficiency.

There are several reasons why we would want the fuel efficiency of a car to be better in the future:

Environmental Concerns: Improving fuel efficiency helps reduce carbon emissions and minimize the environmental impact of vehicles. As the world becomes more conscious of climate change and the need to reduce greenhouse gas emissions, enhancing fuel efficiency plays a vital role in mitigating environmental damage.

Energy Conservation: Better fuel efficiency means using less fuel to travel the same distance. With finite energy resources and the need to conserve them, improving fuel efficiency helps reduce the overall energy consumption in transportation, leading to better resource management.

Cost Savings: Increasing fuel efficiency directly translates to lower fuel consumption and reduced expenses for car owners. With rising fuel prices, having a more fuel-efficient car can significantly cut down on fuel costs, saving money for individuals and businesses.

Technological Advancements: As technology progresses, advancements in engine design, aerodynamics, lightweight materials, and alternative energy sources enable the development of more fuel-efficient vehicles. Striving for improved fuel efficiency encourages innovation in the automotive industry, leading to the creation of more sustainable and eco-friendly transportation options.

Government Regulations: Many governments worldwide have implemented fuel efficiency standards and regulations to reduce fuel consumption and emissions. By meeting or exceeding these standards, car manufacturers contribute to a cleaner and more sustainable transportation sector.

Ultimately, aiming for improved fuel efficiency two years from now aligns with the global push for environmental sustainability, energy conservation, cost savings, technological advancements, and adherence to regulatory standards. It benefits both individuals and society as a whole by promoting a greener and more efficient approach to transportation.

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Answer:

x = 3

Step-by-step explanation:

Formula

CE * DE = AE * BE

Notice how the chords cut each other. Also notice how the segments are equated. See the givens.

Givens

CE = 3

DE = x + 11

AE =x+3

BE = 7

Solution

3*(x + 11) = 7(x + 3)               Remove the brackets

3x + 33 = 7x + 21                 Subtract 21 from both sides

3x + 33 - 21 = 7x                  Combine the left

3x + 12 =7x                          Subtract 3x from both sides

12 = 7x - 3x

12 = 4x                                Divide by 4

12/4 = 4x/4

x = 3

The triangle's sides are b, a, and c, listed from shortest to longest.

The side of triangle ABC opposite angle A is indicated by the letter a.

The letter b stands for the side opposite angle B.

The letter c stands for the side that faces angle C.

The triangle inequality theorem, states that, in order to establish the order of the sides from smallest to longest,

The largest side is the one opposite the largest angle and vice versa.

Hence, we have

B = 38 degrees, thus b.

a = 54 degrees from A

c from C equals 88 degrees.

As a result, the sides are arranged in the following order: b a c.

In other words, the side across from angle B is the smallest, followed by the side across from angle A, and the side across from angle C is the longest.

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It depends on which number has the greatest absolute value.

Think about it as money

If you owe me $10, this is shown as -10

Now  if I give you back 2 dollars  (+2), How much money do I still owe you.

The equation is -10+2

I still owe you 8 dollars which is portrayed as -8

Hope this helps :)

So the total amount received by Sohail is 100 * y². To get the precise amount, we must first determine the value of x.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.

Let's call the number of days Sohail was in town and cleaned the house "y". Then we can write:

y = x - 8 (since he was out of town for 8 days)

And the amount he was promised per day is 10, so the total amount promised is:

10 * y = 10 * (x - 8)

At the end of the break, his mother decided to square the amount due to him, so the final amount he received is:

(10 * y)² = (10 * (x - 8))²

Expanding the square and simplifying, we get:

100 * y²= 100 * (x - 8)²

So the final amount Sohail received is 100 * y². To find the exact value, we need to know the value of x.

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Answer:

30.17feet high

Step-by-step explanation:

Given the following

the distance from the base of the pole to the tip of the shadow = 49feet (hypotenuse)

angle of elevation = 38°

Required

Height of the flagpole (opposite)

Using the SOH CAH TOA identity

Sin theta = opposite/hypotenuse

Sin 38 = H/49

H = 49sin38

H = 49(0.6157)

H = 30.17feet

Hence the flagpole is 30.17feet high

Answer:

Large bucket

Step-by-step explanation:

Sugar water isnt a real life factor in dye. It just makes it sweeter.

But, since it has triple the dye, it has more and therefore darker.

Hope this helps plz hit the crown ;D

Ryan will have to make a monthly payment of $195.41

Answer:

\(\implies x = 1 \quad or -6 \\\\\implies f(x) = -3x^2-15x + 18 \)

Step-by-step explanation:

Given :-

And we need to find out the zeroes of the quadratic function and we need to express it in Standard form. T

Function :-

\(\implies f(x)= -3(x-1)(x+6) \)

\(\implies f(x)=0 \\\\\implies -3(x-1)(x+6)=0 \\\\\implies (x - 1 )(x+6) = 0 \\\\\implies x = 1 \quad or \quad -6 \)

Therefore the zeroes are 1 and -6 .

Expressing in Standard form :-

The standard form of a quadratic equation is ,

\(\implies ax^2+bx + c = 0 \)

And that of a quadratic function is ,

\(\implies f(x) = ax^2+bx + c \)

Simplifying the equation :-

\(\implies f(x)= -3(x-1)(x+6)\\\\\implies f(x) = (-3x +3)(x+6) \\\\\implies f(x) = -3x(x+6)+3(x+6)\\\\\implies f(x) = -3x^2 -18x +3x + 18\\\\\implies f(x) = -3x^2-15x + 18 \)

Hence the Standard form of the equation is -3x² - 15x + 18 .

Answer:

8

Step-by-step explanation:

to get x alone you divide the 2 away on both sides, getting x = 8. To check multiply 8 by 2 and you get 16.

Hope this helps!

Take the root of both sides and solve.

x = 4, −4

False. It is not generally suggested that the sample size in developing a multiple regression model should be at least four times the number of independent variables.

There is no specific rule or guideline that states the sample size in developing a multiple regression model should be at least four times the number of independent variables. The appropriate sample size for a multiple regression model depends on various factors, such as the desired level of statistical power, the effect size, and the level of significance. In general, a larger sample size is preferred as it can increase the statistical power and reliability of the results.

However, the relationship between sample size and the number of independent variables is not fixed at a specific ratio like four times. It is important to consider the specific context of the study and the research question when determining the appropriate sample size for a multiple regression model.

Therefore, it is not accurate to suggest that the sample size should be at least four times the number of independent variables.

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A) The control limits for the x-bar chart are approximately:

Upper Control Limit (UCL) = 55.752 lb

Lower Control Limit (LCL) = 53.748 lb

B) The control limits for the 3-sigma R-chart are approximately:

Upper Control Limit (UCR) = 3.759 lb

Lower Control Limit (LCR) = 1.363 lb

To calculate the control limits for the x-bar chart and the 3-sigma R-chart, we need to use the given information about the sample size and the average range.

a) Control limits for the x-bar chart:

The control limits for the x-bar chart are typically calculated using the formula:

UCL = x(bar) + A₂ × R-bar

LCL = x(bar) - A₂ × R-bar

Where:

UCL = Upper Control Limit

LCL = Lower Control Limit

x(bar) = Overall mean

A₂ = Constant depending on the sample size (from statistical tables)

R-bar = Average range

In this case, the sample size is 7, so we need to find the value of A₂ from the statistical tables. For a sample size of 7, A₂ is approximately 0.577.

Using the given information:

x(bar) = 54.75 lb (Overall mean)

R-bar = 1.78 lb (Average range)

A₂ = 0.577

Substituting these values into the formula, we can calculate the control limits for the x-bar chart:

UCL = 54.75 + 0.577 × 1.78

UCL ≈ 55.752

LCL = 54.75 - 0.577 × 1.78

LCL ≈ 53.748

Therefore, the control limits for the x-bar chart are approximately:

Upper Control Limit (UCL) = 55.752 lb

Lower Control Limit (LCL) = 53.748 lb

b) Control limits for the 3-sigma R-chart:

The control limits for the R-chart can be calculated using the formula:

UCR = D₄ × R-bar

LCR = D₃ × R-bar

Where:

UCR = Upper Control Limit for R-chart

LCR = Lower Control Limit for R-chart

D₄, D₃ = Constants depending on the sample size (from statistical tables)

For a sample size of 7, the values of D₄ and D₃ are approximately 2.115 and 0.765, respectively.

Using the given information:

R-bar = 1.78 lb (Average range)

D₄ = 2.115

D₃ = 0.765

Substituting these values into the formula, we can calculate the control limits for the 3-sigma R-chart:

UCR = 2.115 × 1.78

UCR ≈ 3.759

LCR = 0.765 × 1.78

LCR ≈ 1.363

Therefore, the control limits for the 3-sigma R-chart are approximately:

Upper Control Limit (UCR) = 3.759 lb

Lower Control Limit (LCR) = 1.363 lb

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The complete question is :

35 sample of size 7 each were taken from a fertiliser filling machine at lawm ltd. the result were overall mean = 54.75lb average range = 1.78lb

a) For the given sample size, the control 3-sigma lmits for x bar

Upper Contol Litit (UCL-) = . (round your response to thee decimal places) Lower Control Limit (LCL)= . (round your response to three decimat places).

b) The control lirtits for the 3-sigma R-chart are:

Upper Control Limit (UCR)=  . (cound your rospanse to thee decimal places).

Lower Control Limit (LC,R)=  .(round your response fo three decimal places)

Answer : Rate of change is 2/5 meters per second

Give data:

Time = 5 seconds

Head start = 8 meter

Distance rode, every 5 seconds = 2 meters

Her start line is (0, 8)

Rate of change = distance / time

Rate of change = 2/5

Rate of change = 2/5 meters / second

Since she has a 8 meters head start

Then the slope - intercept equation is

y = 2/5x + 8

Rate of change = 2/5

Answer:

y = -2x + 9

Step-by-step explanation:

The equation of the new line is the same as that of this given line, EXCEPT that the constant will be different.

Start with y = mx + b; substitute 1 for y, 4 for x and -2 for m:

1 = -2(4) + b

Then b = 9, and y = -2x + 9

Answer:

3 stamps

Step-by-step explanation: 42 stamps in equal groups would be 6 stickers/group.

6+3 = 9 stickers in each pile

there was 7 piles so multiply 7 by the 9 stickers in each pile

7· 9 = 63  

5 · 12 = 60, so she gave her friends 60 stickers

63-60 = 3  

Answer:Corporations step up their expansion plans and thus increase their demand for capital.

Step-by-step explanation:

Step-by-step explanation:

Use phytogoras theorem

\( \sqrt{ {29}^{2} } - \sqrt{ {21}^{2} } \\ \\ \\ square \: root \: the \: whole \: eq \\ \\ \\ = 20cm\)

Hope this is correct and helpful

HAVE A GOOD DAY!

a) To find a function f such that \(\mathbf{F} = \nabla f and f(0,0,0) = 0 \\\), we need to find the potential function f(x, y, z) whose gradient is equal to \(\mathbf{F} \\\).

Given \(\mathbf{F} = (z + y)\mathbf{i} + (3z + x)\mathbf{j} + (3y + x)\mathbf{k} \\\), we can find the potential function f(x, y, z) by integrating the components of \(\mathbf{F}\\\) with respect to their corresponding variables:

\(\:f(x, y, z) = \int (z + y) \, dx + \int (3z + x) \, dy + \int (3y + x) \, dz \\\)

Integrating each component:

\(\:f(x, y, z) = \frac{1}{2}zx + yx + g_1(y, z) + \frac{3}{2}zy + g_2(x, z) + \frac{3}{2}yx + g_3(x, y) \\\)

where g_1(y, z), g_2(x, z), and g_3(x, y) are arbitrary functions of their respective variables.

To satisfy the condition f(0, 0, 0) = 0, we set the arbitrary functions g_1(y, z), g_2(x, z), and g_3(x, y) to be zero:

\(f(x, y, z) = \frac{1}{2}zx + yx + \frac{3}{2}zy + \frac{3}{2}yx \\\)

Therefore, the function f(x, y, z) that satisfies \(\mathbf{F} = \nabla f \\\) and f(0, 0, 0) = 0 is:

\(f(x, y, z) = \frac{1}{2}zx + yx + \frac{3}{2}zy + \frac{3}{2}yx \\\)

b) Now, we want to compute the line integral \(\int_C \mathbf{F} \cdot d\mathbf{r} \\\) along any curve C from (0, 0, 0) to (1, 1, 1).

Using the fundamental theorem of line integrals, we can evaluate the line integral by evaluating the potential function f at the endpoints of the curve:

\(\int_C \mathbf{F} \cdot d\mathbf{r} = f(1, 1, 1) - f(0, 0, 0) \\\)

Substituting the values into the potential function:

\(\int_C \mathbf{F} \cdot d\mathbf{r} = f(1, 1, 1) - f(0, 0, 0) \\ \\= \left(\frac{1}{2} + 1 + \frac{3}{2} + \frac{3}{2}\right) - \left(0\right) = \frac{11}{2} \\\)

Therefore, the line integral \(\int_C \mathbf{F} \cdot d\mathbf{r} \\\) along any curve C from (0, 0, 0) to (1, 1, 1) is \(\frac{11}{2} \\\).

Answer:

69 mph

Explanation:

The equation that represents this situation is:

We are required to determine Brian's average speed on the return drive.

To do this, we first find the value of x.

Using the value of x, we find the average speed on the return drive.

Therefore, the average speed on the return drive will be 69 mph.

Answer:

Step-by-step explanation:

C=50+15n

Using the binomial distribution, it is found that:

0.3677 = 36.77% probability that more than 1 of these parts are defective.

-----------------

For each part, there are only two possible outcomes. Either they are defective, or they are not. The probability of a part being defective is independent of any other part, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of a success.

At a certain auto parts manufacturer, the Quality Control division has determined that one of the machines produces defective parts 18% of the time.

This means that \(p = 0.18\)

A random sample of 7 parts produced by this machine is chosen.

This means that \(n = 7\)

Find the probability that more than 1 of these parts are defective.

This is:

\(P(X \geq 1) = 1 - P(X < 1)\)

In which

\(P(X < 1) = P(X = 0) + P(X = 1)\)

Thus

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{7,0}.(0.18)^{0}.(0.82)^{7} = 0.2493\)

\(P(X = 1) = C_{7,1}.(0.18)^{1}.(0.82)^{6} = 0.3830\)

Then

\(P(X < 1) = P(X = 0) + P(X = 1) = 0.2493 + 0.3830 = 0.6323\)

\(P(X \geq 1) = 1 - P(X < 1) = 1 - 0.6323 = 0.3677\)

0.3677 = 36.77% probability that more than 1 of these parts are defective.

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Answer: 4sr+17r−2s4+17−2

Step-by-step explanation: simplify 18r - 3s-r + 4s1r+s

then multiply by one and get 18r-3s-r+4sr+s.

then combine like terms and get 17r-3s-r+4sr+s.

combine like terms again and end up with 17r-2s+4sr

you then want to rearrange the terms to 4sr+17r-2s

and you have your answer .

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

x  = 4

Step-by-step explanation:

hope this helps :)

Answer:

x = 4

Step-by-step explanation:

Distribute 8x + 4 = 27 + 6x - 15

Combine your constants  

8x + 4 = 12 + 6x

Combine like terms by using inverse operations.

2x + 4 = 12

2x = 8

Isolate your variable by using inverse operation

x = 4

The researchers are investigating the perception of three-dimensional shapes on computer screens and specifically examining the components of a square figure or cube necessary for viewers to perceive details of the shape. They vary the stimuli to include fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. Four participants are recruited for an intense study, and their accuracy rates are measured across the three figure conditions. The trials are presented in different orders for each participant using a random-numbers table to determine unique sequences.

In this study, the researchers are interested in understanding how viewers perceive details of three-dimensional shapes on computer screens. They manipulate the stimuli by presenting fully rendered cubes, cubes with incomplete sides, and cubes with missing corner information. By varying these components, the researchers aim to identify which elements are necessary for viewers to accurately perceive the shape.

Four participants are recruited for an intense study, indicating a small sample size. While a larger sample size would generally be preferred for generalizability, intense studies often involve fewer participants due to the time and resource constraints associated with conducting a large number of trials. This approach allows for in-depth analysis of individual participant performance.

The participants are trained on how to detect subtle deformations in the shapes, which suggests that the study aims to assess their ability to perceive and discriminate fine details. After the training, the participants' accuracy rates are measured across the three different figure conditions, likely reported as a percentage of correctly identified shape details.

To minimize potential biases, the trials are presented in different orders for each participant, using a random-numbers table to determine unique sequences. This randomization helps control for order effects, where the order of presenting stimuli can influence participants' responses.

The researchers in this study are investigating the perception of three-dimensional shapes on computer screens. By manipulating the components of square figures or cubes, they aim to determine which elements are necessary for viewers to perceive shape details accurately. The study involves four participants, an intense study design, and measures accuracy rates across different figure conditions. The use of randomization in trial presentation helps mitigate potential order effects.

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Answer:

A. B. and D.

Step-by-step explanation:

Answer:

Volume of the triangular prism = 42 square in.

Step-by-step explanation:

Volume of a triangular prism = Area of the triangular base × Height

Area of the triangular base = \(\frac{1}{2}(\text{Base})(\text{Height})\) [Since, given triangle is a right triangle]

                                             = \(\frac{1}{2}(3)(4)\)

                                             = 6 square in.

Height of the prism = 7 in

Therefore, volume of the triangular prism = 6 × 7

                                                                     = 42 square inch

Answer:

AC = 10

Step-by-step explanation:

We can use proportions to solve

AB         AC

------ = -----------

DE        DF

5        AC

---- = -------

3        6

Using cross products

5*6 = 3 AC

30 = 3AC

Divide by 3

30/3 = AC

10 = AC

Answer:

Step-by-step explanation:

❁ Hello! ❁

AB/DE = AC/DF => 5/3 = AC/6

5/3 = AC/6

5 × 6 = 3 × AC

30 = 3 × AC

30 ÷ 3 = AC

10 = AC

Success! ☺️