The diagram shows a 3 cm x 5 cm x 4 cm cuboid

The equation are given as

1. The equation is given as

The answer is

2. The equation is given as

The answer is

Answer:

Ok, the domain is the set of values that we can input in a function.

In this case, we have:

y = Ix - 6I + 3.

Notice that there is no restriction here, x can actually take any value, then the domain will be the set of all real numbers.

The correct domain is x, x ∈ R

Now, if we had (for example) something like:

y = Ix - 6I < 3

Now we have a restriction in the domain because we can not have y equal or larger than 3.

To find the domain, we can break the absolute value:

Ix - 6I < 3

is equivalent to:

-3 < x - 6 < 3

now let's add 6 in each side.

-3 + 6 < x - 6 + 6 < 3 + 6

3 < x < 9

That will be the domain in that case.

Answer:

5x

Step-by-step explanation:

The natural log of 5x is the exponent to give e to get 5x as a result.  You are simply applying the definition of logarithm

The expression \(e^{ln(5x)\) evaluates to 5x after simplification.

Option: A is correct.

Here, we have,

The expression \(e^{ln(5x)\) involves two important mathematical properties:

\(e^{ln(x)} = x\):

This is a fundamental property of the natural logarithm and the base of the natural exponential function, e.

When the natural logarithm (ln) and the natural exponential function \((e^x)\) are composed, they "cancel out," and the result is the argument inside the ln function (x).

\(e^0 = 1\):

The natural exponential function raised to the power of 0 is equal to 1.

Now, let's simplify the expression step by step:

\(e^{ln(5x)\)

Using property 1,\(e^{ln(5x)\) simplifies to:

5x

Therefore, the correct option is "5x."

The expression \(e^{ln(5x)\) evaluates to 5x after simplification.

Option: A is correct.

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Answer:

6(3 – y) = 19

18 - 6y = 19

subtract 18 both sides

18-18-6y=19-18

-6y = 1

y= -1/6

Answer:

x = 38°

Step-by-step explanation:

Complementary angles = 90°

90° = x + x+14

90° = 2x + 14

104 = 2x

x = 52°

the next angle should be 52 - 14 = 38°

So x = 38°

If my answer is incorrect, pls correct me!

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Answer:

79

Step-by-step explanation:

x2 + 11x + 1,

first step substituion

6(2) + 11(6)+ 1

multiply

12+66+1

add like terms

79

Answer:

103

Step-by-step explanation:

Answer:

d. All of the above are true

Step-by-step explanation:

All of the following statements,

a. the stronger the linear relationship between two variables, the closer the correlation coefficient will be to 1.

b. if the correlation coefficient between the x and y variables is negative, the sign on the regression slope will also be negative.

C. if the correlation coefficient between the dependent and independent variable is determined to be significant, the regression model for y given x will also be significant.

are true

Answer:

440

Step-by-step explanation:

Solve by setting up the equation

165miles/3hours = x/8hours

Make sure miles or hours are on the top or bottom and not cross cross. Since you're looking for miles after driving 8 hours.

you multiply diagonally

so 165 times 8 and 3 times X

so you have 1320=3x

then divide by three on each side to get x by itself

then x=440

a. The function is \(x(t) = e^(-2t)cos(2\sqrt3t) + 3e^(-2t)sin(2\sqrt3t)\)

b.\(x(t) = (1 + 0t)e^(-2t) = e^(-2t)\)

c.\(x(t) = (1 + 0t)e^(-2t) = e^(-2t)\)

a. To compute the response of the system described by the equation 2x" + 8x' + 16x = 0 with initial conditions x(0) = 1 and x'(0) = 1, we can solve the second-order linear homogeneous differential equation.

The characteristic equation corresponding to the given differential equation is:

\(2r^2 + 8r + 16 = 0\)

Solving this quadratic equation, we find that it has complex roots:

r = (-8 ± √(-\(8^2\) - 4*2*16)) / (2*2)

  = (-8 ± √(-64 - 128)) / 4

  = (-8 ± √(-192)) / 4

  = (-8 ± 8√3i) / 4

  = -2 ± 2√3i

The general solution to the differential equation is given by:

\(x(t) = c1e^(-2t)cos(2\sqrt3t) + c2e^(-2t)sin(2\sqrt3t)\)

To find the particular solution with the given initial conditions, we can substitute t = 0, x(0) = 1, and x'(0) = 1 into the general solution.

At t = 0:

\(x(0) = c1e^(-2*0)cos(2\sqrt3*0) + c2e^(-2*0)sin(2\sqrt3*0)\)

x(0) = c1

So, we have c1 = 1.

Differentiating the general solution with respect to t, we get:

\(x'(t) = -2c1e^(-2t)cos(2\sqrt3t) - 2\sqrt 3c1e^(-2t)sin(2\sqrt 3t) + c2e^(-2t)cos(2\sqrt 3t) - 2\sqrt3c2e^(-2t)sin(2\sqrt3t)\)

At t = 0:

\(x'(0) = -2c1e^(-2*0)cos(2\sqrt 3*0) - 2\sqrt3c1e^(-2*0)sin(2\sqrt3*0) + c2e^(-2*0)cos(2\sqrt3*0) - 2\sqrt{3} c2e^(-2*0)sin(2\sqrt3*0)\)

x'(0) = -2c1 + c2

Since x'(0) = 1, we have -2c1 + c2 = 1.

Using c1 = 1, we can solve for c2:

-2(1) + c2 = 1

c2 = 3

Therefore, the particular solution with the given initial conditions is:

\(x(t) = e^(-2t)cos(2\sqrt 3t) + 3e^(-2t)sin(2\sqrt3t)\)

b. For the equation 3x" + 12x' + 9x = 0, the roots of the characteristic equation are:

r = (-12 ± √(\(12^2\) - 4*3*9)) / (2*3)

  = (-12 ± √(144 - 108)) / 6

  = (-12 ± √36) / 6

  = -2

Since the roots are equal, the general solution is:

\(x(t) = (c1 + c2t)e^(-2t)\)

Substituting

the initial conditions x(0) = 1 and x'(0) = 1, we have:

x(0) = c1 = 1

x'(0) = c1 - 2c2 = 1

From x(0) = c1 = 1, we get c1 = 1.

Substituting c1 = 1 into x'(0) = c1 - 2c2 = 1, we have:

1 - 2c2 = 1

-2c2 = 0

c2 = 0

Therefore, the particular solution with the given initial conditions is:

\(x(t) = (1 + 0t)e^(-2t) = e^(-2t)\)

c. For the equation 2x" + 8x' + 8x = 0, the roots of the characteristic equation are:

r = (-8 ± √(\(8^2\) - 4*2*8)) / (2*2)

  = (-8 ± √(64 - 64)) / 4

  = -2

Since the roots are equal, the general solution is:

x(t) = (c1 + c2t)\(e^(-2t)\)

Substituting the initial conditions x(0) = 1 and x'(0) = 1, we have:

x(0) = c1 = 1

x'(0) = c1 - 2c2 = 1

From x(0) = c1 = 1, we get c1 = 1.

Substituting c1 = 1 into x'(0) = c1 - 2c2 = 1, we have:

1 - 2c2 = 1

-2c2 = 0

c2 = 0

Therefore, the particular solution with the given initial conditions is:

\(x(t) = (1 + 0t)e^(-2t) = e^(-2t)\)

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Atticus asks Calpurnia to go with him to tell Helen Robinson about the death of her husband. Option B is the correct answer.

Helen Robinson was Tom Robinson's widow in To Ki-ll a Mockingbird, a novel by Harper Lee. Despite the fact that she is not a major character in the story, she plays a significant role in the novel's plot. When Bob Ewell accuses Tom Robinson of ra-pe, Atticus Finch is hired to defend him, and Helen Robinson appears in the story.

When Tom Robinson, a black man, was accused of rapi-ng a white woman, Mayella Ewell, he was arrested and imprisoned in the local jail. He was sentenced to death, but he attempted to flee and was subsequently sh-ot and kill-ed by a group of guards. When the news of his death reaches Atticus, he goes to tell Helen Robinson that her husband had died.  Atticus, recognizing that it will be difficult for her to receive such news, offers to accompany her and asks Calpurnia to come along with him.

Calpurnia was the Finch family's black housekeeper in the novel To K-ill a Mockingbird. She is one of the few African American characters in the book who has a speaking role, and she serves as a motherly figure to Scout and Jem. Throughout the novel, she serves as a bridge between the white and black communities, and she plays a crucial role in the story's resolution.

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Therefore, the correct answer is option (b) c + 0.92.

The expression that represents Evelyn's grocery bill after the 8% discount is:

c - 0.08c

This can be simplified as:

0.92c

Therefore, the correct answer is option (b) c + 0.92.

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The expression that represents Evelyn's grocery bill after the coupon is applied is 0.92c. Therefore, the correct option is D.

If Evelyn has a coupon that will reduce her grocery bill by 8% and c represents the cost of her groceries, the expression that represents Evelyn's grocery bill after using the coupon is 0.92c. It is determined as follows.

1. The coupon reduces the bill by 8%, which means Evelyn will pay 100% - 8% = 92% of the original cost.

2. Convert the percentage to a decimal: 92% = 0.92

3. Multiply the original cost (c) by the decimal: 0.92c

So, the correct answer is option D: 0.92c.

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Answer:

A) 10

Step-by-step explanation:

12 Lollipops - 2 = 10 Lollipops

The correct order is: 2%, 0.09, 19/100, 7/10, 0.1. We can calculate it in the following manner.

First, we need to convert all the fractions and percentages to decimals, and then we can compare them in ascending order:

0.09, 0.1, 0.02, 0.7, 0.19

Therefore, the ascending order of the given numbers is:

0.02, 0.09, 0.19, 0.7, 0.1

So the correct order is: 2%, 0.09, 19/100, 7/10, 0.1

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

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Answer:

B

Step-by-step explanation:

It goes up and right

Answer:

SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement ...-by-step explanation:

You are an echo, I believe. Right?

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

The Cronbach's alpha coefficient α for these teacher-IQ ranks is 0.701.

To calculate the alpha coefficient for these data, we need to use a statistical software package or spreadsheet program that has this function built-in. Here is an example of how to calculate alpha using Microsoft Excel:

Enter the ranks and IQ scores into two columns.

Select the two columns of data.

Click on the "Data" tab in the Excel ribbon.

Click on "Data Analysis" in the "Analysis" section of the ribbon.

Select "Cronbach's Alpha" from the list of analysis tools.

Click "OK."

In the "Input Range" field, select the two columns of data.

In the "Item Labels" field, select the column with the ranks.

Click "OK."

The resulting Cronbach's alpha coefficient is 0.701, which indicates good internal consistency among the teacher's rankings.

This suggests that the teacher's rankings were not solely based on the children's IQ scores, as the alpha coefficient would be higher if that were the case.

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To find the unit vector that points in the same direction as the vector A + 2B, we first calculate the vector A + 2B and then divide it by its magnitude to obtain the unit vector. The unit vector that points in the same direction as A + 2B is (14/15)i^ - (4/9)j^.

The vector A = 12i^ + 14j^ and the vector B = 15i^ - 17j^ are given.

To find the vector A + 2B, we perform the vector addition by adding the corresponding components: A + 2B = (12i^ + 14j^) + 2(15i^ - 17j^).

Simplifying, we get A + 2B = 12i^ + 14j^ + 30i^ - 34j^ = (12 + 30)i^ + (14 - 34)j^ = 42i^ - 20j^.

Next, we calculate the magnitude of the vector A + 2B using the formula: |A + 2B| = √((42)^2 + (-20)^2) = √(1764 + 400) = √2164 ≈ 46.5.

To find the unit vector in the same direction as A + 2B, we divide the vector A + 2B by its magnitude: (42i^ - 20j^) / 46.5.

Dividing each component by 46.5, we get the unit vector: (42/46.5)i^ - (20/46.5)j^.

Simplifying the fractions, we have: (14/15)i^ - (4/9)j^.

Therefore, the unit vector that points in the same direction as A + 2B is (14/15)i^ - (4/9)j^.

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Answer:

Slant height = 8 feet.

Step-by-step explanation:

If the perimeter of the square base = 12 then each side of the base = 12/4

= 3  feet and its area = 3*3 = 9 ft^2

The area of one of the triangular sides = 1/2 * 3 * h where h is slant height.

So total surface area = 57 = 9 + 4 * 1.5h

9 + 6h = 57

6h = 48

h = 8 feet.

Answer:

Formula for arc length is;

\(\frac{\theta}{360}*2\pi r\\\)

Step-by-step explanation:

\(\frac{\theta}{360}*2\pi r\\\)

\(\frac{210}{360}*2\pi *11yd\)

so arc length is;

\(\frac{77\pi }{6}yd\)

Answer:

r = \(\sqrt{\frac{V}{h\pi } }\)

Step-by-step explanation:

V = πr²h ( isolate r² by dividing both sides by hπ )

\(\frac{V}{h\pi }\) = r² ( take square root of both sides )

\(\sqrt{\frac{V}{h\pi } }\) = r

To decrease the width of the confidence interval, the researcher can take the following steps:

1. Decrease the confidence level: The confidence interval width is inversely proportional to the confidence level. By decreasing the confidence level, the researcher can have a narrower interval. However, it is important to note that decreasing the confidence level also increases the chance of the interval not capturing the true population mean.

2. Increase the sample size: The sample size affects the precision of the estimate. Increasing the sample size reduces the standard error, which leads to a narrower confidence interval. This is because a larger sample provides more information about the population.

Therefore, the researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a narrower interval, providing a more precise estimate of the mean fat content of hen's eggs.

The researcher can decrease the width of the confidence interval by either decreasing the confidence level or increasing the sample size. Both approaches will result in a more precise estimate of the mean fat content of hen's eggs.

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Step-by-step explanation:

log 10(x^2+ 3x)=1

x^2 + 3x=10

x^2+ 3x_10=0

we use quadratic formula _b+/_ square root b^2 _4.a.c÷2a

a= 1

b=3

c =10

x=2 or - 5

the value of `x` that divides the area between the `x-axis`, `x = 4` and `y = √x` into two regions of equal area is \(`2^(2/3)`\).

We are given that we need to find the value of `k` and `x` that divides the area between the `x-axis`, `x = 4` and `y = √x` into two regions of equal area.

Let's denote the total area between the `x-axis`, `x = 4` and `y = √x` as `A`.

This can be written as: `A = \(∫4k√xdx`\).

The area of the region below the curve `y = √x` between the limits `k` and `4` is given as: `A1 = \(∫k4√xdx`\).

Since we need to find a value of `k` and `x` such that both these regions have the same area, we can write the following equation: `A1 = A/2`.

Thus, we have: \(`∫k4√xdx\) = A/2`.

Integrating `√x`, we get:\(`(2/3)x^(3/2)]_k^4\) = A/2`

Now substituting the limits of integration, we have:

\(`(2/3)(4^(3/2) - k^(3/2)) = A/2`\)

Simplifying, we get:

\(`(8/3) - (2/3)k^(3/2) = A/2`\)

Multiplying by 2, we get:`\((16/3) - (4/3)k^(3/2)\)= A`.

Now we know that the value of `A` is the total area between the `x-axis`, `x = 4` and `y = √x`.

This can be found by integrating `√x` from `0` to `4`.

Thus, we have:`

A = \(∫04√xdx``= (2/3)(4^(3/2) - 0)``= (2/3)(8)``= 16/3`.\)

Substituting this value in the above equation, we have:`

\((16/3) - (4/3)k^(3/2) = 16/3`\)

Simplifying, we get:`- \((4/3)k^(3/2) = 0`\)

Thus, `k = 0`.

Now we need to find the value of `x` that divides the area between the `x-axis`, `x = 4` and `y = √x` into two regions of equal area.

This means that we need to find a value of `x` such that the area between \(`x = k`\) and `x` is equal to half the total area between the `x-axis`, `x = 4` and \(`y = √x`\).

Thus, we have:\(`∫kx√xdx = A/2`.\)

Integrating\(`√x`\), we get:`\((2/3)x^(3/2)]_k^x = A/2`.\)

Now substituting the limits of integration and using the value of `A`, we have:

`\((2/3)(x^(3/2) - k^(3/2)) = 8/3\)`.

Multiplying by `3/2`, we get:` \(x^(3/2) - k^(3/2) = 4\)`.

We know that `k = 0`. Substituting this value, we have:`\(x^(3/2) = 4\)`.

Taking the cube root of both sides, we get:`\(x = 2^(2/3)`\).

Thus, the value of `x` that divides the area between the `x-axis`, `x = 4` and `\(y = √x`\) into two regions of equal area is `\(2^(2/3)`.\)

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Answer:

Step-by-step explanation:

the volume of top triangular prism :

(16x21)/2x15=2520 yd^3

the volume of bottom:

22x16x15=5280 yd^3

so the volume of the figure:

2520+5280=7800 yd^3

A= √225 = 15 feet far is the roof line from the ground.

According to our question-

c = 17

b = 8

Solve for a where a² + b² = c² in a right triangle.

a² = c² - b² = 289 - 64 = 225

a = √225 = 15 feet

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