the quotient of 8 and the cube of a number

Answer:

B

Step-by-step explanation:

given

tanΘ = \(\frac{3\sqrt{5} }{2}\) = \(\frac{opposite}{adjacent}\)

this ratio relates to a right triangle, with hypotenuse h and

legs 3\(\sqrt{5}\) and 2

using Pythagoras' identity in the right triangle

h² = (3\(\sqrt{5}\) )² + 2² = 45 + 4 = 49 ( take square root of both sides )

h = \(\sqrt{49}\) = 7

then

cosΘ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{2}{7}\)

Answer:

23.86700

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

11

since it asks the absolute value of -11 it

will be 11 because in absolute value-for negatives it always positive.

Answer:

see attached

Step-by-step explanation:

According to the question, the given expression can be simplified with the help of factors.

Given expression = \(-2\sqrt{-45}-3\sqrt{125}\)

Do the factors of 45 as well as 125 and take the common things out from the square root:

Required expression = \(-2(3)\sqrt{-5}-3(5)\sqrt{-5}= -21i\sqrt{5}\)

In the theory of complex number, \(i^{2} = -1\) is already defined.

Hence, the answer for the given expression is \(-21i\sqrt{5}\).

What is simplification?

Simplification is the process to make the expression as simple for the calculation. That means, to calculate the solution of a complex expression.

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Answer: 3 ft

Step-by-step explanation:

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

x=-5     y=52

x=-1      y=12

x=0      y=2

x=1       y=-8

Step-by-step explanation:

Hope this helps (:

The value of f(5)  in the function are - 9 . Option B

A function can be defined as an expression, rule or law that shows the relationship between a dependent variable or independent variable.

Given the functions;

To determine the value f(5),  substitute the value of x as 5

x > 1 , so we use equation 2

From function (2)

f(5) = 1 - 2x

f(5)  = 1 - 2(5)

f(5) = 1 - 10

f(5)  = - 9

Thus, the value of f(5)  in the function are - 9 . Option B

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Answer:

Area of rectangle = \(\mbox{\large \boxed{\textrm{65 sq. inches}}}\)

Step-by-step explanation:

Let square side = \(a\)

Area of square   \(A = a^2\)

Given \(A = 81\)  and equating it to \(a^2\)
\(a^2\) \(= 81\;in^2\)

\(a = \sqrt{81} = 9\;in\)

Perimeter of square = \(4a = 4\cdot 9 = 36 \;in\)

If \(l\) = length of the rectangle and \(w\) = width

Perimeter P of rectangle = \(2(l + w)\\\)

Given perimeter of rectangle = perimeter of square we get
\(2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18\)

Given

\(w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\\)

\(\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches\)

Answer:

6

Step-by-step explanation:

60-9x

Answer:

i think a

Step-by-step explanation:

Answer: a.) $2.20 dollars per pound of flour.        b.) $5 dollars per hour

Step-by-step explanation:

Answer:

= 1/x^2

Step-by-step explanation:

Possible derivation:

d/dx(-16 - 1/x + y)

Differentiate the sum term by term and factor out constants:

= d/dx(-16) - d/dx(1/x) + d/dx(y)

The derivative of -16 is zero:

= -(d/dx(1/x)) + d/dx(y) + 0

Simplify the expression:

= -(d/dx(1/x)) + d/dx(y)

Use the power rule, d/dx(x^n) = n x^(n - 1), where n = -1.

d/dx(1/x) = d/dx(x^(-1)) = -x^(-2):

= d/dx(y) - -1/x^2

Simplify the expression:

= 1/x^2 + d/dx(y)

The derivative of y is zero:

= 1/x^2 + 0

Simplify the expression:

Answer: = 1/x^2

Rounding up to the nearest whole number, we get a sample size of 543.

To determine the sample size required to estimate the average time college students spent on social media applications in a typical day with a margin of error of 0.1 hrs and a 98% level of confidence, we can use the following formula:

n = \((z \times s / E)^2\)

where:

n is the required sample size

z is the z-score associated with the desired level of confidence (in this case, 2.33, which can be obtained from a standard normal distribution table)

s is the sample standard deviation (1 hr)

E is the desired margin of error (0.1 hrs)

Substituting the values, we get:

n =\((2.33 \times 1 / 0.1)^2\)

n = 542.89

Rounding up to the nearest whole number, we get a sample size of 543.

A sample size of at least 543 college students to estimate, on average, how much time they spent on social media applications in a typical day with a margin of error of 0.1 hrs and a 98% level of confidence.

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The first step in finding the distance between vertex P and vertex V is find the length of diagonal between vertex P and vertex R.

option A.

To find the distance between vertex P and vertex V, we need to draw a diagonal line from vertex P to vertex V.

After drawing the diagonal line, we will notice that we have a new right angle triangle.

So since we know the height of the right triangle, we need to find the base of the right triangle first, which is equal to length of diagonal length PR or TV

So the correct answer will be "find the length of diagonal PR first.".

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You should deposit approximately $340.84 monthly to reach $293,000 in 28 years at a 4.4% annual interest rate compounded monthly.

To calculate the monthly deposit required for an investment plan paying 4.4% interest compounded monthly to reach $293,000 in 28 years, we use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Here, FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of payments. First, convert the annual interest rate (4.4%) to a monthly rate by dividing by 12, which gives 0.0367 (4.4%/12) or 0.00367 as a decimal. The number of payments (n) is 28 years * 12 months/year = 336.

We want to find P, so rearrange the formula:

P = FV / (((1 + r)^n - 1) / r)

Substitute the values:

P = $293,000 / (((1 + 0.00367)^336 - 1) / 0.00367)

P ≈ $340.84

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Answer:

120

Step-by-step explanation:

A hexagon has six sides, and we can use the formula degrees = (# of sides – 2) * 180. Then degrees = (6 – 2) * 180 = 720 degrees. Each angle is 720/6 = 120 degrees.

The probability that it toys will be shipped is option b ) 0.6691 .

Hypergeometric Distribution will be used

P ( X = x ) = h ( x , N , n , k ) = \(C_{k,x}\)\(C_{N-k,n-x}\) / \(C_{N,n}\)

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

According to question,

N = 17

k = 2

n = 3

To find : P ( X = 0 ) ,

P ( X = 0 ) = h ( 0 , 17 , 3 , 2 )

                = \(C_{2,0} C_{15,3} / C_{17,3}\)

                 = 455 / 680

         = 0.6691

So there is 66.91 % probability that toys will be shipped .

Hence , option b ) 0.6691 is the correct answer .

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After four hours, the height of the candles will be the same.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A red candle has an 8-inch height and burns at a 7/10-inch per hour rate. A 6-inch tall blue candle burns at a rate of 1/5 inch per hour.

Let x be the number of hours and y be the height.

y = -0.70x + 8           ...1

y = -0.20x + 6             ...2

From equations 1 and 2, then we have

- 0.20x + 6 = - 0.70x + 8

(0.70 - 0.20)x = 8 - 6

0.50x = 2

x = 4 hours

After four hours, the height of the candles will be the same.

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A residual in regression refers to the difference between the observed value and the predicted value of the dependent variable. It represents the unexplained portion of the data that the regression model fails to capture.

In regression analysis, the goal is to build a model that can predict the value of a dependent variable based on one or more independent variables. The model estimates the relationship between the independent variables and the dependent variable by fitting a line or curve through the data points. However, due to inherent variability or noise in the data, the model may not perfectly predict the observed values of the dependent variable.

Residuals are used to measure the accuracy of the regression model. They represent the vertical distance between the observed values and the corresponding predicted values on the regression line. A positive residual indicates that the observed value is higher than the predicted value, while a negative residual indicates the opposite. By calculating the residuals for each data point and examining their distribution, we can assess how well the regression model fits the data.

Analyzing the residuals can guide model improvements, such as identifying outliers, heteroscedasticity, or nonlinear relationships, and can also be used to assess the statistical assumptions of the regression model, such as independence, normality, and constant variance.

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Missing coordinates for the ordered pairs given are A= 4 and B= 18.

An integer pair used to define a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes Coordinates are two numbers (Cartesian coordinates) or, less frequently, a letter and a number that identify a specific location on a grid, also known as a coordinate plane. They are frequently represented by the x-value and y-value pair (x,y). The x (horizontal) and y (vertical) axes are the two axes of a coordinate plane with four quadrants (vertical)

12/A = 9 / 3

A = 4

Same as above

B/6 = 9/3

B = 18

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Answer:This line contains no two such points. Hence the slope is not defined. A y intercept occurs when we make x equal to 0 . Since this is prohibited by the equation x=−3 , there is no y intercept

Step-by-step explanation:

Answer:

y= x2

x= 1

therefore x2= 1×2

x2=2

therefore y= 2

Answer:33

Step-by-step explanation:

5x-15+30+90=180

5x+105=180

5x-105=-105

5x=75

/5=/5

x=15

Answer:

that would be 1

Step-by-step explanation:

in this equation x=74 and 74/74 equals one

Answer:

See below ↓↓↓↓

Step-by-step explanation:

a) Area of circle with radius 10 units

b) Circumference of circle with diameter 7 units

c) Diameter of circle with area 121π square units

d) Area of circle with circumference 20π units

Area of circle with radius 10 units is 314 square units,

Circumference of circle with diameter 7 units is 22 square units,

Diameter of circle with area 121π square units is 22 units and

Area of circle with circumference 20π units is 314 square units

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

a) Area of circle with radius 10 units

A = πr²

A = 3.14 x (10)²

A = 3.14 x 100

A = 314 sq. units

b) Circumference of circle with diameter 7 units

C = πd

C = 3.14×7

C = 21.98 units

c) Diameter of circle with area 121π square units

A = πr²

121π = πr²

r = √121 = 11 units

d = 2r = 2 x 11 = 22 units

d) Area of circle with circumference 20π units

C = 2πr

20π = 2πr

r = 10 units

A = πr²

A = 3.14 x (10)²

A = 3.14 x 100

A = 314 square units

Hence, Area of circle with radius 10 units is 314 square units, Circumference of circle with diameter 7 units is 22 square units, Diameter of circle with area 121π square units is 22 units and Area of circle with circumference 20π units is 314 square units

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From the question, it was given that the Uranium has a molar mass of 238 grams/mole. It means that for every mole of uranium, its mass will be 238 grams.

Because the question asks the mass of 3 moles of uranium, it will be 3 times the mass of a single mole of it. From this, we can perform the calculation as follows:

Answer:

62.in.2

Step-by-step explanation:

4*8 = 32

(8-4) * (10-4-1.5) = 18

8*1.5 = 12

32+18+12 = 62

The length of the garden will be 14.75 feet.

It was illustrated that the dad has 26 feet of fencing to go around the garden.

Also, the person wants the length of the garden to be 3 1/2 feet longer than the width.

Let the width be given as x.

Therefore the length will be x + 3.5

This will be illustrated as:

x + x + 3.5 = 26

2x + 3.5 = 26

Collect like terms

2x = 26 - 3.5

2x = 22.5

Divide

x = 22.5 / 2

x = 11.25

Therefore, the length will be:

= x + 3.5

= 11.25 + 3.5

= 14.75 feet.

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The equation is (1/3-6m)-(1/4n-8).The equation's difference is -6m-1/4n+25/3.

Given that,

The equation is (1/3-6m)-(1/4n-8)

We have to find the difference of the equation.

What is difference?

Difference in mathematics is produced by one of the most important mathematical operations, which is obtained by deleting two numbers. It displays the difference between two numbers. To determine how many numbers are between the two supplied numbers is the goal of finding the difference in math.

The difference in mathematical notation is minus (-).

To difference between whole numbers and natural numbers, take the following steps:

The values are initially arranged vertically according to their place values. Additionally, make sure that the larger number is on top and the smaller one is at the bottom.

Starting at the ones place, begin removing the numerals.

Take the equation,

(1/3-6m)-(1/4n-8)

Taking least common multiple.

(1-6×3m)/3-(1n-8×4)/4

By multiplication

(1-18m)/3-(n-32)/4

Taking the least common multiple.

4(1-18m)-3(n-32)/3×4

By multiplication

(4-72m-3n+96)/12

Now by adding

(-72m-3n+100)/12

By dividing

-6m-1/4n+25/3

Therefore, The difference of the equation is -6m-1/4n+25/3.

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