Clark gets a savings account that earns an interest rate of 0.5%. Clark starts with principle balance of $120. Use the equation I = prt where I = interest earning, p = principle balance, r = interest rate, and t = time in years. How much interest is earned, in dollars, when t = 10?

The exact value of a trig function can be found by using the unit circle, the trigonometric identities, tables or a calculator.

To find the exact value of a trigonometric function, there are several methods you can use. Below are a few:

1. Using the Unit Circle: The unit circle is a circle with radius 1 centered at the origin in the coordinate plane. The angles in the unit circle are measured in radians and the coordinates of points on the circle can be used to find the exact values of trigonometric functions. For example, given an angle θ in the unit circle, the x-coordinate of the point on the circle corresponding to θ is cos(θ) and the y-coordinate is sin(θ).

2. Using the Trigonometric Identities: There are several trigonometric identities that relate the values of the six trigonometric functions to one another. These identities can be used to find the exact value of a trigonometric function for certain angles. For example, the Pythagorean identity states that for any angle θ, sin²(θ) + cos²(θ) = 1.

3. Using Tables or a Calculator: Trigonometric tables or a scientific calculator can be used to find the exact values of trigonometric functions for certain angles. The values are often given in degrees, so it is important to convert the angle to radians if necessary.

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The required two other expression are d + 49d/100 and 149d/100.

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

We have;

An art teacher enlarged the area of a copy of a painting by 49%. and d represent the area of the original painting.

Given expression is d+ 0.49d

New expressions are

1) d+ 0.49d

= d + 49d/100

2) d+ 0.49d

= d + 49d/100

= 149d/100

Thus, required two other expression are d + 49d/100 and 149d/100.

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$15 is the interest on the amount saved in a year

The formula for calculating simple interest is expressed according to the equation below:

I = PRT

where:

P is the principal = $300

R is the rate = 5% = 0.05

T is the time = 1 year

Substitute to have:

I = 300 * 0.05 * 1

I = $15

Hence the interest that she will earn in a year is $15

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Answer:

Below

Step-by-step explanation:

Put ' - 3' into the equation where 'x' is and compute

6 ( 2(-3)^2 -5) =

6 ( 2*9   -5)

6 ( 18-5)

6(13) = 78

-2 is to be multiplied in the second equation to make the y-values additive inverses.

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

Given are two equations,

3x-4y = -5.....(i)

5x-2y = -6.....(ii)

We need to find the additive inverse of y variable,

The coefficients of y variables in the both equations are ;-

-4 and -2

The additive inverse of -4 is 4,

If we multiply -2 by -2 it becomes 4,

Hence, -2 is to be multiplied in the second equation to make the y-values additive inverses.

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The expression used to find the surface area of the rectangular prism is given as follows:

S = 2 x (1/2 x 3 x 4) + 4 x 2 + 3 x 2 + 5 x 2.

The prism is composed as follows:

The area of each component is given as follows:

The surface area is given by the addition of all these areas.

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Using the concept of proportions and ratios, 684L of natural oil is required to produce 855L of Petrolyn oil.

Proportions are mathematical statements that express the equality of two ratios. A ratio is a comparison of two values, often written as a fraction. For example, if you have 5 apples and 2 bananas, the ratio of apples to bananas can be written as 5/2. A proportion is an equation that sets two ratios equal to each other, such as:

a/b = c/d

In this problem, we need to find the ratio or simply equate and calculate how many liters of natural oil are needed

4L of natural oil = 5L of synthetic oil

xL of natural oil = 855L

cross multiply both sides and solve for x

x = (855 * 4) / 5

x = 684L

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Answer:7/12

Step-by-step explanation:

1/3 = 4/12

1/4=3/12

3/12+4/12 = 7/12

7/12 is the answer

The values are written in commas as x², 6x  and 9

It is important to note that algebraic expressions are expressions that are made of terms, variables, coefficients, factors and constants.

From the information given, we have the quadratic expression as:

(x + 3)^2

Now, take the following steps to determine the values

(x + 3)(x +3)

expand the bracket, we get;

x² + 3x + 3x + 9

Now, collect the like terms and add the values

x² + 6x + 9

Hence, the value is x² + 6x + 9

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Answer:y=-5x+6

Step-by-step explanation:

The expanded form of 916.408 can be written as:

(9 x 100) + (1 x 10) + (6 x 1) + (4 x 0.1) + (8 x 0.01)

Expanded form is a way of writing a number that shows the place value of each digit in the number. In expanded form, a number is expressed as the sum of individual terms, each representing a digit in the number multiplied by its place value.

For example, the number 356 can be written in expanded form as:

3 x 100 + 5 x 10 + 6 x 1

Expanded form can be used to better understand the structure of numbers and how place value works.

So, the numbers should be placed as follows:

(9 x 1,000) + (1 x 100) + (6 x 10) + (4 x 1) + (8 x 0.1)

Therefore, the correct order is:

1000, 100, 10, 1, 0.1

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Answer:

122

Step-by-step explanation:

the question is asking for the area of the whole shape

however, it's split into a trapezoid and rectangle, so all you have to do is find the area of the respective shapes and then add them

the formula for area of a rectangle is [tex]A = L(W)[/tex]

if you substitue, A = 15(6)

so the area of the rectangle is 90

then, you have the trapezoid

area of a trapezoid = [tex]\frac{1}{2} (h)(b_{1} +b_{2})[/tex]

you might assume that you don't have the second base, but it's in the rectangle - 6

A = 1/2(4)(6+10)

A=32

90+32 = 122

Answer: To graph the system of linear equations, you can plot the two lines on the same coordinate plane and look for the point where they intersect. If they intersect, that point represents the solution to the system.

The equation y = x - 6 can be written in slope-intercept form, y = mx + b, where m = 1 and b = -6. The equation of the line will be y = x - 6.

The equation y = -x - 2 can be written in slope-intercept form, y = mx + b, where m = -1 and b = -2. The equation of the line will be y = -x - 2.

Plotting these two lines on the same coordinate plane, we can see that they intersect at the point (2, -4). This means that there is one solution to the system of equations: (2, -4).

Step-by-step explanation:

The height of the cylinder having a volume of 471 cubic centimetres will be 6 cm. The correct option is D.

The volume of the cylinder is defined as the three-dimensional space occupied by the cylinder.

We can use the formula for the volume of a cylinder, which is given:

V = πr²h

Where V is the volume, r is the radius, and h is the height of the cylinder.

We are given that the cylinder is full at 471 cubic centimetres and that the radius is 5 centimetres. Therefore, we can plug in these values into the formula and solve for h:

471 = π(5²)h

471 = 25πh

h = 471 / (25π)

h ≈ 6 centimeters

Therefore, the height of the cylinder is approximately 6 centimetres.

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Answer:

B. 2/3

Step-by-step explanation:

If y directly varies with x, then y = kx where k is a constant

Given that when y = 20 when x = 30 we get the equation: 20 = k x 30

or

20 = 30k

Dividing by 30 both sides and switching sides gives

k = 20/30 = 2/3

The equation becomes
y = 2/3 x

Therefore if x = 1 we get

y = 2/3 x 1 = 2/3

Choice B

Answer:

Step-by-step explanation:53/10

Answer:

36

Step-by-step explanation:

3x+6= 8x-11

3x-8x= -11-6

-5x= -17x

x= 3  2/5

10x+2= 10(3  2/5)+2

         = 34+2

         = 36

Answer:

Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.

Step-by-step explanation:

The given linear regression equation is y=0.775x+950.25, where x represents the square footage of the apartment and y represents the monthly rental price. To find the size of the apartment Grace can expect to rent for $1,500 per month, we can substitute y with 1,500 in the equation and solve for x:

1,500 = 0.775x + 950.25

0.775x = 1,500 - 950.25

0.775x = 549.75

x = 710.32

Therefore, Grace can expect to rent an apartment with a size of approximately 710.32 square feet for $1,500 per month based on the given linear regression equation.

Answer:

Step-by-step explanation:

$\frac{456.232}{4}$

A monomial is an algebraic expression that consists of a single term. A monomial can contain constants and/or variables, which are multiplied together.

The expression 3x²y is a monomial. It contains the constant 3, the variable x squared, and the variable y. The variables can be raised to an exponent, as in this example; however, the exponent must be a whole number.A monomial can also contain coefficients, which are the numbers that are multiplied with a variable. In the example above, the coefficient is 3. If there is no coefficient stated, then the coefficient is assumed to be 1. Therefore, the expression x²y is also a monomial, with the coefficient being 1.Additionally, a monomial can contain a product of numbers and variables, such as the expression 2xyz. This is also considered a single term, since all of the numbers and variables are multiplied together.

Monomials can be used to calculate polynomials, which are algebraic expressions consisting of multiple terms. By adding, subtracting, and multiplying monomials together, you can create a polynomial. For example, the expression (3x²y) + (2xyz) is a polynomial, since it consists of two terms. The first term is the monomial 3x²y, and the second term is the monomial 2xyz.

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Answer 15489 Rupees

Step-by-step explanation:

Total parts= 7+2=9 parts

total salary= 9x
taken salary for car repair= 2x/7
remaining salary= 15000 rupees

9x-2x/7= 15000
(63x-2x)/7=15000
61x/7=15000

61x=105000
x= 105000/61
x= 1721(approx)

Total salary= 9x
                   = 9*1721
                   =15489 rupees


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The required domain and range of the function are (-∞, ∞) and  (2, ∞).

The domain of a function is the set of all possible values of the input variable (x) for which the function is defined. In this case, the function is an exponential function with base 4, which means it is defined for all real numbers.

Therefore, the domain of f(x) is all real numbers, or (-∞, ∞).

The range of a function is the set of all possible values of the output variable (f(x)) for all possible values of the input variable (x).

Since 4^x is always positive (for all x), the value of the function f(x) will always be greater than 2 (the constant added to 5(4)^x), no matter what the value of x is.

As x approaches negative infinity, 5(4)^x approaches zero, so the minimum value of f(x) is 2.

As x approaches positive infinity, 5(4)^x increases without bound, so the range of f(x) is (2, ∞).

Thus, required domain and range of the function are (-∞, ∞) and  (2, ∞).

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Answer:

Step-by-step explanation:

There are 12 months in a year, and 7 of them have more than 5 letters in their names (July, August, September, October, November, December, and January).

The complement of the event is drawing a month with 5 or fewer letters in its name. There are 5 months with 5 letters in their names (May, March, April, June, and August), and 2 months with 4 letters in their names (July and June). Therefore, there are 7 months with 5 or fewer letters in their names.

The probability of drawing a month with 5 or fewer letters in its name is 7/12. The probability of the complement of the event (drawing a month with more than 5 letters in its name) is 1 - 7/12 = 5/12.

Therefore, the probability of the complement of the event is 5/12.

If yall ain't gotta show work just put 5/12 that's the answer the person with the long paragraph

Answer:

Step-by-step explanation:

Given the radius of the base of the cone is 5 cm and the height of the cone is 12 cm, we can find the volume of the toy as follows:

Volume of the cone:

The volume of a cone can be found using the formula: V = (π * r^2 * h) / 3, where r is the radius and h is the height of the cone.

Plugging in the values, we get:

V = (π * 5^2 * 12) / 3 = 100π cm^3

Volume of the hemisphere:

The volume of a hemisphere can be found using the formula: V = (4/3) * π * r^3, where r is the radius of the hemisphere.

Plugging in the values, we get:

V = (4/3) * π * 5^3 = (4/3) * π * 125 = 500π / 3 cm^3

Total volume of the toy:

The total volume of the toy is equal to the sum of the volume of the cone and the volume of the hemisphere:

V = 100π + 500π / 3 = (100 + 500 / 3) * π = 600π / 3 cm^3

So, the total volume of the toy is 600π / 3 cubic centimeters.

Answer:

  a = 1/2

Step-by-step explanation:

You want the solution to 3 +0.5(4a +8) = 9 −2a.

It usually works well to start by simplifying the equation. That is, you eliminate parentheses, combine like terms.

  3 +0.5(4a) +0.5(8) = 9 -2a

  3 + 2a +4 = 9 -2a

  7 +4a = 9 . . . . . . . . . add 2a

  4a = 2 . . . . . . . . . subtract 7

  a = 0.5 . . . . . . divide by 4

The value of a is 1/2.

__

Additional comment

The attached calculator output shows this value of 'a' satisfies the equation.

Answer:

Slope: [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]

y-intercept: [tex]\boxed{-1}[/tex]

Equation: [tex]\boxed{\bf{y=-\dfrac{1}{3}x - 1}}[/tex]

The two boxes at the bottom are asking you to repeat the above information:

the slope is [tex]\bf \boxed{-\dfrac{1}{3}}[/tex]   the y-intercept is [tex]\boxed{-1}[/tex]

Step-by-step explanation:

Actually, you don't have to graph the equation since the graph is already provided

You have to answer the questions based on the provided graph

To find slope

1. Take any two well=defined points on the graph:

2. Find the difference in y-values between P2 - P1. This called rise

3. Find the corresponding difference in x-values: P2 - P. This is called run

4. The slope is computed as rise/run = - 1/3

To find y-intercept

Just note where the line crosses the y-axis and the y-value corresponding to that would be the y-intercept

This is also the y-value at which x = 0

Looking at the graph we see that the line crosses(intercepts) the y-axis at y = - 1
So y-intercept = - 1

To write the equation

The equation of the line is
y = mx + b

where

m = slope

b = y-intercept

So the equation of this particular line is

[tex]\bf{-\dfrac{1}{3}x - 1}[/tex]

If we substitute so every tiny proportion with 0, 1, or 12, the approximate distinction among 7/8 and 6/11 is then equal to 0.

the end result of subtracting two numbers. the difference between two numbers. Example: Subtract five to get the difference between eight and three.

We can substitute each percentage with either a 0, 1, or 12 to calculate the difference between 7/8 and 6/11.

We can round up to one because we know that 7/8 is larger than 1/2 but much less over 1.

For 6/11, we can round up to 1 since we know it is larger than 1/2 but a little less than 1.

As a result, we can calculate the difference as follows:

7/8 - 6/11

= 1 - 1

= 0

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Based on the simulation, we can say that, 95% of proportion of the 95 percent confidence intervals capture the population proportion of 0.3.

Confidence interval in statistics is defined as the certain range of values that you estimate for the unknown parameter lies within.

This means that, if you do your experiment more than once and do resampling, then this is the percentage that the parameters falls within a range.

If we say that the confidence interval is A% for a certain parameter like proportion, mean, standard deviation, etc. to be fall within a range of x and y, then this can be interpreted as that we are A% confident that the parameters fall within x and y.

In other words, A% of the intervals capture the parameters.

Therefore, here, we can say that, 95% of the 95% confidence intervals will capture the population proportion of 0.3.

Hence 95% of proportion of the 95 percent confidence intervals capture the given proportion.

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