f(x) = 5x-10 and g(x) = -x+4
Calculate f(-3)

By using fraction, it can be calculated that--

a) Number of marbles not chosen = 62

b) Number of marbles in the bag before the game = 86

c) Number of blue marbles chosen = 24

What is a fraction?

Suppose there is a collection and a part of a collection has to be taken. The part which is taken is called fraction. In other words, part of a whole is called fraction. The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.

This is a word problem on fraction.

a)Number of blue marbles = 40

Number of white marbles = 46

Fraction of blue marbles chosen = [tex]\frac{3}{5} \times 40[/tex] = 24

Number of marbles not chosen = 40 + 46 -24 = 62

b) Number of marbles in the bag before the game = 40 + 46 = 86

c) Number of blue marbles chosen =  [tex]\frac{3}{5} \times 40[/tex] = 24

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Answer:

Hope the picture will help you

T = 8.80 years is the time required which can be find using simple interest.

Here,

Simple Interest (I) = 3300 (8300-5000)

Principal amount (P) = 5000

Rate of Interest (R) = 7.5%

Time (T) =?

Now using the formula of Simple Interest,

I = P + R+ T

3300 = 5000 + 75/1000 + T

3300/375 = T

T = 8.80 years

What is simple interest?

The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest.

Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest.

Simple interest loans are frequently used for auto loans and short-term personal loans.

Simple interest is calculated by multiplying the principal by the time, interest rate, and time period. "Simple Interest = Principal x Interest Rate x Time" is the written formula.

The straightforward interest computation offers a very fundamental perspective on interest. It serves as a general introduction to the idea of interest. In the actual world, the processes used to calculate interest—whether you're earning it or paying it—are typically more intricate.

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The probability that the sample mean salary will  be less than $29,000 is -1.51.

The central limit theorem implies that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently enough random samples from the population with replacement.

Central Limit Theorem for Sample Means z-score and standard error of the mean: z=ˉx−μx(σx√n)

z=ˉx−μx/(σx/√n)

where

xbar = $29,000

μx = $29,321

σx = $2,120

n = 100

inputing value into the z-formula

(29,000 – 29,321) / (2,120/√100) = -321/212 = -1.51

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The equation of the ellipse in standard form is x² / 36 + y² / 117 = 1.

In this problem we must derive the equation of the ellipse in standard form based on all the information about the foci and vertices. The standard form is described by the following expression:

(x - h)² / a² + (y - k)² / b² = 1, a < b

Where:

And the length of the major semiaxis (b) is found by Pythagorean relationship:

b² = a² + c²

b = √(a² + c²)

Where c is the distance between the center and any of the foci.

First, determine the coordinates of the center by midpoint formula:

(h, k) = 0.5 · (6, 0) + 0.5 · (- 6, 0)

(h, k) = (0, 0)

Second, determine the length of the minor semiaxis:

(a, 0) = (6, 0) - (0, 0)

(a, 0) = (6, 0)

a = 6

Third, find the distance between the center and any foci:

(0, c) = (0, 9) - (0, 0)

(0, c) = (0, 9)

c = 9

Fourth, determine the length of the major semiaxis:

b = √(6² + 9²)

b = 3√13

Fifth, write the equation in standard form:

x² / 36 + y² / 117 = 1

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The value of m∠3 after solving the triangle is 110° and the correct option is a 110°.

A triangle is a plane shape that has three sides.

To find the value of m∠3 in the triangle, we use the formula below.

Formula:

But from the question,

Substitute the value of m∠2 into equation 1

Hence, the correct option is a 110°.

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Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

The mean number of movies that the students saw is 15.

What is mean?

A mean in maths is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Mean =  Sum of the observations/number of observations

Now it is given that,

Number of students = 5

The number of movies they say = 4, 20, 12, 20, 19

So,

the sum of the number of movies = 4 + 20 + 12 + 20 + 19 = 75

Hence,

Mean = sum of the number of movies / Number of students

⇒Mean = 75/5

⇒Mean = 15

Hence, the mean number of movies that the students saw is 15.

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Answer:

x = 1

Step-by-step explanation:

Solve the following system of equations using substitution.

x + y = 4

y = 3x

Take the first equation and substitute in the second for the value of y:

x + (3x) = 4

4x = 4

divide both sides by 4:

4x/4 = 4/4

x = 1

check: if x = 1

1 + (3*1) = 4

1 + 3 = 4

4 = 4

The place value of a digit in a given number can be in either unit, tens, hundred, thousand, hundred of thousand etc.  Therefore the required answer is option B. 0.18.

The place value of a digit is its position in a given number. These could either be as unit, tens, hundred, thousands, ten thousands etc.

This can now be stated as required. This knowledge is required when round off a given decimal number to either a required number of significant figure or decimal places.

So that considering the given question, the place value of 1 in the given number 0.1 is tenths. Therefore, the place value of digit 1 that would make it to have a value of 0.1 is the number 0.18. Thus option B.

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Answer:

Since the slope is undefined, this is a vertical line. Vertical lines have no y-intercept. No y-intercept.

Step-by-step explanation:

hope this helped:)

Answer:

To write the equation of a line in slope-intercept form, we need to first find the slope of the line. The slope is a measure of the steepness of the line, and is calculated as the rise over the run between two points on the line. In this case, we can use the points (-6,-3) and (6,-7) to calculate the slope.

To find the slope, we first need to find the difference between the y-coordinates of the two points, which is -3 - (-7) = 4. We then need to find the difference between the x-coordinates of the two points, which is 6 - (-6) = 12. The slope is then calculated as the rise over the run, which is 4/12 = 1/3.

Once we have the slope, we can use the point-slope formula to write the equation of the line in slope-intercept form. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, we can use the point (-6,-3) and the slope 1/3 to write the equation of the line.

The equation of the line in slope-intercept form is then y - (-3) = 1/3(x - (-6)), which simplifies to y + 3 = 1/3x + 2. This is the equation of the line that passes through the points (-6,-3) and (6,-7) in slope-intercept form.

Therefore, the correct answer is y + 3 = 1/3x + 2.

Step-by-step explanation:

The value of the expression given as 7/4 of 66 is 231 / 2 or 115.5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Given:

7/4 of 66

The above expression is represented by of operation, which means multiplication

7/4 of 66 = 7 / 4 × 66

7/4 of 66 = 7 / 2 × 33

7/4 of 66 = 231 / 2

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The narrowest graph of the quadratic function is y = 5x² + 1.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know the graph a quadratic function y = ax² + bx + c is narrower and narrower with an increase in the value of a > 1.

From the given options we conclude that y = 5x²+ 1 has the narrowest graph.

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Answer:

D is the answer

Step-by-step explanation:

Answer: D

Step-by-step explanation:

Congruent definition: Two triangles are congruent if they have: precisely the same three sides and. precisely the same three angles

the triangle has the same angle measures but different sides.

The answer is D

By using the concept of rotation, it can be inferred that

New coordinate of C (C') = (12, -6)

What is rotation?

Rotation is a mathematical transformation in which an object is turned about a fixed point called the center of rotation. Rotation is a very important tool in mathematics, especially in coordinate geometry.

In this problem, 90° rotation clockwise about the origin has been applied.

We need to find the new coordinate of C after rotation.

Coordinate of C = (6, 12)

C is in the first quadrant

On rotating 90° clockwise, point C will go to fourth quadrant

New coordinate of C (C') = (12, -6)

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Answer:

y = -4

Step-by-step explanation:

x - y = 2

-2 - y = 2

+2.      +2

-y = 4

__  __

-1.    -1

y = -4

The inequality that represents the situation given is option c  x ≥ 1,350

Given,

There are at least 1,350 students at school today.

We have to find the inequality which represents the situation;

Inequality;-

The occurrence of an unfair and/or unequal distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different people and in various settings, the word "inequality" may indicate different things.

Here,

At least means minimum of. That is, greater than or equal to.

So,

x be the number of students.

Then,

x ≥ 1350 represents the number of students.

That is,

x ≥ 1350 (option C) is the inequality which represents the situation given here.

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The total Variance above the standard labor cost  $100

Standard cost to prepare the meal at actual quantity

6,000 x 0.20 = 1,200 x $9.50 = $11,400

Actual incurred = 11500

labor rate variance

11,500 actual - (1,150 actual hours x $9.50 standard rate) = -$575 u

labor efficiency variance =(1,150 actual hours x $9.50 standard rate) - $11,400 = 475 f

The variance contains two components, an unfavorable rate variance, offset by a favorbale efficiency variance. The rate variance is calculated by comparing the actual amount paid to the actual hours at the standard rate.

Add the labor rate variance of $575 and the efficiency variance of ($475) and you get a total variance of $100 above the standard labor cost.

So

The total Variance above the standard labor cost  $100

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Answer:

look it up

Step-by-step explanation:

that is not how to spell answer

Find slope.

Over 4 x, it travels up 3 y.

Slope = rise/run

Slope = 3/4x

At x = 1, y = 3/4

In the context of the problem, this is 75 cents per unit of something.  

Option C

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

The graph of g(x) is a vertical shrink of f(x) by a factor of 1/3 and a reflection across the x-axis

What is Co-ordinate Geometry?

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Solution:

Please refer to the graph attached

The Option B - The graph of g(x) is a vertical shrink of f(x) by a factor of 1/3 and a reflection across the x-axis is correct

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Answer: 8 + 5i

Step-by-step explanation:  P + Q so insert each equation

5 - 2i + 3 + 7i

combine like terms

5 + 3 and 7i - 2i

leaving you with 8 + 5i   in a + bi form

The shape has 2 angles that are acute and equal.

The acute angles

As a general rule, acute angles are angles that are less than 90

In this case, we have

Angles = 55 and 55

This means that it has 2 acute and equal angles

The obtuse angles

As a general rule, obtuse angles are angles that are greater than 90 and less than 180

In this case, we have

Angles = 125 and 125

This means that it has 2 obtuse and equal angles

Right angles

As a general rule, right angles are angles that have a measure of 90 degrees

In this case, we have no angle with a measure of 90 degrees

This means that it has 0 right angle

The best name

In this case, the shape has two parallel sides

So, the best name is a parallelogram

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The three points that are the solution set of the equation, x + 3y = -5, are shown in the graph below as: (-5, 0), (-2, -1), and (7, -4).

If a point is a solution to an equation of a line, it means the point lies on the line and its coordinate values will make the equation true if plugged into the equation.

Given the equation, x + 3y = -5, in slope-intercept form, it can be rewritten as y = -1/3x - 5/3.

This means that the line of this equation will have the following features:

The slope of the line = rise/run = -1/3

The y-intercept is -5/3.

The line is drawn in the graph as shown in the image below.

The solution set plotted on the line are: (-5, 0), (-2, -1), and (7, -4).

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Answer:

0.5

1.The probability of rolling an even number on a die.

2.The probability of flipping a head on a fair coin.

3.The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball, and 3 basketballs. 

0.2

1.The probability of choosing a red block out of a bag containing 1 red, 1 blue, and 3 green blocks.

2.The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls, and 1 squishy ball. 

0.4

1.The probability of choosing a blue marble out of a bag containing 3 red, 1 green, 4 blue and 2 yellow marbles. 

Step-by-step explanation:

HOPE THIS HELPS!!!!

The speed of the ball after one second is given as follows:

9.175 m/s.

The speed function is the derivative of the position function, which is graphed in this problem.

The position function, in meters, for a projectile's height, is given as follows:

h(t) = -4.9t² + v(0)t + h(0).

In which:

From the graph, the initial height is given as follows:

h(0) = 6.

When t = 4, h = 2.5, hence the initial velocity is obtained as follows:

2.5 = -4.9(4)² + 4v(0) + 6

4v(0) = 2.5 - 5 + 4.9(4)²

4v(0) = 75.9

v(0) = 75.9/4

v(0) = 18.975.

Then the position function is of:

h(t) = -4.9t² + 18.975t + 6.

The velocity function is the derivative of the position, hence:

v(t) = -9.8t + 18.975.

Then the velocity after one second is of:

v(1) = -9.8 + 18.975 = 9.175 m/s.

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The balance after 7 years if you invest 400 at 6 percent compounded monthly is  608.15 units.

You invest 400 at 6 percent compounded monthly . The balance after 7 years can be calculated as follows:

Therefore, using compound interest formula, let's find the amount.

[tex]A = p(1 + \frac{r}{n} )^{nt}[/tex]

where

Therefore,

r = 6 / 100 = 0.06

t = 7 years

p = 400

n = 12

Therefore,

[tex]A = 400(1 + \frac{0.06}{12} )^{12(7)}[/tex]

A = 400(1 + 0.005)⁸⁴

A = 608.15 units

Therefore, the balance is  608.15 units

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Answer: 1/10 of a pound

Step-by-step explanation: The original block of cheese was 1/2 a pound, then she cut the block into 5 equal parts. Divide 1/2 by 5 and you get 1/10

Answer:

1/10 of a pound

Step-by-step explanation:

Using this word problem, we can tell that the problem is a division problem:

1/2 ÷ 5 = x

To solve a division problem with fractions, you multiply the first number with the reciprocal (reverse) of the second number:

Now you get the equation:

1/2 x 1/5

To solve this you multiply the numerators together and the denominators together:

1/10 is the answer