a person tosses a coin down from a balcony into a fountain below. substitute 12 for h into the equation h = "-5" - 2 t + 36 to determine how many seconds it will take before the coin passes a sign that is 12 feet above the ground.

The number of years to pay off the loan of principal $14000 in a monthly payment of $400 at rate of 6.8% is 3.3 years

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan. When a loan is taken out it isn't only the principal amount, or the original amount loaned out, that needs to be repaid, but also the interest that accumulates.

The formula for monthly payment is given as ;

Monthly Payment (A) = P {[r(1 + r)ⁿ] / [(1 + r)ⁿ - 1}

Substituting the values into the equation;

400 = 14000 [0.068(1 + 0.068)ⁿ] / [(1 + 0.068)ⁿ - 1]

n = 3.3 year

The number of years for payment is 39 months which is approximately 3.3 years

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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

9. The dilation of the larger solid figure on the coordinate grid to obtain the dashed figure can be represented by the expression in option C

C. (x, y), (-5/8·x, 5/8·y)

A dilation transformation is one in which the dimensions of the sides of the pre-image are increased (enlarged) or decreased to get the image.

9. The dilation of a function, f(x), by a factor k are; f(k·x), and k·f(x), where;

f(k·x) is an horizontal dilation, and k·f(x) is a vertical dilation

The ordered pair (x, y) which can be expressed as (x, f(x)), where, y = f(x), following a dilation by a factor of k is therefore;

[tex](x, \, y) \overset{D_k}\rightarrow (k\cdot x, \ k\cdot f(x)) = (k\cdot x, \ k\cdot y)[/tex]

The representation of a dilation of a point (x, y), by a factor of k is therefore, obtained by multiplying both the x and y-values by the factor k, as follows;

(x, y)   [tex]\overset{D_x} \rightarrow[/tex]   (k·x, k·y)

Similarly, the representation of the reflection of the point (x, y) across the y-axis is the point (-x, y)

The point (-5.8·x, 5/8·y),m is therefore obtained from the dilation of the point (x, y), by a factor of 5/8, followed by a reflection across the y-axis.

The option that represents the dilation is therefore, option C

C. (x, y), (-5/8·x, 5/8·y)

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Answer:

D. [tex]y=-2x+3[/tex]

Step-by-step explanation:

1. Isolate y to convert the original equation to slope-intercept form  [tex](y = mx+b)[/tex]:

[tex]4x+2y=8\\ 2y=8-4x\\ y = \frac{8-4x}{2} \\y = -2x+4\\[/tex]
2. To find the equation parallel to a linear equation, use the original slope and plug in the given point to find b.

We know the slope of the original equation is m = -2, found in step (1).
[tex]y = -2x+ b\\(5) = (-2)(-1) + b \\5-2 =b \\3 = b[/tex]

3. Assemble the final equation:

[tex]y = -2x + 3[/tex]

The height and length of the base of A triangular banner which has an area of 351 cm² is l = 13, and h = 11 / 4 respectively.

One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.

Given data:

A triangular banner has an area of, A =  351 cm²

The length of the base is two centimeters longer than four times the height

Write the equation as shown below,

l = 4h + 2

Here, l = base length, and h = height

Calculate the area,

A = 1 / 2 l × h

351 = 1/2 (4h + 2)h   Substitute the value of l

351 = (2h + 1)h

2h² + h = 351

Solve the quadratic equation to get the value of l,

l = 13 so 4h + 2 = 13

so 4h + 2 = 13

4h = 13 -2

h = 11 / 4

Therefore, the height and length of the base of A triangular banner has an area of 351 cm² is l = 13, and h = 11 / 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!!!!

Answer:

Hope the picture will help you

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:

look it up

Step-by-step explanation:

that is not how to spell answer

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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QR≅SR (given)

PQ ≅ PS (given)

PR = PR (common to both triangles)

∠QPR ≅ ∠SPR (SSS rule)

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

SSS rule (side-side-side)

The three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent.

From the given figure.

QR≅SR (given)

PQ ≅ PS (given)

PR = PR (common to both triangles)

∠QPR ≅ ∠SPR (SSS rule)

Thus,

∠QPR is congruent to ∠SPR by SSS rule.

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The linear equation can be written as:

y = -5*(x + 3) - 4

And its graph can be seen at the end of the answer.

Here we want to graph a line with a slope of -5 that contains the point (-3, -4).

Particularly, for a line with a slope a and a known point (h, k) can be written in the point-slope form as:

y = a*(x - h) + k

So our line can be written as:

y = -5*(x + 3) - 4

Now let's graph it. To graph the line we need to know two points on the line. We already know one that is (-3, -4)

Let's find another, if we evaluate the line in x = 0 we will get:

y = -5*(0 + 3) - 4

y = -5*3 - 4

y = -15 + 4

y = -19

Then the linear equation also contains the point (0, -19), now just let's graph the two known points and connect them with a line. The graph of the g can be seen below.

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If heteroskedasticity is present, the Ordinary Regression Analysis approximations are not the best linearly unbiased estimators.

Heteroskedastic describes a situation in which a regression model's residual term, or measurement error, variance fluctuates significantly. If this is the case, there may be a factor which can explain why it varies in a predictable manner.

When the variances of a predictor are heteroskedastic (or heteroscedastic), it signifies that the variability of the errors is indeed not constant across data. Particularly, estimated coefficients may influence the variability of the mistakes. Non-constant measures are those that are tracked over a range of independent variable values or in relation to earlier time periods.

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The equation of the line shown is; y= -1/2x+2. Also the graph of line with equation y=1/3x-5 is attached.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) and has a gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Where x₁ - x coordinate, y₁ - y coordinate

m - slope

Then Slope line with equation y=1/3x-5

m = 1/3

Now Write the equation for the line shown as;

y= -1/2x+2

Slope = -1/2

Hence, the equation of the line would be;

y= -1/2x+2.

Thus the graph of line with equation y=1/3x-5 is attached below.

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Answer:

length = 10 in.

width = 8 in.

Step-by-step explanation:

volume of cuboid = length(l) * width(w) * height(h)

l = w + 2

(w + 2) * w * 6 = 480

(w + 2) * w = 480/6 = 80 in²

w² + 2w =  80

w² + 2w - 80 =  0

solve for w (AC method):

w² + 10w - 8w - 80 = 0

w(w + 10) - 8 (w + 10) = 0

(w-8)(w+10) = 0

w = 8 or w = -10

As length cannot be negative, w = 8 in.

substitute w with 8:

l = 8 + 2 = 10 in.

10 * 8 * 6 = 480 in³

3.

The value of x is 20°

The value of y is 30.

4.

The value of x is 30°

The value of y is 4.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

3.

An equilateral triangle.

Where all three angles and all three sides are equal and the angle is 60°.

Now,

16 + y = 46

y = 46 - 16

y = 30

And,

180 - 80° = 100°

The sum of the angles must be 180°.

x + 100 + 60 = 180

x = 180 - 160

x = 20°

4.

We have an equilateral triangle and an isosceles triangle.

All the angles in the equilateral triangle are 60°.

The two angles opposite to the equal sides of the isosceles triangle are equal.

So,

5y = 20

y = 4

And,

In the isosceles triangle.

The straight angle.

60 + angle = 180

angle = 180 - 60

angle = 120.

Now,

The sum of the angles of the isosceles triangle = 180.

2x + 120 = 180

2x = 60

x = 30°

Thus,

3.

The value of x and y is 20° and 30.

4.

The value of x and y is 30° and 4.

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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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Answer:

A  -0.16

Step-by-step explanation:

I got it right on edge

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 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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The measure of each angle 2x°, 3x°, 4x°, and x° will be 72°, 108°, 144°, and 36°, respectively.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

The angle 2x and angle 3x is the supplementary angles. Then the value of 'x' is given as,

2x + 3x = 180

5x = 180

x = 36

Then the value of each angle is given as,

2x = 2 × 36 = 72°

3x = 3 × 36 = 108°

4x = 4 × 36 = 144°

 x = 1 × 36 = 36°

The measure of each angle 2x°, 3x°, 4x°, and x° will be 72°, 108°, 144°, and 36°, respectively.

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The rate of change in elevation of the second scuba diver in feet per minute is; 12.5 ft/minute

We are given that;

The elevation of a certain scuba diver changes by 15⁵/₈ ft every minute.

Now, this rate of change was 1¹/₄ times the rate of change for a second scuba diver.

Thus, if the rate of change of elevation for the second scuba diver is x, then it means that;

15⁵/₈ = 1¹/₄x

Converting the fractions to improper fractions gives us;

125/8 = 5x/4

Thus making x the subject gives us;

x = (125 * 4)/(5 * 8)

x = 12.5 ft/minute

This represents the rate of change in elevation of the second diver.

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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 :)

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- Jeron

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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Answer:

13n+8

Step-by-step explanation:

8 more = 8+

product of 13 and n= 13n

8more then 13n

Answer:

Step-by-step explanation:

Eight more than the product of 13 and a number = 13n+8

13n+8=0

13n=-8

n=-8/13

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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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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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:

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