Bookwork code: M47
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Give your answer in the form y = mx + c, where m and c are integers or
fractions in their simplest forms.
5432
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-8-7-6-5-4-3-2-1.01
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The equation that represents the given sitution is 3a-6 = 69. Rita saved $25.

What is an epression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Assume that Rita saved $a.

Given that the cost of a skateboard is $6 less than three times what she has saved.

The mathematical expression of $6 less than three times what she has saved is 3a-6

The actual cost is $69.

According to the question,

3a-6 = 69

Add 6 on both sides:

3a = 69 + 6

3a = 75

Divide both sides by 3:

a = 75/3

a = 25

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The amount compounded after 16 years is $641.88. Therefore, option D is the correct answer.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].

Given that, principal =$400, time period = 16 years and the rate of interest = 3%.

Here, Amount =400(1+3/100)¹⁶

= 400(1.03)¹⁶

= 400×1.605

= $641.88

Therefore, option D is the correct answer.

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I would implement a random sampling approach to determine the rate of smoking among teenagers.

Simple random sampling is a form of probability sampling in which a selection of participants is chosen at random from a population. Each person in the population has an equal probability of getting chosen. The data is then collected from as big a percentage of this random selection as feasible.

The Simple Random Sampling method is a dependable way of gathering information in which every member of a population is picked at random, purely by chance.

Random sampling guarantees that the findings received from your sample are close to those obtained if the full population was surveyed. The simplest random sample gives each unit in the population an equal probability of being chosen.

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The area bounded by the curve y = sin(x) and y = cos(x) for sin(x) = cos(x) as point of intersection is equal to 2√2.

Area bounded by the curve y = sin(x) and y = cos(x).

Point of intersection for sinx = cosx

⇒  x = π/4 and 5π/4

Required area

= [tex]\int_{\frac{\pi }{4} }^{\frac{5\pi }{4}}[/tex]( sinx - cosx)dx

= ( -cosx - sinx ) [tex]|_ {\frac{\pi}{4} }^ {\frac{5\pi}{4} }[/tex]

= [ -cos(5π/4) - sin(5π/4) ] - [ -cos(π/4) - sin(π/4) ]

= [ -( -1 / √2 ) - (-1 / √2 ) ] - [ -1 /√2 - 1 /√2 ]

= ( 1 + 1 ) / √2 + ( 1 + 1 ) / √2

=  ( 2 + 2 ) / √2

= 4 /√2

= 2√2

Therefore, the area bounded by the given curve is equal to  2√2.

The given question is incomplete, I answer the question in general according to my knowledge:

find the area of the region bounded by the curves y = sin(x), y = cos(x), where solution the points of intersection occur when sin(x) = cos(x), that is, when x = π/4 and 5π/4.

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Your lack of cogscitis has a previous probability of 0.5 according to Dr. B.

Prior probability quantifies how likely a theory is to be correct before any supporting data are taken into account. Your lack of cognitis has a previous probability of 0.5 according to Dr. B. This means that according to Doctor B, there is a 50/50 likelihood that you do not have cognitis before any supporting evidence is considered. This impartial viewpoint is frequently employed in scientific research and medical diagnostics. Prior probability is a crucial component of Bayesian inference, which is used to update a hypothesis' probability after all available data has been considered. Prior probability can help scientists and medical practitioners make better decisions.

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The volume of paper in the recycling bin is 6800 cubic inches.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same. Volume of a rectangular prism = Area of a base × Height.

Given that, the area of the bottom of the bin is 400 square inches. Paper completely fills the bin to a height of 17 inches.

So, the volume of recycling bin is 400×17

= 6800 cubic inches

Therefore, the volume of paper in the recycling bin is 6800 cubic inches.

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We can use the distributive property to expand the left side of the equation, which will give us YZ + XY.

Property is a term used to describe an individual's ownership of something tangible or intangible. Property can include real estate, such as a house or land, or personal property, such as furniture, vehicles, and jewelry. Property can also include intangible items such as copyrights, patents, trademarks, and trade secrets. When property is owned, it is the responsibility of the owner to protect it from damage, destruction, theft, or other losses.

We can then use the given equation to substitute WX for YZ on the right side, which will give us WY. Therefore, YZ + XY = WY.

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The probability of rain in a place during a long weekend (Friday, Saturday, and Sunday) is 65% . The risk of rain is between 10% and 30% on all three days.

a) The risk of rain in the destination throughout the long weekend may be calculated by adding the chance of rain on each day, which is 10% + 25% + 30% = 65%. As a result, the probability of rain at the destination throughout the long weekend is 65%.

b) The notion of conditional probability may be used to calculate the likelihood that it will rain in the destination on all three days of the long weekend. It is the likelihood of rain on Sunday given that it has already rained on:

Friday and Saturday × (the probability of rain on Saturday given that it has already rained on Friday) × (probability of rain on Friday) ×( the probability of rain on Friday).

The best lower bound for this probability is the 10% chance of rain on any given day, and the best upper bound is the 30% chance of rain on any given day.

As a result, the likelihood of rain at the destination on all three days of the long weekend is between 10% and 30%.

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When the larger number is divided by the smaller, the quotient is 2 and the remainder is 4 then the two numbers are 18 and 7.

The first number would be x, leaving the other number to be x+11 (which would make it the bigger number) the quotient is:

[tex]$\frac{x+11}{x}[/tex]

Since it had a remainder of 4, it meant that the numerator was 4 more than having the divisor going in evenly ( had 4 left over) or it would have gone in exactly 2 times

It will take away 4 from the number being divided into (for it was just 4 too big for the divisor going in evenly) making

[tex]$\frac{x+11-4}{x}=2$$[/tex]

combine on top

[tex]$\frac{x+7}{x}=2$$[/tex]

Multiply both sides by x so it cancels on the left side with the denominator, giving

x + 7 = 2 x

subtract the x from both sides leaving

7 = x

So 7 was the first number and 18(x+11) is the second number

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Answer:

This time, ratio is 4:1 for you and 24:5 for your friend

Step-by-step explanation:

For You: Using the same method, join (4,1) and (8,2) with a line and extend it
For your friend: Take (24,5) and (48,10), extend line joining them
Done!

Edit: I took the time variable for the y axis, here's the right graph

Answer: in the graph.

Step-by-step explanation:

When you look at the graph you see time is the x axis and cubes are on the y axis. So your first point is (2, 8) for two hours:8 cubes. From zero, go right 2 and up 8 and place your point. From there go right 2 and up another 8 for your 2nd point. Draw your line. For your second line, 5 hours: 24 cubes, so your first point is right 5 and up 24, place your dot. From there, go right 5 and up 24, draw your dot. Now draw your second line. Graph attached.

Answer:

136

Step-by-step explanation:

calculating each area as shown in the picture above

Using right triangle properties, The length of the guy wire, to the nearest foot is 11√(37) ft.

A triangle in which one of the interior angles is 90° is called a right triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the height and the base.

Here, 2 right triangles are formed. One between stake and pole and second between stake and cell tower.

The height of pole = 12 ft.

The distance between stake and pole = 2 ft.

The distance between pole and tower = 9 ft. so the The distance between stake and tower = 2 + 9 = 11 ft.

Let x is the angle between wire and ground.

from first right angled triangle,

tan x = 12/2

tan x = 6

from second right angled triangle

tan x = height of tower/(11)

6 = height of tower/11

height of tower = 66 ft

So, length of wire = √(66² + 11²)

⇒ length of wire = √[(11*6)² + 11²]

⇒ length of wire = √[11²(6²+1)]

⇒ length of wire = √[11²(36+1)]

⇒ length of wire = 11√(37) ft.

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y = x + 1,If you know the value of x, you can solve for y by plugging the value of x into the equation and then solving for y. if x = 4,y = 4 + 1y = 5.

The equation is a mathematical expression that consists of symbols and numbers, and is used to calculate a numerical value or result. The symbols in the equation represent variables or constants, which are either given values or unknowns that need to be solved. An equation can also be used to describe relationships between different concepts, such as physical laws or chemical reactions.

y = 2x - 5

To solve for y, rearrange the equation to isolate y on one side. Subtract 2x from both sides to isolate y on the left side:

y - 2x = -5

Now add 2x to both sides to get y by itself on the left side:

y = 2x - 5

Therefore, the solution for y is 2x - 5.

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Answer: Using the distributive property, an expression equivalent to 34 + 16 is

2 (17 + 8)

If the distance to a star was suddenly cut in half, it would appear four times brighter.

The brightness of a star is directly proportional to the inverse square of its distance from us. This means that if the distance to a star is halved, its brightness will increase by a factor of four.

The relationship between brightness and distance can be expressed as follows:

B = k / d^2

where B is the brightness, k is a constant of proportionality, and d is the distance.

If the distance to the star is halved, it can be expressed as:

d' = d / 2

Plugging this into the equation for brightness, we get:

B' = k / (d / 2)^2

Expanding this and simplifying, we get:

B' = 4 * k / d^2

Since k is a constant, it cancels out and we are left with:

B' = 4 * B

This means that if the distance to a star was suddenly cut in half, it would appear four times brighter. In astronomical terms, this is equivalent to an increase of 2 magnitudes on the logarithmic magnitude scale.

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The linear equation of f(n) would be -3/2 n + 4.

What is linear function f(n) ?

A linear function is one with the equation f(x) = ax + b, where a and b are real values. The gradient of the line is represented by a, while the y-axis intercept is represented by b. (which is sometimes called the vertical intercept).

A linear equation can be represented as f(n) = mn + b, where m is the slope and b is the y-intercept.

To find m and b, we can use two points from the table.

Let's use the points (6, -1) and (4, 2).

The slope, m, can be found using the formula:

m = (f(n2) - f(n1)) / (n2 - n1)

Plugging in the values from the points, we get:

m = (2 - (-1)) / (4 - 6)

m = 3 / (-2)

m = -3/2

Now that we have m, we can use one of the points and the slope to find b. Let's use the point (6, -1).

f(n) = mn + b

-1 = (-3/2)(6) + b

Solving for b, we get:

b = -1 + (3)(3) = 4

So the linear equation of f(n) is:

f(n) = -3/2 n + 4

Thus, The linear equation of f(n) would be -3/2 n + 4.

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Answer:

Below

Step-by-step explanation:

G = 11  + 2w   <===== 11 passed + 2 more per week

P = 8 + 5w     <====== 8 passed and 5 more per week

  When are they equal ?

     Equate   G and P equations:

  11+ 2w = 8 + 5w

   3 = 3w

    w =1     after ONE week they will have the same  G = 13 = P

Answer:

Lin originally had 4 bags * the same amount of apples per bag = 4 * x apples.

After eating 1 apple from each bag, she was left with 4 * x - 4 apples = 28 apples.

Therefore, each bag originally contained x = 28 + 4 = 32 apples.

Answer:

Graph B represents an increasing function

Step-by-step explanation:

If you look at the other graphs, they are either stagnant on one line or going downwards.

Graph B, on the other hand, is growing on both the x and y axis.

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Answer:

The constant of variation for direct variation is k = y/x.

So we have k = y/x = 5/8

To find y when x = 4, we can use the equation y = kx.

y = kx = (5/8) * 4 = 5

So when x = 4, y = 5

The measure of arc KT be 49 and the measure of arc LN be 17 then the measure of ∠M be 30°.

Simply put, the arc measure is the diameter of the arc relative to the circle. Since they both describe the same thing, it is literally the same as the central angle. The arc length is what you were presumably thinking about because it refers to both the length and the distance of the arc.

Divide the arc length by the circle's circumference, then multiply the result by 360 degrees to find the angle's measurement.

Any straight line connecting two places is considered an arc in general. The arc length is the measurement of an arc's length. An ordered pair of adjacent vertices is referred to as a graph arc in a graph. Any section of the circle's circumference (other than the complete curve) is referred to as an arc.

Let the measure of arc KT = 49 and the measure of arc LN = 17

measure of ∠M = 30°.

Therefore, the measure of ∠M be 30°.

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The slope intercept forms of the values are: 1) y--10x -3 (2) y7x+5 (3) y =9/5-4 (4) -5x/4 +5

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope,

The slope-intercept forms of the values are

1) y--10x -3

2) y7x+5

3) y-9/5-4

4) -5x/4 +5

5) Slope is determined by:

a) (7+6)/(-11-17) =13/-18

b) (-5-4) / (-4-3) = -9/-7 = 9/7

c) (15-14) / (11+20) = 1/31

d) (-7+18) / (-1-11) =11/-12

The slopes of the equations are 1) y=2/3x -2 The slope is 2/3

2) y = 9/5x -5 = The slope is 9/5

3) y = -1/2x -2 the slope is -1/2

4) y = -x -1:  the slope is -1

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Answer: There are 850 students total

Step-by-step explanation: First step is to analyze, 34 brought lunch which makes up 4% so to find total we will divide because dividing percentages gives you bigger numbers.

We will do 34/4%= 850

Therefore there are 850 students attending Ridgewood Junior High School

Effect of switching the explanatory response variables have on the regression line is E) The sign and value of m and the value of b all change.

The y-axis dependent variables and x-axis independent variables are shown as a regression line to show their linear relationship. By examining the data pattern the variables' effects have created, the correlation is established.

In a regression graph, the line closest to the data points is shown. By changing the value of x in the regression equation, his statistical tool assists in analyzing the behavior's of a dependent variable y when there is a change in the independent variable x.

Hence, The sign and value of m and the value of b all change.

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Answer:

The product of (px + qy)(ax − by) is pax^2 + qaxby - pbx^2 - qby^2.

Step-by-step explanation:

Answer: apx^2-bpxy+aqxy-bqy^2

Step-by-step explanation: (px+qy)x(ax-by) Multiply each term in the first parenthesis by each term in the second parenthesis (FOIL). That would give you pxax-bpxy+aqxy-qyby. Then calculate the product pxax which would give you apx^2-bpxy+aqxy-qyby. Calculate the other product qyby which would give you apx^2-bpxy+aqxy-bqy^2.  

En 3 años Carlos ganará $12,724 de intereses.

If Carlos deposits $8000 at a monthly interest rate of 2%, he will earn 1440 in interest over the course of three years. This amount is calculated by first multiplying the amount of the deposit (8000) by the interest rate (2%) to determine the amount of interest earned each month (160).

La formula para calcular el interes compuesto es:

I = P(1+r/n)^(nt)

Donde:

I = Interes

P = Cantidad inicial

r = Tasa de interes

n = Numero de periodos por año

t = Numero de periodos

En este caso:

I = 8000 (1+ 0.02/12)^(12 x 3)

I = 8000 (1.0016667)^36

I = 8000 (1.5905350)

I = 12,724

En 3 años Carlos ganará $12,724 de intereses.

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-3.6<- 10/3 is the answer for above question. -3.6 is lesser than -10/3.

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Answer:

yes youre right its 1

Step-by-step explanation:

2% of 50 is

2/100 = x/50

it simplifies to 1/50 = x/50

so x = 1

Answer:

1

Step-by-step explanation:

2%=2/100=0.02

of means multiply

0.02*50=1

u were correct

Answer:

(f•g)(-4) = f(g(-4)) = f(-21) = -43