Stephanie spends $15 each month to belong to a photography club. As a member of the club she can develop rolls of film for $2.50 each. Write and solve an equation to find the total amount Stephanie will spend this month if she develops 5 rolls of film.

Answer:

[tex]\displaystyle y=2\sqrt{6}[/tex]

[tex]\displaystyle x=2\sqrt{2}[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

The longest side of the right triangle is called the hypotenuse and the other two sides are the legs.

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.

The image provided shows a right triangle whose hypotenuse is given. We are required to find the value of both legs.

Let's pick the angle of 30°. Its adjacent side is y. We can use the cosine ration, which is defined as follows:

[tex]\displaystyle \cos 30^\circ=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]

[tex]\displaystyle \cos 30^\circ=\frac{y}{4\sqrt{2}}[/tex]

Solving for y:

[tex]y=4\sqrt{2}\cos 30^\circ[/tex]

Since:

[tex]\cos 30^\circ=\frac{\sqrt{3}}{2}[/tex]

[tex]\displaystyle y=4\sqrt{2}\frac{\sqrt{3}}{2}[/tex]

Simplifying:

[tex]\displaystyle y=2\sqrt{6}[/tex]

Now we use the sine ratio:

[tex]\displaystyle \sin 30^\circ=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]

[tex]\displaystyle \sin 30^\circ=\frac{x}{4\sqrt{2}}[/tex]

Solving for x:

[tex]x=4\sqrt{2}\sin 30^\circ[/tex]

Since:

[tex]\sin 30^\circ=\frac{1}{2}:[/tex]

[tex]\displaystyle x=4\sqrt{2}\frac{1}{2}[/tex]

Simplifying:

[tex]\displaystyle x=2\sqrt{2}[/tex]

The choices are not clear, but it seems like the correct answer is C.

[tex]\boxed{\displaystyle y=2\sqrt{6}}[/tex]

[tex]\boxed{\displaystyle x=2\sqrt{2}}[/tex]

Answer:

x = 35°

y = 55°

Step-by-step explanation:

60° + 50° + 2x = 180° (Sum of angles on a straight line is 180°)

2x = 180° - 110°

x = 70°/2 = 35°

2x + 2y = 180°( Sum of interior angles of a triangle is 180°)

2× 35° + 2y = 180°

70° + 2y = 180°

2y = 180° - 70°

y = 110°/2

y = 55°

Answer:

(D)

Step-by-step explanation:

is the correct because is 1/2

Answer:

C. 1 1/2

Step-by-step explanation:

Answer:

17/24

Step-by-step explanation:

Change the denominators to match

8/24 + 9/24 = 17/24

Answer:

x=3

y=4

Step-by-step explanation:

I'm using 3x+y=13 to find y, then plug y into the second equation.

y= -3x+13

5x-2(-3x+13)=7

find x.

5x+6x-26=7

11x=33

x=3

now plug x into 3x+y=13(you could do it with the other equation too)

3(3)+y=13

y=13-9

y=4

The value of x and y is 3, and 4 respectively by the substitution method.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have a system of equations;

3x +y=13 ...(1)

5x-2y=7​ ...(2)

By using the substitution method.

[tex]\rm 5\cdot \dfrac{13-y}{3}-2y=7[/tex]

y = 4

Plug y = 4 in equation (1)

3x + 4 = 13

x = 3

Thus, the value of x and y is 3, and 4 respectively by the substitution method.

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Answer: y=-1/3x+5

Step-by-step explanation: I presume they want this in the y=mx+b format where m is the slope (change in y/change in x) of the line and b is the y-intercept (what y is when x is equal to 0). To answer this you need to choose any 2 points on this graph. For simplicity's sake, I'm going to choose (0,5) and (9,2). What's good about choosing (0,5) is that we now know the y-intercept is 5. Now, to find slope, subtract the y coordinate 2 from the y coordinate 5. You now know that the change in y is 3. Then, subtract the x coordinate 9 from the x coordinate 0. You now know that the change in y is -9. Finally, divide 3 (change in y) by -9 (change in x) and you should get  -3/9 which can be simplified into -1/3. So now that you have your y-intercept and your slope, all that's left to do in plug it into the format. So your answer should be y=-1/3x+5. Hope this helps you!

Answer:

60.72

Step-by-step explanation:

you multiply 25.3 by 2.4

Answer:

69.04

Step-by-step explanation:

Given that:

Mean (m) = 69.0

Standard deviation (s) = 2.8

Zscore = 0.2

Find the corresponding height (x) ;

Using the relation :

Zscore = (x - m) / s

0.2 = (x - 69.0) / 0.2

0.04 = x - 69.0

0.04 + 69.0 = x

69.04 = x

Hence, the height of a man with a Zscore of 0.2 is 69.04

Answer:

0.40 the actual answer is 3.20 but you said round so

Step-by-step explanation:

Answer:

0.38 is the answer for me

Step-by-step explanation:

Answer:

V(d) = 50d + 250 us the answer

The equation for the function V(d) is V(d) = 5d + 250 if the travel agency is advertising a vacation package that includes $250 for $40a day for a hotel.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

It is given that,

A travel agency is advertising a vacation package that includes $250 for $40a day for a hotel.

The agency also offers the option of eating breakfast and lunch at the hotel for $10 a day for the length of the hotel stay.

The equation for the function can be framed as follows:

Per day expense  = 40 + 10 = 50

Fixed expense = 250

V(d) = 5d + 250

Thus, the equation for the function V(d) is V(d) = 5d + 250 if the travel agency is advertising a vacation package that includes $250 for $40a day for a hotel.

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Answer: The point (5,-20) only satisfies the second inequality statement in the system of inequalities shown.

Step-by-step explanation:

It isn't super clear exactly what you're asking, but the first thing we can do is see if the point (5, -20) satisfies the system of equations.

So, we start by plugging in -20 for y and 5 for x.

y > -2x-3

-20 > (-2)(5) - 3

-20 > -10-3

-20 > -13. - we can see that the coordinates DO NOT satisfy the first inequality, now we can try the second equation.

y ≤ 3x + 2

-20 ≤ 3(5) + 2

-20 ≤ 15 +2

-20 ≤ 17 - this inequality is true because -20 is indeed less than 17.

Answer:

B. rate of water flow.

Step-by-step explanation:

Given that in a research study the explanatory variable is a form of a variable that is independent and it is used by the researcher to make predictions or analyze variations in other variables known as response variables.

Hence, in this case, the Explanatory variable is the "rate of water flow" because it is the variable researcher wishes to utilize in predicting the amount of soil washed away.

Answer:

The perimeter of a rectangle is the sum of both lengths and both widths, which is equal to 54 meters. Let's call Length L and Width W.

The question is saying this: L = 3 meters + 3(W). We have 2 variables, which means we need at least 2 equations to solve. So far we have one, our second equation is from the perimeter.

2 lengths + 2 Widths = 54. Now, it's just a plug and chug.

2(3 + 3W) + 2W = 54.

6 + 6W + 2W = 54

8W = 48

W=6

L = 3 + 3(6) = 21

To double check: 2(21) + 2(6) = 42 + 12 = 54

The Width is 6 meters, and the Length is 21 meters.

Answer:

Grant can purchase 7 baseball card packs for $21. 12/4=3 and 21/3=7.

Answer: 7

Step-by-step explanation:

Answer:

7 packs

Step-by-step explanation:

12/4 = $3 ea.

21/3 = 7 packs

Answer:

(0,6)

(1,5)

(2,4)

(3,3)

(4,2)

Step-by-step explanation:

To solve this table first convert the equation to slope-intercept form (y=mx+b), to do this solve for y in the equation. The slope-intercept form is y=-x+6, where -1 is the slope and 6 is the y-intercept. Then from that, you can get your first point, because you know the y-intercept is 6, therefore when x equals 0 y must be 6. Next, because the slope is -1 that means the y-value decreases by 1 every time the x-value increases by 1. So to find the rest of the y-values simply subtract 1 from the previous y-value.

Answer: -18

Step-by-step explanation: if a=6 then the equation would be (6) - 24 which is -18

Answer:

It's pretty simple. For example, if it says there is a percentage increase on something like there is a jacket for $25 and there was a 15% increase, you multiply 25 by 1.15 to see what the new price is. But say if the same $25 jacket is on sale for 15%, then you can multiply 25 by .15, then subtract that from 25 or originally subtract the 15% from 100 which is 85 and multiply 25x.85 and get the answer directly.

Hope this helps! But this would be easier to explain with an example

Explanation:

The probability of rolling a "2" is 1/6

The probability of rolling a "4" is also 1/6

Multiplying those fractions leads to (1/6)*(1/6) = 1/36. We can multiply the probabilities because the events are independent. Each dice roll does not affect any others.

The probability of rolling a 2 the first time and a 4 the second time is 1/36

There are 6 faces on a die.

Of these 6 faces, one of them is 2 and one of them is 4

So, the probabilities of rolling a 2 and a 4 are:

P(2) = 1/6

P(4) = 1/6

The probability of rolling a 2 the first time and a 4 the second time is calculated as follows:

[tex]\mathbf{Pr = P(2) \times P(4)}[/tex]

This gives

[tex]\mathbf{Pr = \frac 16 \times \frac 16}[/tex]

Multiply

[tex]\mathbf{Pr = \frac 1{36}}[/tex]

Hence, the probability of rolling a 2 the first time and a 4 the second time is 1/36

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Answer: -3

Step-by-step explanation:

18/6 = 3

18/-6 = -3

Answer:

$21600

Step-by-step explanation:

Net income is calculated by deducting all company expenses from its total revenue. Net income is given by the formula:

Net income = Revenue - cost of goods sold - operating expenses - tax.

But Gross margin = gross profit = Revenue - cost of goods sold. Hence:

Net income = Gross margin - operating expenses - tax.

Substituting gives:

Net income = $50000 - $23000 - $5400

Net income = $21600

Step-by-step explanation:

9x² - 36x + 16

= (Ax - B)² = A²x² - 2ABx + B².

By Comparing Coefficients, we have:

A² = 9,

2AB = 36,

B² = 16.

It is obvious that A = 3 and B = 4.

However 2AB = 2(3)(4) = 24 which is not equal to 36.

Hence 9x² - 36x + 16 is not a perfect square trinomial.

Answer:

False

Step-by-step explanation:

The polynomial cannot be factored.

Answer:

3000,

Step-by-step explanation:

5 or above round up, 4 and below keep it the same

Answer:

Yes i think its -96,

if thats what your asking

Answer:

The expected value is 5.6

Step-by-step explanation:

Here, we want to calculate the expected value of x

Mathematically, that will be the probability multiplied by the number of items

In this case, that will be ;

0.28 (28%) * 20 = 5.6

Answer:

nun of the 3 you gave use so the last one the 4th

Step-by-step explanation:

Answer:

as a decimal 0.3 and the percent is 30%

Answer:

in decimal :0.3 and in percent:3/10/total*100%

Step-by-step explanation:

in decimal: 3/10

=0.3

in percent= 3/10/total*100%

Answer:

$49

Step-by-step explanation:

78 - 29 = 49

To get 49, I subtracted 29 from 78.

Answer: