Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if needed.

Answer:

The probability of A and B, denoted as P(A ∩ B) is equal to 0.331.

Step-by-step explanation:

Recall our formula for the probability of A or B:

We are given are variables already, which we can once again define:

To find P(A ∩ B), we start by plugging in the values into our formula:

We can add the RHS of the equation:

Subtracting 0.97 on both sides, we get closer to our answer:

To obtain our final answer, we can simply just divide both sides by -1:

Therefore, the probability of A and B is equal to 0.331.

Answer:

It is similar by AA

Step-by-step explanation:

AA stands for angle-angle. In similar figures, angles are congruent, and the sides are proportional. the corresponding angles are the same. Hope this helps!

The number of soft drinks sold was 4 times the number of fruit juice -> On average, every 4 soft drinks sold, 1 fruit juice is.

-> Every P34.00 of soft drinks sold, P11.00 of fruit juice is.

So, the income is P45.00 everytime.

Since the total income is P900.00, the amount of 4 soft drinks and 1 fruit juice sold is 900 : 45 = 20 times

So, there were 20 x 4 = 80 soft drinks sold.

Recheck : 80 x 8.5 + 20 x 11 = 680 + 220 = 900.

Answer:

352 oz

Step-by-step explanation:

1 lb = 16 oz

22 * 16 = 352

The simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]

Given the surd function expressed as:

[tex]\frac{\sqrt{3} +5}{\sqrt{3} - 5 }[/tex]

Multiply by the conjugate of the denominator to have:
[tex]= \frac{\sqrt{3} +5}{\sqrt{3} - 5 } \times \frac{\sqrt{3} +5}{\sqrt{3} + 5 } \\=\frac{\sqrt{9}+5\sqrt{3}+5\sqrt{3}+25 }{3-25}[/tex]

Simplify the resulting expression
[tex]\\=\frac{3+10\sqrt{3}+25 }{-22}\\=\frac{28+10\sqrt{3}}{-22} \\= \frac{14+5\sqrt{3}}{11}[/tex]

Hence the simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]

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Answer:

x = 4 mm

y = 15 mm

Step-by-step explanation:

x = 12 mm / 3 = 4 mm

y = 3 × 5 mm = 15 mm

Using proportions, it is found that Jimmy should target the rectangular target, as he has hit a higher proportion of throws there.

A proportion is a fraction of a total amount.

In the rectangular target, he has hit it 3 out of 9 times, hence the proportion is:

pR = 3/9 = 0.3333.

In the circular target, he has hit it 2 out of 11 times, hence the proportion is:

pC = 2/11 = 0.1818.

Due to the higher proportion of hits, he should throw at the rectangular target.

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Answer:

g(1) = 1

Step-by-step explanation:

we use the last equation since it can be used when x is not -2 or -1

if we plug in 1 in the equation the answer will be 1

Answer:

4n^2+3n+2

Step-by-step explanation:

9 24 47 78 117

 15  23

     8

8/2 = 4

=4n^2

9-4 = 5 (the minus value come from 4n^2 where n is the position where 9 lays)

24-16 = 8

47-36 = 11

so plus 3 every time so 3n

4n^2+3n for the first value is 7 so you need an extra 2

4n^2+3n+2

The quadratic sequence is 4n² + 3n + 2.

The difference between words always varies by the same amount, which is a characteristic of quadratic number sequences. The "difference between the differences between the words in the sequence is always the same" as a result. The second difference is referred to as constant.

As per the given data:

The given sequence is a quadratic sequence.

The given terms are: 9 24 47 78 117

The difference between the first three consecutive terms:

9 24 47

15  23

Difference of difference:

    8

and 8/2 = 4

∴ The first term is 4n²

9-4 = 5 (the minus value come from 4n² where n is the position where 9 lays)

24-16 = 8

47-36 = 11

so plus 3 every time

∴ The second term to add is 3n

4n² + 3n for the first value is 7, so you need an extra 2

∴ The third term to add is 2

4n² + 3n + 2

Hence, the quadratic sequence is 4n² + 3n + 2

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Answer:

7.5

Step-by-step explanation:

Answer: 30 6/29

Step-by-step explanation: 6132 \ 203 is 30 and 42/203. 42/203 simplified is 6/29

Answer:

Step-by-step explanation:

The equation 4x + 8 = -2 - 2 + 5x has one solution

The equation is given as:

4x + 8 = -2 - 2 + 5x

Collect like terms

4x - 5x = -2 - 2 - 8

Evaluate the like terms

-x = -12

Divide both sides by -1

x = 12

The above means that the equation 4x + 8 = -2 - 2 + 5x has one solution

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Answer:

it does have one solution

Step-by-step explanation:

Answer:

290 8s the answer because 15 mutiplyed by 8 plus 17 multiplyed by 10 give you 290

[tex]\fbox{Surface \: area \: of \: prism = 520 \: sq.in.} [/tex]

Given:

height of prism h = 10 in

length of base of triangle b = 8 in

height of triangle h' = 15in

side A of triangle = 17 in

To find:

Surface area of prism = ?

Solution:

[tex]\begin{gathered}Area \: of \: base \: triangle = \: \frac{1}{2}\cdot{b}{h'} \\ Area \: of \: base \: triangle = \frac{1} {\not2}\cdot{15} \times \not{8} \\ Area \: of \: base \: triangle = 60 \: {in}^{2} \end{gathered}[/tex]\\[tex]\fbox{Area \: of \: base \: triangle \: (B) = 60 \: sq.in. }\\\begin{gathered}Perimeter \: of \: base \: triangle = Side A + Height \: h' + base \: b \\ Perimeter \: of \: base \: triangle = 15 + 17 + 8 \: in\\ Perimeter \: of \: base \: triangle = 40 \: in\end{gathered}

[/tex]

[tex]\fbox{Perimeter \: of \: base \: triangle (p) \: = 40 \: in} [/tex]

[tex]\begin{gathered}Surface \: area \: of \: prism = 2B+ \: ph \\ Surface \: area \: of \: prism = 2 \times 60+ \: 40 \times 10 \\ Surface \: area \: of \: prism = 120 + 400\\ Surface \: area \: of \: prism = 520 \: {in}^{2} \end{gathered} [/tex]

[tex]\fbox{Surface \: area \: of \: prism = 520 \: sq.in.} [/tex]

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Answer:

C. 12/5 kilograms of apples

Step-by-step explanation:

If 5ppl =12kg of apples

then 1 person= ?kg of apples

If more less divides and if less more divides

Therefore

1×12

5

= 12

5

Answer:

9out of 12, 3/4, 75%

Step-by-step explanation:

Red makes up 3 quarters of the spinner, or 9 parts out of 12.

Answer:1.4*10^-9

Step-by-step explanation:

Answer:

1.4×10−x^-{9}

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10.

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Hopefully this helps you!

- Matthew

Answer:

30 .24 m/hr

Step-by-step explanation:

2 hours and 5 minutes  = 2  + 5/60  hours = 2 5/60 hrs

63 miles / (2  5/60) = 30.24 m/hr

Step-by-step explanation:

To find the average speed, we must know this formula :

[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = \dfrac{Distance \: Travelled}{Total \: Time \: Taken}}} \\ \\ [/tex]

Now, substituting the given values in the formula :

[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = \dfrac{63 \: miles}{2.083 \: hr}}} \\ \\ [/tex]

[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = 30.24 \: mph}} \\ \\[/tex]

Therefore,

Answer:

Leanne is correct. It is important that g(x) is subtracted from f(x).

Shiloh is incorrect. She subtracted f(x) from g(x), and subtraction isn't commutative.

*Just took the test, got the answer correct!! Hope this helps!

Answer:

The graph decreases from left to right.

Step-by-step explanation:

Answer:

V = £21,012.50

Step-by-step explanation:

Compound interest formula

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

where:

Given:

Substituting given values into the formula:

[tex]\sf \implies V=20000(1+\frac{0.025}{1})^{(1 \times 2)}[/tex]

[tex]\sf \implies V=21012.5[/tex]

Step-by-step explanation:

what is the problem ? you teacher gave you even the conversion rates in the question.

so, when 1 gallon = 3.79 liters, then how much is 4 gallons ?

4 gallons is 4 times 1 gallon. so, of course, we need to apply the same factor to the other side too.

4 gallons = 4×3.79 = 15.16 ≈ 15 liters

and e do the same for all the other table elements :

8 liters = 8×0.26 = 2.08 ≈ 2 gallons

12.5 liters = 12.5×0.26 = 3.25 ≈ 3 gallons

6 gallons = 6×3.79 = 22.74 liters ≈ 23 liters

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    -2*y-(-4*x+5)=0

STEP 1:

Pulling out like terms

1.1     Pull out like factors :

  -2y + 4x - 5  =   -1 • (2y - 4x + 5)

Equation at the end of step 1:

STEP 2:

Equation of a Straight Line

2.1     Solve   -2y+4x-5  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  -2y+4x-5  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 5/-2 so this line "cuts" the y axis at y=-2.50000

 y-intercept = 5/-2  = -2.50000

Calculate the X-Intercept :

When y = 0 the value of x is 5/4 Our line therefore "cuts" the x axis at x= 1.25000

 x-intercept = 5/4  =  1.25000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -2.500 and for x=2.000, the value of y is 1.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 1.500 - (-2.500) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

    Slope     = 2

Geometric figure: Straight Line

 Slope = 2

 x-intercept = 5/4 = 1.25000

 y-intercept = 5/-2 = -2.50000

Answer:

2

Step-by-step explanation:

y=mx+b where m is the slope

to get y by itself you divide both sides by -2 resulting in

y= 2x+(-5/2)

2=m

Answer:

The complementary angle is 63 degrees and

The supplementary angle is 153 degrees.

Step-by-step explanation:

A complementary Angle has a total of 90 if you subtract 27 from 90 you will get 63

A supplementary adds up to 180 degrees so subtract 27 and you will get 153.

Hope that helps.

Answer:

Supplementary angle = 153°

Complementary angle = 63°

Step-by-step explanation:

Supplementary angles: Two angles that sum to 180°

Complementary angles: Two angles that sum to 90°

Given angle = 27°

⇒ Supplementary angle = 180° - 27° = 153°

⇒ Complementary angle = 90° - 27° = 63°