This hyperbola is centered at the

origin. Find its equation.

Foci: (-4,0) and (4,0)

Vertices: (-3,0) and (3,0)

Answer: Inequality Form: y<-10 or Interval Notation: (-∞,-10)

Answer:

y<-10

Step-by-step explanation:

to remove the fraction then set to 0 and solve

Problem 7

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Explanation:

Let's say we only worried about the colors and the sizes. We have 3 colors and 4 sizes, giving 3*4 = 12 different combos. Think of a table that's 3 rows and 4 columns. We'd have 12 inner cells. Each cell represents a different combo.

This idea extends out to not just two factors, but we can have as many as we want. In short, we simply multiply the values given to us: 3*4*5 = 12*5 = 60 different t-shirts. Your math textbook or your teacher may refer to this method as the counting principle, though they may use another term.

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Problem 8

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Explanation:

We use the same idea as problem 7.

4*7*8 = 28*8 = 224 different coats

As an alternative, you can draw out a tree diagram. However, these types of drawings can get very cluttered.

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Problem 9

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Explanation:

We'll use the same idea as before.

We have 10 choices for the first slot (0 through 9)

Once the first digit is selected, then we have 10-1 = 9 choices left for slot two

Then slot three has 9-1 = 8 choices, and so on.

We have this countdown: 10, 9, 8, 7

The countdown stops once we filled out the four slots. Multiply these values to get the final answer: 10*9*8*7 = 5040. The multiplication step is where we refer to the ideas mentioned in problems 7 and 8 earlier.

Keep in mind that this allows for 0 to be in the first slot. So a number like "0179" is one possibility here. If 0 is not allowed for the first digit, then you'll compute the answer like so:

9*9*8*7 = 4536

This is because we have 9 choices for the first digit, then 9 for the next, and so on. I would ask your teacher for clarification on this one.

Answer:

x=12

Step-by-step explanation:

The side lengths on the big polygon are just the side lengths of the small one by 4.

Answer:

4/4 ?

Step-by-step explanation:

Answer:

4/4

Step-by-step explanation:

Since there are four pieces and none of them is eaten or taken we just do the number of total of pieces as the denominator and the number of pieces taken away on the numerator, since there wasn't any taken away we put it as 4 because there are 4 pieces still there of cake.

Answer:

Step-by-step explanation:

y=1/2x+1

y=mx+b where m=slope and b=y-intercept

in this case, m=1/2, b=1

y-intercept: (0, 1)

---------------------------------

y=-x+4

y=mx+b where m=slope and b=y-intercept

in this case, m=-1, b=4

y-intercept: (0, 4)

------------------------------------

1/2x+1=-x+4

1/2x-(-x)+1=4

1/2x+x=4-1

1/2x+2/2x=3

3/2x=3

x=3/(3/2)

x=(3/1)(2/3)

x=6/3

x=2

substitute x=2, into y=1/2x+1

y=1/2(2)+1=1+1=2

x=2, y=2.

The lines intersect at point (2, 2).

answer:

Y=1/2x+1   M=1/2 and B=1  Y internsept is 1

Y=-x+4   M=-1 and B=4   Y-internsept is 4

Lines will internsept at (2,2)

Answer:

more than 2 triangles

Step-by-step explanation:

well, all triangles have angles add up to 180 degrees, so it is an infinite amount

Answer:

Option (2)

Step-by-step explanation:

From the picture attached,

Length of OG = 16

Length of PE = 9

Let us draw a perpendicular AE to OG which intersects at A.

Length of AG = OG - PE

                      = 16 - 9

                      = 7

Length of AE = OP

                      = OT + TP

                      = OG + PE [Since, OT = OG and TP = PE, radii of the circles]

                      = 16 + 9

                      = 25

By applying Pythagoras theorem in ΔGAE,

GE² = AG² + AE²

GE² = 7² + 25²

GE = √674

GE = 25.96

     ≈ 26

Option (2) will be the correct option.

Answer:

base times height divide by two

26 times 17=442/2=221

the answer is 221

Step-by-step explanation:

Answer:

(a) See attachment for tree diagram

(b) 24 possible outcomes

Step-by-step explanation:

Given

[tex]Urn\ 1 = \{B_1, R_1, R_2, R_3\}[/tex]

[tex]Urn\ 2 = \{R_4, R_5, B_2, B_3\}[/tex]

Solving (a): A possibility tree

If urn 1 is selected, the following selection exists:

[tex]B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2][/tex]

If urn 2 is selected, the following selection exists:

[tex]B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4][/tex]

See attachment for possibility tree

Solving (b): The total number of outcome

For urn 1

There are 4 balls in urn 1

[tex]n = \{B_1,R_1,R_2,R_3\}[/tex]

Each of the balls has 3 subsets. i.e.

[tex]B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2][/tex]

So, the selection is:

[tex]Urn\ 1 = 4 * 3[/tex]

[tex]Urn\ 1 = 12[/tex]

For urn 2

There are 4 balls in urn 2

[tex]n = \{B_2,B_3,R_4,R_5\}[/tex]

Each of the balls has 3 subsets. i.e.

[tex]B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4][/tex]

So, the selection is:

[tex]Urn\ 2 = 4 * 3[/tex]

[tex]Urn\ 2 = 12[/tex]

Total number of outcomes is:

[tex]Total = Urn\ 1 + Urn\ 2[/tex]

[tex]Total = 12 + 12[/tex]

[tex]Total = 24[/tex]

Answer:

0.1711 = 17.11% probability that the class size will be at least 720 students

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

Our random variable X is the number of students not taking admission, which has mean [tex]\mu = 50[/tex] and standard deviation [tex]\sigma = 21[/tex]

a. Suppose 750 students are admitted. What is the probability that the class size will be at least 720 students?

30 or less students do not take admission, which means that this is the pvalue of Z when X = 30.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{30 - 50}{21}[/tex]

[tex]Z = -0.95[/tex]

[tex]Z = -0.95[/tex] has a pvalue of -0.1711

0.1711 = 17.11% probability that the class size will be at least 720 students

Answer:

18.285 in.²

Step-by-step explanation:

3 in. × 4 in. = 12 in.²

A = πr²

A = 12.57 in.²

12.57 in.² ÷ 2 = 6.285 in.²

6.285 in.² + 12 in.²

18.285 in.²

Answer:

it needs me to type more but answer is

-5,-4

Answer:

S will be at (-5,-4)

Step-by-step explanation:

T is located at (0,-4)

To move to the left, the x coordinate moves.

(0-5, -4)

S will be at (-5,-4)

9514 1404 393

Answer:

  85

Step-by-step explanation:

A number will end in 0 if it has a factor of 10. For a number to end in 20 zeros, it must have 20 factors of 10. That means 2^20 and 5^20 must both be factors of the number.

In any group of sequential numbers, the number of them divisible by 2 will exceed the number divisible by 5, so we only need to have 20 factors of 5 in the group.

Every 5th multiple of 5 will have an additional multiple of 5, so 3 groups of 5 multiples of 5 will have 18 factors of 5. That is, the sequential numbers 1 .. 75 will have a total of 18 factors of 5. For two more factors of 5, we need to have two more multiples of 5: 80 and 85.

The sequential numbers 1 .. 85 will have 20 factors of 5 and at least 20 factors of 2. Hence 85! will end in 20 zeros.

Daniel must multiply together 85 sequential counting numbers to have a product ending in 20 zeros. (It will have a total of 129 digits.)

Answer:

11

Step-by-step explanation:

2r - 7 = 15

2r = 15 + 7

2r = 22

r = 22 / 2

r = 11

Answer:

10[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

In the figure below, the areas of rectangles A, B, and C are 12, 24, and 40, respectively. Find the area of rectangle D.

Step-by-step explanation:

here is the picture:

Answer:

48.49 feet

Step-by-step explanation:

The diagrammatic sketch of the information provided in the question was attached in the image below.

From the image below, the distance between the two kites is denoted by (c) and can be determined by using the cosine angle rule which is expressed as:

[tex]c^2 = a^2 + b^2 -2ab cos \ C[/tex]

where;

a = 110

b = 104

Cos C = 26°

Then;

[tex]c^2 = 110^2 + 104^2 -2(110)(104) cos \ 26 \\ \\ c^2 = 12100 + 10816- 22880 ( 0.8988) \\ \\ c^2 = 22916- 20564.544 \\ \\ c^2 = 2351.456 \\ \\ c= \sqrt{2351.456} \\ \\ \mathbf{ c = 48.49 \ feet}[/tex]

Answer:

+12+8＝+20

Step-by-step explanation:

Hope it helps you!

Answer:

[tex]{\huge\red{\fbox{{࿐αɴѕωєя࿐}}}}[/tex]

[tex]( + 12) - ( - 8) \\ = 12 + 8 \\ = + 20[/tex]

[tex]{\boxed{\boxed{\tt { Note :-}}}} \ [/tex]

[tex] - + - = + [/tex]

9514 1404 393

Answer:

  1080 in³

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = LWH

Fill in the given numbers and do the arithmetic.

  V = (10 in)(24 in)(4.5 in) = 1080 in³

Answer:

[tex]\dfrac{6}{10}ab[/tex]

Step-by-step explanation:

Given that,

The first number is [tex]\dfrac{-3a}{7}[/tex]

The second number is [tex]\dfrac{-21b}{15}[/tex]

We need to find the product of the first number and second number. Product means we need to multiply i.e.

[tex]\dfrac{-3a}{7}\times \dfrac{-21b}{15}=0.6ab\\\\=\dfrac{6}{10}ab[/tex]

Hence, the product of the given numbers is equal to [tex]\dfrac{6}{10}ab[/tex].

Given:

The expression is:

[tex]\dfrac{1}{2}(\cos (72)+i\sin (72))^5[/tex]

To find:

The [tex]a+bi[/tex] form for the given expression.

Solution:

According to De Moivre's theorem,

[tex](\cos \theta+i\sin \theta)^n=\cos (n\theta )+i\sin (n\theta )[/tex]

We have,

[tex]\dfrac{1}{2}(\cos (72)+i\sin (72))^5[/tex]

Using De Moivre's theorem, we get

[tex]=\dfrac{1}{2}(\cos (72\times 5)+i\sin (72\times 5))[/tex]

[tex]=\dfrac{1}{2}(\cos (360)+i\sin (360))[/tex]

[tex]=\dfrac{1}{2}(1+i(0))[/tex]

[tex]=\dfrac{1}{2}+0i[/tex]

It is the [tex]a+bi[/tex] form of the given expression. Here, [tex]a=\dfrac{1}{2},\ b=0[/tex].

Therefore, the required expression is [tex]\dfrac{1}{2}+0i[/tex].

Answer:

is the number 2?

Step-by-step explanation:

Answer:

The number could be  

1 1/2 or -2

explanation:

From the data, taking the number to be  x, we write:

2x^2 + x =6

Subtract 6 from both sides.

2x^2 + x - 6 = 0

Factorise.

2x^2 + 4x - 3x - 6 = 0

2x(x + 2) - 3(x + 2) = 0

(2x - 3)(x + 2) = 0

2x - 3 = 0 or x +2 = -2

x = 3/2 = 1 1/2 or x = -2

Answer:

m=Y2–Y1/X2–X1

[tex]m = \frac{ - 9 - (6)}{1 - ( - 4)} \\ m = \frac{ - 15}{5} = - 3 \\ y = mx + b \\ y = - 3x + b[/tex]

Answer: y = -5x - 14

Step-by-step explanation:

first find the difference between the x variables x1 = 1 and x2=-4 to find the slope(m)

-4 - 1 = -5

next find the difference between the y variables to find b

-9 - 6 = -14

Answer:

A) 32

Step-by-step explanation:

f(3)=1/2(4)^(3)

Answer:

x = 24

Step-by-step explanation:

The angles are supplementary therefor

(5x + 13) + (x + 23) = 180

Combine like terms

6x + 36 = 180

Subtract 36 from both sides

6x = 144

Divde both sides by 6

x = 24

Answer:

5x+13+x+23=180°[exterior corresponding angle is supplementary.

6x=180-36

x=144/6

x=24

Answer:

-8

Step-by-step explanation:

The steps are in the photo I attatched

Answer:

16

Step-by-step explanation:

From Point A use -8 subtracted by Point C 8 and get

16. It is positive because the length of side can't be negative.

Step-by-step explanation:

See the photo for the method

Answer:

Step-by-step explanation:

5P4=5×4×3×2=120