Last week Jovanna ran 30 miles more than Rachel. Jovanna ran
47 miles. How many miles did
Rachel run?
A. 30 + x = 47

B. 30 - x = 47

C. 47 + x = 30

D. 47x = 30

Answer: d and e

Step-by-step explanation:

Edge 2021

The option describes graph 4. a vertex at (0, 96), and 5. the center at (0, 0) from the given equation  [tex]\dfrac{y^2}{96^2} - \dfrac{x^2}{40^2} = 1[/tex]

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given equation is

[tex]\dfrac{y^2}{96^2} - \dfrac{x^2}{40^2} = 1[/tex]

From the given equation,

a = 40

b = 96

(h,k) = (0,0),

The vertices are at (0,96) and at (0, -96).

The curves open upward and downward.

c² = a² + b²

c² = 40² + 96²

c² = 10816

c = 104

Therefore the foci are at (0, -104) and (0, 104).

Hence, the option describes the graph

4. a vertex at (0, 96) is correct.

5. the center at (0, 0) is correct.

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Answer:

x = 1

Step-by-step explanation:

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Answer:

[tex]\sigma = 0.831[/tex] --- Standard deviation

[tex]Mode = 10[/tex]

Step-by-step explanation:

Given

[tex]x = 9,8,10,9,8,10,9,10,8,10[/tex]

Solving (a): The population standard deviation

First, we calculate the mean

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x = \frac{9+8+10+9+8+10+9+10+8+10}{10}[/tex]

[tex]\bar x = \frac{91}{10}[/tex]

[tex]\bar x = 9.1[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{\frac{1}{n}\sum (x - \bar x)^2}[/tex]

So, we have:

[tex]\sigma = \sqrt{\frac{1}{10}*[(9 - 9.1)^2+.................+(10- 9.1)^2]}[/tex]

[tex]\sigma = \sqrt{\frac{1}{10}*6.9}[/tex]

[tex]\sigma = \sqrt{0.69}[/tex]

[tex]\sigma = 0.831[/tex]

The mode is:

[tex]Mode = 10[/tex]

10 has the highest frequency of 4

Answer:

8. 24.5

9. 29.6

Step-by-step explanation:

Answer:

8. 24.5

9. 29.6

Step-by-step explanation:

FRACTION. 24.5 as a Fraction in simplest form   24 1/2

29.6 as a fraction is 29 3/5

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Answer:

23=x-13, x=36

9+x=14, x=5

12=x+8, x=4

Step-by-step explanation:

23=x-13. You want to isolate x so you have to add 13 to both sides. x=23+13, x=36

9+x=14. You want to isolate x so you have to subtract 9 from both sides. x=14-9, x=5.

12=x+8. You want to isolate x so you have to subtract 8 from both sides. x=4.

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The price of orange last week was $3.75

An equation is used to show the relationship between two or more numbers and variables.

The price of oranges increases by 20% each week.

The price of oranges this week is $4.50. Hence:

Price of orange last week (x) is given by:

4.5 = x + 20% of x

4.5 = x + 0.2x

1.2x = 4.5

x = 3.75

The price of orange last week was $3.75

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Answer:

There are 180 degrees in the 3 angles of a triangle.

Step-by-step explanation:

Given:

The expression is:

[tex]2.74x-7.9[/tex]

To find:

The expressions that can be set equal to the given expression to form an equation that has no solution.

Solution:

We have,

[tex]2.74x-7.9[/tex]                     ...(i)

An expression whose constant term is different from the given expression but the variable term is same as the given expression, i.e., 2.74, is the required expression.

The expression with same variable term and different constant term is:

[tex]2.74x+7.9[/tex]                    ...(ii)

Because on equating (i) and (ii), we get

[tex]2.74x-7.9=2.74x+7.9[/tex]

[tex]-7.9=7.9[/tex]

This statement is false for any value of x. So, the equation [tex]2.74x-7.9=2.74x+7.9[/tex] has no solution.

Therefore, the correct option is C.

Answer:

81.74% probability that the sum of the 95 wait times you observed is between 670 and 796

Step-by-step explanation:

To solve this question, the uniform probability distribution and the normal probability distribution must be understood.

Uniform distribution:

A distribution is called uniform if each outcome has the same probability of happening.

The distribution has two bounds, a and b.

Its mean is given by:

[tex]M = \frac{b - a}{2}[/tex]

Its standard deviation is given by:

[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Normal 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.

n instances of the uniform distribution can be approximated to the normal with [tex]\mu = nM[/tex], [tex]\sigma = S\sqrt{n}[/tex]

Uniformly distributed over the interval [0,15].

This means that:

[tex]M = \frac{15 - 0}{2} = 7.5[/tex]

[tex]S = \sqrt{\frac{(15-0)^2}{12}} = 4.33[/tex]

95 trains

[tex]n = 95[/tex], so:

[tex]\mu = 95M = 95*7.5 = 712.5[/tex]

[tex]\sigma = S\sqrt{n} = 4.33\sqrt{95} = 42.2[/tex]

What is the approximate probability (to 2 decimal places) that the sum of the 95 wait times you observed is between 670 and 796?

This is the pvalue of Z when X = 796 subtracted by the pvalue of Z when X = 670. So

X = 796

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

[tex]Z = \frac{796 - 712.5}{42.2}[/tex]

[tex]Z = 1.98[/tex]

[tex]Z = 1.98[/tex] has a pvalue of 0.9761

X = 670

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

[tex]Z = \frac{670 - 712.5}{42.2}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

0.9761 - 0.1587 = 0.8174

81.74% probability that the sum of the 95 wait times you observed is between 670 and 796

Answer:

Step-by-step explanation:

c^2 = a^2 - b^2

13^2 - 5^2 = -12

Answer:

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

5x - 24 = 3 * 2

5x - 24 = 6

5x = 30

x = 6

Answer:

Solution given:

AC= 5x - 24, AO= 3.

now

since diagonal bisect each other So,

AC=2 AO

5x-24=2(3)

5x=6+24

x=30/5

x=6

Answer:

131

Step-by-step explanation:TRUST ME IT IS RIGHT

Answer:

x=35

y=72.5

Step-by-step explanation:

Answer:

x=35 , y=72.5

Step-by-step explanation:

I'm not amazing at explaining but x is obviously 35 as its across from it and looks like it's the same angle, we'll be able to test this when we figure out y. Both of the y values are the same number so you just need to figure out

2y + 35 = 180

Minus 35 from both sides

2y = 145

Then we can divide 2 from both sides

y = 72.5

Then we test for x

2y + x = 180

Plug in y

145 + x = 180

Minus 145 from both sides

x= 35

There's your answer! I hope I cleared up any confusion

Answer:

B. All real numbers

Step-by-step explanation:

I calculated it logically

Answer:

B) All real numbers

The graph of the cosine function looks like this: The domain of the function y=cos(x) is all real numbers (cosine is defined for any angle measure), the range is −1≤y≤1 .

Answer:

m<HJK = 40°

Step-by-step explanation:

Given:

m<HJK = 3x - 2

m<KJL = 50°

Required:

m<HJK

Solution:

m<HJK + m<KJL = 90° (complementary angle)

Substitute

3x - 2 + 50 = 90

Add like terms

3x + 48 = 90

3x + 48 - 48 = 90 - 48

3x = 42

3x/3 = 42/3

x = 14

✅m<HJK = 3x - 2

Plug in the value of x

m<HJK = 3(14) - 2 = 42 - 2

m<HJK = 40°

Answer:

1408 packs

2 pens left over

Step-by-step explanation:

5634 / 4 = 1,408.5

half a pack is 2 pens

1408 packs

2 pens left over

Answer:

full length = 25 in.

Step-by-step explanation: .

20% is 1/5 of 100% so in order to find 100% of the length, multiply 5in (20%) by 5 to get to the 100% which will give you 25in.

Answer: 5/27

Step-by-step explanation:

1/9 + 2/27 = ?

1. Find the LCD (Least Common Denominator )

LCD: 27

2.Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD.

(1/9 x 3/3) + (2/27 + 1/1) =

3. Solve

3/ 27   + 2/27  =5/27

Hence, the answer is 5/27

9514 1404 393

Answer:

  64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729

Step-by-step explanation:

The row of Pascal's triangle we need for a 6th power expansion is ...

  1, 6, 15, 20, 15, 6, 1

These are the coefficients of the products (a^(n-k))(b^k) in the expansion of (a+b)^n as k ranges from 0 to n.

Your expansion is ...

  1(2k)^6(-1/3)^0 +6(2k)^5(-1/3)^1 +15(2k)^4(-1/3)^2 +20(2k)^3(-1/3)^3 +...

     15(2k)^2(-1/3)^4 +6(2k)^1(-1/3)^5 +1(2k)^0(-1/3)^6

  = 64k^6 -64k^5 +(80/3)k^4 -(160/27)k^3 +(20/27)k^2 -(4/81)k +1/729

Answer:1/16 for each of us

Step-by-step explanation:

Since only 1/4 is left and you and the teachers are splitting it up,you’d get 1/16 each because the half of 1/4 (1/8) was split into 2 (1/16)

Answer:

a. The scale factor from Drawing 1 to Drawing 2 is 40%

b. The length of the bottom side of Drawing 2 is 7.8 cm

Step-by-step explanation:

5.2 / 13 = 26 / 65 = 2 / 5 = 4 / 10 = 0.4 = 40%

19.5 / 2.5 = 39 / 5 = 78 / 10 = 7.8

9514 1404 393

Answer:

  B, C, D

Step-by-step explanation:

In this diagram, all of the acute angles are congruent. Those are angles 2, 4, 6, and 75°. Similarly, all of the obtuse angles are congruent. They are supplementary to the acute angles, so we have angles 1, 3, (x-15)°, and 5 all have measure 180° -75° = 105°.

This means x = 105° +15° = 120°.

The true statements are ...

  B. angle 2 = angle 6

  C. x = 120°

  D. angle 1 and angle 6 are supplementary

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Answer: 4 units

Step-by-step explanation: IT cant be 2x2 or else it would be a square

so it would have to be that the width is 1 unit and the lenght is 4 units.