Match each equivalent expression with the property that it represents.
Associative Property of Multiplication
3 + (5 + 7) = (3 + 5) + 7
Identity Property of Multiplication
3 + 5 = 5 + 3
Identity Property of Addition
5(1) = 5
Commutative Property of Addition
(3 + 5) + 0 = (3+5)
Associative Property of Addition
[ 3(5) (4) = (3) 5(4)]

Answer:

⬇⬇⬇⬇⬇⬇

⬇⬇⬇⬇⬇⬇

Step-by-step explanation:

1, 3, 4

proof below

(1) The area of the rectangle is 88 square inches

(3) The equation x² – 3x – 88 = 0 can be used to solve for the length of the rectangle.

(4) The triangle has a base of 11 inches and a height of 8 inches.

Area of a rectangle is the sum of the area of two equal right triangle.

Area of rectangle = 2(area of right triangle)

Area of rectangle = 2(44 sq inches) = 88 sq inches

Let the length = x

then the width becomes, x - 3

Area = x(x - 3) = 88

x² - 3x = 88

x² - 3x - 88 = 0

x = 11

width = 11 - 3 = 8

Thus, the statements that are true include;

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Answer:

1085 nuts per day x 17 days = 18,445 nuts in 17 days

Step-by-step explanation:

Answer:509

Step-by-step explanation:600

Answer:

x = 3.5

Step-by-step explanation:

Since the triangles are similar we can use ratios to solve

4           7

------  = ------

(4+2)    ( 7+x)

Using cross products

4(7+x) = 7*(4+2)

Distribute

28+4x = 42

Subtract 28 from each side

4x = 42-28

4x= 14

Divide by 4

4x/4 = 14/4

x = 7/2

Answer:

0.102

Step-by-step explanation:

The number of defective modems in the inventory is 20% * 30 + 8% * 0.50 =10 (out of 80)

Note that the number of defectives in the inventory is fixed i.e. we are told that there is 1/8 probability that a modem in the inventory is defective, but rather that exactly 1/8 of all modems are defective.

The probability that exactly two modems in a random sample of five are defective is :

(10↓2)(70↓3) / (80↓5) = 0.102

Answer:

x ≥-1

Step-by-step explanation:

-1/2x -3 ≤ -2.5

Add 3 to each side

-1/2x -3+3 ≤ -2.5+3

-1/2x ≤ .5

Multiply each side by -2, remembering to flip the inequality

-2 * -1/2x ≥ 1/2 * -2

x ≥-1

Answer:

x≥-7

Step-by-step explanation:

4x+5≥-23

Subtract 5 from each side

4x+5-5≥-23-5

4x≥-28

Divide each side by 4

4x/4≥-28/4

x≥-7

Answer:

X≥-7

Step-by-step explanation:

Step 1: Subtract 5 from both sides.

4x+5-5≥-23-5

4x ≥-28

Step 2: Divide both sides by 4.

4x/4 ≥-28/4

X ≥-7

Answer:

Intervals = (1,064) , (1,036)

Step-by-step explanation:

Given:

Use 95% method

Mean = 1,050

Standard deviation = 7

Find:

Intervals.

Computation:

95% method.

⇒ Intervals = Mean ± 2(Standard deviation)

⇒ Intervals = 1,050 ± 2(7)

⇒Intervals = 1,050 ± 14

⇒ Intervals = (1,050 + 14) , (1,050 - 14)

⇒ Intervals = (1,064) , (1,036)

The Intervals = (1,064) , (1,036)

Given that:

Based on the above information, the calculation is as follows:

Intervals = Mean ± 2(Standard deviation)

Intervals = 1,050 ± 2(7)

Intervals = 1,050 ± 14

Intervals = (1,050 + 14) , (1,050 - 14)

Intervals = (1,064) , (1,036)

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Answer:

$ 1,060.00

Step-by-step explanation:

A = $ 1,060.00

A = P + I where

P (principal) = $ 1,000.00

I (interest) = $ 60.00

Compound Interest Equation

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

Where:

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Answer:

Time = X = 37.14 minutes

Distance they covered= 33.42 miles.

Step-by-step explanation:

Distance= speed * time

And the distance traveled by the two need to be equal.

Speed of storm = 33 mph

Speed of van = 54 mph

But storm is 13 miles away from van.

So

54*x = 33*x+ 13

54x-33x = 13

21x = 13

X= 0.62 hours

X = 37.14 minutes

54 *0.62= 33.42 miles.

Answer:

Isosceles

Obtuse

Step-by-step explanation:

1) When two sides of a triangle are the same length, the triangle is an isosceles triangle.

2) When one angle of the triangle is greater than 90 degrees, the triangle is an obtuse triangle.

I hope this helps! Have a great day!

Answer:

Isosceles, obtuse

Step-by-step explanation:

There are three types of triangles based on their sides:

This triangle here as sides of 28 cm, 16 cm, and 16 cm

There are three types of triangles based on their angles:

This triangle has angles of 26°, 26°, and 128°

Answer:

7.1

Step-by-step explanation:

d = sqrt(7^2 + -1^2)= sqrt(50)=7.1

Answer:

by using distance formula

putting values

d=√(-1-6)²+(-4--5)²

d=√(-7)²+(1)²

d=√49+1

d=√50

d=5√2=7.1

Answer: B

Step-by-step explanation:

Answer:

Step-by-step explanation:That would be the answer

Answer:

25.75 %  interest rate

Step-by-step explanation:

Given:

Amount was invested = r% per quarter  

Amount invested = P

Rate of interest = r %  per quarter

Time (n) = 4  Quarters

Computation:

A = P(1 + r/100)ⁿ

According to question.

⇒ A = P + 1.5P  = 2.5P

⇒ 2.5P = P(1 + r/100)⁴

⇒ 2.5  = (1  + r/100)⁴

⇒ 1 + r/100  =  1.2575

⇒ r/100 = 0.2575

⇒ r = 25.75

25.75 %  interest rate

Answer: About 6.2%

Step-by-step explanation:

He starts with 5500 and gains 893.75 in 2.5 years.

The equation is then 5500*(x)^2.5 = 5500+893.75, or

5500*x^2.5 = 6393.75.

x is about 1.0621, or about 6.2% because it's interest.

Hope that helped,

-sirswagger21

Answer: 137.5%

Step-by-step explanation

Answer:

3,380 combinations

Step-by-step explanation:

26*5*26= 3,380

Answer:

3380

Step-by-step explanation:

Since there are 26 letters, it would be

26*5*26

This is 3380

Answer:

The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 18, \pi = \frac{5}{18} = 0.2778[/tex]

99.5% confidence level

So [tex]\alpha = 0.005[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.005}{2} = 0.9975[/tex], so [tex]Z = 2.81[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 - 2.81\sqrt{\frac{0.2778*0.7222}{18}} = -0.01 = 0[/tex]

We cannot have a negative proportion, so we use 0.

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2778 + 2.81\sqrt{\frac{0.2778*0.7222}{18}} = 0.5745[/tex]

The 99.5% confidence interval for the proportion of all shrubs of this species that will resprout after fire is (0, 0.5745).

Answer:

(2,-2)

Step-by-step explanation:

In the attached file

Answer:

She can fit 9 cubic feet of clothing in the two boxes.

Step-by-step explanation:

She can fit a total of 3 cubic feet of clothing in one box, and the other she can fit a total 6 cubic feet.

3 + 6 = 9

Answer:

9 cu ft.

Step-by-step explanation:

That is the sum of the capacities of the 2 boxes

=  3 + 6

= 9 cu ft.

Answer:  [tex]\bold{P(B|A)=\dfrac{P(B\cap A)}{P(A)}=\dfrac{11}{30}}[/tex]

Step-by-step explanation:

The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)

[tex]P(B|A)=\dfrac{P(B\cap A)}{P(A)}[/tex]

P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)

          (2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)

          (3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)

                    (4, 5), (4, 4), (4, 3), (4, 2), (4, 1)

                              (5, 4), (5, 3), (5, 2), (5, 1)

                                        (6, 3), (6, 2), (6, 1)

       = 30

P(B) = (1, 2), (2, 1)                                   sum = 3

          (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)    sum = 6

          (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)  sum = 9

          (6, 6)                                           sum = 12

      = 12

P(A ∩ B) =  (1, 2), (2, 1)

                  (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

                  (3, 6), (4, 5), (5, 4), (5, 4), (6, 3)

             = 11

Answer:

20°

Step-by-step explanation:

These angles add up to 90° so we have:

x + 2x + x + 10 = 90

4x + 10 = 90

4x = 80

x = 20°

Answer:

g(x)= 2/5

Step-by-step explanation:

g(xl=f(4x-2)+1

5×-2

5x/5

x=2/5

Answer:

Option d

Step-by-step explanation:

The p-value is 0.0516 which is not statistically significant to reject the null hypothesis. Thus we will fail to reject the null hypothesis.

Answer:

Step-by-step explanation:

1) The given inequality is

[tex]|\sqrt{n} \frac{(\bar R_n-p)}{\sqrt{p(1-p)} } |<q_{\alpha /2}| \\\\ \to(\frac{(\sqrt{n} \bar R_n-p)}{\sqrt{p(1-p)} })<q^2_{\alpha /2}[/tex]

[tex]\to n( \bar R _n - p)^2<p(1-p)q^2_{\alpha /2}[/tex]

[tex]\to n\bar R +np^2-2nR_np<q^2_{\alpha /2 p- q^2_{\alpha /2}p^2[/tex]

Arranging the terms  with p² and p, we get

[tex]p^2(n+q^2_{\alpha /2)-p(2n \bar R _n+q^2_{\alpha / 2})+n \bar R ^2 _n <0[/tex]

Hence, the inequality is of the form

Ap² + Bp + c < 0

2. A quadratic equation of the form

Ap² + Bp + c < 0 with A > 0 looks like

Check the attached image

The region where the values are negative lies between p₁ and p₂ ...

The p₁ < p < p₂

Answer:

42

Step-by-step explanation:

Let the number of beanie babies Kaye has be x

according to question

Rachel owns as twice as many beanie babies as Kaye

number of beanie babies Rachel has : 2*x = 2x

Also,

Alexia owns 1/3 as many beanie babies as Rachel

number of beanie babies Alexia has : 1/3(2x) = 2x/3

It is given that Kayes has 63 beanie babies

thus x = 63

Thus,

Number of beanie babies Alexia has = 2x/3 = 2*63/3 =2*21 = 42

Answer: 3 people, 2 people, 4 people, 6 people, 2 people, 3 people, 3 people

Step-by-step explanation:

3 given numbers within 30-39

32, 35, 38

2 given numbers within 40-49

45, 48

4 given numbers within 50-59

51, 52, 54, 59

6 given numbers within 60-69

60, 61, 65, 65, 66, 69

2 given numbers within 70-79

77, 78

3 given numbers within 80-89

83, 83, 84

3 given numbers within 90-99

95, 96, 98

Answer: see Frequency below

Step-by-step explanation:

This is a frequency table.  How many times does a number appear in the data set that falls within the given interval?

Interval             Data                          Frequency

30-39:         35, 38, 32                              3

40-49:         48, 45                                     2

50-59:         59, 51, 52, 54                         4

60-69:         61, 60, 66, 65, 65, 69            6

70-79:          77, 78                                      2

80-89:          83, 84, 83                               3

90-99:          98, 96, 95                               3

Check the total to make sure you included each number from the data set.

Total numbers in the data set = 23, Total Frequency = 23  [tex]\checkmark[/tex]

Answer:

y = x - 2

Step-by-step explanation:

y = x + b

3 = 5 + b

y = x - 2

We can use the slope intercept form of a line.

y = mx+b where m is the slope and b is the y intercept

y = 1x +b

Substitute the point into the equation

3 = 1*5+b

3 = 5+b

Subtract 5 from each side

3-5 = 5+b-5

-2 =b

y = x-2

Answer: ( 77.27 , 83.93)

Therefore at 95% confidence/prediction interval is

= ( 77.27 , 83.93)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 80.6 words per minute

Standard deviation r = 7.2

Number of samples n = 18

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

80.6+/-1.96(7.2/√18)

80.6+/-1.96(1.697056274847)

80.6 +/- 3.33

= ( 77.27 , 83.93)

Therefore at 95% confidence/prediction interval is

= ( 77.27 , 83.93)