Zoe compares the price of a sweatshirt at two stores. At Store A, the sweatshirt costs $25. A friend told her that the sweatshirt costs 30% more at Store B.

Zoe wrote the expression 25+0.3(25) to find the price of the sweatshirt at Store B.


Which equivalent expression could she also use to find the price of the sweatshirt at Store B?

A) (1+0.3)25
B) (1−0.3)25
C) 1+0.3(25)
D) 25 + 0.3

Answer:

The father is 42 years old and the son is 12 years old.

Step-by-step explanation:

Since three years ago the sum of the ages of father and his son was 48 years, and three years hence father's age will be three times that of his are his, to find the present ages of the father and his are his, the following calculations must be performed:

F + S = 48

F + 6 + S + 6 = 3S

34 + 14 = 48 /// 34 + 6 = 40 --- 14 + 6 = 20 (x 3 = 60)

38 + 10 = 48 /// 38 + 6 = 44 --- 10 + 6 = 16 (x 3 = 48)

40 + 8 = 48 /// 40 + 6 = 46 --- 8 + 6 = 14 (x 3 = 42)

39 + 9 = 48 /// 39 + 6 = 45 --- 9 + 6 = 15 (x 3 = 45)

39 + 3 = 42

9 + 3 = 12

Therefore, the father is 42 years old and the son is 12 years old.

Given:

The given sum is:

[tex]\sum _{k=4}^9(5k+3)[/tex]

To find:

The expanded form and find the sum.

Solution:

We have,

[tex]\sum _{k=4}^9(5k+3)[/tex]

The expanded form of given sum is:

[tex]\sum _{k=4}^9(5k+3)=(5(4)+3)+(5(5)+3)+(5(6)+3)+(5(7)+3)+(5(8)+3)+(5(9)+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=(20+3)+(25+3)+(30+3)+(35+3)+(4+3)+(45+3)[/tex]

[tex]\sum _{k=4}^9(5k+3)=23+28+33+38+43+48[/tex]

[tex]\sum _{k=4}^9(5k+3)=213[/tex]

Therefore, the correct option is C.

Answer: 180

Step-by-step explanation: you do 2 divided by 5 and get 0.4 then multiply that by 450

Step-by-step explanation:

Thanks, so cube root of 512 is 8 and reciprocal of 0.4 is 2.5 then:

8 : 2.5 / divide both by 2.5 to get:

3.2 : 1 that's my answer right?

The correct form of the ratio of cube root of 512: reciprocal of 0.4 is 3.2:1

It is a number y such that y to the power 3 is equal to x.

We have to find the ratio of cube root of 512 and the reciprocal of 0.4  which will be as follows

cube root of 512:  reciprocal of 0.4

8: 1/0.4

8=2.5

dividing by 2.5

3.2 : 1

Hence the ratio will be 3.2 :1 of cube root of 512 and the reciprocal of 0.4

Learn more about cube root at https://brainly.com/question/310302

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Answer:

7776pi cubic inches

Step-by-step explanation:

Answer:

a) SAT score = 1075

b) ACT score = 19.2.

c) ACT score = 27.9.

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.

(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score

SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]

51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So

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

[tex]0.025 = \frac{X - 1070}{204}[/tex]

[tex]X - 1070 = 0.025*204[/tex]

[tex]X = 1075[/tex]

SAT score = 1075.

(B) What would be the equivalent ACT score for this student?

ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So

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

[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 0.025*5.2[/tex]

[tex]X = 19.2[/tex]

ACT score = 19.2.

(C) If a student gets an SAT score of 1417, find the equivalent ACT score.

Z-score for the SAT:

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

[tex]Z = \frac{1417 - 1070}{204}[/tex]

[tex]Z = 1.7[/tex]

Equivalent score on the ACT:

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

[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 1.7*5.2[/tex]

[tex]X = 27.9[/tex]

ACT score = 27.9.

Answer:

[tex]6.7159[/tex]

Step-by-step explanation:

[tex]\mu=48.8\\n=35\\\bar{x}=53.8\\\sigma=4.4\\\alpha=1\%=0.01[/tex]

Null and alternative hypothesis :

[tex]H_0:\mu=48.8\\H_a:\mu>48.8[/tex]

Test statistic,

[tex]t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]\Rightarrow t=\frac{53.8-48.8}{\frac{4.4}{\sqrt{35}}}[/tex]

[tex]\Rightarrow t=\frac{5\times 5.91}{4.4}[/tex]

[tex]\Rightarrow t=6.715[/tex]

Test statistic [tex]t=6.715[/tex]

[tex]P-[/tex]value [tex]=P(t>6.715)[/tex]

[tex]P-[/tex] value [tex]=0.0001[/tex]  by the p- table

Significance level [tex]0.01[/tex]

         [tex]p-[/tex]value [tex]<0.01[/tex]

  We reject [tex]H_0[/tex]

Answer:

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).

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].

In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead.

This means that [tex]n = 42, \pi = \frac{26}{42} = 0.619[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 - 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.472[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 + 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.766[/tex]

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).

Answer:

x = 2 , 1

Step-by-step explanation:

Answer:

2.5 or 3.5

Step-by-step explanation:

The quadratic formula is [tex]x = -b +/- \frac{\sqrt{b^2 + 4ac}}{2a}[/tex] .

a, b, and c are determined by the terms in the formula ax^2 + bx + c

They gave you the equation x^2 - 3x - 2, which fits that formula. a is 1, b is -3, and c is -2. So plug those values into the equation:

[tex]x = -(-3) +/- \frac{\sqrt{(-3)^2 + 4(1)(-2)}}{2(1)}[/tex]

[tex]x = 3 +/- \frac{\sqrt{9 -8}}{2}[/tex]

[tex]x = 3 +/- \frac{\sqrt{1}}{2}[/tex]

[tex]x = 3 +/- \frac{1}{2}[/tex]

So x is 3 plus or minus -1/2. 3 plus -1/2 is 2.5

3 minus -1/2 is 3.5

So the 2 possible x values are 2.5 and 3.5.

Answer:

2/45+1/9=

7/45

Have a great day

Answer:

13 minutes

Step-by-step explanation:

The reason why it is 13 minutes is because you subtract 10:41 AM from 10:28 AM and you get 13 minutes.

Answer:

13

Step-by-step explanation:

41-28= 13

the hours don't change so you just need to subtract the minutes

Answer:

Step-by-step explanation:

1/48 + 5/6    

The LCD of 48 and 6 is 48 so we have:

1/48 + 40/48

= 41/38

Answer:

41/48

Step-by-step explanation:

Answer:

[tex]P(Work | Senior) = 0.14[/tex]

Step-by-step explanation:

Given

The attached table

Required

[tex]P(Work | Senior)[/tex]

This is calculated using:

[tex]P(Work | Senior) = \frac{P(Work \ n\ Senior)}{P(Senior)}[/tex]

This gives:

[tex]P(Work | Senior) = \frac{n(Work \ n\ Senior)}{n(Senior)}[/tex]

From the table:

[tex]n(Work \ n\ Senior) = 5[/tex]

[tex]n(Senior) = 25 + 5+ 5 = 35[/tex]

So:

[tex]P(Work | Senior) = \frac{5}{35}[/tex]

[tex]P(Work | Senior) = 0.14[/tex]

Answer:

14%

Step-by-step explanation:

add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

Answer:

4/5 of a fruit bar

Step-by-step explanation:

Answer:

its not loading

Step-by-step explanation:

Answer:

[tex](a)\ Pr = \frac{2}{5}[/tex]

[tex](b)\ Pr = \frac{9}{20}[/tex]

[tex](c)\ E(Orange) = 100[/tex]

[tex](d)\ E(Orange) = 62.5[/tex]

Step-by-step explanation:

Solving (a): Theoretical probability of green or yellow

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 5[/tex] --- i.e. 5 sections

[tex]Yellow = 1[/tex]

[tex]Green = 1[/tex]

So, the probability is:

[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]

[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]

[tex]Pr = \frac{1}{5} + \frac{1}{5}[/tex]

Take LCM

[tex]Pr = \frac{1+1}{5}[/tex]

[tex]Pr = \frac{2}{5}[/tex]

Solving (b): Experimental probability of green or yellow

Here, we consider the result of the experiment

From the attached image, we have:

[tex]n= 40[/tex] --- i.e. 40 spins

[tex]Yellow = 12[/tex]

[tex]Green = 6[/tex]

So, the probability is:

[tex]Pr = P(Yellow)\ or\ P(Green)[/tex]

[tex]Pr = \frac{Yellow}{n} + \frac{Green}{n}[/tex]

[tex]Pr = \frac{12}{40} + \frac{6}{40}[/tex]

Take LCM

[tex]Pr = \frac{12+6}{40}[/tex]

[tex]Pr = \frac{18}{40}[/tex]

Simplify

[tex]Pr = \frac{9}{20}[/tex]

Solving (c): Expectation of orange outcomes in a spin of 500 times, theoretically.

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 5[/tex] --- i.e. 5 sections

[tex]Orange = 1[/tex]

So, the probability of having an outcome of orange in 1 spin is:

[tex]Pr = P(Orange)[/tex]

[tex]Pr = \frac{Orange}{n}[/tex]

[tex]Pr = \frac{1}{5}[/tex]

In 500 spins, the expectation is:

[tex]E(Orange) = Pr * 500[/tex]

[tex]E(Orange) = \frac{1}{5} * 500[/tex]

[tex]E(Orange) = 100[/tex]

Solving (c): Expectation of orange outcomes in a spin of 500 times, base on experiments.

Here, we consider the spinner itself

From the attached image, we have:

[tex]n= 40[/tex] --- i.e. 40 spins

[tex]Orange = 5[/tex]

So, the probability of having an outcome of orange is:

[tex]Pr = P(Orange)[/tex]

[tex]Pr = \frac{Orange}{n}[/tex]

[tex]Pr = \frac{5}{40}[/tex]

[tex]Pr = \frac{1}{8}[/tex]

In 500 spins, the expectation is:

[tex]E(Orange) = Pr * 500[/tex]

[tex]E(Orange) = \frac{1}{8} * 500[/tex]

[tex]E(Orange) = 62.5[/tex]

Answer:

Belle is my fav.

Step-by-step explanation:

She loves to read books like me and I hate people who always go out there and try to impress me with something.

Answer:

the answer is c

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

It's simple, the angle of a line is 180°

∠EFG=90°

Line GD-∠EFG=180°-90°=90°

Please mark brainliest!

Answer:

He can lift 160 pounds

Step-by-step explanation:

125 (from last year) + 35 (more pounds) = 160 (total pounds)

125 + 35 = 160

Answer:

The answer is LINEAR EQUATIONS

Step-by-step explanation:

Hope you have a great day :)

Answer:

speed = 78 miles per hour

Step-by-step explanation:

Speed is distance divided by time

speed = 234 miles / 3 hours

speed = 78 miles per hour

Answer:

3692.64 cm³

Step-by-step explanation:

Answer: 14 units

Step-by-step explanation:

Answer:

I DONT SEE TRIANGLES

Step-by-step explanation:

Answer:

1,408 packs can be made, and 2 pens will be left out.

Step-by-step explanation:

Given that a manufacturer has 5,634 pens to divide into packs of 4 pens, and the manufacturer makes as many packs as possible, to determine how many packs of pens does the manufacturer make, and how many pens are left over, the following must be done calculation:

5.634 / 4 = X

1,408.5 = X

5,634 - (1,408 x 4) = X

5.634 - 5.632 = X

2 = X

Therefore, 1,408 packs can be made, and 2 pens will be left out.

Answer: 1,408 packs can be made and 2 will be left out

Step-by-step explanation:

Answer:

Step-by-step explanation:

First,

7 times 8 = 7 × 8 = 56

Then,

The product divided by 2 = 56 ÷ 2 = 28

Hence,

The required answer is 28