Henry bought a pair of shoes that were on sale for 25% off. The sale price of the shoes was $42. What was the original price?

Answer:

We proceed to use the following operations: (i) Vertical translation downwards ([tex]k = -\frac{1}{2}[/tex]), (ii) Vertical compression ([tex]c = \frac{1}{2}[/tex]), (iii) Vertical translation upwards ([tex]k = \frac{1}{2}[/tex]). The graph is presented below.

Step-by-step explanation:

To transform [tex]y = \frac{5}{4}\cdot x + \frac{1}{2}[/tex] into [tex]y = \frac{5}{8}\cdot x + \frac{1}{2}[/tex], we apply the following steps:

(i) Vertical translation downwards ([tex]k = -\frac{1}{2}[/tex])

[tex]g(x) = f(x) +k[/tex] (1)

(ii) Vertical compression ([tex]c = \frac{1}{2}[/tex])

[tex]g(x) = c\cdot f(x)[/tex] (2)

(iii) Vertical translation upwards ([tex]k = \frac{1}{2}[/tex])

[tex]g(x) = f(x) + k[/tex]

Now, we proceed to transform the primitive expression:

Step 1

[tex]f'(x) = \frac{5}{4}\cdot x[/tex]

Step 2

[tex]f''(x) = \frac{5}{8}\cdot x[/tex]

Step 3

[tex]g(x) = \frac{5}{8}\cdot x + \frac{1}{2}[/tex]

The graph of both function are now presented below. The parent function is the red line and the new function is represented by the blue line.

Answer:

The probability that X is between 1.48 and 15.56 is [tex]P(1.48 \leq X \leq 15.56) = 0.919[/tex]

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4.

This means that [tex]\mu = 8, \sigma = 4[/tex]

The probability that X is between 1.48 and 15.56

This is the pvalue of Z when X = 15.56 subtracted by the pvalue of Z when X = 1.48. So

X = 15.56

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

[tex]Z = \frac{15.56 - 8}{4}[/tex]

[tex]Z = 1.89[/tex]

[tex]Z = 1.89[/tex] has a pvalue of 0.9706

X = 1.48

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

[tex]Z = \frac{1.48 - 8}{4}[/tex]

[tex]Z = -1.63[/tex]

[tex]Z = -1.63[/tex] has a pvalue of 0.0516

0.9706 - 0.0516 = 0.919

Write out the probability notation for this question.

[tex]P(1.48 \leq X \leq 15.56) = 0.919[/tex]

The probability that X is between 1.48 and 15.56 is [tex]P(1.48 \leq X \leq 15.56) = 0.919[/tex]

Answer:

84

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

1344/16=84

Answer:

Approximately [tex]17.6[/tex] percent

Step-by-step explanation:

To find a percentage, take the part, divide it by the whole, and multiply that quotient by 100. As an algebraic expression, that would be [tex]\frac{part}{whole}*100[/tex].

In this case, the part is [tex]12[/tex] and the whole is [tex]68[/tex]. Therefore, our answer is [tex]\frac{12}{68}*100\approx17.6[/tex] percent. Hope this helps!

Answer: About 17.6%

Step-by-step explanation: "Per" means 100. So, to get a percentage, we can divide the numerator by the denominator then multiply the quotient by 100. Or, you can say it like this: [tex]\frac{Numerator}{Denominator} =quotient*100[/tex]

As we see, 12 is the numerator, and 68 is the denominator. Now, we can divide.

12 ÷ 68 = 0.176

We're not done yet, we'll need to multiply the quotient by 100, as in the formula.

0.176 × 100 = 17.6

Hence, 17.6% is the answer.

Let me know if you have any questions or comments.

~ Lily, from Brainly.

Answer:

9.5

Step-by-step explanation:divide area by 12.3

i think it is right

Answer:

u= 19 miles

Step-by-step explanation:

Area of triangle= ½ ×base ×height

Given that the area is 116.85 mi² and height= 12.3 mi,

116.85= ½ ×u ×12.3

6.15u= 116.85

u= 116.85 ÷6.15 (÷6.15 on both sides)

u= 19 mi

Answer:

There is insufficient statistical evidence at 5% significant level to conclude that Brand B machines have a lower variance in quality

Step-by-step explanation:

The given parameters are;

The number of units of the sample from Brand A, n₁ = 12 units

The standard deviation of the quality characteristic of Brand A, s₁ = 15.2

The number of units of the sample from Brand A, n₂ = 20 units

The standard deviation of the quality characteristic of Brand B, s₂ = 10.1

The null Hypothesis; H₀; s₁² = s₂²

The alternative Hypothesis; H₀;  s₂²< s₁²

The difference of two variance formula;

The F test statistic is given as follows;

[tex]F = \dfrac{S_1^2}{S_2^2}[/tex]

Where;

S₁² = The variance of sample (1) = 15.2² =  231.04

S₂² = The variance sample (2) = 10.1² = 102.01

df₁ = n₁ -1 = 12 - 1 = 11

df₂ = n₂ - 1 = 20 - 1 = 19

From the F table, we have the critical value from the F table = 2.66

[tex]F = \dfrac{S_1^2}{S_2^2} = \dfrac{231.04}{102.01} \approx 2.265[/tex]

Therefore, given that F ≈ 2.265 is not larger than the critical F for α = 0.05, we do not reject the null hypothesis, and there is sufficient statistical evidence at 5% significance level to conclude that Brand B machines have the same variance in quality as Brand A machines

Answer: D. The distribution of sample variances tends to be a normal distribution.

Step-by-step explanation:

The properties of the sampling distribution of the​ variance include:

• The expected value of the sample variance is equal to the population variance.

• The mean of the sample variances is the population variance.

• The sample variances target the value of the population variance.

Therefore, the option that isn't a property of the sampling distribution of the variance will be option D "The distribution of sample variances tends to be a normal distribution".

We should note that the sampling distribution came came in place as a result of the central limit theorem. The sample variance gives a true representation of the variance of the population as it is an unbiased estimator.

The one that does not demonstrate a property of variance's sampling distribution would be:

D). The distribution of sample variances tends to be a normal distribution.

The variance's sampling distribution property states that:

As per the question, the fourth statement does not exemplify one of its properties as the distribution displayed by sample variances is inclined towards normal distribution.

Thus, option D is the correct answer.

Learn more about "Variance" here:

brainly.com/question/9431483

Answer:

1. B.

2. C.

Step-by-step explanation:

1. It only has one cell so it needs to rely on other organisms in order for it to survive

2. Chloroplasts are only found in plants you can remember it by "Chloroplants"

Answer:

80 cups

Step-by-step explanation:

There are 640 ounces in 5 gallons so,

640 divided by 8 equals 80, therefore,

The greatest number of cups that can be served are 80

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the volumes.

Here given as, r= 6.2 mm, h = 10.8 mm, π=3.14

hence, the volume of the cone is

Volume = 1/3(πr^2h)

===> vol = 1/3(3.14*(6.2)^2*(10.8))

==> Vol = 1/3*(1303.57)

==> Vol = 434.52 mm^3

Hence the volume of the cone is 434.52 mm^3

Answer:

4800 1 x 24 x 25 x 8

Step-by-step explanation: 1 x 24 x 25 x 8

Step-by-step explanation:

20a + 158+6c=you will expand the brackets

= so it is 120+60+48

20a+158+6c=120+60+48

20a+ 6c=120+60+48-158

20a+6c=70

20a divide by 20+6c divide by 6 on both side

a + c = 0.58

Answer:

a) [tex]f(x) = 45300 + 143x[/tex]

In which 45300 is the current number of miles driven and 143 is the amount of miles she drives each day.

b) 47,016 miles.

Step-by-step explanation:

Question a:

Every day when commuting to and from work, Stefanie drives her car a total of 143 miles for 2.5 hours. Her car already has 45,300 miles on it.

So, after x days of work, the amount of miles driven will be given by

[tex]f(x) = 45300 + 143x[/tex]

In which 45300 is the current number of miles driven and 143 is the amount of miles she drives each day.

Question b:

After 4*3 = 12 days of work. So

[tex]f(12) = 45300 + 143*12 = 47016[/tex]

47,016 miles.

Step-by-step explanation:

x = 65° ----- ( verically opposite Δ )

Answer:

45; 9

Step-by-step explanation:

1) if the rate of the boat in still water is 'b' and the rate of the current is 'c', then it is possible to write the rate of the boat going upstream: b-c, downstream: b+c.

2) the basic formula is: D=r*t, where D - distance, r - rate/velocity, t - time;

3) according to the condition it takes 3 hours to travel 108 km upstream, it means according to  the formula above 3(b-c)=108;

4) according to the condition it takes 2 hours to travel 108 km downstream, it means according to the formula above 2(b+c)=108;

5) if to make up the system of two equations, then:

[tex]\left \{ {{3(b-c)=108} \atop {2(b+c)=108}} \right. \ => \ \left \{ {{b=45} \atop {c=9}} \right.[/tex]

6) rate of the boat in still water: 45 km/h;

rate of the current: 9 km/h.

Answer:

Step-by-step explanation:

they are asking for the triangle the "hangs " off the line, and so that it's in integer units.

by looking at the graph, I think if you were to draw a line on the y =4  ... so a flat horizontal like from the y axis at 4 on the y axis over to your graphed line.. that would do it..  :/   get it?

then the y axis is the "rise" and the line going from the y axis, horizontallly over to the graphed line, from 4.. and staying on 4 to the line... would be the run...  :?   I think this will be tough to get  

8/9 ÷ 4 = 8/36 as simplified as 2/9 in fraction form.

Answer:

8/36

Step-by-step explanation:

I divided  8/9 by 4

Answer:

There is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

Step-by-step explanation:

The population 10 year cumulative incidence of prostrate cancer among 70 year old men, p = 0.06

The number of 50 year old men in the sample, n = 260 men

The number of the sampled men that developed prostrate cancer = 13 men

The significance level, α = 0.05

Let the null hypothesis, H₀: [tex]\hat{p}[/tex] = p

The alternative hypothesis, Hₐ: [tex]\hat{p}[/tex] ≠ p

The standard score, [tex]z_{\alpha /2}[/tex] = 1.96

The test statistic, 'z', is given as follows;

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}[/tex]

[tex]\hat{p}[/tex] = 13/260 = 0.05

q = 1 - p = 1 - 0.06 = 0.94

[tex]Therefore, \ z=\dfrac{0.05-0.06}{\sqrt{\dfrac{0.06 \times 0.94}{260}}} = \dfrac{\sqrt{9165} }{141} \approx -0.68[/tex]

From the z-table, we find the p-value as follows;

P(z ≈ -0.68) = 0.24825

Therefore, given that the p-value, 0.24825 is larger than the significance level, α/2 = 0.025, we fail to reject the null hypothesis, and therefore, there is not enough statistical evidence to conclude that the cumulative incidence of prostrate cancer among 50-year old men differs from that of 70-year old men

Answer:

A = 28 cm

Step-by-step explanation:

equation:

A = [tex]\frac{a + b}{2} h[/tex]

A = [tex]\frac{4 + 10}{2} 4[/tex]

solve:

A = [tex]\frac{14}{2}4[/tex]

A = 7 x 4

A = 28 cm

Answer:

aw ty but is there a question?

Step-by-step explanation:

Answer:

42 - 6 - 6 - 6 - 6 - 6 - 6 - 6 = 0

or

42 - 7 - 7 - 7 - 7 - 7 - 7 = 0

Answer: 10x5

(10 blocks wide, 5 blocks long) or (5 blocks wide, 10 blocks long)

Step-by-step explanation:

3 blocks = 18 meters, so

1 block = 6 meters

60meters/ 6meters= 10 blocks

30 meters/ 6 meters = 5 blocks

Answer:

72 + a (1 + a)

Step-by-step explanation:

The Amount of property taxes you would have to pay per year if the rate was 0.79% is $3,436.50.

If you owned a house and the assessed value was $435,000.00, the amount of property taxes you would have to pay per year

if the rate was 0.79% can be calculated as follows:SolutionTo calculate the amount of property taxes, multiply the assessed value by the tax rate.

We can represent this mathematically as:P = R × Vwhere:P = Property taxesR = Tax rateV = Assessed Value

We are given that:R = 0.79%V = $435,000.00

We need to convert the tax rate to a decimal value before we can use it in our calculation. This can be done by dividing the percentage value by 100. Therefore:R = 0.79 ÷ 100= 0.0079

Using the formula above, we can now calculate the property taxes as:P = R × V= 0.0079 × $435,000.00= $3,436.50

Therefore, the amount of property taxes you would have to pay per year if the rate was 0.79% is $3,436.50.

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