Write an explicit rule to represent the sequence :
4, 10, 16, 22,...

This problem is solved by using the concept of percentage as a part of a whole. We find out that 30% of the total distance equals 6 miles. So by setting up the proportion 30/100 = 6/x, we calculate the total distance is 20 miles.

This question is an application of percentage problems in real-life situations, specifically hiking distance. When you use a percentage to describe a part of a whole thing, the thing is always considered to be '100%'. In this case, Michelle's hiking trip is the 'whole thing' or '100%'.

We are told that 6 miles is 30% of the total distance. To find the total distance, we can set up a proportion to solve for it. The proportion would be 30/100 = 6/x.

Let x represent the total distance. So we can write the proportion as:

6 / x = 30 / 100

To solve for x, we can cross multiply and then divide:

100 * 6 = 30 * x

600 = 30x

x = 20

Therefore, the total number of miles Michelle will walk is 20 miles.. So, the total distance that Michelle will walk is 20 miles.

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Brenda will earn $18.75 in interest after 18 months.

To calculate the interest Brenda will earn after 18 months, we can use the simple interest formula:

Principal x Rate x Time = Interest

According to the question, Brenda deposited $500 in a savings account with a simple interest rate of 2.5% per year. Since the time period given is 18 months, we need to convert it to years. 18 months is equivalent to 1.5 years.

Therefore, the interest Brenda will earn after 18 months can be calculated as:

$500 x 0.025 x 1.5 = $18.75

Brenda will earn $18.75 in interest.

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First, find the median: 30

Then, find the median of the 2 sides from 30 (Q1 and Q3)

The middle value between 2 and 18 is 9. The middle value between 42 and 81 is 71. Now, just subtract 71-9.

The IQR is 62 :)

Final answer:

The interquartile range, or IQR, is the range of the middle 50 percent of the data values, found by subtracting the first quartile from the third quartile. For the given data set, the IQR is determined to be 61.

Explanation:

The interquartile range, represented as IQR, is found by subtracting the first quartile (Q1) from the third quartile (Q3). To find the interquartile range for the data set 2, 5, 9, 11, 18, 30, 42, 48, 71, 73, 81:

Sort the data in ascending order: 2, 5, 9, 11, 18, 30, 42, 48, 71, 73, 81

Calculate Q1 and Q3: Q1 = 10, Q3 = 71

Find IQR: IQR = Q3 - Q1 = 71 - 10 = 61

Answer:

4.8 points per minute

Step-by-step explanation:

Uncle Drew scored 28 points in [tex]5 \frac{5}{6}[/tex] minutes. We have to convert the mixed fraction first:

[tex]t = 5 \frac{5}{6}=\frac{5\cdot 6+5}{6}=\frac{35}{6}[/tex]

So, the time is 35/6 minutes.

In order to find the number of points he scored in a minute, we have to divide the total number of points by the number of minutes, so:

[tex]mean = \frac{28}{35/6}=28 \cdot \frac{6}{35}=4.8[/tex]

So, he scored 4.8 points per minute.

Answer:

4.8

Step-by-step explanation:

Answer:

x=13.6

Step-by-step explanation:

These are vertical angles, so they are equal

8x+16 = 3x+84

Subtract 3x from each side

8x-3x+16 = 3x-3x+84

5x+16 = 84

Subtract 16  from each side

5x+16-16 = 84-16

5x = 68

Divide by 5

5x/5 =68/5

x = 13.6

"A ratio of 4 to 5" means that dividing the two angles (whatever they may be) simplifies to 4/5. One example is 40 degrees and 50 degrees so 40/50 = 4/5. Another example is the pair of angles 20 and 25, so 20/25 = 4/5

For now, we don't know the angles. Let's call them x and y. Based on the info above, we can say

x/y = 4/5

also we know that x and y add to 90 degrees because the angles are complementary. So x+y = 90 which solves to y = 90-x if you isolate y.

Let's cross multiply on the first equation to get...

x/y = 4/5

5*x = 4*y

Now replace y with 90-x. Solve for x

5x = 4(90-x)

5x = 360 - 4x

5x+4x = 360

9x = 360

x = 360/9

x = 40

Use this to find y

y = 90 - x = 90 - 40 = 50

So the two angles are 40 degrees and 50 degrees.

To find two complementary angles with a ratio of 4 to 5, set up the equation 4x + 5x = 90, where x is the common multiplier. Solve for x to find each angle's measure. Check that the sum equals 90 degrees to confirm the solution.

To determine the measures of two complementary angles with a ratio of 4 to 5, you first need to understand that complementary angles add up to 90 degrees. Let's call the angles A and B, with A being the smaller angle. Since they are in a ratio of 4 to 5, we can represent them as 4x and 5x, respectively, where x is a common multiplier. The equation to solve for x is set up based on the definition of complementary angles:

4x + 5x = 90

Combine like terms to simplify:

9x = 90

Now, divide both sides by 9 to solve for x:

x = 90 ÷ 9

x = 10

Once you have the value of x, you can find the measures of the angles:

A = 4x = 4(10) = 40 degrees

B = 5x = 5(10) = 50 degrees

Always check your answer to confirm it makes sense. In this case, A + B should equal 90 degrees, which it does (40 + 50 = 90).

Answer:

Step-by-step explanation:

The point is somewhere on the road. From that point, two poles can be seen at different angles of elevation. One is 30 degrees, and another is 60 degrees.

Call the height of the poles y and the point on the road as x meters away from the base of 60 degree angle to the base pole

(100 - x) * tan(30) = x*tan(60)

The distance to the other pole = 100 - 25 = 75

Answer:

[tex]m\angle N=m\angle R=30^{\circ}[/tex]

Step-by-step explanation:

We are given that

[tex]\triangle RST=\triangle NPQ[/tex]

[tex]m\angle R=-7x+9,m\angle N=-10x[/tex]

We have to find the measure of angle R and measure of angle N.

When two triangles are equal then their angles are equal

Therefore, [tex]m\angle R=m\angle N[/tex]

[tex]-7x+9=-10x[/tex]

[tex]-7x+10x=-9[/tex]

By subtraction property of equality

[tex]3x=-9[/tex]

By combine like terms

[tex]x=\frac{-9}{3}=-3[/tex]

By division property of equality

Substitute x=-3 then we get

[tex]m\angle R=-7(-3)+9=21+9=30^{\circ}[/tex]

[tex]m\angle N=m\angle R=30^{\circ}[/tex]

Answer:

30

Step-by-step explanation:

Answer: Choice A

S9 = (9/2)*(2+26)

===============================================

The formula is

Sn = (n/2)*(a1+an)

where

Sn = sum of the first n terms (nth partial sum)

n = number of terms

a1 = first term

an = nth term

In this case,

n = 9

a1 = 2 (plug in n = 1 into the formula an = 3n-1 and simplify)

an = a9 = 26 (plug n = 9 into the formula an = 3n-1 and simplify)

So,

Sn = (n/2)*(a1+an)

S9 = (9/2)*(2+26)

will help us find the sum of the first 9 terms of this arithmetic sequence

Answer:

A. S9 = (9/2)*(2+26)

The required number of dinosaurs that each of them gets is 39 dinosaurs.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let the number of dinosaurs be x that is distributed among Yolanda and her 3 brothers,
Total persons = 1 + 3 = 4
Total dinosaurs = 156
Each of them gets,
x = 156/4
x = 39 dinosaurs.

Thus, the required number of dinosaurs that each of them gets is 39  dinosaurs.

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Answer:

[tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.

Step-by-step explanation:

unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.

Given the statement: Candy buys 20 ounces of mixed nuts. She puts an equal amount of ounces in each of 3 bags.

Total number of mixed nuts Candy buys = 20 ounces.

As she puts an equal amount of ounces in each of  the 3 bags.

Unit rate per bag = [tex]\frac{20}{3} = 6\frac{2}{3}[/tex] ounces.

therefore, [tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.

Answer:

The correct answer option is 192.

Step-by-step explanation:

We know that f(x) varies directly with [tex]x^{2}[/tex] so we can write it as:

[tex]f(x)[/tex] ∝ [tex]x^{2}[/tex]

Changing it to an equality by the addition of a constant [tex]k[/tex]:

[tex]f(x) = k.x^{2}[/tex]

If f(x) = 75 when x = 5, then we can find the value of k:

[tex]75=k(5)^2[/tex]

[tex]k=\frac{75}{25} =3[/tex]

If k = 3, we can find the value of f(8):

[tex]f(8)=3(8)^2[/tex]

[tex]f(8)=3*64[/tex]

[tex]f(8)=[/tex]192

The claim that people do better with the new edition regarding the given situation is false at 0.01 level of significance.

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

For this case, the hypothesis we'll lay down are:

Null hypothesis: People are performing less than or equal(compared with old performance) with the new edition

Alternate hypothesis: People are doing better with the new edition

This can be symbolically written as:

Null hypothesis: [tex]H_0: \mu_2 \leq 75\\[/tex]
Alternate hypothesis: [tex]H_1: \mu_2 > 75[/tex]

(where [tex]\mu_1[/tex] = 75 is mean test score with old edition, and [tex]\mu_2[/tex] is mean test score with new edition(of the population) )

Mean score with old edition is given to be [tex]\mu_1= 75[/tex]

Mean score with new edition(of the sample) is ratio of sum of scores to total count of scores = [tex]\overline{x} = \dfrac{830}{10} = 83[/tex] ([tex]\overline{x}[/tex] is representative of the population mean with new edition)

The standard deviation for both cases is: [tex]\sigma = 10.5[/tex]

Since sample size = 10 < 30, thus, we'll perform t-test for single mean (as first mean is mean of population and not of any sample).

Degree of freedom =  sample size - 1 = 9

Level of significance = 0.01

t test statistic's value for given case = [tex]\dfrac{\overline{x} - \mu_1}{s / \sqrt{n}} = \dfrac{ 83-75 }{9.82/\sqrt{10}} \approx 2.57[/tex]

(where s is sample standard deviation)

From the p-value calculator, we get the p-value for t = 2.57 at 0.01 level of significance with d.f.= 9 as : p = .015 > level of significance = 0.01

Thus, as p value is bigger than the level of significance, we fail to reject the null hypothesis, and thus, conclude that there is no significant improvement because of the new edition.

Thus, The claim that people do better with the new edition regarding the given situation is false at 0.01 level of significance.

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A one-sample t-test is used to determine if there's a significant difference in mean scores between the old and new textbook. The null hypothesis is not rejected because the t-score is lesser than the critical value, implying that there is not sufficient evidence that the new textbook is more helpful at the 0.01 significance level.

To determine if the newly designed textbook is more helpful for learning material than the old edition, we can use a one-sample t-test. The null hypothesis (H0) is that there is no difference in mean scores between the old and the new textbooks, meaning the mean score with the new textbook is 75. The alternative hypothesis (Ha) is that the mean score with the new textbook is greater than 75.

We're given that the standard deviation (σ) is 10.5, the sample size (n) is 10, and the sample mean (μ) is calculated from the provided scores. To perform the t-test, we first calculate the sample mean (μ) = (92 + 83 + 93 + 74 + 85 + 97 + 88 + 70 + 69 + 79) / 10 = 830 / 10 = 83.

Next, we calculate the t-score using the formula: t = (sample mean - population mean) / (standard deviation / sqrt(n)).

t = (83 - 75) / (10.5 / sqrt(10)) = 8 / (10.5 / 3.162) = 8 / 3.316 = 2.412.

With a significance level of 0.01 and 9 degrees of freedom (n-1), we look up the critical t-value from the t-distribution table or use a statistical software to find that the critical value for a one-tailed test is approximately 2.821. Since our t-score of 2.412 is lesser than the critical value, we do not reject the null hypothesis, suggesting that there is not enough evidence to support that the new textbook is more helpful at the 0.01 significance level.

Answer:

Correct choice is C

Step-by-step explanation:

Points A and B have coordinates (1,-2) and (4,3), respectively.

1. Rotation counterclockwise of 90° about the origin has a rule:

(x,y)→(-y,x).

Then the image of point A is point A'(2,1) and the image of point B is point B'(-3,4).

2. Refection about the x-axis has a rule:

(x,y)→(x,-y).

Then the image of point A' is point A''(2,-1) and the image of point B' is point B''(-3,-4).

3. Rotation counterclockwise of 270° about the origin has a rule:

(x,y)→(y,-x).

Then the image of point A'' is point A'''(-1,-2) and the image of point B'' is point B'''(-4,3).

4.  Refection about the y-axis has a rule:

(x,y)→(-x,y).

Then the image of point A''' is point A(1,-2) and the image of point B''' is point B(4,3).

Answer:

B  2,3,-3

Step-by-step explanation:

If we use the zero product property, we can set each term =0 to find the roots.

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

x-2 =0   x-3 =0   x+3=0

x=2   x=3          x=-3

The roots are -3,2,3

Answer:

f(n) = 10 * 5^(n-1)

an = 15-2.5n

Step-by-step explanation:

{(1, 10), (2, 50), (3, 250), (4, 1250)}

The formula for a geometric sequence is

an = a1 * r ^(n-1)

where a1 is the first term and r is the rate in which it increase

a1 =10

r = 5,  each term goes up by a factor of 5

50/10 = 5

250/50 = 5

etc

f(n) = 10 * 5^(n-1)

What is the explicit rule for the sequence?

13, 10.5, 8, 5.5, 3, 0.5, ...

For an arithmetic sequence the formula is

an = a1 + d(n-1)

where a1 is the first term and d is the common difference

a1= 13 and d = -2.5

10.5 -13 = -2.5

8. - 10 = -2.5

etc

an = 13 - 2.5 ( n-1)

Simplifying

an = 13 -2.5n + 2.5

an = 15-2.5n

Answer:

(0.5446, 0.6554)

Step-by-step explanation:

As the sample is sufficiently large, the formula is used to estimate the proportion shown in the attached image.

Where:

P: sample proportion = 0.6

n: Sample size = 300

[tex]1-\alpha[/tex]: Confidence level = 0.95

α: Significance = 0.05

[tex]Z_{\alpha / 2} = 1.96[/tex] *

* Obtained from the normal standard table.

When introducing these values in the formula shown in the image we obtain:

[tex]0.6 + 1.96 *\sqrt {\frac{0.6*0.4}{300}}[/tex]

[tex]0.6 - 1.96 *\sqrt{\frac{0.6*0.4}{300}}[/tex]

Finally, the confidence interval is:

(0.5446, 0.6554)

Option: B is the correct answer.

The range of the function is:

        B.      5 < y < ∞

Range of a function--

The range of a function is the set of all the values that is attained by the function.

By looking at the graph of the function we see that the function tends to 5 when x→ -∞ and the function tends to infinity when x →∞

Also, the function is a strictly increasing function.

This means that the function takes every real value between 5 and ∞ .

i.e. The range of the function is: (5,∞)

          Hence, the answer is:

                Option: B

The explicit rule for the decreasing arithmetic sequence 13, 10.5, 8, 5.5, 3, 0.5, ... is 'aₙ = 15.5 - 2.5n'. This rule reflects the initial term and the common difference between terms.

The sequence provided is 13, 10.5, 8, 5.5, 3, 0.5, and we are finding the explicit rule for this sequence. To find the explicit rule, we will look at the differences between the terms. The differences are consistently -2.5, thus the sequence decreases by 2.5 each time. Assume the first term corresponds to n=1, the next step is to find the initial value at n=1.

Starting with the first term, when n=1, the value is 13. Keeping in mind the sequence decreases by 2.5 with each step, if we reverse one step back (which would be 0 steps), we would be at the initial value, which is 13 + 2.5 = 15.5. Therefore, the explicit rule can be written in the form aₙ = initial value - difference times (n-1), which simplifies to aₙ = 15.5 - 2.5n.

So, given the options provided, the explicit rule for the given sequence is aₙ = 15.5 - 2.5n.

Answer:

c) 82

Step-by-step explanation:

<ABE and <BEC are supplementary because they form a line.

<ABE + <BEC = 180

116+ x = 180

Subtract 116 from each side.

116-116+x = 180 -116

x = 64

The angles in triangle ECB add to 180 because it is a triangle

<BEC + <ECB + <CBE = 180

x + 34+y = 180

64 + 34+ y = 180

98 + y = 180

Subtract 98 from each side.

98-98+y = 180-98

y = 82

Answer:

The value is 180

Step-by-step explanation:

The formula for z score is given by

       x - mean

z=    -------------

       standard deviation

We know z= 2.4

We know the standard deviation =20

and we know the mean = 132

We can   find  x

         x - 132

2.4 =  ----------------

           20

Multiply each side by 20

2.4 *20 = x-132

48 = x-132

Add 132 to each side

48+132 = x -132+132

180 = x

Answer:

The value that has a z score of 2.4 is 180.

Step-by-step explanation:

Given : If a normal distribution has a mean of 132 and a standard deviation of 20.

To find : What is the value that has a z score of 2.4?

Solution :

The formula of z-score is given by

[tex]z=\frac{x-\mu}{\sigma}[/tex]

where, z=2.4 is z score value

[tex]\mu=132[/tex] is the mean of the normal distribution

[tex]\sigma=20[/tex] is the standard deviation

x is the value of z score.

Substituting all the values in the formula,

[tex]2.4=\frac{x-132}{20}[/tex]

[tex]2.4\times 20=x-132[/tex]

[tex]48=x-132[/tex]

[tex]x=180[/tex]

Therefore, The value that has a z score of 2.4 is 180.

Answer:

length = 100 squared  Width = 80 squared

Step-by-step explanation:

You add the to ratio number ( 4+5 ). You take that number (9) and divide with 180. You receive the answer 20.  Then you multiply 20 by 5 to get the length and multiply 20 by 4 to width. Then you just add back the square operation.

Final answer:

The length and width of the rectangle are found by setting up equations using the given ratio and area. By solving the equations, the length is determined to be 15 inches and the width 12 inches.

Explanation:

To find the length and width of the rectangle with an area of 180 square inches and a ratio of length to width of 5:4, we can set up equations using the ratio and area information. Since the area of a rectangle is equal to the length times the width, we can express the length (L) and width (W) in terms of the ratio:

L = 5x

W = 4x

We know that the area (A) is 180 square inches, so:

A = L × W

180 = (5x) × (4x)

180 = 20x₂

Therefore:

x₂ = 180 / 20

x₂ = 9

x = 3

Now we can find L and W by substituting x back into L = 5x and W = 4x:

L = 5 × 3 = 15 inches

W = 4 × 3 = 12 inches

Hence, the length of the rectangle is 15 inches, and the width is 12 inches.

Answer:

4 rows of 7 plants each

Step-by-step explanation:

To find the number of plants in each row between 5 and 12 requires us to find the factors of the total 28.

28 has factors 1,28 and 2,14 and 4,7. Only 4,7 has a number between 5 and 12. There are 4 rows of 7 plants.

Answer:

168 Km

Step-by-step explanation:

divide 132 Km by 11 to find distance travelled with 1 litre and then multiply this by 14 for distance travelled with 14 litres

= [tex]\frac{132}{11}[/tex] × 14 = 168 Km

Answer: (A) 19.3%

Step-by-step explanation:

[tex]\text{Vodka: }2.5\text{ oz }\times\dfrac{\$35}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$2.59\\\\\text{Vermouth: }0.5\text{ oz }\times\dfrac{\$7.99}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$0.12\\\\\text{Olive: }\$0.15[/tex]

Vodka + Vermouth + Olive = Total Cost

$2.59  +   $0.12      + $0.15 = $2.86

[tex]\dfrac{\text{cost to make}}{\text{selling price}} = \dfrac{\$2.86}{\$15} = 0.19 = 19\%[/tex]

C

You want to choose an assignment of numbers that makes the number of numbers that represent each color be the same.

Numbers 0–33 include 34 numbers. Numbers 0–99 include 100 numbers, so blue blocks are over-represented by scenario A.

Scenario B suffers the same problem as scenario A in that 0–3 includes 4 numbers and 0–9 includes 10 numbers.

Scenario D has the opposite problem: 1–31 is 31 numbers, but 32–63 is 32 numbers. Blue blocks are under-represented in this scenario.

___

Scenario C has 3 of 9 numbers representing each color—just what you want.

Answer: A. y=5/6x-3

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

I'm almost 100% sure this is right.

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have

[tex]m=\dfrac{5}{6},\ b=-3[/tex]

Substitute:

[tex]\boxed{y=\dfrac{5}{6}x-3}[/tex]

Answer:

She should borrow the money for 3.1161... years so that she can afford the monthly payment.

Step-by-step explanation:

Monthly payment formula is:    [tex]M=P*\frac{r(1+r)^n}{(1+r)^n -1}[/tex]  , where

M = Monthly payment amount, P = Loan amount, r = rate of interest per month and n = total number of months.

Given that, Cynthia wants to take out a $8500 loan with a 4.75% APR and she can afford to pay $245 per month.

That means,  [tex]P= 8500, M= 245[/tex] and [tex]r= \frac{0.0475}{12}= 0.0039583[/tex]

Plugging these values into the above formula, we will get........

[tex]245=8500*\frac{0.0039583(1+0.0039583)^n}{(1+0.0039583)^n-1} \\ \\ 245=\frac{33.64555(1.0039583)^n}{(1.0039583)^n -1}\\ \\ 245(1.0039583)^n -245=33.64555(1.0039583)^n\\ \\ 211.35445(1.0039583)^n=245\\ \\ (1.0039583)^n=\frac{245}{211.35445}=1.15919\\ \\ n= log_{1.0039583}(1.15919)=37.39327[/tex]

So, [tex]n= 37.39327 months =\frac{37.39327}{12} years = 3.1161... years[/tex]

That means, she should borrow the money for 3.1161... years so that she can afford the monthly payment.

Answer: 25.13 (choice B)

================================

The formula we'll use is

s = r*theta

with

s = unknown arc length

r = radius = diameter/2 = 12/2 = 6 feet

theta = 4pi/3 radians <--- this angle must be in radian mode for the formula to work

Plug those values into the formula and simplify

s = r*theta

s = 6*(4pi/3)

s = 24pi/3

s = 8*pi

s = 8*3.1416

s = 25.1328

s = 25.13

which is approximate and rounded to the nearest hundredth.