There are 27 questions on an algebra test. All of the questions are multiple choice or constructed response. The number of constructed response questions on the test is six less the ten times the number of multiple choice questions. How many of each.

Answer:

the correct answer is between a and b. So I think the answer is b

Answer:

The answer is B.

Step-by-step explanation:

(5)[tex]\frac{3}{4}[/tex]+[tex]\frac{1}{5}[/tex](4)

[tex]\frac{15}{20}[/tex]+[tex]\frac{4}{20}[/tex]=[tex]\frac{19}{20}[/tex]

The first step is to multiply the left side by 5 and the right side by 4 because you want the denominator to be the same. Then you add [tex]\frac{15}{20}[/tex]+[tex]\frac{4}{20}[/tex] to get [tex]\frac{19}{20}[/tex]:)

5 ÷ 2 * 7 + 5/7

Simplify 2 * 7 to 14

5 ÷ 14 + 5/7

Simplify 14 + 5 to 19

5 ÷ 19/7

Use this rule: a ÷ b/c = a * c/b

5 * 7/19

Simplify

35/19

Convert to a mixed fraction

= 1 16/19

Answer:

[tex]\large\boxed{1\dfrac{16}{19}}[/tex]

Step-by-step explanation:

[tex]5\div2\dfrac{5}{7}\qquad\text{convert the mixed number to improper fraction}\\\\2\dfrac{5}{7}=\dfrac{2\cdot7+5}{7}=\dfrac{19}{7}\\\\=5\div\dfrac{19}{7}=5\cdot\dfrac{7}{19}=\dfrac{(5)(7)}{19}=\dfrac{35}{19}=1\dfrac{16}{19}[/tex]

The y axis? As the graph is symmetrical on either side of it

[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{-2} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\bf \left( -\cfrac{5}{2(3)}~~-2-\cfrac{5^2}{4(3)} \right)\implies \left(-\cfrac{5}{6}~~,~~-2-\cfrac{25}{12} \right)\implies \stackrel{\stackrel{axis~\hfill }{coordinate\qquad }}{\left(-\cfrac{5}{6}~~,~~-\cfrac{49}{12} \right)} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=-\cfrac{5}{6}}~\hfill[/tex]

let's notice, that the squared variable is the "x", and therefore this is a vertical parabola whose axis of symmetry is the vertical line equation of the x-coordinate of its vertex.

To make generalizations from sales data of the Random stationery employees or car salespersons, statistical analysis using histograms, frequency polygons, time series graphs, and box plots is necessary to visually interpret the distribution and variance within the data.

Understanding Sales Data and Statistical Representation

When reviewing the sales data of Random Stationary's employees or the weekly sales of car salespersons, we are engaging in the statistical analysis of a chosen sample. Here, histograms, frequency polygons, time series graphs, and box plots are used to graphically represent data obtained from these samples. These visual tools allow us to interpret data distributions and make generalizations about the overall population from which the sample was taken.

Examples of Data Representation

In the provided example regarding the number of cars sold by 65 randomly selected salespersons, data is summarized in a frequency table. This leads to the construction of a histogram or a box plot where the central tendency and the dispersion of data can be observed. Similarly, in a workplace setting like that of Yoonie’s personnel reviews, the central limit theorem suggests that sampling distributions approach a normal distribution as sample size increases. This is especially true when concluding population averages from sample means.

Making Generalizations from Samples

When looking at the data from Random Stationary’s employees or any other such gathered data, mean, median, mode, range, and standard deviation can provide insights into sales performance. By examining the data visually through box plots, one can comment on the spread and concentration of data, which indicates whether sales performance is consistent or variable across shifts or individuals. Random sampling methods, systematic sampling, and stratified sampling all contribute to acquiring data that can help make valid generalizations when applied correctly.

Morning shift workers generally have lower sales (mean: 32, median: 36, mode: 20) compared to afternoon shift workers (mean: 46, median: 33, mode: 31), with afternoon workers showing a wider range (18).

To make generalizations based on the provided statistical information, let's break down each measure of central tendency and spread for both morning shift workers and afternoon shift workers.

1. **Mean**: The mean is the average value of a set of numbers. It is calculated by adding up all the numbers and then dividing by the total count.

  - For morning shift workers: Mean = (Sum of sales for morning shift workers) / 12 = 32

  - For afternoon shift workers: Mean = (Sum of sales for afternoon shift workers) / 12 = 46

2. **Median**: The median is the middle value in a set of numbers when they are arranged in ascending order. If there is an even number of values, the median is the average of the two middle values.

  - For morning shift workers: Median = 36

  - For afternoon shift workers: Median = 33

3. **Mode**: The mode is the value that appears most frequently in a set of numbers.

  - For morning shift workers: Mode = 20

  - For afternoon shift workers: Mode = 31

4. **Range**: The range is the difference between the largest and smallest values in a dataset.

  - For morning shift workers: Range = Largest value - Smallest value = B - I (not provided)

  - For afternoon shift workers: Range = 62 - 44 = 18

The answer is:

It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.

To find how many seconds Ella took to do a push-up and a sit-up we must write two equations using the given information.

Let be "x" the time needed to push-ups and "y" be the time needed to do sit-ups.

So, writing the equations we have:

First equation,

If she can do 13 push-ups and 7 sit-ups in 60 seconds, we have:

[tex]13x+7y=60[/tex]

Second equation,

If she can do 13 push-ups and 19 sit-ups in 96 seconds, we have:

[tex]13x+19y=96[/tex]

Now, creating a system of equations, and using the reduction method to solve it, we have:

[tex]\left \{ {{13x+7y=60} \atop {13x+19y=96}} \right.[/tex]

Multiplying the first equation by -1, we have:

[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right.[/tex]

[tex]\left \{ {{-13x-7y=-60} \atop {13x+19y=96}} \right\\\\12y=36\\\\y=\frac{36}{12}=3[/tex]

Then, substituting "y" into the first equation, we have:

[tex]13x+7y=60[/tex]

[tex]13x+7(3)=60[/tex]

[tex]13x+21=60[/tex]

[tex]13x=60-21=39[/tex]

[tex]x=\frac{39}{13}=3[/tex]

Hence, we have that It takes Ella 3 seconds to do a push-up and 3 seconds to do a sit up.

Have a nice day!

Answer:

5 rolls

Step-by-step explanation:

If the perimeter around the square footage of the ceiling is equal to 12 + 12 + 12 + 12 = 48, even though the number is 48, in order to have all of the footage covered, Katie would need to buy (at least) 5 rolls.

Hope I helped and please give me brainliest!

Step-by-step explanation:

Mean is the average and that means you add up all the numbers and divide it by its amount.

Interquartile Range is the range of Quartile 3 minus Quartile 1

Range is the highest number minus the lowest number

mean the sum of a set of data divided by the number of items in the set

range the difference between the largest and smallest data points

interquartile range  the difference between the upper quartile and the lower quartile

sin(155)º = sin(180 - 25)º =  sin(25)º

=> B) sin25º

Answer:

Check attached graph

Step-by-step explanation:

Given inequality is [tex]-2a-5>3[/tex].

Now we need to graph the given inequality to find the correct choice.

[tex]-2a-5>3[/tex]

[tex]-2a-5+5>3+5[/tex]

[tex]-2a>8[/tex]

[tex]-\frac{2a}{-2}<\frac{8}{-2}[/tex]

[tex]a<-4[/tex]

that means line will go on the left side of -4.

since we have <, so there will be an open circle at -4.

Hence final graph of the given problem looks like:

Answer:

well a perfect square of trinomial if it can be factored into a binomial multiplied to itself. so theres step by step to

Step-by-step explanation:

For example, in the trinomial x2 - 12x + 36, both x2 and 36 are perfect squares.welcome

Answer is provided in the image attached.

Let S = the amount of sales.

She earns 4% of her sales, this would be written as 0.4S ( you multiply the percent as a decimal by the amount of sales).

You then need to add that amount to her salary so you now have 0.4s + 2100

She wants to earn at least 2900 so the inequality becomes:

2900 ≥ 0.4s + 2100

Her sales would need to be:

800 ≥0.4s

s≥ 800/0.4

s ≥ 2000

Answer:

38

Step-by-step explanation:

0.17 is about 0.2, and 193 is about 190.

0.2 * 190 = 38.

So 0.17 * 193 is about 38

32.81 is your answer

Answer:

[tex]\boxed{\text{a. 111.1 m; b. 56 575 m}^{3}}[/tex]

Step-by-step explanation:

a. Height

(i) Height of prism

The height of the prism is 70 m.

(ii) Height of pyramid

Consider the red triangle in the diagram.

The diagonal of the square base is given by

d² = a² + a² = 2a²

d² = 2(26)² = 2 ×676 = 1352 m²

d = √1352 = 36.77 m

The base of the triangle R is

R = ½d = ½ × 36.77 = 18.38 m

Now,

h² + R² = e²

h² + 18.38² = 45²

h² + 338  = 2025  

h² = 1687

h = 41.07 m

(iii) Total height

Total height = height of prism + height of pyramid = 70 + 41.07 = 111.1 m

b. Volume

(i) Volume of prism

V = lwh

V = 70 × 26 × 26 = 47 320 m³

(ii) Volume of pyramid

The formula for the volume of a square pyramid is  

V = ⅓a²h

V = ⅓ × 26² × 41.07 = 9255 m³

(iii) Total volume

Total volume = volume of prism + volume of pyramid

V = 47320 + 9255 = 56 575 m³

The total height of the building is [tex]\boxed{\textbf{111.1 m}}[/tex]

The total volume of the building is [tex]\boxed{\textbf{56 575 m}^{3}}[/tex]

Answer:

Slope = 6

Step-by-step explanation:

Taking two points on line l to find its slope: (0, 3) and (6, 2).

Slope of line l = [tex]\frac{3-2}{0-6} =-\frac{1}{6}[/tex]

We know that the slope of a line which is perpendicular to another line has a slope which is a negative reciprocal of the other line.

Therefore, the slope of the line which is perpendicular to line l will have a slope of 6.

Answer: 6

Step-by-step explanation: I just got it right lol

Answer:

200 divided by 1700=.1176

move decimal two to the right =11.76% or 12% commission

Answer:

y= 2/3 x

Step-by-step explanation:

First plot the points on a Cartesian plan

You will notice a straight line passing through the origin (0,0)

Find the gradient of the line;

m=change in y/change in x

m=2-0/3-0 =2/3

Find the equation of the line

y-2/x-3 =2/3

3(y-2) = 2(x-3)

3y-6= 2x-6

3y=2x-6+6

3y=2x

y=2/3 x + 0

Answer:

This is a graph of y = -x,

slope of graph = -1,

Y-intercept = 0

This line passes through the origin, so its equation follows the form

[tex]y=mx[/tex]

The slope [tex]m[/tex] can be computed using the "rise over run" technique: each time you increase x by 1, y decreases by 2. So, the slope is -2.

The equation is thus

[tex]y=-2x[/tex]

Hi, it should be written as y = mx + b.

The answer should be:

y = (3/2)r - (5/2)

Answer:

47

Step-by-step explanation:

www.alcula.com/calculators/statistics/median/

Each of these numbers represents the weight of a student in kilograms. Hence, the median of the given data set is 47.

Median is such a number for the arranged data set(ascending or descending order) such that to its left and to its right belong the same number of observations.

Each of these numbers represents the weight of a student in kilograms.

39, 48, 45, 48, 51, 46, 52, 51, 43, 41

We need to find the median of this data set.

In order to find the median, arrange the data in ascending order.

39, 41, 43, 45, 46, 48, 48, 51, 51,  52,

[tex]M= \dfrac{46 + 48 }{2} \\\\M = \dfrac{94}{2} \\\\M= 47[/tex]

Hence, the median of the given data set is 47.

Learn more about median here:

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Answer:

Single Solution of 3.2 (16/5)

Step-by-step explanation:

3x = 8x -16 <--- I combine like terms.

-5x = -16

-16/-5 = x

x = 3.2

BTW Negative times a Negative equals a positive.

To find the solutions to the equation -6y + 13 + 9y = 8y - 3, combine like terms, isolate the variable, and solve for y. The equation has one solution, which is y = 3.2.

To find the solutions to the equation -6y + 13 + 9y = 8y - 3, we need to simplify the equation and solve for y. First, combine like terms by adding the y terms on the left side and the constant terms on the right side. This gives us 3y + 13 = 8y - 3. Next, subtract 3y from both sides to isolate the variable term on the right side. This gives us 13 = 5y - 3. Then, add 3 to both sides to isolate the variable term. This gives us 16 = 5y. Finally, divide both sides by 5 to solve for y. This gives us y = 16/5 or y = 3.2.

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Answer:

The third alternative is correct

Step-by-step explanation:

In hypothesis testing, the null hypothesis H0 is the hypothesis of no difference and as such it always contains an equality sign. The equality sign could be either of the following alternatives;

=, equal to

≤, less than or equal to

≥, greater than or equal to

In the question presented the claim is that students who practice taking all of their regular tests on the computer will do better on the state's final exam than the students taking their regular tests by paper and pencil.  

This implies that the average on the state exam of students using paper and pencil tests is less than the average of the students using computer tests. Since the null hypothesis must contain an equality sign, the third alternative becomes our null hypothesis, H0.

Answer:

The value of x is 1

Step-by-step explanation:

Remember that

The radius of the circle is perpendicular to the lines that are tangent to the circle

Applying the Pythagoras Theorem

[tex]6.1^{2}+(10x)^{2}=6.1^{2}+(9x+1)^{2}[/tex]

Simplify

[tex](10x)^{2}=(9x+1)^{2}[/tex]

[tex]10x=(9x+1)\\ \\ 10x-9x=1\\ \\x=1[/tex]

For this case we have that by definition, the formula to count the total number of different permutations is:

[tex]nP_ {r} = \frac {n!} {(n-r)!}[/tex]

SUstituyendo:

[tex]n = 8\\r = 5[/tex]

We have:

[tex]8P_ {5} = \frac {8!} {(8-5)!} = \frac {8!} {3!} = \frac {8 * 7 * 6 * 5 * 4 * 3!} {3! } = 6720[/tex]

ANswer:

[tex]8P_ {5} = 6720[/tex]

Answer:

112.5 km

Step-by-step explanation:

The lorry needed 45 minutes to travel the remaining 0.4 of the journey and was traveling at 60 km/hr.

First, convert minutes to hours:

45 min × (1 hr / 60 min) = 0.75 hr

Now use distance equation:

distance = rate × time

0.4d = 60 × 0.75

d = 112.5

The distance between the towns is 112.5 km.

Answer:

x = 114

Step-by-step explanation:

Answer:

120°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 6, hence

sum = 180° × 4 = 720°, thus

angle measure = 720° ÷ 6 = 120°

median because there is and outlier

Final answer:

The best measure of spread for the first period is the range, which is found by subtracting the smallest value from the largest value in the dataset.

Explanation:

The best measure of spread for the first period is the range.

The range is found by subtracting the smallest value from the largest value in a dataset. For the first period, the smallest value is 0 and the largest value is 9, so the range is 9 - 0 = 9.

The range is a good measure of spread because it gives the distance between the minimum and maximum values, providing an idea of how much the data values vary.

z÷x

-6÷3

=-2

Answer is -2

Answer:

(-6)/3 = -2

Step-by-step explanation:

you have to change the variables with the numbers

Answer:

[tex]\boxed{\text{15.8 cords}}[/tex]

Step-by-step explanation:

Step 1. Calculate the volume of the room

V = lwh =  5 yd × 5 yd × 3 yd = 75 yd³

Step 2. Convert cubic yards to cubic feet

3 ft = 1 yd

[tex]V = \text{75 yd}^{3} \times \left(\dfrac{\text{3 ft}}{\text{1 yd}} \right)^{3} = \text{2025 ft}^{3}[/tex]

Step 3. Convert cubic feet to cords

128 ft³ = 1 cord

[tex]V = \text{2025 ft}^{3} \times \dfrac{\text{1 cord}}{\text{ 128 ft}^{3}} = \textbf{15.8 cords}\\\\\text{You could fit }\boxed{\textbf{15.8 cords}} \text{ of wood into the room.}[/tex]

The car will travel 800 kilometers in 5 hours.

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given

1 mile = 1.6 km

100 mile = 1.6 * 100 = 160 km

in 1 hr car travels 160 km

in 5 hrs car travels = 160 * 5 = 800 km

The car will travel 800 kilometers in 5 hours.

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In 5 hours, the car will travel 800 kilometers.

To convert the car's speed from miles per hour to kilometers per hour, you multiply by the conversion factor of 1.6 kilometers per 1 mile. Therefore, a speed of 100 miles per hour is equivalent to 100 × 1.6 = 160 kilometers per hour.

Next, to calculate how many kilometers the car will travel in 5 hours at the speed of 160 kilometers per hour, you simply multiply the speed by the time. The car will travel 160 km/h × 5 h = 800 kilometers in 5 hours.