Graph the system of inequalities.
y>4 x-3
3 y-x≤9
Use the graphing tool on the right to graph the system of inequalities.

The low Q₁ is 13 and the median Q₃ is 16.5, the high is 18 and the interquartile range is 3.5

The interquartile range is a measure of dispersion that tells us how spread out the middle 50% of a dataset is. To calculate the IQR, we first need to find the quartiles of the dataset. Quartiles divide a dataset into four equal parts, with the first quartile (Q₁) representing the 25th percentile, the second quartile (Q₂) representing the 50th percentile (also known as the median), and the third quartile (Q₃) representing the 75th percentile.

To find the quartiles of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18}, we first need to order the data in ascending order:

10, 13, 13, 14, 15, 15, 16, 17, 18

The low is the smallest value in the dataset, which is 10.

To find Q₁, we need to find the value that is 25% of the way through the dataset. Since we have 9 values in our dataset, 25% of 9 is 2.25. This means that Q₁ lies between the 2nd and 3rd values in the dataset, which are both 13. To find the exact value of Q₁, we can take the average of these two values:

Q₁ = (13 + 13) / 2 = 13

The median is the middle value in the dataset, which is 15.

To find Q₃, we need to find the value that is 75% of the way through the dataset. 75% of 9 is 6.75, which means that Q₃ lies between the 6th and 7th values in the dataset, which are 16 and 17, respectively. To find the exact value of Q₃, we can take the average of these two values:

Q3 = (16 + 17) / 2 = 16.5

The high is the largest value in the dataset, which is 18.

Now that we have found the quartiles, we can calculate the IQR by subtracting Q1 from Q₃:

IQR = Q₃ - Q₁ = 16.5 - 13 = 3.5

Therefore, the interquartile range of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18} is 3.5. This tells us that the middle 50% of the dataset is relatively tightly clustered around the median, with values ranging from 13 to 16.5.

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The linear factors of the given polynomial is (2x+1)(4x+3) and (3x-2).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given function is f(x)=24x³+14x²-11x-6 and one of the factor is (2x+1).

Here, 24x³+14x²-11x-6 can be written as 24x³+12x²+2x²+1x-12x-6

12x²(2x+1)+1x(2x+1)-6(2x+1)

= (2x+1)(12x²+1x-6)

= (2x+1)(12x²+1x-6)

= (2x+1)(12x²+9x-8x-6)

= (2x+1)[3x(4x+3)-2(4x+3)]

= (2x+1)(4x+3)(3x-2)

Therefore, the linear factors of the given polynomial is (2x+1)(4x+3) and (3x-2).

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Answer:

0.1 is 5% of 2.

Step-by-step explanation:

Steps:

0.1 ÷ 5% = 2%

Answer:

2

Step-by-step explanation:

5% of 2 is 0.1

50% is 1

5% is 0.1

The group of people who participated in the study's sample survey was chosen at random to participate in it by the national grocery store chain. In this instance, the sample comprises the 1,000 customers from throughout the nation that participated in the survey. They are a segment of the total consumer base that frequents the chain's retail outlets.

The chain randomly surveyed 1,000 customers from around the country. It concluded from the study that 80% of all customers who hopped into the chain's stores were interested in the service. The nationwide grocery store chain randomly selected the participants in the study's sample survey from the general public.

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4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

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The expanded form of 12³ is given as follows:

12³ = 12 x 12 x 12 = 1728 cubic feet.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V(a) = a³.

This expression is equivalent to multiplying the side length of the object by itself twice, as follows:

V(a) = a x a x a.

The side length for this problem is given as follows:

a = 12 feet.

Hence the volume of the cube is given as follows:

V = 12³ = 1728 feet³.

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Answer:

B. 42 cubic units

Step-by-step explanation:

The formula for volume of a rectangular prism is given by :

V = lwh, where

In the diagram, the length is 8 units, the width is 1 1/2 units (i.e., 1.5 units), and the height is 3 1/12 units (i.e., 3.5 units).

Thus, we plug in 8 for l, 1.5 for w, and 3.5 for h in the volume formula to find V, the volume in cubic units:

V = (8)(1.5)(3.5)

V = 12(3.5)

V = 42

Thus, the volume of the prism is 42 cubic units (answer choice B.)

The equation that represents the total price of Michigan State University per semester is determined by the number of classes taken (c) and the total cost for the semester, which includes a one-time fee for room and board (t).

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Answer:

3. 100% = 1

3/4 = 0.75

Now, 0.75 is halfway between 0.5 and 1, so Chris is correct.

4. 10% = 10/100 = 0.1

3/5 = 0.6

Now, 0.2 is not halfway between 0.1 and 0.6, so Emily is wrong.

Answer:

3 đúng 4 wrong

Step-by-step explanation:

100%=1

giữa 0, 5 và 1 =(0,5+1)/2=3/4

10%= 0,1

giữa  0,1 và  3/5 =(0,1+3/5)/2=  0,35  #0,2

1. Triangle inequality theorem.

3. The missing lengths and angles are:

<B = 27.07, <C = 98 and c = 32.64.

1. According to triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. To determine the number of triangles that can be formed, we can use the given measurements and check if the triangle inequality theorem is satisfied.

3. We have,

a = 27, b = 15, and A = 55°,

Using the Law of Sines,

sin A/ a = sin B/ b

sin 55 /27 = sin B / 15

0.81915204428 / 27 = sin B /15

0.4550844690444 = sin B

<B = 27.07

Now, <C = 180 - <A - <B = 180 - 55 - 27.07 = 98

Now, Using the Law of Sines

sin A/ a = sin C/ C

0.81915204428 / 27 = sin 98 / c

0.030338964602963 = 0.99026807 /c

c = 32.64

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Answer:

(a)121.5 square inches

(b)196.25 cubic inches

Explanation:

Part A

The dimension of the rectangular tray is 30 inches by 10 inches.

Area of the rectangular tray =30 x 10

=300 square inches

Cylinder

The diameter of the cylinder-shaped bowl = 10 inches

Radius = Diameter/2

= 10/2

= 5 Inches

Square

Side length of the square = 10 inches

Area of the square =10²

=100 square inches

Therefore, the area of the tray not covered

=Area of the tray - (Base Area of the cylinder + Area of the square)

Part B

Height of the cylinder = 2.5 inches

Answer:

(02.02 HC)

The boxes described below have the same volume but different dimensions and surface area. Describe

the relationship between the surface area and the volume of a cell. Analyze the data and explain why cell

shapes can be beneficial.

future: a day, a week, or even a few months from now.

short-term goal

long-term goal

intermediate goal

specific goa

The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is in option (b) 60%.

Proportion: Two ratios are said to be proportional if they express the same relationship.

Given that:

P (households owning mutual funds) = 60% = 0.6

P (households owning individual stocks) = 40% = 0.4

P (households owning both mutual funds and individual stocks) = 20% = 0.2

P (households that own mutual funds but not individual stocks or individual stocks but not mutual funds)

= P(A) only + P(B) only = [P(A) - P(A∩B)] + [P(B) - P(A∩B)]

= 0.4 + 0.2 = 0.6 = 60%.

Please refer to this complete question:

In a certain town, 60% of the households own mutual funds, 40% own individual stocks, and 20% own both mutual funds and individual stocks. The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is

a. 40%.

b. 60%.

c. 80%.

d. 100%

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Complete Question

Newly purchased automobile tires of a certain type are supposed to be filled to a pressure of 30 psi. Let μ denote the true average pressure. Find the P-value associated with each of the following given z statistic values for testing H0: μ = 30 versus Ha: μ 30 when σ is known. (Give the answers to four decimal places.)

calculate for each

(a) z = 2.30

(b) z = -1.7

Answer:

a

\(p-value = 0.021448\)

b

\(p-value = 0.08913\)

Step-by-step explanation:

From the question we are told that

   The population mean is \(\mu = 30 \ psi\)

   The null hypothesis \(H_o : \mu = 30\)

    The alternative hypothesis is  \(H_a : \mu \ne 30\)

Considering question a  

 Here  the test statistics is (a) z = 2.30  

 From the z table  the probability of  (Z >  2.30)  is  

      \(P(Z > 2.30 ) = 0.010724\)

Generally the p-value is mathematically represented as

      \(p-value = 2 * P(Z > 2.30 )\)

=>   \(p-value = 2 * 0.010724\)

=>   \(p-value = 0.021448\)

Considering question b

 Here  the test statistics is (a) z = -1.7

 From the z table  the probability of  (Z <  -1.7)  is  

      \(P(Z < -1.7 ) = 0.044565\)

Generally the p-value is mathematically represented as

      \(p-value = 2 * P(Z < -1.70 )\)

=>   \(p-value = 2 * 0.044565\)

=>   \(p-value = 0.08913\)

Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

(i) In decimals: 0.65

(ii) In percentage: 65%

The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.

Answer:

0.65 or 65%

Step-by-step explanation:

Answer: The length of the rectangle would be 20 inches and the width would be 14 inches.

Step-by-step explanation:

If the length is 20, first, it’s 6 more than 14, and second it would add up to 40. If the width is 14, it’s 6 less than 20, and adds up to 28. If you add those two together, you’d get your total of 68 inches for the perimeter!

The limit of the trigonometric expression is equal to 0.

In this problem we find the case of a trigonometric expression, whose limit must be found. This can be done by means of algebra properties, trigonometric formula and known limits. First, write the entire expression below:

\(\lim_{\Delta x \to 0} \frac{\cos (\pi + \Delta x) + 1}{\Delta x}\)

Second, use the trigonometric formula cos (π + Δx) = - cos Δx to simplify the resulting formula:

\(\lim_{\Delta x \to 0} \frac{1 - \cos \Delta x}{\Delta x}\)

Third, use known limits to determine the result:

0

The limit of the trigonometric function [cos (π + Δx) + 1] / Δx evaluated at Δx → 0 is equal to 0.

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4 1/4 inches

That number is the bottom side of the front, so it will also be the same side as the back.

Answer:

Let b = number of boys and g = number of girls.

g/b = 5/3, so g = (5/3)b

b + g = 136

b + (5/3)b = 136

(8/3)b = 136, so b = 136(3/8) = 51 boys, and g = 85 girls

There are 51 boys and 85 girls at the volleyball summer camp.

The ratio of boys to girls at the camp is 3 to 5. By applying this ratio to the total number of children at the camp (136), we find that there are 51 boys and 85 girls.

The question tells us that for every 3 boys at a camp, there are 5 girls. This means that the ratio of boys to girls is 3:5. This ratio tells us that out of every 8 (3+5) children, 3 are boys and 5 are girls.

Now it's mentioned there are 136 children in total. We divide total children by sum of the ratio to find out the number of boys and girls. 136 divided by 8 equals 17. This means there are 17 sets of 'every 8 children'.

To find the number of boys, multiply 3 (number of boys in one set) by 17 (total sets) and we get 51 boys. Using the same process for the girls, we multiply 5 (number of girls in one set) by 17 (total sets), resulting in 85 girls. Thus, among the 136 children at the camp, there are 51 boys and 85 girls.

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Answer:

987

Step-by-step explanation:



57√56259= 987

Answer:

987

Step-by-step explanation:

56259 ÷ 57 = 987

In the question, we are tasked to determine the coordinates of K after being dilated with a scale factor of 2/3.

Given Point K: (-6,-15)

To be able to dilate the point, we multiply the x and y coordinates by the given scale factor.

We get,

Therefore, the coordinates of point K' is (-4,-10).

The answer is letter B.

Answer:

R(x) = (x + 4)² + 14

Step-by-step explanation:

The equation in vertex form is

a(x - h)² + k

Use the method of completing the square

add/ subtract ( half the coefficient of the x- term)² to x² + 8x

R(x) = x² + 8x + 30

      = x² + 2(4)x + 16 - 16 + 30

     = (x + 4)² + 14 ← in vertex form

Answer:

\(R(x) = (x + 4)^{2} + 14\)

Step-by-step explanation:

Given the quadratic function: \(R(x) = x^{2} + 8x + 30\)

where a = 1, b = 8, and c = 30

Since a > 0, then the parabola is facing upward, and its vertex is the minimum point in the graph. We can determine the vertex (h, k ) through the x and y coordinates of the axis of symmetry:

\(x = \frac{-b}{2a} = \frac{-8}{2(1)} = -4\)

Now that we have the value of x coordinate (or h), plug this value into the quadratic function to solve for the value of the y-coordinate ( k ):

\(R(x) = (-4)^{2} + 8(-4) + 30 = 15 -32 + 30 = 14\)

Therefore, the vertex of the quadractic function is given by (-4, 14).

Now that we have the value of the vertex, we can rewrite the quadratic function into its vertex form:

\(R(x) = (x - (-4)^{2} + 14\)

\(R(x) = (x + 4)^{2} + 14\)

Answer:

314.96in

Step-by-step explanation:

Answer: 30%

Step-by-step explanation:
12/40 = 3/10 = 0.30

0.30*100 = 30%

Answer:

=1−12/3≈−3.67

Step-by-step explanation:

The z-score of x = 1, when x ~ N(12, 3), is approximately -3.6667.

To find the z-score of x when x = 1, we'll use the formula for z-score:

z = (x - μ) / σ

Given:

x = 1

μ (mean) = 12

σ (standard deviation) = 3

Substituting these values into the formula, we get:

z = (1 - 12) / 3

Calculating the numerator:

1 - 12 = -11

Dividing the numerator by the denominator:

-11 / 3 ≈ -3.6667

Therefore, the z-score of x = 1, when x follows a normal distribution with a mean of 12 and a standard deviation of 3, is approximately -3.6667.

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Below, you'll find a list of all the answers to the questions which are solved by using proportional relationship.

The general equation for a straight line is y=mx + c, where m represents the line's slope and expresses the rate of change of y per unit time with respect to x.

The point where the graph crosses the y-axis is called the y-intercept, or c.

Direct proportionality is also represented by y = mx. We can express m as follows: m = y/x

OR

y₁/x₁ = y₂/x₂

In our cafeteria, lemonade is made using a powdered drink mix. The quantity of water required to manufacture a certain amount of powdered drink mix is proportional to the number of scoops required. For every 2 scoops of mix, 1/2 gallon of water is required, and for every 5 scoops,

1 1/4 gallons of water are required.

The proportional formula is written as y = k x.

Using the information provided, we can now write: 2 scoops require 0.5 gallon of water.

1.25 gallon of water is required for 6 scoops.

This means that k = 2/0.5

k = 2/(1/2)

k = 2 x 2

k= 4

Equations describing the relationship can be expressed as y = 4x + c.

0.5 gallon of water is now required for 2 scoops.

2=4(1/2)+c

2=2+c

c=0

Therefore, the formula will be y = 4x.

The end includes a graph for y = 4x.

12 scoops of water:

12=4x

x=3 gallons of water is needed.

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The Central tendency is typically located to the right of the tallest bar.

In a skewed left distribution, the central tendency is typically located to the right of the tallest bar. Skewed left distributions, also known as negatively skewed distributions, are characterized by a tail that extends towards the left side of the distribution.

The central tendency refers to the measure that represents the center or average of a distribution. It provides information about the typical or central value around which the data points tend to cluster. Common measures of central tendency include the mean, median, and mode.

In a skewed left distribution, the mean is usually influenced by the long tail on the left side of the distribution. This tail pulls the mean towards lower values, resulting in a lower mean compared to the median. Therefore, the mean will typically be located to the left of the tallest bar in a skewed left distribution.

On the other hand, the median is less affected by the skewness of the distribution and is relatively robust to extreme values. It represents the value that separates the lower 50% of the data from the upper 50%. In a skewed left distribution, the median will be located closer to the tallest bar or even slightly to the right of it.

The mode, which represents the most frequently occurring value in a distribution, may or may not be influenced by the skewness depending on the shape of the distribution. It can be located anywhere along the distribution, and its position is not necessarily tied to the location of the tallest bar.

To summarize, in a skewed left distribution, the central tendency is typically located to the right of the tallest bar. The median is usually closer to the tallest bar or slightly to the right, while the mean is influenced by the skewness and tends to be located to the left of the tallest bar.

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