What is the simplified form of this expression?
(3 - 13x - 7x?) - (5X2 + 12x - 10)

The number described in the question, whose stated percentage difference is 36, is 80.

Let us represent the number as x. So, the increased number will be -

Increased number = x + 20%×x

Simplify percentage

Increases number = x + 0.2x

Add the digits

Increased number = 1.2x

Similarly, decreased number = x - 25%×x

Converting percentage

Decreased number = x - 0.25x

Subtract the digits

Decreased number = 0.75x

Representing the difference

1.2x - 0.75x = 36

Subtract

0.45x = 36

Divide

x = 80

Hence, the number is 80.

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Answer:

watch a video or use a hint.

Step-by-step explanation:

it say it.

Answer:

- 2/5

Step-by-step explanation:

Step 1:

( 4/5 - 7/5 ) + 1/5

Step 2:

- 3/5 + 1/5

Answer:

- 2/5

Hope This Helps :)

Answer:

d) population is divided into similar groups and a SRS is chosen from each group.

Step-by-step explanation:

Stratified random sampling

can be regarded as "proportional random sampling" and is method of sampling which entails division of a population to more simpler sub- groups, this sub- groups are regarded as " strata". This strata are been formed on the basis of shared attributes of the members. This attribute could be educational attainment as well as income. It should be noted that stratified random sample is population is divided into similar groups and a SRS is chosen from each group.

a. The median number of calls = 55

b. The first and third quartiles, Q1 = 48 and Q3 = 66

c. The first decile and the ninth decile, D1 = 45 and D9 = 71.

d. The 33rd percentile = 52.5

To answer the questions, let's first organize the data in ascending order:

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57 59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

(a) The median is the middle value of a dataset when arranged in ascending order.

Since we have 40 observations, the median is the value at the 20th position.

In this case, the median is the 55th visit.

(b) The quartiles divide the data into four equal parts.

To find the first quartile (Q1), we need to locate the position of the 25th percentile, which is 40 * (25/100) = 10.

The first quartile is the value at the 10th position, which is 48.

To find the third quartile (Q3), we need to locate the position of the 75th percentile, which is 40 * (75/100) = 30.

The third quartile is the value at the 30th position, which is 66.

Therefore, Q1 = 48 and Q3 = 66.

(c) The deciles divide the data into ten equal parts.

To find the first decile (D1), we need to locate the position of the 10th percentile, which is 40 * (10/100) = 4.

The first decile is the value at the 4th position, which is 45.

To find the ninth decile (D9), we need to locate the position of the 90th percentile, which is 40 * (90/100) = 36.

The ninth decile is the value at the 36th position, which is 71.

Therefore, D1 = 45 and D9 = 71.

(d) To find the 33rd percentile, we need to locate the position of the 33rd percentile, which is 40 * (33/100) = 13.2 (rounded to 13). The 33rd percentile is the value at the 13th position.

Since the value at the 13th position is between 52 and 53, we can calculate the percentile using interpolation:

Lower value: 52

Upper value: 53

Position: 13

Percentage: (13 - 12) / (13 - 12 + 1) = 1 / 2 = 0.5

33rd percentile = Lower value + (Percentage * (Upper value - Lower value))

                = 52 + (0.5 * (53 - 52))

                = 52.5

Therefore, the 33rd percentile is 52.5.

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Answer: 0.1630

Step-by-step explanation:

Number of quarters = 10

Number of dimes = 6

Number of nickels = 8

Total number = 10+6+8 = 24

Probability of choosing the first quarter will be: = Number of quarters/Total number of money

= 10/24 = 5/12

Since a quarter has been selected, the total number will reduce to 23 the next time a quarter is choosing and the number of quarters will now be 9. Therefore, the probability of choosing the second quarter will be: = 9/23

Therefore, the probability that two quarters are chosen random from the jar will be:

= 5/12 × 9/23

= 45/276

= 0.1630

The answer is that an appropriate starting resistance for the first set of 12 repetitions for a novice exerciser who can perform a 1-RM bench press at 100 pounds would be around 50-60% of their 1-RM, which would be around 50-60 pounds.

It is important to understand the concept of "training load" when designing a resistance training program. The training load is the amount of weight or resistance that is lifted during an exercise, and it is typically expressed as a percentage of the 1-RM.

For a novice exerciser who is just starting out with resistance training, it is important to start with a relatively low training load to avoid injury and allow the body to adapt to the stress of the exercise. A good starting point is usually around 50-60% of the 1-RM, which is light enough to allow for proper form and technique while still providing enough resistance to stimulate muscle growth and strength gains.

In the case of a novice exerciser who can perform a 1-RM bench press at 100 pounds, a starting resistance of around 50-60 pounds for the first set of 12 repetitions would be appropriate. As the individual progresses and becomes stronger, the training load can be gradually increased over time to continue to challenge the muscles and stimulate further gains in strength and muscle size.

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The growth rate of the sloth population when the population is made up of 275 individuals is 99 individuals per year.

To calculate the growth rate of the three-toed sloth population when there are 275 individuals, we will use the logistic growth model formula:

Growth rate = r * N * (1 - N/K)

where r is the maximum per capita growth rate (0.8 per year), N is the current population size (275 individuals), and K is the carrying capacity of the forest (500 individuals).

Growth rate = 0.8 * 275 * (1 - 275/500)
Growth rate = 0.8 * 275 * (1 - 0.55)
Growth rate = 0.8 * 275 * 0.45
Growth rate ≈ 99 individuals per year

So, the growth rate of the sloth population when the population is made up of 275 individuals is approximately 99 individuals per year.

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Total 2 quarts he have left after solving.

As we know that in 1 cup have 0.25 quarts.

So in 1 quarts = 1/0.25 cups

So in Eight quarts have cups = 8 × 1/0.25

In Eight quarts have cups = 32 cups

He sold 6 cups and then sold 18 cups.

So total sold cups = 6 + 18

Total sold cups = 24

So left cups = Total Number of cups - Total Sold cups

Left cups = 32 - 24

Left cups = 8

As we have to find the total left quarts.

So 1 cup = 0.25 quarts

Then 8 cups = 8 × 0.25 quarts

8 cups = 2 quarts.

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Answer:

I think A or D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

-4y-12+4b

Step-by-step explanation:

Use the Distributive Property:

\( - 4(y + 3 - b)\)

\( - 4y - 12 + 4b\)

\(-4y-12+4b\) is an equivalent expression.

Answer:

50%

Step-by-step explanation:

There are two sides on a penny and there have a 50% chance each

A is invertible if and only if both B and C are invertible.

To prove the converse statement, we need to show that if both B and C are invertible, then A is also invertible.

Assume that B and C are invertible. We need to find the inverse of A.

Let D = BC. Since B and C are invertible, D is also invertible. Moreover, we have:

A = [D 0; 0 I]

where 0 is a square matrix of the same size as B and I is the identity matrix of the same size as C.

To find the inverse of A, we need to find a matrix A-1 such that:

AA-1 = A-1A = I

Let:

A-1 = [E F; G H]

where E, F, G, and H are matrices of appropriate sizes.

Then we have:

AA-1 = [D 0; 0 I][E F; G H] = [DE GF; DG+HI]

and

A-1A = [E F; G H][D 0; 0 I] = [ED FG; GH+I]

Setting these equal to I and equating corresponding entries, we get:

DE = ED = I (since D is invertible)

GF = 0

DG + HI = 0

ED = DE = I (since D is invertible)

FG = 0

GH + I = 0

From the first equation, we have E = D-1. From the second equation, we have F = 0. From the third equation, we have G = -D-1H. Substituting these values into the fourth and sixth equations, we get:

-HD-1H + I = 0

which implies that HD-1H = D-1.

Since D = BC and both B and C are invertible, we have D-1 = C-1B-1. Substituting this into the above equation, we get:

HC-1B-1H = I

which implies that H(BH)-1(C-1H)-1 = I. Since B and C are invertible, BH and C-1H are also invertible. Therefore, H is invertible and we have:

A-1 = [D-1 0; -D-1HC-1B-1 D-1]

Thus, A is invertible if and only if both B and C are invertible.

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C, D, and E are most likely to be right. Its either all of them, one of them, or two of them. A is impossible to use in the equation and if you use b, you get 45.5.

To compute the variance of a geometric distribution with parameter p, we first need to understand the geometric distribution itself.

The geometric distribution represents the number of trials required for the first success in a sequence of Bernoulli trials, where each trial has a success probability of p.

The variance of a geometric distribution with parameter p can be calculated using the formula:

Variance = (1 - p) / p^2

Please note that the Taylor expansion "=1+r+ ir -1" you mentioned does not seem to be relevant to the calculation of the variance of a geometric distribution. The correct formula for the variance is provided above.

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From the Venn diagram , the value of  required probability P(A∪B) is given by :

Option a). 0.6 . The probability that students  takes both Spanish and Chemistry.

Let us consider 'A' be the probability of the students who takes Chemistry.

And 'B' be the probability of the students who takes Spanish.

From the Venn diagram we have,

Probability of A 'P(A) ' = 0.2 + 0.1

                                    = 0.3

Probability of B 'P(B)' = 0.3 + 0.1

                                   = 0.4

Probability of A∩B 'P(A∩B)' = 0.1

Probability of A∪B is given by :

P(A∪B) = P(A) + P(B) - P(A∩B)

Substitute the value we get ,

⇒ P(A∪B) = 0.3 + 0.4 - 0.1

⇒ P(A∪B) =  0.6

P(A∪B) represents the probability of the students that takes both Chemistry and Spanish.

Therefore, the value and explanation of P(A∪B)  is equal to :

Option a). 0.6 , the probability of the students that takes both Chemistry and Spanish.

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The above question is incomplete , the complete question is:

The - Venn diagram below describes the probability of students who will take Chemistry and Spanish at Jefferson High School next year, where A Student takes chemistry and B Students takes Spanish. Suppose one student is chosen at random Use the attached Venn diagram .

Find the value of P(A∪B) and describe in words.

a.) 0.6; The probability that the student takes both chemistry and Spanish.

b.) 0.1; The probability that the student takes both chemistry and Spanish.

c.) 0.1; The probability that the student takes either chemistry or Spanish; but not both.

d.)0.6; The probability that the student takes either chemistry or Spanish, or both.

Venn diagram is attached.

The range of the given function is from 0 to 9, as the highest value is 9 and the lowest value is 0.

The range of the given function is determined by subtracting the lowest value from the highest value. In this case, the highest value is 9 and the lowest value is 0, giving us a range of 9 - 0 = 9. This means the range of the given function is from 0 to 9. This makes sense since all of the values in the function are between 0 and 9. It is important to note that the range of a function is determined by the extreme values, not necessarily the average value of the function. Therefore, even if the values in the function are more clustered around a certain point, the range will remain the same as long as the extreme values remain the same. Understanding the range of a function is an important concept in mathematics that can help us better understand the behavior of functions.

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Answer:

1. 310.5

2. 360

3. 832

4. 1200

Step-by-step explanation:

Answer: A 150mL restaurant serve of white wine is equivalent to 1.4 standard drinks.

Step-by-step explanation:

To determine how many standard drinks are equivalent to a 150mL restaurant serve of white wine, we need to divide the volume of the 150mL serve by the volume of one standard drink, which is 107mL.So, the calculation is: 150 mL ÷ 107 mL/drink = 1.4 standard drinks. Therefore, a 150mL restaurant serve of white wine is equivalent to 1.4 standard drinks.

Given:

Markers are sold in packages of 12 and pens are sold in packages of 8.

To find:

Least amount of markers and pens Rick needs to buy to have an equal number of markers and pens

Solution:

To find the least amount of markers and pens, we need to find the LCM of 12 and 8.

Prime factors of 8 and 12 are

\(8=2\times 2\times 2\)

\(12=2\times 2\times 3\)

To find the LCM, multiply all factors but the common factors are included only once.

\(LCM(8,12)=2\times 2\times 2\times 3\)

\(LCM(8,12)=24\)

Therefore, the least amount of markers and pens Rick needs to buy to have an equal number of markers and pens is 24.

The value of x is 13.85.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

(7x + 1)° and (6x - 1)° makes a straight angle.

This means,

(7x + 1) + (6x - 1) = 180

7x + 1 + 6x - 1 = 180

13x = 180

x = 180/13

x = 13.85

Thus,

x is 13.85°

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The domain of the function in the first graph is \((- \infty, +\infty)\) and the range of the function is \((- \infty, +\infty)\).

And The domain of the function in the second graph is \((- \infty, +\infty)\) and the range of the function is \(( 0, +\infty)\).

We have to find, the domain and the range of each graph given in the question.

The range of a function is the set of all possible outputs of the function. When looking for the range, it may help to make a list of some ordered pairs for the function.

The range of the function in the first graph is \((- \infty, +\infty)\)

And The range of the function in the second graph is \((0, +\infty)\)

The domain of a Function Calculator. Enter the Function want to domain into the editor.

The domain calculator allows you to take a simple or complex function and find the domain in both intervals and set notation instantly.

The domain of the function in the first graph is \((- \infty, +\infty)\)

And The domain of the function in the second graph is \((0, +\infty)\)

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Answer:

C. 58 degrees

To find the measure of angle R in triangle QRS, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Given:

Q = 8x

m/R = 14x + 2 degrees

m/S = 10x + 50 degrees

The sum of angles Q, R, and S is 180 degrees:

Q + R + S = 180

Substituting the given values:

8x + (14x + 2) + (10x + 50) = 180

Simplifying the equation:

8x + 14x + 2 + 10x + 50 = 180

32x + 52 = 180

32x = 180 - 52

32x = 128

x = 128/32

x = 4

Now that we have the value of x, we can substitute it back into the given expressions to find the measures of angles Q, R, and S.

Q = 8x = 8 * 4 = 32 degrees

m/R = 14x + 2 = 14 * 4 + 2 = 58 degrees

m/S = 10x + 50 = 10 * 4 + 50 = 90 degrees

Therefore, the measure of angle R is 58 degrees. So, the correct answer is C. 58°.

I hope you do great and pass this Unit test!!

For an integral value of \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ \) and

\(I_2 = \int_{ 1}^{-2} f(x)dx = -10 \\ \), the computed value of integral \(\int_{ 1}^{3} f(x)dx\) is equals to the -6. So, option(c) is right one.

In mathematics, an integral is the continuous process of a sum, which is used to calculate areas, volumes, and their properties. Integration is a way to sum up parts to the whole.

We have an integral say \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18 \\ \)

\(I_2 = \int_{ 1}^{-2} f(x)dx = 10 \\ \)

We have to determine value of \(\int_{ 1}^{3} f(x)dx\).

Using the properties of integral, consider integral \(I_1 = \int_{ -2}^{3} [2f(x) + 2] dx = 18\\ \)

from distribution property, \(I_1 = \int_{ -2}^{3} 2f(x) dx + \int_{ -2}^{3} 2 dx = 18 \\ \)

\(2 \int_{ -2}^{3} f(x) dx + [ 2x]_{ -2}^{3} = 18\)

\(2 \int_{ -2}^{3} f(x) dx + 10 = 18\)

\(2 \int_{ -2}^{3} f(x) dx = 8\)

\(\int_{ -2}^{3} f(x) dx = 4\)

Now, consider the required integral and rewrite, \(\int_{ 1}^{3} f(x)dx = \int_{ 1}^{-2} f(x)dx + \int_{ -2}^{3} f(x)dx \\ \)

Substitute all known values of integrals

\(\int_{ 1}^{3} f(x)dx = 10 + 4 = 14 \)

Hence, required value is 14.

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The symbols p,x, and s represent sample statistics.

- p (pronounced "p-hat") is the sample proportion. It is used to estimate the population proportion. It is computed as the number of successes in the sample divided by the sample size.

-x (pronounced "x-bar") is the sample mean. It is used to estimate the population mean. It is computed as the sum of all the values in the sample divided by the sample size.

- s is the sample standard deviation. It is used to estimate the population standard deviation. It measures how spread out the data is in the sample. It is computed as the square root of the sum of the squared deviations from the sample mean divided by the sample size minus one.

These sample statistics are used to make inferences about the corresponding population parameters, which are denoted by Greek letters such as μ (mu) for the population mean and σ (sigma) for the population standard deviation.

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A fraction that is sometimes used to approximate pi is 22/7.

One example of a fraction that is sometimes used to approximate pi is 22/7. This fraction is an approximation of pi that has been used for centuries, even though it is not an exact value of pi.

It is a good approximation that is accurate to within about 0.04%, which makes it useful in many practical applications.

The fraction 22/7 comes from dividing the circumference of a circle by its diameter, which is the definition of pi. While the exact value of pi is an irrational number that cannot be expressed as a fraction, 22/7 is a commonly used approximation that is easy to remember and calculate with. However,

there are more accurate approximations of pi that can be used for more precise calculations, such as 355/113 or 3.14159265359.

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Answer:

82.89 cm to the nearest hundredth.

Step-by-step explanation:

Volume = πr^2h     where r = radius, h = height of the water.

r = 1/2 * 48 = 24 cm and the volume = 150 * 100 = 150,000cm^3 (as there are 1000 cm^3 in 1 litre).

So, substituting, we have:

150000 = π*24^2*h

h = 150000/π*24^2

  =  82.893 cm

Answer:  \(x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\)

Step-by-step explanation:

When you subtract b/2a from both sides, you end up with the Quadratic Formula.

Answer:

\(\displaystyle x=\frac{-b \± \sqrt{b^2-4ac} }{2a}\)

Step-by-step explanation:

\(\displaystyle x+\frac{b}{2a} =\±\frac{\sqrt{b^2-4ac} }{2a}\)

Subtract \(\frac{b}{2a}\) from both sides.

\(\displaystyle x+\frac{b}{2a} -\frac{b}{2a} =\±\frac{\sqrt{b^2-4ac} }{2a}-\frac{b}{2a}\)

\(\displaystyle x=\frac{ \± \sqrt{b^2-4ac} -b}{2a}\)

\(\displaystyle x=\frac{-b \± \sqrt{b^2-4ac} }{2a}\)

This is a quadratic formula.

9514 1404 393

Answer:

  (0, 5), (10, 0)

Step-by-step explanation:

It can be useful to graph the equation and plot the points. Alternatively, you can evaluate the equation at the offered points.

Right away, you will notice that x must be even if y is to be an integer. The first point is the y-intercept, which the equation tells you is (0, 5). Then the only remaining candidate point is (10, 0), which also satisfies the equation:

  0 = (-1/2)(10) +5 = -5 +5