Which equation has both 7 and -7 as a
possible value of x?

Answer:

m angle A = 68deg

Step-by-step explanation:

Since they're complementary, they add up to 90deg

you solve this by first finding x

(4x-28) + (x-2) = 90 >> add the left side

5x-30 = 90              >> add 30 from both sides

5x = 120                    >> divide by 5 on both side to get x alone

x = 24

now you know x is 24, you substitute it in m<A since you're finding the measure of it

(4(24) - 28)

96 - 28

68

you can check by finding the value of m<B (22deg) and adding it to m<A and it will equal to 90deg

The measure of ∠A = 68°.

We have two angles ∠A and ∠B which are complementary of each other.

We have to find the measure of ∠A.

Two angles are said to be complementary if their sum is equal to 90°.

Mathematically -   x + y = 90°

According to the question -

∠A = (4x – 28)°

∠B = (x - 2)°

Now, ∠A and ∠B are Complementary angles. Therefore -

∠A + ∠B = 90°

(4x - 28) + (x - 2) = 90

5x - 30 = 90

5x = 120

x = 24

Therefore →

∠A = (4x – 28)° = (4 x 24 – 28)° = 68°

Hence, the measure of ∠A = 68°.

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Therefore, the expression that equals 3B - 3C in standard form is -21x² - 6x + 24.

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated or simplified to obtain a single value or another expression. In algebra, expressions are often used to represent mathematical relationships or formulas, and can be manipulated using various algebraic techniques such as factoring, expanding, simplifying, and solving for unknown variables. Expressions are also used in calculus, probability theory, and many other branches of mathematics to describe mathematical models and relationships.

Here,

We can start by substituting the expressions for B and C into the expression for 3B - 3C and simplifying:

3B - 3C = 3(-3x - 7x²) - 3(-x² - 8 - x)

= -9x - 21x² + 3x² + 24 + 3x

= -21x² - 6x + 24

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Answer:

3/4 for candy 1/4 for chocolate

Step-by-step explanation:

If you buy 3 sodas, the probability that two will be sprite and one will be a root beer is approximately 0.070, or 7%.

To calculate the probability of getting two cans of Sprite and one can of root beer, we'll use the formula for probability:

Probability = (Number of favorable outcomes) / (Total possible outcomes)

First, let's calculate the total number of ways to select 3 sodas from 31 available sodas (14 Cokes, 10 Sprites, and 7 root beers). We'll use combinations for this:

C(n, r) = n! / (r!(n-r)!)

Total outcomes = C(31, 3) = 31! / (3! * (31-3)!)
Total outcomes = 31! / (3! * 28!) = 4495

Now, let's calculate the number of favorable outcomes. This means selecting two Sprites and one root beer:

Favorable outcomes = C(10, 2) * C(7, 1) = (10! / (2! * 8!)) * (7! / (1! * 6!))
Favorable outcomes = (45) * (7) = 315

Finally, we'll divide the number of favorable outcomes by the total number of possible outcomes:

Probability = 315 / 4495 ≈ 0.070

So, the probability of getting two Sprites and one root beer is approximately 0.070, or 7%, rounded to three decimal places.

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Answer:

D

Step-by-step explanation:

The difference between 63y and 35y is 28y. 28/2=14, 28/4=7, 28/7=4, 28/9=not whole number so I'm not doing the math, and to make sure we are right, 28/14=2

Answer:

Step-by-step explanation:

\(63y-35y\\=28y\)

\(\frac{28y}{2} = 14y\\\\\frac{28y}{4} = 7y\\\\\frac{28y}{7} =4y\\\\\frac{28y}{14} = 2y\\\\\frac{28y}{9} =3.1111y\)

Answer: $1562

Step-by-step explanation:

Since the attorney charges a flat fee of $50 and 21% of what he can collect for Lee from customers whose accounts are past due, then if be collected $7200 from last due, the total fee that the attorney will earn will be:

= $50 + (21% × $7200)

= $50 + (0.21 × $7200)

= $50 + $1512

= $1562

Therefore, the amount that the attorney will earn is $1562

To find the greatest common divisor (GCD) of all the numbers that are the product of four consecutive positive integers, let's analyze the pattern and derive a formula for these numbers.

Let's consider the product of four consecutive positive integers as follows:

\(n * (n + 1) * (n + 2) * (n + 3)\)

Expanding this expression:

\(n * (n + 1) * (n + 2) * (n + 3) = n^4 + 6n^3 + 11n^2 + 6n\)

Now, to find the GCD of these numbers, we need to determine the common factors among them.

If we observe the expanded expression, we notice that each term contains at least one factor of n. Therefore, the GCD of the given numbers must have n as a factor.

Next, let's look at the other terms: \(6n^3, 11n^2\), and 6n. All these terms have n as a factor. Additionally, they have a common factor of 6.

Hence, the GCD of the numbers that are the product of four consecutive positive integers is 6n, where n is a positive integer.

The greatest common divisor of all the members of the set containing the numbers that are the product of four consecutive positive integers is 6n, where n is a positive integer.

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Answer:

$360,000

Step-by-step explanation:

Yes, 2x -3y =7 is a Linear equation as the highest power of the variable is linear which is one. Although it has two variables both have one power.

Linear equations are those which have the highest power of variable as one. But it can have n number of different variables. This given equation is called a linear equation with two variables.

Moreover, any expression is called an equation when the expression is equated to some value means the equation is equal to("=") to some other expression, Number, or Zero. And here 2x+3y is being equated to 7 which is a number, So the given expression is an equation.

However if the variables x and y both came together then it will not be linear as x*y will make the power two as one of x and one of y, Which w=makes the highest power of expression two.

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Answer:

t=-28

Step-by-step explanation:

Answer: x=4

Step-by-step explanation:

Given

2(3x+4)-2x=24

Expand parenthesis

6x+8-2x=24

Combine like terms

4x+8=24

Subtract 8 on both sides

4x+8-8=24-8

4x=16

Divide 4 on both sides

4x/4=16/4

x=4

Hope this helps!! :)

Please let me know if you have any questions

To find the orthogonal projection of a vector onto a subspace, we can use the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ,

where A is a matrix whose columns span the subspace, and u is the vector we want to project.

In this case, the subspace W is spanned by the vector v = [0, 0, 0, 1].

Let's calculate the orthogonal projection of u onto W using the formula:

A = [v]

The transpose of A is:

Aᵀ = [vᵀ].

Now, let's substitute the values into the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ

= v⁻¹[vᵀ]u

= [v][(vᵀv)⁻¹vᵀ]u

Substituting the values of v and u:

v = [0, 0, 0, 1]

u = [1, 0, 0, 0]

vᵀv = [0, 0, 0, 1][0, 0, 0, 1] = 1

[(vᵀv)⁻¹vᵀ]u = (1⁻¹)[0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 0]

Therefore, the orthogonal projection of u onto the subspace W is [0, 0, 0, 0].

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Answer:

4 weeks

Step-by-step explanation:

basic math

Answer:

6.5 weeks without parental help, 3.5 weeks with help from your parents.

Step-by-step explanation:

The Equation is:

Y = 20x

Y = Starting price for bikes

X = # of weeks

Therefore:

$130 = 20x

This can be simplified by solving for x

x = 130/20

x = 6.5 weeks

If your parents gave you $60 to help buy the bike the equation would be written as:

Y = 20x + 60

$130 = 20x + 60

Subtract 60 from both sides to get:

$70 = 20x

Solve for x

x = 70/20

x = 3.5 weeks

Answer:

m = 1/3

Step-by-step explanation:

Given two points on a line, we can find the slope of the line using the slope formula, which is given by:

m = (y2 - y1) / (x2 - x1), where

Thus, we can plug in (8, 2) for (x1, y1) and (-7, -3) for (x2, y2) to find m, the slope of the line passing through the two points:

m = (-3 - 2) / (-7 - 8)

m = -5 / -15

m = 1/3

Thus, the slope, m, of the line passing through the points (8, 2) and (-7, -3) is 1/3.

The slope is:

Work/explanation:

Use the slope formula:

\(\bf{m=\dfrac{y_2-y_1}{x_2-x_1}}\)

where m = slope;

(x₁, y₁) is a point;

(x₂, y₂) is another point.

Label the values:

m is unknown;

(x₁, y₁) is (8,2);

(x₂, y₂) is (-7, -3).

Plug in the data:

\(\bf{m=\dfrac{-3-2}{-7-8}}\)

Simplify both the numerator and the denominator

\(\bf{m=\dfrac{-5}{-15}}\)

\(\bf{m=\dfrac{5}{15}}\)

\(\bf{m=\dfrac{1}{3}}\)

Answer:

1/x and x⁻¹

Step-by-step explanation:

(x⁻³)^⅓

x⁻³*⅓

x⁻¹

1/x

I hope this helps

To determine how many scarves Maddie can make and still have at least 3.5 ounces of yarn left over, we can use division and subtraction.

First, we need to figure out how much yarn Maddie will use to make two pairs of mittens:

2 pairs of mittens x 2 mittens per pair x 2.25 ounces of yarn per mitten = 9 ounces of yarn

Next, we can subtract the amount of yarn needed for the mittens from the total amount of yarn Maddie has:

28.14 ounces of yarn - 9 ounces of yarn = 19.14 ounces of yarn remaining

Now, we can divide the remaining amount of yarn by the amount needed for each scarf to find out how many scarves Maddie can make:

19.14 ounces of yarn ÷ 5.25 ounces of yarn per scarf ≈ 3.64 scarves

Since Maddie can't make a fraction of a scarf, we need to round down to the nearest whole number. Therefore, Maddie can make 3 scarves and still have at least 3.5 ounces left over to make two pairs of mittens.

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The appropriate level of precision for the scale depends on the smallest unit of measurement it can accurately determine. In this case, the scale measures weight to the nearest 0.5 lb.

A. 140 lbs. : This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision. B. 148.75 lbs.: This measurement includes decimal places that the scale cannot accurately determine. It exceeds the precision of the scale and does not show an appropriate level of precision. C. 140.5 lbs: This measurement falls within the precision of the scale. It accounts for the nearest 0.5 lb increment and shows an appropriate level of precision. D. 141 lbs: This measurement is rounded to the nearest whole number and does not account for the scale's precision. It does not show an appropriate level of precision.

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The optimal level of Y is option a) 23

TB = \(300Y - 6Y^2\)

MB or Marginal Benefit will result from the first derivative

MB=300-12Y

and TC = 24Y + 108

Marginal Cost, or MC, will result from the first derivative.

MC=24

MC=MB is the level of Y that is ideal.

300-12Y=24

12Y=276

Y=23

The expense that a business incurs when it needs to produce extra units of any goods or services is referred to as a marginal cost.

It is computed by taking into consideration the whole cost of creating the extra items and dividing that sum by the variation in the overall quantity of the produced goods.

Variable costs like materials and labor are included in marginal costs. Additionally, it takes into account any increases in fixed expenses like selling, administration, and overhead.

When a change in production volume is required, the cost change is referred to as the change in the cost of production. More labor and raw resources are needed to produce additional units, changing the overall cost of production.

The volume of output either increases or decreases, which affects quantity. With an increase or decrease in production, there will be a variation in cost.

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The probability that the average final exam score for a sample of 64 students is between 140 and 150 is approximately 0.2893, or 28.93%.

What is normal distribution?

Normal distribution, also known as Gaussian distribution or bell curve, is a probability distribution that is symmetric and bell-shaped. It is widely used in statistics and probability theory to model a wide range of phenomena observed in nature, society, and various fields of study.

To calculate the probability that the average final exam score for a sample of 64 students is between 140 and 150, we need to use the properties of the normal distribution.

Given:

Mean score (μ) = 149

Standard deviation (σ) = 16

Sample size (n) = 64

Step 1: Find the standard deviation of the sample mean (standard error):

The standard deviation of the sample mean, also known as the standard error, is given by the formula:

Standard error (SE) = σ / √n

SE = 16 / √64 = 16 / 8 = 2

Step 2: Convert the values to z-scores:

To work with the standard normal distribution, we need to convert the values of 140 and 150 to z-scores using the formula:

z = (x - μ) / σ

For 140:

z1 = (140 - 149) / 16 = -9 / 16 ≈ -0.5625

For 150:

z2 = (150 - 149) / 16 = 1 / 16 ≈ 0.0625

Step 3: Find the cumulative probability:

Using the z-scores obtained, we can find the cumulative probability for each z-score using a standard normal distribution table or a statistical software.

P(z1 < Z < z2) = P(-0.5625 < Z < 0.0625)

Consulting a standard normal distribution table or using a statistical software, we find that P(-0.5625 < Z < 0.0625) is approximately 0.2893.

Therefore, the probability that the average final exam score for a sample of 64 students is between 140 and 150 is approximately 0.2893, or 28.93%.

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Answer:

ya I am good at personal finance math

Step-by-step explanation:

FOLLOW MY ACCOUNT PLS PLS

The value of (gof)(-7) is 3√6.

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x) = x² + 6 and g(x)=√x-1

We need to find the value of  (gof)(-7).

Let (gof)=g(f(-7))

=g( (-7)² + 6)

=g( 49 + 6)

=g(55)

=√55-1=√54

=√9×6

=3√6

Hence, the value of (gof)(-7) is 3√6.

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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Answer:−6y+9.6z−3

Step-by-step explanation:−(6y−9.6z+3)

−6y+9.6z−3

To find the derivative dy/dx using implicit differentiation, we differentiate both sides of the equation with respect to x, treating y as a function of x.

Given: x*sin(y) - 4y^4 - 6 = 9x

Differentiating both sides with respect to y:

d/dy (x*sin(y) - 4y^4 - 6) = d/dy (9x)

Using the chain rule on the left side:

(d/dx (x*sin(y))) * (dx/dy) - 16y^3 * (dy/dy) = 0

Since dy/dy is simply 1, the equation simplifies to:

x*cos(y) * (dx/dy) - 16y^3 = 0

To find dx/dy, we can isolate it:

xcos(y) * (dx/dy) = 16y^3

dx/dy = (16y^3) / (xcos(y))

Now, given dx = 11, we can substitute it into the equation to find dy/dx.

dx/dy = (16y^3) / (xcos(y))

11/dy = (16y^3) / (xcos(y))

To find dy/dx, we need to take the reciprocal of both sides:

dy/dx = (x*cos(y)) / (16y^3) * 1/11

Therefore, dy/dx = (xcos(y)) / (16y^311)

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The expression that has a value greater than 4,562 is A.4,562 times three-halves

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

In this case, 4,562 times three-halves will be:

= 4562 × 3/2

= 6843

4,562 x 1 is 4562

4,562 times one-half is:

= 4562 × 1/2

= 2281

4,562 times one-fourth is:

= 4562 × 1/4

= 1140.5

Therefore, the correct option is A.

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Answer:

a

Step-by-step explanation:

In order for a sample of the entire population to be considered representative in public opinion polls, it must correctly and fairly reflect the views of the entire population.

Public opinion surveys are used to collect data and information on the opinions and views of people in a given population. For the results of a survey to be valid and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

Public opinion surveys are designed to measure the opinions and views of people in a given population. To ensure the results of the survey are accurate and reliable, the sample of people chosen for the survey must be representative of the entire population. This means that the views of those in the sample must accurately and proportionately reflect the views of the whole population. It is not necessary for the sample to exceed 50% of the targeted population, nor does it need to be based on all registered voters in the population. Therefore, option d. is the correct answer, which states that the sample must be representative in that the views of those in the sample must accurately and proportionately reflect the views of the whole population.

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Complete question :

Abdul's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Abdul $4.25 per pound, and type B coffee costs $5.90 per pound. This month's blend used twice as many pounds of type B coffee as type A, for a total cost of $337.05 . How many pounds of type A coffee were used?

Answer:

21 pounds

Step-by-step explanation:

Pounds of coffee A used = x

Pounds of coffee B = 2x

Cost per pound of A = $4.25

Cost per pound of B = $5.90

Total cost of coffee = $337.05

4.25x + 2x(5.90) = 337.05

4.25x + 11.8x = 337.05

16.05x = 337.05

x = 337.05 / 16.05

x = 21

Hence, 21 pounds of coffee A was used