Use substitution to solve the following system of equations. What is the value of y?
6x + 2y = 4
3x - 5y = 44

y = 7
y = -4.5
y = -7
y = 4.5

The correct answer is the total balance of the account at the end of 24 months is $428.00.

The interest earned on Nicolas's account at the end of 24 months is:$400 x 0.035 x (24/12) = $28.00.

The total balance of the account at the end of 24 months will be the initial deposit of $400 plus the interest earned of $28.00, which gives: $400 + $28.00 = $428.00

Therefore, the total balance of the account at the end of 24 months is $428.00.

The simple interest formula is I = Prt where I is the interest, P is the principal, r is the interest rate as a decimal, and t is the time in years.

For the simple interest, the interest is the product of the principal, the interest rate, and the time.

Simple interest is a basic method of calculating the interest on a loan or an investment. It is called "simple" because it is calculated only on the initial principal amount without taking into account any additional interest that may have accumulated over time.

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The function  which is dependent on x is given by h(x) = 2(x - 1)²

A function is an expression that can be used to represent and show the relationship between two or more variables and numbers.

Given the function h, which is dependent on variable x.

The difference of x and 1 is:

Two times the square  of the difference of x and 1 is:

Therefore:

h(x) = 2(x - 1)²

The function  which is dependent on x is given by h(x) = 2(x - 1)²

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Answer:   51

Step-by-step explanation:

17% of 300 is 51

300 x .17 =51.

Answer:

st 1 _ r 3

st 2 _ r 1

st 3 _ r 2

st 4 _ r 4

The reasonable solution for the number of buttons of each color in one sack is (20, 11), meaning there are 20 black buttons and 11 white buttons in one sack.

Let's solve the system of equations based on the given information:

Let b be the number of black buttons in one sack and w be the number of white buttons in one sack.

From the first equation, we know that the number of black buttons in one sack is 9 more than the number of white buttons:

b = w + 9

From the second equation, we know that the total number of buttons in one sack is 372 divided by the number of sacks (12):

b + w = 372/12

b + w = 31

We can substitute the value of b from the first equation into the second equation:

(w + 9) + w = 31

2w + 9 = 31

2w = 31 - 9

2w = 22

w = 22/2

w = 11

Substituting the value of w back into the first equation, we can find the value of b:

b = 11 + 9

b = 20

Therefore, the reasonable solution for the number of buttons of each color in one sack is (20, 11), meaning there are 20 black buttons and 11 white buttons in one sack.

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As given by the question

There are given that the roll of die.

Now,

In the die, there are total outcomes is 6.

And,

The value in die which is odd number is:

1, 3, 5,

The number that an odd number or a number greater than 2

So, the succesfull outcomes is:

1, 3, 4, 5, 6.

Then,

The probability will be:

Hence, the correct option is B

Answer: 26

Step-by-step explanation: 78÷3 = 26

26x2=52=longer half

26 = shorter half

Answer:

7

Step-by-step explanation:

16+5+16+5+16+5

Answer: 6.875 If it aks you to round it is 7 gallons.

Step-by-step explanation:

The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

What is Standard Deviation?

It is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

To find the approximate wait time for the fastest 4% of passengers, we need to use the normal distribution and the inverse normal distribution function.

The normal distribution is a continuous probability distribution that is symmetrical around the mean, and is defined by the mean and standard deviation. In this case, the mean wait time for passengers with global entry is 40 minutes and the standard deviation is 12 minutes.

The inverse normal distribution function is a mathematical function that takes a probability as input and returns the corresponding value from the normal distribution. In other words, it allows us to find the value that corresponds to a given percentile of the normal distribution.

To find the wait time for the fastest 4% of passengers, we need to find the value that corresponds to the 4th percentile of the normal distribution. To do this, we can use an inverse normal distribution calculator or a normal distribution table.

Plugging in the mean and standard deviation of the wait time and the percentile of 4, we get a value of approximately 29.29 minutes. This is the wait time for the fastest 4% of passengers.

So, The approximate wait time for the fastest 4% of passengers is approximately 29.29 minutes.

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The appropriate choice about the display technique in case of two continuous variables is the scatter plot.

A scatter plot is a graph used to plot two variables, usually as the horizontal and vertical axis, to check for a correlation or connection between them.What is a variable?A variable is a statistical concept that is used to measure the characteristics of a population or a sample.

A variable is an attribute or a feature of an object, event, or person that can be quantified or described numerically. The pie chart is appropriate when you want to display a distribution of a continuous variable. But this technique is not appropriate in this case because you cannot see the distribution of a single continuous variable using a pie chart. A pie chart is best suited for showing percentages of a whole.C.E. A scatter plot is a graphical representation of the relationship between two variables. This technique is appropriate when you want to display two continuous variables. A treemap is best suited for showing the distribution of one categorical variable. F. A pie chart is appropriate when you want to display the distribution of a single continuous variable. A contingency table is appropriate when you want to display the frequency distribution of one categorical and one continuous variable.

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Answer:

18.84, 75.36, 169.56, and 301.44

Step-by-step explanation:

Given:

Annual earnings = $17,500

Asked: What is the gross amount of her semimonthly paycheck?

Solution:

To find the answer, we need to divide first the annual earnings by 12 to get the monthly paycheck. After that, we will divide it by 2 because we are looking for the semimonthly paycheck.

ANSWER: C. $729.17

Answer:

no solution

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Mean is also known as an average value amoung a set of data points, results, and tests.

Mathematically, mean ( average ) is defined as a weighted sum of data points. This can be expressed in a symbolic form as follows:

Where,

We are given with the following set of data points:

And we have a total of:

We will go ahead and plug in the respective values given into the formula for determining the mean value as follows:

Plug in the respective data points as follows:

Evaluate as follows:

The mean ( average ) value for the given set of data points is:

Answer:

\(x=6.5~ units\)

Step-by-step explanation:

\(x=\sqrt{13+29.25}\)

\(= \sqrt{42.25}\)

\(x=6.5\)

After the EEOC completes its investigation in an employment discrimination case, the outcomes can include resolution attempts, lawsuits, or issuing a Notice of Right to Sue to the complainant.

After the Equal Employment Opportunity Commission (EEOC) completes its investigation in an employment discrimination case, several outcomes are possible:

The EEOC may find reasonable cause to believe that discrimination has occurred. In this case, they may attempt to resolve the matter through informal methods such as mediation or settlement negotiations. If these efforts fail, the EEOC may file a lawsuit against the employer on behalf of the aggrieved individual(s).

If the EEOC does not find reasonable cause, they will issue a Notice of Right to Sue to the individual who filed the complaint. This allows the individual to pursue a lawsuit against the employer independently.

In some cases, the EEOC may determine that further investigation is needed, and they may request additional information or evidence from both the complainant and the employer.

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For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

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The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

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1) {p₀, p₁, p₂, p₃} spans the vector space P₂[R].

2) the only solution to the equation is a = b = c = d = 0, indicating linear independence.

vector, in mathematics, a quantity that has both magnitude and direction but not position. Examples of such quantities are velocity and acceleration.

(a) To show that {p₀, p₁, p₂, p₃} is a spanning set of the vector space P₂[R], we need to show that any polynomial in P₂[R] can be expressed as a linear combination of p₀, p₁, p₂ and p₃.

The vector space P₂[R] consists of all polynomials of degree at most two with real coefficients. So, any polynomial in P2[R] can be written as:

f(x) = a + bx + cx²,

where a, b, and c are real coefficients.

Now, let's express f(x) in terms of the given vectors {p₀, p₁, p₂, p₃}:

f(x) = a(1 + x) + b(1 + x + x²) + c(x + x²)

= (a + b)x² + (a + b + c)x + (a).

We can see that f(x) can be expressed as a linear combination of p₀, p₁, p₂ and p₃ with the coefficients (a + b), (a + b + c), and a. Therefore, {p₀, p₁, p₂, p₃ spans the vector space P2[R].

(b) To reduce the set {p₀, p₁, p₂, p₃} to a basis of P₂[R], we need to remove any redundant vectors from the set while still maintaining the spanning property.

From part (a), we know that {p₀, p₁, p₂, p₃} is already a spanning set of P₂[R]. We can reduce it to a basis by removing any linearly dependent vectors.

To check for linear dependence, we set up the equation:

a(1+x) + b(1+x+x²) + c(x+x²) + d(1+x²) = 0,

where a, b, c, d are real coefficients.

Expanding and collecting like terms, we have:

(a + b + c + d) + (a + b + c)x + (b + c)x² + (d)x³ = 0.

For this equation to hold for all values of x, each coefficient must be zero:

a + b + c + d = 0,

a + b + c = 0,

b + c = 0,

d = 0.

From the third equation, we have b = -c.

Substituting b = -c into the second equation, we get:

a + (-c) + c = 0,

a = 0.

Therefore, the only solution to the equation is a = b = c = d = 0, indicating linear independence.

Since the set {p₀, p₁, p₂, p₃} is linearly independent and spans the vector space P₂[R], it is already a basis for P₂[R].

Therefore, the set {p₀, p₁, p₂, p₃} is a basis of the vector space P₂[R].

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Answer:

See below  ----pick the one that you need

Step-by-step explanation:

Total cost = 21   +   21 * .06    +   21 * .15  

               =  21 ( 1 + .06 + .15)

                            = 21(1.21)

Answer:

C=12h+7

Step-by-step explanation:

The total cost = 7 (flat rate) + 12h (12/hour)

Answer:

 =  5

Step-by-step explanation:

This equation can be used to predict the value of y for any given value of x that falls within the Range of the data.

Equation for a line of fit for the given data, we need to first determine the slope and y-intercept of the line. We can use the two ordered pairs (0, 1) and (6, 10) to do this.

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:

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

Substituting the values from the given points, we get:

m = (10 - 1) / (6 - 0) = 1.5

So the slope of the line is 1.5.

Next, we can use the point-slope form of a linear equation to write the equation of the line passing through the point (0, 1) with slope 1.5:

y - y1 = m(x - x1)

Substituting the values of the point (0, 1) and the slope m = 1.5, we get:

y - 1 = 1.5(x - 0)

Simplifying and rearranging, we get:

y = 1.5x + 1

So the equation of the line of fit in y = mx + b form is:

y = 1.5x + 1

This equation can be used to predict the value of y for any given value of x that falls within the range of the data.

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Answer:

a+11b/3

Step-by-step explanation:

Answer:

3 and 2/3b + 1a

Step-by-step explanation:

Simplifying b:

4b - 1/3b = 11/3b = 3 and 2/3b

Simplifying a:

-5a + 6a = 1a

Answer:

yes, it is

Step-by-step explanation:

The table shows a constant rate of change

y-5 7 9 11

5, 5+2, 7+2 ,9+2

The probability of a student having at least one sibling, based on the survey results is 0.8.

Daniel surveyed 120 students at his school and found that 96 of them have at least one sibling. This means that the probability of a student having at least one sibling, based on the survey results, is 96/120 or 0.8.

There are 425 students at Daniel's school, so if we multiply this number by the probability of having at least one sibling (0.8), we can estimate that approximately 340 students at the school have at least one sibling.

To estimate the number of students at Daniel's school who have at least one sibling, we can use this probability to make a prediction.

If we assume that the probability of a student having at least one sibling is the same for all students at the school, then we can apply this probability to the total number of students.

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The acceleration of the car, which comes to a complete stop, is -0.42857 m/s².

The acceleration of the car can be found using the formula:

acceleration = (final velocity - initial velocity) / time.

In this case, the final velocity is 0 m/s, the initial velocity is 15 m/s, and the time is 35 seconds. Plugging these values into the formula gives:

acceleration = (0 - 15) / 35

acceleration = -15 / 35

acceleration = -0.42857 m/s²

Therefore, the car's acceleration is -0.42857 m/s². This means that the car is negatively accelerating, or decelerating, at a rate of 0.42857 m/s².´

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