–
5z+8z+10z+6z+
–
9z

Answer:

8 rides

Step-by-step explanation:

20 + .50x = 24

-20             -20

.50x = 4

/.50    /.50

x = 8

Answer:

8

Step-by-step explanation:

If you have $24 and you buy a $20 ticket to get in, you are left with four dollars.

Since each ride is $0.50 and that is half a dollar, you can multiply four times two. This gives you eight.

Therefore, you can ride 8 rides :)

The probability that the selected student has at least one of the two types of cards is at least 0.2.

To find the probability that the selected student has at least one of the two types of cards, we can use the principle of inclusion-exclusion.

Let's define:

P(A) = probability of having the first type of card,

P(B) = probability of having the second type of card.

The formula for the probability of the union of two events, A and B, is given by:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Given that P(A ∩ B) = 0.2, we can rewrite the formula as:

P(A ∪ B) = P(A) + P(B) - 0.2

Since we want to find the probability of having at least one of the two types of cards, we are interested in P(A ∪ B). Therefore, the probability is at least 0.2, as stated.

This means that even if the probability of having only one of the two types of cards is zero, the probability of having at least one of them is still 0.2 or higher.

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So, you need to deposit $628.86 monthly to accumulate $100,000 in 15 years with an APR of 7%.

To create a college fund for your child, you must determine the amount you need to deposit every month. The fund that offers an APR of 7% will help you accumulate the amount in the future. Here are the steps to find out how much you need to deposit monthly.
Step 1: Determine the total amount required for college funds.
The first step is to determine the total amount you need to pay for college funds. Suppose you want to create a college fund for your child that requires $100,000 in 15 years. Use a present value calculator or online present value calculator to determine the future value of the college fund.
Step 2: Determine the interest rate
The second step is to determine the interest rate you will receive on your savings. Suppose the fund offers an APR of 7%.
Step 3: Determine the number of years
The third step is to determine the number of years you have until you need the money. Suppose you have 15 years.
Step 4: Use the annuity formula
The fourth step is to use the annuity formula to determine how much you need to deposit every month. The formula is:
PMT = FV × i / ((1 + i)n - 1)
Where PMT is the monthly payment, FV is the future value, i is the interest rate, and n is the number of payments.
Using the given values:
PMT = 100,000 × 0.07 / ((1 + 0.07)^15 - 1)
PMT = 100,000 × 0.07 / 11.283
PMT = $628.86

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The line plot is also known as a dot plot.

The given information can be organized as follows:3 students sold 5 candles2 more students sold 6 candles than those who sold 5 candles3 students sold 8 candles1 student sold 12 candles Remaining students sold 9 candles.To create a line plot of candles sold, they will mark an X on the number line for each student's number of candles sold. The number line should go from 0 to the largest number of candles sold. The largest number of candles sold in this case is 12.The number of students selling the same number of candles is used to determine the height of each X mark. For example, 3 students sold 5 candles, so their mark should be placed at the number 5 on the number line with the height of the mark as 3.

A good scale for their line plot is to count by ones (1). This is because the highest number of candles sold is 12, and counting by ones will make it easy to mark an X on the number line for each student's number of candles sold.

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Answer:

See below.

Step-by-step explanation:

Part A

"The graph passes through (0,2), (2,6), (3,12).

If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points.

Using (0,2) and (2,6), the slope would be 2.

Using (2,6) and (3,12), the slope would be 3 1/3.

Since the slope is not constant everywhere, the function is non-linear."

Part B

An example of a linear function is y=2x+6.

An example of a nonlinear function is xy=3.

-hope it helps

The customer have to choose 2002 ways to taste 5 different white wine.

The number of possible ways to choose items from a collection when the order of choice is irrelevant is determined using the combination formula. Combination, to put it simply, is the process of choosing items or things from a bigger group where order is irrelevant.

The combination formula is: n! / (n-r)! r! , where n is the total number of items (14 in this case) and r is the number of items being selected at once (5 in this case),

Plugging our numbers into the formula we get:

= 14! / (14-5)! 5!

= 2002

After simplifying, we get 2002.

So, there are 2002 ways of picking 5 different white wines to taste from a group of 14 local winery bottles.

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Answer:

0.2, 0.6, 0.8, 0.35, 3/4, 1/4, 1/3, 1/2

The absolute values of the three integer roots of the given polynomial are |a| = 0, |b| = 2011, and |c| = 2011.

The given polynomial is x³ - 2011xᵐ.

We are asked to find the absolute values of the three integer roots of this polynomial, denoted as a, b, and c.

To find the roots, we can set the polynomial equal to zero and solve for x:

x³ - 2011xᵐ = 0

Factoring out an x gives us:

x(x² - 2011xᵐ⁻¹) = 0

From this equation, we can see that one of the roots is x = 0.

Now let's focus on the second factor, x² - 2011xᵐ⁻¹ = 0.

This quadratic equation has two roots, which we can find using the quadratic formula:

x = (-b ± √(b² - 4ac))/(2a)

For this equation, a = 1, b = -2011, and c = 0. Substituting these values into the quadratic formula, we get:

x = (-(-2011) ± √((-2011)² - 4(1)(0)))/(2(1))
x = (2011 ± √(4044121))/(2)

Simplifying further, we have:

x = (2011 ± √(2011²))/(2)
x = (2011 ± 2011)/(2)

This gives us two possible values for x:

x = (2011 + 2011)/(2) = 2011
x = (2011 - 2011)/(2) = 0

Now we have three potential roots: x = 0, x = 2011, and x = 2011.

To find the absolute values of these roots, we take the absolute value of each:

|0| = 0
|2011| = 2011
|2011| = 2011

Therefore, the absolute values of the three integer roots of the given polynomial are |a| = 0, |b| = 2011, and |c| = 2011.

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Answer:

\(c \: (x + 5)(x - 1)\)

This value represents the present worth below which the probability is 0.5, indicating a negative present worth.

To estimate the probability that the present worth is negative using the NORM.INV function in Excel,

we need to calculate the present worth of the project and then determine the corresponding probability using the normal distribution.

The present worth of the project can be calculated by finding the sum of the present values of the annual receipts over the 10-year period, minus the initial investment. The present value of each annual receipt can be calculated by discounting it back to the present using the minimum attractive rate of return (MARR).

Using the given information, the present value of the initial investment is $10,000. The present value of each annual receipt is calculated by dividing the expected return of $1,800 by \((1+MARR)^t\),

where t is the year. We then sum up these present values for each year.

We can use the NORM.INV function in Excel to estimate the probability of a negative present worth. The function requires the probability value, mean, and standard deviation as inputs.

Since we have a mean and standard deviation for the present worth,

we can calculate the corresponding probability of a negative present worth using NORM.INV.

This value represents the present worth below which the probability is 0.5. By using the NORM.INV function,

we can estimate the probability that the present worth is negative based on the given data and assumptions.

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The equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3

The equation is

f(x) = 2x - 9

Then it is translated 6 units up

The translation is the process of moving the shape to left/right of up or down. During the translation process the shape and size of the graph will not change. In translation we are only changing the coordinates of the points of the shape.

Here it is translated 6 units up.

During the upward motion it will be positive

g(x) = f(x) + 6

Substitute the value of f(x)

g(x) = 2x-9 + 6

g(x) = 2x-3

Hence, the equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3

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The mean of T is -10 and the standard deviation of T is √425 when X1 and X2 are independent.

To find the mean of T, we can use the properties of expected values. Since T = 11X1 - 2X2, the mean of T can be calculated as follows: E(T) = E(11X1) - E(2X2) = 11E(X1) - 2E(X2) = 11(10) - 2(20) = -10. To find the standard deviation of T, we need to consider the variances and covariance of X1 and X2. Since X1 and X2 are independent, the covariance between them is zero. Therefore, Var(T) = Var(11X1) + Var(-2X2) = 11^2Var(X1) + (-2)^2Var(X2) = 121(2^2) + 4(3^2) = 484 + 36 = 520. Thus, the standard deviation of T is √520, which simplifies to approximately √425. When X1 and X2 have a correlation of -0.76, the mean and standard deviation of T remain the same as in the case of independent variables. To calculate the probability P(T > 30) when X1 and X2 are independent, normally distributed variables, we need to convert T into a standard normal distribution. We can do this by subtracting the mean of T from 30 and dividing by the standard deviation of T. This gives us (30 - (-10))/√425, which simplifies to approximately 6.16.  We can then look up the corresponding probability from the standard normal distribution table or use statistical software to find P(T > 30). The probability will be the area under the standard normal curve to the right of 6.16.

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Answer:

I read it.. I don't know.. It's just saying we can't really cheat, it's not too bad.

The linear programming model would include equation for profit will be Z = 0.85X + 0.9Y and production constraints are 0.3X <= Y <= 0.6X; demand constraints are X <= (5000 + 3A) and Y <= (4000 + 5B); and cost constraint are 0.6X + 0.85Y + A + B <= 16,000.

Optimal values of X, Y, A, and B that maximize profit (Z) can be determined by using Excel Solver.

The linear programming model for the given problem is shown below:

Let X be the number of jars of applesauce produced. Y be the number of bottles of apple juice produced.

The objective function will be to maximize profit, which can be calculated by the following equation:

Profit = revenue - cost

Revenue can be calculated by multiplying the number of units produced by their respective selling prices. Cost can be calculated by multiplying the number of units produced by their respective production costs. The equation for profit will be:

Z = 1.45X + 1.75Y - (0.6X + 0.85Y)

Z = 0.85X + 0.9Y

The marketing manager estimates that the demand for applesauce is a maximum of 5,000 jars, plus an additional 3 jars for each $1 spent on advertising. The maximum demand for apple juice is estimated to be 4,000 bottles, plus an additional 5 bottles for every $1 spent on promoting apple juice. The maximum amount of money that can be spent on production and advertising is $16,000.

Therefore, we can write the constraints as follows:

Production constraints:

0.3X <= Y <= 0.6X

Demand constraints:

X <= (5000 + 3A)

Y <= (4000 + 5B)

Cost constraint:

0.6X + 0.85Y + A + B <= 16,000

Where A and B are the amounts spent on advertising for applesauce and apple juice, respectively.

To solve the model by using the computer, we can use any software that solves linear programming problems.

One such software is Microsoft Excel Solver. We can set up the problem in Excel as follows:

Cell C9: 0.85X + 0.9Y

Cell C12: 0.6X + 0.85Y + A + B

Cell C13: $16,000

Cell C15: 0.3X

Cell C16: XCell C17: 0.6X

Cell C18: 5000 + 3A (for applesauce)

Cell C19: Y

Cell C20: 4000 + 5B (for apple juice)

Cell C21: A

Cell C22: B

We then use Excel Solver to find the optimal values of X, Y, A, and B that maximize profit (Z).

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Step-by-step explanation:

r=21cm

a=135

perimeter=2r+ar

=2×21+135×21

=42+2835

=2877cm

Answer:

x = 2, y = -1

(x,y) = > (2,-1)

Step-by-step explanation:

2x + 5y = -1

3x + 2y = 4

-3(2x + 5y = -1) = > -6x - 15y = 3

2(3x + 2y = 4) = > 6x + 4y = 8

-6x - 15y = 3

6x + 4y = 8

-11y = 11

/-11  /-11

y = -1

2x + 5y = -1

2x + 5(-1) = -1

2x -5 = -1

   +5   +5

2x = 4

/2   /2

x = 2

(x,y) = > (2,-1)

Hope this helps!

Answer:

assuming that the equations are equal to zero the answers would be

3   ,   -3    ,  5

Step-by-step explanation:

one real eigenvalue. find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace.

What is eigenvalue?

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that, when the linear transformation is applied to it, changes at most by a scalar factor. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by lambda.

a) -4

b) 1

c) 1

Step-by-step explanation:

a) The matrix A is given by:

\(A=\left[\begin{array}{ccc}-3 & 0 & 1 \\2 & -4 & 2 \\-3 & -2 & 1\end{array}\right]\\\)

where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:

\(A-\lambda I=\left[\begin{array}{ccc}-3-\lambda & 0 & 1 \\2 & -4-\lambda & 2 \\-3 & -2 & 1-\lambda\end{array}\right]\)

and by taking the determinant:\(\begin{aligned}& {[(-3-\lambda)(-4-\lambda)(1-\lambda)+(0)(2)(-3)+(2)(-2)(1)]-[(1)(-4-\lambda)(-3)+(0)(2)(1-} \\& \lambda)+(2)(-2)(-3-\lambda)]=0 \\& -\lambda^3-6 \lambda^2-12 \lambda-16=0\end{aligned}\)

and the roots of this polynomial is:

\(\begin{aligned}& \lambda_1=-4 \\& \lambda_2=-1+i \sqrt{3} \\& \lambda_3=-1-i \sqrt{3}\end{aligned}\)

hence, the real eigenvalue of the matrix A is -4.

b) The multiplicity of the eigenvalue is 1.

c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)

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Complete Quetion

The matrix A= (−3 0 1, 2 −4 2, −3 −2 1) has one real eigenvalue. Find this eigenvalue, its multiplicity, and the dimension of the corresponding eigenspace. The eigen value = has multiplicity = and the dimension of the corresponding eigenspace is:_______.

Answer: D is the correct answer .

D. h(x)= (x-2)^2(x+4)(x-1)

Step-by-step explanation: For Plato users the correct answer is D .

The function which has three distinct zeroes is h(x) = (x − 2)²(x + 4)(x − 1), the correct option is D.

A function is a law that relates a dependent and an independent variable.

The zeroes of the function are the point at which the function value becomes 0.

The function which have three distinct real zeroes is

h(x) = (x − 2)²(x + 4)(x − 1)

(x-2)² = 0

x = 2

(x+4) = 0

x = -4

x-1 = 0

x = 1

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The result of the given expression as a decimal is - 0.2

Decimals are values containing decimal points. Given the expression below;

-1.56 divide by 7.8

This can also be expressed as:

-1.56/7.8

Convert to fraction

-156/100 ÷78/10
-156/100 * 10/78

-2/10

Hence the result of the given expression as a decimal is - 0.2

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Answer:

100 strawberries

Step-by-step explanation:

multipy 5 by 20 and you'll get 100

The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:

z = (x - μ) / σ

where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:

z = (81 - 65) / 8 = 2.00

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.

Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.

z = (81 - 65) / 8 = 2.00

P(z < 2.00) = 0.9772

Number of students with score < 81 = 0.9772 x 500 = 489

Therefore, we would expect approximately 489 students to earn a score less than 81 points.

The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:

z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70

z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08

Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.

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In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

A circle is a geometric shape defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.

Center: The center is a fixed point in the plane from which all points on the circle are equidistant. It is denoted by the coordinates (h, k), where h represents the x-coordinate and k represents the y-coordinate of the center.

Radius: The radius is the distance between the center of the circle and any point on the circle. It is denoted by the letter "r". The radius is constant for all points on the circle.

Diameter: The diameter is a line segment passing through the center of the circle and with endpoints on the circle. It is twice the length of the radius, and it divides the circle into two equal halves.

In the xy-plane, the unit circle with center at the origin (0, 0) is defined by all the points that are at a distance of 1 unit from the origin.

Point A: (1, 0)

Point A lies on the x-axis and is 1 unit away from the origin. It represents a point on the unit circle.

Point B: (3/5, 4/5)

Point B lies on the unit circle but is not one of the standard points (such as (1, 0), (-1, 0), (0, 1), or (0, -1)). Instead, it represents a point on the unit circle with coordinates (3/5, 4/5). The x-coordinate of B is 3/5, and the y-coordinate is 4/5. The distance between point B and the origin (0, 0) is 1 unit, which satisfies the condition of being on the unit circle.

Therefore, point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

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The simplified expression is (-187.584x + 287.6672) / 6.8, which is equivalent to option A: -2.84x - 1.66.

To simplify the expression 5.3x - 8.14 / 3.6x - 9.8, we can first simplify the division by finding a common denominator for the fractions.

The common denominator for 3.6x and 9.8 is 3.6x * 9.8 = 35.28x.

Next, we can rewrite the expression using the common denominator:
5.3x * (35.28x/35.28x) - 8.14 * (35.28x/35.28x) / 3.6x * (35.28x/35.28x) - 9.8 * (35.28x/35.28x)

Simplifying further, we get:
(5.3 * 35.28x^2 - 8.14 * 35.28x) / (3.6 * 35.28x - 9.8 * 35.28x)

Now, we can simplify the numerator:
(187.584x^2 - 287.6672x) / (-6.8x)

Factoring out an x from the numerator, we have:
x(187.584x - 287.6672) / (-6.8x)

Finally, we can cancel out the x terms:
(187.584x - 287.6672) / -6.8

Therefore, the simplified expression is (-187.584x + 287.6672) / 6.8, which is equivalent to option A: -2.84x - 1.66.

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Answer:

35997

Step-by-step explanation:

Answer:

b and e are the correct numbers

Step-by-step explanation:

i hope this helps :)

The answer to this is 23,440. I got this answer by cheating.

sientific calculator. heh.. :)

Hope this helps!!

The answer would be the first option (x+1)(x+8). You would use the foil method, which will give you the equivalent value of the expression.

Hope this helped

(x+1)(x+8) is the  expression which has an equivalent value to x² + 9x +8 for all values of x.

An expression is combination of variables, numbers and operators.

The given expression is  x² + 9x +8.

We have to find the equivalent expression to the expression x² + 9x +8.

Let us use the factorized form of the expression.

x² + 9x +8.

x² + 8x+x+8

Take common terms and factorize

x(x+8)+1(x+8)

(x+1)(x+8)

Hence, (x+1)(x+8) is the  expression which has an equivalent value to x² + 9x +8 for all values of x.

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