In a deck of 52 cards there are 2 jokers and 4 each of the number cards 1-10. The probability of picking a joker is 2 out of 52 or 2/52. Write as a fraction, the probability of drawing a number 7 card.​

Answer:

28 (0,2,4,14,28)

34 (0,2,17,34)

42 (0,2,6,7,21,42)

the greatest common factor is 2 because it's the greatest number that can be divided by 28, 34 and 42

Answer:

6

Step-by-step explanation:

14-4=10+2=12-6=6+6=12

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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Answer:

2!!!!!

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

do 6/3 easy as pie! (not pi)

Answer:

The midpoint is -4

Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer:

40

Step-by-step explanation:

part        %

------- = ----------

whole    100

8       20

---  =  ---

?        100

8*100/20

40

Answer: 40

Step-by-step explain:

40

Answer: x+y>5 or (x+y)-5

Step-by-step explanation:

There are two potential ways of writing five less than the sum of x and y. You can use an expression or an inequality.

Inequality

By using an inequality, we would use the less than sign because 5 is less than the sum of x and y.

5<x+y

We can also write it where the variables are on the left side, which is usually preferred.

x+y>5

-------------------------------------------------------------------------------------------------------------

Expression

For an expression, we would basically write an equation, but without the equals sign.

(x+y)-5

Since 5 is less than the sum of x and y, we would subtract 5 from x+y. We don't necessarily need to put parentheses around x+y since the order of operations tells us to add or subtract from left to right in order. It is still good to be specific, saying that it is the sum of x and y.

Answer:

\(\textsf{B.} \quad f(x)=\dfrac{1}{(x+2)(x-1)}\)

Step-by-step explanation:

Asymptote: a line which the curve gets infinitely close to, but never touches.

From inspection of the graph, we can see that the asymptotes are:

This means that the function is undefined when x = -2, x = 1 and y = 0.

For a rational function to be undefined, the denominator equals zero.

Therefore,

So the equation of the function is:

\(f(x)=\dfrac{1}{(x+2)(x-1)}\)

Look at the vertical asymptotes

They are

So factor up the denominator

Hence the rational function is 1/(x+2)(x-1)

Option B

The 3rd and 4th expressions cannot be simplified using the quotient rule for exponents

The quotient rule for exponents states that if you have two exponents, and you want to divide them, you can do so by subtracting the exponent of the denominator from the exponent of the numerator.

The general form of the quotient rule:

xᵃ / xᵇ = xᵃ⁻ᵇ

Given:

(3²9⁻¹2³)/(8⁵7⁻²)

(3²9⁻¹2³)/(8⁵7⁻²) = (3² × 3²⁽⁻¹⁾ × 2³)/(8⁵×7⁻²)

                        = (3² × 3⁻² × 2³)/(2³⁽⁵⁾ ×7⁻²)

                        = (3²⁺⁽⁻²⁾ × 2³)/(2¹⁵ × 7⁻²)

                        = (3⁰ × 2³)/(2¹⁵ × 7⁻²)

                        = (1 × 2³)/(2¹⁵ × 7⁻²)

                        = (2³)/(2¹⁵ × 7⁻²)

                       = 2³⁻¹⁵ × 7²    ( quotient rule is used here)

                       = (2⁻¹²) (7²)

(4⁻²x⁻¹)/(4⁻¹x⁻²)

(4⁻²x⁻¹)/(4⁻¹x⁻²) = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾  ( quotient rule is used here)

                       = 4⁻²⁻⁽⁻¹⁾ × x⁻¹⁻⁽⁻²⁾

                       = (4⁻¹) (x¹)

(6x⁻⁸z²)(6⁵x⁻¹z²)

(quotient rule cannot be used to simplify this expression because the two expressions are multiplying each other)

(q⁻⁵r¹¹)/(s⁶t⁻¹⁵)

(quotient rule cannot be used here  because there are no like bases)

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Answer:

9 squares

Step-by-step explanation:

Anne bought a piece of ribbon = 7 over 9 m long = 63 m²

she used = 3 over 18 m = 54 m²

left = 9 m²

maximum number of squares she could form of 1 m = 9

Answer:

each will pay 11.36

Step-by-step explanation:

34.08 divided by 3 is 11.36

Answer:

19.74% of temperatures are between 12.9°C and 14.9°C

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 16.3, \sigma = 2\)

What proportion of temperatures are between 12.9°C and 14.9°C?

This is the pvalue of Z when X = 14.9 subtracted by the pvalue of Z when X = 12.9.

X = 14.9

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{14.9 - 16.3}{2}\)

\(Z = -0.7\)

\(Z = -0.7\) has a pvalue of 0.2420

X = 12.9

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{12.9 - 16.3}{2}\)

\(Z = -1.7\)

\(Z = -1.7\) has a pvalue of 0.0446

0.2420 - 0.0446 = 0.1974

19.74% of temperatures are between 12.9°C and 14.9°C

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer:    8.3 or C  

Eplanation: This is because a half life is 50 percent of a normal life so 50 percent divided by 6 is 8.3

\(8.3\)% is the approximate decay rate of the element after the first day.

What is Radioactive decay ?

Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nuclei is considered radioactive. Three of the most common types of decay are alpha decay, beta decay, and gamma decay, all of which involve emitting one or more particles.

What is decay rate?

The rate of decay, or activity, of a sample of a radioactive substance is the decrease in the number of radioactive nuclei per unit time.

According to question, a radioactive element has a half-life of six days.

A half- life is \(50\)% of a normal life.

So, the approximate decay rate of the element after the first day

\(=\frac{50}{6}\)% \(=8.3\)%

Hence, we can conclude that \(8.3\)% is the approximate decay rate of the element after the first day.

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answer

Equilateral Triangle

Answer:

equilateral triangle

Step-by-step explanation:

Answer:

6 x 39 = 234

Step-by-step explanation:

9 x 6 is 54. 30 x 6 is 180. 180+54 is 234.

Answer:

slope= 3/1

y-intercept (0,2)

y= 3/1 b + 2

The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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This results in the following solution for the system of equations:

x = 2 y = 3 z = 3

To find the inverse of the matrix A and use it to solve the system of equations, you can use the Gauss-Jordan elimination method.

This method involves multiplying a matrix by its inverse to reduce it to its identity matrix. For your system of equations, the matrix A is:

\(A = \begin{bmatrix} 2 & 2 & 3 \ 2 & 2 & -1 \ 3 & -1 & 0 \end{bmatrix}\)

Using the Gauss-Jordan elimination method, the inverse of A can be found by reducing the matrix to its identity matrix. This can be done by performing the following operations on the matrix:

This will result in the identity matrix on the left side, and the inverse of A on the right side. The inverse of A is:

\(A^-1 = \begin{bmatrix} 1 & 0 & 0 \ 2 & 1 & 0 \ -3 & -2 & 1 \end{bmatrix}\)

You can then use this inverse to solve the system of equations by multiplying both sides of the equation by \(A^-1\). This results in the following solution for the system of equations:

x = 2 y = 3 z = 3

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Answer: 1.15

Step-by-step explanation:

23/20 = 1 3/20 = 1.15

Answer:

for the first question, the slope is -2/7 and the y-intercept is 2.

for the second question the slope is -1/3 and the y-intercept is 6

Step-by-step explanation:

Answer:

11 1/2   or    23/2

Step-by-step explanation:

K = 10 + 3/2 = 10 + 1 + 1/2

Answer: 13200 yards

Step-by-step explanation: 1 mile is equivalent to 1760 yards. If you multiply 1760 by 7.5, you get 13200 yards.

method 2: algebra

1. if you set the problem up as an equation, it's y/7.5=1760. Then you cross multiply, so y=13200. (Both methods are different but will get you to the same answer)

Answer:

a. unbounded

e. x ≤ 9

Step-by-step explanation:

The interval means all real numbers less than or equal to 9.

Since all numbers to negative infinity are included, it is unbounded.

a. unbounded

e. x ≤ 9

A sketch looks like a number line with a solid dot at 9 and an line pointing left with an arrowhead at the left pointing left.

Answer:

b. unbounded

e. x ≤ 9

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

A bounded interval is an interval that includes both its endpoints.

For the interval (-∞, 9]:

Therefore, the given interval is unbounded.

Inequality notation

Therefore, the given interval is represented by the inequality x ≤ 9.

To sketch the graph on a number line:

To sketch the graph on a coordinate plane:

The mistake that Katie made in the stem and leaf diagram, was that she D. Missed a length.

Looking at the stem and leaf diagram, we see that there are 14 leaves. This means that there are 14 lengths of caterpillars. However, there are 15 lengths shown on the table.

This means that there is a length missing that Katie failed to account for. Upon close inspection of the stem and leaf plot, we find that the missing length is a second value of 70 because there are two lengths that are 70 but this is shown only once on the stem and leaf plot.

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