real numbers are the set of numbers that includes all rational and irrational numbers

Answer:

  C.  1.05%

Step-by-step explanation:

You want the probability a randomly chosen candidate will be offered admission if only 5% of the 21% called for an interview are offered admission.

The joint probability can be figured from the conditional probability relation:

  P(A&B) = P(A|B)·P(B)

  P(interviewed and admitted) = P(admitted | interviewed) · P(interviewed)

 P(offered admission) = (5%)(21%) = 1.05%

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Answer:

C. 1.05%

Step-by-step explanation:

To find the probability that a candidate will be offered admission, we need to multiply the probability of being called for an interview (21%) by the probability of being offered admission after the interview (5%).

Using the given percentages:

Now, multiply these probabilities:

To express this as a percentage, multiply by 100:

So, the probability that a candidate picked at random from the list of all applicants will be offered admission is 1.05% (Option C).

________________________________________________________

The number of weeks when Jim and Sally would have the same amount of money is 20 weeks.

The expression that can be used to represent the amount of money Jim would have in his account after x weeks is: $1,250 + 27.50x.

The expression that can be used to represent the amount of money Sally would have in his account after x weeks is: $1,400 + $20x.

In order to determine the number of weeks when they would have the same amount of money, the two expressions must be equal to each other.

$1,250 + 27.50x =  $1,400 + $20x

Combine similar terms

$1,400 - $1,250 = $27.50x - $20x

150 = $7.50x

x = 150 / 7.50 = 20 weeks

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Another possible value for j and K is (A) j = 18, k = 2

Note that in inverse variation, one of the variables increases while the other decreases.

From the information given, we have that;

j is inversely related to the cube of k,

This is represented as;

j ∝ 1/k³

Now, find the constant of variation

K = jk³

Substitute the vales

K = 3 × 6³

find the cube value

K = 648

Then, we have that;

j = 648 / 2³ = 81

For option B:

j = 648 / 3³ = 24

For option C:

j = 648 / 2³ = 81

For option D:

j = 648 / 81³ = 0.0008

For option E:

j = 648 / 2³ = 81

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Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

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.

15/8 quart of grape juice is needed for 15/4 quart of sparkling water.

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,

The recipe for sparkling grape juice calls for 1(1/2) quart of sparkling water and 3/4 quart of grape juice,

This means,

1(1/2) quart of sparkling water = 3/4 quart of grape juice

3/2 quart of sparkling water = 3/4 quart of grape juice

Multiply 15/6 on both sides.

15/6 x 3/2 quart of sparkling water = 15/6 x 3/4 quart of grape juice

15/4 quart of sparkling water = 15/8 quart of grape juice

Thus,

15/8 quart of grape juice is needed for 15/4 quart of sparkling water.

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Answer:

3a^2+8/6a^2

Step-by-step explanation:

there ya go hope this helps

Answer:

I got 4

Step-by-step explanation:

I included a picture of how I did it

The statement that is not true concerning PivotTables in Excel is b. PivotTables summarize data for two variables. PivotTables can summarize data for multiple variables, not just two.

PivotTables allow you to analyze and summarize data from various perspectives, including multiple variables, by grouping, filtering, and calculating values based on different criteria. They provide flexibility in summarizing and organizing data in a tabular format, making it easier to extract insights and perform data analysis efficiently.

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The graph of the parent absolute value function is decreasing over the interval (-∞, 0). The function exhibits a decreasing behavior as x moves from negative infinity towards zero, where the absolute value decreases.

The parent absolute value function is defined as f(x) = |x|. To determine where the graph of this function is decreasing, we need to identify the intervals where the function's slope is negative.

Let's analyze the behavior of the parent absolute value function:

For x < 0, the function can be rewritten as f(x) = -x. In this interval, the function is a linear function with a negative slope of -1. As x decreases, f(x) also decreases, indicating a decreasing behavior.

For x > 0, the function remains f(x) = x. In this interval, the function is a linear function with a positive slope of 1. As x increases, f(x) also increases, indicating an increasing behavior.

At x = 0, the function is not differentiable since the slope changes abruptly from negative to positive. However, it is worth noting that the function does not strictly decrease or increase at x = 0.

Therefore, we can conclude that the graph of the parent absolute value function is decreasing over the interval (-∞, 0).

In this interval, as x moves from negative infinity towards zero, the function values decrease. The farther away x is from zero (in the negative direction), the larger the absolute value, resulting in a decrease in the function values.

On the other hand, the graph of the parent absolute value function is increasing over the interval (0, ∞), as explained earlier.

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Answer:

(-8,2)

Step-by-step explanation:The y-value does not change, only the x-value becomes positive.

Answer:

89

Step-by-step explanation:

Answer:

NO

Step-by-step explanation:

is having -$50 bigger than having $50??

The transition matrix from B to B' is given by:

P = [

[10, 12, 3],

[5, 4, -3],

[19, 20, -1]

]

This matrix can be found by multiplying the coordinate matrices of B and B'. The coordinate matrices of B and B' are given by:

B = [

[4, 1, -6],

[3, 1, -6],

[9, 3, -16]

]

B' = [

[5, 8, 6],

[2, 4, 3],

[2, 4, 4]

]

The product of these matrices is given by:

P = B * B' = [

[10, 12, 3],

[5, 4, -3],

[19, 20, -1]

]

This matrix can be used to convert coordinates from the basis B to the basis B'.

For example, the vector (4, 1, -6) in the basis B can be converted to the vector (10, 12, 3) in the basis B' by multiplying it by the transition matrix P. This gives us:

(4, 1, -6) * P = (10, 12, 3)

The transition matrix maps each vector in the basis B to the corresponding vector in the basis B'.

This can be useful for many purposes, such as changing the basis of a linear transformation.

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Answer:

0.121

Step-by-step explanation:

From the given information:

Let X be a hypergeometric random variable. i.e X \(\sim\) h (x;:6,7,12)

To determine the mean and the standard deviation of X of a hypergeometric random variable; we have:

\(\mu_x = E(X)\)

\(\mu_x = 6 \times \dfrac{7}{12}\)

\(\mu_x =1 \times \dfrac{7}{2}\)

\(\mu_x =3.5\)

The standard deviation is :

\(\sigma _x = \sqrt{(\dfrac{12-6}{12-1}) \times 6 \times (\dfrac{7}{12})\times (1-\dfrac{7}{12})}\)

\(\sigma _x = \sqrt{(\dfrac{6}{11}) \times 6 \times (\dfrac{7}{12})\times (\dfrac{5}{12})}\)

\(\sigma _x = \sqrt{\dfrac{35}{44}}\)

\(\sigma _x = 0.892\)

However, the inequality for the event showcasing how X exceeds its mean value by more than 1 standard deviation is :

\(X \geq \mu_x +\sigma_x\)

\(X \geq 3.5 +0.892\)

\(X \geq 4.392\)

\(X \geq 5\)

∴

\(P(X \geq \mu_x + \sigma_x ) = P(X \geq 5)\)

\(P(X \geq \mu_x + \sigma_x ) = 0.121\)

The relationship between the Angles in triangle DEF,  the exact value of side d.

The length of side d in triangle DEF, we can use the Law of Sines, which relates the lengths of the sides of a triangle to the sines of their opposite angles. The Law of Sines states:

a/sin(A) =b/sin(B) = c/sin(C)

In this case, we know that angle D is 47°, side e has a length of 12 units, and side f has a length of 8 units. Let's label side d as x.

Applying the Law of Sines, we have:

x/sin(D) = e/sin(E)

Substituting the known values:

x/sin(47°) = 12/sin(E)

To find the value of sin(E), we can use the fact that the sum of the angles in a triangle is 180°:

E = 180° - D - E = 180° - 47° - E

E = 133° - E

Now we can rewrite the equation as:

x/sin(47°) = 12/sin(133° - E)

To find the value of sin(133° - E), we can use the identity sin(a - b) = sin(a)cos(b) - cos(a)sin(b):

sin(133° - E) = sin(133°)cos(E) - cos(133°)sin(E)

We know that sin(133°) and cos(133°) are fixed values.

Now we can substitute the values into the equation:

x/sin(47°) = 12 / (sin(133°)cos(E) - cos(133°)sin(E))

To find the value of sin(133°) and cos(133°), we can use a calculator

sin(133°) ≈ 0.9781

cos(133°) ≈ -0.2079

Substituting these values into the equation:

x/sin(47°) = 12 / (0.9781cos(E) - (-0.2079)sin(E))

We can rearrange the equation to solve for x:

x = (12 * sin(47°)) / (0.9781cos(E) + 0.2079sin(E))

the relationship between the angles in triangle DEF, we cannot find the exact value of side d.

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Please refer to the attachment for the answer and explanation! Hope it helps!!:))

Answer:

look at the picture I sent

Answer:

Slope = -250

Interpretation: Every month the value of the car goes down $250.

Step-by-step explanation:

The slope of this linear function is -250 because every 4 months, the value goes down by $1000 so...

-1000/4 = -250

Interpretation: Every month the value of the car goes down $250.

Hope this helps!

Answer:100

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer: 7= 1(5)+b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

y = mx + b

Given that the coordinate is (5, -7), you know that x = 5 and y = -7

Variable m represents the slope, so m = -1

Now simply plug in all the numbers:

y = mx + b

-7 = (-1)(5) + b

Answer:

\(\overrightarrow{\sf XJ} \: \textsf{ and } \: \overrightarrow{\sf XE}\)

Step-by-step explanation:

Ray:  Part of a line that has one endpoint and extends infinitely in only one direction. The length of a ray cannot be measured.

When naming a ray, use its endpoint first and then any other point on the ray.

The symbol for a ray is an arrow pointing to the right: \(\Large \text{$\rightarrow$}\)

The given figure is a ray with endpoint X.

Therefore, the given ray can be named as:  XJ and XE.

Answer:Angle x is congruent with the interior angle opposite side 8 (alternate interior angles)

Use tangent:

tan x = 8/15

x = arctan (8/15)

x = 28.1° (rounded)

Step-by-step explanation:

Using it's concept, the equivalent expression for the perimeter of the figure is:

2 + 3x2 + 4x2 + 5x2 + 8

The perimeter of a figure is given by the total length of it's boundary.

Hence, for the figure given in this problem, the perimeter is:

2 + 3 + 3 + 4 + 4 + 5 + 8 + 5

2 + 3x2 + 4x2 + 5x2 + 8

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The alternative hypothesis is that the proportion of smokers in the population is less than 0.151.

In hypothesis testing, the null hypothesis (H₀) represents the assumption or claim being tested, while the alternative hypothesis (H₁) represents the opposing claim. In this case, the null hypothesis is that the proportion of smokers in the population is equal to 0.151.

To determine the alternative hypothesis, we consider the suspected decrease in the proportion of smokers since 2015. The alternative hypothesis will reflect this suspicion. Since we suspect a decrease, the alternative hypothesis would state that the proportion of smokers in the population is less than 0.151.

Formally, the alternative hypothesis can be written as H₁: p < 0.151, where p represents the population proportion of smokers. This states that the true proportion of smokers is smaller than the reported proportion of 0.151, supporting the suspicion of a decrease in the proportion of smokers.

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The simplex method is a widely used algorithm for solving linear programming problems, which involve optimizing a linear objective function subject to linear constraints. False.

However, the simplex method does not explicitly require the variables to be nonnegative in order to find a solution.

The simplex method starts with an initial feasible solution and iteratively improves it by moving along the edges of the feasible region, ultimately reaching the optimal solution. During the iterations, the variables can take any real values, including negative values.

That being said, some variations of the simplex method, such as the dual simplex method, have been developed specifically to handle problems with nonnegativity constraints. These variations can be used when variables are required to be nonnegative.

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Answer:

x = 30°

y = 115°

Step-by-step explanation:

Given = AB ║ DC

            ∠A = 2x + 10

            ∠B = 65

            ∠C = y

            ∠D = 3x + 20

( AD is the transversal on the parallel lines AB and DC)

∴ ∠A + ∠D = 180       and         ∠B + ∠C = 180

 (1)          ∠A + ∠D = 180

              2x + 10 + 3x + 20 = 180

              5x + 30 = 180

              5x = 180 - 30 = 150

                x = 150÷5

                x = 30°

(2)           ∠B + ∠C = 180

               65 + y = 180

                 y = 180 - 65 = 115

                 y = 115°

The ordered pair which is the solution to the system of equations is  (3,-1)

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=3x-10 and 2x+3y=3    

                   putting y=3x-10 in 2x+3y=3

          ⇒      2x+3(3x-10)=3

          ⇒      2x+9x-30=3

          ⇒      11x=33

          ⇒       x=33/11

          ⇒       x=3

Putting x=3 in y=3x-10 ,we get

                          y=3×3-10

                      ⇒    y=9-10

                      ⇒    y=-1

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Answer:

2x^2+3x^4+1

Step-by-step explanation:

a trinomial  is composed by three monomials.

So only A and B can be correct

the degree of a polynomial is the same of the monomial that compose it with the biggest degree

so the answer is B because the monomial with the biggest degree is 3x^4 (its degree is 4)

The resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)

The triangle is a shape that has three sides and angles. Given the coordinate points of the triangle given as:

A(-2, 3)

B (-2, 5)

C (-4, 5)

If the coordinate points is translated by the vector (2, -7), hence the resulting coordinate points will be:

A' = (2+2, 3-7) = (4, -4)

B' = (-2+2, 5-7) = (0, -2)

C' = (-4-2, 5-7) = (-6,-2)

Hence the resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)

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Answer:

60?

Step-by-step explanation: