Elin chose C as the correct answer. Explain how she got her answer.

The amount of grams of each alloy that should be mixed to produce 40 grams of an alloy that is 60% gold are 16 grams and 24 grams respectively.

In order to write a system of linear equations to describe this situation, we would assign variables to the quantity of first alloy (30% gold) and the quantity of second alloy (80% gold) respectively, and then translate the word problem into a linear equation as follows:

Therefore, a system of linear equations to describe this situation can be written as follows;

x + y = 40      .....equation 1.

0.3x + 0.8y = 0.6(40)      .....equation 2.

From equation 2, we have the following:

0.3x + 0.8y = 24

0.3x + 0.8(x - 40) = 24

0.3x + 32 - 0.8x = 24

-0.5x = -8

x = -8/-0.5

x = 16 grams.

y = 40 - x

y = 40 - 16

y = 24 grams.

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When a number is selected at random, the probability that a number that is not a prime number would be selected would be = 3/7.

Prime numbers are defined as those numbers that are greater than one that cannot be divided by a whole number apart from themselves without a remainder.

To calculate the probability of non prime numbers from a game of cards the formula for probability should be used. That is;

Probability = possible outcome/sample space

The possible outcome = 1,4,6 = 3

The sample space = 7

Therefore probability = 3/7

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Answer:

A

Step-by-step explanation:

She earns $15 per poinsettia.

Answer:

A multi-step-word problem is like a puzzle with lots of pieces. Multi-step word problems are math problems that have more than one operation. An operation is addition, subtraction, multiplication, or division. Multi-step word problems can have any combination of these operations

Answer:

14/16 = 0.875

Answer:

the variance of X is 0.126.

Step-by-step explanation:

The number of white balls drawn X follows a hypergeometric distribution with N = 20 (total number of balls), K = 4 (number of balls drawn), and n = 4 (number of white balls). The probability mass function (pmf) of X is given by:

P(X = k) = (nCk)(N-nCk) / (NCk)

where C denotes the combination function.

(a) Expectation of X:

E(X) = np = nK/N = (4/20) * 4 = 0.8

Therefore, the expected number of white balls drawn is 0.8.

(b) Variance of X:

Var(X) = np(1-p)[(N-K)/(N-1)] = nK(N-K)(N-n)/(N^2(N-1)) = (4/20) * 4 * (20-4) * 16 / (20^2 * 19) = 0.126

Therefore, the variance of X is 0.126.

Answer:

The expected number of white balls drawn is 0.4 and the variance of X is 0.24.

Step-by-step explanation:

Answer:

[tex]a. \: 30 + a = 40 \\ a = 40 - 30 \\ a = 10 \\ b. \: 500 + b = 200 \\ b = 200 - 500 \\ b = - 300 \\ c. \: - 1 + c = - 2 \\ c = - 2 + 1 \\ c = - 1 \\ d. \: d +3.567=0 \\ d = 0 - 3.567 \\ d = - 3.567[/tex]

hope it helps:)

The value of 11 3/8 -7/8 is 10 1/2

Subtraction is the operation or process of finding the difference between two numbers or quantities . For examples, if out 100 students In a school , 40 are boys , the number of girls in the school is calculated by subtracting the number of boys from the total number of students.i.e 100 - 40 = 60

Solving 11 3/8 -7/8

= 91/8 - 7/8

= (91-7)/8

= 84/8

= 21/2

= 10 1/2

Therefore the value of 11 3/8 -7/8 is 10 1/2

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The expression that represents the total amount that Ignatio and his friends spent is 15t

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

After spending on t games, we have

f(t) = Rate * t

Substitute the known values in the above equation, so, we have the following representation

f(t) = 15 * t

Evaluate

f(t) = 15t

Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t

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Therefore , the solution of the given problem of probability comes out to be a complete probability model cannot be represented by this list.

The main objective of each considerations technique is to calculate the likelihood that a claim is true or that a particular incident will occur. Anything between 0 and 1, were 0 traditionally denotes a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The probabilities assigned to the outcomes do not add up to 1, hence the following list cannot be a complete probability model.

=> P(2) + P(3) + P(4)

=> 1/12 + 2/3 + 1/4

=>  (1 + 8 + 3) / 12

=> 12 / 12 = 1

In a complete probability model, the total of the probabilities should always be equal to 1, indicating that there is a probability of 1 that one of the events will occur.

In this instance, there is a missing probability since the sum of the probabilities assigned to the possible possibilities is less than 1.

Therefore, a complete probability model cannot be represented by this list.

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Answer:

Step-by-step explanation:

The null and the alternate hypothesis are:

In hypothesis testing, we take the null hypothesis (H₀) and the alternative hypothesis (H₁). The null hypothesis is the opposite of the claim , while the alternative hypothesis states  the claim.

In this case, the null hypothesis is that a majority of adults would not erase their personal information online if they could (i.e., 50% or less of them would do so). The alternative hypothesis is that a majority of adults would erase their personal information online if they could (i.e., more than 50% of them would do so). In symbolic form:

H₀: p ≤ 0.5

H₁: p > 0.5

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Answer:

2v-1

Step-by-step explanation:

9v+-3v+-4v-2+1

=9v-3v-4v-1

=6v-4v-1

=2v-1

Answer:

{-3, √3, -√3, 13/3}

Step-by-step explanation:

Since the polynomial has rational coefficients, any irrational zeros must come in conjugate pairs. So, if √3 is a zero, then so is its conjugate, -√3.

We can write the polynomial with these zeros as:

p(x) = a(x + 3)(x - √3)(x + √3)(x - 13/3)

where a is some constant coefficient. Multiplying out the factors, we get:

p(x) = a(x + 3)(x^2 - 3)(x - 13/3)

To find the remaining zeros, we need to solve for x in the expression p(x) = 0. So we set up the equation:

a(x + 3)(x^2 - 3)(x - 13/3) = 0

This equation is true when any of the factors is equal to zero. We already know three of the zeros, so we need to solve for the fourth:

(x + 3)(x^2 - 3)(x - 13/3) = 0

Expanding the quadratic factor, we get:

(x + 3)(x - √3)(x + √3)(x - 13/3) = 0

Canceling out the (x - √3) and (x + √3) factors, we get:

(x + 3)(x - 13/3) = 0

Solving for x, we get:

x = -3 or x = 13/3

Therefore, the other zeros are -3 and 13/3.

The complete set of zeros is {-3, √3, -√3, 13/3}.

Hope it helps^^

The equation of p(x) in vertex form is p(x) = 3(x + 1)² - 3.

Option C is the correct answer.

Since, Polynomial is an equation written as the sum of terms of the form kxⁿ.

where k and n are positive integers.

We have,

From the table,

From p(x) = 24 to p(x) = -3 the value of p(x) is decreasing and from p(x) = -3 to p(x) = 24 it is increasing.

So,

The vertex is (- 1, -3).

The vertex form of p(x).

p(x) = a ( x - h)² + k

Where (h, k) is the vertex.

Now,

(-1, -3) = (h, k)

Make (- 2, 0) = (x, p(x))

0 = a (- 2 + 1)² + (-3)

0 = a x 1 - 3

a = 3

Thus, The vertex equation of p(x).

p(x) = 3(x + 1)² - 3

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The two trends on the graph are:

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

The graph

The two trends on the graph are:

For the positive correlation, we have

Upward trend from January till August

This is because the function values increase approximately in this domain

For the negative correlation, we have

Upward trend from August till December

This is because the function values decrease approximately in this domain

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Answer:

29

Step-by-step explanation:

she spends $75 on the gift cards, which brings the total down to $175 which is how much money she has left. She then spends $123.5 on the 13 movie passes, she is then left with $51.5 to spend. Then you divide 51.5 by 1.75 to get 29.4 and rounds down to 29.

Answer:

60

Step-by-step explanation:

2$ times 30 luna bars at harmons is $60

Answer:
A and B

Step-by-step explanation:

-10/3= -3.33333333333

(- (-10))/(-3)= -10/3, (negative sign being erased)

=-3.33333333333

hope it helped:)

The strength of the beam is proportional to the width and the square of the depth, so we can express it as Strength = k * width * depth²

where k is the proportionality constant.

In the given figures, the beam is cut from a cylindrical log of diameter d = 24 cm, which means the maximum width and depth of the beam are limited by this diameter. We can see from the figures that the width and depth of the beam change depending on the angle at which it is cut from the log.

In Figure 1, the width and depth of the beam are equal, so we can express the strength of the beam as:

Strength = k * width * depth² = k * x² * (d/2 - x)²

where x is the width and depth of the beam.

In Figure 2, the width and depth of the beam are not equal, so we need to express them separately. Let w be the width and d be the depth, then we can express the strength of the beam as:

Strength = k * width * depth² = k * w * d² = k * ((d/2)sinθ)² * ((d/2)cosθ)²

where θ is the angle at which the beam is cut from the log.

In Figure 3, the width and depth of the beam also vary with the angle θ. We can express the width and depth as follows:

w = d sinθ

d = (d/2)cosθ

Then we can express the strength of the beam as:

Strength = k * width * depth² = k * (d sinθ) * [(d/2)cosθ]²

Therefore, depending on the angle at which the beam is cut from the log, the strength of the beam can be expressed using different equations, but in all cases, the strength is proportional to the width and the square of the depth, with a proportionality constant k.

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Complete question is:

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 24 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle in the figures. (Use k as your proportionality constant.)

The point estimate of the population​ proportion, the margin of error for the following confidence​ interval, and the number of individuals in the sample are:

The point estimate of the population proportion:

= (lower bound + upper bound) / 2

= (0.640 + 0.910) / 2

= 0. 775

The margin of error for the confidence level :

= p - hat - lower bound

= 0. 775 - 0. 640

= 0. 135

The number of individuals in the sample with the specified characteristic (x ) :

= n x p - hat

= 1, 200 x 0. 775

= 930 people

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Step-by-step explanation:

T = 5200 = .2 ( E - 10600)

       5200 / .2 = E - 10600

            E = 5200/.2   + 10 600 = 36600 pounds

Answer:3

Step-by-step explanation: 1/2 X 6 = 3

Answer:

6 x 1/2 = 3 full bottles

Step-by-step explanation:

Answer:

Answer is D.

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she needs to clean 15 uniforms to break even

The volume of the prism is B. 2.5 cubic inches.

According to the question, the prism measures 1/4 of an inch on one side. Now we will assign values to the length, width, and height of this prism as follows:

Length = 2 × 1/4

Width = 5 × 1/4

Height = 3 × 1/4

= 2/4 + 5/4 + 3/4

=  2 2/4

= 2.5 cubic inches.

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The reference angle of given angles are -6π/13 and -5π / 6

To get coterminal angles, you simply have to add or subtract 2π.

a) 32π/13 =

= -32π/13 + 2π

= -32π + 26π / 13

= -6π/13

b) -17π/6 + 2π =

= -17π + 12π / 6

= -5π / 6

Hence the reference angle of given angles are -6π/13 and -5π / 6

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Answer:

If point A (-4,-5) of the trapezoid is reflected across the y-axis, the x-coordinate will change sign while the y-coordinate remains the same. This gives us the point A' (4, -5).

Next, if we shift the point A' by -6 units in the x-direction and 7 units in the y-direction, we get the new point A":

A" = (4 - 6, -5 + 7) = (-2, 2)

Therefore, the coordinates of point A after it is reflected across the y-axis and shifted -6 units in the x direction and 7 units in the y direction are (-2, 2).

Step-by-step explanation:

Answer:

(-2, 2)

Step-by-step explanation:

I did the test

Hope this helps :)

A passenger can travel 6.875 miles for $20 using the given taxi fare function.

To determine how many miles a passenger can travel for $20 using the taxi fare function f(x) = 2.56x + 2.40, we need to set up an equation and solve for x.

The equation we need to solve is:

2.56x + 2.40 = 20

To solve for x, we can start by subtracting 2.40 from both sides of the equation:

2.56x = 17.60

Next, we can divide both sides by 2.56:

x = 6.875

This calculation assumes that the fare is based solely on distance and that there are no additional fees or charges.

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Answer:113

Step-by-step Explanation:

To create an equation to predict the number of seats in any row, we need to start by defining a few variables:

Let's call the number of seats in the first row "a".

Let's call the number of additional seats in each row after the first row "d".

Since we know that each row has 6 more seats than the previous row, we can set d equal to 6:

d = 6

We also know that the first row has 11 seats, so we can set a equal to 11:

a = 11

To find the number of seats in any row, we can use the following formula:

number of seats in a given row = a + (n - 1) * d

Where "n" is the number of the row we are interested in.

Using this formula, we can find the number of seats in row 18:

number of seats in row 18 = 11 + (18 - 1) * 6

= 11 + 102

= 113

Therefore, there are 113 seats in row 18.