The mean score on a physics test was 75 points. Amy’s score was 67 points, which was 2 standard deviations below the mean. What is the variance of the data set? 2 4 8 16.

The maximum value of the objective function from the given vertex points is 60.

The given system of inequalities are {2x + y ≤ 20, 3x + 2y ≤ 30, x , y ≥ 0}.Graph of the given inequalities: The region of feasible solutions is the shaded region below. The vertex points of this system are:(0,0), (0,10), (15,0).Explanation:For the first equation, 2x + y ≤ 20, assume x = 0, then we have y ≤ 20, therefore the line y = 20 is the horizontal boundary for the region of feasible solutions.For the second equation, 3x + 2y ≤ 30, assume x = 0, then we have 2y ≤ 30, which gives us y ≤ 15, therefore the line y = 15 is the horizontal boundary for the region of feasible solutions.For the third equation, x ≥ 0, this implies that the region of feasible solutions is on the right side of the vertical boundary x = 0.For the fourth equation, y ≥ 0, this implies that the region of feasible solutions is above the horizontal boundary y = 0.In part A, we obtained the vertex points of the given system.The vertex points of the given system are (0,0), (0,10), and (15,0). The given objective function is f(z) = 4x + 6y. We need to find the maximum value of the objective function from the given vertex points.Testing vertex points:(0,0): f(0,0) = 4(0) + 6(0) = 0(0,10): f(0,10) = 4(0) + 6(10) = 60(15,0): f(15,0) = 4(15) + 6(0) = 60Therefore, the maximum value of the objective function from the given vertex points is 60.

More about objective function

https://brainly.com/question/33272856

#SPJ11

The simplified expression is -2w/(w+4).

To simplify the expression -2w^2/w^2+4w, we first factor out -2w from the numerator, which gives:

-2w(w+2)/w(w+4)

We can simplify this expression by canceling out the common factor of w+2 in both the numerator and denominator:

-2w/(w+4)

Therefore, the simplified expression is -2w/(w+4).

The excluded value in this expression is w = -4, as this value would make the denominator of the expression equal to zero. Division by zero is undefined, and therefore, w = -4 is not a valid input for this expression.

It is important to always check for excluded values when simplifying rational expressions, as division by zero is not a defined operation. In this case, we found that w = -4 is excluded from the domain of the expression, and all other values of w are valid.

To learn more about Expression :

https://brainly.com/question/1859113

#SPJ11

Answer:

  (1/2, -8 1/2)

Step-by-step explanation:

The enlargement transformation maps point A to one that is 3 times as far from the center of enlargement. If the center is C, then we have the relation ...

  (A' -C) = 3(A -C)

__

Solving for C gives ...

  A' -C = 3A -3C

  2C = 3A -A' . . . . . . . add 3C-A'

  C = (3A -A')/2

Filling in the given coordinates for A and A', we find the center of enlargement to be ...

  C = (3(1, -4) -(2, 5))/2 = (3 -2, -12 -5)/2 = (1, -17)/2

  C = (1/2, -8 1/2)

The center of enlargement is (1/2, -8 1/2).

Answer:

Infinite amount of solutions.

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define equation

6y + 4 - 3y - 7 = 3(y - 1)

Step 2: Solve for y

Here we see that there will be infinite amount of solutions. We can plug in any number y and it will render the equation true.

No solutions.

General Formulas and Concepts:

Order of Operations: BPEMDAS

Regular + Equality Properties

Step-by-step explanation:

Step 1: Define equation

6y + 4 - 3y - 7 = 3(y - 1)

Step 2: Solve for y

Combine like terms:                         3y - 3 = 3(y - 1)

Distribute 3:                                       3y - 3 = 3y - 1

Subtract 3y on both sides:               -3 ≠ -1

Here we see that there will be no solutions of y.

Answer:

B. 60

Step-by-step explanation:

Use cross multiplication to answer this question:

So, multiply 11 by 66 and 12.1 by x. Like this:

12.1 * x = 66 * 11

Simplify now

12.1x = 726                       Multiply both sides

x = 60

With this, x would be equal to 60. B would be the correct answer.

Hope this helps!! If you have questions about my work please ask!

Answer:

It looks like 45 degree for the one on the left and maybe 180 degrees on the right (i'm not sure tbh) but those are my guesses

a.  The probability that this runner will complete this road race: In less than 160 minutes is 0.0764. The correct answer is C.

b.  The probability that this runner will complete this road race: In 215 to 245 minutes is 0.1125 The correct answer is C.

a. To find the probability for each scenario, we'll use the given normal distribution parameters:

Mean (μ) = 190 minutes

Standard Deviation (σ) = 21 minutes

Probability of completing the road race in less than 160 minutes:

To calculate this probability, we need to find the area under the normal distribution curve to the left of 160 minutes.

Using the z-score formula: z = (x - μ) / σ

z = (160 - 190) / 21

z ≈ -1.4286

We can then use a standard normal distribution table or statistical software to find the corresponding cumulative probability.

From the standard normal distribution table, the cumulative probability for z ≈ -1.4286 is approximately 0.0764.

Therefore, the probability of completing the road race in less than 160 minutes is approximately 0.0764. The correct answer is C.

b. Probability of completing the road race in 215 to 245 minutes:

To calculate this probability, we need to find the area under the normal distribution curve between 215 and 245 minutes.

First, we calculate the z-scores for each endpoint:

For 215 minutes:

z1 = (215 - 190) / 21

z1 ≈ 1.1905

For 245 minutes:

z2 = (245 - 190) / 21

z2 ≈ 2.6190

Next, we find the cumulative probabilities for each z-score.

From the standard normal distribution table:

The cumulative probability for z ≈ 1.1905 is approximately 0.8820.

The cumulative probability for z ≈ 2.6190 is approximately 0.9955.

To find the probability between these two z-scores, we subtract the cumulative probability at the lower z-score from the cumulative probability at the higher z-score:

Probability = 0.9955 - 0.8820

Probability ≈ 0.1125

Therefore, the probability of completing the road race in 215 to 245 minutes is approximately 0.1125. The correct answer is C.

Learn more about probability at https://brainly.com/question/32274851

#SPJ11

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

Read more about Equivalent fractions at: https://brainly.com/question/17220365

#SPJ1

There is significant evidence to suggest that parents experience a difference in salary depending on whether or not they have the primary child-rearing responsibilities.

1. Hypotheses:

  - Null hypothesis (H0): There is no significant difference in income between parents with primary child-rearing responsibilities and other parents.

  - Alternative hypothesis (Ha): There is a significant difference in income between parents with primary child-rearing responsibilities and other parents.

2. Calculate the mean difference in income between the primary parent and the other parent:

  Mean difference = Primary parent mean income - Other parent mean income

  Mean difference = $37,122 - $54,219 = -$17,097

3. Calculate the standard error of the difference:

  Standard deviation of the difference = Standard deviation of the difference in income / Square root of the sample size

  Standard deviation of the difference = \($4,311 / \sqrt{74} \approx \$500.97$\)

4. Calculate the t-value:

  t-value = (Mean difference - Expected difference) / Standard error of the difference

  The expected difference is 0 since the null hypothesis assumes no difference.

  t-value = (-$17,097 - 0) / $500.97 ≈ -34.07

5. Determine the degrees of freedom (df):

  df = sample size - 1 = 74 - 1 = 73

6. Find the p-value using the t-distribution:

  By looking up the t-value (-34.07) with df = 73, the p-value is extremely small, close to 0.

7. Interpretation:

  The obtained p-value is highly significant, indicating strong evidence to reject the null hypothesis. Thus, there is significant evidence to suggest that parents experience a difference in salary depending on whether or not they have the primary child-rearing responsibilities. This suggests that the primary parent, on average, has a lower income compared to the other parent in two-parent households with young children.

The complete question must be:

4. (15 points) For a study on the relationship between family responsibility and income, a social science firm recruited 74 households, each of which were two-parent households with at least one young child living in the home. The parents were asked to identify which of them took the primary role in raising the children, and each also reported their salary. The results of this work are collected in the table below.

|   n   | Primary Parent Mean Income | Other Parent Mean Income | Standard Deviation of the Difference |

|:-----:|:-------------------------:|:-----------------------:|:-----------------------------------:|

|   74  |          $37,122          |         $54,219         |               $4,311                |

Use a paired-means hypothesis test to determine whether there is significant evidence that parents experience a difference in salary depending on whether or not they have the primary child-rearing responsibilities. When completing your test, be sure to define your hypotheses, determine the standard error, use the correct t-distribution to find a range for the p-value, and interpret this result in the context of the data.

Learn more about Hypotheses:

https://brainly.com/question/28331914

#SPJ11

Fingerprinting is a technique used by forensic experts and crime scene investigators to identify individuals based on their unique fingerprints. Fingerprints are unique to each individual and have distinct ridge patterns that are used to identify individuals.

It is an effective way of identifying people because fingerprints remain the same throughout a person's life, unlike other physical characteristics.

When fingerprinting a person who is missing fingers, two notations that should be used on the fingerprint card are "amputation" and "absent." The notations on the fingerprint card should indicate that the fingers are missing due to amputation or absence.

Know more about Fingerprinting here:

https://brainly.com/question/3321996

#SPJ11

When fingerprinting a person missing fingers, the two notations that should be used on the fingerprint card are tented arch for a missing middle finger and amputation notation for a completely missing finger.

When fingerprinting a person who is missing fingers, two notations should be used on the fingerprint card:

https://brainly.com/question/34652657

#SPJ12

The counterexample for the conjecture If the perimeter of a rectangle is 40 units, the area must be at least 1 square unit is: A rectangle with length 19.99 units and width 0.01 unit has a perimeter of 40 units and an area of 0.1999 square unit.

What is counterexample?

The term counterexample refers to an instance or example that makes the statement false. This is used in logic to check if a statement is true or not. Counter example tend to counter the statement being discussed with valid points.

The question wants to show the relationship that may exist between perimeter and area of a rectangle.

The counterexample provided the dimensions that gave the perimeter which is 40 but failed to give area of 1 square unit

Learn more about  counterexample at:

brainly.com/question/24881803

#SPJ4

Answer:

216\(\pi\)

Step-by-step explanation:

Given the figure.

And the perimeter in the ratio 4: 2: 1.

Perimeter of smallest circle = \(8\pi\)

To find:

Area of shaded region.

Solution:

To find the area, we need to have radius first.

And radius can be calculated by the given perimeter.

Formula for Perimeter is given as:

Perimeter = \(2\pi r\)

\(8\pi = 2\pi r\\\Rightarrow r = 4\ cm\)

Radius of smallest circle = 4 cm

Ratio of perimeter is equal to the ratio of the radii.

Radius of 2nd smallest circle by the given ratio = 8 cm

Radius of largest circle = 16 cm

Area of a circle is given the formula:

\(A = \pi r^2\)

Area of the smallest circle = \(\pi 4^2 = 16\pi\ cm^2\)

Area of the 2nd smallest circle = \(\pi 8^2 = 64\pi\ cm^2\)

Area of the largest circle = \(\pi 16^2 = 256\pi\ cm^2\)

Area of the shaded region = Area of largest circle + 2 \(\times\) Area of 2nd smallest circle + 3 \(\times\) Area of smallest circle - 2 \(\times\) Area of smallest circle - 3 \(\times\) Area of 2nd smallest circle

Area of the shaded region = Area of largest circle - Area of 2nd smallest circle + Area of smallest circle = \(256\pi - 64\pi +16\pi = 216\pi\)

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Learn more about Laplace Transform

brainly.com/question/30759963

#SPJ11

To find the vector x such that T(x) = (3, 8), we need to solve the system of equations:

x₁ + x₂ = 3

4x₁ + 5x₂ = 8

We can rewrite this system in matrix form as Ax = b, where A is the coefficient matrix, x is the vector of variables, and b is the vector on the right-hand side:

[1 1] [x₁] [3]

[4 5] [x₂] = [8]

To solve this system, we can invert the coefficient matrix A and multiply it by the vector b:

x = A⁻¹ * b

To find A⁻¹, we calculate the inverse of the coefficient matrix A:

A⁻¹ = 1 / (1 * 5 - 4 * 1) * [5 -1]

[-4 1]

Multiplying A⁻¹ by b gives us the solution vector x:

x = [5 -1] * [3]

[8]

= [5 * 3 + (-1) * 8]

[-4 * 3 + 1 * 8]

= [7]

[20]

Therefore, the vector x that satisfies T(x) = (3, 8) is x = (7, 20).

To learn more about vector click here:

brainly.com/question/24256726

#SPJ11

The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

Learn more about expressions on

https://brainly.com/question/1859113

#SPJ4

Part A: greatest common factor: 4.

Part B: Factor of the expression are: x = 4, 1/2.

Part c: Check for the factors are found correct.

The given expression is-

8x² + 28x - 16 = 0

Part A: The highest number that can be taken common is 4.

4(2x² + 7x - 4) = 0

Thus, greatest common factor: 4.

Part B: Factor of the expression.

4(2x² + 7x - 4) = 0

2x² + 7x - 4 = 0

2x² + 8x - x - 4 = 0

2x(x + 4) - (x + 4) = 0

(x + 4)(2x - 1) = 0

x = 4, 1/2

Thus, the Factor of the expression are: x = 4, 1/2.

Part C: Check:

x = 4, 1/2

8x² + 28x - 16

Put x = 4

= 8(4)² + 28(4) - 16

= 0 (satisfies)

Put x = 1/2

= 8(1/2)² + 28(1/2) - 16

= 0 (satisfies)

Thus, the check for the factors are found correct.

To know more about the greatest common factor, here

https://brainly.com/question/219464

#SPJ1

Answer:

6i√6

Step-by-step explanation:

216 is 36 times 6

√36*√6=6√6

But it was negative so keep the i with 6

A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

To learn more about  database click here:

brainly.com/question/31664263

#SPJ11

here this probally will help

Answer:

5, 3

Step-by-step explanation:

Answer:

B = -7

Step-by-step explanation:

P = A + B

- Plug in the values of the values.

36 = 43 + B

- Subtract 43 from both sides.

-7 = B

The Solution:

Given:

We are required to find the probability that the adult selected has IQ greater than 120.

By the Z-statistic formula, we have:

From the Z score tables, we have:

Therefore, the correct answer is 0.091

Answer:

A is the answer half Irish die f Russian stuff right stuff he taught

Step-by-step explanation:

10/94+641=68000

Answer: disagree its backwards

Step-by-step explanation: the x intercept always comes first so its actually (-4,2)

Answer:

Step-by-step explanation:

Now if you look at this wrong, the student would be correct. The student made a common mistake that many make. The mistake they made was they put the X and Y backwards when making the point. All they have to do is make sure they put the X first then the Y. What they should have put is (-4,2). For any other point, you would replace X and Y in the points. (X,Y)

As a result of answering the given question, we may state that When we expressions compare the finished square form\(2(x - 1/4)^2 + 143/8\) to the answer alternatives, we see that option \(D: 2(x - 1/16)`^2.\)

In mathematics, an expression is a set of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that expresses a quantity or value. Expressions might be simple, like "3 + 4", or complex, like "(\(3x^2\) - 2) / (x + 1)". They may also include functions such as "sin(x)" or "log(y)". Expressions can be evaluated by substituting values for the variables and carrying out the mathematical operations in the given order. For instance, if x = 2, the formula "3x + 5" is 3(2) + 5 = 11. In mathematics, expressions are widely used to explain real-world situations, build equations, and simplify complex mathematical issues.

expression is equivalent -

\(2(x^2 - 1/2x) + 18\\2(x^2 - 1/2x + 1/16 - 1/16) + 18\\2((x - 1/4)^2 - 1/16) + 18\\2(x - 1/4)^2 - 1/8 + 18\\2(x - 1/4)^2 + 143/8\\\)

When we compare the finished square form\(2(x - 1/4)^2 + 143/8\) to the answer alternatives, we see that option \(D: 2(x - 1/16)`^2.\)

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

Area = 72 square feet

Step-by-step explanation:

\(4(3x+3y)\)

Multiply the four to the values inside the parentheses to find the "equivalent expression"

\(12x +12y\)

Using the "equivalent expression" we found above, we now want to find the area of Ray's living room, in square feet if \(x=2\) and \(y = 4\)

\(12(2) + 12(4)\)

\(= 24 +48\)

\(= 72\)

Answer:

The answer is  43.9822972 rad but you could just round and put 43.98

Step-by-step explanation:

1. AUB = {a, b, d, e}

2. AUC = {a, b, d, e}

3. BUC = {a, b, d, e}

In each case, the union includes the elements shared between the sets and the unique elements from each set, without repetitions.

To determine the union of the given subsets, we need to combine all the elements without repetition. Let's analyze each case:

1. AUB:

The set A contains the elements {a, b, d}, and the set B contains the elements {b, d, e}. By combining both sets, we obtain the union AUB = {a, b, d, e}. This is the collection of all the elements that appear in either A or B, without duplicates.

2. AUC:

The set A contains the elements {a, b, d}, and the set C contains the elements {a, b, e}. By combining both sets, we obtain the union AUC = {a, b, d, e}. Once again, this set includes all the elements that appear in either A or C, without repetition.

3. BUC:

The set B contains the elements {b, d, e}, and the set C contains the elements {a, b, e}. By combining both sets, we obtain the union BUC = {a, b, d, e}. Similarly, this set represents all the elements that appear in either B or C, without duplicates.

For more such question on  unique elements visit:

https://brainly.com/question/25916838

#SPJ8

Answer:

x>-42

Step-by-step explanation:

I dont have time to explain de but thats the answer