Is it possible for two numbers to have a difference of 5, and a sum of 12?

Answer:

I believe b?

Step-by-step explanation:

I think i took this course

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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Answer:

21 points

Step-by-step explanation:

The difference in points between the two teams is 15-(-6) = 21 points.

Hope this helped!

The Phillips curve describes the relationship between the unemployment rate and the rate of change of wages. Option C is the correct option.

What is  Phillips curve?

The relationship between the rate of inflation and the unemployment rate is represented by the Phillips curve. The analysis of wage inflation and unemployment in the United Kingdom from 1861 to 1957 by A. W. H. Phillips, despite having forerunners, is a significant development in the field of macroeconomics. When unemployment was high, wages rose slowly; when unemployment was low, wages rose quickly, according to Phillips' research.

According to Phillips' hypothesis, as the unemployment rate declines, the labor market becomes more competitive and firms are forced to raise wages more quickly in order to recruit qualified workers. The pressure decreased as unemployment rates rose. The average relationship between wage behavior and unemployment over the course of the business cycle was represented by Phillips' "curve."

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Answer:

49

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

The dashes on the lines show they are equal in length.

Therefore, by inspection of the diagram, we can see that the measures of the sides of the smaller triangle (with base 5x) are half the measures of the sides of the larger triangle (with base 70).

Therefore, creating an equation with this information:

    5x = 1/2 x 70

⇒ 5x = 35

⇒ x = 7

Solution:

Note that:

This means that...

Simplify the equation and solve for x.

The value of x is 7.

Answer:

\(\angle ABC = 122^\circ\)

Step-by-step explanation:

Given

\(\angle ADC = 61^\circ\)

See attachment for circle

Required

Find \(\angle ABC\)

From the attachment, we can see that:

\(\angle ADC\) is at the circumference

\(\angle ABC\\\) is in at the center

From cyclic theorems,

The relationship between ABC and ADC is:

\(\angle ADC = \frac{1}{2} * \angle ABC\)

Make ABC the subject

\(\angle ABC = 2 * \angle ADC\)

Substitute: \(\angle ADC = 61^\circ\)

\(\angle ABC = 2 * 61^\circ\)

\(\angle ABC = 122^\circ\)

The solution to the initial value problem 2y'' - 5y' - 3y = 0, with initial conditions y(0) = -3 and y'(0) = 1, is given by \(y(x) = 2e^{3*x}-3e^{-x}\) The graph of the solution will exhibit exponential growth and decay.

To solve the given initial value problem, we assume the solution has the form \(y(x)=e^{rx}\) and substitute it into the differential equation. We obtain the characteristic equation:

\(2r^{2} - 5r -3 =0\)

Factoring the quadratic equation, we get:

(2r + 1)(r - 3) = 0

Solving for r, we find two distinct roots: r = \(-\frac{1}{2}\) and r = 3.

Therefore, the general solution to the differential equation is given by:

\(y(x) = c_{1} e^{1/2x} + c_{2} e^{3x}\)

To find the particular solution, we use the initial conditions. Applying y(0) = -3, we have:

c₁ + c₂ = -3          (Equation 1)

Next, we differentiate y(x) to find y'(x):

\(y'(x) = -\frac{1}{2} c_{1} e^{-\frac{1}{2x} } + 3c_{2} e^{3x }\)

Applying y'(0) = 1, we have:

\(-\frac{1}{2} c_{1} + 3c_{2} =1\)  (Equation 2)

Solving Equations 1 and 2 simultaneously, we find c₁ = -2 and c₂ = -1.

Therefore, the particular solution is:

\(y(x) = -2e^{(-1/2x)} - e^{3x}\)

Simplifying further, we get:

\(y(x)=2e^{3x}-3e^{-x}\)

The graph of the solution will exhibit exponential growth as the term \(2e^{3x}\) dominates and exponential decay as the term \(-3e^{-x}\) takes effect.

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The 4 name for a rectangle is parallelograms, quadrilaterals, rhombus and polygons.

Given that,

We have to find what are 4 names for a rectangle.

We know that,

Considering that both rhombuses and rectangles have four sides, making them both quadrilaterals.

In addition to rectangles, we also refer to them as parallelograms, quadrilaterals, rhombus and polygons. This is so that it is clear that a rectangle satisfies the definitions of all of these other shapes.

Therefore, The 4 name for a rectangle is parallelograms, quadrilaterals, rhombus and polygons because all are almost similar.

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Answer:

x = 120

Step-by-step explanation:

A regular polygon means all sides and angles are equal.  If a triangle has 180 degrees total, 180 / 3 = 60.  That means each angle is 60 (interior angle).  That is a straight line, which is 180 degrees, 180 - 60 = 120.  

Answer: x-15=0 is x-15

x-4=0 is x=4

Hope this helps :)

Step-by-step explanation:

Answer:

x = -2

Step-by-step explanation:

To solve for x always get x on one side

First add 4 on each side, 4 + 7x - 4 = -18 + 4

Next subtract 18 from 4, making it -14    7x = -14

Now divide 7 on each side, x = -2

The maximum expected increase in exam score if a student studies an extra 3 hours is 4.11 points.

Since we have a 99% confidence interval, we can assume a t-distribution with 31 degrees of freedom (n-1). Using this distribution, we can find the margin of error (E) for the mean difference in exam score (µD) between students who study for an extra 3 hours and those who do not.

E = t* (s/√n), where s is the sample standard deviation and n is the sample size.

We don't have the standard deviation, but we can estimate it using the range rule of thumb, which states that the standard deviation is approximately equal to the range of the data divided by 4.

s ≈ (6.96 - 3.59) / 4 = 0.8425

Using a t-value for a 99% confidence interval and 31 degrees of freedom, we have:

t = 2.750

E = 2.750 * (0.8425/√32) ≈ 0.929

So the 99% confidence interval for the true mean difference in exam score is (3.59 - 0.929, 6.96 + 0.929) = (2.66, 7.89).

To find the maximum expected increase in exam score if a student studies an extra 3 hours, we can subtract the mean difference in exam score from the previous 32 students from the mean difference in exam score between students who study for an extra 3 hours and those who do not.

Mean difference in exam score = (6.96 - 3.59) / 32 = 0.104

Max expected increase in exam score = 0.104 + 3 = 4.11

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Answer:

The surface area of rectangular prism is 390 in²

Step-by-step explanation:

As per given question we have provided that :

Here's the required formula to find the surface area of rectangular prism :

\(\star\boxed{\text{Area}=2(\text{lw}+\text{wh}+\text{lh})}\)

Substituting all the given values in the formula to find the surface area of rectangular prism :

\(\implies \text{Area}=2(\text{lw}+\text{wh}+\text{lh})\)

\(\implies \text{Area}=2[(9\times3)+(3\times14)+(14\times9)]\)

\(\implies \text{Area}=2[(27)+(42)+(126)]\)

\(\implies \text{Area}=2[27+42+126]\)

\(\implies \text{Area}=2[69+126]\)

\(\implies \text{Area}=2[195]\)

\(\implies \text{Area}=2\times195\)

\(\implies \text{Area}=390\)

\(\star\boxed{\text{Area}=390 \ \text{in}^2}\)

Hence, the surface area of rectangular prism is 390 in².

\(\rule{300}{1.5}\)

The expression that is used to describe the given information is 6^(-6).

To discover the equal expression, we are able to simplify the fraction through the usage of the guideline of thumb for exponents that announces that once we divide  powers with the equal base, we are able to subtract the exponents.

An exponent refers back to the wide variety of instances various is elevated through itself.

Using this rule, we get:

(6^(-10)) / (6^4 * 6^0)

= 6^(-10) / 6^4 *1

= 6^(-10+4)

= 6^(-6)

So the equivalent expression is: 1/6^6 = 6^(-6)

The expression that is used to describe the given information is 6^(-6).

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Answer:

Step-by-step explanation:

// Solve equation [2] for the variable  x

 [2]    x = y + 1

// Plug this in for variable  x  in equation [1]

  [1]    (y +1) - 2y = 9

  [1]     - y = 8

// Solve equation [1] for the variable  y

  [1]    y = - 8

// By now we know this much :

   x = y+1

   y = -8

// Use the  y  value to solve for  x

   x = (-8)+1 = -7

Solution :

{x,y} = {-7,-8}

Answer:

interest earned: $105

balance of the account: $455

Step-by-step explanation:

Interest earned and The balance of the account are $105 and $455.

Given:

Amount invested = $350

Interest rate = 3% = 0.03

Number of year = 10 years

Find:

Computation:

simple interest earned = PRT

Interest earned = (350)(0.03)(10)

Interest earned = $105

The balance of the account = 105 + 350

The balance of the account = $455

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Answer:

2x^2 - 4

Step-by-step explanation:

- A "constant" in an equation is a number that stands alone, with no attached variable or exponents.

- A "coefficient" is a number placed before a variable that is multiplying with the variable. For example, 2 would be the coefficient of 2xy, because it is the number you are multiplying "xy" by.

One example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.

Therefore, one example of a parameter is the typical number of hours each night that the entire group of college-enrolled students sleeps.

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The correct question is given below:
A researcher is interested in the sleeping habits of students at the local state college. The average number of hours spent sleeping each night for the entire set of students enrolled at the college is an example of a ____.

Answer:

f(-3)=-1

f(4)=7

f(-1)=-3

f(12) = -24

Step-by-step explanation:

Piecewise Functions

The piecewise functions define different pieces or subfunctions where the domain is divided into parts according to some conditions on the independent variable.

The pieces of the function are defined as shown below:

\(f(x)=\left\{\begin{matrix}-1 &x\le -2\\ 2x-1 &-2<x\le 4 \\ -3x+8 &x>4 \end{matrix}\right.\)

Let's find the values of:

f(-3). Here the variable x is -3. We have to find the interval where x=-3 belongs. Since -3 ≤ -2:

f(-3)=-1

f(4). The variable x is 4 and it belongs to the second interval, thus

f(4)=2*4-1=7

f(4)=7

f(-1). x = -1. It belongs to the second interval, thus:

f(-1)=2*(-1)-1=-3

f(-1)=-3

f(12). x=12 belongs to the last interval since 12 > 4, thus:

f(12)= -3*12+8 = -36 + 8 = -24

f(12) = -24

The system of inequalities that math the graph is; y ≤ 3x and y > –2x – 1

Looking at the attached image, we can see that;

Solid blue line

The solution of the inequality is the shaded area below the solid blue line

The slope of the solid line is positive

The line passes through the origin

The equation of the inequality A is y ≤ 3x

Dashed red line

The solution of the inequality is the shaded area above the dashed red line

The slope of the dashed line is negative

The y-intercept of the dashed line is -1

The equation of the inequality B is; y > –2x – 1

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Answer:

the answer is A

Step-by-step explanation:

Answer:

it's 10

Step-by-step explanation:

2 1/4 = 9/4

22 1/2 = 45/2 × 2 = 90/4 and 90/4 ÷9/4 = 10

Answer: 10 servings.

Step-by-step explanation:Divide 22 1/2 by 2 1/4and it woulwould be 10. Of

Answer:

5000 square ft

Step-by-step explanation:

True , Network analysts should be concerned with these specific properties and patterns that arise in real-world networks since they have important implications for the network's behavior and performance.

Random graphs are mathematical structures that do not have any inherent structure or patterns. They are created by connecting nodes randomly without any specific rules or constraints. Real-world networks, on the other hand, have a certain structure and properties that arise from the way nodes are connected based on specific rules and constraints.

Network analysts use various mathematical models and algorithms to analyze and understand real-world networks. These networks can range from social networks, transportation networks, communication networks, and many others. The goal of network analysis is to uncover the underlying structure and properties of these networks, which can then be used to make predictions, identify vulnerabilities, and optimize their design. Random graphs are often used as a baseline or reference point for network analysis since they represent the simplest form of a network. However, they are not an accurate representation of real-world networks, which are often characterized by specific patterns and properties. For example, many real-world networks exhibit a small-world property, meaning that most nodes are not directly connected to each other but can be reached through a small number of intermediate nodes. This property is not present in random graphs.

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The total number of students that are in the seventh grade are 378 students.

32 student bought ticket at the door.

The number of students that had already bought tickets will be:

= 158 - 32 = 126 students.

Let the number of students present in seventh grade be x

Therefore, based on the information given, the equation to calculate the total students will be:

One-third of the seventh garde class bought ticket for the eventh grade dance.

= (1/3 × x) = 126

x = 3 × 126

x = 378

Therefore, there are 378 students in seventh grade.

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The average charge on arginine at pH 9.20 is +1.

Arginine is an amino acid that contains multiple ionizable groups, including the amino group (-NH2), the carboxyl group (-COOH), and the guanidino group (-NH-C(NH2)2). The average charge on arginine depends on the pKa values of these groups and the pH of the solution.

At pH 9.20, which is alkaline or basic, the carboxyl group (-COOH) and the guanidino group (-NH-C(NH2)2) will be deprotonated and carry a negative charge, while the amino group (-NH2) will be protonated and carry a positive charge.

The pKa values of the ionizable groups in arginine are approximately as follows:

Carboxyl group: pKa ~ 2.17

Amino group: pKa ~ 9.00

Guanidino group: pKa ~ 12.48

To determine the average charge on arginine at pH 9.20, we need to consider the ionization states of these groups. Since the pH is greater than the pKa of the carboxyl group and the guanidino group, these groups will be deprotonated and carry a negative charge. The amino group will be protonated and carry a positive charge.

Therefore, at pH 9.20, the average charge on arginine is +1. This means that, on average, arginine will have a net positive charge of +1 under these conditions.

At pH 9.20, the average charge on arginine is +1. This indicates that, on average, arginine will carry a net positive charge of +1 in a solution with this pH.

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a. The value corresponding to surviving the year is $0, and the value corresponding to not surviving the year is -$90,000.

b. The expected value for the 33-year-old male purchasing the policy is -$579.06.

c. Yes, the insurance company can expect to make a profit from many such policies because the expected profit per 33-year-old male insured for 1 year is $408.06.

a. The monetary value corresponding to surviving the year is $0 because the individual would not receive any payout from the insurance policy if he survives. The monetary value corresponding to not surviving the year is -$90,000 because in the event of the individual's death, the policy pays out a death benefit of $90,000.

b. To calculate the expected value for the 33-year-old male purchasing the policy, we need to multiply the probability of each event by its corresponding monetary value and sum them up. The probability of surviving the year is 0.9988, and the value corresponding to surviving is $0. The probability of not surviving the year is (1 - 0.9988) = 0.0012, and the value corresponding to not surviving is -$90,000.

Expected value = (Probability of surviving * Value of surviving) + (Probability of not surviving * Value of not surviving)

Expected value = (0.9988 * $0) + (0.0012 * -$90,000)

Expected value = -$108 + -$471.06

Expected value = -$579.06 (rounded to the nearest cent)

c. The insurance company can expect to make a profit from many such policies because the expected value for the 33-year-old male purchasing the policy is negative (-$579.06). This means, on average, the insurance company would pay out $579.06 more in claims than it collects in premiums for each 33-year-old male insured for 1 year. Therefore, the insurance company expects to make an average profit of $579.06 on every 33-year-old male it insures for 1 year.

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A number that goes into a greater number with no remainders is called a factor.

A factor is an integer that divides into a greater number without any remainders.

For example, the number 6 is a factor of 18 because when 18 is divided by 6, the answer is 3 with no remainders. Similarly, the number 3 is a factor of 12 because when 12 is divided by 3, the answer is 4 with no remainders.

Factors are important in mathematics because they can be used to solve equations and determine the greatest common divisor (GCD) of two or more numbers. Factors can also be used to determine prime numbers and their multiples.

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The inductive hypothesis of the inductive step of an inductive proof for k≥4, if 2k≥3k, then 2^k+1≥3(k+1) is used in Step 4 of the proof.

The following is the solution to the problem.2^k+1≥2⋅2^k (Step 1)≥2⋅3k (Step 2)≥3k+3k (Step 3)≥3k+3 (Step 4)≥3(k+1) (Step 5)Therefore, the inductive hypothesis is used in step 4 of the proof. Step 4 demonstrates that the statement is correct for k+1.

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