Joey and Nolan are each solving the equation 13x - 42 = 18 - 7x.
Joey's first step was to rewrite the equation as 20x - 42 = 18 while Nolan's first step was to rewrite the
equation as 13x = 60 - 7x.
Who is correctly applying the addition property of equality in the first step of his work?
A. Only Joey
B. Only Nolan
C. Both Joey and Nolan
D. Neither Joey nor Nolan​

Where the above conditions are given,  the correct option is: Plan 1 is a better deal for more than 5 cards purchased.

To determine   which pricing plan is a better deal,we need to compare the total cost for a certain number of game cards purchased.

Let's calculate the   total cost for different numbers  of game cards.

For Plan 1  -

- Admission fee  - $5 (fixed)

- Cost per game card  - $1

For Plan 2  -

- Admission fee  - $2.50 (fixed)

- Cost per game card  - $1.50

Now, let's compare the total cost for different numbers of game cards  -

1. If you purchase 1 game card  -

  - Plan 1  - $5 (admission fee) + $1 (cost per game card) = $6

  - Plan 2  - $2.50 (admission fee) + $1.50 (cost per game card) = $4

2. If you purchase 5 game cards  -

  - Plan 1  - $5 (admission fee) + $5 (cost for 5 game cards) = $10

  - Plan 2  - $2.50 (admission fee) + $7.50 (cost for 5 game cards) = $10

3. If you purchase 8 game cards  -

  - Plan 1  - $5 (admission fee) + $8 (cost for 8 game cards) = $13

  - Plan 2  - $2.50 (admission fee) + $12 (cost for 8 game cards) = $14.50

Based on these calculations, we can conclude that  -

- Plan 1 is a better deal for more than 5 cards purchased.

- Plan 2 is a better deal for more than 8 cards purchased.

Therefore, the correct option is  - Plan 1 is a better deal for more than 5 cards purchased.

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To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then \($g(x) =x^2-10\) exists g(10) = 90.

The value of g(10), we have to substitute in every x of f(x), the

\(f(x) = 2x + 1\) exists f(90) = 181

Therefore, the value of f[g(10)] exists 181.

To estimate the value for g(10), that means that you have to substitute 10 in every x of g(x), then

\($g(x) =x^2-10\)

substitute the value of x = 10

\($g(10) = (10)^2-10\)

simplifying the equation, we get

g(10) = 100 - 10

g(10) = 90

We have the value of g(10), we have to substitute in every x of f(x), then

f(x) = 2x + 1

substitute the value of x = 90

f(90) = 2(90) + 1

simplifying the equation, we get

f(90) = 180 + 1

f(90) = 181

The value of f[g(10)] exists 181.

Therefore, the correct answer is option b) 181.

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Answer:

the answer is 9.6 cm

Step-by-step explanation:

.........................

The measure of arc FD = 236 degree.

In the given figure

The measure of arc FE = 146

And Measure of arc ED is right angle.

We know that right angle = 90 degree

Then,

And Measure of arc ED is right angle.

Since we know,

An "arc" is a smooth curve that connects two locations.

In general, an arc is a section of a circle.  

It is essentially a portion of a circle's circumference.

An arc is a kind of curve. An arc can be a section of another curved form, such as an ellipse, although it most commonly refers to a circle.

From figure,

The arc FD consist of FE and ED

Therefore,

To find the measure of arc FD add the measure of arc FE and ED

So,

mFD = 146 + 90

        = 136

Hence,

⇒ mFD  = 236 degree.

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Answer:

option 1

Step-by-step explanation:

if it goes up 6 then it means plus 6

The angles that are supplementary angles are: ∠SRT and ∠SRO

Angles that are supplementary will give us a sum of 180 degrees when we add the two angles together. One is the supplement of the other.

Some examples of angles that are supplementary angles that are formed when two parallel lines are intersected by a transversal include:

Angle SRT and angle SRO are angles that are adjacent to each other because they share a common side SR and a common vertex R. They line on the straight line OT.

Therefore, angle SRT and angle SRO are two angles that are supplementary angles as shown in the diagram attached below where lines NP and QS are parallel lines. The supplementary angles are therefore angle SRT and angle SRO.

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The appropriate p-value for a t-value of 2.73 with 5 degrees of freedom is approximately 0.05. This indicates that there is a 5% chance of observing a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true.

In statistics, the p-value measures the strength of evidence against the null hypothesis. The null hypothesis states that there is no significant difference or effect in the population being studied. The p-value is calculated by determining the probability of obtaining a test statistic (in this case, the t-value) as extreme as or more extreme than the observed value, assuming the null hypothesis is true.

To determine the appropriate p-value for a t-value, we typically consult a t-distribution table or use statistical software. In this case, with 5 degrees of freedom and a t-value of 2.73, we look up the critical value or use software to find the corresponding p-value. The p-value associated with a t-value of 2.73 and 5 degrees of freedom is approximately 0.05.

The p-value of 0.05 indicates that there is a 5% chance of obtaining a t-value as extreme as 2.73 or more extreme, assuming the null hypothesis is true. Generally, a p-value of 0.05 or lower is considered statistically significant, implying that the observed result is unlikely to have occurred by chance alone. If the p-value is below a predetermined significance level (often denoted as α, commonly set at 0.05), we reject the null hypothesis in favor of an alternative hypothesis. If the p-value is above the significance level, we fail to reject the null hypothesis.

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Answer:

24 miles

Step-by-step explanation:

3x is the miles from downstream

4 (x - 1) is the return trip

Solution:

3x = 4 (x - 1)

3x =4x - 4

-x = -4

x = 4

The outward journey 3x = 12 miles

Return journey is same length

Therefore the distance travel is 24 miles

Answer:

(Choice C)

Slope and a point that is not an intercept

Answer: Decimal form: 19.25

Exact form: 77/4

Mixed number form : 19 1/4

Step-by-step explanation:

Answer:

\(x=10\)

Step-by-step explanation:

Add the numbers.

\(76=4x-1+2x+17\)

\(76=4x+16+2x\)

Combine like terms.

\(76=4x-1+2x=17\)

\(76=6x+16\)

\(76-16=6x + 16 - 16\)

\(60=6x\)

\(\frac{60}{6} = \frac{6x}{6}\)

\(60\) ÷ \(6 = 10\)

\(10 = x\)

Hence, \(x\) equals \(10\).

Hope it helped!

Answer:

7/5

Hope this helps...

Please mark me brainliest

7/5

multiplicative inverse means the number which when multiplied to the given number the product is one.

Answer:

-150.5

Step-by-step explanation:

That's what i got

Answer:

John is 3 and Annie is 5 because to be half of someone's age while being to years younger it would have to be 2 and 4 - but then a year passed and so the are now 3 and 5.

Step-by-step explanation:

The present  age of John is  3 years

The present age of Annie is 5 years  

Given that John is 2 years younger than Annie's age

Let the present age of John be "J"

Let the present age of Annie be "A"

According to the given situation

\(\rm J = A -2........(1)\\\)

One year ago the age of John = \(\rm J-1\)

One year ago the age of Annie = \(\rm A -1\)

According to the given situation

\(\rm\dfrac{A-1}{2}= J-1.........(2)\)

On solving for equations (1) and (2) we get

A = 5 and J = 3

So the present  age of Annie is  5 years

The present age of John is 3 Years  

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If you are 15 years old and Jones is 6 years old, then you are 9 years older than Jones. Therefore, you are 15 + 9 = 24 years old.

To determine your age, we start with the information given: you are currently 15 years old. Since Jones is 6 years old, we can calculate the age difference between you and Jones by subtracting Jones' age from your age: 15 - 6 = 9. This means that you are 9 years older than Jones.

To find your age, we add the age difference to Jones' age. Jones is 6 years old and you are 9 years older, so the calculation is 6 + 9 = 15. Therefore, your age is 15 years old.

Based on the given information that you are currently 15 years old, we can conclude that you are 9 years older than Jones, who is 6 years old. Therefore, your age is 15 + 9 = 24 years old.

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Answer:

It is 2 which represents 20,000

Answer:

31.6in

Step-by-step explanation:

A department store stocks gift boxes for the holiday season. The box has a volume of 500 cubic inches. You also know that the length of the box is 9 inches longer than the width and the height 1/2 as long as the width

Volume of the box = Length * Width * Height

Given

Volume = 500in³

If the length of the box is 9 inches longer than the width, then;

L = W+9

Also if the height is 1/2 as long as the width, then;

H = 1/2 W

Substtute into the volume formula;

V = LWH

500 = (W+9)W(1/2W)

500 = W+9(W²/2)

1000 = W²(W+9)

1000 =W³+9W²

W³+9W² - 1000 = 0

Factorize AND GET w

W³+9W² = 1000

w²(W+9) = 1000

W² = 1000

w = √1000

w = 31.6in

Hence the width of the store is 31.6in

Note that we only looked for the width since are not told what to find

Answer:

Yes it is

Step-by-step explanation:

In order to find it, you just need to find the slope which the equation is y2-y1/x2-x1

Giving you the slope to be -5/3

and the b value is 16 bc it is 16 at 0

slope equation is y= mx + b

plug -5/3X+16 into your graphing calculator and see that it is a straight line and boom.

Answer:

Number 1 4,100$

Number 2 D. The market value of new factories built this year.

Step-by-step explanation:

Answer:

\(5(x - 2) = x + 1 \\ 5x - 10 = x + 1 \\ 5x - x = 1 0+ 1 \\ 4x = 11 \\ x = \frac{11}{4} \)

A. Watchover's expected net interest income at year-end is $7.16 million.

B. The net interest income at year-end, if interest rates rise by 4 percent, is $15.84 million.

C. The change in expected net interest income for a 4 percent increase in interest rates is $1.6 million (positive value indicates an increase).

To calculate Watchover's expected net interest income at year-end, determine the interest income and interest expense for each category of assets and liabilities.

a. Expected Net Interest Income at Year-End:

To calculate the interest income, we multiply the outstanding amount by the corresponding interest rate. For the interest expense, we perform the same calculation for the liabilities.

Interest income:

Floating-rate mortgages: $88 million × 13% = $11.44 million

30-year fixed-rate loans: $104 million × 10% = $10.4 million

Interest expense:

Now deposits: $119 million × 9% = $10.71 million

5-year time deposits: $33 million × 9% = $2.97 million

Net Interest Income at Year-End:

Net Interest Income = Interest income - Interest expense

Net Interest Income = ($11.44 million + $10.4 million) - ($10.71 million + $2.97 million)

Net Interest Income = $20.84 million - $13.68 million

Net Interest Income = $7.16 million

Therefore, Watchover's expected net interest income at year-end is $7.16 million.

b. Net Interest Income at Year-End with 4% Interest Rate Increase:

To calculate the net interest income when interest rates rise by 4 percent, we need to adjust the interest rates and recalculate the interest income and interest expense.

Adjusted interest income:

Floating-rate mortgages: $88 million × (13% + 4%) = $88 million × 17% = $14.96 million

30-year fixed-rate loans: $104 million × (10% + 4%) = $104 million × 14% = $14.56 million

Adjusted interest expense remains the same as in part a.

Net Interest Income at Year-End:

Net Interest Income = Adjusted interest income - Interest expense

Net Interest Income = ($14.96 million + $14.56 million) - ($10.71 million + $2.97 million)

Net Interest Income = $29.52 million - $13.68 million

Net Interest Income = $15.84 million

Therefore, the net interest income at year-end, if interest rates rise by 4 percent, is $15.84 million.

c. Change in Expected Net Interest Income for a 4% Interest Rate Increase using the One-Year Cumulative Repricing Gap Model:

To calculate the change in expected net interest income, we need to use the one-year cumulative repricing gap model. The formula to calculate the change in net interest income is as follows:

Change in Net Interest Income = (Gap) × (Change in Interest Rate)

where Gap is the difference between interest-earning assets and interest-bearing liabilities, and Change in Interest Rate is the increase in interest rates.

Gap = (Interest-earning assets) - (Interest-bearing liabilities)

Gap = ($88 million + $104 million) - ($119 million + $33 million)

Gap = $192 million - $152 million

Gap = $40 million

Change in Net Interest Income = $40 million × 4%

Change in Net Interest Income = $40 million × 0.04

Change in Net Interest Income = $1.6 million

Therefore, the change in expected net interest income for a 4 percent increase in interest rates is $1.6 million (positive value indicates an increase).

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Answer:

168 is the correct value for volume

The correct answer is option (a) n < 27. By dividing both sides of the inequality by -3, we get n > -27.

To solve the inequality -3n < 81, we divide both sides by -3. Remember that when dividing by a negative number, the direction of the inequality sign changes. Dividing both sides by -3 gives us n > -27. So, the correct answer is option (d) n > -27.

The reasoning behind this is that dividing by -3 reverses the inequality sign, which means that the less than ("<") sign becomes a greater than (">") sign.

Option (a) n < 27 is incorrect because dividing by -3 changes the direction of the inequality. Option (b) is stated to be wrong. Option (c) n = 27 is incorrect because the original inequality is strict ("<") and not an equality ("=").

Therefore, By dividing both sides of -3n < 81 by -3, we get n > -27. Therefore, the correct answer is option (a) n < 27.

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Answer:

21a-14b

15b-20a

Step-by-step explanation:

Answer: a + 3b

Step-by-step explanation:

Okay, so...

7(3a - 2b) = 7(3a) - 7(2b) ... distributive property

21a - 14b

5(3b - 4a) = 5(3b) - 5(4a) ... distributive property

15b - 20a

(21a - 14b) + (15b - 20a) = 21a -12b + 15b - 20a =

a + 3b

The names possible to describe the shape Mr Meyer drew are square and rhombus.

A square is a quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles).

A rhombus is a quadrilateral whose four sides are all the same length.

We know a square has 4 sides that are equal and 4 right angles.

And Its properties are acquired by the shape Rhombus with equal sides, and opposite sides that are parallel to each other and angles are of right angle (90 degrees).

And many Quadrilaterals have a right angle but not 4 equal sides.

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The range of the function represented by y = 15x + 20, where y is Kim's daily earnings and x is the number of bikes she assembles, is $20 ≤ y ≤ $110.

The range of a function is the set of values of y possible values of the dependent variable after substituting values for the independent variable(domain).

The total amount she earns can be represented by

y = 15x + 20

where y is her daily earnings and x is the number of bikes she assembles

If Kim's boss daily goal is to assemble no more than 6 bicycles a day, then the value of x will only range from 0 to 6(whole number).

domain : {x| 0 ≤ x ≤ 6}

where x is a whole number

Substituting the minimum and maximum value of x in the function.

y = 15(0) + 20     when x = 0

y = 20

y = 15(6) + 20     when x = 6

y = 110

range : $20 ≤ y ≤ $110

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Answer:

Step-by-step explanation:

Area formula

As per formula the area of a square and length of side are directly proportional

When x = 10 in, area is

Answer: 1.935

Percentage solution with steps:

Step 1: Our output value is 90.

Step 2: We represent the unknown value with x

Step 3: From step 1 above,90=100%

Step 4: Similarly, x=2.15%

Step-by-step explanation:

Let the number be \(\overline{abc}=100a+10b+c\).

\(100a+10b+c=34a+34b+34c \\ \\ 66a-24b-33c=0 \\ \\ 22a-8b-11c=0\)

Taking the equation mod \(11\) yields \(-8b \equiv \pmod{11}\), meaning \(b=0\).

So, \(22a-11c=0 \implies c=2a\).

So, the only possibilites are \((a,c)=(1,2), (2,4),(3,6), (4,8)\).

Therefore, there are \(4\) such numbers.

The probability that a randomly selected group of 16 individuals from the campus will be selected is 0.8023 or 80.23%

Based on the sign in the elevator of the college library, the limit of 16 persons and weight limit of 2,500 pounds need to be adhered to. To ensure compliance with both limits, we need to consider both the number of people and their weight.

Assuming that the distribution of weights of individuals on campus is approximately normal with an average weight of 155 pounds and a standard deviation of 29 pounds, we can use this information to estimate the total weight of a group of 16 randomly selected individuals.

The total weight of a group of 16 individuals can be estimated as follows:

Total weight = 16 x average weight = 16 x 155 = 2480 pounds

To determine if this total weight is within the weight limit of 2,500 pounds, we need to consider the variability in the weights of the individuals. We can do this by calculating the standard deviation of the total weight using the following formula:

Standard deviation of total weight = square root of (n x variance)

where n is the sample size (16) and variance is the square of the standard deviation (29 squared).

Standard deviation of total weight = square root of (16 x 29^2) = 232.74

Using this standard deviation, we can calculate the probability that the total weight of the group of 16 individuals is less than or equal to the weight limit of 2,500 pounds:

Z-score = (2,500 - 2,480) / 232.74 = 0.86

Using a standard normal distribution table or calculator, we can find that the probability of a Z-score less than or equal to 0.86 is approximately 0.8023.

Therefore, the probability that a randomly selected group of 16 individuals from the campus will comply with both the number and weight limits in the elevator of the college library is approximately 0.8023 or 80.23%.

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