20. Find a solution to the following system of equations.
-3x + 3y = -9
-3x+y=7
O
O
O
(5,2)
(-5, -8)
(-2,2)

The option that describes the weight of the contents that Carly can

pack in her bag is: C at most 43.8 pounds

Some of the inequality signs are:

Greater than

Less than

Greater than or equal to

Less than or equal to

Now, we are told that Passenger Bags Can Weigh No More than 50 Pounds.

Since her bag weighs 6.2 pounds empty, then we can say that the maximum weight of the contents that Carly can pack in her bag is:

50 - 6.2 = 43.8 pounds

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without too much fuss, Check the picture below.

so we have roots at -5 and 1, and a point, incidentally the vertex, at (-2 , 9)

[tex]\begin{cases} x = -5 &\implies x +5=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +5 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-2\\ y=9 \end{cases} \\\\\\ a ( -2 +5 )( -2 -1 ) = 9\implies -9a=9\implies a=\cfrac{9}{-9}\implies a=-1 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -( x +5 )( x -1 ) =y \end{array}}~\hfill[/tex]

a. The amount that remains to be refinanced is $175,000

b. The new monthly payment will be $1166.67

c. The gain is $35,000

Simple interest is an interest charge that borrowers pay lenders for a loan. Simple interest is expressed as:

S.I = P× R×T/100

the rate for first 5 years is 5%

SI = 140000 × 5 × 5/100

SI = $35000

Amount after five years = 140000+35000

= $175000

The amount that remains to be refinanced is $175000

For the remaining 10years

SI =[175000× 2× 10/100

= 35000

amount = 175000+35000

= $210,000

The total amount with this package = $210000

The number of months = 15 ×12 = 180

amount that will be paid monthly = 210000/180 = $1166.67

The gain = total amount without package - amount with package

SI = 140000×5×15/100

= $105,000

amount = 140,000+105,000 = $245,000

gain = 245000-210,000

= $35000

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Answer:

Mikas is Saltier

Step-by-step explanation:

Brainliest please.


Jack used 1 tsp to 3 tsp of water Thats a fraction of 1/3

Mika Used 4 tsp to 9 tsp of water which its 4/9

4/9 is greater than 1/3

The radius of the circle that has an area of 380 square inches is calculated as: 11 inches.

The radius of a circle is half of the diameter. It connects from the center of the circle to any point on the circumference on the circle.

We are given the following information about a circle:

Area of the circle = 380 square inches

To find the radius of the circle, recall the formula of the area of a circle which is:

area = πr², where r is the radius, π = 3.14

Therefore:

380 = πr²

380 = 3.14 * r²

380/3.14 = r²

r² = 121.01

r = √121.01

r = 11 inches.

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By answering the presented question, we may conclude that As a result, equation if Quigley Inc. converts from Plan A to Plan B, the ROE will increase by 8.6%.

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance.

TIE is an abbreviation for operating income minus interest expense.

3.2 x $35,000 = $35,000 / Interest cost

Interest cost = $35,000 divided by 3.2 is $10,937.50.

The greatest amount of debt that will cover this interest expense is:

Debt = $10,937.50 / 8.8% = $124,488.64

$200,000 - $124,488.64 = $75,511.36 equity

Debt = $124,488.64

Interest paid = $10,937.50

$35,000 in operating income

$35,000 / $10,937.50 = 3.20 TIE ratio (which meets the 3.2 requirement)

EBT = $35,000 - $10,937.50 = $24,062.50

Taxes = 25% * $24,062.50 = $6,015.63

Net profit = $24,062.50 minus $6,015.63 = $18,046.87

ROE = $18,046.87 / $75,511.36 = 0.239 or 23.9%

The difference in ROE between Plan B and Plan A is as follows:

ROE change = ROE (Plan B) - ROE (Plan A)

ROE change = 0.239 - 0.153 = 0.086 or 8.6%

As a result, if Quigley Inc. converts from Plan A to Plan B, the ROE will increase by 8.6%.

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Answer:

[tex]\large\boxed{\tt x \approx 7.61.}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem we are asked to find the measure of x.}[/tex]

[tex]\textsf{Note that we are given a Right Triangle, which means that we can use one}[/tex]

[tex]\textsf{\underline{Trigonometric Identity} to find the value of x.}[/tex]

[tex]\textsf{These Trigonometric Identities are Sine, Cosine, and Tangent.}[/tex]

[tex]\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Trigonometric Identities;}} \\ \\ \textsf{Trigonometric Identities are trigonometric ratios determined with what's given in order to find a missing value. For a Right Triangle, the Trigonometric Identities are Sine, Cosine, and Tangent. These are used to find missing sides.} \\ \\ \tt Sine = \tt $ \tt \frac{Opposite}{Hypotenuse} \\ \\ Cosine = \frac{Adjacent}{Hypotenuse} \\ \\ Tangent = \frac{Opposite}{Adjacent} \end{minipage}}[/tex]

[tex]\textsf{Because we are focused on the 65}^{\circ} \ \textsf{angle, we will use Cosine. Remember that the}[/tex]

[tex]\textsf{Hypotenuse is the longest side, and the side opposite from the right angle. The}[/tex]

[tex]\textsf{Adjacent Side is the side that the angle is nearest to, or touches. Due to what's}[/tex]

[tex]\textsf{given, we have to find x by using cosine.}[/tex]

[tex]\large\underline{\textsf{Solving for x;}}[/tex]

[tex]\textsf{Let's use cosine to solve for x.}[/tex]

[tex]\tt \cos(65^{\circ}) = \frac{x}{18}[/tex]

[tex]\textsf{Cancel out the fraction by using the \underline{Multiplication Property of Equality}, which}[/tex]

[tex]\textsf{states that expressions are still equal if they're multiplied by the same term.}[/tex]

[tex]\tt 18 \times \cos(65^{\circ}) = \frac{\not{18}x}{\not{18}}[/tex]

[tex]\tt 18\cos(65^{\circ}) = x[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\large\boxed{\tt x \approx 7.61.}[/tex]

In the given problem, solving systematically, the company will pay $3,000 if they purchase 8 computers. (Option C).

To solve this problem, we can use the following steps:

Therefore, the company will pay $3,000 if they purchase 8 computers.

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Answer:

0.066

Step-by-step explanation:

462/7000= 0.066

Answer:

0.66

Step-by-step explanation:

Answer:

A. 11x

B. 3x² +6x

Step-by-step explanation:

If you think math is boring, you're wrong. Math can be very funny, especially when you know some good jokes. Here's one for you:

Q: How do you know that the correct answer is A. 11x and B. 3x² +6x?

A: Because they are both polynomials, and polynomials are always right!

What are polynomials, you ask? Well, they are expressions that consist of one or more terms of non-negative integer powers of a variable. For example, 11x is a polynomial with one term, and 3x² +6x is a polynomial with two terms.

But what about C. 2x²-√x and D. 1-5x²/x? Are they polynomials too? No, they are not, because they contain terms with negative or fractional powers of x. For example, √x is the same as x^(1/2), which is a fractional power of x.

Polynomials are fun, aren't they? They can help you do all kinds of things, like shopping, engineering, and driving a taxi. But did you know that polynomials can also make you laugh? Here are some jokes about polynomials that will tickle your funny bone.

- What do you call a polynomial that is always happy? A jolly-nomial.

- How do you make a polynomial sad? You take away its degree.

- What do you get when you cross a polynomial with a rabbit? A poly-hop-nomial.

- Why did the polynomial go to the dentist? Because it had a root canal.

- How do you know if a polynomial is lying? You check its coefficients.

- What do you call a polynomial that likes to party? A disco-nomial.

- What do you say when you see a polynomial with no terms? Oh, the zero-nomy!

- How do you divide a polynomial by another polynomial? You don't. That's a rational expression.

- What do you call a polynomial that is always angry? A cross-nomial.

- What do you call a polynomial that is afraid of everything? A chicken-nomial.

So, remember: polynomials are always right, and non-polynomials are always wrong. And if you don't believe me, just ask them yourself. They'll tell you the same thing!

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

No, Pete's results are not likely to be representative of the population he is trying to analyze. The sample he selected is not random and is biased towards customers who have purchased the largest number of items. This may not be representative of the general population of customers who have purchased a smaller number of items, and their opinions may differ from those of the selected customers. Additionally, the sample size of 5 is small, which may not provide sufficient statistical power to draw accurate conclusions about the entire population. To obtain a representative sample, a larger sample size should be chosen randomly from the population to reduce the likelihood of bias and increase the precision of the estimates.

I hope you pass class if you need more help on other feel free to ask.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer is 4 because 8 times 4 is 32

Answer: 8·[tex]x[/tex]=32 or 8·4=32

Step-by-step explanation:

The one-step equation 8·[tex]x[/tex]=32 shows how Nina can sort 32 cards into 8 equal groups. To solve, divide 32 by 8. You should get 4. Therefore, an equation to show how Nina can sort 32 cards into 8 equal groups is 8·4=32.

The range is 33.  The interquartile range is 18. The variance is 187.7143 and the standard deviation is 13.69.

The mean deviation is 7.75. The median deviation is 7.38.

Range = maximum value - minimum value

Maximum value = 40

Minimum value = 7

Range = 40 - 7 = 33

The median of the lower half is (7 + 9 + 18 + 22)/4 = 14

The median of the entire set is (7 + 9 + 18 + 22 + 27 + 29 + 32 + 40)/8 = 24.5

The median of the upper half is (27 + 29 + 32 + 40)/4 = 32.

So, Q1 = 14 and Q3 = 32.

Interquartile range (IQR) = Q3 - Q1 = 32 - 14 = 18

Mean (μ) = (7 + 9 + 18 + 22 + 27 + 29 + 32 + 40)/8 = 23

Variance (σ^2) = Σ(xi - μ)^2 / (n-1)

= ((7-23)^2 + (9-23)^2 + (18-23)^2 + (22-23)^2 + (27-23)^2 + (29-23)^2 + (32-23)^2 + (40-23)^2) / (8-1)

= 187.7143

Standard deviation (σ) = √(σ^2) = √(187.7143) = 13.69

Mean deviation (MD) = Σ|xi - μ| / n

= (|7-23| + |9-23| + |18-23| + |22-23| + |27-23| + |29-23| + |32-23| + |40-23|) / 8

= 62 / 8

= 7.75

Median deviation = Σ|xi - M| / n

where M is the median.

M = (22 + 27) / 2 = 24.5

Median deviation = (|7-24.5| + |9-24.5| + |18-24.5| + |22-24.5| + |27-24.5| + |29-24.5| + |32-24.5| + |40-24.5|) / 8

= 59 / 8

= 7.38

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Julie's total time for the race could be any time t < 48.72.

Given that,

Connor finished race at 48.72.

Julie finishes the race before Connor.

We have to find the total time taken by Julie to finish the race.

Julie could finish the race at any time before Connor.

Already we have,

Time that Connor finished race = 48.72

So time that Julie finished the race could be any time t < 48.72.

Hence the time required to finish the race by Julie could be any time t < 48.72.

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The factorization of 7x^2 -6x is x(7x - 6).

It should be noted that to factorize 7x^2 -6x, we need to find two numbers that can multiply to give 7 times the coefficient of x^2 (which is 7), and add to give the coefficient of x (which is -6).

The first step is to factor out the greatest common factor (GCF) of the two terms, which is x:

7x^2 - 6x = x(7x - 6)

Now we can see that the two numbers we need are 7 and -6, since 7 times -6 is -42 and 7 + (-6) is 1. So we can rewrite the expression as:

7x^2 - 6x = x(7x - 6) = x(7x + (-6)) = x(7x - 6)

Therefore, the factorization of 7x^2 -6x is x(7x - 6).

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Factorize 7x^2 -6x

Answer:

1156

Step-by-step explanation:

[tex]\sqrt{x} =34[/tex]

Square both sides. This cancels the square root on the left side.

[tex](\sqrt{x} )^2 = 34^2[/tex]

The x is now free. Square 34 by multiplying it by itself.

x = 1156

Answer:

X=0.8

Step-by-step explanation:

X/Y=3/15

=> X=(3/15)*Y

=> X=(3/15)*4=0.8

To find the additional cost incurred when production is increased from 2 units to 13 units, we need to calculate the difference between the total cost of producing 13 units and the total cost of producing 2 units.

The total cost of producing x units is given by the antiderivative of the marginal cost function:

C(x) = ∫ C′(t) dt = 0.04t^3 - 2t^2 + 80t + C

where C is an arbitrary constant of integration.

To find the value of C, we can use the fact that the total cost of producing 2 units is known:

C(2) = 0.04(2)^3 - 2(2)^2 + 80(2) + C = 162 + C

We know from the problem statement that the total cost of producing 2 units is $162, so we can solve for C:

162 + C = C(2) = 0.12(2)^2 - 4(2) + 80 = 68

C = -94

Now we can find the total cost of producing 13 units:

C(13) = 0.04(13)^3 - 2(13)^2 + 80(13) - 94 = 1956

The additional cost incurred when production is increased from 2 units to 13 units is:

C(13) - C(2) = 1956 - 162 = $1794

Therefore, the additional cost incurred in dollars when production is increased from 2 units to 13 units is $1794.

4 is the answer

Step-by-step explanation:

You will first expand the bracket that will be

2u +6u-30=2

grouping of like terms

2u+6u =2+30

8u =32

dividing both sides by the coefficient u

u =4

Answer:

638.45

Step-by-step explanation:

The interest on the couch will be:

0.13 * $565 = $73.45

So the total amount Sharon paid for the couch with interest is:

$565 + $73.45 = $638.45

Answer:

37.5

Step-by-step explanation:

To find the interquartile range (IQR) for a data set, we need to find the difference between the upper quartile (Q3) and the lower quartile (Q1).

To find Q1 and Q3, we first need to order the data set from lowest to highest:

25, 49, 50, 60, 60, 70, 70, 74, 81, 85, 89, 100

There are 12 data points in this set, so the median is the average of the sixth and seventh numbers:

median = (70 + 70)/2 = 70

To find Q1, we take the median of the first half of the data set (the numbers to the left of the median). There are six numbers in the first half, so the median is the average of the third and fourth numbers:

Q1 = (49 + 50)/2 = 49.5

To find Q3, we take the median of the second half of the data set (the numbers to the right of the median). Again, there are six numbers in the second half, so the median is the average of the ninth and tenth numbers:

Q3 = (85 + 89)/2 = 87

Now we can find the IQR by subtracting Q1 from Q3:

IQR = Q3 - Q1 = 87 - 49.5 = 37.5

Therefore, the interquartile range for the given data set is 37.5.

Answer:

Step-by-step explanation:

Graph crosses x-axis when y=0 (that is f(x)=0).

   [tex](x+3)(x+2)(x-1)=0 \text{ when:}[/tex]

           [tex]x+3=0\text{ or }x+2=0\text{ or }x-1=0[/tex]

           [tex]\text{So }x=-3,-2,1[/tex]

SOLUTION:  Graph crosses x-axis at [tex]x=-3,-2,1[/tex].

The expression, in terms of y, for the perimeter of the rectangle is 4 + 4y

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

Dimensions = y + 2 and y

The perimeter of the rectangle is represented as

P = 2 * (LEngth + Width)

So, we have

P = 2 * (y + 2 + y)

Evaluate

P = 4 + 4y

Hence, the permeter expression is 4 + 4y

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Answer: 1 just like my answer dawg

Step-by-step explanation:

The maximum that the couple can spend on the meal is $40.63

Let's say that the couple spends a total of X.

Then we know that we need to add a tax of 7%, then we need to add a factor of (1.07) to the total cost.

And we also know that they want to pay a tip of 15%, then we need to add a factor of (1.15) to the total cost.

Then the total cost for the meal will be:

C = x*(1.15)*(1.07)

The maximum that the spend is 50, then let's solve this for C = 50

50 = X*(1.15)*(1.07)

50/(1.15)*(1.07) = X

40.63 = X

The maximum that they can spend is $40.63

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Answer:

1) 13

2) 29

3) 61

4) 151

Step-by-step explanation:

1:

Vertical angles are congruent.  Angle A is equal to Angle C

3x - 10 = 29  Add 10 to both sides

3x - 10 + 10 = 29 + 10

3X = 39  Divide both sides by 3

x = 13

2:

29
Vertical angles have the same measurement.

3:

A straight angle (straight line) is 180. The square in the angle means that angle measures 90.

180 - 90 - 29 = 61

4:

180 - 29 = 151

Helping in the name of Jesus.

Answer:

3w+18

Step-by-step explanation:

3 x w = 3w

3 x 6 = 18

So, there is approximately an 85.02% probability that the sample mean will be between 50 and 54.

We'll use the Central Limit Theorem which states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is large enough (n ≥ 30).

In this case, the sample size is 42, so we can apply the Central Limit Theorem.

First, we'll calculate the standard deviation of the sampling distribution (also known as the standard error) using the formula:

Standard error (SE) = population standard deviation / √sample size

SE = 9 / √42 ≈ 1.387

Next, we'll calculate the Z-scores for the lower and upper bounds of the range (50 and 54) using the following formula:

Z = (sample mean - population mean) / standard error

For the lower bound (50):

Z1 = (50 - 52) / 1.387 ≈ -1.44

For the upper bound (54):

Z2 = (54 - 52) / 1.387 ≈ 1.44

Now, we'll use a Z-table or calculator to find the probability that the sample mean lies between these Z-scores. We need to find the area between Z1 and Z2.

P(-1.44 < Z < 1.44) = P(Z < 1.44) - P(Z < -1.44)

Using a Z-table or calculator:

P(Z < 1.44) ≈ 0.9251

P(Z < -1.44) ≈ 0.0749

Now subtract:

P(-1.44 < Z < 1.44) = 0.9251 - 0.0749 = 0.8502

So, there is approximately an 85.02% probability that the sample mean will be between 50 and 54.

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Given a sample of size 42 drawn from a population with a mean of 52 and a standard deviation of 9, what is the probability that the sample mean is between 50 and 54?

The value of the constants a, b and c. are a = 0.145, b = 0.21 and c = 0.645

Given that

X : 0,1,2

P(X = x) : a,b,c

E(X) = 1.5 and Var(X) = 0.54

The formula of expected value is

E(x) = ∑x P(x)

So, we have

0 * a + 1 * b + 2 * c = 1.5

b + 2c = 1.5

The variance of a discrete random variable is

Var(x) = E(x²) - E(x)

Where

E(x²) = ∑x² P(x)

So, we have

E(x²) = 0² * a + 1² * b + 2² * c

E(x²) = b + 4c

Next, we have

Var(x) = E(x²) - E(x)²

b + 4c - (b + 2c)² = 0.54

Evaluate

b + 4c - (b² + 4cb + 4c²) = 0.54

So, we have

b + 4c - (b² + 4cb + 4c²) = 0.54

b + 2c = 1.5

Solve by graphing, we have

b = 0.21 and c = 0.645

The sum of the probabilities is 1

So, we have

a + b + c = 1

This gives

a + 0.21 + 0.645 = 1

Evaluate

a = 0.145

Hence, the value of constant a is 0.145

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