What is the common difference in this equation?

The measure of angle c is 70 degrees.

If angle a and angle b are complementary, it means that the sum of their measures is equal to 90 degrees.

Given:

Measure of angle a = 10x + 10

Measure of angle b = 20

We can set up the equation:

(10x + 10) + 20 = 90

Simplifying the equation:

10x + 30 = 90

Subtracting 30 from both sides:

10x = 60

Dividing both sides by 10:

x = 6

Now, we have found the value of x to be 6.

To find the measure of angle c, we can substitute the value of x into the equation for angle a:

Measure of angle a = 10x + 10

Measure of angle a = 10(6) + 10

Measure of angle a = 60 + 10

Measure of angle a = 70

As a result, angle c has a measure of 70 degrees.

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The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

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Answer:

d is the answer

Step-by-step explanation:

y=mx+b

m being the slope and b being the y intercept

Answer:

X = 7

Step-by-step explanation:

The reflection of the point P(4, -1) over the x-axis is Rx-axis(P) = (4, 1).

To find the reflection of the point P(4, -1) over the x-axis, we need to change the sign of the y-coordinate while keeping the x-coordinate the same.

The reflection of a point over the x-axis will have the same x-coordinate but the y-coordinate will be the opposite sign.

Given the point P(4, -1), the reflection over the x-axis, Rx-axis(P), can be found as follows:

Rx-axis(P) = (4, -(-1))

Simplifying the expression:

Rx-axis(P) = (4, 1)

We must modify the sign of the y-coordinate while maintaining the x-coordinate in order to determine the reflection of the point P(4, -1) across the x-axis.

The x-coordinate of a point reflected across the x-axis will remain the same, but the sign of the y-coordinate will change.

The reflection across the x-axis, Rx-axis(P), for the position P(4, -1), may be obtained as follows:

Rx-axis(P) = (four, minus one).

Condensing the phrase:

(P) = (4, 1) Rx-axis

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Answer:

\(y=\frac{5}{9}\)

Step-by-step explanation:

For the graph of \(y=f(x)\),

the horizontal asymptote becomes \(y=\frac{5}{9}\)

Answer:

it should be 27.6

Step-by-step explanation:

359/13 = 27.61

Answer:

B:  27.6 miles per gallon

Step-by-step explanation:

359/13= 27.6

Answer: a) 45 | b) 60 | c) 150

Step-by-step explanation:

Let's start with what we know. 15x means 15 multiplied times x. So for the different values of x we just plugin different numbers.

a) For the first one 15 * 3 = 45.

b) For the second one 15 * 4 = 60.

c) For the third one 15 * 10 = 150.

So, to my knowledge, the question was just asking you to evaluate different values of x multiplied by 15.

Answer:

y=-1/4x-9/4

Step-by-step explanation:

The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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Answer:

To represent -17/4 on a number line, we first need to find its approximate decimal equivalent. To do that, we divide -17 by 4:

-17 ÷ 4 ≈ -4.25

So, -17/4 is approximately -4.25. To plot it on a number line, we can start by locating -4, which is four units to the left of 0. Then, we can estimate a little bit to the left of -4 to represent -4.25. The resulting point should be closer to -4 than to -5.

Step-by-step explanation:

Hope this helps you~

Answer:

615.75216

Step-by-step explanation:

A=πr2

=π·14^2

≈615.75216

Answer:

\(r = 14cm \\ area = \pi \: r {}^{2} \\ area = 3.14 \times 14 \times 14 \\ area = 3.14 \times 196 \\{area = 615.44}\)

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

The first constraint is a linear equation that relates the variables x1, x2, and x3, and the second constraint is an inequality constraint involving x1 and x2The given problem is a linear programming problem in its primal form.

The objective is to maximize the expression z = 7x1 - 5x2 - 2x3, subject to two constraints.. The goal is to find the values of x1, x2, and x3 that maximize the objective function while satisfying the given constraints.

In the primal problem, the objective is to maximize the expression z, which is a linear combination of the decision variables x1, x2, and x3. The coefficients 7, -5, and -2 represent the weights assigned to each variable in the objective function. The constraints represent the relationships and limitations imposed on the variables. The first constraint is an equality constraint, which means that the left-hand side of the equation must equal the right-hand side. The second constraint is an inequality constraint, indicating that the value of the expression 2x1 + x2 must be less than or equal to a certain value.

To solve this linear programming problem, various optimization techniques such as the simplex method or interior point methods can be applied. These methods iteratively adjust the values of the decision variables to find the optimal solution that maximizes the objective function while satisfying the given constraints. By solving the primal problem, the values of x1, x2, and x3 can be determined, leading to the maximum value of the objective function z.

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Answer:

k<-9

Step-by-step explanation:

First you want to isolate the variable, or k in this case. So you will subtract 12 on both sides which will leave you with -2k<18. Then you will divide both sides by -2. Which turns into k>-9. But since you divided by a negative, the sign changes, so the answer would be k<-9.

Answer:

480

Step-by-step explanation:

Take 20% of 2400

Answer:

1920

Step-by-step explanation:

20% of 2400 = 480

2400-480= 1920

a. A tea bag is considered small if it weighs less than 2.626 grams.

b. The probability that it weighs at least 2.25 grams is 17.07%.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not.

(a) Let X be the weight of a tea bag. Then X ~ N(3.5, 0.53²). We want to find the value of w such that P(X < w) = 0.052. Using the standard normal distribution, we have:

(P(X < w) - P(X < 3.5)) / 0.53 = z

where z is the 0.052 quantile of the standard normal distribution. Using a standard normal table or calculator, we find that z ≈ -1.645. Substituting the values and solving for w, we get:

(w - 3.5) / 0.53 = -1.645

w - 3.5 = -0.874

w ≈ 2.626

Therefore, a tea bag is considered small if it weighs less than 2.626 grams.

(b) We want to find P(X ≥ 2.25 | X < 2.626), which is the conditional probability that a selected tea bag weighs at least 2.25 grams given that it is small. Using the properties of the normal distribution, we have:

P(X ≥ 2.25 | X < 2.626) = P((X - 3.5) / 0.53 ≥ (2.25 - 3.5) / 0.53 | (X - 3.5) / 0.53 < (2.626 - 3.5) / 0.53)

= P(Z ≥ -2.358 | Z < -1.566)

where Z is a standard normal random variable. Using a standard normal table or calculator, we find that:

P(Z ≥ -2.358) ≈ 0.990

P(Z < -1.566) ≈ 0.058

Therefore, P(X ≥ 2.25 | X < 2.626) ≈ 0.990 / 0.058 ≈ 17.07%.

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Answer:

C

Step-by-step explanation:

The dilated point R' of the given point will be (-12,-24). The correct option is A.

Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Given that If QRS is dilated by a scale factor of 6 through the origin, the coordinate will be calculated as:-

The dilation factor is 6 then multiply the coordinates of R by 6 to calculate the value of dilated coordinate.

( -2 , -4) ⇒ Dilated ( -2 x 6 , -4 x 6 )

( -2 , -4 ) ⇒ Dilated ( -12, -24 )

Therefore, the dilated point R' of the given point will be (-12,-24). The correct option is A.

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Answer:

hi

Step-by-step explanation:

The current value of the vending machine is $150,411.90, which is the sum of all discounted future payments.Vending machines are used to offer goods like snacks and beverages to consumers for sale without the need for a salesperson.  

These machines often necessitate cash or debit card payments to operate. Vending machines have become a preferred method of retailing due to their cost-effectiveness and ease of use. The current value of the vending machine can be determined using the present value formula.

The present value is the sum of the future payments, discounted back to their current value. In this case, we must discount the future payments to their present value using the given interest rate. The formula is as follows:PV = Pmt x ((1-(1/(1+r)n))/r).

Where, PV = Present Value Pmt = Payment per period n = Number of periods r = Interest rate per periodIn this scenario, Pmt = $750n = 30 periods (since the payments are made every six months for 15 years, which is 30 periods)r = 5% per period.

Present Value = $750 x ((1-(1/(1+0.05)^30))/0.05) Present Value = $150,411.90.

Therefore, the current value of the vending machine that is expected to pay out $750 every six months for 15 years at a 5% interest rate per annum, and the first payment is made four years after from today is $150,411.90.

In conclusion, the current value of the vending machine is $150,411.90, which is the sum of all discounted future payments.

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Answer:

Step-by-step explanation:

Yasmina:

5.25 x  5 = 26.25 per week

5.25 x 20 = 105 per month

5.25 x 260 = 1365 per year

Camila:

9.75 x 35 = $ 341.25 earnings per week

341.25  x 0.20 = 68.25 saves per week

9.75x35x 4= 1365 earnings per month

1365 x 0.20 = 273 saves per month

9.75 x 35 x 52 =  17745 earnings per year

17745 x 0.20 = 3549 saves per year

Answer:

3

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Angle-Side-Angle. The Angle-Side-Angle Postulate (ASA) states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Answer:

Step-by-step explanation:

They said the defective toys are 3%

Let's see if the prediction matches up.

Prediction:  872 out of 24850

We need to put that info into %.  A percent is a fraction, part over the whole

\(\frac{872}{24850}\)

You can use long division or your calculator to do 872 divided by 24850

= .035      multiply by 100 or move decimal over 2 places to turn into %

=3.5 %      

The prediction is at 3.5%  The prediction is close but a little high because it is a little higher than the 3% they gave you.

The interpretation is that 8% of the variation in the dependent variable can be explained by the variation in the independent variable. (B)

The coefficient of determination, r^2, is a measure of how much of the variation in the dependent variable can be explained by the variation in the independent variable.

It is calculated by squaring the correlation coefficient, r, between the two variables. In this case, r^2 is equal to 0.08, which means that 8% of the variation in the dependent variable can be explained by the variation in the independent variable.

This means that the independent variable has a relatively small effect on the dependent variable, and there are likely other factors that contribute to the variation in the dependent variable.

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Answer:

13.3

Step-by-step explanation:

By using sinus rule

The inequality 3 ≤ x - 2 simplifies to x ≥ 5. This means x can take any value greater than or equal to 5. Therefore, option (E) with a number line from positive 5 to positive 10 is correct.

Given: 3 \(\leq\) x - 2

We need to work out which number line below shows the values that x can take. In order to solve the inequality, we will add 2 to both sides. 3+2 \(\leq\) x - 2+2 5 \(\leq\) x

Now the inequality is in form x \(\geq\) 5. This means that x can take any value greater than or equal to 5. So, the number line going from positive 5 to positive 10 shows the values that x can take.

Therefore, the correct option is (E) A number line going from positive 5 to positive 10.  We added 2 to both sides of the given inequality, which gives us 5 \(\leq\) x. It shows that x can take any value greater than or equal to 5.

Hence, option E is correct.

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