Write the following series in sigma notation.
2+9+16+23+30+37+44

Answer:

(x-6)^2+(y-4)^2=10

Step-by-step explanation:

use the equation of a circle ( x- x coordinate of center)^2+(y-y coordinate of the center)^2=radius squared.

to solve for the radius, make a right triangle from the center to the point on the circle. 1^2+3^2=r^2. So r^2 is 10

Answer:

\((1,\frac{-5}{2} )\)

Step-by-step explanation:

Midpoint Formula: \((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )\)

Simply plug in your coordinates into the midpoint formula to find the midpoint:

\((\frac{0+2}{2},\frac{-4-1}{2} )\)

\((\frac{2}{2},\frac{-5}{2} )\)

\((1,\frac{-5}{2} )\)

The caramel topping demand curve will not change:

The cost of caramel topping is falling; there will be an increase in demand for caramel topping:

Butterscotch topping costs more money;

There will be less demand for caramel topping:

Ice cream now costs more money.

The quantity of caramel topping demanded would increase if the price of the topping dropped. Consequently, the demand curve for caramel topping would go lower.

Ice cream and caramel toppings are complementary products.

Products that are consumed together are said to be complementary.

The amount of ice cream demanded would drop if the price went up. There would be a drop in the number of caramel toppings needed as a result of the fall in demand.

a decline in the popularity of caramel toppings. With less demand, the demand curve for caramel toppings would move inward.

Butterscotch and caramel ice cream toppings serve as stand-ins.

Products that can be used in place of one another are known as substitute goods.

The quantity demanded for butterscotch topping would decline if the price of butterscotch topping rose, making it more expensive overall. Customers might switch to caramel topping. As a result, demand for caramel topping would rise and the demand curve would move outward.

Demand curve: what is it?

The demand curve is a graphical representation of how the cost of an item or service relates to how much is demanded over a given period of time.

To know more about the demand curve visit:

https://brainly.com/question/13131242

#SPJ4

Answer:

∠ ACD = 130°

Step-by-step explanation:

∠ ABC = 180° - 120° = 60° ( adjacent angles on a straight line )

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ACD is an exterior angle of the triangle , then

∠ ACD = 70° + 60° = 130°

The scalar projection of b onto a is -30/7, and the vector projection of b onto a is (90/49, 180/49, 60/49).

To find the scalar and vector projections of vector b onto vector a, we can use the following formulas:

Scalar Projection: comp_b_a = |b| cos(theta)

Vector Projection: proj_b_a = (|b| cos(theta)) * unit vector of a

First, let's calculate the magnitude of vector b:

|b| = sqrt(2^2 + 3^2 + 3^2) = sqrt(4 + 9 + 9) = sqrt(22)

Now, let's find the unit vector of a by dividing vector a by its magnitude:

|a| = sqrt((-3)^2 + (-6)^2 + (-2)^2) = sqrt(9 + 36 + 4) = sqrt(49) = 7

unit vector of a = (a / |a|) = (-3/7, -6/7, -2/7)

Next, let's calculate the cosine of the angle between vectors a and b:

cos(theta) = (a · b) / (|a| * |b|)

= (-32 + -63 + -2*3) / (7 * sqrt(22))

= (-6 - 18 - 6) / (7 * sqrt(22))

= -30 / (7 * sqrt(22))

Now, we can find the scalar projection:

comp_b_a = |b| * cos(theta)

= sqrt(22) * (-30 / (7 * sqrt(22)))

= -30 / 7

Lastly, we can find the vector projection by multiplying the scalar projection by the unit vector of a:

proj_b_a = comp_b_a * unit vector of a

= (-30 / 7) * (-3/7, -6/7, -2/7)

= (90/49, 180/49, 60/49)

Therefore, the scalar projection of b onto a is -30/7, and the vector projection of b onto a is (90/49, 180/49, 60/49).

Learn more about scalar projection here

https://brainly.com/question/30709118

#SPJ11

Answer:

The length of the parallelogram is 18 meters

The width of the parallelogram is 16 meters

Step-by-step explanation:

The perimeter of a parallelogram is 68 meters

LEt x be the length of the parallelogram

Width is 2 meters less than its length

Width =x-2

Perimeter of parallelogram = 2(length + width)

Perimeter of parallelogram =

=

Add 2 on both sides

Divide by 4 on both sides

x=18

The length of the parallelogram is 18 meters

The width of the parallelogram is 18-2= 16 meters

Between 1 and 200, there are 66 numbers that are divisible by either 4 or 6.

To find the numbers between 1 and 200 that are divisible by 4 or 6, we need to determine the count of numbers divisible by 4 and the count of numbers divisible by 6, and then subtract the count of numbers divisible by both 4 and 6 (since they would be counted twice).

Divisibility by 4:

To find the count of numbers divisible by 4, we divide 200 by 4 and round down to the nearest whole number. So, 200 divided by 4 equals 50, meaning there are 50 numbers divisible by 4 between 1 and 200.

Divisibility by 6:

Similarly, to find the count of numbers divisible by 6, we divide 200 by 6 and round down. 200 divided by 6 equals approximately 33.33, so there are 33 numbers divisible by 6 between 1 and 200.

Numbers divisible by both 4 and 6:

To find the count of numbers divisible by both 4 and 6, we need to find the count of numbers divisible by their least common multiple, which is 12. We divide 200 by 12 and round down, resulting in approximately 16.67. Thus, there are 16 numbers divisible by both 4 and 6 between 1 and 200.

Finally, we add the count of numbers divisible by 4 and the count of numbers divisible by 6 and subtract the count of numbers divisible by both 4 and 6 to get the total count of numbers divisible by either 4 or 6. Therefore, there are 50 + 33 - 16 = 67 numbers between 1 and 200 that are divisible by either 4 or 6.

Learn more about Divisibility here:

https://brainly.com/question/2273245

#SPJ11

Answer:

$12.84

Step-by-step explanation:

calculator

The solution to the system of equations is given as follows:

x = 1 and x = 3.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the two equations are:

\(\frac{1}{x - 2} = x - 2\)

Applying cross multiplication:

(x - 2)(x - 2) = 1

x² - 4x + 4 = 1

x² - 4x + 3 = 0

(x - 1)(x - 3) = 0

Hence the solutions are:

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Answer:

No

Step-by-step explanation:

4/9 divided by 5/7 is equal to 4/9 * 7/5 = 28/45. We can see that 63/20 is not equivalent to 28/45 as 28/45 is less than one and 63/20 is greater than one.

Cindy's average tax rate is approximately 13.59%.

To calculate Cindy's average tax rate, we divide the total tax paid by her taxable income and then multiply by 100 to express it as a percentage.

Average tax rate = (Total tax paid / Taxable income) * 100

In this case, Cindy's taxable income is $65,500, and she has calculated that she will owe $8,902 in taxes.

Average tax rate = (8,902 / 65,500) * 100

Average tax rate ≈ 13.59%

Therefore, Cindy's average tax rate is approximately 13.59%.

To study more about Average Tax Rate:

https://brainly.com/question/28962879

Cindy is projecting her earnings to be $90,000, a taxable income of $65,500, and has calculated that she will owe $8,902. Her average tax rate is 13.60%.

How to find the average tax rate?

The average tax rate is determined by dividing the total tax paid by the total income earned. The average tax rate is calculated by dividing the total amount of tax paid by the total taxable income.

Average Tax Rate = Total Tax Paid / Taxable Income Cindy's

The average tax rate can be found as follows:

Average tax rate = (Total tax paid ÷ Taxable income) × 100%

Average tax rate = ($8,902 ÷ $65,500) × 100%

Average tax rate = 0.135994 × 100% ≈ 13.60%

Therefore, Cindy's average tax rate is 13.60%.

To learn more about the average tax rate visit:

https://brainly.com/question/32228027

#SPJ11

(a) In trade equilibrium, the consumption point for the Home consumer can be shown on a graph where wheat is on the x-axis.

(b) If the world relative price increases above 2/3, the Foreign consumer's utility will decrease compared to the benchmark trade equilibrium with a world price of 2/3.

a, Since the relative price of wheat to cloth is 2/3, the Home consumer's consumption point will lie on a budget line with a slope of -2/3. The specific coordinates of the consumption point cannot be determined without additional information about preferences and the Home consumer's budget constraint.

To show that an increase in the relative price of wheat from 2/3 raises Home's utility, we need to consider the concept of substitution effect. When the relative price of wheat increases, it becomes relatively more expensive compared to cloth. The Home consumer will respond by consuming less wheat and more cloth, moving along the budget line to a new consumption point. This movement is driven by the substitution effect, where the consumer substitutes away from the now relatively more expensive wheat towards the relatively cheaper cloth. Since the Home consumer's preferences and utility are not known, the specific utility level cannot be quantified, but it can be concluded that the utility increases due to the substitution effect.

b.  In the benchmark equilibrium, the Foreign consumer maximizes utility given the initial relative price. If the relative price increases, it means that wheat becomes relatively more expensive compared to cloth in the world market.

As a result, the Foreign consumer will have to consume less wheat and more cloth in order to remain on the same budget line. This movement along the budget line leads to a decrease in utility because the consumer has to give up some desired wheat consumption to obtain more cloth. The magnitude of the utility decrease depends on the specific preferences and utility function of the Foreign consumer, but it can be concluded that the utility will be lower when the relative price of wheat increases above 2/3 in the world market.

Learn more about equilibrium here: brainly.com/question/30694482

#SPJ11

Answer:

(-3,12)

Step-by-step explanation:

Answer:

a dog

Step-by-step explanation:

Answer:

Dunno...Dog-man?

Step-by-step explanation:

Lemme think about that

Answer: -5/4

Step-by-step explanation: You can use the graph to count the slope. The change in y is -5 and the change in x is 4, and slope is change in y over change in x.

We would expect about 80 seventh-graders to attend after-school programs.

To estimate the number of seventh-graders attending after-school programs, we can use the proportion of respondents who attend after-school programs from the sample:

28 out of 140 respondents attend after-school programs, which is a proportion of

= 28 / 140

= 0.2.

We can use this proportion to estimate the number of seventh-graders attending after-school programs in the entire population of 400 seventh-graders:

400 * 0.2 = 80

Learn more about proportions at:

https://brainly.com/question/870035

#SPJ1

Step-by-step explanation:

(x² /x² + 7x + 6)÷(9x - 9/x² - 1)

(x²/(x + 1)(x + 6))×((x + 1)(x - 1)/9(x - 1))

(x²/(x + 6))×1/9

x²/9(x + 6)

Answer:

√5, 1.8, -1/4,-1/3,-2

Step-by-step explanation:

Please put brainliest if this helps

Answer:

sqrt5, 1.8, -1/4, -1/3 and -2

Step-by-step explanation:

I. Find the true value of variables

      -2 = -2

     1.8 = 1.8

    -1/3 = -0.333...

    -1/4 = -0.25

  sqrt5 = 2.236

II. Descending is most to least so

 = 2.236, 1.8, -0.25, -0.333, -2

 or sqrt5, 1.8, -1/4, -1/3 and -2

For -0.x, if x is near 0 will be the greatest value,

and +0.x if x is far from 0 will be the greatest value

So Descending is sqrt5, 1.8, -1/4, -1/3 and -2

To determine the number of solutions for the given system of equations:

6x + 3y = -12   (Equation 1)

y = -2x + 4     (Equation 2)

We can analyze the equations to see if they intersect at a single point (one solution), multiple points (infinite solutions), or if they are parallel and do not intersect (no solution).

First, let's rearrange Equation 2 to be in the form y = mx + b, where m is the slope and b is the y-intercept:

y = -2x + 4

Comparing the slopes of the two equations, we see that the slope of Equation 1 is 6/3 = 2, while the slope of Equation 2 is -2.

Since the slopes are different, the two lines represented by the equations are not parallel. Therefore, they will intersect at a single point.

Therefore, the system of equations has one solution.

#SPJ11

If the price on the tag was $30, the price of the phone after the 15% discount but before tax is $25.50.

To calculate the price of the phone after the 15% discount, we need to multiply the original price by the discount rate. The discount rate is 15%, which can be written as 0.15 in decimal form.

The amount of discount can be calculated by multiplying the original price by the discount rate:

Discount = Original Price x Discount Rate

Discount = $30 x 0.15

Discount = $4.50

So the discount on the phone is $4.50.

To calculate the price of the phone after the discount, we need to subtract the discount from the original price:

Price after discount = Original price - Discount

Price after discount = $30 - $4.50

Price after discount = $25.50

To learn more about price click on,

https://brainly.com/question/23714454

#SPJ4

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

To know more about interest visit:

https://brainly.com/question/30393144

#SPJ11

Answer:

the answer is B

x = 1

Step-by-step explanation:

the symmetry is in the middle of the curve like a mirror and the equation of the mirror or symmetry line is x=1

mean: 110

Standard deviation: 15

We have to apply the percentile formula:

z = (score- mean)/ standard deviation

z = (130-110)/15

z= 20/15

z= 1.3333333

Find the percentile with the z score in a z-score chart:

percentile:

Answer:

Brain

Step-by-step explanation:

Brain Brain Brain Brain Brain Brain

The side opposite to angle B is AC. The side adjacent to angle B is BC. The hypotenuse is segment AB.

A pair of sides are referred to as neighboring if they have a shared angle. The term "hypotenuse" refers to a right-angled triangle's longest side as compared to the base and perpendicular lengths. The right angle, the largest angle of the three angles in a right triangle, lies opposite the hypotenuse side. In essence, only the right triangle possesses the hypotenuse feature, not any other triangles.

From the figure we observe that the side opposite to angle B is AC.

The angle adjacent to angle B is BC.

The hypotenuse is segment AB.

Learn more about hypotenuse here:

https://brainly.com/question/16893462

#SPJ1

Answer: the answer to this is true

In the △IGH, the measurement of the angles are m∠G = 114°, m∠H = 49°, and m∠I = 17°.

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Given that,

m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°.

The sum of interior angles of a triangle is 180°.

Therefore,

m∠G + m∠H + m∠I = 180°

Putting m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:

(7x - 5)° + (3x - 2)° + x° = 180°

Combine like terms:

(7x + 3x + x) - (5 + 2) =180

11x - 7 = 180

Add 7 on both sides:

11x = 187

Divide both sides by 11:

x = 187/11

x = 17

Now putting x = 17 in m∠G = (7x - 5)°, m∠H = (3x - 2)°, and m∠I = x°:

m∠G = (7×17 - 5)° = 114°

, m∠H = (3×17  - 2)° = 49°

m∠I =  17°

To learn more about sum of interior angles of a triangle, click on below link:

https://brainly.com/question/18736190

#SPJ1

Answer:

-3

Step-by-step explanation:

Answer:

\( \frac{3}{7} \times \frac{3}{7} = \frac{9}{49 } \)

Answer:

0.67

Step-by-step explanation:

Edge 2021

The probability that Mrs. Barnes does not check homework if the students take a pop quiz will be 0.77. Then the correct option is D.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Mrs. Barnes’s class determined the probability that she will check homework on a randomly chosen day is 0.42.

They also determined the probability that she will give a pop quiz when she checks homework is 0.6, and the probability that she will give a pop quiz when she does not check homework is 0.9.

Then the probability that Mrs. Barnes does not check homework if the students take a pop quiz will be

\(\rm P = 0.42 \times 0.60 + 0.58\times 0.90\\\\P = 0.252 + 0.522\\\\P = 0.774 \approx 0.77\)

More about the probability link is given below.

https://brainly.com/question/795909