What is the surface area of the given figure?

The number of students earning master’s degrees in mathematics or statistics in the country in 2009 was 4474.

We are given that;

g(x) = 7x² -226x + 4941

Now,

To find the number of students in 2009, we need to plug in x = 9 into the function g(x), since 2009 is 9 years after 2000.

g(9) = 7(9)² -226(9) + 4941

g(9) = 7(81) -2034 + 4941

g(9) = 567 -2034 + 4941

g(9) = 4474

Therefore, according to the function g(x) the answer will be 4474.

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Answer:

8.54

Step-by-step explanation:

√(6-9)²+(10-2)2

=√(-3)²+8²

=√9+64

=√73=8.54

The answer is 8.54

Answer: The area of the floor of the hall is approximately 599.2448 square meters.

Step-by-step explanation: Let's assume the breadth of the hall be x meters. Then, the length of the hall will be 2x meters and the height will be 3x meters.

The volume of the hall can be found as follows:

Volume = Length × Breadth × Height

36000 = 2x × x × 3x

36000 = 6x³

x³ = 6000

x = ∛6000 ≈ 17.32 meters

Therefore, the breadth is approximately 17.32 meters, the length is 2 × 17.32 = 34.64 meters, and the height is 3 × 17.32 = 51.96 meters.

The area of the floor can be found by multiplying the length and breadth:

Area = Length × Breadth

Area = 34.64 × 17.32

Area = 599.2448 m²

Therefore, the area of the floor of the hall is approximately 599.2448 square meters.

The value of cos 2θ is determined as 0.442.

The value of cos 2θ is calculated by applying the following trig identities.

sin θ = 28/53

The value of θ is calculated as;

θ = sin ⁻¹ (28/53)

θ = 31.89⁰

The value of cos 2θ is calculated as follows;

cos 2θ = cos (2 x 31.89)

cos 2θ = cos (63.78)

cos (63.78) = 0.442

Thus, the value of cos 2θ is determined by first calculating the value of θ based on the sine function given.

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Answer:

c

Step-by-step explanation:

I hope it help :)

Therefore, using simple division, the price of one pen is calculated to be around $0.27.

In mathematics, division is the process of dividing an integer into equal pieces or groups. It performs multiplication in the other direction. To obtain the quotient or outcome in division, an even number has been divided by another integer, known as the divisor.

We must divide the total expense of the 12-pen pack by the quantity of pens in the box in order to figure out the price of one pen:

Price of one pen is equal to the sum of the pack's pen costs divided by the number of markers in the pack.

In this instance, we may substitute these values as we are aware that the set of 12 pens costs $3.25.

In this instance, we may enter the following values into the calculation as we are aware that the set of 12 markers costs $3.25:

One pen costs $3.25 divided by 12

Long division or using a calculator, we obtain:

One pen costs $0.27.

Consequently, the price of a pen is roughly $0.27.

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Answer:

A

Step-by-step explanation:

I used desmos to graph the equations and A matches

Answer:

Step-by-step explanation:

yes it is b

The metallurgist needs to use 16.714 pounds of the alloy containing 34% aluminum and 28.286 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.

Let x: the number of pounds of the alloy containing 34% aluminum that the metallurgist needs to use,

Let y: be the number of pounds of the alloy containing 69% aluminum.

We want to find values for x and y such that when they are mixed together, they will produce 45 pounds of an alloy containing 56% aluminum.

To solve for x and y, lets set up a system of two equations

x + y = 45 (total weight of the final alloy)....eqn 1

0.34x + 0.69y = 0.56(45) (total amount of aluminum in the final alloy)....eqn 2

Simplifying Eqn 2, we get:

0.34x + 0.69y = 25.2

Now we can solve the system of equations by substitution method

Solve Equation 1 for x in terms of y:

x = 45 - y

Substitute x = 45 - y into Equation 2:

0.34(45 - y) + 0.69y = 25.2

Distribute the 0.34:

15.3 - 0.34y + 0.69y = 25.2

Combine like terms:

0.35y = 9.9

Solve for y:

y = 28.2857... (rounded to 3 d.p)

Now we can use this value of y to find x:

x = 45 - y

x = 16.7142... (rounded to 3 decimal places)

Therefore, the metallurgist needs to use approximately 16.714 pounds of the alloy containing 34% aluminum and 28.286 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.

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The radian measure that is equivalent to 300° is equal to 5π/3. So, correct option is D.

To convert degrees to radians, we use the conversion factor of π/180, which means that one degree is equal to π/180 radians. Therefore, to convert 300° to radians, we multiply 300 by π/180:

300° * π/180 = 5π/3

To understand this conversion, we need to remember that radians are a unit of measurement for angles, just like degrees. However, while degrees divide a circle into 360 equal parts, radians divide a circle into 2π equal parts. One full rotation is equal to 2π radians, which is also equal to 360°.

Since 5π/3 radians is less than one full rotation, it represents an angle that is less than 360°. In fact, 5π/3 radians is equivalent to 300°, which is a well-known angle used in many contexts, such as in geometry, trigonometry, and physics.

In summary, to convert 300° to radians, we multiply it by the conversion factor π/180, which gives us the equivalent angle measure of 5π/3 radians.

So, correct option is D.

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The 10th term of the sequence is 7,257,600. Option D.

To find the 10th term in the sequence, we can use the pattern to generate the next terms:

The first term is 2.

Therefore, to get the 10th term, we can multiply the fifth term by 6, then by 7, then by 8, and then by 9:

Therefore, the 10th term in the sequence is 7,257,600.

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Answer:

[tex]\text{Annual interest rate = 14 \%}[/tex]

Step-by-step explanation:

The formula for computing accrued amount(principal + interest) is given by

[tex]A = P\left (1 + \dfrac{r}{n}\right )^{nt}[/tex]

where

P =principal amount
r = annual interest rate as a decimal
n = number of times compounded per year
t = number of years
A = amount accrued at the end of t years

We are given
A = 62702.95
P = 4000
n = 4 since we are compounding quarterly, i.e. 4 times a year
t = 20

Plugging in known values into the equation we get
[tex]62702.95 = 4000\left(1 +\dfrac{r}{4}\right)^{4 \cdot 20}\\\\62702.95 = 4000\left(1 +\dfrac{r}{4}\right)^{80}\\\\[/tex]

Switch sides and divide both sides by 4000 to get
[tex]\left(1 +\dfrac{r}{4}\right)^{80} = \dfrac{62702.95}{4000}[/tex]

[tex]1 +\dfrac{r}{4}\right) = \left(\dfrac {62,702.95}{4000}\right)^{\dfrac{1}{80}}\\\\\text{Using a calculator,}\\1 +\dfrac{r}{4}\right) = 1.03499\dots \approx 1.035[/tex]

[tex]\dfrac{r}{4} = 1.035 - 1 = 0.035\\\\r = 4 \times 0.035\\\\\\r = 0.14\\\\\\[/tex]

As a percentage that would be

[tex]0.14 \times 100 = 14\%[/tex]

The area of the shaded region of the given figure would be = 47.1.

To calculate the area of the shaded figure, the formula of the area of a sector of a circle is used such as;

area of sector = ∅/360πr²

∅ = 40°

r = 12

area = 40/360 × 3.14× 12×12

= 18086.4/360

= 50.24

Area of the unshaded portion

radius = 12-9 = 3

area = 40/360×3.14×3×3

= 1130.4/360

= 3.14

Therefore area of the shaded portion;

= 50.24- 3.14

= 47.1

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The equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9) is y=5x+26.

Given that, the equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9).

The given equation can be written as y=5x-4.

Now, compare y=5x-4 with y=mx+c, we m=5

The slope of a line parallel to given line is m1=m2

So, the slope of the line parallel to the given line is 5.

Now, substitute m=5 and (x, y)=(-7, -9) in y=mx+c, we get

-9=5(-7)+c

c=-9+35

c=26

So, the equation is y=5x+26

Therefore, the equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9) is y=5x+26.

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Since the calculated F-value of 7.098 is greater than the critical value of 5.79, we reject the null hypothesis and conclude that the population variance of total sales during active price competition is higher than during duopoly and tacit collusion at the 5% level of significance.

For the above issue, the null and alternate hypotheses are as follows:

The population variations of total sales under duopoly, active price competition, and tacit cooperation are all identical.

In contrast to duopoly and implicit collusion, total sales population variance is larger under active price competition.

To test the null  hypothesis, we must use a two-tailed F- test with a 5 % threshold of significance. The ratio of the sample variances is used to determine the F- statistic.

F = s1² / s2²

Where:
s1² - Sample Variance (Active price competition)

s2² -  SAmple variance (Duopoy and Tacit collusion)


Since n1-1 = 3
and n2-1 = 6

F = 114.09 / 16.08
F = 7.098

Having derived same, we know that the critical values of F for a two-tailed test with 3 and 6 degrees of freedom at 5% level of significance are:

Critical Value (3) = 5.14
Critical Value (6) = 5.79

Therefore, since the F-value > Critical Value in both cases, we must reject the null hypothesis.

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Answer:

[2, ∞)

Step-by-step explanation:

We Know

The solution set to x ≥ 2, meaning the 2 ≤ x < ∞

So, the interval notation is [2, ∞)

Answer:

The product of 3 and a number can be represented as:

[tex]3n[/tex]

Step-by-step explanation:

We know that the vertex of the parabola is at the origin, so the equation must have the form:

y = a x^2

where a is a constant.

We also know that the directrix is y = -1.5, which means that the focus is located at (0, 1.5).

Using the formula for the distance between a point (x, y) and a line ax + by + c = 0, which is given by:

d = |ax + by + c| / sqrt(a^2 + b^2)

we can find the value of a. The distance from the vertex (0, 0) to the directrix y = -1.5 is equal to the distance from the vertex to the focus (0, 1.5), so we have:

d = |y - (-1.5)| / sqrt(1^2 + 0^2) = sqrt(x^2 + (y - 1.5)^2) / sqrt(0^2 + 1^2)

Simplifying this equation, we get:

sqrt(x^2 + (y - 1.5)^2) = |y + 1.5|

Squaring both sides, we get:

x^2 + (y - 1.5)^2 = (y + 1.5)^2

Expanding and simplifying, we get:

x^2 = 3y

So the equation of the parabola with vertex at the origin and directrix y = -1.5 is:

y = (1/3)x^2

Therefore, the correct answer is: y = (1/3)x^2.

Answer:

mark me brilliant

Step-by-step explanation:

To calculate Michelle’s monthly credit card payment, we need to find the total amount she owes and then divide it by the number of months she has to pay it off.

First, we need to find the total balance on Michelle’s credit cards:

$4,380 + $1,365 + $2,480 + $5,000 = $13,225

Next, we need to find the weighted average interest rate of her credit cards. To do this, we multiply each balance by its corresponding APR and add up the results. Then we divide by the total balance:

($4,380 x 0.17) + ($1,365 x 0.19) + ($2,480 x 0.23) + ($5,000 x 0.15) = $1,038.55

$1,038.55 ÷ $13,225 = 0.0785, or 7.85%

Now we can use the total balance and the weighted average interest rate to calculate Michelle’s monthly payment using the formula for a fixed payment on a loan:

P = (r(PV)) / (1 - (1 + r)^-n)

Where:

P = monthly payment

r = monthly interest rate (as a decimal)

PV = present value of the loan

n = number of payments

r = 0.16 ÷ 12 = 0.01333 (monthly interest rate)

PV = $13,225

n = 36

P = (0.01333(13,225)) / (1 - (1 + 0.01333)^-36) = $367.36

Therefore, Michelle’s monthly credit card payment would be $367.36 if she consolidated all of her credit card debt into a single credit card with an interest rate of 16% and paid it off in 36 months. The answer is (a) $367.36.

Answer:

x = 13 is the solution.

Step-by-step explanation:

Here is how it looks for this problem:

(-3)* = (-3) 13 Ignore the base and write an equation for the exponents: x = 13 Solve for x by subtracting 13 from both sides: x - 13 = 0 Add 13 to both sides: x = 13 Check your work by plugging x = 13 into the original equation: (-3)* = (-3) 13 (-3) 13 = (-3) 13 True

Answer:

-2 11/12

Step-by-step explanation:

-2 1/3 x 5/4

-7/3 x 5/4 = -35/ 12

-35/-12= -2 11/12

Matt ate 1/6 of the bag of peanut

Matt had 4/6 bag of peanut

He ate a quarter of what was in the bag

The amount of peanut he ate can be calculated as follows

= 4/6 × 1/4

= 4/24

= 1/6

Hence Matt ate 1/6 of the bag of peanut

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The scale factor of the given images above is as follows:

1.) 5/3

2.) 7/10

3.) 7/3

4.) 3/2

For image 1.), the image was scaled down.

scale factor = original image dimensions/scale drawing

= 1.25/0.75

proportional set up = 125/75 = 5/3

For image 2.) the image was scaled up.

scale factor = Bigger dimensions/smaller dimensions

= 3.5/2

proportional set up = 35/20 = 7/10

For image 3.) the image was scaled down.

scale factor = original image dimensions/scale drawing

= 1.75/0.75

proportional set up = 175/75 = 7/3

For image 4.) the image was scaled up.

scale factor = Bigger dimensions/smaller dimensions

= 6/4 = 3/2

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The expression of the perimeter of the triangle is  15h - 6k + 12m.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

The perimeter of a triangle is the sum of the whole three sides of the triangle.

Therefore, let's find the perimeter of the triangle with side length (5h - 4k), (10h + 7m) and  (5m - 2k).

Therefore,

perimeter of a triangle = 5h - 4k + 10h + 7m + 5m - 2k

collect like terms

perimeter of a triangle = 5h + 10h - 4k - 2k + 7m + 5m

Therefore,

perimeter of a triangle = 15h - 6k + 12m

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False. The initial value is 0 gallons every 2 hours because the pool already has 150 gallons of water in it.

Answer:

Step-by-step explanation:

When x≥2 the function is increasing.  you read the graph from left to right

Can also be written [-2, +∞)

Answer:

The Answer may be D

Step-by-step explanation:

The answer is D because it's an one step equation. For something to be linear it must be one step.

The slope of the line that represents the relationship is 0.76.

Slope in mathematics relates to how steep a line is. It measures how much the y-coordinate shifts upward or downward for every unit increment in the x-coordinate. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line is, in other words, the slope of the line.

The following equation can be used to determine a line's slope: slope = (y2 - y1) / (x2 - x1).

where any two points on the line (x1, y1) and (x2, y2).

Positive, negative, zero, or undefinable slopes are all possible. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.

The slope of the line is given by the formula:

slope = (change in y) / (change in x)

Substituting the point from the table we have (0, 0) , (1.3, 1) thus:

m = 1 - 0 / 1.3 - 0

m = 1 / 1.3 = 0.76

Now, using the slope intercept form we have:

y - y1 = m(x - x1)

For (0, 0) we have:

y = 0.76x

Hence, the slope of the line that represents the relationship is 0.76.

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The complete question is: