Represent the following sentence as an algebraic expression, wher
number" is the letter x. You do not need to simplify.
The product of 8 and the sum of a number and 5.
F

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.

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

From the given table, the equation of C(t) is  - t² + 5. that is option C

The standard form is (x - h)² = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The table represents a quadratic function C(t).

t          C(t)

−2           1

−1           4

0           5

1           4

2            1

From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,

C(t) = a(t - 0)² + 5

C(t) = at² + 5

The equation is passing through the point (1, 4), then we have

4 = a (1²) + 5

4 = a + 5

a = - 1

The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.

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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, ∞)

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:

Step-by-step explanation:

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

Can also be written [-2, +∞)

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

Answer:

c

Step-by-step explanation:

I hope it help :)

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 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 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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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 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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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.

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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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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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:

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:

Step-by-step explanation:

yes it is b

Answer:

A

Step-by-step explanation:

I used desmos to graph the equations and A matches

Using a metric standard of 2 meters, then the area of the red triangle would be 54m². The area of the garden would be; 500m²

Using typical walkway widths to 6 ft, to calculate the area the red triangle to be 486 square feet and the area of the garden to be about 4400 square feet, rounding up.

Then it is a right triangle and side a is the altitude or height of the triangle and side b is the base.  

The measurements of the triangle are approximately in the proportion of 3, 4, 5, a typical "Pythagorean Triple" right triangle.

Estimating from rough measurements of the triangle and the dimensions of the garden as shown, the area of the garden is about 18 times the area of the red triangle.

The area of the triangle is half the area of a rectangle with the same side lengths a & b, therefore, 9 ab is a good estimate of the area of the garden.

Area of the triangle estimate:

A = 36ft × 27ft /2

A = 486 square feet

To estimate 2 meter wide sidewalk, the area of the triangle can be reasonably calculated to be;

A = 9m × 12m /2 = 54 m²

The area of the garden = 9 × 54 = 486m²

Then rounded reasonably to 500m²

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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:

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

If P(A) is 0.64, then P(A') is 0.36. P(A) is probability of occurrence of event A.

This question pertains to Probability principles. Probability is a measure of the possibility of an event occurring. Many occurrences cannot be foreseen with absolute accuracy. We can only anticipate the likelihood of an event occurring using it.

A is an occurrence in this context. A' denotes the event's complement.  

For example, if Event A is getting heads on a coin toss, then Event A' is getting tails.

This demonstrates one thing:

A ∪ A' = U, here U is the universal set.

P ( U) = 1

P (A) + P(A') = 1

0.64 + P (A') = 1

P(A') = 1 - 0.64

P (A') = 0.36

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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 slope of line is 400 and plane A's rate of speed is 400 mi/h

The slope of line is 475 and plane B's rate of speed is 475 mi/h

Therefore, Plane B is flying faster.

For Plane A the equation y = 400x represents the relationship between x, the time that a plane flies in hours, and y, the distance the plane flies in miles.

We know the equation of line is y =mx + c

m = slope of line

So, on comparing slope of line is 400 and plane A's rate of speed is 400 mi/h

For Plane B

We know the formula for slope = (y₂-y1)/(x₂ - x₁)

= (950 - 475)/(2 - 1)

= 475

So, slope of line is 475 and plane B's rate of speed is 475 mi/h

Therefore, Plane B is flying faster.

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Answer:

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

[tex]3n[/tex]

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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