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Answer:

200 ft²

Step-by-step explanation:

area = 1/2(BH) = 1/2(20)(20) = 200 ft²

Using equivalent decimals, the correct option regarding which lake lost the least amount of water is:

c. Lake Stockton

For a fraction, we have to divide the numerator by the denominator to find the equivalent decimal.

For a percentage, we just have to divide the percentage by 100%.

Hence, for the three lakes, the equivalent amounts are given by:

Lake Jensen: 1/6 = 0.1666

Lake Parlow: 26% = 26/100 = 0.26

Lake Stockton: 33/200 = 0.165

The smallest equivalent decimal is 0.165,

Hence Lake Stockton lost the least amount of water, and option C is correct.

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Answer:

First of all, this is a simple solution to the equation, by simplifying the equation to x greater than or equal to 12, so option A is in line with the meaning of the problem

Answer: The answer is A & D

Step-by-step explanation:

150x + 200 >_ 2000= x >_12

50x + 1400 >_ 2000= x >_ 12

Your Welcome!

Answer:

y = -3/9x + 6

Step-by-step explanation:

slope = -3/9x

y-intercept = 6

Answer:

i dont know just need points

Step-by-step explanation:

Answer:

x = 62°

Step-by-step explanation:

the top-most angle in the top isosceles triangle must be 73° also

the third angle of the top isosceles triangle is (180 - 73 + 73) which is 34°

the left portion of the right angle must be 56°

you can find by using this equation:  x + x + 56 = 180

2x = 124

x = 62

Answer:

6 x 6

Step-by-step explanation:

None of these options are correct, the correct answer should just be 6x6.

A would be 729.

B would be 18.

C would be 216.

D would be 12.

Answer:

B) 60 degree 50 degree 70 degree is the answer

reason:- 60+50+70=180 In the triangle the sum of all rhe angles is 180

Answer:

\(\boxed {x = \frac{10}{c}}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(3(cx - 7) = 9\)

-Divide \(9\) by \(3\):

\(cx - 7 = \frac{9}{3}\)

\(cx - 7 = 3\)

-Add \(7\) to both sides:

\(cx - 7 + 7 = 3 + 7\)

\(cx = 10\)

-Take \(c\) and divide it on both sides:

\(\frac{cx}{c} = \frac{10}{c}\)

\(\boxed {x = \frac{10}{c}}\)

Therefore, the value of \(x\) is \(\frac{10}{c}\).

Answer:

Area of the triangle is 4.8 square meters using heron's formula to find area of triangle.

Step-by-step explanation:

Formula to find area of triangle when three sides were given is

Semi perimeter s =\(\frac{a+b+c}{2}\)

Where 'a' , 'b' and 'c' are side lengths of the triangle.

Area =\(\sqrt{s(s-a)(s-b)(s-c)}\)

Here, let a=2, b=4.8 and c=5.2

So, semi perimeter s=\(\frac{2+4.8+5.2}{2}\)

Simplify it

s=6

Now use area formula to find area of the triangle.

A=\(\sqrt{6(6-2)(6-4.8)(6-5.2)}\)

Simplify it

A=\(\sqrt{6(4)(1.2)(0.8)}\)

A=\(\sqrt{23.04}\)

A=4.8 square meters.

To find the area of a triangle with the given sides a, b and c we use an expression,

Area = \(\sqrt{s(s-a)(s-b)(s-c)}\)

Where, \(s=\frac{a+b+c}{2}\)

By applying this formula area of the given triangle is 4.8 m².

Side lengths of the triangle are 2m, 4.8m and 5.2m

Therefore, \(s=\frac{2+4.8+5.2}{2}\)

\(s=6\)

Now substitute these values in the formula,

Area = \(\sqrt{6(6-2)(6-4.8)(6-5.2)}\)

        = \(\sqrt{6(4)(1.2)(0.8)}\)

        = 4.8 m²

  Therefore, area of the triangle with the given sides is 4.8 m².

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The required coordinate vector of p(t) = -1 + 15t - 6t^2 relative to B is [2, -2, 3].

The basis for P2 as B = {1 - 4t2, 2 - t, 1 + t - t2}.We need to find the coordinate vector of p(t) = -1 + 15t - 6t2 relative to the basis B of P2.Coordinate vector relative to B means expressing p(t) as a linear combination of the basis vectors, and then finding the scalars (coefficients of the linear combination) and arranging them in a column vector.Consider the vector space P2 consisting of all polynomials of degree less than or equal to 2.Let p(t) be an arbitrary element of P2. Then we need to express p(t) as a linear combination of the given basis vectors, i.e.,p(t) = c1(1 - 4t^2) + c2(2 - t) + c3(1 + t - t^2)where c1, c2, and c3 are scalars. Equating the coefficients of the corresponding powers of t, we get-1 = c1 + 2c2 + c315 = -4c1 - c27 = c1 + c2 - c3Therefore, solving the above equations for c1, c2, and c3, we getc1 = 2, c2 = -2, and c3 = 3.Now, the coordinate vector [P]b of p(t) relative to B is given by[P]b = [2, -2, 3]Hence, the required coordinate vector of p(t) = -1 + 15t - 6t^2 relative to B is [2, -2, 3].Answer: [2, -2, 3].

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The probability that the mean weight of the sample of horses would differ from the population mean by less than 7lbs if 41 horses are sampled at random from the stable is 0.3823

In this question, we have been given  the horses in a large stable have a mean weight of 1124lbs, and a standard deviation of 150lbs.

We need to find the probability that the mean weight of the sample of horses would differ from the population mean by less than 7lbs if 41 horses are sampled at random from the stable.

μ = 1124 lbs, σ = 150 lbs, n = 41,

s = 150/(√41)

  = 23.43

pvalue of Z when X = 1124 + 7 = 1131 subtracted by the pvalue of Z when X = 1124 - 7 = 1117

So by the Central Limit Theorem,

Z = (1131 - 1124)/23.43

Z = 0.2987  has a pvalue of 0.7651

for X = 1117,

Z = (1117- 1124)/23.43

Z = -0.2988 has a pvalue of 0.3828

0.7651 -  0.3828 = 0.3823

Therefore, the probability that the mean weight of the sample of horses would differ from the population mean by less than 7lbs if 41 horses are sampled at random from the stable is 0.3823

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The first partial derivatives of z with respect to x and y in the equation x + sin(y + z) = 0 are ∂z/∂x = -1 and ∂z/∂y = -cos(y + z).

To find the first partial derivatives of z with respect to x and y, we need to differentiate the given implicit equation with respect to x and y while treating z as a function of x and y.

Differentiating the equation with respect to x:

∂/∂x (x + sin(y + z)) = 1 + ∂z/∂x

Differentiating the equation with respect to y:

∂/∂y (x + sin(y + z)) = cos(y + z) (1 + ∂z/∂y)

The term ∂z/∂x represents the partial derivative of z with respect to x, and ∂z/∂y represents the partial derivative of z with respect to y.

So, the first partial derivatives of z are:

∂z/∂x = -1

∂z/∂y = -cos(y + z)

These derivatives indicate how the variable z changes with respect to changes in x and y in the given equation x + sin(y + z) = 0. The value of -1 for ∂z/∂x means that for every unit increase in x, z decreases by 1. The value of -cos(y + z) for ∂z/∂y indicates how z changes with respect to changes in y, with the specific relationship determined by the trigonometric function cos(y + z).

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Answer:

B., C., E.

Step-by-step explanation:

A)  78546 - 60015 = 18531

B)  25972 - 5988 = 19984

C)  43568 - 22185 = 21383

D)  24560 - 5000 = 19560

E)  99756 - 45875 = 53881

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

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By finding the roots we can rewrite our quadratic equation as:

3x² + 10x + 8  =  3*(x + 4/3)*(x + 2)

Here we have a quadratic function which is:

3x² + 6x + 4x + 8

To factorize this we need to simplify it first, we can add the two middle terms because these have the same power of x:

3x² + 6x + 4x + 8  = 3x² + 10x + 8

Now we need to find the zeros, to do so we need to solve:

3x² + 10x + 8  = 0

And using the quadratic formula we will get:

\(x = \frac{-10 \pm \sqrt{10^2 - 4*3*8} }{2*3} \\\\x = \frac{-10 \pm 2 }{6}\)

Then the roots are:

x = (-10 - 2)/6 = -2

x = (-10 + 2)/6 = -8/6 = -4/3

Then we can factorize the quadratic as:

3x² + 10x + 8  =  3*(x + 4/3)*(x + 2)

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Answer:

Step-by-step explanation:

Answer: 9 degrees Celsius, 0 degrees Celsius, -4 degrees Celsius, -12 degrees Celsius

Step-by-step explanation:

Greatest is from Highest to lowest so from 9,0-4,-12 is the correct order

The ratio of the surface area of the front of a person to the total surface area of a sphere with a radius of 2 meters is 1/8.

To calculate the ratio of the surface area of the front of a person to the total surface area of a sphere with a radius of 2 meters,

Determine the specific dimensions of the person and assume that they are approximately spherical in shape.

Since no specific measurements are provided, let us make a general estimation.

Assuming that the person is standing upright with their arms at their sides and their front facing forward,

we can approximate their shape as a hemisphere (half of a sphere) with a diameter equal to their shoulder width.

The surface area of a sphere with radius r is given by the formula,

A = 4πr²

The surface area of a hemisphere is half of the surface area of a full sphere:

Area of hemisphere = (1/2) ×  Area of a sphere

Now, let us calculate the surface area of a sphere with a radius of 2 meters.

Surface area of the front of the person's body,

Assuming the person's shoulder width is approximately 50 cm (0.5 meters),

Area of the front

= (1/2) × Area of sphere

= (1/2) × 4πr²

= (1/2) × 4π(1)²

= 2π square meters

Total surface area of a sphere with a radius of 2 meters,

Area of a sphere

= 4πr²

= 4π(2)²

= 16π square meters

Now, calculate the ratio,

Ratio

= Area of a front / Area of a sphere

= (2π) / (16π)

= 1/8

Therefore, ratio of surface area of the front of a person to the total surface area of a sphere is equal to 1/8.

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Therefore, the general solution to the given differential equation is: \(y(t) = c1e^{(-2t/3)} + c2e^t\) where c1 and c2 are arbitrary constants.

To find the general solution to the given differential equation, we can solve the associated characteristic equation. The characteristic equation for the given differential equation is:

\(3r^2 - r - 2 = 0\)

To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring the equation, we have:

(3r + 2)(r - 1) = 0

Setting each factor equal to zero, we get:

3r + 2 = 0 --> r = -2/3

r - 1 = 0 --> r = 1

The roots of the characteristic equation are r = -2/3 and r = 1.

\(y(t) = c1e^{(-2t/3)} + c2e^t\)

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Given:

The equation is

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)

To find:

The solutions of given equation over the interval \([0,2\pi]\).

Solution:

We have,

The equation is

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\dfrac{\sqrt{3}}{2}\)

\(\sin\left(x+\dfrac{7\pi}{2}\right)=-\sin \dfrac{\pi }{3}\)

\(\sin\left(x+\dfrac{7\pi}{2}\right)=\sin (-\dfrac{\pi }{3})\)

If \(\sin x=\sin y\), then \(x=n\pi +(-1)^ny\).

Over the interval \([0,2\pi]\).

\(x+\dfrac{7\pi}{2}=4\pi-\dfrac{\pi }{3}\) and \(x+\dfrac{7\pi}{2}=5\pi+\dfrac{\pi }{3}\)

\(x=\dfrac{11\pi }{3}-\dfrac{7\pi}{2}\) and \(x=\dfrac{16\pi}{3}-\dfrac{7\pi}{2}\)

\(x=\dfrac{22\pi-21\pi }{6}\) and \(x=\dfrac{32\pi-21\pi }{6}\)

\(x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\)

Therefore, the two solutions are tex]x=\dfrac{\pi}{6}\) and \(x=\dfrac{11\pi }{6}\).

Answer:

C. π/6 & 11π/6

Step-by-step explanation:

If you graph the equation ( Sin (x+7π/2)=-√3/2) and look between 0 & 2π, you'll see that the lines intersect the x-axis at π/6 & 11π/6.

Answer:

1. 795, 23

2. 50, she will finish her candy on November 21 so she won't be able to share with her cousins

3. $276, 71 cars

Step-by-step explanation:

1. your equation: y = 35x + 235

plug in 16 to find how many pictures she will have on may 16: y = 35(16) + 235

you get y = 795

for the second part, you know are trying to find how long it will take to get to 1024 pictures, so you know your y, but you don't know your x

your equation: 1024 = 35x + 235

solve to get x = 22.54

this rounds up to 23, so your answer is 23

2. multiply 8 times 4 to get 32

subtract 32 from 82 to fin how many she has left

you get 50

for the second part, divide 82 by 4 to find how many day it will take to finish her candy

you get 20.5

so no, she will not have candy to share with her cousins, and she will finish her candy on November 21

3. for this, you have a negative y intercept since you need to make $24 to start profiting

your equation: y = 6x - 24

plug in 50 to x: y = 6(50) - 24

you get y = 276

so you make $276 with 50 cars

for the second part, plug in 400 to y: 400 = 6x - 24

solve to get x = 70.66

this rounds up to 71, so your answer is 71

a. The absolute change in city employees who ride the bus to work is 2%.

b. The relative change in city employees who ride the bus to work is approximately 11%.

c. The relative change in city employees who ride the bus to work is approximately 11%.

d. The relative change of around 11% indicates an increase in the proportion of city employees riding the bus to work compared to last year.

a. The absolute change in city employees who ride the bus to work can be calculated as the difference between this year's percentage (20%) and last year's percentage (18%):

Absolute change = 20% - 18% = 2%

b. The absolute change of 2% indicates that the number of city employees riding the bus to work has increased by 2 percentage points compared to last year.

c. The relative change in city employees who ride the bus to work can be calculated as the absolute change divided by the previous year's percentage, multiplied by 100:

Relative change = (Absolute change / Previous year's percentage) * 100

Relative change = (2% / 18%) * 100 ≈ 11%

d. The relative change of approximately 11% implies that the proportion of city employees riding the bus to work has increased by around 11% compared to last year.

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Answer: (0,-6)

Step-by-step explanation:

To find the y-intercept, we can rewrite the equation into slope-intercept form.

3x+5y=-30            [subtract both sides by 3x]

5y=-3x-30             [divide both sides by 5]

y=-3/5x-6

Now that the equation is in slope-interceot form, we know that the y-intercept is -6, we know that the answer is (0,-6).

1.The beginning balance should be $4,000

2.The amount to be adjusted is $2554

3.The ending balance of the account after the adjustment $2554

4. Office Supplies Account is $14846

"Information available from the question"

The Office Supplies account started the year with a $4,000 debit balance

The company purchased supplies for $13,400,

The inventory of supplies available at the end of the year totaled $2,554.

Now, According to the question:

1. The beginning balance should be $4,000

2.The adjusted amount is

Opening balance = 4000

Add: New purchases = 13400

Balance after Purchase = 17400

Less: Year end balance = 2554

3. The ending balance is $2,554

4. The adjusting journal entry is

Dr. Supplies Expense Account is 14846

Adjustment in the year = Cr. 14846 (subtracted from the balance)

Office Supplies Account is 14846

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Answer:

25, 22

Step-by-step explanation: MACHINE 1 fills 3 more cartons per minute than MACHINE 2

Answer:

7.2% ...................

Answer:

yes tell me if I am able then sure

They support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. the correct answer is (d) 0.40.

Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data

set.  The mean, median and mode are the three commonly used measures of central tendency.

To calculate the mean, we need to add the total values given in a datasheet and divide the sum by the total number of

values.

The mean, μ, of the sampling distribution of p can be found using the formula

μ = p,

where p is the proportion of adults in the entire population who support the increase.

In this case, 40% of all adults in Ohio support the increase, so p = 0.40.

Therefore, the mean of the sampling distribution of p is:

μ = 0.40

So the correct answer is (d) 0.40.

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