Find the area of a rectangle with side lengths 8/3 feet and 8:5

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\(\textit{Law of Sines} \\\\ \cfrac{a}{\sin(\measuredangle A)}=\cfrac{b}{\sin(\measuredangle B)}=\cfrac{c}{\sin(\measuredangle C)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{h}{\sin(157^o)}=\cfrac{240}{\sin(6^o)}\implies h\sin(6^o)=240\sin(157^o) \\\\\\ h=\cfrac{240\sin(157^o)}{\sin(6^o)}\implies h\approx 897.1~cm\)

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The radius of the spherical ball, correct to one decimal place, is approximately 8.5 cm.

To find the radius of a spherical ball when the volume is given, we can use the formula for the volume of a sphere:

\(Volume = (4/3) * π * r^3\)

Given that the volume of the ball is 5000 cm^3, we can set up the equation as follows:

\(5000 = (4/3) * π * r^3\)

To find the radius, we need to isolate it in the equation. Let's solve for r step by step:

1. Divide both sides of the equation by (4/3) * π to isolate r^3:

 \(r^3 = 5000 / [(4/3) * π]\)

2. Simplify the right side of the equation:

  r^3 = 3750 / π

3. Take the cube root of both sides to solve for r:

  r = (3750 / π)^(1/3)

Using a calculator, we can approximate the value of r:

  r ≈ 8.532

Therefore, the radius of the spherical ball, correct to one decimal place, is approximately 8.5 cm.

It's important to note that the value of π used in the calculation should be accurate to the required level of precision. In this case, we have used the standard value of π (approximately 3.14159).

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Answer:

B) y - 2 = (-1/4)(x - 2)

Step-by-step explanation:

Start with the equation of the given line: y = 4x + 7.

Determine the slope of the given line, which is 4.

Since the perpendicular line has a negative reciprocal slope, the perpendicular line's slope is -1/4.

Use the point-slope form of a linear equation: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.

Substitute the values x₁ = 2 and y₁ = 2 into the point-slope equation: y - 2 = (-1/4)(x - 2).

Simplify by distributing -1/4 to (x - 2): y - 2 = (-1/4)x + 1/2.

Add 2 to both sides to isolate y: y = (-1/4)x + 1/2 + 2.

Simplify further: y = (-1/4)x + 5/2.

The equation in point-slope form for the line passing through (2, 2) and perpendicular to y = 4x + 7 is y - 2 = (-1/4)(x - 2), which matches option B.

Answer:

woah lol

Step-by-step explanation:

I can't tell if this is a question or not

Answer: its a taco

Step-by-step explanation: taco

Answer: neither

Step-by-step explanation:

sandwich is a sandwich, a taco is a taco.

The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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Answer:

c

Step-by-step explanation:

Answer:

30(A)+39(B)

Step-by-step explanation:

Here are the answers to the above questions:

To calculate the locator and percentile, we need to first arrange the scores in ascending order:

6, 8, 11, 12, 14, 17, 20, 34, 36, 38, 47, 48, 49

a) To calculate the locator for the 52nd percentile, we use the following formula:

Lp = (p/100) * (N + 1)

where Lp is the locator for the pth percentile, p is the percentile we are interested in, and N is the total number of scores.

For the 52nd percentile, p = 52 and N = 13. Substituting these values into the formula, we get:

L52 = (52/100) * (13 + 1) = 6.72

Therefore, the locator for the 52nd percentile is 6.72.

b) To determine the 52nd percentile, we need to find the score corresponding to the locator L52. Looking at the ordered list of scores, we see that the score at position 6 is 17 and the score at position 7 is 20. Since the locator L52 falls between positions 6 and 7, we can use linear interpolation to estimate the 52nd percentile:

P52 = (7 - L52) / (7 - 6) * 50 + (L52 - 6) / (7 - 6) * 50

P52 = (7 - 6.72) / (7 - 6) * 50 + (6.72 - 6) / (7 - 6) * 50

P52 = 38 + 0.48 * 50

P52 = 61.4

Therefore, the 52nd percentile is approximately 61.4.

c) To find the percentage of scores that are above the 52nd percentile, we subtract the 52nd percentile from 100:

100 - 52 = 48

Therefore, approximately 48% of the scores in the dataset are above the 52nd percentile.

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Answer: -5x^2 + 2

Step-by-step explanation:

The function has three distinct real zeros.

The correct answer is A.

To determine the statement about the zeros of the graphed function, let's analyze the given information.

We have the following points on the graph:

(0.8, 4), (2, -4), (4.6, 0.5), (6, 0), and (7.5, 8)

Additionally, the function intercepts the x-axis at 1, 4, and 6 units.

To find the zeros of the function, we need to identify the x-values where the function intersects the x-axis.

From the given information, we know that the function intersects the x-axis at 1, 4, and 6 units.

These three x-values correspond to three distinct real zeros of the function.

The correct statement about the zeros of the graphed function is:

The function has three distinct real zeros.

The correct answer is A.

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Answer:

0.443 hours

Step-by-step explanation:

time = total distance / mph

time = 50 / 112.9094

time ≈ 0.443 hours

Answer:

0.443 hours

Explanation:

Given following:

Formula:

\(\sf time \ taken = \dfrac{distance}{speed}\)

Substitute values to find time taken:

\(\sf \rightarrow time = \dfrac{50}{112.9094 }\)

evaluate

\(\sf \rightarrow time = 0.4428329262\)

rounded to nearest thousandth

\(\sf \rightarrow time = 0.443\)

Answer:

C

Step-by-step explanation:

Answer:

48ab+72a/4

Step-by-step explanation:

it is a fraction

So, the spread of the numbers 4, 6, 7, 9, 9 is 5.

Spread can refer to different things depending on the context. Here are a few examples:

In finance, spread refers to the difference between the bid price and the ask price of a security or asset. The bid price is the highest price a buyer is willing to pay for a security, while the ask price is the lowest price a seller is willing to accept. The spread represents the cost of trading that security or asset and is typically measured in basis points (hundredths of a percentage point).

In sports betting, spread refers to the point spread or handicap that is assigned to a team in order to make the betting odds more even. For example, if a football team is favored to win by 7 points, they may be assigned a -7-point spread, meaning they would have to win by more than 7 points for a bet on them to be successful.

In epidemiology, spread refers to the transmission of a disease from one person to another. The spread of a disease can be influenced by a variety of factors, including the infectiousness of the disease, the proximity and frequency of contact between people, and the effectiveness of measures to prevent transmission (such as vaccines or masks).

In cooking, spread can refer to a variety of ingredients that are used to spread on bread or crackers, such as butter, jam, or peanut butter.

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Step-by-step explanation:

2/x^2-1 = 1/ x +1 + 1/ x-1

2/x^2-1 = 1

2=x^2-1

x^2 = 3

x= root 3

100 miles in a day the truck should have to cover so that the rental costs for company A and company B are same

Company A rented a truck for  ​$70 a day and $.5 per mile will be added accordingly. Similarly, Company B rented a truck for  ​$30 a day and $.9 per mile will be added as per distance covered.

Let the number of miles travelled by the truck be x.

Then, we can depict the given information in terms of equation and will equate them further to solve according to the question need.

So, total rent to be pay to company A = ​$(70+0.5x)

and total rent to be pay to company B = ​$(30+0.9x)

Now, the number of miles in a day at which the rental costs for Company A and Company B are the same will be

70+0.5x = 30+0.9x .............(1)

Now, solve equation (1) in order to calculate the value of x.

70-30 = 0.9x-0.5x

40 = 0.4x

40/0.4 = x

400/4 = x

100 = x

∴ x = 100

Hence, 100 miles in a day the truck should have to cover so that the rental costs for company A and company B are same.

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Answer:

1/36 will be ur ans__________

Answer:

? = 36

Step-by-step explanation:

If you count all the options, there are 36 options/number combinations in all.

However, the only combination that would equal 12 is 6,6

This is because 6 + 6 = 12. No other numbers together would equal 12.

The expression |-4| has a value of 4 when evaluated

From the question, we have the following parameters that can be used in our computation:

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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Answer:

Weak negative correlation

Step-by-step explanation:

The scatter plot shown in the graph above indicates a negative correlation between the x-variables and the y-variables, because, as the variables on the x-axis increases, the variables on the y-axis decreases.

Also, the if we are to draw a line of best fit to connect some of the data points on a straight line, we would see that a number of the data points would be far apart from each other away from the line. The data points are not much clustered around the line of best fit, therefore, this shows that the negative correlation between the variables is a weak one.

The data represented on the scatter plot show a weak negative correlation.

Option 2 is the answer.

No. on tickets sold = 6000

Proceedings of the tickets sold = $78,000

Cost of tickets for children = $8

Cost of tickets for adults = $16

Cost of tickets for seniors = $12

2 times more adults were present than the children.

Let the number of children be 'c.'
Let the number of adults be 'a.'
Let the number of seniors be 's.'

Since 2 times more adults were present than the children, we get the equation,

a = 2c

No. of tickets sold will be equal to the total no, of people.

∴ c + a + s = 6000

The proceedings will be equal to the sum of the amounts and number of people who bought tickets with that amount,

∴ 8c + 16a + 12s = $78,000

Thus, we have the three equations,

c + a + s = 6000
8c + 16a + 12s = $78,000
a = 2c

This series of equations are given in option 2 Thus, option 2 is the answer.

Answer) Option 2.

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The depth of the aquarium is approximately 4 feet when rounded to the nearest whole number (since 3.64 is closer to 4 than it is to 3 when rounded to the nearest whole number).

To calculate the depth of the aquarium, we need to use the formula for volume of a rectangular prism,

which is V = lwh where V is the volume, l is the length, w is the width, and h is the height (or depth, in this case).

Given that the aquarium holds 11.35 cubic feet of water, the volume of the aquarium can be represented by V = 11.35 cubic feet.We are also given that the length of the aquarium is 2.6 feet and the width is 1.1 feet.

Substituting these values into the formula for volume,

we get:11.35 = 2.6 × 1.1 × h

Simplifying this expression:

11.35 = 2.86h

Dividing both sides by 2.6 × 1.1,

we get:h ≈ 3.64 feet (rounded to two decimal places)

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Answer:

58

Step-by-step explanation:

Here, we are given rectangle FGHI and we want to find the area.

To do so we must first find the lengths of the sides and then we can calculate the area using the formula "area = length x width"

We can find the lengths of the sides by using the distance formula \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\) where (x1,y1) and (x2,y2) are from the points of the line. To make it easier its best to list the coordinates of the vertices.

Given coordinates of F and I are (3,5) and (8,3)

Defining our variables, we get (x1,y1) = (3,5) and (x2,y2) = (8,3)

This means that x1 = 3 , y1 = 5, x2 = 8 and y2= 3

We now want to plug these values into the formula

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

==> plug in x1 = 3 , y1 = 5, x2 = 8 and y2= 3

\(d=\sqrt{(8-3)^2+(3-5)^2}\)

==> simplify subtraction

\(d=\sqrt{(5)^2+(-2)^2}\)

==> evaluate exponents

\(d=\sqrt{25+4}\)

==> simplify addition

\(d=\sqrt{29}\)

So the side width or smaller side has a length of √29

Given coordinates of I and H are (8,3) and (4,-7)

Defining our variables we get (x1,y1) = (8,3) and (x2,y2) = (4,-7)

This means that x1 = 8, y1 = 3, x2 = 4 and y2 = -7

We now plug in these values into the formula

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

==> plug in x1 = 8, y1 = 3, x2 = 4 and y2 = -7

\(d=\sqrt{(4-8)^2+(-7-3)^2}\)

==> simplify subtraction

\(d=\sqrt{(-4)^2+(-10)^2}\)

==> evaluate exponents

\(d=\sqrt{16+100}\)

==> simplify addition

\(d=\sqrt{116}\)

==> simplify radical

\(d= 2\sqrt{29}\)

So the length of IH is 2√29

Now that we have the lengths of the sides of the rectangle we can find the area of the rectangle.
We know that the area of a rectangle is equivalent to the length multiplied by the width.

Here, we've identified that the length is 2√29 and the width is √29

This means that the area would be :

\(2\sqrt{29} *\sqrt{29}\)

==> simplify using the rule : \(b\sqrt{a}*\sqrt{a}=b\sqrt{a^2} =b(a)\)

2(29)

==> multiply 2 and 29

=58

The area of the rectangle is 58

Answer:

Step-by-step explanation:

To find out how much money Chelsea will earn next week, you need to multiply her hourly wage by the number of hours she plans to work.

First, convert the number of hours to a decimal by dividing the number of minutes by 60. In this case, 20 1/2 hours is equal to 20.5 hours.

Then, multiply Chelsea's hourly wage by the number of hours she plans to work:

14.60 * 20.5 = 297.3

Therefore, Chelsea will earn $297.30 next week.

Answer:

hope this helps

Step-by-step explanation:

To determine its end behavior, look at the leading term of the polynomial function. Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph

Answer:

73.5

Step-by-step explanation:

Answer:

21.3 seconds

Step-by-step explanation:

PLS GIVE BRAINLIEST

Answer:

21.3 seconds

Step-by-step explanation:

600 ft (200 yds x 3) divided by 90 ft (length to a base) would be 6.6666667

6.6666667 times 3.2 equals 21.3

iinm

Answer:

7

Step-by-step explanation:

16/28 = 4/x

16 ÷ 4 = 4

28 ÷ 4 = x

x = 7

Answer:

x = 7 ..................

Answer:

d) 1/12

Step-by-step explanation:

Answer:

x-4+(20)/(x+4)