A box is 24 inches long, 10 inches wide, and 10 inches deep. About how many cubic feet is the box?

The calculated value of the surface area of the cuboid is 188cm²

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

This means that

Height = 168/24 = 7

Length = 24/4 = 6

The surface area of the cuboid is then calculated as

Area = 2 * (lw + wh + lh)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (4 * 6 + 4 * 7 + 7 * 6)

Evaluate

Area = 188

Hence, the area is 188cm²

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The answer is 2.5, but if you say it isn't then maybe it can be as a fraction  \(\frac{10}{4}\) or \(\frac{5}{2}\).

The slope-point form is:

where (x0,y0) is a point in the line and m is the slope.

A) If the equation is written in slope-point form, we have:

Then, the point is (5,0) and the slope is m=2.

Answer: Point = (5,0)

Slope = 2

B)

Answer: Point (0,-3)

Slope = 5

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

\({ \bf{ \underbrace{Given :}}}\)

Radius of the circle "\(r\)" = 9 in.

\({ \bf{ \underbrace{To\:find:}}}\)

The circumference of the circle.

\({ \bf{ \underbrace{Solution :}}}\)

\(\sf\orange{The\:circumference \:of\:the\:circle\:is\:56.52\:in.}\)

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

We know that,

\(\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }\)

\( = 2 \times 3.14 \times 9 \: in \\ \\ = 56.52 \: in\)

Therefore, the circumference of the circle is 56.52 in.

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}\)

The solution is,  the time of the note in days is 95 days.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

A business owner in England signs a 15% discount note for 30,000 English pounds (£30,000) with a bank in London.

If the proceeds are £28,835.16.

Since it's not mentioned in the problem, it can be safely assumed that the discount rate is 15%.

For this problem, we use the formula:

F = P(1+rn)

where

r is the discount rate

n is the number of days

P is the original amount

so, we get,

£28,835.16 =£30,000(1+0.15*n)

by, solving we get,

n = 94.5

i.e. 95 days

Hence, The solution is,  the time of the note in days is 95 days.

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Step-by-step explanation:

1. By assigning women at random. It would make these 2 groups comparable abc the result from the research or investigation would be more useful and valid. It is very important that there are two comparable groups.

2. A control group is useful in comparing both groups. It would help us to check if there's really an effect or if there is none. If all women were in in art group then all would likely make improvements and there would be no means of verifying this.

Answer:

27n³+125n³ = 152n³

5.337n)(5.337n)(5.337n)

Answer:

Step-by-step explanation: use math-way a chegg service

When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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Answer:

- sinu

Step-by-step explanation:

using the difference identity for sine

sin(a - b) = sinacosb - cosasinb

then

sin(u - π )

= sinucosπ - cosusinπ

= sinu(- 1) - cosu(0)

= - sinu - 0

= - sinu

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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Answer:

Step-by-step explanation:

False. They have one point in common meaning there is only 1 solution.

Answer:

The median Number of touchdowns for team X is less than the median number of touchdowns for team Z

Step-by-step explanation:

The statement, median Number of touchdowns for team X is less than the median number of touchdowns for team Z isn't supported by the boxplot Given :

Median value for Number of touchdowns for team X = 3

Median value for Number of touchdowns for team Z = 2

Since 3 > 2

Then, team X median number of touchdowns is greater than team Z median number of touchdowns.

Answer:3.657            hope this helps

Step-by-step explanation:

The volume of the solid whose base is the semicircle y = √(16 - x²), where -4 < x < 4 and whose cross section perpendicular axis are squares is 256/3 unit³

To obtain the volume of a 3D shape, the cross-section area is discovered and then integrated across a predetermined limit. This technique is known as the cross-sectional method of volume fining. The area of the square base is determined in the given problem, and it is then integrated to determine the overall volume.

To find the volume we will first find the cross-sectional area and then integrate it with respect to x from -4 to 4.

Thus the volume is given as follows:

y = √(16 - x²)

V = ₋₄∫⁴ (√(16 - x²))² dx

V = ₋₄∫⁴ (16 - x²) dx

V = [16x - x³/3]₋₄⁴

V = (64 - 64/3 + 64 -64/3)

V = 256/3 unit³

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The total volume of the composite figure is; 381 m³

The formula for volume of a prism is;

V = Bh

where;

B is area of triangular base

h is height of prism

Thus;

V = (¹/₂ * 3 * 5) * 6

V = 45 m³

Volume of bottom cuboid is given by the formula;

V = Length * width * height

Thus;

V = 16 * 7 * 3

V = 336 m³

Total volume of composite figure = 45 m³ + 336 m³

Total volume of composite figure = 381 m³

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Answer/Step-by-step explanation:

✔️Find EC using Cosine Rule:

EC² = DC² + DE² - 2*DC*DE*cos(D)

EC² = 27² + 14² - 2*27*14*cos(32)

EC² = 925 - 756*cos(32)

EC² = 283.875639

EC = √283.875639

EC = 16.85 cm

✔️Find the area of ∆DCE:

Area = ½*14*27*sin(32)

Area of ∆DCE = 100.15 cm²

✔️Since ∆DCE and ∆ABE are congruent, therefore,

Area of ∆ABE = 100.15 cm²

✔️Find the area of the sector:

Area of sector = 105/360*π*16.85²

Area = 260.16 cm² (nearest tenth)

✔️Therefore,

Area of the logo = 100.15 + 100.15 + 260.16 = 460.46 ≈ 460 cm² (to 2 S.F)

The distance between the fire and station B is 10.7miles

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

The angle at A = 90- 35

= 55°

The angle at B = 90-49

= 41°

Angle at the fire = 180-(41+55)

= 180-96 = 84°

Using sine rule

sin84/13 = sin55/x

xsin84 = 13sin55

0.995x = 10.65

x = 10.65/0.995

x = 10.7 miles

Therefore the distance between the fire and station B is 10.7 miles.

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Answer:

Step-by-step explanation:

10 months=10/12=5/6 years.

Amount=Principal+ Interest

A=P+I

A=P+P×r×t

A=P(1+rt)

18500=P(1+4%×5/6)

18500=P(1+20/600)

18500=P(1+1/30)

18500=P(31/30)

P=18500×30/31≈17903.2258≈17903.23

The mean of a distribution is 217, while the median is 217.The statements is likely to be true about the distribution is  option  D. It is not symmetrical.

The distribution is likely to be asymmetrical if the mean and median have different values. If the mean and median of a distribution are equal, it is likely that the distribution is symmetrical, which means it has equal tail sizes on both sides. However, if the mean and median are not equal, it indicates that the distribution is skewed.

A negatively skewed distribution means that the mean is less than the median, whereas a positively skewed distribution means that the mean is greater than the median.In this case, since the mean and median of the distribution are equal, it is likely to be symmetrical. Since none of the options say "symmetrical," option D, "It is not symmetrical," is the correct answer.

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Answer:

125

Step-by-step explanation:

90+145=235

360-235=125

Answer:

x=35

Step-by-step explanation:

Because with two angles making up one side of a straight line like that, their total will always be 280 degrees, Seein g that one of the angles is 145. 180-145= x or 35

Answer:

For maximum area: Its a square of dimensions 7.25 * 7.25.

Step-by-step explanation:

We can use calculus to solve this:

Let the length of the rectangle be L and the width be W then we have

2L + 2W = 29

L + W = 14.5

W = 14.5 - L

Area = WL

A = L(14.5 - L)

A = 14.5L - L^2

We need this to be a maximum.

Finding the derivative:

dA/dW = 14.5 - 2L = 0   for a maximum

2L = 14.5

L = 7.25

Also W = 14.5 - L

= 14.5 - 7.25 = 7.25.

So the dimensions for maximum area are 7.25 * 7.25.

The  figure is a SQUARE.

The perimeter of a rectangle, is the sum of its side lengths.

The rectangle that has the maximum area when the length is 7.25 and the width is 7.25

The perimeter is given as:

\(\mathbf{P = 29}\)

Let the dimensions be l and w.

So, we have:

\(\mathbf{2( l + w) = 29}\)

Divide both sides by 2

\(\mathbf{l + w = 14.5}\)

Make l the subject

\(\mathbf{l = 14.5 - w}\)

The area of a rectangle is:

\(\mathbf{A = lw}\)

Substitute \(\mathbf{l = 14.5 - w}\)

\(\mathbf{A = (14.5 - w)w}\)

Open brackets

\(\mathbf{A = 14.5w - w^2}\)

Differentiate

\(\mathbf{A' = 14.5 - 2w}\)

Set to 0

\(\mathbf{14.5 - 2w = 0}\)

Collect like terms

\(\mathbf{2w = 14.5}\)

Divide both sides by 2

\(\mathbf{w = 7.25}\)

Recall that: \(\mathbf{l = 14.5 - w}\)

So, we have:

\(\mathbf{l = 14.5 - 7.25 = 7.25}\)

Hence, the rectangle that has the maximum area when the length is 7.25 and the width is 7.25

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Answer: B i think

Step-by-step explanation:

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms.

Answer:

Step-by-step explanation:

(a) Step 1

Distance ran by Finn = 3.2

Distance ran by Jake = 3.9

Total Distance of team A = 7.1

   Step 2

Distance ran by team B = 7.2

Hence team B ran further

(b) Difference in distances ran by team A and B = 7.2 -7.1

                                                                                   = 0.1 km

Hence team B ran 0.1 km more than team A

The value of function which cross the y-axis at point (0, 7) will be;

⇒ y = x + 7

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The point which cross the function = (0, 7)

Now,

Since, The point which cross the function = (0, 7)

Hence, The point must be satisfy the function.

By option (1);

⇒ y = x + 7

Put (x, y) = (0, 7)

⇒ 7 = 0 + 7

⇒ 7 = 7

Thus, The correct function which passes through the point (0, 7) is,

⇒ y = x + 7

Option (i) is true.

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There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.

To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.

Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):

Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.

Therefore, the probability that a randomly selected student scored A or B

in Biostatistics is:

Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.

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The system of equations has one solution.

To check this, we can graph the two equations of the system:

y = (-1/3)x + 7

y = -2x³ + 5x² + x - 2

On the same coordinate axis, and check how many times do the graphs intercept.

The graph can be seen in the image at the end, there you can see that there is only one intecept point. Thus, the system of equations has only one solution.

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Answer:

16

Step-by-step explanation:

3^x +1 = f(X)

2x-4 = g(x)

find f(2)-g(-1)

we substitute in function f(X) by value (2), and in function g(X) by value (-1)

1. 3^x +1 becomes 3^2+1 =9+1=10

2. 2(-1)-4= -2-4=-6

then f(2)-g(-1)

= 10-(-6) =10+6=16

Answer: B

Step-by-step explanation:

The pair of equations that can be used to find x and y are:

x + y = 62

(1.02)x = 7

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here, we have,

The form of the pair of equations would be:

hours worked last week + hours worked this week = total hours worked both weeks equation 1

(1 + percent increase/100) x hours worked last week = hours worked this week equation 2

x + y = 62 equation 1

(1 + 20/100) ×x = y

(1.02)x = 7 equation 2

The two equations can be solved using either of these three methods:

elimination method

substitution method

graph method

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complete question:

Jillian worked 62 hours this week and last week. She worked x hours last week and y hours this week. She worked 20% more hours this week than last week. What pair of equations can be used to find x and y?