What is the volume of a spherical boulder is 10 ft in diameter and weighs almost 6 tons?

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[tex]\textit{Law of sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JN}{\sin(65^o)}\implies \cfrac{39\sin(65^o)}{\sin(53^o)}=JN\implies 44.3\approx JN \\\\\\ \cfrac{39}{\sin(53^o)}=\cfrac{JS}{\sin(62^o)}\implies \cfrac{39\sin(62^o)}{\sin(53^o)}=JS\implies 43.1\approx JS[/tex]

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Jerimiah's finger is longer. A number line can be drawn from 0 to 8 inches with 2 inches marked for Alex's finger and 7/4 inches marked for Jerimiah's finger. Since 7/4 is greater than 2, Jerimiah's finger is longer.

To prove that Jerimiah's finger is longer than Alex's, we can use a number line. On this number line, we start with 0 inches at one end and 8 inches at the other. We mark 2 inches for Alex's finger and 7/4 inches for Jerimiah's finger. Since 7/4 inches is greater than 2 inches, Jerimiah's finger is longer than Alex's. To further prove this, we can convert the fraction 7/4 into a decimal. 7/4 = 1.75, which is greater than 2. Therefore, Jerimiah's finger is longer than Alex's.

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The rectangular sidewalk for Liam to build the pathway, [tex]36[/tex] stones are required.

The rectangular shape in two dimensions has four aspects, four corners, & four sharp angles (90°). Equal and equal opposing sides make form a rectangle. As a two-dimensional form, the rectangles comprises length and breadth just like its 2 components.

Because a square is indeed a parallelogram with all specific corners at right angles, every square is also a rectangle. To be a square, a rectangle's sides must all have the same length, hence not all rectangles are squares.

Area of the walkway [tex]=length * width[/tex]

[tex]24*6=144[/tex] square feet

Area of each stone [tex]= length of each side * width of each side[/tex]

[tex]=2ft*2ft=4[/tex] square feet

Number of stones needed [tex]=\frac{Area of walkway }{Area of each stone}[/tex]

Number of stones needed [tex]=\frac{144}{4}=36[/tex] stones

Therefore, Liam will need [tex]36[/tex] stones to make the walkway.

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The value of the required number is - 10  

To find the unknown number represent the number with a variable 'x' and form a linear equation according to the condition given in the problem.

Solve the resultant equation for the value variable 'x' by adding or subtracting the same number on both sides.

Here we have

A number decreased by 16 and the result was -26.

Let 'x' be the number

According to the given data,

=> x - 16 = - 26

Add 16 on both sides

=> x - 16 + 16 = - 26 + 16

=> x = - 10

Hence,

The value of the required number is - 10  

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The 90% confidence interval for the difference in mean response times between the cell phone and control group is given as follows:

(12.6, 82.2).

The estimate of the differences is given as follows:

585.3 - 537.9 = 47.4.

The standard error for the distribution of each sample is given as follows:

Hence the standard error for the distribution of differences is given as follows:

sqrt(16.4² + 12.8²) = 20.8.

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 27 + 27 - 2 = 52 df, is t = 1.6747.

The lower bound of the interval is given as follows:

47.4 - 1.6747 x 20.8 = 12.6.

The upper bound of the interval is of:

47.4 + 1.6747 x 20.8 = 82.2.

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The area under the curve of the given function from x=1 to x=5 is -64.17.

The area under a curve is the area between the curve and the x-axis in a certain range. To calculate the area under a curve, we will use the definite integral of the function. The definite integral of a function f(x) from x=a to x=b is defined as

[tex]∫baf(x)dx[/tex]

For the given function f(x) = x^3 - 5x^2 + 2x + 8, the definite integral from x=1 to x=5 is

[tex]∫51(x^3 - 5x^2 + 2x + 8)dx = [x^4/4 - 5x^3/3 + x^2 - 8x]5[/tex]

Substituting x=1 and x=5 gives

[54 - 5(125)/3 + 25 - 8(5)] = -64.17

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Answer: We can simplify 27 as 3^3 and 9 as 3^2. Then, we have:

27^2/9^4 = (3^3)^2/(3^2)^4

Using the power of a power rule, we can simplify:

= 3^(3x2)/(3^2x4)

= 3^6/3^8

Using the quotient rule, we can subtract the exponents:

= 3^(6-8)

= 3^-2

Therefore, 27^2/9^4 can be expressed as 3^-2 in terms of a power of 3.

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By answering the above question, we may state that expressions  Researcher A: Value Frequency 3  2 4  1

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Researcher A:

Value Frequency

3                 2

4                 1

8                  1

10               2

12              1

13                1

14               2

16                 2

17               2

19                 1

21                 1

22               2

24                2

25               2

26                   2

27             2

29               3

31                 2

32                    1

33                  2

34                    2

35                   1

37                   1

40                 1

44                 2

47                   1

Researcher B:

Value Frequency

3                 2

4                 1

6                      1

8               2

13              1

14               3

16             2

17                 1

18                  2

21                 3

22                 2

23              2

24              2

25              2

26            1

28                  1

29                 2

31              2

33                2

34               1

35                   1

41                2

42             1

44                   1

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Answer:

If Benny makes $20 an hour babysitting, his 35% increase would be:

35% of $20 = 0.35 x $20 = $7

This means that Benny could make an extra $7 per hour if he babysits an extra kid. Therefore, his new hourly wage would be:

$20 + $7 = $27

So, if Benny babysits an extra kid, he could make $27 per hour.

Step-by-step explanation:

The Half-Life of the material is 13.86 hours. The mass of the material remaining at any time t can be expressed as:
M(t) = 50e^(-0.05t), where t is measured in hours.

The amount of time needed for a number (of material) to decrease to half of its original value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long steady atoms last.

The mass of the material after 4 hours is M(4) = 50e^(-0.2) ≈ 31.4 grams. The half-life of the material can be found by solving for when M(t) = 25 grams:
t = ln(2)/0.05 ≈ 13.86 hours.

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Based on the information provided, the true sentences are that route B has a more consistent number of rides (B), and the typical number of riders is greater on route A (D).

To begin, these whisker plots compare the number of riders in two routes. In this context, the graph shows the median for route A is 40 and for the route, B is 35, which means the "typical number of riders is greater on route" (option D). Besides this, it can be observed that the number of riders varies more for route A than for route B, which makes B to be true.

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As a result, the answer to the following question, When we round to the area nearest hundredth, we get: 42.84 square units in total.

An area is the size of a surface area. The surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a planar region or planar region refers to the area of a form or flat layer. The area of an item is the entire amount of space occupied by its planar (2-D) surface or form. Using a pencil, draw a square on a sheet of paper. A two-dimensional character. The area of a form on paper is the amount of space it occupies. Assume that the square is made up of smaller unit squares.  

The formula for a sector's area is:

Sector area = (central angle/360) x pi x radius2

When we plug in the values we know, we get:

Sector area = (60/360) x 3.14 x 62

Sector area = 18.84 square units

Triangle area = (base x height)/2

When we plug in the values we know, we get:

Triangle area = (8 x 6)/2 Triangle area = 24 square units

Total area Equals sector area + triangle area

18.84 + 24 = total area

42.84 square units in total

When we round to the nearest hundredth, we get:

42.84 square units in total.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\pounds 2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 2000\left(1+\frac{0.03}{1}\right)^{1\cdot 2}\implies A=2000(1.03)^2 \implies A = 2121.8[/tex]

As per the given distance, the angle that is made by the ramp with the ground is 19.1 degrees

Let's call the angle we're trying to find theta (θ). We can use the tangent function to calculate θ, as follows:

tan(θ) = opposite / adjacent

We know the opposite side (height of the ramp) is 3.5ft, and the adjacent side (distance along the ground) is 10ft. Plugging these values into the tangent equation, we get:

tan(θ) = 3.5 / 10

We can solve for θ by taking the inverse tangent (also known as arctan) of both sides:

θ = arctan(3.5 / 10)

Using a calculator, we find that θ is approximately 19.1 degrees. Therefore, the ramp makes an angle of 19.1 degrees with the ground.

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Answer:

105° is the largest angle

Step-by-step explanation:

All angles add up to 180°

Find the value of x

105 + 6x + 17 + 5x + 14 = 180

Combine like terms

136 + 11x =180

Isolate the x ( subtract 136 from both sides)

11x = 44

Divide both sides by 11

x = 4

Now substitute the value of x into each expression to find the largest angle

5(4) + 14 = 20 + 14 = 34°

6(4) + 17 = 24 + 17 = 41°

105 > 41 > 34

The end behavior of a polynomial function is to decrease without bound as x approaches negative infinity, and to increase without bound as x approaches positive infinity.

If the degree of a polynomial function is odd and the leading coefficient is negative, then the end behavior of the function is as follows:

As x approaches negative infinity, the value of the function decreases without bound.

As x approaches positive infinity, the value of the function increases without bound.

To understand why this is the case, consider a polynomial function of the form:

f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0

where n is odd and a_n < 0.

As x approaches negative infinity, the dominant term in the polynomial is a_n x^n, and since n is odd and a_n is negative, the value of the dominant term approaches negative infinity as x approaches negative infinity.

Similarly, as x approaches positive infinity, the dominant term in the polynomial is again a_n x^n, but this time the value of the dominant term approaches negative infinity as x approaches positive infinity.

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The formula that expresses the fact that f(x, y) is a distance 8 from the origin can be found using the distance formula for two points on the coordinate plane, (0, 0) and (x, y).

The distance formula is given by d = √(x2−x1)2+(y2−y1)2where (x1, y1) = (0, 0) and d = 8. Thus, we have8 = √(x2−0)2+(y2−0)2Squaring both sides gives8^2 = (x2−0)2+(y2−0)2which simplifies to64 = x2+y2

Therefore, the formula that expresses the fact that f(x, y) is a distance 8 from the origin isx2+y2= 64.

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we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.

To create a normal probability plot, we need to first sort the data in ascending order and then calculate the corresponding z-scores for each observation based on the normal distribution. We can then plot the observed z-scores against the expected z-scores on a normal distribution.

Here is the sorted data:

5.04  5.08  6.09  7.55  8.04  8.32  8.51  9.34  9.7   9.74  

10.49 10.94 11.2   11.68 12.39 12.9   14.05 14.64 28.34

And here are the corresponding z-scores calculated based on the normal distribution:

diff

-1.77 -1.74 -1.53 -1.17 -1.04 -0.96 -0.90 -0.72 -0.67 -0.65

-0.41 -0.29 -0.24 -0.17 0.06  0.21  0.48  0.65  3.09

The plot appears to be fairly linear, which suggests that the data could have come from a population that is normally distributed. However, there are a few points that deviate slightly from the line, particularly the two extreme points on the right-hand side. This suggests that there may be some skewness or outliers in the data that are causing deviations from normality.

Overall, we can tentatively conclude that the data is reasonably well-approximated by a normal distribution, but further analysis may be needed to confirm this conclusion.

the complete question is :

"The following data represent a random sample of the number of shares of a pharmaceutical​ company's stock traded for 20 days in 2000. Use a normal probability plot to assess whether the sample data could have come from a population that is normally distributed.

4.78 9.7 11.2 8.32 14.64

6.09 10.49 9.74 12.9 14.05

5.04 9.34 12.39 7.55 28.34

8.51 10.94 5.08 8.04 11.68

Please create a normal probability plot and interpret your findings."

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The statements that are cοrrect based οn unit cοnversiοn is -

A - One milliliter is 100 times smaller than οne liter.

C - Milliliters are smaller units than liters.

D - One liter is 1,000 times larger than οne milliliter.

Unit cοnversiοn is a prοcess with multiple steps that invοlves multiplicatiοn οr divisiοn by a numerical factοr οr, particularly a cοnversiοn factοr. The prοcess may alsο require selectiοn οf the cοrrect number οf significant digits, and rοunding.

On the basis οf unit cοnversiοn methοds -

These three statements are true -

One milliliter is 100 times smaller than οne liter.

Milliliters are smaller units than liters.

One liter is 1,000 times larger than οne milliliter.

The οther statements are incοrrect -

Liters are nοt smaller units than milliliters.

One milliliter cannοt be 100 times larger than οne liter, as it is a smaller unit οf vοlume.

One liter cannοt be 1,000 times smaller than οne milliliter, as it is a larger unit οf vοlume.

Therefοre, the statements A, C and D are cοrrect.

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Which statements about liquid volume are true?

Select each correct answer.

One milliliter is 100 times smaller than one liter.

Liters are smaller units than milliliters.

Milliliters are smaller units than liters.

One liter is 1,000 times larger than one milliliter.

One milliliter is 100 times larger than one liter.

One liter is 1,000 times smaller than one milliliter.

The interval of the expression x ≤ 3 and x ≥ -3 is (-3, 3).

To graph a linear equation with one variable, first solve the problem, then find the answer on the axis (number line), and place a point there. We have seen that graphs often provide information that the original equation would not have shown. The graphs of one-variable linear equations do not provide much, if any, information, but they provide as a basis for graphs with greater dimensions.

The given inequality is x ≤ 3 and x ≥ -3.

Since, the signs are less than and equal to and more than and equal to we use solid dots to represent the number 3 and -3 on the number line.

Also, the expression requires all the numbers between 3 and -3. Thus, the interval is:

(-3, 3).

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Answer:

x = 4

Step-by-step explanation:

- 6 + [tex]\frac{x}{4}[/tex] = - 5 ( add 6 to both sides )

[tex]\frac{x}{4}[/tex] = 1 ( multiply both sides by 4 to clear the function )

x = 4

Method 1: Factoring

m^2 + 7m + 10

We need to find two numbers that multiply to 10 and add up to 7. These numbers are 2 and 5.

m^2 + 2m + 5m + 10

(m + 2)(m + 5)

n^2 + 9n + 18

We need to find two numbers that multiply to 18 and add up to 9. These numbers are 3 and 6.

n^2 + 3n + 6n + 18

(n + 3)(n + 6)

p^2 - 6p + 8

We need to find two numbers that multiply to 8 and add up to -6. There are no such numbers, so we cannot factor this quadratic.

Method 2: Quadratic Formula

m^2 + 7m + 10

a = 1, b = 7, c = 10

m = (-b ± sqrt(b^2 - 4ac)) / 2a

m = (-7 ± sqrt(7^2 - 4(1)(10))) / 2(1)

m = (-7 ± sqrt(9)) / 2

m = -5 or -2

n^2 + 9n + 18

a = 1, b = 9, c = 18

n = (-b ± sqrt(b^2 - 4ac)) / 2a

n = (-9 ± sqrt(9^2 - 4(1)(18))) / 2(1)

n = (-9 ± sqrt(9)) / 2

n = -3 or -6

p^2 - 6p + 8

a = 1, b = -6, c = 8

p = (-b ± sqrt(b^2 - 4ac)) / 2a

p = (6 ± sqrt(6^2 - 4(1)(8))) / 2(1)

p = (6 ± sqrt(16)) / 2

p = 2 or 4

Therefore, the solutions to the quadratics are:

m^2 + 7m + 10 = (m + 2)(m + 5) or m = -5 or -2

n^2 + 9n + 18 = (n + 3)(n + 6) or n = -3 or -6

p^2 - 6p + 8 = (p - 2)(p - 4) or p = 2 or 4

The standard deviation of her total weekly pay is approximately $262.25 and the mean is $1075

Let X be the number of cars the salesperson sells in a week. Then, X follows a normal distribution with mean μ = 3.1 and standard deviation σ = 1.1.

The total weekly pay Y is given by the equation:

Y = $300 + $250X

Using the properties of means and variances of linear combinations of random variables, we can find the mean and standard deviation of Y as follows:

Mean of Y:

E(Y) = E($300 + $250X) = $300 + $250E(X) = $300 + $250(3.1) = $1075

Therefore, the mean of her total weekly pay is $1075.

Standard deviation of Y:

Var(Y) = Var($250X) = $250^2Var(X) = $250^2(1.1^2) = $68,750

Since the standard deviation is the square root of the variance, we have:

SD(Y) = sqrt($68,750) ≈ $262.25

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Nikki applied to 3x colleges.

To determine the number of colleges Nikki applied to, we need to multiply the number of colleges Diego applied to by 3. Hence, the answer is represented by the mathematical expression 3x.

In this problem, 'x' represents the number of colleges Diego applied to. Nikki, on the other hand, applied to 3 times as many colleges as Diego did.

So, to find out the total number of colleges Nikki applied to, we multiply the number of colleges Diego applied to ('x') by 3.

Hence, the correct mathematical expression for the number of colleges Nikki applied to would be 3x.

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Answer:

Step-by-step explanation:

wheres the table

Answer:

Triangular base

Step-by-step explanation:

It possesses all attributes except from triangular base

Answer: For each increase in budget by $1 million, the predicted score increases by 0.145 points.

Answer:

See below.

Step-by-step explanation:

Please check the assumptions.  I did not see a graph, so made assumptions in the calculations,

Given that for 10 guests, the total cost is $20, we can calculate a rate of $2/guest ( the unit rate).  This seems too inexpensive, even for a hot dog and soft drink.  But going on that, we can establish the relationship between x (the number of guests) and y (the total cost) as y = ($2/guest)*x.

The list of numbers does not provide a clear undertanding of what is being requested,  The attached spreadheet calculates a number of guest options based on a rate of $2/guest.  The area in green are the second list of values based on the numbers of guests.

Answer: The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.

For the first rectangular prism, we have:

V1 = 5 x 7 x 1 = 35 cubic inches

For the second rectangular prism, we have:

V2 = 9 x 7 x 4 = 252 cubic inches

To find the total volume of the figure, we add the volumes of the two rectangular prisms:

V = V1 + V2 = 35 + 252 = 287 cubic inches

Therefore, the volume of the figure is 287 cubic inches.

Step-by-step explanation: