Find the missing side lengths. Leave your answers as radicals in simplest form.

a) If two similar solids have a scale factor of 2 : 5, the ratio of their volumes is 8:125, expressed in the lowest terms.

b) If cone with volume 2625 m³ is dilated by a scale factor of 15, the volume of the resulting cone is 10,640,625 m³.

(a) When two solids are similar, their corresponding linear dimensions are in the same ratio, which is known as the scale factor. For example, if two similar solids have a scale factor of 2:5, it means that the corresponding sides of the two solids are in the ratio 2:5.

The volume of a solid is proportional to the cube of its linear dimensions. Therefore, if the linear dimensions of two similar solids are in the ratio 2:5, the ratio of their volumes would be:

(2/5)³ = 8/125

(b) The volume of a cone is given by the formula:

V = (1/3)πr²h

where V is the volume, r is the radius, and h is the height of the cone.

When a cone is dilated by a scale factor of k, its linear dimensions increase by a factor of k, and its volume increases by a factor of k³. Therefore, if the volume of a cone is V and it is dilated by a scale factor of k, the volume of the resulting cone would be:

V' = k³V

In this case, the volume of the original cone is given as 2625 m³, and it is dilated by a scale factor of 15. Substituting these values in the formula, we get:

V' = 15³(2625)

V' = 15³(2625/1)

V' = 10640625

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Answer:

Step-by-step explanation:
To test the null hypothesis that the proportion of red light runners is the same at both intersections, we can use a two-sample z-test for proportions.

Let p1 be the proportion of red light runners at the first intersection, and p2 be the proportion of red light runners at the second intersection. We want to test the null hypothesis:

H0: p1 = p2

against the alternative hypothesis:

Ha: p1 ≠ p2

We can use the following formula to calculate the test statistic:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of red light runners at the two intersections, and n1 and n2 are the sample sizes.

For the first intersection, we have x1 = 24 and n1 = 127. For the second intersection, we have x2 = 29 and n2 = 164.

The pooled sample proportion is:

p_hat = (x1 + x2) / (n1 + n2) = (24 + 29) / (127 + 164) = 0.167

The test statistic is:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2)) = (0.189 - 0.177) / sqrt(0.167 * (1 - 0.167) * (1/127 + 1/164)) = 0.99

Using a standard normal distribution table, we can find that the probability of getting a z-value of 0.99 or greater is 0.160. Since this is greater than the significance level of 0.01, we fail to reject the null hypothesis.

Therefore, we cannot conclude that the proportion of red light runners differs between the two intersections.

The sum of both numbers is 107/12

One number is 6 3/4

The other smaller number is 2 1/6

The sum of both numbers can be calculated as follows

= 6 3/4 + 2 1/6

= 27/4 + 13/6

= 162 + 52/24

= 214/24

= 107/12

Hence the sum of both numbers is 107/12

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Answer:

[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]

Step-by-step explanation:

Simplify

[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}[/tex]

The first-level numerator is
[tex]\dfrac{16}{x-4}-\dfrac{4}{x-2}\\\\\\= \dfrac{16(x-4) - 4(x - 2)}{(x-2)(x-4)}\\\\\\= \dfrac{16x -64 - 4x + 8}{(x-2)(x-4)}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)}[/tex]

The first-level denominator is
[tex]\dfrac{16}{x}-\dfrac{x-4}{x-2}\\\\\\= \dfrac{16(x-2) - x(x-4)}{x(x-2)}\\\\\\\\= \dfrac{16x - 32 -x^2 +4x}{x(x-2)}[/tex]

[tex]= \dfrac{-x^2+20x-32}{x\left(x-2\right)}[/tex]

Therefore
[tex]\dfrac{\dfrac{16}{x-2}-\dfrac{4}{x-4}}{\dfrac{16}{x}-\dfrac{x-4}{x-2}}\\\\\\= \dfrac{12x -56}{(x-2)(x-4)} \div\dfrac{-x^2+20x-32}{x\left(x-2\right)} \\\\\\[/tex]

Use the fraction rule: [tex]\dfrac{a}{b} \div \dfrac{d}{c} = \dfrac{a}{b} \cdot \dfrac{d}{c}[/tex]

[tex]= \dfrac{12x -56}{(x-2)(x-4)} \cdot \dfrac{x(x-2)}{-x^2 +20x -32}}[/tex]

The (x-2) term cancels out resulting in:
[tex]\dfrac{\left(12x-56\right)x}{\left(x-4\right)\left(-x^2+20x-32\right)}[/tex]

The solution of the inequality, log₂ 2m > log₂ (m + 5) is {m | m > 5 / 2}.

An inequality is an expression that have <, >, ≤ and ≥ . Therefore, let's solve the logarithmic inequality for the variable m.

Hence,

log₂ 2m > log₂ (m + 5)

Therefore, let's divide both sides by log₂.

Hence,

2m > m + 5

subtract m from both sides of the inequality

2m > m + 5

2m - m > m - m + 5

2m > 5

divide both sides by 2

2m / 2 > 5 / 2

Therefore,

m > 5 / 2

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Answer:

See explanation.

Step-by-step explanation:

Let's analyze each solution to determine if it's viable or non-viable based on the given constraints: Johnnie and Amy have $38.50, and they cannot buy more than 7 lunches.

1. 8 slices of pizza and 0 hamburgers

This solution is non-viable because they are not allowed to buy more than 7 lunches. In this case, they would be buying 8 lunches.

2. 5 slices of pizza and 2 hamburgers

Cost: 5×4.75+2×5.55=23.75+11.10=34.85

This solution is viable because the total cost is within their budget, and they are buying 7 lunches.

3. 4 slices of pizza and 3 hamburgers

Cost: 4×4.75+3×5.55=19.00+16.65=35.65

This solution is viable because the total cost is within their budget, and they are buying 7 lunches.

4. 3 slices of pizza and 2 hamburgers

Cost: 3×4.75+2×5.55=14.25+11.10=25.35

This solution is non-viable because they are only buying 5 lunches, which is less than the maximum allowed. But if it is acceptable to only buy below 7 lunches, then this solution can be viable.

5. 2 slices of pizza and 6 hamburgers

Cost: 2×4.75+6×5.55=9.50+33.30=42.80

This solution is non-viable because the total cost exceeds their budget.

6. 0 slices of pizza and 7 hamburgers

Cost: 7×5.55=38.85

This solution is non-viable because the total cost exceeds their budget.

In conclusion, the viable solutions are:

5 slices of pizza and 2 hamburgers

4 slices of pizza and 3 hamburgers

Possible in being viable:

3 slices of pizza and 2 hamburgers

Answer:

The distribution is symmetric

Step-by-step explanation:

Because in both sides it has the same structure, so that means that the value is the same in both sides

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Answer:

It is a graphical representation that discusses the relationship between two or more quantities or things

Step-by-step explanation:

The graphical method is used to optimize the two-variable linear programming. If the problem has two decision variables, a graphical method is the best method to find the optimal solution. In this method, the set of inequalities are subjected to constraints. Then the inequalities are plotted in the XY plane.

Graphical methods are commonly used for determining whether the data support an interpretation of mixing of two potential sources or fractionation of a single source.

A graphic solution can be done by hand (on graph paper), or with the use of a graphing calculator. Graphing a system of linear equations is as simple as graphing two straight lines. When the lines are graphed, the solution will be the (x,y) ordered pair where the two lines intersect (cross).

GIVE NICE GUY BRAINLINEST PLEASE

We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

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The converse of the statement "A → B: If x = 3, then x + 8 = 11" is Option(c) which is "B → A: If x + 8 = 11, then x = 3."

The "Converse" of a "conditional-statement" can be expressed by interchanging the hypothesis and the conclusion of "original-statement".

In this case, The "conditional-statement" is given to be "A → B: If x = 3, then x+8=11", which is read-as that if "x" is equal to 3, then expression "x + 8" is equal to 11.

So, The converse statement would say that if "x + 8" is equal to 11, then x must be equal to 3.

Therefore, the correct option is (c).

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Answer:  A and yes

Step-by-step explanation:

1.  A is the answer. You must balance an equation.  Whatever you do to one side you have to do to the other side. There are no like terms to combine on one side so C, D are out.

2.  Yes, because the equations are balance and will get same answers

Answer:

5,340x.095=507.3

507.3÷5=101.46

101.46÷12=$8.45 interest

5,340÷5=1068

1068÷12= $89

89+8.45=$97.45

answer $97.45 a month

Note that adding one pair does not make the table a function. This is why it is trickly. For the table to be a function, each value of x must be related to only one unique value of y and vice versa.

For the table to become a function, we must eliminate any repeated ordered pairs such as (3, 8) and (7, 8)

For example, we can say (3, 6) and (7, 8) then pick the last to be (5, 10)

So the table becomes a function when you have:

X    Y

6     0

3     6

9     12

7     8
5     10

The word linear function in mathematics refers to two separate but related concepts: A linear function in calculus and related fields is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.

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Answer:

1. The function that gives the lion population size P(t), t years from today is:

P(t) = 325(0.95)^t

2. To find the population in 4 years, we can substitute t=4 in the function:

P(4) = 325(0.95)^4

P(4) = 279.14

So the population will be approximately 279 lions in 4 years.

3. The exponential function for all three years is the same as in part 1:

P(t) = 325(0.95)^t

According to the information, the dilated rectangle would have the dimensions of 2.66cm on the side and 5cm on the base.

To calculate the dimensions of each side of the dilated figure we must identify the dilation factor. In this case it is 3, so we must divide the length of each side into the number of the expansion factor as shown below:

According to the above, the dilated rectangle would remain with the dimensions of 2.66cm on the side and 5cm on the base.

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Answer:

Set your calculator to degree mode.

Please sketch the figure to confirm my answer.

cos(38°) = 320/d

d•cos(38°) = 320

d = 320/cos(38°) = 406.1 feet

mean = 11+20+38+5+4/5 = 78/5 = 15.6

The length of AB is 27.3m and AD is 113 m.

Using Trigonometry in Triangle ABC

tan 50. 8 = P / B

tan 50.8 = AB / 22.3

1.2261 = AB/ 22.3

AB =  27.34 m

Now, again using Trigonometry

tan 25.4 = P / B

tan 50.8 = AD / 27.34

0.474 = AD/ 27.34

AD =  12.95916 m

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The weight of the empty tank is given as follows:

4 pounds.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The weight of the empty tank is the intercept of the function, which is of b = 4, hence:

4 pounds.

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The matrix formed by performing the row operation 4R₂ + R₃ — R₃ will result to R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₂ + R₃ — R₃, we have;

4(-6) + (-9) = -33 {row 3 column 1}

4(5) + 4 = 24 {row 3 column 2}

4(-1) + (-5) = -9 {row 3 column 3}

4(8) + 0 = 32 {row 3 column 4}

Therefore, the matrix formed by performing the row operation 4R₂ + R₃ — R₃ will give a new one with R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]

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The correct answers are:

They are inverses of one another

They are symmetric over the line y=x

When a number is too big or too little, exponential notation can express it as a single number and 10 increased to the power of the appropriate exponent.

The exponential form [tex]y=5^x[/tex]

The logarithmic form [tex]y = log_5\ x[/tex] are inverse functions of each other.

If we [tex]y = 5^x[/tex], then [tex]x = log_5\ y[/tex].

As long as x is a real number and y is positive, this is true for any value of x and y.

The graphs of [tex]y = 5^x[/tex] and [tex]y = log_5\ x[/tex] are symmetric over the line y = x.

We obtain the other graph by reflecting the first graph across this line.

Over the line y = x, the inverse functions are always symmetric.

If we swap the x and y coordinates of any point on one graph, we get a comparable position on the other graph.

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For the given data set of temperatures, the median temperature is 72.5 degree Fahrenheit.

In order to find the median temperature, we first need to arrange the temperatures in order from lowest to highest:

The temperatures arranged in order is : {66, 70, 72, 72, 73, 75, 79, 81}

There are 8 temperatures in total, which is an even-number, so the median will be the average of fourth and fifth day temperature.

In this case, the temperature of the fourth day is 72, and fifth day is 73,

The average will be = (72+73)/2 = 72.5,

Therefore, the median high daily temperature in the city is 72.5 degrees Fahrenheit.

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The given question is incomplete, the complete question is

The data set shown below represents the distribution of daily high temperatures in a city for 8 days.

79,73,72,70,72,66,81,75.

What is the median high daily temperature, in degrees Fahrenheit, in the city?

The percentage of time that the machine will dispense from 7. 5 oz to 7. 9 oz is 62.47% of the time.

Find the Z-scores for both 7. 5 oz and 7. 9 oz :

Z = ( X - μ ) / σ

For 7. 5 oz :

Z = ( 7.5 - 7.6 ) / 0.2

Z = -0. 1 / 0. 2

Z = -0. 5

For 7.9 oz:

Z =  (7. 9 - 7.6 ) / 0.2

Z = 0. 3 / 0. 2

Z = 1. 5

Using the z - values from the table, the percentage of time is:

0.9332 - 0.3085 = 0.6247

= 62. 47 %

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Answer:

4/5

Step-by-step explanation:

The percent of the increase, rounded to the nearest tenth of a percent, concerning the sales of boxes of cookies that Molly sold last month and this month, is 11.5%.

The percentage increase can be determined by finding the difference or the amount of increase in sales.

This difference is divided by the previous month's sales and multiplied by 100.

The total number of boxes of cookies Molly's Scout Troop sold last month = 148

The total number sold this month = 165

The increase = 17 (165 - 148)

Percentage increase = 11.5% (17 ÷ 148 x 100)

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The value of sin(A-B) is 2334/6625

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Example of trigonometric identity include;

cos 2 θ + sin 2 θ = 1 cos 2 θ + sin 2 θ = 1.

1 + cot 2 θ = csc 2 θ 1 + cot 2 θ = csc 2 θ

1 + tan 2 θ = sec 2 θ 1 + tan 2 θ = sec 2 θ

Sin(A-B) = = sin A cos B- cos Asin B

if tan A = 4/3, then 4 is the opp and 3 is the adj,

hyp² = 4²+3²

= 16+9

hyp² = 25

hyp = √25

= 5

cos A = 3/5 and sinA = 4/5

if sinB = 28/53, then opp is 28 is the opp and 53 is the hyp

adj = √ 53²-28²

adj = √ 2809 - 784

adj = √2025

adj = 45

cos B = 45/58

sin(A-B) = 4/5 × 45/58 - 3/5× 28/53

= 18/29 - 84/265

= (4770-2436)/6625

= 2334/6625

therefore the value of sin(A-B) = 2334/6625

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Answer:

B

Step-by-step explanation:

Notice that all y-intercepts are the same (doesn't give a clue to the answer).

The line has a downward slant as you move from left to right, so the slope is negative (eliminating A & C as answers).

Determine the actual slope by identifying the y-intercept and x-intercept, and calculate Rise over Run:

  Rise = -6 (goes from +6 to 0)

  Run = +12

  -6/12 = -1/2

Answer:

A) circle.

When a sphere is cut by a horizontal plane, the resulting cross section is a circle. This is because a sphere is a three-dimensional object that is perfectly symmetrical in all directions, so any plane that intersects it will create a circular cross section.

Answer: