What is the volume of the cube shown? 2 1/4

The expression in the blank spaces -3x, 5x-8, -4x+7, 3x-10, 4x-9 and -2x+5 represented with A, B, C, D, E and F respectively

This is a problem involving algebraic expressions

Since the total for each row and column is the same

First, start from the second because it is complete. Add up all the expressions to get the total:

2x-3 + 3 + 2-x + x = 2x-2

Check the attached image. I labeled the boxes with alphabets for convenience.

A = 2x-2 -(1-2x) - (4x-1)-(3x-2)              (Remember: 2x-2 is the total)

A = 2x-2 -1 +2x - 4x+1-3x+2  =  -3x

B = 2x-2 -(8-3x) - (2x-3) -(1-2x)

B = 2x-2 -8+3x - 2x+3 -1+2x = 5x-8

C = 2x-2 -B -(6-5x) -(6x-7)             where B = 5x-8

C = 2x-2 -5x+8 -6+5x -6x+7 = -4x+7

D = 2x-2 -3 -(4x-1) -(6-5x)

D = 2x-2 -3 -4x+1 -6+5x = 3x-10

E = 2x-2 -C -(2-x) -(3x-2)

E = 2x-2 +4x-7 -2+x-3x+2 = 4x-9

F = 2x-2 -A -x -(6x-7)

F  = 2x-2 +3x -x -6x +7 = -2x+5

Therefore, the blank spaces should be filled with the expressions -3x, 5x-8, -4x+7, 3x-10, 4x-9 and -2x+5 represented with A, B, C, D, E and F respectively

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

\(4\)

Step-by-step explanation:

The total number of cars Ms. Owens has is \(15\).

The number of cars left after Ms. Cook took some were \(11\).

The number of cars taken by Ms. Cook will be the difference of the total number of cars and the number of cars left. So,

\(15-11=4\)

Hence, the number of cars taken by Ms. Cook were \(4\).

x/2, which is a contradiction. So, the statement is true.Let x = 1,

then x² + x + 41 = 43

which is a prime.

If we take x = 2,

then x² + x + 41 = 47

which is also a prime. But,

when x = 40,

then x² + x + 41 = 1681

which is not a prime.

So, the statement is false.

b) ∀x∃y(x + y = 0). For every x,

there exists y = -x,

such that x + y =

x - x = 0.

So, the statement is true.

c) Let x = 2,

y = 1.

Then x > 1 and y > 0,

but  \(y^x = 1^2\)

= 1 ≤ x.

So, the statement is false.

d) Let a = 6,

b = 3,

c = 4.

Then a divides bc, but a does not divide b or a does not divide c. So, the statement is false.

e) Let a = 2,

b = 5,

c = 3, and

d = 1.

Then a divides (b-c) and a divides (c-d), but a does not divide (b-d). So, the statement is false.

f) x² - x ≥ 0 can be written as x(x-1) ≥ 0. If x > 1,

then both x and x-1 are positive and hence their product is positive.

If 0 ≤ x < 1, then x is positive and x-1 is negative, so their product is negative.

But, the statement is true only for positive real numbers. So, the statement is true.

g) Subtracting x+1 on both sides, 2x - (x+1) > 0 or x > 1. So,

the statement is true only for x > 1.

h) For any positive real number x, choose y = x/2.

Then for any positive real number z, yz ≥ z.

So, the statement is true.

i) For any positive real number x,

choose y = x/2.

Then if y < x, 0 < x-y < x.

If y > x,

then y > x/2 > x-x/2

= x/2,

which is a contradiction. So, the statement is true.

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The number of ways to plan her schedule of menus for the 20 school days is 10^20.

To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.

For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.

The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.

How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?

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The number that best completes the sequence is 7.

A sequence is a list of numbers arranged in a specific order. Each number in the sequence is called a term or element. Sequences can be finite or infinite.

To find the number that best completes the given sequence, let's examine the pattern:

⇒ 100 - 48 = 52

⇒ 52 - 24 = 28

⇒ 28 - 12 = 16

⇒ 16 - 6 = 10

From this pattern, we can observe that each term in the sequence is obtained by subtracting a decreasing even number.

If we subtract 48, 24, 12, and 6 successively.

Therefore, to continue the pattern, we subtract the next even number, which is 3. So, we subtract 3 from 10 ⇒ 10 - 3 = 7

Hence,

The number that best completes the sequence is 7.

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Answer:

One candy bar cost $4.02

Step-by-step explanation:

14.19 - 5.79 = 8.4 (total candy bar cost)

8.4 / 2 = 4.2 cost of one candy bar

Answer:

4.2

Step-by-step explanation:

14.18-5.79 = 8.4

8.4/2 = 4.2

Using adjacent angles, The value of a given figure, the value of E = 132°

What is an Adjacent angle?

When two angles have a similar vertex and side, they are referred to as neighboring angles. The vertex of an angle is the point at which the rays that make up its sides come to an end. When adjacent angles have a same vertex and side, they can be a complimentary angle or supplemental angle.

draw a line EOF parallel to AB

now EF || AB and CD||AB

∵ AB || EF and AO is a transversal

we have

∠AOF+∠OAB=180°

∠AOF+108 = 180 °

∠AOF=72 °

∵ EF|| CD and OC is transversal

so

∠COF+∠OCD=180°

∠COF+112° = 180°

∠COF=60°

∴∠AOC=∠AOF+∠COF

=72 ° + 60°

=132°

Hence the value of E = 132°

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For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

A coincidental discrepancy between the observed and true values of anything is known as a random error (e.g., a researcher misreading a weighing scale records an incorrect measurement).

It's not always a mistake when there is random error; rather, it happens when measurements are made. Even when you measure the same item repeatedly, there will always be some variation in your results because to changes in the environment, the instrument, or your own perceptions.

Your measurements are equally likely to be greater or lower than the genuine values due to random error, which has unexpected effects.

According to the given data,

For a result to be considered significant, the chances of its occurring as a result of random error are often less than 5 percent.

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Answer:

4.30 and 0.70 if you round of to the nearest tenth

Step-by-step explanation:

pls mark as brainliest lol

Answer:

Triangle

Step-by-step explanation:

It forms a triangle because when you plot the points and connect a dot its a triangle

Answer:

3( n + \(\frac{17}{6}\) )² - \(\frac{361}{12}\) = 0

Step-by-step explanation:

3n² = 6 - 17n ⇔ 3n² + 17n - 6 = 0

3( n² + 2 × \(\frac{17}{6}\) n + ( \(\frac{17}{6}\) )² - ( \(\frac{17}{6}\) )² - 2 ) = 0

3( n + \(\frac{17}{6}\) )² - 3 × \(\frac{289}{36}\) - 6 = 0

3( n + \(\frac{17}{6}\) )² - \(\frac{361}{12}\) = 0

The basic postulate of collision theory states that the rate of a reaction is proportional to the number of effective collisions per second among reactant molecules, requiring proper orientation and a minimum molecular kinetic energy.

The basic postulate of collision theory states that the rate of a reaction is proportional to the number of effective collisions per second among the reactant molecules. To have an effective collision, the reacting molecules must fulfill two requirements:

Proper orientation: The molecules must collide in a specific geometric arrangement that allows the necessary atomic rearrangement for the reaction to occur. The proper orientation is independent of the energies of the colliding molecules.

Minimum molecular kinetic energy: The colliding molecules must possess a minimum amount of kinetic energy to overcome the energy barrier or activation energy required for the reaction to take place. This minimum energy requirement is independent of the orientation of the molecules.

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We can use the general form of a quadratic model:

We can find the parameters a, b and c by taking some pair of values from the table, like this:

Let's take the pair (0,0), if we replace these values for y and x into the above model we get:

Now let's take the pair (1, 2.4), by replacing these values into the above model for x and y, we get:

From this equation, we can solve for a to get:

By taking the pair (2, 9.4) we get:

We can replace the expression that we got previously a = 2.4 - b into the above equation to get:

From this expression, we can solve for b like this:

Now we can replace it into the equation a = 2.4 - b, then we get:

a = 2.4 - 0.1 = 2.3

Then we get the expression:

Now we just have to evaluate 10 km into the equation, then we get:

Then, the best prediction of the time required for the oil spill to reach a diameter of 10 km is 233 days

The solution to the given IVP is y(t) = e^4t(2cos(4t) + sin(4t)), satisfying the initial conditions y(0) = 2 and y'(0) = -1.


The given differential equation is a homogeneous linear second-order equation with constant coefficients. The characteristic equation is r^2 - 8r + 16 = 0, which can be factored as (r - 4)^2 = 0. Thus, the characteristic roots are r = 4 with multiplicity 2.

Since the roots are repeated, the general solution takes the form y(t) = (C1 + C2t)e^(4t), where C1 and C2 are constants to be determined.

Using the initial condition y(0) = 2, we have 2 = C1. Then, differentiating y(t), we get y'(t) = (C1 + C2t)e^(4t) + C2e^(4t). Evaluating at t = 0 and applying the second initial condition, we find -1 = C1 + C2. Solving these equations, we obtain C1 = 2 and C2 = -3.

Thus, the solution to the IVP is y(t) = 2e^(4t)(cos(4t) - 3sin(4t)).

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Answer:

The ratio of senior members to junior members at the company is 1 : 3

Step-by-step explanation:

The given average number of years of experience of the senior employees, x = 16 years

The given average number of years of experience of the junior employees, y = 7 years

Let a represent the number of senior employees in the company, and let b represent the number of junior workers in the company, we have;

(16·a + 4·b)/(a + b) = 7

∴ (16·a + 4·b) = (a + b) × 7 = 7·a + 7·b

16·a - 7·a = 7·b - 4·b

9·a = 3·b

a/b = 3/9 = 1/3

a/b = 1/3

The above equation, expressed as a ratio is, a : b = 1 : 3

Therefore;

The ratio of senior members to junior members at the company, a : b = 1 : 3.

To calculate the probability of the next call arriving within 2 minutes, we need to convert the given arrival rate from hours to minutes. With a call arrival rate of 25 calls per hour, we can determine the average rate of calls per minute. Then, using the exponential distribution, we can calculate the probability of a call arriving within 2 minutes. The probability that the next call will arrive within 2 minutes is approximately 0.0083 or 0.83%.

the arrival rate of 25 calls per hour, we need to convert it to minutes. Since there are 60 minutes in an hour, the arrival rate would be 25/60 calls per minute, which simplifies to approximately 0.4167 calls per minute.

To calculate the probability that the next call will arrive within 2 minutes, we can use the exponential distribution formula: P(x ≤ t) = 1 - e^(-λt), where λ is the arrival rate and t is the time in minutes.

Plugging in the values, we have P(x ≤ 2) = 1 - e^(-0.4167 * 2). Using a calculator, this simplifies to approximately 0.0083 or 0.83%.

Therefore, the probability that the next call will arrive within 2 minutes is approximately 0.0083 or 0.83%.

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To  have a total mass of 1 googol kilograms, 1.674480911 × 10 ⁷⁵ earths are needed

Given that:

1 googol = 10¹⁰⁰

Earth's mass is 5.972×10²⁴ kilograms

In order to find how many earths are needed to have a total mass of 1 googol kilograms, you need to divide  1 googol kilograms by Earth's mass (5.972×10²⁴ kilograms). Thus:

Number of earths needed =  10¹⁰⁰ / 5.972×10²⁴

Number of earths needed = 1.674480911 × 10 ⁷⁵ earths

Therefore, 1.674480911 × 10 ⁷⁵ earths are needed to have a total mass of 1 googol kilograms

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Answer:

x = 4/5

Step-by-step explanation:

3x - 7x = x - 4

-4x = x - 4

(Subtract x on both sides)

-4x - x = x - x - 4

-5x = -4

(Subtract by -5 on both sides)

-5/-5x = -4/-5

x = 4/5

Answer: \(x=\frac{4}{5}\)

Explaination: math :)

To rewrite the equation 56x + 7y + 21 = 0 as a function of x, we need to isolate y on one side of the equation.

Starting with the given equation: 56x + 7y + 21 = 0.  First, subtract 21 from both sides to get: 56x + 7y = -21.  Next, subtract 56x from both sides:

7y = -56x - 21.  To isolate y, divide both sides by 7:y = (-56x - 21) / 7. Simplifying further:y = -8x - 3.  Therefore, the equation 56x + 7y + 21 = 0 can be rewritten as a function of x: f(x) = -8x - 3.

Hence after rewriting  the following equation as a function of x. 56x 7y 21 = 0 we get , f(x) = -8x - 3.

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The hypothesis test is left-tailed because the financial analyst wants to test if the proportion of stock portfolios containing high-risk stocks is lower than 0.10.

In other words, they are interested in determining if the proportion is significantly less than the specified value of 0.10. A left-tailed hypothesis test is used when the alternative hypothesis suggests that the parameter of interest is smaller than the hypothesized value. In this case, the alternative hypothesis would be that the proportion of stock portfolios with high-risk stocks is less than 0.10.

By conducting a left-tailed test, the financial analyst is trying to gather evidence to support their claim that their clients have a lower proportion of high-risk stock portfolios. They want to determine if the observed data provides sufficient evidence to conclude that the true proportion is indeed less than 0.10, which would support their claim of a lower proportion of high-risk stocks.

Therefore, a left-tailed hypothesis test is appropriate in this scenario.

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Answer:

$125

Step-by-step explanation:

I = Prt

I = ($500)(.05)(5) = $2,500(.05) = $125

Answer:

Step-by-step explanation:

Refer to attached

Finding the required coordinate is shown on the graph

Answer: x = -4 or 8

Step-by-step explanation:

    To solve, we will isolate the x-variable. Since this is a parabola (as shown by the square) we will either have 1 or 2 answers.

    Given:

6(x - 2)² + 7 = 223

    Subtract 7 from both sides of the equation:

6(x - 2)² = 216

    Divide both sides of the equation by 6:

(x - 2)² = 36

    Square root both sides of the equation:

* Since we square rooted, we will have the positive and negative result

x - 2 = 6           x - 2 = -6

    Add 2 to both sides of the equation, for both equations:

x = 8           x = -4

          x = -4 or 8

9b²+30b+25

Step-by-step explanation:

15b+25+9b²+15b

9b²+30b+25

Answer:

487=3x-17

487+17=3x-17+17

3x=53

3x/3=53/3

x=168

Step-by-step explanation:

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

Yes

Step-by-step explanation:

Because it’s a trapezoid and those can be trapezoid because they have one pair of parallel sides and a parallelogram has two pairs of parallel sides so a parallelogram is also a trapezoid.