Two 6-sided dice, one red and one green, are rolled. What is the probability that the red die shows an odd number and the green die shows a number that is a perfect square

Answer:

3/15 in the simplest form is 1/5....

when you divide by 3 it gives 1/5.

The fraction 3/15 in simplest form is 1/5.

A fraction is in its simplest form if the numerator and denominator have no common factors other than 1.

In other words, you cannot divide the top and bottom any further and have them still be whole numbers. The simplest form is also called lowest terms.

In this case, 3 and 15 have a common factor, which is 3. Thus, 3/15 in simplest form will be:

3/15 = 1/5  (divide both numerator and denominator by 3)

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Answer:

11 3/8 ft

Step-by-step explanation:

convert mixed fractions then multiply them

13/4×7/2

11 3/8

The baking soda that each mixing bowl will need is A. 1/9 cups.

A fraction simply means the part of a whole number. It's represented as a/b where a = numerator and b = denominator.

In this case, it can be seen that in the visual diagram, the value of B occurs in 3 places out of the 27 alphabets written.

This will be illustrated as:

= Number of B / Total alphabets

= 3 / 27

= 1/9.

Therefore, there'll be 1/9 cups.

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In 700 years the population of Transylvania will double  

What is growth rate ?

the typical annual rate of population change during a particular period for a certain nation, region, or geographic area. In most cases, a factor of 100 is used to describe the ratio between the annual growth in population size and the total population for the year.

Growth rate equals Absolute Change divided by Previous Value. Calculate the percentage of change: Percent of change = Growth rate x 100 is the formula that may be used to calculate the percent of change.

To calculate in how many years the population of Transylvania double

= 70 / 0.1

= 700 years

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The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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Therefore, the requirements of Rolle's Theorem are not fulfilled, and the absence of a number c with f'(c) = 0 does not contradict the theorem.

To show that f(0) = f(π), we substitute the values into the function:

f(0) = tan(0) = 0

f(π) = tan(π) = 0

Hence, we have f(0) = f(π), indicating that the function values at x = 0 and x = π are equal.

To investigate the derivative, we differentiate f(x) = tan(x) with respect to x:

f'(x) = sec^2(x)

Next, we need to determine if there exists a number c in the interval (0, π) such that f'(c) = 0. Let's evaluate f'(x) at the endpoints of the interval:

f'(0) = sec^2(0) = 1

f'(π) = sec^2(π) = 1

Since f'(x) is always positive (1) for any x in the interval (0, π), there is no number c in that interval for which f'(c) = 0.

This observation does not contradict Rolle's Theorem because Rolle's Theorem requires three conditions to be satisfied:

The function must be continuous on the closed interval [a, b].

The function must be differentiable on the open interval (a, b).

The function values at the endpoints must be equal, i.e., f(a) = f(b).

In this case, f(x) = tan(x) fails to satisfy the second condition because the derivative, f'(x) = sec^2(x), is never zero in the interval (0, π).

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Answer:

Step-by-step explanation:

the product of two and a number x is 2•x

so the sum of seven and the product of two and a number x is:

7 + 2x

Answer:

14.9cm

Step-by-step explanation:

20sin40= b

b= 14.9022

b = 14.9cm

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable(b).

In the analysis of variance procedure (ANOVA), "factor" refers to the independent variable. ANOVA is used to determine if there is a significant difference between the means of two or more groups, and the factor is the variable being studied that is believed to have an effect on the outcome. Variance is a measure of the variability or spread of the data, and ANOVA compares the variance between groups to the variance within groups to determine if there is a significant difference. The different levels of a treatment are also referred to as levels of the factor.

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Answer:

x = 25

y = 6

Step-by-step explanation:

In a parallelogram, opposite angles are equal.

2x and 50 are opposite angles,

2x = 50

Divide 2 on both sides,

x = 50 / 2

x = 25

In a parallelogram opposite sides are equal.

y + 5 and 11 are opposite sides,

y + 5 = 11

y = 11 - 5

y = 6

Answer:

x=25

y=6

Step-by-step explanation:

from the diagram,

2x= 50(opposite angles of a parallelogram)

2x= 50

dividing bothsides by 2

2x/2=50/2

x= 25

then,

y+5=11(opposite sides of a parallelogram)

y= 11-5

y= 6

Answer:

-16

Step-by-step explanation:

2(8)=16, 25+(-16)=current debt after 8 weeks

The velocity of the particle after time t can be determined using calculus by taking the derivative of the displacement equation. The resulting equation for velocity is v(t) = 1/2 cos(t).

The displacement equation for the particle is given as s(t) = 5 + (1/2) sin(t), where s is measured in centimeters and t is measured in seconds. To find the velocity of the particle after time t, we need to take the derivative of the displacement equation with respect to time.

Differentiating the equation s(t) with respect to t gives us v(t) = (d/dt)(5 + (1/2) sin(t)). The derivative of a constant term (5) is zero, and the derivative of sin(t) with respect to t is cos(t). Therefore, the velocity equation becomes v(t) = (1/2) cos(t).

This means that the velocity of the particle at any given time t is given by v(t) = (1/2) cos(t). The velocity is measured in centimeters per second, and the cosine function determines the magnitude and direction of the velocity. The coefficient 1/2 in front of the cosine function scales the velocity appropriately.

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There are 30 different types of jeans available from the Super Duper Jean company,

To determine the number of different types of jeans available, we can use the concept of combinations.

For each design (3 options), there are 2 choices for the length (short or long). Similarly, for each design, there are 5 color patterns to choose from.

To find the total number of combinations, we multiply the number of choices for each characteristic together:

Number of different designs × Number of length options × Number of color patterns = 3 × 2 × 5 = 30.

Therefore, the correct answer is C. 30.

There are 30 different types of jeans available from the Super Duper Jean company, considering the combinations of designs, length, and color patterns.

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40 oz of a 65% iron alloy contains 40 × 0.65 = 26 oz of iron.

x oz of a 42% alloy contains 0.42x oz of iron.

To end up with an alloy of 50% iron, Donna needs to use x oz of the 42% alloy such that

(26 + 0.42x) / (40 + x) = 0.50

Solve for x :

26 + 0.42x = 0.50 (40 + x)

26 + 0.42x = 20 + 0.50x

6 = 0.08x

x = 75

Using a calculator, it can be found that

Rounding to three decimal places,

If 12 out of 18 students prefer summer sports, then the fraction of students prefer winter sports is 33.33%

Total number of students = 18

The number of student prefer summer sports = 12

Then the number of student who prefer winter sports = Total number of students - The number of student prefer summer sports

= 18 - 12

= 6 students

The percentage is number that can be represented as the fraction of 100.

It is denoted by the percentage sign "%"

Then the fraction of students who prefer winter sports = (Number of student who prefer winter sports /Total number of students )×100

= (6/18) × 100

= 33.33%

Hence, if 12 out of 18 students prefer summer sports, then the fraction of students prefer winter sports is 33.33%

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The optimal solution for the given linear programming problem using the Big-M method is x₁ = 4, x₂ = 2, with a maximum value of Z = 22.

To solve the given linear programming problem using the Big-M method, we first convert it into standard form by introducing slack, surplus, and artificial variables.

The objective function is to maximize Z = 4x₁ + 3x₂. The constraints are 2x₁ + x₂ ≥ 10, -3x₁ + 2x₂ ≤ 6, x₁ + x₂ ≥ 6, and x₁, x₂ ≥ 0.

We introduce slack variables s₁, s₂, and s₃ to convert the inequalities into equalities. The initial Big-M tableau is set up with the coefficients and variables, and the artificial variables are introduced to handle the inequalities. We set a large positive value (M) for the artificial variables' coefficients.

In the first iteration, we choose the most negative coefficient in the Z-row, which is -4 corresponding to x₁. We select the s₂-row as the pivot row since it has the minimum ratio of the RHS value (6) to the coefficient in the pivot column (-3). We perform row operations to make the pivot element 1 and other elements in the pivot column 0.

After multiple iterations, we find that the optimal solution is x₁ = 4, x₂ = 2, with a maximum value of Z = 22. This means that to maximize the objective function, x₁ should be set to 4 and x₂ should be set to 2, resulting in a maximum value of Z as 22." short

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What problems will two decimal places have in the product? Select all that apply.

A 7.5 × 10

B 6.3 × 3

C 3.2 × 4.7

D 5 × 0.85

E 5.47 × 100

Integral ∫(x/√(x² - 1)) dx using the substitution x = sec(θ) is ln|x| + (1/4)(x² - 1)² + C, Integral  ∫(1/(x² + 25)²) dx using the substitution x = 5tan(θ) is tan⁻¹(x/5) + C and Integral ∫(x²/√(4 - x²)) dx using the substitution x = 2sin(θ) is 2sin⁻¹(x/2) - sin(2sin⁻¹(x/2)) + C.

1. Evaluating ∫(x/√(x² - 1)) dx using the substitution x = sec(θ):

Let x = sec(θ), then dx = sec(θ)tan(θ) dθ.

Substituting x and dx, the integral becomes:

∫(sec(θ)/√(sec²(θ) - 1)) sec(θ)tan(θ) dθ

Simplifying, we get:

∫(sec²(θ)/tan(θ)) dθ

Using the trigonometric identity sec²(θ) = 1 + tan²(θ), we have:

∫((1 + tan²(θ))/tan(θ)) dθ

Expanding the integrand:

∫(tan(θ) + tan³(θ)) dθ

Integrating term by term, we get:

ln|sec(θ)| + (1/4)tan⁴(θ) + C

Substituting back x = sec(θ), we have:

ln|sec(sec⁻¹(x))| + (1/4)tan⁴(sec⁻¹(x)) + C

ln|x| + (1/4)(x² - 1)² + C

2. Evaluating ∫(1/(x² + 25)²) dx using the substitution x = 5tan(θ):

Let x = 5tan(θ), then dx = 5sec²(θ) dθ.

Substituting x and dx, the integral becomes:

∫(1/((5tan(θ))² + 25)²) (5sec²(θ)) dθ

Simplifying, we get:

∫(1/(25tan²(θ) + 25)²) (5sec²(θ)) dθ

Simplifying further:

∫(1/(25sec²(θ))) (5sec²(θ)) dθ

∫ dθ

Integrating, we get:

θ + C

Substituting back x = 5tan(θ), we have:

tan⁻¹(x/5) + C

3. Evaluating ∫(x²/√(4 - x²)) dx using the substitution x = 2sin(θ):

Let x = 2sin(θ), then dx = 2cos(θ) dθ.

Substituting x and dx, the integral becomes:

∫((2sin(θ))²/√(4 - (2sin(θ))²)) (2cos(θ)) dθ

Simplifying, we get:

∫(4sin²(θ)/√(4 - 4sin²(θ))) (2cos(θ)) dθ

Simplifying further:

∫(4sin²(θ)/√(4cos²(θ))) (2cos(θ)) dθ

∫(4sin²(θ)/2cos(θ)) (2cos(θ)) dθ

∫(4sin²(θ)) dθ

Using the double-angle identity, sin²(θ) = (1 - cos(2θ))/2, we have:

∫(4(1 - cos(2θ))/2) dθ

Simplifying, we get:

∫(2 - 2cos(2θ)) dθ

Integrating term by term, we get:

2θ - sin(2θ) + C

Substituting back x = 2sin(θ), we have:

2sin⁻¹(x/2) - sin(2sin⁻¹(x/2)) + C

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Complete Question:

Evaluate each integral using the recommended substitution.

\(\displaystyle \int {\frac{x}{\sqrt{x^2 - 1}} dx\) let x = secθ

\(\displaystyle \int \limits^5_0 {\frac{1}{(x^2 +25)^2}} dx\) let x = 5tanθ

\(\displaystyle \int {\frac{x^2}{\sqrt{4-x^2}} dx\) let x = 2sinθ

In order to solve this system using the inverse of a matrix, first let's put the system in the matrix form:

Now the system is in the form AX = B, where A, X and B are matrices.

To solve this system, we can do the following:

So we need to calculate the inverse matrix of A. We can do this as follows:

Now we have:

So the solution of this system is x = -2.5 and y = 0.5

The vertical component of velocity can be zero at specific points in the motion of an object.

What is Velocity?

Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.

The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.

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Answer:

D

Step-by-step explanation:

To find the inverse we'll switch x and f(x).

That means we have:

x = 5/3 * f(x) + 5

5/3 f(x) = x - 5

f(x) = 3(x - 5)/5

After answering the presented question, we can conclude that  it will function take 36 months for the total cost to reach $2005.

In mathematics, a function appears to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.

inverse function

\(c(x) = 55x + 25\\c(x) - 25 = 55x\\x = (c(x) - 25) / 55\\c^(-1)(x) = (x - 25) / 55\\c(x) = 55x + 25 = 2005\\55x = 1980\\x = 36\\\)

it will take 36 months for the total cost to reach $2005.

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When an inequality is multiplied or divided by a negative number, the inequality sign will flip, meaning it will change its direction. For example, if you have a > b and you multiply or divide both sides by a negative number, the inequality will become a < b. This is because the relationship between the values reverses when multiplied or divided by a negative number.

Explanation:

When an inequality is multiplied or divided by a negative number, the direction of the inequality sign is flipped. This is because multiplication or division by a negative number, results in a reversal of the order of the numbers on the number line.

To see why this happens, consider the following example:

Suppose we have the inequality x < 5. If we multiply both sides of this inequality by -1, we get -x > -5. Notice that we have flipped the inequality sign from "<" to ">". This is because multiplying by -1 changes the sign of x to its opposite, and also changes the sign of 5 to its opposite, resulting in a reversal of the order of the numbers on the number line.

Similarly, if we divide both sides of the inequality x > 3 by -2, we get (-1/2)x < (-3/2). Here, we have again flipped the inequality sign from ">" to "<". This is because dividing by a negative number also changes the order of the numbers on the number line.

In general, if we have an inequality of the form a < b or a > b, where a and b are real numbers, and we multiply or divide both sides by a negative number, we obtain:

If we multiply by a negative number, the inequality sign is flipped. For example, if a < b and c < 0, then ac > bc.

If we divide by a negative number, the inequality sign is also flipped. For example, if a > b and c < 0, then a/c < b/c.

Therefore, it is important to be mindful of the signs of the numbers involved when performing operations on inequalities. If we multiply or divide by a negative number, we must flip the direction of the inequality sign accordingly.

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Step 1. The two points we have are:

we will label these points as (x1,y1) and (x2,y2):

Step 2. Now that we have labeled the points, we can use the slope formula to find the slope ''m'' of the line:

Substituting the known values:

Step 3. Simplify the signs in the operations.

-(-37) is +37,

and -(-26) is +26:

Step 4. Make the operations:

The result of this division is:

The slope of the line is 4.

Answer:

4

Answer: -3, -4, -5 are the integers

Step-by-step explanation: I don't get what you mean in this problem. You said the sum was -12 but then you are asking for the sum again? Do you want the integers? If so they are -3 -4 and -5 and if you want the sum then it is -12

I hope this helps and brainliest would be appreciated

Answer:

i think its the third one

Step-by-step explanation: im srry if im wrong doe

a) The test statistic is less than the z-critical value of -2.33, we reject the null hypothesis.

b) The result obtained in part a is statistically significant. c) i. The magnitude of the z-statistic increases as the sample size increases.; ii. The magnitude of the z-statistic decreases as the value of x moves closer to jo.

a) The null hypothesis is that the average number of cars served per hour is equal to 50 while the alternate hypothesis is that the average number of cars served per hour is less than 50.

The sample average cars served per hour is x = 46 and the sample standard deviation is s = 12.

The standard error of the mean is equal to s / sqrt(n) = 12 / sqrt(30) = 2.19.

The test statistic is z = (x - mu) / (s / sqrt(n)) = (46 - 50) / 2.19 = -1.83.

Since the test statistic is less than the z-critical value of -2.33, we reject the null hypothesis and conclude that the population mean for cars served per day is less than 50 with a 1% significance level.

b) Statistically significant means that the results of a statistical hypothesis test are unlikely to have occurred by chance. The result obtained in part a is statistically significant because the test statistic falls in the rejection region and we reject the null hypothesis at the 1% significance level.

c) i. The magnitude of the z-statistic increases as the sample size increases. This is because the standard error of the mean decreases as the sample size increases, which makes the estimate of the population mean more precise.

ii. The magnitude of the z-statistic decreases as the value of x moves closer to jo. This is because the difference between the sample mean and the hypothesized population mean decreases, which makes the estimate of the population mean more accurate.

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