A triangle has angles measuring 25 degrees and 45 degrees. What is the measure of the triangle's third angle

The answers are:

a. population standard deviation σ = 0.1 ounce

b. standard deviation of the sampling distribution sx = 0.0268 ounce.

Given,

Sample size = n = 15

Mean weight = 2 ounces

Standard deviation = s = 0.12 ounces

Population standard deviation = σ = 0.1 ounces

The formula to calculate the standard deviation of the sampling distribution of the sample mean is given as:

σx = σ/√n

Where, σx is the standard deviation of the sampling distribution of the sample mean.

σ is the population standard deviation.

n is the sample size.

Now, substitute the given values in the above formula:

σx = 0.1/√15

σx ≈ 0.0268

So, the standard deviation of the sampling distribution of the sample mean is σx = 0.0268.

Therefore, the answers are:

a. σ = 0.1 ounce

b. σx = 0.0268 ounce.

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The correct term for a sample obtained in such a way that every element in the population has an equal chance of being selected is a "random sample."

In a random sample, each member of the population has an equal probability of being chosen, providing a representative subset of the population. This sampling method helps to reduce bias and ensures that the sample is more likely to accurately reflect the characteristics of the entire population.

Random sampling is a fundamental principle in statistics and research, allowing for generalizations and inferences to be made about the population based on the characteristics observed in the sample. It is widely used in various fields, such as social sciences, market research, and opinion polls, to draw meaningful conclusions about a larger population.

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The solution to the original equation is approximately 1.4422.

To continue with the bounds found in part d, we need to use the interval [1.4, 1.5] as the initial approximation for the next iteration. Using the Newton-Raphson method, we get the following approximations:

- Iteration 2: x1 = 1.4428
- Iteration 3: x2 = 1.4422

Based on these two iterations, we can conclude that the solution to the original equation is approximately 1.4422. This is because the difference between the approximations in the last two iterations is only 0.0006, which is a small enough difference to suggest that the approximation has converged to a solution.

In other words, the Newton-Raphson method has been successful in finding a solution to the equation f(x) = x^3 - x^2 - x - 1 = 0 within the given interval [1.4, 1.5]. The method works by using the tangent line to the graph of f(x) at each iteration to approximate the root of the equation. By repeating this process, we are able to get closer and closer to the actual solution.  

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Answer:

Step-by-step explanation:

Given,

\( {( \frac{5}{2} )}^{x} + {( \frac{5}{2} )}^{x + 3} \)

\( = {( \frac{5}{2}) }^{x} + {( \frac{5}{2}) }^{x} \times {( \frac{5}{2} )}^{3} \)

\( = ( \frac{5}{2} ) ^{x} (1 + {( \frac{5}{2} )}^{3} \)

\( = {( \frac{5}{2} )}^{x} (1 + \frac{125}{8} )\)

\( = {( \frac{5}{2} )}^{x} ( \frac{1 \times 8 + 125}{8} )\)

\( = {( \frac{5}{2}) }^{x} ( \frac{8 + 125}{8} )\)

\( {( \frac{5}{2} )}^{x} ( \frac{133}{8} )\)

Comparing with A • \( {( \frac{5}{2}) }^{x} \)

A = \( \frac{133}{8} \)

Hope this helps...

Good luck on your assignment...

Answer:

t = -3

Step-by-step explanation:

To minimize costs, the optimal distribution schedule for Finnish Furniture would involve shipping 130 units from Reno to Phoenix, 20 units from Denver to Cleveland, and 160 units from Pittsburgh to Chicago. This allocation is determined by using the transportation algorithm, specifically the Vogel's Approximation Method (VAM), which considers the lowest shipping costs per unit for each source-destination combination. By following this approach, the total cost for the distribution is calculated to be $4,360.

To determine the optimal distribution schedule that minimizes costs, we need to allocate the available supplies from the manufacturing facilities to the retail stores based on the shipping costs per unit. We can achieve this by employing the transportation algorithm, such as the North-West Corner Rule or the Vogel's Approximation Method (VAM).

Using VAM, we begin by identifying the lowest shipping cost per unit for each row and column in the given table. We then select the highest difference between the two lowest costs, considering both rows and columns. This difference indicates the most cost-effective allocation.

In this case, the VAM suggests shipping 130 units from Reno to Phoenix since the shipping cost per unit is 10, which is the lowest for the Reno row. For Cleveland, Denver has the lowest cost at 14, so we allocate 20 units from Denver to Cleveland. Lastly, we allocate 160 units from Pittsburgh to Chicago, as the cost per unit is the lowest at 12 for the Pittsburgh column.

Now, let's calculate the total cost. The cost of shipping 130 units from Reno to Phoenix is 130 x 10 = $1,300. Shipping 20 units from Denver to Cleveland costs 20 x 14 = $280. Lastly, shipping 160 units from Pittsburgh to Chicago costs 160 x 12 = $1,920. Adding these costs together gives us a total cost of $1,300 + $280 + $1,920 = $4,360.

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Answer:

If he walks 1 dog he will make 8$ if he walks two dogs he will earn 16$ if he walks 3 dogs he will make 24$

The number of hours Ella worked before school was 8 hours and after school was 16 hours.

Hours worked is the number of hours actually worked, defined as the sum of all periods spent on direct and ancillary activities to produce goods and services.

Given that, Ella works two part-time jobs, before and after school, Before school, she earns $11.25/hour, and after school she earns $11.75/hour. Last week, she earned a total of $278. She works twice as many hours after school.

We are asked to find how many hours did she work at each job,

We will solve this question by using an equation,

Let the number of hours she worked before school be x and after school 2x,

Therefore, establishing the equations,

x(11.25)+2x(11.75) = 278

11.25x+23.5x = 278

34.75x = 278

x = 8

Hence, the number of hours Ella worked before school was 8 hours and after school was 16 hours.

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Answer:

The answer is vjapur

Step-by-step explanation:

divide population by literates then get the percentage, higher percentage is answer.

Rampur has a greater literacy rate than Vijaypur

First, find the literacy rate of each town in percentage.

A. Rampur

175,600/200,000

= 1,756/2,000

= 87.8%

B. Vijaypur

105,400/160,000

= 1054/1600

= 65.8%

From this, we can easily say that Rampur has a greater literacy rate than Vijaypur

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

D is correct.

0 is greater than -2.

-1 is greater than -2.

5 is greater than -2.

-3 is smaller than -2.

Hope this helps!

Answer:

there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Step-by-step explanation:

To choose three different members from the club to be president, vice president, and treasurer, you can follow these steps:

Step 1: Calculate the number of ways to choose the president:

Since there are 15 club members in total, the number of ways to choose the president is 15.

Step 2: Calculate the number of ways to choose the vice president:

After selecting the president, there are 14 remaining members. The number of ways to choose the vice president from these 14 members is 14.

Step 3: Calculate the number of ways to choose the treasurer:

After selecting the president and vice president, there are 13 remaining members. The number of ways to choose the treasurer from these 13 members is 13.

Step 4: Calculate the total number of ways to choose the president, vice president, and treasurer:

Since each step is independent, you can multiply the number of choices at each step: 15 * 14 * 13 = 2,730.

Therefore, there are 2,730 different ways to choose a president, vice president, and treasurer from the student club consisting of 10 computer science majors and 5 mathematics majors.

Answer:

No

Because Bradley's carton is taller than Josh's, Bradley would drink more milk.

Let us assume that Bradley carton has 100 quarts . If he drank 1/4, he would drink 25 quarts of milk. If Josh carton is 80 quarts full of milk, he would drink 20 quarts of milk. this example shows that they would not drink the same amount of milk

Step-by-step explanation:

A taller carton would contain more ounces of milk.

Answer:

Multiply by 1/7

Step-by-step explanation:

14*1/7=2

21*1/7=3

The equivalent expression of the statement is as follows:

\((\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}\)

The expression is as follows:

Quantity y raised to the negative third power times z raised to the fifth power end quantity over quantity z raised to the negative fourth power times y raised to the sixth power end quantity all raised to the negative second power

The equivalent expression of the statement is as follows:

\((\frac{y^{-3} X z^{5} }{z^{-4} X y^{6} }) ^{2}\)

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Answer:

Point C represents 2/3

Answer:

C.

Step-by-step explanation:

Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3

Slope - point form:

y - y1 = m(x -x1)

y - 5 = 3(x - 4)

y - 5 = 3x - 12

- 3x + y = - 12 + 5

- 3x + y = - 7

Answer:

Option C is the correct option.

Step-by-step explanation:

A line passes through ( 2 , -1 ) and ( 4 , 5 )

The equation of line:

\( \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} \)

Plug the values

\( \frac{ y - ( - 1)}{x - 2} = \frac{5 - ( - 1)}{4 - 2} \)

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

\( \frac{y + 1}{x - 2} = \frac{5 + 1}{4 - 2} \)

Add the numbers

\( \frac{y + 1}{x - 2} = \frac{6}{4 - 2} \)

Subtract the numbers

\( \frac{y + 1}{x - 2} = \frac{6}{2} \)

Reduce the numbers with 2

\( \frac{y + 1}{x - 2} = 3\)

Apply cross product property

\(3x - 6 = y + 1\)

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

\(3x - y = 1 + 6\)

Add the numbers

\(3x - y = 7\)

\( - 3x + y = - 7\)

Hope this helps...

Best regards!

Answer:

\(\frac{-1}{2}ab^{12}\)

\(\frac{w^{10}}{3y^4}\)

Step-by-step explanation:

Given the expression;

\(\frac{-2a^2b^4}{4ab^{-8}}\\= \frac{-2}{4}*a^{2-1}b^{4-(-8)}\\= \frac{-1}{2}ab^{12}\)

Similarly for the expression;

\(\frac{-5w^4y^{-2}}{-15w^{-6}y^2}\\= \frac{-5}{-15}*w^{4-(-6)}y^{-2-2}\\= \frac{1}{3}w^{10}y^{-4} \\= \frac{w^{10}}{3y^4}\)

The density of glycerin at 60°C is approximately 19.9592 g/cm³.

To find the density of glycerin at 60°C, we can use the volume expansion coefficient and the given density at 20°C.

The formula for volume expansion is:

ΔV = β * V₀ * ΔT

where:

ΔV is the change in volume,

β is the volume expansion coefficient,

V₀ is the initial volume, and

ΔT is the change in temperature.

In this case, we want to find the change in density, so we can rewrite the formula as:

Δρ = -β * ρ₀ * ΔT

where:

Δρ is the change in density,

β is the volume expansion coefficient,

ρ₀ is the initial density, and

ΔT is the change in temperature.

Given:

ρ₀ = 20 g/cm³ (density at 20°C)

β = 5.1 x 10⁻⁴ °C⁻¹ (volume expansion coefficient)

ΔT = 60°C - 20°C = 40°C (change in temperature)

Substituting the values into the formula, we have:

Δρ = - (5.1 x 10⁻⁴ °C⁻¹) * (20 g/cm³) * (40°C)

Calculating the expression:

Δρ = - (5.1 x 10⁻⁴) * (20) * (40) g/cm³

≈ - 0.0408 g/cm³

To find the density at 60°C, we add the change in density to the initial density:

ρ = ρ₀ + Δρ

= 20 g/cm³ + (-0.0408 g/cm³)

≈ 19.9592 g/cm³

Therefore, the density of glycerin at 60°C is approximately 19.9592 g/cm³.

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Answer: $234.5

Step-by-step explanation: when you get a 40% off that means you would pay 60% but then you have to play 7% so you have to pay 67% of 350 wich is 234.5

Answer:

$149.8

Step-by-step explanation:

40% of 350 is 140

7% of 140 is 9.8

This is an example of a one-sample of t-test for the difference in muscle strength between the left and right hands of a random sample of 15 left-handed men, with a one-sided alternative hypothesis that the left hand is stronger.

In this example, the researcher was interested in testing whether left-handed men have stronger left hands than right hands, given that they live in a world designed for right-handed people. Muscle strength was measured on both hands of a random sample of 15 left-handed men, and the difference between the left and right hand strength was calculated for each individual.

A one-sample t-test was used to test the null hypothesis that the mean difference in muscle strength between the left and right hands is zero, against the alternative hypothesis that the mean difference is greater than zero (indicating that the left hand is stronger). The resulting t-statistic was 1.80, which would have a corresponding p-value associated with it.

If the p-value is less than the chosen level of significance (e.g., 0.05), then the null hypothesis can be rejected in favor of the alternative hypothesis, providing evidence to support the claim that left-handed men have stronger left hands than right hands in a world designed for right-handed people.

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Answer:

The signs of each monomial in the second polynomial are changed.

When subtracting two polynomials, the subtraction affects each monomial in the second polynomial by inverting the sign of each coefficient. That is, every coefficient in the second polynomial is multiplied by -1.

Polynomials are mathematical expressions that contain one or more terms. These terms are made up of coefficients and variables raised to powers, like x^2, y, or z^3.

When subtracting two polynomials, we need to keep in mind that each term within the polynomial is affected.

Example: Consider the following polynomial:

2x^2 + 3xy + 4y^2

When we subtract the polynomial 3x^2 - 2xy - 5y^2 from the above polynomial, we need to invert the sign of each coefficient in the second polynomial. That is, we have:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

Now, inverting the sign of each coefficient in the second polynomial, we get:

-3x^2 + 2xy + 5y^2

So the final result is:

2x^2 + 3xy + 4y^2 - (3x^2 - 2xy - 5y^2)

= 2x^2 + 3xy + 4y^2 - 3x^2 + 2xy + 5y^2

= -x^2 + 5xy + 9y^2

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The slope indicated in the table is 5.

To find the slope of the line passing through the points in the table, we can use the slope formula, which is (change in y)/(change in x). Using any two points in the table, we can calculate the change in y and change in x between those points, and then divide the change in y by the change in x to get the slope.

For example, if we choose the points (2, 10) and (-4, 20), the change in y is 20 - 10 = 10, and the change in x is -4 - 2 = -6. Dividing the change in y by the change in x gives us the slope of (10)/(-6) = -5/3.

However, we need to be careful here because the table doesn't show a line with a negative slope. Instead, the table shows a line with a positive slope, which means we need to choose different points that give a positive slope. If we choose the points (2, 10) and (8, 40), the change in y is 40 - 10 = 30, and the change in x is 8 - 2 = 6. Dividing the change in y by the change in x gives us the slope of (30)/(6) = 5. Therefore, the slope indicated in the table is 5.

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Answer:

Option D: x = -2; x = 3/4

Step-by-step explanation:

Hello!

We can factor this expression and then find the zeroes to find our solutions.

We have to factor by grouping. Multiply the 1st and last term, 4x² and -6 is -24x², and find two factors that equal to -24x² and add up to the second term, 5x. 8x and -3x work for this.

Now, set the equation equal to zero.

Remember, if two numbers, a and b, multiply to 0, either a or b or both numbers must be zero. So now we set both factors to zero, hence the zero-product property.

And the next one:

The solutions are x = -2, and x = 3/4, or Option D

Answer:

f(- 2) = - 4

Step-by-step explanation:

Step-by-step explanation:

To evaluate f(- 2) substitute x = - 2 into f(x) , that is

f(- 2) = (- 2)² + 3(- 2) - 2 = 4 - 6 - 2 = - 4

Answer:

8 m

Step-by-step explanation:

Diagonal: Hypotenuse

Let the hypotenuse (diagonal) be c, Stafford street be a, and let Silvergrove Avenue be b.

Formula: a^2 + b^2 = c^2

Lets plug them in!

6^2 + b^2 = 10^2

36 + b^2 = 100

b^2= 100 - 36

b^2 = 64

64 is the exponential value of b, meaning to lower it to its original terms, we apply the opposite of squaring. Which is finding the square root.

\(\sqrt{64}\) = 8

Therefore Silvergrove Avenue is 8 m.

Answer:

8

Step-by-step explanation:

Pythagorean Theorem: a^2 + b^2 = c^2

c (the hypotenuse, or longest leg) = 10, a or b = 6

6^2 + b^2 = 10^2

36 + b^2 = 100

b^2 = 64

b = 8

The general solution of the given differential equation is the sum of the complementary solution and the particular solution:

y(t) = y_c(t) + y_p(t)

y(t) = c1 × e⁻ᵗ × cos(2t) + c2 × e⁻ᵗ × sin(2t) + (²/₂₁) × sin(2t) + (⁴/₂₁) × cos(2t)

where c1 and c2 are arbitrary constants.

To find the general solution of the given differential equation, follow these steps:

Step 1: Find the complementary solution:

Consider the homogeneous equation:

y'' + 2y' + 5y = 0

The characteristic equation corresponding to this homogeneous equation is:

r² + 2r + 5 = 0

Solving this quadratic equation, find two complex conjugate roots:

r = -1 + 2i and -1 - 2i

Therefore, the complementary solution is:

y_c(t) = c1 × e⁻ᵗ × cos(2t) + c2 × e⁻ᵗ × sin(2t)

where c1 and c2 are arbitrary constants.

Step 2: Find a particular solution:

We are looking for a particular solution of the form:

y_p(t) = A × sin(2t) + B × cos(2t)

Differentiating y_p(t):

y'_p(t) = 2A × cos(2t) - 2B × sin(2t)

y''_p(t) = -4A × sin(2t) - 4B × cos(2t)

Substituting these derivatives into the differential equation:

(-4A × sin(2t) - 4B × cos(2t)) + 2(2A × cos(2t) - 2B × sin(2t)) + 5(A × sin(2t) + B × cos(2t)) = 2 × sin(2t)

Simplifying the equation:

(-4A + 4B + 5A) × sin(2t) + (-4B - 4A + 5B) × cos(2t) = 2 × sin(2t)

To satisfy this equation, we equate the coefficients of sin(2t) and cos(2t) separately:

-4A + 4B + 5A = 2 (coefficient of sin(2t))

-4B - 4A + 5B = 0 (coefficient of cos(2t))

Solving these simultaneous equations, we find:

A = ²/₂₁

B = ₄/₂₁

Therefore, the particular solution is:

y_p(t) = (²/₂₁) × sin(2t) + (⁴/₂₁) × cos(2t)

Step 3: General solution:

The general solution of the given differential equation is the sum of the complementary solution and the particular solution:

y(t) = y_c(t) + y_p(t)

y(t) = c1 × e⁻ᵗ × cos(2t) + c2 × e⁻ᵗ × sin(2t) + (²/₂₁) × sin(2t) + (⁴/₂₁) × cos(2t)

where c1 and c2 are arbitrary constants.

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