Brendon finished an obstacle course in 22.5 minutes. Tobias finished the course 85 seconds after Brendon. How long did it take Tobias to finish?

Without this information, it is not possible to determine if the sample accurately represents the overall distribution of eggs at the farmers' market.

It is impossible to say if the sample of eggs at the farmers' market is likely to be representative based on the information supplied. Jackson appears to have bought 17 eggs from each farmer, which suggests that he did so in an equal amount. It does not, however, provide data on the total number of farmers present at the market or their overall distribution of eggs.

Additional data, such as the total number of farmers present at the market, the average number of eggs each farmer generally has, and the variability in the number of eggs among the farmers, would be required to evaluate the sample's representativeness.

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The property that should be used to simplify the expression 1/t⁻³ is [tex]\frac{1}{a^-m}[/tex] = [tex]a^m[/tex] (where a ≠ 0). Option A

In the given scenario or expression, this property implies that 1/t⁻³ = t³. The negative exponent in the denominator becomes a positive exponent when moved to the numerator.

Here is the step-by-step solution

1/t⁻³ = 1/(t⁻³)

1/(t⁻³) = (t⁻³)⁻¹

(t⁻³)⁻¹ = t⁽⁻³⁾ˣ⁽⁻¹⁾

t⁽⁻³⁾ˣ⁽⁻¹⁾ = t³

Therefore, the simplified expression is t³.

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Answer:

x = 5.7

Step-by-step explanation:

Use the pythagorean theorem, which says a^2+b^2 = c^2 where c is the hypotenuse (longest side of a right triangle, always opposite the 90 degree right angle).

7^2 + x^2 = 9^2

49 + x^2 = 81

x^2 = 32

now take the square root of both sides

x = 5.65685424949

Round to the nearest tenth.

x = 5.7

Answer:

5.7

Step-by-step explanation:

x^2 + 7^2 = 9^2

x^2 + 49 = 81

x^2 = 81 - 49

x^2 = 32

x = the square root of 32

x = 5.657

round to the nearest tenth

x = 5.7

Answer:

I estimate it is around 340 because 34 times 10 is 340 the product of 34 times 12 is 408

Step-by-step explanation:

Answer:

The answer is 5

Step-by-step explanation:

c²=3²+4²

c²=9+16

c²=25

[tex] \sqrt{ {c}^{2} } = \sqrt{25} [/tex]

c=5

The value of c is :

↬ c = 5, c = -5

Solution:

First off, we should square the numbers:

[tex]\sf{3^2+4^2=c^2}[/tex]

[tex]\sf{9+16=c^2}[/tex]

[tex]\sf{25=c^2}[/tex]

Now I square-root each side :

[tex]\sf{5=c}[/tex]

[tex]\sf{-5=c}[/tex]

This means that :

[tex]\sf{c=5,\:c=-5}[/tex]

How did this happen? We should know that once we take the square root of a number, we end up with two solutions that are opposites of each other. This phenomenon is explained below.

When we square 5, we get 25. When we square -5, we also get 25.

So then, when taking the square root of 25, we get both 5 and -5. And now, we know why.

To determine whether there is a difference of opinion between doctors and nurses regarding a new postoperative procedure, the researcher conducted a survey and tabulated the data in a table form. The next step is to analyze the data using statistical methods and a significance level of 5%.

To begin the analysis, the researcher can use a statistical test such as the chi-square test for independence. This test will examine whether there is a significant association between the opinions of doctors and nurses regarding the procedure.

The chi-square test will compare the observed frequencies in each category (e.g., doctors who feel differently, doctors who feel the same, nurses who feel differently, nurses who feel the same) with the frequencies that would be expected if there was no association between the profession and opinion.

If the calculated chi-square value exceeds the critical value at a significance level of 5%, it suggests that there is a significant difference in opinion between the two groups.

The researcher should calculate the chi-square value, degrees of freedom, and compare it to the critical value from the chi-square distribution table.

If the calculated chi-square value exceeds the critical value, the researcher can conclude that there is a significant difference of opinion between doctors and nurses regarding the postoperative procedure.

It is important to note that statistical significance does not imply practical significance. Even if there is a significant difference, the magnitude of the difference should be considered in the context of the study.

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John William is entitled to purchase 15,000 shares before the offering is made to the public.

a. To calculate the percentage of the total vote John William will control, we need to find the proportion of shares he owns out of the total shares represented at the meeting.

John William owns 6,000 shares out of the 20,000 shares offered so far. Therefore, the proportion of shares he owns is 6,000/20,000, which simplifies to 3/10 or 0.3.

To convert this proportion to a percentage, we multiply by 100:

Percentage of the total vote = 0.3 * 100 = 30%

Thus, John William will control 30% of the total vote at the.         shareholder meeting.    

b. Preemptive rights allow existing shareholders to purchase new shares before they are offered to the public. To determine the number of shares John William is entitled to purchase, we need to calculate the proportion of his current ownership.

John William owns 6,000 shares out of the total shares offered so far, which is 20,000. Therefore, his ownership proportion is 6,000/20,000, or 3/10.

If Peixotto Media plans to issue 50,000 new shares, John William's entitlement would be:

Entitlement = (3/10) * 50,000 = 15,000 shares.

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Except You can invest your 401(k) into a wider variety of asset types than you can with an IRA. All are the advantages. Option B

A) You don't pay taxes on your investments' growth each year: One of the main advantages of a 401(k) plan is the tax advantage it provides.

Contributions to a traditional 401(k) are made on a pre-tax basis, meaning that the money you contribute is not subject to income tax. Additionally, the growth of investments within the 401(k) account is tax-deferred until you make withdrawals in retirement.

C) Your employer may match some of your 401(k) contributions: Many employers offer a matching contribution to their employees' 401(k) plans. This means that for every dollar you contribute to your 401(k), your employer will contribute a certain percentage, up to a specified limit.

D) You can contribute more money into a 401(k) than into an IRA: 401(k) plans generally allow for higher contribution limits compared to Individual Retirement Accounts (IRAs).

In 2021, the annual contribution limit for a 401(k) is $19,500 (with an additional $6,500 catch-up contribution for individuals aged 50 or older).

In contrast, the annual contribution limit for an IRA is $6,000 (with an additional $1,000 catch-up contribution for individuals aged 50 or older). The higher contribution limits of a 401(k) allow individuals to save more for retirement on a tax-advantaged basis.

In summary, the correct answer is B. The ability to invest in a wider variety of asset types is not an advantage of a 401(k) plan. However, the other options listed (A, C, and D) are all advantages of a 401(k) plan.

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24. The length RT is 18 units

25. The equation of the circle graphed is x² + (y - 3)² = 16

The length RT can be calculated using the intersecting secants equation

So, we have

11 * (11 + x) = 9 * (9 + 13)

So, we have

11 + x = 18

This gives

RT = 18

The equation of the circle graphed is represented as

(x - a)² + (y - b)² = r²

Where, we have

So, we have

(x - 0)² + (y - 3)² = 4²

Evaluate

x² + (y - 3)² = 16

Hence, the equation of the circle graphed is x² + (y - 3)² = 16

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The area of the rectangular shaped kitchen floor is A = 96 feet²

Given data ,

The side length of each tile is 2ft, then the area of each tile is:

Area of a tile = side x side = 2ft x 2ft = 4 sq ft

Since there are 6 rows of tiles, each row has 4 tiles, therefore the total number of tiles is:

Total number of tiles = 6 x 4 = 24 tiles

So, the total area covered by the tiles is:

Total area covered by tiles = Area of a tile x Total number of tiles

= 4 sq ft/tile x 24 tiles

= 96 sq ft

Hence , the area of the kitchen floor is 96 feet²

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The total cost of materials needed to build the house is $4374.75.

Calculate the area of the front and back of the house.

Area = Length x Width

Area = 3.5 m x 2.5 m = 8.75 m²

Calculate the area of the sides of the house.

Area = 2 x Length x Height

Area = 2 x 3.5 m x 5 m = 35 m²

Calculate the total cost of glass.

Cost of glass = Area x Cost per square meter

Cost of glass = 8.75 m² x $37 / m² = $323.75

Calculate the total cost of roof tiles.

Cost of roof tiles = Area x Cost per square meter

Cost of roof tiles = 35 m² x $95 / m² = $3325

Calculate the total cost of reinforcement metal.

Cost of reinforcement metal = Perimeter x Cost per meter

Cost of reinforcement metal = 2 x (Length + Width) x $54 / m = $726

Add the costs of glass, roof tiles, and reinforcement metal to get the total cost of materials.

Total cost = $323.75 + $3325 + $726 = $4374.75

Therefore, the total cost of materials needed to build the house is $4374.75.

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The variable that is contained in the given expression is y. Therefore, option C is the correct answer.

The given expression is 7y+2y² +3.

In the given expression there are 3 terms, so it is called trinomial.

In the term 7y, y is the coefficient of 7.

In the term 2y², y² is the coefficient of 2.

3 is the constant term.

Therefore, option C is the correct answer.

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Answer:

3/8 = (3 + AD)/20

8(3 + AD) = 60

24 + 8AD = 60

8AD = 36

A = 4 1/2

B is the correct answer.

The sales tax on the computer is $69.93.

To calculate the sales tax on the computer, we need to multiply the price of the computer by the sales tax rate. Here's how you can do it:

Price of the computer: $999.00

Sales tax rate: 7% (which can be expressed as 0.07)

Sales tax = Price of the computer * Sales tax rate

Sales tax = $999.00 * 0.07

To find the sales tax in dollars and cents, we can perform the calculation:

Sales tax = $999.00 * 0.07

Sales tax = $69.93

Therefore, the sales tax on the computer is $69.93.

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ANSWER: 100% of 2000000000 is 2000000000

What is 100 Percent of 2000000000?

100 percent *2000000000

= (100/100)*2000000000

= (100*2000000000)/100

= 200000000000/100 = 2000000000

Now we have: 100 percent of 2000000000 = 2000000000

Question: What is 100 percent of 2000000000?

We need to determine 100% of 2000000000 now and the procedure explaining it as such

Step 1: In the given case Output Value is 2000000000.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 2000000000 = 100%.

Step 4: In the Same way, x = 100%.

Step 5: On dividing the pair of simple equations we got the equation as under

2000000000 = 100% (1).

x = 100% (2).

(2000000000%)/(x%) = 100/100

Step 6: Reciprocal of both the sides results in the following equation

x%/2000000000% = 100/100

Step 7: Simplifying the above obtained equation further will tell what is 100% of 2000000000

x = 2000000000%

Therefore, 100% of 2000000000 is 2000000000

Answer:

Therefore, the y-intercept of the line is (0, 4/3).

Step-by-step explanation:

To find the y-intercept of the line 12x - 18y = -24, we need to set x = 0 and solve for y.

12(0) - 18y = -24

Simplifying, we get:

-18y = -24

Dividing both sides by -18:

y = 4/3

Therefore, the y-intercept of the line is (0, 4/3).

The values of a and b are a = -3 and b = 42. The solutions for x can be written as:

x = -3 - √42

x = -3 + √42

To solve the quadratic equation 2x² + 12x = 66 by completing the square, we need to follow these steps:

Step 1: Move the constant term to the right side:

2x² + 12x - 66 = 0

Step 2: Divide the equation by the leading coefficient (2):

x² + 6x - 33 = 0

Step 3: To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation:

x² + 6x + (6/2)² = 33 + (6/2)²

x² + 6x + 9 = 33 + 9

x² + 6x + 9 = 42

Step 4: Rewrite the left side as a perfect square:

(x + 3)² = 42

Step 5: Take the square root of both sides:

√(x + 3)² = ±√42

x + 3 = ±√42

Step 6: Solve for x:

x = -3 ± √42.

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The amount of money that will produce Rs. 15000 at the end of 6 month for 10years at 16% is Rs. 3750

Compound interest is the interest you earn on interest.

For example, if you have $100 and it earns 5% interest each year, you'll have $105 at the end of the first year. At the end of the second year, you'll have $110.25.

Compound interest is expressed as;

A = P( 1+r/n) ^{nt}

where A is the amount

n is the number of time its compounded

t is time

A = 15000

r = 16/100 = 0.16

n = 6/12 = 0.5

t = 10 years

15000 = P( 1 + 0.16/0.5) ^{ 0.5× 10}

15000 = P( 1 + 0.32)⁵

15000 = P( 1.32)⁵

15000 = 4P

P = 15000/4

P = Rs. 3750

Therefore the amount that will be deposited to give Rs. 15000 is Rs. 3750.

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Answer:

7/10

Step-by-step explanation:

[tex]1 - \frac{3}{10} \\ = \frac{10}{10} - \frac{3}{10 } \\ = \frac{7}{10} [/tex]

The solution to the System of equations is x = -9 and y = 8

We have the equation x - y = -1 and the equation x = -9. We can use the second equation to substitute the value of x in the first equation and solve for y.

Given x = -9, we substitute this value into the first equation:

(-9) - y = -1

Simplifying, we have:

-9 + y = -1

To isolate y, we can add 9 to both sides of the equation:

-9 + 9 + y = -1 + 9

This gives us:

y = 8

Therefore, the solution to the system of equations is x = -9 and y = 8.

We can check this solution by substituting the values of x and y back into the original equations:

Equation 1: x - y = -1

Substituting x = -9 and y = 8:

-9 - 8 = -1

Simplifying, we have:

-17 = -1

The equation is true, so our solution is valid.It is important to note that the solution provided is derived from the given equations and standard algebraic methods.

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The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

Using the Central Limit Theorem.

The Central Limit Theorem states that for a large enough sample size, the distribution of sample means will be approximately normally distributed, regardless of the shape of the population distribution. In this case, we have a sample size of 30, which is considered large enough for the Central Limit Theorem to apply.

Calculate the standard error of the mean (SEM):

SEM = σ / √n

SEM = 0.52 / √30

SEM ≈ 0.095

Calculate the z-scores for the lower and upper limits:

z1 = (94.7 - μ) / SEM

z2 = (95.3 - μ) / SEM

z1 = (94.7 - 95) / 0.095 ≈ -0.526

z2 = (95.3 - 95) / 0.095 ≈ 0.316

Find the area under the normal distribution curve between the z-scores using a standard normal distribution table or a calculator. The area represents the probability.

Using a standard normal distribution table or a calculator, the area between -0.526 and 0.316 is approximately 0.436.

Therefore, the probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.

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Based on this graph, a measurement which represent the best estimate for the mean length of bass in the lake include the following: 17 inches.

In Mathematics and Statistics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean of a data set can be calculated by using the following formula:

Mean = [F(x)]/n

By critically observing the graph (histogram) shown in the image attached below, we can logically deduce that the distribution is symmetrical. This ultimately implies that, the mean length of bass in the lake would be in the middle, with an estimated value of 17 inches.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Complete Question:

A university professor and his students did a study to determine the mean length of bass in a lake. Each time a bass was caught, its length was measured in inches, and then it was released. The distribution of the lengths is shown in the graph below. Based on this graph, which measurement represents the best estimate for the mean length of bass in the lake?

12 inches

17 inches

20 inches

23 inches

Answer:

-3x + 3

Step-by-step explanation:

To find the equation of a line perpendicular to the line passing through (-2, 1) and (4, 3), we need to determine the slope of the original line first. Then, we can use the negative reciprocal of that slope to find the slope of the perpendicular line. Finally, we can use the point-slope form to write the equation of the perpendicular line.

Step 1: Find the slope of the original line.

Slope (m) = (change in y) / (change in x)

m = (3 - 1) / (4 - (-2))

m = 2 / 6

m = 1/3

Step 2: Determine the slope of the perpendicular line.

The slope of the perpendicular line is the negative reciprocal of the original line's slope.

Perpendicular slope = -1 / (1/3)

Perpendicular slope = -3

Step 3: Use the point-slope form to write the equation.

The point-slope form is given by:

y - y1 = m(x - x1)

Using the point (-2, 9) and the perpendicular slope (-3), we can write the equation as:

y - 9 = -3(x - (-2))

y - 9 = -3(x + 2)

y - 9 = -3x - 6

y = -3x + 3

Therefore, the equation of the line perpendicular to the line passing through (-2, 1) and (4, 3) and passing through (-2, 9) is y = -3x + 3.

The expression x = (2 ± √(-12)) / 2 is negative, this quadratic equation does not have real solutions.

The quadratic formula, we need the quadratic equation in the form ax^2 + bx + c = 0. The given equation is x^2 + 1 = 2x - 3. To set it up correctly, we need to move all terms to one side of the equation to have a zero on the other side.

Rearranging the equation, we get x^2 - 2x + 4 = 0. Now we can identify the coefficients a, b, and c.

The correct expression to set up the quadratic formula is:

B) x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 2x + 4 = 0, we have:

a = 1

b = -2

c = 4

Plugging these values into the quadratic formula, we have:

x = (-(-2) ± √((-2)^2 - 4 * 1 * 4)) / (2 * 1)

Simplifying further, we get:

x = (2 ± √(4 - 16)) / 2

x = (2 ± √(-12)) / 2

Since the expression inside the square root is negative, this quadratic equation does not have real solutions.

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Note the full question may be :

Consider the quadratic equation 2x^2 + 5x - 3 = 0. Which expression correctly sets up the quadratic formula?

A) x = (-b ± √(b^2 - 4ac)) / (2a)

B) x = (-b ± √(b^2 + 4ac)) / (2a)

C) x = (-b ± √(4ac - b^2)) / (2a)

D) x = (b ± √(b^2 - 4ac)) / (2a)

Answer:

Step-by-step explanation:

Answer:181,250

Step-by-step explanation:

Basically, the cost would go up 5 percent, and you’re asking how much it would go up in 5 years. So 5x5=25, so you’d multiply 145,000 by 25%, which is 36,250. So, you’d add that to 145,000 which would get you 181,250.

Given statement solution :- The correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

To make the best estimate for the number of beats in 60 seconds, we need to find the proportion that relates the beats per second in the given scenario to the desired duration of 60 seconds.

Let's set up the proportion using the given information:

Heart beats per second (beats/sec) = 48 beats / 40 seconds

We want to find the number of beats in 60 seconds (x beats / 60 seconds).

The correct proportion would be:

48 beats / 40 seconds = x beats / 60 seconds

Therefore, the correct proportion to make the best estimate for the number of beats in 60 seconds is:

A. 48/40 = 60/x

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Answer:

20 square feet

Step-by-step explanation:

area of a triangle = (1/2) base x height

The "base" for this one gigantic triangle is the 'top' of the diagram - - - - it's the entire 3+7 = 10 side. (We can calculate the area of the whole thing at once. We don't have to do the left and the right halves separately!!!)

The height is 4.

So area = (1/2) base x height

= (1/2) * 10 * 4

= 20 square feet

The equation of the graph in the required form is y = 5|x| - 5

From the question, we have the following parameters that can be used in our computation:

The graph (see attachment)

The graph is an absolute value graph

And it can be expressed in the form of y = a|x – h| + k

Where

Vertex = (h, k)

The vertex of the graph is (0, -5)

So, we have

y = a|x| - 5

Using the point on the graph, we have

a|1| - 5 = 0

So, we have

a = 5

This means that the equation of the graph is y = 5|x| - 5

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