Carlos went to buy a television the same size as his friend’s. When he got to the store, he found that televisions are measured along the diagonal. Which equation will help him find the size he wants?

2 triangles are connected at their hypotenuse to form a rectangle. The rectangle has a length of 35 inches and width of 20 inches.
20 squared + 35 squared = d squared
d squared + 20 squared = 35 squared
d squared + 35 squared = 20 squared
35 squared minus 20 squared = d squared

Answer:

lets do it.

f-¹(X) = 1/X+4

f -¹(4) = 1/4+4

= 1/8

D.kite

youre welcome hihihi

Answer:

see explanation

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = - 2 and d = a₂ - a₁ = 5 - (- 2) = 5 + 2 = 7 , then

\(a_{n}\) = - 2 + 7(n - 1) = - 2 + 7n - 7 = 7n - 9

Use this formula to find a₁₀

a₁₀ = 7(10) - 9 = 70 - 9 = 61

The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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Answer:

{t|60 <= t <= 85}

Step-by-step explanation:

The temperatures were measures at different times, but does not stop the values being real numbers (i.e. not discrete, or integer values).

So the range of the function is the set of all values between the minimum and maximum measured during the measuring interval (domain) of hours two and twenty-two.

The minimum value = 60F

The maximum value = 85F

So the interval of the range is [60,85], in interval notation.

In set-builder notation, it is

{t|60 <= t <= 85}

A non-directional study hypothesis, on the other hand, would merely assert that there is a difference between the variables being examined without specifying which way the difference will go.

A type of statistical hypothesis known as a null hypothesis claims that a particular collection of findings has no significance in statistics. The viability of theories is evaluated using sample data. an an an a The assumption made by researchers is that there is some connection between the factors. The null hypothesis, on the other hand, asserts that such a relationship does not exist. Although it might not seem significant, the null hypothesis is an important part of study.

"h1: 1 > 2" denotes the direction of the study. Indicating that one variable (1) will have a higher impact or value than the other variable (2), this hypothesis forecasts the direction of a connection between the variables under study. (2). A non-directional study hypothesis, on the other hand, would merely assert that there is a difference between the variables being examined without specifying which way the difference will go.

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Answer:The plant growth 1/2 inches each week

Step-by-step explanation:

Answer:

The one you picked

Step by Step explanation

The probability that m balls is P(m balls in first compartment) = (nCm) * ((n-1)^(n-m)) / (n^n).

The total number of possible arrangements of distributing n balls into n compartments is given by n^n. Each ball has n choices for which compartment to fall into, and since there are n balls, we multiply n by itself n times.

Now, let's consider the number of ways m balls can fall into the first compartment. We can choose m balls out of the n balls to go into the first compartment in nCm ways, which is the binomial coefficient.

The remaining (n-m) balls can go into any of the remaining (n-1) compartments in (n-1)^(n-m) ways. Therefore, the probability that m balls will fall into the first compartment is given by:

P(m balls in first compartment) = (nCm) * ((n-1)^(n-m)) / (n^n)

This formula calculates the ratio of favorable outcomes (m balls in the first compartment) to the total number of possible outcomes (all possible arrangements of distributing n balls into n compartments).

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Answer:

Between 6 and 7

Step-by-step explanation:

Step 1:  Determine where square root of 46 lies

\(6^2 = 36\)

\(7^2 = 49\)

Since 46 lies between 36 and 49, our square root value lies between 6 and 7

Answer:  Between 6 and 7

B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

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Answer:

37%

Step-by-step explanation:

37/100

If we allow the number of edges between any two nodes to be more than two, we would need to use the adjacency matrix to accurately store that graph information.

The adjacency matrix is a matrix representation of a graph where the rows and columns represent the vertices and the values in the matrix represent the number of edges between two vertices.

In this case, we could have values greater than 1 in the matrix to represent multiple edges between two vertices.

On the other hand, the adjacency list data structure would not be able to accurately store this information, as it represents each vertex and its adjacent vertices in a linked list format.

It would be difficult to represent multiple edges between two vertices using this data structure.

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Answer:

135min = 2hours and 15 minutes

Step-by-step explanation:

85.5F - 78F = 7.5F

it takes -7.5F to cool 85.5F to 78F

Since it takes 18 minutes to lower the temperature -1

18 × 7.5 = 135

135 minutes = 2 hours and 15 minutes

it takes 2 hours and 15 minutes to cool a room from 85.5 to 78 F

If you doubled a penny every day, you would have $5,368,709.12

You can see that the decision is rather straightforward: having a single penny that doubles every day for a month are preferable to receiving $1 million upfront. This is due to compound interest's strength.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.

It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.

Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

If I double this particular penny every day, I would have 30 extra pennies, plus my original one. I have $0.31 literal dollars

On day 30, if you doubled a penny every day, you would have $5,368,709.12.

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Answer:

$2907.89

General Formulas and Concepts:

Symbols

Pre-Algebra

Order of Operations: BPEMDAS

Algebra i

Compounded Continuously Formula: \(\displaystyle A = Pe^{rt}\)

Step-by-step explanation:

Step 1: Define

Identify variables

P = 930

t = 19

r = 6% = 0.06

Step 2: Find Interest

Answer: \(-5000\)

Step-by-step explanation:

Hint: "below" the ocean depths

Answer:

 \(\frac{x-7}{4} =f^{-1}( x)\)

Step-by-step explanation:

→ Replace f(x) with y

y = 4x + 7

→ Minus 7 from both sides

y - 7 = 4x

→ Divide both sides by 4

\(\frac{y-7}{4} =x\)

→ Replace y's with f⁻¹(x)

\(\frac{x-7}{4} =f^{-1}( x)\)

Given the expression:

Dividing complex numbers:

Finding the conjugate:

If the firm increases its production and sales from 3 to 4 units per day, the profit margin increases.

The correct answer option is option B

Total profit = Total revenue - Total cost

Total revenue = number of units × price of each Units

At 3 units:

Total profit = Total revenue - Total cost

= (3 × 2500) - $3000

= $7,500 - $3000

Total profit = $4,500

At 4 units:

Total profit = Total revenue - Total cost

= (4 × $2,500) - $4,100

= $10,000 - $4,100

= $5,900

In conclusion, the profit margin when production is increased from 3 to 4 units will also increase.

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Answer:

2,160

Step-by-step explanation: since M is proportional to L^3 so when L=2 then L^3=8 so M=160 which means if L = 3

When L = 3, the value of M is 540. The relationship between M and L³ holds true.

When two variables, M and L, are directly proportional, it means that their ratio remains constant.

In this case, M is directly proportional to L³, which can be written as M = k × L³, where k is the constant of proportionality.

To find the value of k, we can use the given information when L = 2, and M = 160:

160 = k × 2³

160 = k × 8

k = 160 / 8

k = 20

Now that we have the value of k, we can find the value of M when L = 3:

M = 20 × 3³

M = 20 × 27

M = 540

So, when L = 3, the value of M is 540. The relationship between M and L³ holds true for any value of L when multiplied by the constant of proportionality k, which we found to be 20 in this case.

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The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³

To know the amount of juice the cup can hold, we shall obtain the volume of the cup.

We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:

Volume = πr²h

Volume = 3.14 × 4² × 12

Volume = 3.14 × 16 × 12

Volume = 602.88 cm³

Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³

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Dividing 9x³ + 3x² + 10x + 3 by 3x + 2. will yield a quotient of 3x² - x + 4 and a remainder of -5 that is (3x² - x + 4) -5/(3x + 2).

Applying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.

We shall divide the 9x³ + 3x² + 10x + 3 by 3x + 2. as follows;

9x³ divided by 3x equals 3x²

3x + 2. multiplied by 3x² equals 9x³ + 6x²

subtract 9x³ + 6x² from 9x³ + 3x² + 10x + 3 will result to -3x² + 10x + 3

-3x² divided by 3x equals -x

3x + 2 multiplied by -x equals -3x² - 2x

subtract -3x² - 2x from -3x² + 10x + 3 will result to 12x + 3

12x divided by 3x equals 4

3x + 2 multiplied by 4 equals 12x + 8

subtract 12x + 8 from 12x + 3 will result to a remainder of -5

Therefore by the long division method, 9x³ + 3x² + 10x + 3 divided by 3x + 2 gives a quotient 3x² - x + 4 and a remainder of -5 and can be written as (3x² - x + 4) -5/(3x + 2).

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If you work 40 hours this week, your net pay after all of the withholding taxes are taken out is $386.75.

The net pay is the difference between the gross pay (total earnings for the period) and the payroll deductions (e.g. withholding taxes).

Hourly pay rate = $12.50

Work week hours = 40 hours

Total earnings for the week = $500 ($12.50 x 40)

Federal withholding tax = 15%

Social Security = 6.2%

Medicare = 1.45%

Total withholding taxes = 22.65%

= $113.25 ($500 x 22.65%)

Net earnings for the week = $386.75 ($500 - $113.25)

Thus, for working 40 hours this week, your net pay will be $386.75.

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The equation of the line with slope 2/3 and y-intercept at ( 0, - 2) is y = ( 2/3 )x - 2.

The slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible.

We have the slope 2/3 of a line and the y-intercept at ( 0, - 2 ).

Now, we know that

The slope-intercept form of the equation of a line with slope m and y-intercept at the point (0, c) is given by:

y = mx + c

The slope of the line is :

m = 2/3

And, the y-intercept is (0, c) = ( 0, -2)

Hence, the equation of the line in the slope-intercept form will be:

y = mx + c

y = ( 2/3 )x + ( - 2)

y = ( 2/3 )x - 2

Therefore, the slope-intercept form of the equation of the line is y = ( 2/3 )x - 2.

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Answer:

b, d

Step-by-step explanation: