A triangle with area 28 square inches has a height that is six less than twice the width. Find the height and width of the triangle. [Hint: For a triangle with base b and height h , the area, A , is given by the formula

a. The null hypothesis (H₀): The mean annual interest paid on household debt is equal to or greater than $8,000.

The alternate hypothesis (H₁): The mean annual interest paid on household debt is less than $8,000.

b. The value of test statistic is -1.518

c. at the 0.05 significance level, it is not reasonable to conclude that these households paid less than $8,000 of interest per year.

a. The null hypothesis (H₀): The mean annual interest paid on household debt is equal to or greater than $8,000.

The alternate hypothesis (H₁): The mean annual interest paid on household debt is less than $8,000.

b. To compute the value of the test statistic, we need to calculate the sample mean and the sample standard deviation.

Sample mean (\(\bar{X}\)) = (7,077 + 5,744 + 6,753 + 7,381 + 7,625 + 6,636 + 7,164 + 7,348 + 8,060 + 5,848 + 9,275 + 7,052) / 12 = 7,222.33

Sample standard deviation (s) = √([Σ(x - \(\bar{X}\))²] / (n - 1))

= √([Σ(7,077 - 7,222.33)² + (5,744 - 7,222.33)² + ... + (7,052 - 7,222.33)²] / (12 - 1))

≈ 1,066.11

Now we can calculate the t-value using the formula:

t = (\(\bar{X}\) - μ) / (s / √(n))

where μ is the hypothesized mean under the null hypothesis.

t = (7,222.33 - 8,000) / (1,066.11 / sqrt(12))

≈ -1.518

The value of test statistic is -1.518

c. To determine whether it is reasonable to conclude that these households have less debt, we need to compare the computed t-value to the critical t-value at the 0.05 significance level for a one-tailed test with (n - 1) degrees of freedom.

Since the alternative hypothesis states that the mean interest paid is less than $8,000, it is a one-tailed test in the left tail.

Looking up the critical t-value from a t-distribution table or using a t-distribution calculator with 11 degrees of freedom at a 0.05 significance level, we find the critical t-value to be approximately -1.796.

Since the computed t-value (-1.518) is greater than the critical t-value (-1.796), we fail to reject the null hypothesis.

Therefore, at the 0.05 significance level, it is not reasonable to conclude that these households paid less than $8,000 of interest per year.

Learn more about test statistic here

https://brainly.com/question/31746962

#SPJ4

Answer:

1

Step-by-step explanation:

32/4=8

no remainder so it is i^4

i^4=1

Answer:

b<-7 or b>-1

Step-by-step explanation:

explanation: -6b>42 turns into -42>6b then divide by 6 on both sides and you get -7>b

for the other inequality, you  take 4b+6>2 and then subtract6 from both sides, from there you will get 4b>-4 and that will be b>-1

Answer:

Her wages in a week, if she worked 48 hours, is;

Explanation:

Given that Helen earns $22.60 per hour as a grocery clerk and She receives time-and-a-half pay for any hours she works over 40 in a week.

Given that she worked 48 hours;

So, her wages in a week will then be;

Therefore, her wages in a week, if she worked 48 hours, is;

Answer: x + 5

Step-by-step explanation:

Answer:

B=5

Step-by-step explanation:

a2+b2=c2

12squared+b2=13squared

144+b2=169 Subtract by 144 on both sides

b2=25 Find square root of 25

b=5

To multiply a square root by a square root and a whole number, you can use the distributive property of multiplication

Given data ,

Let the numbers be represented by the expression A

Now , the value of A is

A = √2 × 3√5

First, you can simplify each square root:

√2 = 1.4142 (rounded to 4 decimal places)

3√5 = 5.1962 (rounded to 4 decimal places)

Next, you can multiply the two simplified square roots and the whole number:

√2 × 3√5 = 1.4142 × 5.1962 × 3

= 22.3607 × 3

= 67.0821

Hence , the expression is A = √2 × 3√5 = 67.0821

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Answer:

18

Step-by-step explanation:

We are to determine the value of a

to do this we have to make a the subject of the formula. this can be achieved by taking the following steps

divide both sides of the equation -  2(42 - a) = 48 - by 2

42 - a = 24

take a to the right hand side and bring 24 to the left hand side

a = 42 - 24

a = 18

Answer:

Neither

Step-by-step explanation:

-12x + 3y = 3

y = 4x + 1

y = mx + b

The second equation given is set up in the correct form already (y = 4x + 1)

We have to convert the first equation into the same format

-12x + 3y = 3

Isolate the y

3y = 3 + 12x

Divide the 3 from the y and the other side

y = 1 + 4x

y = 4x + 1

This is the same as the first equation

They can only be parallel if their slope (m or 4 in this case) is the same and their y-intercepts (b or 1 in this case) are different. Since the equations are the exact same and do not fit the y-intercept criteria for parallel, they cannot be parallel. If they were perpendicular, their lines must cross. This means they have to contain reciprocals or opposite slopes. Our slope here for both of them is 4 or 4/1. Since neither are the opposite (which would be 1/4), it is not perpendicular. Therefore, the answer is neither

The ordered pairs that could be points on a parallel line are:

(-8, 8) and (2, 2)

(-2, 1) and (3, -2)

Parallel lines have the same slope. Thus, we have to find ordered pairs with a slope of -3/5.

We have:

slope of the line is -3/5.

Thus, m = -3/5

Formula for slope between two coordinates is;

m = (y₂ - y₁)/(x₂ - x₁)

A) At (–8, 8) and (2, 2);

m = (2 - 8)/(2 - (-8))

m = -6/10

m = -3/5

B) At (–5, –1) and (0, 2);

m = (2 - (-1))/(0 - (-5))

m = 3/5

C) At (–3, 6) and (6, –9);

m = (-9 - 6)/(6 - (-3))

m = -15/9

m = -5/3

D) At (–2, 1) and (3, –2);

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

m = -3/5

E) At (0, 2) and (5, 5);

m = (5 - 2)/(5 - 0)

m = 3/5

Learn more about slope on:

brainly.com/question/18957723

#SPJ1

The temperature at which ΔrG° = 0.00 kJ is 1,596 K.


We know that:

ΔrG° = ΔrH° - TΔrS°

where ΔrG° is the standard free energy change of the reaction, ΔrH° is the standard enthalpy change of the reaction, ΔrS° is the standard entropy change of the reaction, and T is the temperature.

For ΔrG° to equal 0.00 kJ, we can rearrange the equation to solve for T:

T = ΔrH°/ΔrS°

Plugging in the values we have:

T = (2112 kJ)/(132.9 J/K)
T = 1,596 K

Therefore, the temperature at which ΔrG° = 0.00 kJ is 1,596 K.

Learn more about entropy here:

https://brainly.com/question/32484278

#SPJ11

Answer:

24 meters

Step-by-step explanation:

8*3=24

Given:

The graph of a function and a blue line.

To find:

The correct name for the blue line.

Solution:

Domain: It is the set of inputs. These are the x-values for which the function is defined.

Range: It is the set of outputs. These are the y-values for the function.

Asymptote: The function approaches to a line as x approaches to -∞ or ∞ but not intersect the line, then the line is known as asymptote.

y-intercept: It is the intersection point of the function and the y-axis.

From the given graph it is clear that the function approaches to the blue line as x approaches to -∞ but not intersect the blue line.

So, the blue line is an asymptote of the function.

Look at the graph shown below the blue line represents an asymptote of the graph.

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

For such more question on interest

https://brainly.com/question/25720319

#SPJ8

Obtaining the average monthly cell phone bill for all high school students in the state of Florida would be an example of a population parameter estimation.

In statistics, population parameter estimation involves using a sample to estimate unknown characteristics of a population. The average monthly cell phone bill for all high school students in Florida is a population parameter because it represents a characteristic of the entire population of interest. However, it is often impractical or impossible to collect data from every individual in a population. Therefore, researchers rely on sampling techniques to select a representative subset of the population.

In this case, the researcher is interested in the average monthly cell phone bill for all high school students in Florida. To estimate this parameter, the researcher would need to collect data from a sample of high school students in the state. By calculating the average cell phone bill for the selected sample, the researcher can make an inference about the average bill for the entire population.

The process of obtaining an estimate of the population parameter is known as point estimation. In this scenario, the researcher would calculate the sample mean of the monthly cell phone bills and use it as an estimate of the population mean. This estimate provides valuable insights into the average cell phone bill for high school students in Florida, even though the researcher did not survey every student in the state.

Learn more about average here:

https://brainly.com/question/28280622

#SPJ11

Answer:

1202404.6

Step-by-step explanation:

1,200,000 + 2400 =1202400

1202400 + 4.6 = 1202404.6

The solution to the system of equations that includes functions f(x) and g(x) is given by: (1,7).

A linear function is modeled by:

y = mx + b

In which:

The linear function g(x) goes through point (0,5), hence the y-intercept is of 5. The function also goes through point (1,7), hence the slope is of 2 and the function is:

g(x) = 5 + 2x.

The solution to the system of equations is found as follows:

f(x) = g(x)

2x² + x + 4 = 5 + 2x

2x² - x - 1 = 0

Which is a quadratic equation with coefficient a = 2, b = -1, c = -1, hence:

When x = 1, f(x) = g(x) = 7, hence the solution of the system is of (1,7).

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

Answer:

D. (1,7)

Step-by-step explanation:

I took the exam

Answer:

The bench mark values might be 10/120 - 30/80

Step-by-step explanation

The value represents the climber's change in elevation during the first minute of the training session is  1/5.

Given,

During the second minute of a two-minute training session, a rock climber completed a 12-meter ascent up the wall. The climber returned to the identical location she had been in at the beginning of the two-minute session.

Let x be the distance climbed by the climber is x m

During the first minutes(60 seconds): distance climbed =\(\frac{x}{60}\)

In the 2nd minute, they climbed 12 m higher than in the 1st minute.

Now, the distance climbed by the climbed in the Second minute = \(\frac{x+12}{60}\)

Now, the change in the elevation during the first minute of the training session= \(\frac{x+12}{60}-\frac{x}{60} = \frac{12}{60}=\frac{2}{10}=\frac{1}{5}\)

Hence, the value represents the climber's change in elevation during the first minute of the training session is \(\frac{1}{5}\)

To read more about change, visit https://brainly.com/question/17270104

#SPJ4

Answer:

2

Step-by-step explanation:

it makes more sense and what was the last answer?

The Poisson probability law states that the probability of at least two changes every day is 0.0263. Thus, 0.0263% of changes happen twice or more each day.

The mathematical method it explains for calculating probability calculates all the probabilities of something occurring in the setting of specific random events. A probability's proximity to the value or, alternatively, its distance from zero can make one less confidence in the outcome. The confidence level is based on how close the probability value is, which is calculated using a number range from 0 and 1.

Here,

calculation

The probability distribution function for X is the average number of times the event happens over a specific period of time.

In this experiment, the frequency, or x, at which an event occurs is counted.

The likelihood of the event happening throughout each period is equal.

The number of occurrences in one period is independent of the number in other intervals.

the first step is to set the discrete random variable X to the number of website content updates.

Let's say that there are on average x content changes every day.

The Poisson probability law states that the probability of at least two changes every day is 0.0263.

Consequently, 0.0263% of changes that occur twice or more

To know more about probability visit :-

brainly.com/question/30034780

#SPJ1

The number of silver and bronze medals that France won are 9 silver and bronze medals.

Since there are 60 medals awarded, and there were 20 each of bronze, silver, and gold. This means that there are 20 gold, 20 bronze and 20 silver.

Since U.S. swim team won 13 gold medals and Spain won 5gold medals, then the gold won by France will be:

= 20 - (13 + 5)

= 20 - 18

= 2 gold medals

France won 2 gold medals.

Since France won one-third of all the medals, the number of medals won by France will be:

= 1/3 × 60

= 20 medals

Since France won 2 golds medals, then the number of silver and bronze will be:

= 20 - 2

= 18 silver and bronze medals.

Since France won equal number of silver and bronze medals. This will be:

= 18/2

= 9 silver and bronze medals.

Read related link on:

https://brainly.com/question/19972449

Answer:

6

0

2

Step-by-step explanation:

I assume we are taking the y-value and dividing it by x, as indicated by the y/x

-6/-1

6

0/1

0

6/3

2

Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

MARK AS BRAINLIEST!!!

The factorial or ratio of p / q approximately is 1199.5.

Calculate p (number of ways to place 5 queens randomly on a chessboard):

A chessboard has 64 squares. We can place the first queen in any of the 64 squares, the second queen in any of the remaining 63 squares, and so on.

So, the number of ways to place 5 queens randomly is: p = 64 * 63 * 62 * 61 * 60 However, since the order in which we place the queens does not matter, we need to divide by the number of ways to arrange the 5 queens,

which is 5! (5 factorial). p = (64 * 63 * 62 * 61 * 60) / (5 * 4 * 3 * 2 * 1) 2=8,048,640

Calculate q (number of ways to place 5 queens column-wise):

We need to find the value of q. Here, we place 5 queens column-wise. In the first column, there are 8 possible squares to place the first queen. In the second column, there are only 7 possible squares left because one square is already blocked by the first queen.

Similarly, in the third column, there are only 6 possible squares left, and so on. Therefore, the total number of ways to place the 5 queens column-wise is: 8 × 7 × 6 × 5 × 4= 6,720

Calculate the ratio p / q:

Now that we have values for p and q, we can find the ratio p / q. p / q ≈ ((64 * 63 * 62 * 61 * 60) / (5 * 4 * 3 * 2 * 1)) / (8 × 7 × 6 × 5 × 4) ≈ 1199.5

Therefore, the ratio of p / q approximately is 1199.5.

To know more about factorial refer here:

https://brainly.com/question/30136880

#SPJ11

To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

To learn more about cash : brainly.com/question/31754110

#SPJ11

Given the differential equation dy/dx = y(8x^2+1)We have to find the general solution of the given differential equation and express it explicitly as a function of the independent variable.

We can solve this differential equation by the method of separating variables. Let's start solving. \(dy/dx = y(8x^2+1)Divide both sides by y(8x^2+1)\).So, we get\(1/y dy = (8x^2+1) dx\)Integrating both sides, we get\(∫ 1/y dy = ∫ (8x^2+1) dx On integrating, we get ln |y| = (8/3)x^3 + x + C\) where C is an arbitrary constant of integration.

Raise e to both sides, we \(get |y| = e^(8/3)x^3+xe^CNow, |y| = e^(8/3)x^3.e^C\)On putting a positive constant of integration, we can write |y| = Ke^(8/3)x^3 where K is a positive constant of integration. Since |y| can be either positive or negative, therefore,\(y = ±Ke^(8/3)x^3\)Therefore, the general solution of the given differential equation is\(y = Ke^(8/3)x^3\)where K is a positive constant of integration.

To know more about   differential equation  visit:

brainly.com/question/32645495

#SPJ11

Answer:

The answer is "\(v = \frac{50b}{v} = 50 \times b\)".

Step-by-step explanation:

A single bottle of supercharging includes the equivalent of 50 vitamins.

Number of vitamins v = Total number of vitamins

b = the number of bottles that were used

Because each bottle contains one vitamin, you should multiply this total number of bottles (b) by the total amount of vitamins (50 vitamins).

\(v = \frac{50b}{v} = 50 \times b\) so, Both are the same.

Answer:

i just did it- here ya go

Step-by-step explanation:

Given a linear transformation (LT) L: R2 → R2 and a basis S = {v1, v2} for R2, where v1 = (1, -1) and v2 = (4, -2), and that L(v1) = (-2, 1) and L(v2) = (4, -1), here need to find L(v) when v = (-1, 3) using the Reduced Row Echelon Form (RREF) method.

To find L(v) when v = (-1, 3), it can express v as a linear combination of the basis vectors v1 and v2. Let's call the coefficients of this linear combination x and y. Therefore, we have:

v = xv1 + yv2

Substituting the given values for v1 and v2:

(-1, 3) = x*(1, -1) + y*(4, -2)

Expanding this equation, get a system of equations:

-1 = x + 4y

3 = -x - 2y

It can represent this system of equations in matrix form as [A | B], where A is the coefficient matrix and B is the augmented column matrix:

| 1 4 | -1 |

| -1 -2 | 3 |

To find the values of x and y,  can perform row operations on the augmented matrix [A | B] until  obtain the Reduced Row Echelon Form (RREF). Applying row operations, get:

| 1 4 | -1 |

| 0 -6 | 2 |

From the RREF, it can read the values of x and y. In this case, we have:

x = -1/6

y = 1/3

Now, we can find L(v) by substituting x and y into the expression:

L(v) = L(xv1 + yv2)

= L((-1/6)(1, -1) + (1/3)(4, -2))

= L((-1/6, 1/6) + (4/3, -2/3))

= L((4/3 - 1/6, -2/3 + 1/6))

= L((7/6, -1/6))

Using the information given that L(v1) = (-2, 1) and L(v2) = (4, -1), we can conclude that:

L(v) = (7/6)L(v1) + (-1/6)L(v2)

= (7/6)(-2, 1) + (-1/6)(4, -1)

= (-14/6, 7/6) + (-4/6, 1/6)

= (-18/6, 8/6)

= (-3, 4/3)

Therefore, L(v) is equal to (-3, 4/3) when v = (-1, 3) using the RREF method.

To learn more about transformation -  brainly.com/question/32510058

#SPJ11

Answer:

17,964.9 cubic meters

Step-by-step explanation:

Hey there!

The formula for finding the area of a sphere is:

\(V=(4/3)\pi r^3\)

Where V is volume, and r is radius

The question already tells us that the diameter is 32.5m

*Remember, the diameter isn't the radius. It is the radius times two*

Now, we have to divide 32.5 by 2 to get the radius

32.5/2 is 16.25

Now we can plug this into the formula

16.25 cubed is 4291 after being rounded to the nearest tenth

Now we multiply 4291 by 3.14 (pi)

4291 x 3.14 is 13473.7 after being rounded to the nearest tenth

Now multiply 13473.7 by 4/3 and then you will get the volume to the sphere

13473.7 x 4/3 is 17964.93333333...

Since it is asking us to round to the nearest tenth of a cubic meter;

The volume of the sphere will be 17,964.9 cubic meters

\(\rule{300}{1}\)

\(\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}\)

What is the volume of a sphere with a diameter of 32.5 m, rounded to the nearest tenth of a cubic meter (m³)?

\(\dashrightarrow\large\textsf{\textbf{\underline{Answer and how to solve:-}}}\)

We are asked to find the volume of a sphere, which we can find using the following formula:-

\(\bold{V=\dfrac{4}{3} \pi r^3}\)

\(\bold{r=d\div2}\)

Replace d with 32.5:-

\(\bold{r=32.5\div2}\)

Therefore, the sphere's radius is as follows:-

\(\bold{r=16.25}\) m

\(\rule{300}{1}\)

Now, let's find the sphere's volume, which, as I mentioned earlier, can be found with the help of this formula:-

\(\bold{V=\dfrac{4}{3} \pi r^3}\)

Replace r with 16.25:-

\(\bold{V=\dfrac{4}{3} \pi (4291)}\)           Next, we replace π with 3.14:-

\(\bold{V=\dfrac{4}{3} \times3.14\times4291}\)

On simplification,

\(\bold{V=\dfrac{4}{3} \times13,473.74}\)

On further simplification,

\(\bold{V=17,964.9\:m^3}\Longleftarrow\sf{volume\:of\:the\:sphere}\)

\(\rule{300}{1}\)