What is the volume of this rectangular prism?

890 apples.

Hope this helps

The required number of children and adults for sitting in the theater are 300 and 50 respectively.

A equation is supposed to be linear equation in two factors in the event that it is written as hatchet + by + c=0, where a, b and c are genuine numbers and the coefficients of x and y, i.e an a and b separately, are not equivalent to nothing. For instance, 10x+4y = 3 and - x+5y = 2 are straight equation in two factors.

Let be consider number of children be x and that of adults is y.

We have,

x + y = 350-------(1)

y = 350 - x

And 5x + 10y = 2000------------------(2)

Put value of y in equation (2)

5x + 10( 350 - x) = 2000

5x + 3500 - 10x = 2000

-5x = -1500

x = 300

Then

y = 350 - x = 350 - 300 = 50

Thus, There will be 300 children and 50 adults in the  theater .

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The Annual yield is approximately 2.92%.

To determine the cost per share and the annual yield, we need to perform some calculations based on the given information.

a. Cost per share:

The cost per share can be calculated by dividing the total cost (including the commission) by the number of shares.

Total cost = Cost of shares + Commission

Total cost = $3,945.90

Number of shares = 60

Cost per share = Total cost / Number of shares

Cost per share = $3,945.90 / 60

Cost per share ≈ $65.76

Therefore, the cost per share is approximately $65.76.

b. Annual yield:

The annual yield is the dividend per share divided by the cost per share, expressed as a percentage.

Dividend per share = $1.92

Annual yield = (Dividend per share / Cost per share) * 100

Annual yield = ($1.92 / $65.76) * 100

Annual yield ≈ 2.92%

Therefore, the annual yield is approximately 2.92%.

In summary:

a. The cost per share for Comerica Inc. is approximately $65.76.

b. The annual yield for Comerica Inc. is approximately 2.92%.

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Answer:

163

Step-by-step explanation:

\(2*(7^{2}) +9(7)+2\)

\(2*(49)+9(7)+2\)

\(98+63+2\)

\(=163\)

Answer:

x- intercept = 4 , y- intercept = - 2

Step-by-step explanation:

To find the x- intercept let f(x) = 0 , that is

\(\frac{x-4}{-x+2}\) = 0

The denominator cannot be zero as this would make f(x) undefined

Equating the numerator to zero

x - 4 = 0 ⇒ x = 4 ← is the x- intercept

To find the y- intercept let x = 0 , that is

f(0) = \(\frac{0-4}{-0+2}\) = \(\frac{-4}{2}\) = - 2 ← is the y- intercept

Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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The 95% prediction interval for the adjusted distribution volume of a single healthy individual is approximately 12.03 to 76.89.

To calculate a 95% prediction interval for the adjusted distribution volume of a single healthy individual based on the given data, follow these steps:

1. Calculate the mean (µ) and standard deviation (σ) of the sample:
Mean (µ) = (22+39+40+42+43+46+51+57+64+65+68+69+72) / 13 = 578 / 13 = 44.46
Standard deviation (σ) = √(Σ(x-µ)² / (n-1)) = 15.15 (approx.)

2. Find the t-value corresponding to a 95% prediction interval for 12 degrees of freedom (n-1) from a t-distribution table or calculator (e.g., online t-table or calculator). The t-value for 12 degrees of freedom and 95% prediction interval is 2.179 (approx.).

3. Calculate the prediction interval using the following formula:
Prediction interval = µ ± t * σ * √(1 + (1/n))
Prediction interval = 44.46 ± 2.179 * 15.15 * √(1 + (1/13))

4. Compute the final values:
Lower bound: 44.46 - 2.179 * 15.15 * √(1 + (1/13)) = 12.03 (approx.)
Upper bound: 44.46 + 2.179 * 15.15 * √(1 + (1/13)) = 76.89 (approx.)

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Answer:

-5/2

Step-by-step explanation:

Slope intercept form = y=mx+b

M=Slope

B=y-intercept

Answer:

-5/2 is the slope

Step-by-step explanation:

the form that it is currently in is slope intercept form

( y= mx+b ) m is the is the slope and x is a variable. -5 is the y intercept.

Answer:

y = (10r - 24)/9

Step-by-step explanation:

10r - 9y = 24

-9y = -10r + 24

y = (10r - 24)/9

g(x) has the greatest x-intercept.

Option(A) is correct.

What is the x-intercept of the function?

To find the x-intercept of a function, we set y = 0 and solve for x. The x-intercept is the point where the graph of the function intersects the x-axis.

To find the x-intercept of a function, we set y = 0 and solve for x.

For g(x) = 3/2 * x + 1, setting y = 0 gives:

0 = 3/2 * x + 1

Solving for x:

x = -2/3

So the x-intercept of g(x) is -2/3.

For h(x), there is no x-intercept because all the y-values are negative.

For f(x), setting y = 0 gives:

0 = 3/2 * x + 1

Solving for x:

x = -2/3

So the x-intercept of f(x) is also -2/3.

For j(x), we don't have enough information to determine the function. Therefore, we cannot compare it with the other functions in terms of x-intercepts.

So, between g(x), h(x), and f(x), the function with the greatest x-intercept is g(x) because it has an x-intercept of -2/3, which is larger than the x-intercepts of f(x) and h(x).

Hence, g(x) has the greatest x-intercept.

Option(A) is correct.

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The values that satisfy the inequality are -45 , -50 , -56.23 etc..

Algebraic expressions are contrasted in a mathematical statement known as an inequality using the greater-than (>), less-than (<), and other inequality symbols. A pair of inequalities connected by and or or form a compound inequality. In this lesson, linear and compound inequalities in one variable will be resolved using the properties of inequalities. The study of absolute-value equations and inequalities continues.

Solving inequalities is very like solving equations, we do most of the same things , but we must also pay attention to the direction of the inequality.

The given inequality is of the form n < -15 . Since no other information is given about n we will consider n to be a Real number.

Hence any real number that is less that -15 will satisfy the inequality.

Therefore the values that satisfy the inequality are -45 , -50 , -56.23 etc..

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a. To find the relationship between Q and p, we can express Q as a function of p using the equation Q = e^(-BQ).

b. Expressing p as a function of Q, we have p = e^(-BQ).

c. To differentiate e^(-BQ) with respect to Q, we use the chain rule. The derivative is dp/dQ = -B * e^(-BQ).




The log-linear demand for a product can be expressed as ln(Q) = -BQ, where Q represents the quantity demanded and B is a constant coefficient. In order to find the relationship between price (p) and quantity (Q) and calculate the derivative dp/dQ, let's follow the steps below:

a. Express Q as a function of p:

To find the relationship between Q and p, we need to exponentiate both sides of the equation ln(Q) = -BQ. This gives us:

Q = e^(-BQ).

Now, we can solve for Q in terms of p by substituting p for Q:

p = e^(-Bp).

To calculate dp/dQ, we differentiate the expression with respect to Q:

dp/dQ = d/dQ(e^(-BQ)).

b. Express p as a function of Q and find dp/dQ:

To express p as a function of Q, we start with the equation p = e^(-Bp) and solve for p:

p = e^(-BQ).

To find dp/dQ, we differentiate the expression with respect to Q:

dp/dQ = d/dQ(e^(-BQ)).

c. Show mathematical steps for differentiation:

To differentiate e^(-BQ) with respect to Q, we can use the chain rule. Let's denote f(Q) = e^(-BQ), then:

df/dQ = (df/dQ)(dQ/dQ) = (d/dQ(e^(-BQ))) * 1 = -B * e^(-BQ).

Therefore, dp/dQ = -B * e^(-BQ).

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Answer:

VII

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

57/220=0.259090909090

It is important for researchers to carefully consider these factors when designing studies and analyzing data to ensure that their results are accurate and reliable.

Small Sample Size: With only 40 participants remaining in the experimental group after 6 months, the sample size may have been too small to detect any significant differences between the experimental and control groups.

Sampling Error: Even with random assignment to groups, there is always a chance that the groups will differ on some important characteristic that could affect the results.

Statistical Power: The statistical power of a study refers to its ability to detect a true effect if one exists. With a small sample size, the statistical power of the study may have been too low to detect any real differences between the groups.

Data Analysis: The way in which the data was analyzed could have influenced the results. For example, if the researchers used an inappropriate statistical test or did not correct for multiple comparisons, it could have led to faulty results.

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there is no flow chart

Answer:

WHAT FLOWCHART?

Step-by-step explanation:

Answer:

h=60 2h=120

Step-by-step explanation:

the sum of 4 angles of a quadrilateral is 360 degree. so h+h+2h+2h=360

h=60 and 2h=120

Answer:

I hope it helps mate

as I promised I will help you

I will always help you understanding your assingments

enjoy your day

#Captainpower:)

The intervals of convergence for f'(x) are (-1, 1).

The intervals of convergence for f''(x) are (-1, 1).

To find the interval of convergence for the function f(x) = Σ(xⁿ/n²), where the summation is from n = 1 to infinity, we can use the ratio test.

The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges. Mathematically, the ratio test can be written as:

lim |(a[n+1] / a[n])| < 1

Let's apply the ratio test to f(x):

f(x) = x + x²/2² + x³/3² + x⁴/4² + ...

First, let's calculate the ratio of consecutive terms:

|r| = |(x⁽ⁿ⁺¹⁾ / (n+1)²) / (xⁿ / n²)|

= |(x⁽ⁿ⁺¹⁾ × n²) / ((n+1)² × xⁿ)|

= |x × (n² / (n+1)²)|

Taking the limit as n approaches infinity:

lim |x × (n² / (n+1)²)|

= |x × 1|

Since the absolute value of x is independent of n, we can drop it from the limit.

Therefore, for the series f(x) to converge, |x × 1| < 1.

This implies -1 < x < 1.

Hence, the interval of convergence for f(x) is (-1, 1).

Now let's find the intervals of convergence for f'(x), the derivative of f(x).

Differentiating f(x) term by term, we get:

f'(x) = 1 + x/2 + x²/3²+ x³/4² + ...

We can apply the ratio test to find the intervals of convergence for f'(x):

|r| = |(x⁽ⁿ⁺¹⁾ / (n+1)²) / (xⁿ / n²)|

= |(x⁽ⁿ⁺¹⁾ × n²) / ((n+1)² × xⁿ)|

= |x × (n² / (n+1)²)|

Taking the limit as n approaches infinity:

lim |x × (n² / (n+1)²)|

= |x × 1|

Since the absolute value of x is independent of n, we can drop it from the limit.

Therefore, for the series f'(x) to converge, |x × 1| < 1.

This implies -1 < x < 1.

Hence, the intervals of convergence for f'(x) are (-1, 1).

Finally, let's find the intervals of convergence for f''(x), the second derivative of f(x).

Differentiating f'(x) term by term, we get:

f''(x) = 0 + 1/2 + x/3² + x²/4²+ ...

Again, we can apply the ratio test to find the intervals of convergence for f''(x):

|r| = |(x⁽ⁿ⁺¹⁾ / (n+1)²) / (xⁿ / n²)|

= |(x⁽ⁿ⁺¹⁾ × n²) / ((n+1)² × xⁿ)|

= |x ×(n² / (n+1)²)|

Taking the limit as n approaches infinity:

lim |x × (n² / (n+1)²)|

= |x × 1|

Since the absolute value of x is independent of n, we can drop it from the limit.

Therefore, for the series f''(x) to converge, |x × 1| < 1.

This implies -1 < x < 1.

Hence, the intervals of convergence for f''(x) are (-1, 1).

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Answer:

$1331 compounded annually after three years

Step-by-step explanation:

Given the following question:

1000 dollars invested (princpal)....
You invest that 1000 dollars for three years (time)....

Assuming it's compounded annually we need to substitute the values into the formula to calculate compound interest.

\(A=P(1+\frac{r}{n} )^{nt}\)
\(P=1000\)
\(\frac{r}{n} =\frac{10}{100} =10\div100=0.1\)
\(nt=(1)(3)\)
\(A=1000(1+0.1)^{(1)(3)}\)
\(1\times3=3\)
\(A=1000(1+0.1)^{3}\)
\(1+0.1=1.1\)
\(1.1^3=1.1\times1.1\times1.1=1.331\)
\(A=1000\times1.331\)
\(1000\times1.331=1331\)
\(=1331\)

Which means after a intital investment of 1000 dollars you will have "1331 dollars" after three years compounded annually.

Hope this helps.

Answer:  The middle school has 652 students.

Step-by-step explanation:  Divide the number of student in the high school by 4.5

\(\frac{2934}{4.5}\) = 652

10 ft pls like if it helped

Answer:

x = -23/6 4x = -46/3

Step-by-step explanation:

1st no. = 4x

2nd = x

as per the ques:

6 × 4x + 4 = 4

24x + 4 = 4

x = 4/24 - 4

= 1/6 - 4

x = -23/6

4x = 4 × -23/6

= -46/3

Jerome can save an amount of R33377.27 per month which is the larger amount.

A ratio is a quantitative or qualitative connection between two things: "On the building site, the male-to-female ratio was 10 to one." This indicates there were 10 males and one lady present.

Here

He earns R52450 per month

He separated his earnings in a ratio 7: 4

If he saves a larger amount, then the required solution would be as:

⇒ 52450 × 7/(7+4)

⇒ 52450 × 7/11

Apply the multiplication operation, and we get the amount of savings:

⇒ 33377.27

Therefore, he can save an amount of R33377.27 per month.

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Answer:

1/2 of an answer is zero answer.

Step-by-step explanation:

Answer:

a. Solve for x. x=16

b. The lenght of the missing side is 10 units.

Step-by-step explanation:

a.

        x-6>0      x>6

According to the Pythagorean theorem: a²+b²=c².

Hence,

\((x-6)^2+24^2=26^2\\x^2-2*x*6+6^2+24*24=26*26\\x^2-12x+6*6+576=676\\x^2-12x+36+576-676=676-676\\x^2-12x-64=0\\x^2-12x-4x+4x-64=0\\x^2-16x+4x-64=0\\(x*x-16x)+(4x-64)=0\\x*(x-16)+4*(x-16)=0\\(x-16)*(x+4)=0\\x-16=0\\x_1=16\\x+4=0\\x_2=-4\notin\\\)

b.

\(16-6=\\10\)

Answer:

22

Explanation:

The cell phone plan costs $39.99 per month plus $0.18 for each text message.

Let the number of text messages sent or receive = t

The cost, C in a month will be:

If you have at most $44 to spend, it means the cost can be less than or equal to $44.

We then solve the inequality for t.

Since text messages cannot be decimal, the maximum number of text messages that you can send or receive next month is 22.

9514 1404 393

Answer:

  c.)  2000

Step-by-step explanation:

In 2 minutes, the motorcycle travels a distance of ...

  (6300 ft/min)(2 min) = 12600 ft

The circumference of the tire is ...

  C = 2πr = 2π(1 ft) = 2π ft

The distance traveled is n times the circumference, where n is the number of revolutions of the tire.

  12600 = 2π·n

  12600/(2π) = n = 6300/π ≈ 2005.4

The tire makes about 2000 revolutions in 2 minutes.

Answer:

it's a bit hard to see in green.