if the volume of a rectangular prism is 26,214 m3 and it has a height of 17 m what is the value of b , the area of the base ? A. 13,062 m2 B. 13,062 m3 C.1,542 m2 D. 1,542 m3

Answer:

the surface area of the rectangular prism is 572cm².

Step-by-step explanation:

The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:

2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²

So the surface area of the rectangular prism is 572 square centimeters.

The next "three-umbers" in the pattern "2,0,6,-4,10,-8,..." are 14, -12, and 18.

To find the next three numbers in the pattern 2, 0, 6, -4, 10, -8, we need to analyze the pattern and identify the rule for it.

The pattern seems to be alternating between adding and subtracting the "odd-multiples" of 2.

The pattern is as follows : 2 - (2×1) = 0,

0 + (2×3) = 6,

6 - (2×5) = -4,

-4 + (2×7) = 10,

10 - (2×9) = -8,

Using this rule, we can find the next three numbers in the pattern as follows:

Add 22 because : -8 + (2×11) = 14,

Subtract 26 because : 14 - (2×13) = -12,

Add 30 , because : -12 + (2×15) = 18,

Therefore, the next three numbers in the pattern are 14, -12, and 18.

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The integer which is closest to the radius of a circle with a circumference of 50.27 as required is; Choice A; 8.

It follows from the task content that the integer which is closest to the radius of the circle whose circumference is; 50.27 is to be determined.

Recall; Circumference, C = 2πr

r = C / 2π

r = 50.27 / 2π

r = 8.000718989

Ultimately, the integer which is closest to the radius is; Choice A; 8.

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The value of arc CD is 110⁰.

The value of arc AD is 120⁰.

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)

angle DEC = ¹/₂ (360 - 200)

angle DEC = 80⁰

The value of arc CD is calculated as follows;

80 = ¹/₂ (CD + 50) (intersecting chord theorem)

2 x 80 = CD + 50

160 = CD + 50

CD = 110⁰

Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)

arc AD = 120⁰

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When a student is chosen at random, the student is more likely to be from Mrs Johnson's class.

The probability that the student got A in the first semester will be 0.15.

When a student is chosen at random, the student is more likely to be from Mrs Johnson's class. It should be noted that this is because 152 students out of 300 are from her class compared to Dixon who has 148 students.

The probability that the student got A in the first semester will be:

= 46 / 300

= 0.15

The probability for the last question will be:

= 14 / 148

= 0.095.

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If Alonso pays the monthly payment each month for the full term. Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.

To calculate the total amount that Alonzo will repay over the 6-year term of the loan, we need to use the formula for the monthly payment on an amortized loan:

M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)

where:

M is the monthly payment

P is the principal amount

r is the monthly interest rate (which is the annual interest rate divided by 12)

n is the total number of payments (which is the number of years multiplied by 12).

Using the values given in the problem, we have:

P = $49,000

r = 6.55% / 12 = 0.005458333 (monthly interest rate)

n = 6 years * 12 months/year = 72

Substituting these values into the formula, we get:

M = $49,000 * 0.005458333 * (1 + 0.005458333)^72 / ((1 + 0.005458333)^72 - 1)

= $824.85 (rounded to the nearest cent)

To find the total amount he will repay, we can simply multiply the monthly payment by the number of payments:

Total amount =$824.85 * 72

Total amount = $59,389.2

Therefore, Alonzo will repay a total of $59,389.2 over the 6-year term of the loan if he makes the monthly payment each month.

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The speed limit for the highway in rounded to the nearest whole is 33 mi/h.

The speed is the ratio of the distance in a given time interval. The distance is represented by a unit of length and the time is represented by a unit of time.

There are different units for the length or distance. In the International System Units (SI), the standard unit of distance is the meter (m) and the standard unit of time is the second (s). Nonetheless, there are others units, for example: inches (in), miles (mi) and  yards (yd).

For solving this exercise, you need to know the relation between the given units for distance and time.

The question gives - 100 km/h. The kilometer (km) is a multiple of the  standard unit of distance -  the meter (m) and the hour is a submultiple of the  standard unit of time  - the second (s)

For solving this question, it is necessary that you know the relation between km/h and mi/h. See  below.

[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]

Now you can solve the question from a math tool - Rule of three. Thus,

[tex]\text{1 km/h}= 0.6213712 \ \text{mi/h}[/tex]

[tex]100 \ \text{km/h}= \text{x mi/h}[/tex]

[tex]\text{x}= 100 \times 0.6[/tex]

[tex]\text{x}=33 \ \text{mi/h}[/tex]

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Here, We provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.

To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:

25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22

The sum of the values is:

25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813

Dividing by the number of values (30), we get:

Mean = 813/30 = 27.1

To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.

To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:

20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34

There are 30 values, so the median is the 15th value, which is 28.

To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:

Range = 34 - 20 = 14

To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:

20-24, 25-29, 30-34

The frequency table would look like this:

Interval | Frequency

20-24 | 4

25-29 | 18

30-34 | 8

To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:

Proportion = Frequency/Total frequency = 18/30 = 0.6

Angle = Proportion x 360° = 0.6 x 360° = 216°

We can repeat this calculation for each interval to obtain the angles for the pie chart.

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Note that in the proof stated above, there is no incorrect statement.

The evidence is that when four lines are drawn starting from a point and making two right angles, the two angles between those lines are equal.

The proof begins by stating that when you have a right angle, the two angles that add up to produce the correct angle are referred to as complementary angles.

The Congruent Complements Theorem is then used to demonstrate that the two angles in the centre are equal.

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Answer:

The quotient is

[tex]8 {x}^{2} + 15x - \frac{1}{8} [/tex]

and the remainder is

[tex] \frac{63}{64} [/tex]

Answer:

Step-by-step explanation:

To determine which flight will have the most no-shows, we need to compare the probabilities of no-shows for each flight.

The probability of a no-show for the afternoon flight is 1/10, which means that on average, 1 out of every 10 passengers on the afternoon flight will not show up.

The probability of a no-show for the morning flight is 1/20, which means that on average, 1 out of every 20 passengers on the morning flight will not show up.

Since 1/10 is greater than 1/20, the afternoon flight will have a higher number of no-shows, on average. Therefore, the afternoon flight is more likely to have the most no-shows.

the cruising speed of the blue whale is approximately 3.16 meters per second.

What are  velocity?

a velocity is a unit of measurement for the Distance an object travels in a

the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by

dividing the total Distance traveled by the journey time.

In this case, we know the mass of the blue whale (m = 170,000 kg) and its kinetic energy (KE = 890,000 J), but we need to solve for its velocity (v).

Rearranging the formula, we get:

v = √(2 * KE / m)

Plugging in the values we know, we get:

v = √(2 * 890000 J / 170000 kg)

Simplifying this expression, we get:

v = √10 = 3.16 m/s

Therefore, the cruising speed of the blue whale is approximately 3.16 meters per second.

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The equation for L in terms of tea, representing the length of the candle, remaining on burn in inches, tea hours, after the candles lit is 15 in - (1.25 in/hr)t

Given  the initial length of a candle is 15 inches and the candle burns at a rate of 1.25 in./h

L(t) is a function of time, t:

L(t) = 15 in - (1.25 in/hr)t

Note that when the candle has burned down to nothing, L(t) = 0.

Set 15 in - (1.25 in/hr)t equal to zero and solve for t:

(1.25 in/hr)t = 15 in, or

t = 15/  1.25 in/hr

t = 12 hrs

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The maximum profit that for the equation p(x) = 2800x - 85x² - x³ - 109000 is $672500

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Given the profit function:

p(x) = 2800x - 85x² - x³ - 109000

The profit is maximum at:

p'(x) = 0

p(x) = 2800 + 170x - 3x²

2800 + 170x - 3x² = 0

x = 70

p(70) = 2800(70) - 85(70)² - (70)³ - 109000 = 672500

The maximum profit is $672500

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The percentage of females that do not satisfy the requirement is given as follows:

55.17%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as follows:

[tex]\mu = 998, \sigma = 202[/tex]

The proportion that does not satisfy the requirement is the p-value of Z when X = 1025, hence:

Z = (1025 - 998)/202

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

Hence the percentage is given as follows:

0.5517 x 100% = 55.17%.

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The conjecture that can be made about the other number is option A: the other number is odd.

Let's assume that the two even numbers are x and y. Then, we can write their sum as x + y = 2a, where a is some even number.

Now, let's consider the sum of 6 and another number, which we can represent as 6 + z, where z is some unknown number. If this sum is even, then we can write it as 2b, where b is some even number.

So, we have the equations:

x + y = 2a (since the sum of two even numbers is even)

6 + z = 2b (since the sum of 6 and another number is even)

We can subtract 6 from both sides of the second equation to get:

z = 2b - 6

Now, we can substitute this expression for z into the first equation:

x + y = 2a

And we get:

x + y + z - 2z = 2a

x + (y + z) - 2z = 2a

x + (2b - 6) - 2z = 2a

x + 2b - 2z - 6 = 2a

This equation tells us that x + 2b - 2z - 6 is an even number (since 2a is even). Since x and 2b are even, the expression -2z - 6 must also be even. Therefore, -2z must be even. This means that z is odd (since an even number minus an even number is even, and -6 is even).

So, we can conclude that the other number (z) is odd. Option A is the correct answer.

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The angle of the turn at Deer Trail is of 105 degrees.

Notice that both of the lines that go up to the left are parallel, thus, the angles formed betwen the intersections are all equal (for the respective lines).

Now, also know that two adjacent angles in an intersection should add up to 180°.

We can see that the angle to the right of deer trail has a measure of 75°, then the angle to the left (which is adjacent) must have a measure M such that:

M + 75° = 180°

M = 180° - 75°

M = 105°

That is the angle of the turn.

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a) Yes, the function is in standard form.

  Degree = 2

  Exponent = 2

  Constant term = -1

b) No, the function is not in standard form.

   And it doesn't have the degree, exponent and constant term.

Firstly, let's consider the function f(x) = x(x-1). To determine if it is a polynomial function, we need to check if all of its terms have non-negative integer exponents. In this case, we see that f(x) can be written as x² - x, which has only two terms, and each term has a non-negative integer exponent. Therefore, f(x) is a polynomial function.

In this case, the degree of f(x) is 2 because the highest exponent of x is 2.

In this case, the leading term of f(x) is x², and its leading coefficient is 1.

Finally, the constant term is the term that does not have the variable in it. Here, the constant term of f(x) is -1.

Next, let's consider the function f(x) = 3 - 1/2 x. We can see that f(x) is not a polynomial function because it has a term with a negative exponent.

Polynomial functions must have non-negative integer exponents on all terms.

Therefore, the answer to the first question is 'no.'

Since f(x) is not a polynomial function, it does not have a degree, leading term, or constant term.

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Answer: y=16x - 86

Step-by-step explanation:

The three types of rock are igneous, sedimentary, and metamorphic.

There are three types of rocks as explained below.

Igneous rocks are formed from the cooling and solidification of molten rock, either on the Earth's surface (extrusive) or beneath the surface (intrusive). Examples of igneous rocks include basalt, granite, and pumice.

Sedimentary rocks are formed from the accumulation and cementation of sediment particles (such as sand, silt, and clay) or the precipitation of minerals from a solution. Examples of sedimentary rocks include sandstone, limestone, and shale.

Metamorphic rocks are formed from the alteration of pre-existing rocks by heat, pressure, and chemical reactions. Examples of metamorphic rocks include marble, slate, and gneiss.

The rock cycle is the process by which one type of rock can be changed into another type of rock.

The rock cycle involves three main processes:

Therefore, one type of rock can be changed into another type of rock through the rock cycle by undergoing weathering, erosion, deposition, lithification, metamorphism, melting, and solidification, depending on the specific conditions and processes involved.

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The solution set for the inequality is x < -10

The different signs for representing inequalities are;

From the information given, we have that;

−4x−38<2

To solve for the value of x, take the steps;

collect the like terms

-4x> 2 + 38

Add the values

-4x> 40

Divide both sides by the coefficient of x, we have;

x > -10

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The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.

In statistics, mean is a measure of central tendency that represents the average value of a set of data. It is commonly referred to as the "arithmetic mean" or simply the "average." To calculate the mean, you add up all the values in the data set and divide the total by the number of values. For example, if you have the following data set: 2, 5, 8, 9, 12, the mean would be calculated as follows:(2 + 5 + 8 + 9 + 12) ÷ 5 = 7.2 . So the mean of this data set is 7.2. The mean is a useful measure of central tendency because it takes into account all the values in the data set and provides a single representative value that can be used to describe the overall characteristics of the data.

given

For a population receiving pharmacological treatments, the mean wake time was estimated with a 95% confidence interval.

where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.

When we enter the provided values, we obtain:

s = 23.3

n = 23

t0.025,22 = 2.074

The mean wake time estimate with a 95% confidence interval for a population receiving medication is thus:

82.1 ± 2.074 * (23.3/√23)

which is equivalent to:

(71.4, 92.8)

The absence of the value 105.0 from the interval shows that the medication therapy significantly reduces wake time.

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Answer: 2.5

Step-by-step explanation:

the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5

hope it helped:)

The equation of the quadratic function in standard form is f(x) = 5x² - 3x - 7

To write an equation for a quadratic function in standard form, we need to use the general form of the equation, which is: f(x) = ax² + bx + c where a, b, and c are constants that determine the shape and position of the graph of the function.

Let's choose the points (-2, -16), (-1, -15), and (0, -12) from the table. Substituting these values into the equation above, we get:

-16 = 4a - 2b + c -15 = a - b + c -12 = c

We can use the third equation to solve for c, which is -12 in this case. Substituting this value into the first two equations, we get:

-16 = 4a - 2b - 12 => 4a - 2b = 4 -15 = a - b - 12 => a - b = 3

Now we have two equations in two unknowns, which we can solve by substitution or elimination. Let's use substitution to solve for b first:

a - b = 3 => b = a - 3

Substituting this into the first equation, we get:

4a - 2(a - 3) = 4 => 2a = 10 => a = 5

Now we can substitute the values of a and b into one of the original equations to find c:

-15 = 5 - b + c => -15 = 5 - (5 - 3) + c => c = -7

Therefore, the equation of the quadratic function in standard form is:

f(x) = 5x² - 3x - 7

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The grams of each food she feeds this group of rats each day is 80 grams of food A and 100 grams of food B each day.

Let us consider that the researcher feeds x grams of food A and y grams of food B each day. Then we can restructure the  two equations on the basis of  the amount of niacin and retinol present in the food
0.11x + 0.35y = 28.4 (equation 1)
190x + 95y = 37,335 (equation 2)

We can evaluate this system of equations applying the substitution or elimination method.
Let us apply substitution method:
In case of equation 1, we can evaluate concerning x:
x = (28.4 - 0.35y) / 0.11
Staging this value for x in equation 2
190[(28.4 - 0.35y) / 0.11] + 95y
= 37,335
Applying simplification and evaluating for y
y = 100
Staging this value for y in equation 1 to evaluate x

x = 80

Then, the researcher feeds 80 grams of food A and 100 grams of food B each day.
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the deductible, and the coinsurance. Here are the steps to calculate the total out-of-pocket expense: the total out-of-pocket expense for one month is $ [tex]154[/tex] .

To calculate the out-of-pocket expense for one month, we need to take into account the monthly premium.

Step 1: Calculate the deductible

The deductible is the amount that the insured person needs to pay before the insurance starts covering the costs.

In this case, the deductible is $500 because that's the threshold for the 90% coverage. Since the family will fill 6 prescriptions per month, we need to calculate the average cost per prescription:

Average cost per prescription = Total prescription costs / Number of prescriptions

Average cost per prescription = $ [tex]850 / 6 = $141.67[/tex]

Since the deductible is $500, the insurance will cover 90% of the first $500, which is $450. The remaining $50 will be paid by the insured person. Therefore, the deductible is $  [tex]500 - $450 = $50.[/tex]

Step 2: Calculate the coinsurance

After the deductible is met, the insurance will cover 80% of the remaining prescription costs, and the insured person will be responsible for the remaining  [tex]20[/tex] %.

To calculate the coinsurance, we need to subtract the deductible from the total prescription costs and multiply the result by 0.2:

Coinsurance = (Total prescription costs - Deductible) x 0.2

Coinsurance = [tex]($850 - $500) \times 0.2[/tex]

Coinsurance = $ [tex]70[/tex]

Step 3:

Calculate the total out-of-pocket expense

The total out-of-pocket expense is the sum of the monthly premium, the deductible, and the coinsurance:

Total out-of-pocket expense = Monthly premium + Deductible + Coinsurance

Total out-of-pocket expense = $  [tex]34 + $50 + $70[/tex]

Total out-of-pocket expense = $154

Therefore, the total out-of-pocket expense for one month is $ [tex]154[/tex] .

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The difference in what you have as a balance in your check register versus your online statment by 11/18 is $34.78.

The combined total of the 2 transactions they have in common is $206.99.

Use the amount in 11/1 as your balance, then compute by deducting the checks (chk) and debit purchases and adding the deposits. Then get the difference.

Check Register:

Total = 397.45 - 50.32 - 16.32 + 190.67

Total = 521.48

Online Statement:

Total = 486.44 - 84.80 - 19.73 - 16.32 + 190.67

Total = 556.26

Difference = online - check register

Difference = 34.78

On 11/10 and 11/18, check and online have the same transactions (same date, same amount) which are 16.32 and 190.67. Add them together to get 206.99

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Answer:

25$ if the tickets were involved it would be 70$

Santiago would have to pay $87 in total if he bought 6 snacks for everyone to share. The cost increases to $60 + 4.5*x when a variable number of snacks, represented by x, are bought.

The topic of this question is

Mathematics

, specifically about using multiplication and addition in problem-solving.

Firstly, Santiago is going to see a movie with his 3 kids. Therefore, he needs to buy 4 tickets. If each ticket costs $15, then the total cost for movie tickets will be 4 * 15 = $60.

Secondly, if Santiago buys 6 snacks for everybody to share with each snack costing $4.50, the total cost for snacks will be 6 * 4.5 = $27. The total money Santiago would have to pay for his family would then be the sum of the costs of the tickets and snacks, which is 60 + 27 = $87.

Regarding the case when Santiago bought x snacks for everybody to share, the total cost would become 60 + 4.5*x. This formula gives the total cost based on the given number of snacks.

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Answer:

the answer is:l only

because -10 only states the true statement while -1 and 6 gave False Staments...