The volume of the prism is 1368 cubic feet.
We have,
The three steps that should be taken to calculate the volume of the prism are:
- Use the formula A = b h to find the area of the base, where b is the length of the base and h is the width of the base.
For a rectangular prism, the base is a rectangle, so the formula is:
A = length x width.
- Use the formula V = B h to find the volume of the prism, where B is the area of the base and h is the height of the prism.
For a rectangular prism, the formula.
V = length x width x height.
- Substitute the given values into the formulas and solve for the volume. For the given rectangular prism with a length of 9 and one-half feet, a width of 24 feet, and a height of 6 feet, we can find the volume by using the formula V = B h.
First, we find the area of the base by using the formula:
A = length x width:
A = (9.5 ft) x (24 ft)
= 228 sq ft
Next, we use the formula V = B h to find the volume:
V = (228 sq ft) x (6 ft)
= 1368 cubic feet
Therefore,
The volume of the prism is 1368 cubic feet.
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Convert the following binary to decimal numbers 1112
[tex]1\cdot2^2+1\cdot2^1+1\cdot2^0=4+2+1=7\\\\111_2=7_{10}[/tex]
What is the exact value of cos 30°?
Enter your answer, as a simplified fraction, in the box.
cos 30° can be evaluated using the trigonometric identity: cos 30° = cos(π/6) = (√3)/2.
Therefore, the exact value of cos 30° is (√3)/2.
Answer:
cos30 = √3 / 2
or cos30 ≈ 0.8660254037
Joe has to take two quizzes tomorrow. He has only enough time to study for one of them.
• The science quiz has 7 true-or-false questions.
• The English quiz has 5 multiple-choice questions.
Joe calculates the probability that he will get each question correct by guessing.
Science
English
To get 100% correct:
Answer 7 of 7 correctiv
Answer 5 of 5 correctiv
P(guess is correct)
0.5
0.25
Joe will study for the quiz on which he is likely to do worse by guessing. Which quiz should he study for?
• A. Science, because the probability of getting all questions correct is
(0.008), which is lower than for English (0.125).
• B. English, because the probability of getting all questions correct is 0.001, which is lower than for science (0.008).
• c. English, because the probability of getting all questions correct is
(0.125), which is lower than for science (0.5).
• D. Science, because he must get more questions correct.
Answer: B
Step-by-step explanation:
English: 0.25^5=0.001
Science:0.5^7=0.008
English is harder to get 100% on, since the probability 0.001 is lower than 0.008.
The figure on the right shows the cross-section of a pipe. The internal radius is 5cm and the thickness of the metal is 6mm. What is the external circumference of the pipe? (Take π = 22)
The external circumference of the metal pipe is approximately 31.4 centimeters.
We know that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We are given that internal radius is 5cm and the thickness of the metal is 6mm.
The circumference of the external circle = 2πr
= 2 x 3.14 x 5
= 31.4
The circumference of the metal pipe is approximately 31.4 centimeters.
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746x75755 tell me the answer please because its my only answer
Answer: number is the number so we can be a number
Step-by-step explanation:
Answer:
56,513,230
Step-by-step explanation:
Hope this helps! pls mark as brainiest!
Drag the tiles to the correct boxes to complete the pairs.
Match each function with the graph of its inverse function. fx=5x-1 fx= 1/5 x fx=x-5 fx=7x+1
The inverse of the functions are solved
Given data ,
Let the inverse of the function be represented as f⁻¹ ( x )
a)
f(x) = 5x - 1
y = 5x - 1
x = 5y - 1
x + 1 = 5y
y = (x + 1)/5
Inverse: f⁻¹(x) = (x + 1)/5
b)
f(x) = (1/5)x
y = (1/5)x
x = (1/5)y
y = 5x
Inverse: f⁻¹(x) = 5x
c)
f(x) = x - 5
y = x - 5
x = y - 5
y = x + 5
Inverse: f⁻¹(x) = x + 5
d)
f(x) = 7x + 1
y = 7x + 1
x = 7y + 1
x - 1 = 7y
y = (x - 1)/7
Inverse: f⁻¹(x) = (x - 1)/7
Hence , the inverse of the functions are solved
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What is the measure of an interior angle of a regular 12-gon?
Answer:
150°
Step-by-step explanation:
Measure of and interior angle of 12-gon:
[tex]\sf \boxed{\text{\bf Sum of all angles of n-polygon = (n -2) * 180}}[/tex]
n is the number of sides.
Sum of all angles of 12-gon = (12 - 2) * 180
= 10 *180
= 1800°
In a regular 12-gon, all the interior angles will be equal.
[tex]\text{\bf Measure of each interior angle = $\bf \dfrac{Sum \ of \ all \ the \ angles}{number \ of \ sides}$}[/tex]
[tex]\sf = \dfrac{1800}{12}\\\\=150^\circ[/tex]
Enter the number that belongs in the green box 11 12 20
The number that belongs in the green box, using the law of cosines, is given as follows:
15.97º.
What is the law of cosines?The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:
c² = a² + b² - 2abcos(C)
For this problem, the parameters are given as follows:
c = 11, a = 12, b = 20.
Hence the missing angle measure is given as follows:
11² = 12² + 20² - 2 x 11 x 20cos(C)
440cos(C) = 423
cos(C) = 423/440
C = arccos(423/440)
C = 15.97º.
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{1, √2, √√3, 2, √5, ...}
need help knowing the sequence and the 3 next terms
Answer:
3, 2√2, √7
Step-by-step explanation:
compute the square roots of the next three prime numbers:
√7
√11
√13
Therefore, the next three terms of the sequence are:
{1, √2, √3, 2, √5, √7, √11, √13}
chatgpt
chat
help me with the question below
The value of the x is 31.4 mm
Surface area = 282.6
According to the given figure,
Radius of circle = 5 mm
The length of x is the circumference of the circle,
⇒ x = 2πr
Here r is the radius of the circle,
Therefore, r = 5
Then put it into the circumference expression,
⇒ x = 2x3.14x5
= 31.4 mm
Total surface area,
= 2 x area of circle + area of rectangle
= 2(πr²) + (LxW)
= 2xπx5² + 10xπx4
= 50π + 40π
= 90 π
= 90x3.14
= 282.6
Hence,
Surface area = 282.6 mm³
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what is the inverse of the function? pls help thank you sm
Step-by-step explanation:
y= rad(x+3)
y²=x+3
x= y²-3
change the variables
y= x²-3
Three brothers share some money. The oldest 5/11 of the money. The next boy gets gets 7/12 of the remainder. What fraction of the money does the youngest boy get?
The fraction of the money the youngest boy does get is 5x/22.
Given that, three brothers share some money. The oldest 5/11 of the money.
Let the total money be x.
Share of oldest boy = 5/11 ×x
= 5x/11
Remainder = x-5x/11
Remainder = 6x/11
The next boy gets 7/12 of the remainder.
Share of next boy = 7/12 × 6x/11
= 7x/22
Share of youngest boy = 6x/11 - 7x/22
= (12x-7x)/22
= 5x/22
Therefore, the fraction of the money the youngest boy does get is 5x/22.
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4. Graph the exponential function y = 2* and its inverse y = log₂ x. Table of values: (3 marks) Graph: y (2 marks)
The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Here, Functions are,
⇒ y = 2ˣ
And, Its inverse function is,
⇒ y = log₂ x
Thus, The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.
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A certain disease has an incidence rate of 0.4%. If the false negative rate is 6% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
A car travels 200 kilometres in 5 hours. How far does it travel in 7 hours at the same speed?
Answer:
Speed =distance divide by time
=200 kilometres divide by 5
=40km/h
Distance =speed multiple by time
=40 multiple by 7 hours
=280km
A laptop has a listed price of $710.98 before tax. If the sales tax rate is 7.25%, find the total cost of the laptop with sales tax included.
Answer:
$762.53
Step-by-step explanation:
think of 710.98 as the whole.
then 7.25% = an increase of 0.0725.
710.98 X (1 + 0.0725)
= $762.53 (to nearest cent)
In a data distribution that is skewed left.
The median will be greater than the mean in a left-skewed distribution
We have,
In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.
A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.
When the data is skewed left, it means that the distribution is being pulled towards the left side.
This is because there are a few extreme values on the left side that are pulling the mean in that direction.
In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.
For a left-skewed distribution,
The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.
In a data distribution that is skewed left, the mean will be less than the median.
This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.
Therefore,
The median will be greater than the mean in a left-skewed distribution
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Makayla’s local movie theater has a moviegoer club. The charts in the annual registration fee of $25. However movie tickets are discounted remembers at six dollars per ticket instead of the regular nine dollars per ticket. Let him represent the number of movie tickets Makayla’s purchase a need to write a function tomorrow the amount of money Makayla spent going to the movies doing the club
Answer:
m = 25 + 6n
Step-by-step explanation:
To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.
A company introduces a customer service app. They track the number of customers who use it over an 8-month period. The scatter plot shows the data and a good line of fit. Write an equation of the line. Then predict the number of customers that will use the app after 12 months. Show your work.
The Y-intercept (b), we can substitute one of the points into the equation y = mx + b and solve for b.
The equation for the line of fit on the scatter plot, we need to determine the slope and y-intercept. Then, using the equation, we can predict the number of customers that will use the app after 12 months.
Given that we have a good line of fit, let's assume the equation of the line is in the form y = mx + b, where y represents the number of customers and x represents the number of months.
the scatter plot, we can determine two points on the line of fit. Let's say the coordinates of the first point are (x1, y1) and the coordinates of the second point are (x2, y2).
Next, we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
the y-intercept (b), we can substitute one of the points into the equation y = mx + b and solve for b.
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Given f(x) = x − 2 and g(x) = 5x + 3, evaluate the function for f(g(4))?
pls help guys calculus 30pts
Find the value of x.
Answer: x = 11
Step-by-step explanation:
We know that vertical angles are congruent to each other. We will create an equation to help us solve. Then, will isolate the x-variable with inverse operations.
128° = 8x + 40°
8x + 40° = 128°
8x = 88°
x = 11
If the variance for a set of data equals 8.1, find the standard deviation.
The standard deviation for this set of data is approximately 2.85.
To find the standard deviation, we first need to take the square root of the variance. Therefore, the standard deviation for the given data set is the square root of 8.1, which is approximately 2.846.
To find the standard deviation of a set of data when the variance is given, you simply need to take the square root of the variance. In this case, the variance equals 8.1.
Step 1: Identify the variance, which is 8.1.
Step 2: Take the square root of the variance.
Standard Deviation = √(Variance) = √(8.1)
Step 3: Calculate the square root of 8.1.
Standard Deviation ≈ 2.85
So, the standard deviation for this set of data is approximately 2.85.
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Based on the values in the table below, find the slope and y-intercept to write the equation of the line in the form y=mx+b.
The y-intercept of the line is 2. the equation of the line in the form y=mx+b is y = 2x + 2.
To find the equation of the line in the form y=mx+b, we need to first find the slope (m) and the y-intercept (b).
Looking at the table:
x | y
--|--
1 | 4
2 | 6
3 | 8
We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1, 4) and (2, 6):
m = (6 - 4) / (2 - 1)
m = 2 / 1
m = 2
So the slope of the line is 2.
To find the y-intercept, we can use the formula:
b = y - mx
Let's use the first point (1, 4) and the slope we just found:
b = 4 - (2)(1)
b = 4 - 2
b = 2
So the y-intercept of the line is 2.
Putting it all together, the equation of the line in the form y=mx+b is:
y = 2x + 2.
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select ALL the correct answers.
Which data set could be used to create the box plot below?
Im sorry but I dont see a Box Plot.
Answer:
provide more data
Step-by-step explanation:
no solution
What is the side length of AB
Answer:
AB ≈ 8.1
Step-by-step explanation:
using the cosine ratio in the right triangle
cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{6.2}{AB}[/tex] ( multiply both sides by AB )
AB × cos40° = 6.2 ( divide both sides by cos40° )
AB = [tex]\frac{6.2}{cos49}[/tex] ≈ 8.1 ( to the nearest tenth )
Si la secuencia es 7,12,17,22 y la regla es agregar 5 cuales son los siguentes dos terminos ?
the next two terms in the sequence would be 12 and 17.
Encuentra el siguen termino de la sucesión 23,18,13
Answer: 8
Step-by-step explanation:
We see that each term is 5 less than the previous one. We will subtract 5 from 13 to find the next term in the sequence.
13 - 5 = 8
simplify the expression (x+6)^2
The simplified expression for (x+6)^2 is x^2 + 12x + 36.
The expression (x+6)^2 represents the square of the sum of x and 6. To simplify this expression, we need to use the formula for expanding a binomial squared, which is (a+b)^2 = a^2 + 2ab + b^2.
Applying this formula to our expression, we get:
(x+6)^2 = x^2 + 2(x)(6) + 6^2
Simplifying further:
(x+6)^2 = x^2 + 12x + 36
In summary, to simplify the expression (x+6)^2, we use the formula for expanding a binomial squared and simplify the resulting terms to get the simplified expression x^2 + 12x + 36.
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Find the mean of 7,9,4,3,9,4 graphically
Answer:
6
Step-by-step explanation:
To find the mean you've got to add 7, 9,4,3,9 and 4 (which gives you 36) and divide that by the number of figures/numbers (which is 6 numbers in total) and it gives you 6
