The cross-section of the rectangular pyramid, obtained by slicing it parallel to the longer sides of the base and through the top vertex, forms a 9-12-15 right triangle. The area of the cross-section is 54 square inches (Option C).
The rectangular pyramid has a base with sides of 5 inches and 12 inches, and diagonals measuring 13 inches. The height of the pyramid is 9 inches.
The cross-section obtained by slicing the pyramid parallel to the longer sides of the base and passing through the top vertex will form a right triangle with legs of 9 inches and 12 inches, and a hypotenuse of 13 inches (as given by the diagonals).
This right triangle is a 3-4-5 right triangle scaled up by a factor of 3, making it a 9-12-15 right triangle. The area of a right triangle is given by [tex]\(\frac{1}{2} \times \text{base} \times \text{height}\).[/tex]
So, the area of the cross-section is [tex]\(\frac{1}{2} \times 12 \times 9 = 54\)[/tex] square inches.
Therefore, the correct answer is (C) 54 square inches.
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Need help with finding the volume of this cone for #35
What is 0.(24) ̅ (the 24 is repeating) expressed as a fraction in simplest form?
What is 0.24 ̅ (the 4 is repeating) expressed as a fraction in simplest form?
What is 0.24 expressed as a fraction in simplest form?
PLEASE SHOW YOUR WORK
A bag contains 5 red marbles, 7 white marbles, and 6 blue marbles. Find P(red or blue).
Answer:
P(red or blue) = 5/18 + 6/18 = 11/18
if a ship sailed due south from iceland to antarctica, it would sail through an angle of rotation of about 140 degrees around Earth's center. Find this measure in radians. Then, using 3960 miles for Earth's radius, find how far the ship would travel
the ship would travel approximately 9685.82 miles from Iceland to Antarctica.
To convert the angle from degrees to radians, we use the conversion factor[tex]\( \pi \)[/tex]radians = 180 degrees.
[tex]\[ \text{Angle in radians} = \frac{\text{Angle in degrees} \times \pi}{180} \][/tex]
In this case, the angle in degrees is 140 degrees:
[tex]\[ \text{Angle in radians} = \frac{140 \times \pi}{180} \]\[ \text{Angle in radians} = \frac{140}{180} \times \pi \]\[ \text{Angle in radians} = \frac{7}{9} \pi \][/tex]
Next, we'll find how far the ship would travel using Earth's radius. The distance traveled on a circle is given by the formula:
[tex]\[ \text{Distance} = \text{radius} \times \text{angle in radians} \][/tex]
Given Earth's radius as 3960 miles and the angle in radians as [tex]\( \frac{7}{9} \pi \)[/tex], we can calculate the distance:
[tex]\[ \text{Distance} = 3960 \times \frac{7}{9} \pi \]\[ \text{Distance} = 3080 \pi \]\[ \text{Distance} \approx 9685.82 \text{ miles} \][/tex]
So, the ship would travel approximately 9685.82 miles from Iceland to Antarctica.
What’s $54.00 for 3 tickets in unit rate
help me pls with the answers pls, identify each pair of angles as complementary,supplementary, or neither
Dirk can clean a playground in 5 hours. Geralyn can clean a playground in only 4 hours. Which of the following can be used to determine the amount of time it would take for Dirk and Geralyn to clean a playground together?
Which of the following sets of numbers could be the lengths of the sides of a triangle? A. 81 mm, 7 mm, 6 mm B. 81 mm, 7 mm, 72 mm C. 81 mm, 7 mm, 88 mm D. 81 mm, 7 mm, 77 mm
The correct option is B. 81 mm, 7 mm, 72 mm could be the lengths of the sides of a triangle.
To determine if a set of numbers could be the lengths of the sides of a triangle, the Triangle Inequality Theorem must be satisfied. The theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this theorem to each set of numbers:
A. 81 mm, 7 mm, 6 mm
- The sum of the two smallest sides is 81 + 6 = 87 mm, which is greater than the third side, 7 mm. However, the sum of the two smallest sides, 7 + 6 = 13 mm, is not greater than the largest side, 81 mm. Therefore, these lengths cannot form a triangle.
B. 81 mm, 7 mm, 72 mm
- The sum of the two smallest sides is 7 + 72 = 79 mm, which is greater than the third side, 81 mm. This set satisfies the Triangle Inequality Theorem.
C. 81 mm, 7 mm, 88 mm
- The sum of the two smallest sides is 81 + 7 = 88 mm, which is equal to the third side, 88 mm. According to the Triangle Inequality Theorem, the sum must be strictly greater than the third side, so these lengths cannot form a triangle.
D. 81 mm, 7 mm, 77 mm
- The sum of the two smallest sides is 7 + 77 = 84 mm, which is greater than the third side, 81 mm. However, the sum of the two smallest sides, 81 + 7 = 88 mm, is not greater than the third side, 77 mm. Therefore, these lengths cannot form a triangle.
Based on the Triangle Inequality Theorem, the only set of lengths that can form a triangle is option B: 81 mm, 7 mm, 72 mm.
What is the decimal equivalent of the fraction?
4/30
A) 0.13⎯⎯⎯⎯
B) 0.13
C) 0.1⎯⎯3
D) 0.13⎯⎯
Answer:
Option A [tex]\frac{4}{30}=0.13333...=0.1\bar3[/tex]
Step-by-step explanation:
Given : Expression [tex]\frac{4}{30}[/tex]
To find : What is the decimal equivalent of the fraction?
Solution :
Step 1 - Write the fraction
[tex]\frac{4}{30}[/tex]
Step 2 - Divide the numerator by denominator,
[tex]\frac{4}{30}=0.13333...[/tex]
or [tex]\frac{4}{30}=0.13333...=0.1\bar3[/tex]
Therefore, Option A is correct.
A rectangular bathtub is 5 1/2 feet Long, 1 1/2 feet wide, and 3 feet high. Daniel fills the tub to a depth of 2 feet. What is the volume of the water in the tub?
A hamster wheel has a diameter of 8.5 in. How many inches does the hamster run in one revolution? Use 3.14 to approximate for π .
As hamster wheel is circular so for revolution we will find the circumference.
Diameter of the Hamster wheel = 8.5 in
One revolution of the wheel = circumference of the wheel
Circumference = π × d
π = 3.14 and d = 8.5
So, Circumference = 3.14 × 8.5
Circumference = 26.69 in
So in one revolution the hamster wheel travels a distance of 26.69 in
If a PENNY has a circumference of 59.69 millimeters, what is the radius?
The radius of the penny is 9.54 millimeters.
What is circumference?The circumference means the length of the literal line that surrounds and forms a circle.
What is the formula for the circumference of circle?The formula for the circumference of the circle is given by
[tex]circumference = 2\pi r[/tex]
Where,
r is the radius
and π = 3.14
What is radius?A radius is a straight line from the center of a circle to the circumference of a circle.
According to the given question.
We have a penny whose circumference is 59.69 millimeters.
Let r be the radius of the penny and 2πr be the circumference of the penny.
Since we know that, the shape of the penny is circular.
Therefore,
The radius, r of the penny is given by
[tex]2\pi r= 59.69[/tex]
[tex]\implies r = \frac{59.69}{2\pi }[/tex]
[tex]\implies r = \frac{59.69}{2(3.14)}[/tex]
[tex]\implies r = \frac{59.69}{6.28}[/tex]
[tex]\implies r = 9.54\ millimeters[/tex]
Hence, the radius of the penny is 9.54 millimeters.
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Giovanni justifies whether the expression -4x-8 is equivalent to -2(x+1)-2(x+3)by letting x=3 in both expressions. What is the value of each expression when x=3
3 and -20
4 and 4
-20 and -20
3 and 4
which equation models the population (in millions), p, of austinberg t years after january 1, 2000
Perry divides up some candy to give equally to his six friends. If c represents the total amount, write the expression to represent how much candy each friend receives.
Latoya drives 8 miles to work in 13 minutes what is her average rate
At what position does the ball have its maximum potential energy
A) a
B) d
C) f
D) g
write an equation that represents each mixed number as a sum of whole numbers and unit fractions 4 1/4
The equation that represents each mixed number as a sum of whole numbers and unit fractions of [tex]4\frac{1}{4}[/tex] is [tex]4\frac{1}{4}[/tex] = 4 + 1/4.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
We have the mixed fraction,
[tex]4\frac{1}{4}[/tex].
Converting the mixed fraction to an improper fraction,
[tex]4\frac{1}{4}[/tex] = 17/4
We need to write it as a sum of whole numbers and unit fractions:
So, it becomes,
[tex]4\frac{1}{4}[/tex] = 4 + 1/4
[tex]4\frac{1}{4}[/tex] = (16 + 1)/4
[tex]4\frac{1}{4}[/tex] = 17/4
Therefore, [tex]4\frac{1}{4}[/tex] = 4 + 1/4 is the required equation.
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What is the surface area of the ramp in square feet and if each square foot of wood on the ramp is sold for three dollars how much would the ramp sell for
Kevin had 6 nickles and 4 dimes in his pocket. If he took out one count and then a second coin without replacing the first coin-
what is the probability that both coins were nickels?
what is the probability that both coins were dimes?
what is the probability that the first coin was a nickel and the second a dime?
In this detailed answer, the probabilities of drawing two coins from Kevin's pocket - with 6 nickels and 4 dimes - are explained. The probabilities of both coins being nickels and dimes are 0 due to the lack of replacement, while the probability of one nickel and one dime is 4/15.
To calculate the probabilities of drawing coins from Kevin's pocket, where he has 6 nickels and 4 dimes:
Probability both coins are nickels: Since each draw affects the remaining number of nickels and dimes, the probability is 0.
Probability both coins are dimes: Similarly, as the draws are not independent, the probability here is also 0.
Probability of one nickel and one dime: Since Kevin has 6 nickels and 4 dimes, the probability of drawing a nickel first is 6/10 (6 nickels out of 10 coins) and drawing a dime second is 4/9 (4 dimes remaining out of 9 coins), which equals 24/90 or 4/15.
Use the Babylonian method to estimate √80 to the nearest hundredth.
Seed corn was $5 per bag, whereas dog food cost only $3 per bag. Wewoka bought 50 bags and spent $190. How many bags of dog food did she buy?
Answer:
30 bags
Step-by-step explanation:
Nc + Nd = 50
5Nc + 3Nd = 190
Multiply by -5 becomes:
-5Nc - 5Nd = -250
5Nc + 3Nd = 190
Equals:
-2Nd= -60
simplify:
-2Nd/-2 and -60/-2 = Nd= 30 bags
Find the area of the trapezoid.
A) 18 cm2
B) 22.5 cm2
C) 27 cm2
D) 45 cm2
Answer:
27 cm2
Step-by-step explanation:
The answer is 27 cm 2 because if you use length x base x height you would get your answer. So 6 x 3 x 3 = 54 and then if you divide that by 2 you would get 27
Answer:
the answer is C), 27 cm2
Step-by-step explanation:
write and solve an inequality for this situation. To honor 50 years of business, All Strikes Bowling is having an anniversary special. Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes, how many games can he bowl?
To honor 50 years of business, All Strikes Bowling is having an anniversary special. The game he can bowl is 25.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
To honor 50 years of business, All Strikes Bowling is having an anniversary special.
Shoes rent for $1.25 and each game is $0.75. If Charlie has $20 and needs shoes.
Charlie can bowl 25 games.
= 20 - 1.25
= 18.75
So, he can bowl game
= 18.75/ 0.75
= 25 games
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Factor completely 2x3 + 10x2 + 4x + 20.
2(x3 + 5x2 + 2x + 10)
2[(x + 5)(x2 + 2)]
(2x + 10)(x2 + 2)
(x + 5)(2x2 + 4)
Answer:
Step-by-step explanation:
Alright, lets get started.
The given expression is :
[tex]2x^3+10x^2+4x+20[/tex]
taking 2 common factor
[tex]2(x^3+5x^2+2x+10)[/tex]
[tex]2(x^3+2x+5x^2+10)[/tex]
[tex]2[(x+5)(x^2+2)][/tex]
So, the correct answer is option B : answer
Hope it will help :)
The function f(x) = 68(1.3)x represents the possible squirrel population in a park x years from now. Each year, the expected number of squirrels is ____ the number the year before. A. 3 times B. 1.3 times C. 3 more than D. 0.3 times
A recipe for dessert calls for 2/4 cup of powdered sugar and 1/6 cup of brown sugar . What is the total amount of sugar needed for the recipe
A scientist conducted an experiment to determine whether an organic cleaner is as effective as a non-organic cleaner in killing germs that cause colds and the flu. To conduct the experiment, the scientist randomly selected 50 doorknobs in a hospital. He cleaned 25 of the door knobs with the organic cleaner, and he cleaned the remaining 25 door knobs with the non-organic cleaner. After cleaning and testing all of the doorknobs, the scientist reported that the organic cleaner killed 90% of germs that cause colds and the flu on the doorknobs, while the non-organic cleaner killed 95% of germs that cause colds and the flu on the doorknobs. What can be concluded from the scientist's report?
Therefore, an organic cleaner is not as effective as a non-organic cleaner in killing germs that cause colds and the flu.
Alfonso went to famous Sam’s appliance store
toothbrushes are $4.00 each. there is a 10% discount but also 6% sales tax. What is the new price?