calculate the cost of fuel. 40 L at 65.7cents/L
HELP!!! A pentagonal pyramid is sliced parallel to its base. what shape does it make?
solve for x:
4/x-3 + 2/x^2-9 = 1/x+3
a. -17/3
b.13/3
c.19/3
d.-5
The Mississippi River is about 4,000 kilometers long. An M&M is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer. Estimate how many M&Ms it would take to measure the length of the Mississippi River
To measure the approximately 4,000 km long Mississippi River with M&Ms, we will need about 400,000,000 M&Ms, as there are 100 cm in a meter and 1,000 m in a km.
The question involves estimating the length of the Mississippi River using the size of M&Ms as a unit of measurement. Since the river is about 4,000 kilometers long and the standard unit of length in the SI system is the meter, we need to convert kilometers to centimeters to match the size of an M&M, which is about 1 centimeter long. There are 100 centimeters in a meter, and 1,000 meters in a kilometer. Therefore, we have:
Convert kilometers to meters: 4,000 km x 1,000 m/km = 4,000,000 m.Convert meters to centimeters: 4,000,000 m x 100 cm/m = 400,000,000 cm.Now, since each M&M is 1 centimeter, the number of M&Ms needed to measure the length of the Mississippi River is equal to the total number of centimeters:
400,000,000 M&Ms would be required to measure the approximate length of the Mississippi River.
write three different equivalent expressions for the following expression:
16x^8
Three different equivalent expressions for 16x^8 are [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex], [tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex].
Expressing [tex]\(16x^8\)[/tex] in three different equivalent forms:
1. Expanded Form:
[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2 \cdot x)^4 \cdot x^4 = (2x)^4 \cdot x^4 \][/tex]
2. Factored Form:
[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \][/tex]
3. Exponential Form with a Common Base:
[tex]\[ 16x^8 = 2^4 \cdot x^8 = (2x)^4 \cdot x^4 = 2^{4 + 4} \cdot x^{4 + 4} = 2^8 \cdot x^8 \][/tex]
These expressions show the flexibility in representing the original expression using different algebraic manipulations. The key is to recognize patterns, use properties of exponents, and factor out common terms.
A person at ground level measures the angle of elevation to the top of a building to be 74 degrees. If at this point the person is 34 feet away from the base of the building, then how tall is the building? (Please round to the tenths place; please show work/steps and provide units with your answer) WILL GIVE BRAINIEST
to find the height of the building multiply the distance ( 34 feet) by the tangent of the angle(74)
34 * tan(74) = 118.57 feet
The length of a rectangle is one unit shorter than one-sixth of the width, x. Which expression represents the perimeter of the rectangle? 7/3x−2 1/3x−4 1/3x−2 7/3x−8
Answer: [tex]\dfrac{7}{3}x-2[/tex]
Step-by-step explanation:
Let x be the width of the rectangle , then the length of the rectangle will be :_
Length = [tex]\dfrac{1}{6}x-1[/tex]
We know that the perimeter of a rectangle is given by :-
[tex]P=2(l+w)[/tex]
Substitute the value of length and width we get,
[tex]P=2(\dfrac{1}{6}x-1+x)[/tex]
Combine like terms, we get
[tex]P=2(\dfrac{1+6}{6}x-1)\\\\\Rightarrow\ P=2(\dfrac{7}{6}x-1)\\\\\Rightarrow\ P=2\times\dfrac{7}{6}x-2\times1\\\\\Rightarrow\ P=\dfrac{7}{3}x-2[/tex]
Hence, the expression represents the perimeter of the rectangle : [tex]\dfrac{7}{3}x-2[/tex]
192 beads to make a necklace and bracelet. 5 times as many beads to make a necklace than a bracelet. How many beads are used to make a the necklace?
What are the solutions of 2x2 + 8x = −26
The Boardman family walked 2/5 of a mile in 2/7 of an hour. What is their unit rate in miles per hour? 20 points
The Boardman family's walking speed is 1.4 miles per hour, which is calculated by dividing the distance walked (2/5 mile) by the time it took (2/7 hour).
A unit rate defines how many units of the first type of quantity correspond to one unit of the second type of quantity. In this case, we need to find out how many miles they walk in one hour.
To calculate the unit rate, we divide the distance by the time. They walked 2/5 of a mile in 2/7 of an hour. Setting up the division, we have:
(2/5) miles / (2/7) hours = (2/5) × (7/2) miles per hour = 7/5 miles per hour
After simplifying, we get that the Boardman family's walking speed is 1.4 miles per hour.
Determine the intercepts of the line. 7x-5=4y-6/7x−5=4y−6
Answer:
x.(-1/7,0)
y.(0,1/4)
Step-by-step explanation:
We have found the least squares line for predicting coral growth y from mean sea surface temperature x to be y = 11.6921 − 0.30305x. (a) use the equation to obtain the seven residuals step by step. that is, find the prediction y for each observation and then find the residual y − y. (round your answers to three decimal places.)
From the above equation putting the value of x. we get yhat and reducing it from actual value of y we will get residual
Therefore, as shown on the image below,
the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8. what is the value of w
The value of 'w' using the given slope is [tex]\frac{9}{2}[/tex]
Given :
the slope of the line that passes through the points (-6,w) and (-10,4) is 1/8
apply slope formula
[tex]slope =\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the values given in the points and make it equal to 1/8
[tex]slope =\frac{4-w}{-10+6}=\frac{1}{8} \\\frac{4-w}{-4}=\frac{1}{8}\\(4-w)(8)=-4(1)\\32-8w=-4\\-8w=-4-32\\-8=-36[/tex]
Divide both sides by -8
[tex]w=\frac{-36}{-8} =\frac{9}{2}[/tex]
The value of 'w' is [tex]\frac{9}{2}[/tex]
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What happens to the arrangement of water molecules as ice melts?
A. Molecules gain enough energy to escape as vapor.
B. Molecules release enough energy to escape as vapor.
C. Molecules release enough energy to move from their fixed positions.
D. Molecules gain enough energy to move from their fixed positions.
An athletic director pays $90 for 12 sun visors for the softball team. a. How much will the athletic director pay to buy 15 more sun visors?
The base of a skyscraper is a triangle bordered by three streets: Main Street, Elm Street, and Maple Street. The Elm Street side is 1 ft shorter than twice the Maple Street side. The Maple Street side is 8 ft shorter than half the Main Street side. The Main Street side is 206 ft. The base of a skyscraper is a triangle bordered by three streets: Main Street, Elm Street, and Maple Street. The Elm Street side is 1 ft shorter than twice the Maple Street side. The Maple Street side is 8 ft shorter than half the Main Street side. The Main Street side is 206 ft.
Part 1 out of 2
(a) Find the two unknown side lengths.
Maple Street is
ft.
Elm Street is
ft.
solve each inequality. Justify each step (y-) - 4 + 2y > 11
The perimeter of a rectangle is 42 cm. The longer side has length of 7 cm more than the shorter side. Find the length of longer side
What is the mean of the following set of numbers?
{-7, 23, -5, 4}
A. 3.75
B. 9.75
C. -9.75
D. -3.75
the mean is the average
-7+23 -5 +4 = 15
15 / 4 = 3.75
Answer is A
Exercise 26 proposes modeling iq scores with n(100, 16). what iq would you consider to be unusually high? explain.
Course hero from a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. in how many ways can it be done?
Find the equation of the ellipse with the following properties. The ellipse with x-intercepts (2, 0) and (-2, 0); y-intercepts (0, 4) and (0, -4).
An m-bit password is required to access a system. a hacker systematically works through all possible m-bit patterns. let x be the number of patterns tested until the correct password is found. find the conditional pmf of x given that the password has not been found after k tries
Final answer:
The conditional pmf of x, the number of patterns tested until the correct m-bit password is found, given that the password has not been found after k tries, is uniformly distributed with 1/(2^m - k) for x = k+1, k+2, ..., 2^m.
Explanation:
The question deals with the topic of probability and specifically centers around the concept of a conditional probability mass function (pmf). Given that an m-bit password is systematically being guessed by a hacker and has not been found after k attempts, we need to find the conditional pmf of x, where x is the number of patterns tested until the password is found.
Since the password has not been guessed within the first k tries, the conditional probability is based on the remaining 2m - k possibilities. The distribution of x will be uniform because each subsequent attempt has an equal probability of being correct. The conditional pmf of x given that the password was not found after k tries is 1/(2m - k) for x = k+1, k+2, ..., 2m.
For a normal distribution, the proportion in the tail beyond z = 0.30 is p = 0.1179.
a. True
b. False
Using the normal distribution, it is found that the statement is False, thus the correct option is b.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.The area on the tail beyond z is the proportion that is above z, that is, 1 subtracted by the p-value of z.For this problem, z = 0.3 has a p-value of 0.6554.
1 - 0.6554 = 0.3446
The proportion in the tail beyond z = 0.30 is p = 0.3446, thus, the statement is False.
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which one of the following items is an example of software
suppose you deposit $25,000 in to a fund for which the annual interest rate is 5.3% compounded continuously. find the number of years it will take to double in value (round your answer to the nearest tenth of a year)
The table shows the amount that each person spend on snacks, games, and souvenirs the las time they went to the carnival.
Sinea- snacks $5/ games $8/ souvenirs $12
Ren- snacks $10/ games $8/ souvenirs $20
Suppose Sinea and Ren each spend $40 on snacks, and each person spends money using the same ratios as on their last trip. Who spends more on souvenirs? Explain
A bus can carry 50 people per run. At least how many times does the bus have to run in order to transfer 25,000 people?
Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 256 ft^3 of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?
To solve the problem we must know about the volume and the surface area of cuboids.
The length of the aquarium is 4, and the width of the aquarium is 8.
Given to us
The aquarium must hold 256 ft^3 of water.We know that the base of the aquarium should be a square, therefore, the length and the breadth of the aquarium will be the same.
Volume of the AquariumLength x breadth x height = 256 ft³
Length x Length x height = 256 ft³
Length ² x height = 256 ft³
[tex]L^2\times H = 256\\\\H = \dfrac{256}{L^2}[/tex]
Surface Area of the AquariumSurface Area of the Aquarium
= Area of the base + (4 x Area of the 4 sides)
[tex]= L^2 + 4(L\times H)[/tex]
Substituting the value of H,
[tex]= L^2 + 4L(\dfrac{256}{L^2})[/tex]
Length of the AquariumLet the surface area be a function of L, therefore,
[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})[/tex]
Differentiating the function to get the minimum,
[tex]f(L) = L^2 + 4L(\dfrac{256}{L^2})\\\\f(L) = L^2 + (\dfrac{1024}{L})\\\\f'(L) = 2L - (\dfrac{1024}{L^2})[/tex]
Equating against zero,
[tex]2L - (\dfrac{1024}{L^2}) = 0\\\\\dfrac{2L^3-1024}{L^2} = 0\\\\2L^3-1024 = 0\\\\L = 8[/tex]
Substituting the value of L,
[tex]H = \dfrac{256}{L^2}\\\\H = \dfrac{256}{8^2}\\\\H = 4[/tex]
But this way the area will be more, therefore, replace the value of L with 8,
L = 4
H = 8
Hence, the length of the aquarium is 4, and the width of the aquarium is 8.
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how much smaller is the value of the 5 in 57,800 than the value of the 5 in 526,300