Answer:
21 waysStep-by-step explanation:
Given
Wilbur has 7 subjects' homeworkHe can only do 5 of themCombination Formula
ⁿCₓ = n! / (n - x)! x!Number of possible ways
⁷C₅ = 7! / 2! x 5!⇒ 7 x 6 x 5! / 2! x 5!⇒ 7 x 6 / 2⇒ 7 x 3⇒ 21 ways
13-18 Express the quantity as a single logarithm.
13. [tex]2 \ln x+3 \ln y-\ln z[/tex]
[tex]2 \ln x+ 3 \ln y - \ln z\\\\=\ln x^2 + \ln y^3 - \ln z\\\\=\ln(x^2 y^3) - \ln z\\\\=\ln \left( \dfrac{x^2y^3}{z} \right)[/tex]
A man traveled 24 miles in 20 minutes and 18 miles in 15 minutes. Assume that the distance varies linearly with time. How far will he travel in 30 minutes
Step-by-step explanation:
First we need to get his speed:
speed = distance / time
If he travelled 24 miles in 20 mintues, his speed is 24 / 20 = 1.2 miles per minute
If he travelled 18 miles in 15 minutes, his speed is 18 / 15 = 1.2 miles per minute
Those two should give us the same answer since it says that the distance varies linear with time, which means that his speed is constant.
Then after 30 minutes he will have traveled: 1.2 x 30 = 36 miles
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Find the volume of the pyramid.
A pentagonal pyramid with base labeled as B equals 210 square inches. The height of the pyramid is 30 inches.
Answer:
6300in
Step-by-step explanation:
vol=base area x height
210x30
=6300in
On the map below 1/4 inch represents one mile. Candler, Canton, and Oteen are three cities on the map. If Candler and Oteen are 3 1/2 inches apart on the map, what is the actual distance between Candler and Oteen in miles?
14 miles
Step-by-step explanation:Let "Candler" be known as "C" and "Oteen" as "O"
Given:
0.25 inch = 1 mileDistance between "C" and "O" (In inches): 3.5 inches3.5 ------> 3.50
⇒ Distance between "C" and "O" (In inches): 3.50 inchesComparing the rate (inches/mile) and the distance:
⇒ 0.25x = 3.50Multiplying both sides by 100:
⇒ 25x = 350Clearly, 350 is divisible by 25 as "50" is divisible by 25.
Divide both sides by 25 to isolate x:
⇒ 25x/25 = 350/25⇒ x = 14The actual distance between the two cities is 14 miles.
Answer:
14 miles
Step-by-step explanation:
Given:
[tex]\sf Scale=\dfrac14\:in : 1\:mile[/tex]distance between Candler and Oteen is 3 1/2 inLet [tex]x[/tex] be the distance between Candler and Oteen in miles.
[tex]\implies \dfrac14:1=3 \frac12:x[/tex]
[tex]\implies \dfrac{\frac14}{1}=\dfrac{\frac72}{x}[/tex]
[tex]\implies \dfrac14x=\dfrac72[/tex]
[tex]\implies x=\dfrac72 \div \dfrac14[/tex]
[tex]\implies x=\dfrac72 \times \dfrac41[/tex]
[tex]\implies x=\dfrac{28}{2}[/tex]
[tex]\implies x=14[/tex]
The cost of beef decreases weekly at a rate of 10.2%. If beef cost $15.75 per pound today. How much will it cost in 2 years? ( round to the nearest cent (2 decimal places) )
Answer:
$ 383 854.28 per pound ====> See below !!
Step-by-step explanation:
Increases 10.2 % per WEEK (?? Per WEEK?))
2 years is 104 weeks (this is going to be a HUGE number)
15.75 (1+.102)^104 =
If increase is YEARLY
15.75 ( 1 + .102)^2 = $ 19.13 per pound <<<<after two years
What does 4! Equal?show the equation and what it equals
Answer:
[tex]\boxed{\sf{24}}[/tex]Step-by-step explanation:
To solve this problem, first, you have to use the order of operations.
PEMDAS stands for:
ParenthesesExponentsMultiplyDivideAddSubtract4!Use the fractional rule.
[tex]\Longrightarrow: \sf{n!= 1*2*3*4}[/tex]
First, multiply.
1*2=2
2*3*4
2*3=6
6*4=24
[tex]\Longrightarrow: \boxed{\sf{24}}[/tex]
Therefore, the correct answer is 24.I hope this helps. Let me know if you have any questions.
Cosx(tanx+cotx)=
Pls Help
Answer:
Answer is csc(x)
Step-by-step explanation:
I convert tan(x)= sin(x)/cos(x) and cot(x)= cos(x)/sin(x).
Then distribute the cos(x).
Then turn it into fractor that has same denominator.
Simplified the numerator sin^2(x)+cos^2(x)=1
[tex]cos(x)*\((tan(x)+cot(x))\\\\cos(x)*(\frac{sin(x)}{cos(x)} +\frac{cos(x)}{sin(x)})\\\\sin(x)+\frac{cos^2(x)}{sin(x)}\\\\sin(x)*\frac{sin(x)}{sin(x)}+\frac{cos^2(x)}{sin(x)}\\\\\frac{sin^2(x)}{sin(x)}+\frac{cos^2(x)}{sin(x)}\\\\\frac{sin^2(x)+cos^2(x)}{sin(x)}\\\\\frac{1}{sin(x)}\\\\csc(x)[/tex]
Answer:
→cosecx
Step-by-step explanation:
[tex]\hookrightarrow cosx(tanx+cotx)\\\\\hookrightarrow cosx(\frac{sinx}{cosx} +\frac{cosx}{sinx} )\\\\\hookrightarrow cosx(\frac{sinx \times sinx + cosx \times cosx}{cosx*sinx} )\\\\\hookrightarrow cosx(\frac{sin^{2}x+cosx^{2}x}{cosx*sinx} )\\\\\hookrightarrow cosx(\frac{1}{cosx*sinx} )\\\\\hookrightarrow cosx \times \frac{1}{cosx} \times \frac{1}{sinx} \\\\\hookrightarrow 1\times\frac{1}{sinx} \\\\\hookrightarrow \frac{1}{sinx} \\\\\hookrightarrow cosecx[/tex]
A store is currently offering a 60% discount on all items purchased. Your cashier is trying to convince you to open a store credit card and says to you, “ In addition to the 60% discount you are receiving for purchasing these items on sale today you will get an additional 20% off for opening a credit card account. That means you are getting 80% off!
If we were getting 60% discount early and then again we are receiving 20% discount for using credit card then it means that we are getting 80% discount.
What is discount?Discount means the amount which is deducted by sellers from the amount to be payable by buyers.
How to calculate discount?Let the total price to be paid by us to store is $100.
Discount received because on purchase on sale day=100*60%
=60
Discount received due to use of credit card=100*20%
=20
Total discount received from store=60+20
=80
Percentage=80/100*100
=80%
Hence the total discount received by us from store is 80%.
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Change the following fraction to a mixed number with the fraction part reduced to lowest terms. 84/42
Answer:
2
Step-by-step explanation:
since you have 84/42, and you are supposed to convert the improper fraction to a mixed number, the easiest place to start is to divide the two numbers and find the remainder. In this case, however, there is no remainder, as 84 divided by 42 is exactly 2. Therefore, the most simplified fraction would be 2 (although it does not look like a fraction the most simplified form of the fraction is 2/1 --> which is just 2). Hope this helps!
In the decimal 14.8765 the 5 is in the
place.
Answer:
The 5 is in the thousandths place
8 is the 'ones'
7 is the tenths
6 is the hundredths
5 is the thousandths
Step-by-step explanation:
A standard deck of cards has 13 cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, ace) in each
of 4 suits (hearts, clubs, diamonds, spades). The hearts and diamonds cards are red. The
clubs and spades cards are black. You choose a card from a standard deck of cards at
random. What is the probability that you do not choose a club?
The probability that you do not choose a club is
Answer:
3/4
Step-by-step explanation:
Prob to pick a club is 13/52
Prob not to pick a club is 1 - 13/52
1 - 13/52 = 3/4
Logic question.
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Thanks :)
Select the expressions that have a value less than -1.
A. -7 ÷ (-4)
B. – (3 ÷ 2)
C. -8/5 x (-5/8)
D. -5/-3
E. (-9) ÷ 6
Answer:
B and E
Step-by-step explanation:
A. -7 ÷ (-4) = -7/-4 = 7/4 = 1.75
B. -(3 ÷ 2) = -(1.5) = -1.5
C. -8/5 * (-5/8) = (8/5) * (5/8) = 1
D. -5/-3 = 5/3 ≈ 1.667
E. -9 ÷ 6 = -9/6 = -1.5
50 points each question. Please help. How do I solve?
[tex]~~~~~7e^{xy} +2x^2 -4y^2 =13\\\\\\\implies \dfrac{d}{dx}\left(7e^{xy} +2x^2 -4y^2\right) =\dfrac d{dx} (13)\\\\\\\implies 7\left[e^{xy} \dfrac{d}{dx} ( xy)\right] +2 \cdot 2x -4\cdot 2y \dfrac{dy}{dx} = 0\\\\\\\implies 7e^{xy} \left( x \dfrac{dy}{dx} +y\right) +4x -8y \dfrac{dy}{dx} =0\\\\\\\implies 7xe^{xy}\dfrac{dy}{dx} + 7ye^{xy} +4x -8y\dfrac{dy}{dx} = 0\\\\\\\implies \left(7xe^{xy} -8y \right) \dfrac{dy}{dx}=-7ye^{xy} -4x\\\\\\[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{-7ye^{xy} -4x}{7xe^{xy} -8y }[/tex]
A rectangular window has a height of 5 1/2 feet and a width of 1 1/2 feet. What is the perimeter of the window?
A. 7 feet
B. 13 feet
C. 14 feet
D. 28 feet
Answer:
Your answer is C, 14ft
Step-by-step explanation:
Your Given Measurements (in feet):
Height = 5 1/2 ; Width = 1 1/2
___________________________________________________
The Perimeter Formula:
L + W + L + W = P
In this case, the "L" which is length going to get substituted as Height.
5 1/2 is 5.5 because if you do 1/2 on the calculator, you get 0.5 which you can add 5 to get 5.5.
1 1/2 is 1.5 which is the same as the 5 1/2.
____________________________________________________
Now do 5.5 + 1.5 + 5.5 + 1.5 = perimeter
5.5 + 1.5 = 7
7 + 7 = 14ft
Your answer is C: 14 ft
According to the rules of NCAA volleyball, there must be exactly 6 players on the court at all times and each player has a unique designated position on the court. How many different starting position configurations are possible for the 6 starting players of an 8-member volleyball team that follows this rule? Please answer quick.
Answer:
20160Step-by-step explanation:
This is a permutation of 6 out of 8
Use formula
P(n, r) = n!/(n-r)!Find the number of starting positions
P(8,)6 = 8!/(8 - 6)! = 8!/2! = 1*2*3*4*5*6*7*8/1*2 = 20160The difference between two consecutive cube numbers is always odd or even?
Answer:
odd
Step-by-step explanation:
take example of 2^3 +3^3 it's odd
now others try yourself
Can yall help me with this pls
kvnaebivaebriebhaeibnebaeb g
Find the value of X.
Answer:
Step-by-step explanation:
Vertically opposite angles are congruent.
-2x - 6 = 40
Add 6 to both sides
-2x = 40 + 6
-2x = 46
Divde both sides by (-2)
x = 46/(-2)
x = -23
You want to buy a television priced at $479 with a 6.5% sales tax. What is the final cost of the television, after-tax? Round to the nearest cent.
Answer:
On Knewton May 15,2022 $510.14
Step-by-step explanation:
A rectangular tabletop will be made of maple
wood that weighs 43 pounds per cubic foot. The
tabletop will have a length of eight feet, a width
of three feet, and a thickness of one inch.
Determine and state the weight of the tabletop,
in pounds.
A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot. The weight of the tabletop, in pounds, is 1032.
What is the volume of the rectangular tabletop?The volume of the rectangular tabletop is the product of the length, breadth, and height of the given tabletop.
Volume of rectangular tabletop= (length x width x height)
The tabletop will have a length of eight feet, a width of three feet, and a thickness of one inch.
Volume of rectangular tabletop= (length x width x height)
= [tex]8 \times 3 \times 1\\\\24[/tex]
A rectangular tabletop will be made of maple wood that weighs 43 pounds per cubic foot.
The weight of the tabletop, in pounds = 43 x 24
= 1032 pounds
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A teacher wants to assign 4 of the 15 practice problems at the end of the lesson. How many different assignments are possible?
Answer:
15/4= 3.75
Step-by-step explanation:
Pls help me
Pls show your answer pls and thank you
Answer:
Step-by-step explanation:
Beth's position over time is constant, which makes the problem a lot easier. You are asked for the rate of position versus time, so begin by doing that. Since the rate is constant, clearly from the table, you can take any two data points and take their ratio. Her rate would be 11 feet every 5 seconds, or equivalently 2.2 feet every second. To graph the data, put position on the x-axis and time on the y-axis. The slope will be 2.2 at every point along her bike ride.
Moving on to the third part. If Amy traveled at a rate of 75 feet every 30 seconds, then she would be traveling 2.5 feet every second. Amy's rate is larger than Beth's rate. Since the rate corresponds to the slope of the postion vs. time graph, Amy's graph will have a steeper incline since the slope is 2.5
Use log 2=a, log 3=b to evaluate log 216
Answer:
answer = 3(a +b)
Step-by-step explanation:
[tex] log(2) = a \: log(3) = b \: \: \\ log(216) = log(2 \times 2 \times 2 \times 3 \times 3 \times 3) \\ = log( {2}^{3} \times {3}^{3} ) \\ = log(2^{3} ) + log( {3}^{3} ) \\ = 3 log(2) + 3 log(3) \\ = 3(a) + 3(b) \\ = 3(a + b) \\ \\ log(216) = 3(a + b)[/tex]
Here are the test scores for 15 students in Mr. M's class.
96, 85, 59, 63, 76, 68, 94, 97, 89, 100, 93, 96, 72, 46, 78
What is the percentage of these test scores that are less than 90?
Answer:
60%
Step-by-step explanation:
If you look through the data, it is clear that 46, 59, 63, 68, 72, 76, 78, 85, and 89 are all less than 90. There are 9 elements total that are less than 90.
For percentages, you take the number you have and divide by the total. Since we know that there are 15 students, we can do 9 / 15. This gives us 0.6 which is 60%
Algebra Write an expression representing the volume of the composite figure
formed by a hemisphere with radius r and a cube with side length 2r.
The expression that represents the volume of the composite figure is 16/3πr³ + r³
The expression that represents the volume?The given parameters are:
Hemisphere radius = rCube length = rThe volume of a cube is:
V = l³
So, we have:
V = r³
The volume of a hemisphere is:
V = (2/3)πr³
So, we have:
V = (2/3)π(2r)³
Evaluate
V = (2/3)π * 8r³
This gives
V = 16/3πr³
Add both volumes
Volume = 16/3πr³ + r³
Hence, the expression that represents the volume of the figure is 16/3πr³ + r³
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Find the surface of the rectangular prism
Answer:
yes multiply the 3 sides 3 times together with the number 2
Help! This one step for solving standard deviation I don't understand...
When I got it wrong it tells me what to do but I don't get it? (2nd image)
x = 10
hope it helps...!!!
The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is y+7= -5/2(x-10)What
is the standard form of the equation for this line ?
One way we can organize a linear equation is in standard form:
[tex]Ax+By=C[/tex]
A, B and C are typically integersAnother way we can organize a linear equation is in point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
m is the slope[tex](x_1,y_1)[/tex] is a point that falls on the lineSolving the QuestionWe're given:
Line passes through (-5,-1) and (10,-7)Point-slope form is [tex]y+7=-\dfrac{5}{2}(x-10)[/tex]We only need the point-slope form equation to find the stand form of the equation for this line. All we have to do is rearrange the numbers to get them in the right places.
[tex]y+7=-\dfrac{5}{2}(x-10)[/tex]
⇒ First, multiply both sides by 2 to get rid of the fraction:
[tex]2y+14=-5(x-10)[/tex]
⇒ Now, open up the parentheses:
[tex]2y+14=-5x+50[/tex]
⇒ Move -5x to the other side:
[tex]5x+2y+14=50[/tex]
⇒ Move 14 to the other side:
[tex]5x+2y=50-14[/tex]
⇒ Combine like terms:
[tex]5x+2y=36[/tex]
Answer[tex]5x+2y=36[/tex]