Answer:
1680 ways.
Step-by-step explanation:
This question is solved using Permutation formula.
Permutation formula is given as
nPr = n! / (n -r)!
In the above question we are to find how many ways we can answer 8 multiple choice questions with 4 options(A, B,C,D)
Therefore,
n = 8 multiple choice questions
r = 4 options
nPr = n! / (n - r)!
8P4 = 8! / ( 8 - 4) !
8P4 = 8! / 4!
8P4 = (8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1)
8P4 = 40320 / 24
8P4 = 1680 ways
Therefore, the number of ways to answer 8 multiple choice questions with 4 options (A, B, C, D) for each is 1680 ways.
Answer:
65,536 ways.
Step-by-step explanation:
The Fundamental Counting Principle states that:
"If decision M can be made m ways and decision N can be made n ways, then the two decisions can be made m⋅n ways"
Therefore, we can create a model of the eight questions by drawing eight blanks:
_ _ _ _ _ _ _ _
Then, filling in each "question" with the number of options for each, which is four:
4 4 4 4 4 4 4 4
And finally, we can multiply the fours together, which would be 4⋅4⋅4⋅4⋅4⋅4⋅4⋅4 or 4⁸, which is equal to 65,536.
I hope this helps! :D
35×712÷2710==============================================
Answer:
9.19
Step-by-step explanation: please give brainliest
Seth made a small rectangular table from his workroom the sides of the table or 1.3 mm and 2.8 mm what is the length of the diagonal of the table
Answer:
3.08mm
Step-by-step explanation:
use Pythagorean Theorem. 1.3^2 + 2.8^2 = 9.53 sqrt of 9.53 = 3.08
Answer:
3.087
Step-by-step explanation:
[tex] = \sqrt{ {1.3}^{2} + {2.8}^{2} } \\ = \sqrt{1.69 + 7.84} \\ = \sqrt{9.53} \\ = 3.087[/tex]
On Saturday Elena biked 10 miles. On Sunday she biked 50% of that distance. How far did she travel on Sunday?
50% is one half.
One half of 10 miles would be 5 miles.
You can either divide 10 by 2 or multiply 19 by the decimal for 50% which is 0.5 , they will both get you the answer of 5 miles.
PLZ HELP !! no guessing
Answer:
9 /16 cups
Step-by-step explanation:
Take the number of cups and divide by the number of servings
2 1/4 ÷ 4
Change to an improper fraction
9/4 ÷4
Copy dot flip
9/4 * 1/4
9 /16
Answer: 9/16
Step-by-step explanation: First, take the number of cups and divide by the number of servings. So we have 2 and 1/4 ÷ 4.
Now, rewrite 2 and 1/4 as the improper fraction 9/4 an 4 as 4/1.
So we have 9/4 ÷ 4/1.
Now, dividing by a fraction is the same as multiplying by its reciprocal. In other words, we can change the division sign to multiplication and flip the second fraction. So 9/4 ÷ 4/1 can be rewritten as 9/4 × 1/4.
Now, multiply across the numerators and denominators to get 9/16.
So there are 9/16 cup of raisins in each serving.
An above-ground swimming pool is leaking. After 1/2 an hour the pool has leaked 3/4 of a gallon of water. How many gallons of water per hour is the swimming pool leaking?
Answer:
1.5 GPH.
Step-by-step explanation:
Hello there!
Since we are given the amount that leaked out in half an hour, we can multiply it by 2 to get the final amount in gallons per hour (GPH).
:)
Answer: [tex]\frac{3}{2}[/tex] gallons of water per hour
Step-by-step explanation:
If [tex]\frac{3}{4}[/tex] of a gallon of water are leaked in half an hour, I conclude that if I multiply that by 2, it will give the result of gallons of water leaking per hour.
[tex]\frac{3}{4}*2=\frac{3}{2}[/tex]
what is the value of z?
z=2³
Answer:
8
Step-by-step explanation:
Ok here's the solution. I'm typing this to get 20+ characters:
2^3 = 2 x 2 x 2
= 8
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{z = 2^3}[/tex]
[tex]\mathsf{2^3 = z}[/tex]
[tex]\mathsf{2^3}[/tex]
[tex]\mathsf{= 2 \times 2 \times 2}[/tex]
[tex]\mathsf{= 4 \times2}[/tex]
[tex]\mathsf{= \bf 8}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Therefore, your answer is: z = \bf 8 (Option A)}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]whats the perimeter
Perimeter is the sum of the outside dimensions:
4 + 5 + 1 + 5 + 9 = 24 inches.
Your answer should be a polynomial in standard form. ( − 2 h + 9 ) ( 9 h − 2 ) = (−2h+9)(9h−2)=
Answer:
[tex]-18\cdot h^{2} + 85\cdot h - 18[/tex]
Step-by-step explanation:
The polynomial in standard form is:
[tex](-2\cdot h + 9) \cdot (9\cdot h - 2)[/tex]
[tex]-18\cdot h^{2} + 81\cdot h +4 \cdot h - 18[/tex]
[tex]-18\cdot h^{2} + 85\cdot h - 18[/tex]
2+3x=-4(5+2x) need help for this question.
Answer:
x=-2
Step-by-step explanation:
2+3x=-20-8x
22=-11x
x=-2
Answer:
[tex]x = -2[/tex]
Step-by-step explanation:
[tex]2 + 3x = - 4(5 + 2x) \\ 2 + 3x = - 20 - 8x \\ 3x + 8x = - 20 - 2 \\ 11x = - 22 \\ \frac{11x}{11} = \frac{-22}{11} \\ x =- 2[/tex]
What is the equation of the line that passes through 1,2 and is parallel to the line whose equation is 2x + y - 1 = 0
Answer:
Step-by-step explanation:
Use the point-slope formula.
y - y_1 = m(x - x_1) you have : x_1 =1 and y_1 =2
m the slope m= -2 (same slope for the line : 2x+y-1=0 because this lines are parallel and you can write y=-2x-1
an equation for this line is : y-2 = -2(x-1)
Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year's value. At this rate, what can Dan expect the approximate value of the computer to be after 7 years?
Answer:
$120.1355
Step-by-step explanation:
We can model this as an exponencial function:
P = Po * (1+r)^t
Where P is the final value, Po is the inicial value, r is the rate and t is the amount of time.
For this case, we have that Po = 900, r = -25% = -0.25 and t = 7, so we can find the value of P
P = 900 * (1 - 0.25)^7 = $120.1355
The price after 7 years will be $120.1355.
To calculate the value of Dan's computer after 7 years of 25% annual depreciation, we use the exponential decay formula. The approximate value of the computer after 7 years is $120.14.
To calculate the approximate value of Dan's computer after 7 years with a depreciation rate of 25% per year, we can use the formula for exponential decay:
[tex]V = P(1 - r)^t[/tex]
V is the future value of the computer.P is the original price of the computer ($900).r is the rate of depreciation (25% or 0.25).t is the time in years (7 years).Plugging in the values, we get:
[tex]V = $900(1 - 0.25)^7[/tex]
[tex]V = $900(0.75)^7[/tex]
V = $900 * 0.1334838867
Therefore, the approximate value of the computer after 7 years is:
V = $120.14
Dan can expect the computer to be worth approximately $120.14 after 7 years.
If the surface area of a cube is 390 sq cm. Which best describes the length of the side of the cube?
The length of the side of a cube with a surface area of 390 sq cm is approximately 8.06 cm.
Explanation:The student's question relates to finding the length of a side of the cube, given the total surface area of the cube. In the case of a cube, all sides are equal in length. Furthermore, a cube has six equal sides. Therefore, to find the length of one side, we can use the formula of the surface area of a cube, which is 6 * side² = Total Surface Area. For our problem, side² = 390 / 6 = 65. Hence, the length of the side would be the square root of 65, which is approximately 8.06 cm.
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The best description of the length of the side of the cube is Option C. between 8 and 9.
To determine the length of the side of a cube given its surface area, we first recall the formula for the surface area (SA) of a cube:
SA = 6s²
where s is the length of one side. We are given a surface area of 390 cm². We substitute this value into the formula and solve for s:
390 = 6s²
s² = 390 / 6
s² = 65
s = √65
To find the exact value of √65, we use a calculator:
√65 ≈ 8.06
Therefore, the length of the side of the cube is approximately 8.06 cm, which falls between 8 and 9. Hence, the correct answer is:
Option C. between 8 and 9
Complete question:
If the surface area of a cube is 390 cm^2. Which best describes the length of the side of the cube?
A. less than 7
B. between 7 and 8
C. between 8 and 9
D. greater than 9
What is the area of the 8 ft by 12 ft rectangle
Answer:
96
Step-by-step explanation:
Multiply 8 and 12.
The nth term of a sequence is 2n-6 work out the tenth term
Answer:
Tenth term=14
Step-by-step explanation:
The nth term of a sequence=2n-6
Find the 10th term
If 2n-6= nth term
Then,
Tenth term=2(10)-6
=20-6
=14
Therefore,
Tenth term =14
Select the correct locations on the graph.
There are 10 students in Jenna’s skating class. The data gives the ages and the heights of these students. Select the points that represent this data.
Age (years) Height (cm)
11 140
12 145
12 151
13 160
14 155
14 161
15 170
15 179
16 175
16 179
It should look like the photo I've attached.
The points that represent the data are of the form (age, height), and the graph can be seen below.
Which points represent the data?
Here we have the table:
Age (years) Height (cm)
11 140
12 145
12 151
13 160
14 155
14 161
15 170
15 179
16 175
16 179
Then the points that represent the data are of the form (age, height).
So we have 10 points:
(11, 140), (12, 145), (12, 151), (13, 160), (14, 155), (14, 161), (15, 170), (15, 179), (16, 175), (16, 179).
The graph of these 10 points can be seen below:
If you want to learn more about graphing:
https://brainly.com/question/14323743
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David picks a card at random.
Without putting the first card back, he picks a second card at random.
Are these two events dependent or independent?
Answer:
dependent
Step-by-step explanation:
This question assumes that we're working with a standard full deck of cards. There are 52 unique cards in such a deck.
If David picks a card at random and doesn't put it back, then the number of unique cards left in his deck is 51.
These two events are dependent because the withdrawal of 1 card changes the probability of drawing any other of these 51 cards
Your friend is investing in a 401(k) that promises 2% annual growth. He plans on investing $250 each month for 25 years. Excel returns a value of $97,205.28 for the balance in the 401(k) after 25 years. How much interest is earned in the account after 30 years?
Final answer:
After 30 years of monthly $250 contributions to a 401(k) with a 2% annual growth rate, the interest earned on the account is approximately $65,961.73.
Explanation:
To calculate the amount of interest earned in the 401(k) after 30 years with a 2% annual growth rate, we first need to figure out the future value of the account. We use the formula for the future value of an annuity, as the investments are made at regular intervals (monthly).
The formula is: FV = P *rac{(1 + r)^n - 1}{r}
Where:
FV is the future value of the annuity.
P is the payment amount per period.
r is the interest rate per period.
n is the total number of payments.
Since contributions are made monthly, the annual interest rate (2% or 0.02) is divided by 12 to get the monthly rate, and the total number of contributions is multiplied by 12 to account for monthly contributions over 30 years.
For an investment of $250 per month at a monthly rate of 0.02/12, over 360 months (30 years), we get:
FV = $250* rac{(1 + 0.02/12)^{360} - 1}{0.02/12}
Now we calculate the future value:
FV ≈ $250 * rac{(1 + 0.0016667)^{360} - 1}{0.0016667}
FV ≈ $250 * rac{(1.0016667)^{360} - 1}{0.0016667}
FV ≈ $250 * rac{2.0398873 - 1}{0.0016667}
FV ≈ $250 * 623.8469386
FV ≈ $155,961.73
The total amount invested over 30 years is $250 * 12 *30 = $90,000.
The interest earned is therefore:
Interest = FV - Total amount invested
Interest ≈ $155,961.73 - $90,000
Interest ≈ $65,961.73
So the interest earned on the account after 30 years is approximately $65,961.73.
Martina ordered x cans of paint at a cost of $18.95 per can along with $55 worth of paintbrushes.
Martina can use the equation x = 18.95y + 55 to find the total cost, y, of her order.
A- true
B- false
Answer:
False
Step-by-step explanation:
Cost of 1 can = $18.95
Cost of x cans = 18.95x
Cost of paintbrushes = $55
Total cost = 18.95x+55
Let y be the total cost
y=18.95x+55
So, Equation that can be used : y=18.95x+55
We are given that Martina can use the equation x = 18.95y + 55 to find the total cost, y, of her order.
So, It is False
The graph of y = f '(x), the derivative of f(x), is shown below. Given f(-4) = 2, evaluate f(4).
The options are:
0
2
8
10
Answer:
2
Step-by-step explanation:
f'(x) is an odd function (symmetrical about the origin), therefore f(x) is an even function (symmetrical about the y-axis). So f(x) = f(-x).
Since f(-4) = 2, f(4) = 2.
We can also show this using integrals:
f(-4) = ∫₀⁻⁴ f'(x) dx + C
2 = ½ (-4)(-2) + C
2 = 4 + C
C = -2
f(4) = ∫₀⁻⁴ f'(x) dx − 2
f(4) = ½ (4)(2) − 2
f(4) = 4 − 2
f(4) = 2
Easy Question, Easy points
Topic: Volume
Focus on question 12
Answer: 0.6 meters cubed.
Step-by-step explanation:
To find the answer to this, first find the volume of the cube.
Volume is equal to the side cubed. In this case, 1 cubed is 1, so the area of the cube is 1 meter cubed.
The depth of the water is 0.4 meters, so the water makes a shape of a rectangular prism, where the length and width are 1 meter, and the height is 0.4 meters.
The volume of a rectangular prism is l*w*h, so the volume of this rectangular prism is 0.4 * 1 * 1, or 0.4 meters cubed.
As such, the volume of the air in the tank is 1 - 0.4, or 0.6 meters cubed.
Answer:
0.6 meters CUBED
Step-by-step explanation:
hope it helps
Lila lives in a house that is 12 meters below sea level. Lila goes to school every day, which is 6 meters above sea level. How many meters does Lila travel, in altitude, when going from home to school?
Answer:
18 meters
Step-by-step explanation:
12 + 6 = 8
Lila travels an absolute altitude difference of 18 meters from home to school, considering she travels from 12 meters below sea level to 6 meters above sea level.
Explanation:The question presents a situation where Lila travels from an altitude of 12 meters below sea level to an altitude of 6 meters above sea level. Here, instead of adding these two numbers, we consider the absolute values of these heights. Thus, when Lila travels from her home to school, she first climbs up 12 meters to reach sea level and then another 6 meters to reach her school. So, in total, Lila travels 18 meters in altitude when going from home to school.
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Sue has 18 sweets.
Tony also has 18 sweets.
Sue gives Tony x sweets.
Sue then eats 5 of her sweets.
Tony then eats half of his sweets.
Write expressions for the number of sweets Sue and Tony now have.
Answer:
s = 13 - x
t = [tex]\frac{18+x}{2}[/tex]
Step-by-step explanation:
To start out with:
s = 18
t = 18
Sue gives Tony x sweets
s = 18 - x
t = 18 + x
Sue then eats 5 of her sweets
s = 18 - x - 5 = 13 - x
t = 18 + x
Tony eats half of his sweets
s = 13 - x
t = [tex]\frac{18+x}{2}[/tex]
(Possible constraint that [tex]x\mod 2 = 0[/tex])
When Sue gives Tony x sweets, and then eats 5, she has 13 - x sweets left. Tony, having received x from Sue and then eats half of his total, has 9 + 0.5x sweets.
Explanation:The question begins with Sue and Tony each having 18 sweets. First, Sue gives Tony 'x' sweets which results in Sue having 18 - x sweets and Tony having 18 + x sweets. Sue then eats 5 sweets resulting in her having 18 - x - 5 = 13 - x sweets. Tony then eats half of his sweets, resulting in him having (18 + x) / 2 = 9 + 0.5x sweets. So, the expressions summarizing the number of sweets Sue and Tony have now are 13 - x for Sue and 9 + 0.5x for Tony respectively.
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Name 2 decimals with a difference of 0.35.
Answer:
1.00 and 0.65
Step-by-step explanation:
:D
To find two decimals with a difference of 0.35, you can start with any decimal and add or subtract 0.35 from it.
Explanation:To find two decimals with a difference of 0.35, we can start with any decimal and add or subtract 0.35 from it. Here are two examples:
Decimal 1: 3.65 - 0.35 = 3.3Decimal 2: 5.45 + 0.35 = 5.8These decimals have a difference of 0.35 between them.
If Ryan paid $63 for shoes that were regularly priced at $90, what was the percent discount of the
sale?
Answer:
30% off
Step-by-step explanation:
63 is 70% of 90 which means that 30 percent of the price is off.
Please mark me brainliest. I need it. Hope this helps
write -4-10 in addition
Answer:
14
Step-by-step explanation:
In mathematics, sum can be defined as the result or answer we get on adding two or more numbers or terms.
(-4)-10=14
Determine whether triangle RST or triangle LMN is similar to triangle ABC?
Answer:
triangle LMN is similar to triangle RST
Step-by-step explanation:
Investigate the link between Pascal's triangle and 2 and its powers
Answer:
Outside of probability, Pascal's Triangle is also used for: Algebra, where coefficient of polynomials can be used to find the numbers in Pascal's triangle. Pascal's Triangle is an arithmetical triangle you can use for some neat things in mathematics.
The entries in Pascal's triangle are actually the number of combinations of N take n where N is the row number starting with N = 0 for the top row and n is the nth number in the row counting from left to right where the n = 0 number is the first number.
The mathematical formula for the number of combinations without repetition is N!/(n!(N-n)!).
Step-by-step explanation:
To construct Pascal's triangle, start with a 1. Then, in the next row, write a 1 and 1. It's good to have spacing between the numbers. In the third row, we have 1 and 1 on the outside slopes. The 2 comes from adding the two numbers above and adjacent. Thus, we are adding the number on the left, 1, with the number on the right, 1, to get 1 + 1 = 2.
In the next row, the 3 comes from adding the 1 and the 2. This particular Pascal's triangle stopped at 1 5 10 10 5 1, but we could have continued indefinitely.
What is true about the solution of x^2/2x-6=9/6x-18?
Answer:
x = ±√3
Step-by-step explanation:
In order to avoid extraneous answers, I like to work these by transforming to an expression equal to zero.
[tex]\dfrac{x^2}{2x-6}=\dfrac{9}{6x-18}\\\\\dfrac{x^2}{2(x-3)}-\dfrac{9}{6(x-3)}=0\\\\\dfrac{x^2-3}{2(x-3)}=0\\\\x^2=3\\\\\boxed{x=\pm\sqrt{3}}[/tex]
__
If you do this the usual way, by clearing fractions to start, you will get an extraneous solution of x=3.
What is the volume of a cylinder with base radius 2 and height 9?
True or false help pls
Answer:
Answer: False
Step-by-step explanation:
Answer:
False :)
Step-by-step explanation: