Answer:
1680 ways
Step-by-step explanation:
From the question,
nPr = n!/(n-r)!.................. Equation 1
Where, n = Total number of books to chose from, r = number of books to be arranged in the shelf.
Given: n = 8 books, r = 4 books.
Substitute into equation 1
8P4 = 8!/(8-4)!
8P4 = 8!/4!
8P4 = (8×7×6×5×4!)/4!
8P4 = 1680 ways.
Hence the number of ways 4 books can be arranged in a shelf if there are 8 books to chose from is 1680 ways
simplify the expression. explain when answering please!
Hello!
This question is relating powers and simplification.
Let's look at the term in the denominator first, which is [tex]d^0[/tex].
The zero exponent rule states that anything to the 0th power, will be 1.
Meaning that we can simplify this expression to [tex]6c^{-3}[/tex].
Now let's look at the term we have left.
The negative exponent rule states that anything to the negative power can be moved to the other side of the fraction and have its exponent turn into a positive exponent.
Meaning that we can simplify [tex]6c^{-3}[/tex] to [tex]\frac{6}{c^3}[/tex].
Hope this helps!
Write an equation of the perpendicular bisector of the segment with endpoints M(1,5) and N(7,−1).
Answer:
y = x - 2
Step-by-step explanation:
Going from M to N, the run (increase in x) is 6, from 1 to 7. The rise (which is actually a decrease here) is -6, from 5 to -1. Thus, the slope of the line segment MN is m = rise / run = -6/6, or -1.
The slope of the perpendicular bisector is the negative reciprocal of this m = -1, and is +1.
This bisector passes through the midpoint of segment MN. The x-coordinate of this midpoint is (1 + 7)/2, or 4, and the y-coordinate is (5 - 1)/2, or 2: (4, 2).
Knowing both a point on this bisector (4, 2) and the slope of the bisector (+1), we can modify the point-slope form of the equation of a straight line, y - k = m(x - h), to obtain y -2 = 1(x - 4), or y = 2 + x - 4, or y = x - 2
OMG PLS HELP WITH THIS IM PANICKING OMG I GOT A F IN MATH MY MOM JUST YELLED AT ME IM CRYING PLS HELP WITH THS-
Number 3 is 18
Number 4 is 32
Number 5 is 8
Number 6 is 46
Number 7 is 24 since you add every side (2+2+10+10) and it gives you 24
Find (8°f)(3)
f(x) = (x + 2
g(x) = -x^2
Answer:
A) -25
Step-by-step explanation:
[tex]f(x)=|x+2|\\[/tex]
[tex]g(x)=-x^{2}[/tex]
[tex](gof)(x)=g(f(x))=g(|x+21|)\\[/tex]
[tex](gof)(x)=-(|x+21)^{2}[/tex]
[tex](gof)(3)=-(13+21)^{2}[/tex]
[tex](gof)(3)=-(151)^{2}[/tex]
[tex]=-(5)[/tex]
[tex](gof)(3)=-25\\--------[/tex]
hope it helps...
have a great day!!
Can someone please answer all parts of this question with STEP BY STEP EXPLANATION? I'm struggling with this.
Answer for question A:
find three numbers that have a mode of 4 and a mean of 6
Answer:
4, 4, 10
Step-by-step explanation:
4, 4, 10
4 appears the most so that's the mode.
Mean = (Sum of numbers)/(3 numbers)
Mean = (4 + 4 + 10)/3
Mean = (18)/3
Mean = 6
The three numbers that have a mode of 4 and a mean of 6 are 4, 4, and 10.
What is mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data. A set of data values mode is the value that appears the most frequently.
The three numbers that have a mode of 4 and a mean of 6 will be calculated below:-
Let us suppose the three numbers are 4, 4, and 10 the mean will be calculated as:-
Mean = (Sum of numbers)/(3 numbers)
Mean = (4 + 4 + 10)/3Mean = (18)/3
Mean = 6
Therefore, the three numbers that have a mode of 4 and a mean of 6 are 4, 4, and 10.
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A bag contains 18 balls. There are 6 red balls, 6 yellow balls, and 6 green balls. A ball is drawn at random and returned. Then another ball is drawn at random. Select ALL statements that are true.
A. The expected probability of drawing a green ball first is the same as the expected probability of drawing a green ball second.
B.There are six possible outcomes.
C.The probability of drawing a red ball first is the same as not drawing a red ball second.
D.The expected probability of drawing a red ball and then a yellow ball is 19.
Answer:
There are 18 balls in the bag:
6 are red
6 are yellow
6 are green.
A ball is drawn at random and then returned.
Then another ball is drawn.
Now, let's analyze each option and let's see if it is true or not.
A) The probability of drawing at random a green ball is equal to the quotient between the number of green balls and the total number of balls.
Then for the first draw, the probability is 6/18
Because the drawn ball is returned, for the second draw we still have 6 green balls and 18 balls in total, then the probability still is 6/18
Statement A is true
B) if we define the notation:
YR
as:
Yellow in the first draw, red in the second draw.
The possible outcomes are:
YR
YG
YY
RR
RG
RY
GR
GG
GY
So we have a total of 9 outcomes, we also can calculate this in the following way:
For the first event (first draw) we have 3 possible outcomes (Y, G, and R)
For the second event (second draw) we have again 3 possible outcomes.
The total number of outcomes is the product between the possible outcomes for each event, this is:
3*3 = 9
Then statement B is false.
C) The probability of drawing a red ball first is:
p = 6/18
The probability of NOT drawing a red ball second, is equal to the probability of drawing a yellow or green ball second (we have 12 balls that are green or yellow, and 18 total balls) then this probability is:
q = 12/18
The probabilities are different, then we can conclude that statement C is false.
fD) The expected probabilty of drawing a red ball and then a yellow ball is the product of the individual probabilities, this is:
prob of drawing a red ball first = 6/18
prob of drawing a yellow ball second = 6/18
Joint probability:
P = (6/18)*(6/18) = (1/3)*(1/3) = 1/9
So statement D is true. (it says 19, i suppose that there is a mistake in this sentence and it actually should say 1/9)
Zaharia is 4/5 as tall as Zayden. Zayden is 3/5 as tall as Eric. Eric is how many times as tall as Zaharia?
Answer: rttgyt5tgot4h5uioyh
Step-by-step explanation:
hudshviowuerbgp
One number is 6 more than other number. Also, 7 times the smaller number is equal to 6 times the
larger number. Find the two numbers.
Answer:
The numbers are 36 and 42
Step-by-step explanation:
Represent the two numbers by m and n, m being the larger number and n the smaller. Then
m = n + 6. also, 7n = 6m
Substitute n + 6 for m in the second equation: 7n = 6(n + 6).
Performing the indicated multiplication, we get 7n = 6n + 36, or n = 36.
Then m = n + 6, which here is m = 36 + 6 = 42.
The numbers are 36 and 42.
Which is the graph of the equation y - 1 =[tex]\frac{2}{3}(x-3)[/tex]
Answer:
Step-by-step explanation:
A function is shown in the table.
Xg(x)
-3 17
-1 -3
0 -4
2 13
Which of the following is a true statement for this function? (5 points)
Answer:
the answer here its a -3 17
PLEASE HELP!!!!!!!!!!
Find the volume of the figure please.
Answer:
1568 in^3
Step-by-step explanation:
Answer:
Volume = 1,568
Step-by-step explanation:
V = Bh
B = 17.5 x 14 = 245
h = 6.4
245 x 6.4 = 1,568
The easier way:
17.5 x 14 x 6.4 = 1,568
Let me know if this helps!
Explain what independent and dependent variables mean
Answer:
please give me brainlist and follow
Step-by-step explanation:
You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause, while a dependent variable is the effect. In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable.
2. Write down a number that has a value less than |14.7|
Absolute Value of 14.7 is 14.7 any number below 14.7.
find the measure of the missing angle
Answer:
60°
.....................
Answer:
60
Step-by-step explanation:
This is a complementary angle which means two angles that sum up to 90 so 60+30=90
Greg has two coupons for a bicycle.
Coupon A: $19 rebate on a $81 bicycle
Coupon B: 20% off of a $81 bicycle
Choose the coupon that gives the lower price.
The price of Coupon A will be less than the price of Coupon B. Coupon A gives the lower price.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Greg has two coupons for a bicycle.
Coupon A: $19 rebate on an $81 bicycle. Then the price of a bicycle will be
⇒ $81 - $19
⇒ $62
Coupon B: 20% off of an $81 bicycle. Then the price of a bicycle will be
⇒ $81 x 0.80
⇒ $64.8
The price of Coupon A will be less than the price of Coupon B. Coupon A gives the lower price.
More about the Algebra link is given below.
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(-2, 7) and (-2, 14)
Slope
Answer:
slope is undefined
This February only one quarter of the days had an average temperature above freezing (32 degrees). How many days in February were below freezing?
Answer:
21 days
Step-by-step explanation:
February has 28 days
28/4=7
1 quarter of 28 is 7
Since one quarter was above freezing, 3 were below freezing
3x7=21
21 days is the final answer
Answer:
21 days
Step-by-step explanation:
There are 28 days in February.
If one quarter of the days had a temperature above freezing, that means that three quarters of the days had a temperature below freezing.
Find how many days were below freezing by multiplying 28 by 3/4
28(3/4)
= 21
So, 21 days in February were below freezing.
Determine how many x-intercepts the quadratic function in the graph has and identify the intercept points.
Question 6 options:
A)
Two x-intercepts, (2.5,0), (5.5,0)
B)
Two x-intercepts, (2,0), (6,0)
C)
Two x-intercepts, (0,2), (0,6)
D)
One x-intercept, (4,–2)
Answer:
B . The graph intercept at two points, (2,0) and (6,0)
Answer: (4,-2)
Step-by-step explanation:
(4,-2)
You invest $1700  in account earning 8% annual interest compounded continuously write an exponential function for the amount in the account after T years
An exponential function for the amount in the account after T years if the interest of 8% is compounding annually on initial amount 1700 is: P_T = 1700(1.08)^T
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
How does compound interest works?Instead of calculating the interest on the initial amount, the compound interest repeats calculating interest on (old amount + interest to be paid).
For this case, we're specified that:
Initial amount deposited = $1700Rate of interest = 8% annual = 0.08 (converted percent to fraction).Let P be the inital amount, and r be the rate of interest compounding per unit of time (in decimal)
Let [tex]P_t[/tex] be the amount after t unit of time(same unit as the interest).
Then after 1 year, the new amount would be:
[tex]P_{t+1} = P_t + 100r \%\text{ of }P_t}\\P_{t+1}= P_t + P_t \times r\\P_{t+1} = P_t(1+r)[/tex]
Thus, we get:
[tex]P_t = P_{t-1}(1+r) = P_{t-2}(1+r)(1+r) = P_{t-2}(1+r)^2\\\\P_t = P_{t-t} (1+r)^t = P_0(1+r)^t[/tex]
where P₀ is the initial amount (as amount at t = 0 is initial amount)
Thus, we get:
[tex]P_t = P(1+r)^t[/tex]
Here, putting P = 1700, r = 0.08, and t = T, we get:
[tex]P_T = 1700(1.08)^T[/tex]
Thus, an exponential function for the amount in the account after T years if the interest of 8% is compounding annually on initial amount 1700 is: [tex]P_T = 1700(1.08)^T[/tex]
Learn more about compound interest here:
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Reflect on your Learning Check to move forward. What topics were covered on your learning check? What topics do you have mastery of? What topics do you need clarification?
Step-by-step explanation:
I feel like you need help figuring out what to write
For the first one say something like
These topics..... were covered in my learning check
I feel like I am pretty good with ..... topics
I feel like I need some help with ..... topics
Correct me if I'm wrong but this is what I assume your asking
What is the surface area
Answer: b
Step-by-step explanation:
How many solutions does the following equation have?
9z-6+7z=16z-6
Answer:
This equation has infinite solutions
Step-by-step explanation:
9z - 6 + 7z = 16z - 6
16z - 6 = 16z - 6
z = z
A cardboard box has edges of length 2.3 in, 6.5 in, and 9.7 in. What is the volume of the box?
Answer:
volume = 145.02 in³
Step-by-step explanation:
volume = 2.3 x 6.5 x 9.7 = 145.02 in³
Kala is a software saleswoman. Her base salary is $1800, and she makes an additional $110 for every copy of Math is Fun she sells.
Let P represent her total pay (in dollars), and let N represent the number of copies of Math is Fun she sells. Write an equation relating P to N. Then use this
equation to find her total pay if she sells 29 copies of Math is Fun.
Equation:
8
Х
Total pay if Kala sells 29 copies: s[
Answer:
1800 + 110n = P
4990 * 8 = 39,920
Step-by-step explanation:
So first, the best way to solve linear word problems is to define your variables (which was given to you)
Second, construct your equation. From the information, we know that $1,800 is her starting amount. So that will be the y-intercept. Then, we see that she gets additional $110 for every copy she sells.
A real estate agent sold a house for $250,000 and received a
5.5% commission on the sale. How much was the commission?
Answer:13,750
Step-by-step explanation:5.5% of 250,000 is 13,750.
Answer:
13,750
Step-by-step explanation:
Find x in each triangle.
Answer:
where’s the triangles?
help Plz
If the slice of pizza below has an area of 18.86 cm?, what is the measure of the central angle to the nearest
degree?
8 cm
Answer:
Step-by-step explanation:
Help Plz
If the slice of pizza below has an area of 18.86 cm?, what is the measure of the central angle to the nearest
degree?
8 cm
Please help BY tomorrow
A truck leaves a garage and travels east at a rate of 55 miles per hour. A car leaves the same garage 15 minutes later and travels east at a rate of 66 miles per hour. After how many minutes from the time the car leaves does the car overtake the truck?
Answer:
think yourself........
Step-by-step explanation:
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