For this case we have that by definition, the formula to count the total number of different permutations is:
[tex]nP_ {r} = \frac {n!} {(n-r)!}[/tex]
SUstituyendo:
[tex]n = 8\\r = 5[/tex]
We have:
[tex]8P_ {5} = \frac {8!} {(8-5)!} = \frac {8!} {3!} = \frac {8 * 7 * 6 * 5 * 4 * 3!} {3! } = 6720[/tex]
ANswer:
[tex]8P_ {5} = 6720[/tex]
A sequence is defined as t1=1 and
t(n+1)=tn+3. which is the nth term of the
sequence ?
A) 3n-2
B) 4n-3
C) n^2-n+1
D) 5n-4
E) 6n-5
I need this for a test :(( in t1, the 1 is a subscript and in t(n+1) the (n+1) is a subscript.
The recursive rule tells you that
[tex]t_2=t_1+3[/tex]
[tex]t_3=t_2+3=(t_1+3)+3=t_1+2\cdot3[/tex]
[tex]t_4=t_3+3=(t_1+2\cdot3)+3=t_1+3\cdot3[/tex]
and so on, with the general rule
[tex]t_n=t_1+(n-1)\cdot3[/tex]
Then with [tex]t_1=1[/tex], you have
[tex]t_n=1+3(n-1)\implies\boxed{t_n=3n-2}[/tex]
Given: BD is a diameter
m 1 = 100°
m BC= 30°
m 4 =
100
150
330
Answer:
150
Step-by-step explanation:
bc is along a straight line with section 4 straight lines are 180° if bc is 30° then 180°-30°=150°
Answer:
The measure of ∠4 is 150°
Step-by-step explanation:
Given the figure in which BD is the diameter of circle and
m∠1=100°
m(arc BC)=∠3=30°
we have to find the measure of ∠4.
As BD is a straight line as BD is diameter therefore
∠4 and ∠3 forms a linear pair
⇒ ∠4 and ∠3 are supplementary i.e these angles adds up to 180°
∠4 + ∠3 = 180°
∠4+30°=180°
∠4=180°-30°=150°
Hence, the measure of ∠4 is 150°
Using the numbers -4,10,8,2,-3,-5 create two expressions that equal 6
Try this option:
1.
[tex]\frac{10-4}{(-3)*(-5)+8*2}=6[/tex]
2.
[tex]\frac{8+2-4}{\frac{10}{-5}-(-3)} =6[/tex]
Can anyone help with this please
For this case we have a function of the form [tex]y = f (x)[/tex], where:
[tex]f (x) = \frac {5 + x} {6 + 3x}[/tex]
We must evaluate the function at[tex]x = a-1[/tex]
So:
[tex]g (a-1) = \frac {5+ (a-1)} {6 + 3 (a-1)}\\g (a-1) = \frac {5 + a-1} {6 + 3a-3}\\g (a-1) = \frac {4 + a} {3 + 3a}[/tex]
Thus, the value of the function is:
[tex]\frac {4 + a} {3 + 3a}[/tex]
Answer:
[tex]g (a-1) = \frac {4 + a} {3 + 3a}[/tex]
Find the area of the figure
Answer:
215 yd²Step-by-step explanation:
It's a parallelogram.
The formula of an area of a parallelogram:
[tex]A=bh[/tex]
b - base
h - height
We have
[tex]b=17\dfrac{1}{5}yd=17\dfrac{1\cdot2}{5\cdot2}yd=17\dfrac{2}{10}yd=17.2yd\\\\h=12\dfrac{1}{2}yd=12.5yd[/tex]
Substitute:
[tex]A=(17.2)(12.5)=215\ yd^2[/tex]
Ryan has a school bag. He has 6 books, of which 2 are math books. What is the probability that a randomly selected book will be a math book?
1/3
2 of the books are math books and there are 6 books. This is 2/6. Now, divide both sides of the fraction by 2 to simplify it. This gives you a final answer of 1/3.
Two passenger train, A and B, 450 km apart, star to move toward each other at the same time and meet after 2hours.
If train B, travels 8/7 as fast as train A. Find the speed of each train
Let [tex]v[/tex] be the speed of train A, and let's set the origin in the initial position of train A. The equations of motion are
[tex]\begin{cases}s_A(t) = vt\\s_B(t) = -\dfrac{8}{7}vt+450\end{cases}[/tex]
where [tex]s_A,\ s_B[/tex] are the positions of trains A and B respectively, and t is the time in hours.
The two trains meet if and only if [tex]s_A=s_B[/tex], and we know that this happens after two hours, i.e. at [tex]t=2[/tex]
[tex]\begin{cases}s_A(2) = 2v\\s_B(2) = -\dfrac{16}{7}v+450\end{cases}\implies 2v = -\dfrac{16}{7}v+450[/tex]
Solving this equation for v we have
[tex]2v = -\dfrac{16}{7}v+450 \iff \dfrac{30}{7}v=450 \iff v=\dfrac{450\cdot 7}{30} = 105[/tex]
So, train A is travelling at 105 km/h. This implies that train B travels at
[tex]105\cdot \dfrac{8}{7} = 15\cdot 8=120 \text{ km/h}[/tex]
train A travels at 210 km/h and train B travels at 240 km/h.
The student's question involves finding the speeds of two trains moving towards each other when certain conditions are provided. We know that the two trains are 450 km apart and meet after 2 hours. Train B travels at 8/7 the speed of train A.
Let's denote the speed of train A as v km/h. Then, the speed of train B would be 8/7 * v km/h. Since they meet after 2 hours, we can add their distances to equal the total distance between them.
Speed of train A: v km/h
Speed of train B: 8/7 × v km/h
Total distance: 450 km
Time to meet: 2 hours
The total distance both trains cover can be expressed as:
(Speed of train A + Speed of train B) × Time = (v + 8/7 × v) × 2 hours
Since the sum of the two distances covered by the trains is the initial distance between them which is 450 km, we get:
(1 + 8/7)v * 2 = 450 km
We simplify this equation to find the value of v. The equation becomes:
15/7 v × 2 = 450 km
v = (450 × 7) / (15 × 2)
v = 210 km/h
Now, we find the speed of train B by multiplying the speed of train A by 8/7:
Speed of train B = 8/7 × 210 km/h = 240 km/h
Therefore, train A travels at 210 km/h and train B travels at 240 km/h.
What is the distance between points -3 , 10 and 5 , 0
Answer:
5/4
Step-by-step explanation:
Use the slope formula
Answer:
9.43398
Step-by-step explanation:
The formula is square root of (x2-x1)^2 + (y2-y1)^2.
So if you plug in the equation, it is 9.43398.
based on the function F(x)=x^4-3x^2-1 and the graph of G(x) below, which of the following statements is true?
Answer:
Step-by-step explanation:
A function has a root only if cuts the x axis .
If it cuts once it means it has one real root, if twice then two roots and so on .
Here in the graph of G(x) shown ,it never crosses the x axis so we can say that there is no real root of the given function G(x).
It means the option A which states G(x) has zero roots is correct.
Adult panda weights are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. The largest pandas weigh over 250 pounds. Using the empirical rule, approximately what percent of the adult pandas weigh over 250 pounds?
16%
32%
47.5%
95%
Answer:
16%
Step-by-step explanation:
THERE
Answer: 16%
Step-by-step explanation:
Given: Mean : [tex]\mu = 200\text{ pounds}[/tex]
Standard deviation : [tex]\sigma=50\text{ pounds}[/tex]
The formula for z score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Now, for x=250
[tex]z=\dfrac{250-200}{50}=1[/tex]
The P-value [tex]= P(z>1)=1-P(z<1)[/tex]
[tex]=1-0.8413=0.1587\approx16\%[/tex]
Hence, the percent of the adult pandas weigh over 250 pounds is about 16%.
2. For f(x) = 2(x+3) - 5, name the type of function and describe each of the
three transformations from the parent function f(x) = x
Answer:
The function is a linear function
The function is translated 3 units to the left,then stretched vertically
by factor 2, then translated 5 units down
Step-by-step explanation:
* Lets revise some transformation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
- If the function f(x) stretched vertically, then g(x) = k · f(x), where
k > 1 (multiplying each of its y-coordinates by k)
- If the function f(x) compressed vertically, then g(x) = k · f(x), where
0 < k < 1 (multiplying each of its y-coordinates by k)
* Now lets solve the problem
∵ f(x) = 2(x + 3) - 5
- The greatest power of the function is 1 (degree of the function)
∴ f(x) is linear function
- The parent function f(x) = x
∵ f(x) changed to f(x + 3)
∴ f(x) translated 3 units to the left
# Each x-coordinate of the points on the function subtracted by 3
∵ f(x + 3) changed to 2f(x + 3)
∵ 2 > 1
∴ f(x + 3) stretched vertically by factor 2 (k = 2)
# Each y-coordinate of the points on the function multiplied by 2
∵ 2f(x + 3) changed to 2f(x + 3) - 5
∴ 2f(x + 3) translated 5 units down
# Each y-coordinate of the points on the function subtracted by 5
14 workers, working at the same pace, can lay 36000 bricks in one day. How many workers will be needed to lay 54000 bricks in the same period of time?
[tex]\bf \begin{array}{ccll} workers&bricks\\ \cline{1-2} 14&36000\\ x&54000 \end{array}\implies \cfrac{14}{x}=\cfrac{36000}{54000}\implies \implies \cfrac{14}{x}=\cfrac{2}{3} \\\\\\ 42=2x\implies \cfrac{42}{2}=x\implies 21=x[/tex]
Answer:
21 workers would be your answer.
a restaurant uses 60 cups of mushrooms to make 12 gallons of mushroom soup. jesse wants to make 3 gallons of soup using this recipe. how many cups of mushrooms should he use?
Answer:
15
Step-by-step explanation:
Write a proportion:
60 cups / 12 gallons = x cups / 3 gallons
Cross multiply:
12x = 180
Divide:
x = 15
He should use 15 cups.
Jesse should use 15 cups of mushrooms to make 3 gallons of mushroom soup, based on the restaurant's recipe. Devon will be making 37.5 liters of soup for the party of 100 guests.
Explanation:To solve Jesse's question about how many cups of mushrooms he should use to make 3 gallons of mushroom soup, we need to find the proportion between the amount used in the restaurant's recipe and the desired amount for Jesse's smaller batch.
The restaurant uses 60 cups of mushrooms to make 12 gallons of soup. To find out how many cups are needed for 1 gallon, we divide the number of cups by the number of gallons:
60 cups / 12 gallons = 5 cups per gallon
Jesse wants to make 3 gallons of soup. Multiplying the amount needed for one gallon by 3 gives us the answer:
5 cups/gallon × 3 gallons = 15 cups of mushrooms.
Devon, on the other hand, is preparing soup for a party. Calculating the total amount for 100 guests using 375 milliliters per person, we get:
375 milliliters/guest × 100 guests = 37500 milliliters.
Since 1 liter is equivalent to 1000 milliliters, we can convert the milliliters to liters:
37500 milliliters / 1000 = 37.5 liters of soup for 100 guests.
What is the length of leg s of the triangle below ?
Answer:
4
Step-by-step explanation:
In a 45-45-90 triangle, the length of the hypotenuse is √2 times the legs.
s√2 = 4√2
s = 4
Each leg is 4 units long.
Each length of the side of the triangle is 4 units long.
We have given that side is s and hypotenuse is 4root2.
and also the angle is 45-45-90degrees.
We have to determine the length of the sides
In a 45-45-90 triangle, the length of the hypotenuse is √2 times the legs.
What is the 45°−45°−90° triangle?45°−45°−90° triangle is a commonly encountered right triangle whose sides are in the proportion 1:1:√2 .
s√2 = 4√2
s = 4
Therefore each length of the side of the triangle is 4 units long.
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You are doing yardwork with a friend. You can finish mowing the lawn in 57 minutes, while your friend can do the same amount of work in 54 minutes. How long will it take to complete the job if you work together? Round your answer to the nearest whole number.
Answer:
28 minutes
Step-by-step explanation:
Speed = distance / time
Your speed is 1 lawn / 57 minutes. Your friend's speed is 1 lawn / 54 minutes. Working together, your combined speed is:
1/57 + 1/54
So the time it takes working together is:
Speed = distance / time
1/57 + 1/54 = 1 / t
t = 27.7 minutes
Rounded to the nearest whole number, it takes 28 minutes.
Choose the correct answers.
Bill Campbell gets a student rate for medical insurance of $25.00 a month. There is a $250 deductible.
He recently received treatment for a covered condition. The bill was $2,350.00
Bill's insurance company provided payment of 80% of the bill less the deductible.
What was the insurance company's payment? $
What was Bill's share of the charge? $
The insurance company's payment is $1,680.00 and Bill's share of the charge is $670.00.
Explanation:To calculate the insurance company's payment, we first need to determine the amount after the deductible is applied. Since the bill was $2,350.00 and the deductible is $250, we subtract the deductible from the bill: $2,350.00 - $250 = $2,100.00. The insurance company covers 80% of this amount, so we multiply $2,100.00 by 80%: $2,100.00 x 80% = $1,680.00. Therefore, the insurance company's payment is $1,680.00.
Bill's share of the charge is calculated by subtracting the insurance company's payment from the total bill: $2,350.00 - $1,680.00 = $670.00. Therefore, Bill's share of the charge is $670.00.
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i need help on this question
What is 9 kg in grams
Answer:
9,000
Step-by-step explanation:
multiply the mass value by 1000
Answer:
9000 grams!!!
I hope this helped! :)
Point R, located at (-5, 3), is reflected over both axes. What are the coordinates of R?
a (-5, -3)
b(5.-3)
c (5,3)
b(-3,5)
It’s going to be b which is positive 5 and negative 3
2. Give two ways to write the expression 7t in words.
a. the product of 7 and t
t more than 7
7 multiplied by t
1 added to 7
b. t subtracted from 7
d. the quotient of 7 and
t less than 7
7 divided by t
Answer:
The product of 7 and t and 7 multiplied by t
Step-by-step explanation:
What is the domain of the function f(x) = (x + 3)2? A) all integers B) all real numbers C) all integers greater than zero D) all real numbers greater than zero
Answer:
Option B is correct
Step-by-step explanation:
We have function f(x)=(x+3)2
The domain of the function is the set of values for which the function is defined and real.
In our case if x belong to all real numbers the function will be real and defined as given in Option B as function has no undefined points.
All other options are subset of real numbers.
So, option B is correct.
Can someone help me with this?
Answer:
y=0
Step-by-step explanation:
For the x axis, the value of y is zero
y=0
Factor 6x4 – 5x2 + 12x2 – 10 by grouping. What is the resulting expression?
Answer:
(6x² - 5)(x² + 2)
Step-by-step explanation:
Given
6[tex]x^{4}[/tex] - 5x² + 12x² - 10 ( factor the first/second and third/fourth terms )
= x²(6x² - 5) + 2(6x² - 5) ← factor out (6x² - 5) from each term
= (6x² - 5)(x² + 2)
Answer:
(x^2 + 2)(6x^2 – 5)
Step-by-step explanation:
6x^4 – 5x^2 + 12x^2 – 10
=(6x^4 – 5x^2) + (12x^2 – 10)
=x^2 (6x^2 – 5) + 2(6x^2 – 5)
=(x^2 + 2)(6x^2 – 5)
Answer
(x^2 + 2) and (6x^2 – 5) are factors of the expression 6x^4 – 5x^2 + 12x^2 – 10
Mrs. Karabin wants to paint the inside of her brand new two-car garage. The garage is 20 feet wide, 24 feet long, and 12 feet tall. She wants to paint the walls and the ceiling (not the floor). What’s the surface area of the parts she wants to paint?
Answer:
The surface area is [tex]1,536\ ft^{2}[/tex]
Step-by-step explanation:
we know that
The surface area is equal to
[tex]SA=B+PH[/tex]
where
B is the area of the ceiling
P is the perimeter of the base
H is the height of the walls
substitute the given values
[tex]SA=(20)(24)+2(20+24)(12)[/tex]
[tex]SA=480+1,056=1,536\ ft^{2}[/tex]
Mrs. Karabin will be painting a total of 1536 square feet in her garage. This includes 1056 square feet for the walls and 480 square feet for the ceiling.
Explanation:To solve this, we need to calculate the surface area for the walls and ceiling of the garage. Because all sides of this garage are rectangular, we can find the area by multiplying the length by times width for each side.
For the walls: There are two walls that are 12 feet high and 24 feet long and two walls that are 12 feet high and 20 feet wide. So, we calculate (12x24)x2 + (12x20)x2 = 576 + 480 = 1056 square feet.
For the ceiling: The ceiling is 20 feet wide and 24 feet long, so we calculate 20x24 = 480 square feet.
Adding these together, Mrs. Karabin will be painting 1056 (for the walls) + 480 (for the ceiling) = 1536 square feet in total.
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these are many question in one because I only have 31 points.
what is 1/20 as a decimal and a percentage
what 1/10 as a decimal and a percentage
what 12 1/2% as a decimal and a percentage
what is 0.2 as a fraction and a percentage
what is 25% as a decimal and fraction
what is 30% decimal and fraction
what is 1/3 as a decimal and percentage
what's is 0.375 as a fraction and percentage
what is 0.4 as a fraction and percentage
what is 1/2 as a decimal and percentage
what is 0.6 as a fraction and percentage
what is 0.625 as a fraction and percentage
what is 66 1/2% as a decimal and fraction
sorry for the many questions. its my homework so pls leave the work. I will be back in 30 minutes to check up on this. thx to those of you who answered this
Answer:
what is 1/20 as a decimal and a percentage: 0.05 and 5%
what 1/10 as a decimal and a percentage : 0,1 and 10%
what 12 1/2% as a decimal and a percentage: 12.5% it's already as a percentage, as a fraction 1/8
what is 0.2 as a fraction and a percentage: 1/5 and 20%
what is 25% as a decimal and fraction: 0.25 and 1/4
what is 30% decimal and fraction : 0.3 and 3/10
what is 1/3 as a decimal and percentage : 0.33 and 33%
what's is 0.375 as a fraction and percentage : 3/8 and 37.5%
what is 0.4 as a fraction and percentage : 4/10 and 40%
what is 1/2 as a decimal and percentage : 0.5 and 50%
what is 0.6 as a fraction and percentage : 3/5 and 60%
what is 0.625 as a fraction and percentage: 5/8 and 62.5%
what is 66 1/2% as a decimal and fraction: 0.665 and 665/1000, 133/200
Step-by-step explanation:
These are basically 3 problems, so I won't explain two items for every one of your 13 similar questions. Here's the explanation for every 3 cases asked in your questions... and the answers. All you have to do is replace the numbers in the explanations for the ones in each other question asking the same thing.
To express a fraction in percentage, you simply have to put the fraction with a denominator of 100..., for example:
[tex]\frac{1}{20} * \frac{5}{5} = \frac{5}{100}[/tex]
So, 1/20 is 5%.
[tex]\frac{1}{2} * \frac{50}{50} = \frac{50}{100}[/tex]
And 1/2 is 50%
To express a percentage as a fraction, you take that percentage and place it over a denominator of 100 and you simplify, like this:
[tex]\frac{12.5}{100} = \frac{1}{8}[/tex]
[tex]\frac{30}{100} = \frac{3}{10}[/tex]
To convert a decimal number to a fraction, the easiest way is to express this number up to the 2nd decimal... then take that as a %.
Examples:
0.2 you can say 0.2 = 0.20... so it's 20 hundredths, or 20 per 100... so 20%
0.375, it's already expressed in more than hundredths, so you simply move the dot 2 spots right to get 37.5%
what is 1/20 as a decimal and a percentage: 5% (see above)
what 1/10 as a decimal and a percentage : 10% (save as above)
what 12 1/2% as a decimal and a percentage: 12.5%, it's already as a percentage, if you mean as a fraction... 1/8 (see above)
what is 0.2 as a fraction and a percentage: 1/5 and 20% (see above)
what is 25% as a decimal and fraction: 0.25 and 1/4
what is 30% decimal and fraction : 0.3 and 3/10
what is 1/3 as a decimal and percentage : 0.33 and 33%
what's is 0.375 as a fraction and percentage : 3/8 and 37.5%
what is 0.4 as a fraction and percentage : 4/10 and 40%
what is 1/2 as a decimal and percentage : 0.5 and 50%
what is 0.6 as a fraction and percentage : 3/5 and 60%
what is 0.625 as a fraction and percentage: 5/8 and 62.5%
what is 66 1/2% as a decimal and fraction: 0.665 and 665/1000, 133/200
At a high school movie night, the refreshment stand sells popcorn and soft drinks. Of the 100 students who came to the movie, 62 bout popcorn and 47 bought a drink. 38 students bought both popcorn and a drink. What is the probability that a student buys a drink?
The answer is 19/50 or 38%.
Hope this helps!
Answer:
The probability that a student buys a drink is 0.47.
Step-by-step explanation:
Given : At a high school movie night, the refreshment stand sells popcorn and soft drinks. Of the 100 students who came to the movie, 62 bout popcorn and 47 bought a drink. 38 students bought both popcorn and a drink.
To find : What is the probability that a student buys a drink?
Solution :
Total number of students are T=100 who came to the movie.
Student who bought popcorn = 62
Student who bought drink = 47
Students who bought both popcorn and a drink = 38
We have to find the probability that a student buys a drink.
Favorable outcome F=47
Probability is [tex]P=\frac{F}{T}[/tex]
[tex]P=\frac{47}{100}[/tex]
[tex]P=0.47[/tex]
Therefore, The probability that a student buys a drink is 0.47.
If 5 bags cost 255.35 how much would 2 bags cost
[tex]255.35 \div 5 = 51.07 [/tex]
[tex]51.07 \times 2 = 102.14[/tex]
Answer:
102.14
Step-by-step explanation:
The area of the triangle below is __sq units ?
The picture is above !
The correct answer is C. you multiply the 16x5
Answer:B) 40 sq units
Step-by-step explanation:
use formula [tex]\frac{1}{2}[/tex] base × height
= (0.50)(16) × (5)
= 40 sq units
For the inverse variation equation p = 8/V, what is the value of V when p = 4?
Answer:
V=2
Step-by-step explanation:
p=8/v
substitute p=4,
4=8/v
multiply both sides by v,
4(v)=8(v)/v
4v=8
divide 8 by 4,
v=2
Answer: choice c. 2 edge 2023
Step-by-step explanation:
If two coins are flipped, what is the probability that both coins will not land on heads?
0%
25%
50%
75%