To solve the problem we must know about Permutation and Combination.
The number of different types of shirts available from this company is 42.
Given to us
A shirt company has 3 designs each of which can be made with short or long sleeves. There are 7 color patterns available.As given to us there are 3 designs available,
Number of designs = [tex]^3C_1[/tex],Number of ways the sleeves can be made = [tex]^2C_1[/tex] (short or long sleeves),Number of color patterns available = [tex]^7C_1[/tex]Total number of ways in which a shirt can be madeTotal number of ways in which a shirt can be made [tex]= ^3C_1\times ^2C_1\times ^7C_1[/tex]
= 3 x 2 x 7
= 42 ways
Hence, the number of different types of shirts available from this company is 42.
Learn more about Permutation and Combination:
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What is the distance to the nearest tenth of a unit between point H ( -4,6 ) and point I ( 2,-3 )
Answer:
10.81 units
Step-by-step explanation:
Given data
point H ( -4,6 ) and point I ( 2,-3 )
x1= -4
y1=6
x2= 2
y2=-3
The formula for the distance between two points is
d=√((x_2-x_1)²+(y_2-y_1)²)
d=√((2-(-4))²+(-3-6)²)
d= √(2+4)²+(-9)²)
d= √(6)²+(-9)²)
d= √36+81
d=√117
d= 10.81 units
Hence the distance between the points is 10.81 units
what is the pattern to 1,2,4,7,11
Answer:
1+1=2
2+2=4
4+3=7
7+4=11
so the patter is number + natural numbers (serially)
Step-by-step explanation:
4, -4, 0 are examples of-
i. irrational numbers.
ii. natural numbers.
iii. integers.
v. none of these.
4, -4, 0 are examples of-iii. integers.
they are not in fractional.
Given: x + 3.8 > -10.02.
Choose the solution set.
Answer:
x > -13.82
Step-by-step explanation:
The first step in finding the solution set is to subtract 3.8 from both sides of the given inequality:
x > -10.02 - 3.8. or
x > -13.82
Which of these values for p and a will cause the function f(x)=Pax to be an exponential growth function
The option are missing in the question. The options are :
A. P = 2, a = 1
B. [tex]$P=\frac{1}{2} ; a =\frac{1}{3}$[/tex]
C. [tex]$P=\frac{1}{2} ; a =1$[/tex]
D. P = 2, a = 3
Solution :
The given function is [tex]$f(x)= Pa^x$[/tex]
So for the function to be an exponential growth, a should be a positive number and should be larger than 1. If it less than 1 or a fraction, then it is a decay. If the value of a is negative, then it would be between positive and negative alternately.
When the four option being substituted in the function, we get
A). It is a constant function since [tex]$2(1^x)=2$[/tex]
B). Here, the value of a is a fraction which is less than 1, so it is a decay function. [tex]$f(x)=\frac{1}{2}\left(\frac{1}{3}\right)^x$[/tex]
C). It is a constant function since the value of a is 1.
D). Here a = 3. So substituting, as the value of x increases by 1, the value of the function, f(x) increases by 3 times.
[tex]$f(x)=2(3)^x$[/tex]
Therefore, option (D). represents an exponential function.
Answer:
Its P = 1/5 ; a = 2
Step-by-step explanation:
I am doing the test; I got it right.
What is the degree of the polynomial 4x4 + 3x3 - 6x2 + 7x + 4?
1
Answer:
4
Step-by-step explanation:
The degree is equal to the highest power of the polynomial.
find the common difference of the arithmetic sequence -2, -11/4, -7/2
Answer = 3/4
First, change them all into like fractions.
-2, -11/4, -7/2 = -8/4, -11/4, -14/4
Therefore the common difference of their arithmetic sequence is 3/4
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Which pair of x and y values below are the solution to the simultaneous equations? x+2y=6
x-2y=2
x = 4, y = 1
Step 1: use the equations given to find an equation with only 1 term. Here I used x.
(x + 2y) + (x - 2y) = 2x = 6 + 2 = 8
2x = 8
x = 4
Step 2: substitute x = 4 into either given equation. Here I used the first equation x + 2y = 6.
(4 + 2y) = 6
2y = 6 - 4 = 2
y = 1
This solution can also be done by finding y in step 1 or using the other given equation in step 2.
Hope this helped!
I need help for this question
9514 1404 393
Answer:
a) Cat
b) 8
c) 6
Step-by-step explanation:
a) Each line contains one large square, at least. The smallest additional area is on the Cat line. Apparently, the fewest people preferred cats.
__
b) The smaller symbols appear to represent 1/4, 1/2, and 3/4 of the larger square. On that basis, we can add all of the symbols to discover there are a total of 10 of them:
1 1/4 +1 3/4 +2 1/2 +1 1/2 + 3 = 8 + (1/4 +3/4) +(1/2 +1/2) = 8 +1 +1 = 10
Since 10 symbols represent 80 people, each large square symbol must represent 8 people.
__
c) The number preferring dogs is (1 3/4)(8) = 14. The number preferring giraffes is (2 1/2)(8) = 20. Then 20 -14 = 6 more people preferred giraffes.
Answer:
cat,8,6
Step-by-step explanation:
i think im not sure
Estimate 86 x 904 plz answerrr fastt
Answer:
81, 000
Step-by-step explanation:
86 = 90
904 = 900
90 x 900 = 81, 000
Answer:
81,000
Step-by-step explanation:
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please I need help.
Part of a stained glass window is shown at the right. Each square in the grid is 1 in. long. Find the perimeter and area of the dark gray parallelogram.
Answer:
Perimeter: 5 in
Area: 9 in^2
Step-by-step explanation:
y=-5(-4)^2 - 40(-4) + 10
Answer:
Step-by-step explanation:
y=-5(16)-160+10
y=-80+160+10
y=90
∠E and ∠F are vertical angles. If m∠E=(5x+55)° and m∠F=(11x-53)°, find m∠E
Answer:
145° = m∠E
Step-by-step explanation:
Vertical Angles: always congruent, therefore, to find Angle E first find "x" ;
5x + 55 = 11x - 53
55 = 6x - 53
108 = 6x
108/6 = x
18 = x
Now that we know x-value is 18, u can substitute that in for the equation for Angle E for "x";
=> 5(18) + 55 = m∠E
=> 145° = m∠E
Hope this helps!
What is the inverse of f(x)=1.5^x+4
Answer:
Step-by-step explanation:
The inverse function of [tex]f(x) = 1.5^x + 4[/tex] is [tex]f^{-1}(x) = \log1.5(x - 4)[/tex]
In other words, the required answer is [tex]f^{-1}(x) = \log1.5(x - 4)[/tex]
To find the inverse of the function[tex]f(x) = 1.5^x + 4[/tex], we need to swap the roles of x and y and solve for y.
Start with the original function:
[tex]y = 1.5^x + 4[/tex]
Swap x and y:
[tex]x = 1.5^y + 4[/tex]
Solve for y:
Subtract 4 from both sides:
[tex]x - 4 = 1.5^y[/tex]
Take the logarithm (base 1.5) of both sides:
[tex]\log1.5(x - 4) = y[/tex]
Rewrite the equation with y as the subject:
y = log1.5(x - 4)
Therefore, the inverse function of [tex]f(x) = 1.5^x + 4[/tex] is [tex]f^{-1}(x) = \log1.5(x - 4)[/tex]
In other words, the required answer is [tex]f^{-1}(x) = \log1.5(x - 4)[/tex]
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What is the appropriate equation used to find the value of n?
Answer:
B
Step-by-step explanation:
It's B, because it's the only way to find n on both sides
In Parallelogram WXYZ, diagonals WY and XZ intersect at A. WA=x2−24 and AY=2x.
What is WY?
Enter your answer in the box.
WY=
units
Answer:
[tex] \displaystyle WY = 24[/tex]
Step-by-step explanation:
refer the attachment
remember that,
the diagonals of Parallelogram bisect each other so WA=AY
thus our equation is
[tex] \displaystyle {x}^{2} - 24 = 2x[/tex]
move left hand side expression to right hand side and change its sign:
[tex] \displaystyle {x}^{2} - 2x - 24 =0[/tex]
rewrite 2x and 4x-6x:
[tex] \displaystyle {x}^{2} + 4x -6x - 24 =0[/tex]
factor out x:
[tex] \displaystyle x ({x}^{} + 4) -6x - 24 =0[/tex]
factor out -6:
[tex] \displaystyle x ({x}^{} + 4) -6(x + 4) =0[/tex]
group:
[tex] \displaystyle ({x}^{} + 4) (x - 6) =0[/tex]
recall that,
When the product of factors equals 0 then at least one factor is 0 so
[tex] \displaystyle \begin{cases} {x}^{} + 4 = 0 \\ x - 6 =0 \end{cases}[/tex]
[tex] \displaystyle \begin{cases} {x}^{} = - 4\\ x =6 \end{cases}[/tex]
since the length cannot be negative negative x isn't available
therefore
[tex] \displaystyle \therefore x = 6[/tex]
since WA and AY are the part of WY we acquire:
[tex] \displaystyle WY = {x}^{2} - 24 + 2x[/tex]
substitute the got value of x:
[tex] \displaystyle WY = {6}^{2} - 24 + 2.6[/tex]
simplify square:
[tex] \displaystyle WY = 36 - 24 + 2.6[/tex]
simplify multiplication:
[tex] \displaystyle WY = 36 - 24 + 12[/tex]
simplify addition:
[tex] \displaystyle WY = 48- 24[/tex]
simplify substraction:
[tex] \displaystyle WY = 24[/tex]
hence,
[tex] \displaystyle WY = 24[/tex]
Diagonals bisect each other
WA=AYx²-24=2xx²-2x=24x²-2x-24=0x²-6x+4x-24=0x(x-6)+4(x-6)=0(x+4)(x-6)=0Take it positive
x=6Now
AY=2(6)=12WY=12(2)=24A tree that is 12 feet tall casts a shadow that is 9 feet long. At the same time a nearby stop sign casts a shadow that is 6 feet long. What is the height, h , of the stop sign?
A. 4.5 ft
B. 7.3 ft
C. 8 ft
D. 9 ft
Answer:
height / shadow = height / shadow until sun moves or earth tilts
12/9 = h / 6
h = 6*12 /9 = (3*2*3*4 ) / (3*3) = 2 * 4 = 8
So C. 8ft
PLEASE QUICK I ONLY HAVE 11 MINS I NEED THIS ONE QUICK!
WILL GIVE BRAINLY
Answer:
the answer is 7 feet
2πr/2π=14π/2π
r=7 feet
Miriam measures the water level at the end of a dock each day. On Monday, she marked where the water level was on one of the dock pilings. On Tuesday, the water level was 412 inches lower. On Wednesday, the water level was 2 inches lower than the day before. On Thursday, Miriam marked the water level on the piling again. The water level was 534 inches higher than the day before.
How does the height of Thursday's mark compare to the height of the mark Miriam made on Monday?
Answer:
Thursday's mark is 3/4 inch below Monday's mark.
What is the volume of a rectangular prism that has the dimensions of 12 feet, 14 feet, and 6 feet? HINT: Remember to label your answer correctly for full credit!
The formula is V=lwh (Or volume equals length times width times height).
V=12 x 14 x 6
12 x 14 = 168
168 x 6 = 1,008
V=1,008
length: is how long the object is.
width: is the depth of the object, like how wide it is.
height: is how tall it is.
Y is 5 times more than x
Answer:
y = 5x
Step-by-step explanation:
Form the equation:
y = 5 times x or y = 5x
If my answer is incorrect, pls correct me!
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heyy! i’ll give brainliest please help
Answer:
they held yearly elections so I would say democracy but I'm not 100% sure
if r = 1 and 0 = 7pi /6 what is the approximate arc length
0 = theta
A.)1.75
B.)5.498
C.)21.991
D.)7.330
Answer:
[tex]l = 3.66[/tex]
Step-by-step explanation:
Given
[tex]r =1[/tex]
[tex]\theta = \frac{7\pi}{6}[/tex]
Required
The arc length (l)
This is calculated as:
[tex]l= r\theta[/tex]
So, we have:
[tex]l = 1 * \frac{7\pi}{6}[/tex]
[tex]l = \frac{7\pi}{6}[/tex]
So, we have:
[tex]l = \frac{7*3.14}{6}[/tex]
[tex]l = 3.66[/tex]
None of the options is correct
Right triangles 1, 2, 3 are given with all their angle measures
Answer:
6.4/7.7 is the ratio
Step-by-step explanation:
The bottom triangle matches the 50 40 90 angle, so the ratio of the triangle length is consistent
- Gage Millar, Algebra 2 tutor
Find x.
A. 6/6
B. 24v3
C. 18
D.912
Answer:A
Step-by-step explanation:
What is the measurement of ∠B ?
Answer: 82 degrees
Step-by-step explanation:
Brand A green beans costs $7.00 for a 16 ounce pack and Brand B green beans costs $9.00 for a 20 ounce pack.
a. Which brand of green beans has the lowest price per ounce?
b. Explain your reasoning. Be specific (include the price per ounce for each brand in your explanation).
Andre sells T-shirts. He charges
customers $19 per T-shirt, plus a delivery
fee of $8 per order. The amount, y, that
Andre charges for an order of x T-shirts is
represented by the equation y = 19x + 8. A
customer paid $217 for an order of
T-shirts. How many T-shirts did the
customer order?
Answer:
11
Step-by-step explanation:
217 = 19x + 8
209 = 19x
x = 209/19
x = 11
Question 2
Which of the following sets of numbers could represent side lengths of a right triangle?
6m, 10m, 16m
06m, 8m, 10m
6m, 8m, 9m
6m, 6m, 11m
Bob has a coin cup with four $1 tokens and two $5 tokens in it. He also has two $10 tokens and one $25 token in his pocket.
He randomly draws a token froin the cup, and then randomly draws a token from his pocket. What is the probability that he
will draw $30 in tokens?
OB.
. В
We want to find the probability that Bob will randomly draw $30 in tokens. We will find that the probability is P = 1/6 = 0.167
Finding the probability.
The only case where he draws $30 randomly is when:
He takes one $5 token from the coin cupHe takes the $25 token from his pocket.Then we need to find the probabilities for these two events.
For the first one, the probability will be equal to the quotient between the number of $5 tokens and the total number of tokens in the cup. There are 6 tokens in the cup and 2 of these are $5 tokens, then the probability is:
p = 2/6 = 1/3
For the second event the probability is computed in the same way, he has two tokens in his pocket and one of them is a $25 token, then the probability is:
q = 1/2
The joint probability, the probability that both of these events happen at the same time, is given by the product of the individual probabilities, so we get:
P = p*q = (1/3)*(1/2) = 1/6 = 0.167
So the probability that he draws $30 in tokens is P = 1/6 = 0.167.
If you want to learn more about probability, you can read:
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Answer:
4/9
Step-by-step explanation: