The number of ways to choose the colors is 36
How to determine the number of ways?The given parameters are:
Colors = 9
Colors to choose = 7
Since order does not matter, then it is combination
This is calculated using:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^nC_r = \frac{9!}{7!2!}[/tex]
Evaluate
[tex]^nC_r = 36[/tex]
Hence, the number of ways is 36
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DO NOT PUT A WRONG ANSWER OR ELSE I WILL START TO REPORT YOU!!!
A person who is 6 feet tall is walking away from a lamp post at the rate of 40 feet per minute. When the person is 10 feet from the lamp post, his shadow is 20 feet long. Find the rate at which the length of the shadow is increasing when he is 30 feet from the lamp post.
Square root of (-16)^2
Answer: [tex]\sqrt{(-16)^{2} } =16[/tex]
Step-by-step explanation:
I looked it up on my calculator. I hope this helps!! :)
Each year the Royal London company gives
its employees a gift box containing 6 bags of
coffee, 4 boxes of tea, and 2 boxes of biscuits.
If in the first three years, the number of
employees grew from 2 to 12 to 18, what was
the total quantity of coffee, tea, & biscuits
distributed by the company in those years?
The total number of tea received in three years is 192.
The total number of coffee received in three years is 128.
The total number of biscuits received in three years is 64.
What is the total quantity of tea, coffee and biscuits distributed in the three years?The total quantity of tea, coffee and biscuits received in the first year = (6 x 2) , (4 x 2) , (2 x 2) = 12, 8, 4 respectively
The total quantity of tea, coffee and biscuits distributed in the second year = (6 x 12) , (4 x 12) , (2 x 12) = 72, 48, 24 respectively
The total quantity of tea, coffee and biscuits distributed in the third year = (6 x 18) , (4 x 18) , (2 x 18) = 108, 72, 36 respectively
Total number of tea received in three years = 108 + 72 + 12 = 192
Total number of coffee received in three years = 8 + 48 + 72 = 128
Total number of biscuits received in three years = 4 + 24 + 36 = 64
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Solve the following compound inequality: x greater-than-or-equal-to negative 1 or x less-than 2.
a.
Negative 1 less-than-or-equal-to x less-than 2
c.
x greater-than-or-equal-to negative 1
b.
no solution
d.
all real numbers
Answer:
x greater than equal to (-1)
x less than 2
all no. greater than -1 = -1,1, 0 , 1 ,2 ......
no. less than2 = 1, 0, -1,.......
-1,0, 1
Option CA clothing store is having a 15% off sale on t-shirts. If you will save $3.75 on a shirt, what was the original price before the sale? Show your work.
Answer:
$25
Step-by-step explanation:
3.75 is 15% of 25.
15% × 25 = 3.75
Base of a prism is a right triangle with legs 3 feet and 4 feet. The height is 13 feet , what is the volume?
Answer:
Triangular prisms
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h
Step-by-step explanation:
A cooler contains five colas, seven root beers, and four ginger ales. Three people grab a drink at random, one at a time. a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?
The probabilities are:
a) P = 0.024
b) P = 0.5
How to get the probabilities?
a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.
There are 5 colas, and 16 drinks in total, so the probability is:
P = 5/16
The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:
Q = 4/15
Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:
Z = 4/14
The joint probability is:
prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024
b) If the two first persons grabed colas, then in the cooler we have:
3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.
Then the probability of grabbing a root beer is:
p = 7/14 = 1/2 = 0.5
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In the diagram, DG = 15, GF = 5, EH = 12, and DE = 8.
Triangle D F E is shown. Line segment G H is drawn from side D F to side E F to form triangle G F H. The length of D G is 15, the length of G F is 5, the length of E H is 12, and the length of D E is 8.
To prove that △DFE ~ △GFH by the SSS similarity theorem using the information provided in the diagram, it would be enough additional information to know that
To prove that △DFE ~ △GFH by the SSS similarity theorem, the correct answer is; Option C: HF is 4 units and GH is 2 units
How to prove the similarity theorem?The SSS Similarity theorem states that two triangles are similar If all the three sides of one of the triangles are in same proportion to the three sides of the other triangle.
Since triangle DFE is similar to triangle GHF as seen in the attached diagram, then we can say that;
DF/GF = DE/GH
20/5 = 8/GH
GH = 2 units
Also:
EF/HF = DF/GF
(12 + HF)/HF = 20/5
HF = 4 units
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A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 7-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
Answer:
1/(7^5)=1/16807
Step-by-step explanation:
Assuming 7-key mean zero up to 7,
# of possible codes = 17^5 = 16807
=====
Probability of first try correct = 1/7^5
how would i solve this problem
Answer:
30
Step-by-step explanation:
1500/50=30
X+(x^2+2)+y=4
Find 2 coordinates
(X,y) (x,y)
Answer: (-2,0) and (1,0)
Step-by-step explanation:
If y=0, then:
[tex]x+x^2 + 2=4\\\\x^2 + x-2=0\\\\(x+2)(x-1)=0\\\\x=-2, 1[/tex]
So, the points (-2,0) and (1,0) lie on the curve.
The points (-2,0) and (1,0) lie on the curve.
If y=0, then:
[tex]x+(x^2+2)+0=4\\x^2+x+2=4\\[/tex]
What is the coordinate of the axis?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
[tex]x^2+x-2=0[/tex]
[tex]=\left(x^2-x\right)+\left(2x-2\right)[/tex]
[tex]=x\left(x-1\right)+2\left(x-1\right)[/tex]
[tex]=\left(x-1\right)\left(x+2\right)[/tex]
[tex]x=-2,x=1[/tex]
So, the points (-2,0) and (1,0) lie on the curve.
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which of the following are identities? check all that apply A. cot^2x+1=csc^2x B.tan^2=1-sec^2x C.sin2^x=1=cos^2x D.sin^2x+cos^2x=1
Need help ASAP!! Will give Brainliest
Answer:
B
Step-by-step explanation:
The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006? Round your answer to the nearest integer.
The expected number of employees working at Sprockets R Us in 2006 will be 8069.45.
What are percentages?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006?
The number of the employees in 2006 will be calculated as:-
Number of employees decreased = 0.5% x 8110
Number of employees decreased = (0.5/100) x 8110
Number of employees decreased = 40.55
The number of the employees in 2006 will be
N = 8110 - 40.55 = 8069.45
Therefore the expected number of employees working at Sprockets R Us in 2006 will be 8069.45.
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find 2^x=4x, find x
Whatever... I'll try to solve the first two problems.
[tex]2^x=4x\\4x=e^{\ln 2^x}\\4x=e^{x\ln 2}\\\dfrac{1}{4x}=e^{-x \ln 2}\\-\dfrac{\ln 2}{4}=-x\ln 2e^{-x \ln 2}\\-x\ln 2=W\left(-\dfrac{\ln 2}{4}\right)\\x=-\dfrac{W\left(-\dfrac{\ln 2}{4}\right)}{\ln 2}[/tex]
1.
[tex]x=\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}\qquad\left( x\geq0\right)\\\\x=\sqrt{13+\sqrt{5+x}}\\\\x^2=13+\sqrt{5+x}\\\sqrt{5+x}=x^2-13\\\\D:5+x\geq0 \wedge x^2-13\geq 0\wedge x\geq 0\\D:x\geq-5 \wedge x^2\geq13\wedge x\geq 0\\D:x\geq \sqrt{13} \vee x\leq-\sqrt{13}\wedge x\geq0 \\D:x\in[\sqrt{13},\infty)\\\\ 5+x=x^4-26x^2+169\\x^4-26x^2-x+164=0\\\vdots\\(x - 4) (x^3 + 4 x^2 - 10 x - 41) = 0\\x-4=0\\x=4[/tex]
One solution is [tex]x=4[/tex], and [tex]4\in D[/tex], therefore[tex]\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}=4[/tex].
We can ignore other possible solutions of the polynomial equation, because the expression can not be equal to two different values simultaneously.
A rectangular bedroom has an area of 117 ft. the length of the bedroom is 4ft more than the width. find the length and the width of the bedroom
Answer: Length = 13 ft. , Width = 9 ft.
Step-by-step explanation:
Rectangle area = Length x width
Area = 117 ft.
Length = x + 4
Width = x
To solve
(x)(x + 4) = 117
x^2 + 4x = 117
x^2 + 4x - 117 = 0
(x - 9)(x + 13)
x = 9, -13
x = 9 (measurement cannot be negative)
Length
x + 4
9 + 4 = 13
6. The diagram on the right shows the cross-section of a cylindrical pipe with water lying in the bottom. a) If the maximum depth of the water is 2 cm and the radius of the pipe is 7 cm, find the area shaded. b) What is the volume of water in a length of 30 cm?
Answer:
404 cm³ Anyway... Look down here for my explanation.
Step-by-step explanation:
Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.
We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)
44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°
The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.
Shaded area 88.8/360*area of circle - ½*7*788.8°
= 88.8/360*π*7² - 24.5*sin 88.8°
13.5 cm²
(using area of ∆ = ½.a.b.sin C for the triangle)
Volume of water = cross-sectional area * length
13.5 * 30 cm³
404 cm³
What is 9 lbs 6 oz converted to ounces?
Answer:
150 ounces
Step-by-step explanation:
in quadlateral wxyz wc equals 2X +5 and CY equals 3X +2 what must x equal
The value of x in the given quadrilateral is; x = 3
How to find the angle in a quadrilateral?
The diagonals of a parallelogram bisect each other.
Thus, from the image attached, we can say that;
WC = CY.
Thus;
2x + 5 = 3x + 2
Subtract 2x from each side to get;
5 = x + 2
Subtract 2 from each side to get;
5 - 2 = x + 2 - 2
x = 3
The complete question is;
In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?
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A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of a red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. What is the expected value of the game?
The expected value of the game is $2.00.
To Find: The fair price to pay to play the game of rolling a colored die with three red sides, two green sides, and one blue side
Now the question arises how to find the Fair Price
We are told that in the game of rolling the colored die;
A roll of a red loses.
A roll of blue pays 5.00 and A roll of green pays 2.00.
Now, the best game to get the fairest price is to play; RRRGGB i.e (RED, RED, RED, GREEN, GREEN,BLUE)
Fair price = 2(3/6) + 6(1/6) + 0(2/6)
Fair price = $2
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Find the midpoint of the segment with the following endpoints.
(-3,-3) and (1, 2)
[tex]\left(\frac{-3+1}{2}, \frac{-3+2}{2} \right)=\boxed{\left(-1, -\frac{1}{2} \right)}[/tex]
HELPPP!!! can someone turn 3x−2=13 into a WORD problem. (i already know answer)
Write 4 1/7 as an improper fraction?
Answer:
29/7
Step-by-step explanation:
4 1/7 = 4 + 1/7
4 = 28/7
then:
4 1/7 = 28/7 + 1/7 = (28+1) / 7
= 29/7
Find the equation of a line containing the points (−2,−4) and (1,−3).
PLEASE HELP!!!!!!!!!
Answer:
correct answer is B.
Step-by-step explanation:
for more information see the attachment.
Answer:
no 2/B is the correct answer
To estimate the height of a totem pole, Jorge uses a small square of plastic. He holds the square up to his eyes and walks backward from the pole. He stops when the bottom of the pole lines up with the bottom edge of the square and the top of the pole lines up with the top edge of the square. Jorge's eye level is about 2 m from the ground. He is about 3 m from the pole. Which of the following is the best estimate of the height of the totem pole?
Answer:
6.5 meters
Step-by-step explanation:
Analyze the diagram below and answer the question that follows
How many faces does the solid have?
A. 4
B. 5
C. 6
D. 8
Answer:
C.6
Step-by-step explanation:
The following data represent the high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population. Complete parts (a) through (c
Temperature Lower Limit Upper Limit Days
50-59 50 59 4
60-69 60 69 316
70-79 70 79 1426
80-89 80 89 1532
90-99 90 99 345
100-109 100 109 7
Answer:
The Mean and Standard deviation for the given data would be as follows:
μ =79.7
б =7.81
Step-by-step explanation:
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.
Frequency Distribution
Given that,
Temperature Lower Limit Upper Limit Days([tex]f_{i}[/tex])
50-59 50 59 2
60-69 60 69 313
70-79 70 79 1419
80-89 80 89 1503
90-99 90 99 319
100-109 100 109 9
Average([tex]x_{i\\}[/tex])
[tex]\frac{50+59}{2} = 54.5\\ \\\frac{60+69}{2} = 64.5\\ \\\frac{70+79}{2} = 74.5\\\\\frac{80+89}{2} = 84.5\\ \\\frac{90+99}{2} = 94.5\\ \\\frac{100+109}{2} = 104.5[/tex]
As we know,
Mean (μ) =∑ [tex](x_{i}f_{i})[/tex]/∑[tex]f_{i}[/tex]
= { (54.5 * 2) + (64.5 * 313) +(74.5 * 1419)+(84.5*1503)+(94.5*319) + (104.5*9)/ (2+313+1419+1503+319)
∵ μ = 79.7
As we know,
Standard Deviation:-
[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]
by putting the values, we get
∵ б = 7.81
Hence, μ = 79.7 and б=7.81 are the correct answers.
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Which choices are equivalent to the expression below? Check all that apply. √8 × √8
A. √ 8
B. 8
C. 64
D. 8
E. 16
F. √64
Answer:
the answers are B and F since √8 x √8 = √64 which simplifies to 8.
Given the functions, fx) = 3x-6 and g(x)= x² + 5x+7, perform the indicated operation. When applicable, state the
domain restriction.
f(g(x))
Hope this helps
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
I did this already
