There are 10 different ways to select a committee of 2 people from a group of 5 candidates.
Explanation:To calculate the number of ways to select a committee of 2 people from a group of 5 candidates, we can use the combination formula. The number of combinations of n items taken r at a time is given by the formula:
nCr = n! / (r!(n-r)!)
Here, n is the total number of candidates (5) and r is the number of people to be selected for the committee (2). Plugging in the values, we get:
5C2 = 5! / (2!(5-2)!)
Simplifying this expression:
5C2 = (5 * 4) / (2 * 1)
Therefore, there are 10 different ways to select the committee.
find the value of x
This is the first part of a three-part problem. express $18\sqrt 8$ in the form $a\sqrt b$, where $a$ and $b$ are integers and $b$ is as small as possible.
Answer:
[tex]18\sqrt{8}=36\sqrt{2}[/tex]
Where a=36 and b=2 with b is small.
Step-by-step explanation:
Given problem [tex]18\sqrt{8}[/tex]
We have to write the given problem in form of [tex]a\sqrt{b}[/tex], where a and b are integers and b is as small as possible.
Consider the given problem [tex]18\sqrt{8}[/tex]
8 can be written in factored form as 2 × 2 × 2
Substitute, in given problem, we have
[tex]18\sqrt{8}=18\sqrt{2 \times 2\times 2}[/tex]
This can be written as,
[tex]18\sqrt{2 \times 2\times 2}=18(\sqrt{4}\sqrt{2})[/tex]
We know [tex]\sqrt{4}=2[/tex] , thus,
[tex]18(\sqrt{4}\sqrt{2})=18\cdot 2\sqrt{2}=36\sqrt{2}[/tex]
Thus,[tex]18\sqrt{8}=36\sqrt{2}[/tex]
Where a=36 and b=2 with b is small.
An initial deposit of $5325 was made into an account that compounds interest semi-annually. No other deposits were made. At the end of 13 years, the balance in the account had doubled. Find the interest rate on this account.
6 cards are drawn from a standard deck without replacement how many different 6 card hands are possible if the drawing is done without replacement
A triangle has an area of 30 cm². The base and height are scaled by a factor of 4.
What is the area of the resulting triangle?
Enter your answer in the box.
Answer:
480cm². Verified by correct test results.
Noah was asked to find the median of the following numbers.
115, 109, 117, 136, 127, 131
Noah’s work is shown below.
109, 115, 117, 127, 131, 136
mc006-1.jpg
What error, if any, did Noah make?
A)He forgot to put the numbers in order first.
B)He crossed off the high/low number pairs incorrectly.
C)He left out a number when putting the numbers in order.
D)He did not make any error.
Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be filled, and after 5 minutes, he had 25 cups left to be filled. Mary’s progress is shown in the table of values below. Assuming that both Jorge and Mary are filling cups at a constant rate, which statement is correct?
Mary’s Cup-Filling Progress
Time (minutes)
0.5
1
1.5
2
2.5
Cups Remaining
99
81
63
45
27
Jorge is filling 14 cups per minute, which is faster than Mary.
Jorge is filling 28 cups per minute, which is faster than Mary.
Mary is filling 18 cups per minute, which is faster than Jorge.
Mary is filling 36 cups per minute, which is faster than Jorge.
Answer:
Mary is filling 36 cups per minute, which is faster than Jorge.
Step-by-step explanation:
Lets get Jorge's time :
As the rate is constant, we can find the slope to know the number of cups he is filling per minute.
Slope is found using: [tex]\frac{y2-y1}{x2-x1}[/tex]
= [tex]\frac{53-25}{5-3}[/tex]
= [tex]\frac{28}{2}=14[/tex]
From the table lets get Mary's time:
[tex]\frac{99-81}{1-0.5}[/tex]
= [tex]\frac{18}{0.5}=36[/tex]
Another data: [tex]\frac{63-45}{2-1.5}[/tex]
= [tex]\frac{18}{0.5}=36[/tex]
Therefore, we can see that Mary is filling 36 cups in a minute and Jorge is filling 14 cups.
Hence, the correct answer is : Mary is filling 36 cups per minute, which is faster than Jorge.
Answer:
Mary is filling 36 cups per minute, which is faster than Jorge.
Step-by-step explanation:
Express 8.12 as a mixed number.
△BQH∼△SFN
What is FN ?
Answer:
23.4 in
Step-by-step explanation:
The only side of SFN we know the measurement of is FS, which is 18.2. We see from the similarity statement that FS corresponds to QB, which is 14. This gives us the ratio
14/18.2.
From the similarity statement, we see that FN corresponds to QH; this gives us the ratio
18/x
Together this gives us the proportion
14/18.2 = 18/x
Cross multiplying gives us
14(x) = 18.2(18)
14x = 327.6
Divide each side by 14:
14x/14 = 327.6/14
x = 23.4
OUCH MY BRAIN IS HURTING AFTER TRYING TO SOLVE THIS QUESTION
which statement best describes the function below?
f(x)=2x^2-3x+1
A.It is a one-to-one function.
B.It fails the vertical line function.
C.It is a many-to-one function.
D.It is not a function.
f(x)=2x^2-3x+1
the graph of the function is attached with the answer
As we can see that equation is quadratic and its graph is a parabola facing upward.
As we can see it passes the Vertical line test
As it passes the Vertical line test , So it is a function
And two values of x has one value of y
So it is a many to one function.
When a standard six sided die is rolled, what is the probability of getting a 9?
A theater charges $25 for adults and $15 for children. When the price of a child's ticket increases to $18 next year,the cost for a dance club to attend the theater will increase from $450 to $480. Write and solve a system of equations to find how many adults are in the dance club.
8j -k+148j−k+148, j, minus, k, plus, 14 when j=0.25j=0.25j, equals, 0, point, 25 and k=1k=1
Answer:
15. It was right for me, not sure for anyone else
Step-by-step explanation:
If BE is parallel to CD, the. The value of x is:
A. 10
B. 6
C. 9
CD←→ is tangent to circle A at point B.
What is the measure of ∠ABD?
45º
60º
90º
180º
The measure [tex]\angle ABD[/tex] is C. [tex]90^{\circ}[/tex]
Given,CD is tangent to the circle A at point B.
We have to find the measure of [tex]\angle[/tex][tex]ABD[/tex].
Tangent:We know that,
Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent on a point to circle. The Tangent makes an angle of [tex]90^{\circ}[/tex] with the radius of the circle at the point of contact.Hence [tex]\angle ABD[/tex] is [tex]90^{\circ}[/tex].The correct option is C. [tex]90^{\circ}[/tex]
For more details about tangent, follow the link:
https://brainly.com/question/1503247
In two or more complete sentences, define the key features of the graph below and explain how to write its equation using function notation.
Answer:
The function notation of the graph is f(x) = |x-3| - 2
Step-by-step explanation:
From the graph it is evident that it is the graph of the absolute value of the function i.e. f(x) = |x| and we know that 'Translation' is a transformation that shifts the graph of a function in any direction.
Now, as we can see that the graph is shifted towards the right of the y-axis at point x=3, this means that it is translated by 3 units to the right of y-axis.
Therefore, the function becomes f(x) = |x-3|.
Furthermore, it is also shifted downwards at the point x= -2, this means that it is translated by 2 units downward from the x-axis.
Hence, the new function is f(x) = |x-3| - 2.
It can also be seen from the figure below that the graph of above f(x) is same as that of the provided image.
A rectangular solid is dilated by a factor of 0.5.
How many times larger is the volume of the resulting solid than the volume of the original solid?
Enter your answer as a decimal in the box.
Answer:
0.125 took test
Step-by-step explanation:
Volume of the resultant solid will be 0.125 times of the original solid.
Volume scale factor of a rectangular solid:If the sides of a rectangle solid is dilated by a scale factor 'k',Volume of the solid will be given by the expression,
Volume = (k)³(Volume of the original solid)
If a rectangular solid is dilated by a scale factor 'k' = 0.5
Volume of the resultant solid = (0.5)³(Volume of the original solid)
= 0.125(Volume of the original solid)
Therefore, volume of the resultant solid will be 0.125 times of the original solid.
Learn more about the dilation of a rectangular solid here,
https://brainly.com/question/2919998?referrer=searchResults
You want to draw an enlargement of a design that is printed on a card that is 4 in. by 5 in. You will be drawing this design on a piece of paper that is 8one half in. by 11 in. What are the dimensions of the largest complete enlargement you can make?
Answer:
The dimensions are
[tex]8\frac{1}{2}\ in[/tex]
[tex]10\frac{5}{8}\ in[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the scale factor is the ratio of its corresponding sides
step 1
Divide [tex]8\frac{1}{2}[/tex] by [tex]4[/tex]
[tex]8\frac{1}{2}=\frac{8*2+1}{2}=\frac{17}{2}\ in[/tex]
so
[tex]\frac{17}{2}/4=2.125[/tex]
step 2
Divide [tex]11[/tex] by [tex]5[/tex]
so
[tex]\frac{11}{5}=2.2[/tex]
step 3
Find the largest complete enlargement
The scale factor is the smaller of the two previous values
so
The scale factor is [tex]2.125[/tex]
The dimensions are
[tex]4*2.125=8.5=8\frac{1}{2}\ in[/tex]
[tex]5*2.125=10.625=10\frac{5}{8}\ in[/tex]
Answer:
8 1/2 in. by 10 5/8 in.
Step-by-step explanation:
What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)
What is the exact value of the trigonometric expression in simplest form? 2 cos(3π/4)−4 sin(7π/6)
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]
Let us find the value of cos([tex] \frac{3\pi}{4} [/tex]) and [tex] sin(\frac{7\pi}{6} ) [/tex]
[tex] cos(\frac{3\pi}{4} )=cos(\pi -\frac{\pi}{4} ) [/tex]
The angle [tex] \pi -\frac{\pi}{4} [/tex] lies in second quadrant.
So, [tex] cos(\frac{3\pi}{4} )=-cos(\frac{\pi}{4} ) =-\frac{1}{\sqrt{2}} [/tex]
[tex] So, cos(\frac{3\pi}{4} )=-\frac{1}{\sqrt{2}} [/tex]
Now, Let us find the value of [tex] sin(\frac{7\pi}{6} ) [/tex]
[tex] sin(\frac{7\pi}{6} ) =sin(\pi +\frac{\pi}{6} )=-sin(\frac{\pi}{6} ) =\frac{-1}{2} [/tex]
[tex] sin(\frac{7\pi}{6} ) =\frac{-1}{2} [/tex]
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6}) [/tex]=2*[tex] \frac{-1}{\sqrt{2}} [/tex]-4*[tex] \frac{-1}{2} [/tex]
=[tex] \frac{-2}{\sqrt{2}} +\frac{4}{2} [/tex]
=[tex] \frac{-2\sqrt{2}}{2} +\frac{4}{2} [/tex]
=[tex] \frac{-1\sqrt{2}}{1} +\frac{2}{1} [/tex]
=[tex] -\sqrt{2} +2 [/tex]
=[tex] 2-\sqrt{2} [/tex]
[tex] 2 cos(\frac{3\pi}{4})-4sin(\frac{7\pi}{6})=2-\sqrt{2} [/tex]
Which set does not contain –3?
the set of all whole numbers
1.66666666667 rounded to the tenth
Find the retail price of a backpack that has a wholesale price of $25 and is marked up 40%. Multiply $25 and 40% in decimal form to find the markup amount. 25(0.40) = $10 Add the wholesale price to the markup amount. What is the selling price? $10 $15 $35 $65
Answer:
35 35 35 35
Step-by-step explanation:
it 35
which pair of ratios form a true proportion
a) 1/2=6/10
b) 6/8=5/20
c) 3/5=6/10
d) 3/9=7/80
Which stem-and-leaf plot represents the data 80, 81, 91, 92, 66, 55, 54, 30, 55, 79, 78?
Answer:The answer is below Hope this help and tthanjs for answer please like and vote excellent thanks and have a good day.
Step-by-step explanation
3 0
4
5 455
6 6
7 89
8 01 9 12A cylindrical container holding sugar has a height of 15 inches and a diameter of 4 inches. Which of the following is the closest to the volume of the sugar container?
A.
707 cubic inches
B.
94 cubic inches
C.
754 cubic inches
D.
188 cubic inches
Using the formula V = πr²h, the volume of the cylinder is calculated as 188.4954 cubic inches, which can be rounded to 188 cubic inches, corresponding to answer choice D.
To calculate the volume of the cylindrical container holding sugar, we can use the formula for the volume of a cylinder, which is V = πr²h. Here, π is a constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.
The diameter of the container is given as 4 inches, so the radius (r) is half of the diameter, which is 2 inches. The height (h) is given as 15 inches. Plugging these values into the volume formula, we get:
V = π(2 inches)²(15 inches)
= π(4 square inches)(15 inches)
= 60π cubic inches
Using 3.14159 as the value for π, the volume calculates to:
V = 60 * 3.14159 cubic inches = 188.4954 cubic inches
So, the closest estimate to the volume of the sugar container would be 188 cubic inches, which corresponds to answer choice D.
A baker used the equation y = kx to find how many cupcakes he needs to fill 22 identical boxes. He found that he would need 176 cupcakes. How many cupcakes fit into each box?
What is the future value of $1,600 in 17 years assuming an interest rate of 10 percent compounded semiannually?
How do you make 3ln2+2ln4 a single logarithm?
Given that f(x) = x2 − 3x + 3 and g(x) = the quantity of x minus one, over four , solve for f(g(x)) when x = 5. (1 point)
Answer:
The answer is 1
Step-by-step explanation: