Answer: Second Option
C(8,8)=1
Step-by-step explanation:
We must calculate a combination
The combination [tex]C (n, r) =\frac{n!}{r!(n-r)!}[/tex]
Where n is the number of elements that you can combine and you choose "r" from them.
So
C (8, 8) is the combination of 8 in 8.
Therefore
[tex]n = 8\\r=8[/tex]
[tex]C(8,8)= \frac{8!}{8!(8-8)!}\\\\C(8,8)=\frac{8!}{8!(0)!}\\\\C(8,8)=\frac{1}{1*1}\\\\C(8,8)=1[/tex]
The answer is the second option
The value of [tex]\( C(8, 8) \)[/tex] is 1 because choosing all 8 items from 8 yields only 1 combination.
The expression [tex]\( C(8, 8) \)[/tex] represents choosing 8 items from a set of 8 items without regard to order, which is also known as a combination. Here's how we can evaluate it step by step:
Step 1: Recall the formula for combinations.
The formula for combinations is [tex]\( C(n, k) = \frac{n!}{k!(n - k)!} \),[/tex] where [tex]\( n \)[/tex] is the total number of items and [tex]\( k \)[/tex] is the number of items to choose.
Step 2: Substitute the values into the combination formula.
In this case, [tex]\( n = 8 \) and \( k = 8 \),[/tex] so the expression becomes:
[tex]\[ C(8, 8) = \frac{8!}{8!(8 - 8)!} \][/tex]
Step 3:
Simplify the expression.
[tex]\[ C(8, 8) = \frac{8!}{8!0!} \][/tex]
Step 4:
Recall that [tex]\( n! = n \times (n - 1) \times (n - 2) \times \ldots \times 1 \)[/tex] and [tex]\( 0! = 1 \).[/tex]
[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 \times 1} \][/tex]
Step 5:
Cancel out the common terms.
[tex]\[ C(8, 8) = \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \][/tex]
[tex]\[ C(8, 8) = 1 \][/tex]
So, [tex]\( C(8, 8) = 1 \).[/tex]
Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.
Check the picture below.
The answer is a=8 btw
PLEASE HELP ASAP i will give brainliest!!
Write an inequality to represent the real-world problem. Then complete the statements. Jasmine’s computer cost more than $300.
The variable in the inequality represents _______
The inequality symbol needed is ________
The constant is _______
The inequality that correctly represents the problem is ______
Answer:
1. the cost of the computer (c)
2. > (greater than)
3. how much ($300)
4. c > 300
The variable in the inequality represents the cost of the computer.
The inequality symbol needed is > (greater than)
The constant is how much ($300)
The inequality that correctly represents the problem is cost of the computer > 300
What is problem-solving?Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
Problem-solving starts with identifying the issue. As an example, a trainer may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.
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what is 3 3/5 x ( -8 1/3)
Answer: -30
I really hope this helped you
To solve 3 3/5 x (-8 1/3), we convert the mixed numbers into improper fractions, multiply them, and simplify to get the answer -30.
The student is asking to perform multiplication between a mixed number and a mixed number with a negative sign. To compute 3 3/5 x (-8 1/3), we first convert the mixed numbers into improper fractions. The number 3 3/5 can be converted to 18/5 (since 3*5 + 3 = 18) and -8 1/3 can be converted to -25/3 (since -8*3 + 1 = -25). Multiplying these two improper fractions gives us (18/5) * (-25/3). To multiply fractions, we multiply the numerators together and the denominators together, giving us -450/15. Simplifying this fraction, we get the final answer, which is -30.
Help URGENT! I WILL MARK BRAINLIEST!!!!!!!! JUST HELP MR FIND THE ANSWER OF THE PROBLEM IN THE IMAGE ABOVE!!!!! Worth 20 points!!!
Answer: -8n^4 + 3n^2
(The ^ is the exponent)
Which is equivalent to ?
I do not see an illustration.
16 POINTS!
WILL GIVE BRAINLIEST!
A class tracked the hours each student played games per month. Answer the questions below.
Based on the data in the line plot, show all work to calculate the following:
a) The mean
b) The median
c) The mode
d) What percentage of the students play video games for more than 4 hours in a month?
Answer: The mean
Step-by-step explanation: a) The mean:
To find the mean, we just simply need to add the hours spent by the students playing games and divide by the number of hours.
Mean = = 2.85
b) The median:
We will arrange the number of hours for in ascending order and the middle value will be the median.
Median = 3
c) The mode:
Mode is the number which occurs most frequently. So in this case Mode = 2, 3.
d)Percentage of the students play video games for more than 4 hours in a month = = 45%
A square piece of gold has an area of 36 square millimeters. How long is each is each side?
Answer:
9
Step-by-step explanation:
What you're going to do is
-take the area and divide it by the amount of sides (a square has 4)
36/4=9
Given: m∠ELG = 124°
Prove: x = 28
Answer:
Angle addition postulate and 2x=56
Step-by-step explanation:
The value of x is 28 degree.
What is linear pair?Linear pair of angles are formed when two lines intersect each other at a single point.
Given:
m∠ELG = 124
as, m∠ELG and m∠ELD are in linear pair.
So, 124 + 2x =180
2x =56
x -28
Hence, the value of x is 28 degree
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10 Points! Drag the tiles to the correct boxes to complete the pairs.
Match each expression to the correct verbal description.
The answers are:
First box: 7 times the cube of the sum of x and 8
Second box: 8 added to the cube of 7x.
Third box: 8 added to 7 and x cubed.
Fourth box: the cube of the sum of 7x and 8.
Why?We are given the expression and we need to macth to the correct verbal description, so we have:
First box:
[tex]7(x+8)x^{3}[/tex]
It's 7 times the cube of the sum of x and 8
Second box:
[tex](7x)^{3}+8[/tex]
We have that "7x" is cubed and then, added to 8, so, it's 8 added to the cube of 7x.
Third box:
[tex]7x^{3}+8[/tex]
We have "7" times "x" cubed and added to 8, so it's 8 added to 7 and x cubed.
Fourth box:
[tex](7x+8)x^{3}[/tex]
We have "7x" added to 8, and the expression is cubed, so, it's the cube of the sum of 7x and 8.
Have a nice day!
The average of six numbers is 4. If the of two of those numbers is 2, what is the average of the other four numbers?
Answer:
5
Step-by-step explanation:
total sum of the 6 numbers
= 4 ×6
= 24
sum of numbers without the two 2s
= 24 - 2(2)
= 20
average of other 4 numbers
= 20 ÷ 4
= 5
The average of the other four numbers is 5.
How to find the average?
The average of six numbers is 4. If the of two of those numbers is 2.
The total sum of the 6 numbers
= 4 ×6
= 24
The sum of numbers without the two 2s
= 24 - 2(2)
= 20
The average of other 4 numbers
= 20 ÷ 4
= 5
Hence, The average of the other four numbers is 5.
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Help please !!!!! Math 3
Answer:
A
Step-by-step explanation:
The degree of a polynomial is determined by the largest exponent in the terms of the polynomial. The leading coefficient is the coefficient of the term with the largest exponent.
Given
f(x) = 2x³ + 2x² - [tex]\frac{1}{x}[/tex]
The term - [tex]\frac{1}{x}[/tex] means that f(x) is not a polynomial
Since terms with division by a variable are not allowed.
A wooden board in the shape of a rectangular prism measures 1.5 meters by 0.75 meter by 0.2 meter and has a mass of 146.25 kilograms.
What is the density of the board?
Enter your answer in the box.
kg/m³
Answer:
650 kg/m³
Step-by-step explanation:
The density is the ratio of mass to volume. The volume is the product of the dimensions of the prism.
density = (146.25 kg)/((1.5 m)(0.75 m)(0.2 m)) = 146.25/0.225 kg/m³
= 650 kg/m³
Answer:
650 kg/m³
Step-by-step explanation:
calculate the volume of each geometric shape:
a) cylinder with radius of 5 inches and height of 3 inches.
b) sphere with diameter of 12 inches.
Answer:
a) 235.62in³
b) 904.78in³
Step-by-step explanation:
a) The formula to find the volume of a cylinder is:
[tex]V = \pi r^2h[/tex]
We are given that r = 5 and h = 3, so we can just plug in and solve:
[tex]V = \pi(5)^2(3) = 235.62in^3[/tex]
b) The formula to find the volume of a sphere is:
[tex]V = \frac{4}{3}\pi r^3[/tex]
We are given that the diameter is 12in, which means that the radius (r) must be 6in (half the diameter). Now, we can plug in and solve:
[tex]V = \frac{4}{3}\pi (6)^3 = 904.78in^3[/tex]
the equation y=-3x^2 describes a parabola what way does the parabola open
Answer:
Downwards.
Step-by-step explanation:
The coefficient of x^2 is negative (-3) so it opens downwards. All values of x will be 0 or negative.
1.
A photo of a painting has a scale of 3 inches = 2 feet. If the photo is 7.5 inches long, how many feet long is the painting?
45
11.25
5
1.25
Divide the total inches by the scale inches:
7.5 / 3 = 2.5
Multiply that by the scale feet:
2.5 x 2 = 5 feet.
Answer: 5
Step-by-step explanation:
Find the area of the kite QRST. HELP PLEASE!!!
A. 90m^2
B. 108m^2
C. 216 m^2
D. 135 m^2
ANSWER
D. 135 m^2
EXPLANATION
The area of a kite is half the product of the diagonals.
The first diagonal is
9m+6m=15m
Note that the vertical diagonal is the axis of symmetry of the kite.
This diagonal bisect the kite
Therefore the second diagonal is
2(9m)=18m
The area of the kite
[tex] = \frac{1}{2} \times 18 \times 15[/tex]
[tex] = 9 \times 15[/tex]
[tex] = 135 {m}^{2} [/tex]
Answer:
[tex]A_{T}=135 m^{2[/tex]
Step-by-step explanation:
Hello
To solve this problem we can divide the kite into simpler geometric figures to find its area, we have four triangles
the area of a triangle =(b*h)/2
b is the base and his the heigth
Step 1
triangle 1 (LEFT UP)
[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{1} =40.5\ m^{2}[/tex]
Step 2
triangle 2 (RIGHT UP)
[tex]b=9\ m\\\ h= 9\ m\\A=\frac{9 m* 9m}{2}\\\\A_{2} =40.5\ m^{2}[/tex]
Step 3
triangle 3 (LEFT DOWN)
[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{3} =27\ m^{2}[/tex]
Step 4
triangle 4 (RIGHT DOWN)
[tex]b=9\ m\\\ h= 6\ m\\A=\frac{9 m* 6m}{2}\\\\A_{4} =27\ m^{2}[/tex]
Step 5
Total Area
the total area is
[tex]A_{T}=A_{1}+A_{2}+A_{3}+A_{4} \\A_{T}=(40.5+40.5+27+27)m^{2} \\A_{T}=135 m^{2}[/tex]
Have a great day
Two
coins
are
flipped
to
decide
who
has
to
do
the
chores.
If
two
heads
are
flipped,
Matt
has
to
do
the
chores.
If
two
tails
are
flipped,
Mark
has
to
do
the
chores.
If
neither
of
these
results
is
met,
they
flip
both
coins
again.
a. How
many
different
outcomes
are
there
after
flipping
both
coins?
b. What
is
the
probability
that
Matt
has
to
do
chores?
c. What
is
the
probability
that
Mark
has
to
do
chores?
d. Is
the
method
of
decision
fair?
e. What
is
the
likelihood
that
they
must flip again?
Answer:
Step-by-step explanation:
If you flip coins, you can get,
HT TH HH TT
There are 4 possible outcomes.
Out of these 4, Matt has to do chores if two heads are flipped. It is 1/4 chance.
Out of these 4, Mark has to do chores if two tails are flipped. Again, 1/4 chance.
The method of decision is far since both guys have the same chance of being picked to do chores.
To flip again, they would have to get either HT or TH out of the 4 choices. So 2/4=1/2 is the likeihood they must flip again.
12 Times 15
My calculator said it was 160
Answer:
False
Step-by-step explanation:
12 × 15 = 180
12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 180
Answer:
180.
Step-by-step explanation:
Something wrong there. Mine says 180.
12 * 15 = 12*10 + 12*5
= 120 + 60
= 180.
Find the zeros of the function. y=1/2(2x+5)(x+4)
I think the answers are X=-2.5 and X=-4 but I'm not sure about the -2.5 Pls Help
0=1/2(2x²+13x+20)
0=x²+6,5x+10
[tex]x = \frac{ - 6.5 + \sqrt{2.25} }{2} \\ x = - 2.5 \\ x = - 4[/tex]
Answer:
x = - 2.5, x = - 4
Step-by-step explanation:
To find the zeros, set y = 0, that is
[tex]\frac{1}{2}[/tex](2x + 5)(x + 4) = 0
Equate each of the factors to zero and solve for x
2x + 5 = 0 ⇒ 2x = - 5 ⇒ x = - 2.5
x + 4 = 0 ⇒ x = - 4
Answers choices
<4
<3
<1
<2
Answer:
4
Step-by-step explanation:
An angle of depression is measured from the horizontal downwards
From the given diagram this is represented by angle 4
The point (2, –4) is reflected across the line y = –1. What are the coordinates of the image?
ANSWER
The coordinates of the image are (2,2)
EXPLANATION
The mapping for a reflection across the line y=k is :
[tex](x,y)\to (x,2k-y)[/tex]
We want to find the image of the point (2,-4) after a reflection in the line y=-1.
In this case k=-1.
[tex](2, - 4)\to (2,2( - 1)- - 4)[/tex]
This simplifies to,
[tex](2, - 4)\to (2, - 2 + 4)[/tex]
[tex](2, - 4)\to (2, 2)[/tex]
Hence the image is (2,2)
The square of the sum of two consecutive positive even integers is 4048 more than the sum of the squares of these two numbers. Find the two numbers.
PLZZZZZ I NEED LE HELP FROM LE FELLOW STUDENTS!!!
Answer:
The numbers are 44 and 46
Step-by-step explanation:
Let
x, x+2 ----> the two consecutive positive even integers
we know that
[tex](x+x+2)^{2} =4,048+x^{2} +(x+2)^{2} \\ \\(2x+2)^{2} =4,048+x^{2} +x^{2}+4x+4\\ \\4x^{2}+8x+4=2x^{2}+4x+4,052\\ \\2x^{2} +4x-4,048=0[/tex]
Solve the quadratic equation using a graphing calculator
The solution is x=44
see the attached figure
x+2=44+2=46
therefore
The numbers are 44 and 46
7x^2/2x+6 divided by 3x-5/x+3
Answer:
[tex]\large\boxed{\dfrac{7x^2}{6x-10}}[/tex]
Step-by-step explanation:
[tex]\dfrac{7x^2}{2x+6}\div\dfrac{3x-5}{x+3}=\dfrac{7x^2}{2(x+3)}\cdot\dfrac{x+3}{3x-5}\\\\\text{cancel}\ (x+3)\\\\=\dfrac{7x^2}{2}\cdot\dfrac{1}{3x-5}=\dfrac{(7x^2)(1)}{(2)(3x-5)}\\\\\text{use the distributive property}\ a(b-c)=ab-ac\\\\=\dfrac{7x^2}{6x-10}[/tex]
What is the answer to this? I need your help!! 10 points
Answer: 6 units
Step-by-step explanation:
Area = 1/2 (base1 + base2) X height <-------- Formula for a trapezoid
24 = 1/2 (2 + 6) X h <----- We know that the area of the trapezoid is 24 units
squared and that both of the bases are 2 units and 6 units.
24 = 1/2 (8) X h <------- Add 6 + 2
24 = 4 X h <----- Half of 8 is 4
h = 6 <------ 6 X 4 = 24 , therefore the height is 6 units.
Hope this helps!
Given: circle k(O), m LM = 164°, m WK = 68°, m∠MLK = 65°. Find: m∠LMW
Answer:
The measure of angle LMW is [tex]m\angle LMW=67\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc MW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK][/tex]
substitute the given values
[tex]65\°=\frac{1}{2}[arc\ MW+68\°][/tex]
[tex]130\°=[arc\ MW+68\°][/tex]
[tex]arc\ MW=130\°-68\°=62\°[/tex]
step 2
Find the measure of arc LK
we know that
[tex]arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°[/tex] -----> by complete circle
substitute the given values
[tex]164\°+62\°+68\°+arc\ LK=360\°[/tex]
[tex]294\°+arc\ LK=360\°[/tex]
[tex]arc\ LK=360\°-294\°=66\°[/tex]
step 3
Find the measure of angle LMW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK][/tex]
substitute the given values
[tex]m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°[/tex]
Applying the inscribed angle theorem, the measure of angle LMW is found as: 67°.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that is intercepted.
Given:
m(LM) = 164°m(WK) = 68°m∠MLK = 65°Find m(MK):
m(MK) = 2(m∠MLK) (inscribed angle theorem)
Substitute
m(MK) = 2(65°)
m(MK) = 130°
Find m(LK):
m(LK) = 360° - m(LM) - m(MK) (full circle)
Substitute
m(LK) = 360° - 164° - 130°
m(LK) = 66°
Therefore:
m∠LMW = 1/2[m(LK) + m(WK) (inscribed angle theorem)
Substitute
m∠LMW = 1/2[66° + 68°]
m∠LMW = 1/2[134°]
m∠LMW = 67°
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The sum of two numbers is 13. Two times the first number minus three times the second number is one. If you let x stand for the first number and y for the second number what are the two numbers?
please and thanks!
Answer: X = 8 And Y = 5 "First Choice Letter A"
Step-by-step explanation: x + y = 13......x = 13 - y
2x - 3y = 1
2(13 - y) - 3y = 1
26 - 2y - 3y = 1
-2y - 3y = 1 - 26
-5y = -25
y = -25/-5
y = 5
x + y = 13
x + 5 = 13
x = 13 - 5
x = 8
so, x = 8 and y = 5
Which angles are vertical angles and, therefore, congruent?
a d
a g
a e
a f
Answer:
a and f
Step-by-step explanation:
Vertical angles are directly opposite each other, created by two lines intersecting.
∠A and ∠F are congruent to each other because they are vertically opposite angles. Then the correct option is D.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Vertically opposite angle - When two lines intersect, then their opposite angles are equal.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
∠A and ∠F, ∠B and ∠E, ∠C and ∠H, and ∠D and ∠G are congruent to each other because they are vertically opposite angles.
Then the correct option is D.
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Need a two step equation for number 3
so the bike costs $129, but she already has $24 saved, then she'll be saving $3 per week so let's take a peek at a table of those savings
week 1..................... total amount......... 24 + 3(1)
week 2..................... total amount......... 24 + 3(2)
week 3..................... total amount......... 24 + 3(3)
week 4..................... total amount......... 24 + 3(4)
week 5..................... total amount......... 24 + 3(5)
week w..................... total amount......... 24 + 3(w)
[tex]\bf \stackrel{\textit{total savings}}{s(x)}=\stackrel{\textit{initial amount}}{24}+\stackrel{\textit{weekly savings}}{3w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{cost of the bike}}{129}=24+3w\implies 105=3w\implies \cfrac{105}{3}=w\implies 35=w[/tex]
Answer:
24 + 3x = 129
35 weeks
Step-by-step explanation:
She already has 24 dollars saved, but will save 3 dollars every week. Use x to represent the number of weeks. In total she will save 129.
Solve for x using the equation:
24-24 + 3x = 129-24
3x = 105
3x/3 = 105/3
x= 35
What is the area of the scalene triangle shown (ABC), if AO = 10 cm, CO = 2 cm, BC = 5 cm, and AB = 12.20 cm? (Triangle AOB is a right triangle.)
Answer:
The area of triangle ABC is [tex]25\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of triangle ABC is equal to the area of triangle ABO minus the area of triangle ACO
see the attached figure to better understand the problem
step 1
Find the area of triangle ABO
The area is equal to
[tex]A=\frac{1}{2}(AO)(BO)[/tex]
substitute values
[tex]A=\frac{1}{2}(10)(5+2)=35\ cm^{2}[/tex]
step 2
Find the area of triangle ACO
The area is equal to
[tex]A=\frac{1}{2}(AO)(CO)[/tex]
substitute values
[tex]A=\frac{1}{2}(10)(2)=10\ cm^{2}[/tex]
step 3
Find the area of triangle ABC
[tex]35\ cm^{2}-10\ cm^{2}=25\ cm^{2}[/tex]
A farmstand sells two types of grapes. the cost of green grapes can be represented by the equation Y= 1.5X, where Y is the total cost for X pounds. the graph represents the cost of black grapes which statement must be true?
A. Three pounds of green grapes cost $6.00.
B. Black grapes cost less per pound than green grapes l.
C. Black grapes cost more per pound than green grapes.
D. Two pounds of black grapes cost $3.00.
PLEASEEEE HELP
Answer:
C. Black grapes cost more per pound than green grapes.
Step-by-step explanation:
Verify each statement
A. Three pounds of green grapes cost $6.00
The statement is False
Because
For x=3 pounds
y=1.5x
y=1.5(3)=$4.5
B. Black grapes cost less per pound than green grapes
The statement is False
Because
For x=1 pound
The green grapes cost ----> y=1.5(1)=$1.5
Observing the graph
For x=1 pound
The black grapes cost $2
C. Black grapes cost more per pound than green grapes.
The statement is True
D. Two pounds of black grapes cost $3.00.
The statement is False
Because
Observing the graph
Two pounds of black grapes cost $4
An equation is formed of two equal expressions. The third statement is true.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
A.) The cost of a pound of green grapes is,
Y = 1.5X = 1.5×3 = 4.5
Hence, the first statement is false.
B.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the second statement is false.
C.) The cost of a pound of green grapes is $1.5, while the cost of a pound of black grapes is $2. Thus, the third statement is true.
D.) As per the graph, the cost of 2 pounds of grapes is $4. Thus, the fourth statement is wrong.
Hence, the third statement is true.
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