Answer:
1176 Combinations
Step-by-step explanation:
As mentioned in the question, there are total 8 boys and 7 girls.
Our objective is to create a team with 5 boys and girls each.
To select 5 boys out of 8, we will use combination.
=> 8C5 = [tex]\frac{8!}{5!(8-5!)}[/tex]
=> [tex]\frac{8.7.6.5!}{5!.3!}[/tex]
=> [tex]\frac{8.7.6}{6}[/tex]
=> 56
Similarly,
5 girls are selected using 7C5
=> 21
Therefore, the total combination of players are 56 * 21 = 1176
Identify the area of the rhombus. HELP PLEASE!!
Answer:
A = (x^2 - 2x - 8) m^2
Second option
Step-by-step explanation:
Area of rhombus = 1/2 d1 * d2
= 1/2(2x+4)(x-4)
= 1/2 (2x^2 -8x + 4x - 16)
= 1/2 (2x^2 - 4x - 16)
= x^2 - 2x - 8
1. the domain set of C = {( 2, 5), (2, 6), (2, 7)} {2} 2. the range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)} domain = range = {all real numbers} 3. the range and domain of F = {(x, y ) | x + y =10} domain = {all real numbers}: range = {y: y = 3} 4. the range and domain of P = {(x, y ) | y = 3} {3, 4, 5, 6}
For the given sets, the domain of set C is {2}, and its range is {5, 6, 7}. Set E has both domain and range as {3, 4, 5, 6}.
A set of ordered pairs is defined as a relation. The domain of a relation is the set of all the first elements of the ordered pairs, and the range is the set of all the second elements. Let's look at the listed sets and determine their domains and ranges.
For set C = {( 2, 5), (2, 6), (2, 7)}, the domain is {2}, because 2 is the only first element in all the pairs. The range for set C is {5, 6, 7} since those are all the second elements in the pairs.The range of set E = {(3, 3), (4, 4), (5, 5), (6, 6)} is the set of y-values or second elements of the ordered pairs, which is {3, 4, 5, 6}. Since each pair has the same x and y values, the domain of E is also {3, 4, 5, 6}.For the relation F = {(x, y) | x + y = 10}, if the domain is all real numbers, then the range must also include all real numbers that can be paired with a number from the domain to sum up to 10.For relation P = {(x, y ) | y = 3}, regardless of the x values, if y is always 3, then the range is {3}. The domain can include any real number as x, but the specific domain provided is {3, 4, 5, 6}.A function is a special type of relation where each element of the domain is associated with exactly one element in the range. This condition is also known as the vertical line test when graphing the relation on a coordinate plane.
Ummm Hey,I don't know the answer for this question,when I solve the problem my answer always 6 but the real answer is 2 so I need help right now.
umm ok then its 2...
What are the zeros of the function? f(x)=x(x−2)(x+6)
Select each correct answer.
−6
−2
0
2
6
Answer:
-6,0,2
Step-by-step explanation:
f(x)=x(x−2)(x+6)
To find the zeros of the function, set the function equal to zero
0 =x(x−2)(x+6)
Using the zero product property
x=0 x-2 =0 x+6=0
Solve each equation
x=0 x=2 x=-6
There are three zero's
-6,0,2
A 2012 Gallup survey of a random sample of 1014 American adults indicates that American families spend on average $151 per week on food. The report further states that, with 95% confidence, this estimate has a margin of error of ±$7 . (a) This confidence interval is expressed in the form: “estimate ± margin of error.” What is the range of values (lower bound, upper bound) that corresponds to this confidence interval? (Enter your answers as a whole number.) lower bound: upper bound: (b) What is the parameter captured by this confidence interval? What does it mean to say that we have " 95% confidence" in this interval? The parameter captured by this interval is the population mean weekly spending on food ???? for all American adults. " 95% confidence" means that this interval was found using a procedure that produces correct results 95% of the time. The parameter captured by this interval is the populations weekly spending on food ???? for all American adults. " 95% confidence" means that this interval is correct 95% of the time. The parameter captured by this interval is the population mean weekly spending on food ???? for all American adults. " 95% confidence" means that this interval represents 95% of the population of American adults. The parameter captured by this interval is the populations weekly spending on food ???? for all American adults. " 95% confidence" means that this interval was found using a procedure that produces correct results 95% of the time.
Answer:135.9
Step-by-step explanation:you just have to multiply
PLEASE HELP!
What is the measure of angle C?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
[tex] R = 10.39^\circ [/tex]
Step-by-step explanation:
Since you have the lengths of all the sides, you can use sine, cosine, or tangent to find the answer. Let's use the tangent ratio.
For angle C, AB is the opposite leg, and BC is the adjacent leg.
[tex] \tan C = \dfrac{opp}{adj} [/tex]
[tex] \tan C = \dfrac{22}{120} [/tex]
[tex] C = \tan^{-1} \dfrac{22}{120} [/tex]
[tex] C = 10.39^\circ [/tex]
Applying the tangent ratio (tan ∅ = opposite length/adjacent length), the measure of angle C, to the nearest hundreth, is: 10.39°
What is the Tangent Ratio?In a given right triangle, the tangent ratio is given as, tan ∅ = opposite length/adjacent length.
Given the following:
∅ = ∠COpposite = 22Adjacent = 120Applying the tangent ratio:
tan C = 22/120
m∠C = tan^(-1)(22/120)
m∠C = 10.39° (nearest hundreth)
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I’ll give brainliest!! Help!! Paige has $213.84 deducted from her paycheck for her 401(k). Her gross paycheck amount is $1944. What percent of her gross paycheck amount does she have deducted for her 401(k)
9%
11%
13%
Answer:
11 %
Step-by-step explanation:
Percent = Amount deducted/original amount × 100 %
= 213.84/1944 × 100 %
= 11.00 %
Paige has 11.00 % of her paycheck deducted for her 401(k).
Answer:
11%
Step-by-step explanation:
A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 206 like rock, 161 like country, and 118 like jazz. Moreover, 30 like rock and country, 27 like rock and jazz, 22 like country and jazz, and 11 like all three types of music. What is the probability that a randomly selected student likes neither rock nor country? Note: A Venn diagram may be useful here.
Answer:
163/500 = 0.326
Step-by-step Explanation:
Drawing a Venn diagram for this, we will have 3 circles. One will represent rock, one will represent country, and one will represent jazz.
There are 11 students that like all 3 types of music. This means the number 11 goes in the intersection of all 3 circles.
There are a total of 30 students that like rock and country; taking out the 11 that like all 3, this leaves 30-11 = 19 students in the intersection of just rock and country.
There are a total of 27 students that like rock and jazz; taking out the 11 that like all 3, this leaves 27-11 = 16 students in the intersection of just rock and jazz.
There are a total of 22 students that like country and jazz; taking out the 11 that like all 3, this leaves 22-11 = 11 students in the intersection of just country and jazz.
There are 206 students that like rock; taking out the 11 that like all 3, the 19 that like rock and country, and the 16 that like rock and jazz, we have
206-(11+19+16) = 206-(46) = 160 in just rock.
There are 161 students that like country; taking out the 11 that like all 3, the 19 that like rock and country, and the 11 that like country and jazz, we have
161-(11+19+11) = 161-(41) = 120 in just country.
There are 118 students that like jazz; taking out the 11 that like all 3, the 16 that like rock and jazz, and the 11 that like country and jazz, we have
118-(11+16+11) = 118-38 = 80 in just jazz.
This leaves
500-(80+120+160+11+11+19+16) = 500-417 = 83 students that like none of the 3 types of music.
This means for the probability that a student likes neither rock nor country, they either like just jazz or none of the 3; this is (83+80)/500 = 163/500 = 0.326.
The probability that a randomly selected student likes neither rock nor country is;
P(R' ∩ C') = 0.326
Let us denote them as follows;
Number that like rock music be R
Number that like Country music be C
Number that like Jazz music be J
Thus, as we are given we have;
R = 206
C = 161
J = 118
R ∩ C = 30 - 11 = 19
R ∩ J = 27 - 11 = 16
C ∩ J = 22 - 11 = 11
R ∩ C ∩ J = 11
Thus, number that liked only jazz music is;n(only jazz) = J - [(R ∩ J) + (C ∩ J) + (R ∩ C ∩ J)]
n(only jazz) = 118 - (16 + 11 + 11)
n(only J) = 80
Number of students that liked only Rock music;n(only Rock) = R - [(R ∩ C) + (R ∩ J) + (R ∩ C ∩ J)]
n(only Rock) = 206 - (19 + 16 + 11)
n(only R) = 160
Number of students that liked only country music;n(only country) = C - [(R ∩ C) + (C ∩ J) + (R ∩ C ∩ J)]
n(only country) = 161 - (19 + 11 + 11)
n(only C) = 120
Now, the number of students that like neither of the 3 music is;
A' ∩ B' ∩ C' = 500 - [(R ∩ C) + (R ∩ J) + (C ∩ J) + (R ∩ C ∩ J) + n(only J) + n(only R) + n(only C)]
⇒ 500 - (80 + 120 + 160 + 19 + 16 + 11 + 11)
⇒ A' ∩ B' ∩ C' = 83
Thus, number of students that likes neither rock nor country is;
n(A' ∩ B') = (A' ∩ B' ∩ C') + n(only C)
n(A' ∩ B') = 83 + 80
n(A' ∩ B') = 163
Thus, probability that a randomly selected student likes neither rock nor country = 163/500 = 0.326
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Yadira's mom is buying hot dogs and hot dog buns for the family barbecue. Hot dogs come in packs of 1 and hot dog buns come in packs of 9. The store does not sell parts of a pack and Yadira's mom wants the same number of hot dogs as hot dog buns. What is the smallest total number of hot dogs that Yadira's mom can purchase?
Answer:
Nine
Step-by-step explanation:
The smallest number of buns is one pack or 9 buns.
If there is one hot dog per bun, the smallest number of hot dogs is nine.
Answer:
36 hotdogs
Step-by-step explanation:
Mathematically, we say that 36 is the least common multiple of 12 and 9. In math notation this looks like:
lcm of 9 and 12 is 36
The smallest total number of hot dogs that Yadira's mom can purchase is , 36.
The following system has a solution: x=10, y=-3, z=14
In this problem, we have the following System of Three Equations in Three Variables, so our goal is to determine whether [tex]x=10, \ y=-3, \ z=14[/tex] is the solution to this system, that is, the ordered triple [tex]P(x,y,z)[/tex] where three planes intersect.
The easier way to find the answer is to plug in the x, y and z values in the equations and figure out whether the equations satisfy the solutions. Then:
[tex]First \ Equation: \\ \\ 3(10)+7(-3)-14=-5 \\ \\ It \ satisfies \ the \ first \ equation \\ \\ \\ Second \ Equation: \\ \\ 9(10)-(-3)-4(14)=37 \neq 17 \\ \\ It \ doesn't \ satisfy \ the \ second \ equation[/tex]
STOP HERE! Since the x, y an z values doesn't satisfy the second equation, the [tex]x=10, \ y=-3, \ z=14[/tex] is not the solution to the system of equations.
Factor completely, then place the factors in the proper location on the grid. 2a 2 + 2b 2 - 5ab
Answer:
[tex](2a-b)(a-2b) = 0[/tex]
Step-by-step explanation:
We can use the quadratic formula to factor this expression
For a quadratic function of the form:
[tex]na ^ 2 + ma + c[/tex]
Whe have:
[tex]2a^2 + 2b^2 - 5ab[/tex]
Then:
[tex]n = 2\\\\m = -5b\\\\c = 2b^2[/tex]
The quadratic formula is:
[tex]a =\frac{-m\±\sqrt{m^2-4nc}}{2n}[/tex]
Then the solutions are:
[tex]a= \frac{-(-5b)\±\sqrt{(-5b)^2 -4(2)(2b^2)}}{2(2)}\\\\a = \frac{5b\±\sqrt{25b^2-16b^2}}{4}\\\\a = \frac{5b\±3b}{4}\\\\a_1=2b\\\\a_2 =\frac{b}{2}[/tex]
Finally The factored expression is:
[tex]a-\frac{b}{2} = 0\\\\2a -b = 0\\\\[/tex]
and
[tex]a-2b= 0[/tex]
Then
[tex]2a^2 + 2b^2 - 5ab = (2a-b)(a-2b) = 0[/tex]
What is the sum of the given polynomials in standard from? (x^2 -3x) + (-2x^2+5x-3)
The pic will help you
Good luck:))
A circle has a circumference of 11{,}30411,30411, comma, 304 units. What is the diameter of the circle?
Answer:
The diameter of the circle is [tex]3,600\ units[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
In this problem we have
[tex]C=11,304\ units[/tex]
assume [tex]\pi=3.14[/tex]
substitute the values and solve for D
[tex]11,304=(3.14)D[/tex]
[tex]D=11,304/(3.14)=3,600\ units[/tex]
Answer: 3,600 units
Step-by-step explanation:
Given a triangle with angles of 23, 90, 67, what type of triangle is it: acute, equiangular, obtuse, or right?
Answer:
It is a right triangle because if it contains a 90 degree angle (a right angle), it's a right triangle.
Step-by-step explanation:
It would be a right angled triangle because all triangles with a 90 degree angle are right angle triangles : 90 degrees is a right angle
Which is NOT a major expense category?A) housingb) transportationc) electricityd) food???
Answer: the one that is not a magor epense catgortuy is c : transportation
Step-by-step explanation:
the answer is: C) transportation
A company advertises that there are an average of 25 grams of potato chips in each bag of chips. A consumer group has collected a sample and wants to perform a test to see if the company is providing less than it advertises. H0: μ = 25 Ha: μ < 25 Which type of significance test should be used for this situation?
Answer:
one sample t-test will be appropriate in this case
Step-by-step explanation:
We are carrying out a hypothesis test of the mean with the population standard deviation being unknown. We shall estimate the population standard deviation with the sample equivalent, s in determining the value of the test-statistic.
Answer:
A left-tailed test
Step-by-step explanation:
Examine the right triangle. What is the length of the hypotenuse, c?
Answers are in the pic
a^2+b^2=c^2 <----- the equation to find out sides for a right triangle
Every right triangle follows the pythagorean theorem: given the legs [tex]a[/tex] and [tex]b[/tex] and the hypothenuse [tex]c[/tex] we have
[tex]a^2+b^2=c^2 \implies c=\sqrt{a^2+b^2}[/tex]
In your case, a=3 and b=5, so we have
[tex]c=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}[/tex]
Which equation is an identity?
8 – (6v + 7) = –6v – 1
5y + 5 = 5y – 6
3w + 8 – w = 4w – 2(w – 4)
6m – 6 = 7m + 9 – m
Answer:
Equation 3
Step-by-step explanation:
An identity is, simply put, an equation that is always true. 1 = 1, 2 = 2, and x = x are all examples of identities, as there's no case in which 1 ≠ 1, 2 ≠ 2, and x ≠ x. Essentially, if we can manipulate and equation so that we end up with the same value on either side, we've found an identity. Let's run through and try to solve each of these equations to see which one fulfills that condition:
8 - (6v + 7) = -6v - 1
8 - 6v - 7 = -6v - 1
1 - 6v = -6v - 1
1 = -1
This is clearly untrue. Moving on to the next equation:
5y + 5 = 5y - 6
5 = -6
Untrue again. Solving the third:
3w + 8 - w = 4w - 2(w - 4)
2w + 8 = 4w - 2w + 8
2w + 8 = 2w + 8
If we created a new variable z = 2w + 8, we could rewrite this equation as
z = z, which is always true. We can stop here, as we've now found that equation 3 is an identity.
The identity among the given equations is 3w + 8 - w = 4w - 2(w - 4), as it simplifies to a true statement 2w + 8 = 2w + 8 for all values of w.
Explanation:The student asked which equation is an identity. To find the identity, we simplify and solve each equation:
8 – (6v + 7) = –6v – 1: When we simplify, we get 8 - 6v - 7 = -6v - 1, which further simplifies to 1 - 6v = -6v - 1. Adding 6v to both sides, we have 1 = -1, which is not true, so it's not an identity.
5y + 5 = 5y – 6: Simplifying this we simply subtract 5y from both sides, and we are left with 5 = -6, which is not true, so this is not an identity either.
3w + 8 – w = 4w – 2(w – 4): Simplifying we get 2w + 8 = 4w - 2w + 8, which reduces to 2w + 8 = 2w + 8. This is true for all values of w, therefore, this is an identity.
6m – 6 = 7m + 9 – m: Simplifying gives us 6m - 6 = 6m + 9. Subtracting 6m from both sides, we get -6 = 9, which is not true and thus not an identity.
The identity is the equation 3w + 8 – w = 4w – 2(w – 4) because it simplifies to a true statement regardless of the value of w.
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A quadrilateral has all sides the same length and no right angels.What is the name of the quadrilateral
I think it's possibly a rhombus
There are x boys playing in the park. The number of girls playing in the park is equal to the square root of the number of boys. If the total number of boys and girls playing in the park is 42, find the number of boys. A. 36 B. 6 C. 49 D. 7
Answer:
Option A. 36
Step-by-step explanation:
Let
x-------> the number of boys
y------> the number of girls
we know that
[tex]x+y=42[/tex] -----> equation A
[tex]y=\sqrt{x}[/tex] -----> equation B
using a graphing tool to solve the system of equations
Remember that the solution is the intersection point both graphs
The solution is the point (36,6)
see the attached figure
therefore
The number of boys is 36
A yield sign measures 30 inches on all three sides. what is the area of the sign
Answer:
450
Step-by-step explanation:
To find an area of the triangle, you must first multiply the base and the height.
△ABC is a right triangle with right angle at ∠B . AB=34 cm AC=55 cm What is the measure of ∠C , to the nearest degree? Enter your answer in the box.
Answer:
38°
Step-by-step explanation:
One side length is 34cm and the hypotenuse is 55cm. Used SOH-CAH-TOA to find what trig function to use. You have the opposite side and the hypotenuse, so use sine. SinC = 34/55. You can input this into a calculator as 34/55 and press sin^-1 to get the angle value, which is approximately 38°.
Answer:
△ABC is a right triangle with right angle at ∠B.
AB=34 cm
AC=55 cm
What is the measure of ∠C, to the nearest degree?
Enter your answer in the box.
38°
Step-by-step explanation:
The area of rectangle bathroom floor is 53 5/8 feet. If the bathroom is 6 1/2 feet wide, what is the length
Answer:
The length is [tex]8\frac{1}{4}\ ft[/tex]
Step-by-step explanation:
we know that
The area of a rectangle is equal to
[tex]A=LW[/tex]
In this problem we have
[tex]A=53\frac{5}{8}\ ft^{2}[/tex]
[tex]W=6\frac{1}{2}\ ft[/tex]
convert to an improper fraction
[tex]A=53\frac{5}{8}=\frac{53*8+5}{8}=\frac{429}{8}\ ft^{2}[/tex]
[tex]W=6\frac{1}{2}=\frac{6*2+1}{2}=\frac{13}{2}\ ft[/tex]
substitute in the formula and solve for L
[tex]\frac{429}{8}=L\frac{13}{2}[/tex]
[tex]L=\frac{429*2}{8*13}=\frac{858}{104}\ ft[/tex]
Convert to mixed number
[tex]L=\frac{858}{104}=\frac{832}{104}+\frac{26}{104}=8\frac{1}{4}\ ft[/tex]
The length of the bathroom floor in this case is 8 1/4 feet.
The area of a rectangle is calculated by multiplying its length by its width. In this case, with the bathroom floor having an area of 53 5/8 square feet and a width of 6 1/2 feet, we can find the length as follows:
Area = Length x Width
53 5/8 = Length x 6 1/2
Length = 53 5/8 / 6 1/2
Length = 8 1/4 feet
Therefore, the length of the bathroom floor is 8 1/4 feet.
Find the value of y. m angle 1 = 4y+22
I believe y = 41
Hope this helped!
The answer would be -21/4
Here’s how you solve it!
First move the variable to the left side which makes it change the sign to a negative
-4y➕1=22
Then you move the constant to the other side and change the sign
-4y=22-1
Now you subtract
22-1=21
-4y=21
Then divide both sides by -4
Then you are left with your answer
Y=-21/4
Hope this helps! :3
If Logan's family can drive 23 1/8 miles on 1 gallon of gas,how far can they drive on 17 gallons
[tex]\bf \begin{array}{ccll} miles&\stackrel{gas}{gallons}\\ \cline{1-2}\\ 23\frac{1}{8}&1\\\\ x&17 \end{array}\implies \cfrac{23\frac{1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{23\cdot 8+1}{8}}{x}=\cfrac{1}{17}\implies \cfrac{\frac{185}{8}}{x}=\cfrac{1}{17} \\\\\\ \cfrac{\frac{185}{8}}{\frac{x}{1}}=\cfrac{1}{17}\implies \cfrac{185}{8}\cdot \cfrac{1}{x}=\cfrac{1}{17}\implies \cfrac{185}{8x}=\cfrac{1}{17} \\\\\\ 3145=8x\implies \cfrac{3145}{8}=x\implies 393\frac{1}{8}=x[/tex]
Alaska is the biggest state in the United States of America , write this as a biconditional statement
Final answer:
A biconditional statement regarding Alaska's size is 'Alaska is the biggest state in the United States of America if and only if no other state in the United States has more territory than Alaska.' This statement clarifies that Alaska's status as the largest state is based on a measurable, verifiable fact.
Explanation:
A biconditional statement is a logical assertion that combines two statements into one, where one statement implies the other, and vice versa. In this context, the statement 'Alaska is the biggest state in the United States of America' can be written as a biconditional statement as follows:
'Alaska is the biggest state in the United States of America if and only if no other state in the United States has more territory than Alaska.'
This biconditional statement emphasizes the fact that Alaska's status as the largest state is contingent on the condition that all other states must have less territory. This is a fact that is verifiable and not subject to opinion, underscoring the importance of factual accuracy in research and the careful use of evidence.
Problem Eight days ago, I put 50 sheets of paper in my binder. I used the same number of sheets each day. Now I only have 2 sheets left. How many sheets of paper did I use each day?
As given,
Number of sheets of paper put in the binder 8 days ago = 50 sheets
Current number of sheets left after 8 days = 2 sheets
So, number of sheets used in 8 days = [tex]50-2=48[/tex] sheets
As it is stated that the same number of sheets are used each day, so number of sheets used per day = [tex]\frac{48}{8}=6[/tex] sheets.
Hence, 6 sheets of paper were used each day.
Answer:
6
Step-by-step explanation:
What is the solution to the system of equations? Use the substitution method. Y=?3x+12x+5y=18
The answer is
[tex]y = - 3x + \frac{18}{5} [/tex]
Bob started mowing his lawn at 9:55. It took 70 minutes. At what time did bob finish mowing?
60 minutes = 1 hour
55 + 5 = 60 70 - 5 = 65 10:00
10:00 + 60 min = 11:00 65 - 60 = 5
11:00 + 5 min = 11:05
Bob finished mowing at 11:05
a car insurance company paid 1758.90 to repair a car that has been rear ended. this was 75% towards the total cost of the repair. what was the total cost
Answer:
Step-by-step explanation:
$2345.20
The total cost price of the car is $2,345.2.
Given that, a car insurance company paid 1758.90 to repair a car that has been rear-ended. This was 75% of the total cost of the repair.
We need to find what was the total cost price of the car.
What is the cost price?The amount paid to purchase an article or the price at which an article is made is known as its cost price. The cost price is abbreviated as C.P. Selling Price: The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.
Let the total cost price be x.
Now, 75% of x=1758.90
⇒0.75×x=1758.90
⇒x=$2,345.2
Therefore, the total cost price of the car is $2,345.2.
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