The different combinations of 5 friends could possibly receive the tickets are 56.
What is combination?
A combination is a choice made from a set of distinct items in mathematics where the order of the choices is irrelevant.
The definition of a combination is "An arrangement of objects where the order in which the objects are chosen does not matter." A combination is a "selection of things" where the importance of the order of the things is negligible.
Given:
A group of 8 friends (5 girls and 3 boys) plans to watch a movie.
We have to find the different combinations of 5 friends could possibly receive the tickets.
Here there are total 8 friends.
We have to select 5 from 8 in 8C5 ways.
[tex]8_C_5 = \frac{8!}{5!*(8-5)!} \\8_C_5 = \frac{8!}{5!*3!} \\8_C_5 = \frac{6*7*8}{1*2*3}\\ 8_C_5 = 56[/tex]
Hence, the different combinations of 5 friends could possibly receive the tickets are 56.
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Darren had 20 minutes to do a three problem quiz he spent 10 1/4 minutes on question A and 5 4/5 minutes on question B how much time did he have left for question C
Adding the times on A and B gets you 16 minutes and 3 seconds. 20 minutes minus 16 minutes and 3 seconds will leave you with
3 minutes, 57 seconds
In the data set shown below, what is the value of the quartiles?
{56, 58, 64, 68, 72, 75, 78}
PLEASE LOOK AT THE NUMBERS CAREFULLY
A. Q1 = 58; Q2 = 68; Q3 = 73.5
B. Q1 = 61; Q2 = 68; Q3 = 73.5
C. Q1 = 75; Q2 = 68; Q3 = 58
D. Q1 = 58; Q2 = 68; Q3 = 75
Answer:
To find the value of the quartiles, we need to first find the median of the data set. The median is the middle value of the data set, or the value that separates the lower half of the data from the upper half. In this data set, the median is 68, as it is the middle value when the data is arranged in ascending order.
Once we have the median, we can find the first and third quartiles. The first quartile, also known as Q1, is the median of the lower half of the data set, and the third quartile, also known as Q3, is the median of the upper half of the data set. In this data set, the lower half of the data is {56, 58, 64}, and the upper half of the data is {72, 75, 78}. The median of the lower half is 58, and the median of the upper half is 75.
Therefore, the value of the quartiles is Q1 = 58, Q2 = 68, and Q3 = 75.
Option D, Q1 = 58; Q2 = 68; Q3 = 75, is the correct answer.
Step-by-step explanation:
tina spends 65$ on supplies to start a dog washing business. she earns $21 every time she washes a dog. what is w, the number of dogs tina must wash to earn a profit of $40
By solving an equation, we know that the value of w or the number of dogs Tina must wash to earn a profit of $400 is 5.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, using the information given, the equation can be formed as:
21w - 65 = 40
Now, solve for the subject w to get the value of w as follows:
21w - 65 = 40
21w = 40 + 65
21w = 105
w = 105/21
w = 5
Therefore, by solving an equation, we know that the value of w or the number of dogs Tina must wash to earn a profit of $400 is 5.
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The equation y = ax^2 describes a parabola. If the value of a is positive, which
way does the parabola open?
• A. Up
• B. Left
• C. Down
• D. Right
Solve for the legs of the 45-45-90 triangle.
Answer:
1st answer option
Step-by-step explanation:
the 45° side angles make this an isoceles triangle (both legs are equally long).
therefore, x = y.
Pythagoras gives us
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), and a and b being the legs.
so, we have
(5 × sqrt(2))² = x² + y² (remember, x = y)
(5 × sqrt(2))² = x² + x²
25 × 2 = 2x²
25 = x²
x = 5
because of x = y
y = 5
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In the diagram, the measures of ∠2, ∠6, and ∠7 are 25°. The measure of ∠1 is 155°. Are lines c and d parallel?
Answer: Yes
Step-by-step explanation:
Parallel means that the lines are a constant distance away from each other and they never touch. As you can see lines C and D never touch.
The Lines D and C are Parallel since Parallel lines never touch
Hope this helps!
A truck driver is driving from Nome, Alaska, to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (2 points)
Part B: Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points)
Part C: In January 1989, the temperature in Nome, Alaska, dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not? (4 points)
(A) The required inequality is, -40°F < x < 140°F.
(C) The gas has freezing point of -40°F, that means below that temperature the gas will freeze.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
(A) Let the liquid range is from -40°F to 140°F.
Let x be the range.
So, the required inequality is,
-40°F < x < 140°F
(B) The graph of inequality is attached below.
(C) Since the gas has freezing point of -40°F, that means below that temperature the gas will freeze.
(-49°F < 40°F)
Hence, the gas will freeze.
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PLS LOOK AT PIC AND HELP ME!! I’m being timed pls help :((
What’s the difference between fundamental theorem of calculus part 1 and 2? (Simple explanation pls bc I don’t understand)
The difference between fundamental theorem of calculus part 1 and 2 is explained below:
What is fundamental theorem of calculus?The basic theorem of calculus is a theorem that connects the ideas of differentiating and integrating functions. A constant value that relies on where one begins to compute area makes the two procedures the inverses of one another. The relationship between the integral and derivative is established by the calculus fundamental theorem. Simply put, it says that the height of the area at a point x equals the rate of change of the area under the curve up to that point. We can find definite integrals with the aid of this theorem.
The connection between the integral and the derivative is demonstrated in The Fundamental Theorem of Calculus, Part 1. Take note. A definite integral can be assessed in terms of an antiderivative of its integrand using the Fundamental Theorem of Calculus, Part 2. This formula will calculate the total area under a curve.
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a club has 6 men and 2 women. a committee of two people is selected randomly. Find the expected number of women on the committee
The required expected number of women on the committee is 1/2 or 0.5.
The expected number of women on the committee can be found by calculating the probability that a woman is selected for the committee and then multiplying that probability by the number of people on the committee.
There are a total of 6 + 2 = 8 people in the club, and the committee has 2 people.
Given the committee is selected randomly, the probability that a particular person is selected for the committee is 2/8 = 1/4.
There are 2 women in the club, so the probability that a woman is selected for the committee is 2/8 = 1/4.
The expected number of women on the committee is the probability that a woman is selected for the committee multiplied by the number of people on the committee, which is (1/4) * 2 = 1/2.
Thus, the expected number of women on the committee is 1/2 or 0.5.
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Find the measure of ∠ 1
a 180°
b 30°
c 60°
d 120°
Answer:
120
Step-by-step explanation:
Using the theorems of geometry, you know that all angles of a triangle add up to 180º. We can use an equation after looking at both angles, and the total:
30 + 30 + x = 180
60 + x = 180
x = 180 - 60
x = 120
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Which of the following statements about BC and BD is true?
Answer: Its. C. Line BC is longer than line BD
Step-by-step explanation:
Type the correct answer in the box. Spell all words correctly. Consider these four statements about a line that passes through two points on a plane. Statement A: The line is on a different plane from the points. Statement B: The line lies on only one plane. Statement C: The line is on the same plane as the points. Statement D: The line passes through only one plane. Only statement is true. Reset Next
Statement C is correct
The line lies on the same plane as the points.
What is a 3d Plane?A 3-d or three-dimensional plane is called a hyperplane.
The three axes X-axis, Y-axis, and Z-axis are mutually perpendicular to each other.
We can represent a plane in vector form using the following equation. (p — p₀) . n = 0
Let the line is passing through two points on a given plane. Then, this is the line joining the two points and so all the points lying on this line must also lie on the plane. This clearly tells that the line completely lies on the same plane as the points.
the correct option is Statement C. The line is on the same plane as the points
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toby buys a new mp3 player for the price of 45.5. what is the total amount his credit card is charged if the sales tax is 7%
(HURRY HURRY HURRY!)
A function of x is given by f(x) = 2x – 3. Which of these describes the meaning of f(-1)?
A.
The output value for the function f when x = -1.
B.
The input value for the function f when 2 is added to -3.
C.
The input value for the function f when x = -1.
D.
The output value for the function f when 2 is added to -3.
Answer:
A. The output value for the function f when x = -1.
Step-by-step explanation:
x is input.
f(x) is output.
f(-1) is the output when x = -1.
Answer:
A. The output value for the function f when x = -1.
If Triangle ABC has been translated 4 units to the right into Triangle DEF, what are the coordinates of Point E?
Triangle ABC has been translated 4 units to the right into triangle DEF. Then, the coordinates of point E is (6, -2).
What is the translation?A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
Given that, triangle ABC has been translated 4 units to the right into Triangle DEF.
From the given coordinate plane A(-8, -2), B(2, -2) and (-4, -9)
When the shape is moved towards the right by k units, then replace x with x + k.
Now,
A(-8, -2) → D(-8+4, -2)=D(-4, -2)
B (2, -2) → E(2+4, -2)=E(6, -2)
C (-4, -9) → F(-4+4, -9)=F(0, -9)
Therefore, the coordinates of point E is (6, -2).
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Solve equation:
8n-7=-12+3n
Answer:
n = -1
Subtract and isolate
To solve this problem, the first thing we have to do is regroup the terms so that we can then subtract, simplify, subtract, and finally simplify again.
But first we must know.
¿What are the equations?Equations are those mathematical equalities divided between two expressions which are called members and separated by their equal sign, in which known elements and unknown or unknown data appear, related by mathematical operations.
We solve the problem:8n - 7 = -12 + 3n8n - 7 = 3n - 128n - 7 - 3n = -125n - 7 = -125n = -12 + 75n = -5N = -1Now we must check our results.
8n -7 = -12 + 3n
8 × - 1 - 7 = -12 + 3 × - 1
- 8 - 7 = - 12 - 3
- 15 = - 12 - 3
- 15 = - 15
So, our results are correct, the answer is n = - 1
¡Hope this helped!
find the price of a toy that wholesales for 2.25 and is marked up 100% for retail
Each piece of lead for a mechanical pencil is 65 mm long. Find the total length in centimeters of the lead in a package with 25 pieces.
Answer:
cis theanswerforthequwstion
Mary says the digits in the quotient of 381.109+0.86 are 44315.
but she doesn't know where to place the decimal point. How can
Mary use number sense to place the decimal point?
The correct place to the decimal is after 4 digits, that is 4431.5
What is decimal?Decimals are the numbers, having two parts, a whole number part and a fractional part separated by a point that point is called the decimal. For example, 7.5 is a decimal number.
Given that, Mary says the digits in the quotient of 381.109÷0.86 are 44315.
but she doesn't know where to place the decimal point.
The division is 381.109/0.86
Placing the decimals in numerator and removing from denominator,
Since, in the denominator the decimal is two digits before, so multiply numerator and denominator by 100,
38110.9/86
According to rule, put the decimal point in the answer at the same place it is at in the dividend,
38110.9/86 = 4431.5
Hence, she should put decimal before digit 5.
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HELP HELP MEEEEE PLEASE Oliver is knitting a Scarf with 76 rows. He plans to knit 8 rows each week Part A Oliver drew this array to determine how long it will take for him to complete the scarf. What division sentence does the drawing show? O A 76÷8=9 OB 76÷8=9 R4 C. 76 ÷ 9 = 8 R2 D. 76 ÷ 9 = 8 R6 CHOOSE WORDS FROM THE DROP-DOWN MENUS TO EXPLAIN HOW LONG IT'LL TAKE FOR HOWEVER TO COMPLETE THE SCARF Oliver Will knit eight rows each week for A 4 B 8 C 9 weeks after that he will still have a 4 B 6 c9 Rows to knit
Answer:
Answer: C. Oliver will knit eight rows each week for nine weeks and then he will still have nine rows to knit.
Step-by-step explanation:
Use synthetic division to find the result when 2x4 - 8x³ - 3x² +28x - 3 is
divided by x-3.
you think I know
Step-by-step explanation:
bro what
Which equation correctly solves for x in △RST?
The equation that correctly solves for x in △RST is; x² + 11x - 42 = 0
How to find the lengths of similar triangles?We are given that ΔDEF ∼ △RST.
This means that ΔDEF is similar to △RST.
From the concept of similar triangles, all corresponding sides are usually in the same ratio. Thus, applying this to our given triangles, we have;
DE/RS = EF/ST = DF/RT
This means when we plug in the relevant values, we will get;
(x + 5)/12 = (x + 7)/(x + 12) = 6/(x + 6)
Thus, we can say that;
(x + 5)/12 = 6/(x + 6)
Cross multiply to get;
(x + 5)(x + 6) = 72
x² + 11x + 30 - 72 = 0
x² + 11x - 42 = 0
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Complete question is;
In the figure shown, ΔDEF ∼ △RST . Which equation can be used to find the value of x?
Sine, Cosine, Tangent question below
Answer:
3 / 5
Step-by-step explanation:
TOA-CAH-SOHTOA-CAH-SOH are 3 trigonometry ratios. They are:
TOA - tan(theta) = Opposite ÷ Adjacent
CAH - cos(theta) = Adjacent ÷ Hypotenuse
SOH - sin(theta) = Opposite ÷ Hypotenuse
SolutionWe are finding Cos(A)
Cos(A) = Adjacent ÷ Hypotenuse
= AB ÷ AC
=
[tex] \frac{30}{50} \\ = \frac{3}{5} [/tex]
Therefore Cos(A) = 3 / 5.
Which ordered pair is a solution to the inequality 3x - 4y < 16?
(-3, -3)
(0, -4)
(4, -1)
(2, -3)
Answer: (-3,-3)
Step-by-step explanation:
Sub in the numbers
3(0)-4(-4)<16
16<16 wrong
3(-3)-4(-3)<16
-9+12<16
3<16 Correct
(-3,-3)
Help answer the questions below
-----------------------------------------------------------------------------------------------------------
1. Reminder: Assume all dimensions are feet.
Task: Surround the given figure with a fence. Estimate that you will need 10% more than the actual perimeter in case of mistakes.
Cost: $26 for 4 feet of fence
Cost of Task =
----------------------------------------------------------------------------------------------------------
2. Reminder: Assume all dimensions are feet.
Task: Surround the given figure with a fence. Estimate that you will need 15% more than the actual perimeter in case of mistakes.
Cost: $25 for 4 feet of fence
Cost of Task =
-----------------------------------------------------------------------------------------------------------
3. Reminder: Assume all dimensions are feet.
Task: Surround the given figure with a fence. Estimate that you will need 20% more than the actual perimeter in case of mistakes.
Cost: $28 for 5 feet of fence
Cost of Task =
-----------------------------------------------------------------------------------------------------------
4. Reminder: Assume all dimensions are feet.
Task: Surround the given figure with a fence. Estimate that you will need 4% more than the actual perimeter in case of mistakes.
Cost: $27 for 4 feet of fence
Cost of Task =
The cost of the tasks to surround the figures with a fence, equivalent to perimeter of the fence and an extra percentage are as follows;
1. $143
2. $143.75
3. $147.84
4. $224.64
What is the perimeter of a geometric figure?The perimeter of a figure is the length of the line that surrounds the plane area covered by the figure.
1. The perimeter of the fence = 2 ft + 4 ft + 2 ft + 4 ft + 2 ft + 4 ft + (4 ft - 2 ft) = 20 ft
The perimeter needed = 110/100 × 20 ft = 22 ft
The cost of 4 feet of fence = $26
Cost per feet of fence = $26/4 = $6.5/ft
Cost of the task = 22 feet × $6.5/ft = $143
2. The perimeter of the fence = 3 ft + 3 ft + 2 ft + 3 ft + 1 ft + 2 ft + 1 ft + 2 ft + 3 ft = 20 ft
The perimeter of the fence needed = 115/100 × 20 ft = 23 ft
Cost of 4 feet = $25
Cost per ft = $25/4 = $6.25
Cost of the fencing = 23 ft × $6.25/ft = $143.75
3. The perimeter of the fence = 5 ft + 3 ft + (6 ft - 5 ft) + 2 ft + 6 ft + 2 ft + 3 ft = 22 ft
The fence needed = 120/100 × 22 ft = 26.4 ft
The cost of 5 ft of fencing = $28
The cost per feet = $28/5 ft = $5.6/ft
The cost of the fencing = 26.4 ft × $5.6/ft = $147.84
Cost of the Task = $147.84
4. The perimeter of the fence = 8 ft + 6 ft + (8 ft - 6 ft) + (8 ft - 6 ft) + 6 ft + 8 ft = 32 ft
The fencing needed = 104/100 × 32 ft = 33.28 ft
The cost for 4 feet = $27
The cost per feet = $27/4 ft = $6.75/ft
The cost of the task = 33.28 ft × $6.75/ft = $224.64
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Factor the terms below.
1. 46xyz^5
Answer:
2. 19n^8 y^3
Answer:
3. 62d^3 f
Answer:
4. 36ab^4
Answer:
The factors of 46xy[tex]z^5[/tex] are 46, x, y, z, z, z, z, and z.
The factors of 19[tex]n^8y^3[/tex]are 19, n, n, n, n, n, n, n, n, y, y, and y.
The factors of 62d³f are 62, d, d, d, and f.
The factors of 36a[tex]b^4[/tex] are 36, a, b, b, b, and b.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
46xy[tex]z^5[/tex]
The factors are 46, x, y, z, z, z, z, and z.
19[tex]n^8y^3[/tex]
The factors are 19, n, n, n, n, n, n, n, n, y, y, and y.
62d³f
The factors are 62, d, d, d, and f.
36a[tex]b^4[/tex]
The factors are 36, a, b, b, b, and b.
Thus,
The factors are given above.
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An angle measures 76.6° less than
the measure of its
complementary
angle. What is the measure of each
angle?
What is the slope? Simplify your answer and write it as a proper fraction, improper fraction, or integer
Answer: 2/1
Step-by-step explanation:
You can decide this by looking at the rise over the run.
kevin has 5 fish in his fish tank.Jasmine has 4 times as many fish as kevin has.How many fish does Jasmine have?
Answer:
20
Step-by-step explanation:
5 x 4 = 20