There are 990 ways to select 6 starters from a possible 14 using precisely two of the three triplets.
= C(3,2) = 3! / ( 2! x 1! ) = 3
To select the final 4 starters out of the 11 players ,
= C(11,4) = 11! / (4!7!)
= 330
There are a total of 6 ways to select starters.
= 3*330 = 990
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method.
The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
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WILL VOTE BRAINLIEST IF POSSIBLE!!
What is the relationship between the following two sequences? Sequence 1: 0, 1, 2, 3, 4, 5… Sequence 2: 0, 4, 8, 12, 16, 20… Group of answer choices The terms in Sequence 2 are four times as large as the terms in Sequence 1. The terms in Sequence 2 are twice as large as the terms in Sequence 1. The terms in Sequence 2 are three times as large as the terms in Sequence 1. The terms in Sequence 2 are half as large as the terms in Sequence 1.
Answer:
The terms in Sequence 2 are four times as large as the terms in Sequence 1.
Step-by-step explanation:
If we take a look at the numbers,
Sequence 1: 0, 1, 2, 3, 4, 5
Sequence 2: 0, 4, 8, 12, 16, 20
We can see that 0 × 4 = 0,
1 × 4 = 4,
2 × 4 = 8,
And so on.
We can also see in sequence 2 that 4 is added to each of the numbers every time, whereas the first sequence is simply counting up.
Therefore, we can conclude that the terms in Sequence 2 are four times as large as the terms in Sequence 1.
Mr. Radmanic and Mrs. Chin both fill up their cars with gasoline at the beginning of the week. The equation compares the number of miles driven, x, to the amount of gasoline in the tank, y. Find and compare the y-intercepts for the models and interpret their real world meanings
The y-intercepts for the models are equal to 13.2.
What is slope?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all
Any two different points on a line can be used to calculate the slope of any line.
A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-
P1 = (x1, y1) and P2 = (x2, y2)
Hence, The y-intercepts for the models are equal to 13.2.
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hree people are asked to throw a fair die. what is the probability that all of them get the same number
The probability that all of them get the same number is 1/36.
Given :
Three people are asked to throw a fair die.
Probability :
Probability is a branch of mathematics that deals with the occurrence of a random event.
In one dice probable outcomes 1, 2, 3, 4, 5 and 6
Total out comes in three dice = ( 6 * 6 * 6 = 216 )
Probability of getting 1 = 1/216
Similarly for 2, 3, 4, 5 and 6
Probability of getting same number = 6 * 1/6 * 1/6 * 1/6
= 6*1/6 * 1 * 1 / 6 * 6
= 6/6 * 1/36
= 1 * 1/36
= 1/36
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7) Skyler buys 8 T-shirts and 5 hats for $220. The next week, he buys 5 T-shirts and 1 had for $112. How
much does each T-shirt and each hat cost? Write a system of equations that can be used to solve the problem.
Step-by-step explanation:
As given in question that Skyler buys 8 T-shirts and 5 hats for $220.
The next day, he buys 5 T-shirts and 1 hat for $112.
We have to find the cost of T-shirt and hat each.
Let the cost of T-shirt and hat is x and y respectively.
According to the question,
8x + 5y = 220 ............(i)
5x + 1y = 112 ............(ii)
Multiply by 5 in eq. (ii)
25x + 5y = 560 ............(iii)
Now subtract eq. (iii) - eq. (i)
25x + 5y = 560
- 8x + 5y = 220
17x = 340
[tex]x = \frac{340}{17}[/tex]
∴ x = 20
Put the value of x in eq. (ii)
5 x 20 + y = 112
100 + y = 112
y = 112 - 100
∴ y = 12
Hence the cost of each T-shirt and each hat is $20 and $12 respectively.Charlotte is working two summer jobs, making $7 per hour washing
cars and making $15 per hour clearing tables. In a given week, she can
work at most 16 total hours and must earn a minimum of $150. If x
represents the number of hours washing cars and y represents the
number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
Inequality 1: y
Inequality 2:y
The value of the inequality is ( 45/4 , 19/4 )
What is Inequality ?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.
According to the given information
Number of hours spent in washing cars = x
Number of hours spent in clearing tables = y
Amount paid per hour for washing the car = $7
Amount paid per hour for clearing the tables = $15
Earnings
7x + 15y ≥ 150
x + y ≤ 16
7x + 15y = 150 ........ (i)
x + y = 16 ........(ii)
Multiply (ii) by 7
7x + 7y = 112 ..... (iii)
Subtract (i) and (iii)
8y = 38
y = 19/4
Putting the value of y in (ii)
x + 19/4 = 16
x = 16 - 19/4
x = 45/4
The value of the inequality is ( 45/4 , 19/4 )
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Isaac owns a food truck that sells tacos and burritos. He only has enough supplies to make 130 tacos or burritos. He sells each taco for $4.25 and each burrito for $8.50. Isaac must sell a minimum of $850 worth of tacos and burritos each day. If xx represents the number of tacos sold and yy represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
By solving linear inequation, it can be calculated that
x = 60 , y = 70 is one possible solution.
What is linear inequation?
Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by <, >, ≤, ≥
A one degree inequation is known as linear inequation
Let the number of tacos sold be $x and the number of burrito sold be $y
He only has enough supplies to make 130 tacos or burritos.
x + y [tex]\leq[/tex] 130 ... (1)
He sells each taco for $4.25 and each burrito for $8.50.
Isaac must sell a minimum of $850 worth of tacos and burritos each day.
4.25x + 8.5y [tex]\geq[/tex] 850
x + 2y [tex]\geq[/tex] 200 ... (2)
The inequalities has been solved graphically
One possible solution is x = 60, y = 70
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Margaret said the exact product of 602 and 341 is 205,282 . Is she correct prove it by showing an algorithm:
Yes, she is. The exact product of 602 and 341 is 205,282.
What is algorithm in math?In mathematics, an algorithm is a process, a description of a series of steps that can be used to solve a problem; however, they are now far more prevalent than that. Although many areas of research (and daily life) use algorithms, long division's step-by-step process is probably the most prevalent example.
To determine the exact product of 602 and 341, both numbers must be multiplied, obtaining the result. To do this, said number can be decomposed, to facilitate the operation and to be able to corroborate the accuracy of the result.
So, we can multiply 602 by 300, plus 602 by 40 and 602 by 1, and add the results.
Therefore, since 602 times 300 is equal to 180,600 (602 x 300 = 180,600); that 602 times 40 is equal to 24,080 (602 x 40 = 24,080); and since 602 times 1 is equal to 602, all those values must be added.
So 180,600 plus 24,080 equals 204,680. And in turn, 204,680 plus 602 equals 205,282. Therefore, the proposed result is correct.
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17
ning:
of
2
Find the Missing Angle
Instructions: Find the measure of the indicated angle.
Check
to
70°
The values of as shown in the isosceles triangle x is 55°
What is an isosceles triangle?An isosceles triangle is a type of triangle that have two equal sides.
To calculate the value of x in the isosceles triangle, we use the formula below.
Note: The sum of the angle in a triangle is 180°.
Formula:
180 = a+b+c............. Equation 1Where:
a,b,c = The three sides of the triangle respectively.From the image,
Given:
a = 70°b = c = xSubstitute these values into equation and solve for x
x+x+70 = 1802x = 180-702x = 110x = 110/2x = 55°Hence, the values of x is 55°
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The equation of a line is y = 2x - 4. If the equation is changed to y = 2x - 2, how will the graph of the line change?
Responses
A The line will become less steep.The line will become less steep.
B The line will shift right 2 units.The line will shift right 2 units.
C The line will shift up 2 units.The line will shift up 2 units.
D The line will shift left 2 units.The line will shift left 2 units.
E The line will shift down 2 units.
The equation of a line is y = 2x - 4. If the equation is changed to y = 2x - 2, how will the graph of the line change?
A The line will become less steep.
B The line will shift right 2 units.
C The line will shift up 2 units.
D The line will shift left 2 units.
E The line will shift down 2 units.
the quotient of four and a number increased by ten as an algebraic expression
Answer:
(x/4)+10
Step-by-step explanation:
Quotient=division, so x/4
Increased by 10, so (x/4)+10
A pair of shoes are priced at $35.99 but is on sale for 20% off. What is the sale price of the shoes?
Answer: $28.79
Find 20% of $35.99.
Then subtract that answer (7.2) from $35.99
your answer is
The shoes where on sale for $28.79
For each part below, use the figure to fill in the blank.
If necessary, you may learn what the markings on a figure indicate.
(a) Find m
The measure of m∠x is 110°
What is the Isosceles Triangle?
Isosceles triangles are those triangles that have at least two sides of equal measure. We know that triangles are three-sided enclosed polygons and they are classified as equilateral, isosceles, and scalene, based on the length of their sides.
We have,
given the triangle Δwxy,
m∠y = 35°, and
there are two similar sides to the triangle wx ≅ xy,
Properties of an Isosceles Triangle are:
The two sides are congruent with each other.
The third side of an isosceles triangle which is unequal to the other two sides is called the base of the isosceles triangle.
The two angles opposite to the equal sides are congruent with each other. That means it has two congruent base angles and this is called an isosceles triangle base angle theorem.
The angle which is not congruent to the two congruent base angles is called an apex angle.
The altitude from the apex of an isosceles triangle bisects the base into two equal parts and also bisects its apex angle into two equal angles.
The altitude from the apex of an isosceles triangle divides the triangle into two congruent right-angled triangles.
The two angles opposite to the equal sides are congruent with each other.
so, m∠w = m∠y = 35°
The sum of measure of the angles of the isosceles triangles is 180.
so,
m∠w + m∠x + m∠y = 180
35 + 35 + m∠x = 180
m∠x = 180 - 70
m∠x = 110°
Hence, the measure of m∠x is 110°.
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Extra Points if you answer and if the answer is correct.
Find the value of y? Round to the nearest tenth: 42, 85 and 31
What does y equal to?
The value of the unknown side y for the given triangle will be 46.15.
What is the triangle?In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
The sine law, also known as the law of sines, states that the ratio of a triangle's side length to the sine of its opposite angle is constant for all three sides. It's sometimes referred to as the sine rule.
We have to find the value of the side as y.
Apply Sin law in the given triangle,
SinA/a=SinB/b=SinC/c
Sin42/31=sin85/y
0.6691/31=0.9962/y
y=30.8822/0.6691
y=46.15
Thus, the value of the unknown side y for the given triangle will be 46.15.
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Which represents a side length of a square that has an area of 450 square inches? in. In. 112. 5 in. 115. 5 in.
If a square has an area of 450 square inches then according to Area = 2(length of a side), the length of one side of that square will be 225 inches.
What is the formula of area and perimeter of square?The formula of Area of a Square is ,
area = side × side = side² square units
whereas the perimeter of square is = 4 x side
What is a square simple definition?A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at right angles or at 90 degrees.
let the length of a side of a square is x
area of square is = 450 square inches
as area of square is found as
Area = 2(length of a side)
2x = 450 square inches
x =450/2
x=225 inches
so the length of each side of square is 225 inches.
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Ms. Wilson purchased a welcome mat for her front porch that is a semicircle. The straight side of the mat is 38 inches. To the nearest hundredth, what is the area of the porch mat?
Answer:
567.06 in.²
Step-by-step explanation:
The mat is a semicircle.
The straight side is a diameter.
d = 38 in.
r = d/2 = 19 in.
Area of circle = πr²
Area of semicircle = πr²/2
A = 3.14159 × (19 in.)² / 2
A = 567.06 in.²
Find the volume of this right solid. The base is a square with
sides 6 meters long. The cylindrical hole has a diameter of 3 m.
Round answer to 2 decimal places.
The volume of the cylinder is 21.2m³
Volume of a CylinderThe volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. The formula is given as πr²h, where r is the radius of the circular base and h is the height of the cylinder.
V = πr²h
v = volumer = radius = diameter / 2h = heightradius = diameter / 2
radius = 3 /2
radius = 1.5m
v = π × 1.5² × 3
v = 21.2m³
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(2x)/(25)=(0.4)/(0.15)
how many times does one go into 3
Answer:
Step-by-step explanation: 3?
Describe the correlation in the scatter plot below.
Answer:
Step-by-step explanation:
The scatter plot shows positive correlation because as the plotted values of x increase, the values of y generally increase.
When x and y both increase, you have a positive correlation. When one increases and the other decreases then you have a negative correlation.
write the following algebraically using x as unknown
"i think of a number , take away 1 and multiply the result by 3
Answer: (x-1) 3
Step-by-step explanation:
This is equation you want
x is unknown -1 in the mark and then times 3!
HELP!!! NEED ANSWER FAST
Answer:
y = 1.3x + 10
Step-by-step explanation:
as, y = 1.3 * 5 + 10
= 16.5
Answer: y = 1.3x + 10
Step-by-step explanation: 1.3 x 0 = 0→ 0 + 10 = 10
1.3 x 5 = 6.5→ 6.5 + 10 = 16.5
1.3 x 10 = 13→ 13 + 10 = 23
1.3 x 15 = 19.5→ 19.5 + 10 = 29.5
1.3 x 20 = 26→ 26 + 10 = 36
Hope this helps.
make g the subject of 3e+4g=7+9eg
Answer:
g= 7-3e / 4 - 9e
Step-by-step explanation:
I assume you need to solve for g. Please let me know if that is not the case
round the fraction or mixed number to the nearest 1/2.
4 and 8/9
answers
4
4 and 1/2
5
Basic Triangle Proofs (Congruence Only - No CPCTC)
Given:
AB⊥ BC
AD⊥ DC
BC≅ AD
Prove: △ABC≅△CDA
The given triangles are congruent following the side angle side (SAS) congruency .
Given,
AB⊥ BCAD⊥ DCBC≅ AD∴ ∠ A = ∠ B = ∠ C = ∠ D =90°
In Δ ABC and Δ CDA
AB = CD
∠ BAC= ∠ DAC
AB= AD
∴ By Side Angle Side congruent property
Δ ABC ≅ Δ CDA
Congruent refers to figures that are similar in all respects, primarily in terms of size and shape. Congruence describes how two congruent figures relate to one another.
The relationship between two figures that are congruent is referred to as congruence. Let's talk about the triangle SAS congruence now. We don't necessarily need to look into all the sides and angles to determine whether the two triangles are identical.
Triangles must be congruent to mean,
There are no different comparable angle pairs.
It is equal on all comparable sides.
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Find the equation of a line parallel to y=-3 passing through the coordinate (2 6).
The equation of line parallel to y = -3 passing through (2,6) is y = 6
The slope-intercept form of straight line is used to find the equation of line. It is given as y =mx + b
where m is a slope of line
b is y-intercept
According to the question,
The required line is parallel to line y = -3
Slope of given line : m₁
m₁ = 0
When two lines are parallel to each other then their slopes are equal
Therefore , slope of required line is m₂ = m₁ = 0
Also , given that the line is passing through the coordinate (2,6)
So , 6 = 0(2) + b
=> b = 6
Substituting the values of slope and intercept
y = 6 is required equation of line
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Consider y=1/2x+1. a. Complete the table for the equation. x y 0 2 4
The table can be completed as follows x = 0, 2, 4 we get y = 1, 2, 3 for the linear equation [tex]y = \frac{1}{2}x + 1[/tex].
What is a Linear Equation ?If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equal to zero, then it is said to be a linear equation in two variables.
Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
Such an equation has a pair of numbers as its solution, one for x and one for y, which further equalises the two sides of the equation.
A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.
Basically, there are infinitely many solutions to a linear equation with two variables.
The equation is :
[tex]y = \frac{1}{2}x + 1[/tex]
So, when x = 0
y = 1,
when x = 2
y = [tex]\frac{1}{2}*2 + 1[/tex] = 1 + 1 = 2
and , when x = 4
y = [tex]\frac{1}{2}*4 + 1[/tex] = 2+ 1 = 3
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due a cupple days ago pls help meee
Answer:
(0, 2 )
Step-by-step explanation:
If the dilatation is centred at the origin then the original coordinates are multiplied by the scale factor , that is
B (0, 4 ) → ( [tex]\frac{1}{2}[/tex] (0), [tex]\frac{1}{2}[/tex] (4) ) → (0, 2 )
PLEASE HELP< I DONT UNDERSTAND THIS
y=1/3x+4 is the equation of line passing through (3, 5) and parallel to -x+3y=6
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
-x+3y=6
3y=6+x
Divide both sides by 3
y=2+1/3x
y=1/3x+2
slope is 1/3
In parallel lines the slope will remain same
We need to find the equation of line passing through (3, 5) and parallel to 3y=6+x
5=1/3(3)+b
5=1+b
b=4
Hence, y=1/3x+4 is the equation of line passing through (3, 5) and parallel to -x+3y=6
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Jordan and his children went into a restaurant and he bought $26 worth of drinks and tacos. Each drink costs $2. 50 and each taco costs $2. He bought 4 more tacos than drinks. Write a system of equations that could be used to determine the number of drinks and the number of tacos that jordan bought. Define the variables that you use to write the system.
Using the equations 2x+2.5y=26 and x=y+4, Jordan also brought 4 beverages and 8 tacos.
What is equation?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. A mathematical sentence with two equal sides and an equal sign is called an equation. An example of an equation is 4 + 6 = 10.
Here,
Let x be the tacos and y be the drinks,
cost of each drink=$2.5
cost of each tacos=$2
2x+2.5y=26
x=y+4
2(y+4)+2.5y=26
2y+8+2.5y=26
4.5y=18
y=18/4.5
y=4
x=y+4
x=8
Jordan brought 8 tacos using the system of equation as 2x+2.5y=26 and x=y+4 as well as 4 drinks.
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a certain statistic dˆ is being used to estimate a population parameter d. the expected value of dˆ is not equal to d. what property does dˆ exhibit?
Using the Central Limit Theorem for proportions, the correct option is:
E. The statistic is biased.
What is Central Limit Theorem?
The central limit theorem in probability theory proves that, even if independent random variables are not normally distributed in themselves, in many cases, when they are added together, their properly normalised sum tends toward a normal distribution.
The central limit theorem states that the distribution of the sample means will be roughly normally distributed if you have a population with mean and standard deviation and take sufficiently large random samples from the population with replacement.
The Central Limit Theorem establishes that for a proportion p in a sample of size n:
- The expected value is[tex]$\mu=p$[/tex].
- The standard error is [tex]$s=\sqrt{\frac{p(1-p)}{n}}$[/tex]
In this problem, the expected value is different of the expected of [tex]$\mu=p$[/tex], hence, the statistic is biased, and the correct option is [tex]$\mathbf{E}$[/tex].
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