The total number of students that are on the team is e. 210 if the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6
As the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6, we can write the number of students as;
Freshmen = 1x
Sophomores = 3x
Juniors = 4x
Seniors = 6x
As the number of juniors on the team is 60, therefore;
4x = 60
To determine the value of x we divide both sides by 4;
4x/4 = 60/4
x = 15
Now the total number of students can be found by substituting the value of x;
1x + 3x + 4x + 6x
1(15) + 3(15) + 4(15) + 6(15) = 210
Hence, the total number of students on the team is 210.
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ctagse autosave question4409071.1stems withvalues.)Construct a back-to-back stem-and-leaf diagram for the winning and losing scores given in the table below. (Enter numbers from smallest to largest separated by spaces. Enter NONE forSuper Bowl Results, 1967-201135-1033-1416-7 23-716=324-314-724-716-621-1732-1426-2135-31 31-19 27-1038-938-1646-1039-20$2-10 20-16 55-10 20=1937-2452-17 30-13 49-2635-2131-24 34-19 23-16 34-720-17 48-21 32-29 24-21 21-1029-1717-14 27-2331-25Winning Scores vs. Losing ScoresWinningLosina
Given
Values of winning and losing scores
Find
Make a stem and leaf ploy for the given values
Explanation
Final answer
Above is the
The ratio of small dogs to large dogs at the dog show is 4:3. If there are 60 dogs in the
show, how many are large dogs?
Answer:
45 large dogs
Step-by-step explanation:
Step 1:
60 x 3 = 180
180 ÷ 4 = 45
Christopher earns $5.80 an hour and time-and-a-half for all hours worked over 40 hours. How much did he earn the week he worked 44.5 hours?
Answer:
$271.15
Step-by-step explanation:
Assuming that "time-and-a-half for all hours worked over 40 hours" means that all time spent past that is 1.5X the paycheck, then its 40 times 5.80=$232. then (5.8 times 1.5) times 4.5 = $39.15
$232+$39.15=$271.15
Evaluate the numerical expression open parentheses 5 to the power of negative 4 close parentheses to the power of one half.
Answer:
1/25 or 0.04
Step-by-step explanation:
evaluated in fraction and decimal form i hope this helped :)
A study on students drinking habits wants to determine the true average number of alcoholic drinks all uf graduate students have in a one week period. We know from preliminary studies that the standard deviation is around 1. 8. How many students should be sampled to be within 0. 25 drink of population mean with 95% probability?.
The number of the students should be sampled to be within 0.25 alcoholic drinks of population mean with 95% probability is 62.
What is termed as the Margin of error?The margin of error measures the degree of uncertainty in the parameter estimates of parameter results.The reliability of a estimates decreases as the margin of sample error increases.α is the result of subtracting one from confidence interval as well as dividing by two.
α = (1 - 0.95) ÷ 2 = 0.25
Find z in the Z-table because z does have a p-value of 1 - α.
As a result, the p-value of z is (1 - 0.025) = 0.975.
Thus, z = 1.96
Now find M as;
M = z × (σ ÷ √n)
In which,
n is the sample size σ = population standard deviation.When M = 1,
The standard deviation, in accordance with the question, is approximately 1.
σ = 1
M = z × (σ ÷ √n)
0. 25 = 1.96 × (1 ÷ √n)
√n = 1.96 × (1 ÷ √n)
Squaring both sides,
(√n)² = ((1.96 × 1) ÷ 0.25)²
n = (7.84)²
n = 61.4656
n ≈ 62
Thus, the number of the students should be sampled to be within 0. 25 alcoholic drink of population mean with 95% probability is 62.
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100 points pls helppppp
Answer:
[tex](g \circ f)(0)=216[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=2x+6\\g(x)=x^3\end{cases}[/tex]
(g o f)(x) is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function (g o f)(0) means to substitute the function f(x) when x=0 in place of the x in function g(x).
[tex]\begin{aligned}\implies (g \circ f)(0)&=g[f(0)]\\& = g(2(0)+6)\\&=g(0+6)\\&=g(6)\\&=6^3\\&=216\end{aligned}[/tex]
Could someone please help? You do not have to draw a diagram.
The biggest area of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.
What is area of a quadrilateral?A quadrilateral made up of two triangles.Area of the quadrilateral = 2 * area of the traingleIf the diagonal and the length of the perpendiculars from the vertices are given, then the area of the quadrilateral is calculated as: Area of quadrilateral = (½) × diagonal length × sum of the length of the perpendiculars drawn from the remaining two vertices.GIVEN:
The circumference of the circle is 20π units.The biggest area of a quadrilateral that can fit in a circle is of square.Deduce the radius of the circle.SOLVING:
2πR =20πr = 10 unitsArea of the quadrilateral is
100*2= 200 sq unitshence,The biggest area of a quadrilateral we can fit in a circle of a 20π units is 200 sq units.
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Complete the function for this graph
Determine the values of A, B, and C when y – 7=3(x−4) is written in standard form, Ax+By=C.
Answer:
Step-by-step explanation:
rearrange this equation y – 7=3(x−4) into this Ax+By = C
its pretty simple if you think about it :)
firstly, lets multiply the 3 with x - 4
y - 7 = 3x -12
we are going to bring the 3x to the right side to make the arrangement possible
-3x - y = -5 (minus twelve plus seven)
therefore, A is -3, B is -1 and C is -5
Select the statement that correctly compares two numbers. (2 points) 3.02 = 3.020 4.05 < 4.05 5.17 < 5.07 6.08 > 6.08 hurry up
The statement that correctly compares two numbers is: A. 3.02 = 3.020
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more numbers such as integers, and variables in an equation based on any of the following arguments (symbols):
Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).Next, we would evaluate the given inequalities in order to determine the correct statement as follows:
3.02 = 3.020 (True).
4.05 < 4.05 (False) because 4.05 is equal to 4.05.
5.17 < 5.07 (False) because 5.17 is greater than 5.07.
6.08 > 6.08 (False) because 6.08 is equal to 6.08.
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For a project in his Geometry class, Yusuf uses a mirror on the ground to measure the
height of his school building. He walks a distance of 10.25 meters from the building,
then places a mirror flat on the ground, marked with an X at the center. He then
walks 1.65 more meters past the mirror, so that when he turns around and looks
down at the mirror, he can see the top of the school clearly marked in the X. His
partner measures the distance from his eyes to the ground to be 1.55 meters. How tall
is the school? Round your answer to the nearest hundredth of a meter.
Answer:
x = 9.629 meters
Step-by-step explanation:
x / 10.25 = 1.55 / 1.65
x = 1.55 / 1.65 * 10.25
x = 9.629 meters
As Sandra drives, her music player randomly selects music from her playlist. Sandra’s playlist contains:
3 traditional country songs
6 traditional rock songs
4 hip-hop rap songs
5 contemporary country songs'
1 Latin rap song
3 traditional pop songs
What is the probability that the player will select some rap music next?
Find P (traditional), that is, the probability that the player will randomly select traditional music of any kind.
Find P (traditional pop)
Find P (not country), the probability that the next song is NOT country music.
In the given question, the following information is given
Sandra music player randomly selects music from her playlist. Sandra’s playlist contains:
traditional country songs = 3
traditional rock songs = 6
hip-hop rap songs = 4
contemporary country songs' = 5
Latin rap song = 1
traditional pop songs = 3
Total sample space = 3 + 1+ 5 + 4+ 6+3 = 22 songs
We need to find the probability, that her music player will play a rap song = [tex]\frac{Number of sample sample space for rap song}{Total space} \\[/tex]
= [tex]\frac{4 + 1}{22}[/tex] = [tex]\frac{5}{22}[/tex]
P (traditional), that is, the probability that the player will randomly select traditional music of any kind = [tex]\frac{Number od sample space for traditional song}{total sample space}[/tex]
= [tex]\frac{3 + 6+3}{22}[/tex]
= [tex]\frac{12}{22}[/tex] = [tex]\frac{6}{11}[/tex]
P (traditional pop) = [tex]\frac{sample space for pop songs}{total sample space}[/tex]
= [tex]\frac{3}{22}[/tex]
P (country), the probability that the next song is country music = [tex]\frac{Sample space fpr country music}{total sample space}[/tex]
= [tex]\frac{8}{22}[/tex]
= [tex]\frac{4}{11}[/tex]
P (not country), the probability that the next song is NOT country music.=
1 - [tex]\frac{4}{11}[/tex]
= [tex]\frac{11 -4}{11}[/tex]
= [tex]\frac{7}{11}[/tex]
Hence, this is the final answer.
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I need help with this page for my math class
Answer:
(1) Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity. Example, 1, 2, 3, 4,... are natural numbers.
Step-by-step explanation:
(2) Number Trick 1:
Let the single digit be: 1
Multiply by 2: 1 x 2 = 2
Add 8 to your answer: 2 + 8 = 10
Divide your answer by 2: 10 ÷ 2 = 5
Subtract original number: 5 - 1 = 4
(3) Final result is 4.
The trick will always work for all NATURAL NUMBERS.
Someone please complete. will mark brainliest. 30 points given!!
The answer to all the subparts of the congruency of triangles is shown:
ΔABC and ΔPQR are congruent - SSS congruence.ΔGHJ and ΔUVW are congruent - SSS congruence.ΔGHJ and ΔPQR are not congruent.ΔPQR and ΔUVW are not congruent.What is the Congruence of a triangle?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance.In ΔABC and ΔPQR
AB = PQAC = PRBC = QRThus from SSS congruence, we get ΔABC ≅ ΔPQR
In ΔGHJ and ΔUVW
GH = UVJH = WVJG = UWThus from SSS congruence, we get ΔGHJ ≅ ΔUVW
However, ΔGHJ and ΔPQR are not congruent because there are no two sides that are equal.
Also, ΔPQR and ΔUVW are not congruent because of the same reason mentioned above.
Therefore, the answer to all the subparts of the congruency of triangles is shown:
ΔABC and ΔPQR are congruent - SSS congruence.ΔGHJ and ΔUVW are congruent - SSS congruence.ΔGHJ and ΔPQR are not congruent.ΔPQR and ΔUVW are not congruent.Know more about the Congruence of a triangle here:
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Find the x- and y-intercepts of the graph of x+y=18. State each answer as an integer or an improper fraction in simplest form
The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.
What is the x-intercept of a function?The x-intercept of a function of variable x ( y = f(x) ) form is an intersection fo the x-axis and the curve of the function. The x-intercept for a function y = f(x) is a solution to the equation f(x) = 0 because at that value of x, the function f(x) lies on x-axis, where y is 0. Values of x-intercept for a function f(x) are also called roots or solution of f(x) = 0 equation.
For x intercept, y = 0
x + y = 18
x + 0 = 18
x = 18
Hence, the x-intercept is (18, 0)
For y intercept, x = 0
x + y = 18
0 + y = 18
y = 18
Hence, the y-intercept is (0, 18)
The x- and y-intercepts of the graph of x+y=18 are; (18, 0) and (0, 18) respectively.
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Which represents a total cost of 3 dance tickets at a price of c for each, less a one-time $2 discount?
A 2(c) - 3
B 3(2) - c
C 3(c - 2)
D 3(c) - 2
The correct answer is option D
3(c) - 2 represents the total cost of three dance tickets at a cost of c each, less a one-time $2 discount.
Explanation:A linear equation is one with a leading degree of one.A linear equation is an algebraic equation With only a constant and a first-order (linear) term of the formy = mx+b, where m is the slope and b is the y-intercept.
The above is sometimes referred to as a "linear equation of two variables," where y and x are the variables.Based on the question. We have the parameters listed below.
The total cost of three dance tickets is 3c (at c for each)
One-time offer = $2
Because discounts are always subtracted from the total cost,
the equation represents,
the total cost of three dance tickets at a cost of c each, less a one-time discount $2
= 3(c) - 2
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Which one of them is right?
Answer:
neither of them are right
Comparing Attributes of 2-D Figure, (points, brainliest, stars)
The given figure is a Rhombus hence the last diagram is correct.
In planar Euclidean geometry, a rhombus—also known as a rhombi or rhombus—is a quadrilateral having four sides of equal length.
A quadrilateral with equally sized sides is referred to as a "equilateral quadrilateral." While the name "diamond" is usually used to refer to a rhombus with a 60° angle because it resembles the projection of an octahedral diamond from the playing card's diamond suitThe term "lozenge" is occasionally used to specifically refer to a rhombus with a 45° angle.Every single rhombus is a unique example of a parallelogram and a kite, and it is straightforward (does not self-intersect). A right-angled rhombus is a square.The given figure is a rhombus. All the sides are equal but the angles are not 90°. Hence its is not a square or a rectangle.
The correct diagram is attached below.
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the quotient of 98 and a number
Answer:
98 ÷ 98 = 1 OR 98 ÷ 1 = 98
Step-by-step explanation:
Division is breaking something up into equal parts. The "dividend" is the whole you start with, the "divisor" is what you use to divide up the whole, and the "quotient" is the answer like this: Dividend ÷ Divisor = Quotient. So, the quotient of 98 and a number would be represented as such: 98 ÷ 1 = 98 or 98 ÷ 98 = 1
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PLS HURRY ILL GIVE BRAINLIEST!! Which number sentence is true?
Answer:
B
Step-by-step explanation:
Let's go through each, step-by-step and simplify to see if we find a true number sentence:
A)
[tex]3\frac{1}{3} < \sqrt{7}?[/tex]
[tex]3.3333 < 2.64575?[/tex] Not true
B)
[tex]4.8 < \sqrt{32}?[/tex]
[tex]4.8 < 5.65685?[/tex] True
Knowing B is true, we have found our answer and don't need to go any further.
- student claims that there is no solution to the system of inequalities shown.
y≥x² + 3
y< x + 1
2
PART A (2 POINTS): Explain a method for proving that the student's claim is correct.
peaker notes
The system of inequalities has no solution because the lines do not meet at any point
How to prove the student's claim?The system of inequalities is given as
y ≥ x² + 3
y < x + 1
From the above system of inequalities, we can see that the function types are
Parabola: y ≥ x² + 3Linear: y < x + 1Next, we plot the graph of both inequalities in the system (see attachment for the graph)
From the graph, we can see that the lines and the curves of the functions do not intersect
This means that the system has no solution
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An insurance agent is paid a salary of 200 and a commission of 3% on all sales over 2000 per month. If his total income in a particular month was 530 what was the amount of his sales for that month
The amount of the insurance agent's sales for the month is 11,000.
What is the amount of sales?The total income can be modelled as a linear equation. A linear equation is an equation that has one variable that is raised to the power of one. The form of a linear equation is:
y = mx + b
Where:
m = slope b = intercept530 = base salary + (percentage x value of sales over 2000)
530 = 200 + 3% x s
530 = 200 + 0.03s
530 - 200 = 0.03s
330 = 0.03s
s = 330 / 0.03
s = 11,000
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what are the name of these polygons
The names of the polygons are;
a. Heptagon
b. Octagon
c. Pentagon
d. Hexagon
What are polygons?A polygon can be defined as a plane figure described by a known number of straight line segments which are connected to form a closed chain.
Polygon are also described as figures which are enclosed by line segments known as sides.
It is important to note that polygons are 2- dimensional shapes.
Depending on the number of sides, the types of polygons are;
three sides = trianglefour sides = QuadrilateralFive sides = pentagonSix sides = HexagonSeven sides = HeptagonEight sides = OctagonNine sides = NonagonTen sides = Decagona. It has seven sides = Heptagon
b. It has eight sides = Octagon
c. It has five sides = pentagon
d. It has six sides = Hexagon.
Hence, the number of sides determines the name.
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50 Points Halp Me With This Question Pls and Ty
Angle 6, Angle 16 and Angle 11 are not congruent.
We need to check ∠5 is not equal to which angle from the figure.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Here,
Angle 5 = Angle 2 (Vertically opposite angles)
Angle 5 = Angle 7 (corresponding angles are equal)
Angle 5 = Angle 13 (corresponding angles are equal)
Therefore, Angle 6, Angle 16 and Angle 11 are not congruent.
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Answer:
B) Angle 6
C) Angle 16
E) Angle 11
Step-by-step explanation:
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Corresponding Angles Theorem
When a straight line intersects two parallel straight lines, the angles in the same relative position are congruent.
According to the corresponding angles theorem:
∠5 = ∠13 = ∠7 = ∠15∠2 = ∠10 = ∠4 = ∠12According to the vertical angles theorem:
∠5 = ∠2Therefore:
∠5 = ∠2 = ∠4 = ∠7 = ∠10 = ∠12 = ∠13 = ∠15As angle 5 is not a right angle, the angles that angle 5 is not equal to are:
Angles 1, 3, 6, 8, 9, 11, 14 and 16Which recieves the more interest per annum:$150 invested at 4% or $180 invested at 3 1/2%? What is the annual difference
Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time. When the total principal amount and the rate of interest for a certain amount of time surpass the due date for payment, this is known as compound interest.
What do compound and simple interest mean?Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued. S.I. = (P, T, and R) x 100 is the formula.For Example : $150 put up at 4%Total to Calculate Interest on - $150
Annual Interest Rate - 4%
Monthly interest - $0.50
Yearly interest - $6.00
Investing $180 at 3 1/2%Total to Calculate Interest on - $180
Annual Interest Rate - 3.5
Monthly interest - $0.53
Yearly interest - $6.30
Consider making a $100 (the principal) investment at a 5% yearly rate for a year. The computation for simple interest is as follows: $100 x.05 interest x 1 year = $5 in simple interest after a year.To learn more about Simple interest refer to:
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Please answer my first question
[tex]\textit{area of a rectangle}\\\\ A=bh ~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=2x^2+5x+4\\ h=5x^3 \end{cases}\qquad \begin{array}{llll} \\\\\\ A~~ = ~~ \end{array} \begin{array}{cllll} 2x^2+5x+4\\\\ \times ~~ 5x^3\\\cline{1-1} 10x^5+25x^4+20x^3 \end{array}[/tex]
A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs $80. A season ski pass costs $300. The skier would have to rent skis with either pass for $25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive then the daily passes?
Answer: I think it's 9 days.
Step-by-step explanation:
11. (0, 2) and (4, -4)
12. (-2,-4) and (-3, -3)
Answer:
11. -3/2
12. -1
Step-by-step explanation:
To find slope, subtract the y's and put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction. Simplify if you can.
Subtract y's 2 - -4 is
2+4 which is 6, put that on top.
0 - 4 is -4 put it on the bottom.
Slope is 6/-4. Simplified, this is -3/2
The other question, same thing:
y-y over x-x
-4 - -3 / -2 - - 3
= -4+3 / -2 + 3
= -1 / 1
= -1
Derek filled the pitcher with 8 fluid ounces of lemonade. What was the percent error if the actual measurement was 10 fluid ounces?
Answer: 80%
Step-by-step explanation:
To find percent error all you have to do is divide the estimate by the actual then multiply it by 100
8/10×100=80%
The percent error of the actual measurement of 10 fluid ounces is 25%.
Percent error:
Percent error means the difference between the exact or known value of something and its approximate or actual value, in percentage form.
The formula to calculate the percent id defined as
δ = |(A - E)/E| x 100%
Where
δ = percent error
A = actual value observed
E = expected value
Given,
Derek filled the pitcher with 8 fluid ounces of lemonade.
Here we need to find the percent error if the actual measurement was 10 fluid ounces.
According to the percent error formula, the actual value in the given question is 10 and the expected value is 8.
Then we have to apply the value on the formula, then we get,
Percent error = [(10 - 8)/8] x 100%
Percent error = [2/8] x 100%
Percent error = 0.25 x 100%
Therefore, the percent error in the given situation is 25%.
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y+2=-3(x+2) in slope intercept form
y = -3x - 8
Slope-intercept form: y = mx + b
Given: y + 2 = -3(x + 2)
Simplify:
y + 2 = -3x - 6
y = -3x - 6 - 2
y = -3x - 8
We have: m = -3, and b = -8
Answer:
y=-3x-8
Step-by-step explanation:
First make y by itself
y=-3(x+2)-2
Distribute the -3
y=-3x-6-2
Combine like terms
y=-3x-8