Let's say there are $v$ varsity players and $j$ JV players.
The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:
$\sf\implies\:(2/3)v$
And the number of JV players partnered with a varsity player is:
$\sf\implies\:(3/5)j$
Since these two numbers represent the same group of paired players, they must be equal:
$\sf\implies\:(2/3)v = (3/5)j$
To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:
$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired
$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired
So the total fraction of players who are paired is:
$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)
Simplifying:
$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$
Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.
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[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]
what is the value for 43.7 x 0.25
Answer:
43.7 x 0.25 is 10.925
Step-by-step explanation:
To multiply decimals, we can use the following steps:
1. Multiply the numbers as if they were whole numbers, ignoring the decimal points.
2. Count the total number of decimal places in the factors being multiplied. This will be the number of decimal places in the product.
3. Place the decimal point in the product so that it has the same number of decimal places as the total counted in step 2.
Using these steps, we can find the product of 43.7 and 0.25 as follows:
1. 437 x 25 = 10925
2. There are two decimal places in 43.7 and two decimal places in 0.25, so there are a total of four decimal places in the factors being multiplied.
3. Place the decimal point in the product so that it has four decimal places: 10.925
Therefore, the value of 43.7 x 0.25 is 10.925.
Starting from rest, an object travels at a constant speed of 150 cm/s (centimeters per second) along a straight line. If d is the total distance in cm that the object has traveled at time t seconds, then which of the following gives the equation expressing d as a function of t, and the total distance d in meters that the object has traveled at time t = 2 seconds?
The equation expressing d as a function of t can be found by using the formula for distance traveled with constant speed:
d = vt
where d is the distance, v is the constant speed, and t is the time elapsed.
In this case, the speed is 150 cm/s, so the equation is:
d = 150t
To find the total distance traveled in meters at t = 2 seconds, we need to first find the total distance traveled in centimeters at t = 2 seconds:
d = 150t
d = 150(2)
d = 300 cm
To convert to meters, we divide by 100:
d = 300/100
d = 3 meters
Therefore, at t = 2 seconds, the object has traveled a total distance of 3 meters.
Evaluate the following expression.
If x=12,y=8, and z=6.
X2y-2z over 4
The value of the expression "(x²y - 2z)/4", when x = 12 , y = 8 and z = 6, is (c) 285.
An "Expression" is defined as a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, which are written using mathematical symbols and follow certain rules.
We have to evaluate the expression : (x²y - 2z)/4, if x = 12 , y = 8 and z = 6,
To evaluate , we substitute x = 12 , y = 8 and z = 6, in the expression,
So, We have,
⇒ (12² × 8 - 2×6)/4,
⇒ (144 × 8 - 12)/4,
⇒ (144 × 8 - 12)/4,
⇒ (1152 - 12)/4,
⇒ 1140/4,
⇒ 285,
Therefore, the value of the given expression, when x=12, y=8, and z=6, is 285, the correct option is (c).
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The ratio of two numbers is 7 to 3 and the sum of their squares is 232. Find the numbers.
Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer: 100.48 cubic feet
Step-by-step explanation:
I need help with the answer to the photo provieded
Answer:
26
Step-by-step explanation:
On a scale drawing of a soccer field, 0.5 cm equals 8 m.
If the drawing has dimensions 6.5 cm X 3.25 cm, what is the actual length of the soccer field, in meters?
[tex]\sf Length\, of\,the\,field=\boxed{\sf 104(m)}}.[/tex]
Step-by-step explanation:1. Create a conversion factor.A conversion factor is just a fraction that contains an equivalence. We make the numerator be the unit we want to have as a result and the denominator is the current unit that we have.
The problem states that 0.5 cm equals 8 m, and we want to convert from cm to m, therefore, a conversion factor for this problem is:
[tex]\sf \dfrac{8(m)}{0.5(cm)}[/tex]
2. Use the conversion factor to convert each unit,To use the conversion factor, just multiply each measure by the fraction:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}[/tex]
Here the centimeters (cm) cancel out each other and the ending answer is expressed in meters:
[tex]\sf 6.5(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 104(m)}.[/tex]
For the other measure:
[tex]\sf 3.25(cm) \dfrac{8(m)}{0.5(cm)}=\boxed{\sf 52(m)}.[/tex]
So a soccer field, as you may already know, is always longer than it is wide, therefore, the greatest measure (104m) should be the length of the field.
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Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation.
United States Birth Rate (per 1000)
Birth Rate
A graph titled United States Birth Rate (per 1000) has year on the x-axis and birthrate on the y-axis. Points trend in a negative line.
Year
Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
a.
no correlation
b.
positive correlation; as time passes, the birth rate increases.
c.
positive correlation; as time passes, the birth rate decreases.
d.
negative correlation; as time passes, the birth rate decreases.
A negative correlation may be seen on the graph. The birth rate declines over time. This indicates that the number of births per 1000 persons in the US has been declining over time.
A bug crawls 5 1/2 feet in 28.6 seconds. At that pace, how many seconds does it take the bug to crawl one foot?
Answer:
5.2 seconds
Step-by-step explanation:
To get one foot, we need to divide by 5.5
Set up a proportion:
[tex]\frac{5.5}{5.5}=\frac{28.6}{5.5}[/tex]
Solve:
[tex]1ft.=5.2secs.[/tex]
NEED HELP ASAP PLS AND THX PIC IS ATTACHED
The trigonometry functions when evaluated are shown below
Evaluating the trigonometry functionsIn trigonometry, sine (sin), cosine (cos), and tangent (tan) are three basic functions that relate angles to the sides of a right triangle.
They are defined as follows:
sin A = opposite side/hypotenuse.
cos A = adjacent side/hypotenuse.
tan A = opposite side/adjacent side.
So, we have
Figure 1
sin A = 6/9cos A = √5/3tan A = 6/√5Figure 2
sin A = √2/2cos A = √2/2tan A = 1Figure 3
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A college student takes the same number of credits each semester. They had 19 credits when they started, and after 6 semesters, they had 67 credits. Which of these expresses the rate at which they is earning credits?
As per the given variables, the rate at which they earn credits is 8 credits per semester
Total number of credits = 19
Total number of semesters = 6
Credits after six semesters = 67
Calculating the change in credits -
Change in credits -
Credits after six semesters - Inital credits
= 67 - 19
= 48 credits
Total time = 6 semesters
Calculating the change in credits over the six semesters and dividing by the total time to get the pace at which the college student is acquiring credits.
Therefore, the rate at which the college student is earning credits is:
Rate = Change in credits / Total time
= 48 credits / 6 semesters
= 8 credits per semester
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Factor by grouping. Then supply the term that is missing below. 4mn+3m+8n+6=(m+2)(?+3)
Answer:
4mn + 3m + 8n + 6 = (m + 2)(4n + 3)
The missing term is 4n.
For two programs at a university, the type of student for two majors is as follows. find the probability a student is a graduate student, given they are a history major.
The probability that a student is a graduate student given they are a history major is approximately 0.16.
What is probability?The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.
According to question:We are given the following information:
Total number of students who are history major: 463
Total number of graduate students: 261
Number of graduate students who are history major: 73
We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:
P(graduate | history) = P(graduate and history)/P(history)
P(graduate | history) = 73/463
P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)
Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.
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An equilateral triangle is shown inside a square inside a regular pentagon inside a regular hexagon. Write an expression for the exact area of each shaded region in the figure. Then find the approximate area of the entire shaded region, rounded to the nearest whole unit.
An expression for the exact area of each shaded region in the figure include the following:
Shaded area = area of the regular hexagon - area of the regular pentagon + area of the square - area of the equilateral triangle.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using the following formula:
Area of a regular polygon = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.Based on the diagram (see attachment), the area of the first shaded region is given by;
Area of first shaded region = Area regular hexagon - Area regular pentagon
For the area of the second shaded region, we have;
Area of second shaded region = Area of a square - Area of the equilateral triangle
Therefore, the total area of all of the shaded regions is given by;
Total shaded area = {area of the regular hexagon - area of the regular pentagon} + area of the square - {area of the equilateral triangle}.
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PLEASE HELP! Showing all work, solve for x and why and round to nearest tenth
Answer:
x = 7.9 (nearest tenth)
y = 24.6° (nearest tenth)
Step-by-step explanation:
Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to find the length of the hypotenuse, x:
[tex]\begin{aligned}3.2^2+7^2&=x^2\\10.24+49&=x^2\\59.24&=x^2\\x^2&=59.24\\x&=\sqrt{59.24}\\x&=7.6967525...\\x&=7.9\; \sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 7.9.
[tex]\hrulefill[/tex]
The tangent ratio is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
As we have been given the lengths of the sides that are opposite and adjacent angle y, we can use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3.2}{7}\\y&=\tan^{-1}\left(\dfrac{3.2}{7}\right)\\y&=\vphantom{\dfrac12}24.5671713...^{\circ}\\y&=24.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 24.6°.
Find the equation of the line that passes through the point (3,−5) and is perpendicular to the line y=1/5x-2
Casey is going to wear a gray sportscoat and is trying to decide what tie he should wear to work. In his closet, he has 29 ties, 15 of which he feels go well with the sport coat. If Casey selects one tie at random, determine the probability and the odds of the tie going well or not going well with the sport coat.
The probability of Casey selecting a tie that goes well with the sport coat is 0.517.
The probability of Casey selecting a tie that does not go well with the sport coat is 0.483
What are the probability and the odds of the tie going well or not going well with the sport coat?The probability of Casey selecting a tie that goes well with the sport coat is:
P(goes well) = 15/29
P(goes well) ≈ 0.517
The probability of Casey selecting a tie that does not go well with the sport coat is:
P(does not go well) = 1 - P(goes well)
P(does not go well) = 1 - 15/29 = 14/29
P(does not go well) ≈ 0.483
The odds in favor of the tie going well with the sport coat are:
P(goes well) : P(does not go well) = 15/29 : 14/29
P(goes well) : P(does not go well) = 15:14
The odds against the tie going well with the sport coat are:
P(does not go well) : P(goes well) = 14/29 : 15/29
P(does not go well) : P(goes well) = 14:15
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Line g has an equation of y = 2x + 1. Line h includes the point (-5, 2) and is perpendicular
to line g. What is the equation of line h?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
Submit
Enter your answer, rounded to the nearest tenth, in the box.
Answer:
[tex]f(0) = 6.2 \sqrt{4.5} + 18 = 31.2[/tex]
the line is parellel to graph of 2x-3y=7 and contains the point (-3,-3)
The equation of the line parallel to the graph of 2x - 3y = 7 and containing the point (-3,-3) is y = (2/3)x - 1.
What is the equation of the parallel line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the equation of the graph: 2x - 3y = 7.
First, we need to rearrange the given equation into slope-intercept form (y = mx + b) by solving for y:
2x - 3y = 7
-3y = -2x + 7
y = (2/3)x - 7/3
The slope of the given line is 2/3.
Hence, any line parallel to it will also have a slope of 2/3.
Using the point-slope form, we determine the equation of the line that passes through (-3,-3) and has a slope of 2/3:
y - y1 = m(x - x1)
y - (-3) = (2/3)(x - (-3))
y + 3 = (2/3)x + 2
y = (2/3)x - 1
Therefore, the equation of the line is y = (2/3)x - 1.
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Find the side lengths of each triangle.
Answer:
9) 36 36 and 36 (all three sides equal)
10) 3.1 3.1 and 3.3 (two sides equal)
Step-by-step explanation:
#9
This is an equilateral triangle so all three sides are equal
Expressions for two of the sides are 6y and 4y + 12
Set these expressions equal to each other and solve for y:
6y = 4y + 12
6y - 4y = 12
2y = 12
y =6
So the side with expression 6y becomes 6 · 6 = 36
Since it is an equilateral triangle, each of the three sides is 36
#10
This is an isosceles triangle with side 2x + 1.7 = x + 2.4
Solve for x:
2x + 1.7 = x + 2.4
2x - x = 2.4 - 1.7
x = 0.7
So the side with x + 2.4 = 0.7 + 2.4 = 3.1 same as the side with 2x + 1.7
The third side with 4x + 0.5 = 4(0.7) + 0.5 = 2.8 + 0.5 = 3.3
So the sides of this triangle are 3.1, 3.1 and 3.3
Write the standard form of the following polynomial.
(2x-3)²-3(x-2)(x+4)-7
X² ? X+ ?
‼️‼️‼️‼️WILL MARK BRAINLIEST‼️‼️‼️‼️
Answer:
S = 2π(14^2) + 2π(14)(154)
= 2π(196) + 2π(2,156)
= 4,704π = 14,778.1 ft^2
Using 3.14 for π:
S = 4,704(3.14) = 14,770.6 ft^2
2raised to power m-3 = 1
Answer:
m = 3
Step-by-step explanation:
Given:
[tex]2^{m-3}[/tex] = 1
Take the logarithm of both sides (logarithm of 1 is 0):
m - 3 = 0
Add 3 to both sides:
m - 3 + 3 = 0 + 3
m = 3
Hence, m = 3.
Logarithm is the power to which a number must be raised in order to get some other number. For example:
The base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. Meaning [tex]10^{2}[/tex] = 100.Solve x²-3x+ 5 = 0.
A.
3+√-29
+VE
2
and
3-
2
-29
B. 3+√29 and 3-√29
O c. 3+√-11 and 3-√-11
2
2
D. 3+√11 and 3-√11
Using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.
What is the quadratic formula?The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem.
In addition to the quadratic formula, other methods of solving quadratic equations include factoring, completing the square, graphing, and others.
A second-order equation of the form ax² + bx + c = 0 denotes a quadratic equation, where a, b, and c are real number coefficients and a 0.
So, we have the equation:
x²-3x+ 5 = 0
Now, solve it using the quadratic formula as follows:
x²-3x+ 5 = 0
a = 1
b = -3
c = 5
x = -(-3)±√(-3)² -4*1*5/2
Solve this further:
x = 3±√11/2
Therefore, using the quadratic formula to solve the equation x²-3x+ 5 = 0, the resultant answer is (D) 3+√11/2 and 3-√11/2.
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Correct question:
Solve x²-3x+ 5 = 0.
A.3+√-29 +VE/2 and 3- 2-29
B. 3+√29 and 3-√29
C. 3+√-11 and 3-√-11/2
D. 3+√11/2 and 3-√11/2
Factor the expression. x^2-14x-32
Answer:
[tex](x-2)(x+16)[/tex]
Step-by-step explanation:
Use graphing calculator and find the x-intercepts.
PLS HELP IM FAILING ALGEBRA
if 3x+2y=36 and (5y)/(3x)=5, what is the value of x+y?
Answer:
16
Step-by-step explanation:
5y/3x = 5
3x = 5y/5
3x = y
3x + 2y = 36
y + 2y = 36
3y = 36
y = 36/3
y = 12
3x = y
3x = 12
x = 12/3
x = 4
x + y
= 4 + 12
= 16
x + y = 16
A rainwater collection system uses a cylindrical storage tank with a diameter of 50 cm and a height of 80 cm what is the total volume of water in cubic centimeters that can be collected
Answer:
157,000
Step-by-step explanation:
π r² h
The perimeter of the quadrilateral is 34 centimeters. Find the length of each side.
x+8
x +4
2x - 2
x²-2x
Answer: x=4, sides = 12, 8, 6, 8
Step-by-step explain
Perimeter means the sum of all sides of a shape, in this example there are four sides add the sides and set it equal to 34.
X+8+x+4+2x-2+x²-2x=34
x²+2x+10=34
x²+2x-24
(x-4)(x+6)
x=4, x=-6
x can not be -6 because then the x+4 side would be -2, therefore it is extraneous and x=4 is the correct answer.
Now to find side lengths just plug in 4 for x
4+8=12
4+4=8
2*4-2=6
4*4-2*4=8