There were 2350 people supporting the home team
How to determine the number of supporters?The given parameters are:
Total = 2500
Proportion that supports the visiting team= 6%
Let the number of people that supports the team be x.
So, we have:
x = (1 - Proportion that supports the visiting team) * Total
This gives
x = (1 - 6%) * 2500
Evaluate
x = 2350
Hence, there were 2350 people supporting the home team
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The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.
Speed
(s kilometres per hour) Frequency
40 < s 50 10
50 < s 60 16
60 < s 70 19
70 < s 80 23
80 < s 90 12
(a) Write down the modal class
(b) Work out an estimate for the mean speed of the motorbikes as they pass under the bridge.
Give your answer correct to 3 significant figures.
The modal class is 70 - 80 and the mean speed is 66.4
How to determine the modal class?The table of values is given as:
Speed Frequency
40 - 50 10
50 - 60 16
60 - 70 19
70 - 80 23
80 - 90 12
The modal class is the class with the highest frequency
The class 70 - 80 has the highest frequency of 23
Hence, the modal class is 70 - 80
How to determine the mean?Rewrite the frequency table to include the class midpoints
x f
45 10
55 16
65 19
75 23
85 12
The estimate of the mean speed is then calculated as:
[tex]\bar x =\frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{45* 10 + 55 * 16 + 65 * 19 + 75 * 23 + 85 * 12}{80}[/tex]
Evaluate
[tex]\bar x = 66.4[/tex]
Hence, the mean speed is 66.4
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2x + 4y = 15
6x +12y = 45
What would the solution to the system of equations be?
Answer:
They both have an infinite number of solutions.
Step-by-step explanation:
Given system of equations:
a) 2x + 4y = 15
b) 6x + 12y = 45
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Rewrite both equations into slope-intercept form:
a) 2x + 4y = 15
⇒ 2x + 4y = 15 [subtract 2x from both sides]
⇒ 2x - 2x + 4y = 15 - 2x
⇒ 4y = - 2x + 15 [divide both sides by 4]
⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
b) 6x + 12y = 45
⇒ 6x + 12y = 45 [subtract 6x from both sides]
⇒ 6x - 6x + 12y = 45 - 6x
⇒ 12y = - 6x + 45 [divide both sides by 12]
⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
New equations:
[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.
System of equations can have the following:
No Solution: the same slope (both lines will be parallel)
One Solution: different slopes and different y-intercepts
Infinitely Many Solutions: the same slope and y-intercept
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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.
Slope-Intercept Form ⇒ [tex]y = mx + b[/tex]m = slopeb = y-interceptEquation #1
Subtract 2x from both sides
[tex]2x + 4y = 15[/tex][tex]2x - 2x + 4y = 15 - 2x[/tex][tex]4y = -2x + 15[/tex]Divide both sides by 4
[tex]\frac{4y}{4} = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = -0.5x + 3.75[/tex]Equation #2
Subtract 6x from both sides
[tex]6x + 12y = 45[/tex][tex]6x - 6x + 12y = 45 - 6x[/tex][tex]12y = -6x + 45[/tex]Divide both sides by 12
[tex]\frac{12y}{12} = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = -0.5x + 3.75[/tex]Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other. Therefore, there are infinite solutions as they will always continue on top of each other.
Umberto plants a garden with an area of 16 square feet. What is the area of the garden in square inches
Answer:
2,304 inches
Step-by-step explanation:
1 square foot = 144 square inches
16 x 144 = 2,304 square inches
What is the value of F(x)=-x+9 if x=-7
Answer: F = - 2/7
Step-by-step explanation:
[tex]f(x) = x + 9\\f(-7) = -7 + 9\\f(-7) = 2\\f = -\frac{2}{7}[/tex]
Work out the length of
x.
Give your answer rounded to 3 significant figures.
The triangle is an isosceles right triangle. Then the value of x will be 1.27 cm.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The right-angle triangle is given below.
The given triangle is an isosceles right triangle.
P = B = x
Then we have
1.8² = x² + x²
2x² = 3.24
x² = 1.62
x = 1.27 cm
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what is the volume of the solid
Answer:
A.264
Step-by-step explanation:
((Area Of triangle*height)=Volume
Area of triangle is the base of the triangle multiplied by height of triangle divided by 2
((8*6)/2)*11=264
what is 0.02 to the power of 4? HELP NEEDED SOON
Answer:
1.6e-7, or .00000016
Step-by-step explanation:
8 3/8 + 3 3/8 + 2 3/8 + 3/8
what is the answer of this ?
The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have an expression:
[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]
After simplification:
[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]
[tex]= \dfrac{67+27+19+3}{8}[/tex]
= 116/8
= 29/2
[tex]= 14\dfrac{1}{2}[/tex]
Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
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Answer:
i dont understand your question
Step-by-step explanation:
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a jack .
Answer:
2/52 so the chance is unlikely.
Step-by-step explanation:
well I think I’m right because sometimes when my family has time we play blackjack in my house for fun or another card game so I should be right.
what is the decimal equivalent for 15 1/4
Answer:
15.25
Step-by-step explanation:
1/4 is also 0.25 in decimals so add that to your 15 and you get 15.25.
Step-by-step explanation:
the fraction 1/4 is also equivalent to the decimal for of .25 + 15 equals 15.25
Find the missing side of this right
triangle.
30
X
[?]
X = 1
Enter the number that belongs in the green box.
Answer:
see the attachment photo!
What is the solution to this equation? (1/27)2-x =9^3x
Answer:
x = -2
Step-by-step explanation:
Prime factorize, 27 and 9
27 = 3 *3 * 3 = 3³
9 = 3*3 = 3²
[tex]\sf \left(\dfrac{1}{27}\right)^{2-x}=9^{3x}\\\\[/tex]
[tex]\left(\dfrac{1}{3^3}\right)^{2-x}=9^{3x}\\\\(3^{-3})^{2-x}=(3^2)^{3x}\\\\3^{(-3)*(2-x)}=3^{2*3x}\\\\3^{-6+3x} = 3^{6x}[/tex]
Bases are same, so now compare the exponents
-6 + 3x = 6x
3x = 6x + 6
3x - 6x = 6
-3x = 6
x = 6/(-3)
[tex]\sf \boxed{\bf x = -2}[/tex]
Exponent law:[tex](x^m)^n=x^{m*n}\\\\\left(\dfrac{1}{a^{m}}\right)=a^{-m}\\[/tex]
2 x 3 4/5 as a mixed number.
Answer:
7 3/5
Step-by-step explanation:
2 x 3 4/5
2 x 19/5
2x19/1x5 = 38/5 = 7 3/5
what is the range of exponential function f(x)=9*2^x
Answer:
uhm smhtn
Step-by-step explanation:
i really just want points.
Answer:
(0,infinity)
Step-by-step explanation:
.
If 8x + y = -1 is a true equation, what would be the value of y + 8x
Solve for D: 70D + 2 - 14D = 79 + 12D - 20
70d+2-14d= 79+12d-20
70d-14d-12d= 79-20-2
44d= 57
d= 57/44
A board game uses a deck of cards that players draw from to move tokens around the board. The probability of selecting a card that moves a player's token forward is 32%. Over the course of a game, the deck is shuffled and reused as necessary. Approximately how many cards must be drawn from the deck before players' tokens move forward 50 times?
Using the binomial distribution, it is found that approximately 156 cards must be drawn from the deck before players' tokens move forward 50 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q successes is:
[tex]E_s(X) = \frac{q}{p}[/tex]
In this problem, the parameters are given as follows:
q = 50, p = 0.32.
Hence:
[tex]E_s(X) = \frac{50}{0.32} = 156[/tex]
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The y-intercept is the place where a line crosses the y-axis. hat is true about the y-intercept?
A. It always has an x coordinate of 0.
B. It always has any coordinate of 0
C. Both x and y coordinates are 0.
Answer:
It always has an x coord of 0
The first step that we must take before attempting to solve a problem is to understand what it is asking for and what is given to us to help solve the problem. Looking at the problem statement, we can see that they are asking what is true about the y-intercept. We are given the information that the y-intercept is the place where a line crosses the y-axis.
Now that we have collected all that information, let us move onto understanding and solving the problem. So first of all, using the information that was given to us, we know that the y-intercept is the place where a line crosses the y-axis. The y-axis occurs where the x-coordinate is 0 and the x-axis occurs where the y-coordinate is 0. Therefore, the option that would best fit the description that we have would be option A, it always has an x coordinate of 0.
6-2 6 grade home work
Answer:
list five solution to the energy crisis of nepal
add 6370 square to 6370 square
L=24 B=12 area=______
Perimeter=_______
Answer:
Area= 288
Perimeter= 72
Step-by-step explanation:
In order to get the area of a rectangle, you multiply the length by the width, 24x12=288.
In order to find the perimeter just add all of the sides, there are 2 sides with a length of 24, and two sides with a width of 12.
24+24+12+12=72
Which smallest number is subtracted from the number 12675 to make it a perfect square?
A particle is moving along the curve y= 4sqrt(5x+11) . As the particle passes through the point (5,24) , its -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant
The rate of change of the distance from the particle to the origin at this instant is 3 units per second.
What is the rate of change?The instantaneous rate of change is the rate of change at a particular instant.
A particle is moving along the curve
[tex]y= 4\sqrt{5x+11} .[/tex]
The rate of change of y is given as:
dy / dx = 2
by differentiating both sides,
[tex]\dfrac{dy}{dx} = 4\dfrac{1}{2\sqrt{5x+11} } 5\dfrac{dx}{dt} \\\\\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\[/tex]
From the question, we have:
(x, y) = (5,24)
Substitute 5 for x and dy / dx = 2
[tex]\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\\\5= \dfrac{10}{\sqrt{5(5)+11} }\dfrac{dx}{dt}\\\\\\\sqrt{5(5)+11} = 2\dfrac{dx}{dt}\\\\\\\dfrac{dx}{dt} = 6/ 2 = 3[/tex]
Hence, the rate of change of the distance from the particle to the origin at this instant is 3 units per second.
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The ratio of boys to girls is 3:2. f the class has 27 boys. How many pupils are in the class?
Answer:
the answer is 45
see the attachment photo!
6 kids play a tennis game. Each play each other once. How many games did they play altogether
a quadrilateral is inscirbed in circle o. the angle measures the quadrilateral in degrees are given by the expressions shown in the figure.
what is the measure of angle c?
(will mark branliest + 20points)
Answer:
A. 65 degrees
Step-by-step explanation:
The required measure of the angle c in the quadrilateral is given as 65°.
As mentioned in the question,
A quadrilateral is inscribed in a circle o. the angle measures the quadrilateral in degrees is given by the expressions shown in the figure.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
In a quadrilateral, the sum of the composite angle is equal to 180°,
∠A + ∠C = 180
130 -x + 95 -2x = 180
-3x = 180 - 225
x = 15
Now,
∠c = 95 - 2x
∠c = 95 - 2×15
∠c = 65
Thus, the required measure of the angle c in the quadrilateral is given as 65°.
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Find the equation of the exponential function represented by the table below:
Y
8
0
1
2
3
3
12
48
192
no I dont feel like it is the answer
f(x)=√x +3. Find the inverse of f(x) and its domain.
Answer:
f(x) = √x + 3
y = √x + 3
√x = y - 3
x = (y - 3)²
Hence inverse of f(x) = (x - 3)² and its domain is x >= 3.
Step-by-step explanation:
hope this helps
help?
what fraction of a dollar is 236 cents?
236/100, 59/25, or 2 9/25
Step-by-step explanation:
There are 100 cents in a dollar, so 236/100 is your starting fraction. The simplest improper fraction would be 59/25. But if you're looking for a mixed number, you get 2 9/25.
236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.
To solve this problem,
We need to convert 236 cents into dollars.
Since there are 100 cents in one dollar,
we can divide 236 by 100 to get the equivalent dollar value.
⇒ 236 cents ÷ 100 cents per dollar = 2.36 dollars
Now that we know that 236 cents is equivalent to 2.36 dollars,
we can express it as a fraction of a dollar.
To do this, we'll use the fact that one dollar is equivalent to 100 cents, which means that one dollar can be expressed as the fraction 100/100.
To find the fraction of a dollar that 2.36 dollars represents,
we'll divide 2.36 by 1.
⇒ 2.36 ÷ 1 = 2.36/1
To express this as a fraction of a dollar,
Multiply both the numerator and denominator by 100 to get,
⇒ (2.36 x 100) / (1 x 100) = 236/100
Simplifying this fraction, we get,
⇒ 236/100 = 118/50
Therefore,
236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.
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Please solve the whole page please please
1d) ↑ (Do the same but turned if that's easier)
1a) 199
1b) 193
1c) 217
1e) Based on the box plot, we can for example, find the lowest and greatest values, the range (largest - smallest), the mean (all values / # values), and the median middle value or q2 given by the second line in the box.
2b) 7
2c) 9.5
2d) ↑
2e) because the data is not ordered, it is difficult to determine the quartile data. Once it is ordered like 6, 7, 7, 7, 8, 8, 9, 10, 10. The data can be visualized alot easier. With the box plot we can determine q3 of the data by looking at the 3rd line, using the whiskers of the box to find the minimum and maximum values.
3)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be: 4,6,8,8,9,11,12,14,14,16.
[4, 6, 8, 8, 9] [] [11, 12, 14, 14, 16]
4 is the minimum, 16 is the maximum, q1 is 8, q3 is 14, and median is 10.
4) ↑
5)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be:
45, 45, 50, 55, 60, 70, 70, 75, 80, 85
[45, 45, 50, 55, 60] [] [70, 70, 75, 80, 85]
45 is the minimum, 85 is the maximum, q1 is 50, q3 is 75, and median is 65.
6) ↑