Probability that the person selected at random from the sport centre of 125 people is a fraction of 1/4 or 0.25.
Probability of an eventThe probability of an event is the fraction of the required number of outcome divided by the number of possible outcomes.
We shall determine the answer to the question as follows;
People in the sport centre = 125
People who used the 3 facilities = 6
People who accessed only gym = 59 - (6 + 11 + 19) = 26
People who accessed only track event = 55 - (6 + 11 + 24) = 14
People who accessed only swimming pool event = 70 - (6 + 19 + 24) = 21
People who accessed only gym and swimming pool events = 29 - 6 = 19
People who accessed only gym and track events = 17 - 6 = 11
People who accessed only swimming pool and track events = 30 - 6 = 24
Total number of people who accessed at least any one of the facilities = 121
The number of people who did not access any of the facility = 125 - 121 = 4, which is the number of possible outcomes for our required outcome.
Therefore, the probability that the person selected doesn't use any facility = 1/4
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Look at this table:
England
Wules
Birth rate per 1000 population
1961
1994
17.6
17.0
12.2
(a) In England, from 1961 to 1994, the birth rate fell by 26.1%
What was the birth rate in England in 1994? Show your working.
(b) In Wales, the birth rate also fell.
Calculate the percentage fall from 1961 to 1994. Show your working.
The birth rate in England in 1994 is 13 and the percentage fall in Wales is 28.23%
(a)In England, from 1961 to 1994, the birth rate fell by 26.1%
We need to find the birth rate in England in 1994
Birth rate in 1961 is 17.6
Birth rate in 1994 = 17.6 - 17.6 x26.1/100
= 17.6 - 17.6 x261/1000
= 17.6 - 4.6
= 13
(b) In Wales, the birth rate also fell.
The birth rate in 1961 is 17.0
The birth rate in 1994 is 12.2
Percentage fall is 100 x (17.0 - 12.2)/17.0
Percentage fall is 28.23 %
Therefore, the birth rate in England in 1994 is 13 and the percentage fall in Wales is 28.23%
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1.2.1 The number of pieces of ropes for FIVE cuts. 1.2.2 The general formula (Ta), for the number of rope pieces. 1.2.3 How many rupe cuttings will make up 153 rope pieces? 1.2.4 How many ropes pieces will result from 11 cuttings? 5 Please tu
Step 1
The number of pieces for 5 cuts is
[tex]7+4=11[/tex]Step 2
The general formula Tn, for the number of rope pieces is
[tex]\begin{gathered} a=3 \\ d=2 \\ T_n=3+(n-1)2 \\ T_n=2n+1 \end{gathered}[/tex]Step 3
How many rope cuttings will make up 153 rope pieces
[tex]\begin{gathered} 153=2n+1 \\ 152=2n \\ \frac{152}{2}=\frac{2n}{2} \\ n=76\text{ rope cuttings} \end{gathered}[/tex]Step 4
How many ropes pieces will result from 11 cuttings
[tex]\begin{gathered} T_n=2(11)+1 \\ T_n=23\text{ rope pieces} \end{gathered}[/tex]Question is in the image. I need help with #19
EXPLANATION
Replacing the given functions into the following:
[tex]\frac{f(x+h)-f(x)}{h}[/tex][tex]\frac{x^2-1+h-(x^2-1)}{h}[/tex]Removing the parentheses and simplifying:
[tex]\frac{x^2-1+h-x^2+1}{h}[/tex]Simplifying like terms:
[tex]\frac{h}{h}=1[/tex]Hence,
[tex]\frac{f(x+h)-f(x)}{h}=1[/tex]given the figure, find the value of y for which the quadrilateral must be a parallelogram
For the figure to be a parallelogram, then y must be equal to 12
Here, we want to get the value of y for which the the quadilateral must be a parallelogarm
Mathematically, the diagonals of a parallelogarm bisects each other
That means the lengths on either sides are equal
Mathematically, we can get two equations as follows;
[tex]\begin{gathered} 3x\text{ = y} \\ 2x\text{ + 2y = 32} \\ \text{From the second equation;} \\ 2(x+y)\text{ = 2(16)} \\ x\text{ + y = 16} \\ \text{From this, we have that;} \\ x\text{ = 16-y} \\ we\text{ can put this in the first equation;} \\ 3(16-y)\text{ = y} \\ 48\text{ - 3y = y} \\ y\text{ + 3y = 48} \\ 4y\text{ = 48} \\ y\text{ = }\frac{48}{4} \\ y\text{ = 12} \end{gathered}[/tex]The ice cream shop sells cones for two dollars and sundaes for three dollars. Rachel makes a table to compare the cost of the ice cream treats. Part A: complete the pattern on the table for the cost of 0, 1, 2, and 3 ice cream treats. Then write the ordered pair for each row.
Given:
The cost of the cone is $2.
The cost of sundaes is $3.
Required:
Cost of cone and sundaes for different values.
The table for the data is:
Cost of ice-cream cone cost of ice-cream sundaes ordered pair
0 0 (0,0)
2 3 (2,3)
4 6 (4,6)
6 9 (6,9)
Hence, the missing values of the table is obtained.
Seth buys last year's best-selling novel, in hardcover, for $21.75. This is with a 25% discount from the original price. What was the original price of the novel?
Price after the 25% discount: $21.75
This means that $21.75 is 75% of the original price. If x is the original price, then:
[tex]\begin{gathered} 75\text{\% of }x=21.75 \\ \frac{75}{100}\cdot x=21.75 \\ x=\frac{100\cdot21.75}{75} \\ \Rightarrow x=\text{ \$}29 \end{gathered}[/tex]Write the equation of the line that is perpendicular to the line y=3x+5 and passes through point (9,5)
The equation of the required perpendicular line is x + 3y = 24.
What is the slope relation for two perpendicular lines?
For two perpendicular lines on a plane, the product of their slopes always equals (-1).
What is the equation of line with slope 'm' and passing through the point (x₁, y₁)?
The standard equation of the line with slope 'm' and passing through the point (x₁, y₁) is y - y₁ = m(x - x₁).
Given, the required line is perpendicular to line given by y = 3x + 5 with slope, m₁ as 3, on analysis with standard equation of line; also the line passes through the point (9, 5) i.e. (x₁, y₁).
Let the slope of the required line be = m₂
As per statement established in the literature above, we have:
Slope of two perpendicular lines = -1
∴m₁ × m₂ = -1 ⇒ 3m₂ = -1 ⇒ m₂ = (-1)/3
Again, equation of the required perpendicular line is:
y - 5 = [(-1)/3][x - 9] ⇒ 3y - 15 = 9 - x ⇒ x + 3y = 24
Thus, the equation of the required perpendicular line is x + 3y = 24.
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40 ounces of granola cost $6.52 how much does a granola cost per ounce(give your answer to the nearest cent)
Answer: $0.2
Step-by-step explanation:
To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)
what is the slope of the line represented by the equation 4/5x -3
The slope of the line represented by the equation; 4/5x - 3 is; 4/5.
What is the slope of the line represented by the equation 4/5x - 3?It follows from the task content that the slope of the line represented by the equation; (4/5)x - 3 is to be determined.
Recall, from line geometry and equation of lines;
The slope-intercept form of the equation of a line, y is given as; y = mx + c.
Where, m is the slope and c is the y-intercept.
Therefore, by comparison of the equation defined as; 4/5x - 3; it follows that the slope of the equation is; 4/5.
Ultimately, the required slope is; 4/5.
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Two freight trains are delivering cargo. One freight train is delivering coal, and the other freight train is delivering grain. Their respective distances traveled after x hours is represented in the table and graph below.
Solution
- In order to find which of the trains is moving faster, we should calculate the average speeds of both trains and compare them.
- The y-values of both trains are the Distance in Miles and the x-axis is the time in hours.
- Thus, the best way to calculate their average speeds is to find the slope of both datasets.
- The formula for calculating the slope is given below:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where,} \\ (x_1,y_1)\text{ and (}x_2,y_2)\text{ are coordinates chosen} \end{gathered}[/tex]- Thus, with the above information, we can proceed to solve the question
Speed of Coal Freight Train:
[tex]\begin{gathered} \text{ Choosing } \\ (x_1,y_1)=(1,49) \\ (x_2,y_2)=(2,98) \\ \\ m_C=\frac{y_2-y_1}{x_2-x_1}=\frac{98-49}{2-1} \\ \\ \therefore m_C=49\text{miles per hour} \end{gathered}[/tex]Speed of Grain Freight Train:
[tex]\begin{gathered} \text{Reading off the graph that passes through the origin, we choose:} \\ (0,0)\text{ and }(1,45) \\ \\ \therefore m_G=\frac{45-0}{1-0}=45 \\ \\ m_G=45\text{miles per hour} \end{gathered}[/tex]- From the above calculations, we can easily observe that the Speed of the Coal Freight Train is greater than the speed of the Grain Freight Train
Final Answer
"The Coal Freight Train is traveling at a faster speed" (OPTION 2)
a newsletter publisher believes that 60`% of their readers own a laptop. is there sufficient evidence at the 0.050.05 level to refute the publisher's claim? state the null and alternative hypotheses for the above scenario.
The null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].
What is null and alternative hypothesis?
The null hypothesis is that the statement that researchers usually aim to disprove by performing tests of significance on the dataset. the most purpose of the null hypothesis is to help disprove a hypothesis or nullify it in favor of the alternate hypothesis that the researchers want to prove.
Let the percentage of readers who own a laptop be [tex]x.[/tex]
As newsletter publisher believes that [tex]60[/tex]`% of their readers own a laptop.
Therefore the null hypothesis is [tex]H_{0} : x=0.60[/tex] and alternative hypothesis is [tex]H_{1} :x\neq 0.60[/tex].
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Find the y intercept: y=3.5x-7
The y-intercept of the function y = 3.5x - 7 is ( 0, - 7 ).
A function is an association between inputs in which each input has a unique link to one or more outputs. Each function has a range, codomain, and domain.
Consider the function,
y = 3.5x - 7
The equation of a straight line is expressed in the slope-intercept form (a linear function). It takes the formula y = mx + b, where m is the slope, b is the y-intercept, and y and x serve as variables.
The value of y at x = 0 can be used to determine the y-intercept. The graph's intersection with the y-axis occurs at this location.
Then,
y = 3.5x - 7
y = 3.5( 0 ) - 7
y = - 7
The y-intercept of the function is ( 0, - 7).
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The list price of an air conditioner is $ 1260. The store offers an off season discount of 16% on it. Find its selling price.
Answer: $1058.40
Step-by-step explanation:
16% of 1260
10%=126
5%=63
1%=12.6
10% divide by 10
5% divide by 10 then divide by 2
1% divide by 100
126+63+12.6=201.6
$201.60
Because it is on a discount we know subtract it with the original price
1260-201.6=1058.4
$1058.40
in 15 of the 100 trials of the simulation none of the 10 passengers chosen was seated in first class. does this result provide convincing evidence that the tsa officers did not carrry out a truly random samplw?
The result provides convincing evidence that the tsa officers did not carrry out a truly random sample.
What is a random sample?A simple random sample is a subset of a statistical population in which each member has an equal chance of being selected.
In statistics, a simple random sample is a subset of individuals picked at random from a larger set, with all individuals having the same probability. It is the process of selecting a sample at random.
In this case, it's important to note that the fact that all the people chosen were first class members means that it was bias and not a random sampling.
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Help please. Was absent due to medical issues and trying to catch myself up and learn it now.
We paint with:
• red the regions where the function is decreasing,
,• green the regions where the function is increasing.
From the graph, we see that the function is:
• decreasing in the intervals (-∞, -1.5) and (2, ∞),
,• increasing in the interval (-1.5, 2).
Answer
• Increasing on the interval(s): ,(-∞, -1.5), (2, ∞)
,• Decreasing on the interval(s): ,(-1.5, 2)
-3/2 = -2/3w - 4/5 solve for w and simplify your answer as much as possible
Hello!
Here are all three solutions to the given equation.
Exact Form:
[tex]w=\frac{21}{20}[/tex]
Decimal Form:
[tex]w=1.05[/tex]
Mixed Number Form:
[tex]w=1\frac{1}{20}[/tex]
Hope this helps!
Determine the intervals on which the function is increasing, decreasing, and constant.
A) Increasing on (- 5, - 3) and (2, 5) Decreasing on (- 3, 0) Constant on (0, 2) B) Increasing on (- 3, - 1) Decreasing on (- 5, - 2) and (2, 4) Constant on (- 1, 2) C) Increasing on (- 3, 1) ; Decreasing on (- 5, - 3) and (0, 5) ; Constant on (1, 2) D ) Increasing on (- 3, 0) Decreasing on (- 5, - 3) and (2, 5); Constant on (0, 2)
The intervals on which the function is increasing, decreasing and constant are (-5,-3) and (2,5) on increasing (-3,0) on decreasing and (0,2) on constant.
What is intervals?
An interval in math is the measured in terms of the numbers. An interval to includes all the numbers that come between two of particular numbers. This is the range includes all of the realistic numbers between those two of numbers. Real numbers are the any kind of number you can definitely think of.
Sol-by showing in the figure the function is increasing on the (-3,0)
Decreasing on (-5,-3) and (2,5)
Constant on (0,2)
Thus, the correct option is A
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Salesman A gets paid $300 a month plus $8 for every sale he makes. Salesman B gets paid $1500 a mont. Write and equation and solve to see how many salesman a must make in order to make the same amount of salesman b
The salesman A must make 150 order to make the same amount of salesman B .
In the question ,
it is given that ,
Salesman A gets paid $300 per month
for every sale salesman A get $8 .
let the number of sales made by salesman A be "x" .
So, amount made by salesman A = 300 + 8x
Salesman B earns per month = $1500 .
To make the amount earned by both the salesman same ,
300 + 8x = 1500
8x = 1500 - 300
8x = 1200
x = 1200/8
x = 150
Therefore , The salesman A must make 150 order to make the same amount of salesman B .
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what is the absolute value for this equation? : |-x| = 3
Answer:
The answer is |-3|
Step-by-step explanation:
The absolute value of a negative number will always be the same number but positive. Like the absolute value of |-4| will be 4.
Isaiah's school is having a spring carnival. When Isaiah carries a bin of water balloons outside for the balloon toss, he trips and breaks 12 balloons. He counts the remaining water balloons, and there are 14 left. Which equation can you use to find the number of water balloons w in the bin before Isaiah trips?
Solve this equation for w to find the number of water balloons in the bin. Water balloons
Equation: w - 12 = 14
Answer: 26
Step-by-step explanation:
Lost 12, left with 14.
Let W be water balloons before the trip.
w - 12 = 14
14 + 12 = 26
Proof:
26 - 12 = 14
Write an equation of the line passing through the point (2, -9) that is perpendicular to the line V=x+6.
The equation of the line that is perpendicular to y = x + 6 is expressed as: y = -x - 7
How to Write the Equation of a Line?The equation of a line can be written as y = mx + 1. The value of m is the slope while the value of b is the y-intercept.
The slopes of two lines that are perpendicular to each other are negative reciprocals. This means, if we multiply their slope values together, we will get -1.
Given the line, y = x + 6, the slope of the line is 1. The slope of the line it is perpendicular to is -1, because -1 is the negative reciprocal of 1.
Substitute m = -1 and (x, y) = (2, -9) onto y = mx + b to find the value of b:
-9 = -1(2) + b
-9 = -2 + b
-9 + 2 = b
-7 = b
b = -7
To write the equation of the perpendicular line, substitute m = -1 and b = -7 into y = mx + b:
y = -x - 7
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You start at (2, -5). You move up 5 units and right 3 units. Where do you end?
the answer would be (0,5)
A manufacturer has been selling 1250 television sets a week at $450 each. a market survey indicates that for each $13 rebate offered to a buyer, the number of sets sold will increase by 130 per week.
The demand function of the number of sets sold will increase by 130 per week is p(x) = (-1 ÷ 13)x + 550.
Determine the coordinates of two points mostly online. Estimate the difference in y-coordinates between these two places. Estimate the difference in x-coordinates between these two places. Divide the y-coordinate difference by the x-coordinate difference.
Let p(x) denote the demand function, with x denoting the number of TV sets desired. As stated in the issue, a $10 decrease in p(x) causes a 130 rise in x. As a result, the slope of the demand function graph is -13 ÷ 130 = -1 ÷ 10.
Given p(1250) = 450,
-1 ÷ 10 = (p(x) - 450) ÷ (x - 1250)
p(x) = (-1 ÷ 13)x + 550
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(3x(2)+4x+2)-(7x(2)+2x+5)
how do we solve it please someone help
The simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].
In the given question,
The given expression is [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex].
We have to solve the given expression.
To solve this question we use have to follow some rule.
Some Rules are
We have to remove parentheses from each side of the equation and combine similar phrases to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.In this given question to solve the expression we firstly solve the bracket.
When we multiply the term under the bracket with minus sign then all sign under the bracket will also be changed
Now simplifying the expression.
[tex]=3x^2+4x+2-7x^2-2x-5[/tex]
Now we combine the similar term.
[tex]=(3x^2-7x^2)+(4x-2x)+(2-5)[/tex]
[tex]=-4x^2+2x-3[/tex]
Hence, the simplified form of the expression [tex](3x^2+4x+2)-(7x^2+2x+5)[/tex] is [tex]-4x^2+2x-3[/tex].
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8g - 7 = 18 + 3g
SOLVE EQUATION PLEASE
Answer:
g = 5
Step-by-step explanation:
8g - 7 = 18 + 3g
add 7 to both sides:
8g - 7 + 7 = 18 + 3g + 7
8g = 25 + 3g
subtract 3g from both sides:
8g - 3g = 25 + 3g - 3g
5g = 25
divide both sides by 5:
5g/5 = 25/5
g = 5
What number should be the exponent on the 10 so that the two numbers are equivalent? 75.6 - 10% = 0.00756 y = -3 C y = 3 c y y = 4 y = 4 =
Answer:
y = -4
Explanation:
Given the equation:
[tex]75.6\times10^y=0.00756[/tex][tex]\begin{gathered} 0.00756=7.56\times10^{-3} \\ =75.6\times10^{-4} \end{gathered}[/tex]Thus, the number is -4.
what is the equation of the line that passes through the point (-2, 14) and is perpendicular to the with the following equation? y = -2/5x - 1
Answer: the y = -2/5x - 1
Step-by-step explanation: hoped this help you two
Solve the equation b over 27 equals negative 3 for b.
81
9
−9
−81
Solve the equation 42 = v + 35 for v.
−77
77
−7
7
Solve the equation −128 = 4x for x.
−124
132
−32
32
The solution of the equation is as follows;
b = -81v = 7x = -32How to solve equations?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
In other words, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The expression can be solved as follows:
b / 27 = - 3
cross multiply
b = -3 × 27
b = - 81
42 = v + 35
subtract 35 from both sides of the equations.
42 - 35 = v + 35 - 35
v = 42 - 35
v = 7
- 128 = 4x
divide both sides of the equations by 4
4x / 4 = - 128 / 4
x = - 32
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Answer:
b = -81v = 7 x = -32Step-by-step explanation:
1) b/27 = -3, then b = ?
→ b/27 = -3
→ b = -3 × 27
→ [ b = -81 ]
Thus, value of b is -81.
2) 42 = v + 35, then v = ?
→ v + 35 = 42
→ v = 42 - 35
→ [ v = 7 ]
Thus, value of v is 7.
3) -128 = 4x, then x = ?
→ 4x = -128
→ x = -128/4
→ [ x = -32 ]
Thus, value of x is -32.
PLSSSSSS ANSWER SOON!!!!!!!
There is a pic
solve for P
Answer:
48x
Step-by-step explanation:
15+2+7+15+2+7=48 + x = 48x
Hope this helps!
Hi please help explain. Image attached. Thanks!
