Answer:
1.4
Step-by-step explanation:
tickets for a cinema costs £4 and £5. There were 223 customers who paid a total of £936. How many bought £4 tickets
The number of people who bought £4 tickets are 139.
How to illustrate the equation?Let £4 tickets be x
Let £5 tickets be y.
Therefore based on the information given, this will be:
x + y = 223 ..... i
4x + 5y = 936 ..... ii
From equation i
x = 213 - y
Put this into equation ii
4x + 5y = 936
4(213 - y) + 5y = 936
852 - 4y + 5y = 936
Collect like terms
y = 84
This implies that the number of £5 tickets is 84.
Recall that x + y = 223
x + 84 = 223
x = 223 - 84
x = 139
The number of £4 tickets is 139
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The perimeter (adding up all the sides) of a rectangular
piece of land is 228 feet. The length of the land can be
shown by x and its width can be shown by (2x + 6).
The perimeter (adding up all the sides) of a rectangular piece of land is 228 feet. The length of the land is 74 feet and its width is 154 feet.
Define perimeter.The perimeter of a closed plane figure is referred to in geometry. You might have studied perimeter calculations in school. An equilateral triangle has a 27-foot perimeter if each of its nine sides is the same length. The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimeter, meters, inches, and feet.
Given,
Perimeter = 228 feet
Length = x
Width = 2x + 6
Perimeter of rectangle = Length + Width
228 = x + 2x + 6
228 = 3x + 6
228 - 6 = 3x
222 = 3x
x = 74
The length of the land is 74 feet and its width is 154 feet.
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Ginny is 53 3/4
inches tall. Jillian is 1 3/8
inches shorter than Ginny and Jane is 1 1/5
inches shorter than Jillian. How tall is Jane?
Answer:
51.425
Step-by-step explanation:
make x the subject
........................................
Step-by-step explanation:
Find the attached picture
Find the circumference of a circle with a diameter of 20 centimeters. Round your answer to the nearest centimeter.
The circumference of circle with the diameter is 62.8cm
The Circumference of the circle is the measurement of the boundary of the circle.
If we open a circle and make a straight line out of it , then its length is circumference.
The circumference of a circle = 2πr
where r is radius of circle
we can write circumference in terms of diameter,
diameter of circle = 2r
so , the circumference = πd
Given in the question,
the diameter of circle = 20cm
Therefore , the circumference will be πd
taking 3.14 value of π
= (3.14)× 20
=62.8 cm
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Given that x is a nonnegative number, a student conjectured that x+5 < x²
Which value of x is a counterexample to the student's conjecture?
0 x=-1²
x=-5
x=0
x=5
The value of x that is a counterexample to the student's conjecture is of:
x = 0.
What is a counter example?A counter example to a conjecture is a statement that makes the conjecture false.
In the context of this problem, the conjecture is presented as follows:
x + 5 < x².
The conjecture is only true for non-negative numbers, hence the counter example also has to be a non-negative number, meaning that these following options are removed, as they are negative numbers:
x = -1.x = -5.For x = 0, the conjecture is given as follows:
0 + 5 < 0²
5 < 0
Which is a false statement, hence x = 0 is the counterexample to the student's conjecture.
At x = 5, the conjecture is given as follows:
5 + 5 < 5².
10 < 25.
Which is true, however, the conjecture has already been shown to be false at x = 0.
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If the area of a circle is 114 cm2, what is its circumference?
Answer: ≈ 18.91 cm
Step-by-step explanation:
r²= 114 ÷ pi/3.14 = 5700/157
r = √r²
≈ 6.025
Circumference = r × pi/3.14
≈ 18,91 cm
What is the change to the graph of y=−3x−2 when the slope is changed to −1/3?
The slope of the graph will be changed. The graph is still a straight line, But it becomes steep.
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
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You have a credit card with an initial balance of $3,168. 00 and an interest rate of 12. 75% apr. If you make no payments on the card for three months, how much is your balance by the end of the third month?.
When the interest rate is 12.75%, your balance at the conclusion of the third month is $3270.06.
When provided,
P=$3168
R=0.1275/12
= 0.010625
n=3
Interest rate = 12. 75%
Using the formula
A=P(1+r)^n
we can now insert the values
A=3168(1+0.010625)^3 and
A=3270.06
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A line passes through the point (5,9) and has a slope of 4. write an equation in point slope form for this line
Answer: y = 4x -11
Remeber the slope is the gradient -> m
Our equation to find the problem:
y-y1 = m(x-x1)Substitude:
y-9 = 4(x-5) because y1= 9, x1 = 5 and m = 4
y-9 = 4x - 20 multiply by 4 with the numbers in the bracets
y = 4x -11 - 9 on both sides
therfore our equation that passes through the point (5,9) and has a slope of 4 is y = 4x -11
there are 3 siblings that are each 1 year apart in age the total of their age is 54. How old are they ?
Answer:
56
Step-by-step explanation:
Step-by-step explanation:
54÷3
=18
one is 17
one is 18
the other is 19
ITEM 14 - from the lesson Modeling with Linear Inequalities
Catherine is practicing math and science questions to prepare for her upcoming exams. It takes her 12 minutes to do a math question and 5 minutes to answer a science question.
Among the following options, which one should she choose if she wants to spend less than an hour practicing?
Hint: Set up an equation to represent the scenario. Here is how you should set your equation up.
A. 3 math questions and 5 science questions
B. 2 math questions and 7 science questions
C.5 math questions and 1 science question
D.4 math questions and 3 science questions
The option she should choose based on the given condition is Option B 2 math questions and 7 science questions.
What are linear inequalities?
When two linear expressions are compared using the inequality symbols, that is an expression of a linear inequality.
Given, Time is taken for solving single math question = 12 minutes
Time is taken for solving single science question = 5 minutes
Let 'x' be the total number of math questions and 'y' be the total number of science questions.
Then,
The total time taken for 'x' math questions = 12x minutes
The total time taken for 'y' science questions = 5y minutes
So, as defined in the question, we get
Total time she wants to spend practicing < 60 minutes
i. e. 12x + 5y < 60 .................... (i)
Now, we check this condition for each answer choice
A) x = 3 and y = 5, substituting values in equation (i)
So, 12*3 + 5*5 < 60
or, 36+25 < 60
or, 61 < 60 (Not valid)
B) x = 2 and y = 7, substituting values in equation (i)
So, 12*2 + 5*7 < 60
or, 24+35 < 60
or, 59 < 60 (Valid)
So, Option B is valid.
Hence, the required answer of choice is Option B i.e. 2 math questions and 7 science questions.
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write an expression for twice a number W, increased by 12
Answer:
2w+12
Step-by-step explanation:
twice a number: doubled or multiplied by 2
Increased: means to add
Hopes this helps please mark brainliest
Answer:
W2+12
Step-by-step explanation:
twice a number means to multiply by two
increased by 12 means to add 12
so W2+12 is the answer
A survey of all beings on planet Vreel found that 25% preferred vreel juice to all other juices. If 3 beings preferred vreel juice, how many beings were surveyed altogether?
Answer:
12.
Step-by-step explanation:
[tex]\text{let } x = \text{ number of people who participated in the survey}[/tex]
3 = 25% of x. We can rewrite that as an equation.
[tex]\frac3x \times 100 = 25 \text{ // Divide by 100}\\ \\\frac3x = \frac14 \text{ // Cross multiply}\\\\12 = x[/tex]
The side lengths of the state flag is the ratio 4:7. If the flag is 28 feet long. What is its height? Show your work.
Answer:
16 ft
Step-by-step explanation:
We are here given that the side lengths of the state flag are in ratio 4:7 . Let us take the ratio to be [tex] 4x:7x[/tex] .
Now we are given that the flag is 28 ft. long. So ;
[tex]\longrightarrow 7x = 28\\[/tex]
Divide both sides by 7 ,
[tex]\longrightarrow x = 4 [/tex]
Therefore the height of the flag will be ,
[tex]\longrightarrow h = 4x [/tex]
Substitute for x ,
[tex]\longrightarrow h = 4(4) ft [/tex]
Multiply,
[tex]\longrightarrow\underline{\underline{ h = 16ft}} [/tex]
And we are done!
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The amount owed at the end of the 6 years duration is $10865
How to determine the amount owed in six years?The given parameters about the compound interest are
Principal Amount, P = $5300
Interest Rate, R = 8%
Time, t = 6 years
To calculate the amount owed, we make use of the following formula
A = P + CI
Where
Compound interest, CI = P(1 + R)^t - P
So, the equation becomes
A = P + P(1 + R)^t - P
Evaluate the like terms
A = P(1 + R)^t
In this question, the formula is given as
A = P(1 + r/n)^nt
Where
n = 12, i.e compounded monthly
Substitute the known values in the above equation
A = 5300 * (1 + 8%/12)^(6*12)
Express 8% as decimal
A = 5300 * (1 + 0.08/12)^(6*12)
Evaluate the sum
A = 5300 * (1.01)^(6*12)
Evaluate the exponent
A = 5300 * 2.05
Evaluate the product
A = 10865
Hence, the value of the amount after 6 years is $10865
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-5.5+10.63+(—3.7)+10.63
Answer:
12.06
Step-by-step explanation:
-5.5+10.63+(-3.7)+10.63
1) Remove parentheses.
-5.5 + 10.63 - 3.7 + 10.63
2) Simplify -5.5 + 10.63 to 5.13.
5.13 - 3.7 + 10.63
3) Simplify 5.13 - 3.7 to 1.43.
1.43 + 10.63
4) Simplify.
12.06
Audrey and Sam divided money in the ratio of 3 to 5. Audrey obtained $36, how much money do they have altogether?
8:20 is the same as 2:5.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
= 12 + SS= (2/5)AS= (2/5)(12+S)5S = 24 + 2S3S = 24S = 24/3 = 8 = what Sam receivedA= 8+12 = 20 = what Audreyreceived8:20 is the same as 2:5divide both 8 and 20 by 4 to get the 2 to 5 ratio.hence,8:20 is the same as 2:5.
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What is mean absolute deviation in math example?.
The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We can determine how "spread out" the values in a data set are by looking at the mean absolute deviation.
What is mean absolute deviation?The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data collection. A measure of variance in a data collection is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation. Take the absolute value of each digit in the data set, then deduct the mean. Next, add up the absolute values. The mean absolute deviation is then calculated by dividing the aforementioned sum by the total number of values in the data set. Finally, tenths should be rounded.
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Please someone help me out with my math homework .
Answer:
you see that Square on the corner of B use that unit box and trace it and then go to E and Trace two unit boxes at the top
PLEASE HELP DUE IN 2 MINUTES
Patel is solving 8x2 16x 3 = 0. which steps could he use to solve the quadratic equation? select three options. 8(x2 2x 1) = â€""3 8 x = â€""1 plus or minus startroot startfraction 5 over 8 endfraction endroot x = â€""1 plus or minus startroot startfraction 4 over 8 endfraction endroot 8(x2 2x 1) = 3 1 8(x2 2x) = â€""3
Answer: 8(x2 + 2x) = –3
8(x2 + 2x + 1) = –3 + 8
x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
Step-by-step explanation: I hope i did this right?
Answer:
A. 8(x2 + 2x + 1) = –3 + 8
B. x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot
E. 8(x2 + 2x) = –3
Step-by-step explanation:
On edge 2022
the basis for a statistical process control chart is a(the) multiple choice process capability. sampling distribution. control limit. sample range. sample mean.
The correct statement is 'the basis for a statistical process control chart is a(the) sampling distribution'
In this question, we have been given a statement.
We need to select the correct option to complete the given statement.
Given statement:
the basis for a statistical process control chart is a(the) ............
We know that statistical process control chart or graph is used to study how a process changes over time with data plotted.
A statistical process control chart is nothing but a line graph showing a measure in consecutive order, with the measure on the y-axis and time or observation number on the horizontal x-axis. The use of statistical process control chart in the monitoring and maintaining of the quality found in a sample.
Therefore, the correct statement is 'the basis for a statistical process control chart is a(the) sampling distribution'
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the mean of this sample is 264.4 yards. his driving distance is known to be normally distributed with a population standard deviation of 20 yards. test jean's claim that jack's driving distance is less than 275 yards at a 0.05 significance level. calculate the test statistic to 2 decimal places.
After solving, the test statistic value of z is -2.65.
In the given question,
Sample Mean x=264.4
Population standard deviation σ=20
sample size (n) = 25
significance level α=0.05
To test Jean's claim that Jack's driving distance is less than 275 yards
The null and alternative hypothesis are
H(0): μ=275
H(α): μ<275
Test Statistic Z is:
Z = (x-μ)/(σ/√n)
Z = (264.4-275)/(20/√25)
Z = -10.6/(20/5)
Z = -10.6/4
Z = -2.65
Hence, the test statistic value of z is -2.65.
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The right question is:
Jack tells Jean that his average drive of a golf ball is 275 yards. Jean is skeptical, she thinks he has overstated is driving distance and asks for substantiation. So Jack takes a random sample of 25 of his drives. The mean of this sample is 264.4 yards. His driving distance is known to be normally distributed with a population standard deviation of 20 yards. Test Jean's claim that Jack's driving distance is less than 275 yards at a 0.05 significance level. Calculate the test statistic to 2 decimal places.
Elion has three more quarters than dimes in his pocket, for a total of 2.50 write an equation that could be used to determine the number of dimes, d, in his pocket
pls show work
The equation that could be used to determine the number of dimes, d, in his pocket is: 0.35d + 0.75 =2.50.
How to find the equation?Let the number of dimes be d
Let number of quarters be q
Hence,
d + q = 2.50
q = d+3
1 dimes = $0.10
1 quarters = $0.25
0.10d +0.25q = 2.50
Substitute value of q into 0.10d +0.25q = 2.50
0.10d +0.25 (d+3) = 2.50
0.10d +0.25d +0.75 = 2.50
0.35d + 0.75 =2.50
Hence, the equation is : 0.35d + 0.75 =2.50.
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48% percent of Mrs.Cano's students are in athletics. If there are 25 students in her class then how many are in athletics?
The percentage is used to denote the fraction of a quantity present.
The number of athletics students are 4. The correct answer is option A.
What is Percentage ?The percentage is defined as the portion of quantity present.
It is converted into fraction by dividing it by 100.
The percentage of students in athletics are 48%.
Total number of students in the class is 25.
The number of students in athletics is given as,
N = 48% of 25
=> N = 48 / 100 × 25
=> N = 48 / 4
=> N = 12.
Hence the number of athletics students in Mrs. Cano's class is 12.
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The elimination method was used to solve the following system of equations:
x − 6y = 30
5x − 2y = −46
Which of the following is the correct y-coordinate of the solution?
−12
−7
7
12
Answer:
-7
Step-by-step explanation:
To solve this system of equations, let's solve for x first. We can move 6y to the other side of the first equation by adding it to both sides. Now we know what x equals:
x = 30 + 6y.
Now, we can substitute that equation in for every x in the 2nd equation, then solve for y.
The second equation becomes:
5(30+6y) - 2y = -46
(150 + 30y) - 2y = -46
Simplify.
150 + 28y = -46
Subtract 150 from both sides
28y = -196
Divide by 28 (to get y by itself)
y = -7
Answer:
y = -7
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}x-6y = 30\\5x-2y =-46\end{cases}[/tex]
Multiply the first equation by -5:
[tex]\implies -5(x-6y)=-5(30)[/tex]
[tex]\implies -5x+30y=-150[/tex]
Add this to the second equation to eliminate the term in x:
[tex]\begin{array}{crcrcl}& 5x & - & 2y & = & \:\:-46\\+&(-5x&+&30y&=&-150)\\\cline{2-6}&&&28y&=&-196\\ \cline{2-6}\end{array}[/tex]
Solve the equation for y:
[tex]\implies 28y=-196[/tex]
[tex]\implies \dfrac{28y}{28}=\dfrac{-196}{28}[/tex]
[tex]\implies y=-7[/tex]
x+5y-3z=19
2x-3y+4z=-11
4x+y-2z=0
The solution of the system of equations is
x = -13/20 , y = 9/2 , z = 19/20
Given, a system of equations
x + 5y - 3z = 19
2x - 3y + 4z = -11
4x + y - 2z = 0
On multiplying eq (1) by 2, we get
2x + 10y - 6z = 38
On subtracting eq (1) and (2), we get
13y - 10z = 49 ... (4)
Now, On multiplying eq (2) by 2, we get
4x - 6y + 8z = -22
On subtracting eq (3) and (2), we get
7y - 10z = 22 ... (5)
Now, on subtracting eq (4) and (5), we get
6y = 27
y = 9/2
On substituting the value of y in Eq (5), we get
z = 19/20
Now, On substituting the value of y & z in Eq (1), we get
x + 5(9/2) - 3(19/20) = 19
x + 45/2 - 57/20 = 19
x + 393/20 = 19
x = -13/20
Hence, the solution of the system of equations is
x = -13/20 , y = 9/2 , z = 19/20
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Which of the following is the graph of y=-1/2x+2
Lines f and g are graphed on top of each other below.Does the system of linear equation on the below graph represent infinitely many solution?
True or False
The required answer is True.
What are Graphing Systems of Linear Equations?
There exists an endless number of valid solutions for both equations if the graphs of the equations are identical.
For the given graph,
The equations are simply multiples or rearrangements of one another if graph lines meet. Every set of numbers that satisfies one of the equations also satisfies the other.
Hence, the system of the linear equation on the below graph represents infinitely many solutions and it is True.
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