The value of y that satisfies the equation is 41.
What is the arithmetic operation?
Arithmetic operations involve the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
To solve this equation for y, you can divide both sides by 4:
4y/4 = 164/4
This simplifies to:
y = 41
Hence, the value of y that satisfies the equation is 41.
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Christian went into a movie theater and bought 8 drinks and 10 candies, costing a total of $94. Dianelys went into the same movie theater and bought 9 drinks and 6 candies, costing a total of $79.50. Write a system of equations that could be used to determine the price of each drink and the price of each candy. Define the variables that you use to write the system.
The cost of each drink is $5.5
The cost of each candy is $5
What is elimination method ?Using the elimination method, you may either add or subtract the equations to produce an equation in one variable. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
According to the given information
Let number of drinks = x
Let number of candies = y
Christian bought 8 drinks and 10 candies and it costed $94
So the equation becomes
8x + 10 y = $94
Other guy bought 9 drinks and 6 candies and it costed $79.50
So the equation becomes
9x + 6y = $79.50
By applying elimination method
9x + 6y = $79.50
Dividing by 2
3x + 2y = $26.5
multiplying the above equation by 5
15x + 10y = $132.5
8x + 10 y = $94
Subtract the following equation
7x = 38.5
x = 5.5
substituting the value of x in above one equation we get
y = 5
So the cost of each drink is $5.5
the cost of each candy is $5
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Answer:
D = the price of each drink
C = The price of each candy
One drink costs d. So 8 drinks cost 8d. Same thing with candies except a different variable. One candy costs c. Therefore 10 candies cost 10c. So the first equation here would be :
8d + 10c = 94
Same thing with the second equation but with different numbers :
9d + 6c = 79.50
If you're also looking for a solution to this answer. You use a process called the elimination method.
Let me know if you have any questions ! <3
help!! please! i don’t understand
Answer:
[tex] 2 \sqrt[3] {60}~mm [/tex]
Step-by-step explanation:
The volume of a cube is the side cubed, so each edge is the cubic root of the volume.
V = 480 mm³
[tex] s = \sqrt[3] {V} [/tex]
[tex] s = \sqrt[3] {480~mm^3} [/tex]
[tex] s = \sqrt[3] {2^3 \times 2^2 \times 3 \times 5~mm^3} [/tex]
[tex] s = \sqrt[3] {2^3} \times \sqrt[3] {2^2 \times 3 \times 5~mm^3} [/tex]
[tex] s = 2 \sqrt[3] {60}~mm [/tex]
213. Sandy has 1 quart and 1 pint of soda.
How many cups can she divide this
amount into?
simplify the expression: 5(1+2m)
Answer:
Hi!
The answer would be: 5 + 10m
I hope this helped you! :)
Answer:
[tex]\bf 5+10m[/tex]
Step-by-step explanation:
[tex]\bf 5\left(1+2m\right)[/tex]
Apply the distributive law:-
[tex]\bf 5\left(1+2m\right)=5\times \:1+5\times\:2m[/tex]
[tex]\bf 5\times\:1+5\times \:2m[/tex]
[tex]\bf 5+10m[/tex]
___________________
Hope this helps!
Have a good one!
Use the image below to answer the next two questions.
ABCD pictured below is a square.
Categorize the angles as either 45° or 90°.
The measure of angle ABC is 90° and the the measure of angle BDC is 45°.
Square ABCD is given.
What is a square?A square is a quadrilateral with four equal sides. There are many objects around us that are in the shape of a square. Each square shape is identified by its equal sides and its interior angles that are equal to 90°.
Diagonals bisects the angles in square and intersect each other at right angle.
Now, ∠ABC=90°
∠AED=90°
∠BAC=45°
∠DBC=45°
∠BDC=45°
Hence, the measure of angle ABC is 90° and the the measure of angle BDC is 45°.
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Explain the steps in solving 2.14x - 12.18 = -5.76, and write the solution to the equation.
WRITER
Someone please help me with this!!!
Answer:
x = 3
Step-by-step explanation:
You want to solve for x, so you want to get x on one side of the equation. To do this, you can add the -12.18 to both sides of the equation (you add since it's negative).
2.14x - 12.18 = -5.76
2.14x = 6.42
Then you want to get x by itself, without the 2.14 in front of it. To do this, you can divide both sides of the equation by 2.14.
This will give you,
x = 3
7. What is the equation of a line that is parallel to -x+3 y=6 and passes through the point (3,5) ?
y=___ x +_____
The equation of a line that is parallel to -x + 3y = 6 and passes through the point (3,5) is y = 1 / 3 x + 5
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of a line that is parallel to -x + 3y = 6 and passes through the point (3,5) can be found as follows:
Parallel lines have the same slope.
-x + 3y = 6
3y = x + 6
y = 1 / 3 x + 2
Therefore, the slope is 1 / 3. Let's find the y-intercept using (3, 5).
y = 1 / 3 x + b
5 = 1 / 3 (3) + b
b = 5
Therefore, the equation is y = 1 / 3 x + 5
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Consider the expression 40+24 . Find the greatest common factor of the two numbers, and rewrite the expression using the distributive property.
The greatest common factor of 40 and 24 would be; 8.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We can rewrite this expression for distribution using the amount of times 8 goes into both numbers as;
8(5 + 3)
Using the distributive property, we get:
8(5) + 8(3) = 40 + 24.
Threfore,
The greatest common factor of 40 and 24 would be; 8.
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Find a polynomial f(x) of degree 4 with real coefficients and the following zeros. 1 (multiplicity 2) , 1+2i
Answer:
Factorization
Step-by-step explanation:
determine the sample size needed to construct a 95 % confidence interval to estimate the population proportion is 0.54, and the margin of error is 0.06. use two decimal places for the critical value and round to the nearest integer for your final answer. eg. 48.47
The sample size needed is at least 311.17.
We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2. So:
α = [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of 1-α
So it is z with a p-value of , so
1-0.025 = 0.975, so z = 1.96
Now, find the margin of error M as such
[tex]M = z*\frac{sd}{\sqrt{n} }[/tex]
where sd = σ = standard deviation
At least n, in which N is found when M= 0.06 and σ = 0.54. So
[tex]M = z*\frac{sd}{\sqrt{n} } \\0.06 = 1.96 * \frac{0.54}{\sqrt{n}} \\\sqrt{n} = \frac{1.96*0.54}{0.06} \\\sqrt{n} = 17.64\\n = 311.1696\\[/tex]
Rounding off to the nearest integer, we get n = 311.17.
Thus, the sample size needed is at least 311.17.
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There is a fee to enter the county fair, plus a fixed amount to play each game. The
line shows the money spent at the fair, y, when a games are played.
Money Spent at the Fair
Money Spent ($)
y
Write an equation for the line in slope-intercept form.
Drag a number into each box to write the equation.
Y
An equation for the line in slope-intercept form is y=(6/5)x+8
What is a slope?The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.
The steepness, incline, or grade of a line can be approximated by the slope's absolute value. The slope of a line determines how steep it is.
From the graph,
The line passes through the points (0,8) and (5, 14)
Slope m=(14-8)/(5-0)
m=6/5
(0, 8) passes through the line y=mx+c
So, 8=6(0)/5+c
Then, c=8
An equation for the line in slope-intercept form is y=(6/5)x+8.
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a) Work out the minimum number of dogs that could have a mass of more than 24 kg
b) Work out the maximum number of dogs that could have a mass of more than 24 kg}.
Mass(kg) Frequency
0≤x<10 2
10≤x<20 7
20≤x<30 12
30≤x<40 6
a) A minimum number of dogs that could have a mass of more than 24 kg is 6.
b) The maximum number of dogs that could have a mass of more than 18 kg is 20.
How to find the minimum and maximum value mean?We will rearrange the function using fundamental algebraic concepts to process the value of x when the derivative equals 0. This response gives us the x-coordinate of the function's vertex, which is the point that the maximum or minimum will occur. To find the minimum or maximum, we will start by rewriting the solution into the original function.
From the given parameters, we can see that the minimum of the values present in the interval 20 to 40 is 6
From the given parameters, we can see that the maximum of the values present in the interval 20 to 40 is;
(12 + 6) = 18
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Write an equation for a rational function with:
Vertical asymptotes at x = 6 and x = 3
x intercepts at x = 1 and x = -1
y intercept at 5
Answer:
Making a fraction is the easiest way to do this.
The x-intercepts give solutions to a problem that equals zero.
The vertical asymptotes are values x cannot be, in a fraction the denominator can not be zero.
Horizontal asymptotes are the values y approaches. This can be accomplished by making the leading term have a coefficient of 6
Step-by-step explanation:
A standard queen bed hotel room at the Posh Inn is currently priced at $ 135 a day, after a 17 % markup to offset inflation costs. What was the daily charge for the room before the increase?
the regular daily charge is "x", oddly enough that's the 100%.
so the new charge is 17% up, that means the new charge is 100% + 17% = 117%, and we know that's $135, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 135& 117 \end{array} \implies \cfrac{x}{135}~~=~~\cfrac{100}{117} \\\\\\ 117x=13500\implies x=\cfrac{13500}{117}\implies x=\cfrac{1500}{13}\implies x=115\frac{5}{13}[/tex]
Question 5 id points
Do not round or enter wards, use a decimal answer.
You are playing a carnival game. You will spin the two spinners below.
Rule 1: To win the grand prize, you need to spin an "A" and a "1". What is the probability that you win a bōsic prize?
Answer:
Rule 2: To win you a basic prize, you need to spin an "A" or a "1". What is the probability that you win a basic prize?
Probability of winning a grand prize is 1/10
Probability of winning a basic prize is 11/20
What is the probability of two independent events?
If A and B are two independent events, then P(A and B) = P(A) * P(B).
If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).
Solution:
P(A) = no. of A / total possibility
= 4/10
P(B) = no. of 1's/total possibility
= 3/12
= 1/4
Now,
To win a grand prize you need an "A" and "1" .
∴ P(A and B) = P(A) × P(B)
= 4/10 × 1/4
P(A and B) = 1/10
Now ,
To win a basic prize you need to spin an "A" or a "1"
∴ P(A or B) = P(A) + P(B) - P(A and B)
= 4/10 + 1/4 - 1/10
= 3/10 + 1/4
∴ P(A or B)= 11/20
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Probability of winning a grand prize is 1/10
Probability of winning a basic prize is 11/20
What is the probability of two independent events?If A and B are two independent events, then P(A and B) = P(A) * P(B).
If Events A and B are independent, the probability that either Event A or Event B occurs is: P(A or B) = P(A) + P(B) - P(A and B).
Evaluating :P(A) = no. of A / total possibility
= 4/10
P(B) = no. of 1's/total possibility
= 3/12
= 1/4
Now,
To win a grand prize you need an "A" and "1" .
∴ P(A and B) = P(A) × P(B)
= 4/10 × 1/4
P(A and B) = 1/10
Now ,
To win a basic prize you need to spin an "A" or a "1"
∴ P(A or B) = P(A) + P(B) - P(A and B)
= 4/10 + 1/4 - 1/10
= 3/10 + 1/4
∴ P(A or B)= 11/20
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Write this ratio as a fraction in simplest form without any units 27 feet to 8 yards
The ratio of 27 feet to 8 yards is 9/8 while converting feet to yards and the ratio is also 9/8 while converting yards to feet.
What are yards and feet?Yards and feet are units use to measure the length of geometrical shapes.
1 foot equal to 0.333 yards and similarly 1 yard equal to 3 feet. There is proportional relationship between them.
what did you get from the above fraction value?We got the same fraction value from the ratio of two units which implies that the two units are proportional.
1 foot =0.333 yard so
27 feet = 9 yards
similarly, 1 yard = 3 feet
so, 8 yard = 24 feet
hence, the ratio is 9/8
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Simplify to create an equivalent expression.
2(-n -3) -7(5+2n)
Answer:
-16n-41
Step-by-step explanation:
Suppose a simple random sample of 30 students from this district is selected. What is the probability that at least half of them have brown eyes? (Use technology. Round your answer to three decimal places.)
In the simple random sample, the probability that at least half of the students have brown eyes is 0.400
How to calculate probability of an event at a particular time?Probability is defined as the chance of occurrence of an event.
Probability is defined as follows:
P(E)=[tex]\frac{no of required outcome}{total of possible outcomes}[/tex]
The given parameters are:
The sample size= 30 students
Number with brown eye=40%
40% x 30 = [tex]\frac{40}{100} * 30[/tex]
=12
This means that there 12 students out of 30 that have brown eyes.
Applying the probability formula
[tex]\frac{12}{30}[/tex]= 2/5
In conclusion 0.400 of the students have brown eyes.
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(a) Solve the given inequality 3 (x +2) ≥ 5 (x + 1).
(b) Find the greatest possible value of x, if it is;
1. a rational number
2. an integer
3. a prime number
The following information matrices shows how many of each Video Game Consoles that each
electronics store sold during one weekend and the price that is charged for each gaming console at all
3 stores.
Micro Middle store sold the least number of video game consoles.
What is a 2D matrix?The two dimensions of a matrix are represented by rows and columns. The row index and the column index are the two subscripts that each element is specified by.
The rows and columns in a matrix stand in for the two dimensions. The row index and the column index serve as two subscripts that each define an element. A 2D matrix is expanded into a multidimensional array, which uses additional subscripts for indexing.
The total no. of consoles sold by each store is:
Game Go = 53+21+48 = 122
Better Buy = 65+34+70 = 169
Micro Middle = 18+11+15 = 44
The least number of consoles were sold by Micro Middle(44).
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Simplify. (3x² - 2x + 2) - (x² + 5x-5) A. 2x² - 7x+7 B. 2x²-3x - 3 C. 2x² + 3x - 3 D. 4x² + 3x 3
The equivalent expression is 2x² - 7x + 7
Option A is the correct answer.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
2x + 6 - 9 is an expression.
3x = 9 is an expression.
We have,
(3x² - 2x + 2) - (x² + 5x - 5)
Remove the parenthesis.
3x² - 2x + 2 - x² - 5x + 5
Add like terms.
2x² - 2x + 2 - 5x + 5
Add like terms
2x² - 7x + 7
Thus,
The final expression is 2x² - 7x + 7
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Output(y) 8 less than 3 times x
Answer:
y = 3x - 8
Step-by-step explanation:
A football club sells, on average, 23000 tickets per match. In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?
Answer:
On average, the football club sells 1,058,000 tickets per season.
Step-by-step explanation:
[tex]23000[/tex] × [tex]46 = 1058000[/tex]
Where does the line f(x) = x-1 cross the parabola g(x) = (x+2)^2-9?
Answer:
The line and the parabola cross at x = -4 and x = 1
Step-by-step explanation:
Set f(x) = g(x)
[tex]x-1 = (x+2)^2-9\\x - 1 = x^2+4x+4-9\\x = x^2 + 4x - 4\\0 = x^2 + 3x - 4\\Factor\\0 = (x - 1) (x + 4)\\x = 1, -4[/tex]
Write an inequality with x isolated on the left side that is equivalent to the given inequality.
Fx+Wy>R; Assume F > 0.
The equivalent inequality with x isolated on the left side is
Need help asap
The inequality Fx + Wy > R written with x isolated to the left sides is
x > (R - Wy) / FHow to write the inequality with x isolated to the left hand sideInequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe given inequality in the problem has greater than sign and it is written as Fx + Wy > R
rearranging the inequality gives
Fx + Wy > R
Fx > R - Wy
divide through by F
Fx / F> R/F - Wy/F
x > (R - Wy) / F
isolating x to the left side gives x > (R - Wy) / F
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Question
the third term of GP is 4 the product of its first 5 term is
please solve it
Don't Spam
[tex] \huge{ \bold{ \color{purple}{Solution }}}[/tex]
Let a be the first term and r be the common ratio
Now,
[tex] \large{ \sf{T _3 = 4}}[/tex]
[tex] \large{ \sf{ {ar}^{2} = 4}}[/tex]
[tex]\large{ \sf{ \therefore \: product \: of \: first \: 5 \: term \: = a _1 \times a_2 \times a_3 \times a_4 \times \: a _5}}[/tex]
[tex] \large{ \sf{ = a(ar)( {ar}^{2} )( {ar}^{3} )( {ar}^{4} ) = {a}^{5} r {}^{10} }}[/tex]
[tex] \large{ \sf{ \red{(ar {}^{2} ) {}^{5} = {4}^{5} }}}[/tex]
[tex] \rule{150pt}{5pt}[/tex]
A employee must create 140 gallons of slash burn fuel that must have a ratio of 8 parts diesel to 2 parts gas. How much diesel and gas are needed to create this mixture?
The amount of diesel required to create slash burn fuel is = 112 gallons
The amount of gas required to create slash burn fuel = 28 gallons
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
The total amount of slash fuel = 140 gallons
The ratio of diesel to gas in slash fuel is = 8 : 2
Let the amount of diesel required to create slash burn fuel be = 8x
Let the amount of gas required to create slash burn fuel be = 2x
So , the equation of proportion is given by
Total amount of slash fuel = amount of diesel required to create slash burn fuel + amount of gas required to create slash burn fuel
Substituting the values in the equation , we get
Total amount of slash fuel = 8x + 2x
8x + 2x = 140
10x = 140
Divide by 10 on both sides of the equation , we get
x = 14 gallons
Substituting the value of x in the above expressions , we get
Amount of diesel required to create slash burn fuel = 8x
Amount of diesel required to create slash burn fuel = 8 x 14
Amount of diesel required to create slash burn fuel = 112 gallons
And ,
Amount of gas required to create slash burn fuel = 2x
Amount of gas required to create slash burn fuel = 2 x 14
Amount of gas required to create slash burn fuel = 28 gallons
Hence ,
The amount of diesel required to create slash burn fuel is = 112 gallons
The amount of gas required to create slash burn fuel = 28 gallons
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plssss helpppp right answers only and explaintion.
The equivalent of the expression 2³/2⁷ using the law of indices is (a) 1/2⁴
How to determine the equivalent expression?From the question, we have the following parameters that can be used in our computation:
2³/2⁷
The above expression can be solved using the law of indices
When the law of indices is applied, we have the following representation
2³/2⁷ = 2(³ ⁻ ⁷)
Remove the bracket in the above expression
So, we have the following representation
2³/2⁷ = 2³ ⁻ ⁷
Evaluate the difference
This gives
2³/2⁷ = 2⁻⁴
Rewrite as
2³/2⁷ = 1/2⁴
Hence, the solution is (a) 1/2⁴
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b is the midpoint of segment ac. a has coordinates (-3, 4) and b has coordinates (-1 1/2, 1). find the coordinates of c
The coordinates point C of the given line segment AC is C(0, -2) whose midpoint is at B.
How to calculate a midpoint of a line segment?To calculate the midpoint of a line segment, find the average for the coordinates of the endpoints of the line segment. I.e.,
Consider a line segment AC, B is its midpoint.
So, the coordinates of B are (Where we have A(x1, y1) and C(x2, y2))
B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
Calculation:It is given that, B is the midpoint of a line segment AC.
Where A has coordinates as (-3, 4) and B has coordinates as (-1 1/2, 1).
So, the coordinates of the other end point C of the given line segment are calculated as
B(x, y) = [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex]
⇒ (-1.5, 1) = [tex](\frac{-3+x2}{2}, \frac{4+y2}{2})[/tex]
⇒ -1.5 = (-3 + x2)/2 and 1 = (4 + y2)/2
⇒ -3 = -3 + x2 and 2 = 4 + y2
⇒ x2 = 0 and y2 = 2 - 4 = -2
Therefore, point C has coordinates as (0, -2).
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Find the volume of the solid. When appropriate, use 3.14 and round to the nearest hundredth.
Answer:
904.32 cm³
Step-by-step explanation:
Assuming 12cm is the diameter.
The given solid is a sphere, we must find the volume.
Given radius:
[tex]6[/tex]6
Use the equation [tex]v=\frac{4}{3} \pi r^3[/tex] to find the volume of the sphere.
[tex]\frac{4}{3} \times\pi\times6^3[/tex]
≈ 904.77868
Rounding, 904.32 cm³