Answer: A
Step-by-step explanation: To solve this problem, we can set up a system of equations to represent the information given in the problem. Let x represent the cost of a plate of spring rolls, y represent the cost of a plate of chicken tenders, and z represent the cost of a plate of pretzel dippers.
The first group spent $23 on 2 plates of chicken tenders and 1 plate of pretzel dippers, so the equation for this group is:
2y + z = $23
The second group spent $30.75 to buy 3 plates of spring rolls and 1 plate of chicken tenders, so the equation for this group is:
3x + y = $30.75
The third group spent $22.25 on one of each appetizer, so the equation for this group is:
x + y + z = $22.25
Now that we have three equations, we can use algebraic techniques to solve for the value of x, which represents the cost of a plate of spring rolls.
First, we can solve the second equation for y:
y = $30.75 - 3x
Substituting this expression for y into the first equation, we get:
2($30.75 - 3x) + z = $23
Solving for x, we find that x = $7.75.
Therefore, the cost of a plate of spring rolls is $7.75, so the answer is A.
HELP DUE TODAY THE 16TH OF DEC
Simplify fraction with 8 minus 4 times 3 in the numerator and the cube root of 8 plus 5 in the denominator.
twelve sevenths
negative twelve sevenths
four sevenths
negative four sevenths
THANK YOU AND HELP I’m VERY CONFUSED
Answer:
The first one is the answer
Write 2/5 and 1/4 with the same denominator
Answer:
Make the denominators equal by L.C.M
--> 8/20 + 5/20
--> 13/20
Example An investor Saved #120,000 For 7 years in a bank which pays interest of 11½% per annum Calculate the a. Interest which accrued b balance if # 25,000 was withdrawn from the account (N 28,276) 00
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$120000\\ r=rate\to 11.5\%\to \frac{11.5}{100}\dotfill &0.115\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per annum, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases}[/tex]
[tex]A=120000\left(1+\frac{0.115}{1}\right)^{1\cdot 7} \implies A \approx 257101.92 \\\\\\ \underset{earned~interest}{\stackrel{257101.92 - 120000}{\text{\LARGE 137101.92}}}\hspace{10em}\underset{adjusted~balance}{\stackrel{257101.92 - 25000}{\text{\LARGE 232101.92}}}[/tex]
Ariana has 6 posters she wants to hang on the wall. How many different ways
can the posters be arranged in a row?
What are the values of x and y in the figure?
PLEASE HELP ASAP!!!!
Answer:
statements 2 and 3 are true
Step-by-step explanation:
using the rule of exponents
[tex]a^{0}[/tex] = 1
then
1 [tex]a^{0}[/tex]≠ a ← lie
2 [tex]x^{0}[/tex] = 1 ← true
3 [tex]5^{0}[/tex] = 1 ← true
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Eliana and her friend Greta are each baking apple pies and tarts for a bake sale, using the
same recipes. Eliana baked 2 apple pies and 6 apple tarts, using a total of 38 apples. Greta
made 2 apple pies and 8 apple tarts, which used 46 apples. How many apples does each
dessert require?
An apple pie uses
Submit
apples and an apple tart requires
C
zoom
apples.
O
An apple pie requires 7 apples and an apple tart requires 4 apples
How to write a system of equations to describe a situation?To set up this problem, we can let p represent the number of apples needed for one pie and t represents the number of apples needed for one tart.
We can then set up the following system of equations to represent the information given in the problem:
2p + 6t = 38
2p + 8t = 46
To solve this system, we can subtract the first equation from the second to eliminate the p terms:
2p + 8t - 2p - 6t = 46 - 38
2t = 8
t = 4
Substituting this value back into the first equation, we get:
2p + 6(4) = 38
2p = 14
p = 7
Thus, an apple pie requires 7 apples and an apple tart requires 4 apples.
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Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $210. Now the cost is $320. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
The percent increase is 56%
The percent increase if the airline charges an additional $50 baggage fee with the new ticket price is 76%
How to determine the percent increaseThe formula for determining percent increase is expressed as;
Percent increase = x₂ - x₁/x₁ × 100/ 1
Where;
x₁ is the initial valuex₂ is the final valueNow, substitute the values, we have;
Percent increase = $320 - $210/$210 × 100/ 1
Find the difference
Percent increase = $110/$210 × 100/ 1
Percent increase = 0. 52 × 100/ 1
Multiply through
Percent increase = 52%
If there is an increase of $50
Percent increase = $370-210/210 × 100/ 1
= 160/210 × 100/ 1
= 76%
Hence, the values are 52% and 76% respectively,
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What is an algebraic expression for 16 more than the product of 43 and a number?
A: 16 − 43y
B: 43y(16)
C: 43y − 16
D: 43y + 16
The algebraic expression that can be represented by the statement is 43y + 16
How to make a algebraic expression that can be represented by the statement?From the question, we have the following statement that can be used in our computation:
16 more than the product of 43 and a number
Represent the variable with y
So, we have the following representation
16 more than the product of 43 and y
Express the product as an actual product
So, we have the following representation
16 more than 43y
more than as used here means addition
So, we have
43y + 16
Hence, the expression is (d) 43y + 16
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Answer: 43y + 16
Step-by-step explanation:
i did the test
Molly wants to put a triangular fence around her garden. Use the diagram below to answer the questions.
Molly would need 43 feet of fencing to fence the triangular area.
What is Pythagorean theorem?
Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).
According to the given question:
We can see that the area is in the form of a right-angled triangle. Since only two sides of the triangle is given, we could utilize Pythagoras theorem to our advantage to find out the third side.
In Δ ABC
AB² (base) + AC² (perpendicular) = BC² (hypotenuse)
Substituting the values of AB as 10 feet and BC as 18 feet
AC²= BC²- AB ²
∴AC²= 224
∴AC= 14.96 cm
Amount of fence required by molly would equal perimeter of the area.
⇒The perimeter of the area would equal AB+BC+AC
⇒Summing up the values of AB, AC and BC
Perimeter= 10+14.96+18= 42.96 feet which is about 43 feet
Hence, Molly would require 43 feet of fencing.
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Whats the scale factor of triangle PQR to triangle STU.
PR =8 SU=12
RQ=6 UT=9
QP=10 TS=15
The scale factor of triangle PQR to triangle STU is 3/2
How to find the scale factor of the two trianglesScale factors are used to increase or decrease image. The situation of increment is usually called magnifying.
Taking a point of reference say PR and SU
PR = 8
SU = 12
let the scale factor be r such that
8 * r = 12
r = 12 / 8
r = 3/2
checking with other sides
PR to UT
6 * 2/3 = 9 correct
QP to TS
10 * 3/2 = 15 correct
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Dean is training for a 20 kilometre race. He wants to beat his personal best time of 3 hr 14 min 45 sec. If it takes him 9 minutes and 30 seconds to run one kilometre, will he beat his personal best? Calculate by how much will Dean beat/not beat his personal best time?
Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the personal best time of Dean be = A
Now , the value of A = 3 hours 14 minutes 45 seconds
And ,
The time taken by Dean to complete 1 km = 9 minutes 30 seconds
Now , the total distance of the race lap = 20 km
So , the equation will be
Total time taken by Dean to complete 20 km race B = 20 x time taken by Dean to complete 1 km
Substituting the values in the equation , we get
Total time taken by Dean to complete 20 km race = 20 x 9 minutes 30 seconds
Total time taken by Dean to complete 20 km race = 20 x 9 minutes + 20 x 30 seconds
Total time taken by Dean to complete 20 km race = 180 minutes + 600 seconds
1 hour = 60 minutes
1 minute = 60 seconds
180 minutes = 3 hours
600 seconds = 10 minutes
So , the equation is
Total time taken by Dean to complete 20 km race B = 3 hours 10 minutes
So , the value of B < value of A
Therefore , the Dean will beat his personal best time and the race is completed in 3 hours 10 minutes
Hence , Dean will take a total time of 3 hours and 10 minutes to complete the race and will beat his personal best time
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The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The Scooter Company's total profit function is represented by -2x²+250x-2000.
Total profit of a company is the difference between total revenue and total cost.
What is gain or profit?The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
Company earns a total revenue that can be determined by the function R(x) = 400x - 2x²
Each scooter cost $150 to produce, and the company has a fixed cost of $2,000.
Variable cost = Cost of each scooter × Number of scooter sold
Total cost = fixed cost + variable cost
= 2000 + (150×x)
Cost, C(x) = 2000 + 150x
Revenue, R(x) = 400x - 2x²
Total profit = Revenue - Cost
= 400x-2x²-(2000 + 150x)
= 400x-2x²-2000-150x
= -2x²+250x-2000
Therefore, the Scooter Company's total profit function is represented by -2x²+250x-2000.
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A school sold 461 tickets for the school play. Student tickets cost $3 and adult tickets cost $4. Ticket sales totaled $1624.
Part A. Write and solve a system of equations to model this situation.
Part B. Then explain the meaning of your solution.
The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
Given that,
461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students. Sales of tickets totaled $1624.
We have to find the system of equations to model.
We know that,
We get,
a + s = 461
s = 461 -a
The student tickets sold = s × 3 = 3 × (461-a)
The adult tix sold = 4 a
Summed they total 1624
We get system of equations as
s = 461-a
3 (461-a) + 4a = 1624
1383 -3a +4a = 1624
a = 241
Then
s = 461 -a = 220
Therefore, The system of equations to model is s=220 and a=241 when 461 tickets for a school performance were sold. Adult tickets are $4 and cost $3 for students.
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Please help, I'm having trouble.
Compared to the graph of y = x graph y = -x/3 is a negative slope
Compared to the graph of y = x graph y = -x/3 intersects the y axis at same point
Compared to the graph of y = x graph y = x - 2 is a parallel line
Compared to the graph of y = x graph y = x - 2 intersects the y axis at 2 units down
How to make the graph comparisonThe two graphs compared are linear function graphs
A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
y = x
slope = 1
c = 0
y = -x/3
slope = -1/3
c = 0
y = x - 2
slope = 1
equal slopes means the lines are parallel
c = -2 (down 2 units)
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What is the equation of the parabola with focus (1, 6) and directrix y = 1?
An equation of the parabola with focus (1, 6) and directrix y = 1 is: C. y = 1/10(x²) - 1/5(x) + 18/5
How to determine the equation of a parabola?Mathematically, the standard equation of the directrix lines for any parabola is given by:
y = a(x - h)² + 2.
Where:
h and k are the vertex.a is a point.Since the directrix is horizontal, the axis of symmetry would be vertical. Therefore, the equation of this parabola would be modeled by this standard mathematical expression;
(x - h)² = 4p(y - k)
Where:
h = 1
In Mathematics, the focus for either a right or left parabola is modeled by this mathematical expression (h + p, k) while its directrix is modeled by this mathematical expression x = h - p;
k + p = 6
k - p = 1
Solving the set of linear equations simultaneously, we have:
2k = 7
k = 7/2
For the value of p, we have;
p = 6 - k
p = 6 - 7/2
p = 5/2
Substituting the given parameters into the formula, we have;
(x - 1)² = 4(5/2)(y - 7/2)
x² - 2x + 1 = 10(y - 7/2)
x² - 2x + 1 = 10y - 35
10y = x² - 2x + 1 + 35
10y = x² - 2x + 36
y = (x² - 2x + 36)/10
y = x²/10 - x/5 + 18/5
y = 1/10(x²) - 1/5(x) + 18/5
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if a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?
The given statistic is said to be an "unbiased estimator". In this statistic, the mean is equal to the true value of the estimated parameter.
What is an unbiased estimator?In a statistic, if the mean is equal to the estimated parameter, then that statistic is said to be an unbiased estimator. It is used to estimate a population parameter.
Calculation:Consider a statistic.
"A statistic describes a portion of the target population".
"A parameter describes the whole population".
In a statistic, the mean of the sampling distribution is equal to the true value of the estimated parameter.
I.e., μ = E(x)
So, that statistic is said to be an unbiased estimator.
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Write ONE equivalent ratio for the following: 6 : 4
classify the polynomial 2x^3-5+9x^2
The category of the polynomial 2x³ - 5 + 9x² is a trinomial
How to determine the category of the expression?From the question, we have the following expression that can be used in our computation:
2x^3-5+9x^2
Rewrite this expression properly
So, we have the following representation
2x³ - 5 + 9x²
This expression can be further rewritten as
2x³ + 9x² - 5
The degree of a polynomial is the highest power of the polynomial
In this case, the degree of the above polynomial is 3
As a general rule, a trinomial is any polynomial that has a degree of 3
Hence, the expression is a trinomial
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Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135. What was the total of his sales for that week?
The total of his sales for that week is $49,500.
Given :
Nate Belloir earns a weekly commission of 2. 5% on sales of $50,000 or less and 3. 0% on sales in excess of $50,000. One week Nate's commission was $2,135.
Let x be the total sales.
2135 = 2.5 % * 50000 + 3 % (x - 50000 )
= 2.5 * 50000 / 100 + 3/100 ( x - 50000 )
1235 = 2.5 * 500 + 0.03x - 0.03 * 50000
1235 = 1250 + 0.03x - 1500
0.03x = 1235 - 1250 + 1500
0.03x = -15 + 1500
0.03x = 1485
multiply by 100 on both sides
0.03x * 100 = 1485 * 100
3x = 148500
x = $49500
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convert 5 centimeters into yards rounded to nearest hundredth
Answer:
.05 yd
Step-by-step explanation:
5/91.44=.05468066
[tex]3(x+7)=7x-48[/tex] I can't solve this question can you help me please !!!
Therefore the value of x from the given equation comes out to be 13.5
What is equation?A statement proving the equality of two mathematical expressions is known as an equation. The equal sign (=) is used to represent an equation between two mathematical expressions. Anything that contains the equal sign is an equation, to put it simply. Examples of equations include x=7, 2x+5=7, etc.
Here,
The equation given is 3(x+2)=7x-48
thus we find the value of x from the given equation
=> 3(x+2)=7x-48
=> 3x+6=7x-48
=> 7x-48-3x-6=0
=> 4x-54=0
=> 4x=54
=> x=54/4
=> x=13.5
Therefore the value of x from the given equation comes out to be 13.5
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Below are the steps to solve an equation:
Step 1: x 5+2=5
Step 2: x - 5] 5-2
Step 3: x 5 = 3
Which of the following is a correct next step to solve the equation? (1 point)
Ox+5=-3
O-x-5-3
Ox-5--3
Ox+5=3
Jack is running on a treadmill at a speed of 7. 2 miles per hour a slim y equals total distance and x equals number of hours
Need help pls important!!!!!!!!
Given that he is running on a treadmill at a pace of 7.2 miles per hour, the necessary expression will be y=7.2x.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
Here,
Speed of him=7.2 miles/hour
Let y be the total distance and x be the number of hours,
speed=distance/time
7.2=y/x
y=7.2x
The required expression will be y=7.2x as he is running on a treadmill at a speed of 7. 2 miles per hour.
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geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 microgram of 206pb for 1.000 microgram of 238u present. approximately how old is the sample? yrs
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately 3.7973 × 10⁹ years old is the sample.
What is decay constant?The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.
According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.
t1/2 of U₂₃₈ is 4.5 × 10⁹ years
moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles
moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles
Now, U₂₃₈ → Pb₂₀₆
As Pb₂₀₆ comes from U₂₃₈ hence,
moles of U₂₃₈ decayed = moles of Pb₂₀₆
= (0.686 × 10⁻⁶ / 206) moles
Therefore, initial moles of U₂₃₈:
N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles
and N = (1 × 10⁻⁶ / 238) moles
Now, λ (decay constant) = 0.693 / (t1/2)
= 0.693 / ( 4.5 × 10⁹ years)
So,
t = 2.303 / λ × log (N₀ / N)
t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]
t = 14.95 × 10⁹ × 0.254
t = 3.7973 × 10⁹ years.
Thus, the sample is: 3.7973 × 10⁹ years old.
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Describe a set of data in which it would be most appropriate to use the mode as the measure of central tendency.
Answer:
It would be most appropriate to use the mode for categorical data, such as favorite ice cream flavor. This is because you can't use mean or median for flavors such as chocolate or vanilla, so mode would make the most sense there.
Help me please before my assignment is due
Greta's current age is m + n years.
What is an expression?An algebraic expression in mathematics is an expression that is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
In other words, algebraic expressions are combinations of variables, numbers, and at least one arithmetic operation
Therefore, let's convert the word's expression to an algebraic expression.
Greta was m years old n years ago. Her age now is as follows:
n years ago Greta was m years old. This simply means n years ago Greta was m years old. Her current age will be the sum of her current age and the number of years ago.
Therefore,
(m + n) years
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The expression below is the factorization of what polynomial? Write
exponents with the caret (^). For example, enter x² as x^2.
(2x+3)(3x + 5)
Twice last month, Judy Carter rented a car from a car rental company and traveled around the Southwest on business. The company rents its car for a daily fee, plus an
additional charge per mile driven. Judy recalls that her first trip lasted 4 days, she drove 450 miles, and the rental cost her $256.00. On her second business trip she drove
200 miles in 3 days, and paid $159.00 for the rental. Find the daily fee, and find the mileage charge.
Answer:
the daily fee is 37 and the mileage charge is .24 per mile.
Step-by-step explanation:
256 = 450x + 4b
159 = 200x + 3b
Multiple the top equations by -3 all the way through the bottom equations by 4 all the way through then add the equation together.
-768 = -1350x -12b
636 = 800x + 12b
-132 = -550x Divide both sides by -550
.24 = x This is the charge per mile.
Plug in .24 for x into either of the original 2 equations to solve for b which is the daily fee.
256 = 450(.24) = 4b
256 = 108 + 4b Subtract 108 from both sides
148 = 4b Divide both sides by 4
37 = b This is the daily fee.