Two hungry football players ordered lasagna and salad. The first order 3 pieces of lasagna and two salads and spent $17.63. The second orders four pieces of lasagna and one order of side salad and spent $18.69. How much would five pieces of lasagna and 3 salads cost?
Answers
Using a system of equations, five pieces of lasagna and 3 salads cost $28.42.
What is a system of equations?A system of equations involves two or more equations solved simultaneously or concurrently.
Lasagna Salads Total Costs
The first order 3 2 $17.63
The second order 4 1 $18.69
Let the unit cost of Lasagna = x
Let the unit cost of Salads = y
Equations:3x + 2y = 17.63 ...Equation 1
4x + y = 18.69 ...Equation 2
Multiply Equation 2 by 2:
8x + 2y = 37.38 ...Equation 3
Subtract Equation 1 from Equation 3:
8x + 2y = 37.38
-
3x + 2y = 17.63
5x = 19.75
x = 3.95
Substitute x = $3.95 in either Equation:
3x + 2y = 17.63
3(3.95) + 2y = 17.63
11.85 + 2y = 17.63
2y = 5.78
y =2.89
Cost of 5 Lasagna and 3 Salads:
5(3.95) + 3(2.89) =
19.75 + 8.67 = $28.42
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Related Questions
What is the population standard deviation?
{5,8,8,5}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2.
Answers
5, 8, 8, 5 has a population standard deviation of 3
Given,
The population is
{5, 8, 8, 5}
The population's mean is calculated as follows:
Sum of terms / Number of terms
Calculate the values and then replace them in the equation.
Sum equals 5 + 8 + 8 + 5 = 26
Number of terms = 4
The population's average is 26 / 4 = 6.5
The population's variance is equal to (5 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (8 - 6.5) (8 - 6.5)² + (5 - 6.5)²
= (-1.5) (-1.5)² + (1.5) (1.5)² + 1.5² + (-1.5) (-1.5)²
= 2.25 + 2.25 + 2.25 + 2.25
= 9
The population's standard deviation is equal to
= 3
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Is (x-1) a factor of 2x3 - 15x2 + 22x + 15
Answers
Answer:
Step-by-step explanation:
If x - 1 is a factor of the cubic, then 1 should result in 0 when you put it in the cubic for x. Does it?
f(1) = 2(1)^3 - 15(1)^2 + 22(1) + 15
f(1) = 2 - 15 + 22 + 15
f(1)= 24.
No the result is not zero. So x - 1 is not a factor.
However there must be something that makes this cubic go to zero. The easiest way to find it is to graph it.
The numbers that do make this zero are -0.5, 3, 5
Which mean that the factors are (2x+1)(x-3)(x - 5)
If a loading ramp is placed next to a truck, at a height of 8
feet, and the inclined portion of the ramp is 17 feet long, what angle (in degrees) does the ramp make with the ground?
Round your answer to one-tenth of a degree.
Answers
The angle that the ramp makes with the ground is approximately 28.07 degrees.
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The sin of the angle θ is the ratio of the opposite side (height of the ramp) to the adjacent side (length of the inclined portion of the ramp):
Sin(θ) = 8/17
We can use a calculator to find the inverse sin of this ratio to get the angle θ:
θ = sin⁻¹(8/17)
θ ≈ 28.07 degrees
Therefore, the angle that the ramp makes with the ground is approximately 28.07 degrees.
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6.
Circumference is the same as the area of a circle.
a. True
b. False
Answers
Answer:
TRUE
Step-by-step explanation:
i just know it :>
Look for factors that will help you determine what type of economy exists in Country A.
Based on the clues in this passage, what type of economy does Country A have?
developed
developing
transitioning
command
Answers
developing:
a low GDP
an economy based on agriculture
Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.
A certain punch recipe contains fruit juice and seltzer. The ratio of fruit juice to seltzer in the recipe is 3:8. If a teenager follows the recipe ratio and makes a total of 11 cups of the punch, which statement is true?
A. The teenager puts 3 cups of seltzer in the recipe.
B. The teenager puts 5 cups of fruit juice in the recipe
C. The teenager puts 8 cups of seltzer in the recipe.
D. The teenager puts 11 cups of fruit juice in the recipe.
THIS IS NOT A COLLEDGE QUESTION IT IS A SIXTH GRADE QUESTION
Answers
Graph the function shown below
Answers
Answer:
.
Step-by-step explanation:
Answer:
Hi!
The graph will look something like this
I hope this helped you!
Divide. Write your answer in simplest form.
8/7÷4
Answers
Answer:
8/7 ÷ 4/1 = 7/32
Step-by-step explanation:
4/1 is the same as 4, flip all the Fractions so the bottom number is on the top and top on bottom and then multiply top x top and bottom x bottom
Hey there!
First, let's convert 4 into a fraction:
4=4/1
Now, divide the fractions:
\(\bold{\displaystyle\frac{8}{7} :\frac{4}{1}}\)
Now, flop the second fraction over and multiply the first fraction times the second one:
\(\bold{\displaystyle\frac{8}{7} *\frac{1}{4}}\)
Multiply the numerator (8) times the numerator of the second fraction (1) and multiply the denominator (7) times the denominator of the second fraction (4):
\(\bold{\displaystyle\frac{8}{28}}}\)
Also, this fraction can be reduced:
\(\bold{\displaystyle\frac{4}{14}}\)
We can divide by 2 again.
Hence, the answer is
\(\boxed{\boxed{\bold{\displaystyle\frac{2}{7}} }}}\)
Hope everything is clear.
Let me know if you have any questions!
:-)
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\(\rule{200}{2}\)
The Mannings prepared an expense summary. They had planned to spend $164.50
on utilities for the previous month but actually spent $187.25. How much more or less did they spend on utilities than they had budgeted for?
Answers
Answer:
$22.75 more
Step-by-step explanation:
Solve
-12 + 23
A. -35
B. -11
C. 11
D. 35
Answers
Answer:
C. 11
Step-by-step explanation:
This can be rewritten as
23 - 12
This is equal to 11.
Answer:
11
Step-by-step explanation:
-12 + 23 = 11
since the 12 is negative subtract it from 23 and you get 11 as your answer
Please help me on this question ASAP if you do ill give you brainliest!
Answers
Answer:
1. 2/21
2. 7/45
3. 9/26
4. 4/61
5. 3/29
6. 8/61
Step-by-step explanation:
I'll just explain number one, since you can do the same thing to solve all the others.
You start with 10 1/2. You can make this an improper fraction by multiplying 10 and 2, then adding one. This leaves you with 21/2. The reciprocal of a fraction is just the numerator and denominator of the fraction flipped. So, you get 2/21.
Hope this helps!
5 times 100 times 105
Answers
Answer:
52500
Step-by-step explanation:
first do 5*105 to get 525 then mutiply by 100 to get 52500
For the following event, state whether you think the difference between what occurred and what you would expect by chance is statistically significant. Explain.
An airline with a 95% on-time departure rate has 16 out of 300 flights with late departures.
Answers
The difference between the observed and expected number of late departures is statistically significant, we need to perform a binomial test by calculating the probability of observing 16 or more late departures out of 300 flights assuming the null hypothesis is true. If the resulting p-value is less than 0.05, we can conclude that the difference is statistically significant.
Based on the given information, an airline with a 95% on-time departure rate has 16 out of 300 flights with late departures. The question asks whether the difference between what occurred (16 late departures) and what you would expect by chance is statistically significant.
To determine if the difference is statistically significant, we need to conduct a hypothesis test. In this case, we can use a binomial test since we are dealing with two possible outcomes: on-time departure or late departure.
The null hypothesis (H0) assumes that the observed number of late departures is equal to what would be expected by chance. The alternative hypothesis (Ha) assumes that there is a significant difference between the observed and expected values.
In this case, the expected number of late departures can be calculated by multiplying the total number of flights (300) by the expected on-time departure rate (95%). This gives us an expected value of 300 * 0.05 = 15.
To perform the binomial test, we can calculate the probability of observing 16 or more late departures out of 300 flights, assuming the null hypothesis is true. This probability can be calculated using the binomial probability formula or by using statistical software.
If the resulting probability (also known as the p-value) is less than the significance level (usually 0.05), we can reject the null hypothesis and conclude that the difference between what occurred and what would be expected by chance is statistically significant. Otherwise, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that the difference is not statistically significant.
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Use Law of sines to solve for this problem. Round your answer to the nearest TENTH.
Answers
We will have the following:
AB:
\(\begin{gathered} \frac{15}{sin(70)}=\frac{AB}{sin(45)}\Rightarrow AB=\frac{15sin(45)}{sin(70)} \\ \\ \Rightarrow AB=11.28730979...\Rightarrow AB\approx11.3 \end{gathered}\)So, the measure of segment AB is approximately 11.3 units.
BC:
\(\begin{gathered} \frac{BC}{sin(65)}=\frac{15}{sin(70)}\Rightarrow BC=\frac{15sin(65)}{sin(70)} \\ \\ \Rightarrow BC=14.46708903...\Rightarrow BC\approx14.5 \end{gathered}\)So, the measure of segment BC is approximately 14.5 units.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Simplify the expression 8x2y2/ 10x2y3 and find the missing terms. The simplest form of 8x2y2/10x2y3 has in the numerator and in the denominator.
Answers
The simplest form of the expression (8x²y²) / (10x²y³) has 4 in the numerator and 5y in the denominator. The missing terms are 4 and 5y.
What is the greatest common factor?The greatest number that can divide the numbers in equal parts.
It is called as greatest common factor.
The given expression,
(8x²y²) / (10x²y³)
In order to simplify the expression,
factor out the greatest common factor.
Here, GCF is 2x²y².
That means,
(8x²y²) / (10x²y³) = (2x²y²)4 / (2x²y²)(5y)
(8x²y²) / (10x²y³) = 4/(5y)
This is required, the simplest form of the expression.
And it has 4 in the numerator and 5y in the denominator.
Therefore, the simplest form of the expression has 4 in the numerator and 5y in the denominator.
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In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC?
Answers
Answer:
\(\angle ADB \cong \angle CDB\)
\(\angle DBA \cong \angle DBC\)
\(BD = BD\)
Step-by-step explanation:
Given
\(\triangle ABD \cong \triangle CBD\)
Required
The congruent segments by CPCTC
From the question, we have:
\(\angle ADB \cong \angle CDB\) --- given
\(\angle DBA \cong \angle DBC\) --- given
Both triangles share a common side (length BD);
So, we have:
\(BD = BD\)
Hence, the congruent segments are:
\(\angle ADB \cong \angle CDB\)
\(\angle DBA \cong \angle DBC\)
\(BD = BD\)
A LOT OF POINTS!!!! PLZ ANSWER
Answers
Answer:
f(3x)= 3x+5/6x+2
substitute the value of X in the given question.
if u want simplified form then u can try rationalising.
f(3x)= 3x+5/6x+2 hope helped thanks for points
let be the amount of coffee (in ounces) that an undergraduate student at uiuc drinks per day. suppose we know that has a mean of 10 oz and a standard deviation of 5.2 oz. suppose there are 120 students in stat 107. assuming stat 107 students are a random sample, calculate the standard error of the average amount of coffee a stat 107 student drinks per day . is greater than 12.7 oz.
Answers
0.137606 the standard error of the average amount of coffee a stat 107 student drinks per day is greater than 12.7 oz.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Statisticians can assess if the data fits into a normal distribution or another mathematical connection using the standard deviation. The average, or mean, data point will be within one standard deviation of 68% of the data points if the data follow a normal curve.
Given that,
Standard deviation (σ) = 5.2 oz
mean (μ) = 10 oz
Number of students (n) = 120
As we know,
P ( z > 12.7 oz.) = P (z > [{x(avg.) - μ\(\sqrt{n}\)}/σ])
= P (z > [{12.7 - 10\(\sqrt{120}\)}/5.2])
= P (z > 1.86)
= 1 - P ( z < 1.86)
= 1 - 0.862394
= 0.137606
Thus, P( z > 12.7 oz.) = 0.137606
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Solve the equation. 10g + 8 = 14g
Answers
Hello there! :)
\(\huge\boxed{g = 2}\)
10g + 8 = 14g
Subtract 10g from both sides:
10g - 10g + 8 = 14g - 10g
8 = 4g
Divide both sides by 4:
8/4 = 4g/4
g = 2.
Hey there!
\(Answer:\boxed{g=2}\)
\(Explanation:\)
\(10g+8=14g\)
In our first step, we will subtract 14g from both sides of the equation.
\(10g+8-14g=14g-14g\\-4g+8=0\)
Now we will have to subtract 8 from both sides of the equation.
\(-4g+8-8=0-8\\-4g=-8\)
In our third/final step, we will divide both sides by -4.
\(\frac{-4g}{-4}=\frac{-8}{-4} \\g=2\)
\(\boxed{g=2}\text{ is your answer.}\)
Hope this helps!
\(\text{-TestedHyperr}\)
show that the volume of the unit cube is one
Answers
Check the picture below.
How do I solve this diagram map? Diagram shows the following:
1 - 3
2 - 5
3 - .....?
?..... - 17
10 - ......?
100 - ......?
Answers
The complete diagram map is given as,
1 - 3
2 - 5,
3 - 7,
8 - 17,
10 - 21
100 - 201
Given that,
To complete the map diagram,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
The given map diagram follows the general term as nth term = 2n + 1
So for n = 3
= 2 [3] + 1
= 7
Similarly,
10th = 21
100th = 2001
For the value 17
17 = 2n + 1
n = 8
So the 8th term is 17 in the map diagram,
Thus, The complete diagram map has been shown.
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Last year and investor purchased 115 shares of stock A at $90 per share
Answers
The difference in overall loss or gain between sell at the current day's high price or low price is found tp be the difference in overall gain as $280.10
The third option is correct.
How do we calculate?For stock A:High price value: 115 shares * $105.19 per share = $12,084.85
Low price value: 115 shares * $103.25 per share = $11,858.75
For stock B:High price value: 30 shares * $145.18 per share = $4,355.40
Low price value: 30 shares * $143.28 per share = $4,298.40
The overall value at high price:
$12,084.85 + $4,355.40
= $16,440.25
The overall value at low price:
$11,858.75 + $4,298.40
= $16,157.15
In conclusion, the difference in overall gain or loss:
$16,440.25 - $16,157.15 = $280.10
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-4x + 5y = 12. Value of y when x equals -13
Answers
Answer:
y = -8
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
-4x + 5y = 12
x = -13
Step 2: Solve for y
Substitute in x: -4(-13) + 5y = 12Multiply: 52 + 5y = 12[Subtraction Property of Equality] Isolate y term: 5y = -40[Division Property of Equality] Isolate y: y = -8Answer:
-8
Step-by-step explanation:
-4x + 5y =12
-4(-13) + 5y =12
52 + 5y =12
5y= -52 + 12
5y/5 = -40/5
y= -8
Which of the following properly describe slope select all that apply 
Rise/run
Run/rise
Ratio of the change in Y values rice for a segment of the graph to the corresponding chain with X values run
Y2-y1
————
X2-x1
X2-x1
———-
Y2-y1
Answers
Choose which option shows the plan and which option shows the front elevation of this 3D shape.
Answers
Answer:
Think about what surfaces on are the indicated front side. And protrustions like the one shown will have a divider that separates the high side from the low side answer c
Gavyn, Richard and Stephen share some sweets in the ratio 4:2:3. Gavyn gets 10 more sweets
than Stephen. How many sweets does Richard get?
Answers
Answer:
13 is richard
Step-by-step explanation:
Answer:
10 sweets.
Step-by-step explanation:
So all of them share the sweets in a ratio of 4:2:3. Since Gavyn gets 10 more sweets than Stephen, and the ratio of Gavyn's sweets to Stephens sweets is 4:3, which means that x=10. To clarify, a ratio can be written as 4x:3x, so x=10. So now you do Richards ratio (2x) and you just plug in x and you get 20. So Richard gets 20 sweets.
Which expression is NOT equivalent to 24 + 6x?
A. 2(3x + 12)
B. 28 + 4x – 4 + 2x
C. 5x + 7 + x + 17
D. 3(8 + 3x)
Answers
Answer:
D
the answer is D because when you multiply 3(8 + 3x), it will give you 24+9x
3(8 + 3x) is not equivalent to 24 + 6x.
Option D expression is not equivalent to 24 + 6x.
What is an expression?An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
According to the question
Expression is NOT equivalent to 24 + 6x
A . 2(3x + 12)
= 2(3x) + 2(12)
= 6x + 24
= 24 + 6x
B. 28 + 4x – 4 + 2x
= (28 - 4) + (4x + 2x)
= 24 + 6x
C. 5x + 7 + x + 17
= (5x + x) + (7 + 17)
= 6x + 24
= 24 + 6x
D. 3(8 + 3x)
= 3(8x) + 3(3x)
= 24 + 9x
Hence, Option D is not equivalent to 24 + 6x.
3(8 + 3x) is not equivalent to 24 + 6x.
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Use the graph of the parabola to fill in the table Also find the equation of the axis of symmetry
Answers
According to the given graph:
a. The parabola opens downward.
b. The coordinates of the vertex, which in this case is the point at the top of the parabola, are (-4, 1).
c. The y intercept is: (0, -3)
The x intercepts are: (-2, 0), (-6, 0).
d. The equation of the axis of symmetry is:
x=-4.
The length of a rectangular fish pond is 5 feet more than its width. The area of the fish pond is 143 squarefeet. Find the dimensions of the fish pond and its perimeter.What is the length of the fish pond? (Select]What is the width of the fish pond? Select]What is the perimeter of the fish pond? (Select]
Answers
We know that the length of the rectangle is 5 feet more than the width. Let x be the width of the rectangle, then its length is x+5. This can be see in the next picture
We also know that the area of the fish pond is 143 and that the area is given by
\(A=wl\)Plugging the values we have that
\(143=x(x+5)\)writting the equation in standard form we have that
\(\begin{gathered} 143=x(x+5) \\ 143=x^2+5x \\ x^2+5x-143=0 \end{gathered}\)We know that any quadratic equation can be solve by
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)using it for our equation we have
\(\begin{gathered} x=\frac{-5\pm\sqrt[]{(5)^2-4(1)(-143)}}{2(1)} \\ =\frac{-5\pm\sqrt[]{25+572}}{2} \\ =\frac{-5\pm\sqrt[]{597}}{2} \\ \text{then} \\ x_1=\frac{-5+\sqrt[]{597}}{2}=9.72 \\ \text{and} \\ x_2=\frac{-5-\sqrt[]{597}}{2}=-14.72 \end{gathered}\)As we know the quadratic equation leads to two solutions. Nevertheless the negative solution is not right in this case, since the distances have to be positive. Then x=9.72.
Once we have the value of x we can know the width a lenght
\(\begin{gathered} l=9.72 \\ w=14.72 \end{gathered}\)And the perimeter is
\(\begin{gathered} P=2w+2l \\ =2(14.72)+2(9.72) \\ =48.88 \end{gathered}\)The perimeter is 48.88 ft.
What is the length of line segment AC?
Answers
Using geometry, we can find that the length of the line segment AC as per the distance between two points is= 18 ft.
What are line segments?
In geometry, a line segment's borders are determined by two distinct points on the line. Any portion of a line that connects two places is referred to as a line segment.
A segment has an endpoint, whereas a line doesn't.
What are some examples of line segments in the real world?
a scale, a ruler, a stick, and a boundary line.
Thus, the length of the line segment AC is = 18ft.
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