Answer:
21 hot dogs
9 pizza slices
Step-by-step explanation:
Given information:
Group = 30 peopleCost of a hot dog = $2.50Cost of a slice of pizza = $3.25Total bill = $81.75Define the variables:
Let x = the number of hot dogs purchased.Let y = the number of pizza slices purchased.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad x + y = 30[/tex]
[tex]\textsf{Equation 2}: \quad 2.5x+3.25y=81.75[/tex]
Rewrite Equation 1 to make x the subject:
[tex]\implies x=30-y[/tex]
Substitute this into Equation 2 and solve for x:
[tex]\implies 2.5(30-y)+3.25y=81.75[/tex]
[tex]\implies 75-2.5y+3.25y=81.75[/tex]
[tex]\implies 75+0.75y=81.75[/tex]
[tex]\implies 0.75y=6.75[/tex]
[tex]\implies y=9[/tex]
Substitute the found value of y into the rewritten form of Equation 1 and solve for x:
[tex]\implies x=30-9[/tex]
[tex]\implies x=21[/tex]
Solution
Hot dogs purchased = 21Pizza slices purchased = 9Learn more about systems of equations here:
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Answer:
Number of hot dogs purchased = 21
Number of pizza slices purchased = 9
Step-by-step explanation:
Let the number of people buying hot dogs be represented by the variable H and the number of people buying pizzas be represented by the variable P
Since H hot dogs were purchased and each hot dog costs $2.50, total amount spent on hot dog purchase = $2.50H
Since P slices of pizza were purchased and each slice of pizza costs $3,25, total amount spent on hot dog purchase = $3,25P
Total amount spent (in $) = 2.50H + 3.25P and we are given that this total amount is $81.75
So we have an equation in two variables
2.50H + 3.25P = 81.75 (1)
We know the number of people is 30 and that should equal the number of hot dogs and pizza slices purchased
So
H + P = 30 (2)
Multiply Equation (2) on both sides by 2.50
==> 2.50(H + P) = 2.50 x 30
2.50H + 2.50P = 75 (3)
Subtract equation (3) from equation (1) to eliminate the H terms
(1) - (3):
2.50H + 3.25P - (2.50H + 2.50P) = 81.75 -75
2.50H + 3.25P - 2.50H - 2.50P = 6.75
Collect like terms and simplify
==> (2.50H -2.50H) + (3.25P - 2.50P) = 6.75
==> 0.75P = 6.75
Divide both sides by 0.75
==> 0.75P/0.75 = 6.75/0.75
==> P = 9
So number of people who bought pizza slices = 9
This is the same as the number of pizza slices that were bought
Substitute for P in Eq (2) H + P = 30
==> H + 9 = 30
Subtract 9 from both sides
==> H + 9 - 9 = 30 - 9
==> H = 21
So number of people who bought hot dogs = 21
This is the same as the number of hot dogs purchased
Use the slope formula to find the slope
The slope of line: 1. m= 6 , 2. m= -6 , 3. m= 2.5, 4. m= .5
The slope of the line :
In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.
The net change in the y-coordinate is represented by Δy and the net change in the x-coordinate is represented by Δx.
Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,
m = change in y/change in x = Δy/Δx
Where “m” is the slope of a line.
Tan θ = Δy/Δx can also represent the slope of the line
So, tan θ to be the slope of a line.
Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The letter ‘ m’ usually represents the slope.
If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:
Slope,
m = Change in y-coordinates/Change in x-coordinates
m = (y2 – y1)/(x2 – x1)
Therefore, based on the above formula, we can easily calculate the slope of a line between two points.
In other terms, the slope of a line between two points is also said to be the rise of the line from one point to another (along the y-axis) over the run (along the x-axis). Therefore,
Slope, m = Rise/Run
1.
(-1,-1) & (0,5)
m = (y2 – y1)/(x2 – x1)
m = (5 – (-1)) /(0– (-1))
m = (5 +1)/(0 +1)
m = (6)/(1)
m = 6
2.
(3,5) & (4,-1)
m = (-1 – 5)/(4 – 3)
m = (-6)/(1)
m = -6
3.
(2,1) & (4,6)
m = (6 – 1)/(4 – 2)
m = (5)/(2)
m = 2.5
4.
(-5,-2) & (3,2)
m = (2 – (-2))/(3 – (-5))
m = (2 +2/(3 +5)
m = (4)/(8)
m = (2/(4)
m = (1)/(2)
m = 0.5
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A box of Tyler's favorite snack, Cheesy Snaps, is 13 centimeters tall and 6 centimeters wide.
It is twice as long as it is wide. What is the volume of a box of Cheesy Snaps?
Answer: 156
Step-by-step explanation:
13x2=26
26x6=156
The required volume of the box is given as 936 cubic centimeters.
Given that, A box of Tyler's favorite snack, Cheesy Snaps, is 13 centimeters tall and 6 centimeters wide. It has twice as long as it is wide.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
height = 2 × width
height = 2 × 6 = 12
The volume of the box = length × width × height
= 13 × 6 × 12 = 936
Thus, the required volume of the box is given as 936 cubic centimeters.
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Four times the lesser of two consecutive even integers is less than twice the greater number. Find the integers.
There exists no even integer with the given parameters
How to determine the two consecutive even integers?Consecutive even integers are integers that have a difference of 2
i.e x and x + 2
Where x is the lesser number
Using the given mathematical statement, we have
4x < 2(x + 2)
Divide by 2
2x < x + 2
Subtract x from both sides
x < 2
There is no even number less than 2
Hence, there exists no even integer with the given parameters
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Later you have another chocolate bar. This time, after you give away 1/3 of the bar, a
friend breaks off 3/4 of the remaining piece. What part of the origina chocolate bar do you have
left? Answer this question by drawing a diagram
Answer:
Step-by-step explanation:
The trapezoids are similar. What is the value of x? 50 75 35 7 10
Answer:
The correct value of x is 15.
Step-by-step explanation:
Each side of the larger trapezoid is 5 times each corresponding side of the smaller trapezoid.
Is this a function ?
Answer:
no
Step-by-step explanation:
Functions are wavy lines
Answer:
yes
Step-by-step explanation:
write the expression (-10) . (-10) . 3 . 3 .3 .3 .3 using exponents
Explain your thinking please
The exponential form is a way of writing numbers using bases and powers. (-10)^2*3^5 is the expression in exponent form for expression (-10) . (-10) . 3 . 3 .3 .3 .3 .
What is Exponential form?The exponential form is a way of writing numbers using bases and powers.
Given expression is (-10) . (-10) . 3 . 3 .3 .3 .3, we need to write in exponent form.
An exponential function is defined by the formula f(x) = a^x, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.
(-10) is 2 times and 3 is five times,
we can write in the form (-10)^2.(3)^5
Therefore the required answer is (-10)^2.(3)^5 for expression (-10) . (-10) . 3 . 3 .3 .3 .3 .
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Given the following data, find the weight that represents the 42nd percentile.
Weights of Newborn Babies
8.3 6.5 6.0 5.4 6.7
6.5 8.1 9.2 6.4 8.0
6.8 9.0 8.7 9.3 8.0
The weight represents the 42nd percentile.
=6.712
This is further explained below.
Find the weight that represents the 42nd percentile.?Generally, the given data is
8.3,6.5,6,6,5,4,6.7,6.5,8: 1,9.2,6.4,8 0,6.8,9.0,8.7,9.3,8.0
The ascending order of the data is
5.4,6.0,6.4,6.5,6.5,6.7,6.8,8.0,8.0,8.1,8.3,8.7,9.0
n=15.
42ndPercentile
=P_{42}
[tex]=42\left(\frac{n+1}{100}\right)^{\text {th }} \text { term } \\[/tex]
[tex]&=42\left(\frac{16}{100}\right) \text { th term } \\[/tex]
=6.72th term
=6th+0.72(72nd -6th) term
=6.7+0.72(6.8-6.7)
=6.712
In conclusion, the weight represents the 42nd percentile.
=6.712
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The sum of 4,7, and a number amounts to 16 find the number
Answer:
The unknow number is 5.
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1. To solve, first wrote it into an equation. Also, the letter x will stand for the unknown number.
4 + 7 = 11
11 + x = 16
2. Isolate the varable by subtracting 11 from both sides of the equation.
11 + x = 16
- 11 - 11
x = 5
The unknow number is 5.
Check:
11 + 5 = 16
16 = 16
True statement.
8
LO
5
15
4
1
In the figure shown above, all the corners form right angles. What is the area of the figure in squ
O 33 square units
O 66 square units
O 70 square units
O 120 square units
The area of the given figure is 70 square units, that is, option 3.
The area of a rectangle = length × breadth
Here, we need to find the area of the shaded region.
To do this, we will subtract the area of the smaller rectangle from the larger one.
The area of the larger rectangle = 8 × 15
= 120 square units
Now, the we have one side of the smaller rectangle which is 5, the other side will be (15 - 4 - 1) = 10 units.
The area of the smaller rectangle = 10 × 5
= 50 square units
Thus, the area of the shaded region = 120 - 50
= 70 square units
Hence, the area of the figure is 70 square units.
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Your question was incomplete. Please find the missing figure below.
PLEASE HELP! TRIGONOMETRY:
A passenger in an airplane at an altitude of 10 kilometers sees two towns directly to the east of the plane. The angles of depression to the towns are 24° and 53° (see figure). How far (in km) apart are the towns? (Round your answer to one decimal place.)
Using relations in a right triangle, it is found that the distance between the towns is of 15 km.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.For the first town, we have that:
The internal angle of the triangle 90 - 53 = 37º.The opposite side to the angle is the horizontal position xA.The adjacent side to the angle is of 10 km.Hence:
tan(37º) = xA/10
xA = 10 x tan(37º).
xA = 7.5 km.
For the second town, we have that:
The internal angle of the triangle 90 - 24 = 66º.The opposite side to the angle is the horizontal position xB.The adjacent side to the angle is of 10 km.Hence:
tan(66º) = xB/10
xB = 10 x tan(66º).
xB = 22.5 km.
Hence the distance is:
22.5 km - 7.5 km = 15 km.
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Calculate the magnitude of the repulsive force between a +500μC charge and a +100μC charge which are 5 m apart. [k=9×109 Nm2C-1]
The magnitude of the repulsive force between a +500μC charge and a +100μC charge which are 5 m apart is 2N.
The repulsive force between two charges = (k q₁ q₂)/r²
q₁ q₂ are the charges
r is distance between the charges
k= 9×10⁹ Nm²C²
F= (500μC) (+100μC)9×10⁹/25
= 2N
A movement between two charges that are same or comparable is referred to as repulsion. The tension between two electrons (negative charge). Two charges of a different sort are drawn toward one another by the force of attraction, which is defined as "a force between two charges that are distinct or different."
At a distance, magnetism is an attractive or repulsive force. The repulsive force gives rise to a metric that measures how a system's gravitational mass changes. According to the force-based approach, the forces that attract and repel other atoms come from their subatomic arrangement and control how they behave.
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What is the BEST first step for calculating the LCM of 15 and 20
Step-by-step explanation:
The commonly used methods to find the LCM of 15 and 20 are:
1) Division Method
2) Prime Factorization Method
3)Listing Multiples
Lydia is buying some jewelry for her fried Michelle for her birthday. Each set is $5 and shipping is $4 flat. If Lydia buys 4 jewelry sets, how much will she spend?
When Lydia buys 4 jewelry sets, the amount spent is $24.
How to calculate the value?From the information given, we are told that Michelle is preparing for her birthday and that each set is $5 and shipping is $4 flat. If Lydia buys 4 jewelry sets.
Therefore, the equation will be:
4 + (5 × x)
where x = number of set
4 + 5x
4 + (5 × 4)
= 4 + 20
= $24
The amount is $24.
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For the rational function f(x)=2−x4x+6, find the point on the graph at the function value f(x)=1.
The point on the graph at the function value f(x)=1 is x = -4/5
How to find the point on the graph at the function value f(x)=1?The equation of the function is given as:
f(x) = 2 - x4x + 6
Rewrite the rational function, properly as follows:
f(x) = 2 - x/4x + 6
When f(x) = 1, we have:
2 - x/4x + 6 = 1
Cross multiply
2 - x = 4x + 6
Collect the like terms
4x + x = 2 - 6
Evaluate the like terms
5x = -4
Divide by 5
x = -4/5
Hence, the point on the graph at the function value f(x)=1 is x = -4/5
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What is the least common multiple of 70, 60, and 50?
60
180
210
2,100
210,000
If a linear function has the points (−5,4) and (−2,−2) on its graph, what is the rate of change of the function?
The rate of change of the linear equation that has the given points on its graph is; -2.
How to Find the Rate of Change of a Linear Function?The rate of change of a linear function can be determined by using the following formula:
Rate of change = change in y / change in x = y2 - y1 / x2 - x1.
Given the following points on a graph of a linear function:
(−5,4) = (x1, y1)
(−2,−2) = (x2, y2)
Plug in the values
Rate of change = change in y / change in x = (-2 - 4) / (-2 -(-5))
Rate of change = -6 / 3
Rate of change = -2 / 1
Rate of change = -2
Thus, the rate of change of the linear equation that has the given points on its graph is; -2.
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Name the property shown 0+8=8
Answer:
Step-by-step explanation:
commutative
5. identify
H E L P :(
What is the ratio of fiction novels to all novels? 11 to 5 2:5 5/11 5 to 2
Answer:
5/11
Step-by-step explanation:
make sure next time to say how much books do you have I have answered a similar question with this wording so I hope this helps :))
Round to the nearest ten
thousand.
123,045,067
Answer: 123050000
Step-by-step explanation:
don't take this down again :)
What is the solution to
this equation?
5x + 3 = 2x - 6
The solution to this equation is x = -3
How to determine the solution to this equation?
The equation is given as
5x + 3 = 2x - 6
Collect the like terms
5x - 2x = -3 - 6
Evaluate the like terms
3x = -9
Divide both sides by 3
x = -3
Hence, the solution to this equation is x = -3
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Find the area of the figure.
Answer:
[tex]18 {m}^{2} [/tex]
Step-by-step explanation:
The figure shown in the image is a parallelogram.
To find the area of a parallelogram we use the following formula:
A = b • h (b: base, h: height)
The height is 4.5m while the base is given as 4m
(4.5) • 4 = 18
Since the area is put in square units the answer is
[tex]18 {m}^{2} [/tex]
Factor out the greatest common factor.
4x³+16x² +8x
The greatest common factor for 4x³+16x² +8x is 4x(x2- 4x - 2).
This solution focuses on simplification:
4x(x2-4x-2)
(4(x3)-24x2)-8x
(22x3-24x2) -8x
Take similar factors aside:
4x3-16x2-8= 4x(x2-4x-2)
Factoring x2 - 4x - 2
x2 is the initial term, and it has a coefficient of 1.
The coefficient of the intermediate term, which would be -4x, is 4.
"The constant," the final term, is -2.
Multiply the constant by the coefficient of the first term. 1 -2 = -2
The second step is to find two -2 factors whose sum is equal to the -4 coefficient of the middle word.
-2 + 1 = -1
-1 + 2 = 1
No two of these factors can be discovered!!
Trinomial cannot be factored.
Hence, The greatest common factor is 4x(x2- 4x - 2).
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help pls and tysm ;0
Answer:
At least 20
Hope this helps :)
Step-by-step explanation:
85 ÷ 3.5 = 24.2857142857
24.2857142857 is approximately rounded to 20.
So she need at least 20 pieces of ribbon (which means greater than or equal to 20 pieces).
if we multiply by 5 to the difference of 1 out of six part of Times of 15 and 3 then find the number
Answer:
1 out of 6 part of time 15 and 3 mains time 15 and 3 has 6 parts and that you should take one out of this six paths
1/6 (15 x 3) = 1/6. x 45 = 15/2
then,multiple by 5
15/2 × 575/2 = 37 1/2
another way to write m-9
The expression written in another way is -9 + m
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and constants
How to rewrite the expression in another way?The expression is given as:
m - 9
By the subtraction property of an equation, we have
a - b = -b + a
x - y = -y + x
Using the above equations as a guide, we have
m - 9 = -9 + m
Hence, the expression written in another way is -9 + m
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Your weight on the Moon is about 1/6 of your weight on Earth. Write and solve an equation to show how much a person weighs on Earth if he weighs 16 pounds on the moon. How could you check that your answer is reasonable??
Answer:
1/6(x) = 16
Step-by-step explanation:
You can just solve for x which goes as follows:
6 * 1/6 = 6 * 16 - Multiply both sides by 6.
x = 96
Answer:
x=96
Step-by-step explanation:
To figure out the weight of the person on the moon we would need to take their weight and divide by 6. we don't know the weight so it's x. We know the final weight so the x divided by 6 should be 16.
this translates to:
x/6=16
x=16*6
x=96
Find the midpoint of the line segment with the endpoints A and B.
A(10,4); B(8,2)
The midpoint of the line segment is
(Type an ordered pair.)
explain how to graph the equation on a coordinate plane: y = 3x - 5
lations below are also functions?
To graph an equation on the co-ordinate plane we plot points that satisfy the given equation .
The graph of a linear equation is two variables gives a straight line on the co-ordinate plane.
To graph a straight line on the co-ordinate plane we take three points or solution of the equation on the line and join them.To calculate the solutions(points) of the line we take some values of x and calculate the corresponding values of y.Then we make a table of the points and graph the equation of the line by joining the points.the given equation is y=3x-5
at x=0 ,y=3×0-5 or y=-5
at x=2 , y=(3×2)-5 or y=1
at x=-1,y=(3×-1)-5 or y=-8
Now we make the table to get the desired points.
x y point
0 -5 A (0,-5)
2 1 C(2,1)
-1 -11 B (-1,-8)
The graph for the equation y=3x-5 is drawn.
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500,000 in expanded form
Answer:
500,000 =
5 × 100,000
+ 0 × 10,000
+ 0 × 1,000
+ 0 × 100
+ 0 × 10
+ 0 × 1
Step-by-step explanation:
there are more then one ways of writing this so here's another example
500,000 =
500,000
+ 0
+ 0
+ 0
+ 0
+ 0