6 small sizes, 3 medium sizes, and 7 large size pizzas were delivered.
What is a system of equations?
A system of linear equations is a set of two or more linear equations involving the same variables. The variables represent unknown quantities that we want to find, and the linear equations are mathematical statements that describe the relationships between these variables.
Let a = number of small pizzas delivered
Let b = number of medium pizzas delivered
Let c= number of large pizzas delivered
(1) a + b + c = 16
(2) 4a + 9b + 11c = 128
(3) 3a + 5b + 10c = 6 * 16 + 7
--------------------------------------------
(3) 3a + 5b + 10c = 103
Multiply both sides of (1) by 3
and subtract (1) from (3)
(3) 3a + 5b + 10c = 103
(1) - 3a - 3b - 3c = - 48
--------------------------------------------
2b + 7c = 55
---------------------------------------
Multiply both sides of (1) by 4
and subtract (1) from (2)
(2) 4a + 9b + 11c = 128
(1) - 4a - 4b - 4c = - 64
5b + 7c = 64
Subtract:
5b + 7c = 64
- 2b - 7c = - 55
3b = 9
b = 3
and,
5 * 3 + 7c = 64
7c = 64 - 15
7c = 49
c = 7
(1) a + b + c = 16
(1) a + 3 + 7 = 16
(1) a = 6
Hence, 6 small sizes, 3 medium sizes, and 7 large size pizzas were delivered.
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Hi can someone please send me answers?
Answer:
61 campers will focus on hockey.
Step-by-step explanation:
86+53=139
139-200=61
Which Property of Addition does 9 + 0 = 9 illustrate ? A. Distributive Property B. Identity Property C. Zero Property D. Commutative Property
Answer:
B. Identity Property
Jeff has 19 packages he wants to mail. 18 identical packages weigh 12 7/8 pounds each. A nineteenth package weighs 19 times the cost of one package. How many pounds do all the packages weigh together?
An arrow is shot from 3 ft above the top of a hill with a vertical upward velocity of 108 ft/s. If it strikes the plain below after 9.5 s, how high is the hill?
If the arrow is launched at t0, then write an equation describing velocity as a function of time?
The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),
To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:
h = h0 + v0t + 1/2at^2
where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).
In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.
At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:
v = v0 + at
we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:
0 = 108 - 32.2t
t = 108/32.2 ≈ 3.35 s
Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.
Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:
h_hill = h0 + v0t + 1/2at^2 - h_top
where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:
h_top = h0 + v0^2/2a
Plugging in the given values, we get:
h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft
Plugging this into the first equation, we get:
h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78
h_hill ≈ 25.73 ft
If the arrow is launched at t0, the equation describing velocity as a function of time would be:
v(t) = v0 - gt
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Help me please please
Here is a frequency distribution table (FDT) for a small data set: data value frequency 14 14 15 11 16 23 17 10 18 13 Find the following measures of central tendency: mean (I (Please show your answer to one decimal place.) median (Please enter an exact answer:) mode (Please enter an exact answer: )
The mean is 14.7, the median is 16, and the mode is 16.
To find the mean, we need to calculate the sum of all the data values and divide it by the total number of observations.
The sum of the data values is:
14 x 14 + 15 x 11 + 16 x 23 + 17 x 10 + 18 x 13 = 196 + 165 + 368 + 170 + 234 = 1043
The number of observations is:
14 + 11 + 23 + 10 + 13 = 71
The mean is calculated as follows,
1043 / 71 = 14.7 (rounded to one decimal place)
The median is the central value in the data collection. To find the median, we need to arrange the data values in ascending order and find the middle value. In this case, we have an odd number of observations, so the median is simply the middle value.
14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18
The median is 16.
The mode is the value that appears most repeatedly in the data set. In this case, the mode is 16 since it occurs the most (23 times).
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The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answer:
A) Mr. Simpson's class; it has a larger median value 14.5 pencils.
Step-by-step explanation:
A box plot is a visual display of the five-number summary:
Minimum value = The value at the end of the left whisker.Lower quartile (Q₁) = The left side of the box.Median (Q₂) = The vertical line inside the box.Upper quartile (Q₃) = The right side of the boxMaximum = The value at the end of the right whisker.From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:
Mr Johnson's class:
Median = 11IQR = Q₃ - Q₁ = 14 - 8 = 6Range = max - min = 45 - 7 = 38Mr Simpson's class:
Median = 14.5IQR = Q₃ - Q₁ = 21 - 12 = 9Range = max - min = 50 - 0 = 50In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.
The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.
The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).
As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.
In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.
please help me please please
without graphing, describe the transformation of each parabola or absolute value function y = 2 |x|+ 1
Remember the following transformations of a function:
\(c\cdot f(x)\)This transformation stretches the function over the vertical axis if c>1 and shrinks it if 0
If c is positive, the orientation is mantained, and if c is negative, the function is also flipped over (it shrinks if -1
\(f(x)+c\)This transformation moves the function vertically c units. It goes up if c>0 and down if c<0.
Therefore, starting with the absolute value function:
\(\lvert x\rvert\)Multiply the function by 2:
\(2\cdot\lvert x\rvert\)Since 2>1, then this is a vertical stretching by a factor of 2.
Next, add 1:
\(2\cdot\lvert x\rvert+1\)This will translate the stretched absolute value function one unit upwards.
Therefore, the complete description of the transfromation would be:
\(y=2\cdot\lvert x\rvert+1\)Is a vertical stretching of the absolute value function by a factor of 2, translated 1 unit upwards.
Please break down how to do these pls
The value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
Simplifying an equation is simply another way of saying solving a math problem. When you simplify a phrase, you are attempting to write it in the simplest way feasible. In conclusion, there should be no more adding, subtracting, multiplying, or dividing to do.
Given expression 1. -4\(x^{-2}\) + 3\(y^{0}\) 2. 2\(x^{0}\)\(y^{-2}\)
Expression for x =2 and y=5
-4x-2 + 3y0
= -4(2)-2 + 3(5)0
= 16+3
=19
Now
2x0y-2
= 2(2)0x(5)-2
= 2 x (1/25)
= 2 x 0.04
= 0.08
Therefore the value of given expressions is -4\(x^{-2}\) + 3\(y^{0}\) = 19 and 2\(x^{0}\)\(y^{-2}\) = 0.08
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A mechanic earned $983.88 for 42.5 hours of work . Which is the best estimate of how much the mechanic earned per hour
Match the following graph with the name of the graph
Absolute value: C
Quadratic: D
Constant: A
Square root: E
Linear: B
There are the equations for the graphs on the bottom:
y=2 is constant because the y value never changes
y=x is linear because the y value changes at a constant rate
y= |x| is absolute value because |x| is the absolute value of x
y=x^2 is quadratic because quadratic functions have a degree of 2
y=sqrt(x) is a square root because y= square root of x
Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2/1/2+2/3/4+3=8/1/4 pounds
The correct total weight of the bags of granola is 8 1/4 pounds.
One thing that can be done to improve Roberto's reasoning is to ensure the accuracy of the calculations.
In his conclusion, Roberto added the weights of the bags of granola (2 1/2, 2 3/4, and 3) and claimed that the total weight was 8 1/4 pounds. However, the sum of these weights does not equal 8 1/4 pounds.
To address this, Roberto should recheck his calculations. Adding mixed numbers involves adding the whole numbers separately and then adding the fractions separately. In this case, 2 1/2 + 2 3/4 + 3 can be calculated as follows:
2 + 2 + 3 = 7 (sum of whole numbers)
1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1 1/4 (sum of fractions)
Thus, the correct sum is 7 + 1 1/4 = 8 1/4 pounds.
By double-checking the calculations and providing the accurate sum, Roberto's reasoning would be more precise, reliable, and free from errors.
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The probable question may be:
Roberto made a line plot to show the weight in pounds of the bags of granola in his store he concluded that the total weight of the granola was 2 1/2+2 3/4+3=8 1/4 pounds.
what is one thing that you could do to Roberto's Reasoning
The figure below shows a rope that circles the Earth. The radius of the Earth is 6371 kilometers.
Assuming the rope makes a perfect circle, what is the length of this rope?
Give your answer in terms of pi.
Simplify (3.8 x 10^-2)(5.14 x 10^-10). Write the final answer in scientific notation.
Answer:
1.9532×10⁻¹¹
Step-by-step explanation:
You want the product (3.8 × 10^-2)(5.14 × 10^-10) in scientific notation.
ProductThe product is computed in the usual way, making use of the rules of exponents.
(3.8 × 10^-2)(5.14 × 10^-10) = (3.8×5.14) × (10^-2)(10^-10)
= 19.532 × 10^(-2-10) = 19.532 × 10^-12
Moving a factor of 10 from the coefficient to the exponent gives ...
= 1.9532×10^-11 . . . . . . final answer in scientific notation
__
Additional comment
Scientific notation has 1 digit to the left of the decimal point in the coefficient.
Here, we had to divide by 10 to put the coefficient decimal point in the right place. To keep the number at the same value, we had to increase the exponent of 10 by 1 from -12 to -11.
Your calculator can display the product in scientific notation for you, as can any spreadsheet.
Sometimes it is convenient to adjust the exponents before the multiplication. Here, you can see the product of the coefficients will be greater than 10, so will ultimately need to be divided by 10. One way to get there is rewriting the problem as (0.38×10^-1)(5.14×10^-10). This will give a product coefficient between 1 and 10 with an exponent of -11.
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Can someone solve this, please?
AND FAST
Answer: 40
Step-by-step explanation: yes make me brainlist (its the crown)
have a good holiday guys
Answer:
Well thank you so much you too
Step-by-step explanation:
Answer:
u too homie!
Step-by-step explanation:
i want free points
Please help asap need this answer fast.
Answer:
D
Step-by-step explanation:
Because 2×2 is 12 and 12×5 is 60
A right rectangular prism is thee times as long as it is wide. Its height is twice its length. The width is 5 centimeters. What is the volume (in cubic centimeters)
Answer:
I think its 50centimeters
Hope this helps
Write the ratios of each for the given triangle below
SinA=
CosA=
TanA=
SinB=
CosB=
TanB=
Answer:
i have made it in above picture
Consider the two circles shown.
(-5,6)
To show that circle P is similar to circle Q. circle P is translated t units to the right.
The image is then dilated about its center by a scale factor of s.
What are the values of t and s?
Fill t in blank 1 and s in blank 2. Do not round.
A
6)
A
The values of t and s are 13 and 1.75, respectively.according to the given conditions
What are similar circle ?
Similar circles are circles that have the same shape, but different sizes. More specifically, if two circles are similar, then their corresponding radii are proportional and their corresponding centers are collinear. In other words, if you can transform one circle into the other by uniformly scaling it, then the circles are similar.
To show that circle P is similar to circle Q, we need to show that their corresponding radii are proportional, and their corresponding centers are collinear.
Let's first find the equation of the line that passes through the centers of the two circles:
The equation of the line passing through (-5, 6) and (8, 6) is:
y = 6
Therefore, the centers are collinear.
The radius of circle P is 4, and the radius of circle Q is 7. Therefore, the ratio of their radii is:
7/4 = 1.75
To find the value of t, we need to translate the center of circle P to the right until it coincides with the center of circle Q. Since the x-coordinate of the center of circle P is -5, and the x-coordinate of the center of circle Q is 8, we need to translate circle P by:
t = 8 - (-5) = 13 units to the right
To find the value of s, we need to dilate the image about its center. The center of the image after translation is:
(-5 + 13, 6) = (8, 6)
Therefore, the center of dilation is (8, 6). The scale factor of dilation is the ratio of the radii, which is 1.75. Therefore,
s = 1.75
Hence, the values of t and s are 13 and 1.75, respectively.
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5/9+ (-4/5)
A. 1/4
B. 11/45
C. -9/14
D. -11/45
PLEASE HELP ILL GIVE BRAINLIST
Hey team can spend no more than $300 on shirts the team has already spent $80 how many more shirts for $15 each can I still buy Rite in inequality that represents the situation
He can buy less οr equal tο 14 shirts with the mοney left and The inequality that represents this situatiοn is s (stands fοr shirts) ≤ 14.
What is inequality?In Mathematics, it is the relatiοnship between twο values that are nοt equal. Inequality means twο values that are nοt equal. When the situatiοn is tο cοmpare the values, '≤' οr '≥' sign are used.
Hey team can spend nο mοre than $300 οn shirts the team has already spent $80.
300- 80 = 220
220/ 15 = 14.6
Let us say s be the number οf shirts.
Then the inequality will be s≤14
As the numbers οf shirts cant be a fractiοnal term sο we cοnvert the fractiοnal term tο the integer οne.
Hence, the inequality that represents the situatiοn is s≤14.
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please
\(2x {}^{2} + 2y {}^{2} - 6y - 12y = 3 \)
I need help
A square pyramid is shown. Select the net of the square pyramid. Then, use the net to select the surface area.
The surface area of the square pyramid is 28.2 square units
How to determine the surface area of the shapeFrom the question, we have the following parameters that can be used in our computation:
The square pyramid
A square pyramid when split has 1 square and 4 triangles
Using the above as a guide, we have the following:
The net is net (a)
So, the surface area is
Area = 3 * 3 + 4 * 0.5 * 3 * 3.2
Evaluate
Area = 28.2
Hence, the surface area of the shape is 28.2 square units
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What is 10% of 10$ plz
Answer:
1 dollar
Step-by-step explanation:
Answer:
1 dollar
Step-by-step explanation:
Hope this helps!
What is the value of Y
Answer:
100
Step-by-step explanation:
The measure of an arc is twice the measure of the inscribed angle that intercepts it. The arc y° is intercepted by an inscribed angle marked 50°, so ...
y = 100
Which ratio represents the number of vowels to total letters in the word JACKSONVILLE?
Step-by-step explanation:
4:12 there are four vowels and 12 letters?
If Jonny was 21 years old . He is 3 times as old as Becky determined Becky’s age
Answer:
Becky is 7 years old.
Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.
Answer:
Becky's 7 seven years old
Step-by-step explanation:
If 21 = 3x
x = 21/3
x = 7
Hope this helps :)
Pls brainliest...
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 5 milliliters of compound
B. If a chemist wants to make 728 milliliters of the drug, how many milliliters of compound A are needed?
? milliliters of compound A
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
What do you mean by compound?A compound in chemistry is a material comprised of two or more separate chemical elements mixed together in a certain proportion. Chemical connections that are challenging to break are created when the elements interact with one another.
Compound A:Compound B ratio in the medication is 3:5. In other words, there are 3 millilitres of compound A and 5 millilitres of compound B for every 3+5=8 millilitres of the medicine.
We may set up a percentage using the ratio of compound A to the total volume of the medicine to determine how much compound A is required to make 728 millilitres of the drug:
3 ml x 3 ml x 3 ml
-------- = ----------
728 ml total, 8 ml overall
If we cross-multiply, we obtain:
8(x) = 3(728)
To find x, we use the formula x = 3(728)/8 = 273
In order to create 728 millilitres of the medication, 273 millilitres of component A are required.
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273 milliliters of compound A are needed to make 728 milliliters of the drug.
What are proportions?
In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:
a/b = c/d
To determine the amount of compound A needed to make 728 milliliters of the drug, we need to use the given ratio of 3 milliliters of compound A to 5 milliliters of compound B.
Let's start by finding the ratio of compound A to the total amount of ingredients (A+B) in the drug:
3 : (3+5) or 3:8
This means that for every 8 milliliters of the drug, 3 milliliters of compound A are used.
To find out how many milliliters of compound A are needed for 728 milliliters of the drug, we can set up a proportion:
3/8 = x/728
where x represents the amount of compound A needed.
To solve for x, we can cross-multiply:
8x = 3*728
8x = 2184
x = 273
Therefore, 273 milliliters of compound A are needed to make 728 milliliters of the drug.
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