Tommy's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 51 regular sodas and 34 diet sodas. What percentage of the sodas served were regular?
Answer:
72
Step-by-step explanation:
Max bought a 100-page journal and writes 1 page per day. Pat bought a 200-page journal and writes 3 pages per day. The equation below can be solved to find the number of days ( d ) until they will have the same number of pages left in their journals. −d + 100 = −3d + 200 In how many days ( d ) will Max and Pat have the same number of pages left in their journals?
Answer:
d=50
Step-by-step explanation:
-d+100=-3d+200
Subtract 100 from both sides
-d+100-100=-3d+200-100
Simplify
-d=-3d+100
Add 3d to both sides
-d+3d=-3d+100+3d
Simplify
2d=100
Divide both sides by 2
\frac{2d}{2}=\frac{100}{2}
Simplify
d=50
Answer:
In 50days
Step-by-step explanation:
Since the equation below can be used to find the number of days (d) until they will have the same number of pages left in their journals −d + 100 = −3d + 200, this equations will be solved to get 'd'
Given the equation;
−d + 100 = −3d + 200
Collecting like terms we will have;
-d+3d = 200-100
2d = 100
d = 50
This shows that Max and Pat will have the same number of pages left in their journals in 50days.
I have the first part but I don't know how to do the second part
h e l p
[tex]\bf \begin{array}{cll} \stackrel{ordinal}{position}&\stackrel{term}{value}\\ \cline{1-2} 1&12\\ 2&12+d\\ 3&12+d+d\\ 4&12+d+d+d\\ &12+3d \end{array}\qquad \implies ~\hfill \begin{array}{llll} \stackrel{\textit{4th term}}{12+3d}~~=~~\stackrel{\textit{4th value}}{3}\\\\ 3d=-9\implies d = \cfrac{-9}{3}\\\\ \stackrel{\textit{common difference}}{d = -3} \end{array}[/tex]
well, we know the common difference is -3, to go from the 4th term to the 8th term, we need to add "d" 4 times or namely 3+4(-3), likewise to go from the 13th term to the 19th term we have to add "d" 6 times, or namely -24 + 6(-3).
[tex]\bf \stackrel{\textit{8th term}}{3+4(-3)}\implies 3-12\implies -9 \\\\\\ \stackrel{\textit{19th term}}{-24 + 6(-3)}\implies -24-18\implies -42[/tex]
7+(8+4) order of operations
Answer:
19
Step-by-step explanation:
8+4=12 +7=19
gcf of 35 and 15 and 3
Answer:
1
Step-by-step explanation:
Greatest Common Factor is the highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions.
No number (except 1) is divisible by both 35, 15, and 3. Therefore, the GCF is 1.
Answer:
35: 5×7 GCF: 5×3=15
15: 5×3
3: 1×3
Step-by-step explanation:
35 15 3
/ \ / \ / \
5 × 7 3 × 5 1 × 3
Use the pythagorean theorem to find the distance between from A(5, -3) to B (6,0)
A. 1.43
B.2.18
C. 3.16
D.11.40
Please explain
C. 3.16 is the right answer
Step-by-step explanation:
The distance formula used in coordinate geometry is derived from the Pythagorean theorem.
The distance formula is give by:
[tex]d=\sqrt{(x_2-x_2)^2+(y_2-y_1)^2}[/tex]
Here (x1,y1) are the coordinates of first point and (y1,y2) are the coordinates of second point
Here,
(x1,y1) = (5,-3)
(x2,y2) = (6,0)
Putting the values in the formula
[tex]AB = \sqrt{(6-5)^2+(0-(-3))^2}\\=\sqrt{(1)^2+(0+3)^2}\\=\sqrt{(1)^2+(3)^2}\\=\sqrt{1+9}\\=\sqrt{10}\\=3.16\ units[/tex]
The distance between two points is 3.16 units.
Hence,
C. 3.16 is the right answer
Keywords: Coordinate geometry, Pythagorean Theorem
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Josef is on a planning committee for the eighth-grade party. The food, decoration, and entertainment costs a total of $350. The committee has $75 already. If the committee sells the tickets for $5 each, at least how many tickets must be sold to cover the remaining cost of the party?
Answer:
At least 55 tickets must be sold to cover the remaining cost of the party.
Step-by-step explanation:
Total money needed for the party = $350
The money already with the committee = $75
Now, the money yet to be collected = Total Party Budget - Money present
= $350 = $75 = $275
Now, the cost of 1 ticket = $5
Let us assume the number of tickets sold to cover the cost of party = m
⇒ The cost of m tickets = 5 m
The renaming cost = Total cost of m tickets
or, 5 m = $275
⇒ m = 275/5 = 55
or, m = 55
Hence, at least 55 tickets must be sold to cover the remaining cost of the
party by Josef.
What is the measure of each interior angle of a regular hexagon?
Answer:
120°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
A hexagon has 6 sides, thus
sum = 180° × 4 = 720°
To find the measure of each interior angle divide by 6, that is
interior angle = 720° ÷ 6 = 120°
Answer: 120°
Step-by-step explanation: Let's start by finding the sum of the measures of the interior angles. The sum of the measures of the interior angles of a polygon can be found using the formula 180 (n - 2) where n represents the number of sides in the polygon.
Since a regular hexagon has 6 sides, we can plug a 6 in for n in our formula and we have 180 (6 - 2) where 6 represents the number of sides. We can simplify this by subtracting 2 from 6 inside the parentheses to get 180 (4) which is 720.
So the sum of the measures of the interior angles of a regular hexagon is 720°.
However, we want to know the measure of each interior angle. Since the angles of a regular hexagon are all congruent, we simply divide the sum of the measures of the angles which is 720 by the number of angles or sides which is 6 to get 120.
So the measure of each interior angle of a regular hexagon is 120°.
So the formula for finding the measure of each interior angle of a regular polygon is simply the sum of the interior angles 180 (n - 2) divided by the number of sides which is n.
Image provided.
The area of a rectangle is 27ft squared, and the length of the rectangle is 3ft less than twice the width. Find the dimensions of the rectangle.
Answer:
width =4.5ft
length=6ft
Step-by-step explanation:
w = x
L = 2x-3
area = L*w
27 = x(2x-3)
[tex]27=2x^{2} -3x[/tex]
[tex]2x^{2} -3x-27=0[/tex]
[tex]2x^{2} +6x-9x-27=0[/tex]
2x(x+3)-9(x+3)=0
(2x-9)(x+3)=0
2x-9=0
2x=9
x=9/2
x=4.5
L=2x-3=2*4.5-3 =9-3=6
The dimensions of the rectangle are; width = 4.5ft and length = 6ft.
What is the area of the rectangle?The area of the rectangle is the product of the length and width of a given rectangle.
The area of the rectangle = length × Width
The length of the rectangle is 3ft less than twice the width.
Let width = x
Length = 2x - 3
The area of the rectangle = length × Width
27 = x(2x-3)
2x² - 3x = 27
2x² - 3x - 27 = 0
2x(x + 3) - 9(x + 3) = 0
(2x-9)(x+3)=0
The solutions are;
2x-9=0
2x=9
x=9/2
x = 4.5
(x+3) = 0
x = -3
The width cannot be negative.
So,
Length = 2x-3 = 2*4.5-3 = 9 - 3
Length = 6
Hence, The dimensions of the rectangle are; width = 4.5ft and length = 6ft.
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What is the solution to the linear equation?
d – 10 – 2d + 7 = 8 + d – 10 – 3d
d = –5
d = –1
d = 1
d = 5
The solution to the linear equation d – 10 – 2d + 7 = 8 + d – 10 – 3d is d = 1.
EquationAn equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
d – 10 – 2d + 7 = 8 + d – 10 – 3d
Simplifying:
-d - 3 = -2d - 2
Collecting like terms:
-d + 2d = -2 + 3
d = 1
The solution to the linear equation d – 10 – 2d + 7 = 8 + d – 10 – 3d is d = 1.
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In the following expression 5x2−7x+11
, the number 11 is an example of __________________? term
coefficient
constant
variable
Answer:
constant
It is the unchanging value, and the coefficiant is the numbers with the variables because the variable changes the number. The variable is the letter that is either alone or with a number.
A store owner sells two pairs of running
shoes for each pair of high tops.
He plans to order 144 pairs of shoes
How many pairs should be high tops?
Answer:
He will order 72 pairs of high tops
Explanation:
Given the store owner sells two pairs of running shoes for each pair of high tops
For every pair of high tops, he sells 2 pairs of running shoes
1 high top = 2 running shoes
He has planned to order 144 pairs of shoes
Therefore, 144 pair of running shoes = 144/2 = 72 pairs of high tops
Therefore, he will order 72 pairs of high tops
a. How many bushels of seed potatoes a
needed to plant 76 rows if 3 pecks are
planted per row?
Answer:57
Step-by-step explanation:
Conversion factor is
1 US bushel = 4 US pecks
76 rows x 3 pecks= 228 pecks
228 pecks / 4 = 57
To plant 76 rows of seed potatoes, with 3 pecks per row, we would need a total of 57 bushels, as there are 0.75 bushels per row and this is multiplied by the number of rows.
Explanation:To answer this question, we first need to understand the relationship between bushels and pecks. There are 4 pecks in one bushel. If 3 pecks are planted per row, then each row requires 0.75 bushels (because 3/4 = 0.75). So, to find the number of bushels needed for 76 rows, we multiply 76 by 0.75.
First, determine how many bushels are in a peck, which is 0.25.Then multiply that amount by the number of pecks per row (3 pecks) to get the bushels per row (0.75 bushels).Finally, multiply the bushels per row by the number of rows (76 rows) to find the total amount of bushels needed.The final calculation is: 0.75 bushels/row * 76 rows = 57 bushels.
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25 divided by 1750 if u know the answer ur smart
Answer:
70 would be the answer to this question....apparently.
Step-by-step explanation:
Answer:
70
Step-by-step explanation:
25 divided by 1750 = 70
subtract 1750 to 175 =
00 subtract 00 = 00
overall 70 is your answer in long division
The figures below show a pattern.
Find the expression that could be used to determine the number of squares in the nth figure.
Answer:
The number of blocks in the nth figure will be (3n + 1).
Step-by-step explanation:
See the attached figure where few arrangements are there.
The number of blocks in the first arrangement is (3 + 1)
Now, the number of blocks in the second arrangement is (3 × 2 + 1)
Again, the number of blocks in the third arrangement is (3 × 3 + 1)
So, the pattern says that the number of blocks in the nth arrangement will be (3 × n + 1) = (3n + 1) (Answer)
You have a truck with two gas tanks. The volume of the larger tank is "8x2 + 2x − 1" in3 and the volume of the smaller tank is "7x2 − 2x + 1" in3. Find a single expression that represents the capacity of both gas tanks combined.
A) 15x2
The combined volume of both tanks is: Option A: 15x^2
Step-by-step explanation:
Given
Volume of larger tank = V_L = [tex]8x^2+2x-1[/tex] in^3
Volume of smaller tank = V_S= [tex]7x^2-2x+1[/tex] in^3
To find the combined volume, we have to add both volumes
[tex]V = V_L+V_S\\=8x^2 + 2x - 1 + (7x^2 - 2x + 1)\\=8x^2+2x-1+7x^2-2x+1\\Combining\ like\ terms\\=8x^2+7x^2+2x-2x-1+1\\=15x^2[/tex]
Hence,
The combined volume of both tanks is: Option A: 15x^2
Keywords: Expressions, Polynomials
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Which expression is equivalent to 1/5(15+10x-5)
Answer:
simplify the expression: 2x+2
Step-by-step explanation:
The equivalent expression of the given expression is is 2 + 2x
To solve this expression, we should simply proceed to multiply the value outside the bracket and simplify.
steps required;
collect like termsmultiply through the bracket by the value outsideCollect like termsThis is done to add up or subtract similar or like values with each other.
[tex]\frac{1}{5}(15+10x-5)=\frac{1}{5}(15-5+10x)=\frac{1}{5}(10+10x)\\[/tex]
Multiply ThroughMultiply the entire value inside the bracket by 1/5.
[tex]\frac{1}{5}(10+10x)=2+2x[/tex]
This is the simplified expression of what we are given.
The equivalent expression is 2 + 2x.
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What percent of 20 is 10
Answer:
50%
Step-by-step explanation:
cause 50% is 1/2 and 1/2 of 20 is 10
Answer: 50%
Step-by-step explanation:
10 is half of 20.
Half converted to a percent is 50%
What is 1/6 times 1/5
Answer: 1/30
Step-by-step explanation:
This package of cheese costs $2.97 (there are 11 slices of cheese)
How much would a package with 18 slices cost at the same pruce per slice?
Answer:
$4.86
Step-by-step explanation:
2.97/11 =.27 .27 x 18= 4.86
Answer:
4.86
Step-by-step explanation
telephone company charges a fixed monthly rate plus a rate per megabyte of data used. The company charges $120 for 100 megabytes of data and $95 for 50 megabytes of data. An equation can be written to show the relationship between the total megabytes of data used (x) and the total monthly charges (y). Which of the following best describes the steps to draw the graph?
Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 0.50
Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 2
Draw a graph that joins the points (120, 100) and (95, 50) and has a slope = 2
Draw a graph that joins the points (120, 100) and (95, 50) and has a slope = 0.50
Answer:
The correct answer is A. Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 0.50
Step-by-step explanation:
1. Let's review the information given to us for solving the question:
Total of megabytes of date used = x
Total monthly charges = y
x₁ = 50 Megabytes, x₂ = 100 Megabytes
y₁ = US$ 95, y₂ = US$ 120
2. Let's find out the best description of the steps to draw the graph and the slope.
Slope = (y₂ - y₁)/ (x ₂- x₁)
Slope = 120 - 95/ 100 - 50
Slope = 25/50 = 1/2 = 0.50
Remember that the coordinates of the points in the line are written this way:
(x, y) ⇒ (Total of megabytes of date used, Total monthly charges)
The correct answer is A. Draw a graph that joins the points (100, 120) and (50, 95) and has a slope = 0.50
Answer:
a
Step-by-step explanation:
100% on test
The product of 576 and 684 is irrational or rational
The product of 576 and 684 is a rational number since it results in an integer, which is a subset of rational numbers.
Explanation:The product of 576 and 684 is asked to be classified as rational or irrational. The multiplication of two integers will always produce another integer, as is the case with 576 multiplied by 684. Since all integers are rational numbers (they can be expressed as the ratio of two integers), the product, in this case, is also a rational number.
Therefore, the product of 576 and 684 is rational because it can be expressed as a ratio of the two integers (the product itself over 1), fitting the definition of a rational number which includes integers, fractions, finite decimals, and repeating decimals.
Final answer:
The product of 576 and 684 is a rational number because the multiplication of two integers always results in another integer.
Explanation:
The question asks whether the product of 576 and 684 is rational or irrational. A rational number is a number that can be expressed as a ratio of two integers. Since both 576 and 684 are integers, their product will also be an integer, as the multiplication of two integers always results in another integer. Therefore, this product is definitely a rational number. An irrational number, by contrast, cannot be expressed as such a ratio, and is typically found with non-repeating, non-terminating decimal expansions or with numbers like the square root of a non-square number. However, as there is no square root or any other irrational operation involved in multiplying 576 and 684, the result is rational.
Postage stamps cost $0.37 each. How much does a book of 50 stamps cost?
Answer:
$18.50
Step-by-step explanation:
.37×50 = 18.5
$18.50
Answer:
$18.50
Step-by-step explanation:
GIven
1 stamp ----> $0.37
50 stamps ------> $0.37 x 50 = $18.50
0.0398 rounded to the nearest cent
Answer:
0.04
Step-by-step explanation:
0.0398
when rounding if its over 5 you round up if its under you round down
The number 0.0398 rounded to the nearest cent; is 0.04.
According to the question;
We are required to round off 0.0398 to the nearest cent.To round off to the nearest cent;
We must know that cents is synonym for Hundredths;
The number to be rounded off is 0.0398In essence, since 9 which is after the digit, 3 which occupies the hundredth position is greater than 5; it is rounded off to 1 and added to 3.Consequently; 0.0398 rounded to the nearest cent is 0.4
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A package of five pairs of insulated gloves cost $29.45 what is the cost of a single pair of gloves
Answer:
$5.89
Step-by-step explanation:
29.45/5=5.89
Answer:
$5.89
Step-by-step explanation:
I divided 29.45 and 5 and got the product+cost of a single pair of the gloves; $5.89
Sand Castles
Juan built a sand castle like the one shown. The castle is shaped like a rectangular prism with a rectangular pyramid on top. How much sand did it take Juan to build it?
Answer:
80in^3
Step-by-step explanation:
Answer:
80 in^3
Step-by-step explanation:
I just did this
What is the value of the discriminant of the quadratic equation -2x =-8x+8, and what does its value mean about the number
of real number solutions the equation has?
Final answer:
The value of the discriminant is 36, which means that the quadratic equation -2x = -8x + 8 has two distinct real solutions.
Explanation:
The given equation -2x = -8x + 8 can be rearranged into a quadratic equation: -8x + 8 + 2x = 0. Combining like terms gives: -6x + 8 = 0. To find the discriminant of this quadratic equation, we look at the coefficient of x^2, which is 0. Since the discriminant D = b^2 - 4ac, where a = coefficient of x^2, b = coefficient of x, and c = constant term, in this case, a = 0, b = -6, and c = 8. Plugging these values into the formula, we have: D = (-6)^2 - 4(0)(8) = 36 - 0 = 36.
The value of the discriminant is 36. The discriminant tells us about the number of real number solutions the equation has. If the discriminant is positive (D > 0), then the equation has two distinct real solutions. If the discriminant is zero (D = 0), then the equation has one real solution. If the discriminant is negative (D < 0), then the equation has no real solutions.
In this case, since the discriminant is positive (D = 36), the quadratic equation has two distinct real solutions.
Kate and Miley are selling girls scout cookies Kate sold 27 boxes in 45 minutes Miley sold 12 boxes in 30 minutes at the same rates how many total boxes will the girls have sold in one hour
The total number of boxes will be 60 that the girls have sold in one hour.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
We have to determine the total number of boxes will the girls have sold in one hour
Let Kate sold x boxes in 60 minutes
As per the given situation, we can write the ratio would be as:
27 boxes : 45 minutes = x boxes : 60 minutes
⇒ 27/45 = x/60
Apply the cross-multiplication operation,
⇒ x = (60×27)/45
⇒ x = 36
Let Miley sold y boxes in 60 minutes
⇒ 12/30= y/60
Apply the cross-multiplication operation,
⇒ y = (12×60)/30
⇒ y = 24
So, the total number of boxes = x + y = 36 + 24 = 60
Thus, the total number of boxes will be 60 that the girls have sold in one hour.
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Final answer:
Kate sells 36 boxes and Miley sells 24 boxes in one hour. So, they will have sold a total of 60 boxes in one hour.
Explanation:
To find the total number of boxes sold by both Kate and Miley in one hour, we need to calculate the rate at which each of them sells boxes. Kate sells 27 boxes in 45 minutes, which can be converted to 0.6 boxes per minute (27 boxes / 45 minutes = 0.6 boxes per minute). Miley sells 12 boxes in 30 minutes, which can be converted to 0.4 boxes per minute (12 boxes / 30 minutes = 0.4 boxes per minute).
To find the total number of boxes sold in one hour, we add the number of boxes each of them sells in one minute and multiply it by 60 (the number of minutes in an hour). Kate sells 0.6 boxes per minute, so in one hour she would sell 0.6 boxes/minute * 60 minutes = 36 boxes. Miley sells 0.4 boxes per minute, so in one hour she would sell 0.4 boxes/minute * 60 minutes = 24 boxes. Therefore, the total number of boxes sold by both Kate and Miley in one hour would be 36 + 24 = 60 boxes.
The sum of 3 times a and b
Answer:
3+(axb)
Step-by-step explanation:
The algebraic representation of the expression The sum of 3 times a and b is 3a + b
How to determine the algebraic representation of the expressionFrom the question, we have the following parameters that can be used in our computation:
The sum of 3 times a and b
By definiton:
sum means plus
Using the above as a guide, we have the following:
3 * a + b
When solved, we have
3a + b
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Question
Translate the sentence into an algebraic expression
The sum of 3 times a and b
The data below shows the age distribution of cases
of a certain disease reported during the year at a
hospital
34 17 25 37 19 19 27 19 44 24
24 22 32 12 13 16 18 14 12 16
14 17 10 16
20 15 15 10 10
14 17 20 18 19 13 13 B 18 30
24 34 44 31 43 40 28 31 18 22
15 31 18 27 35 35 20 32 38 32.
22
Organising the data into a frequency distribution
lor table, calculate the coefficient of Skewness
and kur tosis and interpret your results
Answer:
I would line up the numbers in order
The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.
We have,
To calculate the coefficient of skewness and kurtosis, we first need to organize the data into a frequency distribution table.
Age | Frequency
10 | 3
12 | 2
13 | 4
14 | 5
15 | 5
16 | 5
17 | 4
18 | 6
19 | 4
20 | 3
22 | 4
24 | 4
25 | 1
27 | 3
28 | 1
30 | 2
31 | 4
32 | 3
34 | 3
35 | 3
37 | 1
38 | 1
40 | 1
43 | 1
44 | 2
To calculate the coefficient of skewness, we use the formula:
Coefficient of Skewness = (mean - mode) / standard deviation
Mean = (10 * 3 + 12 * 2 + 13 * 4 + ... + 44 * 2) / 100 ≈ 20.49
Mode = 18 (the most frequent value in the dataset)
Standard Deviation
= √[((10 - mean)² * 3 + (12 - mean)² * 2 + ... + (44 - mean)² * 2) / 100]
≈ 9.63
Coefficient of Skewness = (20.49 - 18) / 9.63 ≈ 0.26
To calculate the kurtosis, we use the formula:
Kurtosis = ∑[((x - mean) / standard deviation)⁴ * frequency] / (n * standard deviation⁴) - 3
Kurtosis = [((10 - mean) / standard deviation)⁴ * 3 + ((12 - mean) / standard deviation)⁴ * 2 + ... + ((44 - mean) / standard deviation)⁴ * 2] / (100 * standard deviation⁴) - 3 ≈ -0.84
Interpretation:
Coefficient of Skewness:
The coefficient of skewness is positive (0.26), indicating that the data is slightly skewed to the right (positively skewed). This means that there is a longer tail on the right side of the distribution.
Kurtosis:
The kurtosis value is approximately -0.84. Since it is less than 3, the distribution is considered platykurtic. This means that the distribution has lighter tails and is flatter compared to a normal distribution.
Thus,
The coefficient of skewness is 0.26, indicating slight positive skewness and the kurtosis is approximately -0.84, indicating a platykurtic distribution.
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