26 possible letters for each of the first two positions and 10 possible digits for each of the last 4 positions gives a total of 676,000,000 license plates.
(1) 26 possible letters for each of the first two positions and 10 possible digits for each of the last 4 positions gives a total of
26 x 26 x 10 x 10 x 10 x 10 = 676,000,000 license plates.
(2) The number of possible license plates where the digits must be different is the number of permutations of 10 items taken 4 at a time, or 10P4 = 5040. Multiplying by 26 x 26 gives a total of
5040 x 26 x 26 = 3,636,160 possible license plates.
(3) To find the number of license plates that begin with "A" and don't have a 7, we first find the number of license plates that start with "A" and don't have any restriction on the last 4 digits. This is
26 x 10 x 10 x 10 x 10 = 676,000
Then, we find the number of license plates that have a 7, which is
9 x 26 x 10 x 10 = 23,760
Subtracting this from the total number of license plates that start with "A" gives us
676,000 - 23,760 = 652,240 possible license plates.
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What is 16% of 175 I need help
Answer: 28
Step-by-step explanation:
16% = 0.16
Percents are just decimals!
Now you can put this in your calculator, and you will get 28.
However:
It might help you later to know that x% of y = y% of x
In other words, 16% of 175 is the same thing as 175% of 16
This problem is easier, since we can break 175% into 1 and 3/4th. 3/4th of 16 is easy to calculate, (its 12), and so we can add 12 to 16 to find the answer, which is still 28 :)
No calculator needed!
Please help!
Solve for x
The value of x is 8 by using the concept of similar shapes and angles.
Ratios of similar shapes and angles.When one triangle can be generated from the other by equally scaling, the two triangles are said to be similar. The ratio of any two pairs of comparable sides of similar shapes is said to be equal to the ratio of the sides of any two similar shapes. The similarity of the two shapes indicates that all related angle pairs and sides are equal and proportionate.
From the given information, equating the similar sides in order to determine the unknown side is expressed as follows;
24/(3x+6) = 32/40
Cancel the common factor (3) from the left-hand side
8/(x + 2) = 32/40
Cancel the common factor (8) from the right-hand side.
8/(x+2) = 4/5
Cross multiply
4x + 8 = 40
4x = 40 - 8
4x = 32
x = 32/4
x = 8
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Describe the graph of the function at its roots.
f(x) = (x − 2)3(x + 6)2(x + 12)
At x = 2, the graph
the x–axis.
For the graph of given function, At x = 2, the graph crosses x axis At x = - 6, the graph touches x axis, At x = - 12, the graph crosses x axis.
What's an Equation?
The description of an equation in algebra is a fine statement proving the equivalency of two fine expressions.
The two equations 3x 5 and 14 are separated by the" equal" sign in the equation 3x 5 = 14, for illustration.
In mathematics, an equation is a relationship between two expressions that's equal on both sides of the equal to subscribe. An equation is commodity like 3y = 16.
Equation of a function f( x) = ( x − 2) 3( x 6) 2( x 12)
Lets find out the roots and dissect
lets set each factor = 0 and break for x
Exponent in each factor tell us the multifariousness. Using multifariousness we check whether crosses or traces x axis
When multifariousness is odd also graph crosses x axis.
when multifariousness is indeed also graph touches x axis.
f(x) = (x-2)^3(x+6)^6(x+12)
⇒(x-2)^3
⇒x-2 = 0
⇒ x = 2
Root is x = 2 with multifariousness 3. 3 is odd
At x = 2, the graph crosses x axis
⇒ (x+6)^2
⇒ (x+6)=0
⇒ x = -6
At x = - 6, multifariousness is 2 that's indeed.
At x = - 6, the graph touches x axis
x + 12 = 0
x = -12
x = - 12 with multifariousness 1. 1 is odd
At x = - 12, the graph crosses x axis.
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A line is graphed on the coordinate plane.
Type in the equation for this line? Use x as your independent variable and y as the dependent variable.
The equation of the given line is [tex]y= \frac{1}{3}x+2[/tex]
What is the slope of a line?
A line's steepness and direction are measured by the line's slope. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
Given a straight line in a graph, we need to find the equation of this line
from the graph, we can see that the line passes through the axes at (0, 2) and (-6, 0)
now, the slope of the line is [tex]\frac{y2 - y1}{x2 - x1}[/tex]
[tex]= \frac{0 - 2}{-6 - 0} \\= \frac{1}{3}[/tex]
The line makes an intercept of 2 on the Y-axis, as we can see clearly
The slope-intercept form of the line is y = mx + c, where 'c' is the intercept and 'm' is the slope of the line
The equation of the given line is [tex]y = \frac{1}{3}x + 2[/tex]
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At a carnival game, you randomly throw two darts at the board and break two balloons. What is the probability that both of the balloons you break are purple? Write your answer in simplified fraction form
If randomly throw two darts at the board and break two balloons, then [tex]\frac{2}{35}[/tex] is the probability that both of the balloons you break are purple.
Considering what is meant by probability,
However, you must be aware that probability refers to the likelihood—greater or lesser—of a given event occurring.
In other words, probability creates a connection between the total number of conceivable events and the number of favorable events.
Then, the ratio between the number of favorable circumstances (cases in which event A may or may not occur) and the total number of possible cases is used to define the likelihood of any event A. Laplace's Law is what governs this.
[tex]P(A)=\frac{number of favorable cases}{number of possible cases}[/tex]
If the occurrence of one of them has an impact on the occurrence of the other, then two occurrences A and B are dependent. The likelihood for events that are dependent is:
P(A and B)= P(A)× P(B|A)
The phrase "the probability of B, provided that A has occurred" is denoted by the symbol P(B|A).
In this instance:
[tex]P(A)=\frac{4 balloons}{15 balloons} =\frac{4}{15}[/tex]
If the first balloon is purple, there are still 3 purple balloons available out of the total of 14. P(B|A) then equals [tex]\frac{3}{14}[/tex].
[tex]P(A and B)=\frac{4}{15} *\frac{3}{14}[/tex]
[tex]P(A and B)=\frac{2}{35}[/tex]
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y=3x+2
-4x+2y=8
graph
Answer:
Y=3x+2
Graph the line using the slope and y-intercept or two points
Slope: 3 Y-intercept: (0,2)
Point 1: (0,2) Point 2: (1,5)
-4x+2y=8
Graph the line using the slope and y-intercept or two points
Slope: 2 Y-intercept: (0,4)
Point 1: (0,4) Point 2: (1,6)
how many times larger is a centigram than a milligram? 10times | 100 times| 1000 times| 0.1 time
A centigram is 100 times larger than a milligram. So, the option b) 100 times is correct for this question.
1 centigram = 100 milligrams. A centigram is a unit of mass in the metric system, equivalent to one hundredth of a gram. A milligram, on the other hand, is a unit of mass in the metric system, equivalent to one thousandth of a gram. Therefore, a centigram is 100 times larger than a milligram. The conversion between the two units can be easily calculated as 1 centigram is equal to 100 milligrams. The use of centigrams is limited in common applications, with milligrams being the preferred unit for expressing very small masses, while grams and kilograms are used for larger masses.
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Which is larger? Circle A with an area of 10562.96 cm squared, or circle B with a circumference of 357.96 cm?
Circle A is larger.
Circle A's radius is 58 cm and circle B's radius is 57 cm.
What is a circle?A circle is a two-dimensional figure with a radius and circumference of 2πr.
We have,
Area of a circle = πr²
Circumference of a circle = 2πr
Circle A:
Area of a circle = 10562.96
πr² = 10562.96
r² = 3364
r = 58 cm ____(1)
Circle B:
Circumference = 357.96
2πr = 357.96
r = 357.96/6.28
r = 57 cm ______(2)
From (1) and (2)
58 > 57
So,
Circle A is larger.
Thus,
Circle A is larger.
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Solve the following system of inequalities graphically on the set of axes below. State
the coordinates of a point in the solution set.
Y >1/2x-1
Y ≥-3/4x-6
The solution to the inequality are the region in the shaded area
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
Y >1/2x-1
Y ≥-3/4x-6
Represent properly
y > 1/2x - 1
y ≥ -3/4x - 6
Next, we make a plot of the system to determine the solution
The shaded area in the plot represent the solution to the inequality
In this case, one of the coordinates in the shaded area has a coordinate of (-4, -3)
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PLEASE HELP ME!!!!!!
In 5-7 sentences, give real-world examples of the following math vocabulary terms:
1. Rotation
2. Reflection
3. Translation
4. Dilation
Answer: are have a raztation speed of 20 rotation a min
Step-by-step explanation:W anwer
2. Mick recorded the lengths of 10 Steller sea lions. Which length occurs most often?
3. Make a line plot. Draw a dot for each value. Stack dots for values that occur more than once.
Steller Sea Lion Lengths
−2
81/1/21
9 911 9/1/201
Length (in feet)
DATA
Steller Sea Lion Lengths (in feet)
9: 9 8/3/10
9
91/1
8
9 1/1 9 1/1/0
9/1/12
1438
9/3/3
91/1
18
Answer:feet occurs most often. Mick recorded the lengths of 10 Steller sea lions.
Step-by-step explanation:feet occurs most often. Mick recorded the lengths of 10 Steller sea lions.
Someone please help with this question
A business owner wants to have the front window of her store painted and is considering two artists for the job. Mariana has quoted a flat rate of $135 for the job. Vincent's quote is $34 per hour, plus $67 to cover the cost of materials. Depending on how long it takes Vincent to paint the window, these two could end up charging the same amount. How much would it cost? How long would Vincent have to take?
Answer:
Step-by-step explanation:
Mariana's quote: 135
Vicent's quote: 34x+67
Say x=1, 34(1)+67=101
For 1 hour of Vincent's work it would be $101.
Say x=2. 34(2)+67=135
Vincent would have to work for two hours to charge the exact same as Mariana.
Change the denominator of the fraction
p/p-2 to 4-p^2
n = the numerator of the fraction
[tex]\cfrac{p}{p-2}~~ = ~~\cfrac{n}{4-p^2}\implies \cfrac{p(4-p^2)}{p-2}~~ = ~~n\implies \cfrac{p(-1)(p^2-4)}{p-2}=n \\\\\\ \stackrel{ \textit{difference of squares} }{\cfrac{p(-1)(p^2-2^2)}{p-2}}=n\implies \cfrac{-p(p-2)(p+2)}{p-2}=n \\\\\\ \boxed{-p(p+2)=n}\hspace{5em}\cfrac{-p(p+2)}{4-p^2}[/tex]
Fill each square with a number to make the addition results correct
If the array includes just the positive integers [tex]{\displaystyle 1,2,...,n^{2}}{\displaystyle 1,2,...,n^{2}}[/tex], the magic square is said to be normal. Some authors take magic square to mean normal magic square.
A magic square is a square grid of numbers that has the same sum for every row, column, and diagonal. It is a mathematical puzzle that has been known and studied for thousands of years. Magic squares can be of different sizes, but the most common are those with odd numbers of rows and columns.
The concept of magic squares dates back to ancient China, where they were believed to have mystical properties. In India, they were used for divination and as part of religious rituals. In Europe, magic squares were popularized in the 16th century, where they were used as a form of mathematical entertainment. Magic squares are not only interesting mathematical puzzles but also have practical applications.
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Complete Question: -
Fill the given squre with numbers from 0 to 8 ( using each of them exactly once) in such a way that the sum of the numbers in the first second and third rows are third rows are in the ratio 1 : 2 : 3. At the same time the sum of the numbers in the first second and third columns also have to be in the same ratio.
verify the identity (cos 2x)/(sin x)=csc x-2sinx
Use identities:
cos 2x = 1 - 2sin² xcsc x = 1 / sin xThen apply to the left side of the given equation:
cos 2x / sin x = Substitute(1 - 2sin² x) / sin x = Distribute1 / sin x - 2sin² x / sin x = Simplifycsc x - 2sin x AnswerProved
Emma is starting a cupcake business and borrows money from Dixons dynamite deals (DDD) .she agrees to pay back the loan after 10 years by making one payment of 80,000 , interest is compounded and fixed at 14,6% per annum.hpw much did emma borrow from (DDD) ?
The amount (present value) that Emma borrowed from Dixons Dynamite Deals (DDD) to repay after 10 years with a one-time payment of $80,000 at 14/6% compounded interest per annum is not more than $20,475.94.
Step-by-step explanation:
To find out how much Emma borrowed from Dixons Dynamite Deals (DDD), we can use the formula for the future value of a loan with compound interest:
Future Value (FV) = Principal Amount (P) * (1 + r)^n
Where:
P = Principal amount (the amount borrowed)
r = Interest rate per period (in decimal form)
n = Number of periods
In this case:
Future Value (FV) = $80,000 (the payment Emma will make after 10 years)
Interest rate (r) = 14.6% per annum = 0.146 (in decimal form)
Number of periods (n) = 10 years
Now, let's calculate the principal amount (P):
$80,000 = P * (1 + 0.146)^10
Now, let's solve for P:
P = $80,000 / (1.146)^10
P ≈ $80,000 / 2.97804
P ≈ $26,874.94
So, Emma borrowed approximately $26,874.94 from Dixons Dynamite Deals (DDD) to start her cupcake business.
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Find the missing number so that the equation has infinitely many solutions.
– 2x+18=blank x+18
The missing term in the equation is n = -2
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 equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the missing term be represented as n
-2x + 18 = nx + 18
Subtracting 18 on both sides of the equation , we get
-2x = nx
Divide by x on both sides of the equation , we get
n = -2
Therefore , the missing term is n = -2
Hence , the equation is n = -2
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Solve For n !
[tex] \large \frak{2n + 5 = 6( {n}^{2} - 5) }[/tex]
Thank You!:)
The solution to the equation 2n + 5 = 6( n² - 5 ) is n = ( 1 - √(211 )) / 6 and n = ( 1 + √(211 )) / 6
What is the solution to the quadratic equation?Given the quadratic equation in the question;
2n + 5 = 6( n² - 5 )
First we simplify the given equation;
2n + 5 = 6( n² - 5 )
2n + 5 = 6n² - 30
6n² - 2n - 5 - 30 = 0
6n² - 2n - 35 = 0
To solve for n, we use the quadratic formula.
n = (-b±√(b² - 4ac)) / (2a)
Compare 6n² - 2n - 35 = 0 to the quadratic equation in its standard form an² + bn + c = 0.
a = 6b = -2c = -35Plug the values into the quadratic formula
n = (-b±√(b² - 4ac)) / (2a)
n = ( -(-2) ±√( (-2)² - 4 × 6 × -35 )) / (2 × 6 ))
n = ( 2 ±√( 4 + 840 )) / ( 12 )
n = ( 2 ±√( 844 )) / ( 12 )
n = ( 2 ±2√(211 )) / ( 12 )
n = ( 1 ± √(211 )) / 6
n = ( 1 - √(211 )) / 6 or n = ( 1 + √(211 )) / 6
Therefore, the values of n are ( 1 - √(211 )) / 6 and ( 1 + √(211 )) / 6.
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4
ASSIGNMENT (USE YOUR ASSIGNMENT NOTE)
1. James runs 400m every day. Work out how far James runs in one week. Give your
[3 marks]
answer in kilometres.
2. Here is a signpost
Town Center
3.5km
Park
650m
How far apart are the Town Centre and the Park?
Give your answer in kilometres.
(3 marks)
3. A bottle contains 1.75 litres of lemonade.
A can contains 330 ml of lemonade. Phil has 2 bottles of lemonade and 6 cans of
lemonade. How much lemonade does he have in total? Give your answer in millilitres.
For question 1,
James runs 400m in a day
In a week = 7 days
400m × 7 days = 2800m
To convert 2800m to km
1km = 1000m
So, 2800m/1000m
= 2.8 km
For question 2,
How far are the Town Center and the Park
3.5 km and 650m
650m to km
1km = 1000m
To km = 0.65km
The distance = 3.5km - 0.65km
= 2.85km
So, they are 2.85km apart
For question 3,
A bottle = 1.75 liters of lemonade
A can = 330 ml of lemonade
1.75 liters to milliliters
1 liter = 1000 milliliter
= 1.75 × 1000 ml
= 1750 ml
2 bottles of lemonade
1750ml × 2
= 3500 ml
6 cans of lemonade
330ml × 6
= 1980 ml
In total, 3500ml + 1980ml
= 5480 ml
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What percentage of calls with the Chicago service center answer within 10 seconds in January of 1994?
Answer:
Option B
Step-by-step explanation:
The green graph represents the percentage of calls with the Chicago service center.
For December 1993, the percentage of calls is coming out to at least 95 percent. In addition, the graph is increasing as months go by. Based on these two analysis, the estimate percentage of calls within 10 seconds in January of 1994 is:
Option B: 98
a rectangular bedroom is 5 ft longer than it is wide. its area is 84 ft2. what is the width of the room?
The width of the bedroom is approximately 7.32 feet.
A rectangle is a four-sided figure with opposite sides being equal and parallel. The area of a rectangle is given by multiplying the length and width of the rectangle.
Let's assume that the width of the bedroom is 'x' feet. We know that the length of the room is 5 feet longer than its width. Therefore, the length of the room will be (x+5) feet.
Now, we can use the given area of the bedroom to set up an equation:
Area of rectangle = Length x Width
84 = (x+5) x x
Simplifying this equation, we get:
84 = x² + 5x
Rearranging, we get:
x² + 5x - 84 = 0
This is a quadratic equation that can be solved using the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
In this case, a = 1, b = 5 and c = -84. Substituting these values in the formula, we get:
x = (-5 ± √(5² - 4(1)(-84)))/2(1)
Simplifying this, we get:
x = (-5 ± √721)/2
We can ignore the negative root since the width of the bedroom cannot be negative. Therefore, the width of the bedroom is:
x = (-5 + √721)/2
x ≈ 7.32 feet
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a necklace is made from purple pyramids and yellow spheres in a 1 : 6 ratio
By simplifying the ratio and adding the fractions, we found that 1/7 of the beads are purple pyramids.
Ratios are used to compare two quantities or values. They are often expressed in the form of a fraction or as a percentage.
The given ratio of purple pyramids to yellow spheres is 1:6. This means that for every 1 purple pyramid, there are 6 yellow spheres. We can express this ratio as a fraction:
Purple pyramids : Yellow spheres = 1 : 6
This can be simplified by dividing both sides by 6:
1/6 Purple pyramids : 1 Yellow sphere = 1/6 : 1
Now, we can add the two fractions to get the total fraction of pyramids in the necklace:
1/6 + 1 = 7/6
This means that out of every 7 beads, 1 is a purple pyramid. We can express this as a fraction:
1/7 of the beads are purple pyramids.
So, the fraction of the beads that are pyramids is 1/7.
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Complete Question:
A necklace is made from purple pyramids and yellow spheres in a 1:6 ratio . What fraction of the beads are pyramids?
Which set of steps shows how to find f(-3) when f(c)=-4x-5?
Answer:
7
Step-by-step explanation:
f(-3)
f(x) = -4x-5
f(-3) = -4(-3) - 5
f(-3) = 12 - 5
f(-3) = 7
In a density curve, proportion of data is represented by__
A. area above the curve. B. area under the curve.
C. the shape of the curve.
D. intervals of values on the vertical axis.
E. intervals of values on the horizontal axis.
F. the length of the curve.
Option B. Area under the curve. In a density curve, the proportion of data is represented by the area under the curve.
The area under the curve represents the proportion of data points that fall within a certain range of values, and the height of the curve at any given point represents the relative frequency or density of data points at that value. The total area under the curve is equal to 1, indicating that the sum of the proportions of data points in all possible intervals is equal to 100%.
It's important to note that the total area under the curve is equal to 1, indicating that the sum of the proportions of data points in all possible intervals is equal to 100%. This means that the density curve provides a complete picture of the distribution of the data, and the shape of the curve can be used to make inferences about the distribution, such as whether it is symmetrical, skewed, bimodal, etc.
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. a school has 100 business majors, 60 math majors, and 40 psych majors. every student at the school belongs to one and only one of these majors. three different students are chosen to be interviewed for a focus group. how many ways are there to choose this focus group where all three students do not all come from the same major?
Number of ways are there to choose this focus group where all three students do not all come from the same major is 240,000
It is given that a school have three majors i.ie, business, math and psych
Number of students in business majors is 100
Number of students in math majors is 60
Number of students in psych majors is 40
Total number of students (100+60+40) = 200 students
Three different students are chosen to be interviewed for a focus group.
Therefore, number of student in focus group = 3
Now, number of ways are there to choose this focus group where all three students do not all come from the same major
= [tex]^{100}C_{1} \times ^{60}C_{1}\times^{40}C_{1}[/tex]
= 100×60×40
= 240,000 ways
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ouise used this figure to model the expression 20 divided by 4.
A number line going from 0 to 20. An arrow goes from 4 to 8, from 8 to 12, from 12 to 16, and from 16 to 20.
What error did Louise make in her model?
The small arrows are pointed in the wrong direction.
The small arrows should all end in the same place as the large one.
The arrows should start at zero.
There should be one large arrow and 20 small arrows.
The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.
What is error model?
Error modelling is used to describe the variability in how well a parameter describes the data.
The error that Louise made in her model is that "the small arrows should all end in the same place as the large one.
" The model as described shows four small arrows going from 4 to 8, 8 to 12, 12 to 16, and 16 to 20, respectively, and one large arrow going from 0 to 20. Since the expression is 20 divided by 4, the model should show four equal parts from 0 to 20, and each part should have a length of 5.
The arrows should start at the beginning of each part and end at the end of each part, resulting in four equal segments.
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weinstein, mcdermott, and roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies. one part of the study asked students to prepare for a test by reading a passage. in one condition, students generated and answered questions after reading the passage. in a second condition, students simply read the passage a second time. all students were then given a test on the passage material and the researchers recorded the number of correct answers. a. identify the dependent variable for this study. b. is the dependent variable discrete or continuous?
a. The dependent variable for this study is the number of correct answers on the test given.
b. The dependent variable in this study is a discrete variable.
a. The dependent variable for this study is the number of correct answers on the test given to the students after they prepared for the test by either generating and answering questions or reading the passage a second time.
b. The dependent variable in this study is a discrete variable because the number of correct answers can only take on whole numbers (e.g., 0, 1, 2, 3, etc.). It is not possible to have fractional or continuous values of correct answers on the test.
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This morning, Brendan tock a history test. There were 20 multiple-choice problems on the
test and Brendan answered 85% of them correctly. How many problems did Brendan get
right?
1. Which of the following are methods for solving systems of equations (select all that apply)
a) graphing
b) substitution
c) Using a Protractor
d) elimination
Answer:
1- graphing
2- substitution
3- elimination.
Each month, Tomas buys 4 boxes of crunchy granola bars and 2 boxes of chewy granola bars for his family. Crunchy granola bars come in boxes containing x bars, and chewy granola bars come in boxes containing y bars. Write two equivalent expressions for the total number of granola bars Tomas buys after 5 months. (5(__x+__y) and __x+__y)
The two equivalent expressions for the total number of granola bars Tomas buys after 5 months is 5(4x + 2y) and 20x + 10y
In mathematics, an expression is a combination of symbols (such as numbers, variables, and operators) that represent a mathematical object or value.
Tomas buys 4 boxes of crunchy granola bars and 2 boxes of chewy granola bars each month. Let's assume that each box of crunchy granola bars contains x bars and each box of chewy granola bars contains y bars.
To express the total number of granola bars that Tomas buys in one month, we can use the following expression:
4x + 2y
This expression shows that Tomas buys 4 boxes of crunchy granola bars, each containing x bars, and 2 boxes of chewy granola bars, each containing y bars.
To find the total number of granola bars that Tomas buys after 5 months, we need to multiply the expression by 5, since he buys granola bars each month for 5 months. This gives us the expression:
5(4x + 2y) = 20x + 10y
Alternatively, we can also express the total number of granola bars that Tomas buys in 5 months using the following expression:
5x(4) + 5y(2) = 20x + 10y
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