Given:
Total shelves: 6
Books per shelve: 72
Total books = ?
Solution:
Total books: 6 * 72 = 432
Total books = 432
Part 2:Given:
Fiction books = 1/3 of total books
Solution:
Nonfiction books = Total books - 1/3 of total books
= 432 - 1/3 * 432
= 432 - 166 = 266
Non- fiction books = 266
If the water level at the lake continued to change at the same rate for 3 months in a row, explain how you could estimate the total change in water level at the end of the 3 month period.
The fraction is 7/8 is really close to 1, so you could estimate that the water level
changes by approximately -5 inches per month. The total change in the water
level at the end of the 3 month period would be approximately -15 inches.
Answer:
If the water level at the lake is decreased by the rate r each month, then the total change in water level at the end of the 3 month period is -3r.
Step-by-step explanation:
It is given that the water level at the lake continued to change at the same rate for 3 months in a row.
Let the water level at the lake is decreased by the rate r each month.
Change in the water level for 1 month period = -r units
Change in the water level for 2 month period = -2r units
Change in the water level for 3 month period = -3r units
So, we conclude that if the water level at the lake is decreased by the rate r each month, then the total change in water level at the end of the 3 month period is -3r.
A student has some $1 and $5 bills in his wallet. He has a total of 19 bills that are worth $55. How many of each type of bill does he have?
To solve the problem, we use a system of linear equations. We find that the student has 14 $1 bills and 5 $5 bills.
Explanation:This problem can be solved using a system of linear equations. Let's define two variables: x represents the number of $1 bills and y represents the number of $5 bills . From the problem, we can set up the following two equations:
x + y = 19 (since the total number of bills is 19) $1x + $5y = $55 (since the total worth of the bills is $55)
Solving these equations simultaneously, we find that x = 14 and y = 5. Thus, the student has 14 $1 bills and 5 $5 bills.
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To model 15 – 11 on a number line, begin at _______ and travel 11 units to the left.
The answer is 15 cause you start at 15 and go from there
15 is the correct answer to the fill-in-the-blanks in this problem.
Simplify step by step 1/3+6(2/3−1/6)2
To solve this problem you must apply the proccedure shown below:
1- Solve the substraction in the parenthesis and square it:
[tex]\frac{1}{3}+6(\frac{1}{2})^2\\\frac{1}{3}+6(\frac{1}{4})[/tex]
2- Apply the distributive property and solve the addition:
[tex]\frac{1}{3}+\frac{6}{4}\=\frac{11}{6}[/tex]
The answer is: [tex]\frac{11}{6}[/tex]
[tex]\frac{1}{3} +6(\frac{2}{3} - \frac{1}{6})^2[/tex]
first we simplify the parenthesis
To simplify the fractions inside the parenthesis , we make the denominators same
[tex]\frac{1}{3} +6(\frac{2*2}{3*2} - \frac{1}{6})^2[/tex]
[tex]\frac{1}{3} +6(\frac{4}{6} - \frac{1}{6})^2[/tex]
[tex]\frac{1}{3} +6(\frac{3}{6})^2[/tex]
Simplify the fraction 3/6
[tex]\frac{1}{3} +6(\frac{1}{2})^2[/tex]
Now we square 1/2
[tex]\frac{1}{3} +6(\frac{1}{4})[/tex]
Multiply 6 inside the parenthesis
[tex]\frac{1}{3} +\frac{6}{4}[/tex]
[tex]\frac{1}{3} +\frac{3}{2}[/tex]
Now make the denominators same to add fractions
[tex]\frac{1*2}{3*2} +\frac{3*3}{2*3}[/tex]
[tex]\frac{2}{6} +\frac{9}{6}[/tex]
[tex]\frac{11}{6}[/tex]
Which numbers are a distance of 3 units from 12 on a number line? A number line ranging from negative 5 to 17. Select each correct answer.
The distance between A and B is d = |B - A|
We have d = 3 and A = 12.
Substitute:
[tex]|B-12|=3\iffB-12=3\ \vee\ B-12=-3\qquad|\text{add 12 to both sides}\\\\B=15\ \vee\ B=9[/tex]
Answer: 9 and 15.Graph y<1−3x .
Please only answer if you know what you're doing
y < 1 - 3x can alse be written as y < -3x + 1 (which crosses the y-axis at 1 and has a slope of -3 (aka rise over run of: down 3 and to the right 1)
The symbol (<) represents a dashed line that is shaded below.
Answer: A
Leah loves chicken a wings and is comparing the deals at three diffrent restaurants. Buffalo bills has 8 wings for $7 .Buffalo milds wings has 12 wings for $10 .Wingers has 20 wings for $17 .Which restaurant offers the lowest price per wing?
For each, divide the amount by the number of wings
7 divided by 8: 0.875 = $0.88 per wing
10 divided by 12: 0.8333 = $0.83 per wing
17 divided by 20: 0.85 = $0.85 per wing
Looking at each result, the middle one (the $10 for 12 wings) is the best deal
Do 0.3 and 3.0 have the same value? I’m not sure they aren’t but i’m checking
2. At Algorithms Pizza they have the exponential pizza, which is a 24-inch cheese pizzoa that costs $17.50. Each topping for the pizza costs $2.35. If Connor ordered the exponential pizza and was charged $29.25, how many toppings were on his pizza? Justify your answer by using an algebraic equation to solve this problem step by step.
Answer:
Connor ordered 5 toppings on his pizza.
Step-by-step explanation:
17.50 + (2.35 * x) = 29.25
Remove the parentheses
17.50 + 2.35x = 29.25
Subtract 17.50 from both sides
2.35x = 29.25 - 17.50
Subtract
2.35x = 11.75
Divide both sides by 2.35
x = 5
Answer:
29.25 - 17.50 = 11.75
11.75 divided by 2.35 = 5
So that he had 5 toppings on his pizza.
Step-by-step explanation:
17.6 make a budget go math page 651 and 652
Doesn’t make sense !
Answer:179383764382340279370974087283506230757326520
Step-by-step explanation:ugly ms.smith order 5000000000 pizza and got fat like druwisfat and explosed and died bye bitsh
Kiley had a piece of bamboo skewer that measured 15 3/5 inches long. She wanted to cut it into toothpicks that were each 3 1/5 inches long. How many toothpicks can she make?
4 is the max number of toothpicks you can make
4* 3 1/5= 12 4/5
5* 3 1/5=16 that's too many
Use the substitution method to solve the system of equations. Choose the correct ordered pair.
2y + 4x = 18
2y – 3x = 4
A. (6, –3)
B. (5, –1)
C. (2, 5)
D. (3, 3)
Answer:
Option C is right answer.
Step-by-step explanation:
Given two equations as
2y + 4x = 18
2y – 3x = 4
We have to use substitution method.
From first equation find the value of y.
2y = 18-4x
Or y = 9-2x
Substitute this in II equation.
2(9-2x)-3x =4
18-4x-3x =4
-7x = 4-18 = -14
Divide by -7
x =2
Since y = 9-2x, substitute x=2 to get y
y = 9-2(2) = 5
Answer is (2,5)
To verify:
Substitute (2,5) in the given two equations to check.
2(5)+4(2) = 18 is right
2(5)-3(2) = 4 is also right.
Hence solution is (2,5)
Answer:
C. (2,5)
Step-by-step explanation:
Frances gets 6 paychecks in 1w weeks how many paychecks does she get in 52 weeks
The question says that Frances gets 6 paychecks in 1 week.
To find the number of paychecks that Frances gets paid in 52 weeks we need to know the number of paychecks she gets each week.
She gets 6 paychecks each week,
So that means,
1 w = 6 paychecks
So, in 52 weeks she will get:
[tex]6 \times 52=312[/tex] paychecks.
Over the duration of 52 weeks, Frances gets 312 paychecks.
If 7/12x-1/3=1/2+3/8 what is the value of x
[tex]\dfrac{7}{12}x-\dfrac{1}{3}=\dfrac{1}{2}+\dfrac{3}{8}\\\\LCM(12,\ 3,\ 2,\ 8)=24\\\\\text{multiply both sides by 24}\\\\24\cdot\dfrac{7}{12}x-12\cdot\dfrac{1}{3}=12\cdot\dfrac{1}{2}+24\cdot\dfrac{3}{8}\\\\2\cdot7x-8=12+3\cdot3\\\\14x-8=12+9\\\\14x-8=21\qquad|\text{add 8 to both sides}\\\\14x=29\qquad|\text{divide both sides by 14}\\\\x=\dfrac{29}{14}[/tex]
To solve the equation, convert all fractions to have the same denominator. Then simplify the equation, and finally divide the obtained number by the coefficient of x to get the value of x.
Explanation:To solve the equation 7/12x-1/3=1/2+3/8, we first need to simplify both sides of the equation by converting all the fractions to have the same denominator, which, in this case, is 24.
So we obtain the equation:(14/24)x-8/24=12/24+9/24. After simplifying this equation, we get: (14/24)x = 29/24. Diving 29/24 by 14/24 will give us the value of x.
This process is very similar to the one used for solving linear equations, you must combine like terms and isolate the variable on one side of the equation to find the solution.
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During a particular year, 77 graduating boys chose to attend a 4-year college, while 34 boys attended a 2-year college; 83 girls chose a 4-year college, and 33 attended a 2-year college. What conclusion can be drawn?
A) If you are a boy in this group, you are more likely to attend a 2-year college than a 4-year college..
B) If you are a girl in this group, you are more likely to attend a 2-year college than a 4-year college..
C) If you are a girl in this group, you are more likely to attend a 4-year college than a 2-year college..
D) Knowing if a person attended a 4-year college will help determine gender.
C) If you are a girl in this group, you are more likely to attend a 4-year college than a 2-year college..
The girls who are likely to attend 2-year college are 39.76% and who are likely to attend a 4-year college are 60.24%. That is option C is correct.
What is the conclusion?It is a process of making an important decision.
Given
During a particular year, 77 graduating boys chose to attend a 4-year college, while 34 boys attended a 2-year college.
83 girls chose a 4-year college, and 33 attended a 2-year college.
How to give a conclusion?The boys who are likely to attend 2-year college are 44.16% and who are likely to attend a 4-year college are 55.84%.
Similarly,
The girls who are likely to attend 2-year college are 39.76% and who are likely to attend a 4-year college are 60.24%.
Then, option C is correct.
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The diagram shows a sphere with center O and a radius of 6 inches that has been cut by a plane. The cross-section formed by the plane is shaded.
Which shape is a possible representation of the cross-section?
The cross-section of a sphere, cut by a plane, is always a circle, and the radius of this circle would be the same as the sphere, which is 6 inches.
Explanation:Given the description of the scenario in the question, the cross-sectional shape of the sphere formed after a plane cuts it is a circle. A spacer is always a circle when cut by a plane, no matter what direction the cut is made. If we think of the sphere as Earth, no matter where you slice it, you’ll get a circle. The diameter of this new circle would be identical to the diameter of the sphere, and hence, it’s got a radius of 6 inches.
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please help me with this .....
Use the elimination method to solve the system of equations. Choose the correct ordered pair. 2x – 5y = 2 3x + 2y = –16
A. (–4, –2)
B. (2, –11)
C. (4, –14)
D. (–9, –4)
Answer:
It is -4,-2
Step-by-step explanation:
Answer:
The solution is (-4, -2)
Step-by-step explanation:
Given two equations
[tex]2x-5y=2[/tex] → (1)
[tex]3x+2y=-16[/tex] → (2)
we have to solve the system of equations by elimination method
Multiply (1) by 3 and (2) by 2 and then subtracting we get
[tex]3(2x-5y)-2(3x+2y)=6-(-32)[/tex]
[tex]6x-15y-6x-4y=38[/tex]
[tex]-19y=38[/tex]
[tex]y=-2[/tex]
⇒ [tex]2x=2+5(-2)=2-10=-8[/tex]
[tex]x=-4[/tex]
Hence, the solution is (-4, -2)
Option A is correct
If a = 5 and b = 7, what is the measure of ∠A? (round to the nearest tenth of a degree)
With assumptions about it being a *right* triangle and a and b being the legs, the answer is:
B) 35.5°
Solve the following multiplication and division problems.
a. 3 km 5 hm × 15 =
b. 19 m 44 cm × 32 =
c. 1,140 m ÷ 12 =
d. 3 km 6 hm 7 dam 5 m ÷ 15 =
Answer:
a. 22.5 km
b. 267.52 m
c. 95 m
d. [tex](4.2)(10^{-5})[/tex] km
Step-by-step explanation:
a. You can convert from hectometers to kilometers, and then you can make the multiplication:
[tex]\frac{5hm}{10}=0.5km[/tex]
[tex](3km)(0.5km)(15)=22.5km[/tex]
b. You can convert from centimeters to meters, and then you can make the multiplication:
[tex]\frac{44cm}{100}=0.44m\\(19m)(0.44m)(32)=267.52m[/tex]
c. You only need to divide 1,140 meters by 12:
[tex]\frac{1,140m}{12})=95m[/tex]
d. You can convert from hectometers to kilometers, from decameters to kilometers and from meters to kilometers, and divide this by 15:
[tex]\frac{6hm}{10}=0.6km[/tex]
[tex]\frac{7dam}{100}=0.07km[/tex]
[tex]\frac{5m}{1000}=0.005km[/tex]
[tex]\frac{(3km)(0.6km)(0.07km)(0.005km)}{15}=(4.2)(10^{-5})[/tex] km
The actual length of Lake Superior is 350 miles and the width is 160 miles. What's the length and width of the lake on a map if the scale is "1 cm = 25 miles"?
A. length: 6.4 cm, width: 14 cm
B. length: 14 cm, width: 6.4 cm
C. length: 7 cm, width: 3.2 cm
D. length: 3.2 cm, width: 7 cm
The correct option is: B. length: 14 cm, width: 6.4 cm
Explanation
The actual length of Lake Superior is 350 miles and the width is 160 miles.
The scale is given as: 1 cm = 25 miles
Suppose, the length and width of the lake on the map are [tex]x[/tex] cm and [tex]y[/tex] cm respectively.
First, the equation according to the ratio of scaled length to the actual length will be....
[tex]\frac{x}{350}=\frac{1}{25}\\ \\ 25x=350\\ \\ x=\frac{350}{25}=14[/tex]
Now, the equation according to the ratio of scaled width to the actual width will be....
[tex]\frac{y}{160}=\frac{1}{25}\\ \\ 25y=160\\ \\ y=\frac{160}{25}=6.4[/tex]
Thus, the length and width of the lake on the map will be 14 cm and 6.4 cm respectively.
Willie changes the quadratic function f(x)=x2?6x+14 to vertex form f(x)=a(x?h)2+k. If Willie does this correctly, what is the value of k?
Answer:
The value of k is 5.
Step-by-step explanation:
Since we know we can convert function's quadratic form to vertex form by completing the square.
f(x)=x2?6x+14
We will add and subtract 9 to our equation in order to complete the square.
[tex]1(x^{2} ?6x+9)-9+14[/tex]
Upon completing the square and combining like terms we will get,
[tex]1(x?3)^{2} +5[/tex]
Upon comparing Willie's vertex form with our expression we can see that k is 5.
Therefore, the value of k is 5.
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A bicycle wheel with radius 26" rotates through an arc that measures 80°. What is the length of the arc of the tire that touched the ground?
2.88pi inches
5.78pi inches
11.56pi inches
hang on just a seci think i got it
Answer:
Option C is the correct answer.
Step-by-step explanation:
We have arc length = Radius x Angle in radian
Radius = 26 inches
[tex]\texttt{Angle rotated }= 80^0=80\times \frac{\pi}{180}=\frac{4\pi}{9}[/tex]
Arc length = [tex]l=\frac{4\pi}{9}\times 26=11.56\pi[/tex]
Length of the arc of the tire that touched the ground = 11.56π
Option C is the correct answer.
Graph 24x+25=−6y+7 .
Use the line tool and select two points on the line.
I just need someone to explain where they would go on a graph
To graph 24x + 25 = -6y + 7, first rearrange it to the form y = mx + b. In our case, y = -4x -3. Plot the y-intercept (0, -3) first, then use the slope (-4) to find a second point (1, -7). Connect these points to form the graph.
Explanation:To graph the equation 24x + 25 = -6y + 7, the first step is to rewrite the equation in slope-intercept form, or y = mx + b, where m is the slope of the line and b is the y-intercept (where the line crosses the y-axis).
Add 6y to both sides of the equation 24x + 25 = -6y + 7 to get 6y = 24x + 25 - 7. Then, rearrange the equations and divide all terms by 6 to get y = -4x - 3.
Now, we can identify the slope and y-intercept. The slope (m) is -4 and the y-intercept (b) is -3. Using these, we can plot two points on a graph. The first point is the y-intercept which is at (0, -3), the point where the line crosses the y-axis.
The slope of -4 means for every step to the right on the x-axis, we go down 4 steps. Therefore, our second point would be at (1, -7). Connect these two points with a straight line, and you have graphed the equation.
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Simplify each expression using the order of operations. Then, match the expression (term) on the left with its solution (definition) on the right.
Match Term Definition
42 + 3 − 2(3) A) 18
22 ⋅ 8 ÷ 2 + 2 B) 44
(42 + 16) + 12 C) 75
8 ⋅ 32 + 3 D) 13
Using the order of operations, none of the provided expressions match with the given definitions (18, 44, 75, 13). It seems there's a mistake in the definitions.
Explanation:This question requires you to use the order of operations, sometimes remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
For 42 + 3 − 2(3), first perform the multiplication: 2*3 = 6. Then add and subtract from left to right: 42+3-6 = 39. So it matches with none of the options given.For 22 ⋅ 8 ÷ 2 + 2, perform the multiplication and division from left to right: 22*8 ÷ 2 + 2 = 88+2 = 90. So it matches with none of the options given.For (42 + 16) + 12, handle the operations in the parentheses first: (42 +16) = 58. Then add 12: 58+12 = 70. So it matches with none of the options given.For 8 ⋅ 32 + 3, perform the multiplication first: 8*32 = 256. Then add 3: 256+3 = 259. So it matches with none of the options given.It appears there may be a mistake in the definitions, as none of the terms match with their respective definitions.
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You ask 150 people about their pets. The results show that 925 of the people own a dog. Of the people who own a dog, 16 of them also own a cat. A. What fraction of the people own a dog and a cat? Of the people own a dog and a cat. B. How many people own a dog but not a cat? People own a dog but not a cat.
Let us assume the total number of people surveyed be = 1500
People who own a dog = 925
People who also own a cat along with dog = 16
So, people who own only dog = 925-16 = 909
A.
The fraction of people who own both a dog and a cat are = [tex]\frac{925}{1500}[/tex]
= [tex]\frac{37}{60}[/tex]
B.
Number of people who own a dog and not a cat are = 909
In fraction it will be [tex]\frac{909}{1500}=\frac{303}{500}[/tex]
Which ordered pair comes from the table?
x y
3 4
4 4
5 2
6 5
A. (4, 3)
B. (5, 6)
C. (6, 5)
D. (2, 5)
Answer:
Option C is correct
(6, 5) ordered pair comes from the table
Step-by-step explanation:
For this, we must indicate which of the ordered pairs shown belongs to the given table.
x y
3 4
4 4
5 2
6 5
The ordered pair is in the form of (x, y).
Option A:
(x, y) = (4, 3)
This pair is not found in the given table.
Option B:
(x, y) = (5, 6)
This pair is not found in the given table.
Option C
(x, y) = (6, 5)
This pair is found in the last row of the given table.
Option D:
(x, y) = (2, 5)
This pair is not found in the given table.
Therefore, (6, 5) ordered pair comes from the table
Which set of ordered pairs in the form of (x, y) does not represent a function of x?
A. {(1, 1.5), (2, 1.5), (3, 1.5), (4, 1.5)}
B. {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}
C. {(1, 1.5), (–1, 1.5), (2, 2.5), (–2, 2.5)}
D. {(1, 1.5), (–1, –1.5), (2, 2.5), (–2, 2.5)}
Answer:
Option B
Step-by-step explanation:
For answering this question we must understand what is a function.
A function is different from mapping.
Mapping is just a subset of AxB where A and B are two sets.
But function is constrained to the point that elements of I set will have unique image in second set.
We find From the options
But in option B,, we find that 1 has two images 3.3 and 4.5. i.e. 1 does not have unique image. Hence not a function.
All other options the first element in ordered pair have a unique image.
Hence all other options are functions.
Only option B is not a function.
Kyle swann 450 yards in 5 minutes. What is the average number of yards he swam per minute show the work
[tex]\frac{450 (yards)}{5 (minutes)} = \frac{90 (yards)}{1 (minute)}[/tex] = 90 yards per minute
Graphing Polynomial Functions
Let's assume
'a' , 'b' are zeros
so, we will find total zeros from graph
We can curve touches x-axis
Let's assume it touches at x=b
so, there would be two zeros at x=b
it also crosses origin
so, another zero is at x=0
it crosses x-axis one more time
Let's assume that zeros at x=a
so, we have got four zeros
x=a,0,b,b
now, we can set up function
[tex]f(x)=(x-0)(x-a)(x-b)(x-b)[/tex]
we can also write as
[tex]f(x)=x(x-a)(x-b)^2[/tex].................Answer
What is the LCM of xy2 and xz?
xyz
xy2z
x2y2z
x
xy² = x · y · y
xz = x · z
LCM(xy², xz) = x · y · y · z = xy²z