The cost of shelving Nathaniel’s DVD collection is 15.75×27=$425.25.
We are given that;
Dimensions =7.5in, 5.3in, 0.6in
To find the cost of shelving Nathaniel’s DVD collection, we need to find how many shelves he needs and multiply that by the price of each shelf. To find how many shelves he needs, we need to find how many DVDs can fit on one shelf and divide that by the total number of DVDs.
Since the shelves are 31.5 inches wide and the DVDs are 5.3 inches wide, we can fit 5.331.5≈5.94 DVDs on one shelf. We round this down to 5 DVDs per shelf because we cannot fit a partial DVD on a shelf.
Since Nathaniel has 132 DVDs in his collection, he needs 5132=26.4 shelves. We round this up to 27 shelves because we cannot use a partial shelf.
Therefore, by algebra the answer will be 15.75×27=$425.25.
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With workings, please help
Answer:
Step-by-step explanation:
What is the fraction and mixed number for this decimal 0.5
Answer: 1/2
Step-by-step explanation:
The fraction equivalent of 0.5 is 1/2.
To convert it into a mixed number, we can divide the numerator by the denominator:
1 ÷ 2 = 0 with a remainder of 1
So, the mixed number is 0 1/2.
You are biking to the library. When you are 75% of the way there, you realize you forgot a book. So you turn around and head back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library. How far do you live from the library? please explain step by step process.
According to the information, the distance from your starting point to the library is 4 miles.
How to calculate how far do you live from the library?To calculate how far do you live from the library we have to assume that the distance from the starting point to the library is "x" miles.
According to the problem, when you are 75% of the way there, you realize you forgot a book. It means you have traveled 75% of the distance, which is 0.75x miles.
Now, you turn around and bike back. When you are 1/3 of the way back, you realize you don't need the book, so you turn around again and bike 3.2 miles to the library.
From the starting point, you have traveled 0.75x miles to the point where you forgot the book, and then you traveled back 1/3 of 0.75x miles, which is (1/3)*0.75x = 0.25x miles.
Now you turn around again and bike 3.2 miles to the library. It means that the distance between the point where you realized you don't need the book and the library is 3.2 miles.
Therefore, the total distance from your starting point to the library is:
0.75x + 0.25x + 3.2 = xSimplifying the equation:
1x = 4.0Thus, the distance from your starting point to the library is 4 miles.
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20 Per Question, Algebra 2, Thanks :)
The answer to the expression is (x+3)/(x-1)
What is a quadratic expression?You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0
The given expressions are
(x² - 3x - 18) / (x²- 7x +6
(x²-6x +3x +19) / (x²-x -6x +6)
This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}
⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]
This means that [(x+3)(x-6)] / [(x-6)(x-1)]
Dividing by (x-6) to have
Therefore the value of the expression is (x+3)/(x-1)
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Translate A’B’C by the directed line segment from (0,0) to (-3,-2)
By translation, the image of the vertices of the figure A'B'C' are A''(x, y) = (1, - 3), B''(x, y) = (- 2, - 1) and C''(x, y) = (- 3, - 5), respectively.
How to find the image of the figure by rigid transformations
In this problem we must determine the image of the figure A'B'C', whose vertices are A'(x, y) = (4, - 1), B'(x, y) = (1, 1), C'(x, y) = (0, - 3), by translation, whose definition is shown below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original pointT(x, y) - Translation vector.P'(x, y) - Resulting pointIf we know that T(x, y) = (- 3, - 2), then the image of the vertices of the figure A'B'C' are:
A''(x, y) = (4, - 1) + (- 3, - 2)
A''(x, y) = (1, - 3)
B''(x, y) = (1, 1) + (- 3, - 2)
B''(x, y) = (- 2, - 1)
C''(x, y) = (0, - 3) + (- 3, - 2)
C''(x, y) = (- 3, - 5)
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Jamal and his dad went scuba diving. They went on a 54-foot dive, descending from a motor boat located on the Gulf of Mexico. The boat was located
at sea level.
Where on a number line would you plot a point to represent the boat's location?
The last customer of the day is a loyal customer who brings in a $15.00 off coupon. She purchases two paint brushes, one dozen colored pencils, and one sketch book.
What percent did she save by using her coupon?
~info of the art supplies~
*Paint brush- $10.50
*Colored pencils- $7.88
*Sketch Book- $16.12
The total cost of the art supplies without the coupon is:
2 paint brushes x $10.50 per brush = $21.00
1 dozen colored pencils x $7.88 per dozen = $7.88
1 sketch book x $16.12 per book = $16.12
Total cost without coupon = $21.00 + $7.88 + $16.12 = $45.00
With the $15.00 off coupon, the total cost becomes:
$45.00 - $15.00 = $30.00
The amount saved by using the coupon is:
$45.00 - $30.00 = $15.00
The percentage saved can be calculated as:
Percentage saved = (Amount saved / Total cost without coupon) x 100%
Percentage saved = ($15.00 / $45.00) x 100%
Percentage saved = 33.33%
Therefore, the customer saved 33.33% by using her coupon.
A fair six sided number cube has the following faces 1,1,2,2,5,6 this number cube is rolled 50 times what is the probability that fewer than 30% of the rolls result in a two
The probability that fewer than 30% of the rolls result in a two is given as follows:
0.3085 = 30.85%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].2 out of the six faces are two, and there will be 50 trials, thus the parameters n and p are given as follows:
n = 50, p = 2/6 = 1/3 = 0.3333.
The mean and the standard error are given as follows:
[tex]\mu = p = 0.3333[/tex][tex]s = \sqrt{\frac{0.3333 \times 0.6667}{50}} = 0.0667[/tex]The probability that fewer than 30% of the rolls result in a two is the p-value of Z when X = 0.3, hence:
Z = (0.3 - 0.3333)/0.0667
Z = -0.5
Z = -0.5 has a p-value of 0.3085.
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Circle 1 is centered at (−5, 4) and has a radius of 15 units. Circle 2 is centered at (−5, −3) and has a radius of 9 units. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the boxes. The circles are similar because you can translate Circle 1 using the transformation rule ( , ) and then dilate it using a scale factor of .
The circles are similar because you can translate Circle 1 using the transformation rule (0, -7) and then dilate it using a scale factor of 3/5.
Translation involves moving an object in a straight line without changing its size or shape. In this case, we can translate Circle 1 7 units down to match the y-coordinate of Circle 2. The transformation rule for this translation is (0, -7), since we are not changing the x-coordinate.
Dilation involves uniformly scaling an object, either making it larger or smaller. We can dilate Circle 1 by a scale factor of 3/5 to make it have the same radius as Circle 2. The scale factor is determined by taking the ratio of the radii:
scale factor = radius of Circle 2 / radius of Circle 1
scale factor = 9 / 15
scale factor = 3/5
The center of dilation is the center of Circle 1, since we want to preserve its position.
Therefore, we can transform Circle 1 into Circle 2 by translating it 7 units down and dilating it by a scale factor of 3/5. The transformation rule is:
(0, -7) followed by dilation with a scale factor of 3/5
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Find the endpoint of the directed line segment starting at (8,19) that is divided in a 1:5 ratio by the point (13,14)
Please help Image Attached!
Please answer these I’m so confused
The solution set of the inequality 2.5x ≥ 20 is x ≥ 8 and as such, Sebastian is incorrect based on his graph.
The graph of the solution set of -48 < -8t is shown below.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
Next, we would determine the solution to the given inequality as follows;
2.5x ≥ 20
x ≥ 20/2.5
x ≥ 8 (Sebastian was wrong)
-48 < -8t
-48/-8 < -8t/-8
6 < t
t > 8
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Ten upright dominos of increasing height are lined up to be knocked down. The dominos are numbered 0 to 9. The smallest domino, #0, is 3.00 inches tall and will be toppled by a person to start the chain reaction. Each subsequent domino is 15% taller than the one before. What is the height of domino #9?
Answer:
8.604 in.
Step-by-step explanation:
We can use the formula for compound interest to find the height of domino #9:
A = P(1 + r)^n
where A is the final amount, P is the initial amount, r is the growth rate, and n is the number of compounding periods. In this case, P is the height of domino #0, r is 15% or 0.15, and n is 9 (since we want to find the height of domino #9).
Substituting the given values:
A = 3.00 in * (1 + 0.15)^9
Simplifying:
A = 3.00 in * 2.86797199
A ≈ 8.604 in
Therefore, the height of domino #9 is approximately 8.604 inches.
X-2 = x-1 +2
____________
x-1 =. x+1 + x-1
Evaluating the expression (x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1), we get x = 1
Evaluating the expressionFrom the question, we have the following parameters that can be used in our computation:
(x - 2)/(x - 1) = (x - 1 + 2)/(x + 1)(x - 1)
Evaluating the like terms, we have
(x - 2)/(x - 1) = (x + 1)/(x + 1)(x - 1)
Cancel out the common factors
So, we have
(x - 2) = 1
Add 2 to both sides
x = 3
Hence, the solution is 3
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1/9 times 3 to the 3rd power minus 2(1/6+2/3)
The value of the expression is 28 2/3
How to determine the valueTo determine the value of addition, we need to know that fractions are described as part of a whole number or variables.
From the information given, we have that;
1/9 times 3 to the 3rd power
This is represented as;
(1/9 × 3)³
Divide the values, we get
(3)³
Find the cube
27
Then, we have;
27 + 2(1/6+2/3)
Solve the bracket
27 + 2( 1+ 4 /6)
27 + 2(5/6)
Divide the values
27 + 5/3
81 + 5/3
86/3
Divide the values
28 2/3
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I need help with this please
Answer: C
Step-by-step explanation:
Right angles (or 90 degree angles) are indicated by little squares in the corners of the figures that have them.
A triangle has two 90° angles and a side 12 centimeters in length.
Select True or False for each statement about this type of triangle.
The triangle with 2 angles as 90° is not possible and the statement is false.
Given data ,
Let the triangle be represented as ∠ABC
Now , the measures of the angles of the triangle are
A triangle has two 90° angles and a side 12 centimeters in length
So , ∠ABC = ∠BAC = 90°
And , For a Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
Therefore, a triangle cannot be formed with 2 angles as 90°
Hence, the statement, the third angle is 90° is False
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Mathematics
Direction. Answer the following questions.
- what is the short meaning of percentage, rate, and base?
- How we use percentage, rate and base in our daily lives. give example for each one.
(P=BxR) , (B=P/R) , (R=P/B)
The concepts of percentage, rate, and base can be defined as follows:
Percentage is the representation of a fraction or portion in relation to a whole expressed as a ratio out of 100.Rate refers to the quantitative measurement of something over a specified period, which is often expressed in terms of specific units like miles per hour or dollars per hour. Base denotes the starting point for any calculation or comparison.How to use the concepts in our daily livesIn our daily lives, we utilize these three concepts in many different ways, some examples of which are outlined below:
When we go shopping, we frequently come across discounts or sale prices offered as percentages off the original price. For example, if an item was initially $40 but is now available at a discount of 20%, it will be priced at $32.
Rates enable us to measure speed when we are driving or running with unit-based measurements. In addition, rates allow us to compare prices during grocery shopping, where we might need to know the cost per pound of apples and/or calculate interests on investments or loans.
Bases have utility while dealing with ratios or proportions. For instance, if we wish to prepare food for eight people instead of four, one can take the existing recipe as a base and adjust ingredient quantities proportionally.
The formulas P = B × R, B = P / R, and R = P / B are basic calculations that correspond to different values based on the given percentage, rate, or base. For instance, P = B × R allows us to obtain the value of P given the input of B and R.
Meanwhile, B = P / R enables us to get the value of B by punching in P and R much like calculating interest paid out each month in compound-interest cases.
Finally, R = P / B yields the value of R using inputs for P and B. These formulas find rampant use in fields like finance, economics, and mathematics.
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james baked 5 1/4 dozen peanut butter cookies and 4 5/6 dozen oatmeal cookies for a bake sale what it is the estimate the number of dozen of cookies he baked
The members of a volleyball team were asked what their favorite colors were. The results are shown in the Venn diagram below.
How many players included red and purple as their favorite colors?
A. 0
B. 2
C. 3
D. 4
The number of players who included red and purple as their favorite colors is 0.
option A.
What is the number of people?
The number of people who included red and purple as their favorite colors are calculated as follows;
We are going to determine this number based on the given Venn diagram.
Check the intersection of red and purple, you will notice it is empty, so there is volleyball team member who included red and purple as their favorite colors.
So the answer is zero (0) since the intersection or connection point between red and purple is empty.
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Use the graph to answer the question.
B
3
D
Determine the line of reflection.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 5
Reflection across y = 6
8
C
D'
9
10
E'
11
12
B'
A'
13
The line of reflection of the graph is y = -3
Determining the line of reflection.The given graph is added as an attachment
From the graph, we can see that the shapes are symmetrical about the line y = -3
When shapes are symmetrical about a point or a line, then the point or the line is the point of reflection
This means that the line of reflection is y = -3
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Answer:
The calculated line of reflection of the graph is y = -3
Step-by-step explanation:
If you apply the changes below to the quadratic parent function, F(x) = x²,
what is the equation of the new function?
• Shift 6 units right.
• Shift 4 units down.
A. G(x) = (x-4)² +6
B. G(x) = (x − 4)² – 6
C. G(x) = (x + 6)² − 4
D. G(x) = (x − 6)² – 4
The equation for the translated function is the one in option D:
G(x) = (x - 6)² - 4
What is the equation of the new function?We start with the parent quadratic function:
F(x) = x²
We apply two translations, one of 6 units to the right which can be written as:
G(x) = F(x - 6)
And a translation of 4 units down, which is written as:
G(x) = F(x - 6) - 4
Replacing F(x) we will get:
G(x) = (x - 6)² - 4
The correct option is D.
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The table represents a quadratic function f(x).
x f(x)
−4 7
−3 6
−2 7
−1 10
0 15
1 22
2 31
If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?
A) 3
B) 6
C) 16
D) 22
Answer:
B) 6
Step-by-step explanation:
Calculate the value of c by substituting point (0, 15) into the quadratic equation formula:
[tex]f(x)=ax^2+bx+c[/tex]
[tex]\begin{aligned}f(0)=a(0)^2+b(0)+c&=15\\0+0+c&=15\\c&=15\end{aligned}[/tex]
Therefore:
[tex]f(x)=ax^2+bx+15[/tex]
Substitute the point (1, 22) into the formula and create an equation for a in terms of b:
[tex]\begin{aligned}f(1)=a(1)^2+b(1)+15&=22\\a+b+15&=22\\a+b&=7\\a&=7-b\end{aligned}[/tex]
Therefore:
[tex]f(x)=(7-b)x^2+bx+15[/tex]
Finally, substitute another point from the table (-3, 6) and solve for b:
[tex]\begin{aligned}f(-3)=(7-b)(-3)^2+b(-3)+15&=6\\(7-b)9-3b+15&=6\\63-9b-3b+15&=6\\78-12b&=6\\-12b&=-72\\b&=6\end{aligned}[/tex]
Therefore, the value of b is 6.
Answer:
6
Step-by-step explanation:
The table shows the distribution, by age and gender, of the million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 2534 age range.
The probability which is selected randomly from a lot of people living alone in the area in the 25-34 age range is 0.1487
The total digit of individuals living independently in the area = 31.6
The digit of individuals living in the area who fall within the 25 - 34 age range = 4.7
The probability formula will be applied ed as
P = required outcome / Total possible outcomes
From the information that is provided above the given data is:
P(range 25 - 34) = 4.7 / 31.6
= 0.1487
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The question is incomplete, Complete question probably will be is:
The table shows the distribution, by age and gender, of the 31.6 million people who live alone in a certain region. Use the data in the table to find the probability that a randomly selected person living alone in the region is in the 25-34 age range.
The probability is ___.
(Type an integer or decimal rounded to the nearest hundredth as needed.)
Find an equation of the line passing through the given points. Use function notation to write the equation.
(−2,−3) and (−4,−4)
Answer:
Step-by-step explanation:
Let A(-2,-3), B(-4,-4).
Line f(x) = y = ax + b (C)
The line passes through these points so when substituting their coordinates into (C), we get:
-3 = -2a + b
-4 = -4a + b
Solving this set of equations gives us a = 1/2; b = -2.
So the equation of this line is [tex]f(x)=\frac{1}{2}x-2[/tex]
A rectangular brochure is designed so that it has an area of 30 square inches and a perimeter of 23 inches. Find the width and height of the brochure. Assume the height is greater than the width.
The width of the brochure is 3/2 inches and the height is 10 inches.
Let's assume that the width of the brochure is x and the height is y.
The area of the brochure is given as 30 square inches:
xy = 30
The perimeter of the brochure is given as 23 inches:
2x + 2y = 23
We can use the second equation to solve for one variable in terms of the other.
2x + 2y = 23
2x = 23 - 2y
x = (23 - 2y)/2
Now we can substitute this expression for x into the equation for the area:
xy = 30
[(23 - 2y)/2]y = 30
23y/2 - y^2 = 60/2
y^2 - 23y/2 + 30 = 0
We can solve for y using the quadratic formula:
y = [23/2 ± sqrt((23/2)^2 - 4(1)(30))]/(2)
y = [23/2 ± sqrt(529/4 - 120)]/2
y = [23/2 ± sqrt(289/4)]/2
y = [23/2 ± 17/2]/2
y = 10 or y = 3/2
Since the height must be greater than the width, we can eliminate y = 3/2 as a solution.
So, y = 10 and
x = (23 - 2y)/2 = (23 - 20)/2 = 3/2
Therefore, the width of the brochure is 3/2 inches and the height is 10 inches.
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Tarea de rendimiento
12
La señora Ericson preparó sándwiches para sus 4 hijos. Todos los sándwiches tenían
el mismo tamaño. Después del almuerzo, a cada niño le quedaba una fracción
diferente de su sándwich. Matt tenía, Elisa tenía
7
3, Carl tenía 2, y Riley tenía 8
8
4
A Usa esta información para escribir un problema en que se comparen dos fracciones
con el mismo numerador.
The word problem is given thus: Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?
How to solveFour sandwiches were prepared by Mrs. Ericson, each identical in size, for her offspring: Matt, Elisa, Carl, and Riley.
The children consumed varying portions of their respective sandwiches during the shared midday meal.
Post-lunch investigations denoted different fractions residual from each child's original sandwich quantity.
Matt kept 7/8 of his portion while Elisa held on to 3/4 of hers. Meanwhile, two halves (2/4) constitute what remained of Carl's sandwich with Riley retaining 4/8 for himself.
Given this gridlock, which child between Matt and Riley still had more proportionate remaining sandwich contents provided they both possess a shared 4/8 numerator?
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The question in English is:
Mrs. Ericson made sandwiches for her 4 children. All the sandwiches had
The same size. After lunch, each child had a fraction left.
different from your sandwich. Matt had, Elisa had
7
3, Carl was 2, and Riley was 8
8
4
Use this information to write a problem comparing two fractions
with the same numerator.
A 105 kg halfback runs north and is tackled by a 156 kg opponent running south at 6 m/s. The collision is perfectly inelastic. Just after the tackle, both players move at a velocity of 3 m/s north. Calculate the velocity (m/s) of the 105 kg player just before the tackle. Answer to one decimal place.
We can solve this problem using the conservation of momentum and the law of conservation of energy. Here's how:
Let v be the velocity of the 105 kg player just before the tackle. Then the velocity of the 156 kg player just before the tackle is -6 m/s, since he is running south. After the tackle, the two players move at a velocity of 3 m/s north, so we have:
Total momentum before = Total momentum after
(105 kg)(v) + (156 kg)(-6 m/s) = (105 kg + 156 kg)(3 m/s)
Simplifying and solving for v, we get:
v = (105 kg + 156 kg)(3 m/s) + (156 kg)(6 m/s) / 105 kg
v = 2.85 m/s
Therefore, the velocity of the 105 kg player just before the tackle was 2.85 m/s north.
Solve for c ;;; upside down triangle 156.5° / 117.5°
Check the picture below.
I’m confused. Can somebody help me?
Answer:
The Correct answer is D and F
Rewrite this non-statistical
question as a statistical
question.
How many brothers do you
have?
Answer:
0
Step-by-step explanation: