Answer:
5 single rolls or 3 double rolls.
Step-by-step explanation:
Ignoring doors and windows, we need to find the lateral surface ares. We are not papering the ceiling or floor.
The lateral surface areas = P*h
= 2(l+w) * h
= 2(10+12) * 8
= 2(22)*8
=352 ft^2
A single roll covers 72 ft^2 so we divide the number of ft^2 that we need (352^2) by the amount of a single roll
352/72 =4.88888(repeating)
Rounding up since we need to buy in full rolls.
We will need 5 rolls
Assuming a double roll will cover twice that of a single roll
2*72 = 144 ft^2
Take 572/144 =2.4444444
Rounding up since we need to buy in full rolls.
We will need to buy 3 double rolls
Adia will need 5 single rolls or 3 double rolls of wallpaper to cover her 10' by 12' bedroom with 8' ceilings.
Adia needs to calculate the amount of wallpaper needed to cover the walls of her bedroom. To find the total wall area, we calculate the perimeter of the room and multiply it by the ceiling height. The perimeter is two times the length (12 feet) plus two times the width (10 feet), giving us 44 feet. Multiplying the perimeter by the ceiling height (8 feet) gives us the total wall area: 44 feet × 8 feet = 352 square feet.
Since each single roll covers 72 square feet, dividing the total wall area by the coverage of one roll gives us the number of rolls needed: 352 square feet / 72 square feet/roll = 4.89, which means Adia will need 5 single rolls of wallpaper.
For double rolls, we need to consider that each double roll is equivalent to two single rolls.
Therefore, we divide the number of single rolls needed by 2 to get the number of double rolls: 5 single rolls / 2 = 2.5, which means Adia will need 3 double rolls (since she can't purchase half a roll, she'll have to round up).
brenda deposits $500 in a saving account that pays a simple interest rate of 2.5% per year. How much interest will Brenda earn after 18 months?
Brenda will earn $18.75 in interest after 18 months.
Explanation:To calculate the interest Brenda will earn after 18 months, we can use the simple interest formula:
Principal x Rate x Time = Interest
According to the question, Brenda deposited $500 in a savings account with a simple interest rate of 2.5% per year. Since the time period given is 18 months, we need to convert it to years. 18 months is equivalent to 1.5 years.
Therefore, the interest Brenda will earn after 18 months can be calculated as:
$500 x 0.025 x 1.5 = $18.75
Brenda will earn $18.75 in interest.
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Uncle Drew scored 2828 points in 5 5/6 ? minutes during a game of basketball. How many points did he average per minute during that 5\dfrac565 6 5 ? minutes?
Answer:
4.8 points per minute
Step-by-step explanation:
Uncle Drew scored 28 points in [tex]5 \frac{5}{6}[/tex] minutes. We have to convert the mixed fraction first:
[tex]t = 5 \frac{5}{6}=\frac{5\cdot 6+5}{6}=\frac{35}{6}[/tex]
So, the time is 35/6 minutes.
In order to find the number of points he scored in a minute, we have to divide the total number of points by the number of minutes, so:
[tex]mean = \frac{28}{35/6}=28 \cdot \frac{6}{35}=4.8[/tex]
So, he scored 4.8 points per minute.
Answer:
4.8
Step-by-step explanation:
Candy buys 20 ounces of mixed nuts. She puts an equal amount of ounces in each of 3 bags. How many ounces of mixed nuts will be in each bag? Write the answer as a whole number and a fraction.
Answer:
[tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.
Step-by-step explanation:
unit rate is defined as the rates are expressed as a quantity of 1, such as 3 feet per second or 6 miles per hour, they are called unit rates.
Given the statement: Candy buys 20 ounces of mixed nuts. She puts an equal amount of ounces in each of 3 bags.
Total number of mixed nuts Candy buys = 20 ounces.
As she puts an equal amount of ounces in each of the 3 bags.
Unit rate per bag = [tex]\frac{20}{3} = 6\frac{2}{3}[/tex] ounces.
therefore, [tex]6\frac{2}{3}[/tex] ounces of mixed nuts will be in each bag.
Michelle is hiking on a weekend camping trip. She has walked 6 miles so far. This is 30% of the total distance What is the total number of miles she will walk
This problem is solved by using the concept of percentage as a part of a whole. We find out that 30% of the total distance equals 6 miles. So by setting up the proportion 30/100 = 6/x, we calculate the total distance is 20 miles.
Explanation:This question is an application of percentage problems in real-life situations, specifically hiking distance. When you use a percentage to describe a part of a whole thing, the thing is always considered to be '100%'. In this case, Michelle's hiking trip is the 'whole thing' or '100%'.
We are told that 6 miles is 30% of the total distance. To find the total distance, we can set up a proportion to solve for it. The proportion would be 30/100 = 6/x.
Let x represent the total distance. So we can write the proportion as:
6 / x = 30 / 100
To solve for x, we can cross multiply and then divide:
100 * 6 = 30 * x
600 = 30x
x = 20
Therefore, the total number of miles Michelle will walk is 20 miles.. So, the total distance that Michelle will walk is 20 miles.
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What is the interquartile range of this data set 2,5,9,11,18,30,42,48,71,73,81
First, find the median: 30
Then, find the median of the 2 sides from 30 (Q1 and Q3)
The middle value between 2 and 18 is 9. The middle value between 42 and 81 is 71. Now, just subtract 71-9.
The IQR is 62 :)
Final answer:
The interquartile range, or IQR, is the range of the middle 50 percent of the data values, found by subtracting the first quartile from the third quartile. For the given data set, the IQR is determined to be 61.
Explanation:
The interquartile range, represented as IQR, is found by subtracting the first quartile (Q1) from the third quartile (Q3). To find the interquartile range for the data set 2, 5, 9, 11, 18, 30, 42, 48, 71, 73, 81:
Sort the data in ascending order: 2, 5, 9, 11, 18, 30, 42, 48, 71, 73, 81
Calculate Q1 and Q3: Q1 = 10, Q3 = 71
Find IQR: IQR = Q3 - Q1 = 71 - 10 = 61
Which calculation should be used to calculate s9 for the arithmetic sequence an=3n-1
Answer: Choice A
S9 = (9/2)*(2+26)
===============================================
The formula is
Sn = (n/2)*(a1+an)
where
Sn = sum of the first n terms (nth partial sum)
n = number of terms
a1 = first term
an = nth term
In this case,
n = 9
a1 = 2 (plug in n = 1 into the formula an = 3n-1 and simplify)
an = a9 = 26 (plug n = 9 into the formula an = 3n-1 and simplify)
So,
Sn = (n/2)*(a1+an)
S9 = (9/2)*(2+26)
will help us find the sum of the first 9 terms of this arithmetic sequence
Answer:
A. S9 = (9/2)*(2+26)
HELP BECAUSE IM STUPID!
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
an=15+2.5n
an=15.5+2.5n
an=15−2.5n
an=15.5−2.5n
The explicit rule for the decreasing arithmetic sequence 13, 10.5, 8, 5.5, 3, 0.5, ... is 'aₙ = 15.5 - 2.5n'. This rule reflects the initial term and the common difference between terms.
The sequence provided is 13, 10.5, 8, 5.5, 3, 0.5, and we are finding the explicit rule for this sequence. To find the explicit rule, we will look at the differences between the terms. The differences are consistently -2.5, thus the sequence decreases by 2.5 each time. Assume the first term corresponds to n=1, the next step is to find the initial value at n=1.
Starting with the first term, when n=1, the value is 13. Keeping in mind the sequence decreases by 2.5 with each step, if we reverse one step back (which would be 0 steps), we would be at the initial value, which is 13 + 2.5 = 15.5. Therefore, the explicit rule can be written in the form aₙ = initial value - difference times (n-1), which simplifies to aₙ = 15.5 - 2.5n.
So, given the options provided, the explicit rule for the given sequence is aₙ = 15.5 - 2.5n.
Write the equation of the line that passes through the point (2, 6) and is perpendicular to the line x = 4
Answer:
The perpendicular line would be y = 6
Step-by-step explanation:
In order to get this, we must first recognize that the equation given is a vertical line. If our new line is to be perpendicular to it, it must be a horizontal line. All horizontal lines are written as y = (a number). Since we have a point it goes through, we can get that value in the ordered pair. The ordered pair has a y value of 6, which means the equation would be y = 6
Shawn drew a rectangle that had a width of 4.2 inches and a length of 8.1 inches. Find the perimeter of Shawn's rectangle
Answer: 24.6 inches
Step-by-step explanation: Since it's a rectangle, and not a rectangular prism, that means it's 2D. Length is the long sides on the top and bottom, and width is the shorter sides on it's left and right. So since there's two of each, just do 8.1 + 8.1 + 4.2 + 4.2 and you have your answer!
A line has slope 5/6 and y-intercept −3.
Which answer is the equation of the line?
A.y=5/6x−3
B.y=3x+5/6
C.y=−3x+5/6
D.y=5/6x+3
Answer: A. y=5/6x-3
Step-by-step explanation:
y=mx+b
m=slope
b=y-intercept
I'm almost 100% sure this is right.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have
[tex]m=\dfrac{5}{6},\ b=-3[/tex]
Substitute:
[tex]\boxed{y=\dfrac{5}{6}x-3}[/tex]
The area of a rectangle is 180 squared in2. The ratio of the length to the width is 5 : 4Find the length and the width. The length of the rectangle is nothing in.
Answer:
length = 100 squared Width = 80 squared
Step-by-step explanation:
You add the to ratio number ( 4+5 ). You take that number (9) and divide with 180. You receive the answer 20. Then you multiply 20 by 5 to get the length and multiply 20 by 4 to width. Then you just add back the square operation.
Final answer:
The length and width of the rectangle are found by setting up equations using the given ratio and area. By solving the equations, the length is determined to be 15 inches and the width 12 inches.
Explanation:
To find the length and width of the rectangle with an area of 180 square inches and a ratio of length to width of 5:4, we can set up equations using the ratio and area information. Since the area of a rectangle is equal to the length times the width, we can express the length (L) and width (W) in terms of the ratio:
L = 5x
W = 4x
We know that the area (A) is 180 square inches, so:
A = L × W
180 = (5x) × (4x)
180 = 20x₂
Therefore:
x₂ = 180 / 20
x₂ = 9
x = 3
Now we can find L and W by substituting x back into L = 5x and W = 4x:
L = 5 × 3 = 15 inches
W = 4 × 3 = 12 inches
Hence, the length of the rectangle is 15 inches, and the width is 12 inches.
Two poles of equal heights are standing opposite to each other on either side of a road, which is 100 meters wide .From a point between them on the road, the angles of elevation of their tops are 30? and 60? .Find the position of the point and also, the height of the poles. ( use = 1.73)
Answer:
Distance to the pole from the vertex of the 60o angle = 25 mDistance to the second pole from the vertex of the 30o angle = 75 mHeight of the pole = 43.3Step-by-step explanation:
The point is somewhere on the road. From that point, two poles can be seen at different angles of elevation. One is 30 degrees, and another is 60 degrees.
Call the height of the poles y and the point on the road as x meters away from the base of 60 degree angle to the base pole
Tan(60) = y/xTan(30) = y/(100 - x) Isolate y for both equations(100 - x) * tan(30) = x*tan(60)
Using exact values (from the unit circle) tan(30) = sqrt(3)/3tan(60) = sqrt(3)(100 - x) * sqrt(3)/3 = x*sqrt(3) Divide both sides by sqrt(3)(100 - x)/3 = x Multiply both sides by 3 100 - x = 3x Add x to both sides100 = 4x Divide by 4x = 25The distance to the other pole = 100 - 25 = 75
y = x * sqrt(3)y = 25 * 1.73y = 43.3If a standard vodka martini recipe at La-ti-da Lounge calls for 2.5 oz of premium vodka that sells for $35/liter, .5 oz of dry vermouth that sells for $7.99 a liter, and one jumbo gourmet olive for 15 cents, and the martini sells for $15, what is the drink cost percentage?
a. 19.3 percent
b. 14.7 percent
c. 12.5 percent
d. 16.5 percent
Answer: (A) 19.3%
Step-by-step explanation:
[tex]\text{Vodka: }2.5\text{ oz }\times\dfrac{\$35}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$2.59\\\\\text{Vermouth: }0.5\text{ oz }\times\dfrac{\$7.99}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$0.12\\\\\text{Olive: }\$0.15[/tex]
Vodka + Vermouth + Olive = Total Cost
$2.59 + $0.12 + $0.15 = $2.86
[tex]\dfrac{\text{cost to make}}{\text{selling price}} = \dfrac{\$2.86}{\$15} = 0.19 = 19\%[/tex]
Soft drinks cost $1.89 and refills cost $0.25 each. With $3.80 to spend on the soft drink and refills, what is the maximum number of refills that you can get? Refills (Hint: Do not answer with a fraction because you can not get a partial refill. Your answer should be an integer). 2 Game Bonus Solve equations with inequalities word problems
The number of times of the soft drink that refills will be 7.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
Soft drinks cost $1.89 and refills cost $0.25 each.
With $3.80 to spend on the soft drink and refills.
Then the maximum number of refills will be given as
Let x be the number of refills.
1.89 + 0.25x ≤ 3.80
0.25x ≤ 1.91
x ≤ 7.64
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given parallelogram abcd, find the value of y.
a) 64
b) 26
c) 82
d) 180
Answer:
c) 82
Step-by-step explanation:
<ABE and <BEC are supplementary because they form a line.
<ABE + <BEC = 180
116+ x = 180
Subtract 116 from each side.
116-116+x = 180 -116
x = 64
The angles in triangle ECB add to 180 because it is a triangle
<BEC + <ECB + <CBE = 180
x + 34+y = 180
64 + 34+ y = 180
98 + y = 180
Subtract 98 from each side.
98-98+y = 180-98
y = 82
Guillermo bought some reams of paper for $5 each and a $200 printer.He spent a total of $450.Write and solve an equation to find the number reams of paper Guillermo purchased
If f(x) varies directly with x^2, and f(x) = 75 when x = 5, find the value of f(8).
192
256
25
40
Answer:
The correct answer option is 192.
Step-by-step explanation:
We know that f(x) varies directly with [tex]x^{2}[/tex] so we can write it as:
[tex]f(x)[/tex] ∝ [tex]x^{2}[/tex]
Changing it to an equality by the addition of a constant [tex]k[/tex]:
[tex]f(x) = k.x^{2}[/tex]
If f(x) = 75 when x = 5, then we can find the value of k:
[tex]75=k(5)^2[/tex]
[tex]k=\frac{75}{25} =3[/tex]
If k = 3, we can find the value of f(8):
[tex]f(8)=3(8)^2[/tex]
[tex]f(8)=3*64[/tex]
[tex]f(8)=[/tex]192
What is the range of the function graphed below?
Option: B is the correct answer.
The range of the function is:
B. 5 < y < ∞
Step-by-step explanation:Range of a function--
The range of a function is the set of all the values that is attained by the function.
By looking at the graph of the function we see that the function tends to 5 when x→ -∞ and the function tends to infinity when x →∞
Also, the function is a strictly increasing function.
This means that the function takes every real value between 5 and ∞ .
i.e. The range of the function is: (5,∞)
Hence, the answer is:
Option: B
A cell phone company sold 4,000 cell phones in the month of November. In December, the company held its annual sale and sold 22% more cell phones than it did in November. In January, the company experienced its slowest month, managing to sell only 50% of the number of cell phones sold during the month of December. What is the total number of cell phones sold by the company during the three months combined? Select one: A. 10,450 B. 10,900 C. 11,320 D. 11,710
help please, 30 pts
Sean places 28 tomato plants in rows. All rows contain the same number of plants. There are netween 5 and 12 plants in each row. How many plants are in each row?
Answer:
4 rows of 7 plants each
Step-by-step explanation:
To find the number of plants in each row between 5 and 12 requires us to find the factors of the total 28.
28 has factors 1,28 and 2,14 and 4,7. Only 4,7 has a number between 5 and 12. There are 4 rows of 7 plants.
What are the zeros of the function? Y=(x-2)(x-3)(x+3)
Answer:
B 2,3,-3
Step-by-step explanation:
If we use the zero product property, we can set each term =0 to find the roots.
0=(x-2)(x-3)(x+3)
x-2 =0 x-3 =0 x+3=0
x=2 x=3 x=-3
The roots are -3,2,3
What is the value of x?
13.6
68
84
9.09
Answer:
x=13.6
Step-by-step explanation:
These are vertical angles, so they are equal
8x+16 = 3x+84
Subtract 3x from each side
8x-3x+16 = 3x-3x+84
5x+16 = 84
Subtract 16 from each side
5x+16-16 = 84-16
5x = 68
Divide by 5
5x/5 =68/5
x = 13.6
given RST = NPQ R=-7x+9, N=-10x find R and N
Answer:
[tex]m\angle N=m\angle R=30^{\circ}[/tex]
Step-by-step explanation:
We are given that
[tex]\triangle RST=\triangle NPQ[/tex]
[tex]m\angle R=-7x+9,m\angle N=-10x[/tex]
We have to find the measure of angle R and measure of angle N.
When two triangles are equal then their angles are equal
Therefore, [tex]m\angle R=m\angle N[/tex]
[tex]-7x+9=-10x[/tex]
[tex]-7x+10x=-9[/tex]
By subtraction property of equality
[tex]3x=-9[/tex]
By combine like terms
[tex]x=\frac{-9}{3}=-3[/tex]
By division property of equality
Substitute x=-3 then we get
[tex]m\angle R=-7(-3)+9=21+9=30^{\circ}[/tex]
[tex]m\angle N=m\angle R=30^{\circ}[/tex]
Answer:
30
Step-by-step explanation:
Yolanda and her 3 brothers shared a box of 156 toy dinosaurs . About how many dilnosaurs did each kid get
The required number of dinosaurs that each of them gets is 39 dinosaurs.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the number of dinosaurs be x that is distributed among Yolanda and her 3 brothers,
Total persons = 1 + 3 = 4
Total dinosaurs = 156
Each of them gets,
x = 156/4
x = 39 dinosaurs.
Thus, the required number of dinosaurs that each of them gets is 39 dinosaurs.
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Adam drove his car 132 km and used 11 liters of fuel. How many kilometers will he cover with 14 liters of fuel?
Answer:
168 Km
Step-by-step explanation:
divide 132 Km by 11 to find distance travelled with 1 litre and then multiply this by 14 for distance travelled with 14 litres
= [tex]\frac{132}{11}[/tex] × 14 = 168 Km
PLEASE HELP PLEASE PLEASE
Answer: 25.13 (choice B)
================================
The formula we'll use is
s = r*theta
with
s = unknown arc length
r = radius = diameter/2 = 12/2 = 6 feet
theta = 4pi/3 radians <--- this angle must be in radian mode for the formula to work
Plug those values into the formula and simplify
s = r*theta
s = 6*(4pi/3)
s = 24pi/3
s = 8*pi
s = 8*3.1416
s = 25.1328
s = 25.13
which is approximate and rounded to the nearest hundredth.
If you shift the linear parent function, f(x) = x, down 7 units, what is the equation of the new function? A. G(x) = 7x B. G(x) = x + 7 C. G(x) = x – 7 D. G(x) = x
Answer:
The correct answer is C. f(x) = x - 7
Step-by-step explanation:
In order to find this, you simply need to know that vertical shifts can be added on to the end of parent equations as constants. Since this is a downward shift, we use a negative number.
Help!! im stupid and just need these 2 questions HELP!!!!!
WILL GIVE BRAINLIEST
The ordered pairs model an exponential function, where j is the function name and e is the input variable.
{(1, 10), (2, 50), (3, 250), (4, 1250)}
What is the function equation in sequence notation?
Enter your answer in the box.
je=
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
an=15+2.5n
an=15.5+2.5n
an=15−2.5n
an=15.5−2.5n
Answer:
f(n) = 10 * 5^(n-1)
an = 15-2.5n
Step-by-step explanation:
{(1, 10), (2, 50), (3, 250), (4, 1250)}
The formula for a geometric sequence is
an = a1 * r ^(n-1)
where a1 is the first term and r is the rate in which it increase
a1 =10
r = 5, each term goes up by a factor of 5
50/10 = 5
250/50 = 5
etc
f(n) = 10 * 5^(n-1)
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
For an arithmetic sequence the formula is
an = a1 + d(n-1)
where a1 is the first term and d is the common difference
a1= 13 and d = -2.5
10.5 -13 = -2.5
8. - 10 = -2.5
etc
an = 13 - 2.5 ( n-1)
Simplifying
an = 13 -2.5n + 2.5
an = 15-2.5n
Given that line segments are taken to line segments of the same length during rigid transformations, which transformation maps the line segment AB onto itself?
A) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → x-axis reflection
B) rotation counterclockwise of 90° → y-axis reflection → rotation counterclockwise of 270° → y-axis reflection
C) rotation counterclockwise of 90° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
D) rotation counterclockwise of 180° → x-axis reflection → rotation counterclockwise of 270° → y-axis reflection
Answer:
Correct choice is C
Step-by-step explanation:
Points A and B have coordinates (1,-2) and (4,3), respectively.
1. Rotation counterclockwise of 90° about the origin has a rule:
(x,y)→(-y,x).
Then the image of point A is point A'(2,1) and the image of point B is point B'(-3,4).
2. Refection about the x-axis has a rule:
(x,y)→(x,-y).
Then the image of point A' is point A''(2,-1) and the image of point B' is point B''(-3,-4).
3. Rotation counterclockwise of 270° about the origin has a rule:
(x,y)→(y,-x).
Then the image of point A'' is point A'''(-1,-2) and the image of point B'' is point B'''(-4,3).
4. Refection about the y-axis has a rule:
(x,y)→(-x,y).
Then the image of point A''' is point A(1,-2) and the image of point B''' is point B(4,3).
A study found that out of 300 people 60% of them prefer to eat hamburgers rather than hot dogs. Find the 95% confidence interval for the true proportion of people who prefer to eat hamburgers rather than hot dogs in the entire population.
Answer:
(0.5446, 0.6554)
Step-by-step explanation:
As the sample is sufficiently large, the formula is used to estimate the proportion shown in the attached image.
Where:
P: sample proportion = 0.6
n: Sample size = 300
[tex]1-\alpha[/tex]: Confidence level = 0.95
α: Significance = 0.05
[tex]Z_{\alpha / 2} = 1.96[/tex] *
* Obtained from the normal standard table.
When introducing these values in the formula shown in the image we obtain:
[tex]0.6 + 1.96 *\sqrt {\frac{0.6*0.4}{300}}[/tex]
[tex]0.6 - 1.96 *\sqrt{\frac{0.6*0.4}{300}}[/tex]
Finally, the confidence interval is:
(0.5446, 0.6554)