The fraction of the total number of marbles is left in the bag after removing and giving part to her friend is 3/8
Fractionlet
Number of marbles in her bag = xNumber of marbles removed from her bag = 1/2xRemaining marbles = x - 1/2x
= (2x-x) / 2
= x/2
= 1/2x
Number of marbles given to her friend = 1/4 of 1/2x
= 1/4 × 1/2x
= 1/8x
Number of marbles left in the bag = Remaining marbles - Number of marbles given to her friend
= 1/2x - 1/8x
= (4x-x) / 8
= 3x/8
= 3/8x
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How many gallons of a 60% antifreeze solution must be mixed with 70 gallons of 15% antifreeze to get a mixture that is 50% antifreeze?
There are 245 gallons of antifreeze solution required.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Here, Let 60% antifreeze solution volume = x
15% antifreeze solution volume = 15%
Final concentration 50%
Process
0.6x + 0.15(70) = 0.5(70 + x)
Simplification
0.6x + 10.5 = 35 + 0.5x
0.6x - 0.5x = 35 - 10.5
0.1x = 24.5
x = 24.5/0.1
x = 245 gallons
Thus, There are 245 gallons of antifreeze solution required.
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Pls help me with my math
Answer:
d.
Step-by-step explanation:
Left line is defined when x < 1 (x is less than 1). The point is not full and that means that x = 1 is not included.
Right line is defined when x is greater or equal to one x ≥ 1.
Options that have x < 1 and x ≥ 1 are b and d, so the answer is one of those.
Equations of the lines are in slope-intercept form y = mx + b, where m is slope and b is y-intercept.
Right line has steeper slope than left line, so the slope of right line will have bigger absolute value. That is the case with option d. (Left line has slope -1 and right one has slope -2, absolute value of right slope is bigger.)
You could also check with y-intercepts. Left line has y-intercept at y = 2 and left line is defined when x < 1. Only option d meets these conditions.
find value o x 235 degree arc
The length of the arc given in the question is; 4.1r
How to find the length of an arc?We are given;
Angle at which arc is subtended; θ = 235°
Formula for arc length subtended at an angle θ is;
Arc Length = (θ/360) * 2πr
where r is radius of circle.
Thus;
Arc Length = (235/360) * 2πr
Arc Length = 4.1r
The complete question is;
Find the value of the length of an arc that subtends an angle of 235 degrees to the circle's center.
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Help me with this question please and thank you!!! :):)
Answer:
A intersection B = ( elements which are common in both)
= ( 2,4,7,19)
A union B = ( all the elements which are either in A or in B).
= ( 2, 4, 7 , 13, 14, 19, 20 , 3, 5, 6, 10,11, 12 , 15,17 , 18 , 19 )
What is the area of triangle ABD?
a 4.5 cm 2
b 3.5 cm 2
c 7 cm 2
d 6 cm 2
Answer: [tex]4.5 \text{ cm}^{2}[/tex]
Step-by-step explanation:
[tex]A=\frac{1}{2} bh\\\\A=\frac{1}{2}(3)(3)\\\\\boxed{A=4.5 \text{ cm}^{2}}[/tex]
The area of the triangle will be equal to 4.5 square centimeters.
What is an area?The space occupied by any two-dimensional figure in a plane is called the area. The space covered by the triangle in the two-dimension is called an area of the triangle.
The area of the triangle ABD will be calculated as:-
Area = [tex]\dfrac{1}{2}[/tex] x Base x height
Area = [tex]\dfrac{1}{2}[/tex] x 3 x 3
Area = 4.5 cm.
Therefore the area of the triangle will be equal to 4.5 square centimeters.
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The Rainbow Motor Motel is a 50-room facility with a restaurant to accommodate its guests. The motel is open 365 days a year, even on leap years; as Lurena Boucha, the proprietor, closes down the facility every February 29, her birthday, for an all day celebration of four years of successful operations. On the average, 98% of the rooms are available for sale. For the year just ended, the actual number of rooms sold totaled 15,000 and the number of guests for the year totaled 20,000. The projected occupancy rate for the next year is 82% of the available rooms based on past experience. The food information is as follows:
Sales $150,000, Beg Inventory 8,000, Purchases $70,000, Ending Inventory, $ 13,000 Consumption by employees (free of charge) $3,000, Number of checks 64,139. Cost of sales ?
From the information given, the cost of sales is $65,000. See the explanation below.
What is the definition of cost of sales?Add your initial inventory to the purchases made over the time period, remove that amount from your ending inventory, and that is your cost of sales.
Cost of Sales = (Bi + P) - Ei
Where Bi is Beginning Inventory
P is Purchases; and
Ei is Ending Inventory.
So the derivation of the solution above is?Beginning Inventory = 8,000
(add) Purchase = 70,000
Bi + P = 78,000
Ending Inventory = 13,000
Cost of sales = 78,000 - 13,000
= $65,000
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Determine the value(s) for which the rational expression −5u+12−2u+2 is undefined. If there's more than one value, list them separated by a comma, e.g. u=2,3.
The value(s) for which the rational expression −5u+12−2u+2 is undefined is u = 1.
What is radial expression?The expression or an equation which can be undefined at some point is a celled the radial expression.
f(u) = -5u +12 / -2u +2
For the function to be undefined, denominator must be equal to zero.
-2u +2 =0
-2u =-2
u = 1
Thus, the value for which the given expression is undefined is 1.
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The function f(x) = 2·5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function? 2 5 10 32
The multiplicative rate of change of the function f(x) = 2 × 5ˣ is 5.
What is Exponential Function?An exponential function is a type of function in math that involves exponents. A basic exponential function is of the form f(x) = bˣ, where b > 0 and b ≠ 1.
The function is given as:
f(x) = 2 X 5ˣ
The above function is an exponential function.
An exponential function is represented as:
f(x) = abˣ
Where b represents the multiplicative rate
By comparison;
b = 5
Thus, the multiplicative rate of change of the function is 5.
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Answer:
B!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
The table shows the heights of three different plants.
Answer:
7/4 meters
Step-by-step explanation:
the tallest plant is 19/8
since they have all the same denominaters we can just compare the top numbers
so
the smallestp lant is 5/8
19/8 - 5/8 = 14/8
7/4 is your final answer after simplifying
evaluate-4x + 2y - z if x = - 2, y = 3, and z = -4
Answer:
-4(-2)+2(3)-(-4)
8+6+4
16 is the answers
Step-by-step explanation:
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Evergreen Landscaping bought 4 tons of topsoil and 3 tons of mulch for $1460. The next week the
firm bought 5 tons of topsoil and 2 tons of mulch for $1391. Find the price per ton for each item.
Answer: The price per ton of topsoil is $179
and price per ton of mulch is $248.
Step-by-step explanation:
Let price of 1 ton of topsoil be x
and price 1 ton of mulch be y
According to question
4x + 3y = $1460 -(i)
and 5x + 2y = $1391 -(ii)
Now solving these linear equations
By multiply (i) equation with 5 and divide it by 4
we get 5x + [tex]\frac{15}{4}[/tex]y = $1825 -(iii)
Subtract equation (ii) from equation (iii)
5x +[tex]\frac{15}{4}[/tex] y - 5x - 2y = $1825-$1391
[tex]\frac{7}{4}[/tex]y=$434
y = $434х[tex]\frac{4}{7}[/tex] = $248
put value of y in equation (i)
4x + 3($248) = $1460
4x - $744 =$1460
4x = $716
x = $179
The price per ton of topsoil is $179
the price per ton of mulch is $248.
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y = 4/5 + square root x + 0.2 - 5x
Answer:
5
Step-by-step explanation:
20
Find the standard deviation of
the given data rounded to the
nearest hundredth.
12, 53, 141, 219, 500
Σ (x-mean)2
n
0 =
σ= [?]
The standard deviation of the data to the nearest hundredth is 173.01.
What is standard deviation?Standard deviation is used to determine how the values in a group differs from the mean of the values in the group. It is a measure of variation.
In order to determine the standard deviation, take the following steps:
Determine the mean of the observation: 185
Determine the difference between each value and the mean and then square the result:
Determine the mean of the sum of the squared differences and then find the square root of the mean:
Following these steps, the standard deviation is 173.01
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The high temperature on Friday was 8 degrees above zero. The low temperature was 3 degrees below zero. Which expression gives the average of the low and high temperatures?
Negative (3 + 8) divided by 2
(negative 3 + 8) divided by 2
(negative 3 + 8) divided by (negative 2)
Left-bracket negative 3 + (negative 8) right-bracket divided by (2) Right-bracket
Using the mean concept, the expression that gives the average of the low and high temperatures is:
(-3 + 8)/2.
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem, the two observations are -3 and 8, hence their average is given by:
(-3 + 8)/2.
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A retailer purchases postcards for $0.50 and sells them for $0.70. What is the markup?
0.70 -0.50 = 0.20 cent mark up
0.20/0.50 = 0.40 = 40% markup
Hamish and Harry work as plumbers. harry earns a dollar more than 5/4 the amount Hamish earns per hour. the amount Harry earns per hour is 2$ less than 7/5 the amount Hamish earns per hour. how much to both of them earn per hour?
Answer:
Hamish earns $20 per hour, and Harry earns $26 per hour.
Step-by-step explanation:
Harry earns
$1+(5/4)•x and also (7/5)•x-$2
$1+(5/4)•x = (7/5)•x-$2
$1+$2= (7/5)•x-(5/4)•x
3=(7•4•x-5•5•x)/20
3=3x/20
3•20=3x
X=20, Hamish earns $20
Substitute x in one of the expressions
1+(5/4)•20=1+25=26, Harry earns $26
which number is the
same distance away from -12 as 2?
Answer:
-26
Step-by-step explanation:
2 is 14 away from -12. The other number that is 14 away from -12 is -26.
-12 + x = 2
x = 14
-12 - 14 = -26
The slope of the line below is 0.8. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side. Coordinates (-2,-3)
The equation of the line is y = 0.8x - 1.4 if the slope of the line is 0.8 and line passes through coordinates (-2,-3)
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope m = 0.8
The line passing through coordinates (-2,-3)
y = mx + c
y = 0.8x + c
Plug the point in the equation.
-3 = 0.8(-2) + c
c = -1.4
y = 0.8x - 1.4
Thus, the equation of the line is y = 0.8x - 1.4 if the slope of the line is 0.8 and line passes through coordinates (-2,-3)
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
36 meters
48 meters
80 meters
89 meters
The width of the cooling tower at the base of the structure will be A. 36 meters.
How to calculate the width?From the information given, the towers walls are modeled by x²/324 - (y² - 90)²/1600.
Therefore, the width of the cooling tower at the base of the structure will be:
= 2 × ✓324
= 2 × 18
= 36
In conclusion, the width is 36 meters.
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Answer:
It is actually D
Step-by-step explanation:
Simplify each expression and state whether each is a volume, an area, or neither.
a) n(4)2 x
b) lw+lw+wh+wh+lh+lh
c) 8y2(10y2)
a. 2n^4b, neither a volume nor an area
b. 2Iw + 2wh + 2Ih, It is an area
c. 80 y^4, neither a volume nor an area
How to simply the algebraic expressionsa. n(4) 2 x b
n * n * n* n* 2 * b
2n^4b
It is neither an area nor a volume
b. lw+lw+wh+wh+lh+lh
Collect like terms
2Iw + 2wh + 2Ih
It is an area
c. 8y2(10y2)
8y^2 * 10 * y^2
80 y^4
It is neither a volume nor an area
Thus, the expressions are simplified as a. 2n^4b, b. 2Iw + 2wh + 2Ih, c. 80 y^4
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A geometric seqerence 1.5, -3, 6, -12 .... How many regative terms in the sequencs greater than
- 6000 ?
The total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have:
A geometric sequence 1.5, -3, 6, -12 ....
The common ratio r = -3/1.5 = -2
1.5, -3.6, 6, -12, 36, -108, 324, -972, 2916, -8748
The total negative terms = 4
Thus, the total negative terms are 4 which are greater than -6000 if the geometric sequence 1.5, -3, 6, -12 ... with a common ratio -3.
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For the function f(x)=|x−7|−4, evaluate f(x+1).
Answer:
[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]
Step-by-step explanation:
To evaluate [tex]\displaystyle{f(x+1)}[/tex], substitute [tex]\displaystyle{x}[/tex] to [tex]\displaystyle{x+1}[/tex] so we should have:
[tex]\displaystyle{f(x+1) = |x+1-7|-4}[/tex]
Evaluate the expression and finally, we have:
[tex]\displaystyle{f(x+1)=|x-6|-4}[/tex]
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a model airplane has two engines. it can fly if one engine fails but is in serious trouble if both engines fail. The engines function independently of one another. On any given flight, the probability of a failure is 0.10 for each engine. Design a simulation to estimate the probability that the airplane will be in serious trouble the next time it goes up.
Using the binomial distribution, it is found that there is a 0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.1, n = 2.
The plane is in serious trouble if both engines fail, that is, the probability is P(X = 2), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.1)^{2}.(0.9)^{0} = 0.0001[/tex]
0.0001 = 0.01% probability that the airplane will be in serious trouble the next time it goes up.
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look at the picture
Answer:
The x-intercept is 2.
Step-by-step explanation:
[tex]2 \sqrt[3]{x - 10} + 4 = 0[/tex]
[tex]2 \sqrt[3]{x - 10} = - 4[/tex]
[tex] \sqrt[3]{x - 10 } = - 2[/tex]
[tex]x - 10 = - 8[/tex]
[tex]x = 2[/tex]
Choose the function that includes the given points.
(0,−2),(5,13),(−2,−8),(4,10)
The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
What is the function about?Note that all function of (0,−2),(5,13),(−2,−8),(4,10) can be seen as all the brackets are placed in the form (X, Y), Y=P(x)
In the case above, how we arrived at the answer, you have to fill up the X's in the brackets using the X's in the Options.
Then since P(x) is the number one see in place of Y in the brackets, then that the top Right option is correct as it has −2.
Therefore, The function that includes the given points of (0,−2),(5,13),(−2,−8),(4,10) is the second encircled option by the top right in the image attached.
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Use the Distributive Property to find $(n-6)(n-4)$ .
Answer:
n^2 -10n + 24
Step-by-step explanation:
Given expression:
(n-6)(n-4)
Solution:
Apply distributive property,then simplifying using PEMDAS,we obtain
n^2 - 4n - 6n + 24n^2 -10n +24Hence,n^2 -10n -24 is the answer.
The account balance of each of three children at the end of a month is shown below:
Daniel has −$1.25
Libby has −$2.00
Sandra has as much savings in her account as the amount Daniel owes the bank.
Part A: On a blank paper, draw a number line from −4 to +4. Plot points on the number line to show the account balances of the three children. Label the points using the name of each child. Describe in detail how you created and labeled this number line, and what it looks like in detail. (5 points)
Part B: Determine whether Daniel or Libby owes the bank more. Use absolute values and inequalities to write statements that justify your conclusion. (5 points)
Answer:
Using the concept of number line, we find that Libby owes more than Daniel.
Step-by-step explanation:
Given that the account balance of Daniel is -$1.25 and of Libby is -$2.00. Sandra has as much savings in her account as the amount Daniel owes the bank. So, her account balance is +$1.25.
The numbers to be plotted on the number line are -2.00, -1.25 and 1.25.
The number line is in the attachment.
These numbers are related as: -2 < -1.25 < 1.25.
From the number line, all the names that come left to the origin owe some amount to the bank while all the names that come right to the origin have some money as savings in their account.
Clearly, Daniel and Libby owe the bank.
But since Libby comes before Daniel, Libby owes more than Daniel.
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five percent of a batch of fuel was found faullty if 27 fuses were faulty how many were inspected the price of internet service is decreased by 7% to 52.00 what is the original price
There are 540 fuses in total and the original price of the internet is $55.91
How to work with percentages?
a) We know that 5% of the fuses are faulty, and there are 27 faulty fusses, then we can write:
5% = 27
100% = x
We want to find x, to do that, we can write:
x = 27*(100%/5%) = 27*20 = 540
There are 540 fuses in total.
b) Now we know that the original price is P, and when we decrease it by 7%, then new price is $52.00
Then we can write:
$52.00 = P*(1 - 7%/100%)
$52.00 = P*(0.93)
$52.00/0.93 = P = $55.91
The original price is $55.91
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What is the surface area of prism below?
Answer:
Aprism = 483.246 yd2
Step-by-step explanation:
The surface area is the sum of the 2 circles areas and the rectangle area.
Ac1 = PI*r2
Ac1 = (3.14)*(11.4/2)2
Ac1 = 102.0186 yd2
Ac1 = Ac2 then
Ac2 = 102.0186 yd2
Now the perimeter of the circle is one the sides of the rectangle:
Pc = 2PI*r
Pc = 2*3.14*(11.4/2)
Pc = 35.796 yd
Now the area of the rectangle is:
Ar = 7.8yd*35.796yd
Ar = 279.2088 yd2
Then, the surface area of prism is:
Aprism = Ac1 + Ac2 + ArAprism = 102.0186yd2 + 102.0186yd2 + 279.2088yd2Aprism = 483.246 yd2If a 103 pound man can have 1292 mg of a medicine in a day, how much can a 102 pound woman have? (round answer to one decimal place) She can have mg
Answer:
1279.5mg
Step-by-step explanation:
103 pound man takes -1292mg of medicines
102 pound woman will take -xmg of medicine
cross multiply
102x1292=103x
131784=103x
x=131784/103
x=1279.5mg
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Women will have 1279.5mg of medicine in a day.
How much can a 102-pound woman have?103-pound man takes -1292mg of medicines.
102-pound woman will take x mg of the medicine.
By cross multiply
102x1292=103x
131784=103x
x=131784/103
x=1279.5mg
What is an example of a word problem?Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?
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