The teacher will have a total of 120 pens if 12 sets of pens are ordered.
To find the total number of pens a teacher will have if 12 sets of pens are ordered, we can start by finding the total number of pens in one set and then multiply it by 12.
In one set, there are 4 blue pens, 3 black pens, 2 red pens, and 1 purple pen. To find the total number of pens in one set, we can simply add the number of pens of each color:
Total pens in one set = 4 + 3 + 2 + 1 = 10
Therefore, the numerical expression to represent how many pens a teacher will have if 12 sets of pens are ordered is:
12 × 10 = 120
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Find a linear inequality with the following solution set. Each grid line represents one unit.
The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.
How to derive the inequality that represents the image
Herein we have an representation of a inequality of the form y ≤ f(x), where f(x) is a linear function, that is, a first grade polynomial. By geometry we know that a equation of the line can be known from two distinct points set on Cartesian plane:
Slope
m = [- 4 - (- 2)] / [4 - (- 2)]
m = (- 2) / 6
m = - 1 / 3
Intercept (m = - 1 / 3, (x, y) = (4, - 4)
b = y - m · x
b = - 4 - (- 1 / 3) · 4
b = - 4 + 4 / 3
b = - 8 / 3
Then, we find that the inequality is:
y ≤ (- 1 / 3) · x - 8 / 3
8 / 3 ≤ (- 1 / 3) · x - y
(- 1 / 3) · x - y ≥ 8 / 3
The linear inequality that represents the solution set is (- 1 / 3) · x - y ≥ 8 / 3.
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Can someone please explain how [tex](3^{\frac{1}{5} } )^{2}[/tex] can be written as the radical expression [tex]\sqrt[5]{9}[/tex] ???
We can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
What is a radical expression?A radical expression is an expression of the form ⁿ√x where it is called the nth root of x.
Now, to write [tex](3^{\frac{1}{5} } )^{2}[/tex] as the radical expression [tex]\sqrt[5]{9}[/tex], we use following laws of indices
The power law of indices. [tex](x^{\frac{1}{b} } )^{a} = (x^{a} )^{\frac{1}{b} }[/tex] and root law of indices [tex]x^{\frac{1}{a} } = \sqrt[a]{x}[/tex]So, [tex](3^{\frac{1}{5} } )^{2} = (3^{2} )^{\frac{1}{5} }[/tex]
[tex](3^{2} )^{\frac{1}{5} } = 9^{\frac{1}{5} } = \sqrt[5]{9}[/tex]
Thus, we can to convert the expression [tex](3^{\frac{1}{5} } )^{2}[/tex] to the radical expression [tex]\sqrt[5]{9}[/tex]. by using the laws of indices.
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What is the value of z?
Answer:
(B). 25.25
Step-by-step explanation:
z + 54° + (3z + 1)° + 204° = 360°
4z + 259 = 360
z = 101 ÷ 4
z = 25.25 (B).
A 393939-meter ladder is sliding down a vertical wall so the distance between the bottom of the ladder and the wall is increasing at 101010 meters per minute. At a certain instant, the bottom of the ladder is 363636 meters from the wall. What is the rate of change of the distance between the top of the ladder and the ground at that instant (in meters per minute)
The rate at which the distance between the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.
Given length of ladder 39 m and the rate at which the wall is increasing is 101, the bottom of the ladder is 36 m from the wall.
Let bottom is x and the length of wall be y.
We have to find the rate at which the distance between the top of the ladder and the ground at that instant.
we have to find dy/dt.
We have to apply pythagoras theorem first.
[tex]x^{2} +y^{2} =39^{2}[/tex]---------------1
[tex]x^{2} +y^{2} =1521[/tex]
put the value of x=36 in the above equation
[tex]36^{2} +y^{2} =1521[/tex]
[tex]y^{2} =225[/tex]
y=15 m
We have to find the derivative of equation 1 with respect to t.
2x*dx/dt+2y*dy/dt=0
Because it is given that bottom is increasing at 101 meters per minute so dx/dt=101
2x*101+2y*dy/dt=0
put the value of y=15
2x*101+2*15*dy/dt=0
2x*101+2*15*dy/dt=0
dy/dt=-3030/2*36
dy/dt=-42.08
Hence the rate at which the rate at which the top of the ladder and the ground at that instant is decreasing at 42 meters per minute.
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Question is wrong so it includes ladder length be 39 meters and the rate of increasing of bottom of ladder from bottom of wall is 101 meters per minute and the bottomis 36 m from the wall.
{10, 11, 12, ..., 55}
How many numbers in the above set are divisible by 2 but not by 10?
(A) 17
(B) 18
(C) 19
(D) 21
Considering concepts of divisibility, the amount of numbers in the set that are divisible by 2 but not by 10 is:
(C) 19.
What are the rules for division by 2 and by 10?Numbers that finish in 0, 2, 4, 6, and 8 are divisible by 2, that is, even numbers are divisible by 2.Numbers that finish in 0 are divisible by 10. Hence, every number that is divisible by 10 is also divisible by 2.The data-set has (55 - 10) + 1 = 46 numbers, hence 23 are divisible by 2. 20, 30, 40 and 50 are also divisible by 10, that is, 4 numbers have to be removed, hence the amount is:
23 - 4 = 19.
Which means that option C is correct.
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what are the more approprite measures of center and spread for this data set? select two choices: one for the center and one for the spread. please help asap!!
Based on the data set, B. Better measure of center: median. C. Better measure of spread: interquartile range (IQR).
What measures of center and spread are best?The measure of center should be the median because the mean will be affected by the outliers on the left side.
The IQR will be the best measure of spread because the standard deviation is also affected by the outliers.
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If AD BD, which of the following relationships can be proved and why?
B
OA. AACD ABCD, because of AS.
OB. AACD ABCD, because of ASA.
OC. There is not enough information to prove a relationship.
D. AACD ABCD, because of SAS.
IfIf AD BD, the following relationships that can be proved and why is: D. ΔACD ΔBCD, because of SAS.
Relationship that can be proved if AD=BDThe relationship that can be proved is ΔACD ΔBCD, because of SAS.
The reason is that m<CDA=M<CDB=90°
CD=CD
AD=BD
Hence, ΔACD=ΔBCD because of SAS. SAS congruence can tend to be proved when the length of the two side correspond and when the angle between the two side is equal.
Therefore the correct option is D.
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The price of a new television is $423. This price includes VAT in 17 1/2%.
a) Work out the cost of the television before VAT was added.
By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. The value of a television was $423 at the start of the year.
b) Work out the value of the television at the end of the third year. Give your answer to the nearest penny.
The cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3
What is the meaning of VAT ?VAT is an acronym for Value Added Tax. This is a tax attach to goods and products.
Given that the price of a new television is $423. This price includes VAT in 17 1/2%.
a) The cost of the television before VAT was added is calculated below.
Let the initial cost = C
(17.5 + 100)/100 x C = 423
117.5/100 x C = 423
1.175C = 423
C = 423/1.175
C = $360
b. By the end of the year, the value of a television has fallen by 12% of its value at the start of that year. If the value of a television was $423 at the start of the year, the value of the television at the end of the third year will be calculated by using the formula
A = P(1 - R%)^3
Substitute all the parameters
A = 423(1 - 12/100)^3
A = 423 x [tex]0.88^{3}[/tex]
A = 288.3 dollars
Therefore, cost of the television before VAT was added is $360 and the value of the television at the end of the third year is $288.3
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5.5(x+6 1/2)-(x+9 1/3)-(19-x)
The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12
What is the simplified form of the expressionGiven the expression;
5.5(x+6 1/2) - (x+9 1/3) - (19-x)
First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction
6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2
So, we have
(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )
Next, we remove the parentheses
11x/2 + 143/4 - x - 28/3 - 19 + x
11x/2 + 143/4 - 28/3 - 19
11x/2 + 317/12 - 19
11x/2 + 89/12
Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.
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A rectangular equation that is a function will be a function in any coordinate system. true or false ?
Answer:
True.
Step-by-step explanation:
In this true or false question, the answer is true.
Hope this helps!
Answer:
False
Step-by-step explanation:
Not every function in a rectangular plane will be a function in every plane. Hope this helps
please help will r8 5 + brainliest
Answer:
Option C more peaked and more widely spread.
Step-by-step explanation:
15 + 35 + 18 + 30 + 25 + 21 + 32 + 16
80 + 78 + 34
192/8 = 24
24 + 22 + 27 + 28
46 + 55 = 101/4 = 25.2
One-eight of 32 students in the class went abroad for fall break. how many students went aboard
Answer:4
Step-by-step explanation: 32\8 = 4
You are hiking. The total weight of your backpack
and its contents is 13 3/8 pounds. You want to carry no more than
15 pounds. How many extra water bottles can you add to your
backpack if each bottle weighs 3/4 pound?
By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .
What is the number of bottles we can add in the backpack ?It is given that the total weight of your backpack and its contents is 13 3/8 pounds.
Also given , we want to carry no more than 15 pounds.
Let the number of bottles we can carry be x.
Each bottles weigh 3/4 pounds.
Total weight of the bottles = 3x/4 pounds.
Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .
Thus the statement equation formed is -
⇒ 107/8 + 3x/4 = 15
⇒ 3x/4 = 13/8
⇒ x = 13/6 = 2.166
∴ x ≈ 2
Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .
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-9(z+8)=-9z-72
Llllllll
Answer:
true
-9(z+8)
-9*z +(-9)*8
-9z-72
Write the equation of the circle whose center is at the origin and whose diameter is 12.5
The equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625
Equation of a circleThe formula for finding the equation of a circle is expressed as:
(x-a)² + (y - b)² = r²
where
(a, b) is the centre
r is the radius
Given the following
(a, b) = (0, 0)
r = 12.5/2 = 6.25
Substitute
(x-0)² + (y - 0)² = 6.25²
x²+y²=39.0625
Hence the equation of the circle whose center is at the origin and whose diameter is 12.5 is x²+y²=39.0625
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Time Remaining
55:45
Circles C and D overlap. The distance from point C to point D is 7 centimeters.
What is the sum of the areas of circle C and circle D?
7Pi units squared
14Pi units squared
49Pi units squared
98Pi units squared
The sum of the areas of circle C and circle D is 98 units square. Option D
How to determine the areaIt is important to note that the if the circles overlap each other, then the most have the same radius
Also, the formula for area of a circle is given as;
Area = [tex]\pi r^2[/tex]
For Circle C
The value for π = 3. 142
radius = 7cm
Substitute the values into the formula
We have
Area = π × 7 × 7
Area = 49 π units square
For Circle D
Substitute the values into the formula
Area = [tex]\pi r^2[/tex]
Area = π × 7 × 7
Area = 49 π units square
Sum of the areas of circle C and circle D = area of circle C and area of circle D
Sum of the areas of circle C and D = 49π + 49 π
= 98 units square
The sum of the areas of the circles is 98 units square
Thus, the sum of the areas of circle C and circle D is 98 units square. Option D
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Consider rolling a fair die thrice and tossing a fair coin sixteen times. Assume that all the tosses and rolls are independent. The chance that the total number of heads in all the coin tosses equals 12 is (
The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.
Given a fair dice and tossing a fair coin sixteen times.
We have to find the probability that the total number of heads in all the coin tosses equals 12.
The probability lies between 0 and 1.
Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.
Let X shows the sum of heads while tossing.
P(X=12)=?
We can find the probability using binomial theorem.
=[tex]16C_{12} (0.5)^{12} (0.5)^{2}[/tex]
We have to toss sixteen times and out of 16 times we need head 12 times.
=16!/12!4!*0.00024*0.0625
=1820*0.000015
=0.0273
Hence the probability that the total number of heads in all the coin tosses equals 12 is 0.0273.
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Solve for x please anyone?
Answer: x=11
Step-by-step explanation:
The lines are parallel, which you can tell by the two arrows. 4x-8 is a corresponding angle to 3x+3, meaning they are congruent.
4x-8 = 3x+3
x=11
Answer:
x = 11
Step-by-step explanation:
these angles are corresponding angles so they are equal to each other.
4x - 8 = 3x + 3 Subtract 2x from both sides
x - 8 = 3 Add 8 to both sides
x = 11
Plug 11 back into the equations find the angle measurements
4(11) -8 = 36 degrees
3(11) + 3 = 36degrees
13. Rod earned $60 in one week working for a
lawn-care service. He worked for 6 hr. How
much did he earn per hour?
A chemist has three different acid solutions. the first acid solution contains 20 % acid, the second contains 30 % and the third contains 60 % . he wants to use all three solutions to obtain a mixture of 54 liters containing 45 % acid, using 2 times as much of the 60 % solution as the 30 % solution. how many liters of each solution should be used? the chemist should use liters of 20 % solution, liters of 30 % solution, and liters of 60 % solution.
Let [tex]a,b,c[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% acid solutions, respectively. These quantities then contain [tex]0.20a[/tex], [tex]0.30b[/tex], and [tex]0.60c[/tex] liters of acid.
The chemist wants to end up with a total volume of 54 liters, so
[tex]a + b + c = 54[/tex]
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
[tex]0.20a + 0.30b + 0.60c = 24.3[/tex]
He will also use twice as much of the 60% solution as the 30% solution, so
[tex]c = 2b[/tex]
Substitute this into the first two equations and solve for [tex]a,b[/tex].
[tex]\begin{cases} a + 3b = 54 \\ 0.20a + 1.50b = 24.3 \end{cases}[/tex]
Eliminating [tex]b[/tex], we have
[tex](a + 3b) - 2 (0.20a + 1.50b) = 54 - 2(24.3) \implies 0.60a = 5.4 \implies \boxed{a = 9}[/tex]
Solve for [tex]b[/tex].
[tex]9+3b=54 \implies 3b=45 \implies \boxed{b=15}[/tex]
Solve for [tex]c[/tex].
[tex]c = 2(15) \implies \boxed{c=30}[/tex]
a = 9, b = 15 and c = 30 liters of each solution should be used.
What liter means?According to the metric system, a liter is a unit for measuring volume. A bottle of Coke that holds 33.76 ounces, or 1.0567 quarters, is an example of a liter. 2. The fundamental metric unit of liquid volume or capacity, which is equivalent to 1.06 quarts or 2.12 pints.What is a liter of water?Let's examine this with the help of the following justification. Despite the fact that there is no established standard size for glasses, their capacity varies. In contrast, we estimate that a glass of water holds 8 ounces, and a liter holds 32 ounces.According to the question:
Let a, b, and c stand for the relative volumes (in liters) of the 20 percent, 30 percent, and 60 percent acid solutions. The amount of acid in these amounts is 0.20a, 0.30b, and 0.60c liters.
a+b+c = 54 because the chemist wishes to have a final volume of 54 liters.
and a concentration of 45% acid. This comes out to 0.45×54 = 24.3 total liters of acid, so
0.20a + 0.30b + 0.60c = 24.3
Additionally, he will consume twice as much of the 60% solution as the 30% solution, thus c = 2b.
Substitute this into the first two equations and solve for a,b
a + 3b = 54
0.20a + 1.50b = 24.3
Eliminating b, we have[tex](a+3 b)-2(0.20 a+1.50 b)=54-2(24.3) \\0.60 a=5.4[/tex]
a = 9.
Solve for b.9+3b = 54
3b = 45
b = 15.
Solve for c.c = 2(15)
c = 30.
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Sara's telephone service costs $31 per month plus $0.25 for each local call. Long-distance calls are extra. Last month, Sara's bill was $54.35, including $8.35 in long-distance charges. How many local calls did she make?
Answer:
60 local calls
Step-by-step explanation:
Total price minus the long-distance charges: 54.35 - 8.35 = $46.00
46 minus the fixed per month cost: 46-31 = $15
15 divided by the cost of each local call: 15/0.25 = 60 calls
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours
The correct option is (b) h=0.5cos([tex]\pi[/tex]/6t)+9.5.
The equations can be used to model the height as a function of time, t, in hours is h=0.5cos([tex]\pi[/tex]/6t)+9.5.
Equation of cosine function:The following is a presentation of the cosine function's generic form;
y = a + cos(bx - c) + d
amplitude = a
b = cycle speed
Calculation for the model height;
The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.
Obtain amplitude 'a' as
[tex]\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}[/tex]
The time 'T' is calculated as-
[tex]\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}[/tex]
Now, calculate 'd'
[tex]\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}[/tex]
Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:
h=0.5cos([tex]\pi[/tex]/6t)+9.5
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The complete question is-
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.
A. h=0.5cos([tex]\pi[/tex]/12t)+9.5
B. h=0.5cos([tex]\pi[/tex]/6t)+9.5
C. h=cos([tex]\pi[/tex]/12t)+9
D. h=cos([tex]\pi[/tex]/6t)+9
Describe the sample variance using words rather than a formula. do the same with the population variance
A. The sample variance is the sum of the deviations from the mean divided by the number of measurements minus one. The population variance is the average of the distances of the measurements on all units in the population from the mean.B. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements. The population variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.C. The sample variance is the sum of the deviations from the mean divided by the number of measurements. The population variance is the sum of the deviations from the mean divided by the number of measurements minus one.D. The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
The option D is the correct option.
According to the statement
we have to define the sample variance in the words.
So,
The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.
and in the case of the population variance it becomes
The population variance is the average of the squared distances of the measurements on all units in the population from the mean.
This is the method by which we define the sample variance and population variance.
So, The option D is the correct option.
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Help with this word problem!
Answer:
2.0 km
Step-by-step explanation:
The Law of Cosines can be used to find the third side of a triangle in which two sides and the angle between them are given.
SetupThe law of cosines tells us ...
c² = a² +b² -2ab·cos(C)
Using the given values, we have ...
c² = 4.2² +4.5² -2(4.2)(4.5)cos(26°)
SolutionSimplifying the equation, we get ...
c² = 37.89 -37.8cos(26°) ≈ 3.91559
c ≈ 1.979 . . . . km
The width of the strait is about 2.0 km.
(x 2 + 3) (x 3 + 4x)(x 2 + x - i - xi) = 0
The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.
What are the possible values of x?The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;
(x²+3) (x³+4x) (x²+x-i-xi) = 0.
Hence, by further factorisation; we have;
x(x²+3) (x²+4) (x-i) (x+1) = 0.
The possible values of x are therefore;
x = 0;
x²+3 = 0; x = ±√3i
x² +4 = 0; x = ±2i
x -i = 0; x = i.
x +1 = 0; x = -1
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I know this is a supervised data mining task because (choose all that apply) A. Because the target belonged to the same group as some thine else B. We have historical data on the target. C. There a specific quantifiable target that we are interested in or trying to predict. D. We were able to group the target with other variables
Answer:
The answer to your question is C. There a specific quantifiable target that we are interested in or trying to predict.
Step-by-step explanation:
I hope this helps and have a good day!
Wayne is holding a can of juice that has a diameter of 4 inches. there is a price tag stuck to the side of the can. wayne places the can on its with side with the sticker on the bottom and rolls it across a table top at a constant speed. the can reaches wayne's friend at the other end of the table in 5 seconds and completes 4 full rotations. which function could represent the price tag's height relative to the table top, , after it has been rolling for t seconds?
The function that could represent the price tag's height relative to the table top is h(t) = 4sin (22) +4
Disclaimer!!The question is incomplete because the options are not given and hence the correct option is shown below
Which function could represent the price tag's height relative to the table top, h(t), after it has been rolling for e seconds?
A n(t) = 2008(832) +2
B. h(t) =-2005(522) +2
C h(t) = –2sin(572) +2
D. h(t) = 4sin (22) +4
Given diameter is 4 inches and the time given is 5 seconds and
the number of rotations given is 4
We need to find the function that could represent the price tag's height relative to the table top .
Diameter = 4
So, Radius will be D/2 = 4/2
Radius=2
time given is 5 seconds and
the number of rotations given is 4
So , 5/4 = 2π/w
Therefore ,
W = 8π / 5
Therefore
h(t) = h(t) = 4sin (22) +4
Hence The function that could represent the price tag's height relative to the table top is h(t) = 4sin (22) +4
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Clarice was late paying her credit card bill of $249. She was charged a 5% late fee. What was the amount of the late fee?
Answer:
You subtract 249 minus 5
Which function in vertex form is equivalent to f(x) = x² + x +1?
○ f(x) = (x + 1/ 1³² + 1 ²1/0
3
4
○ f(x) = (x + 1)² + 2/1/2
○ f(x) = (x + ²/2 1²³ + ²/
4
5
f(x) = (x + 1/2-1² + ²/1/2
4
Answer:
[tex]\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
Step-by-step explanation:
NOTE :
[tex]x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}[/tex]
………………………………………
f(x) = x² + x +1
[tex]=x^{2}+2\times \frac{x}{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1[/tex]
[tex]=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}[/tex]
When a large cake is cut into piece that each weighs 3 ounces, it yields 120 pieces. How many pieces would the cake yield if it were cut into 2- ounce pieces instead
when the cake is cut into [tex]2[/tex] ounce pieces instead of [tex]3[/tex] pieces it yields [tex]180[/tex] pieces.
How to find large cake pieces ?
Given in the question when cake cuts into piece that each weight is [tex]3[/tex] ounce it yields [tex]120[/tex]
So original large cake weight is
[tex]w=120*3\\\\w=360[/tex]
So we can find cake pieces when cake cuts into weight [tex]2[/tex] each piece
[tex]pieces=\frac{360}{2}\\=180[/tex]
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