Answer:
1.3×10⁻² = 0.013
Step-by-step explanation:
The "E" stands for "×10^", so 1.3E-2 means 1.3×10^-2.
Of course 10^-2 = 1/10^2 = 1/100 = 0.01, so
1.3E-2 = 1.3×10^-2 = 1.3×0.01 = 0.013
_____
This notation was used by early computers to print results where the character set was limited and superscripts could not be printed.
6.
What is the value of x?
24
30
40
38
You must do pythagorean theorem:
a^2 + b^2 = c^2
a and b are the legs and c is the hypotenuse
In this triangle...
a = 16
b = x
c = 34
so...
16^2 + x^2 = 34^2
256 + x ^2 = 1156
x^2 = 900
Then to isolate x square root both sides. This will get rid of the square on the x value.
This will give you...
30
x is 30
Hope this helped!
Answer: second option
Step-by-step explanation:
You need to apply the Pythagorean theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.
In the figure you can observe the value the hypotenuse of the right triangle and the value of one of this leg. Then, you need to solve for the other leg from [tex]a^2=b^2+c^2[/tex]:
[tex]b^2=a^2-c^2[/tex]
[tex]b=\sqrt{a^2-c^2}[/tex]
Substituting values, you get that the value of "x" is:
[tex]b=\sqrt{(34)^2-(16)^2}[/tex]
[tex]b=30[/tex]
Match each term with the appropriate example
1.
Absolute value
2.
All real numbers
3.
x = -5
4.
No solution
5.
Adding the opposite to both sides of the equation.
a.
|2x| = -10
b.
3x = 3x
c.
5x = -25
d.
| - 7| = 7
e.
Canceling
Answer:
1. Absolute value : d. | - 7| = 7
2. All real numbers : b. 3x = 3x
3. x = -5 : c. 5x = -25
4. No solution : a. |2x| = -10
5. Adding the opposite to both sides of the equation. : e. Canceling
Step-by-step explanation:
1. Absolute value : d. | - 7| = 7
The absolute value is considered the distance to 0... so if there's a negative sign in the value, the negative sign disappears.
2. All real numbers : b. 3x = 3x
If we divide both sides by 3, we have x = x, which will always be true.
3. x = -5 : c. 5x = -25
If we multiply each side by 5, we have 5(x) = 5(-5) thus 5x = -25
4. No solution : a. |2x| = -10
The result of an absolute value cannot be a negative number. So, that has no solution since there's no value of x that would make this true.
5. Adding the opposite to both sides of the equation. : e. Canceling
If you have for example (x = -5) and you add 5 on both sides, you cancel the value on the right side... (becomes x + 5 = 0).
This results when you flip the numerator and denominator of a fraction. what do you call this?
Answer:
the multiplicative inverse or reciprocal.
Step-by-step explanation:
The price of a sweatshirt at a local shop is twice the price of a pair of shorts. The price of a T-shirt at the shop is $4 less than the price of a pair of shorts. Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.
19Let w represent the price of one sweatshirt, t represent the price of one T-shirt, and h represent the price of one pair of shorts. Write a system of three equations that represents the prices of the clothing.
20= Solve the system. Find the cost of each item.
Answer:
Price of sweatshirt = $24
Price of t-shirt=$8
Price of shorts= $12
Step-by-step explanation:
Let
w be the price of one sweat shirt
t be the price of t-shirt
h be the price of shorts
The first statement is:
The price of a sweatshirt at a local shop is twice the price of a pair of shorts.
w=2h Eqn 1
Then,
The price of a T-shirt at the shop is $4 less than the price of a pair of shorts.
t=h-4 Eqn 2
And
Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for a total cost of $136.
3w+2h+5t=136 Eqn 3
Putting the value of w and t in equation 3
3w+2h+5t=136
3(2h)+2h+5(h-4)=136
6h+2h+5h-20=136
13h=136+20
h=156/13
h=12
So the price of pair of shorts is $12.
Putting the value of h in equation 1
w=2(12)
w=24
Price of sweatshirt is: $24
Putting the value of h in eqn 2:
t=12-4
t=8
Price of T-shirt is $8 ..
Find the coordinates of the point on the directed segment from (3,2) to (6,8) that divides into a ratio of 1:3.
a. (4.5, 5.5)
b. (5.25, 6.25)
c. (3.75, 3.5)
d. (4,4)
Answer:
c. (3.75, 3.5)
Step-by-step explanation:
Let's call the given segment AB, and the dividing point P. Then you want AP:PB = 1:3.
There are a couple of ways you can get there.
1. Recognize that when you subtract the coordinates of A from P, the difference will be 1/4 of the result of subtracting A from B. That is, ...
P-A = (1/(1+3))·(B-A)
We can see that B-A = (6,8) -(3,2) = (3, 6), so 1/4 of that is (3/4, 3/2) = (0.75, 1.5). Adding these values to the coordinates of A gives ...
P = A + (.75, 1.5) = (3.75, 3.5)
__
2. Finish working out the equation above to solve for P:
4(P -A) = B -A
4P = B + 3A
P = (3A + B)/4 . . . . . note the multiplier for A is the relative length of PB and vice versa
P = (3(3, 2) +(6, 8))/4 = (15/4, 14/4) = (3.75, 3.5)
_____
Comment on choosing an answer
You only need to determine one of the coordinates in order to pick the correct answer. Finding both coordinates can help give you assurance that you have worked it out correctly.
On the first day of the month, John counted his money and found he had 28.35. Since then, he has received an additional 17.26 from the jobs he does after school. How much money does he have now
Answer: He has 45.61
Step-by-step explanation:The answer is 45.61 because you add the decimals, 28.35+17.26, then you aline the decimal points and add, then get 45.61
1 1
28.35
+ 17.26
45.61
Total money John has now is 45.61.
On the first day of the month, John had $28.35 and received an additional $17.26.
To find out how much money John has now, you need to add the initial amount to the additional money he received. Therefore, John now has
28.35 + 17.26 = 45.61 money
Please please help me out
Answer:
angle x will be 17
Step-by-step explanation:
ATP,
3x+4=72–x
3x+x=72–4
4x=68
x=68/4
x=17
Answer:
x = 17
Step-by-step explanation:
Since triangles are similar then corresponding angles are congruent.
∠I and ∠ P are corresponding and congruent, hence
3x + 4 = 72 - x ( add x to both sides )
4x + 4 = 72 ( subtract 4 from both sides )
4x = 68 ( divide both sides by 4 )
x = 17
A box without a top is made from a rectangular piece of cardboard, with dimensions 6 ft by 8 ft, by cutting out square corners with side length x. Which expression can be used to determine the greatest possible volume of the cardboard box? (8−2x)(6−2x)x (6−x)(8−x)x (8x−6)(6x−8) (8−6x)(6−8x)
The answer is:
The first option:
[tex]Volumen_{max}=(8-2x)(6-2x)*x[/tex]
Why?From the statement, we know the dimensions of the box, and the length of the sides to be cut (x).
So,
Working with the length of the box, we have:
Let be 8 the length of the cardboard for the length of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(8-(x+x))=(8-2x)[/tex]
Now,
Working with the width of the box, we have:
Let be 6 the length of the cardboard for the width of the box, so, if we cut out the side of length "x", we have:
[tex]Length=(6-(x+x))=(6-2x)[/tex]
Now that we already know the length and the width of the box, we know that the bottom of the box will have the same length "x", so, the greatest possible volume of the cardboard box will be:
[tex]Volumen_{max}=Length*Width*Bottom=(8-2x)(6-2x)*x[/tex]
Have a nice day!
solve the equation32x – 1 = 16x + 4
PLEASE HELP:(
Answer:
x = 5/16
Step-by-step explanation:
"Solving this equation" means determining the x value that makes the equation true. Since it's a linear equation, there can be only one solution.
Starting with 32x – 1 = 16x + 4, subtract 16x from both sides, obtaining:
16x - 1 = 4
and then add 1 to both sides, obtaining 16x = 5. Then x = 5/16.
Which transformation represents a reflection over the y-axis? (x, y) → (−x, y) (x, y) → (x , −y) (x, y) → (y, x) (x, y) → (−y, x)
Answer:
(x, y) → (−x, y)(x, y)
Step-by-step explanation:
To do a transformation over the Y-axis, you just have to change the sign on the x in order to create a matching point on the other side of the Y axis, for example if you wish to make a reflection of the point (8,9), the reflection over the Y axis would be (-8,9), the same with X and Y, if you wish to make a reflection of (x,y) you just change the sign of the x like this: (-x,y)
The correct answer is option 1. [tex](x,y) \rightarrow (-x,y)[/tex]
To determine which transformation represents a reflection over the y-axis, we examine the options provided:
[tex](x,y) \rightarrow (-x,y)[/tex][tex](x,y) \rightarrow (x,-y)[/tex][tex](x,y) \rightarrow (y,x)[/tex][tex](x,y) \rightarrow (-y,x)[/tex]A reflection over the y-axis transforms the x-coordinate of a point to its opposite while keeping the y-coordinate unchanged. Therefore, the correct transformation is [tex](x,y) \rightarrow (-x,y)[/tex].
Reflection over the y-axis results in the point (x, y) being mapped to (−x, y). This is because the x-coordinate is negated while the y-coordinate remains the same.
The complete question is:
Which transformation represents a reflection over the y-axis?
1. [tex](x,y) \rightarrow (-x,y)[/tex]
2. [tex](x,y) \rightarrow (x,-y)[/tex]
3. [tex](x,y) \rightarrow (y,x)[/tex]
4. [tex](x,y) \rightarrow (-y,x)[/tex]
Please help me with this
Answer:
[tex]\frac{\sqrt{51} }{10}[/tex]
Step-by-step explanation:
Using the Pythagorean identity
sin²x + cos²x = 1 ⇒ cosx = ± [tex]\sqrt{1-sin^2x}[/tex], hence
cosΘ = [tex]\sqrt{1-(7/10)^2}[/tex]
= [tex]\sqrt{1-\frac{49}{100} }[/tex]
= [tex]\sqrt{\frac{51}{100} }[/tex]
= [tex]\frac{\sqrt{51} }{\sqrt{100} }[/tex] = [tex]\frac{\sqrt{51} }{10}[/tex]
Determine if triangle XYZ with coordinates X(1, 1), Y(5, 6), and Z(6, 2) is a right triangle.
Answer:
Yes.
Step-by-step explanation:
If you graph it you can see that they all the points match up to the perfect right triangle. You may have to rotate it to see it though. Point Z is the angle of the triangle that is the corner of the 90 degree triangle.
The dimensions of a rectangular garden were 5m by 12 m. Each dimension was increased by the same amount. The garden then had an area of 120 m^2. Find the dimensions of the new garden.
Here is the set up:
We know the given dimensions are increased by the same number.
Let x be that number.
The garden is a rectangle.
Area = length times width.
5m = 5 meters
12m = 12 meters
Area is 120 meters^2.
Here is your equation:
120 = (5 + x)(12 + x)
Take it from here.
Find a cubic function with the given zeros. 7, -3, 2 (1 point)
ANSWER
[tex]f(x) =x^3-6x^2-13x+42[/tex]
EXPLANATION
The zeros of the cubic function is given as:
x=7,x=-3,x=2
This implies that, x-7,x+3,x-2 are factors of the given cubic polynomial function.
We can write the completely factored form as a function of x to get:
[tex]f(x) = (x - 7)(x + 3)(x - 2)[/tex]
We expand to get:
[tex]f(x) = (x - 7)(x^2+ x-6)[/tex]
[tex]f(x) =x^3-6x^2-13x+42[/tex]
This is a cubic function because the highest degree is 3.
Find the next term of the arithmetic sequence shown. 23, 28, 33, 38, . . .
A) 42
B) 43
C) 45
D) 48
ANSWER
B) 43
EXPLANATION
The given arithmetic sequence is 23, 28, 33, 38, . . .
We can observe the following pattern,
23+5=28
28+5=33
33+5=38
To obtain the subsequent terms, we add 5.
Therefore the next term is
38+5=43
Gavin and Jack are practicing shots against their goalie. On their last 15 attempts, Gavin made 6 and Jack made 7. Based on this performance, what is the probability that they both make their next shot?
Answer:
[tex]\dfrac{14}{75}[/tex]
Step-by-step explanation:
Gavin made 6 out of 15 shots, so the probability that Gavin's next shot will be successful is
[tex]\dfrac{6}{15}=\dfrac{2}{5}[/tex]
Jack made 7 out of 15 shots, so the probability that Jack's next shot will be successful is
[tex]\dfrac{7}{15}[/tex]
The probability that they both make their next shot successfully is
[tex]\dfrac{2}{5}\cdot \dfrac{7}{15}=\dfrac{14}{75}[/tex]
Lester was solving an equation but he made a mistake. What is the mistake and what is the correct answer? X + 17 = 22 –22 –22 x = 0
subtract 17, not 22, from both sides. 17 – 17 = 0 and 22 – 17 = 5. The answer should be x = 5.
Step-by-step explanation:
An equation between two variables that gives a straight line when plotted on a graph.
Lester made mistake in first steps he subtract 22 from the equation.
The correct solution of the equation is x =5.
GivenLester was solving an equation but he made a mistake.
The given equation is;
[tex]\rm x + 17 = 22[/tex]
What is a linear equation?An equation between two variables that gives a straight line when plotted on a graph.
The equation represents the linear equation and to solve the equation following all the steps given below.
Then,
The correct way to solve the equation is,
[tex]\rm x + 17 = 22\\\\x+17-17 = 22-17\\\\x +0=5\\\\x=5[/tex]
Hence, the correct solution of the equation is x =5.
To know more about the Linear equation click the link given below.
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If the parent function f(x)=\root(3)(x) is transformed to g(x)=\root(3)(x+2-4), which is the graph of g(x)?
(Photos of graphs included)
(15 points)
ANSWER
A.
EXPLANATION
The parent function is
[tex]f(x) = \sqrt[3]{x} [/tex]
This function is transformed to obtain
[tex]g(x) = \sqrt[3]{x + 2} - 4[/tex]
The +2 is a horizontal translation, that shifts the graph of the parent function to the left by 2 units.
The -4 is a vertical translation, that shifts the graph of the parent function down by 4 units.
The correct option is A.
Answer:
A)
Step-by-step explanation:
First we will graph th parent function which is a cube root and we can see it in the attachment #1.
In this excercise there are two types of transformations of the parent function:
[tex]f(x)=\sqrt[3]{x}[/tex]
First:
[tex]f(x+b)[/tex] shifts the function b units to the left.(Attachment #2 )
[tex]f(x)=\sqrt[3]{x+2}[/tex]
[tex]b=2[/tex]
Second:
[tex]f(x)-c[/tex] shifts the function c units downward. (Attachment #3)
[tex]f(x)=\sqrt[3]{x+2}+4[/tex]
[tex]c=4[/tex]
Which value for x satisfies the equation 3x - 6 = 15 ?
Answer:
7
Step-by-step explanation:
3x - 6 = 15
+6 +6
____________
3x = 21
3x = 21/3
x = 7
The value of x that satisfies the equation 3x - 6 = 15 is x = 7. This was calculated by isolating x and solving the equation.
Explanation:The equation provided is 3x - 6 = 15, and the value for x that satisfies this equation is what we are looking for. To solve for x, we can start by adding 6 to both sides of the equation to isolate 3x on one side which results in 3x = 21. Finally, we divide each side by 3 to find the solution which gives us x = 7. Therefore, the solution to the equation 3x - 6 = 15 is x = 7
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Linda received the following scores on her essay tests.
64, 65, 63, 66, 60, 65, 66, 68, 69, 66, 63
What is the mean of her scores?
A.64.5
B.65
C.65.5
D.66
The answer to your question is B. 65
Answer:
b
Step-by-step explanation:
you add them all together and divide 11 because there are 11 numbers.
i used to have problem on mean, median, and mode too.
In a plane, if a line is _____ to one of two parallel lines, then it is perpendicular to the other.
a. parallel
b. perpendicular
c. skew
d. intersecting
Answer:
Perpendicular
Step-by-step explanation:
Think of a ladder. It has 2 long sides that are parallel to each other. If a step is perpendicular to one long side then it is perpendicular to the other long side BECAUSE the 2 long sides are parallel to each other.
In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
In a plane, two lines which are parallel exist in the same axis.In essence, any line which is perpendicular to one of two parallel lines is also perpendicular to the other.This concept is evident in the model of ladders, where each of the vertical lines are perpendicular to the parallel step lines(horizontal lines).Read more;
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Solve 8 sin ( 5 x ) = 3 for the two smallest positive solutions a and b, with a < b
The two smallest positive solutions, with a < b, are approximately
x ≈ 0.384 and x ≈ 1.64.
We have,
Isolate the sine function by dividing both sides by 8.
sin(5x) = 3/8
The inverse sine function (also called arcsin) is on both sides of the equation.
5x = arcsin(3/8).
Divide both sides by 5.
x = (1/5) arcsin(3/8)
Now,
arcsin(3/8) is approximately 0.4115.
So,
x = (1/5) * 0.4115
x = 0.384.
Since the sine function repeats itself every 2π radians, we add multiples of 2π/5 to the solution to find other valid values of x.
The second smallest positive solution
x = 0.384 + (2π/5) = 1.64.
Therefore,
The two smallest positive solutions, with a < b, are approximately
x ≈ 0.384 and x ≈ 1.64.
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The equation 8 sin(5x) = 3 is solved by isolating the variable term, using inverse sine to get an angle, and considering the period of the sine function when finding additional solutions.
Explanation:To solve the equation 8 sin (5x) = 3, we first isolate the term involving the variable 'x'. Start by dividing both sides by 8. We get sin(5x) = 3/8.
The inverse sine (also known as arcsin or sin^-1) is used to get the angle whose sine is 3/8. So we have 5x = sin^-1(3/8).
To solve for 'x', we then divide both sides by 5: x = sin^-1(3/8) / 5.
This value of 'x' is a solution, but sine function repeats every 2π intervals, so we add multiples of 2π/5 to 'x' to get additional solutions.
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△WKT∼△NRP
What is PR?
Enter your answer, as a decimal, in the box.
_____ in.
Answer:
The answer is 31.5
Step-by-step explanation:
Similar triangles have their corresponding sides to be in equivalent ratios
The length of PR is 31.5 inches
△WKT∼△NRP means that, the following sides are similar
WK and NRWT and NPTK and PRSo, we have the following equivalent ratio
[tex]WK : TK = NR : PR[/tex]
From the complete question, we have the following parameters:
WK = 14TK = 18NR = 24.5So, the ratio becomes
[tex]14 : 18 = 24.5 : PR[/tex]
Express the ratio as fraction
[tex]\frac{18}{14}= \frac{PR}{24.5 }[/tex]
Multiply both sides by 24.5
[tex]\frac{18}{14} \times 24.5= PR[/tex]
This gives
[tex]\frac{441}{14} = PR[/tex]
Divide 441 by 14
[tex]31.5 = PR[/tex]
Rewrite the above equation as
[tex]PR = 31.5[/tex]
Hence, the length of PR is 31.5 inches
Read more about similar triangles at:
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Write an equation in slope-intercept form, y=mx+b, for the lines with the following information:
y-intercept 3 and slope -6
Slope intercept formula: y = mx + b where m equals slope and b equals the y-intercept.
Answer: y = -6x + 3
Final answer:
The equation in slope-intercept form for a line with y-intercept 3 and slope -6 is y = -6x + 3, showing a line decreasing by 6 units in y for each unit increase in x.
Explanation:
To write an equation in slope-intercept form, which is y = mx + b, we need to know the slope (m) and the y-intercept (b). In this case, we have a y-intercept of 3 and a slope of -6. Plugging these values into the slope-intercept form, we get the equation of the line:
y = -6x + 3
This equation tells us that the line crosses the y-axis at (0, 3) and for each unit increase in x, the value of y decreases by 6 units, since the slope is negative. This is a direct application of the algebra of straight lines and the concepts of slope and y-intercept.
Internet provider A charges $9.95 per month for the first 10 hours of use and $1.69 per hour for all those over 10. Provider B charges a flat fee of $19.95.What would be the maximum number of hours you could use each month for Provider A to be the best value for you?
15 hours is the answer to this
1.69×5+9.95
Answer:
15 hours.
Step-by-step explanation:
In order to solve this, we just have to create an inequality, for ti to be more convenient for us to work with the first company we shouldn´t be spending more than 19.95 a month, otherwise we would be better off with the second one, so the total would be 19.95, and the base fee is $9.95 for the first ten hours, so X would be the number of extra hours we will use:
[tex]Base+Extra,hours=Budget[/tex]
Now we just insert the values in to the formula:
[tex]10+1.68x=19.95\\[/tex]
We clear X:
[tex]10+1.68x=19.95\\[/tex]
[tex]1.68x=19.95-10\\[/tex]
[tex]1.68x=9.95\\[/tex]
[tex]x=\frac{9.95}{1.69}[/tex]
[tex]x=5.91\\[/tex]
So the as the number of extra hours that we could use without going over the budget is 5.91, and the company wouldn´t charge us the .91, the number of extra hours is 5, plus the base hours, the total number of hours would be 15.
the surface area of the figure below is 50.80m^2 True or False
For this case we have that by definition, the surface area of a cone is given by:
[tex]SA = \pi * r * s + \pi * r ^ 2[/tex]
Where:
A: It's the radio
s: It's the slant
Substituting according to the data we have:
[tex]SA = \pi * 2.1 * 5.6 + \pi * (2.1) ^ 2\\SA = 36.9264 + 13.8474\\SA = 50.7738 \ m ^ 2[/tex]
If we round:
[tex]SA = 50.8 \ m ^ 2[/tex]
Answer:
True
A rabbit and a turtle were to start a race at the same place. the rabbit was feeling very confident and slept for 8 hours before starting. the turtle ran at a pace of 1 mile per hour, and the rabbit ran at 5 miles per hour. the race was a distance of 10 miles. who won the race?
Answer:
Step-by-step explanation:
D=RT
10=1T
T=10 HOURS FOR THE TURTLE.
10=5(T-8)
10=5T-40
5T=10+40
5T=50
T=50/5
T=10 HOURS FOR THE RABBIT.
LOOKS LIKE A TIE .
Students volunteering at a charity event work 1/2- hour shifts.Zack volunteered for 4 hours.He incorrectly divided one half by four to find the number of shifts he worked. How should zack have calculated the number of his shifts
Answer:
He should have divided 4 by [tex]\frac{1}{2}[/tex]:
[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]
Step-by-step explanation:
You know that the students work [tex]\frac{1}{2}[/tex]-hour shifts at the charity event and Zack worked in the event for four hours.
Then, to calculate the number of shifts he worked, he should not have divided [tex]\frac{1}{2}[/tex] by 4. He should have divided 4 by [tex]\frac{1}{2}[/tex].
Let's make the correct procedure to calculate the number of shifts Zack worked at the charity event. This is:
[tex]shifts=\frac{4}{\frac{1}{2}}\\\\shifts=8[/tex]
Therefore, he worked 8 shifts.
To calculate the number of shifts Zack worked, we need to follow these steps:
1. Determine the length of one shift. According to the information provided, one shift lasts 1/2 hour.
2. Determine the total amount of time Zack volunteered. Zack volunteered for 4 hours.
3. To find out the total number of shifts Zack worked, we need to divide the total number of hours he volunteered by the length of one shift.
So, we take the total volunteer time (4 hours) and divide it by the shift length (1/2 hour):
\[ \text{Number of shifts} = \frac{\text{Total volunteer time}}{\text{Shift length}} \]
\[ \text{Number of shifts} = \frac{4}{1/2} \]
Now, when dividing by a fraction, you can multiply by its reciprocal. The reciprocal of 1/2 is 2/1, or just 2.
\[ \text{Number of shifts} = 4 \times 2 \]
\[ \text{Number of shifts} = 8 \]
So Zack should have determined that he worked 8 shifts in total during his volunteer time.
a candle maker has 301.59 cubic centimeters (cm3) of liquid wax to make cone shaped candles. Each Candle has a circular base with a diameter of 3 cm and a height of 5 cm. what is the maximum number candles that can be made from the liquid wax?
A. 6
B. 7
C. 25
D. 26
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ h=5 \end{cases}\implies V=\cfrac{\pi (1.5)^2(5)}{3}\implies V=\cfrac{11.25\pi }{3} \\\\\\ V= 3.75\pi \implies V\approx 11.78~cm^3\qquad \leftarrow \textit{for one candle} \\\\\\ \stackrel{\textit{how many times does 11.78 go into 301.59?}}{301.59\div 11.78\implies 26}\qquad \leftarrow \textit{rounded up}[/tex]
The volume of the cone is one-third of the product of its base area and its height. The maximum number of candles that can be made from the liquid wax is 25.
What is the volume of a cone?The volume of the cone is one-third of the product of its base area and its height. It is given by the formula,
The Volume of Cone = (1/3) × π × (d/2)² × h
The volume of wax that is needed to make a single candle with a diameter of 3 cm and height of 5 cm is,
The Volume of Cone = (1/3) × π × (d/2)² × h
The Volume of Candle = (1/3) × π × (3/2)² × 5 = 11.78 cm³
The total wax available is 301.59 cm³, while the amount of wax needed to make a candle is 11.78 cm³, therefore, the number of candles that can be made with the total wax is,
The Number of candles = (301.59 cm³/ 11.78 cm³) = 25.5999
Since a half candle can not be produced, therefore, the maximum number of candles that can be made from the liquid wax is 25.
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A worker takes a random sample of 200 bolts and finds that 30 of them are either too long or Too Short thus making them unusable. Estimate the number of unusable bolts and a production of 17,000 bolts.
A. 1,610 Bolts
B. 2,550 Bolts
C. 2,140 Bolts
D. 2,260 Bolts
I got D. I just need to be sure it is the right answer.
Answer:
B
Step-by-step explanation:
30 are unusable in 200. So how many are unusable in 17,000??
We can set up a ratio and figure out the answer right away! Let x be the number of unusable bolts in 17,000, so we can write:
[tex]\frac{30}{200}=\frac{x}{17,000}\\200x=30*17000\\200x=510,000\\x=\frac{510,000}{200}\\x=2550[/tex]
THus, number of unusable bolts is 2550. B is right.