The number of cubes of dimensions of [tex]\frac{1}{8}[/tex] foot that can fit into a rectangular prism of a length of 1 foot, a width of 1 [tex]\frac{3}{8}[/tex] foot, and a height of [tex]\frac{5}{8}[/tex] foot is 55.
Volume of cuboid = l * b * h
where l is the length
b is the breadth
h is the height
l = 1 foot
b = 1 [tex]\frac{3}{8}[/tex] foot = [tex]\frac{11}{8}[/tex] foot
h = [tex]\frac{5}{8}[/tex] foot
Volume of cuboid = 1 * [tex]\frac{11}{8}[/tex] * [tex]\frac{5}{8}[/tex]
= [tex]\frac{55}{64}[/tex] cubic foot
Volume of cube = [tex]s^3[/tex]
where s is the side
s = [tex]\frac{1}{8}[/tex] foot
Volume = [tex]\frac{1}{8}^3[/tex]
= [tex]\frac{1}{64}[/tex] cubic foot
Number of cubes = [tex]\frac{\frac{55}{64} }{\frac{1}{64} }[/tex]
= 55
The number of cubes that fit into the prism is 55.
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When you don’t replace the marble for the second draw what kind of probability is it?
If you do not replace the marble after the first draw, the probability calculation depends on whether you are dealing with a dependent or an independent event.
The possibility or chance of an event occurring is measured by probability. It is a number between 0 and 1 (inclusive), where 0 denotes an impossibility and 1 denotes a certainty. By dividing the number of favorable outcomes by the total number of potential outcomes, the probability of an occurrence is determined. The field of mathematics known as probability studies the possibility that a certain event will take place. It is a way to quantify the possibility or likelihood that something will really happen.
For an independent event, assuming that the first draw had no bearing on the outcome of the second draw, in the case of an isolated occurrence, the chance of drawing a specific marble on the second draw would be the same as the likelihood of drawing that same marble on the first draw. For a dependent event, the outcome of the first draw would determine the possibility of drawing a specific marble on the second draw.
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The cost after the coupon is $21. 25 she decides to add a 20% tip. How much is she adding for a tip
If the cost after the coupon is $21.25 and she decides to add a 20% tip, she will be adding $4.25 for the tip.
Find out how much a 20% tip would be on a cost of $21.25 after applying a coupon.
Identify the total cost after the coupon.
In this case, the cost is $21.25.
Determine the percentage for the tip.
The tip percentage is given as 20%.
Convert the percentage to a decimal.
To do this, divide the percentage by 100. So, 20% divided by 100 is equal to 0.2.
Multiply the total cost by the tip percentage in decimal form.
Now, multiply $21.25 (total cost) by 0.2 (tip percentage as a decimal).
$21.25 x 0.2 = $4.25
Calculate the tip amount.
The tip amount is $4.25.
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The original selling price of a jacket was s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by 0. 85 (1. 4s). Which expression could explain what happened to the price of the jacket?
The expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.
The original selling price of the jacket was s dollars.The store owner made the first change, increasing the selling price by 40%. This can be represented by multiplying the original price (s) by 1.4: 1.4s.The store owner then made a second change, reducing the selling price by 15%. This can be represented by multiplying the new price (1.4s) by 0.85: 0.85(1.4s).So, the expression 0.85(1.4s) explains what happened to the price of the jacket through the two changes made by the store owner.
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Find-F+2G+H-R using the Graphical Tail-to-Tip method.
F = 45.0 N [S 45° W]
G= 25.0 N[35° N of W]
H=70.0 N [E 15° S]
To find -F+2G+H-R using the Graphical Tail-to-Tip method, measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.
How to solveTo find the vector sum F+2G+H-R using the graphical tail-to-tip method, follow these steps:
Draw vector F: 45.0 N [S 45° W]Draw 2G: Multiply G by 2: 2 x 25.0 N [35° N of W] = 50.0 N [35° N of W]Draw vector H: 70.0 N [E 15° S]Draw vector R: Since we want to find the sum F+2G+H-R, R should be drawn in the opposite direction to balance the equation.Now, place the vectors tail-to-tip in the following order: F, 2G, H, and R (in opposite directions).
The sum of these vectors can be found by connecting the starting point (tail of F) to the endpoint (tip of R in the opposite direction).
Measure the magnitude and direction of this resultant vector to find the sum F+2G+H-R.
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on a standardized test, phyllis scored 84, exactly one standard deviation above the mean. if the standard deviation for the test is 6, what is the mean score for the test?
The mean score for the test Phyllis scored 84, exactly one standard deviation above the mean is 78.
One of the statistics used in the generalised Cochran-Mantel-Haenszel tests is the mean score statistic. When the answer levels (columns) are assessed using an ordinal scale, it is applicable.
The chi-square distribution with (R-1) degrees of freedom, where R is the number of treatment groups, serves as the asymptotic distribution of the mean score statistic if the two variables are independent of one another in all strata (rows).
If the mean scores of the response differ between the treatment groups in at least one stratum, the mean score statistic tends to have larger values. The term "nonparametric ANOVA statistic" also applies to this statistic.
x = 84
[tex]\sigma=6[/tex]
since, x is 1 standard deviation above mean so,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]1=\frac{84-\mu}{6}\\ \\[/tex]
[tex]\mu[/tex] = 84-6
[tex]\mu[/tex] =78.
therefore, mean = 78.
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At the start of an observation, there are 7286.9 grams of a radioactive element present. The number of years t that must pass before N grams remain is given by the natural logarithm equation
t = 7,286.9 - 1,252 In(IV).
, dit
Find dt/dn When N = 15. Round to 2 decimal places, if necessary.
The value of dt/dN when N = 15 is -0.00509.
We are given the equation t = 7,286.9 - 1,252 ln(N/IV) which relates the number of years t that must pass before N grams of a radioactive element remain. We want to find the rate of change of t with respect to N, i.e., dt/dN when N = 15.
We can start by taking the derivative of both sides of the equation with respect to N:
dt/dN = -1252 / (N*ln(2))
Now we can substitute N = 15 into this equation to get:
dt/dN = -1252 / (15*ln(2))
Evaluating this expression, we get dt/dN ≈ -0.00509 (rounded to 2 decimal places). Therefore, the rate of change of t with respect to N when N = 15 is approximately -0.00509 years per gram.
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Please help this is for a test and i need a good grade lollll
"the wind force f on a sail varies jointly as the area al of the sall and the square of the wind speed w.
the force on a sail with area an area of 500 p? is 64.8 pounds when the wind speed is 18 mph. what
would be the force for a sail with an area of 250 f12 with a wind speed of 35 mph"
please show step by step work tysmmmm <3
The force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.
How to find force on sail?We are given that the wind force F on a sail varies jointly as the area A and the square of the wind speed W. We can represent this relationship mathematically using the equation:
F = k * A * W²
where k is a constant of proportionality.
We are also given that the force on a sail with an area of 500 p and wind speed of 18 mph is 64.8 pounds. We can use this information to solve for k:
64.8 = k * 500 * 18²
Solving for k, we get:
k = 64.8 / (500 * 18²)
k = 0.0000768
Now, we can use the equation to find the force for a sail with an area of 250 f12 and a wind speed of 35 mph:
F = 0.0000768 * 250 f12 * 35²
F = 108.72 pounds
Therefore, the force on a sail with an area of 250 f12 and a wind speed of 35 mph would be 108.72 pounds.
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Which is true about the relationship between 1 inch and 1 foot?
A. 1 inch is 12 times as long as 1 foot. B. 1 foot is 12 times as long as 1 inch. C. 1 foot is 6 times as long as 1 inch. D. 1 inch is 6 times as long as 1 foot
Option B is true about the relationship between 1 inch and 1 foot.
What is conversation?
A unit's use depends on the context; for example, a room's area is expressed in meters, yet a pencil's length and thickness are expressed in centimeters and millimeters, respectively. Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion. When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
There are 12 inches in 1 foot. This means that 1 foot is 12 times longer than 1 inch. Therefore, option B is correct. Option A is incorrect because it states that 1 inch is 12 times as long as 1 foot, which is the opposite of the correct relationship. Option C is incorrect because it states that 1 foot is 6 times as long as 1 inch, which is half of the correct relationship. Option D is incorrect because it states that 1 inch is 6 times as long as 1 foot, which is the opposite of the correct relationship.
Hence, Option B is true about the relationship between 1 inch and 1 foot.
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Exercise 11. 3. 1: Applying the pigeonhole principle - heights and times. About Apply the pigeonhole principle to answer the following questions. If the pigeonhole principle can not be applied, give a specific counterexample. (a) A team of three high jumpers all have a personal record that is at least 6 feet and less than 7 feet. Is it necessarily true that two of the team members must have personal records that are within four inches of each other
To apply the pigeonhole principle, we need to determine the number of pigeonholes and the number of pigeons. The pigeonhole principle cannot be applied to this question.
In this case, the" holes" are the high minidresses and the" lockers" are the ranges of particular records. Let's assume that the range of particular records is from 6 bases( 72 elevation) to 7 bases( 84 elevation). The difference between the upper and lower bounds of the range is
84- 72 = 12 elevation.
We can divide this range into five subintervals of length2.4 elevation( 72,74.4),(74.4,76.8),(76.8,79.2),(79.2,81.6), and(81.6, 84).
Since there are only five subintervals, but we've three high minidresses, it isn't inescapably true that two of the platoon members must have particular records that are within four elevation of each other. For illustration, if the three high minidresses have particular records of 6 bases 3 elevation( 75 elevation), 6 bases 7 elevation( 79 elevation), and 7 bases( 84 elevation), also none of them have particular records within four elevation of each other.
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The tax on a bicycle costing $400 is $32 how much will the tax be on a bicylce costing $700 if the tax remains the same
The tax on a bicycle costing $700, with the tax remaining the same as a bicycle costing $400 with a tax of $32, will be $56.
To calculate the tax on a bicycle costing $700, we need to know the percentage of tax charged on the $400 bicycle. The tax on the $400 bicycle is $32. To find the tax rate, we divide the tax by the cost of the bicycle and multiply by 100 to get a percentage.
tax rate = (tax / cost of bicycle) x 100%
tax rate = (32 / 400) x 100%
tax rate = 8%
Therefore, the tax rate is 8%. We can use this tax rate to calculate the tax on a bicycle costing $700.
tax on $700 bicycle = (tax rate / 100) x cost of bicycle
tax on $700 bicycle = (8 / 100) x $700
tax on $700 bicycle = $56
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!!PLEASE HELPP!! (check if I’m right pls)
Answer: It's correct
Step-by-step explanation:
Consider the following series: (-1)^ 71n n We will test this series for convergence or divergence. (i) What test(s) is(are) applicable to test this series? Click for List (i) Determine whether this series converges or diverges. O Converges O Diverges (iii) What is the sum of the series? Note: Write the exact answer not the decimal approximation (for example write 1 / not 0.8). Answer: The sum of the series is PO
The series given is (-1)^71n*n. To test for convergence or divergence, the alternating series test as the series alternates in sign. Also, the absolute value of the terms of the series is decreasing as n increases. In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
According to the alternating series test, if a series alternates in sign, and the absolute value of its terms is decreasing as n increases, then the series converges.
Thus, the series converges.
To find the sum of the series, we use the formula for the sum of an alternating series:
Sum = (-1)^71*1 - (-1)^71*2 + (-1)^71*3 - (-1)^71*4 + ...
= (-1)^71*(1 - 2 + 3 - 4 + ...)
= (-1)^71*(n(n+1)/2)
= 0
Therefore, the sum of the series is 0.
I'd be happy to help you with your question. To determine the convergence or divergence of the series (-1)^71n * n, we can follow these steps:
(i) Since the series has terms that alternate in sign, we can use the Alternating Series Test to test for convergence.
(ii) To apply the Alternating Series Test, we must first verify that the sequence of positive terms is decreasing and has a limit of zero. In this case, the sequence of positive terms is given by "n". As "n" goes to infinity, the sequence increases, not decreases, and the limit is not zero. Therefore, the series (-1)^71n * n does not pass the Alternating Series Test, and it diverges.
(iii) Since the series diverges, it does not have a finite sum.
In conclusion, the given series (-1)^71n * n diverges, and it does not have a finite sum.
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The International Links long-distance phone company charges no monthly fee but charges 18 cents per minute for long-distance calls. The World Connections long distance company charges $50 per month plus 10 cents per minute for long-distance calls. Compare the World Connections long-distance plan to that of International Links. Under what circumstances is it cheaper to use International Links?
If the number of minutes used is less than 625 per month, it is more affordable to use International Links if not, you can go for World Connections.
Let us assume that the number of minutes used = x
Cost per minute = 18 cents
Total cost for International calls = 0.18x
Basci cahrge = 50 per month
If we use x number of minutes for calls for world connections then the total cost will be:
50 + 0.10x
To find the value of x where International Links cost is less than the total cost for World Connections
0.18x < 50 + 0.10x
0.08 < 50
8x < 50
x < 625
Therefore, we can infer that if the number of minutes used is less than 625 per month, it is cheaper to use International Links.
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Please Help me with this problem! No links or files, I will report.
The area of the preimage is 400units²
What is dilation?Dilation is a transformation, which is used to resize a given object. We can use dilation to either make the objects larger or smaller.
A scale factor shows the relationship between the old shape and new shape.
The scale factor is expressed as ;
scale factor = dimension of the new length / dimension of old length
scale factor = 3/2 = 1.5
old length = x
therefore 1.5 = 30/x
1.5x = 30
divide both sides by 1.5
x = 30/1.5 = 20units
therefore the area of the preimage = l²
= 20²
= 400units²
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B. Constructing a parallel through a point (rhombus method) Steps: 1. Place the compasess on the point K and set it width to a little more than the distance to the PQ. The exact distance is not important. 2. Draw a wide arc from the right of K around so it crosses the PQ at two points. Label the left point J.
3. Without adjusting the opening of the compass, move the compass to J and draw an arc across the PQ Label this point E.
4. Without adjusting the span of the compass , move the compass to E and draw an arc across the large arc to the right of K. Label this point S.
5. Draw a straight line through points K and S.
6. Done. The KS is parallel to the PQ.
please paki sagot po.
The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential.
Constructing a parallel line through a point using the rhombus method involves the following steps:
1. Place the compass on point K and set its width slightly more than the distance to line PQ. The exact distance is not crucial.
2. Draw a wide arc from the right of K, crossing line PQ at two points. Label the left point J.
3. Without adjusting the compass opening, move the compass to point J and draw an arc across line PQ. Label this point E.
4. Keeping the compass width unchanged, move the compass to point E and draw an arc across the large arc to the right of K. Label this point S.
5. Draw a straight line through points K and S.
6. The line KS is now parallel to line PQ, as desired.
The rhombus method is a useful technique for constructing parallel lines, especially in geometry problems where creating accurate drawings is essential. The process relies on the compass's fixed width to ensure the angles and distances remain consistent, resulting in parallel lines.
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Yuriy and anduray will mail rectangular packages that meet the weight and height requirements of their delivery service. their packages are described in
the table.
yurly's package
package
height
4 in.
7 in.
length
21 in.
18 in.
width
9 in.
14 in.
part 1. the delivery service also requires that both the length and width of the packages to be 22 inches or less and that the length plus the width be no
more than 30 inches. write a system of inequalities to represent this situation. don't forget to define your variables and show your work
The complete system of inequalities for Anduray's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
14xy ≤ 3696
Let's define:
x: length of the package in inches
y: width of the package in inches
Then, the system of inequalities that represents the delivery service requirements is:
x ≤ 22 (length must be 22 inches or less)
y ≤ 22 (width must be 22 inches or less)
x + y ≤ 30 (length plus width must be no more than 30 inches)
We also know that Yuriy's package has a height of 7 inches, so we can add the following constraint:
4xy ≤ 840 (the product of length, width, and height must be no more than 840 cubic inches)
Therefore, the complete system of inequalities for Yuriy's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
4xy ≤ 840
Anduray's package has a height of 14 inches, so we can add the following constraint to his system of inequalities:
14xy ≤ 3696 (the product of length, width, and height must be no more than 3696 cubic inches)
Therefore, the complete system of inequalities for Anduray's package is:
x ≤ 22
y ≤ 22
x + y ≤ 30
14xy ≤ 3696
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A baker makes 20 loaves of bread
each day. The loaves are either
white or brown.
The ratio of white loaves to brown
loaves is always 7 : 3.
After how many days would the
baker have made 180 loaves of
brown bread?
Every day, a baker produces 20 loaves of bread. The loaves come in white or brown. It would take him 30 days to make 180 loaves of brown bread.
Let the ratio be x,
We have been given the ratio of 7 : 3 in which 3 part is of brown bed.
So the number of brown bread will be 3x and white bread will be 7x.
Now, we have to find out the days for 180 loaves of brown bread. This means that 3x = 180. Now we will find out the value of x to find the total loaves of bread from this equation.
3x = 180
x = 180 / 3
x = 60
So, the total amount of bread = brown bread + white bread
Total amount of bread = 3x + 7x
= 10x
= 10 × 60
= 600
We know that in 20 loaves of bread are made in one day, so
time taken to make 600 loaves of bread = 600 / 20
= 30 days
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Please help me with this
Answer:
B f(x)=1(8)^x
Step-by-step explanation:
1 is the 0 value, you can see it's exponential by the rapid growth and how it grows by a lot each time
Find the difference. Express the answer in scientific notation. (8. 64 times 10 Superscript 20 Baseline) minus (7. 83 times 10 Superscript 20 Baseline) 8. 1 times 10 Superscript 19 0. 81 times 10 Superscript 20 8. 1 times 10 Superscript 21 0. 81 times 10 Superscript 40
In scientific notation, the difference between (8.64 x 10^20) and (7.83 x 10^20) is expressed as 8.1 x 10^19.
To find the difference between (8.64 x 10^20) and (7.83 x 10^20), we subtract the second number from the first:
8.64 x 10^20 - 7.83 x 10^20 = 0.81 x 10^20
Since the difference is less than one, we express the answer in scientific notation by moving the decimal point one place to the left and increasing the exponent by one:
0.81 x 10^20 = 8.1 x 10^19
Therefore, the difference between (8.64 x 10^20) and (7.83 x 10^20) expressed in scientific notation is 8.1 x 10^19.
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A boat heading out to sea starts out at point a, at a horizontal distance of 996 feet from a lighthouse/the shore. from that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 6^{\circ} ∘. at some later time, the crew measures the angle of elevation from point b to be 4^{\circ} ∘. find the distance from point a to point b. round your answer to the nearest foot if necessary.
The distance from point A to point B is approximately 998 feet (rounded to the nearest foot).
Let's denote the distance from point A to the lighthouse as "x", and the distance from point B to the lighthouse as "y". Also, let's denote the height of the lighthouse as "h". Then we have the following diagram:
Lighthouse
|\
| \
| \ h
| \
|θ2 \
|____\
x y
A B
From the diagram, we can see that:
tan(6°) = h/x (equation 1)
and
tan(4°) = h/y (equation 2)
We need to find the value of "d", the distance from point A to point B. We can use the following equation:
d^2 = x^2 + y^2 (equation 3)
We can solve equation 1 for h:
h = x tan(6°)
Substitute this into equation 2:
x tan(6°) / y = tan(4°)
Solve for y:
y = x tan(6°) / tan(4°)
Substitute this into equation 3:
d^2 = x^2 + (x tan(6°) / tan(4°))^2
Simplify:
d^2 = x^2 (1 + tan^2(6°) / tan^2(4°))
Solve for d:
d = x sqrt(1 + tan^2(6°) / tan^2(4°))
Substitute the given values:
d = 996 sqrt(1 + tan^2(6°) / tan^2(4°))
Using a calculator, we get:
tan(6°) / tan(4°) = 0.1051
So,
d = 996 sqrt(1 + 0.1051^2) ≈ 998.38 feet
Therefore, the distance from point A to point B is approximately 998 feet (rounded to the nearest foot).
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Which relationship does not represent a direct proportion?
A. y = −
3
8
x
B.
Pounds Cost
3 $3.87
5 $6.45
8 $10.32
C. A dog groomer charges $15 per hour.
D.
The correct relationship which does not represent a direct proportion is,
⇒ A dog groomer charges $15 per hour.
Given that;
The graph is shown relation between number of minutes and Distance.
Take two points on the line are,
(2, 100) and (4, 150)
Hence, From graph we get;
The equation of line is,
⇒ y - 100 = (150 - 100)/ (4 - 2) (x - 2)
⇒ y - 100 = 25 (x - 2)
⇒ y - 100 = 25x - 50
⇒ y = 25x - 50 + 100
⇒ y = 25x + 50
Thus, The correct relationship which does not represent a direct proportion is,
⇒ A dog groomer charges $15 per hour.
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Your gross pay is $2,500 and your net pay is $1,750. How much was withheld from your pay?
a: $250
b: $500
c:750
d:4,250
$750 was withheld from my pay after deductions form the gross pay
How to calculate the amount of money that was withheld from my pay?
Gross pay is the money that an employee gets before tax and other deduction are made
Net pay is the amount of money given to am employee after deduction of tax and other mandatory expenses
The gross pay is $2,500
The net pay is $1,750
The money withheld can be calculated as follows
= 2500 - 1750
= 750
The money withheld from the gross pay is $750
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Find the absolute maximum and absolute minimum values off on each interval. (If an answer does not exist, enter DNE.) F(x) = 2x² - 16x + 850 (a) (0,4) Absolute maximum: Absolute minimum: (b) (0,4) Absolute maximum: Absolute minimum:
From the above information we get:
Absolute maximum: 850
Absolute minimum: 800
To find the absolute maximum and minimum values of the function f(x) = 2x² - 16x + 850 on the given interval (0,4), we will follow these steps:
1. Find the critical points by taking the first derivative of f(x) and setting it equal to zero.
2. Determine if the critical points are within the interval (0,4).
3. Evaluate f(x) at the critical points and endpoints of the interval.
4. Identify the absolute maximum and minimum values based on the results.
Step 1: Find the critical points
f'(x) = 4x - 16
Setting f'(x) equal to zero:
4x - 16 = 0
4x = 16
x = 4
Step 2: Determine if the critical point is within the interval (0,4)
The critical point x = 4 is within the interval (0,4).
Step 3: Evaluate f(x) at the critical points and endpoints of the interval
f(0) = 2(0)² - 16(0) + 850 = 850
f(4) = 2(4)² - 16(4) + 850 = 850 - 64 + 850 = 800
Step 4: Identify the absolute maximum and minimum values based on the results
Absolute maximum: f(0) = 850
Absolute minimum: f(4) = 800
To answer the question:
(a) Interval (0,4)
Absolute maximum: 850
Absolute minimum: 800
(b) It seems you have repeated the interval (0,4), so the answer remains the same.
Absolute maximum: 850
Absolute minimum: 800
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the circumstances of the base is 48π cm. if the volume if the cone is 8640π cm cubed, what is the height?
Answer:
h = 15 cm
Step-by-step explanation:
Given:
C (base's circumstance) = 48π cm
V (volume) = 8640π cm^3
Find: h (height) - ?
[tex]c = 2\pi \times r[/tex]
[tex]2\pi \times r = 48π[/tex]
[tex]r = 24[/tex]
We found the radius
[tex]v = \frac{1}{3} \times \pi {r}^{2} \times h[/tex]
[tex] \frac{1}{3} \times \pi \times {24}^{2} \times h = 8640π[/tex]
Multiply the whole equation by 3 to eliminate the fraction:
[tex]1728\pi \times h = 25920\pi[/tex]
[tex]h = 15[/tex]
Identify the angle or side that is common to triangle SUT and triangle SVT
A. B. SV
C. D. ST
Angle S, Angle T and side ST are common to triangle SUT and triangle SVT.
To identify the angle or side that is common to triangle SUT and triangle SVT, based on given information, we can evaluate them as follows:
A. Angle S is common to both triangles SUT and SVT, as it is the vertex where the two triangles share a point.
B. Side SV is not common to both triangles, as it is only a side of triangle SVT.
C. Side ST is common to both triangles SUT and SVT, as it connects the shared vertex S to points U and V in each respective triangle.
D. Angle T is also common to both triangles SUT and SVT, as it is the other vertex where the two triangles share a point.
Therefore, Angle S, side ST, and Angle T are all common to triangle SUT and triangle SVT.
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A large diamond with a mass of 2138. 7 grams was recently discovered in a mine. If
8
the density of the diamond is 3. 51 cm", what is the volume? Round your answer to
the nearest hundredth. (5 points)
O 1)
141. 84 cm3
2) 609. 3 cm3
3) 717. 06 cm3
O 4
8169. 8 cm3
WILL GIVE BRAINLIEST!!
The volume of the diamond is 609.3 cm³.
To find the volume of the diamond, we can use the formula:
Volume = Mass / Density
Given:
Mass = 2138.7 grams
Density = 3.51 g/cm³
Substituting these values into the formula:
Volume = 2138.7 g / 3.51 g/cm³
Calculating the division:
Volume ≈ 609.3 cm³
Therefore, the volume of the diamond is approximately 609.3 cm³.
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Bus stops A, B, C, and D are on a straight road. The distance from A to D is exactly 1 km. The distance from B to C is 2 km. The distance from B to D is 3 km, the distance from A to B is 4 km, and the distance from C to D is 5 km. What is the distance between stops A and C? AC=_ km
The distance between bus stops A and C is exactly 1 km.
To find the distance between bus stops A and C, we can use the fact that the distance from A to D is 1 km and the distance from C to D is 5 km.
This means that the total distance from A to C, passing through D, is 6 km (1 km + 5 km).
However, we need to subtract the distance between B and D (3 km) and the distance between B and C (2 km) since we don't want to double count the stretch between B and D.
Therefore, the distance between A and C is 6 km - 3 km - 2 km = 1 km.
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A track has the dimensions shown.
36.5 m
ISTAN
SAMANT
men komm
84.4 m
Ta
inside of track
outside of track
. The track has 8 lanes
• Each lane is 2.1 meters wide
36.5 m
O
TI
16. To the nearest tenth of a meter, what is
the perimeter of the outside of the
track?
Byp
*REQUIRED
ANA
1
√x
Sign out
Answer:
Step-by-step explanation:
Find a formula for the slope of the graph of fat the point (x, f(x)). Then use it to find the slope at the two given points.
The slope at the given points are -1/36 and -1/16 respectively.
Given is a function f(x) = 1/x+6 we need to find the slope of the function,
The slope of a function is given by dy/dx, therefore,
dy/dx = -1/(x+6)²
Therefore, at point (0, 1/6),
The slope = -1/(0+6)² = -1/36
At point (-2, 1/4),
The slope = -1/(-2+6)² = -1/16
Hence the slope at the given points are -1/36 and -1/16 respectively.
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Sally earns a weekly salary of $450 plus a 6. 5% commission on sales at a boutique. How much would she make in a work week if she sold $650 worth of merchandise?
To find out Sally's total earnings for the week, we need to consider her base salary and the commission on her sales. Her base salary is $450, and she earns a 6.5% commission on $650 worth of merchandise.
First, let's calculate her commission:
6.5% of $650 = 0.065 * $650 = $42.25
Now, we can add her base salary to the commission:
Total earnings = Base salary + Commission
Total earnings = $450 + $42.25
Total earnings = $492.25
So, Sally would make $492.25 in a work week if she sold $650 worth of merchandise.
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