Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.
What is a prism?A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.
According to the given information:Both Jeremy and Aksa could be right, depending on how they are counting the cubes.
If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.
However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.
Therefore, the answer depends on the shape of the prism and how the layers are counted.
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A cylinder has a height of 9 millimeters and a radius of 14 millimeters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
As a result, the cylinder's volume is roughly **5541.48 mm³**.
DEFINE THE CYLINDER'S VOLUME?The capacity of a cylinder is defined as its volume, and this definition aids in determining how much material the cylinder can hold .The volume of a cylinder—which corresponds to how much material can be transported inside of it or immersed in it—determines its density.. The formula r²πh, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.
V = r²πh, where V is the volume, r is the radius of the cylinder's base, and h is the cylinder's height, is the formula for calculating a cylinder's volume.
When we enter the specified values into the formula, we obtain:
V = π(14)²(9)
V = 1764π
Rounding to the closest hundredth using 3.14, we obtain:
V ≈ 5541.48 mm³
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Find the amount of the payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period.
$85,000; money earns 8% compounded semiannually for 4 1/2
years
The amount of payment to be made into the sinking fund is approximately $71,207.16, using the compound interest formula.
What is compound interest?
Compound interest is the interest calculated not only on the initial principal amount of a loan or investment but also on the accumulated interest from previous periods. In other words, it is interest that is added to the original amount (principal), and then interest is calculated on the new total (principal + accumulated interest) for subsequent periods.
According to the given information:
To find the amount of payment to be made into a sinking fund, we can use the formula for compound interest:
A = P(1 + r/n)ⁿt
where:
A = the accumulated amount
P = the payment made at each period
r = the annual interest rate (expressed as a decimal)
n = the number of compounding periods per year
t = the number of years
In this case, we have:
A = $85,000 (the accumulated amount)
r = 8% per year, compounded semiannually, so r = 0.08/2 = 0.04 (since there are two compounding periods in a year)
n = 2 (since the interest is compounded semiannually)
t = 4.5 years
Plugging these values into the formula, we get:
$85,000 = P(1 + 0.04/2)⁹
Now we can solve for P by dividing both sides of the equation by (1 + 0.04/2)^(2 * 4.5):
P = $85,000 / (1 + 0.04/2)⁹
P = $85,000 / (1.02)⁹
P = $85,000 / 1.193
P ≈ $71,207.16
So, the amount of payment to be made into the sinking fund is approximately $71,207.16.
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bridge is raised so that it forms a 15° angle with the ground. It is then raised some more so that it forms a 43° angle with the ground. How many degrees was the draw bridge raised from its first position to its second position?
Answer: If you minus it the answer is -0.488692191 rad
I think
Step-by-step explanation:
How do you find the second of an angle?
The whole part of the measure of an angle in decimal degrees is the whole number of degrees. Multiplying the decimal part by 60 gives the number of minutes. If this number of minutes has a decimal part, then multiplying this decimal part by 60 gives the number of seconds.
These are my opinion
During filming, an IMAX camera uses 65-mm film at a rate
of 5.6 ft/s.
a. At what rate per minute does the camera go through film?
b. How quickly does the camera use a 500-foot roll of 65-mm film? Round to the
nearest second.
Answer:
a. To find the rate per minute, we need to convert the rate from feet per second to feet per minute:
5.6 ft/s * 60 s/min = 336 ft/min
Therefore, the camera goes through film at a rate of 336 feet per minute.
b. The camera uses 500 feet of film at a rate of 336 ft/min, so we can use the formula:
time = distance/rate
where the distance is 500 feet and the rate is 336 ft/min.
time = 500 ft / 336 ft/min
time ≈ 1.49 min
To convert minutes to seconds, we can multiply by 60:
1.49 min * 60 s/min ≈ 89.4 s
Therefore, the camera uses a 500-foot roll of 65-mm film in approximately 89 seconds.
4. Assuming that the rectangles have whole number side lengths, why is it possible to draw two different rectangles that have an area of 30 square inches but not possible to draw two rectangles with an area of 7 square inches?
Answer:
hm
Step-by-step explanation:
The reason why it is possible to draw two different rectangles that have an area of 30 square inches is that there are multiple pairs of whole numbers that multiply to 30. For example, a rectangle with dimensions 5 inches by 6 inches has an area of 30 square inches, and so does a rectangle with dimensions 2 inches by 15 inches.
However, the number 7 is a prime number, which means it can only be divided evenly by 1 and itself. Therefore, the only way to get an area of 7 square inches for a rectangle is by multiplying 1 and 7, which means the dimensions of the rectangle would be 1 inch by 7 inches. Since there are no other pairs of whole numbers that multiply to 7, it is not possible to draw two different rectangles with an area of 7 square inches.
When I divide an integer by 15, the remainder is an integer from 0 to 14. When I
divide an integer by 27, the remainder is an integer from 0 to 26.
For instance, if the integer is 100 then the remainders are 10 and 19, which are
different.
How many integers from 1 to 1000 leave the same remainders after division by 15
and after division by 27?
Answer: 119
Step-by-step explanation:
We know that we must find the least common multiple of 15 and 27 in order to solve the problem because when we are finding remainders that are the same, there must be some relationship between the integer and the two dividing numbers.
Thus, we have the least common multiple 135 and its multiples which will all have a 0 remainder when divided by 15 and by 27.
We can take each of the numbers (7) and the 15 consecutive numbers after each of them, because of modulo becoming the same after 15. If we take the total of all these numbers, which will have the same remainder after division by 15 and 27, we are left with:
15 * 8 - 1 = 119
Four lines are drawn on a coordinate plane to form trapezoid WXYZ.
A coordinate grid with 4 lines. Line X W is drawn with point W at (negative 4, 1) and passes through (0, 2) with and (3, 3). Line Y X is drawn with point Y at (3, 0) and passes through (0, 3). Line Z W is drawn with point Z at (0, negative 3) and point W at (negative 4, 1). LIne Z Y is drawn with point Y at (3, 0) and point Z at (0, negative 3).
Which statements are true about the lines? Select three options.
Line WZ has the same slope as line XY.
Line YX has a greater slope than line ZY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line YZ.
Line XY has a lesser y-intercept than line XW
The three statements that are true about the lines are: Line WZ has the same slope as line XY. Line YX has a greater slope than line ZY, and Line XW has a lesser slope than line YZ.
What is slope-intercept form?A linear equation has the form y = mx + b, where m is the slope of the line and b is the y-intercept, or the y-coordinate of the line's intersection with the y-axis. The slope measures how steep a line is, or how quickly the y-coordinate changes for every unit change in the x-coordinate. A line has a positive slope if it is moving upward from left to right, and a negative slope if it is moving downward. The line's intersection point with the y-axis, or the value of y when x is equal to 0, is known as the y-intercept.
Because both lines travel through the same point (0, -3) and have a slope of 1/3, line WZ and line XY have the same slope.
Given that both lines pass through the same point (3, 0), line YX has a bigger slope than line ZY.
Because line XW passes through points (-4, 1) and (3, 3), which have a little change in y over a large change in x, as opposed to line YZ, which passes through points (0, -3) and (3, 0), which have a large change in y over a small change in x, line XW has a lower slope than line YZ.
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Much help would be greatly needed!
For a $85,000 mortgage, the borrower was charged the following closing costs.
Loan origination fee (1% of mortgage) $
Broker loan fee $1640
Lender document and underwriting fees $350
Lender tax and wire fees $210
Fee to title company $225
Title insurance fee $320
Title reconveyance fee $70
Document recording fee $40
Compute the total closing costs for this mortgage:
Answer:
hope this helps
Step-by-step explanation:
The total closing costs for this mortgage can be calculated as follows:
Loan origination fee: 1% of $85,000 = $850
Broker loan fee: $1,640
Lender document and underwriting fees: $350
Lender tax and wire fees: $210
Fee to title company: $225
Title insurance fee: $320
Title reconveyance fee: $70
Document recording fee: $40Total closing costs = $850 + $1,640 + $350 + $210 + $225 + $320 + $70 + $40
Total closing costs = $3,705
Therefore, the total closing costs for this mortgage are $3,705.
A rectangle has an area of 108 square
centimeters. Its width is 9 centimeters.
What is the perimeter of the
rectangle?
Therefore, the perimeter of the rectangle is 42 centimeters.
What is area?The concept of area is used in many areas of mathematics, science, and everyday life. It is used in geometry to calculate the area of various shapes, such as triangles, circles, and polygons. It is also used in physics to calculate the amount of surface area of an object that is exposed to air or water, and in architecture and engineering to determine the amount of material needed to construct a building or structure.
Here,
To find the perimeter of a rectangle, we need to know its length and width. We are given that the width of the rectangle is 9 centimeters, and the area of the rectangle is 108 square centimeters.
We can use the formula for the area of a rectangle:
Area of rectangle = length x width
Plugging in the values we have:
108cm² = length x 9cm
Solving for the length, we can divide both sides by 9cm:
length = 108cm² / 9cm
length = 12cm
So, the length of the rectangle is 12 centimeters.
To find the perimeter of the rectangle, we can use the formula:
Perimeter of rectangle = 2 x (length + width)
Plugging in the values we have:
Perimeter of rectangle = 2 x (12cm + 9cm)
Perimeter of rectangle = 2 x 21cm
Perimeter of rectangle = 42cm
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Is 1/8 equal to 1/5 or less than or is it grater than or
Answer: less then
Step-by-step explanation:
Im pretty sure
4. Greta's neighborhood is having a picnic to celebrate the end of the school year. She has been
asked to prepare potato salad. Greta actually has to work at 2pm when the picnic is scheduled, so
she asks Lynn, the neighbor coordinating food, if she can drop off the potato salad at the park
when she goes into work at 10am. Lynn is not sure this will work. Describe why Lynn is hesitant
and what might happen if Greta's potato salad sits out in the sun until the picnic begins at 2pm.
Then offer at least one suggestion to solve Greta and Lynn's problem.
Lynn is hesitant to allow Greta to drop off the potato salad at 10am .
How to solve Greta and Lynn's problem?Greta could make the potato salad the night before and keep it in the refrigerator to solve the problem she and Lynn were having. She could then transport the potato salad at a safe temperature in a cooler filled with ice packs on the day of the picnic.
She could ask Lynn to store the potato salad in a cooler or refrigerator until the picnic starts when she gets to the park. Along these lines, the potato salad will be protected to eat and won't represent a gamble of food contamination.
The mayonnaise in Greta's potato salad will spoil, leading to the growth of bacteria that could result in foodborne illness, if it is left outside in the sun until the picnic begins at 2 p.m. The potato salad may cause nausea, vomiting, diarrhea, and stomach cramps in those who consume it.
Because food safety guidelines state that perishable foods, like potato salad, should not be kept at room temperature for more than two hours, Lynn is hesitant to let Greta drop off the potato salad at 10 a.m.
If the potato salad is left out in the sun from 10 a.m. to 2 p.m., bacteria can grow on it, and eating it could make you sick.
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Rewrite in simplest terms: 4(0.7n-6n-0.3)-0.4n
Answer:
21.6n-1.2
Step-by-step explanation:
=2.8n-24n-1.2-0.4n
=21.6n-1.2
7.
Choose the measurement that is the most precise.
A.350 cm
B.3,575 mm
C.3 m
D.They are all of equal precision.
Answer:
To determine which measurement is the most precise, we need to look at the number of decimal places or significant figures in each measurement.
A. 350 cm has one significant figure.
B. 3,575 mm has four significant figures.
C. 3 m has one significant figure.
Therefore, the measurement that is the most precise is B. 3,575 mm, since it has the highest number of significant figures.
find four points that are 10 units away from the point (1,6) consider the fact that 3,4,5 is a Pythagorean triple
The four points that are 10 units away from (1,6) are:
(4,10)
(1,12)
(1,0)
(9,6)
What is Pythagoras' Theorem?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
To find four points that are 10 units away from the point (1,6), we can use the Pythagorean theorem to calculate the x and y coordinates of the points.
Since 3, 4, 5 is a Pythagorean triple, we can use it to simplify our calculations. Let's start by finding the coordinates of a point that is 5 units away from (1,6). We can do this by considering a right triangle with sides of length 3, 4, and 5:
Move 3 units to the right of (1,6) to get to the point (4,6).
Move 4 units up from (4,6) to get to the point (4,10).
Now we have a point that is 5 units away from (1,6). To find the other three points that are 10 units away, we can use the same idea:
Starting from (1,6), move 6 units up to get to the point (1,12).
Starting from (1,6), move 6 units down to get to the point (1,0).
Starting from (1,6), move 8 units to the right to get to the point (9,6).
Therefore, the four points that are 10 units away from (1,6) are:
(4,10)
(1,12)
(1,0)
(9,6)
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A company determines an employee's starting salary according to the number of years of experience, as detailed in the table.
Using technology, determine the line of fit, where represents the number of years of experience and y represents the salary.
A) y = - 2525x + 40000
B) y = 2525x + 40000
C) y = -2233.3x + 39940
D) y = 2233. 3x + 39940
The correct option is D) y = 2233. 3x + 39940, determines the best line of fit.
Explain about the best line of fit:The straight line that best depicts the overall picture that the collected data is showing is known as the line of best fit, also known as a trendline or a linear regression. It aids in determining whether the two things under study are related or have a correlation.
In this case, the pay would be plotted upon that y-axis of the scatter plot and the employee's years of experience will be plotted on the x-axis.We may rationally and logically conclude that the equation again for line of best fit is supplied by: by carefully examining the scatter plot that models the data in the provided table.y = 2233.3x + 39940
The employee's starting salary with seven years of experience would thus be predicted using the equation for such line of best fit as follows:
y = 2233.3(7) + 39940
y = 15,633.1 + 39940
y = 55,573.1 ≈ $55,573.
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Please answer this question ASAP!
Answer:
The third choice (the bottom one)
Step-by-step explanation:
By law of sin, an angle over the side opposite of the angle is equal to another angle over side opposite of the angle. If that doesn't make sense, refer to the picture below. The first option is not applicable because y is not opposite the angle measuring 100 degrees. Therefore, law of sin cannot be applied. The second option is not applicable because y is not opposite the angle measuring 46 degrees. The third option is applicable because the side measuring 21 unites is opposite the angle measuring 46 degrees and side y is opposite the angle measuring 34 degrees.
You can afford a $1000 per month mortgage payment. You've found a 30 year loan at 5.3% interest.
a) How big of a loan can you afford? (Round to the nearest cent, as needed.)
$
b) How much total money will you pay the loan company? (Round to the nearest cent, as needed.)
$
c) How much of that money is interest? (Round to the nearest cent, as needed.)
Answer:
a) To find out how big of a loan you can afford, we can use the formula for the monthly payment of a mortgage:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1 ]
where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (which is the annual interest rate divided by 12), and n is the number of monthly payments (which is the number of years times 12).
In this case, we know that M = $1,000, i = 0.053/12, and n = 30 x 12 = 360. We want to solve for P, the principal we can afford.
Substituting these values into the formula, we get:
$1,000 = P [ 0.004416(1 + 0.004416)^360 ] / [ (1 + 0.004416)^360 - 1 ]
Simplifying and solving for P, we get:
P = $183,928.72
Therefore, you can afford a loan of approximately $183,928.72.
b) The total money paid to the loan company will be the monthly payment multiplied by the number of payments over the life of the loan. In this case, we have:
Total money paid = $1,000 x 360 = $360,000
Therefore, the total amount of money paid to the loan company will be $360,000.
c) To find out how much of that money is interest, we can subtract the principal from the total amount paid. In this case, we have:
Interest paid = Total money paid - Principal = $360,000 - $183,928.72 = $176,071.28
Therefore, the amount of money paid in interest will be $176,071.28.
Is this statement true or false ?
Answer:
False
Step-by-step explanation:
Formula
Circumference of circle = 2πr
Its not just πr
if each square is equivalent to 1 cm what would be the perimeter of this object?
Answer:
the answer would be 12 cm
Step-by-step explanation:
you take the lines that were on the outside of the shape, and you sum them up, each being 1 cm long
A local department store can sell 100 gaming systems at a price of $180 each. Research
shows that for each $18 price increase, the store will sell 4 fewer systems, and vice versa.
a. Find a linear price equation for the gaming system. That is, express the price, p, as a
function of the quantity, q. (2 points)
b. Use your answer from (a) to find the revenue equation.
c. Use your knowledge of quadratic functions to find the price and quantity sold that will maximize revenue.
Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
What is the unit price?
In order to find the unit price of a certain item, we just need to divide the total price paid (or total cost) by the number of items bought.
According to given information
a. Let x be the number of $18 price increases from the original price of $180, and let y be the corresponding decrease in the number of gaming systems sold. Then we have the data point (x, y) = (0, 0) and the slope of the line is -4/18 = -2/9. Using the point-slope form of a linear equation, we have:
y - 0 = (-2/9)x
y = (-2/9)x
Substituting x = 18n, where n is the number of $18 price increases, we have:
y = (-2/9)(18n) = -4n
Let q be the quantity of gaming systems sold at a price of $180. Then the equation for the price of the gaming system as a function of the quantity sold is:
p(q) = 180 + 18n = 180 + 18(q - q0)/4 = 180 + (9/2)(q - q0),
where q0 is the quantity of gaming systems sold at the original price of $180.
b. The revenue equation is given by R(q) = q*p(q). Substituting the expression for p(q) found in part (a), we have:
R(q) = q*(180 + (9/2)(q - q0)) = (9/2)q^2 + (180 - 9q0/2)q
c. To find the price and quantity sold that will maximize revenue, we can differentiate the revenue equation with respect to q, set the derivative equal to zero, and solve for q:
R'(q) = 9q - 9q0/2 = 0
q = q0/2
Substituting q = q0/2 into the revenue equation, we have:
R(q0/2) = (9/2)(q0/2)^2 + (180 - 9q0/2)(q0/2)
R(q0/2) = (9/8)*q0^2 + (45/2)*q0
To find the corresponding price, we can use the expression for p(q) found in part (a):
p(q0/2) = 180 + (9/2)(q0/2 - q0)
p(q0/2) = 135
Therefore, the price that maximizes revenue is $135, and the quantity sold at that price is q0/2.
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runner a takes 45s to run 400m
runnerb takes 48 to run the same distance
which runner has a grater average speed??
Answer:
The answer the runner who took 45 sec to run 400m
Step-by-step explanation:
let the runner who took 45 sec to run 400m be x
let the runner who took 48sec to run 400m be y
Average speed=Total distance(m)/time taken(s)
A(x)=400/45≈9m/s
A(y)=400/48≈8m/s
You have a jar of marbles, each marble is numbered 1-35. 10 Marbles are Blue, 12 Marbles are Green, and 13 Marbles are Red. You draw a random marble.What is the probability that you pull out a marble that is Green or an even number.
The probability of drawing a marble that is green or even-numbered is 28/35
Calculating the probabilityThe total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.
We need to find the probability of drawing a marble that is green or an even number.
First, let's find the number of even-numbered marbles.
Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).
There are 12 green marbles, and 17 even-numbered marbles,
Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.
The probability of drawing a marble that is green or even-numbered is
28/35
So the probability of drawing a marble that is green or even-numbered is 28/35
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1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
a. How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)
A. There are 9 sample spaces.
B. The probability of choosing Chocolate, Fudge, and Rainbow is 1/9
What is meant by sample spaces?
In probability theory, a sample space is the set of all possible outcomes of a random experiment or process. It is used to define the space of events and calculate probabilities.
What is meant by probability?
Probability is a measure of the likelihood of an event occurring, expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. It is calculated by dividing the number of favourable outcomes by the total number of possible outcomes.
According to the given information
A. There are 9 possible combinations (3 ice cream flavors x 3 toppings x 1 sprinkle color), so there are 9 sample spaces.
B. The probability of choosing Chocolate, Fudge, and Rainbow is 1/9, assuming all combinations are equally likely.
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Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^,
3/4 ≤ ≤ 3/2
The area of the region bounded by the curve [tex]r = {e}^{x} [/tex] and the specified sector is 1/4 [tex](e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )[/tex].
What is area?
Area is a mathematical term that refers to the amount of space inside a two-dimensional shape or region. It is a measure of the extent or size of a surface or a planar region. In geometry, area is usually expressed in square units, such as square meters (m²) or square feet (ft²). The formula for finding the area of a shape or region depends on the type of shape or region.
The given curve is [tex]r = e^x[/tex], which is a polar equation for an exponential curve in the polar coordinate system.
The specified sector is the region enclosed by the rays emanating from the origin at angles 3/4 and 3/2 radians, as shown below:
To find the area of this region, we need to integrate the area element dA over the given sector,[tex]dA = \frac{1}{2} r^2 dθ[/tex] where θ varies from 3/4 to 3/2, and [tex]r = e^x[/tex]
.We can express r as a function of θ by solving the polar equation for x in terms of θ,
[tex]r = e^x \\ x = ln(r) \\ r = e^{(ln(r))} \\ r = r[/tex]
Therefore,
[tex]r = e^{ln(r)} = e^{(θ)}[/tex]
Substituting this into the area element,
[tex]dA = \frac{1}{2} (e^{(2θ)}) dθ[/tex]
Integrating this from θ = 3/4 to θ = 3/2, we get,
[tex]A = \int( \frac{3}{2} )( \frac{3}{4} ) \frac{1}{2} (e^{(2θ)}) dθ \\ =[ \frac{1}{4} (e^{(2θ)}]( \frac{3}{4} )^{( \frac{3}{4} )} \\ = \frac{1}{4} (e^{ \frac{3}{2} } - e^{ \frac{3}{4} }[/tex]
Therefore, the area of the region bounded by the curve [tex]r = e^x[/tex] and the specified sector is 1/4 [tex](e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )[/tex].
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Correct question is "Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^x, 3/4 ≤ x ≤ 3/2."
7. Fill in the bubbles to indicate whether each expression is linear or not linear.
5x Linear or Nonlinear
6x+1 Linear or Nonlinear
10xy Linear or Nonlinear
17 Linear or Nonlinear
4x^2 Linear or Nonlinear
5x is Linear , 6x+1 is Linear , 10xy is Nonlinear , 17 is Linear , 4x² is Nonlinear
what is Nonlinear ?
Nonlinear refers to a function, equation, or expression that does not have a constant rate of change. In other words, the value of the dependent variable does not increase or decrease at a constant rate as the independent variable changes.
In the given question,
5x: Linear. This is a linear expression because it is a first-degree polynomial with a single variable, x. It has a constant rate of change, meaning that the value of y increases or decreases at a constant rate as x increases or decreases.
6x+1: Linear. This is also a linear expression because it is a first-degree polynomial with a single variable, x. It has a constant rate of change, meaning that the value of y increases or decreases at a constant rate as x increases or decreases.
10xy: Nonlinear. This expression is not linear because it contains a product of two variables, x and y. A linear expression can only have terms that involve a single variable raised to the first power. This expression has a degree of 2, which makes it a quadratic expression.
17: Linear. This is a linear expression because it is a constant value. It has a slope of 0, which means that the value of y does not change as x changes.
4x²: Nonlinear. This expression is not linear because it contains a variable, x, raised to the power of 2. A linear expression can only have terms that involve a single variable raised to the first power. This expression has a degree of 2, which makes it a quadratic expression.
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Question 1 of 5
Which expression is equivalent to?x1/3
Answer:
[tex]\frac{?x1}{3}[/tex] is the answer as in ?x1/3 the ?x1/3 is = to ÷3.
so therefore the answer could also be [tex]\frac{?x1}{3}[/tex].
( please note that the [tex]\frac{x}{above}[/tex] symbolises ×by )
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Good luck with studies.
consider a collection of enveloped consisting of 2 red, 1 blue, 2 green envelopes, and 2 yellow envelopes. If two envelopes are selected at random, with replacement, determine the probability that at least one envelope is a yellow envelope.
Can I get a detailed answer so that I can use it to study?
Answer:
The probability of picking a yellow envelope is 2/7
Step-by-step explanation:
red envelope =2
blue " " =1
green " "=2
yellow " " =2
Total envelope =2+1+2+2=7
Probability thay at least one envelope will be yellow
P=number of yellow envelope/Total envelope
P=2/7
1/2x + 2y, when x = 7 and y=8 help me please
Answer:
39/2 or 19.5
Step-by-step explanation:
To evaluate the expression 1/2x + 2y when x = 7 and y = 8, we can substitute the values of x and y into the expression and perform the necessary calculations.
Given:
x = 7
y = 8
Plugging these values into the expression, we get:
1/2(7) + 2(8)
Now, we can follow the order of operations (PEMDAS/BODMAS) to simplify the expression:
1/2(7) + 2(8)
= 1/2 * 7 + 2 * 8 (Multiplication has higher precedence than addition)
= 7/2 + 16 (Performing the multiplications)
= 7/2 + 32/2 (Finding the common denominator for addition)
= (7 + 32)/2 (Adding the numerators)
= 39/2 (Simplifying the fraction)
So, the value of the expression 1/2x + 2y when x = 7 and y = 8 is 39/2 or 19.5.
A flag in the shape of a right triangle has one side length equal to 4.0 feet, and the length of the hypotenuse is 6.5 feet. Approximately what are the three interior
angles of this triangle?
A.10°,22°,90°
B.30°,60°,90°
C.38°,52°,90°
D.40°,65°,90°
The three interior angles of the triangle are answer (C): 38°, 52°, 90
What do you understand by the term Hypotenuse in Trigonometry ?Hypotenuse: This is the largest side of the triangle. It is also opposite the right angle of the triangle. Base: The side on which a right triangle stands is called its base. We can use trigonometric ratios to find the angles of this right triangle.
Let's call the angle between the hypotenuse and the side of the 4 legs "A" and the angle between the hypotenuse and the other leg "B". Then we have:
sin(A) = opposite/hypotenuse = 4/6.5 = 0.615
cos(A) = adjacent/hypotenic =√ (1 - sin²(A)) = 0.789
tan(A) = opposite/adjacent = 4/√(6.5² - 4²) = 0.646
We also have:
sin(B) = opposite/hypotenuse = 6.5/6.5 = 1
cos(B) = adjacent/hypotenuse = 4/6.5 = 0.615
tan(B) = opposite/adjacent = √(6.5² - 4²)/4 = 1.361
Since angle A is opposite the 4-foot side, it is the smallest angle of the triangle. Therefore, the answer must be either A or C.
To distinguish between the two, we can use the fact that the sum of the angles of a triangle is always 180 degrees. So if you add A, B and the right angle (90 degrees) you should get 180 degrees.
A + B + 90 = 180
A + B = 90
Using the values we calculated for the tangent of A and B, we can solve for their sum:
tan(A) + tan(B) = 0.646 + 1.361 = 2.007
We can then use the inverse tangent function to find the angle whose tangent is 2.007:
[tex]tan^-1(2.007)[/tex] = 63.4 degrees
Since A B = 90, we can subtract 63.4 from 90 to find the value of angle A:
A = 90 - 63.4 = 26.6 degrees
Therefore, the answer is C: 38°, 52°, 90
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A bag contains some tiles. Each tile has the number 1, 10, 100, or 1000 written on it The table shows the frequency of each number in the bag. A tile is chosen at random. Find each probability.
P(1000)
Fraction:
Percent: %
Likelihood: Impossible, unlikely, equally likely, likely, certain
P(not even)
Fraction:
Percent: %
Likelihood: impossible, unlikely, equally likely, likely, certain
Fraction: 0/4
Percent: 0%
Likelihood: Impossible
Answer:
1.fraction 1/4
percentage 25%
unlikely
2.same as number one
