When we find the area of a 3D figure, we label our answer as "units 2 (squared)".
When we find the volume of a 3D figure, what do we label our answers as? "units
Need help with this one thanks
By answering the presented question, we may conclude that For slope example, if a figure's measures are in metros, the volume will be in cubic metros (m3).
what is slope?The slope of a line determines how steep it is. The gradient is expressed mathematically as gradient overflow. The slope is computed by dividing the vertical difference (run) between two locations by the height difference (rise). The curve form of an expression is used to describe the straight line equation, which is written as y = mx + b. The y-intercept of the line is located where the inclination is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7. (0, 7). The y-intercept is placed where the slope of the path is m, b is b, and (0, b).
When we calculate the volume of a 3D figure, we call our solution "units 3 (cubed)".
The term "cubed" is used since volume is calculated by multiplying three dimensions (length, breadth, and height), resulting in a unit raised to the power of three. For example, if a figure's measures are in metres, the volume will be in cubic metros (m3).
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How do I solve tanx +secx=1
Answer:
Step-by-step explanation:
tan^2 x +1=sec^2 x
1= sec^2 x-tan^2 x
First person to answer gets brainilest.
Answer:
74 + 4 π ft^2
Step-by-step explanation:
Just a bit of a piecemeal.
2 rectangles and a half circle. We have all the dimensions.
1. Let's solve the big one first A = lw, putting in the numbers A = 4*15 = 60
2. The smaller one A = lw, putting int eh numbers A = 2 * 7 = 14
3. Now, the semi-circle. We know the diameter by deducting 12 from the total length, which is 9 + 7 = 16 in = 4 ft
The radius of the circle is half of the diameter, so the radius is 2 ft
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
Substituting the values, we get:
A = π(2)^2
A = 4π
The area of the circle is 4π square ft^2
Add: 60 + 14 + 4π = 74 + 4 π ft^2
Help me please!!!
Line A has equation y = -4x + 1 and line B contains the points (-2,1) and (1,-11). Select any statement(s) below that are true.
Line B has a slope of -5.
Line A has a slope of -4.
Line A and line B have the same slope.
Line B has a flatter slope than line A.
Line A has a flatter slope than line B.
In response to the question, we may say that Line A has a slope of -4, which is lower than that of line B.
what is slope?The slope of a line determines how steep it is. A mathematical expression for the gradient is gradient overflow. The vertical change (run) between two spots is divided by the height change (rise) between the same two locations to get the slope. The equation of a straight line, written as y = mx + b, is represented by the curve form of an expression. The inclination is m, b is b, and the line's y-intercept is located at these points (0, b). As an example, consider the y-intercept and slope of the equation y = 3x - 7. (0, 7). The y-intercept is situated when the slope of the path is m, b is b, and (0, b).
With the two provided points, we must first establish whether of the following claims is true:
Slope of line B = (Y) / (X) = (-11 - 1) / (1 - (-2)) = -12 / 3 = -4
As a result, we can identify the following claims as being true:
The slope of line B is -5. (False)
The slope of line A is -4. (Really) The slope of lines A and B is the same. (False) Line B slopes more gently than line A. (False) Line A slopes more gently than line B. (True)
The following propositions are true:
Line A has a slope of -4, which is lower than that of line B.
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please help give me an answer
Which of the following represents the intersection between 6x
-2 2-8 and 7x + 6 ≤ 13 ?
Answer:
The answer is x = 2/7
Step-by-step explanation:
To find the intersection between 6x - 2 and 2 - 8x, we need to solve the equation:
6x - 2 = 2 - 8x
Adding 8x to both sides, we get:
14x - 2 = 2
Adding 2 to both sides, we get:
14x = 4
Dividing both sides by 14, we get:
x = 4/14 = 2/7
To find the values of x that satisfy the inequality 7x + 6 ≤ 13, we need to solve the inequality:
7x + 6 ≤ 13
Subtracting 6 from both sides, we get:
7x ≤ 7
Dividing both sides by 7, we get:
x ≤ 1
Therefore, the intersection between 6x - 2 and 2 - 8x for values of x that satisfy 7x + 6 ≤ 13 is x = 2/7. Since 2/7 is less than or equal to 1, it satisfies the inequality.
So the answer is x = 2/7.
Hope this helps! Sorry if it's wrong. If you need more help, ask me! :]
Which of the following are equations?
Check all that are true.
z = 14
3x + 2y = 30
X - 2
1/3 + x
b + 5
Answer:
z = 14
3x + 2y = 30
Step-by-step explanation:
z = 14
3x + 2y = 30 are the equations because they have an equal sign, =, in them.
The others are "expressions" because they don't have the equal sign.
To increase sales, an online clothing store began giving a 50% off coupon to random customers. Customers didn't know whether they would receive the coupon until after the final sale. The website claimed that one in five customers received the coupon. Six customers each made purchases from the website. Let X = the number of customers that received the 50% off coupon. Part A: Is X a binomial random variable? Explain. (3 points) Part B: What is the mean and standard deviation of X? Provide an interpretation for each value in context. (4 points) Part C: Two of the six customers receive the coupon with their purchase. Is the store's claim accurate? Compute P(X ≥ 2) and use the result to justify your answer. (3 points)
Part a: the success, with a probability of p = 1/5.
Part b:The mean of X is μ = np = 6(1/5) = 1.2.
Part c:The probability of at least two customers receiving the coupon can be computed using the binomial distribution formula, P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - [tex](6C1)(1/5)^1(4/5)^5 - (6C0)(1/5)^0(4/5)^6[/tex]
Part A: Yes, X is a binomial random variable. A binomial random variable is the number of successes in a sequence of n independent trials, where each trial has a probability p of success. In this case, X is the number of customers that receive the 50% off coupon, which is the success, with a probability of p = 1/5. There are also a total of n = 6 independent trials, which is the number of customers that made purchases from the website.
Part B: The mean of X is μ = np = 6(1/5) = 1.2. This means that, on average, the store can expect 1.2 customers to receive the 50% off coupon. The standard deviation of X is σ = √(np(1 - p)) = √(6(1/5)(1 - 1/5)) = 0.9. This means that there is a large degree of variability in the number of customers that receive the 50% off coupon.
Part C: The store's claim is accurate. The probability of at least two customers receiving the coupon can be computed using the binomial distribution formula, P(X ≥ 2) = 1 - P(X ≤ 1) = 1 - [tex](6C1)(1/5)^1(4/5)^5 - (6C0)(1/5)^0(4/5)^6[/tex]
≈ 0.477,
which is close to the claimed probability of 1/5.
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(x+2)(2x-3)=5(x+2)...
Answer:
Step-by-step explanation:
x = 4 or x = -2
(12x^3 + 9x^2 -3) ÷ 3x
A. 12x^2 +3x-1/x
B. 4x^2+3x-1/x
C. 4x^2+6x-1/x
D. 4x^2 + 3x 1
The solution to the expression (12x³ + 9x² - 3) / 3x is (4x³ + 3x² - 1) / x
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
Given the expression:
(12x³ + 9x² - 3) / 3x
To solve, we need to factorize the numerator to get:
= 3(4x³ + 3x² - 1) / 3x
= (4x³ + 3x² - 1) / x
The solution to the expression is (4x³ + 3x² - 1) / x
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What is the duration of the compression event? Use the following information • Intake valve opens 8 degrees BTDC • Intake valve closes 50 degrees ABDC • Exhaust valve opens 50 degrees BBDC • Exhaust valve closes 8 degrees ATDC 130 180 150
The duration of the compression event is 100 degrees of crankshaft rotation by using the number of degrees of crankshaft rotation between the point where the intake valve closes (IVC) and the point where the exhaust valve opens (EVO).
To determine the duration of the compression event, we need to find the number of degrees of crankshaft rotation between the point where the intake valve closes (IVC) and the point where the exhaust valve opens (EVO).
Intake valve opens (IVO) at 8 degrees before top dead center (BTDC)
Intake valve closes (IVC) at 50 degrees after bottom dead center (ABDC)
Exhaust valve opens (EVO) at 50 degrees before bottom dead center (BBDC)
Exhaust valve closes (EVC) at 8 degrees after top dead center (ATDC)
First, we need to determine the position of the piston at each of these valve events. We know that the stroke of the engine is 180 degrees, so we can use this information to calculate the position of the piston at each event:
IVO: piston is at 8 degrees BTDC
IVC: piston is at 180 - 50 = 130 degrees ATDC
EVO: piston is at 180 + 50 = 230 degrees ATDC
EVC: piston is at 360 - 8 = 352 degrees BTDC
To find the duration of the compression event, we need to calculate the number of degrees of crankshaft rotation between IVC and EVO. We can do this by subtracting the position of the piston at IVC from the position of the piston at EVO:
Duration of compression event = EVO - IVC
= 230 - 130
= 100 degrees
Therefore, the duration of the compression event is 100 degrees of crankshaft rotation.
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1. a. List the sample space for the experiment: "Toss three
coins."
b. List the elements of the event, E: "Get exactly two
heads"
c. What is the probability of the event, E
2. If you toss two dice, what is the probability that the sum is
a. 10?
b. a divisor of 10?
The probability of getting a sum that is a divisor of 10 is:P(sum is a divisor of 10) = 4/36= 1/9.
The sample space for the experiment "Toss three coins" is given by:{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}b. The event, E: "Get exactly two heads" consists of the following elements:{HHT, HTH, THH}c. The probability of the event, E: "Get exactly two heads" is given by:P(E) = number of favorable outcomes / number of possible outcomes= 3/8For the experiment of rolling two dice, the sample space is given by the set of all possible ordered pairs {(i, j)}, where i and j are numbers from 1 to 6. Thus, the sample space contains 6*6 = 36 elements.a. For the sum to be 10, the pairs that satisfy the condition are (4, 6), (5, 5), and (6, 4). Thus, the probability of getting a sum of 10 is:P(sum = 10) = 3/36= 1/12b. For the sum to be a divisor of 10, we need the pairs (2, 8), (4, 6), (6, 4), and (8, 2). Thus, the probability of getting a sum that is a divisor of 10 is:P(sum is a divisor of 10) = 4/36= 1/9.
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Water fills a tank at a rate of 150 litres during the first hour, 125 litres during the second, 150 litres during the third and so on. Find the number of hours necessary to fill a rectangular tank 16m x 6m x 5m
Water fills a tank at a rate of 150 liters during the first hour, 125 liters during the second, 150 liters during the third, and so on. The number of hours necessary to fill a rectangular tank 16m x 6m x 5m is 103 hours.
The volume of the rectangular tank can be found by multiplying its length, width, and height:
The volume of the tank = Length x Width x Height
Volume of tank = 16m x 6m x 5m
The volume of the tank = 480 cubic meters
We need to convert this volume to liters in order to compare it to the flow rate of water. Since 1 cubic meter is equal to 1,000 liters, we have:
Volume of tank = 480 x 1,000 = 480,000 liters
Now we can add up the flow rate of water over time until it exceeds the volume of the tank. The flow rate starts at 150 liters and then alternates between 125 liters and 150 liters for each subsequent hour. We can express this pattern as:
[tex]150 + 125 + 150 + 125 + 150 + ...[/tex]
This is an arithmetic sequence with a first term of 150, a common difference of -25 (since each subsequent term is 25 less than the previous one), and an unknown number of terms. We can use the formula for the sum of an arithmetic sequence to find the number of terms:
Sum = (n/2)(first term + last term)
where n is the number of terms.
We want to find the number of terms that will give us a sum greater than or equal to 480,000 liters. We can set up an inequality:
(n/2)(150 + (150 + (n-1)(-25))) ≥ 480,000
Simplifying and solving for n, we get:
n ≥ 102.4
Since we need a whole number of terms, we can round up to 103 terms. This means it will take 103 hours to fill the tank.
Therefore, the number of hours necessary to fill the rectangular tank is 103 hours.
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Please i need this answer right now
Please write the answer with clear explanation also
Answer:
orange box = [tex]1 \frac{1}{4}[/tex]
blue box = [tex]1\frac{3}{4}[/tex]
Step-by-step explanation:
We are counting up in quarters (1/4) so we add 1/4 (or a quarter) on every time.
1/4 + 1/4 = 2/4 = 1/2 (equivalent fractions)
2/4 + 1/4 = 3/4
3/4 + 1/4 = 4/4 = 1 whole = 1
1 + 1/4 = 1 1/4 = orange box
1 1/4 + 1/4 = 1 1/2 or 1 2/4
1 2/4 + 1/4 = 1 3/4 = blue box
etc
hope this makes sense.
A cone has a radius of 2.5 inches and a height of 1.6 inches. what is the volume of the cone? use 3.14 for pi. round to the nearest tenth. responses 4.0 in³ 4.0 in³ 10.5 in³ 10.5 in³ 12.0 in³ 12.0 in³ 23.1 in³
The volume of the cone is 10.5 in³.
Given that,
The radius of the cone = 2.5 in
The height of the cone = 1.6 in
The volume of the cone = [tex]\frac{1}{3}\pi r^{2} h[/tex]
= [tex]\frac{1}{3}[/tex] × 3.14 × (2.5)²× 1.6
=[tex]\frac{1}{3}[/tex] × 3.14 × 6.25 × 1.6
= 10.5 in³
Therefore, the volume of the cone = 10.5 in³.
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If the length is 3 times longer than the width in a rectangle with an area of 36 cm, what is the width
In a rectangle having an area of 36 cm, if the length is three times more than the width of the rectangle is approximately 3.46 cm.
Let's assume that the width of the rectangle is "w" cm-
According to the problem, the length of the rectangle is three times longer than the width. Therefore, the length of the rectangle would be 3w cm.
The area of the rectangle is given as 36 cm². We know that the formula for the area of a rectangle is A = length x width.
So, we can substitute the values we have and get:-
36 = (3w) x w
Simplifying the equation, we get:-
36 = 3w²
Dividing both sides by 3, we get--
12 = w²
Taking the square root of both sides, we get--
w = √12
w ≈ 3.46
Therefore, the width of the rectangle is approximately 3.46 cm.
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Ross has a fourth of the amount needed to buy a new computer. The computer costs $213 and the additional software costs $55. Does the expression (213 + 55) ÷ 4 show how you could calculate the amount of money Ross has? Explain. Yes. Dividing the total cost by 14
is the same as multiplying by 14. No. There is no way to tell how much money Ross has from this expression. Yes. Dividing the total cost by 4 is the same as multiplying by 4. Yes. Dividing the total cost by 4 is the same as multiplying by 14
The statement "the expression (213 + 55) ÷ 4 show how you could calculate the amount of money Ross has" is true. Dividing the total cost by 4 is the same as multiplying by 4. The correct answer is (c).
The expression (213 + 55) ÷ 4 represents the calculation of the total cost of the computer and software divided by four, which is the amount of money Ross has. The total cost of the computer and software is $213 + $55 = $268. Dividing $268 by 4 gives $67, which is a fourth of the total cost. Therefore, Ross has $67.
Dividing by 4 is the same as multiplying by 1/4. So, another way to write the expression is (213 + 55) × (1/4). Both expressions represent the same calculation and give the same result.
Therefore, option (c) is the correct answer, and the expression (213 + 55) ÷ 4 shows how to calculate the amount of money Ross has.
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Complete question is:
Ross has a fourth of the amount needed to buy a new computer. The computer costs $213 and the additional software costs $55. Does the expression (213 + 55) ÷ 4 show how you could calculate the amount of money Ross has? Explain.
a) Yes. Dividing the total cost by 14 is the same as multiplying by 14.
b) No. There is no way to tell how much money Ross has from this expression.
c) Yes. Dividing the total cost by 4 is the same as multiplying by 4.
d) Yes. Dividing the total cost by 4 is the same as multiplying by 14
3 pts Suppose a college apparel clothing manufacturer would like to estimate the population mean height for college students. Assume the population standard deviation of student height is 9.48 centimeters. Find the sample size needed to obtain a 95% confidence interval with a 1.2 centimeters margin of error. We cannot find the an appropriate critical value to use since we do not know the degrees of freedom 239,75 239 240
We need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.
We need to find the sample size needed to obtain a 95% confidence interval with a 1.2 centimeters margin of error.Given that population standard deviation of student height is 9.48 centimeters.Using the formula of margin of error, we getME = z* σ/√nHere, σ = 9.48, ME = 1.2, and confidence interval = 95%.Since we do not know the degrees of freedom, we can use the Z-distribution to find the z-score.For 95% confidence interval, α/2 = 0.025The z-score for the 0.025 level of significance (two-tailed test) can be found using Z-table or calculator or Excel function= NORMSINV(0.025) = -1.96ME = z* σ/√n1.2 = -1.96 * 9.48 /√n√n = 1.96 * 9.48 /1.2= 15.42n = (15.42)^2= 238.1764≈ 239Therefore, we need a sample size of 239 to estimate the population mean height for college students with 95% confidence interval and 1.2 cm margin of error.
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The balance of a certain loan increases at a rate that is proportional at any time to the balance at that time. The loan balance is $1600 initially, and it is $1920 after one year (365 days). What is the balance of the loan after 90 days?
By answering the presented question, we may conclude that As a result, proportionality the loan debt after 90 days is roughly $1713.17.
what is proportionality?Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two remains constant at all levels. The diameter and circumference of a circle serve as an example.
Let B represent the loan balance at any moment t. (t).
k * B d(B(t))/dt (t)
where k is a proportionality constant.
This differential equation may be solved by separating the variables.
k * dt = d(B(t))/B(t).
When both sides are combined, the following results:
B(t) ln(t) = k*t + C
where C is an integration constant.
ln(B(0)) = k*0 + C
ln(1600) = C
So,
[tex]k*t + ln(B(t)) = ln(B(t)) (1600)\\= k*1 + ln(B(1)) (1600)\\ln(1920) = k + ln (1600)\\k = ln(1920) - ln (1600)\\k = ln(1.2) (1.2)[/tex]
Therefore,
[tex]ln(B(t)) = ln(1600) * 1.2 * t\\1600 * 1.2t = ln(B(t))\\B(t) = 1600 * 1.2^t\\[/tex]
To calculate the loan balance after 90 days, enter t=90/365:
[tex]B(90/365) = 1600 * 1.2^(90/365)\\B(90/365) ≈ $1713.17\\[/tex]
As a result, the loan debt after 90 days is roughly $1713.17.
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You receive two job offers: Job A:$46,000starting salary, with5%annual raises Job B:$55,000starting salary, with2%annual raises How many years will it take for your salary at job A to exceed your salary at job B? Solve by setting up equations and solving algebraically.
It will take approximately 7.78 years for your salary at job A to exceed your salary at job B.
To solve this problem, we need to set up an equation. Let x represent the number of years that it will take for your salary at job A to exceed your salary at job B. We can use this equation to solve for x:
$46,000(1.05)^x > $55,000(1.02)^x
Now, let's simplify this equation to solve for x:
(1.05)^x > (1.02)^x * (55000/46000)
Taking the natural log of both sides of the equation:
xlog(1.05) > log(1.02) + log(55000/46000)
Solving for x:
x > [log(1.02) + log(55000/46000)]/log(1.05) ~ 7.78
It will take approximately 7.78 years for your salary at job A to exceed your salary at job B.
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The expression 9+5(3+y) is simplified in several steps below.
For each step, choose the reason that best justifies it.
Step
9 + 5(3 + y)
9 + 15 + 5y
24 + 5y
5y + 24
Reason
Given expression
Choose one
Choose one
Choose one
X
S
According to the distributive property of algebraic expressions, each term in an expression's sum or difference must be multiplied by a number outside of the parenthesis. A number is used as the value outside of the parenthesis, with the total or difference.
What is the use of distributive property in the expression?By employing the distributive property of multiplication in step 2, we can reduce the expression by multiplying 5 by both 3 and y. So, our total is [tex]9 + 15 + 5y[/tex] .
In step 3, we use the commutative characteristic of addition to reorder the terms in the phrase. We now have [tex]15 + 9 + 5y,[/tex] which equals [tex]24 + 5y[/tex] .
Step 4 involves applying the commutative property of addition to rearrange the equation's terms once more. This leads to the final simplified formulation, which is [tex]5y + 24[/tex] .
Therefore, The justification offered in step 1 is provided expression because it is the first expression provided and doesn't need to be further explained.
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Convert the rate of 6 pt/d to an equivalent rate measured in qt/wk.
O A. 15 qt/wk
O B. 10 qt/wk
O C. 12 qt/wk
O D. 21 qt/wk
The equivalent rate measured in qt/wk is 5.25 qt/wk, which is closest to option C. 12 qt/wk.
To convert units of measurement, you need to use conversion factors, which are ratios that relate to the two units of measurement. The conversion factor is derived from the relationship between the two units of measurement, and it ensures that the numerical value of the quantity does not change, only the unit.
In this case, we are converting a 6 pt/d to an equivalent rate measured in qt/wk. We need to use conversion factors for both volume and time to do this.
First, we need to convert pints to quarts. Since there are 2 pints in a quart, we can use the conversion factor 2 pt/1 qt. Multiplying by this conversion factor gives:
6 pt/d x (1/8 qt/pt) x (7 d/wk) = 21/4 qt/wk = 5.25 qt/wkTherefore, the equivalent rate measured in qt/wk is 5.25 qt/wk, which is closest to option C. 12 qt/wk.
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due in 5 minute's 1/2x+8≤10
Answer:
x≤4
Step-by-step explanation:
Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.
WX=
; XZ=
; m∠W=
33
°
The answer of the given question based on the right triangle the answer is, the right triangle has side measures of WX ≈ 16.8, XY ≈ 28.5, and XZ ≈ 32.5, and angle measures of m∠W = 33°.
What is An angle?A angle is geometric figure formed by two rays that share common endpoint called vertex. The two rays are called sides or legs of angle, and angle is typically denoted by vertex letter, with small arc between two sides to indicate angle.
Let's start by labeling the sides and angles:
/|
/ |
/ |
WX/___| Z
Y
WX is opposite to angle W
XY is adjacent to angle W
XZ is the hypotenuse of the triangle
Using the given information, we know that:
m∠W = 33°
XZ = WX / sin(W) (using the sine ratio)
We can solve for XZ as follows:
XZ = WX / sin(W)
XZ = XY / cos(W) (using the complementary angle of 90° - 33° = 57°)
We don't know the length of XY, but we can find it using the Pythagorean theorem:
XY² + WX² = XZ²
XY² + WX² = (WX / sin(W))²
XY² = (WX / sin(W))² - WX²
XY = sqrt((WX / sin(W))² - WX²)
Plugging in the given values, we get:
XY = sqrt((WX / sin(33°))² - WX²)
With WX rounded to the nearest tenth, we get:
WX = 16.8
XY = 28.5
XZ = 32.5
Therefore, the right triangle has side measures of WX ≈ 16.8, XY ≈ 28.5, and XZ ≈ 32.5, and angle measures of m∠W = 33°.
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What is meant by Limacons, Cardioids etc. In Polar Form?
Limaçons, Cardioids, and other polar curves are curves described in polar form by their radial distance from the origin and the angle they make with a fixed reference line
In polar form, curves are described in terms of their radial distance from the origin and the angle they make with a fixed reference line.
Here are the definitions of some common polar curves:
Limaçons: A limaçon is a polar curve defined by the equation r = a + b cos(θ) or r = a + b sin(θ), where a and b are constants. The shape of the limaçon depends on the values of a and b. If a > b, the curve has a loop that encloses the origin; if a = b, the curve is a cardioid; and if a < b, the curve has a dimple that encloses the origin.
Cardioids: A cardioid is a special case of a limaçon where a = b. The equation of a cardioid is r = a + a cos(θ) or r = a + a sin(θ), where a is a constant. A cardioid looks like a heart-shaped curve.
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A circle with circumference of 10 has area of 100.
true
false
False. The area of a circle is equal to 7.854.
The formula for the circumference of a circle is C = 2πr,
where C is the circumference and r is the radius. We can rearrange this formula to solve for the radius:
r = C/2π.
In this case, we are given that the circumference is 10, so we can calculate the radius as:
r = 10/2π
r = 5/π
To calculate the area of a circle, we use the formula
[tex]A = \pi r^2[/tex]
Substituting the value we found for r, we get:
[tex]A = \pi (5/\pi )^2\\A = \pi (25/\pi^2)\\A = 25/\pi[/tex]
This is approximately equal to 7.9577, which is not equal to 100. Therefore, the statement "A circle with a circumference of 10 has an area of 100" is false.
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Can someone please explain how to solve this step by step really stuck
Answer:
[tex]x=\frac{b-a}{ab}[/tex]
Step-by-step explanation:
[tex]\frac{1}{ax} -\frac{1}{bx} =1\\\frac{1}{ax} *\frac{b}{b} -\frac{1}{bx} *\frac{a}{a} =1\\\frac{b}{abx} -\frac{a}{abx}=1\\\frac{b-a}{abx}=1\\b-a=abx\\x=\frac{b-a}{ab}[/tex]
In rhombus ABCD, if DB = 2x - 4 and PB = 2x - 9, find PD.
The answer of the given question based on the rhombus ABCD finding PD the answer is PD = -5.
What is Diagonal?In geometry, diagonal is straight line segment that connects two non-adjacent vertices of polygon. A polygon is any two-dimensional shape with straight sides, like triangle, rectangle, square, or any other n-sided figure.
In a rectangle, diagonal is line segment that connects two opposite corners of rectangle.
Let's label the points as shown in the diagram:
A
/ \
/ \
/ \
D-------B
P
We know that DB = 2x - 4 and PB = 2x - 9. We need to find PD.
Since diagonals of rhombus bisect with each other, we have:
PD = PB - BD
Substituting the given values, we get:
PD = (2x - 9) - (2x - 4)
Simplifying, we get:
PD = 2x - 9 - 2x + 4
PD = -5
Therefore, PD = -5.
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Complete question is
In rhombus ABCD, if DB = 2x - 4 and PB = 2x - 9, find PD.
the diagram is also provided in the answer. you can refer there.
Can someone pretty please help me
Answer: [tex]\frac{10}{3}[/tex]
Step-by-step explanation:
7+3(5-4)=10
2+1=3
Therefore, 10/3.
Given:-
[tex] \sf \: u = 2 [/tex][tex] \: [/tex]
[tex] \sf \: v = 5[/tex][tex] \: [/tex]
Solution:-
[tex] \sf \: \frac{7 + 3 ( v - 2u ) }{u + 1} [/tex][tex] \: [/tex]
put the given values in the equation
[tex] \sf \: \frac{7 + 3 ( 5 - 2 ( 2 )}{2 + 1} [/tex][tex] \: [/tex]
[tex] \sf \: \frac{7 + 3 ( 5 - 4 )}{3} [/tex][tex] \: [/tex]
[tex] \sf \: \frac{7 + 15 - 12 }{3} [/tex][tex] \: [/tex]
[tex] \sf \: \frac{7 + 3}{3} [/tex][tex] \: [/tex]
[tex] \boxed{ \sf \color{hotpink} {\frac{10}{3} }}[/tex][tex] \: [/tex]
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hope it helps ⸙
A bicycle manufacturer makes two styles of bicycles: a road bike and a touring bike. The road bike
sells for $400 and the touring bike sells for $200. To meet the minimum requirements of a supply
contract, the manufacturer needs to produce at least 60 road bikes and at least 120 touring bikes.
Each bicycle is produced using the same frames and tires. The touring bike takes one hour of labor
for assembly and painting, while the road bike takes 3 hours of labor. There are 400 frames and 600
hours of labor available for production. How many of each model should be produced to maximize
revenue? What is the maximum revenue?
The manufacturer can maximize their revenue by producing 60 road bikes and 120 touring bikes. The maximum revenue of the manufacturer is $24,000.
What is revenue?Revenue is the total amount of money earned by a business from its activities. It is calculated by subtracting the cost of goods sold from the total sales of goods and services. Revenue indicates how well a company is doing financially and serves as a key indicator of a company's performance. Revenue is an important factor in calculating the company's profitability.
This satisfies the minimum requirements of the supply contract, while also utilizing all of the available resources, frames and labor.
The total cost of producing 60 road bikes and 120 touring bikes is 400 frames and 900 hours of labor. This leaves no frames or labor unused. The total revenue from selling these bicycles is $24,000 (60 x $400 + 120 x $200). Therefore, the maximum revenue of the manufacturer is $24,000.
To maximize their revenue, the manufacturer should produce 60 road bikes and 120 touring bikes. This will ensure that all of their resources are used and they will get the highest return on their investment. This will also help them meet the minimum requirements of the supply contract.
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