Answers
The required probabilities are,
1. P(A and B) = 7/100.
2. P(AIB) = 16/25
3. P(AIB) = 0.495
4. P(A and B) = 0.7.
What is conditional probability?Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.
1. Given:
The probabilities are,
P(A) = 1/5, P(BIA) = 7/20.
P(A and B) = P(A ∩ B) = P(BIA) x P(A)
Now, P(A and B) = 7/20 x 1/5 = 7/100.
2. Given:
P(B) = 3/4, P(A and B) = P(A ∩ B) = 12/25
P(AIB) = P(A ∩ B) /P(B) = 12/25 x 4/3 = 16/25
3. Given:
P(B) = 0.5, P(A and B) = P(A ∩ B) = 0.2475
P(AIB) = P(A ∩ B) /P(B) = 0.2475/0.5 = 0.495
4. Given:
P(A) = 0.5, P(BIA) = 0.35.
P(A and B) = P(A ∩ B) = P(BIA) x P(A)
Now, P(A and B) = 0.35/0.5 = 0.7.
Therefore, all the required values are given above.
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Related Questions
At a bank, ECS2.60 is equivalent to US$1.00. For every US$1.00 exchanged, ECS0.10 is deducted as an exchange fee. How much EC dollars will Leon receive if he exchanges US$100.00? (A) (B) (C) (D) $ 90.90 236.34 $ $ 250.00 $ 260.00
Answers
Leon will receive ECS250.00 dollars if he exchanges US$100.00 at this bank.
How determine how much EC dollars Leon will receive if he exchanges US$100.00?If ECS2.60 is equivalent to US$1.00, then the exchange rate from US dollars to EC dollars is 1:2.60.
To find out how much ECS dollars Leon will receive for US$100.00, we first need to convert US$100.00 to EC dollars using the exchange rate:
US$100.00 * 2.60 = ECS260.00
So, Leon will receive ECS260.00 for US$100.00 before any exchange fees are deducted.
The exchange fee for every US$1.00 exchanged is ECS0.10. Therefore, the exchange fee for US$100.00 will be:
US$100.00 * ECS0.10 = ECS10.00
To find out how much Leon will receive after the exchange fee is deducted, we need to subtract the fee from the initial amount:
ECS260.00 - ECS10.00 = ECS250.00
Therefore, Leon will receive ECS250.00 if he exchanges US$100.00 at this bank.
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Felix is selling hats and T-shirts to raise money to pay for his summer camp registration, and he will use any additional money he raises as spending money while at camp. He plans to sell each hat for $8 and each T-shirt for $12. In order to pay for his summer camp registration, Felix must raise at least $288, and he wants to sell at least 32 hats and T-shirts altogether. Let h represent the number of hats Felix sells, and let t represent the number of T-shirts he sells. One of the graphs below shows the system of inequalities that represents this situation, with it's solution region shaded in. Answer the following questions. Which graph shows the system of inequalities that represents this situation with the solution region shaded in? If Felix sells 28 hats and 5 T-shirts, is it enough to cover the cost of his summer camp registration?
Answers
Felix needs to sell more hats and/or T-shirts in order to raise enough money to pay for his summer camp registration.
This situation's inequality system is as follows:
h + t ≥ 32 (Felix hopes to sell a total of at least 32 hats and t-shirts)
(Felix needs to raise at least $288.) 8h + 12t = 288
The second inequality can be rearranged as follows:
2h + 3t ≥ 72
The graph with the lines h + t = 32 solid and the region above it shaded, and 2h + 3t = 72 dashed and the region above it shaded, is the one that depicts the system of inequalities with the solution region shaded in. The offered image's option D corresponds to this graph.
We may change h = 28 and t = 5 into the inequality to see if selling 28 hats and 5 T-shirts is enough to pay for Felix's summer camp registration:
h + t ≥ 32\s28 + 5 ≥ 32\s33 ≥ 32 (Because this inequality is real, at least 32 hats and t-shirts were sold.)
8h + 12t ≥ 288\s8(28) + 12(5) ≥ 288\s224 + 60 ≥ 288\s284 ≥ 288 (Because this imbalance is untrue, Felix's summer camp registration costs cannot be covered by selling 28 caps and 5 T-shirts.)
Felix must therefore sell more hats and/or T-shirts to raise enough cash to cover the cost of his summer camp registration.
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The Jayden family eats at a restaurant that is having a 15% discount promotion. Their meal costs $78.97 before the discount, and they leave a 20% tip. If the tip applies to the cost of the meal before the discount, what is the total cost of the meal? Round your intermediate calculations and answer to the nearest cent.
Answers
Answer:
The discount is 15% of the cost of the meal before the discount, so the discounted cost is:
Discounted cost = $78.97 - 0.15($78.97) = $67.12
Now we need to calculate the tip on the cost before the discount. The tip is 20% of the cost before the discount, so the tip amount is:
Tip = 0.20($78.97) = $15.79
Adding the discounted cost and the tip, we get the total cost of the meal:
Total cost = $67.12 + $15.79 = $82.91
Therefore, the total cost of the meal, including the discount and tip, is $82.91.
PLS HURRY 100 POINTS BRAINLIEST
A box contains 4 bags of sugar. The mass of each bag is 6 kilograms. What is the total mass of the box in grams?
240,000 grams
24,000 grams
2,400 grams
240 grams
Answers
Answer:
24,000 grams
Step-by-step explanation:
<3
Write as an equation: The sides of a triangle are 7, x and (x+1). The perimeter is 30.
Answers
Answer:
8 + 2x = 30
Step-by-step explanation:
The sides of the triangle add up to the perimeter:
7 + x + x + 1 = 30
Simplify by combining like terms:
8 + 2x = 30
Micah wants to divide a block of content on a web page and set it apart with different formatting. Which tag should Micah use to accomplish this?
Answers
Micah can use the <div> tag.
What is Tag?
A tag is given as the label that has been attached to someone or something in order to add identification to the particular thing. The tag in the HTML or any other language has been used for the conversion of the HTML document into web pages. The tags are braced in the < >.
Micah can use the <div> tag to divide a block of content on a web page and set it apart with different formatting.
The <div> tag is a container tag that is used to group and separate HTML elements on a web page.
Micah can give the <div> tag a class or an ID attribute and use CSS to apply different formatting to the content within that tag.
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Evaluate the expression X to the power of 3 + X to the power of 2 X = 4.
Answers
Answer: I need to woo
Step-by-step explanation: your exciting boy come find me
Find the surface area of the rectangular prism. The figure is not to scale. Use pencil, paper, and a ruler. Draw a net for the prism that is to scale. Then draw a more accurate sketch of the prism.
Answers
the above question, we may state that Hence, the surface area rectangular prism has a surface area of 148 square centimeters.
what is surface area ?An object's surface area is a measure of how much space it takes up overall. The entire amount of space around a three-dimensional form is its surface area. The total surface area of a three-dimensional form is referred to as its surface area. By summing the areas of each face, one may get the surface area of a cuboid with six rectangular faces. Instead, you may identify the box's dimensions using the following formula: Surface (SA) equals 2lh, 2lw, and 2hw. The total amount of space occupied by the surface of a three-dimensional form is measured as surface area.
Shown above is a rectangular prism. We may apply the formula: to determine the surface area.
2lw + 2lh + 2wh = Surface Area
where the prism's length, breadth, and height are indicated by l, w, and h, respectively.
As we look at the image, we can see that it is 6 cm long, 4 cm wide, and 5 cm tall. These values can be used as substitutes in the formula:
Surface Area = (2,6,4,2,6,5,2) (5)
Area of Surface = 48 + 60 + 40
Area of Surface = 148
Hence, the rectangular prism has a surface area of 148 square centimeters.
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What is the total surface area of the rectangular prism shown?
Answers
Hence, the total surface area of the rectangular prism is 736 in².
Provide an example to help people understand what surface area is.A 3D object's surface area is calculated as the total of all of its faces. For instance, if we wanted to figure out how much paint we would need to paint a cube, we would use the cube's surface area.
To calculate the total surface area of the rectangular prism, we need to find the area of each of its six faces and add them together.
The area of the top and bottom faces, which are identical, is:
Length x Breadth = 16 in x 8 in = 128 in².
The area of the front and back faces, which are also identical, is:
Height x Breadth = 10 in x 8 in = 80 in².
The area of the left and right faces, which are also identical, is:
Height x Length = 10 in x 16 in = 160 in².
Therefore, the total surface area of the rectangular prism is:
2(Length x Breadth) + 2(Height x Breadth) + 2(Height x Length)
= 2(16 in x 8 in) + 2(10 in x 8 in) + 2(10 in x 16 in)
= 256 in² + 160 in² + 320 in²
= 736 in²
Hence, the total surface area of the rectangular prism is 736 in².
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Consider the price of a stock at the end of each day. Suppose that whether the price tomorrow will go up or down depends on the price movement in the last two days. If the stock price went up for the last two days, then it will go up tomorrow with probability 0.8. If the stock price went up today but not yesterday, then it will go up tomorrow with probability 0.6. If the price went up yesterday but not today, then it will go up tomorrow with probability 0.5. If the price went down in the last two days, then it will go up tomorrow with probability 0.35.
b) Model the price movement as a Discrete time Markov chain, and write the transition matrix. a) Draw the state transition diagram.
Answers
The probability of transitioning from the UU state to the UD state, which is 0.2
a) The state transition diagram for this Discrete time Markov chain can be represented as follows:
``
0.8 0.2
UU -------> UU <------- UD
^ | ^
| | |
| | |
| V |
| 0.4 0.5
| DD <------- DU
| ^ |
| | |
| | |
| | V
| 0.35 0.5
|-------- DD <------- DD
0.2 0.65
```
Where UU represents the state where the stock price went up for the last two days, UD represents the state where the stock price went up today but not yesterday, DU represents the state where the stock price went up yesterday but not today, and DD represents the state where the stock price went down in the last two days.
b) The transition matrix for this Discrete time Markov chain can be represented as follows:
```
| UU UD DU DD |
|-------------------|
UU | 0.8 0.2 0.0 0.0 |
UD | 0.0 0.0 0.6 0.4 |
DU | 0.0 0.5 0.0 0.5 |
DD | 0.2 0.0 0.0 0.8 |
```
Where the rows represent the current state and the columns represent the next state. Each entry in the matrix represents the probability of transitioning from the current state to the next state. For example, the entry in the first row and second column represents the probability of transitioning from the UU state to the UD state, which is 0.2.
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Answer this plsssssssssssss
Need help SOS
Answers
PLSS HELP ASAPPP , PLS SOLVE NUMBER 3
Answers
The constant of proportionality (k) for the data points on this graph is 7.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the data points on this graph as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 7/1 = 14/2 = 21/3 = 28/4 = 35/5
Constant of proportionality, k = 7.
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a bullet travels at 5*10^(6 )feet per hour. If it strikes a target in 2*10^(-4) hours, how far has it traveled?
Answers
The distance traveled by the bullet is 1000 feet.
The distance traveled by the bullet can be calculated by multiplying its speed by the time it takes to hit the target:
Distance = Speed x Time
Substituting the given values, we get:
[tex]Distance = 510^6 feet/hour * 210^{-4} hours[/tex]
Simplifying this expression, we get:
Distance = 1000 feet
Therefore, the bullet has traveled 1000 feet before striking the target.
In summary, the distance traveled by the bullet can be calculated by multiplying its speed by the time it takes to hit the target. In this case, the distance traveled is 1000 feet.
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The standard deviation and arithmetic mean of the distribution are 1.456 and 44,5 respectively then the coefficient of variation of a distribution is a. 30.56 b. 3.27 c. 44.5 d. 305.63
Answers
The coefficient of variation (CV) of a distribution is the ratio of the standard deviation to the arithmetic mean. Therefore, in this case the CV is:CV = (1.456/44.5) x 100 = 3.27
The correct answer is therefore B: 3.27
The coefficient of variation (CV) is a measure of relative variability. It is the ratio of the standard deviation to the mean (average) of a distribution. The formula for calculating the coefficient of variation is:
CV = (standard deviation / mean) × 100
In this case, the standard deviation is 1.456 and the mean is 44.5. Plugging these values into the formula gives:
CV = (1.456 / 44.5) × 100
CV = 0.0327 × 100
V = 3.27
Therefore, the correct answer is b. 3.27. The coefficient of variation of this distribution is 3.27.
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a. Use the elimination method to solve the fol 7.4x-y=-255 12.1x-y=-233 The solution, rounded to the nearest whole nun
Answers
To use the elimination method to solve the system of equations 7.4x-y=-255 and 12.1x-y=-233, we need to eliminate one of the variables. We can do this by multiplying one of the equations by a constant to make the coefficients of one of the variables the same, and then subtracting the equations.
1. Multiply the first equation by -1 to make the coefficients of y the same:
-7.4x + y = 255
2. Subtract the second equation from the first equation:
-7.4x + y = 255
-12.1x + y = -233
---------------------
4.7x = 488
3. Solve for x:
x = 488/4.7
x ≈ 103.83
4. Substitute the value of x back into one of the original equations to find y:
7.4(103.83) - y = -255
765.342 - y = -255
y = 765.342 + 255
y ≈ 1020.342
5. Round the solution to the nearest whole number:
x ≈ 104
y ≈ 1020
So the solution to the system of equations is (104, 1020).
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Working alone, it takes Stephanie seven hours to clean an attic. Shayna can clean the same attic in 12 hours. Find how long it would take them if they worked together.
Answers
The answer would take Stephanie and Shayna approximately 4.42 hours to clean the attic if they worked together.
Working alone, it takes Stephanie seven hours to clean an attic. Shayna can clean the same attic in 12 hours. To find how long it would take them if they worked together,
we can use the formula:
1/T = 1/t1 + 1/t2
Where T is the time it takes for both to complete the task together, t1 is the time it takes for the first person to complete the task alone, and t2 is the time it takes for the second person to complete the task alone.
Plugging in the given values, we get:
1/T = 1/7 + 1/12
1/T = 12/84 + 7/84
1/T = 19/84
T = 84/19
T = 4.42 hours
Therefore, it would take Stephanie and Shayna approximately 4.42 hours to clean the attic if they worked together.
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Can anyone help me with this I can't figure it out
Answers
60Answer: it would be 60
Step-by-step explanation:
it’s going up and down by 10
Describe the sequence that you’ll map triangle ABC to A’B’C.
Answers
Answer:
First we would shrink by a factor of 3
Then translate 6 units on the x axis
Then reflect across x=6
The library in Geotown has a large room with enough tables and chairs to seat 236 people. some of the tables are in the shape of a hexagon and seat six people each. The rest of the tables are octagonal and seat eight people each. if there are 35 tables in the room, how many are hexagons and how many are octagons?
Answers
The library in Georgetown has 35 tables, 5 of which are hexagons and 30 of which are octagons.
What are octagons?An octagon is a two-dimensional shape with eight sides and eight angles. It is a regular polygon, meaning that all of its sides and angles are equal. Octagons are often seen in everyday life, such as in stop signs, tiling, and in some types of architectural structures.
In order to answer this question, we must first solve a simple equation. We know that the total number of tables in the room is 35, and we know that each hexagonal table seats six people, while each octagonal table seats eight people. Therefore, we can set up an equation to represent the total number of people being seated at all of the tables: 6x + 8y = 236, where x is the number of hexagonal tables and y is the number of octagonal tables.
By solving this equation, we can determine that x = 5 and y = 30. This means that there are 5 hexagonal tables and 30 octagonal tables in the room. Therefore, the library in Georgetown has 35 tables, 5 of which are hexagons and 30 of which are octagons.
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Combining like terms in a quadratic Simplify the following expression. 12x^(2)+9-8x-6x^(2)-14x
Answers
The final simplified expression is: [tex]6x^(2) - 22x + 9[/tex]
To simplify the given expression, we need to combine like terms. This means that we need to add or subtract terms that have the same variable and exponent.
The given expression is: [tex]12x^(2)+9-8x-6x^(2)-14x[/tex]
First, let's combine the terms with the same variable and exponent:
[tex]12x^(2) - 6x^(2) = 6x^(2)[/tex]
[tex]-8x - 14x = -22x[/tex]
Now, let's substitute these simplified terms back into the expression:
[tex]6x^(2) + 9 - 22x[/tex]
This is the simplified expression. There are no more like terms to combine, so we cannot simplify it further.
The final simplified expression is: [tex]6x^(2) - 22x + 9[/tex]
Answer: [tex]6x^(2) - 22x + 9[/tex]
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For number 6, how you find the population in 2023? I just need to know how because I forgot how to do that stuff.
This is 9th grade algebra
Answers
Answer:
y=2500(0.15)^x
y=375^x
Step-by-step explanation:
Dave travel of 120 km/h it takes him 90 minutes to reach his destination It takes him. How far is his destination
Answers
Javier is saving money at a constant rate to buy a new car. After saving for 2 months, Javier has $920 . After saving for 4 months, Javier has $1,030 . Construct a function that models the relationship between the amount of money Javier has saved and the number of months he has saved for. Show or explain how you constructed the function. Respond in the space provided.
Answers
Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.
What is equation of a straight line?
The formula for a straight line is y=mx+c where c is the height at which the line intersects the y-axis, often known as the y-intercept, and m is the gradient.
After 2 months, Javier has saved a total of $920. Therefore, we can write the following equation:
2m = 920
Simplifying this equation, we get:
m = 460
This means that Javier is saving $460 each month.
After 4 months, Javier has saved a total of $1030. Using the same logic as before, we can write:
4m = 1030
Simplifying this equation, we get:
m = 257.5
This means that Javier is saving $257.5 each month.
To model the relationship between the amount of money Javier has saved and the number of months he has saved for, we can use the equation of a straight line:
y = mx + b
where y is the amount of money saved, x is the number of months, m is the monthly savings rate, and b is the starting amount saved.
Using the values we found earlier, we can write two equations:
y = 460x + b (for the first two months)
y = 257.5x + b (for the first four months)
To find the value of b, we can substitute the values of x and y for one of the points:
920 = 460(2) + b
Simplifying, we get:
b = 0
So the final equation that models the relationship between the amount of money Javier has saved and the number of months he has saved for is:
y = 460x (for the first two months)
y = 257.5x (for the first four months)
This means that Javier is saving $460 per month for the first two months, and $257.5 per month for the first four months.
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If you are solving to find a missing hypotenuse should you add or subtract
Answers
Answer:
It depends on what's given in the problem.
Step-by-step explanation:
There's a few ways to find the hypotenuse of a triangle, but we must have something given to us.
A Few Methods (Most Common to Least Common):
The Pythagorean Theorem. 2 legs of a right triangle are given. You should add the 2 legs together to find the hypotenuse.
[tex]a^2 + b^2 = c^2[/tex]
Sine, or Cosine. This is only used when there's a given angle, and/or at least one given side.
[tex]Sin \ (\theta) = \frac{opposite}{hypotenuse}[/tex]
[tex]Cosin \ (\theta)=\frac{adjacent}{hypotenuse}[/tex]
Rare, but possibly we need to find the area of the triangle. There needs to be at least 1 angle given.
This is the formula we need to find the Hypotenuse:
[tex]Area = \frac{1}{2} \times h^2 (hyp.) \times sin (angle) \times cos(angle)[/tex]
This is a lot to learn. Let me know if you have any questions.
Determine whether each statement is true or false. If false, tell why. See Example 4. 53. \( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ}+\cos 60^{\circ} \) 54. \( \sin 30^{\circ}+\sin 60^{
Answers
Both statements are false because the sum of two angles does not equal the sum of their cosines or sines.
Statement 53 is false. This is because the sum of two angles does not equal the sum of their cosines. The correct equation for the sum of two angles in terms of their cosines is:
\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)
Using this equation, we can calculate the correct value of the cosine of the sum of the two angles:
\( \cos \left(30^{\circ}+60^{\circ}\right)=\cos 30^{\circ} \cos 60^{\circ} - \sin 30^{\circ} \sin 60^{\circ} \)
\( \cos 90^{\circ}=\frac{\sqrt{3}}{2} \cdot \frac{1}{2} - \frac{1}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \cos 90^{\circ}=0 \)
Statement 54 is also false. This is because the sum of two angles does not equal the sum of their sines. The correct equation for the sum of two angles in terms of their sines is:
\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)
Using this equation, we can calculate the correct value of the sine of the sum of the two angles:
\( \sin \left(30^{\circ}+60^{\circ}\right)=\sin 30^{\circ} \cos 60^{\circ} + \cos 30^{\circ} \sin 60^{\circ} \)
\( \sin 90^{\circ}=\frac{1}{2} \cdot \frac{1}{2} + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} \)
\( \sin 90^{\circ}=1 \)
In conclusion, both statements are false because the sum of two angles does not equal the sum of their cosines or sines. The correct equations for the sum of two angles in terms of their cosines and sines are shown above.
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What are the solutions to the quadratic equation x^2-3x+4=0
Answers
Answer:
[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]
[tex]x=\frac{3}{2} + i\frac{\sqrt{7}}{2}[/tex]
Step-by-step explanation:
We can use the quadratic formula to solve the equation:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = -3, and c = 4. Substituting these values into the formula, we get:
x = (3 ± sqrt((-3)^2 - 4(1)(4))) / 2(1)
x = (3 ± sqrt(9 - 16)) / 2
x = (3 ± sqrt(-7)) / 2
Since the square root of a negative number is not a real number, the solutions to the quadratic equation are complex numbers. Therefore, the answer is:
[tex]x=\frac{3}{2}+i\frac{\sqrt{7} }{2}[/tex]
[tex]x=\frac{3}{2} - i\frac{\sqrt{7}}{2}[/tex]
Why is the interest rate of a loan one of the most important things to consider when shopping around for loans?
Responses
Interest rates vary between lenders and can drastically change the monthly payment.
Interest rates do not vary between lenders so it won't effect the monthly payment.
The interest rate effects the amount of time you have to pay back a loan.
Interest rates are not important when making financial decisions.
Answers
Answer: The correct response is "Interest rates vary between lenders and can drastically change the monthly payment."
The interest rate is one of the most important things to consider when shopping around for loans because it determines the cost of borrowing money. Different lenders offer different interest rates, and even a small difference in interest rates can have a big impact on the total cost of the loan. A higher interest rate will result in a higher monthly payment, and a longer repayment period, which can make the loan more expensive overall. Therefore, it is important to shop around and compare interest rates from different lenders to find the best deal.
Step-by-step explanation:
If the aspect ratio of a white board is 16:9 and the width is 64in, what is the height of the white board?
Answers
The height of the white board for the given aspect ratio is found as 36 in.
Explain about the aspect ratio?A proportional association among an image's height and width is known as an aspect ratio. It essentially describes the contour of a picture. Aspect ratios are expressed as a width-to-height formula, such as 3:2. A square image, for instance, has a 1:1 aspect ratio because its width and height are equal. Aspect ratio, in its most basic form, is the proportion between an image's width and height. That affects how readers compose your picture and how huge it will be, which is why it's so crucial.Aspect ratio of a white board = 16:9 .
Width = 64 in
Let the height be 'h'.
So, using proportions.
16/9 = 64/h
h = 64*9 /16
h = 36
Thus, the height of the white board for the given aspect ratio is found as 36 in.
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which equation can be used to represent the distance d for the times given in the table rebeka chose A as the the correct answer.how did she get that answer
Answers
Answer:
Step-by-step explanation:
Pls give simple working
Jesse would like to determine if the following are inverse functions. f(x)=3x-4,g(x)=4-3x
Answers
Yes, f(x) and g(x) are inverse functions.
An inverse function is a function that "undoes" the original function. In other words, if we plug the output of the original function into the inverse function, we will get the original input back.
To determine if two functions are inverses of each other, we can use the following steps:
1. Plug the first function into the second function, replacing x with f(x). In this case, we will plug f(x) = 3x - 4 into g(x) = 4 - 3x:
g(f(x)) = 4 - 3(3x - 4)
2. Simplify the expression:
g(f(x)) = 4 - 9x + 12
g(f(x)) = 16 - 9x
3. Now plug the second function into the first function, replacing x with g(x):
f(g(x)) = 3(4 - 3x) - 4
4. Simplify the expression:
f(g(x)) = 12 - 9x - 4
f(g(x)) = 8 - 9x
5. If the two simplified expressions are equal to each other, then the functions are inverses of each other. In this case, g(f(x)) = 16 - 9x and f(g(x)) = 8 - 9x are not equal to each other, so the functions are not inverses of each other.
However, if we rearrange the equation for g(x) to solve for x, we get:
g(x) = 4 - 3x
3x = 4 - g(x)
x = (4 - g(x))/3
This is the same as the equation for f(x), but with g(x) in place of x. Therefore, f(x) and g(x) are inverse functions.
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