The expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).
To express the function g(x) in terms of f(x), we need to understand the relationship between the two functions.
The given expression g(x) = f(x) + indicates that the function g(x) is obtained by adding a certain value or expression to the function f(x). expression for g(x) in terms of f(x).
In general, if we have the function g(x) = f(x) + c, where c is a constant value, then g(x) can be expressed in terms of f(x) as:
g(x) = f(x) + c
In this case, g(x) is obtained by adding the constant value c to the corresponding values of f(x).
It's important to note that without additional information about the specific relationship between f(x) and g(x), such as a functional equation or given values, we cannot provide a more precise expression for g(x) in terms of f(x).
Therefore, the expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).
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Answer: 3
Step-by-step explanation: just 3
Edge 2020
The pie charts below show information about the animals that were treated in a veterinary surgery during one weekend. 300 animals were treated on Saturday. 125 animals were treated on Sunday. What percentage of all the animals treated during the weekend were tortoises? Give your answer to the nearest 1%. 22% 19% Saturday 3% 56% Animals treated Sunday 4% 48% 28% 12% 8% Key Tortoise Rabbit Cat Dog Hamster Not drawn accurately
X^2+y^2-6x+2y-38>0
Find the center and radius of the circle
I've been stuck on this problem for a minute, anyone able to show me what to do?
Use the following duration times (seconds) of 24 eruptions of the Old Faithful geyser in Yellowstone National
Park. The duration times are sorted from lowest to highest.
110 120 178 213 234 234 235 237 240 243 245 245
250 250 251 252 254 255 255 259 260 266 269 273
Describe how to calculate the limits to determine outliers for this data set? Identify any outliers.
Answer:
1. 01= 234, 03= 255 (since the data is
already sorted)
2. I0R = 255 - 234= 21
3. Lower limit = 234- 1.5 * 21= 203.5
Upper limit = 255+ 1.5 * 21= 285.5
4. Outliers: 110, 120, 178 (below the
lower limit), and 273 (above the upper
limit)
Suppose that an object is thrown upward from ground level with an initial velocity of 160ft/sec. Its height after t seconds is a function h given by h(t)=-16t^2 +160t.
a) Find an equivalent expression for h(t) by factoring out a common factor with a negative coefficient.
b) Check your factoring by evaluating both expressions for h(t) at t=1.
The factored expression is
a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.
b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.
a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:
h(t) = [tex]-16(t^2 - 10t)[/tex]
Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:
h(t) = -16t(t - 10)
Therefore, the factored expression for h(t) is -16t(t - 10).
b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.
Using the original expression:
h(1) = [tex]-16(1)^2 + 160(1)[/tex]
h(1) = -16 + 160
h(1) = 144
Using the factored expression:
h(1) = -16(1)(1 - 10)
h(1) = -16(1)(-9)
h(1) = 144
Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.
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Vinay buys some fruits. He buys 7 fruits more than the place value of 2 in the number 37,523. Find out the number of fruits that vinay buys and write the same in number names.
Vinay buys "two thousand seven" fruits.
To find the number of fruits that Vinay buys, we need to determine the place value of 2 in the number 37,523 and add 7 to it.
In the number 37,523, the digit 2 is in the thousands place.
The place value of 2 in the thousands place is 2,000.
Adding 7 to the place value of 2, we get:
2,000 + 7 = 2,007.
Therefore, Vinay buys 2,007 fruits.
In number names, we can write 2,007 as "two thousand seven."
So, Vinay buys "two thousand seven" fruits.
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What is the value of x in equation 2/3(1/2x+12)=1/2(1/3x+14)-3
Answer:
x=-24
Step-by-step explanation:
2/3*1/2x = 2/6x
2/3*12=8
1/2*1/3x=1/6x
1/2*14=7
2/6x+8=1/6x+7-3
2/6x+8=1/6x+4
Takeaway 1/6x both sides to make x on one side
1/6x+8=4
take away 8 both sides to make x on its own
1/6x=-4
divide 1/6 both sides
x=-24
Hope this helps, (brainliest pleasee thanks)
What type of association does the following scatter plot represent?
Graph shows 0 to 10 on x and y axes at increments of 1. Dots are made at the ordered pairs 0, 10 and 1, 9 and 2,8 and 3,7 and 4,6 and 5,5 and 6,4.5 and 7,4 and 8,3.8 and 9,3.8 and 10,3.8
Positive linear association
Negative linear association
Positive nonlinear association
Negative nonlinear association
The data points form a straight line, suggesting a negative linear association.
Based on the given scatter plot, the association can be described as a negative linear association. A linear association refers to a relationship between two variables where the data points tend to cluster around a straight line. In this case, as the x-values increase, the corresponding y-values consistently decrease.
The scatter plot displays a clear negative slope, indicating that as the x-values increase, the y-values decrease in a linear fashion. This pattern suggests an inverse relationship between the two variables: as one variable increases, the other decreases proportionally.
The dots are arranged in a downward trend, with a clear linear pattern. This is characteristic of a negative linear association. The relationship between the variables can be described by a negative slope or a negative correlation coefficient.
It's worth noting that the scatter plot does not exhibit any curvature or nonlinear patterns. If there were a curvature present, indicating a non-linear relationship, it could be further classified as either positive or negative based on the direction of the curve.
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Purchasing a Car
Now you have to decide how to save enough money to purchase a used car in three years. You have the
$1000 that you saved up and you plan to continue working. According to your estimates, you can save an
additional $60 per month to put towards the car purchase. After conducting some research at the banks,
you have decided on two options (see below). You need to figure out which option will yield the most
money after the three years.
Option #1-CD for 3 years
Interest rate of 3% compounded monthly.
No money can be added to the CD.
However you can save your money on the side.
Option # 2-CD for 1 year
Interest rate of 2% compounded quarterly.
You can add money at the end of each year.
You will renew it each year for 3 years.
Work Shown:
Answer:
Step-by-step explanation:
To determine which option will yield the most money after three years, let's calculate the final amount for each option.
Option #1 - CD for 3 years:
Principal (initial investment) = $1000
Interest rate = 3% per year (compounded monthly)
No additional money can be added
To calculate the final amount, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Final amount
P = Principal (initial investment)
r = Interest rate (as a decimal)
n = Number of times the interest is compounded per year
t = Number of years
For Option #1:
P = $1000
r = 3% = 0.03 (as a decimal)
n = 12 (compounded monthly)
t = 3 years
A = $1000 * (1 + 0.03/12)^(12*3)
Calculating the final amount for Option #1, we get:
A = $1000 * (1 + 0.0025)^(36)
A ≈ $1000 * (1.0025)^(36)
A ≈ $1000 * 1.0916768
A ≈ $1091.68
Option #2 - CD for 1 year:
Principal (initial investment) = $1000
Interest rate = 2% per year (compounded quarterly)
Money can be added at the end of each year
To calculate the final amount, we need to consider the annual additions and compounding at the end of each year.
First Year:
P = $1000
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1000 * (1 + 0.02/4)^(4*1)
A ≈ $1000 * (1.005)^(4)
A ≈ $1000 * 1.0202
A ≈ $1020.20
At the end of the first year, the total amount is $1020.20.
Second Year:
Now we add an additional $60 to the previous amount:
P = $1020.20 + $60 = $1080.20
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1080.20 * (1 + 0.02/4)^(4*1)
A ≈ $1080.20 * (1.005)^(4)
A ≈ $1080.20 * 1.0202
A ≈ $1101.59
At the end of the second year, the total amount is $1101.59.
Third Year:
Again, we add $60 to the previous amount:
P = $1101.59 + $60 = $1161.59
r = 2% = 0.02 (as a decimal)
n = 4 (compounded quarterly)
t = 1 year
A = $1161.59 * (1 + 0.02/4)^(4*1)
A ≈ $1161.59 * (1.005)^(4)
A ≈ $1161.59 * 1.0202
A ≈ $1185.39
At the end of the third year, the total amount is $1185.39.
Comparing the final amounts:
Option #1: $1091.68
Option #2: $1185.39
Therefore, Option #2 - CD for 1 year with an interest rate of 2% compounded quarterly and the ability to add money at the end of each year will yield the most money after three years.
Find the slope of the slope of a line passing through (-4,7)(-4,1)
Answer:
m = undefined
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-4,7) (-4,1)
We see the y decrease by 6 and the x stay the same, so the slope is
m = undefined
[tex]\pmb{Question}[/tex]
Find the slope of a line passing through (-4,7) (-4,1).
[tex]\pmb{Answer}[/tex]
Not Defined
[tex]\pmb{Formula}[/tex]
[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\pmb{Where}[/tex]
m = slope(x₁,y₁) and (x₂, y₂) are two points on the line[tex]\pmb{Plug\:in\:the\:data}[/tex]
[tex]\sf{m=\dfrac{1-7}{-4-(-4)}}[/tex]
[tex]\sf{m=\dfrac{-6}{-4+4}}[/tex]
[tex]\sf{m=-\dfrac{6}{0}}[/tex]
[tex]\sf{Slope=Not\;De fined}[/tex]
∴ the slope is undefined
[tex]\rule{350}{3}[/tex]
[tex]\frak{-star-}[/tex]
I need help please!!
Answer:
25,
-7
Step-by-step explanation:
r ° q= r(q(x))= (-x+2) ^2
So, using perfect square trinomial,
[tex](-x+2)^{2} =x^{2} -4x+4[/tex]
Thus q(-3)=25
q(r(x))= (-x^2)+2=-7
Where will the hand of a clock stop if it
(a) starts at 12 and makes 1/2 of a revolution,clockwise?
(b) starts at 2 and makes 1/2 of a revolution,clockwise?
(c) starts at 5 and 1/4 of a revolution,clockwise?
(d) starts at 5 and makes 3/4 of a revolution,clockwise?
(a) Starting at 12 and making 1/2 revolution clockwise, the hand stops at 6.
(b) Starting at 2 and making 1/2 revolution clockwise, the hand stops at 8.
(c) Starting at 5 and making 1/4 revolution clockwise, the hand stops at 8.
(d) Starting at 5 and making 3/4 revolution clockwise, the hand stops at 11.
To determine where the hand of a clock will stop, we need to consider the fractions of a revolution made by the hand starting from different positions.
(a) If the hand starts at 12 and makes 1/2 of a revolution clockwise, it will stop at 6.
This is because a half revolution corresponds to the hand moving from 12 to 6 on the clock face.
(b) If the hand starts at 2 and makes 1/2 of a revolution clockwise, it will stop at 8.
Again, a half revolution corresponds to the hand moving from 2 to 8 on the clock face.
(c) If the hand starts at 5 and makes 1/4 of a revolution clockwise, it will stop at 8.
A quarter revolution corresponds to the hand moving from 5 to 8 on the clock face.
(d) If the hand starts at 5 and makes 3/4 of a revolution clockwise, it will stop at 11.
A three-quarter revolution corresponds to the hand moving from 5 to 11 on the clock face.
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step 3: Describe how to convert from vertex form to standard form. (Daredevil Danny)
To convert the vertex form back to standard form, simply square the binomial, distribute a, and add the constants.
Example :
[tex]y=3(x+1)^2+5[/tex]
[tex]y=3(x^2+2x+1)+5[/tex]
[tex]y=3x^2+6x+3+5[/tex]
[tex]y=3x^2+6x+8[/tex] , This is the original standard form of the equation.
The vertex form of a quadratic equation is written as [tex]y = a(x - h)^2 + k[/tex] , where (h, k) represents the coordinates of the vertex.
To convert from vertex form to standard form, expand the equation using the distributive property:
[tex]y = a(x - h)^2 + k[/tex]
[tex]y = a(x^2 - 2hx + h^2) + k[/tex]
[tex]y = ax^2 - 2ahx + ah^2 + k[/tex]
Next, combine like terms by grouping the x^2 and x terms:
[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]
[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]
Finally, rearrange the terms in standard form:
[tex]y = ax^2 - (2ahx) + (ah^2 + k)[/tex]
[tex]y = ax^2 - 2ahx + ah^2 + k[/tex]
The resulting equation is in standard form, which is written as y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = a, b = -2ah, and c = ah^2 + k.
By converting from vertex form to standard form, we express the quadratic equation in a different but equivalent format, allowing for different types of analysis and calculations.
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If mZA = (4x - 2)° and mZB= (6x-20), what is the value of x?
To find the value of x, we can set the two angle measures equal to each other and solve for x.
Given:
mZA = (4x - 2)°
mZB = (6x - 20)°
Setting them equal to each other:
4x - 2 = 6x - 20
Now, we can solve for x:
4x - 6x = -20 + 2
-2x = -18
Dividing both sides by -2:
x = -18 / -2
x = 9
Therefore, the value of x is 9.
Answer:
The answer is 9.
Step-by-step explanation:
We need to use the fact that the sum of the angles in a triangle is 180 degrees. Let A, B, and C be the three angles in the triangle. Then we have:
mZA + mZB + mZC = 180°
Substituting the given values, we get:
(4x - 2)° + (6x - 20)° + mZC = 180°
Simplifying the left side, we get:
10x - 22 + mZC = 180°
Next, we use the fact that angles opposite congruent sides of a triangle are congruent. Since we know that segment AC and segment BC are congruent, we have:
mZA = mZB
Substituting the given values and simplifying, we get
4x - 2 = 6x - 20
Solving for x, we get:
x = 9
Therefore, the value of x is 9.
Deepak wrote out the steps to his solution of the equation StartFraction 5 Over 2 minus 3 x minus 5 plus 4 x equals negative StartFraction 7 Over 4 EndFraction – 3x – 5 + 4x = –.
The solution to the given equation is x = -1/4.To solve the equation, let's break down the steps as outlined by Deepak:
Combine like terms: Starting with the left side of the equation, combine the x terms and the constant terms separately. On the left side, we have -3x and 4x, which can be combined to give x. Similarly, we have -5 and 5, which cancel each other out, leaving us with zero.
Simplify both sides: Now, the equation becomes x = -7/4 - 3x.
Move all the x terms to one side: To isolate the x term on one side, we can add 3x to both sides of the equation. This gives us 4x + 3x = -7/4.
Combine like terms: On the left side, we have 4x and 3x, which can be added to give 7x. The equation now becomes 7x = -7/4.
Solve for x: To solve for x, we divide both sides of the equation by 7. This yields x = -1/4.
Therefore, the solution to the given equation is x = -1/4.
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Solve the following questions:
1. name the properties of multiplication used
Answer:
a) Commutative Property of Multiplication
b) Associative Property of Multiplication
c) Distributive Property of Multiplication over Addition
d) Inverse Property of Multiplication
e) Zero Property of Multiplication
Step-by-step explanation:
The Commutative Property of Multiplication states that the order of factors in a multiplication operation can be rearranged without changing the end result.
a × b = b × aThe Associative Property of Multiplication states that the grouping of factors in a multiplication operation by parentheses in a different way does not affect their product.
(a × b) × c = a × (b × c) = (a × c) × bThe Distributive Property of Multiplication over Addition states that multiplying a number by the sum of two other numbers is equivalent to multiplying the number separately by each of the two numbers and then adding the results.
a(b + c) = ab + acThe Inverse Property of Multiplication states that if a number is multiplied by its reciprocal (multiplicative inverse), the product is always equal to 1.
a × 1/a = 1The Zero Property of Multiplication states that the product of any number and zero is always zero.
a × 0 = 0how to write a decimal as a mixed number
Answer:
Here's an example:
convert 2.5 into a mixed number.
Make the denominator less than the original.
The easy way for this is to do 25/10
when you put it through a calculator it ends up being 2.5
(essentially the mixed number and the decimal are the SAME numbers.)
Hope this clarified. :)
To convert a decimal to a mixed number, follow these steps:
Step 1: Identify the whole number part of the decimal. This is the part of the decimal before the decimal point.
Step 2: Identify the decimal part. This is the part of the decimal after the decimal point.
Step 3: Express the decimal part as a fraction by using the place value of the last digit.
Step 4: Simplify the fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
Step 5: Combine the whole number part, the fraction, and simplify if necessary.
Here's an example:
Let's say we have the decimal 2.75.
Step 1: The whole number part is 2.
Step 2: The decimal part is 0.75.
Step 3: To express 0.75 as a fraction, we write it as 75/100. Since 75 and 100 have a common factor of 25, we can simplify it to 3/4.
Step 4: The fraction 3/4 is already in its simplest form.
Step 5: Combining the whole number part and the fraction, we have 2 3/4.
So, the decimal 2.75 can be written as the mixed number 2 3/4.
Remember to always simplify the fraction part if possible.
A sample of size n = 10 is drawn from a population. The data is shown below.
115.6
109.3
126
104.9
131.9
113.7
119.8
98.6
131.9
131.9
What is the range of this data set?
What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, reporting 2 more decimal places than the original data.
Answer:
first, arrange the numbers from least to greatest order. (Actually this is a longer step, if you also want to find the median. But since you are only asking for range and standard deviation, I won't do that here.) So, just find the lowest number and the highest number. Subtract the lowest from the highest. That is your range.
Your problem:
lowest: 98.6
highest: 131.9
subtract: 131.9 - 98.6 = 33.3 ← this is your range
Now, standard deviation.
Standard deviation is the amount of variety you have in your data sample.
Step 1: Find the mean
Add up all your numbers and divide by how many numbers you have.
You have 10 numbers in your sample.
115.6 + 109.3 + 126 + 104.9 + 131.9 + 113.7 + 119.8 + 98.6 + 131.9 + 131.9
total = 1,183.6
now divide this by 10. (n is the variable used here, so n = 10. This is because you have ten numbers. )
so n = 10
and 1,183.6/10 = 118.3
Now subtract each number by 118.3.
115.6 - 118.3 = -2.7
109.3 - 118.3 = -9
126 - 118.3 = 7.7
104.9 - 118.3 = -13.4
131.9 -118.3 = 13.6
113.7 - 118.3 = -4.6
119.8 - 118.3 = 1.5
98.6 - 118.3 = -19.7
131.9 - 118.3 = 13.6
131.9 - 118.3 = 13.6
now square all these numbers
7.29
81
59.29
179.56
184.96
21.16
0.75
388.09
184.96
184.96
Find the sum of these squares now. (We're almost done!)
sum = 1,292.02
remember our n?
it was n=10
now the formula for this is,
sum of squares ÷ n-1
substitute all this in.
1,292.02 ÷ 9 = 143.55
Remember. This is the VARIANCE. NOT the standard deviation.
The last step to find the standard deviation is, to find the square root of what we got. (143.55)
√143.55
= 11.9812353286 this is the number, but rounded two more decimal places is..
11.98 is the standard deviation.
Hope this helped!
Devaughn's age is three times Sydney's age. The sum of their ages is 80 . What is Sydney's age?
[tex]\qquad\displaystyle \rm \dashrightarrow \: let \: \: Sydney's \: \: age \: \: be \: \: 'y'[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: Devaughn's \: \: age \: \: will \: \: be \: \: 3y[/tex]
Sum up ;
[tex]\qquad\displaystyle \tt \dashrightarrow \: 3y + y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 4y = 80[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 80 \div 4[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: y = 20[/tex]
So, Sydney's age is 20 years, n that of Devaughn is 20 × 3 = 60 years
Answer:
Sydney= 20, Devaughn= 60
Step-by-step explanation:
Let Sydney's age be 'x'
Devaughn's age = 3 times x = 3x
We Know That
The sum of their ages is 80.
So,
3x + x = 80
4x = 80
If we shift the 4 to the 80 side
x = 80/4
x = 20
So, Sydney's age is 20
Therefore, Devaughn's age =
3x = 3 times x
= 3 times 20
= 60
Simplify the f(x) and g(x) to get it
Answer:
(fg)(x)= (x²+6)(x²-x+9)
multiply the terms:
(fg)(x)= x²(x²-x+9) +6(x²-x+9)
add the like terms:
(fg)(x)= (x⁴-x³+9x²)+(6x²-6x+54)
and you get your final answer:
(fg)(x)= x⁴-x³+15x²-6x+54
What is the place value of the 6- digit in the number 205.876?
Answer:
thousandths place value
Step-by-step explanation:
Given the calculator output below, determine the following: (round all answers to four decimal places)
LinReg
y=ax+b
a=.1186440678
b=3.677966102
r2=.0353407862
r. 1879914523
a.) What is the value of the correlation coefficient?
b.) What is the value of the slope of the regression line?
c.) What is the value of the coefficient of determination?
d.) What is the value of the y-intercept of the regression line?
Answer:
a) r = .1880
b) a = .1186
c) r² = .0353
d) b = 3.6780
Rotate point (-3, 2) about the origin 180 degrees clockwise. Where will the new point be?
Answer: the answer is (3,-2)
Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)
therefore
(-3,2) becomes (3,-2)
I'm pretty sure
In a class of 34, girls 21 play tennis and 18 play netball. If all the girl play at least one of the Games, how many of them play both games.
Solution:
Formula: Total = Group 1 + Group 2 - Both + Neither
where:
- Total = total number of girls in the class (34)
- Group 1 = number of girls playing tennis (21)
- Group 2 = number of girls playing netball (18)
- Both = number of girls playing both games (what we want to find)
- Neither = number of girls playing neither game (0, since all the girls play at least one game)
Plugging in the values, we get:
34 = 21 + 18 - Both + 0
Simplifying:
34 = 39 - Both
Both = 39 - 34
Both = 5
30+((-2×(25- (13-3)))
Hello,
Answer:
[tex]30+((-2\times(25- (13-3)))[/tex]
[tex]=30+((-2\times(25- 10))[/tex]
[tex]=30+(-2\times 15)[/tex]
[tex]=30+(-30)[/tex]
[tex]=30-30[/tex]
[tex]=\boxed{0}[/tex]
Select the sentence that contains no errors in subject-verb agreement.
Group of answer choices
Those people whose long lives are about to end feels reassured by this belief.
Those people whose long lives are about to end feel reassured by this belief.
A person whose long life is about to end feel reassured by this belief.
A person whose long life are about to end feels reassured by this belief.
The sentence that contains no errors in subject-verb agreement is: "Those people whose long lives are about to end feel reassured by this belief."
This sentence correctly matches the plural subject "Those people whose long lives are about to end" with the plural verb "feel." The verb "feel" agrees in number with the subject "people."
The other sentences have subject-verb agreement errors:
"Those people whose long lives are about to end feels reassured by this belief."
The verb "feels" does not agree with the plural subject "Those people." It should be "feel."
"A person whose long life is about to end feel reassured by this belief."
The verb "feel" does not agree with the singular subject "A person." It should be "feels."
"A person whose long life are about to end feels reassured by this belief."
The verb "are" does not agree with the singular subject "A person." It should be "is."
Therefore, the sentence with no errors in subject-verb agreement is: "Those people whose long lives are about to end feel reassured by this belief."
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5. A person observes that from point A, the angle of elevation to the top of a cliff at D is 30°. Another person at point B, notes that the angle of elevation to the top of the
cliff is 45°. If the height of the cliff is 80.0 m, find the distance between A and B. Show the steps of your solution.
Answer:
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.
In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.
AB = AC - BC = (80√3 - 80) meters
= 80(√3 - 1) meters
= about 58.56 meters
The distance between points A and B is approximately 138.6 meters.
To find the distance between points A and B, we can use the concept of trigonometry and the given information.
Let's denote the distance between points A and B as x.
From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:
tan(30°) = opposite/adjacent
tan(30°) = 80.0/x
Simplifying the equation, we have:
x = 80.0 / tan(30°)
Using a calculator, we can find the value of tan(30°) ≈ 0.5774.
Substituting the value, we get:
x = 80.0 / 0.5774
Calculating the value, we find:
x ≈ 138.6 meters
In light of this, the separation between positions A and B is roughly 138.6 metres.
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a house is covers by a rectangle of ground 15.7m by 12.3m on the plan of the house the length of the rectangle is 78.5cm what is the scale of the plan in form 1:n ? find width if the house on the plan
The width of the house on the plan is 0.615 meters.
To find the scale of the plan in the form 1:n, we can compare the measurements on the plan to the actual measurements of the house.
Length of the rectangle on the plan = 78.5 cm
Actual length of the house = 15.7 m
We need to convert the actual length of the house to the same unit as the length on the plan, which is centimeters.
1 meter = 100 centimeters
So, the actual length of the house in centimeters = 15.7 m [tex]\times[/tex] 100 cm/m = 1570 cm
Now, we can find the scale of the plan by dividing the length on the plan by the actual length of the house:
Scale = Length on the plan / Actual length of the house
= 78.5 cm / 1570 cm
Simplifying this fraction, we get:
Scale = 1/20
Therefore, the scale of the plan is 1:20.
To find the width of the house on the plan, we can use the same scale.
Width of the house in actual measurements = 12.3 m.
Width of the house on the plan = (Width of the house in actual measurements) / Scale
= 12.3 m / 20
= 0.615 m.
So, the width of the house on the plan is 0.615 meters.
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13. Tonia and Trinny are twins. Their friends give them identical cakes for their birthday. Tonia eats ⅛ of her cake and Trinny eats ⅙ of her cake. How much cake is left?
Answer:
If Tonia eats 1/8 of the cake, then the fraction of the cake left is:
1 - 1/8 = 7/8
If Trinny eats 1/6 of the cake, then the fraction of the cake left is:
1 - 1/6 = 5/6
Since Tonia and Trinny have identical cakes, the amount of cake left is the same for both of them. Therefore, the amount of cake left is:
(7/8 + 5/6) / 2 = 41/48
So there is 41/48 of the cake left.
A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres
Answer:
2 Litres
Step-by-step explanation:
A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres
find Volume ( Volume = L x W x h)20 * 10 * 10 = 2000cm^3
Convert cubic centimeters to litres1000 cm^3 = 1 Litres
2000 cm^3 = 2 Litres
PLEASE HELP ME
How are conditional probability and independent events related?
Select the correct phrase or notation from each drop-down menu to complete the explanation.
The notation P(A|B) reads the probability of Event
choose... (A occurring given that Event B has occurred) or (B occurring given that Event A had occurred)
. If two events are independent, then the probability of one event occurring
Choose... (affects the probability of the other event occurring) or (Does not affect the probability of the other event occurring)
. Events A and B are independent if
Choose... P(A|B)= P(A), P(B|A)= P(B), P(A|B)= P(B|A)
.
Conditional probability, denoted as P(A|B), represents the probability of event A occurring given that event B has occurred. If events A and B are independent, P(A|B) = P(A) and P(B|A) = P(B).
The notation P(A|B) reads the probability of Event (A occurring given that Event B has occurred). If two events are independent, then the probability of one event occurring (does not affect the probability of the other event occurring). Events A and B are independent if (P(A|B) = P(A), P(B|A) = P(B), P(A|B) = P(B|A)).
To understand the relationship between conditional probability and independent events, let's consider two events A and B. The conditional probability P(A|B) represents the probability of event A occurring given that event B has already occurred. It measures the likelihood of event A happening under the condition that event B has already taken place.
On the other hand, if two events A and B are independent, it means that the occurrence or non-occurrence of one event has no effect on the probability of the other event happening. In other words, the probability of event A happening is not influenced by the occurrence or non-occurrence of event B, and vice versa.
Mathematically, if events A and B are independent, it implies that P(A|B) = P(A) and P(B|A) = P(B). This means that the probability of event A occurring is the same whether or not event B has occurred, and the probability of event B occurring is the same whether or not event A has occurred.
Therefore, the concepts of conditional probability and independent events are related in the sense that if two events are independent, the conditional probabilities P(A|B) and P(B|A) become equal to the unconditional probabilities P(A) and P(B) respectively.
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