The value of the probabilities are
a. P(X < 4) = 0
b. P(X > 3.5) ≈ 0.796875
c. P(4 < X < 5) ≈ 0.5625
d. P(X < 4.5) ≈ 0.703125
e. P(X < 3.5 or X > 4.5) = 0
a. P(X < 4):
To calculate P(X < 4), we need to find the area under the curve of the function f(x) = x/8 for values of x less than 4. However, the given function is only defined for the range 3 < x < 5. Therefore, we cannot directly calculate P(X < 4) using this function. The probability of X being less than 4 is zero since the function does not cover that range.
b. P(X > 3.5):
To calculate P(X > 3.5), we need to find the area under the curve of the function f(x) = x/8 for values of x greater than 3.5. Since the function is defined for 3 < x < 5, we can calculate this probability by integrating the function over the range 3.5 to 5.
Integrating f(x) from 3.5 to 5:
∫[3.5, 5] (x/8) dx = [x²/16] evaluated from 3.5 to 5
= [(5²/16) - (3.5²/16)]
= (25/16) - (12.25/16)
= 12.75/16
= 0.796875
Therefore, P(X > 3.5) ≈ 0.796875.
c. P(4 < X < 5):
To calculate P(4 < X < 5), we need to find the area under the curve of the function f(x) = x/8 for values of x between 4 and 5. We can calculate this probability by integrating the function over the range 4 to 5.
Integrating f(x) from 4 to 5:
∫[4, 5] (x/8) dx = [x²/16] evaluated from 4 to 5
= [(5²/16) - (4²/16)]
= (25/16) - (16/16)
= 9/16
= 0.5625
Therefore, P(4 < X < 5) ≈ 0.5625.
d. P(X < 4.5):
To calculate P(X < 4.5), we need to find the area under the curve of the function f(x) = x/8 for values of x less than 4.5. We can calculate this probability by integrating the function over the range 3 to 4.5.
Integrating f(x) from 3 to 4.5:
∫[3, 4.5] (x/8) dx = [x²/16] evaluated from 3 to 4.5
= [(4.5²/16) - (3²/16)]
= (20.25/16) - (9/16)
= 11.25/16
= 0.703125
Therefore, P(X < 4.5) ≈ 0.703125.
e. P(X < 3.5 or X > 4.5):
To calculate P(X < 3.5 or X > 4.5), we can calculate the sum of probabilities P(X < 3.5) and P(X > 4.5). However, as mentioned earlier, the function f(x) = x/8 is not defined for values less than 3 or greater than 5. Therefore, the probability of X being less than 3.5 or greater than 4.5 is zero.
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18. If the expansion, in ascending powers of x, as far as the term in x², of (2-x)(1+ ax)^6 is (1 + bx²+....) find the value of a and of b.
The value of a = 1/3 and b = 2.
We can expand the given expression using the binomial theorem:
Binomial theorem statement that for any positive integer n the nth power of the sum of two numbers a and b may be expressed as the sum of n + 1 terms of the form in the sequence of terms, the index r takes on the successive values 0, 1, 2,…, n.
Equation.
(2-x)(1+ax)⁶ = (2-x) × [1 + 6a x + 15a² x² + ...]
Multiplying this out gives:
(2-x)(1+ax)⁶ = 2 + (6a-2x) x + (15a² - 12ax + x²) x² + ...
Comparing the coefficient of x and x² with the given expansion we get:
6a - 2 = 0 (coefficient of x)
15a² - 12a + 1 = b (coefficient of x²)
From the first equation, we get:
6a = 2
a = 1/3
Substituting this value of a into the second equation, we get:
15(1/3)² - 12(1/3) + 1 = b
5 - 4 + 1 = b
b = 2
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Sandals are on sale for 75% off. The original price of one pair of sandals is $30. What is the new cost of the sandals after discount?
Answer:$7.50
Step-by-step explanation:The original cost of the sandals is $30 and the discount if is 75%.That means only 25% of the original cost of the sandals remain so we do 30x.25=$7.50
Find the measures for the following:
A=
B=
Answer:
a is 90
b is 90
Step-by-step explanation:
I'm not 100 percent sure about A but I think it is right
Answer:
a=5 b=7.07
Step-by-step explanation:
a(sin45)=5sin45
a=5sin45/sin45
a=5
bsin45=5sin90/45
b=7.07
Cho sells kakigori, a Japanese frozen dessert flavored with sweet syrup, at a street stand.
The scatter plot shows the daily high temperature and the number of servings of kakigori
Cho sells each day for 12 days. Based on a line of best fit for the data, about how many
servings of kakigori will Cho sell on a day when the high temperature is 29° Celsius?
Number of Servings Sold
115
110
105
100
95
90
85
80
75
70
65
60
55
50
0
18 19 20 21 22 23 24 25 26 27 28 29 30
Temperature (°C)
94
101
88
111
We can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.
Based on the line of best fit for the data, we can estimate the number of servings of kakigori Cho will sell on a day when the high temperature is 29° Celsius.
From the scatter plot, we can see that the line of best fit is increasing as the temperature increases.
By estimating the value on the line of best fit for the temperature of 29° Celsius, we can approximate the number of servings sold. Based on the scatter plot, it appears that the number of servings sold is around 100 when the temperature is 29° Celsius.
Therefore, we can estimate that Cho will sell around 100 servings of kakigori on a day when the high temperature is 29° Celsius.
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in the diagram, points B and C are points of tendency. Solve for x
The value of the variable x is 7
What is point of tangency?Point of tangency is described as the point where tangent meets the circle.
It is perpendicular to the radius of the circle, with which it intersects
From the information given, we have that;
BD = 46
CD = x² - 3
Since tangent lines are equal
We have that;
46 = x² - 3
collect the like terms, we get;;
x² = 46 + 3
Add the values
x² = 49
Find the square root of both sides, we have;
x = √49
Find the value
x = 7
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What is the value of a + c? Explain or show your reasoning
Answer:
a + c = 90° because BC is a tangent to circle A, meaning that angle B is a right angle.
Can you help me please
The perimeter of the tree house floor is 27.62 meters and area of the tree house floor is 30 square meters.
To find the perimeter of the tree house floor, we need to add up the lengths of all four sides of the rectangular floor.
We can use the distance formula to calculate the length of each side:
Length of side AB =√(6-0)² + (4-4)²) = √(36) = 6 meters
Length of side BC =√(6-0)² + (-1-4)²) = √61 = 7.81 meters
Length of side CD = √(0-6)² + (-1-4)² = √61= 7.81 meters
Length of side DA = √(0-6)²+ (4-4)²) =√36= 6 meters
Therefore, the perimeter of the tree house floor is:
Perimeter = AB + BC + CD + DA
Perimeter = 6 + 7.81 + 7.81 + 6
Perimeter = 27.62 meters
To find the area of the tree house floor, we can use the formula for the area of a rectangle:
Area = base x height
The base of the rectangle is the length of side AB, which is 6 meters.
The height of the rectangle is the distance between points B and C, which is 4-(-1) = 5 meters. Therefore, the area of the tree house floor is:
Area = base x height
Area = 6 x 5
Area = 30 square meters
Hence, the area of the tree house floor is 30 square meters.
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If 1/64 = 4^2s-1. 16^2s+2, what is the value of s? a. -1
b. 0
c. 1
d.no solution
Answer:
a ) -1
Step-by-step explanation:
[tex]\frac{1}{64} = 4^{2s-1} . 16^{2s+2}\\ 4^{-3} = 4^{2s-1+4s+4}\\ 4^{-3} = 4^{6s+3}\\ 6s + 3 = -3\\6s = -6\\s = -1[/tex]
Fourteen years ago, your parents set aside $7,500 to help fund your college education. Today, that fund is valued at $26,180. What rate of interest is being earned on this account?
Select one:
a. 7. 99 percent
b. 9. 34 percent
c. 8. 51 percent
d. 8. 36 percent
The interest rate being earned on the college education fund set aside by your parents 14 years ago is 8.51 percent. This rate of interest has resulted in the value of the fund increasing from $7,500 to $26,180 over the period.
The calculation of the interest rate is based on the concept of compound interest, where the interest earned is added to the initial principal amount, and subsequent interest is calculated on the new balance. Using the formula for compound interest, the rate can be determined as follows:
$26,180 = $7,500(1 + r/100)^14
Solving for the interest rate, r, gives a value of 8.51 percent. This means that the fund has been growing at a rate of 8.51 percent per year for the past 14 years. It is worth noting that the actual rate of return may vary due to factors such as fees, taxes, and market fluctuations, but the calculated rate provides a good estimate of the average growth rate of the fund.
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Why is f(x) = cos^2x + sin^2x a straight line
Answer:
The function f(x) = cos^2x + sin^2x is not a straight line, but rather a constant function that always evaluates to 1 for any value of x.To see why this is the case, recall the trigonometric identity that states that the square of the cosine of an angle added to the square of the sine of the same angle equals 1:cos^2x + sin^2x = 1Since this identity holds for all values of x, it follows that f(x) = 1 for all x. Therefore, the graph of this function is a horizontal line at y = 1, not a straight line.
Step-by-step explanation:
What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y-4=(x-6) and passes through the point (-2,-2)?
0 y=-x-10
Oy=-3x+10
Oy=2x-1
O y = 2x+1
Answer:
y = (3/2)x + 1
Step-by-step explanation:
straight line equation format is y -y1 = m(x - x1)
where y1 is y-coordinate of a point, x1 is x-coordinate of the same point, m is the slope (gradient).
slope of y - 4 = -2/3 (x - 6) is -2/3, since that's the number before x.
this means that slope of perpendicular line = -(1/ (-2/3)) = 3/2.
it passes through (-2, -2)
equation is y - -2 = 3/2 (x - - 2)
y + 2 = 3/2 (x +2) = (3/2) x + 3
subtract 2 from both sides
y = (3/2)x + 1
if the probability of me shopping on saturday is inversely correlated with the probability i shop on sunday, which of the above numbers is the true probability closer to?
the above numbers (Saturday or Sunday) the true probability is closer to. Inverse correlation implies that as the probability of shopping on Saturday increases, the probability of shopping on Sunday decreases, and vice versa.
If the probability of shopping on Saturday is inversely correlated with the probability of shopping on Sunday, we can infer that as the likelihood of shopping on one day increases, the likelihood of shopping on the other day decreases.
Without specific numbers or additional information, it is impossible to determine which probability is closer to the true probability.
Let's consider two scenarios to illustrate this point.
In Scenario A, the probability of shopping on Saturday is high (e.g., 80%), suggesting a low probability of shopping on Sunday (e.g., 20%).
In Scenario B, the probability of shopping on Saturday is low (e.g., 20%), indicating a high probability of shopping on Sunday (e.g., 80%).
Both scenarios exhibit an inverse correlation between the two probabilities.
In Scenario A, the true probability is closer to 80% for shopping on Saturday, while in Scenario B, the true probability is closer to 80% for shopping on Sunday.
Thus, without specific values or additional information, it is not possible to determine which probability is closer to the true probability.
The inverse correlation only tells us about the relationship between the two probabilities, not their actual values.
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Bookwork code: M47 allowed
This distance-time graph shows part of the journey of a bee travelling away from
its hive.
Calculate the average speed of the bee for this part of the journey,
If your answer is a decimal, give it to 1 d.p.
The average speed for this part of the journey is 6 m/s.
Velocity is given by the change in the distance divided by the change in the time, hence the following equation is built to model the relationship between these three variables:
v = d/t.
The parameters for this problem are given as follows:
Change in distance of 90 - 30 = 60 m.
Change in time of 10 - 0 = 10 s.
Hence the average speed for this part of the journey is given as follows:
60/10 = 6 m/s.
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Find the measure of the missing angles.
PLEASEE ANSWER FAST!!!
I've already tried x = 52 and y = 90 but it won't work
Answer:
x= 52° and y= 142°
Step-by-step explanation:
x combined with angle next to it make a right angle, so you can find x by subtracting 38 from 90. y would be 90 plus 52 because the other angle is the same as x.
Answer:
x = 52° and y = 142°
Step-by-step explanation:
38 + x + the right angle are on straight line.
angles on straight line add up to 180.
so x = 180 - 90 - 38 = 52.
y is the big angle, not the 90.
again, angles on straight line:
y = 180 - 38 = 142
HELP PLEASE!!!!!!!!!!!!
Answer:
Anything you want
Step-by-step explanation:
This is a problem where you have your own choice about whether you agree or disagree with the choice.
Great make greatest 5 digit number 4 2 and 0
To create the greatest 5-digit number using the digits 4, 2, and 0, we need to place the highest value digit in the leftmost position. Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.
By arranging the digits in this order, you ensure that you have the largest possible value while still using only the given digits 4, 2, and 0. In this case, the digit 4 is the highest value digit. So we place it in the ten-thousands place. This gives us 40,000. Now we need to fill in the remaining four digits. Since we want to create the greatest possible number, we need to use the next highest digit, which is 2, in the thousands place. This gives us 42,000. We can then use the remaining digit, which is 0, in the hundreds, tens, and ones places. to create the greatest 5-digit number, we need to start with the highest value digit and place it in the leftmost position. Then, we fill in the remaining digits with the next highest value digits in descending order. This ensures that we create the greatest possible number.
The greatest 5-digit number using the digits 4, 2, and 0, you can repeat the digits as needed. Place the largest digit (4) in the leftmost position to maximize the value, and then fill in the remaining positions with the next largest digit (2), followed by the smallest digit (0).
Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.
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how many cards would you need to draw to ensure that you have at least two of the same denomination?
To ensure that you have at least two cards with the same denomination, you would need to draw five cards.
This problem is a variation of the pigeonhole principle, also known as the birthday paradox. There are 13 denominations in a standard deck of cards (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King), and drawing five cards creates five pigeonholes. Since there are more pigeonholes than there are denominations, it is guaranteed that at least two of the cards will have the same denomination. To see this, note that drawing six cards will also guarantee two cards with the same denomination, since there would be six pigeonholes and only 13 denominations.
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Help me pls need this done
Answer:
B
Step-by-step explanation:
The positive 9 shows that it's moving up 9 units, the negative in front of the square root reflects the equation over the x-axis, and the positive 3 shows that it has been moved to the left 3 units.
Outside of equation: positive numbers translate up, negative translate down. (ex: [tex]x^{2}+3, x^{2}-3[/tex]. The three would move the equation up or down.)
Inside of equation: positive numbers translate left, negative translate right. (ex: [tex](x-3)^{2},(x+3)^{2}[/tex]. The 3 would move left or right.)
help pleeeeaseeeee 20 points
Answer:
54
Step-by-step explanation:
686779496080807
In 2010, the population of a city was 246,000. From 2010 to 2015, the population grew by 7%. From 2015 to 2020, it fell by 3%. To the nearest 100 people, what was the population in 2020?
The population of the city in 2020 is approximately 255 100
How to determine the population in 2020To find the population in 2020 we first need to find the population in 2015 after the 7% growth from 2010.
Population in 2015 = 246 000 + 0.07 x 246 000 = 263,220
we need to find the population in 2020 after the 3% decrease from 2015
Population in 2020 = 263 220 - 0.03 x 263,220 = 255 027.6
Rounding to the nearest 100 people the population in 2020 is approximately 255 100
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Which improper fraction is equal to the decimal 2.8?
Answer: 14/5
Step-by-step explanation:
2.8 = 28/10
this can be simplified to 14/5
Answer:
14/5
Step-by-step explanation:
the height of a cylinder is decreasing at a constant rate of 2 feet per second, and the volume is decreasing at a rate of 264 cubic feet per second. at the instant when the radius of the cylinder is 11 feet and the volume is 26 cubic feet, what is the rate of change of the radius?
the rate of change of the radius at the instant when the radius is 11 feet and the volume is 26 cubic feet is -10 feet per second.
What is Volume?
Volume is the amount of three-dimensional space enclosed by a closed surface, such as the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using an SI-derived unit, the cubic meter
To find the rate of change of the radius at the instant when the radius of the cylinder is 11 feet and the volume is 26 cubic feet, we can use the related rates of change between the height, radius, and volume of the cylinder.
Let's denote the height of the cylinder as h, the radius as r, and the volume as V. We are given that the height is decreasing at a constant rate of 2 feet per second, and the volume is decreasing at a rate of 264 cubic feet per second.
We know the formula for the volume of a cylinder is V = πr^2h.
Differentiating both sides of the equation with respect to time (t), we have:
dV/dt = d(πr^2h)/dt
Using the product rule, we can rewrite this as:
dV/dt = π(2rh(dr/dt) + r^2(dh/dt))
Since we are given the values of dV/dt (rate of change of volume) and dh/dt (rate of change of height), and we want to find the rate of change of the radius, we can substitute these values into the equation along with the known values of r (radius) and V (volume) at the given instant.
dV/dt = -264 (volume is decreasing at a rate of 264 cubic feet per second)
dh/dt = -2 (height is decreasing at a rate of 2 feet per second)
r = 11 (radius is 11 feet)
V = 26 (volume is 26 cubic feet)
Plugging in these values, we have:
-264 = π(2(11)(dr/dt) + 11^2(-2))
Simplifying further:
-264 = π(22(dr/dt) - 22)
Dividing both sides by π(22), we get:
-12 = dr/dt - 2
Adding 2 to both sides, we have:
dr/dt = -12 + 2 = -10
Therefore, the rate of change of the radius at the instant when the radius is 11 feet and the volume is 26 cubic feet is -10 feet per second. Note that the negative sign indicates that the radius is decreasing.
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Calculate the perimeter and area of each of the following figures. All curves are semicircles or quadrants.
The perimeters and areas of each figures are
Area = 4.48 m²; Perimeter = 11.312 metersArea = 3400 cm²; Perimeter = 393 centimetersArea = 98.125 m²; Perimeter = 39.25 metersArea = 12.46 cm²; Perimeter = 9.03 centimetersArea = 392.5 cm²; Perimeter = 54.95 centimetersCalculating the perimeters and areas of each figuresGiven that all curves are semicircles or quadrants., we have
Figure 1
The area is calculated as
Area = 1.6 * 2.8
Area = 4.48 m²
The perimeter is calculated as
Perimeter = 2 * (1.6 + 2.8) + 3.14 * 1.6/2
Perimeter = 11.312 meters
Figure 2
The area is calculated as
Area = 50 * 68
Area = 3400 cm²
The perimeter is calculated as
Perimeter = 2 * (50 + 68) + 3.14 * 50
Perimeter = 393 centimeters
Figure 3
The area is calculated as
Area = 3.14 * 5² + 2 * 3.14 * (5/2)² * 1/2
Area = 98.125 m²
The perimeter is calculated as
Perimeter = 2 * 3.14 * 5 + 2 * 1/2 * 3.14 * 5/2
Perimeter = 39.25 meters
Figure 4
The area is calculated as
Area = 3.14 * (4.6/2)²/2 + 3.14 * (2.3)²/4
Area = 12.46 cm²
The perimeter is calculated as
Perimeter = 3.14 * (4.6/2) + 3.14 * (2.3)/4
Perimeter = 9.03 centimeters
Figure 5
The area is calculated as
Area = 3.14 * (15)²/2 + 2 * 3.14 * (5)²/2 - 3.14 * (5)²/2
Area = 392.5 cm²
The perimeter is calculated as
Perimeter = 3.14 * (15) + 2 * 3.14 * (5)/2 - 3.14 * (5)/2
Perimeter = 54.95 centimeters
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3. Find the measure of Arc BED. *
O 180 degrees
O142 degrees
O218 degrees
O 72 degrees
The measure of arc BED is:
180 degrees
How to find the measure of Arc BED?The arc of a circle is the segment or part of the circumference of a circle. The measure of an arc is the angle at which the arc is subtended.
You will notice that AD is the diameter of the circle.
Since the measure of arc CD is 90°.
Thus, the measure of arc AB is:
90 - 52 = 38°
Arc ED = arc AB (vertically opposite angles are equal)
Therefore, the measure of Arc BED will be:
Arc BED = Arc BC + arc CD + arc ED
Arc BED = 52° + 90° + 38°
Arc BED = 180°
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use the area and circumstance formulas to find the radius or diameter
The radius and diameter of each measure to their approximation is as follows;
7) 14 km 8) 5 yards 9) 23 inches 10) 20 feet 11) 17.5 mm 12. 22.5 cm
13) 95feet² 14) 92.2 mm 15) 119.6 m 16)227 inches²
How do we find the radius and diameter of a circle using area?For each problem, we use the formulas;
Area of a circle: A = πr²
Circumference of a circle: C = 2πr or C = πd
a) Find the radius of a circle with an area of 615.75 square kilometers.
A = πr²
∴ r = √(A/π)
√(615.75/π)
= 14 km
b) Find the diameter of a circle with a circumference of 15.71 yards.
C = πd
∴ d = C/π
15.71/π = 5 yards
c) Find the diameter of a circle with an area of 415.48 square inches.
A = πr²
∴ r = √(A/π)
√(415.48/π) = 11.5 inches,
∴ d = 2r = 23 inches
d) Find the radius of a circle with a circumference of 125.66 feet.
C = 2πr
∴ r = C/(2π)
125.66/(2π) = 20 feet
e) Find the diameter of a circle with an area of 240.25 square millimeters.
sqrt(240.25/π) = 8.75 mm,
∴ d = 2r = 17.5 mm
f) Find the radius of a circle with a circumference of 45π centimeters.
45π/(2π) = 22.5 cm
g) Find the area of a circle with a circumference of 11π feet.
11π/(2π) = 5.5 feet,
A = πr² = π×(5.5)² = 95 feet²
h) Find the circumference of a circle with an area of 676 square millimeters.
A = πr²
∴ r = √A/π) =√(676/π) = 14.67 mm,
∴ C = 2πr = 2π×14.67 = 92.2 mm
i. Find the circumference of a circle with an area of 1,134.11 square meters.
√(1,134.11/π) = 19.03 m,
C = 2πr = 2π×19.03 = 119.6 m
j. Find the area of a circle with a circumference of 53.41 inches.
C = 2πr
∴ r = C/(2π) = 53.41/(2π) = 8.5 inches,
∴ A = πr² = π×(8.5)² = 227inches²
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Grant is going to drain his hot tub. The volume, in gallons, after the pool has been drained can be modeled by 45t^2 − 108t + 63, where t is the time in seconds.
Choose the correct expression to solve for the amount of time it takes to drain the hot tub.
A) (9t - 9)(5t - 7)
B) (9t + 9)(5t + 7)
C) 450(0)^2 - 108(0) + 63
D) 9(5t^2 -12t + 7)
I know that the correct answer is A, but I don't understand what the correct process is.
The correct expression to solve for the amount of time it takes to drain the hot tub is: A) (9t - 9)(5t - 7)
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.By using the sum-product pattern, we have the following:
45t² − 108t + 63
45t² − 63t - 45t + 63
By writing the common factor from the two pairs, we have the following:
(45t² − 63t) - (45t + 63)
9t(5t - 7) - 9(5t - 7)
By rewriting in factored form, we have the following:
(9t - 9)(5t - 7)
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Calcular el ángulo de elevación del Sol en el momento en que un árbol de 32.5m de altura proyecta una sombra de 75 m.
The angle of elevation of the Sun is approximately 23.85 degrees.
This problem can be solved using the tangent trigonometric ratio.
If we call "x" the angle of elevation of the Sun, then we can write:
tan(x) = height of the tree / length of the shadow
tan(x) = 32.5 / 75
To find the value of x, we can take the inverse tangent (tan⁻¹) of both sides of the equation:
x = tan⁻¹ (32.5 / 75)
x ≈ 23.85 degrees
Therefore, the angle of elevation of the Sun is approximately 23.85 degrees.
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need help with #3, 4, 5
1. It will cost Dave $646.62 to refill his truck's fuel tank.
2. The cost of concrete for Greg's driveway will be $9,720.
3. Total cost of the topsoil needed from suppliers is $726.90 from Holland Growers and $919.55 from Night Growers.
How much will it cost Dave to refill his truck?A refill refers to filling something again with more of same thing such as fuel, water etc.
We need to convert the fuel capacity of Dave's truck from gallons to liters.
1 US gallon = 3.78541 liters
So, 180 US gallons will give us:
= 180 * 3.78541 liters
= 681.37 liters
We will calculate total cost of refilling Dave's truck which is:
= 681.37 liters * 0.949 dollars/liter
= $646.62013
= $646.62.
2. To get volume of concrete needed, we will convert thickness of the driveway from inches to meters. 4 inches is equal to 0.1 meters.
The volume of the driveway is:
V = l x w x h
V = 20m x 36m x 0.1m
V = 72 cubic meters
The cost of the concrete for the driveway is:
= Volume x Price per cubic meter
= 72 cubic meters x $135/cubic meter
= $9,720.
3. To get total cost of the topsoil, we have to calculate volume of soil required for each planter box:
Volume = Length x Width x Depth
Volume = 44" x 24" x 18"
Volume = (44/36) yards x (24/36) yards x (18/36) yards
Volume = 1.22 yards³
Since she needs to build 35 planter boxes, the total volume of soil required is:
= 1.22 yards³ x 35
= 42.7 yards³
The cost from Holland Growers will be:
= Total Volume x $17/yd
= 42.7 yards³ x $17/yd
= $726.90
The cost from Night Growers will be:
= Total Volume x $21.50/yd²
= 42.7 yards³ x $21.50/yd²
= $919.55.
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an angle in standard position measures startfraction pi over 2 endfraction radians, and p(0, 1) is on the terminal side of the angle. what is the value of the cosine of this angle?
An angle in standard position measures π/2 radians, and p(0, 1) is on the terminal side of the angle, the value of the cosine of this angle is 1.
So, we have:
cos θ = adjacent/hypotenuse
cos θ = x/1
cos θ = x
Now, the given angle is π/2 radians, and the point P (0, 1) lies on the terminal side of the angle. From the point P (0, 1), we can move left towards the origin to make a right-angled triangle.
Since the angle measures π/2, one leg will be on the x-axis (the horizontal leg) and the other leg will be on the y-axis (the vertical leg). Let's construct a right triangle using the point P (0, 1) and the origin (0,0) as two of the vertices: So, the opposite side is equal to 0, and the adjacent side is equal to 1.
Thus, the value of the cosine of this angle is cos θ = adjacent/hypotenuse = 1/1 = 1.
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Answer:
0
Step-by-step explanation:
let $f(x) = ax+b$, where $a$ and $b$ are real constants, and $g(x) = 2x - 5$. suppose that for all $x$, it is true that $g(f(x)) = 3x + 4$. what is $a+b$?
For the given function the answer is a + b = 3/2 + 9/2 = 12/2 = 6.
What is function?A function is an association between inputs in which each input has a unique link to one or more outputs.
To find the values of a and b, we can substitute the expressions for f(x) and g(x) into the equation g(f(x)) = 3x + 4 and solve for a and b.
We have:
g(f(x)) = 3x + 4
Substituting the expressions for f(x) and g(x), we get:
g(ax + b) = 3x + 4
Since g(x) = 2x - 5, we can replace g(ax + b) with 2(ax + b) - 5:
2(ax + b) - 5 = 3x + 4
Expanding and simplifying, we have:
2ax + 2b - 5 = 3x + 4
Rearranging terms, we get:
(2a - 3)x + (2b - 9) = 0
For this equation to hold for all values of x, the coefficient of x must be zero, and the constant terms must also be zero.
Therefore, we have the following system of equations:
2a - 3 = 0 (coefficient of x)
2b - 9 = 0 (constant term)
Solving these equations simultaneously, we find:
2a = 3 --> a = 3/2
2b = 9 --> b = 9/2
Therefore, a + b = 3/2 + 9/2 = 12/2 = 6.
Hence, a + b = 6.
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