Answer:To make the equality 1+23+45=65 true by inserting parentheses, you can group the numbers and operations in the following way:
(1+2)*(3+4)*5 = 65
This can be calculated as:
3 * 7 * 5 = 65
So, by adding parentheses as (1+2)(3+4)5, the equality 1+23+45=65 becomes true.
∫( , ,) = .(2 ―4 + ) + ( 4 + ) +(3 ― ) ,over the curve C with vertices (1,0,0), (0,1,0) ), and (0,0,1).
A curve C with Vertices (1,0,0), (0,1,0), and (0,0,1). These points define a triangle in three-dimensional space, not a curve.
The integral you provided seems to be incomplete and contains placeholders instead of actual functions or expressions. Additionally mentioned a curve C with vertices (1,0,0), (0,1,0), and (0,0,1). These points define a triangle in three-dimensional space, not a curve.
an integral over a region or a surface bounded by the given triangle in three-dimensional space. However, without the specific function or expression to integrate expression that needs to be integrated over the region or surface.
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What is 2 5 ⋅ 3 4 5 2 ⋅ 4 3 in its most reduced form?
The expression [tex]2^{5}*3^{4}/5^{2}*4^{3}[/tex], in its most reduced form, is equal to 81/50.
To simplify the expression [tex]2^{5}*3^{4}/5^{2}*4^{3}[/tex], we can perform the calculations step by step using the exponent rules and simplifying each term.
Let's simplify each component of the expression separately:
[tex]2^{5}[/tex] = 2 * 2 * 2 * 2 * 2 = 32
[tex]3^{4}[/tex] = 3 * 3 * 3 * 3 = 81
[tex]5^{2}[/tex] = 5 * 5 = 25
[tex]4^{3}[/tex] = 4 * 4 * 4 = 64
Now we substitute the simplified values back into the expression:
32 * 81 / 25 * 64
Next, we perform the multiplication and division from left to right:
(32 * 81) / (25 * 64) = 2592 / 1600
To reduce the fraction, we find the greatest common divisor (GCD) of the numerator and denominator:
GCD(2592, 1600) = 16
Dividing both the numerator and denominator by 16:
2592 / 1600 = (2592 / 16) / (1600 / 16) = 162 / 100
Now, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD) again:
GCD(162, 100) = 2
Dividing both the numerator and denominator by 2:
162 / 100 = (162 / 2) / (100 / 2) = 81 / 50
Therefore, the expression [tex]2^{5}*3^{4}/5^{2}*4^{3}[/tex], in its most reduced form, is equal to 81/50.
In summary, we simplified each term by evaluating the exponents and then performed the necessary multiplication and division. Finally, we reduced the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor.
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what is 2x=10, find x?
Answer:
Step-by-step explanation:
. Start with the equation: 2x = 10.
2. To isolate the variable x, we need to get rid of the coefficient 2. We can do this by performing the inverse operation, which is dividing both sides of the equation by 2.
Divide both sides of the equation by 2:
(2x)/2 = 10/2.
Simplifying, we have x = 5.
3. Therefore, the solution to the equation 2x = 10 is x = 5.
Select the correct answer.
What does it mean when the correlation coefficient has a positive value?
A.
О в.
O C.
O D.
When x increases, y decreases, and when x decreases, y increases.
When x increases, y increases, and when x decreases, y decreases.
When x increases, y decreases, and when x is constant, y equals zero.
When x increases, y increases, and when x is constant, y decreases.
When the correlation coefficient has a positive value, it means that as x increases, y tends to increase, and as x decreases, y also tends to decrease.
The correct answer is:
D. When x increases, y increases, and when x decreases, y decreases.
When the correlation coefficient has a positive value, it indicates a positive linear relationship between two variables.
This means that as one variable (x) increases, the other variable (y) also tends to increase.
Similarly, as x decreases, y tends to decrease. A positive correlation coefficient suggests that there is a consistent and direct relationship between the two variables.
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Solve the equation for x.
4-3x-2=60
Answer:
x = 19.34
Step-by-step explanation:
add like terms first
-3x + 2 = 60
isolate the -3x
-3x = 58
divide both sides by -3 to get x
x = 19.34
Find 5 consecutive integers such that: the sum of 7the first and 7 times the third is equal to 70 less than 4 times the sum of the second, fourth, and fifth
Answer:
The five consecutive integers are -26, -25, -24, -23, -22.
Step-by-step explanation:
Let's assume the first consecutive integer is "x."
The five consecutive integers can be represented as follows:
x, x+1, x+2, x+3, x+4
According to the given condition:
7 times the first (7x) plus 7 times the third (7(x+2)) is equal to 70 less than 4 times the sum of the second (4(x+1)), fourth (4(x+3)), and fifth (4(x+4)).
Mathematically, we can express this as:
7x + 7(x+2) = 4[(x+1) + (x+3) + (x+4)] - 70
Simplifying the equation:
7x + 7x + 14 = 4(3x + 8) - 70
14x + 14 = 12x + 32 - 70
14x + 14 = 12x - 38
2x = -52
x = -26
Substituting the value of x back into our assumption, we get:
The five consecutive integers are -26, -25, -24, -23, -22.
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Answer: 13
Step-by-step explanation:
The integers will be represented as
X, X+1, X+2,X+3,X+4 since they are consecutive
The equation will be
X+7(x+2)=4(x+1+x+3+x+4)-70
multiply to get rid of parentheses then add like terms
x+7x+14= 4x+4+4x+12+4x+16-70
8x +14= 12x-38
Subtract 8x from both sides
Add 38 to both sides
52=4x
divide by 4
x=13
the five consecutive integers are 13,14,15,16,17
Find the area 20 points!
[tex]A_{\triangle}=\dfrac{1}{2}\cdot 12\text{ in}\cdot 4\text{ in}=24\text{ in}^2\\\\A_{\square}=12\text{ in}\cdot 9\text{ in}=108\text{ in}^2\\\\A_{\text{Figure}}=A_{\triangle}+A_{\square}=24\text{ in}^2+108\text{ in}^2=132\text{ in}^2[/tex]
Answer:
132
Step-by-step explanation:
First calculate the area of the triangle, Triangle area formula is 1/2 B x H meaning we'd have to do 4 x 12 which gives us 48. Then we half 48 and get 24. We then calculate the area of the rectangle which is L x W so we do 9x 12 and get 108 we add the two numbers and get 132.
If the trinomial x² + 4x + 4 represents the area
of a triangle and the binomial x + 2 represents
the base, what expression represents the height
of the triangle?
Answer:
To find the expression that represents the height of the triangle, we need to use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the trinomial x² + 4x + 4 represents the area of the triangle, and the binomial x + 2 represents the base.
Using the formula, we can rearrange it to solve for the height:
Area = (1/2) * base * height
x² + 4x + 4 = (1/2) * (x + 2) * height
Now, we can solve for the height by isolating it on one side of the equation:
2 * (x² + 4x + 4) = (x + 2) * height
2x² + 8x + 8 = (x + 2) * height
Divide both sides by (x + 2) to solve for height:
height = (2x² + 8x + 8) / (x + 2)
Therefore, the expression that represents the height of the triangle is (2x² + 8x + 8) / (x + 2).
In measuring the mass of sack of rice, which of the following units of measure should you use?
a. milligram
b. gram
c. pound
d. kilogram
The most suitable unit of measure would be the kilogram (option d).
What is the unit?The unit milligram (option a), which is frequently employed for accurate measurements of small quantities, is too small. Gram (option b) is a good option for little quantities of rice, but it would be more practical to utilize kilograms when working with a sack of rice because the bulk is simpler to comprehend and handle.
The kilogram is the standard unit within the International System of Units (SI) and is generally acknowledged and used globally for measuring mass. The pound (option c) is an imperial unit that is frequently used in some locations.
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Scrumptious Snacks Inc. manufactures three types of snack foods: tortilla chips, potato chips, and pretzels. The company has budgeted the following costs for the upcoming period:
Factory depreciation $26,550
Indirect labor 65,797
Factory electricity 7,503
Indirect materials 15,584
Selling expenses 36,939
Administrative expenses 20,778
Total costs $173,151
Factory overhead is allocated to the three products on the basis of processing hours. The products had the following production budget and processing hours per case:
Budgeted Volume
(Cases) Processing Hours
Per Case
Tortilla chips 4,800 0.10
Potato chips 4,200 0.12
Pretzels 5,100 0.15
Total 14,100
a. Determine the single plantwide factory overhead rate.
Answer: The single plantwide factory overhead rate is approximately $66.03 per processing hour.
Step-by-step explanation: To determine the single plantwide factory overhead rate, we need to divide the total factory overhead costs by the total processing hours.
Total factory overhead costs = Factory depreciation + Indirect labor + Factory electricity + Indirect materials
= $26,550 + $65,797 + $7,503 + $15,584
= $115,434
Total processing hours = (Processing hours per case for tortilla chips x Budgeted volume for tortilla chips)
+ (Processing hours per case for potato chips x Budgeted volume for potato chips)
+ (Processing hours per case for pretzels x Budgeted volume for pretzels)
= (0.10 x 4,800) + (0.12 x 4,200) + (0.15 x 5,100)
= 480 + 504 + 765
= 1,749
Single plantwide factory overhead rate = Total factory overhead costs / Total processing hours
= $115,434 / 1,749
≈ $66.03 per processing hour
Therefore, the single plantwide factory overhead rate is approximately $66.03 per processing hour.
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Conclusión de densidad ?
Answer:
yes
Step-by-step explanation:
evaluate 8x-4y when x=2 and y=3
(a)4
(b)28
(c)22
(d)18
Olga is using spherical beads to create a border on a picture frame. Each bead has a diameter of 1.5 millimeters. Find the volume of each bead. Round to the nearest tenth.
The Volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.
The volume of each bead, the volume of a sphere using its diameter. The formula for the volume of a sphere is given by:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere.
Given that the diameter of each bead is 1.5 millimeters, we can calculate the radius as half of the diameter:
r = 1.5 mm / 2 = 0.75 mm
Now, we can substitute the value of the radius into the volume formula:
V = (4/3) * π * (0.75 mm)^3
Using the value of π ≈ 3.14 and performing the calculations:
V ≈ (4/3) * 3.14 * (0.75 mm)^3
V ≈ (4/3) * 3.14 * 0.421875 mm^3
V ≈ 1.767 mm^3 (rounded to the nearest tenth)
the volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.
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Keyser Mining is considering a project that will require the purchase of $980,000 in new equipment. The equipment will be depreciated straight-line to a zero book value over the 7-year life of the project. The equipment can be scraped at the end of the project for 5 percent of its original cost. Annual sales from this project are estimated at $420,000. Net working capital equal to 20 percent of sales will be required to support the project. All of the net working capital will be recouped. The required return is 16 percent and the tax rate is 35 percent. What is the amount of the after-tax salvage value of the equipment?
A. $17,150
B. $31,850
C. $118,800
D. $237,600
E. $343,000
The after-tax salvage value of the equipment is $31,850, which corresponds to option B.
To calculate the after-tax salvage value of the equipment, we need to consider the tax implications of the scrap value. Here are the steps to find the answer:
Calculate the annual depreciation expense:
Depreciation expense = Equipment cost / Project life
Depreciation expense = $980,000 / 7 = $140,000 per year
Determine the book value of the equipment at the end of the project:
Book value = Equipment cost - (Depreciation expense * Project life)
Book value = $980,000 - ($140,000 * 7) = $980,000 - $980,000 = $0
Calculate the taxable gain or loss on the sale of the equipment:
Taxable gain or loss = Scrap value - Book value
Taxable gain or loss = 0.05 * $980,000 - $0 = $49,000
Calculate the tax payment on the gain or loss:
Tax payment = Taxable gain or loss * Tax rate
Tax payment = $49,000 * 0.35 = $17,150
Calculate the after-tax salvage value:
After-tax salvage value = Scrap value - Tax payment
After-tax salvage value = 0.05 * $980,000 - $17,150 = $49,000 - $17,150 = $31,850
Therefore, the after-tax salvage value of the equipment is $31,850, which corresponds to option B.
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Which characteristic is correct for the function f(x)=2x^5-3x
both even and odd
odd
neither even nor odd
even
a rectangular park is 16 miles long and 8 miles wide. how long is the pedestrian route that runs diagonally across the park
Answer:
17.89 miles long.
Step-by-step explanation:
The pedestrian route that runs diagonally across the rectangular park is the hypotenuse of a right triangle whose legs are the length and width of the park. We can use the Pythagorean theorem to find the length of this diagonal route.
According to the Pythagorean theorem, the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of its legs. In this case, one leg of the right triangle is 16 miles long and the other leg is 8 miles long. So, we have:
d² = 16² + 8²
d² = 256 + 64
d² = 320
d = √320
d ≈ 17.89
So, the pedestrian route that runs diagonally across the park is approximately 17.89 miles long.
Find the requested values below.
ADC =
X=
Submit Answer
Check the picture below.
[tex]3x+5=\cfrac{260-100}{2}\implies 6x+10=160\implies 6x=150 \\\\\\ x=\cfrac{150}{6}\implies x=25\hspace{9em}\stackrel{\measuredangle ABC}{3(25)+5}\implies 80^o[/tex]
baez has hit 31.25% of the time he is at bat for hte last 7 games. If he has 10 hits how many total at bats does he have?
Baez has had a total of 32 at bats in the last 7 games.
31.25% = 10/32
which is true.
To solve this problem, we can use a proportion. We know that Baez has hit 31.25% of the time, which means he has hit 31.25 out of 100 times. If we let x be the total number of at bats Baez has had, we can set up the proportion:
31.25/100 = 10/x
To solve for x, we can cross-multiply:
31.25x = 1000
x = 32
It's important to note that hitting percentage is calculated by dividing the number of hits by the number of at bats,
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Use the order of operations to simplify thise expression. Enter a numerical answer only: 3 • −8 + 5 − 4 ÷ 2
The Simplified expression 3 • (-8) + 5 - 4 ÷ 2 equals -21.
The expression 3 • (-8) + 5 - 4 ÷ 2 using the order of operations, we follow the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
First, we perform the multiplication operation:
3 • (-8) + 5 - 4 ÷ 2 = -24 + 5 - 4 ÷ 2
Next, we perform the division operation:
-24 + 5 - 4 ÷ 2 = -24 + 5 - 2
Now, we perform the addition operation:
-24 + 5 - 2 = -19 - 2
Finally, we perform the subtraction operation:
-19 - 2 = -21
Therefore, the simplified expression 3 • (-8) + 5 - 4 ÷ 2 equals -21.
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maths question! please help
The graph of f(x) approaches q as x approaches negative infinity then the horizontal asymptote of f(x) is also y = q
To find the values of x for which a/(x+p) = bˣ+c, we can set the two equations equal to each other:
a/(x+p) = bˣ+c
To simplify the equation, we can multiply both sides by (x+p):
a = (x+p)(bˣ+c)
To find the values of x for which bˣ+c - a/(x+p) ≤ q, we can rearrange the inequality:
bˣ+c - a/(x+p) - q ≤ 0
To find the values of x for which f(x) ≤ g(x), we can substitute the given equations:
a/(x+p) + q ≤ bˣ + c
The x-intercept of a function occurs when the value of y is zero.
To find the x-intercept of f(x), we set f(x) = 0 and solve for x:
a/(x+p) + q = 0
To solve for x, we can rearrange the equation:
a/(x+p) = -q
Multiply both sides by (x+p):
a = -q(x+p)
Now, solve for x:
x = -p - (a/q)
So the x-intercept of f(x) is (-p - (a/q), 0).
The y-intercept of f(x) occurs when the value of x is zero. Substitute x = 0 into the equation for f(x):
f(0) = a/(0+p) + q = a/p + q
So the y-intercept of f(x) is (0, a/p + q).
To find the equations of the asymptotes of f(x), we can analyze the behavior of the function as x approaches positive or negative infinity.
As x approaches positive infinity, the term a/(x+p) approaches zero. Therefore, the graph of f(x) approaches q as x approaches positive infinity.
This means the horizontal asymptote of f(x) is y = q.
As x approaches negative infinity, the term a/(x+p) also approaches zero.
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Mrs. Harper is randomly selecting four students to give their presentation today if there are 16 boys and 14 girls in the class what is the probability that the first two . students selected are girls and the next two are boys
The probability that the first two students selected are girls, and the next two are boys, is approximately 5.2%.
To find the probability of selecting two girls followed by two boys, we need to calculate the probability of each event occurring and multiply them together.
First, let's determine the probability of selecting two girls from the class of 14 girls. The probability of selecting the first girl is 14/30 because there are 14 girls out of the total 30 students. After one girl has been selected, there are now 13 girls left out of the remaining 29 students. Thus, the probability of selecting a second girl is 13/29.
Next, we need to calculate the probability of selecting two boys from the class of 16 boys. After selecting the two girls, there are 16 boys left out of the remaining 28 students. Therefore, the probability of selecting the first boy is 16/28, and after one boy has been selected, there are 15 boys left out of the remaining 27 students. So, the probability of selecting a second boy is 15/27.
To obtain the overall probability, we multiply the individual probabilities together:
Probability = (14/30) × (13/29) ×(16/28) × (15/27)
Now, let's calculate this probability:
Probability = (182/870) × (240/812) × (4/7) × (5/9)
Probability ≈ 0.052 or 5.2% (rounded to one decimal place)
Therefore, the probability that the first two students selected are girls, and the next two are boys, is approximately 5.2%.
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daily methadone dosage in milligrams 0 to 49 frequency 4 50 to 99 frequency 9 00 to 149 frequency 11 50 to 199 frequency 5 00 to 249 frequency 2 based on the frequency distribution using the midpoint of each data class estimate the mean daily methadone dosage for the patients
The estimated mean daily methadone dosage for the patients is approximately 54.9 milligrams.
How to find the estimated meanLlet's find the midpoint for each data class. The midpoint is calculated by averaging the lower and upper limits of each class interval.
Midpoint of 0 to 49: (0 + 49) / 2 = 24.5
Midpoint of 50 to 99: (50 + 99) / 2 = 74.5
Midpoint of 100 to 149: (100 + 149) / 2 = 124.5
Midpoint of 150 to 199: (150 + 199) / 2 = 174.5
Midpoint of 200 to 249: (200 + 249) / 2 = 224.5
Next, we calculate the weighted average by multiplying each midpoint by its corresponding frequency, summing up the products, and dividing by the total frequency.
Weighted average = (24.5 * 4 + 74.5 * 9 + 124.5 * 11 + 174.5 * 5 + 224.5 * 2) / (4 + 9 + 11 + 5 + 2)
Weighted average = 1702.5 / 31
Weighted average ≈ 54.9
Therefore, the estimated mean daily methadone dosage for the patients is approximately 54.9 milligrams.
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It took 2 weeks for them to canoe 110 miles down the Hulahula River. They sometimes took days off to hike or rest. What was the average number of miles they paddled per day? Round to the nearest tenth.
The average number of miles they paddled per day, rounded to the nearest tenth, is approximately 7.9 miles.
To find the average number of miles they paddled per day, we need to divide the total number of miles they canoed by the number of days they were actively paddling.
Given that it took 2 weeks for them to canoe 110 miles down the Hulahula River, we need to determine the number of days they were actively paddling. Since a week consists of 7 days, 2 weeks would be 2 * 7 = 14 days.
Let's calculate the average number of miles they paddled per day:
Average miles per day = Total miles / Number of days
Average miles per day = 110 miles / 14 days
Average miles per day ≈ 7.857 miles per day (rounded to the nearest tenth)
Therefore, the average number of miles they paddled per day, rounded to the nearest tenth, is approximately 7.9 miles.
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You need a 20% alcohol solution. On hand, you have a 15 mL of a 5% alcohol mixture. You also have 25% alcohol mixture. How much of the 25% mixture will you need to add to obtain the desired solution?
Answer:
Let x be the number of mL of 25% alcohol mixture needed.
.05(15) + .25x = .20(15 + x)
.75 + .25x = 3 + .20x
.05x = 2.25
x = 45 mL
Write x^2 - 8x + 10 in the form
(x + a)^2 + B
[tex]x^2-8x+10=x^2-8x+16-6=(x-4)^2-6[/tex]
Find the Value of X.
The value of x is 33.2
What are similar triangles?Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent or equal.
Also the ratio of corresponding sides of similar triangles are equal.
Therefore;
Triangle EHG and EFG are similar
39/36 = 36/x
36 × 36 = 39x
39x = 1296
divide both sides by 39
x = 1296/39
x = 33.2
Therefore the value of x is 33.2
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Whats the length of a dollar bill
The measurements are designed to fit within standard wallets, cash registers, and monetary Handling equipment.
The length of a dollar bill can vary slightly depending on the country. In the United States, a standard US dollar bill has a length of approximately 6.14 inches or 155.956 mm. The width of a US dollar bill is approximately 2.61 inches or 66.294 mm. The bill is rectangular in shape and has a portrait of a historical figure on the front, such as George Washington, and various symbols and designs on both sides.
It's important to note that the dimensions of a dollar bill may vary slightly due to production and printing variations. Additionally, different countries have their own currency and dimensions for their respective bills.
The size and dimensions of currency notes are regulated by central banks or government authorities to ensure consistency and prevent counterfeiting. These measurements are designed to fit within standard wallets, cash registers, and other monetary handling equipment.
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Insurance company executives surveyed 200 young adults about their first motor vehicle. The results of the survey are given in the following two-way table. A 4-column table with 3 rows. Column 1 has entries 4, 6, 8. Column 2 is labeled car with entries 118, 16, 2. Column 3 is labeled truck with entries 6, 12, 6. Column 4 is labeled S U V with entries 18, 20, 2. The columns are titled motor vehicle and the rows are titled cylinders. A survey participant is randomly selected. Let F be the event that the participant’s first motor vehicle had four cylinders and let C be the event that the participant’s first motor vehicle was a car. 0.59 0.68 0.71 0.80
The probability that a randomly selected survey participant had a car as their first motor vehicle, given that it had four cylinders, is 0.83 or 83%.
The two-way table indicates that out of the 200 young adults surveyed, 118 individuals had cars with four cylinders, six had trucks with four cylinders, and 18 had SUVs with four cylinders. Thus, the probability that a survey participant's first motor vehicle had four cylinders is:
P(F) = (118 + 6 + 18) / 200 = 0.71
Similarly, out of the 118 individuals who had cars with four cylinders, 118 itself were cars. Thus, the probability that a survey participant's first motor vehicle was a car, given that it had four cylinders, is:
P(C | F) = 118 / 142 = 0.83
It's important to carefully read and interpret the table when forming probabilities, and then apply the relevant formulas to compute the desired probabilities.
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Note: The complete question is- Find the probability that a survey participant who had a four-cylinder motor vehicle for their first vehicle also had a car for their first vehicle, i.e., P(C|F).
907, 000 in scientific notation.
Answer:
9.07*10⁵
Step-by-step explanation:
Scientific notification is in the form a*10^n, where a is between 1 and 10.
9.07*100,000
100,000=10^5
Therefore, 9.07*10⁵
Feel free to tell me if I did anything wrong! :)
125ml castor sugar,convert the sugar to
cups
Answer:
To convert 125 ml of castor sugar to cups, we need to know the conversion factor between milliliters and cups. The conversion factor commonly used is 1 cup = 237 ml.
So, to convert 125 ml of castor sugar to cups, we can use the following calculation:
125 ml * (1 cup / 237 ml) ≈ 0.527 cups
Therefore, 125 ml of castor sugar is approximately equal to 0.527 cups.
Step-by-step explanation:
Answer:
According to some online sources , 125 ml of castor sugar is equivalent to about **0.53 cups**. Therefore, if you want to convert the sugar to cups, you can use this conversion factor. For example, if a recipe calls for 250 ml of castor sugar, you can use about 1.06 cups instead. However, keep in mind that different types of sugar may have different densities and weights, so the conversion may not be exact. It is always better to use a kitchen scale or measuring cups to measure your ingredients accurately.
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