Answer:
(4,2) represents the number of ways to choose 2 items from a set of 4 distinct items. The formula for C(n,r) is n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values for C(4,2), we get: C(4,2) = 4! / (2! * (4-2)!) = 24 / (2 * 2) = 6 Therefore, there are 6 ways to choose 2 items from a set of 4 distinct items.
0 / 350
The value of the given combination C(4, 2) by applying the combination formula in factorial form is equals to option 6.
To evaluate C(4, 2), we use the combination formula, also known as "n choose r" or "C(n, r)",
which calculates the number of ways to choose r items from a set of n distinct items without considering their order. The formula for C(n, r) is:
C(n, r) = n! / (r! × (n - r)!)
Where "!" denotes the factorial of a number, which is the product of all positive integers up to that number.
For example,
4! = 4 × 3 ×2 × 1
= 24.
Now, let's plug the values into the formula for C(4, 2):
C(4, 2) = 4! / (2! × (4 - 2)!)
= 4! / (2! × 2!)
= (4 × 3 × 2 × 1) / ((2 × 1) × (2 × 1))
= (24) / (4)
= 6
Therefore , the value of the combination C(4, 2) equals to option 6.
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a visitor is staying in a cottage that is 10 miles east of the closest point on a shoreline to an island. the island is 7 miles due south of the shoreline. the visitor plans to travel from the cottage to the island by running and swimming. if the visitor runs at a rate of 5 mph and swims at a rate of 3 mph, how far should the visitor run to minimize the time it takes to reach the island?
The visitor should run 1.2 miles to minimize the time it takes to reach the island.
Consider the following figure.
Let us assume that x (CD) represents the distance covered when visitor runs at a rate of 5 mph
So, the time taken by visitor would be:
t₁ = x/5
Let the distance covered 10 - x when visitor swims at a rate of 3 mph
From figure consider right triangle ABC.
Using Pythagoras theorem,
BC² = 7² + (10 - x)²
BC = [tex]\sqrt{49 + (10-x)^2}[/tex]
Now the times taken by visitor when he swims at a rate of 3 mph,
t₂ = [tex]\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]
so, the total time would be:
t = t₁ + t₂
[tex]t=\frac{x}{6}+\frac{ \sqrt{49 + (10-x)^2}}{3}[/tex]
Differentiating with respect to x we get,
[tex]\frac{dt}{dx}=\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}[/tex]
consider dt/dx = 0
[tex]\frac{1}{6} -\frac{(10-x)}{ \sqrt{49 + (10-x)^2}}=0[/tex]
If we solve above equation for x we get, x = 11.2 and x = 8.8
The distance the visitor should run to minimize the time would be:
10 - 8.8 = 1.2 miles
Therefore, the required distance is 1.2 miles
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A package of 6 pairs of insulated gloves costs $34.14. What is the unit price of the pairs of gloves ?
Answer:
$5.69
Step-by-step explanation:
To find the unit price (price per pair) of the gloves, we need to divide the total cost by the number of pairs:
Unit price = Total cost / Number of pairs
In this case, the total cost is $34.14 and the number of pairs is 6, so:
Unit price = $34.14 / 6
Unit price = $5.69 (rounded to the nearest cent)
Therefore, the unit price of the pairs of insulated gloves is $5.69.
What does the differences between the price after value added tax (VAT) and price after discount of any article give us?
Answer:
The difference between the price after value added tax (VAT) and the price after discount of an article gives us the actual amount of money saved by the customer.
The price after VAT is the price of the item including the tax imposed by the government, whereas the price after discount is the price of the item after any promotional or discounted price reduction. By subtracting the price after discount from the price after VAT, we can determine the actual amount saved by the customer, which is the discount amount minus any VAT paid on the original price.
For example, if an item originally cost $100 with a 10% VAT, the price after VAT would be $110. If the item was discounted by 20%, the price after discount would be $80. The difference between the price after VAT and the price after discount would be $30, which is the actual amount saved by the customer ($20 discount minus $10 VAT paid on the original price).
Step-by-step explanation:
To calculate the actual amount saved by the customer, we need to follow these steps:
Determine the original price of the item. For example, let's say the original price of the item is $100.
Calculate the VAT amount paid on the original price. To do this, multiply the original price by the VAT rate as a decimal. For example, if the VAT rate is 10%, then the VAT amount would be:
VAT amount = original price x VAT rate
VAT amount = $100 x 0.1
VAT amount = $10
So, the VAT amount paid on the original price of $100 is $10.
Determine the discounted price of the item. For example, let's say the item is discounted by 20%, so the discounted price is:
Discounted price = original price - (original price x discount rate)
Discounted price = $100 - ($100 x 0.2)
Discounted price = $80
So, the discounted price of the item is $80.
Calculate the actual amount saved by the customer. To do this, subtract the discounted price from the price after VAT. For example:
Actual amount saved = price after VAT - discounted price
Actual amount saved = $110 - $80
Actual amount saved = $30
So, the actual amount saved by the customer is $30, which is the discount amount minus the VAT paid on the original price.
every water sample from a river has a 10% chance of containing a specified pollutant. suppose the samples are independent. a. compute the probability that 2 of the next 20 samples contain that pollutant. b. compute the probability that at least four of the next 20 samples contain the pollutant. c. compute the probability that more than 2 and less than 7 of the next 20 samples contain the pollutant. d. compute the average number of samples (out of 20) that will contain the pollutant
The average number of samples (out of 20) that will contain the pollutant is 2.
a. Probability that 2 of the next 20 samples contain the pollutantTo calculate the probability that 2 of the next 20 samples contain the pollutant, we use the binomial distribution. We can use the formula below:P(X=k) = (nCk) pk(1-p)n-kwhere:n = 20, the number of samples; k = 2, the number of samples containing the pollutant; p = 0.10, the probability that a sample contains the pollutant; q = 1 - p = 0.90, the probability that a sample does not contain the pollutant.Using the above formula, we get:P(X=2) = (20C2) (0.10)2(0.90)18= (190) (0.01) (0.2066)≈ 0.3979Therefore, the probability that 2 of the next 20 samples contain the pollutant is approximately 0.3979.
b. Probability that at least four of the next 20 samples contain the pollutantTo calculate the probability that at least four of the next 20 samples contain the pollutant, we need to calculate the probability of P(X ≥ 4).We can use the complement of P(X < 4) and use the binomial distribution formula to calculate this. We get:P(X ≥ 4) = 1 - P(X < 4)P(X < 4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)P(X=0) = (20C0) (0.10)0(0.90)20= (1) (1) (0.1216)≈ 0.1216P(X=1) = (20C1) (0.10)1(0.90)19= (20) (0.10) (0.2296)≈ 0.4593P(X=2) = (20C2) (0.10)2(0.90)18= (190) (0.01) (0.2066)≈ 0.3979P(X=3) = (20C3) (0.10)3(0.90)17= (1140) (0.001) (0.2753)≈ 0.2059Therefore, P(X < 4) ≈ 0.1216 + 0.4593 + 0.3979 + 0.2059 ≈ 1.185P(X ≥ 4) = 1 - P(X < 4)≈ 1 - 1.185= -0.185This is not a valid probability. Therefore, we have made an error in our calculations, and the probability cannot be calculated using this method.
c. Probability that more than 2 and less than 7 of the next 20 samples contain the pollutant. To calculate the probability that more than 2 and less than 7 of the next 20 samples contain the pollutant, we can use the binomial distribution formula again. We need to calculate P(3 ≤ X ≤ 6).We can use the formula:P(3 ≤ X ≤ 6) = P(X=3) + P(X=4) + P(X=5) + P(X=6)P(X=3) = (20C3) (0.10)3(0.90)17= (1140) (0.001) (0.2753)≈ 0.2059P(X=4) = (20C4) (0.10)4(0.90)16= (4845) (0.0001) (0.3112)≈ 0.1516P(X=5) = (20C5) (0.10)5(0.90)15= (15504) (0.00001) (0.3544)≈ 0.0583P(X=6) = (20C6) (0.10)6(0.90)14= (38760) (0.000001) (0.3919)≈ 0.0121Therefore,P(3 ≤ X ≤ 6) ≈ 0.2059 + 0.1516 + 0.0583 + 0.0121 ≈ 0.4279Therefore, the probability that more than 2 and less than 7 of the next 20 samples contain the pollutant is approximately 0.4279.
d. Average number of samples (out of 20) that will contain the pollutantThe expected value or average number of samples that will contain the pollutant can be calculated using the following formula:E(X) = npwhere:n = 20, the number of samples; p = 0.10, the probability that a sample contains the pollutant.Using the above formula,E(X) = np= 20 (0.10)= 2.
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Use the information below to answer the question Diego rode his bicycle 12.6 miles in 1.5 hours. If Diego rides at the same average rate how many miles will he ride in 2.5 hours?
A.15.1
B.16.8
C.21.10
D.25.2
Diego will ride 21 miles in 2.5 hours as a result, which is answer option C as 8.4 miles per hour divided by 2.5 hours equals 21 miles.
what is unitary method ?Mathematicians use the unitary technique to address proportional relationship issues involving two or more quantities. To answer problems involving rates, ratios, and proportions, it is frequently employed in academics and everyday life. With the unitary technique, the value with one unit is first determined, and the value of the desired amount of units is then determined using this value. The unitary technique can be used, for instance, to determine the price of 1 pen if the price of 4 pens is $8. Cost of 1 pen equals the sum of the costs of 4 other pens. One pen costs $8 plus $4. One pen costs $2.
given
Diego will cover 2.5 miles in that time, according to the following formula:
Rate times distance
Diego's bicycle travels at an average speed of:
Rate: Distance x Time
Hence, we may determine his rate as:
12.6 miles divided by 1.5 hours equals 8.4 miles per hour.
Now that we know this rate, we can calculate how far Diego will travel in 2.5 hours:
8.4 miles per hour divided by 2.5 hours equals 21 miles in the formula for distance.
Diego will ride 21 miles in 2.5 hours as a result, which is answer option C as 8.4 miles per hour divided by 2.5 hours equals 21 miles.
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I need help w/ my Math, it’s a series of questions starting from 10-18 but not 16. ⚠️I NEED HELP TO SIMPLIFY THEM, NOT ANSWER THEM⚠️
10. 8-3(2-3+1)the power of 2 divided by 8x2)
11. 3 to the power of 2 +5(2+9)
12. 7 to the power of 2-8x3+6
13. 3x5-(3 to the power of 2+2)+72 divided by 8
14. 8-3-(24-4 to the power of 2) divided by 2
15. 11+3(19+2)
17. 10+2[18 divided by(5+1)]
18 (6-2)x0+8
Answer:
10. 8
11. 64
12. 31
13. 13
14. 1
15. 74
17. 16
18. 8
Step-by-step explanation:
:))
Represent the reflection across the y-axis using coordinates.
(x,y) ——-> ( __ x , __ y )
Answer:
(x,y) ——-> ( - x , y )
Step-by-step explanation:
When reflected across the y-axis, the sign of the x will change. So, the answer to this is (x,y) ——-> ( - x , y )
In ΔKLM, m = 5.2 cm, k = 8.3 cm and ∠L=162°. Find ∠M, to the nearest 10th of a degree.
The measure of angle M in triangle KLM is approximately 47.3 degrees, to the nearest 10th of a degree.
Solving for nearest 10th of degree:
To find the measure of angle M in triangle KLM, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. The Law of Cosines states that:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
where c: length of the side opposite angle C, and a & b are the lengths of the other two sides.
In this case, we wish to find the measure of angle M, which will be opposite the side of length m. We are aware that the lengths of the other two sides, k and l, and measure of angle L. To find l, we use the Law of Cosines:
[tex]l^2 = k^2 + m^2 - 2km cos(L)[/tex]
Substituting:
[tex]l^2 = 8.3^2 + 5.2^2 - 2(8.3)(5.2) cos(162 degree)[/tex]
Solve for the l, we get:
l = 10.038 cm
We will use Law of Cosines again to find the measure of angle M:
cos(M) = [tex](k^2 + l^2 - m^2) / (2kl)[/tex]
Substituting:
cos(M) = [tex]([/tex][tex]8.3^2 + 10.038^2 - 5.2^2)[/tex] [tex]/ (2(8.3)(10.038))[/tex]
Simplifying:
cos(M) = 0.665
To get the measure of angle M, we take the inverse cosine:
M = 47.3°
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in one town, 39% of all voters are democrats. if two voters are randomly selected for a survey, find the probability that they are both democrats. round to the nearest thousandth if necessary. group of answer choices
0.148 is the probability that they are both democrats.
In one town, 39% of all voters are democrats.
If two voters are randomly selected for a survey, the probability that they are both democrats can be calculated as follows.
P(A) = 0.39 is the probability of selecting a democrat in the first draw.
P(B|A) = 0.38
is the probability of selecting a democrat in the second draw if the first draw selects a democrat.
P(B|A') = 0.39 is the probability of selecting a democrat in the second draw if the first draw does not select a democrat.
The probability that both voters are democrats is:
P(A) x P(B|A) = 0.39 x 0.38 = 0.1482
The result is 0.1482, which means the probability that two voters are both democrats in one town is 0.1482 to the nearest thousandth.
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How many points of intersection are there between the graphs of the two hyperbolas?
3x^2−5y^2+5x−7y+2=0
3x^2−2y^2+5x−y+2=0
o 0
o 1
o 2
o 4
Since an ellipse and a hyperbοla can intersect at mοst fοur pοints, the answer is 4.
What is hyperbοla?A hyperbοla is a type οf cοnic sectiοn, which is a curve that is created when a plane intersects a dοuble cοne. A hyperbοla is fοrmed when a plane intersects bοth halves οf a dοuble cοne, resulting in twο distinct curves that mirrοr each οther.
Tο find the pοints οf intersectiοn between the graphs οf the twο hyperbοlas, we need tο sοlve the system οf equatiοns:
[tex]3x^2-5y^2+5x -7y+2=0[/tex]
[tex]3x^2-2y^2+5x-y+2=0[/tex]
We can simplify the system by subtracting the secοnd equatiοn frοm the first:
[tex]-3x^2 - (-2y^2) - 6y = -6[/tex]
Simplifying further:
[tex]3x^2 + 2y^2 + 6y = 6[/tex]
Nοw we can cοmplete the square fοr the y terms:
[tex]3x^2 + 2(y+1)^2 = 9[/tex]
Dividing by 9, we get:
[tex]x^2/3 + (y+1)^2/4 = 1[/tex]
This is the equatiοn οf an ellipse cantered at (-√3, -1) and (√3, -1), with the majοr axis alοng the x-axis and a minοr axis alοng the y-axis.
Therefοre, an ellipse and a hyperbοla can intersect at mοst fοur pοints, the answer is ο 4.
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MODELING REAL LIFE You ride your bicycle 40 meters. How many complete revolutions does the front wheel
make?
32.5 cm
The bicycle makes complete revolutions.
Answer:
19
Step-by-step explanation:
r = 32.5 cm
C = 2πr = 2(3.14159)(32.5 cm) = 204.20 cm
40 m = 40 m × (100 cm)/m = 4000 cm
4000 cm / 204.2 cm = 19.588
Answer: 19
One angle of a triangle measures 85°. The other two angles are in a ratio of 9:10. What are the measures of those two angles?
Answer:
Let x be the first unknown angle, and y be the second unknown angle.
We know that the sum of the three angles in a triangle is 180 degrees, so:
85 + 9kx + 10kx = 180
where k is a constant representing the ratio of the other two angles.
Simplifying the equation, we get:
19kx = 95
Dividing both sides by 19k, we get:
x = 5/k
Since the ratio of the other two angles is 9:10, we know that:
y = 9kx = 9k(5/k) = 45
So the measures of the two unknown angles are:
x = 5/k and y = 45
We cannot find the exact measures of x and y without more information, but we know that x and y are in a ratio of 9:10 and their sum is 180 - 85 = 95 degrees. We can set up the following equation to solve for k:
5/k + 45/k = 95
50/k = 95
k = 50/95
Using this value of k, we can find the measures of x and y:
x = 5/k = 5/(50/95) = 9.5
y = 9kx = 9(50/95)(9.5) = 47.37
Therefore, the measures of the two unknown angles are x = 9.5 degrees and y = 47.37 degrees (rounded to two decimal places).
Step-by-step explanation:
Write an algebraic expression for the sum of 12 and 4
The requires algebraic expression is (12 + 4)
Algebraic expression:An algebraic expression is a mathematical phrase that consists of variables, constants, and mathematical operations.
Algebraic expressions can represent a wide range of mathematical concepts and can be used to solve problems in various fields such as physics, engineering, economics, and more.
Here we have
the sum of 12 and 4
Here the sum of 12 and 4 implies the addition of 12 and 4
Hence, we need to use the symbol '+' to write the expression
Hence,
The requires algebraic expression is (12 + 4)
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Find the volume & surface area of each figure. Round your answers to the nearest hundredth, if necessary.
Answer:
15) surface area = 791.68, volume = 1693.32
16) surface area = 138.23, volume = 113.1
17) surface area = 650.87, volume = 1073
18) surface area = 34.87, volume = 10.52
19) surface area = 153.94, volume = 179.59
20) surface area = 314.16, volume = 523.6
Step-by-Step Explanation:
sorry I didn't add the cm or inches or km in my answers :)
Find the equation of a line perpendicular to 2x+y=−9 that passes through the point (8,9)
What is the equivalent fraction of two ones and two hundredths
The equivalent fraction of two ones and two hundredths is 101/50 by converting the whole number part to a fraction, then add it to the fraction part.
Two ones and two hundredths can be represented as a mixed number, which is [tex]2 \frac{2}{100}[/tex].
To convert this mixed number to an equivalent fraction, we need to first convert the whole number part to a fraction by multiplying it by the denominator of the fraction part, and then adding the numerator of the fraction part. So, we have:
2 + 2/100 = (2 * 100 + 2) / 100 = 202/100
Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
202/100 = (2 * 101) / (2 * 50) = 101/50
Therefore, the equivalent fraction of two ones and two hundredths is 101/50.
In summary, to convert a mixed number to an equivalent fraction, we first convert the whole number part to a fraction, then add it to the fraction part, and finally simplify the resulting fraction if possible.
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How do you do these step by step thank uu
Answer:
y = x + 3
Step-by-step explanation:
The question is y is 3 more than x.
We know that "more" means addition.
and since y is the greater number here, the answer would be y = x + 3!
Simple!
:)
Is EG ⊥ DF? Why or why not?
The length of XF is equal to 13 units.
Is EG ⊥ DF: D. impossible to tell; not enough information is given.
What is a rhombus?In Mathematics and Geometry, a rhombus is a type of quadrilateral that is composed of four (4) equal sides and opposite interior angles that are congruent (equal).
Additionally, a rhombus typically has two (2) diagonals that bisect each other at right angles (90 degrees);
3x - 5 = 2x
3x - 2x = 5
x = 5
Next, we would determine the length of the diagonal DF;
Diagonal DF = 5x + 1
Diagonal DF = 5(5) + 1
Diagonal DF = 26 units.
XF = DF/2
XF = 26/2
XF = 13 units.
In conclusion, it is impossible to determine whether side EF is perpendicular to side DF because information about the side length was not provided.
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17.Two paddocks in the shapes shown below are to be fenced with wire. If the same total
amount of wire is used for each paddock, what are the dimensions of each paddock in
metres?
you know that i have gave wrong Ans
explanation: because i need points
Answer:
Step-by-step explanation:
where’s the figure ?
What is the value of x?
Answer:x = 4
Step-by-step explanation:
9. Divide the following: please helppp
a.
x4 x3
b.
s3
s5
c.
z12
z10
Answer:
a. x
b. 1/s^2
c. z^2
Step-by-step explanation:
I need help on these three pages please asap. Thank you!
Step-by-step explanation:
Example 1:
Given pair: (3;2)
{2x + 3y = 12,
{x - 4y = -5;
Make x the subject from the 2nd equation:
x = -5 + 4y
Replace x in the 1st equation:
2 × (-5 + 4y) + 3y = 12
-10 + 8y + 3y = 12
11 y = 12 + 10
11y = 22 / : 11
y = 2
y = 2x = -5 + 4 × 2 = -5 + 8 = 3
The answer: (3;2)
The given pair is the solution of the system of equations
.
Example 2:
Given pair: (0; -4)
{x + y = -4,
{x - 5y = 20;
x = -4 - y
(-4 - y) - 5y = 20
-4 - y - 5y = 20
-6y = 20 + 4
-6y = 24 / : (-6)
y = -4
y = -4x = -4 - (-4) = -4 + 4 = 0
The answer: (0; -4)
The given pair is the solution
.
Example 3:
Given pair: (3;3)
{x + 2y = 9,
{4x - y = 15;
x = 9 - 2y
4(9 - 2y) - y = 15
36 - 8y - y = 15
-9y = 15 - 36
-9y = -21 / : (-9)
[tex]y = 2 \frac{1}{3} [/tex]
[tex]x = 9 - 2 \times 2 \frac{1}{3} = 9 - 2 \times \frac{7}{3} = 9 - \frac{14}{3} = \frac{13}{3} = 4 \frac{1}{3} [/tex]
The given pair is not the solution
.
Example 4:
Given pair: (1; -2)
{2x - 3y = 8,
{3x + 2y = -1;
2x = 8 + 3y / : 2
x = 4 + 1,5y
3(4+1,5y) + 2y = -1
12 + 4,5y + 2y = -1
6,5y = -1 - 12
6,5y = -13 / : 6,5
y = -2
y = -2x = 4 + 1,5 × (-2) = 4 - 3 = 1
The given pair is the solution
.
Example 5:
Given pair: (1;5)
{5x - 2y = -5,
{3x - 7y = -32;
-2y = -5 - 5x / : (-2)
y = 2,5 + 2,5x
3x - 7(2,5 + 2,5x) = -32
3x - 17,5 - 17,5x = -32
-14,5x = -32 + 17,5
-14,5x = -14,5 / : (-14,5)
x = 1
x = 1y = 2,5 + 2,5 × 1 = 5
The given pair is the solution
.
Example 6:
Given pair: (-1; -3)
{3x + y = -6,
{2x = 1 + y;
y = -6 - 3x
2x = 1 + (-6 - 3x)
2x = 1 - 6 - 3x
2x + 3x = 1 - 6
5x = -5 / : 5
x = -1
x = -1y = -6 - 3 × (-1) = -6 + 3 = -3
The given pair is the solution
100 points!
can someone help me with this !!! please and thank you :)
The value of x that makes the shape a kite is determined as 4.
What is the special property of kite shape?
One special property of a kite shape is that it has two pairs of adjacent sides that are congruent (i.e., they have the same length). In other words, the two shorter sides are equal in length, and the two longer sides are equal in length, but the shorter and longer sides are not equal to each other.
The value of x is calculated by applying this special property of kite;
6x - 3 = 21 --- (1)
4x + 1 = 17 --- (2)
Solving equation (1)
6x = 24
x = 24/6
x = 4
Solving equation (2);
4x = 17 - 1
4x = 16
x = 16/4
x = 4
So the shape is kite if the value of x is 4.
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Find dy/dt at x=1 and y=x^2+3 if dx/dt=4
Using derivative of the function dy/dt = 6.
How to find dy/dt at x = 1?Differentiation involves finding the derivative of a function, which is a new function that describes the rate of change of the original function at each point.
Since we have x term and we are differentiating with respect to t, we need to apply the chain rule. This means we first differentiate with respect to x and then multiply by dx/dt. That is:
dy/dt = d[x² + 3]/dt
dy/dt = (2x) dx/dt
dy/dt = 2(1) + 4 (Since x=1 and dx/dt= 4)
dy/dt = 2 + 4
dy/dt = 6
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1 5. (1.2 x 10)+4 DAO 1:3-5÷4 6. (5 x 107) x (3 x 10°) 15 x 10-¹1 1.5-10° 15×1= 'T Answer each of the following questions. Show all of your work. The diameter of the Sun is approximately 1.3 x 106 km. The diameter of the Earth is approximately 1.3 x 10 km. The diameter of the Sun is how many times larger than the diameter of the Earth?
To find how many times larger the diameter of the Sun is than the diameter of the Earth, we need to divide the diameter of the Sun by the diameter of the Earth:
(1.3 x 10^6 km) / (1.3 x 10^4 km)
Simplifying:
= (1.3 / 1.3) x (10^6 / 10^4)
= 100
Therefore, the diameter of the Sun is 100 times larger than the diameter of the Earth.
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at the mp donut hole factory, niraek, theo, and akshaj are coating spherical donut holes in powdered sugar. niraek's donut holes have radius $6$ mm, theo's donut holes have radius $8$ mm, and akshaj's donut holes have radius $10$ mm. all three workers coat the surface of the donut holes at the same rate and start at the same time. assuming that the powdered sugar coating has negligible thickness and is distributed equally on all donut holes, how many donut holes will niraek have covered by the first time all three workers finish their current donut hole at the same time?
Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.
The time it takes to coat a donut hole is directly proportional to the surface area of the donut hole.
The surface area of a sphere is given by the formula:
Surface Area = 4πr²
Here, r is the radius of the sphere.
Comparing the surface areas of the donut holes:
Niraek's donut hole: Surface Area = 4π(6²)
Theo's donut hole: Surface Area = 4π(8²)
Akshaj's donut hole: Surface Area = 4π(10²)
Now, let's find the LCM of the surface areas to determine the time it takes for all workers to finish:
LCM(144π, 256π, 400π) = 57600π mm²
This means that it will take the same amount of time for all three workers to finish their current donut holes when they have covered a total surface area of 57600π mm².
Number of donut holes = (Total surface area) / (Surface area of Niraek's donut hole)
= (57600π mm²) / (144π mm²)
= 57600 / 144
= 400
Therefore, Niraek will have covered 400 donut holes by the time all three workers finish their current donut holes at the same time.
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what is the diameter of 100km
Answer: The diameter of a circle is the distance across the circle passing through the center.
To find the diameter of a circle with a radius of 100 km, we can simply double the radius, since the diameter is twice the length of the radius.
Therefore, the diameter of a circle with a radius of 100 km is:
2 x 100 km = 200 km
So the diameter is 200 km.
Step-by-step explanation:
Which choice is equivalent to the expression below when x ≥ 0?
√32x^3 - √16x^3 + 4√x^3 - √2x^3
A. 3√2x
B. 4x√2x
C. 3x√2x
D. √18x^3
The response is: [tex]$32x^{3}-16x^{3}+4x^{3}-2x^{3}$[/tex] equals 2x (4x - x²) equals 3x²x (Option C)
what is expressiοn ?An expressiοn is a grοup οf digits, variables, and mathematical οperatοrs (such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, etc.) that depicts a quantity οr relatiοnship. Expressiοns can be straightfοrward οr intricate, and they can cοntain any number οf different mathematical οperatiοns and values.
Fοr instance, "3 + 5" is a straightfοrward statement that denοtes the additiοn οf 3 and 5, whereas "2x² + 5xy - 7" is a mοre intricate expressiοn that uses expοnents and variables. In algebra and οther branches οf mathematics, expressiοns are frequently emplοyed tο illustrate relatiοnships and address issues.
Let's first simplify each phrase that appears after the square rοοt:
√32x^3 = √(16x²) * √(2x) = 4x√2x √16x³ = √(16x²) * √x = 4x√x 4√x³ = 4√(x²) * √x = 4x√x √2x³ = √(2x²) * √x = √2x * x√x
Cοmbining the οriginal statement with these simplificatiοns results in:
32x³ - 16x³ + 4x³ - 2x³ = 4x²x - 4xx + 4xx - xx = 4x²x - xx = 2x (4x - x²).
As 4x and x2 are bοth nοn-negative because x 0, their difference is alsο
non-negative.
Hence, the response is: [tex]$32x^{3}-16x^{3}+4x^{3}-2x^{3}$[/tex] equals 2x (4x - x²) equals 3x²x (Option C) .
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The membership in a performing arts club increased by 120% compared to the previous year. How many squares would be shaded on 10 × 10 grids to represent 120%?
220 squares would be shaded on 10 x 10 grids to represent an increase of 120%.
An increase of 120% means that the new value is 100% + 120% = 220% of the previous value.
If we let the previous value be x, then the new value is 2.2x.
To represent this increase on a 10 x 10 grid, we can shade in 220 out of 100 squares, or:
The new value would be 2.2 times the previous value, since an increase of 120% means that the new value is 220% of the previous value.
If we let the previous value be x, then the new value is:
new value = x + 120% of x
220/100 x 10 x 10 = 220 squares
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If there are two figures a parallelogram and a rectangle with a base of 12in and a height of 6in how are they related
The parallelogram and rectangle have the same base and height, they have the same area of 72 in2.
The parallelogram and the rectangle are related because they both have the same base and height. The area of the parallelogram is calculated by multiplying the base of the parallelogram (b) by the height (h): Area = b × h. In this case, the area of the parallelogram is 12 in × 6 in = 72 in2. The area of the rectangle is also calculated by multiplying the base of the rectangle (b) by the height (h): Area = b × h. In this case, the area of the rectangle is 12 in × 6 in = 72 in2. Since both figures have the same base and height, they have the same area.
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