Imran can row at 3 m/s against the current and at 6 m/s with the current. Find the speed of the current.​

As per the given costs, 80 notebooks were sold at the student government fundraiser.

Let the number of notebooks sold be = N

Let the number of t-shirts sold be = T

Setting the equation, representing the total number of items sold

N + T = 90

or N = 90 - T.

Setting the equation, representing the total amount -

6N + 12T = 600

Substituting this value of N into the second equation -

6(90 - T) + 12T = 600

540 - 6T + 12T = 600

6T = 600 - 540

6T = 60

T = 60 / 6

T = 10

Substituting the value of T back into the first equation to find the value of n or total notebooks -

N + 10 = 90

N = 90 - 10

N = 80

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Therefore, the limit of the given expression as x approaches 0 is 3125/120.

First, we will find the Maclaurin series for sin(5x). The Maclaurin series for sin(x) is given by:
sin(x) = x - (x^3)/6 + (x^5)/120 - ...
So, the Maclaurin series for sin(5x) is:
sin(5x) = 5x - (5x)^3/6 + (5x)^5/120 - ...
Now, substitute this into the expression and simplify:
lim (sin(5x) - 5x + 125x^3/6) / x^5 as x→0
lim (5x - (5x)^3/6 + (5x)^5/120 - 5x + 125x^3/6) / x^5 as x→0
lim (-(5x)^3/6 + (5x)^5/120 + 125x^3/6) / x^5 as x→0
Now, divide each term by x^5:
lim (-5^3x^2/6 + 5^5x^0/120 + 125x^(-2)/6) as x→0
As x approaches 0, x^(-2) approaches infinity, and 5^5x^0 approaches 5^5. Therefore:
lim = -125/6 + 5^5/120
Combine the terms:
lim = (5^5 - 125*20) / 120
lim = 3125 / 120

Therefore, the limit of the given expression as x approaches 0 is 3125/120.

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Answer:

The area if the triangle is 15 yd^2

Step-by-step explanation:

The formula to find the area if a triangle is base × height ÷ 2. So for this question it is 10×3÷2=15

The probability that the events do not occur is 0.6778`.

The probability that the events do not occur is given by `P(Ac)=1-P(A)` and `P(Bc)=1-P(B)`.

The given probabilities are `P(A)=0.2272` and `P(B)=0.4506`.

Using the formula `P(A∪B)=P(A)+P(B)-P(A∩B)`, we have `P(A∩B) = P(A) + P(B) - P(A∪B)`

Using the fact that the two events are mutually exclusive, we get `P(A∩B) = 0`.

Thus, `P(A∪B) = P(A) + P(B) = 0.2272 + 0.4506 = 0.6778`.

The probability that either A or B but not both occurs is given by `P(AΔB) = P(A∪B) - P(A∩B) = 0.6778 - 0 = 0.6778`.

Hence, the required probability is `P(AΔB) = 0.6778`.

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Increase the length of the tube.

The natural frequency of a tube is determined by the speed of sound in the material of the tube and the length of the tube. Increasing the length of the tube will increase the wavelength of the standing waves that can be formed inside the tube, which in turn will increase the natural frequency of the tube. Decreasing the length of the tube will have the opposite effect, decreasing the natural frequency. Making holes in the tube will change the boundary conditions and may affect the natural frequency, but it is not a guaranteed way to increase it. Changing the composition of the tube will change the speed of sound in the material, which may increase or decrease the natural frequency depending on the new material's properties.

I hope this helps :)

Answer:

< 40, 28, 72 >

Step-by-step explanation:

Given

y = < 2, 6, 8 > and z = < 7, - 2, 6 > , then

6y + 4z

= 6 < 2, 6, 8 > + 4 < 7, - 2, 6 >

Multiply each component by the scalar quantity

= < 6(2), 6(6), 6(8) > + < 4(7), 4(- 2), 4(6) >

= < 12, 36, 48 > + < 28, - 8, 24 >

Add corresponding components

= < 12 + 28, 36 - 8, 48 + 24 >

= < 40, 28, 72 >

Answer:

a=corresponding sides of congruent triangles

b= by SAS condition ( ac=ce, acb=oce,oc=cb)

Answer:

1st option.

\(\sum_{k=1}^{6} \frac{1}{2k-1}\)

Step-by-step explanation:

The given sequence is as follows:

\(1 + \dfrac{1}{3}+ \dfrac{1}{5}+ \dfrac{1}{7}+ \dfrac{1}{9}+ \dfrac{1}{11}\)

Here, we can see that the denominator is in AP and the sequence is:

1, 3, 7, 9, 11

first term, a  = 1

Common difference, d = 2

We know that nth term for an AP:

\(a_n = a+(n-1)d\)

where a is the first term and

d is the common difference.

So, nth term for above AP:

\(a_n = 1+(n-1)\times 2\\\Rightarrow 2n-1\)

Here, we have 'k' in place of 'n':

\(a_k = 2k-1\)

And as per the given sequence in the question, the kth term is simply the reciprocal:

i.e. \(\dfrac{1}{2k-1}\)

and sum is to be done up to k = 6 from k = 1.

Hence, the summation notation for the sequence

\(1 + \dfrac{1}{3}+ \dfrac{1}{5}+ \dfrac{1}{7}+ \dfrac{1}{9}+ \dfrac{1}{11}\)

is:

\(\sum_{k=1}^{6} \frac{1}{2k-1}\)

Answer:

100

Step-by-step explanation:

In 17.92, the 7 is in the ones digit, so its value is 7.

In 92.17, the 7 is in the hundredth digit, so its value is 0.07

7 is 100 times 0.07

Answer:

0.5

Step-by-step explanation:

The slope of the line is 1/2, so the answer is 0.5

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Answer:

GIVE ME MY RAMEN

Step-by-step explanation:

3.

add like terms

30 + 7k = 100

100-30 = 70

70 divided by 7k = 10

k = 10

4. add the z's together

2z - 6 -2 = -10

+ 6 + 2

-10 will be -2 now since we dragged the -6 and -2 to the other side

2z = -2

z = -1

5. 3.2x - 1.7x = 1.5x

1.5x + 5.5 = 10

10 would be 4.5 since we dragged 5.5 to the other side so it would be 10 - 5.5

3.2x = 5.5

x = 1.71875

6.

3/4x - 1/4x = 2/4x

14 - 3 = 11

2/4x = 11

x = 22

Answer:

8 balloons

Step-by-step explanation:

We want to find how many she kept for herself.

She brought 24 balloons to the picnic.

She gave 1/3 to Karen.

She will be left with 2/3 of the balloons:

2/3 * 24 = 16

She will be left with 16 balloons.

She gave 1/2 of what was left to Tim. She will be left with 1/2 of the balloons:

1/2 * 16 = 8

She will be left with 8 balloons.

we can still express its behavior as x approaches positive infinity by stating that the limit is equal to -∞.

To determine whether the given limit leads to a determinate or indeterminate form, we must first examine the limit as x approaches positive infinity:

lim (x→+∞) (4-x)

As x becomes infinitely large, the expression (4-x) becomes increasingly negative, approaching negative infinity. Since the limit approaches a specific value, in this case, -∞, it is considered a determinate form.

The given limit, lim (x→+∞) (4-x), is a determinate form because as x approaches positive infinity, the expression (4-x) becomes increasingly negative, ultimately approaching negative infinity.

The limit of the given expression, lim (x→+∞) (4-x), is a determinate form and evaluates to -∞.  about existence, the limit does not exist in the conventional sense, as it does not approach a finite value. However, we can still express its behavior as x approaches positive infinity by stating that the limit is equal to -∞.

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The percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.

According to statement we have given

239 of the 500 households in the sample had internet access.

So, find sample percentage then

Sample percentage= 500/239 =0.478=47.8%

Thus we estimate the percentage as 47.8%.

The box contains 25,000 tickets of which 47.8% are 1's and the remaining 52.2% tickets are 0's. We will draw 500 tickets from the box.

Number of draws=500

Now, find the SD then

\(SD= (Big number - Small number) * \sqrt{Fraction with big number * fraction with small number}\)

Substitute the values then

\(SD= (1 - 0) * \sqrt{0.478 *0.522}\)

\(SD=0.4995\)

Now find the standard error of sum then

The standard error of the sum is the product of the square root of the number of draws and the standard deviation of the box.

\(SE sum =\sqrt{Number of draws} * SD box\)

\(SE sum =\sqrt{500} * 0.4995\)

\(SE sum =11.16\)

Now find the standard error of percentage then

The standard error of the percentage is the standard error for the sum divided by the sample size.

SE percentage= SE for number/Number of draws ×100%

= 50011.1692×100%

≈0.022×100%

=2.2%

​

Thus the percentage of households in the town with internet access is estimates as 47.8%, give or take 2.2% or so.

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Answer:

The correct answer is option C: 5

Step-by-step explanation:

Each large box weighs 50 pounds, and each small box weighs 5 pounds.

Let's assume the weight of a large box is L pounds, and the weight of a small box is S pounds. We can set up a system of equations based on the given information.

From the given information, we know that the combined weight of a large and small box is 55 pounds, so we have the equation: L + S = 55. This equation represents the total weight of the boxes.

We also know that the truck is transporting a total of 130 boxes, which is the sum of 70 large boxes and 60 small boxes: 70L + 60S = 3700. This equation represents the total weight of all the boxes on the truck.

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 1, we can express L in terms of S: L = 55 - S.

Substituting this value of L into the second equation, we have: 70(55 - S) + 60S = 3700.

Simplifying the equation, we get: 3850 - 70S + 60S = 3700.

Combining like terms, we have: -10S = -150.

Dividing both sides by -10, we find: S = 15.

Substituting this value of S back into Equation 1, we can solve for L: L + 15 = 55, which gives L = 40.

Therefore, each large box weighs 40 pounds, and each small box weighs 15 pounds.

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The greatest acceleration when the unbalanced force is applied will be experienced by the least weighted box ( i.e., the mass of 2 kg)

Acceleration: it is defined as rate of change of velocity with respect to time.

Unbalanced Force:  it means that the force applied in one direction is greatest than the force applied in the opposite direction.

Given that, F = 8n.

let us assume that the boxes are of 2kg, 4 kg, 6 kg and 8 kg.

According to the 2nd law of motion: the external unbalanced force is directly proportional to rate of change of momentum or Force is equal to the product of mass and acceleration.

                         F = m × a

                 ⇒     a = F/ m

where,  F is Force, m is mass and a is acceleration.

Now, acceleration of the box of 2kg = 8÷2 = 4 m/s²

         acceleration of the box of 4kg = 8÷ 4 = 2 m/m²

         acceleration of the box of 6 kg = 8÷ 6 = 1.34 m/s²

         acceleration of the box of 8kg = 8÷ 8 = 1 m/s²

∴ the box with mass of 2kg experience the greatest acceleration.

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Answer:

4(6+7)

Explanation:

24+28

(4×6)+(4×7)

4(6+7)

Answer:

x ≤ 3

Step-by-step explanation:

The equation of the solid line is x = 3

The shaded region to the left of x = 3 is less than 3 , thus

x ≤ 3 matches the graph

The probability that it will rain both days is \(\frac{1}{4}\).

According to the question

Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.

Assuming that the chance of rain is independent of the day

Probability is the chance that some event will happen.

It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.

Probability = Number of ways it can occur/Total number of outcomes

Probability of rain on first day = 1/2

Probability of rain on second day = 1/2

Then

Probability of rain on both days = \(\frac{1}{2}\) × \(\frac{1}{2}\) = 1/4

Hence,

The probability that it will rain both days is \(\frac{1}{4}\).

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Answer:

(3,2) and (-2,7)

Step-by-step explanation:

Look for the intercepts of both graphs.

Mark me brainliest pls

Answer:

√10+√15-√14-√21

Explanation:

(√2 * √5) = √10

(√2 * -√7) = -√14

(√3 * √5) = √15

(√3 * -√7) = -√21

Put it all together: √10 + √15 - √14 - √21

Hope this helped :)

The simplified form of the expression  (√2+√3)(√5-√7) is √10-√14+√15-√21

An expression is combination of variables, numbers and operators.

The given expression is (√2+√3)(√5-√7)

√2(√5-√7) + √3(√5-√7)

We have to apply  distributive property

√2.√5 - √2.√7 + √3.√5 -√3.√7

√2×5 -√2×7 +√3×5 -√3×7

√10-√14+√15-√21

Hence, the simplified form of the expression  (√2+√3)(√5-√7) is √10-√14+√15-√21

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Answer:

The answer is 2+/- 2 over(/) 3

Step-by-step explanation:

You use the discriminant formula :)

Given:

The function is,

a) The graph of the given function us,

Answer: option B)

b) f(1) and f(5) is,

Answer:

c) the domain of the function is,

Aaron can arrange the 13 songs on the CD in 6,227,020,800 different ways.

To determine the number of different ways Aaron can arrange the 13 songs on the compact disk (CD), we need to find the total number of permutations for the songs. Since there are 13 songs, we can calculate this using the formula:

Permutations = 13!

Step-by-step explanation:

1. Calculate the factorial of 13 (13!).
2. The factorial function is the product of all positive integers up to that number (e.g., 5! = 5 x 4 x 3 x 2 x 1).

So, 13! = 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 6,227,020,800

Therefore, Aaron can arrange the 13 songs on the CD in 6,227,020,800 different ways.

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Answer:

your answer is 15.6

Step-by-step explanation:

5x divided by 3= 26

multiply 3 by each side

5x = 78

divide 5 by each side to get x by itself

x= 15.6

The slope of a plot of the natural log of the vapor pressure of a substance versus 1/t is  - e.

What is slope?

\(l_{n} P = \frac{- Delta H_{vol} }{R} ( 1 T ) + C\)

Yy = mx + c

\(m = \frac{- Delta H_{vol} }{R}\)

m = slope

Ans = - e

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Answer: Median is 5

Step-by-step explanation: To find the median, we first need to arrange the numbers in order from least to greatest:

0 0 3 7 10 27

The median is the middle number, or the average of the two middle numbers if there are an even number of values. In this case, there are 6 values, so the median is the average of the two middle numbers:

median = (3 + 7) / 2

median = 5

Therefore, the median of the given numbers is 5.