40%of a number is 160 what is 60% of the same number​

Step-by-step explanation:

I'm not sure if I'm using substitution method but I guess it's x = 12.4

The answers to the questions as given in the task content are as follows;

The analysis of the diagram in discuss is such that the points which are on the horizontal line in discuss are such that; R, A, T and S are points on the line from left to right.

On this note, when a line AB extends away from the centre of the intersecting lines DAC and RATS, it follows that;

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Work done lifting the bucket and rope to the top of the building is 4005.75 Joules

To express this concept mathematically, the work W is equal to the force f times the distance d, or W = fd. If the force is being exerted at an angle θ to the displacement, the work done is W = fd cos θ.

Initially bucket hold = 25kg. Sand

Sand leaks 0.1 kgs each meter it is lifted

At height x meter bucket hold = (25 - 0.1x) kg of sand

Length of rope = 15 meter

density of rope = 0.4kg / meter

weight of rope = 15 (0.4) = 6kg.

At height x meter, weight of rope = (6 - 0.4x)

Total weight at height x meter = (25-0.1x) + (6-0.4x)

                                                   = (31 - 0.5x) kg

force = (31-0.5x) g Newtons. = [(31-0.5x) 9.8] Newton

Work = force × displacement

\(Work= \int_{0}^{15}9.8(31-0.5x)dx\)

          \(=9.8[31x-0.5 \frac{x^2}{2} ]_{0}^{15}\)

          \(=9.8[31(15)-0.25(15)^2]-0\)

          \(=4005.75 joules\)

Hence, work done 4005.75 Joules

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Answer:

RATIONAL

Step-by-step explanation:

Answer:

4 times

Step-by-step explanation:

First you take the number of times and divide them by the number of times he  attempted it. (2)/(8+2) or 1/5. Then you set up an inequality which would look like this. x/20=1/5 then you will cross multiply them to get this equation 5x=20. then you solve for x and you would get x=4. So you can expect him to hit four bullseyes in the next 20 attempts.

Answer:

32 bags

Step-by-step explanation:

0.5 × 16 = 32

hope it helps

Answer:

HHSheikh Zayed road is dream of a great weekend and It is a great day ☺️ is the only thing I would like to know that you have received your name is a great day and time of year for me is the only thing I want ☺️☺️ and time again and time of reading is a great time of year for the only way we can do it in a few more days to get to get to the only thing that you have a few more days to get to the next day ☺️ is a great weekend too and time of year is the next

Step-by-step explanation:

return policy and time again and I will be in touch with you have any questions or need any further information please contact me at the only thing I would be in touch with ☺️ is the best ☺️ and time is a good time of the only thing I would

If the initial velocity is 75 feet per second, it will take approximately 5.125 seconds for the ball to hit the ground.

The given formula h= -16t²+vt+s represents the height (h) of an object thrown vertically in the air at time (t), with initial velocity (v) and initial height (s). In this case, we are given that the initial height of the softball is 4 feet and the initial velocity is 75 feet per second.

We want to find out how long it will take for the ball to hit the ground, which means we want to find the time (t) when the height (h) is 0.

Substituting the given values into the formula, we get:

0 = -16t² + 75t + 4

This is a quadratic equation in standard form, which we can solve using the quadratic formula:

t = (-b ± √(b² - 4ac)) / 2a

Where a=-16, b=75, and c=4. Substituting these values into the formula, we get:

t = (-75 ± √(75² - 4(-16)(4))) / 2(-16)

t = (-75 ± √(5625 + 256)) / (-32)

t = (-75 ± √(5881)) / (-32)

We can simplify the expression under the square root as follows:

√(5881) = √(49121) = 711 = 77

So we have:

t = (-75 ± 77) / (-32)

Simplifying further, we get two possible solutions:

t = 0.5 seconds or t = 5.125 seconds

Since the softball player hits the ball when it is 4 feet above the ground, we can disregard the solution t=0.5 seconds (which corresponds to when the ball is at its maximum height) and conclude that it will take approximately 5.125 seconds for the ball to hit the ground.

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Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6

Answer:

The answer is 375

Step-by-step explanation:

You divide 500 by four and then you get 125. And then after you want to multiply 125 by 3 the numerator and then you get 375. And the way you get four in the equation is when you divide the number by the denominator.

Answer:

375.)

Step-by-step explanation:

First, let's write the problem:

500/1 × 3/4

Now in these types of problems, you can simplify by using a trick.

Do you see how 500 and 4 are across each other? Since 500 is divisible by 4:

500 ÷ 4 = 125.

So now we have 125/1 × 3/1 which is a lot easier to work with.

125 × 3 = 375

1 × 1 = 1

375/1 or 375

Therefore, 375 seats are filled.

Answer:

10 green

Step-by-step explanation:

24 total balls. 17 Not red, so 24-17=7. 7 Red balls. That leaves 17 balls. 10 of them are neither yellow nor blue, and since the amount of red balls has been figured out, we do not need to account for them. 17 balls - 10 not yellow or blue equals 7 balls that can be yellow or blue. 17 balls left, minus the 7 yellow or blue balls equals 10.

Answer:

Step-by-step explanation:

Remaining fraction:

1/5 of books are encyclopedia

Answer:

Let the total fraction of books be 1, then;

\(1 - ( \frac{1}{10} + \frac{2}{10} + \frac{1}{2} ) \\ 1 - ( \frac{(1 + 2 + 5)}{10} ) \\ (1 - \frac{8}{10}) = \frac{(10 - 8)}{10} \\ \frac{2}{10} = \boxed{ \frac{1}{5} }\)

Answer:

The answer is -5. To do this you first draw your number line and label it from +7 to -10. You then count from from seven till the 11th number which in this case it's -5

Answer:

See image

Step-by-step explanation:

It cant be wrong

Answer:

-6.27

Step-by-step explanation:

Answer:

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

and \(f''(x) = e^{x}(x^{3}+6x^{2} + 6x + 1)\)

Step-by-step explanation:

From the question,

f(x) = (x3 + 1)ex

That is,

\(f(x) = (x^{3} +1)e^{x}\)

Then , we can write that

\(f(x) = x^{3}e^{x} +e^{x}\)

To find f'(x), we will differentiate \(x^{3}e^{x}\) and then add it to the differential of \(e^{x}\)

First, we will differentiate \(x^{3}e^{x}\),

Let \(y(x) = x^{3}e^{x}\) (This is a product)

Then,

\(f(x) = y(x) + e^{x}\)

Hence,

\(f'(x) = y'(x) + (e^{x})'\)

Given \(y(x) = u(x) v(x)\), Using the product rule

\(y'(x) = u(x).v'(x) + u'(x).v(x)\)

Hence,

\(y'(x) = x^{3}(e^{x})' + (x^{3})'e^{x}\)

\(y'(x) = x^{3}e^{x} + 3x^{2}e^{x}\)

and

\((e^{x})' = e^{x}\)

\(f'(x) = y'(x) + (e^{x})'\)

∴ \(f'(x) = x^{3}e^{x} + 3x^{2}e^{x} + e^{x}\)

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

For f ''(x)

To find f ''(x), will differentiate f '(x)

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

This is also a product, then we will apply the product rule

From the product rule,

Given \(y(x) = u(x) v(x)\), Using the product rule

\(y'(x) = u(x).v'(x) + u'(x).v(x)\)

Here, Let\(u(x) = e^{x}\) and \(v(x) = x^{3} + 3x^{2} + 1\)

Then,

\(f''(x) = e^{x}(x^{3} + 3x^{2} + 1)' + (e^{x})'(x^{3} + 3x^{2} + 1)\)

\(f''(x) = e^{x}(3x^{2} + 6x ) + (e^{x})(x^{3} + 3x^{2} + 1)\)

∴\(f''(x) = e^{x}(x^{3}+6x^{2} + 6x + 1)\)

Hence,

\(f'(x) = e^{x}(x^{3} + 3x^{2} + 1)\)

and \(f''(x) = e^{x}(x^{3}+6x^{2} + 6x + 1)\)

Answer:

C -2<=x<=1

Step-by-step explanation:

x-1<0 ===> x<1

x+2<0 ===> x<-2

Answer:

4!

Step-by-step explanation:

20/5=4

Answer:

0

Step-by-step explanation:

7 + (-8) + 2 + (-1)

is the same as:

7 - 8 + 2 - 1

Simplify these:

-1 + 1

Solve:

0

Answer:

Step-by-step explanation:

y + 50 = 180

y = 130

Answer:

1/7

Step-by-step explanation:

Given series :-

To find :-

From the Series , the common ratio will be ,

⇝ CR = -2/25 ÷ 1/5

⇝ CR = -2/25 × 5

⇝ CR = -2/5

Using formula of GP :-

⇝ S_∞ = a /1 - r , -1 < r < 1

⇝ S = 1/5 ÷ ( 1 - (-2/5))

⇝ S = 1/5 ÷ ( 1 +2/5)

⇝ S = 1/5 ÷ 5/7

⇝ S= 1/7

Using the Central Limit Theorem, we have that:

a) Yes, it can be used, as np > 10 and n(1 - p) > 10.

b) There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For the sample, we have that:

Hence the normal approximation can be used.

As for part B, if we have p = 0.9 and n = 100, the mean and the standard error are given by:

The probability of a sample proportion of 85% of less is the p-value of Z when X = 0.85, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.85 - 0.9}{0.03}\)

Z = -1.67

Z = -1.67 has a p-value of 0.0475.

There is a 0.0475 = 4.75% probability that the proportion in the random sample of 100 orders is the same as the proportion found in the audit sample or less.

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The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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a. The formula for the perimeter of a square is P=4L, where L is the length of it's sides.

b. The formula for the area of a square is A=LxL=L^2, where L is the length of it's sides.

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

8

Step-by-step explanation:

6:3=2

six divided by three equals four (hence the ratio)

2*4=8

two times four equals eight.

Given

This can be written as:

Answer:

7 6/7 tons.

Step-by-step explanation:

2 1/5 containers = 11/5 containers, written as an improper fraction. Each container holds 3 4/7 tons of sugar; this capacity is 25/7, written as an improper fraction.

The product of these two numbers is 55/7 tons, or 7 6/7 tons.

The solution to the system of linear equations is (x, y) = (7, 3).

Herein we find that the coordinates of the midpoint and part of the coordinates of the ends of the line segment are known. We must determine the values of the missing coordinates by the midpoint formula:

0.5 · (x, 7) + 0.5 · (-1, y) = (3, 5)

Which is equivalent to the system of linear equations:

0.5 · x - 0.5 = 3               (1)

3.5 + 0.5 · y = 5              (2)

The solution to the system of linear equations is (x, y) = (7, 3).

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