a) Solve 3(x – 5) = 18

Answer:A

Step-by-step explanation: 1 Gallon is equal to 8 pints.

Answer:

A

Step-by-step explanation:

pint=1/8 of a gallon

therfor 7 pints = 7/8

7/8<1gal

Answer:

300 raisins

Step-by-step explanation:

sum the parts of the ratio, 3 + 27 = 30 parts

Divide the total by 30 for the value of one part of the ratio.

3000 ÷ 30 = 100 ← value of 1 part of the ratio , then

3 parts = 3 × 100 = 300 ← number of raisins in a box

To correctly identify formatted scientific notation, we need to look for numbers expressed in the form of a × 10^b, where "a" is a number between 1 and 10, and "b" is an integer.

Here are the correctly formatted scientific notations from the options provided:

- 8 × 10^6 (this is equivalent to 8,000,000)
- 6.1 × 10^12 (this is equivalent to 6,100,000,000,000)
- 0.802 × 10^4 (this is equivalent to 8,020)
- 4.532 × 10^-9 (this is equivalent to 0.000000004532)

The other options are not in the correct scientific notation format.

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Answer:

200 is the answer since you round up

Step-by-step explanation:

Quartile Formula:

Formula for Lower quartile (Q1) = N + 1 multiplied by (1) divided by (4)

Formula for Middle quartile (Q2) = N + 1 multiplied by (2) divided by (4)

Formula for Upper quartile (Q3) = N + 1 multiplied by (3) divided by (4)

Formula for Interquartile range = Q3 (upper quartile) – Q1 (lower quartile)

i don't know how to work it out but i gave you some information.

The indefinite integral of x^11 sin(3x^(13/2)) dx is -(2/13) * \(x^11 * cos(3x^(13/2)) / (9x^3) + (16/271) * sin(3x^(13/2)) + C\), where C is the constant of integration.

Substituting these into the integral, we get: integral of x^11 sin(3x^(13/2)) dx

= integral of sin(u) * x^11 * (2/39)u^(-9/13) du

= (2/39) integral of sin(u) * x^11 * u^(-9/13) du

Next, we can use integration by parts with u = x^11 and dv = sin(u) * u^(-9/13) du. Solving for dv, we get:

dv = sin(u) * u^(-9/13) du

= (1/u^(4/13)) * sin(u) du

Solving for v using integration, we get:

v = -cos(u) * u^(-4/13)

Now we can apply integration by parts:

integral of sin(u) * x^11 * u^(-9/13) du

= -x^11 * cos(u) * u^(-4/13) - integral of (-4/13) * x^11 * cos(u) * u^(-17/13) du

Substituting back u = 3x^(13/2) and simplifying, we get:

integral of x^11 sin(3x^(13/2)) dx

= -(2/39) * x^11 * cos(3x^(13/2)) * (3x^(13/2))^(-4/13) - (8/507) * integral of x^11 cos(3x^(13/2)) * x^(-3/13) dx + C

Simplifying further, we get:

integral of x^11 sin(3x^(13/2)) dx

= -(2/13) * x^11 * cos(3x^(13/2)) / (9x^3) - (8/507) * integral of x^(-28/13) cos(3x^(13/2)) dx + C

Finally, we can evaluate the last integral using the same substitution as before, and we get:

integral of x^11 sin(3x^(13/2)) dx

= -(2/13) * x^11 * cos(3x^(13/2)) / (9x^3) + (16/271) * sin(3x^(13/2)) + C

Therefore, the indefinite integral of x^11 sin(3x^(13/2)) dx is -(2/13) * x^11 * cos(3x^(13/2)) / (9x^3) + (16/271) * sin(3x^(13/2)) + C, where C is the constant of integration.

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Answer:

=64x^14+169

Step-by-step explanation:

happy to help ya :)

Answer:

2c(c - 3)(c - 8)

Step-by-step explanation:

Hello!

Factor:

Think: What two numbers multiply to 24, and add up to -11?

Answer: -8 and -3

Split up the -11c into -8c and -3c:

Answer:

(5x+6)(2x+5)-(2x+4)(x+8) simplified is 8x^2+17x-2

Step-by-step explanation:

Answer:

13x²+16x+28

Step-by-step explanation:

S=(5x+6)×(3x+2)=15x²+28x+12

2x+5-x-3=x-2

5x+6-3x+2=2x+8

(x-2)×(2x-8)=2x²-12x+16

15x²+28x+12-2x²-12x+16=13x²+16x+28

For a discrete random variable X valid on non-negative integers, The main answer is that Pr(X ≤ 2) cannot be determined based solely on the given information.

To determine Pr(X ≤ 2), we need additional information about the random variable X, such as its probability mass function (PMF) or cumulative distribution function (CDF). The given information provides the expected value of z^X, but it does not directly give us the probabilities of X taking specific values.

Without knowing the PMF or CDF of X, we cannot determine Pr(X ≤ 2) solely based on the given information. Additional information about the distribution of X is required to calculate the desired probability.

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Answer:

36

Step-by-step explanation:

3=3

9=3*3 = 3^2

12=2*2*3 = 2^2*3

lcm = 2^2*3^3

      = 4*9

therefore lcm= 36

Answer:

36

Step-by-step explanation:

\(\bold{3} \times \bold{12} = 36\\\bold{9} \times 4 = 36\)

The solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

To solve the given differential equation (DE), we can use the integrating factor method. The steps are as follows:

1. Multiply both sides of the DE by the integrating factor, which is the exponential of the integral of the coefficient of y. In this case, the coefficient of y is (x + 2), so the integrating factor is e^(∫(x+2)dx) = e^(x^2/2 + 2x).

So, we have: (x + 1) e^(x^2/2 + 2x) dy/dx + (x + 2) e^(x^2/2 + 2x) y = 2x e^(x^2/2 + 2x) e^(-xy)

2. Notice that the left-hand side of the DE is the product of the derivative of y with respect to x and the integrating factor, so we can apply the product rule of differentiation to obtain:

d/dx [ e^(x^2/2 + 2x) y ] = 2x e^(x^2/2 + 2x) e^(-xy)

3. Integrate both sides of the previous equation with respect to x to obtain:

e^(x^2/2 + 2x) y = - e^(-xy) + C

where C is the constant of integration.

4. Solve for y by dividing both sides by the integrating factor:

y = [- e^(-xy) + C] e^(-x^2/2 - 2x)

This is the general solution of the given DE.

Note that the solution involves an integral that cannot be evaluated in closed form, so the answer cannot be simplified further.

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Answer:

Add 5 to both sides.

Step-by-step explanation:

3.7 = x + (-5)

3.7 + 5 = x + ( -5) + 5

5 cancels on the right

8.7 = x

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3.7=x+(-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 3.7=x-5

Add 5 to both sides of an equation, we get

3.7+5=x-5+5

x=8.7

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

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Answer:

EF=35

EG=22

Step-by-step explanation:

EF

7y-14=2y+21

5y=35

y=7

EF=7(7)-14=49-14=35

EG

15x+7=12x+10

3x=3

x=1

EG=15(1)+7=15+7=22

Answer:

(a). 35 units ; (b). 44 units

Step-by-step explanation:

(a). 7y - 14 = 2y + 21 ⇒ y = 7

EF = 7(7) - 14 = 35 units

(b). EJ = JG

15x + 7 = 12x + 10 ⇒ x = 1

EG = 2 × (15(1) + 7) = 44 units

To convert grams to moles per gram, you need to find the molar mass of the substance in grams per mole. Then, divide the number of moles by the given mass to get moles per gram.

To convert grams to moles per gram, you first need to determine the molar mass of the substance you are interested in. The molar mass is the mass of one mole of the substance, expressed in grams. Once you know the molar mass, you can use it to convert grams to moles, and then divide by the total mass to get moles per gram.

Here are the steps to follow:

Determine the molar mass of the substance. This is the sum of the atomic masses of all the atoms in the molecule, expressed in grams per mole. You can find the atomic masses on the periodic table.

Convert the given mass from grams to moles, using the formula:

moles = mass / molar mass

where mass is the given mass in grams, and molar mass is the calculated molar mass in grams per mole.

Divide the number of moles by the given mass, to get the moles per gram. This gives you the number of moles of the substance per gram of the sample.

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Using a system of linear equation, the cost of each shirt and pant is $9 and $11 respectively.

A system of linear equations is a collection of one or more linear equations that contain two or more variables. The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system.

A linear equation is an equation that can be written in the form of ax+by=c, where x and y are variables, and a, b, and c are coefficients.

In this problem, we need to define our variables and the solve the equations.

Let;

x + 2y = 31 ...eq(i)

3x + y = 38 ...eq(ii)

Solving both equations

x = 9, y = 11

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Using the permutation formula, it is found that the probability that joseph will be able to unlock the phone on his first attempt is \(\frac{1}{5040}\)

The number of possible permutations of x elements from a set of n elements is given by:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

In this problem, 4 numbers are taken from a set of 10, hence the number of possible permutations is:

\(P_{10,4} = \frac{10!}{6!} = 5040\)

Then the probability that he gets the correct number is:

\(p = \frac{1}{5040}\)

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Answer:

Step-by-step explanation:

You want to know angles x, y, and z in the given figure where parallel lines 'a' and 'b' are crossed by a transversal. The sum of these angles is 290°.

Angles y and z are called consecutive interior angles. As such, they are supplementary, so their sum is 180°.

  x + y + z = 290°

  x + 180° = 290°

  x = 110°

Angles x and y are vertical angles, so are congruent.

  y = x = 110°

Then z is found from ...

  y + z = 180°

  110° + z = 180°

  z = 70°

The measures of x, y, and z are 110°, 110°, and 70°, respectively.

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Answer: 24+6=30

Step-by-step explanation:

Football(6)  rugby(2)  hiking(3)

the order it gave you the info was football then rugby then hiking they way it gave you the number was 6,2,3 so football was said first and the number 6 was said first so football matches up with 6 therefore just add the two number and you get 30

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

5^10

Step-by-step explanation:

Hope I helped!

According to the question Rounding to the nearest whole number, it will take Mary approximately 5 years to repay the loan. The answer is 5 years.

To calculate the time it will take for Mary to repay the loan, we can use the formula for the number of years (t) needed to repay a loan:

t = loan amount / annual payment,

where the loan amount is $8,000 and the annual payment is $1,500.

Substituting the given values into the formula, we have:

t = $8,000 / $1,500 ≈ 5.3333.

Rounding to the nearest whole number, it will take Mary approximately 5 years to repay the loan. The answer is 5 years.

Therefore, the answer is 5 years.

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Answer: To find the equation of a line passing through two points, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of one of the points, and m is the slope of the line.

To find the slope, we can use the formula:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

So, let's plug in the values we have:

m = (-8 - 3)/(-8 - (-10)) = (-8 - 3)/2 = -11/2

Now we can use either point to find the equation. Let's use (-10, 3):

y - 3 = (-11/2)(x - (-10))

y - 3 = (-11/2)x - 55/2

y = (-11/2)x - 49/2

So the equation of the line through (-10, 3) and (-8, -8) is:

y = (-11/2)x - 49/2.

The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532.

150 x 22,500 equals the total salary before correction, or Rs.

After rectification, the total salary equals

(150-2)*22500 + 25760 + 18590, or Rs. 339060.

Correct mean pay is equal to Rs. 339060 / 150, or Rs. 22532.

Initial reports stated that the mean wage for 150 workers was Rs. 22500 per month. Further examination revealed, however, that two employees' salary had been put incorrectly as Rs 25760 and Rs 19590, respectively. The two employees' actual pay were Rs. 27760 and Rs. 18590. The total salary before rectification was therefore 150*22,500, or Rs. 337,000. After two employees' pay were adjusted, the total salary was (150-2)*22500.The average monthly pay for 150 employees was Rs 22500; however, after two employees' salaries were incorrectly inputted, the actual average monthly pay for employees was Rs 22532 (150-2)*22500 + 25760 + 18590 = Rs339060. Consequently, it was determined that Rs339060 / 150 = Rs22532 was the proper mean wage paid to employees. After correcting the two incorrectly reported salaries, the average monthly wage for the organization's employees came to Rs22532.

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Answer:

the bin, 60-69 has the most data values

Step-by-step explanation:

since it has the highest frequency it has the most data values

Answer:

Step-by-step explanation:

The bin 60-69, contains the most data 100% positive that this is correct

Answer:

g( \(\frac{3}{2}\) ) = - \(\frac{35}{4}\)

Step-by-step explanation:

substitute x = \(\frac{3}{2}\) into g(x) , that is

g( \(\frac{3}{2}\) )

= - 2( \(\frac{3}{2}\) )³ - \(\frac{4}{3}\) × \(\frac{3}{2}\)

= - 2 × \(\frac{27}{8}\) - 2

= = - \(\frac{27}{4}\) - \(\frac{8}{4}\)

= - \(\frac{35}{4}\)

The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 115 grams of a radioactive isotope

If we start with 115g of the isotope, after one half-life the quantity will diminish to \(\frac{115g}{2} = 57.5\) which is half the original quantity.

This can be written mathematically as: \(115g(\frac{1}{2})^{1}\)

After the second half life: \(\frac{57.5g}{2} = 28.75 = \frac{115g}{4} = (115g)\frac{1}{2}^{2}\)

After the third half life: \(\frac{28.75g}{2} = 14.37g = \frac{115g}{8} = (115g)(\frac{1}{2}) ^{3}\)

But now we can see a pattern developing, because for each new half-life we are dividing the quantity by 2 to a power that increases as the number of half-lives.

Then we can take the original quantity and quickly compute for 6 half-lives:

\((115g)(\frac{1}{2})^{6} = (115g)(\frac{1}{64}) = \frac{115g}{64} = 1.79g\)

The time it takes for the isotope to do this will depend on the isotope in question. For some it will be microsecond, and for others it will be years and decades. The isotope will typically decay to become another element or isotope.

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Answer:

none dogs dont live 65 years?

Step-by-step explanation: