One number chosen randomly from the integers 1 to 20. Find the probability of getting a number that is odd and prime.

Based on the amount of oranges bought, those sold at a profit and those sold at a loss, the overall profit is 14.2%

Assume that the buying price was $1 each.

The amount earned from 60% of them is:

= 60% x 100,000 x 1

= $60,000

The profit from selling 50% of the remaining is:

= (50% x 40,000) x 1.60

= $32,000

The loss from selling the other 50%:

= (50% x 40,000) x 0.90

= $22,222.22

Total selling price:

= 60,000 + 32,000 + 22,222.22

= $114,222.22

Total profit:

= (114,222.22 - 100,000) / 100,000

= 14.2%

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The rounding off a given number implies approximating the number to the required value. Thus the answer to the given question is 6 000 mm.

Rounding off a given number implies approximating the number to the required value. This can be done in two major ways: rounding up or rounding down.

Rounding up implies considering the required digit if it is up to or greater than 5, which turns to 1. Rounding down requires no consideration of digits less than 5 which turns to 0.

Thus considering the given question, Since the second digit is 4 which is lesser than 5, then it turns to a zero. So that;

rounding off 6 400 mm would give 6 000 mm.

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The end behavior of the function is as:

as →∞, f(x)→+∞ and as x→-∞, f(x)→+∞

The x-axis "endpoints" of a function's graph are referred to as its "end behavior" in this context.

choosing the polynomial function's greatest degree. The highest degree term will dominate the graph since it will expand more quickly than the other terms as x gets very big or very small.

Function f(x)=2∛x has the following graph:

The behavior of the function at its conclusion is because it leads to infinity.

as  x→∞, f(x)→+∞ and as x→-∞, f(x)→+∞

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Answer:g(x)

Step-by-step explanation:1/5 g (x)

For starters,

[tex]\cos(6t+\pi) = \cos(6t) \cos(\pi) - \sin(6t) \sin(\pi) = -\cos(6t)[/tex]

Now by the fundamental theorem of calculus, integrating both sides gives

[tex]\displaystyle \frac{ds}{dt} = s'(0) + \int_0^t 36 \cos(6u) \, du = 100 + 6 \sin(6t)[/tex]

Integrating again, we get

[tex]\displaystyle s(t) = s(0) + \int_0^t (100 + 6\sin(6u)) \, du = \boxed{100t - \cos(6t) + 1}[/tex]

Alternatively, you can work with antiderivatives, then find the particular constants of integration later using the initial values.

[tex]\displaystyle \int \frac{d^2s}{dt^2} \, dt = \int 36\cos(6t) \, dt \implies \frac{ds}{dt} = 6\sin(6t) + C_1[/tex]

[tex]\displaystyle \int \frac{ds}{dt} \, dt = \int (6\sin(6t) + C_1) \, dt \implies s(t) = -\cos(6t) + C_1t + C_2[/tex]

Now,

[tex]s(0) = 0 \implies 0 = -1 + C_2 \implies C_2 = 1[/tex]

and

[tex]s'(0) = 100 \implies 100 = 0 + C_1 \implies C_1 = 100[/tex]

Then the particular solution to the IVP is

[tex]s(t) = -\cos(6t) + 100t + 1[/tex]

just as before.

Using proportions, it is found that 68 more people prefer vanilla than do strawberry.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Researching this problem on the internet, it is found that, out of 400 people:

Hence the amounts are:

The difference is:

140 - 72 = 68.

68 more people prefer vanilla than do strawberry.

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Answer:X=12/7

Step-by-step explanation:

Y [tex]\alpha[/tex] X

⇒Y=KX

Where K is the constant

From the question,k=7

⇒ When Y=12,

y=KX

12=7X

X=12/7

Answer: 1223.07

Step-by-step explanation: you don't round up

Answer: 45

Step-by-step explanation: Given the way the formula is formatted, the first term is 1. The common difference can be found by subtracting a number from the number that follows (ex. 3-2 or 4-3), therefore it's 1. The desired term is what you're trying to find so 44-1=43. When you put it all together, the formula should be 2+1(44-1) which equals 45 when you follow the rules of PEMDAS.

The equilibrium expression is written as  [NH3]^2/[N2] [H2]^3.

A reaction involves the conversion of reactants to products. Now we know that the number that shows us the extent to which we can convert the reactants to products is given by the equilibrium constant. If the equilibrium constant is large and positive, then the reaction tends towards the conversion of reactants to products. on the other hand, when the reaction has a small equilibrium constant, then the reaction tends towards the reactants.

Thus, the magnitude of the equilibrium constant tells us how easily reactants are converted into products and this is necessary when we are trying to predict the direction in which a reaction will go or make calculations.

Given a reaction; N₂(g) + 3H₂(g) ----> 2NH3(g) we can now write the expression for the equilibrium of the reaction as;

K = [NH3]^2/[N2] [H2]^3

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Answer: B

Step-by-step explanation:

We can rearrange the equation to get [tex]x^2=-\frac{2}{3}[/tex], which clearly has complex roots.

Answer:

[tex]a = 8[/tex]  or [tex]a = -\frac{14}{3}[/tex]

Step-by-step explanation:

[tex]13(a+4)+24(a+5) = 3(a^{2} +9a+20)[/tex]

[tex]3a^{2} -10a-112=0[/tex]

[tex](3a+14)(a-8)=0[/tex]

[tex]a = 8[/tex]  or [tex]a = -\frac{14}{3}[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13}{a + 5} + \cfrac{24}{a + 4} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13(a + 4) + 24(a + 5)}{(a + 5)(a + 4)} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{13a + 52+ 24a + 120}{a {}^{2} + 5a + 4a + 20} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ 37a + 172}{a {}^{2} +9a + 20} = 3[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3( {a }^{2} + 9a + 20) = 37a + 172[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} + 27a + 60 = 37a + 172[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} + 27a - 37a + 60 - 172 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} - 10a - 112= 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {a}^{2} - 24a + 14a - 112 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3a(a - 8) + 14(a - 8) = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \: (a - 8) + (3a + 14) = 0[/tex]

So, required values of " a " are :

[tex]\qquad \sf  \dashrightarrow \: a = 8 \: \: \: or \: \: \: a = - \cfrac{ 14}{3} [/tex]

Answer:

You did not list any choices but if you simplify that the answer is 6√2x-3√2

Step-by-step explanation:

If they want you to factor it instead of simplifying the answer is 3√2(2x-1)

Answer:

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Step-by-step explanation:

So you haven't provided any options, but I'm assuming they want it in most simplified form.

To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.

So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y

[tex]5xy-3y+xy[/tex]

So in here, think of y as the variable and the 5x, -3, and x as the coefficients.

In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))

[tex](5x-3+x)y[/tex]

Simplify this expression to get

[tex](6x-3)y[/tex]

Now just plug the sqrt(2) back in as y and you get the expression

[tex](6x-3)\sqrt{2}[/tex]

Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Answer:

Work(W)=7.5*10⁴J

Step-by-step explanation:

Greetings !

[tex]firstly \: recall \: the \: work \: power \: equation \\ w = pt \\ substitute \: known \: variables \: to \: the \: equation \\ w = (500)(150) \\ change \: 2.5min \: to \: second = 150second \\ solve \: for \: work \\ w = 7.5 \times 10 {}^{4} j[/tex]

The correct statements about the solids are:

To find which statements are correct:

Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.

The volume of the first triangle is: [tex]2x^{2} h[/tex]

The volume of the second triangle is: [tex]x^{2} h[/tex]

Therefore, the correct statements about the solids are:

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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.

A) The bases are congruent.

B) The solids are similar.

C) The ratio of the volumes of the first solid to the second solid is 8:1.

D)The volume of the first solid is twice as much as the volume of the second solid.

E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more

surface area than the second solid.

the number of gallons that must be applied is 94 gallons.

Density is simply defined as the ratio of the mass to the volume occupied by an object or substance.

It is denoted with rho, 'ρ'

The formula for density is given as;

Density = mass/ volume

From the information given, we have that

To determine the volume, we need to make it the subject from the formula

Volume = density × mass

Volume = [tex]\frac{9. 4}{100}[/tex]

Volume = 0. 094

The number of gallons is given as;

= Volume × 1000

= 0. 094 × 1000

= 94 gallons

Thus, the number of gallons that must be applied is 94 gallons.

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The height of the pyramid is 14.4 cm.

volume of a pyramid = 1 / 3 Bh

where

Therefore,

volume of the cube = L³

where

Hence,

volume of the cube = 10³

volume of the cube = 1000 cm³

The volume of the pyramid is the same with the  volume of the cube.

Hence,

1000 = 1 / 3 Bh

The height of the pyramid is the same as the square base.

Therefore,

1000 = 1 / 3 (h²)h

1000 = 1  / 3 h³

cross multiply

3000 = h³

h = ∛3000

h = 14.4224957031

Hence, the height of the pyramid is 14.4 cm.

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The factors of the trinomial based on the information given include:

C. x – 7

E. x + 2

It should be noted that a trinomial is an algebraic expression that has three non-zero terms. Here, the examples of a trinomial expression: x + y + z is a trinomial in three variables x, y and z. Also, 2a² + 5a + 7 is a trinomial in one variables.

In this case, the algebra tile configuration has 0 tiles are in the Factor 1 spot and 0 tiles are in the Factor 2 spot. 24 tiles are in the Product spot: 1 is labeled + x squared, 7 are labeled negative x. Here, the trinomial is x² - 5x - 14.

The factors will be:

x² - 5x - 14.

x² + 2x - 7x - 14

x(x + 2) - 7(x + 2)

= (x + 2)(x - 7)

A polynomial with three terms is called a trinomial.

In conclusion, the correct options are C and E.

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There is a maximum value of 6 located at (x, y) = (1, 6).

The function given to us is f(x, y) = xy.

The constraint given to us is 6x + y = 12.

Rearranging the constraint, we get:

6x + y = 12,

or, y = 12 - 6x.

Substituting this in the function, we get:

f(x, y) = xy,

or, f(x) = x(12 - 6x) = 12x - 6x².

To find the extremum, we differentiate this, with respect to x, and equate that to 0.

f'(x) = 12 - 12x ... (i)

Equating to 0, we get:

12 - 12x = 0,

or, 12x = 12,

or, x = 1.

Differentiating (i), with respect to x again, we get:

f''(x) = -12, which is less than 0, showing f(x) is maximum at x = 1.

The value of y, when x = 1 is,

y = 12 - 6x,

or, y = 12 - 6*1 = 6.

The value of f(x, y) when (x, y) = (1, 6) is,

f(x, y) = xy,

or, f(x, y) = 1*6 = 6.

Thus, there is a maximum value of 6 located at (x, y) = (1, 6).

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The provided question is incomplete. The complete question is:

"Find the extremum of f(x, y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x, y)=xy; 6x+y=12.

Part A: Sasha's solution of the equation incorrect. The solution x = 7.

Part B: The equation have They are unique solutions.

According to the question,

Sasha solved an equation, as shown below:

Step 1: 8x = 56

Step 2: x = 56 – 8

Step 3: x = 48

Step 2 is incorrect, the correct steps to find x, we would divide both sides by 8 so,

8 / 8x = 8 / 56

x = 7.

An equation can have infinitely many solutions only if  the system of an equation has infinitely many solutions when the two lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line. Then the have infinitely many solutions.

But, the given equation have unique solutions. Thus, x=7.

Hence, Part A: Sasha's solution incorrect. The solution x = 7.

Part B: They are unique solutions solutions.

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Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.

At the null hypothesis, it is tested if the average cost is still of $50,000, that is:

[tex]H_0: \mu = 50000[/tex]

At the alternative hypothesis, it is tested if the average cost is decreasing, that is:

[tex]H_1: \mu < 50000[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are:

[tex]\overline{x} = 49450, \mu = 50000, \sigma = 2500, n = 100[/tex]

Hence:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{49450 - 50000}{\frac{2500}{\sqrt{100}}}[/tex]

z = -2.2.

Using a z-distribution calculator, for a left-tailed test, as we are testing if the mean is less than a value, with z = -2.2, the p-value is of 0.0139.

Since the p-value is less than 0.05, there is evidence to support the claim that the average cost of private universities are decreasing.

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Answer:

46 and 22

Step-by-step explanation:

let the father b (f) and d son is (s)

so

f=3s.....(1)

(f+10) +(s+10)=68 .... (2)

substitute f=3s in equation (2)

we have

(3s+10)+(s+10)=68

4s+20=68

4s=68-20

4s=48

s=12 .......(3)

substitute (3) in (1)

f=3*12

which f=36

in 10 year time

f+10 =46

s+10=22

Answer:

As the number of files increases, the storage space used increases.

Given same lengths and slopes of the opposite sides and nature of the angle between adjacent sides, we have;

The given points are;

L(-5, 4), M(2, 2), N(0, -3), S(-7, -1)

Lengths of the sides are;

Length of LM = √((2-(-5))²+(2-4)²) ≈ √(53)

Length of MN = √((2-0)²+(2-(-3))²) ≈ √(29)

Length of NS = √((0-(-7))²+((-3)-(-1))²) ≈ √(53)

Length of LS = √(((-7)-(-5))²+((-1)-4)²) ≈ √(29)

Therefore;

Slope of LM = (2-4)/(2-(-5)) = -2/7

Slope of MN = (2-(-3))/(0-2) = 5/2

Slope of NS = ((-3)-(-1))/(0-(-7)) = -2/7

Slope of LS = ((-1)-4)/(-7-(-5)) = 5/2

Therefore;

The quadrilateral created by the points L(-5, 4), M(2, 2), N(0, -3), S(-7, -1) is therefore;

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Answer:

D) subtract 6 from the previous term

Step-by-step explanation:

27-6=21, 21-6=15, 15-6=9, and 9-6=3

Answer:

Step-by-step explanation:

There are 1.40 groups of 5/7 in 1.

8 divided by 5/7 is  11 1/5.

Here is the completed table:

Length (cm)       Percentage

  12                          60% of Ehecatl's old hair

   4                         20% of Ehecatl's old hair

  20                           100% of Ehecatl's old hair

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

In order to determine how many groups of 5/7 are in 1, divide 1 by 5/7

1 ÷ 5/7

1 x 7/5 = 7/5  = 1.40

8 ÷  5/7

8 x 7/5

= 56 / 5

= 11 1/5

The first step is to determine the length of her hair before she cut it

Length of the hair before it was cut = new length / 60%

12 / 0.6 = 20

60% x 20 = 12cm

20% x 20 = 4cm

100% x 20 = 20cm

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Step-by-step explanation:

I just answered this. how often did you post that question ?

she added 54-48 = 6g.

how many % of 48g are these 6g ?

100% = 48

1% = 100%/100 = 48/100 = 0.48g

how many % are 6g ?

as many as how often 1% (0.48g) fits into 6g :

6 / 0.48 = 12.5%

Step-by-step explanation:

I assume the measuring cylinder measures the cm³ of its normally liquid content.

because for anything else we would need more information about the dimensions of the cylinder.

and so, originally the cylinder shows 40 cm³.

after dropping the stone in, how many cm³ of water is the cylinder then showing ?

let's first mention some facts we are going to use :

water weighs 1 kg (1000 g) per liter.

and 1 liter fits exactly into a cube of

10 cm × 10 cm × 10 cm = 1000 cm³

so, 1 cm³ water weighs exactly 1 g and has therefore a density of 1 g / cm³.

the stone has a density of 8.6 g / cm³, is therefore heavier than water and sinks (and replaces water correspondingly).

how many cm³ does the stone have (and replaces water) ?

well, it has 129 g, and 8.6 g of the stone fill a cm³.

so, it has

129 / 8.6 = 15 cm³

therefore, as these 15 cm³ of stone replace 15 cm³ of water, this is the same as putting 40 + 15 = 55 cm³ of water into the measuring cylinder.

and the cylinder reads now 55 cm³.

FYI : but there is still only 40 cm³ of water in there.

this is actually used to calculate the density of objects (by first weighing and then dropping them into the water to see how much water they replace).

Answer: 55 cm³.

Step-by-step explanation:

[tex]\displaystyle\\m_{stone}=129\ g\ \ \ \ \ \rho_{stone}=8,6\ \frac{g}{cm^3} \ \ \ \ \ V_{water}=40\ cm^3\ \ \ \ \ V=?.\\ \boxed {\rho=\frac{m}{V} }\\V=\frac{m}{\rho} \\V=V_{water}+V_{stone}\\V_{stone}=\frac{m_{stone}}{\rho_{stone}} \\V_{stone}=\frac{129}{8,6}\\V_{stone }=15\ cm^3.\\V=40+15\\V=55\ cm^3.[/tex]