In a group of 40 pupils, 15 play the flute only. 7 play the piano only. 5 play both instruments. A student is chosen at random. What is the probability the student plays neither instrument?

Step-by-step explanation:

Let’s start with y.

Because they are opposite angles on 2 180 degrees lines 102 = y-17

Now solve

102 = y - 17

Now add 17 to both sides

119 = y

For x

Because it is on a 180 degree line

102 + 3x = 180

Now subtract 102 from both sides

3x = 78

Now divide each side by 3 to get x alone

x = 26

This proves the answer is in fact A

In the morning, the train went 170 miles. in the afternoon the train went 50 more miles. The Train ended up going 220 miles in total.

In the morning, the train traveled 170 miles.

In the afternoon, it traveled an additional 50 miles.

To find the total distance traveled by the train, we need to add the distance traveled in the morning and the distance traveled in the afternoon:

Total distance = Distance traveled in the morning + Distance traveled in the afternoon

Total distance = 170 miles + 50 miles

Total distance = 220 miles

So, the train ended up traveling a total of 220 miles.

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Answer:

x = 1.523

Step-by-step explanation:

Given
[tex]\quad\quad e^{x-1} = 3^{2-x}[/tex]

we are asked to solve for x

Take natural logs on both sides:
[tex]\ln \left(e^{x-1}\right)=\ln \left(3^{2-x}\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)}\\\\\ln \left(e^{x-1}\right)=\left(x-1\right)\ln \left(e\right)\\\\\rightarrow \left(x-1\right)\ln \left(e\right)=\ln \left(3^{2-x}\right)[/tex]substitute on left side of original eqn

[tex]\ln \left(3^{2-x}\right)=\left(2-x\right)\ln \left(3\right)\\\\[/tex]

Therefore we get
[tex]\left(x-1\right)\ln \left(e\right)=\left(2-x\right)\ln \left(3\right)[/tex]

But ln(e) = 1

So we get
[tex]x - 1 = (2-x)\;\ln(3)\\\\[/tex]

So the expression becomes

[tex]x - 1 = (2- x) \ln(3)\\\\x - 1 = 2\ln(3) - x \ln(3)[/tex]

Add [tex]x\ln(3)[/tex] on both sides:

x + x ln(3) - 1 = 2ln(3)

Add 1 to bot sides:
x + x ln(3) = 2ln(3) + 1

x(1 + ln(3)) = 2 ln3 + 1

ln(1 + \ln(3)) = 2.09861

2ln(3) + 1 =3.1972

So we get

x(2.0986) = 3.1972

x = 3.1972/2.0986 = 1.52349

Rounded to 3 decimal places, the answer is 1.523

Answer:

To calculate the cost of painting the top surface of 20 engine parts, we need to find the surface area of one engine part and then multiply it by 20.

To find the surface area, we need to find the length of the curved surface. We can do this by using the Pythagorean theorem to find AB and then use that to find the circumference of the curved surface.

AB^2 = BO^2 + AO^2 = 9 + 36 = 45

AB = sqrt(45) = 3 sqrt(5)

Circumference = 2 * pi * AB = 2 * pi * 3 sqrt(5) = 6 pi sqrt(5)

Using the fact that the reflex angle BÔC is 240 degrees, we can find the length of the curved surface:

240° / 360° = 2/3 of the circumference

Curved surface length = 2/3 * 6 pi sqrt(5) = 4 pi sqrt(5)

Finally, we can find the surface area of one engine part:

Surface area = (2 * 6 * 3) + (4 pi sqrt(5) * 6) = 36 + (24 pi sqrt(5))

To paint 20 engine parts, the cost would be:

20 * surface area * 15p = 20 * 36 + 20 * 24 pi sqrt(5) * 15p = 720 + (24 * 20 * 15 * pi * sqrt(5)) p = 720 + 720 pi sqrt(5) p

Since 1 pound is equal to 100 pence, the cost in pounds would be:

720 + 720 * pi * sqrt(5) / 100 = 720 + 720 * 0.177 / 100 = 720 + 1.264

So, the cost to paint the top surface of 20 engine parts would be 721.264 pounds.

The solution of the equations will be x = 241 and y = -89.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are -16y=22+6x and -11y-4x=15. The equations by elimination method will be calculated as:-

-16y=22+6x

-11y-4x=15

Write the equations in the following way:-

6x + 16y = -22

-4x - 11y = 15

24x + 64y = 88

-24x - 66y = 90

____________

0     - 2y = 178

           y = 89

The value of x will be:-

-11y-4x=15

-11 x -89 - 4x = 15

979 - 4x = 15

-4x = -964

x = 241

Therefore, the value of x is 241 and the value of y is -89.

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Answer:

$55.44 is the price of the sunglasses

Step-by-step explanation:

Price Of Sunglasses = $56

10% Discount = $5.6

So, $56-$5.6 = $50.4 <------ Applying Discount

10% of $50.4 = $5.04 <------ Price of Processing Fee for Discounted Price

$50.4+$5.04 = $55.44 <------ Total Price

The discounted price is $50.4 and we take 10% of that [discounted price] and we add it to the discounted price. 10% of that is $5.04. = $55.44

Answer:

$55.44

Step-by-step explanation:

56 - 56(0.10) = 50.40  price with 10% off

50.40 + 50.40(0.10) = 55.44   10% processing fee added to discounted price

Answer:

Subtracting an expression is similar to distributing a -1 because it cancels out the numbers in the expression.

Step-by-step explanation:

Answer:

314 ft^3

Step-by-step explanation:

The equation that needs to be set up is 1/3 × pi × r^2 ×h which r is the radius and h is the height. If we substitute 1/3 × pi × 5 × 12= 100 × pi. Once you finish the equation out by multiplying 100 and pi (3.14) It can be rounded to 314 ft ^3

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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Repeatedly  sample variance from a small population without replacement leads to the outcomes in our sample being non-independent, as the same individuals may be chosen multiple times.

Repeatedly  sample variance from a small population without replacement can lead to skewed results, as the same individuals may be chosen multiple times. This can be problematic when the sample size is small, as the same individuals may be overrepresented in the sample. This can lead to outcomes that are not representative of the population and can lead to inaccurate results. As the same individuals are chosen multiple times, the outcomes in the sample are not independent; the outcomes of one individual can influence the outcomes of other individuals in the sample. This can lead to bias in the results and should be avoided when possible. When sampling from a small population without replacement, it is important to ensure that the sample size is large enough that the same individuals are not chosen multiple times, otherwise the results may be skewed or biased.

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Sampling repeatedly from a small population without replacement leads the outcomes in our sample to be dependent.

In dependent samples, subjects in one group do provide information about subjects in other groups.

y=8x is the direct variation equation that shows the relationship between x and y.

Two or more expressions with an Equal sign is called as Equation.

In a direct variation, y=16 when x=2.

y=kx

We have to find the relationship between x and y.

16=2k

Divide both sides by 2

k=8

Now plug in the value of k in the above equation.

y=8x

Hence, y=8x is the direct variation equation that shows the relationship between x and y.

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Answer:

Below

Step-by-step explanation:

12 + 3s + 9s + 2 =

(3s+9s) + (12+2) =

12s + 14           ( or   2 (6s+7)   )

The two solutions of the quadratic equations are 8,-4 and the negative solution -4

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: when 32 subtracted from the square of a number and the result is 4 times the number.

Let x be the number then we have

x²-32=4x

x²-4x-32=0

x²-8x+4x-32=0

x(x-8)+4(x-8)=0

(x-8) (x+4) =0

Thus the two solutions of the quadratic equations are 8,-4

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Answer: To find the mean hourly wage, you need to sum up the total wages of all employees and then divide by the number of employees. The total hourly wage for 25 phone operators is 25 * $22.85 = $571.25. The total hourly wage for 5 supervisors is 5 * $27.25 = $136.25. The combined total is $571.25 + $136.25 = $707.50. The mean hourly wage for the 30 employees is $707.50 / 30 = $23.58. So, the answer is approximately $23.58.

Step-by-step explanation:

The polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. -5, -1, 2 is,

⇒ f (x) = x³ + 4x² - 7x - 10

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

For a polynomial,

A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Now, We know that;

The standard polynomial is given by:

⇒ f (x) = a (x - p) (x - q) ...

Where, 'a' is leading coefficient and p, q, .. are zeroes.

Here, A leading coefficient = 1,

And, the given zeros = -5, -1, 2

Hence, The polynomial is,

⇒ f (x) = 1 (x - (-5)) (x - (- 1)) (x - 2)

⇒ f (x) = (x + 5) (x + 1) (x - 2)

⇒ f (x) = (x + 5) (x² - 2x + x - 2)

⇒ f (x) = (x + 5) (x² - x - 2)

⇒ f (x) = x³ - x² - 2x + 5x² - 5x - 10

⇒ f (x) = x³ + 4x² - 7x - 10

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Step-by-step explanation:

x+4y=0

2x−y=18

​To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

x+4y=0,2x−y=18

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign.

x+4y=0

Subtract 4y from both sides of the equation.

x=−4y

Substitute −4y for x in the other equation, 2x−y=18.

2(−4)y−y=18

Multiply 2 times −4y.

−8y−y=18

Add −8y to −y.

−9y=18

Divide both sides by −9.

y=−2

Substitute −2 for y in x=−4y. Because the resulting equation contains only one variable, you can solve for x directly.

x=−4(−2)

Multiply −4 times −2.

x=8

The system is now solved.

x=8,y=−2

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Answer:

$150.35

Step-by-step explanation:

Total commission taken from sale = $155,000 * 5% = $7,750.

Broker = $7,750 * 2% = $155.

Office assistant = $7,750 * 1% = $77.5.

Debby's profit = $7,750 - $155 - $77.5 = $7,517.5 * 2% = $150.35.

Check the picture below.

Answer:

Let's call the measure of the first angle "x". Then, the equation can be written as:

x = 3y - 8

Since the angles are supplementary, their measures add up to 180 degrees, so:

x + y = 180

We can substitute the first equation into the second equation to solve for y:

3y - 8 + y = 180

4y = 188

y = 47

Now that we know the measure of y, we can substitute it back into the first equation to find x:

x = 3(47) - 8 = 133

So the measure of the larger angle is 133 degrees.

The simplified expression 2-6/-2-4-12/6x-3 is given as follows:

-2 - 2x.

The expression for this problem is defined as follows:

[tex]2 - \frac{6}{-2} - 4 - \frac{12x}{6} - 3[/tex]

The division operation has a higher precedence over the subtraction operations, hence:

Hence the expression can be written as follows:

2 - (-3) - 4 - 2x - 3 = 2 + 3 - 4 - 2x - 3.

Then combining the like terms, which are the constant, the simplified expression is given as follows:

-2 - 2x.

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Answer:

Geometry in Mathematics is the study of shape and figures.

Answer:

Geometry refers to a branch of mathematics which is focused on the measurement and relationship of lines, angles, surfaces, solids and points. For instance, the calculation of a triangle's angles is an example of geometry.

Answer:

x = 0.4

Step-by-step explanation:

1.5 * x = 0.6

x = 0.6 / 1.5

x = 0.4

Answer:

0.4

Step-by-step explanation:

To solve the equation 1.5 * ? = 0.6 for the value of ?, we need to isolate the variable ? on one side of the equation.

First, we can divide both sides of the equation by 1.5 to isolate the variable:

1.5 * ? / 1.5 = 0.6 / 1.5

Simplifying, we get:

? = 0.4

Therefore, the value of ? that makes the equation 1.5 * ? = 0.6 true is 0.4.

The zeroes of the quadratic function 2x² - 7x - 4 is 1 and 4,

known as roots.

A quadratic equation is an algebraic expression in the form of variables and constants.

itsA quadratic equation has two roots as it's degree is two.

We know, The general form of a quadratic equation is x² + bx + c.

Let, y = x² + bx + c.

At, (0, - 2).

- 2 = 0 + 0 + c.

c = - 2.

At, (4, 0).

0 = 4² + 4b - 2.

0 = 14 + 4b.

b = - 7/2.

So, It is x² - (7/2)x - 2 = 0.

2x² - 7x - 4 = 0.

2x² - 8x + x - 4 = 0.

2x(x - 4) - 1(x - 4) = 0.

(x - 4)(x - 1) = 0.

So, the zeroes of the function are 4 and 1.

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Answer:

1. We can think of the beaver population as a function of time in years because it shows how the population changes over time. The graph shows a direct correlation between the number of years after 1995 and the number of beavers in the forest, indicating that the population of beavers is dependent on the number of years that have passed since 1995.

2. The point labeled Q represents the exponential growth rate of the beaver population.

3. An equation using function notation to represent this situation would be: P(t) = P0 * e^kt, where P(t) is the population at time t (in years after 1995), P0 is the initial population of beavers in 1995, and k is the constant exponential growth rate.

If jack has three packs of gum and sam has 4 packs of gum, then the total amount of gum they have together is 7 packs.

What is the addition?

The addition is putting numbers together to make a sum or total. The plus sign + tells you to add two numbers. = is an equals sign. It shows that things on either side of it are equal.

We have given,

Jack has 3 packs of gum and Sam has 4 packs of gum.

To find the total number of packs of gum they have together, we simply add their individual amounts:

3 packs (Jack) + 4 packs (Sam) = 7 packs

Therefore, the total amount of gum they have together is 7 packs.

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Step-by-step explanation:

Solution: Let the current ages of the father be F and that of the son, S.

Three years ago their ages were (F-3) and (S-3) and the sum was 48, or

F+S = 48+3+3 = 54, or

F = 54-S …(1)

(F+3) : (S+3) = 3:1, or

F+3 = 3S+9, or

F = 3S+6 …(2)

Equate (1) and (2): 54-S = 3S+6, or

4S=48, or S = 12 and So F = 42.

The father is 42 years and the son 12 years,

Answer:

+3 year after now Dad = 45; Son = 15 ====>   30 years old

now                       Dad = 42; Son = 12 ====>   30 years old

-3 year after now Dad = 39; Son = 9 =====>   30 years old

Step-by-step explanation:

Before 3 year is 48 so after 3 year is + 6 right???

so ==> 48 + 6(father and son so it's 2) + 6(same same) ==> 60

the ratio is 3:1 so son gets 1 dad gets 3 right?

==> 4 is the sum

So son is 60/4x1 = 15

Dad is 60/4x3(dad have three remember?) = 45

so now dad and son will be:

Dad = 45 -3 (only dad ok?) = 42

Son = 15-3(only son) = 12

so you can find the before to by minus 3 again ok??

Thanks for seeing

Tell me if it's wrong or right :P | XD | (❁´◡`❁)

There, ages are as follows:

Madhu's grandfather age = 72 years

Madhu father's age = 46 years

Madhu age = 17 years

Madhu's father is 26 years younger than Madhu's grandfather and 29 years older than Madhu.

The sum of the ages of all three is 135 years.  

Therefore, let's find their ages as follows:

Let

Madhu's grandfather age = x

Madhu father's age = x - 26

Madhu age = x - 26 - 29 = x - 55

Therefore,

x + x - 26 + x - 55 = 135

3x = 135 + 81

3x = 216

divide both sides by 3

x = 216 / 3

x = 72

Hence,

Madhu's grandfather age = 72 years

Madhu father's age = 72 - 26 = 46 years

Madhu age = x - 26 - 29 = 72 - 55 = 17 years

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Answer:

rectangular prism has 6 faces, 8 vertices (or corners) and 12 edges.

Step-by-step explanation:

hopefully this is the answer you are looking for.

Answer:

Step-by-step explanation:

Lin counts 5 bacteria under a microscope. She counts them again each day for four days, and finds that the number of bacteria doubled each day—from 5 to 10, then from 10 to 20, and so on.

Is the population of bacteria a function of the number of days? If so, is it linear? The population of bacteria is a function. The relationship is linear.

Answer:

x = 2/3

y = 5

Step-by-step explanation:

6x + y = 9

3x -4y = -18

Times the second equation by -2

6x + y = 9

-6x + 8y = 36

9y = 45

y = 5

Now put 5 in for y and solve for x

6x + 5 = 9

6x = 4

x = 2/3

Let's check

6(2/3) + 5 = 9

4 + 5 = 9

9 = 9

So, x = 2/3 and y = 5 is the correct answer.