consider a group of hundred students. out of them, eighty students can speak either english or spanish. suppose twenty-five students can speak only english. how many students can speak spanish?

Using composite functions, we have that:

a) f(x) = x² + 3.

b) [tex]g(x) = \sqrt{x}[/tex]

c) f(g(x)) = x + 3.

d) [tex](g \circ f)(6) = \sqrt{39}[/tex]

The composite function of f(x) and g(x) is given by:

(f ∘ g)(x) = f(g(x)).

For item a, we want a non-linear function, which has a highest exponent different of 1, that does not go through the origin, hence the function can be:

f(x) = x² + 3.

For item b, we also want a non-linear function with a radical, hence the function can be:

[tex]g(x) = \sqrt{x}[/tex].

For item c, the composite function is:

[tex]f(g(x)) = f(\sqrt{x}) = (\sqrt{x})^2 + 3 = x + 3[/tex]

For item d, the composite function is:

[tex]g(f(x)) = g(x^2 + 3) = \sqrt{x^2 + 3}[/tex]

At x = 6, we have that:

[tex](g \circ f)(6) = \sqrt{6^2 + 3} = \sqrt{39}[/tex]

More can be learned about composite functions at https://brainly.com/question/13502804

#SPJ1

The average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given,

The function f(x)=80(1.5)x

where x is the time in hours

Then,

f(4)=80(1.5)4=480

f(8)=80(1.5)8=960

f(0)=80(1.5)0=0

Then the average rate of change between 4 and 8 hours =[tex]\frac{960-480}{4}[/tex]

=120 units per hour

The average rate of change between 0 and 4 hours=[tex]\frac{480-0}{4}[/tex]

=120 units per hour

Hence, the average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

Learn more about function here

brainly.com/question/12431044

#SPJ4

Step-by-step explanation:

24-(14)

10

use bidmas...

The expression after combining the like terms is 14uv+ 3s³t²

Expression:

Mathematical expression consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Variable:

A variable in algebra is an alphabet that is used to symbolise the unknowable integer. It stands in for the value. An amount that can fluctuate depending on the mathematical issue is referred to as a variable.

⇒9uv + 3s³t² + 5uv

⇒ 14uv+ 3s³t² { addition of like terms}

Therefore,The expression after combining the like terms is 14uv+ 3s³t²

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ4

[tex]Answer: the\ number\ is\ \boxed{-26}[/tex]

Step-by-step explanation:

[tex]2(n-4)=3(n+6)\\2(n)-2(4)=3(n)+3(6)\\2n-8=3n+18\\2n-8-18=3n+18-18\\2n-26=3n\\2n-26-2n=3n-2n\\-26=n\\Thus,\\n=-26[/tex]

The slope for plane A is 375, this means its rate of speed is 375 ml/h.

The slope for plane B is 445, this means the rate of speed for Plane B is 445 ml/h.

The slope of a linear equation = change in y / change in x.

A linear equation that is given as, y = mx + b or y = mx, has a slope that is represented as m.

Slope of Plane A:

Given the equation for Plane A as, y = 375x, the slope is, 375.

This means its rate of speed is: 375 ml/h.

Slope of Plane B:

Using two points, (1, 445) and (2, 890)

Slope for plane B = (890 - 445)/(2 - 1)

Slope for plane B = 445

This means the rate of speed for Plane B is: 445 ml/h.

Learn more about the slope on:

https://brainly.com/question/24907633

#SPJ1

The value of the expression a^3 is 3 3/8

The given parameters can be represented as

If a = 3, then 5a = 15.

Also, we have the value of the variable a to be

a = 1 1/2

Express the value of the variable a as an improper fraction

So, we have

a = 3/2

When a = 1 1/2 or a = 3/2, the value of a³ is calculated using the following formula

a³ = (1 1/2)³ = (3/2)³

Rewrite the formula as

a³ = (3/2)³

Evaluate the exponent in the above equation

So, we have

a³ = (27/8)³

Evaluate the quotient in the above equation

So, we have

a³ = 3 3/8

Hence, the value of the expression a³ is 3 3/8

Read more about expressions at

https://brainly.com/question/723406

#SPJ1

The length of line AB with coordinates A (-5, -2) and B (7, 4) is;  6√5 units

The formula for distance of a line between two coordinates is;

D = √[(x2 - x1)² + (y2 - y1)²]

From the coordinates given as A (-5, -2) and B (7, 4), we can say that;

x1 = -5

x2 = 7

y1 = -2

y2 = 4

Thus;

D = √[(7 - (-5))² + (4 - (-2))²]

D = √(12² + 6²)

D = √180

D = 6√5 units

Thus, we conclude that the length of line AB with coordinates A (-5, -2) and B (7, 4) is;  6√5 units

Read more about Distance between coordinates at; https://brainly.com/question/7243416

#SPJ1

Complete question is;

Find the distance of the line AB with coordinates A (-5, -2) and B (7, 4).

Answer:

[tex]\textsf{(a)} \quad -4 < x\leq 1[/tex]

[tex]\textsf{(b)} \quad [3, 19)[/tex]

Step-by-step explanation:

Given compound inequality:

[tex]\dfrac{9+x}{5} < 5+x\leq 6[/tex]

[tex]\textsf{If\: $a < u\leq b$ \:then\: $a < u$ \:and\: $u\leq b$}.[/tex]

[tex]\textsf{Therefore \:$\dfrac{9+x}{5} < 5+x$ \:and\: $5+x\leq 6$}[/tex]

Solve the inequalities separately:

Inequality 1

[tex]\begin{aligned}\dfrac{9+x}{5} & < 5+x\\9+x & < 5(5+x)\\9+x & < 25+5x\\9+x -5x& < 25+5x-5x\\9-4x & < 25\\ 9-4x-9 & < 25-9\\-4x & < 16\\-x & < 4\\x & > -4\\ \end{aligned}[/tex]

Inequality 2

[tex]\begin{aligned} 5+x & \leq 6\\ 5+x-5 & \leq 6-5\\x & \leq 1 \end{aligned}[/tex]

Combine the intervals:

[tex]-4 < x\leq 1[/tex]

Given equation:

[tex]y=x^2+3[/tex]

As the domain is restricted to  -4 < x ≤ 1, the range is also restricted.

The vertex (minimum point) of  [tex]y = x^2 + 3[/tex]  is when x = 0.

As x = 0 lies within the restricted domain, y = 3 is the lowest value of the range.

[tex]x=-4 \implies y=(-4)^2+3=19[/tex]

Therefore, the range is:

When the nursery is recording the heights of its available fruit trees. the display that can be used to represent the data, is A. Bar chart, because tree height is numerical.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

When displaying the distribution of data points or comparing metric values across several subgroups of your data, a bar chart is employed. A bar graph allows us to determine which groupings are most numerous or prevalent as well as how different groups stack up against one another.

Learn more about bar chart on:

https://brainly.com/question/24741444

#SPJ1

Answer:

The answer would be B.

Step-by-step explanation:

Since we are doing heights, it would make since to have a box plot, since that includes minimum, maximum, median, Q1, & Q2. :)

that makes it easier to record height

z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.

important is that the ratio between each succeeding pair of Fibonacci numbers approaches 1.618, or its inverse, 0.618, as the numbers get bigger. The holy proportion, the golden ratio, and the golden mean are some additional names for this proportion. Then why is this number so important? The fact that so many items in nature have dimensions characteristics that conform to the 1.618 ratio suggests that it plays a fundamental role for the components of nature. Due to its visual appeal compared to other proportions, the golden ratio is frequently used in the arts. The Great Pyramid in Giza, the Mona Lisa by Da Vinci, and the Parthenon in Athens are all.

z1 =........=zm = 0 and n=m

z1 =........=zm = 0 and n=m because n0 cannot be expressed in the +ve Phi / golden ratio form.

To know more about golden ratio visit ::-

https://brainly.com/question/2263789

#SPJ4

The correct options are:

The elevation is 15,976 feet

A good expression would be 18,492 + -2,516

When a person goes up a mountain, the sign used to represent their height above sea level is a positive sign (+). When a person goes down a mountain, the sign used to represent their height above sea level is a negative sign (-). So, the sign in front of 18,492 would be positive and the sign in front of 2516 would be negative.

The expression that can be used to evaluate the elevation of the second campsite :

height of the first campsite - feet descended

18,492 - 2,516 =  15,976 feet

To learn more about subtraction, please check: https://brainly.com/question/854115

#SPJ1

To decide the power of 10 multiplies an equation with repeating digits; Round the equation to the required significant numbers.

when the numerator of an equation is divided by the denominator and the result is not a whole number ( i.e. number with some decimals)and sometimes the decimal places are unending. to present the result properly we have to round off the number to the nearest significant number, then you can multiply the equation with the power of 10, in relation to the number of significant places you rounded off.

Example :

5/200 = 0.025

To express this answer with the power of 10

0.025 = 2.5 * 10 ^-2

For more information on decimal points click on the link below:

https://brainly.com/question/26090574

#SPJ4

Final answer:

The best term that describes the number of solutions that will maximize the function is one optimal solution (a)

A practicable solution is one that complies with all limitations and specifications. When all of the requirements and constraints cannot be satisfied by any combination of decision variable values, a solution is deemed to be infeasible. The parabola's highest or lowest point represents the ideal value. If only the parabola expands down words, the optimal value, also known as the vertex of the parabola, would be maximal. The minimal value is one opening upwards. The vertex's "Y" coordinate is it.

An option for making a judgment or a resolution that does not adhere to one or more constraints. The corners of the entire model's graph would contain the ideal answer.

Explanation:

(Assume that [tex]x > 0[/tex] and [tex]y > 0[/tex].)

[tex]x + 2 < 5x-y < 2[/tex]

[tex]F(x,y) = 2x+y[/tex]

So , the equation becomes a optimal solution.

To learn more about feasible solution, visit

brainly.com/question/28169083

#SPJ4

Answer:8

Step-by-step explanation:add them all together and divide by however many numbers you have

Answer:

the mean(average) is 5

Step-by-step explanation:

Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

The possible numbers are

( 9 , 9 ,2 ) ;( 9 , 8 , 3 );( 9 , 7 , 4 );( 9 , 6 , 5 )

All 4 combinations have the sum of 20 .

To know more about  number system ,

https://brainly.com/app/ask?q=number+system

Answer: 10x + 19 = 519              x = 50

Step-by-step explanation:

We are looking for the number of students that rode in each bus, so first lets subtract out those that drove in cars.

519-19=500

So 500 students rode on 10 buses. So now we divide the students onto the buses.

500/10 = 50

Each bus drove 50 students.

An equation to represent the total number of students as a function of those on the buses would be

10x + 19 = 519

x = 50 (the number of students on each bus)

According to the given statement

P(D) 0.7, P(E) = 0.2 and P(D and E) = 0.15.

P(DIE):0.75

The possibility of an event or outcome occurring conditional on the occurrence of a prior event or outcome is known as conditional probability. The conditional probability is calculated by multiplying the probability of the previous event by the present probability of the upcoming, or conditional, occurrence.

Contrast Unconditional probability with conditional probability. The possibility that an event will occur regardless of whether any previous occurrences have occurred or any other circumstances are present is known as Unconditional probability.

According to the given value;

P(DIE): 0.15/0.2

            =0.75.

hence,P(DIE):0.75.

To know more about Conditional Probability, visit;

https://brainly.com/question/16456973

#SPJ9

Step-by-step explanation:

this creates a right-angled triangle, with the pure coordinate changes being the legs, and the actual distance being the Hypotenuse (the side opposite of the 90° angle).

and so, we can use Pythagoras :

distance² = leg1² + leg2² = 300² + 500² =

= 90000 + 250000 = 340000

distance = sqrt(340000) = sqrt(10000×34) = 100×sqrt(34) =

= 583.0951895... km ≈ 583 km

According to the question, to investigate through an experiment by telling people to smoke a pack of cigarettes each day by putting their health at risk. This causes serious health issues. And the other half are told not to smoke but might smoke at their own discretion. In the end, it is very difficult to keep track of 50 years of both types of people. That means people who are smoking and others who are not smoking. And, after 50 years, checking their consistency has become extremely difficult, if not impossible. Therefore, this experiment is not possible in both ways, that is, experimental or observational.

To learn more about the observational experiments  from the given link:

https://brainly.com/question/10992959

#SPJ4

The coordinates of its center will be (2,10)

(x - h)²+ (y - k)² = r² is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius.

A circle with a radius of r and a center is represented as

(x - a)² + (y - b)² = r² where (a, b) is the center of the circle.

Circle passes points (-4, 2) and (2, 0):

Both (-4 - a)² + (2 - b)² and (2 - a)² + (-b)² are equal to r²

Currently, the center's x coordinate (a) is 2 due to the tangent at (2, 0)

The equations then read:

6² + (2 - b)² = r²

b² = r²

⇒ 36 + (2 -b)² -b² = 0

⇒ 36 + 4 + b² - 4b - b² = 0

⇒ 4b = 40

⇒ b = 10.

So, the center is (2,10)

To learn more about equation of the circle from given link

https://brainly.com/question/17064049

#SPJ4

1/[tex]\sqrt{3}[/tex] is the exact trigonometric ratios for the angle x whose radian measure is given.

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.

Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.

The right triangle's three sides are as follows:

sin(4π/3) = sin(π + π/3)

               = - sin(π/3)

               = - [tex]\sqrt{3}[/tex]/2

CSC(4π )/3) = csc(π  + π /3)

               = - csc(π /3)

               = - 2/[tex]\sqrt{3\\[/tex]

cos(4π /3) = cos(π  + π  /3)

               = - cos(π /3) = - 1/2

sec(4 π /3) = sec(π  + π/3)

               = - sec(π /3) = - 2

tan(4π )/3) = tan(π + π /3)

               = tan(π/3) = [tex]\sqrt{3}[/tex]

Cot (4π/3 )= cot(π  + π/3)

              = Cot π/3 = 1/[tex]\sqrt{3}[/tex]

To learn more about the, trigonometric ratios visit:

https://brainly.com/question/1201366

#SPJ4

Answer: 2/9 of the book left

Step-by-step explanation: 5/9 + 2/9= 7/9

9/9- 7/9= 2/9

Answer:

[tex] \sqrt{7 \times 2} \sqrt{7 + 4 \sqrt{7} } \\ 14 + 4 \sqrt{7} [/tex]

The slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.

Given the following data:

Points on x-axis = (-12, 6).

Points on y-axis = (14, -1).

A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

Substituting the given points into the formula, we have;

Slope = (6 + 12)/-1 - 14)

Slope = -18/15

Slope = -6/5

Mathematically, the standard form of the equation of a straight line is given by;

y = mx + c

Where:

At point (-12, 14), we have:

14 = -6/5(-12) + c

8 = 72/5 + c

40 = 72 + 5c

5c = 72 - 40

c = 32/5

In conclusion, we can reasonably and logically deduce that the slope-intercept form of the equation of the line described is y = -6x/5 + 32/5.

Read more on slope-intercept form here: brainly.com/question/1884491

#SPJ1

The sample standard deviation is 0.89

In the given statement is:

A sample n = 5 scores which means that there are 5 sample having m = 20 which is the arithmetic mean (A.M.)of these samples, and [tex]s^{2}[/tex] = 4 is the variance of these samples.

Let us know the :

What is meant by Sample Standard deviation?

The sample standard deviation (s) is the square root of the sample variance and is also measure of the spread from the expected values.

Standard deviation is the square root of the variance.

Therefore, [tex]s^{2}[/tex] =4 => s = 2

(Where, s denotes sample standard deviation ,σ)

Also, Standard error of the sample S(E) = Sample standard variance / [tex]\sqrt{number of samples}[/tex]

= σ /[tex]\sqrt{n}[/tex] = 2/[tex]\sqrt{5}[/tex]

and, root 5 = 2.24

put the value of root 5

=2 / 2.24

= 0.89

Hence, The sample standard deviation is 0.89

Learn more about The sample standard deviation at:

https://brainly.com/question/15518357

#SPJ4

Answer:

Pretty sure A would be the answer

Step-by-step explanation:

Jayden's maximum and minimum walkie-talkie will reach mile marker is:

|x + 253| = 3

x = 253

The range of Jayden's walkie-talkie is three miles.

At mile 253, Jayden is moving straight along a highway.

Find the least and maximum milepost that Jayden's walkie-talkie will reach from 253 by solving the absolute-value equation.

range of 3 miles.

mile marker 253.

Find maximum and minimum of walkie talkie will reach

|x + 3| - 253 = 3x

                   = 253 or x

                   = 250

|x + 3| = 253

      x = 250 or x

         = -256|x - 253|

         = 3

x = 256 or x

  = 250

|x + 253| = 3

x = 253

Therefore, Jayden's minimum and maximum mile marker from 253 that walkie-talkie will reach is

|x + 253| = 3

x = 253

learn more about minimum and maximum:

https://brainly.com/question/1841403

#SPJ4