A class of 40 students has 11 honor students and 10 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student. Round to the nearest thousandth.

Answer:

409.86

Step-by-step explanation:

First find the mark up

230 *65%

230 * .65 = 149.50

The new cost of the tent is the original cost plus the mark up

230 + 149.50

379.50

Now we need to find the tax

379.50 * 8%

379.50 *.08

30.36

The total cost is the cost of the tent plus the tax

379.50 + 30.36

409.86

Answer:

409.86

is the correct answe rfor this question

Answer:

733 inches

Step-by-step explanation:

V= 3.14*5^2*28/3

Order of Operations (PEMDAS)

5^2=25

25*3.14= 78.5

78.5*28= 2198

2198/3=732.66

Round to nearest cubic inch

733 inches

Answer:

c. When a > 0 and b > 1, the function models exponential growth.

Step-by-step explanation:

You have exponential decay when a > 0 and 0 < b < 1.

The statement that is always true about the function y=a•b^xc is this: C. When a > 0 and b > 1, the function models exponential growth.

Exponential growth is a type of growth that occurs as there is an addition of numbers. This is reflected in the upward movement of the graph if such growth is represented in a graph.

So, the statement that best reflects this meaning of exponential growth is that when in a function, a > 0 and b > 1, then exponential growth is modeled. Thus, the correct option number is C. "When a > 0 and b > 1, the function models exponential growth."

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Answer:

c = -2

Step-by-step explanation:

The two functions are given as:

f(x) =  x^2 - 2x

g(x) = 6x + 4

To find:

(f+g)(x) = 0

We can evaluate (f+g)(x) using the given functions.

We know that:

(f+g)(x) = f(x) + g(x)

= x²- 2x + 6x + 4

= x² + 4x + 4

Now, we have for x = c:

c² + 4c + 4 = 0

x² + 2c + 2c + 4 = 0

c(c+2) + 2(c+2) = 0

(c+2)² = 0

c+2 = 0

c = -2

Answer:

I can't see Mathieu's work but I will show the right steps and maybe you can find where Mathieu went wrong.

f(x)=x^2+4x+3

f(x)=(x+3)(x+1)       Since 3*1=3 and 3+1=4

The x-intercepts can be found by setting y to 0 and solving for x

(in other words replace that f(x) thing with 0 and solve for x)

0=(x+3)(x+1)

Now set both factors equal to 0

x+3=0       or      x+1=0

x   =-3                    x=-1

The x-intercepts are at (-3,0) and (-1,0)

A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

The x-intercepts of the function f(x) = x² + 4x + 3 can be found as shown below.

f(x) = x² + 4x + 3

0 = x² + 4x + 3

0 = (x+3)(x+1)

x = -3, -1

Now, it can be seen that Mathieu has actually set the factored expressions equal to each other, which was wrong.

Hence, the correct option is C.

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Answer:

The equation is y=-x+6.

Step-by-step explanation:

To find the slope of this equation, we use the equation m=y2-y1/x2-x1, where m is the slope. Take one y coordinate and subtract it from the other and do the same with the x coordinates. Then, divide the difference of the y coordinates by the difference of the x coordinates. For example, 6-2/0-4. This gets us 4/-4. You can also do 2-6/4-0 which gets us -4/4. No matter what, we get -1 for each (we don't include the 1 in front of the x). To find the y-intercept, plug in the coordinates. For example, do 6=0(-1)+b or 2=4(-1)+b. No matter which you use, you get an answer of b=6. This gives you an equation of y=-x+6. Hope this helps :)

The equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x

To determine the equation for the line that passes through the points (4,2) and (0,6),

We will use the formula for the determining the equation of a line with two given points

The formula for the determining the equation of a line with two given points is

[tex]\frac{y-y_{1} }{x-x_{1} }=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

The given points are (4,2) and (0,6)

Therefore,

x₁ = 4

y₁ = 2

x₂ = 0

y₂ = 6

Now, putting these into the formula,

We get

[tex]\frac{y-2}{x-4}=\frac{6-2}{0-4}[/tex]

This becomes

[tex]\frac{y-2}{x-4}=\frac{4}{-4}[/tex]

[tex]\frac{y-2}{x-4}=-1[/tex]

Then, the equation becomes

[tex]y-2 = -1(x-4)[/tex]

[tex]y-2 = -x +4[/tex]

[tex]y = 4+2-x[/tex]

[tex]y = 6-x[/tex]

Hence, the equation of the line that passes through the points (4,2) and (0,6) is y = 6 - x

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Answer:

y = 5x - 4

see attached for graph

Answer:

3

Step-by-step explanation:

The digit in the tenths place of 25.391 is 3.

Answer: [tex]3[/tex]

Step-by-step explanation:

It is important to know that, in order to find the digit in the tenth place of a decimal number, you need to indentify the first digit located to the right of the decimal point.

Therefore, knowing this and having the decimal number provided in the exercise:

 [tex]25.391[/tex]

You can observe that the  first digit to the right of the decimal point is 3.

Therefore, the digit in the tenths place of ths decimal number is: [tex]3[/tex]

Answer:

(a) 15/3 = 100/x

(b) There are 20 toddlers in the class.

Step-by-step explanation:

(a)

The total number of students is 100% of the students.

Let the total number of students be x.

15% of students is to 3 as 100% of students is to x.

15/3 = 100/x

(b)

15/3 = 100/x

Cross multiply the equation.

15x = 3 * 100

15x = 300

Divide both sides by 15.

x = 20

Answer: There are 20 toddlers in the class.

Answer:

Rule is (x, y+k)

New point is (-3,9)

Step-by-step explanation:

A point translated vertically k units up means the x coordinate remains the same in the translation but the y coordinate is increased by k units

This can be represented mathematically as;

Let;s assume the point to be A with coordinates (x,y) then to get the image of the point under  a vertical translation k units up you add k to the y coordinate value.

Given ;

[tex]A=(\frac{x}{y} )\\\\T=(0,k)\\\\A'=(\frac{x}{y} )+(\frac{0}{k} )=(\frac{0+x}{y+k} )\\\\A'=\frac{x}{y+k} =(x,y+k)[/tex]

where T is the translation

In the question

Given (-3,-6) and T is (0,5) the new coordinate will be

[tex]=(\frac{-3}{4}) +(\frac{0}{5} )=\frac{-3}{9} =(-3,9)[/tex]

To cover the distance of 14 miles at a speed of 14 miles per hour Brian will take 1 hour means 60 minutes.

The speed is the rate of distance covered by a person or a vehicle in a particular time.

We have been given the distance=14 miles

Speed=14 miles per hour

We have also been given the formula of distance which is

d=rt

we have to rearrange it to calculate time

t=d/r

so the time will be calculated as t=14/14

t=1 hour because the speed is of per hour.

Hence Brian will take 60 minutes to cover the required distance.

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Answer:

B???

Step-by-step explanation:

Answer:

The correct option is A. Figure B repeats in the tessellation shown below.

Step-by-step explanation:

Tessellation can be defined as the arrangement of geographical patterns that are closely attached together to form a particular pattern.

The given figure is formed by the arrangement off figure B.

This large pattern is formed by the repetition of this smaller pattern,

Figure B repeats in the tessellation shown below. Therefore, the correct option is A.

Answer:

see explanation

Step-by-step explanation:

The perimeter (P) is the length of all 3 sides of the triangle

The triangle is isosceles with 2 equal sides 20 - 7xy

P = 20 - 7xy + 20 - 7xy + 12 = 52 - 14xy

When x = 2, y = 1, then

P = 52 - 14(2)(1) = 52 - 28 = 24

49 ___ 3 + 32 ÷ 23

49 ___ 3 + 1.39

49 ___ 4.39

49 > 4.39 is the only possible answer. 49 is greater than 4.39.

To determine the correct symbol for the expression 49 ___ 3 + 32 ÷ 23, first calculate the right side following PEMDAS, resulting in 7. Then compare it with the left side (49), which shows that 49 is greater than 7, so the correct symbol is '>'.

The question asks which symbol makes the mathematical statement true for the expression 49 ___ 3 + 32 ÷ 23. We need to solve the right side of the equation first before we can determine the correct symbol to use.

To solve 3 + 32 ÷ 23, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division as they appear from left to right, Addition and Subtraction as they appear from left to right). First, we solve the exponent 23, which equals 8. Then, we perform the division: 32 ÷ 8 = 4. Finally, we add 3 to the result: 3 + 4 = 7. So, our expression on the right side of the equation is equal to 7.

Now we compare the left side of the equation (49) with the result we calculated (7). It is evident that 49 is greater than 7, so the correct symbol to use would be '>'. Therefore, the complete and true mathematical statement would be: 49 > 3 + 32 ÷ 23 or 49 > 7.

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Answer:

$17.10

Step-by-step explanation:

Bracelet cost  $15

4% sales tax:  0.04($15) = $0.60

10% Fed tax:  0.10($15) = $1.50

Summing these three amounts, we get a total cost of $17.10.

Answer:

x^2 +8x+12

Step-by-step explanation:

(X+2)(x+6)

Foil

first: x*x = x^2

outer: x*6 = 6x

inner : 2*x = 2x

last: 2*6 = 12

Add them together:  x^2 +6x+2x+12 = x^2 +8x+12

[tex]\bf \textit{lateral area of a cylinder}\\\\ LA=2\pi rh~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=4\\ h=5 \end{cases}\implies LA=2\pi (4)(5)\implies V=40\pi[/tex]

Answer:

3BC

Step-by-step explanation:

8BC - 9BC + 10BC - 6BC = BC(8 - 9 + 10 - 6) = BC(3) = 3BC

There you go in the attached.

Answer:

72 campers.

Step-by-step explanation:

You can do this with a simple equation. 180% = 1.8 as a decimal fraction. Let x be this  year's attendance. Then:

x = 1.8* 40

x = 72 campers.

Answer:

72 Campers

Step-by-step explanation:

Hope this helps:)

Base x height

To find the base, do pi r squared.

Answer: $17.80

Step-by-step explanation:

2.80 + 3(5) = x

2.80 + 15 = x

17.80 = x

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The total amount paid by Jacob is $17.8.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

Jacob bought a magazine for $2.80. Also, three candy bars for $5 each. Therefore, the amount paid by Jacob is,

Amount paid by Jacob = $2.80 + (3 × $5)

                                      = $17.8

Hence, the total amount paid by Jacob is $17.8.

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Answer with explanation:

→Draw a Line segment of any length on a piece of paper.Measure the length of segment with the help of Straightedge.

→Now if it is a number divisible by 3,with the help of compass divide the length of segment by 3 and by placing the compass on the straightedge open the compass starting from 0 up to that length.

→If the number is not divisible by 3, round the number to nearest rational number.

→And then Mark arc with the help of Compass from starting of line segment the length being equal to the number obtained after dividing by 3,and after obtaining the first point taking the same width mark second arc from the point obtained.

This is required trisected line segment.

⇒The Statement is True which is we can trisect a line segment using only a straightedge and a compass.

Answer:

True

Step-by-step explanation:

Just did the test :)

Answer:

1.48 m

Step-by-step explanation:

mean height of 14 boys is 1.56 m, so their total height is 14 * 1.56 = 21.84 m

mean height of 32 students is 1.515 m, so their total height is 48.48

48.48 - 21.84 = 26.64 (total height of the girls)

mean height of the girls is 26.64/18 = 1.48 m

Answer:

1.48 m.

Step-by-step explanation:

There are 32 - 14 = 18 girls in the class.

Total height of the whole class = 1.515 * 32

= 48.48 m..

Total height of all the boys = 14 * 1.56 =  21.84 m.

So the total height of the 18 girls = 48.48 - 21.84

= 26.64 m.

Therefore the mean height of the girls

= 26.64 / 18

= 1.48 m.

The number of wheels on a group of buses involves mathematical calculations and can be analyzed using multiplication, probability, and physics, particularly when combined with other factors such as passenger capacities or mechanical variables like angular velocity of a flywheel within the bus.

The question about the number of wheels on a group of buses relates to mathematical calculations, specifically pertaining to multiplication and potentially to probability and combinatorics if one were analyzing how to most efficiently deploy a fleet of buses for transportation or which bus to take based on passenger load and capability.

A practical example of a bus-related math problem would be: if a bus has 6 wheels, then a fleet of 10 buses would have a total of 60 wheels. This is a straightforward multiplication problem (10 buses x 6 wheels per bus = 60 wheels).

In the context of probabilistic analysis, considering a situation where buses have different passenger capacities, we might use the expected value formula E(X) = Σx₁p(x₁) to calculate the best option for transportation based on various factors, including the number of passengers each bus can transport.

Moreover, buses also have a place in physics problems. For instance, calculating the angular velocity a bus's flywheel must have to achieve a certain speed involves understanding the concepts of rotational kinetic energy and its transformation into translational energy. This more complex application lies within the realm of physics but has roots in mathematical computation.

Answer:

4,444097208657794

Step-by-step explanation:

c = 20ft

b = 19.5ft

just use the pythagorean theeorem

Answer:

‭1.267650600228229401496703205376e+130‬

Step-by-step explanation:

√400 =20

20¹⁰⁰ = ‭1.267650600228229401496703205376e+130‬

Hope this helps!

Answer:

B = 65

C = 115

Step-by-step explanation:

Givens

ABCD is a parallelogram

It is lettered in such a way that B is opposite D

B = 3n+20

D = 6n-25

Solution

<B = <D                      Property of Parallelogram

3n + 20 = 6n - 25      Add 25 to both sides

3n + 20 + 25 = 6n      Combine

3n +45 = 6n                Subtract 3n from both sides

3n +45 = 6n-3n           Combine

45 = 3n                        Divide by 3

45/3=3n/3                    

n = 15                            Value of n    

B = 3n + 20                  Find B. Let n = 15

B= 3*15+20                   Combine

B = 45 + 20                 Combine

B = 65                                

==================

B and C are supplementary. They add up to 180

B + C = 180

65 + C = 180

C = 180-65

C = 115

Answer:

Step-by-step explanation:

Rewrite X^2+22x=31, leaving space after the "22x:"

X^2+22x                          = 31

The coefficient of x is 22.  Take half of that, obtaining 11.  

Square this result:  11^2 = 121.

Write in "+121      -121" after the x term:

X^2+22x  + 121 - 121 = 31

Rewrite X^2+22x + 121 as

          (x + 11)^2  -121 =  31

Add 121 to both sides:

           (x + 11)^2 = 152

Take the square root of both sides:

            x + 11 = ±√152 = ±2√38

Finally, x = -11 ±2√38.

This is "solution by completing the square"

Answer: OPTION A

Step-by-step explanation:

We have this quadratic equation: [tex]x^2+22x=31[/tex]

In order to complete the square the first step is to pick the coefficient of the x term, divide it by 2 and square it. Then:

[tex](\frac{22}{2})^2=11^2[/tex]

Now we must add 11² to both sides of the equation:

[tex]x^2+22x+11^2=31+11^2[/tex]

Therefore, after complete the square and factor, we get:

[tex](x+11)^2=152[/tex]

This matches with the option A.

Answer:

Step-by-step explanation:

You use latex very well. Nice work.

sqrt(17) = 4.123

sqrt(5) = 2.236

==============

pi + 7

=====

5

3.14 + 7

======

5

10.14/5 = 2.028

Answer

B. \frac{\pi +7 }{5}   2.028

C. \sqrt{5}               2.236

A. \sqrt{17}              4.123