Sammy has $125 saved from his summer lifeguarding job. Sammy has to take the bus to get to school this semester. Each week, Sammy uses $10.50 for bus fare. A. Function s represents the remaining amount, in dollars, in his savings account, as a function of the number of weeks, w, since school started. Complete the table: 6 weeks = 10 weeks = w = = is the dollars remaining in savings B. Use function notation to write a rule that defines function s C. Graph function s on a coordinate plane. D. Solve the equation s(w) = 41 and explain what the solution means.

168 students are enrolled in both classes.

This is a problem from set theory. We can solve this problem by following a few steps easily.

First of all, we have to calculate the students present in both classes.

Student present in both classes = the total student - the student not enrolled in both classes.

So the percentage of the students enrolled in both classes or any of one class is ( 100% - 42% ) = 58%.

Now, the students only enrolled in chorus class is ( 58% - 34%) = 24%

So, the students who joined both classes is ( 28%- 24%)= 4%

The total student is 1200, then 4% of the total student is

( 1200 × 14 )/100 = 168 students.

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Since the total interest he paid on the loan was $336. Then, The annual interest rate of Juan's loan if there are 365 days in a year  will be as at 8.4%.

Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

For example, when a person takes a loan of Rs. 5000, at a rate of 10 p.a. for two years, the person's interest for two years will be S.I. on the borrowed money.

The formula of simple interest is given as:

S.I = PRT

Where:

Substituting the values and solving for the rate on the loan

r = {A} {PT}\r

= {5336} {5000*292}

r = 8.4 %

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6 men complete the work in 20 days.

In 1 day it takes:

6 x20 = 120 men

You need to do the same work done in 20 days, in one day. (more manpower)

So, to finish the work in 12 days:

120 men / 12 days = 10 men

Using the vector form of velocity, it is possible to calculate the airspeed and bearing, which are 165.33 mph and 0.7 degrees respectively.

Given:

A plane may go 360 miles straight north in 2.0 hours if the wind is blowing at 15 mph and 331 degrees from the north.

You can use the following formula to calculate airspeed.

[tex]V^{2} =V_{x} ^{2} + V_{y} ^{2}- 2v_{x} v_{y}cos\beta \\[/tex] ...........equation (1)

[tex]v_{x}[/tex] is the velocity of the wind and [tex]v_{y}[/tex] is the velocity of the plane.

[tex]\beta = 331-180 = 151 degree[/tex]

Putting [tex]v_{x}, v_{y} , \beta[/tex] in equation (1)

[tex]V^{2}= 15^{2} +180^{2} -2*15*180*cos151\\ V^{2} = 225 + 32400 - 5400*cos151\\V^{2} = 27336.49\\V = 165.33[/tex]

Hence, The airspeed of the plane is 165.33 mph

Now,

[tex]\frac{sin\alpha }{v_{x} } =\frac{sin\beta }{V} \\\frac{sin\alpha }{15 } =\frac{sin151 }{165.33} \\\\sin\alpha = 10*0.00122\\\alpha = 0.7[/tex]

Hence bearing required is 0.7 degrees.

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Given:

A table represents a survey to know if residents would like a dog.

a) What is an appropriate first step in finding the experimental probability that a household has 2 or more dogs?

The first step is to find the total households

So, the answer will be option C

Find the sum of the number of households for each category.

b) What is the experimental probability that a household has 2 or more dogs?

First, the total number of households = 513 + 218 + 129 = 860

And the number of households has 2 or more dogs = 129

So, the probability = 129/860 = 0.15 = 15%

So, the answer will be 15%

To solve the following calculation

You have to keep in mind the order of operations. Which states that multiplications and divisions are to be solved before additions or subtractions.

So the first step is to solve the multiplication "4*2" and the division "10÷2"

Now all that is left is to add the numbers when you have to perform the same operation several times, you have to solve them from lef

Given:

The slopr of line is m = -7.

The line passes through point (-6,8).

Explanation:

The equation of line in slope-intercept form is,

Substitute the valus in the equation to determine the value of c.

So equation of line is y = -7x - 34.

Answer:

there were 246 chemistry textbooks and 169 psychology textbooks sold

Step-by-step explanation:

Let

c = the number of chemistry textbooks sold

p = the number of psychology textbooks sold

a textbook store sold a combined total 415 chemistry and psychology textbooks in a week

c + p = 415

the number of chemistry textbooks sold was 77 more than the number of psychology textbooks sold

c = 77 + p

by solving the system of equations

c + p = 415

c = 77 + p

we find

c = 246 chemistry textbooks

p = 169 psychology textbooks

By solving a proportional relation, we conclude that he needs 81 hooks to catch 189 fish.

We assume there is a proportional relationship of the form:

F = k*H

where:

We know that with 3 hooks he catches 7 fish, then we can replace that:

7= k*3

7/3 = k

So the proportional relation is:

y = (7/3)*x

Then if he wants to get 189 fish we can write:

189 = (7/3)*x

And solve this for x:

189*(3/7) = x =81

He will need 81 hooks.

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Answer:

  9

Step-by-step explanation:

You want the minimum value of objective function C=6x+3y, given the constraints x>1, y≥1, 4x+2y<32, and 2x+8y<56.

The objective function has positive coefficients for both x and y, so it will be minimized when x and y are at their minimum values. The constraints tell you these minimum values are x=1 and y=1, so the minimum value of C is ...

  C = 6(1) +3(1) = 9

The minimum value of C is 9.

__

Additional comment

The value of x cannot actually be 1, so the value of C cannot actually be 9. However x may be arbitrarily close to 1, so C may be arbitrarily close to 9.

  C = 6x +3y   ⇒   x = (C -3y)/6

The x-constraint requires ...

  x > 1

  (C -3y)/6 > 1

  C -3y > 6 . . . . . . multiply by 6

  C > 6 +3y . . . . . . add 3y

The minimum value of y is exactly 1, so we have ...

  C > 6 +3(1)

  C > 9

-3(x+1)<15 ​

Divide both-side of the inequality by -3

(x + 1) > -5

subtract 1 from both-side of the inequality

x > -5 - 1

x > -6

Answer:

Step-by-step explanation:

-3(x+1)<15

Divide the inequality by -3, so we need to change the sides of the less than into greater than

x+1 > -5

x > -5 - 1

x > -6

The average rate of change of a function in the interval [a,b] is given by:

In this case we have that a=1 and b=6; plugging these values in the formula above we have:

Therefore, the average rate of change in the interval is -15

Ok, so

The point slope form of the line is given by the following formula:

Where

Is a point of the line, and m is the slope.

If we replace our values:

Slope = 7

Point = (-6, 1)

We obtain that the equation is:

To find the slope intercept form of the equation, we distribute in the brackets:

And the equation of our line in the slope intercept form will be:

y=7x+43

Answer:21

Step-by-step explanation:

To direct variations use a rule of three, as follow:

ANSWER:

33.3%

STEP-BY-STEP EXPLANATION:

We can calculate the value of the percentage starting from the following equation:

We solve for x:

The percentage that decreased was 33.3%

Answer:

1280 ft²

Step-by-step explanation:

Perimeter is the addition of all sides of the shape added together. Therefore, if the backyard is the rectangular shape you know that two of the sides are 40 feet wide. By adding both sides you get a total of 80 feet. Subtract the total from the perimeter in order to get the total of the unknown sides. 144 minus 80 is equivalent to 64. Now that you have the total of the unknown sides, divide by two in order to get the single unknown length. So, 64 divided by 2 is equal to 32. The area is the multiplication of two sides with quadrilaterals. Therefore, 40 times 32 equals an area of 1280 feet squared.

The decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25

The given mixed fraction = [tex]14\frac{25}{100}[/tex]

The mixed fraction is the fraction that consist of one whole number and the simple fraction.

The simple fraction is the fraction that consist of numerator and denominator as whole number. The top term of the simple fraction is called numerator and bottom term is called denominator

The decimal number is a number that consist of one whole number and the fractional part. The fractional parts are separated by a decimal point.

The number is [tex]14\frac{25}{100}[/tex]

Convert the mixed fraction to simple fraction

[tex]14\frac{25}{100}[/tex] = (100×14+25)/100

= 57/4

Convert the simple fraction to decimal number

57/4 = 14.25

Hence, the decimal number of the fraction [tex]14\frac{25}{100}[/tex] is 14.25

The complete question is:

Rewrite the decimal fraction as a decimal number.

[tex]14\frac{25}{100}[/tex]

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Step-by-step explanation:

you do know what a percent is ?

1% is the 1/100 part of a whole.

when we have

100,000,000 (one hundred million),

how many 1/100 parts of that are

45,000,000 (45 million)?

well, 45.

45,000,000 is 45/100 of 100,000,000

in other words 45%.

Answer:

12-3x=14

Step-by-step explanation:

Answer:

The axis of symmetry is -4 because the axis of symmetry is equal to h, in the vertex form!

Answer:i have no idea good luck

Step-by-step explanation:

Answer:

4,3 DONT BE MAD IF IM WRONG

Answer:

1,857.21

Explanation:

In the number: 1,857.205

The digit after 0 is 5.

Since it is a number between 5 and 9, we round up to obtain:

The numeric value for the given expression is as follows:

[tex]\frac{j(x + h) - j(x)}{h} = \frac{4^{x - 2}(4^h - 1)}{h}[/tex]

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.

In the context of this problem, the function j(x) is given as follows:

[tex]j(x) = 4^{x - 2}[/tex]

At x = x + h, the numeric value of the function is found replacing the lone instance of x by x + h as follows:

[tex]j(x + h) = 4^{x + h - 2}[/tex]

For the fraction, the subtraction at the numerator is given as follows, applying properties of exponents:

[tex]j(x + h) - j(x) = 4^{x + h - 2} - 4^{x - 2} = 4^{x - 2}(4^h - 1)[/tex]

As the x - 2 term is common to both exponents.

Just dividing by h, the numeric value of the entire expression is given as follows:

[tex]\frac{j(x + h) - j(x)}{h} = \frac{4^{x - 2}(4^h - 1)}{h}[/tex]

Which means that the third option is correct.

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The given function is:

f(x) = 1.5x + 7

Then, since x represents the age of the baby, in months, in order to find its weight with 5 months, that is, f(5), we need to replace x by 5 in the above equation:

f(5) = 1.5 * 5 + 7 = 7.5 + 7 = 14.5

Therefore, the last option is correct.

Given the following equation:

You need to solve for "x" in order to find its value and solve the equation. To do this, you can follow the steps shown below:

1. You need to apply the Subtraction property of equality by subtracting 2 from both sides of the equation:

2. Now you can apply the Additio property of equality by adding "4x" to both sides of the equation:

Therefore, you get that the solution is:

Budget: $40

Fruit: $4/pound

Granola bars: $1 each

At least 20 granolas

Let's call

f: number of pounds of fruit

g: number of granola bars

Therefore

The total cost of fruit is given by: $4 · f

The total cost of granola is given by: $1 · g

The total cost of everything is given by: $4 · f + $1 · g

Since budget: $40 then

$4 · f + $1 · g = $40

4f + g = 40

g > 20 means we have at least 20 granolas

4f + g > 20 means that we have at least 20 granolas, that cost $20, since 4f + g = 40 and 40 > 20

The number when increased by twenty is at least 85, the possible values  of the numbers for this are: 35, 33, 40 and 34.

Given, according to the statement in the question, frame the equation:

2x+20 ≥ 85

⇒ 2x + 20 ≥ 85

⇒ 2x ≥ 85 - 20

⇒ 2x ≥ 65

⇒ x ≥ 65/2

⇒ x ≥ 32.5

hence the numbers greater than or equal to 32.5 are 35, 33, 40 and 34.

Hence the possible values of the number are 35, 33, 40 and 34.

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SOLUTION; Concept

Step1: Identify the giving information in the question

BOX A contains

BOX B contains

Step2: Find the probability of each event

Event 1: Choosing a green pen from the Box B

Event 2: Choosing a black pen from the Box B

Event 3: Choosing a yellow or black pen from the Box A

Since Box A contains only a yellow or black pen then the probability is

Event 4: Choosing a yellow pen from box A

Since there are 9 yellow pens in box A, the probability of choosing the yellow pen is

Probability describes the likelihood of the event.

Hence From least likely to most likely the occurrence of the event is arranged as follows according to the probability of each event

EXPLANATION:

To calculate the number of independent events that occur, the product of the probabilities of the individual events occurring must be calculated.

Therefore if A and B are independent events then:

P (A and B) = P (A) • P (B)

The exercise is as follows:

NOTE:

To obtain the product of two fractions, the numerators must be multiplied with each other and the denominators must also be multiplied with each other.