John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. He wrote the inequality 4+5x≤15 to solve for all the possible values of x , the number of pounds of chocolate John could buy

The total number of each type of bill and coin are

$5 bills x 5,

$1 bills x 10,

quarters x 16,

dimes x 9.

Equations are mathematical expressions with two algebraic expressions flanking the equals (=) sign on either side. It shows the relationship of equality between the expression written on the left side with the expression written on the right side.

Now in the given question,

$5 bills = x, total = 5x

$1 bills = 2x, total = x

Quarters = 3x + 1, total = 0.25(3x + 1)

Dimes = 3x + 1 - 7= 3x - 6, total = 0.1(3x - 6)

Equation below as the sum, solve for x:

5x + 2x + 0.25(3x + 1) + 0.1(3x - 6) = 39.9

7x + 0.75x + 0.25 + 0.3x - 0.6 = 39.9

8.05x  - 0.35 = 39.9

8.05x = 40.25

x = 40.25/8.05

x = 5

Number of each bill and coin:

$5 bills = 5

$1 bills = 2*5 = 10

Quarters = 3*5 + 1 = 16

Dimes = 3*5 - 6 = 9

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There are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers. Hence, the accurate answer is option (b) 28.

To determine the number of ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers, we will use the formula for combinations, which is given by -

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items to be selected, and ! denotes the factorial function (the product of all positive integers up to a given number).

Here, we are given n = 8 fish and k = 2 fish.

Thus, the number of ways to select and place 2 fish from 8 fish will be -

8C2 = 8! / (2!(8-2)!) = (8 x 7) / (2 x 1) = 28

Therefore, there are 28 ways to randomly select 2 fish from 8 fish and put each of the 2 selected fish into different containers.

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The company must make 100 X-ray machines to minimize the unit cost.

A differential equation is an equation that contains one or more functions with its derivatives.

To minimize the unit cost, we need to find the value of x that minimizes the function C(x) = 0.9x² - 180x + 20985.

We can start by taking the derivative of C(x) with respect to x and setting it equal to zero:

C'(x) = 1.8x - 180 = 0

Solving for x, we get:

x = 100

Therefore, the company must make 100 X-ray machines to minimize the unit cost.

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Doubling the down payment reduces the total cost of the vehicle, and increasing the down payment or extending the loan term are two ways to lower the monthly payment.

Let's assume that you're planning to buy a car worth $20,000. The down payment is the initial amount you pay towards the purchase of the car, and it is usually expressed as a percentage of the total cost of the car. Let's assume that the down payment is 10% of the total cost, which means you have to pay $2,000 initially.

If you double the down payment from 10% to 20%, you will have to pay $4,000 initially. This means that the amount you borrow from the bank to buy the car will be reduced. As a result, the total cost of the vehicle will decrease because the interest on the loan will also decrease.

Now, let's move on to ways to lower your monthly payment.

Increase the down payment: As we discussed earlier, making a higher down payment reduces the loan amount, which, in turn, reduces the monthly payment. So, if you can increase the down payment, you can lower the monthly payment.

Increase the loan term: The loan term is the length of time you have to repay the loan. If you extend the loan term, the monthly payment will be lower. However, keep in mind that a longer loan term means you'll end up paying more interest over the life of the loan, which will increase the total cost of the vehicle.

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Answer:

A one-sample t-test for a population mean is the appropriate test for the researchers' hypothesis. In this case, they want to test the hypothesis that the mean battery life of their new battery is greater than a known mean battery life of their older version. The one-sample t-test allows them to compare the mean of a sample to a known population mean and determine if the difference between them is statistically significant.

1. The area of the marble is 6.6m² and the cost is

$3491.4

2. The area of the marble is 42.84m² and the cost is $22662.36

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

1. The area of the marble is

A=( 3.7 × 1.2 ) + 0.9 × 2.4

A= 4.44 + 2.16

A= 6.6m²

if the cost is 23 dollars /meter

per meter square = 23² = $ 529 / meter square

1 meter square = 529

6.6 meter square = 529 × 6.6 = $3491.4

2. The area of the marble is obtained by cutting it into rectangle and trapezium

A= ½(8.8+4.8) 3.9 + 4.8 × 3.4

A= ½(13.6× 3.9) + 16.32

A= 26.52+ 16.32

A= 42.84 m²

The cost will be 529 × 42.84

= $22662.36

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The probability of spinning green and then rolling an even number is 1/36

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

The probability of spinning green is 1/6 because there are 6 equally likely outcomes and 1 of them is green.

The probability of rolling an even number is 3/6 because there are 6 equally likely outcomes and 3 of them are even numbers (2, 4, and 6).

The probability of spinning green and then rolling an even number is the product of the probabilities of each event. To find this, we multiply the probability of spinning green (1/6) by the probability of rolling an even number (3/6):

(1/6) * (3/6) = 1/36

So, the probability of spinning green and then rolling an even number is 1/36.

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I agree with Kofi that the circumference of a circle equals pi times the diameter. This is because the formula for the circumference of a circle is given by:

C = 2πr

Where C is the circumference, π is pi, and r is the radius of the circle. To find the diameter, we can double the radius, so we can write:

C = 2π(r) = π(2r) = πd

Where d is the diameter of the circle.

So, the formula for the circumference of a circle is indeed pi times the diameter, not just pi times the radius.

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

Explanation:

Let's label the sides of the triangle a, b, and c.

Furthermore, let's have 'a' & b represent known sides and  [tex]b \ge a[/tex] be the case. For a triangle to be possible, the missing side c must have these restrictions placed on it:

b-a < c < b+a

This inequality is valid because of a modification to the Triangle Inequality Theorem. I'll leave the proof to the reader.

-------

In this case we have a = 3 and b = 8 which lead to...

b-a < c < b+a

8-3 < x < 8+3

5 < x < 11

The third side is between 5 and 11, excluding both endpoints. We cannot have x = 5. Furthermore, we cannot have x = 11 either. If x were either of those endpoints, then we'd form a straight line rather than a triangle.

Having x be an integer leads to the roster set notation {6,7,8,9,10} to represent all possible values of x. For instance, we could have a triangle with side lengths 3, 8, and 6. I recommend getting slips of paper of these lengths to try it out yourself. Or you can use software such as GeoGebra to see why this works.

A scatter plot would best display the relationship between the number of hours a student spent studying for several tests and the student's grade on each test.

A scatter plot is a graph that displays the relationship between two continuous variables. In this case, the number of hours a student spent studying is the independent variable, which would be plotted on the x-axis. The student's grade on each test is the dependent variable, which would be plotted on the y-axis. Each data point would represent a single test, with the x-coordinate indicating the number of hours studied for that test and the y-coordinate indicating the grade received.

By using a scatter plot, you can easily identify any patterns or relationships between the number of hours studied and the student's grades on each test. It can also help to identify any outliers or anomalies in the data.

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The radius of the circle is √17.

The center of the circle is (4, 2).

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

The equation of a circle with radius r and center (h, k) is

(x - h)² + (y - k)² = r²

Now,

x² + y² - 4 y - 8x + 3 = 0

x² - 8x + y² - 4y + 3 = 0

x² - 8x + 4² - 4² + y² - 4y + 2² - 2² + 3 = 0

(x - 4)² + (y - 2)² - 16 - 4 + 3 = 0

(x - 4)² + (y - 2)² = 16 + 4 - 3

(x - 4)² + (y - 2)² = √17

This means,

radius = √17 and center = (4, 2)

Thus,

The radius and center of the circle are √17 and (4, 2).

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Answer:

x = 3

Step-by-step explanation:

Take the first equation-  x + 2y = (-1)

Multiply both sides by 2

2(x + 2y) = 2(-1)
2x + 4y = -2

Add first and second equations

(2x + 4y = -2)

+(4x -4y = 20)
= 6x = 18

x = 18/6

x= 3

Extra info- This method is also called as Elimination method in which Elimination (whether by addition of equations or subtraction) of any variable is done.

Hope it helps

Answer:

SOLVE IT!

Step-by-step explanation:

A. 45.50+0.11= answer

B. 65.50+0.17= answer

Minus A plus B to get answer!

Answer:

firstly, I would fill up the 10-oz glass with juice and use it to fill the 6-oz glass. This would leave me with 4 oz left in the 10-oz glass

Step-by-step explanation:

Answer:

The length of each leg would be 4 units

Step-by-step explanation:

The hypotenuse of a 45-45-90 is √2 times bigger than either side length since they're the same lengths.

Answer:

25.85 cubic feet

Step-by-step explanation:

Volume of a cylinder is

Base Area • height

The Base Area of a cylinder is a circle. The area of a circle is pi•r^2.

Vol = pi•r^2•h

They gave the diameter of the circle as 2.8, so the radius is half of that.

r = 1.4

The height was given

h = 4.2

Fill in radius and height and 3.14 for pi. Square the radius and then multiply everything.

see image.

Round to two decimal places.

hi i just did the test and the answer is 25.85 cubic feet

and it was correct btw other person deserves brainly have a nice day!

The value of (f - g)(-1) is 5.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -5x³ - 8x² - 4x + 3

g(x) = 3x³ - 2x² - 8x - 4

Now,

(f - g)(x)

= f(x) - g(x)

= -5x³ - 8x² - 4x + 3 - (3x³ - 2x² - 8x - 4)

= -5x³ - 8x² - 4x + 3 - 3x³ + 2x² + 8x + 4

= -8x³ - 6x² + 4x + 7

Now,

(f - g) (-1)

Substitute x = -1.

= -8(-1)³ - 6(-1)² + 4(-1) + 7

= -8 x -1 - 6 - 4 + 7

= 8 - 6 - 4 + 7

= 8 - 10 + 7

= 15 - 10

= 5

Thus,

(f - g)(-1) = 5

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The probability of selecting a jury composed of 12 women from a pool of 30 people that includes 12 men and 18 women is extremely low, only 0.0657%.

The probability of an event happening is the measure of how likely that event is to occur.

In this case, we need to find the probability of selecting a jury of 12 women from a pool of 30 people. To calculate this probability, we can use the formula:

Probability = Number of favorable outcomes / Total number of outcomes

The total number of outcomes is the number of ways in which we can select 12 people from a pool of 30. We can calculate this number using the combination formula:

Total number of outcomes = C(30,12) = 30! / (12! * (30-12)!) = 28,238,760

Now, we need to calculate the number of favorable outcomes, which is the number of ways in which we can select 12 women from a pool of 18. We can calculate this number using the combination formula as well:

Number of favorable outcomes = C(18,12) = 18! / (12! * (18-12)!) = 18,564

Therefore, the probability of selecting a jury composed of 12 women is:

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 18,564 / 28,238,760

Probability = 0.000657 or 0.0657%

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A regular polygon with 18 sides has a central angle that is 20 degrees in size.

A polygon's total number of central angles equals 360 degrees.

As a result, the regular polygon's centre angle has a ratio of 360 to its number of sides. It may be expressed as,

[tex]$C_a=\frac{360}{n}[/tex]

Here, (n) denotes the regular polygon's number of sides.

The polygon in the provided issue has an overall total of 18 sides. Using the method above, it is possible to determine the polygon's centre angle, which has 18 sides. Thus,

[tex]$& C_a=\frac{360}{18} \\[/tex]

[tex]$& C_a=20^{\circ}[/tex]

Therefore, a regular polygon with 18 sides has a central angle that is 20 degrees in size.

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The probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).

What is Probability?

Probability is a mathematical concept used to measure the likelihood of a particular event occurring. It is a way of expressing the chance or possibility of an event happening, ranging from 0 (impossible) to 1 (certain).

In probability theory, an event is a subset of the possible outcomes of an experiment or a random process. Probability can be expressed in terms of fractions, percentages, or decimals.

The symbol for the event that a college student is female is A, as given in the statement. The symbol for the event that a college student has financial aid is B, as given in the statement.

So, A={A student is female} and B={A student has financial aid}.

These events are mutually exclusive because one does not necessarily affect the other. For example, a male student can have financial aid and a female student may not have financial aid. Hence, the occurrence of one event does not influence the occurrence of the other event.

Therefore, the probability of a college student being either female or having financial aid can be represented as the union of the events A and B. It can be denoted as P(A ∪ B) and is calculated as:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Where P(A ∩ B) represents the probability of a student having both characteristics, i.e., being female and having financial aid.

However, as these events are mutually exclusive, P(A ∩ B) = 0. So the probability of a college student being either female or having financial aid is simply the sum of their individual probabilities:

P(A ∪ B) = P(A) + P(B) - 0

P(A ∪ B) = P(A) + P(B)

Hence, the probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).

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Step-by-step explanation:

We know all angles on a traingle equal 180

We also know one angle is a right angle which is 90

180 - 90 = 90, indicating the other two angles equal 90

[tex](2x - 1) + (3x + 6) = 90[/tex]

Now we will combine the X's and constants

[tex]5x +5 = 90[/tex]

Now to subtract 7

[tex]5x = 85[/tex]

Lastly, divide by 5

[tex]x = 17[/tex]

Answer: Yes, No, No, Yes, No

Step-by-step explanation:

I think Graphing is the best way to tackle this. But I prefer algebra:

A) 2(-8) + 6(7) = 26

-16 + 42 = 26

26 = 26

The answer for A is Yes. I wont show work for the others, i think its pretty intuitive, (just substitute the coordinates for x and y, and check if the resulting statement is true)

B. No

C. No

D. Yes

E. No

a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

A relation is a function if it has only One y-value for each x-value.

Given that a  Function G takes a student's first name for its input and gives the number of letters in the first name for its output.

a.

Given that G(Jada) = 4

In the above function Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. We need to find the value of G(Diego)

In the above function Diego is the input and 5 will be output, the output is 5 because there are 5 letters in Diego word.

G(Diego) =5

Hence, a. Jada is the input and 4 is output, the output is 4 because there are 4 letters in Jada word.

b. G(Diego) =5

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The answer choices  50(1.15)  and 57.5 below are equivalent to 50(1+0.15)

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The order of operations is a rule that specifies the right procedure to follow when evaluating a mathematical equation. Using the acronym PEMDAS, we can memorize this order: parentheses, exponents, multiplication, and division (left to right), addition and subtraction (from left to right).

50(1+0.15)

Add the numbers

= 50(1.15)

Multiply the  numbers

= 57.5

The answer choices  50(1.15)  and 57.5 below are equivalent to 50(1+0.15)

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Using the diagram in the problem angle TQU is solved to be

The angle at U is 90 degrees, Using the concept of adjacent angles the three angles at U is solved

Using the trigonometry relations of right triangle we solve for angle PQT'

tan (angle PQT) = 1 / 3

angle PQT = arc tan (1 / 3)  

angle PQT = 18.43

angle PQT = angle UQS and

angle PQT + angle UQS  + angle TQU = 90 degrees adjacent angles

2 * 18.43 * angle TQU = 90

angle TQU = 90 - 2 * 18.43

angle TQU = 53.14 degrees

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The required Jodi will consume 180 calories if she eats 5 chocolates.

When two quantities are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage. As gas costs increase, the cost of food may as well as well.

We can use proportionality to solve this problem. Since the number of calories consumed varies directly with the number of chocolates eaten, we can write:

calories consumed / chocolates eaten = constant

Let's call this constant k. We can solve for k using the information given:

72 calories / 2 chocolates = k

k = 36 calories/chocolate

Now we can use this constant to find the number of calories Jodi will consume if she eats 5 chocolates:

calories consumed / chocolates eaten = k

calories consumed / 5 chocolates = 36 calories/chocolate

calories consumed = 5 chocolates * 36 calories/chocolate

calories consumed = 180 calories

Therefore, Jodi will consume 180 calories if she eats 5 chocolates.

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Answer:

to help navigate the answer

Using the ratio formula the unknown numbers are found to be 6 and 9.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

The original ratio value is 2 : 3.

Three is added to the ratio.

The new ratio value is 3 : 4.

Let the unknown numbers be 2x and 3x.

The equation will be -

2x + 3 / 3x + 3 = 3/4

Solve the equation -

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

8x + 12 = 9x + 9

8x - 9x = 9 - 12

-x = -3

x = 3

Substitute the value of x in the unknown numbers -

2x = 2(3) = 6

3x = 3(3) = 9

Therefore, the numbers are 6 and 9.

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