The price of a pen set can be determined by the equation:P=$2n,Where p is the price and n is the number of pens What is the constant of proportionality (unit rate)

We have the following:

We calculate the number of inches per month as follows:

therefore:

The table is:

Month Growth (inches)

1 3.4

2 6.8

3 10.2

4 13.6

5 17

6 20.4

Answer:

Step-by-step explanation:

Let the number of jars is x.

80 liters distributed, each jar has:

Redistribution with 4 less jars, each jar now has:

Each jar has now twice the amount:

She prepared 8 jars at the start

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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Answer:

The approximate value of \(P(0.45<\bar X<0.50)\) is 0.3686.

Step-by-step explanation:

The pdf of X is:

\(f(x) = 6x(1-x), 0 < x < 1\)

Compute the mean as follows:

\(\mu=\int\limits^{1}_{0} {x\times 6x(1-x)} \, dx \\\\=\int\limits^{1}_{0} {6x^{2}-6x^{3}} \, dx\\\\=[\frac{6x^{3}}{3}]-[\frac{6x^{4}}{4}]|^{1}_{0}\\\\=2-\frac{3}{2}\\\\=0.50\)

Compute the variance as follows:

\(\sigma^{2}=E(X^{2})-(\mu)^{2}\)

\(E(X^{2})=\int\limits^{1}_{0} {x^{2}\times 6x(1-x)} \, dx \\\\=\int\limits^{1}_{0} {6x^{3}-6x^{4}} \, dx\\\\=[\frac{6x^{4}}{4}]-[\frac{6x^{5}}{5}]|^{1}_{0}\\\\=\frac{3}{2}-\frac{6}{5}\\\\=0.30\)

\(\sigma^{2}=E(X^{2})-(\mu)^{2}\\\\\sigma=\sqrt{E(X^{2})-(\mu)^{2}}\\\\=\sqrt{0.30-(0.50)^{2}}\\\\=0.2236\)

According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.  

Then, the mean of the sample means is given by,

\(\mu_{\bar x}=\mu\)

And the standard deviation of the sample means is given by,

\(\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}\)

The sample selected is of size n = 64 > 30. Thus a central limit theorem can be applied to approximate the sampling distribution of sample mean.

Compute the value of \(P(0.45<\bar X<0.50)\) as follows:

\(P(0.45<\bar X<0.50)=P(\frac{0.45-0.50}{0.2236/\sqrt{64}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{0.50-0.50}{0.2236/\sqrt{64}})\)

                                \(=P(-1.12<Z<0)\\\\=P(Z<0)-P(Z<-1.12)\\\\=0.50-0.13136\\\\=0.36864\\\\\approx 0.3686\)

Thus, the approximate value of \(P(0.45<\bar X<0.50)\) is 0.3686.

Answer:

it's 60

Step-by-step explanation:

Step-by-step explanation:

The situation described can be modeled using a linear equation, where the balance of the savings account increases by a fixed amount every month. Specifically, the equation that represents this situation is:

balance = $5000 + $825 * months

where "months" represents the number of months that have passed since the account was opened. The slope of this line is constant at $825, indicating that the balance is increasing by the same amount every month.

Therefore, the model for this situation is linear.

The average number of enrollments per day at the Sunnyside Daycare is 21.

An average is a result obtained by summing some numerical values and then dividing the total by the number of values or variables.

An average is the mean, which is one of the central tendency values.

Day          Number of Enrollments

Monday                 17

Tuesday                19

Wednesday         23

Thursday              14

Friday                  25

Saturday             28

Total =               126

Average enrollments = 21 (126/6)

Thus, the average number of enrollments per day at the Sunnyside Daycare is 21.

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What was the average number of enrollments per day?

Answer: The answer is Multiplicative Inverse.

Step-by-step explanation: I hope this helps.

The area of the figure we need to use Rectangle, Triangle and Circle formulas:

Identify the shape: Depending on the figure you have, it could be a rectangle, triangle, circle, or a more complex shape. If it's a composite figure, break it down into simpler shapes.
Use the appropriate formula: Each shape has a specific formula to calculate the area.
- Rectangle: Area = length × width
- Triangle: Area = (base × height) / 2
- Circle: Area = π × (radius²)
Measure the necessary dimensions: Measure the required dimensions (length, width, base, height, or radius) using appropriate units (e.g., meters, centimeters, inches).
Plug the values into the formula: Insert the measured dimensions into the corresponding formula.
Perform calculations: Carry out the necessary mathematical operations to get the area.
Include units: Express the area with the appropriate square units (e.g., square meters, square centimeters, square inches).
(For composite figures) Add or subtract areas: If the figure is composed of multiple shapes, add or subtract their areas accordingly to get the total area of the figure.

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Answer:

A fraction is in simplest form when the top and bottom cannot be any smaller, while still being whole numbers.

Step-by-step explanation:

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

y2-y1/x2-x1= 36-8/8-4 and that gives you 31

Step-by-step explanation:

this is your slope formula y2-y1/x2-x1

YOU MUST PLUG IN YOUR X & Y VALUES

Answer:

23.45 meters

Step-by-step explanation:

To solve, you do 3.35*7, which gives you 23.45

The expression (-3)0 has a value of 0 when evaluated because a number multiplied by 0 gives 0

From the question, we have the following parameters that can be used in our computation:

(-3)0

The above statement is a product expression that multiplies the values of -3 and 0

Also, there is no need to check if there are like terms in the expression or not

This is  because we are multiplying the factors

So, we have

(-3)0 = 0

This means that the value of the expression is 0 i.e a number multiplied by 0 gives 0

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TJohn's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

To represent the given problem as a system of equations, we can use the following information:

John is 70 years younger than Sharon: j = s - 70

Sharon is 4 times as old as John: s = 4j

Let's plot the graph for this system of equations:

First, let's solve equation (2) for s:

s = 4j

Now substitute this value of s in equation (1):

j = s - 70

j = 4j - 70

3j = 70

j = 70/3

Substitute the value of j back into equation (2) to find s:

s = 4j

s = 4(70/3)

s = 280/3

The solution to the system of equations is j = 70/3 and s = 280/3

In the graph d, the solution to the system of equations is represented by the point (70/3, 280/3), which is approximately (23.33, 93.33) on the graph.

Therefore, John's age is approximately 23.33 years, and Sharon's age is approximately 93.33 years.

And the correct graph is D.

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Answer:

BC = 21 cm

Step-by-step explanation:

In similar triangles the corresponding sides are in same proportion.

Its given in the sum that AC = 12 cm; DF = 20 cm and EF = 35 cm.

      \(\sf \dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{AC}{DF}\\\\\\\dfrac{AC}{DF}=\dfrac{BC}{EF}\\\\\dfrac{12}{20}=\dfrac{BC}{35}\)

     \(\sf \dfrac{12}{20}*35=BC\\\\\\\dfrac{12}{4}*7=BC\\\\\\3*7=BC\\\\ \boxed{BC = 21 cm}\)

The area of a square inscribed in a circle is 25, then the area of the circle is 25π/2 or approximately 39.27 square units.

To solve this problem, we can use the relationship between the area of a square inscribed in a circle and the area of the circle itself.

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. Let's assume that the side length of the square is 's' and the radius of the circle is 'r'.

We are given that the area of the square is 25, so we can find the side length of the square:

Area of square = \(s^2 = 25\)

Taking the square root of both sides, we get:

s = √25 = 5

Since the diagonal of the square is equal to the diameter of the circle, we can find the diameter of the circle:

Diagonal = Diameter = s√2 = 5√2

The radius of the circle is half the diameter, so:

Radius = 5√2 / 2 = (5√2)/2

Now, we can calculate the area of the circle using the formula:

Area of circle = \(\pi r^2\)

Substituting the value of the radius, we get:

Area of circle = π((5√2)/\(2)^2\) = π(25/2) = 25π/2

Therefore, the area of the circle is 25π/2 or approximately 39.27 square units.

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a) He needs 500 g of sugar to make apple crumble for 16 people.

b) She needs 45 g of flour to make apple crumble for 2 people.

c) 500g of apples is enough to make apple crumble for 6 people.

The amounts for this problem are obtained according to the proportions given in the problem.

For 8 people, the amount of sugar needed is of 250 g. For 16 people, the  number of people doubles, hence the amount of sugar needed will also double, as follows:

2 x 250 = 500 g.

For 2 people, the amount of each item is divided by 4, hence the amount of flour needed is given as follows:

180/4 = 45 g.

The amount of apple needed per people is of:

700/8 = 87.5 grams.

For 6 people, the amount is given as follows:

6 x 87.5 = 525 grams.

Hence 500g of apples is enough to make apple crumble for 6 people.

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Answer:

1/2, 5/2

Step-by-step explanation:

To find the midpoint add up the x coordinates and divide by 2 and the y coordinates and divide by 2

(-3+4)/2, (-2 +7)/2

1/2, 5/2

Answer:

\((\frac{1}{2}, \frac{5}{2} )\)

Step-by-step explanation:

Use the midpoint formula:

\((\frac{-3+4}{2} , \frac{-2+7}{2} )\)

The points are:

\((\frac{1}{2}, \frac{5}{2} )\)

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

Answer:

4x+15y

Step-by-step explanation:

If you want it simplified

Answer:

Option A

Step-by-step explanation:

Given:

To find:

Solution:

a)  3x-5= 3x + 5

Add 5 to both sides

3x-5= 3x + 5

3x - 5 + 5 = 3x + 5 + 5

Simplify

(Add the numbers)

3x - 5 + 5 = 3x + 5 + 5

3x = 3x + 5 + 5

(Add the numbers)

3x  = 3x + 5 + 5

3x = 3x + 10

Subtract 3x from both sides

3x = 3x + 10

3x - 3x = 3x + 10 - 3

Simplify

(Combine like terms)

3x -3x = 3x + 10 - 3

0 = 3x + 10 - 3

(Combine like terms)

0 = 3x + 10 - 3

0 = 10

The input is a contradiction: it has no solutions

b)  3x-5= 3x - 5

Since both sides equal, there are infinitely many solutions.

c)  3x - 5 = 2x+5

Add 5 to both sides

3x = 2x + 5 + 5

Simplify  2x + 5 + 5 to 2x + 10

3x = 2x + 10

Subtract 2x from both sides

3x - 2x = 10

Simplify 3x - 2x to x.

x = 10

d) 3x-5 = 2x + 10

Add 5 to both sides

3x = 2x + 10 + 5

Simplify 2x + 10 + 5 to 2x + 15

3x = 2x + 15

Subtract 2x from both sides

3x - 2x = 15

Simplify 3x -2x to x.

x = 15

--------------------------------------------

Answer:

As you can see all c and d both have solutions, eliminating them as options. Option B has infinite solutions leaving Option A which has no solutions.

Therefore, Option A is the linear equation that has no solution.

The total volume of the crayon is 4,650.2 mm³.

The total surface area of the crayon is 2,300.33 mm².

The volume and surface area of one crayon is calculated by applying the following formula as follows;

The volume of the cylinder is calculated as;

V = πr²h

where;

V = π x (4.25)² x (80)

V = 4539.6 mm³

The volume of the cone is calculated as;

V = ¹/₃ πr²h

V = ¹/₃ π(6.5/2)² x (10)

V = 110.6 mm³

Total volume of the crayon = 4539.6 mm³ + 110.6 mm³  = 4,650.2 mm³

The surface area of the cylindrical part of the crayon is calculated as;

S.A = 2πrh + πr²

S.A = 2π(4.25)(80) + π(4.25)²

S.A = 2,193.03 mm²

The surface area of the cone part of the crayon is calculated as;

S.A = πrs

where;

s = √ (10² + 3.25²)

s = 10.51 mm

S.A = π x 3.25 mm  x  10.51 mm

S.A = 107.3 mm²

The total surface area of the crayon = 107.3 mm² +  2,193.03 mm² = 2,300.33 mm²

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True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

Step-by-step explanation:

You want to know a thermometer's reading 4 minutes and 9 minutes after begin brought into a room with a temperature of 36 °C if its initial reading is 10 °C, and it rises to 14 °C after 2 minutes.

Newton's law of cooling tells you the temperature difference of 36 -10 = 26 °C will decline exponentially. If it declines to 36 -14 = 22 °C after 2 minutes, then the temperature reading can be modeled by ...

  T = 36 -26·(22/26)^(t/2)

At times of t=4 and t=9, the temperature readings will be ...

__

Additional comment

The time constant of this thermometer is about 12 minutes, so it will take about 67 minutes to read within 0.1 °C of the room temperature.

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Answer:

25

Step-by-step explanation:

range = largest value - smallest value (123-25)

The answer is 12, 15, 30