2 Riley eats of one small pizza with p slices. Enter an expression to represent the number of slices of pizza Riley eats. ​

Answers

Answer 1

The expression representing number of slices of pizza ate by Riley is equal to (2/3 ) of total slices of one small pizza is given by  n = (2/3) × p.

Let us consider 'n' represents the number of slices of pizza Riley eats

Here 'p' represents the total number of slices of one small pizza.

If Riley eats two-thirds (2/3) of a small pizza with p slices,

Then the number of slices of pizza Riley eats can be represented by the expression,

Number of slices of pizza Riley eats  

= ( 2/3 ) × Total number of slices of one small pizza

⇒ n = (2/3) × p

Therefore, the expression represents two-thirds of the total number of slices in the pizza, which is the amount that Riley eats is equal to n = (2/3) × p

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The above question is incomplete, the complete question is:

Riley eats 2/3 of one small pizza with p slices. Enter an expression to represent the number of slices of pizza Riley eats. ​


Related Questions

In an expression using the logical operator ____, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. a. OrElse b. Nor c. AndAlso d. Xor

Answers

In an expression using the logical operator And Also, as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false.

The And Also operator is a short-circuiting operator that is used to combine two or more Boolean expressions. It evaluates the left-hand expression first and then the right-hand expression only if the left-hand expression evaluates to true

. If the left-hand expression evaluates to false, then the right-hand expression is not evaluated at all. This helps to improve the performance of the code by avoiding unnecessary evaluations of expressions that would not change the outcome of the overall condition.

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In an expression using the logical operator And Also , as soon as one of the compound conditions is found to be false, no further conditions are tested and the expression evaluates to false. Therefore option c. And Also correct.

This is because the AndAlso operator employs short-circuit evaluation, meaning it stops evaluating once it encounters

the first false condition since the overall result will definitely be false.

In an expression using AndAlso, if the first condition is false, the entire expression is evaluated as false without testing

any further conditions. This is also known as short-circuit evaluation.

In contrast, the OrElse operator evaluates to true as soon as one of the compound conditions is true, without testing

any further conditions. The Nor and Xor operators are less commonly used and have different behavior.

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when sampling from a population with , which of the following sample means is more surprising? why? sample a: a random sample of 9 pell grant recipients with a mean award amount of $2750. sample b: a random sample of 36 pell grant recipients with a mean award amount of $2750.

Answers

Sample mean in sample b to be less variable and more representative of  population mean than sample mean in sample a.

Standard error measures the variability of sample means around the population mean.

It decreases as sample size increases.

Using the formula for the standard error of the mean,

Calculate the standard errors for each sample,

Standard error of sample a

= s/√(n)

= 850/√(9)

= 283.33

Standard error of sample b

= s/√(n)

= 850/√(36)

= 141.67

Where s is the sample standard deviation

And n is the sample size.

The standard error of sample b is smaller than the standard error of sample a.

Sample mean in sample b is more likely to be closer to true population mean than sample mean in sample a.

Therefore, sample mean b is more surprising as larger sample size makes it more likely and accurately represents population mean.

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Please use Triangle Inequality to solve, I'm having a bit of trouble. I'd also appreciate if you just help me.

Answers

The value of x for the given triangle through which the perimeter of the given relation is satisfied is 10.

What about perimeter of triangle?

The perimeter of a triangle is the total length of its boundary, which is the sum of the lengths of its three sides. The perimeter can be thought of as the distance around the triangle, and it is measured in units of length such as centimeters, meters, or feet. The perimeter of a triangle is an important geometric property that is used in many practical applications, such as calculating the amount of fencing needed to enclose a triangular-shaped garden or determining the length of wire required to form a triangular circuit.

According to the given information:

The perimeter of triangle is sum of all sides of the triangle

In which,

2x + 4 + 3x - 8 + x - 2 = 54

6x - 6  = 54

6x = 60

x = 10

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How do you find the period of a cosine function of the form y = cos bx?

Answers

The period of a cosine function of the form y = cos bx is equal to T= 2π/b where 'T' is the period of the cosine function and b is the coefficient of x in the function.

This formula tells us that the period of the cosine function is equal to the length of one complete cycle of the function.

it represents  the distance along the x-axis for the cosine function to complete one full oscillation.

The period of a cosine function of the form y = cos bx, first identify the coefficient b.

Use the formula T= 2π/b  to calculate the period 'T'.

For example,

Consider cosine function y = cos 2x,

The coefficient of x is 2.

Using the formula above, the period is equal to

Period = 2π/2

           = π

So the period of the function y = cos 2x is π.

This implies that the cosine function completes one full oscillation every π units along the x-axis.

Therefore, the formula used to calculate the period of the cosine function y = cos bx is given by T= 2π/b.

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Which expression has a solution of 4, if r = 9?

A. r + 4

B. 13 - , r

C. 5 - r

D. r, + 5

Answers

Answer: B. 13 - , r

Step-by-step explanation:

The expression that has a solution of 4 when r = 9 is:

B. 13 - r

The length of one leg of a right triangle is 2 times the length of the other, and the
length of the hypotenuse is 12. What is the length of the longest leg?

Answers

Answer:

[tex]\frac{24\sqrt{5} }{5}[/tex]

Step-by-step explanation:

Let's start by assigning one of the unknown legs with the variable x.

We know that the other leg is 2 times the length of x, so we can write:

2x

We also know that the length of the hypotenuse is 12.

From here, we can use the Pythagorean Theorem.

Recall that the Pythagorean Theorem is:

[tex]a^2+b^2=c^2[/tex]

where a is the length of one leg, b is the length of the other leg, and c is the length of the hypotenuse.

Let's substitute the values. We have:

[tex]x^2+(2x^2)=12^2=\\x^2+4x^2=144=\\5x^2=144=\\x^2=\frac{144}{5}=\\x=\frac{12}{\sqrt{5} }[/tex]

Let's rationalize the denominator by multiplying the numerator and denominator by [tex]\sqrt{5}[/tex], like so:

[tex]\frac{12}{\sqrt{5} } =\\\frac{12\sqrt{5} }{5}[/tex]

Therefore, [tex]x=\frac{12\sqrt{5} }{5}[/tex]

Let's solve for 2x:

[tex]2x=\\2(\frac{12\sqrt{5} }{5})=\\ \frac{24\sqrt{5} }{5}[/tex]

So, the length of the longest leg is [tex]\frac{24\sqrt{5} }{5}[/tex]

Find the 11th term of the geometric sequence shown below.
-9x²,-18x7, -36x¹2
12
"...

Answers

the 11th term in the given geometric sequence is equal to [tex]-9216x^{52}[/tex]

What is a geometric sequence.

A sequence is a list of numbers indexed by the natural numbers 1,2,3,4,5.. A common notation for a sequence is [tex]a_1,a_2,a_3,\cdots[/tex]. Most often for interesting sequences there is some pattern in the list of numbers, and there is some formula to generate the nth number in the sequence. A sequence is called a geometric sequence if the next number number is got from the previous number by multiplying it by a fixed number r. This number is called the common ratio r of the sequence. So if the first number is a, then the second number is ar, the third is [tex]ar^2[/tex]... So that the nth number [tex]a_n = ar^{n-1][/tex].  

For example 1 ,3,9,27,81,.... The sum of the first n terms of such a sequence is equal to [tex]$S_n = \frac{a(r^n-1)}{r-1}$[/tex]. if the absolute value of r, [tex]|r| < 1[/tex], then the sum to infinity is [tex]$S = \frac{a}{1-r}$[/tex].

In our question we are given a geometric sequence whose first term :

[tex]$a = -9x^2\,,\textrm{ and common ratio : r } = 2x^5$[/tex] .

So the 11th term is [tex]$ar^{10} = (-9x^2){(2x^5)}^{10} = (-9x^2)(1024x^{50}) = -9216x^{52}$[/tex]

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A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.
On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.


Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.

Answers

Answer: First choice 480t = 300t + 900

Step-by-step explanation:

A factory has two assembly lines, M and N, that make the same toy. On Monday, only assembly line M was functioning and it made 900 toys.  

On Tuesday, both assembly lines were functioning for the same amount of time. Line M made 300 toys per hour and line N made 480 toys per hour. Line N made as many toys on Tuesday as line M did over both days.

Write an equation that can be used to find the number of hours, t, that the assembly lines were functioning on Tuesday.

ANS

Let say t is time in hrs for Which Both Assembly line worked

M made 300 toys per hr on Tuesday

Toys made on Tuesday at Assembly line M = 300 × t  = 300t  toys

N made 480 toys per hr on Tuesday

Toys made on Tuesday at Assembly line N = 480 × t  = 480t  toys

Toys Made by N on Tuesday  = Toys made by M on Tuesday + Toys made by M on Monday

480t = 300t + 900

=> 180 t = 900

=> t = 900/180

=> t = 5 hr

N capacity on tuesday Per hour * t  = M capacity on tuesday per hour  * t  + Toys made by M on Monday

N = N capacity on tuesday Per hour

M = M capacity on tuesday Per hour

=> t (N - M ) = 900

=> t = 900/(N-M)

Triangle UVW has vertices at U(−2, 0), V(−3, 1), W(−3, 3). Determine the vertices of image U′V′W′ if the preimage is rotated 90° counterclockwise.

U′(0, −2), V′(−1, −3), W′(−3, −3)

U′(0, −2), V′(1, −3), W′(3, −3)

U′(2, 0), V′(3, −1), W′(3, −3)

U′(−2, 0), V′(−3, 0), W′(3, −3)

Answers

Answer:

The vertices of the image after rotating triangle uvw 90 degrees counterclockwise are u′(0, −2), v′(1, −3), w′(3, −3).

Step-by-step explanation:

4. A fish tank is in the shape of a cuboid. It
has a base of width 80cm and length of 1.2 m.
Water is put into the tank to a depth of 70cm.
There are 700 000 small fish in the tank. Each
one of them needs a litre of water.
Is there enough water for the fish in the tank?

Answers

The volume of water in the tank won't be enough for the fish.

What is volume of a cuboid?

A cuboid is a solid shape or a three-dimensional shape. The volume of a cuboid is expressed as;

V = l×w× h

where l is the length, w is the width and h is the height.

The volume of water needed by the fish is 700,000× 1litre = 700,000 litres.

The volume of water the tank can occupy is

V = l× b× h

V = 80× 1200× 70

V = 6,720,000cm³

in litres ;

V = 6,720,000/1000

V = 6720litres

therefore the volume water in the tank is not enough for the fish

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solve the proportion b+4/5=7/4

Answers

Step-by-step explanation:

When adding or subtracting fractions, they must have a common denominator....20 is the easiest for these...this then becomes

b +  16/20  = 35/20     now subtract 16/20 from both sides of the equation

b = 35/20 - 16/20

b = (35-16)/20 =  19/20      

.


Which equation is a step in solving the equation |5 − 3x| + 2 = 19?

A.
5 − 3x = -17
B.
|5 − 3x| = -17
C.
5 + 3x = -17
D.
|5 + 3x| = 17

Answers

Answer:

Step-by-step explanation:

The absolute value (or modulus) | 5 - 3x | of a real number  5 - 3x is the non-negative value of 5 - 3x without regard to its sign.

| 5 - 3x| + 2 = 19

| 5 + 3x | = 19 - 2

| 5 + 3x | = 17

Ans: D

the table shows several packages of assorted spools of thread available at a store. what is the price per spool of each kind of thread?

Answers

I'm sorry, but I cannot provide a definitive answer to your question as I do not have access to the table you are referring to.

However, in general, to find the price per spool of each kind of thread, you would need to know the total price of the package and the number of spools in the package.

To calculate the price per spool, you would divide the total price of the package by the number of spools in the package. For example, if a package costs $10 and contains 50 spools of thread, the price per spool would be $0.20 ($10 ÷ 50 = $0.20).

You can use this method to find the price per spool for each type of thread in the table you are looking at.

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Solve for all values of x by factoring.
x² + 6x-41 = 6x - 5

Answers

The solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.

Solving for all values of x by factoring.

To solve for all values of x by factoring x² + 6x - 41 = 6x - 5, we can first simplify the equation by combining like terms:

x² + 6x - 41 = 6x - 5

x² - 41 = -5

Next, we can bring all the terms to one side of the equation:

x² - 41 + 5 = 0

x² - 36 = 0

Now we can factor the left side of the equation:

(x - 6)(x + 6) = 0

Setting each factor equal to zero and solving for x, we get:

x - 6 = 0 or x + 6 = 0

x = 6 or x = -6

Therefore, the solutions to the equation x² + 6x - 41 = 6x - 5 are x = 6 and x = -6.

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the mean weight of an adult is 62 kilograms with a variance of 144 . if 195 adults are randomly selected, what is the probability that the sample mean would be greater than 59.5 kilograms? round your answer to four decimal places.

Answers

The probability is 0.9835 where the sample mean would be greater than 59.5 kilograms.

The central limit theorem can be used to approximate the sampling distribution of the sample mean as a normal distribution.

where the mean equals the population mean (μ = 62 kg) and the standard deviation equals the population standard deviation divided by the square root of sample size (σ/sqrt (n) = sqrt(144 / 195) = 2.4287 kg).

Next, find the probability that the sample mean is greater than 59.5 kilograms.

z = (59.5 - 62) / (2.4287 / square (195)) = -2.1295

Using an ordinary regular table or calculator, we know that the probability of a Z-score less than -2.1295 is 0.0165.

Therefore, the probability that the sample mean exceeds 59.5 kilograms is

1 - 0.0165 = 0.9835

Rounding to four decimal places gives a probability of 0.9835.

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Fruit Smoothle
O E. Talia can use 1
cup orange juice
cup yogurt
8 cup strawberries
8 cup blueberries
cup of ice
Blend all ingredients. Serve cold.
Makes 1 serving.
Which statement about the recipe is true? Mark all that apply.
cup strawberries to double the recipe.
O A. Talia can use
OB. Talia can use
OC. Talia can use
12 cup yogurt to make 3 servings.
cup blueberries to make 4 servings.
OD. Talia can use
1
cups orange juice to make 4 servings.
cup of ice to make 5 servings.

Answers

A. Talia can use 1 and 3/4 cup strawberries to double the recipe. B. Talia can use 1 and 1/3 cup yogurt to make 3 servings. D. Talia can use 2 cups orange juice to make 4 servings.

What is proportion?

In statistics, a proportion is a fraction or a percentage that reflects the proportion of a population's or sample's members who share a particular attribute to the population's or sample's overall size. It is a kind of ratio where the denominator is the entire population or sample size and the numerator is the number of people who possess a specific trait or attribute.

From the given ingredients and the serving size we can see that the correct statement is:

A. Talia can use 1 and 3/4 cup strawberries to double the recipe.

B. Talia can use 1 and 1/3 cup yogurt to make 3 servings.

D. Talia can use 2 cups orange juice to make 4 servings.

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The complete question is:

Harry is organizing a picnic. He can spend at most $24. 00 on beverages. Iced tea costs $2. 00 per gallon and lemonade costs $2. 50 per gallon. If x represents the number of gallons of iced tea and y represents the number of gallons of lemonade, which inequality shows the number of gallons of each drink that he can buy? Identify the number of gallons of iced tea that Harry can buy if he buys 5 gallons of lemonade.

Answers

Harry can buy 5 gallons of tea.

Some working out:
5y = (2.50x5)
5y = 12.50 (lemonade)

24-12.50 = 11.50
11.50/2 = 5 r 1.5

Therefore Harry can buy 5 gallons of lemonade and 5 gallons of iced tea and still have $1.50 left over from his original $24 dollar budget

Answer:

Harry can buy 5 gallons of lemonade and 5 gallons of iced tea and still have $1.50 left over from his original $24 dollar budget

Step-by-step explanation:

the time it takes to cover the distance between two cities by car varies inversely with the speed of the car. the trip takes hours for a car moving at . how long does the trip take for a car moving at ?

Answers

The time takes by car to cover the distance between two cities by car varies inversely with the speed of car. Total 5 hours will consume to complete the trip with a car moving at 40 mph.

Time is taken in traveling a particular distance is proportional to the distance traveled which means more distance covered in more time.

The speed of an object is defined as the 'distance traveled per unit time'. Formula is written as [tex]Speed(s ) = \frac{Distance(d)}{Time(t)}[/tex]

Distance(d) = Speed(r)×Time(t)Time(t) = Distance(d)/Speed(s)

Now, Speed of car (s) = 50 miles per hour

Car takes 4 hours to complete the trip. Let the distance travelled by car in 4 hour during the trip be 'x'. Applying the speed formula, [tex]50 mph = \frac{ x}{4 \: \: hours}[/tex]

=> x = 4 × 50 miles

=> x = 200 miles

Now, if the speed of car (s') = 40 mph in the trip. We have to determine the time taken by car to complete the trip with 40 mph speed. So, we know the speed of car and total distance travelled by car on trip. Using the time formula,[tex]time ( t') = \frac{distance (x) }{ speed( s')} [/tex]

=> [tex] time (t') = \frac{ 200 \: miles}{ 40 \: mph}[/tex]

= 5 hours.

Hence, required value of time is 5 hours.

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Complete question :

The time it takes to cover the distance between two cities by car varies inversely with the speed of the car. The trip takes four hours for a car moving at 50 mph. How long does the trip take for a car moving at 40 mph?

a man can hit his target 25% of the time if he fires 4 shots in succession what is the probability that he will hit his target

Answers

The probability that the man will hit his target at least once in 4 shots is calculated using the complementary probability of him missing all 4 shots. Since he hits his target 25% of the time, he misses it 75% of the time.

The probability of missing all 4 shots is (0.75)^4 = 0.3164.

Now, to find the probability of hitting the target at least once, subtract the probability of missing all shots from 1:

1 - 0.3164 = 0.6836 or 68.36%.

So, the probability that the man will hit his target at least once in 4 shots is approximately 68.36%.

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HELP ME PLEASE!!!!!!!

Answers

Answer:

Step-by-step explanation:

Graph #          Matching equation

1                             |-3x|

2                            |-x|

3                           -|2x|

You can tell which one matches by finding the slope and whether the V points up or down

A pre-image has coordinates A(3, -5), B(3, 1) and C(-2, 0). The image has coordinates A'(3, 5), B'(3, -1) and C'(-2, 0). What type of reflection occurred? Explain how you know.

Answers

For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the x-axis refection.

Explain about the reflection about x axis:

The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).

The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

Given data:

pre-image coordinates - A(3, -5), B(3, 1) and C(-2, 0).

Image coordinates A'(3, 5), B'(3, -1) and C'(-2, 0).

As its is clear from the given coordinates that value of x is same while the value of y gets change by negative.

(x,y) ---> (x, -y) , shows the refection about the x axis.

Thus, For the image with coordinates A'(3, 5), B'(3, -1) and C'(-2, 0) occurred after the refection about the x axis.

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The volume of a volleyball is approximately 113 in ^3. What is its diameter? Round your answer to the nearest whole number.

A. 13 in
B. 6 in
C. 2 in
D. 5 in

will give brainliest ​

Answers

If the  volume of a volleyball is approximately 113 in³, then the diameter of the volleyball is approximately option (D) 5 inches.

The formula for the volume of a sphere is

V = (4/3)πr³

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

We are given the volume of the volleyball as 113 in³, so we can solve for the radius as follows

113 = (4/3)πr³

r³ = 113 / ((4/3)π)

r³ ≈ 21.50

r ≈ 2.8

To find the diameter, we double the radius:

d = 2r ≈ 5.6

Rounding this to the nearest whole number

d = 5 in

Therefore, the correct option is (D) 5 in

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4. The radius of a cylinder is 3x-2 cm. The height of the cylinder is x +3 cm. What is the
surface area of the cylinder? Use the formula A=2x²+2xrh.
02x (3x2+10x-8)
O 27(12x+7x-2)
O 27(12x²-2x+13)
O 27(12x²-5x-2)

Answers

Answer:

D: 27(12x² - 5x - 2).

Step-by-step explanation:

The formula for the surface area of a cylinder is: A = 2πr² + 2πrh

Given that the radius of the cylinder is 3x - 2 cm and the height is x + 3 cm, we can substitute these values in the formula and simplify:

A = 2π(3x - 2)² + 2π(3x - 2)(x + 3)

A = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6)

A = 18πx² - 24πx + 8π + 6πx² + 14πx - 12π

A = 24πx² - 10πx - 4π

A = 2π(12x² - 5x - 2)

Therefore, the answer is option D: 27(12x² - 5x - 2).

Answer:

D

Step-by-step explanation:

2㏒_[6](2)+3㏒_[6](3)+㏒_[6](12)

Answers

Answer: 4

Step-by-step explanation:

Given:

   [tex]2log_62+3log_63+log_612[/tex]

Rewrite using the power property:

   [tex]log_62^2+log_63^3+log_612[/tex]

Rewrite by adding the logarithms together (multiplying) since they all have a common base of 6:

   [tex]log_6(2^2*3^3*12)[/tex]

Simplify by multiplying:

   [tex]log_6(4*27*12)[/tex]

   [tex]log_6(1,296)[/tex]

Evaluate the logarithm:

   [tex]log_6(1,296)[/tex]

   4

One gallon of paint covers 400 square feet. What is the least amount of paint needed to paint the walls of a room in the shape of a rectangular prism with a length of 17 feet, a width of 15 feet, and a height of 12 feet? Write your answer as a decimal. Gal

Answers

We need at least 3.465 gallons of paint to paint the walls of this room.

The area of the two rectangular faces on either end of the prism is:

length x height = 17 x 12 = 204 square feet

The area of the two rectangular faces on the sides of the prism is:

width x height = 15 x 12 = 180 square feet

The area of the top and bottom faces of the prism is:

length x width = 17 x 15 = 255 square feet

The total surface area of the prism is:

2(204) + 2(180) + 2(255) = 1386 square feet

Now, we divide surface area by coverage of one gallon of paint:

1386 / 400 = 3.465

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*MATH* PLS HELP! THE PROBLEM IS IN THE IMAGE!

(PLEASE show your work or explain how you got that answer)

Answers

The scale factor that takes triangle C to triangle D is 3/10.

What is scale factor?

Scale factor is a number by which the size a geometrical figure or shape can be changed with respect to its original size.

To find the scale factor that takes triangle C to triangle D, we use the formula below

Formula:

S.F = Length of triangle D/Corresponding Length of triangle C

Where:

S.F = Scale factor

From the diagram in the question,

Given:

Hypotenus of triangle D = 3.36Hypotenus of triangle C = 11.2

Substitute these values into equation 1

S.F = 3.36/11.2S.F = 0.3 = 3/10

Hence, the scale factor is 3/10.

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i need some help with this problem i don’t really understand it

Answers

Answer:

-34x+29

Step-by-step explanation:

[tex]7(5-x)-3(9x+2)=7.5-7x-3.9x-3.2=35-7x-27x-6\\=-34x+29[/tex]

Ms. Yamato's gross pay is $2644. Her deductions total $548.30.

What percent of her gross pay is take-home pay?
A. 84%
B. 79%
C. 21%
D. 18%

Answers

Thus, the correct Percent response is B) 79%.

what is a percent?

Percentage refers to a portion of every hundred. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, it is frequently shown using the percent sign, "%".

If you have 100 apples and distribute 10 of them, for instance, you have distributed 10% of your total apple supply.

We deduct Ms. Yamato's deductions from her gross income to determine her take-home pay:

$2644 - $548.30 = $2095.702.

By dividing her take-home pay by her gross pay and multiplying the result by 100%, we can determine what proportion of her gross pay is taken home:

($2095.70 / $2644) * 100% = 79%

Thus, the correct response is B) 79%.

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let p(n) be the statement that 1^3 +2^3+ 3^3 ... +n^3 = (n(n 1)2)^2 for the positive integer n. we will have completed the basis step of the proof if we show that

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Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

To complete the basic step of the proof, we need to show that the statement p(n) is true for the smallest positive integer n, which is 1.

Let's plug n = 1 into the statement p(n):[tex]1^3 = (\frac{1(1 + 1))}{2})^2[/tex]

Simplifying the equation, we get:
[tex]1^3 = (1(2)/2)^2\\1^3 = (1^2)^2\\1 = 1[/tex]

Since the statement p(n) holds true for n = 1, we have successfully completed the basic step of the proof.

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The statement is true for n=1, and we have completed the basis step of the proof.

To complete the basis step of the proof for the statement p(n), we need to show that it is true for the smallest positive

integer n, which is 1.

Our statement is:

[tex]1^3 + 2^3 + 3^3 + ... + n^3 = (n(n+1)/2)^2.[/tex]

For the basis step, let n = 1:

Left side: [tex]1^3 = 1[/tex]

Right side:[tex](1(1+1)/2)^2 = (1(2)/2)^2 = (1)^2 = 1[/tex]

Since the left side and the right side are equal, we have successfully completed the basis step of the proof for the statement p(n).

Therefore, the statement is true for n=1, and we have completed the basis step of the proof.

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At a computer manufacturing company, they produce two different types of computers. They can make 70 laptops per day while making 55 desktops per day. The company has a total of 14 machines to make computers. They can make a total of 905 computers per day. How many machines make laptops and how many make desktops?
Write a system of equations and solve.

Answers

Answer:

Yo wassup bro, at this computer factory, they be making two types of computers, laptops and desktops. They churn out 70 laptops a day and 55 desktops a day. They got a total of 14 machines to make these computers. And they make a total of 905 computers a day. We gotta figure out how many machines are making laptops and how many are making desktops, ya know?

Alright, let's set up a system of equations to solve this. Let's call the number of machines making laptops "x" and the number of machines making desktops "y".

So, we got two equations here:

The total number of computers they make in a day is 905, so we can write: x laptops + y desktops = 905.

They got a total of 14 machines, so we can write: x + y = 14.

Now, let's solve this system of equations to find the values of x and y, man. Once we got those, we'll know how many machines are making laptops and how many are making desktops at this computer factory, yo!

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