A 300-g package of pepperoni costs $4.29.

a) What is the cost per 100 g?

b) How much would 1 kg cost?

c) How much pepperoni could you buy with $20?

The derivative of 1/logx is With the chain rule.

1log(x)=log(x)−1 is ,= -1xlog(x)2 .

The by-product of logₐ x (log x with base a) is 1/(x ln a). Here, the thrilling issue is that we have "ln" withinside the by-product of "log x". Note that "ln" is referred to as the logarithm (or) it's miles a logarithm with base "e".

The by-product of 1/log x is -1/x(log x)^2. Note that 1/logx is the reciprocal of log.

\(With the chain rule. \\

1log(x)=log(x)−1 \\

So you follow the chain rule to the electricity after which to the log: \\

ddxlog(x)−1=−1⋅log(x) \\ \\−2⋅ddxlog(x)

\\ =−1log(x)21x

\\ =−1xlog(x)2 .\)

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The simplest form of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Both given expressions are not equivalent.

What is an expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given expression is 3x + 14 – x + \(1\frac{1}{2}\)

Now combine like terms:

= (3x - x) + (14 + \(1\frac{1}{2}\))

= 2x +  (14 + \(1\frac{1}{2}\))

Convert mixed fraction to improper fraction:

= 2x +  (14 + 3/2)

= 2x + 31/2

= 2x + \(15\frac{1}{2}\)

The equivalent expression of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Therefore, 3x + 14 – x + \(1\frac{1}{2}\) is not equivalent to 4x + \(1\frac{3}{4}\).

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Both options (a) and (b) represent real numbers that are constructible.

To determine whether a real number is constructible or not, we need to check if it can be obtained using a finite sequence of additions, subtractions, multiplications, divisions, and taking square roots.

(a) √5 + 7:

√5 is constructible since it is obtained by taking the square root of 5.

Adding 7 to √5 is also constructible since addition is allowed.

Therefore, √5 + 7 is constructible.

(b) (4 + √3):

√3 is constructible since it is obtained by taking the square root of 3.

Adding 4 to √3 is also constructible since addition is allowed.

Therefore, (4 + √3) is constructible.

Both options (a) and (b) represent real numbers that are constructible.

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Answer:

height = 5 in

Step-by-step explanation:

Area =h x (b1+ b2)/2

50 = h x (12 + 8)/2

50 = h x 10

h = 5

Answer:  The slope-intercept form is y = -2x + 10

Step-by-step explanation:

Step 1: The y-intercept is the point where x=0, so that is (0,10)

Step 2: Use the points (-2,14) and (-1,12) to find the slope

Slope (m) = ΔY/ΔX = -2/1 = -2

Step 3: The slope-intercept form is:

y = mx+b

y = (step 2 value) x + (step 1 value)

y = -2x+10

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Alternative and null hypotheses are always based on populations.

A population cannot have both the alternative hypothesis and the null hypothesis be true. A hypothesis test determines whether to accept or reject the null hypothesis based on sample data.

null assumption (H0)

Under the null hypothesis, a population parameter (such as the mean, standard deviation, and so on) is equal to an assumed value. Often, the first claim that constitutes the null hypothesis is based on prior research or expert knowledge.

alternative hypotheses (H1)

A population parameter is either less, greater, or different from the value assumed by the alternative hypothesis, according to the former. The alternative hypothesis is what you could believe to be accurate or what you aim to prove.

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the absolute extrema of the linear equation f(x) =  12x^2 -11x +2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

What are the absolute extrema of a linear equation within a closed interval?

According to the functions theory, linear equations have no absolute extrema for all real numbers, but things are different for any closed interval as absolute extrema are the ends of linear function. Now we proceed to evaluate the function at each point:

Absolute maximum

f(- 8) =   12x^2 -11x +2

f(- 8) = 27

Absolute minimum

f(4) = - 3 · 4 + 3

f(4) = - 9

By means of functions theory and the characteristics of linear equations, the absolute extrema of the linear equation f(x) = 12x^2 -11x+2  are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).

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Answer:

x-intercepts = (8, 0) and (-4, 0)

y- intercept = (0, 8)

vertex = (2, 9)

Step-by-step explanation:

Sorry if its wrong but I think it's where the coordinates are according to the graph. The x-int would hit at the x-axis, y-int would hit the y-axis, and the vertex would be where it's highest point is

Answer:

x = t(a+p)/4

Step-by-step explanation

Given the expression

​a=4x/t - p

We are to make x the subject of the formula

a=4x/t - p

Add p to both sides

a+p = 4x/t - p+p

a+p = 4x/t

Cross multiply

t(a+p) = 4x

Rearrange

4x = t(a+p)

Divide both sides by 4

4x/4 = t(a+p)/4

x = t(a+p)/4

I hope this helps you

The quadrilaterals WXYZ and its image will be congruent  

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

The transformation of WXYZ by

The above transformations are rigid transformations

This means that the image and the transformed figure would be congruent

This is so because the transformation does not change side lengths and angle measures

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Question

Quadrilateral wxyz will be reflected across the x axis and then rotated 90 degrees counterclockwise about the origin.

What are the true statements about the quadrilateral and/or the transformed quadrilateral

The cost of a CD is $5.94 more than the cost of a DVD. Let's assume that the cost of a DVD is "x" dollars, then the cost of a CD is "x+5.94" dollars.

Using this information, we can write the following equations:

5(x+5.94) + 2x = 113.63 (cost of 5 CDs and 2 DVDs)

6(x+5.94) + 2x = ? (cost of 6 CDs and 2 DVDs)

Solving the first equation for "x", we get x = 12.21. Substituting this value in the second equation, we get the cost of 6 CDs and 2 DVDs as $83.64.

Therefore, the cost of 6 CDs and 2 DVDs would be $83.64 at All Bets Are Off Electronics if 5 CDs and 2 DVDs cost $113.63, and CDs cost $5.94 more than DVDs.

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Without using a calculator, the trigonometric expressions simplify to:

1. sin^(-1)(sin(θ/6)) = θ/6

2. cos^(-1)(cos(5/4)) = 5/4

3. tan^(-1)(tan(5/6)) = 5/6.

To compute the trigonometric expressions without using a calculator, we can make use of the properties and relationships between trigonometric functions.

1. sin^(-1)(sin(θ/6)):

Since sin^(-1)(sin(x)) = x for -π/2 ≤ x ≤ π/2, we have sin^(-1)(sin(θ/6)) = θ/6.

2. cos^(-1)(cos(5/4)):

Similarly, cos^(-1)(cos(x)) = x for 0 ≤ x ≤ π. Therefore, cos^(-1)(cos(5/4)) = 5/4.

3. tan^(-1)(tan(5/6)):

tan^(-1)(tan(x)) = x for -π/2 < x < π/2. Thus, tan^(-1)(tan(5/6)) = 5/6.

Hence, without using a calculator, we find that:

sin^(-1)(sin(θ/6)) = θ/6,

cos^(-1)(cos(5/4)) = 5/4,

tan^(-1)(tan(5/6)) = 5/6.

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Answer:

angle A = 32

Step-by-step explanation:

angle A = 180 - (58+90) {by angle sum property of a triangle.}

angle A = 32

Answer:

volume: 49280 cm³  and   curved S.A = 5826.64 cm²

Explanation:

using similarities:

\(\sf \frac{45 + h2}{28} = \frac{h2}{7}\)

\(\sf 315 + 7h2 = 28h2\)

\(\sf 315 = 28h2-7h2\)

\(\sf 315 = 21h2\)

\(\sf 15 = h2\)

total height of the cone: 45 + 15 = 60 cm

solve for volume:

\(\sf volume \ of \ cone \ = \frac{1}{3} \pi r^2 h\)

\(\sf volume \ of \ cone \ = \frac{1}{3} \pi (28)^2 (60)\)

\(\sf volume \ of \ cone \ = 15680\ *\frac{22}{7}\)

\(\sf volume \ of \ cone \ = 49280 \ cm^3\)

First find the slant height using Pythagoras theorem -

\(\sf l^2 = r^2 + h^2\)

\(\sf l =\sqrt{ r^2 + h^2}\)

\(\sf l =\sqrt{ (28)^2 + (60)^2}\)

\(\sf l =66.212 \ cm\)

solve for curved surface area:

\(\sf curved \ surface \ area = \pi rl\)

\(\sf curved \ surface \ area = \pi (28)(66.2)\)

\(\sf curved \ surface \ area =5826.64 \ cm^2\)

The image point of the point is (-12,8)

A dilation is a transformation that changes the size of a figure but not its shape.

In a dilation with respect to the origin, a point (x, y) is transformed to a point (kx, ky) where k is a scale factor.

In this case, the point (-3, 2) is transformed under a dilation of 4 with respect to the origin.

So the image point is (kx, ky) = (-34, 24) = (-12, 8)

So the image point of (-3,2) under a dilation of 4 with respect to the origin is (-12,8)

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Complete question

find the image point when the indicated transformation is applied to the given pre-image point

(-3,2) under a dilation of 4 with respect to the origin

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The statements that are true include option A, D and E. The statements are true according to the triangle properties.

Let's verify each statement:

Option A: The sum of m∠3 and m∠4 is 180°.

Here, an angle of 180° will always form a straight line. The line is called as a straight angle. Any line interfering the line will make a change in the lines angle corresponding to the line but the total angle for the line of 180°.

Option D: m∠4 = m∠1 + m∠2.

Here, ∠3+∠4=180°. Also ∠1+∠2+∠3=180° ---------eq(1)

⇒ ∠3=180°-∠4 ------- eq(2)

Substitute eq (2) in eq(1)

⇒ ∠1+∠2+180°-∠4=180°

⇒ ∠1+∠2 = ∠4

Hence proved.

Option E: m∠1 + m∠2 + m∠3 = 180°

It should be noted that the sum of angles that are in a triangle equals 180°. Therefore, m∠1 + m∠2 + m∠3 = 180°.

Therefore, Option A,D and E are correct according to the triangle laws.

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To determine the percentage of a number in relation to another, you divide the first number by the second number and multiply by 100. This formula can be used in various scenarios, such as calculating discounts, proportions, or ratios.

1. First, divide the number you want to find the percentage of by the number you want to compare it to.
  For example, let's say you want to find out what percentage 25 is of 100. You would divide 25 by 100, resulting in 0.25.

2. Next, multiply the result from step 1 by 100 to get the percentage.
  Using our previous example, you would multiply 0.25 by 100, giving you 25%.

Therefore, 25 is 25% of 100.

Here's another example to help solidify the concept:

Suppose you want to find out what percentage 60 is of 200.

1. Divide 60 by 200, which equals 0.3.

2. Multiply 0.3 by 100, resulting in 30%.

Hence, 60 is 30% of 200.

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Answer:

30

Step-by-step explanation:

20 % of his toys are 6. 20 % of a number could only be 100, 100 / 20 = 5
Multiply 5 by 6 and u get 30 :D

Answer: X is the missing value.

Step-by-step explanation:

Answer:

Perimeter of the given figure is :---

\((2n) + (2n) +( n + 5) + (n + 5) + (3n + 3) \\ = 2n + 2n + n + 5 + n + 5 + 3n + 3 \\ = \boxed{9n + 13}✓\)

Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.

To calculate the size of the container Camillo should buy, we need to find a container size that can accommodate the required 2,400 oz of peanut butter.

By comparing the given container sizes, we can see that the 40-oz container is the largest one available. As Camillo needs 2,400 oz of peanut butter, he would need to purchase multiple containers.

To find out how many of those containers Camillo will need, we can divide the total amount of peanut butter needed (2,400 oz) by the size of each container (40 oz). This gives us:

Number of containers = Total amount needed / Size of each container

Number of containers = 2,400 oz / 40 oz

Number of containers = 60 containers

So Camillo would need to buy 60 of the 40-oz containers to meet his requirement.

To calculate the total cost of those containers, we need to multiply the number of containers (60) by the price of each container. The price for each 40-oz container is $12.40. Therefore:

Total cost = Number of containers * Price per container

Total cost = 60 containers * $12.40

Total cost = $744.00

Hence, the total cost of the 60 containers would be $744.00.

In summary, Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.

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Complete Question

Camillo needs 2,400 oz of peanut butter.

What size container should Camillo buy?

How many of those containers will he need?

What will be the total cost of those containers?

Container Size    Price          Unit Price

12-oz                   $2.52           $0.21/oz

16-oz                   $4.00           $0.25/oz

32-oz                  $5.12             $0.16/oz

40-oz                  $12.40           $0.31/oz

Answer:

9.6 feet

See attached image

The longest and the shortest distances are 1 mile and 5 miles

The greatest number of miles left is 4.5 miles

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

Luke = 3 miles

Logan = 2 miles

This means that

Shortest = 3 - 2 = 1 mile

Longest = 3 + 2 = 5 miles

Represent the distance with x

So, we have

3 - 2 < x < 3 + 2

Evaluate

1 < x < 5

The number line is | 1 | 2 | 3 | 4 | 5 |

In (a), we have

Longest = 5 miles

So, we have

Greatest = 5 - 0.5

Greatest = 4,5 miles

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Answer:

x = 90

y = 60

Step-by-step explanation:

Let x = student

Let y = non-student

x + y = 150

4x + 8y = 840 <—— Use elimination/addition ethos for both equations

8 (x + y = 150)

-1 (4x + 8y = 840) <—— Let’s eliminate y

8x + 8y = 1200

+ -4x - 8y = -840

—————————————

4x = 360

x = 90

x + y = 150 <— substitute for x from above

90 + y = 150

- 90 = - 90 <— subtract from both sides

y = 60

Answer:

I got 115.5/214 which is less than one so I think what I got is wrong.

Step-by-step explanation:

I did 7/214=x/16.5 and then did cross multiplication to get 115.5=214x. After that I solved for x.

Answer:

5.5 feet

Step-by-step explanation: