How many liters of pure water should be mixed with a 5 liter solution of 80% acid to produce a mixture that is 70% water?

Simple Interest Consider making an investment of $100 (the principal) at a 5% yearly rate for a year. Simple interest is calculated as follows: $100 multiplied by.05 percent per year for a total of $5 after a year.

Let x represent the sum of money invested at a simple interest rate of 6%. Let y represent the sum of money invested at a simple interest rate of 10%.

Decimalize the interest rates as follows: 6% equals 0.06 and 10% equals 0.10. The interest earned on the first account is equal to 0.06 times the interest rate multiplied by the amount invested.

Similar to the first account, the second account's interest earnings are calculated as the interest rate times the amount invested, or 0.10*y.

Now that we have the data from the problem, we need to model the scenario with two equations. Because it is less hazardous, the man invests twice as much in the lower-yielding account. Otherwise put,

[the investment amount at 6%] = [2] * [the investment amount at 10%]

We can represent this relationship in algebra as

x=2y

Therefore, the amount the man earns in interest is $4,180.

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P(140 < x < 150) is 0.1915 when x is normally distributed with mean 140 and standard deviation 20.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value

μ = mean = 140

σ = standard deviation = 20

z-score(x = 140) = (140 - 140) / 20

z-score(x = 140) = 0

z-score(x = 150) =(150 - 140) / 20

z-score(x = 150) = 0.5

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 0   probability = 0.5000

z-score = 0.5   probability = 0.6915

This means that there's a probability of 0.500 and 0.6915 that the value of x is less than 140 and 150, respectively.

P(140 < x < 150) = 0.6915 - 0.5000 = 0.1915

Therefore, the probability that the value of x is between 140 and 150 is 0.1915.

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None of the sequence of transformation not produce the same image

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A reflection across the x-axis, then a counter-clockwise rotation 90 degrees

The rule of reflection across the x-axis is:

(x, y)--->(x, -y)

The rule of 90 degrees counter-clockwise rotation is:

(x, y)--->(-y, x)

So, we have:

(x, -y)--->(y, x)

(x, y) and (y, x) are different.

Hence, this sequence of transformation does not produce the same image

Hence, none of the sequence of transformation not produce the same image

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Answer:

A, C, D

Explanation:

I just did the assignment on edge

Someone can't pay exactly 87 to have their windows washed.

A company charges a 5 flat fee plus 3 per window to wash windows. Therefore, let's find if someone can pay exactly 87 units to have there window washed.

Hence, using equation,

y = 5 + 3x

where

Using the equation, let's find if someone can use exactly 87 units for the service.

87 = 5 + 3x

87 - 5 = 3x

82 = 3x

divide both sides by 3

x = 82 / 3

x = 27.33

Therefore, someone can't use exactly 87 units because the number of windows washed is in decimal.

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Answer:

B-1/2 MILE

Step-by-step explanation:

Leona ordered 25 boxes of pen

Ahmed sells pens for $8 and rubber bands for $4

Leona ordered a total of 30 cartons for $220

The number of boxes that Leona ordered can be calculated as follows

Let x represent the boxes of pen

Let y represent the boxes of rubber bands

x + y= 30.........equation 1

8x + 4y= 220.......equation 2

From equation 1

x= 30 - y

Substitute 30-y for x in equation 2

8(30-y) + 4y= 220

240 - 8y + 4y= 220

240-4y= 220

-4y= 220-240

-4y= -20

y= 20/4

y= 5

Substitute 5 for y in equation 1

x + y= 30

x + 5= 30

x= 30-5

x= 25

Hence Leona ordered for 25 boxes of pen

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Answer: 10

Step-by-step explanation:

Assuming that pi = 3.14

The height of the cylinder in inches is 10.

When two equal or identical and parallel bases are connected in a three-dimensional solid form makes a cylinder. These bases resemble spherical disks.

Given:

A cylindrical shape is given.

And the surface area of the shape is 78π.

And the radius of the cylinder is 3 inches.

That means,

2πrh + 2πr² = 78π

3h + 9 = 39

Subtracting 9 from both sides,

we get,

3h = 39 - 9

h = 30/2

h = 10

The height = 10 inches.

Therefore, the height is 10 inches.

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Answer:

b = 21.93

Step-by-step explanation:

This can be solved using Pythagorean theorem. Basically your hypotenuse or c is the length of the ladder, your base or a value is 12 and you're trying to find the height of the wall which is your b

[tex]a^2 + b^2 = c^2\\c^2 - a^2 = b^2\\(25)^2 - (12)^2 = b^2\\625 - 144 = b^2\\b= \sqrt{481} \\b = 21.93...\\b = 21.93[/tex]

Step-by-step explanation:

Whenever you have brackets, you have to multiply the outside with all of the insides.

6 + 4x(3+4) = 6 + [ (4x×3) + (4x×4) ]

= 6 + [ 12x + 16x ]

= 6 + 28x

Answer: 6+28x

D) 15 tablespoons of parsley she needs.

Let's call the number of tablespoons of parsley she needs "x". We know the recipe uses 5 parts thyme to 3 parts parsley, so the total number of parts is 5 + 3 = 8.

Since she's making 40 tablespoons of the mix, each part is equal to 40 / 8 = 5 tablespoons.

So x, the number of tablespoons of parsley, is equal to 3 parts * 5 tablespoons/part = 15 tablespoons.

The answer is D) 15 tablespoons of parsley she needs.

Therefore, we can say she needs 15 tablespoons of parsley.

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The measure best describes the typical route time is, Median. So option C is correct.

The middle number or piece of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the mode, median, and mean. The measures of central tendency are this trio of measurements.

Median = {(n+1)/2}th term (for odd)

Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)

The median is the middle value in a set of data, and is often used to describe the typical or central value in a dataset. Unlike the mean, which can be affected by extreme values, the median is not sensitive to outliers and provides a better representation of the typical value in the dataset.

For example, if the bus route times are listed in a frequency table, the median can be found by ordering the values and finding the middle value (or the average of the two middle values, if the number of observations is even).

In the context of driving a school bus, the median route time would give the most accurate representation of the typical time it takes to complete the daily route, and would provide a better indicator of the bus driver's performance than the mean or any other measures of central tendency.

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Answer:

39 ckfiffiofods9odoxdo

The difference of the algebraic expressions is 3x² - 11x + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The difference of two algebraic expressions means the subtraction of the expressions. That is:

(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1

                                 =  3x² - 11x + 4

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The average velocity for the time period from t = 1 to t = 4 is 6 feet/s.

The distance driven in a car is shown by

s(t) = t^2 + t

The distance driven in a car at t = 1

s(1) = (1)^2 + 1

s(1) = 1 + 1

s(1) = 2

The distance driven in a car at t = 4

s(4) = (4)^2 + 4

s(4) = 16 + 4

s(4) = 20

Let at t = 1, it is t(1) and at t = 4 it is t(2)

Displacement of car between t(1) and t(4) = s(2) - s(1)

Displacement of car between t(1) and t(4) = 20 - 2

Displacement of car between t(1) and t(4) = 18 feet

Time travel between t(1) and t(4) = 4 - 1

Time travel between t(1) and t(4) = 3

Now,

Average velocity = Displacement of car between t(1) and t(4)/Time travel between t(1) and t(4)

Average velocity = 18/3

Average velocity = 6 feet/s

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Answer:

area: 64
perimeter: 32

Step-by-step explanation:

Answer:

Perimeter: 32 inches Area: 64 inches²

Step-by-step explanation:

1) Perimeter

2) Area

Answer: The quotient of 60 divided by k is 60/k.

Step-by-step explanation:

The quotient of 60 divided by k refers to the result of dividing the number 60 by another number k. The division operation can be represented mathematically as 60/k.

In other words, the quotient of 60 and k is a mathematical expression that returns the number that results from dividing 60 by k. The result of this division is a single value which can be a fraction or a whole number, depending on the value of k.

The value for the function f(x) = z² + 3/z² for f(2) is 4.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range.

Given:

f(x) = z² + 3/z²

Also we have f(1)= 2 then

f(1) = z² + 3/z²

2 = z² + 3/z²

2z² = [tex]z^4[/tex] + 3

-3 = [tex]z^4[/tex] - 2z²

-3 = z²(z²-2)

So, z²= -3  or z²-2 = -3

z= ±√3i or z =i

Now, F(2) we get

F(2) = z² + 3/z²

      = (-1)² + 3/ (-1)²

      = 1 + 3

F(2) = 4

Hence, the value of F(2) is 4.

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The height of the cylinder with a volume of 1000 cubic centimeters is 1000/49π cm or 6.5 cm.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Given that;

Plug the given values into the above formula and solve for h.

V = π × r² × h

1000 = π × ( 7 )² × h

1000 = 49π × h

h = 1000 / 49π

h = 1000/49π cm or 6.5 cm

Therefore, the value of the height h is 1000/49π cm or 6.5 cm.

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Answer:

1109

Step-by-step explanation:

4563 = 4b + 127  Subtract 127 from both sides

4436 = 4b  Divide both sides by 4

1109 = b

16% is the Percentage of individuals from this population who will have LDL level 1.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given the distribution of LDL levels is normal, with a mean of 123 mg/dL and a standard deviation of 41 mg/dL. If an individual's LDL is at least 1 standard deviation or more above the mean, he or she will be monitored carefully by a doctor.

one standard deviation 68% of data- -95% of data- -3 -2 -1 0

So we want a percentage of individuals with LDL level 1 or more sd above the mean.

So from the above graph, we basically want to know what percentage of the scores are to the right of 1 on the x-axis because we want a percentage of individuals with LDL level 1 or more sd above the mean.

Right of 0 on the x-axis we have 50% of the data.

So by simple calculations

Percentage = 50-34=16%

therefore, the Percentage of individuals from this population who will have LDL level 1  is 16%.

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Answer: A

Step-by-step explanation:

Answer:

  B

Step-by-step explanation:

You want to know why ∛4 = 4^(1/3).

The applicable rule of exponents is ...

  (a^b)^c = a^(bc)

  a^1 = a

The cube root of a number is the value that, when cubed, gives the original number.

Let x represent the exponent of a cube root. Then the cube root of 4 must satisfy ...

  (4^x)^3 = 4

Simplifying, using the rules of exponents, we have ...

  4^(3x) = 4^1

Equating the powers tells us ...

  3x = 1

  x = 1/3 . . . . . divide by 3

That is, ...

  (4^(1/3))^3 = 4^(3/3) = 4^1 = 4 . . . . . . . matches answer choice B

__

Additional comment

By extension, the n-th root is equivalent to the power 1/n.

We can prove that a cube root of 4 is equal to 4 to the one-third power by the rule of the exponent.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given, a cube root of 4 equal to 4 to the one-third power

Rules of exponents

Since The applicable rule of exponents is

 (a^b)^c = a^(bc)

 a^1 = a

Cube root:

The cube root of a number is the value that, when cubed, gives the original number.

Cube root of 4:

Let x represent the exponent of a cube root. Then the cube root of 4 will be:

 (4^x)^3 = 4

Simplifying, using the rules of exponents

 4^(3x) = 4^1

Equating the powers

 3x = 1

 x = 1/3 . . . . . divide by 3

therefore,

=>  (4^(1/3))^3 = 4^(3/3) = 4^1 = 4

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(a). Revenues = $6,600.

(b). Expenses = $10400

(c). Net income = $3800

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

For the year ending April 30,

Urology Medical Services Co. mistakenly omitted to adjust entries for (1) $1,400 of supplies that were used,

(2) unearned revenue of $6,600 that was earned,

and (3) insurance of $9,000 that expired.

(a). Revenues = $6,600.

(b). Expenses = ($1,400 + $9,000).

= $10400

(c). Net income =

($10,400 – $6,600).

= $3800

Therefore, all the required values are given above.

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Drainage density is a measure of the frequency and spacing of stream channels within a drainage basin, expressed as the ratio of the total length of streams within a given area to the total area of the drainage basin.

Drainage density is used to quantify the efficiency of the drainage system in carrying water away from the land surface and helps in understanding the hydrological and geomorphological processes that shape the landscape.

Therefore, a measure of the frequency and spacing of stream channels within a drainage basin, expressed as the ratio of the total length of streams within a given area to the total area of the drainage basin is drainage density.

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Answer:

see below

Step-by-step explanation:

pennies = x+2

nickels = x

x*0.05 + (x+2)*0.01 =0.68

0.05x+0.01x+0.02 =0.68

0.06x=0.66

x=11 nickels

pennies = x+2 =13

When teaching an 8th grade lesson on problem solving, Sylvia begins by utilizing a short video clip. Sylvia uses this video clip as a discrepant event because students attached with science it would look like magic for them.

A discrepant occurrence is an unexpected, counterintuitive result that differs from what an observer would typically anticipate. Oobleck is a classic illustration of a discrepant event.

Most kids (who have never seen it before) wouldn't anticipate that it would have both solid and liquid qualities. They didn't anticipate it to spread out right away once the "ball" was placed on the table instead of rolling into a ball and taking shape.

The main factor is that pupils will develop an obsession with science. They will see this as "magic," and they will be very interested in learning how it worked. After that, they'll be prepared to "amaze" their friends with both the "trick" and their subsequently displayed "smarts."

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The probability of earning a total of exactly 10 points in 2 turns is 1/8.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:

(4, 6) or (6, 4)

The probability of getting a 4 in first try and 6 in second try is:

(4, 6) = 1/4 * 1/4 = 1/16

The probability of getting a 6 in first try and 4 in second try is:

(6, 4) = 1.4 * 1/4 = 1/16

The possibilities to earn exactly ten points occur when the scores in first and second turn are as follows:

(4, 6) or (6, 4) = 1/16 + 1/ 16 = 2/16 = 1/8

Hence, the probability of earning a total of exactly 10 points in 2 turns is 1/8.

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Answer:

measure them goofy

Step-by-step explanation:

stop being dumn

The value of y. (∂w / ∂x) + x. (∂w / ∂y) is,

⇒ - 4xy f ' (x² - y², y² - x²)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The two-variable function is,

⇒ w = f (x² - y², y² - x²)

Now, We can differentiate the function as;

⇒ (∂w / ∂x) = f ' (x² - y², y² - x²) × (2x , - 2x)

⇒ (∂w / ∂y) =  f ' (x² - y², y² - x²) × (- 2y , 2y)

Thus, The value of y. (∂w / ∂x) + x. (∂w / ∂y) is,

⇒ y. (∂w / ∂x) + x. (∂w / ∂y)

⇒ y × f ' (x² - y², y² - x²) × (2x , - 2x) + x × f ' (x² - y², y² - x²) × (- 2y , 2y)

⇒ - 2xy × f ' (x² - y², y² - x²) - 2xy × f ' (x² - y², y² - x²)

⇒ - 4xy f ' (x² - y², y² - x²)

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An event that is impossible has a probability of 0.

What is the probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

The probability of an event that is impossible is 0. This means that there is no chance or likelihood of it occurring.

In probability, 0 represents the complete absence of any possibility of an event happening, while 1 represents a certain or guaranteed event.

All other values between 0 and 1 represent varying levels of uncertainty or likelihood.

Hence, An event that is impossible has a probability of 0.

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