4x - y = 3
3x + y = 4

Answer:

Step-by-step explanation:

You want the costs of an oscilloscope and a multimeter when the sum of their costs is $574, and the difference of their costs is $356.

Let o and m represent the costs of the oscilloscope and multimeter, respectively. Then the costs can be described by ...

  o +m = 574

  o -m = 356

Adding these two equations gives ...

  2o = (574+356) = 930

  o = 465 . . . . . . . . . . . . divide by 2

Subtracting the second equation from the first gives ...

  2m = 574 -356 = 218

  m = 109 . . . . . . . . . . . . divide by 2

The oscilloscope costs $465; the multimeter costs $109.

__

Additional comment

This is the generic solution to a "sum and difference" problem: the higher value is half the sum of the given numbers, and the lower value is half their difference.

The volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

What is frustum of pyramid?

The top of a conventional pyramid is removed to create the frustum, which is a pyramid. It is known as a truncated pyramid for this reason. The height of a pyramid is represented by the letter h and is the distance from its base to its summit. Similar to it, it has two bases and a slant height indicated by the letter "s" (top and bottom).

We are given frustum of a pyramid with square base of side 22, square top of side 13 and height 20.

We know that volume of frustum of pyramid(V) = h(b^2 + a^2 + ab)/3

We are given b = 22, a = 13 and h = 20

From this, we get

⇒V = h(b^2 + a^2 + ab)/3

⇒V = 20(22^2 + 13^2 + 22*13)/3

⇒V = 20(484 + 169 + 286)/3

⇒V = 20(939)/3

⇒V = 20*313

⇒V = 6260 cubic units

Hence, the volume of a frustum of a pyramid with given dimensions is 6260 cubic units.

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The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let r be the radius of the circle. Then the area of the circle will be

A = πr² square units

The area of the circle is 4π x² + 12πx + 9π. Then the radius is given as,

A = 4π x² + 12πx + 9π

πr² = π [(2x)² + 2 · 2x · 3 + 3²]

r² = (2x + 3)²

r = 2x + 3

The value of the radius should be more than zero. Then we have

r > 0

2x + 3 > 0

x > - 3/2

The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.

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The complete question is given below.

The area of a circle is 4π x 2 + 12πx + 9π.

a. What is an expression for the radius of the circle?

b. What is the least possible integer value of x for the circle to exist? Explain.

Answer:

Here is a table that can be used to solve the equation:

Operation Result

38.2 38.2

+ (-1) 37.2

= 11 False

The equation 38.2 + (-1) = 11 is not true for any value of x. There is no solution for this equation.

Oh, hello there! Let's work on this equation together.

38.2 + -1 = 11

Let's create a table to keep track of our work.

-1 38.2 11

+1 37.2 12

As you can see, we added 1 to both sides to cancel out the negative 1.

So now, our equation is 37.2 = 12.

Let's subtract 12 from both sides.

-12 37.2 11

-12 25.2 -1

And there you have it! The solution is 25.2.

The cubic function g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The cubic parent function f(x) = x³ has been transformed to the function g(x) = −2(x + 4)³ − 5 through a combination of translations, scaling, and reflection.

Translation: The parent function has been shifted 4 units to the right, resulting in x + 4 instead of x in the argument of the function.

Scaling: The parent function has been scaled vertically by a factor of -2, resulting in a coefficient of -2 in front of the argument.

Reflection: The parent function has been reflected on the x-axis, resulting in the negative sign in front of the argument.

Thus, g(x) = -2(x + 4)³ - 5 can be obtained from f(x) = x³ by a translation of 4 units to the right, a vertical scaling by a factor of -2, and a reflection about the x-axis.

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Answer: Let x be the number of miles driven.

The cost of renting the car and driving x miles is 80 + 0.25x.

We want to find the maximum number of miles that can be driven given a budget of $110, so we set 80 + 0.25x = 110 and solve for x:

80 + 0.25x = 110

0.25x = 110 - 80

0.25x = 30

x = 120

So the maximum number of miles that can be driven is 120.

Step-by-step explanation:

Answer:

two of the sides are x and the other two sides are x+2

x+x+x+2+x+2 = 36

4x = 32

x = 8

the sides are 8, 8, 10, 10

area is length x width

8 x 10 = 80

answer: 80ft

Step-by-step explanation:

The hypothesis and conclusion are -

(a) Hypothesis : n is a prime number.

Conclusion : n² has three positive factors.

(b) Hypothesis : a and b are irrational numbers.

Conclusion : a · b is an irrational number .

(c) Hypothesis : p is a prime number.

Conclusion : p = 2 or p is an odd number .

(d) Hypothesis : ap is a prime number and p≠2 .

Conclusion : p≠2, p is an odd number .

(e) Hypothesis : p≠2 and p is a even number.

Conclusion : p is not a prime number .

What is irrational number?

A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio.

The hypothesis of a conditional statement is the phrase immediately following the word if.

The conclusion of a conditional statement is the phrase immediately following the word then.

(a) If n is a prime number, then n² has three positive factors.

Hypothesis : n is a prime number.

Conclusion : n² has three positive factors.

(b) If a is an irrational number and b is an irrational number, then a⋅b is an irrational number.

Hypothesis : a and b are irrational numbers.

Conclusion : a · b is an irrational number .

(c) If p is a prime number, then p=2 or p is an odd number.

Hypothesis : p is a prime number.

Conclusion : p = 2 or p is an odd number .

(d) If p is a prime number and p≠2 or p is an odd number.

Hypothesis : ap is a prime number and p≠2 .

Conclusion : p≠2, p is an odd number .

(e) p≠2 or p is a even number, then p is not prime.

Hypothesis : p≠2 and p is a even number.

Conclusion : p is not a prime number .

Therefore, the hypothesis and conclusions are made.

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The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

Then the equation of the line is given as,

(y - 5) = [(10 - 5) / (14 - 7)](x - 7)

y - 5 = (5/7)x - 1

y = (5/7)x + 4

At x = 63, the value of 'y' is given as,

y = (5/7)63 + 4

y = 45 + 4

y = 49

The equation is y = (5/7)x + 4. Then the value of the pattern y at x = 63 will be 49.

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The standard form of the equation of the sphere with center (0, -1, 3) and a radius of square root of 5 is given as follows:

x² + (y + 1)² + (z - 3)² = 5.

The two parameters for the equation of a sphere are given as follows:

Then the equation for the sphere is given as follows:

(x - x*)² + (y - y*)² + (z - z*)² = r².

The parameters for this problem are given as follows:

Hence the equation of the sphere is defined as follows:

x² + (y + 1)² + (z - 3)² = 5.

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The triangle will by a right triangle if the sum of the squared side lengths is equals to the squared length of the hypotenuse.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

Hence, a triangle will only be a right triangle if the Pythagorean Theorem is respected, hence the sum of the squared side lengths must be compared to the square of the hypotenuse length.

The problem is incomplete, hence the procedure to verify whether the triangle is a right triangle was presented.

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The concept is the Chi-square test, a statistical test for comparing observed results to expected results. The answer is option A.

The test statistic x^2 is equivalent to the test statistic Z. Homogeneity 2x2 The chi-square statistic (and the test) is equivalent to a two proportion test.

The chi-square test is a statistical test used to compare observed results to expected results.The purpose of this test is to determine whether the difference between the observed and expected data is due to chance or to the relationship between the variables being studied. The

Two Ratio Z-Test is a statistical hypothesis test used to determine whether two ratios are different from each other. When you run the test, the z-statistic is calculated from two independent samples, and the null hypothesis is that the two proportions are equal.

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Hi there, here's your answer:

The general formula of a circle:

[tex](x-h)^{2} +(y-k)^{2}=r^2\\[/tex]

Where the ordered pair (h, k) is the center of the circle.

Given (h, k) = (-6, -2)

We also have that the circle passes through a point (7, 12)

Which means that (7, 12) lies on the circumference of the circle.

Let this be labelled as [tex](x_{1}, y_{1})[/tex]

Since this point lies on the circumference of the circle, it must satisfy the equation when substituted in for (x, y).

Thus, we substitute [tex]x_{1}[/tex] for x and [tex]y_{1}[/tex] for y.

We get the final equation to be:

[tex](7+6)^2 + (12+2)^2 = r^2[/tex]

Or

[tex]169 + 196 = r^2[/tex]

[tex]r^2 = 365[/tex]

Thus, we get the final equation of the circle to be [tex](x+6)^2 + (y+2)^2 = 365[/tex]

Hope it helps!

The child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.

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

The distance between the kite and the child's hand level "d".

By using the Pythagorean theorem, we can write:

d² + h² = s²

Simplifying and solving for d, we get:

d² = s²-h²

d = √(s²-h² )

Let's call the length of the cord "L". Then, we can write:

d² + L² = s²

Differentiating both sides with respect to time (t), we get:

2d (dd/dt) + 2L (dL/dt) = 2s (ds/dt)

We want to find (dL/dt) when L = s and d = √(s²-h² )

(dd/dt) = 0 as the height of the kite above the child's hand level is constant.

(dL/dt) = (s(ds/dt) - d (dd/dt)) / L

Substituting in the values we found for d and L, we get:

(dL/dt) = s(ds/dt)) / √(s²-h² )

Therefore, the child is paying out cord at a rate of s(ds/dt)) /√(s²-h²) feet per second when "s" feet of cord are out.

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Answer:

Step-by-step explanation:

y=8x-7

9=8x-7

9+7=8x-7+7

16=8x

16/8=8x/8

2=x

If m/n is the probability that you do not eat green candy after you eat a red candy, then m + n is 6.

A bag contains 8 green candies and 4 red candies. If you eat five candies, there are relatively prime positive integers m and n so that m/n is the probability that you do not eat green candy after you eat a red candy. Below list the ways to accomplish this ordering along with their respective probabilities:

GRRRR : [tex]\frac{8}{12}\times\frac{4}{11} \times\frac{3}{10} \times\frac{2}{9} \times\frac{1}{8}[/tex]

GGRRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{4}{10} \times\frac{3}{9} \times\frac{2}{8}[/tex]

GGGRR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{4}{9} \times\frac{3}{8}[/tex]

GGGGR : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]

GGGGG : [tex]\frac{8}{12}\times\frac{7}{11} \times\frac{6}{10} \times\frac{5}{9} \times\frac{4}{8}[/tex]

The sum is [tex]\frac{8\times3\times4(2+14+42+70+70)}{12.11.10.9.8}[/tex]

Probability that you do not eat green candy after you eat a red candy =[tex]\frac{1}{5}[/tex]

so m = 1 and n = 5

m + n =6

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After evaluating these expression it seems to be the option (a) math.hypot(3,4) == math.sqrt(25) evaluate that is True

The math.hypot function calculates the Euclidean distance between two points in a 2D space, which is equivalent to the length of the hypotenuse of a right triangle with sides of length a and b (where a and b are the arguments to math.hypot).

In this case, math.hypot(3, 4) calculates the length of the hypotenuse of a right triangle with sides of length 3 and 4, which is equal to 5.

The expression math.sqrt(25) calculates the square root of 25, which is equal to 5. Since math.hypot(3, 4) and math.sqrt(25) both evaluate to 5, the expression math.hypot(3, 4) == math.sqrt(25) evaluates to True.

The other expressions are not evaluating to True:

b. math.hypot(2,5) != math.trunc(2.5)

c. math.hypot(2,5) != math.true(2.5)

d. math.cell(2,5) does not exist. It is likely a typo for math.ceil which is not equal to math.floor(2.5)

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Answer:

The actual distance between two cities that are 3 7/8 inches apart on the map is 279 miles.

Step-by-step explanation:

To find the actual distance between two cities, we need to convert the distance on the map to miles. The scale of the map is 3/4 inch equals 72 miles, which means 1 inch on the map is equal to 72/3=24 miles.

So, the actual distance between two cities on the map that are 3 7/8 inches apart is 24 * 3 7/8 = 279 miles.

A word problem for the given expression is the division of 3/4 cups of juice among two friends equally.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given is an expression [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex].

Suppose that there are 3/4 cups of juice available.

There are two friends who are in need of this.

The total amount of juice has to be divided equally among these two friends.

Amount of cups of juice each friend gets = [tex]\frac{3}{4}[/tex] ÷ 2.

[tex]\frac{3}{4}[/tex] ÷ 2 = [tex]\frac{3}{4}[/tex] × [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex]

So each friend gets 3/8 cups of juice.

Hence the division of a total of 3/4 cups of juice among two friends equally is a word problem for the given expression.

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Answer: The best-fitting model for the data is a parabolic equation with the form y = ax^2 + bx + c. The coefficients a, b, and c represent the parameters that best describe the relationship between the time (x) and the height (y) of the baseball.

Based on the information provided, the best-fitting model is:

y = 1.553x^2 + 15.178x + 3.37

where y is the height of the baseball (in feet), x is the time (in seconds), 1.553 is the coefficient for x^2, 15.178 is the coefficient for x, and 3.37 is the constant term. This equation represents the best fit of the data to a parabolic function.

Step-by-step explanation:

Of the lists of properties you provided, only the list of "identity, solubility, melting point" contains only those that are characteristic properties of a substance.

Identity refers to the name or chemical formula of the substance, which is unique to that substance and can be used to identify it.

Solubility refers to the ability of a substance to dissolve in a solvent, such as water. The solubility of a substance can also be used to identify it, as different substances have different solubility's.

Melting point refers to the temperature at which a solid substance will change into a liquid. Like solubility, the melting point of a substance is also a characteristic property that can be used to identify it.

On the other hand, boiling point, mass, and density are not always characteristic properties of a substance. While they can give us information about a substance, they are not unique to that substance and cannot be used to identify it.

Volume and temperature are not considered characteristic properties of a substance, as they are dependent on external factors, such as the pressure and the amount of the substance being measured.

In conclusion, the list of "identity, solubility, melting point" contains only those properties that are characteristic of a substance and can be used to identify it.

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Answer: The number of bacteria in the people of a town with a population of 200 thousand would be 200,000 * 600 million = 120 x 10^9 bacteria.

Step-by-step explanation:

Answer:

C = 10m

Step-by-step explanation:

when c=20, m=2

when c=40, m=4

we can see that c is equals to 10 times the value of m

Therefore c = 10m

The rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.

Two or more expressions with an Equal sign is called as Equation.

Let's call the number of items sold at a price of $p as x(p).

Based on the information given, we can write an equation for x(p) as:

x(p) = 2000 - 400(p - 30)

The profit from selling the items at a price of $p is given by the product of the number of items sold and the price:

Profit(p) = x(p)×p

Taking the derivative of the profit function with respect to the price, we can find the rate of change of the profit:

dProfit/dp = dx/dp×p + x(p)

= -400 p + 400 ( 30) + 2000 - 400(p - 30)

= -400 p + 12000

When p = 30, the rate of change of the profit is:

dProfit/dp = -400(30 )+ 12000

= 3600

So the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.

Hence,  the rate of change of the profit when the item price is $30 is $3600 per dollar increase in price.

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Answer: The function that models the cost of the house over time can be written as y = 200,000 * (1 + 0.03)^x, where x is the number of years and y is the value of the house.

To find the value of the house at the end of ten years, we need to plug in x = 10 into the function:

y = 200,000 * (1 + 0.03)^10 = 200,000 * 1.33489 = 266,978.8

So the value of the house at the end of ten years is $266,978.8.

Step-by-step explanation:

Answer: 107.1

Step-by-step explanation:

4 or less down

5 or more up

In this case, we round to 1 decimal place, so we look at the hundredths column.

It is 6, so we round up.

The range of the function is 8.75.

And the domain is all the positive integers.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

Given:

Alice decides to finish her trip by riding a train 700 miles to Washington, D.C.

The train travels at an average speed of 80mph.

Let s be the average speed.

So, speed = distance / time

s = 700/t

t = 700/80

t = 8.75 hours.

The range of the function is 8.75.

And the domain is all the positive integers.

Therefore, the time it will take is 8.75 hours.

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Answer:

2^4*2^5=2^(4+5)=2^9

Step-by-step explanation:

When dealing with operations with exponents and multiplication, the exponent operations always come first.  So while the exponent 9 is correct for the answer, 4 is incorrect.

For example, if you were to solve each operation and eliminate every exponent, you would have

2^4*2^5=16*32=512 which is the same as 2^9=512.

As you can see, the exponent operation must come before the multiplication.

The row with the most sucktastic runtime is the one with[tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes.

No, we do not have any non-integer answers.

Second: 72

Minute: 1000

Hour: [tex]2^(17)[/tex]

Day: [tex]2^25[/tex]

Month: [tex]2^30[/tex]

Year: [tex]2^35[/tex]

Second: f(n) = 72 => n = 72

Minute: f(n) = 1000 => n = 1000

[tex]Hour: f(n) = 2^n = > n = 17Day: f(n) = 2^n = > n = 25 Month: f(n) = 2^n = > n = 30Year: f(n) = 2^n = > n = 35[/tex]

Seconds: The runtime for an input of size n is 72 microseconds, so the largest input that can be calculated in a second is 72.

Minutes: The runtime for an input of size n is 1000 microseconds, so the largest input that can be calculated in a minute is 1000.

Hours: The runtime for an input of size n is[tex]2^n[/tex] microseconds, so the largest input that can be calculated in an hour is [tex]2^17.[/tex]

Days: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a day is [tex]2^25[/tex]

Months: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a month is [tex]2^30.[/tex]

Years: The runtime for an input of size n is [tex]2^n[/tex] microseconds, so the largest input that can be calculated in a year is [tex]2^35.[/tex]

The row with the most sucktastic runtime is the one with [tex]2^n[/tex], as it takes exponentially longer to run than the other runtimes. Therefore, the longer the time period, the larger the input size that can be calculated. No, we do not have any non-integer answers as the runtimes of the inputs are in microseconds and the input size is given as an integer.

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