Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?
2 y + x = 5. 5 x minus y = 3.
2 x + y = 5. 5 y minus x = 3.
2 y + x = 5. y minus 5 x = 3.
2 x + y = 5. x minus 5 y = 3.

Grape flavor has the smallest ratio of mix to water.

What is ratio proportion?

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or number that is dividing is referred to as the consequent. A ratio compares two numbers by division.

Here, we have

The ratios of punch mix to water for several fruit drinks as Grape mix (1 Grape flavor has the smallest ratio of mix to water.

cup to 3 cups), Cherry mix (5 cups to 12 cups), Lemon mix (7 cups to 12 cups), and Orange mix (2 cups to 3 cups).

We have to find which flavor has the smallest ratio of mix to water.

So, we compare all the given proportions by having a common base.  

Proportions of grape, cherry, lemon, and orange mixed in water = 1/3, 5/12, 7/12, 2/3

Now let us have a common denominator 12 as LCM of 3 and 12 is 12.  

Proportions of grape, cherry, lemon, and orange mixed with water = 1×4/3×4, 5/12, 7/12, 2×4/3×4

Proportions of grape, cherry, lemon, and orange mixed with water = 4/12, 5/12, 7/12, 8/12

Hence, the Grape flavor has the smallest ratio of mix to water.

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40 pounds of salami are purchased by a deli for its renowned grinder sandwiches. An illustration of an intermediate good is salami.

Given fill-in-the-blank;

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of___ goods.

The answer for this case is Intermediate.

A deli buys 40 pounds of salami for its famous grinder sandwiches. the salami is an example of Intermediate goods.

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If On December 31, a corporation determines that they have income taxes expense of $20,000, with $15,000 currently due. the journal entry is Debit Income taxes expense $20,000, Credit income taxes payable $15,000 Credit Deferred income tax liability $5,000.

Based on the given information the appropriate journal entry to record the transaction is"

Journal entry

Debit Income taxes expense $20,000

Credit income taxes payable $15,000

Credit Deferred income tax liability $5,000

($20,000 -$5,000)

(To record income taxes)

Therefore the entry is Debit Income taxes expense ,Credit income taxes payable and Credit Deferred income tax liability.

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The equation of the volume of the cylinder is V = A× h where a is base area and h is height.

Given that,

We have to find the equation of the volume of the cylinder.

We know that,

Given that a cylinder and a prism have similar shapes, but a cylinder differs from a prism in that it has a curved side face, we can determine a cylinder's volume using the same formula. We are aware that the formula, which is used to determine a prism's area,

Where V = A× h

A = the base's area

height is h.

Using the formula above, the volume (V) of a right circular cylinder is,

V = πr²h

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The rate of change of y with respect to x for a given line is 4/5.

What is the rate of change?

The rate of change is measured by a line's slope. It is frequently used when discussing momentum and is typically expressed as a ratio of one variable's change to another's corresponding change. This ratio is graphically represented by a line's slope.

The rate of change of y with respect to x for a given linear function is simply the slope expressed as:

dy/dx = (y2 - y1)/(x2 - x1)

Let us take the first 2 coordinates from the graph which are:

(0, 3) and (5, 7)

Thus;

dy/dx = (7 - 3)/(5 - 0)

dy/dx = 4/5

Hence, the rate of change of y with respect to x for a given line is 4/5.

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The types of angles include the supplementary, complementary, adjacent and vertical angles.

An angle is defined as the common point that is being formed when two straight lines meet at a common endpoint.

There are various types of angles that include the following:

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A function is a relationship between inputs and outputs, while a power is a mathematical operation that represents repeated multiplication.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by equations, which specify the relationship between the inputs and outputs.

A power, on the other hand, is a mathematical operation that represents repeated multiplication of a number by itself. The number that is being multiplied is called the base, and the number of times it is multiplied is called the exponent. For example, in the power 3⁴, the base is 3 and the exponent is 4, which represents 3 multiplied by itself 4 times, or 333*3.

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The long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

A variable is a quantity that could alter when used in a mathematical problem or experiment. Normally, a variable is denoted by a single letter. Common generic symbols used for variables include the letters x, y, and z.

Any traits, figure, or amount that can be gauged or counted is referred to as a variable. An alternative name for a variable is a data item. Age,  business earnings and expenses, country of birth, capital expenditures, class grades, eye color, and car kind are a few examples of variables.

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Although part of your question is missing, you might be referring to this full question: Use the exponential regression equation that best fits the data (10, 4), (12, 20), (13, 35), and (16, 300) to estimate y when x = 15.

The estimated y value at x = 15 is 147.

The exponential regression equation in general has form y = a*b^x.

And from the attached graph, it is shown that:

a ≈ 0.0038

b ≈ 2.0223

So, using the exponential regression calculator, the exponential model created by the data is:

y = a*b^x

y = 0.0038*(2.0223)^x

And when x = 15, thus:

y = 0.0038*(2.0223)^15

y ≈ 147

Hence, the estimated y value at x = 15 is 147.

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Debit Common Dividends Payable $ 234,850 ; credit Cash $ 234,850.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addi - tion, subtraction, multiplication, division, exponents, and root extraction. The Peano axioms, developed by the Italian mathematician Giuseppe Peano in the 19th century and still vital to the modern study of mathematical logic, formalised arithmetic. There are only a few ancient artefacts that can be used to date the invention of addition and subtraction. The best-known of these is the disputedly interpreted Ishango bone from africa, which dates to between 20,000 and 18,000 BC.

Main Body:

Debit Common Dividends Payable $100,100; credit Cash $100,100.

= $0.55 * (456,000 shares - 19,000 shares)

= $0.55 *427,000 shares

= $ 234,850

Hence ,debit Common Dividends Payable $ 234,850 ; credit Cash

$ 234,850.

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In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

What is ellipse?

In addition to being drawn outside the ellipse, the directrix of the ellipse is parallel to its latus rectum. There are two directions on the ellipse that are parallel to its principal axis. The ratio of distances between any point on an ellipse and its foci, as well as the directrix of the ellipse, is used to define an ellipse's eccentricity, and it is less than 1.

6x^(2)+2y^(2)+18x-10y+2=0

[tex]\frac{\left(x-\left(-\frac{3}{2}\right)\right)^2}{2^2}+\frac{\left(y-\frac{5}{2}\right)^2}{\left(2\sqrt{3}\right)^2}=1[/tex]

[tex]\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:a=2,\:b=2\sqrt{3}[/tex]

[tex]\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(-\frac{3}{2},\:\frac{5}{2}\right),\:\:b=2\sqrt{3},\:\:a=2[/tex]

Hence, In the ellipse, the center is (-3/2,5/2) semi-major axis is 2√3 and the semi-minor axis is 2.

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Answer:

1.3 to the twenty-eighth power over 1.2 to the twenty-first power

Step-by-step explanation:

The equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven is 1.3 cubed over 1.2 raised to the fourth power.

To find the equivalent expression, we need to use the rule that x^a / x^b = x^(a-b) for any value of x except 0.

In this case, we have 1.2^3 / 1.3^4 raised to the power of -7. Applying the rule, we get:

(1.2^3 / 1.3^4)^-7 = (1.2^(-4) / 1.3^3)^7

Since the exponent of a number raised to a power is the same as the power, we can rewrite the expression as:

1.2^(-47) / 1.3^(37)

Simplifying, we get:

1.2^(-28) / 1.3^(21)

Which is the same as:

1.3^(21) / 1.2^(28)

This is the same as the expression 1.3 cubed over 1.2 raised to the fourth power. Therefore, the equivalent expression for 1.2 cubed over 1.3 raised to the fourth power all raised to the power of negative seven is 1.3 cubed over 1.2 raised to the fourth power.

For the  given  quadratic function, the  highest  point  that the object  reaches is  (5, 768).

Since we are given with the quadratic function of h(t)=−16t2+160t+368, where  Let a = -16, b = 160, and c = 368, so the vertex for the equation will be  :t = -b/2a = -(160)/2(-16) = -160/(-32) = 5, so substituting this value  in the equation for the value of t is

h(5) = -16(5)2 + 160(5) + 368 = -400 + 800 + 368 = 768

Here the highest point that the object reaches is (5, 768), which means that  at a time of 5 seconds, the object reaches the building after being launched at the height of  768 feet  

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We are standing on the top of a 368 feet tall building and launching a small object upward. The object's vertical position, measured in feet, after t seconds is

We are standing on the top of a 1200 feet tall building and launch a small object upward. The object's vertical position, measured in feet, after t seconds is  What is the highest point that the object reaches?

The number of hours to operate the mines to minimize cost are Mine 1 hour = 30 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                             Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             350

Low grade               17                             10              610

Operating cost      7000                     29000

Time                        54                              27

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 7000x + 29000y

Subject to:

5x + 20y ≥ 350

17x + 10y ≥ 610

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (30, 10)

This means that

Mine 1 hour = 30 hours

Mine 2 hour = 10 hours

Hence, the number of hours are 30 and 10 hours

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The speed of the boat in still water is 3 miles per hour

Given that,

A boat travels 40 miles upstream in 4 hours and 48 miles downstream in 3 hours.

To find : The speed of the boat in still water

We use the distance formula. D = r * t

48/3 = 16 mph | Trip 1 |

40/4= 10mph | Trip 2 |

16-10 = 6 mph difference traveling upstream or downstream. Thus the speed of the current is 3 miles per hour.

Therefore, The speed of the boat in still water is 3 miles per hour.

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Question 1

[tex]a=1, r=1/2 \implies S_{\infty}=\frac{1}{1-(1/2)}=\boxed{2}[/tex]

Question 2

[tex]d=10, a_1+5d=52 \implies a_1=2 \\ \\ a_{15}=a_1+14d=2+14(10)=\boxed{142}[/tex]

The value of the expression on evaluation is 96π / 5.

Here we have to find the value of the expression.

∫∫∫x² dV

E is indeed the solid that exists inside the cylinder x² + y² = 4 above the surface z =0.

E's precession through into xy-plane is x² + y² ≤4 where r≤2 with Ф[0, 2π].

∫∫∫ x² dV = ∫[tex]\int\limits^2\pi _0 {} \, \int\limits^2_0{} \, \int\limits^3r_0[/tex] r² cos² Фrd dФ

             = [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 \int\limits^3r_z=0 {} \,[/tex]r³ cos²Ф dz dr dФ

            = [tex]\int\limits^2\pi _0 {} \, \int\limits^2_0 {} \,[/tex] 3[tex]r^{4}[/tex]cos²Ф dr dФ

           = 3 [tex]\int\limits^2\pi _0 {} \,[/tex] 1/2 [tex]2^{5}[/tex]/ 5 ( 1 + cos² Ф )dr dФ

           = 48 / 5 [( Ф + 1/2 sin 2Ф)[tex]]^{2\pi } _{0}[/tex]

            = 96π / 5

Therefore the value of the expression is 96π/5.

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The cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

What is cumulative distribution function?

The cumulative distribution function of a real-valued random variable X, or simply the distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x in probability theory and statistics.

We have to find the c.d.f  of ax + b for a > 0 and a < 0.

F(x) = P(X < x)

a>0:

P(aX + b < x) = P(aX < (x - b)) = P(X < (x - b)/a) = F((x - b)/a)

a < 0 :

P(aX + b < x) = P(aX < (x - b)) = P(X > (x - b)/a) = 1 - P(X < (x - b)/a) =

1 -  F((x - b)/a).

Hence, the cumulative distribution function, for

a > 0 is  F((x - b)/a) and for  a < 0 is 1 -  F((x - b)/a).

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Answer:

somone in my class is literally a new York rat

Step-by-step explanation:

Answer:

(x - 3 i) (x + 3 i) (x + 3)

Step-by-step explanation:

Answer: 1980

Step-by-step explanation:

1. If 4 sessions is 330 dollars, and how much is 24 sessions you have to multiply 4 times 6 and the answer is 24.

2. If 4 times 6 is 24 you have to multiply 330 by 6

3. We break down 330 dollars, so 300 times 6 is 1800, i like to take away  the zeros so 3 times 6 is 18 and we add 2 zeros becuase 300 has 2 zeros. And we do the same think with 30, but this time add 1 zero because 30 has 1 one zero.

4. the answer is 1800 dollars, you're welcome!

The greatest common factor for the fraction is 26.

What is fraction?

A fraction represents a district of an entire or, additional typically, any range of equal components. once spoken in everyday English, a fraction describes what number components of an exact size there area unit.

Main body:

According to the question,

fraction = 52/78

to find its common factor , we need to write it in form of multiples of its factors,

52 = 2*2*13

78 = 2*3*13

from this it is clear that both 52, 78 has factor as 2*13

Hence the greatest common factor for the fraction is 26

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The prime number that cannot be in the set is A . 2.

Prime number:

In math, prime number is a natural number greater than 1 that is not a product of two smaller natural numbers

Given,

Here we need to find the prime number that is not in the set, if if the sum of a set of ten different positive prime numbers is an even number.

Here we know that, all prime numbers except the first prime number are odd except 2.

And here we assume that the two prime numbers are different,

So, if one of the prime number is 2 which is even, the other prime number would be odd and hence sum of the prime numbers would be odd as sum of an even and an odd number is always odd.

Where as if none of the prime numbers are odd, then both the prime numbers would be odd and hence sum of the prime numbers would be even as sum of two odd numbers is always even.

There the correct option is A. 2.

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The total amount that will ba paid altogether is $710.

From the information, the person borrow 500 for 6 years at an annual interest rate of 7%.

It should be noted that interest is calculated as:

= Principal × Rate × Time

= 500 × 7% × 6

= $210

The total amount will be:

= Principal + Interest

= $500 + $210

= $710

The total amount is $710

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Answer:

  x = √41

Step-by-step explanation:

Given a right trapezoid with bases 10 and 14, and height 5, you want the length of the angled side, x.

The length x is the hypotenuse of a right triangle with one leg 5 units and the other leg (14 -10) = 4 units. It can be found using the Pythagorean relation:

  c² = a² +b²

  x² = 5² +4² = 25 +16 = 41

  x = √41 . . . . . take the square root

Yes, it is possible that one-to-one function and its inverse are true. If f(f(x)) = x then function and its inverse coincide.

If each x-value corresponds to exactly one y-value, the function is said to be one-to-one.  Inverse function graphs are reflections of the y = x line. This indicates that there can be only one y-value for each x-value. One-to-one functions are those that fit this description.

Inverse of function is represented by [tex]f^{-1} (x)[/tex].

Test to check inverse function: If and only if no horizontal line intersects the graph of f at more than one location, then the function f is one-to-one and possesses an inverse function.

Example: f(x) = 5-x

f(f(x))= 5- (5-x) = x

So above function is one to one and inverse of itself.

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If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

If a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, then we have to explain what she can:

decrease the sample size.

increase the confidence level.

increase the sample size.

increase the sample size.

As we know that;

The formula of Margin of Error is;

ME = Z(α)× √σ^2/n

where; ME = margin of error

α = confidence level

z(α) = quantile

σ = standard deviation

n = sample size

So as we can see that Margin of Error is inversely proportion to sample size.

So, if a decision maker wishes to reduce the margin of error associated with a confidence interval estimate for a population mean, she can decrease the sample size. So the option a is correct.

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At tα/2= -1.66, we reject H0.

What is the Null hypothesis?

The null hypothesis is a standard statistical theory that contends there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Data provided

sample size is 100, and

sample mean, 52.0 for x

The standard deviation of the sample, s= 22.0

Average population, = 60.0

Level of significance, = 0.05

Theorem testing

The alternate and the null hypothesis is

H0: u = 60

Ha: u < 60

Crucial component:

value crucial at 0.05

tα/2= -1.66

Region of rejection:

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Answer: 3 pieces

Step-by-step explanation:

This problem can be solved by modeling the problem using equivalent fractions.

We know Stephanie put icing on 9 of her 15 pieces, this gives us a fraction of [tex]\frac{9}{15}[/tex].

Tammy cut her cake in 5 pieces, but we do not know how many were iced, the pieces of iced cake will be our variable, x, so her fraction is [tex]\frac{x}{5}[/tex].

Both of the fractions need to be equivalent so [tex]\frac{9}{15} =\frac{x}{5}[/tex], which can be solved for x = 3 pieces.

The probability that a student chosen randomly from the class plays both basketball and baseball is 39%.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given:

In a certain Algebra 2 class of 23 students, 11 of them play basketball and 13 of them play baseball.

There are 8 students who play neither sport.

Either (or both) sports = (23 - 8) = 15 students play

Both = [11 basketball and 13 baseball) - 15] = 9 must play both

Probability=9/23

Probability=0.39 or 39%

Hence, the probability that a student chosen randomly from the class plays both basketball and baseball is 39%.

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