Which equation is equivalent to pq=r?
Responses

A) p=logR q
B) p=logQ r
C) q=logR p
D) q=logP r

Yes, W_2 = {p_2 = a_2t_2 + a_1t + a_0 ∈ ℙ_2 | a_0 = 2} is a subspace of the vector space ℙ_2.

Yes, W_1 = {[a b c; d 0 0] ∈ M_{2x3} | b = a + c} is a subspace of the vector space M_{2x3}.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, ℙ_2 is the set of all 2nd degree polynomials with the usual polynomial addition and scalar multiplication with reals.

Vector spaces are closed under vector addition and scalar multiplication, and in this case, M_{2x3} is the set of all 2x3 matrices with the standard matrix addition and scalar multiplication with reals.

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Answer: $22.50

Step-by-step explanation:

Let x be the cost per pound of the secret-formula coffee beans.

The total cost of the secret-formula beans is 12x dollars.

The total cost of the other beans is 15 × 18 = 270 dollars.

The total cost of the mix is (12 + 15) × 20 = 540 dollars.

Since the barista mixed 12 pounds of the secret-formula beans with 15 pounds of the other beans, the total weight of the mix is 12 + 15 = 27 pounds.

We can set up an equation based on the total cost of the mix:

12x + 270 = 540

Subtracting 270 from both sides:

12x = 270

Dividing both sides by 12:

x = 22.5

Therefore, the barista's secret-formula coffee beans cost $22.50 per pound.

Answer:

P = [tex]2y^{2}[/tex] + 4xy +4

Q = [tex]-3y^{2}[/tex] + 7 -3xy

R = -3xy +8

Step-by-step explanation:

Therefore, we have the values of:

a = -g(x) for -10 < x < -8

b = lower limit of the range where g(x) = -6

c = -C for -1 < x < 1

d = upper limit of the range where g(x) = 4

e = we cannot determine the value of e based on the given information.

In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It 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 a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.

Here,

We can find the values of a, b, c, d, and e by examining the given information:

For -15 < x < -10: g(x) = -(-10) = 10

For -10 < x < -8: g(x) = -a

For -1 < x < 1: g(x) = -C

For b < x < l: g(x) = -(-6) = 6

For 10 < x < 15: g(x) = -8

For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.

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the sale price of the cell phone after the 35% discount is $315.25.

How to solve and what is sale?

To find the sale price of the cell phone, we need to apply the discount of 35% to the regular price of $485. We can do this by multiplying the regular price by 0.35 and then subtracting the result from the regular price:

Sale price = Regular price - Discount amount

Sale price = $485 - (0.35 x $485)

Sale price = $485 - $169.75

Sale price = $315.25

Therefore, the sale price of the cell phone after the 35% discount is $315.25.

A sale is a temporary reduction in the price of a product or service. Sales are often used by businesses to attract customers and increase sales volume. Sales can be offered for many reasons, such as to clear out inventory, promote a new product, or attract customers during a slow period.

In a sale, the price of a product or service is discounted, either by a fixed amount or by a percentage of the regular price. For example, a store might offer a 20% discount on all clothing items, or a car dealership might offer a $5,000 discount on a particular model of car.

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Answer:

x = 45.

Step-by-step explanation:

Given a straight line with the equation.

First collect like terms:

2x + x = 180 - 45

Then calculate:

3x = 135

Finally after dividing both sides by 3:

x = 45

The Length of AB in square ABCD is 30 feet.

Since the squares ABCD and EFGH are similar, their corresponding sides are proportional, so we can set up the following relation:

AB/EF = 1/4

We can also use the fact that the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. Therefore,

AB²/EF² = (Area of square ABCD)/(Area of square EFGH)

Substituting the given values:

AB²/EF² = (Area of square ABCD)/(14400)

Since the areas of squares are proportional to the square of their sides, we can write,

Area of square ABCD/Area of square EFGH = (AB/EF)²

Substituting this into the above equation and solving for AB, we get,

AB²/EF² = (AB/EF)²

AB² = (AB/EF)² * EF²

AB² = (1/4)² * 14400

AB² = 900

AB = 30 feet

Therefore, the length of the side AB of square ABCD is 30 feet.

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Answer:

Step-by-step explanation:

Answer:

Length = 53 feet

Width = 22 feet

Step-by-step explanation:

Perimeter = 2(length + width)

Then:

a = 2w + 9            Ec. 1

150 = 2(a + w)       Ec. 2

a = length

w = width

From Eq. 1:

a - 9 = 2w            Eq. 3

From Eq. 2:

150 = 2*a + 2*w

150 = 2a + 2w

150 - 2a = 2w        Eq. 4

Equalizing Eq. 3 and Eq. 4

a - 9 = 150 - 2a

a + 2a = 150 + 9

3a = 159

a = 159/3

a = 53

From Eq. 1:

a = 2w + 9

53 = 2w + 9

53 - 9 = 2w

44 = 2w

44/2 = w

w = 22

Check:

From Eq. 2

150 = 2(a+w)

150 = 2(53+22)

150 = 2*75

(a) Symbol used for sample standard deviation is “s” or “σˆ” (s-hat). The unit for the sample standard deviation is grams, as it is calculated from a sample.

(b) Symbol used for population standard deviation is “σ” (sigma).The unit for the population standard deviation is also grams, as it is calculated for the entire population.

The population standard deviation is a parameter, which is a fixed value calculated from every individual in the population.

A sample standard deviation is a statistic. This means that it is calculated from only some of the individuals in a population. Since the sample standard deviation depends upon the sample, it has greater variability.

(c) Symbol used for sample variance is “s²” or “σ²ˆ” (sigma-hat squared). The unit for the sample variance is grams², as it is calculated from a sample.

(d) Symbol used for population variance is “σ²” (sigma squared). The unit for the population variance is also grams², as it is calculated for the entire population.

Population variance refers to the value of variance that is calculated from population data, and sample variance is the variance calculated from sample data.

Due to this value of denominator in the formula for variance in case of sample data is ‘n-1’, and it is ‘n’ for population data. As a result both variance and standard deviation derived from sample data are more than those found out from population data.

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Answer: Let x be the number of hamburgers sold.

Then, the number of cheeseburgers sold is 3x.

The total number of burgers sold is x + 3x = 4x.

Given that the total number of burgers sold is 416, we have:

4x = 416

x = 416/4

x = 104

Therefore, 104 hamburgers were sold.

Step-by-step explanation:

Answer:

If the GM between √2 and 2√2 is a find the value of a.​

Step-by-step explanation:

To find the geometric mean between two numbers, we simply take the square root of their product.

In this case, we want to find the geometric mean between √2 and 2√2.

Their product is:

√2 * 2√2 = 2√4 = 2*2 = 4

So, the geometric mean between √2 and 2√2 is the square root of 4, which is:

√4 = 2

Therefore, the value of a is 2.

The  value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

(a) To verify that C(3) < C(6), we have to find the values of C(3) and C(6).The given function is C(x) = s(x x+3)The order size is measured in hundreds. So, when x = 3, the order size is 300 and when x = 6, the order size is 600.Therefore, C(3) = s(3 x 3+3) = s(18) and C(6) = s(6 x 6+3) = s(39)Now, as s(x) > 0, we can see that C(6) > C(3). Hence, C(3) < C(6).(b) According to Rolle's Theorem, the rate of change of the cost must be 0 for some order size in the interval (3 < x < 6).We know that the function is continuous and differentiable in the interval (3 < x < 6). Now, the rate of change of the cost is given by the derivative of the function C(x) with respect to x.C(x) = s(x x+3)C'(x) = s[1 + (x + 3) . 1] = s(1 + x + 3) = s(x + 4)As per Rolle's Theorem, there must exist a value of x in the interval (3 < x < 6) such that C'(x) = 0.So, s(x + 4) = 0x + 4 = 0x = -4Thus, the order size is -4 x 100 = -400. However, this is an absurd answer as the order size cannot be negative. Therefore, there is no value of x in the interval (3 < x < 6) for which the rate of change of the cost is zero.

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In the following question, among the given options, the statement is said to be, The pooled estimate of the standard deviation for the data given is √(54.14^2/10 + 24.26^2/10) = 22.74.

According to the rule for examining standard deviations in ANOVA from Chapter 12 (page 560), the within-group standard deviation should be no more than twice the size of the between-group standard deviation. In this case, the between-group standard deviation is 44.85 and the within-group standard deviation (22.74) is less than twice the size of the between-group standard deviation, so it is reasonable to use a pooled standard deviation for the analysis of these data.

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Answer:

- 1 and 7

Step-by-step explanation:

to find h(0) substitute x = 0 into h(x)

h(0) = 4(0) - 1 = 0 - 1 = - 1

to find h2) substitute x = 2 into h(x)

h(2) = 4(2) - 1 = 8 - 1 = 7

A bin can hold 28 pounds. each toy car weighs 7 ounces., so the bin can hold 64 toy cars.

To determine the number of toy cars the bin can hold, we must first convert the weight limit of the bin and the weight of the toy cars to a uniform unit of measure.

We'll then divide the weight limit of the bin by the weight of one toy car. After that, we'll multiply the resulting value by the number of ounces in one pound (16).

Here's how to solve the problem:

1 pound = 16 ounces

Therefore, a bin that can hold 28 pounds can hold:28 × 16 = 448 Ounces

The weight of one toy car is 7 ounces.

Divide the weight limit of the bin (448 ounces) by the weight of one toy car (7 ounces):

448 ÷ 7 = 64

Therefore, the bin can hold 64 toy cars.

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As per the equations, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

Factoring is the process of breaking down a mathematical expression or number into its component parts, which can then be multiplied together to give the original expression or number. In algebra, factoring is often used to simplify or solve equations.

An equation is a statement that shows the equality of two expressions, typically separated by an equals sign (=). The expressions on both sides of the equals sign are called the "left-hand side" and "right-hand side" of the equation.

In the given question,

Let's call the age of the first dog "x" and the age of the second dog "y". We know that their ages add up to 15, so we can write:

x + y = 15

We also know that their ages multiply to 44, so we can write:

x * y = 44

Now we have two equations with two unknowns, which we can solve simultaneously to find the values of x and y.

One way to do this is to use substitution. From the first equation, we can solve for one variable in terms of the other:

y = 15 - x

We can substitute this expression for y into the second equation:

x × (15 - x) = 44

Expanding the left side, we get:

15x - x^2 = 44

Rearranging and simplifying, we get a quadratic equation:

x^2 - 15x + 44 = 0

We can factor this equation as:

(x - 11)(x - 4) = 0

Using the zero product property, we know that this equation is true when either (x - 11) = 0 or (x - 4) = 0.

Therefore, the possible values of x are x = 11 and x = 4.If x = 11, then y = 15 - x = 4, which means that the ages of the two dogs are 11 and 4.

If x = 4, then y = 15 - x = 11, which means that the ages of the two dogs are 4 and 11.

Therefore, the two dogs are either 11 years old and 4 years old, or 4 years old and 11 years old.

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Answer: 54 square in

Step-by-step explanation:

I don't know if this is the same person but I answered this same question just now please check my profile or comment if you want the explanation

The three examples of contracts are:

Contracts are legal agreements between two or more parties that involve the exchange of goods, services, or money. They can be classified as unilateral or bilateral, express or implied, executed or executory.

Here are three examples of contracts that a person can be a part of:

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Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

The triangle is right-angled

In a right-angled triangle, the following equality holds

[tex]\tan x = \dfrac{\text{Side Opposite x}}{\text{Side adjacent to x}}\\\\\tan 30 = \dfrac{4}{x}\\\\[/tex]

[tex]\tan 30 = \dfrac{1}{\sqrt{3}}\\\\\dfrac{1}{\sqrt{3}} = \dfrac{4}{x}\\\\[/tex]

Cross multiply:
[tex]1 \times x = 4 \times \sqrt{3}\\\\x = 4\sqrt{3}[/tex]

The answer to the question is 334 kittens.

Given that a cat gave birth to 333 kittens who each had a different mass between 147 g and 159 g. Then the cat gave birth to a 4th kitten with a mass of 57 g.

First of all, we will find out the range of the mass of kittens. The range is given as follows;Range = Maximum Value - Minimum Value Range = 159 g - 147 g Range = 12 g

Now, the cat gave birth to a 4th kitten with a mass of 57 g, we can say that the minimum value of kitten's mass is 57 g.So, the maximum value of kitten's mass can be calculated as follows;Maximum Value = 57 g + Range Maximum Value = 57 g + 12 g Maximum Value = 69 g Now, we can say that all kittens with a mass of 69 g or less would be born because the minimum value of kitten's mass is 57 g and the range of mass is 12 g.

Therefore, the answer to the question is 334 kittens.

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Answer:

To find the point that partitions the line segment AB in a ratio of 1:3, we can use the following formula:

P = (3B + 1A) / 4

where P is the point that partitions the line segment in a ratio of 1:3, A and B are the endpoints of the line segment, and the coefficients 3 and 1 represent the ratio of the segment we are dividing.

Substituting the values, we get:

P = (3*(-1, -5) + 1*(-5, 3)) / 4

P = (-3, -7)

Therefore, the point that partitions the line segment AB in a ratio of 1:3 is (-3, -7).

Step-by-step explanation:

The given conditional statements are false, true, false, True.

They are determined by following:

(a) False - The statement "If 10<7,10<7, then 3=43=4" is false, since 10 is not less than 7.
(b) True - The statement "If 7<10,7<10, then 3=43=4" is true, since 7 is less than 10.
(c) False - The statement "If 10<7,10<7, then 3+5=83+5=8" is false, since 10 is not less than 7.
(d) True - The statement "If 7<10,7<10, then 3+5=83+5=8" is true, since 7 is less than 10.

Conditional statements are used in mathematics and logic to express relationships between events and conditions. These statements consist of an "if-then" structure, where the "if" clause is the antecedent or condition, and the "then" clause is the consequent or outcome.

The truth value of the conditional statement depends on whether the condition is true or false. If the condition is true, then the outcome is also true, and the statement is considered true.

If the condition is false, then the outcome may be true or false, and the statement is considered false. Conditional statements are widely used in mathematical proofs, programming, and reasoning to establish logical connections between different events and conditions.

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There are 169 outcomes in the complement of the given event.

To find the number of outcomes in the complement of the given event, which is that out of 344 high school students in their senior year, 175 are left-handed, you need to follow a few steps. So, let's get started. To find the number of outcomes in the complement of the given event, you will first find the total number of students that are right-handed, which can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169Therefore, there are 169 right-handed students.

Next, to find the number of outcomes in the complement of the given event, you will need to subtract the number of outcomes in the given event from the total number of possible outcomes. Since the number of possible outcomes is equal to the total number of students, the number of outcomes in the complement of the given event can be found by subtracting the number of left-handed students from the total number of students:344 - 175 = 169 Therefore, there are 169 outcomes in the complement of the given event.

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As a result, Lara made a $6,262.71 initial deposit into her savings account.

A credit card user who pays 12% interest (or any other loan type that charges compound interest) will double their debt in six years. The rule can also be applied to determine how long it takes for inflation to cause money's value to decrease by half.

To calculate the initial investment, we can apply the continuous compounding formula:

A = Pe(rt)

Where:

A = the current balance ($7,000.00)

P = the initial deposit (unknown)

r = the annual interest rate (11% or 0.11 as a decimal)

t = the time in years (1 year)

Plugging in these values, we get:

$7,000.00 = Pe(0.11 * 1)

A shorter version of the exponential expression:

$7,000.00 = Pe0.11

$7,000.00 = P * 1.1166 (rounded to 4 decimal places)

Dividing both sides by 1.1166:

P = $6,262.71 (rounded to the nearest cent)

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Answer:

To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.

We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.

So we have:

556 = 16 x 34 + 48 + 4

This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.

Simplifying the remainder, we have:

48 + 4/16 = 48 + 1/4 = 48.25

Therefore, the quotient of 556 and 16 is:

556/16 = 34 1/4

The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.

When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.

Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.

Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.

There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.

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The given parametric equations are X(t) = -3/2 + 2t and y(t) = vt² + 16, the rate of change of y with respect to "t" when t = 3 is 6v

We have the parametric equations that are X(t) = -3/2 + 2t and y(t) = vt² + 16.

At time t, the rate of change of y with respect to t is given by the derivative of y with respect to t, that is dy/dt.

So, y(t) = vt² + 16

Differentiating with respect to t, we get

⇒ dy/dt = 2vt.

Now, t = 3 gives us,

y(3) = v(3)² + 16 ⇒ 9v + 16.

Therefore, the rate of change of y with respect to t at t = 3 is

dy/dt ⇒ 2vt ⇒ 2v(3) ⇒ 6v.

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Answer:

10 sides

Step-by-step explanation:

We can use the formula for the sum of the interior angles of a polygon to solve this problem. The formula for the sum of the interior angles of a polygon with n sides, where S is the sum of the interior angles, and n is the number of sides of the polygon is:

S = (n - 2) x 180 degrees

If the sum of the interior angles is 1440 degrees, we can set this equal to the formula and solve for n:

1440 = (n - 2) x 180

Dividing both sides by 180, we get:

8 = n - 2

Adding 2 to both sides, we get:

n = 10

Therefore, a polygon with a sum of interior angles of 1440 degrees has 10 sides.

Jen has 54 pages left to read to meet her assignment requirement.

The inequality that represents this situation is p ≥ 85 - 31

To find how many pages Jen has left to read, we can subtract the number of pages she has already read from the minimum number of pages she needs to read.

The minimum number of pages Jen needs to read is 85, and she has already read 31 pages. So, the number of pages she has left to read, p, can be found by:

p = 85 - 31

p = 54

Therefore, Jen has 54 pages left to read.

To represent this situation with an inequality, we can use:

p ≥ 85 - 31

This inequality states that the number of pages Jen still needs to read, p, must be greater than or equal to the difference between the minimum number of pages she needs to read (85) and the number of pages she has already read (31).

Solving for p:

p ≥ 85 - 31

p ≥ 54

This means that Jen must read at least 54 more pages to meet her assignment requirement.

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a) To write the ratio of the number of machines to the number of crates packed per day in the form 1: n, we need to find the number of crates packed per day per machine. We can do this by dividing the total number of crates packed per day by the number of machines:

Number of crates packed per day per machine = 150 crates/day ÷ 60 machines = 2.5 crates/machine/day

Therefore, the ratio of the number of machines to the number of crates packed per day in the form 1: n is 1:2.5 or 2:5.

b) To find out how many crates of limes 70 of these machines would pack per day, we can use the ratio from part (a) to set up a proportion:

1 machine : 2.5 crates/day = 70 machines : x crates/day

Solving for x, we get:

x = (70 machines × 2.5 crates/day) / 1 machine = 175 crates/day

Therefore, 70 of these machines would pack 175 crates of limes per day.

Step-by-step explanation:

a) The ratio of the number of machines to the number of crates packed per day can be written as:

60 : 150

To simplify this ratio, we can divide both sides by 10:

6 : 15

Finally, we can divide both sides by 3 to get the ratio in the form 1 : n:

1 : 2.5

Therefore, the ratio of the number of machines to the number of crates packed per day is 1 : 2.5.

b) If 60 machines can pack 150 crates per day, then one machine can pack:

150/60 = 2.5 crates per day

So, 70 machines can pack:

70 × 2.5 = 175 crates per day

Therefore, 70 machines can pack 175 crates of limes per day.