the perimeter of an isosceles triangle is 56 in. the ratio of the sides is 5:4. find the lengths of the sides and the base of the triangle

An expression for the number of amoebas after 24 hours is 1 × 2²⁴ = 16,777,216

Single-celled creatures knοwn as amοebas reprοduce asexually. An amοeba begins tο reprοduce when its genetic material dοubles, twο nuclei are fοrmed, and it begins tο alter shape by develοping a thin "waist" in the centre. Typically, this prοcedure gοes οn until the cells are finally divided intο twο.

Amοeba reprοduce typically asexually thrοugh a prοcess called binary fissiοn. The cell splits intο twο daughter cells οf equal size fοllοwing the replicatiοn οf its genetic material by mitοtic divisiοn.

a. It is given that an amοeba divides tο fοrm twο amοebas after οne hοur sο there are 2 amοebas after 1 hοur.

b. It is given that οne hοur later, each οf the twο amοebas divides tο fοrm twο mοre amοebas sο there are 2×2=4 amοebas after 2 hοurs.

c. The number οf amοebas is dοubling after each hοur since each amοeba divides intο twο amοebas every hοur. This means that the number οf amοebas after 6 hοurs can be fοund by multiplying the οriginal number οf amοebas, which was 1, by 2 six times. The number οf amοebas after 6 hοurs is then 1 × 2⁶ = 2⁶= 64 amοebas.

d. Using the same pattern frοm part (c), the number οf amοebas after 24 hοurs is 1 × 2²⁴ = 2²⁴ = 16,777,216 amοebas.

Expression = 1 × 2²⁴ = 16,777,216

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The width of the rectangular garden is 9.5 feet.

Given that the perimeter of a rectangular garden is 43.8 feet and its length is 12.4 feet.

Let's assume the width of the rectangular garden be "w".

Now we need to find the width of the garden.

Solution: Perimeter of a rectangular garden is given by the formula: P = 2(l + w)

where l = length and w = width.

Substituting the given values in the above formula,

we get43.8 = 2(12.4 + w)

We can solve for "w" by simplifying the above equation.

43.8 = 24.8 + 2w43.8 - 24.8 = 2w19 = 2w

Dividing both sides by 2,we get

w = 9.5 feet.

Therefore, the width of the rectangular garden is 9.5 feet.

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The repair costs $90 for parts, plus $70 per hour for labor describes the situation. The solution has been obtained by using the equation.

What is an equation?

An equation is an assertion that two expressions containing variables and/or numbers are equivalent. The basic driving factors behind the growth of mathematics have been the attempts to rationally answer equations, which are essentially questions.

We are given an equation of the function as C(x) = 90 + 70x.

This depicts that $90 is fixed cost whereas $70 is variable cost and is dependent on the value of x.

So, the statement that describes the given situation is that the he repair costs $90 for parts, plus $70 per hour for labor.

Hence, the fourth option is the correct option.

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The sample space for rolling the game piece is S = {A, B, C, D}

In mathematics, a set is a well-defined collection of distinct objects, which can be anything like numbers, letters, people, or even other sets. A set is usually denoted by curly braces {} enclosing its elements separated by commas. For example, the set of natural numbers less than or equal to 5 can be denoted as {1, 2, 3, 4, 5}.

Sets can also be described by various methods such as by listing its elements, by set-builder notation, or by using a Venn diagram to visualize relationships between sets. A set can have any number of elements, including none (empty set), and can also have infinite number of elements.

Sets can be combined through set operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements that belong to either A or B (or both). The intersection of two sets A and B is a set that contains all the elements that belong to both A and B. The complement of a set A is the set of all elements that are not in A.

The sample space for rolling the game piece can be represented by the set of possible outcomes, which are the labels on the faces of the game piece. Therefore, the sample space is:

S = {A, B, C, D}

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Answer: Rectangular prism & Cylinder

Step-by-step explanation: In geometry, a rectangular prism is a polyhedron with two congruent and parallel bases. It is also called a cuboid. A rectangular prism has six faces, and all the faces are in a rectangle shape and have twelve edges. Because of its cross-section along the length, it is said to be a prism.

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The line segment joining the two centers is the axis, that denotes the height of the cylinder.

If an automobile manufacturer of a certain model of car wants to estimate the mileage this model car gets in highway driving. The manufacturer needs to sample at least 39 cars.

We can use the formula for the margin of error in a confidence interval for a mean:

Margin of Error = z* (σ/√n)

Where:

z* is the critical value of the standard normal distribution for the desired level of confidence, which is 90% in this case.

σ is the known population standard deviation, which is 5.7 mpg.

n is the sample size we want to determine.

We want the margin of error to be 1.5 mpg, so we can set up the equation:

1.5 = 1.645 * (5.7 / √n)

where 1.645 is the z-score for 90% confidence level.

Simplifying this equation, we get:

√n = 1.645 * (5.7 / 1.5)

√n = 6.251

Squaring both sides, we get:

n = 39.07

Rounding up to the nearest integer, we get:

n = 39

Therefore, the manufacturer needs to sample at least 39 cars to estimate the highway mileage with a 90% confidence interval and a margin of error of 1.5 mpg.

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This problem is a classic example of applying the stars and bars combinatorial method.

To solve this problem, we need to distribute 23 identical objects into 7 distinct containers so that none of the containers is empty. Let's start by assuming that each container has at least one object. This means we have distributed 7 objects, leaving 16 objects to be distributed.

We can now use the stars and bars method to distribute these 16 objects. Imagine placing all 16 objects in a line, and placing 6 dividers between them to separate them into 7 groups (one for each container). Each group will then receive the objects that are to the left of the divider.

For example, if we have the sequence OO|OOO|O|OOO|OO|OO|O, this corresponds to 2 objects in the first container, 3 objects in the second container, 1 object in the third container, and so on.

The number of ways to place the 6 dividers in the sequence of 16 objects is the same as the number of ways to choose 6 positions out of 16 to place the dividers. This can be computed using the formula for combinations:

$${16 \choose 6} = \frac{16!}{6!(16-6)!} = 8008$$

Therefore, there are 8008 ways to distribute 23 identical objects into 7 distinct containers so that no container is empty.

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The equation that can be used to find the sale price, s, of the pizza is S = 0.8(15).

It is the final amount paid for a product or service and is often lower than the original asking price.

This equation uses the percentage discount of 20%, which can be represented as 0.8, to find the sale price.

To calculate the sale price, the equation multiplies the regular price of $15 by the discount, 0.8.

0.8*15 =12

Therefore, the sale price of the pizza is $12.

The other equations are not correct because they do not take into account the percentage discount of 20%.

S = 0.1(15) does not consider the discount of 20%, as it is multiplying the regular price of $15 by 0.1, which is equivalent to 10%, not 20%.

Similarly, S = 0.115 is incorrect because it is multiplying the regular price of $15 by 1.15, which is equivalent to 115%, not 20%.

Lastly, S=0.8 15 is incorrect because it is not multiplying the regular price of $15 by the discount of 20%, which is 0.8.

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Answer: 3/2

Step-by-step explanation:

To find the slope of the line that passes through the points (2, 1) and (0, -2), we can use the formula:

m = (y2 - y1) / (x2 - x1)

where:

m = slope of the line

(x1, y1) = coordinates of the first point

(x2, y2) = coordinates of the second point

Plugging in the values we have, we get:

m = (-2 - 1) / (0 - 2)

m = -3 / -2

m = 3/2

Therefore, the slope of the line that passes through the points (2, 1) and (0, -2) is 3/2.

If your grade is 88 but you have a test that counts for 25 percent of your total grade and you get an 80, your grade will be 86.

Test scores are an essential aspect of an educational system. Teachers use them to evaluate how well students have grasped concepts or learned material from a class or course. They help in establishing the academic strength and weaknesses of the student.

The test score you got is 80, which makes 25% of the total grade you can have for this course. This means that 0.25*80 = 20 marks will be added to your final grade. Your previous grade was 88, which will not be counted with the test marks.

Hence the marks you will have for the final grade will be 88 + 20 = 108. Divide this number by 1.25 (as 25% is equivalent to 0.25), which results in 86.4. You can round it off to the nearest integer, which is 86.

Therefore, your final grade will be 86.

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The number of nickels Bill has is 10.

Therefore, Bill has 10 nickels and 30 dimes.

The given question is as follows.

Bill has a collection of 40 nickels and dimes.

Together, they add up to $3.50.

Bill have of each coin :

To solve the given problem, let's consider the following steps.

Step 1: Let x be the number of nickels and y be the number of dimes.

Based on the given data, we can form the following two equations:

x + y = 40 ... (1) (because Bill has 40 nickels and dimes)

0.05x + 0.10y = 3.50 ... (2) (because the sum of 40 nickels and dimes is $3.50)

Step 2: Solve the equations (1) and (2) by elimination method by multiplying equation (1) with 0.05 and subtracting it from equation (2).

0.05x + 0.05y = 2 ... (3)0.05x + 0.10y = 3.50 ... (4)

Subtracting equation (3) from equation (4),

we get0.05y = 1.50

Dividing both sides by 0.05, we get

y = 30

Therefore, the number of dimes Bill has is 30.

Step 3: Now, substitute the value of y in equation (1), we get

x + 30 = 40

Subtracting 30 from both sides, we get x = 10.

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Answer:

The equation 3^4 x 2^3 = 6^4+3 is incorrect.

To evaluate the left side of the equation, we first simplify each term using exponent rules:

3^4 = 3 x 3 x 3 x 3 = 81

2^3 = 2 x 2 x 2 = 8

So 3^4 x 2^3 = 81 x 8 = 648

To evaluate the right side of the equation, we simplify the exponent first:

6^4+3 = 6^4 x 6^3 = 1296 x 216 = 279936

Therefore, the corrected equation should be:

3^4 x 2^3 = 648 = 6^4 - 288

Notice that 6^4 - 288 is equal to the original value of 279936, but the equation has been written correctly by moving the 3 to the other side of the equation and changing the operation from addition to subtraction.

From the given information provided, Laura can cut 3 one-thirds strips from the 1 meter long ribbon.

If Laura has a strip of ribbon 1 meter long, we need to find out how many one-thirds strips can be cut from it.

To do this, we need to divide the length of the ribbon by the length of each one-third strip:

Number of one-thirds strips = Length of ribbon / Length of one-third strip

The length of each one-third strip is 1/3 meters, since one-third of a meter is required to make each strip.

So we can substitute these values into the formula:

Number of one-thirds strips = 1 meter / (1/3 meter)

Number of one-thirds strips = 1 meter x (3/1)

Number of one-thirds strips = 3

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The number of license plates that can be made if repetition of letters and digits is allowed is:

67,600

Can be found by multiplying the number of possibilities for each position.

License plates are made using 2 letters followed by 2 digits. In this case, repetition is allowed, which means that each of the 2 letters can be any of the 26 letters of the English alphabet, and each of the 2 digits can be any of the 10 digits from 0 to 9. Thus, the total number of possible license plates can be found by multiplying the number of possibilities for each position.

There are 26 choices for each of the two letter positions, and 10 choices for each of the two digit positions, so the total number of possible license plates is:

26 x 26 x 10 x 10 = 67,600

Therefore, there are 67,600 plates that can be made if repetition of letters and digits is allowed.

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Therefore , the solution of the given problem of angles comes out to be m∠G= 63° is the response to the second component of the query.

The curved lines which make up the ends of a skew are divided by its highest and bottom walls using Cartesian measurements. There is a possibility who two poles will collide at an intersection. Another result of two objects interacting is an angle. They most closely mimic dihedral shapes. Two line beams can be arranged in different ways between their extremities to form a two-dimensional curve.

Here,

m∠E + m∠F + m∠G = 180°

Additionally, we are aware that mE = (5x + 6)°, mF = (4x - 6)°, and mG = (5x - 2)°. When we enter these numbers into the formula above, we obtain:

=> (5x + 6)° + (4x - 6)° + (5x - 2)° = 180°

When we simplify and find x, we obtain:

=> 14x - 2 = 180

=> 14x = 182

=> x = 13

Now that we know the three vectors' values:

=> m∠E = (5x + 6)° = (5(13) + 6)° = 71°

=> m∠F = (4x - 6)° = (4(13) - 6)° = 46°

=> m∠G = (5x - 2)° = (5(13) - 2)° = 63°

In light of this, mE = 71°, mF = 46°, and mG = 63°.

The first portion of the question has the following solution:

=>  m∠EFG = m∠E + m∠F + m∠G = 71° + 46° + 63° = 180°.

m∠G= 63° is the response to the second component of the query.

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Answer: 60%

Step-by-step explanation:

As mentioned earlier, we need to know the number of senior nutrition majors and sophomore non-nutrition majors to calculate the exact probability. Without this information, we cannot provide a specific answer to the question.

However, we can provide a general formula for computing the probability, assuming that the selections are made without replacement and the population of students is large enough to assume independence:

Probability of selecting a senior nutrition major and then a sophomore non-nutrition major = (Number of senior nutrition majors / Total number of students) × (Number of sophomore non-nutrition majors / (Total number of students - 1))

Once we have the values for the number of senior nutrition majors and sophomore non-nutrition majors, we can substitute them into this formula to obtain the probability, which will be a decimal number rounded to four decimal places.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 850\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years \end{cases} \\\\\\ 850 = 500[1+(0.1)(t)] \implies \cfrac{850}{500}=1+0.10t\implies \cfrac{17}{10}=1+0.10t \\\\\\ \cfrac{17}{10}-1=0.10t\implies \cfrac{7}{10}=0.10t\implies \cfrac{7}{(10)(0.10)}=t\implies 7=t[/tex]

The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:

P(x=0) = (p^5)*(q^0) = p^5

In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.

For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.

To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.

The correct question is:

A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective

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Answer: The correct answer is "Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim."

Step-by-step explanation:

I took the test

The probability of selecting a vowel from a hat with letters of the alphabet is 5/26 or approximately 0.1923. There are 5 vowels and 26 total letters.

There are 5 vowels in the English alphabet: A, E, I, O, and U. Therefore, the number of favorable outcomes (i.e., the number of vowels in the hat) is 5.

There are a total of 26 letters in the English alphabet. Therefore, the number of possible outcomes (i.e., the number of letters in the hat) is 26.

The probability of selecting a vowel is the ratio of the number of favorable outcomes to the number of possible outcomes:

P(vowel) = number of favorable outcomes / number of possible outcomes

P(vowel) = 5 / 26

Therefore, the probability of selecting a vowel is 5/26 or approximately 0.1923 (rounded to four decimal places).

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Answer:

5

26

5/26

19

Step-by-step explanation:

Answer:

................

Step-by-step explanation:

.................

Answer:

To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.

Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.

Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.

Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.

The 90% confidence interval for the population proportion is (0.1171, 0.1829).

To calculate the confidence interval, we first need to find the point estimate of the population proportion. The point estimate is the sample proportion which is given by:

p-bar = x/n = 60/400 = 0.15

where x is the number of items that failed the test and n is the sample size.

Next, we need to find the margin of error, which is given by:

ME = z*√(p_bar(1-p_bar)/n)

where z is the z-score corresponding to the confidence level, p_bar is the sample proportion, and n is the sample size.

For a 90% confidence level, the z-score is 1.645 (using a standard normal distribution table). Substituting the values, we get:

ME = 1.645*√(0.15(1-0.15)/400) = 0.0329

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:

CI = p_bar ± ME = 0.15 ± 0.0329 = (0.1171, 0.1829)

Therefore, we are 90% confident that the true population proportion of items that will fail the test is between 0.1171 and 0.1829.

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Rounded to two decimal places, the value of the test statistic is 0.41.

The value of the test statistic to compare the publisher's reported percentage of 75% and the marketing executive's claim that the actual percentage is different can be found by using the formula z = (p1 - p2)/(sqrt[p*(1-p)*((1/n1)+(1/n2))]), where p is the pooled proportion, p1 is the proportion of the publisher's readers owning the particular make of car, p2 is the proportion of the random sample owning the particular make of car, n1 is the total number of the publisher's readers, and n2 is the total number of the random sample.

In this case, p = [tex](75% + 69%)/2 = 72%, p1 = 75%, p2 = 69%, n1[/tex]is unknown, n2 = 250. Thus, the test statistic is z =[tex](75%-69%)/(sqrt[72%(1-72%)((1/n1)+(1/250))]) = 0.41.[/tex]

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The inequality to determine how much more money he needs to save so he can buy the shoes is x ≥ $45

Let x be the amount of money Jordan still needs to save to buy the shoes.

The total cost of the shoes is $75, and Jordan has already saved $30. Therefore, the amount of money he still needs to save is:

x = $75 - $30

Simplifying the right side:

x = $45

So, the inequality that represents how much more money Jordan needs to save is:

x ≥ $45

This means that Jordan needs to save at least $45 more to be able to buy the shoes.

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Yuri will spend $ X more on concrete than on soil and wood.

When answering questions on Brainly, it is important to be factually accurate, concise, and professional.

It is also important to provide a step-by-step explanation of how you arrived at your answer.

The question is asking about the cost of materials for a patio, garden, and deck.

Let's break down the information we have.

Area of the patio = enter your response

Here

Cost of concrete = $ enter your response

Here

Area of the garden = enter your response

here

Cost of soil = $ enter your response

here

Total area of the deck = enter your response

here

Cost of wood = $ enter your response

here

Yuri will spend $ enter your response here more on concrete than on soil and wood.

To find the cost of each material, we need to multiply the area by the cost per unit area.

For example, the cost of concrete would be the area of the patio multiplied by the cost of concrete per unit area.

Let's call the cost per unit area for concrete C, the cost per unit area for soil S, and the cost per unit area for wood W.

Area of patio = P

Cost of concrete = C

Area of garden = G

Cost of soil = S

Total area of deck = D

Cost of wood = W

Yuri will spend X more on concrete than on soil and wood.

To find the values of P, C, G, S, D, and W, we need to use the information given in the question.

However, some values are missing.

We can use the given information to create equations that will help us find these values.

For example, we know that the total area of the deck is the sum of the area of the patio and the area of the garden, so we can write:

D = P + G

Similarly, we can write an equation for the cost of each material.

For example, the cost of concrete is the area of the patio multiplied by the cost per unit area for concrete, so we can write:

C = P * C

Similarly, we can write equations for the cost of soil and wood:

S = G * W, W = D * W

Now we have three equations and three unknowns: P, G, and D. We can solve this system of equations to find these values.

Let's solve for P and G first.

We'll use the equation

D = P + G

to eliminate G from the equations.

C = P * CS = G * WP = D - G

Substitute P = D - G into the first two equations.

C = (D - G) * CW = D * W - G * W

Now we have two equations and two unknowns: D and G.

We can solve for these values.

We'll use the equation

W = D * W - G * W

to eliminate W from the equations.

C = (D - G) * CS = G * SD = P + G = 2G - (W / C)

Substitute D = P + G into the first two equations.

C = P * C + G * CS = G * SW = P + G - DC = P * C + (D - P) * C + (W / C) * C = 2P * C + W

We can now solve for P, G, and D.

P = (C + S + W / C) / 2G = (S + W / C) / 2D = P + G = (C + S + W / C) / 2 + (S + W / C) / 2P = enter your response

here

C = enter your response

here

S = enter your response

here

W = enter your response

here

G = enter your response

here

D = enter your response

here

Now we can find the value of X, which is the difference between the cost of concrete and the combined cost of soil and wood.

X = C - (S + W)X = enter your response.

The area of the patio is enter your response here ​, so the cost of concrete is ​$ enter your response here. The area of the garden is enter your response here ​, so the cost of soil is ​$ enter your response here. The total area of the deck is enter your response here ​, so the cost of wood is ​$ enter your response here.

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Question:

Yuri bought a new house. The diagram shows the layout of his backyard. Yuri is designing improvements that he wants to make. Yuri plans to fill the patio with concrete, the garden with a special soil mixture, and the remaining areas that surround the hot tub with a wood deck. The table shows the costs associated with each project. How much more will Yuri spend on concrete than on soil and wood?

Answer:

remember, in order to calculate the weight on earth, we need to multiply the mass of the object with the force of Gravity (9.8 m/s^2 on earth)

so, her weight would be:

48 x 9.8 = 470.4 >>>>>>> Will be 470 if we round it to the nearest whole number.

Step-by-step explanation: Hope this helps. Mark me brainliest!! :)))

Answer: 470

Step-by-step explanation:

The correct option is c: 46lb x (16 oz / 1lb). Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

The same attribute is expressed using a unit conversion, but in a different measurement unit. For example say, time can be mentioned in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Measurements are frequently offered in one set of measurements, like feet, but are required in another set, like chains. A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.

Given data:

ratio of ounces to pounds = 16:1

16 ounce / 1 pound

Let the weight of dog in ounce be 'x'.

weight of dog in pounds = 46 pounds.

ratio : x ounce /  46 pounds

Equating both ratios:

16 ounce / 1 pound = x ounce /  46 pounds

Cross multiplying:

x = 16*46  ounce

x = 736 ounce

The correct option is c: 46lb x (16 oz / 1lb)

Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

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Complete question is-

The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight

ounces. Which ratio shows the conversion to ounces?

The full question is attached.

The theoretical probability of drawing a blue marble from a jar containing 21 brown and 19 blue marbles is 19/40, or 0.475.

To calculate this, divide the number of blue marbles by the total number of marbles in the jar. 19 divided by 40 equals 0.475, or 19/40. This means that there is a 47.5% chance of drawing a blue marble from the jar.

The probability of drawing a specific marble from the jar can be expressed using the formula P(A) = n(A)/n(T).

In this example, the probability P(A) is the chance of drawing a blue marble, n(A) is the number of blue marbles (19) and n(T) is the total number of marbles in the jar (40). Therefore, P(A) = 19/40 = 0.475.

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