A veterinarian uses a specific formula to calculate the dosage of an antibiotic given to dogs with bacterial infections. For each 10 pounds of a dog's weight, she treats the dog with 50 mg of antibiotic per dose. Which of the following graphs describes the relationship between a dog's weight and the antibiotic dosage used to treat it?

The system of equations where the combination of the candies gives you a total of 22 points are:

x + y = 9

2x + 3y = 22

To create the equations, we shall first define the variables:

x = the number of purple candies

y = the number of yellow candies

Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.

Then, we would make sure that the total number of candies selected is 9.

The first equation represents the total number of candies selected:

x + y = 9

The second equation represents the total number of points obtained:

2x + 3y = 22

Therefore, the system of equations is:

x + y = 9

2x + 3y = 22

This is a system of linear equations.

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The fountain will occupy a fraction of 50/173 of the Total area of the courtyard.

Let A be the area of the courtyard and F be the area of the fountain.

We know that the area of the stone-covered part of the courtyard is 246 square feet.

So, the area of the whole courtyard is A = 246 + F square feet.

The fraction of the area of the courtyard occupied by the fountain is given by:

F / A = F / (246 + F)

We can simplify this expression by multiplying the numerator and denominator by the reciprocal of the denominator:

F / A = F / (246 + F) * (1 / (246 + F))

F / A = F / (246 * (246 + F))

F / A = 1 / (246 / F + 1)

We don't know F yet, but we can use the fact that the fountain is rectangular to set up an equation relating the length and width of the fountain:

F = L * W

where L is the length of the fountain and W is the width of the fountain.

We also know that the perimeter of the fountain is 50 feet:

2L + 2W = 50

Simplifying this equation, we get:

L + W = 25

Solving for one variable in terms of the other, we get:

L = 25 - W

Substituting this expression for L into the equation for F, we get:

F = (25 - W) * W

Expanding this expression, we get:

F = 25W - W^2

We also know that the cost of the fountain is $600, which includes installation. So, we can set up another equation relating the cost of the fountain to its dimensions:

1.5LW = 600

Substituting 25 - W for L, we get:

1.5(25 - W)W = 600

Expanding and simplifying this equation, we get:

W^2 - 25W + 400 = 0

Solving this quadratic equation, we get:

W = 20 or W = 5

We reject the solution W = 5 because it implies a negative length for the fountain, which is not physically possible. Therefore, the width of the fountain is W = 20 feet and its length is L = 25 - W = 5 feet.

The area of the fountain is therefore:

F = L * W = 5 * 20 = 100 square feet

The fraction of the area of the courtyard occupied by the fountain is

F / A = 100 / (246 + 100) = 100 / 346 = 50 / 173

So, the fountain will occupy a fraction of 50/173 of the total area of the courtyard.

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Answer:

1. 23

2. 8

Step-by-step explanation:

☆Cross multiply.

\( \frac{2}{10} = \frac{4}{a - 3} \\ \\ 40 = 2(a - 3) \\ 40 = 2a - 6 \\ \frac{ + 6 = \: \: \: \: \: \: \: \: + 6}{ \frac{46}{2} = \frac{2a}{2} } \\ \\ 23 = a\)

--------

\( \frac{k}{6} = \frac{4}{3} \\ \\ \frac{24}{ 3} = \frac{3k}{3} \\ \\ 8 = k\)

Answer:

(a) Approximately 68 % of women in this group have platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7.

(b) Approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.

Step-by-step explanation:

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 257.62 and a standard deviation of 62.1

Let X = the blood platelet counts of a group of women

So, X ~ Normal(\(\mu=257.62, \sigma^{2} =62.1^{2}\))

Now, the empirical rule states that;

(a) The approximate percentage of women with platelet counts within 1 standard deviation of the mean, or between 195.5 and 319.7 is 68% according to the empirical rule.

(b) The approximate percentage of women with platelet counts between 71.3 and 443.9 is given by;

       z-score of 443.9 =  \(\frac{X-\mu}{\sigma}\)

                                   =  \(\frac{443.9-257.62}{62.1}\)  = 3

       z-score of 71.3 =  \(\frac{X-\mu}{\sigma}\)

                                =  \(\frac{71.3-257.62}{62.1}\)  = -3

So, approximately 99.7% of women in this group have platelet counts between 71.3 and 443.9.

Answer:

4 2/3

Step-by-step explanation:

8×21=168

168÷36(1 yard in inches)=4 with a remainder of 24

24/36 can both be divided by 12 so its now been reduced to 2/3

9514 1404 393

Answer:

  54 3/5 mi/h

Step-by-step explanation:

To find miles per hour, divide miles by hours.

  (18 1/5 mi)/(1/3 h) = (18 1/5)(3/1) mi/h = 54 3/5 mi/h

Answer:

88 percent

Step-by-step explanation:

100/25 is 4 so 4 times 22 is 88 percent

Answer:

54

Step-by-step explanation:

Answer:

54

Step-by-step explanation:

Answer:

P(8) = 1/9

Step-by-step explanation:

There are 9 balls, 1,2,3,4,5,6,7,8,9

We want to get ball 8

P(8) = number of balls marked 8/ total number of balls

       = 1/9

Answer:

P = 1/9

Step-by-step explanation:

Probability of selecting the ball marked with 8

\(\sf Probability = \dfrac{Number\: of \:favorable\: outcomes }{ Total \:number\: of\: possible\: outcomes}\\\\\sf Probability = \dfrac{1 }{9}\)

The Division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

To find the division of the sum of (7/8), (15/4), and (1/12) by their multiplication, we first need to calculate the sum and multiplication of the given fractions.

The sum of the fractions is:

(7/8) + (15/4) + (1/12)

To add these fractions, we need a common denominator. The least common multiple of 8, 4, and 12 is 24. Let's convert each fraction to have a denominator of 24:

(7/8) = (21/24)

(15/4) = (90/24)

(1/12) = (2/24)

Now we can add the fractions:

(21/24) + (90/24) + (2/24) = (113/24)

The multiplication of the fractions is:

(7/8) * (15/4) * (1/12)

To multiply fractions, we multiply the numerators and denominators:

(7*15*1) / (8*4*12) = (7/96)

Now we can divide the sum of the fractions by their multiplication:

(113/24) / (7/96)

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:

(113/24) * (96/7) = (2712/168)

Therefore, the division of the sum of (7/8), (15/4), and (1/12) by their multiplication is (2712/168).

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Answer: To calculate the growth factor, you would need to determine the slope of the line of best fit, which is typically calculated using linear regression. The slope represents the change in the y-variable (in this case, age) per unit change in the x-variable (in this case, diameter).

Step-by-step explanation: So if the slope of the line of best fit is, for example, 5 years per inch, then the growth factor for the tree would be 1/5 (or 0.2) inches per year. This means that for every inch of diameter growth, the tree would grow 0.2 years in age.

It's important to note that the growth factor can vary depending on the particular species of tree, environmental factors, and other variables.

The answer of the given question based on the equation is , the unknown number is 6.

An equation is the  mathematical statement that asserts equality of the two expressions. It typically consists of the two expressions separated by equal sign " = ". The expressions can include variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Solving an equation involves finding the value(s) of the variable(s) that make the equation true.

The statement can be translated into an equation as follows:

2(y - 2) = 8

Simplifying the equation, we can distribute the 2 on the left-hand side:

2y - 4 = 8

Then, we can add 4 to both sides to isolate the variable:

2y = 12

Finally, we divide both sides by 2 to solve for y:

y = 6

Therefore, the unknown number is 6.

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Answer: $18.75

Step-by-step explanation:

1 - 3/8 = 5/8

12 x 5/8 = 7.5

7.5 x 2.5 = 18.75

Dave spent $18.75, in filling his car's tank of capacity 12 gallons up to the capacity, which was 3/8th filled already, at the unit rate of $2.50 per gallon of gas.

The unit rate is the quantity (cost/distance/time, etc.) for one unit of another quantity (cost/distance/time, etc.).

In the question, we are informed that the gas tank of Dave's car has a capacity of 12 gallons. The tank was 3/8 full before Dave filled it to capacity. It cost him $2.50 per gallon of gas.

We are asked the amount Dave spent.

The unit rate of gas is $2.50 per gallon.

To find the total amount spent by Dave, we need to find the volume of gas he filled and then multiply that volume with the unit rate.

The capacity of Dave's car's tank = 12 gallons.

Gas it already had = 3/8th of capacity,

or, gas it already had = 3/8 * 12 = 4.5 gallons.

Therefore, the volume of gas Dave filled = 12 - 4.5 gallons = 7.5 gallons.

The amount spent by Dave = Volume filled*Unit rate = $ 7.5 * 2.5 = $18.75.

Therefore, Dave spent $18.75, in filling his car's tank of capacity 12 gallons up to the capacity, which was 3/8th filled already, at the unit rate of $2.50 per gallon of gas.

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Answer:

A - Rational

B - Not Rational

C - Not Rational

Hope this helps!

Step-by-step explanation:

Answer:

I think they are all irrational, but im not 100% sure

Step-by-step explanation:

The relation that is a function is relation (b)

The ordered pairs in the option represent the given parameters

For a relation (i.e. the ordered pairs) to be a function, the following must be true:

Each y value on the ordered pair must have exactly one x value

i.e. no x value must point to the different y value

Having said that the relation that is a function is relation (b)

Hence, the the relation that is a function is relation (b)2

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The conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.

According to the question,

We have the following information:

Mercury travels at a rate of approximately 30 miles per second.

We know that there are 1/60 minutes in 1 second.

So, we have the following expression for conversion:

30/(1/60) miles per minute

30*60

1800 miles per minute

Now, we know that following formula is used to find distance:

Distance = speed*time

Distance = 1800*3

Distance = 5400 miles

Hence, the conversion of 30 miles per second into miles per minute is 1800 miles per minute and Mercury will travel 5400 miles in 3 minutes at this rate.

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By algebra properties and trigonometric formulas, the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b².

In this problem we must prove that the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b², this can be done both by algebra properties and trigonometric formulas. First, write the given expression:

(a · cos A + b · sin A)² + (a · sin A - b · cos A)²

Second, expand the expression by algebra properties:

a² · cos² A + 2 · a · b · cos A · sin A + b² · sin² A + a² · sin² A - 2 · a · b · cos A · sin A + b² · cos² A

(a² + b²) · cos² A + (2 · a · b - 2 · a · b) · cos A · sin A + (a² + b²) · sin² A

(a² + b²) · (cos² A + sin² A)

Third, use the fundamental trigonometric formula:

a² + b²

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Answer:

I dont think you can read whats below so te amo and sorry i couldnt answer your question

Step-by-step explanation:

Who ever is reading this:

I love u.

U matter.

The world needs u

hang in there ik it may be bad but u deserve the world <3

ur beautiful no matter ur shape, size, color, gender.. anything

don't give up i need u to live.

i wish i could take everyones problems so yall wouldn't have to have em but i cant so just know ily and if anyone needs to talk u can talk to me

Pls pass this on. Everyone deserves to know this. ♥️♥️

Answer:

e. The mayor uses a significance level of 0.05 and n = 1,000 voters.

Step-by-step explanation:

Power of a test:

For a high power of a test, two conditions are needed:

Large significance level.

Large sample.

In this question:

A significance level of 0.05 will lead to a higher power than a significance level of 0.01, which means that the answer is between options d and e.

A test with a sample of 1000 has a higher power than a test with a sample of 500, and thus, the answer is given by option e.

Answer:

If they are asking amount it is $4800.893013; $4800 (nearest dollar)

If they are asking the amount for interest is $900.8930129; $900 (nearest dollar)

Step-by-step explanation:

Compound interest Formula:

Amount = principle( 1+ rate/100)^n

Information from the question.

-So how you put it is the principle is $3900; the rate is 2.1%; the n is 10.

How to apply it?

- Just substitute in the values;

Amount=3900(1+2.1/100)^10

=4800.893013

~4800 ( nearest dollar)

》That is for amount.

Interest=4800.893013-3900

=900.893013

~900 ( nearest dollar)

》That is for interest.

Hope it helps!!!!:))

Answer:

Step-by-step explanation:

A=Pert=3900e(0.021)(10)≈4811.34

The account is worth $4811 after 10 years.

Answer:

Volume : 94

Step-by-step explanation:

2(4 x 5) = 40

2(3 x 5) = 30

2(3 x 4) = 24

------------------

40 + 30 + 24 = 94

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

Answer:

3 cups of orange juice.

Step-by-step explanation:

Multiply 1/4 by 4 to get 1

Also multiply 3/4 to get 3

Answer:

For this problem, x has multiple values, so we will solve for both.

Step-by-step explanation:

\(x^2+10x-11=11-11\\x^2+10x-11=0\\\)

Quadratic rule

\(x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

\(\mathrm{For\:} a=1,\:b=10,\:c=-11\)

\(x_{1,\:2}=\frac{-10\pm \sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}}{2\cdot \:1}\)

Dealing with radicals

\(\sqrt{10^2-4\cdot \:1\cdot \left(-11\right)}\\=\sqrt{10^2+4\cdot \:1\cdot \:11}\\=\sqrt{10^2+44}\\=\sqrt{100+44}\\=\sqrt{144}\\=\sqrt{12^2}\\=12\\\)

Multi-solution expression

\(x_1=\frac{-10+12}{2\cdot \:1},\:x_2=\frac{-10-12}{2\cdot \:1}\)

Solve for x₁

\(\frac{-10+12}{2\cdot \:1}\\=\frac{2}{2\cdot \:1}\\=\frac{2}{2}\\=1\)

Solve for x₂

\(\frac{-10-12}{2\cdot \:1}\\=\frac{-22}{2\cdot \:1}\\=\frac{-22}{2}\\= -\frac{22}{2}\\= -11\)

Thus, x has 2 values for 2 different numbers:

x₁ = 1

x₂ = -11

➲ Hope this helps!

The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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The number of hot dogs sold is an illustration of a linear equation

The number of hot dogs sold in 9 commercials is 90

The linear equation that represents the amount of hot dogs is given as:

\(y = 10x\)

Where x represents the number of commercial timeouts

So, we have:

\(y = 10 * 9\)

\(y = 90\)

Hence, the number of hot dogs sold in 9 commercials is 90

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If the straight angle is bisected then we get two equal angles so it is nothing but right angles.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. The angle that lies in the plane does not have to be in the Euclidean space. Angles are referred to as dihedral angles if they are created by the intersection of two planes in a space other than Euclidean. The sign "" is used to denote angles. The Greek letter,,, etc. can be used to represent the angle measurement between the two rays. If the Angles are measured in relation to a line, and there are two sorts of angles: positive angles and negative angles.

Positive Angle: A positive angle is one that is in the counterclockwise direction.

Negative Angle: A negative angle is one that is measured in the clockwise direction.

If the straight angle is bisected then we get two equal angles so it is nothing but right angles.

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Answer: 11,

Step-by-step explanation: