This graph shows the amount of medicine in a patient after receiving an injection.

How much medicine was in the patient after `4` hours?
729 mg
144 mg
2/3 mg
4 mg

Answer: 816

Step-by-step explanation:

h(3) = 1248 - 160(3) + 16(3)

h(3)= 1248 - 480 + 48

h(3)= 816

Answer:

2

Step-by-step explanation:

[tex] \: \: \: \: \: \: \: \large{\frac{5}{8}} \: \div \large{\frac{5}{16}} \\ \\ = \frac{5}{8} \times \frac{16}{5} \\ \\ = \green 2 \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:

2

Step-by-step explanation:

(5/8) ÷ (5/16)

= (5*16) ÷ (8*5)

= 80 ÷ 40

= 2

Calculating the likelihood of experiments happening is one of the branches of mathematics named as probability. The probability that none of the 2 vials have hairline cracks is 0.0565.

The study of probabilities, which exists defined by the ratio of favorable occurrences to probable cases, exists comprehended as probability.

The probability that there won't be any hairline cracks = 13/53

If you choose two vials at random from the delivery

Probability (avoiding hairline cracks) = 13 - 1/53 - 1

Probability (avoiding hairline cracks) = 12/52

To find the chance that neither of the two vials has a hairline crack is

(13/53) × (12/52) = 0.2452 × 0.2307

= 0.0565

The probability that none of the 2 vials have hairline cracks is 0.0565

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Step-by-step explanation:

420x1800=756000

so 756k items in 30 minutes

|x-5| + 7 = 13 is equal to x= -11 and x = 1.

[tex]|x-5|+7=13[/tex]

Subtract 7 from both sides

[tex]|x-5|+7-7=13-7[/tex]

Simplify

[tex]|x-5|=6[/tex]

Apply absolute rule: If [tex]$|u|=a, a > 0$[/tex] then [tex]$u=a$[/tex] or [tex]$u=-a$[/tex] [tex]$x-5=-6$[/tex] or [tex]$x-5=6$[/tex]

[tex]$$x-5=-6 \text { or } x-5=6$$[/tex]

[tex]$$x=-1 \text { or } x=11$$[/tex]

Making something simpler is making it less intricate or crowded. When you describe a complex mathematical idea to a youngster in words they can easily comprehend, you are simplifying. When you eliminate many of the tasks that were keeping you occupied and stressed out, you have simplified.

Making something simpler refers to making it simpler to accomplish or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers.

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The solution of the differential equation as given in the task content is; ln(5p +a)/5 + C = t

It follows from the task content that the solution of the differential equation is required.

Given;

dp/dt=5p +a

To find; solution to the differential equation;

By variable separation; the resulting equation is;

dp/(5p +a) = dt

By integrating both sides of the equation; we have;

ln(5p +a)/5 + C = t

Ultimately, although both sides of the equation integrated yield a constant of integration as the integral is indefinite, the two constants have been combined into constant, C as in the equation above.

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Answer:

25

Step-by-step explanation:

180 - 25 = 155

180 - 155 = 25

Answer:

a. [tex]y=38x[/tex].

Step-by-step explanation:

Let y represent distance in miles and x represent gallons of gas.    

a. First of all, we will find mileage of Ann's car by dividing total distance traveled by total fuel consumed.

Since Ann's can travels 38 miles per gallon, so distance covered by using x gallons on gas would be [tex]38x[/tex] .

Therefore, our required equation would be [tex]y=38x[/tex].

In tape diagram, The number of visits Juan must make to earn a free movie ticket

20 + 7.5V = 125

What is a tape diagram in math?

How a tape diagram appears?

represents the number of visits Juan must make to earn a free movie ticket

20 + 7.5V = 125

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Power of a number 3⁶⁰ is the simplest form of math equation.

What is the power of a number?

What are power and exponent?

3^2*5*2*3 = 3⁶⁰

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Interest is Rs.96  and Total amount payback is Rs.3096.

Principal (P) = Rs.3000

Rate of  interest (R) = 1.6%

Number of years (N) = 2 yrs

Simple interest = PNR/100

= (3000*1.6*2)/100

=(9600/100

=96Rs

Total Amount (A) = P+I

=3000+96

=3096Rs

The principal, or initial balance of your account, is where interest is calculated. This could be the initial sum of a loan or an investment. The simplest way to compute interest is as a percentage of the principal .Only relatively short-term loans frequently include one-time basic interest charges. Interest is frequently paid on a daily, monthly, quarterly, or annual basis for loans with longer terms. In that scenario, interest would be consistently earned.

Hence, the interest for the above principle is 96Rs and the total amount to be payback is 3096Rs.

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Answer:   w > 50

This is because we are focusing on weights (w) that are larger than 50

We won't have an "or equal to" as part of this.

An inequality for the given scenario is;

⇒ w > 50

Here,

The given scenario is;

For safety, all dogs at a dog park who weigh, w, more than 50 pounds must play in Area 2.

We have to find the inequality.

What is Inequality?

An inequality compares two values, showing if one is less than, greater than.

Now,

Weight of all dogs = w

And, Weight of all dogs w is more than 50 pounds.

Hence, An inequality for the given scenario is;

⇒ w > 50

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Answer:

x [tex]\leq[/tex] 28

Step-by-step explanation:

lets say you chose 27 . 27 - 13 = 14 . thats not enough . but everything 28 and above would work for x . so x would be equal to or greater than 28 . hope this helps :)

Answer:

314.0063694

Step-by-step explanation:

You will have to use the pythogoras. triple to solve the equation

Answer:

Step-by-step explanation:

the diagonal is the hypotenuse of the two triangles that form the rectangle (see figure) we solve with Pythagoras

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

a² = b²+ c²

a² = 250² + 190²

a² = 62500 + 36100

a² = 98600

a = √98600

a = 314 m

Answer:

21 seconds

Step-by-step explanation:

First let's find out how long it would take for them to have the same score.

160 + 5s = 100 + 8s

160 = 100 + 3s

60 = 3s

20 = s

Since it takes 20 seconds to get the same score and Raul get's more points every second, it would take 21 seconds for Raul to take the lead.

A(0,-3), B(3,-2), C(1, -1) (B) is  the coordinates of ΔA'' B'' C'' after a reflection in the x -axis and a rotation of 180.

What does the term "coordinates" mean?

A 180 degree clockwise rotation will change the coordinates as follows (x,y) --> (-x,-y)

A(-3, 0), B(-2, 3), C(-1, 0) -->

A(3, 0), B(2, -3), C(1, -1)

Reflection across the line y=-x will change the coordinates as follows (x,y) --> (-y,-x)

A(3, 0), B(2, -3), C(1, -1) -->

A(0,-3), B(3,-2), C(1, -1) (B)

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By algebraic simplification, the expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to the expression 2 · b.

In this question we need to simplify the division of two expressions that comprises powers and square roots, the complete procedure requires the use of algebra properties:

The expression [(3 · a · b²) / (5 · b²)] ÷ √[(9 · a²) / (100 · b²)] is equivalent to 2 · b.

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The width of the message as shown in the image attached is 3 inches.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the width of the message. The area of the postcard is 24 square inches, hence:

(b + 3)4 = 24

4b + 12 = 24

b = 3

The width of the message as shown in the image attached is 3 inches.

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The relationship between the ∠1 and ∠5 is that both are corresponding angles

Given,

The angles = ∠1 and ∠5

Here,

∠1 and ∠5 are lies on the same side of the two lines and on the same side of the transversal

So, ∠1 and ∠5 are corresponding angles

Hence, The relationship between the ∠1 and ∠5 is that both are corresponding angles

The complete question is:

Classify the relationship between the pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

∠1 and ∠5

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Answer:

23 dollars.

Step-by-step explanation:

She spent a total of 174 - 13 = 161 dollars.

So, the cost of each book = 161/7

= 23 dollars.

Answer:

9.81....

Step-by-step explanation:

x = 432/44

x = 9.81...

The shortest length of fabric, in inches, that Kirk could use to make the tablecloth without putting any separate pieces of fabric together is 30 inches

Given data

diameter of the table = 3 feet

hang down dimension = 5 inches

sew down dimension = 1 inch

width of rectangular fabric = 60 inches

The question seeks for area of the table cloth, for a circular table area of a circle = pi * r^2

required radius of cloth

= radius of the table + hang down dimension + sew down dimension

= 3 feet / 2 + 5 inches + 1 inch

= 1.5 * 12 inches + 5 inches + 1 inch

= 18 + 5 + 1

= 24 inches

Area of required cloth

= pi * 24^2

= 1809.557 square inches

Area of fabric =  Area of required cloth

length * wide = 1809.557 square inches

length * 60 = 1809.557 square inches

length = 1809.557 / 60 square inches

length = 30.159 inches ≈ 30 inches

Therefore option H which is 30 inches is the answer

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The reactants in the chemical equation C7H16 + O2 = CO2 + H2O have a total of 7 atoms in them.

The chemical formula of a compound indicates how many atoms are present in the substance.

The number of atoms of each element present in a molecule is noted in a chemical formula.

The answer to this query provides the following description of the chemical interaction between heptane and oxygen:

O2 + C7H16 = CO2 + H2O

Hexane's chemical composition reveals that the reactant side of the reaction has 7 carbon atoms.

Therefore, there are 7 atoms total in the reactants of the chemical equation C7H16 + O2 = CO2 + H2O.

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Step-by-step explanation:

f(x) = 5|x - 1| - 5

f(x) will be positive that means >= 0, if

5|x - 1| - 5 >= 0

5|x - 1| >= 5

|x - 1| >= 1

that will be true for x <= 0 or x >= 2

f(x) will be negative for the other cases.

so, 0 < x < 2

f(x) is increasing in

[1, infinity)

the value "1" is for sure included, as it starts the increasing part.

f(x) is decreasing in

(-infinity, 1]

"1" is again included, because it ends the decreasing part.

end behavior means for x going to infinity and -infinity : in both cases f(x) goes to infinity.

The discriminant of the quadratic equation is q · (q + 8) < 0. The solution set of this inequality is (0, - 8).

The nature of the roots of quadratic equations of the form a · x² + b · x + c = 0 can be inferred by the understading of its discriminant under the following condition:

b² - 4 · a · c < 0

Where a, b, c are the coefficients of the polynomial.

If we know that a = 2 · q, b = q and c = - 1, then the equation of the discriminant is:

q² - 4 · (2 · q) · (- 1) < 0

q² + 8 · q < 0

And by algebraic handling, we find the set of possible values of q:

q · (q + 8) < 0

The solution set of this inequality is (0, - 8).

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Answer:

graph B would be the answer.

Step-by-step explanation:

-

The density of the material is  0.4 kg/cubic cm.

Given that:-

Height of the cylinder = 54.5 mm

Diameter of the cylinder = 53.0 mm

Weight of the cylinder = 1 kg

We have to find the density of the cylinder.

We know that,

Density  = mass/volume

Here, mass = 1 kg

We know that,

Volume of a cylinder = [tex]\frac{1}{3} \pi r^2 h[/tex]

Where,

r is the radius of the cylinder, and

h is the height of the cylinder

Here, h = 54.5 mm, and

r = 53/2 = 26.5 mm

Hence,

Volume of cylinder = (1/3)*(22/7)*(26.5)(26.5)*54.5 ≈ 2566.088 ≈ 2566 cubic mm. = 2566/(10*10*10) cubic cm = 2.566 cubic cm

Density of cylinder = 1kg/2.566 cubic cm  ≈ 0.3897  ≈ 0.4 kg/cubic cm.

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The circumference of the children's ball to the nearest centimeter is 52 centimeters.

If a regulation volleyball has a circumference of about 66 centimeters, solve for its radius using the formula for the circumference of a circle given by:

C = 2πr

66 centimeters = 2πr

r = 33/π centimeters

Then, solve for the surface area of this regulation volleyball using the formula given by:

A = 4πr^2

A = 4π(33/π centimeters)^2

A = 4356/π square centimeters

If the ratio of the surface area of that ball to the surface area of a children's ball is approximately 1.6 : 1, then

surface area of regulation volleyball : surface area of a children's ball = 1.6 : 1

surface area of a children's ball = 4356/π square centimeters/1.6

surface area of a children's ball = 2722.5/π square centimeters

If  the children's ball has a surface area of 2722.5/π square centimeters, solve for its radius using the formula for the surface area given by:

A = 4πr^2

2722.5/π square centimeters = 4πr^2

r = 26.0887907/π centimeters

Solving for the circumference:

C = 2πr

C = 2π(26.0887907/π centimeters)

C = 52.17758139 centimeters

Rounding off to the nearest centimeter.

C = 52 centimeters

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How do you find equivalent expressions?

Image result for what is equivalent to (5x/6)

Combine any like terms on each side of the equation: x-terms with x-terms and constants with constants. Arrange the terms in the same order, usually x-term before constants. If all of the terms in the two expressions are identical, then the two expressions are equivalent.