Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h at time t seconds after launch is h(t) = -16(t)^2 +80t. Find the domain of the function.

4.0 mL of marcaine will be needed to draw up to equal the 1%.

Marcaine is a brand name for the medication bupivacaine, which is a local anesthetic used to numb a specific area of the body during a surgical or medical procedure.

To determine the amount of marcaine that is needed to be drawn up to equal the 1% lidocaine, we can use the following formula:

(Concentration of Lidocaine) / (Concentration of Marcaine) = (Volume of Lidocaine) / (Volume of Marcaine)

In this case, we know that the concentration of lidocaine is 1% and the concentration of marcaine is 0.25%. So we can plug these values into the formula:

1 / 0.25 = (Volume of Lidocaine) / (Volume of Marcaine)

To solve for the volume of marcaine, we can multiply both sides of the equation by the volume of lidocaine:

(Volume of Lidocaine) / (Volume of Marcaine) = 4

Therefore, 4.0 mL of marcaine will be needed to draw up to equal the 1%.

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According to the diagram, there are eight fractions of 3/8 in three.

We are shown a diagram of three equal parts divided into eight equal parts.

Divide 3 by 8 to get the value of the equal part.

As a result, the value of each can be given as 3/8.

Therefore There are 8 groups of 3/8 in 3 as per the given diagram.

The diagram is attached below:

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After 11 years, the amount (future value) in Zahra's account will be $58 more than the amount in Christopher's.

The future value can be determined by using the FV table or formula.

We can also ascertain the future value using an online finance calculator as follows:

N (# of periods) = 11 years

I/Y (Interest per year) = 8.625%

PV (Present Value) = $8,800

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $21,863.03

Total Interest = $13,063.03

N (# of periods) = 4015 days (11 years x 365)

I/Y (Interest per year) = 8.25%

PV (Present Value) = $8,800

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $21,805.22

Total Interest = $13,005.22

Zahra's = $21,863.03

Christopher's = $21,805.22

Difference = $57.81 ($21,863.03 - $21,805.22)

Thus, with a slightly higher interest rate, Zahra's account will generate $58 more in future value than Christopher's investment.

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If the GCF of a term and 12x²y is 4xy , then (a) The term is 8xy , The expression is 4xy(2 + 3x) .

The Greatest Common Factor of the two terms is 4xy ,

where , the first term is 12x²y , we have to find the second  term ,

Consider Option(a) : where the second term is 8xy ,

So , GCF of 8xy and 12x²y is

= 2(4xy) and  3x(4xy)

= 4xy(2 + 3x )      ....taking 4xy common from both the terms ,

Therefore , Yes , the second term is 8xy and the expression is 4xy(2+3x) .

The given question is incomplete , the complete question is

What term and 12x²y have a GCF of 4xy? Write an expression that shows the monomial factored out of the polynomial , choose the correct answer below :

(a) The term is 8xy , The expression is 4xy(2 + 3x)

(b) The term is 16xy , The expression is 4xy(4xy + 3x)

(c) The term is 3x , The expression is 12x²y(3x + 4xy)

(d) The term is 4x²y , the expression is 4xy(1 + 3x) .

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Answer:

sold 23 Tickets and 8 General Admission Tickets

Step-by-step explanation:

y = General Admission tickets

x = tickets

4x + 6y = 170

x + y = 31

Use the Substitution method:

4x + 6(31 - x) = 170

4x + 186 - 6x = 170

4x - 6x = -16

-2x = -16

x = 8

y = 31 - 8 = 23

Answer: - 8c - 25

Step-by-step explanation:

Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.

Answer: The graph of g(x) = 4x - 6 is a translation of the graph of f(x) = 4x - 3.

A translation of a function results in a shift of the graph of the function, either horizontally (left or right) or vertically (up or down).

When the graph of a function is shifted down, the y-coordinates of all the points on the graph decrease. When it's shifted to the left, the x-coordinates of all the points on the graph decrease.

In this case, the graph of g(x) = 4x - 6 is a vertical translation of 3 units down from the graph of f(x) = 4x - 3.

The y-coordinates of all the points on the graph of g(x) = 4x - 6 are 3 units less than the y-coordinates of the corresponding points on the graph of f(x) = 4x - 3.

Therefore, the correct answer is:

Translation of 3 units down.

Step-by-step explanation:

Gary would need 15.2 oz. of glue and 7.6 oz. of glitter to make 4 bottles.

The correct option is D.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

Given in the table,

Bottles   Glue   Glitter

1              3.8       1.9

Therefore

1 bottle = 3.8 oz. of glue + 1.9 oz. of glitter

Now,

Multiply 4 on both sides.

4 bottle = 4 x (3.8 oz. of glue + 1.9 oz. of glitter)

4 bottle = 15.2 oz. of glue + 7.6 oz. of glitter

Hence, 15.2 oz. of glue and 7.6 oz. of glitter is needed to make 4 bottles.

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Students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a hypothesis.

A hypothesis is a proposed explanation or prediction about a phenomenon, based on limited information or data. It is a tentative statement about the relationship between variables that can be tested through further investigation or experimentation.

In scientific research, a hypothesis provides a framework for designing and conducting experiments to gather evidence to support or reject the hypothesis. It acts as a starting point for scientific inquiry and helps guide the research process.

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The number for an empty cell would be 20 so any number below this benefit South Korea and above this benefit the United States. This also makes it impossible for trade between these two countries.

If a country can manufacture a significant number of goods with the same resources as another country, it has an absolute advantage. If a country can manufacture a certain commodity more cheaply and with higher quality than another country, it has a comparative advantage.

In the given scenario, 1000÷10=100 autos are sacrificed by the United States to manufacture one airplane which is the opportunity cost. In comparison to the United States, South Korea requires twice (2000÷1000) as long to construct an airplane.

a) The number of hours for South Korea to produce one auto would be 2×10=20. Because of this, South Korea would benefit from any number below 20, while the US would benefit from any number above 20.

b) The empty cell value would be 20 for South Korea to have the same opportunity cost as the United States. So mutually beneficial trade cannot exist without comparative advantage.

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The average rate of change for the given function from x = −1 to x = 2 is -4/3

The average rate of change of a function over an interval is a measure of how much the output of the function (y-value) changes as the input (x-value) changes over that interval. This is also the slope of the function or line.

average rate of change = (y2-y1)/(x2-x1)

From the graph, x1 = -1, y1 = 4 and x2 = 2, y2 = 0

average rate of change = (0-4)/(2-(-1)) = -4/3

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These are functions that almost have to be memorized but can be understood through Desmos for example:

a: W

b: Z

c: X

d: Y

e: V

The ratio of the volume of the cone to the volume of a prism is equal to one.

Three-dimensional space is quantified by volume. It is frequently measured quantitatively with SI-derived units (such the cubic metre and litre) or with a variety of imperial or US-standard units (such as the gallon, quart, cubic inch). Volume and height are related in how they are defined (cubed). The volume of a container is typically thought of as its capacity, or the amount of fluid (gas or liquid) that it could hold, as opposed to the amount of space the container occupies. Utilizing naturally occurring containers of a comparable shape and subsequently, standardized containers, volume is measured. Arithmetic formulas make it simple to determine the volume of some basic three-dimensional shapes.

We know that

The volume of the cone = area of the base. height/3

The volume of Prism = area of the base. height

Since the area of the base and height are the same hence the volume will also be . so the ratio will be 1.

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Answer:

0.2

Step-by-step explanation:

1. distribute 8 to 1 and 5

2. Now its 8+40x

3. Divide on both sides

4. 40x/40 cancels out

5.  8/40=0.2

The length of the third side of the triangle is x + 13.

A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.

The perimeter of a triangle is the sum of the length of all three sides of the triangle.

Given the data in the question;

To find side C, equate the sum of all three sides of the triangle to the perimeter and simplify.

Side A + Side B + Side C = P

5x + ( 3x - 7 ) + Side C = 9x + 6

5x + 3x - 7 + Side C = 9x + 6

8x - 7 + Side C = 9x + 6

Side C = 9x + 6 - ( 8x - 7 )

Side C = 9x + 6 - 8x + 7

Side C = x + 13

Therefore, side C is x + 13.

Option A) x + 13 is the correct answer.

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Answer:

x + 13

Step-by-step explanation:

i took the test xx

The approximate percentage of total pay that fringe benefits make up is 10%

The term called percentage in math is defined as a number or ratio that can be expressed as a fraction of 100

Here we have to find the approximate percentage of total pay that fringe benefits make up.

As the total compensation offered to the workers or employees by employers in different countries can usually be bifurcated into two broad components.

Here we have to know that the first one is based on wages & salaries components and the second one is the fringe benefits component.

Here this one includes the benefits components usually consist of supplementary benefits such as gratuity, pension contribution, transportation service, accommodation facility, etc.

Here as per the report published by the Bureau of Labor Statistics, U.S. Department of Labor in 2020 said that the approximate of the total pay that the fringe benefits make up usually range from 26.1% - 37.3%.

Based on that the percentage of fringe benefits could vary from the type of industry such as the goods-producing industry or service-providing industry.

So, the increased percentage is calculated as

=> 37.3 - 26.1

=> 11.2

Therefore, the correct option is (b).

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A customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.

Charge for first 5 charged = $ 4.50

Charge for additional time = $ 0.50 per minute

Starting time = 9:35 p.m.

End time = 11:15 p.m.

Total minutes = 100 minutes

Total charge = 4.50 + (95 x 0.50)

                  = 4.50 + 47.50

                  = 52.00

Hence, a customer would  be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.

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Answer:

the percentage increase is 27.4%

Step-by-step explanation:

To find the percentage increase, we can use the formula:

(New cost - Old cost) / Old cost x 100% = Percentage increase

(79 - 62) / 62 x 100% = 27.41%

The percentage increase is 27.41%. Rounded to the nearest tenth of a percent, the percentage increase is 27.4%

Difference of $62 and $79 is 24.1%

62 - 79/((62 + 79)/2) = 17/70.5 =

0.24113475177305 x 100 = 24.113475177305%

Step-by-step explanation:

that is really simple, because the additional half-circle compensates for the missing half-circle on the other side.

so, the area is plain and simple the area of the rectangle, which is

13×12 = 156 = 156.0

The perimeter of the square piece of paper is 40 cm .The perimeter of the rectangular piece of paper is 50 cm and the length of the rectangular piece of paper is 15 cm.

A. The perimeter of the square piece of paper is 40 cm.
This is calculated by multiplying the length of each side of the square by 4.

Length of each side = 10cm
Perimeter of square = 4 x 10 cm = 40 cm

B. The perimeter of the rectangular piece of paper is 50 cm.
This is calculated by multiplying the length and width of the rectangle by 2.

Length = 15 cm
Width = 15 cm
Perimeter of rectangle = 2 x (15 + 15) cm = 2 x 30 cm = 50 cm

C. The length of the rectangular piece of paper is 15 cm.
This is given in the question.

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Answer:

x = 3

Step-by-step explanation:

x+5=8

x+5-5=8-5

X=3

Answer:

x = 3

Step-by-step explanation:

basically 2 ways

1st: Transposing

1) x + 5 = 8

2) transpose or transfer +5 to the other side

NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)

3) x = 8 - 5

x = 3

2nd: Property of Equality (whatever u do one one side, you do the same to the other)

1) x + 5 = 8

2) x + 5 - 5 = 8 - 5

x = 3

the main focus is to isolate x, or to make it be alone in one side of the equation

Answer:

20/C=X

Step-by-step explanation:

C= swim caps

X=How many swim caps each swimmer gets

It would take 2 hours for this space shuttle to travel 7. 2 x 108 miles

As per the given data, a certain space shuttle travels at a speed of 3. 6 x

104 miles per hour.

Here we have to determine that how many hours would it take this space shuttle to travel 7. 2 x 108 miles.

The relation between the speed and the distance is:

Speed = Distance × Time

Speed = 3. 6 x 104 miles per hour

Time = 1 hour

3. 6 x 104 = Distance × 1

Distance = 374.4 miles

The distance to be covered 7. 2 x 108 miles

= 777.6 miles

Hours taken to travel 7. 2 x 108 miles.

Time =  [tex]\frac{777.6 }{374.4}[/tex]

≅ 2 hours.

Therefore the time taken to travel 7. 2 x 108 miles is 2 hours.

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The volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis is π/2.

We have to determine the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis.

We will rotate the region near the y-axis using the disc method. Consequently, the curve's equation should be expressed in terms of y.

y = x^2

Taking square root on both side, we get

x = √y

We can write it as

x = y^{1/2}

The volume integral formula is

V = [tex]\pi\int_{a}^{b}R(x)^2dx[/tex]

The values of a and b are taken from the y-axis since the equation for the curve we need is expressed in terms of y.

Using the curve's equation, if x = 0, y = 0, and if x = 1, y = 1, respectively.

Thus, a = 0 and b = 1 are the values.

Now, we may use definite integral to express the volume.

V = [tex]\pi\int_{0}^{1}\left[y^{1/2}\right]^2dx[/tex]

Now simplify

V = [tex]\pi\int_{0}^{1}ydx[/tex]

Now integrating

V = [tex]\pi\left[\frac{y^2}{2}\right]_{0}^{1}[/tex]

V = [tex]\pi\left[\frac{(1)^2}{2}-\frac{(0)^2}{2}\right][/tex]

V = [tex]\pi\left[\frac{1}{2}-0}\right][/tex]

V = π/2

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Answer:

EG = 44

Step-by-step explanation:

EG, the whole thing, is 10x - 16. It says that at the top of the image. But also, under the segment, we can put together two small pieces, EF and FG. So, the whole thing could also be 4x + 20.

The two expressions both describe EG. They are equal to each other. Write an equation.

10x - 16 = 4x + 20

subtract 4x

6x - 16 = 20

add 16

6x = 36

divide by 6

x = 6

They are asking for EG. Use either expression.

EG = 4x + 20

= 4(6) + 20

= 24 + 20

= 44

or,

EG = 10x - 16

= 10(6) - 16

= 60 - 16

= 44

Actually, its a neat check to do both ways bc it should come out the same.

EG = 44

The equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a).

The Latin word secant, which means to cut, is used in mathematics to define a line that passes through the points P and Q of any arbitrary curve whose equation is y=f(x).

Slope is the term used to describe when one end or side of a surface is higher than the other. A Secant line is a straight line that connects two points on a function. formula for secant line slope.

A secant line's slope through two points is equal to y 2 y 1 x 2 x 1. On the secant line, locate two spots.Discover the line's slope between the two spots.To get the line's equation, enter one of your points and your slope into the point slope form of your line.

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The width of the given rectangular frame of perimeter of 52 inches is; 12 inches.

The formula for perimeter of rectangle is;

Perimeter = 2(Length + width)

Now, we have the parameters as;

Perimeter = 52 inches

Length = 14 inches

Thus, plugging in the relevant values into the perimeter equation gives;

52 = 2(14 + width)

52/2 = 14 + width

14 + width = 26

Width = 26 - 14 = 12 inches

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