Use the tables of values of f and g to answer the problem.
(g ∘ f)(2)

Answer:   πr2h

=  π×282×34

=  26656π

=  83742.29377409 centimeters3

Step-by-step explanation:

Answer:

The volume of the composite figure is 12,719 cm³ to the nearest whole number.

Step-by-step explanation:

The composite figure is composed of a cone and a half-sphere.

To calculate the volume of the figure, sum the volume of the cone and the volume of the half-sphere.

[tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a cone}\\\\$V=\dfrac{1}{3} \pi r^2 h$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]     [tex]\boxed{\begin{minipage}{4 cm}\underline{Volume of a half-sphere}\\\\$V=\dfrac{2}{3} \pi r^3$ \\\\ where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\\end{minipage}}[/tex]

Therefore, the equation for the volume of the composite figure is:

[tex]V=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3[/tex]

From inspection of the given diagram:

As the diameter of a circle is twice its radius, r = 14 cm.

Substitute the values of r, h and π into the equation and solve for V:

[tex]\begin{aligned}\implies V&=\dfrac{1}{3} \pi r^2 h+\dfrac{2}{3} \pi r^3\\\\&=\dfrac{1}{3} (3.14) (14)^2 (34)+\dfrac{2}{3} (3.14) (14)^3\\\\&=\dfrac{1}{3} (3.14) (196) (34)+\dfrac{2}{3} (3.14) (2744)\\\\&=6974.98666...+5744.10666...\\\\&=12719.09333...\\\\&=12719\;\sf cm^3\;\;(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, the volume of the composite figure is 12,719 cm³ to the nearest whole number.

The terms from the highest to lowest power of the variable are 10b⁶, -b², -9b, -9.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
To write the terms from the highest to the lowest power of the variable, we need to first simplify the given expression by combining the like terms.

The given expression can be simplified as follows:

= 9b² + 10b⁵b + 4 + 7b² - 6 - 15b² - 9b

= 10b⁶ + (9b² + 7b² - 15b²) - 9b + (4 - 6)

= 10b⁶ - b² - 9

Now, we can write the terms from highest to lowest power of the variable as follows:

10b⁶ is the term with the highest power of the variable.

The next highest power of the variable is b². Therefore, we have -b².

The next term is -9b, which has the power of the variable 1.

Finally, the constant term is -9, which has no power of the variable.

Therefore, the terms from the highest to lowest power of the variable are 10b⁶, -b², -9b, -9.

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The volume of water that Keith's kitchen kettle holds when it is full is 1800 ml.

Assume that Keith's kitchen kettle has a "x" ml capacity when it is full.

The kettle is initially 80% full, which means it holds 0.8x ml of water, according to the problem.

20% of the water is poured out, leaving 80% of the original amount of water in the kettle, which is:

0.8x * 0.8 = 0.64x ml

We are informed that the 1152 ml of water that is left equates to:

0.64x = 1152

By multiplying both sides by 0.64, we obtain:

x = 1800

Consequently, Keith's cooking kettle has an 1800 ml capacity when it is full.

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If A file that is 278 megabytes is being downloaded and the download is 19.7% complete, then you just need to multiply the 278 megabytes with 19.7%

The calculation would be: 278 megabytes x 0.197 = 54.766 megabytes.

If you round up the answer to nearest tenth it will be 54.8 megabytes.

Michelle biked approximately 37.68 miles in the shape of a circle.

A circle's diameter and radius are connected because the diameter is twice as long as the radius. Mathematically, this connection may be written as d = 2r, where d stands for the diameter and r for the radius. On the other hand, we can alternatively state that the radius is equal to half the diameter's length: r = d/2

The circumference of a circle can be found using the formula:

C = πd

Given that,

Michelle biked around the trail 4 times.

The circumference is:

C = π x 3 = 9.42 miles

Also,

4 x 9.42 = 37.68 miles

Hence, Michelle biked approximately 37.68 miles in the shape of a circle.

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The statement, Angle 1 and angle 5 are complementary angles,

As ∠2 = ∠5.

We know when a transversal intersects two parallel lines at two distinct points,

Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.

We know when the sum of two angles is 180° they are supplementary.

Two angles are said to be adjacent angles if they share a common side.

Two angles are said to be complementary when the sum is 90°.

We know vertically opposite angles are in equal measure when a transversal intersects two parallel lines.

Therefore, ∠2 = ∠5.

Hence, ∠1 + ∠2 = ∠1 = ∠5 = 90°.

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Answer:

90

Step-by-step explanation:

Answer:

$104,000

Step-by-step explanation:

For simple interest,

I = Prt

where I = interest earned

P = principal, amount invested

r = annual interest rate

t = time in years

I = $40,000 × 0.08 × 20

I = $64,000

The total amount saved is the principal amount plus the interest.

$40,000 + $64,000 = $104,000

The average rate of change on that interval is r = 7/3.

For any function f(x), we define the average rate of change on an interval [a, b] as

r = ( f(b) - f(a))/(b - a)

here, we have,

In this case, the interval is [0, 6], using the graph we can find the values of the function for these inputs:

f(0) = -8

f(6) =6

Replacing that we get:

r = (6 - (-8))/(6 - 0)

r = (6 + 8)/6

r = 14/6

r = 7/3

The average rate is 7/3.

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The common feature of the two functions is given as follows:

Vertical asymptote.

For this problem, neither of the functions is defined at x = -4, hence x = -4 is the vertical asymptote for both of the functions.

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Total amount/Working days

Step-by-step explanation:

As a result, there is roughly 0.4664 of an area under the standard normal curve between Z= -1.83 and Z= 0.

Area is the overall space occupied by a three-dimensional object's surface. Square units like square meters or square feet are used to quantify it. By adding up the areas of all an item's faces or surfaces, the surface area of the object can be calculated. For instance, since a cube has six faces, the surface area of a cube can be determined by finding the area of one face and multiplying it by six. Similar to this, one can determine the surface area of a sphere by calculating the area of its surface using the formula 4r2, where r is the sphere's radius.

given

To determine the region under the standard normal curve between Z=-1.83 and Z=0, we can use a standard normal chart or a calculator.

Using a normalised standard table:

Z=-1.83 corresponds to a region of 0.0336. (from the table).

The region is 0.5 to the west of Z= 0. (from the table).

Therefore, 0.5 - 0.0336 = 0.4664 is the region between Z= -1.83 and Z= 0.

Calculator usage

Calculator's normalcdf algorithm can be used to determine the region between Z=-1.83 and Z=0. We calculate normalcdf(-1.83, 0) = 0.4664 using the tool.

As a result, there is roughly 0.4664 of an area under the standard normal curve between Z= -1.83 and Z= 0.

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According to the given values London's statement is incorrect.

Simple interest is a type of interest that is calculated based on the principal amount of a loan or investment and the length of time for which the money is borrowed or invested. It is called "simple" because the interest is calculated only on the initial principal amount and does not take into account any interest that may have accrued in previous periods.

Let's calculate the interest earned by each person after one year:

London:

The amount deposited by London is $100. The simple interest rate is 3.4%. Therefore, the interest earned by London after one year is:

[tex]$$\text{Interest}[/tex] = [tex]\text{Principal} \times \text{Rate} \times \text{Time}[/tex] = [tex]$100 \times 3.4%[/tex] [tex]\times 1[/tex]= [tex]$3.40$$[/tex]

Chen:

The amount deposited by Chen is $200. The simple interest rate is 2.2%. Therefore, the interest earned by Chen after one year is:

[tex]$$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}[/tex]= [tex]$200 \times 2.2%[/tex] [tex]\times 1[/tex] = [tex]$4.40$$[/tex]

As we can see, even though London's interest rate is higher than Chen's, Chen will earn more interest in one year because he deposited a larger amount of money.

Therefore, according to the given values London's statement is incorrect.

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Answer: B. 50

Step-by-step explanation:

  To solve this, we will isolate the variable b.

   Given:

[tex]\frac{1}{5}[/tex]b + 4 = 14

   Subtract four from both sides of the equation:

[tex]\frac{1}{5}[/tex]b = 10

   Multiply both sides of the equation by 5:

b = 50

        B. 50

Note that with respect to the above problem,

Plan:

Let P1 be the proportion for the treatment group (low-fat diet), and P2 the proportion for the control group (normal diet).

State the hypotheses for your test:

H₀: P1 = P2 (There is no significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups)

Ha: P1 ≠ P2 (There is a significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups)

To test this claim, we can use a two-sample z-test for proportions. We calculate the test statistic as follows:

z = (p1 - p2) / sqrt(p*(1-p)*(1/n1 + 1/n2))

where p1 and p2 are the sample proportions, n1 and n2 are the sample sizes, and p is the pooled proportion. The pooled proportion is calculated as:

p = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of successes in each sample.

Using the given data, we have:

p1 = 1642/3311 = 0.495

p2 = 1480/3176 = 0.466

n1 = 3311

n2 = 3176

x1 = 1642

x2 = 1480

p = (1642 + 1480) / (3311 + 3176)

p = 0.480

Then, the test statistic is:

z = (0.495 - 0.466) / sqrt(0.480*(1-0.480)*(1/3311 + 1/3176))

z = 3.22

Using a standard normal distribution table or calculator, we find the p-value associated with a two-tailed z-score of 3.22 is approximately 0.001.

Therefore, the p-value is 0.001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that there is a significant difference in the proportion of women with a family history of breast cancer between the low-fat and normal diet groups.

Answer: The difference between the sample proportions is significant at the 0.10 significance level. Therefore, we reject the null hypothesis and conclude that there is evidence that the two proportions differ.

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The value of x in the equation below 18 = x - 10 is equal to 28.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

18 = x - 10

By rearranging and collecting like-terms, we have the following:

x = 18 + 10

x = 28.

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Complete Question:

Find the value of x in the equation below. 18 = x - 10

25 pi^2

The circumference is diameter by pi. So you have to divide 50pi by pi, which gives you 50. Then, divide that by 2 to get your radius. 25. A=pi r^2. So you have to multiply 35 by pi, 25pi, and then make it squared.

Answer:

The greatest possible distance between two points on the walls in the room is 17 feet.

Step-by-step explanation:

The room can be modelled as a rectangular prism with the following dimensions:

The greatest possible distance between two points on the walls in the room is the line between diagonally opposite corners. This is marked as the blue line (x) on the attached 3D diagram.

This distance is the hypotenuse of a right triangle with a base of the diagonal of the floor and a height of the height of the room.

The diagonal of the floor (marked "y" on the attached diagram) is the hypotenuse of a right triangle with legs of the width and length of the room.  To calculate the diagonal of the floor, use Pythagoras Theorem.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Substitute a = 8, b = 12 and c = y into the formula and solve for y:

[tex]\implies 8^2+12^2=y^2[/tex]

[tex]\implies 64+144=y^2[/tex]

[tex]\implies y^2=208[/tex]

[tex]\implies y=\sqrt{208}\; \sf ft[/tex]

Therefore, the diagonal of the floor (y) is √(208) feet in length.

We can now use Pythagoras Theorem again to find the length x.

Substitute a = y, b = 9 and c = x into the formula:

[tex]\implies y^2+9^2=x^2[/tex]

Substitute the found value of y and solve for x:

[tex]\implies (\sqrt{208})^2+9^2=x^2[/tex]

[tex]\implies 208+81=x^2[/tex]

[tex]\implies 289=x^2[/tex]

[tex]\implies x=\sqrt{289}[/tex]

[tex]\implies x=17 \sf \; ft[/tex]

Therefore, the greatest possible distance between two points on the walls in the room is 17 feet.

Janice packed 32 cookies.

A system of equations is a set of two or more equations that are to be solved simultaneously. The solutions to a system of equations are the values that satisfy all the equations in the system. There are different methods to solve systems of equations, such as substitution, elimination, and graphing. Systems of equations are used in many areas of mathematics, science, engineering, and economics to model and solve real-world problems.

Substitution method is a common technique for solving systems of equations. In this method, one equation is solved for one of its variables in terms of the other variable, and then the expression for that variable is substituted into the other equation. This results in an equation in one variable that can be solved using algebraic methods. Once the value of one variable is found, it can be substituted back into one of the original equations to solve for the other variable.

In the given question,

Let's use a system of equations to solve the problem:

Let x be the number of cookies Janice packed.

Let y be the number of cookies Siti packed.

Let z be the number of cookies Huiling packed.

From the problem, we know:

x + y = 146 (equation 1)

x + z = 374 (equation 2)

z = 3y (equation 3)

We can use equation 3 to substitute z in equation 2:

x + 3y = 374

We can then use equation 1 to substitute y in the new equation:

x + (146 - x)/2 * 3 = 374

Simplifying and solving for x, we get:

x + 219 - 3x/2 = 374

2x/2 - 3x/2 = 374 - 219

-x/2 = 155

x = -2 * 155

x = -310 (discard this solution)

Since we can't have negative number of cookies, we discard the solution x = -310. Therefore, we can conclude that Janice packed:

x = 146 - y

x = 374 - z

z = 3y

Substituting z in the second equation, we get:

x = 374 - 3y

Substituting this expression for x in the first equation, we get:

374 - 3y + y = 146

Simplifying and solving for y, we get:

-2y = -228

y = 114

Therefore, Siti packed 114 cookies, and since Janice and Siti packed 146 cookies altogether, we have:

x + y = 146

x + 114 = 146

x = 32

So Janice packed 32 cookies.

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Answer:

[tex]x=1[/tex]

Step-by-step explanation:

First, square both sides.

[tex]\left(\sqrt{3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}}\, \right)^2= 3^2[/tex]

[tex]3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6} = 9[/tex]

This eliminates the square root over the entire left side of the equation.

Next, multiply both sides by 6 to get rid of the fraction on the left side.

[tex]6\left(3+\dfrac{\left(4 + \sqrt{x+3} \, \right)^2}{6}\right) = 6( 9)[/tex]

[tex]6(3) + \left(4 + \sqrt{x+3} \, \right)^2 = 6(9)[/tex]

[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54[/tex]

Then, subtract 18 from both sides to isolate the squared term.

[tex]18 + \left(4 + \sqrt{x+3} \, \right)^2 = 54\\\underline{-18 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 18}[/tex]

[tex]\left(4 + \sqrt{x+3} \, \right)^2 = 36[/tex]

Now, we can square root both sides.

[tex]\sqrt{\left(4 + \sqrt{x+3} \, \right)^2} = \sqrt{36}[/tex]

[tex]4 + \sqrt{x+3} = \pm 6[/tex]

Remember to use apply the even root property, so that the right side (6) is positive or negative (indicated by the plus or minus sign).

Next, subtract 4 from both sides.

[tex]4 + \sqrt{x+3} = \pm 6 \\ \underline{-4\ \ \ \ \ \ \ \ \ \ \: } \ \ \ \ \ \underline{ - 4}[/tex]

[tex]\sqrt{x+3} = \pm 6 - 4[/tex]

Then, square both sides to get rid of the square root on the left side.

[tex]\left(\sqrt{x+3}\right)^2 = (\pm 6 - 4)^2[/tex]

[tex]x+3 = 2^2[/tex]    OR    [tex]x+3 = (-10)^2[/tex]

We can see that there are two resulting expressions, each of which we can solve individually.

[tex]x+3 = 4[/tex]    OR    [tex]x+3 = 100[/tex]

[tex]\boxed{x = 1}[/tex]                 [tex]\boxed{x\ne97}[/tex]

The reason that x = 97 is crossed out is because when we plug that x-value back into the original equation, it does not come out to be true. Therefore, 97 is an extraneous solution.

Also, see the attached image for another solution (that implores another method).

Answer:

  x = 1

Step-by-step explanation:

You want to solve for x:

  [tex]\sqrt{3+\dfrac{(4+\sqrt{x+3})^2}{6}}=3[/tex]

At any stage where there is a root, you isolate the radical and raise both sides of the equation to a power sufficient to eliminate the radical. Repeat as necessary.

The radical is already on one side of the equation by itself, so we simply square both sides:

  [tex]3+\dfrac{(4+\sqrt{x+3})^2}{6}=9\\\\(4+\sqrt{x+3})^2=6^2\qquad\text{subtract 3, multiply by 6}\\\\|4+\sqrt{x+3}|=6\qquad\text{take the square root}[/tex]

At this point, we note that the sum cannot be negative, so the absolute value bars are irrelevant. Isolating the radical and squaring both sides, we can finish the solution.

  [tex]4+\sqrt{x+3}=6\\\\\sqrt{x+3}=2\qquad\text{subtract 4}\\\\x+3=4\qquad\text{square both sides}\\\\\boxed{x=1}\qquad\text{subtract 3}[/tex]

This is the only solution, as the attached graph shows.

__

Additional comment

Generally, the square root symbol means the positive square root. That is, √z is usually considered to be non-negative.  This is why we use ±√z when we want both signs of the root.

In this problem, the only root we're taking as part of the solution is the root of a square. The possibility of a negative value for the term being squared is handled by using the absolute value brackets: √(z²) = |z|.

For solving these using a graphing calculator, we like to rewrite the equation to the form f(x)=0. That way, the solutions are the x-intercepts.

The length of the mid segment is 8 feet.

The bases of a trapezoid have lengths of 6 feet and 10 feet. Let's find the length of the mid segment of the trapezoid.

A midsegment of a trapezoid is the line segment connecting the midpoints of the two non-parallel sides of a trapezoid.

The length of the midsegment of trapezoid is half the sum of the lengths of the two parallel sides

Hence,

mid segment = 1  /2 (6 + 10)

mid segment = 16 / 2

mid segment = 8 feet

Therefore,

mid segment = 8 feet.

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The sample space for spinning the spinner two times is -

{Blue, Orange} {Blue, Red} {Orange, Red}

{Blue, Blue} {Red, Blue} {Orange, Blue}

{Red, Red} {Orange, Orange}

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

The sample space for spinning the spinner two times can be found by listing all possible outcomes of the two spins.

Each spin has three possible outcomes, so the total number of outcomes for two spins is 3 x 3 = 9.

One way to list the sample space is to use a table where the rows and columns represent the outcomes of the first and second spins, respectively.

The entries in the table represent the ordered pairs of outcomes, with the first entry corresponding to the first spin and the second entry corresponding to the second spin.

Using this method, the sample space for spinning the spinner two times is -

Blue | Blue | (Blue, Blue) | Blue | Orange | (Blue, Orange) | Blue | Red | (Blue, Red)

Red | Blue | (Red, Blue) | Red | Orange | (Red, Orange) | Red | Red | (Red, Red)

Orange | Blue | (Orange, Blue) | Orange | Orange | (Orange, Orange) | Orange | Red | (Orange, Red)

Alternatively, we can list the outcomes as an unordered set of two elements, where the order of the elements does not matter.

In this case, the sample space for two spins would be -

{Blue, Orange} {Blue, Red} {Orange, Red}

{Blue, Blue} {Red, Blue} {Orange, Blue}

{Red, Red} {Orange, Orange}

Therefore, the sample space is obtained.

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It will take 6.5 minutes to grade 338 test by the electronic grading machine.

The quality of the answer papers is a key element. The machine might not be able to reliably scan and evaluate the answers if the answer sheets are not filled out completely or if the paper has rips or smudges on it. Similar to this, the computer might not be able to recognize the right answers if the answer sheets are not properly aligned.

Given that, the machine can grade 52 test in 1 minute.

The, we can calculate the time taken to grade 338 test as follows:

time = number of tests / rate of grading

Plugging in the given values, we get:

time = 338 / 52 = 6.5 minutes

Hence, it will take 6.5 minutes to grade 338 test by the electronic grading machine.

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The amount that I spent by using the equation y = 1/2x , according to my friend's expense is $7.5.

In its simplest form in algebra, the definition of an equation is a mathematical statement that two mathematical expressions are equal. For example, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two terms separated by an equal sign. 

There are two types of equations:

Identities and conditionals. The identity applies to all values ​​of the variable. Constraint expressions apply only to specific values ​​of variables. Equations are written as two expressions separated by an equal sign ("="). 

Solution:

Given, amount spent by friend = $15

           Equation: y = 1/2x

So, amount spent by me is as follows

y = (1/2)×15

  =15/2

y  = $7.5

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The amount of money you are spending is $7.50 according to the given equation.

A mathematical equation is a statement that expresses the relationship between two values using mathematical symbols. An equation typically involves a variable, which is a symbol that stands for a number that can change, and an equals sign. Equations can be used to solve a variety of problems in mathematics.

The equation y = 1/2x states that 'y' is equal to one half of 'x'. This equation can be used in many different ways to solve real-life problems. In this case, 'x' represents the amount of money your friend spent at the carnival. 'y' represents the amount of money you spent. To solve for 'y', we divide the value of 'x' by 2.

In the question, your friend spent $15 at the carnival. Therefore, 'x' is equal to 15. We then divide 15 by 2, which gives us 7.5. This means that you spent $7.50 at the carnival.

The equation y = 1/2x is a simple but powerful tool for solving problems. It can be used for a variety of tasks, including finding out how much money you spent at the carnival if you spent half as much as your friend. All you have to do is plug in the value of 'x' and divide it by two.

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Answer: Y = X2

Step-by-step explanation:
A and C aren't proportional and D is increasng

Answer:

7.75 ; 7.81 ; 7.77 ; 7.84

for a f(5) is 1 and f(7) is 1/4

for b the domain is 16-1/4

for c the value is decreasing by 1/2 every time

Answer:

A. Lancaster

Lancaster is on the edge of the yellow area.

The growth rate of the plant shown in the graph is 1/2 centimeter per week

From the question, we are to determine the growth rate of the plant

To determine the growth rate of the plant, we will determine the slope of the line

To determine the slope of the line passing through the points (1, 1/2) and (3, 1 1/2), we can use the slope formula:

Slope = (Change in y) / (Change in x)

We first calculate the change in y by subtracting the y-coordinate of the first point from the y-coordinate of the second point:

Δy = 1 1/2 - 1/2 = 1

Next, we calculate the change in x by subtracting the x-coordinate of the first point from the x-coordinate of the second point:

Δx = 3 - 1 = 2

Finally, we can calculate the slope by dividing the change in y by the change in x:

Slope = Δy / Δx = 1 / 2

The slope of the line is 1/2.

Hence, the growth rate is 1/2 centimeter per week

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