For the graph, find the average rate of change on the intervals given

See attached picture b

Answer:

The area of the triangle is 9.8 inches.

Using triple angle formula the evaluation of the trigonometric identity cos(2a) are 1 and 1/2.

We can use the trigonometric identity cos(2a) = 1 - 2sin^2(a) to evaluate cos(2a), but first we need to find the value of sin(a) from the given equation.

Given: sin(3a) = 2sin(a)

We can expand sin(3a) using the triple angle formula:

[tex]sin(3a) = 3sin(a) - 4sin^3(a)[/tex]

Substituting the given equation into this, we get:

[tex]2sin(a) = 3sin(a) - 4sin^3(a)[/tex]

Simplifying, we can rearrange to get:

[tex]4sin^3(a) - sin(a) = 0[/tex]

Factorizing, we get:

[tex]sin(a)(4sin^2(a) - 1) = 0[/tex]

So, either sin(a) = 0 or 4sin^2(a) - 1 = 0.

If sin(a) = 0, then

[tex]cos(a) = \±1\\cos(2a) = cos^2(a) = 1.[/tex]

If 4sin^2(a) - 1 = 0, then we can solve for sin(a) to get:

[tex]sin(a) = \±\sqrt{(1/4)} = \±1/2[/tex]

If sin(a) = 1/2, then

[tex]cos(a) = \sqrt{(1 - sin^2(a))} = \sqrt{(1 - 1/4)} = \sqrt{3/2}[/tex]

Using the identity cos(2a) = 1 - 2sin^2(a), we can then calculate:

[tex]cos(2a) = 1 - 2sin^2(a) = 1 - 2(1/4) = 1/2[/tex]

If sin(a) = -1/2, then cos(a) = -√3/2, and using the same identity we get:

[tex]cos(2a) = 1 - 2sin^2(a) = 1 - 2(1/4) = 1/2[/tex]

So, we have two possible values for cos(2a): 1 and 1/2.

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Answer:

Step-by-step explanation:

Let X be the lifespan of an item. We are given that X is normally distributed with a mean of μ = 5 years and a standard deviation of σ = 1.3 years.

We want to find the probability that an item will last longer than 6 years. Let Y be the random variable that represents the lifespan of an item in excess of 6 years, i.e. Y = X - 6. Then we want to find:

P(Y > 0)

Using the properties of normal distribution, we can standardize Y to get a standard normal variable Z:

Z = (Y - μ) / σ = (X - 6 - 5) / 1.3 = (X - 11) / 1.3

So we want to find:

P(Z > (6 - 11) / 1.3) = P(Z > -3.85)

Using a standard normal distribution table or calculator, we can find that the probability of Z being greater than -3.85 is very close to 1 (in fact, it is essentially 1). Therefore, the probability of an item lasting longer than 6 years is essentially the same as the probability of Y being greater than 0, which is 1.

Therefore, the probability that a randomly purchased item will last longer than 6 years is approximately 1.

The central limit theorem states that the distribution of the sample mean will be approximately normal if the sample size is sufficiently large.

Specifically, the  central limit theorem states that if the sample size (n) is greater than or equal to 30, then the sample mean (X) will be approximately normally distributed with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n). Mathematically X~N(μ, σ/√n)

For example, if a population has a mean of 10 and a standard deviation of 2, then a sample of size 30 taken from that population will have a sample mean (X) that is approximately normally distributed with a mean of 10 and a standard deviation of 2/√30, or 0.6.

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we can see, the function f(x) = 3x - 5 produces the desired range for the given domain.

The range of numbers that can be plugged into a function is known as its domain. The x values for a function like f make up this collection.(x). A function's range is the collection of values it can take as input. After we enter an x number, the function outputs this set of values.

The function that produces the range of {−11,−5,1,7,13} given a domain of {−2,0,2,4,6} is:

f(x) = 3x - 5

To see why, we can plug in each value from the domain into the equation and see if it produces the corresponding value in the range:

f(-2) = 3(-2) - 5 = -11

f(0) = 3(0) - 5 = -5

f(2) = 3(2) - 5 = 1

f(4) = 3(4) - 5 = 7

f(6) = 3(6) - 5 = 13

As we can see, the function f(x) = 3x - 5 produces the desired range for the given domain.

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The plane travels a distance of 11710 feet from point A to point B.

Why are trig ratios important?

As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

The figure representing the situation is given below.

From triangle AOC,

tan 19° = AC / OC

tan 19° = 7425 / OC

OC = 7425 / tan 19°

OC = 21563.77 feet

Similarly for triangle BOD,

tan 37° = BD / OD

tan 37° = 7425 / OD

OD = 7425 / tan 37°

     = 9853.31 feet

AB = CD

    = OC - OD

    = 21563.77 feet - 9853.31 feet

    = 11,710.46 feet

    ≈ 11710 feet

Hence the distance plane travelled from point A to point B is 11710 feet.

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Accοrding tο the data, the answers tο Questiοns 1 and 2 are: Harris shοuld anticipate spinning a sum οr less 10 apprοximately 367 times and a tοtal that is 10 οr larger apprοximately 133 times.

Yοur example is an equatiοn since an equatiοn that's any statement with an equal's sign. The usage οf equatiοns in mathematical expressiοns is widespread because mathematicians adοre equal signs. An equatiοn is a cοllectiοn οf guidelines fοr prοducing a specific οutcοme.

Part A: Tο calculate the likelihοοd that Harris will spinning a sum οr less 10, multiply the οverall number οf spins by the chance οf οbtaining a sum οr less 10. The οutcοmes οf the first spinner's spin are 1, 2, and 3, while the results οf the secοnd spinner's spin are 4, 5, 6, 7, and 8. Hence, the amοunts οr less 10 are:

1 + 4 = 5

1 + 5 = 6

1 + 6 = 7

1 + 7 = 8

1 + 8 = 9

2 + 4 = 6

2 + 5 = 7

2 + 6 = 8

2 + 7 = 9

3 + 4 = 7

3 + 5 = 8

3 + 6 = 9

There are 11 amοunts that cοuld be less than ten. The number οf successful results divided by the entire number οf pοssibilities, which is 11/15, represents the likelihοοd οf receiving a payοut οf less than 10 in a single spin. Harris will therefοre spin a tοtal less than 10 times, and the equatiοn tο estimate this is:

11/15 = x/500

After finding x, we οbtain:

x = (11/15) x 500

x = 366.67, which rοunds up tο 367

Sο, Harris shοuld expect tο spin a sum less than 10 abοut 367 times.

Part B: Tο determine hοw frequently Harris shοuld anticipate spinning a sum οf ten οr mοre, we can deduct the times that he shοuld anticipate spinning a sum lοwer than ten frοm the οverall number οf spins:

500 - 367 = 133

Therefοre, Harris shοuld expect tο spin a sum that is 10 οr greater abοut 133 times.

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find the velocity function from the derivative of s

v=s'=-32t+vo

set that equal to 64, solve for time t.

In your average velocity, you should have had a negative distance, which would have made a negative velocity (meaning downward). see the original equation for the negative sign.

Mark me brainiest!

Step-by-step explanation:

The formula to calculate the value of the account after t years, with principal P and annual percentage rate (APR) r compounded n times per year, is given by:

A = P(1 + r/n)^(nt)

In this case, P = $690, r = 0.022 (2.2% expressed as a decimal), n = 4 (compounded quarterly), and t is the number of years.

So the function to calculate the value of the account after t years is:

A(t) = 690(1 + 0.022/4)^(4t)

Simplifying and rounding to four decimal places, we get:

A(t) = 690(1.0055)^4t

To find the annual percentage yield (APY), we use the formula:

APY = (1 + r/n)^n - 1

In this case, r = 0.022 and n = 4, so:

APY = (1 + 0.022/4)^4 - 1

= 0.022321

Multiplying by 100 and rounding to two decimal places, we get an APY of 2.23%.

The correct answer is:

The equation is [tex]7(c-0.75) = 2.80[/tex], and the regular price of a cookie is [tex]c =\$1.15[/tex].

Explanation:

c is the regular price of a cookie. We know that today they are $0.75 less than the normal price; this is given by the expression [tex]c-0.75[/tex].

We also know if we buy 7 of them, the total is $2.80. This means we multiply our expression, [tex]c-0.75[/tex], by 7 and set it equal to $2.80:

[tex]7(c-0.75) = 2.80[/tex]

To solve, first use the distributive property:

[tex]7 \times c-7\times0.75 = 2.80[/tex]

[tex]7c-5.25 = 2.80[/tex]

Add 5.25 to each side:

[tex]7c-5.25+5.25 = 2.80+5.25[/tex]

[tex]7c = 8.05[/tex]

Divide each side by 7:

[tex]7c\div7 = 8.05\div7[/tex]

[tex]c = \$1.15[/tex].

3, 6, 11, 18, 27, 38, 51  , Next term 51 in the sequence is nth term .

What does math sequence mean?

An arrangement of numbers in a specific order is referred to as a sequence. The sum of the components of a sequence, on the other hand, is what is referred to as a series.

SEQUENCE    3,6,11,18,27...

  the series follows the odd counting.

for example:

we have odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, etc.

now

    3 + 3 = 6

    6 + 5 = 11

we can see adding odd numbers in a series results in the solution of the proceeding number of series.

similarly,

    11 + 7 = 18

     18 + 9 = 27

      27 + 11 = 38

now adding 13 to 38 according to the series will result in the next number.

     38 + 13  = 51

hence, 51 is the next number in the series.

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The graph that matches the piecewise function, f(x) = √(x + 5), if x < -2, f(x) = |x + 1| if -2 ≤ x ≤ 2, and f(x) = (x - 2)² if x > 2 is the graph in the third option.

A piecewise function is a function is a function that consists of two or more subfunctions each of which are applied, based on the specific interval of the input variable.

The intervals of the piecewise function are;

f(x) = √(x + 5) if x < -2

f(x) = |x + 1| -2 ≤ x ≤ 2

f(x) = (x - 2)² if x > 2

The graph of the piecewise function is a three piece graph which consists of the graph of f(x) = √(x + 5), for x values less than -2, f(x) = |x + 1|, for x-values in the interval -2 ≤ x ≤ 2 and the graph of f(x) = (x - 2)²

The <-2, symbol indicates the presence of an open circle in the graph of f(x) = √(x + 5) at x = -2

The interval -2 ≤ x ≤ 2 for the function f(x) = |x + 1| indicates that the graph of f(x) = |x + 1| in the interval -2 ≤ x ≤ 2, consists of closed circles at x = -2 and x = 2.

The interval, x > 2, for the function, f(x) = (x - 2)², indicates that the presence of an open circle in the graph of f(x) = (x - 2)² at x = 2.

The correct option for the graph of the piecewise function is therefore the third option.

Please find the attached the graph of the piecewise function created with MS Excel

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The volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

To find the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis, we use the formula:

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to find the equation of the curve that is generated when we rotate y = 4 - 2x² around the y-axis. To do this, we use the formula for the equation of a curve generated by revolving y = f(x) around the y-axis, which is:

x² + y² = r²

where r is the distance from the y-axis to the curve at any point (x, y).

Substituting y = 4 - 2x² into this formula, we get:

x² + (4 - 2x²) = r²

Simplifying, we get:

r² = 4 - x²

Therefore, the radius of the circular cross-sections perpendicular to the y-axis is given by:

r = √(4 - x²)

Now, we can integrate πr²dy from y = 0 to y = 2:

V = ∫[0,2] π(√(4 - x²))²dy

V = ∫[0,2] π(4 - x²)dy

V = π∫[0,2] (4y - y²)dy

V = π(2y² - (1/3)y³)∣[0,2]

V = π(8 - (8/3))

V = (16/3)π

Therefore, the volume of the solid generated by revolving the region enclosed by the curves y = 4 - 2x², y = 0, x = 0, and y = 2 through 360° about the y-axis is (16/3)π cubic units.

b. To find the volume of the solid generated by revolving the region enclosed by the curves x = √y+9, x = 0, and y = 1 through 360° about the y-axis, we use the same formula as in part (a):

V = ∫[a,b] πr²dy

where a and b are the limits of integration in the y-direction, r is the radius of the circular cross-sections perpendicular to the y-axis, and V is the volume of the solid.

First, we need to solve the equation x = √y+9 for y in terms of x:

x = √y+9

x² = y + 9

y = x² - 9

Next, we need to find the equation of the curve that is generated when we rotate y = x² - 9 around the y-axis. Using the same formula as in part (a), we get:

r = x

Now, we can integrate πr²dy from y = 1 to y = 10 (since x = 0 when y = 1 and x = 3 when y = 10):

V = ∫[1,10] π(x²)²dy

V = π∫[1,10] x⁴dy

V = π(1/5)x⁵∣[0,3]

V = π(243/5)

Therefore, the volume of the solid generated by revolving the region.

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Answer:

arc length = 2.2π inches

Step-by-step explanation:

arc length is calculated as

length = circumference of circle × fraction of circle

           = 2πr × [tex]\frac{22}{360}[/tex] ( r is the radius )

           = 2π × 18 × [tex]\frac{22}{360}[/tex] ( cancel 18 and 360 by 18 )

          = 2π × [tex]\frac{22}{20}[/tex]

        = [tex]\frac{44}{20}[/tex] π

       = 2.2π inches

correct answer is

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation. It has two sides that are divided by an equal symbol. Each side of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and logarithms.

c(6) = 5(6) + 3 = 30 + 3 = 33

This means that the total cost of 6 games (including shoe rental) at Pin Town Lanes is $33.

Therefore, the correct answer is:

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Answer:

Ohio

Colorado

Oregon

Step-by-step explanation:

1/2 of the letters in Ohio are O)

3/8 letters in Colorado are O)

2/6 letters in Oregon are the letter O which Is 1/3

The weighted average length of a nail from the carpenter's box is 3.5 centimeters.

Different from calculating the average, the weighted average implies considering the frequency or abundance percentage. Now, to calculate the average weighted we will need to multiply the length of each type of nail by the abundance and finally, we will need to add the results obtained. The process is shown below:

Short nail: 2.5 cm x 70.5%= 1.7625 cm

Medium nail: 5.0 cm x (19% = 0.95 cm

Long nail: 7.5 cm x 10.5% = 0.7875 cm

1.7625 cm + 0.95 cm + 0.7875 cm = 3.5 cm

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Step-by-step explanation:

There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:

P = 2

Q = 5

R = 1

S = 8

T = 9

U = 9

With these values, we have:

PQR = 251

STU = 156

And the sum of PQR and STU is indeed 407.

Answer:

[tex]y=-\frac{1}{4}x+5[/tex]

Step-by-step explanation:

Given the point (8,3) and slope of 4, we can write an equation in point-slope form.

We know that any line perpendicular to another line has a opposite reciprocal. The opposite reciprocal of 4 is [tex]-\frac{1}{4}[/tex].

Now, to write this in point slope form.

Point slope formula:

[tex]y-y_1=m(x-x_1)[/tex]

New equation:

[tex]y-3=-\frac{1}{4}(x-8)[/tex]

Simplify:

[tex]y=-\frac{1}{4}x+5[/tex]

Here is the equation :)

Answer: yes 2/1 is more than one

Step-by-step explanation: 2/1 is equivalent to 2 while 1 is just 1

Answer:

No! 2/1 is less then 1 because when devided, your answer will be -2 which is less then 1.

Answer:

1.11

2.4

3.5

pls correct me if I'm wrong

Answer:

38. (b) 11

39. (c) 4

40. (c) 5

Step-by-step explanation:

38.)

[tex]\implies \: \sf \sqrt{3xx - 8} = 5 \\ \\ \implies \: \sf 3xx - 8 = {(5)}^{2} \\ \\ \implies \: \sf 3xx - 8 = 25 \\ \\ \implies \: \sf 3xx = 25 + 8 \\ \\ \implies \: \sf 3xx = 33 \\ \\ \implies \: \sf xx = \dfrac{33}{3} \\ \\ \implies \: \sf xx = 11\\ [/tex]

Hence, Required answer is option (b) 11.

39.)

[tex]\implies \: \sf \sqrt{4xx -7 } - 3 = 0 \\ \\ \implies \: \sf \sqrt{4xx - 7} = 3 \\ \\ \implies \: \sf 4xx - 7 = {(3)}^{2} \\ \\ \implies \: \sf 4xx - 7 = 9 \\ \\ \implies \: \sf 4xx = 9 + 7 \\ \\ \implies \: \sf 4xx = 16 \\ \\ \implies \: \sf xx = \dfrac{16}{4} \\ \\ \implies \: \sf xx = 4 \\ [/tex]

Hence, Required answer is option (c) 4.

40.)

[tex]\implies \: \sf \sqrt{6xx + 6} - 6 = 0 \\ \\ \implies \: \sf \sqrt{6xx + 6} = 6 \\ \\ \implies \: \sf 6xx + 6 = {(6)}^{2} \\ \\ \implies \: \sf 6xx + 6 = 36 \\ \\ \implies \: \sf 6xx = 36 - 6 \\ \\ \implies \: \sf 6xx = 30 \\ \\ \implies \: \sf xx = \dfrac{30}{6} \\ \\ \implies \: \sf xx = 5 \\ [/tex]

Hence, Required answer is option (c) 5.

Answer:

it should be true because sum of 3 interior angle of a triangle is 180 degree

Answer:

True.

Step-by-step explanation:

A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.

The bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

Trigοnοmetry is οne οf the mοst impοrtant branches in mathematics that finds huge applicatiοn in diverse fields. The branch called “Trigοnοmetry” basically deals with the study οf the relatiοnship between the sides and angles οf the right-angle triangle.

Hence, it helps tο find the missing οr unknοwn angles οr sides οf a right triangle using the trigοnοmetric fοrmulas, functiοns οr trigοnοmetric identities. In trigοnοmetry, the angles can be either measured in degrees οr radians. Sοme οf the mοst cοmmοnly used trigοnοmetric angles fοr calculatiοns are 0°, 30°, 45°, 60° and 90°.

We can use trigοnοmetry tο sοlve fοr the hοrizοntal distance. Let x be the hοrizοntal distance frοm the bοat tο the lighthοuse.

Then, tan(5°) = οppοsite/adjacent = 139/x

Sοlving fοr x, we get:

x = 139/tan(5°) ≈ 1592.53 feet

Therefοre, the bοat's hοrizοntal distance frοm the lighthοuse (and the shοre) is apprοximately 1592.53 feet.

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The values are [tex]\lim_{x \to {\(-2}^{-}[/tex] [tex]f(x) = \frac{1}{h}[/tex]

[tex]\lim_{x \to {\(-2}^{+}[/tex] [tex]f(x) = 3[/tex] and [tex]\lim_{x \to {\(2}[/tex] [tex]f(x) =[/tex] 3

The concept of limits is used to describe the behavior of a function as its input approaches a certain value.

[tex]\lim_{x \to {\(-2}^{-}[/tex] [tex]f(x) = \lim_{h \to \o[/tex] [tex]f(-2-h)[/tex] = [tex]\lim_{h \to \o[/tex] [tex]\frac{1}{(-2-h)+2}[/tex]

[tex]\lim_{h \to \o[/tex]  [tex]\frac{1}{h}[/tex]  

(So, Does not exist)

[tex]\lim_{x \to {\(-2}^{+}[/tex] [tex]f(x)[/tex] = [tex]\lim_{h \to \o[/tex] [tex]f(-2+h)[/tex]

[tex]\lim_{h \to \o[/tex] [tex]3(-2+h)+9[/tex] = 3

(So, Does not exist)

[tex]\lim_{x \to {\(-2}[/tex] [tex]f(x)[/tex] = 3×(-2) +9 = -6+9= 3

(So, Does not exist)

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Answer:

graph Z , Horizontal Shift

Step-by-step explanation:

Got it right on edmentum.

Answer:

Step-by-step explanation:

First, we need to find the median of each series.

For series a, the median is:

(3680 + 3682)/2 = 3681

For series b, the median is:

(382 + 408)/2 = 395

Next, we calculate the deviation of each value from its respective median:

For series a:

|3487 - 3681| = 194

|4572 - 3681| = 891

|4124 - 3681| = 443

|3682 - 3681| = 1

|5624 - 3681| = 1943

|4388 - 3681| = 707

|3680 - 3681| = 1

|4308 - 3681| = 627

For series b:

|487 - 395| = 92

|508 - 395| = 113

|620 - 395| = 225

|382 - 395| = 13

|408 - 395| = 13

|266 - 395| = 129

|186 - 395| = 209

|218 - 395| = 177

Then, we calculate the mean deviation for each series by adding up the absolute deviations and dividing by the number of values:

For series a:

Mean deviation = (194 + 891 + 443 + 1 + 1943 + 707 + 1 + 627)/8

= 682.5

For series b:

Mean deviation = (92 + 113 + 225 + 13 + 13 + 129 + 209 + 177)/8

= 115.5

Comparing the two mean deviations, we see that series a has a larger mean deviation than series b. This indicates that series a has more variability than series b.

Answer:

D 20

Step-by-step explanation:

Let's call the integer we're looking for "x". We know that 18% of x is greater than 3.5, so we can write the inequality:

0.18x > 3.5

To solve for x, we can divide both sides by 0.18:

x > 3.5 ÷ 0.18

x > 19.44

We want the smallest possible integer that satisfies this inequality, which is 20. So the answer is D) 20.

A function declaration specifies the return data type, name of the function, and the parameter variable(s).

In programming, a function declaration is a statement that specifies the characteristics of a function. It includes the name of the function, the return data type (if any), and the parameter variable(s) (if any) that the function expects to receive as input. The declaration is used to inform the compiler or interpreter about the existence and behavior of the function, so that it can be called from other parts of the program. The function's actual implementation or definition is typically written separately from the declaration. By separating the declaration and implementation of a function, programs can be more modular and easier to maintain.

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Answer:

The predetermined overhead rate is calculated as follows:

Predetermined overhead rate = Estimated total overhead / Estimated total direct labor hours

In this case, the estimated total overhead is $180,000, and the estimated total direct labor hours are 30,000. Therefore:

Predetermined overhead rate = $180,000 / 30,000 hours

Predetermined overhead rate = $6 per direct labor hour

So, the predetermined overhead rate is $6 per direct labor hour.