What's the circumference of a
circle with a radius of 4 inches?
Use 3.14 for I.
C = [?] inches
Enter the number that belongs in the green
box. Do not round your answer.
Hint: C = 2+r
I cant find the answer anywhere HELP!!!

The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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Answer:

21

Step-by-step explanation:

3(6) +4(2) - 5

18 + 8 - 5

26 - 5

= 21

The geometric figure which is most likely the next step in the series include the following: C. heptagon.

In Mathematics, a series can be defined as a sequence of real and natural numbers in which each term differs from the preceding term by a constant numerical quantity.

By critically observing the given series, we can logically deduce that the first geometric figure represent a square with four (4) sides, the second geometric figure represent a pentagon with five (5) sides, the third geometric figure represent a hexagon with six (6) sides. This ultimately implies that, each of the sides of the geometric figure increases by one (1).

In this context, the next geometric figure in the series must be a heptagon with seven (7) sides.

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Answer:

x = 7 1/2

Step-by-step explanation:

We can use proportions to solve

12         5

----- = -----

18          x

Using cross products

12x = 18*5

12x = 90

Divide by 12

12x/12 = 90/12

x = 7 1/2

12/18 = 5/x

12x = 18 × 5

12x = 90

x = 90 ÷ 12

x = 7,5 => x = 7 1/2

Answer:

Natural

Step-by-step explanation:

Ln in mathematics mean natural log. Natural log is the log of a number with base e where e=2.71828. For understanding if the number is 2.71828^10 then the ln of 2.71828^10 is 10.

The surface area of the complex figure given two cuboids is 626 \(yd^{2}\)

Surface area of Cuboid is equal to the sum of the areas of it’s 6 rectangular faces, which is given by:

Surface Area of a Cuboid (SA) = 2 (lw + wh + lh)

Given two cuboids in the complex solid

Surface area Cuboid 1 = 2(lw + wh + lh)

Given Length = 12 yd

Width = 3 yd

Height = 11 yd

Surface area = 2{(12*3) + (3*11) + (12*11)

SA = 2(36 + 33 + 132)

SA = 2(201)

SA = 402 \(yd^{2}\)

Surface area of Cuboid 2 = 2(lw + wh + lh)

Where Length = 12 yd

Width = 4 yd

Height = 4 yd

Surface area = 2{(12*4) + (4*4) + (12*4)}

SA = 2(48 + 16 + 48)

SA = 2(112)

SA = 224 \(yd^{2}\)

Surface area of the complex solid = 402\(yd^{2}\) + 224\(yd^{2}\)

Surface area = 626 \(yd^{2}\)

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Answer:

\(\sf 6)\quad \dfrac{3}{25}=12\%\)

\(\sf 7) \quad \dfrac{1}{11}=9.1\%\)

\(\sf 8) \quad \dfrac{7}{48}=14.6\%\)

Step-by-step explanation:

\(\boxed{\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}}\)

The events of the first spin landing on an odd number and the second spin landing on 2 are independent events because the outcome of the each spin does not affect the outcome of the other spin. Therefore, the probabilities remain the same for each spin.

Since the spinner has an equal chance of landing on each of its five numbered regions, we can determine the probability of the first spin landing on an odd number and the second spin landing on 2 by multiplying the probabilities of each individual event.

There are three odd numbers (1, 3, and 5), so the probability of the first spin landing on an odd number is:

\(\sf P(X=odd)=\dfrac{3}{5}\)

There is only one region on the spinner with the number 2, therefore the probability of the second spin landing on 2 is:

\(\sf P(X=2)=\dfrac{1}{5}\)

To find the probability of both events happening, multiply the individual probabilities:

\(\sf Probability=\dfrac{3}{5} \times \dfrac{1}{5}=\dfrac{3}{25}\)

Therefore, the probability that the first spin lands on an odd number and the second spin lands on 2 is 3/25 or 12%.

\(\hrulefill\)

When you choose a mystery novel for the first book, the number of mystery novels and the total number of remaining books change. This means that the probability of selecting a mystery novel for the second book is influenced by the previous selection. Therefore, the events are dependent because the outcome of the first book selection affects the probability of the second book selection.

To find the probability that both books chosen are mystery novels, we need to calculate the probability of selecting a mystery novel for the first book and then, given that the first book was a mystery novel, the probability of selecting another mystery novel for the second book.

There are a total of 4 mystery novels out of the 12 books available. So, the probability of selecting a mystery novel as the first book is:

\(\sf P(Mystery\;1)=\dfrac{4}{12}=\dfrac{1}{3}\)

After selecting a mystery novel for the first book, there will be 3 mystery novels remaining out of the total 11 remaining books. Therefore, the probability of selecting another mystery novel for the second book, given that the first book was a mystery novel, is:

\(\sf P(Mystery\;2)=\dfrac{3}{11}\)

To find the probability of both events happening, multiply the individual probabilities:

\(\sf Probability=\dfrac{1}{3} \times \dfrac{3}{11}=\dfrac{3}{33}=\dfrac{1}{11}\)

Therefore, the probability of randomly selecting two mystery novels is 1/11 or approximately 9.1%.

\(\hrulefill\)

The events in this scenario are dependent because the total number of shirts changes after the first selection, which affects the probability of the second selection.

To calculate the probability of wearing a blue shirt on Monday and a white shirt on Tuesday, we need to consider the number of blue shirts and white shirts, as well as the total number of shirts remaining after the first selection.

There are a total of 7 blue shirts out of the 16 shirts available. So, the probability of selecting a blue shirt on Monday is:

\(\sf P(Blue\;on\;Monday)=\dfrac{7}{16}\)

After selecting a blue shirt on Monday, we have all 5 white shirts still available, but the total number of shirts is reduced to 15 (since one shirt has been chosen). Therefore, the probability of selecting a white shirt on Tuesday, given that a blue shirt was worn on Monday, is:

\(\sf P(White\;on\;Tuesday)=\dfrac{5}{15}=\dfrac{1}{3}\)

To find the probability of both events happening, multiply the individual probabilities:

\(\sf Probability=\dfrac{7}{16} \times \dfrac{1}{3}=\dfrac{7}{48}\)

Therefore, the probability of wearing a blue shirt on Monday and a white shirt on Tuesday is 7/48 or approximately 14.6%.

Answer:

\(g(x)=\log_3(x+4)\)

Step-by-step explanation:

Translations

For \(a > 0\)

\(f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}\)

\(f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}\)

\(f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}\)

\(f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}\)

Parent function:

  \(f(x)=\log_3x\)

From inspection of the graph:

If there was a vertical translation, the end behaviors of both g(x) and f(x) would be the same in that the both functions would be increasing from -∞ in quadrant IV.

As the x-intercepts of both functions is different, and g(x) increases from -∞ in quadrant III, this indicates that there has been a horizontal translation of 4 units to the left.

Therefore:

\(g(x)=f(x+4)=\log_3(x+4)\)

Further Proof

Logs of zero or negative numbers are undefined.

From inspection of the graph, \(x=-3\) is part of the domain of g(x).

Therefore, input this value of x into the answer options:

 \(g(-3)=\log_3(-3)-4\implies\) undefined

 \(g(-3)=\log_3(-3)+4\implies\) undefined

 \(g(-3)=\log_3(-3-4)=\log_3(-7)=\implies\) undefined

 \(g(-3)=\log_3(-3+4)=\log_3(1)=0\)

Hence proving that \(g(x)=\log_3(x+4)\)

The equation that represents g(x) is:  \(g(x) = log_3(x + 4)\)

The correct answer is: the fourth option:

\(g(x) = log_3(x + 4)\).

Here, we have to find the equation that represents g(x) using f(x), we need to consider how the graph of g(x) is related to the graph of f(x).

The graph of f(x) = log base 3 of x starts from negative infinity in quadrant four, passes through (0, 1), and increases to positive infinity.

The graph of g(x) is increasing from negative infinity in quadrant two, passes through (0, -3), and increases to positive infinity.

So, we can see that the graph of g(x) is the graph of f(x) shifted 4 units to the left along the x-axis.

Therefore, the equation that represents g(x) is:

\(g(x) = log_3(x + 4)\)

The correct answer is: the fourth option:

\(g(x) = log_3(x + 4)\).

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The probability of patients are females older than 30 years of age who are not admitted to the hospital is 0.19

The probability of patients who are females and are admitted will be 0.15. The probability of those younger than 30 years will be 0.21.

The proportion of the patients are females older than 30 years of age who are not admitted to the hospital will be:

= [(1 - 0.45) - 0.21] - 0.15

= 0.19

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Carson's work is correct for solving the equations.

Given that;

Carson wants to solve this system of equations.

y = x² + 5x − 6

y = x − 1

Now, We can solve first equation as;

y = x² + 5x - 6

y = x² + 5x - 6 = 0

⇒ x = - 5 ± √5² - 4×1×- 6 / 2

⇒ x = - 5 ± √25 + 24 / 2

⇒ x = - 5 ± √49 / 2

⇒ x = - 5 ± 7/2

⇒ x = - 5 + 7 / 2

⇒ x = 2/2

⇒ x = 1

⇒ x = - 5 - 7 / 2

⇒ x = - 12 / 2

⇒ x = - 6

Hence, From (ii);

⇒ y = x - 1

At x = 1;

y = 1 - 1

y = 0

At x = - 6;

y = - 6 - 1

y = - 7

Hence, Carson's work is correct.

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The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

   = 1.67

Z - score for X = 156:

Z = (156 - 120)/18

  = 2

So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471

Rounding off to four decimal places,

P(150 < X < 156) = 0.0247

Thus, the required probability is 0.0247.

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The value of the variable w associated to the two line segments is equal to 3.5.

In this question we find two line segments that are supposed to be of equal length. We need to determine the value of a variable w both by definitions and theorems from Euclidean geometry and algebra properties. The complete procedure is now shown:

Step 1 - Given:

JK = LM, JK = 4 · w + 1,

Step 2 - Given:

LM = 6 · w - 6

Step 3 - Steps 1 & 2 / Algebra properties:

4 · w + 1 = 6 · w - 6

Step 4 - Algebra properties:

2 · w = 7

Step 5 - Algebra properties / Result

w = 3.5

The value of the variable w is equal to 3.5.

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Answer: a = 2√3

First method (Pythagoras theorem):

a² + b² = c²

a² + 2² = 4²

a² = 16 - 4

a = √12

a = 2√3

Second method (sine rule):

opposite/hypotenuse = sin(x)

a/4 = sin(60)

a = 4sin(60)

a = 2√3

Third method (tan rule):

opposite/adjacent = tan(x)

a/2 = tan(60)

a = 2tan(60)

a = 2√3

Answer:

2√3

Step-by-step explanation:

From inspection of the given triangle:

As we cannot be sure that ΔABC is a right triangle since it is not marked as such, use the cosine rule to find the exact length of side a.

Cosine Rule

\(a^2=b^2+c^2-2bc \cos A\)

where a, b and c are the sides and A is the angle opposite side a

Given:

Substitute the given values into the formula and solve for a:

\(\implies a^2=2^2+4^2-2(2)(4) \cos 60^{\circ}\)

\(\implies a^2=4+16-16\left(\dfrac{1}{2}\right)\)

\(\implies a^2=20-8\)

\(\implies a^2=12\)

\(\implies a=\sqrt{12}\)

\(\implies a=\sqrt{4 \cdot 3}\)

\(\implies a=\sqrt{4}{\sqrt{3}\)

\(\implies a=2\sqrt{3}\)

Therefore, the exact length of side a is 2√3.

To find out if ΔABC is a right triangle, use Pythagoras Theorem to solve for side a:

\(\implies a^2+b^2=c^2\)

\(\implies a^2+2^2=4^2\)

\(\implies a^2+4=16\)

\(\implies a^2=12\)

\(\implies a=\sqrt{12}\)

\(\implies a=2\sqrt{3}\)

As the measure of side a is the same as the solution found when using the cosine rule, we can conclude that ΔABC is a right triangle.

Answer:

51 deg

Step-by-step explanation:

By corresponding parts of congruent polygons, <BAD is congruent to <FEH.

m<BAD = m<FEH = 51 deg

Answer: 51 deg

Answer:

51 degrees

Step-by-step explanation:

The answer is 51 degrees because the two pyramids shown are congruent which means that since we are given the degree measure of angle FEH then we can plug in that measure to find the measure of angle BAD. We can also use what we know about degrees to figure out that because angle CBA is equal to 129 degrees then angle BAD is equal to the difference between the measure of angle CBA and 180 degrees which is 59 degrees.

The required value of the given sum is given as 4.8. Option B is correct.

Given that,
To estimate the sum of 3.62 + 1.16 by rounding each addend to the nearest tenth.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.

Here,
Given expression,
= 3.62 + 1.16
Round the values to the nearest tenth,
= 3.6 + 1.2
= 4.8

Thus, the required value of the given sum is given as 4.8. Option B is correct.

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The period of a simple harmonic oscillator is given by

Then, if k = 5 and the period has to be 6 seconds, we can find the mass m as:

NOTE: as T is in seconds, we assume standard units for the constant k. Then, the mass is in kg.

Answer: the mass has to be approximately 4.56 kg.

Answer:

$1,233.50

Step-by-step explanation:

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Using proportions, the commissions are given as follows:

5. a. $200. b. $0. c. $0. d. $200.

6. a. $250. b. $200. c. $0. d. $490.

7. a. $250. b. $800. c. $300. d. $1350.

8. a. $250. b. $800. c. $1250. d. $2300.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item 5, the amount is less than $5,000, hence there is a single commission of 5%, as follows:

0.05 x 4000 = $200.

Hence the amounts are:

a. $200. b. $0. c. $0. d. $200.

For item 6, the commissions are divided as follows:

For a total of $490, as 250 + 240 = 490.

Hence the amounts are:

a. $250. b. $200. c. $0. d. $490.

For item 7, the commissions are divided as follows:

For a total of $1,350, as 250 + 800 + 300 = 1350.

Hence the amounts are:

a. $250. b. $800. c. $300. d. $1350.

For item 8, the commissions are divided as follows:

For a total of $2,300, as 250 + 800 + 1250 = 2300.

Hence the amounts are:

a. $250. b. $800. c. $1250. d. $2300.

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Answer:

2.5

Step-by-step explanation:

the length has increased by 7.5/3 = 2.5.

so the scale factor is 2.5

The value of x when y = 117 is 13 as y varies directly with x.

Proportional relationships are relationships between two variables where their ratios are equivalent.

Direct variation equation is a linear equation in two variables.

This is expressed as; y varies directly with x

y ∝ x,  then y = kx

Where k is the proportionality constant.

Given that;  x = 4 and y = 36, we find the proportionality constant k.

y = kx

k = y / x

k = 36/4

k = 9

Now, when y = 117, x will be?

y = kx

x = y / k

x = 117/9

x = 13

Therefore, the numerical value of x is 13.

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Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Answer:

z = 2.1

Step-by-step explanation:

\(z=\frac{x-\mu}{\sigma}\\ \\z=\frac{121-79}{20}\\ \\z=\frac{42}{20}\\ \\z=2.1\)

This tells us that the person's score of 121 places them 2.1 standard deviations above the mean score of 79.

The scenarios that can be considered a seller-based discount are:

A. The offer by Wire and Cable

B. Carfna's Fine Foods

C. Mouser Electronics offer

E. Carchex Car Maintenance

A seller-based discount is a discount that is offered by a seller for the early purchase of a product. The goal of the seller in this case is to get cash as he or she is in an immediate need for cash.

The most outstanding example is that of Carchex Car Maintenance where an offer is made by the seller for the early purchase of products.

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