A string measures 30 centimeters. About how many inches long is the string?
A. 11

B. 11.8

C. 15

D. 20

Answer:

x = 8°

Step-by-step explanation:

Given the three angles with measurements, m < 90°, m < 40°, and m < (6x + 2)°, in which the sum of their measurements equal 180°,

We can establish the following formula to solve for the value of x:

180° = m < 90° + m < 40° + m < (6x + 2)°

180° = 90° +  40° + 6x + 2

180° = 132° + 6x

Subtract 132° on both sides of the equation:

180°- 132° = 132° + 6x - 132°

48° = 6x

Divide both sides by 6 to solve for x:

\(\frac{48}{6} = \frac{6x}{6}\)

x = 8°

To verify whether this is the correct answer, plug in the value of x into the original equation:

180° = m < 90° + m < 40° + m < (6x + 2)°

180° = 90° +  40° + 6(8)° + 2°

180° = 90° +  40° + 48° + 2°

180° = 180°

Therefore, we derived the correct value for x = 8°.

Let's solve the given problem. Suppose v is an eigenvector of a matrix A with eigenvalue 5 and an eigenvector of a matrix B with eigenvalue 3.

We are to determine the eigenvalue λ corresponding to v as an eigenvector of 2A² + B².We know that the eigenvalues of A and B are 5 and 3 respectively. So we have Av = 5v and Bv = 3v.Now, let's find the eigenvalue corresponding to v in the matrix 2A² + B².Let's first calculate (2A²)v using the identity A²v = A(Av).Now, (2A²)v = 2A(Av) = 2A(5v) = 10Av = 10(5v) = 50v.Note that we used the fact that Av = 5v.

Therefore, (2A²)v = 50v.Next, let's calculate (B²)v = B(Bv) = B(3v) = 3Bv = 3(3v) = 9v.Substituting these values, we can now calculate the eigenvalue corresponding to v in the matrix 2A² + B²:(2A² + B²)v = (2A²)v + (B²)v = 50v + 9v = 59v.We can now write the equation (2A² + B²)v = λv, where λ is the eigenvalue corresponding to v in the matrix 2A² + B². Substituting the values we obtained above, we get:59v = λv⇒ λ = 59.Therefore, the eigenvalue corresponding to v as an eigenvector of 2A² + B² is 59.

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Answer:

526

758

393

146

115

Step-by-step explanation:

The relative frequency for private vehicles is 97%, the relative frequency for public transport is 0 and the relative frequency for others is 2.

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell by the total frequency.

We know the formula for the relative frequency:

\(\rm Rf = \frac{Frequency}{Total \ frequency}\)

From the data given the Rf value for the private vehicle:

\(\rm Rf = \frac{1887}{1928} \times100\)

Rf = 0.97×100 = 97%

For public transport:

= 0.005×100

= 0.5

= 0  (whole value)

For other:

= 0.022×100

= 2.2

=2 (whole value)

Thus, the relative frequency for private vehicles is 97%, the relative frequency for public transport is 0 and the relative frequency for others is 2.

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Answer:

x=40

Step-by-step explanation:

120=3x due to vertical angles theorem

120/3

40

x=40

Tthe area enclosed by the lemniscate is 4 units squared.

The lemniscate is symmetric about the x-axis and y-axis, so we can find the area in the first quadrant and multiply it by 4.

In polar coordinates, the equation of the lemniscate can be written as:

r^2 = 4cos(2θ)

Squaring both sides, we get:

r^4 = 16cos^2(2θ)

Converting to Cartesian coordinates, we have:

x^2 + y^2 = 16cos^2(2θ)

Using the identity cos(2θ) = (1/2)(cos^2θ - sin^2θ), we can simplify the equation to:

x^2 + y^2 = 8(cos^4θ - cos^2θsin^2θ)

Multiplying both sides by r, we get:

r^2 = 8r(cos^4θ - cos^2θsin^2θ)

Substituting x = rcosθ and y = rsinθ, we get:

x^2 + y^2 = 8(x^2 - xy + y^2)(x^2 + y^2)

Simplifying, we get:

x^4 - 2x^2y^2 + y^4 = (1/8)

This is the equation of a quartic curve, which is symmetric about the x-axis and y-axis.

To find the area enclosed by the lemniscate in the first quadrant, we can integrate over the range 0 ≤ θ ≤ π/4:

A = 4 ∫[0,π/4] ∫[0,r(θ)] r dr dθ

where r(θ) = 2√cos(2θ).

Evaluating the integral, we get:

A = 4 ∫[0,π/4] ∫[0,2√cos(2θ)] r dr dθ

= 4 ∫[0,π/4] (1/2)(2√cos(2θ))^2 dθ

= 4 ∫[0,π/4] 2cos(2θ) dθ

= 4[sin(π/2) - sin(0)]

= 4

Therefore, the area enclosed by the lemniscate is 4 units squared.

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According to the question the solution to the limit \(\(\lim_{x \rightarrow -2^+} \frac{|2x+4|}{\sqrt{x+2}}\) is 0.\)

To solve the limit \(\(\lim_{x \rightarrow -2^+} \frac{|2x+4|}{\sqrt{x+2}}\)\), we need to evaluate the expression as \(\(x\)\) approaches \(\(-2\)\) from the positive side.

Since the limit is one-sided, we only consider values of \(\(x\)\) that are greater than \(\(-2\).\)

Let's first simplify the expression:

\(\[\lim_{x \rightarrow -2^+} \frac{|2x+4|}{\sqrt{x+2}} = \lim_{x \rightarrow -2^+} \frac{2|x+2|}{\sqrt{x+2}}\]\)

Next, let's evaluate the limit using the properties of limits:

\(\[\lim_{x \rightarrow -2^+} \frac{2|x+2|}{\sqrt{x+2}} = \frac{2|-2+2|}{\sqrt{-2+2}} = \frac{0}{0}\]\)

The expression \(\(\frac{0}{0}\)\) is an indeterminate form, which means further simplification or evaluation is required.

To proceed, we can apply L'Hôpital's rule by taking the derivative of the numerator and denominator:

\(\[\lim_{x \rightarrow -2^+} \frac{2|x+2|}{\sqrt{x+2}} = \lim_{x \rightarrow -2^+} \frac{2}{\frac{1}{2\sqrt{x+2}}} = \lim_{x \rightarrow -2^+} 4\sqrt{x+2} = 4\sqrt{0} = 0\]\)

Therefore, the solution to the limit \(\(\lim_{x \rightarrow -2^+} \frac{|2x+4|}{\sqrt{x+2}}\) is 0.\)

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The probability of obtaining a sum of 18 when rolling four dice and taking the sum of the three highest values can be calculated by determining the number of favorable outcomes and dividing it by the total number of possible outcomes.

When rolling four dice, each die can have six possible outcomes, ranging from 1 to 6. To find the probability of obtaining a sum of 18, we need to determine the number of favorable outcomes. In this case, we are interested in the three highest values summing up to 18.

To calculate this, we can use combinations. The three highest values that can result in a sum of 18 are 6, 6, and 6. We can choose these three values from the four dice in only one way. The remaining die can have any value from 1 to 6, giving us six possible outcomes.

Therefore, the number of favorable outcomes is 1, and the total number of possible outcomes is 6^4 (since each die has six possible outcomes and we are rolling four dice). Dividing the number of favorable outcomes by the total number of possible outcomes gives us the probability: 1/(6^4) ≈ 0.00077, or approximately 0.077%. Thus, the probability of obtaining a sum of 18 when rolling four dice and taking the sum of the three highest values is very low.

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Answer:

Since they're both equated to y...

7x² + 6x – 13 = 3x – 3

Bringing all the left

7x² + 3x – 10 = 0

Solving for x

you have

x = 1 or x = –10/3

Now substitute to get y

y = 0 or –13

On solving the provided question, we can say that equation let x =amount of copies sold  = > 37,600is = .073  X x = 515,068.4932.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x =amount of copies sold to date.

37,600is = .073  X x

t x = 37,600 / .073

= 515,068.4932.

round to nearest 515,068.

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Answer: 0.13 cents per minute.

Step-by-step explanation:

7.80 divided by 60(min per hour.)= .13 cents.

The price we have to pay for the disc after 10% discount is 1467 dollars.

Percentage is the value per hundredth.

According to the given question we bought a disc which costs 1630 dollars there's a 10% discount we have to find how much i have to pay.

10% of 1630 dollars will be

= (10/100) × 1630 dollars.

= 16300/100 dollars.

= 163 dollars.

So, the price we have to pay for the disc after 10% discount is

= (Total amount - Discount amount)

= ( 1630 - 163 ) dollars.

= 1467 dollars.

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The dataset consists of 5 observations: 23, 39, 29, 34, and 70. By calculating the interquartile range (IQR) and applying the 1.5 * IQR rule, we can identify outliers.

However, in this case, none of the observations fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR, indicating that there are no outliers present in the dataset. To determine if there are any outliers in a dataset, we need to understand the concept of outliers and apply appropriate statistical techniques. In this scenario, we have a dataset with five observations: 23, 39, 29, 34, and 70. To identify outliers, one commonly used method is the interquartile range (IQR). By calculating the IQR, which is the difference between the third quartile (Q3) and the first quartile (Q1), we can assess the spread of the middle 50% of the data. The dataset of five observations exhibits no outliers based on the calculated interquartile range and the application of the 1.5 * IQR rule.

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The percentage of 39/100 can be written as 39% as given in the question.

A percentage is a figure or ratio stated as a fraction of 100. The abbreviations "pct.", "pct," and "pct" are also used. A% is a dimensionless (pure) number with no unit of measurement.

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento. The "cento" symbol was developed from two circles divided by a horizontal line.

As money denominations expanded in the Middle Ages, computations with a denominator of 100 were increasingly prevalent, to the point where it became normal for mathematics texts to incorporate such computations from the late 15th to the early 16th centuries

We write 39/100 in the percentage as 39%

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Answer:

The mean is the average of all the numbers

Step-by-step explanation:

Add all the numbers up and divide by how many numbers there are

Answer:

The answer is explained below

Step-by-step explanation:

The question is not complete, the complete question is Suppose you revolve the plane region completely about the given line to sweep out a solid of revolution. Describe the solid. Then find its surface area in terms of pi.

i) about the y axis

ii) about the x axis

Also the image is attached below.

Answer:

i) about the y axis

If it is revolved about the y axis, the solid produced is a cone with a radius of of 4 units (r = 4) and a height of 3 units (h = 3). The surface area of the cone is:

Surface area = πr (r + √(r² + h²)) = π × 4 (4 + √(4² + 3²)) = 4π (4 + √25) = 4π (4 + 5) = 4π × 9 = 36π unit²

ii) about the x axis

From the image attached, If it is revolved about the x axis, the solid produced is a cone with a radius of of 3 units (r = 3) and a height of 4 units (h = 4). The surface area of the cone is:

Surface area = πr (r + √(r² + h²)) = π × 3 (3 + √(4² + 3²)) = 3π (3 + √25) = 3π (3 + 5) = 3π × 8 = 24π unit²

where is the figure? I can't see it

The the fewest number of tire rotations is 42 to travel the entire distance of the driveway.

It is given that the driveway that is 200 feet long and the tire diameter is 18 inches.

It is required to find the fewest number of tire rotations a tire will make to travel the entire distance of the driveway.

It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).

Driveway length = 200 feet

Diameter of the tire = 10 inches

For converting it to feet divide by 12.

Now the diameter of tire = 18/12 = 1.5 feet

Radius of the tire = 0.75 feet

We know the perimeter of the circle:

\(\rm P = 2\pi r\)

P = 2(π)(0.75)

P = 4.71 feet   ( π =3.14 and P = 0.75)

\(\rm number \ of \ tire \ rotations = \frac{Driveway \ length}{Perimeter \ of tire}\)

\(= \frac{200}{4.71}\)

Number of tire rotation = 42.462 ≈ 42

Thus, the the fewest number of tire rotations is 42 to travel the entire distance of the driveway.

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Step-by-step explanation:

for this you take the midpoints of every interval, multiply them with the corresponding frequency, sum this all up, and divide the result by the total number of cases (here 31 for the 31 days in December).

2 × 12 = 24

7 × 8 = 56

12 × 7 = 84

17 × 4 = 72

--------

236

236 / 31 = 7.612903226... ≈ 7.6

there were estimated 7.6 accidents per day.

a) The equation of the line with a gradient of -1/3 passing through the point (1,1) is y = (-1/3)x + 4/3.

b) The equation of the line passing through the points (-3,5) and (-2,-4) is y = -9x - 22.

c) The equation of the line passing through the points (1,-1) and (2,-3) is y = -2x + 1.

a) To determine the equation of a line with a gradient of -1/3 passing through the point (1,1), we can use the point-slope form of a linear equation.

The point-slope form is given by:

y - y1 = m(x - x1)

where (x1, y1) represents a point on the line, and m represents the gradient.

Substituting the given values, we have:

y - 1 = (-1/3)(x - 1)

Expanding and rearranging the equation:

y - 1 = (-1/3)x + 1/3

y = (-1/3)x + 4/3

Therefore, the equation of the line with a gradient of -1/3 passing through the point (1,1) is y = (-1/3)x + 4/3.

b) To determine the equation of a line passing through the points (-3,5) and (-2,-4), we can use the slope-intercept form of a linear equation.

The slope-intercept form is given by:

y = mx + b

where m represents the gradient, and b represents the y-intercept.

First, let's calculate the gradient (m) using the two given points:

m = (y2 - y1) / (x2 - x1)

= (-4 - 5) / (-2 - (-3))

= (-9) / (1)

= -9

Now, let's choose one of the given points (let's use (-3,5)) to find the y-intercept (b):

y = mx + b

5 = (-9)(-3) + b

5 = 27 + b

b = 5 - 27

b = -22

Therefore, the equation of the line passing through the points (-3,5) and (-2,-4) is y = -9x - 22.

c) To determine the equation of a line passing through the points (1,-1) and (2,-3), we can again use the slope-intercept form.

First, let's calculate the gradient (m) using the two given points:

m = (y2 - y1) / (x2 - x1)

= (-3 - (-1)) / (2 - 1)

= (-3 + 1) / (2 - 1)

= -2

Now, let's choose one of the given points (let's use (1,-1)) to find the y-intercept (b):

y = mx + b

-1 = (-2)(1) + b

-1 = -2 + b

b = -1 + 2

b = 1

Therefore, the equation of the line passing through the points (1,-1) and (2,-3) is y = -2x + 1.

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Volume without holes = 3 x 6 x 11 = 198 cubic inches.

Calculate volume of one hole:

3.14 x 0.5^2 x 3 = 2.355 cubic inches

There are 3 holes: 3 x 2.355 = 7.065

Subtract volume of the holes from the brick:

198 - 7.065 = 190.935 cubic inches.

Rounded to the nearest tenth: 190.9 cubic inches.

Answer:

190.9 inches^3

Step-by-step explanation:

First of all we have to find the total volume:

V = dimension 1 x dimension 2 x dimension 3

V = 3 x 6 x 11 = 198 inches^3

now we have to find the volume of the cylinders:

V= radius^2 x pi x height = 0.5^2 x 3.14 x 3 = 2.355 inches^3

the cylinders are three so:

V = 2.355 x 3 = 7.065 inches^3

at least we have to subtract this value at the total volume:

V= 198 - 7.065 = 190.935 = 190.9 inches^3

The Highest Common Factor (HCF) of 12, 18, and 48 is 6. This means that 6 is the greatest number that can be evenly divided into all three numbers without leaving a remainder.

1. List out the factors of each number:

12: 1, 2, 3, 4, 6, 12

18: 1, 2, 3, 6, 9, 18

48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

2. Find the common factors of all three numbers:

1, 2, 3, 6

3. The greatest number of these common factors is 6, so 6 is the HCF of 12, 18, and 48.

The Highest Common Factor (HCF) is the greatest number that can be evenly divided into all the numbers in a set. To find the HCF of a set of numbers, we must first list out the factors for each number. The factors are the numbers that can be evenly divided into the original number. For instance, 1, 2, 3, 4, 6, and 12 are the factors of 12. We then compare the lists of factors of all the numbers and find the common factors. The greatest number of these common factors is the HCF. For example, the HCF of 12, 18, and 48 is 6, because 6 is the greatest number that can be evenly divided into all three numbers without leaving a remainder

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Answer:

10× + 25y ≤ 25

Answer:

0.1x + 0.25y ≤ 25

Step-by-step explanation:

A call within the US is $0.10, a call to France is $0.25, and you have $25.00. Your total amount of money spent depends on how many calls you make. Now, turn this information into an inequality.

Answer:

x+68=90 degrees

Step-by-step explanation:

Answer:

90-68 or 68+22

Step-by-step explanation:

this works becuz it is a 98 degree angle

The probability to obtain the sum of two rolled dice as a multiple of 6 or a multiple of 4 is 13/36.

When comparing the likelihood of an outcome to all other possible outcomes, we use a sort of ratio known as probability.

Given that a dice is rolled twice. Sum of the two rolls has following possibilities,

2,3,4,5,6,7,8,9,10,11,12

A multiple of 6 is obtained when the sum is either 6 or 12.

Sum of 6 is obtained when the two rolls are (1,5) , (2,4) , (3,3), (4,2) , (5,1)

Probability for each is 1/36. Therefore total probability to obtain sum of 6 is 5/36.

Sum of 12 is obtained only when the two rolls (6,6).

Probability to obtain sum of 12 is therefore 1/36.

Similarly for a sum of 4, the probability is 3/36.

For a sum of 8, the probability is 4/36.

Therefore the required probability is the sum of above calculated probabilities,

Required probability = 5/36 + 1/36 + 3/36 + 4/36 = 13/36

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C

Carl wheezer told me

The interest on a note of $32,000 at 9% for three months is $720.

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.

It is given that,

Principal(P) = $32,000

Rate(R) = 9%

Time(T) = 3/12 = 0.25 years

Interest(I)=?

Automobile loans that are amortized monthly and retailer installment loans that are also calculated monthly are examples of simple interest; the interest increases as the loan balance decreases with each monthly payment. Using simple interest, certificates of deposit (CDs) pay a predetermined amount of interest on a predetermined date.

The formula for the simple interest is,

I=(P×R×T)/100

Substitute the given value as

I=(P×R×T)/100

I=(32,000×9×0.25)/100

I=$720

Thus, the interest on a note of $32,000 at 9% for three months is $720.

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Reflection of point 1 over X axis is (-4, -2)

Reflection of point 2 over Y axis is (2, 3)

Reflection of point 3 over x = 1 is (2, 1)

Reflection of point 4 over y = x is  (2, -1)

What is Reflection of a point?

A reflection point occurs when a figure is constructed around a single point known as the point of reflection or center of the figure. For every point in the figure, another point is found directly opposite to it on the other side.

According to the given question:

1. Reflection of point 1 over X axis (x, -y) ⇔ (x, y)

 ∴ Reflection of (-4, 2) over X axis is (-4, -2)

2. Reflection of point 2 over Y axis (x, y) ⇔ (-x, y)

 ∴ Reflection of (-2, 3) over Y axis is (2, 3)

3. Reflection of point 3 over x = 1

 ∴ Reflection of (-2, 1) over x = 1 axis is (2, 1)

4. Reflection of point 4 over y = x is  (x, y) ⇔ (y, x)

 ∴ Reflection of (-1, 2) over X axis is (2, -1)

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Answer:

y=2x

Step-by-step explanation:

hope this helps

:) :3