In the right triangle, find the length of the side not given. Give an exact answer and an approximation to three decimal
K
places
a=15, b=15

the exact value of C is

the approximate value of c is

The arc length of the sector is 10π inches, and the area of the sector is 60π square inches.

What is the arc length and area of the sector of a circle?

Arc length = [tex] \frac{ \theta}{ {360}^{o} } \times 2\pi \: r[/tex]

Area of sector = [tex] \frac{ \theta}{ {360}^{o} } \times \pi \: {r}^{2} [/tex]

Where r is the radius of the circle, angle is the central angle in degrees, and π is the mathematical constant pi (approximately equal to 3.14159).

Given that the angle is 150° and the radius is 12 inches, we can substitute these values into the formulas to get:

Arc length

[tex]= \frac{150}{360} \times 2π(12) \\ = \frac{5}{12} \times 2π(12) \\ = 10π \: inches[/tex]

Area of sector

[tex]= \frac{150}{360} \times π(12)^2 \\ = \frac{5}{12} \times π(144) \\ = 60π \: square \: inches[/tex]

Therefore, the arc length of the sector is 10π inches, and the area of the sector is 60π square inches.

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Answer:

A. The rate of change of the table is equal to the rate of change of the graph.

The solution to the system of equations is x = 5 and y = 3.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.

To solve the system using addition, we want to add the two equations together in a way that eliminates one of the variables. In this case, we can add the two equations directly because the x term will cancel out:

X - 4.7y = -9.1

+(-x + 5.8 = 12.4)

1.1y = 3.3

Now we can solve for y by dividing both sides by 1.1:

y = 3.3 ÷ 1.1

y = 3

Substituting y = 3 back into one of the original equations, we can solve for x:

x - 4.7y = -9.1

x - 4.7(3) = -9.1

x - 14.1 = -9.1

x = 5

Therefore, the solution to the system of equations is x = 5 and y = 3.

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Answer:

  cos(L) = (√46)/11

Step-by-step explanation:

You want cos(L) in simplest terms, given right triangle side lengths LK=√46 and JK=√75.

The cosine is the ratio ...

  Cos = Adjacent/Hypotenuse

The side adjacent to vertex L is LK. The hypotenuse of the triangle is LJ. This means the desired ratio is ...

  cos(L) = LK/LJ

The length of hypotenuse LJ can be found using the Pythagorean theorem.

  LJ² = LK² +JK²

  LJ² = (√46)² +(√75)² = 46 +75 = 121

  LJ = √121 = 11

Then the desired ratio is ...

  cos(L) = (√46)/11

Answer:

[tex] \frac{25}{121} [/tex]

Step-by-step explanation:

Given:

r (dartboard) = 11 m

r (shaded area) = 5 m

π = 3,14

First, let's find the area of the dartboard:

A (dartboard) = πr^2 = 3,14 × 121 = 379,94 m^2

A (shaded area) = 3,14 × 25 = 78,5 m^2

Let's call this event A:

A - "A dart must hit the shaded area":

All outcomes:

n = 379,94

Favorable outcomes:

m(A) = 78,5

[tex]p(a) = \frac{78.5}{379.94} = \frac{25}{121} [/tex]

I assume, this is the right answer

Answer:

y in (7,y) = 14

Step-by-step explanation:

A General Linear function is as the following:

y = mx + c, Where: m: slope of the line, c: y-intercept

Given that:

Point 1 (P1) = (1,5)

Point 2 (P2) = (3, 11)

Point 3 (P3) = (7,y)

By substituting in the linear function with P1:

5 = m + c  ---> (1)

By substituting in the linear function with P2:

11 = 3m + c   ---> (2)

By multiplying equation (1) times 3 and subtracting eq. (2) from it:

(15 = 3m + 3c) - (11 = 3m + c) =

4 = 2c

Then, c = 2

By substituting with "c" in eq. (1):

5 = m + 2

Then, m = 3

Hence,

the function of this line is:

y = 3x + 2

So,

to get "y" in P3, we are going to substitute with 7:

y = 3(7) + 2

then "y" in P3 = 23


Another Solution:

by getting the slope of the line:

[tex]Slope = \frac{\triangle y}{\triangle x}[/tex] Where: Δy: change in y points, Δx: change in x points

by utilizing P1 & P2 in slope formula:

[tex]slope = \frac{11 - 5}{3 - 1} = \frac{6}{2} = 3[/tex]

By substituting with P1 in the linear function:

5 = 3 + c

Then, c = 2

the function of the line is:

y = 3x + 2

So,

to get "y" in P3, we are going to substitute with 7:

y = 3(7) + 2

then "y" in P3 = 23



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The equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).

The definitiοn οf an equatiοn οf the line is a linear equatiοn with degree 1. X and Y are twο variables in the equatiοn fοr the line. The slοpe οf the line, which reflects the elevatiοn οf the line, is the third parameter.

The general fοrm οf the equatiοn οf the line:-

y = mx + c

m = slοpe

c = y-intercept

Given that Line, v has an equatiοn οf y=–109x–3. Perpendicular tο line v is line w, which passes thrοugh the pοint (2,3).

The slοpe οf the required line will be inverse and the οppοsite οf the given line,

m = 1/109

The intercept will be calculated as,

y = mx + b

3 = (1/109)2 + b

3 = 2/109 + b

327/109 = 2/109 + b

325/109 = b

The equatiοn οf the line is written as,

y = (1/109)x + (325/109)

Therefοre, the equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).

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The area of the parallelogram is 140 cm².

A parallelogram is a quadrilateral having two pairs of parallel sides (a four-sided polygon). This indicates that opposing sides of a parallelogram are parallel, and opposite angles have the same size.

Given :

Base of parallelogram = 10 cm

Height of parallelogram = 14 cm

Area of Parallelogram = B × H  

Area = 10 × 14

Area = 140 cm²

Area of parallelogram is 140 cm².

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The complete question is:

Answer:

B

Step-by-step explanation:

a² + 14a - 51 = 0 ( add 51 to both sides )

a² + 14a = 51

to complete the square

add ( half the coefficient of  the x- term )² to both sides

a² + 2(7)a + 49 = 51 + 49

(a + 7)² = 100 ( take square root of both sides )

a + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )

a = - 7 ± 10

then

a = - 7 + 10 = 3

a = - 7 - 10 = - 17

Answer: the value of x is 29

Step-by-step explanation:

Answer:

it's in the attachment

Step-by-step explanation:

the one that are the same value as the given value on the transversals are either opposite interior angles or opposite exterior angles

the ones that have different values as the given value on the transversal are subtracted from 180⁰

No, Johnny does not have enough fruit to make smoothies for his 5 friends because he is short 383.51 ounces of juice.

The relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."

Lοοking at the given pοints, we can see that the input x = -5 has an οutput y = 1, and the input x = 5 alsο has an οutput y = 1.

This means that there are twο different inputs (x-values) that cοrrespοnd tο the same οutput (y-value), viοlating the definitiοn οf a functiοn.

Tο determine if the relatiοn is a functiοn, we need tο check if fοr each input (x-value), there is exactly οne οutput (y-value).

Therefοre, the relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."

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Therefore, the probability that a student who did not complete the homework passed the test is 2/5 or 0.4 (or 40%).

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 because there is one favorable outcome (getting heads) out of two possible outcomes (getting heads or tails).

Let's define the following events:

A: passing the test

B: completing the assignment

We know that:

[tex]P(A) = 18/28 = 9/14[/tex] (since 18 students out of 28 passed the test)

[tex]P(B) = 19/28[/tex] (since 19 students out of 28 completed the assignment)

P (A ∩ B) = P(B) = 19/28 (since every student who completed the assignment also took the test)

We want to find P (A | not B), which represents the probability of passing the test given that the student did not complete the assignment.

Using Bayes' theorem, we have:

P (A | not B) = P (not B | A) * P (A) / P (not B)

We know that:

P (not B | A) = P (A' ∩ B') / P(A') = 7/28 / 10/28 = 7/10 (since 7 students failed the test and did not complete the assignment)

P (not B) = 1 - P(B) = 9/28 (since not completing the assignment is the complement of completing the assignment)

Plugging in these values, we get:

[tex]P(A | not B) = (7/10) * (9/14) / (9/28)[/tex]

[tex]P(A | not B) = 2/5[/tex]

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According to the given question, the center of the circle is (-9, 46) and its radius is approximately 11.09.

The equation of a circle is a formula that describes the relationship between the x and y coordinates of any point on the circle.

The standard equation of circle is:

(x - h)²+(y - k)²=r²

This equation states that the sum of the squares of the differences between the x-coordinate and the center, and the y-coordinate and the center, is equal to the square of the radius.

The equation of the circle is given by (x+9)² + (y-46)² = 123.

Comparing this to the standard equation of a circle, (x-h)² + (y-k)² = r², we can see that the center of the circle is (-9, 46) and the radius is √(123) = 11.09.

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Proof that one million boards aren't enough. .Therefore, one million boards are not enough to reach (2023, 2023).

A total of 2023 boards are needed to reach (2023, 2023).

This problem is a mathematical puzzle that involves traversing a hazardous area to reach a specific point using a limited number of resources.

The problem is set in the Cartesian plane, where the first quadrant (i.e., the region where both x and y coordinates are positive) is covered with lava, making it impossible to traverse.

Let's assume that we can reach (2023, 2023) with one million boards. We know that each board can cover a distance of at most 1. Therefore, the total distance we can cover with one million boards is at most one million. However, the distance between the origin (0, 0) and (2023, 2023) is ✓2023² + ✓2023² = 2855.9

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To multiply two numbers in scientific notation, we multiply their coefficients and add their exponents. So:

(0.4x10^-6)(0.7x10^-2) = (0.4)(0.7)x10^(-6-2) = 0.28x10^-8

Therefore, the answer is 0.28 x 10^−8 in scientific notation.

Answer:

true

Step-by-step explanation:

After answering the presented question, we can conclude that expression Therefore, the value of 5310² - 5330 × 5290 when p = 5330 and q = 10 is 400.

An expression in mathematics is a collection of representations, digits, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, division, and exponentiation. Expressions are often used in arithmetic, mathematics, and form. They are employed in the representation of mathematical formulas, the solving of equations, and the simplification of mathematical relationships.

(i)

(p - 2q)² = p² - 4pq + 4q²

p(p - 4q) = p² - 4pq

(p - 2q)² - p(p - 4q) = (p² - 4pq + 4q²) - (p² - 4pq)

(p - 2q)² - p(p - 4q) = 4q²

(ii)

(5330 - 2×10)² - 5330(5330 - 4×10) = 4×10²

(5310)² - 5330 × 5290 = 400

Therefore, the value of 5310² - 5330 × 5290 when p = 5330 and q = 10 is 400.

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The brace must be approximately 38.1 cm long.

To find the length of the brace for the closet rod holder,

we can use the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the vertical side is 15 cm and the horizontal side is 35 cm.

Let's call the length of the brace (the hypotenuse) "c".

According to the Pythagorean theorem:
[tex]c^2 = (15 cm)^2 + (35 cm)^2[/tex]
[tex]c^2 = 225 cm^2 + 1225 cm^2[/tex]
[tex]c^2 = 1450 cm^2[/tex]
Now, to find the length of the brace, we need to take the square root of both sides:
[tex]c = \sqrt{(1450 cm^2)}[/tex]
c ≈ 38.1 cm.

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classify the different measurement systems into one of the four types

of scales. (Exercise)

1. Your checking account number as a name for your account.

2. Your checking account balance as a measure of the amount of money you

have in that account

3. The order in which you were eliminated in a spelling bee as a measure of your

spelling ability.

4. Your score on the first statistics test as a measure of your knowledge of

statistics.

5. Your score on an individual intelligence test as a measure of your

intelligence.

6. The distance around your forehead measured with a tape measure as a

measure of your intelligence.

7. A response to the statement "Abortion is a woman's right" where "Strongly

Disagree" = 1, "Disagree" = 2, "No Opinion" = 3, "Agree" = 4, and "Strongly

Agree" = 5, as a measure of attitude toward abortion.

8. Times for swimmers to complete a 50-meter race

9. Months of the year Meskerm, Tikimit…

10.Socioeconomic status of a family when classified as low, middle and upper

classes.

11. Blood type of individuals, A, B, AB and O.

12.Pollen counts provided as numbers between 1 and 10 where 1 implies there is

almost no pollen and 10 that it is rampant, but for which the values do not

represent an actual counts of grains of pollen.

13.Regions numbers of Ethiopia (1, 2, 3 etc.)

14.The number of students in a college;

15.the net wages of a group of workers;

16.the height of the men in the same town;

The mean of the sampling distribution of sample means is approximately 5.2 ± 0.1339.

When a sampling distribution is created using samples of the ages at which 48 children begin reading, the mean of the sampling distribution of sample means can be calculated by dividing the population mean by the square root of the sample size. This is known as the standard error of the mean and is denoted as SE.

The formula for calculating the standard error of the mean is:

SE = σ / √n

where σ is the population standard deviation and n is the sample size.In this case, the sample size is 48 children. Since the population standard deviation is not given, it is assumed that the sample standard deviation is used as an estimate of the population standard deviation. The formula for calculating the sample standard deviation is:

S = √[(Σ(x - μ)²) / (n - 1)]

where S is the sample standard deviation, Σ is the sum of the squared deviations from the mean, x is the value of each observation, μ is the mean of the sample, and n is the sample size.Using the data given, the sum of the squared deviations from the mean is:

Σ(x - μ)² = (6 - 5.2)² + (8 - 5.2)² + (7 - 5.2)² + (9 - 5.2)² + (4 - 5.2)² + (7 - 5.2)² + (6 - 5.2)² + (5 - 5.2)² = 2.56 + 5.76 + 1.44 + 12.96 + 1.44 + 1.44 + 0.36 + 0.04 = 26.4

The sample standard deviation is:S = √[26.4 / (48 - 1)] = 0.9197Using the formula for standard error of the mean, the mean of the sampling distribution of sample means is:

SE = σ / √n= 0.9197 / √48≈ 0.1339

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The estimated amount Franklin will pay in finance charges on his $1,520 purchase is $35.07.

What is annual percentage rate?

Annual Percentage Rate (APR) is the annual rate charged for borrowing or earned through an investment and is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or investment.

The finance charges on a credit card purchase can be calculated using the following formula:

finance charges = (APR/365) * balance * number of days

Where APR is the annual percentage rate, balance is the amount of the purchase, and the number of days is the time period for which the finance charges are being calculated.

Assuming that Franklin does not make any payments towards his credit card balance during the billing period, the number of days for which finance charges will be calculated will be equal to the billing cycle. Let's assume a billing cycle of 30 days for this example.

Using the formula above, we can calculate the finance charges as follows:

finance charges = (28.2%/365) * $1,520 * 30

= (0.00077397) * $1,520 * 30

= $35.07 (rounded to the nearest cent)

Therefore, the estimated amount Franklin will pay in finance charges on his $1,520 purchase is $35.07.

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The area of the path running around the square field is 475 square meters.

To find the area of the path running around a square field with a side of 45 meters and a path width of 2.5 meters,

Calculate the area of the entire square (including the path):

Side of the larger square = 45 M (side of the field) + 2.5 M (width of the path on one side) + 2.5 M (width of the path on the opposite side) = 50 M

Area of the larger square = (Side of the larger square)²

                                          = (50 M)²

                                          = 2500 M²

Calculate the area of the square field (without the path):

Side of the field = 45 M

Area of the square field = (Side of the field)²

                                       = (45 M)²

                                       = 2025 M²

Subtract the area of the square field from the area of the entire square to find the area of the path:

Area of the path = Area of the larger square - Area of the square field

                           = 2500 M² - 2025 M²

                           = 475 M²

So, the area of the path running around the square field is 475 square meters.

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Answer:

381.7 cubic inches.

The solutions for y are:

We can simplify the expression sqrt(160) by factoring 160 into its prime factors:

160 = 2^5 * 5

Taking the square root of each factor, we get:

sqrt(160) = sqrt(2^5 * 5) = sqrt(2^4 * 2 * 5) = 2^2 * sqrt(2 * 5) = 4 * sqrt(10)

Therefore, we can simplify the expression for y as follows:

y = (7 +- sqrt(160))/10 = (7 +- 4sqrt(10))/10

So the solutions for y are:

y = (7 + 4sqrt(10))/10

y = (7 - 4sqrt(10))/10

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The possible lengths x for the side of square A. The possible lengths x for the side of the square is the interval [-7,7].

Since the area of a square is given by the formula A = x^2, where x is the length of the side, we can solve for x to find the possible lengths of a square with area 49 square feet or less.

A ≤ 49

x^2 ≤ 49

|x| ≤ 7

So the possible lengths for the side of the square are any values of x between -7 and 7, inclusive.

Therefore, the answer is: A. The possible lengths x for the side of the square is the interval [-7,7].

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f(x) = 12x and  [tex]g(x)= \sqrt{x-12}[/tex] both include domain values of [12, ∞), and both functions increase over the interval (12, ∞).

The set containing all input values is known as a function's domain while a function's range is the collection of all possible output values.

Function f(x) is defined by: f(x) = 12x.

Function g(x) is defined by: [tex]g(x)= \sqrt{x-12}[/tex]

Therefore, the correct option is (d) Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).

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