Estimate √487 plsssssss

The measurement of acute triangle ABC we can find by direct substitution of the labeled measures in the Law of Sines is,

a/ sin a = b/sin b

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sine rule for a triangle ABC is, a/sinA = b/sinB = c/sinC .

In the diagram, there are two identified sides and if you use the sine rule, you can find the opposed angles easily.

Side a, with angle A.

Side b, with angle B.

If you input these into the sine rule, it would be, a/ sin a = b/sin b

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Answer:

Below

Step-by-step explanation:

Circumference = pi * d = 22/7 * d

2517 = 22/7 * d             ( are you sure 2517 is correct??)

d = 2517 * 7/22 = 800.86 inches    ( a VERY large pie)

radius = 1/2 * d = 400.43 inches

Area = pi r^2

        = 22/7   * (400.43)^2 = 503 943 in^2

The fifth term of the expansion by using Binomial Expansion is +1008x¹⁵y¹⁴.

When algebraic identities cannot be employed to extend a binomial, the binomial expansion formulae are used to determine the powers of the binomials.

The expansion of (x + y)^n is given by this binomial expansion formula, where n is a natural number. There are (n + 1) terms in the expansion of (x + y)^n.

Given that:

[tex]=(\dfrac{1}{2}x^3y^2-4y)^9[/tex]

Use the binomial expansion theorem to find each term. The binomial theorem states [tex](a+b)^n = \sum \limits^n_{k=0}nCk*(a^{n-k}b^k)[/tex]

[tex]\sum \limits^9_{k=0} \dfrac{9!}{(9-k)!k!}* (\dfrac{1}{2}*(x^3y^2))^{9-k}*(-4y)^k[/tex]

Expand the summation.

[tex]=\dfrac{9!}{(9-0)!0!}*(\dfrac{1}{2}*(x^3y^2)^{9-0}*(-4y)^0+ \dfrac{9!}{(9-1)!1!}*(\dfrac{1}{2}*(x^3y^2)^{9-1}*(-4y)^1+...+\dfrac{9!}{(9-9)!9!}*(\dfrac{1}{2}*(x^3y^2)^{9-9}*(-4y)^9[/tex]

Simplify the exponents for each term of the expansion.

[tex]=1*(\dfrac{1}{2}*(x^3y^2)^{9}*(-4y)^0+ 9*(\dfrac{1}{2}*(x^3y^2)^{8}*(-4y)^1+...+1*(\dfrac{1}{2}*(x^3y^2)^{0}*(-4y)^9[/tex]

Simplify the polynomial result.

[tex]=\dfrac{x^{27}y^{18}}{512}-\dfrac{9x^{24}y^{17}}{64}+\dfrac{9x^{21}y^{16}}{2}-84x^{18}y^{15}+1008x^{15}y^{14}-8064x^{12}y^{13}+43008x^9y^{12}-147456x^6y^{11}+294912x^3y^{10}-262144y^9[/tex]

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Check the picture below.

so the triangle with the 35° angle is an isosceles, namely a triangle with twin sides stemming from the center of the circle, well, twin sides make twin angles, and since the center of the circle makes a central angle, well, any arc will get its degrees from that.

The normal probability plot can reveal information about the population from which the data were drawn. A straight line pattern indicates normality, whereas deviations from the straight line indicate non-normality.

A normal probability plot is a graphical method for determining whether a set of data values is normally distributed. The plot depicts sample data values on the y-axis and theoretical normal deviate values on the x-axis.

If the plotted points follow a roughly straight line, the population is likely to be normally distributed. If the points plotted deviate significantly from a straight line, the population is not normally distributed.

As a result, the shape of the normal probability plot can provide insight into the normality of the population from which the data were drawn. A straight line pattern indicates that the distribution is normal, whereas deviations from the straight line indicate non-normality.

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In ΔJKL using the angle bisector theorem the value for x is obatined as 48.6 units.

What is angle bisector theorem?

The opposite side of a triangle is divided into two pieces by the angle bisector in proportion to the other two sides. If the interior point of a triangle is equally spaced from its two sides, that point will be on the angle bisector of the angle created by the two line segments.

The measurement for line segment JK = 54 units.

The measurement for line segment LK = x units.

The measurement for line segment LM = 36 units.

The measurement for line segment JM = 40 units.

In ΔJKL line segment KM is an angle bisector.

So, according to the angle bisector theorem -

JM / LM = JK / LK

Substitute the values in the equation -

40 / 36 = 54 / x

Simplify to find the value of x -

x = (54 × 36) / 40

x = (27 × 9) / 5

x = 48.6 units

Therefore, the value of x is 48.6 units.

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Answer:

Step-by-step explanation:

You want to solve the triangle with A=35°, B=60°, and c=10.

When two angles and a side are given, the Law of Sines is useful for providing a solution. In order to use it, we need to know an angle and its opposite side. That is, we need angle C.

Using the sum of angles of a triangle, we have ...

  A +B +C = 180°

  C = 180° -A -B = 180° -35° -60° = 85°

Now, we can use ...

  a/sin(A) = b/sin(B) = c/sin(C)

  b = c·sin(B)/sin(C) = 10·sin(60°)/sin(85°) ≈ 8.69

  a = c·sin(A)/sin(C) = 10·sin(35°)/sin(85°) ≈ 5.76

Using the graph we will see that line q can be written as:

y = (-1/2)*x + 3

Remember that the general linear equation is written as:

y = a*x +b

Where a is the slope and b is the y-intercept.

We know that if the line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

Using the graph we can identify the two points (0, 3) and (2, 2), then the slope is:

a = (2 - 3)/(2 - 0) = -1/2

And the y-intercept is y = 3, then the linear equation is:

y = (-1/2)*x + 3

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(a) The markup is $3.9.

(b) The selling price of the CD is $11.70.

The markup of the CD is calculated by applying the following formula.

The markup = 50% x $7.80

The markup = ( 50 / 100 ) x $7.80

The markup = 0.5 x $7.80

The markup = $3.9

The selling price of the CD is calculated as follows;

selling price = $7.80 + $3.9

selling price = $11.7

Thus, the selling price of the CD is a function of the cost price, and mark up price. So the final selling price of the CD is $11.7 while the mark up is $3.9

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Sam can jump 4 steps at a time and Nina can jump 5 steps at a time. on 20th of the steps will both meet if both start jumping together. we can find it out with the help of HCM and LCM

GIVEN

Sam can jump four steps at a time and Nina can jump five steps at a time.

TO DETERMINE

On which of the steps will both meet if both start jumping together

EVALUATION

Here it is given that Sam can jump 4 steps at a time and Nina can jump 5 steps at a time.

Now we find the LCM of 4 and 5

Since 4 and 5 are prime to each other

So LCM of 4 and 5 = 4 × 5 = 20

Hence after 20 steps both meet if both start jumping together

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The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is,

⇒ g (x) = 6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

Now, The value of function are,

At x = - 2;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x ≤ 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (- 2) = 0

At x = 4;

⇒ g (x) =  6 ; - 8 ≤ x < - 2

           = 0 ; - 2 ≤ x < 4

           = - 4 ; 4 ≤ x ≤ 10

⇒ g (4) = - 4

Thus, The values of the function when x = -2 and when = 4 are,

⇒ g (-2) = 0

⇒ g (4) = - 4

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The length Thebe the HCF (highest common factor) of the given dimensions that are 168mm and 196 mm. Hence, the length of each square will be equal to 28mm.

The greatest of all their common factors is the Highest Common Factor (HCF) of two or more numbers. As a result, it is also known as the greatest common factor (GCF). If M is the greatest common factor of N, then M is the greatest possible number that divides N.

The length of the each square will be given by the HCF of the dimensions that are 168mm and 196mm.

[tex]168=2*2*2*3*7\\196=2*2*7*7[/tex]

So, the length of the each square paper=[tex]2*2*7=28mm.[/tex]

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the greatest distance the dog can be from the origin is 15 feet.

A Cartesian plane (named after French mathematician Rene Descartes, who formalized its use in mathematics) is defined by two perpendicular number lines: the x-axis, which is horizontal, and the y-axis, which is vertical. Using these axes, we can describe any point in the plane using an ordered pair of numbers.

Well first we have to find the distance from the origin to the point (4,3). Now to do this we use the distance formula. I didn't want to type this out so i found a picture.

Now the origin point is (0,0) So now we have two points we can plug in to find the difference between them. Now the X1 and X2 as well as y1 and y2 are interchangeable within their brackets.

So D= [tex]\sqrt{(4)^{2} } + (3^{2} )[/tex] Which means D= the square root of 25 which is 5. This means the distance from the origin to (4,3) is 5 feet. Now the dog can go 10 more feet in the opposite direction of the origin so 5 + 10 (pretty easy math) = 15. The dog can be (at its farthest) 15 feet from the origin.

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The two forms of representing her hair length are (3/4)H cm and 0.75H cm.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, On Monday, Florencia's hair was H centimeters long.

Therefore, After the hair cut her hair length will be,

= (75/100)×H.

= (3/4)H cm.

Now, We can also write it in terms of decimals which is,

= (75/100)×H.

= 0.75H cm.

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A) (i) (1, 5) is possible solution of equation.

(ii) (-2, 0) is not possible solution of equation.

B)  Solution of graph 1);

⇒ (- 2, - 2)

And, Solution of graph 2);

⇒ (4, 1)

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

A) Substitute the given coordinate in system of equation and check it is solution or not as;

1) System of equation are,

⇒ - 5m + 6n = 25

⇒ - 7m + 8n = 33

Coordinate = (1, 5) = (m, n)

Substitute in equations;

⇒ - 5m + 6n = 25

⇒ - 5 (1) + 6(5) = 25

⇒ - 5 + 30 = 25

⇒ 25 = 25

⇒ - 7m + 8n = 33

⇒ - 7(1) + 8(5) = 33

⇒ - 7 + 40 = 33

⇒ 33 = 33

Thus, (1, 5) is possible solution of equation.

2) System of equation are,

⇒ 8x - 3y = - 16

⇒ - 9x - 2y = 50

Coordinate = (- 2, 0) = (x, y)

Substitute in equations;

⇒ 8x - 3y = - 16

⇒ 8(-2) - 3(0) = - 16

⇒ - 16 = - 16

⇒ - 9x - 2y = 50

⇒ - 9(-2) - 2(0) = 50

⇒ 18 ≠ 50

Thus, (-2, 0) is not possible solution of equation.

B) The solution of graph of lines are intersection point of both lines.

Hence, Solution of graph 1);

⇒ (- 2, - 2)

And, Solution of graph 2);

⇒ (4, 1)

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Answer: 90

Step-by-step explanation:

The number that you need to find because it is missing in the equation is 48.

Let's assume the number we're trying to find is "x."

According to the problem, one-third of the number is (1/3)x, and one-fourth of the number is (1/4)x.

We're told that the sum of one-third of the number and one-fourth of the number is 28, so we can write the equation as follows:

(1/3)x + (1/4)x = 28

To solve this equation, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can rewrite the equation as:

(4/12)x + (3/12)x = 28

Combining the fractions, we get:

(7/12)x = 28

To isolate x, we multiply both sides of the equation by the reciprocal of (7/12), which is (12/7):

x = 28(12/7)

Simplifying the right side of the equation, we have:

x = 48

Therefore, the number we're looking for is 48.

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To find the average, one adds up all the scores and then divides by the total number of scores.

Joan had to find the average of the scores of her friends. To find the average, one adds up all the scores and then divides by the total number of scores. In this case, Joan had to find the sum of 10 different scores of her friends and then divide by 10. This will give her the average of the scores of her friends, which is a single value representing the central tendency of the scores. The average is a commonly used statistical measure that provides an overall idea of the data. In this case, the average of the scores of Joan's friends will give her an idea of the overall performance of her friends in the test she is preparing for.

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Answer:

you take the perimeter and subtract 2*the length. Then you divide that answer by 2

Step-by-step explanation:

This is because a rectangle is made up of 2 pairs of heights. 2 equal sides represent the height and 2 equal sides represent the width.

When we subtract the lengths of the 2 sides that represent the height we get a number that we then have to divide by 2 to get the width of the triangle.

Hope this helps. It's a little difficult to explain but the answer is correct :)

The conclusion is that there is sufficient evidence at the 0.01 level to support the mayor's claim that under 62% of the residents favor construction of the bridge.

The mayor rejects the null hypothesis at the 0.01 level, which means that the results from the hypothesis test show that the actual proportion of residents who favor construction is less than 62%. The alternative hypothesis would be that the true proportion is less than 62%. After gathering information from 110 voters, the results of the hypothesis test were used to make a decision on whether to reject or fail to reject the null hypothesis. If the hypothesis test showed that the null hypothesis could be rejected at the 0.01 level, it means that there was sufficient evidence to support the mayor's claim that less than 62% of the residents favor the bridge construction. However, it's important to note that hypothesis testing is not a perfect method and other factors such as sample size and sampling method should also be considered when interpreting the results.

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The required quarts of frozen yogurt made in 36 hours as per the given information is equal to 720 quarts.

Quarts of frozen yogurt made by factory is equal to 100 quarts

Time required to make 100 quarts of frozen yogurt is equal to 5 hours

Let 'x' quarts of frozen yogurt made in 36 hours

5 hours = 100 quarts of frozen yogurt

⇒ 1hour = ( 100 / 5 ) quarts of frozen yogurt

⇒ 36 hours =  ( 100 / 5 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 20 ) × ( 36 ) quarts of frozen yogurt

⇒ 36 hours =  ( 720 ) quarts of frozen yogurt

Therefore, the quarts of frozen yogurt made in 36 hours is equal to 720 quarts.

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Answer:The coefficient in this expression is 3.

Step-by-step explanation:

What is a Coefficient?

By definition, a coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic.

What is a variable?

A variable is a symbol that represents a mathematical object. So for example, 9p + 2. In this equation, the variable would be the letter "p."

The correct answer is Stratified Random Sampling

Given that,

In a study, the sample is selected by dividing the class into gender-based groups, then choosing 10 men and 10 women.

Researchers split a population into homogeneous subpopulations called strata (plural of stratum) depending on particular traits in a stratified sample (e.g., race, gender identity, location, etc.).

In order to estimate statistical measures for each subpopulation, each stratum is then sampled using a different probability sampling technique, such as cluster sampling or simple random sampling.

When a population's traits are varied and researchers want to make sure that each characteristic is accurately represented in the sample, they rely on stratified sampling. This aids in the study's validity and generalizability while preventing biases in the research process like undercoverage bias.

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The graph of the inequality -3x + y ≥ 1 is given below.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality:

-3x + y ≥ 1.

The intercepts are (0, 1) and (-0.33, 0)

The graph of the inequality is given in the attached image.

Therefore, the graph is given.

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The length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.

The owner of the used tire store wants to construct a fence to enclose a rectangular outdoor storage area. The side of the store is 240 feet long and there are 460 feet of fencing available for the other three sides. The formula for the area of a rectangle is A=LxW, where A is the area, L is the length, and W is the width. To find the dimensions of the outdoor enclosure with the most area, the length and width must be equal so that all of the fencing is used. Therefore, the length and width each need to be 230 feet, and the area of the outdoor enclosure will be A=(230)(230)=52900 sq. ft.

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Answer:

x=-2.083

or x=-25/12

Step-by-step explanation:

Answer:

x = -25/12

Step-by-step explanation:

We can solve for x by isolating x:

[tex]((-12x-7)=18)+7\\((-12x=25)/12\\x=-25/12[/tex]

The slope of these lines are:

Slope can be calcualted by comparing the change in y-axis with the change in x-axis. Then, let's discuss every lines we have:

1. We take 2 points: (3, 1) and (-2, -1)

m = y₂ - y₁

      x₂ - x₁

m = -1 - 1

      -2 - 3

m = - 2/ -5

m = 2/5

2. We take 2 points: (2, 2) and (-3, -3)

m = y₂ - y₁

      x₂ - x₁

m = -3 - 2

     -3 - 2

m = -5/-5

m = 1

3. We take 2 points: (1, 3) and (-1, -2)

m = y₂ - y₁

      x₂ - x₁

m = -2 - 3

      -1 - 1

m = -5 / -2

m = 5/2

4. We take 2 points:  (1, 0) and (-1, -2)

m = y₂ - y₁

      x₂ - x₁

m = (-2 - 0) / (-1 - 1)

m = -2/-2 = 1

We subtitute one point: (1, 0)

y = mx + c

0 = 1 (1) + c

c = -1 --> y = x - 1

5. We take 2 points:  (3, -1) and (-2, -2)

m = y₂ - y₁

      x₂ - x₁

m = -2 - (-1)

      -2 - 3

m = -1 / -5 = 1/5

We subtitute one point: (3, -1)

y = mx + c

-1 = 1/5 (3) + c

-5/5 = 3/5 + c

c = -8/5 --> y = 1/5 x - 8/5

6. We take 2 points: (2, -1) and (-1, 3)

m = y₂ - y₁

      x₂ - x₁

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

m = 4/(-3)

m = - 4/3

We subtitute one point: (2, -1)

y = mx + c

-1 = - 4/3 (2) + c

-3/3 = -8/3 + c

c =5/3 --> y = -4/3 x + 5/3

7. m = Δy / Δx

m = 8/24

m = 1/3

8. m = Δy / Δx

m = 100/1000

m = 1/10

9. (1, 3) and (4, 7)

m = y₂ - y₁

      x₂ - x₁

m = (7 - 3) / (4 - 1)

m = 4/3

10. (3, 5) and (2, 6)

m = y₂ - y₁

      x₂ - x₁

m = (6 - 5) / (2 - 3)

m = 1 / (-1) = -1

11. (4, 0) and (5, 5)

m = y₂ - y₁

      x₂ - x₁

m = (5 - 0) / (5 - 4)

m = 5/1 = 5

Please refer to the graphs attached below for the graph number 4, 5, and 6.

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Answer: 35 is 70% of 50

Step-by-step explanation:

Steps to solve "35 is 70 percent of what number?"

We have, 70% × x = 35

or,

70

100

× x = 35

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 35 ×

100

70

x = 50

If you are using a calculator, simply enter 35×100÷70, which will give you the answer.

Answer:

50

Step-by-step explanation:

35 + 15 = 50

---------------------------

15 is 30% of 50 There fore 50 is the correct answer

I took this exam, its the 5.08 Ratios and rates practice exam right?

Have an amazing Day and good luck (:

The standard deviation of x is 3 cars. So the option A is correct.

Suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the Poisson distribution.

If the mean of x is equal to 9 cars, then we have to determine the standard deviation of x.

An indicator of how much variance from the mean there is is the standard deviation, which can be expressed as spread, dispersion, or spread. A "typical" departure from the mean is represented by the standard deviation. As a result of returning to the data set's original units of measure, it is a well-liked measure of variability.

The Mean = 9 cars

Standard Deviation = Square Root of Mean

Standard Deviation = √9

Standard Deviation = 3 cars

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