what is the square root of 4761

The measure of angle x in the isosceles triangle is 40 degrees.

Let's call the two congruent sides of the isosceles triangle "a" and the remaining side "b". Since the angle opposite one of the congruent sides (let's call it "a") is 70 degrees, the other angle opposite "a" must also be 70 degrees due to the property of isosceles triangles. Let's call this angle "y".

So we have two angles that add up to 140 degrees (70 + 70 = 140). We also know that the sum of the angles in any triangle is always 180 degrees. Therefore, we can find the measure of angle "x" as follows:

x + y + 70 = 180

Substituting y = 70, we get:

x + 70 + 70 = 180

Simplifying the equation, we get:

x + 140 = 180

Subtracting 140 from both sides, we get:

x = 40

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The given question is incomplete, the complete question is :

The angles opposite the congruent sides of an isosceles triangle are congruent. find the value of x in the triangle. show all your work.

The function 1/5f(x) compares to the parent function f(x) given as follows:

Vertical shrink/compression by a factor of 1/4.

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

For a vertical compression or stretch, the definitions are given as follows:

As k = 0.2 < 1, the transformation is a vertical shrink by a factor of 1/5.

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A scatter plot of the data is shown below.

The best-fitting line for the data is y = -10t + 165.8.

The predicted number of adult softball teams in 2010 is 56 thousands adult softball teams.

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the number of years would be plotted on the x-axis of the scatter plot while the number of teams (thousands) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the number of years and teams (thousands), a linear equation for the line of best fit is given by:

y = -10t + 165.8

Next, we would determine the predicted number of adult softball teams in 2010:

Years, t = 2010 - 1999 = 11 years.

y = -10(11) + 165.8

y = -110 + 165.8

y = 55.8 ≈ 56 thousands adult softball teams.

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The area of the figure composed of the square and four semicircles is approximately 242.4 square units.

A semicircle is a two-dimensional geometric shape that is half of a circle. It is formed by drawing a diameter of a circle and then drawing the arc that connects the two endpoints of the diameter. The diameter divides the circle into two equal parts, each of which is a semicircle.

A semicircle has several important properties, including:

It has one straight side, which is the diameter of the circle.

The other side is curved, and it is a half-circle.

The radius of the semicircle is equal to half the diameter of the circle.

The circumference of a semicircle is half the circumference of the circle.

The area of a semicircle is half the area of the circle.

Semicircles are used in many applications of geometry and trigonometry, including in the study of angles, arcs, and circles. They are also used in architecture and engineering to design buildings, bridges, and other structures that have semicircular features.

In addition to being a geometric shape, a semicircle can also refer to a half-circle that is used as a decorative element or design motif. Semicircles are often used in art, architecture, and graphic design to create visually interesting patterns and compositions.

To find the area of the figure composed of a square and four semicircles, we need to first find the area of the square and the area of the four semicircles. Then, we can subtract the area of the four semicircles from the area of the square to get the total area of the figure.

The area of the square is simply the side length squared, so in this case it is:

Area of square = (22)^2 = 484 square units

The diameter of each semicircle is equal to the side length of the square, so the radius is half of that or 11 units. Therefore, the area of each semicircle is:

Area of semicircle = (1/2) * π * r^2 = (1/2) * π * 11^2 = 60.4 square units

Since there are four semicircles, the total area of the four semicircles is:

Total area of semicircles = 4 * Area of semicircle = 4 * 60.4 = 241.6 square units

To get the area of the entire figure, we need to subtract the area of the four semicircles from the area of the square:

Area of figure = Area of square - Total area of semicircles

Area of figure = 484 - 241.6 = 242.4 square units

Rounding this to the nearest tenth gives:

Area of figure = 242.4 (rounded to the nearest tenth)

Therefore, the area of the figure composed of the square and four semicircles is approximately 242.4 square units.

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Answer:

48

Step-by-step explanation:

3 x 16 = 48

OR

16 + 16 + 16 = 48

48

16 x 3 = 48.

Simple :)

Answer:

53 minutes

Step-by-step explanation:

The initial value of the investment is denoted by 480 in the function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

V(t) = 480 [tex](1.065)^t[/tex]

V is the total value after t years.

Now,

480 is constant and it indicates the initial value of the investment.

1.065 indicates that there is an increase of 6.5% each year.

Thus,

480 in the function denotes the initial value of the investment.

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Answer:

a. 651

Step-by-step explanation:

To solve the problem, you can start by finding out how many students bike or walk to school by multiplying the total number of students by the percentage that bike or walk:

1860 x 0.45 = 837

Next, you can subtract the number of students who drive to school to find out how many students travel by bus:

1860 - 837 - 372 = 651

Therefore, the answer is 651, so the option (a) is correct.

Answer:

a. 651

Step-by-step explanation:

We first need to find the number of students that bike or walk.

We can do this by plugging the numbers into this equation:

[tex]\frac{is}{of} = \frac{percent}{100}[/tex]

We know that the percent is 45, and we know the total amount of students, 1860, so we are solving for is.

[tex]\frac{x}{1860} = \frac{45}{100}[/tex]  where x = is.

To solve this, we cross multiply:

1860(45) = 100x

83,700 = 100x

837 = x

Now we know that 837 students bike or walk, and 372 drive.

We can calculate how many students travel by bus by subtracting these numbers from the total number of students, 1860.

1860 - 837 - 372 = 651

Therefore, 651 students travel to school by bus.

The greatest common factor (GCF) of 42, 126, and 210 is 42.

To find the GCF, you can use several methods such as prime factorization or the Euclidean algorithm. One way to find the GCF using prime factorization is to express each number as a product of its prime factors:

42 = 2 × 3 × 7

126 = 2 × 3² × 7

210 = 2 × 3 × 5 × 7

Then, identify the common prime factors and their smallest exponent across all three numbers. In this case, the common prime factors are 2, 3, and 7. The smallest exponent of 2 is 1, the smallest exponent of 3 is 1, and the smallest exponent of 7 is 1. Therefore, the GCF is

= 2 × 3 × 7

= 42

Another method to find the GCF is the Euclidean algorithm, which involves finding the remainder of dividing the larger number by the smaller number repeatedly until the remainder is zero. The GCF is the last nonzero remainder. However, in this case, the prime factorization method is simpler and quicker.

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Answer:

100.48ft

Step-by-step explanation:

Use circumference formula

C=2(pi)r

Applying the angles addition postulate, m<KJL = 132°.

The Angles Addition Postulate is a fundamental property of angles in geometry that explains how to find the measure of an angle that is formed by two adjacent angles. According to this postulate, the measure of the larger angle, which is formed by two adjacent angles, is equal to the sum of the measures of the two smaller adjacent angles.

Given the following:

m <1 =79°

m<2 = 53°

Thus, we have:

m<KJL = m<1 + m<2

Substitute:

m<KJL = 79 + 53

m<KJL = 132°

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The angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure of m∠KJL = 132°.

We can observe that the angles m∠1 and m∠2 are between the angle m∠KJL hence the sum of the two angles m∠1= 79° and m∠2 = 53° will give the measure of m∠KJL as follows:

m∠1 + m∠1 = m∠KJL

79° + 53° = 132°

m∠KJL = 132°

Therefore, the angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure m∠KJL = 132°

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The height of the​ heater is 5 feet.

The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs.

Given:

The length of one side of the base is 12 feet.

The slant height is 13 feet.

Using Pythagorean theorem we get

H² = slant height² - 1/2 base diagonal²

H² = 13² - 12²

H² = 169- 144

H² = 25

H= 5 feet

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The two possible locations of point B on the number line are 0.1 and 1.1.

A number line is a graphic depiction of numbers organized in a straight line in mathematics. Positive numbers appear to the right of zero and negative numbers to the left of zero when it is displayed horizontally. At the line's intersection, the number zero serves as a standard against which other numbers' magnitudes can be measured.

Many forms of numbers, including whole numbers, integers, fractions, decimals, and even irrational numbers, can be represented on a number line. The distance between any two points on the number line, which stands for the difference between any two matching numbers, corresponds to a distinct number.

Number lines are frequently used to graph functions and equations as well as to execute basic arithmetic operations including addition, subtraction, multiplication, and division. They are also helpful for comprehending ideas like magnitude, distance, and absolute value.

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You kayak 140 feet further in 5 minutes going downstream than you do in 5 minutes going upstream.

Speed is determined by dividing the distance traveled by the time taken to travel it. It gives the distance traveled and the amount of time it took to travel that distance.

Speed is directly Proportional to Distance and Inversely proportional to Time. Hence,

Distance = Speed X Time.

Given: You paddle a kayak 168 feet up a river every two minutes.

Hence, 168/2 = 84 feet per minute.

Therefore you go up  84 feet in one minute.

You reach 84*5 = 420 feet in 5 minutes.

Given: As you paddle back down the river, you cover 56 feet every 30 seconds.

Speed is determined by distance traveled divided by time, therefore when traveling downward, 56/0.5 equals 112 feet per minute.

In one minute, you descend by 112 feet.

You descend 560 feet in 5 minutes, or 5*(112) feet.

As a result, you will move on 140 feet (560 - 420)=140 feet further .

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The amount owed at the end of that period is given as follows:

$334.

An exponential function is modeled as follows:

y = ab^x.

In which:

For a decreasing exponential function, the rate of change b is given as follows:

b = 1 - r.

In which r is the decay rate.

The parameters for this problem are given as follows:

a = 390, r = 0.05, b = 0.95.

Hence the function giving the amount owed after x months is given as follows:

y = 390(0.95)^x.

After three months, the amount owed is given as follows:

y = 390(0.95)^3

y = $334.

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Answer:

$334.37

Step-by-step explanation:

At the start, Sai owes his mum $390. After the first month, his mum reduces his debt by 5% of $390, which is 0.05 x $390 = $19.50. So at the end of the first month, he owes his mum $390 - $19.50 = $370.50.

After the second month, his mum reduces his debt by 5% of $370.50, which is 0.05 x $370.50 = $18.53. So at the end of the second month, he owes his mum $370.50 - $18.53 = $351.97.

After the third month, his mum reduces his debt by 5% of $351.97, which is 0.05 x $351.97 = $17.60 (rounded to the nearest cent). So at the end of the third month, he owes his mum $351.97 - $17.60 = $334.37.

Therefore, Sai owes his mum $334.37 at the end of three months.

Answer: I think its B, C, and F

Step-by-step explanation: Im not sure but i am so sorry if im wrong

The probability that he would have done at least this well if he had no ESP is 0.4335,

The probability of a man correctly predicting the outcome of a coin flip without having extrasensory perception (ESP) can be calculated by using probability theory.

In this case, we can calculate the probability of correctly predicting 16 or more coin flips out of 22, given that the man has no ESP. To do this, we first need to calculate the probability of correctly predicting each coin flip individually. Since each coin flip is an independent event, the probability of correctly predicting each coin flip is 0.5, or 50%.

Therefore, the probability of correctly predicting 16 or more coin flips out of 22 can be calculated as the sum of the probabilities of correctly predicting each coin flip, multiplied by the number of ways in which 16 or more coin flips can be correctly predicted. This can be expressed as

=> P(x ≥ 16) = 0.5²² x C(22, 16) + 0.5²² x C(22, 17) +…+ 0.5²² x C(22, 22),

where C is the combination operator.

Using this formula, the probability of correctly predicting 16 or more coin flips out of 22 without having ESP is 0.4335, meaning that it is highly unlikely that the man has ESP

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Brackets are used for multiplication to expand and simplify an expression.

We must multiply out the brackets in order to extend and simplify an expression. The resulting phrase is then made simpler by grouping like terms together. Our method for removing brackets is known as expanding brackets or multiplying them out. Factorization is being done in reverse.

In some non-standard or informal contexts, such as with some programming languages or computer systems, brackets are employed as multiplication signs. When accessing items of an array or list in various programming languages, square brackets may also be used to denote multiplication in specific circumstances. As an example, the formula 2(3) instructs you to multiply 2 by 3 to generate the number 6.

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The limit definition of a derivative is a mathematical method used to calculate the instant rate of change of a characteristic at a particular point. it is based at the idea of the limit of a function because the input techniques a certain cost.

The limit definition of a derivative is expressed as follows:

[tex]f'(x) = lim (h → 0) [f(x + h) - f(x)] /h[/tex]

Wherein f'(x) represents the derivative of the function f(x) at a particular factor x. The expression [tex]( f(x + h) - f(x)) / h[/tex] represents the common price of alternate of the characteristic over a small interval of size h, focused at x. The limit of this expression as h approaches 0 represents the instant fee of change of the characteristic at x, or the slope of the tangent line to the function at that factor.

The limit definition of a derivative is a fundamental concept in calculus and is used to calculate the slopes of tangent lines, to find maximum and minimum factors, and to clear up optimization issues in a huge variety of packages.

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No es posible determinar si lo que dice Luis es correcto sin conocer el porcentaje de descuento aplicado en la compra de la casaca.

Si el precio original de la casaca es de $80 y después de aplicar un descuento el precio final es de $55, entonces se puede determinar el porcentaje de descuento utilizando la fórmula:

descuento = (precio original - precio final) / precio original

descuento = (80 - 55) / 80 = 0.3125 = 31.25%

Si el porcentaje de descuento es del 31.25%, entonces Luis tiene razón en su afirmación de que está comprando la casaca con un descuento. Sin embargo, si el porcentaje de descuento es diferente, entonces su afirmación podría ser incorrecta.

Por lo tanto, es importante conocer el porcentaje de descuento para determinar si lo que dice Luis es correcto o no.

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When each vertex of the square is located on the circumference of the circle, each side of the square measures 5.971 cm.

As per Geometry and trigonometry, a square has equilateral triangle sides and four equal angles, making itself an equilateral quadrilateral. Other name for it is a triangle with two adjacent vertices that are the same length. An equilateral quadrant is one that has four equal ends and four equal angles, like a square. Angles that are 90 degrees or straight are square angles. The downtown's diagonals are also split at a right angles and are evenly spaced. a rectangle with approximately consecutive sides that is adjacent. a trapezoid with four equal sides and straight angles on all four sides. a parallelogram with two adjacent sides that seem to be equal and make a right angle. rhombus has straight sides.

given

If the square perfectly fits the circle, then the circle's diameter is the same as the square's diagonal. The square's diagonal also has a length of cm because each side of the square is cm long. The square's diagonal can be determined using the area of the circle, as shown below:

area = [tex]\pi[/tex]*r *r

r*r = 56/pi

r = 4.22

As the square's diagonal and the circle's diameter are equal, x = 5.971 cm.

When each vertex of the square is located on the circumference of the circle, each side of the square measures 5.971 cm.

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A graph of the line with slope 3/4 passing through the point (5, 2) is shown in the image attached below.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (5, 2), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

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

y - 2 = 3x/4 - 15/4

y = 3x/4 - 1.75

In conclusion, we would use an online graphing calculator to plot the above linear equation as shown in the graph attached below.

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Answer:

The number line with the added values would look as follows:

< -40/8 -5 ⟳ √3 -4 5/8 -3 √16 -2 7/12 -1 0 1 2 3 ^3√27 4 5 >

The volume of the triangular prism is 144 cm³.

What is the volume of the triangular prism?

We know that the volume of the prism = base area × Length of the prism. Therefore, the volume of the prism, in this case, is calculated using the same formula, Volume of triangular prism = (1/2) bh × L.

We have given:

b = 8cm,

h = 3 cm

l = 12 cm

So, the Volume of the triangular prism = (1/2) bh × L.

= (1/2) 8*3 × 12.

= 12 * 12

= 144

Hence, the volume of the triangular prism is 144 cm³.

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Answer:

12 feet

Step-by-step explanation:

Let h be the height of the tree. We set up and solve this proportion:

[tex] \frac{h}{24} = \frac{3}{6} [/tex]

[tex]6h = 72[/tex]

[tex]h = 12[/tex]

Answer:

h ≈ 29.98

Step-by-step explanation:

diameter = 12m

volume = [tex]1130m^{3}[/tex]

radius = 6m

The equation to find the height given radius and volume:

[tex]h = \frac{3(V)}{\pi r^2}[/tex]

Plug in values

Answer:

Given:-

Diameter=12m

Volume=1130m³

Takeπ=3.14

To find:-

Height of cone=?

Step-by-step explanation:

Solution:-

Radius=d/2

= 12/2

=6m

Volume of cone=1/3πr²h

h= 3v/πr²

= 3×1130/3.14× 6²

= 3390/113.04

= 29.98m

hence, the height of cone is 30m.

The probability that the moderate number of moths in 60 traps is more significant than 0.4 is approximately 0.9738 or 97.38%.

(a).

The mean number of moths =  60 traps

Now, the properties of normal distribution and central limit theorem are used.

mean of the individual moth counts = 0.5.

The standard deviation = the Standard deviation of the individual moth counts, divided by the square root of the sample size.

standard deviation = (0.7 / [tex]\sqrt{60}[/tex])

standard deviation = 0.0905

the mean number of moths and standard deviation of the average number of moths in 60 traps are 0.5 and 0.0905.

(b) .

By using the central limit theorem

The average number of moths in 60 traps = 0.4

The z-score formula is to be calculated by using:

Z = (sample mean - population mean) / (standard deviation/sqrt (sample size))

Substituting the given values, we have:

Z = (0.4 - 0.5) / (0.7 / sqrt(60))

Z = -1.94

The probability of a Z-score greater than -1.94 is approximately 0.9738.

Hence, we can conclude that the probability that the average number of moths in 60 traps is greater than 0.4 is approximately 0.9738.

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The volume of the solid is 342.9 sq. cm.

The volume of an object is the amount of substance that the object can contain. Th three dimensions of the object is required in order to determine its volume.

Considering the question,

volume of a cylinder = [tex]\pi[/tex]r^2h

Where r is the radius and h is the height of the cylinder.

volume of the hole = length*width*height

Thus,

The volume of a cylinder = [tex]\pi[/tex]r^2h

                   = 22/7*4^2*10

                   = 502.86

The volume of the cylinder is 502.86 sq. cm.

The volume of the hole = length*width*height

                                     = 4*4*10

                                     = 160 sq cm.

The volume of the solid = volume of a cylinder  - volume of the hole

                                         = 502.86 - 160

                                      = 342.86

The volume of the solid is 342.9 sq. cm.

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