Two sides of a triangle have the following measures. Find the range of possible measures for the third side (x).

11, 8

a) after 30 minutes, they will 12.5 m apart

b)  25  is the distance between the boats changing 30 minutes after they leave port

The direction of movement of both boats forms a right angle triangle. The distance travelled due south and due east by both boats represents the legs of the triangle. Their distance apart after t hours represents the hypotenuse of the right angle triangle.

Let x represent the length the shorter leg(west) of the right angle triangle.

Let y represent the length the longer leg(south) of the right angle triangle.

Let z represent the hypotenuse.

Applying Pythagoras theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

 = 20^2+15^2

 z = 25

but after 30 minutes one travels 10mph

and another 7.5mph

then

z= 12.5

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Answer:

13.5

Step-by-step explanation:

Step 1:

x - 16 = 3x + 11      Equation

Step 2:

- 16 = 2x + 11     Subtract x on both sides

Step 3:

- 27 = 2x     Subtract 11 on both sides

Step 4:

x = - 27 ÷ 2

Answer:

x = 13.5

Hope This Helps :)

Answer:

\(x = -\frac{27}{2}\)

Step-by-step explanation:

I hope this helps!

The result of the integral is (10/5)sin^5(x) - (20/7)sin^7(x) + (10/9)sin^9(x) + c. To evaluate the integral ∫10cos^5(x)sin^4(x)dx, we can use a trigonometric identity and a substitution.

To simplify the integrand, we can use the trigonometric identity cos^2(x) = 1 - sin^2(x) and substitute u = sin(x).

Apply the trigonometric identity: cos^5(x) = (1 - sin^2(x))^2 * cos(x) = (1 - u^2)^2 * cos(x). Now we have the integrand as 10(1 - u^2)^2 * cos(x) * u^4.

Use the substitution: Let u = sin(x), then du = cos(x)dx. We can rewrite the integral as ∫10(1 - u^2)^2 * u^4 * du.

Expand the integrand: 10u^4 - 20u^6 + 10u^8.

Integrate each term: The integral of u^4 is u^5/5, the integral of u^6 is u^7/7, and the integral of u^8 is u^9/9.

Substitute back: Replace u with sin(x) in the antiderivative expression obtained in the previous step.

Add the constant of integration, c, to obtain the final result.

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The solution is,

1.   a, 99%       b71%

2. 64%, 44%

3. Number of particles   0, 1, 2, 3, 4,  5, 6, 7,  8, 9, 10, 11, 12, 13, 14

frequencies:                 1, 2, 3, 12, 11, 15, 18, 10,  12, 4, 5, 3, 1, 2, 1

Relative frequencies  0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04,                        0.05,0.03,0.01,0.02,0.01

A histogram is an approximate representation of the distribution of numerical data.

here, we have,

Number of particles: 0, 1, 2, 3, 4, , 5, 6, 7

Frequency: 1, 2, 3, 12, 11, 15, 18, 10

Number of particles: 8, 9, 10, 11, 12, 13, 14

Frequency: 12, 4, 5, 3, 1, 2, 1

we solve by saying that  . one of th smaples wafer is with  any particles. we get the proportion by subtracting 1 from the total  divided by 100

100-1/100

.99

at least five particles , then we can subtract the number of those with particles less than five from 100 , divided by 100

100-(11+12+3+2+1)=71/100

0.71 or 71%

b. those particles within 5 and 10 inclusive

15+18+10+12+4+5=64/100

0.64

0r 64%

five and 10 exclusively will be

18+10+12+4=44/100

0.44

44%

c. Draw an histogram. first we have frequency table first

Number of particles    0, 1, 2, 3, 4,  5, 6, 7,  8, 9, 10, 11, 12, 13, 14

frequencies:                 1, 2, 3, 12, 11, 15, 18, 10,  12, 4, 5, 3, 1, 2, 1

Relative frequencies  0.01, 0.02,0.03,0.12,0.11,0.15, 0.18,0.1, 0.12,0.04,                        0.05,0.03,0.01,0.02,0.01

Relative frequencies is derived by dividing each frequencies over the total frequencies

we can say that it is unimodal or say that it is slightly positively skewed

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The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.

The endpoints are (2, -5) and (-3,1).

The standard form equation for a circle is known as

\((x-a)^2+(y-b)^2=r^2\)

where (a, b) are the center's coordinates and (r) is the radius.

Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.

Calculating the midpoint is as follows:

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)\)

where, \((x_{1},y_{1})\) and \((x_{2},y_{2})\) are two points.

Now putting the values

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)\)

Now we determine the equation of circle.

The center (2, 1) and the terminal are the two points (-2, 3).

r = \(\sqrt{(-2-1)^2+(3-1)^2}\)

r =\(\sqrt{(-3)^2+(2)^2}\)

r = \(\sqrt{9+4}\)

r = √13

Now we can write the equation of circle as:

(x - 1)^2 + (y - 1)^2 = (√13)^2

(x - 1)^2 + (y - 1)^2 = 13

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The complete question is:

Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).

Write the standard equation for the circle.

Answer:

Priya, Hailey, Shetal

Step-by-step explanation:

Let's pretend the clock is currently at 4. Hailey auditioned 10 mins before, so she auditioned at 3:50.

Priya auditioned 30 mins before Hailey, meaning she auditioned at 3:20.

Then, Shetal auditioned 5 mins before 4, meaning she auditioned at 3:55.

So, going in time, the order will be  3:20, 3:50, 3:55

So, Priya, Hailey, Shetal

1) Estimate value of the product of 2/3 and 0.55 is, 2/3.

2) The fraction part is, 55 / 100

3) The product of the two numbers is, 11/30

We have to given that,

Estimate the product of 2/3 and 0.55.

And, Convert the decimal 0.55 to a fraction.

And, The product of the two numbers.

Now,

Estimate the product of 2/3 and 0.55,

So, we can round 0.55 to the nearest whole number, which is 1.

Then, multiply 2/3 by 1 to get an estimate of the product.

so, The correct answer is 2/3.

Now, we can convert the decimal 0.55 to a fraction,

= 0.55

= 55/100

= 11/20

Thus,  The correct answer is, 55/100.

And,  the product of 2/3 and 0.55,

= 2/3 x 55/100

= 110/300

= 11/30.

Hence, The correct answer is, 110/300 or 11/30

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Given:

It can be written as follows.

Dividing 5.44 by 6.8, we get

Hence the quotient is

Its less than i think yeah

To evaluate the integral ∫2^9x dx, we can use the definite integral formula. Let's divide the interval [2, 9] into n subintervals of equal width.

The width of each subinterval can be found by taking the difference between the endpoints of the interval and dividing it by the number of subintervals: Δx = (9 - 2)/n. The ith endpoint, denoted as xi, can be determined by multiplying the width of each subinterval by i and adding it to the lower endpoint: xi = 2 + iΔx. We can evaluate f(xi) = 9xi at the ith endpoint by substituting xi into the function. Finally, we can evaluate the integral using the definite integral formula: ∫2^9x dx = lim(n→∞) Σ[i=1 to n] f(xi)Δx.

In summary, to evaluate the integral ∫2^9x dx, we divide the interval [2, 9] into n subintervals of equal width. The width of each subinterval is given by Δx = (9 - 2)/n. The ith endpoint, xi, is determined by multiplying the width of each subinterval by i and adding it to the lower endpoint. We evaluate f(xi) = 9xi at the ith endpoint by substituting xi into the function. Finally, we can find the integral by taking the limit of the sum of f(xi)Δx as n approaches infinity.

Now let's explain the steps in more detail. We start by finding the width of each subinterval. The interval [2, 9] has a difference of 7, and we divide it into n equal subintervals. Thus, the width of each subinterval is Δx = (9 - 2)/n.

Next, we determine the ith endpoint, xi, for each subinterval. We multiply the width of each subinterval, Δx, by i and add it to the lower endpoint of the interval. In this case, the lower endpoint is 2. Therefore, xi = 2 + iΔx.

To evaluate f(xi) = 9xi at the ith endpoint, we substitute xi into the function f(x) = 9x. This gives us f(xi) = 9(2 + iΔx).

Finally, we can evaluate the integral by taking the limit of the sum of f(xi)Δx as the number of subintervals, n, approaches infinity. The integral is expressed as ∫2^9x dx = lim(n→∞) Σ[i=1 to n] f(xi)Δx.

By following these steps and taking the limit as n approaches infinity, we can evaluate the integral.

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True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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Answer:

(a) is 15

(b) is 30

75 divide by 15 times 90 divide by 15 is 30

Answer:

Step-by-step explanation:

Highest common factor of 75 and 90 will be the largest possible length of the square.

75 = 5 * 5 * 3

90 = 3 * 3 * 2 * 5

GCF = 5 * 3 = 15

Length of the side of square = 15 cm

b) Number of squares =  Area of sheet ÷ Area of square

                                    \(= \frac{75*90}{15*15}\\\\= 5 * 6\\\\= 30\)

Total number of square = 30

How is anyone gonna know that lol

9514 1404 393

Answer:

  y = -x +3

Step-by-step explanation:

The point-slope form can be a useful place to start.

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

You require the line ...

  y -(-4) = -1(x -7)

  y = -x +7 -4 . . . . . . . . eliminate parentheses, add -4

  y = -x +3 . . . . . . . . . slope-intercept form

Henry's claim is accurate.

Area is a quantity which explains the sai chowk to dimensional cigarette there for flannel armenia of the plane it is been thoughts as a payment of purpose that is a safe colour calculator the area of a sea for surface candy important step.

As the number of triangles increases, the estimated area will approach the actual area of the circle as the base lengths and heights of the triangles decrease. This is because the area of each triangle will approach zero, resulting in a more accurate estimate of the circle's area. Additionally, when n is large enough, the sum of the base lengths will be equal to the circumference of the circle, which is equal to the area.

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(a) Circumference of Earth in kilometers: 40,075.017 km

(b) Surface area of Earth in square kilometers: 510.1 million km^2

(c) Volume of Earth in cubic kilometers: 1.08 trillion km^3

To calculate these values, we use mathematical formulas that relate to the sphere shape of the Earth.

For (a), we use the formula for the circumference of a circle, C = 2 * pi * r, where r is the radius of the Earth in meters (6.37 x 10^6 m). We then convert this result to kilometers by dividing by 1000.

For (b), we use the formula for the surface area of a sphere, A = 4 * pi * r^2, where r is the radius of the Earth. Again, we convert this result to square kilometers.

For (c), we use the formula for the volume of a sphere, V = (4/3) * pi * r^3, where r is the radius of the Earth. We then convert this result to cubic kilometers by dividing by 10^9.

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Step-by-step explanation:

Philipp Heinrich Scheidemann was a German politician of the Social Democratic Party of Germany. In the first quarter of the 20th century he played a leading role in both his party and in the young Weimar Republic. Wikipedia

Born: July 26, 1865, Kassel, Germany

Died: November 29, 1939, Copenhagen, Denmark

Party: Social Democratic Party of Germany

Spouse: Johanna Dibbern (m. 1889–1926)

Previous offices: Mayor of Kassel (1919–1925), Chancellor of the German Reich (1919–1919), More

Books: The Making of New Germany: The Memoirs of Philipp Scheidemann

Nationality: German, Weimar

Answer: 2:1

Step-by-step explanation:

the probability that they get they get the silver cars and someone else gets the white is 2:1

The domain restrictions of the expression q²−7q−8/q²+3q−4 are q ≠ -4 and q ≠ 1. (option c)

The denominator of the expression is q²+3q−4. To determine the values that would make the denominator equal to zero, we can set it equal to zero and solve for q:

q² + 3q - 4 = 0

Now, we can factorize the quadratic equation:

(q + 4)(q - 1) = 0

To find the values of q, we set each factor equal to zero and solve for q:

q + 4 = 0 or q - 1 = 0

Solving these equations, we get:

q = -4 or q = 1

So, the values of q that would make the denominator equal to zero are q = -4 and q = 1. These are the values we need to exclude from the domain of the expression to avoid division by zero.

Therefore, the correct answer is option c) q ≠ 1 and q ≠ -4.

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Complete Question:

What are the domain restrictions of q²−7q−8/q²+3q−4?

a) q≠1 and q≠−8

b) q≠−1 and q≠4

c) q≠1 and q≠−4

d) q≠−1 and q≠8

The 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).

Suppose that mean retail price per gallon of regular grade gasoline 3.43.

empirical rule explains that  approximately 68%,95% and 99.7% of data lies between (µ ± 1*σ) ,(µ ± 2*σ) and (µ ± 3*σ) respectively.

⇒If some data {x} are normally distributed, the corresponding {z} will be normal with mean 0 and standard deviation 1 where the correspondence between the {x} and {z} is given by

Such z's are called z-scores.

(µ ± 1*σ)=68%

(µ ± 2*σ)=95%

(µ ± 3*σ)=99.7%

a)

P(3.23<x<3.63) =\(P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ]\)

=P[( \(\frac{3.23-3.43}{0.10}\) < z < \(\frac{3.63-3.43}{0.10}\) ]

=P[-2 < z < 2 ]

=0.95

=95.0 %

b)

P(3.23<x<3.53) =\(P[ \frac{(x1- \mu)}{\sigma} < z < \frac{(x2- \mu)}{\sigma}} ]\)

=P[( \(\frac{3.23-3.43}{0.10}\) < z < (\(\frac{3.53-3.43}{0.10}\) ]

=P[-2 < z < 1 ]

=0.815

=81.5 %

c)

P(x>3.53) =\(P[ z > \frac{x-\mu}{\sigma} ]\)

=P[ z > \(\frac{3.53-3.43}{0.10}\) ]

=P[ z > 1 ]

=0.16

=16.0 %.

Therefore, 95% of regular grade gasoline sells for between $3.23 & $3.63 and per gallon (to decimal) and 85% of regular grade gasoline sells for between $3.23 & $3.53 and per gallon (to decimal) and 16% percentage of regular grade gasoline sells for less than $3.53 per gallon (to decimal).

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A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output.

The process of evaluating a function is typically straightforward when we have the function in the form of a formula. For instance, it is possible to evaluate the function f(x)=53x2 by first squaring the input number, multiplying by 3, and then subtracting the result from 5.

The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x.

To determine the outcome, simplify the values. The abscissa is the x value of the point (x, y). It shows how far a point is from the origin or from the x-axis' horizontal axis. 

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Answer:

wow

Step-by-step explanation:

Answer:

The answer is B. When we count to the left the second digit is tens place

Answer:

35 multiplied by 12

Step-by-step explanation:

Because either you multiply it or you do sohcahtoa

Answer:

Do as a which is c if I'm not than rost me

Step-by-step explanation:

Answer:

15.2

Step-by-step explanation:

The explanation is in the photo.. but basically this question is about similar triangles and you need to find the scale factor to find the height.

Hope it helps

the height of the tree is approximately 15.2 meters.

To find the height of the tree, we can set up a proportion between Andrew's height and the height of the tree based on their respective shadow lengths.

Let's denote the height of the tree as "h" meters.

The proportion between the height and shadow lengths can be written as:

h / 28.0 = 1.9 / 3.5

Now, we can solve for "h":

h = (1.9 / 3.5) * 28.0

h ≈ 15.2 meters

To the nearest tenth of a meter, the height of the tree is approximately 15.2 meters.

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The answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

The equation x3 + y3 = 9 is a cubic equation and is a non-linear equation. As such, it does not have any tangent lines that are horizontal. A tangent line is a line that just touches a point on a curve and has the same slope as the curve at that point. Since the equation is non-linear, the slope of the curve changes at each point, meaning that there cannot be any horizontal tangent lines.

To calculate the slope of the curve at any point (x,y), we use the formula m = (dy/dx) or m = 3*(x2/y2). At these points, the slope of the curve will not be zero, meaning that there is no horizontal tangent line at any point on the curve.

Therefore, the answer to the question is that there are no points on the curve x3 + y3 = 9 in the xy-plane that have a tangent line that is horizontal.

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there are 5 white blocks and 4 gray blocks.

so the ratio of the gray square to white square is,

multiply numerator and denominator by 5.

so the answer is option D

The value of c such that f(c) is the average value of the function f(x) = 4x on the interval [0, 2] is c = 1. Option A

The average value of a function on an interval [a, b] is given by the formula:

Average value = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, the interval is [0, 2] and the function is f(x) = 4x.

Average value = (1 / (2 - 0)) * ∫[0, 2] 4x dx

Simplifying the integral:

Average value = (1 / 2) * [\(2x^2]\) evaluated from x = 0 to x = 2

Average value =\((1 / 2) * (2(2)^2 - 2(0)^2)\)

Average value = (1 / 2) * (2 * 4 - 0)

Average value = (1 / 2) * 8

Average value = 4

Now, we want to find the value of c such that f(c) is equal to the average value, which is 4.

f(c) = 4

Substituting the function f(x) = 4x:

4x = 4

Dividing both sides by 4:

x = 1

Therefore, the value of c such that f(c) is the average value of the function f(x) = 4x on the interval [0, 2] is c = 1.

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