A circle with a radius of 10 inches is placed inside a square with a side length of 20 inches. Find the probability that a dart thrown will land inside the circle.

a. 87.5%
b. 75.8%
c. 57.8%
d. 78.5&

Answer: [tex]x=128\°[/tex]

Step-by-step explanation:

It is important to remember the following:

[tex]Angle\ formed\ by\ two\ chords=\frac{1}{2}(Sum\ of\ intercepted\ arcs)[/tex]

In this case you can observe in the figure that "x" is an Angle formed by two chords, therefore, you can find its value applying the formula.

Therefore, the value of "x" is this:

[tex]x=\frac{1}{2}(202\°+54\°)\\\\x=\frac{1}{2}(256\°)\\\\x=128\°[/tex]

Question 2

Answer: 1.20

---------

To get this answer, you divide the total amount of royalties (300) over the number of books (250) to get 300/250 = 1.20

Another way to see this is through the ratio of

300 dollars: 250 books

then you divide both parts of that ratio by 250 so that the "250 books" turns into "1 book" like so...

300 dollars: 250 books

300/250 dollars: 250/250 books

1.20 dollars: 1 book

Indicating that his royalties per book is 1.20 dollars. The rate of change is often expressed as a unit rate, meaning that we want the royalties for 1 book (which then scales up).

=========================================================

Question 3

Answer: slope is -1/10 or -0.1; slope tells us how much the candle height is decreasing each minute, y intercept is the starting candle height (see below for further explanation)

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

Explanation:

The y intercept is at 25, as this is where the diagonal line crosses the vertical y axis. Similarly, the x intercept is 250. The y and x intercept lead to the two points (0,25) and (250,0). Let's use the slope formula to find the slope of the line through these two points

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

m = (0 - 25)/(250 - 0)

m = -25/250

m = -1/10

m = -0.1

The slope of the line is -1/10 or the decimal equivalent -0.1

What does the slope tell us? It tells us how much of the candle's height is changing as each minute ticks by. Specifically, the slope -0.1 means that the candle height is going down by 0.1 cm for each minute gone by. A shorter way to say this is to say "the height is decreasing by 0.1 cm per minute" (think of it like a speed such as miles per hour)

The y intercept is the starting height of the candle due to the fact that x = 0 here. Therefore, the starting height of the candle is 25 cm.

Side note: the x intercept of 250 tells us how long the candle burns for, which in this case is 250 minutes (4 hrs, 10 min) because y = 0 for the x intercept, and y is the height of the candle at time x. Anything beyond x = 250 is not possible in realistic sense as we can't have a negative y height value.

Answer:

associative property

Step-by-step explanation:

This illustrates the associative property.  It doesn't matter in which order you combine the terms here.

This is an example of associative property which states,

[tex]a+(b+c)=(a+b)+c[/tex]

Hope this helps.

r3t40

Answer:

[tex]\frac{2}{9}[/tex]

Step-by-step explanation:

THe most common mistake would be to think 1/4th of the kites flew, BUT 1/4th of the trapezoidal kites flew.

Hence, 1/4th of 8/9th of the TOTAL KITES FLEW, that is:

[tex]\frac{1}{4}*\frac{8}{9}=\frac{2}{9}[/tex]

hence, 2/9th of the kites flew

The number 19,761 is divisible by the following numbers: 1, 3, 7, 21, 941, 2,823, 6,587, and 19,761.

When 19,761 is divided by any of these numbers, we obtain a whole number without any remainder.

In other words, the factors of 19,761 include 1, 3, 7, 21, 941, 2,823, 6,587, and 19,761.

19,761 ÷ 1 = 19,761

19,761 ÷ 3 =  6,587

19,761 ÷ 7 = 2,823

19,761 ÷ 21 = 941

19,761 ÷ 941 = 21

19,761 ÷ 2,823 = 7

19,761 ÷ 6,587 = 3

19,761 ÷ 19,761 = 1

Thus, we describe a number as divisible by another number or factor when the quotient shows a whole number and there is no remainder.

Answer:

55

Step-by-step explanation:

bisect means to cut in half so it is half of 110 so it is 55

Answer:

I believe the answer is 55°.

Step-by-step explanation:

Sense line Y is cut between angle AXB, you would need to find the half of 110°.

So, 110 ÷ 2 = 55.

Therefore, 55° is the correct answer.

Answer:

The vertex is the point (-5,3)

Step-by-step explanation:

we know that

The equation of a vertical parabola in vertex form is equal to

[tex]y=a(x-h)^{2}+k[/tex]

where

a is a coefficient

(h,k) is the vertex

If a > 0 the parabola open upward and the vertex is a minimum

If a < 0 the parabola open downward and the vertex is a maximum

In this problem we have

[tex]y=2(x+5)^{2}+3[/tex]

a=2

so

the parabola open upward and the vertex is a minimum

h=-5, k=3

therefore

The vertex is the point (-5,3)

Answer:

y + 3 = -6(x + 9) or y = -6x - 57

Step-by-step explanation:

We can use the point-slope form for this situation.

Point-slope form: y - y₁ = m(x - x₁), where m = slope and (x₁, y₁) are given coordinates.

Plug in: y + 3 = -6(x + 9)

This can be changed to the more common slope-intercept form.

Multiply: y + 3 = -6x - 54

Subtract: y = -6x -57

Answer:

y=-6x-57 (this answer is in slope-intercept form)

I don't know what your choices are and if you can select multiple answers or not.

Step-by-step explanation:

y=mx+b is an equation for a line with slope m and y-intercept b.

We are given m=-6 so we will plug this in giving us: y=-6x+b.

Now we need to find b, the y-intercept.  Let's use a point (x,y) we know is on the line of y=-6x+b to find b.

We know (x,y)=(-9,-3) is on that line.  So our line should satisfy this point.  We must pick a b so that happens.  Plug (x,y)=(-9,-3) into the equation now.

-3=-6(-9)+b

-3=54+b

-3-54=b

-57=b

So the equation is y=-6x-57

A proportion

[tex]a\div b = c\div d[/tex]

is nothing but a comparison between two fractions: we can rewrite it as

[tex]\dfrac{a}{b}=\dfrac{c}{d}[/tex]

So, we can multiply both sides by the two denominators b and d to get

[tex]\dfrac{a}{b}=\dfrac{c}{d} \iff ad = bc[/tex]

In other words, a proportion is true if the product of the inner terms is the same as the product of the outer terms.

In your case, we have the check is the following:

[tex]24 \div 40 = 4\div 7 \iff 24\cdot 7 = 40\cdot 7 \iff 168 = 280[/tex]

which is clearly false. So, 24:40 = 4:7 is not a true proportion. In fact, if we convert fractions into numbers, we have

[tex]\dfrac{24}{40} = 0.6,\quad \dfrac{4}{7} = 0.\overline{571428}[/tex]

which makes even more clear that the proportion doesn't hold.

Answer:

x^4+2x^2y+y^2

Step-by-step explanation:

first we expand the brackets

(x^2+y)(x^2+y)

the it will become

x^4+x^2y+yx^2+y^2

then finally the answer will become

,x^4+2x^2y+y^2

Answer:

x⁴+2x²y+y²

Step-by-step explanation:

Given the equation( x²+y)², to expand, we will open the bracket by multiplyimg the function x²+y by itself to have;

(x²+y)² = (x²+y)(x²+y)

(x²+y)² = x⁴+x²y+x²y+y²

(x²+y)² = x⁴+2x²y+y²

Therefore the expansion form of (x²+y)² is x⁴+2x²y+y²

Answer:

x = 8 + 7y

Step-by-step explanation:

Given

x - 7y = 8 ( isolate x by adding 7y to both sides )

x = 8 + 7y

Linear equation is the equation in which the highest power of the unknown variable is one.The value of the variable x for the given expression is,

[tex]x=7y+8[/tex]

The given linear equation is,

[tex]x-7y=8[/tex]

Linear equation is the equation in which the highest power of the unknown variable is one. The linear equation are used to find out the value of unknown variable.

In the above linear equation the coefficient of the variable x is one and the coefficient of the variable y is negative seven.

The number eight is the constant which is equal to the given expression of variables.

To solve the equation for x refers to get the value of the variable x. As there is only one linear equation and the unknown variables are two. Thus the value of variable x can be obtained in the form of the variable y.

Let solve the given equation,

[tex]x-7y=8[/tex]

Add [tex]7y[/tex] both sides of the equation. thus,

[tex]x=8+7y[/tex]

[tex]x=7y+8[/tex]

Thus the value of the variable x for the given expression is,

[tex]x=7y+8[/tex]

Learn more about the linear equation here;

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Answer:

Option B k > 0

Step-by-step explanation:

we know that

Observing the graph

The slope of the line is positive

The y-intercept is negative

we have

[tex]3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)[/tex]

The slope of the line is equal to

[tex]m=\frac{1}{3}[5k+2][/tex]

Remember that the slope must be positive

so

[tex]5k+2> 0\\ \\k > -\frac{2}{5}[/tex]

The value of k is greater than -2/5

Analyze the y-intercept

[tex](2-\frac{4}{3}k) < 0\\ \\ 2 < \frac{4}{3}k\\ \\1.5 < k\\ \\k > 1.5[/tex]

1.5 is greater than zero

so

the solution for k is the interval ------> (1.5,∞)

therefore

must be true

k > 0

Answer:

x = -(38/3)

Step-by-step explanation:

Well first you have to isolate the square root on the left hand side.

Then eliminate the radical on the left hand side.

Last step

Solve the linear equation :

Rearranged equation

3x + 38 = 0

Subtract 38 from both sides

3x = -38

Divide both sides by 3

A possible solution is :

x = -(38/3)

For this case we must solve the following equation:

[tex]\sqrt {3x + 54} + 6 = 10[/tex]

Subtracting 6 from both sides of the equation:

[tex]\sqrt {3x + 54} = 10-6\\\sqrt {3x + 54} = 4[/tex]

We square both sides of the equation squared:

[tex]3x + 54 = 4 ^ 2\\3x + 54 = 16[/tex]

We subtract 54 from both sides of the equation:

[tex]3x = 16-54[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]3x = -38[/tex]

We divide between 3 on both sides:

[tex]x = \frac {-38} {3}\\x = - \frac {38} {3}[/tex]

Answer:

[tex]x = - \frac {38} {3}[/tex]

Answer:

The answer would be 12.8

Step-by-step explanation:

I looked it up and found the answer on another website

it is 12.8

By using the sine rule we got the value of a is 8 units.

Given that, in triangle ABC, angle A = 45, c= 17, and angle B = 25.

We need to find the measure of side a.

The sine rule formula is sinA/a=sinB/b=sinC/c.

Now, sin45°/a=sin25°/b=sin110°/17

⇒sin45°/a=0.9397/17

⇒0.7071/a=0.0854

⇒a=8.27≈8

Therefore, the value of a is 8 units.

To learn more about sine rule visit:

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x^3 + 7x^2 -8x -3x^2 -21x +24

x^3 + 4x^2 -29x +24

For this case we must simplify the following expression:

[tex](x-3) (x ^ 2 + 7x-8)[/tex]

We must apply distributive property:

[tex]x * x ^ 2 + x * 7x-8 * x-3 * x ^ 2-3 * 7x + 3 * 8 =\\x ^ 3 + 7x ^ 2-8x-3x ^ 2-21x + 24 =[/tex]

Adding similar terms we have:

[tex]x ^ 3 + 4x ^ 2-29x + 24[/tex]

Answer:

The simplified expression is:

[tex]x ^ 3 + 4x ^ 2-29x + 24[/tex]

Answer:

i) 4π

ii) An isosceles triangle

iii) 8 cm^2[/tex]

iv)  [tex](4\pi - 8)cm^2[/tex]

Step-by-step explanation:

The radius of the circle is 4 cm and the measure of the central angle is 90°.  

We know that the area of sector of a circle = [tex]\frac{central angle}{360} *\pi *r^2[/tex]

Given: r = 4 and central angle = 90

Now plug in these values in the above formula, we get

Area of the sector = [tex]\frac{90}{360} *\pi *4^2\\= \frac{1}{4} *\pi *16\\= 4\pi[/tex]

i) 4π

ii) In the triangle, the two sides are equal in measure, because the two sides represents the radius of the circle. The radius are the same in measure in a circle.

Therefore, the triangle is the second is an isosceles triangle.

iii) Area of a right triangle = [tex]\frac{1}{2} *base*height[/tex]

Here base = 4 and height = 4, plug in these values in the triangle formula, we get

The area of the triangle = [tex]\frac{1}{2} *4*4\\= 2*4\\= 8 cm^2[/tex]

iv) The area of the segment of the circle is (4π - area of the triangle).

= [tex](4\pi - 8)cm^2[/tex]

The area of a sector is calculated using:

[tex]A = \frac{\theta}{360} \times \pi r^2[/tex]

So, we have:

[tex]A = \frac{90}{360} \times \pi \times 4^2[/tex]

[tex]A = \frac{1}{4} \times \pi \times 4^2[/tex]

[tex]A = 4\pi[/tex]

Hence, the area of the sector is [tex]4\pi[/tex]

One of the angles in the triangle is 90 degrees.

So, the triangle is a right-angled triangle

The area of the triangle is then calculated as:

[tex]A = \frac 12 bh[/tex]

This gives

[tex]A = \frac 12 \times 4 \times 4[/tex]

[tex]A = 8[/tex]

Hence, the area of the triangle is 8, and the triangle is a right triangle

This is the difference between the areas of the circle and the triangle.

So, we have:

[tex]A = 4\pi - 8[/tex]

Hence, the area of the segment is [tex] 4\pi - 8[/tex]

Read more about areas at:

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Answer:

7560 million

Step-by-step explanation:

here is the answer for your question

Answer:

[tex]f(2)=\frac{37}{4}[/tex]  or [tex]f(2)=-(-\frac{37}{4})[/tex]

Step-by-step explanation:

we have

[tex]f(x)=2x^{2} +\frac{5}{x+2}[/tex]

Find f(2)

we know that

f(2) is the value of f(x) when the value of x is equal to 2

so

For x=2

substitute

[tex]f(2)=2(2)^{2} +\frac{5}{2+2}[/tex]

[tex]f(2)=8 +\frac{5}{4}[/tex]

[tex]f(2)=\frac{37}{4}[/tex]

or

[tex]f(2)=-(-\frac{37}{4})[/tex]

Answer:

3 people

Step-by-step explanation:

We can write a proportion, putting lbs of beef over people

21 lbs            7 lbs

-----------   = ------------

9 people         x people

Using cross products

21x = 7*9

21x = 63

Divide each side by 21

21x/21 = 63/21

x =3

You can have 3 people

For the equation cross multiplication is key. i do recommend you take in the fact it takes 2.3333etc. to make each persons portion

but none the less the quation should look like 7x9=63 then 63/21 which gives you 3.

you could also do 12/9=2.3, then 7/2.3= 3.04 for a more accurate answer

Answer:

There are 32 words total on the list.

Step-by-step explanation:

24*4=96;  

96÷3=32;  

There are 32 words total on the list.

Answer:

gfrwkmsvfbs

Step-by-step explanation:

dfffve

Answer:

A. Drusilla

Step-by-step explanation:

The line of random numbers is used for numbered population.

As we can see that the students are already labelled we have to divide the random number line in pairs of 2 digits

59,78,44,43,12,15,95,40,92,33,00,04,67,43,18,02,61,05,73,96,16,84,33,84,54

We have to keep in mind that our serial numbers are till 29.

So read the pair of numbers one by one

59 can't be used as it is greater than 29. Similarly 78,44,43 cannot be used.

The first student will be: 12 Kiefer

Then 15 and 00 will be second and third.

So the fourth student will be: 04 Drusilla

Hence option A is correct ..

Answer:

[tex]\dfrac{3}{2}[/tex]

Step-by-step explanation:

If 2x - 3 is a factor of P(x), then  3/2 is a zero of P(x).

[tex]\begin{array}{rcl}2x - 3 & = & 0\\2x & = & 3\\\\x & = & \mathbf{\dfrac{3}{2}}\end{array}\\\\\mathbf{P(\frac{3}{2})} \text{ will equal zero if $(2x-3)$ is a factor of $P(x)$}[/tex]

Answer:

270 7/16 in^2.

Step-by-step explanation:

The surface area equals the sum of the  areas of 3 pairs of congruent rectangles.

These are  2 * 8 * 1 3/4 + 2 * 8 * 12 1/2 + 2 * 1 3/4 * 12 / 1/8

= 16 * 7/4  +  16 * 25/2 + 2 * 7/4 * 97/8

=  28 + 200 + 42 7/16

= 270 7/16 in^2.

Answer: Option 'A' is correct.

Step-by-step explanation :

Since we have given that

Number of medals = 2

Number of runners = 8

We need to find the number of ways to award the medals.

We would use "fundamental theorem of counting" to find the number of ways.

So, number of ways is given by

8 × 7 = 56

Hence, option 'A' is correct.

Answer:

A. 56

Step-by-step explanation:

You take 8 and then find the next number down and multiply them.

8*7= 56

(Also, I just did this on APEX)

Answer:

f(x) reflects across the x-axis and translate left 2 ⇒ 2nd answer

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

- If the function f(x) translated vertically up  

 by k units, then the new function g(x) = f(x) + k

- If the function f(x) translated vertically down  

 by k units, then the new function g(x) = f(x) – k

* Lets solve the problem

∵ f(x) = x²

∵ The parent function is f(x) = - (x + 2)²

- There is a negative out the bracket means we change f(x) to -f(x)

∴ f(x) is reflected across the x-axis

- The x is changed to x + 2, that means we translate the f(x) to the

  left two units

∵ x in f(x) is changed to (x + 2)

∴ f(x) is translated 2 units to the left

∴ f(x) reflects across the x-axis and translate left 2

The function f(x) = -(x + 2) ^2 is a reflection over the x-axis and a horizontal shift to the left by 2 units.

The given function, f(x) = -(x + 2) ^2, is a transformation of the parent function, f(x) = x^2. The negative sign in front of the function reflects it over the x-axis, making it an upside-down parabola. The addition of 2 inside the parentheses shifts the graph 2 units to the left. Therefore, the transformation is a reflection over the x-axis and a horizontal shift to the left by 2 units.

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Answer:

=12 units

Step-by-step explanation:

When a square is cut along one diagonal, it forms a right angled triangle whose legs are the sides of the square and the hypotenuse is the diagonal of the square.

Therefore, the Pythagoras theorem is used to find the hypotenuse.

a² + b² = c²

(6√2)²+(6√2)²=c²

72+72=c²

c²=144

c=√144

=12

The diagonals of the square measure 12 units each.

Answer:

It is not a function!

Step-by-step explanation:

It is not a function!

A function can't have two y-values assigned to the same x-value. In this case, you can se that for x=1 we have two y-values, which are y= -2 and y= -3.

We can have have two x-values assigned to the same y-value, that's why it's okay that for x=1 and x=3 we have the same y-value y=-2

Answer:

x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6 thus NO, x^2 - (7 x)/3 = -4  would be correct.

Step-by-step explanation:

Solve for x:

3 x^2 - 7 x + 12 = 0

Hint: | Write the quadratic equation in standard form.

Divide both sides by 3:

x^2 - (7 x)/3 + 4 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 4 from both sides:

x^2 - (7 x)/3 = -4

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 49/36 to both sides:

x^2 - (7 x)/3 + 49/36 = -95/36

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 7/6)^2 = -95/36

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 7/6 = (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6

Hint: | Look at the first equation: Solve for x.

Add 7/6 to both sides:

x = 7/6 + (i sqrt(95))/6 or x - 7/6 = -(i sqrt(95))/6

Hint: | Look at the second equation: Solve for x.

Add 7/6 to both sides:

Answer:  x = 7/6 + (i sqrt(95))/6 or x = 7/6 - (i sqrt(95))/6

Answer:

Joseph's work wasn't accurate

Step-by-step explanation:

Take a look at the image to understand the procedures

Answer:

B -0.104

Step-by-step explanation:

Step 1: Write the formula for correlation

r =    total xy

√Total x² x Total y²

Step 2: Make a table to calculate all values

Table is attached in the picture below

Step 3 : Solve

Mean of X = Total X/ Total number of X

                  = 507/12

                  = 106.33

Mean of Y = Total Y/ Total number of Y

                  = 1276/ 12  

                  = 42.25

r =    total xy

√Total x² x Total y²

r = -352.05/ √3656.25 x 3122.66698

r = -0.104

-0.104 is negative

This negative correlation means there is an inverse correlation between variables.

Answer:

B. According to this data, there is a negative correlation between age and IQ.

Step-by-step explanation:

Correlation shows the strength of relation between two variables. The formula used to calculate correlation is:

[tex]Correlation(r) = \frac{Cov(x, y)}{\sigma_{x}\sigma_{y}}= \frac{E(x-\mu_{x})(y-\mu_{y})}{\sigma_{x}\sigma_{y}}[/tex]

where, Cov(x,y) = Covariance of x and y

[tex]\sigma_{x} [/tex] = standard deviation of x

[tex]\sigma_{y} [/tex] = standard deviation of y

[tex]\mu_{x} [/tex] = mean of x

[tex]\mu_{y} [/tex] = mean of y

and, E denotes the Expectation.

The value of the correlation lies between -1 to +1.

If the value of correlation lies between -1 to 0 then it is known as a negative correlation.

and, If the value of correlation lies between 0 to 1 then it is known as a positive correlation.

Using the above formula of correlation we get Correlation (r) = -0.1225.

Thus, there is negative correlation between age and IQ.

We can also use a correlation calculator for getting the value of correlation.

Hence, option (B) is correct.