which of the following can be determined from the table above?

A. events D and A are independent

B. events D and B are independent

C. events A and B are independent

D. events E and B are independent

10y + 7 + 3(3y + 7) = 180

10y + 7 + 9y + 21 = 180

19y + 28 = 180

19y = 180 - 28

19y = 152

y = 152/19

y = 8

Plug back into Q and S.

Q = 10y + 7

Q = 10(8) + 7

Q = 80 + 7

Q = 87

S = 3(3y + 7)

S = 9y + 21

S = 9(8) + 21

S = 72 + 21

S = 93

Without solving for x to find the other angles, we can easily see that the answer is choice C.

Answer:

P = 61°

Q = 87°

R = 119°

S = 93°

Done!

The formula is d=C/π.

The diameter is 2 times the radius

The formula for the circumference using the radius is 2πr.

in order to do this backwards, we would have to do 16÷2÷π, but we're not looking for the radius.

Therefore, we take out the ÷2 part, which would be 16÷π

16 is the circumference

16÷π=d

d=C÷π

Answer:

d = /π

Step-by-step explanation:

Answer:

2x^3 - 2x^2  - 12x

Step-by-step explanation:

2x(x - 3)(x + 2)

= 2x ( x^2 + 2x -3x - 6)

= 2x (x^2 - x - 6)

= 2x^3 - 2x^2  - 12x (answer).

Answer:

Step-by-step explanation:

Find the product

2x(x - 3)(x + 2)

OA. 4x - 1

B. 2x3 -X-6 Find the product

2x(x - 3)(x + 2)

OA. 4x - 1 Find the product

2x(x - 3)(x + 2)

OA. 4x - 1

B. 2x3 -X-6

C. 2x3 - 2x2 - 12x

2x3-12x|

B. 2x3 -X-6

C. 2x3 - 2x2 - 12x

2x3-12x|

C. 2x3 - 2x2 - 12x

2x3-12x|Find the product

2x(x - 3)(x + 2)

OA. 4x - 1

B. 2x3 -X-6

C. 2x3 - 2x2 - 12x

2x3-12x|

Jenna is correct because the square root of a rational number can still be irrational.

Take for example the square root of 2. It is an irrational number than goes 1.41421...

If you multiply just the first however many digits of the result by itself, you will never end up with a perfect 2, because the square root is irrational.

Answer:

Jenna is correct because not all square roots are rational.

Step-by-step explanation:

Margret sold a total of 3,332 meatballs on Friday and Saturday by adding the meatballs sold on each day (1,392 on Friday and 1,940 on Saturday).

To find out how many meatballs Margret sold on Friday and Saturday combined, we simply add the number she sold on each day. On Friday, she sold 1,392 meatballs and on Saturday, she sold 1,940 meatballs.

The total number of meatballs sold over the two days is:

1,392 (meatballs on Friday)
+ 1,940 (meatballs on Saturday)
3,332 (total meatballs)

So, Margret sold a total of 3,332 meatballs on Friday and Saturday.

Check the picture below.

Answer:

The correct answer is 23

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(1500)(0.05)(1)\implies I=75[/tex]

Chris will earn $75 in interest in the first year by depositing $1,500 into a savings account with an annual interest rate of 5%, calculated using the simple interest formula.

To calculate the amount of interest Chris will earn in the first year the money is in the savings account, we will use the formula for simple interest, which is Interest = Principal × Rate × Time. In this case, the principal amount is $1,500, the annual interest rate is 5% or 0.05 when expressed as a decimal, and the time is 1 year since we are looking for the interest for the first year only.

Therefore, the interest Chris will earn after one year is calculated as follows:

Interest = $1,500 × 0.05 × 1

Interest = $75

Thus, at the end of the first year, Chris will have earned $75 in interest.

ANSWER

[tex]\frac{x - 4}{2x - 2} [/tex]

EXPLANATION

The given expression is;

[tex] \frac{2 {x}^{2} + 5x + 3}{ {x}^{2} - 3x - 4} \div \frac{4 {x}^{2} + 2x - 6}{ {x}^{2} - 8x + 16} [/tex]

We factor to obtain;

[tex] \frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \div \frac{2(x - 1)(2x + 3)}{(x - 4)(x - 4)} [/tex]

Multiply by the reciprocal of the second fraction

[tex]\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \times \frac{(x - 4)(x - 4)}{2(x - 1)(2x + 3)} [/tex]

Cancel out common factors to get,

[tex]\frac{1}{1} \times \frac{(x - 4)}{2(x - 1)} [/tex]

[tex]\frac{x - 4}{2x - 2} [/tex]

Answer:

X-4/2x-2

Step-by-step explanation:

Answer:

Here's a possible example:

Step-by-step explanation:

[tex]f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}[/tex]

Each piece is linear, so the pieces are continuous by themselves.

We need consider only the point at which the pieces meet (x = 3).

[tex]\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)[/tex]

The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.

Final answer:

A piecewise function with a jump discontinuity at x = 3 could be f(x) = 2x for x < 3 and f(x) = 2x + 1 for x ≥ 3. It fails the 3-step test for continuity at x = 3 in the second step, as the limits on either side of the point x = 3 do not match.

Explanation:

To write the equation of a piecewise function with a jump discontinuity at x = 3, we can define one function for values of x less than 3, and another for values of x equal to or greater than 3. For instance:

Now, to determine where the piecewise function fails the 3-step test for continuity at x = 3, we assess the following criteria:

Therefore, the function has a jump discontinuity at x = 3 because it fails the second step of the 3-step test for continuity, where the left and right-hand limits are not equal.

Answer:

  7/4 yard

Step-by-step explanation:

36 is a suitable common denominator for expressing these fractions. All measures are in yards.

  2/3 + 4/9 + 23/36 = (12·2)/(12·3) + (4·4)/(4·9) + 23/36

  = 24/36 + 16/36 + 23/36

  = 63/36 = (9·7)/(9·4)

  = 7/4 = 1 3/4 . . . . . yards

Answer:

170 ft²

Step-by-step explanation:

First let's calculate the height of this trapezoid.  Call it 'h.'  Look at the triangle on the right; the base is equal to (22 ft - 12 ft), or (10 ft).  Using the tangent function, we can find h:

                    h

tan 45° = ---------- = 1  and so we know that h = 10 ft

                  10 ft

The formula for the area of a trapezoid is

A = (average length)*(width)

Here we have:

A = [ (12 ft + 22 ft) / 2 ] * 10 ft, or

A  =           (17 ft)*(10 ft) = 170 ft²

Answer: 5,000

Step-by-step

Answer:

5,000

Step-by-step explanation:

just got my paper graded

[tex]\bf b=ar^{n-1}~~ \begin{cases} b=1024\\ a=16\\ r=2 \end{cases}\implies 1024=16(2^{n-1})~~ \begin{cases} 1024=&2^{10}\\ 16=&2^4 \end{cases} \\\\\\ 2^{10}=2^4(2^{n-1})\implies \cfrac{2^{10}}{2^4}=2^{n-1}\implies 2^{10}\cdot 2^{-4}=2^{n-1}\implies 2^{10-4}=2^{n-1} \\\\\\ 2^6=2^{n-1}\implies \stackrel{\textit{same base, the exponents must be the same}}{6=n-1\implies 7=n}[/tex]

The value of n when b = 1,024, a = 16, and r = 2 is 7.

The student is asking to solve for n in the formula of the nth term of a geometric series given the formula b = ar^(n-1) and the values of b, a, and r. To find the value of n, we can substitute the known values into the formula and solve for n.

b = 1,024

a = 16

r = 2

Using these values:

Substitute the known values into the formula: 1,024 = 16 imes 2^(n-1)

Divide both sides by 16: 64 = 2^(n-1)

Recognize that 64 is 2 to the power of 6: 2^6 = 2^(n-1)

Therefore, n - 1 = 6

Add 1 to both sides to find n: n = 7

The value of n when b = 1,024, a = 16, and r = 2 is 7.

7068.58 cubic feet is the volume

Answer:

Step-by-step explanation:

Answer:

$934.30

Step-by-step explanation:

We have been given that Alfred invest $60 a month in annuity that earns 4% APR and is compounded monthly. We are asked to find the future value of Alfred's account after 5 years.

[tex]FV=C_0\cdot (1+r)^n[/tex], where,

[tex]C_0=\text{Initial value}[/tex],

[tex]r=\text{APR in decimal form}[/tex],

[tex]n=\text{Number of times interest is compounded per year}[/tex].

[tex]r=4\%=\frac{4}{100}=0.04[/tex]

[tex]FV=\$60\cdot (1+0.04)^{12*5}[/tex]

[tex]FV=\$60\cdot (1.04)^{70}[/tex]

[tex]FV=\$60\cdot 15.57161835[/tex]

[tex]FV=\$934.2971[/tex]

[tex]FV\approx \$934.30[/tex]

Therefore, the future value of Alfred's account in 5 years would be $934.30.

Answer:

D) 8.6

Step-by-step explanation:

The Law of Sines tells you ...

c/sin(C) = a/sin(A)

The sum of angles in a triangle tells you ...

C = 180° -A -B = 180° -50° -60° = 70°

Then ...

c = a·sin(C)/sin(A) = 7·sin(70°)/sin(50°) ≈ 8.6 . . . . . above equation multiplied by sin(C)

_____

There are apps available for phone or tablet for solving triangles. Many graphing calculators have functions that will do the same. Also, there are on-line triangle solvers that will give you the answer.

We include the working here because you're supposed to know how to work the problem. If all you want is the answer, that can be found faster a number of different ways.

Answer:

The answer is D

Step-by-step explanation:

for every increase in the product sold, the earnings increase by 300 respectively

Since p = x² - 7, you can substitute/plug in p for x² - 7

So:

(x² - 7)² - 4x² + 28 = 5

(p)² - 4x² + 28 = 5      You can factor out -4 from (-4x² + 28)

p² - 4(x² - 7) = 5        Plug in p

p² - 4p = 5        Subtract 5

p² - 4p - 5 = 0        Your answer is C

To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, substitute x^2-7 with p. The equation equivalent to (x^2-7)-4x^2+28 in terms of p is -4x^2+p+28.

To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, we can substitute x^2-7 with p. So we have (p)-4x^2+28. Now, we combine like terms by adding the coefficients of p and -4x^2, which gives us -4x^2+p+28.

Answer:

1/4, 0.25, 25%

Step-by-step explanation:

There are 8 letters in total and 2 K's out of those 8. Therefore the fraction is 2/8, and simpfied it would be 1/4. 1/4 is equal to 0.25 and 25%.

Answer:

3/4,  0.75, 75%.

Step-by-step explanation:

J, K , L, J, K, M, N, P.

There are 8 letters and 2 of them are K, therefore 6 of them are not K.

Probability ( Not picking K) =  6/8

= 3/4 or 0.75 or 75%.

Answer:  D) (-5, 1)

Step-by-step explanation:

Inverse is when the x's and y's are swapped.

f(x) has the coordinate (1, -5) --> the inverse of that is (-5, 1), which is option D.

Answer:

Step-by-step explanation:

If the point is translated across the y axis then the x coordinate will change sign.

If the point is translated upwards then the y coordinate will increase by 3

So the answers are B and D.

take the square root of 36 and subtract 2 because √36= 6-2=4x

Answer:

take the square root of 36 and subtract 2 because √36= 6-2=4x

Step-by-step explanation:

Yes.

The triangle inequality theorem states that a triangle is possible if the sum of two sides is larger than the 3rd side.

In this case, the sides are 4, 5 and 6.

4+5 is bigger than 6

4 + 6 is bigger than 5

5 + 6 is bigger than 4.

The sum of any 2 sides is always larger than the 3rd side, so this triangle is possible.

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

Answer:   Yes

Answer:

True

Step-by-step explanation:

The hypotenuse angle theorem, also known as the HA theorem, states that "If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent."

In triangles MNP and QRS:

Then, triangles MNP and PRS are congruent by HA theorem.

True

Answer:

True (just did it on a pex)

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

All of these questions use the external angle theorem, that is

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

18

∠3 = 43° + 22° = 65°

19

∠2 + 71 = 92 ( subtract 71 from both sides )

∠2 = 21°

20

90 + ∠4 = 123 ( subtract 90 from both sides )

∠4 = 33°

21

2x - 15 + x - 5 = 148

3x - 20 = 148 ( add 20 to both sides )

3x = 168 ( divide both sides by 3 )

x = 56

Hence ∠ABC = x - 5 = 56 - 5 = 51°

22

2x + 27 + 2x - 11 = 100

4x + 16 = 100 ( subtract 16 from both sides )

4x = 84 ( divide both sides by 4 )

x = 21

Hence ∠JKL = 2x - 11 = (2 × 21) - 11 = 42 - 11 = 31°

Answer:

[tex]\large\boxed{\left(-\dfrac{11}{2};\ -\dfrac{11}{2}\right)}[/tex]

Step-by-step explanation:

The formula of a midpoint of the segment"

[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points W(-3, -7) and X(-8, -4).

Substitute:

[tex]x=\dfrac{-3+(-8)}{2}=\dfrac{-11}{2}\\\\y=\dfrac{-7+(-4)}{2}=\dfrac{-11}{2}[/tex]

The coordinates of the midpoint of a line segment with endpoints (-3, -7) and (-8, -4) are (-5.5, -5.5) using the midpoint formula.

The subject of this question is Mathematics, specifically dealing with geometry. The student is asked to find the midpoint of a line segment whose endpoints are given. The coordinates of the endpoints of the line segment are W(-3, -7) and X(-8, -4).

The formula to calculate the coordinates of a midpoint in a Cartesian plane is M = [(x1 + x2)/2, (y1 + y2)/2], where M denotes the midpoint, (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.

Thus, the midpoint M of the line segment WX is calculated as follows: M = [(-3 -8)/2, (-7 -4)/2] =  [-11/2, -11/2]. So, the coordinates of the midpoint of the line segment WX are (-5.5, -5.5).

https://brainly.com/question/28224145

#SPJ3

Answer:

(x,12x-18)

Step-by-step explanation:

Answer:

Check attached graph

Step-by-step explanation:

Given equation of the parabola is [tex]y=-2x^2+12x-14[/tex].

Nowe we need to use the parabola tool to graph the quadratic function. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Compare Given equation with [tex]y=ax^2+bx+c[/tex] we get: a=-2 and b=12

then x-coordinate of vertex [tex]=x=-\frac{b}{2a}=-\frac{12}{2\left(-2\right)}=3[/tex]

plug x=3 into given function

[tex]y=-2x^2+12x-14[/tex]

[tex]y=-2(3)^2+12(3)-14=4[/tex]

Hence vertex is (3,4).

Plug any x-value say x=0 into given function to find other point

[tex]y=-2(2)^2+12(2)-14=2[/tex]

Hence second point is (2,2)

now graph the parabola using both points as shown below:

Answer:

Step-by-step explanation:

The (x - 4) indicates side-to-side movement, and the -3 at the end indicates up and down movement.  This log graph has moved 4 units to the right (x - (4)) and down 3 units (-3)

Final answer:

The transformation consists of a horizontal shift to the right by 4 units and a vertical shift downward by 3 units from the parent function f(x) = log x to g(x) = log(x - 4) - 3.

Explanation:

The transformation of the parent function f(x) = log x to g(x) = log(x - 4) - 3 involves a horizontal shift to the right by 4 units and a vertical shift downward by 3 units. This is because for the horizontal shift, the logarithmic function is now evaluating (x - 4) instead of x, indicating a move to the right on the x-axis by 4 units. Similarly, subtracting 3 from the whole function log(x - 4) indicates that every value of the function will be decreased by 3 units on the y-axis.

Answer:

0.3

Step-by-step explanation:

Final answer:

The approximate area of a 212-degree sector with a 45m radius is 3371.26 m², and the approximate area of a 92-degree sector with a 9m diameter (4.5m radius) is 16.2 m².

Explanation:

To find the approximate area of a sector of a circle, we use the formula for the area of a circle, A = πr², and then adjust it for the sector by multiplying by the ratio of the central angle to 360 degrees. For Question 1, the central angle θ is approximately 212 degrees and the radius is 45 m. The formula for the sector area becomes A = (π × (45 m)² × (212/360)). A quick calculation gives us the following area:

For the first sector with a 212-degree angle and a radius of 45m:

A = 3.1415927 × (45 m)² × (212/360) = 3.1415927 × 2025 m² × 0.5889 ≈ 3371.26 m²

For Question 2, the central angle θ is approximately 92 degrees and the diameter is 9m, which makes the radius 4.5m. The formula for the sector area then becomes A = (π × (4.5 m)² × (92/360)). The calculation yields the following area:

A = 3.1415927 × (4.5 m)² × (92/360) = 3.1415927 × 20.25 m² × 0.2556 ≈ 16.2 m²