Use the Distributive Property to simplify

1/7 x (56 - 1/4)

Answer:

16π

Step-by-step explanation:

2 * π * 8

16π

Answer:

16π

Hope this helps out!

Answer:

x = -2

Step-by-step explanation:

The first thing we can notice about this figure is that the two small outer triangles are congruent because of the given side congruence markings as well as the fact that the large triangle ABC is isosceles, thus angle A is congruent to angle C.

Using the above information, we can construct the equation:

3x + 2 = 2x

and solve it for x.

x = -2

The equation we constructed simply equates the corresponding sides of the two small outer triangles, as they are congruent by the CPCTC theorem.

Answer:

linked the graph!

Step-by-step explanation:

Answer:

Using the slope-intercept form, the slope is −5

y=0,-1

Step-by-step explanation:

Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Answer:

it is B

Step-by-step explanation:

he is putting in by the 3/5

Answer:

C.

Step-by-step explanation:

Why its C...

You can tell that on the top it say that the total is 15 so it can not be a. So now our answer choices are B, C, ad D.

Now it says that there are 3/5 highlighted but since the rest say 3/5 we can not eliminate yet.

Next we would multiply 3 x 3 to get 9 for how many dollars there are. Cross out B.

Between C and D, C is the most reasonable answer because it says how much did he put in the bank while the other one (D) says how much did he spend?

So it would be C

Hope this helps :)

Answer: 7/2

Step-by-step explanation:

3  1/2 in a/b form = 7/2

Hope it helped u,

pls mark as the brainliest

^_^

Answer:

322.19

Step-by-step explanation:

RECTANGLE AREA =L × B

=12 × 8

AREA OF CIRCLES= 4(1/2×PIE×6×6)

TOTAL AREA= 12 × 8+ 4(1/2×PIE×6×6)

=322

HOPE IT HELPSS!!

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

We have,

To determine how long it will take for there to be 150mg of aspirin left in the bloodstream, we can use the concept of half-life.

The half-life of aspirin is given as 6 hours, which means that after every 6 hours, the amount of aspirin in the bloodstream reduces by half.

Let's calculate the number of half-lives required to reach 150mg:

Initial amount of aspirin = 625mg

Final amount of aspirin = 150mg

625mg / 150mg = 4.17

This means it will take approximately 4.17 half-lives for the amount of aspirin in the bloodstream to reduce from 625mg to 150mg.

Since each half-life is 6 hours, we can calculate the total time it will take:

Total time = Number of half-lives * Half-life duration

Total time = 4.17 x 6 hours

Total time ≈ 25 hours and 1 minute

Therefore,

It will take approximately 25 hours and 1 minute for there to be 150mg of aspirin left in the bloodstream.

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Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

In a poker hand consisting of 5 cards, the probability of holding 3 kings is   0.0009 .  

The probability of holding 3 kings in a poker hand of 5 cards can be calculated as follows:

The number of ways to choose 3 kings from a deck of 4 kings is= ⁴C₃ = 4.

The number of ways to choose 2 other cards from the remaining 48 cards is = ⁴⁸C₂ = 1128.

The total number of 5-card hands from a standard deck of 52 cards is = ⁵²C₅ = 2598960.

So , the probability of holding 3 kings in a 5 card hand is

⇒ (4 × 1128)/2598960

⇒ 4512/2598960  .

⇒ 0.00085148 .

Therefore , probability of holding 3 kings in a 5card hand is approximately 0.0009 .

The given question is incomplete , the complete question is

In a poker hand consisting of 5 cards, find the probability of holding  3 kings .

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Answer:

Hello,

Answer 31

Step-by-step explanation:

\(3*log_2(x+1)-2=13\\\\3*log_2(x+1)=13+2\\\\log_2(x+1)=5\\\\\\x+1=2^5\\\\x=32-1\\\\\boxed{x=31}\\\)

The required statistical parameters has been computed as follows:

Range = 15.

Standard deviation, SD = 4.4441.

Variance = 19.75.

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 36 - 21

Range = 15.

Mathematically, the mean for these data sets would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 22 + 29 + 21 + 24 + 27 + 28 + 25 + 36

F(x) = 212.

Mean = 212/8

Mean = 26.5

Next, we would calculate the standard deviation by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × ∑(22 - 26.5)² + 1/5 × ∑(29 - 26.5)² + 1/5 × ∑(21 - 26.5)² + 1/5 × ∑(24 - 26.5)² + 1/5 × ∑(27 - 26.5)² + 1/5 × ∑(28 - 26.5)² + 1/5 × ∑(25 - 26.5)² + + 1/5 × ∑(36 - 26.5)²)

Standard deviation, SD = 4.4441.

In Statistics, the standard deviation of a data sample is the square root of the variance and this is given by this mathematical expression:

Variance = δ²

Variance = 4.4441²

Variance = 19.75.

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Answer:

x = 23

Step-by-step explanation:

Add 4x to the left and add 86 to the right.

5x = 115

Now, divide 5 on both sides to get x.

x = 23.

The result is 23.

Answer:

x= – 115/3

Step-by-step explanation:

I don’t know what exact form you want so I’ll give you mixed number form.

Answer: I think food 2 $2 per kilogram.

Step-by-step explanation:

Answer:

B. [3,5]

Step-by-step explanation:

You had it right.

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

Work Shown:

ED/DF = AB/AC

x/24 = 12/16

16x = 24*12

16x = 288

x = 288/16

x = 18

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

Explanation:

Because the triangles are similar, we can form the proportion shown above. There are many variations of the proportion that can happen, but they all lead to the same result x = 18.

So for instance, another proportion you could solve is ED/AB = DF/AC.

The key is to keep up the same pattern when forming the ratios.

What I mean by that is when I formed ED/DF I divided the vertical side over the horizontal side for triangle EDF. So to form the second fraction, we must do the same division (vertical over horizontal) for triangle ABC.

Answer:

152 units

Step-by-step explanation:

Two sides of the rectangle are 27 units long and the other two sides are 49 units wide. You just add all the numbers up (27+27+49+49). When you do that, you get 152. I hope this helps!

Check the picture below, so the ellipse looks more or less like so.

\(\textit{ellipse, vertical major axis} \\\\ \cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=3\\ k=-8\\ a=5 \end{cases}\implies \cfrac{(x-3)^2}{b^2}+\cfrac{(y-(-8))^2}{5^2}=1 \\\\\\ \stackrel{\textit{we also know that}~\hfill }{c=3\hspace{3.5em} 3=\sqrt{5^2 - b^2}} \implies 3^2=5^2-b^2\implies b=\sqrt{5^2-3^2} \implies \boxed{b=4} \\\\\\ \cfrac{(x-3)^2}{4^2}+\cfrac{(y-(-8))^2}{5^2}=1\implies \cfrac{(x-3)^2}{16}+\cfrac{(y+8)^2}{25}=1\)

Therefore, the reference angle of 7π/4 is 3π/4, and tan 0 = 1.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, especially right triangles. It involves the study of trigonometric functions such as sine, cosine, tangent, and their inverses, as well as their applications in various fields such as physics, engineering, and navigation. Trigonometry is an important tool for solving problems involving angles, distances, and heights, among others.

Here,

The reference angle for an angle θ is the positive acute angle formed by the terminal side of θ and the x-axis.

To find the reference angle for 7π/4, we can subtract π from it since the angle is in the fourth quadrant.

Reference angle = 7π/4 - π

= 3π/4

To find tan 0, we need to use the tangent function:

tan θ = opposite/adjacent

Since we don't know the sides of the triangle, we need to use the reference angle to find the ratio.

The reference angle of 3π/4 is in the second quadrant, where x is negative and y is positive. We can draw a triangle with sides of length 1, 1, and √2, where the hypotenuse is the line with angle 3π/4.

Then, tan(3π/4) = opposite/adjacent

= 1/-1

= -1

So, tan 0 = tan (7π/4)

= tan (3π/4 + π)

= -tan(3π/4)

= -(-1)

= 1.

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Answer:

1/6y + 1/6(y + 12) - 2

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

Step-by-step explanation:

The 84 represents 80% of your grade and the 100 is 20 percent :

84 * 80%   + 100 * 20% =

84 (.8) + 100(.2) = 87.2 %

Answer:

16801.2cm²

Step-by-step explanation:

Cone :

SA = πrl

SA = π · 28 ·  45                     90-45 = 45

SA = 3958.406744

Cylinder :

SA = 2 · π · r · ( r+h)

SA = 2 · π · 28 ( 28 +45 )

SA = 2 · π · 28 (73)

SA = 12842.83077

12842.83077 + 3958.406744 =

16801.2cm²

Answer:

y = 10/1x - 5

Step-by-step explanation:

y=mx+b

m=slope  b=y-intercept

therefore

y=10/1x -5

(10/1 is a fractions just too lazy to make it a fraction on here)

Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) +             2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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Answer:

0.5 or 1/2

Step-by-step explanation:

hope this helps

have a good day

Answer:

Step-by-step explanation:

10(a)+5(c)=310

a= number of adult

c= number children

EXPLANATION

If we draw two clubs on consecutive draws with replacement from a standard deck with 52 cards and 13 clubs, we can apply the following relationship:

The probability that both cards are clubs is as follows:

If both cards are clubs, we will receive $9, therefore:

0.0625 * (9) = 0.5625

If both cards are not clubs, we will pay $4:

1 - 0.0625 = 0.9375

Now, in this case we will need to pay:

0.9375 * (4) = -3.75

Hence, the Expected Value of the bet is:

0.5625 - 3.75 = -3.19

In conclusion, the Expected Value is $ -3.19

Answer

Option B is correct.

the solutions to the system of equations include

(-3, 7) and (1, -1)

Step-by-step Explanation

The question is to solve the system of equations

y = x² - 2 ..... equation 1

y = -2x + 1 ..... equation 2

To solve this, we can just equate the expression given for y in equation 1 to the expression given for y in equation 2.

y = x² - 2

y = -2x + 1

Since

y = y

x² - 2 = -2x + 1

x² + 2x - 2 - 1 = 0

x² + 2x - 3 = 0

This gives a quadratic equation which we will now solve

x² + 2x - 3 = 0

x² + 3x - x - 3 = 0

x (x + 3) - 1 (x + 3) = 0

(x - 1) (x + 3) = 0

So,

x - 1 = 0 or x + 3 = 0

x = 1 or x = -3

If x = 1,

y = x² - 2

= 1² - 2

= 1 - 2

= -1

x = 1, y = -1

If x = -3

y = x² - 2

= (-3)² - 2

= 9 - 2

= 7

x = -3, y = 7

So, the solutions to the system of equations include

x = -3, y = 7, that is, (-3, 7)

And

x = 1, y = -1, that is, (1, -1)

Hope this Helps!!!