Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). A six-sided die of unknown bias is rolled 20 times, and the number 3 comes up 6 times. In the next three rounds (the die is rolled 20 times in each round), the number 3 comes up 6 times, 5 times, and 7 times. The experimental probability of rolling a 3 is %, which is approximately % more than its theoretical probability. (Round off your answers to the nearest integer.)

Answer:

ASA

Step-by-step explanation:

You are given 2 equal sets of angles.

<ABD and <ACD    (right angles)

<BAD and <CDA    (bisected angle)

You can get <ADB = <ADC because every triangle has 180 degrees. You know two of the angles: you can show that  the 3 rd set are equal a subtraction postulate.

AD = AD              (Reflexive property)

The triangles are congruent by ASA

If AAS is acceptable then it is correct in this case.

AD = AD

The two right angles are equal

The two angles created by the angle bisector are equal.

These three facts give AAS, but please see my comment below.

Answer:

The correct answer is AAS.

Step-by-step explanation:

Answer:

a segment cd only

Step-by-step explanation:

segment cd is the only line that passes through segment ab at a right angle

Answer:

[tex]f\left(x\right)=x^2-3x-54[/tex]

Step-by-step explanation:

Given function is [tex]f\left(x\right)=x^2-3x-54[/tex].

Now we need to rewrite that equation in standard form.

Given equation is a polynomial function. So to write that in standard form, we need to rearrange terms in descending order of exponents of the variable (x).

We see that exponents of variable x are 2, 1  and 0.

Terms are already written in descending order of exponents.

Hence final answer is given function itself. [tex]f\left(x\right)=x^2-3x-54[/tex]

Answer:

Step-by-step explanation:

The formula of an area of a circle:

[tex]A=\pi r^2[/tex]

r - radius

We have the diameter d = 16ft.

d = 2r, therefore r = (16 ft) : 2 = 8 ft.

Substitute:

[tex]A=\pi(8^2)=64\pi\ ft^2[/tex]

[tex]\pi\approx3.14\to A\approx(64)(3.14)=200.96\ ft^2[/tex]

Answer:

C) 200.96 ft²

Step-by-step explanation:

Area formula of a circle: A = πr²

radius = circumference/2 = 8 ft

Plug in: A = π(8)²

Multiply: A = 64π

Approximate+ Multiply: π ≈ 3.14 --> A ≈ 200.96 ft²

[tex]

3x-4y=16 \\

5x+2y=44 \\ \\

3x-4y=16 \\

10x+4y=88 \\ \\

13x=104 \\

x=\boxed{104\div13=8}\\ \\

3\times8-4y=16 \\

24-4y=16 \\

-4y=-8 \\

y=\boxed{2}

[/tex]

Answer:

They intersect but not perpendicular.

Answer:

The answer is D

Step-by-step explanation:

(12 + 6) x ( 11 - 7) = 72

18 x 4 = 72

72 = 72

Answer:

The answer is D.

Step-by-step explanation:

The only equation that equals 72 is letter D. if you add 12 + 6 you get 18 so now the equation is 18 * (11 - 7) = 72 then you do 11 - 7 and get 4 so now the equation is 18 * 4 = 72 and 18 * 4 equals 72 so your answer is correct.

The area for one side is S^2 where S is the length of one side.

The area for one side = 1/2^2 = 1/4 square foot.

A cube has 6 sides. Total surface are = 1/4 x 6 = 1 1/2 square feet.

Volume of a cube is S^3

1/4^3 = 1/64 cubic foot.

Answer:

40/3

Step-by-step explanation:

Here you're dividing the fraction -5/3 by the fraction -1/8.

Right off, we can simplify this by recalling that (-)(-) = (+), and so we have:

Divide 5/3 by 1/8.

There's a rule for dividing by a fraction:  Invert the fraction and multiply.  So, applying that rule here, we get:

5      8

---- * ---- = 40/3

 3      1

Answer:

7. C

8. D

Step-by-step explanation:

7. The interest rate is 8% or .08. You find that by solving I=Prt (interest=original amount*rate*time in years)

8. The discounted price would be $48 (80*(1-.40)) Then you multiply that 48 by .08 and add that amount to the $48.

Answer: false

Step-by-step explanation:

Final answer:

The probability of any number from 0 to 4 appearing in a randomly generated list is 1/5, not 1/4. The false notion might come from misinterpreting randomness or falling prey to the gambler's fallacy.

Explanation:

Your question pertains to the concept of probability in a random distribution of numbers. Specifically, you are asking whether the probability of each number occurring in a randomly generated list of numbers from 0 to 4 is 1/4. This statement is false. Since there are five possible outcomes (0, 1, 2, 3, and 4), and assuming that each number has an equal chance of being selected, the correct probability of each number occurring would be 1/5, not 1/4.

The misconception that the probability is 1/4 likely arises from a misunderstanding of randomness and probability. People often have a preconceived notion of what randomness looks like, influenced by incidents of the gambler's fallacy, where they believe past events affect the likelihood of future events. Which is not mathematically accurate. For example, the gambler's fallacy is when someone thinks that after flipping a coin and getting heads multiple times, tails is 'due' to occur. However, each flip is independent, and the probability remains at 50% for heads or tails, regardless of past flips.

Understanding true randomness means recognizing that each outcome in a set of distinct outcomes has an equal chance of occurring, and that chance is determined by dividing 1 by the total number of possible outcomes. In the scenario with the list of numbers from 0 to 4, since there are 5 possible outcomes, the correct probability should be calculated as 1/5.

Answer:

3544

Step-by-step explanation:

This is a problem of compound growth. The formula is

[tex]F=P(1+r)^t[/tex]

Where F is the value in the future (in this case, the population after 13 years)

P is the intial amount (here, the initial population of 2000, so P = 2000)

r is the rate of growth (here, it is 4.5%, in decimal, 0.045)

t is the time frame (here, it is 13 years, so t = 13)

we can plug the numbers into the formula and solve for F:

[tex]F=P(1+r)^t\\F=2000(1+0.045)^{13}\\F=2000(1.045)^{13}\\F=3544.4[/tex]

rounded to the nearest whole number, the population after 13 years would be 3544

Answer:

The  population after 13 years = 3544

Step-by-step explanation:

Points to remember

Compound interest

A = P[1 +R/n]^nt

Where A - amount

P - principle amount

R = rate of interest

t -   number of years

n - number of times compounded yearly

Here we have to consider compounded growth.

To find the population

Here P = 2000 , R = 4.5% = 0.045% and n = 13 years

A =  P[1 +R/n]^nt

 = 2000[1 + 0.045/1]^(1 * 13)

 = 2000 * 1.77

 = 3544

Therefore the  population after 13 years = 3544

Answer: OPTION C

Step-by-step explanation:

Given the quadratic equation [tex]x^2 - 7x + 10[/tex] and the value of the variable "x" [tex]x = -2[/tex], you need to substitute the given value of the variable. Then:

[tex]=(-2)^2 - 7(-2) + 10[/tex]

And finally, you need to evaluate.

Remember the multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Therefore, you get the following result:

[tex]=4+14 + 10[/tex]

[tex]=28[/tex]

This matches with the option C.

Answer:

a.  [tex]\frac{1}{6}[/tex]

b.  [tex]\frac{67}{450}[/tex]

Step-by-step explanation:

Theoretical probability is what we expect to happen and experimental probability is what actually happens.

a. In theoretical probability, it doesn't matter what happened in the past. So basically we want to know the probability of rolling a 3 when a number cube is rolled.

There are 6 faces (from 1 to 6) in a number cube. And there is 1 "3". So the probabilty of rolling a 3 is:

1/6

b. In experimental probability, we need to know what happened before. When the cube was rolled 450 times, it came up "3", 67 times.

Hence the experimental probabilty of rolling a "3" is:

67/450

Let [tex]x[/tex] be the amount of the 30% alloy and [tex]y[/tex] the amount of the 60% alloy the metalworker will use. However much is used, the final alloy will have a mass of

[tex]x+y=100[/tex]

kilograms. For each kg of the 30% alloy used, 0.3 kg is copper; similary, each kg of the 60% alloy contributes 0.6 kg, so that

[tex]0.3x+0.6y=0.54(x+y)=54[/tex]

Now,

[tex]x+y=100\implies y=100-x[/tex]

[tex]\implies0.3x+0.6(100-x)=54[/tex]

[tex]\implies60-0.3x=54[/tex]

[tex]\implies0.3x=6[/tex]

[tex]\implies x=20[/tex]

[tex]\implies y=100-20=80[/tex]

Answer:

log(M/N) = 4, log(P/N) = 5

log M - log N = 4

log P - log N = 5

log P - log M = log(P/M) = 1

P/M = 10

P = 10M

The correct answer is C.

Since it is evident that P is in fact ten times larger than M, the right response is P = 10M Option C is correct.

To solve this problem

Given that log(M/N) = 4, log(P/N) = 5 and both logarithms have the same base, let's consider the relationship between M and P

Since Log (M) = 4 this implies that M =[tex]10^4[/tex]

Similarly, Log ( P) = 5 this implies that P = [tex]10^ 5[/tex]

Now, we can compare P and M :

[tex]P = 10^5[/tex]

[tex]M = 10^4[/tex]

Since it is evident that P is in fact ten times larger than M, the right response is:

C . P = 10M

Therefore, This reflects the relationship that P is 10 times M.

Answer:

The value of the missing side is [tex]x=2\ units[/tex]

Step-by-step explanation:

In this problem i assume that the length side x is tangent to the circle

so

the length side x is perpendicular to the radius

Applying the Pythagoras Theorem in the right triangle

we have that

[tex](1.5+1)^{2}=1.5^{2}+x^{2}[/tex]

Solve for x

[tex](2.5)^{2}=1.5^{2}+x^{2}[/tex]

[tex]x^{2}=2.5^{2}-1.5^{2}[/tex]

[tex]x^{2}=4[/tex]

[tex]x=2\ units[/tex]

Answer:

x=2

Step-by-step explanation:

4 + 4= 8/2= 4

the median number is 4

The answer is 24.

Hope this helps!

Answer:

17 4/5

Step-by-step explanation:

Fist, add the whole numbers.

5 + 6 + 5 = 16

Now add the fractions.

2/3 and 1/3 have the same denominator so you can add easily.

2/3 + 1/3 = 3/3 = 1

Now 16 + 1 = 17

Then what's left is Mr. Caswall's 4/5 and then we add that to 17.

So it's 17 4/5

Hope this helps!

Answer:

17 4/5 miles.

Step-by-step explanation:

First add the integer parts of the mixed numbers:

5 + 5 + 6 = 16 miles.

Now add the fractions:

2/3 + 1/3 + 4/5

LCD of 3 and 5 is 15 so we have:

10/15 + 5/15 + 12/15

= 27/15

= 9/5

= 1 4/5 miles.

So our answer is 16 + 1 4/5

= 17 4/5 miles.

She bought 2 fancy shirts and 5 plain shirts.

2 x 28=$56, and 5x15=$75. 75 plus 56 is 131

Answer:

its an obtuse

Step-by-step explanation:

The triangle is:

               A.   Scalene.

               E.  Acute

Scalene triangle--

A triangle is said to be scalene if the length of all the three sides of a triangle are different.

Right triangle--

A triangle is said to be a right triangle if one of the angle is right angle i.e. measure of one of the angle is: 90 degrees.

Equilateral triangle--

A triangle is said to be equilateral if all of the sides of a triangle are equal.

Obtuse triangle--

A triangle is said to be obtuse if measure of one of the angle is more than 90 degrees but less than 180 degrees.

Acute triangle--

A triangle is said to be acute triangle if the measure of all the three angles of a triangle are less than 90 degrees.

Based on the diagram we observe that all the sides of a triangle are different and all the three angles of a triangle are less than 90 degrees.

Hence, the triangle is scalene and it is a acute triangle.

Answer:

x = 1.36

Step-by-step explanation:

We are given the following equation;

7^x = 14

we are required to determine the value of x;

the first step is to introduce natural logs on both sides of the equation;

[tex]ln(7^{x})=ln(14)\\\\xln(7)=ln(14)\\\\x=\frac{ln(14)}{ln(7)}\\\\x=1.3562[/tex]

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

2 divided by 6 is [tex]\frac{1}{3}[/tex]

To confirm it,

[tex]6 * \frac{1}{3} =2[/tex]

40; base it off of the y-intercept [C]. What is the unit of measurement?

Answer:

The maxima is the point where it is the highest it can possibly get. I promise this isn't a scam but I have a picture that shows what I mean

Step-by-step explanation:

So this graph shows that (1.75, 89) is the maximum height

I hope this helps:)

Answer:

-288

Step-by-step explanation:

n=1/2 divided by -144. You then just plug that number which is .00347 into n in the equation and use a scientific calculator to find the answer.

The sum of the  infinite geometric series is:

                                 -288

We know that the sum of the infinite geometric series:

[tex]\sum_{n=1}^{\infty} ar^{n-1}[/tex]

is given by the formula:

[tex]Sum=\dfrac{a}{1-r}[/tex]

The series is given by:

     [tex]\sum_{n=1}^{\infty} (-144)\cdot (\dfrac{1}{2})^{n-1}[/tex]

By looking at the series we observe that the first term of the series is:

            [tex]a=-144[/tex]

and the common ratio of the series is:

[tex]r=\dfrac{1}{2}[/tex]

Hence, the sum of the series is:

[tex]Sum=\dfrac{-144}{1-\dfrac{1}{2}}\\\\Sum=\dfrac{-144}{\dfrac{1}{2}}\\\\Sum=-144\times 2\\\\Sum=-288[/tex]

Answer:

y = 2x + 3

Step-by-step explanation:

The y-intercept is clearly marked:  it's b = 3 (or 0, 3).

Going from the point (-3, -3) to the point (0, 3),

x increases by 3 and y increases by 6.  Thus, the slope of the line through these two points is m = rise / run = 6 / 3, or m = 2.

Starting with the slope-intercept form of the equation of a straight line:

y = mx + b, we substitute 2 for m and 3 for b, obtaining:

y = 2x + 3

Answer:

y = 2x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, - 3) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3+3}{0+3}[/tex] = [tex]\frac{6}{3}[/tex] = 2

note the line crosses the y- axis at (0, 3) ⇒ c = 3

y = 2x + 3 ← equation of line

Answer:

11.76%

Step-by-step explanation:

use % error formula:[tex]\frac{|approx-exact|}{exact}[/tex]

where approx is 60

and exact is 68

so

[tex]\frac{|60-68|}{68}[/tex]

[tex]\frac{|-8|}{68}[/tex] =0.1176

0.1176=11.76%

hope this helps!

Tessellation is possible only for equilateral triangles, squares and regular hexagons. Therefore, there are only three regular polygons that tessellate.

Tessellation is possible, if each interior angle of a polygon is a factor of 360 degrees.

Now, in the given image, pentagon and octagon cannot tessellate.

And the triangle does not seem to be an equilateral triangle. But in general we can say that triangle tessellates.

So, the answer might be triangle (if its equilateral)

Answer:

1.7

Step-by-step explanation:

( 5x + 2y = 7 ) 2

( - 2x + 6y = 9 ) 5

10x + 4y = 14

-10x + 30y = 45

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

34y = 59

y = 1.7

The y-coordinate of the solution to the system of equations 5x + 2y = 7 and -2x + 6y = 9 is 1.8 when rounded to the nearest tenth.

To solve the system of equations 5x + 2y = 7 and -2x + 6y = 9, we'll use the method of substitution or elimination. I will demonstrate the elimination method:

This is the y-coordinate of the solution for the given system of equations.

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