Please help me on this

Answer:

The correct answer on USATestprep is B.

Step-by-step explanation:

Final answer:

To simulate the probability of obtaining more than one tyrannosaurus rex toy in five cereal boxes, we can use a deck of cards (Option B). Drawing five cards in 10 trials and counting the number of spades mirrors the conditions of the cereal box toy scenario. The law of large numbers ensures that this simulation's results will approach the actual probability with enough trials.

Explanation:

The question asks about the probability of obtaining more than one tyrannosaurus rex toy when buying five cereal boxes, each with an equal chance of containing one of four different dinosaur toys. To simulate this situation accurately, the experiment must mimic the conditions of the actual scenario by having four equally likely outcomes and a sample size of five.

Option B is the most suitable simulation for this situation because it replicates these conditions using a deck of cards. If we consider each dinosaur to be analogous to a suit in a standard deck of cards, then drawing five cards and recording the number of a particular suit (such as spades) simulates the probability of getting a particular dinosaur toy. We then repeat this simulation in multiple trials to estimate the probability based on the relative frequency of getting more than one spade, which would represent obtaining more than one tyrannosaurus rex toy.

Through simulations and the law of large numbers, we can acquire an empirical probability that approximates the theoretical probability. However, it's crucial to conduct a sufficient number of trials to ensure a sound approximation of the probability.

In a given week, there are seven possible outcomes for Kay's birthday falling on a particular day. Five of these outcomes are weekdays, so the probability of Kay's birthday falling on a weekday is 5/7 or 0.714, making the event likely.

In this problem, we are dealing with the concept of probability in mathematics. Probability refers to the branch of mathematics that deals with the likelihood of occurrence of particular events.

1. List the sample space for this problem:

The sample space, which is the set of all possible outcomes, is all the days in a week. Therefore, the sample space in our case consists of these seven outcomes: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

2. Which outcome (or outcomes) of the sample space composes the event?

The event in this case is Kay’s birthday falling on a weekday. Thus, the outcomes that compose the event are: Monday, Tuesday, Wednesday, Thursday and Friday.

3. Express the probability of Kay’s birthday falling on a weekday as a fraction and as a decimal:

The probability of an event is the ratio of the favorable outcomes to the total outcomes in the sample space. Here, the favorable outcomes are 5 (number of weekdays) and the total outcomes are 7 (total number of days in a week). As a fraction, the probability is 5/7. This can be expressed as a decimal by dividing 5 by 7, giving approximately 0.714.

4. Describe the probability of Kay’s birthday falling on a weekday as impossible, unlikely, neither likely nor unlikely, likely, or certain:

Given that the probability is 5/7 or 0.714, this event is likely to occur because the probability value is more than 0.5 or 50%.

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Answer:

  12 cm

Step-by-step explanation:

The square of the length of the tangent segment is equal to the product of near and far distances to the circle from the point of intersection of the secant and tangent:

  (8 cm)^2 = (4 cm)(4 cm +x)

  16 cm = 4 cm +x . . . . . . divide by 4 cm

  12 cm = x . . . . . . . . . . . . subtract 4 cm

Ashley ran on the track for 4 miles. Option C is correct.

Solving word problems.

In the track event (joggling), the distance of the track is 1 mile (i.e. it represents a single mile).

It was noted that Ashley jogged for 4 times. Now, the length of the joggling time multiplied by the numbers of time Ashley jogged on this track will be how far Ashley ran on the track.

How far Ashley ran on the track = 1  × 4

How far Ashley ran on the track = 4 miles.

Thus, Ashley ran on the track for 4 miles.

The complete question.

The jogging track is of a mile long. If Ashley jogged around it 4 times, how far did she run? A.2 miles  B. 1/2 miles  C. 4 miles D. 5 miles.

Answer:

  $311.74

Step-by-step explanation:

A financial calculator computes the payment amount to be $311.74.

___

Your graphing calculator may have the capability to do this. Certainly, such calculators are available in spreadsheet programs and on the web.

___

The appropriate formula is the one for the sum of terms of a geometric series.

  Sn = a1·((1+r)^n -1)/(r) . . . . . where r is the monthly interest rate (0.005) and n is the number of payments (480). Filling in the given numbers, you have ...

  $620827.46 = a1·(1.005^480 -1)/.005 = 1991.4907·a1

Then ...

  $620827.46/1991.4907 = a1 ≈ $311.74

To achieve a retirement income of $4000 per month with a 6% APR compounded monthly, a nest egg of $620,827.46, and a retirement plan spanning 40 years, one should deposit about $288.69 into the account each month.

This question pertains to the concept of future value and annuities in finance. The purpose is to determine the monthly deposits required to achieve a specified future value, which in this case is the desired retirement income. Here, we use the future value of a series formula: FV = P * [((1 + r)^nt - 1) / r], where P is the monthly payment, r is the monthly interest rate, n is the number of times interest is compounded per year, and t is the time in years. Given that the future value FV is $620,827.46, the interest rate r is 0.06/12 (since it's compounded monthly), n is 12 (compounded twelve times a year), and t is 40 years. The aim is to solve for P, the monthly payment: P = FV / [((1 + r)^nt - 1) / r]. Plugging in the given values, the result is approximately $288.69. Thus, to receive a retirement income of $4000 per month, you should deposit about $288.69 into the account each month.

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Let [tex]s_n[/tex] denote the number of seats in the [tex]n[/tex]-th row. [tex]s_n[/tex] is arithmetic, so

[tex]s_n=s_{n-1}+d[/tex]

for some constant [tex]d[/tex].

We're told [tex]s_5=22[/tex] and [tex]s_{10}=37[/tex], so that

[tex]s_{10}=s_9+d[/tex]

[tex]s_{10}=(s_8+d)+d=s_8+2d[/tex]

[tex]s_{10}=(s_7+d)+2d=s_7+3d[/tex]

and so on up to

[tex]s_{10}=s_5+5d\implies37=22+5d\implies5d=15\implies d=3[/tex]

The pattern continues:

[tex]s_5=s_4+3[/tex]

[tex]s_5=(s_3+3)+3=s_3+2\cdot3[/tex]

and so on up to

[tex]s_5=s_1+4\cdot3\implies22=s_1+12\implies\boxed{s_1=10}[/tex]

Answer:

8

Step-by-step explanation:

Answer:

5/4

Step-by-step explanation:

slope is rise/run, 5 is the amount rising or going up and  is running straight

Answer:

16.84

Step-by-step explanation:

For perimeter, you are basically solving 2 different 1/2 circles

for the larger one, you do the equation: 3.14 x 4 = 12.56

For the smaller one, you do the equation: 3.14 x 2 = 6.28

12.56 + 6.28 = 18.84

and since I think you are putting em together you are supposed to remove 2 so the answer would be : 16.84

So, for the calculations (if doing area), you are gonna have to split the figures apart.

ok, for the first part, the 1/4 circles

Pi*2^2=12.566

12.566/4=3.1415

Since there is 2 of the same figure, you can do 1 of 2 ways

A. 3.1415x2 = 6.283

B. 12.566 / 2 = 6.283

Now for the 1/2 circle:

pi*1^2=3.142

3.142/2 = 1.571

Now to add:

1.571 + 6.283 = 7.854

Answer:

the answer is in the image attached

Hope this helps

Answer:

x = ± 2i

Step-by-step explanation:

The equation has no real roots, gut has complex roots

Given

x² = - 4 ( take the square root of both sides )

x = ± [tex]\sqrt{-4}[/tex]

  = ± [tex]\sqrt{4(-1)}[/tex]

[ Note that [tex]\sqrt{-1}[/tex] = i ]

  = ± [tex]\sqrt{4}[/tex] × [tex]\sqrt{-1}[/tex] = ± 2i

The weight of the water in the pool to the nearest pound is 280,800 pounds.

To find the weight of the water in the swimming pool, we need to calculate the volume of the pool in cubic feet and then use the density of water to determine the weight.

Convert dimensions to consistent units:

The depth of the pool is given in feet (2 feet), so we need to convert the length and width from yards to feet.

1 yard = 3 feet

Length = 25 yards × 3 feet/yard = 75 feet

Width = 10 yards × 3 feet/yard = 30 feet

Calculate the volume of the pool:

Volume = length × width × depth

Volume = 75 feet × 30 feet × 2 feet = 4,500 cubic feet

Calculate the weight of the water:

Weight of water = volume × density

Density of water = 62.4 pounds per cubic foot

Weight = 4,500 cubic feet × 62.4 pounds/cubic foot = 280,800 pounds

Answer:

0.184

Step-by-step explanation:

There are 38 seniors, of which 7 prefer evening classes.

7/38 ≈ 0.184

The question involves mathematical sampling techniques to generate categorical data from a high school population, which is shown in a pie chart and involves creating a stratified sample by selecting students from each year.

The question pertains to a mathematical concept used in the selection of a sample from a population, which in this scenario, is a group of high school students. This involves using a random number generator to select two class years (freshman, sophomore, junior, or senior) and then including all students from those two years in the sample. The sampling process will result in categorical data, which can be represented in a pie chart as shown in Solution 1.10.

Moreover, organizing the students' names by classification and selecting 25 students from each (a, d) ensures a stratified sample of high school students across different academic stages.

In the context of the presented educational tasks, students might explore how their learning experiences have intersected with personal and global changes, engaging in an analysis of polymorphism, continuous variation, and clinal distribution based on surveyed traits among their peers (Conclusion).

domain for a graph as shown (where the lines never stop) is always (Negative Infinity,Positive Infinity).

Answer:

Step-by-step explanation:

The domain of an exponential function is "the set of all real numbers."

Answer:

sin⁡(α+β)/sin⁡(α-β) ==(tan⁡ α+tan ⁡β)/(tan ⁡α-tan ⁡β )

Step-by-step explanation:

We have to complete

sin⁡(α+β)/sin⁡(α-β) = ?

The identities that will be used:

sin⁡(α+β)=sin⁡ α cos ⁡β+cos ⁡α sin ⁡β

and

sin⁡(α-β)=sin⁡ α cos⁡ β-cos⁡ α sin⁡ β  

Now:

=   sin⁡(α+β)/sin⁡(α-β)  

=(sin⁡ α cos⁡ β+cos ⁡α sin⁡ β)/(sin ⁡α cos ⁡β-cos ⁡α sin ⁡β)

In order to bring the equation in compact form we wil divide both numerator and denominator with  cos⁡ α cos⁡ β  

=  (((sin ⁡α cos ⁡β+cos ⁡α sin ⁡β))/(cos ⁡α cos ⁡β ))/(((sin α  cos ⁡β-cos ⁡α sin ⁡β))/(cos ⁡α  cos ⁡β))

=((sin⁡ α cos⁡β)/(cos ⁡α cos ⁡β )+(cos ⁡α sin ⁡β)/(cos ⁡α cos ⁡β ))/((sin ⁡α cos ⁡β)/(cos ⁡α  cos ⁡β )-(cos ⁡α sin ⁡β)/(cos ⁡α cos ⁡β))  

=(sin⁡ α/cos ⁡α + sin ⁡β/cos ⁡β )/(sin ⁡α/cos ⁡β - sin ⁡β/cos ⁡β)

=(tan ⁡α+tan ⁡β)/(tan ⁡α-tan ⁡β )

So,

sin⁡(α+β)/sin⁡(α-β) ==(tan⁡ α+tan ⁡β)/(tan ⁡α-tan ⁡β)

Answer:

  about 0.39 (inelastic)

Step-by-step explanation:

Elasticity of supply is the ratio of percentage supply change to a corresponding percentage of price change. Here, that is ...

  eos = (410/380 -1)/(0.20) = 0.78947/0.2 ≈ 0.3947

Values below 1 are said to correspond to an inelastic supply, one not very sensitive to price.

Answer:

  a) center: (-3, 2)

  b) radius: √65

  c) equation: (x +3)² +(y -2)² = 65

Step-by-step explanation:

a) The center (point A) is the midpoint of the diameter, so its coordinates are the average of the endpoint coordinates:

  A = (P +Q)/2 = ((-10, -2) +(4, 6))/2

  = (-10+4, -2+6)/2 = (-6, 4)/2

  A = (-3, 2)

__

b) The radius is the distance from the center to one end of the diameter. The distance formula can be used to find that.

  r = √((x2 -x1)² +(y2 -y1)²) = √((4-(-3))² +(6 -2)²) = √(49+16)

  r = √65

__

c) The circle centered at (h, k) with radius r has formula ...

  (x -h)² +(y -k)² = r²

So the formula for this circle is ...

  (x +3)² +(y -2)² = 65

The parallel line of RU would need to be the mid point S and midpoint M

Segment SM would be the parallel line.

Answer:

Though I'm not quite sure (as this is a bit of a trick Question) the only Parallel to Line/segment to RU would MS. Given the question they are asking MS are the only two points that run adjacent/parallel to RU. Hope this helps

Step-by-step explanation:

ANSWER

The height of the basketball hoop is

[tex]14 \frac{2}{3} ft[/tex]

EXPLANATION

Let the height of the basketball hoop be x feet.

The shadow of the basketball hoop is 9 ft long.

The height of Jack is 5.5 feet.

Jack's shadow is 9 ft long.

By similar triangles,

[tex] \frac{x}{5.5} = \frac{24}{9} [/tex]

Multiply both sides by 5.5

This gives us,

[tex]x = \frac{24}{9} \times 5.5[/tex]

[tex]x = \frac{132}{9} [/tex]

[tex]x = 14 \frac{2}{3} [/tex]

The height of the basketball hoop is 14⅔ feet

Answer:

Each element is either included or not in a subset.

--> 2^6 = 64

Hope this helps you out!

64. 2 to the 6th power

Give me a few minutes and ill tell you the answer : )

Answer:

~24.4%

Step-by-step explanation:

A circle is 360 degrees, we all know this.

The angle representing Techno is 28° While Country has a 60°. Combine this and we get 88° of people total chose country or techno. 88° divided by 360° gives us 0.2444444... With percentages, we move the decimal two places to the right, giving us:

~24.4%

Answer:

Step-by-step explanation:

1. Use the conversions 1 yd = 3 ft, 1 ft = 12 in.

  (12 yd +2 ft +10 in) +(6 yd +1 ft +8 in) +(16 yd +2 ft +9 in)

  = (12 +6 +16) yd + (2 +1 +2) ft + (10 +8 +9) in

  = 34 yd + 5 ft + 27 in

  = 34 yd +5 ft + (2 ft +3 in) . . . . convert 27 in to feet and inches

  = 34 yd + 7 ft + 3 in . . . . . . . . . add feet

  = 34 yd + 2 yd + 1 ft + 3 in . . . . convert 7 ft to yards and feet, then add yards

  = 36 yd + 1 ft + 3 in

__

2. Use the conversions 1 yr = 12 mo, 1 mo = 30 da. (To be more accurate, we need to know the starting date of each time period.)

  (8 yr +9 mo +23 da) +(12 yr +11 mo +16 da) +(19 yr +7 mo +28 da)

  = (8 +12 +19) yr +(9 +11 +7) mo +(23 +16 +28) da

  = 39 yr +27 mo +67 da

  = 39 yr + 27 mo + 2 mo +7 da . . . . . convert 67 da to mo and da

  = 39 yr + 2 yr + 5 mo + 7 da . . . . . . . convert 29 mo to yr and mo

  = 41 yr +5 mo +7 da

__

3. Use the conversion 1 lb = 16 oz.

  (15 lb +12 oz) +(19 lb +15 oz) +(23 lb +7 oz)

  = (15 +19 +23) lb +(12 +15 +7) oz

  = 57 lb +34 oz

  = 57 lb +2 lb + 2 oz . . . . . convert 34 ounces to pounds and ounces

  = 59 lb +2 oz

Using the mid point formula

(x1 +x2)/2 , (y1 +y2)/2

F is the midpoint of A and B

F = (2+10)/2 , (4+6)/2 = 12/2 , 10,2 = 6,5

F should be (6,5)

Now you have A, F and B, use the midpoint formula to find the other coordinates:

D is the midpoint of A and F and is (4,4.5)

C is the midpoint of A and D and is (3,4.25)

E is the mid point of D and F and is (5,4.75)

H is the midpoint of F and B and is (8,5.5)

G is the midpoint of F and H and is (7, 5.25)

I is the midpoint of H and B and is (9,5.75)

The following are matched coordinates:

D is the midpoint of A and F and is (4,4.5)

C is the midpoint of A and D and is (3,4.25)

E is the mid point of D and F and is (5,4.75)

H is the midpoint of F and B and is (8,5.5)

G is the midpoint of F and H and is (7, 5.25)

I is the midpoint of H and B and is (9,5.75)

Answer:

B. 0.588

Step-by-step explanation:

There are 40 non-face cards in the deck, so the probability of drawing the first one is 40/52. After doing that, the probability of drawing the second one is 39/51, since the number of non-face cards is 1 fewer, as is the size of the deck.

The joint probability is then ...

(40/52)·(39/51) ≈ 0.588

Final answer:

To determine the total number of mini pizzas, multiply the number of people sharing the pizzas (Mark, his sister, and 4 friends, totaling 6) by the number of pizzas per person (5). Thus, there are 30 mini pizzas in total.

Explanation:

The student's question involves a basic arithmetic calculation related to multiplication. Mark, his sister, and his 4 friends add up to a total of 6 people (Mark + Mark's sister + 4 friends). Each of these 6 individuals will receive 5 mini pizzas each. To find the total number of mini pizzas, we need to multiply the number of people by the mini pizzas each person receives.

Therefore, the calculation is as follows:

Total number of mini pizzas = Number of people × Mini pizzas per person

Now, we execute the multiplication:

Total number of mini pizzas = 6 × 5 = 30 mini pizzas

So, the total number of mini pizzas in the box is 30.

Answer:

  B.  1

Step-by-step explanation:

The amplitude is the measure from the midline (0) to the peak (1). It is ...

  1 - 0 = 1

Answer:

yes

Step-by-step explanation:

It is the factored form of a 2nd-degree polynomial, so is a quadratic function.

the answer is.... 39.988

Let [tex]X[/tex] denote the event that the two [tex]C_1[/tex] flips yield the same faces (1 if the same faces occur, 0 if not), so that

[tex]P(X=x)=\begin{cases}2{p_1}^2-2p_1+1&\text{for }x=1\\2p_1-2{p_1}^2&\text{for }x=0\\0&\text{otherwise}\end{cases}[/tex]

For example,

[tex]P(X=1)=P(C_1=\mathrm{HH}\lor C_1=\mathrm{TT})=P(C_1=\mathrm{HH})+P(C_1=\mathrm{TT})={p_1}^2+(1-p_1)^2[/tex]

Let [tex]Y[/tex] denote the outcome (number of heads) of the next three flips of either [tex]C_2[/tex] or [tex]C_3[/tex]. By the law of total probability,

[tex]P(Y=y)=P(Y=y\land X=1)+P(Y=y\land X=0)[/tex]

[tex]P(Y=y)=P(Y=y\mid X=1)P(X=1)+P(Y=y\mid X=0)P(X=0)[/tex]

and in particular we have

[tex]P(Y=y\mid X=1)=\begin{cases}\dbinom3y{p_2}^y(1-p_2)^{3-y}&\text{for }y\in\{0,1,2,3\}\\\\0&\text{otherwise}\end{cases}[/tex]

[tex]P(Y=y\mid X=0)=\begin{cases}\dbinom3y{p_3}^y(1-p_3)^{3-y}&\text{for }y\in\{0,1,2,3\}\\\\0&\text{otherwise}\end{cases}[/tex]

Then

[tex]P(Y=y)=\begin{cases}\dbinom3y{p_2}^y(1-p_2)^{3-y}(2{p_1}^2-2p_1+1)+\dbinom3y{p_3}^y(1-p_3)^{3-y}(2p_1-2{p_1}^2)&\text{for }y\in\{0,1,2,3\}\\\\0&\text{otherwise}\end{cases}[/tex]

Jack wants to find [tex]P(X=1\mid Y=y)[/tex] for some given [tex]y[/tex].

a. With [tex]y=1[/tex], we have

[tex]P(X=1\mid Y=1)=\dfrac{P(X=1\land Y=1)}{P(Y=1)}[/tex]

[tex]P(X=1\mid Y=1)=\dfrac{P(Y=1\mid X=1)P(X=1)}{P(Y=1)}[/tex]

[tex]P(X=1\mid Y=1)=\dfrac{\binom31p_2(1-p_2)^2(2{p_1}^2-2p_1+1)}{\binom31p_2(1-p_2)^2(2{p_1}^2-2p_1+1)+\binom31p_3(1-p_3)^2(2p_1-2{p_1}^2)}[/tex]

[tex]P(X=1\mid Y=1)\approx\dfrac{0.1498}{0.2376}\approx0.6303[/tex]

b. With [tex]y=0[/tex], we'd get

[tex]P(X=1\mid Y=0)=\dfrac{P(X=1\land Y=0)}{P(Y=0)}[/tex]

[tex]P(X=1\mid Y=0)=\dfrac{P(Y=0\mid X=1)P(X=1)}{P(Y=0)}[/tex]

[tex]P(X=1\mid Y=0)\approx\dfrac{0.0333}{0.1128}\approx0.295[/tex]

Answer:

m = 2.8

Step-by-step explanation:

Multiply both sides of the equation by the inverse of the coefficient of m. That coefficient is 1/7, so its inverse is 7/1 = 7. Then you have ...

7·2/5 = 7·m/7

14/5 = m . . . . . . . . simplify

m = 2 4/5 = 2.8 . . express the number in a manner that makes sense to you

Answer:

2.8

Step-by-step explanation:

Given that

[tex]\dfrac{2}{5}=\dfrac{m}{7}[/tex]

Multiply both sides by 7 to isolate m

[tex]\dfrac{2}{5}\times7=\dfrac{m}{7}\times7[/tex]

You'll be left with:

[tex]\dfrac{2}{5}\times7=m[/tex]

Then simply do the operations to get the value of m:

[tex]\dfrac{2}{5}\times7=m[/tex]

[tex]\dfrac{2\times7}{5}=m[/tex]

[tex]\dfrac{14}{5}=m[/tex]

2.8 = m