Valentino sells ice cream cones and ice cream tubs.

The ice cream flavours are chocolate, strawberry and vanilla.

On Sunday, 120 people each bought one ice cream from Valentino. The two-way table shows some information about these ice creams.

One of the 120 people is picked at random.

Find the probability that this person bought a vanilla ice cream cone.

The approximate probability that the random sample of 1000 letters will contain 7.4% or fewer is 0.242.

We have taken a random sample of 1000 letters and counted the number of t's. We have to find the approximate probability that this random sample will contain 7.4 % or fewer t's. We are given an estimation that the letter 'T' makes up 8% of a certain language.

Proportion(p) = 8 % = 0.08

n = 1000

q = 1 - p

q = 1 - 0.08

q = 0.92

The mean is equal to the proportion. Therefore;

μ = p = 0.08

Now, we will apply the formula for standard deviation;

σ = \(\sqrt{\frac{pq}{n} }\)

σ = \(\sqrt{\frac{(0.08)(0.92)}{1000} }\)

σ = 0.0858

The z-score will be calculated by;

z = (x - μ )/σ

z = (0.074 - 0.08)/0.00858

z = -0.70

From the z-score calculator, we get the p-value as;

P(Z< -0.70) = 0.242

Therefore, the approximate probability that the random sample of 1000 letters will contain 7.4% or fewer is 0.242.

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The complete question is "The letter "T" makes up an estimated 8% of a certain language. Assume this is still correct. A random sample of 1000 letters is taken from a randomly selected, large book, and the t's are counted. find the approximate probability that the random sample of 1000 letters will contain 7.4% or fewer t's​"

Answer:

13,000

Step-by-step explanation:

We are 30 years away from 1990 which is double of 15 years so if you double 6,258 you get close to 13,000

Answer:

C, 13,000

I have attached a graph to help you out:

Hope this helps!

Our conjecture is that PO is two-thirds the length of PQ.

As A is the midpoint of PQ, B is the midpoint of PA, and C is the midpoint of PB, we can make a conjecture about the algebraic relationship between PO and PQ.

Conjecture: The segment PO is two-thirds the length of PQ.

To support this conjecture, we can examine the properties of midpoints. A midpoint of a line segment divides the segment into two equal parts.

In this case, since A is the midpoint of PQ, we can say that PA is equal in length to AQ. Similarly, since B is the midpoint of PA, PB is equal in length to BA, and since C is the midpoint of PB, PC is equal in length to BP.

Using this information, we can express the length of the segments in terms of each other:

PA = AQ

PB = BA

PC = BP

Now, we can consider the relationship between PO and PQ. We know that:

PO = PA + AO

PQ = PA + AQ

Since PA is common to both expressions, we can substitute AQ for PA in the expression for PQ:

PQ = PA + AQ

PQ = PO + AQ

Rearranging the equation, we get:

AQ = PQ - PO

Based on our previous findings, AQ is half the length of PQ (since A is the midpoint of PQ). Substituting this information into the equation, we have:

1/2(PQ) = PQ - PO

Simplifying further:

1/2(PQ) = PQ - PO

PQ/2 = PQ - PO

PQ = 2(PQ - PO)

PQ = 2PQ - 2PO

2PO = PQ

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Answer:

\(o \: f(x) = 500 {(x)}^{2} \)

Step-by-step explanation:

\(f(x) = 500 {(x)}^{2} \\ f(0) = 500 {(0)}^{2} \\ = 500\)

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

Step-by-step explanation:

X-coordinates are domain and y-coordinates are range

Domain= {1,2,3,4}

Range= {2}

Answer:

domain: 1,2,3,4. range:2

Step-by-step explanation:

domain is the input aka the x- values, and the range is the output aka the y-values

Answer:

The restaurant owner can infer that most customers like pie  

Step-by-step explanation:

Answer: The owner can infer that "Pie" is what customers like the most.

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

according to the condition it is possible to calculate the values of ∠DEF; ∠CDE and ∠DCF:

1) m∠DEF=m∠BAE=104°;

2) m∠CDE=180-m∠BAE=180-104=76°;

3) m∠DCF=m∠BAE-m∠BCF=104-60=44°;

the required value of the angle EFC is:

4) m∠EFC=360- (m∠DEF+m∠CDE+m∠DCF)=360-104-76-44=136°

5) the correct answer is: C. 136°.

The basketball league has 576 games in total.

A mathematical procedure called addition combines two or more numbers to determine their sum or total.

It is indicated by the plus sign ("+"). The effect of adding numbers is unaffected by the sequence in which the numbers are added.

The sum is the name given to the outcome of an addition operation.

In the east conference, each team plays against the other seven teams from the same conference four times.

Since there are eight teams in the east conference, the total number of games within the east conference can be calculated as follows:

Total games in the east conference = 8 teams × 7 opponents × 4 games per opponent

Similarly, in the west conference, each team plays against the other seven teams from the same conference four times. So the total number of games within the west conference can be calculated as:

Total games in the west conference = 8 teams × 7 opponents × 4 games per opponent

Now, each team from the east conference plays against all eight teams from the west conference twice. Thus, the total number of games between the conferences is:

Games between the conferences = 8 teams × 8 opponents × 2 games per opponent

To find the total number of games, we sum up the games within each conference and the games between the conferences:

Total games = Total games in the east conference + Total games in the west conference + Games between the conferences

Plugging in the values:

Total games = (8 × 7 × 4) + (8 × 7 × 4) + (8 × 8 × 2)

= 224 + 224 + 128

= 576

Therefore, there are a total of 576 games in the basketball league.

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The required probabilities for the events in question are:

Based on the parameters given :

Number of red slots = 18

Number of black slots = 18

Number of green slots = 2

Total number of slots = 18+18+2 = 38

A.)

Probability of green slots 2 or more times :

(2/38)² × (36/38)²³ = 0.00080

B.)

Probability of ball not entering the green slots

1 - P(green slots)

P(not entering green slot ) = 1 - 0.0008 = 0.9992

C.)

probability that ball falls into black slot 15 or more times :

(18/38)¹⁵ * (20/38)¹⁰ = \(2.21\times10^{-8}\)

D.)

Probability that ball falls into red slot 10 or less times :

(10/38)¹⁰ * (28/38)¹⁵ = \(1.63\times10^{-8}\)

Therefore, the required probabilities are :

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Answer:

x = 8

Step-by-step explanation:

I hope this helps!

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

x = # of 5 cent coins

y = # of 50 cent coins

x+y=25

.05x+.5y=7.1

y=25-x

(.05x+.5(25-x)=7.1)100

5x+50(25-x)=710

5x+1250-50x=710

-45x=-540

x=12

You have 12, 5 cent coins and 13, 50 cent coins.

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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The lower end of the 95% confidence interval can be calculated using the margin of error and the sample mean.

To calculate the lower end of the 95% confidence interval, we need the sample mean and the margin of error. The margin of error is determined by multiplying the critical value (1.96 for a 95% confidence level) by the standard deviation of the sample or population, depending on the case.

Once the margin of error is calculated, we subtract it from the sample mean to obtain the lower end of the confidence interval. For example, if the sample mean is 50 and the margin of error is 2.5, the lower end of the 95% confidence interval would be 50 - 2.5 = 47.5.

It is important to note that the actual values used in the calculation will vary depending on the specific context and data. Therefore, the exact lower end of the interval cannot be provided without the specific sample mean and margin of error.

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Answer:

17 stops on 1 ticket

Step-by-step explanation:

Answer:

17 stops on 1 ticket

Step-by-step explanation:

When compared to a normal distribution, a t-distribution with a small degrees of freedom has heavier tails, indicating a higher probability of extreme values. As the degrees of freedom increase, the shape of the t-distribution approaches that of a normal distribution.

The shape of a t-distribution with a small degrees of freedom (df) differs from that of a normal distribution. The first paragraph provides a summary of the answer, and the second paragraph explains the details of the comparison.

A t-distribution with a small degrees of freedom has a shape that is similar to a normal distribution, but with heavier tails. As the degrees of freedom decrease, the t-distribution becomes more spread out and has a higher probability of extreme values compared to a normal distribution.

The tails of the t-distribution are fatter or thicker than those of a normal distribution. This means that the t-distribution has a higher probability of extreme values, making it more likely to observe values far away from the mean. In contrast, the normal distribution has thinner tails, indicating a lower probability of extreme values and a higher concentration of data around the mean.

The shape of the t-distribution approaches that of a normal distribution as the degrees of freedom increase. When the degrees of freedom are large (typically above 30), the t-distribution becomes very similar to a normal distribution, and the differences between them become negligible.

The t-distribution is widely used in statistical inference, especially in situations where the sample size is small or when the population standard deviation is unknown. It provides a more appropriate distribution for estimating population parameters when the underlying data exhibit variability.

In summary, compared to a normal distribution, a t-distribution with a small degrees of freedom has heavier tails, indicating a higher probability of extreme values. As the degrees of freedom increase, the shape of the t-distribution approaches that of a normal distribution.

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Answer:

23,154* 3/4 >23,164

Step-by-step explanation:

Is this what you need

If not, then I'm sorry. :(

Hello russell6333!

\( \huge \boxed{\mathfrak{Question} \downarrow}\)

Solve for x.

\( \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}\)

\(1) \: \: \: 144 = 12x \\ \frac{144}{12} = x \\ \boxed{ \boxed{ \bf12 = x}}\)

__________________

\(2) \: \: \: 45 = 4x - 27 \\ 45 + 27 = 4x \\ 72 = 4x \\ \frac{72}{4} = x \\ \boxed{ \boxed { \bf18 = x }}\)

__________________

\(3) \: \: \: 2x - 2 = 14 \\ 2x = 14 - 2 \\ 2x = 12 \\ x = \frac{12}{2} \\ \boxed{ \boxed{ \bf \: x = 6}}\)

__________________

\(4) \: \: \: 12x = 44 - 10x \\ 12x + 10x = 44 \\ 22x = 44 \\ x = \frac{44}{22} \\ \boxed{\boxed{ \bf \: x = 2}}\)

__________________

__________________

Hope it'll help you!

ℓu¢αzz ッ

Answer:

25

Step-by-step explanation:

60·\(\frac{1}{3}\)= 20

60·\(\frac{1}{4\\}\)= 15

60- 20+ 15= 60-35 = 25

Answer:

32 cm

Step-by-step explanation:

The volume of the container is:

V= area of the base * the heigth

Since the container has a rectangular base the area of it is:

A = length * width

Let L be the missing length

A = L * 10

V = 10* 25 * L

The container can hold 8 Liters when it's completely full to its brim.

8 liters is 8000 cm^3 ( multiply by 1000)

8000 = 10*25*L

8000 = 250 *L

L = 8000/250

L = 32 cm

v=8litres which is 8 × 1000

l=?

b=10

h=25

since, v=lbh (volume of cuboid)

8000=l × 10 × 25

l=8000/250

l=32

therefore the length is 32cm

The m∠GLK of the circle is 63°.

Arc of a circle is the part or segment of the circumference of a circle. A straight line  drawn by connecting the two ends of the arc is called a chord of a circle.

Since the measure of inscribed angle is half the measure of its intercepted arc. Thus, we can say:

∠KLJ = 1/2 * arc KJ

∠KLJ = 1/2 * 118

∠KLJ = 59°

m∠GLK = 180 - 59 - 58  (sum of angle on a straight line is 180°)

m∠GLK = 63°

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Complete Question

Check the attached image

Answer:

\(2.75,\ 0.1x\)  

\(2.75\)

Step-by-step explanation:

In the expression \(2.75+0.1x\) the number \(2.75\) represents the cost of a movie ticket in 1980 and \(x\) represents the years after 1980. So increase per year is represented by \(0.1x\).

If the cost of the ticket in 1982 is needed that means 2 years have passed after 1980, \(x\) will be \(2\).

In 1980, zero years have passed so, \(x=0\)

Therefore the cost of movie tickets is represented by \(2.75+0.1\times 0=2.75\)

Answer:

-7/8

= (7/9) × (-9/8)

=-7/8

To determine the required sample size for a political poll with a 4% margin of error and a 97.5% confidence level, a formula can be used. For this scenario, the sample size required would be approximately 862 respondents.

To calculate the sample size needed for a political poll with a 4% margin of error and a 97.5% confidence level, the following formula can be used:

n = (Z^2 * p * (1-p)) / E^2

Where:

n is the sample size

Z is the Z-score associated with the desired confidence level (in this case, it is 2.24)

p is the expected proportion of support for the candidate (this value is typically unknown, so a conservative estimate of 0.5 is often used to get the maximum sample size)

E is the margin of error

Plugging in the values for this scenario, we get:

n = (2.24^2 * 0.5 * (1-0.5)) / 0.04^2

n ≈ 862

Therefore, the required sample size for this political poll is approximately 862 respondents. This sample size would provide a margin of error of 4% at a 97.5% confidence level, meaning that there is a 97.5% chance that the true proportion of support for the candidate lies within the range of the survey results plus or minus the margin of error.

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The volume of the cylinder is 81π cubic meters.

The volume of a cylinder

Volume = π × radius² × height

The diameter of the cylinder is 6m, we can determine the radius by dividing the diameter by 2

Radius = diameter / 2 = 6m / 2 = 3m

Since the height is triple the radius

Height = 3 × radius = 3 × 3m = 9m

Now we can substitute these values into the volume formula

Volume = π × (3m)² × 9m

Volume = π × 9m² × 9m

Volume = 81π m³

Therefore, the volume of the cylinder is 81π cubic meters.

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Answer:

4 + 9 = 13

Step-by-step explanation:

Start by prime factorizing 108. 108 is equal to \(2^2 \cdot 3^3\). This conveniently makes the a and b we need, as we are looking for \(a^2 \cdot b^3\). We get \(a=2,b=3\). Now, plug this into \(2a+ 3b\). We get \(2 \cdot 2 + 3 \cdot 3 = 4 + 9 = 13\).

Answer:

3 times 10 Superscript 9 feet

Step-by-step explanation:

your welccome

The feet the jet would fly in the given time is 3 x \(10^{9}\).

Multiplication is the process of determining the product of two or more numbers by following a set of mathematical principle.

The feet travelled can be determined by multiplying the rate per hour by the total time.

1.3 x 10^3 x 2.8 x 10^6 = 3 x 10^9

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Answer:  E is located at (-2, 6)

Explanation:

The rule for reflecting over y = x is \((x,y) \to (y,x)\)

The x and y coordinates swap places.

Point E' is located at (6, -2) so that means point E must be located at (-2, 6)