In a certain board game, a 12-sided number cube showing numbers 1–12 is rolled. If 4 such number cubes are rolled, what is the probability that at least 1 number cube will show a number 8 or larger?

Answer:(20, 100).

Step-by-step explanation:

Formation of inequalities and their solution,

To form an inequality choose the variables.

Point lying in the common region of the inequalities will be the solution of the inequalities.

Given in the question,

Cost of student ticket = $5 each

Cost of adult ticket = $9.5 each

Let the number of student tickets sold = x

And the number of adult tickets sold = y

First statement states," Auditorium can hold a maximum of 130 people".

Inequality for the statement will be,

x + y ≤ 130 --------(1)

Second statement states, "The drama club must make at least $950 from the tickets sale to cover the show's cost".

Inequality for the statement will be,

5x + 9.5y ≥ 950 ------ (2)

Now use the utility to graph the inequality,

Since, a point (20, 100) lies in the common region (solution area) of the inequalities,

Answer:

12

Step-by-step explanation:

(5/3)y-8 = (7/3)y-16

(5/3)y- (7/3)y = 8 -16

(-2/3) y = -8

y = 3*8/2

y=24/2

y=12

Answer:

11.25

Step-by-step explanation:

Answer: C) y = 0.25m + 30

Step-by-step explanation:

Since the rental fee (y) of the car is $30 plus $0.25 per mile (m), then the cost will be:

= $30 + $0.25(m)

= 30 + 0.25m

For example, to calculate the cost of someone who rented the car and used 20 miles will be:

= 30 + 0.25m

= 30 + 0.25(20)

= 35

The volume of a cylinder changes when you adjust the height or radius as the volume either increases or reduces.

Let's assume that the height and radius are 14cm and 7cm. The volume will be:

= πr²h

= 3.14 × 7² × 14

= 2154.04cm³

When the radius and height are reduced to 5cm and 9cm, the volume will be:

= πr²h

= 3.14 × 5² × 9

= 706.5cm³

This illustrates that the volume reduces when the height and radius reduces.

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Answer:

for the first time i have no idea

Step-by-step explanation:

Good!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

the area of envelope surface is 54

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The total number of customers in the second week is 140.

It is given that during its first week in business, a craft shop had 50 customers. During the second week, the shop had 160% more customers than during the first week.

Assume that the number of customers in the shop during the second week be {x}. So, we can write -

{x} = 50 + {160% of 50}

{x} = 50 + {160/100 x 50}

{x} = 50 + 16 x 5

{x} = 50 + 90

{x} = 140

Therefore, the total number of customers in the second week is 140.

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The solution for question a is -2.00. The solution for question b is  0.6687. The solution for question c is 10 students. We can show the working in the following manner.

a. What is the probability of completing the exam in one hour or less (to 4 decimals)?

To answer this question, we need to convert the time of one hour (60 minutes) to a z-score using the mean and standard deviation provided. We have:

z = (60 - 80) / 10 = -2.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in one hour or less is approximately 0.0228, rounded to 4 decimal places.

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?

To answer this question, we need to find the probability of completing the exam in less than 75 minutes and subtract the probability of completing the exam in less than 60 minutes. We have:

z1 = (60 - 80) / 10 = -2.00

z2 = (75 - 80) / 10 = -0.50

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in less than 75 minutes is approximately 0.6915 and the probability of completing the exam in less than 60 minutes is approximately 0.0228, as calculated in part a.

So, the probability of completing the exam in more than 60 minutes but less than 75 minutes is approximately:

0.6915 - 0.0228 = 0.6687, rounded to 4 decimal places.

c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

To answer this question, we need to find the number of students whose exam time is greater than 90 minutes, which is the maximum time allowed. We can use the normal distribution with the given mean and standard deviation to calculate this.

First, we need to find the z-score corresponding to a time of 90 minutes:

z = (90 - 80) / 10 = 1.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in more than 90 minutes is approximately 0.1587.

Therefore, the expected number of students who will be unable to complete the exam in the allotted time is:

60 x 0.1587 = 9.52, which rounds up to 10 students (to the next whole number).

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Answer:

55.5 ÷ 100 = 0.555

Step-by-step explanation:

When you ask, "What is 55.5 as a decimal?", we assume you want to know what 55.5 percent is as a decimal. In other words, 55.5 percent converted to decimal.

First, we will tell you why it is useful to know 55.5 as a decimal.

Normally, to calculate 55.5 percent, you would multiply a number by 55.5 percent and then you would take the product of that and divide it by 100 to get the answer.

Instead, you can simply multiply a number by 55.5 as a decimal to get the answer.

55.5 percent means 55.5 per hundred. Therefore, to get 55.5 as a decimal, all you have to do is divide 55.5 by 100 like so:

55.5 ÷ 100 = 0.555

Answer:

55.5% = 0.555

Step-by-step explanation:

55.5% = 55.5/100 = 0.555

Answer:

3/4 of a hour

Step-by-step explanation:

2 miles  = 0.5 hours

Divide by 2

1 mile = 0.25 hours

Multiply by 3

3 mile = 0.75 hours

Answer:

45 minutes or .75 of an hour or 3/4 of an hour

Step-by-step explanation:

if you walk 2 miles in a half-hour (30 minutes) , how long will it take to walk 3 miles. Well the answer is simple, we need to use proportions to solve it though. For example:

\(\frac{miles}{hours}\)   =    \(\frac{2}{.5}\)

therefore, half of .5 is .25

so for someone to complete 1 mile, it takes .25 of an hour. .25 of an hour is 15 minutes. Therefore, the correct simplified proportion is : \(\frac{1}{.25}\)

Now we need to find out what the denominator (bottom number/time) would be when the numerator (top number of the fraction) is =3.

Since we have the simplified version as a 1, we can just multiply .25 by 3 which is .75, and .75 of an hour is 45 minutes. Therefore the answer is 45 minutes.

If the curve passes through the points (2,16) and (5,250), then its equation is y = 78x - 140.

In order to find the equation of the curve which passes through the points (2,16) and (5,250), we use the "point-slope" form of a linear equation, which is :

⇒ "Point-slope" form is : "y - y₁ = m×(x - x₁)",

where (x₁, y₁) is point on curve, m = slope of curve, and (x, y) = coordinates of any point on curve,

First, we find slope (m) using the two points, (x₁, y₁) = (2, 16), (x₂, y₂) = (5, 250),

Substituting the values,

We get,

⇒ Slope = (y₂ - y₁)/(x₂ - x₁),

⇒ m = (250 - 16)/(5 - 2),

⇒ m = 234/3,

⇒ m = 78,

Now, we use slope and the points to write equation of curve,

We use the point (2,16),

we get,

⇒ x₁ = 2, y₁ = 16, m = 78;

Substituting the values, in point-slope form equation,

We get,

⇒ y - 16 = 78(x - 2),

⇒ y - 16 = 78x - 156,

⇒ y = 78x - 156 + 16,

⇒ y = 78x - 140,

Therefore, the required curve-equation is "y = 78x - 140".

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The given question is incomplete, the complete question is

Find the equation of the curve that passes through the points (2,16) and (5,250).

The angle between string and horizontal decreases at the rate of 0.02 rad/sec

A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s.

The horizontal decreasing when 200 ft of string have been let out.

We have to find out at what rate is the angle changing means \($\frac{\mathrm{d} \theta}{\mathrm{dt}}$\)

Given, \($$\frac{\mathrm{dx}}{\mathrm{dt}}=8$$\)

from figure\($\therefore \tan \theta=\frac{100}{\mathrm{x}}$, and $\sec \theta=\frac{200}{\mathrm{x}}$\)

Differentiating w.r.tt, we get

\($$\begin{aligned}& \sec ^2 \theta \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{100}{\mathrm{x}^2} \frac{\mathrm{dx}}{\mathrm{dt}} \\& \left(\frac{200}{\mathrm{x}}\right)^2 \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{100}{\mathrm{x}^2} \frac{\mathrm{dx}}{\mathrm{dt}} \\& \frac{40,000}{\mathrm{x}^2} \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{100}{\mathrm{x}^2} \times 8 \\& \frac{\mathrm{d} \theta}{\mathrm{dt}}=-\frac{800}{40,000} \\& =-0.02\end{aligned}$$\)

Therefore, the the angle (in radians) between the string and the horizontal is \(-0.02\).

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Answer:

The inverse of a function is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function. In plain English, finding an inverse is simply the swapping of the x and y coordinates.

Step-by-step explanation:

Answer:

Step-by-step explanation:

6c + 18-4c + 16

Solving like terms

2c + 34

Answer: 2c + 2

6(c + 3) - 4(c + 4)

= 6c + 18 - (4c + 16)

= 6c + 18 - 4c - 16

= 2c + 2

Step-by-step explanation:

The probability that there will be no accidents during the first 2 weeks of January is calculated to be approximately 0.778 or 77.8%.

The first two weeks of January consist of 14 days, so we want to find the probability that no accidents occur in 14 days given that the probability of an accident occurring on any given day is 30/365. We can use the binomial distribution to solve this problem.

Let X be the number of accidents in 14 days. Then X follows a binomial distribution with n = 14 and p = 30/365. The probability of no accidents in 14 days is P(X = 0), which is given by the formula:

P(X = 0) = (n choose 0) x p⁰ x (1-p)⁽ⁿ⁻⁰⁾

where "n choose 0" is the number of ways to choose 0 accidents out of n days, which is simply 1.

Substituting n = 14 and p = 30/365, we get:

P(X = 0) = (1) x (30/365)⁰ x (1 - 30/365)⁽¹⁴⁻⁰⁾ ≈ 0.778

Therefore, the probability that there will be no accidents during the first 2 weeks of January is approximately 0.778 or 77.8%.

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Answer:

22 divided 5 I would think

Step-by-step explanation:

Answer:

It will be 1 since s=1 and (1^2)=1

If s ≥ 0, then  √s² is equal to s, option C is correct.

A number system is defined as a system of writing to express numbers.

If s ≥ 0, then  √s² is equal to S

s is greater than or equal to zero then we have to find the value of square root of s square.

The square root of a number is always non-negative, so  √s² would be equal to s, regardless of whether s is positive or zero.

Hence, if s ≥ 0, then  √s² is equal to s, option C is correct.

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Answer:

B. h(x) = -3x + 4.

Step-by-step explanation:

I am assuming that the vertical shift is upwards,

A refection in the x axis gives -3x

Vertical shift upwards of 4 gives -3x + 4.

The minimum dimensions of the box will be; 7 cm × 6 cm × 6 cm

Since the dimension is described as the measurement of something in physical space such as length, width, or height.

Given that the there will be maximum dimension when the height of the cylinder and the radius of the hemisphere are aligned together.

Maximum height = 4 cm + 3 cm = 7 cm

Maximum diameter = 2 × 3 cm = 6 cm

Therefore, we can see that the minimum dimensions of the box are :

7 cm × 6 cm × 6 cm.

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Answer:

<1=134 degrees

<2=46 degrees

Step-by-step explanation:

Ans in attachment

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The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

In this case, we have two figures, LMNO and HIJK, and we know that LMNO is a reflection of HIJK. This means that there is an axis of reflection that maps HIJK onto LMNO.

When a shape is reflected across a line of symmetry, its angles are preserved. That is, if two angles in the original shape are congruent, then their images in the reflected shape are also congruent.

In this case, ZH is an angle in HIJK, and we want to find the angle in LMNO that corresponds to it. To do this, we need to find the line of symmetry that maps HIJK onto LMNO.

Once we have identified this line, we can draw the perpendicular bisector of ZH and find where it intersects the line of symmetry. The angle formed by this intersection point and the corresponding point on LMNO is congruent to ZH.

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The best statement of the conclusion for your meeting would be: C. There is not sufficient evidence that the mean body temperature of women is < 98.6 degrees F.

Based on the given options, the best statement of the conclusion would be option C, which states that there is not sufficient evidence that the mean body temperature of women is less than 98.6 degrees Fahrenheit.

To elaborate further, the conclusion is drawn based on the hypothesis testing that was conducted to test whether the mean body temperature of women is significantly different from the commonly accepted value of 98.6 degrees Fahrenheit.

The null hypothesis (H0) in this case would be that the mean body temperature of women is equal to 98.6 degrees Fahrenheit, while the alternative hypothesis (Ha) would be that the mean body temperature of women is less than 98.6 degrees Fahrenheit.

The hypothesis testing would involve calculating the test statistic, which in this case could be the t-statistic, and comparing it with the critical value from the t-distribution, based on the level of significance and degrees of freedom. If the calculated test statistic is greater than the critical value, then the null hypothesis would be rejected, indicating that there is sufficient evidence to support the alternative hypothesis.

On the other hand, if the calculated test statistic is less than the critical value, then the null hypothesis would fail to be rejected, indicating that there is not enough evidence to support the alternative hypothesis.

In this scenario, the conclusion states that there is not sufficient evidence to reject the null hypothesis, which means that the mean body temperature of women is not significantly different from 98.6 degrees Fahrenheit.

It is important to note that the conclusion is not a definitive statement, but rather a statistical inference based on the sample data collected. Further research and analysis could be conducted to verify the results and draw more concrete conclusions.

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The equation of the plane with normal vector =⟨−5,2,5⟩ passing through the point =(4,1,8) in scalar form is 5x + 2y + 5z = 22.

1. Recall the equation of a plane in scalar form: Ax + By + Cz = D, where ⟨A, B, C⟩ is the normal vector of the plane, and (x, y, z) are the coordinates of any point on the plane.

2. In this case, the normal vector is given as ⟨−5, 2, 5⟩. Therefore, A = -5, B = 2, and C = 5.

3. The plane passes through the point (4, 1, 8). We can use this point to find the value of D. Substitute the point's coordinates into the equation: -5(4) + 2(1) + 5(8) = D.

4. Calculate the value of D: -20 + 2 + 40 = 22.

5. Now, we can write the equation of the plane in scalar form using the values of A, B, C, and D: -5x + 2y + 5z = 22.

So, the equation of the plane with normal vector ⟨−5, 2, 5⟩ passing through the point (4, 1, 8) in scalar form is: -5x + 2y + 5z = 22.

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answers are in the pictures

Answer:

Function A: Linear

Function B: Nonlinear

Step-by-step explanation:

1. When looking at tables, an easy way to tell if it's linear or not is to determine if the slope is the same between different coordinates.

Try (3,5) (6,10)

y2-y1/x2-x1

10-5/6-3

5/3

Now try (6,10) (9,15)

15-10/9-6

5/3

The slopes are the same, so this function is in fact linear.

2. For graphs, linear functions form a straight line. The line in this graph is clearly curved, so it is not linear.

Answer: 2.4 weeks

Step-by-step explanation:

Answer:

2.4 wk

Step-by-step explanation: