A fair 10 sided die rolled until a 7 is first seen. What is the probability of rolling the die six times?

Answer:

Step-by-step explanation:

In this problem, we are expected to calculate the change in the price of a particular stock

Given that the days high is 80 1/4

and also that the days low is 50 1/2

we can calculate the change by subtracting the days low from the days high

i.e 80 1/4- 50 1/2= 321/4-101/2= (321-202)/4= 119/4 = 29 3/4

hence the change for the day is 29 3/4

Also we can calculate the percentage change as

%change = (high-low)/low*100

%change= 80 1/4- 50 1/2/50 1/2= 29 3/4/50 1/2 *100

%change= 119/4*2/101 *100= 119/202*100= 0.589*100= 58.9%

%change= 58.9%

The given equation is:

Recall that:

Suppose (4c - 10) < 0, it follows that:

Suppose (4c - 10) ≥ 0, it follows that:

Therefore, the solution is:

c = -10 and c =15

.

James will fully clear the loan after approximately 12 years when the remaining balance reaches zero.

To determine the number of years it will take for James to fully clear the loan, we need to calculate the remaining balance after each payment and divide the initial loan amount by the annual payment until the remaining balance reaches zero.

The loan amount is 9000 euros, and James pays off 770 euros each year. Since the interest is charged at a rate of 3% of the original amount per annum, the interest for each year will be \(0.03 \times 9000 = 270\) euros.

In the first year, James pays off 770 euros, and the interest on the remaining balance of 9000 - 770 = 8230 euros is \(8230 \times 0.03 = 246.9\)euros. Therefore, the remaining balance after the first year is 8230 + 246.9 = 8476.9 euros.

In the second year, James again pays off 770 euros, and the interest on the remaining balance of 8476.9 - 770 = 7706.9 euros is \(7706.9 \times 0.03 = 231.21\) euros. The remaining balance after the second year is 7706.9 + 231.21 = 7938.11 euros.

This process continues until the remaining balance reaches zero. We can set up the equation \((9000 - x) + 0.03 \times (9000 - x) = x\), where x represents the remaining balance.

Simplifying the equation, we get 9000 - x + 270 - 0.03x = x.

Combining like terms, we have 9000 + 270 = 1.04x.

Solving for x, we find x = 9270 / 1.04 = 8913.46 euros.

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The equation of the tangent line to the function \(y = x^3 + 3x^2 - 5x + 3\) at the point (1, y(1)) is y = 4x + (y(1) - 4), and the equation of the normal line is y = -1/4x + (y(1) + 1/4). The value of y(1) represents the y-coordinate of the function at x = 1, which can be obtained by substituting x = 1 into the given function.

To find the equation of the tangent and the normal of the given function at the indicated point, we need to determine the derivative of the function, evaluate it at the given point, and then use that information to construct the equations.

Find the derivative of the function:

Given function: \(y = x^3 + 3x^2 - 5x + 3\)

Taking the derivative with respect to x:

\(y' = 3x^2 + 6x - 5\)

Evaluate the derivative at the point x = 1:

\(y' = 3(1)^2 + 6(1) - 5\)

= 3 + 6 - 5

= 4

Find the equation of the tangent line:

Using the point-slope form of a line, we have:

y - y1 = m(x - x1)

where (x1, y1) is the given point (1, y(1)) and m is the slope.

Plugging in the values:

y - y(1) = 4(x - 1)

Simplifying:

y - y(1) = 4x - 4

y = 4x + (y(1) - 4)

Therefore, the equation of the tangent line is y = 4x + (y(1) - 4).

Find the equation of the normal line:

The normal line is perpendicular to the tangent line and has a slope that is the negative reciprocal of the tangent's slope.

The slope of the normal line is -1/m, where m is the slope of the tangent line.

Thus, the slope of the normal line is -1/4.

Using the point-slope form again with the point (1, y(1)), we have:

y - y(1) = -1/4(x - 1)

Simplifying:

y - y(1) = -1/4x + 1/4

y = -1/4x + (y(1) + 1/4)

Therefore, the equation of the normal line is y = -1/4x + (y(1) + 1/4).

Note: y(1) represents the value of y at x = 1, which can be calculated by plugging x = 1 into the given function \(y = x^3 + 3x^2 - 5x + 3\).

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The truth value of the conditional statement is false, and the counterexample of this statement is corresponding angles

The conditional statement is given as:

If two angles are congruent, then they are vertical angles.

The above statement is false because not all congruent angles are vertical angles

A counterexample of this statement is a corresponding angle

i.e. corresponding angles are congruent angles, but they are not vertical angles

Hence, the truth value of the conditional statement is false, and the counterexample of this statement is a corresponding angle

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Bar charts or bar graphs are generally small and show simple trends rather than all the details regarding the horizontal and vertical axes that you would expect on a normal graph.

Bar charts are a type of data visualization that represent categorical data using rectangular bars. Each bar represents a specific category, and the length or height of the bar corresponds to the value or frequency of that category.
Here's how you can create a bar chart:
1. Identify the categories or variables you want to compare. For example, if you want to compare the sales of different products, the categories would be the product names.
2. Determine the scale for the horizontal and vertical axes. The horizontal axis typically represents the categories, while the vertical axis represents the values or frequencies. The scale should be appropriate to fit the data without cutting off any bars.
3. Draw a horizontal line for the x-axis and a vertical line for the y-axis.
4. Mark the categories along the x-axis. You can use labels or tick marks to indicate each category.
5. Mark the values or frequencies along the y-axis. Again, you can use labels or tick marks depending on the range of values.
6. Draw bars for each category. The length or height of each bar corresponds to the value or frequency of that category. You can use rectangles or vertical lines to represent the bars.
7. Label the bars if necessary to provide additional information or clarity.

Bar charts are often used to compare discrete data or categories, such as sales by product, population by country, or survey responses by option. They are easy to read and interpret, making them a popular choice for visualizing data in a simple and straightforward way. However, bar charts may not provide the same level of detail as other types of graphs, such as line graphs or scatter plots.

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The number of candidates (n) and the number to be selected (r) were not provided in the question, I am unable to provide a specific numerical answer. There are 252 ways to select a list of 5 candidates from a pool of 10 candidates.

If we assume that the number of candidates is n and the boss wants to select a list of k candidates, then the number of ways to select the list can be calculated using the combination formula.
The formula for combination is: n choose k = n!/k!(n-k)!
Using this formula, we can find the number of ways to select the list of k candidates from the n candidates.
For example, if there are 10 candidates and the boss wants to select a list of 5 candidates, then the number of ways to select the list would be:
10 choose 5 = 10!/5!(10-5)! = 252
Therefore, there are 252 ways to select a list of 5 candidates from a pool of 10 candidates.
In general, the number of ways to select a list of k candidates from a pool of n candidates can be calculated using the combination formula as n choose k = n!/k!(n-k)!.
Hi there! It seems that your question is incomplete, but I'll try my best to provide a helpful answer using the information provided. It appears you are asking about the number of ways to select a list of candidates to submit to a boss for a final decision.
To calculate the number of ways to select a list of candidates, we will use the concept of combinations. A combination is a way of selecting items from a larger set, without considering the order in which they are chosen. The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
where C(n, r) represents the number of combinations, n is the total number of candidates, r is the number of candidates to be selected, and ! denotes a factorial (e.g., 5! = 5 x 4 x 3 x 2 x 1).
However, If you can provide the values for n and r, I would be happy to help you calculate the number of ways to select the list of candidates to submit to the boss.

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Reject the null hypothesis because \($p$\)-value \($=0.0045$\) is less than the Significance level x=0.025.

The null hypothesis is a widely used statistical theory that states that for any given single observable variable, there is no statistical relationship or significance between any two sets of observed data and measured events.

According to the given information

\(& H_0: \mu=57 \\\)

\(& H_a ; \mu > 57 \\\)

\(& \alpha=0.025 \\\)

\(& \text { Test Statistic }=2.61\)

So,

This is right tailed test

\(& \text { Using } z \text { table } \\\)

\(& p(z > 2.61) \\\)

\(&= 1-p(z < 2.61) \\\)

\(&= 1-0.9955 \\\)

\(& p \text {-value }= 0.0045\)

Reject the null hypothesis because \($p$\)-value \($=0.0045$\) is less than the Significance level x=0.025.

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Answer:

Step-by-step explanation:

If an angle measures x degrees, the measure of its supplement is (180-x) degrees.

This means that x-62.4 = 180-x, meaning that x=121.2.

So, the angles are 121.2 and 58.8 degrees.

Answer:

The mean temperature is O

Step-by-step explanation:

Answer:

A

Hope that helps!

Step-by-step explanation:

The expression that represents all clothing is being marked down 15%.

is A) 0.85x.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

We know fractions and percentages are related.

Assuming the cost of clothing to be 'x'.

∴ After the markdown of 15% it is,

= {(100 - 15)/100}×x.

= {85/100}×x.

= 0.85x

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The cost of making the chest with these dimensions is approximately $3.83.

Let's start by finding an expression for the cost of making the chest in terms of its dimensions. The cost of the oak top and sides is given by:

cost of oak = 2lw + 2lh

where l is the length and w is the width of the chest, and h is the height (which we don't know yet). The cost of the pine bottom is given by:

cost of pine = lw

The total cost of making the chest is the sum of these two costs:

total cost = cost of oak + cost of pine

= 2lw + 2lh + lw

We want to minimize this cost subject to the constraint that the volume of the chest is 0.25 cubic metres. The volume of a rectangular box is given by:

volume = length × width × height

= lwh

Since the volume is given as 0.25 cubic metres, we have:

lwh = 0.25

We also know that the length is twice the width, so we can write:

l = 2w

Substituting this into the expression for volume, we get:

\(2w^{2h} = 0.25\)

Solving for h, we get:

\(h = 0.125/w^2\)

Substituting this expression for h into the expression for the total cost, we get:

total cost = \(2lw + 2(0.125/w^2)w + lw\)

= 2lw + 0.25/w

To minimize this cost, we can take the derivative with respect to w and set it equal to zero:

d(total cost)/dw =\(2l - 0.25/w^2 = 0\)

Solving for w, we get:

w = \(\sqrt{0.125/l)}\)

Substituting this value for w back into the expression for h, we get:

h = \(0.125/w^2 = 8l\)

Therefore, the dimensions that will minimize the cost of making the chest are:

length = 2w = \(2\sqrt{(0.125/l)}\)

width = w =\(\sqrt{0.125/l)}\)

height = h = 8

To find the cost of making the chest, we can substitute these values into the expression for the total cost:

total cost = 2lw + 0.25/w

= \(2\sqrt{(0.125/l} ) \times \sqrt{0.125/l)} \times 2 + 0.25/\sqrt{(0.125/l)}\)

= 4 × 0.125 + 0.25 × sqrt(l/0.125)

= 0.5 + 2\(\sqrt{2\) ≈ 3.83

Therefore, the cost of making the chest with these dimensions is approximately $3.83.

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The expected number of customers in the system is 0.96.

Given that the arrivals to the drive-up teller window occur at a rate of 0.4 customers per minute, and the service times are exponentially distributed, we can use queuing theory to determine the operating characteristics of the system.

What is the expected number of customers waiting in line?

We can use the queuing formula Lq = (λ^2) / (μ(μ-λ)), where λ is the arrival rate and μ is the service rate. Here, λ = 0.4 and μ is the reciprocal of the average service time, which we need to calculate.

Assuming the bank tellers can serve customers in an average of 2 minutes, then μ = 1/2 = 0.5.

Plugging these values into the formula, we get:

Lq = (0.4^2) / (0.5(0.5-0.4)) = 0.16 customers

Therefore, the expected number of customers waiting in line is 0.16.

What is the expected time a customer spends in the system?

We can use the queuing formula W = (1/μ) + (Lq/λ), where μ is the service rate and λ is the arrival rate, and Lq is the expected number of customers waiting in line.

Using the same values of λ and μ as before, we can calculate Lq as 0.16 customers. Plugging these values into the formula, we get:

W = (1/0.5) + (0.16/0.4) = 2.4 minutes

Therefore, the expected time a customer spends in the system is 2.4 minutes.

What is the expected number of customers in the system (i.e., both waiting and being served)?

We can use the queuing formula L = λW, where λ is the arrival rate and W is the expected time a customer spends in the system.

Plugging in the values of λ and W that we calculated earlier, we get:

L = 0.4 x 2.4 = 0.96 customers

Therefore, the expected number of customers in the system is 0.96.

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Answer:

20 students

Step-by-step explanation:20 students cos 88 divided by 4 =22 and it said she had 8 left so 20 student in her class

a) The expected number of people to die before their 71st birthday is given as follows: 128.

b) The probability that a 67 year old woman will live to her 68th birthday is given as follows: 0.8876 = 88.76%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

0.025679 of the 70 year old men die, hence the expected number out of 5000 is given as follows:

0.025679 x 5000 = 128.

The probability for item b is given as follows:

0.016798/0.018925 = 0.8876 = 88.76%.

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Answer:

127.2

Step-by-step explanation:

The area of a semicircle is:

\(\frac{\pi r^{2} }{2}\)

So to figure it out we first find the diameter:

18÷2=9

Then we plug it into the equation

\(\frac{9^{2}\pi }{2} = \frac{81\pi}{2}\) Which we can put into a calculator to get 127.2345... so we round to 1 d.p to get our answer, 127.2 (the fifth digit, 3, rounds down)

The required inequality represented by the number line is 54≤x<58

A number line is a pictorial representation of numbers on a straight line. In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

here, we have,

Number line and graph

From the given number line, you can see that the circle is on the 53 value and closed. The closed circle shows that the inequality sign will contain the equal sign.

For the direction of arrow, the direction is towards the positive side of the number line showing that the required inequality is:

54≤x<58.

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An inequality which could be used to determine the lengths that would make the area of the rectangular base of the tree house greater than 293 square inches is W² + 7W > 293.

Mathematically, the area of a rectangle can be calculated by using this formula;

A = LW

Where:

For the length and area of the rectangular base, we have:

L = W + 7

A > 293

Substituting the given parameters into the formula, we have;

L × W > 293

(W + 7) × W > 293

W² + 7W > 293

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Complete Question:

Adam built a tree house with a rectangular base. The length of the base is 7 inches more than its width. If w represents the width of the tree house, which inequality could be used to determine what lengths would make the area of the base of the tree house greater than 293 square inches?

W + 7 > 293

202 + 286 > 2,051

w² + 7w > 293

12 + 293 > 293

Answer:

(a)0.7

(b)0.42

Step-by-step explanation:

Definition: Mutually exclusive events are events that occur independently of one another.

The table below gives the distribution of the patrons in the restaurant.

\(\left|\begin{array}{c|c|c|c}&$Male&$Female&$Total\\---&---&---&---\\$Under 10 years old&6&5&11\\10-55&13&22&35\\$Over 55 years old&5&9&14\\---&---&---&---\\$Total&24&36&60\end{array}\right|\)

(a)P(Female or under 10)

These are not mutually exclusive events, therefore:

\(P$(Female or under 10)=P(Female)+P(Under 10)-P(Female and Under 10)\\=\dfrac{36}{60}+ \dfrac{11}{60}-\dfrac{5}{60}\\=\dfrac{42}{60}\\\\=0.7\)

(b) P(Under 10 or over 55)

These are mutually exclusive events, therefore:

\(P$(Under 10 or over 55)=P(Under 10)+P(Over 55)\\=\dfrac{11}{60}+ \dfrac{14}{60}\\=\dfrac{25}{60}\\\\=0.42\)

When the sides are the same then the triangles are congruent.

Identical lines through the sides of a triangle indicate that the sides are congruent.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

Congruent triangles are two triangles that are identical in terms of size and shape. One of two congruent triangles remains congruent even if it is rotated, flipped, or turned. Two triangles must have the same sides in order for them to have the same angles and, as a result, to be congruent.

Thus, identical lines through the sides of a triangle indicate that the sides are congruent.

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We can use the truth table for the expression as shown below:

A B C A+BC0000101000111101111

A truth table is a table showing the inputs and outputs of a logical circuit or system.

It provides an outline of all possible outcomes of an experiment and is commonly used in data processing, computer science, and electrical engineering.

The table usually contains two columns: one for inputs and another for outputs.

In the case of the expression (A + BC) (A . BC), the truth table is shown below:

ABCA.BC(A + BC) (A . BC)0000000100000110000110100011110111001011111100111100111The next step is to simplify the expression.

We can use the distributive law to simplify the expression, as shown below:

A + BC + A.BC = A (1 + BC) + BC

= A + BC

The simplified expression is A + BC.

The final step is to draw the circuit diagram and the truth table for the simplified expression.

The circuit diagram is shown below:

We can now use the truth table for the simplified expression as shown below:

A B C A+BC0000101000111101111

The circuit diagram and truth table for the simplified expression are shown above.

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Answer:

Hello! answer: y = 76

Because there vertical angles they Will have the same measure therefore y = 76 Hope that helps!

The combined area of dark pieces is 253.5 in².

First, Area of 5 light pieces

= length x width

= 3 3/4 x 39

= 15/4 x 39

= 146.25 in²

Now, Area of board

= L x W

= 29 x 39

= 1131 in²

Thus, the combined area of dark pieces

= 1131 - 146.25 x 6

= 253.5 in²

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Answer:

I believe it's either equation one or three. hope that helps :)

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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Answer:

y intercept: (0,-13)

x intercept: (13/5, 0)

Step-by-step explanation:

To find the y intercept, x has to equal zero. So, plug it in. The equation becomes y=-13.

Since x is zero, the point becomes (0,-13)

To find the x intercpet, y has to equal zero. So, plug it in. The equation becomes 0=5x-13.

move 13 to the other side

13=5x

divide by 5

13/5=x

Since y is zero, the point becomes (13/5,0)

hope this helps!

Answer:

y = 5x - 4

for the x values..

y = -4

y = 1

y = 6

Step-by-step explanation:

Answer: 4sr+17r−2s4+17−2

Step-by-step explanation: simplify 18r - 3s-r + 4s1r+s

then multiply by one and get 18r-3s-r+4sr+s.

then combine like terms and get 17r-3s-r+4sr+s.

combine like terms again and end up with 17r-2s+4sr

you then want to rearrange the terms to 4sr+17r-2s

and you have your answer .

No, it is not safe to assume that the sampling distribution of the sample means is about normal given the sample size.

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Answer: x³-4x²-2x-4

Tips:

Bring down top values, then multiply by the outside value, then put it under the next value, add, and repeat