Nine more than twice a number is less than negative eleven. Find all numbers that make the statement true

The probability that at least one pair of people have the same birthday, with 30 people in a classroom is approximately 0.7063.

To solve this problem, we can use the concept of the complement of an event. The complement of the event "at least one pair of people have the same birthday" is the event "no pair of people have the same birthday." So, we can find the probability of this complement event and subtract it from 1 to get the probability of the original event.

The probability that the first person has a unique birthday is 1, since there are no other people in the room yet. The probability that the second person also has a unique birthday is (364/365), since there are 364 remaining days in the year that they could be born on.

Similarly, the probability that the third person has a unique birthday is (363/365), and so on, down to the 30th person, whose probability of having a unique birthday is (336/365).

To find the probability that no pair of people have the same birthday, we can multiply these probabilities together:

P(no pair share a birthday) = 1 * (364/365) * (363/365) * ... * (336/365) ≈ 0.2937

Therefore, the probability that at least one pair of people have the same birthday is:

P(at least one pair share a birthday) = 1 - P(no pair share a birthday) ≈ 1 - 0.2937 = 0.7063

So the probability that at least one pair of people have the same birthday is approximately 0.7063, which is quite high. This is known as the birthday problem or birthday paradox.

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Answer: E

Step-by-step explanation:

The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.

Answer:

Not equal and Congruent should be your answers

The blood platelet count is an illustration of normal distribution Approximately 95% of the data lies within 2 standard deviations of the mean. There are approximately 99.7% of women with platelet count between 65.2 and 431.8

The given parameters are:

μ = 248.5

[tex]\sigma = 61.1\\[/tex]

(a) The percentage within 2 standard deviation of mean or between 126.3 and 370.7

Start by calculating the z-score, when x = 126.3 and x = 370.7

[tex]Z = \frac{(x-u)}{\sigma}[/tex]

So, we have:

x = -2

Also,

x = 2

The empirical rule states that:

Approximately 95% of the data lies within 2 standard deviations of the mean.

Hence, there are approximately 95% of women with platelet count within 2 standard deviations of the mean.

(b) The percentage with platelet count between 65.2 and 431.8

Start by calculating the z-score, when x = 65.2 and x = 431.8

So, we have:

Z =-3

Also:

Z = 3

The empirical rule states that:

Approximately 99.7% of the data lies within 3 standard deviations of the mean.

Hence, there are approximately 99.7% of women with platelet count between 65.2 and 431.8

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Answer: Look below :)

Step-by-step explanation:

Hello again Sarah!

a. the dashed line indicated our answer will use > or <

furthermore, we can see two points, (0,2) and (1,6) on the graph.

So the slope is: 4/1 = 4

and the y intercept can be visually seen as 2

Since the shaded part is to the right, we will use <

The final equation is: y < 4x + 2

I wont show working for the others, but its pretty similar:

b. [tex]y \geq 0.5x - 3[/tex]

c. y < 0.75x - 2

[tex]above \: the \: line[/tex]

The sampling technique best described here is systematic sampling. Systematic sampling is a type of probability sampling in which the elements in the population are selected in a systematic way

This sampling technique is used when the population size is too large to survey the entire population. In this example, the population size is 300 passengers and the sampling interval is determined by dividing the population size by the sample size. For example, if the sample size is 30, the sampling interval is[tex]10 (300/30=10).[/tex] This means that every 10th passenger is randomly selected for the survey. The selection starts with a randomly chosen passenger and then the ninth passenger after that is selected and so on. The formula for Systematic sampling is n = N/n, where N is the population size and n is the sample size.

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The function [tex]f(x) = 4x^3 - 4[/tex] is a polynomial function. It takes an input value x and returns an output value f(x) based on the expression [tex]4x^3 - 4.[/tex]So the value of f(-1/2) is -4.5.

When we evaluate f(-1/2), we substitute -1/2 for x in the expression for f(x). This gives us:

[tex]f(-1/2) = 4(-1/2)^3 - 4[/tex]

The expression inside the parentheses, [tex](-1/2)^3,\\[/tex] is the cube of -1/2. To simplify this expression, we need to first raise -1/2 to the power of 3:

[tex](-1/2)^3 = (-1/2) * (-1/2) * (-1/2) = -1/8[/tex]

Next, we substitute this value back into the expression for f(-1/2):

f(-1/2) = 4(-1/8) - 4

Now we can simplify the expression by multiplying 4 and -1/8:

f(-1/2) = -1/2 - 4

Finally, we subtract 4 from -1/2 to get the final answer:

f(-1/2) = -4.5

So the value of f(-1/2) is -4.5.

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Given the function f(x) = 4x^3 - 4, find the value of f(- 1/2)?

The length of the unknown side is 11.2ft

Using the Pythagorean theorem which states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

From the image shown,we have the parameters as;

Now, substitute the values, we have;

x² = 10² + 5²

Find the squares

x² = 100 + 25

Add the values

x ² = 125

Find the square root

x = 11.2 ft

Hence, the value is 11.2ft

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The area of the composite figure is equal to 254 m² square metres.

The composite figure can be observed to be a vertical rectangle, a square and an horizontal rectangle, so we shall calculate for the areas of the three figures and then add the result to get the total area of the composite figure as follows:

area of the vertical rectangle = 19 m × 7 m

area of the vertical rectangle = 133 m²

area of the square = 5 m × 5 m

area of the square = 25 m²

area of the horizontal rectangle = 16 m × 6 m

area of the horizontal rectangle = 96 m²

total area of the composite figure = 133 m² + 25 m² + 96 m²

total area of the composite figure = 254 m²

Therefore, the area of the composite figure is equal to 254 m² square metres.

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The measure of angle DBC is 60 degrees

Any triangle's three angles always sum to 180 degrees. Therefore, if you only have two angles available, add them up, and then take 180 away from the result.

The computation of the measure of angle ABC is shown below:

Given that

Angle ABC is 120 degrees

And, the measure of angle BAC is 60 degrees

So based on the above information

The  measure of angle  is

= Angle ABC - Angle ABD

= 120 degrees - 60 degrees

= 60 degrees

hence, the measure of angle DBC is 60 degrees

Q - Angle ABC is equal to 120 degrees. The measure of angle ABD is 60 degrees. What is the measure of angle DBC?

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The greater probability is the probability of winning through the use of regular defense.

If out of the 100 games that were reviewed, the defense games were 50 and the prevent defense games were 50 as well

Out of the regular 50, there are 38 wins and then 12 loses. Out of the prevent games, there 29 wins and 21 loses.

The probability to win by regular is 38 / 50 = 0.76

the probability to win by prevent defense is 29 / 50 = 0.58

0.76 is greater than 0.58 hence the decision would be to win the game by playing the regular defense.

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A football coach is trying to decide: When a team is ahead late in the game, which strategy is better?

Play the "regular" defense.

Play a "prevent" defense that guards against long gains but makes short gains easier.

The coach reviews the outcomes of 100 games.

Compare the probability of winning when playing regular defense with the probability of winning when playing prevents defense. Draw a conclusion based on your results.

Answer:

Step-by-step explanation:

6(x + 4)/5(x - 7) * 9(x - 7)/7(x + 4) =

Cancel the x + 4 and x - 7

54/35

Answer:

bro do u have a pic i will give u your points back but i need a pic to help

Step-by-step explanation:

The expression has 3 terms and 3 factors

The terms are the constant, the r term and the t term

The factors that are in the equation are 1500, 1 and 12

An exponential equation is an equation that involves an exponential function, which has the form f(x) = a^x, where "a" is a constant base and "x" is the exponent. Exponential equations are used to model phenomena that grow or decay at a constant relative rate. The solutions to exponential equations can be found by manipulating the equation algebraically to isolate the variable in the exponent, taking logarithms of both sides, or by using exponential rules such as the power rule or the product rule.

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The vector equation for a line segment that joins two points P and Q can be found by subtracting the position vectors of P and Q and representing the result as a vector from P.

The position vector of point P is given by [0, -4, 4] and the position vector of point Q is given by [1/2, 1/3, 1/4]. So, the direction vector of the line segment is found by subtracting the position vectors:

d = Q - P = [1/2, 1/3, 1/4] - [0, -4, 4] = [1/2, 5/3, -3/4]

The vector equation of the line segment can be written as:

r(t) = P + t * d = [0, -4, 4] + t * [1/2, 5/3, -3/4] = [t/2, -4 + 5t/3, 4 - 3t/4]

where t is a scalar parameter that varies from 0 to 1 to give the points on the line segment between P and Q.

The parametric equations of the line segment are:

x(t) = t/2

y(t) = -4 + 5t/3

z(t) = 4 - 3t/4

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Find a vector equation and parametric equations for the line segment that joins P to Q?

P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )

vector equation r(t)

parametric equations x(t), y(t), z(t)

If the scale factor of figure A to figure B is 3:8, the value of x is 9.

We are given Figure A and Figure B, along with their respective scale factors. To solve the problem, we must utilize the proportion rule. The ratio of the two figures is 3:8, so we can write the equation for proportion as follows -

3/8 = x/24

Applying the cross-multiplication rule, we get,

3 * 24 = 8 * x

Further solving for the value of x, we get,

x = (3 * 24) / 8

x = 9

Hence, the value of x is 9.

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The complete question is -

If the scale factor of figure A to figure B is 3:8 find the value of x.

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

According to graph, the value of p(x) = 8, when x = -2, as this point lies on the curve ~

Now, put the value of x in each of the choices provided to check if its equal to 8.

[tex]\qquad \sf  \dashrightarrow \: p( x) = (0.35) {}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = (0.35) {}^{ - 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = \dfrac{1}{(0.35 ){}^{2} } [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = \dfrac{1}{0.1225} [/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) = 8.1632[/tex]

[tex]\qquad \sf  \dashrightarrow \: p( - 2) \approx 8[/tex]

Since the value satisfy the first equation, the correct choice will be (A)

In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

In order to determine how much a normal family of four should budget for food in 9 years, we must take inflation into consideration.

To account for inflation, we can use the formula below to determine the future worth of the current food expenditures:

Future value = Present value * (1 + inflation rate)^n

where:

Present value = $897.20/month

Inflation rate = 4% per year

n = number of years

When we substitute the specified values, we get:

Future value = $897.20 * [tex](1 + 0.04)^9[/tex]

= $897.20 * 1.3981

= $1254.77 (to two decimal places in rounding)

Therefore, In 9 years, assuming a 4% annual inflation rate, a typical family of four should budget $1254.77 a month for food.

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The required mixed number of 26/9 is given as  2 8/9.

A mixed number is a number that consists of a whole number and a proper fraction. It is written in the form "a b/c", where "a" is the whole number, "b" is the numerator of the proper fraction, and "c" is the denominator of the proper fraction.

Here,
To rewrite 26/9 as a mixed number, we need to divide the numerator (26) by the denominator (9) and express the result as a whole number and a proper fraction.

26 ÷ 9 = 2 with a remainder of 8

The whole number part is 2, and the proper fraction part is 8/9, since 8 is the remainder and 9 is the denominator.

Therefore, 26/9 as a mixed number is 2 8/9.

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The area of the figure is given as follows:

100.56 mm².

The figure in this problem is composed as follows:

The areas for each region are given as follows:

Hence the total area is of:

48 + 14 + 20 + 6 + 12.56 = 100.56 mm².

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Answer: To determine the amount in Heidi's 401(k) account after 15 years, we need to calculate her total contribution each month and the interest earned on that contribution over the 15-year period.

First, let's calculate Heidi's contribution each month:

11% of $3,250 = $357.50

Next, let's calculate her employer's contribution each month:

6% of $3,250 = $195

Since Heidi's contribution is $357.50, and her employer matches her contribution up to 6% of her salary, her employer will contribute $195 each month.

So, Heidi's total contribution each month is $357.50 + $195 = $552.50

Next, we can use the formula for compound interest to calculate the balance in her 401(k) account after 15 years:

A = P * (1 + r/n)^(nt)

where:

A is the balance in the account after t years

P is the principal (initial deposit)

r is the interest rate

n is the number of times the interest is compounded in a year

t is the number of years

In this case, n = 12 (because interest is compounded monthly) and t = 15 (because the calculation is for 15 years). The principal P is $552.50 (Heidi's total contribution each month). The interest rate r is 6.25%.

Plugging in the values, we get:

A = $552.50 * (1 + 0.0625/12)^(12 * 15) = $552.50 * (1.00520833)^180

Using a calculator or spreadsheet software, we can calculate this value to be approximately $27,973.81.

So, the amount in Heidi's 401(k) account after 15 years, rounded to the nearest cent, is $27,973.81.

Step-by-step explanation:

The blank in the statement should be filled in with "ΔVYZ." which is proven by the definition of congruence.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.

Since S, T, and U are midpoints in ΔVYZ, it follows that:

ST is a median of ΔVYZ, meaning it bisects the side VZ into two equal parts.

TU is a median of ΔVYZ, meaning it bisects the side VY into two equal parts.

SV is a median of ΔVYZ, meaning it bisects the side YZ into two equal parts.

Using the definition of congruence, two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure. Since medians bisect their corresponding sides, it follows that all three pairs of corresponding sides in ΔYST, ΔTUZ, and ΔSVU are equal in length.

Furthermore, since the medians divide the triangle into two smaller triangles that are similar to the original triangle, it follows that the corresponding angles in ΔYST, ΔTUZ, and ΔSVU are equal in measure.

Therefore, ΔYST ≅ ΔTUZ ≅ ΔSVU ≅ ΔVYZ.

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The probability distribution of the random variable Y is 0.63, 0.25, 0.12. The mean of y is 0.4899 and the std deviation of y is 0.6999 and the mean of the selling price for the fat quarters sold by Company G is $4.4 and the std deviation for the same is $0.99

a) x = number of defects on a fat quarter

to be sold, X must be, X ≤ 2

y = number of defects on the sellable fat quarter,

now from the table, P [fat quarter being sellable]

=P [X ≤ 2]

=0.58 + 0.23 + 0.11

= 0.92

Therefore, P[y-0] = P[x=0Ix≤2]

=[tex]\frac{P[x=0][x < 2]}{P[x < 2]}[/tex]

=P[y=0] = 0.63

P[y=1] = P[x=1Ix≤2]

P[y=1] = [tex]\frac{0.23}{0.92}[/tex]

=0.25

P[y=2] = P[x=2Ix≤2]

P[y=2] = [tex]\frac{0.11}{0.92}[/tex]

= 0.12

y------------------0--------1---------2

probability---0.63----0.25----0.12

b)mean of y = E(y)

=0²×0.063+1×0.25+2×0.12

=0.25+0.24

=0.49

now we know that E(y²) = 0²×0.63+1²×0.25+2²×0.12

=0.25+0.48

=0.73

E(y²) - [E(y)]²

=0.73-0.49²

=0.4899

std deviation of y = 0.6999

c) now that we have E(G) = 0.40, √v(G) = 0.66

let s be selling price of fat quarters, then s = 5.00 - 1.50 × (G)

therefore = 5-1.5×0.4

=5-0.6

=$4.4 is the mean selling price.

now for the standard deviation price = v[5-1.5G]

=v(5)+1.5² v(G)

=0+2.25×0.66²

=v(s)= 0.9801

standard deviation of sp =√v(s)

=$0.99

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The sides of the right triangle are as follows:

x = 18 units

y = 15.6 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, let's find the sides of the right triangle using trigonometric ratios

tan 30° = opposite / adjacent

tan 30° = 9 / y

cross multiply

y = 9 / tan 30

y = 15.5884645362

y = 15.6 units

Let's find x

sin 30 = opposite / hypotenuse

sin 30° = 9 / x

x = 9 / 0.5

x = 18 units

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The answer to the given fill in the blanks is "Residual". in a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the Residual come from a normal distribution.

In linear regression, we make several assumptions about the relationship between the predictor variable and the response variable. One of these assumptions is that the residuals (the differences between the predicted values and the actual values) follow a normal distribution with a mean of zero and constant variance. To check this assumption, we can create a normal quantile plot of the residuals. A normal quantile plot is a graphical method that compares the distribution of the residuals to a normal distribution. If the residuals are normally distributed, the plot should follow a straight line. If the plot deviates from a straight line, it suggests that the residuals are not normally distributed. A non-normal distribution of residuals can have several implications, such as indicating the presence of outliers or influencing the accuracy of the model’s prediction. Therefore, checking for normality of residuals is a crucial step in evaluating the model's assumptions and determining whether the model is appropriate for the data.

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Answer:

In trapezium PQRS, AB is parallel to PS and PS is parallel to QR. Since we know the lengths of PA, AQ, and BR, we can calculate the length of SB as follows:

SB = PA + BR - AQ = 3 + 2.1 - 1.4 = 3.7 cm