Given a standardized normal distribution​ (with a mean of 0 and a standard deviation of​ 1), determine the following probabilities.
a. ​P(Z >1.06​) b. ​P(Z <-0.29)
c.P(-1.96 d.What is the value of Z if only 30.85% of all possible​ Z-values are​ larger?

71.2 was the mean of dr. ringo star's biology final exam when z-score of 1.5 .

What does "z-score" mean?

X - μ/σ = Z

85 - μ/9.2 = 1.5

μ = 85 - ( 1.5 * 9.2 )

μ = 71.2

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To find the value of x + 2 that ensures the given model is a valid probability model, we need to check if the given conditions for a probability model are satisfied:

1. The sum of all probabilities should be equal to 1.

2. Each probability should be between 0 and 1.

Let's check these conditions for the given model. P(x) = x! for x = 0, 1, 2, …Here, x! denotes the factorial of x. So, P(x) is the factorial of x divided by itself multiplied by all smaller positive integers than x. Therefore, P(x) is always positive. Also, P(0) = 1/1 = 1.

Hence, the probability P(x) satisfies the second condition. Now, let's find the sum of all probabilities.

P(0) + P(1) + P(2) + … = 1/1 + 1/1 + 2/2 + 6/6 + 24/24 + …= 1 + 1 + 1 + 1 + 1 + …This is an infinite series of 1s. The sum of infinite 1s is infinite, and not equal to 1. Therefore, the sum of all probabilities is not equal to 1. Hence, the given model is not a valid probability model. To make the given model a valid probability model, we need to modify the probabilities such that they satisfy both the conditions.

We can modify P(x) to P(x) = x! / (x + 2)! for x = 0, 1, 2, …Now, let's check the conditions again. P(x) = x! / (x + 2)! is always positive.

Also, P(0) = 0! / 2! = 1/2.

Hence, the probability P(x) satisfies the second condition. Now, let's find the sum of all probabilities.

P(0) + P(1) + P(2) + … = 1/2 + 1/6 + 1/24 + …= ∑ (x = 0 to infinity) x! / (x + 2)!= ∑ (x = 0 to infinity) 1 / [(x + 1)(x + 2)]= ∑ (x = 0 to infinity) [1 / (x + 1) - 1 / (x + 2)]= [1/1 - 1/2] + [1/2 - 1/3] + [1/3 - 1/4] + …= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...= 1

This is a converging infinite series. The sum of the series is 1. Therefore, the given modified model is a valid probability model. Now, we need to find the value of x + 2 that ensures the modified model is a valid probability model.

P(x) = x! / (x + 2)! => P(x) = 1 / [(x + 1)(x + 2)]

For P(x) to be valid, it should be positive. So, [(x + 1)(x + 2)] should be positive. This means x should be greater than -2. Hence, the smallest value of x is -1. Therefore, the value of x + 2 is 1.

The modified model is P(x) = x! / (x + 2)! for x = -1, 0, 1, 2, …The probability distribution table is: x P(x)-1 1/2 0 1/6 1 1/3 2 1/12...The value of x + 2 that ensures the modified model is a valid probability model is 1.

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Difference of -148 and 27 is -175.

Correct option is C.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-).

It is used to find difference of numbers.

Given numbers,

-148 and 27

Difference of numbers

= -148 - 27

= -175

Hence -175 is difference of the numbers -148 and 27.

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Answer:-175

Step-by-step explanation:

x - 12 = 18 is the the equation that represents ."Twelve less than a number, ×, is 18."

given the number is x

the equation of the given statement

x - 12 = 18

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Probability is a fundamental concept in statistics and is used to make predictions, estimate risks, and make decisions in various fields such as finance, sports, medicine, and engineering.

We have,

Probability is a measure of how likely an event is to occur.

It is a way of quantifying uncertainty and making predictions based on incomplete information.

For example,

When we toss a fair coin, there are two possible outcomes: heads or tails. Since the coin is fair, each outcome has an equal chance of occurring, so the probability of getting heads is 1/2 or 50%, and the probability of getting tails is also 1/2 or 50%.

Another example of probability is when we roll a six-sided die.

There are six possible outcomes, each of which has an equal chance of occurring.

Therefore, the probability of rolling a specific number, say 4, is 1/6 or approximately 17%.

Thus,

Probability is a fundamental concept in statistics and is used to make predictions, estimate risks, and make decisions in various fields such as finance, sports, medicine, and engineering.

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The critical value of t for constructing a 99% confidence interval with a sample size of 30 and a sample standard deviation of 0.05 is 2.7564.

A confidence interval is a range of values within which the population parameter is estimated to lie with a certain level of confidence. In this case, we are constructing a 99% confidence interval for the population mean. The critical value of t is used to determine the width of the confidence interval.

The formula for calculating the confidence interval for the population mean is:

Confidence interval = sample mean ± (critical value) * (standard deviation of the sample / square root of the sample size)

Given that the sample size is 30 (n = 30) and the standard deviation of the sample is 0.05 (S = 0.05), we need to find the critical value of t for a 99% confidence level. The critical value of t depends on the desired confidence level and the degrees of freedom, which is equal to n - 1 in this case (30 - 1 = 29). Looking up the critical value in a t-table or using statistical software, we find that the critical value of t for a 99% confidence level with 29 degrees of freedom is approximately 2.7564.

Therefore, the 99% confidence interval for the population mean would be calculated as follows: sample mean ± (2.7564) * (0.05 / √30). The final result would be a range of values within which we can be 99% confident that the true population mean lies.

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The sentences describing the ratio of small balls (S) to total balls (T) should be completed as follows:

There are 9 small balls for every 15 total balls.

There are 3 small balls for every 5 total balls.

What is ratio?

Ratio can be defined as a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

What is a proportion?

A proportion can be defined as an expression which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By critically observing the image (see attachment) and counting the number of balls, we have the following information:

Number of small balls, S = 9 small balls.

Total balls, T = 15 balls.

In this context, the ratio of small balls (S) to total balls (T) is given by:

S:T = 9:15 = 3:5.

In conclusion, we can infer and logically deduce that the sentences describing the ratio of small balls (S) to total balls (T) should be completed as follows:

There are 9 small balls for every 15 total balls.

There are 3 small balls for every 5 total balls.

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Answer:

The anwer is 1/2

\(P=N_Y/Total=3/6=1/2\)

Answer:

neither parallel nor perpendicular

if you need an explanation, put it in the comments :)

Answer:

F = FIRST TERM

S = SECOND TERM

L = LAST TERM

Step-by-step explanation:

1- (x+1)² = x²+2x+1

F = x²

S = 2x

L = 1

2- (x+2)² = x² + 4x + 4

F = x²

S = 4x

L = 4

3- (x+3)² = x² + 6x +9

F = x²

S= 6x

L= 9

4 (x+ y)² = x²+2xy +y²

F = x²

S = 2xy

L = y²

The best estimate for the total amount of money, d, after 25 days of the fund-raiser is $45.

To find the best estimate of the total amount of money, d, after 25 days, we can calculate the daily contributions and sum them up.

On the first day, the principal put $1.50 into the barrel.

On the second day, the collective body of students put in 20% more than the previous day, which is $1.50 + (20% of $1.50).

On the third day, they put in 20% more than the second day's contribution, and so on.

To calculate the total amount of money, we need to sum up the contributions for each day:

Total amount = $1.50 + ($1.50 + 20% of $1.50) + ($1.50 + 20% of $1.50 + 20% of ($1.50 + 20% of $1.50)) + ...

We can simplify this calculation by using a loop or a mathematical formula, but for a quick estimate, we can use the following approximation:

Each day's contribution is roughly 20% more than the previous day's contribution. So, we can assume that the average daily contribution is 20% more than $1.50.

Average daily contribution = $1.50 + (20% of $1.50)

= $1.50 + $0.30

= $1.80

Therefore, the best estimate of the total amount of money, d, after 25 days is:

d = 25 days × $1.80 per day

= $45

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The centroid of the region bounded by the curves y = 12x and y = √x is (72,1.88).

To find the centroid of the region bounded by the given curves y = 12x and y = √x, the following steps should be followed.

Step 1: Sketch the region bounded by the two curves to have an idea of what the region looks like.

Step 2: Determine the area of the region bounded by the two curves. The area A can be computed by evaluating the definite integral of the difference between the two functions. \(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx\]\)  We solve for this integral below.\(\[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = 64 - 1728 + \frac{2}{3}\sqrt{6}\] \[\int\limits_{0}^{144} (\sqrt{x}-12x)dx = -1663.30\]\)

Step 3: To find the centroid of the region, we need to determine the x and y coordinates of the centroid. The x-coordinate of the centroid is given by the formula below.

\(\[x = \frac{1}{A}\int\limits_{a}^{b} \frac{1}{2}(y_1^2-y_2^2)dx\]\)

where A is the area of the region, and y1 and y2 are the upper and lower functions, respectively. Substituting values, we obtain

\(\[x = \frac{1}{-1663.30}\int\limits_{0}^{144} \frac{1}{2}((\sqrt{x})^2-(12x)^2)dx\]  \[x = 72\]\)

 The y-coordinate of the centroid is given by the formula below.

\(\[y = \frac{1}{2A}\int\limits_{a}^{b}(y_1+y_2)\sqrt{(y_1-y_2)^2+4dx}\]\)

 Substituting values, we obtain \(\[y = \frac{1}{2(-1663.30)}\int\limits_{0}^{144}(12x+\sqrt{x})\sqrt{(\sqrt{x}-12x)^2+4dx}\]  \[y = 1.88\]\)

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Since the interval for t is 0 ≤ t ≤ π/4, the correct bounds for the integral are from 0 to π/4, the length of the curve is approximately 0.3763

The length of a curve can be determined using the arc length formula, which is given by the integral of the magnitude of the derivative of the vector function over the given interval.

In this case, the vector function is r(t) = (sin t, cos t, tan t), and we want to find the length of the curve for 0 ≤ t ≤ π/4.

The derivative of r(t) is dr/dt = (cos t, -sin t, sec² t), and the magnitude of the derivative is |dr/dt| = √(cos² t + sin² t + sec⁴ t).

To find the length of the curve, we need to integrate |dr/dt| over the interval 0 to π/4:

Length = ∫[0, π/4] √(cos² t + sin² t + sec⁴ t) dt

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Answer:

D. y= 0.3x2

Step-by-step explanation:

In quadratic functions, the value of a affects the wideness of the graph. The smaller the absolute value of a, the wider the graph. In these choices, 1/3 and 0.3 are the smallest. To understand which is smaller convert both to decimals; 1/3 is 0.3333 repeating. Therefore, 0.3 is slightly smaller and wider.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

cylinders

h = 9 in

radius = r (in )

V = volume (in ³ )

Step 02:

a.

volume of a cylinder:

V = π r ² h

radius = 1 in

V1 = π (1 in)² * 9 in = 9 π in³

radius = 2 in

V1 = π (2 in)² * 9 in = 36 π in³

radius = 3 in

V1 = π (3 in)² * 9 in = 243 π in³

Table

radius Volume

row 1 1 9 π

row 2 2 36 π

row 3 3 243 π

Step 03:

b. Is there a linear relationship between the radius and the volume of these cylinders?

Yes, because the greater the radius, the greater the volume.

Step 04:

c.

cylinder pitcher:

h = 9 in

r = r

V = π r ² h

Vcp = π r ² 9 in = 9 π r ² in ³

cylinder:

h = 9 in

r = 2r

V = π r ² h

Vc = π (2r) ² 9 in = 36 π r ² in ³

# pitchers = Vc / Vcp

= 36 π r ² in ³ / 9 π r ² in ³

= 4

It can fill 4 pitchers

That is the full solution.

The stretch of an exponential decay function is y = 2(1/5)ˣ

From the question, we have the following parameters that can be used in our computation:

The list of exponential functions

An exponential function is represented as

y = abˣ

Where

In this case, the exponential function is a decay function

This means that

The value of b is less than 1

An example of this is, from the list of option is

y = 2(1/5)ˣ

Hence, the exponential decay function is y = 2(1/5)ˣ

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Complete question

Which is a stretch of an exponential decay function?

Of(x) = -(5)ˣ

Of(x) = 5(2)ˣ

O fix) = 2(1/5)ˣ

Answer: 1.465 : 1

Step-by-step explanation:

Slope of the line segment:

m = (5 - 3)/(4 - (-2)) = 2/6 = 1/3

The equation of the line which the line segment lies on is found by:

(y - 3)/(x - (-2)) = 1/3

(y - 3)/(x + 2) = 1/3

(y - 3)/(x + 2) * (x + 2) = 1/3 * (x + 2)

y - 3 = (x + 2)/3 = 1/3 x + 2/3

y = 1/3 x + 11/3

The equation of the line given:

4x + 5y = 21

5y = -4x + 21

y = -4/5 * x + 21/5

Set them equal to each other and solve for x to find their intersection:

1/3 x + 11/3 = -4/5 * x + 21/5

15(1/3 x + 11/3) = 15(-4/5 * x + 21/5)

5 x + 55 = -12 x + 63

17x = 8

x = 8/17

y = 1/3 (8/17) + 11/3 = 8/51 + 181/51 = 189/51

Point (8/17, 189/51)

Distance from right end of segment to intersection:

s = SQRT((4 - 8/17)^2 + (5 - 189/51)^2) = SQRT((60/17)^2 + (66/51)^2) = 3.759

length of segment = SQRT((5–3)^2 + (4 - (-2))^2) = SQRT(4 + 36) = SQRT(40) = 6.324

Distance from the left end to interseciton:

6.324 - 3.759 = 2.555

Ratio of right end to left end:

3.759/2.565 = 1.465

Answer:

1 is 25% of 4, so 75% decrease

Step-by-step explanation:

The total perimeter of the shape = 64.62 cm

The total area of the shape = 187.4cm²

Here,

we have,

in the given figure,

we get two shapes.

1st part:

it is a square with side = 11.6cm

so, perimeter = 4 * 11.6 = 46.4 cm

and, area = 11.6 * 11.6 = 134.56 cm²

2nd part:

it is a semicircle with diameter = 11.6 cm

so, perimeter = 1/2 × π × 11.6 = 18.22 cm

and, area = 1/2 × π × 11.6/2× 11.6/2  = 52.84 cm²

so, we get,

The total perimeter of the shape = 64.62 cm

The total area of the shape = 187.4cm²

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Using the normal distribution, it is found that the probability that the association would observe 654 or less people who drink milk in the sample is of 0%.

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For the binomial distribution, the parameters are given as follows:

n = 800, p = 0.87.

Hence, the mean and the standard deviation of the approximation are given by:

The probability that the association would observe 654 or less people who drink milk in the sample, using continuity correction, is \(P(X \leq 654.5)\), which is the p-value of Z when X = 654.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{654.5 - 696}{9.5121}\)

Z = -4.36

Z = -4.36 has a p-value of 0.

0% probability that the association would observe 654 or less people who drink milk in the sample.

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Answer:

6

Step-by-step explanation:

If you push two triangle tables together you just multiply 3*2

The probability of an even number being spun all 3 times is 8/125.

Given that a circular spinner is divided into 5 equal parts.

We need to find the probability that an even number is spun all 3 times.

To find out the probability of an event, we need to use the following formula;

P(event) = Number of favorable outcomes/Total number of outcomes

So, let us first determine the total number of outcomes.

There are 5 equally likely outcomes on the spinner.

Since we spun the spinner 3 times, the total number of outcomes will be:

Total number of outcomes = 5 × 5 × 5 = 125

Now, we will find out the number of favorable outcomes.

To get an even number, we can only spin the number 2 or 4.

Therefore, the total number of favorable outcomes will be:

Number of favorable outcomes = 2 × 2 × 2 = 8

Hence, the probability of an even number being spun all 3 times is:

P(an even number is spun all 3 times)

= Number of favorable outcomes/Total number of outcomes

= 8/125

Therefore, the probability of an even number being spun all 3 times is 8/125.

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we have, the opposite angles at the vertex have the same measure, therefore:

then,

and we have the sum of all 4 angles is equal to 360 and as I said before, the opposite angles by the vertex have equal measure, so:

answer: x = 2 and z = 104

Answer:

6 roll for 8.89

Step-by-step explanation:

4roll for 6.79 you pay 1.60 per roll and 6 roll for 8.89 you pay roughly 1.40 per roll

Answer:

the gym that has 150, will take 2 months and the gym that has 50 will take 6 months

first gym:

150

300

second gym:

50

100

150

200

250

300

The answer is x = 1, assuming that the space is meant to be an equal sign.

Answer:

The slope, or m, is equal to 1/2.

Step-by-step explanation:

m = y2 - y1/x2 - x1

m = 2 - 4/3 - 7

m = -2/-4

m = 1/2

Answer:

15.00

Step-by-step explanation:

8+0.75+0.75+1.50+1.50+1.50=

The mass of the wire is found to be 40π√2 units.

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = \(\int_a^b \delta\left|r^{\prime}(t)\right| d t\)

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

\(\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}\)

Further simplifying;

\(\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}\)

Now, use integration to find the mass of the wire;

       \(\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}\)

Therefore, the mass of the wire is estimated as 40π√2 units.

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The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5