Question 2 of 10 Which of the following is equal to the fraction below? (5/8)

After answering the presented question using a z-score table, we can conclude that

P(z > -0.84)  = 0.7995

P(z < 1.89) = 0.9693

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails).

Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

We can use a z-score table to determine the likelihood of a standard normal random variable having values above or below a given z-score.

We can find P(z > -0.84) by looking up -0.84 in the z-score table and subtracting it from 1.

The result for -0.84 is 0.2005, which means:

P(z > -0.84) = 1 - 0.2005 = 0.7995

As a result, the likelihood of a standard normal random variable exceeding -0.84 is around 0.7995.

We can look up the value for 1.89 in the z-score table to determine P(z 1.89).

The result for 1.89 is 0.9693, which means:

P(z < 1.89) = 0.9693

As a result, the likelihood of a standard normal random variable being less than 1.89 is roughly 0.9693.

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Answer:

--------------------------

Multiply the first equation by 2 and the second equation by 5

Add up the equations

Answer:

x = 7

Step-by-step explanation:

Given system of equations:

\(\begin{cases}2x+5y=-1\\3x-2y=27\end{cases}\)

Multiply the first equation by 2:

\(\implies 2(2x+5y)=2(-1)\)

\(\implies 4x+10y=-2\)

Multiply the second equation by 5:

\(\implies 5(3x-2y)=5(27)\)

\(\implies 15x-10y=135\)

Add the two equations to eliminate the term in y:

\(\begin{array}{crcccl}& 4x & + & 10y & = & \:-2\\+ & (15x & - & 10y & = & 135)\\\cline{2-6} & 19x & & & = & 133\\\cline{2-6}\end{array}\)

Solve the equation for x:

\(\implies 19x=133\)

\(\implies \dfrac{19x}{19}=\dfrac{133}{19}\)

\(\implies x=7\)

Answer:

d=150 when t=3

Step-by-step explanation:

First you would need to find what d equals when t=1

100 ÷ 2 =50

d=50 when t=1

Then you need to find the total

100 + 50 = 150

d=150 when t=3

If the numbers 6, 8, and 10 are each multiplied by the same natural number, the resulting numbers are Pythagorean triples as well.

To prove that if the numbers 6, 8, and 10 are each multiplied by the same natural number, the resulting numbers are Pythagorean triples, we need to show that the squared sum of the two smaller numbers is equal to the squared value of the largest number.

Let's assume the natural number multiplier is represented by 'n'.

We will multiply each of the given numbers by 'n' to obtain the new numbers: 6n, 8n, and 10n.

Now, let's calculate the squared sum of the two smaller numbers (6n and 8n) and compare it to the squared value of the largest number (10n).

Squared sum of the two smaller numbers:

(6n)^2 + (8n)^2 = 36n^2 + 64n^2 = 100n^2

Squared value of the largest number:

(10n)^2 = 100n^2

We can see that the squared sum of the two smaller numbers (36n^2 + 64n^2 = 100n^2) is equal to the squared value of the largest number (100n^2).

Therefore, the resulting numbers, 6n, 8n, and 10n, form a Pythagorean triple.

This result holds true for any natural number 'n'. Multiplying the numbers 6, 8, and 10 by the same natural number 'n' will always yield a Pythagorean triple.

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(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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True. Empirical research involves using observation and experience to gather data and test hypotheses. This process is primarily logical, as it involves reasoning and making sense of the data. While mathematical tools may be used in some aspects of empirical research, they are not the foundation of the process.

True. Empirical research is primarily a logical operation rather than a mathematical one. Empirical research involves observation and gathering of data through direct experience, experiments, or measurements and hypotheses, which requires logical reasoning and analysis to draw conclusions. While mathematical operations and calculations can be a part of the empirical research process, they are not the main focus. The primary focus is on using logic to interpret the collected data and determine the validity of the results.

By quantifying the evidence or understanding the evidence in a qualitative way, researchers can answer empirical questions that need to be articulated and answered with the data collected (often called data). Research designs vary by field and research question. Many researchers, especially in the social sciences and education, have provided good and varied observation models to better answer questions that cannot be studied in the laboratory.

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-8 = -7 + X

- 8 + 7 = X (Adding 7 to both sides of the equation)

-1 =x (Subtracting)

The answer is x=-1.

the answer of -8 = -7 +Xx is x= -1

Answer: what are the questions

Step-by-step explanation:

i dont know  what they are

Answer:

Aids Guilt Memorial Project

Answer:

C. The area of the blue circle is equal to the sum of areas of green square and black circle.

Step-by-step explanation:

The area of a circle is the circumference of the circle measured with its diameter. In the given scenario the area of the blue circle is greater than the area of black circle. This is because of the difference in diameter of the two circles. The area of green square plus the area of black circle equals the blue circle.

Answer:

sqrt 23,  180%, 1 2/7, (sqrt49)/7, pi-5

Step-by-step explanation:

sqrt 23 is between the integers 4 and 5 and closer to 5 and we can use these two reference points to base off the rest of our numbers

180% is essentially 180/100 which again is equal to 1.8 and is far less than sqrt 23s rough estimation of 4

1 2/7 is roughly 1.3 when they are made into decimal form and so that is rounded up and is closer to something around 1.28 but for our purposes, we shouldn't need to use this and 1.3 is just an easier number to work with.

sqrt49 is essentially a question asking what times itself becomes 49. That is 7 and 7/7 is just 1.

pi - 5 is like asking what is 3.14159 -5 and we dont even need to use this complex decimal. We can turn it to 3.5 rounding far up and still get a negative number which is far less than any other number on the list

2x-3=7

The answer would be 5.

Answer:

x=5

Step-by-step explanation:

2x−3=7

Add 3 to both sides.

2x=7+3

Add 7 and 3 to get 10.

2x=10

Divide both sides by 2.

x=10/2

Divide 10 by 2 to get 5.

x=5

Answer: 39/100 and percentage is 39%

Step-by-step explanation:

The height of Jane's shadow who is 5.9 feet tall is appoximately 6.3 feet

Given that, a tree 54 feet tall casts a shadow 58 feet long and Jane is 5.9 feet tall.

To find the height of Jane's shadow, we can use proportions and ratios.

Hence:

(Height of the tree) : (Length of the tree's shadow) = (Height of Jane) : (Length of Jane's shadow)

Plug in:

Height of the tree = 54

Length of the tree's shadow = 58

Height of Jane = 5.9

Let Length of Jane's shadow = x

54 feet : 58 feet = 5.9 feet : x

54/58 = 5.9/x

Cross multiply:

54 × x = 58 × 5.9

54x = 342.2

x = 342.2/54

x = 6.3 feet

Therefore, the measure of her shadow is approximately 6.3 feet.

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The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

V = x³ + 11x² + 12x

Step-by-step explanation:

calculate the volume (V) using the formula

V = lwh ( l is the length, w the width and h the height )

here l = 2x + 3 , w = x , h = x + 4 , then

V = (2x + 3)(x)(x + 4)

  = x(2x + 3)(x + 4) ← expand the factors using FOIL

  = x(2x² + 8x + 3x + 12)

  = x(2x² + 11x + 12) ← distribute terms in parenthesis by x

  = 2x³ + 11x² + 12x

Answer:

It drove 30.08 kilometers in an hour.

Step-by-step explanation:

This question is solved by proportions, using a rule of three.

In this question:

177 kilometers in 5*60 + 53 = 353 minutes.

How many kilometers in 1 hour = 60 minutes?

177 km - 353 min

x km - 60 min

\(353x = 60*177\)

\(x = \frac{60*177}{353}\)

\(x = 30.08\)

It drove 30.08 kilometers in an hour.

it A

Step-by-step explanation:

We can say with 90% confidence that the true mean GPA of all accounting students at this university lies between 2.7107 and 3.0493.

We are given:

Sample size n = 21

Sample mean X = 2.88

Sample standard deviation s = 0.16

Confidence level = 90% or α = 0.10 (since α = 1 - confidence level)

Since the sample size is small and population standard deviation is unknown, we will use a t-distribution to construct the confidence interval.

The formula for the confidence interval is given by:

X ± t(α/2, n-1) * s/√n

where t(α/2, n-1) is the t-score with (n-1) degrees of freedom, corresponding to the upper α/2 percentage point of the t-distribution.

Using a t-table with (n-1) = 20 degrees of freedom and α/2 = 0.05, we find the t-score to be 1.725.

Plugging in the values, we get:

2.88 ± 1.725 * 0.16/√21

= (2.7107, 3.0493)

Therefore, we can say with 90% confidence that the true mean GPA of all accounting students at this university lies between 2.7107 and 3.0493.

Note: The confidence interval can also be written as [2.71, 3.05] rounding to two decimal places.

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Answer:

100-2=98

2250/100x98=2450

100-3 = 97

2450/100 X 97= 2376.50

Answer:

\(a_n=4n-11\)

Step-by-step explanation:

The common difference is \(d=4\) with the first term being \(a_1=-7\), so we can generate an explicit formula for this arithmetic sequence:

\(a_n=a_1+(n-1)d\\a_n=-7+(n-1)(4)\\a_n=-7+4n-4\\a_n=4n-11\)

here ...

let us suppose breadth of the room be x.

then, length = 2x

now ,the cost of plastering the floor is RS 1080 at rate of RS 15 per ...

hence

the area of floor{length *breadth} =1080/15

x*2x=72

or,2x^2=72

or,x=√(72/2)

hence, the value of x= 6m

(ie. breadth {x}=6. &. length {2x}=12)

again....

we have ,

volume of the room (length *breadth*height)is 396m^3

12*6*height=396

72*height=396

height=396/72

hence , height=5.5

we know,

the area of 4 walls = 2( length+breadth)*height

=2(12+6)*5.5

=198

hence the cost of plastering 4 walls at the rate of RS 20 per SQ meter = 198*20=RS 3960

The arrow point to the left for the inequality x < 17.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that inequality is x < 17. When the inequality is plotted on the graph it will highlight the values that are less than the number 17. The graph of the inequality is attached with the answer below.

Hence, the arrow for the given inequality will point to the left side.

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As the sample size (n) increases, the power of the statistical test also increases.

The power of a statistical test measures the ability of the test to detect a true effect or reject a false null hypothesis. In this case, the investigator states that the power of his test at a significance level of 1% is 0.87. If the sample size (n) increases, the power of the test increases.

Increasing the sample size generally leads to an increase in the power of a statistical test. This is because a larger sample size provides more information and reduces the variability in the data. With a larger sample size, the test has a greater chance of detecting a true effect and rejecting the null hypothesis when it is false. Consequently, the power of the test increases.

In summary, as the sample size (n) increases, the power of the statistical test also increases. This is because a larger sample size enhances the test's ability to detect true effects and reject false null hypotheses, resulting in higher statistical power. Therefore, in this scenario, increasing the sample size would lead to an increase in the power of the test.

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Answer:

is 14.14

Step-by-step explanation:

These are the following dimensions:

1

.

base

=

5

f

t

2

.

hypotenuse

=

15

f

t

3

.

height

=

?

f

t

To solve for the height, use the Pythagorean Theorem, which is:

a

2

+

b

2

=

c

2

where:

a

=

height

b

=

base

c

=

hypotenuse

Substitute your known values into the equation to find the height:

a

2

+

b

2

=

c

2

a

2

+

(

5

)

2

=

(

15

)

2

a

2

+

25

=

225

a

2

=

200

a

=

√

200

a

=

10

√

2

⇒

simplify the radical

a

≈

14.14

f

t

∴

, the ladder goes approximately  

14.14

f

t

up the building.

Answer:

The answer is 7

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

Because this shape is a parallelogram, the line segment measuring 6x must be equal to the line segment on the other side of E, which measures 144 units. 144 ÷ 6 = 24

To find the constants m and b in the linear function f(x) = mx + b, we can use the given conditions f(7) = 9 and a slope of -3.

The value of f(7) represents the y-coordinate of the point on the line when x = 7. So, substituting x = 7 into the equation, we get 9 = 7m + b.

The slope of a linear function is given by the coefficient of x, which in this case is -3. So, we have m = -3.

Now, we can substitute the value of m into the equation obtained from f(7). We get 9 = 7(-3) + b, which simplifies to 9 = -21 + b.

Solving for b, we find b = 30.

Therefore, the constants for the linear function f(x) = mx + b that satisfy the given conditions are m = -3 and b = 30.

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