Find the missing side

The null hypothesis is found as: H0: μ = 5.0

The  alternative hypothesis is found as: Ha: μ ≠ 5.0

The null hypothesis, denoted as H0, states that there is no significant difference between the mean GPA of students in the university and the reported value of 5.0 (out of 7.0).

In symbols, the null hypothesis can be represented as:
H0: μ = 5.0

The alternative hypothesis, denoted as Ha, states that there is a significant difference between the mean GPA of students in the university and the reported value of 5.0 (out of 7.0).

In words, the alternative hypothesis can be stated as:
Ha: μ ≠ 5.0

Where μ represents the population mean GPA. The alternative hypothesis indicates that there is a difference, either higher or lower, between the mean GPA of students in the university and the reported value.

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Answer:

D)

\(5 \times {10}^{ - 12} \)

Step-by-step explanation:

velocity(v) = distance/time

but distance =

\(3 \times {10}^{ - 4} \)

and velocity =

\(6 \times {10}^{7} \)

\(6 \times {10}^{7} = \frac{3 \times {10}^{ - 4} }{time} \)

\(time = \frac{3 \times {10}^{ - 4} }{6 \times {10}^{7} } \)

\(time = 5 \times {10}^{ - 12} \)

Point S represent the point which is opposite to the number -5 \(\frac{1}{2}\).

Number line is a straight line drawn horizontally where the integers are place in an equal intervals, usually 1 unit apart.

Number line includes negative integers, 0 and positive integers. 0 is located in the middle of the number line.

Midpoint of the number line is 0.

So the number opposite to a negative number must be at the positive side with the same magnitude.

-5 \(\frac{1}{2}\) is actually -5.5, which is located at the exact middle in between -5 and -6.

Then the opposite of the number -5 \(\frac{1}{2}\) is +5 \(\frac{1}{2}\).

+5 \(\frac{1}{2}\) lies in the positive side in between 5 and 6, which is represented by point S.

Hence point S represents the number opposite the number -5 \(\frac{1}{2}\).

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In public opinion polling, a sample as small as about 1,500 people can faithfully represent the "universe" of Americans.

The size of a sample needed for accurate representation of a larger population, known as the "universe," depends on several factors, including the desired level of confidence and margin of error. While larger sample sizes generally provide more precise estimates, they also require more resources and time. Statistically, a sample size of around 1,500 is often considered sufficient for accurately representing the opinions and characteristics of the larger American population.

The principle behind this is known as the "law of large numbers" and the "central limit theorem." These statistical concepts suggest that as the sample size increases, the sample's distribution becomes closer to the population's distribution. By using appropriate sampling techniques, such as random sampling, stratified sampling, or quota sampling, pollsters aim to select a diverse and representative subset of the population. Through statistical analysis, they can estimate the views and preferences of the larger population based on the responses collected from the sample. A well-designed and properly conducted survey with a sample size of around 1,500 individuals can provide reliable insights into the opinions and attitudes of Americans as a whole.

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If both populations are known to be normal, the size of the samples required to complete the inference procedures will depend on the desired level of confidence and the margin of error.

Generally, a larger sample size will result in a more accurate estimate of the population parameters. In order to determine the appropriate sample size, statistical calculations can be used based on the desired level of confidence and margin of error. These calculations take into account factors such as the standard deviation of the populations and the level of significance. Once the appropriate sample size is determined, the inference procedures can be completed using statistical tests such as t-tests or z-tests to compare the means or proportions of the two populations.
To determine the required sample sizes to complete the inference procedures when both populations are known to be normal, you need to follow these steps:

1. Identify the desired level of confidence (e.g., 95% or 99%) and the acceptable margin of error.
2. Determine the population variances (σ₁² and σ₂²) or use estimates of the variances from previous studies or pilot samples.
3. Utilize a formula for calculating the required sample sizes for the inference procedures. For comparing two means using independent samples, the formula is:
n₁ = n₂ = (Zα/2 * √(σ₁² + σ₂²) / Margin of Error)²
where n₁ and n₂ are the required sample sizes for the two populations, Zα/2 is the critical value for the desired level of confidence, and σ₁² and σ₂² are the variances of the two populations.
4. Calculate the sample sizes using the formula, rounding up to the nearest whole number if necessary.
By following these steps, you can determine the required sample sizes to complete the inference procedures when both populations are known to be normal.

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Journal articles and research reports are widely recognized as the most common types of secondary sources used in education. In the field of education, secondary sources play a crucial role in providing researchers and educators with valuable information and scholarly insights.

Among the various types of secondary sources, journal articles and research reports hold a prominent position. These sources are often peer-reviewed and published in reputable academic journals or research institutions. They provide detailed accounts of research studies, experiments, analyses, and findings conducted by experts in the field. Journal articles and research reports serve as reliable references for educators and researchers, offering up-to-date information and contributing to the advancement of knowledge in the education domain. Their prevalence and credibility make them highly valued and frequently consulted secondary sources in educational settings.

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Answer:

275 - 11=264

Step-by-step explanation:

The system of equations y = 10x - 5 and y = 10x - 5 has infinitely many solutions.

The system of equations you provided consists of two identical equations:

y = 10x - 5

y = 10x - 5

These equations represent the same line in a coordinate plane.

The equation y = 10x - 5 is a linear equation with a slope of 10 and a y-intercept of -5.

Since the two equations are identical, any point (x, y) that satisfies one equation will automatically satisfy the other.

Graphically, the equations represent a straight line that is completely overlapped.

This means that every point on the line is a solution to the system. In other words, there are infinitely many solutions to the system of equations.

To understand this concept, consider that the system of equations represents two different representations of the same relationship between x and y.

Both equations express that y is always equal to 10x - 5, so there is no unique solution to the system.

Instead, any value of x can be chosen, and the corresponding value of y will satisfy both equations.

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We can write 2 equations from the information given.

Let the amount invested in CD be "x" and the amount invested in bond be "y".

The total amount invested is $600,000. Thus, we can write,

The CD pays 2% (0.02) and the bond pays 8.5% (0.085). Total interest needed is $27,000. Thus, we can craft another equation,

Solving the first equation for "x", we can substitute it into the second equation and solve for "y" first. The steps are shown below:

Now, we can find "x",

Rounded to the nearest dollar, we write our answer >>>

Answer:

y-187.50= 1.50(x-125)

this is in point slope, but in slope intercept it would be y=1.50x+0

Step-by-step explanation:

Answer:

\(y-187.50=1.50(x-125)\)

Step-by-step explanation:

Slope = $1.50

\(x=125\)

\(y=$187.50\)

The given integral is∫ (π/2)0 Ie sin(2x) dxWe can integrate it by substitution method. Let u= 2x, then du/dx = 2 and dx = du/2Now substitute the value of x and dx in the integral:

∫ (π/2)0 Ie sin u/2 du/2

Now, integrate sin u/2,

we get, -2cos u/2 from 0 to π/2

=(-2(cosπ/4 - cos0)/2\

=-1/√2 - (-2(cos0)/2)

=-1/√2 + 1

Thus, the value of the integral is -I(e) [1/√2 - 1]

= I(e) (1-1/√2)

= I(e) (1/√2) (2 - √2)

Therefore, the value of the given integral is I(e) (1/√2) (2 - √2).

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Step-by-step explanation:

no solution as √x is a positive value

no solution as √x is a positive value

#1

If square root is over x only x=3²=9

#2

No solutions as -10 is <0

#3

If root is over x only then no solutions

#4

√x=0.1

x=0.01

The value of the machine 7 years from now.

To determine the value of the machine 7 years from now, we can use the formula for exponential decay:

V(t) = V(0) * e^(-kt)

Where:

V(t) is the value of the machine at time t

V(0) is the initial value of the machine

k is the decay constant

t is the time in years

We are given that the machine was purchased 9 years ago for $77,000, so V(0) = $77,000. We also know that the current value of the machine is $35,000, so V(t) = $35,000.

We can plug in these values to find the decay constant:

$35,000 = $77,000 * e^(-k * 9)

Dividing both sides by $77,000:

e^(-k * 9) = $35,000 / $77,000

Taking the natural logarithm of both sides:

-ln(e^(-k * 9)) = ln($35,000 / $77,000)

Simplifying:

9k = ln($35,000 / $77,000)

Now we can solve for k:

k = ln($35,000 / $77,000) / 9

Now we can use this value of k to find the value of the machine 7 years from now:

V(7) = $77,000 * e^(-k * 7)

Substituting the value of k we found:

V(7) = $77,000 * e^(-ln($35,000 / $77,000) / 9 * 7)

Calculating this expression will give us the value of the machine 7 years from now.

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The value of the machine 7 years from now, based on the exponential decay model, will be about $17960.33.

This question pertains to exponential decay. In mathematics, we often use the formula for exponential decay to analyze the decline of asset values over time. The formula is V(t) = V0 * e^(-kt), where V(t) is the value at time t, V0 is the initial value, k is the decay constant, and e is the base of natural logarithms (approximately equal to 2.71828).

Given that the initial value of the machine was $77000 and it is now worth $35000 after 9 years, we first solve for the decay constant k using the equation: 35000 = 77000 * e^(-9k). Solving for 'k', we find that k is approximated to 0.0613.

Now, to find the value of the machine 7 years from now (16 years total from the original purchase), we substitute these values into our formula, getting V(16) = 77000 * e^(-0.0613*16), which gives us a machine value of approx $17960.33, rounded to the nearest cent.

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The water level after 4 weeks will be 29.2 feet.

The water level of the lake will increase by 10% each week during the winter rainstorms. This means that each week, the water level will increase by 0.10 × 20 = <<0.10*20=2>>2 feet.

After the first week, the water level will be 20 + 2 = <<20+2=22>>22 feet.
After the second week, the water level will be 22 + 2 = <<22+2=24>>24 feet.
After the third week, the water level will be 24 + 2 = <<24+2=26>>26 feet.
And so on.

We can use the formula A = P(1 + r)^n to find the water level after n weeks, where A is the final amount, P is the initial amount, r is the rate of increase, and n is the number of weeks.

In this case, P = 20, r = 0.10, and n is the number of weeks.

So, the water level after n weeks will be:

A = 20(1 + 0.10)^n

We can plug in different values of n to find the water level after a certain number of weeks.

For example, to find the water level after 4 weeks, we can plug in n = 4:

A = 20(1 + 0.10)^4 = 29.2 feet

So, the water level after 4 weeks will be 29.2 feet.

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Answer:

130 degrees

Step-by-step explanation:

When two lines intersect, the opposite angles are equal, therefore, in this example, 7c+36 = 5c+40. We can find c using this equation.
7c+36 = 5c+40
7c-5c = 40-36
2c = 4
c = 4/2 therefore c=2

now that we know c is equal to 2, we can find out both of those angles.
therefore 5c+40 = (5*2)+40 = 10+40= 50
and 7c+36 = (7*2)+36 = 14 +36 = 50

now we know that those two angles add up to 100.

to find the sum of x and the angle opposite to x, subtract 100 from 360
360-100 = 260

since the angle opposite of x is equal to x, x+x = 260
2x=260
x=260/2 = 130

x is 130 degrees

Answer:

x = 130

Step-by-step explanation:

7c + 36 and 5c + 40 are vertically opposite angles and are congruent , so

7c + 36 = 5c + 40  ( subtract 5c from both sides )

2c + 36 = 40 ( subtract 36 from both sides )

2c = 4 ( divide both sides by 2 )

c = 2

Then

7c + 36 = 7(2) + 36 = 14 + 36 = 50

5c + 36 and x are a linear pair and sum to 180° , that is

50 + x = 180 ( subtract 50 from both sides )

x = 130

The interest rate would be = 8.9%

An interest rate is defined as the percentage of money that should be received by an individual for a particular period of time following an investment made.

The principal amount (p) = £9400

The simple interest = £11,907 - 9400 = 2507

The time given(T) = 3 years

The rate (R)= x%

The rate can be calculated from the formula of simple interest = P×T×R/100

make R the subject of formula;

R = 100×SI/P×T

R = 100× 2507/9400×3

R = 250700/28200

R = 8.89%

R= 8.9%

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Answer:

option c, x = 3

Step-by-step explanation:

Given:

Since both equal f(x) they must be equivalent as well,

\(3^{x} = 27\\\)

Apply exponent rule, 3 x 3 x 3 = 27

hence x = 3

The probability of picking the letter "I" from the box containing all the letters that form the word "Equilibrium" is 3/11 or approximately 0.273 (27.3%). This is calculated by dividing the number of desired outcomes (3 occurrences of "I") by the total number of possible outcomes.

In order to calculate the likelihood of selecting the letter "I" from a box containing all the letters that make up the word "Equilibrium," we must take into account how frequently the letter "I" appears in the word. Three times in the word "Equilibrium" is the letter "I." The total number of outcomes is equal to the number of letters in the word, which is 11, because each letter in the box has an equal chance of being chosen. As a result, it is easy to determine the likelihood of selecting the letter "I" by dividing the number of desired outcomes (3 desired outcomes) by the total number of available outcomes (11).As a result, the likelihood of selecting the letter "I" is 3/11, which is equivalent to about 0.273 or 27.3%.

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Answer:

14/25

0.56

56%

Step-by-step explanation:

1. Turn it into a fraction (28/50)

2. Divided the numerator (28) and the denominator (50) by the greatest common factor (2), which makes the answer: 14/25

3. Divide the numerator (14) by the denominator (25) to get the decimal (14÷25=0.56)

4. Multiply the decimal (0.56) by 100 to get the percentage (0.56×100=56%)

Answer:

17 and 5

Step-by-step explanation:

Interesting question!

Turn both sentences to equations:

\(a=4b-3\\a-2b=7\)

a is the first number, and b is the second number.

A system of equations! A graphing calculator will do the work:

(See picture)

The y in the picture is a, and the x in the picture is b.

So the solution is a=17 and b=5

Answer:

6f + 2

Step-by-step explanation:

The 9 and the - 7 are "like terms"

They are both constants. That is, they don't have a variable. The terms will be considered "like terms" if they have the same variables to the same power.

So we can combine 9 and - 7.

9 + - 7 is 2.

9 + 6f - 7

= 6f + 9 - 7

= 6f + 2

Within-groups design compares the same subjects across time. In this design, participants are measured or observed on multiple occasions, such as before and after an intervention or at different time points.

The purpose of the within-groups design is to examine changes within individuals over time, allowing researchers to assess the impact of an intervention or the natural progression of a phenomenon within the same group of subjects.

By comparing the same subjects across time, within-groups designs help to control for individual differences and increase the internal validity of the study.

This design allows researchers to evaluate the effectiveness of an intervention by assessing changes within individuals and determining if those changes are statistically significant.

It also allows for a more precise assessment of the impact of an intervention or the stability of a phenomenon over time.

Within-groups designs are commonly used in fields such as psychology, education, and medicine to study changes in behavior, cognition, or health outcomes.

They provide valuable insights into individual responses to interventions or the natural course of development or disease progression within a specific group of subjects.

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We need to find the probability of exactly three successes in six trials of a binomial experiment. Probability of success 50% (no success is 50%).

To find this probability, we need to use the following formula for Bernoulli Trials (or Binomial Experiment):

The combinations are given by:

Then, we have:

Thus, the probability of exactly three successes in six trials of a binomial experiment (which the probability of success is 50%) is 0.0625.

Rounding to the nearest tenth is about p = 0.1 (1/10) or 10%.



1. P-adic Numbers:

P-adic numbers are a specialized alternative not commonly used as a continuity strategy in mathematics. They are an extension of the real numbers that provide a different way of measuring and analyzing numbers. P-adic numbers are based on a different concept of distance, known as the p-adic metric. This metric assigns a measure of closeness or distance between numbers based on their divisibility by a prime number, p. P-adic numbers have unique properties and can be useful in number theory, algebraic geometry, and other branches of mathematics. However, they are not typically employed as a continuity strategy in practical applications.

2. Nonstandard Analysis:

Nonstandard analysis is a mathematical framework that provides an alternative approach to calculus and analysis. It introduces new types of numbers called "infinitesimals" and "infinite numbers" that lie between the standard real numbers but are infinitely smaller or larger than any real number. Nonstandard analysis allows for more rigorous treatment of infinitesimal quantities and provides a different perspective on limits, continuity, and differentiation. While nonstandard analysis has theoretical implications and can provide valuable insights in mathematical research, it is not commonly used as a continuity strategy in practical applications where standard analysis and calculus are more prevalent.

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The value of y in the triangle is 64.

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

We need to find the value of y,

The other two angles of triangle are 79⁰ and 37⁰

We have to use angle sum property of triangle

The sum of three angles of a triangle is 180⁰

y+ 79⁰+37⁰=180⁰

y+116⁰=180⁰

Subtract 116⁰ from both sides

y=180⁰- 116⁰

y=64⁰

Hence, the value of y in the triangle is 64.

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Answer:

Step-by-step explanation:

the value of X will be 62,575 and the divisor and remainder are 104 and 71 respectively.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given,  X/ 104=601 R71

Simplifying this expression

=> X/104 = 601 R71

=> X/104 = 601 + 71/104

multiply by 104 on both sides

=> X  = 601 *104 + 71

=> X = 62575

Since,

A divisor is a number that divides another number either completely or with a remainder. A divisor is represented in a division equation as Dividend ÷ Divisor = Quotient.

Thus in our case divisor is 104

The quotient is the number of times a division is completed fully, while the remainder is the amount left that doesn't entirely go into the divisor.

In our case remainder is 71.

Therefore, the value of X will be 62,575 and the divisor and remainder are 104 and 71 respectively.

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Complete question:

Answer:

JKL = 117

Step-by-step explanation:

63 and JKL form a straight line and their sum is 180

63+ KJL = 180

Subtract 63 from each side

63+ KJL - 63 = 180-63

JKL = 117

The expression is equivalent to "\(z^4 * (z + 6)^2 + (z + 6)\)".

To clarify, I understand the expression as: "z * (z + 6) * z * (z + 6) * z + (z + 6)". Let's break down the expression and simplify it step by step:

Distribute the multiplication:

z * (z + 6) * z * (z + 6) * z + (z + 6)

becomes

z * z * z * (z + 6) * (z + 6) * z + (z + 6)

Combine like terms:

z * z * z simplifies to \(z^3\)

(z + 6) * (z + 6) simplifies to (z + 6)^2

The expression now becomes:

\(z^3 * (z + 6)^2 * z + (z + 6)\)

Multiply \(z^3\) and z:

 \(z^3 * z\) simplifies to \(z^4\)

The expression becomes:

  \(z^4 * (z + 6)^2 + (z + 6)\)

So, an equivalent expression to "z (z + 6)z (z + 6)z + (z + 6)" is "\(z^4 * (z + 6)^2 + (z + 6)\)".

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Answer: Let's set up 1/5 and 1/4 side by side so they are easier to see:

\(\frac{1}{5} x\frac{1}{4}\)

The next step is to multiply the numerators on the top line and the denominators on the bottom line:

1 x 1

5 x 4

From there, we can perform the multiplication to get the resulting fraction:

1 x 1

5 x 4 = \(\frac{1}{20}\)

The complete answer is below (simplified to the lowest form):

1/20

Convert 1/5 times 1/4 to Decimal

Here's a little bonus calculation for you to easily work out the decimal format of the fraction we calculated. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal:

\(\frac{1}{20}\) = 0.05

Answer: 567

Step-by-step explanation: cause im smart i think