Determine whether each set of numbers could represent the sides of a triangle (Yes or No)

1. {9,11,16}

2. {12,7,20}

3. {13,9,6}

4. {25,50,75}

5. {14,14,14}

6. {4.5,7.3,2.8}

7. {15,6,9}

8. {10.5,4.5,6.5}

Answer: 6 square inches

Step-by-step explanation:

Since the pizza is 16 inches and there is 8 slices divide.

16 inches ÷ 8 slices = 2 inches per slice

Each slice is 2 inches.

Since each slice is 2 inches multiply by 3 slices to get how many square inches she ate.

2 inches per slice x 3 slices = 6 square inches

Therefore she ate 6 square inches of pizza.

Answer:

Given equation of motion of a particle is,

To find the velocity function of t, value of t when the velocity is zero and acceleration of the particle.

Explanation:

we know that, velocity of a particle is rate of change of the object’s position with respect to a frame of reference and time.

we get,

Substitute for s(t), we get

Differenting we get,

Required velocity function is,

when velocity equal to 0, we get

Dividing by 12, we get

we get,

Taking (t+4) as common we get,

we get,

The values of t are,

t=-4 and t=-2

To find acceleration of a particle.

we know that,

Acceleration a(t) is the rate at which velocity (speed) is changing.

we get,

Substitute v(t), we get,

we get,

The acceleration of a particle is,

The length of one edge of the tabletop is 4.89 feet.

We know that square is a shape that has all the side equal. Based on this using the formula to find the length of edge of the tabletop.

The area of square table is given by the formula -

Area of square table = side²

We will keep the value of area of square table to find the value of side which will be length of edge

24 = side²

Side = ✓24

Taking square root for the value on right side of the equation

Side = 4.89

Hence, the length of one edge of the tabletop is 4.89 feet.

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Answer:

A.

Step-by-step explanation:

4 + 8 = 12 which is < 13.

Answer:

4+8 is 12

Step-by-step explanation:

12 is less than 13 which cannot make this a triangle

The value of test specific round to decimal places is 0.31 .

Given,

57 subjects , 36 successes .

Sampling Distribution of Proportion: The random sample of size n is taken from the population with proportion

The sample proportion has mean p

standard deviation : √p(1-p)/n

Moreover, the sample proportion follows normal distribution for large sample size n.

Statistical hypotheses testing: Hypotheses testing is used to make inferences about the population based on the sample data. The hypotheses test consists of null hypothesis and alternative hypothesis.

Null hypothesis: The null hypothesis states that there is no difference in the test, which is denoted by \(H_{0}\) .

P-value: The probability of getting the value of the statistic that is as extreme as the observed statistic when the null hypothesis is true is called as P-value.

The formula of sample proportion is given as,

proportion = x/n

The formula for test statistic of sample proportion is given below:

z = sample proportion - mean proportion/√p(1-p)/n

Now,

The sample proportion value is obtained below:

From the information, a random sample of 57 subjects and 36 successes.

Sample proportion = x/n

Sample proportion = 36 /57

Sample proportion = 0.63 .

The test statistic value is obtained below:

Null hypothesis: \(H_{0} : p = 0.61\\\)

Alternative hypothesis: : \(H_{0} : p \neq 0.61\\\) .

The population proportion value is 0.61 . So p value is 0.61 .

Test statistic = 0.63 - 0.61/ √0.61(1- 0.61)/57

z = 0.31 .

Thus the value of test specific is 0.31 .

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Let's call the number "x". If we add x to itself, it is the same as multiplying x by 2 (2x). So the sentence "A number added to itself equal 4 less than the number" can be translated into an equation like this: 2x = x - 4.

Now we can solve for x by isolating it on one side of the equation: 2x - x = -4x = -4. Therefore, the number that satisfies the condition of "A number added to itself equal 4 less than the number" is -4.

We can use algebra to solve many real-life problems, including problems that involve numbers and unknown variables. One type of problem that can be solved with algebra is a word problem. Word problems require us to read the problem carefully, identify the key information, and translate it into an equation that we can solve.

Once we have the equation, we can use algebraic techniques to solve for the unknown variable.In this problem, we were given the sentence "A number added to itself equal 4 less than the number". We recognized that the unknown variable was a number, which we called "x".

We then used algebraic notation to represent the sentence as an equation: 2x = x - 4.

To solve the equation, we isolated the variable on one side by subtracting x from both sides: 2x - x = -4.

This simplified to x = -4, which was our final answer.

The process of solving a word problem with algebra requires several steps. It is important to read the problem carefully and make sure we understand what is being asked.

We then need to identify the unknown variable and use algebraic notation to represent the information in the problem. We can then solve the equation using algebraic techniques to find the solution.

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The answers to all parts are shown below.

Based on the given data, we can observe the following:

Based on this data, we can conclude that there is an inverse relationship between the distance from a magnet and the number of paper clips attracted.

In most cases, the strength of a magnet's attraction decreases with an increase in distance.

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Answer:

\( m\angle PQR =(8x - 4)\degree\)

Step-by-step explanation:

Since, QS bisects angle PQR.

Therefore,

\(m\angle PQR = m\angle PQS = m\angle RQS\\

m\angle PQR =5x - 11 + 3x +7\\

m\angle PQR =5x + 3x + 7 - 11\\

\huge \red {\boxed {m\angle PQR =(8x - 4)\degree}} \)

Answer:

OD

Step-by-step explanation:

The zero x=8 will make the factor (x-8) = 0 and the zero x=3 will make the factor (x-3) = 0.

so it's (x-8) and (x-3)

Let X be the number of fixed points of a random permutation of n elements. A fixed point is an element that remains in the same position after the permutation. Thus, the probability that an element is fixed is 1/n, and the probability that it is not fixed is (n-1)/n.

Using the linearity of the expected value, we can calculate the expected value of X as:

E(X) = E(X1 + X2 + ... + Xn) = E(X1) + E(X2) + ... + E(Xn)

where Xi is the indicator random variable that is equal to 1 if the i-th element is fixed and 0 otherwise. Since the probability of an element being fixed is 1/n, we have E(Xi) = 1/n. Therefore,

E(X) = n * (1/n) = 1

To find the variance of X, we need to compute E(X^2) - E(X)^2. We can use the fact that X^2 = X1 + X2 + ... + Xn, where Xi is the indicator random variable that is equal to 1 if the i-th and j-th elements are both fixed and 0 otherwise. Then,

E(X^2) = E(X1 + X2 + ... + Xn)^2 = E(X1^2 + X2^2 + ... + Xn^2) + 2 E(X1X2 + X1X3 + ... + X(n-1)n)

Since there is only one way to fix two elements out of n, we have E(XiXj) = 1/(n(n-1)). Therefore,

E(X^2) = n * (1/n) + n(n-1) * (1/(n(n-1))) = 1 + 1/n

Finally, the variance of X is

Var(X) = E(X^2) - E(X)^2 = 1 + 1/n - 1^2 = 1/n

Therefore, the variance of the number of fixed elements of a randomly selected permutation of n elements is 1/n.

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we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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Answer:

1) y=2x+6

Step-by-step explanation:

2) y=2×7+6=20ft

Answer:

y = 2x + 6 and the height is 20 feet after seven years.

Step-by-step explanation:

Hello we meet again.

You substitute the x with 7 and then it will be 2(7)+6. 2 times 7 is 14 plus 6 equals 20 so good luck.

In performing an ANOVA with a fixed total sample size, as the number of groups being compared increases, the power decreases i.e., the correct option is B.

The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false.

In the context of ANOVA (analysis of variance), power refers to the ability of the test to detect significant differences among the group means.

When comparing the means of multiple groups in ANOVA, the fixed total sample size is divided among the groups, resulting in smaller sample sizes for each group as the number of groups increases.

With smaller sample sizes, the ability to detect significant differences becomes more challenging, leading to a decrease in power.

Power is influenced by factors such as the sample size, effect size, and significance level.

In this case, the fixed total sample size means that as the number of groups increases, the sample size per group decreases.

This reduction in sample size limits the ability of the ANOVA test to detect small or moderate differences between group means, thereby decreasing the power of the test.

It is important to consider the trade-off between the number of groups being compared and the power of the ANOVA test.

Increasing the number of groups may provide more detailed comparisons but may result in decreased power and lower sensitivity to detect significant differences among the groups.

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Given that the correlation between two variables is r=0.23. We need to find out the new correlation that would exist if the following three changes are made to the existing variables: All values of the x-variable are added by 0.14. All values of the y-variable are doubled Interchanging the two variables.  the correct option is B. 0.37.

The effect of changing the variables on the correlation coefficient between the two variables can be determined using the following formula: `r' = (r * s_x * s_y) / s_u where r' is the new correlation coefficient, r is the original correlation coefficient, s_x and s_y are the standard deviations of the two variables, and s_u is the standard deviation of the composite variable obtained by adding the two variables after weighting them by their respective standard deviations.

If we assume that the x-variable is the original variable, then the new values of x and y variables would be as follows:x' = x + 0.14 (since all values of the x-variable are added by 0.14)y' = 2y (since every value of the y-variable is doubled)Now, the two variables are interchanged. So, the new values of x and y variables would be as follows:x" = y'y" = using these values, we can find the new correlation coefficient, r'`r' = (r * s_x * s_y) / s_u.

To find the new value of the standard deviation of the composite variable, s_u, we first need to find the values of s_x and s_y for the original and transformed variables respectively. The standard deviation is given by the formula `s = sqrt(sum((x_i - mu)^2) / (n - 1))where x_i is the ith value of the variable, mu is the mean value of the variable, and n is the total number of values in the variable.

For the original variables, we have:r = 0.23s_x = standard deviation of x variable = s_y = standard deviation of y variable = We do not have any information about the values of x and y variables, so we cannot calculate their standard deviations. For the transformed variables, we have:x' = x + 0.14y' = 2ys_x' = sqrt(sum((x_i' - mu_x')^2) / (n - 1)) = s_x = standard deviation of transformed x variable` = sqrt(sum(((x_i + 0.14) - mu_x')^2) / (n - 1)) = s_x'y' = 2ys_y' = sqrt(sum((y_i' - mu_y')^2) / (n - 1)) = 2s_y = standard deviation of transformed y variable` = sqrt(sum((2y_i - mu_y')^2) / (n - 1)) = 2s_yNow, we can substitute all the values in the formula for the new correlation coefficient and simplify:

r' = (r * s_x * s_y) / s_ur' = (0.23 * s_x' * s_y') / sqrt(s_x'^2 + s_y'^2)r' = (0.23 * s_x * 2s_y) / sqrt((s_x^2 + 2 * 0.14 * s_x + 0.14^2) + (4 * s_y^2))r' = (0.46 * s_x * s_y) / sqrt(s_x^2 + 0.0396 + 4 * s_y^2)Now, we can substitute the value of s_x = s_y = in the above formula:r' = (0.46 * * ) / sqrt( + 0.0396 + 4 * )r' = (0.46 * ) / sqrt( + 0.1584 + )r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = (0.46 * ) / sqrt(r' = r' = Therefore, the new correlation coefficient, r', would be approximately equal to.

Hence, the correct option is B. 0.37.

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Answer:

Famous mathematician Archimedes of Syracuse did the first calculation of pi around 250 BC. Without pi, we cannot calculate the ratio of the circumference of a circle to its diameter. Pi is made up of 31.4 trillion digits. Within pi, you can find your birthday, social security number, and every word ever if put into alphabetic values (1=a, 2=b, etc). You can get your entire life story from beginning to end just from pi!

hope this helps:)

\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

The six main criteria to define normality and abnormality include statistical infrequency, personal distress, others' distress, unexpected behavior, highly consistent/inconsistent behavior, and maladaptiveness/disability.

1. Abnormality as statistical infrequency: This criterion defines abnormality based on behaviors or characteristics that deviate significantly from the statistical norm.

2. Abnormality as personal distress: This criterion focuses on the individual's subjective experience of distress or discomfort. It considers behaviors or experiences that cause significant emotional or psychological distress to the person as abnormal.

For instance, someone experiencing intense anxiety or depression may be considered abnormal based on personal distress.

3. Abnormality as others' distress: This criterion takes into account the impact of behavior on others. It considers behaviors that cause distress, harm, or disruption to others as abnormal.

For example, someone engaging in violent or aggressive behavior that harms others may be considered abnormal based on the distress caused to others.

4. Abnormality as unexpected behavior: This criterion defines abnormality based on behaviors that are considered atypical or unexpected in a given context or situation.

For instance, if someone starts laughing uncontrollably during a sad event, their behavior may be considered abnormal due to its unexpected nature.

5. Abnormality as highly consistent/inconsistent behavior: This criterion involves comparing an individual's behavior to both their own typical behavior and the behavior of others. Consistent or inconsistent patterns of behavior may be considered abnormal.

For example, if a person consistently engages in risky and impulsive behavior, it may be seen as abnormal compared to their own usually cautious behavior or the behavior of others in similar situations.

6. It considers behaviors that are maladaptive, causing difficulties in personal, social, or occupational areas. For instance, someone experiencing severe social anxiety that prevents them from forming relationships or attending school or work may be considered abnormal due to the disability it causes.

The medical model and classification systems used in physical illnesses have both value and limitations when applied to psychological disorders. They provide a structured framework for understanding and diagnosing psychological disorders, allowing for standardized assessment and treatment. However, they can oversimplify the complexity of psychological experiences and may lead to overpathologization or stigmatization.

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There are 5040 different permutations of the set {a, b, c, d, e, f, g}.

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

The set {a, b, c, d, e, f, g} has seven elements, so there are 7! (7 factorial) permutations possible. The factorial of a number is the product of all the numbers up to and including that number. In this case,

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

This means that there are 5040 different permutations of the set

{a, b, c, d, e, f, g}.

A permutation is defined as an arrangement of elements in a specific order. In this case, the elements are {a, b, c, d, e, f, g} and the order can be changed in any way, as long as all elements are included. For example, one possible permutation is bfgdeca.

This is one of the 5040 possible permutations of the set.

As the set contains seven elements, there are 7! (7 factorial) possible permutations. This means that there are 5040 different permutations of the set {a, b, c, d, e, f, g}.

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If we reject the null hypothesis, we conclude that there is not enough statistical evidence to infer that the null hypothesis is true.

In hypothesis testing, the researcher makes a claim about the population and then uses a sample of the population to determine whether or not the claim is accurate. Before the sample is drawn, the degree of significance—or the predicted error—must be determined. The validity of a claim is determined by the value of a test statistic.

The researcher rejects the provided null hypothesis if the test statistic's value is significant. When the null hypothesis is rejected, there is no discernible difference between the hypothesized value and the sampled observations. If the null hypothesis is rejected, it is determined that there is insufficient statistical support to draw the conclusion that it is true.

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The person who worked out the first 31,415,926,535,897 digits of pi is not known.

However, there are several people who have contributed to its calculation over time. Some of the notable names include:

a. William Shanks (1812-1882), an English mathematician, was the first to calculate 707 digits of pi, but later calculations revealed that he made a mistake in the 528th digit. William Shanks (1812-1882) was an English mathematician who is known for his work on the calculation of pi. In 1853, he published a book titled "Contributions to Mathematics, Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals," in which he claimed to have calculated pi to 707 decimal places.

However, in 1945, it was discovered that there was an error in Shanks' calculation, and only the first 527 decimal places were correct. Despite this mistake, Shanks' work on the calculation of pi was still significant for its time, and he made important contributions to other areas of mathematics as well.

b. Richard Brent, an Australian mathematician, calculated the first 1,000,000 digits of pi in 1989 using a supercomputer. The current world record for calculating the most digits of pi is held by Timothy Mullican, who calculated over 31 trillion digits in 2019 using a cloud-based virtual machine.

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See attachment for math work and answer.

Answer:

y = -(x - 2)^2.

Step-by-step explanation:

Vertex form is a(x - b)^2 + c   where  a is a constant and (b, c) is the vertex.

Here b = 2 and c = 0

So we have:

y = a( x - 2)^2 + 0

When x = 4 y = -4 so:

-4 = a( 4 - 2)^2

a = -4/2^2 = -1

So the required equation is

y = -(x - 2)^2.

Step-by-step explanation:

Out of 14 people choose 9  :

14 C 9 = 14! / (5! 9! )  =   2002 ways

Using the combination formula is still the best way, but it can also be approached a bit differently.

We can choose the first person in 14 ways, the second one in 13 ways (one has been already chosen), the third one in 12 ways (two have been already chosen, etc. until the ninth person.

Therefore, we can choose 9 people in \(14\cdot13\cdot12\cdot11\cdot10\cdot9\cdot8\cdot7\cdot6=726485760\) ways.

However, this method accounts for the order of choosing, and we don't care about the order. Therefore, we have to divide the above result by the number of permutations of 9 people, which is \(9!=362880\)

Therefore, the number of groups of 9 that can be formed is \(\dfrac{}{}\)\(\dfrac{726485760}{362880}=2002\).

Answer:

12

Step-by-step explanation:

The expression 3c + 24 represents the amount of cookies you sell and the expression 5c represents the amount of cookies your sister sells. If we want to find when they become equal, we must set them equal to each other:

3c + 24 = 5c

24 = 2c

12 = c

Therefore, the answer is 12.

The capacity to overcome opposition or hesitancy to accept is referred to as convincing.

Convincing can also be described by other words like cogent, sound, telling, and valid.

Despite the fact that all of these words have the same meaning—"having such force as to compel serious attention and typically acceptance”—convincing denotes the ability to go over resistance or hesitation to accept.

When you say that someone or something is compelling, you indicate that they persuade you that something is real, accurate, or true.

Three fundamental strategies for persuading a listener to agree with you are ethos, logos, and pathos.

A more appropriate translation today may be "picture."

The audience's perception of the speaker's character, according to Aristotle, is referred to as ethos.

Therefore, the capacity to overcome opposition or hesitancy to accept is referred to as convincing.

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The magnitude of the resultant force upon the piling is 3710 pounds.

To find the resultant force, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the forces exerted by the bulldozers form the two sides of a right triangle.

The force exerted by the first bulldozer in the westerly direction is 1850 pounds, and the force exerted by the second bulldozer in the northerly direction is 3250 pounds.

Using the Pythagorean theorem, we can calculate the magnitude of the resultant force as follows:

Resultant force =\(√(1850^2 + 3250^2)= √(3422500 + 10562500)= √(13985000)≈ 3710 pounds.\)

Therefore, the magnitude of the resultant force upon the piling is approximately 3710 pounds.

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