Which number line models the sum of 8 + (-12) correctly?

Answer:

After correcting the error, IQR remains unchanged while standard deviation reduced drastically from 26.3 to 2.04

Step-by-step explanation:

Given the data:

3 5 6 7 7 8 8 8 9 9 9 10 102

Ordered data: 3, 5, 6, 7, 7, 8, 8, 8, 9, 9, 9, 10, 102

The interquartile range (IQR) for the data:

IQR = Q3 - Q1

Q3 = 3/4(n + 1) th term.

n = sample size = 13

Q3 = 3/4(14) = 10.5th term

Q3 = (10 + 11)th term / 2 = (9+9)/2 = 9

Q1 = 1/4(14) = 3.5th term

Q3 = (3 + 4)th term / 2 = (6+7)/2 = 6.5

IQR = Q3 - Q1 = 9 - 6.5 = 2.5

THE STANDARD DEVIATION :

Sqrt[Σ(X - m)²/n-1]

Using calculator :

Standard deviation = 26.3

Correcting error in the data:

3 5 6 7 7 8 8 8 9 9 9 10 10.2

Q3 = 3/4(n + 1) th term.

n = sample size = 13

Q3 = 3/4(14) = 10.5th term

Q3 = (10 + 11)th term / 2 = (9+9)/2 = 9

Q1 = 1/4(14) = 3.5th term

Q3 = (3 + 4)th term / 2 = (6+7)/2 = 6.5

IQR = Q3 - Q1 = 9 - 6.5 = 2.5

THE STANDARD DEVIATION :

Sqrt[Σ(X - m)²/n-1]

Using calculator :

Standard deviation = 2.04

After correcting the error, IQR remains unchanged while standard deviation reduced drastically from 26.3 to 2.04

Based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid.

The teacher surveyed his homeroom class about their post-graduation plans. He found out that most of his students plan to become soldiers.

An inference is a conclusion that can be drawn from a given set of data. In this case, the inference that can be made is that a significant number of students in the homeroom class plan to become soldiers.Therefore, the inference is valid based on the data provided.

However, it is essential to keep in mind that the sample size in the homeroom class is relatively small and may not be representative of the entire population. If the teacher had surveyed a more extensive and diverse population, the results might have been different.

In conclusion, based on the information provided, the inference that a significant number of students in the homeroom class plan to become soldiers is valid. However, this may not apply to the entire population, and it is crucial to consider the sample size when drawing inferences.

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Answer: One root

Reason:

The term "root" refers to the x intercept.

We plug in y = 0 and solve for x to get the x intercept

y = 2x-12

0 = 2x-12

2x = 12

x = 12/2

x = 6

The root is 6.

The single x intercept is located at (6,0).

Answer:

FALSE

TRUE

TRUE

Step-by-step explanation:

For median,

Arrange your numbers in numerical order.

Count how many numbers you have.

If you have an odd number, divide by 2 and round up to get the position of the median number.

If you have an even number, divide by 2. Go to the number in that position and average it with the number in the next higher position to get the median.

Source: https://www.verywellmind.com/how-to-identify-and-calculate-the-mean-median-or-mode-2795785

So for April median: 2.5, 3, 3.5, 3.5 (since we have 4 numbers we divide by 2 and we count by 2 places from left. Since we have even number data, we average 3 with the next higher position to get the median so (3+3.5)/2 = 3.25

For May apply same concept and you get median to be 2.25.

Median difference is 3.25-2.25 = 1

Therefore, statement 1 is false and statement 2 is true.

For average in May, add all numbers and divide by the number of data points so May= (2.5+3+3.5+3.5)/ 4 = 3.13

Apply same concept you for April and you get 2.38 as mean.

Mean difference is 3.13-2.38 = 0.75

Therefore, statement 3 is correct (true)

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

To test the claim that the proportion of American adults who eat salad once a week is equal to 80%, we will conduct a hypothesis test.

Claim: p = 0.80

Opposite: p ≠ 0.80

The test is a two-tailed z-test.

Sample proportion (p) = 374/445 = 0.8404

Test statistic= (0.8404 - 0.80) / sqrt((0.80 * (1 - 0.80)) / 445)

z = 2.53 (rounded to 2 decimals)

Significance level (α) = 0.005, so the critical values for a two-tailed test are -2.576 and 2.576.

Since the test statistic (2.53) falls within the critical values (-2.576 and 2.576), we fail to reject the null hypothesis.

Conclusion: There does not appear to be enough evidence to reject the claim that the proportion of American adults who eat salad once a week is equal to 80%.

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Answer:

The expression that can be used to approximate the expression "logax" for all positive numbers a, b, and x, where a=1 and b=1 is:

log1x = 0

Answer:

in secret

Step-by-step explanation:

correct answer is in a secret

Answer: √195 or 13.96424004

Step-by-step explanation:

Answer:

\(\sqrt{195}\)

Step-by-step explanation:

Given:

\(\sqrt{3} \cdot \sqrt{5} \cdot \sqrt{13}\)

\(\textsf{Apply the radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:\)

\(\implies \sqrt{3 \cdot 5 \cdot 13}\)

\(\implies \sqrt{15 \cdot 13}\)

\(\implies \sqrt{195}\)

This cannot be simplified any further.

Given:

The function is:

Find-:

Graph of function

Explanation-:

The function is:

So, the graph is:

Answer:

36.8

Step-by-step explanation:

5/8 = 23/x

5x=23*8

5x=184

x=184/5

x=36 and 4/5 or 36.8

Answer:

Step-by-step explanation:

Answer:

so the answer is 1 whole and 3/7 hope this helps :)

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ \theta =\frac{\pi }{2}\\[1em] r=\frac{8}{3} \end{cases}\implies A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot\left( \cfrac{8}{3} \right)^2 \\\\\\ A=\cfrac{1}{2}\cdot \cfrac{\pi }{2}\cdot \cfrac{64}{9}\implies A=\cfrac{16\pi }{9}\implies A\approx 5.59\)

Answer: 5

Step-by-step explanation:

Answer:

x = 67

y = 169

Step-by-step explanation:

We know that (x-1) + 52 + (y-7) = 180 because they're all on the same straight line. We also know that x-1 = 66, because they are alternate interior angles.

Solve for x:

x-1 = 66

x = 67

Now solve for y:

(67-1) + 52 + (y-7) = 180

y = 169

Answer:

Step-by-step explanation:

To work out the given expression without a calculator, we need to convert the numbers from their respective bases to decimal form and then perform the arithmetic operations. Let's break it down step by step:

11101010 base 2: To convert a binary number to decimal, we multiply each digit by the corresponding power of 2 and sum the results. So, let's calculate:

1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 0 * 2^4 + 1 * 2^3 + 0 * 2^2 + 1 * 2^1 + 0 * 2^0 = 234.

2122 base 8: To convert an octal number to decimal, we multiply each digit by the corresponding power of 8 and sum the results. Let's calculate:

2 * 8^3 + 1 * 8^2 + 2 * 8^1 + 2 * 8^0 = 1090.

ABC base 16: To convert a hexadecimal number to decimal, we multiply each digit by the corresponding power of 16 and sum the results. Let's calculate:

10 * 16^2 + 11 * 16^1 + 12 * 16^0 = 2748.

123 base 8: We already know that 123 is in base 8 (octal), so we can directly convert it to decimal:

1 * 8^2 + 2 * 8^1 + 3 * 8^0 = 83.

Now, let's perform the arithmetic operations:

234 + 1090 + 2748 - 83 = 3989.

Therefore, the result of the given expression in decimal form is 3989.

Answer:

10

Step-by-step explanation:

Round up if this number is greater than or equal to  

5  and round down if it is less than  5

To determine the function that models the data, we need to analyze the relationship between the cost per photo and the number of photos a customer buys. From the given information, we can observe that the cost per photo varies inversely with the number of photos. This implies that as the number of photos increases, the cost per photo decreases, and vice versa.

To model this relationship, we can use the inverse variation equation, which can be expressed as:

y = k/x

Here, y represents the cost per photo, x represents the number of photos, and k is the constant of variation.

Let's examine the data given in the table to find the value of k:

Number of Photos (x) Cost per Photo (y)

10 10

25 4

50 2

100 1

We can see that as the number of photos increases, the cost per photo decreases. We can use any pair of values from the table to solve for k. Let's choose the pair (50, 2):

2 = k/50

Solving for k:

k = 2 * 50 = 100

Now that we have the value of k, we can write the function that models the data:

y = 100/x

Therefore, the function that models the data is y = 100/x, where y represents the cost per photo and x represents the number of photos a customer buys.

Answer:

$223,787

Step-by-step explanation:

r = 0.02

C = 191,000

t = 8

S = 191,000 (1 + 0.02)⁸

Follow order of operations (PEMDAS).

S = 191,000 (1.02)⁸

S = 191,000 (1.171659381)

S = 223,786.9

(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)

Rounding, S = 223,787

Answer: 2x + 3

Step-by-step explanation:

f(x) = 4x + 6

g(x) = 1/2 * f(x)

Plug f(x) into the g(x) equation.

g(x) = 1/2 * (4x + 6)

Now simplify,

g(x) = 2x + 3

Answer:

-8

Step-by-step explanation:

Replace the x in f(x) = 2 • 2x with -2

f(-2) = 2 × 2 × (-2) ➡ f(-2) = -8

Each row will have 4 blueberry bushes and 7 raspberry bushes.

What is Greatest common divisor?

Greatest common divisor (GCD) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest positive integer that is a factor of two or more integers.

We are required to find the greatest common divisor (GCD) of 56 and 98.

we can factorize these numbers as follows :

56 = 2 x 2 x 2 x 7

98 = 2 x 7 x 7

The GCD is the product of the common prime factors, raised to the lowest power they appear in either factor:

GCD = 2 x 7 = 14

Therefore, Gemma can plant 14 rows. To find how many blueberry and raspberry bushes will be in each row, we can divide the total number of bushes by the number of rows:

No. of blueberry bushes per row = 56 / 14 = 4

No. of raspberry bushes per row = 98 / 14 = 7

So, each row will have 4 blueberry bushes and 7 raspberry bushes.

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answer

symbolic materials ?

Answer:

\(z=\frac{256-266}{\frac{16}{\sqrt{20}}}=-2.795\)    

The p value for this case can be calculated with this probability:

\(p_v =P(z<-2.795)=0.0026\)  

Step-by-step explanation:

Information provided

\(\bar X=256\) represent the sample mean

\(\sigma=16\) represent the population standard deviation

\(n=20\) sample size  

\(\mu_o =266\) represent the value that we want to test

z would represent the statistic

\(p_v\) represent the p value

Hypothesis to verify

We need to conduct a hypothesis in order to see if inadequate food intake should have shorter gestation times, the system of hypothesis would be:  

Null hypothesis:\(\mu \geq 266\)  

Alternative hypothesis:\(\mu < 266\)  

The statistic is given by:

\(z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}\)  (1)  

Replacing the info given we got:

\(z=\frac{256-266}{\frac{16}{\sqrt{20}}}=-2.795\)    

The p value for this case can be calculated with this probability:

\(p_v =P(z<-2.795)=0.0026\)  

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172