Question 11 of 50
Which of the following best describes the term common notion?
A. A statement that is not officially defined but that is understood to
be common sense
B. A precise statement of the qualities of an idea, object, or process
C. A logical arrangement of deductions that leads to the conclusion
that a statement is always true
D. A statement that is assumed to be true without proof

Answer:

Step-by-step explanation:

the little triangle is  1/3 of the big one.  we know that b/c of the  6/18  sides and that's  also 1/3, I mean the fraction 6/18 , reduces to  1/3

so we know that 1/3 of the 42 is the small triangle and that 2/3 of 42 is the rest of that distance,  so  

42 * 2/3  = ?

28 = ?

so that part that they want to know is 28 units...  :)

Answer: You can't answer this without the graph

Step-by-step explanation:

The amount of peanut butter needed using a proportion: Mrs. Cunningham should use 2 cups of peanut butter for her huge batch of cookies.

According to Mrs. Cunningham's recipe, she uses 1 cup of peanut butter for every 1/2 cup of oil (12 of a cup is equivalent to 1/2 cup).

Since today she wants to use 1 cup of oil, we can calculate the amount of peanut butter needed using a proportion:

Peanut butter / Oil = 1 cup / 1/2 cup

To find the value of Peanut butter, we can cross-multiply:

Peanut butter = (1 cup / 1/2 cup) * 1 cup

Peanut butter = 1 cup * (2/1)

Peanut butter = 2 cups

Therefore, Mrs. Cunningham should use 2 cups of peanut butter for her huge batch of cookies.

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The angular measure L is : 47°

Angles are formed when two lines meet.

Analysis:

Firstly, we calculate for m using cosine rule.

\(m^{2}\) = \(510^{2}\) + \(820^{2}\) -2(510)(820) cos 20

\(m^{2}\) = 260100 + 672400 -83600(0.9396)

\(m^{2}\) = 146618.56

m = \(\sqrt{146618.56}\) = 382.9cm

using sine rule to find ∠L

382.9/sin20 = 820/sinL

sinL = 820sin20/382.9

sinL = 820(0.342)/382.9

sinL = 0.732

L = sin inverse of 0.732 = 47°

In conclusion, ∠L is 47°

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Answer:

180 cups of hot chocolate and 95 cups of coffee

Step-by-step explanation:

multiply the cups by the price and add them together and it adds up to the total sales they got

Answer:

9

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

Arranging the numbers in ascending order,

9,11,11,12,13,13,14,14,17,17,18,19,22,23,25

Median = 14

Answer:

Point slope:y - y1 = m(x -x1)y - y1 = m(x -x1)

Given values: (x1 , y1) = (2 , 3)m = 3

Solution: y - 3 = 3(x - 2

Step-by-step explanation:

hope this helps if not let me know have a good day

Answer:

A. 10

Step-by-step explanation:

The perimeter is the sum of all the outside lengths

Therefore, to find the value of x, you must do:

x + x + 5 + x + 7 = 42

3x + 12 = 42

3x = 30

x =10

Answer:

1 point. O (0,0)

Step-by-step explanation:

Hi

Invariant points are those points who remain on the same location after a given transformation.

1.  Plotting OABC we have it below:

2. Whenever we dilate centered, the image O'A'B'C' will be determined by the following points:

\(O'(0,0) \:A'(3,0) B'(6,6) \:and\:C'(0,6)\)

Since the Scale factor is (2)

3. Check it out O'A'B'C' below

4. On the perimeter of O'A'B'C' (enlarged OABC) we have left 1 point invariant.

Answer:

The answer would be 2

Answer:

( -2, 2 )

Step-by-step explanation:

plug the points into the midpoint formula

\(x=\frac{-4+0}{2}=\frac{-4}{2}=-2\\\\y=\frac{7-3}{2}=\frac{4}{2}=2\)

Based on a one-sample t-test with a sample mean of 411 grams, a sample standard deviation of 25 grams, and a significance level of 0.0125 (adjusted for a one-tailed test), there is sufficient evidence to conclude that the bags are overfilled. The test statistic and resulting p-value will determine the level of significance and strength of the evidence.

The null and alternative hypotheses can be stated as follows:

Null Hypothesis (H0): The mean weight of the bags filled by the machine is equal to 402 grams.

Alternative Hypothesis (Ha): The mean weight of the bags filled by the machine is greater than 402 grams.

In this scenario, we are testing whether the bags are overfilled, which means we are interested in determining if the mean weight is greater than the specified setting of 402 grams.

To assess the evidence, we will perform a one-sample t-test since we have a sample mean, sample standard deviation, and the assumption of approximately normal population distribution.

The significance level is given as 0.025, which indicates a two-tailed test. Since the alternative hypothesis is one-tailed (greater than), we need to adjust the significance level to account for this.

Therefore, the new significance level for the one-tailed test is 0.025 divided by 2, which equals 0.0125.

In the subsequent steps, we will calculate the test statistic, degrees of freedom, and compare the p-value against the adjusted significance level to make a conclusion about whether there is sufficient evidence to support the claim that the bags are overfilled.

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The extremizer point is x=(1,1].

Consider the problem min 22 – (21 – 2)3 + 3 subject to X2 > 1. The given problem can be written in the following form: minimize f(x)= 22 - (21 - 2)3 + 3 subject to g(x) = x2 > 1.The extremizer point is the point that satisfies the conditions that have been given in the question. Therefore, the extremizer point in this problem is x=(1,1].In order to find the extremizer point of a problem, we need to calculate the derivative of the objective function and then equate it to zero to find the point where it attains its minimum value. Here, however, we have only one point to choose from that satisfies the given constraint, so it is the extremizer point.

A point in a convex set that does not lie on any open line segment connecting two points in the set is referred to as an extreme point in mathematics.

The terms "extreme point" and "extremal point" can also mean:

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Answer:

0.42

Step-by-step explanation:

The original price of the old hardcover books was sold for b dollars. But the manager markdown the hardcover books by 42%.

The expression of the markdown using a decimal can be represented below.

Recall the markdown is 42 %. If you want to convert from percentage to a decimal, you have to move the decimal point two places to the left . The percentage sign is removed at this stage and the value is represent in decimal.  Or you can just divide the percentage value by 100.

In our case the percentage value can be solved as 42/100 = 0.42 in decimal or by just simply moving the decimal points two places to the left which is 0.42.

Answer:

$1256.85

Step-by-step explanation:

1140 (1.05) = $1197 cost

$1197* 1.05 = 5% profit

We have to solve this equation:

We have two variables and one equation that is linear.

We can make a table by giving values to x and then calculating the corresponding value of y.

Then, first we have to clear y from the equation.

We can do this as:

Then, we can calculate 3 points to make a table of values.

In a calculator, we have to press the keys '4', '-', '2', 'x' and the value we assigned to x.

For example if we start with x = 0, we would press: 4, -, 2, x, 0, = and obtain the value of y that correspond to x = 0.

We than can complete the table as:

x | y

-----|------

0 | 4

1 | 2

2 | 0

We can assign another values to x and obtain new values of y.

Answer:

its B

Step-by-step explanation:

3.14 then pi (3.14159) then 22 ÷ 7 (3.1428) then square root of 10 (3.16)

Answer:

B

Step-by-step explanation:

pi=3.141592654

square root of 10=3.16227766

3.14=3.14

22/7=3.142857143

Answer:

x = 4; y = 8

Step-by-step explanation:

y=2x

y=x+4

2x = x + 4

x = 4

y = 2x = 2(4)

y = 8

Solution: x = 4; y = 8

Answer: area is height x width

Step-by-step explanation:

1.

3 x 7 = 21

11 x 3 = 33

2.

8 x 11 = 88

5 x 9 = 45

Box plot describes 5 important description of the data set it represents. The true statement according to the box plot specified is given by: Option C: The data is skewed and shows that she was equally likely to work more than 3. 5 hours or less than 5 hours.

A box plot has 5 data description.

IQR(inter quartile range)  is the dfference between third and first quartile.

Range = Maximum value of the data set - Minimum value of the dataset

Data is symmetric if the median is in the mid of the box plot and the box is mid to the line connecting both whiskers(since in that case, the frequencies are more likely to be distributed symmetric to the middle).

For the given case, it is described that:

Whiskers range from 2 and 7 thus, minimum of data set = 2, maximum value = 7

and the box ranges from 3. 5 to 7 (so first quartile is 3.5, and third quartile is at 7)

The line dividing box is at 4, thus, median or second quartile is 4.

Average of box's limit is (3.5 + 7)/2 = 5.25  

this is not coinciding with median, and actually lying ahead of median.

That means data is leaning on right side(skewed negatively).

That means she worked more that median(the central measure here) thus, the data is skewed and shows that she was equally likely to work more than 3. 5 hours or less than 5 hours. (option C)

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Step-by-step explanation:

1-phenyl-3-methyl-4-stearoyl- 5-pyrazolone1-phenyl-3-methyl-4-stearoyl- 5-pyrazolone

13) The scientific notation is        1.4354125 * 10⁸. 14) The scientific notation is        1.4354125 * 10⁻¹. 15) The scientific notation is 22366.0992. 16) The scientific notation is 1.55 * 10¹⁰.

Let's solve the given expressions and write the answers in scientific notation:

13) \((6.125*10^3) * (2.345*10^4)\)

To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:

\((6.125 * 2.345) * (10^3 * 10^4) = 14.354125 * 10^(3 + 4) = 14.354125 * 10^7 = 1.4354125 * 10^8\)

\(= 1.4354125 * 10^8\)

14) \((6.1258*10^3) * (2.345*10^{-4})\)

To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents:

\((6.125 * 2.345) * (10^3 * 10^{-4}) = 14.354125 * 10^{3 - 4} = 14.354125 * 10^{-1} = 1.43541258* 10^{-1}\)

\(= 1.4354125 * 10^{-1}\)

15) \(3700.13 * (6.04*10^4)\)

To multiply a decimal number and a number in scientific notation, we simply multiply the decimal by the coefficient of the scientific notation:

3700.13 × 6.04 = 22366.0992

Since the answer does not need to be expressed in scientific notation, the result is 22366.0992.

= 22366.0992

16) \((6.2*10^4) / (0.4*10^{-5})\)

To divide numbers in scientific notation, we divide the coefficients and subtract the exponents:

\((6.2 / 0.4) * (10^4 / 10^{-5}) \\= 15.5 * 10^{4 - (-5}) \\= 15.5 * 10^9 \\= 1.55 * 10^{10}\\= 1.55 * 10^{10}\)

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The percentage of American women that have shoe sizes that are at least 11.1 is; 0.0015

Empirical Rule

We are given;

Mean; x' = 8.04

Standard deviation; σ = 1.53

Using the empirical rule, we can have the data either 1, 2, or 3 standard deviations from the mean.

Thus;

At 1 standard deviation from the mean, we have;

8.04 ± 1(1.53)

⇒ (6.52, 8.56)

At 2 standard deviations from the mean, we have;

8.04 ± 2(1.53)

⇒ (5, 11.08)

At 3 standard deviations from the mean, we have;

8.04 ± 3(1.52)

⇒ (3.48, 12.6)

We can see that the one with at least 12,6 is 3 standard deviations from the mean which from the empirical rule is 99.7%

Thus;

percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%

P(x ≥ 12.6) = 0.15% = 0.0015

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The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

To find the observed z value we have to use the principles to create a formula.

The formula for finding the value of z is

z = ( x - μ)/(σ/√n)

here,

x = sample mean

μ = population mean

σ = standard deviation of the population

n = sample size

for the given question the values are

x = 50

μ = 45

σ = 5

n = 1

staging the values in the formula

z = (50-45)/(5/√1)

z = 1

The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.

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Answer: 3/8

Step-by-step explanation:

there are 8 slots and three of them are blue if you need decimal form then here: 0.375.  The percentage is: 15% i think

I hope i helped you! :)

Answer:

Hey can we talk if you are there please

Answer:

3 to 4

Step-by-step explanation:

A. To calculate the probability P(X > 7.6), we need to find the area under the normal distribution curve to the right of 7.6.

B. To calculate the probability P(7.4 ≤ X ≤ 10.6), we need to find the area under the normal distribution curve between 7.4 and 10.6.

C. To find the value x such that P(X > x) = 0.025, we need to determine the z-score corresponding to a cumulative probability of 0.975 and then transform it back to the original scale.

D. To find the value x such that P(x ≤ X ≤ 2.5) = 0.4943, we need to determine the z-scores corresponding to the cumulative probabilities of 0.25285 and 0.74715 and then transform them back to the original scale.

A. By standardizing the variable X using the z-score formula, we can calculate the probability P(Z > z), where Z is a standard normal variable. Substituting the given values and solving for z, we can find the probability P(X > 7.6) using a standard normal distribution table or calculator.

B. Similar to part A, we can standardize the values 7.4 and 10.6 using the z-score formula. Then, by finding the probabilities P(Z < z1) and P(Z < z2), where z1 and z2 are the standardized values, we can calculate P(7.4 ≤ X ≤ 10.6) as the difference between these probabilities.

C. To find the value x such that P(X > x) = 0.025, we can determine the z-score corresponding to a cumulative probability of 0.975 (1 - 0.025) using a standard normal distribution table or calculator. We then use the inverse z-score formula to transform the standardized value back to the original scale.

D. Similarly, to find the value x such that P(x ≤ X ≤ 2.5) = 0.4943, we need to determine the z-scores corresponding to the cumulative probabilities of 0.25285 and 0.74715. By applying the inverse z-score formula, we can obtain the values of x on the original scale.

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For solving this question, you need to apply trigonometric ratios and/or Pythagoras Theorem for each of the right triangles.

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  In this triangle from the trigonometric ratios or the Pythagoras Theorem (\(hypotenuse^2=(side_1)^2 + (side_2)^2\)), it is possible finding angles or sides.

The main trigonometric ratios are presented below.

\(sin(x)=\frac{opposite\,side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\,side}{hypotenuse}\\ \\ tan(x)=\frac{sin(x)}{cos(x)}= \frac{opposite\,side}{hypotenuse}* \frac{hypotenuse}{adjacent\,side}= \frac{opposite\,side}{adjacent\,side}\)

                                     \(hypotenuse^2=(side_1)^2 + (side_2)^2\\ \\ 29^2=20^2+s^2\\ \\ 841=400+s^2\\ \\ s^2=441\\ \\ s=\sqrt{441}=21\)

For angle D you will find:

                        \(sin(D)=\frac{opposite\,side}{hypotenuse}=\frac{20}{29} \\ \\ cos(D)=\frac{adjacent\,side}{hypotenuse}=\frac{21}{29} \\ \\ tan(D)=\frac{sin(D)}{cos(D)}= \frac{opposite\,side}{adjacent\,side}=\frac{20}{21}\)

For angle E you will find:

                       \(sin(E)=\frac{opposite\,side}{hypotenuse}=\frac{21}{29} \\ \\ cos(E)=\frac{adjacent\,side}{hypotenuse}=\frac{20}{29} \\ \\ tan(E)=\frac{sin(E)}{cos(E)}= \frac{opposite\,side}{adjacent\,side}=\frac{21}{20}\)

The question gives an angle (62°) and the adjacent side (25) from the angle 62° of the right triangle. Therefore, you can find x from the trigonometric ratio of tan (62°):

                           \(tan(62^{\circ \:})= \frac{opposite\,side}{adjacent\,side}=\frac{x}{25}\\ \\ \tan \left(62^{\circ \:}\right)=1.881 \\ \\ Then,\\ \\ 1.881=\frac{x}{25} \\ \\ x=25*1.881=47.025\\ \\ x=47.0\)

The question gives an angle (26°) and the opposite side (11) from the angle 26° of the right triangle. Therefore, you can find x from the trigonometric ratio of sin (26°):

                          \(sin(26^{\circ \:})=\frac{opposite\,side}{hypotenuse}=\frac{11}{x} \\ \\ sin(26^{\circ \:})=0.438\\ \\ Then,\\ \\ 0.438=\frac{11}{x} \\ \\ 0.438x=11\\ \\ x=\frac{11}{0.438} \\ \\ x=25.1\)

The question gives an angle (48°) and the hypotenuse (32) of the right triangle. Therefore, you can find x from the trigonometric ratio of sin (48°):

                        \(sin(48^{\circ \:})=\frac{opposite\,side}{hypotenuse}=\frac{x}{32} \\ \\ sin(48^{\circ \:})=0.743\\ \\ Then,\\ \\ 0.743=\frac{x}{32} \\ \\ x=32*0.743\\ \\ x=23.8\)

The question gives an angle (12°) and the adjacent side (29) from the angle 12° of the right triangle. Therefore, you can find x from the trigonometric ratio of cos (12°):

                           \(cos(12^{\circ \:})=\frac{adjacent\,side}{hypotenuse}=\frac{29}{x} \\ \\ cos(12^{\circ \:})=0.978\\ \\ Then,\\ \\ 0.978=\frac{29}{x} \\ \\ 0.978x=29\\ \\ x=\frac{29}{0.978} \\ \\ x=29.6\)

The question gives the adjacent side (14) from the angle x and the hypotenuse (15) of the right triangle. Therefore, you can find x from the trigonometric ratio of cos(x) :

                        \(cos(x)=\frac{adjacent\,side}{hypotenuse}=\frac{14}{15} \\ \\ cos(x)=0.933\)

After that, you should calculate the arccos(x).

                      \(\arccos \left(\frac{14}{15}\right)=21.0^{\circ \:}\\ \\ Then,\\ \\ x=21.0^{\circ \:}\)

The question gives the adjacent side (23) from angle x and the opposite side (19) from angle x of the right triangle. Therefore, you can find x from the trigonometric ratio of tan (x) :

                        \(tan(x)= \frac{opposite\,side}{adjacent\,side}=\frac{19}{23}\\ \\ \tan \left(x}\right)=0.826\)

After that, you should calculate the arctan(x).

                      \(\arctan \left(\frac{19}{23}\right)=39.6^{\circ \:}\\ \\ Then,\\ \\ x=39.6^{\circ \:}\)

The question gives the adjacent side (9) from angle x and the hypotenuse (17) of the right triangle. Therefore, you can find x from the trigonometric ratio of cos(x) :

                        \(cos(x)=\frac{adjacent\,side}{hypotenuse}=\frac{9}{17} \\ \\ cos(x)=0.529\)

After that, you should calculate the arccos(x).

                      \(\arccos \left(\frac{9}{17}\right)=58.0^{\circ \:}\\ \\ Then,\\ \\ x=58.0^{\circ \:}\)

The question gives the opposite side (43) from angle x and the hypotenuse (45) of the right triangle. Therefore, you can find x from the trigonometric ratio of sin(x) :

                        \(sin(x)=\frac{opposite\,side}{hypotenuse}=\frac{43}{45} \\ \\ sin(x)=0.956\)

After that, you should calculate the arcsin(x).

                      \(\arcsin \left(\frac{43}{45}\right)=72.9^{\circ \:}\\ \\ Then,\\ \\ x=72.9^{\circ \:}\)

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The point p(x, y) lies on the terminal side of an angle theta = startfraction 3 pi over 4 endfraction in standard position. Then x values are negative and the y values are positive.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. When the two rays are creating an exact 180-degree angle, an angle is considered to be straight. It gets its name from the fact that two lines at an angle of 180 degrees resemble one single straight line. Angles, whose measure is always non-negative, have some standard language.

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