Answer:
Rational
Step-by-step explanation:
Quick Easy Eliminations:
We can get rid of positive integer as the sum of these roots is a decimal which is not a whole number. Hence, we can eliminate 2 options, C. Positive integer and D. Whole Number.
First solve:
6√14 + √14
= 7√14 (Decimal form: 26.191602)
What we need is the decimal form in order to determine if it's rational or irrational.
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Rational
Maria divided 16 by 4. below is her work 16/4=x
x=4 , Chelsea multiplies 16 by 4 below is her work 16x4=y y=64
Both Maria and Chelsea approached the calculation of 16 divided by 4 (16/4) and 16 multiplied by 4 (16x4) differently.
Maria's work shows that she divided 16 by 4 and assigned the result to the variable x. Therefore, x = 4.
On the other hand, Chelsea multiplied 16 by 4 and assigned the result to the variable y. Hence, y = 64.
Maria's approach represents the quotient of dividing 16 by 4, resulting in x = 4. This means that if you divide 16 into four equal parts, each part will have a value of 4.
Chelsea's approach, multiplying 16 by 4, gives us the product of 64. This indicates that if you have 16 groups of 4, the total value would be 64.
It's important to note that division and multiplication are inverse operations, and the results will differ depending on the approach chosen. In this case, Maria obtained the quotient, while Chelsea obtained the product.
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Mr. Roosevelt has 48 nails that each weigh 1.35 ounces. What is the weight of these nails in ounces?
Answer:
64.8 ounces
Step-by-step explanation:
48 nails times 1.35 ounces gives you 64.8 ounces.
What is the mode of the data shown in the table?
Scores: 5, 12, 13, 18
Frequency: 3, 2, 5, 4
A. 12
B. 13
C. 51.5
D. 12.5
Answer: Option B - 13
Explanation:
The mode is the value that appears most frequently in a data set
So 13 appears 5 times so it is the mode
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Answer:
B
Step-by-step explanation:
The mode is the score which occurs most often.
From the table a score of 13 occurs 5 times, that is
The mode is 13 → B
Find the length of the unknown leg of the right triangle. Use pencil and paper.
Draw the triangle on graph paper and measure to verify the answer.
Answer:
15Step-by-step explanation:
Use Pythagorean:
x² + 2.75² = 15.25²x² = 15.25² - 2.75²x² = 225x = √225x = 15Step-by-step explanation:
Perpendicular=p=2.75Hypotenuse=h=15.25we know that
\( \boxed{ \sf \: h {}^{2} = {p}^{2} + {b}^{2} } \\ \rm \mapsto \: {(15.25)}^{2} = {(2.75)}^{2} + {b}^{2} \\ \rm \mapsto \: {b} {}^{2} = {(15.75)}^{2} - {(2.75)}^{2} \\ \rm \mapsto \: b = \sqrt{ {(15.25)}^{2} - {(2.75)}^{2} } \\ \rm \mapsto \: b = \sqrt{232.5 - 7.5} \\ \rm \mapsto \: b = \sqrt{225.5} = 15.07=15(approx)\)
Transcribed image text: F1 In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent ОА categorical data O B quantitative data C e ither categorical or quantitative data. O D since the numbers are sequential, the data is quantitative. Unanswered Save
Answer:
The correct answer is B. Quantitative data, because the numbers represent numerical values that can be measured and compared.
what is the probability of no significant rainfall on a day, if there was no significant rainfall on the prior day?
The probability of no significant rainfall on a day, if there was no significant rainfall on the prior day, is dependent on various factors such as the location, climate, and season.
However, assuming a stable weather pattern, the probability of no significant rainfall on a day following a day with no significant rainfall would be higher than if there was significant rainfall on the prior day. This is because weather patterns tend to persist for several days, meaning that if there was no significant rainfall on the prior day, it is more likely that there will be no significant rainfall on the following day as well. Additionally, if the region is experiencing a dry season, the probability of no significant rainfall on a day would be higher regardless of the prior day's weather. The probability of no significant rainfall on a day, given that there was no significant rainfall on the prior day, depends on the weather patterns and climate in your specific location.
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How do you find the measure of an angle in a triangle isosceles?
To find the measure of an angle in a triangle that is isosceles, you can use the fact that the two equal sides of the triangle are congruent to each other. The measure of each of these angles can be found by subtracting the measure of the third angle from 180 degrees.
Determine which two sides of the triangle are equal in length (these are called the "congruent sides").
Find the measure of the angle opposite one of the congruent sides. This angle is called the "base angle."
Subtract the measure of the base angle from 180 degrees. This will give you the measure of the other two angles in the triangle (since the three angles in any triangle must add up to 180 degrees).
For example, if the measure of the base angle is x degrees, then the measure of the other two angles would be (180-x) degrees.
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The measure of angles in an isosceles triangle can be found using the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.
To find the measure of an angle in a triangle isosceles, you can use the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in any triangle is 180 degrees. Therefore, if you know two of the angles in the triangle, you can find the third angle by subtracting the sum of the two known angles from 180.
Let's look at an example. Suppose you have an isosceles triangle and you know that two of its angles measure 50 degrees and 60 degrees. To find the measure of the third angle, you would subtract 110 (the sum of the two known angles) from 180. This gives you 70 degrees as the measure of the third angle.
In addition to the Triangle Angle Sum Theorem, you can also use the Isosceles Triangle Theorem to find the measure of an angle in an isosceles triangle. The Isosceles Triangle Theorem states that the angles opposite the two equal sides of an isosceles triangle are equal. This means that if you know one of the angles in the triangle, you can determine the measure of the other two angles, since they will both be equal to the measure of the known angle.
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Identify the error in the student solution shown below. Find the correct answer. 2ln(x) = ln(3x) - [ln(9) - 2ln(3)] ln(x^2) = ln(3x) -0 in(x^2) = in(3x/0); division by 0, undifined
The correct answer is x = 9.
How do you compute a logarithm?Making use of the logarithm table, Compute the characteristic that the provided integer's whole number component dictates. Using the significant digits of the given number, find the mantissa. Add a decimal point after combining the characteristic and mantissa.
The student's solution has a division by zero error. The wrong step is when ln(x2) = ln(3x) - 0. It would have been better to first simplify the addition of ln(9) - 2ln(3) as follows:
The formula is ln(9) - 2ln(3) = ln(9) - ln(32) = ln(9/32) = ln(1/3).
When we substitute this number into the first equation, we get:
ln(1/3) - ln(3x) = 2ln(x)
ln(3x/1/3) = 2ln(x)
2ln(x) = ln (9x)
If we multiply both sides by their exponential, we get:
E = 2ln(x) + eln (9x)
x^2 = 9x
x^2 - 9x = 0
x(x - 9) = 0
As a result, the solutions are x = 0 and x = 9, but since ln(0) is undefined, we must determine whether x = 0 is a valid solution. So x = 9 is a workable answer.
Hence, the right response is x = 9.
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What is thirty five sixths times twenty five twelfths
Answer: 12.152
Step-by-step explanation:
Answer:
12.15 or 875/72
Step-by-step explanation:
35/6 = 5.8333333
25/12 = 2.083333
or
35/6 turns to 70/12
70/12 x 25/12 = 1750/12
1750/144 turns to 875/72
In a sampler box of candy there are 20 mints, 10 fudges and 20 toffees. A sweet is taken at random from the packet. What is the probability that it is fudge? Write the answer as a percentage.
Answer:
98%
Step-by-step explanation:
have a great day
Answer:
2% chance.
Step-by-step explanation:
20 + 20 + 10 equals 50. 1 divided by 50 equals 0.02, which is 2 percent.
Which answer choice shows a solution set in which all values, when input for x, will be true?
482x<12
{2, 4, 6, 8}
{4, 6, 8}
{1, 3, 5}
{1, 2, 3, 4}
can you help me with this math
Answer: B
Step-by-step explanation:
203.95-11.95=192
192/4=48
One ticket cost 48 dollars, and the service fee is $11.95. Therefore, c=11.95+48t
7/9 - 1/5 =. put answer in simplest form
35-9/45 = 26/45
The answer is 26/45.
Answer:
26/45
Step-by-step explanation:
35/45-9/45=26/45
The circumference of a circle is 98.596 millimeters. What is the radius of the circle? Use 3.14 for π.
197.2 mm
49.3 mm
31.4 mm
15.7 mm
Answer: D) 15.7
Step-by-step explanation:
Start with the formula C=2 πr
Then solve for r r=C2π = 98.62·π = 15.69(7)204
The radius of the circle is 15.7 mm.
What is Circumference?The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
We have,
The circumference of Circle = 2πr
Also, The circumference of a circle is 98.596 millimeters.
So, circumference of Circle = 2πr
98.596 = 2πr
98.596 = 6.28r
r= 98. 596 / 6.28
r = 15.7 mm
Thus, the radius is 15.7 mm.
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In 1999 the stock market took big swings up and down. A survey of 998 adult investors asked how often they tracked the portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily?
ANSWER
Option D
\(\frac{235}{998};0.235\)EXPLANATION
Given:
Total number of investors = 998
Number of investors tracking daily stock = 235
Determine the probability
\(\begin{gathered} Prob=\frac{number\text{ of investors tracking daily stock}}{total\text{ number of investors}} \\ =\frac{235}{998} \\ =0.235 \end{gathered}\)-2(x+2)+5x-
\( - 2(x + 2) + 5x - 1\)
I NEED HELP!!!!!!NOW!!!!!
Answer: Your answer is 6x-9
Step-by-step explanation: Hope I helped
Answer:
6x-9
Step-by-step explanation:
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a school district wants to justify building a new elementary school in the district because it believes that the expected number of students will start to exceed the capacity of the schools in the district. which statistical method would be most appropriate? group of answer choices binomial distribution confidence interval hypothesis test regression analysis
The answer is that regression analysis is the most appropriate method.
The most appropriate statistical method to justify building a new elementary school in the district would be regression analysis. This method can be used to examine the relationship between the expected number of students and the capacity of the schools in the district.
Regression analysis is a statistical method that helps to determine the relationship between two or more variables. In this case, the expected number of students would be the independent variable, while the capacity of the schools in the district would be the dependent variable. By analyzing the relationship between these variables, the school district can make predictions about how many students will need to be accommodated in the future and whether a new elementary school is necessary.
In contrast, binomial distribution is a statistical method that is used to calculate the probability of a specific number of successes in a set of trials, which would not be suitable for this situation. Confidence intervals and hypothesis tests are statistical methods used to draw conclusions about populations based on sample data, but may not be the most appropriate method for this situation.
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6. an economics researcher wants to estimate the mean number of hours worked by all grocery store employees in the county. how many employees must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean? a previous study showed that the population standard deviation is 7.9. the critical value for a level of confidence of 95% is 1.96.
The number of employees that must be included in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean is 107 employees.
To estimate the mean number of hours worked by all grocery store employees in the county with 95% confidence and a margin of error of 1.5 hours, we can use the sample size formula:
n = (Z * σ / E)²
where:
- n is the required sample size
- Z is the critical value (1.96 for a 95% level of confidence)
- σ is the population standard deviation (7.9 from the previous study)
- E is the margin of error (1.5 hours)
Plugging in the given values:
n = (1.96 * 7.9 / 1.5)²
n ≈ 106.56
Since you cannot have a fraction of an employee, you need to round up to the nearest whole number. Therefore, the researcher must include 107 employees in the sample to be 95% confident that the sample mean is within 1.5 hours of the population mean.
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help with khan academy
Answer:218 degrees
Step-by-step explanation:c
What is the length of the prism if the volume is 540 cm cube
Answer:
8.14 or 8.15
Step-by-step explanation:
Just do cube root of 540, which is about 8.14 Or 8.15.
The length of the prism would be 10 cm when the base of the prism is a rectangle with dimensions of 10 cm by 6 cm.
What is the volume of the cube?The volume of a cube is equal to the product of the length, width, and height of a cube.
The volume of a cube is given by the formula as
The volume of a cube = length × breadth × height
To determine the length of a prism based on its volume, you need to know the formula for the volume of a prism and the values of the other dimensions of the prism. The formula for the volume of a prism is V = Bh, where B is the area of the base of the prism and h is the height of the prism.
If the volume of the prism is 540 cm cube, and you know the values of B and h, you can use the formula V = Bh to solve for the length of the prism.
Assume, that the base of the prism is a rectangle with dimensions of 10 cm by 6 cm, and the height of the prism is 9 cm, then the volume of the prism would be V = Bh = (10 cm)(6 cm)(9 cm) = 540 cm cube. In this case, the length of the prism would be 10 cm, since that is one of the dimensions of the base of the prism.
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Endpoint: (7,1), Midpoint: (-8,-9)
Answer:
Step-by-step explanation:
(x+7)/2= -8
x + 7 = -16
x = -9
(y + 1)/2 = -9
y + 1 = -18
y = -19
(-9, -19)
Two farmers sell peanuts. The table and the graph below represent the two farmers where f(x) is the cost in dollars for x pounds of peanuts. What is the difference in the rate of change for the two functions
Answer:
number 2
Step-by-step explanation:
What is the tangent in a unit circle? How are calculations regarding the tangent done?
Answer:
Below
Step-by-step explanation:
TANGENT is defined as the opposite leg / adjacent leg of the right triangle formed by the angle in the unit circle
this is y / x in the image below :
Drag the answers to match the inequality and the situation it represents.
This is worth 100 points. Please answer. Do not skip over this question. Do not give incorrect or absurd answers.
Explain how to solve 3x − 4 = 6 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.
Answer:
x=3.333(approximated to thousanths)
3x3.3 - 4 = 6
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the greatest common factor of 12x-18
Answer:
6
Step-by-step explanation:
The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.
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Solve the equation for d.
Answer:
\(d=\frac{f+4}{3}\)
Step-by-step explanation:
3d - 4 = f
add 4 to both sides
3d = f + 4
divide both sides by 3
d = f/3 + 4/3
You are required to determine the relationship between Gibbs-Duhem equation and the activity coefficient of a selected binary chemical mixture (chemical A and chemical B ) in chemical industrial process. The following model is represented the excess Gibbs energy for the selected binary chemical mixture (chemical A and chemical B ). RT
G E
=X 1
lnγ 1
+X 2
lnγ 2
The Gibbs-Duhem equation says that, in a mixture, the activity coefficients of the individual components are not independent of one another but are related by a differential equation. In a binary mixture the Gibbs-Duhem relation is; x 1
( ∂x 1
∂lnγ i
) T,P
=x 2
( ∂x 2
∂lnγ 2
) T,P
The Gibbs-Duhem equation relates the activity coefficients of the individual components in a mixture. It states that the activity coefficients are not independent of each other but are related by a differential equation.
In the case of a binary mixture (chemical A and chemical B), the Gibbs-Duhem relation can be written as:
x1 * (∂x1/∂lnγ1)T,P = x2 * (∂x2/∂lnγ2)T,P
Here, x1 and x2 represent the mole fractions of chemical A and chemical B, respectively. The activity coefficients for chemical A and chemical B are denoted as γ1 and γ2, respectively.
The equation shows that the change in mole fraction of one component (x1) with respect to the change in the logarithm of its activity coefficient (lnγ1) is proportional to the change in mole fraction of the other component (x2) with respect to the change in the logarithm of its activity coefficient (lnγ2).
This relationship helps us understand how changes in the activity coefficients of the components affect each other in a binary mixture. By studying this relationship, we can gain insights into the behavior of the mixture and make predictions about its properties.
For example, let's consider a mixture of ethanol (chemical A) and water (chemical B). If the activity coefficient of ethanol (γ1) decreases, the Gibbs-Duhem equation tells us that the mole fraction of ethanol (x1) will also decrease. Similarly, if the activity coefficient of water (γ2) increases, the mole fraction of water (x2) will increase.
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What is this (College Math)
Hi, Which math? Alegbra,calculus, or geometry?) lol
Step-by-step explanation: