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What is the answer to this question?
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a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

Answer:

Step-by-step explanation:

Answer:

Volume = 7.912

Step-by-step explanation:

V = πr²h

V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )

V = 3.14 × 9/16 ×18/4

V = 3.14 × 0.56 × 4.5

V = 7.912

Answer:

The probability that all five lines will be in use when a customer calls customer service is 1/7776.

What is probability?

The proportion of favorable cases to all possible situations that can occur indicates how likely an event is to occur.

Step-by-step explanation:

Given that there are 5 lines and the probability for each line to be engaged in working hours is 1/6.

So, for all 5 lines to be engaged is

= 1/6 * 1/6 * 1/6 * 1/6 * 1/6

= \(\frac{1}{6} ^{5}\)

= \(\frac{1}{7776}\)

Therefore, the probability that all five lines are engaged is 1/7776.

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The five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

Measures of statistical dispersion, or the spread of the data, include the interquartile range. In addition to the IQR, other names for it include the midspread, middle 50%, fourth spread, and H-spread.

To find the five-number summary and interquartile range for this data set, we first need to find the quartiles.

Step 1: Find the median (Q2)

When a data collection is sorted from least to largest, the median is the midway value. Since there are 12 values in this data set, the median is the average of the sixth and seventh values:

Median (Q2) = (41 + 46)/2 = 43.5

Step 2: Find the lower quartile (Q1)

The lower quartile is the median of the lower half of the data set. Since there are 6 values below the median, we take the median of those values:

Q1 = (32 + 32)/2 = 32

Step 3: Find the upper quartile (Q3)

The upper quartile is the median of the upper half of the data set. Since there are 6 values above the median, we take the median of those values:

Q3 = (50 + 51)/2 = 50.5

Now we have all the information we need to construct the five-number summary and interquartile range:

Minimum: 29

Lower quartile (Q1): 32

Median (Q2): 43.5

Upper quartile (Q3): 50.5

Maximum: 53

Interquartile range (IQR) = Q3 - Q1 = 50.5 - 32 = 18.5

the five-number summary for this data set is 29, 32, 43.5, 50.5, and 53, and the interquartile range is 18.5.

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Step-by-step explanation:

the amplitude is the height of the wave.

like with sound - the further away you are, the lower the volume of the sound (as the sound volume is the indicator of the amplitude of a sound wave, or the brightness of a light is the indicator of the amplitude of a light wave).

the same for any other type of wave (like the seismic wave of an earthquake).

so, the larger the distance, normally the smaller the amplitude.

the area of the shaded quadrilateral is equal to the sum of area of triangle  AOC and BOC is equal to 110 unit square.

Suppose area of  triangle CEO = x and area of COD =y

OE : OB = 16:20 (Ratios of the areas of AEO and AOB)

Hence, Area of CEO : Area COB = 16:20

Area of CEO : (Area of COD +Area of DOB) = 16;20

x : (y+10) = 16:20

10x=5(y+10) ........(1)

AO : OD = 20:10 (Ratios of the areas of AOB and DOB)

Hence, Area of AOC : Area DOC = 20:10

(Area of AOE + Area of COE) : Area of DOB= 20:10

(16+x) : y = 20:10

16+x=2y.......(2)

From (1) and (2)

x=68 and y=42

so the area of quadrilateral is 110.

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a. It will take 7 months to pay off the credit card.

b. it will take 4 months to pay off the credit card.

Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.

We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

n = 6.18

Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

n = 3.43

Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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Answer:

77.91 units²

or

77.91 square units

Step-by-step explanation:

the area of a circle is A=pi*r²

since we only need a certain fraction, we will multiply it with 62/360

62° is the given angle. 360° would be the full circle

A = pi * 12² * 62/360

note that the answer is in square units, bc in "r²" the units themselves get squared, even tough we don't know if its inch or kilometers, its definitely squared

Answer:

$61.29 per day.

Step-by-step explanation:

Checking account balance on February 1st: $443

Checking account balance on February 7th: $872

Difference in balances: $872 - $443 = $429

Number of days between February 1st and February 7th: 7 days

Rate of change = Difference in balances / Number of days

Rate of change = $429 / 7 days

To find the rate of change per day, divide the difference in balances by the number of days:

Rate of change = $429 / 7 days ≈ $61.29 per day

Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.

The statement that describes inverse function best is the amount of time she has walked (in hours) when she is kilometers from tomsville i.e. option A

According to the question,

The given function denotes the distance travelled by Kira in kilometers from tomsville after hours of walking

D(t) =  10.4 - 4t

The inverse of the function is D⁻¹(x)

=> D(t) =  10.4 - 4t

Converting equation in terms of t,

=>  D(t) + 4t = 10.4

=> 4t = 10.4 - D(t)

=> t = 10.4 - D(t) /4

Inverse function =  D⁻¹(x) = 10.4 - D(x) /4

It denotes the amount of time she has walked (in hours) when she is kilometers from tomsville.

From the following statements in the question

Option (a) is correct about inverse function

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Answer:

I believe it is Inductive Reasoning.

Step-by-step explanation:

Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.

Deductive Reasoning is a basic form of valid reasoning.

According to the solving the explicit rule:

y = 52000 - 58000 * x

The explicit formula for an arithmetic sequence is a = a + (n - 1)d, and each term of the sequence may be computed without knowing the previous terms of the sequence. In general, the explicit formula is the nth term of an arithmetic, geometric, or harmonic sequence.

An implicit function is a function containing numerous variables, one of which is a function of the other set of variables. An explicit function is one in which the dependent variable may be clearly stated in terms of the independent variable.

Initial = 52000

Rate = 58000 each year

Determine the equation of the graph:

The equation can be used:

Amount = initial - rate * years

We used minus (-) because, the amount reduces as the student pays.

So,

y = amount

x = years

we have:

y = initial  - rate * x

putting the values we get:

y = 52000 - 58000 * x

According to the solving the explicit rule:

y = 52000 - 58000 * x

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Answer:

2 days 5 minuts 14 seconds

Step-by-step explanation:

 1 1   1 1    1

 18   19   26

+25  45  48

1 24   05  14

The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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Answer:

y = 7

Step-by-step explanation:

3y + (y+1) + (4y-3) = 54

3y + y + 4y + 1 - 3 = 54

8y - 2 = 54

8y = 54 + 2

8y = 56

y = 56/8

y = 7

Check:

3*7 + (7+1) + ((4*7)-3) = 54

21 + 8 + 28-3 = 54

29 + 25 = 54

sinθ = t/o

cosθ = m/o

tanθ = t/m

cscθ = o/t

secθ = o/m

cotθ = m/t

Answer:

1st option: -2 < x ≤ 3

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

We see that our x-values span from -2 to 3. Since -2 is an open dot, we cannot include it in our domain:

(-2, 3] or -2 < x ≤ 3

1.333...percent

Hope it helps

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

Step-by-step explanation:

Let h(x) = y

The exponentail function is of the form :

\(y = ab^x\)

We have :

\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)

Given points : (4, 9) and (5, 34.2)

We have:

\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)

Writing the equation with x, y and b:

\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)

a = 0.043

b = 3.8

When x = 6, y will be:

\(y = (0.043)(3.8^6)\\\\y = 128.47\)

This is not the y value in the question y = 59.4

Therefore (6, 59.4) does not lie on the graph h(x)

Answer:

Step-by-step explanation:

add both the equations then you will get

3x^3-x^2+2

but in the standard form there should be an x^1 term or x term since there is no term like that we write it as 0x

so the equation will be

3x^3-x^2+0x+2

The area of the parallelogram with vertices p(3, 3, 2), q(5, 6, 4), r(9, 10, 12), and s(7, 7, 10) is √336≈18.34 units.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighboring sides, but it must have opposite sides that are parallel for it to be a parallelogram.

Calculate the length of PQ → Position vector of Q - Position vector P

PQ→ (5-3)i + (6-3)j + (4-2)k

PQ→ 2i + 3j + 2k

Calculate the length of PS →Position vector of S - Position vector P

PQ→ (7-3)i + (7-3)j + (10-2)k

PQ→ 4i + 4j + 8k

Area of parralelogram = \(\left[\begin{array}{ccc}i&j&k\\2&3&2\\4&4&8\end{array}\right]\)

= √16² + 8² + 4²

=√336

=18.34 units

The area of a parallelogram is the region bounded by the parallelogram's four sides. It is measured in square units like cm2, m2, and inch2 and can be computed if we know the size of the parallelogram's base and height.

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To calculate the percentage of questions Danielle got correct on her math test, we can divide the number of questions she got correct by the total number of questions on the test and then multiply by 100. In this case, Danielle got 23 out of 25 questions correct, so we can calculate her percentage as follows: (23/25) * 100 = 92%. Therefore, Danielle got 92% of the questions correct on her math test.

Percent = amount per 100

23/25 = amount per 25

25 x 4 = 100

23 x 4 = 92

92/100 = 92%

Answer = 92%

Hope this helps!

It took Rapunzel approximately 14.58 minutes to clean her room.

Cleaning refers to the process of removing dirt, dust, and other unwanted substances from a surface or an object.  

Let's start by converting the time to minutes.

15 1/2 minutes = 15.5 minutes

Let's now subtract the time she finished cleaning from the time she started cleaning:

15.5 - 0.92 = 14.58 minutes

Therefore, it took Rapunzel approximately 14.58 minutes to clean her room.

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Answer:

Researcher B

Step-by-step explanation:

Normally, when all other things being equal, we usually say that power is higher when the standard deviation is small than when it is large.

Now, from researcher A, standard deviation is 110 while from researcher B, standard deviation is 60.

We can see that the standard deviation for researcher B is smaller than that of researcher A.

Therefore, we can conclude that since the standard deviation for researcher B is lesser than that of researcher A, it means that Researcher B will have more power to detect an effect.

Answer:

an estimation is 30000

Step-by-step explanation:

An estimate is a number that is close, so we round 395 to 400 and 76 to 75

Answer:

30020

estimate 395 x 75 = 29625

the answer is reasonable

Step-by-step explanation: