Diana filled a bucket with 5/6 of a gallon of water. Later, she poured out 1/6 of a gallon
of the water. How much water is left in the bucket?
Write your answer as a fraction or as a whole or mixed number.

Answer:

120, The answer is 120

Step-by-step explanation:

Determine the measure of the interior angle at vertex C.

A. 120

B. 180

C. 90

D. 200

Mean absolute percentage error is used in situations where you need to compare forecasting methods for different time periods.

The most used metric for gauging forecast accuracy is mean absolute percent error. It belongs to the category of scale-independent percentage errors, which may be used to compare series on various scales.

MAPE = mean (| eᵢ |/yᵢ )*100

where eᵢ is the error term and yᵢ is the actual data at the time i.

The drawback of MAPE is that it loses definition if the actual figure for any observation in the data has a value of 0.

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Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.

Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,

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Answer:

63.57817848

Step-by-step explanation:

all will be in degrees:

cos 40 sinx - sin 40 cos x = sin(x - 40) by the formula sin(A − B) = sinA cosB − cosA sinB

sin(x - 40) = 2/5

x - 40 = arcsin(2/5)

x - 40 = 23.57817848

x = 63.57817848 degrees

Answer:

x =  63.57817848

x = 196.4218215

Step-by-step explanation:

cos 40 sin x - sin 40 cos x = 2/5

sin x cos 40 - cos x sin 40 = 2/5

Using trig identities   sin(α – β) = sin(α) cos(β) – cos(α) sin(β)

sin ( x - 40) = 2/5

Rewriting as m = x-40

sin ( m) = 2/5

Taking the inverse sin of each side

sin ^-1 sin m = sin ^-1 (2/5)

m = 23.57817848

m = 180 -23.57817848  = 156.4218215

now find x

x -40 = m

x = m+40

x = 23.57817848 +40 = 63.57817848

x = 156.4218215 + 40 = 196.4218215

Answer:

multiplicative identity property

Step-by-step explanation:

Any number times 1 give it itself.

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

To create a box and whisker plot for the given dataset {69, 88, 94, 73, 78, 90, 68}, follow these steps:

Step 1: Arrange the data in ascending order:

68, 69, 73, 78, 88, 90, 94

Step 2: Find the five-number summary:

Minimum: The smallest value in the dataset, which is 68.

First quartile (Q1): The median of the lower half of the dataset. In this case, it's the median of {68, 69, 73}, which is 69.

Median (Q2): The middle value of the dataset. In this case, it's 78.

Third quartile (Q3): The median of the upper half of the dataset. In this case, it's the median of {88, 90, 94}, which is 90.

Maximum: The largest value in the dataset, which is 94.

Step 3: Create the box and whisker plot:

Draw a number line with a range from the minimum (68) to the maximum (94).

Mark the first quartile (Q1) at 69.

Mark the median (Q2) at 78.

Mark the third quartile (Q3) at 90.

Draw a box from Q1 to Q3.

Draw a vertical line (whisker) from the box to the minimum (68) and another vertical line from the box to the maximum (94).

The resulting box and whisker plot for the given dataset would look like this:

  |

 94|                 ▄

  |                ╱ ╲

 90|              ╱   ╲

  |             ╱     ╲

 88|            ▇       ▂

  |            ▇       ▂

 78|            ▇       ▂

  |            ▇       ▂

 73|          ╱         ╲

  |         ╱           ╲

 69|        ▃             ▃

  |       ╱               ╲

 68|      ╱                 ╲

  |_________________________________

    68     73     78     88     94

This plot represents the distribution of the given dataset, showing the minimum, maximum, first quartile (Q1), median (Q2), and third quartile (Q3).

The five-number summary for the dataset are Minimum: 68, Q1: 69, Median: 78, Q3: 90 and Maximum: 94.

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The correct Answer is D

s1 = s2 and r1 = r2

The two data sets have the same range. The first data set has a range of 88 − 56 = 32, and the second data set has a range of 112 − 80 = 32.

This relationship is sometimes referred to as the range rule for standard deviation. The range rule tells us that the standard deviation of a sample is approximately equal to one-fourth of the range of the data. In other words s = (Maximum – Minimum)/4.

The standard deviation is a more effective measure of variation than the range. Range of the data is a measure of variation which gives the difference in the maximum and the minimum observation of the dataset. It is only based on two observations, the maximum and the minimum.

Alternatively, it can be seen visually that the ranges are the same because the two dot plots are aligned, the scales of the graphs are the same, and the graphs have the same width. The two data sets have different standard deviations. Both dot plots show distributions that have a mean near the center value of the dot plot. The first dot plot shows most values clustered near the mean, while the second dot plot shows most values farther from the mean. Therefore, the standard deviations of the two data sets are not equal—the data represented by the second dot plot has a greater standard deviation.

Choices A, B, and C are incorrect because they incorrectly assert either that the standard deviations are the same or that the ranges are different.

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Answer:

(A): As year increases the number of pikas reduces.

(B): As year increases the number of pikas increases as opposed to when the rate reduces.

Step-by-step explanation:

See comment for complete question

Given

\(a = 144\) --- Initial Population

\(r = 8\%\) --- rate

(A) WHEN THE RATE DECREASES

First, we need to write out the function when the population decreases.

This is given as:

\(f(x) = a(1-r)^x\)

Substitute values for a and r

\(f(x) = 144(1-8\%)^x\)

Convert % to decimal

\(f(x) = 144(1-0.08)^x\)

\(f(x) = 144(0.92)^x\)

Next, we calculate the average rate of change for both intervals using:

\(Rate = \frac{f(b) - f(a)}{b-a}\)

For 1 to 5:

\(Rate = \frac{f(5) - f(1)}{5-1}\)

\(Rate = \frac{f(5) - f(1)}{4}\)

Calculate f(5) and f(1)

\(f(x) = 144(0.92)^x\)

\(f(1) = 144*0.92^1 =144*0.92=132.48\)

\(f(5) = 144*0.92^5 =144*0.66=95.04\)

\(Rate = \frac{95.04 - 132.48 }{4}\)

\(Rate = \frac{-37.44}{4}\)

\(Rate = -9.36\)

For 6 to 10:

\(Rate = \frac{f(10) - f(6)}{10-6}\)

\(Rate = \frac{f(10) - f(6)}{4}\)

Calculate f(6) and f(10)

\(f(x) = 144(0.92)^x\)

\(f(6) = 144*0.92^6 =144*0.61=87.84\)

\(f(10) = 144*0.92^{10} =144*0.43=61.92\)

\(Rate = \frac{61.92-87.84}{4}\)

\(Rate = \frac{-25.92}{4}\)

\(Rate = -6.48\)

So, we have:

\(Rate = -9.36\) for year 1 to 5

This means that the number of pikas reduces by 9.36 yearly

\(Rate = -6.48\) for year 6 to 10

This means that the number of pikas reduces by 6.48 yearly

So, we can say that, as year increases the number of pikas reduces.

(B) WHEN THE RATE INCREASES

First, we need to write out the function when the population decreases.

This is given as:

\(f(x) = a(1-r)^x\)

Substitute values for a and r

\(f(x) = 144(1+8\%)^x\)

Convert % to decimal

\(f(x) = 144(1+0.08)^x\)

\(f(x) = 144(1.08)^x\)

Next, we calculate the average rate of change for both intervals using:

\(Rate = \frac{f(b) - f(a)}{b-a}\)

For 1 to 5:

\(Rate = \frac{f(5) - f(1)}{5-1}\)

\(Rate = \frac{f(5) - f(1)}{4}\)

Calculate f(5) and f(1)

\(f(x) = 144(1.08)^x\)

\(f(1) = 144(1.08)^1 = 144*1.08= 155.52\)

\(f(5) = 144(1.08)^5 = 144*1.47= 211.68\)

\(Rate = \frac{211.68 - 155.52}{4}\)

\(Rate = \frac{56.16}{4}\)

\(Rate = 14.04\)

For 6 to 10:

\(Rate = \frac{f(10) - f(6)}{10-6}\)

\(Rate = \frac{f(10) - f(6)}{4}\)

Calculate f(6) and f(10)

\(f(x) = 144(1.08)^x\)

\(f(6) = 144(1.08)^6 = 228.52\)

\(f(10) = 144(1.08)^{10} = 310.89\)

\(Rate = \frac{310.89-228.52}{4}\)

\(Rate = \frac{82.37}{4}\)

\(Rate = 20.59\)

So, we have:

\(Rate = 14.04\) for year 1 to 5

This means that the number of pikas increases by 14.04 yearly

\(Rate = 20.59\) for year 6 to 10

This means that the number of pikas increases by 20.59 yearly

So, we can say that, as year increases the number of pikas increases as opposed to when the rate reduces.

Answer:

Step-by-step explanation:

x = 20

Answer:

20

Step-by-step Explanation:

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).

An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.

Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:

(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)

Note that this vector has length 3, so we can divide it by 3 to get a unit vector:

(-3/3, 0/3, 0/3) = (-1, 0, 0)

So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).

To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.

Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):

v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)

= (0, 1, 0) - 0 / 9 * (-3, 0, 0)

= (0, 1, 0)

We can then normalize this vector to get a unit vector:

v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)

So, the second row of the orthogonal matrix A is (0, 1, 0).

To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:

(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)

We normalize this vector to get a unit vector:

v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)

So, the third row of the orthogonal matrix A is (0, 0, -1).

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

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The entropy change during the isothermal reversible expansion of one mole of an ideal gas from a volume of 5 dm³ to a volume of 60 dm³ at 300 K is approximately 36.48 J/K.

The entropy change (ΔS) of an ideal gas during an isothermal reversible process can be calculated using the formula:

ΔS = nR ln(V₂/V₁)

where ΔS is the entropy change, n is the number of moles of gas, R is the gas constant (8.314 J/(K·mol)), V₁ is the initial volume, and V₂ is the final volume.

In this case, we have one mole of gas (n = 1), an initial volume of 5 dm³ (V₁ = 5 dm³), and a final volume of 60 dm³ (V₂ = 60 dm³). The temperature is given as 300 K.

Plugging these values into the formula, we get:

ΔS = (1 mol) * (8.314 J/(K·mol)) * ln(60 dm³/5 dm³)

Calculating the natural logarithm term:

ln(60/5) = ln(12)

Using a calculator, ln(12) is approximately 2.4849.

Substituting this value back into the equation:

ΔS = (1 mol) * (8.314 J/(K·mol)) * 2.4849

Calculating the result:

ΔS ≈ 20.69 J/K

So, the entropy change during the process is approximately 20.69 J/K.

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Answer:

2 5/8 inches

Step-by-step explanation:

There are 2 pieces 5 3/4 inches long.

There is 1 piece 5 1/2 inches long.

There are 4 pieces 5 1/4 inches long.

The seventh longest piece is one of the pieces measuring 5 1/4 inches.

Juan's piece is 1/2 as long as 5 1/4 inches.

1/2 × 5 1/4 inches = 1/2 × 21/4 = 21/8 inches = (16/8 + 5/8) = 2 5/8 inches

Answer:

(9-7)+6

2+6

8...........

Answer:8

Step-by-step explanation:9-7=2. 2+6=8

Answer:

False

Step-by-step explanation:

An acute angle can be scalene

Eg - 2 angles of 20 degrees , and 1 angle of 50 degre

HOPE THIS WILL HELP YOU

Step-by-step explanation:

\( \frac{ \sin(81) }{x} = \frac{ \sin(40) }{7} \\ x \times \sin(40) = 7 \times \sin(81) \\ x = \frac{7 \times \sin(81) }{ \sin(40) } = 10.75 = 10.8 \: cm\)

Answer:

x is 10.8 cm

Step-by-step explanation:

from Lami's theorem:

\( \frac{7}{ \sin(40 \degree) } = \frac{x}{ \sin(81 \degree) } \\ \\ x = \frac{7 \sin(81 \degree) }{ \sin(40 \degree) } \\ \\ x = 10.8 \: cm\)

Answer:0.48

Step-by-step equation:

Answer:

587

Step-by-step explanation:

Answer:

Hill 1: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 3: F(x) = 4(x - 2)(x + 5)

Step-by-step explanation:

Hill 1

You must go up and down to make a peak, so your function must cross the x-axis six times. You need six zeros.

Also, the end behaviour must have F(x) ⟶ -∞ as x ⟶ -∞ and F(x) ⟶ -∞ as x⟶ ∞. You need a negative sign in front of the binomials.

One possibility is

F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2

Multiplying the polynomial by -½ makes the slopes shallower. You must multiply by -2 to make them steeper. Of course, flipping the hills converts them into valleys.

Adding 3 to a function shifts it up three units. To shift it three units to the right, you must subtract 3 from each value of x.

The transformed function should be

F(x)  = -2(x +1)(x)(x -2)(x -3)(x - 6)(x - 7)

Hill 3

To make a shallow parabola, you must divide it by a number. The factor should be ¼, not 4.

The zeroes of your picture run from -4 to +7.

One of the zeros of your parabola is +5 (2 less than 7).

Rather than put the other zero at ½, I would put it at (2 more than -4) to make the parabola cover the picture more evenly.

The function could be

F(x) = ¼(x - 2)(x + 5).

In the image below, Hill 1 is red, Hill 2 is blue, and Hill 3 is the shallow black parabola.

Answer:

15

Step-by-step explanation:

Answer:

43

Step-by-step explanation

-6 x -4 - -10 - -9

First - simplify the expression

-6 x -4 + 10 + 9

remember that 2 negatives is equal to a positive

second - multiply -6 and -4

24 + 10 + 9

negative times a negative is a positive and 6 x 4 is 24

third - add

24 + 10 = 34

34 + 9 = 43

If you don't understand anything or are still confused, lmk

Multiply and divide (left to right) -6(-4): 24

= 24 - (-10) - (-9)

Add and subtract (left to right) 24 - (-10) - (-9): 43

= 43

The answer is 43

Trinomials are the polynomials with triplets. Ok, now let's solve the given question.

For The Better Preference, Plz have a look of the handwritten answer which i had solved in the above attachment.

So, the answer of the product of the following polynomials are:‐ 4m² – 3n² – 2p² + mn – 2mp + 5 np.

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The trigonometric ratios for each triangles are:

Please note that all angles B are the right angle, then:

cos B = 1; sin B = 0; tan B = -

The trigonometric ratio of sin, cos, tan, can be formulated as:

(please refer to the attached triangle below for reference)

cos A = side adjacent to A / Hypotenuse

Cos A = b/c

Sin A = side opposite to A / Hypotenuse

Sin A = a/b

Tan A = Side opposite to A / Side adjacent to A

Tan A = a/b

From these formulas, we can find that:

Triangle 1

Cos A = 40/50 = 4/5

Sin A = 30/50 = 3/5

Tan A = 30/40 = 3/4

Cos C = 30/50 = 3/5

Sin C = 40/50 = 4/5

Tan C = 40/30 = 4/3

Triangle 2

Cos A = 27/45 = 3/5

Sin A = 36/45 = 4/5

Tan A = 36/27 = 4/3

Cos C = 36/45 = 4/5

Sin C = 27/45 = 3/5

Tan C= 27/36 = 3/4

Triangle 3

Cos A = 15/17

Sin A = 8/15

Tan A = 8/15

Cos C = 8/17

Sin C = 15/17

Tan C = 15/8

Please note that all angle B on the three triangles are all a right angle, then:

Cos B = 1

Sin B = 0

Tan B = -

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The given pattern 5/7, 8/7, 11/7, 2, ....... is in the form of the arithmetic progression AP. The next 3 terms are  17/7, 20/7, 23/7.

An arithmetic progression is a sequence whose terms continue to increase and otherwise decrease by a constant number. The common difference is the set amount through which they either increase or decrease.

The following arithmetic progression formulas are frequently utilized to solve various AP problems for the initial term 'a' of an AP and the common difference 'd'-

Now, as per the stated question;

The AP given as; 5/7, 8/7, 11/7, 2, ...........

The series consists of four given terms.

Consider the initial term be 'a₁' = 5/7.

Then, the second term be 'a₂' = 8/7.

And, the third term be 'a₃' = 11/7.

And, the fourth term is 'a₄' = 2.

The AP have the same common difference. so,

d = a₃ - a₂

Substitute the values.

d = 11/7 - 8/7

d = 3/7

Thus, the common difference is 3/7.

or d = a₄ - a₃ (Put the values)

d = 2 - 11/7

d = 3/7

As, a₃ - a₂ = a₄ - a₃

Thus, we can conclude that the given sequence is in AP.

The fifth term will be; a₅ = a₄ + d = 2 + 3/7

a₅ = 17/7

Now, the 6th term will be; a₆ = a₅ + d = 17/7 + 3/7

a₆ = 20/7

Similarly, the 7th term will be; a₇ = a₆ + d = 20/7 + 3/7

a₇ = 23/7

Therefore, it can be said that the given sequence is in AP next three terms be 17/7, 20/7, 23/7.

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Answer:

(x2 +2x+1)+(y2+4y)=31+1

(x+1)2 +(y2+4y)=32

(x+1)2 +(y2+4y+4)=32+4

(x+1)2 +(y+2)2=36

The equation can be written in the form (x-p)2 +(y-q)2=r2

so it represents a circle with the radius r=6  and the center (-1,-2)

Step-by-step explanation:

Answer:

6 units is the amswer

Step-by-step explanation:

here you gooo

Determining the monthly payment as $668.54, it seems that Jax cannot buy this car since he wants his monthly payment to be under $500.

The monthly payment is the periodic payment that must be made by Jax to settle the credit or car loan, including the finance charges.

The monthly payment can be determined using an online finance calculator.

N (# of periods) = 60 months (5 years x 12)

I/Y (Interest per year) = 5.5%

PV (Present Value) = $35,000

FV (Future Value) = $0

Results:

Monthly Payment (PMT) = $-668.54

The sum of all periodic payments = $-40,112.44

Total Interest = $5,112.44

Thus, Jax must pay $668.54 monthly to finance the car and cannot based on his budget.

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Step-by-step explanation:

x+a= 180

x+ 52= 180

x= 180-52

x= 128°

Answer: Its 76!

Step-by-step explanation:

52+52=104

180-104=76

Hope this helps!

Sorry if im wrong, im just leanring this in class too!

The proportion of the area under the curve that lies to the right of t = 2.015 in a t-distribution with 5 degrees of freedom can be calculated using the t-distribution function in a statistical software package such as R.

The answer is approximately 0.9522. This means that 95.22% of the area under the curve lies to the right of t = 2.015. This indicates that the probability of observing a value of t greater than 2.015 is quite high.

This is because the t-distribution with 5 degrees of freedom has a larger spread than the normal distribution, which means that the probability of observing values further from the mean is greater.

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Answer:

This graph shows a function because no vertical line passes through more than one point on the graph.

Step-by-step explanation:

Answer:

Answer Picture:

Step-by-step explanation:

Answer:

6/25

Step-by-step explanation:

.24 = 24/100 = 6/25

Answer:

6/25

Step-by-step explanation:

step 1 The decimal number = 0.24

step 2 Write it as a fraction

0.24/1

step 3 Multiply 100 to both numerator & denominator

(0.24 x 100)/(1 x 100) = 24/100

It can be written as 24% = 24/100 or 24/100

step 4 To simplify 24/100 to its lowest terms, find LCM (Least Common Multiple) for 24 & 100.

4 is the LCM for 24 & 100

step 5 divide numerator & denominator by 4

24/100 = (24 / 4) / (100 / 4)

= 6/25

6/25 is a simplest fraction for the decimal point number 0.24