What is the remainder when 17^77 is divided by 35?

The mean profit per day, calculated using a working mean of N3,300, is N3,272.50 for 16 consecutive days.

To calculate the mean profit per day,

We simply need to add up all the profits for the 16 days, and then divide by 16 (the number of days).

Here are the steps,

Add up all the profits,

⇒ N3 290 + N3350 + N3270 + N3210 + N3 400 + N3 300 + N3380 + N3260 + N3 280 + N3320 + N3300 + N3 360 + N3430 + N3250 + N3330 + N3230 = N52 360

Divide by 16,

⇒  N52 360 ÷ 16 = N3 272.50

So the mean profit per day is N3 272.50,

which is slightly lower than the working mean of N3 300.

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Answer:

20

Step-by-step explanation:

Total no of plants in a garden = 36

The ratio of tomato plants to cucumber plants to be 4:5.

Let tomato plants are 4x and cucumber plants is 5x.

ATQ,

4x+5x=36

9x = 36

x = 4

For cucumber plant, 5x = 5(4) = 20

So, there are 20 cucumber plants will be in Reggie's garden

Answer:

He added $25 to the contents of his wallet.

Step-by-step explanation:

Here's what's happening, symbolically:

$6 + m = $31, or m = $25.  Jake added $25 (represented by m) to the contents of his wallet.

Answer:

Ross = 15 hours

Russel = 40 hours

Step-by-step explanation:

Let Ross have used their sprinklers for x hours

Let Russell  have used their sprinklers for y hours

Together they used 55 hours

x+y = 55 hours

The output of Ross is 35 liters per hour and Russell is 30 liters per hour for a total of 1725

35x + 30y = 1725

Multiply the first equation by -30

-30(x+y=55)

-30x -30y = -1650

Add this to the second equation to eliminate y

-30x -30y = -1650

35x + 30y = 1725

-----------------------------

5x =75

Divide each side by 5

x = 15

Now find y

x+y = 55

y = 55-15

y = 40

Answer:

------------------

Let the amount deposited be x. It is assumed we are talking about simple interest.

After 4 years the interest amount is:

95% of this amount is Rs 4940:

Mrs Majhi deposited Rs 20000.

Mrs. Majhi deposited Rs 20000 in her bank account. This was calculated by first finding the total interest (before tax) and then using the formula for simple interest to determine the principal amount.

The question is based on the concepts of Simple Interest and taxation. We know that Mrs Majhi received Rs 4940 as net interest after 4 years and this amount is 95% of the total interest (since 5% was paid as income tax). The total interest can be calculated as (4940 / 95) * 100 = Rs 5200.

The rate of interest is given as 6.5% per annum. Thus, the money deposited (Principal) by her can be calculated using the formula for simple interest (I = PRT/100), where P is the Principal, R is the rate of interest, and T is the time. Re-arranged to calculate the Principal (P), it becomes P = I / (R*T) = 5200 / (6.5*4) = Rs 20000.

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Answer:

D) 216cm²

Step-by-step explanation:

Triangles: a=1/bh

a=1/2(6)(8)

a=24 (2 of them)

Base: 6x7=42

Back: 8x7=56

Front Rectangle: 7x10=70

24+24+42+56+70=216cm²

The mean of the given data set is 3.5, the variance is 5.056, and the approximate mean using the grouped data table is 0.428.

The average of a set of values is referred to as the mean. To calculate the mean of a dataset, add up all of the values and divide by the number of values.

We can calculate the mean of the given data set as follows:

Mean = (9 + 6 + 2 + 0 + 2 + 3 + 5 + 2 + 1 + 5)/10

Mean = 3.5

Variance:Variance is a measure of how much a set of data varies. In other words, variance tells us how far each value in the dataset is from the mean. The variance formula is as follows:

σ² = (Σ(x - μ)²) / N

Where σ² is the variance, Σ is the sum, x is each value in the data set, μ is the mean of the data set, and N is the number of values in the data set.

Using the above formula, we can calculate the variance for the given data as follows:

First, we need to calculate the mean of the data set.x f(x)

xf(x)4 1 45 3 15 6 4 24 7 4 28 8 2 16

Total 14 128

Mean (μ) = 128 / 14 = 9.14

σ² = (Σ(x - μ)²) / N

σ² = [1(4 - 9.14)² + 3(5 - 9.14)² + 4(6 - 9.14)² + 4(7 - 9.14)² + 2(8 - 9.14)²] / 14

σ² = 5.056

Approximating the Mean:

We can use the midpoint of each interval as an approximate value for the entire interval. We can calculate the approximate mean as follows:

Mean = Σ(midpoint × proportion of stocks)

Mean = (-0.80 × 0.03) + (-0.40 × 0.03) + (0.00 × 0.2) + (0.40 × 0.44) + (0.80 × 0.16) + (1.20 × 0.06) + (1.60 × 0.05) + (2.00 × 0.03)

Mean = 0.428

Therefore, the mean of the given data set is 3.5, the variance is 5.056, and the approximate mean using the grouped data table is 0.428.

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The perimeter of the rectangle when the width is 15 inches, would therefore be 90 inches

The width of the rectangle is said to be half of the length which means that because the width is 15 inches, then the length would be:

= 2 x width

= 2 x 15

= 30 inches

As we now have the length as 30 inches and the width as 15 inches, the perimeter of the rectangle would therefore be :

= 30 + 30 + 15 + 15

= 60 + 30

= 90 inches

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The full question is:

The width of a rectangle is half of the length. What is the perimeter of the rectangle when the width is 15 inches?

5k² = 60 - 20k

5k² + 20k - 60 = 0

k² + 20/5k - 60/5 = 0 dividing by 5 at both sides

k² + 4k - 12 = 0

If we compute (k+2)², we get:

(k+2)² = k² + 2*k*2 + 2² = k² + 4k + 4

Then,

k² + 4k - 12 + 4 - 4 = 0

(k² + 4k + 4) + (-12 - 4) = 0

(k+2)² - 16 = 0

(k+2)² = 16

k + 2 =√16

This has two solutions

k + 2 = 4 or k + 2 = -4

k = 4 - 2 k = -4 - 2

k = 2 k = -6

Answer:

58,928.6 rotations

Step-by-step explanation:

2.2 in x (2.54cm/in) x (1m/100cm)= .056 m/circumference

3300m/(.056m/rotation) = 58,928.6 rotations

Answer:

Bru how can u not know that

Step-by-step explanation:

1. 2 pieces

2. 0.008

3. 4 pieces

4.0.016

5. 8 pieces

6.0.32

7.16

8.0.64

Answer

The average for the next test would be 60

Step-by-step explanation:

50+50+50+50+100= 300

then divide by 5 students

300/5 = 60

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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Answer:

$6.81 or 681 US Cents

Step-by-step explanation:

100 - 19 = 81

7 - 1 = 6

$7.00 - .19 = $6.81

or 681 US Cents.

To analyze the increasing boiling points as carbon chains grow longer, we need to consider the intermolecular forces that come into play. The primary intermolecular force involved in hydrocarbon boiling points is London dispersion forces, also known as van der Waals forces.

London dispersion forces arise from temporary fluctuations in electron distribution, leading to temporary dipoles in molecules. These temporary dipoles induce dipoles in neighboring molecules, resulting in attractive forces. The strength of London dispersion forces depends on the size of the electron cloud, which is influenced by molecular mass and shape.

As the carbon chains grow longer, the molecular mass increases. Larger molecules have more electrons, leading to larger electron clouds, and consequently, stronger London dispersion forces. Therefore, longer carbon chains generally exhibit higher boiling points compared to shorter chains.

Regarding the isomers of a compound, different isomers can have different boiling points. Isomers are compounds with the same molecular formula but different structural arrangements. The arrangement of atoms in a molecule affects its shape, which, in turn, influences the strength and nature of intermolecular forces.

For example, consider the isomers of pentane: n-pentane, 2-methylbutane, and 2,2-dimethylpropane. N-pentane has a linear structure, while the other two isomers have branched structures. The linear structure allows for closer molecular packing, leading to stronger intermolecular forces and a higher boiling point compared to the branched isomers. Therefore, in this case, the isomers of pentane have different boiling points.

In general, isomers with more compact and symmetrical structures have weaker intermolecular forces and lower boiling points compared to their more linear or less symmetrical counterparts. However, it is important to note that other factors, such as functional groups and molecular polarity, can also influence boiling points and may lead to exceptions to this general trend.

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15 inches is the height of the pyramid

Step-by-step explanation:

The volume of a cube is a³

Given a = 5 inches

→ Volume = a³

= 5³

= 5×5×5

= 125 in²

The volume of a pyramid is \( \frac{1}{3} {a}^{2}h\)

Given a = 5 inches , h = height of pyramid

\( = > \frac{1}{3} {a}^{2} h\)

\( = > \frac{1}{3}(5)^{2}h\)

\( = > \frac{1}{3} \times 25 \times h\)

\( = > \frac{25}{3}h\)

then,

\(125 = \frac{25h}{3}\)

\( = > 25h = 125 \times 3\)

\( = > 25h = 375\)

\( = > h = \frac{375}{25} \)

\( = > h = 15\)

Hence, the height of pyramid is 15 inches

Answer:

I don't know

Step-by-step explanation:

Because I don't have a protractor and a scaled representation of the image you sent.

Answer:

D.) AFD and EFD

Step-by-step explanation:

supplementary angles equal 180° and this is the only set that produces 180 when added together. the supplementary angle is basically the whole straight line

The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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Answer:

Step-by-step explanation:

The statements that are true regarding undefined terms are;

The reason these statements above are true are as follows:

Examples of undefined terms includes a point, a plane, a line and a set

A point is for representing a position in space. It has no dimensions

Therefore, the statement, A point has no length or width is true

A plane is defined as an interconnected set of points that lay on the same flat surface, and extends infinitely along the surface in all directions

A line is defined as an infinite set of points that are arranged in straight path and extends without end in opposite directions

Therefore, the statement, a line consists of an infinite number of points is true

Therefore, a plane can be considered as being made up of an infinite set of lines that are located on a flat surface

Therefore, the statement, a plane consists of an infinite set of lines is true

Answer:

  a) 48 gigabytes

  b) 250 minutes, or 4 hours 10 minutes

Step-by-step explanation:

For D(t) = 75 -0.3t modeling the number of remaining gigabytes to download after t minutes, you want to find D(90) and t such that D(t) = 0.

  D(90) = 75 -0.3·90 = 48

After 90 minutes, 48 gigabytes are left to download.

The time required to complete the entire download is given by ...

  0 = 75 - 0.3t

  0 = 250 -t . . . . . divide by 0.3

  t = 250 . . . . . . add t

It will take 250 minutes, or 4 hours 10 minutes to download the entire game.

__

Additional comment

The attached calculator screen shows conversion to hours and minutes. Hours, minutes, seconds are computed "base-60" the same way that Degrees, minutes, seconds are computed "base-60". 250 minutes is converted to hours by dividing by 60 min/hour. We can use the →DMS function of the calculator to show decimal or fractional hours in hours : minutes : seconds. In this use of that function, degrees represents hours.

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Answer:

224

Step-by-step explanation:

If c = 1 and d = 2:

(-1³ + 2⁴)² - (-1 + 2)³

(-1 + 16)² -(1)³

(15)² -1

225 -1

224

The raw score associated with a z-score of -0.76 is approximately 11.1908.

To determine the raw score associated with a given z-score, we can use the formula:

Raw Score = (Z-score * Standard Deviation) + Mean

Substituting the values given:

Z-score = -0.76

Standard Deviation = 1.47

Mean = 12.31

Raw Score = (-0.76 * 1.47) + 12.31

Raw Score = -1.1192 + 12.31

Raw Score = 11.1908

Therefore, the raw score associated with a z-score of -0.76 is approximately 11.1908.

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a) Population of city in 2015 = 640000

b) Population of city in 2019 = 777924

Population-growth happens when an initial population increases by the same percentage or factor over equal time increments or generations.

Given,

Population of city in 2017 (P) = 705600

Rate per annum r = 5% = 0.05

a) Population of city in 2015 (p) = ?

Time difference 2015 and 2017 = 2 years

Population of city in 2017

P = p(1 + r)ⁿ

705600 = p(1 + 0.05)²

p = 705600/1.05²

p = 705600/1.1025

p = 640000

b) Population of city in 2019 = ?

Time difference 2017 and 2019 n = 2 years

Population of city in 2019

= P(1 + r)ⁿ

= 705600(1+0.05)²

=  705600(1.05)²

= 705600 × 1.1025

= 777924

Hence, 640000 is population of city in 2015.

777924 is population of city in 2019

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Opposite angles of a cyclic quadrilateral are supplementary, so

\(x+17+6x-5=180 \\ \\ 7x+12=180 \\ \\ 7x=168 \\ \\ x=24 \\ \\ \\ \implies \angle QRO=2(24)+19=\boxed{67^{\circ}}\)

(a) To find the average value of f(x) = ln(x) on the interval [1, 3], we can use the formula for the average value:

f = (1/(b-a)) * ∫[a,b] f(x) dx

In this case, a = 1 and b = 3. Let's calculate the integral:

∫[1, 3] ln(x) dx

Using integration by parts:

Let u = ln(x), dv = dx

du = (1/x) dx, v = x

∫ ln(x) dx = x ln(x) - ∫ (x * (1/x)) dx

= x ln(x) - ∫ dx

= x ln(x) - x + C

Now, let's evaluate the integral from 1 to 3:

∫[1, 3] ln(x) dx = [3 ln(3) - 3] - [1 ln(1) - 1]

= 3 ln(3) - 3 - 1 ln(1) + 1

= 3 ln(3) - 2

Finally, we calculate the average value:

f = (1/(b-a)) * ∫[a,b] f(x) dx

= (1/(3-1)) * (3 ln(3) - 2)

= (1/2) * (3 ln(3) - 2)

= (3/2) ln(3) - 1

Therefore, the exact value of f is (3/2) ln(3) - 1.

(b) To find the error bound in calculating the average value using the Trapezoidal Rule with n = 5, we can use the formula:

Error Bound = \(((b-a)^3 / (12 * n^2)) * Max|f''(x)|\)

In this case, a = 1, b = 3, and n = 5. We need to find the maximum value of the second derivative of f(x) = ln(x) on the interval [1, 3].

First, let's find the second derivative of f(x):

f'(x) = 1/x

\(f''(x) = -1/x^2\)

Since f''(x) = -1/x^2, we can observe that f''(x) is always negative on the interval [1, 3]. Therefore, the maximum value of f''(x) occurs at x = 1.

\(Max|f''(x)| = |-1/(1^2)| = 1\)

Now, let's calculate the error bound:

Error Bound = \(((b-a)^3 / (12 * n^2)) * Max|f''(x)|\)

\(= ((3-1)^3 / (12 * 5^2)) * 1\)

\(= (2^3 / (12 * 25)) * 1\)

= (8 / 300)

= 2/75

Therefore, the error bound in calculating the average value using the Trapezoidal Rule with n = 5 is 2/75.

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The domain and the range of the quadratic function in this problem are given as follows:

The function is defined for all real values, as x assumes all the values on the graph.

The maximum value of y on the graph is of y = 3, hence the range of the function is given by the values of 3 or less as follows:

y ≤ 3.

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Given that three charges (-25 nC, 79.1nC, and −55.9nC) are placed at three of the four corners of a square with sides of length 22.2 cm. We need to determine the value of the electric potential (in V) at the empty comer if the positive charge is placed in the opposite corner.

The formula for the electric potential at a point in space is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) + ….. ]where;k = Coulomb's constant (8.99 × 10^9 Nm²/C²)q1, q2, q3,…. are the charges at the cornersr1, r2, r3,…. are the distances from the corner to the point whose potential is being calculated Now we can calculate the electric potential at the empty corner as follows;The three charges can be represented as shown below:Charges at corners of a square

The distance from any corner to the opposite corner (where the positive charge is placed) is given by d = √[ (22.2 cm)² + (22.2 cm)² ] = 31.4 cmTherefore, the electric potential at the empty corner is given by;V = k [ (q1 / r1) + (q2 / r2) + (q3 / r3) ]Here, q1 = -25 nC, q2 = -55.9 nC, q3 = 79.1 nC, r1 = r2 = r3 = d = 31.4 cm = 0.314 mPlugging in the values we get;V = 8.99 × 10^9 [ (-25 × 10^-9 / 0.314) + (-55.9 × 10^-9 / 0.314) + (79.1 × 10^-9 / 0.314) ]= 8.99 × 10^9 [ -0.0795 - 0.1783 + 0.252 ]= 8.99 × 10^9 × 0.0052= 46.8 VTherefore, the value of the electric potential at the empty comer if the positive charge is placed in the opposite comer is 46.8 V.

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The equation for the function which would have the given graph is:

f(x) = { 2x - 8, for -12 ≤ x ≤ -2}, { 0.5x + 6, for -2 < x ≤ 6}, {-2x + 10, for 6 < x ≤ 12}.

The given graph is shown below:

The graph shows that the function has three separate line segments which means the function may have different equations for different intervals.

Therefore, we can determine the function equation using each line segment.

First interval: The interval is from -12 to -2 with a slope of 2 and y-intercept -8. f(x) = 2x - 8.

Second interval: The interval is from -2 to 6 with a slope of 0.5 and y-intercept 6. f(x) = 0.5x + 6.

Third interval: The interval is from 6 to 12 with a slope of -2 and y-intercept 10. f(x) = -2x + 10.

Thus, the equation for the function which would have the given graph is:

f(x) = { 2x - 8, for -12 ≤ x ≤ -2}, { 0.5x + 6, for -2 < x ≤ 6}, {-2x + 10, for 6 < x ≤ 12}.

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Answer:

Option B

Step-by-step explanation:

=> \(f(x) = 3x+5\)

=> \(g(x) = x^2\)

Subtracting both

=> \((f-g)(x) = 3x+5-x^2\)

Assembling

=> \((f-g)(x) = -x^2+3x+5\)