Determine which expression is equivalent to
3
4
−
x
(
1
2
−
5
8
)
+
(
−
3
8
x
)
4
3
​
−x(
2
1
​
−
8
5
​
)+(−
8
3
​
x).
A
−34x−
4
3
​
x
B
12x
2
1
​
x
C
18−78x
8
1
​
−
8
7
​
x
D
34−14x
4
3
​
−
4
1
​
x

We may conclude after answering the presented question that derivatives Therefore, the derivative of y = ln(cos(x)) with respect to x is: dy/dx = -tan(x)

In mathematics, the derivative of a function with real variables measures how sensitively the function's value varies in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. Because it is frequently the slope of a straight line, it should be enclosed in quotation marks. Derivatives are rate of change metrics that apply to almost any function.

To find dy/dx when y = ln(cos(x)), we'll need to use the chain rule and the derivative of the natural logarithm.

[tex]dy/dx = (dy/du) * (du/dx)\\d/dx [ln(u)] = 1/u * du/dx\\dy/du = 1/u = 1/cos(x)\\dy/dx = (dy/du) * (du/dx) = (1/cos(x)) * (-sin(x)) = -tan(x)\\[/tex]

Therefore, the derivative of y = ln(cos(x)) with respect to x is:

dy/dx = -tan(x)

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As a result, the cylinder's capacity is roughly 11,088 cubic metres.

The diameter of a circular is the distance measured through its middle. The radius of a circle is the distance to the middle to any spot on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d .

First, we need to find the radius of the cylinder. We know that the diameter is 28 meters, so the radius is half of that, which is 14 meters.

Using the formula for the volume of a cylinder, V = πr²h, we can now substitute the given values:

V = (22/7) x 14² x 4.5

Simplifying this expression:

V = (22/7) x 196 x 4.5

V = 11,088 cubic meters

Therefore, the volume of the cylinder is approximately 11,088 cubic meters.

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Answer:

1.986 x 10 to the tenth power

Step-by-step explanation:

Step-by-step explanation:

It is an ODD  number  due to statement 1

it is a multiple of 5   due to the last statement

5   15   25   35   45  55  65  75    85  95  105   .....

When you divide by 3    there is a R 1

25    55    85    115    145

When you divide by 4  there is a R = 1

25   is the lowest number    next possible number is 145    then another posssible is 265    etc

Answer:

; Simplified =

Let "Zoe" = z

Let "Luke" = x

x = 16/2 + 3 is your equation

You're expression is

~

Step-by-step explanation:

i hope it's helpful for you

Answer:

Sandra's curiosity led her to sift through recycling and trash bins, wearing gloves to keep her hands clean. She counted the plastic type of each bottle and noted which ones were properly disposed of. It's important to be mindful of our recycling behaviors and make sure we're doing our part to protect the environment. Let's all strive to recycle properly and reduce our waste!

Answer:

The first term of the sequence is -3 and the common difference is -1/3. Therefore, the second term of the sequence can be found by adding the common difference to the first term:

second term = first term + common difference

second term = -3 + (-1/3)

second term = -10/3

Similarly, we can find the third term by adding the common difference to the second term:

third term = second term + common difference

third term = -10/3 + (-1/3)

third term = -11/3

And we can find the fourth term by adding the common difference to the third term:

fourth term = third term + common difference

fourth term = -11/3 + (-1/3)

fourth term = -4

Therefore, the first four terms of the sequence are -3, -10/3, -11/3, and -4.

Answer:

Put the point a tiny bit more than half way between 14 and 15.

Step-by-step explanation:

If you are allowed to use a calculator, put in sqrt215 and you get out 14.66, that goes a little bit more than halfway between 14 and 15.

If you are not allowed to use a calculator, think of the numbers on the numberline in terms of answers to *perfect square* questions.

So 12 is sqrt 144.

13 is sqrt 169.

14 is sqrt 196.

15 is sqrt 225.

So the 215 in your question is in between 196 and 225.

215 is closer to 225 (than to 196) so put the point closer to sqrt 225. That is, in between 14 and 15 and just a tad bit closer to 15.

A) The completed table is given as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

B) the graph is attached accordingly.

C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.

We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.

D(L) = ceil(L/6)

Using this formula, we can complete the table as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).

b) The graph is attached.

c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.

So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.

In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

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Answer:

31000 - y = x

Step-by-step explanation:

Solve for x

[tex]12000\times5=9500+9500+10000+x+y[/tex]

Add and multiply the integers

[tex]60000=29000+x+y[/tex]

Subtract 29000 on both sides

[tex]31000=x+y[/tex]

Subtract y on both sides

[tex]31000-y=x[/tex]

The amount Elsa earns per week, which is $150 more than Anna per week and Elsa had saved $2400 more than Anna when Anna had saved $2880, found by solving the simultaneous equations obtained is $650.

Simultaneous equations are equations that share the same variables.

Let x represent the amount Elsa earn per week, we get;

The amount Anna earns per week + 150 = The amount Elsa earns per week

Therefore; The amount Anna earns per week = x - 150

The amount each girl spent per week = $320

The amount saved per week = The rest of their weekly earning

The mount more Elsa add saved when Anna saved $2880 = $2400

Let n represent the number of weeks after which Anna had saved $2,880, we get the following equations;

n × (x - 150 - 320) = 2800

n × (x - 470) = 2800...(1)

n × (x - 320) = 2880 + 2400 = 5280

n × (x - 320) = 5280...(2)

The above simultaneous equations (1) and (2) indicates;

n × (x - 470) = 2800

x - 470 = 2880/n

x = 2880/n + 470

n × (x - 320) = 5280

x - 320 = 5280/n

x = 5280/n + 320

2800/n + 470 = 5280/n + 320

5280/n - 2880/n = 470 - 320 = 150

(5280 - 2880)/n = 150

n = (5280 - 2880)/150 = 16

n = 16

x = 5280/n + 320

Therefore;

x = 5280/16 + 320 = 650

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The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

A Z-score is a statistical measurement that indicates how many standard deviations a data point is from the mean of a distribution.

It is calculated by subtracting the mean of the distribution from the data point and then dividing the result by the standard deviation of the distribution.

Here we have

The cumulative area is 0.3897

Using the standard normal table, we can find the z-score that corresponds to a cumulative area of 0.3897 as follows:

1. Locate the entry in the body of the table that is closest to 0.3897. In this case, the closest entry is 0.3897 in the body of the table.

2. Identify the corresponding row and column headers for this entry. The row header is 0.0 and the column header is 0.08.

3. The z-score that corresponds to the area of 0.3897 is the value at the intersection of the row and column headers. In this case, the value is 0.25.

Therefore,

The z-score that corresponds to a cumulative area of 0.3897 is 0.25.

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Step-by-step explanation:

72 inches = 6 feet

There are 12 inches in a foot, so to convert inches to feet, you divide the number of inches by 12.

72 inches / 12 inches/foot = 6 feet

Therefore , the solution of the given problem of angles comes out to be  the engraved angle ACB is 16 degrees in size.

Using Cartesian coordinates, the top and bottom walls divide the circular lines that make up a skew's ends. There is a chance that two poles will meet at a junction point. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various ways at their extremities.

Here,

A circle's inscribed angle has a measure that is half that of the interrupted arc. As a result, the inscribed angle ACB intersecting arc AB with a measure of 32 degrees will have a measure of:

=> Angle ACB = 32 / (1/2)

=> ACB = 16 degree angle

As a result, the engraved angle ACB is 16 degrees in size.

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The predicted Iife expectancy οf maIes in 2006 is 71.7 years.

A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.

Tο find the Iinear functiοn E(t) that fits the data, we need tο find the equatiοn οf the Iine that passes thrοugh the twο given pοints: (0, 65.2) and (5, 67.7), where t = 0 cοrrespοnds tο the year 1993 and t = 5 cοrrespοnds tο the year 1998.

Using the sIοpe-intercept fοrm οf a Iinear equatiοn, we have:

E(t) = mt + b

where m is the sIοpe οf the Iine and b is the y-intercept.

We can find the sIοpe by using the fοrmuIa:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (0, 65.2) and (x2, y2) = (5, 67.7):

m = (67.7 - 65.2)/(5 - 0) = 0.5

Sο the equatiοn οf the Iine is:

E(t) = 0.5t + b

Tο find the y-intercept, we can use οne οf the given pοints. Let's use (0, 65.2):

65.2 = 0.5(0) + b

b = 65.2

Therefοre, the Iinear functiοn E(t) that fits the data is:

E(t) = 0.5t + 65.2

Tο predict the Iife expectancy οf maIes in 2006, we need tο find t when the year is 2006:

t = 2006 - 1993 = 13

Sο we can use t = 13 in the equatiοn:

E(13) = 0.5(13) + 65.2

E(13) = 6.5 + 65.2

E(13) = 71.7

Therefοre, the predicted Iife expectancy οf maIes in 2006 is 71.7 years.

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Answer:

Step-by-step explanation:

modal weight:  the weight that appear most often

4.5 kg  appears 3 times

6-sided polygon:  even though it is an irregular polygon, the interior angles still add up to (6 - 2)180 = 720

therefore, angle f = 720 - 576 = 144      (the sum of a+b+c+d+e is very blurry in the image, it looks like 576--please double check that!)

modal score:  read this right off the graph.  The score with the highest frequency is the modal score:  14   (meaning, 9 contestants got this score)

Step-by-step explanation:

I just did in the other posting. how often did you post it ?

this is a trick question. the triangle at the top is not an isoceles triangle.

we use Pythagoras for an the steps.

so, the left part of the baseline (split by the height) is calculated by

12² = 10² + part²

144 = 100 + part²

part = sqrt(44) = 6.633249581... ft

the other part is then

20 - 6.633249581... = 13.36675042... ft

and the second leg of the large triangle is

leg² = 10² + 13.36675042...² = 278.6700168...

leg = 16.69341238... ft

P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈

≈ 64.69 ft

please see the answer to the other posting for more details.

According to the question 560 cups divided by 20 cups per week equals 28 weeks.

Division is a mathematical operation that involves splitting a number or quantity into equal parts. It is an essential process in mathematics, used to solve problems and find solutions. Division involves dividing a number, or a set of numbers, by another number. The result of the division is known as the quotient. Division can also be used to find fractions or ratios, as well as to divide a number into its parts.

Assuming the bag of dog food is a large bag and Carl is feeding his dog 2 1/2 cups daily, the maximum number of days Carl can feed his dog from one full bag is 28.
This is because 2 1/2 cups equals 20 cups per week, and a large bag typically contains approximately 560 cups.
Therefore, 560 cups divided by 20 cups per week equals 28 weeks.

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The entire number of kilometres driven by Roland's family can be determined by using the phrase [tex]=\frac{69}{10}[/tex]

To determine the total number of kilometres driven by Roland's family, the distance from their home to the gas station and the distance from the gas station to the shop must be added.

There are [tex]4\times \frac{6}{10}[/tex] kilometres between their home and the gas station, which can also be stated incorrectly as follows:

[tex]4\times \frac{6}{10}=\frac{(4\times 10+6)}{10} \\\\=\frac{46}{10}[/tex]

The formula for expressing the distance between the gas stop and the store is 2 30/100 kilometers, which can be written as follows:

[tex]2\times\frac{30}{100} =\frac{(2\times100+30)}{100} \\\\=\frac{230}{100}[/tex]

To calculate the overall distance traveled, we add the two distances:

[tex]\frac{46}{10} +\frac{230}{100}[/tex]

To combine these fractions, we need to find a common denominator. Only one unique digit, 100, can be used to divide both 10 and 100. In light

of this, we can rewrite the equation as follows using 100 as the common denominator:

[tex](\frac{46}{10} )\times (\frac{10}{10} )+(\frac{230}{100} )\times (\frac{1}{1} )[/tex]

That amounts to:

[tex]\frac{46}{100} +\frac{230}{100} =\frac{690}{100}[/tex]

Therefore, we can reduce this fraction by multiplying the numerator and denominator by their ten largest common factor:

[tex]\frac{690}{100} =\frac{(69/10)}{(100/10)} \\\\=\frac{69}{10}[/tex]

Consequently, the phrase that follows may be used to determine the overall number of kilometres driven by Roland's family:

[tex]2\times\frac{30}{100} +4\times \frac{6}{10} =\frac{69}{10}\ km[/tex]

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Rest of the question is,

They drove 2 30/100 kilometers from the gas station to the store. Which expression can be used to determine the number of kilometer Ronald's family drove altogether.

Answer:

I'm stuck too like is so aggravating

Answer:

Step-by-step explanation:

To find the price that maximizes the country's revenue, we need to consider the relationship between price, sales, and revenue.

Let's start by calculating the current revenue for the country:

Revenue = Price × Sales

Revenue = $80/barrel × 7 million barrels/day

Revenue = $560 million/day

Now let's consider the effect of a price increase on sales. According to the problem, a $1 increase in price will result in a decrease of 100,000 barrels/day in sales. This means that the new sales rate at a price of $81/barrel will be:

New sales = 7 million barrels/day - 100,000 barrels/day per $1 increase × (81 - 80)

New sales = 6.9 million barrels/day

The new revenue at a price of $81/barrel will be:

New revenue = $81/barrel × 6.9 million barrels/day

New revenue = $559.9 million/day

We can repeat this process for a range of prices to see how revenue changes:

Price Sales (million barrels/day) Revenue (million $/day)

 80                            7.0                             560.0

 81                            6.9                             559.9

 82                            6.8                             544.0

 83                            6.7                             534.1

 84                            6.6                             528.0

 85                            6.5                             520.0

From this table, we can see that the price that maximizes revenue is $84/barrel. At this price, the country will sell 6.6 million barrels/day, and generate revenue of $528 million/day.

Therefore, the price that will maximize the country's revenue is $84/barrel, and it will sell 6.6 million barrels/day at that price.

Answer:

m∠WUV=135°

Hope this helps.

Answer:

[tex]k = - 3[/tex]

Step-by-step explanation:

[tex]y = kx[/tex]

[tex]k \times ( - 1) = 3[/tex]

[tex] - k = 3[/tex]

[tex]k = - 3[/tex]

Answer:

[tex]k = -3[/tex]

Step-by-step explanation:

Step 1: Substitute

To solve this problem you are going to need to substitute the values of y and x into the problem y=kx.  Which would give you the problem of 3=-1k or 3 = -k to make things easier.

Step 2: Using properties of equality

In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]

Step 3: Check

In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct

The area of Desert 1 is 28,000,000 square miles and the area of Desert 2 is 4,000,000 square miles.

Let's assume that the area of Desert 2 is x square miles.

According to the problem statement, the area of Desert 1 is seven times that, or 7x square miles.

We are also given that the sum of their areas is 32,000,000 square miles:

x + 7x = 32,000,000

Simplifying the left side of the equation:

8x = 32,000,000

Dividing both sides by 8:

x = 4,000,000

Now that we know the area of Desert 2 is x = 4,000,000 square miles, we can find the area of Desert 1 by multiplying by 7:

7x = 7(4,000,000) = 28,000,000

Therefore, the area of Desert 1 is 28,000,000 square miles and the area of Desert 2 is 4,000,000 square miles.

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The balance of the savings plan after 4 years with an APR of 8% and monthly payments of $150 is approximately $7,456.76.

As a result, the savings plan formula for such challenges is as follows: final saving = number of periods * (first and last period savings) / 2.

To calculate the balance of the savings plan after four years, we can use the formula for the future value of an annuity with regular payments:

P * ((1 + r/n)(n*t) - 1) / (r/n)

Where P is the monthly payment amount, which is $150.

r = 8% annual interest rate

n = the number of times annual interest is compounded = 12 (since we have monthly payments)

4 t = the number of years

We get the following results when we plug these values into the formula:

FV = 150 * ((1 + 0.08/12)^(12*4) - 1) / (0.08/12) ≈ $7,456.76

As a result, the savings plan balance after four years with an APR of 8% and monthly payments of $150 is approximately $7,456.76.

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Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

The quantity of punch produced by the recipe is:

If the punch bowl has an 8-quart capacity and the recipe fills it 3/4 full.

=> 6 pints =  8 * 3/4.

The formula yields 6 quarts of punch as a result.

Therefore , the solution of the given problem of unitary method comes out to be yields 6 quarts of punch as a result.

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Mr. Oppong's chargeable income for the year of assessment 2022 is GH¢109,100.

Taxes must generally be paid on all types of income, even those derived from a business or profession. Employment. Dividends.

We must take into account Mr. Kwesi Oppong's salary, benefits, and any deductions when determining his chargeable income for the assessment year of 2022.

Let's start by figuring out his gross revenue for 2022. The annual wage scale for Mr. Oppong is GH85,000 X GH5,000 - GH130,000, which denotes a salary range of GH85,000 to GH130,000. To make things easier, we might suppose that his pay is the midpoint of the range, or GH107,500.

His annual acting allowance is GHC 5,000, so the following would be his total income from salary and allowances:

GH107,500 plus GH5,000 plus (GH300 x 12) plus (GH250 x 12) equals GH114,500.

Next, we must look at his advantages. Mr. Oppong is given a vehicle with a designated driver and free fuel, as well as a furnished place to stay. They are taxable benefits, but in order to estimate their worth, we need more details.

Mr. Oppong also holds a life insurance policy with a GHC 70,000 capital and GHC 8,000 yearly premium. This is not a necessary component of his chargeable income.

Let's now explore the inferences made by Mr. Oppong. 5.5% of his income is put into Social Security by him. Since the Social Security rate is set at GH450 every month, Mr. Oppong can only contribute a maximum of GH5,400 (GH450 x 12) in a given year.

As a result, the following would be Mr. Oppong's chargeable income for the year of assessment 2022:

GH114,500 minus GH5,400 equals GH109,100.

Thus, GH 109,100 will be Mr. Oppong's chargeable income for the assessment year 2022.

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The student can purchase no more than four books, or k. This can be represented so the correct answer option (A) is  8.50k +2.25(k+ 4) ≤ 43

Symbol for inequality: Comparing two numbers that are not equal requires the use of an inequality symbol. (>) More Than: The larger number is always on the left when using this symbol, and the smaller number is always on the right.

First, let's define some variables. Let b be the quantity of books the student purchases, and p represent the quantity of pens. Since the student purchases four more pens than books, the total cost of the purchase is $43, and we know that p = b + four. This can be expressed as an equation:

8.50b + 2.25p = 43

By replacing p = b + 4, we obtain:

8.50b + 2.25(b + 4) = 43

If we simplify, we get:

10.75b + 9 = 43

9 is subtracted from either side, resulting in:

10.75b = 34

By multiplying both sides by 10.75, we obtain:

b ≈ 3.16

The student may purchase either 3 or 4 books because the total number of books must be a whole number. Let's use the initial equation to verify these values:

If the student purchases three books, then p = 3 + 4 = seven pens are needed. 8.50(3) + 2.25(7) = 38.25, or less than $43, is the total price.

If the student purchases four books, then p = four plus four equals eight pens. 8.50(4) + 2.25(8) = 43, or precisely $43, is the total price

As a result, the student can purchase no more than four books, or k. This can be represented as:

8.50k + 2.25(k + 4) ≤ 43

Answer (A) is the right selection.

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As a text-based AI, I am unable to use drawing tools or interact with grids. However, I can still help you understand the terms you mentioned and provide guidance on how to approach the problem.

1. "Delete": This term typically refers to removing an element or a part of the content you're working on. When working with a grid, you may need to delete some lines, shapes, or text that are not needed.

2. "Reset": Resetting refers to reverting a grid or a drawing tool to its original state, essentially starting from scratch. This can be useful if you've made multiple changes and want to begin anew without having to manually undo each step.
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