On Babylonian tablet YBC 4652, a problem is given that translates to this equation:

X + + x plus StartFraction x Over 7 EndFraction plus StartFraction 1 Over 11 EndFraction left-parenthesis x plus StartFraction x Over 7 EndFraction right-parenthesis equals 60.(x + ) = 60
What is the solution to the equation?

x = 48.125
x = 52.5
x = 60.125
x = 77

Answer:

Step-by-step explanation:

75

If two samples are to be taken for each possible configuration, then 32 samples are to be taken. And  3003 are the number of ways in which the committee can be formed. Also, there are 1050 different ways the committee can be formed with 4 faculty representatives and 1 ex-officio member.

1. To determine the bacterial communities in the aquatic environment with different configurations, you need to consider the number of options for each configuration and multiply them together.

- Type of water: 2 options (salt water or fresh water)

- Season of the year: 4 options (winter, spring, summer, autumn)

- Environment: 2 options (urban or rural)

To calculate the total number of samples, you multiply the options for each configuration:

2 (type of water) × 4 (season of the year) × 2 (environment) = 16

Since you are taking two samples for each configuration, you multiply the total number of samples by 2:

16 (total configurations) × 2 (samples per configuration) = 32 samples to be taken.

Therefore, you need to take a total of 32 samples.

2. To calculate the number of different ways the special committee of 5 members can be formed from the academic senate of 15 members, you need to use the combination formula.

The number of ways to choose 5 members out of 15 is given by the combination formula:

C(15, 5) = 15! / (5! × (15 - 5)!) = 3003

Therefore, there are 3003 different ways the committee can be formed.

3. In this case, the special committee must have 4 faculty representatives and 1 ex-officio member. We can calculate the number of ways to choose 4 faculty representatives from the 10 available and 1 ex-officio member from the 5 available.

The number of ways to choose 4 faculty representatives out of 10 is given by the combination formula:

C(10, 4) = 10! / (4! × (10 - 4)!) = 210

The number of ways to choose 1 ex-officio member out of 5 is simply 5.

To calculate the total number of ways the committee can be formed, we multiply these two numbers together:

210 (faculty representatives) × 5 (ex-officio members) = 1050

Therefore, there are 1050 different ways the committee can be formed with 4 faculty representatives and 1 ex-officio member.

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Answer:

(a+2)(a-12)

Step-by-step explanation:

\(a^2-10a-24\\\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(a^2+2a\right)+\left(-12a-24\right)\\\\\mathrm{Factor\:out\:}a\mathrm{\:from\:}a^2+2a\mathrm{:\quad }a\left(a+2\right)\\\\\mathrm{Factor\:out\:}-12\mathrm{\:from\:}-12a-24\mathrm{\\:\quad }-12\left(a+2\right)\\=a\left(a+2\right)-12\left(a+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}a+2\\=\left(a+2\right)\left(a-12\right)\)

Answer:

(a + 2)(a - 12)

Step-by-step explanation:

a^2 - 10a - 24

using splitting method

a^2 - 12a + 2a - 24

taking separate common from both pairs

a(a - 12) + 2(a - 12)

(a + 2)(a - 12)

Answer:

4th answer is correct

Step-by-step explanation:

First, let us make x the subject.

\(\sf \frac{x+4}{4} =\frac{y+7}{7}\)

Use cross multiplication.

\(\sf 7(x+4)=4(y+7)\)

Solve the brackets.

\(\sf 7x+28=4y+28\)

Subtract 28 from both sides.

\(\sf 7x=4y+28-28\\\\\sf7x=4y\)

Divide both sides by 7.

\(\sf x=\frac{4y}{7}\)

Now let us find the value of x/4.

To find that, replace x with (4y/7).

Let us find it now.

\(\sf \frac{x}{4} =\frac{\frac{4y}{7} }{4} \\\\\sf \frac{x}{4} =\frac{4y}{7}*\frac{1}{4} \\\\\sf \frac{x}{4} =\frac{4y}{28}\\\\\sf \frac{x}{4} =\frac{y}{7}\)

The expression is simplified to -105

An integer can be defined as a whole number, with no fractional or decimal form which can be positive, negative or zero.

Negative integer values are  the additive inverses of their corresponding positive numbers.

Integers are a collection of whole numbers and negative values.

The types of integers are;

From the information given, we have;

10(-3)(4) - (-15)

expand the bracket

10(-12) - ( -15)

expand further

-120 + 15

Add the values

-105

Hence, the value is -105

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Answer:

Divide by 2 each time.

Step-by-step explanation:

The rule is dividing by 2 each time.

64/2=32

32/2=16

16/2=8

8/2=4

Hope this helps you!! Have an amazing day, and happy thanksgiving ^^

The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

Step-by-step explanation:

99(v + 9) is all you need here.

Answer:

Step-by-step explanation:

Let the number of rooms is x.

Each room is built to hold 6 puppies, so x rooms hold 6x puppies.

The equation for this is:

And the solution is 13 rooms.

The present value, or the amount Jerry would need to deposit today, is approximately $47,120.23.

To calculate the amount Jerry would need to deposit today, we can use the formula for present value:

Present Value = Future Value / (1 + Interest Rate)ⁿ

Where:

Future Value is $85,000

Interest Rate is 8% (or 0.08 as a decimal)

n is the number of years, which is 9

Plugging in these values into the formula, we have:

Present Value = $85,000 / (1 + 0.08)⁹

Simplifying the expression:

Present Value = $85,000 / (1.08)⁹

Calculating this expression using a calculator or spreadsheet software, we find that the present value, or the amount Jerry would need to deposit today, is approximately $47,120.23.

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Answer:

720°

Step-by-step explanation:

The sum of the exterior angles of a polygon = 360°

Divide by 60 to find number of sides (n)

n = 360° ÷ 60° = 6

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

The sum of the exterior angles of a regular polygon is 360º

Each exterior angle of a regular polygon is 60º/n

360º/n=60º

360/60=n

6=n

A polygon with 6 sides is a hexagon.

Use the formula (n-2)×180

(6-2)*180=4*180=720º

another solution...

you have 6 interior angles (hexagon)

if an exterior angle is 60º, the corresponding interior angle is 180-60=120º

you have 6 of these 120º angles

6*120=720º

Answer:

b

Step-by-step explanation:

The values of p and for the class might differ from the same frequencies reported for the North American population due to a variety of reasons. Some of these reasons include:

a) The class data is based on a small population of individuals. This can lead to sampling bias and can result in inaccurate representation of the larger population.

b) Natural selection is occurring in the population for PTC tasters. This can result in certain alleles becoming more or less prevalent in the population over time, leading to a difference in the frequencies of PTC tasters in the class and the larger population.

c) Migration of individuals from other parts of the world may be affecting the gene pool. This can introduce new alleles into the population and change the frequencies of PTC tasters.

d) Random mutations affect the alleles of PTC tasters at different rates for those in the class. This can result in changes in the frequencies of PTC tasters over time.

e) Mating selection occurs for those who cannot taste PTC. This can lead to a change in the frequencies of PTC tasters in the population over time.

Overall, there are a variety of reasons why the values of p and for the class might differ from the same frequencies reported for the North American population. These reasons include sampling bias, natural selection, migration, random mutations, and mating selection.

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Answer:

The answer is A and C

A The class data is based on a small population of individuals

C Migration of individuals from other parts of the world may be affecting the gene pool.

Step-by-step explanation:

The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.

Now, According to the question:

What is meant by ratio?

Therefore, simplifying the equation then we get,

if you take the ranges (y) and subtract one from the other you get 0.42.

(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42

(23.26 - 22.84)/(3 - 2) = 0.42

(23.68 - 23.26)/(4 - 3) = 0.42

Hence, The common difference is 0.42

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Answer:

Step-by-step explanation:

Given:

This figure gives us 180 degrees of angles.

Calculate the angle of x in the figures according to the term x on one side of the equation.

The angle relationship should be represented by 2x.

2x+75=180

First, subtract by 75 from both sides.

2x+75-75=180-75

Solve.

Subtract the numbers from left to right.

180-75=105

2x=105

Divide by 2 from both sides.

2x/2=105/2

Solve.

Divide the numbers from left to right.

105/2=52.5

x=105/2=52.5

I hope this helps. Let me know if you have any questions.

=========================================================

Explanation:

A diagram is optional, but I find it helps sometimes. The diagram is shown below.

Opposite the 10 degree angle is h. So we consider h the opposite side.

The hypotenuse is 12. The hypotenuse is always opposite the 90 degree angle.

Apply the sine ratio to solve for h

sin(angle) = opposite/hypotenuse

sin(10) = h/12

12*sin(10) = h

h = 12*sin(10)

h = 2.08377813200317 which is approximate

h = 2.1 miles is the plane's altitude which is also approximate

Side note: 2.1 miles is equal to 11,088 feet (multiply by 5280 to convert from miles to feet).

The value of the length of SP is 15 inches. So option C is true.

Used the concept of Pythagoras's theorem that states,

The well-known geometric theorem is that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Given that,

VW = 40

VG = 20

ST = 20

and, PT=25

Now, using Pythagoras's theorem

\(ST^2+SP^2=PT^2\)

Substitute the given values,

\(20^2+SP^2=25\)

\(400+SP^2=625\)

Subtract 400 on both sides,

\(PS^2 = 225\)

Taking square root on both sides,

\(SP=15\text{ inches }\)

Therefore, the length of SP is 15 inches. So, option C is true.

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The complete question is shown in the image.

Answer:

37

Step-by-step explanation:

296 ÷ 8 = 37

Sorry I couldn't explain more, but I hope this helps!

Answer:

The unit rate is 37 words per minute.

Step-by-step explanation:

296 divided by 8 is 37

Using the given information we found that the equation of the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

For a parabola with vertex (h, k), the equation is:

y = a*(x - h)^2 + k

Here the vertex is (3, 5), so the equation is:

y = a*(x - 3)^2 + 5

And the y-intercept is y = 1, this means that:

1 = a*(0 - 3)^2 + 5

1 = a*9 + 5

1 - 5 = a*9

-4/9 = a

So the parabola is:

y = (-4/9)*(x - 3)^2 + 5

And its graph is below.

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Answer:

  (a)  -5

Step-by-step explanation:

The vertical scale factor for the graph and the function can be found by comparing the y-value of a point on f(x) to the y-value of a point on g(x). The graph conveniently marks two corresponding points with these y-values:

  f(-2) = 2

  g(-2) = -10

The value of k in g(x)=k·f(x) is the ratio of these y-values:

  k = g(-2)/f(-2) = -10/2 = -5

The value of the vertical scale factor k is -5.

Answer:

11/3

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 33 on the left side and the dividend 9 on the right side like this:

 3 3 ⟌ 9    

Step 2:

The divisor (33) goes into the first digit of the dividend (9), 0 time(s). Therefore, put 0 on top:

       0    

 3 3 ⟌ 9    

Step 3:

Multiply the divisor by the result in the previous step (33 x 0 = 0) and write that answer below the dividend.

       0    

 3 3 ⟌ 9    

       0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (9 - 0 = 9) and write the answer below.

       0    

 3 3 ⟌ 9    

     - 0    

       9    

You are done.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 9 divided by 33 calculated using Long Division is:

0

9 Remainder

Answer: Robin has 50 nickels, 60 dimes, and 120 quarters.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Now we will look at two famous irrational numbers,  and e and calculate their approximate decimal expansions. As you may remember, pi is used in geometry and has been around for over 4000 years. It is used to find area of a circle, surface area and volume of a sphere, cone, and cylinder. Its value is used in many real world calculations such as mechanics, architecture, nature, art, and even medicine. The value e is called Euler’s number and is very important in exponential functions such as finance. Let’s approximate the value of these two numbers, e and .

Example 5:

To determine the decimal expansion of , we will use the fact that the number  is the area of a unit circle together with counting the total squares inside a circle on a grid. Remember, . The unit circle is a circle with a radius of 1. Since the area of a unit circle is equal to  and we will be counting squares, we can decrease our work by focusing on the area of just  of the circle. Take a look at the illustrations below to help you understand our premise.

Unit Circle Area using grids

A = (1)2

A =  Area of circle = total number of squares inside circle

Let’s take a look at  of the unit circle using a 10 x 10 grid. It is difficult to count the number of squares inside the quarter circle because some are not whole squares.

We have inner squares inside the quarter circle, and outer squares outside of the quarter circle. Next, we mark a border inside the circle and outside the circle, as close as possible to the circle. The inside border should enclose all the whole squares inside the quarter circle, (red). The outside border contains all the whole squares within the quarter circle and parts of the squares that are outside the circle (black). Now let’s estimate the area of the unit circle to approximate .

Let r2 equal all inner squares and s2 equal all the squares within the black border and quarter circle. There are 69 inner squares and 89 inner and outer squares. Algebraically, r2 <  < s2.

If we consider the area of the square with side length equal to 10 squares of the grid paper, then the area of r2 =  and area of s2 = .

Therefore,

r2 <  < s2

We know this is accurate because 2.76 < 3.14 < 3.44. Of course we can improve our estimate of  by including more of the partial grid squares inside the quarter circle. By combining the partial squares there appears to be about 7 more inside the circle. We then add 7 to the 69. This gives us,

We can reason the same way as before to estimate s2 to 80, instead 86.

We are getting closer to approximating pi. Suppose we divide each square horizontally and vertically instead of having 100 squares, we have 400 squares.

Multiplying by 4 throughout, we have

By looking at partial squares we can estimate r2 = 310 and s2 is 321. Then, the inequality is

We can continue the process to get closer and closer estimates,

3.14159 <  < 3.14160

and then continue on to get an even more precise estimate of . By now, we have a very close one already.

We conclude by making one final observation about  and irrational numbers. When we take the square of an irrational number such as , we are doing so without knowing the exact value of . Since we can use a calculator to show that 3.14159 <  < 3.14160, we also know

3.141592 <  < 3.141602

9.8695877281 <  < 9.86965056

Notice that the first 4 digits, 9.869 are the same on both sides of the inequality. Therefore, we can say that ^2=9.869 is correct to 3 decimal digits.

Example 6:

Estimate the value of the irrational number (12.03801...)2

Solution:

The estimated value is 144.91 and correct up to 2 decimal digits.

To estimate this, we truncate to one digit higher for the number on the right. Then we square.

12.038012 < (12.03801...)2 < 12.038022

144.91585161 < (12.30791)2 < 144.91825924

The first two decimal places are the same, therefore (12.03801...)2 = 144.91 is correct up to 2 decimal digits.

Example 7:

Estimate the value of the irrational number (9.204107...)2

Solution:

The estimated value is 84.715, which is correct up to 3 decimal digits.

9.2041072 < (9.204107...)2 < 9.2041082

84.715585667449 < (9.204107...)2 < 84.715604075664

(9.204107...)2 = 84.715 is correct up to 3 decimal digits.

Answer:

it is 6 dude

Step-by-step explanation:

Tom's preferences, the value of b in the function W(x, y) = 160xᵇ y⁶⁸ should be greater than 1.

A utility function is a mathematical representation used in economics to quantify the preferences or satisfaction a consumer derives from consuming different goods or bundles of goods. It assigns a numerical value, known as utility, to each possible combination of goods or services, reflecting the consumer's preferences.

The utility function is typically denoted as U(x1, x2, ..., xn), where x1, x2, ..., xn represent the quantities of different goods or services consumed. The utility function maps the combination of goods to a real number, indicating the level of satisfaction or utility the consumer derives from that combination.

Utility functions can take different functional forms, depending on the assumptions and models used. Common types include linear utility functions, Cobb-Douglas utility functions, and logarithmic utility functions. These functions capture different patterns of preferences and allow economists to analyze various economic phenomena, such as consumer demand, welfare analysis, and decision-making under uncertainty.

To represent Tom's preferences, the utility function U(x, y) = 24xy is given.

We need to find the value of b in the function W(x, y) = 160x^b y^68 such that it also represents Tom's preferences.

To match Tom's preferences, the two utility functions, U(x, y) and W(x, y), should have the same ranking of preferences. In other words, if U(x1, y1) > U(x2, y2), then W(x1, y1) should also be greater than W(x2, y2).

Let's compare the utility values for two sets of goods (x1, y1) and (x2, y2) using the given utility function U(x, y) = 24xy:

U(x1, y1) = 24x1y1

U(x2, y2) = 24x2y2

For the function W(x, y) = 160xᵇ y⁶⁸, we need to determine the value of b such that W(x1, y1) > W(x2, y2) whenever U(x1, y1) > U(x2, y2).

Comparing the utility values, we have:

24x1y1 > 24x2y2

To maintain the same ranking of preferences, we can equate the corresponding W values:

160x1 y1⁶⁸ > 160x2 y2⁶⁸

Now, canceling out the common factors, we get:

x1ᵇ y1⁶⁸ > x2ᵇ y2ᵇ^68

Since this should hold for any x1, y1, x2, y2, we can compare the exponents of x and y separately:

b > 1

To represent Tom's preferences, the value of b in the function W(x, y) = 160x^b y^68 should be greater than 1.

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The answer is that the value of x such that ex > 1,000,000,000 is x > 14.876 (rounded to three decimal places) and the exponential function f(x) = Cbx whose graph is given is f(x) = 25000e0.03x.

a) To estimate the value of x such that ex > 1,000,000,000, we can use a graph of the exponential function ex. On the graph, we can locate the point (x, ex) = (14.876, 1,000,000,000), which means that when x = 14.876, ex > 1,000,000,000. Therefore, the value of x such that ex > 1,000,000,000 is x > 14.876 (rounded to three decimal places).

b) The exponential function f(x) = Cbx whose graph is given is f(x) = 25000e0.03x.

The answer is that the value of x such that ex > 1,000,000,000 is x > 14.876 (rounded to three decimal places) and the exponential function f(x) = Cbx whose graph is given is f(x) = 25000e0.03x.

The complete question is :

Use a graph to estimate the values of x such that ex > 1,000,000,000. (round your answer to three decimal places.) a) Use a graph to estimate the values of x such that ex > 100,000. (Round your answer to three decimal places.) x >b) Find the exponential function f(x) = Cbx whose graph is given. f(x) = 25000e0.03x.

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Answer:

24:6

Step-by-step explanation:

Simplifying, we get: y - 35 = 2x - 10 or y = 2x + 25 Hence, the equation of the tangent line is y = 2x + 25.

Given that the function is f(x) = x2 - 8x + 50. The slope of the tangent line at x = 5 is 2. To find the equation of the tangent line, we need to find the y-coordinate of the point on the curve at x = 5.

We can do that by plugging x = 5 into the given function:

f(5) = 5² - 8(5) + 50

= 25 - 40 + 50

= 35.

So the point on the curve at x = 5 is (5, 35).

We can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the point on the curve at x = 5 and m is the slope of the tangent line, which we are given is 2.

Substituting the values, we get: y - 35 = 2(x - 5)`Simplifying, we get: y - 35 = 2x - 10 or y = 2x + 25

Hence, the equation of the tangent line is y = 2x + 25.

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Answer:

Slope is 2 and the y-intercept is 2

Step-by-step explanation:

Answer:

slope=2

y-intercept=2

Step-by-step explanation:

i did rise over run and got 4/2=2

y-intercept is when the line hits a number on the y axis which in this case is (0,2)

hope this helps :) have a nice day !!

please let me know if this was wrong

Given

length = 3 times width

Let w = width, and l = 3w

Then the perimeter is

2l + 2w = 20 in

2(3w) + 2w = 20 in

6w + 2w = 20 in

8w = 20 in

w = 2.5 in

l = 3w

l = 3(2.5 in)

l = 7.5 in

Now that we have length and the width, we can now solve for area.

Therefore, the area of the rectangle 18.75 square inches.