How many inches are in 8.43 yards

Answer:

400

Step-by-step explanation:

half of 400 is 200? i need more letterssss

The false statement from the stem-and-leaf plot is given as follows:

b. The data for Paul’s group has two modes.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

4|5 = 45.

The mode of a data-set is the data-set that appears the most times in a data-set.

Hence, for Paul's group, the mode is given as follows:

44.

As it is the only observation that appears the times, hence the data has one mode, and option b gives the false statement.

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Hi there!

~

\((2a^2b+3ab^2-b^3)-(4b^3-3ab^2-6a^2b)\)

Distribute the Negative Sign:

\(= 2a^2 b + 3ab^2 - b^3 + -1(4b^3 - 3ab^2 - 6a^2b)\\= 2a^2 b + 3ab^2 + - b^3 + -1 (4b^3) + -1 (-3ab^2) + -1 (-6a^2b)\\= 2a^2 b + 3ab^2 + -b^3 + -4b^3 + 3ab^2 + 6a^2 b\)

Combine Like Terms:

\(= 2a^2 b + 3ab^2 - b^3 + -4ab^3 + 3ab^2 + 6a^2 b\\= (2a^2 b + 6a^2 b) + ( 3ab^2 + 3ab^2) + (-b^3 + -4b^3) \\= 8a^2 b + 6ab^2 + -5b^3\)

Answer : \(8a^2 b + 6ab^2 + -5b^3\)

Hope this helped you!

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer: the answer is - 4

Step-by-step explanation:

Ok so it decrased by 9 degrees so what you do is 5 - 9 which would be negative four.    -4

Answer:

-4°F

Step-by-step explanation:

Starting temp minus amount dropped gives ending temp.

5 - 9 = -4

Step-by-step explanation:

75 = 3 x 5 x 5    in prime factorization

Answer:

Step-by-step explanation:

3x5x5

Answer:

1. Signed

2. True, -(30/6)=-5, 30/-6=-5, hence they are equal

3. True

Step-by-step explanation:

Answer:

Question 5 is true

Question 4 is false

Step-by-step explanation:

I am not sure about the first question because numbers that are either positive or negative are called integers, however, this is not one of the options.

There are 9444 men and 24555 females are present.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Total students = 34000

For every 5 male students there are 13 female students.

So, the number men are

= 5/18 x 34000

= 9444

and, number of women

= 13/ 18 x 34000

= 24, 555.

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The question attached here is in other language whose translation is given below.

In a school for every 5 male students there are 13 female students. If the total number of students is 34,000, how many men and women are there?

The graph of y=-3x-1 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given equation is  y=-3x-1

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

In the given equation slope is -3.

Let us find few values of x and y.

x    0    1    2     3    4

y    -1   -4   -7    -10  -13

Hence, the graph of y=-3x-1 is given in the attachment.

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The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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The differentiation of the given function f(x) = eˣ+6 is eˣ

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given is function f(x) = eˣ+6, we need to find the derivative of this function,

f(x) = eˣ+6

f'(x) = d / dx (eˣ+6)

= d(eˣ)/dx + d(6)/dx

Since, 6 is a constant and derivative of a constant is zero,

d(eˣ)/dx + d(6)/dx = d(eˣ)/dx + 0

Now, when we differentiate eˣ, we get eˣ itself,

Therefore,

d(eˣ)/dx = eˣ

Therefore, the differentiation of the given function f(x) = eˣ+6 is eˣ

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Answer:

1.811

Step-by-step explanation:

To get the decimal Jenna should type into the computer you simply have to get the decimal value of each fraction and add them all together.

\(\frac{3}{4}=.75\)

\(\frac{1}{8} =.125\)

\(\frac{4}{5}=.8\)

\(\frac{17}{125}=.136\)

Then just add all the decimals together.

let's go like the crab, go backwards, start at the last

if you don't have a Unit Circle, this is a good time to get one, there are many online.

Check the picture below.

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{6}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +6}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{midpoint}{(-5~~,~~-5)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +6}{2}=-5\implies x+6=-10\implies \boxed{x=-16} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-5\implies y+7=-10\implies \boxed{y=-17}\)

Solving the equation the original cost of the shoes before the discount will be obtained as $385.

To find the original cost of the shoes before the discount, you can use the following equation:

original cost = final cost÷ (1 - discount percentage)

In this case:

original cost = $135 ÷  (1 - 0.65)

To find the final cost you need to multiply 135 by 1 - 0.65.

0.65 is the equivalent to 65% when it's represented as a decimal.

0.65 represents the proportion of the original price that was removed (65% or 0.65)

So:

original cost = $135 ÷ (1 - 0.65)

original cost = $135 ÷ (1 - 0.65) = $135 ÷  0.35 = $385

The original cost of the shoes before the discount was $385.

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68

I think, unless if it is multiplied =48

Answer:

48

Step-by-step explanation:

the h value is 8, so multiply 6 and 8,

for future reference, is there is no symbol in the middle, then you always multiply it

Answer:

125

Step-by-step explanation:

All the work is in picture attat

Answer:

X= 2/3

Step-by-step explanation:

-2(x+1/3)+9x=4

Distribute: -2x-2/3+9x=4

Combine: 7x=14/3 ----- 4/1+2/3=12/3+2/3=14/3

Clear the fraction: 21x=14 ------- 7·3x=14/3·3/1

Divide: X=2/3 ------ 14/21÷ 7/7=2/3

X=2/3           Hope This Helps :)

Answer:

\( \sf \large \: x = \frac{2}{3} \)

Step-by-step explanation:

−2(x+1/3)+9x=4

Step 1: Simplify both sides of the equation.

−2(x+1/3)+9x=4

(−2)(x)+(−2)(1/3)+9x=4(Distribute)

−2x+−2/3+9x=4

(−2x+9x)+(−2/3)=4(Combine Like Terms)

7x+−2/3=4

7x+−2/3=4

Step 2: Add 2/3 to both sides.

7x+−2/3+2/3=4+2/3

7x=14/3

Step 3: Divide both sides by 7.

7x/7 = 14/3/7

x=2/3

Answer:D(2,16)

Step-by-step explanation:

Answer: If I did it correctly it should be 150.8

Step-by-step explanation:

The formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2.

Hope this helps!

Step-by-step explanation:

\(y = {2}^{x} \)

This is a basic exponential function.

\(y = {2}^{ - x} same \: as \: y = 0.5 {}^{x} \)

The (-x) exponent makes a reflection in the y-axis.

The answer is C. 236 laptops must be sold to reach the break-even point.

To reach the break-even point, the total revenue must equal the total cost. Let's call the number of laptops sold "x".
Total cost = fixed cost + variable cost * x
Total revenue = price per laptop * x
Setting these equal to each other, we get:
$200,000 + $650x = $1500x
Simplifying this equation, we get:
$850x = $200,000
Dividing both sides by $850, we get:
x = 235.29
Since we can't sell a fraction of a laptop, we must round up to the nearest whole number, which gives us:
x = 236
Therefore, the answer is C. 236 laptops must be sold to reach the break-even point.

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x

\(x + 142 = 180 being \: straight \: line\)

The average speed of the spider is 8 mm per seconds

From the question, we have the following parameters that can be used in our computation:

The graph

The average speed is then calculated as

Average speed = Total distance moved/Total time taken

Using the above and the graph as guides, we have the following:

Total distance moved = 400

Total time taken = 50

So, we have

Average speed = 400/50

Evaluate

Average speed = 8

Hence, the average speed of the spider is 8 mm per seconds

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Answer:

24 and 27

Step-by-step explanation:

√600 = 24.4

√700 = 27.7

So, the numbers should be around 24 and 27

thus you have option 3

The City A and Abilene are nearest to each other

The Austin and Abilene are farthest apart from each other

Here the two angles of the triangle = 59 degrees and 64 degrees

The sum of the angles in a triangle is 180 degrees

Then the third angle will be

59 + 64 + x = 180

123 + x = 180

x = 180 - 123

x = 57 degrees

The third city name is not visible so consider it as city A

Part a

Here the smallest angle is 57 degrees

Opposite side of the angle will be the smallest distance

That is the distance between city A and Abilene

Part b

Here the largest angle is 64 degrees

The opposite side of the angle will be largest distance

That is the distance between Austin and Abilene

Therefore, the City A and Abilene are nearest to each other and Austin and Abilene are farthest apart from each other

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Answer:

The hourly growth rate parameter is of 4.74%

Step-by-step explanation:

Continuous growth model:

The continuous growth model for a population after t hours is given by:

\(P(t) = P(0)(1+r)^t\)

In which P(0) is the initial population and r is the hourly growth rate parameter, as a decimal.

A sample of 1500 bacteria selected from this population reached the size of 1805 bacteria in four hours.

This means that \(P(0) = 1500, P(t) = 1805, t = 4\)

Find the hourly growth rate parameter.

\(P(t) = P(0)(1+r)^t\)

\(1805 = 1500(1+r)^4\)

\((1+r)^4 = \frac{1805}{1500}\)

\(\sqrt[4]{(1+r)^4} = \sqrt[4]{\frac{1805}{1500}}\)

\(1 + r = (\frac{1805}{1500})^{\frac{1}{4}}\)

\(1 + r = 1.0474\)

\(r = 0.0474\)

0.0474*100% = 4.74%

The hourly growth rate parameter is of 4.74%

The approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

To solve the equation 1/x-1 = |x-2| using three iterations of successive approximation, we will start with an initial guess and refine it using an iterative process.

Given that the equation involves absolute value, we will consider two cases:

Case 1: x - 2 ≥ 0

In this case, |x-2| simplifies to x-2, and the equation becomes 1/(x-1) = x-2.

Case 2: x - 2 < 0

In this case, |x-2| simplifies to -(x-2), and the equation becomes 1/(x-1) = -(x-2).

Now, let's perform the successive approximation:

Iteration 1:

Let's start with an initial guess, x = 2.

Case 1: When x - 2 ≥ 0,

1/(2-1) = 2-2,

1/1 = 0,

which is not true.

Case 2: When x - 2 < 0,

1/(2-1) = -(2-2),

1/1 = 0,

which is not true.

Since our initial guess did not satisfy the equation in either case, we need to choose a different initial guess.

Iteration 2:

Let's try x = 3.

Case 1: When x - 2 ≥ 0,

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

1/2 = 1,

which is not true.

Case 2: When x - 2 < 0,

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

1/2 = -1,

which is not true.

Again, our guess did not satisfy the equation in either case.

Iteration 3:

Let's try x = 2.5.

Case 1: When x - 2 ≥ 0,

1/(2.5-1) = 2.5-2,

1/1.5 = 0.5,

which is true.

Case 2: When x - 2 < 0,

1/(2.5-1) = -(2.5-2),

1/1.5 = -0.5,

which is not true.

Our guess of x = 2.5 satisfies the equation in Case 1.

Therefore, the approximate solution to the equation 1/x-1 = |x-2| after three iterations of successive approximation is x ≈ 5/2 or x ≈ 2.5.

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