How many times smaller is 2.9 × 10^3 than 3.654 × 10^5?

126
79
1.26
0.79

Answer:

The domain is equal to (x)=√x

(x)=x is x>0x>0

Answer:

y - 6 = 16(x - (-9))

Step-by-step explanation:

Point slope form is y - (y part of the co-ordinate) = slope(x - x part of the co-ordinate)

x , y

(-9,6)

Answer:

The width of the rectangle is k+4 inches

Step-by-step explanation:

you have \(k^{2}+19k+60\) which can be factorized to (k+4)(k+15)

if the length of the rectangle is k-5 that would mean that we can write \(k^{2}+19k+60\) as (k-5)n which we know is false, so the only one that applies is k+4

The true statement is:

"The width of the rectangle is k + 4"

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

So we want to factorize the area equation, which is a quadratic equation, into a product of two terms.

A = k^2 + 19k + 60

The two zeros are given by Bhaskara's formula:

\(k = \frac{-19 \pm \sqrt{19^2 - 4*1*60} }{2} \\\\k = \frac{-19 \pm 11 }{2}\)

So we have two zeros, these are:

k = (-19 - 11)/2 = -15

k = (-19 +11)/2 = -4

So we can factorize the area as:

A = (k - (-15))*(k - (-4)) = (k + 15)*(k + 4).

From this, the only statement that can be true is:

"The width of the rectangle is k + 4"

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Answer:

A. 3,703 inches squared

Step-by-step explanation:

I took the test and got it right. #platofam

Answer:

the answer 6.5

........

The distance between the points R(0, 1) and S(6, 3.5) is 6.5 units after using the distance formula.

It is defined as the formula for finding the distance between two points. It has given the shortest path distance between two points.

The distance formula can be given as:

\(\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

It is given that:

Two points are:

R(0, 1) and S(6, 3.5)

To find the distance between points R and S we can use the distance formula.

\(\rm d=\sqrt{(6-0)^2+(3.5-1)^2}\\\)

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

d = √(36 + 6.25)

d = √42.25

d = 6.5 units

Thus, the distance between the points R(0, 1) and S(6, 3.5) is 6.5 units after using the distance formula.

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The length of AC is 6.228 cm.

Here the angle of the triangle ∡ABC is 40°, AB = BC = 9.

We have to find the length of AC which is opposite to ∡B.

Let AB = BC = x , AC = c

From the cosine formula, we know that

\(c^{2}\) = \(a^{2}\) + \(b^{2}\) - 2ab cos α

Here c is the length of the side opposite to the angle α, and a, b is the side adjacent to the angle α.

So from the cosine formula we have

\(c^{2}\) = \(x^{2}\) + \(x^{2}\) -2\(x^{2}\)cos α

\(c^{2}\) = 2\(x^{2}\) - 2\(x^{2}\) cos 40°

   = 2\(x^{2}\)(1- cos 40°)

   = 2 ×\(9^{2}\) ( 1 - 0.76)

    = 2 × 81 × 0.24

c = 2 × 9 × 0.2×√3

  =3.6 × 1.73

  = 6.228cm

Therefore the length of the side AC is 6.228cm.

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\(\frac{325}{520}\) fraction of the workforce kept their jobs

What is the Percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

What is Percentage change?

The percentage increase is calculated by subtracting the original number from the new number, dividing that result by the original number, and multiplying that result by 100.

where growth in number equals new number minus initial number.

Similar to how a percentage increase is calculated, a percentage reduction is calculated by subtracting a new number from the original number, dividing that new number by the original number, and multiplying that result by 100.

decreasing number where original number - new number

In other words, there is a percentage decline if the response is negative.

Here, It is given:

In January 520 workers were employed;

In the end, 195 employees were redundant;

So, The fraction of the workforce who kept their job:-

The fraction of the workforce who kept their job=\(\frac{520-195}{520}\)

The fraction of the workforce who kept their job=\(\frac{325}{520}\)

Hence,

The fraction of the workforce who kept their job=\(\frac{325}{520}\)

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Answer: 100

Step-by-step explanation:

An isosceles right triangle therefore has angles of 45 degrees, 45 degrees, and 90 degrees. For an isosceles right triangle with side lengths a, the hypotenuse has length \(\sqrt(2)a\).

Therefore \(x=100\sqrt{2} /\sqrt{2}=100\)

The probability of winning the game before the fourth turn is \(\frac{19}{54}\).

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 represents an event that is impossible to occur, and 1 represents an event that is certain to occur. The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes.

To find the probability of winning the game before the fourth turn, we need to calculate the probability of winning on the first, second, or third turn and then add them together.

On each turn, rolling a standard die has 6 equally likely outcomes (numbers 1 to 6), and tossing a fair coin has 2 equally likely outcomes (heads or tails).

1.Probability of winning on the first turn: To win on the first turn, we need the die to show a 1 or a 6, and the coin to show heads. Probability of rolling a 1 or 6 on the die:  \(\frac{2}{6} =\frac{1}{3}\)

Probability of tossing heads on the coin: \(\frac{1}{2}\)

Therefore, probability of winning on the first turn: \(\frac{1}{3} *\frac{1}{2}\) = \(\frac{1}{6}\)

2.Probability of winning on the second turn: To win on the second turn, we either win on the first turn or fail on the first turn and win on the second turn. Probability of winning on the second turn, given that we didn't win on the first turn:

\(\frac{2}{3} *\frac{1}{3} *\frac{1}{2} \\=\frac{1}{9}\)

3.Probability of winning on the third turn:

To win on the third turn, we either win on the first or second turn or fail on both the first and second turns and win on the third turn. Probability of winning on the third turn, given that we didn't win on the first or second turn:

\(\frac{2}{3} *\frac{2}{3} *\frac{1}{3} \\=\frac{2}{27}\)

Now, we can add the probabilities together:

Probability of winning before the fourth turn =

\(\frac{1}{6}+\frac{1}{9}+\frac{2}{27}\\\\=\frac{9}{54}+\frac{6}{54}+\frac{4}{54}\\\\=\frac{19}{54}\\\)

Therefore, the probability of winning the game before the fourth turn is  \(\frac{19}{54}\).

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The lowest point on the graph occurs at point (3π/2,  -1)

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation

The attached graph shows sine function graph plotted with the interval [0, 2pi]

The lowest point is observed to occur at  (3π/2,  -1)

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Answer:

expression a and c

Step-by-step explanation:

A. 9x-3x-4 = 6x-4

C. 5x+x-4 = 6x-4

hope this helps

Answer:

Expression A and C

Step-by-step explanation:

When Expression A is simplified it is 6x - 4. And for Expression C you add 5x and x, and then it’s 6x - 4. That makes them the same expression. So your answer would be Expression A and C.

I hope it helps! Have a great day!

Muffin ^^

Answer:

Step-by-step explanation:

Given

price of the computer on Friday = $200

price of the computer on Saturday = $149

Difference in price = 200 - 149 = $51

Since the price reduces in price by $51, hence there was a markup in price.

% markup = difference in price/original price * 100%

% mark up = 51/200*100%

% markup = 51/2

% markup = 25.5%

Hence the markup was a 25.5% change

Answer:

25.5 is the answer..........................................................

Step-by-step explanation:

Answer:

f ≥ 35

Step-by-step explanation:

Took the test on Aleks, it was right! :)

Answer:

A. 30 degrees

Explanation:

There are four types of transformations and there are reflection, rotation, dilation, and translation.

Reflection, rotation, and translation are rigid transformations, that is, the preimage and image do not change in size or shape. It also means that the preimage and image will be congruent.

So if triangle BCD is rotated 80 degrees clockwise about the origin to form triangle KLM, and m

Jane has (2/3)d dollars left after buying one beanie boo.

Let's call the cost of one beanie boo "x".

Then, if Jane wants to buy 3 beanie boos, she would spend 3x.

However, she only bought one beanie boo, so she spent x. We know that she spent all of her money, which is "d", so we can set up the equation:

3x = d (the cost of 3 beanie boos is equal to the amount of money Jane has)

To find out how much money Jane has left after buying one beanie boo, we need to subtract the cost of one beanie boo (x) from the total amount of money she has (d). We can solve for x by dividing both sides of the equation by 3:

3x/3 = d/3

x = d/3

Now we can substitute this value of x into our original equation:

3x = d

3(d/3) = d

d = d

So we can see that the amount of money Jane has is "d", and since she only spent "x" to buy one beanie boo, she has "d - x" left:

d - x = d - (d/3)

d - x = (2/3)d

Therefore, Jane has (2/3)d dollars left after buying one beanie boo.

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Answer:

The total number of marbles in the bag is:

6 + 9 + 12 = 27

The probability of drawing a blue marble is:

12/27 = 0.444 or 44.44%

The probability of drawing a green marble is:

9/27 = 0.333 or 33.33%

The probability of not drawing a red marble is:

(9 + 12) / 27 = 21/27 = 0.778 or 77.78%

The odds of not drawing a red marble are:

(6 + 9 + 12) : (9 + 12) = 27 : 21 = 9 : 7

Step-by-step explanation:

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Circle with center C and point D. Triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

What is construction?

In the context of geometry, construction refers to the process of creating geometric figures or shapes using only a compass and straightedge (also called a ruler). The goal of construction is to create accurate and precise geometric figures using only these two tools and a given set of instructions.

To construct an equilateral triangle DEF with points E and F on circle C, we will follow the following steps:

Step 1: Draw a circle with center C and point D on it.

Step 2: Draw a line through points C and D. This line will be the base of our equilateral triangle DEF.

Step 3: Construct the perpendicular bisector of line CD. This can be done by drawing two circles with centers at C and D, both with radius greater than half the length of CD. The two circles will intersect at two points, and the line passing through these two points will be the perpendicular bisector of CD.

Step 4: Let G be the intersection point of the perpendicular bisector and circle C that is closest to point D. Draw lines from G to points C and D. These lines will intersect circle C at points E and F, respectively.

Step 5: Check that the length of CE is equal to the length of CF. This can be done using a compass and ruler.

Step 6: Finally, draw lines from points E and F to point D. The resulting triangle DEF will be equilateral.

To prove that triangle DEF is equilateral, we can show that DE = EF = FD. We already know that CE = CF from step 5. Since C is the center of the circle, CE = CF = CD. By construction, angle ECD and angle FCD are both 60 degrees, since they are inscribed angles that intercept the same arc.

Therefore, triangle CDE and triangle CDF are both equilateral, and we have DE = EF = FD.

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Answer:

160 degrees

Step-by-step explanation:

We can split up the angle into two sections:

One section is the right side which is a right angle so it is 90 degrees. The left side is already given (70 degrees).

So we just add them two together

70+90=160

according to the question,

given data in the question,

the type of rigid transformation is the equivalent of two across intersecting lines

Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.

The intersection of the two reflection lines is the center of rotation.

An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.

The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation

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The type of transformation that is equivalent to 2 reflections across intersecting lines is rotation

A slide or a shift is a translation. By executing two composite reflections along parallel lines, translations may be produced. Translations maintain orientation and are isometric.

An isometry is made up of two other isometries. The translation is equal to the combination of two reflections over two parallel lines.

according to the question,

the type of rigid transformation is the equivalent of two across intersecting lines

Rotation is the process of changing the orientation of a shape by mirroring two intersecting line segments.

The intersection of the two reflection lines is the center of rotation.

An isometric drawing is a composite of two isometric drawings. The combination of two reflections on two parallel lines corresponds to translation.

The configuration of the two reflections is either translational or rotational. A translation occurs when a reflection is followed by a parallel reflection. Reflections following reflections from intersecting lines cause rotation

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1 cup is equivalent to 16 tablespoons.

Taking the ratio, 40 cups will be equivalent to,

Answer:

-2/3x + 3

Step-by-step explanation:

Standard form is just ax^2 + bx + c

In this equation, there is no ax^2. So we have 2/3x + 3.

We don't have to make any changes because the equation is already in standard form.

Solution

We have the following info:

Grades Credits

B 2

B 5

B 5

C 2

And we know that A= 4, B= 3, C=2

So we can do this:

then the weighted average is 2.86

We need to find the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45.

In order to find this probability, we need to find the number of doctors that are General Practitioner or under under the age of 45. Then, divide that number by he total of 17.

We know that 7 doctors are General Practitioners. And 2 of them are also under the age of 45.

Therefore, since ther are 4 doctors that are under the age of 45, there are 2 additional doctors, besided those 2 that follow in both categories, there are under the age of 45.

Summarizing, the number of doctors that are General Practitioner or a doctor under the age of 45 is:

Notice that this result can also be obtained by the formula:

where A is the set of General Practitioners, B is the set of doctors under the age of 45, and the symbol |...| represents the number of elements in that set:

Therefore, the required probability is:

Answer

Answer:

It's equivalent to the 3rd answer choice: y4 − 16y3 + 96y2 − 256y + 256

hope this helps! <3

The expression (y − 4)⁴ is equivalent to the expression y⁴ − 16y³ + 96y² − 256y + 256 option (C) is correct.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

\(\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n\)

It is given that:

=  (y − 4)⁴

After expanding:

= (y - 4)²(y - 4)²

After multiplication and simplifying:, we get:

y⁴ − 16y³ + 96y² − 256y + 256

Thus, the expression (y − 4)⁴ is equivalent to the expression y⁴ − 16y³ + 96y² − 256y + 256 option (C) is correct.

The options are:

y⁴ − 48y³ + 8y² − 4

y³ − 12y² + 48y − 64

y⁴ − 16y³ + 96y² − 256y + 256

y⁴ + 16y³ + 96y² + 256y + 256

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Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.

The area of a rectangle of length l and width w is given as follows:

A = lw.

In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:

Then:

l(l + 2) = 80

l² + 2l - 80 = 0

(l + 10)(l - 8) = 0.

We need the positive measure, hence:

l -  8= 0 -> l = 8 units.

w = l + 2 = 10 units.

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True. approximately 95% of the households had sizes in the range 2.07 to 2.33 people

To determine if approximately 95% of the households had sizes in the range of 2.07 to 2.33 people, we need to consider the concept of confidence intervals.

A confidence interval is a range of values that we can be reasonably confident contains the true population parameter. In this case, we are interested in the average household size.

Given that the sample size is large (900 households) and the standard deviation is known (2 people), we can use the Z-distribution to calculate the confidence interval.

For a 95% confidence interval, we consider the critical Z-value at the 2.5% and 97.5% percentiles (since we want to capture the middle 95% of the distribution).

Using a statistical table or software, the critical Z-value is approximately ±1.96.

The formula for the confidence interval is:

CI = X ± Z * (σ/√n)

where X is the sample mean, Z is the Z-value, σ is the population standard deviation, and n is the sample size.

Plugging in the given values, we have:

CI = 2.2 ± 1.96 * (2/√900)

Simplifying the equation, we get:

CI = 2.2 ± 1.96 * (2/30)

Calculating the values, we find:

CI ≈ 2.2 ± 0.271

CI ≈ (1.929, 2.471)

Since the range 2.07 to 2.33 falls within this confidence interval, it is true that approximately 95% of the households had sizes in that range.

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The value of x in the given triangle is 61 degrees.

In the given triangle, we have an exterior angle of 67 degrees formed by extending one side of the triangle. Let's label the interior angles of the triangle as A, B, and C, with angle A being the exterior angle of 67 degrees.

According to the property of exterior angles of a triangle, the exterior angle is equal to the sum of the two interior opposite angles. Therefore, we have the equation:

A = B + C

Substituting the given values, we have:

67° = B + C

Now, we can observe that angle C is the interior angle labeled as x degrees. So we rewrite the equation as:

67° = B + x

Since the sum of the interior angles in a triangle is always 180 degrees, we have the equation:

A + B + C = 180°

Substituting the given values and rearranging the equation, we get:

67° + B + x = 180°

Simplifying further:

B + x = 180° - 67°

B + x = 113°

Now, we can equate the two expressions for B + x:

B + x = 113°

Since B is given as 52 degrees, we can substitute this value:

52° + x = 113°

Subtracting 52 from both sides, we find:

x = 113° - 52°

x = 61°

Therefore, the value of x in the given triangle is 61 degrees.

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Answer:

a) 3⁴

b)7⁵

c)10²

d)5⁷

Step-by-step explanation:

a) 3²*3², add the exponents if multiplying(subtract if division)

b) add the other 7, cause 7⁴ is 7*7*7*7 and since you're doing another *7 just add a number to the exponent

c)10⁹/10⁷ is 9-7, and take that and use it as the exponent

d)since there is no exponent but it is basically the same as b, but switched. Instead of adding an exponent you take one away

Answer:

A) 27

Step-by-step explanation:

3 x 3 = 3²

3 x 3 = 9

9 x 9

27