Estimate the quotient of 42.4 ÷ 7.28.

Answer:

2.5

Step-by-step explanation:

It looks like it's 2.5.

Answer:

) The number of men who attended the sessions can be obtained by summing up the number of males in each session:

Total number of men = 12 + 18 + 17 = 47

Therefore, 47 men attended the sessions.

b) The number of people who attended Session 3 can be obtained by summing up the number of males and females in Session 3:

Total number of people in Session 3 = 17 (males) + 5 (females) = 22

Therefore, 22 people attended Session 3.

c) The sample size refers to the total number of attendees across all sessions. We can calculate it by summing up the number of males and females in each session:

Sample size = (12 + 8) + (18 + 9) + (17 + 5) = 69

Therefore, the sample size is 69.

d) To calculate the probability that a randomly selected person is male, we need to divide the number of males by the sample size:

Probability of selecting a male = Number of males / Sample size = 47 / 69 ≈ 0.6812

Therefore, the probability that a randomly selected person is male is approximately 0.6812 (rounded to four decimal places).

e) To calculate the probability that a randomly selected person attended Session 3, we need to divide the number of people who attended Session 3 by the sample size:

Probability of attending Session 3 = Number of people in Session 3 / Sample size = 22 / 69 ≈ 0.3188

Therefore, the probability that a randomly selected person attended Session 3 is approximately 0.3188 (rounded to four decimal places).

f) To calculate the probability that a randomly selected person is male and attended Session 3, we need to divide the number of males in Session 3 by the sample size:

Probability of being male and attending Session 3 = Number of males in Session 3 / Sample size = 17 / 69 ≈ 0.2464

Therefore, the probability that a randomly selected person is male and attended Session 3 is approximately 0.2464 (rounded to four decimal places).

The probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth is 0.443

Out of 217 visitors who came to Nayeli's website, none of them purchased a costume. Therefore, the number of visitors who may purchase a costume is 217 less than the total number of visitors:

Total visitors - No. of visitors who didn't purchase a costume = 217

Total visitors - 217 = No. of visitors who may purchase a costume

Total visitors = 113 + 217+36 = 336

Out of the remaining visitors, 113 purchased exactly one costume, and 36 purchased more than one costume. Therefore, the number of visitors who purchased one or more costumes is:

No. of visitors who purchased one or more costumes = 113 + 36 = 149

Therefore, the probability that the next person will purchase one or more costumes can be expressed as:

Probability = No. of visitors who purchased one or more costumes / Total visitors

Probability = 149 /336 = 0.443

The probability that the next person will purchase one or more costumes as a decimal to the nearest hundredth is 0.443

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Answer:

Step-by-step explanation:

.44

The algebraic expression "difference of 4 and a number" where the number is letter x is represented as 4 - x.

Algebra is an elementary branch of mathematics that deals with the numbers and the basic mathematics operations of addition, subtraction, division and multiplication. Algebraic expression involves arithmetic where the use of unknown quantities along with numbers.

From the question, we have the mathematical statement "difference of 4 and a number" and the number is "a number" is represented with the letter x.

the word difference in mathematics implies Subtraction (-)

Therefore, the mathematical statement "difference of 4 and a number" is represented as 4 - x.

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Complete Question

Assume that adults have IQ scores that are normally distributed with a mean μ=100 and a standard deviation σ=15. Find the probability that a randomly selected adult has an IQ between 81 and 119.

Answer:

The probability is  \(P( x_1 < X < x_2) = 0.79474\)

Step-by-step explanation:

From the question we are told that

   The standard deviation is  σ = 15.

    The mean μ= 100

     The range we are considering is \(x_1 = 81 , \ x_2 = 119\)

Now given that IQ scores are normally distributed

    Then the probability that a randomly selected adult has an IQ between 81 and 119 is mathematically represented as

               \(P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <\frac{X - \mu }{\sigma } < \frac{x_2- \mu }{\sigma } )\)

 Generally

                \(\frac{X - \mu }{\sigma } = Z(The \ standardized \ value \ of \ X )\)

So

              \(P( x_1 < X < x_2) = P(\frac{x_1 - \mu }{\sigma } <Z < \frac{x_2- \mu }{\sigma } )\)

substituting values

               \(P( x_1 < X < x_2) = P(\frac{81 - 100 }{15 } <Z < \frac{119- 100 }{15 } )\)

               \(P( x_1 < X < x_2) = P( -1.2667 <Z <1.2667 )\)

               \(P( x_1 < X < x_2) = P(Z <1.2667 )-P( Z < -1.2667 )\)

From the standardized Z table

               \(P(Z <-1.2667 ) = 0.10263\)

And        \(P(Z <1.2667 ) = 0.89737\)

So

            \(P( x_1 < X < x_2) = 0.89737 - 0.10263\)

            \(P( x_1 < X < x_2) = 0.79474\)

Answer:

\(x= 8\sqrt{2}\)

Step-by-step explanation:

This is a 45, 45, 90-degree triangle.

You can tell because whenever there is a 90 degree angle (right angle) and a 45-degree angle, the last angle must be 45, too, making it 45, 45, 90.

In such a triangle, the hypotenuse is equal to some number (x) times the square root of 2.

To get 16, you must eliminate that radical 2, so you have to multiply by a square root. We know that the square root of 2 times the square root of 2 is 2, so then now we only need to get a constant to multiply it by 16.

This constant would be 8.

We know this because sqrt(2) times 8(sqrt 2) gives us 2 times 8, or 16.

Now that we know what x is, we have the solution.

The legs of a 45,45,90 degree triangle are equal to the number we need to multiply the square root of 2 by to get 16, 8(sqrt 2)

That is our answer: 8(sqrt 2)

The nearest Whole percent, the percent increase of women students is approximately 21%.

The percent increase of women students, we need to compare the number of women students in 2005 and 2006.

In 2005, the number of women students was 123.

In 2006, the number of women students was 149.

To find the increase, we subtract the initial value (2005) from the final value (2006):

Increase = Final Value - Initial Value

Increase = 149 - 123

Increase = 26

Next, we need to calculate the percent increase. The percent increase is given by the formula:

Percent Increase = (Increase / Initial Value) * 100

Plugging in the values:

Percent Increase = (26 / 123) * 100

Calculating the percent increase:

Percent Increase ≈ 21.14%

Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.

Therefore, the answer is 21%.

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Answer:

number 21; x =80°

Step-by-step explanation:

1) 180 - 118 = 62° because all angles on straight lines add to 180.

2) 62°+38°= 100

3) 180 - 100 = 80°

Answer: 803.84cm3

Step-by-step explanation:
The formula for finding the volume of a cylinder is πr2h.
In other words, the area of the top face's circle times the height.

To find the circle's area, we first find the radius of the circle. Since the diameter is 8cm, we divide by 2 to get the radius, which is 4cm.

4cm squared is 4cm x 4cm, which is 16cm. 16cm times 3.14 is 50.24cm squared.

Now, we have the area of the circle. 50.24cm squared!

The height is 16cm, so to find the cylinder, we times the area of the circle by the height of the cylinder! So,

16cm x 50.24cm squared = 803.84cm cubed.

The volume of the can of soup is 803.84cm cubed.

Foreign direct investment helps improve the economic situation of a recipient country by increasing employment opportunities in the country that the company invests in.

When foreign companies invest in a recipient country, they often establish or expand their operations, which requires hiring local workers. This leads to job creation and reduces unemployment rates in the recipient country.

Increased employment opportunities result in more individuals having access to income and improved standards of living.

Foreign direct investment also contributes to the transfer of technology, knowledge, and skills to the recipient country. Multinational companies often bring advanced technologies, production techniques, and management practices that may not have been available or widely adopted in the recipient country.

Furthermore, foreign direct investment stimulates domestic investment and encourages the growth of local businesses. When foreign companies invest in a recipient country, they often form partnerships or engage in supply chain relationships with local firms.

Overall, foreign direct investment increases employment opportunities, fosters technology transfer, and stimulates domestic investment, all of which contribute to improving the economic situation of a recipient country.

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The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.

To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.

Add the square of half of the coefficient of x to both sides of the equation:

x² + 2x + (2/2)² = 319 + (2/2)²

x² + 2x + 1 = 320

The left-hand side of the equation can now be factored as a perfect square:

(x+1)² = 320

This is the equation in the form (x+a)²=b, where a=1 and b=320.

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The complete question is as follows:

What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?

x² + 2x = 319

Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB. Option C

The steps involved in constructing a perpendicular bisector are:

Thus, Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB. Option C

The complete question

Eric was attempting to construct a perpendicular bisector to the segment AB with a compass and straight edge. Which of the below statements explains what Eric may have done wrong?

a. Eric should have started by putting the compass needle point at the midpoint of the segment AB.

b. On the second step, Eric should have placed the compass needle point where the first arc intersected the segment AB.

c. Erick just needed to open the compass more to create arcs that have a radius of more than half the length of the segment AB.

d. Erick didn’t do anything wrong he just needs to connect the opposite endpoints of each arc to finish the construction.

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Answer:

4800

Step-by-step explanation:

length = 20mm X 3 = 60mm

width = 20mm X 4 = 80mm

area = length X width = 60 X 80 = 4800 m\(m^{2}\)

I hope it helps you!

Answer:

This is the answer: 4160 mm^2

Answer:

1. False

2. True

3. True

4. True

5. False

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. False   3/10 x 5 = 15/50 not 12/50

2. True    1/2 x 2 = 6/12

3. True    5/6 x 2 = 10/12

4. True    5/7 x 3 = 15/21

5. False   3/8 x 2 = 6/16 not 6/15

Answer:

200ft

Step-by-step explanation:

100ft = 1/2 ft

12in = 1 ft

1/2 * 2= 1ft

1ft or 12in = 200ft

Answer:

5b + 2

Step-by-step explanation:

Frank is going to plant b vegetable seeds in one garden and 4b + 2 vegetable seeds in another.

We need to find how many seeds is frank going to plant.

It is equal to the sum of vegetable seeds in one garden and the vegetable seeds in another.

Sum = b + 4b + 2

Sum = 5b + 2

So, there are "5b + 2" seeds frank going to plant.

Answer:

70

Step-by-step explanation:

\(~~~~~~~~~y= 2x^3 -2x^2 -3x+1\\\\\\\implies \dfrac{dy}{dx} =\dfrac d{dx} \left( 2x^3 -2x^2 -3x +1\right)\\\\\\~~~~~~~~~~~=2 \dfrac{d}{dx}\left(x^3\right) - 2 \dfrac d{dx} \left(x^2\right) - 3 \dfrac d{dx} (x) +\dfrac{d}{dx}(1)\\ \\\\~~~~~~~~~~~=2\cdot 3x^2 -2\cdot 2x-3 +0~~~~~~~;\left [ \dfrac d{dx} x^n = nx^{n-1}\right]\\\\\\~~~~~~~~~~~=6x^2 -4x -3\)

\(\text{The derivative is}~6x^2 -4x -3\)

The length of the hypotenuse of the triangle is the solution to the question.

The length of the hypotenuse can be found using the Sine Trigonometric Ratio given to be:

From the image, we have the following parameters:

Therefore, we have:

To solve for AC, we can cross-multiply:

Recall the identity:

Therefore, the equation will be:

The SECOND OPTION is correct.

The distance that the box has to travel to move from point A to point C is equal to the length of side AC of the right triangle ABC. Since angle ACB is 62 degrees and side AB is opposite this angle, we can use the definition of sine to find the length of side AC. The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, we have:

$$\sin(62°)=\frac{AC}{AB}$$

Substituting the known values, we get:

$$\sin(62°)=\frac{AC}{10}$$

Solving for AC, we get:

$$AC=10\sin(62°)$$

So, the distance that the box has to travel to move from point A to point C is **10 sin 62°** feet.

Answer:

Independent variable causes an effect on the dependent variable. Example: How long you sleep (independent variable) affects your test score (dependent variable). This makes sense, but: Example: Your test score affects how long you sleep

Answer:

A. Reflection

Step-by-step explanation:

I believe the answer would be reflection

Answer:

1/10 = 0.1

Step-by-step explanation:

The value of a 4 in the one thousands place = 4000

the value of a 4 in the ten thousands

= 40000

In fraction,The value of a 4 in the one thousands place to the value of a 4 in the ten thousands place

= 4000/40000

= 4/40

= 1/10

= 0.1

Answer:

I kept coming up with $3.56

Step-by-step explanation:

Answer:

$2.00 each

Step-by-step explanation:

9514 1404 393

Answer:

  (5, -6)

Step-by-step explanation:

x-coordinates measure the distance to the right of the y-axis. Moving a point 4 units to the right adds 4 to its x-coordinate.

y-coordinates measure distance up from the x-axis. Moving a point 4 units down subtracts 4 from its y-coordinate.

  (1, -2) +(4, -4) = (1 +4, -2 -4) = (5, -6) . . . . image of translated point

The intermediate step in completing the square is\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\)

To complete the square for the equation \($(x+a)^2=b$\), we can follow these steps:

1. Expand the left side of the equation: \($(x+a)^2 = (x+a)(x+a) = x^2 + 2ax + a^2$\).

2. Rewrite the equation by isolating the squared term and the linear term: \($x^2 + 2ax = b - a^2$\).

3. To complete the square, take half of the coefficient of the linear term, square it, and add it to both sides of the equation:

\($x^2 + 2ax + (a^2) = b - a^2 + (a^2)$\).

4. Simplify the right side of the equation: \($x^2 + 2ax + (a^2) = b$\).

This step can be represented as: \(\[x^2 + 2ax + (a^2) = b - a^2 + (a^2)\]\)

This intermediate step helps us rewrite the equation in a form that allows us to factor it into a perfect square.

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