Assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that the heights of men be between 64 and 78 inches. If 500 men want to enlist in the U.S. Marine Corps, how many would you not expect to meet the height requirements?

The equation in the form at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex], the magnitude of the velocity is 7.81 m/s, the direction of the velocity is 50.19°.

Consider the flow field:

u=2+y & v=2 y

Determine the streamline equation by using the following equation:

[tex]& \frac{d x}{u}=\frac{d y}{v} \\ \frac{d x}{2+y}=\frac{d y}{2 y} \\\\& \int d x=\int\left(\frac{2+y}{2 y}\right) d y \\\\& x=\ln y+\frac{y}{2}+C[/tex]

(A)

Since the stream line passes through (3,2).

[tex]$$\begin{aligned}& x=\ln y+\frac{y}{2}+C \\& 3=\ln 2+\frac{2}{2}+C \\& C=2-\ln 2 \\& C=1.31\end{aligned}$$[/tex]

Substitute the value of C in equation (1).

[tex]& x=\ln y+\frac{y}{2}+C \\\\& x=\ln y+\frac{y}{2}+1.31 \\\\& 2 x-1.31 \times 2=2 \ln y+y \\\\& \ln y^2+y=2 x-2.62[/tex]

Therefore, the equation of streamline equation at point (3m, 2m) is [tex]$\ln y^2+y=2 x-2.62$[/tex].

(B).

Calculate the magnitude of the velocity of a particle located at point (5m , 3m).

[tex]V & =\sqrt{u^2+v^2} \\\\& =\sqrt{(2+y)^2+(2 y)^2} \\\\& =\sqrt{(2+3)^2+(2 \times 3)^2} \\\\& =\sqrt{5^2+6^2} \\\\& =7.81 \mathrm{~m} / \mathrm{s}[/tex]

Therefore, the magnitude of the velocity of a particle located at point (5m , 3m) is 7.81m/s.

(C).

Calculate the direction of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x-axis is

[tex]\tan \theta & =\frac{v}{u} \\\\& =\frac{2 y}{2+y} \\\\& =\frac{6}{5} \\\\& =50.19^{\circ}[/tex]

Therefore, the direction of the velocity of a particle located at point (5m , 3m) is 50.19°.

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A flow field for a fluid is described by u=(2+y) m/s and v=(2y) m/s, where y is in meters.

      A.) Determine the equation of the streamline that passes through point (3m, 2m). Write the equation in the form

 x={x(y)}, where y is in meters.

      B.) Find the magnitude of the velocity of a particle located at point (5m , 3m).

      C.) Find the direction ? of the velocity of a particle located at point (5m , 3m) measured counterclockwise from the positive x axis.

Answer:

mn/100

Step-by-step explanation:

m% = m/100

m% of n = m% × n = m/100 × n = mn/100

I believe the answer is x= 12

Answer:

15 cm

Step-by-step explanation:

a² + b² = c²

(9 cm)² + (12 cm)² = c²

81 cm² + 144 cm² = c²

225 cm² = c²

c = √(225 cm²)

c = 15 cm

Answer: 15 cm

To determine the number and type of solutions to the quadratic equation x^2 - x = -1/4, we can use the discriminant, which is the part of the quadratic formula that determines the number of solutions. The quadratic formula is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation. In this case, the coefficients of the equation are a = 1, b = -1, and c = -1/4. Plugging these values into the formula gives us:

x = (1 +/- sqrt(1^2 - 4(1)(-1/4))) / (2(1))

x = (1 +/- sqrt(1 + 1)) / 2

x = (1 +/- sqrt(2)) / 2

Therefore, the quadratic equation has two solutions: x = (1 + sqrt(2)) / 2 and x = (1 - sqrt(2)) / 2. These solutions are both real numbers.

Answer: 49/60 mins.

Step-by-step explanation:

First lap time = 5/6 minute

Second lap time = 11/12 minute

Third lap = ?

To find the 3rd lap mins, we need to find 5 x 6, which is 30. Then, we need to find 1 1/12 more than 30. Then, when we get that answer, we need to find 1 1/10 fewer mins to get the 3rd lap time. If you do it all right, you should end up with 49 mins or 49/60 mins as a fraction (The denominator was changed to 60 to make the problem more realistic and easier) I hoped this helped.

Answer:

Wdym what to put for 1 and 2??

Step-by-step explanation:

there’s no picture on my screen ;-;

A coordinate system is a two-dimensional number line, for example, two perpendicular number lines or axes.

This is a typical coordinate system:

coordinate plane1

The horizontal axis is called the x-axis and the vertical axis is called the y-axis.

The center of the coordinate system is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0).

An ordered pair contains the coordinates of one point in the coordinate system. That is named by its ordered pair of the form of (x, y).

The first number corresponds to the x-coordinate and the second to the y-coordinate.

To graph a point, we have to draw a dot at the coordinates that correspond to the ordered pair. It is one of the best ways to start at the origin.

The x-coordinate shows how many steps have to take from positive to negative on the x-axis, the same as the y-coordinate tells how to have many steps from positive to negative on the y-axis.

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As per the concept of unitary method, the another way to express 8 feet is 2 [tex]\frac{2}{3}[/tex] yards.

In math, unitary method is known as a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.

Here we have given that a clothesline rope is 8 feet long.

Now we need to find another way to express 8 feet

We know that the formula to convert the measurement it to divide the length by the conversion ratio.

As we know that one yard is equal to 3 feet, then we can use this simple formula to convert is written as

yards = [tex]\frac{feet}{3}[/tex]

Then we have to convert the improper fraction into mixed fraction from, then we get,

2[tex]\frac{2}{3}[/tex] yards

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Answer:

- 4, - 3, - 2, - 1, 0, 1

Step-by-step explanation:

- 15 < 3n < 6 ( divide each interval by 3 )

- 5 < n < 2

then integer value of n are - 4, - 3, - 2, - 1, 0, 1

We may demonstrate via a contrapositive assertion that if the total of two real numbers is less than 50, then at least one of the numbers must be less than 25.

The purpose is to demonstrate the following using contraposition:

Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite. Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement.

Contrapositive assertions, in other words, result from adding "not" to both component claims and reversing the order of the given conditional statements.

Two real numbers will have a sum that is larger than or equal to 50 if neither of them is smaller than 25.

Assume for all real numbers r and s r≥25, s≥25

By using inequality algebra,

r+s≥25+25

≥50

This demonstrates that two numbers will add up to a value more than or equal to 50 if neither of them is less than 25.

Hence, r + s<50, then r<25, s<25 by contrapositive statement.

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At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge.

The unitary method is used to calculate the value of a single unit and then multiply that value by itself in order obtain the desired value. Unitary refers to a single, unique, or solitary unit. As a result,

this method's objective is to establish values in terms of a single unit. If a car can drive 44 kilometer two litres of gas, for instance, the unitary approach can be used to calculate how many kilometers it can travel on one litre of gas. The value of a single unit is determined by the unitary technique, and also the value of the required quantity of units can then be calculated using this value.

given,

 0.76 miles = (4024/5280) miles

Speed =20 miles per hour

Time: =(Distance / Speed) = (0.76/20)

= 0.038 ( in hours )

into minutes = 2 min

At a continuous speed of 20 miles per hour, it takes 2 minutes to cross this bridge

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Answer:

Slope: 3

y-intercept: ( 0, −5)

Graph a solid line, then shade the area above the boundary line since

y is greater than 3x −5.

y ≥ 3x −5

Answer: 6.4 miles

Step-by-step explanation:

Take 30 divided by 4 = 1 mile every 7.5 minutes

Then take 48 divided by 7.5 = 6.4 miles in 48 minutes

In an effort to reduce wait times in the emergency room. Eighty patients were polled at random by the investigating committee. And, the upper-bound 95% confidence interval is found to be 1.64.

For small sample numbers or unidentified changes, the t-distribution is used in statistics to calculate the significance of population parameters.

Given sample mean [tex]\overline{X}[/tex] is 1.5 hours, sample size n is 80, and sample standard deviation s is 0.7 hours. Then, the standard error for the mean is,

[tex]\begin{aligned}SE_x&=\frac{s}{\sqrt{n}}\\&=\frac{0.7}{\sqrt{80}}\\&=0.07826\end{aligned}[/tex]

The degree of freedom is given by, df = n-1 = 80-1 = 79.

From the t-distribution table, [tex]t_{\alpha/2, 79}=1.7735[/tex]

Then, the upper-bound 95% confidence interval is calculated as,

[tex]\begin{aligned}\overline{X}+t_{\alpha,(n-1)}\frac{s}{\sqrt{n}}&\geq \mu\\&=\overline{X}+t_{0.08, 79}\frac{s}{\sqrt{n}}\\&=1.5+1.7735\left(\frac{0.7}{\sqrt{80}}\right)\\&=1.5+1.7735(0.07826)\\&=1.5+0.13879\\&=1.63879\\&\approx1.64\end{aligned}[/tex]

The required answer is 1.64.

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To find the constant of variation in this situation, we need to use the formula for inverse variation, which is:

y = k / x

where y is the number of cigarettes a person smokes, x is the length of time they can hold their breath, and k is the constant of variation.

In this case, we are given that y = 10 cigarettes and x = 50 seconds. We can solve for k by multiplying both sides of the equation by x:

k = y * x

= 10 cigarettes * 50 seconds

= 500

Therefore, the constant of variation in this situation is 500. This means that for every 50 seconds of breath-holding time, a person will smoke approximately 10 cigarettes.

Answer:

7

Step-by-step explanation:

4+3=7

7-4=3

7-3=4

Answer:

C

Step-by-step explanation:

[tex]\frac{6y }{x^{8} } . \frac{4y}{x^{14} }\\\\\frac{24y^{2} }{x^{8+14} } \\\\\frac{24y^{2} }{x^{22} }[/tex]

The solutions for the given equation is (1, 12), (2, 18), (3, 24), (4, 30) and (5, 36).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=6x+6.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Substitute, x=1, 2, 3, 4, 5,.....

When x=1

y=6x+6

y=12

When x=2

y=6x+6

y=6(2)+6

y=18

When x=3

y=6x+6

y=6(3)+6

y=24

When x=4

y=6x+6

y=6(4)+6

y=30

When x=5

y=6x+6

y=6(5)+6

y=36

Therefore, the solutions for the equation is (1, 12), (2, 18), (3, 24), (4, 30) and (5, 36).

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Answer:

Step-by-step explanation:

Given angles of elevation of 10° and 50° measured 10 seconds apart from an observation point 1.5 miles away, you want to know the vertical change in distance, and the average speed of the shuttle between the two observations.

The tangent relation tells you ...

  Tan = Opposite/Adjacent

Then the height of the shuttle at the observed angles was ...

  Opposite = Tan · Adjacent

  h1 = tan(10°)·(1.5 mi) ≈ 0.264490 mi

  h2 = tan(50°)·(1.5 mi) ≈ 1.787630 mi

The amount of vertical travel in the 10-second interval was ...

  1.787630 mi -0.264490 mi = 1.523240 mi

The space shuttle traveled about 1.523 miles vertically in the 10-second interval.

In miles per second, the average speed during that time was about ...

  (1.523 mi)/(10 s) = 0.1523 mi/s

In miles per hour, that's about ...

  (0.1523 mi/s)(3600 s/h) ≈ 548 mi/h

Answer:

answer on the picture..........

A circle of radius 4.6 cm is drawn with its center at the origin. The diameter XY of the circle is also drawn, along with two chords XP and YQ connecting the endpoints of the diameter.

A circle of radius 4.6 cm is drawn with its center at the origin, which is labeled as O. The diameter XY of the circle is also drawn and labeled, with the endpoints X and Y. Two chords XP and YQ are then drawn connecting the endpoints of the diameter. The chord XP starts at X and ends at P, while the chord YQ starts at Y and ends at Q. This diagram demonstrates the idea of a circle and its diameter, as well as how two chords can be drawn from the same two endpoints of a diameter. The circle and its diameter can also be used to calculate the circumference of the circle and the length of the diameter.

Circumference of circle = 2 * π * 4.6 = 28.96 cm

Length of diameter = 2 * 4.6 = 9.2 cm

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Answer:

x = 4.083

Step-by-step explanation:

6(2x+5)+19=0

12x+30+19=0

12x+49=0

12x=-49

x=4.083

Answer:

f(2x + 5) = 6x + 19

= 6(2x + 5) + 19

= 12x + 30 + 19

= 12x + 49

f(2) = 12x + 49

= 12(2) + 49

= 73

Step-by-step explanation:

The correct statements are:

1) Leena consumed 1,500 calories at dinner.

2) The equation  2/3(x + 400 + 350) = x

In this question we have been given Leena consumes 400 calories at breakfast and 350 calories at lunch. she consumes 2/3 of her daily calories at dinner.

We need to select a statement that describes the situation  if x represents the calories consumed at dinner.

Let x be the calories consumed at dinner.

Leena consumes 400 calories at breakfast and 350 calories at lunch.

So, the daily calories consumed by her:

400 + 350 + x

Given that she consumes 2/3 of her daily calories at dinner.

From given conditions we get an equation,

x = 2/3(x + 400 + 350)

3x = 2(x + 750)                          ............(multiply both sides by 3)

3x = 2x + 1500                

3x - 2x = 2x + 1500 - 2x            ...............(subtract 2x from both sides)

x = 1500 calories

Therefore, Leena consumed 1500 calories at dinner.

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Answer:3.3

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

the difference between 51.2 and a number is  :   51.2 - x

 Now multiply this by 6  :   6 x (51.2-x)    

     and this equals 68.3  :      6 x (51.2-x) = 68.3

Answer:

36,015.

Step-by-step explanation:

To calculate the cost-of-living increase, you would first multiply the current salary by the percentage increase: $35,000 * 0.029 = $1,015.

Then, to find the new salary, you would add the cost-of-living increase to the current salary: $35,000 + $1,015 = $36,015.

So, the woman's new salary would be $36,015 per year.

a) The probability that an apple from the tree has a weight greater than 90 grams is of: 0.2514 = 25.14%.

b) i) The p-value of the test is of: 0.0045.

b) ii) The conclusion of the test is given as follows: There is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B, as the p-value of the test is less than the significance level.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the weight of the apples are given as follows:

[tex]\mu = 85, \sigma = 7.5[/tex]

The probability that an apple from the tree has a weight greater than 90 grams is one subtracted by the p-value of Z when X = 90, hence:

Z = (90 - 85)/7.5

Z = 0.67

Z = 0.67 has a p-value of 0.7486.

1 - 0.7486 = 0.2514 = 25.14%.

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the mean by the standard error of the distribution of differences, hence:

z = 4.2/1.61 = 2.61.

Using the z-table, with z = 2.61, the p-value is of:

0.0045.

As the p-value is less than the significance level, there is enough evidence to conclude that the mean weight of apples from tree A is greater than the mean weight of apples from tree B.

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The result of the subtraction of the algebraic expression (5.62n − 2.8) − (4 + 14.3n) is -8.68n - 6.8 Third option is correct.

What is algebraic expression?

An algebraic expression is a mathematical phrase that uses numbers, operations such as addition and multiplication, and variables (letters or symbols that represent unknown values). Algebraic expressions are used to represent real-world problems and situations. Algebraic expressions can be combined and simplified, and they can also be used to solve equations. Algebraic expressions can be used to describe anything from the area of a circle to the cost of a car. Algebraic expressions are an essential part of algebra, and they are used to help students understand mathematics concepts in a more concrete way.

The given algebraic expressions are 5.62n - 2.8 and 4 + 14.3n

Now,

(5.62n − 2.8) − (4 + 14.3n)

5.62n - 2.8 - 4 - 14.3n

-8.68n - 6.8

Third option is correct

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Answer:

the answer is b

Step-by-step explanation:

If the two expression be 14 - 3a and 7a - 9 then the combined term exists 4a + 5.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. An expression has the following structure: Expression: (Math Operator, Number/Variable, Math Operator).

The addition, subtraction, multiplication, and division mathematical operations are used to create mathematical expressions.

Let the two expression be 14 - 3a and 7a - 9

Expression one - 14 - 3a

Expression two - 7a - 9

Combining both two terms

14 - 3a + (7a - 9)  = 14 - 3a + 7a - 9

simplifying the above equation, we get

= (-3a + 7a) + 114 - 9)

=  4a + 5

If the two expression be 14 - 3a and 7a - 9 then the combined term exists 4a + 5.

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