Which expression is equivalent to...

The height of the man from the given question is; 37.5 ft

This question will form a triangle where;

Height of building = 30 ft

Height of man = h ft

Initial height of shadow = 40 ft

Additional height of shadow = 10 ft

Using similarity theorem, we have;

h/30 = (40 + 10)/40

h/30 = 5/4

h = (30 * 5)/4

h = 37.5 ft

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Answer:

B = 49/5 - 7a/5

A = = -5b/7 + 7

Step-by-step explanation:

Given that,

7a+ 5b= 49

Solution:

Solving for a:

Add -5b to both sides:

Divide both sides by 7:

Hence,a = -5b/7 + 7.

Solving for b:

Add -7a to both sides:

Divide both sides by 5:

Hence,b = 49/5 - 7a/5.

Answer:

Using the rational root theorem, we know to divide the function by (x - 1).

(7x³ + 9x² - 12x - 4) / (x - 1) = 7x^2 + 16x + 4

Now we can further factorize 7x^2 + 16x + 4 into (7x + 2) and (x + 2).

Therefore, the original function can be rewritten as (x - 1) (7x + 2) (x + 2).

Using the factorized form above, the zeros of the function are 1, -2/7, and -2.

The area of the region bounded by the line y =3x -6 and line y=-2x+8 is  12/5 units

y = 3x - 6

y = -2x + 8

Set these two equations equal to each other.

3x - 6 = -2x + 8

Add 2x to both sides of the equation.

5x - 6 = 8

Add 6 to both sides of the equation.

5x = 14

Divide both sides of the equation by 5.

x = 14/5  

Find the y-value where these points intersect by plugging this x-value back into either equation.

y = 3(14/5) - 6

Multiply and simplify.

y = 42/5 - 6

Multiply 6 by (5/5) to get common denominators.

y = 42/5 - 30/5  

Subtract and simplify.

y = 12/5

These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.

Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.

Set both equations equal to 0.

(I) 0 = 3x - 6  

Add 6 both sides of the equation.

6 = 3x

Divide both sides of the equation by 3.

x = 2  

Set the second equation equal to 0.

(II) 0 = -2x + 8

2x = 8

x = 4

The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.

The height of the triangle is 12/5 units.

A = 1/2bh

Substitute 2 for b and 14/5 for h.

A = (1/2) · (2) · (12/5)

A = 12/5

The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.

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Answer:

60200 cm^2

Step-by-step explanation:

I believe I've answered this question on another post: https://brainly.com/question/27987703

Answer:

x = 19.5 (nearest tenth)

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

[tex]\theta[/tex] is the angle

Use the cos ratio to find the measure of the altitude (the perpendicular drawn from the vertex of the triangle to the opposite side):

[tex]\implies \cos(47^{\circ})=\dfrac{a}{18}[/tex]

[tex]\implies a=18\cos(47^{\circ})[/tex]

Now use the sin ratio to the the measure of side x:

[tex]\implies \sin(39^{\circ})=\dfrac{a}{x}[/tex]

[tex]\implies x=\dfrac{a}{\sin(39^{\circ})}[/tex]

[tex]\implies x=\dfrac{18\cos(47^{\circ})}{\sin(39^{\circ})}[/tex]

[tex]\implies x=19.50671018[/tex]

Therefore, x = 19.5 (nearest tenth)

Answer:

{x | x = -6, -1, 0, 3}

(first option listed)

Step-by-step explanation:

The domain of a function is all possible x-values for that function

So, we can see (from the x-value portion of our table) that the possible x-values are:

-6 , -1, 0, and 3

We write domain and range in lowest - highest number value order, so we write our domain as such:

{x | x = -6, -1, 0, 3}

{range is all possible y-values, and this would include -7 , 1, 9, and -2}

hope this helps!!

Answer:

Area = 3.36 in²

Step-by-step explanation:

[tex]Area\space\ of \space\ trapezium = \frac{a \space\ + \space\ b}{2} h[/tex] ,

where a and b are the two parallel sides, and h is the height.

[tex]Area = \frac{1.3 \space\ + \space\ 3.5}{2} (1.4)\\\\Area = 3.36 \space\ in^{2}[/tex]

The histogram of the distribution plotted on the y - axis and the interval for the length of time on the x - axis is attached below.

The first bar denotes the length of time between 0 and 10 having a frequency of 8. The second bar denoted the interval between 10 and 15 with a frequency of 15

The third bar denoted the interval between 15 and 20 with a frequency of 10. The fourth bar denoted the interval between 20 and 30 with a frequency of 11

Therefore, the histogram of the distribution is attached below.

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The amount invested at each rate

Investment at 7% = $25000

Investment at 2%  = $11,000

Investment definition is an asset acquired or invested in to build wealth and save money from the hard earned income or appreciation.

Given:

Larry Mitchell invested = $36,000 at 7% annual simple interest

the rest at 2% annual simple interest.

Total investment = 36000

let the investment at 7% is x

then, invested at 2% = 36000 - x

Total interest earned = $1,970

Simple interest = principal * rate * time

Investment at 4%:

(x * 0.07) + [(36000 - x) * 0.02] = 1970

0.07x + 720 - 0.02x= 1970

0.05x = 1970-720

0.05x = 1250

x= 25000

Hence,

Investment at 7% = $25000

Investment at 2% = $36,000 - $25000 = $11,000

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Option D is the correct answer.

All real numbers greater than or equal to 0 and less than 4.

The domain of a function is the set of its possible inputs, i.e., the set of input values where for which the function is defined.

Here, The function of the car value is given as:

V(x) = 20000 X (0.84)ˣ

When the car reaches half its value, we have:

V(x) = 10000

Substitute V(x) = 10000 in V(x) = 20000 * (0.84)ˣ

10000 = 20000 X (0.84)ˣ

Divide both sides by 20000

0.84ˣ = 0.5

Take the logarithm of both sides

x log(0.84) = log(0.5)

Divide both sides by log(0.84)

           x = 4

This means that the maximum value of x is 4.

Thus, all real numbers greater than or equal to 0 and less than 4.

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Answer:

09

Step-by-step explanation:

09

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

The rate at which the oil burns.

1 hour = 2/3 ounce

At 12 noon = 193/3 = 64.33 ounces

At 2 pm = 63 ounces

At 5 pm = 61 ounces

The amount of oil at 12 noon is 64.33 ounces.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

A camper lights an oil lantern at 12 noon and lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant rate each hour.

At 2 p.m., the amount of oil left in the lantern is 63 ounces.

At 5 p.m., the amount of oil left in the lantern is 61 ounces.

This means,

Amount of oil burnt in the lantern from 2 pm to 5 pm.

= 63 ounces - 61 ounces
= 2 ounces

Now,

3 hours = 2 ounces

2 hours = 1.33 ounces

1 hour = 0.67 ounces

Now,

The number of hours from 12 noon to 2 pm.

= 2 hours

So,

The amount of oil at 12 noon.

= 63 + 4/3

= (189 + 4) / 3

= 193/3 ounces

Thus,

The amount of oil at 12 noon is 65 ounces.

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Answer:

1

Step-by-step explanation:

It has only 1 line of symmetry. The line is a vertical line that passes through the top vertex.

Answer: 1

The equation of the circle, ellipse, and hyperbola will be x² + y² = 3², x² + y² / 3² = 1, and x² / 2² - y² / 3² = 1, respectively.

The curve that is derived from the section of the cone is known as conic section.

The following equations are given below.

x² + y² = 3², this is the equation of the circle.

x² + y² / 3² = 1, this is the equation of the ellipse.

x² / 2² - y² / 3² = 1, this is the equation of the hyperbola.

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The number of cars that have passed through the intersection is 245.

Direct variation is when two variables move in the same direction. If one variable increases, the other variable increases.

The equation that represents direct variation is; c = wk

Where:

1085 = k31

k = 1085 / 31

k = 35

c = 7 x 35

c = 245

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Answer:

domain is all reals

Step-by-step explanation:

sorry I couldn't find the range

Step-by-step explanation:

-| 12/3 - 1| 2-(-3)

-|12-3/3|5

-5|9/3|

-5|3|

-5×3 & -5×-3

-15 & 15

I think it is the answer

I presume you meant [tex]y=-2\sqrt{x-3}+2[/tex].

The graph is shown in the attached image.

15-(5)/5-10=10/-5=-2 hope it helps!

Answer: The height is 15

Step-by-step explanation:

Vcone =  pi * r^2 * h  / 3

Area of the base  =  pi*r^2  = 70   so...

350  = 70 * h / 3  

350  = (70/3) * h     multiply both sides by 3/70

350 (3/70)  = h  = 15 m

Answer:

√2/4, √3/4, and √5/4.

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively

The table of values is given as:

Savings Lower Limit Upper Limit     Frequency

0-199         0         199                       345

200-399   200   399                         97

400-599   400   599                         52

600-799   600   799                         21

800-999   800   999                         9

1000-1199 1000  1199                         8

1200-1399 1200  1399                      3

Rewrite the table to include the class midpoint and the frequency

x               f

99.5         345

299.5        97

499.5        52

699.5        21

899.5        9

1099.5        8

1299.5        3

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\bar x = 233.331775701[/tex]

Approximate

[tex]\bar x = 233.3[/tex]

Hence, the approximation of the mean is 233.3

The standard deviation is calculated as:

[tex]\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}[/tex]

So, we have:

[tex]\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}[/tex]

Evaluate

[tex]\sigma = 229.82[/tex]

Hence, the approximation of the standard deviation is 229.82

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Answer:

I think non response bias because response bias includes answering incorrectly on a survey to get it over with so that is my answer

Step-by-step explanation:

Answer:

4mm

Step-by-step explanation:

you have to add both sides after substituting each of the 4 sides by 1mm

which gives you the total of 4

The number of hours that Bret can hike with 9 liters of water is 9.6 hours.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given,

Water needed = 0.75 liters per hour

For x number of hours = 0.75x liters

Reserved water = 1.8 liters.

Total water needs for x hours = (0.75x + 1.8)

The number of hours that can be hiked with 9 liters will be as,

(0.75x + 1.8) = 9

x = 9.6 hours.

Hence "The number of hours that Bret can hike with 9 liters of water is 9.6 hours".

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The required work done is 62400 J.

work done to lift a 1500 N object from the ground to the top of a 40 m building if the cable weighs 3 N per m

work done, is define as the product of force and displacement.

since,
work done to lift 1500N to height of 40 m is:
W= FS
   =  1500 x 40 = 60000J
now work done for rope
  is given by
w = mgΔx(40-x)
w= [tex]\int _0^{40}\left mg(40-x\right)dx[/tex]
w=[tex]3\int _0^{40}\left(40-x\right)dx[/tex]
w= 3[tex][40x-x^2/2]\left \{ {{40} \atop {0}} \right.[/tex]
w= 3[1600-800]
w = 2400
Total work done for lifting 1500N to 40m height
= 6000+2400=62400J

Thus the required work done to lift 1500N weight to 40m is 62400J.

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The value of minimum usual value is, [tex]\mu-2\sigma=-119.2[/tex]

The value of maximum usual value is, [tex]\mu+2\sigma=1311.2[/tex]

Given the values of the parameters of Binomial Distribution are,

Total number of trials (n) = 1490

probability of success in one trial is (p) = 2/5

The probability of failure in on trial is given by,

[tex]q=1-p=1-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}[/tex]

For Binomial distribution we know that,

Mean [tex](\mu)=np=1490\times\frac{2}{5}=596[/tex]

and Standard Deviation [tex](\sigma)=\sqrt{npq}=\sqrt{1490\times\frac{2}{5}\times\frac{3}{5}}=357.6[/tex]

Now, calculating the required measurement we get,

The minimum usual value is given by,

Mean -2 Standard Deviation [tex]=\mu-2\sigma=596-2\times357.6=-119.2[/tex]

The maximum usual value is given by,

Mean + 2 Standard Deviation [tex]=\mu+2\sigma=596+2\times357.6=1311.2[/tex]

Hence the minimum and maximum usual values are -119.2 and 1311.2 respectively.

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Answer:

Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 4 inches.

(a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.)

z1 = (70-71)/4 = -0.25

z2 = (72-71/4 = 0.25

P(70<X<72) = p(-0.25<z<0.25) = 0.1974

Answer: 0.1974

(b) If a random sample of thirteen 18-year-old men is selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.)

z1 = (70-71)/(4/sqrt(13)) = -0.9014

z2 = (72-71/(4/sqrt(13)) = 0.9014

P(70<X<72) = p(-0.9014<z<0.9014) = 0.6326

Answer: 0.6326

please mark me the brainiest

Answer: all real numbers

Step-by-step explanation:

I assume you meant to write:

[tex]f(x)+g(x)=(x+5)+(x+4)=2x+9[/tex]

Since this is a linear function, the domain is all real numbers.

Answer:

well the answer is 4 have a good day