The daily upper limit for vitamin C is 2,000 milligrams. In the morning, Marcelo takes a vitamin containing 500 milligrams of vitamin C. An orange contains 100 milligrams of vitamin C. Let x be the number of oranges Marcelo can eat without reaching the daily limit for vitamin C. Choose the correct inequality.

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Given:

Area of the triangle, A = 70 square meters

Base of the triangle, b = 10 meters

To find the height, h, of the triangle, use the area of the triangle formula below:

Rewrite the formula for h:

To find the height, h, we have the equation:

Input values into the equation:

Therefore, the height of the triangle is 14 meters

ANSWER:

14 meters

The cosine function graphed is defined as follows:

y = 2.5cos(4x) + 1.5.

The function is at it's maximum value at the origin, hence it is a cosine function, defined as follows:

y = Acos(Bx) + C.

The parameters are given as follows:

The maximum value of the function is of 4, while the minimum value of the function is of -1, for a difference of 5, hence the amplitude is given as follows:

2A = 5

A = 5/2

A = 2.5.

Without vertical shift, the function would oscillate between -2.5 and 2.5, but it oscillates between -1 and 4, hence the vertical shift is given as follows:

C = 1.5.

The shortest distance between repetitions is of π/2, hence the period is of π/2 and the coefficient B is obtained as follows:

2π/B = π/2

B = 4.

Hence the function is given as follows:

y = 2.5cos(4x) + 1.5.

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a. The slopes of the lines are:

Slope of line 1 = 1/4

Slope of line 2 = -4

Slope of line 3 = -1/3

b.

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

From the question, we are to determine the slope of each of the given lines:

Using the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

m = (-3 - 0) / (-4 - 8)

m = (-3) / (-12)

m = 1/4

m = (2 - 6) / (0 - (-1))

m = (-4) / (1)

m = -4

m = (-7 - (-4)) / (6 - (-3))

m = (-3) / (9)

m = -1/3

b.

NOTE: Two lines are said to be parallel if they have equal slopes; and they are said to be perpendicular if the slope of one is the negative reciprocal of the other.

Thus,

Line 1 and Line 2 : Perpendicular

Line 1 and Line 3 : Neither

Line 2 and Line 3 : Neither

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Answer:

117

Step-by-step explanation:

Hi, If you were to add 75 to 42, you would get 117. Since a triangle's angles all have to add up to 180, the last angle would be 63. However, you are looking for the outside angle, which would then just be 117. Hope this is right!

Option C.88ft².

Answer:

Solution given:

side 1=19ft

side 2=25ft

height=4ft

now

area =½height (side 1+side 2)

=½*4*(19+25)=88ft²

Answer:

The area of trapezoid is 88 ft ² .

Step-by-step explanation:

The, area of trapezoid is given by

= 1 / 2 ( Base ¹ + Base ² ) × Height

Where,

Base ¹ and Base ² are the length of parrallel side and Height is the perpendicular distance between them.

1 / 2 ( Base ¹ + Base ² ) × Height

Where, given that

Substitute the values

Area = 1 / 2 × ( 19 ft + 25 ft ) × 4 ft

add the both parallel sides of trapezoid

Area = 1 / 2 × 44 ft × 4 ft

multiply the values , we get

Area = 176 ft ²/ 2

Divide and we get

Area of trapezoid = 88 ft ²

Therefore, the area of trapezoid is 88 ft ².

The definite integral for this problem has the result given as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}\)

The definite integral for this problem is defined as follows:

\(\int_1^5 x^2 + 2x - \tan{x} dx\)

We have an integral of the sum, hence we can integrate each term, and then add them.

For the first two terms, applying the power rule, the integrals are given as follows:

The integral of the tangent is given as follows:

ln|sec(x)|

Then the integral is given as follows:

I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.

Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:

I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)

I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|

I = 212 - ln|sec(5)| + ln|sec(1)|.

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The median age of the 120 people seated in the first five rows of the concert was 31.

Value is an important concept in economics and business. It is the worth of goods, services, or assets that is determined by the market or by an individual. It can be measured in terms of money, time, or effort. Value is also used to describe a person’s sense of worth or importance. Values can be seen as the principles, standards, or goals that guide an individual’s actions and decisions. Ultimately, value is subjective and is held by each person and can change over time.

The box and whisker plot provided by the sponsor shows the ages of the 120 people seated in the first five rows of the concert. The box and whisker plot shows a minimum value of 18, a maximum value of 45, a median of 31, a first quartile of 24, and a third quartile of 37. This indicates that 50% of the 120 people in the first five rows had an age of 31 or below, and 50% of the 120 people had an age of 37 or above. The median age of the 120 people seated in the first five rows of the concert was 31.

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Answer:

y=-8

Step-by-step explanation:

y-y1=m(x-x1)

y-(-8)=0(x-6)

y+8=0

y=0-8

y=-8

Answer:

1.97497

Step-by-step explanation:

Using my calculator, I just put in log(94.4).

Answer:

if you meant (b+3)+(2^b-2), the answer is b+1+2^b

Step-by-step explanation:

but if you meant (b+3)+(2b-2), the aanswer is 3b+1

Answer:

3b+1

Step-by-step explanation:

(b+3)+(2b-2)

b+3+2b-2

3-2

b+1+2b

b+2b

3b+1

The correct word form of 8.16 is b. eight and sixteen hundredths

Since the number is 8.16, we have 8.16 = 8 + 0.16 = 8 + 16/100

Since we have 8 in the units place, it is pronounced eight.

Also, we have our decimal part 0.16 = 16/100 which is pronounced as sixteen hundredths.

So, combining both we have eight and sixteen hundredths.

So, the correct word form of 8.16 is b. eight and sixteen hundredths

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The no. of cars that must drive by until a white one drives by is 40.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is

\(^nC_xp^Xq^{n-x}\).

We know the expected value of a binomial distribution E(x) = np.

Given, Suppose that 40% of the cars in a certain town are white.

Therefore 50% of cars in the town are not which.

Let, The no. of cards in the town be 'n'.

So, p = 40/n and q = 60/n

Therefore from the formula E(x) = np we get,

E(x) = n×40/n

E(x) = 40.

So, The expected value of X is 40.

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Answer: We expect 2.5 cars to

The expected value of X is 2.5.

Step-by-step explanation:

In this case, it is a geometric distribution because we do not have a fixed number of trials.

We use the formula of a geometric distribution to find the mean (the expected value) such that mu_x = 1/p.

In this case:

mu_x=1/0.4 = 2.5

In this case, we do not round up or down even if we cannot have half a car because we want the expected value (mean).

A perceiving type of person tend to make more use of intuition in their approach of life.

The word "Perceive" means to become aware of through the personal senses.

Therefore, they perceive situation automatically as they are use to that way of life approach.

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Answer:

38

Step-by-step explanation:

1) 1/2(10q-7q)

2) 1/2(10*9 - 7*2)

3) 1/2(90-14)

4) 1/2(76)

5) 38

Answer:

38

Step-by-step explanation:

firstly let us subtitute the values in the equation

1/2(10×9-7×2)

1/2(90-14)

1/2(76)

=38

Answer:

Step-by-step explanation:

Answer:

i think the answer is

\(f(x) = \\ - \frac{45x {}^{2} }{(1 + x {}^{3}) {}^{2} }\)

None of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

To find the slope of the red line given that it is perpendicular to the green line with a slope of 2, we can use the property that perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the green line is 2. To find the slope of the red line, we take the negative reciprocal of 2. The negative reciprocal is obtained by taking the reciprocal (flipping the fraction) and changing the sign.

Reciprocal of 2: 1/2

Negative reciprocal: -1/2

Therefore, the slope of the red line is -1/2.

However, none of the given answer options (-10, 10, 16, ¾/1) correspond to the correct slope of -1/2.

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If the sun is 69° above the horizon, the length of the shadow cast by a building 91 ft tall

You should understand that the length of the shadow is the distance between a point to the foot of the tenth

This makes an angle of depression, with 69 degrees

Remember that the angle on top of the tenth is 90-69 = 21 degrees

therefore, using the trigonometrical ratio

We have Tan∅ = opposite of adjacent

Tan 21⁰ = x/9

x= 9*tan 21⁰

x = 9*0.3839

The distance is 3.45

Therefore the length of the shadow cast by a building is approximately 3.5 feet long

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Answer:

60=5k

Step-by-step explanation:

k=12

I did it on Khan and got it right!

5 minutes in bike and by walking 1 hours 3 minutes

Traci Lynn saves getting to class each morning if she were to ride  6.12 minute

The formula is used to find the value of time is;

Time = Distance/speed

Given that Traci Lynn currently walks to school from her apartment, which is 1.3 miles away from her first class.

If she goes to school from the apartment by walking, then it will take time is;

Time = 1.3/3

Time = 0.43 hours

If she goes to school from the apartment by bicycle, then it will take time is;

Time = 1.3/5

Times = 0.26 hours

Therefore,

The time in minutes could Traci Lynn save getting to class each morning if She ride the bike is;

0.43 - 0.26

= 0.17 hours

= 0.17 x 36 = 6.12 minute

Hence, Traci Lynn saves getting to class each morning if she were to ride  6.12 minute

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Answer:

Step-by-step explanation:

Check THe picture attached, hope it helps ❤️

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

9514 1404 393

Answer:

  525 km

Step-by-step explanation:

Let d represent the distance to the town. Let s represent the nominal speed of the car. The relation between time, speed, and distance is d = st.

  t1 = d/s

  t2 = d/(s+15)

  t1 : t2 = 6 : 5 . . . increasing the speed reduces the time

Substituting for t1 and t2, we have ...

  (d/s)/(d/(s+15)) = 6/5

  (s +15)/s = 6/5

  1 +15/s = 1 +1/5

  s = 5·15 = 75 . . . . nominal speed in km/h

__

Decreasing the speed increases the time.

  d/75 +(105/60) = d/(75-15)

  d(60/75) +105 = d . . . . . . multiply by 60

  105 = d/5 . . . . . . . . . . . subtract 4/5d

  525 = d . . . . . . . . . . multiply by 5

The distance traveled by the car is 525 km.  

Answer: y = 3x - 1

Step-by-step explanation:

y = 3x + c

-1 = 3(0) + c

-1 = 0 + c

-1 - 0 = c

-1 = c

y = 3x - 1

Answer:

"Cubic functions are functions with a degree of 3 (hence cubic ), which is odd. Linear functions and functions with odd degrees have opposite end behaviors. The format of writing this is:

x → ∞ ,  f ( x ) → ∞

x → − ∞ ,  f ( x ) → − ∞

For example, for the picture below, as x goes to  ∞

, the y value is also increasing to infinity. However, as x approaches - ∞

, the y value continues to decrease; to test the end behavior of the left, you must view the graph from right to left!!

graph{x^3 [-10, 10, -5, 5]}

Here is an example of a flipped cubic function, graph{-x^3 [-10, 10, -5, 5]}

Just as the parent function (

y = x 3

) has opposite end behaviors, so does this function, with a reflection over the y-axis.

The end behavior of this graph is:

x → ∞ ,  f ( x ) → − ∞x → − ∞ ,  f ( x ) → ∞

Even linear functions go in opposite directions, which makes sense considering their degree is an odd number: 1."

-website

Step-by-step explanation:

Answer:

7 girl gifts and 4 boy gifts

Step-by-step explanation:

7 girls gifts = $14
4 boy = $4
total = 18