Final answer:
The chicken quesadilla contains a total of 542 kilocalories, which is derived by summing the caloric contributions from protein, carbohydrate, and fat.
Explanation:
To calculate the number of kilocalories in a chicken quesadilla with 28 grams of protein, 40 grams of carbohydrate, and 30 grams of fat, we use the known caloric values for each macronutrient. Protein and carbohydrate each have 4 Calories per gram, while fat has 9 Calories per gram.
Protein: 28 grams × 4 Calories/gram = 112 Calories
Carbohydrate: 40 grams × 4 Calories/gram = 160 Calories
Fat: 30 grams × 9 Calories/gram = 270 Calories
Adding up these amounts, we have:
112 Calories (from protein) + 160 Calories (from carbohydrate) + 270 Calories (from fat) = 542 Calories
To convert Calories into kilocalories, we remember that 1 kilocalorie = 1 Calorie. Therefore, the chicken quesadilla contains 542 kilocalories.
The current global human population is about 6.1 billion and is growing at an annual rate of 1.35 percent. If world population were to grow at this rate for the next year, approximately how many people would be added?
Answer:
Step-by-step explanation:
The current global population is growing at an annual rate of 1.35 percent. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r)^t
Where
A represents the population after t years.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 6.1 × 10^9
r = 1.35% = 1.35/100 = 0.0135
t = 1
Therefore
A = 6.1 × 10^9(1 + 0.0135)^1
A = 6.1 × 10^9(1.0135)^1
A = 6182350000
The number of people that would be added is
6182350000 - 6100000000
= 82350000
If the world population were to keep growing at 1.35%, we number of people who would be added next year is 82,350,000 people.
The population of the world is growing at 1.35%. This means that next year, the number of people added will be 1.35% of the current population.
The current population is 6.1 billion so the number of people who will be added is:
= Population x Incremental rate
= 6,100,000,000 x 1.35%
= 82,350,000 people
In conclusion, 82,350,000 people will be added.
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A man claims to have extrasensory perception. As a test, a fair coin is flipped 10 times and the man is asked to predict the outcome in advance. He gets 7 out of 10 correct. What is the probability that he would have done at least this well if he had no ESP?
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠D.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠D = °
Answer:
27° (as an integer)
Step-by-step explanation:
From the figure given;
Triangle BCD is a right triangle;We are given the two shorter sides;DC = 8 units
BC = 4 units
We are required to determine m∠D
We need to use the appropriate trigonometric ratio;
In this case, DC is adjacent and BC is opposite to m∠D
Therefore, the appropriate trigonometric ratio is tangent;
That is;
Tan m∠D = BC ÷ DC
= 4 ÷ 8
= 0.5
Thus;
m∠D = Tan^-1 (0.5)
= 26.57
= 27 (as an integer)
Thus, m∠D is 27°
When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 32% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 60 of the dragon eggs to incubate. Consider all the possible samples of 60 dragon eggs.What is the usual number of yellow eggs in samples of 60 eggs? (Give answers as SENSIBLE whole numbers.)minimum usual number of yellow eggs =maximum usual number of yellow eggs
Answer:
19
Step-by-step explanation:
If the scientist chooses 60 random eggs then the overall probability of selecting yellow eggs is 32%. So, there's a chance of he randomly collecting 60 eggs out of which 19 could be yellow.
(60/100) x 32 ~ 19...
The usual number of yellow dragon eggs expected in a sample of 60, given a 32% probability, is 19 when rounded to the nearest whole number.
The question at hand involves finding the expected number of yellow eggs in a sample size of 60, given a known probability of a yellow egg occurrence.
Since we know that 32% of the dragon eggs on planet Pern are yellow, we can calculate the usual number of yellow eggs in the samples by multiplying the sample size (60 eggs) by the probability of getting a yellow egg (0.32).
Therefore, the expected or usual number of yellow eggs in the sample would be 60 × 0.32 = 19.2.
Considering that we cannot have a fraction of an egg, the usual number of yellow eggs in samples of 60 eggs would typically be rounded to the nearest whole number, which is 19.
suppose the model boat were traveling at a rate of 4 feet per second. How long would it take the model boat to get from the edge of the pond to the center
Answer:
[tex]25\ seconds[/tex]
Step-by-step explanation:
Hi,
Time, speed and distance are related by a very simple formula:
[tex]Distance = Time \times Speed[/tex]
Which can easily be used here to solve the question.
To find the time, we require:
Speed:
This is given in the question as 4 ft/ sec.
Distance:
On a circle, the distance from the end of the circle to the centre is referred to as "Radius". We shall assume the radius here is [tex]r[/tex].
To calculate the radius, we can use the formula of the circumference: [tex]C = 2 \pi r[/tex]
Were are given that C = 628 feet.
Using the formula: [tex]r = \frac{628}{2 \pi} = 100\ feet[/tex]
The distance the boat needs to travel is 100 feet.
Time:
To calculate time, we alter the provided formula to: [tex]Time = \frac{Distance}{Speed}[/tex]
Substituting the values in this: [tex]Time = \frac{r}{4}[/tex]
[tex]Time = \frac{100}{4} = 25\ seconds[/tex]
The boat requires 25 seconds to travel from the edge of the pond to centre.
The 5th grade is getting a special lunch to celebrate the end of first grading period.The cafeteria manager is planning to buy 0.3 pound of turkey for each student. If turkey is on sale for $0.79 per pound, what will it cost to give turkey to 100 students.
Final answer:
To calculate the cost, multiply the amount of turkey per student (0.3 pounds) by the number of students (100), then multiply the total pounds needed (30) by the cost per pound ($0.79), resulting in a total cost of $23.70 for turkey for 100 students.
Explanation:
The question asks us to calculate the cost of providing turkey to 100 students if each student requires 0.3 pounds of turkey, and turkey costs $0.79 per pound. To find the total amount of turkey needed, we multiply the amount each student gets by the total number of students: 0.3 pounds/student × 100 students. This calculation results in 30 pounds of turkey required for 100 students.
Next, to determine the total cost, we multiply the total pounds of turkey needed by the cost per pound: 30 pounds × $0.79/pound. This calculation gives us a total cost of $23.70 for the turkey.
Therefore, it will cost $23.70 to give turkey to 100 students.
Rebecca is three years younger than twice Anthony's age. Write an expression that represents the relationship of Rebecca's age in terms of Anthony's age.
Answer:
X=2y-3
Step-by-step explanation:
Let Rebecca's age be x
Let Anthony's age be y
Twice Anthony =2y
Rebecca's age (x) to be 3 years younger than twice Anthony's =2y-3
So, it's x=2y-3
a hexagonal aquarium is 15.5 on each side of its base and 28.5cm high. whats the area
Answer:
17807cm2
Step-by-step explanation:
Surface area of a hexagonal prism is =( (3√3)/2) a^2 h
= 2.598 * 15.5^2 *28.5
= 2.598* 240.5* 28.5
=17807.34cm2
A triangle has sides with lengths a,b,and c.The longest side is b.Write An Equation or inequality that shows the relationships of the lengths of the three sides
the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
In a right triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. So, we have:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
This equation represents the relationship among the side lengths of a right triangle.
Therefore, the equations are:
[tex]\[ c^2 = a^2 + b^2 \][/tex]
[tex]\[ a^2 = c^2 - b^2 \][/tex]
[tex]\[ b^2 = c^2 - a^2 \][/tex]
This completes the three relations among a, b, andc.
The complete Question is given below:
A right triangle has side lengths of a,b , and c units. The longest side has a length of c units. Complete each equation show three relations among a,b , and c .
Type the answers in the boxes below.
c^(2)= _____
a^(2)= _____
b^(2)= _____
Three fair dice are rolled, one red, one green and one blue. What is the probability that the upturned faces of the three dice are all of different numbers?
Answer: [tex]\dfrac{5}{9}[/tex]
Step-by-step explanation:
When we throw a die , Total outcomes =6
When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]
Given : Three fair dice are rolled, one red, one green and one blue.
Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed
By Permutations , the number of favorable outcomes = [tex]^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120[/tex]
The probability that the upturned faces of the three dice are all of different numbers = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{120}{216}=\dfrac{5}{9}[/tex]
The probability that the upturned faces of the three dice are all of different numbers is [tex]\dfrac{5}{9}[/tex] .
Last spring Janessa made 30 to one cup serving of lemonade for a lemonade stand this year she will make two times the amount I live in a that she made last year how many gallons of lemonade will Janessa make this year
Answer:
3.75 gallons
Step-by-step explanation:
The headline "Drugs shown in 98 percent of movies" accompanied a news story that described a "government study" claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals. Discuss whether the headline accurately represents the story.
Answer:
Discussed below.
Step-by-step explanation:
The headline states that 98% of all movies show imagery of drugs. There are a few assumptions that the wording can insinuate:
By stating "drugs shown" it is not specified what kind of drugs are shown nor whether the consumption of these drugs is also shown (showing drug can allude to the consumption of drugs).Drugs can have different meanings in different contexts, some are not harmful such as pharmaceutical drugs. Without any specification, one assumes the worst. 98% of movies refers to 98% of all movies produced thus one can assume that 98% of the total output of movie production show imagery of drug use, which is highly unlikely.However, the story refers to a more specific statistic: that not 98% of all movies but 98% of the top movie rentals depicted drug use, drinking or smoking.
The key differences:
the story is more specific as to what the statistic is referring to (not the total movie output but the top rented movies)the story specifically mentions the use of drugs is shown the story also mentions other types of harmful substances such as smoking and drinkingThus, the headline misrepresents the content of the story which may lead one to make broader and misplaced conclusion about imagery of drugs in movies.
The headline accurately reflects the information provided in the news story, but the accuracy is dependent on the credibility and methodology of the government study.
Explanation:The headline "Drugs shown in 98 percent of movies" accompanied a news story about a "government study" claiming that drug use, drinking, or smoking was depicted in 98% of the top movie rentals.
First, it's important to note that the headline accurately reflects the information provided in the news story. However, the accuracy of the headline is dependent on the credibility and methodology of the government study being referenced.
Without additional information about the study, such as the sample size, selection criteria, and methodology, it is difficult to fully assess the accuracy of the headline. It's always important to critically evaluate the sources of information and consider multiple perspectives in order to draw accurate conclusions.
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(9x90)+(8x11)+(4x5) if someone can help please
Answer:
918
Step-by-step explanation:
Use distributive property.
(810) + (88) + (20) = 918
Answer:
918
Step-by-step explanation: hope it was helpful
How many positive integers $n$ with $n\le 500$ have square roots that can be expressed in the form $a\sqrt{b}$ where $a$ and $b$ are integers with $a\ge 10$?
Answer:
23
Step-by-step explanation:
We take a methodical approach by considering the different possible values of b when asqrtb is the simplest form of sqrtn.
Case 1: b=1. We can't forget the perfect squares! If n=100, for example, then sqrt100 can be written as 10sqrt1. So, we must include the perfect squares from 10^2=100 up through 22^2 = 484. (All greater squares are greater than 500.) There are 13 such squares.
Case 2: b=2. If b=2, then we have asqrtb = asqrt2 = sqrta^2 x sqrt2 = sqrt2a^2. We still must have a {>_} 10, but now we need 2a^2 to be no greater than 500. This means that a^2 must be no greater than 250, so a can be 10, 11, 12, 13, 14, or 15. There are 6 such values.
Case 3: b=3. We then have asqrtb = asqrt3 = sqrt3a^2. Since 3a^2 {<_} 500, we know that a^2 is less than 167. We still need a {>_} 10, so there are only 3 values of a in this case: 10, 11, 12.
We skip b=4 because then asqrtb would not be in simplest form.
Case 4: b=5. We then have asqrtb = sqrt5a^2, and a=10 is the only possible value for this case.
For any greater value of b, the resulting value of n is greater than 500 when a {>_} 10. So, there are no more possible numbers asqrtb that satisfy the problem. Since each of the 13+6+3+1 = 23 possibilities listed above represent different simplified forms, they give us 23 different possible values of n that satisfy the problem.
There are infinitely many positive integers less than 500 that have square roots in the form of a√b, where a and b are integers with a≥10.
The number of such positive integers n is infinite, as there is no finite value for the count.
Here,
We are looking for positive integers n that are less than 500.
The square roots of these integers can be expressed in the form a√b.
And [tex]a\ge 10[/tex]
To find the number of positive integers less than 500 that have square roots in the form of a√b,
Analyze the possible values of a and b separately:
For a,
We know that it must be an integer greater than or equal to 1. So,
We have a total of a = 10, 11, 12 ..., and so on. (since a ≥ 10)
As for b,
it can be any perfect square less than or equal to 500.
Let's list a few examples:
b = 1, since 1√1 = 1
b = 4, since 1√4 = 2
b = 9, since 1√9 = 3
b = 16, since 1√16 = 4
...
b = 484, since 1√484 = 22
Now, we can count the number of possibilities for a and b.
We have an infinite number of possibilities for a, but b has a finite number of perfect squares less than or equal to 500.
There are 22 perfect squares within this range.
Therefore, the total number of positive integers n, with n < 500, that have square roots in the form of a√b is 22 x infinity = infinity.
Since there are infinitely many possible values for n,
Hence,
We can conclude that there is no finite value for the number of positive integers n that satisfies this condition.
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The RideEm Bicycles factory can produce 100 bicycles in a day at a total cost of $10,500. It can produce 120 bicycles in a day at a total cost of $11,000. What are the company's daily fixed costs, and what is the marginal cost per bicycle?
Answer:
The company's daily fixed cost=$8000
The marginal cost per cycle=Slope=$ 25
Step-by-step explanation:
We are given that
Factory produces bicycle in a day=[tex]x_1=[/tex]100
Total cost,[tex]y_1=[/tex]$10,500
Factory produces bicycles in a day,[tex]x_2[/tex]=120
Total cost=[tex]y_2=[/tex]$11,000
There are two points (100,10500) and (120,11000)
Slope =[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the formula
[tex]m=\frac{11000-10500}{120-100}=\frac{500}{20}=25[/tex]
Slope-intercept form
[tex]y=mx+c[/tex]
Where m=Slope of line
c=y-intercept
Substitute the values
[tex]10500=25(100)+c[/tex]
[tex]10500=2500+c[/tex]
[tex]c=10500-2500=8000[/tex]
y-intercept=8000
Substitute the values in the equation
[tex]y=25x+8000[/tex]
Therefore, company's daily fixed cost=$8000
The marginal cost per cycle=Slope=$ 25
Suppose Rick has 40 ft of fencing with which he can build a rectangular garden.Letxrepresent the length of the garden and letyrepresent the width.(a) Write and inequality representing the fact that the total perimeter of thegarden is at most 40 ft.(b) Sketch part of the solution set for this inequality that represents all possiblevalues for the length and with of the garden. (Hint:Note that both the lengthand the width must be positive.)
Answer:
20 >= x + y
Step-by-step explanation:
Given:
- The length of garden = x
- The width of the garden = y
- Total fence available = 40 ft
- Rectangular garden
Find:
(a) Write and inequality representing the fact that the total perimeter of thegarden is at most 40 ft.
(b) Sketch part of the solution set for this inequality that represents all possiblevalues for the length and with of the garden.
Solution:
- The perimeter of the rectangular garden is P at most 40 ft:
P >= 2*x + 2*y
40 >= 2*x + 2*y
20 >= x + y
- The sketch of the graph will be all points in the shaded region denoted by the inequality as follows:
y =< 20 - x
- See the triangular shaded region.
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since Rick has 40ft of fencing
Then, the perimeter cannot be more than 40ft if he decided to lay the block on a single layer and not on each other
Then if the length is x
And the breadth is y
Perimeter of a rectangle is 2(l+b)
Therefore,
Perimeter is less than or equal to 40ft
2(l+b) ≤ 40
b. 2(l+b)≤ 40
Then divide both side by 2
l+b≤ 20.
Then l ≤ 20-b
Also, b ≤ 20-l
Check attachment for graph
If you invest $500 at 3% compounded monthly for 2 years, how much interest you do earn? Show work.
Answer:
$30.88
Step-by-step explanation:
The account value is given by ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, t is the number of years, n is the number of times interest is compounded per year.
The amount of interest earned is the account value less the initial investment:
I = A - P = P(1 +r/n)^(nt) -P = P((1 +r/n)^(nt) -1)
Filling in the given values, we get ...
I = 500((1 +.03/12)^(12·2) -1) = 500(1.0025^24 -1) ≈ $30.88
The amount of interest earned is $30.88.
What is the 6th value in the sequence with the explicit formula an=−2n−14?
Answer:
-26
Step-by-step explanation:
a(6)=-2(6)-14
a(6)=-12-14
a(6)=-26
Hope this helped!
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The 6th value in the sequence = an=−2n−14 = -4.3
Take n = 6
⇒ a6 = -2·6 -14 = -12-14 = -26
∴ a= [tex]\frac{-26}{6}[/tex] = -4.3
Explicit formulaThe explicit formula for an arithmetic sequence is an = a + (n - 1)d, and any term of the sequence can be computed, without knowing the other terms of the sequence. In general, the explicit formula is the nth term of arithmetic, geomrietc, or harmonic sequence.
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Let us first concentrate on the central value. take f0 = n and 0 = . find the central value of fx, in n
Answer:
Fx=N177.007
Step-by-step explanation:
Let us first concentrate on the central value. Take F0 = 325 and theta 0 = 57 degrees. Find the central value of Fx, in N
can be pu as thus from an online resource
To resolve forces into the horizontal component , we have
Fx=fCosФ
Fx=325Cos57
Fx=N177.007
Take Note that a force is that which tends to change a body's state of rest or uniform motion in a straight line.
Bryce, a previous winner of the contest, made a trip of 360 miles in a 6.5 hours. At this same average rate of speed, how long will it take Bryce to travel an additional 300 miles so that he can judge the contest?
Answer:
5.42 hours
Step-by-step explanation:
Let x represent time taken to complete 300 miles.
We have been given that Bryce a previous winner of the contest, made a trip of 360 miles in a 6.5 hours.
We will use proportions to solve our given problem since rates are same for both distances.
[tex]\frac{\text{Distance covered}}{\text{Time taken}}=\frac{360\text{ Miles}}{6.5\text{ Hours}}[/tex]
Upon substituting our given values in above proportion, we will get:
[tex]\frac{300\text{ Miles}}{x}=\frac{360\text{ Miles}}{6.5\text{ Hours}}[/tex]
Cross multiply:
[tex]x\cdot 360\text{ Miles}=300\text{ Miles}\times6.5\text{ Hours}}[/tex]
[tex]x=\frac{300\text{ Miles}\times6.5\text{ Hours}}{ 360\text{ Miles}}[/tex]
[tex]x=\frac{300\times6.5\text{ Hours}}{360}[/tex]
[tex]x=5.41666\text{ Hours}\approx 5.42\text{ Hours}[/tex]
Therefore, it will take approximately 5.42 hours to travel additional 300 miles.
7. In which reaction is mass converted to energy by the process of fission?
If Alex and Brandon work together, they will clean the school in 15 hours. Working alone, Brandon can finish the same job in 20 hours. How long will it take Alex to do the job by himself?
Answer:
I think it is 5 but don't take my word for it
Step-by-step explanation:
I think you minus 20 - 15 which equals to 5 so 20 - 15 = 5 hopefully i was a little helpful just try that if its not correct i'm so sorry i will practice my math and answer this question again thank you for being so understanding
Answer:
Correct answer: Alex can finish the same job in 60 hours
Step-by-step explanation:
The appropriate equation for this situation is:
1/20 + 1/x = 1/15 => (x + 20) / 20x = 1/15 => 15 · (x + 20) = 20x =>
15x + 300 = 20x => 5x = 300 => x = 300/5 = 60 hours
x = 60 hours
God is with you!!!
The level of a lake in inches is falling linearly . The lake level is 452 inches on Jan 1 and then 378 inches on Jan 21. Find a function to represent the lake level
Answer:
[tex]y=-\frac{74}{21}x+452[/tex]
Step-by-step explanation:
Given:
The level of a lake is falling linearly.
On Jan 1, the level is 452 inches
On Jan 21, the level is 378 inches.
Now, a linear function can be represented in the form:
[tex]y=mx+b[/tex]
Where, 'm' is the rate of change and 'b' is initial level
[tex]x\to number\ of\ days\ passed\ since\ Jan\ 1[/tex]
[tex]y\to Lake\ level[/tex]
So, let Jan 1 corresponds to the initial level and thus b = 452 in
Now, the rate of change is given as the ratio of the change in level of lake to the number of days passed.
So, from Jan 1 to Jan 21, the days passed is 21.
Change in level = Level on Jan 21 - Level on Jan 1
Change in level = 378 in - 452 in = -74 in
Now, rate of change is given as:
[tex]m=\frac{-74}{21}[/tex]
Hence, the function to represent the lake level is [tex]y=-\frac{74}{21}x+452[/tex]
Where, 'x' is the number of days passed since Jan 1.
Final answer:
The lake level can be represented by a linear function L(t) = -3.7t + 452, where L(t) is the lake level in inches and t is the time in days from January 1st.
Explanation:
To find a function representing the lake level as it drops linearly over time, we need to determine the linear equation that corresponds to the change in the lake level.
We are given that the lake level is 452 inches on January 1st and 378 inches on January 21st.
First, we will define the variables where L(t) is the lake level in inches and t is the time in days with t=0 corresponding to January 1st.
We are given two points on the linear function: (0, 452) and (20, 378), since January 21st is 20 days after January 1st.
Next, we calculate the slope of the line using the formula:
slope = (change in lake level) / (change in time) = (378 - 452) / (20 - 0) = -74 / 20 = -3.7 inches per day.
Now, we can use the slope and a point to write the equation of the lake level as a function of time in the slope-intercept form:
L(t) = mt + b
where m is the slope and b is the y-intercept. Plugging in the slope and the point (0, 452):
L(t) = -3.7t + 452
This equation represents the function of the lake level over time.
19 in2 17 in2 12 in2 22 in2
Answer:22in2
Step-by-step explanation:
very confused on how to approach??? pls helpppp
Answer:
The height of the wall is 52.2 feet.
Step-by-step explanation:
Given:
From the figure shown, HT is the height of Carlos, 'V' is the position of mirror.
So, TV = 4 ft, VS = 36 ft, HT = 5.8 ft.
Let the height of the wall be 'x'. So, JS = 'x'
Now, consider the two triangles HTV and JVS
Statements Reasons
1. ∠ HTV ≅ ∠ JSV Right angles are congruent
2. ∠ HVT ≅ ∠ JVS Given in the figure
Therefore, ΔHTV and Δ JVS are similar triangles by AA postulate.
Now, from definition of similar triangles, corresponding sides of two similar triangles are in proportion to each other. Therefore,
[tex]\frac{HT}{JS}=\frac{TV}{VS}=\frac{HV}{JV}[/tex]
Considering the first two pair of fractions, we have:
[tex]\frac{5.8}{x}=\frac{4}{36}\\\\36\times 5.8=4\times x\\\\x=\frac{36\times 5.8}{4}\\\\x=9\times 5.8=52.2\ ft[/tex]
Therefore, the height of the wall is 52.2 feet.
a particle is moving on the x-axis, where x is in centimeters. it has velocity v(x) in cm/s, when it is at the co-ordinate x, given by v(x)=x^3-2x+3 find the acceleration of the particle when it is at the point x=2. express youre answer as a number rounded to the nearest whole number
Answer:
10cm/s²
Step-by-step explanation:
Acceleration is the change in velocity of an object with respect to time.
Given velocity v(x) to be x³-2x+6
Acceleration = ∆v/∆x
Differentiating the velocity function to get acceleration we have,
Acceleration = dv/dt = 3x²-2
Acceleration of the particle at x = 2 will give;
dv/dt @ x = 2 is 3(2)²-2
= 12-2 = 10cm/s²
Triangle MNO is an equilateral triangle with sides measuring 16 StartRoot 3 EndRoot units. Triangle M N O is an equilateral triangle with sides measuring 16 StartRoot 3 EndRoot units. A perpendicular bisector is drawn from point N to point R on side M O splitting side M O into 2 equal parts. What is the height of the triangle? 12 units 24 units 36 units 72 units
Answer:
The correct option is second one i.e 24 units.
Therefore the height of the triangle is
[tex]NR=24\ units[/tex]
Step-by-step explanation:
Given:
An equilateral triangle has all sides equal.
ΔMNO is an Equilateral Triangle with sides measuring,
[tex]NM = MO = ON =16\sqrt{3}[/tex]
NR is perpendicular bisector to MO such that
[tex]MR=RO=\dfrac{MO}{2}=\dfrac{16\sqrt{3}}{2}=8\sqrt{3}[/tex] .NR ⊥ Bisector.
To Find:
Height of the triangle = NR = ?
Solution :
Now we have a right angled triangle NRM at ∠R =90°,
So by applying Pythagoras theorem we get
[tex](\textrm{Hypotenuse})^{2} = (\textrm{Shorter leg})^{2}+(\textrm{Longer leg})^{2}[/tex]
Substituting the values we get
[tex](MN)^{2} = (MR)^{2}+(NR)^{2}\\\\(16\sqrt{3})^{2}=(8\sqrt{3})^{2}+(NR)^{2}\\\\(NR)^{2}=768-192=576\\Square\ rooting\ we\ get\\NR=\sqrt{576}=24\ units[/tex]
Therefore the height of the triangle is
[tex]NR=24\ units[/tex]
Answer:
b 24
Step-by-step explanation:
The unit price on a 100-pound container of a swimming pool chlorine is $.06 per pound less than the unit price on a 75-pound container. If the 100-pound container costs $55.50 more than the 75-pound container, find the cost of each.
Answer:
100 lb: $24075 lb: $184.50Step-by-step explanation:
Let u represent the unit price of the 100 lb container. Then u+.06 is the unit price of the 75 lb container.
The difference in prices is ...
100u - 75(u+.06) = 55.50
25u -4.50 = 55.50
25u = 60
u = 60/25 = 2.40
The cost of the 100 lb container is 100u = 240. The cost of the 75 lb container is $55.50 less: 240 -55.50 = 184.50.
The 100 lb container costs $240. The 75 lb container costs $184.50.
Aaron and Blake both wrote down equation. Their equation has the same slope, But Aaron's y-intercept was negative and Blake's y-intercept was positive. How many solutions for their system of equations have? Explain your reasoning
Answer:
Parallel lines do not intersect therefore the system of equations cannot have any solution. Therefore there no solutions to the given system of equations.
Step-by-step explanation:
Aaron and Blake both wrote down equation. Their equation has the same slope, But Aaron's y-intercept was negative and Blake's y-intercept was positive.
Therefore both equations will represent lines that are parallel.
Parallel lines do not intersect therefore the system of equations cannot have any solution.
Suppose the average price for new cars in 2012 has a mean of $30,100 and a standard deviation of $5,600. Based on this information, what interval of prices would we expect at least 89% of new car prices to fall within?
Answer:
($13,300,$46,900)
Step-by-step explanation:
We are given the following in he question:
Mean, μ = $30,100
Standard Deviation, σ = $5,600
Chebyshev's Theorem:
According to theorem atleast [tex]1 - \dfrac{1}{k^2}[/tex] percent of data lies within 2 standard deviations of mean.For k = 3,[tex]1 -\dfrac{1}{(3)^2} = 0.889 \approx 89\%[/tex]
Thus, 89% of data lies within three standard deviation of mean.
[tex]\mu - 3(\sigma) = 30100 - 3(5600) = 13300\\\mu + 3(\sigma) = 30100 + 3(5600) = 46900[/tex]
Thus, we expect at least 89% of new car prices to fall within ($13,300,$46,900)