A triangle has sides of length 5 cm and 11 cm. What can you say about the length of the third side?
Final answer:
The length of the third side of the triangle must be greater than 6 cm and less than 16 cm, as per the triangle inequality theorem.
Explanation:
According to the triangle inequality theorem, the length of any side of a triangle must be less than the sum of the other two sides and greater than the difference between them. Therefore, the third side of a triangle with sides of length 5 cm and 11 cm must be longer than 6 cm (11 cm - 5 cm) and shorter than 16 cm (11 cm + 5 cm). To clarify, for any triangle with sides a, b, and c, where c is the longest side, the following must always be true: a + b > c and |a - b| < c.
After 15 minutes a train has moved 9/2 miles towards its destination. How many miles per minute is the train moving
What statement correctly describes the key features of the graph of f(x) = 4(one half)x + 1 − 3?
A. Y-intercept of (0, −1), starts up on the left, gets closer to y = −3 on the right
B. Y-intercept of (0, −1), starts down on the left, gets closer to y = −3 on the right
C. Y-intercept of (0, 1), starts up on the left, gets closer to y = −3 on the right
D. Y-intercept of (0, 1), starts down on the left, gets closer to y = −3 on the right
Answer: The correct option is B.
Explanation:
The given function is,
[tex]f(x)=4(\frac{1}{2})^{(x+1)} -3[/tex]
Put x=0 to find the y-intercept.
[tex]f(x)=4(\frac{1}{2})^{(0+1)} -3[/tex]
[tex]f(x)=4(\frac{1}{2}) -3[/tex]
[tex]f(x)=2-3[/tex]
[tex]f(x)=-1[/tex]
At x=0 the value of f(x) is -1, therefore the y- intercept is (0,-1).
Since it is an exponential function in the form of,
[tex]g(x)=ma^x+n[/tex]
Where, 0<a<1, so,
[tex]f(x)\rightarrow \infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow -3\text{ as }x\rightarrow \infty[/tex]
Therefore the starts up on the left, gets closer to y = −3 on the right. So the option B is correct.
Answer: the correct answer is B
Step-by-step explanation:
Part 1: Mr. Nicholson accepts a job that pays an annual salary of $60,000. In his employment contract, he is given the option of choosing a) an annual raise of $3,500 or b) an annual raise of 5% of his current salary.
Procedures:
1. Use the provided information to identify each of Mr. Nicholson's earning opportunities as arithmetic or geometric. For each opportunity, include all the common difference or ratio.
2. Model each of Mr. Nicholson's salary options with a recursive model that includes his potential earnings for the first three years of employment.
a. $60,000 salary with an annual raise of $3,500
b. $60,000 salary with an annual raise of 5% of his current salary
3. Suppose Mr. Nicholson plans on working for his new employer for at least 9 years. use each of the recursive models to determine Mr. Nicholson plans on working for his new employer for at least 9 years. Use each of the recursive models to determine Mr. Nicho
Answer:
See belowStep-by-step explanation:
1. Arithmetic: Add 3,500
The annual raise of 3,500 means add 3,500 to the previous year's salary
60,000 + 3,500 = 63,500
63,500 + 3,500 = 67,000
67,000 + 3,500 = 70,500
70,500 + 3,500 = 74,000
74,000 + 3,500 = 77,500
Geometric: Multiply by 1.05
The annual raise by 5% of his current salary means multiply by 1.05.
60,000 x 1.05 = 63,000
63,000 x 1.05 = 66,150
66,150 x 1.05 = 69,457.50
69,457.50 x 1.05 = 72,930.38 rounded
72,930.375 x 1.05 = 76,576.89
The first sequence is arithmetic because we add the same number (3,500) to the preceding term. The second sequence is geometric because we multiply the preceding term by the same number always (1.05.)
2a. Arithmetic - New salary is $3,500 greater each year than last year's salary
S = 60,000 + 3500(n-1)
Geometric - New salary is 5% more each year than last year's salary
60,000 + (1.05)^(n-1)
2b. Arithmetic Earnings over 3 years
60,000 + 63,500 + 67,000 = 190,500
Geometric Earnings over 3 years
60,000 + 63,000 + 66,150 = 189,150
There is a 1,000 dollar difference. In this case, the arithmetic increase of 3,500 dollars would be better for Mr. Nicholson. 1,000 dollars may or may not be considered a big difference. In my opinion, I'd say there is a slight difference between the two
3.Arithmetic
a(9) = 3,500 + a(9-1)
a(9) = 3,500 + 89,000
a(9) = 92,500
Geometric
a(9) = 1.05 x a(9-1)
a(9) = 1.05 x 84,425.90
a(9) = 88,647.20
4. In this case, both the 3 year and 9 year time frames favor the arithmetic increase of $3,500. At 3 years, he would have 190,500 compared to the geometric salary of 189,150. However, this is a small difference. If he is going to be at the company for 9 years, then definitely he should choose the first opportunity. 92,500 is significantly more money than 88,647.20. So, longer time frames only make the first opportunity, which is better to begin with, shine even more.
I'm always happy to help :)
The problem analyses two salary options: a regular increase (arithmetic sequence) and a percentage increase (geometric sequence). It involves using recursive models to calculate potential earnings over a specified period. Over the long term, the geometric sequence provides a greater total income.
Explanation:The subject is about Mr. Nicholson's two different salary options. An arithmetic sequence series represents option a) where Mr. Nicholson's salary increases by a steady $3,500 per year. The difference, or increase, remains constant.
On the other hand, option b) represents a geometric sequence where Mr. Nicholson's salary increases by 5% of his current salary each year. The ratio, or multiplier remains constant at 1.05 (current salary * 5%).
To calculate his earnings for the first three years using the recursive model: Option a) Year 1: $60,000 Year 2: 60,000 + 3,500 = $63,500, Year 3: 63,500 + 3,500 = $67,000. Option b) Year 1: $60,000, Year 2: 60,000 * 1.05 = $63,000, Year 3: 63,000 * 1.05 = $66,150.
For a period of 9 years, continually apply the recursive model for each year. It becomes apparent that with the geometric sequence (option b), the amount of raise will increase per year because it is based on a percentage of his increasing salary, providing a higher total over time compared to the arithmetic sequence (option a).
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Marianne has 5/8 pound of peas. She cooks 2/3 of those peas for 5 people. If each person is served an equal amount, how much peas did each person get?
Raj is writing 3/2000 as a percent. Find his mistake and correct it.
3/2000 = 0.0015 = 15%
The percentage of the given fraction is 0.15%. Raj has done the mistake in his calculation instead of multiplying 100 he multiplied 1000.
Given that, 3/2000.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Now, percentage = 3/2000 × 100
= 0.0015 × 100
= 0.15%
The percentage of the given fraction is 0.15%. Raj has done the mistake in his calculation instead of multiplying 100 he multiplied 1000.
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A discount store marks up the merchandise it sells by 55% if the whole sale price of a particular item is $25 what should the retail price be set at
Mary lost 14 pounds, which is 10% of her starting weight. What was her original weight?
Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?
As the number of people in a sample gets larger, the distribution of means
Which of the following is a unit of density?
Cubic meters
Square meters
Liters per cubic gram
Kilograms per cubic centimeter
The unit of density is:
Kilograms per cubic centimeter.
Step-by-step explanation:We know that the density of a substance is defined as the ratio of the mass of a substance to it's volume.
i.e.
[tex]\text{Density}=\dfrac{\text{Mass}}{\text{Volume}}[/tex]
Now, we know that the standard unit of the mass of a substance is: Kilograms(kg)
and the standard unit for a volume is: cubic centimeters(cm³)
Hence, we will get the unit for density as:
Kilograms per cubic centimeter
4 gallons of paint cover 1,400 square feet. How much does 7 gallons of paint cover? (Solve with Porportion)
Give the value of x that makes this equation true.
(3)(-4)(x) = (3)(-4)
0
4
1
-3
if the length of the rectangle is twice the width and the perimeter of the rectangle is 30 centimeters what is the length of the current width of the rectangle
Please help thank you.
A(n) ____ consists of equations that state what a value is for one or more base cases and one or more recursive cases.
Suppose you put $500 into a bank account today. interest is paid annually and the annual interest rate is 8 percent. the future value of the $500 after 2 years is
A total of 645 tickets were sold for the school play. They were either adult tickets or student tickets. There were 55 fewer student tickets sold than adult tickets. How many adult tickets were sold?
Answer: 350 adult tickets
Step-by-step explanation:
number of adult tickets sold = x
number of student tickets sold = x-55
x-55+x=645
2x-55=645
2x=700
x=350
(5h3−8h)+(−2h3−h2−2h)
What does it mean by "completing the square" and how do u do it?
Final answer:
Completing the square is a technique used to solve quadratic equations by transforming the equation into a perfect square trinomial format. It involves a series of steps to find the value(s) of the variable.
Explanation:
Completing the square is a technique used to solve quadratic equations. It involves transforming the equation into a perfect square trinomial format. Here's how you can complete the square:
Move the constant term to one side of the equation.
Take half of the coefficient of the variable term and square it.
Add the squared value to both sides of the equation.
Factor the perfect square trinomial.
Solve for the variable term by taking the square root of both sides.
Get the value(s) of the variable.
Find the value of 21 - 18 ÷ 3 · 2
Use the graph showing Jamie's account balance to answer the question what is the interest rate on Jamie's account?
A. 1.9%
B. 2.2%
C. 18.3%
D. 22.5%
Answer: 12 yers
Step-by-step explanation:
The amount that results when $2,000 is compounded at 8% annually over six years.
jessie uses 20 liters of gasoline to travel 200kilometers, how many liters of gasoline will he use on a trip of 700 kilometer?
Answer: He will use 70 liters of gasoline on a trip of 700 kilometer.
Step-by-step explanation:
Given : Jessie uses 20 liters of gasoline to travel 200 kilometers.
We assume that the rate of consumption of gasoline is contant.
By UNITARY METHOD, the amount of gasoline required for 1 kilometer distance = [tex]\dfrac{20}{200}=\dfrac{1}{10}[/tex] liter
Now, the amount of gasoline required for 700 kilometer distance = [tex]700\times\dfrac{1}{10}=70[/tex] liters
Hence, He will use 70 liters of gasoline on a trip of 700 kilometer.
To calculate how many liters of gasoline Jessie will use for a 700 km trip, the fuel efficiency is first determined to be 10 km/L from the given data. Using this information, it is found that Jessie will need 70 liters of gasoline for the 700 km trip.
Jessie uses 20 liters of gasoline to travel 200 kilometers. To determine how much gasoline Jessie will use on a trip of 700 kilometers, we first need to find the fuel efficiency of the vehicle. By dividing the distance traveled by the amount of gasoline used, we get the fuel consumption rate:
Fuel efficiency = Distance / Gasoline
Fuel efficiency = 200 km / 20 L
Fuel efficiency = 10 km/L
Now we know that the vehicle uses one liter of gasoline to travel 10 kilometers. To find out how many liters are needed for a 700 km trip, we apply the following:
Gasoline needed = Trip distance / Fuel efficiency
Gasoline needed = 700 km / (10 km/L)
Gasoline needed = 70 liters
Therefore, Jessie will use 70 liters of gasoline to travel 700 kilometers.
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If p is true and q is false, the p -> q is always, sometimes, never true.
When p is false and q is true, then p or q is always, sometimes, never true.
If p is true and ~ q is false, then p -> ~ q is always, sometimes, never false.
If p is true and q is true, then ~ p -> ~ q is always, sometimes, never true.
If p -> q is true and q is true, then p always, sometimes, never is
1. If p is true and q is false, the p -> q is never true.
2. When p is false and q is true, then p or q is always true.
3. If p is true and ~ q is false, then p -> ~ q is never false.
4. If p is true and q is true, then ~ p -> ~ q is always true.
5. If p -> q is true and q is true, then p is always true.
Further Explanation:
The logic gates are used here.
Here, the symbol -> is for implication. Implication p-> q means that if p is true then q must be true.
So let us look at all the questions one by one.
1. If p is true and q is false, the p -> q is always, sometimes, never true.
p -> q
true -> false
The true should imply true so the given statement will never be true.
2. When p is false and q is true, then p or q is always, sometimes, never true.
false or true
We know that in or gate even if one input is true, the whole output is true. So this statement will be always true given p is false and q is true.
3. If p is true and ~ q is false, then p -> ~ q is always, sometimes, never false.
This translates to:
true -> true
So it will never be false.
4. If p is true and q is true, then ~ p -> ~ q is always, sometimes, never true.
This translates to:
false -> false
This will always be true.
5. If p -> q is true and q is true, then p is always, sometimes, never true.
If p->q is true and q is true then p will always be true. "Implies to" states that in p->q, in order for q to be true p has to be true. So p will always be true.
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Answer:
Your answer is: Always true
Step-by-step explanation:
Kerrie is tiling the floor of a kitchen. The kitchen floor measures 11.3 feet by 9.25 feet. She orders enough tiles for 99 square feet. Which statement about the amount of tiles is correct? Kerrie estimated correctly by rounding down. She has enough tile. The exact area is 104.5 square feet. Kerrie estimated correctly by rounding up. She has enough tile. The exact area is 104.5 square feet. Kerrie did not estimate correctly by rounding up. She does not have enough tile. The exact area is 104.5 square feet. Kerrie did not estimate correctly by rounding down. She does not have enough tile. The exact area is 104.5 square feet.
Kitchen = 11.3 * 9.25 = 104.525 square feet
Kerrie did not estimate correctly by rounding down. She does not have enough tile. The exact area is 104.5 square feet.
Kerrie did not estimate correctly by rounding down. She does not have enough tile. The exact area is 104.5 square feet.
What is an expression?
The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Kerrie is tiling the floor of a kitchen. The kitchen floor measures 11.3 feet by 9.25 feet. She orders enough tiles for 99 square feet.
Kitchen = 11.3 x 9.25 = 104.525 square feet
Therefore, Kerrie did not estimate correctly by rounding down. She does not have enough tile. The exact area is 104.5 square feet.
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Padraig is a financial advisor. He earned a salary of $80,000 last year and sold stocks for $5,000. Which of the following types of income did Padraig have?
I earned income
II passive income
III capital gains income
a.
I and II
b.
I and III
c.
II and III
d.
III
Answer:
The answer is b. I and III
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
To Answer this question we need to first understand what each type of income is.
Earned Income refers to the an amount of money received from the act of providing goods or services. Such Income includes Salaries, Paychecks, Sub-contracting work etc.
Passive Income is a periodic inflow of cash received with little to no effort on the part of the beneficiary.
Capital Gains Income refers to the money made on selling a certain asset above the value of purchase.
Know that we have this information we can see that Padraig has two types of incomes. Both Earned Income from his salary and Capital Gains Income from the stocks that he sold. Therefore the answer is b. I and III
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
For how many hours did edison's best light bulb stay lit?
Find the taylor polynomial of degree three for the function x^0.2 about the point a=7. (your answers should include the variable x when appropriate.)
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is _____ . 5, 3, 2.5, or 0.2
The slope represents __________. the total cost of the taxi ride, the total number of miles traveled, the cost per mile traveled, or the initial cost of the ride
1. To find for the value of the slope, we need to have the graph. But you forgot to include the graph in your question. So I will just help you find for it.
In the graph, find for any two pairs of x and y. Then use the equation:
m = (y2 – y1) / (x2 – x1)
where m is the slope, y2 is the 2nd y, y1 is the 1st y, x2 is the x of the 2nd y, x1 is the x of the 1st y
2. Actually the slope m represents the:
the cost per mile traveled
Answer:
The correct answer to this the slope is 2.5. And the slope represents the cost per miles traveled
Step-by-step explanation:
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