Final answer:
To simplify the expression 5.5a - 1 + 21b + 3a, combine like terms to get 8.5a + 21b - 1, which is the simplified form of the original expression.
Explanation:
To simplify the expression 5.5a - 1 + 21b + 3a, we need to combine like terms, which are terms that have the same variable raised to the same power. Here, 5.5a and 3a are like terms, and they can be combined by addition. There are no like terms for 21b or the constant -1, so they remain as they are.
Step 1: Combine the coefficients of like terms 5.5a and 3a: 5.5a + 3a = 8.5a.
Step 2: Rewrite the simplified expression with the combined like term: 8.5a + 21b - 1.
This is the simplified form of the original expression.
help me please i dont know how to do all of this ill really appreciate it please
what is statistics what is the definition of statistics
Statistics is a branch of mathematics dealing with data collection, analysis, interpretation, and presentation, consisting of two main types: descriptive and inferential. Statistical models use probability distributions to describe expected behaviors and variability within observations.
Explanation:About Statistics
The field of statistics is an essential discipline within mathematics that entails the collection, analysis, interpretation, and presentation of data. In our daily lives, we encounter data in various forms, which can be meticulously examined and understood through statistical methods. Two main types of statistics exist: descriptive statistics and inferential statistics. Descriptive statistics summarize and describe the features of a specific data set, providing a way to visualize data through graphs, charts, and summary measures like the mean and standard deviation. On the other hand, inferential statistics allow us to make predictions or inferences about a population based on a sample of data.
Statistical models are used to describe phenomena, utilizing probability distributions to account for the expected behavior and variability of observations. When researchers collect data, they often use a random sample to represent the larger population. A statistic is a numerical characteristic derived from the sample that helps estimate the corresponding population parameter, which is a characteristic of the entire population.
Statistics and probability are intertwined; as we gather and inspect data, we use statistical tools to distinguish good data from bad and create accurate predictions. Properly understanding and applying statistics can lead to more informed decisions in science, business, policy-making, and virtually every other field where data is essential.
The base of a square pyramid has side lengths of 9 inches. The height of the pyramid is 21 inches. What is the volume of the pyramid?
A. 189 in3
B. 567 in3
C. 850.5 in3
D. 1701 in3
You invest $5,000 in a savings account paying 4% interest compounded quarterly. How much is in the account after 5 years if there are no withdrawals and no additions to the account?
The price of a shirt was $38. It was reduced by 20% and then again by 10%.
a. What is the final price of the shirt?
b. What would the price of the shirt be if it were reduced by 30% from the original?
c. Explain why the two prices in a. and b. differ.
Answer:
A- The final price of the shirt was $27.36.
B- If it were reduced by 30% from the original price, the price of the shirt would be $26.6.
C- There is a difference between both prices because in the first case, the discount is split, making a first discount on a larger basis, and the second on a smaller basis, already made the first discount.
In contrast, at the second price, the entire percentage is made on the major basis. Therefore, the discount is larger.
Step-by-step explanation:
A- The final price of the shirt is determined by the following calculation:
(38 x 0.8) x 0.9 = FINAL PRICE
38 is multiplied by 0.8 because the price was reduced by 20% (0.2 is the 20% of 1, that is, of a unit. Therefore, the remaining price would be that 0.8 or 80%)
Then, using the same logic, we have to multiply that result by 0.9 in order to get the final price.
Therefore:
(38 x 0.8) x 0.9 = 30.4 x 0.9 = 27.36
B- Here, we would have to multiply 38 x 0.7, which gives a result of 26.6
Bill is a car salesman he earns $200 for every car he sales plus a 3% commission if Bill sells three cars in one week for a total of $32,343 what are his total earnings for this week
what is the answer
solve 4.8+n=6.2
Solve the recurrence relation for the variables indicated below: bn = 8bn-1 - 15bn-2 b1 = 2 b2 = 16 If the explicit formula for the sequence is written in the form bn = u(s1)n + v(s2)n then find s1 and s2 .
The recurrence relation is given by bn = 8bn-1 - 15bn-2 with b1 = 2 and b2 = 16.
How to depict the solution?Since it is linear homogeneous recurrence relation ,so first find its characteristic equation.
r² - 8r + 15 = 0
( r - 3 )( r - 5 ) = 0
r = 3 , 5
So, the general solution of the given recurrence relation is
bn = u(3)n + v(5)n ------------ ( 1 )
Now use the initial conditions b1 = 2 and b2 = 16.
From ( 1 ) , b1 = u(3)1 + v(5)1
2 = 3u + 5v ---------- ( 2 )
and b2 = u(3)2 + v(5)2
16 = 9u+ 25v------- ( 3 )
Solving ( 2 ) and ( 3 ) , we get u= - 1 and v = 1
Therefore, the required solution is bn = - (3)n + (5)n
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to function properly, rainwater outflow pipe must drop exactly 1 inch for every 25 inches of horizontal distance. A 40 foot long rain water pipe runs under the edge of a roof. What is the vertical distance, in inches, the pipe bust drop between its ends? Round your number to the nearest tenth.
Answer: Hence, There is vertical distance of 19 inches the pipe must drop between its ends.
Step-by-step explanation:
Since we have given that
Rainwater outflow pipe must drop exactly 1 inch for every 25 inches of horizontal distance.
For 1 inch = 25 inches of vertical distance the pipe must drop.
If there is a 40 foot long rain water pipe runs under the edge of a roof.
Then, we need to find the vertical distance in inches the pope must drop.
First, we change 40 feet into inches.
Since 1 foot = 12 inches
40 feet = 40×12 inches = 480 inches
So, Vertical distance the pipe must drop is given by
[tex]\dfrac{480}{25}\\\\=19.2\ inches[/tex]
Hence, There is vertical distance of 19.2 inches ≈ 19 inches the pipe must drop between its ends.
What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 5.5? A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm. Perimeter = 50 cm, area = 155.25 cm2 Perimeter = 50 cm, area = 1,452 cm2 Perimeter = 154 cm, area = 155.25 cm2 Perimeter = 154 cm, area = 1,452 cm2
Answer:
the answer is 154 cm, area = 1,452 cm2 I took the test
Step-by-step explanation:
PLEASE HELP
Law of sines:
Which represents the value of c?
What is the slope of the line in the graph?
The slope of the line in the given graph with the coordinates (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) is equal to 1.
The slope of a line is calculated by rise over run.
Here is the formula for calculating the slope of a line:
Slope = (y₂ - y₁) / (x₂ - x₁)
Here, the points (x₁ , y₁ ) = (4, 5) and (x₂ , y₂) = (2, 3) are on the line. Plugging these points into the formula, we get:
Slope
= (3 - 5) / (2 - 4)
= (-2) / (-2)
= 1
Therefore, the slope of the line is 1.
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I am a closed shape made of 6 line segments. I have two angles less than right angle & no right angles. What shape am I?
The unit of measure of an area equal to 1 km by 1m
Compare the volumes of the rectangular prisms shown below. Which of the containers will hold more, X or Y? In your final answer, include all of your calculations.
The volumes of the rectangular prism 'X' (126 cu.cm.) is greater than the volumes of the rectangular prism 'Y' (110 cu.cm.).
What is the volume of the rectangular prism?[tex]V=l\times w\times h[/tex]
where, 'l' be the length of the rectangular prism,
'w' is the width of the rectangular prism,
'h' is the height of the rectangular prism
For given question,
We have been given two rectangular prisms 'X' and 'Y'.
The dimensions of the rectangular prism 'X',
[tex]l=7~cm,w=3~cm,h=6~cm[/tex]
Using the formula for the volume of the rectangular prism,
[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=7\times 3\times 6\\\\\Rightarrow V=126~cu.cm.[/tex] ...................(i)
The dimensions of the rectangular prism 'Y',
[tex]l=5~cm,w=2~cm,h=11~cm[/tex]
Using the formula for the volume of the rectangular prism,
[tex]\Rightarrow V=l\times w\times h\\\\\Rightarrow V=5\times 2\times 11\\\\\Rightarrow V=110~cu.cm.[/tex] ...............(ii)
From (i) and (ii),
the volume of the rectangular prism 'X' is greater than the volume of the rectangular prism 'Y'.
Therefore, the volume of the rectangular prism 'X' (126 cu.cm.) is greater than the volume of the rectangular prism 'Y' (110 cu.cm.)
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Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable. What is the smallest number of new spools that Ted will need for this job ??
The smallest number of new spools that Ted will need for this job is 8 spools of cable.
Given that, Ted is installing lighting in a new block of 12 apartments. He will need 60 metres of cable for each apartment. Each new spool holds 100 metres of cable.
We need to find the smallest number of new spools that Ted will need for this job.
What are the spools?A cylindrical device on which film, magnetic tape, thread, or other flexible materials can be wound; a reel.
Now, 60 meters per apartment x 12 apartments =720 total meters for all 12 apartments.
720 meters / 100 meters per spool =7.2 spools
so, Ted will need at least 8 spools of cable.
Therefore, the smallest number of new spools that Ted will need for this job is 8 spools of cable.
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Carl spends 9 hours each day working at her job. what percentage of her day does she spend at work
Helppppppppppppppppppp
Jeremy and Caitlin collect baseball cards. the ratio of Jeremy’s cards and Caitlin’s cards was 9 to 3. After Jeremy gave 12 carss to Caitlin, they had an equal number of cards. How many cards did Caitlin and Jeremy have at first? Explain.
Louis,Michelle, and Tonya were asked to find an equation for a function that passed through the points (1,6) and (8,12) Louis gave the function y 6(2)-112 Michelle gave the function y V2)22 Tonya gave the function y-6 3(x-1) Which students are correct?
Ethan is 3 years older than twice his brother Adrian’s age write an expersion to represent Ethan’s age ; if Adrian is 6 how old is Ethan;
PLEASE HELP!
Drag a reason to each box to complete this proof.
If 5x-4+13=5 , then x=1/2
JEWELRY is to FILIGREE as ____ is to ____?
A. Music is to din
B. Clothing is to lace
C. Cyclone is to vortex
D. Forest is to tree
E. Ice cream is to flavor
The correct answer is B. Clothing is to lace. The analogy asks to draw a comparison between an object and a characteristic of that object, so filigree is to jewelry as lace is to clothing.
Explanation:The correct answer is B. Clothing is to lace. This analogy asks you to draw a comparison between an object and a characteristic or feature of that object. In the case of 'JEWELRY is to FILIGREE', filigree is a detailed, intricate design often found in jewelry. Similarly, in 'Clothing is to lace', lace is a material often found in clothing and contributes to the design or style of the clothing piece, much like filigree does for jewelry.
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suppose F varies inversely with G and that f equals 40 when g equals 5 what is the value of f when g equals 10
The value of F when G equals 10 is 20.
Explanation:The given problem states that F varies inversely with G. In other words, as G increases, F decreases, and vice versa. The inverse variation can be represented by the equation F = k/G, where k is a constant.
We are given that when G = 5, F = 40. To find the value of F when G = 10, we can use the equation F = k/G and substitute the given values.
F = k/5, and when F = 40, we have 40 = k/5. Solving for k, we get k = 40 x 5 = 200.
Now, we can substitute k = 200 and G = 10 into the equation F = k/G. F = 200/10 = 20.
What percent of students ran the mile in 12 minutes or less?
Find the length of side AB in the right triangle shown.
Answer:
72
Step-by-step explanation:
Kayleen left home at noon and drove to boston.she got there at 4:00.if boston is about 280 miles away,what was kayleens average speed
three of the angle measures of a parallelogram are 60°, 120°, and 60°. What is the measure of the fourth angle?
What's the name of the line segment in the diagram below? A. B. C. D.
Thomas correctly spell 18 out of 20 words on his last spelling quiz. What decimal represent the portion of the rights that Thomas spelled correctly
Final answer:
Thomas spelled 18 out of 20 words correctly, which, when divided, gives us 0.9. This decimal represents the portion of the words he spelled correctly on his quiz.
Explanation:
To find the decimal that represents the portion of words Thomas spelled correctly on his quiz, we follow a simple process of division and conversion to a decimal.
Thomas spelled 18 out of 20 words correctly. So, we divide 18 by 20 which equals 0.9. This is the decimal that represents the portion of words Thomas spelled correctly.