Answer:
In (3x)^2, you are squaring both the 3 and the x:
9x^2
in 3x^2, you are squaring just the x:
3x^2
Answer:
(3x)^2=9x^2
(3x^2)=3x^2
Step-by-step explanation:
The difference between the two is that
(3x)^2 means the square applied to both the 3 and the x to give 9x^2
But on the other side
(3x^2) means that the square only applies to x without involving 3 which gives 3x^2
So there is difference between them
Chinedu sat down to do his homework, which included 30 math problems. He solved 2 problems each minute. Let f(n) be the number of problems left for Chinedu to solve at the beginning of the nth minute.
f is a sequence. What kind of sequence is it?
IS IT GEOMETRIC OR ARITHMETIC AND TELL ME THE EXPLICIT FORMULA
Answer:
Arithmetic sequence
f(n)=30-2(n-1)
Step-by-step explanation:
Chinedu's problem-solving sequence is arithmetic. The explicit formula for the sequence is f(n) = 32 - 2n.
Chinedu's homework problem involves a sequence where he solves 2 problems each minute, starting with 30 problems. To determine the number of problems left at the beginning of the nth minute, we can use an arithmetic sequence since the number of problems decreases by a constant amount (2 problems) each minute.
In an arithmetic sequence, the nth term can be expressed using the formula:
f(n) = a + (n - 1)d
where a is the first term and d is the common difference.
Steps:
Identify the first term (a), which is 30 (the total number of problems initially).Identify the common difference (d), which is -2 (since Chinedu is solving 2 problems each minute).Apply the formula:f(n) = 30 + (n - 1)(-2) = 30 - 2(n - 1) = 32 - 2n
So, the explicit formula for the sequence is f(n) = 32 - 2n.
what basic trig identity would you use to verify that cotxsinx+cosx
Answer:
You use cotx = cosx/sinx.
Step-by-step explanation:
I guess you mean cotx sinx = cosx.
You substitute the identity cotx = cosx / sinx:
cotx sinx = (cosx / sin x) * sin x
The sin x ' s cancel to give cosx.
Final answer:
To verify that cot(x)sin(x) + cos(x) is a basic trigonometric identity, we can use the Pythagorean Identity which states that sin²(x) + cos²(x) = 1. The expression cot(x)sin(x) + cos(x) simplifies to 2cos(x), which confirms that it is a basic trigonometric identity.
Explanation:
To verify that cot(x)sin(x) + cos(x) is a basic trigonometric identity, we can use the Pythagorean Identity which states that sin²(x) + cos²(x) = 1. Let's start by expressing cot(x) in terms of sin(x) and cos(x). Since cot(x) = cos(x)/sin(x), we can substitute this into the equation:
cot(x)sin(x) + cos(x) = cos(x)/sin(x) * sin(x) + cos(x) = cos(x) + cos(x) = 2cos(x).
So, the given expression reduces to 2cos(x), which is indeed a basic trigonometric identity.
Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Your answer is t=
To find the time required for an investment to grow to a certain amount with compound interest, we can use the formula Final Balance = Principal(1 + interest rate/number of compounding periods)^(number of compounding periods * time). In this case, the investment of $5000 will take approximately 4.08 years to grow to $6000 at an interest rate of 7.5% per year, compounded quarterly.
Explanation:To find the time required for an investment to grow to a certain amount with compound interest, we can use the formula:
Final Balance = Principal(1 + interest rate/number of compounding periods)^(number of compounding periods * time)
In this case, the initial principal is $5000, the final balance is $6000, the interest rate is 7.5% (or 0.075), and the interest is compounded quarterly (so there are 4 compounding periods per year).
Convert the interest rate to a decimal: 0.075Substitute the known values into the formula: 6000 = 5000(1 + 0.075/4)^(4*time)Divide both sides by 5000: 1.2 = (1 + 0.075/4)^(4*time)Take the natural logarithm of both sides: ln(1.2) = ln((1 + 0.075/4)^(4*time))Divide both sides by ln((1 + 0.075/4)^(4*time)): time = ln(1.2)/ln((1 + 0.075/4)^(4*time))Using a calculator, we can solve for time to find that the investment will take approximately 4.08 years to grow from $5000 to $6000.
A storage locker measures 5 feet by 6 feet by
14 feet. How much space in the warehouse will
the storage locker occupy?
Answer:
[tex] 420 \: {feet}^{3} [/tex]
Step-by-step explanation:
Space occupied by storage locker in the warehouse will be equal to its volume.
[tex] \therefore \: volume \: of \: storage \: locker \\ = 5 \times 6 \times 14 \\ = 30 \times 14 \\ = 420 \: {feet}^{3} [/tex]
Hence, storage locker will occupy 420 cubic feet of space in the warehouse.
Started at 15 degrees and dropped 1/2 degrees each minute
Answer:
based on how many minutes it pass, it the time pass one minute it will be 14.5 degrees.
Solve the quadratic equation for x.
(x−4)(x+6)=0
Answer:
X = 4, -6
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x = 4 and x = -6
Step-by-step explanation:
We can use the Zero Identity Property, which states that 0 * n = 0, where n is any number.
Here, in order for (x - 4)(x + 6) = 0 to be true, either x - 4 must equal 0 or x + 6 must equal 0. So set each of them equal to 0 and solve for x:
x - 4 = 0
x = 4
x + 6 = 0
x = -6
The answers are x = 4 and x = -6.
Hope this helps!
Stuck on this question.
Please help.
Answer:
I think it is -1.333...
Step-by-step explanation:
I did cross-multiply
15 y
__ = ___
-18 1.6
which is -1y=24
y= -1.333
I may be wrong though...
Which real-world situation can be represented by the equation y = 12x?
Group of answer choices
Dale buys pencils that come in packs of 12. He gets y total pencils for buying x packs.
Tanisha has 12 pens, and she buys x more. She now has a total of y pens.
Mary buys juice drinks that come in packs of 12. She gets x total juice drinks for buying y packs.
Seth has 12 trading cards, and he buys y more. He now has a total of x trading cards.
Answer:
Dale buys pencils that come in packs of 12. He gets y total pencils for buying x packs.
Step-by-step explanation:
12x in the equation is the 12 pencils in each pack times the number of packs (x). In the equation, y is the total, and the answer says he gets y total pencils.
Hope this helps! ☺
Simple 3c-9d+7c+5d
Please help me
At a car dealership, the sales records of weekdays and weekends were examined. Ten of the days examined were weekdays and 10 of them were weekend days. The following statistical information was calculated from the number of sales made during weekdays and weekends.
Weekday
Sales Weekend
Sales
Mean 15 18
Median 13 19
Mode 14 21
Range 10 13
Based on these samples, what generalization can be made?
A.
Not enough information is provided to draw any of these conclusions.
B.
More cars were sold on the weekdays than on the weekends.
C.
The same number of cars were sold on the weekends as on the weekdays.
D.
Less cars were sold on the weekdays than on the weekends.
Answer:
I believe D is the answer
Step-by-step explanation:
determine the slope of (5,6) & (3,9)???
Answer:
3/-2
Step-by-step explanation:
A box of a dozen breakfast bars costs $3.72, while a different box of six breakfast bars cost $1.92. Which is the better deal for the consumer and by how much?
Answer:
Better deal : dozen bars for $3.72 (It is a better deal by 12 cents)
Step-by-step explanation:
Since one has half of the amount that the other has, you multiply the price by two, and you end up with (for a dozen) $3.72, (and for 2 boxes of 6) $3.84. So, the singular box of a dozen bars wins.
:) Hope this helps! <3
Answer: the box of dozen is cheaper by 0.12
Step-by-step explanation:
3.72 /12= 0.31
1.92*2= 3.84
3.84/12= 0.32
3.84-3.72=0.12
Haley’s work evaluating (Negative 2) Superscript 8 is shown below.
(Negative 2) Superscript 8 = (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) (negative 2) = negative 256
Which statement best describe Haley’s first error?
Answer:
D
Step-by-step explanation:
The statements are shown below:
A) She used the wrong number as a repeated factor and should have evaluated -2x2x2x2x2x2x2x2.
B) She used the wrong number as a repeated factor and should have evaluated -(8x8).
C) She misinterpreted the exponential form and should have multiplied -2 and 8.
D) She made a sign error when multiplying and should have had 256 as a final answer.
Solution:
The problem to simplify is:
[tex](-2)^{8}[/tex]
Haley's steps are shown below:
[tex](-2)^{8}=(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)=-256[/tex]
Generally,
[tex](a)^b[/tex] is actually "a" multiplied "b" times.
So, Haley wrote "-2" eight times multiplied together. That is okay.
Now,
We are dealing with negative numbers.
When negative numbers are multiplied "odd" number of times, the answer is negative.When negative numbers are multiplied "even" number of times, the answer is positive.Haley wrote "-2" eight times, which is EVEN number of times, so the answer would be POSITIVE. But, Haley's answer is negative. Which is wrong. But "256" is right.
Haley's error is:
Answer choice D
Answer:
the answer is D
Step-by-step explanation:
Find two numbers a+b is -4 and difference a-b is 4 what's your answer
Answer:
a=0, b=-4
Step-by-step explanation:
a+b=-4.....(1)
a-b=4.......(2)
(1)+(2): 2a=0
a=0
0+b=-4
b=-4
(a, b) =(0,-4)
Factor the expression:
16x^2 - 16xy^3 + 4y^6
Answer:
(4x - 2y³)²
Step-by-step explanation:
a² - 2ab + b² = (a - b)²
16x² = 4²x² = (4x)² , Therefore, a = 4x
4y⁶=2²(y³)² = (2y³)² = b² , Therefore, b = 2y³
2ab = 2*4x*2y³ = 16xy³
16x² - 16xy³ + 4y⁶ = (4x)² - 2* 4x * 2y³ + (2y³)²
= (4x - 2y³)²
Answer:(4x - 2y³)²
Step-by-step explanation:
Y = x - 1
-x + 3/2 = -y
Answer:
It has more than one equal sign but set up like this:
Step-by-step explanation:
Let's solve for x.
y+x−1+
3
2
=−y
Step 1: Add -y to both sides.
x+y+
1
2
+−y=−y+−y
x+
1
2
=−2y
Step 2: Add (-1)/2 to both sides.
x+
1
2
+
−1
2
=−2y+
−1
2
x=−2y+
−1
2
Answer:
x=−2y+ -1/2
The graph shows the salaries of 23 employees at a small company. Each bar spans a width of $50,000 and the height shows the number of people whose salaries fall into that interval. Which inequality correctly describes the relationship between the mean and the median? A) mean < median < $250,000 B) median < mean < $250,000 C) median < $250,000 < mean D) mean < $250,000 < median
Answer:
b
Step-by-step explanation:
The mean is heavily influenced by the outlier salary of $5,000,000, making it much higher than the stable median of $30,000. The correct inequality reflecting the relationship between the mean and the median salaries in this skewed distribution is median < mean < $250,000. The correct choice is option B) median < mean < $250,000.
Given the information about the salaries, the distribution has a significant skew due to the presence of an outlier. This outlier is the one employee earning $5,000,000, which is vastly different from the rest of the group who earn $30,000. When an outlier is present, the mean will be greatly affected, whereas the median will remain a more stable measure of central tendency.
The median salary in this scenario would be $30,000, as 49 out of 50 salaries are at this amount, and thus the middle value of the ranked list would not be impacted by the outlier. However, the mean would be significantly higher because it includes the $5,000,000 salary in the calculation. Since the question describes an inequality relationship between the mean and median, the correct answer is that the median is less than the mean, but both the median and the mean are less than $250,000, which leads to the correct inequality: B) median < mean < $250,000.
Evaluate the following.
15:5+3+4x6
Answer:
15:32
Step-by-step explanation:
15:5+3+4×6
Using BODMAS rule
15:5+3+(4×6)
15:5+3+24
So add up
15:32
Since the two cannot be divided by the same number,we will have to leave the answer as
15:32
The Vehicle assembly building at Kennedy space center is a rectangular prism. It is 218 m long, 158 m wide and 160 m tall. There are four 139 m tall doors in the building, averaging 29 m in width. What is the buildings outside surface area when the doors are open?
Answer:
104,196 square meter
Step-by-step explanation:
This question can be solved by using the formula of area of four side in a
rectangular prism
In the given problem we have
Length of building = 218m
width of building = 158m
height of building = 160
Area of four walls is given by formula = 2*(L + B) * H
where L is length of rectangular prism
B is width of rectangular prism
H is height of rectangular prism
Therefore total surface area of building = 2*(218 + 158)* 160 = 376*320= 120,320
___________________________________________________
No of doors in the building = 4
length of door = 139m
width of door = 29 m
area of one door = length * width = 139* 29 = 4,031
area of four door = 4* 4,031 = 16,124
___________________________________________________
we have to find surface area of building when doors are open
To find this we can subtract total area of four door from total surface area of four walls which we have calculated above
total surface area of four walls - total area of four door
=> 120,320 - 16,124 = 104,196
104,196 is the buildings outside surface area when the doors are open
A triangle has an area of 70 square inches. The height of the triangle is 8 inches. Write and solve an equation to find the length of the base of the raingle
Answer:
70 = 1/2 b *8
17.5 inches =b
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
We know the area and the height
70 = 1/2 b *8
70 = 4b
Divide each side by 4
70/4 = 4b/4
17.5 =b
The area of a square can be expressed by the polynomial expression 16x^4 -16x^2 +4. What is the polynomial expression for the length of a side?
Answer:
4x+2
Step-by-step explanation:
[tex]16x^{4}-16x^{2}+4=16x^{2}+4[/tex]
[tex]\sqrt{16x^{2}+4}[/tex]
[tex]\sqrt{16}*(\sqrt{x^{2}})+\sqrt{4}=4(x) +2=4x+2[/tex]
Hometown Buffet has tables that can seat 6 people and booths that can seat 4 people. The restaurant has 38 seating units for seating a total of 188 people. How many tables and booths are at the restaurant?
Solution:
Let "x" be the number of tables
Let "y" be the number of booths
The restaurant has 38 seating units
Therefore,
x + y = 38
x = 38 - y ------- eqn 1
Hometown Buffet has tables that can seat 6 people and booths that can seat 4 people
Total of 188 people
Therefore,
6x + 4y = 188 ------ eqn 2
Substitute eqn 1 in eqn 2
6(38 - y) + 4y = 188
228 - 6y + 4y = 188
2y = 40
y = 20
Substitute y = 20 in eqn 1
x = 38 - 20
x = 18
Thus there are 18 tables and 20 booths are at the restaurant
Find the height of the parallelogram in which A= 7.5 m^2
Step-by-step explanation:
Given the area of the Parallelogram
[tex]A=\:7.5\:m^2[/tex]
The area of a parallelogram is defined as the multiplication of its base and height.so
A = base × height
Plugging A = 7.5 m² in above equation
7.5 m² = base × height
height = base ÷ 7.5 m²
Therefore, height of the parallelogram with area 7.5 m² is : base ÷ 7.5 m²
Plot the point ( 2, - /4
Answer:
A.
Step-by-step explanation:
The first number is 2, so 2 must be plotted on the X radius (because it goes by X first). B plots X on the Y axis so therefore, by process of elimination, A is the answer.
What is the next arithmetic sequence 1 3 5 7 9
Answer:
11
Step-by-step explanation:
You are adding 2 every time:
1+2=3
3+2=5
5+2=7
7+2=9
9+2=11
The next term in the sequence is 11.
Therefore the complete the series is : 1, 3, 5, 7, 9, 11 .
Arithmetic sequence : Sequence in which the difference between two consecutive terms is same .
Given, Arithmetic sequence : 1, 3, 5, 7, 9 .
So, after analyzing the sequence the common difference between two consecutive terms is 2.
Thus in the sequence add 2 to the first term , then the next term is obtained. Like,
1 + 2 = 3
3 + 2 = 5
5 + 2 = 7
7 + 2 = 9
Therefore the next term will be,
9 + 2 = 11
Know more about arithmetic sequence,
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Angel and Jayden were at track practice.The track is 25 kilometers around.
•Angel ran 1 lap in. 2 min
• Jayden ran 3 laps in 5 min.
1.How many minutes does it take angel to run one kilometer what about Jayden?
2.how far does angel run in one minute?what about Jayden?
3.Who runs the fastest? How do u know ?
Please help especially with 1 and 2 plzz my parents are mad at me and I don’t understand A bit it’s already missing I will get a. 0
Answer:
1. Angel - 0.08 mins, Jayden - 0.067 mins
2. Angel - 12.5 km, Jayden - 15 km
3. Jayden runs faster.
Step-by-step explanation:
The length of the track (1 lap) is 25 km.
Angel ran 1 lap in 2 mins. That means he ran 25 km in 2 mins.
Jayden ran 3 laps in 5 mins. That means he ran 75 km (3 * 25 km) in 5 mins.
1. To find the time it takes to run 1 km, we divide the total time taken by the total distance run.
The number of minutes it takes Angel to run 1 km will be:
T = 2 / 25 = 0.08 minutes
The number of minutes it takes Jayden to run 1 km will be:
T = 5 / 75 = 0.067 minutes
2. To calculate the distance they run in 1 min, we divide the total distance run by the total time taken.
The distance Angel runs in 1 min is:
D = 25 / 2 = 12.5 km
The distance Jayden runs in 1 min is:
D = 75 / 5 = 15 km
3. Jayden runs faster because he runs more kilometres per minutes (15 km/min) than Angel (12.5 km/min).
In other words, Jayden clocks a faster speed than Angel.
Andre says, “I multiplied 4 by 5, then cubed the result.” Select all expressions that equal Andre’s answer.
The expressions which have the final answer 8000 will be equal to Andre's answer.
What is Multiplication?Multiplication is the process of adding a number repeatedly up to the times as that of the another number which is being multiplied with the given number.
For example 2 × 3 means 2 is added to itself 3 times or 3 is added to itself 2 times.
Andre says, “I multiplied 4 by 5, then cubed the result.”
Mathematically the expression is (4 × 5)³.
(4 × 5)³ = (4 + 4 + 4 + 4 + 4)³
= 20³
Now a number cubed means it is multiplied to itself 3 times.
20³ = 20 × 20 × 20
= 8000
Hence the resultant of the expression (4 × 5)³ = 8000. So all expressions which will result in an answer of 8000 will be equal to Andre's answer.
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which expression represents 7 times the difference between 300 and 28
Answer:
(300-28)7
Step-by-step explanation:
You always do parenthesis first and then the 7 means to do multiplication if it is right next to the parenthesis
Answer:
7(300-28)
Step-by-step explanation: All you have to do is put the 300-28 in parentheses (300-28) and then you would put the 7 on the outside of the parentheses and your answer would be 7(300-28)
Can someone help please?
Fill in the missing number
√□=14
For the square root of a number to be a whole number, we would need to have a perfect square. 14 is given to us, so to find the missing number, all we have to do is square 14 (or multiply it by itself).
14 x 14 = 196
The missing number is 196.
Hope this helps! :)
What is the measure of Angle A? (picture included)
Answer:
19.4
Step-by-step explanation:
10x-14=180
Answer:
19.4
Step-by-step explanation:
we know a + b + c = 180 so:
x + 5x + 4x -14 = 180
10x = 180 + 14
10x = 194
x = 19.4 degrees