Answer:
Step-by-step explanation:
The formula to find density of a sphere is mass/volume.
Density in simple words means the relation between weight and size of a substance. It is basically related to the compactness of a substance.It is a very useful characteristic and every material has density.
To calculate density, we must calculate the mass and volume of the substance.
p=m/v
where p= density, m= mass of substance, v= volume of substance
Formula to calculate the volume of a sphere = 4/3 [tex]\pi r^{3} \\[/tex]
Therefore, density p =[tex]m/4/3\pi r^{3}[/tex]
p = 3m/4 [tex]\pi r^{3} \\[/tex]
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how to do inverse of functions
Answer:
Step-by-step explanation:
First, replace f(x) with y
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y .
Replace y with f−1(x) f − 1 ( x ) .
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
Final answer:
To find the inverse of a function, you reverse the original operation, whether it's an exponential with its natural log, a square with a square root, or logarithms with their exponential counterpart. These inverses, like ln(e^x) = x, demonstrate how they 'undo' each other. The inverse log can be used to find the original number from its logarithm.
Explanation:
Understanding Inverse Functions
To find the inverse of a function, you essentially want to reverse the original operation. For example, an exponential function and its inverse, the natural logarithm (ln), undo each other. If you have an equation y = ex, taking the natural logarithm of both sides would give you ln(y) = x, which effectively isolates x. This demonstrates that ln(ex) = x and eln(x) = x, showing how these functions are inverses of each other.
Similarly, other function pairs such as sine and arcsine, or a power function and its corresponding root function, act as inverse operations. For instance, if you have a2 = c2 - b2, as in the Pythagorean Theorem, you would take the square root of both sides to find a. This 'undoes' the square, showing that (√()2) is the inverse function of squaring.
When it comes to logarithms, the process of finding an inverse is similar. If you take a logarithm of a number, you can find the original number by taking the inverse log or calculating 10to the power of the logarithm. If you have log10(x) = y, then 10y = x.
What is the distance between the following points?
NOOOOOOO
-3-2
+
1
2
3
4
5
6
7
Answer: You can use the formula [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] (SEE EXPLANATION)
Step-by-step explanation:
Since the points are not written correctly, I will give you a general explanation about the procedure you should follow in order to find the distance between the two points.
By definition, the distance between two points can be calculated with the following formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
As you can observe, if you have two points:
[tex](x_1,y_1)\\\\(x_2,y_2)[/tex]
The steps you must follow in order to solve the exercise, are the shown below:
Step 1. You can substitute the values of [tex]x_1,y_1,x_2[/tex] and [tex]y_2[/tex] into the formula [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)}[/tex].
Step 2. You must evaluate in order to find the distance between those two points.
Lake Mead contains approximately 28,945,000 acre feet of water and there are about 326,099 gallons in 1 acre-foot. The approximate number of gallons of water in lake Mead is 9.4x10^a what is the value of a ?
Answer:
12
Step-by-step explanation:
Let x be the number of gallons of water in lake Mead.
Given that there is 326099 gallons in 1 acre-foot, we calculate Mead's gallons as:
[tex]1 acrefoot=326099g\\28945000acrefoot=x\\\\x=\frac{28945000acrefoot\times326099g}{1acrefoot}\\\\x=9.4\times 10^{12} \ gallons[/tex]
We now equate x to [tex]9.4\times10^a[/tex];
[tex]9.4\times 10^a=9.4\times 10^{12}\\\\a=12[/tex]
Hence, a=12
expand the brackets
1.
[tex]3(2x + 5)[/tex]
2.
[tex]7(p + 3q)[/tex]
3.
[tex]3m(n - 2m)[/tex]
[tex]1)\ 3(2x + 5) = 6x + 15\\\\2)\ 7(p + 3q) = 7p + 21q\\\\3)\ 3m(n - 2m) = 3mn - 6m^2\\\\[/tex]
Solution:
Given that,
We have to expand the brackets
Use distributive property,
a(b + c) = ab + bc
Multiply the number in front of parenthesis with each term inside the parenthesis and then add them together
1)
[tex]3(2x + 5) = 3 \times 2x + 3 \times 5\\\\3(2x + 5) = 6x+15[/tex]
-------------------------------------------------
2)
[tex]7(p + 3q) = 7 \times p + 7 \times 3q\\\\7(p + 3q) =7p + 21q[/tex]
----------------------------------------------------
3)
[tex]3m(n-2m) = 3m \times n - 3m \times 2m\\\\3m(n-2m) = 3mn - 6m^2[/tex]
Thus the given expressions are expanded using distributive property
Geese are tagged and released in a wildlife area. Each year, about 60% of the tagged geese
still live in the same wildlife area. There are an estimated 1,500 geese still living in the wildlife
area this year. Based on the data, about how many tagged geese are expected to be living in the wildlife
area next year?
Multiply the number of geese by the percent that will be alive:
1500 x 0.60 = 900
There will be 900 geese alive next year.
Answer:
900 geese
Step-by-step explanation:
Each year they decrease by 40%
part/whole
x/1500 = 60/100
60 x 1500 = 90000
90000/100 = 900
8993.2
x 103
Enter
I need help with This I don’t know the answer
Answer: the answer is 926299.6
Step-by-step explanation: I hope this helps you
Answer:
[tex]926,299.6[/tex]
Step-by-step explanation:
[tex]8993.2 \\ \times 103 \\ =926,299.6[/tex]
thanks
hope this helps....
In 2004, 520,000 acres of farmland in a region were devoted to growing nuts. By 2011, the number of acres used to grow nuts had increased to 850,000. Find the average rate of change in the number of acres in a region used to grow nuts from 2004 to 2011. The average rate of change was about acres per year. (Round to the nearest integer as needed.)
Answer:
see attachment
Step-by-step explanation:
The average rate of change in the number of acres used to grow nuts from 2004 to 2011 is approximately 47,143 acres per year when rounded to the nearest integer.
To find the average rate of change in the number of acres in a region used to grow nuts from 2004 to 2011, we can apply the formula for the rate of change, which is:
(Change in Quantity) / (Change in Time)
In this case, the quantity is the number of acres used for nut farming, and the time is the number of years between 2004 and 2011. The calculation is as follows:
Change in Quantity = Final value - Initial value = 850,000 acres - 520,000 acres = 330,000 acres
Change in Time = 2011 - 2004 = 7 years
Therefore, the average rate of change is:
Average rate of change = (330,000 acres) / (7 years) = 47,143 acres per year
Rounded to the nearest integer, the average rate of change is 47,143 acres per year.
If CJ=2x+3, CT=53, and JT=9x+6, find JT
If CJ is given 2x + 3, CT is given 53 and JT is given 9x +6, then the value of x by the solving the equation is 4. So the value of JT is 42.
Explanation:To find the value of JT, we first need to establish the value of x.
Given the equation CJ + JT = CT or 2x + 3 + 9x + 6 = 53.
We can simplify that by adding 2x and 9x and 3 and 6 together to give us 11x + 9 = 53.
We then subtract 9 from both sides of the equation which gives us 11x = 53 - 9 or 11x = 44.
Then by dividing both sides of the equation by 11 we solve for x, which gives us x = 44 / 11 or x = 4.
Now we can substitute the value of x into the equation JT = 9x + 6.
Substituting 4 for x gives us JT = 9 × 4 + 6 or JT = 36 + 6.
So JT = 42.
Therefore, the value of JT is 42 when the value of x is 4.
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3 to the third power + (5 - 2) divided by 3 + (5 - 3 to the second power)
Answer:6
Step-by-step explanation:quick maths
What is equivalent to 4^7 x 4^-5
Answer:
16
Step-by-step explanation:
Answer:
[tex] {4}^{2} [/tex]
Step-by-step explanation:
[tex] {4}^{7} \times {4}^{ - 5} [/tex]
when the bases are same we add the powers to find the multiplier
So the answer is 7 + (-5) = 2
plzzzzzzzzzzzzzzzzz help quick
Answer:
y=-2x-7 D
Step-by-step explanation:
Cherie was building a fort with her friend jaylah . Cherie built a fort that was 181 inches tall and jaylah built a fort that was 62 inches taller than cheries fort. How tall was jaylah fort?
Height of Jaylah's fort = 243 inches
Step-by-step explanation:
Step 1:
Height of Cherie's fort = 181 inches
Height of Jaylah's fort = 62 inches taller than Cherie's fort
We need to find the actual height of Jaylah's fort
Step 2 :
Since we are given that Jaylah's fort is 62 inches taller than Cherie's fort the actual height of Jaylah's fort can be determined by adding the height of Jaylah's fort to that of Cherie's fort.
Hence
Height of Jaylah's fort = 181 + 62 = 243 inches
Step 3 :
Answer :
Height of Jaylah's fort = 243 inches
Union employees vote for a representative to negotiate on behalf of all workers. This representative negotiates 3%
increase in wages, but requires workers to contribute 15% of their $10,000/year health insurance rather than 10% last year. What is the net
gain or loss each worker (on average) receives or pays if the average worker makes $39,000 per year when both issues are factored?
a) $500 loss
b) $670 gain
c) $1,170 gain
d) $3,000 gain
Answer:
670$ gain
Step-by-step explanation:
After accounting for both the wage increase and the increased health insurance contribution, on average, each worker experiences a net gain of $670 annually.
Explanation:The first step is to calculate the increase in wages due to the 3% increase in salary. This is calculated as follows: 3% of $39,000 is $1,170.
Next, we need to calculate the additional amount contributed toward health insurance, which has increased from 10% to 15%. This represents an increase of 5%. Thus, the added cost of health insurance is 5% of $10,000, which equals $500.
Finally, we can calculate the net change for the worker. This is achieved by subtracting the increase in health insurance contributions from the increase in wages. So, $1,170 - $500 equals $670 gain.
Hence, the correct option is (b), $670 gain.
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⚠️ P L E A S E H E L P
Fill in the blank with the correct response. What is the scale factor?
?
——
?
Answer:
x = 11 | Scale factor = 2
Step-by-step explanation:
As you can see, the 3 turns into a six meaning it multiplied by 2. Apply this to 5.5 to get 11. The 2 is your scale factor.
Answer:
it is 2 but whats under or over 2 because no one reads the question or says the right question or answer
Step-by-step explanation
ill just put 2/2
Assume the lines are parrel.
Step-by-step explanation:
[tex]x = 70 \degree..(vertical \: \angle s) \\ \\ y = 70 \degree..(alternate \: \angle s) \\ \\ 2z = 70 \degree..(corresponding \: \angle s) \\ \\ \therefore \: z = 35\degree[/tex]
I NEED HELP ASAP FOR THIS QUESTION URGENTTTT
Step-by-step explanation:
[tex]10x - 4x + 6x = 12x = 6x + 6x \\ \\ 8(1 + 9y) = 8.1 + 8.9y = 8 + 72y[/tex]
Answer:
12x, 6x+6x for row one
8*1+8×9y, 8+72y for row two
Step-by-step explanation:
10x-4x is 6x, because they're like terms. 6x+6x=12x
Using the Distributive Property, 8(1+9y)=
(8*1)+(8*9y)
=
8+72y
An amount of $4000 was deposted in a bank of 7% compounded quarterly for 2 years. The rate the increased to 10% and was compounded quarterly for the next 2 years. If no money was
balance at the end of this time?
The balance was $=
(Round to the nearest cant as needed)
Answer:
$5599.20
Step-by-step explanation:
The quarterly interest rate for the first two years was ...
7%/4 = 0.0175
So, the multiplier each quarter for those 8 quarters was 1+0.0175 = 1.0175. At the end of the first 8 quarters, the account value had been multiplied by ...
1.0175^8
For the next 8 quarters, the quarterly interest rate was 10%/4 = 0.025. So at the end of those 8 quarters, the balance had been multiplied by ...
1.025^8
Then the balance at the end of 4 years was ...
$4000(1.0175^8)(1.025^8) ≈ $5599.20
The balance was $5599.20.
Find the product.
3.456 x (2.05 x 10") = ?
The diameter of a sphere is 2,160 mm. The diameter of a second sphere is 7,520 mm. Approximately how many times larger is the volume of the second sphere than the volume of the first sphere?
Answer:
Approximately 42 times larger
Step-by-step explanation:
The diameter of a sphere is 2,160 mm.
The diameter of a second sphere is 7,520 mm.
To see how many times larger is the diameter of second sphere is than the diameter of the second sphere, we divide to get:
[tex]k = \frac{7520}{2160} [/tex]
[tex]k = 3.481[/tex]
To see how many times larger the volume is, we cube both sides
[tex] {k}^{3} = {3.481}^{3} [/tex]
This implies that
[tex] {k}^{3} = 42.181[/tex]
Therefore the volume of the second sphere is approximately 42 times larger
6,010,499,999 rounded to the nearest hundred thousand
Answer:
6,010,500,000
Step-by-step explanation:
0.4 + (0.5 + 0.2) divided by 7
Answer:
0.16
To two decimal places
Step-by-step explanation:
0.4 + (0.5 + 0.2)
A question with more than one sign will be solved using the rule of BODMAS. Bracket Of Division, Multiplication, Addition and Subtraction.
In this question, we have Bracket and addition and it will be answered in that order.
0.4 + (0.5 + 0.2)
0.4+(0.7)
1.1 divided by 7
0.16
To 2 decimal places
what is the distance between S( -9, 8) & T(8 , -6) ?
Answer:
Exact Form:
√485
Decimal Form:
22.02271554…
Step-by-step explanation:
A cube made out of lead has mass 12 grams. A side of the cube has length 1 cm. What would be the mass of a lead cube whose sides have length 1.5 cm?
Answer:
The mass of a lead cube whose sides have length 1.5 cm is 40.5 grams
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Mass of the cube made out of lead = 12 grams
Side of the cube = 1 cm
2. What would be the mass of a lead cube whose sides have length 1.5 cm?
For answering the question, let's calculate the volume of the cube and then its density, this way:
Volume = Height * Width * Length
Volume = 1 * 1 * 1
Volume = 1 cm³
Let's recall the formula of the density:
Density = Mass/Volume, therefore:
Density of the lead = 12/1 = 12 gr/cm³
Now, let's calculate the volume of the second cube:
Volume = Height * Width * Length
Volume = 1.5 * 1.5 * 1.5
Volume = 3.375 cm³
Finally, let's calculate the mass, using the density of the lead we already know:
Density = Mass/Volume
12 = Mass/3.375
Mass = 12 * 3.375
Mass = 40.5 grams
What is the equation of the line described below written in slope-intercept form?
the line passing through point (-1,5) and parallel to the line whose equation is x+y=10
y = x-4
y = x + 4
y = -x + 4
Answer:
y=-x+4
Step-by-step explanation:
Since the two lines are parallel, the slope would be negative x and the y intercept is 4
Answer:
y= - x + 4
Step-by-step explanation:
the two lines are parallel so the slope would be negative
Ms. Martina filled her truck's gas tank with
28.7 gallons of gas. If she drove 100 miles
on the same tank of gas, how much gas did
she use per mile?
Answer:
i think the answer is 0.287
Step-by-step explanation:
i divided 28.7/100 which gave me 0.287
nere are 1,800 pastries in a bakery shop. 45% of them are pretzels and the rest are croissants.
30% of the pretzels are coated with chocolate. 70% of the croissants are coated with chocolate.
a How many croissants are there in the bakery shop?
55% of radhat
1800 is 990
b How many pretzels are coated with chocolate?
c How many croissants are coated with chocolate?
Answer:
a. 990 b. 243 c. 693
Step-by-step explanation:
a. 1,800 * 0.55 = 990
b. 1,800 * 0.45 = 810
810 * 0.3 = 243 pretzels
c. 1,800 * 0.55 = 990
990 * 0.7 = 693 croissants
There are 990 croissants in the bakery shop. Out of 810 pretzels, 243 are coated with chocolate, and out of 990 croissants, 693 are coated with chocolate.
Explanation:Number of Croissants and Coated Pastries
Let's begin by calculating the number of croissants in the bakery shop. If 45% of the pastries are pretzels, then the remaining 55% are croissants. We can calculate the number of croissants as follows:
Number of croissants = 55% of 1800
= 0.55 × 1800
= 990
This means there are 990 croissants in the bakery shop.
Next, let's find out how many pretzels are coated with chocolate. We already know that 45% of the pastries are pretzels, so first we determine the total number of pretzels:
Number of pretzels = 45% of 1800
= 0.45 × 1800
= 810
Now, 30% of these pretzels are coated with chocolate:
Chocolate-coated pretzels = 30% of 810
= 0.30 × 810
= 243
So, 243 pretzels are coated with chocolate.
Finally, we need to calculate how many croissants are coated with chocolate. We determined that there were 990 croissants, and 70% of them are coated with chocolate:
Chocolate-coated croissants = 70% of 990
= 0.70 × 990
= 693
Therefore, 693 croissants are coated with chocolate.
Isabel runs 6 miles in 55 minutes how many miles will she run in 44 minutes
Answer:
4.8 miles
Step-by-step explanation:
6 : 55
X : 44
X/44 = 6/55
X = 4.8
x/44 = 6:55
6(44) = 55
6 (44) = 264
55x = 264
Divide both sides by 55
55x/ 55 = 264/55
Cancel out: 55x/55 because that gives you 1
Keep: 264/55 because it gives us our answer
Thus x = 4.8
Your answer: 4.8
Good luck on your assignment and enjoy your day!
~LoveYourselfFirst:)
It took me 3 hours to visit my friend in Maine, averaging a speed of 58 miles per hour. If it took me 15 minutes less to get back home, what was my average speed coming home?
Answer:
The average speed coming home was 63.27 miles per hour
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Speed from home to Maine = 58 miles per hour
Time of the first leg of the trip = 3 hours or 180 minutes
Time of the second leg of the trip = 15 minutes less = 180 - 15 = 165 minutes or 2 hours 45 minutes
2. What was my average speed coming home?
Let's calculate the distance from home to Maine, this way:
Speed = Distance/Time
Distance = Speed * Time
Distance = 58 * 3 = 174 miles
Now, let's calculate the speed of the second leg, as follows:
Speed = Distance/Time
2 hours 45 minutes = 2.75
Speed = 174/2.75
Speed = 63.27 miles per hour
zahra earns $80 each day plus a 6% commission on her sale at an appliance store. on friday zahra has $900in sales.how much does zahra earn on friday including commission
Solution:
Given that,
zahra earns $80 each day plus a 6% commission on her sale at an appliance store
zahra has $900 in sales
Find the commission amount
commission amount = 6 % of 900
[tex]commission\ amount = \frac{6}{100} \times 900\\\\commission\ amount = 54[/tex]
Zara earnings including commission amount = 80 + 54 = 134
Thus Zara earned $ 134 on friday including commission
HELP!!!!!!! WILL MARK BRAINLIEST.
See attachment.
Answer:
Humberto multiplied 4 by 3, but that is incorrect, you are supposed to first do 3^2 and the multiply the answer by 4 to get 36.
The correct value is: 36
Step-by-step explanation:
Step 1: Set t to 3
4t^2
4(3)^2
4(9) -> Correct way
36 -> Correct
Humberto
4(3)^2
(12)^2 -> Made mistake
144 -> Incorrect
Humberto multiplied 4 by 3, but that is incorrect, you are supposed to first do 3^2 and the multiply the answer by 4 to get 36.
The correct value is: 36