Answer:
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
x
=
3
V
Answer:
Vx = 3
Step-by-step explanation:
The answer below is because you move all terms not containing Vx to the right side of the equation.
What is the unit's digits in the product 7³⁵×3⁷¹×11⁵⁵
A.1
B.3
C.7
D.9
Answer:
A.1
Step-by-step explanation:
Apply exponent rule [tex](3^{7}) ^1(11^{5} *7^{3} )^{5}[/tex]
[tex]=55240493^{5}(3^{7})^{1}[/tex]
Apply rule a^1=a = [tex]3^{7} *55240493^{5}[/tex]
[tex]=55240493^{5}*2187[/tex]
= 1.2496......E42
:)Hope you enjoy this:)
Soda cans A machine that fills cans with soda fills according to a Normal model with mean 12.1 ounces and standard deviation 0.05 ounces. a. If the cans claim to have 12 ounces of soda each, what percent of cans are under-filled
Answer:
The percentage is [tex]p = 4.55\%[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 12.1 \ ounce[/tex]
The standard deviation is [tex]\sigma = 0.05 \ ounce[/tex]
The value of soda each can claims to have is [tex]X = 12 \ ounce[/tex]
Generally the z-score is mathematically represented as
[tex]z = \frac{ X- \mu }{\sigma }[/tex]
=> [tex]z = \frac{ 12-12.1 }{0.05}[/tex]
=> [tex]z = -2[/tex]
From the z table the area under the normal curve representing the proportion of under filled cans is
[tex]P(x <-2 \ or\ x > 2)= 0.0455[/tex]
Converting to percentage
[tex]p = 0.0455 *100[/tex]
=> [tex]p = 4.55\%[/tex]
For f(x)=2x+1 and g(x) = x + 14, find (f o g) (x).
A. 2x^3+x^2-14x-7
B 2x+29
C. 2x^2-6
D. 4x^2+4x-6
Answer && Step-by-step explanation:
f o g x
== f(g(x))
plug g(x) into x variables
f(x)=2x+1 , g(x)=x+14
2(x+14)+1
2x+28+1
==2x+29
b is the answer
A rectangular building is to have a volume of 8000 fr^3. Annual heating and cooling costs will amount to $2/ft^2 for its top, front, and back, and $4/ft^2 for the two end walls. What dimensions of the building would minimize these annual heating and cooling costs?
Answer:
the dimensions that will minimize the cost are; 25.2 ft × 25.2 ft × 12.6 ft
Step-by-step explanation:
If the length, width and height of the building are represented by a, b and c, then we have:
Volume = abc
We are given volume as 8000 ft³. Thus;
abc = 8000
Top area = ab
Front area = ac
Back area = ac
End walls area = bc
We are told that cooling costs will amount to $2/ft² for its top, front, and back, and $4/ft² for the two end walls.
Thus, cooling cost equation is;
X = 2(ab) + 2(ac) + 2(ac) + 4bc + 4bc
X = 2ab + 4ac + 4bc
Now, from the volume equation where abc = 8000.
c = 8000/ab
Thus;
X = 2ab + 4a(8000/ab) + 4b(8000/ab)
X = 2ab + 32000/b + 32000/a
To minimize, we will find the a and b derivative and set the equation to zero in both cases.
Thus;
dX/da = 2b - 32000/a² = 0
2b = 32000/a² - - - eq(1)
Also;
dX/db = 2a - 32000/b² = 0
2a = 32000/b² - - - (eq 2)
Making a the subject in eq 2 gives;
a = 32000/2b²
a = 16000/b²
Putting 16000/b² for a in eq (1) gives;
2b = 32000/(16000/b²)²
2b = 32000b⁴/256000000
2b = b⁴/8000
Multiply both sides by 8000 to get;
2b × 8000 = b⁴
16000b = b⁴
Divide both sides by b to get;
16000 = b³
b ≈ 25.2 ft
Putting 25.2 for b in a = 16000/b², we have;
a = 16000/25.2²
a ≈ 25.2
Putting a and b = 25.2 in the volume equation, we have;
25.2 × 25.2 × c = 8000
c = 8000/(25.2 × 25.2)
c = 12.6 ft
Thus, the dimensions that will minimize the cost are; 25.2 ft × 25.2 ft × 12.6 ft
One beehive produces 64 pounds of honey per year. How many
beehives does it take to produce 5,504 pounds of honey?
Answer:
86 beehives, Hope I helped!
Step-by-step explanation:
I'm to lazy :P
PLEASE HELP ASAP!!!! I WILL MARK BRAINLIEST!!!!
After getting 5 new rocks, George gave half of his rock collection to Susan. If George gave 36 of his rocks to Susan, which equation could be used to determine how many rocks George started with?
A. 1/2 x = 36 + 6
B. 1/2 (x-5) = 36
C. 1/2x+5=36
D. 1/2 (x+5) = 36
One pump can fill a gasoline storage tank in 8 hours. With a
second pump working simultaneously, the tank can be filled in 3
hours. How long would it take the second pump to fill the tank
operating alone?
Answer:
eight hours long to operate
3 cups of cashews : 2 cups of almonds a rate, a proportion, or only a ratio?
Answer:
5 cups
Step-by-step explanation:
can someone help asap
pls do this will give brainliest
Answer:
I think it might be b
Step-by-step explanation:
sorry if its wrong
Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of days that have passed.
Answer:
2+
Step-by-step explanation:
what is the value what is the value of x in this equation 3(4x-6) - 2x + 1 = 3 - (3x - 6)
Answer:
x=2
Step-by-step explanation:
What is the sum of the integers less than 100 that have both 6 and 9 as divisors?
Answer:
The sum of the integers less than 100 that have both 6 and 9 as divisors is 270
Step-by-step explanation:
To determine the integers less than 100 that have both 6 and 9 as divisors,
First, we will list the multiples of 6 and 9 that are less than 100, and the common multiples will give the integers less than 100 that have both 6 and 9 as divisors.
Multiples of 6 less than 100 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.
Multiples of 9 less than 100 are:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.
Hence, the integers less than 100 that have both 6 and 9 as divisors are 18, 36, 54, 72 and 90.
Then, the sum of the integers less than 100 that have both 6 and 9 as divisors is
18 + 36 + 54 + 72 + 90 = 270
Hence, the sum of the integers less than 100 that have both 6 and 9 as divisors is 270.
Evaluate the expression 263 + 5 when b= 3.
Answer:
59
Step-by-step explanation:
2b^3+5 when b=3
Plug in the value of b
2*3^3+5 = 2*27+5 = 54+5 = 59
Four cats and five mice enter a race. In how many ways can they finish with a mouse placing first, second, and third
The requried, there are 240 possible ways the race can finish with a mouse placing first, second, and third.
To find the number of ways the race can finish with a mouse placing first, second, and third, we can use the concept of permutations.
Since the mouse is guaranteed to finish first, there are 5 mice to choose from for the first position.
Once the first place is determined, there are 4 mice left for the second position.
After the first two positions are filled, there are 3 mice left for the third position.
Now, we need to determine the order of the cats. There are 4 cats to choose from for the fourth position.
The total number of ways the race can finish with a mouse placing first, second, and third is given by the product of these choices:
Number of ways = 5 (for first place) * 4 (for second place) * 3 (for third place) * 4 (for fourth place)
Number of ways = 5 * 4 * 3 * 4
Number of ways = 240
There are 240 possible ways the race can finish with a mouse placing first, second, and third.
Learn more about permutation here:
https://brainly.com/question/33149025
#SPJ12
Assume that when adults with smartphones are randomly selected, 39% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 24 of the use their smartphones in
meetings or classes
The probability is .
(Round to four decimal places as needed)
Answer:
n = 10
p = 0.56
Step-by-step explanation:
(a) Suppose that a person has an average heart rate of 72.0 beats/min. How many beats does he or she have in 2.0 y
Answer:
[tex]7.56\times 10^7\ \text{beats}[/tex]
Step-by-step explanation:
It is given that,
A person has an average heart rate of 72.0 beats/min.
We need to find how many beats does he or she have in 2.0 years, t = 2 Y
Converting years to min.
[tex]t=2\text{year}\times \dfrac{365\ \text{days}}{\text{year}}\times 24\dfrac{h}{\text{day}}\times \dfrac{60\text{min}}{\text{hour}}\\\\t=1051200\ \text{min}[/tex]
So, no of beats in 2 years is given by :
[tex]b=72\ \text{beats/min}\times 1051200\ \text{min}\\\\b=7.56\times 10^7\ \text{beats}[/tex]
Hence, the required answer is [tex]7.56\times 10^7\ \text{beats}[/tex].
PLZ HELP
A train travels at an average speed of 67.5 miles per hour. At this speed, how far could the train travel in 3.25 hours?
Answer:
219.375 miles
Step-by-step explanation:
1 hour the train can go for 67.5 miles
so multiply the 67.5 with 3.25 and then you will get 219.375
Steve has 54 stamps in his collection of 13 cent, 29 cent, and 45 cent stamps, totaling a value of $15.98. If the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80. Find the number of each type of stamp in his collection.
Answer:
Number of 13 cents stamp = 14
Number of 29 cents stamp = 24
Number of 45 cents stamp = 16
Step-by-step explanation:
We are told he has 54 stamps in total.
These stamps are;13 cent, 29 cent, and 45 cent stamps.
Let's call number of 13 cent($0.13) stamp A
Call number of 29 cent($0.29) stamp B
Call number of 45 cent($0.45) stamp C
Thus;
A + B + C = 54
We are told the total value of the 3 stamps are $15.98.
Thus;
0.13A + 0.29B + 0.45C = $15.98 - - - (eq2)
Now we are told that if the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80.
Thus;
2(0.13A) + 0.29B + 0.45C = 17.8
0.26A + 0.29B + 0.45C = 17.8 - - - (eq 3)
Solving the 3 equations simultaneously, we have;
A = 14
B = 24
C = 16
We have;
Number of 13 cents stamp = 14
Number of 29 cents stamp = 24
Number of 45 cents stamp = 16
Find the percentage of area under a normal curve between the mean and the given number of standard deviations from the mean.1.68
Answer:
0.4532
Step-by-step explanation:
Given the question :
Find the percentage of area under a normal curve between the mean and the given number of standard deviations from the mean.1.68
Number of standard deviations from the mean = 1.68
I. 68 standard deviations below the mean :
Mean = 0(normal distribution)
P(Z < 0) = 0.5
1.68 standard deviations above the mean = + 1.68
P(Z < 1.68) = 0.95352
P(0 < x < Z) = (0.95352 - 0.5) = 0.4532
Suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. Previous research indicates the population mean is $20 per week. The population standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21
Answer:
The probability is 0.9545
Step-by-step explanation:
To find this probability, we shall use the z-score formula
Mathematically;
z-score = (x - mean)/SD/√n
where mean = 20
SD = 5
n = 100 and so √100 = 10
So for 19, we have ;
(19-20)/5/10 = 1/0.5 = -2
For 21, we have
(21-20)/5/10 = 1/0.5 = 2
So the probability we want to calculate is
P( -2 < z < 2)
we can use the standard normal distribution table for this
Using this table;
P(-2<z<2) = 0.9545
Sean and his crew operate a fishing charter company. They caught a blue
marlin and an amberjack. The weight of the blue marlin was 12 times as
great as the weight of the amberjack. The combined weight of both fish was
1,014 pounds. How much did each fish weigh?
factor the GCF: 12x^4y-9x^3y^2+3x^2y^3
Answer:
3x^2y
Step-by-step explanation:
May i please have brainliest :)
B. Indicate whether the normal balance of the given account is a debit or a credit and whether the increase or
decrease in such account should be a debit or a credit. Check the appropriate box.
Normal Balance
Effect in the Account
Particulars
Debit
Credit
Debit
Credit
1. Equipment was sold for P 350,000.00
2. Notes Recievable was collected in full
3. Loans Payable in bank was paid in full
4. Office furnishings was acquired for
P 35,000.00
5. Insurance in premium for one year was
paid in November
Answer:
given below
Step-by-step explanation:
1. Equipment is credited and cash is debited.
2. Notes receivable is credited and cash is debited
3. Loan Payable is debited and cash account is credited
4.Office furnishings are debited and cash is credited.
5. Insurance in premium is debited and cash is credited.
Summary
1) addition to an asset account is a debit
2) subtraction from an asset account is a credit
3) addition to a liability account is a credit
4) subtraction from a liability account is a debit
5) Bank account is credited when cash is added to it and debited when cash is withdrawn from it
Normal Balance Effect in the Account Debit Credit
1) Equipment 350,000.00 decrease in asset Cash Equipment
2. Notes Recievable Cash N/R
3. Loans Payable Dec. Accounts /Rec Loans Payable Cash
4. Office furnishings 35,000.00 Office furnishings Cash
5. Insurance in premium (+aasets) Insurance in premium Cash
2. There was increase in cash and decrease in notes receivable.