Answer:
Amount of water pumped out by the motor = 1117.46 liters
Step-by-step explanation:
Amount of water pumped out by the motor pump = 6704.76 liters
Time taken by the motor to pump the water = 6 hours
Rate at which the motor pumps out the water = [tex]\frac{\text{Amount of water pumped out}}{\text{Time taken to pump the water}}[/tex]
= [tex]\frac{6704.76}{6}[/tex]
= 1117.46 liters per hour
Therefore, amount of water pumped out by the motor = 1117.46 liters
Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using this relationship, what is the value of each function composition?
(h o k) (3)=
(k o h)(-4b) =
Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
Help please. Thank you
9514 1404 393
Answer:
(x, y) = (1, -3)
Step-by-step explanation:
The x-term has a coefficient of 1 in the first equation, making it easy to write and expression that can be substituted for x:
x = -3y -8
Using this in the second equation, we have ...
4(-3y -8) -3y = 13
-15y -32 = 13
-45 = 15y
-3 = y
Then the value of x is ...
x = -3(-3) -8 = 1
The solution is (x, y) = (1, -3).
A payday loan company charges a $90 fee for a $500 payday loan that will be repaid in 16 days.
Treating the fee as interest paid, what is the equivalent annual interest rate?
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Interest amount paid on loan = $90
Principal value, amount borrowed = $500
Period, t = 16 days
The equivalent annual interest :
Using the simple interest formula :
simple interest = principal * rate * time
Using, days of year = 365
Plugging in the values into the formula :
90 = 500 * rate * (16/365)
90 = 500 * rate * 0.0438356
90 = 21.917808 * rate
Rate = 90 / 21.917808
Rate = 4.10 = 4.10 * 100% = 410%
If days of year = 360 is used :
90 = 500 * rate * (16/360)
Rate = 90 / 22.222
Rate = 4.05 = 4.105 * 100% = 405%
4. The electrical resistance of a wire varies inversely as the square of its radius. If the resistance is 0.80 ohm when the radius is 0.4cm. Find the resistance whom the radius is 0.7cm.
9514 1404 393
Answer:
0.261 ohm
Step-by-step explanation:
If the radius increases by a factor of 0.7/0.4= 7/4, the square of this factor is (7/4)^2 = 49/16. The inverse of this square is 16/49, which is the factor by which the resistance changed.
The resistance of the larger wire is ...
(16/49)(0.80 ohm) ≈ 0.261 ohm
A company manufactures two products. Market research and available resources require the following
constraints:
• The number of units of product A manufactured, 2, is at most 500 units more than twice the number
of units of product B. y.
• The square of the company's profit is equal to the sum of 35 times the number of product A units
sold and 50 times the number of product B units sold.
If the company expects weekly profits to exceed $22,500, which pair of inequalities represents these
constraints?
will give brainliest + 50 points :)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of product A and y represent the number of product B, hence:
x ≤ 500 + 2y (1)
Also:
35x + 50y > 22500² (2)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
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The rectangular ground floor of a building has a perimeter of 780 ft. The length is 200 ft more than the width. Find the length and the width.
The length is ___ and the width is ___
Answer:
L = 295ft
W = 95ft
Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
If the length is 200 ft more than the width, then:
L = 200+W
Substitute
P = 2(200+W+W)
780 = 2(200+2W)
780 = 400+4W
4W = 780-400
4w = 380
W = 380/4
W = 95ft
Since L = 200+w
L = 200+95
L = 295ft
Set up an equation and find the missing value of x.
Answer:
x = 35
Step-by-step explanation:
The angles shown are vertical angles
Vertical angles are congruent
Hence, 80 = 2x + 10
( Note that we just created an equation that we can use to solve for x )
We now solve for x using the equation we created
80 = 2x + 10
Step 1 subtract 10 from each side
80 - 10 = 70
10 - 10 cancels out
We now have 70 = 2x
Step 2 divide each side by 2
70/2 = 35
2x / 2 = x
We're left with x = 35
rule for 15,19,23 please I need it urgently
Answer:
[tex]a_{n}[/tex] = 4n + 11
Step-by-step explanation:
There is a common difference between consecutive terms, that is
19 - 15 = 23 - 19 = 4
This indicates the sequence is arithmetic with explicit rule
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 15 and d = 4 , then
[tex]a_{n}[/tex] = 15 + 4(n - 1) = 15 + 4n - 4 = 4n + 11
Why should people conserve energy? (Please don’t get the answer form the internet)
A burger place sells vanilla and chocolate shakes in two sizes, small and large. If 62% of shakes sold are vanilla flavor, 46% are size large, and 23% are large vanilla shakes which size/flavor combination is the most popular? (i.e. has the highest percentage)
Answer:
25 gfstuhfujjjjjgredeetuu
7 - 9m = 11
explain step by step
Answer:
[tex]m=-\frac{4}{9}[/tex]
Step-by-step explanation:
Given:
[tex]7-9m=11[/tex]
Subtract 7 from both sides
[tex]-9m=4[/tex]
Divide both sides by -9 to get m alone
[tex]m=-\frac{4}{9}[/tex]
Hope this is helpful
3x-6y-2z=-17
−6x+4y+5z=13
−3x−4y−3z=22
Answer:
1) x = -17 +6y + 2z/3
2) x= -13 - 4y - 5z/6
3) x= -22 +4y + 3z/3
Step-by-step explanation:
1) 3x-6y-2z=-17
3x- 6y -2z- (-6y -2z)= - 17 - ( 6y -2z )
3x=-17+6y+2z
3x/3= -17/3 +6y/3 + 2z/3
x = -17 +6y + 2z/3
2) −6x+4y+5z=13
-6x+4y+5z- ( 4y + 5z )= 13 - ( 4y + 5z )
-6x=13-4y-5z
-6x/-6= 13/-6 - 4y/-6 - 5z/-6
x= -13 - 4y - 5z/6
3) −3x−4y−3z=22
-3x=22+4y+3z
-3x/-3 = 22/-3 + 4y/-3 +3z/-3
x= -22 +4y + 3z/3
Consider all four-digit numbers that can be made from the digits 0-8 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is less than or equal to 4000
Answer:
The probability is:
P = 0.375
Step-by-step explanation:
First, we need to find the total number of four-digit numbers that can be made with the digits 0-8, such that the first digit can not be zero.
To do this, we first need to find the number of selections that we have, in this case, there are 4, one for each digit in our 4-digit number.
Now let's count the number of options that we have for each one of these selections:
first digit: we have 8 options (because the 0 can not be here)
second digit: we have 9 options (because now the zero can be taken)
third digit: we have 9 options
fourth digit: we have 9 options.
The total number of combinations is equal to the product of all the numbers of options, this is:
C = 8*9*9*9 = 5,832
Now we need to find how many of these are less or equal than 4000.
So now let's count the options again:
first digit: 3 options {1, 2, 3}
second digit: 9 options
third digit: 9 option
fourth digit: 9 options
Total number of combinations:
C' = 3*9*9*9 = 2,187
Here we should also count the combination for the number 4000 itself, as it was not counted in our previous calculation, then we have:
C' = 2,187 + 1 = 2,188 combinations.
The probability of randomly choosing a number that is smaller than or equal to 4000 will be equal to the quotient between the number of combinations that are smaller than or equal to 4000 (2,188 combinations) and the total number of combinations (5,832)
this is:
P = 2,188/5,832 = 0.375
Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 16,12,17,8,15,15,10,11,19,18
Answer:
[tex]Range = 11[/tex]
[tex]\sigma^2 = 12.1[/tex]
[tex]\sigma = 3.5[/tex]
Step-by-step explanation:
Given
[tex]Data: 16,12,17,8,15,15,10,11,19,18[/tex]
Solving (a): Range
This is calculated as:
[tex]Range = Highest - Least[/tex]
Where:
[tex]Highest = 19[/tex]
[tex]Least = 8[/tex]
So:
[tex]Range = 19 - 8[/tex]
[tex]Range = 11[/tex]
Solving (b): The population variance
First, calculate the population mean using:
[tex]\mu = \frac{\sum x}{n}[/tex]
So:
[tex]\mu = \frac{16+12+17+8+15+15+10+11+19+18}{10}[/tex]
[tex]\mu = \frac{141}{10}[/tex]
[tex]\mu = 14.1[/tex]
So, the population variance is:
[tex]\sigma^2 = \frac{\sum(x - \mu)^2}{n}[/tex]
[tex]\sigma^2 = \frac{(16 - 14.1)^2 + (12 - 14.1)^2 +............... + (19- 14.1)^2 + (18- 14.1)^2}{10}[/tex]
[tex]\sigma^2 = \frac{120.9}{10}[/tex]
[tex]\sigma^2 = 12.09[/tex]
[tex]\sigma^2 = 12.1[/tex] --- approximated
Solving (c): The population standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{\sigma^2[/tex]
[tex]\sigma = \sqrt{12.09[/tex]
[tex]\sigma = 3.5[/tex]
Complete the function, count_bases(s). It takes as input a DNA sequence as a string, s. It should compute the number of occurrences of each base (i.e., 'A', 'C', 'G', and 'T') in s. It should then return these counts in a dictionary whose keys are the bases.
Answer:
The function is as follows:
def count_bases(DNA_str):
retDNA = {}
for i in DNA_str:
if i in retDNA:
retDNA[i]+=1
else:
retDNA[i] = 1
return retDNA
Step-by-step explanation:
This defines the function
def count_bases(DNA_str):
This initializes a dictionary
retDNA = {}
This iterates through the dictionary
for i in DNA_str:
If an item exists in the dictionary
if i in retDNA:
The count is updated by 1
retDNA[i]+=1
Otherwise
else:
The count is set to 1
retDNA[i] = 1
This returns the DAN
return retDNA
A box of 20 chocolates, 4 are cream-filled. What is the probability of randomly selecting a cream-filled chocolate?
A. 4/18 ≈ 22%
B. 4/20 = 20%
C. 4/16 = 25%
D. 16/20 = 80%
Answer:
the correct choice is B
Step-by-step explanation:
4 goes into 20 5 times and 20 goes into 100 5 times as in 20x5=100 therefore it is 20%
The probability of randomly selecting a cream-filled chocolate is option (B) 4/20 = 20%.
ProbabilityProbability is the ratio of the fovourable outcome to the total outcomes.
Total number of chocolates in the box is 20 and total number of cream-filled chocolates are 4.
How to find the probability?Favourable number of outcomes is cream-filled chocolate i.e., [tex]4[/tex]
Total number of outcomes are [tex]20[/tex]
Probability of randomly selecting a cream-filled chocolate is-
[tex]P=\dfrac{4}{20}\times 100\\ \text { }=20\%[/tex]
As a result, option B is the correct answer.
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PROBIBILITY HELP ME PLZ Mike is playing a game where a ball is hidden under one of 5 cups. Mike guesses which cup contains the ball 20 times and chooses correctly 6 times. Mike wants to simulate the game to determine if his results are the same as what would be expected by random chance.
Answer:
Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.
Step-by-step explanation:
Given
[tex]Cups = 5[/tex]
[tex]Ball=1[/tex]
[tex]Trials = 20[/tex]
See attachment
Required
Simulate the above experiment (fill in the gaps)
The probability of choosing a ball correctly in each trial are independent, and each probability is calculated as:
[tex]P(Correct) = \frac{Ball}{Cups}[/tex]
This gives:
[tex]P(Correct) = \frac{1}{5}[/tex]
The number of times (i.e. 6) he chose correctly is not a factor in his simulation
So, a correct simulation of the experiment is as follows:
Choose 1 ball from a bag with 1 red ball and 4 white balls. Record the color, replace the ball and repeat the experiment 20 times.
The selected ball represents the number of balls hidden (i.e. 1 ball).
The total number of balls (5 balls; i.e. 1 red and 4 white) represent the number of cups (5 cups)
The 20 times represent the number of times the experiment is repeated.
Lillia total saving y in dollars is given by the equation y= 10 x where x is the number of week
Answer:
$50 dollars saved
Step-by-step explanation:
Given
[tex]y = 10x[/tex]
Required
The amount saved after 5 weeks
We have:
[tex]y = 10x[/tex]
Substitute 5 for x
[tex]y = 10*5[/tex]
[tex]y = 50[/tex]
A city is designing a new trail system that will be
6 1/6 miles long. They plan on placing 49 mileage signs to show the distance. How far apart will each sign be?
Step-by-step explanation:
the answer is 6.125 and its will be divided by 125
arithematic mean between 2-x and 2+x
Answer:
2
Step-by-step explanation:
The mean is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{2-x+2+x}{2}[/tex] = [tex]\frac{4}{2}[/tex] = 2
How would I solve this?
Answer:
20°
Step-by-step explanation:
perpendicular from the center on a chord of a circle always bisects the chord.
AR=BR
∴m arcAC=m arc BC=20°
Which is an x-intercept of the continuous function in the
table?
-2
-1
0
1
2
3
f(x)
-10
48
46
44
-2
0
(0, -6)
(3.0)
O (-6.0)
(0, 3)
Answer:
The x-intercept is the value of the variable x when the value of the function is equal to zero
so
In the table we have
(-1, 0)(−1,0) is a x-intercept, because
For x=-1x=−1 the value of the function is equal to zero
(-6, 0)(−6,0) is a x-intercept, because
For x=-6x=−6 the value of the function is equal to zero
therefore
the answer is
the continuous function in the table has two x-intercepts
(-1, 0)(−1,0)
(-6, 0)(−6,0)
when is 9+10 really equal to 21
Answer:
9 + 10 = 21
Step-by-step explanation:
9 + 10 = 21
Factor out 9 and 10
9 = 3 · 3 10 = 2 · 5
Next multiply 3 by 2
3 × 2 = 6
Then multiply 3 by 5
3 · 5 = 15
Finally add the products
15 + 6 = 21
what is the mode for the data set
x
x x x
x x x x x x
_______ __
5 6 7 8 9 10 options 7.8
5
8
9
Answer:
5
Step-by-step explanation:
The mode of a data set is the number that appears most
To complete a task in 30 days a company needs
4 people each working for 7 hours per day.
The company decides to have
5 people each working for 6 hours per day.
Assuming that each person works at the same rate,
how many days will the task take to complete?
Answer:
28 days
Step-by-step explanation:
4 x 7 x 30= 840 total working hours
5 x 6 x n = 840
= n = 840 ÷ 30
= n = 28 days
The task will take approximately 1 day to complete with 5 people working for 6 hours per day.
Determining the time to complete the taskTotal work done in the first scenario = 4 × 7 × 30
= 840 work hours
Total work done in the second scenario = (5 × 6 × D)
= 4 × 7 × 30
Solving for D:
30D = (4 × 7 × 30) / (5 × 6)
D = (4 × 7) / (5 × 6)
D = 28 / 30
D ≈ 0.9333
Rounding up to the nearest whole day, D = 1
Therefore, the task will take approximately 1 day to complete with 5 people working for 6 hours per day.
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please help me Solve the following equations simultaneously:
solve for x and y
x+3y =6 and 2x+8y=-12
Answer:
x+3y =6
2x+8y=-12
The solutions to your equations are:
x= 42 and y= -12
lets check this
42+-36 =6
84+-96=-12
Hope This Helps!!!
Solve
[tex](6+v)(5v+4)=0[/tex]
Answer:
v = -6 v = -4/5
Step-by-step explanation:
(6+v) ( 5v+4) = 0
Using the zero product property
6+v =0 5v+4 =0
v = -6 5v = -4
v = -6 v = -4/5
What is 2 3 of 99kg?
Step-by-step explanation:
[tex] \frac{2}{3} \times \frac{99}{1} = 66 \: kg[/tex]
Find the Surface Area and the Volume.
Answer:
Surface area = 850 cm²
Volume = 1000 cm³
Step-by-step explanation:
Applying,
A = h(a+b+c+d)................ Equation 1
Where A = Surface area of the trapezoidal prism, a, b, c, d = length of the four sides the trapezium respectively, h = height of the prism.
From the diagram in the question,
Given: h = 25 cm, a = 6 cm, b = 14 cm, c = 7 cm, d = 7 cm
Substitute these values into equation 1
A = 25(6+14+7+7)
A = 25(34)
A = 850 cm²
From the volume,
V = A'h...................... Equation 2
Where A' = Area of the base.
From the diagram,
A' = 1/2(6+14)4
A' = 40 cm²
Therefore,
V = 40×25
V = 1000 cm³
You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford? Round your answer to the nearest dollar.
S
b) How much total money will you pay the loan company? Round your answer to the
nearest dollar.
C) How much of that money is interest? Round your answer to the nearest dollar.
S
Question Help: D Postito forum
Submit Question
9514 1404 393
Answer:
loan: $157,823repaid: $378,000interest: $220,177Step-by-step explanation:
For a loan value of 1, the monthly payment on a 30 year loan at 7% is ...
A = (0.07/12)/(1 -(1 +0.07/12)^(-12·30)) ≈ 0.00665302495
Then the amount repaid after 360 payments is ...
360A = 2.39508898 . . . times the principal amount
__
a) For a monthly payment of $1050, the principal can be ...
$1050/0.00665302495 ≈ $157,823
__
b) The amount repaid to the loan company is ...
$157,823×2.39508898 ≈ $378,000
__
c) The amount that is interest is ...
$378,000 -157,823 = $220,177
