Answers
Answer:
27 and 13
Step-by-step explanation:
let the second number be x then the first number is x - 14
sum the 2 numbers and equate to 40
x - 14 + x = 40
2x - 14 = 40 ( add 14 to both sides )
2x = 54 ( divide both sides by 2 )
x = 27
x - 14 = 27 - 14 = 13
the first number is 27 and the second number is 13
Related Questions
determine whether each of the following conditional statements is true or false. Be sure to use full sentences, and justify your conclusions. (a) If 10 < 7, then 3 = 4. (b) If 7 < 10, then 3 = 4. (c) If 10 < 7, then 3 + 5 = 8. (d) If 7 < 10, then 3 + 5 = 8.
Previous question
Answers
(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
What is a conditional statement?
A hypothesis and a conclusion are both included in conditional statements. An "If-then" statement is another name for it. The conditional statement is false if the hypothesis is correct but the conclusion is incorrect. The entire sentence is untrue if the hypothesis is incorrect.
(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
( 10 is not less than 7 and 3 is not equal to 4)
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
( 7 < 10 and 3 is not equal to 4 )
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
( 10 is not less than 7 , but 3 + 5 = 8 )
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
( 7 < 10 and 3 + 5 = 8, both are true )
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(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
What is a conditional statement?
A hypothesis and a conclusion are both included in conditional statements. An "If-then" statement is another name for it. The conditional statement is false if the hypothesis is correct but the conclusion is incorrect. The entire sentence is untrue if the hypothesis is incorrect.
(a) If 10 < 7, then 3 = 4.
This statement is true. Because False ------> False has the truth value T
( 10 is not less than 7 and 3 is not equal to 4)
(b) If 7 < 10, then 3 = 4
This statement is False. Because True ------> False has the truth value F
( 7 < 10 and 3 is not equal to 4 )
(c) If 10 < 7, then 3 + 5 = 8.
This statement is true. Because False ------> True has the truth value T
( 10 is not less than 7 , but 3 + 5 = 8 )
(d) If 7 < 10, then 3 + 5 = 8
This statement is true. Because True ------> True has the truth value T
( 7 < 10 and 3 + 5 = 8, both are true )
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Dilate H using C as the center and a scale factor of 3. H is 40 mm from C.
Answers
Use technology or a z-distribution table to find the indicated area. The weights of grapefruits in a bin are normally distributed with a mean of 261 grams and a stranded deviation of 9.4 grams. Approximately 20% of the grapefruits weigh less than which amount
• 239 g •247 g •253 g •261 g
Answers
The amount of grape in bin using probability distribution =253 gm
What is probability?Probability is simply the chance that something will happen.
Whenever the outcome of an event is uncertain, we can talk about the likelihood or likelihood of a particular outcome. Analyzing events according to their probabilities is called statistics.
The best example of understanding probability is coin tossing.
Heads or tails, he has two possible outcomes. Crisps
The probability of an event is between 0 and 1 and can also be expressed as a percentage. event probability
P(A)>P(B)P, left parenthesis, A, right parenthesis, greater than, P, left parenthesis, B, right parenthesis, then event
P(A)=P(B)P, left parenthesis, A, right parenthesis, equal, P, left parenthesis, B, right parenthesis, event AA and BB occurs with equal probability.
Now for the given Question:
You need to find the z-score which is closest to .2000 (20%)
Look at your negative z-score table
Look at z= -.84
So -.84 standard deviations below the mean represents 20%
261 - .84 X (9.4) = 253.1 gm
Hence the amount of grapefruit in bin= 253 gm
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Evaluate ∫∫r(x+y)dxdy, where r is the rectangle in the xy plane with vertices (0,1), (1,0), (3,4)and (4,3).
Answers
The double integral [tex]\int\limits^a_b {(x+y)} \, dx dy[/tex]over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.
What do you mean by integration?Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
There are two main types of integration: definite and indefinite integration. The process of integration can be represented symbolically as ∫ (the integral symbol) and the result of an integration is typically represented as an antiderivative. The fundamental theorem of calculus states that differentiation and integration are inverse operations, so the derivative of an antiderivative is the original function.
To evaluate the double integral [tex]\int\limits^a_b {} \, dx dy[/tex]over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3), we first need to find the limits of integration for x and y.
The x-coordinates of the vertices of the rectangle range from 0 to 4, so the limits of integration for x are 0 to 4. The y-coordinates of the vertices of the rectangle range from 1 to 4, so the limits of integration for y are 1 to 4.
So, the double integral becomes:
[tex]\int\limits^a_b {(x+y)} \, dx dy[/tex] = (2 × 4² + 8 × 4) - (2 × 1² + 8 × 1) = 32 - 10 = 22.
Therefore, the double integral [tex]\int\limits^a_b {(x+y)} \, dx dy[/tex] over the rectangle r with vertices (0,1), (1,0), (3,4) and (4,3) is equal to 22.
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Calculate the area of the trapezium 6cm 4cm 5cm 8cm
Answers
Answer:
28 cm^2
Step-by-step explanation:
The area will be the height (4) times the average of the bases (8 and 6 , average = 7 )
4 x 7 = 28 cm^2
The circumference of a circular glazed donut with rainbow sprinkles is 9.42 inches. What is the diameter and radius of the circular donut?
Answers
The formula for the circumference of a circle is given by 2 * pi * r, where r is the radius. If the circumference is 9.42 inches, then we can write the equation:
9.42 = 2 * pi * r
Solving for r, we get:
r = 9.42 / (2 * pi)
The diameter of the circle is equal to 2 * r, so:
d = 2 * r = 2 * (9.42 / (2 * pi)) = 9.42 / pi
So, the radius of the circular donut is approximately 3 inches, and the diameter is approximately 9.42 inches.
the data set shows the january 1 noon temperatures in degrees Fahrenheit for a particular day in each of the past six years. 28 34 27 42 52 15 the five number summary of the data set is15 27 28 34 42 52 the mean of the data set is 33 what is the sum of the squares of the differences between each data value and the mean? use the table to organize your work
Answers
The sum of the squares of the differences between each data value and the mean is given as follows:
828.
How to obtain the sum of the squares?The mean of the data-set in this problem is given as follows:
33.
The data-set is given as follows:
28, 34, 27, 42, 52 and 15.
Hence the sum of the squares of the differences between each data value and the mean is obtained as follows:
(28 - 33)² + (34 - 33)² + (27 - 33)² + (42 - 33)² + (52 - 33)² + (15 - 33)² = 828.
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A tank is full of water. Find the work required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the density of water. Assume r = 6 m and h = 2 m.)
Answers
The work required to pump the water out of the spout is 70.9 * 10⁶ joules which is 71 M Joules approx.
Let the spherical tank be divided into a series of horizontal disks.
Let x be the height of each disk, g = gravity and p = density
Volume of each disk = πr2dx
Where r is the radius of each disk and dx is the thickness
By Pythagoras r² = 6² - x²= 36 -x²
Therefore Volume = π*(36-x²)*dx cubic metres
The distance each disk has to be lifted to escape the top of the spout = 2 + 6-x meters = (8-x)
Work needed to lift each disk to outlet = distance * mass where
mass = volume * density * gravity
= pi(36-x²)*p*g = 9800pi(36-x²)dx
dW = (8-x)* 9800pi(36-x²)dx
Since we have already accounted for the height of the spout, the work required is obtained by integrating the above expression from the bottom of the tank to the top. In other words, - 6 to + 6.
W = ⌠(8-x)*9800pi(36-x2)dx = 9800pi⌠[288 - 36x - 8x² +x³]dx
The odd terms evaluate to zero and we can rewrite the above as 2* I from 0 to 6.
W = 9800pi*2 [288x - 8x³/3] at x = 6 = 1152*19600π Joules = 22579200π joules = 70963200j
Total work required = 70.9 * 10⁶ joules
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Five years ago, a father was six times as old as his son. Two years hence, the age of the father will be 1 year more the three times then age of his son. Find their present ages.
Answers
Answer:
84
Step-by-step explanation:
Let's call the father's present age "F" and the son's present age "S".
Five years ago, the father's age was F - 5 and the son's age was S - 5.
According to the first statement, F - 5 = 6(S - 5), so F = 6S - 35.
Two years in the future, the father's age will be F + 2 and the son's age will be S + 2.
According to the second statement, F + 2 = 3(S + 2) + 1, so F = 3S + 7.
We can now substitute the first equation into the second:
3S + 7 = 6S - 28,
3S - 6S = -35 - 7 = -42,
-3S = -42,
S = 14.
Finally, the father's present age is F = 6S - 35 = 84.
Answer:
The dad is 35 and the son is 10
Step-by-step explanation:
Let f = the father's age
let s - the son's age
In the equations f-5 and s-5 represents the father and son's ages 5 years ago. f + 2 and s +2 represent the father and son's ages two years in the future.
Solve The Following System Of Equations For Z And For Y: System Of Equations: y= 10+2zy=38-5z
Answers
For the system of equations, y = 10 + 2z and y = 38 - 5z the value of y and z are 18 and 4 respectively.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first equation is : y = 10 + 2z
The second equation is : y = 38 - 5z
Subtract equation (1) and (2) -
y - y = 10 + 2z - (38 - 5z)
0 = 10 + 2z - 38 + 5z
Collect the like terms -
2z + 5z = -10 + 38
7z = 28
z = 28/7
z = 4
Substitute the value of z in equation (1) -
y = 10 + 2(4)
y = 10 + 8
y = 18
Therefore, the value of y = 18 and z = 4.
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For each equation draw a tape diagram and find unknown value
Answers
The solutions are:
a. x = 7
b. x = 7
The tape diagrams are given in the image below.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Two equations,
a. x + 9 = 16
b. 4x = 28
Solving the first equation,
x + 9 = 16
x = 7
Solving the second equation,
4x = 28
x = 7
The tape diagrams are given in the image below.
Hence, all the unknown values are given above.
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the math club went on a one day field trip. they visited the math museum. the math club members paid 250.00$ for bus transportation plus 12.00$ per ticket. write an expression to represent the total cost for the field trip for the n members of the club.
a.12n+25-
b.12n-250
c.250n+12
d,250n-12
Answers
12n+250
because you don't know the amount of tickets
The effect of the time of day a science class is taught on test scores is being
studied in an experiment. Which of these is most likely to be an extraneous
factor that could also affect test scores?
O A. Color of the school hallways
B. Principal of the school
OC. Difficulty of test questions
OD. Student clothing
Answers
In linear equation, The effect of the time of day a science class is taught on test scores being studied in an experiment will be the length of the class period.
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
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Answer the questions below
Answers
The triangle is congruent by the Angle side Angle property.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
The Angle side Angle Congruence Theorem (ASA) defines two triangles to be congruent to each other if the included two angles and one side of one are congruent to the included angle and corresponding two sides of the other triangle.
The three parameters that are congruent are:-
BV ≅ BV ( common side)
∠1 ≅ ∠2 ( Bisector)
∠3 ≅ ∠4 ( Bisector)
Hence, the two triangles are congruent with each other.
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M angle 3 = 48 degrees
M angle 3 = 112 degrees
M angle 3 = 88 degrees
M angle 3 = 68 degrees
Answers
The last
M angle 3 = 68 degrees
Step-by-step explanation:
interior angles between parallel lines
sum =180
5. A box containing,74.25 ounces of
pecans was donated to a local store.
The store places the pecans into
8.125-ounce containers and sells each
container for $6.95. Determine which
expression shows how much the store
will earn if they sell all the containers of
pecans. Find the store's earnings.
Answers
The earning of the store is $62.55.
What is an equation?
An equation is expression with one or more variables. It can also have more than 1 degree. it is a linear combination of constants and variables.
We are given that a box contains 74.25 ounces of pecans
These pecans are divided in 8.125 ounces of containers
First let us see how many such containers can be made
To find that we divided the two we get
74.25/ 8.125 = 9 such containers can be made
Now Each container is being sold for $6.95
Hence the total earnings are
9 * 6.95 = $62.55
The earning of the store is $62.55
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Last night, the Dallas Mavs made 12 free throws. If
their free throw percentage is 75%, how many free
throws were attempted?
Answers
Answer: i don't know I just did this so i can get points to ask a question super sorry.
Step-by-step explanation:
On Friday, Thomas the clown sells 16 balloons at the circus. Due to demand, Thomas charges three dollars more per balloon on Saturday. On Saturday, he sells 40 balloons. Let f represent the price of a balloon on Friday and let t represent the total amount he earns on both days combined.
a Write an equation to describe the relationship between the price of a balloon on Friday and the total amount earned.
b Determine the price of a balloon on Saturday if Thomas earns 400 dollars on Friday and Saturday.
Answers
The relationship between the price of balloons and the amount earned is 56f + 120 dollars
The price of the balloons if 400 dollars is earned on friday and saturday is 5 dollars on friday and 8 dollars on saturday
How to solve for the pricea) If f is the price of a balloon on Friday, then the price of a balloon on Saturday would be f + 3 dollars. The total amount Thomas earns on Friday would be 16 balloons * f dollars/balloon = 16f dollars. The total amount Thomas earns on Saturday would be 40 balloons * (f + 3 dollars/balloon) = 40f + 120 dollars. Hence, the total amount earned on Friday and Saturday would be 16f + 40f + 120 dollars = 56f + 120 dollars.
Therefore, the equation to describe the relationship between the price of a balloon on Friday and the total amount earned is: t = 56f + 120 dollars.
b) We are given that Thomas earns 400 dollars on Friday and Saturday, so we can set t = 400 dollars in the equation derived above:
400 = 56f + 120
Solving for f, we have:
280 = 56f
f = 5 dollars
The price of a balloon on Friday is $5, and the price of a balloon on Saturday would be f + 3 = 5 + 3 = $8.
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Practice
Solve for x.
1.x³ = 64
2.x² = 49
3.x³ =25
4.x²=125
Answers
The solutions for all the equations are:
1) x = 4
2) x = ±7
3) x = 5²´³
4) x = ±5³´²
How to solve the equations for x?The first equation is:
x³ = 64
If we apply the cubic root in both sides we will get:
∛x³ = ∛64
x = ∛64 = 4
2) now we have:
x² = 49
If we apply the square root:
√x² = ± √49
(remember the plus minus sign when you use a even degree root)
x = ±7
In this case we have two solutions.
3) x³ =25
Like in the first case:
x = ∛25 = ∛5² = 5²´³
Now we can't simplify this, so we leave it in this way.
4) x² = 125
Remember that 125 = 5³, then:
x² = 5³
x = ±√5³ = ±5³´²
These are all the solutions.
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Because the mean is very sensitive to extreme values, it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10%
trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and delete the top 10% of the values, then calculate the mean of the remaining values. Use the
axial loads (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean.
248 260 267 273 276 278 282 284 284 285
287 287 290 290 293 295 296 299 311 501
Answers
Step-by-step explanation:
Outliers: In this data set, the value of 501 is an outlier as it is significantly higher than the other values.
Median: To find the median, we arrange the data in order and find the middle value. In this case, since there are an odd number of values, the median is the middle value: 290.
Mean: To find the mean, we add up all the values and divide by the number of values:
(248 + 260 + 267 + ... + 311 + 501) / 21 = 293.67
10% Trimmed Mean: To find the 10% trimmed mean, we delete the bottom 10% of the values (2 values) and the top 10% of the values (2 values) and then find the mean of the remaining values:
(278 + 282 + 284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 15 = 286.87
20% Trimmed Mean: To find the 20% trimmed mean, we delete the bottom 20% of the values (4 values) and the top 20% of the values (4 values) and then find the mean of the remaining values:
(284 + 284 + 285 + 287 + 287 + 290 + 290 + 293 + 295 + 296 + 299 + 311) / 12 = 288.92
The median, mean, 10% trimmed mean, and 20% trimmed mean can be compared to see how resistant each measure is to outliers. The median is the most resistant measure as it only considers the middle value, whereas the mean is the least resistant measure as it considers all values in the data set. The trimmed means are intermediate measures that are more resistant to outliers than the mean but less resistant than the median. In this case, we can see that the 10% trimmed mean is more resistant to outliers than the mean but less resistant than the 20% trimmed mean.
1. A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about the
drought's effect on the size of his trees. To decide whether the growth of the trees has been re tard ed, the farmer
decides to take a sample of the heights of 25 trees and obtains the following results (recorded in inches).
60 57 62 69 46 54 64 60 59 58 75 51 49
67 65 44 58 55 48 62 63 73 52 55 50
a. Find the average tree height. _______________ Round your answer to one decimal place. You can use
software for this if desired.
b. Find the median tree height. __________________
c. Find the mode tree height. _____________
d. Find the range of this data _____________
e. Find the standard deviation for this sample. ______________ Round your answer to one decimal place.
You can use software for this if desired.
f. The tree farmer feels the normal height of a tree that was unaffected by the drought would be 65 inches.
Using the information you previously found, find the z-score for a tree that is 65 inches tall, rounding to
two decimal places.
Answers
The following results are:
a. Average height: 58.84
b. Median height: 58
c. Mode height: 55
d. Range of data: 73 - 44 = 29
e. Standard deviation: 8.23
f. Z-score for 65 inches: (65 - 58.84) / 8.23 = 0.83
What is statistics?Statistics is a process in which we collect, interpret, study and understand the data. We took a small sample from the large quantity and then we did study of the sample then according to results, we did our predictions for events which can happen in future.
Given that,
The height of 25 trees,
following results (recorded in inches).
60 57 62 69 46 54 64 60 59 58 75 51 49
67 65 44 58 55 48 62 63 73 52 55 50
a. Average = Sum of height of all the trees/Total number of trees
= 58.84
b. Median = (N + 1)/2th term after arranging into ascending order
= 58
c. Mode = Highest frequency
= 55
d. range = Highest value - Lowest value
= 73 -44
= 29
e. the standard deviation of the given data, you would need to perform the following steps:
Calculate the mean of the data:
(60 + 57 + 62 + 69 + 46 + 54 + 64 + 60 + 59 + 58 + 75 + 51 + 49 + 67 + 65 + 44 + 58 + 55 + 48 + 62 + 63 + 73 + 52 + 55 + 50) / 25 = 58.84
Find the deviation of each data point from the mean:
60 - 58.84 = 1.16, 57 - 58.84 = -1.84, 62 - 58.84 = 3.16, and so on...
Square each deviation:
1.16^2 = 1.3536, (-1.84)² = 3.3876, 3.16^2 = 9.9876, and so on...
Sum all the squared deviations:
1.3536 + 3.3876 + 9.9876 + ... = 519.24
Divide the sum by the number of data points minus 1 (for a sample) or by the number of data points (for a population):
519.24 / 24 = 21.63
Take the square root of the result:
√21.63 = 4.65
The standard deviation of the given data is 4.65.
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how many 3/5 are in two as a tape diagram
Answers
The number of the 3 / 5 in a tape diagram is 3.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator. Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.
Given that the fraction is 3 / 5. When we add the fraction three times we will get the value that is closest to 2.
E = 3 / 5 + 3 / 5 + 3 / 5
E = ( 3 + 3 + 3 ) / 5
E = 9 / 5
E = 1.8 ≅ 2
Hence, in a tape diagram, the 3/5 is represented by the number 3.
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A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 15 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A` (15) and explain its meaning in this situation.
Answers
A'(15) = 2 * 15 = 30.The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm^2 when the side length is 15 mm.
The area A(x) of a square wafer is given by A(x) = x², where x is the side length of the wafer. The derivative of A(x) with respect to x, denoted A'(x), represents the rate of change of the area with respect to the side length. To find A'(15), we need to find the derivative of A(x) at x = 15.
A'(x) = 2x
Therefore, A'(15) = 2 * 15 = 30.
The meaning of A'(15) in this situation is that if the side length of the wafer changes by 1 mm, the area will change by 30 mm² when the side length is 15 mm. This means that for every 1 mm increase in the side length, the area of the wafer will increase by 30 mm², and for every 1 mm decrease in the side length, the area of the wafer will decrease by 30 mm².
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Cooking time 35 minutes to be ready for lunch at 13:00, calculate what time the item should be put in the oven.
Answers
Answer:
he item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.
Step-by-step explanation:
To calculate what time the item should be put in the oven, you need to work backwards from the desired serving time of 13:00 and subtract the cooking time of 35 minutes. Here's how you can do it:
Convert the serving time to 24-hour format: 13:00 is the same as 1:00 PM in 12-hour format. In 24-hour format, it is 13:00.
Subtract the cooking time: Subtract 35 minutes from the serving time of 13:00 to get the time when the item should be put in the oven.
13:00 - 00:35 = 12:25
So, the item should be put in the oven at 12:25 (in 24-hour format) to be ready for lunch at 13:00.
1. Given the image of the circle, identify the length of the radius, diameter, and circumference. Also, find the area. Make sure to show work (area and circumference) to receive credit. Choose a number for the diameter.
Answers
Answer:
Radius = 5 units
Diameter = 10 units
Circumference = 10π units
Area = 25π square units.
Step-by-step explanation:
i choose diameter.
Let's say the diameter of the circle is 10 units.
The radius of the circle can be found by dividing the diameter by 2:
Radius = Diameter / 2 = 10 / 2 = 5 units
The circumference of the circle can be found using the formula:
Circumference = 2πr = 2π * 5 = 10π units
The area of the circle can be found using the formula:
Area = πr^2 = π * 5^2 = 25π square units.
So, for a circle with a diameter of 10 units:
Radius = 5 units
Diameter = 10 units
Circumference = 10π units
Area = 25π square units.
Write the inverse of f(x) = 3x - 1
f -1(x) =
log 3 x + 1
log 3 ( x - 1)
log 3 x - 1
Answers
Answer:
see below
Step-by-step explanation:
we need to write the inverse of ,
[tex]\longrightarrow f(x) = 3x -1 \\[/tex]
Substitute [tex] f(x)=y[/tex] ,
[tex]\longrightarrow y = 3x-1 \\[/tex]
Interchange x and y ,
[tex]\longrightarrow x = 3y -1 \\[/tex]
now solve for y ,
[tex]\longrightarrow 3y = x + 1 \\[/tex]
[tex]\longrightarrow y =\dfrac{x+1}{3} \\[/tex]
replace [tex] y[/tex] with [tex] f^{-1}(x)[/tex] as ,
[tex]\longrightarrow \underline{\underline{ f^{-1}(x) =\dfrac{x+1}{3}}}\\[/tex]
And we are done!
Answer:
[tex]f^{-1}(x)=\log_3(x)+1[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=3^{x-1}[/tex]
To find the inverse of the given function, swap y and x:
[tex]\implies x=3^{y-1}[/tex]
Take the log base 3 of each side of the equation:
[tex]\implies \log_3(x)=\log_{3}3^{y-1}[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \log_3(x)=(y-1)\log_{3}3[/tex]
[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]
[tex]\implies \log_3(x)=(y-1)(1)[/tex]
[tex]\implies \log_3(x)=y-1[/tex]
Add 1 to both sides of the equation:
[tex]\implies \log_3(x)+1=y[/tex]
[tex]\implies y=\log_3(x)+1[/tex]
Replace y for f⁻¹(x):
[tex]\implies f^{-1}(x)=\log_3(x)+1[/tex]
Please answer the question in the image below, thanks
Answers
Based on the volume of the solid, the value of K is 8960.
What is the volume of the solid?The volume of the solid = volume of the cone + volume of the hemisphere
The volume of the cone = ¹/₃hπr²
The volume of the hemisphere = ²/₃πr³
where;
r is radius = 20 cm
h is the height of the cone = ?
The curved surface area of the cone = πrl
The curved surface area of the cone = 580π cm²
πrl = 580π
l = 580/20
l = 29 cm
h = √(29² - 10²)
h = 27.2 cm
The volume of cone = ¹/₃ * 27.2 * 20² * π
The volume of the cone = 3626.7π cm³
The volume of the hemisphere = ²/₃ * π * 20³
The volume of the hemisphere = 5333.3 cm³
The volume of the solid = 5333.3π cm³ + 3626.7π cm³
The volume of the solid = 8960π cm³
The volume of the solid is kπcm³ = 8960π cm³
K = 8960
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Given that 16px + 10q + 10px = 78x + 60. Find the value of P.
Answers
Answer:
p = (39x +30 -5q)/13x
Step-by-step explanation:
16px + 10q + 10px = 78x + 60
Solve for p.
Subtract 10 q from each side.
16px + 10q-10q + 10px = 78x + 60 -10q
16px + 10px = 78x + 60-10q
Combine like terms.
26px = 78x + 60-10q
Factor out p.
p(26x) = 78x + 60-10q
Divide each side by 26x.
p = (78x + 60-10q)/(26x)
Simplify.
p = (39x +30 -5q)/13x
How can you help me with that please also my homework math please
Answers
Which ordered pair is in the solution set of 5x - 2y > 12?
A: (2, -1)
B: (1, 5)
C: (-1, -9)
D: (0.2, 0.5)
Answers
The ordered pair that is in the solution set of the given inequality is (-1, -9). The correct answer would be an option (C).
What is an ordered pair?An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.
We can substitute each of the ordered pairs into the inequality to see if it satisfies the inequality:
A: (2, -1)
5x - 2y > 12
5 × 2 - 2 × -1 > 12
10 - 2 > 12
8 > 12 (False)
B: (1, 5)
5x - 2y > 12
5 × 1 - 2 × 5 > 12
5 - 10 > 12 (False)
C: (-1, -9)
5x - 2y > 12
5 × -1 - 2 × -9 > 12
-5 + 18 > 12 (True)
D: (0.2, 0.5)
5x - 2y > 12
5 × 0.2 - 2 × 0.5 > 12
1 - 1 > 12 (False)
So, the only ordered pair that is in the solution set of the inequality is C: (-1, -9).
Hence, the correct answer would be option (C).
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