what is the smallest number which when divided by 21,45 and 56 leaves a remainder of 7.
Answers
The smallest number that, when divided by 21, 45, and 56, leaves a remainder of 7 is 2527.
To find the smallest number that satisfies the given conditionsThe remaining 7 must be added after determining the least common multiple (LCM) of the numbers 21, 45, and 56.
Find the LCM of 21, 45, and 56 first:
21 = 3 * 7
45 = 3^2 * 5
56 = 2^3 * 7
The LCM is the product of the highest powers of all the prime factors involved:
\(LCM = 2^3 * 3^2 * 5 * 7 = 8 * 9 * 5 * 7 = 2520\)
Now, let's add the remainder of 7 to the LCM:
Smallest number = LCM + Remainder = 2520 + 7 = 2527
Therefore, the smallest number that, when divided by 21, 45, and 56, leaves a remainder of 7 is 2527.
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Related Questions
Help me please !!!!!
Answers
Answer:4.2 ft/sec, 63 feet, -2 points
Step-by-step explanation:
1. 21 feet/5 sec = 4.2ft/sec
2. 15 sec*(4.2ft/sec) = 63 feet
3. 2-5-3+4 = -2 points
Solve the equation 12a2 + a – 35 = 0
Answers
Answer:
Step-by-step explanation:
Factor to solve.
12a2 + a – 35 = 0
>Multiply the first and the last, 12 and -35
(12)(-35) = -420
> Find 2 numbers that multiply to -420 but add to middle term, 1
-20 and +21 multiply to -420 but adds to 1
>Replace the middle term with -20 and 21
12a² + a – 35 = 0
12a² + 20a - 21a – 35 = 0
>Group the first 2 and last 2 terms
( 12a² + 20a) (- 21a – 35) = 0
>Take out GCF from each of the groupings
4a ( 3a + 5) -7(3a + 5) = 0
>Take out GCF (3a + 5)
( 4a - 7) ( 3a + 5) = 0
>Set each =0 and solve for a
( 4a - 7) = 0 ( 3a + 5) = 0
a=7/4 a = -5/3
One and seventy six hundredths in decimal
Answers
Answer:
1.76
Step-by-step explanation:
Answer:
1/76
Step-by-step explanation:
Statement I is false because the study has volunteers, which is not a random selection of the population. We cannot generalize the results to the population of all people with a moderate case of the disease.
Answers
The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.
However, it is important to note that not all studies need to use random sampling in order to draw meaningful conclusions. In some cases, non-random samples may still provide valuable insights into the topic of interest.
In any case, if the study did use volunteers who self-selected to participate, it is important for the researchers to acknowledge this limitation in their conclusions and to avoid overgeneralizing the findings beyond the sample they studied.
The statement is partially correct. because, If the study used volunteers who self-selected to participate, then it may not be a representative sample of the entire population with a moderate case of the disease, and therefore the results may not be generalizable to the population.
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Give the number that is 2 less than its own absolute value
Answers
Answer:
-1
Step-by-step explanation:
l -1 l = 1
1 - -1 = 2
i HOPE U UNDERSTOOD!! :)
look at the picture is it b or c ??
Answers
Answer:
i would say B pls mark brainlest!
Answer:
I would say it is B too.
how do I find X? btw the far right point is C
Answers
X = ?
Then this proportion is valid
104/(2x-8) = 143/22
Now make cross multiply
104•22/143 = (2x-8)
16 = 2x - 8
24 = 2x
Then
x= 24/2= 12
Answer is x=12
list two possible real life situations that can be modeled by using a quadratic function written in standard form, y=ax^2 +bx+c
Answers
Two possible real life situations are: shooting a cannon and hitting a golf ball. In both cases, variable x-variable will represent time (the time after the cannonball was shot and the time after the golf ball was hit), and the y-variable will represent the height of the cannonball and the golf ball.
In both cases, the point (0,0) is included.
Let's suppose that the maximum height reached by the golf ball is 20 ft and it takes 3 seconds to reach that height. The ball will reach the soil after another 3 seconds, making a total of 3 + 3 = 6 seconds. Therefore, the points (3, 20) and (6, 0) will be on the parabola too.
\(\begin{gathered} y=ax^2+bx+c \\ 0=a\cdot0^2+b\cdot0+c \\ 0=c \\ 20=a\cdot3^2+b\cdot3 \\ 20=9a+3b\text{ (eq. 1)} \\ 0=a\cdot6^2+b\cdot6 \\ 0=36a^{}+6b\text{ (eq. 2)} \end{gathered}\)Multiplying equation 1 by 2 and subtracting equation 2 to that result, we get:
2*20 = 2(9a + 3b)
40 = 18a + 6b
40 = 18a + 6b
-
0 = 36a + 6b
------------------------
40 = -18a
40/(-18) = a
-20/9 = a
And the value of b is:
40 = 18(-20/9) + 6b
40 = -40+ 6b
40 + 40 = 6b
80/6 = b
40/3 = b
And the equation is:
\(y=-\frac{20}{9}x^2+\frac{40}{3}x\)This formula has the form:
\(y=-\frac{h}{t^2}x^2+\frac{2h}{t}x\)where the point (t, h) is the vertex of the parabola. So, in the case of the cannonball, let's suppose that the maximum height is 40 ft and it takes 5 seconds to reach that height. Then the equation will be:
\(\begin{gathered} y=-\frac{40}{5^2}x^2+\frac{2\cdot40}{5}x \\ y=-\frac{8}{5}x^2+16x \end{gathered}\)Pls help I will mark u as brainliest!
Answers
Answer: first one, 2,3,6,9
Step-by-step explanation: second is 2,3,5,9,
Rosetta wants to write equations in the form y=mx+by=mx+b for the lines passing through point pp that are parallel and perpendicular to line gg. First she finds the slopes of these two lines. What could she do next to find the yy-intercepts?.
Answers
To obtain the y-intercept of the perpendicular line's b-intercept, she must similarly substitute the slope and the point P into the equation y = mx + b.
The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).
Intercept Form of Equation of a Line: x/a + y/b = 1.
To solve for the y-intercept, b, in the equation y = mx + b, substitute the coordinates of the point P and the slope m.
A P is present in Rosetta. There are lines that cross this location and are both parallel and perpendicular to line g. She is attempting to formulate the equations of the lines in the form of the slope-intercept.
She has already determined the inclinations of these two lines. Similar to line g, the parallel line will also have a slope. The slopes of line g and the perpendicular line will add up to -1.
She must now determine the y-intercepts of each line.
She possesses P, a point on the parallel line, and its slope for the parallel line. In order to find the y-intercept of this line, she only needs to solve for these values in the equation y = mx + b.
Thus, to obtain the y-intercept of the perpendicular line's b-intercept, she must similarly substitute the slope and the point P into the equation y = mx + b.
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What must be true in order for line A to be parallel of line b?
Answers
Answer:
Its the first option.
Step-by-step explanation:
if they are both 180° then they can both go on forever without touching each other.
Answer:
c or (5x-54)°=(3x+16)°
Step-by-step explanation:
Since they are alternate angles, they must be equal. Alternate angles are always equivalent, and since you can't choose more than one answer, then they can't equal 180° or 90°.
a canister of cheese ball measures 12 inches high and its base has a diameter of 6 inches. what is the volume of a canister (rounded to the nearest 10
Answers
The volume of the canister is 339.1 cubic inches.
The volume of a cylinder is calculated by using the formula V=πr²h, where r is the radius of the cylinder and h is the height of the cylinder.
The radius of the cylinder is half of the diameter, so the radius of the canister is 3 inches.
Using the formula, we can calculate the volume of the canister as follows:
V = π×3²×12
V = 108×3.14
V = 339.1 cubic inches
Therefore, the volume of the canister is 339.1 cubic inches.
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what is the distinction between a positive and negative mean deviation in terms of meaning applied to the data values?
Answers
Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.
Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.
In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.
Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.
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The specificheat of a human is approximately 3.47 J/8 ∘
C. Use this information to answer the following questions. (a) If a 1601lb man eats a candy bar containing 287 Cal, how much will his body temperature increase if all of the calories from the candy bar are converted into heat energy? Remember that a food calorie (Cal) is equal to 1kcal, 6
C GOTutorial (b) If a 160lb man eats a roll of candy containing 41.9Cal, how much will his body temperature increase if all of the calories from the candy are converted into heat energy? ∘
C
Answers
(a)the body temperature of the 1601 lb man will increase by approximately 3.0 °C.(b)the body temperature of the 160 lb man will increase by approximately 2.4 °C.
The specific heat of a human is given as 3.47 J/°C. Using this information, we can calculate the increase in body temperature when a certain number of calories are converted into heat energy. In the first scenario, a 1601 lb man consumes a candy bar containing 287 Cal. In the second scenario, a 160 lb man consumes a roll of candy containing 41.9 Cal. We will calculate the increase in body temperature for each case.
(a) To calculate the increase in body temperature for a 1601 lb man who consumes a candy bar containing 287 Cal, we need to convert calories to joules. Since 1 Calorie (Cal) is equal to 4184 joules, we have:
Energy = 287 Cal × 4184 J/Cal = 1.2 × \(10^6\) J
Now, using the specific heat formula Q = mcΔT, where Q is the energy, m is the mass, c is the specific heat, and ΔT is the change in temperature, we can rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
Assuming the mass of the man is converted to kilograms, we have:
ΔT = (1.2 × \(10^6\) J) / (1601 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 3.0 °C
Therefore, the body temperature of the 1601 lb man will increase by approximately 3.0 °C.
(b) For a 160 lb man who consumes a roll of candy containing 41.9 Cal, we repeat the same calculation:
Energy = 41.9 Cal × 4184 J/Cal = 1.75 × \(10^5\) J
ΔT = (1.75 × \(10^5\) J) / (160 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 2.4 °C
Thus, the body temperature of the 160 lb man will increase by approximately 2.4 °C.
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Eddie is arguing with Tana about the probabilities of different outcomes when flipping three coins. They decide to flip a penny, nickel, and a dime.
Answers
Determining the sample space for the 3 events, which are, a penny, nickel and coin flip would best me determined using a tree diagram
Sample space are used to represent the different possible outcomes of an experiment. The Area model are best adopted when two events are involved, such that the possible outcomes of each event are lined as the width and length. The tree diagram is used for more complicated scenarios, usually when the number of events exceeds 2.Therefore, the tree diagram would be best in the scenario described.
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The table below shows labor market statistics for a nation.
Number of Workers Structurally Unemployed: 3 million
Number of Workers Cyclically Unemployed: 4 million
Number of Workers Frictionally Unemployed: 2 million
Number of Workers Officially Classified as Employed: 91 million
Working-age Population: 150 million
What is the nation's unemployment rate?
A
4%
B
5%
C
6%
D
9%
E
66.7%
Answers
According to the table which shows labor market statistics for a nation. There are 3 million structurally unemployed workers, 4 million cyclically unemployed workers, 2 million frictionally unemployed workers, 91 million officially employed workers, and 150 million people of working age.The nation's unemployment rate is 9%
The total number of unemployed workers is the sum of the structurally, cyclically, and frictionally unemployed workers, which is 3 million + 4 million + 2 million = 9 million.
The total number of people in the labor force (employed and unemployed) is the sum of the employed and unemployed workers, which is 91 million + 9 million = 100 million.
The unemployment rate is the ratio of the number of unemployed workers to the total labor force, expressed as a percentage. Therefore, the unemployment rate in the nation is:
(9 million / 100 million) x 100% = 9%
Therefore, the correct answer is option D: 9%.
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Use f to find the probability that at most three grafts fail; that at least two grafts fail
Answers
The probability that at most three grafts fail is 0.98 and the probability that at least two grafts fail is 0.1.
To find the probability that at most three grafts fail, we need to find the sum of the probabilities for x = 0, 1, 2, and 3.
Using the given values of f(x), we get:
P(X <= 3) = f(0) + f(1) + f(2) + f(3)
= 0.7 + 0.2 + 0.05 + 0.03
= 0.98
So the probability that at most three grafts fail is 0.98.
To find the probability that at least two grafts fail, we need to find the sum of the probabilities for x = 2, 3, and 4 and subtract it from 1.
Using the given values of f(x), we get:
P(X >= 2) = 1 - (f(0) + f(1)) = 1 - (0.7 + 0.2) = 0.1
So the probability that at least two grafts fail is 0.1
--The question is incomplete, answering to the question below--
"Grafting the uniting of the stem of one plant with the stem or root of another; is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with hardy root system: Most Florida sweet oranges grow on trees grafted to the root of sour orange variety. The density for X, the number of 'grafts that fail in series of five trials.
For the values of x = 0, 1, 2, 3, and 4 value of f(x) is 0.7, 0.2, 0.05, 0.03, and 0.01 respectively.
Use f(x) to find the probability that at most three grafts fail; that at least two grafts fail."
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Based on an architectural drawing, a roof slopes to a drain along the function represented in the table that defines the edge of slope, where x is the horizontal distance in feet and f(x) is the vertical distance in feet.
If the drain is at the minimum point, how far is it from the wall defined by the y-axis?
0 feet
8 feet
80 feet
160 feet
Answers
The distance from the wall defined by the y-axis will be 8 feet. Then the correct option is B.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The table is given below.
Then the equation of the line will be
(y – 8) = [(8 – 6) / (0 – 20)](x – 0)
y = -0.1x + 8
If the drain is at the minimum point.
Then the distance from the wall defined by the y-axis will be 8 feet.
Then the correct option is B.
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find the angles between the vectors a=7i-4j k, b=3i-k
Answers
The angle between the vectors a and b is approximately 41.4 degrees.
To find the angles between the vectors a=7i-4j+k and b=3i-k, we need to use the dot product formula. The dot product of two vectors a and b is defined as a.b = |a||b|cos(theta), where |a| and |b| are the magnitudes of the vectors, and theta is the angle between them. So, first we need to find the magnitudes of the vectors a and b.|a| = sqrt((7)^2+(-4)^2+1^2) = sqrt(66)
|b| = sqrt((3)^2+(-1)^2) = sqrt(10)
Next, we can find the dot product of the two vectors:
a.b = (7)(3) + (-4)(-1) + (1)(-1) = 24 Now we can plug in all the values we have into the dot product formula:
24 = sqrt(66)sqrt(10)cos(theta)
Solving for cos(theta), we get:
cos(theta) = 24/(sqrt(66)sqrt(10)) Using a calculator, we can find that cos(theta) is approximately equal to 0.753.
Now we can find the angle theta:
theta = cos^(-1)(0.753)
Using a calculator, we get that theta is approximately equal to 41.4 degrees. Therefore, the angle between the vectors a and b is approximately 41.4 degrees.
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Using Linear Pairs to Find an Unknown Value
What is the value of x?
SEE
030
45
т
(3x)
55
70
R
O 60
W
Answers
Answer:
x=45
Step-by-step explanation:
I did it and got it right
What is (-m)-3n if m = 2 and n = -24?
Answers
Answer:
70
Step-by-step explanation:
Knowing both values of variables m and n, you could substitute each of the values inside the equation.
=(-(2))-3(-24)
=(-2)+72
=70
Hope it helped! (:
13. When feeding, a juvenile whale shark filters about 600 cubic meters of water through its
mouth each hour. About 2.8 kilograms of food are filtered out from the water each hour.
120
a. Graph the function that represents the amount a of water filtered by the whale shark as a
function of the number of minutes.
m
b. The whale shark feeds for 7.5 hours each day. Graph the function that represents the amount f
of food (in pounds) filtered by the whale shark as a function of the number d of days.
Answers
Answer:214.29
Step-by-step explanation:600 divided by 2.8
possibly the answer
Select THREE expressions equivalent to –81x + 27.
A. –9(9x – 3)
B. –9(–9x – 3)
C. 3(–27x + 9)
D. –3(27x – 9)
E. –3(–27x + 9)
Answers
Answer:
A, C, and D
Step-by-step explanation:
How do you convert percent to fractions?
Answers
Answer:
put the number over 100 and then simplify it. for example:
50%
50/100 = 1/2
What is the domain of the function?
Answers
Answer: -6 ≤ x < 4
Step-by-step explanation:
Open circles on a graph mean that that point is not included
Filled in circles on a graph mean that that point is included
As a result, the end point (-6, -6) is included while (4, 8) is not
The domain is all possible x-values so the graph can be anywhere from:
-6 ≤ x < 4
Note that there are no possible values for the x-value of 4
What is the greatest common factor of 12 and 30
Answers
Answer:
6
Step-by-step explanation:
We know if we multiply 6x2=12 and 6x5=30. After 6 you can not multiply anything else higher than that. For example 15x2=30 but 15 is not a GCF of 12 and 4x3=12 3 and 4 are not GCFs of 30. So 6 is the GCF of 12 and 30.
Help solve this math problem thing pleasereeee
Answers
Step-by-step explanation:
We have the equation y = 2x - 5
To complete the table of values substitute each of the x values into the equation
When x = 0
y = 2(0) - 5 which means y =(2 × 0) - 5 = -5
The coordinates you plot are (0,-5)
When x = 1
y = 2(1) - 5 which means y = (2 × 1) - 5 = -3
The coordinates you plot are (1,-3)
When x = 2
y = 2(2) - 5 which means y = (2 × 2) - 5 = -1
The coordinates you plot are (2,-1)
When x = 3
y = 2(3) - 5 which means y = (2 × 3) - 5 = 1
The coordinates you plot are (3,1)
When x = 4
y = 2(4) - 5 which means y = (2 × 4) - 5 = 3
The coordinates you plot are (4,3)
When x = 5
y = 2(5) - 5 which means y = (2 × 5) - 5 = 5
The coordinates you plot are (5,5)
The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.3 5.3 million cells per microliter and a standard deviation of 0.3 0.3 million cells per microliter. (a) What is the minimum red blood cell count that can be in the top 23 23% of counts? (b) What is the maximum red blood cell count that can be in the bottom 12 12% of counts?
Answers
Answer:
5.5217
4.9475
Step-by-step explanation:
Given that :
Mean (m) = 5.3
Standard deviation (s) = 0.3
Score
Minimum redbloodcell in top 23% count
Z = (x - m) / s
Z at 0.23 = 0.739
P(z> x) = 0.23 ; Z = 0.739
0.739 = (x - 5.3) / 0.3
0.739 * 0.3 = x - 5.3
0.2217 = x - 5.3
x = 0.2217 + 5.3
x = 5.5217
(b) What is the maximum red blood cell count that can be in the bottom 12% of counts?
Z = (x - m) / s
P(z< x) = 0.12 ; Z = - 1.175 ( Z probability
-1.175 = (x - 5.3) / 0.3
-1.175 * 0.3 = x - 5.3
- 0.3525 = x - 5.3
x = - 0.352 + 5.3
x = 4.9475
_____ refers to the average of all participants on one level of the independent variable, ignoring the other independent variable.
Answers
Marginal means refers to the average of all participants on one level of the independent variable, ignoring the other independent variable.
What is Marginal means?A marginal value can be defined as a value that is valid under specific conditions, the change in a value brought on by a particular change in an independent variable, whether that independent variable or a dependent variable, or any combination of these.
What is independent variable?In statistical modeling, experimental sciences, and mathematical modeling, there are dependent and independent variables. Dependent variables are so named because they are studied in an experiment under the assumption or demand that they are dependent on the values of other variables according to some rule or law.
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Is this correct? (B)
Answers
Yes you are correct. Nice work.
(h,k) = (10,-4) is the center; r = 2 is the radius
(x-h)^2 + (y-k)^2 = r^2
(x-10)^2 + (y-(-4))^2 = 2^2
(x-10)^2 + (y+4)^2 = 4