The HCF of 28 and another number is 4. The LCM is 40. Find the missing number
Answers
The HCF of 28 and another number is 4. The LCM is 40.
The missing number can be either 40, 4, 20, or 8.
Given:
HCF of 28 and the missing number = 4
LCM of 28 and the missing number = 40
To find the missing number, we need to consider the prime factorization of the given numbers.
Prime factorization of \(28: 2^2 * 7\)
Prime factorization of the missing number: Let's assume it as \(x = 2^a * 7^b\)
The HCF of 28 and x is given as 4, so we can equate the powers of common prime factors:
2^min(2, a) * 7^min(1, b) = 2^2 * 7^0
This implies:
2^min(2, a) * 7^min(1, b) = 4 * 1
Simplifying:
2^min(2, a) * 7^min(1, b) = 4
To find the LCM, we multiply the highest powers of prime factors:
LCM of 28 and x = 2^max(2, a) * 7^max(1, b)
The LCM is given as 40, so we can equate the powers of common prime factors:
2^max(2, a) * 7^max(1, b) = 2^3 * 5^1
This implies:
2^max(2, a) * 7^max(1, b) = 8 * 5
Simplifying:
2^max(2, a) * 7^max(1, b) = 40
From these equations, we can determine the possible values of a and b:
For a = 2 and b = 0, we get x = 2^2 * 7^0 = 4.
For a = 3 and b = 1, we get x = 2^3 * 7^1 = 56.
However, 56 is not a possible answer since it does not satisfy the given HCF condition (HCF should be 4).
Therefore, the missing number can be either 40 or 4.
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Related Questions
What is the value of 30-2(7+2)-1?
A. 11
B. 14
C. 17
D. 19
Answers
Answer:
A. 11Step-by-step explanation:
30-2(7+2)-1
= 30 - 2(9) - 1
= 30 - 18 - 1
= 11
Step 1: Think of any number
Step 2: Double the number.
Step 3: Add-5
Step 4: Double your new number.
Step 5: Subtract 6
Step 6: Divide by 4/
Step 7: Subtract your original number
Did you get 1 ? use algebra to show why this works.
Answers
Answer:
Step 1: 20
Step 2: 40
Step 3: 45
Step 4: 90
Step 5: 84
Step 6: 21
Step 7: 1
I did get 1 by following the steps.
A Jewelry company makes and sells necklaces. For one type of necklace, the company uses clay beads and glass beads. Each necklace has no more than 10 clay beads and at least 4 glass beads. For every necklace, four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads. Each clay bead costs $0.20 and each glass bead costs $0.40. The company wants to find the minimum cost to make a necklace with clay and glass beads and find the combination of clay and glass beads in a necklace that costs the least to make. a. Define the variables and write a system of inequalities. Then write an equation for the cost C. b. Graph the system of inequalities and find the coordinates of the vertices of the feasible region. c. Find the number of clay beads and glass beads in a necklace that costs the least to make.
Answers
a. The system of inequalities that models the situation is:
0 ≤ x ≤ 10.y ≥ 4.4y ≤ 8 + 2x.The equation for the cost is: C(x,y) = 0.2x + 0.4y.
b. The graph is given by the image at the end of the answer, and the vertices are (4,4), (10,4) and (10,7).
c. The number of clay beads and glass beads in a necklace that costs the least to make is: 4 clay beads and 4 glass beads.
What is the system of inequalities?The variables for the system are presented as follows:
Variable x: number of clay beads used.Variable y: number of glass beads used.Each necklace has no more than 10 clay beads and at least 4 glass beads, hence the constraints are listed as follows:
0 ≤ x ≤ 10.y ≥ 4.The numbers of each beads are countable amounts, meaning that they cannot assume negative values.
Four times the number of glass beads is less than or equal to 8 more than twice the number of clay beads, hence the final constraint is of:
4y ≤ 8 + 2x.
Each clay bead costs $0.20 and each glass bead costs $0.40, hence the cost function is given as follows:
C(x,y) = 0.2x + 0.4y.
Using the three constraints, the graph is given by the image at the end of the answer, and the vertices are as follows:
(4,4).(10,4).(10,7).The minimum cost is at the vertex with the smallest numeric value of the cost function, hence the numeric values are listed as follows:
C(4,4) = 0.2(4) + 0.4(4) = 2.4. -> minimum cost.C(10,4) = 0.2(10) + 0.4(4) = 3.6.C(10,7) = 0.2(10) + 0.4(7) = 4.8.More can be learned about a system of inequalities at https://brainly.com/question/9195260
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(2x−6)+4(x−3) =
Answer now or I eat ur cookies
Answers
Answer:
(2x−6)+4(x−3)
Use the distributive property to multiply 4 by x−3.
2x−6+4x−12
Combine 2x and 4x to get 6x.
6x−6−12
Subtract 12 from −6 to get −18.
6x−18
at top cruising speed, a mako shark can swim 4 kilometers in 1/10. a blue whale can swim 5 kilometers in 1/4 hour. which animal swims faster at top cruising speed? how much faster?
Answers
Answer:Blue whale
Step-by-step explanation:
The blue whale goes an extra kilometer faster
The Mako shark faster at top cruising speed and by 20km/h.
Given that,
The mamo shark should swim 4 km in one-fourth.While on the other hand, Blue whales should swim 5 km in one-fourth hour.Based on the above information, the calculation is as follows:
We know that
\(Speed = \frac{Distance}{Time}\)
For Mako shark,
\(= \frac{4}{\frac{1}{10} }\)
= 40 km/h
For Blue whales
\(= \frac{5}{\frac{1}{4} }\)
= 20 km/h
Based on the above calculations we can say that the Mako shark should be faster and by 20 km/h.
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Calculate the double integral. SISrycxy da, R= [0, 1] x [0, 3] dA, Х R Need Help? Read It Watch It
Answers
The value of the double integral is 9/4.
To calculate the double integral of f(x, y) = xy over the region R = [0, 1] x [0, 3], follow these steps:
Set up the double integral: ∬R xy dA, with the given region R = [0, 1] x [0, 3].
Express dA in terms of dx and dy: ∬R xy dy dx.
Determine the limits of integration for x and y. The region R is given as [0, 1] x [0, 3], so x goes from 0 to 1 and y goes
from 0 to 3. Your integral now looks like this:
∫(from 0 to 1) ∫(from 0 to 3) xy dy dx
Integrate with respect to y:
∫(from 0 to 1) [(1/2)\(xy^2\) | (from 0 to 3)] dx = ∫(from 0 to 1) [(\(1/2)x(3^2\))] dx
Simplify the expression inside the integral:
∫(from 0 to 1) (9/2)x dx
Integrate with respect to x:
[(9/4)\(x^2\)| (from 0 to 1)]
Evaluate the integral at the limits of integration
[(9/4)(\(1)^2\)] - [(9/4)\((0)^2\)] = 9/4
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video if 10% of the students in a certain school are left-handed, what is the probability that 2 or fewer students are left-handed in a random sample of 70 students from the school? use excel to find the probability. round your answer to four decimal places.
Answers
Using Excel, the probability that 2 or fewer students are left-handed in a random sample of 70 students from a school where 10% of the students are left-handed can be calculated as approximately 0.9999.
To calculate the probability using Excel, we can utilize the binomial distribution function. The binomial distribution is appropriate for situations with a fixed number of independent trials (sampling 70 students) and two possible outcomes (left-handed or not left-handed).
In Excel, the formula to calculate the probability of 2 or fewer left-handed students can be written as "=BINOM.DIST(2, 70, 0.1, TRUE)". Here, "2" represents the number of left-handed students (or fewer) we want to calculate the probability for, "70" is the total number of students in the sample, and "0.1" is the probability of a student being left-handed (10% or 0.10).
Evaluating this formula in Excel yields a probability of approximately 0.9999 when rounded to four decimal places. This implies that there is an extremely high probability (close to 100%) of having 2 or fewer left-handed students in a random sample of 70 students from the school, given that the overall proportion of left-handed students in the school is 10%.
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in a bar chart the horizontal axis is usually labeled with the values of a qualitative variable t/f
Answers
False. In a bar chart, the horizontal axis is usually labeled with the categories or levels of a qualitative variable, not the values.
A bar chart is a graphical representation used to display categorical data. The horizontal axis represents the different categories or levels of a qualitative variable, such as different groups or classes. Each category is typically labeled along the horizontal axis, and the corresponding bars are drawn vertically to represent the frequency, count, or proportion associated with each category.
The length or height of each bar represents the magnitude of the data for that particular category. Therefore, the horizontal axis in a bar chart is labeled with qualitative categories, not the numerical values of the variable.
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The measurements of two sides of a triangular playground are 24 feet and 30 feet. Which length could be the measurement of the third side of the triangular playground?
Answers
Answer: 7 feet
Step-by-step explanation: I did it trust
The length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.
What is triangle inequality theorem?
Triangle inequality theorem of a triangle says that the sum of the two sides of a triangle is always greater than the third side.
Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,
(a+b)>c
(b+c)>a
(c+a)>b
There is a triangular playground. The measurements of two sides of a triangular playground are 24 feet and 30 feet.
Suppose the length of the measurement of the third side of the triangular playground is c meters.
As the two sides are 24 ft and 30 ft long. Thus, by the triangle inequality theorem,
\(24+30 > c\\54 > c\)
For the sides 24 ft and c ft,
\(24+c > 30\\c > 30-24\\c > 6\)
Thus, the length measurement of the third side of the triangular playground whose two sides are 24 ft and 30 ft long should be more than 6 but less than 54.
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Find the area of a segment of a circle, in which the radius of the circle it is in, is 6 cm, and the central angle measures 120o.Round your answer to the nearest tenth
Answers
Answer:
120π
Step-by-step explanation:
radius = 6
angle =120
because a circle is 360, so that's 1/3 of the full circle
full circle area = πr² =36π
so the arc area = 1/3 * 360π = 120π
MARKING BRAINLEIST IF CORRECT PLS ANSWER ASAP
Answers
Answer:
\(c = \sqrt{ {2.2}^{2} + {.6}^{2} } = \sqrt{5.2} = 2.28\)
So the hypotenuse is about 2.3 millimeters.
you'll probably see a lot of questions from me abt math bc i dont wanna fail geometry :)
Answers
Answer:
X=18
Step-by-step explanation:
(4x-3)+(x+8)+(5x-5)=180
10x=180
x=18
Answer: C
Step-by-step explanation: What I did at first was I saw the last two problems and I counted them and all the angles should add up to 180. Hope it is explained well.
A sample of size n = 10 is drawn from a population. The data is shown below. 66.8 58.2 83.3 83.3 44.2 83.3 76.4 54.3 65.2 62.9 What is the range of this data set? range = What is the standard deviatio
Answers
Answer:
25
Step-by-step explanation:
Answer:
Step-by-step explanation:
a. 66.8 58.2 83.3 83.3 44.2 83.3 76.4 54.3 65.2 62.9
Range = highest value - lowest
= 83.3 - 44.2 = 39.1.
b. Mean m = 677.9 / 10
= 67.8
Differences from the mean
= 66.8 - 67.8 = -1.0
-9.6
15.5
-23.6
15.5
15.5
8.6
-13.5
-2.6
-4.9
Now we sqare the above vales:
= 1 , 92.16, 240.25, 240.25, 240.25, 556.96, 73.96, 182.25, 6.76, 24.01
Now the sm of these is 1657.85
Now we divide this by 10 and find the sqare root
= √(165.785)
= 12.86.
Standrad deviation is 12.86.
Quadrilateral PFGH was created by dilating quadrilateral MBGK the length of MB = 4.2 and the
scale factor is 3, what is the length of the corresponding side, PF?
Thank youuu!!
Answers
The corresponding length of the side PF will be 4.2.
What is scale factor? How it is used in Dilating coordinates?Scale factor is used to compare 2 quantities, indicating by how much one quantity is greater than the other. It is denoted by K. Mathematically-
K = a/b.
If a coordinate point (x, y) is dilated by a scale factor of [k], then the coordinate point after dilation will be - (kx, ky).
Given is Quadrilateral PFGH that was created by dilating quadrilateral MBGK such that the length of MB = 4.2 and the scale factor is 3.
When a length MB is dilated by a scale factor of 3, then the new length PF will be equal to -
PF = 3 x 4.2
PF = 12.6
The corresponding length of the side PF will be 4.2.
Therefore, the corresponding length of the side PF will be 4.2.
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On a test called the MMPI-2, a score of 30 on the Anxiety Subscale is considered
very low. Felipe participates in a yoga group at his gym and decides to give this
subscale to 18 people in his yoga group. The mean of their scores is 35.2, with a standard deviation of 10.4. He wants to determine whether their anxiety scores are statistically equal to 30.
What are the groups for this one-sample t-test?
What is the null hypothesis for this one-sample t-test?
What is the value of "?
Should the researcher conduct a one- or two-tailed test?
What is the alternative hypothesis?
What is the value for degrees of freedom?
What is the t-observed value?
What is(are) the t-critical value(s)?
Based on the critical and observed values, should Felipe reject or retain the null
hypothesis? Does this mean that his yoga group has scores that are above 30, below 30, or
statistically equal to 30?
What is the p-value for this example?
What is the Cohen’s d value for this example?
If the " value were dropped to .01, would Felipe reject or retain the null hypothesis?
Calculate a 42% CI around the sample mean.
Calculate a 79% CI around the sample mean.
Calculate a 95% CI around the sample mean.
Answers
The MMPI-2 test is used for the assessment of psychopathology and personality of patients.
It includes 567 true-false questions, resulting in 10 clinical scales, among which one is the anxiety subscale.
A score of 30 or less is usually considered very low.
The questions are answered by the patient, usually in a clinical or research setting.
A one-sample t-test is conducted in the problem, whereby a sample of 18 participants in a yoga group is tested for anxiety scores.
The following are the parameters of the one-sample t-test:Groups:
18 participants
Null hypothesis: The anxiety scores of Felipe's yoga group are statistically equal to 30." value: 30
Type of test: One-tailed test
Alternative hypothesis: The anxiety scores of Felipe's yoga group are greater than 30.
Degrees of freedom: n - 1 = 17T-observed value: (35.2 - 30) / (10.4 / sqrt(18)) = 2.41T-critical value: 1.734
Reject or retain null hypothesis: Since the t-observed value (2.41) is greater than the t-critical value (1.734), Felipe should reject the null hypothesis, which implies that his yoga group's scores are greater than 30.P-value: 0.014Cohen’s d value: (35.2 - 30) / 10.4 = 0.5
If the " value were reduced to 0.01, Felipe would still reject the null hypothesis, since the p-value (0.014) is lower than the alpha level (0.01).
For the sample mean: 35.2CI for 42%: 35.2 ± 0.58CI for 79%: 35.2 ± 1.16CI for 95%: 35.2 ± 2.13
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Can you help me? (BRAINLIEST IF CORREECT! and please dont guess this is important :D)
The Invasion of the Lionfish
What was once just an attractive aquarium fish has recently become one of the biggest menaces in the Atlantic. The lionfish was accidentally introduced into the Atlantic Ocean in the 1990s. Because it has no natural predators, it has adapted quickly to its new home. The lionfish now threatens to destroy native fish populations in the Atlantic, Caribbean, and Gulf of Mexico.
The lionfish spreads quite rapidly. Lionfish spread faster than any other invading species. Experts have called the invasion in the Atlantic the worst marine invasion of all time. The lionfish's success comes from an ability to reproduce all year round. In addition, they are greedy eaters with a fondness for small fish and crustaceans. They will eat anything smaller than they are. Lionfish love the warm waters of the Gulf of Mexico. Since their first sighting, they have rapidly multiplied. In some locations, scientists estimate that lionfish populations exploded by 700 percent between 2004 and 2008 alone.
To combat the invasion, wildlife agencies have sponsored lionfish derbies. In these derbies, local scuba divers are invited to harvest lionfish. In addition, many states offer recipes for preparing and eating lionfish to encourage harvesting. Lionfish have to be handled carefully because of their venomous spines, but they are apparently delicious. Increasing the harvest of lionfish will help. However, scientists estimate that more than a quarter of the population would have to be taken every month to stop the growing population.
The lionfish has targeted our most fragile and important ecosystems. Scientists are working tirelessly to learn as much as they can about this predator. We may never be able to completely remove the threat, but many fishermen and seafood fans are hoping we can figure out how to control it.
Work Cited
Wilcox, Christie. "The Worst Marine Invasion Ever." Slate. July 1, 2013.
http://goo.gl/Vlxpe
Read this line from the text:
In addition, they are greedy eaters with a fondness for small fish and crustaceans.
What does greedy mean in this sentence?
A.They take more than they need.
B.They have little to fear from others.
C.They cannot be controlled.
D.They have a weight problem.
Answers
I hope this is correct and that I’ve helped
kevin has an elm tree in his yard that is $11\frac{2}{3}$ feet tall and an oak tree that is $17\frac{5}{6}$ feet tall. how much taller is the oak tree than the elm tree? express your answer as a simplified mixed number.
Answers
Oak tree is \(6\frac{1}{6}\) feet taller than the elm tree.
we have the height of elm tree = \(11\frac{2}{3}\) feet
the height of oak tree = \(17\frac{5}{6}\) feet
Simplifying the fractions
height of elm tree = 35/3 feet
height of oak tree = 107/6 feet
Now , the difference between the heights of oak tree and the elm tree is given by
difference in height = 107/6 - 35/3
= \(\frac{107 - 70}{6}\)
= 37/6
= \(6\frac{1}{6}\) feet
So the difference between the heights of the oak tree and the elm tree will be \(6\frac{1}{6}\) feet.
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a bag contains 3 red sweets and 5 green sweets. Tim takes a sweet at random and eats it. he then takes another sweet. what is the probability that Tim takes 2 red sweets
Answers
Answer:25% chance
Step-by-step explanation:
easy
Which numbers are 4 units from -2 on this number line?
Drag and drop the two numbers that are 4 units from -2 to their correct position on the number line.
Answers
Answer:
-6 and 2
Step-by-step explanation:
See attached worksheet.
David has a thousand trees.
He wants to plant the trees in rows.
He wants 73 trees in each row.
How many full rows of trees can David plant?
Answers
Answer:
13
Step-by-step explanation:
1000 / 73 = 13.69 , but it asks for full rows so you get rid of the decimal if it can't be round up to a whole number
Answer:
ANSWER:
13
So he can make 13 full rows of 73 trees
and 69 in another row
If AE=3, DE=5, and CE=2, what is the length of BE?
Answers
To determine the length of BE, we can use the concept of the triangle's side lengths and apply the Triangle Inequality Theorem.
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can apply it to triangle ABC, where AC is the longest side.
Given the lengths AE = 3, DE = 5, and CE = 2, we can conclude that AC > AE and AC > CE.
Now, let's focus on triangle ABE. Since AC is the longest side, we can conclude that AB + BE > AE.
Substituting the known values, we have:
AB + BE > 3
Rearranging the inequality, we get:
BE > 3 - AB
To find the length of BE, we need to determine the value of AB. Unfortunately, the length of AB is not provided in the given information. Therefore, without knowing the value of AB, we cannot determine the exact length of BE.
In conclusion, without additional information or the length of AB, we cannot calculate the exact length of BE.
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Pls help me on this problem I’m confused
Answers
Answer:
420 × 2 = 820 feet total
100 yards = 300 feet
125 yards = 375 feet
300 + 375 = 675
820 - 675 = 145 feet
they have 145 feet left
To simplify 8. 3 − 4 1 5 ( 6. 1 + 1 2 ) , which operation must be performed first? Which operation must be performed second? Which operation must be performed last? Which is the simplified expression in the decimal form?
its a mutilpy choice question the choices are addition, multiplication, and subtraction
Answers
Answer:
Step-by-step explanation:
Use PEMDAS to determine order of operations.
P = Parentheses
E = Exponents
M/D = Multiplication/Division
A/S = Addition/Subtraction
The operation in the parentheses must be performed first, which is the addition of 6.1 + 12.
The next operation to perform is multiplication, which is 415 times (6.1 + 12).
The last operation to perform is the subtraction of 415 times (6.1 + 12) from 8.3.
6.1 + 12 = 18.1
8.3 - 415(18.1)
8.3 - 7511.5 = -7503.2
I don't understand how to find the negative. Some of these are wrong and just need help finding my errors
Answers
Answer:
-5pi/4
Step-by-step explanation:
Can 25/119 be simplified?
Answers
WHOEVER ANSER'S THIS WILL GET THE BRAINLESS!!!!!!!!! NEED ANSWER ASAP
Answers
Answer:
I think the last one?
Step-by-step explanation:
I am politely asking for some assistance with, thy questions in quantities above 1. My very brain inside of my cranium is too little to answer thy questions. I am requesting some assistance.
Answers
Answer:
First one, true
Second one, 23/45
Third one, 11/29
Step-by-step explanation:
There's thy answer for thy self t-t
Answer:
1.)true
2.) 23/45
3.)11/29
Step-by-step explanation:
A motorist drives north for 35.0 minutes at 70.5 km/h and then stops for 15.0 minutes. He then continues north, traveling 130 km in. 1.90. h. (a) What is his total displacement? x Your response is within 10 ss of the correct value. This may be due to roundoff emor, of you could have a mistake in yoar calcufation. Carry out all intermediate result to atleast four-digit accuracy to minimize roundoff error. km (b) What is his average velocity? Your response is within.10\% of the conrect vatue. This may be due to roundoff erro, or you could have a misrake in your calcutation. Carry out alf intermediate results to at least four-digit acouracy to minimize roundoff erroc. km/h
Answers
The total displacement is approximately 171.049 km. The average velocity is approximately 68.940 km/h.
- Time of the first leg: 35.0 minutes
- Speed of the first leg: 70.5 km/h
- Time of the second leg: 1.90 hours
- Distance of the second leg: 130 km
(a) Total DisplacementTo find the total displacement, we need to calculate the distance traveled in each leg and sum them up. Since the motorist is traveling north on both legs, we can consider north as the positive direction.
Distance of the first leg = Speed * Time = 70.5 km/h * (35.0 minutes / 60 minutes)
Distance of the second leg = 130 km
Total Displacement = Distance of the first leg + Distance of the second leg
35.0 minutes = 35.0 minutes / 60 minutes = 0.5833 hours
Distance of the first leg = 70.5 km/h * 0.5833 hours
Total Displacement = (70.5 km/h * 0.5833 hours) + 130 km
Distance of the first leg = 41.04865 km (rounded to 5 decimal places)
Total Displacement = 41.04865 km + 130 km
Total Displacement = 171.04865 km
Therefore, the total displacement is approximately 171.049 km.
(b) Average VelocityTo find the average velocity, we need to divide the total displacement by the total time taken.
Total Time = Time of the first leg + Time of the second leg
Time of the first leg = 35.0 minutes / 60 minutes = 0.5833 hours
Time of the second leg = 1.90 hours
Total Time = 0.5833 hours + 1.90 hours
Average Velocity = Total Displacement / Total Time
Average Velocity = 171.04865 km / (0.5833 hours + 1.90 hours)
Average Velocity = 171.04865 km / 2.4833 hours
Average Velocity ≈ 68.940 km/h (rounded to three decimal places)
Therefore, the average velocity is approximately 68.940 km/h.
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what is our number system called
Answers
Step-by-step explanation:
Decimal system, also called Hindu-Arabic number system or Arabic number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Jayden goes to the market and purchase some fruit . There are 10 pieces of fruit in the basket including 4 apples. What is the probable that a randomly selected piece of fruit will be an apple
Answers
Answer:
4/10
Step-by-step explanation:
total number of fruit pieces : 10
number of apple pieces : 4
probabilty of ( picking and apple ) = favourbale outcomes / total outcomes
= 4/10