find the smallest which 108 must be multiplied to get a perfect square
Answer:
The answer is 3
Step-by-step explanation:
x×108=y
x×2²×3³=y
3×108=324
Find the measures of angle a and B. Round to the
nearest degree.
The measure of angle A and B is 29° and 61° respectively
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
tan(tetha) = opp/adj
cos(tetha) = adj/hyp
The opposite is 6 and the adjascent = 11
Therefore tan (tetha) = 11/6 = 1.833
tetha = tan^-1( 1.833)
= 61°( nearest degree)
The sum of angle in a triangle is 180°
therefore,
angle A = 180-( 61+90)
= 180-151
= 29°
therefore the measure of angle A and B is 29° and 61° respectively.
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how many 6 card hands are there (from a standard deck) with at least 3 kings? (enter an integer without commas)
There are 73,701 different 6-card hands (from a standard deck) with at least 3 kings.
To calculate the number of 6-card hands with at least 3 K's, the problem can be divided into:
Case 1:
Exactly 3 Kings
There are 4 ways to choose 3 kings to put in the hand, then there are 48 cards left to choose the remaining 3 cards (because we used 3 cards in a 52-card deck). Therefore, the number of 6-card hands with exactly 3 kings is:
4 * (48 choose 3) = 4 * 17,296 = 69,184
Case 2:
Exactly 4 Kings
There are 4 ways to choose 4 kings to put in the hand, then there are 48 cards left to choose the remaining 2 cards. Therefore, the number of 6-card hands with exactly 4 kings is:
4 * (48 choose 2) = 4 * 1.128 = 4.512
Case 3:
Exactly 5 kings
There are 4 ways to choose the 5 kings in the hand, then there is only one card left to choose from (because we used 5 of the 52 cards in the deck of cards). Therefore, the number of 6-card hands with exactly 5 kings is:
4*1=4
Case 4:
6 cards are king
There is only one way to choose all 6 cards as king.
Therefore, the total number of 6-card hands with at least 3 kings is:
69,184 + 4,512 + 4 + 1 = 73.701
So there are 73,701 different 6-card hands with at least 3 kings.
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If f(x) = 5x - 6, which of these is the inverse of f(x)?
A. f^-¹(x) = x/5 +6
B. f^-¹(x) = x/5 -6
C. f^-¹(x) = x+6/5
D. F^-¹(x) = x-6/5
To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.
So, let's start by swapping x and y in the function f(x) = 5x - 6:x = 5y - 6
Next, we'll solve this equation for y:
x + 6 = 5y
y = (x + 6)/5
Therefore, the inverse of f(x) is f^-1(x) = (x + 6)/5, which is option C.Find the distance, d, of AB.
The distance between A and B is approximately 8.06 units.
In order to find the distance, d, of AB, we need to use the distance formula. The distance formula gives us the distance between two points in a coordinate plane. It is given as:$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where (x1, y1) and (x2, y2) are the coordinates of the two points in question.
In this case, A and B are the two points for which we need to find the distance. Let's assume that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2).
Then the distance formula becomes:
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
$$d = \sqrt{((8 + 4) - 2)^2 + ((5 - 1) - 3)^2}$$
$$d = \sqrt{(10 - 2)^2 + (4 - 3)^2}$$
$$d = \sqrt{(8)^2 + (1)^2}$$
$$d = \sqrt{64 + 1}$$
$$d \approx \sqrt{65}$$
$$d \approx 8.06$$
Therefore, the distance between A and B is approximately 8.06 units.
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HELP!! 10 POINTS
uhm yeah thats all I've got to say
The correct statement regarding the middle 50% of the data-set is given as follows:
C. The box, from 41 to 56.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.The box, from the 25th percentile of 41 to the 75th percentile of 56, shows the middle 50% of the data-set.
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in a certain health center there are 3 doctors, 8 nurses and 2 physicians. in how many ways one can form a group of 5 members consisting of 1 doctor, 3 nurse and 1 physician.
The relationship between the mass m in kilograms of an organism and its metabolism P in Calories per
day can be represented by P = 73.3m³. Find the metabolism of an organism that has a mass of 16 kilograms.
Answer:
The relationship between the mass m in kilograms of an organism and its metabolism p in calories per day can be represented by p = 73.3m³ . To find the metabolism of an organism that has a mass of 16 kilograms, we can substitute m = 16 into the equation:
p = 73.3m³ p = 73.3(16)³ p = 73.3(4096) p = 299,648 calories per day
Therefore, an organism with a mass of 16 kilograms has a metabolism of 299,648 calories per day.
I hope that helps!
Step-by-step explanation:
An organism with a mass of 16 kilograms has a metabolism of 299,708.8 Calories per day according to the given relationship.
We can use the given formula to find the metabolism P of an organism with a mass of 16 kilograms:
P = 73.3m³
where m = 16 kg
Substituting the value of m:
P = 73.3(16)³
P = 73.3(4096)
P = 299,708.8 Calories per day.
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A rock of radioactive material has 500 atoms in it. The number of atoms decreases at a rate of 11% a day. Write an exponential function that models this situation. f(x) type your answer... (1 choose your answer... choose your answer... ✓)^x
Answer:
[tex]f(x) = 500( {.89}^{x} )[/tex]
Any help? Please. Whoever answer it first gets brainliest!
Answer:
[tex]c + 15 > 24[/tex]
[tex]c > 9[/tex]
The additional amount will be more than $9.
given: weight a: 140 pounds at 17 inches aft of datum weight b: 120 pounds at 110 inches aft of datum weight c: 85 pounds at 210 inches aft of datum based on this information, the cg would be located how far aft of datum?
The center of gravity is located 96.7 inches aft of the datum.
To determine the location of the center of gravity (CG) of the system, we need to calculate the moment of each weight about the datum, and then divide the sum of the moments by the total weight of the system.
The moment of each weight is equal to its weight multiplied by its distance from the datum. In this case:
Moment of weight a = 140 pounds x 17 inches = 2,380 inch-pounds
Moment of weight b = 120 pounds x 110 inches = 13,200 inch-pounds
Moment of weight c = 85 pounds x 210 inches = 17,850 inch-pounds
The total weight of the system is:
Total weight = weight a + weight b + weight c = 140 + 120 + 85 = 345 pounds
Therefore, the location of the CG can be calculated as follows:
CG location = (Moment of weight a + Moment of weight b + Moment of weight c) / Total weight
CG location = (2,380 + 13,200 + 17,850) / 345
CG location = 33,430 / 345
CG location = 96.7 inches aft of datum
As a result, the center of gravity is 96.7 inches aft of the datum.
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Please help me so i can finish my homework
Answer:
[tex]\frac{1}{4}[/tex]w + 3
Step-by-step explanation:
Helping in the name of Jesus.
justin developed the below hypothesis. h1: younger adults (18-28 years old) spend more time on social media than the middle-aged (29-65 years old) group and older adults (older than 65 years old). what statistical test should he use to test his hypothesis?
To verify if older adults and middles ages people spend less time on social media, Justin can use the Analysis of variance (ANOVA) test.
ANOVA is used to compare means across two or more groups. Justin can use this test on the different category of younger adults, middle-aged and older adult. This test is done when there is statistically significant difference between the group of samples.
Justin can utilize post-hoc tests (such as Tukey's HSD and Bonferroni) to identify whether particular groups are statistically different from one another if an ANOVA shows a significant difference.
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5 × (10 + 7) = (5 × 10) + (5 ×7)
Answer:
Same equation just using the assocaitive property
Step-by-step explanation:
For example, 8 + (2 + 3) = (8 + 2) + 3 = 13
Hope this helps! =D
21st term: 3,8,13,18 What is the indicated term
The 21st term of the sequence 3, 8, 13, 18, .. is 103
To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as
a(n) = a(1) + (n-1)d
where a(1) is the first term of the sequence, d is the common difference, and n is the term number.
In this case, we have:
a(1) = 3 (the first term)
d = 5 (the common difference)
To find the 21st term, we substitute n = 21 in the formula:
a(21) = a(1) + (21-1)d
a(21) = 3 + 20(5)
a(21) = 103
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2. Tyler leaves his house at 7:00 a.m. to go to school. He walks for 20 minutes until he reaches his school, 1 mile from his house. The function d gives the distance d(t), in miles, of Tyler from his house t minutes after 7:00 a.m. a. Explain what d(5) = 0.25 means in this context. b. On snowy days, Tyler's school has a 2 hour delayed start time (120 minutes). The function is gives Tyler's distance s(t), in miles, from home t minutes after 7:00 a.m. with a 120 minute delayed start time. If d(5) = 0.25, then what is the corresponding point on the function s? c. Write an expression for s in terms of d. A new function, n, is defined as n(t) = d(t +60) explain what this means in terms of Tyler's distance from school.
Answer: a. In this context, d(5) = 0.25 means that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. This is because the function d(t) gives the distance of Tyler from his house t minutes after 7:00 a.m.
b. If d(5) = 0.25, then we know that 5 minutes after 7:00 a.m., Tyler is 0.25 miles away from his house. If there is a 120-minute delayed start time, then Tyler will walk for 20 + 120 = 140 minutes to reach his school. We want to find the corresponding point on the function s, which gives Tyler's distance from home t minutes after 7:00 a.m. with a 120-minute delayed start time. Since Tyler walks the same distance regardless of the delayed start time, we can use the same function for s as we did for d. Therefore, s(145) = 1.25, since Tyler is 1 mile away from his house after walking for 140 minutes and then an additional 5 minutes to account for the delayed start time.
c. Since Tyler walks the same distance regardless of the delayed start time, we can express s(t) in terms of d(t) by adding 120 minutes to the time t. Therefore, s(t) = d(t + 120).
d. The function n(t) = d(t + 60) gives Tyler's distance from his house t minutes after 8:00 a.m. This is because adding 60 minutes to t corresponds to adding one hour to the time, which means that Tyler leaves his house at 8:00 a.m. instead of 7:00 a.m. Therefore, n(t) gives Tyler's distance from school one hour after he leaves his house.
Step-by-step explanation:
When adding or subtracting mixed numbers with like denominators, the numerators ___ , but the denominators ______ .
A. Stay the same
B. change
Answer:
Yo, when you adding or subtracting mixed numbers with the same denominators, the numerators stay chill, they don't change, bro.
But the denominators, they also stay the same, man. It's like keeping things consistent, ya feel me? So the answer is A, dude. Numerators stay put, denominators stay put. It's all good vibes, bro! ✌️
the anova procedure is a statistical approach for determining whether the means of . a. more than two samples are equal b. two or more populations are equal c. two samples are equal d. two or more samples are equal
The means of two or more populations being equal is determined by a statistical approach for the ANOVA procedure. Option B is correct.
The ANOVA (Analysis of Variance) procedure is a statistical method used to determine whether there is a significant difference between the means of two or more groups. To statistically test the equality of means ANOVA uses F-tests.
The repeated-measures ANOVA is a two-stage process that is described as an analysis of dependencies. This test is used to prove an assumed cause-effect relationship between variables. The conditions that must be met for the results of an ANOVA are Independence, Random Sampling, Large Sample Size, and Normality.
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Leo subscribes to a monthly app service that charges him $6 for one month, and each app he purchases costs $0. 90. Lara subscribes to a service that charges $1. 50 per app with no additional monthly fee. After how many apps will they have the same monthly bill?
Iam do not understand what do you mean 1335690964225753897426908224 1335690964225753897426908224 88 9 109 250 10 10 XL 220 10 10 30 250 30 30 30 400
Solve Triangle
Because I Need Answer My Assignment:-)
Good Perfect Complete=Brainlist
Copy Wrong Incomplete=Report
Good Luck Answer Brainly Users:-)
Answer:
x = 4√5 ≈ 8.94 (2 d.p.)
y = 8√5 ≈ 17.89 (2 d.p.)
Step-by-step explanation:
To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).
Geometric Mean Theorem (Leg Rule)The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.
[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]
From inspection of the given right triangle RST:
Altitude = SVHypotenuse = RT = 20Leg 1 = RS = ySegment 1 = RV = 16Leg 2 = ST = xSegment 2 = VT = 4Substitute the values into the formulas:
[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]
Solve the equation for x:
[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]
[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]
[tex]\implies 80=x^2[/tex]
[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{80}[/tex]
[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]
[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]
[tex]\implies x=4\sqrt{5}[/tex]
Solve the equation for y:
[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]
[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]
[tex]\implies 320=y^2[/tex]
[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{320}[/tex]
[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]
[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]
[tex]\implies y=8\sqrt{5}[/tex]
If anyone is reading this, rn i would be so flipping happy if u got this for me ive been waiting for so long and got nothing please answer correctly please
Answer: The answer is A.
Step-by-step explanation: Because I am smart don't underestimate me.
Answer:
C
Step-by-step explanation: (look at attachment)
3x + 4 = -2x -2
By looking at the y-intercepts, you automatically know the answer is C.
The y-intercept of the pink line is 4 because of 3x + 4.
The y-intercept of the blue line is -2, because of -2x - 2.
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches. Which lengths, in inches, could be the length of the third side?
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
Triangle Inequality Theorem:In a triangle, the length of any side must be less than the sum of the lengths of the other two sides and greater than the difference between the lengths of the other two sides.
We can apply this rule to find the possible lengths of the third side of the triangle, given that the lengths of the two sides are 5.2 inches and 3.1 inches.
Here we have
The lengths of two sides of a triangle are 5.2 inches and 3.1 inches
Let's denote the length of the third side as x. Then, we have:
3.1 + 5.2 > x > 5.2 - 3.1
8.3 > x > 2.1
Therefore, the length of the third side x must be greater than 2.1 inches and less than 8.3 inches.
We can write this as an inequality:
2.1 < x < 8.3
Therefore,
The length of the third side between 2.1 inches and 8.3 inches (exclusive) could be a valid length for the third side of the triangle.
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Charlie made the following table to record the height of each person in his family.
If Cheyenne and Hannah lay end to end, how far will they reach?
A. 9
B. 9, 1/2
C. 10
D. 8
Three machines are used to produce nails. The table displays the total number of nails produced by the 3 machines
over different lengths of time.
Nail Production with 3 Machines
Time (minutes)
Number of Nails
(thousands)
15
16
45
48
55
593
ON
If each machine produces nails at the same rate, how many nails can 1 machine produce in 1 hour?
nails
One machine can produce 600,000 nails in one hour.
Finding the total number of nails produced by the three machines in a minute and dividing that number by three to obtain the number of nails produced by a single machine in a minute are the first two steps in the solution to this problem.
The number of nails produced by a single machine in an hour can then be calculated by multiplying that number by 60.
Now, we add up the total number of nails produced during :
(15 + 16 + 45 + 48 + 55 + 59 + 3) / 7 = 30
To find the number of nails produced by one machine in one hour, we multiply by 60: 10,000 x 60 = 600,000
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which combination of factors would definitely cause the confidence interval to become wider? group of answer choices none of these will definitely reduce the width of a confidence interval. use a smaller sample and decrease the level of confidence use a larger sample and increase the level of confidence use a larger sample and decrease the level of confidence use a smaller sample and increase the level of confidence
To reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.
What are the factors?
what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder.
The combination of factors that would definitely cause the confidence interval to become wider is to use a larger sample and increase the level of confidence or to use a smaller sample and increase the level of confidence.
When using a larger sample size, the standard error of the mean decreases, and the interval will become narrower. Conversely, when using a smaller sample size, the standard error of the mean increases, and the interval will become wider. However, increasing the level of confidence will also increase the width of the interval as a wider interval is required to capture the true population parameter with a higher level of confidence.
Therefore, to reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.
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a professor at the university of florida wanted to determine if offering video tutorials for the course software would increase student engagement. the engagement ratings are below for a random sample of 5 students before and after implementing the course change. ratings were on a scale between 0 and 50. the higher scores translated to higher student engagement score. student before after 1 30 40 2 20 40 3 32 37 4 43 46 5 48 44 what is the test statistic for the wilcoxon signed rank test? group of answer choices 1
According to the information, he test statistic for this sample is 5.
How to calculate the test statistic for the Wilcoxon signed-rank test?To calculate the test statistic for the Wilcoxon signed-rank test, we need to calculate the differences between the "before" and "after" engagement ratings and rank them in order of their absolute values.
Student Before After Difference Absolute Difference Rank
1 30 40 10 10 1
2 20 40 20 20 2
3 32 37 5 5 3
4 43 46 3 3 4
5 48 44 -4 4 5
The sum of the ranks for the positive differences is 1 + 2 + 3 + 4 = 10, and the sum of the ranks for the negative differences is 5.
The smaller of the two sums (in this case, the sum of the ranks for the negative differences) is the test statistic for the Wilcoxon signed-rank test.
Therefore, the test statistic for this sample is 5.
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Number 7. I don’t understand, what’s the fraction? How do you get fraction and the + a number.
Answer:
A
Step-by-step explanation:
Equation of a line is: y = mx + b where m = slope b = y axis intercept
To find the slope between any two of the given points :
say 18, 100 and 27, 85
m = slope = (y1-y2) / (x1-x2) = (85-100) / ( 27-18) = -15/12 = -5/3
so now you have
y = - 5/3 x + b we still need to find the value of b
use any point to calculate b
say 15, 106
106 = - 5/3 (15) + b
b = ~ 131
the equation is then y = - 5/3 x + 131 closest to answer 'A'
you place in a dark bag 24 marbles. 12 marbles are red, 5 marbles are blue and 7 marbles are yellow. you select 2 random marbles (one after the other without putting the first back in). what is the probability that the marbles have the same color?
The probability of selecting two marbles with the same color is approximately 0.27 or 27%.
To work out the likelihood that the two marbles drawn have similar variety, we can utilize the accompanying advances:
In the first place, we compute the likelihood of drawing a red marble on the principal pick: 12/24 = 1/2.
On the off chance that the main marble drawn is red, there will be 11 red marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more red marble on the subsequent pick is 11/23.
Likewise, in the event that the principal marble drawn is blue, there will be 4 blue marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more blue marble on the subsequent pick is 4/23.
Furthermore, on the off chance that the main marble drawn is yellow, there will be 6 yellow marbles left taken care of, out of a sum of 23 marbles. So the likelihood of drawing one more yellow marble on the subsequent pick is 6/23.
To get the complete likelihood of drawing two marbles of similar variety, we want to add the probabilities of every one of these cases:
(1/2) x (11/23) + (5/24) x (4/23) + (7/24) x (6/23) = 55/138 or roughly 0.398 or 39.8%.
In this way, the likelihood of drawing two marbles of a similar variety is roughly 39.8%.
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Maggie spent $18. 00 Of $30. 00 In her wallet which decimal represents the fraction of the $30. 00 Maggie spent
The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.
Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.
So, we can write this as a fraction:
$18.00 / $30.00
To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.
$18.00 / $30.00 = 0.6
Another way to say this is that Maggie spent 60% of the money she had in her wallet.
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it is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. an experienced travel agent believes this is wrong. of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. we want to test the travel agent's theory with a hypothesis test. if you used a significance level of 0.05, what is your decision?
Based on the given information, we can set up the following hypotheses for the hypothesis test:
Null Hypothesis (H0): The actual proportion of people taking the cruise within 1 year is equal to the believed proportion of 5%.
Alternative Hypothesis (H1): The actual proportion of people taking the cruise within 1 year is not equal to the believed proportion of 5%.
Let p be the proportion of people taking the cruise within 1 year. We can use the sample proportion, denoted as p-hat, which is calculated as the ratio of the number of people who took the cruise within 1 year (3 in this case) to the total number of people who requested the brochures (100 in this case).
Given that the significance level is 0.05, we can use a z-test to compare the sample proportion with the believed proportion of 5%. The z-test statistic is calculated as:
z = (p-hat - p) / sqrt(p * (1 - p) / n)
where n is the sample size, which is 100 in this case.
Now we can calculate the z-test statistic and compare it with the critical value for a two-tailed test at a significance level of 0.05. If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis; otherwise, we would fail to reject the null hypothesis.
Since the sample proportion p-hat is 3/100 = 0.03, and the believed proportion p is 0.05, we can substitute these values into the z-test formula:
z = (0.03 - 0.05) / sqrt(0.05 * (1 - 0.05) / 100)
Calculating the above expression, we get the value of z. We can then compare this value with the critical value for a two-tailed test at a significance level of 0.05 from a standard normal distribution table or using a statistical calculator.
If the calculated z-test statistic falls outside the critical value, we would reject the null hypothesis and conclude that the actual proportion of people taking the cruise within 1 year is different from the believed proportion of 5%. If the calculated z-test statistic falls within the critical value, we would fail to reject the null hypothesis and not conclude that the actual proportion is different from the believed proportion.
Without the actual values of the calculated z-test statistic and the critical value, we cannot provide a specific decision for this hypothesis test. Please note that hypothesis testing requires careful consideration of the sample size, significance level, and other relevant factors, and should be conducted with caution and in consultation with a qualified statistician or expert in statistical analysis.