Answer:
60 is the larger number
Step-by-step explanation:
Let the two numbers be a and y
x+y = 90
x-y = 30
Add the two equations together
x+y = 90
x-y = 30
-----------------
2x = 120
Divide by 2
2x/2 =120/2
x = 60
x+y =90
60+y = 90
y = 90-60
y = 30
The numbers are 60 and 30
What is the slope-intercept equation of the line below?
10 minutes left
Answer:
y=-3x+4
Step-by-step explanation:
The y intercept is 4 because the line crosses the y axis at the 4 tic mark
The slope will be -3 because the y decreases by 3 every time the x incerases by 1
y=mx+b
y=-3x+4
Anna earned $9 an hour babysitting. She wants
to buy a 16 GB iPod that is $120. Anna has
saved $45 so far. How many more hours of
babysitting does she need to do to earn the rest
to purchase the iPod
Answer:
8.33 hours
Step-by-step explanation:
120-45 = 75
75 ÷ 9 = 8.33
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
The number is 6.
Step-by-step explanation:
[tex]4x-13=x+5\\3x-13=5\\3x=18\\x=6[/tex]
n a history class there are 88 history majors and 88 non-history majors. 44 students are randomly selected to present a topic. What is the probability that at least 22 of the 44 students selected are non-history majors
Answer:
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
Step-by-step explanation:
The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Approximation:
We have to use the mean and the standard deviation of the hypergeometric distribution, that is:
[tex]\mu = \frac{nk}{N}[/tex]
[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]
In this question:
88 + 88 = 176 students, which means that [tex]N = 176[/tex]
88 non-history majors, which means that [tex]k = 88[/tex]
44 students are selected, which means that [tex]n = 44[/tex]
Mean and standard deviation:
[tex]\mu = \frac{44*88}{176} = 22[/tex]
[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]
What is the probability that at least 22 of the 44 students selected are non-history majors?
Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 22}{2.88}[/tex]
[tex]Z = -0.17[/tex]
[tex]Z = -0.17[/tex] has a p-value of 0.4325
1 - 0.4325 = 0.5675
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
find the LCM of 210, 280, 360 by prime factorisation
Answer:
Step-by-step explanation:
210=2x3x5x7
280=2x2x2x5x7
360=2x2x2x3x3x5
Answer:
210= 2×3×5×7
280=2×2×2×5×7
360=2×2×2×3×3×5
common factors=2×2×2×3×5×7=840
uncommon factors=3
L.C.M=Common factors× uncommon factors
L.C.M=840×3
L.C.M=2520
Step-by-step explanation:
i hope it will be helpful
plzz mark as brainliest
Please answer! These r my last questions
Answer:
8. -2a+14
9. w=3/2
Step-by-step explanation:
8.
The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.
For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as
-2 * a + (-2) * (-7) = final answer
= -2 * a + 14
We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out
9.
Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in
(-2/3)w = 4-5 = -1
Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get
w = (-3/2)
To check this, we can plug (-3/2) for w in our original equation, so
(-2/3) * (-3/2) + 5 = 4
-1 + 5 = 4
4 = 4
This works!
You can run at a speed of 4 mph and swim at a speed of 2 mph and are located on the shore, 6 miles east of an island that is 1 mile north of the shoreline. How far (in mi) should you run west to minimize the time needed to reach the island
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Answer:
5.423 miles
Step-by-step explanation:
Let x represent the distance to run. Then the remaining distance to the point that is closest to the island is (6-x) miles. The straight-line distance (d) to the point x from the island is given by the Pythagorean theorem:
d² = 1² +(6 -x)² = x² -12x +37
d = √(x² -12x +37)
The total travel time is the sum of times running and swimming. Each time is found from ...
time = distance/speed
total time = x/4 + d/2 = x/4 +(1/2)√(x² -12x +37)
__
The total time will be minimized when its derivative with respect to x is zero.
t' = 1/4 +(1/4)(2x -12)/√(x² -12x +37) = 0
Multiplying by 4 and combining fractions, we can see the numerator will be ...
√(x² -12x +37) +2x -12 = 0
Subtracting the radical term and squaring both sides, we get ...
4x² -48x +144 = x² -12x +37
3x² -36x +107 = 0
The quadratic formula tells us the smaller of the two roots is ...
x = (36 -√(36² -4(3)(107)))/(2(3)) = (36 -√12)/6 ≈ 5.423 . . . mi
You should run 5.423 miles west to minimize the time needed to reach the island.
__
A graphing calculator solves this nicely. The attached graph shows the time is a minimum when you run 5.423 miles.
Devaughn is 6 years older than Sydney. The sum of their ages is 56 . What is Sydney's age?
Answer:
Devaughn = 31, Sydney = 25
Step-by-step explanation:
(56-6)÷2= 25
So they would both be 25 if they were the same age but Devaughn is 6 years older so 25+6=31
ATQ
[tex]\\ \sf\longmapsto x+x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x+6=56[/tex]
[tex]\\ \sf\longmapsto 2x=56-6[/tex]
[tex]\\ \sf\longmapsto 2x=50[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{50}{2}[/tex]
[tex]\\ \sf\longmapsto x=25[/tex]
What is the volume of a cone with a height of 6m and a diameter of 12m? Nearest meter.
Answer:
0.0005m^3
Step-by-step explanation:
V=1/3hπr²
h=6m
d=12m
r=12÷2=6m
V=1/3×6×(3.14)×36
V=1/2034.72
V=0.0005m^3
Solve each system by graphing.
Answer:
(2,-1)
Step-by-step explanation:
Solved using math.
Answer:
The solution is (2, -1) to show this by graphing do y = -1 by making a straight horizontal line at (0,-1) . And then for the other equation make a line where it starts at (0,4) and passes point (2,-1). Just plot those two points and connect them and you'll have made the line.
Step-by-step explanation:
Both before and after a recent earthquake, surveys were conducted asking voters which of the three candidates they planned on voting for in the upcoming city council election. Has there been a change since the earthquake? Use a level of significance of 0.05. Table shows the results of the survey. Has there been a change in the distribution of voter preferences since the earthquake?
Peter Alan Sui
Before 1838 418 1475
After 1420 329 1140
What is the chi-square test-statistic for this data?
χ2=_____.
Answer:
0.05547
Step-by-step explanation:
Given :
_____Peter __ Alan __ Sui__total
Before 1838 __ 418 ___1475 _3731
After _ 1420 __ 329 ___1140_2889
Total _3258 __ 747 __ 2615 _6620
The expected frequency = (Row total * column total) / N
N = grand total = 6620
Using calculator :
Expected values are :
1836.19 __ 421.006 __ 1473.8
1421.81 ___325.994__ 1141.2
χ² = Σ(Observed - Expected)² / Expected
χ² = (0.00177817 + 0.0214571 + 0.000974852 + 0.00229642 + 0.0277108 + 0.00125897)
χ² = 0.05547
To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used
Answer:
Cluster Sampling
Step-by-step explanation:
Cluster Sampling involves the random sampling of observation or subjects, which are subsets of a population. Cluster analysis involves the initial division of population subjects into a number of groups called clusters . From the divided groups or clusters , a number of groups is then selected and it's elements sampled randomly. In the scenario above, the divison of the population into towns where each town is a cluster. Then, the selected clusters (12) which are randomly chosen are analysed.
I are these orders pairs a function
х,у
0,9
2,8.
4,7
6,6
8,5
10,4
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Answer:
yes
Step-by-step explanation:
No x-value is repeated, so these ordered pairs do represent a function.
An adult can lose or gain two pounds of water ina course of a day. Assume that the changes in water weight isuniformly distributed between minus two and plus two pounds in aday. What is the standard deviation of your weight over a day?
Answer:
The standard deviation of your weight over a day is of 1.1547 pounds.
Step-by-step explanation:
Uniform probability distribution:
An uniform distribution has two bounds, a and b, and the standard deviation is:
[tex]S = \sqrt{\frac{(b-a)^2}{12}}[/tex]
Assume that the changes in water weight is uniformly distributed between minus two and plus two pounds in a day.
This means that [tex]a = -2, b = 2[/tex]
What is the standard deviation of your weight over a day?
[tex]S = \sqrt{\frac{(2 - (-2))^2}{12}} = \sqrt{\frac{4^2}{12}} = \sqrt{\frac{16}{12}} = 1.1547[/tex]
The standard deviation of your weight over a day is of 1.1547 pounds.
Please help quicklyyy!!!
Answer:
Its the 3 one
Step-by-step explanation:
f(x) = - 2x
g(x) = 8x^2 - 5x + 7
Find (f • g)(x).
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Answer:
(f•g)(x) = -16x^3 +10x^2 -14x
Step-by-step explanation:
(f•g)(x) = f(x)•g(x) = (-2x)(8x^2 -5x +7)
Use the distributive property:
(f•g)(x) = -16x^3 +10x^2 -14x
2. What is the length of AB? Round your
answer to the nearest hundredth.
Answer:
The required length of AB is 7.28 units.
I need help to fine the statement that is true
Answer:
option A
Step-by-step explanation:
wx and zy making 90 angle with each other therefore they are perpendicular.
wx and ab making 0 angle with each other therefore they are parallel
Which expression is equivalent to (3 squared) Superscript negative 2?
Answer:
–81
Step-by-step explanation:
Which equation is represented by the graph?
Answer:
I don't knowledge bro sorry
Four people share a taxi to the airport the fare was $36 and they gave the driver a tip equal to 25% of the fair. If they equally share the cost of the fair tip, how How much did each person pay?
Answer:
$11.25
Step-by-step explanation:
Total money given to the taxi driver=36+25% of 36=45
Each person will pay (45/4)=11.25
A square steel bar has a length of 5.1 ft and a 2.7 in by 2.7 in cross section and is subjected to axial tension. The final length is 5.10295 ft . The final side length is 2.69953 in . What is Poisson's ratio for the material
Answer:
The Poisson's ratio for the material is 0.0134.
Step-by-step explanation:
The Poisson's ratio ([tex]\nu[/tex]), no unit, is the ratio of transversal strain ([tex]\epsilon_{t}[/tex]), in inches, to axial strain ([tex]\epsilon_{a}[/tex]), in inches:
[tex]\nu = -\frac{\epsilon_{t}}{\epsilon_{a}}[/tex] (1)
[tex]\epsilon_{a} = l_{a,f}-l_{a,o}[/tex] (2)
[tex]\epsilon_{t} = l_{t,f}-l_{t,o}[/tex] (3)
Where:
[tex]l_{a,o}[/tex] - Initial axial length, in inches.
[tex]l_{a,f}[/tex] - Final axial length, in inches.
[tex]l_{t,o}[/tex] - Initial transversal length, in inches.
[tex]l_{t,f}[/tex] - Final transversal length, in inches.
If we know that [tex]l_{a,o} = 61.2\,in[/tex], [tex]l_{a,f} = 61.235\,in[/tex], [tex]l_{t,o} = 2.7\,in[/tex] and [tex]l_{t,f} = 2.69953\,in[/tex], then the Poisson's ratio is:
[tex]\epsilon_{a} = 61.235\,in - 61.2\,in[/tex]
[tex]\epsilon_{a} = 0.035\,in[/tex]
[tex]\epsilon_{t} = 2.69953\,in - 2.7\,in[/tex]
[tex]\epsilon_{t} = -4.7\times 10^{-4}\,in[/tex]
[tex]\nu = - \frac{(-4.7\times 10^{-4}\,in)}{0.035\,in}[/tex]
[tex]\nu = 0.0134[/tex]
The Poisson's ratio for the material is 0.0134.
Please help! Thank you!!!!!
9514 1404 393
Answer:
f(x) = x² -3g(x) = 6x +7h(x) = 3^xStep-by-step explanation:
f(x) is copied from the problem statement.
g(x) is a symbolic representation of the English wording, using x to represent "a number."
h(x) is the exponential function that corresponds to the geometric sequence in the table. It has a common ratio of 3, and a multiplier of 1 at x=0.
solve the inequality y-6>/2y-4
Answer:
Step-by-step explanation:
Let's solve your inequality step-by-step.
y - 6 > 2y - 4
y - 2y > -4 + 6
-y > 2
now divide by -1 and inequality sign changes
-y/-1 < 2/-1
y < -2
What lines are parallel?
One number is eight less than a second number. Five times the first is 6 more than 6 times the second. Find the numbers.
The value of the first number is -
Answer:
-42/11
Step-by-step explanation:
x = y - 8
5x = 6 - 6y
So now solve the system of equations, divide everything in the second equation by 5 to get it to x = 6/5 - 6y/5
Now...
x = y - 8
x = 6/5 - 6y/5
Now substitute first equation into the second and x is gonna be -42/11 or the first number
Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the length of each of the equal piece of yarn. Since they are 4 equal pieces of yarn, then the total length of the equal pieces of yarn = 4x.
Also, besides cutting the 4 equal pieces of yarn Julie further cuts a yarn 7.75 inches long, therefore if y represent the total length of all the yarn that she ends up cutting, hence:
y = 4x + 7.75
Since the graph produced by this equation have all points connected to each other, hence this is a continuous graph.
If p is true and ~ q is false, then p ~ q is _____ false.
a. sometimes
b. always
c. never
What is the equation of a line that passes through the point (8,-2) and is parallel to the line whose equation is 3x+4y=15?
Answer:
y = -3x/4 + 4
Step-by-step explanation:
slope m = -3/4
-2=(-3/4)×8+b
or, b = 4
y = mx + b
y = -3x/4 + 4
Answered by GAUTHMATH
You take out a 60-day loan for $5000. At the end of the loan, you owe $73.97 in interest. What is the annual percentage rate? Round your answer to the nearest tenth of a percent.
The PERCENTAGE ANNUAL RATE is 9.0% to the nearest tenth using the SIMPLE INTEREST FORMULA
The question is related to a SIMPLE INTEREST problem:
Loan period = 60 days
using 365 days a year ;
converting to years , 60 days = (60 / 365) years
interest on loan = 73.97
principal = 5000
Using the formula:
interest = (principal * rate * time)
73.79 = (5000 * rate * (60/365)
Rate = 73.79/(5000 * (60/365)) =8.977%
rate = 9%
Therefore, PERCENTAGE ANNUAL RATE is 9.0%
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