The required coordinates of E are (2 + 2 √(13), -2) and the coordinates of M are (-4, 2 + 2 √(13)).
What is the midpoint?The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by the formula (x₁ + x₂)/2, (y₁ + y₂)/2.
Since G and O are the midpoints of the sides of square GEOM, the length of each side of the square is the distance between G and O. The distance between the two points can be calculated using the distance formula:
distance = √((x₁ - x₂)² + (y₁ - y₂)²)
Plugging in the coordinates of G and O, we get:
distance = √((-4 - 2)²+ (2 - (-2))²)
distance = √(6² + 4²)
distance = √(36 + 16)
distance = √(52)
distance = 2 √(13)
Thus, the length of each side of the square is 2 √(13).
To find the coordinates of E, we need to move 2 √(13) units to the right of G. Therefore, the coordinates of E are (2 + 2 √(13), -2).
To find the coordinates of M, we need to move 2 √(13) units above O. Therefore, the coordinates of M are (-4, 2 + 2 √(13)).
So the coordinates of E are (2 + 2 √(13), -2) and the coordinates of M are (-4, 2 + 2 √(13)).
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Calculate the equivalent ratio 1.25 : 3.75 : 7.5
The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.
To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.
By multiplying each number in the ratio by 4, we get:
1.25 * 4 = 5
3.75 * 4 = 15
7.5 * 4 = 30
So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.
This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.
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3. Study Hours (Based on Exercise 8.7) Babcock and Marks (2010) reviewed survey data from 2003–2005 and obtained an average of µ = 14 hours per week spent studying by full-time students at 4-year colleges in the United States. To determine whether this average changed over the 10 subsequent years, a researcher selected a sample of = 64 of college students. The data file hours.csv has data consistent with what the researcher found. In this question, you will use the data to if this sample indicates a significant change in the number of hours spent studying.
a. Which of the following are the hypotheses to test if this sample indicates a significant change in the average number of hours spent studying?
i. 0: µ = 14 and 1: µ < 14
ii. 0: µ = 14 and 1: µ ≠ 14
iii. 0: µ = 14 and 1: µ > 14
The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:
0: µ = 14 (null hypothesis)
1: µ ≠ 14 (alternative hypothesis)
Option B is the correct answer.
We have,
The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,
while the alternative hypothesis states that it is different from 14 hours per week.
By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.
Thus,
The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:
0: µ = 14 (null hypothesis)
1: µ ≠ 14 (alternative hypothesis)
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Select ALL of the expressions that are equivalent to 4√5.
A. 2√20
B. 6^1/2-5^1/2
c. 3*5^1/2+5^1/2
D.4*5^1/2
E.2√10
F.3*5^1/2
Answer:
A, C, D
All 3 of those simplfiy to 4√5
4) Ellen deposited $2,500 into a savings account
that earns 5% interest per year. Her friend's
bank offers a 6 1/2% annual interest rate. How
much more money would Ellen's money have
earned in one year if she had deposited her
money at her friend's bank?
A) $12.50
B) $32.50
C) $16.25
D) $37.50
Answer:
c
Step-by-step explanation:
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let ^ p denote the proportion in the sample who say they support the increase. Suppose that 34% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is
Answer:
The standard deviation of the sampling distribution is 0.0122 = 1.22%
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)
A survey asks a random sample of 1500 adults in Ohio
This means that \(n = 1500\)
34% of all adults in Ohio support the increase.
This means that \(p = 0.34\)
The standard deviation of the sampling distribution is
\(s = \sqrt{\frac{0.34*0.66}{1500}} = 0.0122\)
The standard deviation of the sampling distribution is 0.0122 = 1.22%
A pizzeria makes 7 pepperoni pizzas for every 3 cheese pizzas. Yesterday they made 42 pepperoni pizzas. How many cheese pizzas were made?
Answer:
18 cheese pizza's
Step-by-step explanation:
3-7
6*7=42 pepperoni pizza's
3*6=18 cheese pizzas
Ellie the elephant has some peanuts. She eats up 49 peanuts. Now Ellie the elephant has 31 peanuts. How many peanuts did she have before?
Answer:
80
Step-by-step explanation:
do: 49+31=Your answer
Ellie had 80 peanuts before she ate 49 of them.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of peanuts Ellie had before she ate 49 of them.
After eating 49 peanuts, Ellie has 31 peanuts left, so we can write an equation:
x - 49 = 31
To solve for x, we add 49 to both sides of the equation:
x - 49 + 49 = 31 + 49
Simplifying, we get:
x = 80
Therefore, Ellie had 80 peanuts before she ate 49 of them.
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A box contains 50 blue, red and green balls, if 20%are blue and 50% are green, what are the number of red balls?
Answer:
15 - red
Step-by-step explanation:
20/100 × 50 = 10 blue
50/100 × 50 = 25 green
25 + 10 = 35
50 - 35 = 15
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floor of a classroom is 38 feet in length and 34 feet in width. A scale drawing of the floor has a length of 19 inches.
Answer:
38 i think i hope this helps
What is the best description of originality?
nonobvious
special or interesting
convergent
having a low probability, unique
Originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.
Originality refers to the quality of being unique, new, and innovative. It involves creating something that has not been seen or experienced before. The best description of originality is that it is having a low probability and being unique.
An original idea, product, or work of art is something that has not been copied or imitated from others. It represents a new perspective or approach that can offer a fresh insight into a problem or challenge. Originality requires a high level of creativity, imagination, and inspiration, as well as a willingness to take risks and explore new possibilities.
Nonobviousness is also an important factor in originality. It means that the idea or invention is not something that would be obvious to someone skilled in the same field or industry. In other words, an original idea should not be something that could be easily predicted or anticipated.
Special or interesting are also characteristics of originality, but they are not sufficient to define it. An idea or product can be special or interesting without being truly original. For example, a new flavor of ice cream may be interesting, but it may not be original if it has already been created by someone else.
Convergent thinking, on the other hand, involves finding a single solution to a problem. It is the opposite of divergent thinking, which involves generating multiple ideas and possibilities. Convergent thinking is important for finding effective solutions to problems, but it is not the same as originality.
In conclusion, originality is the quality of being unique, new, and innovative. It requires creativity, imagination, inspiration, and nonobviousness. Special or interesting aspects may be present, but they are not sufficient to define originality.
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OMG PLS HELP ME!!!! 30 pts!!!!! I NEED DIS ASAP
A large downtown hotel consists of twenty-four levels. Any level above ground is referred to as a" floor". There are twenty-two floors and each floor corresponds to its number on the number line (2 is second floor, 3 is third floor, etc...) and two underground levels reserved for underground parking. The first level below ground level is Parking A, and the second level below ground level is labeled Parking B.
If you start at Parking B and take the elevator to the fourteenth floor, how many levels have you gone up? [Type your answer as a number.]
Answer:
16
Step-by-step explanation:
there is 2 underground and 14 above so 2 + 14 = 16
I need help in this problem
Step-by-step explanation:
this is first an arithmetic sequence with the first term A1=3(1)+1=4 And the 12th term A12=3(12)+1=37. Then use this formula
S12=12/2 ×(4+37)
=6×41
=246
If you buy a meal from a restaurant that costs $15.00, and the tax is 7%, how much do you pay in taxes? explain pls
Answer: He pays $1.05 in tax
Step-by-step explanation: You multiply 7% by 15.00 (15.00 x 7%) and then you get your tax. If it asks how much the cost is plus tax, you just add the number you got by multiplying 15 by 7 and to the original price, $15.00.
I need help with this question
please help: perimeter of polygon ABCDEF
Answer:
Step-by-step explanation:
what's the answer! Consider having a personal loan that spans 5 years. The loan was only taken out for $6000, but the interest rate was a higher fixed percentage of 5.99%. How much interest will you have paid after it is paid off?
Answer: $179.70
Step-by-step explanation:
The simple interest will be:
= (Principal × Rate × Time) / 100
= ($6000 × 5.99% × 5) / 10
= ($6000 × 0.0599 × 5) / 10
= $1797 / 10
= $179.70
Therefore, the total interest on the loan is $179.70
which function is best represented by this graph
Answer:
Step-by-step explanation:
e
Identify the graph of the inequality 2(2x-1)+7< 13 or -2x+5-10.
From the resulting solution, the correct linear inequality graph is Graph C.
Solving inequality expressionGiven the inequality equation below:
2(2x-1)+7< 13 or -2x+5 ≤ -10.
Simplify the expression
2(2x-1)+7< 13
Expand
4x - 2 + 7 < 13
4x + 5 < 13
4x < 13 - 5
4x < 8
x < 2
For the inequality -2x+5 ≤ -10.
-2x+5 ≤ -10
-2x ≤ -15
x ≥ 7.5
Hence the solution to the given system of inequalities are x < 2 and x ≥ 7.5
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[3r-15] if r is less than 5
When r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.
The expression [3r-15] represents an algebraic expression that depends on the value of r. The condition given is that r is less than 5. To evaluate this expression, we substitute the value of r into the expression and simplify it.
Given that r is less than 5, let's substitute r = 4 into the expression:
[3(4) - 15]
= [12 - 15]
= -3
Therefore, when r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.
It's important to note that this answer is specific to the given condition that r is less than 5. If the condition changes or if r is greater than or equal to 5, the result of the expression may be different.
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What is the ratio of x to y?
5x = 6y
Answer:
6:5
Step-by-step explanation:
Divide both sides by y . ⇒5xy=6y y. ⇒5xy=6. Divide both sides by 5 . ⇒5 x5 y=65. ⇒xy=65. ⇒x:y=6:5.
The ratio between x and y, when 5x = 6y, is 6:5.
Given is an equation 5x = 6y, we need to find the ratio between x and y,
To determine the ratio of x to y in the equation 5x = 6y, we need to isolate one of the variables and express it in terms of the other.
Let's isolate x:
5x = 6y
Divide both sides of the equation by 5:
x = (6y) / 5
Now we have an expression for x in terms of y. The ratio of x to y can be represented as:
x/y = (6y) / (5y)
The y terms cancel out:
x/y = 6/5
Therefore, the ratio of x to y is 6:5.
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6lbs of apples for 33.60
Answer:
If that's the whole question then what exactly are we trying to solve here?
Step-by-step explanation:
help w 16 please. i will mark u brainliest
Answer:
The answer is C.
Hope I helped!
Is the relation shown in the table below a function? (type in yes or no)
Answer:
Yes
Step-by-step explanation:
To know if a table is a function or not, we have to see if 1 input only has 1 output.
Looking at the table each input only has 1 output, so it is a function.
I need help with this one
Answer:
-12
Step-by-step explanation:
Glenn’s favorite number is very special because it reminds him of the day his daughter, Sarah, was born. The factors of this number do not repeat, and all of the prime numbers are less than . What is Glenn’s number? When was Sarah born? BRAINLIEST AND POINTS
Answer:
2/3/10
Step-by-step explanation:
the number is such that its factors do not repeat and factors are all prime numbers less than 12.
CAN SOMEONE HELP WITH THIS QUESTION✨
Answer:
m = √3 ≈ 1.7321b = 1 -π√3/6 ≈ 0.0931Step-by-step explanation:
You want the slope-intercept form equation for the tangent line at point (π/6, 1) on the curve y = 2·sin(x).
SlopeThe slope of the line at the point of tangency is the derivative of the curve at that point:
y' = 2cos(x) = 2·cos(π/6) = 2(√3/2)
m = √3 . . . . . approximately 1.7321
Y-interceptSolving the line's equation for b, we have ...
y = mx +b
b = y -mx = 1 -(√3)(π/6)
b = 1 -π√3/6 . . . . . approximately 0.0931
EquationThe equation of the line is ...
y = mx +b
y = (√3)x +1 -(π√3)/6
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
How much water should be added to 14mL of 9% alcohol solution to reduce the concentration to 7%? We should add mL.
The water that should be added to 14mL of 9% alcohol solution to reduce the concentration to 7% is 4ml.
How much more water must be added to reduce a concentration?Here; In this problem we have a concentration problem, represented by the volume of the solvent divided by the volume of the entire solution. The initial and final concentrations of the solutions are presented in the following formulas;
Given;
14mL of 9% alcohol solution.
Initial concentration;
9/ 100 = x / 14
x = 63/50
Final concentration;
7 / 100 = x / (14 + y)
(14 + y)=x*100/7
y=18-14
y=4
Therefore, water must be added to reduce the concentration will be 4ml.
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In the 2012 Olympics a U.S. athlete Nathan Adrian finished the 100-meter freestyle swim in 47.52 seconds. If nathan swam the same pace in a regular 25-meter pool what would his time have been per lap?
At the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.
To solve this problem
The idea of proportionality can be applied. The time it would take Nathan Adrian to complete one lap in a 25-meter pool is known to be 47.52 seconds for the 100-meter freestyle. Since the tempo is constant while the distance varies, we can establish a ratio:
100 meters / 47.52 seconds = 25 meters / x seconds
where x is the unknown time for one lap in the 25-meter pool.
To solve for x, we can cross-multiply:
100 meters * x seconds = 47.52 seconds * 25 meters
100x = 1188
Dividing both sides by 100, we get:
x = 11.88 seconds
Therefore, at the same rate as his 100-meter freestyle swim in the 2012 Olympics, Nathan Adrian could have completed one loop of a 25-meter pool in 11.88 seconds.
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Evaluate
Check all that apply.
2
5
O The exponent is
O The expanded form is
The expanded form is 2x2x2
5
6
15
8
125
Answer:
a b and e
Step-by-step explanation:
hope this helps
Answer:
it b and e
Step-by-step explanation:
rrrrrrrrrrrrrrr