The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Consequently, it follows that the greatest possible quotient as required is; 25.
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Marvin used the money he received from high school graduation gifts to start a new savings account with a simple interest rate of 7. 5%. After 12 years, the account had earned $288. If there were no other deposits or withdrawals, what was the original amount placed in the account?
The original amount placed in the account is $320.
What is simple interest ?
Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.
The simplest way to compute interest is as a percentage of the principal. For instance, if you borrow $100 from a friend and agree to pay back the money with 5% interest, the interest you would have to pay would simply be 5% of $100, or $5.
Simple Interest is the amount repaid for using the borrowed funds over a predetermined amount of time.
The interest earned is calculated as follows:
I = P*r*t
Where:
I = Interest
P = initial principal balance
r = interest rate
t = time
Marvin is saving money in a savings account with a simple interest rate of r=7.5%=0.075. It's known that after t=12 years, the account had earned $288 interest.
Substituting in the formula:
288 = P*0.075*12
Calculating:
288 = 0.9P
Dividing by 0.9:
P = $320
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Find the surface area of the square pyramid.
A drawing of a square pyramid. The sides of the base are 5 centimeters and the height of the triangular faces is 5 centimeters.
Answer:
add the 5+5 =10
Step-by-step explanation:
5+5=10
hope that helps
Acellus Geometry Question in picture
Pls help me with this question plssss
The average rate of the given function is 2.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given function is h(x)=-x²-x+5 and the interval is -6≤x≤2.
x={-6, -5, -4, -3, -2, -1, 0, 1, 2}
y=-x²-x+5
When x=-2
y=-(-2)²-(-2)+5
y=-4+4+5
y=5
When x=-1
y=-(-1)²-(-1)+5
y=5
When x=0
y=5
When x=1
y=-1-1+5
y=3
When x=2
y=-(2)²-(2)+5
y=-1
Now, rate using (1, 3) and (2, -1), we get
m =(-1-1)/(2-3)
m=2
Therefore, the average rate of the given function is 2.
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*LOOK AT PICTURE*
F) 200.96 feet
G) 602.88 feet
H) 301.44 feet
J) 614.43 feet
Answer:
F 200.96 feet is traveled by the car
Answer:
G) 602.88 feet
Step-by-step explanation:
First find the circumference of the circle:
C = 2πr
If we use 3.14 for pi, we get:
C = 2*3.14(32)
C = 200.96 feet
Because the car takes 3 turns around the circle, multiply the circumference by 3 to find the total distance the car traveled:
200.96*3 = 602.88 feet
8.
Choose the linear inequality that describes each graph.
A. y > – 3x + 5
B. y > – 5x – 3
C. y > – 5x + 3
D. y < – 5x + 3
Answer:
y > -5x + 3
Step-by-step explanation:
Answer:
y > –5x + 3
Step-by-step explanation:
we know that
1) The solution of the inequality is the shaded area above the dashed line
so
The linear inequality could be
y > –5x – 3
y > –5x + 3
y > –3x + 5
2) The slope of the dashed line is negative ----> the three options have slope negative
3) The y-intercept of the dashed line is (0,3)
therefore
The linear inequality is
y > –5x + 3
...............................................................................................................................................
Answer:
Step-by-step explanation:
To find the linear inequality , Let pick two points from the graph
Lets pick (0,3) and (1,-2)
Lets find out slope using the points
Slope m= -5
y intercept b= 3
Equation of the line is y=mx+b
Now we look at the shaded part. we use test point (0,0)
(0,0) is not in the shaded region
0 >3 is false
Does there seem to be a relationship between which type of book her friends like best and the number of books they read this month?
Based on the two-way table, there seems to be a relationship between the type of books Julia's friends like best and the number of books they have read this month, A. Yes, because those who like fiction read one book at a rate four times that of those who read non-fiction books.
What is a two-way table?A two-way table, also called a contingency table, is a statistical table that shows the observed frequency for two variables.
The rows of a two-way table indicate one category and the columns indicate the other category.
For instance, based on the two-way table, one can observe that 80% of Julia's friends prefer fiction while 20% prefer non-fiction.
Among those who read 1 book this month, 80% read fiction against 20% who read non-fiction. Similarly, among those who read 2 books this month, the same 80% read fiction against 20% who read non-fiction.
The number of students who prefer fiction = 60
The number of students who prefer non-fiction = 15
The number of fiction-preferring students who read 1 book this month = 40, which is 80% of the total (40/50 x 100).
The number of fiction-preferring students who read 2 books this month = 20, which is 80% of the total (20/25 x 100).
Thus, we can conclude that Option A is correct.
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Question Completion:The Two-way Table:
Read 1 book Read 2 books Total
Prefer fiction books 40 20 60
Prefer non-fiction books 10 5 15
Total 50 25 75
Ava has a large-screen TV. The TV has a screen with a 51-inch diagonal and a width of 45 in. The base of the TV is 4 in. from the bottom of the screen. 45 in. h in. 51 in 4 in. what is the total height,h,in inches, of the TV?
Answer: Height: 24.9 inch, Width: 44.3 inch
Step-by-step explanation:
The total height of the TV is given by H = 28 inches
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , We can use the Pythagorean theorem to find the height of the TV. Let h be the height of the screen in inches. Then, we have:
h² + 45² = 51²
Simplifying and solving for h:
h² = 51² - 45²
h² = 2601 - 2025
h² = 576
Taking square roots on both sides , we get
h = √(576)
h = 24 inches
Therefore, the height of the screen is 24 inches.
To find the total height of the TV, we need to add the 4 inches from the base to the height of the screen:
Total height of the TV , H = 24 + 4
Total height of the TV , H = 28 inches
Hence , the total height of the TV is 28 inches.
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The complete question is attached below :
Ava has a large-screen TV. The TV has a screen with a 51-inch diagonal and a width of 45 in. The base of the TV is 4 in. from the bottom of the screen. what is the total height,h,in inches, of the TV?
The local store sells small pieces of candy for $0.15 each. Shondra spent
$18.00 on this candy for her class party. The equation below can be used to
determine how many pieces of candy, c, that Shondra bought.
0.15 c = 18.00
How many pieces of candy did Shondra buy for the class party?
Answer:
120 pieces of candy
Step-by-step explanation:
To find c, you need to divide your know values, 18.00 and .15. So 18/.15 = 120.
Shondra bought 120 pieces of candy.
do these form a proportion? please help me!!!
Answer:
yes they do
Step-by-step explanation:
both equal 1/3
8/24 = 1/3
5/15 = 1/3
1/3 = 1/3
Answer:
No, the ratios won't
Step-by-step explanation:
8/25 and 5/15.
they have Similarities, but no proportions.
have a good day!
A steep mountain is inclined 72 degree to the horizontal and rises 4500 ft above the surrounding plain. A cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 900 ft from the base of the mountain. Find the shortest length of cable needed.
Answer:
[tex]l_c=5078.27ft[/tex]
Step-by-step explanation:
From the question we are told that:
Angle of inclination [tex]\angle=72 \textdegree[/tex]
Height [tex]h=4500ft[/tex]
Distance b\w cable base and mountain base [tex]d_{cm}=900ft[/tex]
Generally the equation for length of mountain base [tex]d_{mb}[/tex] is mathematically given by
[tex]Tan\theta=\frac{h}{d_{mb}}[/tex]
[tex]d_{mb}=\frac{h}{Tan\theta}[/tex]
[tex]d_{mb}=\frac{4500}{Tan 72 \textdegree}[/tex]
[tex]d_{mb}=1462.11ft[/tex]
Generally the Pythagoras equation for length of the cable [tex]l_c[/tex] is mathematically given by
[tex]l_c^2=h^2+(d_{mb}+d_{cm}^2)[/tex]
[tex]l_c^2=4500^2+(1462.11}+900}^2)[/tex]
[tex]l_c=5078.27ft[/tex]
calculate the sum of the interior angles of the following polygon 6 sided 15 sided and 3 sided
Answer:
720°, 2340°, 180°
Step-by-step explanation:
Look at the attached image of a regular hexagon. I drew all possible lines from a vertex to other vertices (AC, AD, AE). Drawing in all those diagonals splits the hexagon into 4 triangles, and adding up the measures of all the triangle angles would account for all the interior angles of the hexagon.
♦ Four triangles have an angle sum of 180° x 4 = 720° (180° in each triangle).
See attached image2 to see what happens in an octagon. There are six triangles formed, so the total of all interior angle measures is 6 x 180° = 1080°.
What about a 15-sided regular polygon? How many triangles would be formed by putting in all the diagonals coming from one vertex? There will be 2 fewer triangles than the number of vertices, 13.
♦ The total of interior angle measures in a 15-gon is 13(180°) = 2340°
♦ A polygon with 3 sides is a single triangle; interior angle sum = 180°
assume for a given studey that the null hypothesis asserts that the expected value of a phenomenon is 100
In a given study that the null hypothesis asserts the expected value of a phenomenon is 100 resulting in a 95% confidence interval reported as [98.76, 105.24], then we fail to reject the null hypothesis.
Therefore the answer is d) Fail to reject the null hypothesis.
A 95% confidence interval is a range of values that there is a 95% chance that the true value of a population parameter falls within. In this case, the 95% confidence interval is [98.76, 105.24], which includes the expected value of 100 that is stated in the null hypothesis.
Therefore, we fail to reject the null hypothesis because the data does not provide sufficient evidence to suggest that the true value of the population parameter is different from what is stated in the null hypothesis.
It's worth to mention that, Failing to reject the null hypothesis doesn't mean accepting it, it means that we don't have enough evidence to say that the parameter is different from the null hypothesis, it could be due the sample size, or other factors.
--The question is incomplete, complete question is as follows--
"Assume for a given study that the null hypothesis asserts the expected value of a phenomenon is 100. A research study results in a 95% confidence interval reported as [98.76, 105.24]. What decision would you make based on this confidence interval?
a) A decision cannot be made on a confidence interval; a hypothesis test is required.
b) Retain the null hypothesis.
c) Reject the null hypothesis.
d) Fail to reject the null hypothesis."
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A graphical device used for enumerating sample points in a multiple-step experiment is a a. bar chart b. pie chart c. histogram d. None of the other answers is correct.
None of the listed methods are used for enumerating sample points in a multiple-step experiment. So, option D is the correct answer.
Graphical methods are important mathematical tools that are very helpful when it comes to managing a vast amount of data. These also help when we need to visually represent data. These methods help quite a lot since they make it easier to keep track of data and understand it as well.
A bar chart and a histogram are similar tools that are used to represent data by plotting them as rectangular bars. These can be either vertical or horizontal. A pie chart is also a tool that uses a shape for data visualization. In its case, it represents data in the shape of a circle and all categories/data sets have their slices. So, this means that these three are not methods that can be used for enumerating sample points in a multiple-step experiment. Hence, option D is the correct option.
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Theoretically if you roll a number cube 36 times how many times would you expect to roll the number one?
Answer:
6
Step-by-step explanation:
Since its theoretical, i believe itll be 1/6 x 36 which is 6 times.
hope I helped :)
Answer:
If you were to roll the cube 36 times, theoretically, you would expect that number 1 will be rolled 6 times.
Step-by-step explanation:
The probability of getting a 1 after rolling the number cube is equal to [tex]\frac{1}{6}[/tex]. Now we just multiply the probability by the number of rolls and get...
[tex](\frac{1}{6})(36) = 6[/tex]
Therefore, if we were to roll the cube 36 times, theoretically we would expect that number 1 will be rolled 6 times.
What is the value of the expression below? 2³(3³ – 6) +4 A. 214 B. 172 C. 28 D. 200
Answer:
The answer is C. 28
Im 96% sure
4. The probability that a student is in a category can be approximated by the relative frequency. To the nearest hundredth, what is the probability that a randomly selected student is a girl who wants to go skating?
Ash and her 2 friends went to dinner. If the bill was $124.72, and they left an 18% tip, how much did each person pay
Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.
Which percentage is it?A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Amount of bill = $124.72
and tip they left = 18% of $124.72
total amount is =$124.72 + $124.72*18%=$147.1696
so, each person pay= $147.1696/3=$49.056
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pllzzzzzzzzzzzzzzzzz help
that would be 33 square feet!!!
HELP PLEASE!! there is a .03 chance that Kelly will win the raffle at school. What is the probability that Kellie will not win the raffle?
Answer:
Fraction: 97/100
Decimal: 0.97
Percentage: 97%
Step-by-step explanation:
Hope this helped.
97% you just need to substract
PLEASE HELP ME WITH THIS ILL BRAINLIEST YOU
please help I’m stuck !!!
Answer:
D) 4
Step-by-step explanation:
Take the square root of Miriam's starting bacteria to get your answer [tex](\sqrt{16})[/tex]because the exponent in Jessica's equation is the square of Miriam's.
-2x < -6
Hi, can someone please explain this question?
The answer is x > 3 but I do not know how.
Please explain
Answer:
x > 3
Step-by-step explanation:
This is based on the concept 'when a negative number is multiplied to both sides of the inequality, the sign gets reversed. For example, x > - 2 when it is multiplied by - 1, it becomes - x < 2.'
*only when the number is -ve.
Similarly, in this question, multiply both sides by - 1.
2x > 6
x > 6/2
x > 3
For more : take - 5 > - 2, as you know
Note that 5 is actually greater than 2. To make this true we change signs
Josh has 27 signed baseballs. He places the baseballs equally on 3 shelves. How many baseballs are on each shelf?
Answer:
9
Step-by-step explanation:
27 divided by 3 equal 9
Math help????????????
5 3/8- 4 1/15 thank you if you can help I need a solution
Here is your Answer !!!
HOPE IT HELPS :)
Answer:
1 37/120
Step-by-step explanation:
heyy! i’ll give brainliest please help
Answer:
democratic leader i think im not sure tho
Answer:
an absolute dictator
Step-by-step explanation:
Solve the proportion: Men 45 : ? Women 50 : 10
Answer:
The answer to the proportion is 45:25.
Step-by-step explanation:
To solve this proportion, we can use cross multiplication. That is, we can multiply the numerator of the first ratio (45) by the denominator of the second ratio (10) and the numerator of the second ratio (50) by the denominator of the first ratio (?). This will give us
45 x 10 = 500 and 50 x ? = 500.
If we divide both sides of the equation by 50, we get
? = 25.
Therefore, the answer to the proportion is 45:25.
I want to solve the math problem
Answer:
Here are a few of the factor pairs. The rest you can find in the pdf below.
(-3/4)x + 25 = (1/8)x - 3
Find x and show your work
No links please!
Step one =
-3/4x + 25 -1/8x = 1/8x = 1/8x -3 - 1/8x
-7/8x + 25 = -3
Step two =
-7/8x + 25 - 25 = -3 - 25
-7/8x = -28
Step three =
(8/-7) * (-7/8x) = (8/-7) * (-28)
Answer
X = 32