Okay, so first, we find a number that is between 0 and 1.
A number that qualifies for that condition would be ½.
A property of exponents is x^(n/m) = √x m sqrt(x^n), so x^(1/2) = √x
Therefore, such expression is:
x^(1/2) = 4
Where you now solve for x.
Exponential notation is a common language that is
needed in order to communicate mathematical ideas efficiently and clearly.
Efficiently written repeated multiplication was the reason that this notation was
developed.
An example of this is the division of cells that causes growth to occur in
living organisms. A single type of cell is divided 2 times in an hour,
therefore in 12 hours, the cell will divide into 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2
• 2 • 2 • 2 • 2 time, or as efficiently written, 2^12.
A person in the audience of a game show has a 12% chance of winning free movie tickets. What is the chance that a person in the audience does not win free movie tickets? 24% 38% 72% 88%
A wire that is 22 feet long connects the top of a pole to the ground. The wire is attached to the ground at a point that is 10 feet from the base of the pole.
What is the height of the pole? Round to the nearest hundredth.
12.00 feet
19.60 feet
24.17 feet
38.40 feet
Solution:
Length of wire = 22 feet =AB
Distance between the point where wire is attached to the ground from the point on the ground where pole is fixed= 10 feet=OB
In Right Δ O A B
By Using pythagoras theorem
O A² + OB² = AB²
O A² +10²= 22²
O A²= 484 - 100
O A²= 384
O A= √384= 19.60 (Approximately)
So, the height of pole to nearest hundredth = 19.60 feet
The height of the pole is 19.60 ft
The situation forms a right angle triangle.
Right angle triangleRight angle triangle have one of its sides as 90 degree.
The length of the wire is the hypotenuse of the triangle formed.
The distance of the wire attached to the ground to the base of the pole is the adjacent side of the triangle.
The height of the pole can be found using Pythagoras theorem.
c² = a² + b²
22² - 10² = b²
b² = 484 - 100
b = √384
b = 19.5959179423
b = 19.60 ft
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A juice company did a survey among 100 customers to find their juice preferences. The customers were asked about their preferences for apple or orange juices. Out of the total 35 people who liked apple juice, eight liked orange juice also. There were 20 people who liked orange juice. Part A: Summarize the data by writing the values that the alphabets A to I in the table below represent. (5 points) Like apple juice Do not like apple juice Total Like orange juice A B C Do not like orange juice D E F Total G H I Part B: What percentage of the total people did not like either apple or orange juice? (3 points) Part C: Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer. (2 points)A juice company did a survey among 100 customers to find their juice preferences. The customers were asked about their preferences for apple or orange juices. Out of the total 35 people who liked apple juice, eight liked orange juice also. There were 20 people who liked orange juice. Part A: Summarize the data by writing the values that the alphabets A to I in the table below represent. (5 points) Like apple juice Do not like apple juice Total Like orange juice A B C Do not like orange juice D E F Total G H I Part B: What percentage of the total people did not like either apple or orange juice? (3 points) Part C: Do the people surveyed have more dislike for apple juice than orange juice? Justify your answer. (2 points)
Part A:(This table is a three by three table, with the first top two sections being liked apple juice and didn't like apple juice, and the first left two sections being liked orange juice and didn't like orange juice. The end sections are totals.)
Answer:
Part A: A = 8
B = 20
C = 28
D = 35
E = 37
F = 72
G = 43
H = 57
I = 200
Part B: 18.5%
Part C:
D = People who do not like Orange Juice
B = People who do not like Apple Juice
I use the values of B and D because these are the values that represent dislike for that juice, and also because adding them together creates a value for not liking either juice.
D = 35
B = 20
So there is a greater dislike for Orange Juice.
Step-by-step explanation:
a student scores 71 out of 100 on a test, if the maximum score on the tests is also 100, what score does the student need to maintain at least an average of 78?
Chale bought some packages of pens. He bought one package containing 5 pens and *n* packages containing two pens each. Which of the following expressions could be used to find the total number of pens that Chale bought?
A)7n
B)10n
C)5n+2
D)2n+5
Which statement is true about the solutions for the equation 3y + 4 = −2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
Answer:
B, One solution
Step-by-step explanation:
Suppose $16,537.50 in interest was earned after $75,000 was invested at a simple interest rate of 3.15%. How long (in years) was the money invested?
Answer:
7 Years
Step-by-step explanation:
Find the slope and y-intercept of the line. y = 7/5x – 3
Answer:
Slope is [tex]\frac{7}{5}[/tex]
y-intercept is -3
Step-by-step explanation:
Given equation of line,
[tex]y=\frac{7}{5}x-3[/tex]
Since, the slope intercept form of a line is y = mx + c
Where, m is the slope of the line,
By comparing,
[tex]m = \frac{7}{5}[/tex]
Hence, the slope of the given line is [tex]\frac{7}{5}[/tex]
Now, for y-intercept,
x = 0,
[tex]y=\frac{7}{5}(0) - 3 = -3[/tex]
Hence, the y-intercept of the line is -3.
Plzzz help me with part A ,B and C
A) yes they are similar since both use the same angle P, the angle of line PQ is the same as PA and they are both right triangles.
B) Line AB corresponds to QR - they are both the base of their triangles.
C) Angle A corresponds to angle Q. Q is the lower left angle in triangle PQR and angle A is the lower left angle in triangle PAB and are the same degree
1/5 [4(x+2)-(3-x)]=4
Which polynomial is a difference of two squares?
x2 − 16
x2 + 16
x2 − 8
x2 + 8
which expression is equivalent to 6a + 12
6(a+6)
3(3a+9)
6(a+9)
2(3a+6)
what is the square root of 56x^7
In three more years Miguel's grandfather will be six times as old as Miguel was last year. When Miguel's grandfather present age is added to his grandfathers age is added to his grandfathers present age the total is 68. How old is his grandfather now ?
The table shows the ratio of caramel corn to hot pepper corn in a bag. What is the constant of proportionality?
Hot Pepper Corn | Caramel Corn
5_______________8
10 _____________ 16
15______________ 24
classify the following triangle . check all that apply
Answer:
Option (a) and (d) is correct.
The given triangle is obtuse and isosceles.
Step-by-step explanation:
Given : A triangle with measure of one angle is 120° and two legs of the triangle are given equal in length.
We will have to choose the correct classification for the given triangle.
For a triangle if the measure of one the angles is
1) less than 90 then it is acute triangle ,
2) equal to 90 then right triangle
3) greater to 90 then obtuse triangle
Since the measure of one angle of the triangle is 120° > 90° Thus, the given triangle is obtuse.
For a triangle if all the three sides are equal then it is equilateral triangle, if two sides are equal then it is isosceles and if no side is equal then it is scalene.
Since, for the given triangle, the two legs of the triangle are given equal in length so it is an isosceles triangle.
Thus, the given triangle is obtuse and isosceles.
How many times does 6 go into 22
The number 6√3 is between what two integers and is closer to which integer on the number line.
Between 6 & 7 & is closer to 6
Between 10 & 11 & is closer to 10
Between 6 & 7 & is closer to 7
Between 63 & 64 & is closer to 63
Answer: integer on the number line. Between 6 & 7 & is closer to 6 Between 10 & 11 & is closer to 10 Between 6 & 7 & is closer to 7 Between 63 & 64 & is closer to 63.
Step-by-step explanation:
PLEASE HELP ME!!!
What is the simplified form of the quantity 15 x y squared over x squared minus 5x plus 6 all over the quantity 5 x squared y over 2x squared minus 7x plus 3 ?
Answer: [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]
Step-by-step explanation:
Given problem to simplify is [tex]\frac{\frac{15xy^2}{x^2-5x+6} }{\frac{5x^2y}{2x^2-7x+3} } \\\\=\frac{15xy^2}{x^2-5x+6}\cdot\ \frac{2x^2-7x+3} {5x^2y}............\text{(by fractional division property,the denominator invert and its reciprocal multiply to numerator)}\\\\=\frac{15xy^2}{(x-3)(x-2)}\cdot\frac{(x-3)(2x-1)} {5x^2y}.........\ \text{(factorizing quadratic equation)}[/tex]
[tex]=\frac{3y(2x-1)}{x(x-2)}........\text{(cancelling like terms with same degree and coefficients from numerator and denominator)}[/tex]
so the simplified form of the given problem is [tex]\frac{3y(2x-1)}{x(x-2)}[/tex]
ms campbell invested $7200 for 2 1/2 years. if she earned $756, at what rate did she invest her money. using I=PRT and the answer in percent form
Given I=PRT
Rearrange the formula to find R
I / PT= R
756 / (7200 * 2.5) = R
756 / 18000 = R
0.042 = R
so R = 4.2%
If f(x)=2x-4, find f(q+1)
please show your work!
If the function f(x) = 2x-4, the function f(q + 1) = 2q - 2
What is a function?A function is a mathematical equation that shows the relationship between two variables.
Since if f(x)=2x-4, to find f(q+1), we proceed as follows.
Since we have the function f(x) = 2x - 4, and we want to find f(q + 1). To find the function f(q + 1), we substitute x = q + 1 into the equation. so, we have that
f(x) = 2x - 4
When x = q + 1, we have that
f(x) = 2x - 4
f(q + 1) = 2(q + 1) - 4
Expanding the brackets, we have that
f(q + 1) = 2q + 2 - 4
= 2q - 2
So, f(q + 1) = 2q - 2
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Which list has the numbers in order from least to greatest
The price of an item has been reduced by 80%. The original price was $45. What is the price of the item now?
ANSWER FOR 15 POINTS!!
Which number(s) below belong to the solution set of the inequality? Check all that apply. (Meaning tell me all the ones that apply.)
x + 16 > 51
A. 16
B. 35
C. 80
D. 38
E. 55
F. 34
The Tunnel of Fear ride climbs straight up to its peak 50 meters above the ground. Then, it drops 65 meters into an underground tunnel. What is the elevation of the tunnel relative to the ground?
Answer:
-15
Step-by-step explanation:
find the area of triangle qpm. round the answer to the nearest tenth. a. 5.2 square units b. 6.3 square units c. 6.5 square units d. 12.6 square units
We need to solve for the angles of the smaller triangle in order to solve for the angle of the larger triangle which would help us solve the missing measurement of a side.
Given:
51 degrees.
Cut the triangle into two equal sides and it forms a right triangle. All interior angles of a triangle sums up to 180 degrees.
180 – 51 – 90 = 39 degrees
39 degrees * 2 = 78 degrees.
Angle Q is 78 degrees.
In the bigger triangle, 4.3 is the hypotenuse. We need to solve for the measurement of the long leg which is the opposite of the 78 degree angle.
We will use the formula:
Sine theta = opposite / hypotenuse
Sin(78 deg) = opposite / 4.3
Sin(78 deg) * 4.3 = opposite
4.21 = opposite. This is also the height of the triangle.
Area of a triangle = ½ * base * height
A = ½ * 3units * 4.21units
A = 6.315 square units.
A researcher is interested in estimating the average salary of police officers in a large city. She wants to be 99% confident that her estimate is correct. If the standard deviation is $1050, how large a sample is needed to get the desired information and to be accurate within $200?
the length of a rectangle is 3 centimeters greater than its width the perimeter is 24 cm what are the dimensions of the rectangle
convert 72832 ounces' to tons?
What does interior angle A of the polygon in the figure equal? A. 110 B. 150 C. 230 D. 100