The number 0.7 / 8 is given by the fraction 7 / 80 when expressed in its simplest form
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
A fraction in its simplest terms is given as a/b, where a is the numerator and b is the denominator.
Hence:
0.7 / 8 = 7 / 80
The number 0.7 / 8 is given by the fraction 7 / 80 when expressed in its simplest form
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Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.
Answer:
10
Step-by-step explanation:
2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.
The answer will be either 8 or 4 or 0.
What is a riddle?
A riddle is an intentionally framed ambiguous question or statement that requires ingenuity and critical thinking to solve or understand.
In the given riddle, all the two dogs, four horses, one giraffe and a duck are lying on the bed. Three chickens are flying over a chair.
Assumptions:
1) Bed is placed on the ground.
2) Bed and chair considered are of standard type.
case1:
If we consider the legs of only living organisms, the number of legs on the ground at the given instant will be 0.
case2:
If that's not the case, then a typical chair will have four legs, and a standard bed will also have four legs. So a total of 8 legs will be on the ground or floor of the room.
case3:
And if we consider the possibility of the chair being placed on the bed, then the legs of the chair will not touch the ground. So a total of 4 legs will be on the ground or floor of the room.
∴ From different perspectives, the number of legs on the ground will be either 8 or 4 or 0.
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Using the quadratic formula, solve for "t" in
the function: 0= -16t2 + 5t + 104. Keep in
mind that time CANNOT be "negative'!!!
t = 1.1 s
t = 1.9 s
t=2.71 s
t=2.2 s
For the following exercises, find the x- and y-intercepts of the graphs of each function.
28. f(x) = −2| x +1 | + 6
The x- and y-intercepts of the graphs of the function described are; (2,0) and (4,0) respectively.
What are the x- and y-intercepts of the graph of the function?It follows from the task content that the function given is; f(x) = −2| x +1 | + 6.
Since the x- and y-intercepts corresponds to x and y values for which y and x are zero respectively, it follows that;
x -intercept is;
0 = -2(x+1) + 6
2x = -2 +6
2x = 4
x = 4/2 = 2
y-intercept is;
y = -2(0+1) +6
y = 4.
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Find the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2. a. r= 6/1+2 sin theta b. r= 6/1-2 sin theta c. r= 3/ 1- 2 cos theta d. r= 1/3+2 cos theta
The required polar equation of a conic is given be: [tex]r = \frac{6}{1-2sin\Theta }[/tex]. option b is correct.
For a conic we have directrix = 3 and eccentricity = 2
What is polar equation?Polar equation can be identified as of the form of x= a+b.sinФ.
Which contain simple variable along with trigonometric operators.
Here,
Standard polar equation for the conic is given as,
[tex]r=\frac{ep}{1-esin\theta}[/tex]
By putting given values
[tex]r = \frac{6}{1-2sin\Theta }[/tex].
Thus, the required polar equation for the conic is [tex]r = \frac{6}{1-2sin\Theta }[/tex].
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PLEASE HELP!!!!!!!!!!!!!!
Answer:
The first answer is correct:
[tex]\{\frac{1}{3},-3.45,\sqrt{9}\}[/tex]
Step-by-step explanation:
Since [tex]\frac{1}{3}, -3.45, \sqrt{9}=3[/tex] are all rational numbers, the set that contains those numbers is the set of rational numbers.
In the second set, number [tex]\sqrt{37}[/tex] is irrational number since it can not be written as quotient.
Also in the third and fourth set, numbers [tex]\sqrt{44}[/tex] and [tex]\sqrt{2}[/tex] are irrational numbers.
Therefore, the first answer is correct.
What is the circumference of the given circle in terms of л
Answer:
30π in
Step-by-step explanation:
Circumference of a circle = 2πr
Where r is the radius
In the given diagram, the radius is 15 in
2×π×15 in = 30π in
Minerva starts a savings account with $50. The interest on the account balance is compounded annually. The graph below shows the account balance in terms of x ,the number of years since the account was opened.
After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account.
Cannot be determined from the information given.
False
True
Minerva's account balance will be about $100 , it is True and Option A is the correct answer.
What is meaning of Compounded annually ?Compounded Annually means when the interest is given even on the interest accrued from the principal amount . This is done once a year.
It is given that
Principal Amount = $50
From the graph attached in the answer which was missing in the question ,
It can be confirmed that after 12 years
Minerva's account balance should be about $100.
Therefore it is True and Option A is the correct answer.
The graph missing is attached
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If x is inversely proportional to y, then as x decreases, y decreases.
Answer:
Yes
Step-by-step explanation:
Let's assume that x=1/y.
For y=1, x=1
For y=2, x=0.5
For y=4, x=0.25
And so on
In the diagram, JKLM∼EFGH. Find the perimeter of each polygon.
The perimeter of polygon JKLM = 85 units
The perimeter of polygon EFGH = 34 units.
What is the Perimeter of a Polygon?The perimeter of polygon JKLM = JK + KL + LM + JM
The perimeter of polygon EFGH = EF + FG + GH + EH
Find the missing lengths using the similarity theorem:
JK/EF = KL/FG = LM/GH = JM/EH
Plug in the values
20/8 = KL/11 = LM/3 = 30/EH
20/8 = KL/11
KL = (20 × 11)/8 = 27.5
20/8 = LM/3
LM = (20 × 3)/8
LM = 7.5
20/8 = 30/EH
EH = (30 × 8)/20
EH = 12
The perimeter of polygon JKLM = 20 + 27.5 + 7.5 + 30 = 85 units
The perimeter of polygon EFGH = 8 + 11 + 3 + 12 = 34 units.
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Find the number, d, if the sum of five times d and five times five is a
hundred.
The value of d from the given expression is 15
Word problem leading to equationFrom the given statement the sum of five times d and five times five is a
hundred is interpreted as;
5d + 5(5) = 100
5d + 25 = 100
Subtract 25 from both sides
5d = 100 - 25
5d = 75
d =15
Hence the value of d from the given expression is 15
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A farmer has 45 horses and 20 cows.
(i) Write this as a ratio horses : cows.
Give your answer in its simplest form.
Answer: 9 : 4
Step-by-step explanation:
45 : 20
simplify
9 : 4
If the zeros of a quadratic equation are 7 and - 4 , what would be the factors?
Answer:
(x - 7) , (x + 4)
Step-by-step explanation:
given the zeros of a quadratic equation x = a and x = b , then
the corresponding factors are (x - a) and (x - b)
here the zeros are x = 7 and x = - 4 then factors are
(x - 7) and (x - (- 4) ) , that is
(x - 7) and (x + 4)
4. Point P is not on line . Describe the shortest distance from the point to the line
P
8
Answer:
a line that is perpendicular to the line l
Which of the following completes the two-column proof below?
Given: ∠1≅∠2, p⊥r
Prove: q⊥r
Proof:
1. ∠1≅∠2 (Given)
2. p∥q (?)
3. p⊥r (?)
4. q⊥r (?)
The figure shows lines p and q and transversal r. The intersection of line p and transversal r forms four angles, the top right angle is labeled as a right angle, the top left angle is labeled as 1. The intersection of line q and transversal r forms four angles, the bottom right angle is labeled as 2.
2. Converse of corresponding angles theorem.
3. Given
4. Perpendicular transverse theorem
What is the Converse of Corresponding Angles Theorem?According to the converse of corresponding angles theorem, if two corresponding angles are congruent, then the lines cut by the transversal that both angles line on are parallel to each other.
Thus, given that ∠1 ≅ ∠2, lines p and q will be parallel based on the converse of corresponding angles theorem.
We are given that lines p and r are perpendicular to each other, therefore, we can conclude that, based on the perpendicular transverse theorem, q⊥r.
The missing reasons in the proof are:
2. Converse of corresponding angles theorem.
3. Given
4. Perpendicular transverse theorem
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If 3x + 7 =22, what is the value of x
Answer:
x=5
Step-by-step explanation:
solution,
3x+7=22
or,3x=22-7
or,3x=15
or,x=15/3
:×=5
The value of x in the equation 3x + 7 = 22 is x = 5.
To find the value of x in the equation 3x + 7 = 22, we can solve for x as follows:
Subtract 7 from both sides of the equation:
3x + 7 - 7 = 22 - 7
3x = 15
Divide both sides of the equation by 3 to isolate x:
(3x)/3 = 15/3
x = 5
Therefore, the value of x in the equation 3x + 7 = 22 is x = 5.
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An article marked to give 120% profit originally cost $60. what is the marked price?
Evaluate 3 × 5². A. 30 B. 75 C. 150 D. 225
Answer:
B: 75
Step-by-step explanation:
5^2 is 5 times itself twice, so 5 times 5 = 25
3 times 25 is 75
Answer:
Hello! The answer to your question is B. 75.
Step-by-step explanation:
To solve this question, you have to first convert the exponents:
[tex]5^2 = 25[/tex]
Now that you have converted the exponents, you can multiply:
3 × 25 = 75
Write an equation in slope intercept form for the line with slope -1/2 and y-intercept -5
Answer: -1/2x - 5 = Y
Step-by-step explanation:
- slope intercept form is mx + b = Y
- m is the slope
- b is the y intercept
- leave x and y as variables
- since your y intercept is negative the + will be a -
- so the equation becomes -1/2x - 5 = Y
hope this helps :)
Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance
Answer:
Step-by-step explanation:
Define two ways of painting to be in the same class if one can be rotated to form the other.We can count the number of ways of painting for each specific class .
Case 1: Black-white color distribution is 0-6 (out of 6 total faces)
Trivially [tex]1^{2}[/tex]=1 way to paint the cubes.
Case 2: Black-white color distribution is 1-5
Trivially all [tex]\frac{6}{5}[/tex] =6 ways belong to the same class , so [tex]6^{2}[/tex] ways to paint the cubes.
Case 3: Black-white color distribution is 2-4
There are two classes for this case: the class where the two red faces are touching and the other class where the two red faces are on opposite faces. There are 3 members of the latter class since there are 3 unordered pairs of 2 opposite faces of a cube. Thus, there are [tex]\frac{6}{4}[/tex]-3=12 members of the former class . Thus, [tex]12^{2} + 3^{2}[/tex] ways to paint the cubes for this case.
Case 4: Black-white color distribution is 3-3
By simple intuition, there are also two classes for this case, the class where the three red faces meet at a single vertex, and the other class where the three red faces are in a "straight line" along the edges of the cube. Note that since there are 8 vertices in a cube, there are 8 members of the former class and [tex]\frac{6}{3} -8=12[/tex] members of the latter class. Thus, [tex]12^{2} - 8^{2}[/tex] ways to paint the cubes for this case.
Note that by symmetry (since we are only switching the colors), the number of ways to paint the cubes for black-white color distributions 4-2, 5-1, and 6-0 is 2-4, 1-5, and 0-6 (respectively).
Thus, our total answer is[tex]\frac{2*(6^{2} + 1^{2}+ 12^{2}+ 3^{2})+12^{2}+8^{2}}{2^{12} } =\frac{588}{4096} = \frac{147}{1024}[/tex]
He length of the hypotenuse of a right triangle is 24 inches. if the length of one leg is 8 inches, what is the approximate length of the other leg? 16.0 inches 18.4 inches 22.6 inches 25.3 inches
Answer:
22.6
Step-by-step explanation:
a^2 + b^2 = c^2 We know one of the legs and the hypotenuse. The hypotenuse must be c. The leg that we do know can be a or b. It is our choice. I am going to let it be a
8^2 + b^2 = 24^2 Plug in the numbers that I know
64 + b^2 = 576 Square the numbers that I know
b^2 = 512 Subtract 64 from both sides
b = 22.6 Put this in your calculator to find the square root and round.
Casey was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:
−8, which represents the depth of water in the swimming pool
+7, which represents the height of the slide at the pool
Part A: What does 0 represent in this situation? (3 points)
Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)
Part C: Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)
The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that −8 represents the depth of water in the swimming pool. Hence:
The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.
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A survey of 150 people at a local high school about playing video games was conducted, and the results are posted in the table.
Play Video Games Do Not Play Video Games
Juniors 48 12
Seniors 45 25
Teachers 6 14
What is the probability of choosing a person at random who is a teacher and plays video games? Are these independent events?
The P(teacher and video games) = 4%; the two events are not independent.
The P(teacher and video games) = 4%; the two events are independent.
The P(teacher and video games) = 9%; the two events are not independent.
The P(teacher and video games) = 9%; the two events are independent.
The P(teacher and video games) = 4%; the two events are not independent.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
P(teacher and video games) = number of teachers who play video game / total number of respondents
6/150 = 0.04 = 4%
Independents events are events whose occurrence do not depend on each other. They are random events.
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Answer:
The P(junior and video games) = 32%; the two events are not independent.
Step-by-step explanation:
i got it right aswell
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Considering the definition of an inequality and system of inequalities, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
System of inequalitiesA system of inequalities is made up of two or more inequalities.
The solution will be formed by the intersection of the half-planes of each of the inequalities, that is, it will be the enclosure that all the inequalities have in common. That is, the solution of the system is given by the region of the common plane of the half-planes that define each one of the inequalities.
System of inequality in this caseIn this case:
c represents child bikes.a represents adult bikes.Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. The company is able to have up to 120 hours of building time and 100 hours of testing time for a week.Then, the system of inequality is:
[tex]\left \{ {{4c+6a\leq 120} \atop {4c+4a\leq 100}} \right.[/tex]
On the other hand, the company can build 20 child bikes and 6 adult bikes in the week. So, checking the equations, for given c=20 and a=6:
4×20 + 6×6= 116 < 120
4×20 + 4×6= 104 >100
Finally, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."
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The area and one side of a rectangle are given. Determine the missing dimension
The missing dimension is x + 4
How to determine the missing dimension?The given parameters are:
Area = 4x^2 + 13x - 12
Length = 4x - 3
The width is calculated using:
Width = Area/Length
This gives
Width = (4x^2 + 13x - 12)/(4x - 3)
Expand
Width = (4x^2 + 16x - 3x - 12)/(4x - 3)
Factorize
Width = (4x(x + 4) - 3(x + 4)/(4x - 3)
Factor out x + 4
Width = (4x - 3)(x + 4)/(4x - 3)
Cancel out the common factor
Width = x + 4
Hence, the missing dimension is x + 4
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Select the correct answer.
The product of two numbers is 21. If the first number is-3, which equation represents this situation and what is the second number?
OA The equation that represents this situation is x-3=21. The second number is 24.
OB. The equation that represents this situation is 3x=21. The second number is 7.
OC. The equation that represents this situation is-3x=21. The second number is-7.
OD. The equation that represents this situation is -3+x=21. The second number is 18.
Option B is correct
Why
3x=21
3(7) =21
21=21
Step-by-step explanation:
Answer:
[tex]-3x=21 , -7[/tex]
Step-by-step explanation:
[tex]-3x=21\\x=\frac{21}{-3} =-7[/tex]
A trapezoid has bases measuring 5cm and 9cm, and an area of 42cm. Find the height
The height of the trapezoid is 6 cm
How to find the height?The given parameters are:
Bases = 5cm and 9cm
Area = 42 square cm
The height is calculated using
Area = 0.5 * (Sum of bases) * Height
So, we have:
42 = 0.5 * (5 + 9)* Height
This gives
42 = 7* Height
Divide through by 7
Height= 6
Hence, the height of the trapezoid is 6 cm
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Suppose that $x$ is a multiple of 6 (not necessarily positive). If the square of $x$ is less than 200, how many possible values of $x$ are there
All multiple of 6 under 14 are: -12, -6, 0, 6, 12
How do we get 14 here:
√200= 14.142 (Round to thousandth place)
This is how many x we have found.
A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.
In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.
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math!! please helpp!!!
What is the y intercept of the line below?
( i attached an image)
a) -3
b) 1/3
c) 4
d) (-1.5,0)
e) -1.5
f) (4,0)
g) 3
Answer:
f (4,0)
Step-by-step explanation:
Hope it helps!!!
y=4
x=0
⊱_______________________________________________________⊰
Answer:
4Step-by-step explanation:
[tex]\large\displaystyle\begin{gathered} \sf{The \ y-intercept \ is \ the \ point \ where \ the \ graph \ intercepts \ the \ y \ axis. \\ \sf{Thus, \ assuming \ that \ each \ little \ square \ represents \ one \ unit, \ the \ y-intercept} \\ \sf{is \ 4} \end{gathered}[/tex]
done !!
⊱_______________________________________________________⊰
CαlligɾαρhγType the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.
Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.
Function g is defined as . What is the value of k?
The value of k is
.
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.
Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.
Function g is defined as . What is the value of k?
The value of k is
(1,0)
4^x + 3 = 7 using the change of base formula log y =
log y/log b
Answer:
x=1
Step-by-step explanation:
It's pretty obvious to see that x equals 1 after you subtract 3 from both sides, but this question specifies using change base, so:
log(b)a means log base b with a as the contents
1.
4^x+3-3=7-3
4^x=4
log(4)4^x=log(4)4 (both logs are base 4 in this case to free the x)
x=log(4)4
x=log(10)4/log(10)4 (both logs are base 10 in this case)
x=1
Change base is definitely unnecessary in this problem