Yes the product of two perfect squares is always a perfect square, But the quotient of two perfect squares is not always a perfect square.
What is perfect square?A perfect square is a number that can be expressed as the product of an integer multiplied by itself.
Examples of perfect squares include 4 (2*2), 9 (3*3), and 25 (5*5).
What is quotient of a number?The quotient is the result obtained after performing division of one number by another. It is the number of times that the divisor can be subtracted from the dividend until the remainder is smaller than the divisor.
The product of two perfect squares is always a perfect square because the root of the products is equal to the product of roots as shown below,
let us take the two perfect squares 4 and 9, so the square root of 4*9 is,
[tex]\sqrt{4*9} =\sqrt{4} *\sqrt{9} \ =2*3=6[/tex]
But , the quotient of two perfect squares is a perfect square,
When we divide two perfect squares we are not always going to get a quotient that can be represented as the square of an integer. For example, (36/16) = 9/4 which is not a perfect square.
However, if the numerator and denominator in the quotient are the same perfect square then the quotient will be 1 which is a perfect square.
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Is 0 the middle of a number line?
Zero is the middle point of a number line.
On the number line, all positive (natural numbers) numbers are on the right side of zero, while all negative numbers are on the left. A number's value lowers as we turn to the left. As an illustration, 1 is greater than -2.
A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point. [1]
The integers are frequently represented as specially designated, uniformly spaced dots on a line. It is frequently employed as a teaching tool for basic addition and subtraction, particularly when negative numbers are involved.
The number line may also be referred to as a real line or real number line in advanced mathematics.
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3. A mysterious metal medallion has a mass of 3,088 grams. Water is poured into a graduated glass container with a 10-by-10 cm square base with a water level of 53.0 cm. The medallion is dropped into the container and the water level rises to 54.6 cm. Find the volume and the density of the medallion.
Step-by-step explanation:
Volume of displaced water = (10cm)(10cm)(1.6cm)
= 160 cm^3
density = mass/vol of displaced water
= 3088 grams/160 cm^3
= 19.3 g/cm^3
P.S. This is most likely a pure gold medallion.
You lose 0.3 point for stepping out of bounds during a gymnastics floor routine. Your final score is 9.124. Write and solve an equation to find your score $x$ without the penalty.
Your score without the penalty is 9.424.
To find your score without the penalty, we need to add 0.3 points back to your final score of 9.124. We can use the linear equation:
x = 9.124 + 0.3
This equation represents the original score, represented by x, plus the penalty of 0.3. To solve for x, we need to add 0.3 to 9.124:
x = 9.124 + 0.3
x = 9.424
So your score without the penalty is 9.424.
In this equation, x is being used to represent the original score, before the 0.3-point penalty was applied. The equation x = 9.124 + 0.3 represents that the original score was 9.124 and 0.3 points were taken off due to stepping out of bounds. By solving the equation, we are able to find the original score without the penalty which is 9.424
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PLEASE HELPPP
WILL GIVE BRAINLIEST
Answer:
1 3/16
Step-by-step explanation:
1/8 = 2/16
Answer:
1 3/16
Step-by-step explanation:
HELPPPPPP PLEASEeeeeeeeeeeeeee
Answer:
x > 3
Step-by-step explanation:
6x - 2 - 3x + 9 > 16
3x + 7 > 16
3x > 9
x > 3
A skateboarding ramp is
in the shape of a triangular
prism. If the entire ramp is
to be painted, and a can of
spray paint covers 1,000
square inches, how many
cans will be needed?
Help me please! I only need one more question
Answer:
chicken pot pie
Step-by-step explanation:
ain't good
The number of cans needed will be 3.divide the total surface area by the area the spray paint can cover.
What is surface area ?The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.
The total surface area to be painted;
A = Area 1 + Area 2 +Area 3+Area 4 \\\\\ A= Area of rectangular face 1 + Area of triangular surface 1+Area of triangular face 2 +Area of rectangular face 2
[tex]\rm \ A = 36 \times 50 + \frac{1}{2}\times 48 \times 14 +\frac{1}{2} \times 48 \times 14 + 36 \times 14 \\\\ A = 1800 +672+504 \\\\ A = 2976 \ inch^2[/tex]
The total surface area to be painted is 2976 inch².
To find the number of cans, divide the total surface area by the area that the spray paint can cover;
[tex]\rm n = \frac{2976}{1000} \\\\ n = 2.976 \\\\ n \approx 3[/tex]
Hence, the number of cans required will be 3.
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GIVING BRAINLIEST! HELP
Answer:
The answer is a because the sign should be facing right but not be greater than or equal to.
Write four consecutive numbers with a mean and medium of 14.5
Answer:
13, 14, 15, 16
Step-by-step explanation:
Call the first number n. Then the next three consecutive numbers (assuming integers) are n + 1, n + 2, n + 3.
The mean is the total of the numbers divided by how many there are.
[tex]\frac{n+(n+1)+(n+2)+(n+3)}{4}=14.5[/tex]
Simplify and multiply by 4.
[tex]4n+6=58\\4n=52\\n=13[/tex]
The first number is 13.
The median is 14.5, halfway between the "middle" numbers 14 and 15. This is just a check; no additional equation is necessary.
how do you solve this
Answer:
5^5+4/5^6
5^9/5^6
5^9-6
5^3
125
Step-by-step explanation:
Firstly the powers of 4 adds up
Then net power is formed by (9-6) ie 3
Lastly 5^3 is result which is 125
Describe the distribution of the ages of the Best Actor Oscar winners [LINK]:
A) What is the BEST description of the SHAPE?
- The distribution is not skewed
- The distribution is skewed left.
- The distribution is skewed right.
The correct option is option (c)-"The distribution is skewed right."
The distribution of the ages of the Best Actor Oscar winners is slightly skewed to the right.
A histogram of the ages of the Best Actor Oscar winners shows that the majority of the ages are centered around the mean age, with a few ages on the higher end that extend the right tail of the distribution. This creates a small skewness to the right.
The distribution seems to be centered at around 42-43.
The age distribution ranges from about 30 to about 75, without taking into account an outlier.
It's worth noting that the distribution is not extremely skewed, and the majority of the ages are still grouped around the center of the distribution.
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Find the probability that a point chosen at random in the figure will be shaded region. Write your answer as a percentage rounding to yhe nearwst hundreth in percent
The 7th grade has 159 students. There are twice as many boys in the grade as there are girls.
How many boys are in the 7th grade?
Answer:
106 boys
Step-by-step explanation:
7th grade = 159 students
Boys to girls ratio:
2:1
Find two thirds of 159:
2/3*159 = 106 boys
159-106= 53 girls
Check:
53*2 = 106
Answer:
318 boys
Step-by-step explanation:
Easy mutiplication
159*2=318
PLEASE HELPP
mia has 3 bags the number of toys in each bag is 6, 8 and x what is the number of toys in the third bag if the average number of toys in the three bags is 6?
a. 3
b.6
c.4
d.8
Answer:
b
Step-by-step explanation:
i think b because it makes more sense than a or c
I need help with this ASAP! Its about budgeting.
Answer:
Step-by-step explanation:
I gave you all of the information to fill out the first page
i also answered some of the questions on the 2nd page. They are written sideways on the page. The other questions I didn’t answer yneed calculations after you add all of the expenses together.
put the amounts from each category I listed in the image and put them into the respective category and get the total for each category. Use those totals to fill out page two. If you get stuck I don’t mind helping but I thought this is the best way to get you started.
Bess and Carolina and their 14 classmates write their names on cards. The teacher, Miss Scott, picks two cards without replacing the first card. What is the probability that Bess is chosen first and Carolina is chosen second?
the mean of a 6 number dataset is 20 if one of the numbers is 15 and you remove it from a dataset what us the mean of the remaining 5 numbers in the data?
Answer:
21
Step-by-step explanation:
If the mean of the data set is 20, we know that it is the sum of all the values in the data set, divided by the number of values. So, with s representing the sum, the mean is s/6 = 20
To undo division, multiply 20 by 6. 20*6 = 120.
120 is the sum of all of the values. Since we're taking out the number 15, subtract it from 120. You're left with 105, which is the sum of the rest of the numbers. Since you now only have 5 numbers, divide 105 by 5 and you get the new mean, which is 21.
What does it mean when a problem is undecidable?
An undecidable problem is one that should have a "yes" or "no" answer but has no algorithm that can correctly answer on all inputs.
What is undecidable problem?According to the theories of computational complexity and computability, an undecidable problem is one for which it has been demonstrated that it is impossible to create an algorithm that always yields the right yes-or-no response. As an illustration, it can be shown that there is no algorithm that can accurately predict whether arbitrary programmes will eventually halt when run.
Any question that is simply yes or no on an infinite list of inputs is a decision problem. It is customary to define the decision problem as the set of inputs for which the problem returns yes because of this. Natural numbers as well as values of other kinds, such as strings in a formal language, can be used as these inputs.
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what is 25% more than60
Answer:
1/4 of 60= 15
15+60=75
75 is 125% of 60
Step-by-step explanation:
Someone help plz make sure it’s right will mark brainiest
Which point has coordinates (0, -1) ?
Please help asappp !! I will give 20 points
Answer:
Point E
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
You don't move on the x axis, so no side to side movement.
You do move on the y axis, but only down 1.
D is the only one that can work.
The length of a rectangle is 3cm longer than its width.
If the perimeter of the rectangle is 58 cm, find its length and width.
The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length.
The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
The length of a rectangle is 3cm longer than its width. If the perimeter of the rectangle is 58 cm. Then the equations are given below.
L = 3 + W ...1
2(L + W) = 58
L + W = 29 ...2
From equations 1 and 2, then we have
3 + W + W = 29
2W = 26
W = 13 cm
Then the length of the rectangle will be given as,
L = 3 + 13
L = 16 cm
The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.
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50 POINTS!! Pls make sure the answers are correct and the work is shown
Answer all pls and show work
Answer:
it 33 pts not 50
PLEASE HELP! Jake and Hakeem's rocket's flight is approximately modeled by the equation h(t) = - 12t ^ 2 + 36t + 3 where h(t) is the height in meters of their rocket seconds after launch.
Jake and Hakeem's rocket's flight is approximately modeled by the equation h(t) = - 12t ^ 2 + 36t + 3. The rocket's highest point is 30m
What is the height?Generally, Since we are not instructed on what to look for, we are able to determine the highest point that the rocket ever achieved.
Given that the rocket's flight can be approximated approximatively using the equation,
h(t) = - 12t ^ 2 + 36t + 3
At maximum height dh/dt = 0
dh/dt = --24t + 36
0 = -24t + 36
24t = 36
t= 36/24
t = 1.5s
Find out the maximum height.
h(1.5) = - 12 (1.5)^ 2 + 36(1.5) + 3
h(1.5) = - 12(2.25) + 54 + 3
h(1.5) = -27 + 57
h(1.5) = 30m
As a result, the rocket is only capable of reaching a height of 30 meters at its highest point.
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When treated with an anabiotic, 97% of all the dolphins are cured of an ear infection. if 6 dolphins are treated find the probability that exactly 3 are cured.
The probability is _____
(Round your answer to 4 decimal places.)
Answer:
0.0005
Step-by-step explanation:
this is a binomial experiment -- they are either cured or not, and the outcome is random
probability = n choose r * p^r * q^(n-r)
here, n = number of trials, r = number of successes desired, p = probability event occurs, and q = probability event doesn't occur
probability = n choose r * p^r * q^(n-r) = 6 choose 3 * 0.97^3 * 0.03^(6-3)
= 0.00049284342 rounding to 0.0005
1) Alice decides to take a trip from the East Coast of the United States to the West Coast. While planning, she chooses to drive, fly, and ride a train. Her first leg of the trip is traveling by car, from Sacramento, California to Denver, Colorado. Along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. After driving for many hours, Alice finally makes it to Denver, Colorado spending $874.80 in gas.
a) Let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. Create an equation that models the situation.
Incorrect but attempt was made (1 pt) Partially correct
(2-4 pts) Fully Correct
(5 pts)
b) If Alice purchases 87 gallons for regular unleaded gas, how many gallons of premium gas did she purchase? Show all work to receive full credit.
Provided incorrect answer and no work shown (1 pt) Incorrect answer with work shown or Correct answer with no work shown
(2 pts) Correct with partial work shown (3-4 pts) Fully Correct with all work shown
(5 pts)
a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.
b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.
What is an equation?An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).
The cost per gallon of regular unleaded gas = $4.65
The cost of premium gas per gallon = $4.95
The total cost for gas = $874.80
Let gallons of regular unleaded gas = r
Let gallons of premium gas = p
Equation:4.65r + 4.95p = 874.8
If r = 87, the value of p is:
4.65(87) + 4.95p = 874.8
404.55 + 4.95p = 874.8
4.95p = 470.25
p = 95 gallons
Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.
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WILL MARK BRAINLIEST ASAPPPP
find the volume of the sphere. r = 3 cm. V= cm^3
Answer:
113.1 is the volume of the sphere.
Answer:
[tex]volume = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times 3.14 \times {(3)}^{3} \\ = 113.04 \: {cm}^{3} [/tex]
Solve for x. the formula is cosine
Answer:
Step-by-step explanation:
Which expressions are equivalent to 6x - 18 ?
c.) 3(2x-6)
Reason:-
3(2x-6) = 6x-18
Answer:
C, D, and E are your answers
3 x 2x = 6x, 3 x 6 = 18
6x - 18
x + 5x = 6x
6x - 18
2 x 3x = 6x
2 x 9 = 18
6x - 18
Which of the following ratios is used to determine ones debt-to-income ratio? a. 20/28 b. 20/36 c. 28/30 d. 28/36 Please select the best answer from the choices provided A B C D Mark this and return
Answer:
D 28/36
Step-by-step explanation:
A person's debt-to-income can be calculated by dividing all his/her monthly debt payments by the gross monthly income. This number can be used for determining your ability to manage your monthly payments to repay the money you plan to borrow. In general, 43% is the highest DTI ratio a borrower can have and still get qualified for a mortgage, but lenders prefer a ratio lower than 36%, with no more than 28% of that debt going towards servicing a mortgage or rent payment. Thus, someone should spend at most 28% of his/her gross income on total housing expense and maximum of 36% on total debt service.
Answer:
D
Step-by-step explanation: