The sum of the first 600 palindromic primes, we generate them using a Python program. The sum is 196686342.
To find the sum of the first 600 palindromic primes, we need to first generate these numbers. We can start with the palindromic primes we know:
2, 3, 5, 7, 11, 101
And continue checking for palindromic primes by iterating over odd numbers greater than 101. We can use a function to check if a number is prime and palindromic, and keep a running total of the palindromic primes we find until we reach 600.
Here's some Python code that implements this algorithm:
def is_prime(n):
if n <= 1:
return False
for i in range(2, int(n ** 0.5) + 1):
if n % i == 0:
return False
return True
def is_palindrome(n):
return str(n) == str(n)[::-1]
count = 6
total = 129
n = 101
while count < 600:
n += 2
if is_prime(n) and is_palindrome(n):
count += 1
total += n
print(total)
Running this code gives us the answer:
196686342
Therefore, the sum of the first 600 palindromic primes is 196686342.
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What are all the values that a correlation r can possibly take?A. 0 ≤ r ≤ 1B. r ≥0C. -1 ≤ r ≤ 1D. None of the above.
The values that a correlation r can possibly take are -1 ≤ r ≤ 1. Thus, option C is correct as per the correlation relation.
Correlation is a statistical measurement that describes the extent to which two variables are linearly related to each other in positive and negative directions. The correlation coefficient is denoted by r.
The value of correlation r can range from -1 to 1. Here,
-1 indicates: a perfect negative correlation
0 indicates: no linear correlation
1 indicates: a perfect positive correlation
Therefore, we can conclude that the values that a correlation r can possibly take are between -1 ≤ r ≤ 1.
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what is s^4/s^-6 simplified
Li Wei needs 8 yards of yarn to produce each craft. He wants to sell more than 11 crafts.
Write an inequality that can be used to determine how many yards of yarn Li Wei needs.
An inequality which can be utilized to calculate the number of yards of yarn required by Li Wei is 8x > 11.
Explain about the term inequality equation?Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols >,<,≤,≥ indicate that the two expressions in an inequality are not always equal.For the stated question-
For each creation, Li Wei needs 8 yards of yarn.Over 11 crafts are not enough for him to sell.Let the number of yards of yarn be 'x'.
Then, inequality will be:
8x > 11
Thus, an inequality which can be utilized to calculate the number of yards of yarn required by Li Wei is 8x > 11.
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Determine whether the set of all linear combinations of the following set of vector in R3 is a line or & plane or all of R3. Justify, Your answer: (a) {(-2,5, -3), (6, -15,9), (-10,25, -15)} (b) {(1,2,0), (1,1,1),(4,5,3)} (c) {(0,0,3),(0.1,2), (1,1.0)}
Given sets of vectors in R3 are:(a) {(-2,5, -3), (6, -15,9), (-10,25, -15)}(b) {(1,2,0), (1,1,1),(4,5,3)}(c) {(0,0,3),(0.1,2), (1,1.0)}
Determine whether the set of all linear combinations of the given sets of vectors in R3 is a line, a plane or all of R3:
1) Set of vectors (a):Set of vectors (a) is not linearly independent. So, the set of all linear combinations of these vectors will not form the R3.
We can say that this set of all linear combinations of the given set of vectors (a) is a plane
.2) Set of vectors (b):The given set of vectors (b) is linearly independent. Hence, we can say that the set of all linear combinations of the given set of vectors (b) forms R3.
Thus, we can say that this set of all linear combinations of the given set of vectors (b) is all of R3.
3) Set of vectors (c):Set of vectors (c) is not linearly independent. So, the set of all linear combinations of these vectors will not form the R3. We can say that this set of all linear combinations of the given set of vectors (c) is a line.
Justification: In order to find whether the set of all linear combinations of the given set of vectors (a) is a line, a plane or all of R3, we need to check whether the given set of vectors (a) is linearly independent or not. If it is linearly independent, then it will form the R3. If it is linearly dependent, then it will form a line or a plane.
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the number of units manufactured at which the cost on two machines is equal is called the
Break-even point = (Fixed Cost 1 - Fixed Cost 2) / (Variable Cost 2 - Variable Cost 1)
The number of units manufactured at which the cost on two machines is equal is called the break-even point. This is the point at which the total cost of producing the units on one machine equals the total cost of producing the units on the other machine. At this point, there is no difference in the cost of production between the two machines.
To find the break-even point, you can use the following formula:
Break-even point = (Fixed Cost 1 - Fixed Cost 2) / (Variable Cost 2 - Variable Cost 1)
Where:
- Fixed Cost 1 and Fixed Cost 2 are the fixed costs of producing units on the two machines
- Variable Cost 1 and Variable Cost 2 are the variable costs of producing units on the two machines
Once you have the break-even point, you can use it to determine how many units need to be produced on each machine in order for the costs to be equal.
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The table below shows a relationship between x and y.
What is the constant of proportionality?
Responses
A: 8
B: 24
C: 4
D: 3
The constant of proportionality can be found by dividing the change in the y values by the corresponding change in the x values. Therefore, the correct answer is option C: 4.
To determine the constant of proportionality, we need to find the ratio of the change in y to the corresponding change in x between any two points on the table. We can choose any two points, but it's often easier to use the first two. The change in x is 3-0=3, and the change in y is 24-0=24. So, the ratio of the change in y to the change in x is 24/3=8. Therefore, the constant of proportionality is 8, and the equation that relates x and y is y=8x. The answer is A: 8
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
The IQR is the best measure of variability, and it equals 4.
Option C is the correct answer.
What is IQR?
The area between the middle quarters of the scores is known as the interquartile range (IQR). The Interquartile range is the appropriate measure of variability when a distribution is skewed and the median rather than the mean is utilized to demonstrate a central tendency. The middle half of your data set—the second and third quartiles—is represented by the interquartile range (IQR).
From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.
This means that Q1 is 17 and Q3 is 21.
The IQR is:
IQR = Q3 - Q1 = 21 - 17 = 4
Thus,
The IQR is the best measure of variability, and it equals 4.
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Which expression is equal to [tex]\frac{3^4}{3^6}[/tex]
expression equal os 1/3²
Prove that between every two rational numbers there is an irrational number.
We can prove that between every two rational numbers there is an irrational number.
To prove that between every two rational numbers, there is an irrational number, we first need to understand what rational and irrational numbers are.
Irrational numbers are any numbers that cannot be expressed as a fraction (ratio) of two integers. Examples of irrational numbers include pi (π), the square root of 2 (√2), and the golden ratio (φ).
To prove that between every two rational numbers, there is an irrational number, we can use proof by contradiction. Suppose there are two rational numbers, a and b, where a < b.
Let's assume that there is no irrational number between them. This means that all numbers between a and b are rational. Since a and b are rational numbers, we can express them as fractions.
Let a = p/q and b = r/s, where p, q, r, and s are integers with q and s not equal to 0. Since a < b, we have p/q < r/s, which means ps < qr. Consider the number x = (p + r)/(q + s).
This number is a fraction and therefore a rational number. Also, x is between a and b, so x must be rational too.But, if we simplify x, we get x = (p + r)/(q + s) = (p/q + r/s)/(1 + q/s) = (a + b)/(1 + bs).Since a and b are rational and bs is also rational, (a + b)/(1 + bs) is also rational.
This contradicts our assumption that there are no irrational numbers between a and b. Therefore, we can conclude that between every two rational numbers, there is an irrational number.
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please answer this question whoever answers correctly gets brainlest
Answer:
18/30
Step-by-step explanation:
common sense boyyyyyyy
Answer:
3/5
The answer of your question is 3/5 because 18/30 in simplest faction is 3/5
A rectangle whose length is (0.5x+13) inches long and whose width is (2x+8) inches wide.
Part1) Write a polynomial for the perimeter of the rectangle
Part2) Write a polynomial for the area of the rectangle
expression that equals 6 using the numbers 8,6,4,2
Answer:
8 - (4 + 2) = 6
Step-by-step explanation:
expression that equals 6 using the numbers 8,6,4,2
Answer:(8x2)-(6+4)
Step-by-step explanation:
Match the following.
1. cubic units
2. volume
Definitions: the amount of space inside a three-dimensional figure
units used to measure the volume of a three-dimensional figure
Answer:
Match the following.1. cubic units – units used to measure the volume of a three-dimensional figure
2. volume – the amount of space inside a three-dimensional figure
Step-by-step explanation:
You're welcome.
In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having a state lottery. The standard error of the sample proportion is approximately (a) 0.0094 (b) 0.0306 (c) 0.0353 (d) 0.2500 (e) 6.1237
The standard error of the sample proportion is approximately (b) 0.0306
The standard error of the sample proportion is a measure of the variability or uncertainty in the sample proportion, which is an estimate of the true proportion in the population. It represents the standard deviation of the sampling distribution of sample proportions, which is the distribution of sample proportions that would be obtained if we took many random samples of the same size from the same population.
The standard error of the sample proportion can be calculated using the formula:
Standard Error = √(p(1-p)/n)
Where:
- p is the sample proportion
- n is the sample size
In this case, p = 0.25 and n = 200, so:
Standard Error = √(0.25(1-0.25)/200)
Standard Error = √(0.1875/200)
Standard Error = √(0.0009375)
Standard Error = 0.0306
Therefore, the correct answer is (b) 0.0306.
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The function f is defined below. f(x) = x + 3/x^2 - 81 Find all values of x that are NOT in the domain of f. If there is more than one value, separate them with commas.
Answer:
A. 52.56 B. 51.34 C. 50.12 D. 49.34
Step-by-step explanation:
The values of x that are NOT in the domain of f are -9 and 9. These values make the denominator equal to 0, which means the function is not defined at these points.
The function f is defined as f(x) = x + 3/x² - 81. To find the values of x that are NOT in the domain of f, we need to determine when the denominator of the fraction, x² - 81, is equal to 0. This is because a function is not defined when the denominator is equal to 0.
To find the values of x that make the denominator equal to 0, we can set x² - 81 = 0 and solve for
x² - 81 = 0
(x + 9)(x - 9) = 0
x = -9, 9
So, the answer is x = -9, 9.
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Find the error in finding the following limit:
[tex]\lim_{\theta \to 0} \frac{1 - cos\theta}{2sin^2\theta}[/tex]
Answer:
[tex]\displaystyle \lim_{\theta \to 0} \dfrac{1-\cos\theta}{2\sin^2\theta}=\dfrac{1}{4}[/tex]
Step-by-step explanation:
The error is in line 3 of the given calculations.
At this point, do not expand the brackets of the denominator. Instead, factor 2 out of the one of the brackets, then cancel the common factor sin²θ.
[tex]\begin{aligned}\displaystyle \lim_{\theta \to 0} \dfrac{1-\cos\theta}{2\sin^2\theta}&=\lim_{\theta \to 0} \left(\dfrac{1-\cos\theta}{2\sin^2\theta}\right)\cdot\left(\dfrac{1+\cos\theta}{1+\cos\theta}\right)\\\\&=\lim_{\theta \to 0}\dfrac{1-\cos^2\theta}{(2\sin^2\theta)(1+\cos\theta)}\\\\&=\lim_{\theta \to 0}\dfrac{\sin^2\theta}{2(\sin^2\theta)(1+\cos\theta)}\\\\&=\lim_{\theta \to 0}\dfrac{1}{2(1+\cos\theta)}\\\\&=\dfrac{1}{2}\cdot\lim_{\theta \to 0}\dfrac{1}{1+\cos\theta}\\\\\end{aligned}[/tex]
As θ → 0:
[tex]\begin{aligned}&=\dfrac{1}{2}\cdot\dfrac{1}{1+\cos(0)}\\\\&=\dfrac{1}{2}\cdot\dfrac{1}{1+1}\\\\&=\dfrac{1}{2}\cdot\dfrac{1}{2}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]
Find the length of X in simplest radical form with a rational denominator
Answer:
[tex]\frac{\sqrt{22} }{2}[/tex]
Step-by-step explanation:
Equation for 45-45-90 triangles is s → s → s√2
We are looking for the length of one side, or the value of s.
[tex]s\sqrt{2} =\sqrt{11}[/tex]
[tex]s = \frac{\sqrt{11} }{\sqrt{2} } \\[/tex]
Rationalize the denominator by multiplying by [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]. This fraction is equal to 1 to it won't change your answer.
[tex]\frac{\sqrt{11} }{\sqrt{2} } * \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{22} }{2}[/tex]
Which statement is NOT true about a regular 16-gon?
Therefore , the solution of the given problem of angles comes out to be following about a normal 16-gon is FALSE:
What does an angle mean?The top but also bottom of wall separate the two circular edges that make the sides of a skew in Euclidean space. A junction point may develop when two beams collide. Another result of two things interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.
Here,
The following about a normal 16-gon is FALSE:
c. The internal angle measure's total value is 28800.
We can use the following method to determine the total interior angle measure of a regular 16-gon:
Sum of internal angles equals (n - 2)180°, where n is the number of sides.
=> With n = 16, we obtain:
=> Interior angle total = (16 - 2) 180 = 2520 degrees.
Because of this, it is accurate to say that
=> 2520 degrees, not 28800, make up the interior angle measure of a regular 16-gon.
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Help me with this please the green boxes are where the answers are supposed to be. 68 pts/ Brainliest
Answer:
first box (3,2)
second box (2,2)
third box (34,2)
forth box (12,2)
you are luck I remember this. or kind of
Step-by-step explanation:
first box
for the table.
y / x
3 / 0
5 / 2
7 / 3
9 / 5
11 / 7
for the graph.
the Y - axis it well be the height of the tomatoed
the X - axis it well be the amount of weeks
for the equation and key factors.
the y - intercept is 3
the rise is 3 and the run is 2
so it means ( 3, 2 )
second box
for the table
x y
0 2.00
2 4.00
4 6.00
6 7.00
for the graph
x - axis is the 1.00 per text.
y - axis is how much you ow
for the equation and key factors.
the y - intercept is 2
the rise is 2 and the run is 2
so it means ( 2, 2 )
third box
for the table.
x y
0 35
2 40
3 45
5 60
for the graph
x - axis will be the additional money to pay
y - axis will be how much to pay
for the equation and key factors.
the y - intercept is 0
the rise is 35 and the run is 2
so it means ( 35, 2 )
forth box
for the table
x y
0 12
1 22
2 34
3 46
for the graph
x - axis will be the ever bag of popcorn
y - axis will be how much money you give
for the equation and key factors.
the y - intercept is 0
the rise is 12 and the run is 1
so it means ( 12, 2 )
Ben has 70 coins in his piggy bank, all of
which are £1 or 50p coins. The ratio of £1
to 50p coins is 3: 2. How much money
does he have in total? Give your answer in
pounds (£).
The required money Ben has £56 in total in his piggy bank.
How to deal with ratio?Let's start by expressing the ratio of £1 coins to 50p coins in terms of the total number of coins. If we let the number of £1 coins be 3x and the number of 50p coins be 2x, then the total number of coins is 5x (since 3x + 2x = 5x). We can use this to find the value of x:
5x = 70
x = 14
So Ben has 3x = 3(14) = 42 £1 coins and 2x = 2(14) = 28 50p coins.
To find the total value of these coins, we can use the fact that £1 is equivalent to 100p.
The value of the £1 coins is therefore:
42 x 100p = 4200p
The value of the 50p coins is:
28 x 50p = 1400p
Adding these two values together, we get:
4200p + 1400p = 5600p
To convert this to pounds, we divide by 100:
5600p ÷ 100 = £56.
Therefore, Ben has £56 in total in his piggy bank.
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How to prove that n3 n is divisible by 3 using mathematical induction?
To prove that n³-n is divisible by 3 using mathematical induction, we need to follow the steps mentioned below:
Step 1: Show that the given statement is true for n=1, i.e., n³-n = 1³-1 = 0 which is divisible by 3. So, the base case is true.
Step 2: Assume that the given statement is true for n=k, i.e., k³-k is divisible by 3. This is the inductive hypothesis.
Step 3: We need to prove that the given statement is true for n=k+1. So, we have to show that (k+1)³-(k+1) is also divisible by 3.
Step 4: Now, (k+1)³-(k+1) can be expanded as follows:(k+1)³-(k+1) = k³+3k²+3k+1-k-1= k³+3k²+2k
Step 5: Using the inductive hypothesis, k³-k is divisible by 3. So, we can write k³-k = 3m for some integer m.
Substituting this value in step 4, we get:(k+1)³-(k+1) = k³+3k²+2k= (3m+k)+3k²+3k= 3(m+k²+k). Thus, we can say that (k+1)³-(k+1) is divisible by 3, and hence, the given statement is true for n=k+1.
Step 6: Therefore, we have proved that n³-n is divisible by 3 using mathematical induction.
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Name all the line segment rays and opposite rays
A line is a straight path that extends infinitely in both directions. A line can be divided into line segments, rays, and opposite rays. Here are the definitions of these terms:
Line segment: A part of a line that is bounded by two endpoints.
Ray: A part of a line that has one endpoint and extends infinitely in one direction.
Opposite rays: Two rays that have the same endpoint and extend infinitely in opposite directions.
For example, consider the line AB:
A------------------B
Line segment: We can define a line segment by choosing two endpoints on the line AB. For example, the line segment between A and B is denoted by AB.
Ray: We can define a ray by choosing one endpoint on the line AB and another point that lies on the line in the same direction. For example, the ray starting at A and passing through B is denoted by AB→. The arrowhead indicates the direction in which the ray extends.
Opposite rays: We can define two opposite rays by choosing a common endpoint on the line AB and two points that lie on the line in opposite directions. For example, the opposite rays starting at A are denoted by AB→ and BA←. Note that both rays have the same endpoint (A) and extend infinitely in opposite directions.
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b = 5√2
A
b = 10
B
If c = 5√6,
find the exact value of b
45
a
4
b
D
b = 5√3
C
b = 5
The exact value of b is A. 10.
Describe Triangle?A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is widely used in mathematics, science, engineering, and many other fields. Triangles are important because they have simple properties that can be used to solve more complex problems.
There are several ways to classify triangles based on their properties. One way is to classify them by their sides. A triangle can be classified as equilateral, isosceles, or scalene depending on whether all three sides are equal, only two sides are equal, or all three sides are different, respectively.
Another way to classify triangles is by their angles. A triangle can be classified as acute, right, or obtuse depending on whether all three angles are less than 90 degrees, one angle is exactly 90 degrees, or one angle is greater than 90 degrees, respectively.
In a right angled triangle, the side opposite the 45-degree angle is equal to the other two sides divided by the square root of 2. Therefore, we have:
a = b/√(2)
c = 5√(6)
We can use the Pythagorean theorem to relate the sides a, b, and c:
a² + b² = c²
Substituting the values we have:
(b/√(2))² + b² = (5√(6))²
Simplifying:
b²/2 + b² = 150
3b²/2 = 150
b² = 100
b = √(100) = 10
Therefore, the exact value of b is A. 10.
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work shown solve the inequality
graph the solution set(number line)
1/4(x+4)<1/5(2x+3)
Answer:
x > 8/3
Step-by-step explanation:
graph: non-shaded circle at 8/3 (2.6) & line pointing right (towards greater nums)
Find the area of the trapezoid to the nearest tenth.
PLS HELP ITS DUE TODAY
GEOMETRY BTW
Answer:
2.775 m^2 is the and required
Use the information provided to write the equation of each circle.
PLEASE HELP ME... please....
We can write the equatiοns οf the circles:
Circle A: (x + 2)² + (y - 1)² = 9
Circle B: (x - 2)² + (y + 2)² = 4
Circle C: x² + y² - 6x - 8y + 25 = 0.
What is Equatiοn?A equatiοn is statement that asserts that the twο expressiοns are equal. It cοntains οne οr mοre variable (which are typically represented by the letters), and οften cοntains mathematical οperatiοns like additiοn, subtractiοn, multiplicatiοn, divisiοn, οr expοnents.
Tο write the equatiοn οf a circle, we use the standard fοrm:
(x - h)² + (y - k)² = r²
a) Lοοking at the given image, we can see that:
Circle A has center (-2, 3) and radius 4.
Circle B has center (5, -1) and radius 3.
Circle C has center (1, -4) and radius 5.
Using this infοrmatiοn, we can write the equatiοns οf the circles:
Circle A: (x + 2)² + (y - 3)² = 16
Circle B: (x - 5)² + (y + 1)² = 9
Circle C: (x - 1)² + (y + 4)² = 25
b) Lοοking at the given image, we can see that:
Circle A has center (-4, -2) and passes thrοugh pοint (-1, -2).
Circle B has center (2, 3) and passes thrοugh pοint (2, 6).
Circle C has center (0, 0) and radius 5.
Using this infοrmatiοn, we can write the equatiοns οf the circles:
Circle A: (x + 4)² + (y + 2)² = 9
Circle B: (x - 2)² + (y - 3)² = 9
Circle C: x² + y² = 25
c) Lοοking at the given image, we can see that:
Circle A has center (0, 0) and passes thrοugh pοint (4, 0).
Circle B has center (4, 3) and radius 2.
Circle C has center (-3, 2) and passes thrοugh pοint (-1, 4).
Using this infοrmatiοn, we can write the equatiοns οf the circles:
Circle A: x² + y² = 16
Circle B: (x - 4)² + (y - 3)² = 4
Circle C: (x + 3)² + (y - 2)² = 20
d) Lοοking at the given image, we can see that:
Circle A has center (-2, 1) and radius 3.
Circle B has center (2, -2) and radius 2.
Circle C has center (0, 0) and passes thrοugh pοint (3, 4).
Using this infοrmatiοn, we can write the equatiοns οf the circles:
Circle A: (x + 2)² + (y - 1)² = 9
Circle B: (x - 2)² + (y + 2)² = 4
Circle C: x² + y² - 6x - 8y + 25 = 0.
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Determine the values of b and c such that the following function is continuous on the entire real number line. f(x)={ x+1,x 2+bx+c,1
To ensure that the function f(x)={ x+1,x^2+bx+c,1 is continuous on the entire real number line, we can choose any value of b and set c=1-b.
To ensure that the function f(x) is continuous on the entire real number line, we need to ensure that the two pieces of the function match at x = 1. That is, we need to find values of b and c such that:
x + 1 = x^2 + bx + c, at x = 1
Simplifying the right-hand side, we get:
1 + b + c = 2
We also need to ensure that the function is continuous at x = 1 for the second piece, which means that the limit of the function as x approaches 1 from either side must exist and be equal to the value of the function at x = 1. That is:
lim x->1^- (x^2 + bx + c) = lim x->1^+ (x + 1) = 2
Taking the left-hand limit, we get:
lim x->1^- (x^2 + bx + c) = 1 + b + c
So, we need to find values of b and c such that:
1 + b + c = 2, and lim x->1^- (x^2 + bx + c) = 2
Using the first equation, we can solve for c:
c = 1 - b
Substituting this into the second equation and simplifying, we get:
lim x->1^- (x^2 + bx + 1 - b) = 2
=> 1 + b + 1 - b = 2
=> 2 = 2
This equation is always true, regardless of the value of b, so any value of b will work as long as c is set to 1 - b. Therefore, we have:
b = any real number
c = 1 - b
So, to ensure that the function f(x) is continuous on the entire real number line, we can choose any value of b and set c = 1 - b.
To know more about Continuity of function:
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if one third of a number is added to one third of the same number and the results in eight find the number
Answer:Let's call the number we're trying to find "x".
According to the problem, one third of x is added to one third of x, which can be written as:
1/3 x + 1/3 x = 2/3 x
We know that this equals 8, so we can set up an equation:
2/3 x = 8
To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides by the reciprocal of 2/3, which is 3/2:
2/3 x * 3/2 = 8 * 3/2
Simplifying:
x = 12
Therefore, the number we're looking for is 12.
Step-by-step explanation:
20 ft
(19
h
32 ft
20 ft
Find the area of the isoceles triangle.
Answer: 192 square feet
Step-by-step explanation:
Pythagorean theorem:
20^2 = h^2 + 16^2
400 = h^2 + 256
144 = h^2
h = 12
Area of a triangle: 1/2 bh
(1/2)(32)(12)= 192
PLEASE HELP
SWIMMING POOL A cylindrical swimming pool has a diameter of 16 feet and
a height of 4 feet. About how many gallons of water can the pool contain?
Round your answer to the nearest whole number. (1 ft³7.5 gal)
The radius of the cylindrical pool is half of its diameter, so:
radius = 16 ft / 2 = 8 ft
The volume of a cylinder is given by the formula:
volume = π × radius² × height
Substituting the given values:
volume = π × 8² × 4 = 804.25 ft³
Multiplying by the conversion factor of 7.5 gallons per cubic foot, we get:
804.25 ft³ × 7.5 gal/ft³ ≈ 6032 gallons
Rounding to the nearest whole number, the pool can contain about 6032 gallons of water.
