To find the circumference of the circle, we need to know its radius. However, in this question, we are given the area of a square instead. We can use the relationship between the circle and square to solve the problem.
Explanation:To find the circumference of a circle, we need to know its radius.
However, in this question, we are given the area of a square instead.
We can use the relationship between the circle and square to solve the problem.
First, let's find the side length of the square. The area of the square is given as 144 m².
We can find the side length by taking the square root of the area: √144 = 12 m.
Since the square and circle are related, the side length of the square is equal to the diameter of the circle.
Therefore, the radius (r) of the circle is half of the side length of the square, which is 6 m.
Now, we can find the circumference (C) of the circle using the formula C = 2πr.
Substituting the value of the radius, we get C = 2 × 3.14 × 6 ≈ 37.68 m.
Rounded to the nearest tenth, the circumference of the circle is approximately 37.7 m.
Final answer:
To calculate the circumference of the circle from the area of the square, we find the diameter of the circle (equal to the side length of the square) and divide it by two to get the radius. We then apply the formula C = 2πr using 3.14 for π to find the circumference, which is 37.7 m to the nearest tenth.
Explanation:
To find the circumference of the circle when the area of the square is 144 m², we need to understand the relationship between the square and the circle. First, let's determine the side length of the square. The area of the square (A) is given by the formula A = a², where a is the side length of the square. If the area is 144 m², we take the square root of 144 to find that a = 12 m. Now, since the circle fits perfectly inside the square, the diameter of the circle is equal to the side length of the square, which is 12 m. Hence, the radius (r) of the circle is half of that, so r = 6 m.
Now, we use the formula for the circumference of a circle, which is C = 2πr. Substituting the value of π with 3.14 and r with 6 m, we get C = 2 * 3.14 * 6. This results in a circumference of 37.68 m. To give the answer to the nearest tenth, we round it to 37.7 m. Therefore, the circumference of the circle is 37.7 m.
What is the area of a piece of plywood measuring 2foot8inches long by 2 foot 4 inches wide
A=wl
32 times 28= 896
i converted the feet and inches into just inches btw
What is the slope-intercept form of the linear equation x + 4y = 12?
enter your answer in the box.
plz i need help will give 10 points
y = - [tex]\frac{1}{4}[/tex] x + 3
the equation of a line in slope-intercept form is
y = mx +c ( where m is the slope and c the y-intercept )
rearrange x + 4y = 12 into this form
subtract x from both sides
4y = - x + 12 ( divide all terms by 4 )
y = - [tex]\frac{1}{4}[/tex] x + 3 ← in slope-intercept form
There are 10 cards. Each card has one number between 1 and 10, so that every number from 1 to 10 appears once.
In which distributions does the variable X have a binomial distribution?
Select each correct answer.
When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen.
When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.
When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.
When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen
Answer:
When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen. Here the card is chosen with replacement. This implies probability for choosing a prime number remains the same as the previously drawn card is replaced.
The sample space= {1,2,3,4,5,6,7,8,9,10}
Prime numbers = {2,3,5,7}
Prob for drawing prime number = 4/10 = 0.4
is the same when replacement is done.
Also there are two outcomes either prime or non prime. Hence in this case, X the no of times a prime number is chosen, is binomial with p =0.4 and q = 0.6 and n=5
When a card is chosen at random without replacement three times, X is the number of times an even number is chosen.
Prob for an even number = 0.5
But after one card drawn say odd number next card has prob for even number as 5/9 hence each draw is not independent of the other. Hence not binomial.
When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.
Here since every time replacement is done, probability of drawing a 3 remains constant = 1/10 = 0.3
i.e. each draw is independent of the other and there are only two outcomes , 3 or non 3. Hence here X is binomial.
When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen
Here X is the number of times a card is chosen with replacement till 5 is chosen. This is not binomial. Here probability for drawing nth time correct 5 is P(non 5 in the first n-1 draws)*P(5 in nth draw) = 0.1^(n-1) (0.9)
Because nCr is not appearing i.e. 5 cannot appear in any order but only in the last draw, this is not binomial.
Step-by-step explanation:
Answer:
Step-by-step explanation:
hope this is helpful to anyone in the future!
PLEASE HELPP MEEEEE
A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 8-km rectangle. As the camera zooms out, the length l and width w of the . rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 5 times its original size?
To find the time it takes for the area to be at least 5 times its original size, we need to solve an equation involving the rates of increase for the length and width of the rectangle. The original area is 32 km² and the rates of increase are both 3 km/sec. By substituting these values into the equation and solving for time, we can determine the answer.
Explanation:To determine how long it takes for the area A to be at least 5 times its original size, we first need to find the original area and then solve for the time it takes for the area to reach 5 times that value.
The original area is equal to the length multiplied by the width, so it is A = 4 km * 8 km = 32 km².
Let's denote the rate at which the length and width increase as dl/dt and dw/dt respectively. We know that dl/dt = dw/dt = 3 km/sec.
To find the time it takes for the area to be 5 times its original size, we need to solve the equation 32 + 3l(t) * 3w(t) = 5 * 32, where l(t) and w(t) are the length and width at time t.
Simplifying the equation, we get 9lw - 160 = 0.
Since we're given the rates at which l and w increase, we can substitute l and w with their formulas: l(t) = 4 + 3t and w(t) = 8 + 3t.
Substituting these formulas into the equation, we get 9(4 + 3t)(8 + 3t) - 160 = 0.
Solving this equation will give us the value of t, which represents the time it takes for the area to be at least 5 times its original size.
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Factor the expression over the complex numbers.
x^2+52
Answer: (x - [tex]2i\sqrt{13}[/tex])(x + [tex]2i\sqrt{13}[/tex])
Step-by-step explanation:
x² + 52 = 0
x² = -52
[tex]\sqrt{x^{2} } = \sqrt{-52}[/tex]
x = +/- [tex]\sqrt{52}[/tex]
x = +/- [tex]i\sqrt{2*2*13}[/tex]
x = +/- [tex]2i\sqrt{13}[/tex]
(x - [tex]2i\sqrt{13}[/tex])(x + [tex]2i\sqrt{13}[/tex]) = 0
Byran is pushing his niece, Callie, on a park swing. Her displacement over time can be modeled by the following graph.
How long does it take Callie to complete one full swing?
A.
20 seconds
B.
5 seconds
C.
10 seconds
D.
60 seconds
She takes 20 seconds
Answer: A. 20 seconds
Step-by-step explanation:
We know that if a function has a repeating pattern then it is called a periodic function (like sine or cosine).
The period is the length of the smallest interval that contains exactly one copy of the repeating pattern. It is the horizontal distance required for the graph of a periodic function to complete one cycle.
From the graph it can be seen that, the horizontal distance required for the graph of a periodic function= 20 .
Therefore, it takes 20 seconds by Callie to complete one full swing.
Jackson pays $18 per month for his phone service, plus $0.07 for each long distance minute used. Which of the following correctly describes the y-intercept?
Answer:
The answer is b.
Step-by-step explanation:
You could represent the phone service price with an equation that is
y = 0.07x + 18
So the intercept in y is 18 when x is zero, that is the minimum price of the phone service.
What is the numerical coefficient of the a^8*b^2 term in the expansion of ((1/3)a^2 - 3b)^6 ?
Enter your answer in simplest fractional form.
In the binomial development, the main problem is calculation of binomial coefficients.
If we want to get term a∧8*b∧2 we see that this is the third member in binomial development (n 2) a∧n-2*b∧2
The given binomial is ((1/3)a∧2 - 3b)∧6, the first element is (1/3)a∧2, the second element is (-3b) and n=6 when we replace this in the formula we get
(6 2) * ((1/3)a∧2)∧(6-2) * (-3b)2 = (6*5)/2 * ((1/3)a∧2)∧4 *9b∧2= 15*(1/81)*9 *(a∧8b∧2) =
= 15*9* a∧8b∧2 = 135*a∧8b∧2
We finally get numerical coefficient 135
Good luck!!!
The numerical coefficient of the [tex]a^8*b^2[/tex] term in the expansion of [tex]((1/3)a^2 - 3b)^6[/tex] is -45/16.
Explanation:The numerical coefficient of the [tex]a^8*b^2[/tex] term in the expansion of [tex]((1/3)a^2 - 3b)^6[/tex] can be found using the binomial theorem, which states that [tex](x+y)^n = \sum (n choose k) x^(^n^-^k^) y^k[/tex] where the sum is from k=0 to n. Here, x = [tex](1/3)a^2[/tex], y = -3b, and n = 6.
In the term [tex]a^8*b^2, a^2[/tex] is raised to the 4th power and -3b is raised to the 2nd power. Hence, we are looking for the coefficient in the term in the binomial expansion where [tex](1/3)a^2[/tex] is raised to the 4th power and -3b is raised to the 2nd power.
This can be calculated by multiplying together the coefficient '6 choose 4', the 4th power of [tex](1/3)a^2[/tex], and the 2nd power of -3b.
That leads to coefficient =[tex](6 choose 4)*((1/3)^4)*(-3)^2 * a^8 * b^2[/tex]. After calculation this simplifies to -45/16.
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A ring is now reduced to £840 this is a saving of 40% of the original price whats the original price of the ring
Answer:
1400 dollars
Step-by-step explanation:
Let the original price = 100
Less: saving of 40% = 40
Reduced price = 60
Reduce price of 60 is equivalent to 840 dollars
Hence original price of 100 is equivalent to
100/60 = x/840
Or x = 1400 dollars.
Original price actual = 1400 dollars.
Verify: Original price = 1400
Less: 40% = 560
Reduced price = 1400-560 =840 (given)
Hence verified
Solve for x.
x+5.39>4.48
Enter your answer, as an inequality, in the box.
x + 5.39 > 4.48
-5.39 -5.39
x > -0.91
Answer: x > -0.91
In the next Olympics, the United States can enter four athletes in the diving competition. How many different teams of four divers can be selected from a group of nine divers?
A.
36
B.
126
C.
3,024
D.
6,561
A company sells two versions of an antivirus software. The home edition costs $23.50, and the business edition costs $58.75. Last week, the company earned $29,668.75 from selling 745 copies of the software. If x represents the number of copies of the home edition sold and y represents the number of copies of the business edition sold, which system of equations represents this situation? A. B. C. D.
Answer:
[tex]\left \{ {{x+y=745} \atop {23.50x+58.75y=29,668.75}} \right.[/tex]
Step-by-step explanation:
1. You must analize the information given in the problem.
2. The first equation:
- [tex]x[/tex] represents the number of copies of the home edition sold and [tex]y[/tex] represents the number of copies of the business edition sold.
- A total of 745 copies were sold last week.
- Therefore, if you add the number of copies of the home edition sold and the number of copies of the business edition sold, you will obtain a total of 745 copies, which you can express as below:
[tex]x+y=745[/tex]
3. The second equation:
- The cost of each version is:
[tex]23.50x\\58.75y[/tex]
- If the company earned a total of $29,668.75, you have:
[tex]23.50x+58.75y=29,668.75[/tex]
Use the quadratic formula to find the solutions to the quadratic equation below 2x^2-5x+5=0
Answer:
x = (5 + i sqrt(15))/4 or x = (5 - i sqrt(15))/4
Step-by-step explanation:
Solve for x:
2 x^2 - 5 x + 5 = 0
Hint: | Using the quadratic formula, solve for x.
x = (5 ± sqrt((-5)^2 - 4×2×5))/(2×2) = (5 ± sqrt(25 - 40))/4 = (5 ± sqrt(-15))/4:
x = (5 + sqrt(-15))/4 or x = (5 - sqrt(-15))/4
Hint: | Express sqrt(-15) in terms of i.
sqrt(-15) = sqrt(-1) sqrt(15) = i sqrt(15):
Answer: x = (5 + i sqrt(15))/4 or x = (5 - i sqrt(15))/4
The quadratic equation has an imaginary roots, which is can be calculated using the quadratic formula.
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
2x² - 5x + 5=0
Here a = 2, b = -5, and c = 5
[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(2)(5)}}{2(2)}[/tex]
[tex]\rm x = \dfrac{5 \pm\sqrt{-15}}{4}[/tex]
[tex]\rm x = \dfrac{5 \pm i \sqrt{15}}{4}[/tex] (√(-15) = 15i; i is the iota)
The roots are:
[tex]\rm x = \dfrac{5 + i \sqrt{15}}{4} \\\\\rm x = \dfrac{5 - i \sqrt{15}}{4}[/tex]
Thus, the quadratic equation has an imaginary roots, which is can be calculated using the quadratic formula.
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I really wish I understood this stuff but I don’t. Please help
Choose the number sentence that shows the distributive property of multiplication over addition.
A.
3 × (4 + 5) = (3 × 4) + (3 × 5)
B.
3 × (4 + 5) = (3 + 4) × (3 + 5)
C.
3 × (4 + 5) = (3 × 4) + 5
we know that
distributive property of multiplication over addition:
[tex]a \times (b+c)=a \times b + a \times c[/tex]
now, we will verify each options
option-A:
3 × (4 + 5) = (3 × 4) + (3 × 5)
We can see that both sides match with property
so, this is TRUE
option-B:
3 × (4 + 5) = (3 + 4) × (3 + 5)
We can see that right side does not match with property
so, this is FALSE
option-C:
3 × (4 + 5) = (3 × 4) + 5
We can see that right side does not match with property
so, this is FALSE
HELP ASAP!!!!
Simplify. 4√16x^4y^12 Assume all variables are nonnegative.
Answer:
The given Expression is
[tex]4\sqrt{16x^4y^12[/tex]
= 4 × terms under square root are non negative.so we can break it into different terms.
= 4 × √16 ×[tex]\sqrt{x^4}\times\sqrt {y^{12}}[/tex]
Breaking into factors
= 4 × [tex]\sqrt{2\times2\times\times2\times2 } \times\sqrt{x \times x \times x \times x } \times \sqrt{ y \times y \timesy \times y \timesy \times y \times y \times y \times y \times y \times y \times y \times y \times y[/tex]
= 4× [tex]2 \times2 \times x \times x \times y\times y\times y\times y\times y\times y[/tex]
= 16× [tex]x^{1+1}\times y^{1+1+1+1+1+1}[/tex]
= 16 [tex]x^2 y^6[/tex]
The solution of the expression 4√(16x⁴y¹²) will be 16x²y⁶.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
The given expression is 4√(16x⁴y¹²). The expression will be solved as:-
E = 4√(16x⁴y¹²)
E = 4 √ [( 4 x 4 ) ( x² x x² ) ( x⁶ x x⁶ )]
E = 4 ( 4 x x² x y⁶ )
E = 16x²y⁶.
Therefore, the solution of the expression 4√(16x⁴y¹²) will be 16x²y⁶.
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Walt grew 10 cm in one year. He is now 1.6 m tall. How tall was he 1 year ago?
Maya shaved her head and then began letting her hair grow. She represents the length L of her hair, in centimeters, m months after she shaved her head using the equation L = 1.25m What does 1.25 mean in this situation?
In the given equation (L = 1.25m), 1.25 means that the length of the Maya hair increased by 1.25 centimeters every month.
Given :
Maya shaved her head and then began letting her hair grow. She represents the length L of her hair, in centimeters, m months after she shaved her head using the equation L = 1.25m.The following steps can be used in order to determine the meaning of 1.25:
Step 1 - According to the given data, Maya shaved her head and then began letting her hair grow.
Step 2 - It is also given that, L is the length of the hair in centimeters and m represents the month after she shaved her head.
Step 3 - The equation that represents the given situation is:
L = 1.25m
Step 4 - In the above equation 1.25 means that the length of the Maya hair increased by 1.25 centimeters every month.
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The vertices of triangle rst are r(–1,–2), s(2,–1), and t(4,2). If δjkl ∼ δrst and the length of kl is units , what is the length of jk?
Answer:
3.16 units
Step-by-step explanation:
It has been given that the triangles JKL and the triangle RST are congruent.
That implies that, the length of the side JK, KL, and JL is equivalent to the length of the sides RS, ST, and RT respectively.
Now, to find the length of JK we need to find the length of the side RS. The coordinates of the points R and S are [tex](-1,-2)[/tex] and [tex](2,-1)[/tex].
The length of the side RS is equal to the distance between point R and S.
RS [tex]=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]= \sqrt{(2-(-1))^2+(-1-(-(-2))^2}[/tex]
[tex]=\sqrt{3^2+(-1+2)^2}[/tex]
[tex]=\sqrt{9+1}=\sqrt{10}=3.16[/tex]
Now that we have the length of the side RS, and the triangles JKL and RST are congruent therefore, the length of the side JK is 3.16 units.
Answer:
sq root of 10 over 2
Step-by-step explanation:
took it on edge
Can someone please help me with # 2 #13 thanks show work how it's done, please
Problem 13
10p+10q factors to 10(p+q). If we apply the distributive property, we can distribute the 10 to each term inside (p and q) to get
10(p+q) = (10 times p)+(10 times q) = 10*p + 10*q = 10p+10q
so we get the original expression again. Here 10 is the GCF of the two terms.
--------------------------------------------------------------
Plug p = 1 and q = 2 into the factored form
10*(p+q) = 10*(1+2) = 10*(3) = 30
As a check, let's plug those p,q values into the original expression
10*p+10*q = 10*1+10*2 = 10+20 = 30
We get the same output of 30
A sporting good store sold 2.5 as many footballs as basketballs last year. How many footballs sold for every 2 basketballs said sold?
The store sold 1.25 footballs for every 2 basketballs.
To determine how many footballs were sold for every 2 basketballs, we can set up a ratio based on the information given. Let's denote the number of basketballs sold as [tex]\( B \)[/tex] and the number of footballs sold as [tex]\( F \)[/tex]. According to the problem, the store sold 2.5 times as many footballs as basketballs, which can be expressed as:
[tex]\[ F = 2.5B \][/tex]
Now, we want to find out how many footballs were sold for every 2 basketballs. To do this, we can divide both sides of the equation by 2 to find the number of footballs that correspond to 2 basketballs:
[tex]\[ \frac{F}{2} = \frac{2.5B}{2} \][/tex]
Simplifying the right side of the equation, we get:
[tex]\[ \frac{F}{2} = 1.25B \][/tex]
This means that for every 2 basketballs sold [tex](\( 2B \))[/tex], there were 1.25 footballs sold [tex](\( F \))[/tex]. Therefore, the store sold 1.25 footballs for every 2 basketballs.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!! I CANNOT RETAKE THIS!!
The number of trucks registered in a city increases by 10% each year. Initially, there were 100 trucks registered. There were 110 trucks registered at the end of Year 1.
What is the number of trucks registered in the city at the end of Year 8?
Round the answer to the nearest whole number.
100 (1 + 0.1)^8
= 100 (1.1)^8
= 214
Answer
214 trucks registered in the city at the end of Year 8
Tim counts his friends fingers by fives.He counts six hands.What numbers does he say?
Paolo paid $28 for a hat that was originally priced at $35. By what percent was the hat discounted?
Final answer:
To find the discount percentage, subtract the sale price from the original price, divide the difference by the original price, and multiply by 100. Paolo's hat was discounted by 20%.
Explanation:
To calculate the percentage of the discount that Paolo received on the hat, we need to find the difference between the original price and the sale price, and then divide that difference by the original price. Afterward, we multiply the result by 100 to get the percentage.
The original price of the hat was $35, and Paolo paid $28. The difference between the original price and the sale price is $35 - $28 = $7. Therefore, the discount is $7.
Now, we calculate the percentage discount: ($7 / $35) x 100 = 20%. So, the hat was discounted by 20%.
What number can you cube that is bigger than 600 but smaller than 800
9 to the power of three, or cubed = 720 which is between 600 and 800.
The number you're looking for would be a decimal between approximately 8.375 and 8.6. When these numbers are cubed, they fall in the range of 600 to 800.
Explanation:The question at hand is asking about cubing a number to get a result that is larger than 600 but smaller than 800. We are looking to find the cube root of numbers in this range. The integer cube roots closest to this range are the cube root of 512 (which is 8) and the cube root of 729 (which is 9).
However, neither of these is a number that you could cube to end up in the 600 to 800 range. Therefore, the desired number is not a whole number, but a decimal. If you estimate, any number between 8.375 and 8.6, when cubed, should meet the condition—meaning it would be larger than 600 but still less than 800.
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Need answers!! Will give 20 pts. !!
please help asap 30 pts
Step 1. Subtract 4y from both sides
5y + 18 - 4y = -3.2
Step 2. Simplify 5y + 1.8 -4y to y + 1.8
y + 1.8 = -3.2
Step 3. Subtract 1.8 from both sides
y = -3.2 - 1.8
Step 4. Simplify -3.2 - 1.8 to -5
y = -5
Your answer is A.
[tex]5y+1.8=4y-3.2\qquad|\text{subtract 1.8 from both sides}\\\\5y=4y-5\qquad|\text{subtract 4y from both sides}\\\\\boxed{y=-5}\to\boxed{a.}[/tex]
Is the relationship between Kelvin and degrees Celsius proportional? Justify your answer in two different ways.
The relationship between Kelvin and degrees Celsius is not proportional in any way.
What is temperature?The temperature is the degree of the hotness and the coldness.
We know that
1 Kelvin = -273.15 degree Celsius
Kelvin is a unit of absolute temperature used in measurements and it can also be associated with degrees Celsius.
0 Kelvin is equivalent to -273.15 degrees Celsius.
In order to solve for the unit of temperature, the equation is:
T(Kelvin)= T(degrees Celsius) + 273.15
T(degrees Celsius) = T(Kelvin) - 273.15
The relationship between Kelvin and degrees Celsius is not proportional in any way.
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write 5,400,300 in standard form - help!
Hello,
This number is already in stranded form.
If you want it in scientific notation its : 5.4003*10^6
Hope this helps a bit.
Answer:
[tex]5.4x10^{6}[/tex]
Step-by-step explanation:
The standard form refers to the way of writing large numbers in a smaller expression using power of 10, this is also called scientific notation.
To write this number in standard form, we have to the decimal point to the position between the 5 and the 4, and all spaces jumped represent the exponent of the 10 power, as follows
[tex]5400300=5.4x10^{6}[/tex]
Therefore, the standard form would be
[tex]5.4x10^{6}[/tex]
Jeanine sells a house for 159,000. Her rate of commission is 2.2%. What is her commission on that sale?
Answer:
Her commission on that sale is $3,498
Step-by-step explanation:
1. You have the following information given in the problem above:
- She sells the house for $159,000.
- Her rate of commission is 2.2% (0.022).
2. Therefore, to solve this problem you only need to multiply $159,000 by 2.2% (0.022), as following:
[tex](159,000)(0.022)=3,498[/tex] dollars