Answer:
Beena = 19 years old
Seema = 28 years old
Step-by-step explanation:
Beena = x
Seema = x + 9
x + 9 + 10 = 2x
19 + x = 2x
2x - x = 19
x = 19
You flip 3 coins 20 times and record the number of heads. The results are listed below. 2, 1, 0, 2, 2, 0, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 2, 1, 3, 1 Complete the frequency table. a = ; b = ; c = ; d = Based on these results, which of these statements are true? You would expect to get 0 heads and 3 heads about the same number of times. You would expect to get 1 head and 2 heads about the same number of times. This would be a good experiment to use to find the probability that a family has a dog or a cat. This would be a good experiment to use to find the probability that a family with 3 kids has 1 boy.
The true statements about the result of the coin toss experiment described are :
You would expect to get 0 heads and 3 heads about the same number of times. You would expect to get 1 head and 2 heads about the same number of timesNumber of heads :__0 __ 1 __ 2 __ 3
Frequency _____ :_ 2___7___9___2
Expected Number of 0 heads = 2 Expected Number of 3 heads = 2Expected Number of 1 head = 7Expected Number of 3 heads = 9Therefore, expected Number of 3 and 0 heads are the same. And the expected number of 1 and 2 heads are almost the same.
The experiment cannot be used to model the events in the options as it only gives the number of occurence of a single event.
Hence, only statements 1 and 2 are true.
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The frequency of 0, 1, 2, and 3 heads in the experiment is 2, 7, 10, and 1 respectively. Statement 2 is the most accurate regarding long-term expectations, while statement 4 can be considered conditionally true. Statements 1 and 3 are not related to the probability outcomes of the experiment.
To complete the frequency table based on the given results, we will count the occurrences of each number of heads (0, 1, 2, or 3) in the 20 trials. The frequencies are:
0 heads (a): 2 times1 head (b): 7 times2 heads (c): 10 times3 heads (d): 1 timeBased on these results, we can discuss the truthfulness of the provided statements:
You would not expect to get 0 heads and 3 heads about the same number of times because the probability of getting 0 or 3 heads is lower than 1 or 2 heads when flipping three coins.You would expect to get 1 head and 2 heads about the same number of times in the long term, according to the law of large numbers, which states that as the number of trials increases, the empirical relative frequency of the outcomes approaches the theoretical probability.This would not be a good experiment to use to find the probability that a family has a dog or a cat, as the outcomes of coin flips do not correlate to pet ownership statistics.This could be a relatively good experiment to use to find the probability that a family with 3 kids has 1 boy, assuming that the gender of each child is independent and that the probability of being born a boy is equal to that of being born a girl (each coin flip can represent the birth of a child, with heads representing boys).2 squares area is 125 yards and 5 yards. how many yards would it take to fence the two squares in separately
Answer:
[tex]24\sqrt{5}\ yards[/tex]
Step-by-step explanation:
Let A1 be the area of one square and A2 be the area of second square
So,
A1 = s^2
where s is side of square
[tex]s^2=125\\\sqrt{s^2}=\sqrt{125}\\s=\sqrt{25*5}\\ s= \sqrt{5^2 * 5}\\ s= 5\sqrt{5}[/tex]
So side of one square is [tex]5\sqrt{5}[/tex]
To calculate the length of fence we need to find the perimeter of the square
So,
P1 = 4 * s
[tex]=4*5\sqrt{5} \\=20\sqrt{5}[/tex]
For second square:
[tex]A_2=s^2\\5=s^2\\\sqrt{s^2}=5\\{s}=\sqrt{5}[/tex]
The perimeter will be:
[tex]P_2 = 4*s\\=4 * \sqrt{5} \\=4\sqrt{5}[/tex]
So the total fence will be: P1+P2
[tex]= 20\sqrt{5}+4\sqrt{5} \\= 24\sqrt{5}\ yards[/tex]
One serving of Chad's favorite cereal contains 1 1/4 ounces. How many servings are in a 15 1/3 ounce box
so namely how many times does 1¼ go into 15⅓?
let's firstly convert the mixed fractions to improper fractions and then divide.
[tex]\bf \stackrel{mixed}{1\frac{1}{4}}\implies \cfrac{1\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{5}{4}}~\hfill \stackrel{mixed}{15\frac{1}{3}}\implies \cfrac{15\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{46}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{46}{3}\div\cfrac{5}{4}\implies \cfrac{46}{3}\cdot \cfrac{4}{5}\implies \cfrac{184}{15}\implies 12\frac{4}{15}[/tex]
What is the radius and diameter of the following circle?
Answer:
The radius of the circle is already there, 11cm, and the diameter is 2 times the radius, which is 22
Step-by-step explanation:
First, you look at the radius (which is half of the circle) which is 11, then you multiply that times two to get the diameter. :)
What is 692,119 rounded to the nearest thousand
In order to get the answer to this problem you will have to go to the thousands place value and look at the number next to the place value and if the number is greater then 5 then you round up which will give you your answer.
[tex]692,119[/tex]
[tex]2,119[/tex]
[tex]1<5[/tex]
[tex]= 2000[/tex]
[tex]= 692,000[/tex]
Which means your answer is "692,000."
Hope this helps.
The value 692,119 is rounded to the nearest thousand is 692,000. The nearest thousand for the given number is 2000.
How to round off a number?A number (integer or decimal) is rewritten to the nearest place value (ones, tens, hundreds, thousands, and so on). The rewritten number is said to be the rounded value of the given number. A number is rounded off at any of its place values on the basis of the digit after the digit which is to be rounded.I.e., if the digit after that place is less than 5 (< 5) then round the number down, or if the digit after that place is greater than or equal to 5 ( ≥ 5) then round the number up. If the digit is less than 5, then all the digits after the required place value are rounded as zerosIf the digit is more than 5 or equal to 5, then add 1 to the digit in the required place value and round all the other digits after it as zeros.Rounding the given number to the nearest thousand?The given number is 692,119
The digit in the thousands place of the given number is 2.
The digit after 2 is 1 which is less than 5. So, the digits after the thousand place is rounded as zeros. I.e., 2119 to 2000.
Therefore, the rounded number is 692,000.
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Lorena took a survey of the students in her honors science class to determine how many are going to college. She found that 85% of the students plan to go to college.
Can Lorena make the inference that 85% of all the seniors at her school are going to college?
Answer:
No, Lorena cannot make the inference about all the seniors going to college.
Step-by-step explanation:
We are given that Lorena took a survey of students in her science class to determine how many of them were going to college.
From the survey results, she found that 85% of the students from her science class were going to the college but with these results she cannot infer that 85% of all the seniors at her school were going to college.
This is because the survey was biased as it was not taken from the entire school but only Lorena's science class.
Answer:
No, Lorena’s sample was biased because it was taken only from an honors class.
No, Lorena’s sample was not a random sample of the entire school.
those are the two correct answers, i took the test!
HELP ASAP
What is the area of the triangle?
A)24 square units
B)32 square units
C)48 square units
D)96 square units
Answer:
A. 24 square units
Step-by-step explanation:
length is 8 and height is 6
gets you 48 but you need to divide by 2 because its a triangle so you get 24
Answer:
a
Step-by-step explanation:
classify the system of equations 2x=-3-y 4+y=-2x-2
intersecting
parallel
coincident
please hurry!
Answer:
parallel
Step-by-step explanation:
we have
2x=-3-y
isolate the variable y
y=-2x-3 ----> equation A
4+y=-2x-2
isolate the variable y
y=-2x-2-4
y=-2x-6 -----> equation B
Remember that
If two lines are parallel, then their slopes are the same
Line A and Line B have the same slope m=-2 and different y-intercept
therefore
The lines are parallel
Answer:
Second option: Parallel.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Solve for "y" in each equation:
Equation 1
[tex]2x=-3-y \\\\2x+y=-3\\\\y=-2x-3[/tex]
Equation 2
[tex]4+y=-2x-2\\\\y=-2x-2-4\\\\y=-2x-6[/tex]
You can notice that the slope of the Equation 1 is:
[tex]m_1=-2[/tex]
And the slope of the Equation 2 is:
[tex]m_2=-2[/tex]
Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are: Parallel.
solve the equation 53=-6-17x
Answer:
-59/17 =x
Step-by-step explanation:
53=-6-17x
Add 6 to each side
53+6=-6+6-17x
59 = -17x
Divide each side by -17
59/-17 = -17x/-17
59/-17 = x
-59/17 =x
Given the functions, fx) = x^2-4 and g(x) = x+ 2, perform the indicated operation. When applicable, state the domain
restriction.
F(g(x))
To perform F(g(x)), substitute g(x) into F(x) by squaring g(x) and subtracting 4. The domain of F(g(x)) is all real numbers.
Explanation:The question asks us to perform the composition of two functions - f(x) and g(x). Composition is denoted by (f ∘ g)(x) and involves substituting the output of the inner function (g(x)) into the input of the outer function (f(x)). In this case, we have f(g(x)), which means we need to substitute g(x) into f(x).
First, substitute g(x) into f(x) to get f(g(x)):
f(g(x)) = (g(x))^2 - 4 = (x+2)^2 -4 = x^2 + 4x + 4 - 4 = x^2 + 4x.
The domain restriction is the set of all values that x can take. Since there are no restrictions mentioned in the question, the domain is all real numbers.
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XYZ is a dilation of triangle ABC by a scale factor of 5. Which of the following proportions verified that triangle ABC and XYZ are similar?
Answer:
C. AB/XY = AC/XZ
Step-by-step explanation:
Dilation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The original figure either stretches or shrinks by a certain factor.
In the problem, the dilation is by a factor of 5 and we can see that ABC shrinks to form XYZ.
So, ABC and XYZ are similar triangles which means that the ratio of their corresponding sides will be equal:
AB/XY = AC/XZ = BC/YZ = 5
Answer with explanation:
When ΔABC is dilated by a Scale factor of 5 we will get ΔX Y Z.
Pre-Image = ΔABC
Image = ΔX Y Z
When a triangle is dilated , then the two Triangles that is Original ΔABC and Triangle after dilation ΔX Y Z will be Similar.
⇒Similar triangles has Corresponding sides proportional as well as Corresponding Angles are congruent.
≡Corresponding congruent Angles are
→∠A=∠X
→∠B=∠Y
→∠C=∠Z
≡Corresponding congruent Sides are
[tex]\frac{AB}{XY}=\frac{AC}{XZ}=\frac{BC}{YZ}[/tex]
The Proportionality statement which proves two triangles are Similar
Option B
[tex]\frac{AB}{XY}=\frac{AC}{XZ}[/tex]
Graph the following piecewise function.
Step-by-step explanation:
[tex]for\ 2<x\leq4-\text{the horizontal segment}\ y=2\\\\for\ 4<x<8\to y=x+3\\\\\text{put}\ x=4,\ \text{and}\ x=8\ \text{to the equation}\\\\y=4+3=7\to(4,\ 7)\\y=8+3=11\to(8,\ 11)\\\\for\ x\geq8\to y=2x\\\\\text{put}\ x=8,\ and\ x=9\ \text{to the equation}\\\\y=2(8)=16\to(8,\ 16)\\y=2(9)=18\to(9,\ 18)\\\\==========================[/tex]
[tex]<,\ >\ -\ \text{op}\text{en circle}\\\\\leq,\ \geq\ -\ \text{closed circle}[/tex]
what is the differences between 2^8 and 8^2?
Answer:
The answer is 192
Step-by-step explanation:
2^8 = 256
8^2 = 64
256 - 64 = 192
Remember:
2^8 is really 2*2*2*2*2*2*2*2
Remember:
8^2 is really 8*8
To find the difference, you must subtract the smaller product from the larger product.
<Hope this helps!>
Answer:
192
Step-by-step explanation:
Method 1:
2^8 - 8^2 = 2^8 - 2^6 = 2^6(2^2 - 1) = 64(3) = 192
Method 2:
2^8 - 8^2 = 256 - 64 = 192
TanX= sinX/cosX. Therefore, tan(90-A)= . (All angle measurements are in degrees.)
1/tan(90-A)
1/sin A
1/cos(90-A)
1/tan A
Answer:
tan(90 - A) = 1/tan(A) ⇒ last answer
Step-by-step explanation:
* Lets revise some important information for the right triangle
- In any right triangle
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
∵ The sum of the interior angles of any triangle is 180°
∵ m∠B = 90°
∴ m∠A + m∠C = 180° - 90° = 90°
- If the measure of angle A is x°
∴ The measure of angle C = 90° - x°
- tan(A) = opposite/adjacent
∵ The opposite to ∠A is BC
∵ The adjacent to ∠A is AB
∴ tan(A) = BC/AB ⇒(1)
- tan(C) = opposite/adjacent
∵ The opposite to ∠C is AB
∵ The adjacent to ∠C is BC
∴ tan(C) = AB/BC ⇒ (2)
- From (1) and (2)
∴ tan(A) = 1/tan(C)
∵ m∠A = A , m∠C = (90 - A)
∴ tan(A) = 1/tan(90 - A)
OR
∴ tan(90 - A) = 1/tan(A)
Answer:
LAST OPTION.
Step-by-step explanation:
Remember that:
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
[tex]\frac{cos(x)}{sin(x)}=cot(x)=\frac{1}{tan(x)}[/tex]
[tex]sin(x\±y) = sin(x)cos(y)\±cos(x)sin(y)\\\\cos(x\±y) =cos(x)cos(y)\± sin(x)sin (y) [/tex]
[tex]sin(90\°)=1\\cos(90\°)=0[/tex]
Then, you need to rewrite [tex]tan(90-A)[/tex]:
[tex]tan(90-A)=\frac{sin(90-A)}{cos(90-A)}[/tex]
Applying the identities, you get:
[tex]tan(90\°-A)=\frac{sin(90\°)cos(A)-cos(90\°)sin(A)}{cos(90\°)cos(A)-sin(90\°)sin(A))}[/tex]
Finally, you must simplify. Then:
[tex]tan(90\°-A)=\frac{(1)cos(A)-(0)sin(A)}{(0)cos(A)-(1)sin(A))}\\\\tan(90\°-A)=\frac{cos(A)}{sin(A)}\\\\tan(90\°-A)=\frac{1}{tan(A)}[/tex]
Akira and tori Chang received a total of $48,000 from an estate. They decided to put $9,600 in a trust and divide the remainder. Tori received 3/8 of the remainder. How much did Akira receive?
Answer:
$24,000
Step-by-step explanation:
After putting in trust they have left:
48000 - 9600 = $38,400
If Tori gets 3/8, Akira will get the remaining (1 - 3/8 = 5/8). So Akira will get:
[tex]\frac{5}{8}*38,400=24,000[/tex]
Hence akira will get $24,000
A point has coordinates (0, 3). Where is it located in the coordinate plane?
Choose the best answer from the options below:
A x-axis
B y-axis
C quadrant 3
D quadrant 4
Answer:
A: x-axis
I did a quiz and got it wrong when I choose B: y-axis.
Final answer:
The point with coordinates (0, 3) is on the y-axis, above the origin by 3 units. Therefore, the correct answer is B, the y-axis.
Explanation:
A point with the coordinates (0, 3) is located where the x-coordinate is 0 and the y-coordinate is 3. In the context of a two-dimensional Cartesian coordinate system, this means the point does not move left or right from the origin on the horizontal axis, but it moves up by 3 units on the vertical axis.
Therefore, the correct answer to the question is B, the point is located on the y-axis. It is neither on the x-axis nor in any of the four quadrants since its x-coordinate is zero. Hence, it lies directly above the origin on the y-axis.
What is 1.2 to the tenth power
Answer:
Step-by-step explanation:
that would be written as 1.2^10, and the end result would be the same as you'd get if you use 1.2 as a factor 10 times: 1.2*1.2*1.2* .......1.2
You could use a calculator to evaluate 1.2^10:
Typing in 1.2^10, you'll get 6.191736422.
This is not an exact answer; there are more digits following the ones shown.
Another way in which you could do this problem would be to use logs:
Let y = 1.2^10. Then log y = 10*log 1.2, or log y = 10(0.07918) = 0.791812.
Finding the antilog, we get y = 6.19174
Which statement is the most appropriate comparison of the spreads
Answer:
The answer is C
Step-by-step explanation:
Answer: D. The interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.
Step-by-step explanation:
The interquartile range is most suitable term to compare the spread of two different data displayed by box-whisker plot.
The formula for interquartile range :-
[tex]IQR=Q_3-Q_1[/tex]
For Town A , First quartile : [tex]Q_1=15[/tex]
Second quartile : [tex]Q_2=30[/tex]
[tex]IQR=30-15=15[/tex]
For Town B , First quartile : [tex]Q_1=20[/tex]
Second quartile : [tex]Q_2=40[/tex]
[tex]IQR=40-20=20[/tex]
Clearly , the interquartile range (IQR) for Town A , 15° is less than the interquartile range for town B , 20°.
x=4 is a solution to the equation
2
= x - 8
True
O False
Answer:
False
Step-by-step explanation:
2 = x - 8
Add 8 to each side
2+8 = x-8+8
10 = x
x=4 is not a solution
For this case we have the following equation:
[tex]2 = x-8[/tex]
If we add 8 to both sides of the equation, we have:
[tex]2 + 8 = x-8 + 8\\10 = x[/tex]
Thus, the solution of the equation is [tex]x = 10,[/tex] therefore[tex]x = 4[/tex]is not a solution of the given equation.
Answer:
[tex]x = 4[/tex] is not a solution to the given equation.
False
classify the following triangle
Answer:
Obtuse and Scalene
Step-by-step explanation:
Obtuse means that it is over 90 degrees, in which there is an angle of 102 degrees.
Scalene means that all three side lengths are different.
Answer:
A. Obtuse
C. Scalene
If g(x) = x2 + 2, find g(3). (2 points) 9 8 11 6
For this case we have a function of the form [tex]y = g (x)[/tex]
Where:
[tex]g (x) = x ^ 2 + 2[/tex]
We must find the value of the function when x = 3. Then we substitute:
[tex]g (3) = 3 ^ 2 + 2\\g (3) = 9 + 2\\g (3) = 11[/tex]
Thus, the value of the function when [tex]x = 3[/tex] is [tex]y = 11[/tex]
Answer:
[tex]g (3) = 11[/tex]
Option C
Answer: Third Option
[tex]g(3) = 11[/tex]
Step-by-step explanation:
We have the function [tex]g(x) = x^2 + 2[/tex] and we must find the value of g(3).
To find g (3) we must evaluate the function g(x) for x = 3. That is, we must replace x = 3 in the function
Then
[tex]g(x) = x^2 + 2[/tex]
[tex]g(3) = (3)^2 + 2[/tex]
[tex]g(3) = 9 + 2[/tex]
[tex]g(3) = 11[/tex]
Finally the correct answer is the third option
PLEASEEEE I NEED HELPP
Answer:
∠C = 143°
Step-by-step explanation:
For the quadrilateral to be a parallelogram
Then ∠C = ∠A
Given ∠B = ∠D then consecutive angles are supplementary, that is
∠C + ∠D = 180
∠C + 37 = 180 ( subtract 37 from both sides )
∠C = 143°
what would the answer be
Solve the system of equations.
5x + y = 9
3x + 2y = 4
Answer:
(x,y) (2,-1)
Step-by-step explanation:
Answer:
the first one is 2 the second one is 3
Step-by-step explanation:
what is the 17th term in the arithmetic sequence in which a6 is 101 and a9 is 83
Answer:
The 17th term in arithmetic sequence is 68
Step-by-step explanation:
The general formula of arithmetic sequence is:
aₙ = a₁ + (n – 1)d.
We are given a₆ = 101 and a₉ = 83 and we need to find a₁₇
To find the term a₁₇ we should know a₁ and d. So we would find both
a₆ = a₁ +(6-1)d
101 = a₁ +(5)d
101 = a₁ +5d eq(1)
and
a₉ = a₁ +(9-1)d
83 = a₁ + 8d eq(2)
Subtracting eq(2) from eq(1)
101 = a₁ +5d
83 = a₁ + 8d
- - -
__________
18 = -3d
=> d = 18/-3
=> d = -6
Putting value of d in eq(1)
101 = a₁ + 5d
101 = a₁ + 5(-3)
101 = a₁ -15
=> a₁ = 101+15
=> a₁ = 116
Now finding a₁₇:
aₙ = a₁ + (n – 1)d.
a₁₇ = 116 +(17-1)(-3)
a₁₇ = 116+(16)(-3)
a₁₇ = 116 - 48
a₁₇ = 68
So, the 17th term in arithmetic sequence is 68
Solve 3^(x+1) = 15 for x using the change of base formula
[tex]\bf \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\\\ \textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 3^{x+1}=15\implies \log_{10}(3^{x+1})=\log_{10}(15)\implies (x+1)\log_{10}(3)=\log_{10}(15) \\\\\\ x+1=\cfrac{\log_{10}(15)}{\log_{10}(3)}\implies \stackrel{\textit{change of base rule}}{x=\cfrac{\log_{e}(15)}{\log_{e}(3)}-1}\implies x\approx 1.47[/tex]
Answer:
[tex]x=\frac{log(15)}{log(3)}-1[/tex]
Step-by-step explanation:
[tex]3^{x+1} = 15[/tex]
LEts convert exponential form to log form
[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]
WE apply the same rule to convert the given exponential form to log form
[tex]3^{x+1} = 15[/tex]
[tex]log_3{15} = x+1[/tex]
HEre the base of log is 3. Lets apply change of base formula
[tex]log_b(a)=\frac{log(a)}{log(b)}[/tex]
[tex]log_3{15} = x+1[/tex]
[tex]\frac{log(15)}{log(3)} = x+1[/tex]
Now subtract 1 from both sides
[tex]x=\frac{log(15)}{log(3)}-1[/tex]
Seth bought a T-shirt that costs $21.00. If the tax rate was 8%, what was the total cost of the t-shirt?
Answer:
$22.68
Step-by-step explanation:
21×.08= 1.68
21+1.68=22.68
Total cost =$22.68
Answer:
22.68
Step-by-step explanation:
The first step is to find the amount of tax
tax = original cost * tax rate
= 21 * 8%
= 21 * .08
=1.68
Then we add the tax to the original cost to find the total cost
total cost = original cost + tax
= 21 + 1.68
=22.68
The table and graph both represent the same relationship. Which
equation also represents that relationship?
Answer:
A
Step-by-step explanation:
Just try to label the data in a table for every choice. It is clearly A. If you tried to solve it you will find that =
(-2)² = 4
(-1)² = 1
1² = 1
2² = 4
Brody can fill a bowl with candy in 3 minutes. While Brody fills the bowl, Hudson takes the candy out of the bowl. With Hudson taking candy out of the
bowl, it takes 5 minutes for Brody to fill the bowl.
Which of the following can be used to determine the amount of time it takes for Hudson to empty the bowl if Brody does not add candy?
Answer:
1/3 - 1/x=1/5
Step-by-step explanation:
Let the total work be "1"
Brody Hudson Brody+Hudson
Time 3 mins x min 5 min
Efficiency 1/3 -1/x 1/5
The efficiency of Hudson is negative as he is taking out the candies out of the bowl, since efficiency of Brody + efficiency of Hudson = efficiency of both, which means,
1/3 - 1/x = 1/5....
The density of a American white oak tree is 752 kilograms per cubic meter. If the trunk of an American white oak tree has a circumference of 4.5 meters and a height of 8 meters, what is the approximate number of kilograms of the trunk?
1. 13
2. 9694
3. 13,536
4. 30, 456
Check the picture below.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=4.5 \end{cases}\implies 4.5=2\pi r\implies \cfrac{4.5}{2\pi }=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} h=8\\ r=\frac{4.5}{2\pi } \end{cases}\implies V=\pi \left( \cfrac{4.5}{2\pi } \right)^2(8)\implies V=\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} \cdot \cfrac{20.25}{\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}\underset{\pi }{\begin{matrix} \pi^2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }}(\stackrel{2}{\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}})[/tex]
[tex]\bf V=\cfrac{40.5}{\pi }~cm^3~\hspace{9em} \stackrel{\textit{since density is }752kg~per~cm^3}{density\implies 752\left( \cfrac{40.5}{\pi } \right)}\qquad \approx ~~9694[/tex]
Option 2 is correct. The approximate weight of the trunk of an American white oak tree with a circumference of 4.5 meters and a height of 8 meters is calculated by finding the volume of the trunk and multiplying it by the tree's density, resulting in approximately 9,694 kilograms.
To calculate the approximate weight of the trunk of an American white oak tree, we first need to estimate its volume and then multiply it by the tree's density. Since the tree trunk is cylindrical, we can use the formula for the volume of a cylinder, [tex]V = \(pi \times r^2 \times h\)[/tex], where r is the radius of the base and h is the height of the cylinder. The circumference is given by C = 2 times pi times r, so we can solve for r by rearranging the formula: [tex]\(r = \frac{C}{2 \times \\pi}\)[/tex]. With a circumference of 4.5 meters, the radius is [tex]\(r = \frac{4.5 \text{m}}{2 \times \pi}\approx 0.716m\)[/tex]. Plugging the radius and the height (8 m) into the volume formula gives V approx pi times (0.716m)^2 times 8 m approx 13.07 m^3.
Knowing the volume, we can find the mass of the trunk by multiplying the tree's volume by its density. The density of American white oak is given as 752 kilograms per cubic meter. The mass (m) is then [tex]m = V \times \ext{density} = 13.07 m^3 \times 752 \frac{kg}{m^3} \approx 9,832.64 kg.[/tex] Rounding off gives us approximately 9,694 kilograms, which is option 2 and is the closest answer provided in the question.
What is the value of x in this system of equations? Express the answer as a decimal rounded to the nearest tenth.
-5x - 12y = -8
5x + 2y = 48
Answer:
x = 11.2
Step-by-step explanation:
-5x - 12y = -8
5x + 2y = 48
you can combine all like terms from both equations together:
0x-10y=40
simplified:
-10y=40
y=-4
now you plug in the value of y into either equation:
5x+2(-4)=48
simplify
5x-8=48
add 8
5x=56
divide by 5
x=56/5=11.2