The volume of the ball (sphere) that Jerry needs to determine can be computed with a diameter of 4 inches, rounded to the nearest hundredth, as 33.52 inches³.
What is the volume?The volume refers to the capacity of an object, cylinder, sphere, or box.
Diameter of the ball = 4 inches
Radius = d/2
= 2 inches
The volume can be determined using the radius, which is half of the diameter, as follows:
Volume = ⁴/₃πr³
Volume = ⁴/₃ x ²²/₇ x 2³
Volume = ⁴/₃ x ²²/₇ x 8
Volume = 33.52 inches³
Thus, we can conclude that Jerry's ball has a volume of 33.52 inches³.
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find the complement set of S: U= {1,2,3,4,5,6,7,8,9,10} ,S= {2,4,6,7}
The complement set of S is {1, 3, 5, 8, 9, 10}.
To find the complement set of S, we need to identify all the elements in the universal set U that are not present in set S.
Given:
Universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Set S = {2, 4, 6, 7}
The complement set of S, denoted as S', consists of all the elements in U that are not in S.
Complement set of S (S') = U - S
To find S', we subtract the elements of S from U:
S' = {1, 3, 5, 8, 9, 10}
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Write the expression, 15
-
(6 - 3r), using the fewest possible terms.
Answer: 9 + 3r
Step-by-step explanation:
To reduce the number of terms we need to combine like terms
15 - (6-3r)
Distributive property (distribute the -1)
15 - 6 + 3r
9 + 3r
which number comes next in this series 5, 7, 11, 19, 35
Answer: 67
Step-by-step explanation:
We see a pattern where we multiply the number we added by previously by two.
For example, from 5 to 7, it is 2.
From 7 to 11, we add by 4.
From 11 to 19, we add by 8.
From 19 to 35, we add by 16.
This means the next number would be 32, adding 35 by 32 gives us 67,
Which ordered pairs in the form (x, y) are solutions to the equation 3x−4y=21? Select each correct answer. Responses (−1, −6) begin ordered pair negative 1 comma negative 6 end ordered pair (7, 0) begin ordered pair 7 comma 0 end ordered pair (−3, 3) begin ordered pair negative 3 comma 3 end ordered pair (11, 3) Begin ordered pair 11 comma 3 end ordered pair
To determine which ordered pairs satisfy the equation 3x - 4y = 21, we can substitute the given x and y values into the equation and check if the equation holds true.
Let's check each ordered pair:
1. (-1, -6):
Substituting x = -1 and y = -6 into the equation: 3(-1) - 4(-6) = 3 + 24 = 27, which is not equal to 21. Therefore, (-1, -6) is not a solution.
2. (7, 0):
Substituting x = 7 and y = 0 into the equation: 3(7) - 4(0) = 21, which is equal to 21. Therefore, (7, 0) is a solution.
3. (-3, 3):
Substituting x = -3 and y = 3 into the equation: 3(-3) - 4(3) = -9 - 12 = -21, which is not equal to 21. Therefore, (-3, 3) is not a solution.
4. (11, 3):
Substituting x = 11 and y = 3 into the equation: 3(11) - 4(3) = 33 - 12 = 21, which is equal to 21. Therefore, (11, 3) is a solution.
Based on the calculations, the ordered pairs that are solutions to the equation 3x - 4y = 21 are (7, 0) and (11, 3).
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Which statement is true??
it's the second answer 2 and 3 are same side interior angles
In ΔRST, r = 18 inches, s = 46 inches and ∠T=158°. Find ∠R, to the nearest degree.
Check the picture below.
let's firstly find side "t"
[tex]\textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)\cos(C)\implies c = \sqrt{a^2+b^2-(2ab)\cos(C)} \\\\[-0.35em] ~\dotfill\\\\ t = \sqrt{18^2+46^2~-~2(18)(46)\cos(158^o)} \implies t = \sqrt{ 2440 - 1371168 \cos(158^o) } \\\\\\ t \approx \sqrt{ 2440 - (-1535.42) } \implies t \approx \sqrt{ 3975.42 } \implies t \approx 63.05 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{Law of Sines} \\\\ \cfrac{\sin(\measuredangle A)}{a}=\cfrac{\sin(\measuredangle B)}{b}=\cfrac{\sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin( R )}{18}\approx\cfrac{\sin( 158^o )}{63.05}\implies 63.05\sin(R)\approx18\sin(158^o) \\\\\\ \sin(R)\approx\cfrac{18\sin(158^o)}{63.05} \implies R\approx\sin^{-1}\left( ~~ \cfrac{18\sin( 158^o)}{63.05} ~~\right)\implies \boxed{R\approx 6.14^o}[/tex]
Make sure your calculator is in Degree mode.
find the indicated partial derivative. f(x, y) = y sin−1(xy); fy 4, 1 8
Therefore, the value of fy at (4, 1) is (sin⁻¹(4) + 4/√(-60)) / 8, or approximately -0.105 for given partial derivatives.
To find fy, we need to take the partial derivative of f with respect to y, treating x as a constant. Using the chain rule, we get:
f(x, y) = y sin⁻¹(xy)
∂f/∂y = sin⁻¹(xy) + y(1/√(1 - x²y²))(x)
Now we can substitute the given values of x and y to get:
∂f/∂y (4, 1) = sin⁻¹(4) + 1(1/√(1 - 16))(4)
= sin⁻¹(4) + 4/√(-60)
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.In a multiple regression model, the variance of the error term `eâ is assumed to be the same for all values of the dependent variable.
A)the same for all values of the independent variable
B)zero.
C)the same for all values of the independent variable.
D)one.
In a multiple regression model, the variance of the error term e is assumed to be the same for all values of the independent variable. Therefore, the correct option is C) the same for all values of the independent variable.
In multiple regression, we use several independent variables to predict the values of the dependent variable. The model estimates the relationship between the independent variables and the dependent variable by calculating the coefficients of the independent variables.
The error term e represents the difference between the predicted value of the dependent variable and the actual value of the dependent variable.
The assumption of constant variance of the error term e is known as homoscedasticity. It means that the variance of the errors is the same for all levels of the independent variables.
This assumption is important because, if the errors have different variances across the levels of the independent variable, the model may not accurately capture the relationship between the independent variables and the dependent variable, leading to biased and unreliable results. so, the correct answer is C).
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a laborer charges a fixed amount
of $100.00 for a day's weeding
contract plus an additional amount
for each acre of land cleared per day.
on a particular day, he was paid
$1500.00 for weeding 5 acres
of land, find.
the amount he received per acre
Answer: The laborer charges $100.00 for a day's weeding contract and was paid $1500.00 for weeding 5 acres of land. This means he received $1500.00 - $100.00 = $1400.00 for weeding 5 acres of land.
The amount he received per acre is $1400.00 / 5 acres = $280.00 per acre.
So the answer is 280
3 mi.
1 mi.
a
What is the length of the missing leg? If
necessary, round to the nearest tenth.
a =
miles
Answer:
missing length= 2.8
Step-by-step explanation:
a^2+b^2=c^2
a^2+1^2=3^2
a^2=3^2-1^2
a^2=8
a=2.8284271247461
a=2.8
In 2000, the world population was estimated to be 6. 124 billion people. In 2005, it was 6. 515 billion. Write and exponential growth equation to represent the population y in billions t years after 2000
To represent the world population in billions t years after 2000, an exponential growth equation can be used.
Explanation:
Let y be the world population in billions t years after 2000. Let t be the time elapsed in years since 2000. Let y0 be the world population in billions in the year 2000. Let r be the annual growth rate of the world population as a decimal.
Using the exponential growth equation, we can write:
y = y0 * (1 + r)^t
To find the value of r, we can use the population data from 2000 and 2005. The population growth from 2000 to 2005 can be calculated as:
(6.515 - 6.124) / 6.124 = 0.0638
This means that the world population grew at an annual rate of 0.0638 or 6.38% per year. Therefore, the exponential growth equation for the world population in billions t years after 2000 is:
y = 6.124 * (1 + 0.0638)^t
This equation can be used to estimate the world population in any year t after 2000.
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a bicycle company needs to ship 328 bicycles across the country. if they can fit 50 bicycles in each truck about how many trucks will the company use?
The company will use approximately 7 trucks.
to separate into two or more parts or pieces. : to separate into classes or categories. : cleave entry 2, part.
To calculate the number of trucks needed, divide the total number of bicycles by the number of bicycles that can fit in each truck:
328 bicycles / 50 bicycles per truck = 6.56 trucks.
Since you can't have a fraction of a truck, the company will need to round up to the nearest whole number. Therefore, the company will use 7 trucks to ship the 328 bicycles across the country.
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to use the normal approximation for a test of two proportions, n1 p1 , n1 (1 - p1 ), n2 p2 , and n2 (1 - p2 ) must all be greater than what number?
To use the normal approximation for a test of two proportions, n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2) must all be greater than or equal to 5.
This is because the normal distribution assumes that the sample size is large enough to approximate the binomial distribution, and the rule of thumb is that each cell (n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2)) should have at least 5 expected counts. If any of these cells have fewer than 5 expected counts, then the normal approximation is not reliable and a more appropriate test should be used. It is important to note that this is just a rule of thumb, and other factors such as the size of the effect and the desired level of significance should also be considered when deciding on a statistical test.
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(2power x+y, 3power x-y) = (16, 9)
Answer:
x = 3 , y = 1
Step-by-step explanation:
[tex]2^{x+y} = 16\\2^{x+y} = 2^4\\x + y = 4 ---- (1)\\\\3^{x-y} = 9\\3^{x-y} = 3^2\\x-y = 2 ----- (2)\\\\Adding 1 and 2 , we get ,\\ 2x = 6\\x = 3\\y = 1[/tex]
Answer:
y = 1, x = 3
Step-by-step explanation:
1.) Based on the given, we have [tex]2^{x+y}[/tex] = 16, and [tex]3^{x-y}[/tex]=9. Since [tex]2^4[/tex] is equal to 16, that means that x + y = 4. Since [tex]3^2[/tex] is equal to 9, that means that x - y = 2
2.) Now, we have a system of equations. By using elimination (adding the two together), you get x + x + y - y = 2 + 4. By simplifying, the y cancels out and you get 2x = 6. Finally, you get x = 3.
3.) To end, you need to find y. Since we have x - y = 2, and x = 3, that means that 3 - y = 2, meaning y = 1.
Suppose x = 1, y = -1, and z = 1. What is the output of the following statement? (Please indent the statement correctly first.)
if (x > 0)
if (y > 0)
System.out.println("x > 0 and y > 0");
else if (z > 0)
System.out.println("x < 0 and z > 0");
A. x > 0 and y > 0;
B. x < 0 and z > 0;
C. x < 0 and z < 0;
D. no output
Based on the evaluation of the conditions, the output "x < 0 and z > 0" will be printed. Therefore, the correct answer is B. x < 0 and z > 0.
The correct indentation of the statement would be as follows:
if (x > 0)
if (y > 0)
System.out.println("x > 0 and y > 0");
else if (z > 0)
System.out.println("x < 0 and z > 0");
Given that x = 1, y = -1, and z = 1, let's evaluate the conditions:
The first if statement checks if x > 0, which is true since x = 1.
Since the condition in the first if statement is true, we move to the inner if statement, which checks if y > 0. However, y = -1, so this condition is false.
The inner if statement is followed by an else if statement that checks if z > 0. Since z = 1, this condition is true.
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joann paid $3.80 for each book sale. How much did she spendif she baught 9 books??
Answer: $34.20
Step-by-step explanation:
$3.80 is for 1 book.
Since she would buy 9 books, you would do the equation of 3.80 x 9.
You'll get the answer of 34.2, but then by making that a dollar amount it would be 34.20. Add the dollar sign, $34.20, and wahlah!
What is the diameter of a circle with circumference 264 cm?
a bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. a random sample of 98 homeowners selected from this area showed that they pay an average of $1510 per month for their mortgages. the population standard deviation of such mortgages is known to be $194. a. [3 pts] find the margin of error for a 98% confidence interval (to 3 decimal places) b. [2 pts] give the 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area (rounded to 2 decimal places). [3 pts] if the bank manager wanted to restrict the margin of error to $25, what sample size should the banker use?
The margin of error is approximately $43.51. The 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area is ($1466.49, $1553.51). The banker should use a sample size of at least 285.
a) We want to find the margin of error for a 98% confidence interval. The critical value for a 98% confidence interval with 97 degrees of freedom is 2.326. The margin of error is then:
margin of error = critical value * (standard deviation / sqrt(sample size))
= 2.326 * (194 / sqrt(98))
≈ 43.51
So the margin of error is approximately $43.51.
b) The 98% confidence interval is given by:
sample mean ± margin of error
= $1510 ± 43.51
= ($1466.49, $1553.51)
So the 98% confidence interval for the mean amount of mortgage paid per month by all homeowners in this area is ($1466.49, $1553.51).
c) We want to find the sample size required to have a margin of error of $25. Solving the margin of error formula for sample size, we get:
sample size = (critical value * standard deviation / margin of error)^2
Since we want a 98% confidence interval, the critical value is 2.326. The standard deviation is still $194. Plugging in $25 for the margin of error, we get:
sample size = (2.326 * 194 / 25)^2
≈ 284.87
So the banker should use a sample size of at least 285.
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helppppppp i need help with this
Answer: t = 7°
Step-by-step explanation:
We know that a straight line is equal to 180 degrees and that the little box represents 90 degrees. Using this information we can create an equation to solve for t.
Given:
180° = 90° + 6t° + 6° + 7t° - 7°
Combine like terms:
180° = 89° + 13t°
Subtract 89 from both sides of the equation:
91° = 13t°
Divide both sides of the equation by 13:
t = 7°
7+3x+15=-15
helppppppppppppp i need the answer VERY soon
Brandon's Furniture Store buys a sofa at a wholesale price of $97.00
If the markup rate at Brandon's Furniture Store is %40 what is the markup for the sofa?
Answer:
$38.80
Step-by-step explanation:
Simplify the expression below 6 - 8x + 3
Answer:The given expression is 6 - 8x + 3.
Combining like terms, we have:
6 - 8x + 3 = 9 - 8x
Therefore, the simplified expression is 9 - 8x.
Step-by-step explanation:
THANKS
For each diagram, write down whether the line segments are marked as parallel, perpendicular or equal-length. a) c) b) d) y
The relationships between the line segments in the diagrams are as follows:
a) Equal Length
b) Parallel
c) Perpendicular
d) Equal Length
Let's analyze each diagram and determine the relationships between the line segments.
a) Equal Length:
In this diagram, the two line segments appear to be of the same length. They do not appear to be parallel or perpendicular to each other. When the lengths of two line segments are equal and their orientation doesn't affect this equality, we say they are of equal length. In this case, both line segments simply share the same length without any specific angle relationship.
b) Parallel:
In this diagram, the two line segments run side by side in the same direction and do not intersect. When two lines follow this pattern, they are considered parallel. Parallel lines have the same slope, which means they maintain a constant distance between each other as they extend indefinitely.
c) Perpendicular:
In this diagram, the two line segments meet at a right angle, forming a perfect 90-degree angle where they intersect. When two lines intersect at a right angle, they are referred to as perpendicular. Perpendicular lines have slopes that are negative reciprocals of each other, meaning they intersect at right angles.
d) Equal Length:
Similar to the first diagram, in this case, the two line segments are of equal length. They are not parallel or perpendicular; they simply have the same length.
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Find the mean median and mode of the set of data 10,11,4,7,12,11,16
Answer:
Mean = 10.14,Mode = 11,Median = 11.-------------------------
Given data:
10, 11, 4, 7, 12, 11, 16Put the data in the ascending order:
4, 7, 10, 11, 11, 12, 16The mode, the most repeated term, is 11.
The median is the middle term, also 11.
The mean is the average:
mean = (4 + 7 + 10 + 11 + 11 + 12 + 16)/7 = 10.14 (rounded)Answer & step-by-step explanation:
Let us find the median of the data set
First, you should arrange the data in ascending to descending to find the median.
4, 7, 10, 11, 11, 12, 16
Now let us use the given formula to find the median.
[tex]\sf \dfrac{n+1}{2} =--^t^h data[/tex]
Here,
n → the number of elements
Let us find it now.
[tex]\sf Median= \dfrac{n+1}{2}\\\\\sf Median=\dfrac{7+1}{2} =4^t^h data\\\\Median=11[/tex]
Let us find the mode of the data set.
Mode is the most frequent number in the data set.
∴ mode → 11
Let us find the mean of the data set
Mean is the average of a data set.
To find that, you have to add all the data together and divide it by number of elements.
Mean = Σx ÷ n
Mean = ( 10 + 11 + 4 + 7 + 12 + 11 + 16 ) ÷ 7
Mean = 71 ÷ 7
Mean = 10.14
Work out the value of 5 to the power of a if it equal 1/125
Answer:
a = -3
Step-by-step explanation:
Step 1: Since we're told that 5 to the power of a = 1/125, we can use the following equation to solve for a:
5^a = 1/125
Step 2: Take the log of both sides
log(5^a) = log(1/125)
Step 3: According to the power rule of logs, we can bring a down and multiply it by log(5):
a * log(5) = log (1/125)
Step 4: Divide both sides by log(5) to solve for a:
(a * log(5) = log(1/125)) / log(5)
a = -3
Optional 5: We can check our answer by plugging in -3 for a and seeing if we get 1/125 when completing the operation:
5^-3 = 1/125
1/(5^3) = 1/125 (rule of exponents states that a negative exponent creates a fraction with 1 as the numerator and the base (5) and exponent (-3 becoming 3) as the denominator
1/125 = 1/125
Pls help me w this problem thxxxxxxx
The equation of the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d
Calculating the composite function B(d)From the question, we have the following parameters that can be used in our computation:
T(d) = d² + 20d
A(d) = 12d
The function B(d) is the difference between the functions A(d) and T(d)
Using the above as a guide, we have the following:
B(d) = T(d) - A(d)
In terms of d, we have
B(d) = d² + 20d - 12d
Evaluate the difference
B(d) = d² + 8d
Hence, the composite function B(d) is B(d) = T(d) - A(d) or B(d) = d² + 8d
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Please answer as soon as possible!
The triangle ABC has its coordinates as shown below.
A:(3,3)
, B:(−2,−2)
, and C:(4,−4)
Triangle ABC is translated 2 units up, 3 units left and then dilated by a scale factor of 4 about the origin to form triangle A' B' C'. What are the coordinates of the vertex B' ? Enter your answer in the box below.
The translation of the triangle, 2 units up and 3 units to the left, followed by a dilation by a scale factor of 4 about the origin, indicates;
The coordinates of the vertex B is; (-20, 0)
What is a dilation transformation?A dilation transformation is one in which the size of the pre-image is transformed to produce the image, which may be smaller or increased in size.
The coordinates of the vertices of the triangles are;
A(3, 3), B(-2, -2), and C(4, -4)
The translation applied to the triangle are;
Vertical translation = 2 units up
Horizontal translation = 3 units to the left
The scale factor of the dilation = 4
The center of dilation = The origin
Therefore, we get;
The transformation applied to the vertices are as follows;
A(3 - 3, 3 + 2), B(-2 - 3, -2 + 2), and C(4 - 3, -4 + 2), which produces the coordinate points;
A(0, 5), B(-5, 0), and C(1, -2)
The dilation by a scale factor of 4, with the center of dilation at the origin, therefore, produces;
4 × (0, 5) ⇒ A'(0, 20)
4 × (-5, 0) ⇒ B'(-20, 0)
4 × (1, -2) ⇒ C'(4, -8)
The vertex of the coordinate B are therefore; (-20, 0)
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if f is a one to one function and f(2)=3 what is f^-1(3)
Answer:
2
Step-by-step explanation:
F^-1 IS AN INVERSE, SO F(2)=3 THEREFORE F^-1(3) = 2
True or False? "Some seventh graders" is a set
The statement is False" Some seventh graders" isn't a set.
we know, set is a well- defined collection of distinct objects, which are appertained to as rudiments or members of the set.
For illustration, consider the set A = { 1, 2, 3}. This set contains the rudiments 1, 2, and 3.
It's a expression that describes a group of individualities without furnishing a well- defined collection of rudiments.
A set is a well- defined collection of distinct objects.
To represent a set, we generally use curled braces and list the rudiments within the set.
For illustration,{ 1, 2, 3} is a set containing the rudiments 1, 2, and 3.
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Please help! Find the length of each arc. Do not round. Put answers in terms of pi.
Answer:
14π cm---------------------
Use the formula:
s = (θ/360) × 2πr,where θ is the central angle in degrees, r is the radius
We have:
θ = 315 and r = 8.Substituting the given values, we get:
s = (315/360) × 2π(8)s = (7/8) × 2π(8) s = 14πTherefore, the length of the arc is 14π cm.
