Answer:
72
Step-by-step explanation:
We are told that line AC divides angle BAE in half or "bisects" it. We are also told that line AD divides angle CAE in half as well. Lastly we are giving the value of angle DAE which is 36.
Since line DA split angle CAE in half and we have half of the value, that means that the measure of angle CAE is 36 times 2 which is 72.
72 happens to be our answer for angle BAC because angle BAC is half of the largest angle BAE, which was divided in two by line AC.
Hope this helps!
For a sample size of 85 and a population parameter of 0.2, what is the standard error of the sampling distribution?
Answer:
0.043
Step-by-step explanation:
I hope this helps you! Let me know if you have any questions! :)
find the domain of the function
The domain of the function is { (x, y) ∈ R² | x² + y² ≥ 1 }
What is Domain of function?
A function's domain is the collection of all potential inputs. For instance, all real numbers are in the domain of f(x)=x², and all real numbers are in the domain of g(x)=1/x, with the exception of x=0. Special functions with more constrained domains can also be defined.
According to question
⇒ [tex]z = e^{\sqrt{x^{2}+ y^{2} -1 } }[/tex]
⇒ x² + y² - 1 ≥ 0
⇒ x² + y² ≥ 1
Hence, the Domain of f(x, y) is { (x, y) ∈ R² | x² + y² ≥ 1 }
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Harry owns a rare baseball card that is valued at $13.00. If he originally purchased the card for $5.00, by what percentage has its value increased?
The value of baseball card has increased by 160(%) percentage.
What is the percentage?
A number or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word per cent means. The letter "%" stands for it.
Increase = New Number - Original Number
Then: we divide the increased number by the original number and multiply by 100.
Therefore, % increase = (Increase ÷ Original Number)× 100.
Given, the new price of a baseball card = $13
The original price of a baseball card = $5
Then from the above definition,
Increase = 13-5 = 8
% increase = (8/5)*100 = 160%
Hence, its value has increased by 160 percentage.
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Which relationships have the same constant of proportionality between yyy and xxx as the following table?
x y
7 24.5
9 31.5
Choose 3 answers
Answer:
A,D,E
Step-by-step explanation:
A:
14/4 = 3.5
D:
7/2 = 3.5
E: 14/4 = 3.5
The constant of proportionality for the table is 3.5. Any other table that satisfies the equations x/y = 3.5 will have the same constant of proportionality.
Explanation:To find the constant of proportionality, we can divide the y-values by the corresponding x-values and see if they are the same for all given points. In this case, if we divide 24.5 by 7, we get approximately 3.5. If we divide 31.5 by 9, we also get approximately 3.5. Therefore, the constant of proportionality is 3.5 for this table.
Now, we need to find the relationships that have the same constant of proportionality.
For example, if we have a table with the following values:
x1 y1
x2 y2
x3 y3
and the constant of proportionality is k, then we have the following equations:
x1/ y1 = k
x2/ y2 = k
x3/ y3 = k
So, any other table that satisfies these equations will have the same constant of proportionality as the given table.
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Need help asap.
Calculate the residuals for the scatterplot.
The residuals of the regression are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
How to determine the residuals?The regression equation is given as:
y = 0.138x + 1.166
Next, we calculate the predicted values (y) at the corresponding x values.
So, we have:
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 20 + 1.166 = 3.93
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 16.7 + 1.166 = 3.47
y = 0.138 * 15.5 + 1.166 = 3.31
The residuals are then calculated using:
Residual = Actual value - Predicted value
So, we have:
Residual = 3.7 - 3.65 = 0.05
Residual = 3.69 - 4.19 = -0.5
Residual = 3.8 - 3.65= 0.15
Residual = 4 - 3.93 = 0.07
Residual = 4 - 3.65= 0.35
Residual = 1.11 - 1.26 = -0.15
Residual = 3.69 - 4.19 = -0.5
Residual = 1.11 - 1.26 = -0.15
Residual = 3.5 - 3.47 = 0.03
Residual = 3.92 - 3.31 = 0.61
Hence, the residuals are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
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Answer:
The residuals of the regression are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
How to determine the residuals?
The regression equation is given as:
y = 0.138x + 1.166
Next, we calculate the predicted values (y) at the corresponding x values.
So, we have:
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 20 + 1.166 = 3.93
y = 0.138 * 18 + 1.166 = 3.65
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 21.9 + 1.166 = 4.19
y = 0.138 * 0.7 + 1.166 = 1.26
y = 0.138 * 16.7 + 1.166 = 3.47
y = 0.138 * 15.5 + 1.166 = 3.31
The residuals are then calculated using:
Residual = Actual value - Predicted value
So, we have:
Residual = 3.7 - 3.65 = 0.05
Residual = 3.69 - 4.19 = -0.5
Residual = 3.8 - 3.65= 0.15
Residual = 4 - 3.93 = 0.07
Residual = 4 - 3.65= 0.35
Residual = 1.11 - 1.26 = -0.15
Residual = 3.69 - 4.19 = -0.5
Residual = 1.11 - 1.26 = -0.15
Residual = 3.5 - 3.47 = 0.03
Residual = 3.92 - 3.31 = 0.61
Hence, the residuals are 0.05, -0.5, 0.15, 0.07, 0.35, -0.15, -0.5, -0.15, 0.03 and 0.61
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Step-by-step explanation:
Kiera's lemon cookie recipe calls for 5 cups of sugar. How much sugar would Kiera use to make 3 5/8 batches of cookies?
Answer:18 1/8
Step-by-step explanation:
5x3=15
5x5/8=25/8=3 1/8
15+3 1/8=18 1/8
Work out:
(1.2 × 10′²) × (2 × 10ª)/3 x 10-5
Give your answer in standard
form.
The standard form of the expression is [tex]0.000286 \times 10^a[/tex].
What is a standard form?
A standard form is a document that contains predetermined information in a specific format, such as a contract or agreement. Standard forms are often used to ensure uniformity and efficiency among different parties. Standard forms may include a variety of information, including contact details, payment information, and other important details related to a transaction. By utilizing a standard form, individuals and organizations are able to save time and effort when completing administrative tasks. Standard forms can also be used to ensure that all parties involved in a transaction are aware of the terms and conditions.
The given expression is
[tex]=(1.2 \times 10^2) \times \frac{(2 \times 10^a)}{3} \times 10^{-5}\\\\=129 \times\frac{2}{3}\times\frac{10^a}{3}\times0.00001\\\\=0.000286 \times 10^a[/tex]
Hence, the standard form of the expression is [tex]0.000286 \times 10^a[/tex].
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is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero?
True, is it possible for the results of a study to show a non-zero correlation, even though the correlation for the general population is zero.
When a correlation is statistically significant, it is a significant and strong correlation. Even a very slight association can be statistically significant with a very large sample size.
While the correlation for the entire population is zero, it is nevertheless feasible for a sample to have a true, non-zero correlation.
When there is no association in a correlational analysis, what happens?
The variables fluctuate in opposite directions when there is a negative correlation. There is no association between the variables if there is zero correlation.
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Let the graph of g be a vertical stretch by a factor of 3 and a reflection in the y-axis, followed by a translation 2 units left of the graph of f(x)=x^2-5x+1 . Write a rule for g .
Answer:We may rewrite f(x) = (x-1)^2
We stretch by having 3(x-1)^2
We reflect about the y axis by changing x to -x: 3(-x-1)^2 = 3(x+1)^2
We move to the left by adding 2 to x: 3(x+2+1)^2 = 3(x+3)^2
Step-by-step explanation:A way to verify this: Consider y = x^2 to be the unit parabola. f(x) = (x-1)^2 moves the unit parabola one to the right, so it is symmetric about x = 1; We then vertically stretch it by a factor of 3; reflection about the y-axis moves the parabola to be symmetric about x = -1; moving to the left by 2 means the parabola is now symmetric about x = -3; thus, we have a stretched unit parabola symmetric about x = -3, so g(x) = 3(x+3)^2
We may write g(x) = 3x^2 + 18x + 27, also.
Which system of inequalities is shown?
The equations of inequalities are y < 4 and y > x.
What is inequality?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The line of the graph is not solid. The lines of the graph is dotted. Thus the inequality sign will be less than or greater than.
One graph line is parallel to x-axis and it intersect y axis at (0,4).
The equation of the line that is parallel to x-axis and it intersect y axis at (0,a), then the equation of the line is y = a
The equation of the line parallel to x-axis is y = 4.
The equation of line that passes through origin is y = mx
The line passes through the point (1,1).
Putting x = 1 and y = 1 in y = mx:
1 = m
Therefore the equations of lines are y = x and y = 4
The inequality will be y < x or y > x for the line y = x.
The inequality will be y < 4 or y > 4 for the line y = 4.
(-2,0) is a point on the shaded area.
Putting x = -2 and y = 0 in y > x
0 > -2 true.
The inequality is y > x
Putting x = -2 and y = 0 in y < 4
0 < 4 true.
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PLEASE EXPLAIN AND SHOW YOUR WORK THANK YOU!!
Solve as a MIXED NUMBER:
-2.25 + 0.4x = -2.8
THANK YOU!!!
Answer:
x=-1 3/8
Step-by-step explanation:
-2.25 + 0.4x = -2.8
-2.25 + 2.25 + 0.4x = -2.8 + 2.25 ==> add 2.25 on both sides to isolate x
0.4x = -0.55
(0.4x = -0.55)*20 ==> multiply the equation by 20 to remove decimals
8x = -11
x=-11/8
x=-(3+8)/8 ==> turn x into a mixed number
x=-3/8 - 8/8
x=-3/8 - 1 ==> simplify
x=-1 - 3/8
x=-(1 + 3/8)
x=-1 3/8
a ferris wheel 50 ft in diameter makes one revolution every 40 sec. if the center of the wheel is 30 ft above the ground, how long after reaching the low point is a rider 50 ft above the ground
So, it will take the rider 5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.
The circumference of the ferris wheel is equal to the diameter times pi, or 50*pi=157.08 ft. Since the ferris wheel makes one revolution every 40 seconds, the speed of the ferris wheel is 157.08/40=3.92 ft/sec.
Since the rider starts at a height of 30 ft above the ground and ends up 50 ft above the ground, the total change in height is 50-30=20 ft. Since the speed of the ferris wheel is 3.92 ft/sec, it will take the rider 20/3.92=5.1 seconds to reach a height of 50 ft above the ground after reaching the low point.
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Look at the triangles shown below.
5
Which statement is TRUE?
Answer: B
Step-by-step explanation:
vertical angles are =
100 POINTS IF YOU CAN ANSWER THIS
Which of the following number of selected people having received a ticket would constitute an unusual event?
A. 4
B. 5
C. 1
D. 2
Answer: B
Step-by-step explanation:
Answer: The answer is D. 2 | 0.25
Step-by-step explanation:
I don't really have a good explanation, but I hope it helps!
These figures are similar. The perimeter and area of one are given. The perimeter of the other is also given. Find its area and round to the nearest tenth.
Perimeter= 20m
Area=19.6m^2
Perimeter=34m
What is the Area=
The area of the larger figure that is similar to the smaller one is: 28.2 m².
How to Find the Area of Similar Figures?Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:
Area of figure A / Area of figure B = a²/b².
Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:
Perimeter of smaller figure = 20 m
Area of smaller figure = 19.6 m²
Perimeter of larger figure = 34m
Area of larger figure = x
Therefore:
20/34 = a/b
Simplify:
10/17 = a/b.
Find the area (x) of the larger figure using the formula given above:
10²/12² = 19.6/x
100/144 = 19.6/x
100x = 2,822.4
x = 2,822.4/100
x ≈ 28.2 m²
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What is the slope of y = − 5 + 4x
Given: segment BD bisects angle ABC and segment BD bisects angle ADC. Prove: segment AD is congruent to segment CD
If BD bisects ∠ABC and ∠ADC, then AD is congruent to CD.
What is bisector of an angle?
In geometry, anything is said to have been bisected when it is split into two identical or similar parts, typically by a line. In that case, the line is known as the bisector. The types of bisectors that are most usually taken into account are segment bisectors and angle bisectors..
Since BD bisects ∠ABC, thus ∠ABD = ∠DBC.
Since BD bisects ∠ADC, thus ∠ADB = ∠BDC.
AA theorem: According to the AA similarity theorem, two triangles are similar if two of their triangles are congruent with two of their respective triangles' angles.
Consider △ABD and △DBC:
∠ABD = ∠DBC
∠ADB = ∠BDC
Therefore, △ABD ≅ △DBC
According to CPCT, AD ≅ CD.
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The expression - 270 +18.3y represents a submarine that began at a depth of 270 feet below sea level and ascended at a rate of 18.3 féet par minute. What was the depth
of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A. The submarine ___ was feet below sea level after 8 minutes.
(Type an integer or a decimal:)
B. The submarine will have reached sea level after 8 minutes.
The depth of the submarine after 8 minutes is -123.6 feet below sea level.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Depth of the submarine after y minutes.
= -270 + 18.3y
The depth of the submarine after 8 minutes.
= -270 + 18.3 x 8
= -270 + 146.4
= -123.6
Thus,
The submarine is at -123.6 feet below sea level.
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Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.
Proof of ray BC is the angle bisector of angle ABA' is given.
What are angle bisectors?Angle bisectors are lines that cut across the angle under consideration. The term "bisect" means to divide into two equal portions. The considered angle is therefore divided in half by the bisected halves.
A graph will move exactly to the other side of an axis, such as the x-axis, as if it were a mirror when it is reflected along that axis.
Because it is symmetrical, each point is as far from the axis of reflection as its mirror counterpart.
Triangle A'B'C' is a mirror of triangle ABC over line BC, as shown by the provided issue.
Therefore, <A'B'C' = <ABC
by virtue of congruent triangles' characteristics. Means that if the sides' lengths are equal, the angles' measures are equal, and they may be overlaid.
Therefore, the ray BC is the angle, bisector of angle ABA'.
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a car manufacturer wants to learn more about the brand preferences of electric car owners. there are millions of electric car owners in the world. who should the company survey? 1 point the entire population of electric car owners a sample of car owners who have owned more than one electric car a sample of all electric car owners a sample of car owners who most recently bought an electric car
A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.
What is Survey?A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.
Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.
As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.
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One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs $0.91. There are 3.8 liters in one gallon. How much does one gallon of gas cost in Toronto? Round your answer to the nearest cent.
Answer: One gallon of gas in Toronto would cost approximately $3.43. To find this, first convert the price of gasoline in Buffalo to liters. Since there are 3.8 liters in one gallon, one gallon of gas in Buffalo costs $2.29 * 3.8 liters = $8.69. Next, divide the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.91 / 3.8 liters/gallon = $0.24/liter. Finally, multiply the price per liter in Toronto by the number of liters in a gallon to find the price per gallon in Toronto. This is $0.24/liter * 3.8 liters/gallon = $0.91/gallon. Round this to the nearest cent to find that one gallon of gas in Toronto costs $0.91/gallon = $<<0.91/gallon=0.91>>0.91.
Geometry is hard help
Write a rule for the glide reflection that maps ABC with vertices A(-4,-2), B(-2, 6).
and C(4, 4) to A'B'C' with vertices A'(4, -2), B(6, -6), and C'(12,-4).
The glide reflection that maps ABC to A'B'C' is given as follows:
Reflection over the line y = x - 9.Translation right 8 units.What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.
The midpoint of segment A'B' is given as follows:
x = (4 + 6)/2 = 5.y = (-2 - 6)/2 = -4.The slope of this segment is given as follows:
m = (-6 - (-2))/(6 - 4) = -1.
Then the slope of the reflection line is of:
m = 1.
(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).
Then:
y = x + b.
When x = 5, y = -4, then the intercept b is calculated as follows:
-4 = 5 + b
b = -9.
Thus the reflection line is of:
y = x - 9.
Then the translation is given subtracting the coordinates of one of the vertices, as follows:
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A student rewrites the expression 12⋅16−s as another equivalent expression. Which expression could the student write?
The equivalent expression could be 4×3·4×4−s
What is a equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.
Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.
Let's now have a look at some expressions with variables, such 5x+2.
It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.
The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.
When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.
Here, 4×3=12 and 4×4=16
therefore, 4×3·4×4−s is equal to the expression 12⋅16−s
4×3·4×4−s and 12⋅16−s are equivalent expressions.
Hence, The equivalent expression could be 4×3·4×4−s
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The equivalent expression could be 4×3·4×4−s.
What is a equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.Think about the numbers 3²+1 and 5×2. They both add up to 10. These two expressions are equivalent, so to speak.Let's now have a look at some expressions with variables, such 5x+2.It is possible to rewrite the expression as 5x+2=x+x+x+x+x+1+1.The right side of the equation can be regrouped to 2x+3x+1+1, x+4x+2, or another combination. When the same value is used as x, all of these equations have the same result. These two expressions are equivalent, so to speak.When two expressions have the same value regardless of the value of the variable(s) they contain, they are said to be equivalent.Here, 4×3=12 and 4×4=16
therefore, 4×3·4×4−s is equal to the expression 12⋅16−s
4×3·4×4−s and 12⋅16−s are equivalent expressions.
Hence, The equivalent expression could be 4×3·4×4−s
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Which one. Multiple choice.
In the given relation, 1 is not a domain.
What is domain?The domain of a function is the set of all possible inputs for the function. or we can that in an ordered pair, all the values of x are called domain.
All the values that go into a function. The output values are called the range.
The domain of a function is the set of all possible inputs for the function.
If a function f provides a way to successfully produce a single value y using for that purpose a value for x than that chosen x-value is said to belong to the domain of f.
Given that, a function,
{(5, 1), (4, -3), (3, -1)}
We know, a domain is the set of all "x" values.
Therefore, domain of the function are, 5, 4 and 3
But, if we see, 1 is one of the values of y.
Hence, 1 is not a domain.
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10 points if you answer his question
Point C is 3/4 of the way from point A(−4, −2) to point B(8, 6). What are the coordinates of C?
The coordinates of C are (8/7, 10/7) if point A is (-4, -2) and point B is
(8, 6)
What is section formula?The section formula aids in finding a point's coordinates so that the line connecting two points can be divided in a ratio. This involves both internal and external activities. P (x, y) = (c, m, plus a, plus n, plus d, plus b, plus n). The Section formula is used to determine the ratio by which a line segment is divided by a point either internally or externally in coordinate geometry. It is used to identify a triangle's centroid, incenter, and excenter. Physics uses this technique to determine equilibrium points, the centers of mass of systems, and other things.
A(-4, -2), B(8, 6)
m:n=3:4
((3(8)+4(-4))/(3+4) , ((3(6)+4(-2))/(3+4))
=((24-16)/7, (18-8)/7)
=(8/7, 10/7)
Therefore, the coordinates of C are (8/7, 10/7)
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For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
The snow is needed to build the whole snowman is 19 cubic foot. Hence option A is the correct option.
What is a sphere?
The collection of points in three dimensions that are all the same distance from the center (the radius) or the outcome of rotating a circle around one of its diameters. A sphere's parts and characteristics are comparable to those of a circle.
Given that the diameter of the bottom ball is 3 feet, the diameter of middle ball is 2 feet, and the diameter of the top ball 1.
The radius of a sphere is the half of its diameter.
The radius of the bottom ball is 3/2 feet =1.5 feet
The radius of the middle ball is 2/2 feet = 1 feet.
The radius of the top ball is 1/2 feet = 0.5 feet.
The volume of a sphere is 4/3 × ∏r³.
The volume of bottom ball is 4/3 × ∏ × (1.5)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (1)³ cubic foot.
The volume of middle ball is 4/3 × ∏ × (0.5)³ cubic foot.
The total amount of snow is
4/3 × ∏ × (1.5)³ + 4/3 × ∏ × (1)³ + 4/3 × ∏ × (0.5)³
= 4/3 × ∏ [1.5³ +1³ + 0.5³ ]
= 4/3 × ∏× 4.5
= 18.84
≈ 19 cubic foot
To learn the volume of a sphere, click on below link:
https://brainly.com/question/7473395
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A college student is deciding how many hours to work at a part time job(x) and how many hours to work at an internship (y). The job pays $24 and hour, and the internship pays $12 an hour. The student needs to work less than 15 hours a week but needs to earn at least $240 a week to pay expenses. Write 2 systems of inequalities to represent all the combinations of number of hours the student can work at the job and internship
Answer:
x + y < 152x + y ≥ 20-------------------------------
Total hours worked is x + y.
Earning from the part time job is 24x, from the internship is 12y.
Inequality for the number of hours:
x + y < 15Inequality for the earning:
24x + 12y ≥ 240This can be simplified by dividing all terms by 12:
2x + y ≥ 20Answer:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
Step-by-step explanation:
Part-time job
Let x be the number of hours worked.$24 = pay per hour.Internship
Let y be the number of hours worked.$12 = pay per hour.The student needs to work less than 15 hours a week:
[tex]\implies x+y < 15[/tex]
The student needs to earn at least $240 a week:
[tex]\implies 24x+12y \geq 240[/tex]
Therefore, the system of inequalities is:
[tex]\begin{cases} x+y < 15\\24x+12y \geq 240 \end{cases}[/tex]
The second inequality can be simplified by dividing each term by 12:
[tex]\implies \dfrac{24x}{12}+\dfrac{12y}{12} \geq \dfrac{240}{12}[/tex]
[tex]\implies 2x+y \geq 20[/tex]
Therefore, a second system of inequalities is:
[tex]\begin{cases} x+y < 15\\2x+y \geq 20 \end{cases}[/tex]
To solve the system of equalities, graph both inequalities and shade the overlapping region.
Any (x, y) point in the overlapping region is a solution to the system of inequalities.
Two angles form complements. One angle measure is eight more than twice the other. Find both angles measures.
Answer:
41° and 49°
Step-by-step explanation:
Two angles are said to be complements if the sum of their measures is 90 degrees. Since one angle is eight more than twice the other, we can set up the following equation to represent the situation:
2x + 8 = 90
Solving for x, we get:
2x = 82
x = 41
Since the two angles are complements, their measures must add up to 90 degrees. Therefore, the measure of the other angle is 90 - 41 = 49 degrees.
Therefore, the two angles have measures of 41 and 49 degrees.