Mean is the average. Add the minutes together and divide by 10.
[tex]80 \div10 = 8[/tex]
The answer is C
A boat heading out to sea starts out at Point A, at a horizontal distance of 734 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 14 degrees. At some later time, the crew measures the angle of elevation from point B to be 6 degrees.
Find the distance from point
A to point B. Round your answer to the nearest foot if necessary.
(30 POINTS!!!!!!!! I AM DESPERATE!!!!!!!!!!!)
Answer:
Step-by-step explanation:
the problem that would have to be plugged into the calculator would be as following
Question A) Work out the distance travelled on a cycle in the first 14 seconds. Q B) Work out thr acceleration speed in the first 4 seconds.
The distance travelled in the first 14 seconds would then be 3.57 x 14 = 49.98 metres.the acceleration would be 7.14 - 3.57 = 3.57 metres per second squared.
What is distance?Distance is the numerical measurement of how far apart two objects are. It is measured in units such as kilometers, meters, miles, feet, inches, and more. Distance can be calculated in one, two, or three dimensions. Distance is a key factor in many real-world applications, such as navigation, transport, and communication. Distance can also be used to describe relationships, such as the connection between two people.
A)To work out the distance travelled on a cycle in the first 14 seconds, we must first determine the velocity of the cycle. This can be done by dividing the distance travelled by the time taken. For example, if the cycle travelled 50 metres in 14 seconds, the velocity would be 50 / 14 = 3.57 metres per second. The distance travelled in the first 14 seconds would then be 3.57 x 14 = 49.98 metres.
B) To work out the acceleration speed in the first 4 seconds, we must first determine the change in velocity over the period of time. We can do this by subtracting the initial velocity from the final velocity. For example, if the cycle started at a velocity of 3.57 metres per second, and increased to 7.14 metres per second after 4 seconds, the acceleration would be 7.14 - 3.57 = 3.57 metres per second squared.
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complete question with diagram is
Question A) Work out the distance travelled on a cycle in the first 14 seconds. Q B) Work out thr acceleration speed in the first 4 seconds.
diagram shows trapezium in graph with velocity at y axiz and time at x axis
You and a friend both work two different jobs. The system of linear equations represents the total earnings (in dollars) for x hours worked at the first job and y hours worked at the second job. Your friend earns twice as much as you.
4x+8y=64 You
8x + 16y - 128 Your Friend
a. One week, both of you work 4 hours at the first job. How many hours do you and your friend work at the second job?
b. Both of you work the same number of hours at the second job. Compare the numbers of hours you and your friend work at the first job.
Answer:
Step-by-step explanation:
a. We can start by substituting y = 2x into the second equation to get an equation in terms of x only:
8x + 16y - 128 = 8x + 16(2x) - 128 = 0
Simplifying this equation, we get:
24x = 128
Solving for x, we get:
x = 128/24 = 32/6 = 16/3
So you and your friend work 16/3 hours (or approximately 5.33 hours) each at the second job.
b. If both of you work the same number of hours at the second job, then we can set x = y in the first equation and solve for y:
4x + 8y = 64
4x + 8x = 64
12x = 64
x = 64/12 = 16/3
So both you and your friend work 16/3 hours (or approximately 5.33 hours) at the second job.
To compare the number of hours worked at the first job, we can substitute x = 16/3 into the first equation to find:
4(16/3) + 8y = 64
64/3 + 8y = 64
8y = 64 - 64/3 = 128/3
y = 16/3
So your friend works 16/3 hours (or approximately 5.33 hours) at the first job, which is twice the amount of time you work at the first job.
Find two points on the line to graph the function.
Any lines or curves will be drawn once all required points are plotted.
The two points on the line to graph the function is (3, 4/3) and (-6, 10/3).
Define the term a line?A line is a one-dimensional, straight shape that can go on forever in both directions. It is made up of an infinite number of points that are organized in a straight line.
We are unable to offer two points on the line for graphing in the absence of a line or function.
We consider the function is, [tex]f(x) = 2 - \frac{2}{9} x[/tex]
To graph the function [tex]f(x) = 2 - \frac{2}{9} x[/tex] , we can choose any two values of x, plug them into the equation to find the corresponding values of y, and then plot the points (x, y) on the coordinate plane. Here are two possible sets of points we can use:
Set 1:
Let x = 0:
f(0) = 2 - (2/9)(0) = 2
Therefore, one point on the line is (0, 2).
Let x = 9:
f(9) = 2 - (2/9)(9) = 0
and another point on the line is (9, 0).
Now, we can plot these two points on the coordinate plane and draw a straight line passing through them to graph the function [tex]f(x) = 2 - \frac{2}{9} x[/tex]
Set 2:
Let x = 3:
f(3) = 2 - (2/9)(3) = 2 - (2/3) = 4/3
So one point on the line is (3, 4/3).
Let x = -6:
f(-6) = 2 - (2/9)(-6) = 2 + (4/3) = 10/3
So another point on the line is (-6, 10/3).
Now, we can plot these two points on the coordinate plane and draw a straight line passing through them to graph the function [tex]f(x) = 2 - \frac{2}{9} x[/tex]
Therefore, the two points on the line to graph the function is (3, 4/3) and (-6, 10/3).
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2. Graph the piecewise function.
..
I will solve this equation! Just provide the x value.
Right triangle ABC is on a coordinate plane. Segment AB is on the like y=2 and is 6 units long. Point C is on the line x=-3. What is the y-value of Point C if the area of ABC is 9 units squared
The y-coordinate value of Point C if the area of ABC is 9 units squared is: 5 or -1
How to find the coordinate of the segment?Point A is at (x, 2) and B is at (x + 6, 2). Since AB must lie on the line y=2 and be 6 units long. Point C is on the line x = -3 . So let C be at (-3, y).
Since ΔABC is a right angle, then point C must have the same x-coordinate as point A. Therefore, A(-3, 2) and B(2, 2).
The area of ΔABC is 9. So,
9 = 1/2 (b)(h)
where b is the base and h is the height.
so b = 6 and h = AC
Solving this for AC gives
9 = 1/2 (6)(AC)
18/6 = AC
3 = AC
Point C must lie 3 units above point A or 3 units below the point A. If it lies 3 units above, then it has a y-coordinate of 2 + 3 = 5.
If it lies 3 units below, it has a y-coordinate 2 - 3 = -1.
Therefore, y-coordinate is 5 or -1.
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What data values have a frequency of 2 on the line plot
1) 12 and 58
, 1 half and 5 over 8,
2) 316 and 58
, 3 over 16 and 5 over 8,
3) 12 and 316
, , , 1 half and 3 over 16, , ,
4) 12 and 78
We can identify the data values with a frequency of 2 on the line plot, which are 3/16, 5/8, and 1/2.
A line plot is a visual representation of data that shows the frequency of values in a dataset. In the given line plot, we need to identify the data values that have a frequency of 2.
Firstly, we have a data value of 3/16 that has a frequency of 2. This means that the value 3/16 appears twice in the dataset.
Next, we have a data value of 5/8 that also has a frequency of 2. This means that the value 5/8 appears twice in the dataset.
Lastly, we have a data value of 1/2 that has a frequency of 2. This means that the value 1/2 appears twice in the dataset.
Therefore, the data values that have a frequency of 2 on the given line plot are 3/16, 5/8, and 1/2.
In addition to these, we have some other data values on the line plot. The data value of 4 appears only once, and the data values of 12 and 78 are not present on the line plot. Hence, we cannot determine their frequency from the given information.
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The angle measures of $\triangle ABC$ are $A=54\degree$ , $B=38\degree$ , and $C=88\degree$ . List the sides of the triangle in order from shortest to longest.
The sides of the triangle in order from shortest to longest are b < a < c
How to determine the sides of the triangle in order from shortest to longest.In triangle ABC, the side opposite angle A is denoted by a,
The side opposite angle B is denoted by bThe side opposite angle C is denoted by c.To determine the order of the sides from shortest to longest, we need to use the triangle inequality theorem which implies that
The side opposite the largest angle is the largest side and vice versa
So, we have
b from B = 38 degrees
a from A = 54 degrees
c from C = 88 degrees
Therefore, the order of the sides from shortest to longest is: b < a < c
In other words, the side opposite angle B is the shortest, followed by the side opposite angle A, and the side opposite angle C is the longest.
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Refer to the pie graph that shows the world’s languages and the percentages of the population that speak them.
What percentage of the world’s population does not speak either French or German?
By answering the above question, we may state that Hence, neither expressions French nor German are spoken by nearly 97.7% of the world's population.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
In the image you included, a pie chart illustrating the distribution of the global languages spoken by the entire population can be seen.
We need to figure out what portion of the world's population does not speak either French or German in order to respond to your query.
Around 1.2% of the world's population speaks French, according to the pie chart, and 1.1% speaks German, according to the same data.
Hence, it is possible to determine the proportion of people on Earth who do not speak either French or German as follows:
German: 1.1%; French: 1.2%; 100% = 97.7%
Hence, neither French nor German are spoken by nearly 97.7% of the world's population.
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A pilot was scheduled to depart at 4:00 p.m., but due to air traffic, her departure has been delayed by 16 minutes. Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan. Let x represent the time, in minutes, of her original flight. Create an equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination.
Answer:
The pilot was scheduled to depart at 4:00 p.m.
Her departure has been delayed by 16 minutes.
Air traffic control approved a new flight plan that will allow her to arrive four times faster than she calculated in her original flight plan.
We want to create an equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination.
First, let's represent the time of her original flight as x, in minutes. This means that her original flight plan would have taken x minutes to arrive at her destination.
However, with the new flight plan approved by air traffic control, she will arrive four times faster than she calculated in her original flight plan. This means that her new flight plan will take x/4 minutes to arrive at her destination.
Now, we need to take into account the 16-minute delay in her departure. This means that she will depart at 4:16 p.m. instead of 4:00 p.m., and therefore arrive at her destination x/4 minutes after 4:16 p.m.
So the equation that can be used to predict the number of minutes after 4:00 p.m. she will arrive at her destination is:
Number of minutes after 4:00 p.m. = 16 + x/4
Note that this equation assumes that her flight time is the only factor affecting her arrival time, and does not take into account any other delays or factors that may affect her flight.
Step-by-step explanation:
You and two friends go to the ice cream parlor. The flavors available are Strawberry, Mexican Vanilla, Rocky Road, Belgian Chocolate, Salted Caramel, and Bratwurst. Assuming each of you orders one different flavor, how many outcomes are possible?
Explanation:
There are 6 flavors given. This is the number of choices you have to pick from. After you choose a flavor, the next person has 6-1 = 5 choices. Then there are 5-1 = 4 choices after that. We have this countdown.
Multiply the values mentioned: 6*5*4 = 30*4 = 120
An alternative is to use the nPr permutation formula with n = 6 and r = 3.
The nPr formula is [tex]_nP_r = \frac{n!}{(n-r)!}[/tex] where the exclamation marks mean factorials.
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime to the right.
Horizontal translation
Vertical translation
Reflection across the y-axis
270° counterclockwise rotation
Question 2(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Use the image to determine the direction and angle of rotation.
Graph of polygon ABCD in quadrant 4 with point A at 1 comma negative 5. A second polygon A prime B prime C prime D prime in quadrant 2 with point A prime at negative 1 comma 5.
90° clockwise rotation
270° clockwise rotation
90° counterclockwise rotation
180° counterclockwise rotation
Question 3(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Use the image to determine the direction and angle of rotation.
Graph of triangle ABC in quadrant 1 with point A at 1 comma 3. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 3 comma negative 1.
90° clockwise rotation
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
Question 4(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.
Reflection across the x-axis
180° counterclockwise rotation
Horizontal translation
Vertical translation
Question 5(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Use the image to determine the type of transformation shown.
Graph of polygon VWXYZ with W at point 3 comma 7. A second polygon V prime W prime X prime Y prime Z prime with W prime at point negative 3 comma 7.
Horizontal translation
Reflection across the x-axis
Reflection across the y-axis
270° counterclockwise rotation
Question 6(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Use the image to determine the line of reflection.
Graph of polygon ABCDE with point E at 5 comma negative 1. A second polygon A prime B prime C prime D prime E prime with E prime at 5 comma negative 5.
Reflection across the x-axis
Reflection across the y-axis
Reflection across x = 6
Reflection across y = −3
Question 7(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Use the image to determine the direction and angle of rotation.
Graph of polygon ABCD in quadrant 2 with point A at negative 7 comma 5. A second polygon A prime B prime C prime D prime in quadrant 1 with point A prime at 5 comma 7.
270° clockwise rotation
270° counterclockwise rotation
90° counterclockwise rotation
180° clockwise rotation
Reflection across the y-axis is the transformation used to the polygon ABCD.
What is Polygon?A polygon is closed geometric shape that is made up of straight line segments connected end to end. It is two-dimensional shape that has three or more sides, angles, and vertices.
In a polygon, sides do not cross each other and vertices are points where two sides meet.
1) The type of transformation shown in the image is a Horizontal translation, because the second polygon A'B'C'D' is moved horizontally to the right of the original polygon ABCD while maintaining its size and shape.
2) 90° clockwise rotation
3) 90° counterclockwise rotation.
4) Reflection across the x-axis.
5) Reflection across the y-axis.
6) Reflection across the y-axis
7) the correct answer is 180° clockwise rotation.
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Complete question -
PLEASE HELP QUICK BC I don’t know
Triangle ABC is an isosceles triangle.
Form and solve an equation to find the value of t.
B
25 cm
A
4t - 7 cm
+
2t + 11 cm
C
Answer:
The value of t that satisfies the equation and makes triangle ABC an isosceles triangle is 9 cm.
Step-by-step explanation:
Since triangle ABC is an isosceles triangle, we know that the lengths of AB and AC are equal. Using the lengths given in the diagram, we can set up an equation:
AB = AC
4t - 7 = 2t + 11
Now we can solve for t:
4t - 7 = 2t + 11
2t = 18
t = 9
Therefore, the value of t that satisfies the equation and makes triangle ABC an isosceles triangle is 9 cm.
Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]
Select the correct answer.
Which function is continuous across its domain?
O A.
OB.
C.
D.
f(x) =
ƒ(x) =
f(x) =
f(x) =
x + 6,
0.52,
20
-
3x,
-
x 2,
0.5 ,
25
3x,
x + 4,
0.52,
20
3x,
x + 4,
0.5 2,
25
3x,
-4 ≤ x < -2
-2 ≤ x ≤ 4
4 ≤ x ≤ 8
-4 ≤ x < -2
-2 < x < 4
4 ≤ x ≤ 8
-4 < x < -2
-2 ≤ x < 4
4 ≤ x ≤ 8
-4 ≤ x < -2
-2 ≤ x < 4
4 ≤ x ≤ 8
Function is continuous across its domain is B.
What is domain?The domain of a function is the set of numbers that can go into a given function. In other words, it is the set of x-values that you can put into any given equation. The set of possible y-values is called the range. If you want to know how to find the domain of a function in a variety of situations,
If a real function f is given by a formula, it may be not defined for some values of the variable. In this case, it is a partial function, and the set of real numbers on which the formula can be evaluated to a real number is called the natural domain or domain of definition of [tex]f[/tex].
The function f(x) = 0.52 is a constant function, and constant functions are always continuous across their domain.
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The scale drawing of a building has a height of 10 centimeters. The actual building is 20 feet high. How many centimeters in the scale drawing represent one foot on the actual building?
A. 1/2
B. 2
C. 10
D. 30
1/2cm in the scale drawing represents one foot on the actual building.
What is the scale factor?
The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). When both the original dimensions and the new dimensions are known, the scale factor may be determined. The following is a basic formula to determine a figure's scale factor: Scale factor is equal to the difference between the dimensions of the old and new shapes.
Here, we have
Given: The scale drawing of a building has a height of 10 centimeters. The actual building is 20 feet high.
we have to find how many centimeters in the scale drawing represent one foot on the actual building.
The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter.
Hence, 1/2cm in the scale drawing represents one foot on the actual building.
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I will mark you brainiest!
If the triangle above is translated two units to the right, what is the correct coordinate for A'?
A) A'(5, 5)
B) A'(5, 0)
C) A'(0, 5)
D) A'(0, 0)
Question #2
If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A) A'(0, 5)
B) A'(2, 5)
C) A'(5, 2)
D) A'(-5, -2)
Answer:
1. C
2. B
Step-by-step explanation:
A. A(-2,5) => A' (-2 + 2, 5) or A' (0,5)
B. A(-2,5) => A' (- -2, 5) or A' (2,5)
How to find slope of line line from given table with answer and instructions please
Answer:
The slope of the line is 60.
Step-by-step explanation:
We are given a table of values, and h and c are substitutes from x and y. Judging by this, if we know the formula [tex]\frac{y2-y1}{x2-x1}[/tex] then we can evaluate the slope, we just have to take two of the coordinate points from the table.
Lets take (3,205) and (6,385) and plug it into the formula
[tex]\frac{385-205}{6-3}[/tex]
Evaluate
[tex]\frac{180}{3}[/tex]
Simplify the fraction
[tex]\frac{60}{1}=60[/tex]
The slope of the line is 60.
find the length of blue rectangle2 3 to the length of green rectangle 4 6
the length of blue rectangle 2 to the width of green rectangle 6 is: 2/6 = 0.33 (rounded to two decimal places)
How to find the length of blue rectangle?
To find the length of blue rectangle 2 in relation to the length of green rectangle 4, we need to divide the length of blue rectangle 2 by the length of green rectangle 4.
So, the length of blue rectangle 2 to the length of green rectangle 4 is:
2/4 = 0.5
To find the length of blue rectangle 2 in relation to the width of green rectangle 6, we need to divide the length of blue rectangle 2 by the width of green rectangle 6.
So, the length of blue rectangle 2 to the width of green rectangle 6 is:
2/6 = 0.33 (rounded to two decimal places)
Note that the ratio of the length of blue rectangle 2 to the length of green rectangle 4 is different from the ratio of the length of blue rectangle 2 to the width of green rectangle 6.
A rectangle is a two-dimensional shape that has four sides and four right angles. It is a type of quadrilateral, which means a four-sided polygon.
In a rectangle, the opposite sides are parallel and have equal length. This makes it different from a square, which is also a rectangle but has four equal sides.
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Prove 5^7 + 5^6 is divisible by 6 without calculating
The given expression is divisible by 6 without calculating
What is divisibility?A number can be divided if it divides evenly (leaving no remainder) into another integer. For instance, 2 divides 34 equally, making 34 divisible by 2. 34 is not divided by 3, though, because doing so would leave us with a remainder.
According to question:We can prove that [tex]$5^7 + 5^6$[/tex] is divisible by 6 using modular arithmetic.
First, we can rewrite the expression as [tex]$5^6(5+1)$[/tex], which simplifies to [tex]$5^6 \cdot 6$[/tex].
Since 5 is not divisible by 2, we can use the fact that [tex]$a \equiv b \pmod{m}$[/tex] implies [tex]$ac \equiv bc \pmod{m}$[/tex] for any integer c to simplify our expression to [tex]$(-1)^6 \cdot 6$[/tex], or simply [tex]6 (since $5 \equiv -1 \pmod{6}$)[/tex].
Therefore, [tex]$5^7 + 5^6$[/tex] is divisible by 6.
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NEED ASAP!!!!!!!!!!!!!!!!!1 Identify the formula used to find total surface area, then calculate total surface area. Select the appropriate choices.
Formula:
Total Surface Area:
Answer:
The total surface area of the triangular prism is 556 square units.
Step-by-step explanation:
The given 3D figure is a triangular prism.
The formula to find the total surface area of a triangular prism is:
[tex]\boxed{\textsf{Total Surface Area}= \sf 2 A_B+(a+b+c)h}[/tex]
where:
[tex]\sf A_B[/tex] is the area of one of the triangular bases.a, b and c are the side lengths of the triangular bases.h is the height of the prism.Therefore, the surface area of a triangular prism is the sum of the area of two congruent triangular bases and three rectangles.
The area of a triangle can be calculated by halving the product of the length of its base and height.
The base of the triangles is 17 units and the height is 8 units.
Therefore, the area of each triangular base is:
[tex]\begin{aligned}\implies \sf Area\;of\;triangular\;base\;(A_B)&=\sf\dfrac{1}{2} \cdot17 \cdot8\\&=\sf 68\;square\;units\end{aligned}[/tex]
Therefore, the values to substitute into the total surface area formula are:
a = 11b = 14c = 17h = 10[tex]\sf A_B = 68[/tex][tex]\begin{aligned}\implies \textsf{Total Surface Area}&= \sf 2 A_B+(a+b+c)h\\&= \sf 2 (68)+(11+14+17)10\\&=\sf 2 \left(68\right)+(42)10\\&=\sf 136+420\\&=\sf 556 \; square\;units\end{aligned}[/tex]
Therefore, the total surface area of the given triangular prism is 556 square units.
Find x. Round your answer to the nearest tenth of a degree.
Answer:
63.0°
Step-by-step explanation:
You want the measure of an angle in a right triangle with hypotenuse 11 and adjacent side 5.
CosineThe cosine relation is ...
Cos = Adjacent/Hypotenuse
cos(x) = 5/11
Then the angle is found using the inverse cosine function:
x = arccos(5/11) ≈ 63.0°
The value of x is about 63.0°.
__
Additional comment
The calculator's angle mode needs to be set to "degrees."
Please help, Thanks!
The value of y is 5 when x = -31/3.
What is an Equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
Thus, from the given question, we can see that:
The value of y is -3 when x = -17/5.
The value of y is 0 when x = 1/2.
The equation that represents this relationship is y = (2x - 1) / (x + 6).
However, the value of y cannot be 2 for any value of x that satisfies this equation.
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A fish tank is in the shape of a rectangular prism. What is the volume of the fish tank? Round to the nearest tenth if necessary.
Answer:
The volume is 10 × 20 × 12 = 2,400 square inches.
use rational exponents to rewrite and simplify the expression
the answer is in the photo
Question Number 13 on the worksheet all parts answered
The town with the greatest average rainfall was Milton; the average rainfall in Southport was 0.75 inches more than in Fairview, and the actual rainfall in Fairview was 4.15 inches.
What was the town with the greatest average rainfall?To identify this only observe the table and identify the highest value, in this case, the highest value is 4. 20 in average for Milton.
What is the difference in the average rainfall between Southport and Fairview?4.09 - 3.35 = 0.75 inches
What is the actual rainfall in Fairview?3.35 (information registered) + 0.8 = 4.15 inches
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What is the measure of angle B?
Answer:
58 degrees
Step-by-step explanation:
find x first
8x+2 + 6x + 80 = 180
14x + 82 = 180
14x = 98
x = 7
then substitute it back into the angle measure of B
angle b = 8x + 2
8(7) + 2 = 58
College A has 75% of students on financial aid and College B has 95% of students on financial aid. If you want to compare the sampling distributions between these two colleges, what should the size of your samples be so that the sampling distributions have approximately the same standard deviation?
The sample sizes for the two universities need to be identical in order for their sampling distributions to have about the same standard deviation.
A sample distribution is what?A sampling distribution is a probability distribution that specifies how a statistic—like the mean or standard deviation—behaves when it is generated from population-based samples of a specific size. It is crucial to statistical inference because it makes it easier to calculate the likelihood of receiving specific sample statistics from a population and to draw conclusions about the characteristics of the population from the sample data. The population factors and sample size both have an impact on the form, centre, and spread of a sampling distribution.
The size of the sample for the sampling distributions is given as:
n1 = (s1 / s2) * n2
where n1 and n2 are the sample sizes for College A and College B respectively.
We may assume that the variances of the two populations are identical as we want the sampling distributions to have about the same standard deviation. As a result, we may make the formula as follows by setting s1 = s2:
n1 = n2
We may draw the conclusion that the sample sizes for the two universities need to be identical in order for their sampling distributions to have about the same standard deviation.
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what is the coefficient of y in the equation 3y² - ⅘y + 6 = 0 ?
Answer: -4/5
Step-by-step explanation: To find the coefficient of y in the equation 3y² - ⅘y + 6 = 0, we need to identify the term in the equation that contains y and then extract the coefficient.
In this equation, the term that contains y is -⅘y. The coefficient of y is the number that is multiplied by y in this term, which is -⅘.
Therefore, the coefficient of y in the equation 3y² - ⅘y + 6 = 0 is -⅘.
An investor has $60,000 to invest in a CD and a mutual fund. The CD yields 8% and the mutual fund yields 7%. The mutual fund requires a minimum investment of $8,000, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
Answer:
Step-by-step explanation:
Let's start by defining some variables to represent the amount invested in the CD and the mutual fund. Let:
C = amount invested in the CD
M = amount invested in the mutual fund
From the problem statement, we know that:
C + M = 60,000 (the total investment amount is $60,000)
C >= 2M (twice as much should be invested in CDs as in the mutual fund)
M >= 8,000 (the mutual fund requires a minimum investment of $8,000)
We can use these constraints to write the objective function that we want to maximize, which is the total return on investment:
R = 0.08C + 0.07M
To solve this problem, we can use the following steps:
Substitute C = 2M into the first equation to get:
3M = 60,000
M = 20,000
Since M >= 8,000, we can invest the minimum required amount in the mutual fund and put the rest in the CD:
M = 8,000
C = 60,000 - M = 52,000
Calculate the total return on investment:
R = 0.08C + 0.07M = 0.08(52,000) + 0.07(8,000) = 4,960 + 560 = 5,520
Therefore, the investor should invest $52,000 in the CD and $8,000 in the mutual fund to maximize the return, and the maximum return is $5,520.
Need help will be much appreciated! I did A already Im just stuck with B, I have an hour before my assignment is due please help. :)
A. The inverse of the function f(x) = 3 / (7x + 1) is g(x) = (3 - x)/7x
B. The inverse function is verified, such that f(g(x)) = x
How to find the inverse of the functionThe inverse of the function is solved as follows
f(x) = 3 / (7x + 1)
let f(x) = y, so that y = 3 / (7x + 1)
writing the equation by isolating x
y (7x + 1) = 3
7x + 1 = 3/y
7x = 3/y - 1
7x = (3 - y)/y
x = (3 - y)/7y
interchanging the variables
y = (3 - x)/7x
hence g(x) = (3 - x)/7x
solving for f(g(x)), to verify
f(g(x)) = 3 / (7((3 - x)/7x) + 1)
f(g(x)) = 3 / ((3 - x)/x) + 1)
f(g(x)) = 3 / ((3 - x + x)/x)
f(g(x)) = 3 / 3/x
f(g(x)) = (3 / 3) * x
f(g(x)) = x
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