The values for the cosine and cotangent functions for the angle x is
O cos0 = -√2/2, cot0 =-1
How to find the cosine and cotangent angleLet the angle be x
given that the point [ -√2/2, √2/2] is on the terminal ray of angle x
the x-coordinate of the point is -√2/2 and this is the cos hence
cos x = -√2/2.
To find the cotangent
the y coordinate is the sin therefore sin x = √2/2
tan x = sin x / cosx = (√2/2) / (-√2/2) = -1
and cotangent is the reciprocal of the tangent
cot x = 1 / tan x = -1/1 = -1.
cos x = -√2/2 and cot x = -1.
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if anyone could help me please? :)
The characteristics that shows that the graph is a proportional relationship is: D. The line connecting the points passes through the origin.
What is a graph of a proportional relationship?A graph of a proportional relationship is a straight line that passes through the origin (0, 0) on a coordinate plane, where the points on the line represent pairs of values that are in direct proportion to each other.
From the graph shown above, if we connect the points together, the line will pass through the origin, therefore, the correct answer is: D. The line connecting the points passes through the origin.
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The characteristics that tell you that the graph shows a proportional relationship are: A straight line can be drawn through the points and The line connecting the points passes through the origin. Option B and D are the correct answer.
A proportional relationship is a relationship between two variables where the ratio of their values is constant. This means that if we multiply one of the values by a constant, the other value also gets multiplied by the same constant.
The graph of a proportional relationship is a straight line that passes through the origin. This is because the ratio of the x- and y-values is constant, so the points can be plotted as a straight line.
The ordered pairs all have the same x- and y-values means that the two variables are perfectly correlated. This is not necessary for a proportional relationship, but it is a common characteristic.
The line connecting the points does not need to pass through the origin for the relationship to be proportional. However, if the line does pass through the origin, then the two variables are directly proportional. Option B and D are the correct answer.
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Arianna says that the graphs of both of these functions will grow at the same cale s
she correct? Why or why not?
She is correct They grow at the same rate because
She is not correct. The graph of grows at a faster tale
than the graph of g because each value is mutplied by 4
There is not exgh intymaton to to which graph will
grow at a fasheerale
She is not correct The graph of g grows at a faster ale
than the graph of because & greater than 2
37
Answer:She is not correct The graph of g grows at a faster rate
than the graph of because 8 greater than 2
Step-by-step explanation:
Using PEMDAS, the exponents are done first.
8^3 = 512
4*2^3 = 32
This works for every number that X can be, 3 was just an example.
Maggie bought 50 lbs of clay for her art projects. She used 15.6 lbs to make a sculpture, and 0.84 lbs for each mug. How many mugs did Maggie make if she had 19.28 lbs of clay left over? Solve on paper. Then check your work on Zearn.
The number of mugs that Maggie made with the left over clay that she had would be = 23 mugs
How to calculate the quantity of mug made by Maggie?The total quantity of clay that Maggie bought = 50lbs
The quantity she used for sculpture = 15.6lbs
The quantity of clay she used for mug = 0.84 lbs
The quantity of clay left = 19.28 lbs
If 0.84 = 1 mug
19.28 = X
make X the subject of formula:
X = 19.28/0.84
= 23 mugs
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The box and whisker blot below represent some data set. Which is the maximum value of the data?
The maximum value of the data = 64
We know that in the box and whisker plot with the left end of the whisker represents the minimum value of the data and the right end of the whisker represents the maximum value.
From the attached box and whisker plot, we can observe that between two numbers on the number line there are 5 equal units.
So, the value of each unit length = 4 unit
Here, the left end of the whisker has value 8 and the right end of the whisker has value 64
This means that the meaximum value = 64
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Jasper is using the following data samples to make a claim about the house values in his neighborhood:
House Value
A $150,000
B $175,000
C $200,000
D $167,000
E $2,500,000
Based on the data, should Jasper use the mean or the median to make an inference about the house values in his neighborhood? (10 points)
Group of answer choices
He should use the mean because it is in the center of the data.
He should use the median because it is in the center of the data.
He should use the median because there is an outlier that affects the mean.
He should use the mean because there are no outliers that affect the mean.
Answer:
Jasper should use the median to make an inference about the house values in his neighborhood because there is an outlier that affects the mean. The outlier in this case is the house with a value of $2,500,000, which is significantly higher than the other house values in the sample. The mean is sensitive to outliers, which means that the outlier can significantly affect the value of the mean. In contrast, the median is not affected by outliers, which makes it a better measure of central tendency for this data set. Therefore, Jasper should use the median because it is in the center of the data and is not affected by the outlier. Answer: He should use the median because there is an outlier that affects the mean.
Answer:
The answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &; A & E $150,000 ‘n’ $200,000
Step-by-step explanation:
The outlier is represented as ‘ E ‘ the highest price value and lowest between, $150,000 to $200,000.
But since ‘ E ‘ is represented highest it is an outlier making ‘ E ;
$150,000 ‘n’ $200,000
So ‘ E ‘ is represented as, $150,000 ‘n’ $200,000
The second option for ‘ 10 points ‘ is He should use the median because there is an outlier that affects the mean, being the ‘ Option C ‘
Thus the answer to your problem is, C. He should use the median because there is an outlier that affects the mean. &; A & E $150,000 ‘n’ $200,000
Geometric constructions summative- need help on it.... its my end of year project
The steps for the construction are given below:
It should be noted that to begin, take a ruler and draw a straight line.Next, employ the use of a compass to draw a circle with its center at one end of said line.Maintain your compass width and place it on the opposite end of the line, drawing another circle that collides with the initial circular figure.How to explain the constructionA new line can be created connecting the points where these two circles intersect using just a simple ruler.
Now that you have succeeded in this task, feel free to experiment and manipulate the astonishing construction you've completed using the same innovative tools.
While this is only an elementary blueprint, there are numerous advanced constructions that can be produced by taking advantage of both GeoGebra and traditional paper/pencil/ruler/compass techniques.
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Write an explicit formula that represents the sequence defined by the following recursive formula:
The explicit formula for the sequence defined by the recursive formula a₁ = 150 and aₙ = -1/5 aₙ₋₁ is aₙ = 150 [tex](-1/5)^{(n-1)[/tex].
To find the explicit formula that represents the sequence defined by the given recursive formula, we need to find a pattern in the sequence and express it using a formula.
The first term in the sequence is a₁ = 150. To find the second term, we use the recursive formula: a₂ = -1/5 a₁ = -1/5(150) = -30. To find the third term, we use the recursive formula again: a₃ = -1/5 a₂ = -1/5(-30) = 6.
We can continue this process to find the fourth term: a₄ = -1/5 a₃ = -1/5(6) = -6/5, and so on.
By observing the pattern, we notice that each term is obtained by multiplying the previous term by -1/5. Therefore, the explicit formula for the sequence can be written as:
aₙ = 150 [tex](-1/5)^{(n-1)[/tex]
This formula gives the value of any term in the sequence based on its position n. It can be used to find any term in the sequence without having to recursively calculate all the previous terms.
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Give the coordinates for all three possible
locations of the fourth vertex.
Y
9
8
7
6
5
4
3
2
1
0
X
1 2 3 4 5 6 7 8 9
Answer:
To find the coordinates for all three possible locations of the fourth vertex, we need to consider the three different ways that a parallelogram can be formed on a 9 by 9 grid.
Method 1: The fourth vertex is directly below the first vertex.
In this case, the coordinates of the fourth vertex are (5, 9), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . X
Method 2: The fourth vertex is directly to the right of the first vertex.
In this case, the coordinates of the fourth vertex are (1, 5), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
X . . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
Method 3: The fourth vertex is diagonal to the first vertex.
In this case, the coordinates of the fourth vertex are (5, 5), as shown below:
Y 9 8 7 6 5 4 3 2 1 0
X 1 2 3 4 5 6 7 8 9
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . X . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
Therefore, the coordinates for all three possible locations of the fourth vertex are (5, 9), (1, 5), and (5, 5).
19. Two angles are complementary. The larger
angle is 36 more than the smaller angle. What
is the measure of the larger angle?
Answer:
larger angle = 63°
Step-by-step explanation:
complementary angles sum to 90°
let x be the smaller angle then larger angle is x + 36 , then
x + x + 36 = 90
2x + 36 = 90 ( subtract 36 from both sides )
2x = 54 ( divide both sides by 2 )
x = 27
Then
larger angle = x + 36 = 27 + 36 = 63°
Two animals are experiencing major events in their life cycles.
Animal 1: A panther is a group of cells that are dividing within the mother.
Animal 2: A pelican has hatched from an egg.
Are these animals at the same stage in their life cycle, or different stages, and why?(20 points)
The same stage. Both the panther and the pelican are embryos.
The same stage. Both the panther and the pelican are adults.
Different stages. The panther is an embryo and the pelican is an infant.
Different stages. The panther is an egg and the pelican is an adult.
The two animals are at different stages in their life cycle. Hence option C: Different stages. The panther is an embryo and the pelican is an infant.
What is the life cycles?The two creatures are at distinct points of their developmental process. The panther, denoted as Animal 1, is characterized as a cluster of cells undergoing division within its maternal host. This is one that then shows that the panther is at a very early stage of growth, and that it is in embryonic phase.
The pelican, is one that is also known as Animal 2, that has successfully hatched from its egg, telling us the conclusion of its embryonic phase and the start of the post-embryonic phase.
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Carleigh, Inc., is a pork processor. Its plants, located in the Midwest, produce several products from a common process: sirloin roasts, chops, spare ribs, and the residual. The roasts, chops, and spare ribs are packaged, branded, and sold to supermarkets. The residual consists of organ meats and leftover pieces that are sold to sausage and hot dog processors. The joint costs for a typical week are as follows: Direct materials $84,500 Direct labor 29,000 Overhead 20,000 The revenues from each product are as follows: sirloin roasts, $68,000; chops, $71,000; spare ribs, $33,000; and residual, $9,800. Carleigh’s management has learned that certain organ meats are a prized delicacy in Asia. They are considering separating those from the residual and selling them abroad for $52,000. This would bring the value of the residual down to $2,650. In addition, the organ meats would need to be packaged and then air freighted to Asia. Further processing cost per week is estimated to be $27,500 (the cost of renting additional packaging equipment, purchasing materials, and hiring additional direct labor). Transportation cost would be $12,100 per week. Finally, resource spending would need to be expanded for other activities as well (purchasing, receiving, and internal shipping). The increase in resource spending for these activities is estimated to be $3,120 per week.
Carleigh, Inc. should separate the organ meats from the residual and sell them abroad, as it would increase their total revenue by $17,150 per week.
To determine whether Carleigh, Inc. should separate the organ meats and sell them abroad, we need to calculate the incremental revenue and incremental costs associated with this decision.
The incremental revenue would be the revenue generated from selling the organ meats abroad, which is $52,000 per week. The incremental cost would include the cost of further processing ($27,500 per week), transportation cost ($12,100 per week), and the increase in resource spending for other activities ($3,120 per week).
Therefore, the incremental cost would be $42,720 per week. Subtracting this from the incremental revenue of $52,000, we get an incremental profit of $9,280 per week.
However, this decision would also decrease the value of the residual from $9,800 to $2,650 per week. Therefore, we need to subtract this decrease in value from the incremental profit. This gives us a net increase in profit of $17,150 per week ($9,280 - $7,130).
Thus, it would be beneficial for Carleigh, Inc. to separate the organ meats and sell them abroad.
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why does area and perimeter change in different ways
Answer:
Step-by-step explanation:
Area and perimeter are both measurements used to describe geometric shapes, but they are fundamentally different concepts and therefore change in different ways.The perimeter of a shape is the distance around the outside of the shape. It is a measure of the total length of the boundaries or sides of the shape. Perimeter depends on the length of each side of the shape, and if one or more sides change in length, the perimeter will change accordingly. For example, if you take a square and double the length of one of its sides, the perimeter will double as well.On the other hand, the area of a shape is the measure of the surface enclosed by the shape. It is a measure of the amount of space inside the shape. The area depends on the length and width of the shape, and if one or both of these dimensions change, the area will change accordingly. For example, if you take a square and double the length of one of its sides, the area will increase by a factor of four.In summary, the perimeter of a shape depends on the length of its sides, while the area of a shape depends on its length and width. Therefore, changes to the length of a side will affect the perimeter, but not necessarily the area, while changes to the length or width will affect the area, but not necessarily the perimeter.
I need some assistance with this ? Please
The real solution is 0, and the imaginary solution is 0.5 ± 0.866i.
What are the solutions of x?
The solutions of the equation is calculated as follows;
4x(x² - x + 1) = 0
This equation is satisfied when either 4x = 0 or x² - x + 1 = 0.
If 4x = 0, then x = 0 is a solution,
To find the solutions of x² - x + 1 = 0, we will use formula method;
x = [ -(-1) ± √((-1)² - 4(1)(1)) ] / (2(1))
x = [ 1 ± i√3 ] / 2
x = 0.5 ± 0.866i
Thus, the solutions of the cubic equation involves both real and imaginary solution.
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Prove: 36 + 324 + 900+. . . +(12n − 6)2 = 12n(4n2 − 1)
By mathematical induction, the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
How to solveTo demonstrate our point, mathematical induction can be employed.
We want to prove that the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
Using mathematical induction:
Step 1: Base case (n=1)
S(1) = 6² = 36
12 * 1 * (4 * 1² - 1) = 36
Since S(1) holds true, the base case is proven.
Step 2: Inductive step (Assume it's true for n=k, and show it's true for n=k+1)
Assumption: S(k) = 36 + 324 + 900 + ... + (12k - 6)² = 12k(4k² - 1)
We follow the exhaustive process to prove:
= 12(4k³ + 12k² + 11k + 3)
Since both expressions for S(k+1) are equal, the inductive step is proven.
Thus, by mathematical induction, the given formula holds for all natural numbers n:
S(n) = 36 + 324 + 900 + ... + (12n - 6)² = 12n(4n² - 1)
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The data table shows the numbers of eggs laid by
individual chickens in a year
What is the median number of eggs laid in a year?
A. 231
B. 229
C. 230
D. 234,6
The value of the median number of eggs laid in a year is,
⇒ 231
We have to given that;
The data table shows the numbers of eggs laid by individual chickens in a year.
Now, We can arrange it into ascending order as;
⇒ 222, 229, 229, 231, 234, 235, 262
Since, There are 7 terms
Hence, Median is,
= (7 + 1)/2
= 4th term
= 231
Thus, The value of the median number of eggs laid in a year is,
⇒ 231
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Answer:
A. 229 is correct
answer D.231 is wrong
Find the 8th term of the geometric sequence 10, 50, 250,...
The 8th term of the sequence is 781, 250.
We have geometric sequence 10, 50, 250,...
First term= 10
Common ratio = 50/10 = 5
So, the 8th term of sequence is
= 10 x [tex]r^{8-1[/tex]
= 10 x [tex]r^7[/tex]
= 10 x [tex](5)^7[/tex]
= 10 x 5 x 5 x 5 x 5 x5 x 5 x 5
= 10 x 78125
= 781, 250
Thus, the 8th term of the sequence is 781, 250.
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Rectangle WXYZ is dilated by a factor of 3 to make rectangle W'X'Y'Z. What is the perimeter of rectangle W'X'Y'Z?
The perimeter of rectangle W'X'Y'Z is 16 units
Perimeter of rectangle:he rectangle has four sides. There are two lengths and two widths in a rectangle. Therefore, the perimeter of the rectangle is twice the sum of two adjacent sides that are length and width. The formula is given by:
Perimeter of rectangle = 2(l + b)
We have :
Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'
So, By the image:
The analysis will be the:
Rectangle of WXYZ = 2 × 4
and, The rectangle of W'X'Y'Z' = 2 × WXYZ
= 16
W'X' = 4
W'Z' = 4
Hence, The perimeter of rectangle is = 4 + 4 + 4 + 4 = 16
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The given question is incomplete, So i take the similar question :
Rectangle WXYZ will be the dilated by a scale factor of 1/2 creating rectangle W'X'Y'Z'. What is the perimeter of rectangle W'X'Y'Z?
And also to see the attachment.
Noah tried to prove that
cos
(
�
)
=
sin
(
�
)
cos(θ)=sin(θ)cosine, left parenthesis, theta, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis using the following diagram. His proof is not correct.
A right triangle A B C. Angle B A C is a right angle. Angle A C B is theta.
A right triangle A B C. Angle B A C is a right angle. Angle A C B is theta.
Statement Reason
1
�
∠
�
=
�
m∠B=θm, angle, B, equals, theta The acute angles in a right triangle are congruent.
2
sin
(
�
)
=
�
�
�
�
sin(θ)=
BC
AB
sine, left parenthesis, theta, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Definition of sine.
3
cos
(
�
∠
�
)
=
�
�
�
�
cos(m∠B)=
BC
AB
cosine, left parenthesis, m, angle, B, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Definition of cosine.
4
cos
(
�
)
=
�
�
�
�
cos(θ)=
BC
AB
cosine, left parenthesis, theta, right parenthesis, equals, start fraction, A, B, divided by, B, C, end fraction Substitution.
5
cos
(
�
)
=
sin
(
�
)
cos(θ)=sin(θ)cosine, left parenthesis, theta, right parenthesis, equals, sine, left parenthesis, theta, right parenthesis Substitution
The possible first mistake Noah made in the evaluation of the sine and cosine of the acute angles of a right triangle is that the acute angles are complementary and are not always congruent. The correct option is the option (A).
(A) Angles ∠B and ∠C are complementary, not congruent
What are complementary angles?Complementary angles are angles that when added together are equivalent to 90°
The possible two column table Noah used to attempt to prove that cos(θ) = sin(θ) obtained in a similar proof on the website can be presented as follows;
Statement [tex]{}[/tex] Reason
1 m∠B = θ [tex]{}[/tex] The acute angles in a right triangle are congruent
2 sin(θ) = AB/BC [tex]{}[/tex] Definition of sine
3 cos(m∠B) = AB/BC [tex]{}[/tex] Definition of cosine
4 cos(θ) = AB/BC [tex]{}[/tex] Substitution
5 cos(θ) = sin(θ) [tex]{}[/tex] Substitution
Part of the question is; What is the first mistake in Noah's statement used to prove that cos(θ) = sin(θ)
The first mistake is the statement and reason that angle m∠B = θ because all acute angles are congruent.
The acute angles in the right triangle are ∠B and ∠C
The sum of the acute angles in a right triangle is; ∠B + ∠C = 90°
Therefore the acute angles in a right triangle are always complementary, and not always congruent.
The correct option is therefore the option (A)
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The group thought there was enough food for all 5 group members to complete the trip, with each person getting the required 5600 calories per day. However, they discover that they are missing 28,000 calories. Using the map, create a plan for the rest of the trip that includes taking as many group members as possible to the South Pole, while sending the rest of the group members directly back to base camp. Remember that each person must have 5,600 calories of food per day until he or she gets back to base camp.
Be sure to explain how you came up with your plan. Include all work necessary to support your answer.
Please answer as soon as possible due in an hour. Thank you.
The plan would be to send 2 group members back to base camp with enough food to sustain them for 5 days, while the remaining 3 members continue to receive 5,600 calories per day from the remaining food supply to complete the journey to the South Pole.
To create a plan for the rest of the trip, we need to consider the total number of days it will take for the group to return to base camp from their current location, and the number of group members who can be taken to the South Pole given the remaining food supply.
Given that the group is missing 28,000 calories, we can calculate the number of days of food that are missing by dividing 28,000 by the daily requirement of 5,600 calories per person. This gives us 5 days of missing food. Therefore, the group has enough food for 5 people to continue to receive 5,600 calories per day for 5 days, but not for all 5 members to continue for the entire trip.
To maximize the number of group members who can continue to the South Pole, we can send two members back to base camp immediately with enough food to sustain them for 5 days (2 people x 5 days x 5,600 calories/day = 56,000 calories). This will leave us with 3 group members who can continue to receive 5,600 calories per day for the remaining journey.
Assuming the trip back to base camp takes the same amount of time as the trip to the current location, we can estimate that the total trip duration will be around 20 days. Therefore, the remaining 3 group members will need a total of 20 days x 3 people x 5,600 calories per day = 336,000 calories.
Given the remaining food supply of 28,000 calories, we have a total of 364,000 calories available (28,000 missing calories + 336,000 required calories). Therefore, the 3 remaining group members can continue to receive their required daily calorie intake and complete the journey to the South Pole.
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I need help please geometry not my strong suit
The image point of (-7, -8) after the sequence of transformations is given as follows:
(-4.5, -4).
How to obtain the coordinates of the image point?The original coordinates are given as follows:
(-7, -8)
The first transformation is a dilation with a scale factor of 1/2, meaning that each coordinate is multiplied by 1/2, hence:
(-3.5, -4).
The second transformation is a translation of one unit left, meaning that one is subtracted from the y-coordinate, thus the image point after the sequence of transformations is given as follows:
(-4.5, -4).
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Is y=(1/2)X a linear function
Answer:
linear
Step-by-step explanation:
have a good day God bless :)
Please Help Quickly ASAP Hurry Geometry ASAP
Questions in the picture
Answer:
The answer is Area: 25.5
Step-by-step explanation:
Is y=2x+X+1 a linear function
No, y=2x+X+1 is not a linear function because it contains a term with an exponent of 1 and a term with an exponent of 0. Linear functions are functions of the form y = mx + b, where m and b are constants, and x is the independent variable. The graph of a linear function is a straight line.
In the given function, the term X is not multiplied by a constant, so it does not have a fixed rate of change. Therefore, the graph of this function is not a straight line. Instead, it is a quadratic function, which has a parabolic graph.
A poll showed that 53.2% of Americans say they believe that statistics teachers know the true meaning of life. What is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life. Round to 3 decimal places.
The probability that a statistics teachers do not know the true meaning of life is 46.8%
What is the probability of someone who does not believeFrom the question, we have the following parameters that can be used in our computation:
53.2% of Americans say they believe that statistics teachers know the true meaning of life.
This means that
P(Believe) = 53.2%
For the required probability, we have
P(Not believe) = 1 - P(Believe)
So, we have
P(Not believe) = 1 - 53.2%
Evaluate
P(Not believe) = 46.8%
Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%
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Find the measure of angle A.
60x
O 60°
O 30°
O 23°
O 37°
30x
A
Answer:
Step-by-step explanation:
sum of angles in a triangle=180º
90+60x+30x=180
90+90x=180
90(1+x)=180
1+x=2
x=1
angle A=30º
Given that a/b=3/4 and b/c=5/6 find a:b:c Give you answer in its simplest form
Answer:
LCM of 4 and 5 is 20.
a/b = 3/4 = 15/20
b/c = 5/6 = 20/24
a:b:c = 15:20:24
Identify the area of a regular hexagon with side length 14in. rounded to the nearest tenth.
The area of a regular hexagon with side length 14 inches is 509.22 square inches.
Given that, a regular hexagon with side length 14 inches.
We know that, area of a regular hexagon can be calculated using A=3√3/2 a².
Here, area of a regular hexagon = 3√3/2 ×14²
= 3√3 ×98
= 509.22 square inches
Therefore, the area of a regular hexagon with side length 14 inches is 509.22 square inches.
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A total of $8000 is invested: part at 6% and the remainder at 10%
. How much is invested at each rate if the annual interest is $760
The requried, $1000 is invested at 6%, and $7000 is invested at 10%
Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.
We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.
So we have the system of equations:
x + y = 8000 (1)
0.06x + 0.1y = 760 (2)
We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:
0.06x + 0.06y = 480 (3)
0.1y - 0.06y = 0.04y = 280
y = $7000.
Substituting y = $7000 into equation 1, we get:
x + $7000 = $8000
So x = $1000.
Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.
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An ice block in the form of rectangular prism with a square base is melting at a rate of 550cm^3/min. The base length is decreasing at a rate of 1cm/min. How fast is the surface area of the ice block changning when the base length is 10cm, and height is 20cm?
The speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min
What is the surface area of a rectangular prism?The total area or region that is covered by a rectangular prism's six faces is known as its surface area.
Solids called prisms have identical polygon bases and flat parallelogram sides. Prisms come in a variety of shapes, including triangles, squares, rectangles, pentagons, hexagons, and more.
Thus, it can be seen that the speed at which the surface area of the ice block changes when the base length is 10cm, and the height is 20cm is 180 cm^2 /min
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Write an equation then find the value of y when x =16. Show all work.
Answer:
Answer is A
Step-by-step explanation:
A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.
B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.
