Answers
Using the given clues, we can fill out the table as follows:
Section Number Color
A 3 Green
B 5 Purple
C 9 Brown
D 8 Orange
E 1 Yellow
F 6 Blue
G 4 Pink
Completing the table of valuesUsing this information, we can deduce the values of each section:
The number 8 is in all shapes
So, D = 8
Number C is the largest
So, C = 9 because the numbers used are BETWEEN 0 and 10 i.e. 1 to 9Also, C = BrownFor the blue section, we have
F = Blue
For the triangle, we have
DEF = 48
D + E + F = 15
So, we have
EF = 6
E + F = 7
This means that
(E, F) = (1, 6) or (6, 1)
Number 1 is yellow
So, we have
E = 1 = YellowF = 6 = BlueSince F is not yellow, then
A = Green
A and G add up to 7, and A's number is smaller than G's.
So A and G must be (1, 6), (3, 4) because 2 and 7 are not used
Because of the values of E and F, we have
A = 3 and G = 4
Green and pink are in the rectangle only
So:
G = Pink
Purple and Orange are in the circle
So:
(B, D) = (Orange, Purple), (Purple, Orange)
The purple section is 5 and D = 8
So:
(B, D) = (Purple, Orange) = (5, 8)
The table has been completely filled
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Related Questions
Match the following reasons with the statements to complete the following proof.
Answers
In order to proof that ∠ ABC + m ∠DBE = 180° the correct proof is given as follows:
m ∠CBD - m ∠DBE - Given ∠ABC, ∠CBD are supplementary - Given by the definition of supplementary angels. m ∠ABC + m ∠CBD = 180° - this is is also based on exterior sides in opposite raysm ∠ABC + m ∠DBE = 180° because of the substituted angles.QEDWhat is a supplementary angle?Supplementary angles comprise of angles that are on a straight line and which must add up to 180°
It is right to state therefore, that ∠ABC, ∠CBD are supplementary angels.
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A group of 75 math students were asked whether they
like algebra and whether they like geometry. A total of
45 students like algebra, 53 like geometry, and 6 do
not like either subject.
Algebra vs. Geometry
Likes Algebra
Does Not
Like Algebra
Total
Likes
Geometry
Mark this and return
a
3
53
Does Not
Like Geometry
b
6
e
Total
45
P
75
What are the correct values of a, b, c, d, and e?
a 16, b = 29, c = 22, d = 30, e = 24
a = 29, b = 16, c = 30, d = 22, e = 24
a 16, b = 29, c = 24, d = 22, e = 30
H
a = 29, b = 16, c = 24, d = 30, e = 22
Answers
The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.
For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:
We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.
75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)
Simplifying this equation, we have:
75 = 98 + 6
75 = 104
This equation is incorrect, so we can eliminate options c and d.
Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.
Using the correct values for a and b, we have:
16 + b = 6
b = 6 - 16
b = -10
Since we can't have a negative value for the number of students, option a is also incorrect.
The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.
Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)
Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)
Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)
Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)
All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.
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Show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1
On the interval
(−[infinity], 1),
f is function; therefore f is continuous on
(−[infinity], 1).
On the interval
(1, [infinity]),
f is function; therefore f is continuous on
(1, [infinity]).
Answers
The function \($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\) is continuous on (-∞, ∞).
As per the given data the function f(x) is given by:
\($$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$\)
Here we have to determine that the function f(x) is continuous on (-∞, ∞)
If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)
What are continuous function?
A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.
To show f(x) is continuous at x = 1
\(\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}\) f(x)
\(\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\\)
= 1 - 1
= 0
\(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\\)
= ln 1
= 0
Therefore \(\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0\).
Hence f(x) is continuous on (-∞, ∞)
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Y=? Need help ASAP very much appreciated
Answers
Answer:
8
Step-by-step explanation:
I'm guessing the answer is 8 because when y is -8, x is 4. So, my thought in mind is when x is negative, y is positive. It also says, "If the value of "y" varies directly with "x". So, this means the answer is 8. You're very much welcome! Also, I'm sorry if this is incorrect. I tried my best with this question but I'm pretty sure the answer is 8! Have a great day sunshine!! :)
Answer: y = 8
Step-by-step explanation:
simplify please .....,
Answers
Answer:i simplified it and got 9 so 3 to the second power
Step-by-step explanation:
27. FG L OP, RS LOQ, FG = 33, RS = 36, OP = 14 R a. 12 F P G O X b. 18 S C. 14 d. 21.2
Answers
The radius of the circle and the Pythagorean theorem indicates that the length of the segment OQ = x ≈ 12. The correct option is therefore;
a. 12
What is the Pythagorean theorem?Pythagorean theorem states that the square of the length of the hypotenuse or longest side of a right triangle is equivalent to the sum of the squares of the lengths of the other two sides of the triangle.
The value of x can be found from the length of the radius of the circle, which can be obtained from the length of the chord \(\overline{FG}\) and the segment OP using Pythagorean theorem as follows;
Circle chord theorem states that a chord perpendicular to a radius of a circle is bisected by the circle.
OP bisects \(\overline{FG}\), therefore;
The radius FO = √((FG/2)² + (OP)²)
FO = √((33/2)² + (14)²) = √(468.25)
Similarly, we get; radius RO = √((RS/2)² + (OQ)²)
OQ = x, RS = 36 and the radius RO = FO = √(468.25), therefore;
√(468.25) = √((36/2)² + (x)²) = √(18² + x²)
468.25 = 18² + x²
x² = 468.25 - 18² = 144.25
x = √(144.25) ≈ 12
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If in a population the rate of mutation that converts the A allele to the a allele is 10^-6 and the current frequency of the A allele is 0.75 and the a allele is 0.25, then the frequency of the A and a alleles in the next generation will be
Multiple Choice
O A: 0.74 a: 0.26
O A: 0.75000075 a: 0.24999925
O A: 0.75 a: 0.25
O A: 0.74999925 a: 0.25000075
Answers
The frequency of A allele after a single generation of mutation can be found as follows: Frequency of A allele after a single generationp(A) = p(A) x (1 - m) + q(a) x m
where,
m = mutation rate = 10^-6p(A) = frequency of A allele in initial generation = 0.75q(a) = frequency of a allele in initial generation = 0.25Thus,p(A) = 0.75 x (1 - 10^-6) + 0.25 x 10^-6 = 0.74999925
And the frequency of a allele will beq(a) = 1 - p(A) = 1 - 0.74999925 = 0.25000075
Therefore, the frequency of the A and a alleles in the next generation will beA: 0.74999925 and a: 0.25000075.
This is option D.
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What kind of data might be displayed on a pie chart ?
Answers
Answer: nomial data
Step-by-step explanation:
what is 3/4 doubled as a fraction
Answers
Answer:
1 2/4.....1 1/2...........6/4
Step-by-step explanation:
add two 3/4.
1 2/4.
It is either 1 1/2, or 6/8. Not enough context is given to decide which, you should be able to figure it out though.
The blues band, Jonny and the Silver Toads, charges $25 per ticket at their performances. Their next venue charges them $800 for use of the venue. Based on the inequality below, how many tickets, t, do they need to sell in order to profit at least $1,725?
Answers
If they want to make a profit of $1,725 or more, then they need to sell at least 101 tickets.
How many tickets do they need to sell?We know that each ticket costs $25, then if they sell t tickets the revenue is:
R(t) = 25t
We know that the band has a cost of $800, and they want to make a profit of at least $1,725, then we can write the inequality below:
25t - 800 ≥ 1,725
(remember that the profit is the difference between the revenue and the cost).
Now we can solve that for t.
25t ≥ 1,725 + 800
25t ≥ 2,525
t ≥ 2,525/25
t ≥ 101
They need to sell at least 101 tickets.
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Find the value of k and yz if y is between x and z. x y = 3 k − 2 , y z = 7 k 4 , x z = 4 k 38
Answers
Considering that y is between x and z, we have that:
The value of k is of k = 6.The length of yz is 46 units.How to find the value of k and of yz?We consider that y is between x and z, hence the length of the segment is given by:
xz = xy + yz
The separate lengths are given as follows:
xz = 4k + 38.xy = 3k - 2.yz = 7k + 4.Hence:
4k + 38 = 3k - 2 + 7k + 4.
4k + 38 = 10k + 2
6k = 36
k = 6.
Hence the length of yz is given by:
yz = 7k + 4 = 7(6) + 4 = 42 + 4 = 46 units.
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evaluate the line integral, where c is the given curve. c xey dx, c is the arc of the curve x = ey from (1, 0) to (e9, 9)
Answers
The line integral ∫C xey dx on the arc of the curve x = ey from (1, 0) to (e^9, 9) is (1/3)(e^27 - 1).
How to evaluate the line integral on the given curve?Hi! I'd be happy to help you evaluate the line integral on the given curve. To evaluate the line integral ∫C xey dx, where C is the arc of the curve x = ey from (1, 0) to (e^9, 9), follow these steps:
1. Parameterize the curve: Since x = ey, let y = t, so x = e^t. Thus, the parameterization of the curve is r(t) = (e^t, t), with t ranging from 0 to 9.
2. Compute the derivative of the parameterization: dr/dt = (de^t/dt, dt/dt) = (e^t, 1).
3. Substitute the parameterization into the integrand: xey = (e^t)(e^t) = e^(2t).
4. Compute the dot product of the integrand and dr/dt: (e^(2t)) * (e^t, 1) = e^(3t).
5. Integrate the dot product with respect to t from 0 to 9: ∫(e^(3t)) dt from t = 0 to t = 9.
6. Evaluate the integral: [1/3 * e^(3t)] from t = 0 to t = 9 = [1/3 * e^(27)] - [1/3 * e^0] = (1/3)(e^27 - 1).
So, the line integral ∫C xey dx on the arc of the curve x = ey from (1, 0) to (e^9, 9) is (1/3)(e^27 - 1).
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what is the relationship among the mean, median, and mode in a symmetric distribution? multiple choice they are all equal.
Answers
In a symmetric distribution, the mean, median, and mode are all equal. This means that the center of the distribution is balanced and there is an equal number of values on both sides.
The mean is the average of all the values in the distribution, the median is the middle value, and the mode is the most frequent value. In a symmetric distribution, these three measures of central tendency coincide and provide an accurate representation of the center of the data. This relationship is particularly useful in statistics and data analysis as it simplifies the process of summarizing and interpreting data.
In a symmetric distribution, the mean, median, and mode all have the same value. The mean is the average of all data points, while the median is the middle value when the data is sorted, and the mode is the most frequently occurring value.
Symmetric distributions have a balanced and uniform shape, which causes these measures of central tendency to coincide at the center of the distribution. This relationship holds true for a perfectly symmetric distribution, but might not be applicable to all distributions with some degree of symmetry.
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A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the
period of time the tournament took place was $132,000. This means the tournament took place throughout how many days?
a) 5
b) 7
c) 12
d) 14
Answers
A stadium brought in an average revenue of $11,000 per night for a professional sports tournament. Total receipts for the period of time the tournament took place was $132,000. This means the tournament took place throughout is 12 days
How to find the number of members ?
When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.
A stadium brought in an average revenue of $11,000 per night for a professional sports tournament.
Total receipts for the period of time the tournament took place was $132,000.
This means the tournament took place throughout how many days?
since total divide by per night is equal to number of days
now 132000/11000= 12
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explain why this work is correct
Answers
Ana Maria has applied for United States citizenship. She has studied American history and government for a long time and thinks she is ready to take the citizenship test. When she took the practice test online she answered forty-seven questions correctly and only missed three. What percent of the questions did she get right?
Answers
Answer:
≈93.6
Step-by-step explanation:
percent right = answers right/ anwers wrong
Answers right= 47-3=44
%=44/47
≈93.6
The length of a rectangular cement patio is 3 feet less than three times the width. The sum of the length and width of the patio is 21 feet. Find the length of the patio.
Answers
Answer: The length is 15 feet.
Step-by-step explanation:
L = 3w - 3 (length is 3 feet less than three times the width)21 = w + (3w -3)21 = 4w - 3 (add like terms)24 = 4w (substract 3 from both sides)6 = w <-- widthBut, the problem is asking for the length...
L = 3w - 3L = 3(6) - 3L = 18 - 3L = 15 ftFInd the value of a, b and c
Answers
The angles in the triangle is as follows:
a = 55°b = 97°c = 83°How to find the angle of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the angles a, b and c in the triangle as follows:
c + 44 + 53 = 180(sum of angles in a triangle)
c = 180 - 44 - 53
c = 83 degrees
Therefore, let's find the value of a and b.
b + 83 = 180 (sum of angle on straight)
b = 180 - 83
b = 97 degrees.
Hence,
28 + 97 + a = 180(sum of angles in a triangle)
a = 180 - 28 - 97
a = 55 degrees.
Therefore,
a = 55°
b = 97°
c = 83°
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A vertical 1-meter stick casts a shadow of 0.4 meters. If a tree casts a shadow of 12 meters at the same time, how tall is the tree? a. 13.4 meters b. 12.6 meters c. 30 meters d. 4.8 meters.
Answers
A vertical 1-meter stick casts a shadow of 0.4 meters , then the height of the tree is 30 meters , the correct option is (c) .
We use the concept of proportions to find the height of the tree .
We know that , A vertical stick of 1 meter casts a shadow of 0.4 meters.
We have to find the height of tree which casts a shadow of 12 meter at the same time ,
Let x = the height of the tree in meters.
So , we can write ,
⇒ 1/0.4 = x/12 ,
Simplifying this proportion:
We get ,
⇒ 0.4x = 12 ,
⇒ x = 12/0.4
⇒ x = 30
Therefore, the height of the tree is Option(c) 30 meters.
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The given question is incomplete , the complete question is
A vertical 1-meter stick casts a shadow of 0.4 meters. If a tree casts a shadow of 12 meters at the same time, how tall is the tree?
(a) 13.4 meters
(b) 12.6 meters
(c) 30 meters
(d) 4.8 meters.
Hong needs to memorize words on a vocabulary list for Spanish class. He has memorized 30 of the words, which is five-sixths of the list. How many words are on the list?
Answers
.In this exercise, we see the cumulative effects of inflation. Refer to the CPI table. Find the four-year inflation rate from December 1973 to December 1977. (Round your answer to one decimal place.)
_______%
Answers
Answer:
Step-by-step explanation:
"To find the four-year inflation rate from December 1973 to December 1977, you can use the formula:
Inflation rate = ((CPI in 1977 - CPI in 1973) / CPI in 1973) x 100%
From the CPI table, we can see that the CPI in December 1973 was 146.4, and the CPI in December 1977 was 207.9. So, the inflation rate is:
((207.9 - 146.4) / 146.4) x 100% = 41.9%
Therefore, the four-year inflation rate from December 1973 to December 1977 is 41.9%. Does that help?"
How hectometers equals 102 what
Answers
Find the slope of a line passing through the points (-4,2) and (5,6)
Answers
Step-by-step explanation:
I hope you understand what I did
Joe deposited $2,000 into his savings account. The bank has a rate of 7% interest per year. How much interest did he earn in 5 years?
Answers
Answer:
Joe earned $700 in interest in 5 years
Step-by-step explanation:
To calculate the interest earned by Joe in 5 years at a rate of 7% per year, we can use the simple interest formula:
Interest = Principal x Rate x Time
Where:
Principal is the initial amount deposited, which is $2,000 in this case
Rate is the interest rate per year, which is 7%
Time is the number of years, which is 5 years in this case
Plugging in the values, we get:
Interest = $2,000 x 0.07 x 5
Interest = $700
Therefore, Joe earned $700 in interest in 5 years.
Bea orders takeout. she orders a drink that costs $2.50, an appetizer that costs $8.50, and a sandwich that costs $15.30. what will her total be if there is a 7% sales tax rate and she gives a 20% tip? $33.78 $33.40 $31.56 $28.14
Answers
The total amount Bea spent if there is a 7% sales tax rate and she gives a 20% tip is $33.40. option B
Sales taxCost of drink = $2.50Cost of appetizer = $8.50Cost of sandwich = $15.30Total = $2.50 + $8.50 + $25.30
= $26.30
Sales tax = 7%
= 7% × $26.30
= 0.07 × 26.30
= $1.841
Tips = 20%
= 20% × $26.30
= 0.20 × 26.30
= $5.36
Total cost = $26.30 + $1.841 + $5.36
= $33.401
Approximately,
$33.40
Therefore, the total amount Bea spent if there is a 7% sales tax rate and she gives a 20% tip is $33.40. option B
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what is the smallest font size doug should use in the text on his slides? group of answer choices 20 points 24 points
Answers
The smallest font size that Doug should use in the text on his slides is 24 points.
The reason for this is that smaller font sizes can make the text difficult to read, especially from a distance.
According to industry standards, the recommended minimum font size for slide presentations is 24 points.
This is because smaller font sizes can be challenging to read, especially if the audience is sitting at the back of the room or if the slides are being viewed on a small screen.
While 20 points may seem like a reasonable font size, it's still small enough to make it difficult for some people to read the text.
Therefore, to ensure that all members of the audience can read the text on the slides, it's best to use a font size of at least 24 points.
In addition to using a larger font size, it's also essential to use a clear and legible font.
Sans-serif fonts such as Arial, Helvetica, or Calibri are recommended for presentations as they are easy to read, even from a distance.
It's also important to keep the contrast between the text and the background high to make it easier to read the text.
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Solve for x.
logo(x-2) + log(x + 3) = 2
Answers
Answer:
x=-1-5√17/2
Step-by-step explanation:
logo((x-2)(x+2))=2
logo(x²+3x-2x-6)=2
x²+3x-2x-6=10²
x²+x-6=100
x²+x-106=0
x=-1+5√17/2
Find the measure of the missing angle
Answers
Answer: 149° both
Step-by-step explanation:
The angle B and C are equal as they are on opposite sides.
Angle B and C is equal to 180 - 31 = 149 due to the straight line rule
What are the 3 linear functions?.
Answers
Answer:
point-slope form, standard form, and slope-intercept form
Step-by-step explanation:
The three main types of linear functions are: point-slope form, standard form, and slope-intercept form.
Here is an image with each form
Point K is rotated 90". The coordinate of the pre-image point K was (2,6) and its image K' is at the coordinate (-6, -2) Find the direction of the rotation, The direction of rotation was ???
Answers
Answer:
Clockwise
Step-by-step explanation:
Sorry I answered late
Answer:Clockwise
Step-by-step explanation: