Answers
Answer:
wx = 116 /11
= 10.54
Step-by-step explanation:
plz follow me
Answer: 29
see in the picture, WX is the median of the trapezoid
=> WX = (ST + UV)/2
⇔ 7x + 8 = (10x + 5 + 8x - 1)/2
⇔ 7x + 8 = (18x + 4)/2
⇔ 7x + 8 = 9x + 2
⇔ 2x = 6
⇔ x = 3
with x = 3 => WX = 7.3 + 8 = 21 + 8 = 29
Step-by-step explanation:
Related Questions
The equilibrium prices of three interdependent commodities are given by the system:
2p
1
+4p
2
+p
3
=77
4p
1
+3p
2
+7p
3
=114
2p
1
+p
2
+3p
3
=48
a) Rewrite the equation system in the format Ax=d. b) Use the coefficient matrix A to test the rank of the system and whether the system has a solution. c) If the system has a solution, use Gauss-Jordan elimination to find the solution.
Answers
a) The system can be written as Ax = d.
b) The system has a unique solution.
a) To rewrite the equation system in the format Ax = d, we need to arrange the coefficients of the variables in matrix A and the constants on the right-hand side in vector d. The given system of equations can be written as:
| 2 4 1 | | p₁ | | 77 |
| 4 3 7 | x | p₂ | = | 114 |
| 2 1 3 | | p₃ | | 48 |
Matrix A:
| 2 4 1 |
| 4 3 7 |
| 2 1 3 |
Vector x:
| p₁ |
| p₂ |
| p₃ |
Vector d:
| 77 |
| 114 |
| 48 |
Therefore, the system can be written as Ax = d.
b) To test the rank of the system and whether the system has a solution, we need to find the rank of matrix A. If the rank of A is equal to the rank of the augmented matrix [A | d], and the rank is equal to the number of variables (3 in this case), then the system has a unique solution. Otherwise, if the ranks are not equal or the rank is less than the number of variables, the system either has infinitely many solutions or no solution.
c) To solve the system using Gauss-Jordan elimination, we will perform row operations on the augmented matrix [A | d] until we reach row-echelon form or reduced row-echelon form. However, since the solution is not requested, I will not perform the calculations in this response.
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A circle whose center is at (1, -3) passes through the point (7, 5). whats the radius?
Answers
The distance from the center to any point on the circle exists comprehended as the radius. The radius is 10cm.
What defines the radius of a circle?The radius of a circle is the separation between any two points on the circle and its center. The radius of a circle is the separation between any two points on its circumference. R or r is typically used to indicate it.
The distance along a line connecting a circle's center to a point on its perimeter is known as a circle's radius. Therefore, the radius is equal to half the diameter's length. Therefore, the radius is equal to half the diameter's length.
The radius of a circle is the separation between any two points on the circle and its center.
In this instance (using the Pythagorean Theorem)
r = \(\sqrt{(7-1)^{2}+(5-(-3))^{2} }\)
= √(36 + 64)
r = 10
If a circle whose center is at (1, -3) passes through the point (7, 5) then the radius of the circle exists 10.
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What is the full meaning of Cpct?
Answers
"Corresponding Parts of Congruent Triangles Are Congruent" is represented the CPCTC. The corresponding angles and sides of two or more triangles must also be identical in order for them to be congruent.
Congruence :
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles are of the same size. These triangles can be moved, rotated, flipped, and otherwise manipulated to produce the same effect. When moved, they align with one another. Congruence is a concept used to explain the relationship between an object and its mirror image. Two entities or shapes are considered to be congruent if they superimpose on one another. They are the same size and shape. In the context of geometric figures, line segments with the same length and angles with the same measure are said to be congruent.
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The CPCT stands for Corresponding Parts of Congurent Triangles. It means that when two triangles are congurent the corresponding angles and sides are also congurent.
Congruence :
Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles are of the same size. These triangles can be moved, rotated, flipped, and otherwise manipulated to produce the same effect. When moved, they align with one another. Congruence is a concept used to explain the relationship between an object and its mirror image. Two entities or shapes are considered to be congruent if they superimpose on one another. They are the same size and shape. In the context of geometric figures, line segments with the same length and angles with the same measure are said to be congruent.
Therefore, the appreviation CPCT is Corresponding Parts of Congurent Triangles.
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What is the difference between 30% interest charged for a payday loan and a 30% APR on a credit card?
Answers
The main difference is interest charged for a payday loan is typically over a short period, whereas credit card represents the annualized interest rate over a year.
The payday loan interest is a one-time charge, while the credit card APR accumulates over time if the balance is not paid in full.
For a payday loan, the 30% interest is typically charged over a short period, often within a few weeks.
This means that if you borrow $100, you would need to repay $130, including the $30 interest, within that short timeframe.
On the other hand, a 30% APR on a credit card represents the annualized interest rate charged on the outstanding balance. This interest is spread out over a year.
If you have an outstanding balance of $100 on a credit card with a 30% APR, the interest charged over a year would be $30.
In summary, the main difference is that the 30% interest charged for a payday loan is typically applied over a short period, whereas the 30% APR on a credit card represents the annualized interest rate over a year.
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a wildlife biologist wanted to estimate the size of a deer population because garners were complaining that the deer were destroying their crops. she trapped and tagged the ears of 28 deer in june. in august, she trapped a total of 60 deer and 17 of those had tagged ears. how large was the deer population in that area? the carry capacity is 95. should any permits be inured? if so, how many?
Answers
The estimated size of the deer population in the area is approximately 36.43. Since this is less than the carry capacity of 95, no permits need to be issued for population control.
To estimate the size of the deer population, we can use the mark and recapture method. The biologist tagged 28 deer in June and then trapped a total of 60 deer in August, of which 17 had tagged ears.
The mark and recapture method assumes that the proportion of tagged deer in the second sample represents the proportion of tagged deer in the entire population. We can set up a proportion:
(Tagged deer in the second sample) / (Total population) = (Tagged deer in the first sample) / (Total number of deer in the second sample)
Using the given information:
17 / Total population = 28 / 60
To solve for the total population, we can cross-multiply and solve the equation:
17 * 60 = 28 * Total population
1020 = 28 * Total population
Total population = 1020 / 28
Total population ≈ 36.43
Therefore, the estimated size of the deer population in that area is approximately 36.43.
To determine if any permits should be issued, we need to compare the estimated population size to the carry capacity of 95. Since the estimated population size is less than the carry capacity, no permits need to be issued.
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b If $192 is earned in simple interest on a
principal of $600 invested for 4 years,
what is the rate of interest per year?
Answers
Answer:
8%----------------------
Use the formula for simple interest:
I = PRTwhere:
I = Interest earned,P = Principal,R = Rate of interest ,T = Time (in years).Substituting the given values into the formula, we get:
192 = 600 x R x 4 R = 192/2400R = 0.08 or 8%Therefore, the rate of interest per year is 8%.
A sculpture is formed from a square-based pyramid resting on a cuboid.
the base of the cuboid and the base of the pyramid are both squares
of side 3 cm.
the height of the cuboid is 8 cm and the total height
of the sculpture is 15 cm.
the total mass of the sculpture is 738g.
15 cm
8 cm
3 cm
the cuboid-part of the sculpture is made of iron
with density 7. 8 g/cmº.
the pyramid is made from copper.
calculate the density, in g/cm', of the copper.
[the volume of a pyramid is:
3
-* area of base x perpendicular height. )
[5]
Answers
The density of the copper used in the pyramid is 8.4 g/cm³.
To find the density of the copper used in the pyramid, we first need to determine the volume of the cuboid and pyramid, and then find the mass of the copper.
1. Find the volume of the cuboid (V_cuboid):
V_cuboid = length × width × height
Since the base is a square, the length and width are both 3 cm.
V_cuboid = 3 cm × 3 cm × 8 cm = 72 cm³
2. Find the volume of the pyramid (V_pyramid):
First, find the height of the pyramid: total height (15 cm) - height of the cuboid (8 cm) = 7 cm.
V_pyramid = (1/3) × area of base × perpendicular height
The area of the base is 3 cm × 3 cm = 9 cm².
V_pyramid = (1/3) × 9 cm² × 7 cm = 21 cm³
3. Find the mass of the iron cuboid (m_iron):
Density of iron = 7.8 g/cm³
m_iron = density × V_cuboid = 7.8 g/cm³ × 72 cm³ = 561.6 g
4. Find the mass of the copper pyramid (m_copper):
Total mass of sculpture = 738 g
m_copper = total mass - m_iron = 738 g - 561.6 g = 176.4 g
5. Calculate the density of the copper (density_copper):
density_copper = m_copper / V_pyramid
density_copper = 176.4 g / 21 cm³ ≈ 8.4 g/cm³
The density of the copper is approximately 8.4 g/cm³.
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use function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.
Answers
However, we need to substitute a with s since that is the value we have calculated. Therefore, we get \(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.
Let's consider that s be the length of a side of the regular pentagon.
The perimeter of the regular pentagon will be 5s. Therefore, we have the equation:5s = 140s = 28 cm
Also,
we have the formula for the area of a regular pentagon as:
\($A=\frac{1}{4}(5 +\sqrt{5})a^{2}$,\)
where a is the length of a side of the pentagon.
In order to represent the area of a regular pentagon whose perimeter is 140 cm, we need to substitute a with s, which we have already calculated.
Therefore, we have:\(A(s) = $\frac{1}{{4}(5 +\sqrt{5})s^{2}}$\)
Now, we have successfully used function notation (with the appropriate functions above) to represent the area of a regular pentagon whose perimeter is 140 cm.
The area of a regular pentagon can be represented using function notation (with the appropriate functions above). The first step is to calculate the length of a side of the regular pentagon by dividing the perimeter by 5, since there are 5 sides in a pentagon.
In this case, we are given that the perimeter is 140 cm, so we get 5s = 140, which simplifies to s = 28 cm. We can now use the formula for the area of a regular pentagon, which is\(A = (1/4)(5 + sqrt(5))a^2\), where a is the length of a side of the pentagon.
However, we need to substitute a with s since that is the value we have calculated. Therefore, we get\(A(s) = (1/4)(5 + sqrt(5))s^2.\) This is the function notation that represents the area of a regular pentagon whose perimeter is 140 cm.
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use the properties of geometric series to find the sum of the series. for what values of the variable does the series converge to this sum?
7−14z+28z2−56z3+⋯
sum =
domain =
(Give your domain as an interval or comma separated list of intervals; for example, to enter the region x<−1 and 2
Answers
a) The sum of the given series is 7 / (1 + 2z)
b) The domain of convergence is (-∞, -1/2) U (1/2, ∞).
The given series can be expressed as
7 – 14z + 28z^2 - 56z^3 + ...
This is a geometric series with first term (a) = 7 and common ratio (r) = -2z. The formula for the sum of an infinite geometric series is
sum = a / (1 - r)
Substituting the values of a and r, we get
sum = 7 / (1 + 2z)
So, the sum of the given series is 7 / (1 + 2z).
For the series to converge, the absolute value of the common ratio must be less than 1. That is,
|r| = |−2z| < 1
Simplifying this inequality, we get
1/2 < |z|
So, the domain of convergence of the given series is (-∞, -1/2) U (1/2, ∞).
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Need help solving this to help study for my final exam
Answers
Explanation
To answer this given question, we will make use of the Empirical rule of normal distribution
The Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean. Under this rule, 68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.
The image below helps gives a clearer understanding
So in our case, since the mean is 189 mg/dL and the standard deviation is 23
Then we will have the following values at
\(undefined\)
The backyard of a new home is shaped like a trapezoid with a height of 46 ft and bases of 90 ft and 112ft. What is the cost of putting sod on the yard, if the landscaper charges $ 0.25 per square foot for sod?
Answers
The cost of putting sod on the yard is $1161.5
What exactly is a trapezoid?A trapezoid is a polygon that has just one pair of parallel sides. The two extra sides of a trapezoid, known as the legs, are not parallel.
The price is calculated by multiplying the area in square feet by the price per square foot.
The formula for a trapezoid's area is
A = (1/2)(\(b_{1}\) + \(b_{2}\))h.
where h represents height and \(b_{1}\) and \(b_{2}\) represent base lengths.
The area is
A = (1/2)(90 ft + 112 ft)(46 ft)
= 4646 \(ft^{2}\)
when the supplied information is filled in.
Given that each square foot costs $0.25,
the price for this many square feet (4646\(ft^{2}\) ) is $0.25/\(ft^{2}\) × $989.23.
The cost of sodding the backyard will be $1161.5 according to the landscaper.
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Farmer Ed has 9,500 meters of fencing, and wants to enclose a rectangular plot that boarders on a river. If Farmer Ed does not fence the side along the river, what is the largest area that can be enclosed?The largest area that can be enclosed is____square meters
Answers
Answer:
\(Area_{max}=11,281,250m^{2}\)Explanation:
We were given the following information:
Ed has 9,500 meters of fencing
Ed does not fence the side along the river
\(\begin{gathered} Perimeter=9,500m \\ Perimeter=length+2*width \\ length=9,500-2x \\ width=x \\ The\text{ area of a rectangle is given by:} \\ Area=length*width \\ Area=\lparen9,500-2x)*x \\ Area=9,500x-2x^2 \\ Area=-2x^2+9,500x \\ The\text{ maximum point occurs at the vertex \lparen to obtain the largest area that can be enclosed\rparen:} \\ x=-\frac{b}{2a}=-\frac{9,500}{2\left(-2\right)} \\ x=\frac{9,500}{4}=2,375 \\ x=2,375 \\ Substitute\text{ this into the formula for ''length'', we have:} \\ length=9,500-2\left(2,375\right) \\ length=9,500-4,750=4,750 \\ length=4,750m \\ w\imaginaryI dth=x=2,375m \\ Area_{max}=length*width \\ Area_{max}=4,750*2,375 \\ Area_{max}=11,281,250m^2 \\ \\ \therefore Area_{max}=11,281,250m^2 \end{gathered}\)Therefore, the largest area that can be enclosed is 11,281,250 sq. meters
AB is the angle bisector of ∠CAD. Solve for x.
(I really need help on this one cuz i.dk what I'm doin')
Answers
Answer: x=7
Step-by-step explanation:
Since AB is a bisector, it cuts the angle in half, and since we know that the angle is a right angle, we know it’s 90 degrees, so knowing that you use the equation 7x-4= 45 (since 45 is half of 90), add 4 to both sides so you have 7x=49, the divide 49 by 7 and you get 7, so x= 7
I need help please!!!!
Answers
Answer:
a. 10%
b. 80%
c. 20%
Step-by-step explanation:
Hope this helps!
what is the volume of a solid figure with a height of 2 and a square cross-sectional area where the length of the side of a cross-section at
Answers
The volume of a solid figure with a height of 2 and a square cross-sectional area where the length of the side of a cross-section is x is 2x^2.
To calculate the volume of the solid figure with a height of 2 and a square cross-sectional area, we need to know the length of the side of the cross-section. Let's assume that the length of the side is x.
The cross-sectional area of the figure is the area of the square, which is x^2. The volume of the figure is the product of the cross-sectional area and the height, which is 2x^2.
Therefore, the volume of the solid figure is 2x^2.
It's important to note that the volume of a solid figure is directly proportional to its cross-sectional area. This means that if we increase the cross-sectional area by a factor of 2, the volume will also increase by a factor of 2. This relationship is because the cross-sectional area determines how much material there is to fill up the space. The larger the cross-sectional area, the more material is needed to fill up the same height, resulting in a larger volume.
In conclusion, the volume of a solid figure with a height of 2 and a square cross-sectional area where the length of the side of a cross-section is x is 2x^2.
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The editor of a school magazine polled randomly selected students in the 8th, 9th, and 10th grades. They were asked which activity they enjoyed the most: watching sports, reading, or listening to music. The two-way frequency table shows the data she collected.
(see attachment for table)
Based on the data in the table, what is the approximate probability that a randomly selected student is in the 9th grade, given that he or she enjoys watching sports the most?
A. 0.39
B. 0.37
C. 0.35
D. 0.33
Answers
Answer:
D 0.33
Step-by-step explanation:
based on the table you would just divide 13/39 which is 0.33
I hope i am right
Answer: 0.37
Step-by-step explanation:
Instead of doing 13/39 which is the total number of 9th graders. You have to do 13/35 (35= the total amount of kids who prefer watching sports) because it is saying "what is the approximate probability that a randomly selected student is in the 9th grade, given that he or she enjoys watching sports the most?"
What is the number of degrees of freedom that should be used for finding the critical value ta/2?
Answers
The degree of freedom (df) in statistics is the number of independent values in a calculation that can vary.
When performing a hypothesis test, the number of degrees of freedom is a critical aspect to consider.
The degree of freedom (df) in statistics is the number of independent values in a calculation that can vary freely.
A statistical analysis employs a certain distribution to estimate and test the hypotheses. The number of degrees of freedom varies depending on the number of variables considered and the nature of the data.
It is critical to identify the number of degrees of freedom correctly because this determines the appropriate distribution to use.
When determining the critical value of ta/2, the degrees of freedom should be used to determine the t-score. Therefore, the number of degrees of freedom determines the shape of the distribution when testing hypotheses that depend on the difference between two groups means.
The formula for calculating degrees of freedom is df = n1 + n2 - 2, where n1 and n2 are the sample sizes of the two groups.
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can someone help me with this question?
Answers
Answer:
The answer is D
Hope this helps :)
Your answer would be D. 6/11
Pls solve with all steps
Answers
The results of the expressions involving logarithms are listed below:
Case 1: 1 / 2
Case 2:
Subcase a: 0
Subcase b: 11 / 2
Subcase c: - 11 / 2
How to simplify and evaluate expressions involving logarithmsIn this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:
㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c
㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c
㏒ₐ cᵇ = b · ㏒ₐ c
Now we proceed to determine the result of each case:
Case 1
㏒ ∛8 / ㏒ 4
(1 / 3) · ㏒ 8 / ㏒ 2²
(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)
㏒ 2 / (2 · ㏒ 2)
1 / 2
Case 2:
Subcase a
㏒ [b / (100 · a · c)]
㏒ b - ㏒ (100 · a · c)
㏒ b - ㏒ 100 - ㏒ a - ㏒ c
3 - 2 - 2 + 1
0
Subcase b
㏒√[(a³ · b) / c²]
(1 / 2) · ㏒ [(a³ · b) / c²]
(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²
(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c
(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c
(3 / 2) · 2 + (1 / 2) · 3 + 1
3 + 3 / 2 + 1
11 / 2
Subcase c
㏒ [(2 · a · √b) / (5 · c)]⁻¹
- ㏒ [(2 · a · √b) / (5 · c)]
- ㏒ (2 · a · √b) + ㏒ (5 · c)
- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c
- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c
- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c
- 1 - 2 - (1 / 2) · 3 - 1
- 4 - 3 / 2
- 11 / 2
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in general, assuming > 0, what is the probability that the decoder will know with certainty what the source bit was?
Answers
The characteristics of the channel or transmission medium, and other factors related to the specific system being considered.
What is the probability that the decoder will know with certainty what the source bit was?If we assume that the probability of error (the probability that the decoder will make a mistake) is greater than 0, then the probability that the decoder will know with certainty what the source bit was is 1 minus the probability of error.
Let's denote the probability of error as p_error. The probability that the decoder will know the source bit with certainty (probability of correct decoding) can be expressed as:
P_correct = 1 - p_error
Since we assume that p_error is greater than 0, the probability of correct decoding will be less than 1 but greater than 0.
It's important to note that this is a general concept and the specific value of p_error would depend on the decoding algorithm, the characteristics of the channel or transmission medium, and other factors related to the specific system being considered.
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m(x)=4x+15;m(x)=7
Answer?
Answers
Answer:
M=0
Step-by-step explanation:
(M)=4M+15(M)=7
We move all terms to the left:
(M)-(4M+15(M))=0
We add all the numbers together, and all the variables
M-(+19M)=0
We get rid of parentheses
M-19M=0
We add all the numbers together, and all the variables
-18M=0
M=0/-18
M=0
The figure below is a rectangle. What is the value of x?
Answers
Answer:
1.8
Step-by-step explanation:
\(2x + 10 = 12x + - 8 \\ 10x = 18 \\ x = 1.8 \\ \)
Answer:
1.8
Step-by-step explanation:
12x-8=2(x+5)
12x-8=2x+10
10x=18
x=1.8
"
1) The thicknesses of glass sheets made using process A and process B are recorded in the table below Process Sample Size Sample Mean (mm) Sample Standard Deviation (mm) А 41 3.04 0.124 41 3.12 0.137
a) Does the sample information provide sufficient evidence to conclude that the two processes produce glass sheets that do not have equal thicknesses on average? Use a=0.01. b) What is the P-value for the test in part a? c) What is the power of the test in part a for a true difference in means of 0.1? d) Assuming equal sample sizes, what sample sizes are required to ensure that B=.1 if the true difference in means is 0.1? Assume a=0.01. e) Construct a confidence interval on the difference in means H1 - H2. What is the practical meaning of this interval?
Answers
a) Yes, sample information provides sufficient evidence to conclude that the two processes produce glass sheets that do not have equal thicknesses on average.
Given, Sample 1 mean x1 = 3.04, Sample 1 standard deviation s1 = 0.124, Sample size n1 = 41, Sample 2 mean x2 = 3.12, Sample 2 standard deviation s2 = 0.137, Sample size n2 = 41, Significance level α = 0.01 (two-tailed test)
The null hypothesis and alternative hypothesis are H0: µ1 = µ2, Ha: µ1 ≠ µ2.
The test statistic is given by,
z = [(x1 - x2) - (µ1 - µ2)] / sqrt[s1^2 / n1 + s2^2 / n2]
where µ1 - µ2 = 0.
On substituting the values, we get z = -2.69.
Using the normal distribution table, the p-value for the two-tailed test is 0.007.
Part (a): The given sample information provides sufficient evidence to conclude that the two processes produce glass sheets that do not have equal thicknesses on average because the p-value of the test is less than the level of significance. Therefore, we reject the null hypothesis in favor of the alternative hypothesis.
Part (b): The p-value of the test is 0.007.
Part (c): The power of the test in part a for a true difference in means of 0.1 is the probability of rejecting the null hypothesis when the true difference in means is 0.1. This can be calculated using the formula for the power of a test. The power of the test depends on various factors such as sample size, level of significance, effect size, and variability. Assuming a sample size of 41 for each process, the power of the test is approximately 0.51.
Part (d): To ensure that the power of the test is 0.1 if the true difference in means is 0.1, we need to calculate the sample size required for each process. The sample size can be calculated using the formula for the power of a test. Assuming a significance level of 0.01, the required sample size for each process is 43.
Part (e): We can construct a confidence interval for the difference in means µ1 - µ2
using the formula CI = (x1 - x2) ± zα/2 * sqrt[s1^2 / n1 + s2^2 / n2]`. At the 99% confidence level, the confidence interval is (−0.165, 0.005). This means that we are 99% confident that the true difference in means is between −0.165 and 0.005. The practical meaning of this interval is that the two processes are not significantly different in terms of their thicknesses.
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2. Which of the following is the solution of the system of equations shown? A. (−3, −4) B. (–3, 4) C. (3, 4) D. (3, –4). Please show an explanation
Answers
Which expression represents the prime factorization of 243?
Answers
Answer:
\(\boxed{3^5}\)
Step-by-step explanation:
Hey there!
Look at the image below↓
By looking at the image we can tell the PR expression is \(3^5\).
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Answer:
Below in bold.
Step-by-step explanation:
Dividing by primes:
3 ) 243
3 ) 81
3 ) 27
3) 9
3.
So the prime factors of 243 are 3 * 3 * 3 * 3 * 3 or 3^5.
help asap if you can pls!!!!!
Answers
Answer:
SAS, because vertical angles are congruent.
If you look at a square made up of alternating red and blue stripes for several minutes and then look immediately at a blank white sheet of paper, you will see a square with alternating green and yellow stripes. This effect results from pairs of ________ that work ________.
Answers
The effect of seeing a square with alternating green and yellow stripes after looking at a square made up of alternating red and blue stripes is due to pairs of ganglion cells that work in opposition.
Ganglion cells are neurons located near the inner surface of the retina, whose axons form the optic nerve. They receive visual signals from bipolar cells and then send them to the brain via the optic nerve.
In order to understand why we see a square with alternating green and yellow stripes after looking at a square made up of alternating red and blue stripes, it's important to know that there are three types of cones in the retina that respond to different wavelengths of light: blue, green, and red.
When we look at the square made up of alternating red and blue stripes for several minutes, the cells that are responsible for perceiving red and blue colors become fatigued, while the green cones continue to respond normally. This creates an imbalance between the signals being sent to the brain, which then interprets the remaining signals as a mixture of green and red. This is why we see a square with alternating green and yellow stripes.
Pairs of ganglion cells work in opposition in this phenomenon because each ganglion cell receives input from both types of cones that are sensitive to a particular color. In the case of the square made up of alternating red and blue stripes, one group of ganglion cells is receiving more input from the red-sensitive cones, while the other is receiving more input from the blue-sensitive cones. When we look at the blank white sheet of paper, these ganglion cells continue to work in opposition, leading to the perception of green and yellow stripes.
Know more about Ganglion cells here:
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A recipe requires 1 2/3 cups of sugar. If Mrs.Marina is going to make one and one half of the recipe, then how much sugar does she need
Answers
5/3 + 5/6
10/6 + 5/6
she needs 15/6 or 2 3/6 or 2 1/2 cups of sugar
Mrs. Marina requires 5/2 or 2.5 cups of sugar to make one and one half of the recipe.
What is proportion ?
A proportion is an equation based on the equality of two ratios.
Here it is given that :
A recipe requires 1 (2/3) cups of sugar.
That is 1 recipe requires = 1(2/3) cups of sugars
= 5/3 cups of sugar
Now, Marina is going to make one and one half of the recipe and to find the sugar he needed we simply multiply 1(1/2) both the sides :
1 recipe requires = 5/3 cups of sugar
1(1/2) recipe requires = (5/3) x 1(1/2) cups of sugar
3/2 recipe requires = (5/3) x (3/2) cups of sugar
3/2 recipe requires = 5/2 cups of sugar or 2.5 cups of sugar.
Therefore, Mrs. Marina requires 5/2 or 2.5 cups of sugar to make one and one half of the recipe.
Read more about ratio at:
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What is the sum of the interior angle measures of a convex nonagon?
Answers
Answer:
\(1260^\circ\)
Step-by-step explanation:
The sum of the interior angle measures of a convex n-gon is \(180^\circ(n-2)\), so for a nonagon, the sum would be \(180^\circ(9-2)=180^\circ*7=1260^\circ\).
helpp? determine the intercepts.
Answers
Answer:
(0, 12 ) and (4, 0 )
Step-by-step explanation:
the y- intercept is the point on the y- axis where the line crosses.
the x- coordinate of any point on the y- axis is zero
substitute x = 0 into the equation and solve for y
y = - 3(0) + 12 = 0 + 12 = 12 ← y- intercept , then
y- intercept is (0, 12 )
the x- intercept is the point on the x- axis where the line crosses
the y- coordinate of any point on the x- axis is zero
substitute y = 0 into the equation and solve for x
0 = - 3x + 12 ( subtract 12 from both sides )
- 12 = - 3x ( divide both sides by - 3 )
4 = x ← x- intercept , then
x- intercept is (4, 0 )