Using the theories of prezygotic, we got that in my words prezygotic mechanisms of Reproductive isolation is defined as the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.
Reproductive isolation keeps species from mating with others. Prezygotic mechanisms include the habitat isolation, mating seasons, "mechanical" isolation, gamete isolation and the behavioral isolation.
Hence, in my words, prezygotic mechanisms of reproductive isolation is defined as the mechanism that keeps species from mating with others. Prezygotic isolation actually prevents the fertilization of eggs while the postzygotic isolation prevents the formation of fertile offspring.
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I'm in desperate need on how to solve
Answer:
x = 5; m<1 = 69
Step-by-step explanation:
We know that the two angles with degrees 20x+11 and 25x-14 are vertical angles and are thus congruent or equal. Therefore, we can set the two angles equal to each other to find x:
[tex]20x+11=25x-14\\20x+25=25x\\25=5x\\5=x[/tex]
If we plug in x into any of the two angles, we find the measure of both angles is 111.
The most probable relationship between angle 1 and the other two angles is supplementary, which means that the measure of angle 1 and any of the two angles beside it is 180.
To find m<1, represented as x, we can use the equation:
[tex]180=20(5)+11+x\\180=111+x\\69=x[/tex]
PLS HELPPPP THIS IS URGENT
George was able to solve 36 math problems in 15 minutes. Urban was able to solve 42 math problems in 20 minutes. Who was able to solve math problems at a greater rate? What was the rate?
Question 2 options:
A: George;
B: Urban;
C: George;
Answer:
Urban
Step-by-step explanation:
fifth degree, 4 is a zero of multiplicity 2, −4 is the only other zero, leading coefficient is 2.
The equation of the polynomial equation with a fifth degree is P(x) = (x + 4)³(x - 4)²
How to determine the polynomial equation?The given parameters are
Degree of polynomial = 54 is a zero of multiplicity 2-4 is the only other zeroThe sum of multiplicities of the polynomial equation must be equal to the degree.
This means that the multiplicity of the zero -4 is 3
The equation of the polynomial is then calculated as
P(x) = (x - zero)^multiplicity
Substitute the known values in the above equation, so, we have the following representation
P(x) = (x - (-4))³ * (x - 4)²
Open the inner brackets
P(x) = (x + 4)³ * (x - 4)²
This gives
P(x) = (x + 4)³(x - 4)²
Hence, the equation is P(x) = (x + 4)³(x - 4)²
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Find the equation of a line perpendicular to y= 4/3 x−1 that passes through the point (-4,-8)(−4,−8).
4y = -3x-12 the equation of a line perpendicular to y= 4/3 x−1 that passes through the point (-4,-8).
How do you find the equation of a line parallel or perpendicular?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis.
The slope of parallel lines is the same. The slopes of perpendicular lines are opposing reciprocals. To put it another way, if m=a/b, then m⊥= -b/a.
y= 4/3 x - 1
Slope = 4/3
Equation of line perpendicular to this line
y= -( 3/4) x+b
As slope is -1/m
Now as line passes through (-4,-8)
Plug it in
-8 = (-3/4)(-4) +b
-8= 3+ b
Gives b = -12
So the equation of line will be
y = (-3/4) x -12
or 4y = -3x-12
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Select the expression that is equivalent to x + x + y × y × y.
Answer: x+x+y.y.y = 2x+y^3 ( y cube)
Step-by-step explanation:
Answer:
2x+y^3
Step-by-step explanation:
x's are added while y's are multiplied
Explain why there are no solutions to the equation (2x - 7)² = -9.
Answer:
A square number is always nonnegative. So a quantity squared must be nonnegative.
I need to determine whether the function is a polynomial function, and if so I have to write it in standard form and state it’s degree type and leading coefficient.
f(x) = 7-1.6x² - 5x
Answer:
It is a polynomial, the standard form is -1.6[tex]x^{2}[/tex]-5x+7, and the degree is 2.
Step-by-step explanation:
1. Polynomials can be positive, negative, a zero, a whole number, decimals, or a fraction.
2. When writing a polynomial in standard form arrange the terms from least degree to greatest degree.
3. In this instance the degree of the polynomial is 2 because the term with the highest degree only has x to the second power.
;)
I don't understand a word of this! Due tomorrow and I've been trying all weekend to solve...
Could somebody help me?
The mean price of one of Henry's stamp is $34.7.
The mean number of plays is 6.33.
The mean length of phone call is 11.79.
What is the mean?Mean is the average of a set of numbers.
Mean = ∑(midpoint x frequency) / frequency
Midpoint = (upper boundary + lower boundary) / 2
Stamp price Frequency Midpoint (Midpoint x frequency)
20 - 26 24 (20 + 26) / 2 = 23 552
27 - 33 39 (27 + 33) / 2 = 30 1170
34 - 40 50 (34 + 40) / 2 = 37 1850
41 - 47 37 (41 + 47) / 2 = 44 1628
Sum 150 5200
Mean = 5200 / 150 = 34.7
Number of weeks Frequency Midpoint Midpoint x Frequency
1 - 3 4 (1 + 3) / 2 = 2 8
4 - 6 27 (4 + 6) / 2 = 5 135
7 - 9 16 (7 + 9) / 2 = 8 128
10 - 12 4 (10 + 12) / 2 = 11 44
13 - 15 1 (13 + 15) / 2 = 14 14
Sum 52 329
Mean = 329 / 52 = 6.33
Length of call Frequency Midpoint Midpoint x frequency
1 - 4 3 (1 + 4) / 2 = 2.5 7.5
5 - 8 32 (5 + 8) / 2 = 6.5 208
9 - 12 30 (9 + 12) / 2 = 10.5 315
13 - 16 45 (13 + 16) / 2 = 14.5 652.50
17 - 20 17 (17 + 20) / 2 = 18.5 314.50
Sum 127 1,497.50
Mean = 1497.50 / 127 = 11.79
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Security x has expected return of 9% and standard deviation of 18%. Security y has expected return of 12% and standard deviation of 21%. If the two securities have a correlation coefficient of 0. 4, what is their covariance?.
Their covariance is -0.0151
Given;
The expected return on security x is 9%, whereas the standard deviation is 18%. The expected return on security y is 12%, and the standard deviation is 21%. If the correlation between the two securities is 0.4
Security X:
Expected return E(Rx) = 9% = 0.09
Standard deviation (σx) = 18% = 0.18
Security Y:
Expected return E(Ry) = 12% = 0.12
Standard deviation (σy) = 21% = 0.21
and
Corr(X,Y) = -0.4
We know that,
Corr(X,Y) = Cov(X,Y)/ σx*σy
Substituting the above-given values, we get;
-0.4 = Cov(X,Y)/ 0.18*0.21
-0.4 = Cov(X,Y)/ 0.0378
Cov(X,Y) = -0.4*0.0378
Cov(X,Y) = -0.0151
Therefore, the covariance is -0.0151.
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3/4x+2=9/10 Rewrite the equation below so that it does not have fractions.
Do not use decimals in your answer
Answer:
im not sure if this helps but you can write it with letter like this y = mx + b
Step-by-step explanation:
is smoking during pregnancy associated with premature births? to investigate this question, researchers selected a random sample of 115 pregnant women who were smokers. the average pregnancy length for this sample of smokers was 259 days. from a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. the researchers assume that smoking does not affect the variability in pregnancy length.
The 99% confidence interval is ( 255.157, 262.843 ).
The subset chosen from the larger set to make assumptions is known as a random sample. A range of values is a confidence interval.
According to the given question,
n = number of pregnant women who are smokers
n = 115
μ = average pregnancy length for the sample
μ = 259
σ = standard deviation
σ = 16
At a 99% confidence level,
α = 0.01
z(α/2) = 2.576
The confidence interval is
CI = μ ± z(α/2).(σ/√n)
= 259 ± (2.576)(16/√115)
= 259 ± (2.576)(16/10.724)
= 259 ± (2.576)(1.492)
= 259 ± 3.843
= ( 259 - 3.843, 259 + 3.843)
CI = ( 255.157, 262.843 )
Therefore, the 99% confidence interval to estimate the length of pregnancy for women who smoke is ( 255.157, 262.843 ).
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The complete question is
Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 115 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 259 days. From a large body of research, it is known that the length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length.
Find the 99% confidence interval to estimate the length of pregnancy for women who smoke.
Note: The critical z-value to use is 2.576
-x+3(1 + x) = 3(x +2)
The given equation, -x + 3(1 + x) = 3(x +2), solved for x, is x = -3
Solving linear equationsFrom the question, we are to solve the given equation.
The given equation is
-x + 3(1 + x) = 3(x +2)
To solve this equation, we will determine the value of the variable in the equation.
The variable in the equation is x.
Thus, we will solve for x in the equation.
-x + 3(1 + x) = 3(x +2)
Clear the parentheses by applying the distributive property
-x + 3 + 3x = 3x + 6
Collect like terms
-x + 3x - 3x = 6 - 3
-x = 3
Multiply both sides of the equation by -1
-1 × -x = -1 × 3
x = -3
Hence, the value of x is -3
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ON 7 SESSION 2
Use what you learned to solve these problems.
7
Use linear pairs to find the sum of all the angles labeled in the triangle.
Then use what you know about the interior angles of a triangle to show
that the sum of the measures of the exterior angles of a triangle, one at
each vertex, is 360°.
The sum of the measures of the exterior angles of a triangle, one at each vertex, is 360° and it proved.
Exterior angle
The the angle that is formed with one side and the adjacent extended side of a triangle is known as exterior angle.
Given,
Here we use linear pairs to find the sum of all the angles labeled in the triangle.
And then use what you know about the interior angles of a triangle to show that the sum of the measures of the exterior angles of a triangle, one at each vertex, is 360°.
While we looking into the following figure, we can see that R and Y are the interior and exterior angles of the triangle respectively.
Therefore, here the angles Y and R form a linear pair.
So, we can written it as,
=> Y + R = 180°
Then the value of y is
=> Y = 180° - R
Therefore, when we calculate the value of the full triangle, then we get
=> (Y + R) + (Y + R) + (Y + R) = 180° + 180° + 180°
When we simplify this one,
=> 3Y + 3R = 540° --------- (1)
We already know that, the sum of interior angles of the triangle is as follows,
=> R + R + R = 180°
By using angle sum property of a triangle,
WE can written this like the following,
=> 3R = 180° --------- (2)
Now, substituting the value from equation(2) in equation(1) we get,
Then,
=> 3Y + 180° = 540°
=> 3Y = 540° - 180°
=> 3Y = 360°
Therefore, the sum of exterior angles = 360°
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The sum the sum of the first nine terms of an ap is 126 and the sum of the second nine terms is 369 then
The arithmetic sequence that has the given features is presented as follows:
[tex]a_n = 2 + 3(n - 1)[/tex]
What is an arithmetic sequence?An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and called common difference d.
The nth term of an arithmetic sequence is obtained by the following rule:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term of the sequence.
The sum of the first n terms is presented as follows:
[tex]S_n = \frac{n(a_1 + a_n)}{2}[/tex]
The sum of the first nine terms is of 126, hence:
[tex]S_9 = 126[/tex]
[tex]\frac{9(a_1 + a_9)}{2} = 126[/tex]
[tex]4.5(a_1 + a_9) = 126[/tex]
The ninth term is written as follows:
[tex]a_9 = a_1 + 8d[/tex]
Hence:
[tex]4.5(a_1 + a_1 + 8d) = 126[/tex]
[tex]9a_1 + 36d = 126[/tex]
[tex]a_1 + 4d = 14[/tex]
The sum of the second nine terms is of 369, hence:
[tex]S_{18} = 126 + 369[/tex]
[tex]S_{18} = 495[/tex]
Then:
[tex]\frac{18(a_1 + a_{18})}{2} = 495[/tex]
[tex]a_{1} + a_{18} = 55[/tex]
The 18th term is:
[tex]a_{18} = a_1 + 17d[/tex]
Hence:
[tex]2a_1 + 17d = 55[/tex]
From the first equation, it is found that:
[tex]a_1 = 14 - 4d[/tex]
Hence the common difference is obtained as follows:
2(14 - 4d) + 17d = 55
28 - 8d + 17d = 55
9d = 27
d = 3.
Hence the first term is of:
[tex]a_1 = 14 - 4(3) = 2[/tex]
Thus the definition of the sequence is:
[tex]a_n = 2 + 3(n - 1)[/tex]
Missing InformationThe problem asks for the definition of the arithmetic sequence.
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Kegler bowling buys scorekeeping equipment with an invoice cost of $190,000. The electrical work required for the installation costs $20,000. Additional costs are $4,000 for delivery and $13,700 for sales tax. During the installation, the equipment was damaged and the cost of repair was $1,850. Required: indicate whether each cost should be included in the cost of the equipment or excluded and expensed as incurred.
The total Cost of the equipment is $2,27,700. In which the following included, excluded and expensed as incurred are
Invoicing costs - included in the price
Electrical work required for installation - Included in the price
Delivery costs - included in the price
Sales tax - included in the price
Repair costs - not included or excluded
A machine used by a company to produce products and services is known as a machine tool. It is a vital long-term asset as it speeds up the production process such as transportation, computers and other equipment. These costs will include the costs that were necessary to start opening the plant property. There are equipment costs.
We have given the following details ,
Total Cost DR Machinary DR Expense
Invoice cost $190,000 $190,000
electric work
and $20,000 $20,000
installation cost
delivery cost। $4,000 $4,000
sales tax $13,700 $13,700
repair cost $1,850 $1,850
total $22,9550 $22,7700 $ 1,850
Accordingly, all the mentioned costs except for the repair of the part will be included in the cost of the machinery.
Included in price Excluded
invoice repair cost
electric and installation
delivery
sales tax
Hence , the total equipment cost is $22,7700.
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Jackie travels 60 km to work. Since she began taking a new
route (still 60 km to work) she gets there 30 minutes sooner
because she can drive 10 km/hour faster. Which of the
following equations could you use to solve the problem?
According to the distance-speed-time formula, the equation that could be used to solve this formula is 60/x+10 - 60/x = 1/2
Distance-speed-time
Basically, the formula for speed is speed = distance ÷ time.
In order to work out what the units are for speed, you need to know the units for distance and time.
Given,
Jackie travels 60 km to work. Since she began taking a new route (still 60 km to work) she gets there 30 minutes sooner because she can drive 10 km/hour faster.
Here we need to find the equations could you use to solve the problem.
Let us consider x be the speed of Jackie.
Therefore, the time has been calculated as,
Time1 = 60/ x
Now, the speed is increased as 10, then it can be written as,
=> x + 10
Therefore, the new time Time2 is calculated as,
=> Time2 = 60 / x + 10
So, the equation is obtained by calculating the difference of the times,
So, the equation is,
=> Time 2 - Time1
=> 60/x+10 - 60/x
Now, we know in this one she gets there 30 minutes sooner,
So, it can be written as,
=> 60/x+10 - 60/x = 30/60
=> 60/x+10 - 60/x = 1/2
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How to find a percent change. (Decrease and Increase). Please use simple terms and include a formula. (Also please use a visual demonstration) Thank you!
Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.
What is the mathematical formula for percentage change?Mathematically, the formula for percentage change, C, can be presented as follows;
[tex]C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100[/tex]
Where:C = The percentage change
[tex]x_{1} [/tex] = The original value
[tex]x_{2} [/tex] =The new value
Graphically, percentage change can be presented as follows;
When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;
[tex] C = \dfrac{10-8}{10} = 20\% [/tex]The percentage change is 20%
Initial number of fruits that drops monthly from the tree;
##########
The new number of fruits that drops from the tree on the specified month;
########
The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.
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A humpback whale can swim at a maximum speed of 495 meters per minute. If it is swimming south at one-third of its top speed, how much time will it take the whale to swim 2,310. meters?
Write your answer as a whole number.
(blank) minutes.
Which equation represents the line that passes through point (2,3) and is perpendicular to 4x-5y=7
Answer:
Step-by-step explanation:
First, find the slope of 4x - 5y = 7
Simplify it down to a readable form:
5y = 4x - 7
y = (4x - 7)/5
y = 4/5 x - 7/5
slope = 4/5
slope perpendicular to 4/5 is its opposite reciprocal, which would be -5/4.
given the point (2,3), we can get the equation using point slope form for linear equations: y-k = m(x-h) for point (h,k).
now plug:
y-3 = (4/5)(x-2)
y-3 = (4/5)x - 8/5
There were 20 illustrations in Julio's sketch pad. While at a museum, he drew x more illustrations in the sketch pad. Which expression represents the total number of illustrations in Julio's sketch pad after his museum visit?
The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is given as follows:
Total number = 20 + x.
How to obtain the expression for the total number of illustrations?The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is obtained adding the previous amount of illustrations to the number of illustrations that were added during the visit to the museum, hence:
Total number of illustrations = Previous number of illustrations + number of illustrations added during the visit.
In the context of this problem, the values of these parameters are given as follows:
Previous number of illustrations = 20 -> as stated in the problem.Number of illustrations added during the visit = x.Hence the expression is defined as follows:
Total = 20 + x.
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In triangle OPQ, o=700 cm, p=840 cm and q=620. Find the meaure of ide P to the nearet degree
The measure of side P to the nearest degree is 79 degrees.
Given:
ΔOPQ ,
O = 700 cm,
P = 840cm
Q = 620cm.
To find:
The measure of angle P.
According to the Law of Cosines:
In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:
[tex]cos A = b^{2} +c^{2} - a^{2} / 2bc[/tex]
Using Law of Cosines ΔOPQ, we get,
cos P = o² +q²- p² / 2oq
⇒ cos P = (700)² + (620)² -(840)² /2×700×620
⇒ Cos P = 490000 + 384400 - 705600 / 868000
⇒ Cos P = 168800/868000
on further simplification, we get,
Cos P = 0.19447
P = Cos⁻¹ (0.19447)
P = 78.786236
P = 79.
∴ the measure of angle P is 79 degrees.
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Therefore, the measure of angle P is 79 degrees.
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
Researchers developed a blood test which is quite fair. It gives a positive reaction of 97% people who have that disease and 5% who don't have that disease.
Therefore, the Probability of Type I error if the new blood test is used is 0.025.
H₀ : "the individual does not have the disease"
(a) Probability of Type I error of rejecting when is true =
Probability of concluding the individual has the disease when in fact the individual does not have the disease = 0.025 because the blood test erroneously gives a positive reaction in 2.5% of the people who do not have the disease.
(b) Probability of Type II error = Probability of fail to reject when is true= Probability of concluding the individual does not have the disease when in fact he has the disease = 0.05 because the blood test gives a positive reaction in 97% of the people who have the disease, this implies that the test gives a negative reaction in 5% of the people who have the disease.
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Find an equation of the line passing through the given points. Use function notation to write the equation,
(-1,6) and (-2,11)
f(x) =
Equation of the line passing through the given points is y = -1/5(x) + 29/5.
Given points:
(-1,6) and (-2,11)
slope m = 11 - 6 / -2 - (-1)
= 5/-2+1
= 5/-1
m = -1/5.
substitute m and (-1,6) in y=mx+c.
y = mx + c
6 = -1/5(-1) + c
6 = 1/5 + c
c = 6 - 1/5
= 30 - 1 / 5
c = 29/5.
y = mx + c
y = -1/5(x) + 29/5.
Therefore equation of the line passing through the given points is y = -1/5(x) + 29/5.
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149° + 13x + 5° = 180°
Answer:
Your answer should be x = 2
Step-by-step explanation:
149 + 13(2) + 5 = 180.
Hope this helps.
Answer:
x=2
Step-by-step explanation:
You add 149 and 5, which is 154. Then you take the total which is 180, and subtract it by 154. So 180-154=26 Then you take and do 26/13 which is 2.
149+13(2)+5=180
149+26+5=180
Definitely 2.
Hope this helps!!!
Solve the equation
25^x+3= 1/5
Answer:
X = -4
Step-by-step explanation:
25^(x+3) = 1/5
5^2^(x+3) = 5^(-2)
5^(2x+6) = 5^(-2)
2x+6 = -2
2x = -8
x = -4
Answer:
x = -7/2
or can be written,
x = -3.5
Step-by-step explanation:
25 is a power if 5 and so is 1/5. If you can write both sides as 5 to "some" power. Then the equation is just getting those two exponents equal. See image.
Using logarithms is a nice shortcut. But then you need need a calculator. See image.
find the missing number so that the equation has no solution x+19=2x-4-7x
The missing number so that the equation has no solution is -3 5/6.
What is the missing number?A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that slopes either upwards or downwards.
If the equation has no solution, it means that the value of the left hand equation and the value of the right hand equation are equal.
In order to determine the solution, take the following steps:
x + 19 = 2x - 4 - 7x
Combine similar terms together: 19 + 4 = 2x - 7x - x
Add similar terms together: 23 = -6x
Divide both sides of the equation by -6: x = 23 / - 6
x = -3 5/6
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Of the teacups in Cassie’s Tea Shop, 1/12 are indigo and another 5/12 are teal. What fraction of the teacups are either indigo or teal?
The fraction of the teacups that are either indigo or teal in Cassie's Tea Shop are 1/2.
How to find the fraction?The fraction of teacups in Cassie’s Tea Shop which will either be indigo or teal can be found by adding the fractions of the tea cups which are indigo, to those which are teal.
Fraction of teacups which are indigo = 1/12
Fraction of teacups which are teal = 5/12
The fraction of teacups which are indigo or teal is:
= 1 / 12 + 5 / 12
= 6 / 12
In the simplest form, this is:
= (6 / 6) / (12 / 6)
= 1 / 2
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Answer: The answer to this problem is 1/2.
Step-by-step explanation:
The first thing you do is to add 1/12 and 5/12 together.
1/2 + 5/12 = 6/12
Then you simplify 6/12 to get the answer.
6/12 = 1/2
6/6 = 1
12/6 = 2
This is how you get the answer!
need answers for questions 23-26
The following are the answers:
23. The cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;
The total cost of lessons is; f(x) = y = 10·x + 12 and one lesson costs $22
24. The equation of population of Laredo, Texas is :
p = 92500t/17 + 123000
25. The linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet is T = -(2000/3)x + (4228/3).
26. The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Given:
23. Lydia wants to purchase guitar lessons.
7 lessons = $82
11 lessons = $122
we are asked to determine the linear equation which finds the total cost C for d lessons.
The general equation for the total cost of lessons is;
Let a represent the cost of 7 guitar lessons, and let b represent the cost of 9 guitar lessons, given that the cost increases linearly with the number of lessons, we have;
The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson
Therefore,
slope = b-a/11-7 = b-a/4
Expressing the equation in slope and intercept form, we get:
(y-a) = b-a/4 . (x-7)
y = b-a/4 . x-7 × b-a/4 + a = b-a/4 . x + 11.a-7.b/4
y = b-a/4 . x + 11.a-7.b/4 = 1/4.((b-a).x+11.a-7.b
where a=$82 and b=$122 we ahve:
y = 1/4 . (122-82) . x+1/4 . (11×82-7×122) = 10x+12
The total cost of a lesson is:
y = 10×1+12
= 22
24. Given:
t = the number of years after 1990.
So, for 1990, t = 0. So the coordinate is (0, 123000).
For 2007, t = 17. So the coordinate is (17, 215500).
using point slope formula:
m = 215500-123000/17-0
m = 92500/17
⇒ p = 92500t/17 + 213000
25. The equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
We know the slope is (y₂ - y₁)/(x₂ - x₁).
∴ Here the temperature is y and the height is x.
And the points are (6000, 76) and (12000, 49)
So, slope =(12000 - 6000)/(49 - 76).
Slope = (6000/-27).
Slope = -(2000/9).
Now we have to determine the y-intercept by putting any of the points in y = mx + b.
So, 76 = -(2000/9)×6000 + b.
76 = -(12000/9) + b.
76 = -(4000/3) + b.
b = 4000/3 + 76.
b = 4228/3.
∴ y = -(2000/3)x + (4228/3) or T = -(2000/3)x + (4228/3).
26. The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
he friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.
On first day, they collect = $60
On second day, they collect = $88
Now,
We have to find the equation as;
⇒ R = mc + b
We need to find the value of m and b.
Since, The first point = (15, 60)
The second point = (22, 88)
Hence, Slope (m) = (88 - 60) / (22 - 15)
m = 28 / 7
m = 4
And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,
⇒ R = mc + b
⇒ 60 = 4 x 15 + b
⇒ b = 0
Thus, Substitute m = 4 and b = 0 in equation (i) we get;
⇒ R = mc + b
⇒ R = 4c + 0
⇒ R = 4c
Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Hence we get the required answers.
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What is the method to solve this?
Side-Side-Side can be used to prove this pair of triangles is congruent.
If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent. When two or more triangles are taken that are similar to one another, their corresponding sides and angles are also similar to one another.
According to this question,
Two respective sides of triangles are equal.
One side is common between these two triangles.
Therefore, the third side of the triangles is equal as well.
As all respective sides of the triangles are equal, we can say that the triangles are congruent by Side-Side-Side.
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