The exponential growth rate is approximately 3.1% per year, and the equation is C(t) = 0.22 * e^(0.031t). The cost of a bottle of ketchup in 2012 would be approximately $1.72.
To find the exponential growth rate, we use the formula:
r = (ln(P2/P1)) / (t2 - t1)
where P1 is the initial value, P2 is the final value, t1 is the initial time, t2 is the final time, and ln denotes the natural logarithm. Substituting the values we get:
r = (ln(1.39/0.22)) / (2007-1966) = 0.0271 or 2.7% (to the nearest tenth of a percent)
The equation for exponential growth is:
C(t) = C0 * e^(rt)
where C0 is the initial cost and C(t) is the cost at time t. Substituting the values we get:
C(t) = 0.22 * e^(0.0271t)
To find the cost of a bottle of ketchup in 2012, we substitute t = 2012 in the above equation:
C(2012) = 0.22 * e^(0.0271 * 2012) = $1.72 (rounded to the nearest cent)
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Find the area of the trapezoid below by decomposing it into familiar shapes.
Answer:
168 ft^2
Step-by-step explanation:
18×8=144ft^2 for the area of the rectangle
8×6=48ft^2
48÷2=24ft^2 for the area of the triangle
144+24=168ft^2
help asap will give brainliest!!!!
The value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.
What are exterior angles?External angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle. For each vertex, there are two equivalent exterior angles.
Each vertex typically displays a single external angle. The exterior angles of a triangle are those that are formed outside of it. The exterior angle of a triangle is defined as the angle formed between one of a triangle's sides and its neighboring extended side. As a result, the exterior angle of a triangle is the angle formed by any extended side of a triangle and its neighboring side.
Given that the measure of angle y = 49 degrees.
We observe from the figure that angle a is vertically opposite angle of y thus,
angle y = angle a = 49 degrees.
Now, angle b is exterior angle and,
angle b = angle a + 90
angle b = 49 + 90
angle b = 139 degrees.
Hence, the value of the angle a is 49 degrees and angle b is 139 degrees in the given triangle.
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Can someone just show and tell me which one is the y and x axis that I reflect it off and show me where to move and where 180 is
The coordinates of B is (2, -4).
The coordinates of C is (-2, 4).
The coordinates of D is (5, 8).
The coordinates of E is (-2, -4).
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over the x-axis is represented by this transformation rule (x, y) → (x, -y). Therefore, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
For a reflection over the x-axis, the new coordinates of A is given by:
(x, y) → (x, -y)
A (2, 4) → (2, -(4)) = B (2, -4)
For a reflection over the y-axis, the new coordinates of A is given by:
(x, y) → (-x, y)
A (2, 4) → (-(2), 4) = C (-2, 4)
By applying a translation, the new coordinates of A is given by:
(x, y) → (x + 3, y + 4)
A (2, 4) → (2 + 3, 4 + 4) = D (5, 8)
By applying a rotation 180° clockwise, the new coordinates of A is given by:
(x, y) → (-x, -y)
A (2, 4) → (-(2), -(4)) = E (-2, -4)
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Which angle measures are correct? select three options. m∠x = 55° m∠w = 125° m∠w = 55° m∠z = 125° m∠z = 55°
The correct angle measures of triangle XWZ are m∠x = 55°, m∠w = 125°, m∠z = 125°. The correct options are A, B and D.
The correct angle measures are m∠x = 55°, m∠w = 125°, m∠z = 125°
The option "m∠w = 55°" and "m∠z = 55°" are incorrect. Because "m∠w = 55°" and "m∠z = 55°" are incorrect is that there is only one angle measurement that can be equal to 55°, which is m∠x. This is because in any triangle, the sum of the interior angles is always 180°. Therefore, if m∠x is 55°, then the sum of the other two angles (m∠w and m∠z) must add up to 125° (i.e., 180° - 55°).
So, if m∠w is 125°, then m∠z must also be 55°, and if m∠z is 125°, then m∠w must be 55°. Hence, the options "m∠w = 55°" and "m∠z = 55°" cannot both be correct at the same time. So, the correct answers are A, B and D.
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_____The given question is incomplete, the complete question is given below:
Which angle measures are correct? select three options. A m∠x = 55° B m∠w = 125° C m∠w = 55° D m∠z = 125° E m∠z = 55°.
Answer:
A , B , E
Step-by-step explanation:
Just put A , B , D and got it wrong
can yall pls help me!!!!!!!!!
Answer:
w ≥ 13.5
Step-by-step explanation:
-(4/ 9)w ≤ -6
Multiply both side by - 1
(4/ 9)w ≥ 6
Cross multiply
4w ≥ 54
Divide both side by the coefficient of w
4w/4 ≥ 54/4
w ≥ 13.5
What is the value of m in the equation
Answer:
-1
Step-by-step explanation:
Consider the equation 9-e² = 54.
Solve the equation for z. Express the solution as a logarithm in base-e.
Z=
Approximate the value of z. Round your answer to the nearest
thousandth.
Z≈
The approximate value of z for the given logarithm in base-e is found to be: z = 0.8959 (nearest thousandth).
Explain about the logarithm function?A power wherein a number must all be increased in order to obtain another number is known as a logarithm.
The conception of hyperbolic sectors in calculating the area of a rectangular hyperbola gave rise to the concept of log. Several formats, such as exponential and integration of 1/x, can be used to express a log.
The given expression is-
9. [tex]e^{2z}[/tex] = 54.
On simplification:
[tex]e^{2z}[/tex] = 54 / 9
[tex]e^{2z}[/tex] = 6
Now, taking ㏑ both side:
㏑ [tex]e^{2z}[/tex] = ㏑ 6
using the power rule of ㏑.
2z. ㏑e = ㏑6
we know that, ㏑e = 1
2z * 1 = ㏑6
z = ㏑6 / 2
z = 1.79 / 2
z = 0.8959
Thus, the approximate value of z for the given logarithm in base-e is found to be: z = 0.8959 (nearest thousandth).
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What is the factored form of x2 - 9x + 20?
A. x(x - 9) + 20
B. (x-4)(x + 5)
C. (x - 4)(x - 5)
D. (x2 - 4)(x2 - 5)
-------------------------------------------------------------------------------------------------------------
Answer: Option C, (x - 4)(x - 5)
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{x}^2\textsf{ - 9x + 20}[/tex]
Find: [tex]\textsf{Determine the factored form}[/tex]
Solution: In order to factor the given equation, we need to first determine two numbers which add up to -9 and multiply to become 20. We can think of the factors of 20 which would add up to -9 and the one that matches that description would be -5 and -4. These two numbers multiply to become 20 and combine to become -9. Now that we have that information, we can break up the quadratic into two separate roots using the two numbers that we found.
Therefore, the answer would be Option C, (x - 4)(x - 5).
Instructions: Find the missing side. Round your answer to the nearest tenth.
8
||
75°
24
X
The value of x, the missing side which is the hypotenuse, is approximately 24.85 units.
What is the missing side of the triangle?To solve this problem, we can use the trigonometric function of sine, since we know the opposite side and we want to find the hypotenuse.
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse:
sin(θ) = opposite/hypotenuse
In this case, θ is the angle 75 degrees, the opposite side is 24, and we want to find the hypotenuse x:
sin(75°) = 24/x
To solve for x, we can cross-multiply:
x * sin(75°) = 24
Then, we can divide both sides by sin(75°):
x = 24 / sin(75°)
Using a calculator, we get:
x = 24.85 units
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What is the contrapositive of the following statement?
"If she gets off work early, she will hang out with her friends."
a. If she hangs out with her friends, then she got off work early.
b. If she doesn't get off work early, then she will not hang out with her friends.
c. If she does not hang out with her friends, then she did not get off early.
The contrapositive of the given statement is: She will not hang out with her friends If she did not get off work early
How to determine the contrapositive of the statement?Given that we have the following statement:
"If she gets off work early, she will hang out with her friends."
The contrapositive of a statement is defined as:
Switching the hypothesis and the conclusion in a statementAnd then negate both statementsThe above means that we have the contrapositive of the given statement to be:
She will not hang out with her friends If she did not get off work early,
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3675 m
3
, to the nearest tenth of a meter?
the answer will be 3675.0 m (rounded to one decimal place)
What is rounded off?
Rounding off is a process of approximating a number to a certain degree of accuracy. When we round off a number, we usually need to specify the number of digits we want to keep or the position to which we want to round.
For example, if we want to round off 3.14159 to two decimal places, we would look at the third decimal place (which is 1) and see that it is less than 5, so we would keep the first two decimal places and round off the rest. Thus, rounding off 3.14159 to two decimal places would give us 3.14.
Rounding off is often used to simplify numbers or make them easier to work with, especially in situations where exact values are not necessary or practical.
To round 3675 m to the nearest tenth of a meter, we need to look at the hundredth digit, which is 7. Since 7 is greater than or equal to 5, we need to round up the last digit (tenth digit). Therefore, rounding 3675 m to the nearest tenth of a meter gives us:
Hence the answer will be 3675.0 m (rounded to one decimal place).
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Q3 The following diagram represents the positions and
bearings of three buoys floating in the ocean.
[a] How far west is Buoy B from Buoy C.
[b] How far east is Buoy A from Buoy B.
[c] How far north is Buoy C from Buoy A.
N
Buoy B
N
077⁰
240m
345m
N
314⁰
Buoy A
Buoy C
Q4 A ship sails on a bearing of 074° for 10 miles followed by a
bearing of 131° for 15 miles. Work out the bearing of the
ship from its starting position to the nearest degree.
A ship sails from port a, on a bearing of 050, to port b which is 80km to the east of a. it then sails on a bearing of 062 for 72km until it reaches pot c. West is 270 degrees. Hence Answer would be 80 km.
The minute hand of this clock is shown in two positions. The minute hand first forms a 46° angle with the hour hand. It then forms an 84° angle with the hour hand.
How many degrees did the minute hand turn from its first position to its second position?
Enter your answer in the box.
°
The face of a clock. The hour hand points to the 9. The minute hand is rotated to two positions. In its first position, the minute hand is between 10 and 11 so that it forms a 46 degree angle with the hour hand. In its second position, the minute hand is between 11 and 12 so that it forms an 84 degree angle with the hour hand. The angle formed by the first and second position of the minute hand is labeled with a question mark.
To find the number of degrees the minute hand turned from its first position to its second position, we need to find the difference between the two angles formed by the minute and hour hands.
In the first position, the minute hand forms a 46° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 10 and 11, we know that the hour hand has moved 1/6th of the way from 10 to 11, or 30°. Therefore, the angle between the hour hand and the 12:00 position is 120° + 30° = 150°. So the minute hand is 46° away from 150°, or 104°.
In the second position, the minute hand forms an 84° angle with the hour hand. Since the hour hand is pointing at 10 and the minute hand is between 11 and 12, we know that the hour hand has moved 1/2 of the way from 10 to 11, or 150°. So the minute hand is 84° away from 150°, or 234°.
To find the number of degrees the minute hand turned, we subtract the two angles: 234° - 104° = 130°.
Therefore, the minute hand turned 130° from its first position to its second position.
Anota el valor posicional de las cifras encerradas
The digit information are:
A) 900,000,000
5,000,0006,000B) 40,000
7009What is the Digit numbers about?900,000,000: Nine hundred million. The first three digits (900) represent the hundred millions place, the next three digits (000) represent the ten millions place, and the last three digits (000) represent the ones (or units) place.
5,000,000: Five million. The first digit (5) represents the millions place, and the last six digits (000,000) represent the ones (or units) place.6,000: Six thousand. The first digit (6) represents the thousands place, and the last three digits (000) represent the ones (or units) place.40,000: Forty thousand. The first two digits (40) represent the ten thousands place, and the last three digits (000) represent the ones (or units) place.Lastly, 7009: Seven thousand nine. The first digit (7) represents the thousands place, the next two digits (00) represent the hundreds place (which are omitted since they are zeroes), and the last two digits (09) represent the ones (or units) place.
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See full text below
3.- Anota el valor posicional de las cifras encerradas
=
a) (9) 1(5) 23(6) 470
b) 38(4) 1(7) 6(9)
3.- Write down the place value of the enclosed figures
=
a) (9) 1(5) 23(6) 470
b) 38(4) 1(7) 6(9)
Belle bought 40 pairs of trousers for $2040. She sold them all at the same selling price and made a loss of $200.
(i) How much did each pair of trousers cost Belle to buy?
(ii) How much loss did she make on each pair of trousers?
(iii) What was the selling price of each pair?
Answer:
Let the cost of each pair of trousers be x dollars.
(i) Belle bought 40 pairs of trousers for a total of $2040, so we can set up an equation:
40x = 2040
Solving for x, we get:
x = 2040/40 = 51
Therefore, each pair of trousers cost Belle $51 to buy.
(ii) Belle made a loss of $200 on the entire sale of 40 pairs of trousers. The cost of 40 pairs of trousers is:
40 x $51 = $2040
So, Belle sold 40 pairs of trousers for:
$2040 - $200 = $1840
Belle's cost was $2040, and she sold the trousers for $1840, so her loss was:
$2040 - $1840 = $200
The loss per pair of trousers is the total loss divided by the number of pairs of trousers sold, which is:
$200/40 = $5
Therefore, Belle made a loss of $5 on each pair of trousers sold.
(iii) The selling price of each pair of trousers can be found by adding the loss per pair to the cost per pair:
Selling price = Cost + Loss
Selling price = $51 + $5
Selling price = $56
Therefore, Belle sold each pair of trousers for $56.
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suppose gre verbal scores are normally distributed with a mean of 455 and a standard deviation of 124 . a university plans to offer tutoring jobs to students whose scores are in the top 8% . what is the minimum score required for the job offer? round your answer to the nearest whole number, if necessary.
The minimum score required for the job offer found using normal distribution is 629
To find the minimum score required for the job offer, we have to use the standard normal distribution formula.
Where Z-score can be calculated as,
Z = (x - μ) / σ
Z-score is the number of standard deviations from the mean.
μ = Mean = 455
σ = Standard Deviation = 124
Substituting the values, we get, Z = (x - μ) / σ= (x - 455) / 124
Probability value = 1 - 0.08 = 0.92
The probability of getting scores in the top 8% is 0.92.
By using the standard normal distribution table, we can find the corresponding z-value, where the area under the curve to the right of that value is 0.92.
So, the corresponding Z-value is 1.44.
Z-value = 1.4 = (x - 455) / 124
We can solve the above equation for x (minimum score required for the job offer).
x = Z * σ + μ = 1.4 * 124 + 455 = 628.6 ≈ 629
Round off the answer to the nearest whole number, we get the minimum score required for the job offer is 629.
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I understand how to use and apply the cosine rule but I don't know how to do it without any angles
Answer:
largest angle ≈ 109.6°
Step-by-step explanation:
the largest angle in the triangle is the angle opposite the longest side.
Here that is the angle opposite side of 7.8 cm
let a = 7.8, b = 5.4 , c = 4.1 and A the largest angle , then
cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex]
= [tex]\frac{5.4^2+4.1^2-7.8^2}{2(5.4)(4.1)}[/tex]
= [tex]\frac{29.16+16.81-60.84}{44.28}[/tex]
= [tex]\frac{45.97-60.84}{44.28}[/tex]
= [tex]\frac{-14.87}{44.28}[/tex]
then
A = [tex]cos^{-1}[/tex] ( [tex]\frac{-14.87}{44.28}[/tex] ) ≈ 109.6° ( to 1 decimal place )
Terence applied the associative property to 5 + (9 + 3) = 17. Which of the following might he have used?
Answer:
(5 + 9) + 3 = 17
Step-by-step explanation:
The Associative Property of Addition states that no matter how you group the numbers to be added, the results will still be the same. In this case:
Original:
5 + (9 + 3) = 17
5 + 12 = 17
17 = 17 (True)
Associative Property of Addition:
(5 + 9) + 3 = 17
(14) + 3 = 17
17 = 17 (True)
As you can see, the grouping does not matter as the outcome is still the same.
~
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This figure is a rectangle with a semicircle on the shorter side.
What is the perimeter of this figure?
Use 3.14 for pi.
A. 20.28 ft
B. 30.28 ft
C. 46.28 ft
D. 74.24 ft
The perimeter of the figure which is a rectangle with a semicircle on its shorter side would be =34.28ft
How to calculate the perimeter of the given figure?To calculate the perimeter of the figure, the perimeter of both the rectangle and the semicircle is calculated separately and added together.
The perimeter of rectangle = 2(l+w)
where;
l = 10ft
w = 4ft
perimeter = 2(10+4)
= 2× 14
= 28ft
Perimeter of semicircle = 2πr/2 = πr
where
π = 3.14
r = 4/2 = 2ft
perimeter = 3.14×2 = 6.28
Therefore, the perimeter of the given figure = 28+6.28 = 34.28ft.
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determine if there is an outlier in the given data. if yes, please state the value(s) that are considered outliers. 43,45,24,17,34,18,2,20,13,23,9,53,33,53
Using the interquartile range (IQR) method, the value 2 is considered an outlier in the given data.
To determine if there is an outlier in the given data, we need to calculate the lower and upper bounds using the interquartile range (IQR) method.
First, we need to calculate the first quartile (Q1), second quartile (Q2 or median), and third quartile (Q3) of the data.
Arranging the data in ascending order
2, 9, 13, 17, 18, 20, 23, 24, 33, 34, 43, 45, 53, 53
Q1 = 17
Q2 = 24
Q3 = 43
Next, we can calculate the IQR by subtracting Q1 from Q3
IQR = Q3 - Q1 = 43 - 17 = 26
Now we can calculate the lower and upper bounds
Lower bound = Q1 - 1.5 × IQR = 17 - 1.5 × 26 = -8
Upper bound = Q3 + 1.5 × IQR = 43 + 1.5 × 26 = 79
Any values outside the lower and upper bounds are considered outliers.
In this case, we have a value of 2 that is outside the lower bound of -8. Therefore, 2 is considered an outlier in the given data.
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Is x = 2 a solution to the equation x + 7.6 = 7.8
A. No, because 2 + 7.6 = 7.8 is not true.
B. No, because 2 + 7.6 = 7.8 is true.
C. Yes, because 2 + 7.6 = 7.8 is not true.
D. Yes, because 2 + 7.6 = 7.8 is true.
Answer:
A.
Step-by-step explanation:
the solution to a relation (like an equation, but also inequalities and so on) is the set of values that make the whole thing true (or consistent).
every other value is not a solution.
A function can only have one transformation
happen to it.
True
False
Answer:
False
Step-by-step explanation:
You can transform a function many times
:)
what is the probability that from a sample of 30 indianapolis residents, fewer than 95% were rooting for the giants in super bowl xlvi?
The probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI is approximately 0.304.
This problem can be solved using the binomial distribution, which models the probability of a certain number of successes in a fixed number of independent trials, each with the same probability of success.
Let X be the number of Indianapolis residents in a sample of 30 who wanted the Giants to beat the Patriots. Then X follows a binomial distribution with n = 30 and p = 0.97, since the probability of success (rooting for the Giants) is 0.97 for each resident.
We want to find the probability that fewer than 95% of the sample wanted the Giants to win. That is, we want to find P(X < 0.95*30) = P(X < 28.5), where X has the binomial distribution with parameters n = 30 and p = 0.97.
We can use a continuity correction and approximate this probability by the cumulative distribution function of a normal distribution with mean np and variance np(1-p). That is,
P(X < 28.5) ≈ P(Z < (28.5 - np) / sqrt(np(1-p)))
where Z is a standard normal random variable. Substituting the values of n and p, we get
P(X < 28.5) ≈ P(Z < (28.5 - 300.97) / sqrt(300.97*0.03))
≈ P(Z < -0.51)
Using a standard normal table or calculator, we find that P(Z < -0.51) ≈ 0.304. Therefore, the probability that fewer than 95% of the sample wanted the Giants to win is approximately 0.304.
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The given question is incomplete, the complete question is:
Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city’s own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 97% of Indianapolis residents wanted the Giants to beat the Patriots.
What is the probability that from a sample of 30 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLIV?
a real estate agent has 12 properties that she shows. she feels that there is a 40% chance of selling any one property during a week. the chance of selling any one property is independent of selling another property. compute the probability of selling more than 5 properties in one week. round your answer to four decimal places.
The probability of selling more than 5 properties in a week is 0.7494 (rounded to four decimal places).
The probability of selling more than five properties in a week would be calculated using the binomial distribution method. Binomial distribution is used to calculate the probability of an event happening, given a specific number of trials and assuming that each trial is independent of the others. In this case, we want to know the probability of selling more than five properties in a week.
The formula for the probability of selling more than five properties in a week is:
P(X > 5) = 1 - P(X ≤ 5)
Where P is the probability of selling any one property in a week, and X is the number of properties sold in a week.
Using the binomial probability formula, we can determine the probability of selling exactly k properties in one week:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where
n = 12 (total number of properties)
k = number of properties sold
p = 0.40 (probability of selling any one property in a week)
We can now calculate the probability of selling more than 5 properties in a week:
P(X > 5) = 1 - P(X ≤ 5)
P(X > 5) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5))
P(X > 5) = 1 - [(12 choose 0) * (0.40)^0 * (0.60)^(12-0) + (12 choose 1) * (0.40)^1 * (0.60)^(12-1) + (12 choose 2) * (0.40)^2 * (0.60)^(12-2) + (12 choose 3) * (0.40)^3 * (0.60)^(12-3) + (12 choose 4) * (0.40)^4 * (0.60)^(12-4) + (12 choose 5) * (0.40)^5 * (0.60)^(12-5)]
P(X > 5) = 1 - [0.000015 + 0.0003 + 0.003 + 0.018 + 0.068 + 0.161]
P(X > 5) = 1 - 0.250583
P(X > 5) = 0.749417
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Find an equation of the line that passes through the points (1,2) and (2,3).
Responses
A y = 2x - 1y = 2x - 1
B y = x - 2y = x - 2
C y = x - 1y = x - 1
D y = x + 1
By answering the presented question using inequality, , we may conclude that Therefore, the equation of the line passing through the points (1,2) and (2,3) is
Describe inequality.An inequality in mathematics is a link between two expressions or values that is not equal. As a result, inequality results from imbalance. An inequality in mathematics is a relationship between two values that are not equal. Equality and inequality are not the same thing. The not equal sign is often used to indicate that two values are not equal (). To contrast values, various disparities—no matter how small or large—are used. By changing the two sides until just the variables are left, many fundamental inequalities can be resolved. Yet, a variety of causes fuel inequality: On both sides, negative values are divided or added. Trade right and left.
To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation:
[tex]y-ylm(x-x1) = \\m = (y^2 - y1)/(x^2 − x^1) \\m = (3-2)/(2-1) = 1\\ m = y-2=1\\(x-1) y-2=x-1\\y = x+1[/tex]
Therefore, the equation of the line passing through the points (1,2) and (2,3) is
D) y=x+1
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Please help asap don’t understand any of them
Answer:
#1. A. y=sin x + 2 Is the same as cos.
Step-by-step explanation:
A soccer ball is made using a pattern of black pentagons and white
hexagons. What are the measures of the angles of the shapes that make the soccer ball? Explain. PLEASE HELP
Answer:
Each black pentagon in the soccer ball is surrounded by five white hexagons. Each white hexagon is, in turn, surrounded by three black pentagons and three other white hexagons. This pattern is repeated throughout the soccer ball.
To find the measures of the angles of the shapes that make the soccer ball, we need to first consider the angles of a regular pentagon and a regular hexagon.
A regular pentagon has five sides and five angles that are equal in measure. The formula for finding the measure of each angle in a regular pentagon is:
(angle measure) = (180(n-2))/n, where n is the number of sides.
In the case of a regular pentagon, n=5. Therefore, the measure of each angle in a regular pentagon is:
(angle measure) = (180(5-2))/5 = 108 degrees.
A regular hexagon has six sides and six angles that are equal in measure. The formula for finding the measure of each angle in a regular hexagon is:
(angle measure) = (180(n-2))/n, where n is the number of sides.
In the case of a regular hexagon, n=6. Therefore, the measure of each angle in a regular hexagon is:
(angle measure) = (180(6-2))/6 = 120 degrees.
Now, let's consider the angles of the shapes that make up the soccer ball.
Each black pentagon has five angles that are equal in measure. Therefore, each angle in a black pentagon measures:
(angle measure) = (180(5-2))/5 = 108 degrees.
Each white hexagon has six angles that are equal in measure. Therefore, each angle in a white hexagon measures:
(angle measure) = (180(6-2))/6 = 120 degrees.
Answer:
just do what the guy above me did
Step-by-step explanation:
i checked its correct
amahle makes the minimum salary for an actuary. asaad makes the median salary for a cpa. who makes more money?
Asaad having median salary makes more money in comparison to Amahle who makes minimum salary.
From the attached box plot we have,
Box plot always shows,
First Minimum → Lower quartile → Median → Upper quartile → Maximum
The minimum salary for an actuary is equals to
Approximately 35 dollars
And the median salary for a CPA from the box plot is equals to,
Approximately 60 dollars
Here , by comparing the both the values we have,
Median salary for CPA (60 dollars ) is greater than minimum salary for actuary ( 35 dollars ).
The median salary for a CPA is typically higher than the minimum salary for an actuary.
Therefore, Asaad representing median salary makes more money than Amahle .
learn more about median here
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The above question is incomplete, the complete question is:
Amahle makes the minimum salary for an actuary. Asaad makes the median salary for a CPA. Who makes more money?
Box plot is attached.
PLS HELP ASAP !!! THANKS
The factorizations of the given expressions are:
[tex]9x^{2}-6x+15[/tex] = 3(3x+5)(x-2)
[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)
[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)
[tex]10x^{2}+80x+70[/tex] = 10(x+1)(x+7)
[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)
[tex]x^{2}-16[/tex] = (x+4)(x-4)
Equations[tex]9x^{2}-6x+15[/tex]
We can first factor out the greatest common factor, 3:
[tex]9x^{2}-6x+15[/tex] = 3([tex]3x^{2}-2x-5[/tex])
[tex]3x^{2}-2x-5[/tex] = (3x+5)(x-2)
Putting it all together, we get:
[tex]9x^{2}-6x+5[/tex] = 3(3x+5)(x-2)
[tex]2x^{2}+11x+5[/tex]
We need to find two numbers that multiply to give 2x5=10 and add up to 11. Those numbers are 1 and 10:
[tex]2x^{2}+11x+5[/tex] = (2x+1)(x+5)
[tex]2x^{2}+3x-9[/tex]
We need to find two numbers that multiply to give 2x(-9)=-18 and add up to 3. Those numbers are 6 and -3:
[tex]2x^{2}+3x-9[/tex] = (2x-3)(x+3)
[tex]10x^{2}+80x+70[/tex]
We can first simplify the expression by factoring out 10:
[tex]10x^{2}+80x+70[/tex] = 10([tex]x^{2}+8x+7[/tex])
Now we need to factor the quadratic expression inside the parentheses:
[tex]x^{2}+8x+7[/tex] = (x+1)(x+7)
Putting it all together, we get:
10(x+1)(x+7)
[tex]3x^{2}-8x+4[/tex]
We need to find two numbers that multiply to give 3x4=12 and add up to -8. Those numbers are -2 and -6:
[tex]3x^{2}-8x+4[/tex] = (x-2)(3x-2)
[tex]x^{2}-16[/tex]
This is a difference of squares, which we can factor as:
[tex]x^{2}-16[/tex] = (x+4)(x-4)
To know more about factorizations, click here,
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Unit 5 Systems of equations and inequalities, Homework 10 systems by inequalities
To solve a system of equations, you need to find the values of the variables that satisfy both equations simultaneously. There are different methods to solve systems of equations, including substitution, elimination, and graphing. Here's an example of using substitution:
Solve the system of equations:
2x + y = 5
x - y = 1
From the second equation, we get x = y + 1. Substitute this expression for x into the first equation:
2(y + 1) + y = 5
Simplifying and solving for y, we get:
3y + 2 = 5
3y = 3
y = 1
Then, substitute y = 1 into x = y + 1 to get:
x = 2
So the solution to the system of equations is x = 2 and y = 1.
To solve a system of inequalities, you need to find the values of the variables that satisfy both inequalities simultaneously. There are different methods to solve systems of inequalities, including graphing and substitution. Here's an example of using graphing:
Solve the system of inequalities:
x + y ≤ 3
x - y > 1
First, graph the boundary lines of each inequality. For the first inequality, the boundary line is x + y = 3, which is a line with intercepts (3, 0) and (0, 3). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):
0 + 0 ≤ 3, which is true
Therefore, shade the side of the line that contains the origin.
For the second inequality, the boundary line is x - y = 1, which is a line with intercepts (1, 0) and (0, -1). To decide which side of the line to shade, test a point that is not on the line, such as (0, 0):
0 - 0 > 1, which is false
Therefore, shade the side of the line that does not contain the origin.
The shaded region that satisfies both inequalities is the region that is below the line x + y = 3 and to the right of the line x - y = 1. This region is a triangle with vertices (1, 2), (2, 1), and (2, 2).
I hope this explanation helps you with your homework!