1. Rounding each price per dozen to nearest penny will be $1.6 and $5.4
2. The percent of increase between these 2 years will be
How to calculate the percentageA percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
The percent of increase between these 2 years will be:
= (5.4 - 1.6) / 1.6 × 100
= 3.8/1.6 × 100
= 237.5%
The reason for the change in price of eggs in that time was due to the increase in the feeding of poultry animals.
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the graph shows the linear relationship between the height of the plant(in centimeters) and the time(in weeks) that the plant has been growing
Answer:
The rate of change is 4The rate of change is 4/1The plant grows 4 cm in 1 weekStep-by-step explanation:
You want to identify the rate of change of a graph that has points 1 week apart horizontally and 4 cm apart vertically.
Rate of changeThe rate of change (m) of a curve on a graph is the ratio of rise to run.
Here, the graphed points differ by 4 cm vertically, and 1 cm horizontally. The rate of change is ...
m = rise/run = (4 cm)/(1 week) = 4 cm in 1 week
= 4/1 = 4 . . . . . centimeters per week
The rate of change can be described as ...
44/14 cm in 1 weekIf [tex]f(x)=\frac{5x^{4}}{1-x}[/tex] then [tex]f^{4} (x)[/tex]
Note: There is a way of doing this problem without using the quotient rule 4 times.
Answer:
To find the fourth derivative of f(x), we can use the fact that f(x) can be expressed as:
f(x) = 5x^4 (1 - x)^-1
Then, using the product rule repeatedly, we can find the derivatives of f(x) up to the fourth order:
f'(x) = 20x^3 (1 - x)^-1 - 5x^4 (1 - x)^-2
f''(x) = 60x^2 (1 - x)^-1 + 40x^3 (1 - x)^-2 + 10x^4 (1 - x)^-3
f'''(x) = 120x (1 - x)^-1 + 180x^2 (1 - x)^-2 + 120x^3 (1 - x)^-3 + 20x^4 (1 - x)^-4
f^4(x) = 120 (1 - x)^-1 + 720x (1 - x)^-2 + 1080x^2 (1 - x)^-3 + 480x^3 (1 - x)^-4 + 60x^4 (1 - x)^-5
So, we have found the fourth derivative of f(x) without using the quotient rule four times.
The fourth derivative of the function f(x) = 5x⁴/(1 - x)⁻¹ is,
f''''(x) = 120/(1 - x)⁻¹ + 720x/(1 - x)⁻² + 1080x²/(1 - x)⁻³ + 480x³/(1 - x)⁻⁴
+ 60x⁴/(1 - x)⁻⁵.
What is differentiation?A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.
We have to find the fourth derivative of f(x), f(x) = 5x⁴/(1 - x)⁻¹
The derivatives of f(x) up to the fourth order can then be discovered by continually applying the product rule,
f'(x) = 20x³/(1 - x)⁻¹ - 5x⁴/(1 - x)⁻²
f''(x) = 60x²/(1 - x)⁻¹ + 40x³/(1 - x)⁻² + 10x⁴/(1 - x)⁻³
f'''(x) = 120x/(1 - x)⁻¹ + 180x²/(1 - x)⁻² + 120x³/(1 - x)⁻³ + 20x⁴/(1 - x)⁻⁴
f''''(x) = 120/(1 - x)⁻¹ + 720x/(1 - x)⁻² + 1080x²/(1 - x)⁻³ + 480x³/(1 - x)⁻⁴ +
60x⁴/(1 - x)⁻⁵.
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Which recursive formula can be used to define this sequence for n > 1?
-3, -6, -12, -24, -48, -96, .
Answer:
The recursive formula for this sequence is y(n) = 2 * y(n-1). Starting with y(1) = -3, this formula produces the sequence of -3, -6, -12, -24, -48, and -96.
do yall know this awser?
The missing side length is 7 yd.
What is the missing side length?The object given is made up of two rectangles. The width of the upright rectangle is to be determined. In order to determine this value, the mathematical operation that would be used is subtraction.
Subtraction is the process of determining the difference between two or more numbers. The sign that is used to represent subtraction is -.
Width of the upright rectangle = 15 - 8 = 7 yd
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find the area of polygon ABCD with vertices A(5, -3), B(-1, -3), C(-1, 2), D(5, 6)
The area of polygon ABCD is 31 square units.
What are coordinates?Coordinating refers to the process of organizing or synchronizing different elements or parts to work together in a harmonious and efficient manner towards a common goal or objective. In other words, coordinating involves bringing together various people, resources, activities, or tasks in a way that maximizes their effectiveness and minimizes any conflicts or inefficiencies.
We can find the area of polygon ABCD using the formula for the area of a quadrilateral:
Area = 1/2 * |(x1y2 + x2y3 + x3y4 + x4y1) - (y1x2 + y2x3 + y3x4 + y4x1)|where (x1, y1), (x2, y2), (x3, y3), and (x4, y4) are the coordinates of the vertices of the quadrilateral in order.
Substituting the coordinates of the given vertices, we get:
Area = 1/2 * |(5*(-3) + (-1)2 + (-1)6 + 5(-3)) - (-3(-1) + (-1)5 + 2(-1) + 6*5)|
Simplifying this expression, we get:
Area = 1/2 * |(-15 - 2 - 6 - 15) - (3 + 5 - 2 + 30)|
Area = 1/2 * |-38 - 24|
Area = 1/2 * |-62|
Area = 31
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Which trig function could
be used to solve for the
length of side c using the
50 degree angle?
A. sine
B. cosine
C. tangent
C
14
50°
Answer:
C
Step-by-step explanation:
in the triangle with respect to the 50° angle, the side opposite is c and the adjacent side is 14.
thus using the tangent ratio in the right triangle
tan50° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{c}{14}[/tex] ( multiply both sides by 14 )
14 × tan50° = c , then
c ≈ 16.7 ( to 1 decimal place )
In this problem, the cosine function is used to solve for the length of side C in a right-angled triangle, because the angle and the adjacent side are known. According to trigonometry, the cosine for an angle is the length of the adjacent side divided by the hypotenuse.
Explanation:In the given right-angled triangle, since the length of side C (hypotenuse) is unknown and one of the acute angles (50 degrees) is known, you should use the cosine function to solve for the length of side C. According to Trigonometry, cosine of an angle (in a right-angled triangle) is equal to the adjacent side divided by the hypotenuse. Hence, cos(50) = 14 / C. You could solve this equation for C.
Note that:
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When conducting a survey, which of the following is the most importantreason to avoid using a volunteer sample?
A. In order to get stronger opinions expressed.
B. Your conclusions could not be reliably generalized to a larger population.
C. You might not get a significant result.
D. To ensure truthful answers to the survey's questions.
The most important reason to avoid using a volunteer sample is Your conclusions could not be reliably generalized to a larger population.
Then, we want to determine the most important reason to avoid using a volunteering sample.
A levy sample is a slice system where people can choose whether or not they share in the check. While easier, this system can beget issues statistically.
The primary issue that this slice fashion faces is that the sample won't be arbitrary. You'll probably get people who are more opinioned about the subject the sample enterprises. This means that the sample won't truly be arbitrary, which in turn means it'll not be representative of the population. However, also the conclusions from the sample can not be generalized to the population, If the sample isn't representative of the population.
Thus, the answer is B. Your conclusions couldn't be reliably generalized to a larger population.
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opening a restaurant you are thinking about opening a restaurant and are searching for a good location. from research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. you decide to take a simple random sample of 50 people living near one potential location. based on the mean income of this sample, you will decide whether to open a restaurant there.8
Since we rejected the null hypothesis, you can consider opening a restaurant at that location.
What is the null hypothesis?In order to determine whether the mean income of the sample is sufficient to support the type of upscale restaurant you wish to open, we can perform a hypothesis test.
The null hypothesis (H₀) is that the mean income of the population near the potential location is $85,000 or less.
The alternative hypothesis (Ha) is that the mean income of the population near the potential location is greater than $85,000.
Using a one-sample t-test to test this hypothesis, since the population standard deviation is unknown and the sample size is relatively small (n = 50).
Let's assume that the sample mean income is $90,000 and the sample standard deviation is $10,000.
The test statistic can be calculated as:
t = (sample mean - hypothesized mean) / (sample standard deviation / √n))
t = ($90,000 - $85,000) / ($10,000 / √50))
t = 2.50
The degrees of freedom for this test are n-1 = 49. Using a significance level of 0.05 and a one-tailed test, the critical t-value is 1.676.
Since the calculated t-value (2.50) is greater than the critical t-value (1.676), we can reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean income of the population near the potential location is greater than $85,000.
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A population x of rabbits on an island is modeled by x? = x ? (1/1000)x^2, where the independent variable is time in months. At time t = 0, there are 40 rabbits on the island.
a) Find the solution to the equation with the initial condition.
b) How many rabbits are on the island in 1 month, 5 months, 10 months, 15 months (round to the nearest integer).
a) The solution to the equation with the initial condition is x = 40[tex]e^{(t/1000)}[/tex].
b) Approximately 40, 42, 45, and 49 rabbits on the island after 1, 5, 10, and 15 months.
a) To find the solution to the equation with the initial condition, do we need to solve the differential equation x? = x ? (1/1000)x² with the initial condition x(0) = 40.
Separating variables and integrating, we get:
dx/x = (1/1000) dt
Integrating both sides, we get:
ln|x| = (1/1000) t + C
where C is a constant of integration.
Using the initial condition x(0) = 40, we can solve for C:
ln|40| = C
C = ln|40|
Substituting this value of C, we get:
ln|x| = (1/1000) t + ln|40|
Simplifying, we get:
x = [tex]e^{(ln|40|+(1/1000) t)[/tex] = 40[tex]e^{(t/1000)}[/tex]
Therefore, the solution to the differential equation with the initial condition is x = 40[tex]e^{(t/1000)}[/tex].
b) To find the number of rabbits on the island after 1 month, 5 months, 10 months, and 15 months, we simply substitute the given values of t into the solution and round to the nearest integer.
After 1 month, x = 40[tex]e^{(1/1000)}[/tex] ≈ 40.04, so there are approximately 40 rabbits on the island.
After 5 months, x = 40[tex]e^{(5/1000)}[/tex] ≈ 41.67, so there are approximately 42 rabbits on the island.
After 10 months, x = 40[tex]e^{(10/1000)}[/tex] ≈ 45.26, so there are approximately 45 rabbits on the island.
After 15 months, x = 40[tex]e^{(15/1000)}[/tex] ≈ 49.28, so there are approximately 49 rabbits on the island.
Therefore, there are approximately 40, 42, 45, and 49 rabbits on the island after 1, 5, 10, and 15 months, respectively.
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13. (5 points)
The South Florida Fair is coming to town.
Admission to the fair costs $32.50 and each ride
costs $0.60. You have $52 to spend at the South
Florida Fair including admission.
orth
Part A: Write an inequality that represents this
situation.
Part B: Solve the inequality to determine the
maximum number of rides you can
enjoy at the South Florida Fair?
Part A: Let x be the number of rides you can enjoy at the South Florida Fair. The total cost of admission and rides cannot exceed the $52 you have, so we can write the following inequality:
32.50 + 0.60x ≤ 52
Part B: We can solve the inequality by first subtracting 32.50 from both sides:
0.60x ≤ 19.50
Then, we can divide both sides by 0.60 to isolate x:
x ≤ 32.5
Therefore, the maximum number of rides you can enjoy at the South Florida Fair is 32 rides, since you need to pay for admission and cannot exceed the $52 you have to spend.
Hermes earns $6)an hour for babysitting. He
wants to earn at least($168) for a new video
game system. Determine the number of
hours he must babysit to earn enough money
for the video game system. Then interpret
the solution.
Answer:
Step-by-step explanation:
Just divide the amount he expects to earn between the payment for each working hour.
[tex]Hours -to-babysit=\frac{168}{6}=28[/tex]
Hermes must babysit 28 hours to earn $168 for his new videogame
The units for volume are always BLANK units
The segment that goes all the way across the circle through the center point is called the BLANK
A radius is half of a BLANK
To find the radius, divide the diameter by BLANK
If you don't have a π button on your calculator, you should use BLANK (for accuracy) instead.
FILL IN THE WORDS THAT SAY BLANK!!!
Answer:
A radius is half of a diameter
To find the radius, divide the diameter by 2
If you don't have a π button on your calculator, you should use 3.14159 (for accuracy) instead.
The segment that goes all the way across the circle through the center point is called the diameter.
A radius is half of a diameter.
To find the radius, divide the diameter by 2.
If you don't have a π button on your calculator, you should use an approximation, such as 3.14, instead (for accuracy).
The line y = 3x – 8 cuts the x-axis at point D. what are the coordinates of D?
The coordinates of D on the given line segment is (8/3, 0).
What are the coordinates of midpoint of the line segment AB?Suppose we've two endpoints of a line segment as:
A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
[tex]x = \dfrac{p+m}{2}[/tex]
and
[tex]y = \dfrac{q+n}{2}[/tex]
We are given that;
y = 3x – 8
Now,
When a line cuts the x-axis, its y-coordinate is always 0. Therefore, we can substitute y = 0 into the equation y = 3x - 8 and solve for x:
0 = 3x - 8
3x = 8
x = 8/3
Therefore, the point D has coordinates (8/3, 0).
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8)
Mariah is planting a rectangular rose
garden. In the center of the garden,
she puts a smaller rectangular patch
of grass. The grass is 2 ft by 3 ft. What
is the area of the rose garden?
Rose
Garden
9ft
10ft
Patch of Grass
2ft 3ft
Answer:
Step-by-step explanation:
133 ft
Genevieve is an architect and has just finished the plans for a new library. She built a scale model to take to a planning meeting. The City Council members love her design so much that they have asked her for two new models.
The required for a. Genevieve must multiply the original dimensions with a lower scale factor lower than 1 while for b. Genevieve must multiply the original dimensions with a lower scale factor of more than 1.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
To create a smaller model that fits in a scale model of the entire city, Genevieve will need to use a smaller scale. She can calculate the new measurements by dividing the dimensions of the original model by the desired scale factor. For example, if she wants the new model to be half the size of the original, she would divide all dimensions by 2.
To create a slightly larger model for the entrance of the old library building, Genevieve can use a larger scale. She can calculate the new measurements by multiplying the dimensions of the original model by the desired scale factor. For example, if she wants the new model to be 10% larger than the original, she would multiply all dimensions by 1.1.
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Andy ate breakfast when his
clock had the time shown of 7:05. The clock stopped 12 minutes before breakfast. What time did Andy eat breakfast?
Answer: 7:17
Step-by-step explanation:
Ate breakfast 7:05
Clock stopped 12 minutes before
7:05 + 12 = 7:17
Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data. MLB Batting Averages 0.302 0.278 0.321 0.283 0.311 0.312 0.320 0.276 0.275 0.281 0.305 0.277 0.308 0.303 0.322 0.317 0.305 0.291 0.321 0.277 Copy Data < Answer 6Points Prev Separate multiple answers with commas, if necessary Keypad Selecting a button will replace the entered answer value(s) with the button value. If the button is not selected, the entered answer is used Mean: 0.2293 Median: Modes No mode
From the given information, the mean is 0.3025, the median is 0.3065, and the mode is 0.277 and 0.321.
To find the mean, we need to add up all the values and divide by the total number of values:
Mean = $\frac{0.302 + 0.278 + 0.321 + 0.283 + 0.311 + 0.312 + 0.320 + 0.276 + 0.275 + 0.281 + 0.305 + 0.277 + 0.308 + 0.303 + 0.322 + 0.317 + 0.305 + 0.291 + 0.321 + 0.277}{20} \approx 0.3025$
To find the median, we need to arrange data in the order from smallest to largest:
0.275, 0.276, 0.277, 0.277, 0.278, 0.281, 0.283, 0.291, 0.305, 0.305, 0.308, 0.311, 0.312, 0.317, 0.320, 0.321, 0.321, 0.322, 0.303, 0.302
There are 20 values, so median is average of the 10th and 11th values:
Median = $\frac{0.305 + 0.308}{2} = 0.3065$
To find the mode, we look for the value that appears most frequently. In this case, there are two modes: 0.277 and 0.321.
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is (-6, -8) a solution to this system of equations y=1/2x-3 y=5/2x+7
Since (-6, -8) is not a solution to both equations in the system, it is not a solution to the system of equations.
What is Equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
Now in the given question ,
We can check if (-6, -8) is a solution to the system of equations by plugging in these values for x and y in each equation and verifying if both equations are true.
For the first equation y = (1/2)x - 3, if we substitute x = -6 and y = -8, we get:
-8 = (1/2)(-6) - 3
-8 = -3 - 3
-8 = -6
This is not true, so (-6, -8) is not a solution to the first equation.
For the second equation y = (5/2)x + 7, if we substitute x = -6 and y = -8, we get:
-8 = (5/2)(-6) + 7
-8 = -15 + 7
-8 = -8
This equation is true, so (-6, -8) is a solution to the second equation.
Since (-6, -8) is not a solution to both equations in the system, it is not a solution to the system of equations.
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if m<1= 38 degrees and m<2=78. degrees what is m<3
Given two lines with slopes m<1 and m<2, the slope of a third line that is perpendicular to these lines would be the negative reciprocal of either slope. The negative reciprocal of m<1 is -1/m<1 and the negative reciprocal of m<2 is -1/m<2.
Since m<1 = 38 degrees, the negative reciprocal of m<1 would be -1/38.
And since m<2 = 78 degrees, the negative reciprocal of m<2 would be -1/78.
So, if m<3 is the slope of a line perpendicular to the lines with slopes m<1 and m<2, then m<3 could be either -1/38 or -1/78, depending on which slope is chosen.
find the coordinates of the point r that lies along the directed segment from j (10, -5) to k (-2, -3) and partitions the segment in the ratio of 2 to 7.
The coordinates of the point 'r' that lies along the directed segment from j (10, -5) to k (-2, -3) are equal to the ( 2/3 , -4 ).
We have, coordinates of the point r that lies along the directed line segment from j (10, -5) to k (-2, -3). The ratio of partitions of segment = 2 : 7
Internal section formula, Let consider M(x, y) be the point which divides line segment PQ internally in the ratio m : n. Then, the coordinates of M are calculated by below formula,
M = {[(mx₂ + nx₁ )/(m+n)], [(my₂ + ny₁)/(m+n)]}
j(10, -5) = (x₁,y₁), k(-2,-3) = (x₂,y₂)
Now we can determine the co-ordinate of r by substituting all values, Also, m : n = 2 : 7
r = {[2(10) + 7(-2)/ 2+7 ],[(3(-5) +7(- 3))/2+7 ]}
={[ (20 - 14)/9 ],[(-15 - 21) / 10]}
={6/9 , - 36/9}
= ( 2/3 , -4 )
Hence, required coordinates of r are ( 2/3 , -4 ).
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LOTS OF POINTS IF U ANSWER RIGHT!!
Graph g(2) = 4 cos (2x) - 2.
Use 3.14 for pi.
Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.
Under her cell phone plan, Paisley pays a flat cost of $60 per month and $3 per gigabyte. She wants to keep her bill under $75 per month. Write and solve an inequality which can be used to determine g g, the number of gigabytes Paisley can use while staying within her budget.
Answer:
Step-by-step explanation:
The inequality to determine the number of gigabytes Paisley can use while staying within her budget can be written as:
60 + 3g < 75
Solving for g:
60 + 3g < 75
-60 -60
0 + 3g < 15
/3 /3
g < 5
So Paisley can use up to 5 gigabytes while staying within her budget.
(a) determine the ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius:
The ratio of the volume of a (right circular) cone to the volume of a cylinder with the same height and base radius is 1/3 or 1:3.
The volume of a cone and a cylinder are formulas that are commonly used in geometry. The volume of a right circular cone with height h and base radius r is given by:
V₁ = (1/3)πr^2h
The formula for the volume of a right circular cylinder with height h and base radius r is given by:
V₂ = πr^2h
To find the ratio of the volume of a cone to the volume of a cylinder with the same height and base radius, we can divide the volume of the cone by the volume of the cylinder:
V₁/V₂ = [(1/3)πr^2h]/[πr^2h]
We can simplify this expression by canceling out the factors of π, r^2, and h:
V₁/V₂ = 1/3
Therefore, the ratio of the volume of a cone to the volume of a cylinder with the same height and base radius is 1/3. This means that a cone with the same height and base radius as a cylinder has a volume that is one-third that of the cylinder.
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Quantricide is mixed 2 fl oz to one gallon of water to give the proper dilution for disinfecting. What is the ratio of Quantricide to water?
( please help answer the other questions too below it )
The required ratio of Quantricide to water is 1 fl oz of Quantricide to 64 fl oz of water.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Since we are mixing 2 fl oz of Quantricide with one gallon of water, the ratio of Quantricide to water is, 2 fl oz : 1 gallon
However, it is common to express ratios in simplified form, so we can convert the units of gallons to fluid ounces to get a ratio in terms of fluid ounces,
1 gallon = 128 fl oz (since 1 gallon contains 128 fluid ounces)
So, the ratio of Quantricide to water in terms of fluid ounces is:
2 fl oz : 128 fl oz
This ratio can be simplified by dividing both sides by 2:
1 fl oz : 64 fl oz
Therefore, the ratio of Quantricide to water is 1 fl oz of Quantricide to 64 fl oz of water.
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7. Notice the right triangle inside the pyramid. Given a hypotenuse of 10 in and leg of 8
in, use the Pythagorean Theorem to find the true height (H) of the pyramid. What is
the volume of the pyramid?
The Volume of Pyramid is 512 in³.
What is Volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume.
Given:
Hypotenuse= 10 inch
leg length= 8 inch
Using Pythagorean Theorem
h² = 10² - 8²
h²= 100 - 64
h = 6 inch
So, the Volume of Pyramid
= lwh/3
= 6 x 16 x 16 /3
= 2 x 196
= 512 in³
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Let −2 ≤ x ≤ 5 and a ≤ 4x + 1 ≤ b
If −2 ≤ x ≤ 5 and a ≤ 4x + 1 ≤ b, then the inequality can be written as:
−7 ≤ 4x + 1 ≤ 21
What is expression ?
An expression in mathematics is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a value or a quantity. Expressions can be simple or complex, and they can be written in various forms, such as using variables, exponents, radicals, logarithms, trigonometric functions, and more.
For example, 2x + 5 is an expression that contains a variable x and represents a value that depends on the value of x. Another example is √(a^2 + b^2), which is an expression that contains two variables a and b and represents the square root of the sum of their squares.
According to given condition :
We know that −2 ≤ x ≤ 5. Therefore, the smallest possible value of 4x is −8 (when x = −2) and the largest possible value of 4x is 20 (when x = 5). Adding 1 to both sides of the inequality, we get:
−8 + 1 ≤ 4x + 1 ≤ 20 + 1
−7 ≤ 4x + 1 ≤ 21
So, a = −7 and b = 21.
Therefore, if −2 ≤ x ≤ 5 and a ≤ 4x + 1 ≤ b, then the inequality can be written as:
−7 ≤ 4x + 1 ≤ 21
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Write a function that models the data.
The function that models the data is y = 42 ([tex]\frac{1}{2}[/tex])ˣ.
What are Exponential Functions?Exponential functions are functions where the independent variable, x is in the exponent.
From the graph, it is clear that it is an exponential function.
Exponential functions will be of the form y = k bˣ.
We have the point (0, 42).
Substituting the point,
k b⁰ = 42
k = 42, since any number raised to 0 is 1, b⁰ = 1.
So the function is y = 42 bˣ.
Substituting the point (1, 21),
42 b¹ = 21
b = 21 / 42
b = 1/2
So the function is y = 42([tex]\frac{1}{2}[/tex])ˣ.
Hence the function is y = 42([tex]\frac{1}{2}[/tex])ˣ.
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Harper is going to create a graph of the
equation y = -0.5x + 12. Which of the following
will be true about the graph
The graph of the equation y = -0.5x + 12 will be a straight line
How to determine the true statement about the graphThe equation y = -0.5x + 12 represents a linear function
The slope of the line is -0.5The y-intercept (the value of y when x = 0) is 12Based on the slope -0.5 this means that as the value of x increases, the value of y will decrease.
Additionally, since the y-intercept is 12, the line will cross the y-axis at the point (0, 12).
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Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?
a. 2X1 + X2 − 3X3 ≥ 50b. 2X1+√X2 ≥ 60c. 4X1 - 1/3 X2 = 75d. 3X1+2X2-3x3/ X1+X2+X3 ≤ 0.9e. 3X1^2 +7X2 ≤ 45
The constraint 3X₁² + 7X₂ ≤ 45 has a degree of two and it cannot be used as constraint in a linear programming problem.
The correct answer is an option (e)
We know that a linear constraint in linear programming occurs when linear components are added or subtracted. Also the resulting expression must either increase, decrease, or be exactly equal to a right-hand side value.
Any constraint of a linear programming problem is referred to as linear if all of its terms are of the first order.
We know that the degree of the linear constraint is one, hence the constraint that does not have a degree of one is not a linear constraint.
Here we can observe that the constraint 3X₁² + 7X₂ ≤ 45 has a degree of two and it cannot be used as constraint in a linear programming problem.
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The complete question is:
Which of the following constraints are not linear or cannot be included as a constraint in a linear programming problem?
a. 2X₁ + X₂ − 3X₃ ≥ 50
b. 2X₁ + √X₂ ≥ 60
c. 4X₁ - 1/3 X₂ = 75
d. 3X₁ + 2X₂ - 3x₃ / X₁ + X₂ + X₃ ≤ 0.9
e. 3X₁² + 7X₂ ≤ 45
Divide (-9∠30 ) ÷ (-3∠-30)
After divide, the value of expression (-9∠30 ) ÷ (-3∠-30) is
⇒ (-9∠30 ) ÷ (-3∠-30) = 3
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The expression is,
⇒ (-9∠30 ) ÷ (-3∠-30)
Now, We can divide the expression as;
⇒ (-9∠30 ) ÷ (-3∠-30)
⇒ (-9∠30 ) / (-3∠-30)
⇒ - 9/- 3
⇒ 3
Thus, After divide, the value of expression (-9∠30 ) ÷ (-3∠-30) is
⇒ (-9∠30 ) ÷ (-3∠-30) = 3
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