Answer:
In mathematics, an inequality is a statement that compares two values, indicating that they are not equal, and specifies the relationship between them. In other words, an inequality expresses a relative difference between two values or quantities, rather than an exact equality.
There are different types of inequalities, but the most common ones involve comparisons between numerical values or algebraic expressions using inequality symbols, such as:
Greater than: x > y (read as "x is greater than y")
Less than: x < y (read as "x is less than y")
Greater than or equal to: x ≥ y (read as "x is greater than or equal to y")
Less than or equal to: x ≤ y (read as "x is less than or equal to y")
Inequalities can also involve multiple variables and can be used to describe ranges of values or conditions that must be satisfied. For example, x + y > 5 is an inequality that describes a region of the xy-plane where the sum of x and y is greater than 5.
Inequalities are used extensively in many areas of mathematics, including algebra, calculus, and optimization, and also have applications in other fields such as economics, physics, and engineering.
Step-by-step explanation:
8. A rectangle is inch longer
than it is wide.
Let w = width.
Let = length.
Graph=w+
1
l=w+ 2
To graph the equation l = w + 2, we can use the following steps:
Choose a range of values for the width w that we want to graph. Let's say we choose w = 0 to w = 5.
Plug each value of w into the equation to find the corresponding value of l. For example, when w = 0, l = 0 + 2 = 2. When w = 1, l = 1 + 2 = 3.
w l = w + 2
0 2
1 3
2 4
3 5
4 6
5 7
Plot each point on a coordinate plane using the value of w as the x-coordinate and the value of l as the y-coordinate.
Connect the points with a straight line to create the graph of the equation.
The resulting graph should be a straight line with a slope of 1 and a y-intercept of 2, as shown below:
markdown
Copy code
|
7 |- +
| |
6 |- \
| \
5 |- \
| \
4 |- \
| \
3 |- \
| \
2 |- - - - - - - \
0 1 2 3 4 5 6
w
Note that the graph represents all the possible pairs of width w and length l that satisfy the equation l = w + 2. Since the equation describes a rectangle that is one inch longer than it is wide, we can see that the graph includes all the possible rectangles that fit this description.
|
7 |- +
| |
6 |- \
| \
5 |- \
| \
4 |- \
| \
3 |- \
| \
2 |- - - - - - - \
0 1 2 3 4 5 6
w
Note that the graph represents all the possible pairs of width w and length l that satisfy the equation l = w + 2. Since the equation describes a rectangle that is one inch longer than it is wide, we can see that the graph includes all the possible rectangles that fit this description.
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A normal distribution is informally described as a probability distribution that is "bell-shaped" when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.
Choose the correct answer below.
A.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts on the horizontal scale and rises at a decreasing rate to a central peak before falling at an increasing rate to the horizontal scale.
B.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts above the horizontal scale, falls from the horizontal at an increasing rate, then falls at a decreasing rate to a central minimum before rising at an increasing rate, then rising at a decreasing rate, and finally becoming nearly horizontal.
C.
A symmetric curve is plotted over a horizontal scale. From left to right, the curve starts on the horizontal scale, rises from horizontal at an increasing rate, then rises at a decreasing rate to a central peak before falling at an increasing rate, then falling at a decreasing rate, and finally approaches the horizontal scale.
The correct answer is C. A normal distribution is a symmetric probability distribution that is bell-shaped when graphed. When plotted on a horizontal scale, the curve starts on the horizontal axis, rises to a central peak, and then falls back to the horizontal axis.
The curve is symmetric, meaning that the left and right halves of the curve are mirror images of each other. The curve approaches the horizontal axis but never touches it, which indicates that there is a non-zero probability of observing values at any distance from the mean, although the probability decreases as the distance from the mean increases.
Normal distribution is a type of probability distribution that is commonly found in natural and social phenomena, where the majority of the observations tend to cluster around the mean, with fewer observations further away from the mean.
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In the diagram below ijk~ljm. FIND G
As the triangles are similar to each other, using congruent theorem, we get the value of side g = 2m.
What are similar triangles?Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.
This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".
As per the triangles,
g/5 = 4/10
⇒ g = 4 × 5/10
⇒ g = 2m.
Therefore, we conclude that the value of g = 2m as per the similar triangles' theorem.
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6th grade math, is this correct?
Answer:
No, it is y = - 3x + 7
( negative 3x not positive )
Hope this helps!
Step-by-step explanation:
1. Subtract both sides by 3x
3x + y - ( 3x ) = 7 - ( 3x )
2. Combine like terms
( 3x - 3x ) + y = 7 - ( 3x )
0 + y = 7 - ( 3x )
y = 7 - ( 3x )
y = -3x + 7
About 12% of employed adults in the United States held multiple jobs. A random sample of 66 employed adults is chosen. Use the TI-84 Plus calculator as needed. Part: 0/5 Part 1 of 5 (a) Is it appropriate to use the normal approximation to find the probability that less than 8.4% of the individuals in the sample hold multiple jobs? If so, find the probability. If not, explain why not. It (Choose one) appropriate to use the normal curve, since np (Choose one)
The probability that less than 8.4% of the individuals in the sample hold multiple jobs is approximately 0.0681 or 6.81%.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number outcomes.
To determine whether it is appropriate to use the normal approximation, we need to check whether the conditions for using the normal distribution are met.
We can use the following criteria:
The sample size is large enough: n × p ≥ 10 and n × (1 − p) ≥ 10
The observations are independent
Here, we are given that the sample size is n = 66. To check the first condition, we need to find the expected number of individuals who hold multiple jobs in the sample, which is given by:
np = 0.12 × 66 = 7.92
n(1-p) = 66 - 7.92 = 58.08
Both np and n(1-p) are greater than or equal to 10. So, the sample size is large enough and the first condition is met.
Additionally, we can assume that the observations are independent since the sample is random and represents less than 10% of the population of employed adults in the United States.
Therefore, it is appropriate to use the normal approximation.
To find the probability that less than 8.4% of the individuals in the sample hold multiple jobs, we need to standardize the sample proportion using the formula:
z = (p'- p) / [tex]\sqrt{(p(1-p) / n)}[/tex]
where p' is the sample proportion, p is the population proportion (0.12), n is the sample size (66), and sqrt represents the square root.
Substituting the values, we get:
z = (0.084 - 0.12) / [tex]\sqrt{((0.12)(1-0.12) / 66)}[/tex] = -1.496
Using a standard normal distribution table, we can find that the probability of z being less than -1.496 is approximately 0.0681.
Therefore, the probability that less than 8.4% of the individuals in the sample hold multiple jobs is approximately 0.0681 or 6.81%.
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(4) Practice: Using Visual Cues
Step-by-step explanation:
Refer to pic..........
locate the absolute extrema of the function
on the closed interval
Answer:
To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:
∫[a,b] f(x) dx = F(b) - F(a)
where F(x) is the antiderivative of f(x).
First, we find the antiderivative of f(x):
F(x) = x^2 + (5/3)x + C
where C is the constant of integration.
Next, we evaluate F(5) and F(0):
F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C
F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C
Subtracting F(0) from F(5), we get:
∫[0,5] f(x) dx = F(5) - F(0)
= 25 + (25/3) + C - C
= 25 + (25/3)
= 100/3
Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.
Please figure out #3. I’ll mark brainliest for right answer.
Answer:
We are given the cost equations for Emma's and Madison's text message plans as:
Emma's Plan: y = 0.10x + 10
Madison's Plan: y = 0.15x
where y is the cost in dollars and x is the number of texts sent. We are also told that Emma and Madison paid the same amount in one month. Let's set the two equations equal to each other and solve for x:
0.10x + 10 = 0.15x
Subtracting 0.10x from both sides, we get:
10 = 0.05x
Dividing both sides by 0.05, we get:
x = 200
Therefore, Emma and Madison sent 200 text messages in one month to pay the same amount
Just need help on 7,8, and 9
According to the given information, the missing values in the ratio table are:
7. 6:1/3, 12:2, 6:1, 24:4
8. 1/4:3, 2:6, 1:12, 5/4:15
9. 1/3:8/3, 2/3:2/3, 1:1, 4/3:1.04
What is ratio?
A ratio is a mathematical comparison of two or more quantities. Ratios express the proportional relationship between the quantities being compared. Ratios are often written using a colon (:) or as a fraction, such as "1:2" or "1/2".
7.
We can simplify the ratio of feet to seconds by converting 1/3 to its equivalent fraction with a denominator of 3:
Ratio of feet to seconds = 6 : 1/3 = 6 : (1/3) = 6 : (1/3) x (3/3) = 6 : 1
So, the ratio of feet to seconds is 6 : 1.
Using this ratio and the other ratios given, we can create equations to solve for the missing values:
6 : 1 = 12 : x
Cross-multiplying, we get: 6x = 12
Solving for x, we get: x = 2
y : 1 = 6 : 1
Cross-multiplying, we get: y = 6
6 : 1 = 24 : z
Cross-multiplying, we get: 6z = 24
Solving for z, we get: z = 4
Therefore, the missing values are:
x = 2, y = 6, z = 4
8.
We can set up equations based on the given ratios and solve for the missing values.
1/4 : x = blue ribbon : red ribbon
y : 6 = blue ribbon : red ribbon
1 : z = blue ribbon : red ribbon
5/4 : 15 = blue ribbon : red ribbon
To find x:
1/4 : x = 1 : z (since blue ribbon : red ribbon = 1 : z)
Cross-multiplying, we get:
1z = 4x
z = 4x
To find y:
y : 6 = 1/4 : x (since blue ribbon : red ribbon = 1/4 : x)
Cross-multiplying, we get:
y * x = 6 * 1/4
y * x = 3/2
y = (3/2) / x
To find z:
1 : z = 5/4 : 15 (since blue ribbon : red ribbon = 1 : z)
Cross-multiplying, we get:
1 * 15 = 5/4 * z
z = (1 * 15 * 4) / 5
z = 12
Therefore, the values of x, y, and z are x = 3, y = 2, and z = 12.
9.
To find the values of x, y, and z, we need to first simplify the ratios given.
The ratio between orange fabrics and yellow fabric is:
1/3 : 8/3
We can simplify this ratio by multiplying both sides by 3 to get:
1 : 8
The ratio between 2/3 and x is:
2/3 : x
The ratio between 1 and y is:
1 : y
The ratio between 4/3 and z is:
4/3 : z
We can simplify this ratio by multiplying both sides by 3/4 to get:
1 : (4/3)z or 1 : 1.33z (rounded to two decimal places)
Now we have the following ratios:
Orange : Yellow = 1 : 8
2/3 : x = 2/3 : x
1 : y = 1 : y
1 : (4/3)z = 1 : 1.33z
To solve for x, y, and z, we can use cross-multiplication.
Orange : Yellow = 1 : 8
1/8 = (Orange / Yellow)
8/1 = (Yellow / Orange)
2/3 : x = 2/3 : x
This ratio is already in its simplest form, so x = 2/3.
1 : y = 1 : y
This ratio is already in its simplest form, so y = 1.
1 : (4/3)z = 1 : 1.33z
1 = (4/3)z / 1.33z
1 = 0.96z
z = 1.04
Therefore, the values of x, y, and z are:
x = 2/3, y = 1, z = 1.04
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1 cubic meter = _____ cm cube
Answer:
1 cubic meter = 1000000 cm cubed
Step-by-step explanation:
[tex]1m^3*10^6=1000000cm^3[/tex]
Answer:
1 cubic meter = 10000000 cm cube
Mr. Nkalle invested an amount of N$20,900 divided in two different schemes A and B at the simple interest
rate of 9% p.a. and 8% p.a, respectively. If the total amount of simple interest earned in 2 years is N$3508,
what was the amount invested in Scheme B?
Answer:
Let's assume that Mr. Nkalle invested an amount of x in Scheme A and (20900 - x) in Scheme B.
The simple interest earned on Scheme A in 2 years would be:
SI(A) = (x * 9 * 2)/100 = 0.18x
The simple interest earned on Scheme B in 2 years would be:
SI(B) = [(20900 - x) * 8 * 2]/100 = (3344 - 0.16x)
The total simple interest earned in 2 years is given as N$3508:
SI(A) + SI(B) = 0.18x + (3344 - 0.16x) = 3508
0.02x = 164
x = 8200
Therefore, Mr. Nkalle invested N$8200 in Scheme A and N$12700 (20900 - 8200) in Scheme B. So the amount invested in Scheme B was N$12700.
In the Venn diagram below, event A represents the adults who drink coffee, event B represents the adults who drink tea, and event C represents the adults who drink cola.
List the region(s) which represent the adults who drink both coffee and tea.
(Stats)
Answer:
Regions 1 and 4
Step-by-step explanation:
There are 2 overlapping regions for A (coffee) and B(tea)
These are Region 4 which represents the adults who drink both coffee and tea but not cola
and
Region 1 which represents the adults who drink coffee, tea and cola
So combined these two regions we get all adults who drink both coffee and tea
Find the perimeter of the triangle whose vertices are (−4,3), (−4,1), and (−5,−4). Write the exact answer. Do not round.
Answer:
2 + √[26] + √[50]
Step-by-step explanation:
To find the perimeter of a triangle with vertices given in the coordinate plane, we need to calculate the distance between each pair of vertices and then add them up.
Using the distance formula, the distance between the first two vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-4 - (-4))^2 + (1 - 3)^2] =
√[0 + 4] = 2
The distance between the second and third vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-5 - (-4))^2 + (-4 - 1)^2] =
√[1 + 25] = √[26]
Finally, the distance between the third and first vertices is:
√[(x2 - x1)^2 + (y2 - y1)^2] =
√[(-4 - (-5))^2 + (3 - (-4))^2] =
√[1 + 49] = √[50]
Therefore, the perimeter of the triangle is:
2 + √[26] + √[50]
This is the exact answer, and we cannot simplify it further.
Multiple Choice
Identify the choice that best completes the statement or answers the question.
0
1. What are the pairs of alternate interior angles?
The pairs of alternate interior angles are given as follows:
2 and 8.3 and 5.What are alternate interior angles?Alternate interior angles are pairs of angles that are formed when a transversal intersects two parallel lines. Alternate interior angles are located on opposite sides of the transversal and inside the parallel lines.
From the image given at the end of the answer, the parameters for this problem are given as follows:
The two parallel lines are l and k.The transversal line is t.Hence the pairs of alternate interior angles are given as follows:
2 and 8.3 and 5.As they are between lines l and k, on opposite sides of line t.
Missing InformationThe diagram is given by the image presented at the end of the answer.
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Macy of New York sold LeeCo. of Chicago office equipment with a $6,300 list price. Sale terms were 3/10, n/30 FOB New York. Macy agreed to prepay the $40 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?
The amount that LeeCo pays Macy for the office equipment at the $6,300 list price, sales terms of 3/10, n/30 FOB with payment made within the discount window, is $6,111.
What is a cash discount?A cash discount refers to a reduction in the price of an item due to payment within the discount period.
A cash discount incentivizes the customer to make prompt payments.
The list price of the equipment = $6,300
Sales terms: 3/10, n/30 FOB
Prepaid freight = $40
Cash discount = $189 ($6,300 x 3%)
Payment after the discount = $6,111 ($6,300 - $189)
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A set of sweater prices are normally distributed with a mean of
58
5858 dollars and a standard deviation of
5
55 dollars.
What proportion of sweater prices are between
48.50
48.5048, point, 50 dollars and
60
6060 dollars?
Answer:
0.6267
Step-by-step explanation:
See the picture.
Hope its clear.
I will mark you brainiest!
What is the length of LJ?
A) 23.0
B) 17.0
C) 4.7
D) 3.5
Answer:
The right answer is below
Step-by-step explanation:
4.7 is the length of LJ
A fair coin is tossed five times. What is the theoretical probability that the coin lands on the same side every time??
A) 0.1
B) 0.5
C) 0.03125
D) 0.0625
Answer:
The answer is C
Step-by-step explanation:
Assuming this is a fair coin, the theoretical probability of the coin going on one side, let's say heads, is 50%, or 0.5. So what's the chance the coin lands head 5 times? To do this we do 0.5^5 OR 0.5*0.5*0.5*0.5*0.5. Both of these answers equal 0.03125. So C is the Answer. Hope this helps :D
35% of households say they would feel secure if they had 50000 in savings he randomly selected 8 households and ask them if they would feel secure if they had 50000 in savings find the probability that the number that say that they would feel secure a exactly 5B more than 5 &c at most 5
Probability that precisely 5 people will respond that they would feel comfortable is 0.0808
Probability that more than 5 people will respond that they would feel comfortable is0.1061
Probability that at most 5 people will respond that they would feel comfortable is 0.9747
Probability Definition in MathProbability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence.
Solving the problem:35 percent of households claim that having $50,000 in savings would make them feel comfortable. Ask 8 homes that were chosen at random if they would feel comfortable if they had $50,000 in savings.
Binomial conundrum with p(secure) = 0.35 and n = 8.
the likelihood that the number of people who claim they would feel comfortable is
(a) The number exactly five is equal to ⁸C₅ (0.35)5×(0.65)×3=binompdf(8,0.35,5) = 0.0808.
(b) more than five = 1 - binomcdf(8,0.35,4) = 0.1061
(c) at most five = binomcdf(8,0.35,5) = 0.9747.
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Calculate the derivative of the following function and simplify.
y = [tex]e^{x} csc x[/tex]
Answer:
To find the derivative of this function, we'll use the product rule and the chain rule. Let's begin by writing the function in a more readable form using parentheses:
y = e^x * csc(x) * (1 / x) * csc(x)
Now we can apply the product rule, letting u = e^x and v = csc(x) * (1 / x) * csc(x):
y' = u'v + uv'
To find u' and v', we'll need to use the chain rule.
u' = (e^x)' = e^x
v' = (csc(x) * (1 / x) * csc(x))'
= (csc(x))' * (1 / x) * csc(x) + csc(x) * (-1 / x^2) * csc(x) + csc(x) * (1 / x) * (csc(x))'
= -csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x)
= -csc(x) * [cot(x) * (1 / x) + (1 / x^2) + (cot(x) / x)]
Now we can substitute these into the product rule formula:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] + e^x * (-csc(x) * cot(x) * (1 / x) * csc(x) - csc(x) * (1 / x^2) * csc(x) - csc(x) * (1 / x) * csc(x) * cot(x))
Next, we can simplify this expression. One way to do this is to factor out common terms:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (1 / x) - (1 / x^2) - (cot(x) / x)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]
Now we can simplify further by combining like terms:
y' = e^x * csc(x) * (1 / x) * csc(x) * [-cot(x) * (2 / x) - (1 / x^2)] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + (cot(x) / x)]
= e^x * csc(x) * (1 / x) * csc(x) * [-2cot(x) / x - 1 / x^2 - cot(x) / x^2] - e^x * csc(x) * cot(x) * (1 / x) * csc(x) * [1 + cot(x) / x]
At this point, the derivative is simplified as much as possible.
(please could you kindly mark my answer as brainliest)
Please help and explain what and why you did to get the answer.
For the equation complete the given ordered pairs.
x = -5
(,4), (, -3), (,0)
The ordered pairs of given equation are (3/2,4), (1/3, -3),(5/6,0)
What is ordered pairAn ordered pair is composed of the ordinate and the abscissa of the x coordinate, with two values supplied in parentheses in a specified sequence. Placing a point on the Cartesian plane could be beneficial for visual comprehension.
for example, the ordered pair (x, y) signifies an ordered pair in which 'x' is referred to as the first element and 'y' is referred to as the second element. These items, which can be either variables , have distinct names depending on the context in which they are used. In an ordered pair, the element order is quite significant.
Given Equation of Y=6x−5
First Ordered pair;(,4)
y=4
x=4+5/6
x=3/2
First Ordered pair;(, -3)
y=-3
x=-3+5/6
x=1/3
First Ordered pair; (,0)
y=0
x=5/6
The ordered pairs of given equation are
(3/2,4), (1/3, -3),(5/6,0)
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The complete question is:
For The Equation, Y=6x−5
Complete The Given Ordered Pairs (,4), (, -3), (,0)
HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTS
IF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU
Answer:
The order from least to greatest is:
8.2 x 10^-7 < 5.8 x 10^-5 < 1.2 x 10^3 < 9.7 x 10^3 < 3.4 x 10^6
Answer:
it is already in the correct order
Step-by-step explanation:
Paul borrowed
$
6
,
000
from a credit union for
5
years and was charged simple interest at a rate of
5.45
%
. What is the amount of interest he paid at the end of the loan?
Paul paid $1,635 in interest at the end of the loan.
What is simple interest?Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
According to the given information:The simple interest formula is:
I = P * r * t
where I is the interest, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time in years.
In this problem, P = $6,000, r = 0.0545 (since the interest rate is given as 5.45%), and t = 5 years. Plugging in these values, we get:
I = 6,000 * 0.0545 * 5 = $1,635
Therefore, Paul paid $1,635 in interest at the end of the loan.
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2. write how many degrees are angle between.
a) North and East _______
Answer:
N and E is 90 degrees
N and S is 180 degrees
N and W is 90 degrees
Given, y=a(x−2)(x+4)In the quadratic equation above, a is a nonzero constant. The graph of the equation in the xy-plane is a parabola with vertex (c,d). Which of the following is equal to d?A. -9aB. -8aC. -5aD. -2a
When the graph of the equation y=a(x−2)(x+4) in the xy-plane is a parabola with vertex (c,d), then the value of d is equal to option (A) -9a
To find the vertex of the parabola, we need to complete the square by factoring out the constant term a and adding and subtracting a term that will allow us to write the quadratic in the form
y = a(x - h)^2 + k,
where (h,k) are the coordinates of the vertex. We have
y = a(x - 2)(x + 4) = a(x^2 + 2x - 8x - 8) = a[(x + 1)^2 - 9]
Expanding the square and factoring out the constant term a, we get
y = a[(x + 1)^2 - 9] = a(x + 1)^2 - 9a
Comparing this to the standard form of the quadratic, we see that the vertex is at (-1,-9a). The value of d is -9a
Therefore, the correct option is (A) -9a
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Al's total payment for his loan was $34,267. What was his monthly payment if he
paid it off after making 42 monthly payments? Round to the nearest dollar. Do not
state the units.
Answer: 816
Step-by-step explanation:
Let's denote the monthly payment by x.
Then, Al paid a total of 42x dollars over 42 months.
We know that the total payment for the loan was $34,267. Therefore, we can set up the equation:
42x = 34267
Solving for x, we get:
x = 34267/42
x ≈ 816
So Al's monthly payment was approximately $816.
The data represent the results for a test for a certain disease. Assume one individual from the group is randomly selected. Find the probability of getting someone who tested positive given that he or she had the disease.
Answer:
To find the probability of getting someone who tested positive given that he or she had the disease, we need to use the formula for conditional probability:
P(positive|disease) = P(positive and disease) / P(disease)
From the given data, we can see that there are 136 individuals who tested positive and actually had the disease. Therefore, P(positive and disease) = 136.
We can also see that there are a total of 136 + 8 = 144 individuals who actually had the disease. Therefore, P(disease) = 144.
Substituting these values into the formula, we get:
P(positive|disease) = 136 / 144
Simplifying, we get:
P(positive|disease) = 0.944
Rounding to three decimal places, we get:
P(positive|disease) ≈ 0.944
Therefore, the probability of getting someone who tested positive given that he or she had the disease is approximately 0.944.
Use Mathematical Induction to prove the sum of Arithmetic Sequences:
n
∑
j
=
1
(
a
+
(
j
−
1
)
d
)
=
n
2
(
2
a
+
(
n
−
1
)
d
)
Answer:
We will use mathematical induction to prove the formula for the sum of arithmetic sequences:
For n=1, we have:
∑j=1^1(a + (j-1)d) = a
On the other hand, we have:
n/2(2a + (n-1)d) = 1/2(2a) = a
Thus, the formula holds for n=1.
Assuming the formula holds for n=k, we will prove that it holds for n=k+1.
We have:
∑j=1^(k+1)(a + (j-1)d) = (a + kd) + ∑j=1^k(a + (j-1)d)
Using the formula for n=k, we can write:
∑j=1^k(a + (j-1)d) = k/2(2a + (k-1)d)
Substituting this back into the first equation, we have:
∑j=1^(k+1)(a + (j-1)d) = (a + kd) + k/2(2a + (k-1)d)
Simplifying the right-hand side, we get:
∑j=1^(k+1)(a + (j-1)d) = 1/2(2a + (2k+1)d)
But (k+1)/2(2a + kd + d) = 1/2(2a + (2k+1)d), so the formula holds for n=k+1.
Therefore, by mathematical induction, the formula for the sum of arithmetic sequences is proved.
a. Using the graph above, how many apricots will the United States import at the world price?
As a consequence of this quota, how many apricots will the United States import now?
thousand tons
How many apricots will domestic producers supply?
thousand tons
The graph demonstrates that local producers will provide 8,000 tonnes of apricots at the global price of $400 per tonne.
what is graph ?A graph is a visual representation of data that's frequently used to demonstrate how variables relate to one another or to show how trends change over time. Graphs can come in many various forms, including line graphs, bar graphs, pie charts, scatter plots, and more. Graphs are frequently used to simplify the presentation of complicated data in disciplines like economics, mathematics, science, and the social sciences.
given
The graph indicates that the cost of apricots in the globe is $400 per tonne. In the absence of the quota, the US would purchase 5,000 tonnes of apricots at the market rate. The United States will only be permitted to acquire 3,000 tonnes of apricots under the quota, though.
As a result of this quota, the United States will purchase 3,000 tonnes of apricots at the world price.
The graph demonstrates that local producers will provide 8,000 tonnes of apricots at the global price of $400 per tonne.
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the number of creeping bentgrass shoots on an average size (6000 square feet) well-maintained putting green can range from ______ shoots.
The total number of creeping bentgrass shoots on a 6000 square feet putting green could range from approximately 480,000 to 600,000 shoots.
The United States Golf Association (USGA) suggests that a healthy putting green, which is well-maintained, can support around 80 to 100 creeping bentgrass plants in each square foot. As the given putting green is 6000 square feet, we can calculate the total number of creeping bentgrass plants on this area by multiplying the area by the suggested number of plants per square foot. Therefore, the total number of creeping bentgrass shoots on a well-maintained 6000 square feet putting green could range from approximately 480,000 to 600,000 shoots, based on the given range of suggested plants per square foot.
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