What are inequalities?

Answers

Answer 1
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
Answer 2

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:


Related Questions

Multiple Choice
Identify the choice that best completes the statement or answers the question.
0
1. What are the pairs of alternate interior angles?

Answers

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 Information

The diagram is given by the image presented at the end of the answer.

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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)

Answers

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

I will mark you brainiest!

What is the length of LJ?

A) 23.0

B) 17.0

C) 4.7

D) 3.5

Answers

Answer:

The right answer is below

Step-by-step explanation:

4.7 is the length of LJ

Use Mathematical Induction to prove the sum of Arithmetic Sequences:



n

j
=
1

(
a
+
(
j

1
)
d
)
=
n
2
(
2
a
+
(
n

1
)
d
)

Answers

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.

Calculate the derivative of the following function and simplify.

y = [tex]e^{x} csc x[/tex]

Answers

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.

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locate the absolute extrema of the function
on the closed interval

Answers

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.

1 cubic meter = _____ cm cube

Answers

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

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

Answers

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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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.

Answers

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.

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

Answers

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 Math

Probability 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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2. write how many degrees are angle between.
a) North and East _______

Answers

Answer:

N and E is 90 degrees

N and S is 180 degrees

N and W is 90 degrees

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

Answers

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

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

Answers

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.

Answers

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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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.

Answers

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.

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.

Answers

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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(4) Practice: Using Visual Cues

Answers

Step-by-step explanation:

Refer to pic..........

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)

Answers

The ordered pairs of given equation are (3/2,4), (1/3, -3),(5/6,0)

What is ordered pair

An 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)

8. A rectangle is inch longer
than it is wide.
Let w = width.
Let = length.
Graph=w+
1
l=w+ 2

Answers

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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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?

Answers

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.

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?

Answers

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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Find the perimeter of the triangle whose vertices are (−4,3), (−4,1), and (−5,−4). Write the exact answer. Do not round.

Answers

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.

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)

Answers

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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HELP ASAP WILL GIVE BRAINLYEST AND 100 POINTS
IF YOU DON"T TRY TO ANSWER THE QUESTION RIGHT I WILL REPORT YOU

Answers

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:

Please figure out #3. I’ll mark brainliest for right answer.

Answers

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

In the diagram below ijk~ljm. FIND G

Answers

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?

Answers

The correct answer is y=-3x+7.

Explanation:

Subtract 3x from left and right side to get y=-3x+7

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

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?

Answers

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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Just need help on 7,8, and 9

Answers

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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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?

Answers

Answer:

0.6267

Step-by-step explanation:

See the picture.

Hope its clear.

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