Maths qs
Dot diagram and mean mass

If UV≅PM then UV≅PM → Definition of congruence, EF≅EF → Reflexive property of congruence, If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence.

A statement that is accepted as true without evidence, also referred to as an axiom. Lemmas and theorems are deduced from postulates, which serve as their fundamental building block. For instance, Euclid's postulates, a set of five postulates, provide the foundation of all of Euclidean geometry.

A) If and only if two segments have equal amounts of each, they are congruent.

If UV≅PM then UV≅PM → Definition of congruence

B) An angle, line segment, or shape is always congruent to itself, according to the reflexive characteristic of congruence in geometry.

EF≅EF → Reflexive property of congruence

C) According to the transitive characteristic of congruence, "all sides are congruent to each other if two sides are congruent to the third side."

If AB≅LM and LM≅ST then AB≅ST  → Transitive property of congruence

D) Actually fairly straightforward, equality has the symmetric condition. According to this criterion, if a = b, then b must also be a. In other words, even if two equations' sides are switched, the equation still makes sense.

If AB=XY then XY =AB  → Symmetric property of equality

E) The additive property of equality in an equation asserts that the sides stay equal whether we add or subtract the same amount from both sides of the equation. For entire numbers as well, this property is valid.

If 2x-3=13 then 2x=16 → Addition property of equality

Add 3 on both the sides of equation we get

2x-3+3=13+3

⇒ 2x=16

Therefore, the statement If 2x-3=13 then 2x=16 follows addition property of equality.

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Answer:

The arithmetic sequence in the given series of numbers is 11. The common difference in an arithmetic sequence is the number that is added to each term to get the next term in the sequence. In this case, the common difference is 11, because when we add 11 to the first term, 12, we get 23, which is the second term in the sequence. Similarly, when we add 11 to the second term, 23, we get 34, which is the third term in the sequence, and so on. Therefore, the arithmetic sequence in the given series of numbers is 11

The exponential function best represents the growth of the investment.

What is exponential function?

An exponential function can be used to depict the investment's growth. The formula for an exponential function is y = a * b^x, where an is the starting point (in this case, 45,000), b is the growth factor (in this case,

1 + 0.018 = 1.018), and x is the number of time periods (in this case, the number of months).

For example, if we let x represent the number of months, the function would be:

y = 45,000 * 1.018^x

This function represents the growth of the investment as a function of the number of months. As the number of months increases, the value of the investment will grow exponentially according to the formula.

Hence, the exponential function best represents the growth of the investment.

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The equation of the tangent line to the curve when y = -1 is y = -4x - 1.

To find the equations of all tangent lines to the curve when y = -1, we can use the definition of a tangent line, which is a line that touches a curve at a single point and has the same slope as the curve at that point.

To find the slope of the curve at a given point, we can use the slope formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case, we can set y₁ = -1 and y₂ = -1 + h, where h is a small positive number, and find the corresponding value of x₂ by substituting these values into the equation x - x²y - 2y² = 0. This will give us the slope of the curve at the point (x, -1).

Substituting these values into the equation, we get:

x - x²(-1) - 2(-1 + h)² = 0

Expanding the second term and rearranging, we get:

x - x² + 2(1 - 2h + h²) = 0

This simplifies to:

x - x² + 2 - 4h + 2h² = 0

This can be rewritten as:

x - x² + 2h² - 4h + 2 = 0

To find the slope of the curve at the point (x, -1), we can take the derivative of this equation with respect to x and evaluate it at x = x and h = 0:

slope = (2h² - 4h)'|h=0

= 0 - 4

= -4

Now that we have the slope of the curve at the point (x, -1), we can use the point-slope form of a linear equation to find the equation of the tangent line:

y - (-1) = -4(x - x)

y + 1 = -4x

y = -4x - 1

Therefore, when y = -1, the equation of the tangent line to the curve is y = -4x - 1.

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Reflection of point across x-axis

preimage (-3, 2)         Image (-3, -2)

Reflection of point across y-axis

preimage (-3, 2)         Image (3, 2)

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The reflection to be done is (-3, 2)

Transformation for reflection over x-axis → (-3, -2)

Transformation for reflection over line y-axis  → (3, 2)

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Answer: A. To find the probability that a randomly selected male passenger can fit through the doorway without bending, we need to find the probability that his height is less than or equal to 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, we can use the standard normal distribution to find this probability.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the height of a male passenger from the given distribution to the standard normal distribution by using the formula:

$z = \frac{x - \mu}{\sigma}$

where $x$ is the height of the male passenger, $\mu$ is the mean height of 69 inches, and $\sigma$ is the standard deviation of 2.8 inches. Substituting these values into the formula gives us:

$z = \frac{72 - 69}{2.8} = \frac{3}{2.8} = 1.0714$

Since the standard normal distribution is symmetric, the probability that a male passenger's height is less than or equal to 72 inches is the same as the probability that his height is greater than or equal to 72 inches. We can find this probability by looking up the value of $z = 1.0714$ in a standard normal table, which gives us a probability of 0.8413. Therefore, the probability that a male passenger can fit through the doorway without bending is 0.8413.

B. To find the probability that the mean height of the 175 men is less than 72 inches, we need to find the probability that the sample mean is less than 72 inches. Since the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, the sample mean will also be normally distributed with a mean of 69 inches and a standard deviation of $\frac{2.8}{\sqrt{175}} = 0.32$. We can use the standard normal distribution to find the probability that the sample mean is less than 72 inches.

The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the sample mean from the given distribution to the standard normal distribution by using the formula:

$z = \frac{x - \mu}{\sigma}$

where $x$ is the sample mean, $\mu$ is the mean of 69 inches, and $\sigma$ is the standard deviation of 0.32. Substituting these values into the formula gives us:

$z = \frac{72 - 69}{0.32} = \frac{3}{0.32} = 9.375$

Since the standard normal distribution is symmetric, the probability that the sample mean is less than 72 inches is the same as the probability that the sample mean is greater than 72 inches. We can find this probability by looking up the value of $z = 9.375$ in a standard normal table, which gives us a probability of 0.0000. Therefore, the probability that the mean height of the 175 men is less than 72 inches is 0.0000.

C. When considering the comfort and safety of passengers, the result from part (a) is more relevant than the result from part (b). This is because part (a) tells us the probability that a randomly selected male passenger can fit through the doorway without bending, which is directly relevant to the comfort and safety of the passengers. In contrast, part (b) tells us the probability that the mean height of the 175 men is less than 72 inches, which is not directly relevant to the comfort

D. Women are ignored in this case because the problem only asks about the heights of men. The problem states that the heights of men are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches, and does not provide any information about the heights of women. Therefore, we cannot use the given information to find the probability that a female passenger can fit through the doorway without bending.

Step-by-step explanation:

you did not write this question well

The required solution of the given numerals is,
1. 3 + 4k + k < 43, Option D is correct.
2. The oldest Kim could be 7 years old. Option D is correct.

Given that,
Josh is 3 years older than 4 times Kim's age. The sum of their ages is less than 43. Select the correct inequality for the situation, then determine the oldest age Kim could be.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
J = 4k + 3
And
J + K < 43
4K + 3 + K < 43
5k < 40k
k < 8
K could be K = 7

Thus, the required solution of the given numerals is,
1. 3 + 4k + k < 43, Option D is correct.
2. The oldest Kim could be 7 years old. Option D is correct.

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The percentage of oxygen in the water is 0.0002%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that a 2000 ml sample of water was collected and found to have 0.004 mL of oxygen. Therefore, the percentage oxygen in water is equal to,

Percentage = Volume of oxygen in the water / Volume of water

                   = 0.004 mL / 2000 mL

                   = 0.004 mL / 2 mL

                   = 0.0002% of water

Therefore, the percentage of oxygen in the water is 0.0002%.

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Answer:

12? lol

Step-by-step explanation:

<3

Answer:

L1 = L2 = 16.5 cm and L3 = 7cm

Step-by-step explanation:

Triangle perimeter = L1 + L2 + L3 = 40 cm

L1 = L2 = L

L3 = 7

Then:

40 = 2L +7

33 = 2L

L = 33/2

L = 16.5 cm

Step-by-step explanation:

8x + 3y = 7 --------(1)

2x + y = 2 ----------(2)

y = 2 – 2x ---------(3)

just substitute for y in equation (1)

8x + 3(2–2x) = 7

8x + 6 – 6x = 7

8x – 6x + 6 = 7

2x = 7 – 6

2x = 1

x = ½

since x = ½ just substitute for x in equation(3)

y = 2 – 2x

y = 2 – 2(½)

y = 2 – 1

y = 1

so x = ½,y = 1

i hope this helped

Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

Mathematics deals with the relationship between two numbers or quantities using the notions of ratio and proportion. Two numbers are compared in a ratio, which is often represented as a fraction. For example, the ratio of pounds to oranges in a basket could be 3:2, implying that there are three apples for every two oranges. Contrarily, proportion is the connection between two ratios. It is an equation, in other words, when two ratios are equal. The ratio of apples to oranges in a basket may be 3:2, whereas the ratio of apples to all the other fruits in the basket might be 9:11. In this case, the two ratios are proportionate since 3/2 = 9/11.

How to solve?

Amy buys 12 envelopes for 26p each, so the total cost is 12 x 26 = 312p. She pays with a £5 note, which is equal to 5 x 100 = 500p. Therefore, she gets 500 - 312 = 188p in change. This is equal to £1.88.

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The least number of seats she is setting up 40 seats are needed.

The least number is zero (0). Zero (0) is the smallest natural number and is the additive identity of the set of whole numbers. It is the only number that is neither positive nor negative and is, therefore, regarded as neither odd nor even. Zero (0) is essential in mathematics and is used to represent the absence of a quantity. It is also used to represent the additive identity of real numbers and complex numbers.

Given: Mandy can place 8 seats at each table or 10 seats at each table with no left over.

We have to find the least number of seats needed.

Find the prime factors of 8:

⇒ 8 = 2 x 2 x 2 = 8 = 2³

Find the prime factors of 10:

⇒ 10 = 2 x 5

Find the LCM of 8 and 10:

⇒ 8 = 2³

10 = 2 x 5

LCM = 2³ x 5

LCM = 40

Hence, a minimum of 40 seats are needed.

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Answer:

137

Step-by-step explanation:

triangles always equal 180 degrees for internal angles

20+23-180

Answer: [tex]-\frac{1}{2}, -\frac{1}{4} , -\frac{1}{6}, -\frac{1}{7} , -\frac{2}{3}[/tex]

Step-by-step explanation:

A simple way to find a rational number is to make sure the fraction is between the given numbers. Below are five examples, but there are many more.

[tex]-\frac{1}{2}, -\frac{1}{4} , -\frac{1}{6}, -\frac{1}{7} , -\frac{2}{3}[/tex]

Step-by-step explanation:

y = 160°

take the derivative of both sides

y'= d÷dx(160°)

the derivative of a constant is always 0

y' = 0

On solving the provided question, the capital that is placed at 25% for 3 years, to obtain an interest of $ 1620 will be $3,164.06

interest you receive is equal to as - compound interest. Using simple math, you can see how this works: if you have $100 and it earns 5% interest annually, you will have = $105 at the end of the 1st year. You'll have = $110.25 at the conclusion of the 2ndyear.

To calculate, we will use the following

[tex]First, convert R as a percent to r as a decimal[/tex]

r = R/100

r = 25/100

r = 0.25 rate per year,

Then solve the equation for A

[tex]A = P(1 + r/n)^{(nt)}[/tex]

[tex]A = 1,620.00(1 + 0.25/1)^{(1)(3)}[/tex]

A = 1,620.00(1 + 0.25)(3)

A = $3,164.06

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The total distance Desiree travelled was 14km.

Always remember,

Average speed= Total distance travelled/ Total time taken

So, in this case, we have to find the distance,

Distance= Speed × Time

When she  ran 16km per hour for 30 minutes,

⇒ Distance= 16×30/60

⇒ Distance= 8km --------------------(1)

When she ran 8km per hour for 45 minutes,

⇒ Distance= 8×45/60

⇒ Distance= 6km --------------------(2)

Adding equations (1) and (2) we get,

⇒ Distance = 8+6=14km

Hence, the Total Distance travelled was 14km.

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19.89% is the percentage decrease of the depth of the lake from January to August.

A quantity or ratio can be expressed as a percentage of 100 by using the word "percentage." Comparing two or more numbers and illustrating how significantly one number differs from the other in proportion to the whole is a popular usage for this technique. If a baseball originally costs $12 and is discounted by 20%, for instance, its new price would be $12 x 20/100 = $2.40 less than the original price. In other words, after the reduction, the ball will cost $12 - $2.40 = $9.60. A percentage may often be determined by dividing a quantity by its entirety and multiplying the result by 100. For instance, if a baseball bat costs $100 and is reduced by 30%, its new cost would be $100 x 30/100, which equates to $30 less.

How to solve?

The depth of the lake decreased by 943 - 754.4 = 188.6 feet from January to August.

The percentage decrease is (188.6 / 943) x 100 = 19.89%

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Answer: y=-4x+6

Step-by-step explanation:

Answer:

The answer is 246

Step-by-step explanation:

So,

S₁₂ = 12/2 [2(4) + (12 - 1)3]

S₁₂ = 6 [8 + (11)3]

S₁₂ = 6 × (8 + 33)

S₁₂ = 6 × 41

S₁₂ = 246

Thus, The S₁₂ of given A.P is 246

Answer: I think its 3.5

Step-by-step explanation:

The function is an exponential growth function growth decay percent rate of change of the function is 110 %.

Given :

What type of exponential function is f(x)=0. 75(2. 1)^x what is the function's percent rate of change.

we know that,

exponential growth function in the form of y = a ( 1 + r )^x

on comparing both functions we get ,

1 + r = 2.1

r = 2.1 - 1

r = 21 / 10 - 1

= 21 - 10 / 10

= 11 / 10

= 1.1

converting into percentage:

= 1.1 * 100 %

= 110 %

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Answer:

Each Girl scored 3.71 points

Each boy scored 12 points

Answer:

The range is found by the y axis. Find the length by comparing it to the graph.

Step-by-step explanation:

False, an industry standard is to randomly select 10% of the completed surveys for purposes of making a call-back to validate that the interview was conducted.

What are industries standards?

A collection of standards within an industry referring to how activities are typically carried out in their respective domains of production.

                  In other words, it refers to the standards that are commonly accepted by an industry's participants.

Why is this industry norm?

Industry standards are primarily intended to make products compatible with one another and to ensure that consumers can mix and match products from various brands without risk.

                             Best Industry Standards refers to benchmarks that, taking into account elements like the nature and size of the parties, are in the upper quartile in the relevant industry for the delivery of comparable services that are essentially similar to the Services or the relevant part of them.

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