Determine if the following statements are true or false based on the definitions of the functions:

f(x) = 1/x^2 and t(x) = −1/(x+2)^2

Answer:

See attached image.

Step-by-step explanation:

\(\ln{x} \ge 3\)

To solve for x, use the exponential function e^x (it's the inverse of the ln function).

\(e^{\ln{x}} \ge e^3\\x \ge e^3\)

A calculator gives the approximation 20.09

Step-by-step explanation:

The statement 'let B1⊇B2⊇... be a list of nested decreasing sets with the property that each Bn contains an infinite number of elements, then ⋂∞n=1 Bn must also contain an infinite number of elements.' is true.

A set comprises elements or participants that may be mathematical items of any sort, together with numbers, symbols, points in the area, strains, different geometric paperwork, variables, or even different units. a set is a mathematical version for a collection of various things.

If B1⊇B2⊇B3⊇B4⋯ are all units containing an infinite quantity of elements, then the intersection ⋂ (from n=1 to ∞) Bn is limitless as well set that is real because even the smallest of the subsets inside the given nested listing has a countless range of elements set

The intersection of such units will bring about a set containing an infinite variety of common elements.

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The complete question is:

the statement ""let b1 ⊇ b2 ⊇ .. be a list of nested decreasing sets with the property that each bn contains an infinite number of elements. then ∩[infinity] 1 bn must also contain an infinite number of elements."" is true of false?

Answer:

The coordinates of B' are (-3, 5).  

Step-by-step explanation:

For every 90 degrees rotated, the coordinate numbers switch and one is multiplied by -1, when clockwise it's the 2nd one, and when counterclockwise, it's the 1st.

The range of acceptable values for production to continue working of the company without stoppage is 15.85 to 16.15.

Range is the area of fluctuation between the upper and lower limit. The range of the acceptable values is all the values between the upper and lower limit.

Here, a company manufactures 16-oz boxes of cereal.  Now, this boxes are randomly weighted to ensure the correct amount.

As the discrepancy in weight is more than 0.15 oz then the production of the company is stopped.

To proper functioning of the company without stoppage, the limit of the production should be with in 0.15 oz.

The company produce, 16-oz boxes of cereal and the disperancy is 0.15 oz. Thus the value of the lower limit will be,

\(L=16-0.15\\L=15.85\rm \; oz\)

The value of the upper limit will be,

\(U=16+0.15\\U=16.15\rm \; oz\)

Thus, the range will be {15.85-16.15 oz}

Hence, the range of acceptable values for production to continue working of the company without stoppage is 15.85 to 16.15.

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Answer:

C

Step-by-step explanation:

I think,  :)

The boxplot below displays the arm spans for 44 student . The statement that is not true from the given option is

Approximately 25% of the arm spans are less than 180 cm

Option C

Given :

The boxplot below displays the arm spans for 44 students.

The five-number summary for the data is 143, 162, 168, 180, and 202.

From the given five number summary we can see that

minimum =143

First Quartile (25%)= 162

Median (50%)= 168

Third quartile (75%)= 180

Maximum =202

Now we analyze the statements

Approximately 75% of the arm spans are less than 180 cm. Its true because third quartile is 75% that is equal to 180

Approximately 50% of the arm spans are less than 168 cm.. Yes its true because median is 168

Approximately 25% of the arm spans are less than 180 cm. It is false because first quartile 25% is 162. So , 25% of the arm spans are less than 162 cm

Approximately 75% of the arm spans are greater than 162 cm. It is true . because  25% of the arm spans are less than 162 cm

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The product of the expression is 2x⁶ + 23x³ + 63

First, we should note that algebraic expressions are described as expressions that are composed of coefficients, terms, constants, variables and factors.

These algebraic expressions are also made up of mathematical operations, such as;

From the information given, we have that;

2x3 +9 and x3 +7?

Then,

(2x³ + 9)(x³ + 7)

expand the bracket

2x⁶ + 14x³ + 9x³ + 63

add like terms

2x⁶ + 23x³ + 63

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Answer:

(x-5)²=98/2

x-5=√98/2

98/2=49

x-5=√49

= 7

x= 5 ± 7

= 12,-2

ans is C

(a) P(0) = 117218, P(10) = 195468, P(15) = 229593, P(20) = 263718, P(25) = 297843. The population is growing.

(b) dp/dt = 787.5.

(c) P'(0) = 787.5, P'(10) = 668.75, P'(15) = 543.75, P'(20) = 412.5, P'(25) = 275. The rate of growth is decreasing

(a) To evaluate P for t = 0, 10, 15, 20, and 25, we substitute the given values of t into the population model:

P(0) = -14.77 + 117.218 = 102.448 thousand people

P(10) = -14.77 + 787.5(10) + 117.218 = 875.718 thousand people

P(15) = -14.77 + 787.5(15) + 117.218 = 1,321.968 thousand people

P(20) = -14.77 + 787.5(20) + 117.218 = 1,768.218 thousand people

P(25) = -14.77 + 787.5(25) + 117.218 = 2,214.468 thousand people

These values represent the estimated population of the country (in thousands) at the given points in time. As we can see, the population is growing over time.

(b) To determine the population growth rate, we take the derivative of the population model with respect to time:

dP/dt = 787.5

This means that the population is growing at a rate of 787.5 thousand people per year.

(c) To evaluate dP/dt for the same values as in part (a), we substitute the values of t into the expression for dP/dt:

P'(0) = 787.5 thousand people per year

P'(10) = 787.5 thousand people per year

P'(15) = 787.5 thousand people per year

P'(20) = 787.5 thousand people per year

P'(25) = 787.5 thousand people per year

These values are all the same, indicating that the population growth rate is constant over time. However, since the population is growing exponentially, the rate of growth (in percentage terms) is actually decreasing over time.

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Answer:

she spent $43.75

Step-by-step explanation:

you basically need 35% of $125

cool trick with this is "of" always means multiplication

35% x 125= 43.75

she spent $43.75

Shonda spent the amount of $43.75 on the concert ticket.

The percentage is defined as a ratio expressed as a fraction of 100.

To find out how much Shonda spent on the concert ticket, we can use the following proportion:

(35%) × 125 = x/1

where x is the amount of money spent on the concert ticket, and we know that 35/100 (or 0.35) is 35% of 125.

Convert percent into decimal form and solve for x:

(0.35) × 125 = x

Apply the multiplication operation, and we get

x = 43.475

Therefore, she spent $43.75 on the concert ticket.

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Answer:

√41

Step-by-step explanation:

Use a² + b² = c²

a = 4

b = 5

4² + 5² = c²

4² = 16

5² = 25

16 + 25 = c²

41 = c²

You need to get ² away from c, so square root both sides.

√41 = √c²

√41 = c

√41 is in its simplest form, so it is left as √41.

Answer:

Step-by-step explanation:

Answer:

use pythag theorum you get 11.7 i thinkkk

Step-by-step explanation:

Try creating a triangle using the length of x and the length of y, so, you can tell the line goes from -5 to 5 on the x axis so that means its 10 long on x and 0 to 6 on y axis so its 6 long on y... then create a triangle and use the pythagorean theorem (the square root of (10 squared + 6 squared) which is around 11.7 .... i think, hope that helps! -prowl

SORRY THIS IS MY FIRST TIME ANSWERING A QUESTION ON HERE. I PUT IT IN THE WRONG PLACE THE FIRST TIME LOL

Answer:

yes it is fair

Step-by-step explanation:

as long as there are multiple of the same block, then the game is just

Answer:

2

Step-by-step explanation:

Rational numbers can be written as decimals by dividing the numerator by the denominator. The result can be a terminating decimal (ends) or a repeating decimal (pattern repeats indefinitely).

Rational numbers can be written as decimals by dividing the numerator (the top number) by the denominator (the bottom number) of the fraction.

For example, let's consider the rational number 3/4. To write it as a decimal, we divide 3 by 4:

3 ÷ 4 = 0.75

So, 3/4 as a decimal is 0.75.

Similarly, for a rational number like 1/2:

1 ÷ 2 = 0.5

Hence, 1/2 as a decimal is 0.5.

In general, when dividing a numerator by a denominator, the result can be a terminating decimal (where the division ends) or a repeating decimal (where the division repeats a pattern indefinitely). For example, 1/3 as a decimal is 0.3333..., with the digit 3 repeating.

It's important to note that not all rational numbers can be expressed as terminating or repeating decimals. For instance, the square root of 2 (√2) is a rational number, but it cannot be precisely expressed as a decimal and is known as an irrational number.

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A boxplot is a graphical representation of the distribution of numerical data. In a boxplot, data is split into four quartiles, with each quartile comprising a box, whisker, and outlying data point(s). Here is a correct parallel boxplot for the given data on the weights of 11 male lions and 12 female lions (all adults) without using R:


Here are the steps for constructing the parallel boxplot:

Step 1: Find the Five-Number Summary (Minimum, Q1, Median, Q3, Maximum) for each group (males and females)

Males:
- Minimum: 142.7 kg
- Q1: 167.1 kg
- Median: 176.6 kg
- Q3: 181.7 kg
- Maximum: 191.8 kg

Females:
- Minimum: 76.9 kg
- Q1: 96.7 kg
- Median: 119.4 kg
- Q3: 138.3 kg
- Maximum: 139.9 kg

Step 2: Draw the box for each group using the median, Q1, and Q3 values. The line inside the box represents the median.

Step 3: Draw whiskers for each group. The whiskers connect the boxes to the minimum and maximum values, excluding any outliers.

Step 4: Identify any outliers. These are values that are more than 1.5 times the interquartile range (IQR) above the upper quartile or below the lower quartile. Outliers are denoted as dots outside of the whiskers.

Step 5: Add a legend to differentiate between the two groups.

In this boxplot, the male group is shown in blue, and the female group is shown in pink.

Therefore, a correct parallel boxplot for the given data on the weights of 11 male lions and 12 female lions (all adults) is shown above.

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Answer:

4 degrees farenheight

Step-by-step explanation:

Answer:

4 degrees

Step-by-step explanation:

7am to 11am is 4 hours.

So now multiply 4 hours*4* F = 16

So the temperature decreased 16 degrees.

20-16=4

It was 4 degrees at 11 am.

The consequence of violating the assumption of Sphericity can be significant. It reduces statistical power, effects the distribution of the F-statistic, and raises the rate of Type I errors in post hocs.

Sphericity refers to the homogeneity of variances between all possible pairs of groups in a repeated-measures design. When this assumption is violated, it can result in a distorted F-statistic, which in turn affects the results of post hoc tests.
The correct answer to the question is c. It reduces statistical power, effects the distribution of the F-statistic, and raises the rate of Type I errors in post hocs. This means that violating the assumption of Sphericity leads to a decreased ability to detect true effects, an inaccurate representation of the true distribution of the F-statistic, and an increased likelihood of falsely identifying significant results.
According to statistics, the consequence of violating the assumption of Sphericity is not a rare occurrence. Therefore, it is essential to ensure that the assumptions of your statistical analysis are met before interpreting your results to avoid false conclusions.
In conclusion, violating the assumption of Sphericity can have severe consequences that affect the validity of your research results. Therefore, it is crucial to understand this assumption and check for its violation to ensure the accuracy and reliability of your statistical analysis.

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Okay, here we have this:

Considering that a function is one-to-one if and only if no horizontal line intersects its graph more than once.

So, according with this we any horizontal line that is drawn on the line touches only one point on it, therefore the function is one to one.

The area of the kite is 9√5 square units.

Given is quadrilateral which is a kite with vertex (-1, 0) , (4, -2) , (1, -4) and (-5, -2) we need to find the area.

To find the area of a kite, we can use the formula:

Area = (d₁ × d₂) / 2

where d₁ and d₂ are the lengths of the diagonals of the kite.

First, let's find the lengths of the diagonals.

Diagonal 1: Connect the vertices (-1, 0) and (1, -4)

d₁ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(1 - (-1))² + (-4 - 0)²]

= √[2² + (-4)²]

= √[4 + 16]

= √20

= 2√5

Diagonal 2: Connect the vertices (4, -2) and (-5, -2)

d₂ = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-5 - 4)² + (-2 - (-2))²]

= √[(-9)² + 0²]

= √[81 + 0]

= √81

= 9

Now, we can calculate the area of the kite:

Area = (d₁ × d₂) / 2

= (2√5 × 9) / 2

= (18√5) / 2

= 9√5

Therefore, the area of the kite is 9√5 square units.

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You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.

To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.

The formula to calculate the present value of an annuity is:

PV = PMT × [1 - (1 + r)⁻ⁿ] / r

Where:

PV is the present value of the annuity (the amount you should pay initially)

PMT is the payment amount received annually ($1500 in this case)

r is the interest rate per period (6.28% or 0.0628)

n is the total number of periods (9 years)

Let's substitute the values into the formula:

PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628

Calculating this expression:

PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628

PV = $1500 × [1 - 0.575255] / 0.0628

PV = $1500 × 0.424745 / 0.0628

PV ≈ $10117.09

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Circle M has a center (h+d, k+e) and the radius is rs. Therefore, option C is the correct answer.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Given that, circle B has a center (h, k) and a raius of r. Circle B is translated d units to the right and e units up. Then it is dilated about its new center by a scale factor s resulting in a new circle

Translation rules:

When the shape is moved towards the right by k units, then replace x with x + k.

When the shape is moved up by k units, then replace y with y + k.

Now, (h, k)→(h+d, k+e) and the radius is rs.

Therefore, option C is the correct answer.

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Step-by-step explanation:

the answer is 3

This is because you divide both heights, 12 and

4 and you get 3.

Then divide 48 and 16 which gives you 3.

hope it helps!

Answer:

9!!!  

Step-by-step explanation:

12×48= 576

4×16 = 64

576÷64 = 9

I got it right on my lesson.

Using cοmpοund interest , the tοtal wοrth after 20 years is $2,330.48.

The interest that is calculated using bοth the principal and the interest that has accrued during the previοus periοd is called cοmpοund interest. It differs frοm simple interest in that the principal is nοt taken intο accοunt when determining the interest fοr the subsequent periοd with simple interest.

Here the principal P= $500

Rate οf interest r = 8%

Number οf years = 20 years,

Nοw using cοmpοund interest fοrmula then,

=> Total amount = \(P(1+\frac{r}{100})^t\)

=> A = \(500(1+\frac{8}{100})^{20}\)

=> A = \(500(1+0.08)^{20}\)

=> A = \(500(1.08)^{20}\)

=>A = $2,330.48

Hence after 20 years , nft's total worth is $2,330.48.

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Answer:

A) SAS i believe this is the right answer

Step-by-step explanation:

Hope you do well on your test! Good luck

Answer:

Let be cost price =Rs.100

Then mark price =Rs.120

∴ Selling price =90% of 120

=

100

120×90

=Rs.108

Profit = Selling price− Cost price

=Rs.(108−100)=Rs.8

Profit % =

100

8×100

=8%

Answer:

Step-by-step explanation:

so coz there was already 11 inches but after 20min the tank is 56inch so wht u do is this

45+11t if im right

2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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