Find the domain and solve.
(d) log₄²(1+x²)=0.25

Answer:

Rectangle

Step-by-step explanation:

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A rectangle uses A=lw to calculate area

Where l is length and w is width

Hope this helps,

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Using the cross-multiplication method, we know that the actual height of the building is 91 m.

One might cross-multiply an equation between two fractions or rational expressions in mathematics, more specifically in elementary arithmetic and elementary algebra, to make the equation simpler or to find the value of a variable.

To cross-multiply two fractions, multiply the first fraction's numerator by the second denominator and the second fraction's numerator by the first fraction's denominator.

So, we know that:

The height of the building scale is 14 cm.

The scale is 2 cm and the actual height is 13 m.

Now, the actual height of the building will be:

14/x = 2/13

Use cross-multiplication method as follows:

14/x = 2/13

2x = 14 * 13

2x = 182

x = 182/2

x = 91 m

Therefore, using the cross-multiplication method, we know that the actual height of the building is 91 m.

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The F ratio is 1.2.

What is statistic?

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.

30/25 = 1.2

In an ANOVA, this statistic is used in the F test to test the hypothesis that the group means are not equal to one another. The F ratio is calculated as follows:

Fobs=MSB/MSW

30/25 = 1.2

Where MSB is the mean square between the groups and MSW is the mean square within the groups.

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Therefore, by using mean and standard deviation the required probability is P( 38 ≤ x ≤ 90) = P(-1<x<3) = 0.83999

The mean (also known as the arithmetic mean, as opposed to the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the "average.

A standard deviation (or) is a measure of how dispersed the data is in relation to the mean. A low standard deviation indicates that data are clustered around the mean, whereas a high standard deviation indicates that data are more spread out.

Given:

mean = μ = 51

Standard deviation = σ = 13

as per the question, the probability that X is between 38 and 90 will be

P( 38 ≤ x ≤ 90)

By using the 0.68 - 0.95 - 0.997 rule

P( 38 ≤ x ≤ 90) = P((x-μ)/σ≤z≤(x-μ)/σ)

P( 38 ≤ x ≤ 90) =P((38-51)/13≤z≤(90-51)/13)

from z standard normal table  

P(x<-1) = 0.15866

P(x>3) = 0.0013499

Therefore, by using mean and standard deviation the required probability is

P( 38 ≤ x ≤ 90) = P(-1<x<3) = 0.83999

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Answer: 3,-3  

Step-by-step explanation:

|6x-1| = 17

For absolute value problems there is always two solutions. They will both be the same number, one positive and one negative.

6x-1 = 17

Add 1 to both sides.

6x-1 +1 = 17+1

6x=18

Now, divide by 6.

6x/6=18/6

x = 3

The two answers that would be correct are 3,-3.

Here is the frequency table based on the data:

1 - 200                7

201 - 400            1

401 - 600            2

601 - 800            3

801 - 1000           1

1001 - 1200          1

1201 - 1400

1401 - 1600          1

1601 - 1800         1

A  frequency table is a table that is used to compress a large dataset into a smaller format that can be easily interpreted. A  frequency table is usually made up of a class interval and frequency.

A class is the group of a numbers. The frequency of the class is the total number of times that numbers within the class appear in the dataset.  For example in the class 100 - 200, there are 7 numbers in the dataset that have a value between 100 and 200. This means that the frequency of 100-200 is 7.

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The number of possible wins if the ball lands on red is  4.86 games.

Let there be 100 successive spins,

Random Variable (winnings): $1, -$1

Associated probabilities:

P($1) = 18/38 =9/19

P(-1) = 20/38 = 10/19

Expected winnings is (9/19)*1 + (10/19)*-1

= -1/19 on one spin.

= -2/19 on two spins

= -2/19 on a single spin for $2

= -100/19 on 100 successive spins

since there are 100 spins,  n =100

18 out of 38 spots are red, thus p=18/37 =0.486

expected number of wins = np

= 100* 0.486

=4.86

Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring. Probability is defined as the degree to which something is likely to occur.

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Step-by-step explanation:

be a function, there needs to be one unique

value of +y+ for every +x+

-----------------------------

The 1st set has 5 different values of +y+

for +x+=+1+ and violates definition

--------------

The 2nd set is a function

-----------------------

The 3rd set has

( 1,2 ) & ( 1,1 )

( 2,3 ) & ( 2,2 )

( 3,4 ) & ( 3,3 )

Each of these pairs violates the definition

----------------

The 4th set has ( 2,-7 ) & ( 2,0 ) which

violate definition

Answer:

3x + 12

Step-by-step explanation:

5x + 6(x - 2) - 8(x - 3) ← distribute parenthesis

= 5x + 6x - 12 - 8x + 24 ← collect like terms

==(5x + 6x - 8x) + (- 12 + 24)

= 3x + 12

The numbers, square root of 26 and twenty eight sixths can be compared using the known values of the square root of a number near to 26, such as 25, and inequality symbols, which indicates;

An inequality is a comparison between values that have different measures or magnitude, such that one values may be less than, <, greater than, >, or not equal to, ≠, the other value in the comparison.

The square root of 26 is √(26)

Twenty eight sixths is [tex]\dfrac{28}{6}[/tex]

26 is a larger number than 25, therefore;

√(26) > √(25) = 5

The square root of 26, is larger than 5; √(26) > 5

Expressing the fraction of twenty eight sixths as a proper fraction, indicates

[tex]\dfrac{28}{6} = 4\frac{4}{6} =4\frac{2}{3}[/tex]

Twenty eight sixths is four and two thirds, therefore;

Four and two thirds is less than 5, therefore;

[tex]4\frac{2}{3} < 5[/tex]

Substituting twenty eight sixths with four and two thirds, indicates;

[tex]\dfrac{28}{6} = 4\frac{2}{3} < \sqrt{26} > 5[/tex]

[tex]\dfrac{28}{6} = 4\frac{2}{3} < 5 < \sqrt{26}[/tex]

[tex]\dfrac{28}{6} < \sqrt{26}[/tex]

The correct option is therefore;

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7,701 divided by 36 is 213.91

The division is the process of sharing a collection of items into equal parts and is one of the basic arithmetic operations in mathematics. For example, we can divide a group of 20 members into 4 groups of 5 members

The number 7701 is called the numerator or dividend, and the number 36 is called the denominator or divisor.

The quotient of 7701 and 36, the ratio of 7701 and 36, as well as the fraction of 7701 and 36 all mean (almost) the same:

7701 divided by 36, often written as 7701/36

Therefore, 7701 divided 36 is 213.91

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Solution:

Given:

(-28yx+ 31y²[tex]x^{4}[/tex])/(-4y²[tex]x^{4}[/tex])

[tex]\frac{-28yx}{-4y^{2}x^{4} }[/tex] + [tex]\frac{31y^{2}x^{4}}{-4y^{2} x^{4} }[/tex]

[tex]\frac{7}{x^{3} y}[/tex] + [tex]\frac{31}{4}[/tex]

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After dividing the given equation, the answer in the simplest form is [tex]\frac{7}{x^{3} y}- \frac{31}{4}[/tex]

What do you mean by simplest form?

A fraction with a denominator and numerator that are both relatively prime has the simplest form. It indicates that the fraction's numerator, which is the portion at the top of the fraction, and denominator, which is the portion at the bottom, do not share any factors other than one.

An amount that represents a fraction of a whole is called a fraction. A fraction's reduced form is another name for its simplest form. A fraction with a common factor of one, such as 34, has the simplest form. Although 2/4 can be further simplified and written as 12, it is not the most basic form. The fractions 12 and 2/4 are equivalent in this case, we can also say.

Given:

⇒(-28yx+ 31y²[tex]x^{4}[/tex])/(-4y²[tex]x^{4}[/tex])

⇒ [tex]\frac{-28yx}{-4x^{4}y^{2}}[/tex] + [tex]\frac{31y^{2}x^{4}}{-4y^{2} x^{4} }[/tex]

⇒     [tex]\frac{7} {x^{3} y}[/tex] - [tex]\frac{31}{4}[/tex]

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Answer: 720.0 cm³

Step-by-step explanation:

To convert the volume of the die from millimeters to centimeters, we need to divide the volume by the conversion factor that relates millimeters to centimeters. Since 10 millimeters is equal to 1 centimeter, the conversion factor is 10.

To convert the volume to centimeters, we can divide it by the conversion factor:

7200 mm³ / 10 = 720 cm³

This means that the volume of the die is 720 cm³. Rounded to the nearest tenth, the volume of the die is 720.0 cm³.

Answer:

Step-by-step explanation:

First write the reciprocal of 5/9 which it is 9/5 then multiply by 5 which it equal to 36/5

Answer:

Below

Step-by-step explanation:

from 800 to 1020 is  a  220/800 * 100% = 27.5% increase each year

P(t) = 800 ( 1 + .275)^t    

3300 = 800 ( 1+.275)^t

3300 / 800  = 1.275 ^t     LOG both sides

.615423 / LOG 1.275 = t   = 5.83 years

If each large truck $70,000. Past experience shows that they need twice as many vans as small trucks. The number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.

Since the company intends to purchase 320 vehicle, Let write this equation:

C + S + L = 320 (Eq. 1)

Total cost of the vehicles:

25C + 80S +70L = 16,000 (Eq. 2)  (Divided by 1000 to keep the numbers small)

Number of commercial vans is twice the number of small trucks,

C = 2S

Substituting 2S in place of C in Eq. 1 and Eq. 2

2S + S + L = 320

25(2S) +80S +70L = 16,000

130S + 70L = 16,000

Multiplying the first of those equations by 70

210S + 70L = 22,400

130S + 70L = 16,000

Subtracting the second equation from the first:

80S = 6400

Divide both  side by 80S

S = 6400/80

S = 80 (Small truck)

Then:

C = 2S

C= 2(80)

C= 160 (Commercial van)

So,

C + S + L = 320

160 + 80 + L = 320

L = 320 - 160 - 80

L =80 (Large van)

Therefore  the number of each type of vehicle they can buy is; Small truck 80, Commercial van 160, Large van 80.

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For the given word problem, the cost to rent each chair is $5.25 and each table is $2.625

What is a word problem?

A word problem is a short passage presenting a "real-life" situation where an issue needs to be solved using math. The word problem for groups is a classic example, but there are numerous additional examples as well. This question is in many significant circumstances undecidable, which is a profound conclusion of computational theory.

Let C be the cost per chair

Let T be the cost per table

The total cost to rent 5 chairs and 6 tables is $53.

Then, 5C+6T=42 ................ (i)

The total cost to rent 3 chairs and 2 tables is $21.

Then, 3C+2T=21 ................. (ii)

Now, by solving both equations, multiply (ii) by 3 and subtract (i), we get

9C - 5C = 63 - 42

or, 4C = 21

or, C = $5.25

Then, T = (21-3*5.25)/2 = $2.625

Hence, the cost to rent each chair is $5.25 and each table is $2.625

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Answer: 7% at 6 years would best fit their payment option. They would then be paying $238.69 monthly and which is under $250, I hope this helps!

The vertex and range of y = |4x + 8| - 1 will be (-2, -1) ; -1 ≤ y < ∞ respectively. Using the concept of function -

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predetermined domain and range. This specific sort of connection is what it is called.

Given that,

y = |4x +8| - 1

To get the vertex of y = |4x +8| - 1 as follows.

Where the absolute values are zeros are the vertex points of the absolute value function.

or, |4x +8| = 0

or, 4x +8= 0

or, 4x = -8

or, x = -2

Substitute the value into an original function,

y = |4(-2) + 8| - 1

y= 0 - 1

y = - 1

As a result, the vertex is at (-2, -1)

Remember that the domain is specified in the range of (-∞, ∞) while determining the range.

Given that |4x + 8| ≥ 0 , (absolute value is always 0 or positive)

The result of adding -1 to the inequality's two sides is

|4x + 8| - 1 ≥ - 1

But since |4x + 8| - 1 is identical to f(x) = y, we have y = f(x) - 1, which means that the range is specified for all values larger than -1.

So the range is -1 ≤ y < ∞

Thus,the vertex and range of y = |4x + 8| - 1 will be (-2, -1) ; -1 ≤ y < ∞ respectively.

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In a two-way ANOVA, the two independent variables are known as factors. Two variables, or factors, are supposed to influence the dependent variable.

First, let's understand what is 2-way ANOVA using 2 factors.

To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilized. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.

To evaluate if there is a statistically significant difference between the means of three or more independent groups that have been divided on two factors, a two-way ANOVA is utilized.

Given is that the first factor has 4 levels and the second factor has 9 levels.

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Answer:

$11.25

Step-by-step explanation:

If Stephen receives a 4.5% hourly pay increase each year, his hourly pay will be $10.30 + (4.5% * $10.30) = $10.30 + $0.465 = $10.765 after the first year.

In the second year, his hourly pay will be $10.765 + (4.5% * $10.765) = $10.765 + $0.486 = $11.251.

Therefore, in two years, Stephen's hourly pay will be $11.251. This is closest to the answer choice of $11.25, so it is the correct answer.

the domain =  [1,∞) and range = [4 , ∞) for the given equation.

What is domain and range?

The set of all doable values that qualify as inputs to a operate is understood because the domain of the operate, or it may also be outlined because the entire set of values doable for freelance variables.

The set of all the outputs of a operate is thought because the vary of the operate or when subbing the domain, the whole set of all values attainable as outcomes of the variable.

Main body:

Given equation =

y=8x-4

as x is the number of days

and,y is the weight of the plant.

so x can not be negative

hence the domain of x = [1,∞)

As x is positive , y can not be negative as well.

Hence the domain =  [1,∞) and range = [4 , ∞)

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The value of x is 9 and the value of y is 4.

What is the congruent triangle?

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

The system of equations is

x + 3 = 3y ....(i)

x = y + 5 .....(ii)

Putting x = y + 5 in equation (i):

y + 5 + 3 = 3y

y + 8 = 3y

3y = y + 8

3y - y = 8

2y = 8

y = 4

Putting y = 4 in equation (ii)

x = 4 + 5 = 9

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The inverse of y=-x²+9 is [tex]x=\sqrt{9-y}[/tex]

What is Inverse of a Function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

The output of a function is returned by the inverse function, which also returns the initial value.

If f and g are inverse functions, then f(g(x)) = g(f(x)) = x. The initial value is fetched via a function that is its inverse.

For instance, f(x) = 2x + 5 = y

Therefore, the inverse of f is g(y) = (y-5)/2 = x. (x).

The relationship that results from swapping out an independent variable with a variable that depends on a given equation; the inverse may or may not be a function.

A function is said to be an inverse function if its own inverse is represented by the symbol f-1.

[tex]x^2=9-y\\\\\x=(9-y)^\frac{1}{2}\\\\ x=\sqrt{9-y}[/tex]  is the inverse of y=-x²+9

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Answer:

A. The new maturity value of the loan would be $15,000

B. The maturity data of the loan would be June 20

Step-by-step explanation:

N/A

The inequality and statement about the possible amount of money in the other piggy bank is 0 ≤ PB₂ ≤ 2.69.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10.

∴ PB₁ + PB₂ ≤ 10.

One piggy bank has $7.31 in it.

∴ 7.31 + PB₂ ≤ 10.

PB₂ ≤ 2.69.

So, The amount in PB₂ can be  0 ≤ PB₂ ≤ 2.69.

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Ginny charges $80 for an initial fee, and Bob charges $60 for an initial fee.  Bob charges less for an initial fee.

What is a function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

f(x)=60x+80 is function that represents the charge to Ginny's customers, where x represents the number of hours of labor.

To find initial fee, put x = 0 in the given function.

Put x = 0 in f(x) = 60x + 80:

f(0) = (60×0) + 80

f(0) = 80

The initial fee is $80.

From the table,

When x = 0, cost = $ 60.

The initial fee is $60.

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Answer:

Step-by-step explanation:

if you send 12 messages a day.

and your sister sends and unkown number of texts per day but together you both send 26 number of total texts.

Then, suppose your sister sends X number of texts.

Then

X + 12 = 26

X = 26 - 12

X = 14