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Answer:

14 ×3 = 42 cm.

Step-by-step explanation:

Let's see

#1

#2

Answer:

\(x=\frac{1}{4}\)

Step-by-step explanation:

Given:

\(2log(\frac{2}{3})=\frac{1}{2}log(x)-log(18)+log(16)\)

Use the Power Rule Law:

\(log(\frac{2}{3}^2)=log(x^{1/2})+log(16)-log(18)\)

Use the Quotient Rule Law:

\(log(\frac{4}{9})=log(\sqrt{x})+log(\frac{16}{18})\)

Use the Product Rule Law:

\(log(\frac{4}{9})=log(\frac{16\sqrt{x}}{18})\)

Simplify:

\(log(\frac{4}{9})=log(\frac{8\sqrt{x}}{9})\)

\(\frac{4}{9}=\frac{8\sqrt{x}}{9}\)

\(4=8\sqrt{x}\)

\(\frac{4}{8}=\sqrt{x}\)

\(\frac{1}{2}=\sqrt{x}\)

\(\frac{1}{4}=x\)

Answer:

Working the multiplication part ( that is; 6×8)

Step-by-step explanation:

Answer:

2.5+2.5+45+45

=95.0m

therefore area of the square= 95.0m

45m×0.5=45.5÷95=

Step-by-step explanation:

2.5m

2.5 m tiles are required

\(area = 2.5 \times 45 = 192.5 \: squared \: cenimetre \\ \\ no \: of \: tiles = 0.5 \times 0.5 = 0.25 \\ 192.5 \div 0.25 = 770tiles\)

The correct statements regarding sum and subtraction with negative numbers are given as follows:

When two negative numbers are added, the result is negative, as we keep the signal and then add the absolute amounts of each value, for example:

-5 + (-5) = -(5 + 5) = -10.

Hence the fourth statement is correct, while the first and the third are not.

When we subtract two negative numbers, we first transform the second number to positive, meaning that the result can be either positive or negative, as the result will take the signal of the higher value and their absolute amounts are subtracted.

Hence:

Hence the fifth and the sixth statements are correct.

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Answer:

14

Step-by-step explanation:

Follow BPEMDAS, or PBEMDAS in this case:

PBEMDAS stands for:

Parenthesis

Brackets

Exponents (& Roots)

Multiplication

Division

Addition

Subtraction

~

First, solve the parenthesis:

(7 + 7) = 14

Next, divide:

[14/7] = 2

Finally, multiply:

7 x 2 = 14

14 is your answer.

~

Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

Answer: y = -12x +20

Step-by-step explanation: 1. distribute the -12 into the (x-2), that equals -12+24

2. subtract the 4 from the left side to move it to the right side of the equation

3. add like terms, so 24 + (-4) or 24-4 which equals 20.

4. Answer: y=-12x+20

The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".

A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.

An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.

The quotient of a number"x" and 4 can be written as x/4.

So, one more than the quotient of a number x and 4 can be represented by the expression:

⇒ x/4 + 1,

Therefore, required mathematical expression is "x/4 + 1".

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The given question is incomplete, the complete question is

Write an expression to represent : One more than the quotient of a number x and 4.

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

Answer:

yes

Step-by-step explanation:

Yes it is, assuming we decide to use the Pythagorean Theorem to find the hypotenuse (10) it'll be possible considering the formula is c²=√a²+b²

(c being the longest side of the triangle)

a= 6 and b= 8

Answer:

8)b. 9)d.

Step-by-step explanation:

a biome is a type of group of plants and animals that belong in the same area. This is affected by how much rain a place gets, the temperatures of the place, and many other factors.

the atlantic ocean, russia, chile, central america, and alaska are not continents

Answer:

Question 8: B

Question 9: D

Step-by-step explanation:

8- The three examples explain 3 different climates and how the biomes affect the region.

9- The Continents are Asia, Africa, Europe, Antarctica, North America, South America, and Australia

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Answer:

B

Step-by-step explanation:

assuming you require problem 3

using the Sine Rule in Δ ABC and the exact values

sin45° = \(\frac{1}{\sqrt{2} }\) , sin30° = \(\frac{1}{2}\)

\(\frac{AB}{sin45}\) = \(\frac{BC}{sin30}\) , that is

\(\frac{8}{sin45}\) = \(\frac{BC}{sin30}\) ( cross- multiply )

BC sin45° = 8 sin30°

BC × \(\frac{1}{\sqrt{2} }\) = 8 × \(\frac{1}{2}\) = 4 ( multiply both sides by \(\sqrt{2}\) to clear the fraction )

BC = 4\(\sqrt{2}\)

Answer:

6887

Step-by-step explanation:

given

x + \(\frac{1}{x}\) = 83 ( square both sides )

(x + \(\frac{1}{x}\) )² = 83² = 6889 ← expand factor on left using FOIL

x² + 2( x × \(\frac{1}{x}\) ) + \(\frac{1}{x^2}\) = 6889

x² + 2(1) + \(\frac{1}{x^2}\) = 6889 ( subtract 2 from both sides )

x² + \(\frac{1}{x^2}\) = 6887

The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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Using the binomial distribution, it is found that:

A. The salesperson should expect 1.54 customers until he finds one that makes a purchase.

B. There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

For this problem, the probability of a success on a single trial is of p = 0.65.

The expected number of trials until q successes is:

E(X) = q/p

Hence, for one purchase:

E(X) = 1/0.65 = 1.54.

The salesperson should expect 1.54 customers until he finds one that makes a purchase.

For item B, the probability is P(X = 0) when n = 3 multiplied by 0.65, hence:

p = (0.35)³ x 0.65 = 0.0279.

There is a 0.0279 = 2.79% probability that a salesperson helps 3 customers until he finds the first person to make a purchase.

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To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

\(f(g(x)) = f(x - 4) = (x - 4)^2 + 4\)

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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Answer: 3/4 is greater than 1/2  

                                   >

Step-by-step explanation:

The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321.  the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.

To determine the largest absolute value:

We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.

To determine the smallest absolute value:

We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.

To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.

Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.

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The critical value for a confidence level of 98% with a sample size of 32 is given as follows:

t = 2.4528.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the equation presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are listed as follows:

The critical value, using a t-distribution calculator, for a two-tailed 98% confidence interval, with 32 - 1 = 31 df, is t = 2.4528.

(df is one less than the sample size).

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Based on the distribution of data, the box and whisker plot displays the results of the scientific test for two classes. It is incorrect to say that both sections have the same value for the third quartile.

The formulation of partial differential equation solutions uses distribution generalized functions. The likelihood of a specific value or range of values for a variable is known as the probability distribution. Cumulative distribution function, where the likelihood of a value not exceeding a certain value depends on that value. A list of the values recorded in a sample, or a frequency distribution. In coding theory, there are two types of distribution: inner and outer. distribution of a portion of a manifold's tangent bundle.Term distribution: the state of having all members of a category present. The distributive law from elementary algebra is generalized by the property of binary operations known as distributivity. the distribution.

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Answer:

Step-by-step explanation:

sum of angles in a triangle=180º

90+60x+30x=180

90+90x=180

90(1+x)=180

1+x=2

x=1

angle A=30º

According to the given function,

Domain = \(\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)\)

Vertical Asymptote = 4

Horizontal Asymptote = 0

X - intercept = No x - intercepts

Y - intercept = 1/4

Domain:

The  the domain of a function referred as the set of inputs accepted by the function

Given,

The function is,

\(f(x)=\frac{x-2}{x^2+2x-8}\)

Here we need to find the domain, vertical asymptote, horizontal asymptote,  x - intercept, and y-intercept.

To find the domain and intercepts, we have to plot the graph for the given function.

So, the graph of the function is attached below. It can be drawn using the graphing calculator.

As per the graph,

Domain = \(\left(-\infty, -4\right) \cup \left(-4, 2\right) \cup \left(2, \infty\right)\)

And the values of

x - intercept = No x-intercepts

y - intercept = 1/4

Now, the vertical asymptote is calculated as,

The line x=L is a vertical asymptote of the function f(x), if the limit of the function (one-sided) at this point is infinite.

In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.

So, find the points where the denominator equals 0 and check them.

x = -4

Then,

\(\lim_{x \to -4^+} \frac{1}{x + 4}=\infty\)

Since the limit is infinite, then x=−4 is a vertical asymptote.

And the horizontal asymptote is,

Line y=L is a horizontal asymptote of the function y=f(x), if either '

\(\lim_{x \to \infty} f{\left(x \right)}=L\) or \(\lim_{x \to -\infty} f{\left(x \right)}=L\)  and L is finite.

When we calculate the limits:

\(\lim_{x \to \infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0\\\\\lim_{x \to -\infty}\left(\frac{x - 2}{x^{2} + 2 x - 8}\right)=0\)

Thus, the horizontal asymptote is y=0.

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The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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Answer:

b. 4

c. 90⁰

Step-by-step explanation:

a. is in the diagram

Answer:

Add 16.20+ 40+8

Step-by-step explanation: 16+20+40+8= 84