On a standardized exam, the scores are normally distributed with a mean of 135 and a standard deviation of 20. Find the z-score of a person who scored 115 on the exam.

The logarithm value for the expression → ln(175) is equivalent to 5.17.

Logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number. Mathematically -

[tex]$\log_{b}({b^x})=x[/tex]

Given is the following logarithmic expression, as follows -

ln(175)

We have the expression as -

ln(175)

Solving the expression further, we get -

ln(25 x 7)

ln(25) + ln(7)                                       {Property : log(A x B) = log(A) + log(B)}

ln(5)² + ln(7)

2 x ln(5) + ln(7)

2 x 1.61 + 1.94

5.17

Therefore, the logarithm of the number 175 is equivalent to 5.17.

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The balance of the bank reconciliation statement  is $3,640

A bank reconciliation is is defined as the process by which the bank account balance in an entity’s books of account is reconciled to the balance reported by the financial institution in the most recent bank statement

The bank Reconciliation statement appears thus

Bank reconciliation statement

                                                                      $                         $

Cash book balance                                   11,670

Add unpresented cheque                          5,120

Over cast (400-40)                                         360

                                                                                             17,150

Cheque not credited                                    5120

Less Uncredited cheque                             4910                  

Notes collected                                            2660

Dishonored  cheque                                       770

Bank charges                                                    50

bank interest                                                    140

                                                                                           13500

Balance as per bank statement                                      3640

In conclusion the balance of the Statement is $3640

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The perimeter of the pattern the same as the area of the pattern is 20 cm.

Perimeter of a square is the total length (distance) of the boundary of a square

In a square all the sides are of equal lengths.

Hence, perimeter of a square = 4l

We know that all the sides of a square are equal.

Perimeter of a Square

Perimeter of the square ABCD

                  = AB + BC + CD + AD

                  = 2 cm + 2 cm + 2 cm + 2 cm

                  = (2 × 4) cm

                 = 8 cm

Perimeter of a square is 4 times of s side.

Perimeter of a square = 4 × length of a side..

1st method:

Perimeter of a square PQRS

                 = side + side + side + side

                 = 5 cm + 5 cm + 5 cm + 5 cm

                = 20 cm:

2nd method

Perimeter of a square = 4 times side

                               = 4 × side

                               = 4 × 5 cm

                               = 20 cm

Therefore, Perimeter of a square = 4 × length of one side.

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Question 1

In 2015, [tex]x=5[/tex]. [tex]P(5)=87000(0.9)^5 \approx \boxed{51373}[/tex]

Question 2

[tex]78000(1-0.08)^5 \approx \boxed{51408}[/tex]

Question 3

[tex]51408 > 51373[/tex], so Greene county was more populous.

Answer:

B. g(x) = -x² - 2

Step-by-step explanation:

f(x) = x²

g(x) = -x²

The graph now has a maximum of (0, 0) and is curving downwards. To make the graph go down by -2 subtract 2 from the equation

g(x) = -x² - 2

I hope this helps!

It will take around 0.24 months for the invested money to get doubled.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The formula to calculate the amount is as follows,

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

Substitute all the corresponding values in the above expression to obtain,

A = P[tex](1 + 6/100)^{nt}[/tex]

1800 = 900[tex](1 + 6/100)^{nt}\\[/tex]

=>   [tex](1 + 6/100)^{nt}[/tex] = 1800/900

=>  [tex]1.06^{nt}[/tex] = 2

Since, there are 12 months in one year, n = 12.

[tex]1.06^{12t}[/tex] = 2

=> 12t = log(2) ÷ log(1.06)

=> 12t = 0.275

=> t = 0.02

Which is equivalent to 12 × 0.02 = 0.24 months.

Hence, it will take 0.24 months to double the invested money.

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The simplification of the given expression is (x - 1)²/ (x-2)(x+3) which restrictions on the domain of this expression are x ≠ 1, 2, -3.

The expression is given in the question as:

(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)

To simplify the expression (x+3)(x-1)/(x-2) ÷ (x+3)/(x-1), we can start by multiplying the numerator and denominator of the first fraction by the denominator of the second fraction:

(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)

= (x+3)(x-1) / (x-2) × (x-1) / (x+3)

Then, we can simplify the expression by combining like terms:

= (x - 1)² (x+3)/ (x-2)(x+3)

= (x - 1)²/ (x-2)(x+3)

The restrictions on the domain of this expression are that x cannot be equal to 2 or -3, because these values would make the denominator equal to zero, which is not allowed in a fraction.

Therefore, the domain of the expression is all real numbers except x = 1, x = 2, and x = -3. We can express this as:

Domain: x ∈ R, x ≠ 1, x ≠ 2, x ≠ -3

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The solution to the linear inequality y > 2x - 2 and y > 5x + 8 is -3.33 and -8.67

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥.

Using a graphing calculator, the solution of y > 2x - 2 and y > 5x + 8 is

This will give us a value of x is -3.33 and y is -8.67

Kindly find attached graph below

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Statement                                                  Reason

Z is the midpoint of overline XY             Given

WZ ⊥ XY                                                   Definition of perpendicular lines

angle WZX ≅ angle WZY                        Definition of isosceles triangle

line XA ≅ line YZ                                     Definition of bisection

line WZ ≅ line WZ                                   Reflexive Property of Congruence

Δ WXZ ≅ Δ WYZ                                     Side - Angle - Side (SAS)

< Y ≅ < X       Corresponding Parts of Congruent Triangles are Congruent              

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

The problem requires the prove by Side - Angle - Side = SAS to ensure that the the triangles are congruent

The SAS have it that the two triangles being compared should have their two sides and the included angle equal

Using Corresponding Parts of Congruent Triangles are Congruent CPCTC theorem ∠Y ≅ ∠X .

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The inequality that best represents Soro's situation regarding the number of bus rides he can take between now and the end of this month is :

50 - 2.5y ≥ 20.

        = 50 - 2.5y

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That is a geometric progression.

the common ratio is 1/2.(t2÷t1)

nth term= ar^n-1

16×1/2=8

tn=8^n-1

The number of acres owned for which the average intake is 2200 calories per day is 2 acres obtained by the algebraic expression that relates the acres of land and the calories per day.

It is given that, the number of calories consumed daily by a person owing x acres of land is given by the algebraic expression,

C(x) = 270 ln(x+1) + 1900

The average intake of calories consumed per day is given by C(x) = 2200

Here x is the number of acres of land. Then, the required number of acres of land is

C(x) = 270 ln(x+1) + 1900

⇒ 2200 = 270 ln(x+1) + 1900

⇒ 270 ln(x+1) = 2200 - 1900

⇒ 270 ln(x+1) = 300

⇒ ln(x+1) = 300/270 = 10/9

Applying base 'e' on both sides, we get

⇒ (x+1) = [tex]e^\frac{10}{9}[/tex]

⇒ x+1 = 3.0377

⇒ x = 3.0377 - 1 = 2.0377

When rounding the final answer to the nearest tenths, we get x = 2 acres.

When rounding the final answer to the nearest thousand, we get x = 2.038 acres.

Thus, for an average intake of 2200 calories per day, the number of acres of land owned is approximately 2 acres.

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Answer:

x = 6

Step-by-step explanation:

the opposite sides of a parallelogram are congruent , then

2x + 3 = 15 ( subtract 3 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

If the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that, the value of a commodity decreases at a monthly rate of 0.8%,

We have to find by what percentage the rate decreases in a year.

If there are 12 months in a year, the rate decrease in a year obtained as,

=0.8 × 12

=9.6 %

Thus, if the value of a commodity decreases at a monthly rate of 0.8%, by 9.6 percentage it decreases in a year.

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In a year, the value of commodity decreases by 9.6%, at the monthly rate of 8%.

Ratio basically compares quantities, that means it show value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Monthly decrease rate of change in commodity = 0.8 %,

To find the percentage decrease in year,

Use ratio property,

In 1 month, commodity decreases 0.8%

In 12 months commodity decreases = 12 x 0.8 = 9.6 %

The value of commodity will decrease by 9.6% in a year.

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Answer:

Step-by-step explanation:

6t/6 = 2/3/6

6t/6 = t while were left with 2/3 /6

t = 2/3 / 6.

t = 2/3 x 1/6

t = 2/3 x 1/2(3)

t = 1/3 x 1/3

t = 1 / 3 x 3

t=1/9

decimal form: 0.1

The probability that there are 89/1024 ways in which heads never happen on consecutive tosses.

For the stared question;

Then, for every value of x, I completed casework:

The number of configurations of AAAAAAAAAA is bijective to x=0 and is 1.

The number of configurations of AAAAAAAAB is then bijective to x=1, which really is 9 and so forth.

These variables add up to 89, and there are 1024 different ways to flip them.

P(i + j) = 89/1024

Thus, there are 89/1024 ways in which heads never happen on consecutive tosses.

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Answer:

The slope is 1/3

Step-by-step explanation:

The equation is equivalent to

x - 3y = -14

x = 3y - 14

x + 14 = 3y

(x + 14)/3 = y

The values of x in the first, second, third and fourth triangles are 4 units, 70°, 76° and 80° respectively

To solve this problem, we need some angle geometry knowledge:

For the first triangle:

x = 4 (All sides in a rhombus are identical)

For the second triangle:

The missing side is also equal to x (base of isosceles triangles)

x + x + 40 = 180 (sum of angles in triangle)

2x+40 = 180

2x = 180-40

2x = 140

x = 70°

For the third triangle:

x = 76° (base of isosceles triangles are equal)

For the fourth triangle:

Check the image attached for labeling

m = 180-110 = 70° (angle on a straight line)

y = 70° (base of isosceles triangles are equal)

z = 180-70-70 = 40°

t = 90-40 = 50°

L = 50° (base of isosceles triangles are equal)

Thus, x = 180-50-50 = 80°

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The amount in his savings after 5 years will be  $1507.5.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P = 1500, r = 0.1, t = 5 years.

∴ SI = (1500×0.1×5)/100.

SI = $7.5.

Now, We know Amount = principle + SI.

∴ Amount = 1500 + 7.5 = $1507.5

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The fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) following from the laws of indices is; 8x³ y² / 7.

It follows from the task content that the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) is to be determined.

Since the given expression is; 16x⁵y⁴ / ( 14x²y² ).

As evident in the task content; same base terms are present in the numerator and denominator; we therefore have that;

The expression can be simplified as follows using the laws of indices as follows;

[tex] \frac{16 {x}^{5} {y}^{4} }{14 {x}^{2} {y}^{2} } [/tex]

It follows from the quotient of exponents law of indices; we have that;

[tex] \frac{8}{7} {x}^{5 - 2} {y}^{4 - 2} [/tex]

= 8x³ y² / 7

Therefore, the fully simplified form of the given expression using the laws of indices is; 8x³ y² / 7.

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Answer:

Step-by-step explanation:

10% of 20 is equal to 2. To calculate 10% of a number, we can multiply the number by 10% expressed as a decimal, which is 0.1. For example, 10% of 20 is equal to 20 * 0.1 = 2.

Alternatively, we can calculate 10% of a number by dividing the number by 100 and then multiplying the result by 10. For example, 10% of 20 is equal to (20 / 100) * 10 = 2.

It is necessary to compute in the volume of the rotated region while taking into account that each cross section piece is raised up by a height of h = 4 - y. Scale the results by 62.4 lb/ft3 as well.

The given parabolic region's volume of revolution about the y-axis is a parabolic cylinder. This solid is revolved, and it has circular disks as its cross section. The differential volume of one such disk situated at a differential height y above the x-axis must be determined. The weight of water in this volume can then be calculated by multiplying this volume by the density of water. The depth of this volume is then determined from the tank's top surface. Determine how much differential work is needed to lift this water layer to the top surface. Integrate this differential work now to calculate the overall effort needed to empty the tank.

Rotating the curve x=3y about the y-axis creates the region. Keep in mind that 62.5 = (125 / 2) As a result, using the disk method,

[tex]\int_{0}^{3} \left(\frac{125}{2} \pi (4-y) (3\sqrt{y})^2\right)\, dy \\ &=\int_{0}^{3} \left(\frac{1125}{2} \pi (4-y) y\right)\, dy &\text[/tex]

Integrate in relation to:

[tex]y\text{]} \\ &=\left(-\frac{1125}{2} \pi \left(\frac{y^3}{3}-2 y^2\right)\right)\bigg|_{0}^{3} \\ &=\frac{10125 \pi }{2} \\ &\approx 16045.7 \end{align*} \)[/tex]

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Answer:

-1≤x≤3

Step-by-step explanation:

-3≤2x-1≤5

add 1 to all sides

-2≤2x≤6

divide all sides by 2

-1≤x≤3

Answer: The common factor is 8

Step-by-step explanation:

Each is a variant of the number 8 and 2 but it called for the greater common factor so 8

Answer:: 111

Step-by-step explanation:

111 is greater than 112 I hope it helps!!!!

Answer:

Yes

Step-by-step explanation:

16x^4 x 16x^2= 16x^8

To obtain a confidence interval for a population mean under the t-interval procedure.

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