A textbook store sold a combined total of 429 chemistry and biology textbooks in a week. The number of chemistry textbooks sold was 51 more than the number of biology textbooks sold. How many textbooks of each type were sold?

The function has 2 solutions which is x = 2 and x = 8.

What is a quadratic function?

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

Solution:

Given :

a = 2 , vertex = (5, -18)

f(x) = a(x-h)² + K

f(x) = 2(x - 5)² - 18

f(x) = 2(x² -10x + 25) -18

f(x) = 2x² - 20x +50 - 18

f(x) = x² - 10x +16

∴ x² -10x + 16 = 0

x² - 8x - 2x + 16 = 0

x(x-8) -2(x-8) = 0

(x-2) = 0 and (x-8) = 0

∴ x = 2 and x = 8

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The quadratic function has 2 solutions which is x = 2 and x = 8.

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two. A polynomial of degree two in one or more variables in mathematics is known as a quadratic polynomial. Any polynomial function that is defined by a quadratic polynomial is said to be quadratic.

The terms "quadratic polynomial" and "quadratic function" were almost interchangeable before the 20th century because it was difficult to tell a polynomial from its corresponding polynomial function. This is still true in many elementary courses where "quadratic" is frequently used to refer to both terms.

Solution:

Given :

     a = 2 , vertex = (5, -18)

f(x) = a(x-h)² + K

f(x) = 2(x - 5)² - 18

f(x) = 2(x² -10x + 25) -18

f(x) = 2x² - 20x +50 - 18

f(x) = x² - 10x +16

∴ x² -10x + 16 = 0

x² - 8x - 2x + 16 = 0

x(x-8) -2(x-8) = 0

(x-2) = 0 and (x-8) = 0

∴ x = 2 and x = 8

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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

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 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 required solutions of percentages are below as :

100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.

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

The double number line shows that Henrik has a mass of 60kg.

According to the given question, the required solution would be as:

100% of 60 kg

⇒ (100/100) x 60

⇒ 1 x 60

⇒ 60

So, 100% of 60 kg = 60 kg

20% of 60 kg

20%  is expressed as 20/100 in fractional form

⇒ (20/100) x 60

20/100 is expressed as 0.20 in decimal form

⇒ 0.20 x 60

Apply the multiplication operation, and we get

⇒ 12

So, 20% of 60 kg = 12 kg

40% of 60 kg

⇒ (40/100) x 60

⇒ 0.40 x 60

⇒ 24

So, 40% of 60 kg = 24 kg.

Thus, the required solutions are 100% of 60 kg = 60 kg, 20% of 60 kg = 12 kg, and 40% of 60 kg = 24 kg.

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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:

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

Answer:1.7

Step-by-step explanation:

Answer:

A: AB corresponds to FG

Step-by-step explanation:

The question is asking for which statement if not true/false.

Answer choice A is false because when you turn the rectangle, AB does not end up where FG is. Instead, AB ends up where EF is. Also,  the length of AB is 6 units, while the length of FG is 4 units. So, they cannot correspond to each other.

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!

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

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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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Moment about the pivot must be equal for the seesaw to balance. Initially, the first cat and the bowl are at 2 m from the pivot.

The moment due to cat = 5.3*2 = 10.6 kg.m

The moment due to bowl = 2.5*2 = 5 kg.m

The unbalanced moment = 10.6 - 5 = 5.6 kg.m

Therefore, the 3.7 kg cat should stand at a distance x from the pivot in left to balance the 5.6 kg.m.

That is,

3.7*x = 5.6 => x = 5.6/3.7 = 1.5134 m to the left (on the side of the bowl)

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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

As described in z-distribution the answers are given below:

a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows: (747, 853).

b) The sampling error at 95% confidence level is of: $35.78.

What is a z-distribution ?

The normal distribution with a mean of 0 and a standard deviation of 1 is referred to as the standard normal distribution (also known as the Z distribution) (the green curves in the plots to the right). It is frequently referred to as the bell curve since the probability density graph resembles a bell.

solution:

The bounds of the confidence interval are given as follows:

In which:

is the sample mean.

z is the critical value.

n is the sample size. is the standard deviation for the population.

The parameters for this problem are given as follows:

Hence the lower bound of the interval is of:

800 - 200 x 1.96/square root of 55  = 747.

The upper bound of the interval is of:

800 + 200 x 1.96/square root of 55  = 853.

The sampling error for a sample size of 120 is calculated as follows:

200 x 1.96/square root of 120 = $35.78.

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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

Answer:: 111

Step-by-step explanation:

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

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:

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.

Function f(x)  is 2/9.

f(-2) for f(x) = 2 • 3^x is 2/9.

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Time series forecasts are developed based on time series analysis, which comprises methods for analyzing time series data to extract meaningful statistics and other characteristics of the data.

One of the most often used data science techniques in business, finance, supply chain management, production, and inventory planning is time series forecasting.

A time component is often present in prediction difficulties, necessitating the extrapolation of time series data or time series forecasting. Another crucial field of machine learning (ML) is time series forecasting, which may be viewed as a supervised learning issue.

It can be subjected to ML techniques including regression, neural networks, support vector machines, random forests, and XGBoost. Using models created from historical data to anticipate future observations is known as forecasting.

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Answer:

line | Cartesian equation x + 5 y = 20 | x-intercept = 20 thus: D

Step-by-step explanation:

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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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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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