NEED HELP FAST!! 20 POINTS!!

1.

y= -5x + 4

slope intercept form is y = mx + b (m) being the slope and (b) being the y intercept

The absolute maximum value of the function on the interval is approximately 2.28, and the absolute minimum value is approximately 0.37. Both of these values are expressed in terms of the notiral number, e.

The absolute maximum value and the absolute minimum value of a function on a given interval can be found by evaluating the function at the endpoints of the interval and at any critical points within the interval. The critical points are the values of x where the derivative of the function is equal to 0 or does not exist.

First, let's find the derivative of the function:
\( f'(x)=e^{\operatorname{xin}(x)} \cdot \operatorname{xin}'(x) \)

Using the chain rule, the derivative of \( \operatorname{xin}(x) \) is:
\( \operatorname{xin}'(x)=\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x) \)

So, the derivative of the function is:
\( f'(x)=e^{\operatorname{xin}(x)} \cdot (\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x)) \)

To find the critical points, we need to set the derivative equal to 0:
\( e^{\operatorname{xin}(x)} \cdot (\operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x))=0 \)

Since \( e^{\operatorname{xin}(x)} \) is never equal to 0, we can focus on the second factor:
\( \operatorname{cos}(x)-\operatorname{xin}(x) \cdot \operatorname{sin}(x)=0 \)

This equation cannot be solved algebraically, so we will use a graphing calculator to find the approximate values of x that make the equation true. The values are approximately 0.86 and 4.71.

Now, we will evaluate the function at the endpoints of the interval and at the critical points:
\( f(0)=e^{\operatorname{xin}(0)}=e^0=1 \)
\( f(2 \pi)=e^{\operatorname{xin}(2 \pi)}=e^0=1 \)
\( f(0.86)=e^{\operatorname{xin}(0.86)} \approx 2.28 \)
\( f(4.71)=e^{\operatorname{xin}(4.71)} \approx 0.37 \)

The absolute maximum value of the function on the interval is approximately 2.28, and the absolute minimum value is approximately 0.37. Both of these values are expressed in terms of the notiral number, e.

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The total cost at an activity level of 8,000 units is $55,000.

The total cost at an activity level of 8,000 units can be found by plugging in the value of X into the cost formula Y= $15,000 + $5X.

Step 1: Plug in the value of X into the cost formula:
Y= $15,000 + $5(8,000)

Step 2: Simplify the equation by multiplying $5 and 8,000:
Y= $15,000 + $40,000

Step 3: Add $15,000 and $40,000 to get the total cost:
Y= $55,000

Therefore, the total cost at an activity level of 8,000 units is $55,000. The correct answer is $55,000.

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The value of the painting at t = 4 is $400 (V(4) = $400) and the value of the painting at t = 6 is $800 (V(6) = $800).

To find the value of the painting at t = 4 and t = 6, we can simply plug in these values into the function V(t) = 100 • 2^t/2, for t >= 0 where t is the number of years since the painting was purchased, and V(t) is its value (in dollars) at time t, and simplify.

For t = 4, we have:
V(4) = 100 • 2^4/2
V(4) = 100 • 2^2
V(4) = 100 • 4
V(4) = 400

For t = 6, we have:
V(6) = 100 • 2^6/2
V(6) = 100 • 2^3
V(6) = 100 • 8
V(6) = 800

Therefore, V(4) = $400 and V(6) = $800.

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So the answer is: it took 35.56 minutes to get home on day one.

To find out how long it took to get home on day one, we need to work backwards from day five. Here's how:

On day five, it took 15 minutes to get home. This was 50% faster than on day four, which means that on day four it took 15 minutes / 0.5 = 30 minutes.

On day four, it took 30 minutes, and this was 2 minutes less than on day three. So on day three it took 30 minutes + 2 minutes = 32 minutes.

On day three, it took 32 minutes, and this was 20% longer than on day two. So on day two it took 32 minutes / 1.2 = 26.67 minutes.

On day two, it took 26.67 minutes, and this was 75% of the time it took on day one. So on day one it took 26.67 minutes / 0.75 = 35.56 minutes.

So the answer is: it took 35.56 minutes to get home on day one.

Here's the answer formatted with HTML:

To find out how long it took to get home on day one, we need to work backwards from day five. Here's how:

So the answer is: it took 35.56 minutes to get home on day one.

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The scores of students were normally distributed.

a)Approximately 68% of the students scored between 40 and 62 .

b) The approximately 95% of the students scored between 29 and 73.

We have a nationwide test taken by high school students, Mean score, μ = 51

Standard deviations, s = 12

The scores were normally distributed, that is

X~ N(M= 51, s = 12)

Lower bound of confidence interval= 40

Upper bound of CI = 62

As we know according to empirical rule the percentage of data falls within one,two and three

standard deviations are 68%,95% and 99.7%

respectively.

a) Mean + standard deviations = 51 + 12 = 63 close to 62

= Upper bound

For 2 standard deviations, 51 + 2×12 = 75

Mean - standard deviations= 51 - 12 = 39 close to 40 = lower bound

For 2 standard deviations, 51 - 2×12 = 27

Thus, data falls within one standard deviation

that is under 68% and so, approximately 68% of students scored between 40 and 62.

b) Similarly, the empirical rule demonstrates that 95% of scores falls within two standard deviation.

mean - 2× standard deviations= 51 - 2× 11

= 51 - 22 = 29

mean + 2× standard deviations= 51 + 2×11

= 51 + 22 = 73

Therefore, approximately 95% of students scored

between 29 and 73.

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Complete question:

On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 11

The scores were normally distributed. Complete the following statements.

(a) Approximately ?% of the students scored between 40 and 62 .

(b) Approximately 95% of the students scored between ? and ?

The volume of the right circular cone is approximately 1.6 cubic centimeters (rounding this answer to the nearest tenth of a cubic centimeter).

What is volume ?

Volume is a physical quantity that measures the amount of three-dimensional space that a substance or object occupies.

The volume of a right circular cone is given by the formula

[tex]V = (1/3)\pi r^2h[/tex] , where r is the radius of the base and h is the height of the cone. We are given the height of the cone, which is 14.9 cm. To find the radius of the base, we need to use the given circumference of the base, which is 2.9 cm.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We can rearrange this formula to solve for r, which gives us r = C/(2π). Plugging in the given circumference of 2.9 cm, we get:

r = 2.9/(2π) ≈ 0.461

Now, we can substitute the values of r and h into the formula for the volume of a cone and solve for V:

V = (1/3)π([tex]0.461^2[/tex])(14.9) ≈ 1.564 [tex]cm^3[/tex]

Rounding this answer to the nearest tenth of a cubic centimeter gives us a final volume of approximately [tex]1.6 cm^3[/tex]. Therefore, the volume of the right circular cone is approximately 1.6 cubic centimeters.

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Answer: The answer would be C

Step-by-step explanation:

If we start from 56,60,64,68 and were adding 4 each time the next numbers would be 72,76,80

The pair of functions that are not inverses of each other is (A).

To determine if two functions, g(x) and h(x), are inverses of each other, we need to check if the composition of the two functions, g(h(x)) and h(g(x)), both result in x.

A. g(x) = 2 + 9 = 11, h(x) = 1/2x - 9

g(h(x)) = g(1/2x - 9) = 2 + 9 = 11

h(g(x)) = h(11) = 1/2(11) - 9 = -3/2

Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.

B. g(x) = x - 1, h(x) = x + 1

g(h(x)) = g(x + 1) = (x + 1) - 1 = x

h(g(x)) = h(x - 1) = (x - 1) + 1 = x

Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.

C. g(x) = 3x - 6, h(x) = 1/3x + 2

g(h(x)) = g(1/3x + 2) = 3(1/3x + 2) - 6 = x

h(g(x)) = h(3x - 6) = 1/3(3x - 6) + 2 = x

Since g(h(x)) = x and h(g(x)) = x, the functions g(x) and h(x) are inverses of each other.

D. g(x) = 3x + 4, h(x) = x - 4/3

g(h(x)) = g(x - 4/3) = 3(x - 4/3) + 4 = 3x - 4

h(g(x)) = h(3x + 4) = (3x + 4) - 4/3 = 3x + 8/3

Since g(h(x)) ≠ x and h(g(x)) ≠ x, the functions g(x) and h(x) are not inverses of each other.

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Answer:

60

Step-by-step explanation:

Answer:

The area of the triangle is 60 unit²

Step-by-step explanation:

We know that the area of a triangle is :

[tex]A= \frac{1}{2}(Base \times Height)[/tex]

Since Base = 12 unit and Height = 10 unit

So

[tex]A= \frac{1}{2}(12\times 10)=60\\[/tex]

Hence the area of this triangle is = 60 unit²

a) The sum of their times is of 4x + 3.

b) The property used is the combination of like terms, which we use to add the terms with the variable x.

c) If Doug ran the race in 27 minutes, the total time for the team is of 111 minutes.

Doug finished first, and the times of the other two athletes are as function of Doug, hence the variable x represents the time needed for Doug to finish the race, that is:

D = x.

Kim finished 3 minutes after Doug, hence:

K = D + 3

K = x + 3.

Conner finished with a time that was twice Doug’s time, hence:

C = 2x.

Then the total time is given as follows:

T = D + K + C

T = x + x + 3 + 2x

T = 4x + 3.

If Doug ran the race in 27 minutes, the total time for the team is obtained as follows:

T = 4 x 27 + 3

T = 111 minutes.

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Answer:

2010-36=1974

She was born in 1974.

Answer:1974

Step-by-step explanation:

2010-36=1974

Answer:

The math coach has delivered 4 boxes of books, so the number of boxes she still needs to deliver is b. Each box contains 15 books, so the total number of books she still needs to deliver is 15b. She has 495 books to deliver in total. Therefore, we can write the equation:

15b = 495 - 4(15)

Simplifying the right-hand side:

15b = 495 - 60

15b = 435

Dividing both sides by 15:

b = 29

So the math coach still needs to deliver 29 boxes of books.

Answer: x = p/2

Step-by-step explanation:

x = next one
p = previous

in order to solve the next one, you would do :
x (the one you are trying to solve) = p (the previous one : 1/8) divided by 2
x = p/2

Answer:

15m,20m,25m

Step-by-step explanation:

15 cm, 20cm and 25cm follows the same pattern as the 3-4-5 pattern of the Pythagorean triplet. The Pythagorean triplet holds true.

Answer:

To find the interest rate when given the principal, time, and simple interest, we can use the formula:

Simple Interest = (Principal * Rate * Time) / 100

where:

Simple Interest is the given value of 4252.50

Principal is 18000

Time is 54 months

Rate is the unknown we want to solve for

Substituting the given values, we get:

4252.50 = (18000 * Rate * 54) / 100

Multiplying both sides by 100 and dividing by 18000 * 54, we get:

Rate = (4252.50 * 100) / (18000 * 54)

Rate = 4.398%

Therefore, the interest rate is 4.398% (rounded to three decimal places).

Step-by-step explanation:

Sure! Here is a step-by-step explanation of how to find the interest rate:

Given:

Principal = 18000

Time = 54 months

Simple Interest = 4252.50

Formula:

Simple Interest = (Principal * Rate * Time) / 100

We want to solve for Rate.

Substitute the given values into the formula:

4252.50 = (18000 * Rate * 54) / 100

Simplify by multiplying both sides by 100:

425250 = 18000 * Rate * 54

Divide both sides by 18000 * 54:

Rate = 425250 / (18000 * 54)

Simplify the expression on the right-hand side:

Rate = 0.04398

Convert the decimal to a percentage:

Rate = 4.398%

Therefore, the interest rate is 4.398%.

Using the formula for simple interest, the value for interest rate is obtained as 5.25%.

What is Simple Interest?

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

We can use the formula for simple interest -

I = P × r × t

where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

In this case, the principal is $18,000, the time is 54 months which is 4.5 years, and the simple interest is $4,252.50.

Substituting these values in the formula, we get:

4252.50 = 18000 × r × 4.5

Solving for r, we get -

r = 4252.50 / (18000 × 4.5)

= 0.0525 or 5.25%

Therefore, the interest rate is 5.25%.

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Answer: None of the statements are true.

The expression has only two terms: 17 and (5)(9 + 14y).

No term in the expression equals 23.

The expression has three factors: 17, 5, and (9 + 14y).

The constant in the factor 9 + 14y is 9.

The factors in the expression are 17, 5, 9, and (9 + 14y).

Step-by-step explanation:

The measure of ∠FGH is 28 - 4x.

A three-sided polygon with three angles is known as a triangle. It is a basic geometric shape that can be classified based on its sides and angles.

Since G is the midpoint of DF, we have m∠DGF = m∠FGC (vertical angles are equal), so m∠FGD = m∠CGF = (180 - m∠DGF)/2 = (180 - m∠FGC)/2 = m∠GFC. Similarly, m∠FHE = m∠HEC, so m∠FHE = m∠CGF = m∠GFC.

Using angle sum property, we have:

m∠DEF + m∠FED + m∠FDE = 180

60 - 5x + 2(46 + 2x) + m∠FGH = 180

152 + 4x + m∠FGH = 180

m∠FGH = 180 - 152 - 4x

m∠FGH = 28 - 4x

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The appropriate formula for calculating the dose of diphenhydramine for a pediatric patient is weight (kg) x (age (years)/150) x 33 mg = dose (mg). In this case, the dose would be (9/150) x 33 mg = 2.2 mg, rounded to the nearest tenth of a milligram.

The most appropriate formula to calculate the dose for a pediatric patient is the Clark's rule formula. This formula is used to calculate the dose of a medication for a child based on their weight and the recommended adult dose. The formula is as follows:
Child's dose = (weight of child in pounds / 150) x adult dose
Using this formula, we can calculate the appropriate dose for the 9-year-old patient:
Child's dose = (weight of child in pounds / 150) x 33 mg
Without knowing the weight of the child, we cannot calculate the exact dose. However, once the weight is known, the formula can be used to calculate the appropriate dose and it can be rounded to the nearest tenth of a milligram as necessary.

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This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

It may contain one or more variables, which are symbols that represent unknown quantities or values that can vary. Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships.

For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".

2.077×10⁻⁴ means "2.077 times 10 to the power of -4", which can be rewritten as 0.0002077. This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

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The Big Ideas or Focal Points in the mathematics curriculum for grade 6 are: 1. Ratios and Proportional Relationships
2. The Number System.  3. Expressions and Equations.  4. Geometry.  5. Statistics and Probability.

1. Ratios and Proportional Relationships: Students should be able to understand and use ratios to describe relationships between quantities, and use proportional reasoning to solve problems.

2. The Number System: Students should be able to understand and use negative numbers, and perform operations with multi-digit numbers and decimals.

3. Expressions and Equations: Students should be able to write and evaluate expressions, and use equations to solve problems.

4. Geometry: Students should be able to understand and use the properties of shapes and the relationships between them.

5. Statistics and Probability: Students should be able to use data to make predictions and understand the concept of probability.

These Big Ideas or Focal Points are the key concepts that students should master in grade 6 mathematics in order to be prepared for higher-level math courses.

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The final answer length of the other dimension of the garden is 9x units.

To find the length of the other dimension of the garden, we need to use the formula for the area of a rectangle:

Area = Length x Width

We are given the area and one dimension, so we can plug those values into the formula and solve for the other dimension:

[tex]81x^2-126x[/tex] = (9x-14)(Length)

To solve for the length, we need to divide both sides of the equation by (9x-14):

Length =[tex](81x^2-126x)/(9x-14)[/tex]

Now we can simplify the right side of the equation by factoring out a common factor of 9x:

Length = (9x)(9x-14)/(9x-14)

The (9x-14) terms cancel out, leaving us with:

Length = 9x

So the length of the other dimension of the garden is 9x units.

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Ben is incorrect because, all of Ben's expressions are erroneous since none of them equal the number 108 degrees. The correct equation is (n-2) x 180 / n.

A polygon is a geometric shape with a limited number of sides and two dimensions. The sides or edges of a polygon are formed by joining end-to-end segments of a straight line to form a closed shape. The intersection of two line segments, which results in an angle, is referred to as a vertex or corners.

The formula for calculating an interior angle in a regular polygon with n sides is (n-2) x 180 / n.

An internal angle in a pentagon has a measure of (5-2) x 180 / 5 = 108 degrees.

Substituting the angle in Ben's expression:

xᵒ + (x + 40)° + (2x - 30)° + 3(x - 40)° + 3x°

9x - 27° = 108

We observe that none of the value of x results in 108 degrees.

Hence, all of Ben's expressions are erroneous since none of them equal the number 108 degrees.

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The area of rectangular field is   [tex]\frac{9}{20} \ \text{miles}^2[/tex].

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.

Here the given rectangle , length= [tex]\frac{9}{10}[/tex]miles and Breadth = [tex]\frac{1}{2}[/tex]miles

Now using area of rectangle formula,

=> A = length× breadth square unit.

=> A = [tex]\frac{9}{10}\times\frac{1}{2}[/tex]

=> A =   [tex]\frac{9}{20} \ \text{miles}^2[/tex]

Hence the area of rectangular field is  [tex]\frac{9}{20} \ \text{miles}^2[/tex].

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There were 240 pages in the printer task.

To find the number of pages in the printing task, we can use the relationship between time, rate, and work. The formula for this is:

   time × rate = work.

Let's call the number of pages in the printing task "P" and the rate of printer A "R". We can set up the following equations based on the information given in the question:

   40 minutes × R = P(R + 4) × (40 - 16) = P

We can simplify the second equation to get:

    24R + 96 = P

Now we can set the two equations equal to each other and solve for R:

    40R = 24R + 96

    16R = 96

     R = 6

Now we can plug this value of R back into one of the original equations to find P:

     40 minutes × 6 = P

      P = 240

Therefore, the number of pages in the printing task was 240.

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By following the 6 steps explained, you can find the quotient of a multiple of 10 and any number.

To use place value to find the quotient of a multiple of 10 and a number, you can use the following steps:

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A2: a. The four period moving average forecast method is a technique that is used to calculate the demand for a particular month based on the average demand for the previous four months. In this case, to calculate the demand for the month of April 2020, we will take the average of the demand for the months of December, January, February, and March. The formula for this method is:

Four period moving average forecast = (Demand for December + Demand for January + Demand for February + Demand for March) / 4

= (1,450 + 1,410 + 1,420 + 1,380) / 4

= 5,660 / 4

= 1,415

Therefore, the demand for the month of April 2020 is 1,415 loafs.

b. Based on the demand forecast for the month of April 2020, Al Artz Bakery should decide to maintain their current capacity as the demand is relatively stable and there is no significant increase or decrease in demand. This will ensure that they are able to meet the demand without overproducing or underproducing.

c. If the bakery calculated forecasts for all products it makes, the forecast would be more accurate than the one calculated for just one product. This is because it would take into account the demand for all products and would give a more comprehensive view of the overall demand for the bakery.

d. If the bakery decides to use qualitative methods, it could use sources of opinion such as customer feedback, expert opinion, and market research. These sources of opinion can provide valuable insights into the demand for the bakery's products and can help to improve the accuracy of the demand forecast.

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The correct match of each root word with its meaning are :

(i) Anthropology⇔(d) man

(ii) Psychology⇔(c) mind    

(iii) Economy⇔(e) law  

(iv) Democracy⇔(b) people

(v) Judicious⇔(a) judge

The term (i) Anthropology is related to (d) man because,

The term "Anthropology" is called the study of human-societies and cultures and their development.

The term (ii) Psychology is related to (c) mind ,

The term "Psychology" is defined as the scientific-study of behavior and mental processes of mind;

The term (iii) Economy is related to (e) law,

The Economy can be termed as the social science that deals with the production, distribution, and consumption of goods and services and their management.

The economy and practices of commerce are governed by certain laws or principles. So,  the best option to match economy is law.

The term (iv) Democracy is related to (b) people ,

Democracy is defined as system of government by the whole population or all the eligible members of a state, typically through elected representatives.

The term (v) Judicious is related to (a) judge,

The word "judge" is a derived from the word "judicious", which means, showing and using sound judgement.

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The given question is incomplete, the complete question is

Match the below root of each word to its meaning.

(i) Anthropology       (a) judge

(ii) Psychology          (b) people

(iii) Economy             (c) mind

(iv) Democracy         (d) man

(v) Judicious              (e) law

The probability of rolling a dice less than 3 times is 17/100.

It is a branch of mathematics that deals with the occurrence of a random event.

The total no of times rolling = 200

The probability of rolling 1 = 17 times

And, The probability of rolling 2 = 17 times

So, the probability of rollng a dice less than 3 times is

17+17/200

34/200

17/100

Hence, the probability of rolling a dice less than 3 times is 17/100.

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The value οf x and y in the shape will be 18/5 mm and 15/2 mm respectively.

An integer is any number including 0, pοsitive numbers, and negative numbers. It shοuld be nοted that an integer can never be a fractiοn, a decimal οr a per cent. Sοme examples οf integers include 1, 3, 4, 8, 99, 108, -43, -556, etc.

Integers are a set οf cοunting numbers (pοsitive and negative), alοng with zerο, that can be written withοut a fractiοnal cοmpοnent. As mentiοned abοve, an integer can be either pοsitive, negative οr zerο.

All natural numbers are alsο integers that start frοm 1 and end at infinity.

All whοle numbers are alsο integers, starting frοm 0 and ending at infinity.

An integer is a whοle number withοut any fractiοn οr decimal part.

Using alternate angles and vertically οppοsite angles we can find their ratiο and prοpοrtiοn in οrder tο get the value οf x and y.

[tex]\frac{x}{9} =\frac{3}{y} =\frac{2}{5}[/tex]

x = 2(9)/5 = 18/5 mm

y = 3(5)/2 = 15/2 mm

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