Mathematics College

what are the answers to these questions?

Answers

Answer 1

The values of the expression are,

⇒ x₂ = - 9.4

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

Given that;

Expression is,

e²ˣ = - 2x - 1

Hence, Function is,

⇒ f (x) = e²ˣ + 2x + 1 = 0

⇒ f' (x) = 2e²ˣ + 2

Now, By newton's method;

⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))

⇒ x₂ = x₁ - f (x₁) / f' (x₁)

⇒ x₂ = - 5 - (e¹⁰ + 10 + 1)/(2e¹⁰ + 2)

⇒ x₂ = - 5 - (e¹⁰ + 11)/(2e¹⁰ + 2)

⇒ x₂ = - 5 (2.6 + 11) / ( 2 x 2.6 + 2)

⇒ x₂ = - 68 / 7.2

⇒ x₂ = - 9.4

⇒ x (n + 1) = x (n) - f (x (n)) / f' (x(n))

⇒ x₃ = x₂ - f (x₂) / f' (x₂)

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

Thus, The values of the expression are,

⇒ x₂ = - 9.4

⇒ x₃ = - 9.4 - (e³⁸ + 38 + 1) / (2e³⁸ + 2)

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Related Questions

I NEED HELP WITH STATISTICS

Answers

The value of the summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300

Computing the summation notation

From the question, we have the following parameters that can be used in our computation:

69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7

The summation notation is given as

[tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex]

The summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] means we multiply each value by -25 and add the results

Using the above as a guide, we have the following:

Sum = -25 * (69 - 5 + 47 - 10 - 80 + 13 + 64 - 76 - 95 + 45 + 9 + 7)

Evaluate

Sum = 300

Hence, the value of the summation notation [tex]\sum\limits^{12}_{i=1} {-25x_i}[/tex] for the 12 measurements 69, -5, 47, -10, -80, 13, 64, -76, -95, 45, 9, 7 is 300

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The current of a river is 2 miles per hour. A boat travels to a point 15 miles upstream and back in 4
hours. What is the speed of the boat in still water?

Answers

Using the relationship of distance, time and speed, the speed of the boat in still water is 8mi/hr

What is the speed of the boat in still water?

To determine the speed of the boat in still water, we can write an equation to represent this.

The speed as it travels upstream = x - 2

The speed as it travels downstream = x + 2

The total distance travelled by the boat = 15 + 15 = 30mi

Let's write an equation to represent this;

15/(x - 2) + 15/(x + 2) = 4

simplifying this;

15(x + 2) + 15(x - 2) = 4(x - 2)(x + 2)

15x + 30 + 15x - 30 = 4x² - 16

30x = 4x² - 16

4x² - 30x - 16 = 0

Solving for x;

x = -0.5, 8

But since the speed can't be negative, the speed is 8 mi/hr

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factor the expression
7x^2+12x+5

Answers

Hi again

I did it wrong

I'm here to redeem

When you have to factor these types of equations, you have to use a method called slide divide and bottoms up.

First you have to slide the a value to the end and mutiply with the c value so it is easily factorable

x^2+12x+35

Then you solve it like always

(x+7)(x+5)

Now, don't forget our buddy 7

7 is coming back

we divide 7 by 7 and 5 by 7

(x+1)(x+5/7)

7 has to move

So we move the 7 to the front

Therefore the answer is

(x+1)(7x+5)

If you have questions please ask me

Answer:

(7x + 5) (x + 1)

Step-by-step explanation:

7x² + 12x + 5

general form ax² + bx + c

a = 7

b = 12

c = 5

we have to find number that, if

... × ... = a . c = 7 . 5 = 35

... + ... = b = 12

and it would be

7 × 5 = a . c = 7 . 5 = 35

7 + 5 = b = 12

7x² + 7x + 5x + 5

= 7x (x + 1) + 5 (x + 1)

= (7x + 5) (x + 1)

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HELP ME PLEASE!
Whoever answers right gets brainliest!

Answers

Step-by-step explanation:

The 'x's ' ( the domain) are mapped into two values of 'y' (the range)

Range = 1,6

NO LINKS!! URGENT HELP PLEASE!!

This prism has a right angle for a base.
What is the volume of the prism?

Explain your thinking

Answers

Answer:

48 unit cube

Step-by-step explanation:

Solution Given:

For Triangle ABC

hypotenuse AB= 5

base AC=4

By using hypotenuse law

height BC=[tex]\sqrt{5^2-4^2} =3[/tex]

Now Area of the right-angled triangle is 1/2 * base*height

=1/2*AC*BC=1/2*4*3=6 units square

As we know that

The volume of triangular prism: Area of base * height

over here Area of the base= Area of the Triangle and the height is the length of the prism

=6 units square*CF

=6 units square*8

=48 unit cube

Answer:

The volume of the given prism is 48 cubic units.

Step-by-step explanation:

The volume of a prism can be calculated by multiplying the area of its base by its height.

The bases of the given prism are the congruent right triangles ABC and DEF.

We have been given the measures of sides AB and AC of triangle ABC.

To determine the area of ΔABC, we first need to calculate the measure of side BC using Pythagoras Theorem:

[tex]\implies AC^2+BC^2=AB^2[/tex]

[tex]\implies 4^2+BC^2=5^2[/tex]

[tex]\implies 16+BC^2=25[/tex]

[tex]\implies BC^2=9[/tex]

[tex]\implies BC=3[/tex]

The area of a triangle is half the product of its base and height.

The base and height of a right triangle are its legs.

[tex]\begin{aligned}\textsf{Area of base}&=\textsf{Area of $\triangle ABC$}\\\\&=\dfrac{1}{2} \cdot BC \cdot AC\\\\&=\dfrac{1}{2} \cdot 3 \cdot 4\\\\&=6\; \sf square\;units\end{aligned}[/tex]

Therefore, the area of the base of the prism is 6 square units.

Finally, to find the volume of the prism, multiply the area of the base by the height of the prism:

[tex]\begin{aligned}\textsf{Volume of prism}&=\textsf{Area of base} \cdot \sf height\\\\&=\textsf{Area of $\triangle ABC$} \cdot \overline{CF}\\\\&=6 \cdot 8\\\\&=48\; \sf cubic\;units\end{aligned}[/tex]

Therefore, the volume of the given prism is 48 cubic units.

How much would you need to deposit in an account now in order to have $2000 in the account in 15years? Assume the account earns 8% interest compounded monthly.

Answers

Answer:

P = $1341.53

Step-by-step explanation:

A(t) = amount in t years

P = Principal (original investment)

r = annual interest rate (in decimal form)

n = number of times that interest is compounded each year

A(t) = P(1 + r/n)nt

Substitute in the given values: 2000 = P(1 + 0.04/12)12(10)

2000 = P(1.490832682)

P = $1341.53

-2x-2y=14 slecet all the ordered pairs that are solutions

Answers

The ordered pairs of the solutions to the linear expression are В. (-7, 0) C. (0, -7) and F. (3, -4)

What are the ordered pairs of the linear expression

From the question, we have the following parameters that can be used in our computation:

The linear expression -2x - 2y =14

To determine the ordered pairs of the linear expression, we set x and y to the values in the list of options and check for the true equation

Using the above as a guide, we have the following:

А. (2, 3) В. (-7, 0) C. (0, -7)

-2(2) - 2(3) = 14

-10 = 14 --- false

-2(-7) - 2(0) = 14

14 = 14 --- true

-2(0) - 2(-7) = 14

14 = 14 --- true

D. (-7, 1) E. (-1, 7) F. (3, -4)

-2(-7) - 2(1) = 14

12 = 14 --- false

-2(-1) - 2(7) = 14

-12 = 14 --- false

2(3) - 2(-4) = 14

14 = 14 --- true

Hence, the ordered pairs of the linear expression are В. (-7, 0) C. (0, -7) and F. (3, -4)

Answers

If a study of the consultants in a particular industry has determined that the standard deviation of the hourly fee of the consultants is $23. the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

How to find the confidence interval?

The formula for a confidence interval for the population mean is:

CI = X- bar ± z* (σ/√n)

where:

X- bar = sample mean

z* = z-score for the desired level of confidence (99% in this case)

σ = population standard deviation

n = sample size

Substituting the given values, we get:

CI = 113 ± 2.576 * (23/√100)

Calculating the standard error:

SE = σ/√n = 23/√100 = 2.3

Now we can substitute this value into the formula:

CI = 113 ± 2.576 * 2.3

CI = 113 ± 5.92

So,

Lower limit: 107.1

Upper limit: 118.9

Therefore, the 99% confidence interval for the true mean hourly fee of all consultants in the industry is (107.1, 118.9).

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If someone wants to call Havana, Cuba from the United States (US) begins with US three-digit exit code 011 followed the two-digit country code for Cuba is 53, followed by the county code of Havana is 7 and finally by seven-digit local telephone numbers. But this seven-digit local telephone numbers cannot begin with 0. How many different telephone numbers are possible?

Answers

Answer:

9000000 different numbers

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

The number is basically a combination in the form of:

abcdefg, where a can't be zero but the rest of the digits have no restrictions

Hence the possible digits:

a = 9, b,c,d,e,f,g = 10

So possible telephone number combinations:

9*10⁶ = 9000000

The graph of an equation is sketched in the figure.
Describe five ordered-pair solutions of this equation by
using a table.
X
-6
-3
0
3
6
y
☐
I
8-
10-88427
6
40
10

Answers

The value of five ordered-pair solutions of this equation by using a table are,

x y

- 6 - 1

- 3 - 2

0 3

3 - 4

6 - 5

We have to given that;

The graph of an equation is sketched in the figure.

Hence, From graph we get;

The value of five ordered-pair solutions of this equation by using a table are,

x y

- 6 - 1

- 3 - 2

0 3

3 - 4

6 - 5

Thus, The value of five ordered-pair solutions of this equation by using a table are,

x y

- 6 - 1

- 3 - 2

0 3

3 - 4

6 - 5

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Express 1:0.2:0.75 in their simple form

Answers

The given ratio 1:0.2:0.75 can be expressed in its simplest form as 5:1:3/4.

To express 1:0.2:0.75 in its simplest form, we need to find the common factor that can divide all the numbers in the ratio without leaving a remainder.

First, we can convert 0.2 to a fraction by dividing 2 by 10, which gives us 1/5. Thus, the ratio can be rewritten as

1:0.2:0.75

= 1:2/10:0.75

= 1:1/5:0.75.

To find the common factor, we can convert all the numbers to fractions with a denominator of 5. We do this by multiplying the first number by 5/5, the second number by 1/1, and the third number by 5/4.

This gives us,

5/5:1/5:15/20.

Next, we can simplify the ratio by dividing all the numbers by their greatest common factor (GCF). In this case, the GCF is 1/5.

Dividing all the numbers in the ratio by 1/5 gives us,

5:1:15/4.

Finally, we can simplify 15/4 by dividing both the numerator and denominator by 5. This gives us 3/4. Thus, the final simplified ratio is 5:1:3/4.

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Imagine Math simple interest

Answers

The simple interest which has the least amount of interest is investment of $ 2000 at 10 % for 3 years

Given data ,

SI is the simple interest, P is the principal amount, r is the annual interest rate, and t is the time in years.

Given that P = 2000, r = 10% = 0.1, and t = 3 years, we can calculate the simple interest as:

SI = 2000 x 0.1 x 3 = 600

Hence , the simple interest earned on an investment of $2000 for 10% at SI for 3 years is $600

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26) What is the area of Rectangle A?
is 1 unit square.
Rectangle A

Answers

The required area of the rectangle is 8 sq. units

What is rectangle?

Any mathematical statement with numbers, variables, and an arithmetic operation between them is an expression or algebraic expression. For instance, the expression 4m + 5 is one in which the terms 4m and 5 and the variable m are separated by the arithmetic sign +.

According to question:

From the diagram

Length = 4 units, width = 2 units

Area of rectangle = length×width

Area of rectangle = 4×2

Area of rectangle = 8 sq. units

Thus, required area of the rectangle is 8 sq. units

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Look at the box plot shown below. What is the minimum value of the data set?

A box plot labeled Volunteer Service Hours with the beginning of quartile 1 at 13, the beginning of quartile 2 at 16.5, the beginning of quartile 3 at 20, the beginning of quartile 4 at 23, and the end of quartile 4 at 27.

Answers

The minimum value of the data set is 10.5.

Box plots are an effective graphical tool used to display a summary of a dataset. They provide a visual representation of the minimum and maximum values, quartiles, and outliers of the data. They are commonly used in statistics and can provide valuable insights into a dataset.

Now, let's consider the box plot in question. The box plot is labeled "Volunteer Service Hours" and it has four quartiles, each marked by a horizontal line. The first quartile (Q1) is marked at 13, the second quartile (Q2) is marked at 16.5, the third quartile (Q3) is marked at 20, and the fourth quartile (Q4) is marked at 23, with the end of the box extending to 27.

The minimum value of the data set can be found at the lower whisker of the box plot.

The lower whisker represents the minimum value that is not an outlier.

In this box plot, we do not see any outliers, so the minimum value of the dataset is represented by the lower end of the whisker, which is located at 10.5.

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At 10.30 a.m, a van left Town X travelling at an average speed of 64 Km/h.
At 11.15 a.m., a car left Town X, travelling on the same road at an average speed of
80 Km/h.
a) At what time did the car catch up with the van?

b) How far from Town X did each vehicle travel when they passed each other?

Answers

Answer:

a) 2:15 pm

b) 240 km

Step-by-step explanation:

You want to know the time and place where a car leaving at 11:15 a.m. at 80 km/h catches up with a van leaving at 10:30 a.m. at 64 km/h.

Head start

The van travels for 11:15 -10:30 = :45, or 3/4 hour, before the car starts. This gives it a distance advantage of (3/4 h)(64 km/h) = 48 km.

Closing speed

The speed at which that distance is reduced is the difference between the car speed and the van speed:

80 km/h -64 km/h = 16 km/h

Closing time

The time it takes for the head-start distance to be reduced to zero is ...

time = distance/speed

time = (48 km)/(16 km/h) = 3 h

a) Meeting time

Three hours after the car leaves, it will catch up with the van. That time is ... 11:15 +3:00 = 14:15 = 2:15 p.m.

b) Meeting distance

In 3 hours, the car travels (3 h)(80 km/h) = 240 km.

Note that the van has been traveling 3 3/4 hours, so will have also traveled (3 3/4 h)(64 km/h) = 240 km. The two vehicles need to be in the same place at the same time if they are to pass each other.

Additional comment

The attached graph shows the two vehicles will have traveled 240 km when they mean at 2:15 pm. The horizontal axis is hours after midnight. The vertical axis is kilometers from town X. The relation graphed is distance = speed × time.

50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answers

Answer: C {m | m > 2}

Step-by-step explanation:

write the number in exponential form with the base of 2

2^3m-4 > 2^2

compare the exponents = 3m-4 >2

move the constant to the right and then change the sign

3m> 2+4 add

3m>6 divide

m>2

In problem # 14 solve for y.

Answers

The required value of y is 14 units for the given right triangle.

14. It is required to find the value of y.

According to the attached figure, we have a right triangle that has:

Length of AB = x units

Length of BC = 7 units

Length of AC = y units

∠ABC = 90°

∠BAC = 30°

As per the sine ratio, it can be written as follows:

sin 30° = BC/ AC

1/2 = 7/y

Apply the cross-multiplication, and we get

y = (7)(2)

y = 14 units

Therefore, the required value of y is 14 units for the given right triangle.

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Stephanie bought two rugs. One rug is 15 feet long, and the other rug is 142 feet long. Each rug has a width of 10 feet.
What is the total area in square feet of the two rugs?
A 175 ft²
B 155 ft²
C 147.5 ft²
D 302.5 ft²
*please help me

Answers

The total area of the two rugs in square feet is calculated as: 1570 ft² (none of the options are correct).

How to Find the Total Area of the Rug?

To find the total area of the two rugs, we first need to calculate the area of each rug by multiplying its length and width.

Area of the first rug = 15 ft x 10 ft = 150 ft²

Area of the second rug = 142 ft x 10 ft = 1420 ft²

Now, we can find the total area by adding the area of both rugs:

Total area = 150 ft² + 1420 ft² = 1570 ft²

Therefore, the answer is not one of the options provided.

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Please find the equation of the circle! (Thx)

Answers

Answer:

[tex] {(x - 1)}^{2} + {(y - 2)}^{2} = 5 [/tex]

Oscar buys his lunch in the school cafeteria the cost of 15 school lunches is 33.75 which graph has a slope that best represents the average cost of the lunches in dollar per lunch ?

Answers

Answer:

The graph should be increasing 2.25 each time

Step-by-step explanation:

Since Oscar buys his lunch in school cafeteria and the cost of 15 school lunches is 33.75

Divide them: 33.75 ÷ 15 =

and will represents the average cost of the lunches in dollar per lunch that is 2.25

what is 5w–4w–w+6w simplified

Answers

The value of the expression 5w–4w–w+6w is 6w

What is simplification of expression?

When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

For example, 2( 3a+5) can be simplified by using 2 to multiply both 3a and 5. This will give 6a+10. This means that the simplification of 2(3a+5) = 6a+10.

Similar , 5w-4w-w+6w can be simplified into:

5w+6w-4w-w

= 11w-5w

= 6w.

Therefore,the value of the expression 5w–4w–w+6w is 6w

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Solve for x. Round to the nearest tenth, if necessary.

Answers

Answer:

9.6

Step-by-step explanation:

sin(angle)= opposite/hypotenuse

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

X=9.6

Answer:

Step-by-step explanation:

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

sin(42°)=6.4/X

X*SIN(42°)=6.4

X=6.4/SIN(42)

X=9.6

ALPHABET Which of the following letters
contain at least one acute angle? Which
contain vertical angles? Which contain
adjacent angles?
A E L X

Answers

The letters "L" and "X" both contain adjacent angles, as adjacent angles are angles that share a common vertex and side. In both letters, there are two angles that share a vertex and a side.

What is Acute angle ?

An acute angle is an angle that measures between 0 and 90 degrees. In other words, an acute angle is an angle that is smaller than a right angle, which measures exactly 90 degrees.

The letter "A" contains an acute angle, as the angle between the two lines that form the letter is less than 90 degrees.

None of the letters A, E, L, or X contain vertical angles, as vertical angles are formed by two intersecting lines and none of these letters contain intersecting lines.

Therefore, The letters "L" and "X" both contain adjacent angles, as adjacent angles are angles that share a common vertex and side. In both letters, there are two angles that share a vertex and a side.

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HELP QUICK!
The owners of the pet sitting business have set aside $96 to purchase chewy toys for dogs, x, and collars for the cats, y. They are pricing the items at two different stores and wondering if there are any combinations of these items that could be purchased at both stores for the same price.

Marco’s Market: The price of a chewy toy for dogs is $2 while the price of a cat collar is $8.

Sonia’s Superstore: The price of a chewy toy for dogs is $4 and the price of a cat collar is $4.

Create an equation to represent the quantities of each item that can be purchased at each store. Then, graph the equations on the coordinate axes with proper labels and scale. Use the graph to find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores.

Answers

Answer:Let's assume that the number of chewy toys for dogs purchased at Marco's Market is represented by x, and the number of cat collars purchased at Marco's Market is represented by y. Similarly, let's assume that the number of chewy toys for dogs purchased at Sonia's Superstore is represented by a, and the number of cat collars purchased at Sonia's Superstore is represented by b.

The total cost of chewy toys for dogs and cat collars at Marco's Market is given by:

2x + 8y

The total cost of chewy toys for dogs and cat collars at Sonia's Superstore is given by:

4a + 4b

We want to find values of x, y, a, and b such that:

2x + 8y = 4a + 4b

Simplifying the equation, we get:

x + 4y = 2a + b

We also know that the total amount set aside for the purchases is $96. Therefore, we have:

2x + 8y + 4a + 4b = 96

Simplifying the equation, we get:

x + 4y + 2a + b = 48

Now, we can plot the graph of the equation:

x + 4y = 2a + b

To plot the graph, we can rearrange the equation as follows:

4y - b = 2a - x

y = (2a - x + b)/4

We can choose values of x and b, and then calculate the corresponding values of y and a using the equation. For example, let's choose x = 0 and b = 8. Then, we have:

y = (2a - 0 + 8)/4 = (2a + 8)/4 = 0.5a + 2

Similarly, we can choose other values of x and b, and calculate the corresponding values of y and a. We can then plot the points on the graph and join them to get the line representing the equation.

Here is the graph:

Graph

To find the combination of chewy toys for dogs and cat collars for cats that adds up to the same amount and price at both stores, we need to find the point where the line intersects the line representing the equation of the total cost:

x + 4y + 2a + b = 48

We can find this point by solving the two equations simultaneously. However, we can also use the graph to estimate the point. From the graph, we can see that the point of intersection is approximately (12, 6). This means that we can purchase 12 chewy toys for dogs and 6 cat collars at Marco's Market, and 4 chewy toys for dogs and 10 cat collars at Sonia's Superstore, and the total cost would be $48 at both stores.

Step-by-step explanation:

A bag contains pennies, nickels, dimes, and quarters. There are 50 coins in all. Of the coins, 12% are pennies and 34% are dimes. There are 3 more nickels than pennies. How much money does the bag contain?

Answers

Answer:

i think the bag contains $3.56

Step-by-step explanation:

College Level Trig Question

Answers

Note tha given the above trigonometric expression, the solution is

x = 2π/3 or 4π/3

How did we arrive at that ?

We will start by simplifing the equation by moving all the terms involving sin (x/2) to one side..

2sin (x /2) = √(3)

Then, we can solve for sin(x/2) by dividing both sides by two

sin (x /2) = √(3)/2

This is true when x/2 is π /3 or 2π/3, since these are the values where

sin ( π/3) = √(3)/2 and

sin (2π/3) = √(3)/2.

To find the values of x, we multiply these solutions by two

x = 2pi/3 or 4pi/3

Since we need to make sure that these solutions are in the given interval (0, 2π)

both solutions are in the interval, so our final answer is

x = 2π/3 or 4 π/3

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The questions I need answered are in the picture… help plsss

Answers

The graph of the linear equation y = (1/2)*x + 3 can be seen in the image at the end.

How to graph the linear equation?

Here we want to graph the linear equation:

y = (1/2)*x + 3

To graph it we need to find a few points on the line, graph them on a coordinate axis and then draw a line that connects them.

The first point that we can use is the y-intercept, it is what we get when we evaluate in x = 0.

y = (1/2)*0 + 3

The point is (0, 3)

Then we can get other points by evaluating in different values of x, for example, if x = 2

y = (1/2)*2 + 3 = 1+ 3 =4

If x = 4

y = (1/2)*4 + 3 = 2 + 3 = 5

So we have the points (2, 4) and (4, 5)

Now just graph all these points on a cordinate axis and connect them with a line, you will get a graph like the one in the image below.