Solve for x and graph the solution on the number line below. If possible, resolve your answer to a single inequality. In case of no solution (∅), leave the number line blank.
−3x+4≤−23 and−29≥−3x+4

Matrix A is invertible such that A⁻¹ = - A - 3I. This is solved using the Calely Hamilton Theorem.

This theorem says that every square matrix satisfies its own characteristic equation. In other words, the scalar polynomial

p(λ) = det(λI − σ) also holds for the stress polynomial p(σ).

It also states that The roots λ₁, λ₂........λₙ of a typical equation (aₙλₙ + aₙ₋₁ λⁿ⁻¹ + ...... a₁ λ + a₀)  will indicate the nature of the Matrix A. If either of the roots of the attributes equation is 0, the matrix's determinant becomes zero. As a result, the matrix is non-invertible.

Based on the above, we know that Matrix A fulfills the qualities below::

A²+3A + I = 0

Since every square matrix fulfills its own characteristic

λ₁ + λ₂ = -3

λ₁ x λ₂ = 1 ≠ 0

This is true for any order of a square matrix. That is:
λ₁ x λ₂ x λ₃ x........ x λₙ ≠ 0

Thus

|A| = λ₁ x λ₂ x λ₃ x........ x λₙ

|A| ≠ 0 → Invertibel Matrix

A² + 3A + I = 0
I = -A² - 3A
A⁻¹ x I = A⁻¹ (-A - 3A); hence

A⁻¹ = - A - 3I

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The y-intercept of the function F(x) = x⁴ + 2x - 2 is -2 and the profile is matched to the given graph thus option (B) is correct.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

As per the given graph of the function,

In option (B),

F(x) = x⁴ + 2x - 2

Put x = 0

F(0) = 0 + 0 - 2 = -2

Thus, (0,-2) will be the y-intercept which is matching in the graph.

Hence "The y-intercept of the function F(x) = x⁴ + 2x - 2 is -2 and the profile is matched to the given graph".

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The value of t in the equation can be express as follows:

[tex]t = \frac{V-7\pi r^{2} }{6\pi r}[/tex]

The subject of a formula is the variable that is being worked out. The subject of a formula is the variable which is expressed in terms of the other variables.

The variable to be worked out is t.

Therefore,

V = 6πrt + 7πr²

Therefore, let's make t the subject of the formula,

V = 6πrt + 7πr²

subtract 7πr² from both sides of the equation.

V = 6πrt + 7πr²

V - 7πr² = 6πrt + 7πr² -7πr²

V - 7πr² = 6πrt

divide both sides of the equation by 6πr

Hence,

[tex]\frac{V-7\pi r^{2} }{6\pi r}=t[/tex]

Therefore,

[tex]t = \frac{V-7\pi r^{2} }{6\pi r}[/tex]

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Answer:

Step-by-step explanation:

Remove any grouping symbol such as brackets and parentheses by multiplying factors.

Use the exponent rule to remove grouping if the terms are containing exponents.

Combine the like terms by addition or subtraction

Combine the constants

Simplify 3x2 + 5x2

Solution

Since both terms in the expression are have same exponents, we combine them;

3x2 + 5x2 = (3 + 5) x2 = 8x2

Answer:

58

Step-by-step explanation:

You would have to turn 7 1/4 into a whole fraction.

Do,

7 * 4 = 28

28 + 1 = 29

Your new fraction would be,

29/4

Now you have to make them equal denominators with 1/8.

Lets see,

Now multiply 4 * 2 is 8.

So multiply 29 times 2.

Which is 58.

Your new fraction is,

58/8

So therefore you would have 58 pieces.

According to the given ratio, the hourly pay before the increase for Marta and for Khalid is 1.2

Ratio:

Ratio refers the ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

The ratio of Marta's hourly pay to Khalid's hourly pay is 6:5 Both Marta and Khalid get an increase of £1.50 in their hourly pay. The ratio of Marta's hourly pay to Khalid's hourly pay after this increase is 13:11.

Here we need to work out the hourly pay before the increase for Marta and for Khalid.

So, it can be written as,

=> 6 : 5

And the new pay after the increase is

=> 13 : 11

So, when we equate this, then we get,

=> 6/5 = 13/11

=> 1.2 = 1/2

Therefore, the hourly pay before the increase for Marta and for Khali is 1.2

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a. The researcher should expect each person to get 17 guesses correct under the null hypothesis that the person is guessing.

b. Person A has a smaller p-value because the person's number of successes is further to the hypothesized number of successes.

At the null hypothesis, it is tested if the person is guessing, that is, if the proportion is of 0.5, hence:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, it is tested if there is enough evidence to conclude that the person is not guessing, that is, if the proportion is different than 0.5, hence:

[tex]H_0: p \neq 0.5[/tex]

Considering the tested proportion of 0.5, the expected number of correct guesses on the 34 trials is of:

0.5 x 34 = 17 correct guesses.

The test statistic is given by the equation presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

The parameters that are the same for each person are given as follows:

[tex]p = 0.5, n = 34[/tex]

The sample proportions are given as follows:

Then the test statistics are given as follows:

Person A is farther from the mean due to the higher test statistical, hence it has a smaller p-value.

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In a random sample of 32 times loading Twisting Thunder and 36 times loading Spiral Wonder, the probability is 0.9574.

It's also known as the Gaussian Distribution. It is the most important continuous probability distribution in the world. Because the curve resembles a bell, it is also known as a bell curve.

The average time for riders to board the Twisting Thunder roller coaster is 49 seconds, with a standard deviation of 7.1 seconds.

The likelihood in a random sample of 32 is

z= (x-μ)/σ

z=(32-49)/7.1

z= -2.394

P(x32) =0.0083246 from the Z-Table

The average time to board the Spiral Wonder roller coaster is 44.8 seconds, with a standard deviation of 3.7 seconds.

In a random sample of 36, the probability is

z= (x-μ)/σ

z=(36-44.8)/3.7

z= -2.37838

P(x36) = 0.0086945 from the Z-Table

In a random sample of 32 times loading Twisting Thunder and 36 times loading Spiral Wonder, the probability is P(x32)/P(x36)=0.0083246/0.0086945 =0.9574.

A random sample has a probability of 0.9574.

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Answer: 7,000

Step-by-step explanation: I took the test

Answer:

f(3)=5

Or

(3,5)

Step-by-step explanation:

all you have to do is look at what y axis is on the line when x=3

And y=5

f(3)=5

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The value of test statistic t is -2.39 and P-value is P(t₈< -2.39).

The mean and the standard deviation can be calculated from the below formulae:

Sample mean (X)= (∑xi)/n

Sample standard deviation (s)= √(∑xi- X)²/(n-1)

where, n is sample size = 9

xi= elements in sample

On calculation we get X as,

X = (3.5+6.5+6.5+5.5+19.5+7+12.5+20+10.5)/9 = 10.17

s = √(∑xi- X)²/(n-1)

= √(44.49+13.47+13.47+21.81+87.05+10.05+5.43+96.63+0.11)/8

= √36.57 = 6.04

t would represent the static, it is given by the formula,

t = (X-μ₀)/(s/√n)

where μ₀ = 15 from the data (the value we want to test)

t = (X-μ₀)/(s/√n) = (10.17-15)/(6.04/√9) = -2.39

The formula to find out P value is pv = P(t₈< -2.39)

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Answer:

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

When the ball is punted the value of x is zero, therefore f(0) is:

Answer:

1.5 feet

Step-by-step explanation:

Given function,

→ f(x) = (-16/1225)x² + (7/5)x + 1.5

Required function,

→ f(x) = f(0)

→ f(0) = (-16/1225)x² + (7/5)x + 1.5

Now the needed height is,

→ (-16/1225)x² + (7/5)x + 1.5

→ (-16/1225)(0)² + (7/5)(0) + 1.5

→ 0 + 0 + 1.5

→ 1.5 feet

Hence, the height is 1.5 feet.

Answer:

undefined

Step-by-step explanation:

to find slope it’s y2-y1/x2-x1

9-7/-2-(-2)

2/0

Undefined slope

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For the given confidence interval, the correct statement is Option C. The manager can be 99% confident that the constructed interval captures the true mean number of fish in saltwater tanks.

Confidence interval:

Confidence interval refers the mean of your estimate plus and minus the variation in that estimate.

Given,

Here we need to find which of the following correctly interprets the 99% confidence interval for the true mean number of fish in saltwater tanks.

While we looking into the given question,

We know that, it states that 99% confidence interval for the true mean number of fish in saltwater tanks,

Based on these fact the correct statement is the manager can be 99% confident that the constructed interval captures the true mean number of fish in saltwater tanks.

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The total amount the college student will have in the savings account after 5 years will be $15,095

From the question, we are to determine the amount the college student has in savings.

From the compound interest formula, we have that

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

Where A is the amount

P is the principal

r is the interest rate

n is the number of times compounded per year

and t is the time.

From the given information,

P = $13,000

r = 3%= 0.03

n = 4

t = 5

Putting the parameters into the formula

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

A = 13000(1 + 0.03/4)^(4×5)

A = 13000(1 + 0.03/4)^20

A = $15095.39

A ≈ $15095

Hence, the amount is $15,095

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Using the given information to complete this compounding interest question is as follows:

1. Period Used = 28 quarters

2. Rate Used = 2%

3. PV factor used = 1.14987

4. PV of the amount desired at end of the period = $15,306.04.

Compound interest adds the accumulated interest to the principal amount after each period in order to compute the period's interest.

Compound interest is the opposite of simple interest, which does not add the accumulated interest to the principal before computing another period's interest.

N (# of periods) = 28 quarters (7 x 4)

I/Y (Interest per year) = 2%

PMT (Periodic Payment) = $0

FV (Future Value) = $17,600

Results:

PV = $15,306.04

Total Interest = $2,293.96

PV factor = 1.14987

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In scientific notation, the amount of paper used weekly by the Pittsburgh paper is approximately 5.0 x 10⁷ times more than the amount used by the Newville paper.

Scientific notation is a shorthand or approximated way to write large or small numbers.

Scientists use scientific notations to eliminate the many zeros in a number so that the number is written in a standard form.

In scientific notation, a positive integer is multiplied by another integer (positive or negative) in the power of ten.

The best way to compute the ratio of paper usage at the two newspapers is to rewrite the numbers in long form and convert the answer to scientific notation.

Location     Paper Used (square yards)

Newville     8.0 x 10³ = 8,000

Pittsburgh  4.0 x 10¹¹ = 400,000,000,000

The ratio of Pittsburgh to Newville = 8,000:400,000,000,000

= 1: 50,000,000

= 1: 5.0 x 10⁷

We can also divide 400,000,000,000 by 8,000 to get 50,000,000, which can then be written in standard form as 5.0 x 10⁷.

Thus, expressing the result in scientific notation, the Pittsburgh paper approximately uses 5.0 x 10⁷ more paper than the Newville paper.

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Location     Paper Used (square yards)

Newville     8.0 x 10³

Pittsburgh  4.0 x 10¹¹

The program is an illustration of loops and conditional statements and the part of the complete program is

n = int(input())

for i in range(1,n+1):

  if not(i%3 == 0 or i%5==0):

The program written in Python where comments are used to explain each line is as follows:

#This gets input for n

n = int(input())

#This iterates through n

for i in range(1,n+1):

  #If the current number is not a multiple of 3 and 5

  if not(i%3 == 0 or i%5==0):

      #This prints the number

      print(i,end="")

  else:

      #This prints "Fizz", if the current number is a multiple of 3

      if i%3 == 0:

          print("Fizz",end="")

      #This prints "Buzz", if the current number is a multiple of 5

      if i%5==0:

          print("Buzz",end="")

  #This prints a new line

  print()

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Answer:

X Y

1. 2

2. 3

3. 4

This is the answer to your question

Line e is parallel.

Line h is perpendicular.

Lines f and g are neither.

Answer:

[tex]\frac{3}{4} ft[/tex]

Step-by-step explanation:

at the first piece we can see it stops on the number line at 3/4

Also 3 divided by 4 is 3/4

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Answer:

3/4

Step-by-step explanation:

Look at 1 ft on the ruler below at left. The foot is divided into 4 equal parts, so each small part is 1/4 ft. The length of each piece of wire is 3 of these 1/4 ft lengths, so each piece of wire is 3/4 ft long.

Answer: 3/4

Answer:

The correct answer is: The pizza is heavier

Step-by-step explanation:

(11/5) * 10^3 = 2200 grams of pizza against 1,300 grams of cake

The intersection of two regular pentagons can be hexagon. Therefore, option D is the correct answer.

We need to find the figure formed with the intersection of two regular pentagons.

If all the polygon sides and interior angles are equal, then they are known as regular polygons. In a regular pentagon all the five sides are equal and all the angles are equal in measure.

Here, the intersection of two regular pentagons form a hexagon.

In a shape hexagon there are 7 sides.

The intersection of two regular pentagons can be hexagon. Therefore, option D is the correct answer.

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The total number of transistors in the Titan is equal to 5.950 × 10²¹ transistors.

A supercomputer simply refers to one of the most powerful computers that is designed and developed for handling, evaluating, and solving very complicated problems, calculations, or tasks, better than ordinary desktop or laptop computers.

In order to determine the total number of transistors in the Titan, we would multiply the number of transistors in its central processing unit (CPU) by the number of transistor in its graphics processing unit (GPU) as follows:

Total number of transistors = 4.485 × 10¹⁰ × 1.3268 × 10¹¹

Total number of transistors = (4.485 × 1.3268) × (10¹⁰ × 10¹¹)

Total number of transistors = 5.950 × (10⁽¹⁰ ⁺ ¹¹⁾)

Total number of transistors = 5.950 × 10²¹ transistors.

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Complete Question:

Supercomputers have been developed that are much larger and can perform many more calculations than ordinary desktop or laptop computers. One such supercomputer, the Titan, has 4.485 × 10¹⁰. transistors in its central processing unit (CPU) and another 1.3268 × 10¹¹. transistor in its graphics processing unit (GPU). Find the total number of transistors in the Titan. Show your working and give your answers in standard form.

Answer:

90 books

Step-by-step explanation:

B:C

3:7

X:210

210÷7=30

3*30=90

Answer:

3:7

x:210

=210(3) ÷7

=90

The coordinate of the quadratic function at the intersection with the y-axis is (0, 1).

Given that,

A quadratic function is graphed with a y-intercept of 1.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,

The graph of a quadratic function is shown, whose y-intercept is 1,

by this, we can conclude that when the quadratic function interset the y axis the coordinate of the intersection point is (0, 1).

Thus, the coordinate of the quadratic function at the intersection with the y-axis is (0, 1).

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Answer:

[tex]-1[/tex]

Step-by-step explanation:

Using the graph, when the input, [tex]x[/tex], is 0, the output, [tex]y[/tex] is [tex]-1[/tex].

Answer:

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

Find the line with the given points  (-2, -2) and (2, 0).

Find the slope:

Use point-slope equation and one of the points:

When x = 0, the output is:

Answer:

24663.9!

Step-by-step explanation:

The required cost of the loan is given as $100,966.80.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
Bought a new house for $195,000.
Financed the house and the monthly payments are $822.13 a month for 30 years.

Total money paid against the loan = 822.13 × 30 × 12
                                                    = $295,966.8

Cost of the loan = 295,966.8 - 195,000
                         = $100,966.8

Thus, the required cost of the loan is given as $100,966.80.

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