Which statement correctly describes the relationship between the graph of f (x) and the graph of g(x) = f (x) – 4 ​

Step-by-step explanation:

p = -1, -4

q = -2, 2

p-q = (-1, -4) -1(-2, 2)

= 1, -6

a) \(\[8\int_{-\infty}^{0} e^{-j\theta} d\theta = 1\]\)

To solve this integral, we can use the fundamental property of the exponential function:

\(\[\int e^{ax} dx = \frac{1}{a} e^{ax} + C\]\)

In this case, we have \(\[e^{-j\theta}\].\) Since \(\(j\)\) represents the imaginary unit, we can rewrite it as \(\[e^{-i\theta}\].\)

Using the property of the exponential function, we have:

\(\[8\int_{-\infty}^{0} e^{-j\theta} d\theta = 8 \left[\frac{1}{-j} e^{-j\theta}\right]_{-\infty}^{0}\]\)

Evaluating the limits, we have:

\(\[8 \left(\frac{1}{-j} e^{0} - \frac{1}{-j} e^{-j(-\infty)}\right)\]\)

Simplifying, we get:

\(\[8 \left(\frac{1}{-j} - \frac{1}{-j} \cdot 0\right) = 8 \left(\frac{1}{-j}\right) = 8 \cdot (-j) = -8j\]\)

Therefore, \(\[8\int_{-\infty}^{0} e^{-j\theta} d\theta = -8j\].\)

b) \(\[\int_{0}^{1} 8(1-2)\cos(\theta) d\theta = 0.4 - 2(x-1)\]\)

To solve this integral, we can use the property of the cosine function:

\(\[\int \cos(ax) dx = \frac{1}{a} \sin(ax) + C\]\)

In this case, we have \(\[8(1-2)\cos(\theta) = -8\cos(\theta)\]\). Therefore, we can rewrite the expression as:

\(\[\int_{0}^{1} -8\cos(\theta) d\theta = 0.4 - 2(x-1)\]\)

Using the property of the cosine function, we have:

\(\[-8 \int_{0}^{1} \cos(\theta) d\theta = 0.4 - 2(x-1)\]\)

The integral of the cosine function is given by:

\(\[\int \cos(\theta) d\theta = \sin(\theta) + C\]\)

Evaluating the integral, we get:

\(\[-8 \left[\sin(\theta)\right]_{0}^{1} = 0.4 - 2(x-1)\]\)

Simplifying, we have:

\(\[-8 \left(\sin(1) - \sin(0)\right) = 0.4 - 2(x-1)\]\)

\(\[-8\sin(1) = 0.4 - 2(x-1)\]\)

Finally, we can solve for \(\(x\)\) by isolating it on one side:

\(\[2(x-1) = 0.4 + 8\sin(1)\]\)

\(\[x - 1 = 0.2 + 4\sin(1)\]\)

\(\[x = 1.2 + 4\sin(1)\]\)

Therefore, \(\[\int_{0}^{1} 8(1-2)\cos(\theta) d\theta = 0.4 - 2(x-1)\] simplifies to \(x = 1.2 + 4\sin(1)\).\)

c) \(\[\int_{1}^{2} \sqrt{8(2-1)}e^{2(x-1)} dt = e^{22(x-2)}\]\)

Let's simplify the expression first:

\(\[\int_{1}^{2} \sqrt{8}e^{2(x-1)} dt = e^{22(x-2)}\]\)

We can factor out \(\(\sqrt{8}\)\) from the integral:

\(\[\sqrt{8} \int_{1}^{2} e^{2(x-1)} dt = e^{22(x-2)}\]\)

The integral of \(\(e^{2(x-1)}\)\) can be evaluated using the following property:

\(\[\int e^{ax} dx = \frac{1}{a} e^{ax} + C\]\)

In this case, \(\(a = 2\)\), so the integral becomes:

\(\[\sqrt{8} \left[\frac{1}{2} e^{2(x-1)}\right]_{1}^{2} = e^{22(x-2)}\]\)

Evaluating the limits, we have:

\(\[\sqrt{8} \left(\frac{1}{2} e^{2(2-1)} - \frac{1}{2} e^{2(1-1)}\right) = e^{22(x-2)}\]\)

Simplifying, we get:

\(\[\sqrt{8} \left(\frac{1}{2} e^{2} - \frac{1}{2} e^{0}\right) = e^{22(x-2)}\]\[\sqrt{8} \left(\frac{1}{2} e^{2} - \frac{1}{2}\right) = e^{22(x-2)}\]\)

Simplifying further, we have:

\(\[\sqrt{8} \left(\frac{e^{2}}{2} - \frac{1}{2}\right) = e^{22(x-2)}\]\[\sqrt{8} \left(\frac{e^{2} - 1}{2}\right) = e^{22(x-2)}\]\)

Finally, we can solve for \(\(e^{22(x-2)}\)\) by isolating it on one side:

\(\[e^{22(x-2)} = \sqrt{8} \left(\frac{e^{2} - 1}{2}\right)\]\)

Therefore, \(\[\int_{1}^{2} \sqrt{8(2-1)}e^{2(x-1)} dt = e^{22(x-2)}\] simplifies to \(e^{22(x-2)} = \sqrt{8} \left(\frac{e^{2} - 1}{2}\right)\).\)

To know more about limits visit-

brainly.com/question/30958821

#SPJ11

Answer:10

Step-by-step explanation:

beausepppppp

The side length of the smaller cube inscribed within the sphere is approximately 0.7071.

To find the side length of the smaller cube inscribed within the sphere, which is inscribed in a unit cube, we can follow these steps:
Determine the diameter of the inscribed sphere.
Since the sphere is inscribed in the unit cube, its diameter will be equal to the side length of the unit cube. Therefore, the diameter of the inscribed sphere is 1.
Calculate the radius of the inscribed sphere.
The radius of the sphere is half of its diameter, so the radius is 0.5.
Apply the Pythagorean theorem to the smaller cube.
We can imagine a right triangle formed by half the side length of the smaller cube (let's call this length 's') and the sphere's radius (0.5) as the two shorter sides, and the diagonal of the smaller cube as the hypotenuse.
By applying the Pythagorean theorem, we get:
(s/2)^2 + (s/2)^2 = (0.5)^2
Solve for the side length 's' of the smaller cube.
Expanding the equation, we get:
2 * (s^2 / 4) = 0.25
(s^2 / 2) = 0.25
s^2 = 0.5
s = sqrt(0.5)
Express the side length 's' of the smaller cube.
The side length of the smaller cube, 's', is equal to the square root of 0.5, which can also be written as sqrt(0.5) or approximately 0.7071.
So, the side length of the smaller cube inscribed within the sphere is approximately 0.7071.

for more questions on cube

https://brainly.com/question/10421656

#SPJ11

Answer:

13 more cups of trail mix or 13 1/4 cups

Step-by-step explanation:

1 1/2 (nuts) + 1/4(raisins) + 1/4(pretzels)=2 cups of trail mix

15-2=13

Answer: pi/2

Step-by-step explanation:

This statistic is based on an average of all players in the NFL. The average weight of a random sample of 50 NFL players may be slightly different.

This statistic is based on an average of all players in the NFL. It is not possible to accurately estimate the average weight of a random sample of 50 NFL players without actually measuring the weight of each individual player. The average weight of a random sample of 50 NFL players may be slightly different due to the randomness of the sample and individual player physical characteristics.

In order to accurately determine the average weight of a random sample of 50 NFL players, the weight of each individual player must be measured. The sample size of 50 players is relatively small, and the results may be significantly affected by the inclusion or exclusion of a single player. Additionally, the average weight of the sample may vary due to individual player physical characteristics such as height, body composition, and muscle mass. Furthermore, the average weight could be affected by the age and experience level of the players in the sample. All of these factors should be taken into consideration when attempting to determine the average weight of a random sample of NFL players.

Learn more about statistic here

https://brainly.com/question/14128303

#SPJ4

Answer:

1 cm = 16.5 m

1 m = 1 : 16.5 = 0.060606 cm

480 * 0.060606 = 29.09088 cm ( on the scale drawing )

B :

1.5 in = 0.5 ft

6 ft = 0.5 ft * 12

12 * 1.5 in = 18 inches

Step-by-step explanation:

Answer:

$154,430.64

Step-by-step explanation:

The first step is for us to determine the monthly payment as follows:

Mortgage amount can be found as the present value of all monthly payments, hence, using the formula below we can determine monthly payment as follows:

mortgage amount=monthly payment*(1-(1+r)^-n/r

mortgage amount=$305,500

monthly payment is unknown

r=monthly interest rate=5.75%/12=0.4791667%

n=number of monthly payments in 20years=20*12=240

305,500=monthly payment*(1-(1+0.4791667% )^-240/0.4791667%

305,500=monthly payment*(1-0.31750756 )/0.0047916670

305,500=monthly payment*0.68249244 /0.0047916670

monthly payment=305,500*0.0047916670 /0.68249244

monthly payment=$2,144.87  

Number of months that payments have been made=6*12=72

total paid=$2,144.87*72

total paid for 6 years=$ 154,430.64  

Rote learning is NOT a problem- solving strategy in mathematics.

Mathematics is the study of numbers, shape, quantity, and patterns. Teaching methods of mathematics include problem- solving, lecture, inductive, deductive, analytic, synthetic and Discovery Method. The teacher adopts any method according to the needs and interest of students.

Now, According to the question:

Problem Solving Strategy in Mathematics: In a mathematics class, students at the primary level enjoy learning, solving problems, develop mathematical curiosity and become confident in using mathematics to analyze and solve problems.

Problem - solving is a learner- centered approach that emphasizes learner's active involvement in the learning process. In this approach, teachers create a problematic situation for students and then assists them in perceiving, defining and stating the problems in a fear- free classroom environment.

Hence, Rote learning is NOT a problem- solving strategy in mathematics

Learn more about Solving Strategy at:

https://brainly.com/question/3150777

#SPJ4

The value of data that might affect the statistical measures of spread and center is B. There is a high data value that causes the data set to be asymmetrical for the males.

Outliers stretch out the data further, resulting in a wider range and a higher standard deviation. On the other hand, eliminating outliers reduces data spread, resulting in a lower range and standard deviation.

When an outlier is present, it might change the way the graph looks since it raises the mean. From the chart, there is a high data value in the males which will therefore make the data to be asymmetrical for the males as the larger spread for the males means the data set tilts towards them.

Find out more on spread and center at https://brainly.com/question/28660799

#SPJ1

Answer:

C. (-7, -15)

Step-by-step explanation:

Both the x- and the y-coordinates of a point in the third quadrant are negative.  The given point C. (-7, -15) is the only one of the four choices that satisfies this criterion.

Answer:

8/3

Step-by-step explanation:

1. 2 ÷ 3 = .66

.66 · 4 = 2.6

2. 4 × 2/3 =

4/1 × 2/3 = 8/3

good luck, i hope this helps :)

Answer:

its close 9.45

Step-by-step explanation:

7(x+9)=132

7x+63=132

7x=132-63

7x=69

x=69/7

x=9.45

Answer:

Your answer is 67/9 or 9 6/7

Step-by-step explanation:

Answer: 1. infinitely many solutions

2. no solution

3. one solution

4. no solution

5. infinitely many solutions

Step-by-step explanation:

1. infinitely many solutions - when it is consistent and the number of variables is more than the number of nonzero rows

2. no solution - would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable.

3. one solution - which is when one variable equals one number

4. no solution

5. infinitely many solutions

=============================================

Work Shown:

7(8+4k)+12

7*8+7*4k+12 ..... distributive property

56+28k+12

28k+56+12

28k+68

Answer:

28k + 68? I think

Step-by-step explanation:

expand by distributing terms

56+28k+12

collect lile terms

28k+(56+12)

Simplify

28k+ 68

Step 1: Multiply a and c

a = 1

c = 20

a * c = 20

Step 2: Find factors of +20 that add up to +9

Factors of 20 = 1, 2, 4, 5, 10, 20

The two factors that add up to 9 are 4 and 5.

Step 3: Factor

(x + 4)(x + 5) = 0

Answer: (x + 4)(x + 5) = 0

Hope this helps!

Answer:

C

Step-by-step explanation:

The y-coordinate is the average of 7 and -1 which is 3. This eliminates options A and D. Option B doesn't make sense since 5 is greater than 3, so that leaves us with option C.

Answer:

C.

Step-by-step explanation:

The midpoint is (3+2)/2 , (7 + -1) / 2)

= (5/2, 6/2)

= (5/2, 3)

Answer:

a. 129 meters

Step-by-step explanation:

The given parameters of the tree and the point B are;

The horizontal distance between the tree and point B, x = 125 meters

The angle of depression from the top of the tree to the point B, θ = 46°

Let h represent the height of the tree

The horizontal line at the top of the tree that forms the angle of depression with the line of sight from the top of the tree to the point B is parallel to the horizontal distance from the point B to the tree, therefore;

The angle of depression = The angle of elevation = 46°

By trigonometry, we have;

tan(θ) = h/x

∴ h = x × tan(θ)

Plugging in the values of the variables gives;

h = 125 × tan(46°) ≈ 129.44

The height of the tree, h ≈ 129 meters

According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean. Therefore, the approximate percentage of daily phone calls numbering between 35 and 75 is 95%.

We have been given that the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 55 and a standard deviation of 10.

We are asked to find out the approximate percentage of daily phone calls numbering between 35 and 75 using the empirical rule.

The empirical rule is used to describe how many of the observations fall within a certain distance of the mean in a normal distribution of data.

The empirical rule states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.

To use the empirical rule, we first need to find the z-scores for the values of 35 and 75. We can use the formula

z = (x - μ) / σ,

where x is the value we want to find the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

For x = 35, we have

z = (35 - 55) / 10 = -2, and

for x = 75, we have

z = (75 - 55) / 10 = 2.

So, the values of 35 and 75 are 2 standard deviations away from the mean. According to the empirical rule, approximately 95% of the data falls within two standard deviations of the mean.

Therefore, the approximate percentage of daily phone calls numbering between 35 and 75 is 95%.

Learn more about empirical rule visit:

brainly.com/question/1263320

#SPJ11

Answer:

c

Step-by-step explanation:

\(\text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}\)

==============================================

Reason:

The formula you can use is

\((a+b)^2 = a^2+2ab+b^2\)

This is the perfect square trinomial formula.

In this case,

The square of each gets us

Those form the outer terms, aka 1st and 3rd terms.

The 2ab term in the middle would be 2*x*(1/8) = (1/4)x

That leads us to be able to say \(\left(\text{x}+\frac{1}{8}\right)^2 = \text{x}^2 + \frac{1}{4}\text{x} + \frac{1}{64}\)

You can use the FOIL rule or the box method as two ways to verify this answer. Also a graphing calculator can be used.

Answer:

0.00825

Step-by-step explanation:

Move the decimal point two places to the left to go from a percentage to a decimal.

Answer:

Step-by-step explanation:

are there values for f or b or q? What are we trying to solve?

Two equilateral triangles are always similar.

Similarity is a geometric property that indicates that two shapes have the same shape but possibly different sizes. For equilateral triangles, all angles are equal, and all sides have the same length. Since the definition of an equilateral triangle specifies that all sides and angles are  congruent, any two equilateral triangles will have the same shape.

Therefore, regardless of the size or orientation of the two equilateral triangles, they will always be similar. Their corresponding angles will be equal, and their corresponding sides will be proportional. This is true for any pair of equilateral triangles, making them always similar.

Learn more about equilateral here:

https://brainly.com/question/17264112

#SPJ11

The following are the appropriate notations is P(EIF)=P(E n F) / P(F).

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

As, from the property of conditional probability

P(EIF)=P(E n F) / P(F)

Learn more about conditional property here:

https://brainly.com/question/10567654

#SPJ1

Answer:

\(y = \frac{ - 1}{2} x - 1\)

Step-by-step explanation:

You instructed to write the linear equetion in the form of y=mx+b .

So you must find the y intercept (b) and slop (m) .

the y-intercept is already expressed in the graph which is the line pass through y axis . It is -1 .

and to solve m (slop) we will use (0, -1) or (-2, 0)

It has the same answer . Let's use the 2nd one

y=mx+b

0=m(-2) -1

m(-2)=1

m= -1/2

we get y-intercept -1 and slop -1/2 so the equetion is written as

\(y = \frac{ - 1}{2} x - 1\)

Answer:

2.5 hours

Step-by-step explanation:

If u times 5.50 x 2.5 = 13.75

So 2.5 hours is basically 2h 30min

Answer:

n^2-3n-18 = (n-6)(n+3)        , -3x^2+15x-12 = -3(x-4)(x-1)

Step-by-step explanation:

Answer:

1. (n - 6)(n + 3)

2. -3 (x - 4) (x - 1)

Step-by-step explanation:

In this simplex tableau, x₄, x₅, and z are the basic variables, while x₁, x₂, x₃, x₆, x₇, and x₈ are the nonbasic variables. The values of all the variables associated with this basic feasible solution are x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, and z = 620.

In this tableau, the basic variables are x₄, x₅, and z, while the nonbasic variables are x₁, x₂, x₃, x₆, x₇, and x₈.

The basic variable associated with row 1 is x₄, the basic variable associated with row 2 is x₅, and the basic variable associated with row 3 is z.

The values of all the variables associated with this basic feasible solution are:

x₁ = 0, x₂ = 0, x₃ = 0, x₄ = 620, x₅ = 12, x₆ = 0, x₇ = 0, x₈ = 0, z = 620.

Note that these values correspond to the entries in the tableau in the "BV" column.

Learn more about basic variables here: brainly.com/question/30575036

#SPJ4

The missing tableau is in the image attached below