13. Check all the true statements.

Answer:

The solution is x < 3. To represent that on a number line, you'd have an open (not filled in) circle on 3 and shading to the left.

Step-by-step explanation:

You would only have a closed (solid/filled in) circle if the inequality had a ≤

The Laplace transform of the given function is [tex]f(s)=\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

Given,

[tex]f(t)=\left \{ {{t, 0\leq t < 5} \atop {0,t\geq 5}} \right.[/tex]

Write the function in unit step function.

[tex]f(t)=t(u_{0}(t)-u_{5} (t))[/tex]

      = [tex]t(1-u_{5}(t))[/tex]                       ∵[tex]u_{0} (t)=1[/tex]

      = [tex]t-tu_{5} (t)[/tex]

[tex]f(t)=t-tu_{5} (t)[/tex]

In order to make it easier to take the Laplace transform of the function, we can follow the steps:

[tex]f(t)=t-tu_{5} (t)[/tex]

      = [tex]t-(t-5+5)u_{5} (t)[/tex]

      = [tex]t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]

[tex]f(t)=t-(t-5)u_{5} (t)+5u_{5} (t)[/tex]

We need to find the Laplace transform of f(t).

Apply Laplace transform on both sides,

£[tex][f(t)=[/tex]£[tex](t)-[/tex]£[tex](t-5)u_{5} (t))+5[/tex]£[tex](u_{5} (t))[/tex]

         = [tex]\frac{1}{s^{2} } -e^{-s}[/tex]£[tex](t)+5(\frac{e^{-5s} }{s} )[/tex]

         = [tex]\frac{1}{s^{2} } -e^{-5s} (\frac{1}{s^{2} } )+\frac{5se^{-5s} }{s^{2} }[/tex]

        = [tex]\frac{1-e^{-5s}+5se^{-5s} }{s^{2} }[/tex]

       = [tex]\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

[tex]f(s) =\frac{1-e^{-5s}(1-5s) }{s^{2} }[/tex]

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Answer:

84

Step-by-step explanation:

4 (-4)^2 - 5(-4)

4 × 16 - 5 × -4

64 + 20

84

More than 50% of Americans rely upon television broadcasts for their news.

News, current occasions and ancient programming can help make younger humans extra aware of other cultures and those. Documentaries can help increase vital thinking about society and the arena. television can help introduce teens to classic Hollywood movies and overseas movies that they might not otherwise see.

It broadens the know-how of various cultures, and promotes tolerance and international information of worldwide issues. Through contemporary affairs, discovery, lifestyle, cooking indicates and children's programs, television encourages medical and cultural interest.

Agree with and effect: television is the most relied on a form of marketing and stays maximumly probable to make consumers chortle, circulate them to tears or cause feelings. For example, television is with the aid of a long way the maximum relied on shape of video advertising in Canada. 70% of 18-34-year-olds named tv the most truthful compared to 12% for online video.

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Answer: c = 520

Step-by-step explanation:

     f(2) = 578 means that when x = 2, the value is equal to 578. We will plug these knowns in and then solve for c.

Given:

    f(x) = 4x³ + 7x² - x + c

Substitute:

    578 = 4(2)³ + 7(2)² - (2) + c

Distribute:

    578 = 4 * 2³ + 7 * 2² - 2 + c

Raise to the power of 3 and 2:

    578 = 4 * 8 + 7 * 4 - 2 + c

Multiply:

    578 = 32 + 28 - 2 + c

Add:

    578 = 60 - 2 + c

Subtract:

    578 = 58 + c

Subtract 58 from both sides:

    520 = c

Reflexive property:

   c = 520

[tex] \huge\mathbb{ \underline{SOLUTION :}}[/tex]

Given:

[tex]\longrightarrow\bold{f(x) = 4x^3 + 7x2 −x + c}[/tex]

[tex]\longrightarrow\sf{578= 32+28 −2+ c}[/tex]

[tex]\longrightarrow\sf{578 =58+ c}[/tex]

[tex]\longrightarrow\sf{c = 578-58}[/tex]

[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]

[tex]\longrightarrow\sf{c= 520}[/tex]

Answer:

  (b)  2.175 miles to 2.185 miles

Step-by-step explanation:

When a value is rounded, the original "exact" value is presumed to be within 1/2 of the value of one least-significant unit of the rounded number.

A rounded value of 2.18 has a least-significant digit with a place value of 0.01 units. Half that value is the "margin of error". That is, the range of numbers that would be rounded to 2.18 is ...

  2.18-0.005 ≤ x < 2.18+0.005

  2.175 ≤ x < 2.185 . . . . miles

Answer:

someone please help me check my page

someone please help me check my pageStep-by-step explanation:

By the integral test, the series is convergent.

The sequence [tex]k^3/e^{k^4}[/tex] is clearly positive and decreasing for [tex]k\in\Bbb N[/tex]; then by the integral test,

[tex]\displaystyle \int_1^\infty \frac{x^3}{e^{x^4}} \, dx \le \sum_{k=1}^\infty \frac{k^3}{e^{k^4}}[/tex]

and

[tex]\displaystyle \int_1^\infty \frac{x^3}{e^{x^4}} \, dx = \frac14 \int_1^\infty e^{-u}\, du = \frac1{4e} < \infty[/tex]

By using the integral test, series converges

What is an integral test for convergence and divergence?

⇒ It is used to prove the divergence or convergence of series. This test is called the integral test, which compares an infinite sum to an improper integral. It is important to note that this test can only be applied when we are considering a series whose terms are all positive.

How to know if a series is converging or diverging?

If the limit exists and is a finite number (a number less than infinity), we say the integral converges. If the limit is ±∞ or does not exist, we say the integral diverges.

let aₓ= f (x) is any function

⇒ In order for the integral test to work The function must be positive it has to be continuous and it has to be decreasing when x≥1

If the integral converges it means the series is also converging

If the integral diverges it means the series is also diverging

The sequence [tex]k^{3} /{e^{k^{4} }[/tex] is clearly positive and decreases for k∈N then by the integral test,

[tex]\int\limits^\infty_1 {x^{3} /e^{x^4} dx[/tex] [tex]\leq\displaystyle \sum^{\infty}_{k = 1} {x^{3} /e^{x^{4}[/tex]

and

[tex]\int\limits^\infty_1 {x^{3} /e^{x^4} dx[/tex][tex]=1/4\int\limits^\infty_1 {x^{3} /e^{-u} du[/tex]

⇒ [tex]1/4 < \infty[/tex]

So it comes with a finite value hence the series converges

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9 hours long after the second runner started will the second runner overtake the first runner.

What does it mean to do speed?

Runner I = 6 mph

Runner II = 7 mph

Difference in time= 90 minutes

Train A will have covered 9 miles before Runner II starts

catch up distance= 9 miles

catch up speed = 7-6 mph

catch up speed = 1 mph

Catchup time = catchup distance/catch up speed

catch up time= 9/1

catch up time= 9 hours

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The statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A

It is important to note the following;

"Two triangles are similar when their corresponding angles are equal and corresponding sides are in equal proportion."

The SSS congruence states that ; "Two triangles are congruent if all three sides of a triangle are congruent to corresponding three sides of other triangle."

SSS similarity postulates that;  "Two triangles are similar if all the three sides of a triangle are in proportion to the three sides of another triangle."

SAS similarity postulates that ; "Two triangles are similar if the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle between the two sides in both the triangle are equal."

SAS congruence postulates that ; "Two triangles are congruent if two sides and the angle between these two sides of one triangle are congruent to the corresponding two sides and the included angle of a second triangle."

For given question,

We have been given triangles ABD and CBD.

B is the midpoint of line AC

⇒ AB = BC

For triangles ABD and CBD,

side AB = side CB; since, B is the midpoint of line AC

side BD = side BD ; they have common sides

side AD = side CD = 15 units each

So, by SSS postulates of triangle congruence triangles ABD and CBD are congruent triangles.

Therefore, the statement that best describes the relationship between triangles ABD and CBD is 'Triangles ABD and CBD are congruent by the SSS Congruence postulate'. Option A

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Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept.

we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.

x + 2y = 6

2y = -x + 6

y = -x/2 + 6

The measure of angle C is 35°.

Given that, ΔABC≅ΔDEF, ∠A=70°, ∠E=3x and ∠F=x+10.

Congruent triangles are triangles that have the same size and shape. This means that the corresponding sides are equal and the corresponding angles are equal.

In ΔABC and ΔDEF, corresponding angles are equal.

That is, ∠A=∠D=70°, ∠B=∠E=3x and ∠C=∠F=x+10

Now, ∠A+∠B+∠C=180° (∵angle sum property)

⇒70°+3x+x+10=180°

⇒4x=100°

⇒x=25°

Thus, ∠C=x+10=35°.

Therefore, the measure of angle C is 35°.

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Answer:

Solution:

here,

6 cans cost = 9 dollars

1 can costs = 9÷6 dollars

= 1.5 dollars

Now,

8 cans cost = 8×1.5 dollars

= 12 dollars

Using binomial distribution, the probability of

a. 5 will still be with the company after 1 year is 28%.

b. at most 6 will still be with the company after 1 year is 89%.

The probability of a new employee in a fast-food chain still being with the company at the end of the year is given to be 0.6, which can be taken as the success of the experiment, p.

We are finding probability for people, thus, our sample size, n = 8.

Thus, we can show the given experiment a binomial distribution, with n = 8, and p = 0.6.

(i) We are asked for the probability that 5 will still be with the company.

Thus, we take x = 5.

P(X = 5) = (8C5)(0.6⁵)((1 - 0.6)⁸⁻⁵),

or, P(X = 5) = (56)(0.07776)(0.064),

or, P(X = 5) = 0.27869184 ≈ 0.28 or 28%.

(ii) We are asked for the probability that at most 6 will still be with the company.

Thus, our x = 6, and we need to take all values below it also.

P(X ≤ 6)

= 1 - P(X > 6)

= 1 - P(X = 7) - P(X = 8)

= 1 - (8C7)(0.6)⁷((1 - 0.6)⁸⁻⁷) - (8C8)(0.6)⁸((1 - 0.6)⁸⁻⁸)

= 1 - 8*0.0279936*0.4 - 1*0.01679616*1

= 1 - 0.08957952 - 0.01679616

= 0.89362432 ≈ 0.89 or 89%.

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The provided question is incomplete. The complete question is:

If the probability of new employee in a fast-food chain still being with the company at the end of 1 year is 0.6, what is the probability that out of 8 newly hired people,

a. 5 will still be with the company after 1 year?

b. at most 6 will still be with the company after 1 year?

The value of f(3) is 147.3306

The function is given as:

[tex]f(x)=147+2e^{-0.6x[/tex]

Substitute 3 for x

[tex]f(3)=147+2e^{-0.6*3[/tex]

Evaluate the product

[tex]f(3)=147+2e^{-1.8[/tex]

Evaluate the exponent

f(3)=147 + 2* 0.1653

Evaluate the sum

f(3) = 147.3306

Hence, the value of f(3) is 147.3306

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Answer:

182000

Step-by-step explanation:

4.82 x 10^5

1.

10^5 is equal to 10 being multiplied 5 times. So this can be expressed as:

10 x 10 x 10 x 10 x 10.

When you multiply 10s, you just add the number of zeros next to one.

==> 100000 (5 zeros total)

2.

We multiply 100000 to 4.82.

100000 x 4.82 = 182000

So our final answer will be 182000.

Answer:

482,000.

Step-by-step explanation:

The 5 tells us this number is 6 digits long.

The answer is

482,000

Answer: Answer is B, Mark me brainliest please

Step-by-step explanation:

Answer:

227.02

Step-by-step explanation:

[tex]400.00-172.98 \\ \\ =300 - 72.98 \\ \\ =230-2.98 \\ \\ =228-0.98 \\ \\ =227.02[/tex]

Answer:

227.02

Step-by-step explanation:

[tex]400.00\\-172.98[/tex]

To solve: First subtract 172 from 400, resulting in 228, then you may subtract the 0.98, leaving 227.02.

The vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)

The coordinates of the quadrilateral ABCD are given as:

A(0,0), B(0,3), C(5,3), and D(5,0)

When dilated by a scale factor of 2.5, we have the following equation

A' = A * 2.5

So, we have:

A' = (0,0) * 2.5

A' = (0, 0)

B' = (0,3) * 2.5

B' = (0, 7.5)

C' = (5,3) * 2.5

C' = (12.5, 7.5)

D' = (5,0) * 2.5

D' = (12.5, 0)

Hence, the vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)

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The amount of money that Miguel would save when he earns $120 is  $96.

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

A ratio table can be described as table that shows equivalent values between two or more numbers and helps us to understand the relationship between the numbers.

The first step is to determine the ratio between the money earned and the money saved.

Ratio = money saved / money earned

8/10 = 0.8

Now, multiply the ratio gotten in the previous step by the amount earned to determine the amount saved.

Amount saved = amount earned x ratio

0.8 x 120 = $96

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Answer:

96

Step-by-step explanation:

I took the quiz edge 2022

Answer:

76

Step-by-step explanation:

Formula

[tex]\sf Average=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]

Given values:

Let x be the score of the fourth test.

To find the score of the fourth test, substitute the given values into the formula and solve for x:

[tex]\begin{aligned} \sf Average & =\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}\\\\\implies \sf 80 & = \sf \dfrac{84+78+82+x}{4}\\\sf 80 & = \sf \dfrac{244+x}{4}\\\sf 80 \cdot 4 & = \sf 244 + x \\\sf 320 & = \sf 244 + x\\\implies \sf x & = \sf 320 - 244\\& = \sf 76\end{aligned}[/tex]

Therefore, John scored 76 on his fourth test.

The solution to the equation is x = 1.62

The equation is given as:

[tex]x =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we split the equations as follows:

y = x

[tex]y =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we graph the equations (see attachment)

From the attached graph, the equations intersect at

(x, y)= (1.62, 1.62)

Remove the y value

x = 1.62

Hence, the solution to the equation is x = 1.62

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Rationalize the right side first. Expand and simplify.

[tex]x = \sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}\right) \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x}\right)^2 - \left(\sqrt{1 - \dfrac1x}\right)^2[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(x - \dfrac1x\right) - \left(1 - \dfrac1x\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = x - 1[/tex]

Rearrange terms as

[tex]\dfrac{x - 1}x = \sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}[/tex]

[tex]\dfrac{x - 1}x + \sqrt{\dfrac{x - 1}x} = \sqrt{x - \dfrac1x}[/tex]

Substitute

[tex]y = \sqrt{\dfrac{x-1}x} = \sqrt{1 - \dfrac1x} \\\\ \implies y^2 = 1 - \dfrac1x \implies x = \dfrac1{1-y^2}[/tex]

(noting that [tex]y>0[/tex]) so that

[tex]x - \dfrac1x = \dfrac1{1-y^2} - (1-y^2) = \dfrac{2y^2 - y^4}{1-y^2}[/tex]

and the equation transforms to

[tex]y^2 + y = \sqrt{\dfrac{2y^2 - y^4}{1-y^2}}[/tex]

[tex]y + 1 = \sqrt{\dfrac{2 - y^2}{1-y^2}}[/tex]

Solve for [tex]y[/tex].

[tex](y+1)^2 = \left(\sqrt{\dfrac{2-y^2}{1-y^2}}\right)^2[/tex]

[tex]y^2 + 2y + 1 = \dfrac{2 - y^2}{1 - y^2}[/tex]

[tex]-y^4 - 2y^3 + 2y + 1 = 2 - y^2[/tex]

[tex]y^4 + 2y^3 - y^2 - 2y + 1 = 0[/tex]

[tex]\left(y^4 + 2y^3 + y^2\right) - 2y^2 - 2y + 1 = 0[/tex]

[tex](y^2 + y)^2 - 2(y^2 + y) + 1 = 0[/tex]

[tex]\left(y^2 + y - 1\right)^2 = 0[/tex]

[tex]y^2 + y - 1 = 0[/tex]

[tex]y = \dfrac{-1 \pm \sqrt5}2[/tex]

Since [tex]y>0[/tex], we take the positive root. Then

[tex]y = \sqrt{\dfrac{x-1}x} = \dfrac{-1 + \sqrt5}2[/tex]

Solve for [tex]x[/tex].

[tex]\left(\sqrt{\dfrac{x-1}x}\right)^2 = \left(\dfrac{-1 + \sqrt5}2\right)^2[/tex]

[tex]\dfrac{x-1}x = \dfrac{6 - 2\sqrt5}4 = \dfrac{3 - \sqrt5}2[/tex]

[tex]x - 1 = \dfrac{3-\sqrt5}2x[/tex]

[tex]\dfrac{-1+\sqrt5}2 x = 1[/tex]

[tex]x = \dfrac2{-1+\sqrt5}[/tex]

Rationalize to clean up the answer.

[tex]x = \dfrac2{-1+\sqrt5}\cdot\dfrac{-1-\sqrt5}{-1-\sqrt5} = \boxed{\dfrac{1+\sqrt5}2} \approx 1.6108[/tex]

i.e. the golden ratio constant.

Answer: its C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:  1.51

Step-by-step explanation:

        [tex]\frac{w + 7.1}{3} =2.87[/tex]

   [tex]3(\frac{w+7.1}{3})=3(2.87)[/tex]

      w + 7.1 = 8.61

w + 7.1 - 7.1 = 8.61 - 7.1

               w = 1.51

13.1 = 13.10

---> 13.1 > 13.01

---> 13.01 < 13.1

The correct answer is <

Truth statement exists statements or assertions that exist true yet of whether the constituent premises exist true or false.

There exist five Euclidean Postulates or axioms.

1. Any two ends can be bound by a straight line segment.

2. In a straight line, any straight line segment can be extended indefinitely.

3. A circle can be created utilizing any straight line segment as the radius and one endpoint as the center.

4. Right angles exist all the exact.

5. If two lines meet a third in a manner that the totality of the inner angles on one side exists smaller than two Right Angles, the two lines will inevitably collide on that side if they exist extended far enough.

1. The right angle on the first page of the book offered and the right angles on the last page of the book shown exist all the exact. (Axiom 4)

2. If the string from the Yoyo dangling from the hand in the picture exists circled for 360° such that the length of the string stays equivalent to all thought, and the point from where it exists attached stays fixed, it will trace a circular trajectory. (Axiom 3)

3. The swords held by the fighters can be extended into infinity because they exist in in straight lines. (Axiom 5)

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The expression that represents the volume of the cone is 6aπ.

What is called cone?

Given the data in the question;

Radius r = 3

Height h = 2a

Volume of the cone V = ?

We substitute our given values into the expression above.

V = (1/3) × π × r² × h

V = (1/3) × π × (3)² × 2a

V = (1/3) × π × 9 × 2a

V = 18aπ / 3

V = 6aπ

Therefore, the expression that represents the volume of the cone is 6aπ.

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The complete fractional question given in the above picture is 55/3 = 1 + 52/3 = 2 + 49/3 = 5 + 40/3 = 8 + 31/3 = 10 + 25/3

Let

55/3 = 1 + x/3

55/3 = (3+x) / 3

55/3 × 3 = 3 + x

55 = 3 + x

55 - 3 = x

52 = x

55/3 = 2 + x/3

55/3 =(6+x) / 3

55/3 × 3 = 6+x

55 = 6 + x

55 - 6 = x

49 = x

55/3 = x + 40/3

55/3 = (3x+40) / 3

55/3 × 3 = 3x + 40

55 = 3x + 40

55 - 40 = 3x

15 = 3x

x = 15/3

x = 5

55/3 = x + 31/3

55/3 = (3x+31) / 3

55/3 × 3 = 3x + 31

55 = 3x + 31

55 - 31 = 3x

24 = 3x

x = 24/3

x = 8

55/3 = 10 + x/3

55/3 = (30+x) / 3

55/3 × 3 = 30 + x

55 = 30 + x

55 - 30 = x

25 = x

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