42. (a) find the unit vectors that are parallel to the tangent line to the curve y − 2 sin x at the point sy6, 1d. (b) find the unit vectors that are perpendicular to the tangent line. (c) sketch the curve y − 2 sin x and the vectors in parts (a) and (b), all starting at sy6, 1d.

The flowers on the float would be 6.000 flowers. The result is obtained by using fraction multiplication.

Fraction represents the part of a set of objects. It has two parts separated by a dividing line, namely numerator at the top and denominator at the bottom.

For example:

It means one of four parts and two of five parts.

We have four thousand two hundred carnations on the float. It was 7/10 of flowers needed. Find the whole flowers on the float!

The carnations of a set of flowers is 7/10. It is 4200 carnations.

The carnations part is 7 and the whole part of flowers is 10.

Using fraction, the whole flowers would be

= 10/7 × 4200

= 6.000 flowers

Hence, the number of flowers needed to be on the float is 6.000 flowers.

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Answer:

14s^4-7s^2+15

Step-by-step explanation:

At the beginning the only bracket that is changing is the 3rd one because of the minus. (12s^4-6s^2+4s)+(6s^4-4s+27)-4s^4+s^2+12 then open the rest of the brackets. And start calculating.i will just to show you which ones u calculate together. (I'll separate the numbers depending on what they're squared to).

12s^4+6s^4-4s^4=14s^4

-6s^2-s^2=7s^2

27-12=15

All together is 14s^4-7s^2+15

Answer: A

Step-by-step explanation: 27+9 = 36

Answer:

1. Whereby one square = One unit, we have;

Lengths of the sides of figure C are;

4, √(4² + 2²), √(4² + 2²) which simplifies to 4, 2·√5, 2·√5

Lengths of the sides of figure E are;

2, √(1² + 2²), √(1² + 2²) which simplifies to 2, √5, √5

Figure E is equivalent to figure C scaled down by a factor of 1/2

The trigonometric ratios of the two figures are therefore equal and figure C is similar to figure E but figure C is larger than figure E

2. A transformation that will create figure D from figure C is a rotation, 90° counter clockwise about the point (2, -2)

A transformation that will create figure E from figure D is a dilation of figure D by 1/2 with the midpoint of figure D being the center of dilation

Step-by-step explanation:

Parabolas are used to represent quadratic functions. The x-intercepts of the parabola are -1.969 and 6.01. Vertex of the parabola are 2.02 and 78.002.

A quadratic function is one of the following: f(x) = ax2 + bx + c, where a, b, and c are positive integers and an is not equal to zero. The graph of a quadratic function is a curve called a parabola. Parabolas can open up or down, and their "width" or "steepness" can vary, but they all have the same basic "U" shape.

The function is given as:

f(x) = \(4.9x^{2} + 19.8x+58\)

Next, we plot the graph of the function f(x)

From the graph (see attachment), we have the following features

Vertex = (2.02, 78.002)

Line of symmetry, x = 2.02

x-intercepts = -1.969 and 6.01

Hence, the x-intercepts of the parabola are -1.969 and 6.01 and Vertex of the parabola are 2.02 and 78.002.

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Answer:

nothing

Step-by-step explanation:

Answer:

About 0.417

Step-by-step explanation:

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

The submarine must lower at least 2698 measures and the submarine must rise at least 516.45 measures. Trigonometric angles are the angles in a right- angled triangle using which different trigonometric functions can be represented.

Given that, the sonar system detects an icicle 4000 measures ahead, with an angle of depression of 34 ∘ to the bottom of the icicle.

What are trigonometric angles?

Trigonometric angles are the angles in a right- angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

a) We know that, tan θ = ( vertical/ Base)

Let the number of measures must the submarine lower to pass under the icicle bex.

tan θ = x/ 4000

⇒ tan 34 ° = x/ 4000

⇒0.6745 = x/ 4000

⇒ x = 0.6745 × 4000

⇒ x = 2698 measures

b) Let the number of measures must the submarine rise to pass over the sunken boat bey.

tan θ = y/ 1500

⇒ tan 19 ° = y/ 1500

⇒0.3443 = y/ 1500

⇒ y = 0.3443 × 1500

⇒ y = 516.45 measures

thus, the submarine must lower at least 2698 measures and the submarine must rise at least 516.45 measures.

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A tree with more than one vertex has at least two vertices of degree 1.To show that a tree with more than one vertex has at least two vertices of degree 1, let's extend the argument given in the proof of Lemma.

To extend the argument given in the proof of Lemma, let's first recall the definition of degree in graph theory. The degree of a vertex in a graph is the number of edges incident to it. Now, in a tree, we know that there is a unique path between any two vertices. Therefore, if a vertex has degree 0, it is not connected to any other vertex, and the tree is not connected, which is a contradiction. Now suppose that there is a tree with more than one vertex, and all vertices have a degree of at least 2. Pick any vertex and follow one of its edges to a new vertex. Since the new vertex has degree at least 2, we can follow one of its edges to another new vertex, and so on. Since the tree is finite, this process must eventually lead us to a vertex that we have visited before, which means we have created a cycle. But this contradicts the fact that the tree is acyclic.
Therefore, we must conclude that there exists a vertex of degree 1 in the tree. But can we say that there is only one such vertex? No, we cannot. Consider a tree with two vertices connected by a single edge. Both vertices have degree 1, and there are no other vertices in the tree. So we have at least two vertices of degree 1.In general, if a tree has n vertices and k of them have degree 1, then the sum of the degrees of all vertices in the tree is 2n-2, by the Handshaking Lemma. But each vertex of degree 1 contributes only 1 to this sum, so k=2n-2-k, which implies that k>=2. Therefore, any tree with more than one vertex has at least two vertices of degree 1.

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Answer:

t=1

Step-by-step explanation:

First combine the like terms

3t+5t+2t=6t 3+5-2=6

6t=6t

then divide each side by 6 to simplify

6t=6t

-------

6 6

t=6/6

t=1

The probability of rolling a total of 7 on the two dice is 8/63

Probability:

In Mathematics, Probability is a branch that deals with the occurrence of possible outcomes in a random event or experiment. It is also defined as the ratio of the number of favorable outcomes and the total number of outcomes.

The probability of an event is denoted by P(E). And the probability of all the events in the sample space will equal to 1.  

Probability P(E) = No of favorable outcomes /Total No of outcomes  

Here we have,

The probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die, are in the ratio 1: 2: 3: 4: 5: 6  

Let x, 2x, 3x, 4x, 5x, and 6x are the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die [ since they are in ratio 1: 2: 3: 4: 5: 6 ]  

As we know the total events in a probability = 1

=> x + 2x + 3x + 4x + 5x + 6x = 1  

=> 21 x = 1

=> x = 1/21  

From the above calculations,

The probabilities of rolling 1, 2, 3, 4, 5, and 6 are  \(\frac{1}{21} , \frac{2}{21}, \frac{3}{21}, \frac{4}{21}, \frac{5}{21}, \frac{6}{21}\) respectively.  

The possible combinations of two dies that can give a total of 7 are

(1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)

Therefore, the probability of rolling a total of 7 on the two dice

=  the sum of the probabilities of rolling each combination

=  \(\frac{1}{21} . \frac{6}{21} + \frac{2}{21} .\frac{5}{21} + \frac{3}{21} . \frac{4}{21} + \frac{4}{21} . \frac{3}{21} + \frac{5}{21} .\frac{2}{21} + \frac{6}{21} .\frac{1}{21}\)  

=  \(\frac{6}{441} + \frac{10}{441} + \frac{12}{441} + \frac{12}{441} + \frac{10}{441} + \frac{6}{441}\)  

=  \(\frac{56}{441}\)

=  \(\frac{8}{63}\)

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The complete question is

For a particular peculiar pair of dice, the probabilities of rolling 1, 2, 3, 4, 5, and 6, on each die are in the ratio 1:2:3:4:5:6. What is the probability of rolling a total of 7 on the two dice

Answer:

x = 4

Step-by-step explanation:

expand out the brackets to get   7 - 2x = 2x - 8 - 1

we can then add 2x to both sides to get        7  = 4x - 8 - 1

add 9 to both sides to get       16 = 4x

divide both sides by 4 to get     x = 4

hope that helps

Answer:

Step-by-step explanation:

Here you go mate

→Use PEMDAS

Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction

→Step 1

7-2x=2(x-4)-1  Equation/Question

→Step 2

7-2x=2(x-4)-1  Remove parenthesis

7-2x=2x-9

→Step 3

7-2x=2x-9  Subtract 7

-2x=2x-16

→Step 4

-2x=2x-16  Simplify

-4x=-16

→Step 5

-4x=-16  Divide sides by -4

4

→Answer

∴your answer is x=4

Therefore, the measure of the central angle whose radii define the given arc is approximately 83.077 degrees.

The length of an arc on a circle is given by the formula:

Arc Length = (Central Angle / 360°) * Circumference

In this case, we know the arc length is 6π centimeters, and the radius of the circle is 13 centimeters. The circumference of the circle can be calculated using the formula:

Circumference = 2π * Radius

Substituting the radius value, we get:

Circumference = 2π * 13

= 26π

Now we can use the arc length formula to find the central angle:

6π = (Central Angle / 360°) * 26π

Dividing both sides of the equation by 26π:

6π / 26π = Central Angle / 360°

Simplifying:

6 / 26 = Central Angle / 360°

Cross-multiplying:

360° * 6 = 26 * Central Angle

2160° = 26 * Central Angle

Dividing both sides by 26:

2160° / 26 = Central Angle

Approximately:

Central Angle ≈ 83.077°

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Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to 1.4\%\to \frac{1.4}{100}\dotfill &0.014\\ t=years\dotfill &6 \end{cases} \\\\\\ A=5000[1+(0.014)(6)]\implies A=5000(1.084) \implies A = 5420\)

Answer:

Step-by-step explanation:

Remark

My guess is that what is confusing you is not what you have to do, but why it is disguised as g(n)

What you are doing in effect is setting up a table. You are also not certain where the table starts. And that is a problem. I will start it at zero, but it might be 1.

zero

n = 0

g(0) = 34 - 5*0

g(0) = 34

One

n = 1

g(1) = 34 - 5*1

g(1) = 34 - 5

g(1) = 29

Two

g(2) = 34 - 5*2

g(2) = 34 - 10

g(2) = 24

Three

g(3) = 34 - 5*3

g(3) = 34 - 15

g(3) = 19

Four

g(4) = 34 - 5*4

g(4) = 34 - 20

g(4) = 19

Answer

0      1       2       3      4

34  29     24     19     14

Answer:

Rate is 8.5%

Step-by-step explanation:

Step 1: Write the given terms

Principal (p)=Rs8800

Rate(r)=?

Time(t)=3.5 years

Interest=Rs2618

Step 2: Write the formula for calculating Simple interest

\(i = \frac{prt}{100} \)

Step 3: Make r the subject of the equation

\(by \: cross \: multiplication \\ 100i = prt \\ divide \: both \: sides \: by \: pt \\ r = \frac{100i}{pt} \)

Step 4: Find the value of r by substituting the values in step 1

\(r = \frac{100 \times 2618}{8800 \times 3.5} \\ r = \frac{261800}{30800} \\ r = 8.5\)

Hence, the rate is 8.5%

Answer:

Greater, Less than, Greater

Step-by-step explanation:

Remember anything close to zero will always be greater in negative numbers. Example. -1>-2. Negative one is greater since it it closer to zero than 2.

Answer:

The maximum height of the rocket is 256 feet

Step-by-step explanation:

The vertex form of the quadratic function f(x) = ax² + bx + c is

f(x) = a(x - h)² + k, where

Let us use these rules to solve the question

∵ h(t) = -16t² + 128t

→ Compare it by the form of the quadratic function above

∴ a = -16 and b = 128

∵ a < 0

∴ The vertex (h, k) is a maximum point

∴ The maximum height of the rocket is the value of k

→ Use the rule of h above to find it

∵ h = \(\frac{-128}{2(-16)}\) = \(\frac{-128}{-32}\)

∴ h = 4

→ Substitute x in the equation by the value of h to find k

∵ k = h(h)

∴ k = -16(4)² + 128(4)

∴ k = -256 + 512

∴ K = 256

∴ The maximum height of the rocket is 256 feet

To show that the matrices (1000), (0100), and (0001) generate m2*2(f), we must show that any matrix in m2*2(f) can be written as a linear combination of these three matrices we can show A as a linear combination of the three matrices: A = a(1000) + b(0100) + c(0001)

A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Let A be any matrix in m2*2(f). Then A can be written in the form:
A = (a b)
     (c d)
where a, b, c, and d are elements of the field f.

Now, we can write A as a linear combination of the three matrices:
A = a(1000) + b(0100) + c(0001)
So, the matrices (1000), (0100), and (0001) generate m2*2(f).

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Pack A offers the best value for money because it is sold at a discounted price of £3.40, which is 15% off the normal price of £4. On the other hand, Pack B is sold at its normal price of £4 but with an additional 20% free tea bags.

To compare the value for money offered by both packs of tea bags, we need to calculate the cost per tea bag. Pack A contains 240 tea bags, and with a discount of 15%, it costs £3.40. Therefore, the cost per tea bag is £3.40/240 = £0.014 or 1.4p per tea bag.

Pack B contains 240 tea bags with an additional 20% free, which means a total of 288 tea bags. The price of Pack B is £4, so the cost per tea bag is £4/288 = £0.0139 or 1.39p per tea bag.

Therefore, Pack A is slightly cheaper than Pack B, and it offers the best value for money. It is important to always compare the price per unit (in this case, per tea bag) when comparing different products to determine the best value for money.

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The following probability which  is true: P(1.5 - .02 < X < 1.5 + .02) = 0.68 for the distribution of log-cell counts of red blood cells for women.

Given that the distribution of log-cell counts of red blood cells for women age 25-30 is approximately normally distributed with µ = 1.5 cells/microliter and σ = 0.1 cells/microliter.

In this, the probability of the Z score for a range is asked.

The value of Z is given by:

Z = (X - µ)/σZ

= (1.5 - 1.5)/0.1

= 0

In the Z table, the value of 0 is 0.5.

So, the following probability will be found:

P(1.5 - .02 < X < 1.5 + .02) = P(-0.2 < Z < 0.2)

We know that 0.2 value is in between 0 and 0.25 in the Z table.

P(1.5 - .02 < X < 1.5 + .02) = P(-0.2 < Z < 0.2)

= P(Z < 0.2) - P(Z < -0.2)

= 0.5793 - 0.4207

= 0.1586

≈ 0.16

Therefore, the option which is true is: P(1.5 - .02 < X < 1.5 + .02) = .68.

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Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

What is an Algebraic Expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression. For example, 3x² − 2xy + c is an algebraic expression.

Given,

Total money Preston have = $15

He buys the ticket for = $6.50

And, two snacks = $1.75 each

so the cost of two snacks is = 1.75 * 2 = $3.5

Total cost for ticket and snacks = $3.5 + $6.50 = $10

Now, he spent money on snacks and ticket $10 and he have total money $15 so,

Preston left with = $15 - $10

                           = $5

Therefore, Preston left with $5 and correct expression for to find solution is option(B) i.e, 15 - (6.5 + 2 * 1.75)

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The functions 1/x, 1-x², and 1-3x are linearly independent on any interval that does not contain x=0, but they are dependent at x=0.

To determine whether the functions 1/x, 1-x², and 1-3x are linearly independent, we can use the Wronskian method. The Wronskian of a set of functions f1(x), f2(x), ..., fn(x) is defined as:

W(f1, f2, ..., fn) = det | f1 f2 ... fn |

| f1' f2' ... fn' |

where f1', f2', ..., fn' are the derivatives of the functions with respect to x.

If the Wronskian is nonzero for all values of x in a given interval, then the functions are linearly independent on that interval. If the Wronskian is zero for at least one value of x in the interval, then the functions are linearly dependent on that interval.

For the functions 1/x, 1-x², and 1-3x, we have:

W(1/x, 1-x², 1-3x) = det | 1/x 1-x² 1-3x |

| -1/x² -2x -3 |

| 0 -2x 0 |

Expanding the determinant, we get:

W(1/x, 1-x², 1-3x) = -6/\(x^3\)

Since the Wronskian is nonzero for all values of x except x = 0, the functions 1/x, 1-x², and 1-3x are linearly independent on any interval that does not contain x = 0.

Therefore, the functions are linearly independent except at x = 0.

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Answer:8

Step-by-step explanation: 5 x 3= 15

23-15=8

Answer:

8

Step-by-step explanation:

5 times 3 =15 23 minus 15 is three

Step-by-step explanation:

Yeah i also need the samw ans

The mean value of the radius (r) at which you would find the electron, given the H atom wave function is 100(r), is 0.

The wave function of an electron in the hydrogen atom, denoted by Ψ, describes the probability distribution of finding the electron at different positions around the nucleus. In this case, the given wave function is 100(r), where r represents the radius.

To calculate the mean value of the radius, we need to evaluate the integral of r multiplied by the absolute square of the wave function, integrated over all possible values of r. However, the wave function 100(r) does not provide a valid description of the hydrogen atom's electron distribution. The wave function should be normalized, meaning that the integral of the absolute square of the wave function over all space should equal 1. In this case, the given wave function lacks normalization.

Since the wave function is not properly normalized, we cannot accurately calculate the mean value of the radius. Without normalization, the probability distribution described by the wave function does not provide meaningful information about the electron's position.

In summary, based on the given wave function, the mean value of the radius cannot be determined without proper normalization of the wave function. A properly normalized wave function is necessary to obtain accurate information about the electron's position.

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The expression which is equivalent to 8x²√375x + 2³√3x^7 if x = 0 is; 0.

According to the task content, the expression given is; 8x²√375x + 2³√3x^7.

On this note, it follows that when x=0 is substituted into the expression; the evaluation amounts to zero, 0.

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