What sine function represents an amplitude of 4, a period of pi over 2, no horizontal shift, and a vertical shift of −3?


f(x) = −3 sin 4x + 4

f(x) = 4 sin 4x − 3

f(x) = 4 sin pi over 2x − 3

f(x) = −3 sin pi over 2x + 4

Answer:

[tex]x=\frac{45}{4},  y=-\frac{201}{4}, z=-\frac{61}{2}[/tex]

Step-by-step explanation:

We start by putting our equation in a matricial form:

[tex]\left[\begin{array}{cccc}12&2&1&4\\3&3&-4&5\\2&-2&4&1\end{array}\right][/tex]

Then, we multiply the second row by 4 and substract the first row:

[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\2&-2&4&1\end{array}\right][/tex]

Now, multiply the third row by 6 and substract the first row:

[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&-14&23&2\end{array}\right][/tex]

Next, we will add [tex]\frac{7}{5}[/tex] times the second row to the third row:

[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&0&\frac{-4}{5}&\frac{122}{5}\end{array}\right][/tex]

Now we can solve [tex]\frac{-4}{5} z=\frac{122}{5}[/tex] to obtain

[tex]z=-\frac{61}{2}[/tex]

Then [tex]10y-17\frac{-61}{2}=16[/tex] wich implies that

[tex]y=\frac{16-\frac{17*61}{2}}{10} =\frac{\frac{32-17*61}{2}}{10}=\frac{-1005}{20}=\frac{-201}{4}[/tex]

Finally

[tex]x=\frac{4-2*\frac{-201}{4}+\frac{61}{2}}{12} =\frac{\frac{8+201+61}{2}}{12}=\frac{270}{24}=\frac{135}{12}=\frac{45}{4}[/tex].

[tex]z=-\frac{61}{2}\\ y=-\frac{201}{4} \\x=\frac{45}{4}[/tex]

Step-by-step explanation:

We have 3 given inputs namely P, Q, R and we have to draw a logic circuit which will give the output 1 if , and only if, P and Q have the same value and Q and R have opposite values.

So, first of all we make a truth table for this

P        Q        R        Output(Y)

0        0        0           0

0        0         1           1

0         1        0           0

0         1         1           0

1         0        0          0

1          0        1           0

1          1        0           1

1          1         1           0    

From the truth table we can see that the output, Y can be given by

[tex]Y=\bar{P}\bar{Q}R+PQ\bar{R}[/tex]

So, the logic circuit for the given logic equation can be drawn as shown fig.                  

To design a logic circuit that outputs a 1 if, and only if, P and Q have the same value and Q and R have opposite values, use XOR and AND gates in a specific configuration.

To design a logic circuit that outputs a 1 if, and only if, P and Q have the same value and Q and R have opposite values, we can use logic gates. Here's the step-by-step design:

Thus, the logic circuit will output a 1 if, and only if, P and Q have the same value and Q and R have opposite values.

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Answer:

Step-by-step explanation:

We know that for two similar matrices [tex]A[/tex] and [tex]B[/tex] exists an invertible matrix [tex]P[/tex] for which

[tex][tex]B = P^{-1} AP[/tex][/tex]

∴ [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} \\[/tex]

Also [tex]P^{-1}P = I\\[/tex]

and [tex](P^{-1})^{T} = (P^{T})^{-1}[/tex]

∴[tex](P^{-1})^{T}P^{T} = I[/tex]

so, [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} = (P^{T})^{-1}A^{T} P^{T}\\B^{T} = A^{T} I\\B^{T} = A^{T}[/tex]

Answer:

Step-by-step explanation:

a. The five-number summary is made up of the following summary means:

1. Minimum: 25

2. First Quartile: 30.5

3. Medium: 34.5

4. Third quartile: 43

5. Maximum: 78

6. P30: 32.1

b.

Standard Deviation: 12.72

Rank: 53

Interquartile range: 12.5

C. The interquartile range is 12.5 and 1.5 times the interquartile range is (1.5) (12.5) = 18.75. Third quartile plus 1.5 times the interquartile range is 61.75. The value of 78 exceeds 61.75, then 78 is an outlier.

Answer: 9.70%

Step-by-step explanation:

The formula to find the percentage error is given by :-

[tex]\%\text{ error}=\dfrac{|\text{Estimate-Actual}|}{\text{Actual}}\times100[/tex]

Given : Actual mass of zinc oxide used by pharmacist = 28.35 g

Estimated mass of zinc oxide used by pharmacist =31.1 g

Now, [tex]\%\text{ error}=\dfrac{|31.1-28.35|}{28.35}\times100[/tex]

i.e. [tex]\%\text{ error}=\dfrac{2.75}{28.35}\times100[/tex]

i.e. [tex]\%\text{ error}=9.70017636684\approx9.70\%[/tex]

Hence, the  percentage of error on the basis of the desired quantity.= 9.70%

Answer: This represents a function

Step-by-step explanation: In this problem, we are given a relation in the form of a mapping diagram and we are asked if it represents a function. The easiest way to do this problem is to first translate the mapping diagram into a list of ordered pairs.

(6,-2) (-2,2) (4,1) (-1,1)

Now to determine if the relation is a function, we can simply look at the x coordinates of each ordered pair. Notice that all of them are different so the relation must be a function. It's important to understand that even though two of the Y coordinates are the same, this relation is still a function because the y coordinates do not have any effect on whether or not the relation is a function.

Answer:

% increase =[tex]\frac{\text{ Increased number -Original number }}{\text{Original number}} \times 100\%[/tex]

% decrease =[tex]\frac{\text{ Original number - Decreased number }}{\text{Original number}} \times 100\%[/tex]

Step-by-step explanation:

Percentage Increase:

Let there be an original number. If it increased to a certain value we can calculate the percentage increase value with the help of following formula:

% increase =[tex]\frac{\text{ Increased number -Original number }}{\text{Original number}} \times 100\%[/tex]

Percentage Decrease:

Let there be an original number. If it decreases to a certain value we can calculate the percentage decrease with the help of following formula:

% decrease =[tex]\frac{\text{ Original number - Decreased number }}{\text{Original number}} \times 100\%[/tex]

Answer:

3.5 of the liquid will contain 0.875g of the substance.

Step-by-step explanation:

The problem states that a liquid contains 0.25 mg of a substance per milliliter. And asks how many grams of the substance will 3.5 L contain.

First step: Conversion of 3.5L to ml

Each liter has 1000ml. So:

1L - 1,000mL

3.5L - xmL

x = 1,000*3.5

x = 3,500mL

Second step: How many miligrams are there in 3,500mL?

The problem states that each ml of the liquid contains 0.25mg of a substance. So

1ml - 0.25mg

3,500 mL - xmg

x = 3,500*0.25

x = 875mg

Final step: Conversion of 875mg to g.

Each g has 1000 mg. So

1g - 1000mg

xg - 875mg

1000x = 875

[tex]x = \frac{875}{1000}[/tex]

x = 0.875g

3.5 of the liquid will contain 0.875g of the substance.

To find the mass of the substance in 3.5 L, convert the volume to milliliters and then multiply by the concentration. The mass is 0.875 g.

To find the number of grams of the substance, we need to convert from milliliters to liters and then use the given concentration of 0.25 mg/mL to find the mass.

First, we convert 3.5 L to milliliters by multiplying by 1000: 3.5 L x 1000 mL/L = 3500 mL.

Next, we multiply the volume in milliliters (3500 mL) by the concentration (0.25 mg/mL) to find the mass: 3500 mL x 0.25 mg/mL = 875 mg.

Finally, we convert the mass from milligrams to grams by dividing by 1000: 875 mg / 1000 = 0.875 g.

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Answer:

Angle A = 100°

Angle B = 80°

Step-by-step explanation:

Supplementary angles sum 180°

Angle A to Angle B ratio is 5:4, you can write that ratio using a factor.

Angle A = 5x

Angle B = 4x

Since the sum is 180°

Angle A + Angle B = 180°

5x + 4x = 180°

9x = 180°

x = 20°

Replacing x = 20°

Angle A = 5(20°) = 100°

Angle B = 4(20°) 80°

Answer:

Step-by-step explanation:

In step 2, the result of eliminating parentheses is shown. That is done by using the distributive property to multiply -2 by each of the terms inside parentheses, giving ...

  (-2)(x) +(-2)(12) = -2x -24

In step 3, 2x is added to both sides of the equation. This eliminates the -2x term on the right, and increases the -6x term on the left to -4x.

In step 4, the equation is divided by -4. This makes the coefficient of x become 1.

The equation -6x = -2(x + 12) can be solved by distributing -2 to elements inside the bracket, re-writing the equation, simplifying it, and then finally solving for 'x', leading to x = 6.

The equation shared is a linear equation in one variable, -6x = -2(x + 12). There are main steps to solving this equation:

So, for this equation -6x = -2(x + 12), the solution is x = 6.

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Answer: Hi!, first, Z are the integer numbers, so we only will work with them.

P(x): x ≤ 0

ok, this predicate is true if x is less or equal tan 0, and false if x is greater than 0.

so P(x) is true if { x∈Z, x ≤ 0}

Q(x): x2 = 1

Q(x) is true only if 2*x = 1. now, this means that if x=1/2 is true, but 1/2 isnt an integer, then Q(x) is false ∀ x ∈ Z.

R(x): x is odd

R(x) is true if x is odd, we can write odd numbers as x = 2k + 1, where k is a random integer; then:

R(x) is true if x=2k +1, with k∈Z.

S(x): x = x + 1

S(x) is true if x= x+1, if we subtract x from both sides of the equality, we get that S(x) is true if 0=1, and this is absurd, then:

S(x) is false  ∀ x ∈ Z.

Step-by-step explanation:

To prove this we can use the definition of a sequence converging to its limit, in terms of epsilon:

The sequence [tex] \{ S_n\}[/tex] converges to [tex]L[/tex]

if and only if

for every [tex]\epsilon >0[/tex] there exists [tex]n_0\in \mathbb{N}[/tex] such that

[tex] n>n_0 \implies |S_n-L|<\epsilon[/tex]

if and only if

for every [tex]\epsilon >0[/tex] there exists [tex]n_0\in \mathbb{N}[/tex] such that [tex] n>n_0 \implies |(S_n-L) - 0|<\epsilon[/tex]

if and only if

the sequence [tex]\{S_n-L\}[/tex] converges to 0.

Answer:

The average rate of change is 2, letter a)

Step-by-step explanation:

Given a function y, the average rate of change S of y=f(x) in an interval  [tex][x_{s}, x_{f}][/tex] will be given by the following equation:

[tex]S = \frac{f(x_{f}) - f(x_s)}{x_{f} - x_{s}}[/tex].

In our problem, we have that:

[tex]f(x) = 2x + 7[/tex]

[tex]x_{s} = -1[/tex]

[tex]x_{f} = 0[/tex]

So:

[tex]f(x_{s}) = f(-1) = 2(-1) + 7 = -2 + 7 = 5[/tex]

[tex]f(x_{f}) = f(0) = 2(0) + 7 = 0 + 7 = 7[/tex]

The average rate of change is:

[tex]S = \frac{f(x_{f}) - f(x_s)}{x_{f} - x_{s}} = \frac{7-5}{0 -(-1)} = \frac{2}{1} = 1[/tex]

The average rate of change is 2, letter a)

Answer:

wala akong alam jun

Step-by-step explanation:

i hate math, mathuloggggggg ka, ayieee ?luh asa ka

Answer: a) [tex]N(t) = 10^3\exp(0.046\frac{1}{min}t)[/tex]

b) 1,000,000 bacteria at t = 150 min

Step-by-step explanation:

Hi!!

A colony that grows exponentially has a number of bacteria:

[tex]N(t) = N_0 \exp(\lambda t)[/tex]

In this case at time t = 0:

[tex]N(0)=N_0=10^3[/tex]

We need to find the value of λ. We use the data:

[tex]N(t=50\;min)10^4 = 10^3\exp(\lambda \;50\;min)[/tex]

[tex]ln(10)=2.3=\lambda\;50\;min\\\lambda= \frac{0.046}{min}\\N(t) = 10^3\exp(\frac{0.046}{min}t)\\[/tex]

To find when there will be 1,000,000 bacteria:

[tex]10^6=10^3\exp(\frac{0.046}{min}t)[/tex]

[tex]\ln(10^3)=3\ln(10) = \frac{0.046}{min}t[/tex]

[tex]t = 150\;min [/tex]

Answer:

1. Nominal data 2. Responses here can't be classified as interval or nominal or ordinal data 3.  Responses here can't be classified as interval or nominal or ordinal data  4. nominal

Step-by-step explanation:

1. Heidi's favorite  brand of tenis balls is only a "label" in the set of brands that can be regarded. So, because we are dealing with names or "labels" we should classify responses here as nominal data.

2. Possible values for the number of cars in a parking lot are 0, 1, 2, 3, 4,... Besides we can say that 4 cars is twice than 2 cars, and exist a true zero. We can't say that responses here correspond to interval data, in fact, we can say that responses here correspond to the kind of data called ratio data.

3. You can spend zero hours in your homework, so, there exists an absolute zero, besides, to say that you spend 4 hours in your homework is twice that if you spend 2 hours in your homework is meaningful. We can't classify responses here as interval data or ordinal or nominal. We can classify responses here as ratio data.

4. There are only two different responses here, i.e., You are a US citizen or You are not a US citizen. We are dealing with "labels" again, and in general, we can't say there is a better response or stablish an order.

Final answer:

The correct classifications are: Heidi's favorite brand of tennis balls (Nominal), Number of cars in a parking lot (Nominal, with an explanation), Amount of time spent on homework per week (Interval), and Whether you are a US citizen (Nominal).

Explanation:

To determine whether the listed responses should be classified as interval, nominal, or ordinal data, it is essential to understand what each type of data signifies. Nominal data are categories without any order, ordinal data have a meaningful order or ranking but not necessarily consistent differences between rankings, and interval data have a consistent scale and order, but no true zero point.

Nominal: Heidi's favorite brand of tennis balls. This is a category (brand) without a numerical value or order.

Nominal: Number of cars in a parking lot. Although it involves numbers, it is essentially counting the frequency of an item, which falls under ratio data. However, as the question specifically asks among nominal, ordinal, and interval, the correct identification in this context is not provided.

Interval: Amount of time you spend per week on your homework. Time has a consistent scale and can be ordered, but there is no true zero time (you cannot have negative time).

Nominal: Whether you are a US citizen. This is a categorical variable with no inherent order.

Answer:

[tex]y=11,600x+6,000[/tex]

Yearly sales in 1990: $98,800.

Step-by-step explanation:

We have been given that the sales of a certain appliance dealer can be approximated by a straight line. Sales were $6000 in 1982 and $ 64,000 in 1987.

If at 1982, [tex]x=0[/tex] then at 1987 x will be 5.

Now, we have two points (0,6000) and (5,64000).

[tex]\text{Slope}=\frac{64,000-6,000}{5-0}[/tex]

[tex]\text{Slope}=\frac{58,000}{5}[/tex]

[tex]\text{Slope}=11,600[/tex]

Now, we will represent this information in slope-intercept form of equation.

[tex]y=mx+b[/tex], where,

m = Slope,

b = Initial value or y-intercept.

We have been given that at [tex]x=0[/tex], the value of y is 6,000, so it will be y-intercept.

Substitute values:

[tex]y=11,600x+6,000[/tex]

Therefore, the equation [tex]S=11,600x+6,000[/tex] represents yearly sales.

Now, we will find difference between 1990 and 1982.

[tex]1990-1982=8[/tex]

To find yearly sales in 1990, we will substitute [tex]x=8[/tex] in the equation.

[tex]S=11,600(8)+6,000[/tex]

[tex]S=92,800+6,000[/tex]

[tex]S=98,800[/tex]

Therefore, the yearly sales in 1990 would be $98,800.

Answer:

[tex]f(x) = x +\frac{1}{3}x^{3}+....[/tex]

Step-by-step explanation:

As per the question,

let us consider f(x) = tan(x).

We know that The Maclaurin series is given by:

[tex]f(x) = f(0) + \frac{f^{'}(0)}{1!}\cdot x+ \frac{f^{''}(0)}{2!}\cdot x^{2}+\frac{f^{'''}(0)}{3!}\cdot x^{3}+......[/tex]

So, differentiate the given function 3 times in order to find f'(x), f''(x) and f'''(x).

Therefore,

f'(x) = sec²x

f''(x) = 2 × sec(x) × sec(x)tan(x)

      = 2 × sec²(x) × tan(x)

f'''(x) = 2 × 2 sec²(x) tan(x) tan(x) + 2 sec²(x) × sec²(x)

       = 4sec²(x) tan²(x) + 2sec⁴(x)

       = 6 sec⁴x - 4 sec² x

We then substitute x with 0, and find the values

f(0) = tan 0 = 0

f'(0) =  sec²0 = 1

f''(0) = 2 × sec²(0) × tan(0) = 0

f'''(0) = 6 sec⁴0- 4 sec² 0 = 2

By putting all the values in the Maclaurin series, we get

[tex]f(x) = f(0) + \frac{f^{'}(0)}{1!}\cdot x+ \frac{f^{''}(0)}{2!}\cdot x^{2}+\frac{f^{'''}(0)}{3!}\cdot x^{3}+......[/tex]

[tex]f(x) = 0 + \frac{1}{1}\cdot x+ \frac{0}{2}\cdot x^{2}+\frac{2}{6}\cdot x^{3}+......[/tex]

[tex]f(x) = x +\frac{1}{3}x^{3}+....[/tex]

Therefore, the expansion of tan x at x = 0 is

[tex]f(x) = x +\frac{1}{3}x^{3}+....[/tex].

Step-by-step explanation:

The proof can be done by contradiction. Suppose both a, and b weren't even. So that a, and b are both odd. This means they both look like

[tex]a=2k+1,~~b=2l+1[/tex] (for some integers k and l)

So, let's compute what [tex]a^2-3b^2[/tex] would be in this case:

[tex]a^2-3b^2=(2k+1)^2-3(2l+1)^2=4k^2+4k+1-3(4l^2+4l+1)[/tex]

[tex]= 4k^2+4k+1-12l^2-12l-3=4k^2+4k-12l^2-12l-2 [/tex]

[tex]=4(k^2+k+3l^2-3l)-2[/tex]

which notice wouldn't be divisible by 4. This shows then that since [tex]a^2-3b^2[/tex] is divisible by 4, at least one of the integers a and b is even.

Answer:

There is a 33% probability that this party was received from supplier Z.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

-In your problem, we have:

P(A) is the probability of a defective part being supplied. For this probability, we have:

[tex]P(A) = P_{1} + P_{2} + P_{3}[/tex]

In which [tex]P_{1}[/tex] is the probability that the defective product was chosen from supplier X(we have to consider the probability of supplier X being chosen). So:

[tex]P_{1} = 0.24*0.05 = 0.012[/tex]

[tex]P_{2}[/tex] is the probability that the defective product was chosen from supplier Y(we have to consider the probability of supplier Y being chosen). So:

[tex]P_{2} = 0.36*0.10 = 0.036[/tex]

[tex]P_{3}[/tex] is the probability that the defective product was chosen from supplier Z(we have to consider the probability of supplier Z being chosen). So:

[tex]P_{2} = 0.40*0.06 = 0.024[/tex]

So

[tex]P(A) = P_{1} + P_{2} + P_{3} = 0.012 + 0.036 + 0.024 = 0.072[/tex]

P(B) is the probability of the supplier chosen being Z, so P(B) = 0.4

P(A/B) is the probability of the part supplied being defective, knowing that the supplier chosen was Z. So P(A/B) = 0.06.

So, the probability that this part was received from supplier Z is:

[tex]P = \frac{0.4*0.06}{0.072} = 0.33[/tex]

There is a 33% probability that this party was received from supplier Z.

Answer:  35

Step-by-step explanation:

Given : A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble.

Total = 4+2+1+3+1=11

To find sets of four marbles include none of the red ones, we need to exclude red marbles when we count the total number of marbles.

Then, the total marbles(exclude red) =11-4=7

Now, the combination of 7 marbles taking 4 at a time is given by :-

[tex]^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!3!}=35[/tex]

Hence, the number of sets of four marbles include none of the red ones = 35

Answer: (D) none of the these.

Step-by-step explanation:

If the shape of our data set is multimodal, the it will show two or more peaks which represents the number modes in the data.

Since it has no relation with mean or median of the data, there for the correct option will be "none of these".

In a multimodal distribution, the relationship between the mean and the median cannot be determined without more information on the distribution's skewness and the relative size of the peaks. Thus, the answer is that none of the provided options are necessarily correct.

When dealing with a multimodal distribution, which is a distribution with more than one peak or "mode," the relationship between the mean, the median, and the mode is not as predictable as it is in symmetric distributions. Since multimodal distributions can have multiple peaks at different points, it can alter the typical order of the mean, median, and mode based on where these peaks occur relative to each other.

The presence of multiple modes can pull the mean toward the larger values if one peak represents higher values significantly, or it can pull the mean towards lesser values if a peak represents lower values significantly. However, without additional specific information about the skewness or the relative size of these peaks, we cannot definitively say whether the mean will be less than, equal to, or greater than the median. Therefore, the correct answer is:

(D) none of these.

Answer:

  P = (-18 5/9, 3 13/18, -17 2/3)

Step-by-step explanation:

The given point must satisfy both the equation of the line and that of the plane. We can substitute for x, y, and z in the plane's equation to get ...

  -7(-3-8t) +2(-6+5t) +8(-6-6t) = -4

  21 +56t -12 +10t -48 -48t = -4

  18t -39 = -4 . . . collect terms

  18t = 35 . . . . . . add 39

  t = 35/18 . . . . . .divide by the coefficient of t

The point is ...

  (x, y, z) = (-3-8(35/18), -6+5(35/18), -6-6(35/18))

  P = (x, y, z) = (-18 5/9, 3 13/18, -17 2/3)

To compute the total amount accumulated with compound interest and the interest earned, we utilize the formula for compound interest on the given principal amount, rate of interest, and the period. The interest earned is then computed by subtracting the initial principal amount from the total accumulated amount.

The subject of this question is the calculation of compound interest. Given that the principal amount is $4500, the rate of interest is 5%, and the interest is compounded quarterly over a course of 3 years, we first need to compute the total amount accumulated. Using the formula for compound interest:

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

where:

A is the amount of money accumulated after n years, including interest.

P is the principal amount (the initial amount of money).

r is the annual interest rate (in decimal).

n is the number of times that interest is compounded per year.

t is the number of years the money is invested for.

In this case, P = 4500, r = 0.05 (5% expressed as a decimal), n = 4 (since interest is compounded quarterly), and t = 3. Substituting these values into the formula, we get the total accumulated amount.

The interest earned can subsequently be found by subtracting the original principal amount (P) from the accumulated amount (A).

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Answer:  3600 seconds

Step-by-step explanation:

Use the following conversions: 1 hour = 60 minutes & 1 minute = 60 seconds

[tex]1\ hour \times \dfrac{60\ minutes}{1\ hour}\times \dfrac{60\ seconds}{1\ minute}\quad =\large\boxed{3600\ seconds}[/tex]

Answer:

The means for times for the first round of the 100 meter men’s swim is 52.64789 seconds

The satandar deviation for times for the first round of the 100 meter men’s swim is 7.60182 seconds

Step-by-step explanation:

The sample mean for a set of n data is given by:

[tex]\bar X = \frac{1}{n}\sum{x_i}[/tex]

In other words, the sample mean of the times for 71 times of the first round measured in seconds is:

[tex]\bar X = \frac{1}{71}\sum{x_i} = 52.64789[/tex] seconds

The sample standard deviation for a set of n data is given by:

[tex]S = \sqrt{\frac{1}{n-1}\sum{(x_i - \bar x)^2}}[/tex]

In other words, the sample standard deviation of the times for 71 times of the first round measured in seconds is:

[tex]S = \sqrt{\frac{1}{n-1}\sum{(x_i - \bar x)^2}} = 7.60182[/tex] seconds

Answer: The value of 100 th term is 298 and the value of n th term is 1+3n.

Step-by-step explanation:

Since we have given that

1,4,7,10............

Since it forms an A.P. in which

a = 1

d = [tex]4-1 =3[/tex]

So, the value of 100 th term is given by

[tex]a_{100}=a+(n-1)d\\\\a_{100}=1+(100-1)\times 3\\\\a_{100}=1+99\times 3\\\\a_{100}=1+297\\\\a_{100}=298[/tex]

And the value of n th term is given by

[tex]a_n=1+3n[/tex]

Hence, the value of 100 th term is 298 and the value of n th term is 1+3n.

Answer:

5.9%.

Step-by-step explanation:

We are asked to find the simple interest rate for an amount of $1900 which earned simple interest of $56.28 in 6 months.

We will use simple interest formula to solve our given problem.

[tex]I=Prt[/tex], where,

[tex]I=\text{Amount of interest}[/tex]

P = Principal amount,

r = Interest rate in decimal form,

t = Time in years.

6 months equals 1/2 (0.5) year.

Substituting given values:

[tex]\$56.28=\$1900\cdot r\cdot 0.5[/tex]

[tex]\$56.28=\$950\cdot r[/tex]

[tex]\frac{\$56.28}{\$950}=\frac{\$950\cdot r}{\$950}[/tex]

[tex]0.059242=r[/tex]

Switch sides:

[tex]r=0.059242[/tex]

Convert in percentage:

[tex]0.059242\times 100\%[/tex]

[tex]5.9242\%\approx 5.9\%[/tex]

Therefore, the simple interest rate is approximately 5.9%.

To calculate the simple interest rate, the given values are substituted into the formula for simple interest, which is then re-arranged to solve for the interest rate.

To calculate the simple interest rate, you can use the simple interest formula: I = Prt where I is the interest earned, P is the principal amount (the initial amount of money), r is the rate of interest and t is time.

In this context, you earned $56.28 in 6 months from an initial amount of $1900. Re-arranging the formula to solve for r (the interest rate) we get: r = I / (Pt).

Substituting the given values into the formula, we find: r = $56.28 / ($1900 * 0.5). Carry out the calculations and multiply the result by 100 to get the percentage. This will yield your simple interest rate.

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Answer:

2295, 2286, 2277, 2268, 2259

Step-by-step explanation:

We are dealing with a number of 4 digits, whose first two digits are 2's. So the number looks like [tex]2~2~ d_2 ~d_1[/tex] (where the last 2 digits are to be determined).

The exercise says that the sum of the ones and tens digits is 14. The ones digit is the last digit (the right most digit, which we are denoting by [tex]d_1[/tex]), and the tens digit is the second right most digit (which we are denoting by [tex] d_2[/tex]). So [tex] d_1+d_2=14[/tex]

Since they're digits, their only possible values are 0,1,2,3,4,5,6,7,8,9.

If d1 was 0, d2 would have to be 14 (since they should add up to 14), which is impossible.

If d1 was 1, d2 would have to be 13 (since they should add up to 14), which is impossible.

If d1 was 2, d2 would have to be 12, which is impossible.

And so going through all possibilities, we get that the only possible ones are:

[tex] d1=5~ and~ d_2=9[/tex]

[tex] d1=6~ and~ d_2=8[/tex]

[tex] d1=7~ and~ d_2=7[/tex]

[tex] d1=8~ and~ d_2=6[/tex]

[tex] d1=9~ and~ d_2=5[/tex]

And so the possible 4-digits numbers are 2295, 2286, 2277, 2268, 2259.

We have a vector [tex]\vec F[/tex] with a magnitude [tex]F[/tex] of 86.4 N.

a. Let [tex]\theta[/tex] be the angle [tex]\vec F[/tex] makes with the positive [tex]x[/tex]-axis. The [tex]x[/tex]-component of [tex]\vec F[/tex] is

[tex]F_x=(86.4\cos\theta)\,\mathrm N[/tex]

and has a magnitude of 72.3 N, so

[tex]72.3=86.4\cos\theta\implies\cos\theta=0.837\implies\theta=\boxed{33.2^\circ}[/tex]

b. The [tex]y[/tex]-component of [tex]\vec F[/tex] is

[tex]F_y=(86.4\cos33.2^\circ)\,\mathrm N=\boxed{47.3\,\mathrm N}[/tex]

a) The angle between the vector and the +x axis is approximately 33.196°.

b) The component of the force along the +y axis is approximately 47.304 newtons.

In this question we should apply the concepts of magnitude and direction of a vector to solve each part. The magnitude ([tex]\|\vec F\|[/tex]), in newtons, is a application of Pythagorean theorem and direction ([tex]\theta[/tex]), in degrees, is an application of trigonometric functions.

a) The angle between the vector and the component along the x axis ([tex]F_{x}[/tex]), in newtons, is found by means of the following expression:

[tex]\theta = \cos^{-1} \frac{F_{x}}{\|\vec F\|}[/tex] (1)

([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])

[tex]\theta = \cos^{-1} \left(\frac{72.3\,N}{86.4\,N} \right)[/tex]

[tex]\theta \approx 33.196^{\circ}[/tex]

The angle between the vector and the +x axis is approximately 33.196°. [tex]\blacksquare[/tex]

b) The magnitude of the +y component of the vector force ([tex]F_{y}[/tex]), in newtons, is determined by the following Pythagorean expression:

[tex]F_{y} = \sqrt{(\|\vec F\|)^{2}-F_{x}^{2}}[/tex] (2)

([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])

[tex]F_{y} = \sqrt{(86.4\,N)^{2}-(72.3\,N)^{2}}[/tex]

[tex]F_{y} \approx 47.304\,N[/tex]

The component of the force along the +y axis is approximately 47.304 newtons. [tex]\blacksquare[/tex]

To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13188123

Answer:

5.5 liters

Step-by-step explanation: there are 1000 milliliters in a liter, so divide 5,500/1000

Answer:

5.5 liters

Step-by-step explanation:

because 5500 millilitres is 5.5 liters