The sum of four numbers in arithmetic progression is 16. The square of the last number is the square of the first number plus 48. What are the four numbers?

Answer:

a) The probability is 0.3

b) The probability is 0.1

c) The probability is 0.35

Step-by-step explanation:

Lets call S1 and S2 the events ' he must stop at signal 1 ' and 'he must stop at signal 2' respectively.

a) We know that

0.65 = P(S1 ∪ S2) = P(S1) + P(S2) - P(S1 ∩ S2) = 0.4+0.55-P(S1 ∩ S2) = 0.95 - P(S1 ∩ S2)

Hence P(S1 ∩ S2) = 0.95-0.65 = 0.3

It stops at both signals with probability 0.3

b) Note that, due to the theorem of total probability we have

0.4 = P(S1) = P(S1 ∩ S2) + P(S1 ∩ S2^c) = 0.3 + P(S1∩S2^c)

Where S2^c is the complementary event of S2. Therefore

P(S1∩S2^c) = 0.4-0.3 = 0.1

The probability to stop at the first signal but not at the second one is 0.1

c) The probability of stopping at exactly one signal is equal at the sum of the probabilities of stopping only at the first signal and the probability of stopping only at the second one.

That is P(S1 ∩ S2^c) + P(S1^c ∩ S2) = 0.1 + P(S1^c ∩ S2)

The same way as before:

0.55 = P(S2) = P(S1 ∩ S2) + P(S1^c ∩ S2) = 0.3 + P(S1^c ∩ S2)

Therefore

P(S1^c ∩ S2) = 0.55-0.3 = 0.25

And as a result, the probability of stopping at exactly one signal is 0.25 + 0.1 = 0.35.

The probability that he must stop at both signals 0.30.

The probability to stop at the first signal but not at the second one is 0.1.

The probability that he must stop at exactly 0.35.

Given that,

The probability that he must stop at the first signal is 0.4,

The analogous probability for the second signal is 0.55,

The probability that he must stop at at least one of the two signals is 0.65.

We have to determine,

What is the probability that he must stop.

According to the question,

F = Event that a certain motorist must stop at the first signal.

S = Event that a certain motorist must stop at the second signal.

P(S1 ∪ S2) = P(S1) + P(S2) - P(S1 ∩ S2) =0.65

0.4 +0.55 - P(S1 ∩ S2) = 0.65

0.95 - P(S1 ∩ S2) = 0.65

Hence, P(S1 ∩ S2) = 0.95 - 0.65 = 0.30

It stops at both signals with probability 0.30.

The probability that he must stop at both signals 0.30.

P(S1) = P(S1 ∩ S2) + P(S1 ∩ S2^c)

0.4 = 0.3 + P(S1∩S2^c)

Where S2^c is the complementary event of S2. Therefore

P(S1∩S2^c) = 0.4 - 0.3 = 0.1

The probability to stop at the first signal but not at the second one is 0.1.

= P(S1 ∩ S2^c) + P(S1^c ∩ S2)

= 0.1 + P(S1^c ∩ S2)

Then,

= P(S2) = P(S1 ∩ S2) + P(S1^c ∩ S2) = 0.5

= 0.3 + P(S1^c ∩ S2) = 0.5

Therefore,

P(S1^c ∩ S2) = 0.55 - 0.3 = 0.25

And the probability of stopping at exactly one signal is 0.25 + 0.1 = 0.35.

The probability that he must stop at exactly 0.35.

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Answer:

Step-by-step explanation:

#2 the answer is B, -16/9

do 1/4-5/2

to do this, find the least common denominator. it's 4

1/4-10/4=-9/4

then divide 4 by -9/4. This is the same as 4*-4/9. That is -16/9

#3 the answer is A 9x/x-8

first factor the denominator of the first fraction using special products

x^2-6x-16=(x-8)(x+2)

if you look at the first fraction, you can simplify x+2 leaving you with the fraction 1/x+8

multiply that by 9x, and you get 9x/x-8

#4 the answer is C (2x+1)/2x^2

first add x/4 and 1/8

find the least common denominator. its 8

2x/8 + 1/8 is equal to (2x+1)/8

then multiply that by x^2/4 because dividing a fraction is the same as multiplying its reciprocal

you get (2x+1)/2x^2

#5 the answer is C (x-8)/(x+3)

using special products you can factor the numerator

x^2-4x-32 is the same as (x-8)(x+4)

then, using special products you can also factor the denominator

x^2+7x+12 is the same as (x+4)(x+3)

you can see that both the numerator and the denominator is multiplied by (x+4) you can simplify that. That leaves you with (x-8)/(x+3)

#7 the answer is D 3m

in the numerator in the second fraction, you can factor out 5m^2

leaving you with 5m^2(m-6)/5m^2. simplify the 5m^2 and the m-6

after you simplify both of those, you will get 3m

Answer:

  about 5.52%

Step-by-step explanation:

If Lucius wants an account value of $2000 after 3 years, she can find the interest rate by solving the polynomial ...

  550x³ +600x² +650x -2000 = 0

This equation has one positive real root. It is irrational, so must be found using the rather complicated cubic solution formula or, more simply, a graphing calculator. The latter shows the root to be near 1.05516.

Lucius needs an interest rate of ...

  (1.05516 -1)×100% = 5.516%

The interest rate needed for a balance of $2000 after 3 years is about 5.52%.

Answer:

The answer to your question is below

Step-by-step explanation:

f(x) = 2x + 5

To solve letter a, just multiply each term of f(x) by 3 and subtract 2.

a) 3f(x) - 2 = 3(2x + 5) - 2

                 = 6x + 15 - 2

               = 6x + 13

To f(x) subtract twice g(x)

b) f(x) - 2g(x) = 2x + 5 - 2(x² - 3x + 2)

                    = 2x + 5 - 2x² + 6x - 4

                    = -2x² + 8x + 1

Multiply 5 by each term of f(x) and divide it by g(x)

c)      [tex]\frac{5f(x)}{g(x)} = \frac{5(2x + 5)}{x^{2} - 3x + 2}[/tex]  

                = [tex]\frac{10x + 25}{x^{2}-3x + 2}[/tex]

Answer:

Mrs. Fowler will get [tex]9[/tex] free pizza. And she needs two more coupon for the next pizza.

Step-by-step explanation:

Given that pizza stand gives a free pizza for every [tex]8[/tex] coupons.

And Mrs. Fowler has [tex]78[/tex] coupons.

Part (a)

How many free pizzas can Mrs. Fowler get if she has [tex]78[/tex]coupons?

We will divide total number of coupons [tex]78[/tex] by [tex]8[/tex] coupons.

[tex]\frac{78}{8}=9\frac{6}{8}[/tex]

When we divide we get quotient as [tex]9[/tex], with a remainder of [tex]6[/tex]. So, Mrs. Fowler will get [tex]9[/tex] free pizza.

Now, part (b)

If  Mrs. Fowler adds two more coupons that will turn remainder [tex]6[/tex] into [tex]6+2=8[/tex].

So, she can have next pizza.

Final answer:

To calculate the total number of cherries that the bakery started with, multiply the number of pies by cherries per pie and then add the ones thrown away, resulting in 3026 cherries.

Explanation:

The question asks how many cherries the bakery started with before making the cherry pies. To find the answer, we multiply the number of cherry pies by the cherries used per pie and then add the number of cherries thrown away.

Multiply the number of pies (26) by the number of cherries used for each pie (115).

The result from step 1 gives the number of cherries used to make the pies.

Add the number of cherries thrown away (36) to the result from step 2.

The sum from step 3 is the total number of cherries the bakery started with.

Let's do the calculations:
26 pies × 115 cherries per pie = 2990 cherries
2990 cherries + 36 bad cherries = 3026 cherries

Therefore, the bakery started with 3026 cherries.

-8bits is equivalent yo 1 byte

-bit is(0 or 1)

So each pixel requires 3 bytes

Primary colors are RGB(red,green and blue),so each color represent one byte.

The frame size is:

1280×1024=1310720 pixels

So that the frame contained 1310720 pixels

The size of the frame buffer is equal to the product of RGB and frame pixels:

=3 × 1310720

=3932160 bytes

The minimum size of the frame buffer to store a frame of 1280 x 1024 pixels, with 8 bits used for each of the three primary colors (red, green, blue) per pixel, is 3932160 bytes.

When calculating the size of a frame buffer, you want to take into account the number of pixels in the frame, the number of bits used to represent each primary color per pixel, and the number of primary colors. In this case, the frame is 1280 x 1024 pixels, and 8 bits are used for each of the three primary colors (red, green, blue) per pixel.

Therefore, the calculation will be as follows:

So, the minimum size of the frame buffer to store a frame in this context would be 3932160 bytes.

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Answer:

-15x^4y

Step-by-step explanation:

(-3x^3y^2)(5xy^-1)

-15x^4y^2/y

-15x^4y

Answer:

C.  -15x^4y.

Step-by-step explanation:

(-3x^3y^2) (5xy^-1)

= -3*5 x^(3+1)y^(2 - 1)

= -15x^4y.

Answer:

A frequency distribution lists the number of occurrences of each category of​ data, while a relative frequency distribution lists the proportion of occurrences of each category of data.

Explanation:

A "frequency distribution" is one of the ways in organizing a data, either by listing the information, putting them in a table or showing them in a graph. The items in the list (distinct values) are then counted when it comes to the number of times they've occurred.

Thus, this explains the first answer, "number."

On the other hand, a "relative frequency distribution" refers to the proportion of the overall number of observations in a particular category.  You can get this by dividing each frequency with the total number of data in a sample.

Thus, this explains the second answer, "proportion."

A frequency distribution lists the number of occurrences for each category of data, whereas a relative frequency distribution provides the proportion of occurrences for each category in relation to the total number of data points. Histograms are a common tool to visualize these distributions, with the heights of bars representing either frequency or relative frequency.

The frequency distribution primarily deals with the number of occurrences of each category of data. For instance, in a class of 20 students, if the question is how many students scored in a particular range, the frequency distribution helps identify this - telling us how many students achieved each possible score.

In contrast, a relative frequency distribution showcases the proportion of the total number of data points that each category represents. So, instead of just telling you how many students achieved each score, it would express these amounts as a ratio or percent of the 20 total students, giving you a relative perspective of the categories.

An example of these principles might be visualized in a histogram: a type of graph that can express either frequency or relative frequency. The horizontal axis represents the categories of data (such as score ranges), while the vertical axis reflects frequency or relative frequency, displaying these values through the heights of bars along the graph.

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Answer: T may hold either L or L2

Step-by-step explanation: Going by Landlord and Tenant's law, when L leases a property to T and afterwards assigns his or her own interest to L2. T can either hold L or L2 when a paramount title holder X ejects T from the property.

According to the Law, L (in this case can be referred to as the Landlord) can actually assign all of his or her own rent rights and reversion to L2 (can be referred to as Landlord 2 or assignee). Whatever agreements or contracts made between L and T according to the lease of the property automatically ropes in L2. In this case, T is ejected by X who is a paramount title holder. This goes against the contract agreement between L and T, and therefore gives T the right to hold either L or L2.

I hope this helps.  

Answer:

The answer is 38.7 kg·m/s

Step-by-step explanation:

Considering the definition of average velocity,

The average speed of an object is defined as the distance traveled divided by the time elapsed.

Therefore, If in the frame of 320, the blue dot appears to be at 0 cm  and 24 frames later (at 344), the blue dot appears to be at 11 cm.  24 frames is 1/10 of a second, so

V = 11cm / 0.10s = 110 cm/s = 1.10 m/s

give or take.

Bonus:  initial system (cart only) momentum

p = mv = 23.8kg * 1.80m/s = 42.8 kg·m/s  

final system (cart+disk) momentum

p = (23.8+11.4)kg * 1.10m/s = 38.7 kg·m/s

Answer:

x³ − x² + 9x − 9 = 0

Step-by-step explanation:

Imaginary roots come in conjugate pairs.  So if 3i is a root, then -3i is also a root.

(x − 1) (x − 3i) (x − (-3i)) = 0

(x − 1) (x − 3i) (x + 3i) = 0

(x − 1) (x² − 9i²) = 0

(x − 1) (x² + 9) = 0

x (x² + 9) − (x² + 9) = 0

x³ + 9x − x² − 9 = 0

x³ − x² + 9x − 9 = 0

To find a third-degree polynomial equation with rational coefficients that has the given roots, we consider the conjugate of the complex root. The equation can be written as (x - 1)(x - 3i)(x + 3i) and simplified to x^3 - x^2 + 9x - 9.

To find a third-degree polynomial equation with rational coefficients that has the given roots of 1 and 3i, we need to consider the conjugate of 3i, which is -3i. Therefore, the roots of the equation are 1, 3i, and -3i.

To find the polynomial equation, we start by noting that the polynomials with rational coefficients will have complex conjugate pairs of roots. Thus, we can write the equation as (x - 1)(x - 3i)(x + 3i). Simplifying, we get (x - 1)(x^2 + 9). Expanding further, the equation is x^3 - x^2 + 9x - 9.

Therefore, the desired third-degree polynomial equation with rational coefficients is x^3 - x^2 + 9x - 9.

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Answer:

y/\8

Step-by-step explanation:

(y

4

)

2

​

=y

4⋅2

=y

8

​

This follows from the general rule \left(x^m\right)^{n}=x^{m\cdot n}(x

m

)

n

=x

m⋅n

left parenthesis, x, start superscript, m, end superscript, right parenthesis, start superscript, n, end superscript, equals, x, start superscript, m, dot, n, end superscript.

We can also see this is correct by expanding the powers.

\begin{aligned} \left(y^4\right)^{2}&=\underbrace{y^4\cdot y^4}_\text{2 times} \\\\\\ &=\underbrace{ \underbrace{y\cdot y\cdot y\cdot y}_\text{4 times} \cdot \underbrace{y\cdot y\cdot y\cdot y}_\text{4 times}} _\text{2 times} \\\\ &=y^{8} \end{aligned}

(y

4

)

2

​

=

2 times

y

4

⋅y

4

​

​

=

2 times

4 times

y⋅y⋅y⋅y

​

​

⋅

4 times

y⋅y⋅y⋅y

​

​

​

​

=y

8

​

Hint #22 / 2

In conclusion, \left(y^4\right)^{2}=y^{8}(y

4

)

2

=y

8

left parenthesis, y, start superscript, 4, end superscript, right parenthesis, squared, equals, y, start superscript, 8, end superscript.

To rewrite the expression, divide the digit term in the numerator by the digit term in the denominator and subtract the exponents. The final expression is y^-1/4.

To rewrite the expression in the form yn, we can use the rules of division of exponentials. In this case, we have 1/y5/4.

To divide, we need to subtract the exponents and divide the digit term in the numerator by the digit term in the denominator.

The digit term in the numerator is 1, and the digit term in the denominator is 1.

So, the expression can be rewritten as y1 - 5/4.

Now, let's simplify the exponent. We have 1 - 5/4 = 4/4 - 5/4 = -1/4.

So, the final expression is y-1/4.

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Answer:

this is a left tailed test

   Null hypothesis,  [tex]H_{0} :[/tex] σ = 40 seconds

   Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.

Step-by-step explanation:

i) the standard deviation of duration times in seconds of the old faithful geyser is less than 40 sec. identify the null hypothesis and alternative hypothesis in symbolic form

ii) this is a left tailed test

   Null hypothesis,  [tex]H_{0} :[/tex] σ = 40 seconds

   Alternate hypothesis, [tex]H_{a} :[/tex] σ < 40 seconds.

Answer:

x = 6.

Step-by-step explanation:

Because the the 2 angles are equal

4 / (x + 2) = 3 / (9-3)

4/(x+2) = 3/6

4 / (x + 2) = 1/2

x + 2 = 4*2 = 8

x = 8 - 2 = 6.

Answer:

[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]

Step-by-step explanation:

Given:

The fractions are given as:

[tex]\dfrac{1}{2}\ and\ \dfrac{3}{5}[/tex]

The denominators of the first fraction is 2 and that of the second fraction is 5.

In order to find the common denominator for 2 and 5, we have to find the least common multiple of each of the numbers.

Multiples of 2 = 2, 4, 6, 8, 10, 12,....

Multiples of 5 = 5, 10, 15, 20, 25, 30,....

Therefore, the least common multiple of 2 and 5 is 10. So, the common denominator is 10.

Now, multiply the numerator and denominator of each fraction by the same suitable number such that the denominator becomes 10.

So, for the first fraction, 2 is in the denominator.

So, 2 when multiplied by 5 gives 10.

So, we multiply the numerator and denominator of first fraction by 5. This gives,

[tex]\dfrac{1}{2}=\dfrac{1\times 5}{2\times 5}=\dfrac{5}{10}[/tex]

Now, for the second fraction, 5 is in the denominator.

So, 5 when multiplied by 2 gives 10.

So, we multiply the numerator and denominator of first fraction by 2. This gives,

[tex]\dfrac{3}{5}=\dfrac{3\times 2}{5\times 2}=\dfrac{6}{10}[/tex]

Therefore, the new fractions after making the denominators same are:

[tex]\dfrac{5}{10}\ and\ \dfrac{6}{10}[/tex]

So, the miles covered in fraction with same denominators are:

[tex]\dfrac{5}{10}\ miles\ and\ \dfrac{6}{10}\ miles[/tex]

Answer: The probability of drawing 5 cards in either ascending or descending order out of the deck of 52 standard playing cards is 0.84%.

Step-by-step explanation: We have the following cards in a deck: 1(ace), 2, 3, 4, 5, 6, 7, 8, 9, 10, 12(Jack), 13(Queen), 14(King) (thirteen different in total). There are 4 copies of each of them yielding 52 cards in total. First to draw all of the cards in the ascending order all of the drawn cards need to be different. Imagine you have 13 piles of 4 identical cards. Let us calculate the number of ways you can select 5 different ones (the order matters). First you select 5 different piles (this secures that each card is different) and this is possible to do in [tex]\frac{13!}{(13-5)!}[/tex] (we use the formula for variations since the order matters). Now, each card in the pile can be selected in [tex]4[/tex] different ways so the total number of sequences with [tex]5[/tex] different cards is [tex]4^5\frac{13!}{(13-5)!}[/tex]. Now we select out of these sequences the clases of those that contain exactly the same cards but in different order. Only 4 of the sequences within the same class will be in ascending order out of 4*5! which is the total number of the sequences within the class! This means that we have to multiply our total number of sequences of 5 different cards by [tex]\frac{4}{4\cdot 5!}=\frac{1}{5!}[/tex] and this yields the final answer of total number of ascending sequences to be

[tex]4^5\frac{13!}{(13-5)!5!}.[/tex]  

The total number of possible ways to draw 5 out of 52 cards is just

[tex]\frac{52!}{(52-5)!}.[/tex]

This yields for the probability

[tex]\frac{4^5\frac{13!}{(13-5)!5!}}{\frac{52!}{(52-5)!}}=0.42\%[/tex]

Exactly the same calculation applies for the descending order. So the probabilty of the cards being in either ascending or descending order is just the sum of these two (the events are mutually exclusive, you cannot have both the ascending and descending order at the same time) yielding the final probability of [tex]0.84\%[/tex].

Answer:

Step-by-step explanation:

The car's value was $61,412.50  in the year 2006.

x = no. of years since 2000.

Acc. to ques,

100,000 × (0.85)ˣ = 61,412.50

(0.85)ˣ = 0.614125.

ln((0.85)ˣ) = ln(0.614125).

x × ln(0.85) = ln(0.614125).

x = ln(0.614125) / ln(0.85).

x = 5.832 ≈ 6

Answer: The limit does not exist.

Step-by-step explanation: The limit of a piecewise function f(x) as it approaches "a" will exist if and only if the value of the limit of f(x) as x approaches "a" from the left is the same with the value of the limit of f(x) as x approaches "a" from the right.

From the given question the value are not the same. We have 5 (limit from the left) and -3 (limit from the right). So, we can conclude that the limit of f(x) as x approaches "a" does not exist.

Answer:

Leo is 1 year old.

Step-by-step explanation:

Given:

Lily's age = 5

Leo's age = [tex]3x-14[/tex]

we need to find the Leo's age.

Solution:

Leo's age = [tex]3x-14[/tex]

where x ⇒ Lilly age

But Lilly's age = 5 years (given)

So we will substitute the value of x as 2 in Leo's age expression.

On Substituting we get;

Leo's age = [tex]3x-14 = 3\times5-14 = 15-14 = 1\ year[/tex]

Hence Leo is 1 year old.

Answer:

Bb

Step-by-step explanation:

Final answer:

After applying a 20% discount and a 10% service fee to a pair of shoes originally priced at $75, Martinez ends up saving 12% from the original price.

Explanation:

Martinez is looking to calculate the final price of a pair of shoes after applying a 20% discount and a 10% service fee. She wants to know the overall percentage saved from the original price. First, let's calculate the discount: $75.00 × 0.20 = $15.00. Thus, the discounted price is $75.00 - $15.00 = $60.00. Next, we add the service fee on the discounted price: $60.00 × 0.10 = $6.00. Therefore, the total cost after the discount and service fee is $60.00 + $6.00 = $66.00.

To find the percent decrease from the original price, we can use the formula 'Percent Decrease = ((Original Price - Final Price) / Original Price) × 100%'. Substituting the respective values, we get: ((75 - 66) / 75) × 100% = 12%. Martinez saved 12% off the original price of the shoes after all the adjustments.

To make at least a 25% profit, Cameron should charge a minimum of $1.22 per bag for the mixed candy. The cost per bag is found by adding the total cost of candy corn and M&Ms, then multiplying by 125% and dividing by the number of bags to distribute the cost and profit evenly.

The student's question involves calculating the minimum selling price for candy bags to achieve a certain profit margin, which is a common type of problem in Mathematics, specifically in the field of algebra and business mathematics.

To find the least price Cameron can charge for each of the thirty bags to make at least a 25% profit, we first calculate the total cost of the candy. Cameron bought twelve pounds of candy corn at 79 cents a pound and eighteen pounds of M&Ms at $1.09 a pound.

Now, we calculate the total cost including the desired 25% profit.

Total cost with profit: $29.10 × (1 + 0.25) = $36.375

Since Cameron is making thirty bags, we divide the total cost with profit by the number of bags.

Minimum selling price per bag: $36.375 / 30 bags = $1.2125

However, as prices are generally rounded to the nearest cent, the minimum charge per bag would be $1.22 to ensure a 25% profit.

ANSWER= 0.9772

STEP-BY-STEP EXPLANATION:

We are assuming that there is an underlying distribution of package weights,even though we don´t speciify the shape of that distribution.

Letting [tex]x_{i}[/tex] denote the ith package weight and S=[tex]x_{1} +....x_{100}[/tex] we are trying to find P(S ≤ 1700)

We know that the distribution of S is approximately normal with mean nцХ and variance по²Х

S≈N( 100 * 15, 100 * 10² ) = N (1500.10000) (note that they gave us the standar deviation aove; variances add, so we need to square this). Finally,

P(S ≤ 1700) = P ([tex]\frac{S-1500}{\sqrt{10000} }[/tex] ≤ [tex]\frac{1700 - 1500}{\sqrt{10000} }[/tex])

≈P (Z≤2) = 0.9772

The object's position function is y = 2.5t² - 2t derived using kinematic equations. The speed at time t is |-2 + 5t| m/s where t is the time.

This is a problem of mechanics related to the motion of the object under the influence of a force. First, we need to calculate the acceleration using the formula F=ma. This gives us the acceleration as a = F/m = 20N/4kg = 5m/s². The object is moving upwards so this force is in the positive y direction.

The initial velocity vector is given as vs0d − i2j. The i-component represents the x-direction, and the j-component represents the y-direction. Thus, the initial speed is sqrt((0d)² + (−2)²) = 2 m/s. However, given that this velocity is in the negative y-direction, we determine its initial speed to be -2 m/s.

Now, we can determine the position function for the y-direction using the equation y = y0 + v0y*t + 0.5*a*t², where y0 represents the initial position (origin), v0y is the initial velocity in the y-direction (-2m/s for this case), a is the acceleration (5 m/s²), and t is time. Substituting these values, the equation becomes y = 0 – 2t + 0.5*5t² = 2.5t² - 2t.

For the speed at time t, you can utilize the velocity's magnitude in the y-direction using v = v0y + a*t = -2 m/s + 5t The magnitude ||v|| = sqrt((0)² + (-2 + 5t)²) = |-2 + 5t| m/s as speed is always positive.

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We determined the object's position function to be [tex]\[ \matbf{r}(t) = -t \mathf{i} + 2t \mathf{j} + \frac{5t^2}{2} \mathf{k} \][/tex] and its speed at time t to be |v(t)| = [tex]\sqrt{5 + 25t^2}[/tex]. The calculations involved using Newton's second law and integrating the acceleration and velocity.

To find the position function and speed of the object under the given conditions, we need to use the principles of Newtonian mechanics. Let's break it down step-by-step.

Step 1: Find the acceleration

Given:

- Force ( F = 20 N ) upward

- Mass  (m = 4 kg)

Using Newton's second law (F = ma) , we can find the acceleration:

[tex]\[ \mthbf{a} = \frac{\mahbf{F}}{m} \][/tex]

Since the force is acting directly upward (which we'll take as the ( z )-direction):

F = 20k

Thus,

[tex]\[ \mahbf{a} = \frac{20 \matbf{k}}{4} = 5 \mahbf{k} \][/tex]

So, the acceleration is:

a = 5k

Step 2: Find the velocity function

The initial velocity is given as:

[tex]\[ \matbf{v}(0) = -\matbf{i} + 2\matbf{j} \][/tex]

Acceleration is constant, so we can integrate to find the velocity function:

[tex]\[ \matbf{v}(t) = \mathf{v}(0) + \mathf{a} t \][/tex]

Substituting the known values:

[tex]\[ \mathf{v}(t) = (-\matbf{i} + 2\matbf{j}) + 5 t \mahbf{k} \][/tex]

Thus,

[tex]\[ \matbf{v}(t) = -\matbf{i} + 2\matbf{j} + 5t \mthbf{k} \][/tex]

Step 3: Find the position function

To find the position function, integrate the velocity function:

[tex]\[ \mahbf{r}(t) = \mathf{r}(0) + \int \mathf{v}(t) \, dt \][/tex]

Given that the object starts at the origin:

r(0) = 0

Integrating the velocity function:

[tex]\[ \mathf{r}(t) = \int (-\mathf{i} + 2\matbf{j} + 5t \mathf{k}) \, dt \][/tex]

[tex]\[ \mahbf{r}(t) = (-\matbf{i}t) + (2\matbf{j}t) + \left( \frac{5t^2}{2} \matbf{k} \right) \][/tex]

Thus, the position function is:

[tex]\[ \matbf{r}(t) = -t \mathf{i} + 2t \mathf{j} + \frac{5t^2}{2} \mathf{k} \][/tex]

Step 4: Find the speed at time ( t )

Speed is the magnitude of the velocity vector:

[tex]\[ \mathb{v}(t) = -\mathf{i} + 2\matbf{j} + 5t \mathb{k} \][/tex]

Calculate the magnitude:

[tex]\[ \text{Speed} = |\mathbf{v}(t)| = \sqrt{(-1)^2 + (2)^2 + (5t)^2} \][/tex]

[tex]\[ \text{Speed} = \sqrt{1 + 4 + 25t^2} \][/tex]

[tex]\[ \text{Speed} = \sqrt{5 + 25t^2} \][/tex]

Answer:

  d.  300%

Step-by-step explanation:

The given relation is ...

  60%·A = 20%·B

Dividing by 20%, we see that ...

  3·A = B

Of course, 3 = 3×100% = 300%, so B is 300% of A.

First, let's write the given condition in the form of an equation. If 60% of A is 20% of B, it can be written as:

60/100 * A = 20/100 * B

In order to proceed, we begin simplifying the equation by eliminating the fractions. This can be achieved by multiplying both sides of the equation by 100, turning our equation into:

60A = 20B

Following this, we can further simplify by solving for B. This involves dividing the equation through by 20A which yields:

B = 60A / 20

This simplification results in the following expression:

B = 3A

This means that B equals three times the value of A. However, we have been asked to express B in terms of what percent it is of A. Knowing that 'percent' may be understood as 'per hundred', this corresponds to converting the ratio to a percentage.

We can safely say therefore that B is 300% of A which corresponds to choice (d) among our original options.

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Answer: c. sampling error

Step-by-step explanation:

Since, the sample is a subset of population , so there are chances for unavoidable variation in sample mean from the population mean that varies from sample to sample .

This variation is known as sampling error.

∴ The difference between the value of the sample statistic and the value of the corresponding population parameter is called the sampling error .

Hence,the correct answer is c. sampling error .

The difference between the sample statistic and the population parameter is known as the sampling error. This error occurs due to the sample selected being unrepresentative of the entire population.

The difference between the value of the sample statistic and the value of the corresponding population parameter is referred to as the sampling error. This definition directly fits the option c. Listed among the given options. A sampling error is a discrepancy that occurs due to an unrepresentative selection of observations from the whole population. The nature of statistical sampling means there will always be some level of uncertainty or error because we are making estimates based on a sample from a larger population, rather than the entire population itself.

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Answer:

θ ≈ 71.6°

Step-by-step explanation:

The angle between two lines with slopes m₁ and m₂ is:

tan θ = | (m₂ − m₁) / (1 + m₁m₂) |

Here, m₁ = -2 and m₂ = 1.

tan θ = | (1 − (-2)) / (1 + (-2)(1)) |

tan θ = | 3 / -1 |

tan θ = 3

θ ≈ 71.6°

Answer:

State A has 27 screens and state B has 21 screens.

Step-by-step explanation:

Let the number of screens in state B be 'x'.

Given:

Number of screens in state A is 6 more than state B

Total number of screens = 48.

Now, as per question:

Number of screens in state A = 6 more than state B.

Framing in equation form, we get:

Number of screens in state A = [tex]6+x[/tex]

Now, total number of screens is the sum of the screens in state A and number of screens in state B. Therefore,

Total number of screens = 48

Number of screens in state A + Number of screens in state B = 48

Substituting the given values, we get:

[tex]6+x+x=48\\\\6+2x=48\\\\2x=48-6\\\\2x=42\\\\x=\frac{42}{2}=21[/tex]

So, state B has 21 screens.

State A has = 6 + 21 = 27 screens.

Therefore, state A has 27 screens and state B has 21 screens.

Answer:

168 members are on the marching band but not part of the percussion.

Step-by-step explanation:

Given:

The high school marching band has 196 members,and 28 of them are a part of the percussion.

Now, to find the members on the marching band but not part of the percussion.

Total members of marching band = 196.

Members of them who part of percussion = 28.

So, to get the members of the marching band who are not the part of the percussion we subtract members of them who part of percussion from total members of marching band:

[tex]196-28[/tex]

[tex]=168.[/tex]

Therefore, 168 members are on the marching band but not part of the percussion.

Answer:

D itll go from 87.5 to 70, so it'll drop by 17.5

Step-by-step explanation:

Answer:

The answer is actually D

Step-by-step explanation:

This is true because when you add the scores together you get 350 and then you divide that number by however many data numbers there are in the set.

86+84+90+90=350

because there are 4 numbers in the data set you so divide 350 by 4 which equals 87.5

Then he scores a 0 on the quiz, it will indeed affect the mean.

You add the numbers 86+84+90+90+0 still equals 350, however, instead of 4 numbers in the data set it's 4 because of the zero.

Instead of dividing by 4, you divide by 5

350 divided by 5 equals 70.

the original MEAN was 87.5 and now it is 70, so that means that it decreased by 17.5. there's is your answer. The answer is D 17.5