The times for three runners in a 100-meter race are 9.85 s, 9.6 s and 9.625 s. What is the winning time?

Answer:

continuous.

Step-by-step explanation:

Given function is [tex]f(x)=5x^4-9x^3+x-7[/tex].

and value of a = 7.

Now we need to find if the given function [tex]f(x)=5x^4-9x^3+x-7[/tex] is continuous or not.

By definition of continuity, we know that a function is continuous at a given point if both left and right hand limits are equal.

Left Hand Limit = LHL

[tex]LHL=\lim_{x\rightarrow 7^-}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]

Right Hand Limit = RHL

[tex]RHL=\lim_{x\rightarrow 7^+}f(x)=5(7)^4-9(7)^3+(7)-7=8918[/tex]

Since both limits are equal at a=7 so we can say that given function is continuous at a=7

Answer:

6 books and 10 magazines

Step-by-step explanation:

Answer:

Step-by-step explanation:

(5 - 3i)(6 + 2i)

30 + 10i - 18i - 6i²

i² = - 1

30 - 8i - 6 - (- 1)

30 - 8i + 6

- 8i + 36

36 - 8i

Alternative D

I hope I helped you.

Answer: D

Step-by-step explanation:

  (5 - 3i)(6 + 2i)

= 5(6 + 2i)  -3i(6 + 2i)

= 30 + 10i  -18i - 6i²

= 30 - 8i -6(-1)    because i² = -1

= 30 - 8i + 6

= 36 - 8i

Mario can talk for 384 minutes on his prepaid phone plan, calculated by dividing his plan's cost, $50, by the per-minute rate of $0.13.

To determine how many minutes Mario can talk on his prepaid phone plan, you would divide the total amount of the plan by the cost per minute. Mario has $50 and the cost per minute is $0.13. To calculate the total minutes, use the formula:

Total Minutes = Total Plan Cost / Cost Per Minute

Let's do the math:

Total Minutes = $50 / $0.13

Total Minutes = 384.6154

Since we cannot have a fraction of a minute in this context, we round down to the nearest whole minute.

Therefore, Mario can talk for 384 minutes on his prepaid plan.

Answer:

Any ordered pairs which have a slope of 5/4.

Step-by-step explanation:

The line has a slope of -4/5 which means the y values have a difference of -4 and the x values have a difference of 5. If the line is perpendicular to this line then its slope must be the negative reciprocal which is 5/4. Any points which have a difference in y values of 5 and a difference of x values of 4 will be on some line perpendicular to the original.

Answer:

A. As x→-∞ f(x) →-∞  and as x→∞ f(x) →-∞

Step-by-step explanation:

f(x) = -x^6 +2

As the numbers get very large, the 2 doesn't matter

Let x go to - ∞

f(-∞) = - (- ∞)^6

Anything to an even power is positive

f(-∞) = - ∞

As x →-∞   f(x) →-∞

Let x go to  ∞

f(∞) = - ( ∞)^6

Anything to an even power is positive

f(∞) = - ∞

As x →∞   f(x) →-∞

Answer:

Mean is the sum of all the results included in the sample divided by the number of observations.

Explanation:

Suppose we have the score of 5 randomly selected students in a class.

The scores are:

[tex]45,48,52,65,78[/tex]

Now the mean of the 5 randomly selected students will be:

[tex]Mean = \frac{Sum-of-scores-of-five-students }{Number-of-students}[/tex]

          [tex]=\frac{45+48+52+65+78}{5}[/tex]

          [tex]=\frac{288}{5}[/tex]

          [tex]=57.6[/tex]

Therefore, the mean is 57.6

Answer:

  = 5  * 10 ^ 1/3

Step-by-step explanation:

3 log 2x=4

Divide each side by 3

3/3 log 2x=4/3

log 2x=4/3

Raise each side to the power of 10

10 ^(log 2x)=10 ^(4/3)

2x = 10 ^(4/3)

Divide by 2

2/2x =  1/2 * 10 ^(4/3)

x = 1/2 * 10 ^4/3

10 ^ 4/3  = 10 * 10 ^ 1/3

x = 1/2  ( 10)  10 ^ 1/3

  = 5  * 10 ^ 1/3

According to its Lewis structure, the sulfur dioxide (SO2) molecule forms 0 single bonds, 2 double bonds, has 0 triple bonds, and 1 lone pair of electrons on the central (sulfur) atom.

The Lewis structure of sulfur dioxide (SO2) can be represented as :

:O=S=O:

Here, sulfur is the central atom. It forms one double bond with each oxygen atom. There are no single or triple bonds present, and the sulfur atom has one lone pair of electrons.

Therefore, the correct count of single bonds, double bonds, triple bonds and unshared pairs of electrons on the central atom, in that order, is - 0, 2, 0, 1

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In the Lewis structure for SO2, or sulfur dioxide, there are zero single bonds, two double bonds, zero triple bonds, and one unshared pair of electrons on the central sulfur atom. The correct sequence for SO2 is therefore 0, 2, 0, 1.

SO2, or sulfur dioxide, consists of a central sulfur atom with oxygen atoms on both sides. The Lewis structure for SO2 includes one lone electron pair and double bonds with the two oxygen atoms. To calculate this, we first count the valence electrons from the atoms: sulfur has 6 valence electrons and each oxygen atom has 6 as well, for a total of 18 valence electrons.

To start the Lewis structure, we place the least electronegative atom - sulfur - in the center and the two oxygen atoms on each side. We then place a single bond between the sulfur and each oxygen. This accounts for four valence electrons (2 from each bond), leaving us with 14 more. Next, we distribute the remaining electrons to the oxygen atoms as lone pairs, as necessary, to satisfy the octet rule. If there are still electrons left over, we create double bonds until we have used all of the electrons. Here, it results in double bonds between sulfur and each oxygen atom with one lone pair on the sulfur.

Given these steps, for SO2, we have 0 single bonds, 2 double bonds, 0 triple bonds, and 1 unshared pair of electrons on the central atom, sulphur. So the correct option would be 0, 2, 0, 1.

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Factor 6 from the first two terms.

By factoring out "a", you can better see what "h" needs to be.

Answer:

The dimensions of rectangle a are 6x4 and dimensions of rectangle b are 6x2.

Step-by-step explanation:

We are given a square with area 36 squared cm. Therefore, dimension of the square will be 6 cm.

The square is cut into two rectangles with areas in the ratio 2:1.

Let the dimensions of the rectangles be 6*a and 6*b. Therefore, we can set up the ratio of areas as:

[tex]\frac{6a}{6b}=\frac{2}{1}  \\a=2b[/tex]

Moreover, we can set the combined area of rectangles equal to the area of square to form another equation:

[tex]6a+6b=36\\a+b=6[/tex]

Using substitution method, we can solve for 'a' and 'b' as shown below:

[tex]2b+b=6\\3b=6\\b=2[/tex]

And

[tex]a=2b\\a=2(2)\\a=4[/tex]

Therefore, dimensions of the two rectangles are 6x4 and 6x2, respectively.

[tex]\frac{82}{450}\cdot100\%=\frac{164}{9}\%=18\frac{2}{9}\%[/tex]

Hi there! :)

Answer:

Jaime has 30 dimes in his pocket.

Step-by-step explanation:

First off, you need to know that:

A quarter is equal to = $0.25

A dime is equal to = $0.10

Jaime has 6 quarters, which means that he has 6 times $0.25:

6 × 0.25 = $1.50

Jaime has a total of $4.50 → Subtract the amout of money represented by the quarters and you'll be left with the amout of money represented by the dimes:

4.50 - 1.50 = $3

Jaime has $3 worth of dimes in his pocket. In order to know how many dimes $3 represents, you'll need to divide "3" by 0.10, which is what 1 dime is worth:

3 ÷ 0.10 = 30 → YOUR ANSWER

There you go! I really hope this helped, if there's anything just let me know! :)

Answer:

C

Step-by-step explanation:

We can use the formula for chords ,and tangents

< ABC = 1/2 (ADYC - AC)

61 = 1/2(y - 119)

Answer:

Option C.  [tex]\frac{1}{2}[/tex] ( y-119 ) = 61

Step-by-step explanation:

In the given diagram AB and AC are tangents to circle O.

Length of arc AC = 119°

Inscribed angle between tangents AB and BC is 61°

We have to find the measure 'y' of arc ADC.

As we know the formula

m∠A = [tex]\frac{1}{2}[/tex] [m( arc ADC ) -m(arc AC)]

Now we put the values in this equation

61 = [tex]\frac{1}{2}[/tex] ( y-119 )

So Option C 61 = [tex]\frac{1}{2}[/tex] ( y-119 ) is the answer.

Answer:

it is 20% can you mark me brainless

Step-by-step explanation:

Answer:

18 hours

Step-by-step explanation:

We work in fractions of the job done per hour.

So in the case of Tran alone he does 1/9 of the job per hour.

We have the equation 1/9 + 1/x = 1/6  where x is the time taken for Luis to deliver the newspapers.

1/9 + 1/x = 1/6

Multiply through by the LCM 18x:-

2x + 18 =  3x

18 = x

the answer is:

18 hours !

Answer:

Step-by-step explanation:

The basic and simple way to calculate the probability of an event happening is by using this equation:

Our desired outcomes are picking either red or yellow candies. The number of desired outcomes in this case is the total number of red and yellow candies. 6 red + 3 yellow = 9

Number of desired outcomes = 9

Number of all possible outcomes in this case is the total number of candies in the bag. 10 green + 8 brown + 3 yellow + 8 blue + 6 red = 35

Number of all possible outcomes = 35

Use the formula and we get that the probabbility of drawing out a yellow or red candy is: 9/35, 0.257 or 25.7% (those are 3 different ways to write the probability)

Answer: No; they do not have congruent corresponding angles.

Answer: 40 Boxes

Step-by-step explanation: All you need to do is divide 800 by 20.

Answer:

40

Step-by-step explanation:

Step-by-step explanation:

[tex]3x+\frac{5}{8}\geq 4x-\frac{1}{2}[/tex]

Subtract 5/8 on both sides

To subtract 5/8 we make the denominators same

[tex]3x\geq 4x-\frac{1*4}{2*4}-\frac{5}{8}[/tex]

Addition or Subtraction property of order is used

[tex]3x\geq 4x-\frac{9}{8}[/tex]

Subtract 4x on both sides

Addition or Subtraction property of order is used

[tex]-x\geq -\frac{9}{8}[/tex]

Now divide both sides by -1

Multiplication or Division property of order is used

[tex]\frac{-x}{-1} \geq \frac{-\frac{9}{8}}{-1}[/tex]

Multiplication or Division property of order is used

[tex]x\leq \frac{9}{8}[/tex]

Final answer:

The justification for solving the inequality involves using the Addition or Subtraction property of order to combine like terms and isolate the variable, and the Multiplication or Division property of order to solve for the variable, with an important note that dividing both sides by a negative number reverses the inequality symbol.

Explanation:

The justification for each step in solving the inequality 3x + 5/8 ≥4x − 1/2 can be broken down as follows:

3x + 5/8 ≥4x − 1/2 Given

3x ≥4x − 9/8 Addition or Subtraction property of order, subtracting 5/8 from both sides

−x ≥ − 9/8 Addition or Subtraction property of order, subtracting 4x from both sides

−x / −1 ≥ −9/8 / −1 Multiplication or Division property of order, dividing both sides by −1

x ≤9/8 Multiplication or Division property of order, understanding that dividing by a negative number reverses the inequality symbol

Each step involves manipulating the inequality while maintaining the balance, and the direction of the inequality changes when both sides are multiplied or divided by a negative number.

[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=4,\ a_n=\dfrac{1}{3}\cdot a_{n-1}.\\\\\text{Therefore}\ r=\dfrac{1}{3}.\ \text{Substitute:}\\\\\boxed{a_n=4\left(\dfrac{1}{3}\right)^{n-1}}[/tex]

Answer:

Anne found the 10th term of the following sequence. Her steps are shown below.

3, 7, 11, 15, …

1. common difference = 4, a1 = 3

2. an = 3 + (n - 1)4

3. an = 3 + 4n - 4

4. an = 4n - 1

5. a10 = 4(10) – 1

6. a10 = 39

Analyze Anne’s work. Is she correct? If not, what was her mistake?

Yes, she is correct.

No, she needed to find the common ratio because it is a geometric sequence.

No, she substituted the wrong values into the rule to find the equation that represented the sequence.

No, she solved for the 10th term incorrectly.

Step-by-step explanation:

The function factors as ...

... f(x) = -(x+3)(x+4)/((x-1)(x+4)) = -(x+3)/(x-1) . . . . x ≠ -4

and the quotient is ...

... f(x) = -(1 +4/(x-1))

... f(x) = -1 -4/(x-1) . . . . . x ≠ -4

This has a hole at x = -4 (where the denominator factor cancels the numerator factor), a vertical asymptote at x=1 (where the denominator is zero), and a horizontal asymptote at y = -1 (the value of the function for large values of x).

Answers: (B) (2, -1) and (D) (5, 2)

Step-by-step explanation:

Inverse is when the x's and y's are swapped

Given: (-2, 5), (-1, 2), (0, 1), (2, 5)

Inverse: (5, -2), (2, -1) (1, 0), (5, 2)

The correct answer would be options (B) (2, -1) and (D) (5, 2)

The inverse function is defined as a function obtained by reversing the given function.

To determine the inverse of a function, all you have to do is switch where x and y are and resolve for y.

Given that the set of points is on the graph of a function.

{(−2, 5), (−1, 2), (0, 1), (2, 5)}

We have to find the inverse of the function below :

{(−2, 5), (−1, 2), (0, 1), (2, 5)}

When the values of x and y are switched, the inverse is true.

(-2, 5) ⇒ (5, -2),

(-1, 2) ⇒ (2, -1),

(0, 1) ⇒ (1, 0),

(2, 5) ⇒ (5, 2)

Hence, the points {(5, -2), (2, -1) (1, 0), (5, 2)} are on the graph of the inverse.

The correct answer would be options (B) (2, -1) and (D) (5, 2)

Learn more about the inverse function here:

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Answer: B. (3,9)

Step-by-step explanation:

7x -5y = -24(times by -1)

–9x + 5y = 18

-2x=-6

X= 3

(Substitute 3 in)

-9(3)+5y=18

-27+5y=18

5y=45

Y=9

Answer:

[tex](x-6)[/tex] meters

Step-by-step explanation:

We  have been given that the area of a rectangle is [tex]x^2-11x+30[/tex] square meters and a length of [tex](x-5)[/tex] meters.

Since the area of a rectangle is product of its width and length.

[tex]\text{Area of rectangle}=\text{Width of rectangle*Length of rectangle}[/tex]

We can find width of our rectangle by dividing area of rectangle by length of rectangle.

[tex]\text{Width of rectangle}=\frac{\text{Area of rectangle}}{\text{Length of rectangle}}[/tex]

Let us substitute our given values in above formula.

[tex]\text{Width of rectangle}=\frac{x^2-11x+30}{x-5}[/tex]

Let us factor out numerator by splitting the middle term.

[tex]\text{Width of rectangle}=\frac{x^2-6x-5x+30}{(x-5)}[/tex]

[tex]\text{Width of rectangle}=\frac{x(x-6)-5(x-6)}{(x-5)}[/tex]

[tex]\text{Width of rectangle}=\frac{(x-6)(x-5)}{(x-5)}[/tex]

Upon cancelling out x-5 from numerator and denominator we will get,

[tex]\text{Width of rectangle}=(x-6)[/tex]

Therefore, the expression [tex](x-6)[/tex] meters represents width of the rectangle.

Answer:

the answer is x - 6, have a nice day

Answer:

 degree=2 leading coefficient=4

lowest degree = 3

maximum of 5 x-intercepts

[tex]y=-4x^7-5x+3[/tex] has y intecept 3

y approaches negative infinity

Step-by-step explanation:

(1) [tex]y=4x^2-3x+7[/tex]

Highest exponent is the degree of the function

Highest exponent =2  so degree =2

Coefficient of x^2 is 4, so leading coefficient is 4

(2) from the graph we can see that

As x approaches infinity, the graph goes down

As x approaches -infinity, the graph goes up

The value of y goes on the opposite direction. So it is a odd degree function. If degree =1  then the graph should be a line

Here the graph is like a curve. Also we have 2 x  intercepts . Hence lowest possible degree of the function is 3

(3) y=ax^5+cx^2+f

Here , the degree of the equation is 5

So we will get maximum of 5 x-intercepts

(4) To find the function that has y intercept of 3, we plug in 0 for x in each function

[tex]y=-4x^7-5x+3[/tex]

[tex]y=-4(0)^7-5(0)+3= 3[/tex]

[tex]y=-4x^7-5x+3[/tex] has y intecept 3

(5) [tex]y=-2x^{13}+25x^8-3[/tex]

Here degree is 13 that is odd  and leading coefficient is -2 ( negative)

Degree is odd and leading coefficient is negative so the graph of y goes down on the right side.

the graph of y approaches negative infinity when x approaches infinity

The degree and leading coefficient of the polynomial function y=4x2-3x+7 are 2 and 4 respectively. The maximum of x-intercepts for a polynomial graph y=ax5+cx2+f is 5. The polynomial function y=-4x7-5x+3 has a y-intercept of 3 and as x approaches infinity in the function y=-2x13+25x8-3, y approaches negative infinity.

1. The degree of the function y=4x2-3x+7 is 2 and the leading coefficient is 4. Therefore B. degree=2 leading coefficient=4 is correct.

2. As the image of the function graphed is not provided, it is impossible to definitively say what the lowest degree of the function is.

3. The maximum number of x-intercepts that can be found on a graph with the equation y=ax5+cx2+f is 5, matching the degree of the polynomial, so D. 5 is correct.

4. The polynomial function y=-4x7-5x+3 has a y-intercept of 3, therefore C. y=-4x7-5x+3 is correct.

5. Since the polynomial y=-2x13+25x8-3 has an odd degree and the leading coefficient is negative, as x approaches infinity, y approaches negative infinity. Therefore D. y approaches negative infinity is correct.

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Answer:

Minimum 22 scarves Jenny has to sell in order to make a profit.

Step-by-step explanation:

Let the number of scarves knitted be  'x'.

Then cost price of the scarves = $ (160+4.5x)

Total selling price of the scarves = $ 12x

In order to attain a profit selling price > cost price

Therefore  12x > 160+4.5x

⇒12x - 4.5x > 160

⇒7.5x > 160

⇒ x >160÷7.5

⇒x > 21.33

SO minimum number of scarves should be 22 a whole number.

To find the minimum number of scarves Jenny must sell to make a profit, set up the inequality 12s > 160 + 4.50s, which represents her earnings from selling scarves being greater than her expenses. Solve for s to obtain s > 21.3. As scarves are sold in whole numbers, Jenny must sell at least 22 scarves to make a profit.

To determine the number of scarves that Jenny must sell in order to make a profit, we can set up and solve an inequality. The inequality will represent Jenny's total expenses compared to her total earnings.

Jenny's initial expenses are $160 and it costs $4.50 to make each scarf. This means her total expenses can be represented as 160 + 4.50s, where s is the number of scarves.

Jenny sells each scarf for $12, so her earnings from selling scarves can be represented as 12s.

To establish a profit, Jenny's earnings should be greater than her expenses, so:

12s > 160 + 4.50s

We can solve this inequality by first subtracting 4.50s from each side to isolate the variable:

7.5s > 160

Then, divide both sides by 7.5 to solve for s:

s > 21.3

Since scarves are sold in whole numbers, Jenny needs to sell at least 22 scarves to make a profit.

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