Five weeks after the introduction of a new toy, the manufacturer found that the demand for the toy was modeled by f(x) = x^2 +5x+4/x^2+6x-7 - 1/x , while the company s supply capability was modeled by g(x) = - 0.89x^2 +850x -50/(800x+70.5. Here x is the number of weeks the toy has been on the market, and values of f(x) and g(x) are in millions of toy units. About how many weeks after the toy was introduced did supply equal demand? Round to the nearest whole number of weeks.

Answer:

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{9}{\sqrt{150}} = 1.2[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 40.5 - 1.2 = 39.3 hours

The upper end of the interval is the sample mean added to M. So it is 40.5 + 1.2 = 41.7 hours

The 90% confidence interval for the true mean lifetime of all batteries of this brand is between 39.3 hours and 41.7 hours. The lower limit is 39.3 hours while the upper limit is 41.7 hours.

Answer:

B.

Step-by-step explanation:

So we know right off the bat the angles ABE and CBD are congruent because of vertical angles.

Now we can look at the sides.

The ratio for 27:18 = 3:2

The ratio for 36:24 = 3:2

They check out.

That means that the answer is B. SAS

Answer:

x^4 + 2x + 2

Step-by-step explanation:

The expression in the simplest form is -90p - 102

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given an expression as 9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

Then Rewrite in simplest terms:

9(-6p-4)+3(3p-5) + 9(−6p−4)+3(3p−5)

2 [ 9(-6p-4)+3(3p-5) ]

Solve the like terms;

2 [-54p - 36 + 9p - 15]

2 [-54p + 9p - 15 -  36]

2 x ( -45p - 51)

-90p - 102

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Answer:

98°

Step-by-step explanation:

3x+89+8x+58=180

11x+147=180

11x=180-147

11x=33

x=3

< MON = 3x+89 = 3(3)+89 = 9+89= 98°

Answer:

1.77 percent increase

Answer:

cool i think there are 4 questons

Step-by-step explanation:

Answer:

The probability is 0.7449

Step-by-step explanation:

Given

[tex]n = 12[/tex] ---- total

[tex]r = 5[/tex] --- selection

[tex]Genre =\{Rap(4), Country (5), Heavy\ metal (3)\}[/tex]

Required

Probability of buying at least 1 of each genre

First, we calculate the total possible selection.

To select 5 CDs from a total of 12, we use:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

[tex]^{12}C_5 = \frac{12!}{(12 - 5)!5!}[/tex]

[tex]^{12}C_5 = \frac{12!}{7!5!}[/tex]

Expand

[tex]^{12}C_5 = \frac{12*11*10*9*8*7!}{7!*5*4*3*2*1}[/tex]

[tex]^{12}C_5 = \frac{12*11*10*9*8}{5*4*3*2*1}[/tex]

[tex]^{12}C_5 = \frac{95040}{120}[/tex]

[tex]^{12}C_5 = 792[/tex]

So, the total selection is:

[tex]Total = 792[/tex]

To select at least 1 from each genre, there are 6 possible scenarios.

And they are:

[tex]\begin{array}{ccc}{Heavy\ Metal (3)} & {Rap (4)} & {Country(5)} & {3} & {1} & {1} & 2 & {1} & {2} & {2} & {2} & {1}& {1} & {2} & {2}& {1} & {3} & {1}& {1} & {1} & {3} \ \end{array}[/tex]

The possible selections for the given scenario is:

[tex]Possible = ^3C_3* ^4C_1 * ^5C_1 +^3C_2* ^4C_1 * ^5C_2 +^3C_2* ^4C_2 * ^5C_1 +^3C_1* ^4C_2 * ^5C_2 +^3C_1* ^4C_3 * ^5C_1 +^3C_1* ^4C_1 * ^5C_3[/tex]

Using a calculator, we have:

[tex]Possible = 1*4*5 +3*4*10 +3*6*5 +3*6*10+3*4*5+3*4*10[/tex]

[tex]Possible= 20 +120 +90 +180+60+120[/tex]

[tex]Possible = 590[/tex]

The probability is then calculated using:

[tex]Pr = \frac{Possible}{Total}[/tex]

[tex]Pr = \frac{590}{792}[/tex]

[tex]Pr = 0.7449[/tex]

The three consecutive number are 17 , 18 and 19 respectively

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be = x

Let the second number be = ( x + 1 )

Let the third number be = ( x + 2 )

Now ,

A = 4 times the first decreased by the second is 12 more than twice the third

Substituting the values in the equation , we get

4x - ( x + 1 ) = 12 + 2 ( x + 2 )

On simplifying the equation , we get

4x - x - 1 = 12 + 2x + 4

3x - 1 = 16 + 2x

Subtracting 2x on both sides of the equation , we get

x - 1 = 16

Adding 1 on both sides of the equation , we get

x = 17

Therefore , the value of x is 17

Hence , the consecutive numbers are 17 , 18 and 19

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Answer:

3/20

Step-by-step explanation:

[tex]\frac{0.3}{2}=\frac{0.3*10}{2*10}=\frac{3}{20}[/tex]

Answer:

54°

Step-by-step explanation:

Angles corresponding in parallel lines are the same

Answer:

a) estimated regression equation = ( 2.039e + 04 - 3.79e - 02 millage , - 6.863e + 02 age )  

b) multicollinearity is an issue for this model

Step-by-step explanation:

a) An estimated regression equation

estimated regression equation = price ~ mileage + age = ( 2.039e + 04 - 3.79e - 02 millage , - 6.863e + 02 age )  

Residuals :

Min 1∅ median 3∅ max

- 1053.73 - 542.06 - 19.61  433.55 1560.81

coefficients :

b) multicollinearity is an issue for this  model because the correlation between millage and Fs 0.6681727 is of high degree

attached below is the remaining part of the solution

Answer:

Error is in line 3

Error description: Root of 4 is 2 not 4

Correct answer should be 9*√5 (12*√5 - 3*√5)

Answer:

G

Step-by-step explanation:

only 3 more brailiest and I will become an expert : )

Answer:

The option 'J' is the correct order from least to greatest

The time to build the fence will be 10 hours.

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since construction company is building a fence that is 1 1/3 miles long and they can building the fence 1/6 Mile every hr.

The time to build the fence will be:

= 1 1/3 ÷ 1/6

= 5/3 × 6/1

= 30 / 3

= 10 hours.

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Answer:

She could buy 11 packs of cookies for $43.56.

Step-by-step explanation:

to find the answer you have to find how much 1 pack of cookies costs.

First, you divide 51.48 by 13

51.48/13 = 3.96

now that you know 1 pack of cookies cost $3.96 you can use that to find how many packs you could buy for 43.56

43.56/3.96 = 11

the is answer is probably c

the answer makes sense

Answer:

2(x-3)

Step-by-step explanation: 2 is being multiplied by the difference (subtraction) of x-3.

Answer:

7 cars

11 bikes

Step-by-step explanation:

18 cars would have 72 tires. This is 22 more tires than necessary. If we add a bike, we lose four tires (from the car) and add two (from the bike). This means we lose two tires. 22/2 is 11 so it would be 11 bikes and 7 cars.

11 bikes = 22 tires

7 cars = 28 tires

22+28=50 tires

The sum of the interior angle measures of the polygon is 900 degrees

From the image shown, we can see that the polygon has 7 sides.

A polygon with seven sides is called a heptagon

It is important to note that the number of triangles in a heptagon is 5.

Also, the sum of angles in a triangle is 180 degrees.

Now, the formula for calculating the sum of interior angles of a polygon is expressed as;

= (n - 2) 180

Where; n is the number of sides of the polygon

Substitute the value

= (7-2)180

Subtract the value

= 5(180)

= 900 degrees

Hence, the sum is 900 degrees

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Answer:

3rd term: 24

10th term: 220

Step-by-step explanation:

For the 3rd term

2*3 + 2*(3^2) = 6 + 2*9 = 6 + 18 = 24

For the 10th term

2*10 + 2*(10^2) = 20 + 2*100 = 20 + 200 = 220

Answer:

X=5 y=-2

Step-by-step explanation:

Set them equal to each other so...

-2x+8=3x-7

Simplify by balancing out the equation so

-5x=-1

So x=5

Now plug it into either y equation

-2(5)+8

-10+8

Y=-2

Hope this helps!

Answer:

The child's reading level is at the 3.4th percentile.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 90 words per minute and a standard deviation of 24 words per minute.

This means that [tex]\mu = 90, \sigma = 24[/tex]

You find an individual that reads 46.4 word per minute. At what percentile is the child's reading level?

The percentile is the p-value of Z when X = 46.4, multiplied by 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{46.4 - 90}{24}[/tex]

[tex]Z = -1.82[/tex]

[tex]Z = -1.82[/tex] has a p-value of 0.034.

0.034*100 = 3.4

The child's reading level is at the 3.4th percentile.

The student that has the highest reading rate is Student C who has the highest rate of change of the number of words read of 158 words per minute.

The rate of change of a function is the rate at which the output value changes per unit change in the input value.

The possible data and table obtained from a similar question on the website are presented as follows;

Student A

Number of minutes;         [tex]{}[/tex]1              2             3              4

Number of words read; 150        [tex]{}[/tex]300          450          600

Student B

y = 158·x

Where;

x = The time duration in minutes

y = The number of words read by the student

Student C

The points on the graph representing the reading rate of student C are; (2, 280), (3, 420), (5, 700)

The first difference of the number of words read by Student 1 is constant, indicating that the relationship is a linear relationship, with the reading rate obtained by the rate of change of the number of words read as follows;

Reading rate for Student A = (300 - 150)/(2 - 1) = 150

The reading rate for Student A is 150 words per minute

The equation for the reading rate of Student B; y = 158·x, indicates that Student B reads 158 words per minute

The of the straight ling graph for the reading rate of Student C is found as follows;

Slope = (420 - 280)/(3 - 2) = 140

The slope indicates that the number of words read by Student C increases by 140 words every minute, therefore, the reading rate for Student C is 140 words per minute

The student that reads fastest is therefore, Student C who has a reading reading rate of 158 words per minute

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Answer:

2700 meters

Step-by-step explanation:

2 and a half minutes becomes 150 seconds. 150 seconds divided by 4 seconds, the amount of seconds it takes to cover 72 meters, is 37.5. 37.5 multiplied by 72, the meters covered in 4 seconds, is 2700 meters.

Therefore , the solution is circle Part 1: The central idea ( -5 , 7 ). 2nd part: Radius is 6 in part 2,3rd part: FALSE and Parts 4. There are 10 miles between A and B.

A circular shape called a circle is created by following a moving point in a plane so that its distance from a particular point remains constant. The Greek word kirkos, which means hoop or ring, distance is the source of the English word circle.

Here,

The common circle equation is,

( x - h )² + ( y - k ) ( y - k )

6² = r²

where the circle's radius is r and the center's coordinates are (h, k).

Part 1.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( -5 , 7 )

Consequently, the second choice is the right one.

Part 2.

Using the common circle equation, we obtain,

circle radius is six.

Consequently, the first choice is the right one.

Part 3.

Using the common circle equation, we obtain,

Circle's circumference's coordinate is ( 2 , 3 )

Therefore False.

Part 1.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( -5 , 7 )

As a result, the second choice is the right one.

Part 2.

In comparison to the common circle equation, we obtain,

circle's diameter is six.

As a result, the first choice is right.

Part 3.

In comparison to the common circle equation, we obtain,

Circle's center's coordinates are: ( 2 , 3 )

So, False.

Part 1.

Giving the distance between two points,

Distance between A(-5, 3) and B (5, 3), expressed as:

=> [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} )}[/tex]

= >  [tex]\sqrt{(-5-5)^{2} + (3-3)^{2} )}[/tex]

=> 10

Thus, 3rd Option is correct.

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