8x - 4y = 16
8x+4y= 16

The new mirror must have at least 81 cm² of the area.

The area of the square is defined as the product of the length and width.

As per the given question, we have

Dominic requires a new bicycle mirror. His old mirror was a square with a 9-cm side length.

He wants the replacement mirror to have an area that is as near to his previous bike mirror as feasible.

We have to determine the area of the previous bike mirror.

The area of the previous bike mirror = (side length)²

The area of the previous bike mirror = (9)² = 9 x 9

The area of the previous bike mirror = 81 cm²

So the new mirror must have greater than 81 cm² of area.

Thus, the new mirror must have at least 81 cm² of the area.

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Answer:

5 cm

Step-by-step explanation:

hope this helps

The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]

Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

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Answer: -64

Step-by-step explanation:

(8−2 • 35)−2

8-70-2

8-72

-64

Answer:

(8 - 2 • 35) - 2 = -64

Step-by-step explanation:

Given problem,

→ (8 - 2 • 35) - 2

Let's solve the problem,

→ (8 - 2 • 35) - 2

→ (8 - (2 × 35)) - 2

→ (8 - 70) - 2

→ -62 - 2

→ -64

Hence, the answer is -64.

The probability that Laura does not win the prize is 119 / 175.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of raffle rickets to be sold is 350.

The number of tickets bought by Laura is 12.

Since, the probability of an event is defined as the ratio of favorable outcome to the total outcomes, the probability of winning the prize is,

P = 12 / 350

Thus, the probability of not winning the prize is,

1 - 12 / 350

= 338 / 350

= 119 / 175

Hence, the probability of not winning a prize is 119 / 175.

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Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).

As given in the question,

Focus of the parabola is equal to (-3, -3)

Directrix of the parabola is given by x = 5

Let (x, y) be the point on the parabola.

Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5

⇒√(x +3)² + (y +3)² = | x -5|

⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²

⇒x² +6x +y² +6y +18 = x² -10x +25

⇒y² +6y -7 = -16x

⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.

Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by  x = (-1/16)(y² +6y -7).

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Answer:

0,3

Step-by-step explanation:

it between the 2 and it is negative and positive cases in the -2

Using the concept of average speed we conclude that the space-mean speed of the vehicles is 0.69 km/min.

The average speed of a vehicle traveling a given segment of a highway in a specific time period is called space-mean speed, i.e.

Average mean speed = total distance traveled / average time travel

Given for vehicles are traversing a 1 km segment of highway. Hence total distance is 4km.

Average time = (1.2 + 1.5 + 1.7 + 1.4)/4

= 5.8/4

= 1.45 min

Now Average mean speed = 1/1.45

=0.689

=0.69 km/min

Hence the space-mean speed of the vehicles is 0.69 km/min

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The null hypothesis is a statement which describe the claim of 'no difference'.

Let μ be the population mean.

Given claim : The mean age of bus drivers in Chicago is 50.2 years.

i.e. μ = 50.2

Since "no difference with mean" or statements with an equal sign are used as the null hypothesis.

Then, the null hypothesis for the given situation is

Ηο : μ = 50.2

If the test fails to reject the null hypothesis, it means there is evidence to support the claim that the the mean age of bus drivers in Chicago is 50.2 years.

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided data. Using sample data, hypothesis testing is performed to evaluate a theory' veracity. It is often referred to as just "the null," and its symbol is Hο.

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The probability that Sara will pick a blue marker is 3/20.

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Math's to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given,

the box contains red markers = 5

blue marker = 3

purple marker = 9

pink markers = 3

Total number of markers = 20

The probability that she picks blue marker = 3/20

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Answer:

Total Cost = $186

Step-by-step explanation:

All but 8 means that All of them participated except for 8 of them

Since there is 39 Students in the Club

Then the Number of Students participated = 39 - 8 = 31 Students

Total Cost = (Cost per Student ) * ( Number of Students )

                 =$6 * 31 = $186

Glad to Help

The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.

A function is simply a relationship that maps one input to one output. For relation to qualify as a function,  each x-value can only have one y-value.

Given the data in the question;

To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.

g( a ) = 3a + 2

g( -3 ) = 3( -3 ) + 2

Multiply 3 and -3

g( -3 ) = -9 + 2

Add -9 and 2

g( -3 ) = -7

Therefore, the output value is -7, this forms an ordered pair of (-3,-7).

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By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.

Given,

2x+y=4

x-y=1

By solving above two equations we get,

2x+y=4

x-y=1

3x=5

x=5/3

y=-1+x

y=(5/3)-1

y=2/3

Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

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Answer:

The range of the data set is 16.

Step-by-step explanation:

The range of a box plot is the difference between the maximum and minimum value. To find the range of the given box plot, we can simply subtract the value located at the lower whisker from the value located at the upper whisker.

18 - 2 = 16

Hope this helps :)

14 people can go to the amusement park. Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.

Inequality: 33p + $12.50 ≤ $465

14 people can go to the amusement park

Inequality:

$465= Amount of money they have

$12.50= Parking Cost

$33= Cost of tickets per person

Because they only have $465, they can't spend more than that amount.

Therefore, the inequality would be the ticket cost per person, times the amount of people being payed for (aka x) plus the parking cost is less than or equal to the amount of money they have to spend. Hence the inequality:

33p+ $12.50 ≤ $465

$465- $12.50 = $452.5 (452.5 is how much is left for tickets after subtracting the parking cost)

$33 x1 4 = $462 (14 tickets can be bought for the price of $33)

$462 - $452.5 = $9.5 (9.5 isn't enough for another person)

So, the solution to the inequality is 14 people can go to the amusement park.

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Answer: 45.5p is less than or equal to 465

Answer:

Divide by Three Trick

This is a fun trick. If the sum of the digits in a number can be divided by three, then the number can as well.

Examples:

1) The number 12. The digits 1+2=3 and 12 ÷ 3 = 4.

2) The number 15. The digits 1+5 = 6, which is divisible by 3. It turns out that 15 ÷ 3 = 5

3Justin's estimated Vo2 max is 25.8(mL*kg*min)

What is Vo2 max ?

 The amount (volume) of oxygen used by your body while exercising as hard as you can is referred to as VO2 max. It's a common tool for determining your level of fitness. Knowing your VO2 max can assist you in training for sports, tracking fitness progress, and improving your heart health.

Here using vo2 max fomula 1.5 miles ,

=> VO2 max = 3.5+483/Time

Here Time= 11 min 25 sec = 25/60 = 0.41 min

Then time=11.42 mins. Now,

=> VO2 max = 3.5+ 483/11.41

=> VO2 max = 3.5+42.3

=>VO2 max = 25.8(mL*kg*min)

Hence His estimated Vo2 max is 25.8(mL*kg*min)

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The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8.

A rectangle is a geometrical figure in which opposite sides are equal.

Area of rectangle = length × width.

The angle between any two consecutive sides will be 90 degrees.

As per the given rectangle with dimensions 3 × 5.

The rectangle has been attached below,

The length of the diagonal using Pythagoras' theorem is,

x = √(3² + 5²)

x = √34 = 5.8

Hence "The length of the diagonal for the given rectangular book using Pythagoras' theorem will be 5.8".

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There is no vertex in the graph and the transformations from the parent function are

The graph represents the given parameter

As a general rule, the maximum or the minimum of a graph is the vertex

In this case, there is no maximum or minimum in the graph

This means that that there is no vertex in the graph

Here, we have:

We can see that:

The graph is 4 units to the left of the origin and 2 units below the origin

This means that the function has been shifted down and shifted to the left

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Answer:

x=21

Step-by-step explanation:

The angles of a triangle always add up to 180°

71+62+(2x+5)=180

First add 71 and 62

133+(2x+5)=180

Then you subtract 133

2x+5=47

Subtract 5 too

2x=42

Then divide by 2

x=21

We can check our answer by adding all the angles

71+62+(2*21+5)

71+62+(42+5)

71+62+47=180

Answer:

As a product of prime numbers:

420 = 2 × 2 × 3 × 5 × 7

Probability that the professional other than Tokyo, Kyoto or Osaka is 6803/13839.

Total number of professional train pushers who are diagnosed with carpal tunnel is 13839

Number such professional from Tokyo = 2551

Number such professional from Osaka = 3049

Number such professional from Kyoto = 1436

So, number such professional from other than these three cities = 13839 - (2551+3049+1436) = 6803

Hence the probability that the professional other than Tokyo, Kyoto or Osaka is = 6803/13839

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Answer:

1 piece = 1 slice then the answer is 4/3 = $1.33 (still … 3 slices will be $3.99 rounded to 4). A pizza costs £5.50 and fries cost £1.00, John orders 3 pizzas and 5 fries but the …

The vertex is at (8, -2).The point (10, -22) is also on the parabola.

Step-by-step explanation:

Here is the graph of the function:

The vertex is at (8, -2).

To plot another point on the parabola, we can choose any x-value and plug it into the equation to solve for y.

For example, if we choose x = 10, then we have:

f(x)   = -5(x - 8)² - 2

f(10) = -5(10 - 8)² - 2

f(10) = -5(2)² - 2

f(10) = -5(4) - 2

f(10) = -20 - 2

f(10) = -22

So, the point (10, -22) is also on the parabola.

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As per given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.

As given in the question,

Minimum height require to ride in amusement park = at least 48 inches

Present height of Michael is 42 inches tall

Increase in height every month 1/2 inch.

Let 'm' months taken by Michael to ride in amusement park.

Required equation is:

48 = 42 + (1/2)m

⇒(1/2)m = 48 -42

⇒ m = 6×2

⇒ m =12 months

Therefore, for the given data of at least 48inches height is required to ride in amusement park , Michael is 42 inches tall and grow 1/2 in. every month then total months after which Michael can ride is 12 months.

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The statements that are true are:

It should be noted that the two figures can be regrdedas as one that are similar in the case whereby their corresponding angles are congruent ,also their ratios of the lengths with respect to their corresponding sides would also be equal.

In conclusion, when two figures are similar then it can be concluded that their  corresponding angles are congruent .

Hence, the second and third options are correct.

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Answer:

Corresponding angles of congruent figures are the same.

The corresponding sides of congruent figures are the same.

Step-by-step explanation:

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] have a strong, negative correlation

What is a correlation coefficient?

A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables.

The variables may be two columns of a given data set of observations, often called a sample or two components of a multivariate random variable with a known distribution.

As we know that the correlation coefficient is a measure of the strength of the straight line or linear relationship between two variables. Correlation coefficients are expressed as values between [tex]+1[/tex] and [tex]-1[/tex].

So,

[tex](1,8),(2,3),(3,0),(4,1),(5,2),(6,1)[/tex]

As per the Excel tools i.e., CORREL function the correlation coefficient is [tex]-0.9[/tex].

Hence, the correlation coefficient is [tex]-0.9[/tex], i.e., [tex]x[/tex] and [tex]y[/tex] has a strong, negative correlation.

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Answer:

y=-3/32

Step-by-step explanation:

2-18y=11+78y

-18y-78y=11-2

-96y=9

y=-3/32

The probability that the transistor will last between 12 and 24 weeks is 0.424

the probability that a transistor will last at most 24 weeks is 0.567

The median of the lifetime distribution is less than 24

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

a) X~gamma([tex]\alpha , \beta[/tex])

E(X)= [tex]\alpha \beta[/tex]             [tex]\beta[/tex] =[tex]12^{2}/24[/tex] =6 weeks

V(x)=[tex]\alpha \beta ^{2}[/tex]                 [tex]\alpha[/tex]=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,[tex]\alpha[/tex] ,[tex]\beta[/tex] , False)

P([tex]12\leq X\leq 24[/tex])

P([tex]12/6 \leq X\leq 24/6[/tex])

P([tex]2\leq X\leq 4[/tex])

P= 0.424

Therefore, the probability that the transistor will last between 12 and 24 weeks is 0.424

b) For this case we want this probability:

[tex]P(X\geq 24)=1-P(X\leq 24)[/tex]

In order to find this probability we can use excel with the following code:

=1-GAMMA.DIST(24,4,6,TRUE)

And we got:

[tex]P(X\geq 24)=P(1-X\leq 24)= 0.567[/tex]

c) For this case the median of the lifetime distribution is less than 24

[tex]P(X\leq \alpha )[/tex] = 0.5  (by definition)    So [tex]\alpha[/tex]< 24 because P([tex]X\leq 24[/tex])=0.567 which is greater than 0.5

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