If you translate the square root parent function up three units, and reflect it across the x-axis, what is the equation of the new function?

Answer:

Neither of them are solutions unless you had a typo in the question.

Step-by-step explanation:

1) plug in the known values into both of the equations

First Coordinate:

y-x[tex]\leq[/tex]-5
(1)-(0)[tex]\leq[/tex]-5
1[tex]\leq[/tex]-5 which is not true.
In this case, we do not need to plug in (0,1) into both of the equations because the coordinate cannot be a solution unless the coordinate works in BOTH of the equations.

Second Coordinate:

1)  y-x[tex]\leq[/tex]-5
(-6)-(-1)[tex]\leq[/tex]-5

(-6)+1[tex]\leq[/tex]-5 -->    It becomes a +1 because two negatives make a positive

-5 [tex]\leq[/tex]-5 - -> which means this is true because -5 is less than or equal to -5

2) y-2x>-5
(-6)-2(-1)>-5

-6(2)>-5
-12>-5 NOT TRUE

ANSWER: Neither of them are solutions unless you had a typo in the question.

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

Answer:

[tex]\textsf{Quotient}: \quad 2i^3+4i^2-5i+6[/tex]

[tex]\textsf{Simplified Quotient}: \quad 2-7i[/tex]

Step-by-step explanation:

Long division method

Given rational expression:

[tex]\dfrac{2i^4-6i^3-25i^2 +31i-30}{i -5}[/tex]

Solve using long division:

[tex]\large \begin{array}{r}2i^3+4i^2-5i+6\phantom{)}\\i-5{\overline{\smash{\big)}\,2i^4-6i^3-25i^2 +31i-30\phantom{)}}}\\{-~\phantom{(}\underline{(2i^4-10i^3)\phantom{-b00000000000.)}}\\4i^3-25i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(4i^3-20i^2)\phantom{))))))))))))}}\\-5i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(-5i^2+25i)\phantom{........}}\\6i-30\phantom{)}\\-~\phantom{()}\underline{(6i-30)\phantom{}}\\0\phantom{)}\end{array}[/tex]

Therefore, the quotient is:

[tex]2i^3+4i^2-5i+6[/tex]

Imaginary number rule

[tex]i^2=-1[/tex]

Simplify the quotient:

[tex]\implies 2i^3+4i^2-5i+6[/tex]

[tex]\implies 2i^3+4(-1)-5i+6[/tex]

[tex]\implies 2i^3-4-5i+6[/tex]

[tex]\implies 2i^3-5i-4+6[/tex]

[tex]\implies i(2i^2-5)+2[/tex]

[tex]\implies i(2(-1)-5)+2[/tex]

[tex]\implies-7i+2[/tex]

[tex]\implies 2-7i[/tex]

Using the concepts of statistics, we got that 2004 is the sample size needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence.

The number of observations used to calculate estimates for the certain population is known as the sample size. The sample size was actually determined by drawing from the population. Sampling is a practice of choosing a portion of a population from which to draw conclusions about the characteristics of a entire population. A subset of the population is chosen for analysis based on the number of entities in it.

We have  Margin of error(E)=0.02,

Significance level([tex]\alpha[/tex])=0.01

Proportion(p)=0.13

Therefore, q is defined by =1-p

                =>  q =1-0.13

                =>q=0.87

So, the Z-score is 2.582

Now, we know that sample size(S) is given by

                =>S =[ [ [Z²×p×(1-p)] / e²] / [1+(Z²×p×(1-p)/e²)] ]

               =>S=[ [ ( 2.582)²×0.13×0.87/(0.02)²] / [1 + [(2.582)²×0.13×0.87] / (0.02)²]

               =>S= ([0.754/0.0004] / [1+(0.754/0.0004)])×1000

               =>S=([885.01] / [1+1885.01]) × 1000

                =>S=(0.200351)×1000

                =>S=2003.51=2004 (approx)

Hence, a federal report indicated that 13% of children under age 6 live in poverty in Massachusetts, an increase over previous years in that case size of  sample which is needed to estimate the true proportion of children under age 6 living in poverty in Massachusetts within 2% with 99% confidence is 2004.

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Step-by-step explanation:

There are 185 marbles in a bag. 40% of the marbles are blue and the rest are of other colours.

a. Find the percentage of marbles that are not blue.

100% - 40% = 60%

b. Find the number of marbles that are not blue​.

60% = 0.6

0.6 * 185 = 111 marbles

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

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:

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 :)

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.

Total amount that Mikaela spent on the paddleboard is 578.5065.

According to given data,

original price = 899$ and 40% off.

state tax rate is 7.25%.

Solution:-

Applying formula,

⇒ 899 × (7.25% + 1) × (1 - 40%)

⇒ 899 × 1.0725 × 0.6

⇒ 578.5065.

Total amount that Mikaela spent on the paddleboard is 578.5065.

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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:

£250

Step-by-step explanation:

Divide $405 by $1.62 which is 250.

Multiply that by £1 which is £250.

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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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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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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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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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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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

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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Answer:

2x^2 -x -10 is the answer as a product

3x-3 as a sum

Step-by-step explanation:

Assuming (2x-5)(x+2)=0

Let's distribute.

(2x^2+4x)(-5x-10)=0

Then combine like terms

2x^2 -x -10 is the answer as a product

3x-3 as a sum

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 amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.

From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.

In this case, Omar bought 3.5k of onions are 8.90 per kilo.

The amount that Omar will pay for the onions will be:

= Number of kilograms × Cost per kg

= 3.5 × 8.90

= $31.15

In conclusion, the amount is $31.15.

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The number of terms in the expression 5x - 2 is 2

The number of terms in an expression or equation refers to the values separated by a mathematical operator. A mathematical operator could be

The terms can be like terms or unlike terms

The two terms given is separated by the subtraction operator and are both unlike terms

The first term 5x consist of

The second term is just a constant which is 2

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Answer:

Domain = { -2 , 0 , 2 , 4 }

Range = { 3 }

Step-by-step explanation:

Domain is the x-values that the Function have and Range is the y-values that the Function have corresponding to these x-values

Since the x-values for the Function attached are -2 , 0 , 2 , 4

and the y-values for the Function is 3

Then the Domain = { -2 , 0 , 2 , 4 }

and the Range = { 3 }

Glad to Help

Answer:

the label are marked by numbers

Answer:

length = 13 cm , width = 14 cm

Step-by-step explanation:

let the length be n , then the width is n + 1

the perimeter (P) of a rectangle is calculated as

P = 2(l + w) ← l is the length and w the width

given P = 54 , then

2(n + n + 1) = 54 ( divide both sides by 2 )

2n + 1 = 27 ( subtract 1 from both sides )

2n = 26 ( divide both sides by 2 )

n = 13

n + 1 = 13 + 1 = 14

so, length = 13 cm and width = 14 cm

The actual area represented by 3.5-inches-by-10-inches on map is 995.5 miles.

As the measure of 3/4 inch is provided, working out the calculation for 1 inch.

3/4 inch = 4 miles

1 inch = (4×4)/3

1 inch = 16/3

1 inch = 5.33 miles

Now, the actual area of the region = 3.5 × 10

The actual area of the region = 35 inches²

Converting the area in square miles

The actual area of the region = 35 × (5.33)²

Taking square on Right Hand Side of the equation

The actual area of the region = 35 × 28.4

Performing multiplication on Right Hand Side of the equation

The actual area of the region = 995.5 square miles

Thus, the actual area of the region is 995.5 square miles.

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