You have won a new PS 5 system in a rafflel With a bit of research, you have determined that the cost of a new PS 5 system is $712 with tax. If you know that the value of gaming consoles decreases each year by 12%, based on the previous year's value, what will your PS 5 system be worth after 6 years?

Parent function is represented by the graph is

B. The quadratic parent function

What is Parent function?

A parent function in mathematics is the most basic function within a family of functions that nonetheless upholds the definition of the entire family. For instance, displaystyle y=x2 is the simplest function in the family of quadratic functions with the general form displaystyle y=ax2+bx+c.

A parent function is an equation in the simplest form of a family of functions. There are many forms of parent functions such as: Linear functions: f(x)=x f ( x ) = x , where the degree of the function is 1 and represents a straight line.

The simplest parabola is y = x2, whose graph is shown at the right. The graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions.

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The total area of the Caribbean sea and the South Atlantic ocean is 4.299 × 10⁷ km². The correct option is the second option 4.299 × 10⁷ km²

From the question, we are to determine the total area of the water bodies.

From the given information

"The area of the Caribbean sea is 2.7182 × 10⁶ km²"

and

"The area of the South Atlantic ocean is 4.027 × 10⁷ km²"

To determine the total area, we will add  up the two areas

Total area = 2.7182 × 10⁶ km² + 4.027 × 10⁷ km²

Total area = 0.27182 × 10¹ × 10⁶ km² + 4.027 × 10⁷ km²

Total area = 0.27182 × 10⁷ km² + 4.027 × 10⁷ km²

Total area = 4.29882 × 10⁷ km²

Total area ≈ 4.299 × 10⁷ km²

Hence, the total area is 4.299 × 10⁷ km²

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Answer:

Hence, the total area is 4.299 × 10⁷ km²

Step-by-step explanation:

The ratio of the number of mowers that fail to the overall number of mowers is known as the fraction of mowers that fail the functional performance test. Consequently, 9/500 lawnmowers fail, then the probability of having x failures in the next 100 mowers is = [tex]0.018x[/tex]  

Probability of having x mower fail = 0.018x

Number of mowers that fail = 54

Total number of mowers = 3000

The probability of failure can be defined as,

=  [tex]\frac{Number of mowers that fail}{Total number of mowers}[/tex]

Fraction that failed = [tex]\frac{54}{3000}[/tex]

Fraction that failed = [tex]\frac{9}{500}[/tex]

Fraction that failed = 0.018

Therefore,

The ratio of the number of mowers that fail to the overall number of mowers is known as the fraction of mowers that fail the functional performance test. Consequently, 9/500 lawnmowers fail, then the probability of having x failures in the next 100 mowers is = [tex]0.018x[/tex]

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The value of the numerical expression 70 / (7 - 2) will be 14. Then the correct option is B.

Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.

The numerical expression is given below.

⇒ 70 / (7 - 2)

Simplify the expression, then we have

⇒ 70 / (7 - 2)

⇒ 70 / 5

⇒ 14

The worth of the mathematical articulation 70/(7 - 2) will be 14. Then the right choice is B.

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The correct expression is given below.

70 / (7 - 2)

Alyssa has the money of worth $660

Eric has the money of worth $245

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

Let x be the amount Alyssa has.

Let y be the amount  Eric has.

alyssa has $75 less than three times eric

=> x= 3y - 75

Together they have $905

=> x + y =905

Substitute x

=> 3y - 75  +y = 905

    4y = 905 +75 = 980

    y = 980 /4 = 245

x= 3y - 75  = 3(245) - 75 = 660

Alyssa has  $660

Eric has  $245

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Using the given data, the number of suspects is; 7

The union of two sets A and B is the set of all those elements which are either in A or in B, and which is denoted as A ∪ B.

However, the intersection of two sets A and B is defined as the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B.

Now, we are told that;

Total number of people in the office = 30 people

Number of people wearing a white button down shirts = 22

Number of people wearing black pants = 16

Number of people wearing a multicolored tie = 7

Thus, by definition of intersection of sets, if the suspect was wearing black pants, a white button-down shirt, and a multicolored tie, then;

The number of suspects =  A ∩ B ∩ C = 7 people

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Answer:

C

Step-by-step explanation:

1/18 x³y + 7/18 xy²

1/18 xy (x² + 7y)

The probability that their second child will have blue eyes is 1/4.

Here dark eye is dominant trait and blue eyes is recessive trait.

So both man and woman is heterozygous dominant and the blue eye child is homozygous recessive.

Man and woman will produce four types of genotypes in children. One homozygous dominant (dark eye), one homozygous recessive (blue eye) and two heterozygous dominant (dark eye).

So the probability of any child to be blue eyed (homozygous recessive) will be 1/4.

Hence we get the required answer.

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Answer: -26 feet

Step-by-step explanation:

The original attendance of the video game club was 28.57 members.

To determine the original attendance of the video game club, you can use the following formula:

Original attendance = (Number of members lost) / (Percent of group that left)

Plugging in the values from the problem, we get:

Original attendance = (8 members) / (28%)

To solve this equation, you need to convert the percent to a decimal by dividing it by 100. This gives us:

Original attendance = (8 members) / (0.28)

Then, you can solve the equation by dividing the number of members lost by the decimal equivalent of the percent:

Original attendance = 28.57 members

Therefore, the video gaming club had 28.57 members when it first started.

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Answer:

Step-by-step explanation:

11.1

The approximate value of y - x is 17.2°.

Right angled triangle are those triangle for which one of the angle is 90 degrees.

Given a right triangle LMN.

Using the tangent function,

tan (y) = 19.1 / 14.1

          = 1.3546

y = tan⁻¹ (1.3546) = 53.56°

We know that,

x + y = 90°, since the other angle is 90°.

x = 90 - 53.56° = 36.44°

y - x = 53.56° - 36.44° = 17.12° ≈ 17.2°

Hence the value of y - x is 17.2°.

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The value of y in the isosceles triangle is AC = 6 cm

What Is an Isosceles Triangle?

A triangle with two sides of equal length is an isosceles triangle. The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.

In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

The three types of Isosceles Triangles are :

Isosceles acute triangle

Isosceles right triangle

Isosceles obtuse triangle

Given data ,

Let the triangle be represented as ABC

Now , the angle ∠ABC = 25°

The angle ∠ACB = 25°

So , the 2 angles of a triangle is 25° so , the third angle is 130°

So , the triangle is an isosceles triangle

And , the two sides of the triangle is AB = AC

The measure of side AB = 6 cm

The measure of side AC = measure of side AB

Therefore , the measure of side AC = 6cm

Therefore , the value of AC is 6 cm

Hence , the measure of side AC of triangle is 6 cm

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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

What is the area of the trapezium?

The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.

To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:

A = h(c + d)/2

2A = h(c + d)

2A/h = c + d

c + d = 2A/h

Then, we can subtract d from both sides of the equation to solve for c:

c = (2A/h) - d

Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

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The expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

What is the area of the trapezium?

The formula for the area of a trapezium is A = h(c + d)/2, where h is the height of the trapezium, c is the length of one of the bases, and d is the length of the other base.

To find an expression for c in terms of A, h, and d, we can start by rearranging the formula to solve for c:

A = h(c + d)/2

2A = h(c + d)

2A/h = c + d

c + d = 2A/h

Then, we can subtract d from both sides of the equation to solve for c:

c = (2A/h) - d

Hence, the expression that represents c in terms of A, h, and d would be c = (2A/h) - d.

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Harvey's mistake in this scenario is that he put the pigs on a bed of straw that could infect their belly buttons. Additionally, he did not ensure that they consume colostrum in the first hours of life.

When we have a pregnant sow and we have to manage the postpartum procedure, we must make sure of different necessary procedures so that the piglets are well and their lives are not at risk in the following hours or days.

Among the procedures necessary for the piglets to be well are breathing, feeding and hygiene. In detail, once the piglet is extracted from its mother, we must make sure that it is breathing correctly. Secondly, we must clean it properly and make sure that its navel is completely clean to avoid infections. Finally we must give colostrum as food within the following hours after birth.

Additionally, we must place it in a clean place where it is not exposed to possible bacteria or infections, so the option of putting it on a bed of straw would be ruled out due to hygiene for the pig.

According to the above, Harvey's mistake was that he did not clean the piglets when they were born, did not give them colostrum, and put them on straw. Actually, he made three mistakes.

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If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.  

[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031

X = 89 represent the mean of seventh-grade girls in Midwest school district

s = 15 represent the standard deviation for the sample  

n = 31 sample size  

μ = 100 represent the value that we want to test  

'a' represent the significance level for the hypothesis test.  

't' would represent the statistic (variable of interest)  

[tex]p_{v}[/tex] represent the p value for the test (variable of interest)

State the null and alternative hypotheses,

We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:  

Null hypothesis: μ = 100

Alternative hypothesis: μ ≠ 100

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t = (X-μ) / ([tex]\frac{s}{\sqrt{n} }[/tex] )                (Equation-1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

t = [tex]\frac{89-100}{\frac{15}{\sqrt{31} } }[/tex]

t = -4.08

Calculate the P-value  

First we need to calculate the degrees of freedom given by:  

[tex]df = n-1[/tex]

[tex]df = 31 -1[/tex]

[tex]df = 30[/tex]

Since is a two tailed test the p value would be:  

[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 )

[tex]p_{v}[/tex] = 0.00031

Therefore,

If we compare the p value and a significance level given for example [tex]\alpha = 0.05[/tex] we see that [tex]p_{v} < \alpha[/tex] that the standard deviation of [tex]iq[/tex] scores in this population is known to be 15 the actual true mean is significantly different from 100.  

[tex]p_{v}[/tex] = 2 * p ( [tex]t_{30}[/tex] < -4.08 ) = 0.00031

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The total number of hours Mayerlin worked is 21 and (g + n) respectively.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division. When two whole numbers are added, the sum or total of those values is obtained.

Given that, Mayerlin gets paid $20 per hour to work at the grocery store and $19 per hour to work at the nursery.

Since Mayerlin works 11 hours at the grocery store and 10 hours at the nursery, the total number of hours she worked is:

11 + 10

= 21

Now, if, Mayerline works g hours at the grocery store and n hours at the nursery, the total number of hours she worked is:

g + n

Hence, the total number of hours Mayerlin worked is 21 and (g + n) respectively.

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The number of adult tickets  which were sold that day as calculated from the given data  is 29.

First, we must assign variables to what our "unknowns" are. Assume there are "A" number of adult tickets and "C" number of child tickets. To solve this problem, we will use two equations.

To begin, each adult ticket costs $8.90, and each kid ticket costs $5.30. When the sales totals for both types of tickets are added together, the total sale is $928.

This is represented by the following equation,

$8.90A + $5.30C = $928

Next, we know that multiplying the number of child tickets by three equals the number of adult tickets:

3 * C = A

Now we can answer our first problem by substituting 3 * C for A.

8.9 (3C) + 5.3C = 928

26.7C + 5.3C = 928

32C = 928

C = 29

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The calculation that will give the closest estimate of the sales of soft drinks and hot dogs is 360 * 2 + 220  * 2

From the question, we have the following parameters that can be used in our computation:

Time = one week

Number of cans = 362

Unit price of soft drink = $1.75

Number of hot dogs = 221

Unit price of hot dogs = $2.35

The calculation that will give the closest estimate is represented as

Estimate = Number of cans * Unit price of soft drink + Number of hot dogs * Unit price of hot dogs

Substitute the known values in the above equation, so, we have the following representation

Estimate = 362 * 1.75 + 221  *2.35

Approximate

Estimate = 360 * 2 + 220  * 2

Hence, the expression is 360 * 2 + 220  * 2

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Answer:

1 -  $15

2-  $30

3 - $45

4 - $60

Step-by-step explanation:

$15/hour

1 -  $15 =1*15

2-  $30 =2*15

3 - $45 =3*15

4 - $60=4*15

Answer: 0

Step-by-step explanation: The reasoning behind this is that both functions will never intersect which would mean there are no solutions for the system equation.

The null and different hypotheses for hypothesis test are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

Null hypotheses

Given that:

sample size (η)= 196

sample proposition (p^) = 114/196

Let p denote the population proportion of people who use a loyalty card.

The percentage of shoppers use loyalty cards in their stores has remittent from sixty-three in 2014. [That is, whether or not the proportion has shifted from zero to 1] .63]

Hence, the null and alternative hypothesis are

[tex]H_{0}[/tex] : P =0.63 against [tex]H_{1}[/tex] p [tex]\neq[/tex] 0.63

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The rocket's height after 3 seconds is 6.3 sec.

The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.

A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.

To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:

h = -5*t2 + 30*t + 10

h = -5(2)2 + 30(2) + 10

h = -5(4) + 30(2) + 10

h = -20 + 60 +10

h = 50 m

The height of the rocket 2 seconds after launching it is 50 meters.

To find the x-coordinate of the vertex of a parabola, we use the formula:

[tex]xvertex = -b / 2a[/tex]

t - 3 = ± √(11)

t = 3 ± √(11)

t = 3 ± 3.3

Solving for t, we get two solutions:

t = 3 - 3.3

t = -0.3 sec

and

t = 3 + 3.3

t = 6.3 sec

Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.

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The equation is log_2 (3x - 5) = 9 There are no real solutions to this equation because the logarithm of a negative number is undefined. The left side of the equation would require the argument to be negative, thus making the equation impossible to solve.

This equation cannot be solved because the logarithm of a negative number is undefined. The left side of the equation is of the form log_2 (N), where N is some real number.For the equation to have any real solutions, N needs to be greater than 0. However, in this equation, N is equal to 3x - 5, which can be negative for certain values of x. This means that there is no real number x that can be substituted into the equation to make it true, since the logarithm of a negative number is not defined. Therefore, this equation has no real solutions.

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The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

1. To find out how much prices for filling a cavity vary, an insurance company randomly selects 10 dental practices in California and asks for the cash (non-insurance) price for this procedure.

2. The insurance company then computes the interquartile range of the prices for each practice.

3. The interquartile range of $74 indicates the amount of price variation for filling a cavity at the 10 randomly selected dental practices in California.

The prices for filling a cavity can vary greatly depending on the dental practice. The interquartile range of $74 for 10 randomly selected dental practices in California is an indication of the amount of price variation for this procedure.

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Answer: 120 miles

Step-by-step explanation:

If a car goes 60 miles per hour then in two hours (60×2) it will go 120

The fraction of the pie left that each friend will receive is; 3/8 of the pie

Dividing two fractions is simply the same as multiplying the first fraction by the reciprocal of the second fraction.

The first step in trying to divide fractions is to find the reciprocal of the second fraction. The second step is to multiply the two numerators. Thereafter, multiply the two denominators.

For example, 3/8 divided by 3/4 would be;

3/8 divided by 3/4 = 3/8 * 4/3

Now, we are told that cedric has 3/4 of a pie left.

Now, he wants to share equally among two of his friends, it means that;

Quantity received by each friend = 3/4 ÷ 2 = 3/4 * 1/2 = 3/8

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Complete question is;

Cedric has 3/4 of a pie left. He wants to divide it between his 2 friends. How much of that pie will each friend get?

The less value including 13% VAT in Rs. 3200 than Rs. 3820 is 340 rupees.

A percentage is a ratio or number that may be expressed as a fraction of 100. Additionally, it is denoted by the sign "%."

Here, we have VAT.

A flat charge called value-added tax (VAT) is imposed on a purchase. It resembles a sales tax in some ways, with the exception that with a sales tax, the consumer pays the entire amount due to the government at the moment of sale. With a VAT, several participants to a transaction each pay a piece of the tax amount.

Value on Rs. 3200 with 13% VAT

= 3200 + 30% of 3200

= 3200 + 960

= 4160 rupees

Now, the less value,

= 4160 - 3820

= 340 rupees.

Therefore, the less value is 340 rupees.

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Answer: None of these

Step-by-step explanation:

A. If [tex]x=-32[/tex], then [tex]y=745[/tex], not [tex]10[/tex].

B. If [tex]x=0[/tex], then [tex]y=9[/tex], not [tex]10[/tex].

C. If [tex]x=-1[/tex], then [tex]y=32[/tex], not [tex]1023[/tex].

D. If [tex]x=23[/tex], then [tex]y=-520[/tex], not [tex]10[/tex].

Answer:

x=-3/7

Step-by-step explanation:

Answer:

a. [tex]\frac{x+2}{x+6}[/tex]

Step-by-step explanation:

[tex]\frac{x^2 + 5x+6}{x^2 +9x+18}=\frac{(x+2)(x+3)}{(x+3)(x+6)}=\frac{x+2}{x+6}[/tex]