what is the z score for a soda that costs $1.15 if the population of soda prices has a normal distribution with a mean of $1.00 and a standard deviation of $0.25?

Answer: 5

Step-by-step explanation:

  8-2b=-2

8-2b-8=-2-8

    -2b=-10

-2b/-2=-10/-2

       b=5

Answer:

9x³-9x²+2x

Step-by-step explanation:

Let the expression be given as

(2-3x)(x-3x²)

Expand

= 2(x)-2(3x²)-3x(x)-3x(-3x²)

= 2x - 6x² -3x²+9x³

Rearrange

= 9x³-6x²-3x²+2x

= 9x³-9x²+2x

Hence the simplified form of the expression is 9x³-9x²+2x

The statement (a) ,(b) is disproven because the algorithm with the 12-cent coin does not always produce change using the fewest coins possible for all coin values.

(a) To prove or disprove the statement, we can compare the two algorithms in terms of the number of coins required to produce change. Let's consider an example where the required change is 24 cents. Without the 12-cent coin: The algorithm would likely use 2 dimes and 4 pennies, which makes a total of 6 coins. With the 12-cent coin: Using the 12-cent coin, we can represent 24 cents as 2 dimes and 4 cents. Adding a 12-cent coin to the mix, we would have 1 dime, 1 12-cent coin, and 4 pennies, which also makes a total of 6 coins. In this example, both algorithms result in the same number of coins required for the change of 24 cents. Therefore, the statement (a) is disproven because the algorithm with the 12-cent coin does not produce change using fewer coins compared to the algorithm without the 12-cent coin in this case.

(b) To prove or disprove the statement, we need to show an example where the algorithm with the 12-cent coin does not produce change using the fewest coins possible. Let's consider the example where the required change is 17 cents. Without the 12-cent coin: The algorithm would likely use 1 dime, 1 nickel, and 2 pennies, which makes a total of 4 coins. With the 12-cent coin: Using the 12-cent coin, we can represent 17 cents as 1 dime, 1 nickel, 1 12-cent coin, and 2 pennies, which makes a total of 5 coins. In this example, the algorithm without the 12-cent coin produces change using fewer coins (4 coins) compared to the algorithm with the 12-cent coin (5 coins). Therefore, the statement (b) is disproven because the algorithm with the 12-cent coin does not always produce change using the fewest coins possible for all coin values.

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An equation system's solution is a collection of values for the variable that concurrently fulfill each equation.

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The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution. In order to solve an equation system, all sets of variable values that could possibly exist must be found. The second equation, however, is initially without a solution (5, 4).

The set of values for the variable that simultaneously satisfy all of the equations in an equation system is called the solution.

If both variables are eliminated and you are left with a true statement, there are an infinite number of ordered pairs that satisfy both equations. In reality, the equations' lines are the same.

Let cost token be x and golf games be y, i.e.

16x + 3y = 30

22x + 5y = 43

Lets Solve by using Elimination method both the expression in equal terms

 80x + 15y = 150

- 66x + 15y = 129

14x = 21

x = 21/14

x = 1.5

Then, for y

16(1.5) + 3y = 30

y = 2

Thus, The cost of a battling token is $1.5 and the cost of a miniature golf game is $2.

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Answer:

=36

Step-by-step explanation:

2b is the same as 2×5

so 2b=10

put it back into the brackets

6(10-4)

6×10=60

6×-4=-24

=60-24

=36

Answer:

y = -3/2x + 6

Step-by-step explanation:

Parallel lines have the same slope so slope is -3/2

Using (4,0)

y = mx + b

0 = -3/2(4) + b

0 = -6 + b

b = 6

so y = -3/2x + 6

Answer:

34

Step-by-step explanation:

Substitute the values.

s = 3 and t = -2

8s-5t

8 (3) - 5(-2)

( 8 x 3 ) - ( 5 x -2 )

24 + 10 [ - x - = + ]

= 34

Answer:

This is because the object on the 1st scale weighs (more) than the object on second scale, each pound of error results in a (lesser) percent error. The first scale was (10) pounds off the second scale,was (3) pounds off, so 1st scale was (10)% off 2nd scale was (12)% off.

Answer:

Because the object on Scale 1 weighs more than the object on Scale 2, each pound of error results in a lesser percent error. Scale 1 was 10 pounds off and Scale 2 was 3 pounds off, so Scale 1 was 10% off and Scale 2 was 12% off.

Step-by-step explanation:

Got it right on TTM so yeah! :)

Answer:

Slope = rise/run

Rise = 0

So zero divided by any run is 0.

B

Answer:

B

Step-by-step explanation:

slope or gradient = rise/run

rise=0 0/anything= 0

Line B has no graidient so it is considered as 0.

Answer:

the correct answer is D. 145.8

Answer:

100%

Step-by-step explanation:

they all had allergic reactions

The solutions to the equation √(2)x + 13 - 5 = x are:
x = -16 or x = -8.

A quadratic equation is a polynomial equation of the second degree, which means the highest power of the variable (usually represented by "x") is 2. It can be written in the general form: ax^2 + bx + c = 0

where "a," "b," and "c" are constants, and "a" is not equal to 0. The constants "a," "b," and "c" determine the specific coefficients and values of the quadratic equation.

To solve the equation sqrt(2)x + 13 - 5 = x, we need to isolate the variable x on one side of the equation.
First, we can simplify the left side by combining the constant terms:
√(2)x + 8 = x
Next, we can eliminate the square root by squaring both sides of the equation:
(√(2)x + 8)^2 = x^2
Expanding the left side using FOIL, we get:
2x^2 + 32x + 64 = x^2
Subtracting x^2 from both sides, we get:
x^2 + 32x + 64 = 0
Now we have a quadratic equation that we can solve using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 1, b = 32, and c = 64. Substituting these values into the formula, we get:
x = (-32 ± √(32^2 - 4(1)(64))) / 2(1)
Simplifying the square root, we get:
x = (-32 ± √(576)) / 2
x = (-32 ± 24) / 2
x = -16 or x = -8.

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Considering the vertex of a quadratic equation, the greatest rectangular area that the farmer can enclose with 100 m is of 625 m².

A quadratic equation is modeled by the rule presented as follows:

y = ax^2 + bx + c

The vertex has these following coordinates.

\((x_v, y_v)\)

In which:

Considering the coefficient a, we have that the vertex can represent either a maximum or a minimum point in the function, as follows::

In this problem, the coefficients of the quadratic equation representing the area are given as follows:

a = -1, b = 50.

The greatest rectangular area that the farmer can enclose with 100 m is the y-coordinate of the vertex of the quadratic equation, hence:

\(y_v = -\frac{50^2 - 4(-1)(0)}{4(-1)} = 625\)

The area is of 625 m².

The quadratic equation for the area is:

A(w) = -w² + 50w

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Answer:

625

explanation:

trust

An ogive is used to plot cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class when displaying quantitative data. Option B.

An ogive is a graph that represents a cumulative distribution function (CDF) of a frequency distribution. It shows the cumulative relative frequency or cumulative frequency of each class plotted against the upper limit of the corresponding class. In other words, an ogive can be used to represent data through graphs by plotting the upper limit of each class interval on the x-axis and the cumulative frequency or cumulative relative frequency on the y-axis.

An ogive is used to display the distribution of quantitative data, such as weight, height, or time. It is also useful when analyzing data that is not easily represented by a histogram or a frequency polygon, and when we want to determine the percentile or median of a given set of data. Based on the information given above, option B: "Cumulative frequency or cumulative relative frequency of each class against the upper limit of the corresponding class" is the correct answer.

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Answer:b,c

Step-by-step explanation:i got it correct

Answer:

2.3333333333333333333333333333333 sec

The area of the region d is 1 square unit.

Given that the region d is bounded by y=x^3, y=x^3+1.The area of the region d can be calculated using a double integral. We know that the area is given by A= ∬d dA.

Here, dA is the differential area element, which can be represented as dA=dxdy.

We can write the above equation asA= ∫∫d dxdy. From the given bounds, we know that the limits of integration for y are x^3 to x^3+1, and for x, the limits are from 0 to 1.

\(Thus,A= ∫0^1∫x³^(x³+1) dxdy.\)

Now, we can perform the integration with respect to x and then with respect to y.

\(A= ∫0^1 [(x³+1)-(x³)] dy= ∫0^1 (1) dy= 1\)

The required area is 1 square unit.

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The value of c ≈ 142.65 is the number that approximates 143.7 using the linear approximation method.

We need to find a number c that approximates 143.7 using the linear approximation method. The appropriate function for linear approximation is given by f(x) = xd, where d is the slope of the tangent line at x = 140.

To find the slope d, we need to take the derivative of f(x) with respect to x:

f'(x) = d

Substituting x = 140 and using the given value f(140) = 140d = 196, we get:

140d = 196

d = 196/140

Now we can use the linear approximation formula to find c:

f(c) ≈ f(140) + f'(140)(c - 140)

143.7 ≈ 196 + (196/140)(c - 140)

3.7 ≈ (49/35)(c - 140)

c - 140 ≈ (35/49)(3.7)

c ≈ 140 + (35/49)(3.7)

c ≈ 140 + 2.65

c ≈ 142.65

Therefore, c ≈ 142.65 is the number that approximates 143.7 using the linear approximation method.

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Answer:

what how

Step-by-step explanation:

Answer:

42 km apart

Step-by-step explanation:

1 cm : 7km scale

6 cm apart on map means 6*7km.

6*7 = 42km apart.

Answer:

1. x=6

2. x = -4

3. x³ = 0

Step-by-step explanation:

Step 1: Equation at the end of step 1

((x⁵) - ( 2 · (x⁴)))-(2³· 3x³) = 0

Step 2:

Equation at the end of step 2:

((x⁵)-2x⁴)-(2³ · 3x³) = 0

Step 3: X

Step 4: Pulling out like terms

Pull out like factors :

x⁵ - 2x⁴ -24x³ = x³· (x² - 2x -24)

Trying to factor by splitting the middle term

Factoring  x² -2x - 24

The first term is, x² ts coefficient is  1 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -24  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24  

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -2 .

     -24    +    1    =    -23  

     -12    +    2    =    -10  

     -8    +    3    =    -5  

     -6    +    4    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  4

 x2 - 6x + 4x - 24

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

             Add up the last 2 terms, pulling out common factors :

                   4 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-6)

            Which is the desired factorization

Equation at the end of step

4

:

 x3 • (x + 4) • (x - 6)  = 0  

STEP

5

:

Theory - Roots of a product

5.1    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

5.2      Solve  :    x3 = 0  

 Solution is  x3 = 0

Solving a Single Variable Equation:

5.3      Solve  :    x+4 = 0  

Subtract  4  from both sides of the equation :  

                     x = -4

Solving a Single Variable Equation:

5.4      Solve  :    x-6 = 0  

Add  6  to both sides of the equation :  

                     x = 6

Supplement : Solving Quadratic Equation Directly

Solving    x2-2x-24  = 0   directly  

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

Parabola, Finding the Vertex:

6.1      Find the Vertex of   y = x2-2x-24

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 1 , is positive (greater than zero).  

Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.  

Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.  

For any parabola,Ax2+Bx+C,the  x -coordinate of the vertex is given by  -B/(2A) . In our case the  x  coordinate is   1.0000  

Plugging into the parabola formula   1.0000  for  x  we can calculate the  y -coordinate :  

 y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 24.0

or   y = -25.000

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = x2-2x-24

Axis of Symmetry (dashed)  {x}={ 1.00}  

Vertex at  {x,y} = { 1.00,-25.00}  

x -Intercepts (Roots) :

Root 1 at  {x,y} = {-4.00, 0.00}  

Root 2 at  {x,y} = { 6.00, 0.00}  

Solve Quadratic Equation by Completing The Square

6.2     Solving   x2-2x-24 = 0 by Completing The Square .

Add  24  to both side of the equation :

  x2-2x = 24

Now the clever bit: Take the coefficient of  x , which is  2 , divide by two, giving  1 , and finally square it giving  1  

Add  1  to both sides of the equation :

 On the right hand side we have :

  24  +  1    or,  (24/1)+(1/1)  

 The common denominator of the two fractions is  1   Adding  (24/1)+(1/1)  gives  25/1  

 So adding to both sides we finally get :

  x2-2x+1 = 25

Adding  1  has completed the left hand side into a perfect square :

  x2-2x+1  =

  (x-1) • (x-1)  =

 (x-1)2

Things which are equal to the same thing are also equal to one another. Since

  x2-2x+1 = 25 and

  x2-2x+1 = (x-1)2

then, according to the law of transitivity,

  (x-1)2 = 25

We'll refer to this Equation as  Eq. #6.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

  (x-1)2   is

  (x-1)2/2 =

 (x-1)1 =

  x-1

Now, applying the Square Root Principle to  Eq. #6.2.1  we get:

  x-1 = √ 25

Add  1  to both sides to obtain:

  x = 1 + √ 25

Three solutions were found :

x = 6

x = -4

x3 = 0

Solution:

The volume of the cases in 2001 is given below as

The percentage increase from 2000 is given below as

The exponential function is given below as

By substituting the values, we will have

Hence,

The final answer is YES, THE EXPONENTIAL MODEL FUNCTION IS APPROPRIATE

Therefore,

The exponential model after y years will be

Answer:

Step-by-step explanation:

The function y = -2 is a constant function. It means that the output of the function is always equal to -2, regardless of the input value.

Here is a function table that shows the input and output values for y = -2:

x y

1 -2

2 -2

3 -2

4 -2

5 -2

As you can see, for any value of x, the output is always -2, since y = -2 is a constant function

Answer:

40%

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

Answer:

x=−2/5

y−2

Step-by-step explanation:

5x+2y=−10

Step 1: Add -2y to both sides.

5x+2y+−2y=−10+−2y

5x=−2y−10

Step 2: Divide both sides by 5.

5x

5

=

−2y−10

5

x=

−2

5

y−2

Answer: x- intercept: (-2, 0)   y- intercept:  (0,_5)

Step-by-step explanation:

The equation which can be used to represent the relationship is c = k × v

The constant of proportionality of this relationship is 3.5

v = represent videos streamed

c = represent cost

constant of proportionality = k

c = $24.50

v = 7

c = k × v

24.50 = k × 7

24.50 = 7k

divide both sides by 7

k = 3.5

In conclusion, the equation which represents the situation is c = k × v where k = 3.5.

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The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

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\(\frac{1187.25}{21.25}\) is equal to the maximum number of players the team can bring to the tournament, that is, \(x\).

In this context, we are to represent tape diagrams that could represent the situation where members of a baseball team raised $1187.25 to go to a tournament.

They rented a bus for $783.50 and budgeted $21.25 per player for meals. The tape diagram should be one that represents the context if x represents the number players the team can bring to the tournament.

Tape diagrams, also known as bar models, are pictorial representations that are helpful in solving word problems. They represent numerical relationships between quantities using bars or boxes.

Tape diagrams are used to solve a wide range of word problems, including problems related to ratios, fractions, and percents.

According to the context given, a tape diagram that could represent the situation where x represents the number of players the team can bring to the tournament can be illustrated as follows:
Hence, the tape diagram above represents the given situation if x represents the number of players the team can bring to the tournament.

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Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation: