the density of zinc is 7.13 g/cm3. calculate the probability that a density measurement of the post-1982 pennies made using the caliper method is within 5% of the density of zinc. use the caliper data for the entire lab session to perform your calculation, and assume that the data fits a normal distribution.

1. To get System BBB from System AAA, we can divide both sides of the first equation in System AAA by -3:

-3x + 12y = 15

-3x/ -3 + 12y/ -3 = 15/ -3

x + 4y = -5

So System BBB is obtained by dividing both sides of the first equation in System AAA by -3.

2. Are Systems AAA and BBB equivalent?

Yes, Systems AAA and BBB are equivalent. This means that they have the same solution set, despite having different coefficients in their equations. Equivalent systems of linear equations are systems that have the same solution set, regardless of the coefficients of the equations.

The solution of the system of equation y - 10 = 2x and 1/2 y = x + 5 is

The simultaneous equation is solved by substitution method as follows

y - 10 = 2x and

1/2 y = x + 5

Isolate y in the first equation to get

y = 2x + 10

substitute y in 1/2 y = x + 5

1/2 (2x + 10) = x + 5

x + 5 = x + 5

x = 0

substitute x = 0 into y = 2x + 10

y = 2(0) + 10

y = 10

hence the solution is (0, 10)

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Answer:

256 text

Step-by-step explanation:

Let's call the number of text messages Sarah sends in a month as "x".
So, the total cost of the text messages is $0.25 * x.

The total cost of the phone service and text messages is $35 + $0.25 * x = $99.

So, $35 + $0.25 * x = $99.

Subtracting $35 from both sides, we have:$0.25 * x = $99 - $35 = $64

Dividing both sides by $0.25, we have:x = 256

So, Sarah sent 256 text messages in one month.

The height of the cylinder whose volume has been given above would be = 50cm

The volume of a cylinder can be calculated with the formula = πr²h

Where Volume = 157cm³

radius = 1 cm

height = X cm

π = 3.14

That is, 157 = 3.14 × 1² × X

make X the subject of formula;

X = 157 /3.14

X = 50cm

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The value for  x-5(x - 1)=x- (2x-3) which gives x = 2/3.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

x-5(x - 1)=x- (2x-3)

Now, solving the Equation for x we get

x -5x + 5 = x - 2x + 3

-4x + 5 = -x + 3

-4x + x = 3 -5

-3x = -2

x= 2/3

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The independent variable of the question is c:the number of cars Lamar and Allie wash while the dependent variable is s: the number of hockey sticks Lamar and Allie will be able to purchase

The independent variable is defined as the variable that you change and control in your experiment. The dependent variable is defined as the variable that you don't have control over and is affected by the way that the independent variable reacts.

The parameters given are;

s = the number of hockey sticks Lamar and Allie will be able to purchase

c = the number of cars Lamar and Allie wash

Now, since the number of cars they wash determines how much money they will get to buy a new car, then we can say that c is the independent variable while s is the dependent variable as it depends on c to be actualized.

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Answer:

(2.571, 10.143)

Step-by-step explanation:

Answer:

(4, 3) ordered pair

Step-by-step explanation:

Rearranging the two equations making y the subject of the equations:

[tex]y = -5x + 23[/tex] —-(equation i)

[tex]y = 2x - 5[/tex] ——-(equation ii)

Equating equation i to equation ii and solve for x. Bring all the like terms together:

[tex]2x - 5 = -5x + 23[/tex]

[tex]= 2x + 5x = 23 + 5[/tex]

[tex]= 7x = 28[/tex]

x = [tex]\frac{28}{7}[/tex]

∴ x = 4

Substitute the value of x in any of the two equation to solve for y:[tex]y = 2(4) - 5[/tex]

y = [tex]8 - 5[/tex]

y = 3

Together these x and y values form an ordered pair, which is also the point of intersection for these two equations: [tex](4, 3)[/tex]

The sketch of the front elevation and the side elevation of the prism are added as an attachment

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

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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The probability that it is likely that a randomly selected cookie from the batch will be a chocolate chip cookie.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

If P(chocolate chip) = 0.50, it means that the probability of randomly selecting a chocolate chip cookie from the batch is 0.50 or 50%.

Interpreting this probability, we can say that it is likely that a randomly selected cookie from the batch will be a chocolate chip cookie since the probability is relatively high.

Therefore, the correct answer would be an option (B) Likely.

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In order to determine whether a critical point of a loss function is a global minimum, it is necessary to consider the second derivative of the function.

If the second derivative is positive at the critical point, then we can say with certainty that the critical point is a local minimum. However, this does not necessarily mean that it is a function function. This is because there may be other local minima at points which the second derivative is negative, and in this case, the critical point must be compared to these points to determine if it is indeed the global minimum.

In order to assess whether a local minimum is a global minimum, we must first identify any other local minima. This can be done by locating the points at which the first derivative of the function is equal to zero and then evaluating the second derivative of the function at these points. If the second derivative is negative at any of the points, then we have identified a local minimum. Then, we can compare the value of the loss function at the points function as local minima to the value of the loss function at the critical point. If the value of the loss function at the critical point is lower than the value of the loss function at the other local minima, then the critical point is the global minimum. If the values are equal, then the critical point is a global minimum if and only if it is the only local minimum.Overall, identifying whether a critical point of a loss function is a global minimum requires both sufficiency and necessity. It is necessary to evaluate the second derivative of the function at the critical point in order to determine whether it is a local minimum, and it is also necessary to identify any other local minima and compare the value of the loss function at the critical point to the value of the function at the other local minima in order to determine whether the critical point is the global minimum.

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Jerome saves 337.5$ on the computer.

Jerome buys the computer for 1912.5$.

The total cost of the computer is 2056$ including sales tax.

The total price of the computer not on sale is 2418.75$.

The discount is 15% of the original price:

0.15 x $2250 = $337.50.

If the sales tax is 7.5%,

The price of the computer after the discount is $2250 - $337.50 = $1912.50.

The amount of tax on the computer is 7.5% of $1912.50:

0.075 x $1912.50 = $143.44.

The total cost for the computer is the discounted price plus the tax: $1912.50 + $143.44 = $2055.94.

The total price for the computer not on sale would be the original price plus the tax:

$2250 + $169.13 = $2419.13 (where tax is 7.5% of $2250).

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Answer:

x = 2 and y = -4

Step-by-step explanation:

To solve using substitution, we define one unknown variable in terms of another and sub this into a second equation with both.

We are told y=2x-8 and -3x+4y=-22, so let's sub '2x-8' in for y in -3x+4y=-22:

-3x+4y=-22

-3x+4(2x-8)=-22

-3x+8x-32=-22

5x=10

x=2

If x=2 and y=2x-8, let's sub 2 in for x to find y:

y=2x-8

y=2(2)-8=4-8=-4

The equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z. The solution has been obtained by using angles and line.

What are angles and line?

Straight lines with little depth or width are present. There are many different types of lines, including perpendicular, intersecting, transversal, etc. A figure called an angle is one in which two rays originate from the same point.

We are given that 2 lines intersect to form 4 angles which are 65°, x°, y°, z°.

1. x° + 65° = 180°

We know that angles on a straight line form a linear pair i.e. their sum is 180°. So, this statement is true.

2. x° = z°

We know that vertically opposite angles are equal. So, x° will be equal to z°. Thus, this statement is true.

3. y° = 65°

We know that vertically opposite angles are equal. So, y will be equal to 65°. Thus, this statement is true.

4. x° = 65°

This statement is false because these are the angles on a straight line which must add up to 180°.

5. x° + y° + z° = 115°

We know that angles in a circle add upto 360°. We know one angle as 65°. So, the remaining angles should add upto 295°. Thus, the statement is false.

Hence, the equations x° + 65° = 180°, x° = z° and y° = 65° are true for the values of x, y and z.

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Question: Which equations are true for the values of x, y, and z? Select three options.

2 lines intersect to form 4 angles as shown in the figure. Clockwise, from top, the angles are: 65 degrees, x, y, z.

x degrees + 65 degrees = 180 degrees

x degrees = z degrees

y degrees = 65 degrees

x degrees = 65 degrees

x degrees + y degrees + z degrees = 115 degrees

The coordinates of N are (-38.4, -18.4)

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

M = (-26, -14)

P = (6, -2).

m : n = 2 : 3 i.e. 2/5

The coordinate is then calculated as

N = 1/(m + n) * (mx2 + nx1, my2 + ny1)

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

N = 2/5 * (2 * 6 + 3 * -36, 2 * -2 + 3 * -14)

Evaluate

N = (-38.4, -18.4)

Hence, the coordinate is (-38.4, -18.4)

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Complete question

The point N lies on the segment MP.

Find the coordinates of N so that MN is of MP. 2/5

M- (-26, 14) P- (6,-2)

N(?,?)

Answer:

2x^2 - 12*x/2= Area For Shaded Region

Step-by-step explanation:

This works because you find tha area of both and subtract the shaded area by the unshaded area

Answer: Expression for the area of shades region of the figure = 2[tex]x^{2}[/tex] - 6x

Step-by-step explanation: Area of shaded region = Area of big rectangle - Area of small rectangle

Area of rectangle = length.breadth

Area of big rectangle = 2x.x                                  { . means multiply}

                                     = 2[tex]x^{2}[/tex]

Area of small rectangle = 12.(x/2)

                                         =6x

∴ Area of shaded region = 2[tex]x^{2}[/tex] - 6x

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Answer: 10 times

Step-by-step explanation:

Answer:

x[tex]\leq[/tex]52

Step-by-step explanation:

x[tex]\leq[/tex]52

The estimate for the number of the paintings that are over 70 years old is given as follows:

68 paintings.

The histogram shows the number of observations that appear in each range of the data-set.

24 of the paintings in the gallery are over 90 years old, hence the height of each small square is of:

24/(3 x 4) = 2 units.

Then the estimate of those over 70 years old is given as follows:

Then the total amount is of:

2 x 22 + 24 = 68.

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Answer:

25%

Step-by-step explanation:

Let Dawn’s monthly allowance be 5x. Let Evelyn’s monthly allowance then be 8x.

Percentage increase by 20% is the same as multiplying a number by 1.2

To find the percentage decrease of Evelyn’s monthly allowance, we can equate their allowances after the change of their initial allowance.

1.2 * 5x = k/100 * 8x

k represents the percentage

6x = 8xk/100

Cancel the x’s from both sides

6 = 8k/100

600 = 8k

k = 75

Therefore since 75% of Evelyn’s monthly allowance is equal to Dawn’s increased monthly allowance, this means Evelyn’s monthly allowance was decreased by 25%.

When bisecting a segment using a compass, Sasha's next step would be to swing an arc that intersects the segment. Correct option is B.

To bisect a segment, Sasha needs to find the midpoint of the segment. The compass can help her achieve this by creating two arcs with the same radius from each endpoint of the segment. The intersection of these arcs will be the midpoint of the segment.

Sasha's first step is to place the compass on one endpoint of the segment and open it to a width larger than the length of the segment. Then, she places the compass on the other endpoint and draws an arc that intersects the first arc.

The next step is to swing an arc with the same radius from the other endpoint of the segment, again intersecting the first arc. The intersection of these two arcs will give the midpoint of the segment, which can be marked with a straightedge.

Therefore, Sasha's next step in bisecting a segment using a compass is to swing an arc that intersects the segment.

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Answer:

(8.666666667, -15.66666667)

or in fraction form

(26/3, -47/3)

Step-by-step explanation:

First we want to get both of the equations into y-intercept form

x + y = -7

subtract x from both sides

y = -x - 7

and the other

4x + y = 19

subtract 4x from both sides

y = -4x +19

now we can graph them

(See attached screenshot)

The number of hours taken to have the same number of pages completed is 5 hours.

The solution to the system of equations is (5, 50).

In order to write a system of linear equations that could be used to model the situation and determine the number of hours it would take to complete the workbook, we would assign variables to the number of hours and the number of pages respectively as follows:

Next, we would translate the word problem into system of linear equations as follows:

Isaiah: y = x + 45

Brenna: y = 9x + 5

When the same number of pages are completed, the number of hours taken can be calculated as follows;

x + 45 = 9x + 5

9x - x = 45 - 5

8x = 40

x = 5 hours.

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1. In his newspaper, Peter Zenger published articles criticizing the Governor's use of arbitrary power

2. Because it was against the law to criticize the king or his appointees, the Attorney General accused Peter Zenger of committing" libel.

3. Hamilton believed Zenger was not guilty of this charge because in Zenger's newspaper articles the "truth is told

4. Hamilton felt that more than just Peter Zenger was on trial. He felt that the larger concept of American" liberty was at stake.

Hamilton and Morris agreed that the trial of Peter Zenger was important for American freedom and the defense of liberty.

As for the question about television and newspaper reporters, it is a matter of opinion. Some people believe that the freedom of the press is an important part of democracy, and that reporters should be able to criticize anyone in power, including the president. Others believe that criticism of the president should be limited to protect the dignity and stability of the office. In either case, it is important to strike a balance between free speech and responsible journalism.

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The height of the cell phone tower in feet will be 135 feet high.

The utilization of two or more additional numbers that compares is known as the ratio.

The cell tower that casts a shadow is 100 feet long.

Lia casts shadows 3 feet and 4 inches long.

If Lia is 4 feet 6 inches tall.

Let 'h' be the height of the tower. Then the height of the tower is given as,

h / 100 = (4 + 6/12) / (3 + 4/12)

h / 100 = 4.5 / 3.33

h / 100 = 1.35

h = 135 feet

The height of the cell phone tower in feet will be 135 feet high.

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Mei concluded that

We are 90% confident that the true proportion of times the die would land on the number 4 is between 0.398 and 0.562. Since this includes 0.5, the die appears to be fair.

It is based on a statistical analysis of the data collected by Mei.

The proportion of times the die landed on the number 4 is calculated as 48/100 = 0.48.

Using a statistical method called a confidence interval, we can estimate the range of values that the true proportion of times the die would land on the number 4 is likely to fall within, with 90% confidence.

The confidence interval calculated for this data is 0.398 to 0.562.

Since this interval includes the value of 0.5  (which would be the proportion of times a fair die would land on the number 4), By using statistical method we cannot reject the hypothesis that the die is fair.

Hence,

By using statistical method, we can conclude that the die would land on the number 4 is between 0.398 and 0.562 as 0.5 the die appears to be fair.

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A graph giving us a idea about relationship between the number of days and total amount of sunglasses is mentioned in the image attached below.

In this case, using Microsoft Excel, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot and the total number of sunglasses would be plotted on the y-axis (y-coordinate).

From the scatter plot (attached image) which shows the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 62

Hence, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.

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Answer:C

Step-by-step explanation:

Answer:44

Step-by-step explanation:44444444

The statement is equivalent to numerical value 81.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is the statement as -

"base 3 and exponent 4"

We can write mathematically as -

{x} = 3⁴

{x} = 3 x 3 x 3 x 3

{x} = 81

Therefore, the statement is equivalent to numerical value 81.

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Answer:

C) E=118°, T=118°

Step-by-step explanation:

The angles inside a quadrilateral (shape with four sides) always add to 360°. So this means:

W+E+S+T=360°

29°+E+95°+T=360°

E+T=360°-124°=236°

Note that the shape contains two congruent triangles (they share equal sides) ΔEWS and ΔTWS. This means their angles are the same so E=T

If E=T and E+T=236°, then E=T=236°/2=118°

Answer:

C) E-118°, T=118° is the answer