Ben brought two pizzas to a party. He says that since 1/4 of each pizza is left, the same amount of pizza is left. What is his error? (Show your steps) (Giving brainliest for whoever answers good) (40 points)

Answer:

96

Step-by-step explanation:

40=4x+8

32=4x

x=8

other side x+4 is 12

area is 12×8

96

The value of integer k is -5.

Polynomial equations formed with variables, exponents and coefficients .

Since the polynomial has three integer roots, we can express it as:

(x - r1)(x - r2)(x - r3) = 0

where r1, r2, and r3 are the three integer roots.

Expanding the left-hand side, we get:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Comparing this with the given polynomial, we see that:

r1 + r2 + r3 = 1

r1r2 + r1r3 + r2r3 = k

r1r2r3 = 3

First we need to find the value of k. From the first equation, we see that one of the roots must be 1, since the sum of three integers that are not 1 cannot be 1. Without loss of generality, assume that r1 = 1. Then we have:

r2 + r3 = 0

r2r3 = 3

Since the roots are integers, the only possibility is r2 = -3 and r3 = 1.

Therefore, we have:

k = r1r2 + r1r3 + r2r3 = 1(-3) + 1(1) + (-3)(1) = -5

Therefore, the value of integer k is -5.

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Answer:

When dividing numbers with the same base, you subtract the exponents.

Step-by-step explanation:

For example, 8^5/8^3 = 8^2 or 64

Answer:

44.

Step-by-step explanation:

Given expression: \(3t^2-t\)

To find the value of \(3t^2-t\) where t = 4, we need to substitute t for 4 in the expression.

After substituting, we use PEMDAS (the order of operations) to solve. This is because this problem includes multiple operations.

\(3(4)^2-4\)

\(=3(16)-4\)

\(=48-4\)

\(=48-4=44\)

\(\to \inft3(4)^2-4=44\)

Therefore, the value of \(3t^2-t\) is 44, when t = 4.

The scale factor of the two rectangles is 1.5

According to Euclidean Plane Geometry, a rectangle is a quadrilateral with equal opposed sides and four right angles. In other words, a rectangle is a parallelogram with a right angle of 90 degrees or an equiangular quadrilateral (i.e., 360°/4 = 90°). A rectangle is referred to as a square if its four sides are all the same length.

The ratio of the matching side lengths of two comparable figures is known as the scale factor. We know that the ratio of the respective side lengths of the two rectangles equals equivalent to r since Rectangle A and Rectangle B are similar to one another by the scale factor r.

We can set up the following ratio to determine the scale factor if the lengths of rectangles A and B are 1.5r+2.25 units and 3 units, respectively.

(1.5r+2.25) / 3 = r

Solving for r, we get:

r = (1.5r + 2.25) / 3

multiply both sides of the equation by 3

3r = 1.5r + 2.25

Subtract 1.5r from both sides

1.5r = 2.25

divide both sides by 1.5

r = 2.25/1.5

r = 1.5

Therefore, the scale factor of the two rectangles is 1.5.

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To maximize the volume of an open-top container made from a 13-inch by 48-inch piece of plastic, you need to determine the optimal size of the squares to be cut out from each corner. Let 'x' be the side length of the square removed from each corner. After cutting, the dimensions of the container will be:

- Length: 48 - 2x
- Width: 13 - 2x
- Height: x

The volume of the container can be calculated using the formula: V = L * W * H.  the dimensions, we get:

V(x) = (48 - 2x)(13 - 2x)(x)

To find the maximum volume, we need to identify the value of 'x' that maximizes V(x). This can be achieved using calculus, by finding the critical points where the derivative of the function V(x) is zero or undefined.

Differentiating V(x) with respect to x and setting the derivative equal to zero, we can solve for the optimal value of 'x'. After performing these calculations, we find that the optimal size of the square to be cut out from each corner is approximately 1.52 inches. By removing 1.52-inch squares from each corner and folding up the flaps, the open-top container will have the maximum volume.

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(a) We have shown that there exists an element b ∈ B that is an upper bound for A.

(b) The statement in part (a) is not always the case if we only assume sup A ≤ sup B.

(a) If sup A < sup B, show that there exists an element b ∈ B that is an upper bound for A.

Proof:
1. By definition, sup A is the least upper bound for set A, and sup B is the least upper bound for set B.
2. Since sup A < sup B, there must be a value between sup A and sup B.
3. Let's call this value x, where sup A < x < sup B.
4. Now, since x < sup B and sup B is the least upper bound of set B, there must be an element b ∈ B such that b > x (otherwise, x would be the least upper bound for B, which contradicts the definition of sup B).
5. Since x > sup A and b > x, it follows that b > sup A.
6. As sup A is an upper bound for A, it implies that b is also an upper bound for A (b > sup A ≥ every element in A).

Thus, we have shown that there exists an element b ∈ B that is an upper bound for A.

(b) Give an example to show that this is not always the case if we only assume sup A ≤ sup B.

Example:
Let A = {1, 2, 3} and B = {3, 4, 5}.
Here, sup A = 3 and sup B = 5. We can see that sup A ≤ sup B, but there is no element b ∈ B that is an upper bound for A, as the smallest element in B (3) is equal to the largest element in A, but not greater than it.

This example shows that the statement in part (a) is not always the case if we only assume sup A ≤ sup B.

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Answer:

See below

Step-by-step explanation:

\(1\cdot24=2\cdot12=3\cdot8=4\cdot6=24\)

Answer:

1. 24

2. 12

3. 8

4. 6

Step-by-step explanation:

2 x 12 = 24, 3 x 8 = 24, 4 x 6 = 24

Answer:

\((\frac{12}{-4n^{2}})\)

Step-by-step explanation:

\((\frac{3}{-2n})(\frac{4}{2n})=(\frac{3*4}{-2n*2n})=(\frac{12}{-4n^{2}})\)

Answer:

\( -\dfrac{3}{n^2} \)

Step-by-step explanation:

\( \dfrac{3}{-2n} \times \dfrac{4}{+2n} = \)

\( = \dfrac{3 \times 4}{-2n \times 2n} \)

\( = \dfrac{12}{-4n^2} \)

\( = -\dfrac{3}{n^2} \)

Depends on your level of skills for one. Let's say you can replace a tire on a car within 30 min to 1 hr from the time you open the trunk to get the replacement.

7) 2

8) -3

9) -5/11

10) 2/5

11) -0.5

12) -2

Answer:

X on the graph represents horizontal distance, the x intercept represents when he ends his dive and lands in the water. The x intercept = 8 meaning he is 8 feet away from the diving board when he lands in the water. The y-intercept of y = 13 means the starting point of his dive.

Good luck! :)

Credits: Xin for part A

the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Length of hike = definite integral of velocity from 0 to 10.

What is integral ?

An integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.

The total length of a piecewise-defined function represents the total distance between points on the curve. To calculate this, one can use calculus techniques, such as integration. The definite integral of the function over an interval represents the total length of the curve on that interval. To find the total length of the mountain hike from x=0 to x=10, one needs to evaluate the definite integral of the function over the interval [0,10]. This can be calculated either analytically, using calculus, or numerically, using numerical integration methods. The exact method to be used would depend on the specifics of the function and the desired level of accuracy.

Length of hike = definite integral of velocity from 0 to 10.

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Answer:

Width of the rectangular prism

It is given to us that the volume of the rectangular prism is calculated by the given formula :-

v = lwh

Where,

v = volume

l = length

w = width

h = height

Now,

In the question we are given :-

v = 138.24 cubic inches

h =  9.6 inches

l = 3.2 inches

w = ?

Substitute these values in the volume formula given :-

138.24 = 3.2 * w * 9.6

138.24 = 30.72 * w

w = 138.24/30.72

w = 4.5

⇒ The width of the rectangular prism is 4.5 inches.

The required width of the rectangular prism is 4.5 inches.

Given information:

The volume of the rectangular prism is defined as,

\(V=lwh\)

where l is the length, w is the width, and h is the height of the prism.

The volume of the prism is 138.24 cubic inches.

The height of the prism is 9.6 inches, and the length of the prism is 3.2 inches.

So, the width of the prism can be calculated as,

\(V=lwh\\138.24 =3.2\times w\times 9.6\\138.24 =30.72\times w\\w=\dfrac{138.24}{30.72}\\w=4.5\rm \; inch\)

Therefore, the required width of the rectangular prism is 4.5 inches.

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Answer:

Step-by-step explanation:

Answer:38

Step-by-step explanation:

The length of the rectangular pool is 30 meters.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

a. Here is a sketch of the swimming pool and hot tubs:

 ____________12m__________

|                         |

8m         Pool          8m

|                         |

|_________________________|

b. Let's start by finding the area of the pool and hot tubs combined:

Area of pool = length × width

Area of each hot tub = side length × side length

Area of the pool and hot tubs = Area of pool + 2 × Area of hot tub

= length × 12 + 2 × 8 × 8

= length × 12 + 128

We know that the total area is 488 square meters, so we can set up an equation:

length × 12 + 128 = 488

Simplifying:

length × 12 = 360

Dividing both sides by 12:

length = 30

Therefore, the length of the rectangular pool is 30 meters.

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Answer: cant read it

Step-by-step explanation:

Answer:

A = 54π Km²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{135}{360}\) ( r is the radius )

   = π × 12² × \(\frac{3}{8}\)

   = 144π × \(\frac{3}{8}\) ( cancel 144 and 8 by 8 )

  = 18π × 3

 = 54π Km²

The distance between the given pair of parallel lines is 20 / √10 units.

To find the distance between two parallel lines, we can use the formula:

Distance = |C₁ - C₂| / √(A² + B²)

where the equations of the lines are in the form Ax + By + C₁ = 0 and Ax + By + C₂ = 0.

For the given equations:

Equation 1: x + 3y = 6

Equation 2: x + 3y = -14

In both equations, A = 1, B = 3, and C₁ = 6 for Equation 1 and C₂ = -14 for Equation 2. Substituting these values into the distance formula, we get:

Distance = |C₁ - C₂| / √(A² + B²)

= |6 - (-14)| / √(1² + 3²)

= |20| / √(1 + 9)

= 20 / √10

Therefore, the distance between the given pair of parallel lines is 20 / √10 units.

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The media challenge faced in the scenario is increasing audience fragmentation.

The cost price is abbreviated as C.P.  The price at which an article is sold is known as its selling price. The selling price is abbreviated as S.P.It is a price above the cost price and includes a percentage of profit also.

The media challenge described in the scenario is increasing audience fragmentation. Audience fragmentation occurs when there are numerous media options available, and consumers have different preferences and behaviors regarding media consumption. This makes it challenging for media planners and buyers to identify the most effective media outlets to reach their target audience. In the case of Ford, their media planners and buyers had put a lot of effort into selecting the best media outlets, but still had to pull their campaign due to the challenges posed by audience fragmentation. Therefore, the media challenge faced in the scenario is increasing audience fragmentation.

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Answer:

3rd option

Step-by-step explanation:

becayse y=mx + b and m is slope and b is y intercept

Answer:

y=8x+2

Step-by-step explanation:

Slope formula: y=mx+b

m=slope

b=y-intercept

m=8

b=2

Answer:

a. sine StartFraction pi Over 3 EndFraction = StartFraction opposite Over hypotenuse EndFractionEquals StartFraction opposite Over 1 EndFraction  Equals opposite

The length opposite the angle is the vertical distance from the x-axis on the graph.

Step-by-step explanation:

sin (π/3) = opposite/hypotenuse = opposite/1; The length opposite the angle is the vertical distance from the x-axis on the graph.

Unit circle is a circle centered at the origin, (0,0) with radius(r) i.,e r= 1.

The angle π/3 forms an arc of length S and the x-axis and y-axis divide the coordinate plane and the unit circle as it is centered at (0.0).

Also, the terminal side intersect the circle at (x, y). Thus;

sin (π/3) = opposite/hypotenuse = opposite/1

Thus;

sin (π/3) = opposite

Also, the length opposite the angle is the vertical distance from the x-axis on the graph.

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The better statistics to compare the distribution are given as follows:

A. Mean and standard deviation.

The mean of a data-set is given by the sum of all observations in the data-set divided by the cardinality of the data-set, which represents the number of observations in the data-set.

The standard deviation of a data-set is calculated as square root of the sum of the differences squared between each observation and the mean of the data-set, divided by the cardinality of the data-set.

These two measures should be used as both distributions in this problem are symmetric, meaning that they do not contain outliers.

If the distribution contained outliers, then the median and the IQR should have been used.

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Answer: 16 inches

Step-by-step explanation: well, if you do 76/19, it gives you four, so the ratio is 1-inch costs 4 cents.

Then you just have to do 64/4, which gives you 16. You can buy 16 inches of wire with 64 cents

Answer:

Step-by-step explanation:

Put the left dot on negative 4, and then put the right dot on positive 6.

For each unit of plastics produced , the result would be an external d . cost of $9 .

At the equilibrium point on the graph, we see that the price is $ 21 . This is the equilibrium price .

We also see that the equilibrium social cost is $ 30 .

The external benefit or cost would be:

= Equilibrium price - social cost

= 21 - 30

= - $ 9

This is a negative benefit and so it is an external cost of $ 9.

In conclusion, each unit of plastics leads to an external cost of $9.

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99% Confidence Interval for the Population Percentage of Defective Disks = (0.1004, 0.1196).

Rules for Decimals. Align up the decimal points. To ensure that every one of the values have the same number of places following the decimal, add 0s. Add the same way you would with complete numbers.

Step 1:

Sample Size: n=7002

Number of non-defective disks =6232

Number of defective disks: x = 7002-6232=770

Sample proportion \(\widehat{p}\) = x/n = 770/ 7002 = 0.110

Estimated proportion of disks which are defective: Sample proportion: \(\widehat{p}\) = 0.110

Step 2:

Range of confidence for the population proportion:

\(=\widehat{p}\pm z_{\alpha /2}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(\alpha = (100-99)/100 = 0.01; \alpha/2 = 0.005\)

99% Confidence interval =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

from standard normal tables z0.005 = 2.58

99% Confidence Level for the Population Percentage of Defective Disks =

\(=\widehat{p}\pm z_{0.005}\sqrt{(\widehat{p}(1-\widehat{p}))/n}\)

\(=0.11\pm 2.58\sqrt{(0.11(1-0.11))/7002}\)

\(=0.11\pm 2.58\sqrt{(0.110\times 0.89)/7002}=0.11\pm 2.58\sqrt{\frac{0.0979}{7002}}\)

\(=0.11\pm 2.58\times 0.0037 = 0.11\pm 0.0096 =(0.1004, 0.1196)\)

99% Confidence interval for population proportion of disks which are defective= (0.1004, 0.1196).

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Apply Pythagorean theorem