Jacob received a deck of cards for his birthday. The length, width, and height of the card box are shown below.

A measurement of a cards box bottom as 2 and half in, side as 3 and half in, and width as 2 by 3 in.

What is the volume of the card box?

The triangular base in the xy plane can be described by the equation y = mx + b, where m is the slope of the line and b is the y-intercept.

In the xz plane, the solid has a plane defined by the equation z = f(x). This equation can be derived from the equation of the base by substituting the y values with the corresponding mx + b values. Similarly, in the yz plane, the solid has a plane defined by the equation z = g(y). This equation can be derived from the equation of the base by substituting the x values with the corresponding (y - b)/m values. To calculate the area of the solid, we can use the formula A = 1/2h(b1 + b2), where h is the height of the solid and b1 and b2 are the lengths of the two bases. The area of the solid can then be found by substituting the appropriate values into this formula.

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Answer:

[tex] \sf \: \frac{5 - 3 \sqrt{2} }{3} [/tex]

Step-by-step explanation:

Given expression,

→ (5/3) - √2

Let's simplify the expression,

→ (5/3) - √2

→ (5/3) - ((√2 × 3)/(1 × 3))

→ (5/3) - (3√2/3)

→ (5 - 3√2)/3

Hence, answer is (5 - 3√2)/3.

Answer:

[tex]\dfrac{15+5\sqrt{2}}{7}[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{5}{3-\sqrt{2}}[/tex]

To write the given rational expression in its simplest form we need to rationalise the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of an expression is where we change the sign in the middle of the two terms.  Therefore, the conjugate of the denominator of the given expression is:

Multiply the numerator and denominator by the conjugate of the denominator:

[tex]\dfrac{5}{3-\sqrt{2}} \cdot \dfrac{3+\sqrt{2}}{3+\sqrt{2}}[/tex]

Simplify:

[tex]\implies \dfrac{5(3+\sqrt{2})}{(3-\sqrt{2})(3+\sqrt{2})}[/tex]

[tex]\implies \dfrac{15+5\sqrt{2}}{9+3\sqrt{2}-3\sqrt{2}-2}[/tex]

[tex]\implies \dfrac{15+5\sqrt{2}}{9-2}[/tex]

[tex]\implies \dfrac{15+5\sqrt{2}}{7}[/tex]

Answer:

the answer is alphabet c

The expression that shows the number of cookies that remained is:

C = 45 - n

We know that Crhis baked a total of 45 cookies, and his family ate n of them.

The number of cookies that remained is equal to the difference between the initial amount, which is 45, and the number of cookies that the family ate, which is n.

(Where a difference refers to a subtraction)

Then the expression for the number of cookies that remained is:

cookies = 45 - n

That is the expression that depends on the value n.

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The difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.

A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a broader range.

The standard deviation is a measure of variance or dispersion in statistics.

So, the sampling distribution's standard deviation is calculated as follows:

[tex]\begin{aligned}& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=\sqrt{\frac{0.37 \times(1-0.37)}{28}+\frac{0.89 \times(1-0.89)}{100}} \\& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=0.096\end{aligned}[/tex]

The actual proportional difference between those who believe five minutes is not enough time for pupils to switch courses and those who believe this is generally 0.096.

Therefore, the difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.

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Correct question:

n a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let p hat Subscript Upper F and p hat Subscript Upper S be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the correct shape and justification of the sampling distribution of p hat Subscript Upper F Baseline minus p hat Subscript s ?

Answer:

2 days

Step-by-step explanation:

He was paid 3,250 for 5 days that means 1 day is 3250/5 = 650

So, then 7,800/650 = 12 days(number of days he came to work) but two weeks is 14 days so the number of days he was absent was 14-12= 2

Answer: 0.25

Step-by-step explanation:

1/4 = 0.25

The volume equation of a rectangular prism is:

Where V - volume, l, w, h are dimensions, B - area of base (same as lw)

By substituting values we get:

Answer: 4.4

Step-by-step explanation:

Answer:

400

Step-by-step explanation:

let the number be x

x= (14+6)²

x= 20²

x=400

47

We know the angles in a triangle add up to 180 degrees. Adding the two angles we know, ( 47 and 86) we get 133. Simply subtract 133 from 180 to get 47 degrees.

Answer:

[tex]2x = 5 \\ 2x + 0y - 5 = 0 \\ a = 2 \\ b = 0 \\ c = - 5[/tex]

If the similar figure is smaller than the original then the scale factor is a fraction. If the similar figure is larger than the original then the scale factor is a whole number.

The scale factor is a ratio that compares the corresponding side lengths of two similar figures. If the similar figure is smaller than the original, the scale factor is a fraction less than 1, for example, 2/3 or 3/4. This means that the corresponding side lengths of the similar figure are 2/3 or 3/4 of the corresponding side lengths of the original figure.

On the other hand, if the similar figure is larger than the original, the scale factor is a whole number greater than 1, for example, 2 or 3.

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The slope of a line is calculated as the change in the y-coordinates (rise) divided by the change in the x-coordinates (run). Using the coordinates (9, 10) and (7, 2), we can calculate the slope as:

(10 - 2) / (9 - 7) = 8 / 2 = 4

So, the slope through the line of (9, 10) and (7, 2) is 4.

The solid has a triangular face in the xy-plane.

The solid has a rectangular face in the xz-plane.

The solid has a trapezoidal face in the yz-plane.

The solid has a triangular face in the plane z = 1 - x.

The solid has a rectangular face in the plane y = 9 - 9z.

As x increases, the top of the region decreases.

As y increases, the top of the region remains constant.

The solid whose volume is given by the iterated integral, integral 0 to 1 integral 0 to (1-x) integral 0 to (9 - 9z) dy dz dx. This is a three-dimensional solid, that has been defined by three nested integrals. The outer integral is with respect to x, the second integral is with respect to y and the inner integral is with respect to z.

In the xz-plane, the solid has a rectangular face: the integral bounds for x are 0 to 1 and for z, it is 0 to (9 - 9z)

In the yz-plane, the solid has a trapezoidal face: the integral bounds for y are 0 to (1-x) and for z, it is 0 to (9 - 9z)

In the plane z = 1 - x, the solid has a triangular face: the integral bounds for x are 0 to 1 and z = 1 - x

In the plane y = 9 - 9z, the solid has a rectangular face: the integral bounds for y are 0 to (1-x) and y = 9 - 9z

As x increases, the top of the region decreases: the limit for y decreases from 9 to 0 as x increases from 0 to 1

As y increases, the top of the region remains constant: y = 9 - 9z is a constant value, as y increases, the integral bounds for z decrease from 9 to 0

This solid is a rectangular pyramid with a trapezoidal base. The rectangular face is located in the xz-plane, the trapezoidal face is located in the yz-plane, the triangular face is located in the plane z = 1

--The question is incomplete, answering to the question below

"The solid whose volume is given by the iterated integral,

∫ [0 to 1] ∫ [0 to (1-x)] ∫ [0 to (9 - 9z)] (dy dz dx)

The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the xz-plane.

The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the yz-plane.

The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane z = 1 - x.

The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane y = 9 - 9z.

As x increases, the top of the region (decreases, increases, or remains constant).

As y increases, the top of the region (decreases, increases, or remains constant)."

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The best description of the shape of the sampling distribution is Approximately normal. The correct option is C.

The sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal. A sampling distribution is the distribution of a statistic calculated from a random sample of data. In this case, the statistic is the sample proportion of those who will be cured with the skin cream. The Central Limit Theorem states that the sampling distribution of a statistic will be approximately normal if the sample size is large enough, regardless of the shape of the underlying distribution.

Since the sample size of 100 people is large enough, the sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.

Hence the correct option is C.

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Answer:

The new real state agent earns:

$10,950

Step-by-step explanation:

5% = 5/100 = 0.05

219000 * 0.05 = 10950

Continuity is the formulation of a function that varies with no breaks or jumps. The concepts of limits and continuity have been used to show that the function is continuous at the number a below.

If a graph has no holes asymptotes or breaks at any point then the function is said to be continuous. Or if we can draw the function without lifting our pen then it is called continuous.

The conditions which it should satisfy are,

1)The limit must exist at that point.

2) The function must be defined at that point,  and

3)The limit and the function must have equal values at that point. So,

A function f(x) is said to be continuous at x=a if,

lim f(x) = f(a)

x→a

A function is said to be continuous on the interval [a,b] if it is continuous at each point in the interval.

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132 is the total of all two-digit numbers and their reversal digits. The solution is (C) 9. Nine two-digit numbers, including 21 + 12 = 33, 32 + 23 = 55, 43 + 34 = 77, 54 + 45 = 99, 65 + 56 = 121, 76 + 67 = 143, 87 + 78 = 165, 98 + 89 = 187, and 109 + 901 = 132, meet this characteristic.

132 is the total of all two-digit numbers and their reversal digits. We must look at all potential two-digit numbers and add the number to its reversed digits in order to count the number of two-digit numbers that satisfy this property. The range of the two-digit numbers is 10 to 99. Starting with the number 11, which does not satisfy the stated criteria because 10 + 01 = 11 is not equal to 132. Then, we will look at 11 + 11, which is not equal to 132, and find that it is 22. This method will be repeated until a two-digit number is found that meets the specified attribute. As an illustration, 21 + 12 Equals 33, which is not the same as 132. This technique will be repeated until a two-digit number, such as 65 + 56 = 121, is found that satisfies the property. This operation will be repeated until nine two-digit values, such as 109 + 901 = 132, satisfy the property. As a result, the response is (C) 9.

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The denominator of the function, n(x), is the place where vertical asymptotes can be located. If the numerator, t(x), is not zero for the same value of x, then the vertical asymptotes can be determined by solving the equation n(x) = 0 where n(x) is the denominator.

Despite not being a part of the function graph, a vertical asymptote is a vertical line that serves as a guide.

It happens at an x-value that is outside the function's domain, therefore the graph can never cross it.

1/x^2 -4

Domain of 1/x² - 4 :

Solution : x < -2 or  -2 < x < 2 or x > 2

Interval Notation ; ( -∝ , -2) ∪ (-2 ,2) ∪ (2 , ∝).

Range of 1 / x² - 4 :

Solution : f(x) ≤ - 1/4 or f(x) > 0

Interval Notation : ( -∝ , - 1/4) ∪ (0,∝)

Axis interception points of 1 / x² - 4 :

y Intercepts : (0 , - 1/4)

Asymptotes of  1 / x² - 4:

Verticals x = -2. x = 2,

Horizontal y = 0

Extreme Points of 1/x² - 4 :

Maximum (0, -1/4).

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Answer:

a. Without any additional information provided, it is impossible to determine the probability of Manchester United winning the match. The outcome of a football match can be influenced by many factors such as player performance, tactics, and luck.

b. There are 22 players + 3 officials = 25 people on the pitch. The probability that a person selected at random from the pitch is an official is 3/25.

c. i. Since there are 2 goalkeepers on the pitch, the probability that a player selected at random is a goalkeeper is 2/22 = 1/11

ii. Since there are 3 attackers on the pitch, the probability that a player selected at random is an attacker is 3/22 = 1/7

iii. Since there are 8 defenders on the pitch, the probability that a player selected at random is a defender is 8/22 = 4/11

The probability that the melon will have a diameter greater than 137 mm is 21.19%.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.

Given A grocery store purchases melons from two distributors, J & K,

for distributor J,

mean of melons = μ = 133 mm

standard deviation  = σ = 5 mm

to find the probability  that the melon will have a diameter greater than 137 mm,

x = 137 mm

P(x > 137)

using z score formula

z = (x - μ)/σ

z = (137 - 133)/5

z = 0.8

P-value from Z-Table:

P(x < 137) = 0.78814

P(x > 137) = 1 - P(x < 137) = 0.21186

probability in percent = P(x > 137) = 0.21186*100 = 21.186%

P(x > 137) = 21.19%

Hence probability for melon will have a diameter greater than 137 mm is 21.19%.

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The complete question is,

A grocery store purchases melons from two distributors, J & K. Distributor J provides melons from organic farms. The distribution of the diameters of the melons from distributor J is approximately normal with mean with 133 millimeters and standard deviation 5 mm. For a melon selected at random from distributor J, what is the probability that the melon will have a diameter greater than 137mm?

The slope of the given linear relationship is 5 (A).

From the question, we have 5 different points that create a linear relationship. To determine the slope of the linear relationship, we can choose 2 random sequence points.

We might choose:

Point 1 = (0,-2)

Point 2 = (1,3)

We can find the slope of the relationship using formula of:

m = y2 - y1

       x2 - x1

m = 3- (-2)

        1 - 0

m =   5

        1

m = 5

To ensure our finding, we can choose another pair of random points, for example:

P1 = (-2, -12)

P2 = (-1, -7)

We can use the slope formula:

m = y2 - y1

       x2 - x1

m = -7 - (-12)

        -1 - (-2)

m = 5

        1

m = 5

Hence, the slop of the linear relationship between all the given points are 5.

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Answer:

1.2 Acres

Step-by-step explanation:

The resulting bar chart would show that in Store A, the employees spend 30% of their time on stocking, 40% on cashiering, and 30% on cleaning.

To create a side-by-side bar chart for this data, we would first organize the data into a table with store locations as the rows and tasks as the columns. Each cell in the table would contain the percentage of time spent on that task at that store location.

For example, the table might look like this:

                 Stocking Cashiering Cleaning

Store A         30%             40%            30%

Store B        25%             35%            40%

Store C         35%             25%            40%

To create the bar chart, we would then place the store locations on the x-axis and use different colors to represent the different tasks. The length of each bar would correspond to the percentage of time spent on that task at that store location.

The resulting bar chart would show that in Store A, the employees spend 30% of their time on stocking, 40% on cashiering, and 30% on cleaning.

Similarly, the chart will provide an easy visual representation of the time spent on each task at each store location.

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The complete question is -

The management of a retail company wants to analyze the time spent by employees on different tasks at different store locations. The data collected shows the percentage of time spent on tasks such as stocking, cashiering, and cleaning at three store locations: Store A, Store B, and Store C. Create a side-by-side bar chart to represent this data and analyze the results.

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The McCumber Cube, which bears the name of its inventor, John McCumber, demonstrates the interdependence of the many elements of information security.

What is the McCumber Cube used for?

The McCumber Cube, which bears the name of its inventor, John McCumber, demonstrates how the many elements of information security are interconnected. You may view availability, integrity, and confidentiality on one side. All three of these include crypto in a significant way.

Information Characteristics, Information States, and Security Countermeasures are the three McCumber cube dimensions. The three CIA triangle pillars of confidentiality, integrity, and availability make up information characteristics.

The McCumber Cube, which John McCumber developed in 1991, is a reference framework for developing and assessing information security (also known as information assurance) initiatives. This security model is presented as a grid that resembles the Rubik's Cube in three dimensions.

The McCumber Cube shows three proportions. If theorized, the three dimensions of each axis become a 3 × 3 × 3 cube with 27 cells representing areas that must be addressed to secure today’s information systems. To ensure system security, each of the 27 areas must be properly addressed during the security process (McCumber, 1991).

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Answer: 35

Step-by-step explanation: 20 +15= 35

Answer:

5

Step-by-step explanation:

u just know

Check the picture below, that's just a transformations template

so since we know that f(x) = √x, that means when x = 0, y = 0, so it touches the origin, so f(x) is the graph down below.

now, f(x) has moved to the left by 5 units and up by 4 units, based on the template that means C = 5 and D = 4 whilst B = 1

[tex]g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{5}} ~~ +\stackrel{D}{4}\implies g(x)=\sqrt{x+5} ~~ +4[/tex]

Answer:

A. 9x+5

Step-by-step explanation:

[tex]5(3x-2)-3(2x-5)\\15x-10-6x+15\\9x+5[/tex]

The slope of a secant line or the average rate of change over a relatively brief period of time can be used to approximate the derivative. The closer the interval is to the actual instantaneous rate of change, slope of the tangent line, or slope of the curve, the more accurate the result is.

Therefore,

[tex]& \int_0^6\left|t^2-8 t+12\right| d t \quad \quad \text { Distance traveled over }[a, b] \\[/tex]

[tex]\int_0^2 t^2-8 t+12 d t+-\int_2^6 t^2-8 t+12 d t & \text { distance }=\int_a^b\left|x^{\prime}(t)\right| d t \\[/tex]

[tex]t^2-8 t+12=0[/tex]

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