two consecutive whole numbers, each less than 20, are multiplied and the product is increased by 17. There are exactly two values of the lesser of two consecutive numbers of which the result is not a prime number. Find both values of the lesser numbers?

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:

-4.44

The temperature at 7 A.M. is,

−2 °F.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

Jorge wrote the inequality −14 °F < −2 °F to compare the temperatures at 7 A.M. and 7 P.M.

It was colder at 7 P.M. than at 7 A.M.

That means,

−14 °F is the temperature at 7 P.M.

The temperature at 7 A.M. is,

−2 °F.

Therefore, the temperature at 7 A.M. is −2 °F.

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A combination of loops and random numbers, a unique background and two unique shapes can be created.

The Applab Turtle project uses a combination of loops and random numbers to create a background and two unique shapes. The program starts by setting the background color of the canvas to a random number from 0 to 255. A for loop is then used to create a series of random circles. The loop is set to run 10 times, and each iteration uses the random number function to set the size of the circle and its position, resulting in a unique pattern of circles on the canvas. Following this, two for loops are used to create two unique shapes. The for loops are set to run a set number of times, and each iteration uses the random number function to set the size and position of the shape. By using a combination of loops and random numbers, a unique background and two unique shapes can be created.

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The function f(x) will be : f(x) = 4x and f(2) = 8.

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.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine the order of operations and other aspects of logical syntax.

Given that f(x) is a direct variation function.

Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically -

{K} = y/x = constant

Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.

It is given that -

f(3) = 12

We can write the slope of f(x) as -

m = (12 - 0)/(3 - 0)

m = 12/3

m = 4

So, f(x) will be -

f(x) = 4x

f(2) will be -

f(2) = 8

Therefore, the function f(x) will be : f(x) = 4x and f(2) = 8.

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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

It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.

It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.

1. Two possible events, A and B, are given when a random number generator is used once.

2. It is stated that the two events are mutually exclusive.

3. This implies that the two events cannot occur simultaneously.

4. If event A occurs, event B cannot occur and if event B occurs, event A cannot occur.

It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.

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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?

When we select a random sample of 3 teachers and calculated the sample median from ages of 5 teachers in maths department, we get three samples of sample median 34, four samples of sample median 37 and three samples of sample median 42.

a. To list all 10 possible samples of size 3, we can use the combination formula C(5,3) = 5! / (3! * 2!) = 10.

The possible samples are:

Sample 1: (23, 34, 37) - Sample Median: 34

Sample 2: (23, 34, 42) - Sample Median: 34

Sample 3: (23, 34, 58) - Sample Median: 34

Sample 4: (23, 37, 42) - Sample Median: 37

Sample 5: (23, 37, 58) - Sample Median: 37

Sample 6: (23, 42, 58) - Sample Median: 42

Sample 7: (34, 37, 42) - Sample Median: 37

Sample 8: (34, 37, 58) - Sample Median: 37

Sample 9: (34, 42, 58) - Sample Median: 42

Sample 10: (37, 42, 58) - Sample Median: 42

b. To display the sampling distribution of the sample median, we can create a frequency table that shows how many times each sample median appears in the list of possible samples.

Sample Median Frequency

34                         3

37                         4

42                         3

This table shows that the sample median of 34 appears in 3 out of the 10 possible samples, the sample median of 37 appears in 4 out of the 10 possible samples, and the sample median of 42 appears in 3 out of the 10 possible samples.

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Answer:

I'm pretty sure it's 3. I say that because I get 3 different answers.

x = -1 / 8

x = -0.125

x = -2^3

Those are the answers I got to solve the equation. There also is an answer if I were to rewrite the equation which is... 8x = -1

I hope this helps in any way <3

Step-by-step explanation:

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 ?

We can observe from the graph that plan B is less expensive for the interval [0, 4], however plan A is better if you watch 4 or more movies each month.

We know that Plan A costs $14 per month + $2 each movie, thus the total cost if you see x movies is:

C₁(x) = $14 + $2*x

Plan B costs $10 a month + $3 per movie, therefore the total cost if you see x movies is:

C₂(x) = $10 + $3*x

The graph at the end may now be used to compare expenses. The blue line is C2(x), while the green line is C1(x).

The blue line in the graph may be seen between x = 0 and x = 4.

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Side length of Rhombus ABCD is  8+2√2 unit

EFGH is a rectangle :

We know that ,

E, F , G , H are midpoints of AB, BC, CD , DA respectively

Since ABCD is a rhombus

AB = BC = CD = DA

AB ll CD  and BC ll DA

since,  E, F , G , H are midpoints of AB, BC, CD , DA respectively

from the figure below we can say that ,

1) AB ll CD ll FH and AB= CD = FH

2) BC ll DA ll GE and BC = DA = GE

Using mid point theorem we can say that ,

GH = EF = 1/2 AC and FG= EH = 1/2 BD

Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.

Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )

= 2 x 1/2 ( AC + BD ) = 16

⇒ AC + BD = 16  (1)

now area of a rectangle is given by

A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14

⇒AC x BD = 14 x 4 = 56

from equation (1)

AC ( 16 - AC) = 56

= 16 AC - AC ^2 = 56

⇒ AC^2 - 16 AC + 56 = 0

AC = 8 +/- 2√2

BD = ( 16 - AC) = 8 +/- 2 √2  = side length of rhombus ABCD

Side length of Rhombus ABCD is 8+2√2 unit EFGH is - 1

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The small radius =5 cm; and the Long radius =5+4=9 cm.

Area (a + b) = 106 * pi cm^2 (given)

radius of a = x : radius of b = (x + 4)

Area a =[tex]pi * r^2 = pi * x^2\\[/tex]

Area b = [tex]pi * r^2 = pi * (x + 4)^2[/tex]

Area (a + b) = [tex]pi * x^2 + pi * (x + 4)^2[/tex] = 106 * pi cm^2

Area (a + b) =[tex]pi * x^2 + pi * (x^2 + 8x + 16)[/tex] = 106 * pi cm^2

Area (a + b) = pi * ([tex]2x^2[/tex]+ 8x + 16) = 106 * pi cm^2

Area (a + b) = [tex]2x^2 + 8x - 90 = 0[/tex]

2x^2 + 8x - 90 = x^2 + 4x - 45 = 0

x^2 + 4x - 45 = (x + 9)(x -5) = 0

x = 5 or x = -9

Therefore: radius a = 5 cm and radius b = 9 cm

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The question is incomplete

The sum of the areas of the two circles is 106pi cm^2 and the radius of the larger circle is 4cm longer than the radius Of the smaller circle. How could I find the length of the radii?

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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Answer:

Step-by-step explanation:

It is equivalent

4/12

1/3

1x4=4

         _

3x4=12

None of the transformations followed between the two given triangles. None of the options are correct.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
The graph shows two triangles plotted on a coordinate plane. One triangle is at A (-4, 4), B (-8, 2), and C (-6, -6). Another triangle is at A '(4, -2), B '(2, 2), and C '(6, 0).

As we can see in the graph, the triangles are completely different, so the transformation of either of the ΔABC to ΔA'B'C' or ΔA'B'C' to ΔABC is not possible.

Thus, None of the transformations followed between the two given triangles. None of the options are correct.

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The value of 17% of 279,394 is 47496.98.

percentage, a relative value indicating hundredth parts of any quantity.

We have to find the value of 17% of 279,394

Convert 17% to decimal value by dividing with 100

17/100=0.17

Now multiply 0.17 with 279394

0.17×279394

47496.98

Hence, the value of 17% of 279,394 is 47496.98.

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Answer:

x = 2.5

Step-by-step explanation:

I am assuming that this is the entire equation and that it equates to 0 otherwise the answer will just be [tex]4x + 10[/tex]

[tex]x + 3x +10 = 0 \\4x + 10 = 0\\4x = 10\\x = \frac{10}{4} \\x = 2.5[/tex]

On solving the equations y1 = 41 + 6x and y2 = 32 + 9x, it is obtained that -

For 3 books the cost will be the same.

The cost that will be same is $59.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The cost at Washington Printing is = $41 and $6 per book

The cost at Fairfax University is = $32 and $9 per book

Let the number of books be x.

Let y1 represent the total cost at Washington Printing.

Let y2 represent the total cost at Fairfax University.

So, the equations are -

y1 = 41 + 6x

y2 = 32 + 9x

According to the question -

y1 = y2

41 + 6x = 32 + 9x

Collect all the like terms together -

6x - 9x = 32 - 41

- 3x = - 9

x = 9/3

x = 3

Therefore, the number of books is 3.

The total cost can then be determined by the substituting the value of x in the equations -

41 + 6x = 41 + 6(3) = 41 + 18 = 59

32 + 9x = 32 + 9(3) = 32 + 27 = 59

Therefore, the total cost is $59.

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Answer: 0.25

Step-by-step explanation:

1/4 = 0.25

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:

X ≥ -4

Step-by-step explanation:

Remember domain only focuses on the X values, so we can immediately rule out the answers containing Y. We can observe that the graph has a closed circle over x=-4. This tells us it will be included and so we must have "≥" in the answer choice. By simple process of elimination A, the first answer choice is the correct answer.

Also note that it would be read as "X is greater than or equal to negative 4," which is exactly what our graph depicts. The second choice, which looks like it could be correct at first would be read as "X is greater than negative 4," which excludes negative 4 in the answer. We need that negative 4 for it to be correct.

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:

[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]

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

The expected value for a random variable is defined as the sum of the product of the values and probabilities of the variable.

In this case, the expected value for C is calculated by multiplying each possible value by its probability and adding the products. This is represented mathematically as:

Exp(C) = 0 x 0.60 + 1500 x 0.05 + 5000 x 0.13 + 15000 x 0.22 = 4025

The expected value of C can be interpreted as the average cost that the insurance company can expect to pay out for a randomly selected car of this model. This means that if the company insures a large number of these cars, they can expect the cost per car to average approximately $4025. The expected value does not represent the maximum cost for insuring this car model, or the cost for insuring a set number of cars. Instead, it provides an estimate of what the average cost per car will be.

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The sample space for this experiment is given as follows:

{RR, RB, RY, RG, BG, BB, BY, BG, YR, YB, YY, GG}.

A sample space is a set that contains all possible outcomes in the context of an experiment.

Then the sample space for this problem is composed by two letters, and the meaning of each letter is given as follows:

Hence, as an example, the outcome RB means that the color of the 3-color spinner was red and the color of the 4-color spinner was blue.

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