when the decimal point of a certain positive decimal number is moved four places to the right, the new number is four times the reciprocal of the original number. what is the original number?

Option B is the correct answer, the interval in which the graph of the function is positive is -∞ < x < -1.

What do mean by interval?

In mathematics, a (real) interval is a collection of real numbers that includes all real numbers that fall inside any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 x 1. The set of all real numbers, the set of nonnegative real numbers, the set of positive real numbers, the empty set, and any singleton are additional examples of intervals.

As we can see in the graph provided in the question, the graph of function reach the positive side of the y-axis at x = -1, it means one of the two end point of the interval is going to be -1. And, the graph is constantly and slowing increasing it's value as increase in the x-axis therefore, the other endpoint of the interval cab be considered as negative infinity.

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Answer:

∠

A

=

x

=

32

∘

∠

B

=

3

x

=

3

⋅

32

=

96

∘

∠

C

=

x

+

20

=

32

+

20

=

52

∘

Step-by-step explanation: Every triangle adds up to 180.

1) Radius of the standard tank = 3 feet

2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.

3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.

4)Total volume of the tank is  36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet

5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.

6)Trails of values for r is 4 feet.

What do you mean by Volume?

A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.

What is radius?

A line segment connecting the circumference or boundary surface of a circle or sphere to its center.

Given that;

Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]

                                                [tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]

Volume of new tank = 2 x Volume of standard tank

                                  =  2 x 126π

                                  = 252π

But according to formula, volume of new tank will be;

[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]

where r = radius of new tank

[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]

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If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.

The definition of the MoE, or margin of error, is

MoE = sigma ÷ sqrt(n)

The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.

The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.

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Answer: The answer is C: No solution

Step-by-step explanation:

By squaring the other side (to therefor remove the square off X) you get [tex]x-3=x+6\sqrt{x} +9[/tex]

You then cancel out the equal terms, in this case x, to reach the equation:

[tex]-3=6\sqrt{x} +9[/tex]

This equation, has no solution, as the left side is always negative, and the right side will always be positive, making any statement for x false.

number 9 is 36  12x3 is 36

The probability that the sample mean selling price was more than $210,000 is 0.9772.

The given values are:

The mean selling price(μ) = $215000

Standard deviation(σ) = $25000

The random sample (n) = 100

We have to find the probability that the sample mean selling price was more than $210000.

z-score with z-bar= 210000

z = (x-bar - μ) / (σ/ √n)

 = ( 210000 - 215000) / (25000/ √100)

 = -5000/ 2500

 =-2

Using z-tables, the probability is:

Probability = P[z> -2]

                  = 1 - 0.0228

                  = 0.9772

Therefore the probability is 0.9772.

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The length of the table is 1.51 meters.

Allan is measuring his dining room table to make a tablecloth. The table is 0.45 meter longer than it is wide. The width of the table is 1.06 meter. We need to find out the length of the table.

Let the length of the table be represented by the variable "L". In the context of a mathematical problem or experiment, a variable is a quantity that may vary. The length of the table is the sum of the width of the table and the difference between the two quantities.

L = 1.06 + 0.45

L = 1.51

Hence, the length of the table is 1.51 meters.

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Answer:

216

Step-by-step explanation:

x^3

6^3

6x6x6

36x6

216

Hopes this helps pleas mark brainliest

To do the multiplication, we multiply 0.63 by each of the digits & decimal places of 0.24 (and align the products that we get) then add them together.

0.63 x 4 = 2.52, therefore the first missing spot is a 2.

0.63 x 2 = 1.26, therefore the second missing spot is a 2 (the 0 is so that the decimal point can be aligned for the result.)

Answer: Box 1: 2 Box 2: 2

Step-by-step explanation:

So, for box one it would be 2 because 3 x 4 = 12, put the 2 on the bottom and the 1 on the 6, then 6 x 4 + 1 = 25, then put the 5 on the bottom and the 2 on the top, then 4 x 0 + 2 = 2, so the answer would be 2.

For box 2, 252 + 1?60 = 0.1512, so we have to find the missing number. So, 2 + 0 = 2, so put the two on the bottom, then 5 + 6 = 11, so put the 1 on the bottom and the other 1 on the 2 from the first box, so 2 + 1 = 3, plus 2 more would equal 5, so the second box would be 2.

Hope this helps!

For the given normal distribution, 95% of the values lie between 40 and 60.

Let the said distribution be X

Here it is given that X follows a normal distribution and it has a mean of 50 and a standard deviation of 5.

Therefore we can write X~ N(50, 25)

Now we need to find P(40< X< 60)

= P(40< X< 60) = P(X < 60) - P(X<40)

To find this we need to convert it into the form of a standard normal and then look up the p-values from the Z-table.

To do this we need to use the formula

P(X < x) = Φ[(x - μ) / σ]

where,

μ is the mean

σ is the standard deviation

Therefore we get

P(X < 60) - P(X<40) = Φ[(60 - 50) / 5] - Φ[(40 - 50) / 5]

= Φ[2] - Φ[-2]

Φ(-x) = 1 - Φ(x)

Therefore,

Φ[2] - Φ[-2]

= 2Φ(2) - 1

We get the p-value

2 X .97725 - 1

= 1.9545 - 1

= 0.9545

= 95% (approx)

Hence 95% of the values are between 40 to 60.

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On that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.

The equation u = 0. 99c depicts the value of the US dollar in relation to the Canadian dollar on a specific day.

From the equation,

For  Australian dollar; (from table)

u = 0.95 c   -->

a = 1/0.95 u

a = 20/19 u

(20/19u - u)/ u = 1/19   ....1

For Canadian dollar:

u = 0. 99c

c = 1/0.99 u --> c = 100/99 u

Thus,

(100 u / 99 - u)/ u = 1/99  .....2

From 1 and 2]

1/19 > 1/99

Thus, on that specific day, the US dollar was worth more than the Canadian dollar and less than the Australian dollar.

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The solution set for the given quadratic equation is (-0.62, -5.38).

The given equation is 3x(x+6)=-10.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, 3x(x+6)=-10

⇒ 3x²+18x=-10

⇒ 3x²+18x+10=0

By comparing 3x²+18x+10=0 with ax²+bx+c=0, we get

a=3, b=18 and c=10

Using quadratic formula x = [-b ± √(b² - 4ac)]/2a

= [-18 ± √(18² - 4×3×10)]/2×3

= [-18 ± √(324 - 120)]/6

= [-18 ± √(204)]/6

= [-18 ± √(204)]/6

= [-18 ± 14.28]/6

= [-18 + 14.28]/6 and [-18 - 14.28]/6

= -0.62 and -5.38

Hence, the solution set for the given quadratic equation is (-0.62, -5.38).

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The solution for u in the expression given as 7/u = 3/11 is u = 25.7

From the question, the algebraic expression is given as

7/u = 3/11

There is no constant to add to or subtract from the expression

So, the equation remains the same

7/u = 3/11

Multiply both sides of the equation by u

This gives

u * 7/u = 3/11  * u

Evaluate the products

So, we have the following equation

7 = 3/11u

Multiply both sides of the equation by 11/3

This gives

11/3 * 7 = 3/11u * 11/3

Evaluate the products in the above expression

77/3 = u

So, we have

25.6667 = u

Approximate

25.7 = u

Rewrite as

u = 25.7

Hence, the solution is u = 25.7

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The total amount of the money earned by Paige will be $1591.92.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Paige works at a department store and has a commission rate of 3 per cent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter.

The total amount of earnings will be,

TA = ( 50 x 30 ) + ( 0.02 x 4596)

TA = 1500 + 91.92

TA = $1591.92

Therefore, the total amount of the money earned by Paige will be $1591.92.

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A parabola is a bowl-shaped figure. Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].

And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].

Since the additional point is [tex](3,22)[/tex]

What is a parabola?

A curve formed by the intersection of a cone with a plane parallel to a straight line in its surface: a curve formed by a point moving so that its distance from a fixed point is equal to its distance from a fixed-line. : something that is bowl-shaped.

Here the given quadratic equation is

[tex]y=3x^{2}-x-2[/tex]

The standard form of the quadratic equation is

[tex]y=ax^{2}+bx+c[/tex]

where [tex]a=3,b=-1,c=-2[/tex]

The axis of symmetry is the x-axis  of the vertex

[tex]x=\frac{-b}{2a}\\x=\frac{1}{2(3)}\\x=\frac{1}{6}[/tex]

The y-value of the vertex is determined by substituting [tex]\frac{1}{6}[/tex] for [tex]x[/tex] into the equation and solving it for [tex]y[/tex].

[tex]y=3(\frac{1}{6})^{2}-\frac{1}{6}-2\\y=3(\frac{1}{36})-\frac{1}{6}-2\\y=\frac{3-6-72}{36}\\y=\frac{3-78}{36}\\y=\frac{-75}{36}[/tex]

Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].

Since [tex]a < 0[/tex] the vertex is the maximum point and the parabola opens downward.

X-intercept values of [tex]x[/tex] when [tex]y=0[/tex]

Substituting [tex]0[/tex] for [tex]y[/tex] and solving for [tex]x[/tex] using the quadratic formula

[tex]0=3x^{2}-x-2\\x=\frac{-b+-\sqrt{b^{2}}-{4ac}}{2a}\\x=\frac{1+-\sqrt{1}-{4(3)(-2)}}{2(3)}\\\\x=\frac{1+-\sqrt({1}+{24})}{6}\\\\\\x=\frac{1+-\sqrt(25)}{6}\\\\\\\\x=\frac{1+-5}{6}\\\\\\x=\frac{1+5}{6} , x=\frac{1-5}{6}\\\x=\frac{1+5}{6},x=\frac{1-5}{6}\\\\\x=1,x=\frac{-2}{3}[/tex]

Y-intercept values of [tex]y[/tex] when [tex]x=0[/tex]

Substituting [tex]0[/tex] for [tex]x[/tex] and solving for [tex]y[/tex] using the quadratic formula

[tex]y=3(0)^{6}-0-2\\y=-2[/tex]

Y-intercept [tex](0,1)[/tex]

Now substitute [tex]3[/tex] for [tex]x[/tex] and solve for [tex]y[/tex]

[tex]y=3(3)^{2}-3-2\\y=3(9)-5\\y=27-5\\y=22[/tex]

So the point is [tex](3,22)[/tex].

Hence, the vertex is [tex](\frac{1}{6},\frac{-75}{36})[/tex] and the approximate value is [tex](0.167,-2.08)[/tex].

And the x-intercept is [tex](1,(\frac{-2}{3}))[/tex].

Since the additional point is [tex](3,22)[/tex]

The parabola is of the form

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Answer: a) = 4

b) = 30

Step-by-step explanation:

a) They are asking for the range of the marks so you do 10-6 as 10 is the highest mark and 6 is the lowest

b) You find this out by adding the frequency up 10+4+7+4+5 = 30

There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes. Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how likely it is that a coin will land heads up after being tossed into the air.

Given,

On a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.

Either the wait is over 25 minutes or it is less than 25 minutes. Decimal 1 represents the total of these events' probabilities. So,

P( X ≤ 25) + P(X > 25) = 1

For P(X > 25):

1 -P(X ≤ 25)

1 - e ⁻⁰⁶⁶⁶⁽²⁵⁾

0.1892

There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

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Answer:

no because 60+48+36 is 144

Step-by-step explanation:

please mark brainliest

The total number of people is 144. The data is not consistent.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that at a party, 60 drank malt, 48 drank beer, 36 drank cocacola, 20 drank both beer and cocacola, 18 drank both cocacola and malt, 15 drank malt and beer and 12 drank all the three.

The total number of the people in the party,

60+48+36 is 144

But it is given in the question that there are 100 in the party.

Therefore, the total number of people is 144. The data is not consistent.

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The cluster sample represents the the characteristic of group of same types objects.

What is the cluster sampling?

A population is divided into clusters, such as districts or schools, and some of these clusters are randomly chosen as your sample via the probability sampling technique known as cluster sampling. In a perfect world, each cluster would be a tiny reflection of the entire population.

A researcher intends to carry out a study to evaluate sophomores' abilities in business education across the United States. There is no way to carry out a research study with participants from every university. Instead, the researcher can group the universities from each city into a single cluster by utilizing cluster sampling. The sophomore student population in the United States is then comprised of these clusters. Next, select clusters at random for the research project using either simple random sampling or systematic random sampling. The sophomores from each of these determined groups can then be picked on whom to perform the research study utilizing simple or systematic sampling.

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We have coordinates (-2, -3) and (1, 1)

To find: Slope of a line that passes through these two coordinates

Let (-2, -3) be (x₁ , y₁) and (1, 1) be (x₂, y₂)

We will use the formula of Slope :

m = y₂ - y₁ / x₂ - x₁

Where 'm' stands for slope

m = 1 - (-3) / 1 - (-2)

m = 1 + 3 /  1 + 2

m = 4 / 3

The slope of the line is  4/3

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There is no graph in your question

Answer:

x=-10

Step-by-step explanation:

2(x+3) = 2x+6

2x+6=x-4

2x+6-6=x-4-6

2x=x-10

2x-x=x-10-x

x=-10

Zimbardo did not use a control group. Experiments are performed to reach meaningful conclusions using the appropriate research method. The correct answer is (A).

Experiments whether they are done in natural settings or in a controlled environment need to follow certain ethics. But the Stanford Prison Experiment is an exception. In this experiment, Philip Zimbardo, the Stanford psychologist, took paid participants and asked them to be “guards” in a mock prison at Stanford University.

As soon as the experiment began, the “guards” began mistreating the “prisoners,” in order to provoke evil circumstantially. The conclusion of the study suggested innocent people, thrown into a situation where they have power over others, will begin to misuse that power. And people who are put into a situation where they are powerless will be driven to submission.

The Stanford Prison Experiment has proved to be a Fraud. Philip Zimbardo, the Stanford psychologist who did the experiment, and interviews of the participants, offers convincing evidence that the guards in the experiment were trained to be cruel. This proves that the experiment’s most memorable moment of a prisoner screaming out of rage and proclaiming, “I’m burning up inside!” was the result of the prisoner's acting skills. Many of them think of this study as more of a dramatic demonstration with no real outcomes. The Zimbardo prison experiment is a classic study that has been recently reevaluated and exposed as a fraud.

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The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

The distance covered in a unit of time is known as speed.

Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.

Therefore, the rate of the airplane against the wind is:

7680/8

= 960 km / hr

The rate of the airplane with the wind is:

12420/9

=1380 km / hr

Let the rate of the airplane in still air be a and the rate of the wind be w.

The net rate while flying against the air is:

a - w = 960       (1)

The net rate while flying with the wind is:

a + w = 1380      (2)

Add equations (1) and (2):

2a = 2340

a = 1170 km/hr

Substitute a = 1170 into equation (1):

1170 - w = 960

1170 - 960 = w

210 = w

Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

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A minimum of 71 observations must fall inside the interval (20, 40).

It is true that Chebyshev's Theorem holds true for all conceivable data sets. The minimal percentage of measurements that must fall within one, two, or more standard deviations of the mean is described. The minimum percentage of observations that are within a given range of standard deviations from the mean is calculated using Chebyshev's Theorem. Numerous other probability distributions can be applied with this theorem. Chebyshev's Inequality is another name for Chebyshev's Theorem.

Given,

The data set has 80 observations and has mean 30 and standard deviation 5.

Chebyshev's theorem states that for each data set, the proportion (or percentage) of values ​​that lie within k standard deviations of the mean (that is, the interval (x -ks , x +ks) is at least 1-1/k² . where k > 1.

x = 30

s = 5

Three standard deviations are added to and subtracted from the mean to get the interval (10, 40).

(30 - 3.5, 30 + 3.5) = (10, 40)

According to Chebyshev's Theorem, this interval contains at least 1 -1/3² = 8/9 of the data. Given that 8/9 of  80 is 71.11, the interval must include at least 71.11 observations. However, one cannot make a fractional observation, so we draw the conclusion that the interval must contain at least 71 observations.

A minimum of 71 observations must fall inside the interval (20, 40).

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The value of k for the expression, 3 (2− k) = −3k + 2, does not exist.

According to the question,

We have the following expression:

3 (2− k) = −3k + 2

Now, we will multiply 3 into the bracket:

6-3k = -3k+2

Now, moving -3k from the left hand side to the right hand side will result in the change of the sign from minus to plus:

6-3k+3k = 2

Now, 3k will get subtracted from 3k. So, we do not have any variable left for this equation.

Hence, the value of k  for the expression, 3 (2− k) = −3k + 2, does not exist.

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The value of the expression when a=2 and b=7 is 41.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

From the information, the expression given is 3a + 5b and we want to find the value of the expression when a=2 and b=7.

This will be illustrated thus:

= 3a + 5b

= 3(2) + 5(7)

= 6 + 35

= 41

The value is 41.

The complete question is given below.

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Complete question

The expression given is 3a + 5b. Find the value of the expression when a=2 and b=7

The equation D show the multiplication property of inequality if n+4 =11

What is inequality?

inequality, In mathematics if a statement of an order relationship—greater or greater than or equal to, less than, or less than or equal between two number or algebraic expressions.

An inequality show the relationship between two values in an algebraic equations that are not equal.

Sol-

If n+4 =11

Then by applying the product rule -

(n+4)×2 =11×2

So the correct option is D.

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