Five More Than One Third Of A Number Is Negative 2 What Is The Number?

The amount of candle burn after 6 hours is 4.95 inches.

What is the total amount?

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total.

Here, we have

Given that the 9-inch candle burns in 6 hours.

We know that we first have to calculate how 1 hour how much candles will burn.

Candle burn in 1 hour is :

= 9 / 10

= 0.9 inch

Now,

To find out how far the candle burnt after 6 hours we need to multiply the part of the candle burned by one hour by 11/2 hours.

= 11/2 × 0.9

= 4.95 inches

Hence, the amount of candle burn after 6 hours is 4.95 inches.

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The amounts in each mutual fund are $500 and $1800. By using a system of equations, the required values are evaluated.

It is given that, an investor invested $2300 in two mutual funds.

Consider the amount invested in two mutual funds as fund1 = x and fund2 = y.

So, we can write the equation for the total investment is

x + y = 2300 ...(1)

The percentage of profit earned from the fund1 = 6% = 0.06

The percentage of profit earned from the fund2 = 4% = 0.04

The total profit for the investor = $102

Then, the equation from this statement is

0.06x + 0.04y = 102 ...(2)

Then the system of equations is

x + y = 2300 ...(1)

0.06x + 0.04y = 102 ...(2)

Applying the substitution method to solve the obtained system of equations.

So, from (1), we can write x = 2300 - y

Then, equation (2) becomes

0.06(2300 - y) + 0.04y = 102

⇒ 6(2300 - y) + 4y = 10200

⇒ 13800 - 6y + 4y = 10200

⇒ 13800 - 2y = 10200

⇒ 2y = 13800 - 10200 = 3600

∴ y = 3600/2 = $1800

So, the value of x is x = 2300 - 1800 = $500

Thus, the amount of investment in two mutual funds is $500 and $1800.

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In Herrnstein's matching equation, the letters and numbers to the left of the equals sign refer to behaviour.

THE MATCHING LAW

Herrnstein's Experiment Herrnstein (1961) conducted an experiment with pigeons in a room with two response buttons, red and white. Each key was assigned its own VI gain schedule. For example, under one condition, the left button pick was boosted on a VI 135 second schedule, and the right button pick was boosted on a VI 270 second schedule.

After the birds have learned as much as possible about this electoral situation, how do they distribute their responses? We trained them for days and then measured their reactions. As is often the case with VI schedules, birds returned many responses for each reinforcer received. Most interesting, however, is that in this condition, where two-thirds of the reinforcers came from the left button, the birds performed about two-thirds of the responses with the left button. That is, the proportion of left button responses equaled or matched the proportion of reinforcers delivered by the left button. In another condition, two birds received only about 15% of reinforcers from the left key and responded about 15% to that key.

Based on these results, Herrnstein proposed the following general principle for individual behavior when presented with alternative sequences. So, what you think makes sense rather than other options available at that particular moment.

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Answer:

it travels 25 nautical miles per hour

Step-by-step explanation:

150 nautical miles in 6 hours

150 / 6 = 25

25 nautical miles per hour

Answer: I think it is 25 nautical miles in one hour

Step-by-step explanation:

all you need to do is 150 divided by 6 to get one hour and that is 25 (this might be wrong)

The percentage of Valeria's action figure collection is 47% which she keeps on her wall.

The percentage is defined as a ratio expressed as a fraction of 100.

To find the percentage of Valeria's action figure collection that she keeps on her wall, we need to divide the number of action figures she keeps on her wall by the total number of action figures in her collection and then multiply by 100%.

Since Valeria has a collection of 500 action figures and she keeps 235 of them on her wall, the percentage of her collection that she keeps on her wall is :

⇒ 235 / 500 × 100% = 47%.

Thus, the percentage of Valeria's action figure collection is 47%

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A. y = - (4/3)x + 4.

y = - (4/3)x - 1.

No solution.

B. y = 4x - 5.

y = - 2x + 7.

one solution.

C. 2x + 3y = 8

4x + 6y = 17.

No solution.

D. y = 5x - 15.

y = 5(x - 3).

Infinitely many solutions.

Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.

A system with two or more than two equations has a solution only when they have a common intersection point.

We'll graph each system of equations, If they intersect at one point they have one solution, if they are parallel to each other they have no solution and if they are coinciding with each other they have infinitely many solutions.

y = - (4/3)x + 4.

y = - (4/3)x - 1.

These are parallel lines no solution.

y = 4x - 5.

y = - 2x + 7.

These lines intersect at (2, 3) one solution.

2x + 3y = 8

4x + 6y = 17.

They are parallel to each other.

y = 5x - 15.

y = 5(x - 3).

These are coinciding lines if we distribute the terms hence infinitely many solutions.

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The solution to each of the given algebraic expressions are;

1) 2n - 2 = 10

2) 12n - 1 = 17

3) 4 * 9 = 36

4) 23 - 8 = 15

5) (3 * 7) + 1 = 22

6) ¹/₆ * 42 = 7

7) 3n - 6 = 70

8) y - 2 = 9

9) x = 5 * 12

10) -48 = -4 * 12

11) -32/-8 = 4.

12) (15 - 3)n = 2

13) (5 + 8)n = 42

14) (12 + 6)/2 = 9

15) -4 = -2(5 - 3)

16) x + (x + 1) = 25

17) (x) + (x + 1) = -3

18) 11 - x = -1

1) Two less than twice a number is equal to 10 is expressed as;

2n - 2 = 10

2) 17 is one more than twice a number;

2n - 1 = 17

3) Four times 9 is 36;

4 * 9 = 36

4) Eight less than 23 is fifteen;

23 - 8 = 15

5) One more than 3 times 7 is 22;

(3 * 7) + 1 = 22

6) One sixth of forty two is seven;

¹/₆ * 42 = 7

7) Six less than 3 times a number is equal to seventy;

3n - 6 = 70

8) Two dollars off the regular price of a calculator is $9;

y - 2 = 9

9) A number is equal to five times 12;

x = 5 * 12

10) Negative 4 is a product of the opposite of four and 12;

-48 = -4 * 12

11) Four is the quotient of -32 and -8;

-32/-8 = 4.

12) When 15 minus 3 is multiplied by a number, the product is 2;

(15 - 3)n = 2

13) A number times the sum of five and 8 is 42;

(5 + 8)n = 42

14) 9 is the quotient when 12 + 6 is divided by 2;

(12 + 6)/2 = 9

15) -4 = -2(5 - 3)

16) x + (x + 1) = 25

17) (x) + (x + 1) = -3

18) 11 - x = -1

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Using a system of linear equations the number of quarter and dime present are 1 and 8 respectively

The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.

Let:

1 quarter = $0.25

1 dime = $0.1

A) An equation for the number of coins

q + d = 9 ...eq(i)

B) The amount of money can be represented as;

0.25q + 0.1d = 1.05 ..eq(ii)

C) The number of dimes; solving equation (i) and (ii)

q + d = 9 ..eq(i)

0.25q + 0.1d = 1.05 ...eq(ii)

q = 1, d = 8

There are 8 dimes

D) There is 1 quarter in the money

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Answer:

chronological

or +1 each number up

Step-by-step explanation:

The middle number on the 50th row is 891.5.

The nth row is 18n - 17.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

We see that there are 18 numbers in each row.

The numbers are consecutive natural numbers.

Now,

We can see that,

The first number of each row is 1.

The first number of the second row is 19.

The first number of the third row is 37.

The first number in each row can form a series.

1, 19, 37,....

This series is an arithmetic sequence.

First term = 1

Common difference = 18

The nth term is a + (n - 1)d.

50th term.

= 1 + (50 - 1)18

= 1 + 49 x 18

= 1 + 882

= 883

This means,

The 50th row will have the following series.

883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900.

The middle number is the midpoint of 891 and 892.

= 891.5

The nth row.

= 1 + (n - 1)18

= 1 + 18n - 18

= 18n - 17

Thus,

The middle number on the 50th row is 891.5.

The nth row is 18n - 17.

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The measure of angle JIL is 59°.

We are given that;

Ray IL bisects angle HIJ, we know that the measure of angle HIL is equal to the measure of angle JIL.

Using the given expressions for these angles, we can write:

m∠HIL = m∠JIL

(6x − 7)° = (5x + 4)°

To solve for x, we can subtract 5x from both sides and add 7 to both sides:

x − 7 = 4

x = 11

Now that we have the value of x, we can plug it into the expression for m∠JIL and simplify:

m∠JIL = (5x + 4)°

m∠JIL = (5 × 11 + 4)°

m∠JIL = (55 + 4)°

m∠JIL = 59°

Therefore, by the angle the answer will be 59°.

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The letters of points  below the graph of  y = - 1/3x are  B, C, F, H, J.

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The information about your sample data is summarized and provided by summary statistics.It provides information regarding the values in your data set.This covers the distribution of the mean and the skewness of your data.

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The classification model is used to define the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.

Percentage:

In math,  number or ratio that can be expressed as a fraction of 100 refers the percentage.

Given,

Here we have a dollar general sends out a $5 off coupon to its email subscribers.

And we need to find the percentage of customers between 20 and 30 years of age who lived within 5 miles of the store used the coupon.

Then the model used to define the this type of situation is refers as the classification model, because in this model, we have classify the given group of people based on the constraint.

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Answer:

fourth option

Step-by-step explanation:

to prove that HJ is parallel to KL , then KL divides the sides HG and JG proportionally , that is

[tex]\frac{GK}{HK}[/tex] = [tex]\frac{GL}{LJ}[/tex]

A line plot would be the best data display to highlight every height.

A line plot, also known as a dot plot, is a type of graph that displays data as a series of dots on a number line. Each dot represents a single data point, and the dots are placed above the corresponding value on the number line.

Line plots are useful for displaying small data sets because they provide a simple visual representation of the data. They can quickly show the range of values in the data set, as well as any outliers or clusters of data points. Line plots are commonly used in elementary and middle school classrooms to teach basic data analysis and graphing skills. They are also used in scientific research and statistical analysis to visualize small data sets and identify patterns in the data.

A line plot, also known as a dot plot, displays the data as points on a number line. Each data point is represented by a dot, making it easy to see every height in the data set. Here is an example of a line plot for the given data:

A display that will highlight every height would be a line plot, which would show each individual height as a dot along a number line.

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Answer:

  C.  Yes, SAS

Step-by-step explanation:

You want to know the congruence theorem that lets you say ∆ACD≅∆CAB, given that AB=CD and AB║CD.

The triangles are congruent if an angle or side can be shown congruent, in addition to at least one angle and at least one side.

Here, the sides AB and CD are shown congruent. The side AC is congruent to itself, so we only need the angle(s) between them to show the triangles are congruent.

The Alternate Interior Angles theorem tells you that transversal AC creates congruent angles CAB and ACD with respect to the parallel lines AB and CD.

Hence we can show triangle ACD and CAB are congruent by the SAS congruence theorem.

Yes, The triangle is congruent by Angle - Side - Angle  congruence theorem.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB || CD

Now,

In figure,

⇒ AB || CD

So, In triangle ACD and triangle CAB;

⇒ AB || CD

So, By definition of alternate angles,

⇒ ∠ BAC = ∠ DCA

And, ∠ DAC = ∠ ACB

Here, Line AC is common in both tringle.

Hence, By Angle - Side - Angle  congruence theorem,

⇒ Δ ACD ≅ Δ CAB

Thus, The triangle is congruent by Angle - Side - Angle  congruence theorem.

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The partial fraction decomposition of the expression with repeated factors is given as follows:

[tex]\frac{1}{x} - \frac{2}{x + 4} - \frac{1}{(x + 4)^2}[/tex]

The function in this problem is defined as follows:

(-x² - x - 16)/(x³ + 8x² + 16x).

The decomposition is made considering the factors of the denominator, which are obtained as follows:

x³ + 8x² + 16x = 0.

x(x² + 8x + 16) = 9

x(x + 4)² = 0.

Hence the denominators are as follows:

Then the decomposition is of:

A/x + B/(x + 4) + C/(x + 4)²

Then the expression will be given as follows:

[tex]\frac{A(x + 4)^2 + Bx(x + 4) + Cx}{x^3 + 8x^2 + 16x} = \frac{-x^2-x+16}{x^3 + 8x^2 + 16x}[/tex]

Then the system of equations, equaling the numerators, is given as follows:

Hence:

16A = 16

A = 1.

B = -1 - A

B = -2.

C = -1 - 8A - 4B

C = -1.

Meaning that the third option is correct.

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a) The mean of the sampling distribution of p is of 0.2.

b) The standard deviation of the sampling distribution of p is of: 0.0231, which is the amount that the sample proportions may differ from 0.2.

c) The shape of the sampling distribution of p is approximately normal.

The sampling distribution of p is defined according to the Central Limit Theorem, which states that the sampling distribution of a proportion p in a sample of size n has:

The parameters for this problem are given as follows:

p = 0.2, n = 300.

The 10% condition is given as follows:

Then the standard error of the sampling distribution of p is calculated as follows:

[tex]s = \sqrt{\frac{0.2(0.8)}{300}} = 0.0231[/tex]

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Answer:

Look below

Step-by-step explanation:

There are several methods for solving a system of nonlinear equations, which are a set of equations that cannot be solved using linear methods. Some of these methods include:

Graphical methods: These involve plotting the equations on a graph and finding the points where they intersect, which represent the solutions to the system.

Substitution method: This involves solving one of the equations for one variable in terms of the other, and substituting this expression into the other equation. The resulting equation is then solved for the remaining variable.

Elimination method: This involves adding or subtracting the equations in such a way as to eliminate one of the variables. The resulting equation is then solved for the remaining variable.

Newton's method: This is an iterative method that involves starting with an initial guess for the solution and then using an iterative process to improve the guess until it converges to the true solution.

Broyden's method: This is a variant of Newton's method that involves using a Jacobian matrix to calculate the updates to the solution at each iteration.

To find the composition of two functions f(g(x)) and g(f(x)), you need to apply the outer function to the result of the inner function. For example, if f(x) = x^2 and g(x) = x + 1, then the composition f(g(x)) would be equal to f(x+1) = (x+1)^2, and the composition g(f(x)) would be equal to g(x^2) = x^2 + 1.

To determine if a function is invertible, you need to check if it is one-to-one. A function is one-to-one if every element in the range corresponds to exactly one element in the domain. If a function is one-to-one, it has an inverse function, which is denoted by f^(-1)(x). To find the inverse function, you can solve the original function for the variable in the range and express the variable in the domain in terms of the range. For example, if f(x) = x^2 + 1, then f^(-1)(x) would be the inverse function, which can be found by solving f(x) for x to get x = sqrt(x-1).

The difference quotient is a mathematical concept that is used to approximate the slope of a curve at a particular point. It is defined as the difference between the y-values of two points on the curve, divided by the difference between the x-values of those points. The difference quotient can be written as:

(f(x + h) - f(x))/h

where f is the function, x is the x-value of the point at which the slope is being approximated, and h is a small value that is used to calculate the approximation. To calculate the difference quotient, you can plug the values of f, x, and h into the formula and perform the calculations.

The limit as a definite integral on the interval [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π , 4π] is [tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex].

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

[tex]$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$[/tex]

substitute the values in the above equation, we get

= [tex]$\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$[/tex] on [2π, 4π],

simplifying the above equation

[tex]$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$[/tex]

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From the statistical point of view , the type I error was made , the correct option is (c) .

In the question ,

it is given that ,

the machine was working well, but on the basis of our statistical hypothesis test, it was concluded that the machine was under-filling or over-filling and hence it was shut down .

but after examination by the engineers , there was nothing wrong with the filling machine .

that means that the null hypothesis was rejected when it was actually true .

which refers to the type I error .

Therefore , the correct option is (c) A Type I error was made.  

The given question is incomplete , the complete question is

The result of a hypothesis test is used to prevent a machine from under-filling or overfilling quart size bottles of olive oil. on the basis of sample, the hypothesis is rejected and the machine is shut down for inspection. a thorough examination reveals to engineers there is nothing wrong with the filling machine. from a statistical point of view:

(a) correct decision was made.

(b) Both, a Type I and a Type II errors were made.

(c) A Type I error was made.

(d) A Type II error was made.

(e) None of these answers.

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An approximate 95% confidence interval for the difference in the mean tooth damage is  (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

For sweetened samples

The value of n = 10

The mean of the samples = 6.14

The standard deviation of the sample = 5.0

For unsweetened samples

The value of n = 15

The mean of  the sample = 5.20

The standard deviation of the sample = 15.0

We have to assume that necessary conditions for inference are met

The confidence interval = 95%

The equation will be

(6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

Therefore, the difference in the mean tooth damage is (6.41 - 5.20) ± 2.26[tex]\sqrt{\frac{25}{10}+\frac{225}{15} }[/tex]

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Answer:

I'm sorry I don't know

Step-by-step explanation:

........

There are 1260 eight-digit numbers that have 2 once, 3 twice, and 4 thrice.

There are 10 digits in the number system from 0 to 9.

Let the 8-digit number be represented by

_ _ _ _ _ _ _ _

Here the numbers will have a single 2, a doublet of 3, and a triplet of 4 hence we get

2 3 3 4 4 4 _ _

Now for the last 2 numbers, we have 0, 1, 5, 6, 7,  8, 9. Therefore the last 2 digits can be chosen in ⁷C₂ ways.

= 7!/(2 X 5!)

= 21 ways

There are 6 fixed numbers which can e arranged in 6! ways. Since there are numbers repeated twice and thrice, we can arrange them in

6!/(2! X 3!)

= 6 X 5 X 2

= 60 ways.

Therefore we get

60 X 21 numbers

= 1260 numbers.

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Answer: x=1

Step-by-step explanation:

Assume that "log" is the base-10 logarithm

log (2x)+log (5)=1

log 10{10}(2x)+log (5)=1

Assume that "log" is the base-10 logarithm

\log 10{10}(2x)+\log (5)=1

\log 10{10}(2x)+\log10{10}(5)=1

Apply the logarithm product identity

\log 10{10}(2x)+\log 10{10}(5)=1

log 10{10}(2x x 5)}=1

A company has a monthly time series that regularly shows sales being higher in the summer months, this is an example of Seasonal Component  

A seasonal variation is a calendar-related and systematic effect. One example is an increase in water consumption during the summer due to warmer weather.

Other seasonal effects include trading day effects (the number of working or trading days in a given month varies from year to year, affecting the level of activity in that month) and moving holiday effects (the timing of holidays such as Easter varies, so the effects of the holiday will be experienced in different periods each year).

In the given question,

A company has a monthly time series that regularly shows sales being higher in the summer months,

This is an example of Seasonal variation in times series

As the Sales increases in every summer seasons

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Answer:

Step-by-step explanation:

8^2 = 64

+

4*11 = 44

-> 64 + 44 = 108

Therefore ,The marked point will now have the updated coordinates P' (2, 7).

When a figure is transferred from one area to another without altering its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Here,

On an X-Y coordinate plane, a figure is plotted.

When translating a figure 7 units to the down, we must provide the coordinates of the indicated point in the original figure

"(x, y)" = "(x + m, y + n)"

In response to the query, we have

The specified point's coordinates are: P (5,4).

The new coordinates of the indicated spot after this figure is translated 6 units to the right will be -

P'( 5,4- 7) = P'(5, -3) (5, -3)

As a result, the designated point's new coordinates are P' (5, -3)

The new coordinates of the marked point will be - P'(5, -3)

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Answer:

256

Step-by-step explanation:

((2*2)²)²

(((4)²)²)

(16)²

256