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

An element with mass 420 grams decays by 11.8% per minute. the amount of the element remaining after 16 minutes is 56.3 grams

This is a type of function that are of 3 main parts

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so forth.

Considering the given problem,  

the starting = 420 grams

the base = 1 - r = 1 - 11.8% = 1 - 0.118 = 0.882

the exponents = 16

amount remaining = 420 (0.882)^16

= 56.330895

= 56.3 to the nearest tenths

the amount left is 56.3 g

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the proportionality constant is 20 and in 8 ours it will cover 160 miles.

What is proportional relationship?

When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the term used to describe that constant.

The slope of he given graph will be (30-10)/(2-1) = 20

So here the proportionality constant is 20.

we can write y = 20x

This means in 8 ours it will cover 8*20 = 160 miles.

Hence, the proportionality constant is 20 and in 8 ours it will cover 160 miles.

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Calculating the cost of 4.25 kilogram(kg) is £2.38, by multiplying it by 4.25 kg by 1 kg.

Costs are the expenses incurred in the manufacture, marketing, or preparation of a good or asset for regular use. In other terms, it's the cost incurred to produce a good, buy inventories, sell goods, or prepare equipment for use in a commercial activity.

Given,

2.5 kg cost  £1.40 i.e,

2.5 kg = £1.40

For 1 kg= [tex]\frac{1.40}{2.5}[/tex]

= £0.56

To find the cost of 4.25 kg:

Then,

1 kg = £0.56

4.25 kg = 0.56 x 4.25

= £2.38

£2.38 is the cost of 4.25kg after calculating it.

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Therefore ,we would reject the null hypothesis H0: = 3 in favor of the alternative hypothesis HA: 3. The graph's rejection zone is highlighted in red for visual appeal.

The field of mathematics known as probability studies numerical descriptions of the likelihood of an event occurring or of a statement being true. A number between 0 and 1 is the probabilities of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Here,

Two-Tailed

For the two-tailed test H0, the following two values are critical: = 3 against HA: 3 — one for each tail, with the left tail being denoted by -t(/2, n - 1) and the right tail being denoted by t(/2, n - 1). The t-values t(/2, n - 1) and -t(/2, n - 1) are those where the probability to the left of them is /2 and the likelihood to the right is /2, respectively. It is possible to demonstrate the crucial values -t0.025,14 is -2.1448 and t0.025,14 is 2.1448, respectively, using statistical software or a t-table. This means that if the test statistic t* is less than -2.1448 or more than 2.1448, we would reject the null hypothesis H0: = 3 in favor of the alternative hypothesis HA: 3. The graph's rejection zone is highlighted in red for visual appeal.

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Answer:

2 13/50

Step-by-step explanation:

gogle

On solving the expression 2 + (4/5) - (3/20), we get 53/20.

Given is the expression -

2 + (4/5) - (3/20)

The given expression is -

2 + (4/5) - (3/20)

Now, solving further, we get -

2 + (4/5) - (3/20)

2 + 4/5 - 3/20

(40 + 16 - 3)/20

53/20

Therefore, the given expression 2 + (4/5) - (3/20) is equivalent to 53/20.

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The 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

It is given to us that -

Numbers of items produced per hour by machine a and by machine b are normally distributed

There is a standard deviation of 8.4 items for machine a and a standard deviation of 11.3 items for machine b

The mean hourly amount produced by machine a for a random sample of 40 hours was 130 units

The mean hourly amount produced by machine b for a random sample of 36 hours was 120 units

We have to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines.

Let us say that -

x = Number of units of machine a

y = Number of units of machine b

According to the given information, we have

Number of units of machine a = x⁻ = 130

Standard deviation of machine a = σx = 8.4

Number of hours of machine a = [tex]n_{x}[/tex] = 40

Similarly,

Number of units of machine b = y⁻ = 120

Standard deviation of machine b = σy = 11.3

Number of hours of machine a = [tex]n_{y}[/tex] = 36

We know that mean of the differences can be find out as -

d⁻ = x⁻ - y⁻

=> d⁻ = 130 - 120

=> d⁻ = 10

In order to find out the 95% confidence interval for the difference in mean parts produced per hour by these two machines, we have to make use of the formula mentioned below -

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]  ---- (1)

From the z-score table, for a 95% confidence interval, we have -

α = 0.05

α/2 = 0.025

=> F(z) = 1 - α/2 = 1 - 0.025 = 0.975

For a z-distribution function of 0.975, we have -

[tex]z_{a/2}[/tex] = 1.96

Substituting all the values in equation (1), we have

d⁻ - [tex]z_{a/2}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])] < μd < d⁻ + [tex]z_{a/z}[/tex] √[(σx²/ [tex]n_{x}[/tex]) + (σy²/ [tex]n_{y}[/tex])]

=> [tex]10-1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-1.96\sqrt{1.764+3.54 }[/tex] < μd < [tex]10+1.96\sqrt{\frac{8.4^{2} }{40} +\frac{11.3^{2} }{36} }[/tex]

=> [tex]10-(1.96 * 2.303)[/tex] < μd < [tex]10+(1.96 * 2.303)[/tex]

=> 10 - 4.516 < μd < 10 + 4.516

=> 5.483 < μd < 14.516

=> μd = 10 ± 4.516

Thus, the 95% confidence interval for the difference in mean parts produced per hour by these two machines is given as 10 ± 4.516.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-100\% + 0.58}\\\\\mathsf{= \dfrac{-100}{100} + \dfrac{0.58}{1}}\\\\\mathsf{= -100 \div 100 + 0.58 \div 1}\\\\\mathsf{= -1 + 0.58}\\\\\mathsf{= -0.42}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{-0.42}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

√100000 = 100√10 ≈ 316.227766

10 =2⋅5 has no more square factors, so √10 cannot be simplified further.

So it may be simply

√100000 = 100√10

Unless you want a decimal approximation or an expression using a continued fraction...

Irrational Number

An irrational number is a type of real number which cannot be represented as a simple fraction. It cannot be expressed in the form of a ratio. If N is irrational, then N is not equal to p/q where p and q are integers and q is not equal to 0.

√10 is an irrational number. It cannot be expressed as a fraction. Its decimal representation does not terminate or recur.

If  use a calculator, it will  an approximation like:

√10 ≈ 3.16227766

Then

√100000 = 100√10 ≈ 316.227766

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Answer: QB≈4.24

Step-by-step explanation:

Q(1,0)    B(-2,-3)   QB=?

[tex]\boxed{L=\sqrt{(x_2-x_1)+(y_2-y_1)^2} }\\\\x_1=1\ \ \ \ x_2=-2\ \ \ \ y_1=0\ \ \ \ y_2=-3[/tex]

Hence,

[tex]QB=\sqrt{(-2-1)^2+(-3-0)^2} \\\\QB=\sqrt{(-3)^2+(-3)^2} \\\\QB=\sqrt{9+9} \\\\QB=\sqrt{18} \\\\QB=\sqrt{9(2)} \\\\QB=\sqrt{3^2(2)} \\\\QB=3\sqrt{2} \\\\QB\approx4.24[/tex]

Option (A) ΔDAB ~ΔDAC this similarity statement would be true for the figure.

We know that two triangles are similar if they have the same ratio of corresponding sides and equal of corresponding angles.

The fundamental theorem of similarity states that a line segment splits of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Similar triangles are the triangles that look similar to each other but their sizes might not be exactly the same. Two triangles will be similar if the angles are equal and sides are in the same ratio or proportion. Similar triangles may have different individual lengths of the sides of triangles but their angles must be equal and their corresponding ratio of the length of the sides must be the same.

In Δ DAB and Δ DAC

DA = DA

∠D = ∠D

and AB proportional to AC.

Therefore Δ DAB ~ Δ DAC would be true for the figure.

Given question doesn't provide figure. I have attached figure of triangle to complete the question.

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The amount of loss that the insurance company will pay is $70000

Deductible plus the amount of coinsurance equals the out-of-pocket maximum.

Determine the $1,000 deductible that the insured is required to pay.

Calculate the coinsurance payment due from the insured: 20% of $5,000 equals $1,000.

The coinsurance penalty is calculated using the straightforward formula: the loss multiplied by the amount of insurance that should have been in place, less any deductible, equals the amount that was actually paid.

The following covered losses are subject to the coinsurance provision: Property value: $200,000; policy limit: $140,000; coinsurance: 80%; loss: $100,000; deductible: $250; all other numbers: $200,000; etc.

The insured only had $140,000 when they should have had $160,000 (200,000 x.80).

The coverage will cover the deductible plus $87,500. (140,000/160,000

=.875; $100,000 x .875

= $87,500; $87,500 - $250

= $77,250)

Stop Limit/Value =%, Loss Amount x% = $ Amount Policy Would Pay (-) minus $ Deductible = $ Covered Loss Amount

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The result of the expression is 60.

The given expression can be solved by applying the principle of BODMAS.

BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. The BODMAS is used to explain the order of operation of a mathematical expression.

This indicates that numerous operator expressions must only be spelled out in this order, from left to right. We begin by resolving the brackets, then move on to powers or roots, division or multiplication (depending on which comes first from the left side of the expression), and lastly subtraction or addition (depending on which comes on the left side).

Given, 50+20/10*5 = 50+2*5=50+10=60

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The probability that either a or b occurs is 0.7.

Given :

event  a has a probability of 0.5 , and event b has a probability of 0.4. if a and b are independent events.

P ( a ) = 0.5

P ( b ) = 0.4

we know that,

P ( a or b ) = P ( a ) + P ( b ) - P ( a and b )

if a and b are both independent

P ( a and b ) = P ( a ) * P ( b )

substitute we get

P ( a or b ) = 0.5 + 0.4 - 0.5 * 0.4

= 0.9 - 0.2

= 0.7

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Answer: y = 4x + 1

Step-by-step explanation: Simple...

You have your equation... y=mx+b

You are given a coordinate. That is your x and y, and "m" is given already, and it's your slope.

First, you plug them in. You are solving for the unknown y-intercept or the "b".

5=4(1)+b

Then, you solve!

5=4+b

1=b

Parallel lines have the same slope, so the equation would be...

y=4x+1

Answer:

To put the equation in standard form, we need to get all the terms with variables on one side of the equation and all the constants on the other side. We can start by moving the 4/3 to the right side of the equation:

Y - 2/3 = 4/3(x + 2)

Y = 4/3(x + 2) + 2/3

Next, we can distribute the 4/3 on the right side of the equation to get:

Y = (4/3)x + (4/3)2 + 2/3

Y = (4/3)x + (8/3) + 2/3

Finally, we can combine like terms to get:

Y = (4/3)x + (10/3)

This is the standard form of the equation.

Answer -3y+4x=-10

Step-by-step explanation:

Answer:

0.692

Step-by-step explanation:

Given: The computer that controls a bank's automatic teller machine crashes a mean of 0.5 times per day.

Mean per day = 0.5

Mean per 7 day = 7*0.5 = 3.5

X = Number of times the computer will crash

We have to find:

P( the computer will crash more than 1 time in any seven-day week) =?

P(x >1) = ?

P(X > 1) =1- P(X < or = 1)

P(X < or = 1) = 0.320847

P(X < or = 1) = 0.3208

P(x > 1) = 0.6792

So, the answer is 0.6792

1. Linear pair theorem

2. Substitution property of equality

3. Subtraction property of equality

4. Definition of congruence

The given results can be proved by the linear pair property of angles on a straight lines.

The linear pair property can be defined as the sum of all the angles on the one side of a straight line is equal to 180°.

In the given diagram the following data is given,

The angles ∠DEH and ∠DEF are on the straight line HEF.

And, the angles ∠DEF and ∠FEG are on the straight line DEG.

As per the linear property of angles, it can be written as,

m∠DEH + m∠DEF = 180°.

And,  m∠DEF + m∠FEG = 180°.

Which implies that m∠DEH + m∠DEF = m∠DEF + m∠FEG

Subtract the common terms from both sides to get,

m∠DEH + m∠DEF - m∠DEF = m∠DEF + m∠FEG - m∠DEF

⇒ m∠DEH = m∠FEG

⇒ ∠DEH ≅ ∠FEG

This is also known as the property of vertically opposite angles.

Hence, the given result m∠DEH = m∠FEG is proved by the linear pair property.

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Answer: 45 dogs will eat 135 pounds of dog food.

Step-by-step explanation:

The amount of food required for 45 dogs in a week will be equal to 135 pounds.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Total number of dogs = 9

Amount of food eaten by dogs in a week = 27 pounds

Now, the number of dogs is 45.

Let the amount of food eaten by 45 dogs in a week is x.

So,

x = (27 × 45)/9

x = 1215/9

x = 135 Pounds.

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Answer:

Jeff is Incorrect

Step-by-step explanation:

If x ≤ 1/2, the value will either be 2 or less than 2.

x = 1/2 =>  2(1/2)+1 = 2

x = 0 =>  2(0)+1 = 1

x = -1 =>  2(-1)+1 = 0

Hugo will buy car B.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Car A travels 702 miles on 12 gallons of gasoline.

And, Car B travels 873 miles on 15 gallons of gasoline.

Now,

Since, Car A travels 702 miles on 12 gallons of gasoline.

And, Car B travels 873 miles on 15 gallons of gasoline.

Hence, The distance of car A for travels in per gasoline = 702 / 12

                                                                                      = 58.5 miles

And, The distance of car B for travels in per gasoline = 873 / 15

                                                                                  = 56.2 miles

Since, Hugo wants to buy a car with lower fuel consumption.

Clearly, The car B consume lower fuel.

Hence, Hugo will buy car B.

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The answer of the provided question is  the addition property of equality and then the division property of equality

Regardless of the sequence in which the numbers are added, the total of any two or more numbers is always the same. This characteristic may be expressed in the formula A + B = B + A. For instance, 2 + 4 Equals 4 + 2 = 6. As a result, both sets add up to 6, therefore 2 + 4 = 4 + 2.

We have multiplied both sides of the equation by 5 to move from Step 1 to Step 2:

[tex]-3x -5 +5 = 13 +5\\ -3x = 18[/tex]

We have divided both sides of the equation by -3 to go from Step 2 to Step 3:

[tex]-3x/-3 = 18/-3\\ x = -6[/tex]

These procedures can be categorized as...

first the equality's addition property, then its division property

However, since multiplication and division are the same thing, but with reciprocal numbers, and since addition and subtraction are the same thing, but with opposite numbers, any of the above answers may theoretically be right.

(adjust 5, divide by -3) = (adjust 5, multiply by -1/3)

(subtract 5 and divide by 3) equals (subtract 5 and multiply by 1/3).

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Answer:

Corresponding angels:

a,f

h,b

e,d

c,g

y = 80  Vertical angles are congruent

x = 50 Sum of the interior angles of a triangle is 180

180 - 80 -50 = 50

Step-by-step explanation:

y = 25x + 263 this equation represents how much money she will have, including her saving.

What is the linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The saved amount of $263 by Jenna,

and also she earns $25 per day

if x represents the number of days she works,

and let's take y as the total amount she will have.

Then the equation becomes:
y = 25x + 263

Hence, y = 25x + 263 this equation represents how much money she will have, including her saving.

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The equation of line perpendicular to the given line is,

[tex]y = \frac{5}{2}x - 13[/tex].

What is slope point form of the line?

The general form of a linear equation is y - y1 = m(x - x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Consider the given equation of line,

[tex]y = -\frac{2}{5}x - 1[/tex]

Compare it with y = mx + c

where m is the slope.

⇒ Slope of the line is -2/5.

We have to find the equation of line perpendicular to the given line.

Since the slope of the perpendicular line is negative reciprocal of the slope of given line.

So, the slope of perpendicular line is [tex]-\frac{1}{(\frac{2}{5}) } = 5/2[/tex].

The point passes through (2, -8).

Now consider, the point slope form of the line

[tex]y-y_1 = m(x-x_1)\\[/tex]

Plug [tex](x_1, y_1) = (2, -8) , m = \frac{5}{2}[/tex] in the above equation.

⇒

[tex]y - (-8) = \frac{5}{2}(x-2)\\ y+8 = \frac{5}{2}x - 5\\ y = \frac{5}{2}x-5-8\\ y = \frac{5}{2}x - 13[/tex]

Hence, the equation of line perpendicular to the given line is,

[tex]y = \frac{5}{2}x - 13[/tex].

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The slope of line p is 3, and the slope of line q is -3

From the question, we have the points that can be used in our computation:

Line p

From the line p, we have the following ordered pairs

(2, 2) and (0, -4)

Line q

From the line p, we have the following ordered pairs

(0, 2) and (2, -4)

Rewrite the above points properly

So, we have the following ordered pairs

Line p, (x, y) = (2, 2) and (0, -4)

Line q, (x, y) = (0, 2) and (2, -4)

The slopes of the lines are then calculated using the following slope equation

slope = (y₂ - y₁)/(x₂ - x₁)

Substitute the known values in the above equation

So, we have the following equation

Slope of line p = (-4 - 2)/(0 - 2)

Evaluate

Slope of line p = 3

Slope of line q = (-4 - 2)/(2 - 0)

Evaluate

Slope of line q = -3

Hence, the slopes are 3 and -3, respectively

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The addition is 5x - 2. We can find out our answer using simple arithmetic calculations.

What are arithmetic calculations?

Arithmetic calculations are mathematical operations used to solve equations and perform numerical calculations. They include addition, subtraction, multiplication, and division. Arithmetic is a fundamental part of mathematics, and it is an important part of everyday life. Arithmetic is used to solve problems in a variety of fields, such as engineering, finance, and science. It is also used in everyday tasks such as grocery shopping and budgeting. Arithmetic calculations are essential for most people and can help them understand and solve a variety of problems. By mastering basic arithmetic calculations, people can make more informed decisions and better understand the world around them.

In algebraic expressions ,

same variables are added together and constants together.

In given equation,

2x and 3x are added i.e. 5x

and 5 and -7 are added  i.e. -2

So, the equation is 5x-2.

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Answer:

Monthly cost with 11 slices: $28.75

Monthly cost with x slices: C = 15 + x * 1.25

Step-by-step explanation:

If Austin bought 11 slices of pizza this month, he would have to pay the pizza shop a total of $15 + 11 * $1.25 = 28.75. This includes the cost of the membership fee of $15 and the cost of the 11 slices of pizza at the discounted price of $1.25 per slice.

The monthly cost for x slices of pizza can be represented by the equation C = 15 + x * 1.25, where C is the total cost and x is the number of slices of pizza purchased. This equation shows that the total monthly cost is equal to the membership fee of $15 plus the cost of the x slices of pizza at the discounted price of $1.25 per slice.

Answer:

n=0  or  n=6

Step-by-step explanation:

n² = 6n

n² - 6n = 0

n(n - 6) = 0

n = 0;  or  n - 6 = 0 => n = 6

Linear equations are equations with a leading degree of 1. This shows that there is no solution since 4 =7 is a false statement .

What are linear equations ?

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Solving linear equation

Linear equations are equations with a leading degree of 1. Given the linear equation

Given

13+4x-9=7x+7-3x

Simplify

4 + 4x = 4x + 7

Collect the like terms

4x - 4x = 7 - 4

0x = 3

This shows that there is no solution since 4 =7 is a false statement

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