Combine like terms to create an equivalent expression.
-2.5\left(4x-3\right)−2.5(4x−3)

1. The expression can be simplified as follows: 4 × 5 – 32 × 2 ÷ 6 = 20 – 16 ÷ 6 = 20 – 2 = 18.

2. The expression can be simplified as follows: -2(-9 + 3) = -2(-6) = 12.

3. To solve this equation, we need to isolate the variable a. We can do this by dividing both sides of the equation by -13: -a/13 = 18. Dividing both sides of the equation by -13 gives us a = -18 * 13 = -234.

4. To solve this equation, we need to isolate the variable x. We can do this by moving all terms involving x to one side of the equation and all constants to the other side. This gives us: 7 = 5x + 3(x – 2). We can then distribute the 3 to get 7 = 5x + 3x – 6. Combining like terms, we get 7 = 8x – 6, which we can solve by adding 6 to both sides to get 13 = 8x. Dividing both sides of the equation by 8 gives us x = 13/8.

5. To solve this equation, we need to isolate the variable w. We can do this by moving all terms involving w to one side of the equation and all constants to the other side. This gives us: 11w + 2(3w - 1) = 15 w. We can then distribute the 2 to get 11w + 6w - 2 = 15w. Combining like terms, we get 17w - 2 = 15w, which we can solve by adding 2 to both sides to get 17w = 15w + 2. Subtracting 15w from both sides gives us 2w = 2, which we can solve by dividing both sides by 2 to get w = 1.

6. N' is the complement of the set N. This means that N' contains all elements that are not in the set N. Since the set N contains all factors of 18, N' will contain all natural numbers less than 20 that are not factors of 18. Some elements of N' are 1, 2, 4, 5, 7, 8, 11, 13, 14, 16, and 17.

7. The solution to the inequality 17 - 2a ≤ 29 is all values of a that satisfy the inequality. To find these values, we can first subtract 17 from both sides of the inequality to get -2a ≤ 12. Dividing both sides of the inequality by -2 gives us a ≥ -6. This means that the solution is the set of all values of a that are greater than or equal to -6. This solution can be represented on a number line

8.To solve the inequality 17 – 2a ≤ 29, we first need to isolate the variable on one side of the inequality. To do this, we need to subtract 17 from both sides, which gives us -2a ≤ 12. Dividing both sides by -2, we get a ≥ -6. To graph this inequality, we can use a number line. We would draw a solid line at -6 and shade the region to the right of the line, since a is greater than or equal to -6.

9. To solve the inequality 12c + 6 > 9c – 15, we first need to isolate the variable on one side of the inequality. To do this, we need to subtract 9c from both sides, which gives us 3c + 6 > -15. Next, we need to add 15 to both sides, which gives us 3c + 21 > 0. Finally, we can divide both sides by 3 to get c > -7. To graph this inequality, we can use a number line. We would draw a solid line at -7 and shade the region to the right of the line, since c is greater than -7.

The closure property of addition states that the sum of two whole numbers will always be a whole number.

A whole number is a set of all positive integers from 0 to infinity.  Now we all know that if we add two positive numbers up, the sum will either remain constant (if the number is 0) or be greater than both numbers. This means that the sum of two whole numbers has to be a whole number.

Example 1 If we add 0 and 45

0 + 45

= 45

We already know that 45 is a whole number.

Example 2- If we add 486 and 354

486 + 354

= 840

From the definition, we can say that 840 is a whole number.

This is the closure property.

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[tex]3^4x=9^3x+7[/tex]

Simplify:

[tex]81x=729x+7[/tex]

Subtract 729x from both sides:

[tex]81x-729x=729x+7-729x[/tex]

[tex]-648x=7[/tex]

Divide both sides by -648:

[tex]\dfrac{-648x}{-648} =\dfrac{7}{-648}[/tex]

[tex]\fbox{x = $\dfrac{-7}{-648}$}[/tex]

Answer:

y=-1.25x+7

Step-by-step explanation:

See the image

Answer:

$7,096.55

Step-by-step explanation:

[tex]\frac{1}{6}[/tex] = [tex]\frac{7}{42}[/tex]

[tex]\frac{1}{7}[/tex] = [tex]\frac{6}{42}[/tex]

[tex]\frac{6}{42}[/tex] + [tex]\frac{7}{42}[/tex] = [tex]\frac{13}{42}[/tex]  This Son A and Son B's portion

Son C must be [tex]\frac{42}{42}[/tex] - [tex]\frac{13}{42}[/tex] = [tex]\frac{29}{42}[/tex]

[tex]\frac{29}{42}[/tex] of some number is 29400

[tex]\frac{29}{42}[/tex] x = 29400  Multiple by sides  by [tex]\frac{42}{29}[/tex]

x = [tex]\frac{42}{29}[/tex] x 29400

x = 42579.31  Rounded to the nearest penny

This number is the total

42579.31 x 1/6 = 7096.55 Rounded to the nearest penny

There are 160 possible area codes can be created with this format.

A process determining the number of possible arrangements in a collection of items in which the order of the selection does not matter is called combination.

Given that, When three-digit telephone area codes were first put in place in the United States and Canada, the first number could be any digit from 2 through 9, the second number could only be 0 or 1, and the third number could be any digit from 0 through 9.

So, according to question,

The first digit has about 8 options

The second digit has about 2 options

The third digit has about 10 options

Therefore, the total possible code = 8×2×10=160.

Hence, 160 possible codes are there.

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Values that will satisfy the given inequality be 5,6 and 7.

What do you mean by natural number?

All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

Given inequality:

n > 4

Values that will satisfy the given inequality be 5,6 and 7.

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Answer:

y = 3/5x + 2

Step-by-step explanation:
Parallel lines have the same gradient, so

y = 3/5x + c

Put in your point (-5,-1):

(-1) = 3/5(-5) + c

-1 = -3 + c

-1 + 3 = c

2 = c

So

y = 3/5x + 2

The total urine patient/client has been measuring at home is 2.838 liters.

Given that,

the patient/client has been measuring urine at home with a quart milk carton and states voiding 1 quarts 2 days ago and 2 quarts yesterday.

We know that 1 quart = 0.946 litre

and 2 quarts = 1.892 litre

Therefore total amount = 0.946 + 1.892

                                       = 2.838

Hence the total urine patient/client has been measuring at home is 2.828 litres.

What is Quart?

The quart is an English unit of volume equal to a quarter gallon. It is a quarter of a gallon. Measurement of volume, capacity. Its unit of measurement for liquids, equal to approximately 1.14 litres in the UK, or 0.95 litrs in the US.

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Answer: 7w + 6

Step-by-step explanation:

Your question was "7w + 6". When we simplify this, we get 7w + 6. So your answer is 7w + 6.

Answer:

25

Step-by-step explanation:

Answer:25

Step-by-step explanation:

The shortest length of fence that the rancher can use is 6000ft

Given that

x = width of rectangle

y = length of rectangle

A = area of rectangle = x*y = 1500000 [tex]ft^{2}[/tex]

L = length of fencing needed = 2(x + y) + x = 3x + 2y

L = 3x + 2([tex]\frac{1500000}{x}[/tex]) = 3x + 3([tex]10^{6}[/tex])[tex]x^{-1}[/tex]

As x –> 0+, L –> +inf.

As x –> +inf, L –> (3x)+.

There will be a minimum in Quadrant I.

dL/dx = 3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]

dL/dx = 0:

3 - 3([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 0

3([tex]10^{6}[/tex])[tex]x^{-2}[/tex]= 3

([tex]10^{6}[/tex])[tex]x^{-2}[/tex] = 1

[tex]x^{2}[/tex] = [tex]10^{6}[/tex]

x > 0, so x = 1000 feet for shortest length.

Shortest L = 3000 + 3([tex]10^{6}[/tex])([tex](10^{3} )^{-1}[/tex])= 6000 feet.

The shortest length of fence that the rancher can use is 6000ft

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The value of (x,y) on the given points of the function will be (-2,10),(-1,7),(0,4),(1,1), and (2,-2).

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given function,

f(x) = 3(2 – x) –2

Put x = -2

f(-2) = 3(2 + 2) - 2 = 10 thus, (-2,10)

Put x = -1

f(-1) = 3(2 + 1) - 2 = 7 thus, (-1,7)

Put x = 0

f(0) = 3(2 - 0) - 2 = 4 thus, (0,4)

Put x = 1

f(1) = 3(2 - 1) - 2 = 1 thus, (1,1)

Put x = 2

f(2) = 3(2 - 2) - 2 = -2 thus, (2,-2)

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By using Pythagoras' theorem the required length of the cable  is 85 feets.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem. Perpendicular, Base, and Hypotenuse are the names given to the triangle's sides. The hypotenuse is the longest side in this case because it is opposite the angle of 90°.

The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides of a right-angled triangle. Alternatively, the sum of the squares of a right triangle's two legs equals the square of its hypotenuse.

Given:

Height of the tower = 68 feet = perpendicular

distance of box form tower = 51 feet = base

Let's assume lenght of the cable = L = hypotenous

Acoording to the question by using Pythagoras' theorem,

[tex]hyp^{2}= perpendicular^{2} +base^{2} \\(L)^2 = (68)^2 + (51)^2\\L^2 = 4624 + 2601\\L^2 = 7225\\L =\sqrt{7225}\\L = 85 feet[/tex]

Hence by using Pythagoras' theorem the required length of the cable  is 85 feets.

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The terminal ray of an angle measuring negative startfraction 10 over 9 endfraction pi lies in the Second quadrant. this angle measures 200°.

The standard Cartesian coordinate plane is divided into four quadrants as shown in the figure above.

Angle measure: This is the unit of measure used to determine the distance between two lines joined at a common vertex. Subtract 360 to find the quadrant in degree units.

We have given that,

the angle = - 10π/9°

As we know that , π = 180°

so, - 10π/9° = (-10×180/9)° = - 200°

Now, we check the quadrant for angle - 200°

For this follow the above steps,

So, the required quadrant is second .

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The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. A perpendicular line to Y = -4x + 7 would be Y = 4x + 7.

To find the equation of a line perpendicular to Y = -4x + 7, we need to switch the x and y variables and then change the sign of the slope.

The original equation is in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Since the original equation has a slope of -4, the perpendicular line will have a slope of 4.

Therefore, the equation for the perpendicular line is y = 4x + b.

We can find the y-intercept by plugging in a point from the original equation.

For example, if we plug in (0,7), we get 7 = -4(0) + b, or b = 7.

Therefore, the equation for the perpendicular line is y = 4x + 7.

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The Question is based on concept of Cost Price and selling Price is 5.2$

What is Cost PRice and Selling PRice?

Cost price is the actual price of an object where as selling price is the price in which seller sells it to customer

Solution

Cost Price of batteries = 4$

and shopkeeper can charge upto 30% interest

hence selling price will be 4$ + 30% of 4$

= 4 + 30/100(4)

= 4 + 1.2

5.2$

Hence answer to this Question is 5.2$

and this 5.2$ is the selling price of duracell batteries whereas 4$ was the cost price for the same

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1/5 or -1/9 would both be correct

The negation of the given statement " Everyone failed the quiz today " is given by " No one failed the quiz today."

As given in the question,

Given statement is written as:

S : Everyone failed the quiz today.

Negation of the given statement represent the conversion of true statement into false statement or conversion of false statement into true statement.

Here given statement is true statement.

Convert the given statement into false statement.

So Negation of statement S is represented by ~ S.

~S : No one failed the quiz today.

Therefore, the negation of the given statement is equal to " No one failed the quiz today".

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Answer:

Irrational

Step-by-step explanation:

An irrational number added to any other real numbers still keep its infinitely long and never repeating decimals, leaving it still irrational.

Answer: -3

Step-by-step explanation:

By using the concept of data structure, it can be concluded that-

First option is correct

What is data structure?

Data structure is a group of elements that provides an efficient way of storing and organizing data so that the data can be accessed and used efficiently. Data structure is a very important tool for computer science and computer engineer and especially in IT industry. Nowadays, lots of research work is being done on data structure.

The three main components of data model structure in SAP S/4HANA are,

configuration data, master data and transaction data

First option is correct

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The first term of the geometric progression= 1/5

What is common ratio?

In a geometric sequence, ratio of each term to its immediately preceding term is always constant and is known as common ratio.

Given:

The second term = 3/10

The sixth term = 243/ 160

The formula for the nth term of geometric sequence is given by

an = a1 r^(n-1 ) , a1 = first term , r= common ratio

Substitute n=2

a2 = a1 r^(2-1 ) ..................(1)

3/10 = a1* r

Substitute n=6

243 / 160 = a1 r^5 ..............(2)

dividing equation 2 by 1 , we get

r^4 = 5.0625

=> r = 1.5

Substitute this value of r into equation 1

3/10 = a1 * (1.5)

a1 = 0.2

So, the first term = 1/5

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The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]

Permutations and combinations

permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor

given that

we throw a fair die three times

Due to the fact that each die has a 4 on it, the equation would be [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]+ [tex]\frac{1}{6}[/tex]=[tex]\frac{1}{2}[/tex] if all the dice were added together.

(There are fifteen ways to get 2 fours: 441,414,144,442,424,244.. and so on until 446,464,644; another way to get the solution is using permutations and combinations:

=(1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])+1[tex]C_{1}[/tex])(5[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])+(5[tex]C_{1}[/tex](1[tex]C_{1}[/tex])(1[tex]C_{1}[/tex])/[tex](6C_{1} )^{3}[/tex]

=  [tex]\frac{1+15}{216}[/tex]

=[tex]\frac{2}{27}[/tex]

The probability that there is at least two 4s in the three throws is [tex]\frac{2}{27}[/tex]

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Answer: 4:5

Step-by-step explanation: The lowest form

Answer:

Step-by-step explanation:

4:5

Answer:

Step-by-step explanation:

g

Step-by-step explanation:

16.            +.        5

__.                    ____
7(x+4).                7 (x-3)

The scale factor of the dilation of the triangle ABC is equal to 2.5.

We know that the triangles ABC and A'B'C' are similar.

The scale factor of the dilution is given by -

scale factor = measure of A'B' / measure of AB.

Now, let's find the measure of AB and the measure of A'B' from the graph given below, using the distance formula as follows-

The distance formula is = [tex]\sqrt{(y_{2} - y_{1})^{2} + (x_{2} - x_{1})^{2}}[/tex]

Hence, the distance AB =[tex]\sqrt{(2-2)^{2} + (2-0)^{2}}[/tex]

                                       = [tex]\sqrt{(0)^{2} + (2)^{2}}[/tex]

                                       = [tex]\sqrt{2^{2}}[/tex]

                                       = 2 units

Similarly, we can find the distance A'B'

The distance A'B' = [tex]\sqrt{(-1+1)^{2} + (1+4)^{2}}[/tex]

                             = [tex]\sqrt{(0)^{2} + (5)^{2}}[/tex]

                             = [tex]\sqrt{(5)^{2}}[/tex]

                             = 5 units

Now, the scale factor = measure of A'B' / measure of AB

                                       = 5/2

                                       =2.5

Thus, the scale factor of the dilation is 2.5.

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The complete question is -

Triangle ABC was dilated and translated to form a similar triangle A'B'C'.

What is the scale factor of the dilation?

The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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Answer: nose

Step-by-step explanation: