Which expression is equivalent to −5 + 8 − 6x − 8x?
14x + 13
−14x − 3
−14x + 3
−14x + 13

Answer : -4/9 , -4/7 , -3/5 , -5/6

Answer:  Choice A

The data has little or no linear correlation

======================================================

Explanation:

r = correlation coefficient

The r values are within the interval [tex]-1 \le r \le 1[/tex]

In other words, r is between -1 and 1 inclusive of both endpoints.

For the case r = 0.013, it's very close to r = 0. This suggests there is very weak positive correlation or practically no linear correlation at all.

[tex]\frac{35-32}{32} \times 100=\frac{75}{8}=9.375\%[/tex]

Answer:

9.375%

Step-by-step explanation:

Percentage Error formula

[tex]\textsf{Percentage error}=\sf \left|\dfrac{estimated\:value\:-actual\:value}{actual\:value} \right| \times 100\%[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Percentage error}&= \left|\dfrac{35-32}{32} \right| \times 100\%\\\\&=\left|\dfrac{3}{32} \right| \times 100\%\\\\&=0.09375 \times 100\%\\\\&=9.375\%\end{aligned}[/tex]

Therefore, the percentage error was 9.375%.

The x and y solution of the system  is x = -3 and y = -6

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

6 = −4x + y

− 5x − y = 21

Make -y the subject in the second equation, by adding 5x to both sides of the equation

5x − 5x − y = 21 + 5x

This gives

−y = 21 + 5x

Substitute −y = 21 + 5x in 6 = −4x + y

6 = −4x - 21 - 5x

Evaluate the like terms

5x + 4x = -6 - 21

This gives

9x = -27

So, we have

x = -3

Substitute x = -3 in −y = 21 + 5x

−y = 21 + 5 * -3

Evaluate

−y = 6

So, we have

y = -6

Hence, the solution for the system of linear equations 6 = −4x + y and − 5x − y = 21 is x = -3 and y = -6

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Using the binomial distribution, the mean and the standard deviation for the number of settled complaints among those received are given as follows:

The binomial distribution gives the probability of exactly x successes on n repeated trials, with p probability of a success on each trial. These parameters will be used to find the mean and the standard deviation, with formulas that are presented next.

The mean is given as follows:

[tex]E(X) = np[/tex]

The standard deviation is given as follows:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Considering that a sample of 200 complains are chosen, each with an 90% probability of being settled, the parameters are given as follows:

n = 200, p = 0.8.

Hence the mean is:

[tex]E(X) = np = 200 \times 0.8 = 160[/tex]

The standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200 \times 0.8 \times 0.2} = 5.66[/tex]

The problem states that 200 complaints were received, and asks for the mean and the standard deviation for the number of settled complaints among those received.

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ANSWER

EXPLANATION

We want to find the value of y:

for the values of x.

To do this, for each value of x, substitute the values of x into the equation and simplify.

1. x = 0:

The value of y is undefined for x = 0 since any value divided by 0 is undefined.

2. x = 1:

3. x = 2.5:

4. x = 1/3:

5. x = a:

That is the answer.

The length and width of the rectangle with a perimeter of 378ft are 168ft and 21ft respectively.

The formula used in calculating the perimeter of a rectangle is expressed as;

P = 2( l + w )

Where l is length and w is width.

Given the data in the question;

Let 'x' represent the width of the rectangle.

Plug the given values into perimeter formula and solve for x .

P = 2( l + w )

378 = 2( 8x + x )

378 = 2( 9x )

378 = 18x

18x = 378

x = 378/18

x = 21

Now, we find the length and width of the rectangle.

Width of the rectangle w = x = 21ft

Length of the rectangle l = 8x = 8( 21 ) = 168ft

Therefore, the width of the rectangle is 21ft while its length is 168ft.

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Answer:The answer is 8

Step-by-step explanation:

21-13

The average population density in the county is:

10,137,915 people / 4,751 square miles = 2133.84 people / square mile

Rounding to nearest integer, we have: 2134 people / square mile

Considering the definition of greatest common divisor, the greatest number of backpacks volunteers can prepare using all of the maps and dictionaries is 8.

Considering that a divisor can be formally defined as that number that is contained in another exactly n times, the greatest common divisor is the largest number by which two or more numbers can be divided. That is, the greatest common factor is the highest number by which a set of numbers can be divided, resulting in a whole number.

To calculate the greatest common factor, the following steps must be followed:

In this case, you must calculate the greatest common factor as follows:

2 is the factor common to both numbers, with 3 being the smallest exponent found. Then the greatest common divisor is calculated as:

Greatest common divisor= 2³

Greatest common divisor= 8

This means that they can prepare 8 backpacks.

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The match of the given equations and choices of the properties of equality are;

If a = b and b = c then a = c ; Transitive Property

If a = b then a ÷ c = b ÷ c; Division property of =

a = a; Reflexive property

If x + a = b and x = c then c + a = b; Substitution Property

If a = b then a + c = b + c; Addition Property of =

If a = b then a•c = b•c; Multiplication Property of =

If a•b = a•c then a•c = a•b Symmetric Property

a•(b + c) = a•b + a•c; Distributive property

If a = b then a - c = b - c; Subtraction Property of =

Properties of equality includes; addition, subtraction, transitive, reflexive, and symmetric properties of equality

The transitive property of equality can be stated as follows; If two variables are each equal to a third variable, then the two variables are equal to each other.

Therefore; a = b and b = c then a = c represents the transitive property

The division property states that both sides of an equation remain equal, following a division of both sides by the same non zero number

Therefore;

If a = b then a ÷ c = b ÷ c; represents the division property of equality

The reflexive property of equality states that a measure or number is always equal to itself

Therefore;

a = a represents the reflexive property

Substitution property indicates that if two variables are equal, then one can replace the other in an equation and the results will remain the same

Therefore;

If x + a = b and x = c then c + a = b; represents the substitution property

The statement of the addition (and subtraction) property of equality is that both sides of an equation remain equal following the addition or subtraction of the same amount from both sides the same

Therefore;

If a = b then a + c = b + c; represents the addition property of equality

If a = b then a - c = b - c; represents the subtraction property of equality

This states that both sides of an equation remain equal following the multiplication of both sides by the same value

The symmetric property states that two sides of an equation remain equal when their relative positions are interchanged

This states that two sides of an equation remain equal following a distribution with multiplication over addition or subtraction.

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Answer:

Step-by-step explanation:

=a, log 3 = b Log 2 log 1.5= log 23/20 год 1.5 = = log 3-log 2 b-a The other terms log 1.2 log 0.24, log 0.5, log 0.836 cannot be expressed only. of in terms a or bor both. [Answer: Log 1.5 Option A

Answer:

[tex]\log 72=3a+2b[/tex]

Step-by-step explanation:

Given:

Rewrite 72 as a product of 2s and 3s.

[tex]\implies 72 = 2 \times 2 \times 2 \times 3 \times 3[/tex]

[tex]\implies 72=2^3 \times 3^2[/tex]

Therefore:

[tex]\implies \log 72=\log(2^3 \times 3^2)[/tex]

[tex]\textsf{Apply the log product law}: \quad \log xy=\log x + \log y[/tex]

[tex]\implies \log 72=\log(2^3)+\log(3^2)[/tex]

[tex]\textsf{Apply the log power law}: \quad \log x^n=n\log x[/tex]

[tex]\implies \log 72=3\log2+2\log3[/tex]

Substitute the given values of log 2 and log 3:

[tex]\implies \log 72=3a+2b[/tex]

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Using linear function concepts, it is found that:

a) The amount of lattes sold function is: N(p) = -240p + 1040.

b) The revenue function is: R(p) = -240p² + 1040p.

c) The revenue is maximized when p = $2.17.

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

For this problem, we have a linear function with the points having the following format:

(price, lattes sold).

Hence two points are given as follows:

(2.50, 440), (2.75, 380).

The slope is given by change in y divided by change in x, hence:

m = -60/0.25 = -240.

Then:

N(p) = -240p + b.

When p = 2.50, N(p) = 440, hence we solve for b as follows:

440 = -240(2.5) + b

b = 1040.

Thus the function is:

N(p) = -240p + 1040.

The revenue function is:

R(p) = pN(p)

Hence:

R(p) = p(-240p + 1040)

R(p) = -240p² + 1040p.

Which is a concave down quadratic function, with a = -240 and b = 1040. A concave down quadratic function is maximized when:

p = -b/2a

Hence:

p = -1040/2(-240) = $2.17.

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Answer:

Total price including tax: $ 1,092.00

Sales tax rate: 5%

Step-by-step explanation:

Brainlest, Please!

if we take 1040 to be the 100%, what is 52 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 1040 & 100\\ 52& x \end{array} \implies \cfrac{1040}{52}~~=~~\cfrac{100}{x} \\\\\\ 20=\cfrac{100}{x}\implies 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]

Answer: 16

Step-by-step explanation:

The standard form of a perfect square trinomial is:

[tex](x-a)^{2} = x^{2}-2ax+a^{2}[/tex]

Put the equation into standard form:

[tex]x^{2} -8x+c[/tex]

Compare to to the form of a perfect square trinomial:

[tex]-8x=-2ax\\\frac{-8x}{-2x}=a\\a=4[/tex]

Plug a back into the equation to get c:

[tex]c=a^{2}=4^{2}\\c=16[/tex]

Putting everything back together gives you:

[tex](x-4)^{2} = x^{2}-8x+16[/tex]

The required, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial. Option D is correct.

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the monomial, binomial, and trinomial, etc. ax+b is a polynomial.

To make the expression x² - 8x a perfect-square trinomial, we need to add the square of half of the coefficient of x to the expression.

The coefficient of x is -8, so half of it is -4. The square of -4 is 16.

Therefore, we need to add 16 to the expression x² - 8x to make it a perfect square trinomial.

Answer: 16.

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Answer:

First, let one angle be a variable (eg: x) so that you can form expressions and solve.

Let the first angle be x°.

Then we can form expressions for the second and third angles using the information given.

First angle = x°

Second angle = (x + 10)°

Third angle = (3x)°

Since sum of angles in a triangle is 180°, we can form an equation.

x + (x + 10) + 3x = 180

Simplify and solve for x.

5x + 10 = 180

5x = 170

x = 34

Substitute x into the expressions to find the angles.

First angle = 34°

Second angle = 34 + 10

= 44°

Third angle = 3(34)

= 102°

Annie will receive 66.92 euros after converting the dollars into euros post her trip

The exchange rate between pounds and US dollars: 1 Euro = $1.27

Exchange rate: An exchange rate determines the price at which one currency will be exchanged for another and has an impact on international trade and money transfers.

Euro Annie spends to buy dollars = 500

Equivalent dollars received by Annie for 500 euros = 500*1.27

= $635

The money she spent in dollars = $550

Dollars remaining = 635-550 = $85

Euro she will receive after conversion = Dollars remaining/Conversion rate 85/1.27 = 66.92 Euros

So, After changing the dollars into euros after her vacation, Annie will receive 66.92 euros.

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Given -

a = 2.5 cm

b = 3.6 cm

∠A = 43°

To Find -

Remaining angles and sides =?

Step-by-Step Explanation -

We will start by drawing the diagram:

Now, we know

By, sine rule:

Now, we know N

A + B + C = 180 c°°

43 + B + 79° = 180°°

B = 180° - 799 - 43°°

B = 58°

Now, Side b =

Final Answer -

∠B = 58B°

∠C = 797°

Side, b = 3.1 cm

Answer:

there are 7 severeings of rice

By using fractions, we can conclude that 99 students bring their lunch from home.

So, the Fraction of students eating a cafeteria lunch at her school = 4/5

A fraction of students bring their lunch from home:

495 students attend her school in total.

Several students bring their lunch from home, including:

Therefore, by using fractions, we can conclude that 99 students bring their lunch from home.

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Answer:

d = 7

For step by step explaintion I am so sorry but I don't rember enough of my geometry class to properly explain this, but triangles BDC and ABD are congruent (I swear I can prove this if I dig up my old notes but I really do not feel like doing that) so these 2 equations (sides) are equal. So we just solve for d!

6d + 3 = 10d - 25

(we all know how to solve something this simple so I won't bore you with the details of inverse operations and such)

d = 7

The graph of a function f is the set of all points in the plane of the form (x, f(x)).

Step 1

iven

g(x) is a transformation of the function f(x)we have a root in the function, note that the variable x is inside the root, so we can conclude the basic function is

square tooroot

Step 2

rove

ow, lets's check the transformation of f(x)

a)1 was subtracted form the argument of the fucnction

when you subtract a number b form the argument of the function you are shifting the function b units to the rigth

so

he function was shifteed 1 unit to rigth

) the resulting function was multiplied by 2-

when you multplie by a negavitve constant you are reflecting the funciton acrros x-axis, and is is stretched vertically.

so

he funcition was reflected across x-axis an strtched vertically by a factor of 2

c) 4 was added to the function

when you add a constant b to any function, the graph will be shifted b units up,so

he functinon was shifted 4 units up

hrerefore, we can conclude the answer is

I hope this helps you

Using multiplication we calculate that there are 56 lights in the cross-section.

When two integers are multiplied together in mathematics, the result is a product, or an expression that describes the factors to be multiplied.

Total number of lights in each pole = 2 + 1 + 2 = 5 lights

There are 4 corners

Total number of poles = 5 × 4 = 20

So by multiplication we get there are 20 lights in the intersection.

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Using the percentages formula, we conclude that the percentage increase in life preserves is 40%.

So, the percentage increase in life preserves:

Now, substitute the values in the formula as follows:

Therefore, using the percentages formula, we conclude that the percentage increase in life preserves is 40%.

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Answer: y = -x + 3

Step-by-step explanation:

y = mx + b

We need to find the slope of the equation first.

Change in y: 7 - 0 = 7

Change in x: -4 - 3 = -7

Slope = Change in y / Change in x

slope = 7 / -7 = -1

Now, plug the slope into the equation to find b.

0 = -1(3) + b

b = 3

or 7 = -1(-4) + b

b = 3

Answer:

y = mx

Step-by-step explanation:

It depends on what form of the line that you want.  Usually the slope intercept form is wanted.

y = mx + b  We need to have the m (slope) and the b (the y-intercept)

The slope is the change in y over the change in x.

Ordered pairs are in the form (x,y)

(0,0) and (4,4)  Have x's of 4 and 0, and y's of 4 and 0.  We subtract these to find the changes in y and x.

[tex]\frac{4-0}{4-0}[/tex]  This is [tex]\frac{4}{4}[/tex] which is the same as 1. The slope (m) is 1.

Now we need to find the y -intercept.  The y intercept is the point where x is 0  (0,b).  They give us this point (0,0,)  So the y -intercept is zero.

y = 1m + 0

or y =mx

The probability that x is between -6 and 6 is 18.84%.

For the given question;

The probability of x should line between -6 and 6.

The formula for calculating the z-score is;

z = (x - μ)/σ

μ = mean (-3)

σ = standard deviation (4)

Put the values in the formula.

For x = -6

z = (-6 - (-3))/4

z = -3/4

z = -0.75

Now, x = 6

z = (-6 - 3)/4

z = -9/4

z = -2.25

P(-6 < x < 6) = P(-0.75 < x < -2.25)

Find the probability using negative z score.

P(-6 < x < 6) = 0.197 - 0.0122

P(-6 < x < 6) = 0.1848

P(-6 < x < 6) = 18.84%

Thus, the probability that x is between -6 and 6 is 18.84%.

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Compound Interest

It occurs when the interest is reinvested rather than paying it out.

When it happens interest in the next period is then earned on the principal sum plus previously accumulated interest.

The formula is:

Where:

A=final amount

P=initial principal balance

r=interest rate

n=number of times interest applied per time period

t=number of time periods elapsed

Harry deposited an initial amount of P = $1500.

The savings account gives r = 6% = 0.06 interest

Since the interest is compounded monthly, n = 12 (there are 12 months in a year)

The time is t = 10 years.

Now we apply the formula:

Using a calculator:

A = $2729.095

Rounding to two decimals,

A = $2729.10

Harry will have $2729.10 in his account after 10 years

Now for t = 20 years:

Calculating again:

A = $4965.31

Harry will have $4965.31 in his account after 20 years

The value of the independent variable does not rely on the values of the other variables in an expression or function, and its value determines the values of the other variables.

An independent variable can be defined as the variable that is being manipulated, controlled, and which varies in an experimental or research study for the exploration of its effects.

It is termed “independent” because it's not affected or changed by other variables in an experiment or study.

It is known as a variable that is unaffected in a function and cannot be determined by the other variables in that function.

Other names for an independent variable includes;

Hence, the variable is independent.

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