For each equation, determine whether it is linear.
(a) y=4
Equation
(b) y=-4x²+3
(c) y=7x+2
(d) y=-x
Is the equation linear?
Yes
No

Answer:

Step-by-step explanation:

P+N+2Q=?

P= Pennies

N= Nickels

Q= Quarters

162.5  is the simple interest for one year.

What does the term "simple interest" mean?

The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest.

                   Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

P = $812.50

T = 1 Year

S.I. = ?

R = 20

According to question,

                 S.I. = P * R* T/100

                     = 812.50 * 20 * 1/100

                     = 16250/100

                    = 162.5

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The rules of logarithms, which are derived from the exponent rules, are what make up the attributes of log. The solution is 36.

The rules of logarithms, which are derived from the exponent rules, are what make up the attributes of log.

These logarithm features are used to simplify logarithmic expressions and solve logarithmic problems.

solution to log4(y – 9) + log43 = log481.

log4 (y − 9) + log4 3 = log4 81

We know that log a(b) + loga ( c) = loga ( b*c)

log4 (y − 9) * 3 = log4 81

We know have log a( BC ) = loga ( d)

This means BC = d

(y − 9) * 3  = 81

Divide each side by 3

y - 9 = 81/3

y - 9 = 27

Add 9 to each side

y-9+9 = 27+9

y = 36

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Answer:

y = 36

Step-by-step explanation:

STEP 1:

The given equation is 

log4(y – 9) + log4(3) = log4(81)

STEP 2:

log4(y – 9)(3) = log4(81)

STEP 3:

log4(3y - 27) = log4(81)

STEP 4:

3y - 27 = 81

     +27.   +27

STEP 5:

3y = 108

__   ____

 3.      3

STEP 6:

y = 36

Step-by-step explanation:

Using log properties

[tex] log_{7}(rz {}^{12} ) [/tex]

[tex] log_{7}(r) + log_{7}(z {}^{12} ) [/tex]

Then

[tex] log_{7}(r) + 12 log_{7}(z) [/tex]

Plug in the knowns

[tex] - 7.87 + 12( - 12.59)[/tex]

[tex] - 158.95[/tex]

When we reject the null and the null is true, we have a made a TYPE 1 ERROR

A null hypothesis is either true or false. Unfortunately, we do not know which is the case, and we almost never will. It is important to realize that there is no probability that the null hypothesis is true or that it is false, because there is no element of chance. For example, if you are testing whether a potential mine has a greater gold concentration than that of a break-even mine, the null hypothesis that your potential mine has a gold concentration no greater than a break-even mine is either true or it is false; you just don’t know which. There is no probability associated with these two cases (in a frequentist sense) because the gold is already in the ground, and as a result there is no possibility for chance because everything is already set.

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The range of possible lengths for the third side is [16.52,17.46] for 1st part and [46.13,57.27] for 2nd.

What is pythagoras theorem?

The Pythagorean theorem or Pythagoras' theorem could be a elementary relation in parabolic geometry between the 3 sides of a trigon.

Main Body:

To find range of possible lengths for the third side , we will use Pythagoras theorem : a²+b² = c²

7.     4 cm, 17 cm

4²+17²=c²

16+289=c²

305=c²

To undo the square you have to square root so

√ 305 =17.46

OR

17² = 4²+b²

289 -16 =b²

b = √273 = 16.52

range of possible lengths for the third side is [16.52,17.46]

8.  24 ft , 52 ft​

24² =576

52² =2704

2704+576=3280

√3280 =57.27

OR

52² = 24²+b²

b²= 2704-576

b=√2128

b = 46.13

range of possible lengths for the third side is [46.13,57.27]

Hence the range of third side is found out.

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Answer:

B. x = 3

Step-by-step explanation:

3³ = 27

3 · 3 · 3 = 27

9 · 3 = 27

Answer: (x+5)(2x+10)

Step-by-step explanation: Hope you find it helpful, I am in the rush so can't give you a full explanation on paper yet!

The profit, y, can be written in terms of x, the number of computers sold.  as ​y = 150x

The table that completes the question is added at the end of this solution as an attachment

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

Amount of items sold = x

Profit made by the company = y

The equation of a proportional relationship is represented as

k = Y/X * h

Where

(X, Y) is the coordinate of any ordered pair from the function or table

Using the above as a guide, we have the following:

(X, Y) = (3, 450)

Substitute the known values in the above equation, so, we have the following representation

y = 450/3 * x

Evaluate the quotients in the equation

y = 150 * x

Evaluate the products in the equation

y = 150x

Hence, the equation of the proportional relationship is y = 150x

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An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The number of associates assigned in the case is 7.

The number of partners assigned in the case is 9.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

Number of associates = m

Cost of each associates = $400

Number of partners = n

Cost of each partner = $1000

Now,

Total number of lawyers = 16

Total amount charged = $11800

Now,

m + n = 16

m = 16 - n

400m + 1000n = 11800

Putting m = 16 - n.

400(16 - n) + 1000n = 11800

6400 - 400n + 1000n = 11800

6400 + 600n = 11800

600n = 11800 - 6400

600n = 5400

n = 5400/600

n = 9

Now,

m = 16 - n

m = 16 - 9

m = 7

Thus,

The number of associates assigned in the case is 7.

The number of partners assigned in the case is 9.

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To view the representation of graph of check the attached image.

Given that ;

Stewart's overdue assignment = 36

Per day he complete 4 overdue assignments.

To find : In how many days he complete all the overdue assignments

To complete 36 overdue assignments = 36/4

                                                                = 9 days

Therefore, In 9 days he complete all the overdue assignments

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The total number of hours Tony will he need to work to save amount $1,000 is 242 hours.

The given data for the question is-

Thus,

38%(12.5x - 0.13(12.5x)) = 1000

0.38(10.875x) = 1000

x = 2631.57/10.875

x = 241.98

x = 242

Thus, total number of hours Tony will he need to work to save

$1,000 is 242 hours.

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We can make 19 oatmeal cookies from the bag.

1 pound = 16 ounces

for making a single unit of oatmeal cookie it uses 21 ounces of oats.

We have 25 pound of oats in the bag which means we have 25 X 16 which is equal to 400 ounces of oats in the bag .

To find how much of oatmeal cookies can be made we have to divide the total amount of oats available in the bag divided by the number of ounces required in making of the single unit of oatmeal .

Therefore,

= 400 / 21

= 19.047

Which means 19 overall pieces of oatmeal can be prepared in the 25 pound of oats bag

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The Value of x is 69.78 per given equation.

1/5(4x-2.5) = 5(0.4+10)+3 1/3

0.2(4x-2.5) = 5(0.4+10)+3.33

0.2(4x-2.5) = 5(10.4)+3.33

0.2(4x-2.5) = 52 + 3.33

0.2(4x-2.5)=55.33

4x-2.5 = 276.33

4x = 276.33+2.5

4x = 279.15

x = 69.78

So, the value of x is 69.78

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The greatest amount that a person can receive is 19$. Option D

A word problem is a mathematical exercise which is in the form of a hypothetical question that needs mathematical analysis and equations to be solved.

Total amount = $30

Total number of people = 8

According to the problem, each person gets at least 1$ and also exact amount.Let's consider only one person gets more than 5$ because, we have to find the greatest value.

4 people get more than 1$,that includes the person who gets the maximum amount.

Let the person who gets maximum amount =x

x + 2+2+2+1+1+1+1

Maximum amount = 30- (2+2+2+1+1+1+1+1)= 11$

Hence, the maximum amount will be 19$.

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Answer:

------------------------------------

Let the numbers be:

Geometric means give us:

Then:

Given options give us:

Since all the above options are false, the answer is option D.

(4,3): 2x-5y = -7 is  the ordered pair on the graph lies.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it can be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers. The coordinates of one point in the coordinate system are included in an ordered pair. An ordered pair of the form of a point's name is (x, y). The x-coordinate is represented by the first integer, and the y-coordinate by the second. You must place a dot at the coordinates of the ordered pair in order to graph a point.

Given

We enter the values of the variables into each equation to see if an ordered pair is a solution to the system of two equations. The ordered pair is the system's solution if it makes both equations true.

For this,

(4,3): 2x-5y = -7

Equating values,

2(4) - 5(3)

8 -15

-7

(4,3): 2x-5y = -7 is  the ordered pair on the graph lies.

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The answer is C. 387

Step-by-step explanation:

9+21(13+5)

First do what is in parentheses:

9+21(13+5)

=9+21(18)

Next do 21(18) or 21 x 18:

9+21(18)

=9+378

The last step is to add:

9+378=387

The answer is C. 387

We can not write the polynomial g(x) as a product of linear factors.

What is polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents (No division operation by a variable).

Given:

g(x)=x³ + 3x² - 7x − 3 and x = -1 is a zero of g(x).

Since, if x = a is a zero of the polynomial then (x - a) is a factor of polynomial.

Here (x - (-1)) = (x + 1) is a factor of g(x).

First to check x = -1 is a zero of polynomial or not.

Plug x = -1 in g(x).

g(-1) = (-1)^3 + 3(-1)^2 - 7(-1) - 3

g(-1) = -1 + 3+ 7 - 3

g(-1) = 6

g(-1) ≠ 0

Hence, we can not write the polynomial g(x) as a product of linear factors.

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The amount of money that Noah needs to invest would be = $ 6,558

An interest rate is defined as the rate at which an individual receives an interest on an invested funds over a stipulated period of time.

The interest rate (R) = 7% = 0.07 (decimal form)

The time for the investment (T) = 10 years.

The present value of the account (A) = $12,900

n compounding frequency = 1

Using the formula;

A = P (1 +r/n) ^nt

12,900 = P ( 1 + 0.07) ^ 10

12,900 = P (1.07) ^10

12,900 =P 1.96715

P = 12,900/1.96715

P =$ 6,558

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The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b)

This is incomplete question

Complete question is this:

With a linear regression, what is the aim when choosing the model parameters (aka the slope and coefficient(s))?

Choose the correct option:

Now, According to the question:

Hence, The aim when choosing the model parameters:

Find the parameters that minimize he squared distances, in the y direction, from each point up/down to the regression line

The correct option is (b).

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Answer:

A.   y = -1/2 x + 3/2

Step-by-step explanation:

An x-intercept of 3 means point (3, 0).

The line passes through points (3, 0) and (-5, 4).

y = mx + b

m = (4 - 0)/(-5 - 3) = 4/(-8) = -1/2

y = -1/2 x + b

0 = -1/2 × 3 + b

b = 3/2

y = -1/2 x + 3/2

By using the property of congruency of triangles,

[tex]\angle[/tex]Y [tex]\cong[/tex] [tex]\angle[/tex]X has been proved

What is congruency of triangles?

Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.

There are different axioms of congruency. They are

SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom

Z is the midpoint of XY [Given]

WZ [tex]\perp[/tex] XY  [Given]

[tex]\angle[/tex]WZX [tex]\cong \angle[/tex]WZY [90° each]

XZ [tex]\cong[/tex] YZ [Z is the midpoint of XY]

WZ [tex]\cong[/tex] WZ [Reflexive property of congruency]

[tex]\Delta[/tex] WXZ [tex]\cong \Delta[/tex] WYZ [SAS axiom]

[tex]\angle[/tex]Y [tex]\cong[/tex] [tex]\angle[/tex]X [Corrosponding parts of congruent triangles are congruent]

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When Sam buys 10 tickets for $135 at fundraiser, the amount for each ticket will be $13.50.

It should be noted that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

In this case, Sam buys 10 tickets for $135 at fundraiser, the amount for each ticket will be:

= $135 / 10

=$13.50

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Complete question

Sam buys 10 tickets for $135 at fundraiser. Calculate the amount for each ticket.

The  graph that represents the solution to the inequality −0.96 is greater than or equal to the product of a number and 0.3 number line with a closed circle on point negative 3.2 and arrow shaded to the left

Generally, To solve this inequality, we can start by multiplying both sides by the reciprocal of 0.3, which is 3. Doing so gives us the inequality:

−0.96 * 3 >= x * 0.3 * 3

Simplifying the right side gives us:

−0.96 * 3 >= x * 0.9

Then we can simplify both sides further:

−2.88 >= x * 0.9

Dividing both sides by 0.9 gives us:

−3.2 >= x

The solution to this inequality is all values of x that are less than or equal to -3.2.

The graph of this inequality would be a number line with a solid dot at -3.2, and a solid line extending to the left of -3.2, as shown below:

(graph with number line and solid dot at -3.2, and solid line extending to the left)

This graph represents the solution to inequality.

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The student did better in the test of Geography.

The standard deviation is a measure of the amount of variation or dispersion of a set of values.

To solve this question, we will use the z-score formula to find the w test in which the student scored better. The z-score formula is;

z = (x - μ)/σ

Now, for Geography we have given :

              Test score (x) = 68

                      Mean (μ) = 80

Standard deviation (σ) = 10

Thus, the z-score here will be :

z = (68 - 80)/10

z = -1.2

Similarly, for Mathematics we have given :

              Test score (x) = 249

                      Mean (μ) = 300

Standard deviation (σ) = 34

Thus, the z-score here will be :

z = (249 - 300)/34

z = -1.5

Since the z-score for Geography is less than that of Mathematics, thus, we can conclude that the Geography test is the one in which the student scored better.

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Answer:

DGE and BGA

Step-by-step explanation:

Supplementary angles are two angles whose measures add up to 180°

so BGD + DGE = 180 or BGD + BGA = 180

so both DGE and BGA are supplementary to BGD

For instance, if the multiplication error is 8 x 7 = 56, then the matching division error  56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.

Finding the product of two or more corresponding integers is done mathematically through the action of multiplication. It is frequently represented by the letters "x" or "*." In order to discover the result of multiplication, a multiplicand, also known as the multiplicand, is multiplied by a multiplier, also known as the multiplier. The result of the two integers, for instance, is 56 if the multiplicand and multiplier are both 8. A multiplication process always yields a greater number as the outcome than either of the initial factors. Multiply is also used to describe the process of adding a number to itself a certain number of times, as in "7 multiplied by 3 equals 21."

How to solve?

 For instance, if the multiplication error is 8 x 7 = 56, then the matching division error  56/8 = 7, demonstrating that the result of the division is the other component that was used in the multiplication.

This connection is true for every multiplication and division problem as long as the numbers are utilised consistently in both operations.

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Answer: M=2

y-intercept = (0,7)

x-intercept = (-7/2,0)

Step-by-step explanation:

The slope is already given in the equation, which is 2

M=2

y-intercept = (0,7)

x-intercept = (-7/2,0)