Solve the system using the substitution method. For the system that does not have one unique solution, also state the number of solutions and
whether the system is inconsistent or the equations are dependent. Express numbers as integers or simplified fractions.
y=2x+7
4x+3y=-19

The Formula will be in form of exponential function that is y=$3200(1.09)ˣ

where x= no. of years.

What exactly are exponential functions?

An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.

Growth that is exponential

The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".

The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.

Now,

Initial value=$3200

% increase=9%

then

Amount in x years will  be =3200(1+9/100)ˣ

=3200(109/100)ˣ

=3200(1.09)ˣ

Hence,

           The Formula will be in form of exponential function that is y=$3200(1.09)ˣ

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Answer:

2.016, 2.16, 2.1682, 2.2

How to put anything from least to greatest?

The decimals that you have put are the following:

2.16

2.1682

2.2

2.016

How to do it:

If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.

We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.

Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.

So now here are the decimals from least to greatest:

2.016, 2.16, 2.1682, 2.2

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The function g ( x ) in the graph has one x-intercept , y intercept and an oblique asymptote , a vertical asymptote

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be represented as g ( x )

Now , the value of g ( x ) is

g ( x ) = ( -4x² + 36 ) / ( x + 3 )

On simplifying , we get

g ( x ) = -4 ( x² - 9 ) / ( x + 3 )

On further simplification , we get

g ( x ) = -4 ( x + 3 ) ( x - 3 ) / ( x + 3 )

g ( x ) = -4 ( x - 3 )

g ( x ) = -4x + 12

Now , the function has a vertical asymptote at ( 0 , 12 )

The function has a horizontal asymptote at ( 3 , 0 )

Hence , the function is solved

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Answer:

at least one x-intercept

at least one y-intercept

domain of x

Step-by-step explanation:

took ed2023

It is given that:

20% of the students earned an A in STA 2023.

12% of the students didn't bring their phones to class.

85% of the students who didn't bring their phones to class earned an A.

To answer the following questions, we assume whether all students took STA 2023 and brought their phones to class or not.

a) Let's assume that x% of the students earned an A and brought their phones to class. Then, since the remaining (100% - 12%) = 88% of students brought their phone to class but their grade is not specified, we can set up the following equation:

x% + 85% of 12% = 20%

x% + 0.102 = 0.20

x% = 0.098

Therefore, 9.8% of students earned an A and brought their phones to class.

b) Let's assume that y% of the students didn't earn an A and didn't bring their phones to class. Then, we can set up the following system of equations:

x% + y% = 100% - 12%

0.85*(12%) = y%

Solving for y, we get:

y% = 9.6%

Therefore, 9.6% of students didn't earn an A and didn't bring their phones to class.

STA 2023 is a course code used by some colleges and universities to refer to an introductory course in statistics. The course usually covers topics such as descriptive statistics, probability theory, statistical inference, hypothesis testing, and regression analysis. STA 2023 is often a required course for students majoring in fields such as social sciences, business, and health sciences, as well as for students pursuing degrees in mathematics or statistics. The specific content and level of difficulty of STA 2023 may vary depending on the institution and the instructor.

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Using angle relationships, the missing measures are:

m<3 = 138 degrees.

m<5 = 42 degrees.

m<8 = 138 degrees.

Using angle relationships, each of the measure of the angles can be calculated as follows:

Given that, m<1 = 138 degrees.

m<3 = m<1 [vertical angles are congruent]

Substitute:

m<3 = 138 degrees.

m<5 + m<3 = 180

Substitute:

m<5 + 138 = 180

m<5 = 180 - 138

m<5 = 42 degrees.

m<8 = m<3 [alternate interior angles are congruent]

m<8 = 138 degrees.

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We obtain the sum of the expressions as 5z + 1. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

Four fundamental mathematical operations which can be used to express any real number are known as arithmetic operations. The four  operations are addition, subtraction, multiplication and division.

We are given two expressions as 3z - 4 and 2z + 5.

In order to add the expressions, we will add the like terms.

On adding the like terms, we get

⇒(3z - 4) + (2z + 5)

⇒3z + 2z - 4 + 5

⇒5z + 1

Hence, we get the expression as 5z + 1.

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To fill a 6-inch thick layer of topsoil for a new 28 feet by 17 feet garden, you will need 79.33 cubic yards.

The volume is the product of the multiplication of the thickness, length, and width.

The thickness of the topsoil = 6 inches

12 Inches = 1 Feet

6 inches = 0.5 Feet (6/12)

The length of the garden = 28 feet

The width of the garden = 17 feet

The thickness of the soil = 0.5 feet

Volume of the topsoil = 28 x 17 x 0.5

= 238 ft³

3 Feet to 1 Yard

238 ft³ = 238/3 yards

= 79.33 cubic yards

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The unknown in the similar triangles are as follows;

x = 15 units

x = 16 units

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional to each other.

Let's solve for x in the triangles as follows:

using the proportion,

2.

9 / x = x / 25

cross multiply

25 × 9 = x²

x² = 225

x = √225

x = 15 units

3.

x / 12 = 12 / 9

cross multiply

9x = 144

x = 144 / 9

x = 16 units

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The number that is most likely an irrational number is given as follows:

D. 4.279458105...

Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.

Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.

For this problem, the option D gives the irrational number, as it is the lone non-repeating decimal. For the others, we have that:

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Answer:

541.5 ksh

Step-by-step explanation:

The company can expect to find 125 defective flashlights in a production run of 12,500. The correct option  is B, 125.

Flashlight can be defined as a portable, battery-operated device used for illumination. It typical unit consists of one or more dry cell batteries arranged in a line inside a battery compartment that forms the handle of the light.

Assuming the proportion of defective flashlights remains the same, the number of defective flashlights in a production run of 12,500 would be:

(5/500) x 12,500 = 125

Therefore, the company can expect to find 125 defective flashlights in a production run of 12,500. The answer is option B, 125.

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Answer:

Shortage

Step-by-step explanation:

If the market price of a product is set below the equilibrium price, it will create a shortage of the product because the demand exceeds the supply.

Answer:

3 paintbrushes

Step-by-step explanation:

15 divided by 5 is 3.

So, Mrs. Hamada will put 3 paintbrushes in each cup.

To volume to fill the rectangular garden is 8.99 cubic yard

To determine the volume of amount of sand required to fill the garden, we can simply convert the dimensions from inches and feet into yard.

inch to yard

6 inch = 0.17 yard

Feet to yard

28 feet = 9.33 yard

17 feet = 5.67 yard

The volume of the rectangular garden is given as;

v = l * w * h

Substituting the values;

V = 0.17 * 9.33 * 5.67

v = 8.99 cubic yard

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Answer:

Option D.

Step-by-step explanation:

Negative correlation also called an " inverse correlation " is a relation between 2 variables where-by they behave in opposite manner. When one variable moves ---> in an increasing /\ direction, the other variable moves in a decreasing \/ direction.

Thus, Option D.

(x - 10)² = -12 (y + 4)  represents a parabola with a vertical axis of symmetry, vertex at (10, –4), and p = –3 .

What's a vertical parabola?

A vertical parabola has its axis of symmetry at x = h, and the vertex is (h, v). With this information, you can find the focus and directrix. The focus is the distance from the vertex to the focus is 1/(4a), where a can be found in the equation of the parabola (it is the scalar in front of the parentheses).

we know that

If the axis of symmetry is parallel to the y-axis, then we have a vertical parabola

The equation of a vertical parabola is equal to

4p(y - k) = (x - h)²

where

(h,k) is the vertex

In this problem we have

(h,k) = (10, –4)

p= -3

substitute

4*(-3)(y - (-4)) = (x - 10)²

-12 (y + 4) =  (x - 10)²

or

(x - 10)² = -12 (y + 4)

Hence , option D is correct.

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The correct option is A {-5, 0, 3, 4}.

In mathematics, the domain of a function is the set of all possible input values (independent variable) for which the function is defined. In other words, the domain is the set of values that we can substitute for the independent variable in a function to produce a meaningful output.

For example, consider the function f(x) = 2x. Here, we can substitute any real number for x and get a meaningful output. Therefore, the domain of this function is all real numbers, or (-∞, ∞). However, if we consider the function g(x) = 1/x, we can see that we cannot substitute 0 for x because division by 0 is undefined. Therefore, the domain of this function is all real numbers except 0, or (-∞, 0) U (0, ∞).

The domain of a relation is the set of all possible values for the independent variable (x) for which there exists a corresponding value of the dependent variable (y). In this case, the given coordinates are (1,3), (4,1), and (-5,-4).

The domain of the relation would be the set of x-values that correspond to the given coordinates. So, the domain of this relation is {-5, 1, 4}.

Therefore, the correct answer is A: {-5, 0, 3, 4}.

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Answer:

9 trucks/hour

Step-by-step explanation:

If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.

The probability that the person is under 18 or employed part-time is 179/864.

Experimental probability calculates the probability of some event from the results of experiments.

For an event E, we get the experimental probability of that event

[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]

where,[tex]P_e(E)[/tex] is denoting experimental probability of occurrence of E.

Given that;

The table of age, full time, part time, unemployed

Now,

Total number of people who are between the age group 35-49

= 581+179+104

= 864

Number of people who are employed part time= 179

Number of people employed part time in age group 35-49/ Total people in age group 35-49

= 179/864

Therefore, the probability will be 179/864.

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Answer:

19 < x < 53

Step-by-step explanation:

given 2 sides of a triangle then the third side x is in the range

difference of 2 sides < x < sum of 2 sides , that is

36 - 17 < x < 36 + 17

19 < x < 53

Answer:

Step-by-step explanation:

The time take to fill the pool will be 494 hours.

Inlet pipe fills in  38 hours = 1 pool

Inlet pipe fills in 1 hours = 1/38

Drain pipe empty in 39 hours = 1 pool

Drain pipe empty in 1 hour = 1/39

If both pipes are opened together then in pool fills in 1 hour =  1/38 - 1/39

= 1/1482

Therefore, 1/1482 fills in 1 hour.

. Therefore, 1/3 will be:

= 1/3 × 1482

= 494 hours.

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Side a will be 58cm.In mathematics, a side is a feature of a geometric shape.

The "A-side" of a record, which is the main song, is issued as a single. The "A-side" of an album is the side that this track is on. The word "side" is most frequently employed as a noun, however it can also be used as an adverb or a verb. The shapes we observe are made of points and lines (line segments) (vertices).

Finding the side, we obtain:

Given ∠A= 30°, b =100 cm .

In ΔABC,

tan A = [tex]\frac{a}{100}[/tex],

tan 30°=  [tex]\frac{a}{100}[/tex]

0.577×100=a

a=57.7≅58 cm.

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

Explanation:

Let's go through each answer choice to see which are true and which are false.

A.

The fractions for advertising and rent are 1/6 and 7/12 respectively. The LCD is 12, so let's get 1/6 to have a denominator of 12. Multiply top and bottom by 2 to get 1/6 = 2/12.

Now we can compare the fractions 2/12 (aka 1/6) and 7/12. Clearly 7/12 is larger. It's like saying "having 7 slices of pizza is more than 2 slices of pizza". Therefore, the claim that more was spent on advertising compared to rent is false.

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

B.

1/4 = 3/12 when multiplying top and bottom by 3

3/12 was spent on supplies and 2/12 was spent on advertising

We see that more was spent on supplies, so claim B is true

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

C.

This claim is false because it contradicts claim B.

Another way to see why it's false is to use a calculator to get these decimal values

Since 0.17 is not larger than 0.25, this means 1/6 is not larger than 1/4.

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

D.

We could use any of the methods mentioned in the previous sections, but I'll go another route.

For now assume that the fractions for supplies and rent (1/4 and 7/12 respectively) are equal.

Let's use cross multiplication to say the following:

1/4 = 7/12

1*12 = 4*7

12 = 28

Clearly the two sides are different so the original fractions aren't equal. To fix this error, replace each equal sign with a "less than" sign like so

1/4 < 7/12

1*12 < 4*7

12 < 28

Think of it like working backward up the chain. Start with 12 < 28 which is clearly true, and you can work backwards to end up with 1/4 < 7/12.

The fact we end up with 1/4 < 7/12 shows the claim "The bookstore spends more on supplies than rent" is false. It's the other way around: the bookstore spent more on rent compared to supplies.

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

Summary: We found only choice B to be true. The other statements were false.

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image. Resizing an object is accomplished through the transformation of dilation. The objects can be enlarged or shrunk using dilation. The result of this transformation is an image that has the same shape as the original shape. The size of the shape varies, though. A dilation should either stretch or contract the original shape. The term "scale factor" describes this transformation.

From the diagram:

Scale factor = A'B' / AB = 6/3 = 2

Center = (6, -6)

Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.

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The total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 51 square units.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Divide the figure is into two rectangles and a triangle.

The points B, C, E, and F form a rectangle with base BC and height 7 units.

The points A, D, and G form a rectangle with base AG and height 5 units. The points C, D, and E form a triangle with base CE and height 4 units.

The length of BC is 4 - 4 = 0, so the area of the rectangle with base BC is 0.

The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.

Therefore, the total area of the figure with points A(-5,4), B(4,4), C(4,1),  D(1,1), E(4,-3) F(4,-6), G(-5, -6)  is 45 + 6 = 51 square units.

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A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.

Simple Random Sample (SRS) is a statistical technique for selecting a sample from a population, where each individual or item in the population has an equal chance of being selected for the sample. In other words, a simple random sample is a representative subset of a population where every individual or item in the population has an equal chance of being selected for the sample.

To take a simple random sample, each individual in the population is assigned a unique number, and then random numbers are generated to select the required number of individuals for the sample. This method ensures that the sample is not biased towards any particular subset of the population, and that the sample is representative of the whole population.

A) The data is a random sample from the population of interest. - Yes, it is mentioned that the administrator takes an SRS (Simple Random Sample) of 100 teachers from the statewide database containing every teacher.

B) np^≥10n p^​ ≥10n, p, with, hat, on top, is greater than or equal to, 10 and n(1−p^)≥10n(1− p^​ )≥10n, left parenthesis, 1, minus, p, with, hat, on top, right parenthesis, is greater than or equal to, 10 - Since the problem does not provide the value of p, we cannot determine if the condition np^≥10n and n(1−p^)≥10n are satisfied.

C) Individual observations can be considered independent. - The problem does not provide information about whether the individual observations can be considered independent. However, we can assume that since it is a random sample, the observations are independent.

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Answer: the answer is 5/12