1. What would be a good first step to graph the solution to the following system?
y≥x+3
x<−2
A. Substitute x<−2 into the first inequality and simplify the result.
B.Graph each inequality separately.
C. Change the inequalities to equalities and solve the resulting system of linear equations.
D. Solve the first inequality for x because the second inequality is already solved for x.
2. Which system of inequalities is shown in the graph?
A. y −2x
B. y≥x−3 and y≤−2x
C. y>x−3 and y<−2x
D. y≤x−3 and y≥−2x

The approximate length of the midsegment parallel to xy is 6.63

The midsegment of a triangle is a line segment that connects the midpoints of two sides of the triangle and has the same length as each of the two sides.

To find the midpoint of a line segment, we average the x-coordinates and the y-coordinates of its endpoints.

Since the question stated that the midsegment is parallel to xy, we need to find midpoint of xw and yw.

First, let's find the midpoint of side xw:

Midpoint of xw : ((-14+10)/2, (20+4)/2) = (-2, 12)

Midpoint of yw : ((-14-2)/2, (20-4)/2) = (-8, 8 )

The length of a line segment between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be calculated using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Length line of midpoint xw and midpoint yw :

√((-2-(-8))^2 + (12-(8))^2) = √(6^2 + 4^2) = √(36 + 8) = √44

So, the length of the midsegment is parallel to XY, which is approximately equal to √44 = 6.63

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The simplified form of the expression is y - 1.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is (1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex]

The numerator of the expression can be written as below using the cross multiplication process.

1 - [tex]\frac{1}{y}[/tex] = (y - 1) / y

The whole expression becomes,

(1 - [tex]\frac{1}{y}[/tex] ) / [tex]\frac{1}{y}[/tex] = [(y - 1) / y] / [tex]\frac{1}{y}[/tex]

              = (y - 1) / 1

              = y - 1

Hence the simplified form is y - 1.

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The solution to the inequality is x < -4

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

x+4/2x-1 < 0

Multiply both sides of the inequality

So, we have the following representation

x + 4 < 0

Subtract 4 from both sides of the expression

So, we have the following representation

x < -4

Hence, the solution is x < -4

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In the trash can, there are 648 bricks. when the measurements are 8 by 4 by 2 The right response is so (C).

This same total mass of a three-dimensional shape is referred to as its porous structure. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. The cuboid's length, width, and height can also be labeled, and indeed the surface area (SA) can indeed be calculated using the equation SA=2lw+2lh+2hw.

Based on this equation, surface area is equivalent to two times overall combination of width and length, two times its products of length and height, and two times the ratio of both height and width.

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C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

Two or more expressions with an Equal sign is called as Equation.

Given that Deion pays a cost of $50 per phone produced for materials and labor.

Deon also must pay a daily fixed cost of $200 to rent the building and equipment.

C = 200 + 50p

The above equation represents the total cost, in dollars, of producing p phones in a given day.

Number of phones (p) Total cost (C)

0                                   200

1                                   250

2                                  300

3                                   350

Hence, C = 200 + 50p is the equation represents the total cost, in dollars, of producing p phones in a given day.

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The percent of adult American males could enter this contest is 2.23%

Normal usually refers to the word "normal" in a normal distribution.

The word normal is used when something occurs that has occurred frequently. The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from the mean, its chances decrease.

We solve using z score formula

z = (x-μ)/σ,

where, x is the raw score = < 64 inches

μ is the population mean = 69

σ is the population standard deviation = 2.5

Here Participants must be less than 64 inches tall.

For x < 64 inches

z = 64 - 69/2.5

z = -2

Probability value from Z-Table:

P(x<64) = 0.02275

Converting to percentage;

= 0.02275 × 100

= 2.275%

Approximately = 2.23%

The participants must be less than 64 inches tall to participate in this limbo contest, the percent of adult American males thag could enter this contest is 2.23%

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a. The difference between the highest data speed (74.5 Mbps) and the mean of all 50 data speeds (17.34 Mbps) is:

74.5 - 17.34 = 57.16 Mbps

b. To find the number of standard deviations, divide the difference by the standard deviation:

57.16 / 20.79 = 2.75

So, the difference of 57.16 Mbps is 2.75 standard deviations from the mean.

Mbps known as for “Megabits per second.” This is the standard measure of “speed” or “bandwidth” on home internet connections.

It finds how many bits (units of digital information) can be transferred each second. You’ll normally see speeds ranging from 10-1,000 Mbps advertised for home internet plans.

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An illustrates the abuse of respondents in marketing research is :

Not providing the promised incentive for completing interviews or questionnaires.

The world organization body, the American Marketing Association (AMA), conveys the definition of marketing research is a function that connects customers, consumers, or the general public with marketers through information used to identify marketing problems and opportunities.

Meanwhile, Philip Kotler defines marketing research as the systematic design, collection, analysis, and reporting of data or findings that are relevant to a particular marketing situation faced by a company.

Simply put, marketing research is the identification, collection, analysis, and presentation of systematic and objective information to help companies make decisions related to problem solutions and find opportunities in the marketing process.

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The required probability is 0.9544

A z-score is a quantitative measure obtained when a data point from a normal population with mean μ and standard deviation

σ is transformed. It describes the position of the data point representing its distance from the average value of the normal population measured in number of standard deviations. It is given by:

z =(X − μ)/σ

A standard normal table (z-score table) provides the probability to the left of the z-score so obtained.

Number of randomly selected steady smokers is, n=100.

Sample mean is, M=$20.

The population standard deviation is, σ = $5.

To compute the probability that a sample of 100 steady smokers spend between 19 and 21.

Using the definition of a z-score, computing the z-score for X =$19,

z =(X − μ)/σ /[tex]\sqrt{n}[/tex]

[tex]z = \frac{19-20}{5}/\sqrt{100}[/tex]

z = -2

Again using the definition of a z-score to compute the z-score for X = $21,

z =(X − μ)/σ /[tex]\sqrt{n}[/tex]

[tex]z = \frac{21-20}{5}/\sqrt{100}[/tex]

z = 2

The probability that a sample of 100 steady smokers spend between 19 and 21 is obtained as:

P(19< X < 21) = P(-2 < X < 2)

                     = P(z< 2) - P(z < -2)

                     = P(z < 2) − [1 − P (z < 2)]

                     = 0.9772 - (1 - 0.9772)

                     = 0.9772 - 0.0288

                     = 0.9544

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Answer:

4th

Step-by-step explanation:

first is over y-axis and the linear translation: 6 horizontal and -5 vertical

Equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given that Bananas cost $0.48 per pound.

Since each pound costs $0.85, the cost of one pound is $0.48,

the cost of two pounds is twice that at $0.96

The equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas.

Hence,  equation c=0.48p is used find the cost is $0.48 times the number of pounds of bananas and graph is given in attachment.

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The height of the streetlight is 30 feet.

Let's call the height of the streetlight "h".

When the person is 16 feet from the streetlight, the length of their shadow will be 16 feet * (6 feet / h) = 96 feet / h.

When the person is 5 feet from the tip of the streetlight's shadow, the length of the streetlight's shadow will be h * (16 feet / 5 feet) = 3.2 * h.

Since the length of the person's shadow starts to appear beyond the streetlight's shadow when they are 5 feet from the tip of the streetlight's shadow, we know that 96 / h > 3.2 * h.

Solving for h, we get:

96 / h > 3.2 * h

96 > 3.2h

30 > h

So, the height of the streetlight is less than 30 feet.

To determine the exact height of the streetlight, we can use the equation:

96 / h = 3.2 * h

96 = 3.2h

30 = h

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Check the picture below.

[tex]\begin{cases} ~\hfill 10x+(16y+6)=180\\\\ (4+18y)+(10x-6)=180 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{10x+(16y+6)=180}\implies 10x+16y=174\implies 10x=174-16y \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{substituting on the 2nd equation}}{(4+18y)+(10x-6)=180}\implies 18y+10x-2=180 \\\\\\ 18y+(\underset{10x}{174-16y})-2=180\implies 2y+172=180\implies 2y=8 \\\\\\ y=\cfrac{8}{2}\implies \boxed{y=4} \\\\\\ \stackrel{\textit{since we know that}}{10x=174-16y}\implies 10x=174-16(4)\implies 10x=110 \\\\\\ x=\cfrac{110}{10}\implies \boxed{x=11}[/tex]

The experimental probability of spinning a number less than 3 is 0.46 or 46%.

This can be defined as the likelihood an event occurs or does not occur. Most of the time, the probability is calculated based on the times a specific outcome is obtained versus the number of total outcomes.

To know the probability, let's use the formula getting less than a 3/ total times:

Times they got less than 3: 23 (8+6+9= 23)

Total times: 50

23/50 = 0.46 or 46% (0.46 x 100)

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The probability that the sum of the two rolls equals 4 is  1/12.

Given in the question that a single die with 6 sides is rolled twice, we have to calculate the probability that the sum of the two rolls equals 4.

the set of possible outcomes when we roll a die are {1,2,3,4,5,6}

So when we roll two dice there are 6 × 6 = 36 possibilities

The number of possible combinations that will result in a sum of 4 is (1, 3), (2, 2), and (3, 1). Since there are 6 possible outcomes for each die, the probability of rolling a specific combination is 1/36. There are 3 combinations that will result in a sum of 4, so the probability of rolling a sum of 4 is 3/36 or 1/12.

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A ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, e are informed that the volume is halved, and the pressure increases by a factor of 2.5.

We shall therefore have:

PVγ = 2.5P(0.5V)γ

We'll condense this to:

(1/0.5)γ = 2.5

γ = In2.5/In2

γ = 1.32

The volume temperature relation is written as follows if the volume expands in an adiabatic process:

T1V1∧γ-1 = T2V2∧γ-1

T1V1∧1.32-1 = T2(0.5V1)∧1.32-1

Condensing this results in:

T₁ = 1.24T₂

Therefore, a ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

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The correct option C. Rejecting a true null hypothesis, is the probability in  significance level in hypothesis testing.

By testing an experimental component against a no effect or even no relationship hypothesis based on a specific observation, NHST is a statistical inference technique.

Thus, the likelihood of rejecting a valid null hypothesis determines the significance level in hypothesis testing.

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Answer:

y=-3/5x+

Step-by-step explanation:

slope intercept form;

y= mx+c........... mis the gradient while c is the y-intercept

so it will be; y= -3/5x+

The length and width are possible dimensions for the garden is l = 20 ft; w = 10 ft.

The characteristics of a square and a rectangle in a flat shape are very different. Although both are rectangular, the nature and characteristics of these two buildings are different.

The difference between a square and a rectangle can be seen from the properties they have. These properties are also characteristics of squares and rectangles. For this reason, if we want to mention the difference between the two wakes, then we must know their characteristics.

Your question is incomplete but most probably your full question was:

Which length and width are possible dimensions for the garden?

l = 20 ft; w = 5 ft

l = 20 ft; w = 10 ft

l = 60 ft; w = 20 ft

l = 55 ft; w = 30 ft

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The rate of change of the exponential function in this problem represents a decay, and the rate of decrease is of 3.7%.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which:

The function in this problem is given as follows:

y = 20(0.963)^x.

As 0.963 < 1, this is an exponential decay function, and the decay rate is given as follows:

1 - r = 0.963

r = 1 - 0.963

r = 0.037

r = 3.7%.

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Solving for a in the triangle gives a = 6

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

The figure is a triangle. Since the sum of angles in a triangle is 180°. We can write:

106.2° + (3.8a + 29.7)° + (2.4a + 6.9)° = 180°

106.2 + 3.8a + 29.7 + 2.4a + 6.9 = 180

142.8 + 6.2a = 180

6.2a = 180 - 142.8

6.2a = 37.2

a = 37.2/6.2

a = 6

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Therefore , the solution of the given problem of volume comes out to be volume of cone is  132π cm³.

The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Two examples of cubic units are cm3 and in3. The amount of matter in a thing is measured by its mass, on the other hand. The weight of an object is typically converted into mass quantities like pounds and kilograms.

Here,

Given :

=>height = 11cm

=> radius = 6cm

Volume of cone :

=> 1/3πr²h

=> 1/3*π * 36 * 11

=> 132π cm³

Thus , volume of cone is  132π cm³

Therefore , the solution of the given problem of volume comes out to be volume of cone is  132π cm³.

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From the given graph solution of lines is (32, 5).

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.

In the give graph two lines intersect at (32, 6).

Here, 32 represents the number of kites and 6 represents the total cost.

Therefore, from the given graph solution of lines is (32, 5).

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Answer:

A) Function f is translated up 3 units.

B) Function f is translated to the right 5 units.

Step-by-step explanation:

Given functions:

[tex]f(x)=\sqrt[3]{x+4}[/tex]

[tex]g(x)=\sqrt[3]{x-1}+3[/tex]

To transform function f to function g, first subtract 5 from the x:

[tex]\begin{aligned}f(x-5)&=\sqrt[3]{x-5+4}\\&=\sqrt[3]{x-1}\end{aligned}[/tex]

Now add 3 to the function:

[tex]f(x-5)+3=\sqrt[3]{x-1}+3[/tex]

When a number "n" is subtracted from the x variable of a function, the function is translated "n" units to the right.

When a number "n" is added to a function, the function is translated "n" units up.

Therefore, the transformations performed from function f to function g are:

B. The y-intercept of function A is greater than the y-intercept of function B.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

from the given data, we get,

the 1st line's equation is, y=2x+1

i.e. y-intercept = 1

and,

the 2nd equation is,

1 3 y = 4x - 1

i.e. y-intercept = -1/13

                        =-0.77

as, 1> -0.77

Hence, B. The y-intercept of function A is greater than the y-intercept of function B.

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Check the picture below.

[tex]\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\sin(\measuredangle M)}{m}=\cfrac{\sin(\measuredangle L)}{l}\implies \cfrac{\sin(114^o)}{63}=\cfrac{\sin(42^o)}{l} \\\\\\ l\sin(114^o)=63\sin(42^o)\implies l=\cfrac{63\sin(42^o)}{\sin(114^o)}\implies l\approx 46~inches[/tex]

The ceiling for this problem is given as follows:

450 m.

The three trigonometric ratios are defined as follows:

The parameters for this problem are given as follows:

Hence the value of x is obtained as follows:

tan(71.5º) = x/150

x = 150 x tangent of 71.5 degrees

x = 448.3 m.

Adding 1.7 m, the ceiling is obtained as follows:

448.3 + 1.7 = 450 m.

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Work done to pump the kerosene is equal to W = 126106 ft-lbs

"Information available from the question"

Height of the cylinder = 7 ft.

Diameter of cylinder = 8 ft.

Radius of the cylinder = 4 ft

Weight of the kerosene = 51.2 lb/ft³

Calculating the volume of cylinder for dy height

dV = π r² dy

dV = π 4² dy

dV = 16π dy

Force acting on the cylinder

dF = W x dV

dF = 51.2 x 16πdy...….(1)

We know

Work done = Force x displacement

Displacement = 7 - y

dW = 51.2 x 16πdy x (7 - y)

Now, integrating both side

[tex]\int\limits dW = \int\limits^7_0 {819.2\pi(7-y) } \, dy[/tex]

[tex]W = [819.2\pi (7-y)^2]^0_7[/tex]

By solving, we get

W = 126106 ft-lbs

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