Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation? Group of answer choices
(1)x + y = -2
x - y = -10

(2) x - y = -10
x + y = 2
(3) x + y = -10
x - y = -2
(4) x = -2
y = 5

The sampling method that was used. three representatives from each employee type (faculty, staff, administrators) are chosen for a salary committee. This uses stratified sampling.

In a stratified sample, researchers divide a population into homogeneous subpopulations called strata (the plural of stratum) based on specific characteristics (e.g., race, gender identity, location, etc.). Every member of the population studied should be in exactly one stratum.

Each stratum is then sampled using another probability sampling method, such as cluster sampling or simple random sampling, allowing researchers to estimate statistical measures for each sub-population.

Researchers rely on stratified sampling when a population’s characteristics are diverse and they want to ensure that every characteristic is properly represented in the sample. This helps with the generalizability and validity of the study, as well as avoiding research biases like under coverage bias.

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The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle.

Then the surface area of the triangular prism will be

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

The dimension of the triangle is 13 feet, 5 feet, and 12 feet. And the width of the rectangle is 6 feet.

The surface area of the triangular prism will be given as,

Surface area = 5 x 12 + (5 + 12 + 13) x 6

Surface area = 60 + 180

Surface area = 240 square feet

The area of a triangular prism with dimensions of 13ft, 5 ft, & 12 ft, and 6 ft will be 240 square feet.

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Answer:

x=16

Step-by-step explanation:

x/2=5+3

x/2=8

x=8×2

x=16

I watch a total of 11 hours of TV on Fridays and Ellen watches TV for ten hours every day. 

Let's plot how long Manuel watches TV each day, with M, Harry as H, and Ellen as E.

Manuel knows that from Monday to Friday he watches TV for M hours, so the total amount of time he watches TV in his week is 5 * M = 5M.

On Friday and Saturday he watches TV for H hours a day, so the total amount of time he watches TV in a week is H*2 = 2H.

Ellen watches her E hours TV from Friday to Sunday, so the total amount of time she watches TV in a week is her E*3=3E.

In total, they watch her TV 37 hours a week.

5M + 2H + 3E = 37

I watch a total of 11 hours of TV on Fridays.

M + H + E = 11

We also know that the amount of time Ellen spends watching TV on a given day is twice as much as she does on a given day as Manuel spends watching TV.

E=2M

You can substitute the value of E for M into the second expression.

M+H+2M=11

Combining equal terms gives:

3M+H=11

Now that we have two equations, we can solve the unknowns M and H. Substitute the 3M formula for H from the second formula into the first.

5M + 2H + 3(3M + H) = 37

Expanding the right-hand side, we get:

5M + 2H + 9M + 3H = 37

Combining equal terms gives:

14M + 5H = 37

Now that we have equation 14M + 5H = 37, we can solve for H.

H = (37 - 14 eyes) / 5

Then you can substitute the formula for H with respect to M into the formula for H.

H = (37 - 14 eyes) / 5

Finally, we can solve for M using the value of H.

M = (37 - 5H) / 14

We know that H = (37 - 14M) / 5, so we can substitute this formula into the formula for M.

M = (37 - 5((37 - 14M) / 5)) / 14

Expanding and simplifying the right-hand side, we get:

M = (37 - 37 + 70M) / 14

Solving for M gives:

M=5

So Manuel watches TV for 5 hours every day and Harry watches TV for (37 - 5 * 5) / 5 = 2 hours every day.

Finally, we can use the equation E = 2M to find out how many hours Ellen watches TV each day.

E = 2 * 5 = 10

So Ellen watches TV for ten hours every day. 

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Answer:

a)  Growth rate of 2.737% (3 d.p.) per year

b)  117,897

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$f(t)=ae^{rt}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $r$ is the continuous growth/decay rate.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]

If a > 0 and r > 0, the function is an exponential growth function.

If a > 0 and r < 0, the function is an exponential decay function.

Given exponential function:

[tex]P(t) = 90000\cdot e^{0.027t}[/tex]

As r > 0 the function is an exponential growth function.

The annual growth rate is:

[tex]\begin{aligned}\textsf{Annual growth rate}& = e^{0.027}-1\\&=1.02736780...-1\\&=0.0273678027...\\&=2.73678027...\%\\&=2.737\%\; \sf (3\;d.p.)\end{aligned}[/tex]

To calculate how many residents the model predicts will live in Asheville, NC in 2030, substitute t = 10 into the given function:

[tex]\begin{aligned}\implies P(10) &= 90000\cdot e^{0.027 \cdot 10}\\&= 90000\cdot e^{0.27}\\ &= 90000\cdot 1.30996445...\\&=117896.800...\\&=117897\; \sf (nearest\;whole\;number)\\\end{aligned}[/tex]

Therefore, the model predicts that there will be a population of approximately 117,897 living in Asheville, NC in 2030.

If in a certain large population of adults. the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

Given data:

Mean = 122

Standard deviation = 5

Sample size = 200

Now let find the the standard deviation of the sampling distribution of the mean sample using this formula

Distribution of sample mean = Standard deviation/√Sample size

Let plug in the formula

Distribution of sample mean = 5 /√ 200

Distribution of sample mean = 5/14.14

Distribution of sample mean = 0.35

Therefore the distribution of sample mean iq score is: approximately Normal with mean 122 and standard deviation 0.35.

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The instrument used here is a protractor.

An instrument used to measure angles in degrees is a protractor. When measuring angles using a protractor, it's crucial to check that the vertex of the angle is in the protractor's centre and that the angle's base is lined up with the protractor's baseline.

Acute Angle: - An angle that is less than 90 degrees is considered to be acute. For instance, if the angle is 30 degrees, we would line up the vertex of the angle with the protractor's centre and one of its sides with the baseline. The measurement would be read off the protractor scale, which in this instance would be 30 degrees.

Right Angle: - A right angle is a triangle with a 90 degree angle on each side. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a right angle. The measurement would be read off the protractor scale, which in this instance would be 90 degrees.

Obtuse Angle: - An angle that is more acute than 90 degrees is referred to as an obtuse angle. When using a protractor to measure an obtuse angle, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline. The measurement would then be taken from the protractor scale and would be more than 90 degrees in this instance.

Straight Angle: - A straight angle is one that is 180 degrees in length. Using a protractor, we would line up the vertex of the angle with the protractor's centre and one side of the angle with the baseline to measure a straight angle. The measurement would then be taken from the protractor scale, which would be 180 degrees in this instance.

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It is very important to note that this property is only valid for addition and multiplication. If, AC = AB + BC, then AB + BC = AC by the commutative property.

According to the commutative property, a mathematical principle, the product will not be affected by the order in which we multiply the integers. The commutative property of addition states that the sum is unaffected by the order of the addends.

Only addition and multiplication processes can use the commutative property. So, when adding or multiplying any two integers, we can swap the numbers around or modify their order. This is one of the fundamental characteristics of integers.

Adjective. involving, pertaining to, or involving commutation, exchange, substitution, or interchange. Mathematics. Commutative law for multiplication makes reference to the binary operation's property that one term working on another is equal to another term operating on the first, as in a + b = b a.

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Answer: 6 2/5

Step-by-step explanation:

32 divided by 5 equals 6 with a remainder of 2.

∑[tex](k^2)[/tex] for k = 1 to 6 is the sum in sigma notation for this series of terms.

The series is 1 + 4 + 9 + 16 + 25 + 36. The lower limit of summation is 1, which means, the sum starts at the initial term in the series.

The index of summation is k, which implies, the ongoing term in the series is represented by the variable k.

In the expression [tex]k^2[/tex]  which implies that we are adding up the square of the index of summation.

So, the sigma notation for this series of terms is ∑[tex](k^2)[/tex]  for k = 1 to 6, which means, we are adding up the squares of the numbers from 1 to 6 (1, 4, 9, 16, 25, and 36)

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The required constant of proportionality for the relationship is 1/2.

As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant. In other words, the cost is directly related to the number of gallons pumped.

Let the relation between x and y is

y = kx

Where k is proportionality constant.

Using the given values of x ad y

1 = k(2)

k = 1/2

So, the constant of proportionality for the relationship is 1/2.

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The required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.

Statistic is the study of mathematics that deals with relations between comprehensive data.

Here,
From the table,
Mean = ∑fx / ∑f
Mean = 16010 / 100
Mean = 160.10

Standard deviation,
σ = √∑fd²/∑f
σ = √14265/100
σ = 11.94

The required range of weights from one standard deviation, below the mean is given as
= 160.10 - 11.94 ≤ mean

Thus, the required mean and standard deviation of the frequency distribution of weights is 160.10 and 11.94 respectively.

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The size of the payments that need to be made today and in six months are both $ 6, 961.69.

To find the payment that Caitlin needs to make today and in six months, assume this amount of x.

The payment in 6 months would be:

= (13, 000 - x) ( 1 + 2.4 / 100)⁶

The payment today would be x.

Equate them to find the payment:

x = (13, 000 - x) ( 1 + 2.4 / 100)⁶

x = 14, 988 - 1.1529x

x = 14, 987.979 / 2.1529

= $ 6, 961.69

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Commence at the beginning. The x-coordinate is Negative 3 and 12 units, thus move 3 and 12 units to the right. The difference between 3 and 4 is negative three-half.

A point's exact location on a two-dimensional plane is determined by a pair of numbers called its coordinates. The x and y axes, which are two axes that are at right angles to one another, are known as the coordinate plane's axes. How far along each axis a specific point is located is indicated by its coordinates.

Ordered pairs are a way of describing locations on the coordinate plane. A point's location is revealed by an ordered pair by linking the point's positions along the x-axis (the ordered pair's first value) and the y-axis (the second value of the ordered pair).

To locate points, one uses the numbers on a coordinate grid. Using an ordered pair of numbers, each point may be located.

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Pie charts are used to compare parts of a whole, not the difference between groups. This misleads the viewer to think more than half the people in all three parties voted Yes on Issue #1, when less than half of Republicans and Independents actually voted Yes on Issue #1.

This is a type of graph that resembles a pie because it is a circle that shows the proportion of different groups.

Note: Here is the missing information

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My student ID is 21444367.

The algorithm states that if the digit in the student ID (from left to right) is an even number, then a 0 is placed in the s column in the corresponding row (from top to bottom). If the digit in the student ID (from left to right) is an odd number, then a 1 is placed in the s column in the corresponding row (from top to bottom). Thus, the result of the algorithm applied to my student ID is s = 01101000.

This can be calculated by multiplying the even digits of the student ID by 0 and the odd digits of the student ID by 1 and then adding them together.

For my student ID, 21444367, the calculation would be:

0 * 2 + 1 * 1 + 0 * 4 + 1 * 4 + 0 * 4 + 1 * 3 + 0 * 6 + 1 * 7 = 01101000.

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Answer: Semi-Conservative, and old.

Step-by-step explanation:

The flagpole is visible to the student from 18 feet away and at a 22-degree inclination to the ground. The flagpole is 40.3 feet tall and 50 feet away from the structure.

At an elevation of 22 degrees, the student is looking out of a second-story school window. The building is 50 feet from the flagpole's base, and the window is 18 feet above the ground. We may compute the angle of the triangle formed by the window, the ground, and the top of the flagpole using the tangent ratio to determine its height. The opposing side (the flagpole) divided by the neighboring side equals the tangent of 22 degrees (the window to the ground). Consequently, the flagpole is 40.3 feet tall (50 divided by 1.224). This indicates that the student is 18 feet above the ground and is looking down at the flagpole.

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Equation of a plane perpendicular to a given line with direction ratios <a, b, c> and passing through a point (x1, y1, z1) is given by: a(x - x1) + b(y - y1) + c(z - z1) = 0.

The slope of the line we're looking for is 1/2 since perpendicular lines have opposite-reciprocal slopes. When we enter the supplied point into the equation y = 1/2x + b and solve for b, we obtain b = 6. The line's equation is therefore y = 12x + 6.

Rearranged, it is -x/2 + y = 6. a plane that is outlined by vectors that are perpendicular to a normal. As a result, when given a vector with the coordinates a, b, and c, we can infer that all planes perpendicular to this vector have the form ax+by+cz=d, and any surface with this form is a plane perpendicular to a, b, and c.

Get a direction vector to the two points first, then get the supplied normal from the plane's equation. The normal is then produced by adding the direction vector to the normal.

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Answer:

50 m

Step-by-step explanation:

The angle of elevation of the top of the building from the foot of the tower is 30 and the angle of the top of the tower from the foot of the building is 60. the tower is 50 m high

The graph can be used to determine the median, quartiles, and other statistical measures.

(a). Class width = (maximum value - minimum value)/ number of classes = (109 - 45)/6 = 9

(b).

Class Limits  Class Boundaries Midpoints  Frequencies  Relative Frequencies  Cumulative Frequencies

45 - 54  44.5 - 54.5  49.5  2  0.0741  2

55 - 64  54.5 - 64.5  59.5  7  0.2593  9

65 - 74  64.5 - 74.5  69.5  17  0.6207  26

75 - 84  74.5 - 84.5  79.5  20  0.7407  46

85 - 94  84.5 - 94.5  89.5  14  0.5185  60

95 - 104  94.5 - 104.5  99.5  7  0.2593  67

(c). Histogram

(d). Relative-Frequency Histogram

(e). The basic distribution shape is right-skewed.

(f). Ogive

The ogive graph is a cumulative frequency plot that shows the number of data values that lie at or below each given value on the x-axis. It is constructed by plotting the cumulative frequencies of each data value on the y-axis against the corresponding data values on the x-axis. The points are then connected using closed line segments to form the ogive graph. The graph can be used to determine the median, quartiles, and other statistical measures.

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a. The solutions to the system of equations f(x) = g(x) are given as follows: x = 0 and x = 1.

b. The explanation is that they have the same numeric value at these values of x.

A system of equations is composed by multiple equations.

The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.

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Answer:

see below

Step-by-step explanation:

1-1-2017

H 26K

W 24K

Net income 30K

H salary 12K

W salary 10K

remain: 8K shared EQUALLY so each gets 4K extra

Distribution:

30K - H gets12+4 =16K, and W gets 10+4 = 14K

Answer:

A within-subject variable is a type of variable in which the same subjects are used to measure multiple levels or conditions of the variable. One example of a within-subject variable would be measuring a person's reaction time to a stimulus both before and after a training intervention.

For example: measuring a person's reaction time to a visual stimulus before and after a training program in which the participant learns to react faster to the stimulus, here reaction time is the within-subject variable.

Answer:

$17.32

Step-by-step explanation:

44 hours

52.5 - 44 = 8.5 hours over time for 1.5x regular pay

assume regular pay is x

so 44x + 8.5 * 1.5x =983.15

44x + 12.75x = 983.15

56.75x=983.15

x=17.324

check to see if it's correct

44*17.324 + 12.75*17.324 = 983.14

The two functions such that composition (fog) (x) = H(x) are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

We have a function H(x) = 7 [tex]\sqrt{x-3}[/tex]

We have to find two functions f and g such that (fog) (x) = H(x).

Let f(x) = 7x

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

The composition of these functions is,

(fog)(x) = f (g(x))

           = 7 . g(x)

           = 7 [tex]\sqrt{x-3}[/tex]

           = H(x)

Hence the functions are f(x) = 7x and g(x) = [tex]\sqrt{x-3}[/tex].

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The correct person regarding the classification of quadrilaterals is given as follows:

B. Jamie.

The slopes of each segment are given as follows:

-3 and 1/3.

The multiplication of these slopes is given as follows:

-3 x 1/3 = -1.

As the multiplication of the slopes is of -1, the adjacent sides meet at an angle of 90º, meaning that they are perpendicular, and hence the quadrilateral is classified as a square.

This means that Jamie is correct.

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The distance of IH is 1.089 meters.

Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.

Given that,

Radius = 5.1 meters

EF = EI = 5.1

FG = 6.3 meters

HE is a perpendicular bisector of FG.

FH = HG = 6.3 / 2 = 3.15

Also, FH is the projection of EF in the vertical axis.

FH = EF sin (θ), where θ is the angle FEH.

3.15 = 5.1 sin (θ)

sin (θ) = 0.6176

θ = sin⁻¹ (0.6176)

θ = 38.14°

IH = EI - EH

We have,  EH is the projection of EF into the horizontal axis.

EH = EF cos (θ)

Substituting,

IH = 5.1 -  EF cos (θ)

IH = 5.1 - 5.1 cos (38.14)

IH = 5.1 ( 1 - cos (38.14))

IH = 1.089 meters

Hence the length of the line segment IH is 1.089 meters.

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Answer:

2 is the scale of dilation

The work energy theorem represented as an equation is ΔW = ΔΕ is appropriate option.

Option D is correct.

A fundamental physics principle known as the work-energy theorem asserts that the amount of work done to an object is proportional to the change in its kinetic energy. To put it another way, the kinetic energy of an object is proportional to the net work done to it.

The work-energy theorem can be expressed as an equation because the change in an object's kinetic energy (W) is equal to the change in its work (W). It states that a change in an object's kinetic energy equals the net work done on it. The conservation of energy is a fundamental physics principle that states that energy cannot be created or destroyed; rather, it can only be transferred or converted from one form to another.

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