If a₁ = 15 and d = -8, then 12

The 100 students from a large university represent a sample.

In statistics, a sample is a subset of individuals or observations taken from a larger group known as the population. The purpose of taking a sample is to make inferences and draw conclusions about the population based on the characteristics observed in the sample.

In this scenario, the 100 students from a large university who were asked about their opinion on the new health care program represent a sample. The sample is a smaller group of individuals selected from the larger population of all students at the university. The intention is to gather insights and information about the opinions of the broader population based on the responses obtained from the sample. Statistical inference techniques can be applied to analyze the data collected from the sample and make conclusions or predictions about the entire population.

It is important to note that the sample should be representative of the population to ensure that the conclusions drawn from the sample can be generalized to the larger population accurately. The process of selecting a sample and conducting statistical analyses is an essential part of studying and understanding populations using data and statistics.

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Answer:

x=−12/5

Step-by-step explanation:

2(1.5x−2)=−0.5(−4x−32)

Step 1: Simplify both sides of the equation.

−2(1.5x−2)=−0.5(−4x−32)

(−2)(1.5x)+(−2)(−2)=(−0.5)(−4x)+(−0.5)(−32)(Distribute)

−3x+4=2x+16

Step 2: Subtract 2x from both sides.

−3x+4−2x=2x+16−2x

−5x+4=16

Step 3: Subtract 4 from both sides.

−5x+4−4=16−4

−5x=12

Step 4: Divide both sides by -5.

−5x−5

=12/−5

x=−12/5

Answer:

If you want to know what b is then it is 16

Step-by-step explanation:

38 + b = 54

54- 38 = 16

38 + 16= 54

Answer:

1/4

Step-by-step explanation:

Originally, Kathy has 1/2 of a pizza.

She gave away 1/4 of a pizza.

This can be expressed as:

1/2 - 1/4 =

2/4 - 1/4 =

(2-1)/4 = 1/4

1/4

explanation

1/2-1/4=0.25

and 0.25 to a fraction is 1/4

The equation of the circle with a radius of 111 and a center at (9, 5) is:

To determine the equation of a circle, we use the standard form equation:

\((x - h)^2 + (y - k)^2 = r^2\)

Where (h, k) represents the center coordinates of the circle, and r represents the radius.

In this case, the center of the circle is (9, 5), and the radius is 111. Plugging these values into the equation, we have:

(x - 9)^2 + (y - 5)^2 = 111^2

Expanding and simplifying further:

\((x - 9)^2 + (y - 5)^2 = 12321\)

Therefore, the equation of the circle with a radius of 111 and a center at (9, 5) is:

(x - 9)^2 + (y - 5)^2 = 12321

This equation represents all the points (x, y) that are equidistant from the center (9, 5) by a distance of 111 units, forming a circle shape.

To graphically represent the circle, plot the center point (9, 5) on a coordinate plane and then draw the circle with a radius of 111 units around it. Any point on the graph that satisfies the equation will lie on the circle, while points outside the circle will not satisfy the equation.

It's important to note that the equation of a circle can also be expressed in other forms, such as the general form or parametric form. However, the standard form equation provided above is commonly used for representing circles.

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Answer: 36

Step-by-step explanation:

XZ=XY+YZ

48=12+YZ

48-12=12-12+YZ

YZ=48-12

YZ=36

Answer:

\(16\pi\) \(cm^2\)

Step-by-step explanation:

Area of a circle is equal to \(\pi r^2\), where r is the radius

\(A=\pi r^2\)

A diameter is twice the length of the radius. (\(8/2\))

So the radius is 4 cm.

\(r^2=4^2=16\)

so the Area is \(16\pi\)

Answer:

Step-by-step explanation:

If a 6-ounce bottle of medicine contains 36 doses, we can use a proportion to find how many doses are in a 15-ounce bottle:

6 ounces / 36 doses = 15 ounces / x doses

Cross-multiplying, we get:

6 x = 36 * 15

6 x = 540

Dividing both sides by 6, we get:

x = 90

Therefore, a 15-ounce bottle of the same medicine contains 90 doses.

Explanation:

90° is 90/360 = 1/4 of a full 360° rotation. Meaning that if the central angle of the pizza slice is 90°, then we have four equal slices.

One slice is 7 square inches, so all four slices combine to 7*4 = 28 square inches

Answer:

Step-by-step expla

The statistical technique that combines results of a large number of studies is called meta-analysis.

It means that you will take data from various sources, such as studies, combine them together, and then create this mixture of various results that you can use in your own research. If something occurs often in those studies, it means that it is good and reliable information.

The probability of a defect for this system is approximately 0.0289 or 2.89%.

To determine the probability of a defect for this system, calculate the area under the normal distribution curve that falls outside the specification limits.

First, calculate the z-scores for the upper and lower specification limits using the given mean and standard deviation:

Upper z-score = (Upper Specification Limit - Mean) / Standard Deviation

= (2.019 - 1.96) / 0.031

Lower z-score = (Lower Specification Limit - Mean) / Standard Deviation

= (1.862 - 1.96) / 0.031

Now, use a standard normal distribution table or a statistical calculator to find the probabilities associated with these z-scores.

Using a standard normal distribution table, the probabilities corresponding to the z-scores can be looked up. Denote Φ as the cumulative distribution function (CDF) of the standard normal distribution.

Probability of a defect = P(Z < Lower z-score) + P(Z > Upper z-score)

= Φ(Lower z-score) + (1 - Φ(Upper z-score))

Substituting the values and calculating:

Upper z-score = (2.019 - 1.96) / 0.031 ≈ 1.903

Lower z-score = (1.862 - 1.96) / 0.031 ≈ -3.161

Using a standard normal distribution table or a calculator, we can find:

Φ(1.903) ≈ 0.9719

Φ(-3.161) ≈ 0.0008

Probability of a defect = 0.0008 + (1 - 0.9719) ≈ 0.0289

Therefore, the probability of a defect for this system is approximately 0.0289 or 2.89%.

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The Romberg array is a table of values that is used to estimate the value of a definite integral. To compute the Romberg array, we use the Richardson extrapolation method, which is a process of successive approximation.

To compute the eight rows and columns of the Romberg array, we begin by splitting the integration interval into two equal-length subintervals. The trapezoidal method is then applied to each subinterval to produce two estimates of the integral. The Richardson extrapolation method is then used to get a better estimate of the integral based on these two estimations. This operation is continued, splitting the subintervals into smaller and smaller subintervals, until the Romberg array has the necessary number of rows and columns.

The Romberg array's general formula is as follows:

R(m,n) = (4^n R(m,n-1) - R(m-1,n-1)) / (4^n - 1)

where R(m,n) is the value of the integral estimate at row m and column n in the Romberg array.

The first column of the Romberg array contains the estimates obtained by the trapezoidal rule, while the subsequent columns are obtained by applying the Richardson extrapolation method using the values in the previous column.

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Answer:

t(s(2)) where s(x) = -x + 1, t(x) = -x^2 - 1 = -2

Step-by-step explanation:

The relevant details from the poem and the description of how they develop the subject are:

The fact that the narrator mentions how there are a pair of them means that they are not alone. It means that just because they are a nobody does not mean that they consider themselves to be alone.

The fact that they could be banished means that being a nobody is a bad thing that warrants the punishment of being banished from the society in question.

When a person is deary, it means that they are doing something that can either bring them praise or punishment which means that being somebody can either be positive or negative so it can be a positive to be a nobody.

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Answer:

1.\(40000000000\)
2.\(500000000000000\)
(In case you were asking me to multiply, 20 × 10^24)

Step-by-step explanation:

Given the following questions:
\(4\times10^{10}\)
\(5\times10^{14}\)

In order to find the answers, we take note on how the exponents are positive. We also need to remember how integers always have invisible decimal points.

Question one:

\(4\times10^{10}\)
\(4\times10^{10} =4.0.0.0.0.0.0.0.0.0.0.\)
\(4.0.0.0.0.0.0.0.0.0.0.=40000000000\)
\(40000000000\)

Question two:

\(5\times10^{14}\)
\(5\times10^{14}=5.0.0.0.0.0.0.0.0.0.0.0.0.0.0.\)
\(5.0.0.0.0.0.0.0.0.0.0.0.0.0.0.=500000000000000\)
\(500000000000000\)

In case you were asking me to multiply:

\(40000000000\times500000000000000=20000000000000000000000000\)
\(20000000000000000000000000=20\times10^{24}\)
\(20\times10^{24}\)

Hope this helps.

The function F(A,B,C,D) = B' D + A' D + BD can be expressed as the sum of minterms Σm(1, 3, 5, 7, 9, 11, 13, 15) and as the product of maxterms ΠM(0, 2, 4, 6, 8, 10, 12, 14).

The calculation to express the function F(A,B,C,D) = B' D + A' D + BD as the sum of minterms and as the product of maxterms:

1. Sum of minterms:

F(A,B,C,D) = B' D + A' D + BD

= Σm(1, 3, 5, 7, 9, 11, 13, 15)

To obtain the minterms, we consider each term where the function evaluates to 1:

F(A,B,C,D) = B' D + A' D + BD

= B' D' C' A' + B' D' C' A + B' D' C A' + B' D' C A + B' D C' A' + B' D C' A + B' D C A' + B' D C A

= Σm(1, 3, 5, 7, 9, 11, 13, 15)

2. Product of maxterms:

F(A,B,C,D) = B' D + A' D + BD

= ΠM(0, 2, 4, 6, 8, 10, 12, 14)

To obtain the maxterms, we consider each term where the function evaluates to 0:

F(A,B,C,D) = B' D + A' D + BD

= (B + D) (A + D') (C + D') (A + C') (B + D') (A + D) (C + D) (A + C)

= ΠM(0, 2, 4, 6, 8, 10, 12, 14)

So, the function F(A,B,C,D) = B' D + A' D + BD can be expressed as the sum of minterms Σm(1, 3, 5, 7, 9, 11, 13, 15) and as the product of maxterms ΠM(0, 2, 4, 6, 8, 10, 12, 14).

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Answer:

9\(\sqrt{2}\)

Step-by-step explanation:

9^2 = 81

81 + 81 = 162 = 9\(\sqrt{2}\)

The value of the angle IJK in the image shown is 158°

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depends on other variable while a dependent variable is a variable that depends on other variable.

From the diagram:

m∠IJK = m∠IJZ + m∠ZJK

substituting:

27x - 6 = 16x + 4 + (56)

x = 6

m∠IJk =27(6) - 4 = 158°

The value of the angle IJK in the image shown is 158°

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Answer:

First number is 20, second is 25

Step-by-step explanation:

x + y = 5 + 2x = 45

solve for x first

5 + 2x = 45

x = 20

then solve for y

20 + y = 45

y = 25

hope this helps

The number of times by which 9 × 10⁵ is larger than 5 × 10³ as required to be determined is; 180.

It follows from the task content that the number 9 × 10⁵ is to be compared to 5 × 10³ and determine how larger it is.

On this note, to determine how large 9 × 10⁵ is compared to 5 × 10³; we have that;

(9 × 10⁵) / (5 × 10³)

= (9/5) × (10⁵/10³)

= 1.8 × 100

= 180.

Consequently, the correct answer as required is 180.

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Answer: 180

Step-by-step explanation:

try it and find out........ because it is right -.-

Answer:

-1x -3

Step-by-step explanation:

(3x+4)+(-4x-7)

3x + 4 -4x -7

3x - 4x +4 -7

-1x -3

Hey there!

Plug in the value of x and evaluate:

x²-16x+64

(-4)²+16(-4)+64

16-64+64

16

Hence, the answer is 16.

Hope everything is clear.

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:-)

a < 0 the direction of opening of the graph of the given function is downward.

The given function is: f(x) = –12|x + 3| + 1.

The vertex of the graph of the given function is (-3,1).

The graph of the given function opens downward.Hence, the correct option is: (C) (-3, 1), downward.

We know that the vertex of the graph of f(x) = a|x - h| + k is (h, k).

Comparing the given function f(x) = –12|x + 3| + 1 with the standard form of the absolute function f(x) = a|x - h| + k,

we get

a = -12,

h = -3, and

k = 1.

Therefore, the vertex of the graph of the given function is

(h, k) = (-3, 1).

We know that the direction of opening of the graph of the function

f(x) = a|x - h| + k is upward if a > 0, and the direction of opening of the graph of the function f(x) = a|x - h| + k is downward if a < 0.

Comparing the given function f(x) = –12|x + 3| + 1 with the standard form of the absolute function f(x) = a|x - h| + k,

we get a = -12.

Since a < 0, the direction of opening of the graph of the given function is downward.

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Answer:

4(p + 8) = 8p – 8(p – 6)

4p+32=8p-8p+48

4p=16

p=4

Answer: P=20

Step-by-step explanation:

Hope this helps ;)

Answer: f(0)=11/2

f(n) = f(n - 1) · (-2)

Step-by-step explanation:

f(0)=f(1)*(f(0+1)/f(1+1))

f(0)=f(1)*(f(1)/f(2))

f(0)=-11*(-11/22)

f(0)=-11*(-1/2) ==> -11/22 simplifies to -1/2

f(0)=-11*(-1)/2

f(0)=11/2

f(n) = f(n - 1) · f(2)/f(2-1)

f(n) = f(n - 1) · f(2)/f(1)

f(n) = f(n - 1) · 22/(-11)

f(n) = f(n - 1) · 2/(-1)

f(n) = f(n - 1) · (-2)

Since the line is linear, the sum of the angles should be 180 degrees

x + 28 + 73 = 180

x = 180 - 28 - 73

x = 79 degrees

Hope this helped :)

Answer:

Plot I area= 32.5cm²

Plot II area = 73.09cm²

Plot III area = 35cm²

Plot IV area = 54cm²

Total the area of Field​ = 194.59cm²

Step-by-step explanation:

The field is made up of four plots with different shapes. So we would find the area of the 4 shapes to get the area of the plots.

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Find attached the diagram

Given:

AC = 13cm

AE = 19cm

CF = DE = 7cm

AD = AE - DE

AD =  19-7 = 12cm

GF = 9cm, EH = 15cm

GH = 17cm

Plot I: A right angle triangle

Area = ½ × base × height

Base = CD, height = AD

Using Pythagoras theorem

CD = √(AC² - AD)²

CD = √(13² - 12²) = √(169-144)

CD = √25 = 5

Area = ½ × 5 ×13= 32.5

Area plot I = 32.5cm²

Plot II: An equilateral triangle

Area of the equilateral triangle = a²/4 ×(√3)

√3=1.73

a = side = AC

Area = (13)²/4 ×(√3) = 42.25 × 1.73 = 73.0925

Area of Plot II = 73.09cm²

Plot III: A rectangle

Area of a rectangle = length × width

length = 7cm

width = 5cm

Area of plot III = 7×5 = 35cm²

Plot IV: A trapezium

Area of trapezium = ½(base 1 + base2) × height

Base 1= FE = CD

Base 2= GH

To get height using diagram 2. When you draw the lines from the two points on base1, you would have 1 rectangle in the middle with the two triangles by the side.

We would apply Pythagoras theorem to find h in the two right angled triangles:

Hypotenuse ² = opposite ²+adjacent ²

1st ∆: 9² = h²+a²

h² = 81-a²

2nd ∆: 15² = h² + (12-a)²

225 = h² +144 - 24a+ a²

225-144 = h²-24a+ a²

Insert value for h² in the 2nd

81 = 81-a² - 24a + a²

24a = 81-81

a= 0

h² = 81-0²

h = √81 = 9

Area of trapezium = ½(5+7) × 9

= 6 × 9

Area of plot IV= 54cm²

Total the area of field​ = area of plot I + area of plot II + area of plot III +area of plot IV

= 32.5 + 73.09 + 35+ 54

Total the area of Field​ = 194.59cm²

Answer:

It would take Micheal 22 days.

Step-by-step explanation:

The end goal is to have 80 and we begin with 14

So, 80 - 14 = 66 pieces left to collect

If he collects 3 per day we'll divide 66 by 3, which equals 22

Therefore it takes him 22 days