f(x)=x²+2x²-11; f(-3)

We have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

To apply the Intermediate Value Theorem to the polynomial function f(x) = x^3 - x - 4 and show that it has a real zero between the integers 1 and 7, we need to verify that f(1) and f(7) have opposite signs.

Let's evaluate f(1) and f(7) to determine their signs:

f(1) = (1)^3 - (1) - 4 = 1 - 1 - 4 = -4

f(7) = (7)^3 - (7) - 4 = 343 - 7 - 4 = 332

From the calculations, we can see that f(1) = -4 and f(7) = 332.

Since f(1) is negative (-4) and f(7) is positive (332), they have opposite signs.

According to the Intermediate Value Theorem, if a continuous function changes sign between two points, then it must have at least one real zero between those points.

Since f(1) = -4 (negative) and f(7) = 332 (positive), the polynomial function f(x) = x^3 - x - 4 must have a real zero between the integers 1 and 7.

Therefore, we have demonstrated using the Intermediate Value Theorem that the polynomial function has a real zero between 1 and 7.

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The equations of the lines that passes through the given points are:

Part A:

The slope of the line is given by:

m = (y2 - y1)/(x2 - x1) = (-2 - 3.5)/(10 - (-1)) = -0.5

Using the point-slope form of the equation of a line, where (x1, y1) = (-1, 3.5) and m = -0.5, we get:

y - 3.5 = -0.5(x + 1)

Simplifying, we get:

y = -0.5x + 2

Therefore, the equation of the line passing through the points (-1, 3.5) and (10, -2) is y = -0.5x + 2.

Part B:

The slope of the line is given by:

m = (y2 - y1)/(x2 - x1) = (9 - (-12))/(3 - (-4)) = 21/7 = 3

Using the point-slope form of the equation of a line, where (x1, y1) = (-4, -12) and m = 3, we get:

y - (-12) = 3(x - (-4))

Simplifying, we get:

y = 3x - 0

Therefore, the equation of the line passing through the points (-4, -12) and (3, 9) is y = 3x.

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Answer:

The value of r is 9 and the length of segment EF is 55 units. Opposite sides are equal. Hence, the value of r is 9 and the length of segment EF is 55 units.

Answer:

r = 9

EF = 55

Step-by-step explanation:

9r - 6 = 8r + 3

9r - 8r = 3 + 6

r = 9

4r + 19 = 4(9) + 19 = 36 + 19 = 55

Given ΔPQR, the diagram shows possible segments are:

1.SR, 2. PQ AND PS and 3. QR

Segment:

A segment has two distinct endpoints on a line. The length of a line segment is fixed, that is, the distance between two fixed points. Here, length can be measured in metric units such as centimeters (cm), millimeters (mm) or in conventional units such as feet or inches.

Geometric Mean:

The geometric mean (GM) is an average or mean that expresses the central tendency of a set of numbers by multiplying their values. Basically, we multiply the numbers exactly and take the nth root of the multiplied number, where n is the total number of data values. For example: For a given set of two numbers, say 3 and 1, the geometric mean is equal to √(3×1) = √3 = 1.732.

Given:

Segments                                              Geometric Mean

PS and QS                                           \(\sqrt{(PS)* (QS)}\) or RS

PQ and QR                                                  PR

PQ and QS                                                   QR

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Step-by-step explanation:

a= 1/3 + 3/5

= 5+9/15

= 14/15

b=6/7-2/5

=30-14/35

= 16/35

The object would be age of 5730 years old.

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

If an object contains 50% of its original amount of carbon-14, then the remaining amount is D/D₀ = 0.5, where D₀ is the original amount of carbon-14.

Substituting this value into the equation A = -8267 ln(D/D₀)

A = -8267 ln(0.5/1)

A = 5730 years

Therefore, the object would be age of 5730 years old.

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Answer:

1,708

Step-by-step explanation: does it need an explanation?

if so tell me

1,708

if you multiply 16 by 7 and by 15 equal 1,680. Then you add 11 then add 17 which would give you 1,708

Based on simultaneous equations, Kaun has deposited in each account the following:

When two or more algebraic equations are solved concurrently, we call them simultaneous equations.

We can solve simultaneous equations by graphing, elimination, or substitution methods.

The total deposit in the two accounts = R 5,400

The annual interest in Account A = 3% or 0.03

The annual interest in Account B = 2% or 0.02

The total interest earned from both accounts for the year = R 140

Let Account A be designated as a and Account B be designated as b.

a + b = 5,400 ... Equation 1

0.03a + 0.02b = 140 ... Equation 2

Eliminate a by multiplying Equation 1 by 0.03:

0.03a + 0.03b = 162 ... Equation 3

Subtract Equation 2 from Equation 3:

0.03a + 0.03b = 162

-

0.03a + 0.02b = 140

= 0.01b = 22

b = 2,200

From Equation 1, substitute b:

a + 2,200 = 5,400

a = 3,200 (5,400 - 2,200)

Check:

In equation 2:

0.03a + 0.02b = 140

0.03(3,200) + 0.02(2,200) = 140

96 + 44 = 140

140 = 140

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The area of the circle, as a function of x, will be:

A(x) = 3.14*(3ft + 2x)²

We know that for a circle of radius R, the area is:

A = pi*R²

Where pi = 3.14

In this case we have a circular plot of land with a diameter of 6ft, then the radius (half of that) is:

R = 6ft/2 = 3ft

And then we have a walkway with a width of 2x, then the radius of the circle that includes the walkway is:

R' = 3ft + 2x

Replacing that in the area equation we will get:

A(x) = 3.14*(3ft + 2x)²

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Answer:

1/2

Step-by-step explanation:

Given:

(2 cubed) (2 superscript negative 4)

= (2³)(2^-4)

= (2³) (1 / 2⁴)

= (2³ * 1) / 2⁴

= 2³ / 2⁴

Both numerator and denominator has the same base. Thus, pick one of the bases

Also, in indices, division sign can be translated to subtraction

Therefore,

2³ / 2⁴

= 2^3-4

= 2^-1

= 1/2¹

= 1/2

(2³)(2^-4) = 1/2

Answer:

D

Step-by-step explanation:

bc i said so

Answer:

The rea of walk way is 32 ft^2.

Step-by-step explanation:

width, w = 8 feet

length, L = 10 feet

width of walkway, d = 2 feet

length of outer, L' = 10 + 2 + 2 = 14 feet

Area of outer, A' = L' x w = 14 x 8 = 112 ft^2

Area of inner, A = L x w = 10 x 8 = 80 ft^2

The area of walkway = A' - A = 112 - 80 = 32 ft^2

The rea of walk way is 32 ft^2.

The ratio of boys to girls is 74:62

74 represents the boys

62 represents the girls

Answer:

A. The sampling distribution follows a normal distribution

B. With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28

C. If many groups of 55 randomly selected people were surveyed, then a different confidence interval would be produced for each group. About 90 percent of these confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered  

Step-by-step explanation:

The given parameters are;

The known population standard deviation of the number of names that people can recall after being introduced to 40 people in a party, σ = 6.34 names

The number of people randomly selected in the survey, n = 55 people

The average number of names correctly remembered, \(\overline x_1\) = 18.16

The standard deviation of the group surveyed, s = 4.28

A. Based on the Central Limit Theorem CLT, the sampling distribution follows a normal distribution

B. The 90% confidence interval is given as follows;

\(C.I.=\bar{x}\pm z_{\alpha /2}\cdot \dfrac{\sigma}{\sqrt{n}}\)

Where \(z_{\alpha /2}\) at 90% = 1.65, we have;

\(C.I.=18.16\pm 1.65 \times \dfrac{4.28}{\sqrt{55}}\)

C.I. ≈ 17.20 < μ < 19.11

With 90% confidence the mean number of names that all people can remember when introduced to 40 people at a party is between 17.04 and 19.28

C. The 90% confidence interval gives the certainty that if different groups of 55 randomly selected people were surveyed, then about 90 percent of the confidence intervals will contain the true population mean number of names remembered and about 10 percent will not contain the true population mean number of names remembered.

Answer:

Step-by-step explanation:

∠OAB is 90 degrees, tangent and a radius met at 90 degree angle

∠OCB=90 degrees, tan and radius meet at 90 degrees angle

OB=12

find angle BOC:

triangle BOA is right angle triangle:

cos(AOB)=adj/hyp=7/12=54.33

angle B= 180-(90+54.33)=35.67

angle COB=54.33 equal to angle AOB

angle AOC=54.33+54.33=108.66

the sum of angles of circle =360

360-108.66= 251.34( exterior angle at the center AOC)

length of the arc= angle (251.34 degrees*7)

convert degrees to radians=4.386 (251.34/π)

length=r*angle in radian=4.386*7=30.71

( i hope this is the answer)

The value of  β from the power of test is obtained as 0.02

The chance of rejecting the null hypothesis as untrue, or the likelihood of avoiding a type II mistake, is the power of a test. The probability that a certain investigation will identify a departure from the null hypothesis if one exists is another way to conceptualize power.

In hypothesis testing, power is typically the main concern. Power is defined as the likelihood that we would reject H0 as untrue, i.e., power = 1-β. Power is the likelihood that a test would properly reject a null hypothesis that isn't true.

The specified value for the test's power is 0.98 in the problem.

Hence,

Type II error, β= 1 - Power = 1 - 0.98 = 0.02

So, the value of β is obtained as 0.02.

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Answer:

yes

Step-by-step explanation:

it is a fraction

Answer:

I hope noth your pillows are cold tonight

I appreciate you doing this!!

Answers in bold:

S9 = 2

i = 20

R = -2

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

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

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

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

Compared to small samples, large samples have "less" variability and thus will have a "smaller" error from the population parameters.

Compared to small samples, large samples generally have less variability. This means that large samples are likely to have a more representative distribution of the population, resulting in less random error. In statistical terms, variability is measured by the standard deviation, which is the spread of the data around the mean. When a sample size is increased, the standard deviation of the sample means decreases, leading to less variability.

Less variability in large samples is beneficial because it results in a smaller margin of error from the population parameters. Margin of error is the amount by which the sample statistic may differ from the true population parameter. It is calculated by multiplying the standard error of the mean by a confidence interval, which depends on the sample size. A smaller margin of error implies greater precision and accuracy in estimating the population parameter.

Overall, larger sample sizes provide more reliable estimates of the population parameter, which is the goal of statistical inference. In many cases, larger sample sizes require more resources and time to collect, but they often provide a more accurate representation of the population, leading to more robust and generalizable conclusions. It is important to balance sample size with practical considerations and the objectives of the research question.

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Answer:

2.08 meters

Step-by-step explanation:

From the diagram attached :

We can calculate the height of the shorter building using trigonometry :

s = Height of shorter building

t = height of taller building

Tanθ = opposite / Adjacent

θ = 36°

Adjacent = 12, opposite = s

Tan36° = s / 12

0.7265425 × 12 = s

s = 8.72 meters

s = height of shorter building 8.72 meters ( 2 decimal places)

Height of taller building :

Tanθ = opposite / Adjacent

θ = 48°

Adjacent = t ; opposite = 12

Tan48° = 12 / t

1.1106125 = 12 / t

1.1106125 × t = 12

t = 12 / 1.1106125

t = 10.80 meters ( 2 decimal places)

Height of Taller building = 10.80 meters

Difference in height :

(10.80m - 8.72m) = 2.08 meters

Answer:4.12

Step-by-step explanation: I need brainliest for next rank I’d appreciate it

A predator-prey dynamical system is a type of mathematical model that describes the interactions between two species in an ecosystem, where one species (the predator) hunts and consumes the other (the prey).

In a predator-prey dynamical system, the populations of the predator and prey are modeled as differential equations that describe how their populations change over time. The predator population increases as it consumes prey, while the prey population decreases due to predation. These changes in population are influenced by a variety of factors, including the availability of food, the reproductive rates of the species, and the density-dependent effects of the population on its own growth.

Predator-prey models have been used to study a wide range of ecological systems, from small-scale interactions between insects and plants to large-scale predator-prey relationships in the African savanna. They are also used in fields such as epidemiology, economics, and engineering to model other types of interacting systems.

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Complete question:

what is the predator-prey dynamical system?

Answer:

He should have said that his small brother had 100 small building bricks, but lost 5 in total now.

if the function is divided and we get the remainder of  zero then  it is said to be a factor of a function

According to the Remainder Theorem, by a factor x − an of that polynomial, then you will get a zero remainder. The point of the Factor Theorem is the turnaround of the Remainder Theorem: On the off chance that you synthetic-divide a polynomial by x = a and get a zero remainder, at that point not as it were is x = a, a zero of the polynomial(for the remainder theorem ) but x − a is additionally a factor of the polynomial according to of the Factor Theorem.

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AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides of given triangle.

What is triangle?

A triangle is a two-dimensional geometric shape that has three sides, three angles, and three vertices. It is one of the simplest polygonal shapes and is commonly studied in geometry.

Since we have:

∠A ≅ ∠Y

∠B ≅ ∠X

∠C ≅ ∠Z

We can conclude that the two triangles ABC and XYZ are similar by the Angle-Angle (AA) similarity theorem.

Therefore, the corresponding sides of the two triangles are proportional to each other. We can write this as:

AB : YX = BC : XZ = AC : YZ

where AB and YX are corresponding sides, BC and XZ are corresponding sides, and AC and YZ are corresponding sides.

In other words, the ratio of the length of each side in triangle ABC to the corresponding side in triangle XYZ is constant.

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The number of possible ways such that Biggie and Tupac do not sit next to each other is, 14! - 2 = 87,178,291,200 sections.

There are 14 people having lunch at a round table including Instructor Tiny and 14 TAs. As given, two sections are the same when everybody has the same left neighbor and the same right neighbor. Therefore, the number of sections will be 14. In order to determine the number of possible ways when Biggie and Tupac do not sit next to each other, we have to calculate the total number of ways and then subtract the number of ways when they sit next to each other. There are a total of 14! ways to seat everyone at the table without any restrictions. However, Biggie and Tupac can sit next to each other in two ways (BT and TB), so we have to subtract that from the total number of possible ways. Therefore, the number of possible ways such that Biggie and Tupac do not sit next to each other is:

14! - 2 = 87,178,291,200 sections.

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Answer: x = 0

Step-by-step explanation:

Let's start with what we know:

We know that the line passes through (0,4) and (0,-3). Hmm, this is tricky but we can see that x = 0 for both points which would mean that this line is vertical. Because y changes, but x doesn't change, we know that x = 0 for the whole time.

So the answer is x = 0.

4b+4<20-12b

16b<16

b<1 olur.

İYİ DERSLER!

Answer:

See answer in the image below.

100:27

a  ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

so its also possible to do 100 to 27 but the answer is 100:27 or 100 to 27

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

The realization of the stochastic process implies that the values of the stochastic process are observed at particular points in time. It is denoted by x(t) and takes the form of a function of time t.

If the process is discrete, then the function is a sequence of values at discrete points in time.

A stochastic process is one that evolves over time and the outcomes are uncertain.

The given expression P(X5=3|X4=3,X3=3,X2=1,X1=4, X0=1) gives the probability of X5 being equal to 3 given that X4 is equal to 3, X3 is equal to 3, X2 is equal to 1, X1 is equal to 4, and X0 is equal to 1.

To understand the above expression, suppose we have a stochastic process with values X0, X1, X2, X3, X4, and X5.

The given expression provides the conditional probability of the value of X5 being equal to 3 given that X0, X1, X2, X3, and X4 take specific values.

The given information that X0=1, X1=4, X2=1, X3=3, and X4=3 further restricts the possible values that X5 can take.

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