Solve the inequality -6x+28>=10

By factor theorem and limits, it is found that the end behavior of g(x) is that it goes to negative infinity.

The values of x and g(x) are

x    –4 –1  0  1     5 8 12

g(x) 0  –3  –1  –2 0 3 0

We need to find the end behavior of g(x).

The Factor Theorem states that a function with leading coefficient a and zeros x1,x2,x3...xn  is defined by:

g(x)=(x-x1)(x-x2)(x-x3)..(x-xn)

By definition of factor theorem,

g(x)=a(x-(-4))(x-12)

g(x)=a(x+4)(x-12)

g(x)=a(x2-8x-48)

The end behavior is the limit of g(x) as x goes to infinity, thus:

lim\(lim \lim_{x \to \infty} g(x)= \lim_{x \to \infty} ax^{2} =a*\infty\)

Since the leading coefficient a is negative:

a*infinity= - infinity

Thus the end behaviour of g(x) it goes to negative infinity.

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Answer:

greater than 10 but less than 100

Step-by-step explanation:

700% of 3 is 21, since 100% of 3 is 3, you multiple it 7 times for 700% which gets you 21

when your friend was born, your friend's parents deposited $2000 in an account paying 4.5% interest compounded yearly. Then the account balance be after 18 years is 4416.96

Initial amount deposited into the account is $2000 This means that the principal,

P = 2000

It was compounded yearly. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 4.5%. So

r = 4.5/100 = 0.045

It was compounded for 18 years. So

t = 18

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 2000(1 + 0.045/1)^ 1× 18

A = 2000(1 + 0.045)^18

A= 4416.96

Hence , the amount becomes after 8 years is 4416.96

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Let's start the sum as follows:

x³ = 8

X × X × X = 8

This means there are 3 number which after Multiplication gives answer 8.

If 2 is multtiplied 3 times it will give you 8

Thus the answer of x is 2

x = 2.

x^3 = -8

The cube root of 8 is 2 = 2 x 2 x 2 is 8.

But, the answer is negative, which means that the cube root of -8 must be -2.

-2 x -2 x -2 = -8

x = -2

Hope this helps!

The sample size which will produce sample proportion of 0.3 and 95% confidence interval is 36.

Given sample proportion of 0.3, confidence level 95%.

A confidence interval of proportions is given by:

π±z\(\sqrt{}\)π(1-π)/n

In which :

π is the sample proportion,

z is the critical value

n is the sample size.

Margin of error=z\(\sqrt{}\)π(1-π)/n

z value for confidence level of 95% is 1.96

Margin of error=1.96\(\sqrt{0.3*0.7/n}\)

The widest interval has the highest margin of error, since the margin of error and since the margin of error is inversely proportional to the sample size , a lower sample size generates a higher margin of error.

Hence sample size which is correct is 36.

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Question is incomplete as it also includes options like:

a)46

b)68

c)56

d)36.  

A

Step-by-step explanation:

(1.7×8.0)/3.4 ×10^23-14-23

=4×10^-14

Answer:

yes, it is

Step-by-step explanation:

10 = 4(2) + 2

10 = 8 +2

10 = 10

10  = 2 + 8

10 = 10

Answer:

The answer is yes

*View the attached graph to check your answer graphically.*

Step-by-step explanation:

y = 4x + 2

y = x + 8

For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.

First, I will substitute the second equation, for y, in the first equation:

y = 4x + 2

y = x + 8

x + 8 = 4x + 2

Next, subtract 4x from both sides to isolate x:

x + 8 = 4x + 2

-4x      -4x

-3x + 8 = 2

Then, subtract 8 from both sides:

-3x + 8 = 2

     - 8    - 8

-3x = -6

Now, divide both sides by -3:

-3x = -6

/-3    /-3

x = 2

Now, we find the value of y by substituting 2 for x:

y = 4x + 2

y = 4(2) + 2

y = 8 + 2

y = 10

(x, y) ==> (2, 10)

Therefore, yes (2,10) is a solution to this system of equations.

*View the attached graph to check your answer graphically.*

Hope this helps!

Answer:3−4x/7≤y≤−8+5x

Step-by-step explanation:

Next, multiply the base area by the height of the prism: Volume = 17.5 cm² x 10 cm = 175 cm³.

So, the volume of the triangular prism is 175 cubic centimeters.To find the volume of a triangular prism, you need to multiply the area of the base triangle by the height of the prism.

First, we need to find the area of the base triangle. Since it is a right triangle, we can use the formula A = 1/2 bh, where b and h are the lengths of the legs of the triangle.

A = 1/2 x 5 cm x 7 cm
A = 17.5 cm^2

Now that we have the area of the base triangle, we can find the volume of the prism by multiplying it by the height of the prism.

V = A x h
V = 17.5 cm^2 x 10 cm
V = 175 cm^3

Therefore, the volume of the triangular prism is 175 cubic centimeters.
Hi! To find the volume of a triangular prism, you need to use the formula: Volume = (Base Area) x Height. In this case, the base is a right triangle with legs of length 5 cm and 7 cm, and the prism is 10 cm tall.

First, calculate the base area of the right triangle: (1/2) x base x height = (1/2) x 5 cm x 7 cm = 17.5 cm².

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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1. matches to column 1

2. matches to column 5

3. matches to column 4

4. matches to column 2

5. matches to column 3

Hope it helps.

Answer:

cant see photo lol srry!!!???

Step-by-step explanation:

Answer:

5+d2

Step-by-step explanation:

We'll make d=day

5+d2

5 is the base price

and 2 is the number that increases by day

Please tell me if it's incorrect

Happy Holidays!

Answer:

53.658

Step-by-step explanation:

Answer:131275

Step-by-step explanation: i looked it up :/

To obtain the sampling distribution (likelihood) and the posterior distribution for this scenario, we can use Bayesian inference.

The sampling distribution (likelihood) can be represented as:

p(y|u,02) = (1/sqrt(2*pi*02)^n) * exp(-(1/(2*02)) * sum((yi-u)^2))

where y is the observed data, u is the mean of the normal distribution, and 02 is the variance of the normal distribution.

The non-informative prior for 02 can be represented as:

p(02) « 1/02

Using Bayes' theorem, we can obtain the posterior distribution:

p(u,02|y) = p(y|u,02) * p(02) / p(y)

where p(y) is the marginal likelihood. To simplify the calculation, we can integrate out u from the joint distribution:

p(02|y) = (p(y|02) * p(02)) / p(y)

where p(y|02) is the marginal likelihood for 02:

p(y|02) = (1/sqrt(2*pi*02)^n) * exp(-(n-1)/2)

We can then obtain the posterior distribution for 02:

p(02|y) « 1/02 * exp(-(n-1)/2)

This is a gamma distribution with shape parameter (n-1)/2 and scale parameter 1/2. Therefore, the posterior distribution for 02 is:

02|y ~ Gamma((n-1)/2, 1/2)

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Answer:

B

Step-by-step explanation:

0.25 = 1/4 = 5/20

0.35 = 35/100 = 7/20

5/20 + 7/20 = 12/20 = 6/10 = 3/5

Answer:

Step-by-step explanation:

so first you would do 0.25+0.35= 0.6

now put 0.6 into a fraction= 6/10 because 6 is in the 10th place then simplify 6/10=3/5 which to find that you divide each side by 2

Hope This Helped!

Answer:

x < - 4

Step-by-step explanation:

7(x + 3) < 5x + 13 ← distribute parenthesis on left side

7x + 21 < 5x + 13 ( subtract 5x from both sides )

2x + 21 < 13 ( subtract 21 from both sides )

2x < - 8 ( divide both sides by 2 )

x < - 4

Answer:

a.    \(T = 17s\)

b.    \(D = 72cm\)

Step-by-step explanation:

Given

Direct Variation

\(Distance(D)\ \alpha\ Time (T)\)

D = 264 cm when T = 11 s

Calculating (a)

First, the constant of variation (k) as to be calculated;

Since, there exist a direct proportion; then,

\(D\ \alpha\ T\)

\(D = kT\)

Make k the subject of formula

\(k = \frac{D}{T}\)

D = 264 cm when T = 11 s; So

\(k = \frac{264}{11}\)

\(k = 24\)

So: Solving for (a)

\(D = 408\)

Substitute 408 for D and 24 for k in \(D = kT\)

\(408 = 24 * T\)

Divide both sides by 24

\(\frac{408}{24} = T\)

\(T = \frac{408}{24}\)

\(T = 17s\)

Hence, time to move a distance of 408cm is 17s

Calculating (b)

\(T = 3\)

Substitute 3 for T and 24 for k in \(D = kT\)

\(D = 24 * 3\)

\(D = 72cm\)

Hence, distance covered in 3 seconds is 72cm

The number of followers Rita has is 13086.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of followers Rida has = 6,218

92 people stop following Rida's blog.

This means,

6218 - 92 = 6126

417 people start following Rida's blog.

This means,

6126 + 417 = 6543

The number of followers doubles.

This means,

6543 x 2 = 13086

Thus,

The number of followers Rita has is 13086.

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Answer:

313°

Step-by-step explanation:

Answer:

The zeros are x = -2, x = 0, x = 4.

Step-by-step explanation:

The zeros describe where the function crosses the x-axis, or where the y-value is zero. In this case, the zeros are x = -2, x = 0, x = 4.

The Moon is a natural satellite of the Earth and it takes approximately 27.3 days to complete one rotation around its own axis.

The day and night cycles on the Moon are longer than those on Earth.

The reason for this difference in the length of day and night cycles is due to the Moon's synchronous rotation means that it takes the same amount of time for the Moon to complete one rotation around its own axis as it takes to complete one orbit around the Earth.

The synchronous rotation of the Moon is a result of the gravitational forces between the Earth and the Moon.

These forces have caused the Moon's rotation to gradually slow down over time, until it became synchronized with its orbit around the Earth.

As a result, the same side of the Moon always faces the Earth and the other side is permanently hidden from view.

The longer day and night cycles on the Moon have important implications for the lunar environment.

The extreme temperature variations between the day and night sides of the Moon make it a challenging environment for human exploration.

The daytime temperatures on the Moon can reach up to 127°C (261°F), while the nighttime temperatures can drop to -173°C (-280°F).

The Moon's day and night cycles are longer than those on Earth due to its synchronous rotation with its orbit around the Earth.

This unique phenomenon has important implications for the lunar environment and presents challenges for human exploration of the Moon.

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Answer:

after simplifying, we get,

23/6

Step-by-step explanation:

(2/3+5/2-7/3)+(3/2+7/3-5/6)

We simplify,

\((2/3+5/2-7/3)+(3/2+7/3-5/6)\\(2/3-7/3+5/2)+(3/2+7/3-5/6)\\(5/2-5/3)+(9/6+14/6-5/6)\\(15/6-10/6)+((9+14-5)/6)\\(15-10)/6+(23-5)/6\\5/6+18/6\\(5+18)/6\\23/6\)

To find the point on the line 3x + y = 4 that is closest to the point (-3, 1), we can use the concept of perpendicular distance.

First, let's express the equation of the given line in slope-intercept form (y = mx + b):

y = -3x + 4

Now, we can consider a perpendicular line passing through the point (-3, 1). The slope of the perpendicular line will be the negative reciprocal of the slope of the given line, which is 1/3.

Using the point-slope form of a line (y - y1 = m(x - x1)), we can write the equation of the perpendicular line:

y - 1 = (1/3)(x + 3)

y - 1 = (1/3)x + 1

y = (1/3)x + 2

To find the intersection point of the two lines, we can solve the system of equations:

y = -3x + 4

y = (1/3)x + 2

By equating the two equations, we get:

-3x + 4 = (1/3)x + 2

Simplifying the equation:

-3x - (1/3)x = 2 - 4

-10/3 x = -2

x = 6/5

Substituting the value of x back into either equation, we find:

y = -3(6/5) + 4

y = -18/5 + 20/5

y = 2/5

Therefore, the point on the line 3x + y = 4 closest to the point (-3, 1) is (6/5, 2/5).

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To show that lim x-0 sinx/x=1 using limx-0 cosx-1/x=0, we can use the following trigonometric identity: lim x-0 sinx/x = lim x-0 (cosx-1)/x, Since we are given that limx-0 cosx-1/x=0, we can substitute this into the above identity to get: lim x-0 sinx/x = lim x-0 (cosx-1)/x = 0.

Now, we need to manipulate this expression to get it in the form we want, which is lim x-0 sinx/x=1. We can do this by multiplying the expression by -1/-1, which doesn't change the value but flips the sign: lim x-0 sinx/x = lim x-0 (1-cosx)/x = - lim x-0 (cosx-1)/x.

Now, we can substitute the given limit into this expression to get: lim x-0 sinx/x = - 0 = 0, This is not what we want, so we need to do one more step. We can use the fact that cosx-1 = -2sin^2(x/2) to rewrite the expression: lim x-0 sinx/x = - lim x-0 2sin^2(x/2)/(x/2)^2 * (x/2)^2 = -2 * lim x/2-0 sin^2(x/2)/(x/2)^2 * (x/2)^2. Now, we can use the fact that lim x-0 sinx/x=1 (which is a well-known limit) to get: lim x-0 sinx/x = -2 * 1 * 0 = 0.

This is still not what we want, but we're almost there. We can now use the fact that sinx/x approaches 1 as x approaches 0 (which is a well-known limit) to get: lim x-0 sinx/x = -2 * lim x-0 sin^2(x/2)/(x/2)^2 * (x/2)^2 = -2 * 1 * 0 = 0, Finally, we can multiply by -1/-1 to get the desired result: lim x-0 sinx/x = 1.

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Answer:

To show that lim x-0 sinx/x=1 using limx-0 cosx-1/x=0, we can use the following trigonometric identity: lim x-0 sinx/x = lim x-0 (cosx-1)/x, Since we are given that limx-0 cosx-1/x=0, we can substitute this into the above identity to get: lim x-0 sinx/x = lim x-0 (cosx-1)/x = 0.

Now, we need to manipulate this expression to get it in the form we want, which is lim x-0 sinx/x=1. We can do this by multiplying the expression by -1/-1, which doesn't change the value but flips the sign: lim x-0 sinx/x = lim x-0 (1-cosx)/x = - lim x-0 (cosx-1)/x.

Now, we can substitute the given limit into this expression to get: lim x-0 sinx/x = - 0 = 0, This is not what we want, so we need to do one more step. We can use the fact that cosx-1 = -2sin^2(x/2) to rewrite the expression: lim x-0 sinx/x = - lim x-0 2sin^2(x/2)/(x/2)^2 * (x/2)^2 = -2 * lim x/2-0 sin^2(x/2)/(x/2)^2 * (x/2)^2. Now, we can use the fact that lim x-0 sinx/x=1 (which is a well-known limit) to get: lim x-0 sinx/x = -2 * 1 * 0 = 0.

This is still not what we want, but we're almost there. We can now use the fact that sinx/x approaches 1 as x approaches 0 (which is a well-known limit) to get: lim x-0 sinx/x = -2 * lim x-0 sin^2(x/2)/(x/2)^2 * (x/2)^2 = -2 * 1 * 0 = 0, Finally, we can multiply by -1/-1 to get the desired result: lim x-0 sinx/x = 1.

Step-by-step explanation:

The mean score of the given data set will not change by 1% and the median score of the given data set

Mar x the score recorded as 69%. Therefore, the score recorded as 49% would be (100 - 69)% = 31% or 0.31x. We represent the students' scores by 'S'. And the corrected score of the student whose score was recorded as 49% times 'x'. Since the total number of students is not given, we can consider the score of 100 students.

Therefore, total score of the 100 students = S1 + S2 + S3 + ... + S100

Student's corrected score = x Now, we know that 100x - 31x = S1 + S2 + S3 + ... + S100 (because the student's score is x)

The above formula can be written as

\(69x = S1 + S2 + S3 + ... + S100 + 31x\)

The sum of all the bases before correction is S. And the total number of students is N. Now, we can write

\(S1 + S2 + S3 + ... + S100 = S - 0.31x\)

Therefore

\(69x = S -0.31x + 31x\\100x = S\\x = (1/100) S\\\)

Now, the average score of the given data set is:

Means =  \((S + x) / (N + 1)\)

Average score after correction

\((S + x) / (N + 1) = (S + (1/100) S) / (N + 1) = (101/100) (S / (N + 1))\)

Therefore, the mean score of the given data set discards by 1%. Now, the median score of the given data set is:

median = \((n + 1) / 2\)

Where n is the number of scores in the data set After correction, the total number of scores in the data set remains the same. Therefore, the median score of the given data set will not change.

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

Explanation:

n = diagram number

m = number of matches for diagram n

The given figures show that we have this info so far

\(\begin{array}{|c|c|} \cline{1-2}n & m\\\cline{1-2}1 & 3\\\cline{1-2}2 & 5\\\cline{1-2}3 & 7\\\cline{1-2}\end{array}\)

In other words, we have this sequence of values to represent the number of matches: 3, 5, 7

Each time we generate a new figure, we add 2 matches to the far right side. One match being horizontal and the other vertical.

This shows the common difference of this arithmetic sequence is d = 2.

The starting term is \(a_1 = 3\).

Let's find the nth term.

\(a_n = a_1 + d(n-1)\\\\a_n = 3 + 2(n-1)\\\\a_n = 3 + 2n-2\\\\a_n = 2n+1\\\\\)

Then we can determine the 50th term.

\(a_n = 2n+1\\\\a_{50} = 2(50)+1\\\\a_{50} = 100+1\\\\a_{50} = 101\\\\\)

There are 101 matches in the 50th diagram of the pattern.

Any slice parallel to the base will cut through the pyramid at a right angle and produce a square-shaped cross-section.

When a square pyramid is sliced parallel to the base and halfway up the pyramid, the resulting cross section would be a square.A square pyramid has a square base and four triangular faces that converge to a single point called the apex.

If the pyramid is sliced parallel to the base, the cross-section will always be a square, regardless of where the slice is made. This is because the square base remains intact, while the triangular faces are truncated.

A cross-section is the shape you get when you slice a solid object. The cross-sections of different shapes can vary depending on where they are sliced,

but the cross-section of a square pyramid sliced parallel to its base and halfway up the pyramid will always be a square. This is because the square base is perpendicular to the axis of the pyramid,

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Answer:

y is 11. x is 5 n i think it is 10

Step-by-step explanation:

when you subtract just think what number can it be like 3 + x = 5. so here it is 2

hope this helps

Step-by-step explanation:

y-4=7

y=7+4

y=11(ans)

x-5=0

x=0+5=5(ans)

3(n-2)=48

3n-6=48

3n=48+6

n=54/3=18(ans)

Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9