Use the method of equating coefficients to find the values of a, b, and c: (x+4)(ax2+bx+c)=−2x3−7x2+3x−4.

Using the z-distribution, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

Researching this problem on the internet, 8 out of 39 candies are red, hence the sample size and the estimate are given by:

[tex]n = 39, \pi = \frac{8}{39} = 0.2051[/tex]

Hence the bounds of the interval are:

As a percentage, the 95% confidence interval for the percentage of red candies is of (7.84%, 33.18%). Since 33% is part of the interval, there is not enough evidence to conclude that the claim is wrong.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Answer:

[tex]x=2^{\frac{2}{3}}[/tex]

Step-by-step explanation:

1) Add 8 to both sides.

[tex]2x^3=8[/tex]

2) Divide both sides by 2.

[tex]x^3=\frac{8}{2}[/tex]

3) Simplify [tex]\frac{8}{2}[/tex] to 4.

[tex]x^3=4[/tex]

4) Take the cube root of both sides.

[tex]x=\sqrt[3]{4}[/tex]

5) Rewrite 4 as 2².

[tex]x=\sqrt[3]{2^2}[/tex]

6) Use this rule: [tex]{({x}^{a})}^{b}={x}^{ab}[/tex].

[tex]x=2^{\frac{2}{3}}[/tex]

Decimal Form: 1.587401

__________________________________________

Check the answer:

[tex]2x^3-8=0[/tex]

1) Let [tex]x=2^\frac{2}{3}[/tex].

[tex]2(2^{\frac{2}{3} })-8=0[/tex]

2) Use this rule: [tex](x^a)^b=x^{ab}[/tex].

[tex]2\times2^{\frac{2\times3}{3} } -8=0[/tex]

3) Simplify 2 * 3 to 6.

[tex]2\times2^{\frac{6}{3} } - 8 =0[/tex]

4) Simplify 6/3 to 2.

[tex]2\times2^2-8=0[/tex]

5) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]2^3-8=0[/tex]

6) Simplify 2^3 to 8.

8 - 8 = 0

7) Simplify 8 - 8 to 0.

0 = 0

Thank you,

Eddie

The solution to the equation is 0.07, 0.17, 0.27, 0.38........

The trigonometry equation is given as:

tan(30x - 90°) = -x³

We start by splitting the trigonometry equation as follows, by creating two different equations

y = tan(30x - 90°)

y = -x³

Next, we plot the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³

From the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³, we have the x coordinate of the point of intersection to be:

x = 0.07, 0.17, 0.27, 0.38........

Hence, the solution to the trigonometry equation is 0.07, 0.17, 0.27, 0.38........ .

Read more about trigonometry equations at

https://brainly.com/question/8120556

#SPJ1

Answer:

A., B.

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary, so their sum must equal 180°.

A. 72° + 108° = 180° Answer: yes

B. 66° + 114° = 180° Answer: yes

C. 80° + 90° = 170° Answer: no

D. 64° + 106° = 170° Answer: no

Answer: A., B.

[tex]~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ APY=\left(1+\frac{r}{n}\right)^{n}-1 ~\hfill \begin{cases} r=rate\to 10\%\to \frac{10}{100}\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12 \end{cases} \\\\\\ APY=\left(1+\frac{0.1}{12}\right)^{12}-1\implies APY=\left( \frac{121}{120} \right)^{12}-1\implies APY\approx 0.1047[/tex]

Answer:   so there would be 1

23                                                

3   21

2   20

Step-by-step explanation:

The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².

In this problem we have a quadratic equation in standard form, whose form is defined by f(x) = a · x² + b · x + c, where a, b, c are real coefficients, and we need to transform it into vertex form, defined as:

f(x) - k = C · (x - h)²       (1)

Where:

This latter form can be found by algebraic handling. If we know that f(x) = 2 · x² - 20 · x + 8, then its vertex form is:

f(x) = 2 · x² - 20 · x + 8

f(x) = 2 · (x² - 10 · x + 4)

f(x) + 2 · 25 = 2 · (x² - 10 · x + 25)

f(x) + 75 = 2 · (x - 5)²

The vertex form of the quadratic equation, written in standard form, f(x) = 2 · x² - 20 · x + 8 is f(x) + 75 = 2 · (x - 5)².

To learn more on quadratic equations: https://brainly.com/question/1863222

#SPJ1

Answer:

2583000000000

Step-by-step explanation:

[tex]2.583*10^{12} = 2583000000000[/tex]

The circumference of the pad to the nearest tenth is 39.6 meters

The circumference of a circle is the arc length of the circle, as if it were opened up and straightened out to a line segment. It is also known as the perimeter of a circle.

The formula for calculating the circumference of a circle is expressed as;

C = 2πr

where

π = 3.14

r is the radius of the circle

Given the following parameters

π = 3.14

r = 6.3m

Substitute to have:

C = 2 * 3.14 * 6.3

C = 6.28 * 6.3

C = 39.564

Hence the circumference of the pad to the nearest tenth is 39.6 meters

Learn more on circumference of a circle here: https://brainly.com/question/23986334

#SPJ1

Due to the higher z-score, the correct option regarding the highest relative score is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean, hence the higher the z-score, the higher the score X is relative to other scores.

The respective z-scores for this problem are given by:

Hence the correct option is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

More can be learned about z-scores at https://brainly.com/question/28096232

#SPJ1

Answer:

10x

Step-by-step explanation:

g(x)=5x

f(x)=2x

f(g(x))=f(5x)

f(g(x))=2*5x=10x

Answer:

  1/4

Step-by-step explanation:

The sum of an infinite geometric series is given by the formula ...

  S = a/(1 -r)

where 'a' is the first term, and r is the common ratio.

Here, the first term is 1/12, and the common ratio is ...

  (1/18)/(1/12) = 12/18 = 2/3

Then the sum is ...

  S = (1/12)/(1 -2/3) = (1/12)/(1/3) = 3/12 = 1/4

The sum of the infinite series is 1/4.

The best estimate for the correlation coefficient of the data is: C. 0.5.

Correlation can be defined as a quantitative measure that describes the relationship between variables. Correlation coefficient, r, is a number that ranges from -1 to 1.

The farther the correlation coefficient from 0, the stronger the relationship between two variables, and also, the more closer the data points are on a plotted graph. Also, a negative correlation value will show a trendline on a plot that slopes downward, while positive correlation value will show a trendline that slopes upwards.

In the graph given, the points are moderately closer to each other. Also, the trendline slopes upward, which suggest a positive correlation.

Since the points are moderately spaced from each other, the correlation coefficient would positive and be approximately 0.5.

Therefore, the best estimate for the correlation coefficient of the data is: C. 0.5.

Learn more about the correlation coefficient on:

https://brainly.com/question/4219149

#SPJ1

Answer:

7/18

Step-by-step explanation:

P(sophomore girl) is 7 out of a total 30.

P(girl) is 18 out of 30.

(7/30) / (18/30) = 7/18

If you just look at the girls column you can see this immediately. A given is that we're looking for a girl (18 girls), then what is the chance that it's a sophomore. That is 7 out of 18.

Answer:

The answer would be 7 over 18 in fraction form fill in 7 then 18

Step-by-step explanation:

7/18

The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m

According to the statement

we have given that the Triangular prism of size 0.75 m, 1m and length of 2m.

And we have to find the by which size of advertisement board need to fill the longest side of the shape.

A triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

So, for this purpose,

we know that the longest side of triangular prism is 2m and we have to cover it with the advertising board.

Obviously the length of the advertising board is of 2m to cover the longest side of the shape.

So, The dimensions be of any advertisement that wants to fill the longest side of the shape is of 2m and 1 m and 0.75 m

Learn more about triangular prism here https://brainly.com/question/16595877

#SPJ1

For circumference use C = 2πr because π is the ratio of Circumference to diameter and diameter is 2 x radius.

C = 2 x 3.142 x 9.5 cm ≈ 59.7 cm

Area of a circle is π x r² = 3.142 x (9.5 cm)² ≈ 283.6 cm²

The circumference of a circle with a radius of 9.5 centimeters is about 59.7 centimeters and the area of a circle with radius of 9,5 centimeters is about 283.6 centimeters.

According to the graph, the ships’ paths do not meet at any point.

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x = 5y - 40

-4x + 10y = 20

Make y the subject in the second equation, by adding 4x to both sides of the equation

4x -4x + 10y = 20 + 4x

This gives

10y = 20 + 4x

Divide both sides by 10

y = 2 + 0.4x

Substitute y = 2 + 0.4x in 2x = 5y - 40

2x = 5(2 + 0.4x) - 40

Expand

2x = 10 + 2x - 40

Subtract 2x from both sides of the equation.

2x - 2x = 10 + 2x - 2x - 40

Evaluate the like terms

0 = 10 - 40

Evaluate the like terms

0 = -30

The above equation is not true.

This means that the ships’ paths do not meet at any point.

This can be confirmed using the attached graph.

From the graph, we can see that the lines of 2x = 5y - 40 and -4x + 10y = 20 do not intersect

Hence, we can conclude that the ships’ paths do not meet at any point.

Read more about system of linear equations at

https://brainly.com/question/14323743

#SPJ1

Answer:

(0, -2)

Step-by-step explanation:

The equation of y axis is x = 0. So, the y intercept is located at point (0, b). Therefore we can substitute 0 into x in the given equation to find b and hence the coordinates of the y intercept.

3x - 7y = 14

3*0 - 7y = 14

-7y = 14

y = -2

Answer:

B = - 23

Step-by-step explanation:

5(B + 4) = 3(B - 1) + B ← distribute parenthesis on both sides

5B + 20 = 3B - 3 + B

5B + 20 = 4B - 3 ( subtract 4B from both sides )

B + 20 = - 3 ( subtract 20 from both sides )

B = - 23

Answer:

136

Step-by-step explanation:

While there is no picture for this question, I was able to find this question online, so that should be the correct answer.

By analyzing the end behavior of the graphed function, we conclude that the graphed function is an exponential one.

On the graph, we can see that as the independent variable (the one in the horizontal axis) tends to large negative values, the dependent variable (the one in the vertical axis) tends to zero.

And, as the independent variable increases in the positive domain, also does the dependent variable. So we have an increasing function

Finally, we can see that the range (set of the outputs) of the function is the set of values larger than zero.

These 3 are characteristics of exponential functions, so we conclude that the graphed function is an exponential one, thus the correct option is the first one.

If you want to learn more about exponential functions:

https://brainly.com/question/2456547

#SPJ1

Answer:

Logarithmic

Step-by-step explanation:

HS Teacher

The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

According to the statement

we have given that the some numbers of the songs which are added by the larrisa in her playlist.

And we have to tell the ways which are formed with the help of the combination and permutations.

So, For this purpose we know that the

The first condition we have given that the

"play no more than 4 blues songs" - indicates playlist can contain 0, 1, 2, 3, or 4 blues songs. You need to analyze five different cases and add them up together in the end. From 7 blues songs, you can either "pick" 0, 1, 2, 3, or 4. Since order matters, it's a permutation, not a combination.

Afterwards, it gets tricky. Consider the first case, where we have 0 blues songs. This means that there are 10 spaces for the remaining (3+5+7 = 15) songs, which means that they can be arranged in (7P0 ∙ 15P10) ways.

For the next case, where we have 1 blues songs, it means that there are 9 spaces for the remaining 15 songs, which means that they can be arranged in (7P1 ∙ 15P9) ways. Continue doing this for the cases of 2, 3, and 4 blues songs and add up all the cases together.

And from this way we get the all combinations which are formed.

So, For this purpose

n = (7P0 ∙ 15P10) + (7P1 ∙ 15P9) + (7P2 ∙ 15P8) + (7P3 ∙ 15P7) + (7P4 ∙ 15P6) = 4.43459016×1010,

which rounded to the hundredths place, is 4.43 x 10^10 possible playlists.

So, The total number of ways are formed is 4.43 x 10^10 by rounding to the hundredths place.

Learn more about the combination and permutations here

https://brainly.com/question/3901018

#SPJ1

Answer:

Step-by-step explanation:

Using proportions, it is found that the correct option for when the machine will stop running the algorithm is:

B) 9 P.M. on Saturday.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

The algorithm runs for 972 hours. Each day has 24 hours, hence we apply the proportion to find the number of days as follows:

972/24 = 40.5 days.

The remainder of the division of 40.5 by 7, as a week has 7 days, is of 5.5, which means that the code will finish running 5.5 days after the 9 A. M. Monday, that is at 9 P. M. on a Saturday, which means that option B is correct.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The exponential equation modeling this relationship is given as follows:

f(x) = 8(0.5)^x.

An exponential equation is modeled by:

f(x) = a(b)^x

In which:

For this problem, we have that when x = 0, y = 8, hence a = 8. Then:

f(x) = 8(b)^x.

When x = 1, y = 4, hence b is found as follows:

f(x) = 8(b)^x.

4 = 8b

b = 0.5.

Hence the equation is:

f(x) = 8(0.5)^x.

More can be learned about exponential equations at https://brainly.com/question/25537936

#SPJ1

The equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.

Equations that are equivalent to each other have the same value when evaluated or simplified.

Given the equation, 8x - 6y = 12, to determine which of the given equations in the options is equivalent to, rewrite the equation in slope-intercept form, as y = mx + b.

8x - 6y = 12

Subtract 8x from both sides of the equation

8x - 8x - 6y = -8x + 12

-6y = -8x + 12

Divide both sides of the equation by -6

-6y/-6 = -8x/-6 + 12/-6

y = 4x/3 + (-2)

y = 4x/3 - 2

Therefore, the equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.

Learn more about equivalent equations on:

https://brainly.com/question/2972832

#SPJ1

Answer:

  e)  y = √(x) +5

Step-by-step explanation:

The graph shown is the graph of the square root function shifted upward 5 units. There is no translation left or right.

A function can be translated h units right and k units up by the following:

  g(x) = f(x -h) +k

When the function is f(x) = √x, and it is translated 5 units up, but none left or right, we have ...

  g(x) = f(x-0) +5

  y = √(x) +5 . . . . . . matches choice e

Answer:0.08333333....

Step-by-step explanation:

Answer:

4x²

Step-by-step explanation:

Normally you would use the exponent → roots rule, but this one simplifies easier without that

[tex](8x)^{\frac{2}{3} }[/tex]

8 = 2³

so [tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}}[/tex]

then the threes cancel, since one is a 3 and the other one is [tex]\frac{1}{3}[/tex]

so [tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2[/tex]

then just square the 2 and the x

[tex](8x)^{\frac{2}{3} } = (2^{3}x)^{\frac{2}{3}} = (2x)^2 = 4x^2[/tex]

Answer:

  log(0.0003) = -3.5229

Step-by-step explanation:

The rules of logarithms tell you ...

  log(ab) = log(a) +log(b)

  log(0.0003) = log(3×10^-4) = log(3) +log(10^-4)

  = log(3) -4 = 0.4771 -4

  log(0.0003) = -3.5229

__

Additional comment

If you do much work with logarithms, you find that negative logarithms are generally expressed using a positive mantissa with a negative add-on. Often, that negative add-on is -9, so this would be ...

  5.4771-9

This helps when taking antilogs, as you look up 0.4771 in the table to see that the multiplier is 3.

If you were to look up 0.5229, you would find 3.333, meaning the multiplier is 1/3.333 and the antilog of -3.5229 is (10^-3)/3.333. This may not be a convenient value to work with.