what is the relationship and what does X equal?
help! :)

Answer:

Imaginary roots

Step-by-step explanation:

The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].

Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:

[tex]7x^2-5x+1=0[/tex]

Now assign variables:

The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].

What does this tell us about the roots?

Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.

Answer:

5/8 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

A = 5/6 * 3/4

A = 3/6 * 5/4

A = 1/2 * 5/4

A = 5/8 ft^2

Answer:

1. 1.66in

2. 6.66in

3. 3.33in

4. 1inch

Step-by-step explanation:

the area of a rectangle is found by multiplying the length times width or the two sides.

5 x 1/3 is about 1.66 inches

5 x 4/3 is about 6.66 inches

5/2 x 4/3 is about 3.33 inches

and 7/6 x 6/7 is 1 inch

Answer:

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Step-by-step explanation:

There's a handy formula we can use to find the sum of a geometric sequence, and here it is

[tex]S_n = \frac{a_1 (1 - r^n)}{1 - r}[/tex]

The value n represents the amount of terms you want to sum in the sequence. The variable r is known as the common ratio, and a is just some constant. Let's find those values.

First lets visualize this sequence

[tex]n_1 = 1\\n_2 = 1 + 3\\n_3 = 1 + 3 + 3^2\\n_4=1+3+3^2+3^3\\...[/tex]

Okay so there's clearly a pattern here, let's write it a bit more concisely. For each n, starting at 1, we raise 3 to the (n-1) power, add it to what we had for the previous term.

[tex]S_n = \sum{3^{n-1}} = 3^{1 - 1} + 3^{2 - 1} + 3^{3-1} ...[/tex]

Our coefficients of r, and a, are already here! As you can see below, r is just 3, and a is just 1.

[tex]S_n = \sum{a*r^{n-1}}[/tex]

To finish up lets plug these coefficients in and get our sum after 10 terms.

[tex]S_n = \frac{1 (1 - 3^{10})}{1 - 3} = 29524[/tex]

Answer:

don't know...........

Step-by-step explanation:

Sequence is

4

,

7

,

10

,

13

,

16

,

.

.

.

a

1

=

4

,

a

2

=

7

,

a

3

=

10

,

.

.

.

If it is Arithmetic sequence,

a

2

−

a

1

=

a

3

−

a

2

=

a

4

−

a

3

& so on

In the given sum,

a

2

−

a

1

=

7

−

4

=

3

a

3

−

a

2

=

10

−

7

=

3

a

4

−

a

3

=

13

−

10

=

3

Since the difference between the successive terms is same and

hence

common difference

d

=

3

Answer:

C  -3 < x ≤ 4

Step-by-step explanation:

-9 < 4x + 3 ≤ 19.

Subtract 3 from all sides

-9-3 < 4x + 3-3 ≤ 19-3

-12 < 4x  ≤ 16

Divide by 4

-12/4 < 4x/4 ≤ 16/4

-3 < x ≤ 4

Answer:

Step-by-step explanation:

D={ 6  , -9  , 1 }

R={  0  ,-3 }

Answer:

The range is the set of first coordinates

Observe that the x coords of the roots of a polynomial are,

[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]

Which can be put into form,

[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]

with data

[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]

Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,

[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]

and a will be "lost" in the process.

If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.

Hope this helps :)

a) the cost of a bunch of grapes compared with its weight

GRAAAAAAAAAAAAAAAAAAAAAAAAAAAAPES!!!!!

Answer:

x = -3

Step-by-step explanation:

12 -4x-5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from each side

12-9x-12 = 39-12

-9x = 27

Divide by -9

-9x/-9 = 27/-9

x = -3

Answer:

x = -3

Step-by-step explanation:

12 - 4x - 5x = 39

Combine like terms

12 - 9x = 39

Subtract 12 from both sides

12 - 12 - 9x = 39 - 12

-9x = 27

Divide both sides by -9

-9x/-9 = 27/-9

x = -3

Answer:

n=39/5

Step-by-step explanation:

24=5(n-3)

24=5n-15

-5n= -15-24

-5n=39

n= 39/5

Answer:

605 boys.

Step-by-step explanation:

5:7 means 5 parts consists of boys and 7 parts consist of girls.

Since 7 parts = 847, 1 part = 121 and 5 parts = 605

Hence there are 605 boys.

Hope you have a nice day :)

Answer:

-52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

Answer: -52

Step-by-step explanation:

-4(x + 10) - 6 = -3(x - 2)

Distribute the left side to get:

(-4x + -40) - 6

Now distribute the right side to get:

-3x + 6

Arrange the equation as the following:

-4x - 40 - 6 = -3x + 6

Add the like terms on each side:

-4x - 46 = -3x + 6

Do the inverse operation of each term:

-x = 52

Now we need to get x to become a positive, so we just divide -x by -1 to get x.

And 52/-1 to get our final answer of -52.

Answer:

4/27

Step-by-step explanation:

total number of marbles=9

probability of red=4/9

since you returned the first marble, the total number of marbles remains the same

prob(Blue)=(3/9)=1/3

P(red then blue)=(4/9)*(1/3)

=4/27

Answer:

a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

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

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation:

Answer:

The volume of the resulting solid is π/2 cubic units.

Step-by-step explanation:

Please refer to the diagram below.

The shell method is given by:

[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]

Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.

From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:

[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]

The volume of the resulting solid is π/2 cubic units.

Answer:

pi/2

Step-by-step explanation:

I always like to draw an illustration for these problems.

For shells method think volume of cylinder=2pi×r×h

Integrate(2pi(2-x)(x-x^2) ,x=0...1)

Multiply

Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)

Combine like terms

Integrate(2pi(2x-3x^2+x^3) ,x=0...1)

Begin to evaluate

2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1

2pi(x^2-x^3+x^4/4), x=0...1

2pi(1-1+1/4)

2pi/4

pi/2

Answer:

soory i dont know just report me if you angry

Solution :

Given information :

A sample of n = 10 adults

The mean failure was 24 and the standard deviation was 3.2

a). The formula to calculate the 95% confidence interval is given by :

[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]

Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]

                       = 2.145

Substitute the values

[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]

(26.17, 21.83)

When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]

b). The formula to calculate 95% prediction interval is given by :

    [tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]

   [tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]

   (31.13, 16.87)

Answer:

582-600

1,234-1,200

640-600

770-800

1,104-1,100

Answer:

3.5 inches

Step-by-step explanation:

Sample mean basically means that we need to find the average of the samples.

So the formula for finding average is

Number of observations/ Number of Occurrences

So when we add the values together we get

42.

So there are 12 numbers

So, 42/12 =

3.5 inches

The sample mean of the heights of the plants in Susan's garden is

3.5 inches.

Here,

Susan randomly selected a sample of plants to determine the average height of the total 35 plants in her garden.

She measured the heights (in inches) of 12 randomly selected plants and recorded the data:

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

We have to find the sample mean of the heights of the plants in Susan's garden.

What is Average?

Average value in a set of given numbers is the middle value, calculate as dividing the total of all values by the number of values.

Now,

The recorded data is;

1.0, 1.4, 1.8, 2.0, 2.5, 3.5, 4.2, 4.5, 4.8, 5.0, 5.3, 6.0

To find the sample mean of the heights of the plants in Susan's garden we have to find the average of the recorded data.

Formula for average = [tex]\frac{sum of number of observation}{ number of occurrence}[/tex]

Hence, Average = [tex]\frac{1.0+ 1.4+1.8+2.0+ 2.5+3.5+4.2+4.5+ 4.8+ 5.0+ 5.3+ 6.0}{12} = \frac{42}{12} = 3.5[/tex]

Therefore, The sample mean of the heights of the plants in Susan's garden is 3.5 inches.

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Answer:

4y

They would have the same value if a number was substituted for y

Step-by-step explanation:

y+y+2y =

Combine like terms

4y

These are all like terms

They would have the same value if a number was substituted for y

Let y = 5

5+5+2(5) = 5+5+10 = 20

4(5) =20

9514 1404 393

Answer:

corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)4)

Step-by-step explanation:

In this geometry, "corresponding" angles are in the same direction from the point of intersection of the transversal with the parallel line.

"Alternate" refers to angles on opposite sides of the transversal. "Interior" and "exterior" refer to angles between and outside of the parallel lines, respectively.

Here, we list all angle pairs in each classification, so you can answer questions 1-12 based on this list.

alternate interior: (2, 4), (3, 5)

alternate exterior: (1, 7), (43°, 6)

corresponding: (1, 5), (2, 6), (3, 7), (43°, 4)

__

Additional classifications are also used:

consecutive (same-side) interior: (2, 5), (3, 4)

consecutive (same-side) exterior: (1, 6), (43°, 7)

vertical: (1, 3), (2, 43°), (4, 6), (5, 7)

linear pairs: (1, 2), (1, 43°), (2, 3), (3, 43°), (4, 5), (4, 7), (5, 6), (6, 7)

Answer:

The probability will 4.32%.

The probability that all four are brown is 35/8,64,501.

Given that, A group of hens lays 69 eggs in a single day. On one particular day, there were 7 brown eggs and 62 white eggs.

Probability without replacement means once we draw an item, then we do not replace it back to the sample space before drawing a second item. In other words, an item cannot be drawn more than once.

If four eggs are selected at random, without replacement, the probability that all four are brown is 7/69 × 6/68 × 5/67 × 4/66

= 7/69 × 3/34 × 5/67 × 2/33

=7/23 × 1/17 × 5/67 × 1/33

=35/8,64,501

Therefore, the probability that all four are brown is 35/8,64,501.

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Answer:

8 113/1000(as a mixed number)      8113/1000(as an improper fraction)

Step-by-step explanation:

1. Convert 0.113 to a fraction...113/1000

2. As there is no further simplification needed, add 8 to 113/1000....8 113/1000

3. To convert 8 113/1000 from a mixed number to an improper fraction, multiply 8 (the whole number) and 1,000(the denominator)...8,000. Then add 113 (the numerator) to 8,000...8113. After that, you put 8113 over the denominator of the previous mixed number, getting 8113/1000 as the improper fraction.

Answer:

the probability of taking a clear picture of a California candor is .24

Answer: y = 7x + 18

Step-by-step explanation:

y = mx + b, (-2,4), m = 7

4 = 7(-2) + b

4 = -14 + b

b = 18

y = 7x + 18

Se necesitan 10 micros si queremos que cada 3 micros transporten 90 pasajeros.

En principio, sabemos que 300 pasajeros pueden transportarse en 4 microbuses.

Entonces, el numero de pasajeros que va por cada micro será el cociente entre el numero de pasajeros y el numero de micros:

N = 300/4 = 75

Queremos responder:

¿Cuántos micros se deben aumentar para  que por cada 3 micros se transporten 90 pasajeros?

Definamos X como el numero de grupos de 3 micros que tendriamos en esta situación.

Entonces 300 sobre X, debe ser igual a 90 (el numero de pasajeros que va en cada grupo de 3 micros)

300/X = 90

300 = 90*X

300/90 = X = 3.33...

Notar que el número total de micros sera 3 veces X:

3*X = 3*3.33.... = 10

Se necesitan 10 micros.

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