How many real roots are in 10x^2 +3x+6=0

Based on the given data, the probability that exactly 2 insects will survive is 0.1402 rounded to four decimal places.

The probability mass function for the binomial distribution is given by:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (surviving insects), k is the specific number of successes we're interested in (k=2 in this case), n is the total number of trials (n=11), p is the probability of success (p=0.3), and (n choose k) is the binomial coefficient, which is the number of ways to choose k objects from a set of n objects.

Plugging in the values, we get:

P(X=2) = (11 choose 2) * 0.3² * 0.7²

= (55) * 0.09 * 0.02825

= 0.1402

Therefore, the probability that exactly 2 insects will survive is 0.1402 (rounded to four decimal places).

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The total area of the porch is 329 square feet.

To find the overall area of the porch, we want to calculate the areas of the timber and urban elements one after the other and then add them up. The timber a part of the porch is a right triangle with legs a = 21 ft and b = 28 ft. The region of a triangle is given through the system:

area of triangle = 1/2 × base × height

in this situation, the base and top are the lengths of the legs a and b, respectively. Substituting the values, we get:

area of timber part = 1/2 × 21 ft × 28 feet = 294 ft²

the concrete part of the porch is a square with an aspect length of c = 35 ft. The area of a square is given by using the formula:

area of square = side length²

substituting the value of c, we get:

area of concrete part = 35 ft²

now, we will find the whole area of the porch by using including the regions of the wood and concrete parts:

total area of porch = Area of wooden part + area of concrete element

= 294 ft² + 35 ft²

= 329 ft²

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The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

its c!

Step-by-step explanation:

trust me on this!

Answer:

c

Step-by-step explanation:

the other person

If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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Answer:

-1.031 m/s or  \(\frac{-\sqrt{17} }{4}\)

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is \(\frac{dy}{dt}\) = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =  \(\frac{dx}{dt}\) = ?

for x = 4

Applying Pythagorean Theorem we have

\(1^{2} +x^{2} =y^{2}\)    .... equ 1

solving, where x = 4, we have

\(1^{2} +4^{2} =y^{2}\)

\(y^{2} = 17\)

\(y = \sqrt{17}\)

Differentiating equ 1 implicitly with respect to t, we have

\(2x\frac{dx}{dt} = 2y\frac{dy}{dt}\)

substituting values of

x = 4

y = \(\sqrt{17}\)

\(\frac{dy}{dt}\) = -1

into the equation, we get

\(2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)\)

\(\frac{dx}{dt} = \frac{-\sqrt{17} }{4}\) = -1.031 m/s

Answer:

2x - 15 ≥ 4y

Step-by-step explanation:

The linear function that represents the cost per month is C(x) = $1700 + $39.50x.

A linear function is a function that increases by a constant value. A  linear function when drawn on a graph is a straight line. The straight line can either slope upward or downward.

The form of a linear function is:

f(x) = mx + b

Where:

The fixed cost is the cost that does not change with the unit of the goods produced. The variable cost increases with the unit of goods that is produced.

C(x) = $1700 + $39.50x.

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Answer:

x=3; y=2

Step-by-step explanation:

3x+5(5x-13)=19

28x - 65 = 19

28x=84

x=3

y=5(3) - 13

y=2

The 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).

C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

To construct a 90% confidence interval for the population proportion of adults who believe in UFOs, we can use the formula:

Confidence Interval = Sample Proportion ± Margin of Error

First, we calculate the sample proportion:

Sample Proportion \(\hat{p}\) = Number of adults who believe in UFOs / Total number of adults surveyed = 736 / 2266 ≈ 0.324

Next, we need to calculate the margin of error.

Since we are dealing with a large sample size, we can use the formula for a 90% confidence interval:

Margin of Error\(= Z \times \sqrt{(\hat{p} \times (1 - \hat{p}) / n)}\)

Here, Z represents the z-value for a 90% confidence level, which corresponds to a z-value of 1.645. n represents the sample size.

Margin of Error\(= 1.645 \times \sqrt{(0.324 \times (1 - 0.324) / 2266)}\) ≈ 0.015

Finally, we can construct the confidence interval:

Confidence Interval = 0.324 ± 0.015 = (0.309, 0.339)

Therefore, the 90% confidence interval for the population proportion of adults who believe in UFOs is (0.309, 0.339).

Now, let's interpret the results.

The correct answer is:

C. With 90% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.

This means that we are 90% confident that the true proportion of adults who believe in UFOs falls within the range of 0.309 to 0.339.

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Answer:

Sample Response: The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.

DJ can arrange 88,55 times the first four songs on the playlist.

Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,

Given that,

DJ prepares a playlist of 23 songs.

Since, DJ arranges the first four songs on the playlist,

The ways to arrange the song on the playlist,

= \(^{23}C_4\)

= 23 ! / (4! x (23 - 4)! )

= 23 ! / (4! x 19!)

= (23 x 22 x 21 x 20 x 19!) / (4 x 3 x 2 x 1  x 19!)

= 23 x 11 x 7 x 5

= 8855

There are 8,855 ways to arrange first 4 songs.

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Answer:

  Patty, Karla, Cathy

Step-by-step explanation:

The scoring percentage of goals attempted can be computed by dividing goals made by those attempted, then multiplying the result by 100%.

__

Cathy's rate is ...

  27/54 × 100% = 50%

Karla's rate is ...

  18/45 × 100% = 40%

Patty's rate is ...

  given as 34%

__

By least to greatest scoring rate, the athletes are ...

  Patty (34%), Karla (40%), Cathy (50%)

the two planes will be at the same altitude of approximately 5675.48 feet after 49.45 seconds.

A plane is a flat two-dimensional surface that extends infinitely in all directions. In geometry, a plane is defined as a surface that is completely flat and has no thickness. It is often represented as a coordinate system with two perpendicular axes, usually labeled as the x-axis and y-axis.

Assuming that the two planes maintain their rates of ascent, we can use the following equations to determine when the planes will be at the same altitude:

altitude of plane A = 4000 + 33.5t

altitude of plane B = 3146 + 50.75t

where t represents time in seconds.

To find the time at which the two planes will be at the same altitude, we can set the two equations equal to each other and solve for t:

4000 + 33.5t = 3146 + 50.75tSubtracting 3146 from both sides, we get:

854 + 33.5t = 50.75t

Subtracting 33.5t from both sides, we get:

854 = 17.25t

Dividing both sides by 17.25, we get:

t = 49.45 seconds

Therefore, it will take approximately 49.45 seconds for the two planes to be at the same altitude. To find the altitude at which they will meet, we can substitute this value of t into either equation. Using the equation for plane A, we get:

altitude of plane A = 4000 + 33.5(49.45) = 5645.08 feet

Using the equation for plane B, we get:

altitude of plane B = 3146 + 50.75(49.45) = 5675.48 feet

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Answer:

  x + y = 14

Step-by-step explanation:

The question asks for the final answer to be an equation in standard form. The standard form of the equation for a line is ...

  ax +by = c

where a, b, c are integers with no common factors, and 'a' is positive.

__

When working with parallel and perpendicular lines, standard form is an easy form to work with. The coefficients (a and b) of parallel lines will be the same. All that is different between parallel lines is the value of 'c'.

Given this fact, it is convenient to start by putting the given equation into standard form. For that, we want the x-term on the same side of the equal sign as the y-term.

Adding x to both sides of the given equation puts it in standard form:

  x +y = x +(-x) +3

  x + y = 3 . . . . . simplified

__

Now that we know our equation will be of the form ...

  x + y = (some constant)

we need to find the constant. We can do that by using the given point values for x and y.

For the given point (x, y) = (10, 4), the constant for the parallel line will be ...

  x + y = 10 + 4 = 14

  x + y = 14 . . . equation of parallel line through (10, 4)

Answer:

100

Step-by-step explanation:

5% of 2000 is 100

The position vector of point P, MP, is given by MP = 6i - j.

To find the position vector of point P, which is the midpoint of NO, we can use the midpoint formula.

The midpoint formula states that the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

Midpoint (Mᵖ) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's find the position vector of point P using the given information:

Point N: N = 4i - 5j

Point O: O = 8i + 3j

Using the midpoint formula, we can find the coordinates of point P:

x-coordinate of P: (x₁ + x₂) / 2 = (4i + 8i) / 2 = 12i / 2 = 6i

y-coordinate of P: (y₁ + y₂) / 2 = (-5j + 3j) / 2 = -2j / 2 = -j

Therefore, the position vector of point P, MP, is given by:

MP = 6i - j

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The gestation period of humans ​(266 days) is ​146.3% percent longer than the gestation period of lions (108 days).

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.

Given that, gestation period of humans = 266 days and gestation period of lions = 108 days

Number of days taken more by humans in gestation period =

266-108 = 158

Percentage = 158/108 × 100 = 146.3%

Hence, the gestation period of humans ​(266 days) is ​146.3% percent longer than the gestation period of lions (108 days).

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Answer: 1/343

Step-by-step explanation:

To multiply fractions, combine the numerators and denominators and simplify as shown below.

1/7 x 1/7 x 1/7 can be rewritten as:

(1x1x1)/(7x7x7)

Simplifying the numerator and denominator in the new equation, the result is 1/343.

Thus, 1/7 x 1/7 x 1/7 = 1/343.

I hope this helps!

Answer:

Step-by-step explanation:

y = (x-1)²

vertex (1,0)

y-intercept = (0-1)² = 1

The simplified expression of the radical expression ∛135a¹³ is (135a¹³)¹/³

From the question, we have the following parameters that can be used in our computation:

A radical expression

The radical expression is given as

\sqrt[3]{135^{a13}}

Represent the expression properly

So, we have the following representation

∛135a¹³

Apply the exponent rule of indices

This gives

∛135a¹³ = (135a¹³)¹/³

135 and a¹³ are not perfect cube root expressions

This means that the expression cannot be further simplified

Hence, the solution is (135a¹³)¹/³

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let's firstly convert the mixed fraction to improper fraction and proceed from there.

\(\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div \left(\cfrac{3}{8}\div \cfrac{1}{2} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{8}\cdot \cfrac{2}{1} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{4} \right) \\\\\\ \cfrac{9}{4}\cdot \left(\cfrac{4}{3} \right)\implies \cfrac{9}{3}\cdot \cfrac{4}{4}\implies 3\cdot 1\implies \text{\LARGE 3}\)

To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, the sum of the first 30 terms of this arithmetic sequence is 209. Hoped this helped.

\(BrainiacUser1357\)

Answer:

The sum of first 30 terms of arithmetic sequence is 3225.

Step-by-step explanation:

Here's the required formula to find the sum of the arithmetic sequence :

\( \star{\underline{\boxed{\sf{S_n = \dfrac{n}{2}\Big[2a + (n - 1)d\Big]}}}}\)

Substituting all the given values in the formula to find the sum of arithmetic sequence :

\({\implies{\sf{S_n = \dfrac{n}{2}\Big[2a + (n - 1)d\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[2 \times 6 + (30 - 1)7\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+ (29)7\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+ 29 \times 7\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[12+203\Big]}}}\)

\({\implies{\sf{S_{30} = \dfrac{30}{2}\Big[ \: 215 \: \Big]}}}\)

\({\implies{\sf{S_{30} = 15\Big[ \: 215 \: \Big]}}}\)

\({\implies{\sf{S_{30} = 15 \times 215}}}\)

\({\implies{\sf{S_{30} = 3225}}}\)

\( \star{\underline{\boxed{\sf{S_{30} =3225}}}}\)

Hence, the sum of first 30 terms of arithmetic sequence is 3225.

\(\rule{300}{2.5}\)

Answer:

\(\boxed{\frac{3}{5}}\)

Step-by-step explanation:

The trigonometric functions are described as follows:

\(sin = \frac{opposite}{hypotenuse}\\\\cos = \frac{adjacent}{hypotenuse}\\\\tan = \frac{opposite}{adjacent}\)

Using reference angle ∠A, use the sin trigonometric function. This will be the side opposite (cannot be the hypotenuse) of ∠A over the side adjacent (cannot be the hypotenuse).

The side opposite of ∠A is 3. The hypotenuse of the triangle is 5.

\(\boxed{\frac{3}{5}}\)  is the final answer!

Answer:

3.88 Pints

Step-by-step explanation:

First we need to find the amount of blue paint that was used. We can do that by multiplying 9.7 by 0.60 since that is 3/5 in decimal form

\(9.7*0.60=5.82\)

Now we know how much blue paint was used, now we just need to find how much white paint was used. We can do that by subtracting our amount of blue paint from the total amount of paint used

\(9.7-5.82=3.88\)

thus, 3.88 is the amount of white paint used

Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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The sample proportion of east regional responsibility for all possible samples of size 2 from this population is given by option 1.

The probability distribution of a statistic acquired from a bigger sample size taken from a certain population is known as the sampling distribution. The frequency distribution of a variety of possible outcomes for a population statistic makes up the sampling distribution of a given population.

A population is the total group from which a statistical sample is taken in statistics. An entire group of individuals, things, occasions, medical visits, or measurements can all be referred to as a population. Therefore, a population can be defined as an overall observation of persons clustered together by a shared characteristic.

From all the given combinations we have:

(Andrew, Beth) = 1

(Andrew, Charles) = 1

(Andrew, Diane) = 0.5

(Andrew, Eric) = 0.5

(Beth, Charles) = 1

(Beth, Diane) = 0.5

(Beth, Eric) = 0.5

(Charles, Diane) = 0.5

(Charles, Eric) = 0.5

(Diane, Eric) = 0

Hence, the sample proportion of east regional responsibility for all possible samples of size 2 from this population is given by option 1.

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The correct question is:

There were 8 slices in the whole pizza.

An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign =.  Let us assume the number of slices in the whole pizza is "x".

Since Jim ate two slices which is 25% of the pizza, we will set up the equation:

2 = 0.25x

To solve for "x":

2 / 0.25 = x

x = 8.

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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