by completing the square
1. x2 + 5x + 6= 0
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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

In an ammonium ion (NH+4) ion, there is one nitrogen atom and four hydrogen atoms. Nitrogen has an atomic number of 7 , and hydrogen has an atomic number of 1 , and so the total atomic number of the hydrogens will be 1⋅4=4 . So, there will be a total of 7+4=11 protons.

Step-by-step explanation:

To calculate the ratio of r_l at l=80cm for the thin nichrome wire to the measurement using the thick nichrome wire, we need experimental data for both wires. As it is not provided, it is impossible to provide calculation.

The ratio of r_l at a specific length can be determined by dividing the resistance of the thin nichrome wire at that length by the resistance of the thick nichrome wire at the same length. This ratio will provide information about how  resistance of the thin wire compares to the resistance of the thick wire at a particular length.

However, without the actual experimental data for both wires, including their respective resistances at the specified length of 80cm, it is not possible to generate a specific numerical answer for ratio.

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#complete question

Judging by the image the function graphed has an asymptote at x = 3 and extends forever to -infinity along the x axis.

so the answer would be - infinity not included (because infinity is a concept not a number) to +3 not included because the function infinitely approaches x = 3. this is (-∞,3) in interval notation.  

Answer:A

Step-by-step explanation:

Answer: π / 4

Step-by-step explanation:

Area of a circle = π x r^2

= π x 0.5^2

= π / 4

Answer:

A = 0.25 π m²

Step-by-step explanation:

Area = \(\pi r^2\)

Where r = 0.5 m

A = (0.5)^2 × π

A = 0.25 π m²

The equation for the line in point-(1, 1) is y = -0.5x + 0.5.

Given that the slope of the line below is -0.5. We are to enter the equation for the line in point-(1, 1).The equation for the slope-intercept form of the line is y = mx + c where m is the slope and c is the y-intercept.

Now, the slope of the line is given as -0.5.Therefore, the equation for the slope-intercept form of the line is y = -0.5x + c. Now we need to find the value of c for the equation of the line.

To find the value of c, substitute the values of x and y in the equation of the slope-intercept form of the line.

Given that the point is (-1,1), x=-1 and y=1y = -0.5x + c⇒ 1 = (-0.5) (-1) + c⇒ 1 = 0.5 + c⇒ c = 1 - 0.5⇒ c = 0.5

Therefore, the equation for the line in point-(1, 1) is y = -0.5x + 0.5.The slope of a line refers to how steep the line is and is used to describe its direction. Slope is defined as the vertical change between two points divided by the horizontal change between them.A positive slope moves up and to the right, while a negative slope moves down and to the right. If a line has a slope of zero, it is said to be a horizontal line.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept, or the point at which the line crosses the y-axis. To find the equation of a line with a given slope and a point, we can use the point-slope form of a linear equation.

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Answer:

b140

Step-by-step explanation:

14*10=140 that's all

Answer:

the answer is B

Step-by-step explanation:

because 14*10 is 140

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766). The margin of error is approximately 0.0140.

To construct a confidence interval for the proportion of Americans who drink tea daily, we can use the formula:

Where,

p = the sample proportion

Z = the critical value corresponding to the desired confidence level

n = the sample size

Given:

Now, let's calculate the confidence interval and margin of error:

According to the information, the 95% confidence interval for the proportion of Americans who drink tea daily is approximately (0.2485, 0.2766), with a margin of error of approximately 0.0140.

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Answer:

slope of CE is 2/3

Step-by-step explanation:

used the slope formula: change in y-values / change in x-values

Answer: -4.5 ℉

Step-by-step explanation:

Given: On the coldest day of the year, the temperature at noon = 11℉

By midnight, the temperature had decreased by 15.5℉.

i.e. The temperature at midnight = Temperature at noon - 15.5℉

= 11℉ - 15.5℉

= (11-15) ℉

= -4.5 ℉

Hence, the temperature at midnight was -4.5 ℉.

Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Answer:

3x-10+25+x+15=180

4x+30=180

4x=180-30

4x=150

x=37.5

Answer:

37.5555

Step-by-step explanation:

The ball hits the ground at 0 seconds or 2.5 seconds.

h represents the height of the golf ball after x seconds. The height is given by:

h(x)=-4.8x(x-2.5)

h(x) = -4.8x² + 12x

The time taken for the ball to reach the ground is at h(x) = 0, hence:

0 = -4.8x² + 12x

4.8x² - 12x = 0

x(4.8x - 12) = 0

hence x = 0; or 4.8x - 12 = 0

x = 0; or x = 2.5

Therefore the ball hits the ground at 0 seconds or 2.5 seconds.

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Answer:

squareroot -17

Step-by-step explanation:

squareroot16=4x4

squareroot-9=3x3

squareroot1=1x1

squareroot-17=not possible

The effective interest method is used to amortize the bond premium. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond. The journal entry for bond issuance is as follows: Dr. Cash 205,000, Dr. Premium on Bonds Payable 5,000, Cr. Bonds Payable 210,000

The effective interest method is a method of amortizing bond premium or discount that takes into account the time value of money. The effective interest is the interest that would be earned if the bond were purchased at its market value and held to maturity. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond.

The journal entry for bond issuance records the proceeds from the sale of the bonds, the premium on bonds payable, and the bonds payable. The proceeds from the sale of the bonds are equal to the face value of the bonds plus the premium.

The premium on bonds payable is a liability that represents the excess of the issue price of the bonds over their face value. The bonds payable account is a long-term liability that represents the amount that the company owes to the bondholders.

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Answer:148.38

Step-by-step explanation:

Population Density=Population of country÷Area of country

Population of country=23,023

Area of country=(18*8)+(4*5)=164 m²

Population Density=23023÷164=148.38 people/m²

The probability that he does not select a comedy is 12/23

If we assume that all the movies have the same probability of being randomly selected, then the probability of selecting a movie that is not a comedy is equal to the quotient between the number of movies that aren't comedies and the total number of movies.

There are:

3 action ones.

11 comiedies.

9 dramas

For a total of 23 movies, and 12 of them are not comedies, then:

P = 12/23

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The amount he should sell for one bottle of the fizzy juice to make the 60% profit is 22 Penny.

Orange :  Lemonade

  3  :  5

After buying 2 liters of orange juice and 3 liters of lemonade, cost of each;

Increase the ratio to form divisible by 2 and 3; (L.C.M of 2 and 3 = 6)

(3 x 6L)  :  (5 x 6L)

18L  :  30L      

total fizzy juice = 18L + 30L = 48 liters

bottle of orange = (18 L ÷ 2 L) = 9 bottles

bottle of lemonade = (30 L ÷ 3L ) = 10 bottles

cost of orange = 9 x £1.20 = £10.8

cost of lemonade = 10 x £1.50 = £150

Total cost = £10.8 +  £150 =  £25.80 =  2580 P

250 mL = 0.25 L

0.25L(n) = 48 L

n = 48/0.25

n = 192 bottles

cost = 2580 P/192

cost = 13.44 P

A = 100%(initial cost) + 60%(initial cost)

A = 160%(initial cost)

A = 1.6(initial cost)

A = 1.6 x 13.44 P

A = 21.5 P ≈ 22 P

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The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer:

So the rate of decay is 0.25, or 25%.

Step-by-step explanation:

The variable r gives the rate of decay in the formula f(x) = P(1 − r)x = 16(1 − 0.25)x.

Answer:

Exponential decay, 75% decrease

Step-by-step explanation:

took the test

Answer:

a = -7/17

Step-by-step explanation:

Add -4a to -2a

This makes -6a. Then you add 6a to the left to cancel it out, but you must also add 6a to the right of the =

Then you have -7 = 17a

Divide 17 from both sides and you have -7/17 = a

Answer:

3600 bacterias

Step-by-step explanation:

From P = P'e^(-kt), where

P = final population

P' = initial population

k = decay constant

t = time in hrs

Substituting we have

200 = 170000 x e^(-42k)

1/850 = e^(-42k)

We take natural log (Ln) of both side

Ln (1/850) = Ln (e^(-42k))

-6.745 = -42k

k = 0.16059.

For amount remaining after 24 hrs we find P

P = 170000 x e^(-0.16059x24)

P = 170000 x e^-3.85416

P = 170000 x 0.02119 = 3602.3

Approximately 3600 bacterias.

If 2.7 million tax returns are filed both manually and electronically, the difference in error found in manual returns from electronic returns will be b. 538,650.

This can be found by the formula:

= Errors from manual filing - Errors from electronic filing

Solving gives:

= (20% x 2.7 million) - (0.05% x 2.7 million)

= 540,000 - 1,350

= 538,650 returns.

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Let \(a\) be the first term in the series and \(r\) the common ratio. Then the infinite series converges to

\(a + ar + ar^2 + ar^3 + ar^4 + ar^5 + \cdots = \dfrac a{1-r}\)

Removing the first three terms from the left side effectively multiplies the right side by 27, so

\(ar^3 + ar^4 + ar^5 + \cdots = \dfrac{27a}{1-r}\)

By elimination,

\(a + ar + ar^2 = -\dfrac{26a}{1-r}\)

Solve for \(r\). We can eliminate \(a\) so that

\(1 + r + r^2 = -\dfrac{26}{1-r} \\\\ \implies 1-r^3 = -26 \\\\ \implies r^3 - 27 = 0 \\\\ \implies r^3 = 27 \implies \boxed{r=3}\)

Answer:

Penperdocular

Step-by-step explanation:

Answer:

x=35

Step-by-step explanation:

Answer:

45cm

Step-by-step explanation:

(2/5)d -2=16

(2/5)d =16+2

d=18 ×(5/2)=45cm

The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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Answer:

what is the question, it is unclear