For the equation y = 2x2 − 5x + 18, choose the correct application of the quadratic formula.

Answer:

Option 4

125 × 125

Step-by-step explanation:

5⁶ = 5 × 5 × 5 × 5 × 5 × 5 = 125 × 125

Thus, 5⁶ = 125 × 125

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The probability of selecting two red marbles and one blue marble is \(\frac{4}{15}\)

To calculate the probability, we first determine the total number of possible outcomes. Since three marbles are being selected simultaneously, there are C(6, 3) = 20 different ways to choose three marbles from the six available.

Next, we consider the number of favorable outcomes, which in this case is selecting two red marbles and one blue marble. We can choose two red marbles from the four available in C(4, 2) = 6 ways, and we have only one blue marble to select. Therefore, there are 6 × 1 = 6 favorable outcomes.

Finally, we calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. Thus, the probability of selecting two red marbles and one blue marble is 6÷20, which simplifies to 3÷10 or approximately 0.4.

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Answer:

10.4

Step-by-step explanation:

with reference angle 60

perpendicular (p)= 18

base(b)= x

tan 60 = p/b

\(\sqrt{3}\)  = 18/b

b = 10.4

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Answer:

4 of them would make one cup. Look at it like this 1/4 cup is actually a cup divided into 4 equal parts…. So 1/4 cup is 1 out of the 4 it takes to make a whole cup.So if you need 2 cups you would need 8 of the 1/4 cups.If 4 of them equals one full cup, then you need to do it twice. Altogether 8 of the 1/4 cups makes 2 full cups

Step-by-step explanation:

Answer:

4x^2 - 10x + 1 units

Step-by-step explanation:

(3x - 1) + (x + 2) + (3x^2 - 11x) + (x^2 - 3x)

Adding like terms:

3x^2 + x^2         = 4x^2

-11x - 3x + 3x + x    = -10x

-1 + 2            = 1

Summing it up; the perimeter is
4x^2 - 10x + 1 units

The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

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Answer:

x ≈ 11.7

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos26° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{13}\) ( multiply both sides by 13 )

13 × cos26° = x , then

x ≈ 11.7 ( to the nearest tenth )

The mean temperature is approximately 30.64, the median temperature is approximately 29.5, the highest range of temperature is 37-39, the lowest range of temperature is 25-27, and the modal class is 28-30 with 36 cities.

How to calculate the highest and lowest range of temperature?

To calculate the mean temperature, we need to find the sum of all the temperatures and divide it by the total number of cities:

Mean = (25*25 + 29*36 + 32*30 + 35*22 + 38*15) / (25 + 36 + 30 + 22 + 15)

    = 30.64

Therefore, the mean temperature is approximately 30.64.

To calculate the median temperature, we need to find the middle temperature value. First, we need to arrange the temperatures in ascending order:

25-27, 25-27, 25-27, ..., 25-27 (25 times)

28-30, 28-30, ..., 28-30 (36 times)

31-33, 31-33, ..., 31-33 (30 times)

34-36, 34-36, ..., 34-36 (22 times)

37-39, 37-39, ..., 37-39 (15 times)

The total number of cities is 128. Since 128 is an even number, the median is the average of the two middle values:

Median = (28-30 + 31-33) / 2

      = 29.5

Therefore, the median temperature is approximately 29.5.

The highest range of temperature is 37-39, and the lowest range of temperature is 25-27.

The modal class is the temperature range with the highest frequency, which is 28-30 (36 cities).

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Answer:

80 miles

Step-by-step explanation:

Answer:

the expression is not factorable with rational numbers

Answer:

The equation of a line that passes through the points(-4, 4) and (2, 12) will be:

Hence, option A is true.

Step-by-step explanation:

The slope-intercept form of the line equation

\(y = mx+b\)

where

Given the points

Finding the slope between (-4, 4) and (2, 12)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(-4,\:4\right),\:\left(x_2,\:y_2\right)=\left(2,\:12\right)\)

\(m=\frac{12-4}{2-\left(-4\right)}\)

\(m=\frac{4}{3}\)

Thus, the slope of the line m = 4/3

substituting (-4, 4) and m = 4/3 in the slope-intercept form of the line equation  to determine the y-intercept b

y = mx+b

\(4=\frac{4}{3}\left(-4\right)+b\)

switch sides

\(\frac{4}{3}\left(-4\right)+b=4\)

\(-\frac{16}{3}+b=4\)

Add 16 to both sides

\(-\frac{16}{3}+b+\frac{16}{3}=4+\frac{16}{3}\)

\(b=\frac{28}{3}\)

Thus, the y-intercept b = 28/3

now substituting b = 28/3 and m = 4/3 in the slope-intercept form of the line equation

y = mx+b

y = 4/3x + 28/3

Therefore, the equation of a line that passes through the points(-4, 4) and (2, 12) will be:

Hence, option A is true.

Answer:

the first option : 0.073< 0.73

Step-by-step explanation:

the first option : 0.073< 0.73

Answer:

O 0.073 < 0.73

Step-by-step explanation:

The greater than and less than symbols indicate a difference between two values. The symbol for greater than is " > ", and the symbol for less than is " <",

The value, O 0.073 is lesser then 0.73

hence,0.73 is the correct option

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Therefore, Linda bought 21 yards of ribbon. Hence, Linda bought 94 yards of ribbon.

The number of yards of ribbon Linda bought, we need to calculate the difference between the initial balance on the card and the remaining balance after the purchase.

The initial balance on the card was $20. To find the amount spent on ribbon, we subtract the remaining balance ($17.06) from the initial balance. $20 - $17.06 = $2.94

Now, we need to determine how many yards of ribbon Linda could purchase with $2.94, given that the price of the ribbon is 14 cents per yard.

To find the number of yards, we divide the total amount spent ($2.94) by the price per yard (14 cents): $2.94 ÷ $0.14 = 21

Therefore, Linda bought 21 yards of ribbon.

Hence, Linda bought 94 yards of ribbon.

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Answer: $sin(B) = \frac{\sqrt{2}}{2}$, and $\angle B = \frac{\pi}{4}$.

Step-by-step explanation:

Note that $AB=\sqrt{2x^2+20x+50} = \sqrt{2(x+5)^2;} = (x+5)\sqrt{2}$. Therefore, $sin(B) = AC/AB = \frac{x+5}{(x+5)\sqrt(2)} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$.

This gives $sin(B) = \frac{\sqrt{2}}{2}$, and then taking the inverse sin yields $\angle B = \frac{\pi}{4}, \frac{3 \pi}{4}$. But angle B is acute, so its value is $\frac{\pi}{4}$.

Answer:

The answer is 56 cm^3

Step-by-step explanation:

2 = height

7 = length

4 = width

Formula: LxWxH

2 x 7  x 4 = 56

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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The area of a circle with a radius r is given by the following formula:

In this case we know that the diameter is 8cm which means that its radius is 4cm. Using 3.14 for pie we get:

Then the answer is 50.24 cm².

Answer:

sas means side angle side

aa means angle angle

asa means angle side angle

sss means side side side

hope it helps you

please mark me as brainlist

Answer:

center:(0,4) radius:6

Step-by-step explanation:

Mohammed should deposit approximately $263.16 each month to accumulate $13,000 in the next three-and-a-half years.

To calculate the monthly deposit Mohammed should make, we can use the formula for the future value of an ordinary annuity:

FV = P * [(1 + r)^n - 1] / r,

where:

FV is the future value ($13,000 in this case),

P is the monthly deposit,

r is the monthly interest rate (5.5% divided by 100 and then by 12 to convert it to a decimal),

n is the total number of compounding periods (3.5 years multiplied by 12 months per year).

Plugging in the values, we have:

13,000 = P * [(1 + 0.055/12)^(3.5*12) - 1] / (0.055/12).

Let's calculate it:

13,000 = P * [(1 + 0.004583)^42 - 1] / 0.004583.

Simplifying the equation:

13,000 = P * (1.22625 - 1) / 0.004583,

13,000 = P * 0.22625 / 0.004583,

13,000 = P * 49.3933.

Now, solving for P:

P = 13,000 / 49.3933,

P ≈ $263.16 (rounded to the nearest cent).

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Main Answer:The recurrence relation for the power series solution of the given differential equation is:   a_(n+2) = a_n / (n+2)

Supporting Question and Answer:

How can we find the recurrence relation for the power series solution of a differential equation?

To find the recurrence relation for the power series solution of a differential equation, we can assume the solution can be expressed as a power series and substitute it into the differential equation. By equating the coefficients of like powers of x to zero, we can derive the recurrence relation for the coefficients of the power series. This recurrence relation allows us to express the coefficients in terms of previous coefficients, providing a systematic way to compute the coefficients of the power series solution.

Body of the Solution: To find the recurrence relation for the power series solution of the differential equation y′′(1 - x)y = 0, we can assume that the solution can be expressed as a power series:

y(x) = ∑(n=0)^(∞) a_n x^n

First, to find the first and second derivatives of y(x):

y'(x) = ∑(n=1)^(∞) na_nx^(n-1)

=∑(n=0)^(∞) (n+1)×a_(n+1)×(x)^n

y''(x) =∑(n=2)^(∞) n(n-1)a_nx^(n-2)

= ∑(n=0)^(∞) (n+2)(n+1)×a_(n+2)×(x)^n

Now, substitute these expressions into the differential equation:

∑(n=0)^(∞) (n+2)(n+1)×a_(n+2)×(x)^n× (1 - x) × ∑(n=0)^(∞) a_n x^n = 0

Expand and collect terms:

∑(n=0)^(∞) [(n+2)(n+1)×a_(n+2) - (n+1)×a_n] ×( x)^n - ∑(n=0)^(∞) (n+2)(n+1)×a_(n+2)×(x)^(n+1) = 0

Now, equating the coefficients of like powers of x to zero:

For n = 0:

[(2)(1)×a_2 - (1)×a_0] = 0

a_2 = a_0

For n ≥ 1:

[(n+2)(n+1)×a_(n+2) - (n+1)×a_n] - (n+2)(n+1)×a_(n+2) = 0

a_(n+2) = (n+1)×a_n / ((n+2)(n+1)) = a_n / (n+2)

Final Answer: Hence, the recurrence relation for the power series solution of the given differential equation is:

a_(n+2) = a_n / (n+2);where a_0 is a constant representing the coefficient of x^0 in the power series solution.

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Answer:

C on edge

Step-by-step explanation:

The domains of f(x) and g(x) are different. (answer)

The domains of graph f(x) and g(x) are different.

A mathematical operation is commutative if the numbers used can be changed without changing the outcome. As illustrated here, addition and multiplication are two examples of commutative operations. 2+3 = 5

3+2 = 5

2*3 Equals 6

3*2 Equals 6.

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Answer:

Cobalt (III) iodide CoI₃

Step-by-step explanation:

The name of the compound formed between Cobalt(III) and Iodine is known as Cobalt (III) Iodide.

Answer:

d

Step-by-step explanation:

d

The percentage increase in average commute times between these years = 2.25%

In 2010, the average commute time for wake county workers = 23.9 mins

In 2016, the average commute time for wake county workers = 25 mins.

The increase is = 25- 23.9 = 1.1

The average commute time between the two years,

23.9+25 = 48.9 mins

Therefore, the percentage,

= 1.1/48.9×100

= 110/48.9

= 2.249%

= 2.25% to the nearest two decimal places.

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The value of the account is $165,627.27.

After a certain number of years, the value of an investment account is represented by the expression 10,300(1 + 0.0412)^120. Given expression: 10,300(1 + 0.0412)^120Adding 1 to 0.0412, we get 1.0412. Now, the expression becomes:

=10,300 × 1.0412^120

Using a scientific calculator or spreadsheet software, we can evaluate this expression to get the value of the account as approximately $165,627.27. Therefore, the value of the account is $165,627.27.

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Fix(2.5) is equal to 1. The expected value of X (E(X)) is equal to 13/36. P(X > 0.3 and X < 0.6) is equal to 0.432.

A continuous random variable X has a probability density function (pdf) given by:

fix (x) = {x² + 4/3 x if 0 < x < 1

0 otherwise. Let's solve the questions step-by-step: To find the cumulative distribution function (CDF) Fix(t) of X, we integrate the pdf from 0 to t. To find Fix(-3), we integrate the pdf from 0 to -3, which is not possible since -3 is outside the valid range of x (0 < x < 1). Therefore, Fix(-3) does not exist. To find Fix(0.6), we integrate the pdf from 0 to 0.6:

∫(0 to 0.6) (x² + 4/3 x) dx = [1/3 x³ + 2/3 x²] (0 to 0.6)

= (1/3 × 0.6³ + 2/3 × 0.6²)

= 0.432.

Therefore, Fix(0.6) is equal to 0.432. To find Fix(2.5), we integrate the pdf from 0 to 1 (since the valid range of x is 0 < x < 1):

∫(0 to 1) (x² + 4/3 x) dx = [1/3 x³ + 2/3 x²] (0 to 1)

(1/3 × 1³ + 2/3 × 1²) = 1.

Therefore, Fix(2.5) is equal to 1. To find the expected value of X (E(X)), we need to integrate x times the pdf from 0 to 1:

E(X) = ∫(0 to 1) x × (x² + 4/3 x) dx.

Simplifying the integral:

E(X) = ∫(0 to 1) (x³ + 4/3 xv) dx

= [1/4 x⁴ + 4/9 x³] (0 to 1)

= (1/4 × 1³ + 4/9 × 1³)

= 13/36.

Therefore, the expected value of X (E(X)) is equal to 13/36. To find P(X > 0.3 and X < 0.6), we need to use the definition of conditional probability:

P(X > 0.3 and X < 0.6) = P(X < 0.6) - P(X < 0.3).

Using the CDF we obtained earlier, we have:

P(X > 0.3 and X < 0.6) = Fix(0.6) - Fix(0.3)

= 0.432 - 0

= 0.432.

Therefore, P(X > 0.3 and X < 0.6) is equal to 0.432.

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Answer: I’ll explain it in simpler terms for you. A proportional relationship is one in which two quantities vary directly with each other. Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional. An example of a proportional relationship is simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Hope this helps! :D

Answer: (6 , 3)

Step-by-step explanation: Given

x + 3y =15 ------- equation 1

4x + 2y = 30 --------- equation 2

x = 15 - 3y

Put value of x in equation 2

4 (15 - 3y) + 2y = 30

60 - 12y + 2y = 30

-10y = -30

divide by '-10' on both sides

y = 3

now, put value of y in equation 1

x + 3(3) = 15

x + 9 = 15

x = 15 - 9

x =  6

So , (x , y) = (6 , 3)