If 1,000 liters of oil are sold at $13,000, how much will it cost if they are sold at a 10% discount?

Answer:

\(\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta\)

Step-by-step explanation:

We have the expression:

\(\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}\)

And we want to write the expression in terms of sine and cosine and simplify.

Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:

\(=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}\)

Multiply both layers by cosθ:

\(=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}\)

Distribute:

\(\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}\)

Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:

\(\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}\)

We can convert this to cosecant if we wish.

Answer: candle burns down 1 cm per hour

Step-by-step explanation:

Answer:

d.

Step-by-step explanation:

The probability that a student lives within 3 miles of the school is 75%, and the probability that a student who lives within 3 miles walks to school is 20%. We can find the probability that a student both lives within 3 miles and walks to school by multiplying these probabilities:

0.75 x 0.20 = 0.15

Therefore, the probability that a student lives within 3 miles and walks to school is 0.15 or 15%.

Answer:

0.15  or   15%

Step-by-step explanation:

Answer:

We always start with the x because in the alaphbet x is before y. So it says x=1 and the graph is skipping by 2 so in the middle of where the interact and beside positive 2 on the x row is where the 1 is so you keep it there for now. Now for the y you can see the middle where the interact well that is 0 so you have to keep the dot on the x place because if it said y=2 we would move it but is says 0 so we dont move it!

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Answer:

The LCD of 1/6 and 1/3 is 6.

Step-by-step explanation:

Rewriting input as fractions if necessary:

1/6, 1/3

For the denominators (6, 3) the least common multiple (LCM) is 6.

LCM(6, 3)

Therefore, the least common denominator (LCD) is 6.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

1/6 = 1/6 × 1/1 = 1/6

1/3 = 1/3 × 2/2 = 2/6

As asked by the question, the value of K for a given equation of a line is equal to the slope of the line.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

The value of K for a given line is equal to the slope of the line. Since lines are generally expressed in the form of y = mx +b , where m is the slope of the line and b is the y-intercept of the line. Here , the value of K will be equal to the slope m of the line.

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La masa del sistema es inversamente proporcional a la temperatura del mismo. Existe una relación de proporcionalidad inversa.

En este problema tenemos dos casos de calentamiento sensible en dos muestras de agua, cuya fórmula se describe a continuación:

Q' · Δt = m · c · ΔT

Donde:

A partir de esta fórmula comprobamos que la masa del sistema es inversamente proporcional al cambio de la temperatura del sistema:

m ∝ 1 / ΔT

En consecuencia, a mayor masa, menor cambio en la temperatura.

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The Kivetsky family can claim $8,943.42 as their medical deductions.

To calculate the amount the Kivetsky family can claim as medical deductions, we need to follow these steps:

Step 1: Calculate the threshold for medical deductions:

Threshold = 7.5% of adjusted gross income

Threshold = 0.075 * $119,245.61

Threshold = $8,943.42

Step 2: Calculate the deductible medical expenses:

Deductible Expenses = Medical Expenses - (Medical Expenses * Insurance Coverage)

Deductible Expenses = $14,191 - ($14,191 * 0.8)

Deductible Expenses = $14,191 - $11,352.8

Deductible Expenses = $2,838.2

Step 3: Determine the allowable medical deductions:

Allowable Medical Deductions = Max(Deductible Expenses, Threshold)

Allowable Medical Deductions = Max($2,838.2, $8,943.42)

Allowable Medical Deductions = $8,943.42

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The estimated value of the standard error is approximately $127.05.

The standard error is a measure of the variability or dispersion of the sample mean. It represents the average deviation of the sample means from the true population mean.

To estimate the value of the standard error, we can use the formula:

Standard Error = Standard Deviation / Square Root of Sample Size

In this case, the standard deviation is given as $4021.54 and the sample size is 1000 respondents.

Let's plug these values into the formula:

Standard Error = 4021.54 / √1000

To calculate the square root of 1000, we find that √1000 is approximately 31.62.

So, the standard error is:

Standard Error = 4021.54 / 31.62

Standard Error ≈ $127.05

Therefore, the estimated value of the standard error is approximately $127.05.

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The solution of the recurrence relation is \(a_n=3.2^n\)

For given question,

We have been given a recurrence relation \(a_n = 2a_{n-1}\) for n ≥ 1

and an initial condition \(a_0=3\)

Let \(a_n\) = m², \(a_{n-1}\) = m and \(a_{n-2}\) = 1

So from given recurrence relation we get an characteristic equation,

⇒ m² = 2m

⇒ m² - 2m = 0                     .........( Subtract 2m from each side)

⇒ m(m - 2) = 0                     .........(Factorize)

⇒ m = 0    or  m - 2 = 0

⇒ m = 0   or   m = 2

We know that the solution of the recurrence relation is then of the form

\(a_n=\alpha_1 {m_1}^n + \alpha_2 {m_2}^n\)  where \(m_1,m_2\) are the roots of the characteristic equation.

Let, \(m_1\) = 0   and \(m_2\) = 2

From above roots,

\(\Rightarrow a_n=\alpha_1 {0}^n + \alpha_2 {2}^n\\\\\Rightarrow a_n=0+\alpha_2 {2}^n\\\\\Rightarrow a_n=\alpha_2 {2}^n\)

For n = 0,

\(\Rightarrow a_0=\alpha_2 {2}^0\\\\\Rightarrow a_0=\alpha_2 \times 1\\\\\Rightarrow a_0=\alpha_2\)

But  \(a_0=3\)

This means \(\alpha_2=3\)

so, the solution of the recurrence relation would be \(a_n=3.2^n\)

Therefore, the solution of the recurrence relation is \(a_n=3.2^n\)

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The norm of the linear functional f defined on C[-1, 1) is 1.

To compute the norm, we first consider the absolute value of f(x). Since f is a linear functional, we can split the integral into two parts:

|f(x)| = |∫[-1,1) (L-1)dt - ∫[-1,1) (t * x(t)) dt|

= |∫[-1,1) (L-1)dt| - |∫[-1,1) (t * x(t)) dt|.

Now, let's evaluate each integral separately:

|∫[-1,1) (L-1)dt|:

Since L-1 is a constant function equal to -1, we can rewrite the integral as:

|∫[-1,1) (L-1)dt| = |∫[-1,1) (-1)dt| = |-∫[-1,1) dt|.

Integrating over the interval [-1, 1), we get:

|-∫[-1,1) dt| = |-t| = |1 - (-1)| = 2.

Therefore, |∫[-1,1) (L-1)dt| = 2.

|∫[-1,1) (t * x(t)) dt|:

Here, we need to consider the absolute value of the integral involving the function x(t). Since x(t) is a continuous function defined on the interval [-1, 1), its value can vary. To find the supremum of this integral, we need to analyze the possible values x(t) can take.

Since we're looking for the supremum when ||x|| = 1, we want to consider functions that are "normalized" or have a norm of 1. One example of such a function is the constant function x(t) = 1. Using this function, the integral becomes:

|∫[-1,1) (t * x(t)) dt| = |∫[-1,1) (t * 1) dt| = |∫[-1,1) t dt|.

Evaluating the integral, we find:

|∫[-1,1) t dt| = |[t²/2] from -1 to 1| = |(1²/2) - ((-1)²/2)| = |1/2 + 1/2| = 1.

Therefore, |∫[-1,1) (t * x(t)) dt| = 1.

Now, we can compute the norm of f by taking the supremum of the absolute values obtained above:

||f|| = sup{|f(x)| : x ∈ C[-1, 1), ||x|| = 1}

= sup{|2 - 1|} (using the values obtained earlier)

= sup{1}

= 1.

Hence, the norm of the linear functional f defined on C[-1, 1) is 1.

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Answer:

270

Step-by-step explanation:

Answer:

After 16 years Mr. Jibril will be twice as old as his son.

Step-by-step explanation:

t - age Mr. Jibril

s - son age

t=4s (father is 4 times older than son)

t-4=7(s-4) (4 years ago they both have 4 year old less and father was 7 times older than son)

t=7s-28+4

t=7s-24

7s-24=4s

3s=24

s=8

t=32

x- years after Mr. Jibril will be twice as old as his son.

32+x=2(8+x)

32+x=16+2x

16=x

x=16

The time required for 175 gpm to pass through a 1500-foot length of 12-inch diameter pipeline is d) 8.57 minutes.

To solve this problem, we can use the following formula:

Time = Distance / Velocity

where Velocity = Flow rate / Cross-sectional area

We are given the flow rate (175 gpm) and the dimensions of the pipeline (12-inch diameter), so we can calculate the cross-sectional area:

Area = π x (diameter/2)^2

Area = π x (12/2)^2

Area = π x 36

Area = 113.1 square inches

Next, we can calculate the velocity:

Velocity = Flow rate / Cross-sectional area

Velocity = 175 / 113.1

Velocity = 1.55 feet per second

Finally, we can use the time formula to calculate the time required:

Time = Distance / Velocity

Time = 1500 / (1.55 x 60)

Time = 8.57 minutes (rounded to two decimal places)

Therefore, the answer is option (b) 8.57 minutes.

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Answer:

50 inches.

Step-by-step explanation:

There are 26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰ exponential generating Function to make an arrangement  of Pennies, nickels, dimes and quarters with at least one penny and an odd number of quarters.

Exponential generating Function:

An exponential generator provides a way to encode a sequence as the coefficients of a power series. This encoding helps in many ways.

Therefore, According to the Question:

The exponential generating function is,

G(x) = (x¹/1! + x²/2! + ...)(x¹/1! + x³/3! + x⁵/5! +...)(x°/0! + x¹/1! + x²/2! + ...)²

where the first factor describes the pennies, the second describes the quarters, and the last describes nickels and dimes.

We want the coefficient of  Xˣ /r!.

Using exponential identities we get,

G(x) = \(e^{x} - 1 (\frac{e^{x} - e^{-x} }{2} ) (e^{x} )^2\)

      = \(\frac{1}{2} (e^{4x} -e^{2x} -e^{3x} + e^{x}\)

and the coefficient is

\(\frac{1}{2} (4^r -2^r -3^r +1)\)

The generating function is

G(x) = (x¹/1! + x²/2! + ...)⁴(x°/0! + x¹/1! + x²/2!+...)²² = ()⁴,

and we again want the coefficient of  X¹⁰/10!.

Multiplying we get,

G(x) = \((e^{4x} - 4e^{3x} + 2e^{2x} + 1)e^{22x}\)

       = \(e^{26x} - 4e^{25x} + 2e^{24x} +e^{22x}\)

so the coefficient of  X¹⁰/10! is

26¹⁰ - 4 × (25)¹⁰ + 2 × (24)¹⁰ + 22¹⁰

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Answer:

324, 900, 9

Step-by-step explanation:

When a shape has its size increased by a scale factor, the size of its lengths are multiplied by this scale factor, yet its area is actually multiplied by the scale factor squared. This is due to two lengths being multiplied to contribute to the area, not just one. If it was a volume, you would multiply by the scale factor cubed!

Onto the answer, just follow the advice above:

36 * 3^2 = 36 * 9 = 324 square inches,

36 * 5^2 = 36 * 25 = 900 square inches,

36 * 0.5^2 = 36 * 0.25 = 9 square inches.

Hope this helps :)

Answer:

Solution given:

x+4y=8.......[1]

since slope intercept form is:

y=mx+c where m=slope and c=constant

making equation 1 in slope intercept form:

x+4y=8

4y=8-x

y=\(\frac{-x+8}{4}\)

y=-¼x+2

comparing above equation with y=mx+c we get

m=-¼

So slope is -¼.

The population of Guam is \(18*10^4.\)

To write this as a whole number, we need to multiply 18 by 10,000, which is the same as moving the decimal point four places to the right. So, \(18*10^4.\) is equivalent to 180,000. Therefore, the population of Guam as a whole number is 180,000.

This means that there are approximately 180,000 people living in Guam, according to the given population figure. When dealing with large numbers in scientific notation, it is important to remember that the exponent tells us how many places to move the decimal point to get the whole number equivalent.

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Hey there! I'm happy to help!

LENGTH OF CONVEYOR BELT

We are going to have to use some trigonometry. Let's think of this as a right triangle. The conveyor belt is the diagonal or the hypotenuse, while the ground is  and the height of the room make a right angle as the legs.

We have a sixty degree angle between the conveyor belt and the ground. This is means that the 21 foot height is the opposite side of our right triangle. So, we are dealing with the opposite and the hypotenuse, so we will use the sine. The sine of an angle is equal to the opposite length divided by the hypotenuse length.

We will set up the following equation and solve for the length of our conveyor belt (c).

\(sin60=\frac{21}{c}\)

We multiply both sides by c.

\(c(sin60)=21\)

We divide both sides by sin60.

\(c=\frac{21}{sin60}\)

If we evaluate this with a calculator, we get that c is equal to 24.2487113..., or 24 when rounded to the nearest foot.

So, the supplies travel 24 feet from one end to the other.

DURATION OF TRAVEL

We want to find how long it takes the supplies to move across the conveyor belt. We see that every minute, it moves 75 feet. We want to see how many minutes it will take to move 24 feet, as that is the length of the conveyor belt as we previously solved. Let's set up a proportion.

\(\frac{feet}{minute} =\frac{75}{1} =\frac{24}{m}\)

We cross multiply, giving us the following equation.

75m=24

We divide both sides by 75.

m=0.32

We want to round to the nearest tenth of a minute, so it will take 0.3 minutes for the supplies to move to the second floor.

Have a wonderful day! :D

Answer:

ang tanga mo naman para di malaman ang sagot

Answer:

m>5

Step-by-step explanation:

Let's solve your inequality step-by-step.

m+4>9

Step 1: Subtract 4 from both sides.

m+4−4>9−4

m>5

Answer:

m > 5

Step-by-step explanation:

m + 4 > 9

m + 4 - 4 > 9 - 4

m > 5

The ratio is given as 9 / 26

Total number of miles in the race: 26 miles

Number of miles you've run so far: 17 miles

Miles left to run = Total miles in the race - Miles you've run so far

Miles left to run = 26 miles - 17 miles

Miles left to run = 9 miles

Now, to find the ratio of the number of miles you have left to the total number of miles in the race:

Ratio = Miles left to run : Total miles in the race

Ratio = 9 miles : 26 miles

So the ratio is 9:26.

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Answer:

x=4

Step-by-step explanation:

x-8= x/2 -x-6/3

x-8=x/2-x-2

x-8=-x/2-2

1.5x-8=-2

1.5x=6

x=4

Answer:

domain of the sine and cosine functions is all real numbers

Step-by-step explanation:

range of both the sine and cosine functions is [−1,1]

graph can go left and right to infinity

graph goes up and down between 1 and -1

graph looks like a wave or

like U letters next to each other

UUUU

sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.

mathlibretextsorg

The perimeter of the given figure is 120 units

The perimeter of a figure is the total length of the boundary or the distance around the figure. It is the sum of the lengths of all the sides of the figure. The perimeter is always expressed in units of length, such as centimeters, meters, feet, or inches.

To find the perimeter of this figure, we need to simply add up all the sides;

The perimeter of the figure will be;

P = 16 + 16 + 12 + 4 + 12 + 4 + 24 + 16 + 8 + 8 = 120 units

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