lim(x-0) (sinx-1/x-1)

Answer:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Now we know that point D, which we can write as (x, y), is at a distance of 8 units from the origin.

Where the origin is written as (0, 0)

We also know that point D is 6 units away along the y-axis.

Then point D could be:

(x, 6)

or

(x, -6)

Now, let's find the x-value for each case, we need to solve:

[tex]8 = \sqrt{(x - 0)^2 + (\pm6 - 0)^2}[/tex]

notice that because we have an even power, we will get the same value of x, regardless of which y value we choose.

[tex]8 = \sqrt{x^2 + 36} \\\\8^2 = x^2 + 36\\64 - 36 = x^2\\28 = x^2\\\pm\sqrt{28} = x\\\pm 5.29 = x[/tex]

So we have two possible values of x.

x = 5.29

and

x = -5.29

Then the points that are at a distance of 8 units from the origin, and that are 6 units away along the y-axis are:

(5.29, 6)

(5.29, -6)

(-5.29, 6)

(-5.29, -6)

Part a)

Time:distance

1:3

Part b)

6 hours

Part C)

81km

Answered by Gauthmath must click thanks and mark brainliest

Answer:

t- shirt cost £7, hat cost £3

Step-by-step explanation:

let t represent cost of t- shirt and h represent cost of hat , then

4t + h = 31  → (1)

2t + h = 17 → (2)

Subtract (2) from (1) term by term to eliminate h

(4t - 2t) + (h - h) = 31 - 17 , that is

2t = 14 ( divide both sides by 2 )

t = 7

Substitute t = 7 into either of the 2 equations and solve for h

Substituting into (1)

4(7) + h = 31

28 + h = 31 ( subtract 28 from both sides )

h = 3

t- shirt cost £7 and hat cost £3

Answer:

Step-by-step explanation:

For each game played the chance of winning is 0.05 and losing is 0.95.

If the student wins, they get $5 -$1 = $4, but they lose $1.

Expected value is:

It means you will make $0.75 per average game.

Answer:

21.8

Step-by-step explanation:

Step 1

This is a problem on finding the mean of continuous grouped data. We first find the midpoint of each interval. For example, the first interval or class is 0 - 10. The mid-point of this class will be (0 + 10)/2 = 5.

fullscreen

Step 2

We now calculate the product of mid-point and frequency for each class. Here, the number of athletes in each class is the frequency of that class. For example, for the first class 0 – 10, its frequency is 3.

fullscreen

Step 3

We can now use the formula to calculate mean. Note that t...

Answer:

The minimum number of subjects needed is 385.

Step-by-step explanation:

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].

The margin of error is:

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

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

95% confidence, within 5 percentage points, and a previous estimate is not known.

The sample size is n for which M = 0.05. We don't know the true proportion, so we use [tex]\pi = 0.5[/tex]

Then

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

[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.05})^2[/tex]

[tex]n = 384.16[/tex]

Rounding up:

The minimum number of subjects needed is 385.

Answer: y=2/3X- 4/3

Step-by-step explanation:

Slope = (4-2)/(4-1)=2/3

Y-2=2/3(x-1)

Y-2=2/3x-2/3

Y=2/3X-2/3+2

Y=2/3X-4/3

Answer:

x=6

Step-by-step explanation:

5x - 11 = 19

5x = 30

x = 6

20characters

5x = 19+11 5x = 30 x = 30/5 x = 6

Answer:

the question is incomplete :-')

Answer:

The materials price variance is usually the responsibility of the purchasing manager. The materials quantity and labor efficiency variances are usually the responsibility of production managers and supervisors.

9514 1404 393

Answer:

  7.92 years

Step-by-step explanation:

We want to find t such that ...

  3 = 2^(t/5)

where 2^(t/5) is the annual multiplier when doubling time is 5 years.

Taking logs, we have ...

  log(3) = (t/5)log(2)

  t = 5·log(3)/log(2) ≈ 7.92 . . . years

It will take about 7.92 years for the population to triple.

Volume = πr²h

Radius = 3yd

Height = 12yd

Take π = 22/7

Volume = 22/7×3×3×12

= 2376/7

= 339.4285714yd³

Rounding off to nearest tenth

= 339.43yd³

Answered by Gauthmath must click thanks and mark brainliest

[tex]\large{\underline {\underline {\pmb {\sf {\pink{Answer:}}}}}}[/tex]

Answer:

The largest whole number is the approximate of positive infinity ( to the nearest ones digit )

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{x}{3}[/tex] < 5 ( multiply both sides by 3 to clear the fraction )

x < 15 → C

Answer:

Hi!

Step-by-step explanation:

1234567890987654211234567890......

Step-by-step explanation:

12345678890098764321

9514 1404 393

Answer:

  (a) Yes , the base is 1/e

Step-by-step explanation:

The variable is in the exponent, so this is an exponential function.

The base is the number that has the exponent. The base is (1/e).

Answer:

Step-by-step explanation:

bvxbvxbvxbvcvbbb cv

Answer:

177.3 feet

This is a classic find the vertex of a parabola question.

if this was a calculus class the solution would be to take the derivative and set it equal to zero... -32t+ 105 = 0

BUT i assume that you are not in a calculus class..

so we try plan "B" the  highest (or lowest) point of parabola is it's vertex

the vertex formula is [-b/2a,f(-b/2a)]

in your problem a = -16, b=105, c= 5

so the "X" (TIME) is located at -(105)/(2*-16) = 3.28

plug in 3.28 into -16(3.28)^2 + 105(3.28) + 5 = 177.27

and you will get

Step-by-step explanation:

9514 1404 393

Answer:

  undefined

Step-by-step explanation:

A rational expression is undefined when its denominator is zero.

Answer:

Hello,

Step-by-step explanation:

Let say t the time the hose is left running

235 ≤ t < 245 (in min)

Let say d the amount of water coming out of the hose each minute

2.05 ≤ d < 2.15 (why d : débit in french)

235*2.05 ≤ t*d < 245*2.15

481.75 ≤ t*d < 526.75    (litres)

Answer:

Lower bound: [tex]495\; \rm L[/tex] (inclusive.)

Upper bound: [tex]505\; \rm L[/tex] (exclusive.)

Step-by-step explanation:

The amount of water from the hose is the product of time and the rate at which water comes out.

When multiplying two numbers, the product would have as many significant figures as the less accurate factor.

In this example, both factors are accurate to two significant figures. Hence, the product would also be accurate to two significant figures. That is:

[tex]240 \times 2.1 = 5.0 \times 10^{2}\; \rm L[/tex] ([tex]500\; \rm L[/tex] with only two significant figures.)

Let [tex]x[/tex] denote the amount of water in liters. For [tex]x\![/tex] to round to [tex]5.0 \times 10^{2}\; \rm L[/tex] only two significant figures are kept, [tex]495 \le x < 505[/tex]. That gives a bound on the quantity of water from the hose.

Answer:

$21.9 per gram

Step-by-step explanation:

Take the total price and divide by the number of grams

$162.18/7.4 grams

$21.91621 per gram

Rounding to the nearest tenth

$21.9 per gram

Answer:

$21.90 per gram (to the nearest tenth)

Step-by-step explanation:

Given information:

To find how much the necklace was worth per gram, divide the total cost by the number of grams:

[tex]\sf Worth\:per\:gram = \dfrac{\$162.18}{7.4\:g}=\$21.91621622... \:per\:gram[/tex]

Therefore, the necklace is worth $21.90 per gram (to the nearest tenth).

Answer:

The expected number of items that will be classified into group 1 is 100.

Step-by-step explanation:

For each observation, there are only two possible outcomes. Either it will be classified into group 1, or it will not. The probability of an observation being classified into group 1 is independent of any other observation, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

400 observations

This means that [tex]n = 400[/tex]

Four mutually exclusive groups. The probability of a randomly selected item being classified into any of the four groups is equal.

This means that [tex]p = 0.25[/tex]

Then the expected number of items that will be classified into group 1 is

[tex]E(X) = np = 400*0.25 = 100[/tex]

100 is the answer.

Step-by-step explanation:

hope it will help u

hope it will help u please mark me as brillient...

Answer:

939 is the answer

Step-by-step explanation:

plz Mark me as the brainlist

Answer:

f(x) = 2x + 1, g(x) = 3x - 2 and fg(x) = 5

Step-by-step explanation:

Answer:

[tex] \frac{x}{5} [/tex]

Step-by-step explanation:

[tex]f {}^{ - 1} (x)[/tex]

means inverse.

Find the inverse of the function.

[tex]f(x) = 5x[/tex]

Replace y with and vice versa.

[tex]x = {5y}[/tex]

Solve for y

[tex] \frac{x}{5} = y[/tex]

The inverse function is

[tex] \frac{x}{5} [/tex]

9514 1404 393

Answer:

  35 miles

Step-by-step explanation:

The relevant relation is ...

  distance = speed × time

The total distance the trolley traveled is ...

  d = (20 mi/h) × (3.5 h) = 70 mi

The distance is the same in both directions, so the trolley traveled half this distance in one direction.

The trolley traveled 35 miles in one direction.

Answer:

The two squares are 81 and 100, and their difference is 19

Step-by-step explanation:

Hey there!

Let's take out the square of 1st ten natural numbers to find out the exact answer.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

Now; You can take any of these numbers and subtract from their squares.

So, let's check 6² and 5²

36-25 = 11 which is not equal to 19

Again check for 10²-9²

100 - 81 = 19 (True value)

Therefore, 19 can be expressed as the difference of square of 10 and 9.

Hope it helps!

Answer:

Kindly check explanation

Step-by-step explanation:

H0 : μ = 15.7

H1 : μ < 15.7

This is a one sample t test :

Test statistic = (xbar - μ) ÷ (s/√(n))

n = sample size = 33

Using calculator :

The sample mean, xbar = 15.41

The sample standard deviation, s = 0.419

Test statistic = (15.41 - 15.70) ÷ (0.419/√(33))

Test statistic = - 3.976

Using the Pvalue calculator :

Degree of freedom, df = n - 1 ; 33 - 1 = 32

Pvalue(-3.976, 32) = 0.000187

Decison region :

Reject H0 if Pvalue < α

Since Pvalue < α ; we reject H0

There is significant evidence to conclude that the true average height of the seedlings treated with an extract from Vinca minor roots is less than 15.7 cm.

Answer:

[tex]\boxed {\boxed {\sf x \approx 1.9}}[/tex]

Step-by-step explanation:

We are asked to find x, a missing side in a triangle.

This is a right triangle because there is a small square in the corner representing a 90 degree or right angle. Therefore, we can use right triangle trigonometry. The three main functions are:

Examine the triangle. We will use angle S, measuring 54 degrees, for theta. Side QR, measuring x, is opposite angle S. Side QS, measuring 2.3, is the hypotenuse because it is opposite the right angle. Since we have the opposite and hypotenuse, we will use sine.

[tex]sin \theta = \frac {opposite}{hypotenuse}[/tex]

[tex]sin (54)= \frac{ x}{2.3}[/tex]

We are solving for x, so we must isolate the variable. It is being divided by 2.3 The inverse operation of division is multiplication, so we multiply both sides by 2.3

[tex]2.3* sin (54)= \frac{x}{2.3}*2.3[/tex]

[tex]2.3* sin (54)=x[/tex]

[tex]2.3*0.8090169944=x[/tex]

[tex]1.860739087 =x[/tex]

Round to the nearest tenth. The 6 in the hundredth place to the right tells us to round the 8 up to a 9.

[tex]1.9 \approx x[/tex]

x is approximately 1.9

Answer:

142

Step-by-step explanation:

If the enrollment is five times as big, then that is six different things. So, take 852 and divide it by 6 to get 142. Or in other words:

852÷6=142

142x6=856

I hope this helps. Cheers^^

Step-by-step explanation:

p-cheese wafers

q-chocolate wafers

p2 + q1 = $25

5(2) + 15(1) = $25

Just used numbers that added up to 20 starting from 2 going up