f(x)= x² – 2x +5For f(-3)

Answer:

Step-by-step explanation:

sin28=0,27

cos28=0.88

so b=0.88c

and a =0.27c and from here is easy

Given

To find

we know that

Inserting the value of radius

Step-by-step explanation:

Formula that you need to commit to memory :

  Area of ANY triangle = 1/2 * base * height

             area = 1/2 * 1.2 * . 6 = .36 m^2

Answer: area of the triangle is 0.36m

Step-by-step explanation:

The area of the triangle is mainly defined by the area enclosed by the three sides of any particular triangle. Basically, we calculate it as the area is equal to half of the base times height.

area of the triangle formula : A = 1/2  × b  ×  h

= 1/2 × 1.2m × 0.6 m

=1/2 x 0.72m

=0.36m

Therefore, the area of the triangle will be 0.36m for the base 1.2m and the  height 0.6m

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Answer:

shoot man couldnt tell ya

Answer:

\(506 \frac{2}{3} kg\)

Step-by-step explanation:

50 2/3=

50×2+3/3

=152/3 kg

next 152/3 ×10

=1520/3

=506 2/3

Answer:

The visitor needs to run 5.5 miles before he starts swimming to minimize the time it takes to reach the island.

Step-by-step explanation:

The sketch of the setup described is drawn on the attached image to this question.

Let the distance the visitor has to run be x miles

The distance from that endpoint of running to the closest point on the shoreline to the island is then (7 - x) miles

Using Pythagoras theorem, we can then calculate the distance the visitor has to swim

Let that distance be y

y² = 2² + (7 - x)²

y² = 4 + 49 - 14x + x²

y² = x² - 14x + 53

y = √(x² - 14x + 53)

Speed = (distance/time)

Time = (distance/speed)

Running time = (running distance)/(running speed) = (x/5)

Swimming time = (swimming distance)/(swimming speed) = [√(x² - 14x + 53)]/3

Total time to reach the island

= Running time + Swimming time

T = (x/5) + [√(x² - 14x + 53)]/3

we now want to find the distance that the visitor will run to minimize the time to reach the island

At minimum value of T, (dT/dx) = 0

(dT/dx) = (1/5) + [(2x - 14)(x² - 14x + 53)⁻⁰•⁵]/6

multiplying through by 15

15(dT/dx) = 3 + 5[(x - 7)(x² - 14x + 53)⁻⁰•⁵]

So, at minimum value of T, (dT/dx) = 0

0 = 3 + 5[(x - 7)(x² - 14x + 53)⁻⁰•⁵]

-3[(x² - 14x + 53)⁰•⁵] = 5(x - 7)

-3[(x² - 14x + 53)⁰•⁵] = (5x - 35)

Squaring both sides

9(x² - 14x + 53) = (5x - 35)² = 25x² - 350x + 1225

9x² - 126x + 477 = 25x² - 350x + 1225

25x² - 350x + 1225 = 9x² - 126x + 477

16x² - 224x + 748 = 0

Solving this quadratic equation

x = 8.5 or x = 5.5 miles

Since the Total distance from the cabin to the closest shore point to the island is 7 miles, the only feasible answer is x = 5.5 miles.

Therefore, the visitor needs to run 5.5 miles before he starts swimming to minimize the time it takes to reach the island.

Hope this Helps!!!

The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.

The first step is to determine the dimensions of the quilt.

Dimensions = √35 = 5.92 feet

Now convert the dimensions of the quilt to inches

1 feet = 12 inches

5.92 x 12 = 70.99 inches

Difference in the width of the bed and the quilt = 70.99 - 60 = 10.99

Difference in the length of the bed and the quilt = 80 - 70.99 = 9.01

 Here are the options:

A. The quilt will cover half of the surface of the bed.

O B. The quilt will match up with the length of the bed, but 20 inches will hang over the length. °

C. The quit will be 14.6 inches wider and 15.4 inches shorter than the bed. O D. The quilt will be 10.99 inches wider and 9.01 inches shorter than the bed.

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Answer:

It should be the last one: 57,905.84 inches

Step-by-step explanation:

to solve for m

distribute into parentheses

176 = -16 - 24m

get m on one side

176 + 16 = -24m

192 = -24m

divide by -24

-8 = m

m = -8

Answer:

C. The university surveys 600 randomly selected students who attend the university.

Step-by-step explanation:

If there are 31 horses competing in a show, then the blue, red, and yellow ribbons can be awarded in 26970 different ways.

As per the question statement, 31 horses are competing in a show.

We are required to calculate the number of ways in which the blue, red and yellow ribbons can be awarded.

To solve this question, first, we need to know a basic rule of horse shows, which is the 1st place or the winner is awarded with a blue ribbon, the second place or the runners-up is awarded with a red ribbon and the third place or the second runners-up is awarded with a yellow ribbon.

That is, in simpler terms, we have to calculate the number of different ways, in which the first, second and third places can be achieved between 31 different horses, each having equal probability of winning.

To solve this question, we just need to know the formula of permutation which goes as \([(nPr)=\frac{n!}{(n-r)!} ]\),  i.e., we are to select an ordered set or "r" from a set of "n".

As per our question, (n = 31) and (r = 3), and using these in the above mentioned formula of permutation, we get

\((31C)=\frac{31!}{(31-3)!}=\frac{31!}{28!} =\frac{28!*29*30*31}{28!}=(28*29*30)=26970.\)

That is, the blue, red and yellow ribbons can be awarded in a show with 31 horses as contestants in 26970 different ways.

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The quotient of 7 subtracted from a number c and 4 which is 2 , 4 +3 = 7  and c=3. The quotient is the outcome of splitting two numbers.

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The graph for a line that has a slope of m = -3/2 and the point (-6, 2) is shown below.

The graph of a linear equation can be plotted on a coordinated plane if we are given the slope value, m, and a point (a, b).

The equation of this line can be expressed when we have the value of m (slope), and the value of (a, b), which is a point as y - b = m(x - a) in point-slope form.

Given a line with the following:

Slope (m) = -3/2

A point (a, b) = (-6, 2)

The equation of the line can be written by substituting m = -3/2, a = -6, and b = 2 into y - b = m(x - a):

y - 2 = -3/2(x + 6)

Thus, the graph of this line with the equation, y - 2 = -3/2(x + 6), is shown below.

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Answer:

\( db = 10 log_{10} (\frac{I}{I_o})\)

With db =112 db, \(I_o =10^{-12} W/m^2\) and solving for I the intensity we have:

\( \frac{db}{10}= log_{10} (\frac{I}{I_o})\)

\( \frac{112}{10}= log_{10} (\frac{I}{10^{-12}})\)

Now we can exponentiate with base 10 and we got:

\( 10^{11.2} = \frac{I}{10^{-12}}\)

And solving we got:

\( I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}\)

Step-by-step explanation:

We knwo that the loudnes os 112 db and we want to find the intensity. So then we can use the following formula:

\( db = 10 log_{10} (\frac{I}{I_o})\)

With db =112 db, \(I_o =10^{-12} W/m^2\) and solving for I the intensity we have:

\( \frac{db}{10}= log_{10} (\frac{I}{I_o})\)

\( \frac{112}{10}= log_{10} (\frac{I}{10^{-12}})\)

Now we can exponentiate with base 10 and we got:

\( 10^{11.2} = \frac{I}{10^{-12}}\)

And solving we got:

\( I= 10^{-12} * 10^{11.2} = 0.158 \frac{W}{m^2} = 0.16 \frac{W}{m^2}\)

Answer: 40 ( to the nearest ten)

Step-by-step explanation:

Complete question :

The loudness of a jack hammer is 96 dB . Its sound intensity is about 0.004.

The loudness of a compactor is 94 dB . Its sound intensity is about 0.0025.

The sound intensity of the jack hammer is about 1.6 times the sound intensity of the compactor.

The loudness of a pile driver is 112 dB . About how many times the sound intensity of the jackhammer is the sound intensity of a pile driver? Round to the nearest ten.

Given that:

Sound intensity of jackhammer = 0.004

Sound intensity of compactor = 0.0025

Sound intensity of jackhammer is about 1.6 times the sound intensity of a compactor

Each factor of 10 in intensity corresponds to 10dB

Pile driver with loudness of 112dB ⇒ \(\frac{112}{10}=11.2\)

Hence, 10^11.2 = 1.58489 × 10^11

Hence, sound intensity (I) in watts per m²

I = 1.58489 × 10^11 × 10^-12

I = 1.58489 × 10-1

I = 0.158489

Comparing the intensity of pile driver and jackhammer :

Intensity of piledriver / Intensity of jackhammer

\(\frac{0.158489}{0.004}\)

= 39.622  ≅ 40 ( to the nearest ten )

Answer:

Fred would have earned $31,022.31 after 16 years.

Step-by-step explanation:

To calculate compound interest, the initial capital must be multiplied by the interest rate applied to the capital, and in turn, this number must be exponential by the number of years that the investment lasts. Thus, in the case, the equation would be the following:

12.993 x (1 + 0.0559) ^ 16

In this way, multiplying the result exponentially by 16 years, the final compound interest would be $ 31,022.31.

Answer:

improper fraction would be 3 2/3 and mixed number would be 11/3

Step-by-step explanation:

Answer:

\(\large \boxed{\sf \ \ 9\text{ years} \ \ }\)

Step-by-step explanation:

Hello,

First of all, a few remarks:

>>> 1 year is 12 months, right?

>>> Monthly compounding means that each month we compute the interest and they will be included in the investment for the next month.

>>> 6% is an interest per year, it means that to compute the interest for 1 month we need to compute by 6% multiplied by \(\dfrac{1}{12}\)

Let's do it !

At the beginning, we have:

   $8,000

After 1 month, we will have:

   \(8000 + 8000\cdot \dfrac{6\%}{12}=8000\cdot (1+ \dfrac{6}{1200})= 8000\cdot (1+ \dfrac{1}{200})\)

After 2 months, we will have:

   \(8000\cdot (1+ \dfrac{1}{200})\cdot (1+ \dfrac{1}{200})=8000\cdot \left(1+ \dfrac{1}{200}\right)^2\)

After n months, we will have

   \(8000\cdot \left(1+ \dfrac{1}{200}\right)^n=8000\cdot \left(1.005\right)^n\)

We are looking for n such that

   \(8000\cdot \left(1.005\right)^n=13709.60\\\\ln(8000)+ n\cdot ln(1.005)=ln(13709.60)\\\\\\n = \dfrac{ln(13709.60)-ln(8000)}{ln(1.005)}=108\)

So, we need 108 months to reach this amount, which means 108/12=9 years.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

y = 2x + 3

Step-by-step explanation:

Hi there!

We are given the points (-1, 1) and (3,9) which belong to a line

We want to write the equation of the line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept

First, let's find the slope of the line

The slope (m) can be found using the formula \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

Let's label the values of the points before we start, to avoid confusion and mistakes

\(x_1 = -1\\y_1=1\\x_2=3\\y_2=9\)

Now substitute into the formula (note: the formula has SUBTRACTION, and we have NEGATIVE numbers, so we'll end up subtracting a negative)

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

m = \(\frac{9-1}{3--1}\)

Simplify

m=\(\frac{9-1}{3+1}\)

m=\(\frac{8}{4}\)

Divide

m = 2

The slope of the line is 2

We can substitute this as m in y=mx+b.

y = 2x + b

Now we need to find b

As the equation passes through the point (-1, 1) and (3, 9), we can use either point to help solve for b.

Taking (3, 9) for example:

substitute 3 as x and 9 as y.

9 = 2(3) + b

Multiply

9 = 6 + b

Subtract 6 from both sides

3 = b

Substitute 3 as b in the equation

y = 2x + 3

Hope this helps!

Topic: finding the equation of the line

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Answer: 6

Step-by-step explanation:

hope this is the right answer :)

Answer:

.66

Step-by-step explanation:

1/2 + 1/3 - 1/2 - 1/3 = .66

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

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Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a hexagon has 6 sides , then

sum = 180° × (6 - 2) = 180° × 4 = 720°

12

the polygon has 5 sides , so

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

y + 90 + 120 + 90 + 110 = 540

y + 410 = 540 ( subtract 410 from both sides )

y = 130

13

the polygon has 7 sides , so

sum = 180° × (7 - 2) = 180° × 5 = 900°

sum the interior angles and equate to 900

p + 90 + 141 + 130 + 136 + 123 + 140 = 900

p + 760 = 900 ( subtract 760 from both sides )

p = 140

Answer: 165 miles

Step-by-step explanation: In order to figure out the answer, you must do 55 x 3 because he drove for 3 hours at 55 mph so you could break it up and go 50 x 3 to equal 150 and 5 x 3 to equal 15 and add those to get 165.

Answer:

The answer is 165miles

Step-by-step explanation:

\(distance = speed \times time\)

d=55×3

d=165 miles

Answer:

a = T - 4

Step-by-step explanation:

Simply just subtract 4 on both sides to get the answer!

Answer:

a=T-4

Step-by-step explanation:

subtract 4

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

The probabilities are given as follows:

3. P(rides bus|owns a car) = 1/3.

4. P(red|organic) = 3/5.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item 3, the outcomes are given as follows:

Hence the probability is:

P(rides bus|owns a car) = 8/24 = 1/3.

For item 4, the outcomes are given as follows:

The error was in identifying the total outcomes, and the probability is:

P(red|organic) = 18/30 = 3/5.

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Answer:

the answer should be B:12/5

The standard deviation is 3.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Given, formula for the standard deviation

s = √[1/n(n-1)](n∑x²-(∑x)²)

values: x₁ = 13, x₂ = 16, x₃ = 10

step1: Calculate the square of each data value.

x₁² = 13² = 169

x₂² = 16² = 256

x₃²= 10² = 100

step2: Determine n times the sum of squares of the three values.

n∑x² = n(x₁²+x₂²+x₃²)

=3(169+256+100) = 1575

step3: Calculate the sum of the three values.

∑x = x₁+x₂+x₃

= 13+16+10 =39

step4: Calculate the square of the sum of the three values.

(∑x)² = 1521

step5: Calculate the variance.

[1/n(n-1)](n∑x²-(∑x)²)

=[1/3(3-1)](1575-1521)

=54/6

=9

step6: Calculate the standard deviation.

√[1/n(n-1)](n∑x²-(∑x)²)

= √9

=3

Hence, The standard deviation using the given formula for x₁=13, x₂=16 and x₃=10 is 3.

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