Ben and Susan are truck drivers who start at the same location. Ben drives 300 miles due west and Susan drives 160 miles due south. To the nearest mile, how far apart would they be?

Answer:

x = 34° and y = 62°

Step-by-step explanation:

Complementary angles sum to 90°, therefore 90 = 56 + x which means that x = 34°. The angles formed by an angle bisector are congruent and so are vertical angles; this means that ∠SOR = ∠POU = 56° and ∠POQ = ∠QOR = y. Since POS is a straight line, straight lines have a measure of 180° and because ∠POS = ∠POQ + ∠QOR + ∠SOR, we know that 180 = y + y + 56 → 180 = 2y + 56 → 180 → 2y = 124 → y = 62°.

Answer:

x=nπ3, n∈I

Step-by-step explanation:

sin x + sin 5x = sin 2x + sin 4x

⇒⇒   2 sin 3x cos 2x = 2 sin 3x cos x

⇒⇒   2 sin 3x(cos 2x - cos x) = 0

⇒    sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒    sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I

or    cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x

⇒   2x=2nπ±x  ⇒  x=2nπ, 2nπ3⇒   2x=2nπ±x  ⇒  x=2nπ, 2nπ3 , n∈I, n∈I

But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I

Answer:

  log(1/10) = -1

Step-by-step explanation:

Use the law of exponents and the meaning of logarithm.

  1/10 = 10^-1

  log(10^x) = x

So, you have ...

  log(1/10) = log(10^-1)

  log(1/10) = -1

The arc length is

[tex]S=\displaystyle\int_C\mathrm ds[/tex]

where C is the given curve and ds is the line element. C is defined on 0 ≤ t ≤ 3π by the vector function,

[tex]\mathbf r(t)=(t\cos t,t\sin t)[/tex]

so the line element is

[tex]\mathrm ds=\left\|\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt[/tex]

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm d(t\cos t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm d(t\sin t)}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

[tex]\mathrm ds=\sqrt{1+t^2}\,\mathrm dt[/tex]

So we have

[tex]S=\displaystyle\int_0^{3\pi}\sqrt{1+t^2}\,\mathrm dt\approx46.132[/tex]

10 units squared. Hope this helped.

The area of the triangle is 10 square units.

The given coordinates are A(2,0), B(6,0), and C(8,5).

The formula of area of triangle formula in coordinate geometry is the area of the triangle in the coordinate geometry is:  [tex]A=\frac{1}{2} |x_{1} (y_{2}-y_{3})+x_{2} (y_{3}-y_{1})+x_{3} (y_{1}-y_{2})|[/tex]

Now, Area=1/2|2(0-5)+6(5-0)+8(0-0)|=0.5|20|

=10 square units

Therefore, the area of the triangle is 10 square units.

To learn more about the area of the triangle visit:

https://brainly.com/question/11952845.

#SPJ2

Complete question :

Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an

hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.

Let H represent the whole number of hours that the plumber works.

1) Which inequality describes this scenario?

Choose 1 answer:

A. 28 + 65H < 250

B. 28 + 65H > 250

C. 65 + 28H < 250

D. 65 +28H > 250

2) What is the largest whole number of hours that Anand can afford?​

Answer:

65 + 28H < 250

Number of hours Anand can afford = 6 hours

Step-by-step explanation:

Given the following information :

Initial hourly rate = $65

Hourly rate = $28

Number of hours worked (whole number) = H

Maximum budgeted amount to spend = $250

Therefore ;

(Initial charge + total charge in hours) should not be more than $250

$65 + ($28*H) < $250

65 + 28H < 250

Number of hours Anand can afford :

65 + 28H < 250

28H < 250 - 65

28H < 185

H < (185 / 28)

H < 6.61

Sinve H is a whole number, the number of hours he can afford is 6 hours

Answer:

65 + 28H < 250

6
Step-by-step explanation:

tried it, it worked.
the other answer is correct but hard to understand so give them thanks and 4 star :)

Answer:

AE = 7.5

Step-by-step explanation:

Since <BAC = [tex]90^{0}[/tex], then;

<BAD = <DAE = <CAE = [tex]30^{0}[/tex] (complementary angles)

From ΔABC, applying the Pythagoras theorem to determine the length of side AC;

[tex]/BC/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/AB/^{2}[/tex]

[tex]/10/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/5/^{2}[/tex]

100 = [tex]/AC/^{2}[/tex] + 25

[tex]/AC/^{2}[/tex] = 100 - 25

[tex]/AC/^{2}[/tex] = 75

AC = [tex]\sqrt{75}[/tex]

Applying trigonometric function to ΔCAE,

Cos [tex]30^{0}[/tex] = [tex]\frac{AE}{\sqrt{75} }[/tex]

AE = [tex]\sqrt{75}[/tex] × Cos [tex]30^{0}[/tex]

    = 7.5

Therefore, AE = 7.5

Answer:

Step-by-step explanation:

You have the right numbers, but the wrong accounts.

__

Let x represent the amount invested at 8% (the highest rate). Then the total interest is ...

  .08x +.03(3000 -x) = .04(3000)

  .05x = .01(3000) . . . . subtract .03(3000)

  x = 3000/5 = 600

Matthew invested $600 at 8%, $2400 at 3%.

_____

Comment on checking your answer

You may notice that the overall interest rate is 4%, closer to 3% than to 8%. That means more of the money must be invested at 3% than at 8%.

[tex] \LARGE{ \boxed{ \purple{ \rm{Answers;)}}}}[/tex]

☃️ Degree of the polynomial- The highest degree of any term in a polynomial. Here the highest degree is 5.

⇛ 4x⁴ + 5 + 6x⁵ - 2x(° of polynomial = 5)

☃️ Leading coefficient- The coefficient of the term having the highest degree of the polynomial. Here, the highest degree is 5 and the term is 6x⁵

⇛ 4x⁴ + 5 + 6x⁵ - 2x (Leading coeff. = 6)

☃️ Constant term- It is the term having no coefficients, only a fixed real number. This remains constant in any value of polynomial.

⇛ 4x⁴ + 5 + 6x⁵ - 2x (Constant term = 5)

━━━━━━━━━━━━━━━━━━━━

Answer:

1+5.3=6.3

Step-by-step explanation:

not sure what your asking for with the 2

explain what your looking for with the 2 and maybe we can help you further

(I have to do it the way I did it because the 2 in the question is confusing)

Answer:

For expression 1 + 5.32: 6.32

For expression 1 + 5.3 × 2: 11.6

Step-by-step explanation:

If the expression is 1 + 5.32:

If the expression is 1 + 5.3 × 2:

Answer:

i) [tex]\frac38\pi[/tex]

ii) n = 33

Step-by-step explanation:

For this question you can actually focus on the sine, and forget about the e power. The x-coordinates of the extremes of the curve will be the same as for y=sin(4x)

i) equivalent to solving sin(4x) = -1, so 4x = 3/2 pi, x=3/8 pi

ii) The Tn values are at x = (n·π - π/2)/4

solving  (n·π - π/2)/4 > 25 gives:

n > 1/2 + 100/π, so n > 32.331, but n must be integer, so we get n=33

Answer:

B. 36 square units

Step-by-step explanation:

This is a triangle and to calculate the area of a triangle we multiply height with base and that divided by two

The height of this triangle is 8 units and the base is 9 units

9 × 8 ÷ 2 = 36 square units

Answer:

10 9/20

Step-by-step explanation:

Hey there!

If Hillsboro to Campbell is 16 2/20 and Hillsboro to Oxford is 5 13/20,

we’ll do

16 2/20 - 5 13/20

Imrpoper form

322/20 - 113/20

322 - 113

209/20

10 9/20 miles from Oxford to Campbell.

Hope this helps :)

Answer:

the answer is 18

Step-by-step explanation:

8 is the answer

Answer:

estimated error=±0.725

Step-by-step explanation:

Side of the triangle= 12cm

Opposite of triangle x= 30

h= hypotenose side

Error= =±1

From trigonometry

Sin(x)=opposite/hypotenose

hypotenose=opposite/sin(x)

h=12/sin(x)

h=12Csc(x)

dh=-12Csc(x)Cot(x) dx...............eqn(1)

dx is the possible error in angle measurements

So we need to convert to radius

dx=±1°× (π/180)

=±1°(π/180)

Substitute x and dx into equation (1)

dh= - 12Csc30°Cot30°×[±(π/180)]

= -12(2)(√3)(±(π/180)

==±0.725

Therefore, estimated error=±0.725

Answer:

The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]

(D) is correct option.

Step-by-step explanation:

Given that,

Points (6,5), (7,2), (9,6) and (10,3) are vertices of an inscribed square.

We need to calculate the distance between (7,2) and (9,6)

Using formula of distance

[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

Put the value into the formula

[tex]d^2=(9-7)^2+(6-2)^2[/tex]

[tex]d^2=20\ m[/tex]

The radius will be

[tex]r^2=\dfrac{20}{4}[/tex]

[tex]r^2=5[/tex]

We need to calculate the center of the point (7,2) and (9,6)

Using formula of center point

For x axis,

[tex]h=\dfrac{x_{2}+x_{1}}{2}[/tex]

Put the value into the formula

[tex]h=\dfrac{9+7}{2}[/tex]

[tex]h=\dfrac{16}{2}[/tex]

[tex]h=8[/tex]

For y axis,

[tex]k=\dfrac{y_{2}+y_{1}}{2}[/tex]

Put the value into the formula

[tex]k=\dfrac{6+2}{2}[/tex]

[tex]k=\dfrac{8}{2}[/tex]

[tex]k=4[/tex]

We need to find the equation for the circle

Using formula of equation of circle

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Put the value into the formula

[tex](x-8)^2+(y-4)^2=5[/tex]

Hence, The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]

(D) is correct option.

Answer:

B

Step-by-step explanation:

3x = 2y

One way to solve this is to simply plug in values. If we say the following:

x = 2

y = 3

Then, we can start testing.

A: [tex]x/y = 3/2[/tex]

by plugging 2 and 3 in, we see that A doesn't work.

B: x/2 = y/3

This works! First we should look at the other equations.

C: x/3 = y/2

Nope.

D: x/2 = 3/y

This also works, but only with certain numbers. If we were to make x = 4, and y = 6, this wouldn't work.

You could also find out all of this using algebra. so, our anwser is B.

Answer: hello below is the complete question

How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number

answer : 737 adults

Step-by-step explanation:

confidence interval = 90% = 0.9

( E ) = 4

standard deviation = 66

first we have to calculate the value of a

a = 1 - confidence interval

  = 1 - 0.9 = 0.10      hence  a / 2 = 0.05

next find the value of Z a/2 from table

Z[tex]_{0.05}[/tex]  = 1.645

The number of Adults selected can be determined using this relation

N = [tex](Z_{a/2} * (s/E))^2[/tex]

   = [tex](Z_{0.05} * ( 66/4))^2[/tex]

   = 737

Answer:

1023.75

Step-by-step explanation:

The sum of a geometric sequence is

sum = a( 1 - r^n) / (1-r)

where a is the first term  r is the common ratio and  r^n is the nth term

We need to find the common ratio

r = 256/512 = 1/2

sum = 512 ( 1 - 1/2^12) / ( 1-1/2)

       =512( 1-.000244141) / (.5)

       =512(.999755859) /.5

     =1023.75

Answer:

1023.75

Step-by-step explanation:

sum = a( 1 - r^n) / (1-r)

a1 = 512

n = 12

r = 256 / 512 = 1/2

                              512 (1 - 1/2¹²)

therefore.. sum =  ------------------ = 1023.75

                                   1 - 1/2

Answer:

Population Size

Step-by-step explanation:

When sampling with replacement, we can expect that the population size will remain the same. Sampling with replacement occurs when a unit or subject for research is chosen from a population at random. This chosen unit can be returned to the population and another random selection done with the possibility that a unit that was chosen before could be chosen again. So in applying this system of selection, the population size is not taken into consideration. When samples are chosen in this form, it can be referred to as a simple random sample.

So, when determining the sample size necessary for estimating the true population mean, using the sampling with replacement method, the population size is not considered.

Answer:

157

Step-by-step explanation:

135+144+116+132=527

527+136.8=762.8

762.8÷5= 157

Answer:

1284 m^2

Step-by-step explanation:

Front face and back face:

2 * [28 m * 5 m + (22 m - 5 m) * 6 m] = 484 m^2

Left face and right face:

2 * 22 m * 8 m = 352 m^2

Bottom face and top face:

2 * 28 m * 8 m = 448 m^2

total surface area = 484 m^2 + 352 m^2 + 448 m^2 = 1284 m^2

Answer:

15.5846.>

Step-by-step explanation:

Answer:

B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.

Step-by-step explanation:

The rules for linear transformations are that

 g(x) = a·f(b·(x-c)) +d

stretches the graph vertically by a factor of "a" (before the shift)

compresses the graph horizontally by a factor of "b" (before the shift)

shifts it to the right by amount "c"

shifts it up by amount "d".

Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.

The appropriate choice of description is ...

 b) the graph of g(x) is horizontally stretched by a factor of 3

Answer:

B

Step-by-step explanation:

Correct on Plato

Answer:

Hey there!

q is 1, and n=-2.

q-n=1-(-2), which is 3.

n-q=-2=1, which is -3.

q is 1.

Thus, the least value is n-q, and the greatest value is q-n. Closest to zero would be q.

Let me know if this helps :)

Answer:

Least: n-q

Greatest: q-n

Closest to zero: q

Answer: The value of (f*g)(7) is 66.

Step-by-step explanation:

Given functions: [tex]f(x)= 4x-6\text{ and } g(x)=\sqrt{x+2}[/tex]

Since, product of two functions: [tex](u*v)(x)=u(x)\times v(x)[/tex]

[tex](f*g)(x)=f(x)\times g(x)\\\\=4x-6\times \sqrt{x+2}\\\\\Rightarrow\ (f*g)(x)=(4x-6) \sqrt{x+2}[/tex]

[tex](f*g)(7)=(4(7)-6)\sqrt{7+2}\\\\=(28-6)\sqrt{9}\\\\=22\times 3=66[/tex]

Hence, the value of (f*g)(7) is 66.

Answer:

I know the answer

Step-by-step explanation:

If we use 150 the answer would be 6(150) - 200 = 700. The answer is 200.

Brooklyn Burn sold 150 bottles of hot sauce every month, 700 is the profit they make eachmonth.

Answer:

James town is 5 meters higher than Takoradi​ .

Step-by-step explanation:

Given:

Height of James town = 2 meters below sea level

Height of Takoradi town = 7 meters below sea level

To find:

How much higher is James town that Takoradi = ?

Solution:

As we can see the standard of height is how much the town is below the sea level.

So, the height of town having lesser value will be at a higher level.

Value of Height of James town is lesser than that of Takoradi town.

Therefore, James town is at a higher level.

Difference of height = 7 meters - 2 meters = 5 meters

So, the answer is:

James town is 5 meters higher than Takoradi.

Answer: 0.0215 .

Step-by-step explanation:

Let X denotes the weekly wages at a certain factory .

It is normally distributed , such that

[tex]X\sim N(\mu=400,\ \sigma= 50)[/tex]

Then, the probability that a worker  selected at random makes between

$250 and $300:

[tex]P(250<X<300)=P(\dfrac{250-400}{50}<\dfrac{x-\mu}{\sigma}<\dfrac{300-400}{50})\\\\=P(\dfrac{-150}{50}<z<\dfrac{-100}{50})\ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(-3<z<-2)\\\\=P(z<-2)-P(z<-3)\\\\=1-P(z<2)-(1-P(z<3))\\\\=P(z<3)-P(z<2)\\\\=0.9987-0.9772\\\\=0.0215[/tex]

Hence,the required probability = 0.0215 .

Answer:

x=-2/3 and 1

Step-by-step explanation:

3x^2-x-2=0

(3x+2)(x-1)

3x=-2

x=-2/3

x=1