[tex]\frac{63,756×60}{70×5,280}[/tex]

Answer:

the red car is traveling at 102.44 ft/s along the road

Step-by-step explanation:

From the given information:

Let consider p be how far the car is up the road and  q be how far the police is off the road.

Also, suppose that r is the distance between the police and the car.

Then, we can have a right triangle in which  we can use the Pythagorean Theorem to calculate the r (distance between the cop and the car)

NOW,

p² + q² = r²

r² = 40² + 180²

r² = 1600 + 32400

r² = 34000

r = [tex]\sqrt{34000}[/tex]

r = 184.39

If we consider q'  to be how fast the car is traveling down the road.

And, p' be how fast the police is traveling toward the road.

r' be how fast the distance between the police and the car is changing.

then , the derivative of our equation, p² + q² = r² with respect to time can now be:

2p(p') +2q(q') = 2r(r')

p(p') +q(q') = r(r')

By replacing our values; we have:

40(0) +180(y') = [tex]\sqrt{34000} \times 100[/tex]    (given that the police is not moving p' =0)

180(y') = [tex]\sqrt{34000} \times 100[/tex]

[tex](y') = \dfrac{\sqrt{34000} \times 100}{180}[/tex]

[tex](y') = \dfrac{184.39 \times 100}{180}[/tex]

[tex]\mathbf{(y') = 102.44 \ ft/s}[/tex]

the red car is traveling at 102.44 ft/s along the road

Answer:

There is not sufficient evidence to support a claim of linear correlation between the two variables.

Step-by-step explanation:

The data provided is as follows:

X        Y

78       5.5

79       8.8

56.2      3.3

68.3       1.7

77.9      10.8

38.2       0.1

(a)

The scatter plot is attached below.

(b)

Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.

The correlation coefficient between the number of internet users and the award winners is,

r = 0.797.

(c)

The test statistic value is:

[tex]t=r\sqrt{\frac{n-2}{1-r^{2}}}[/tex]

  [tex]=0.797\times\sqrt{\frac{6-2}{1-(0.797)^{2}}}\\\\=0.797\times 3.311372\\\\=2.639163484\\\\\approx 2.64[/tex]

The degrees of freedom is,

df = n - 2

   = 6 - 2

   = 4

Compute the p-value as follows:

[tex]p-value=P(t_{n-2}<2.64)=0.057[/tex]

*Use a t-table.

p-value = 0.057 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.

Answer:

a) 55 degrees

b) 350 ft.

Step-by-step explanation:

a- the sum of angles of triangle=180

( since it is right angle , one angle is 90 degrees), x be the acute angle

x+35+90=180

x=180-125

x=55 degrees

b) tan 35= height of a tree/ length of a shadow

height of a tree=tan35*500=350.103≅350 ft ( rounded to nearest tens)

c)  hypotenuse²=350.1²+500²

c=√350.1²+500²

c=610.385 ft

d) no because the distance is more than 500

Answer:

B. Multiply each term in x - 12y = 2 by 4 and add it to the other original equation.

Step-by-step explanation:

The expression are two linear equation and can be solved simultaneously

[tex]x - 12y = 2------------------1[/tex]

[tex]-4x + 7y = 12----------------------2[/tex]

1. we need to multiply each term in eqn 1 by 4 and add it to the other

original equation(2).

[tex]4x - 48y = 8----------------3\\-4x + 7y = 12---------------2\\\\[/tex]

Adding both 3 and 2 we have

[tex]4x - 48y = 8----------------3\\-4x + 7y = 12---------------2\\\\\\[/tex]

2. once we have gotten the value of y

we then substitute it in any of the equations to solve for x

Answer:

Step-by-step explanation:

To find the length of a we use the cosine rule

That's

a² = b² + c² - 2bc cos A

We have

a² = AB ² + AC ² - 2(AB)(AC) cos A

From the question

AB = 6

AC = 5

A = 20°

Substituting the values into the above formula we have

a² = 6² + 5² - 2(6)(5) cos 20

a² = 36 + 25 - 60cos 20

a² = 61 - 56.38

a² = 4.62

Find square root of both sides

a = √4.62

We have the final answer as

Hope this helps you

To build the fleet of ships, Astrid must consider each of the given rates (i.e.  the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.

Given that:

Required quantities

[tex]Wood = 40\ tons[/tex]

[tex]Sailors = 300[/tex] per ship

Available quantities

[tex]Wood = 4\ tons[/tex] daily

[tex]Days = 100[/tex] at most

First, we calculate the total tons of woods Astrid can receive.

[tex]Total = Days \times Wood\ Available[/tex]

[tex]Total = 100 \times 4[/tex]

[tex]Total = 400\ tons[/tex] ---- in 100 days

Next, we calculate the number of ships that can be made from the 400 tons.

[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]

So, we have:

[tex]Ships = \frac{400}{40}[/tex]

[tex]Ships = 10[/tex]

This means that Astrid can build up to 10 ships

The number of sailors the ship can accommodate is:

[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]

So, we have:

[tex]Sailors = 10 \times 300[/tex]

[tex]Sailors = 3000[/tex]

It means the 10 ships can accommodate 3000 sailors.

3000 sailors is greater than 2100 sailors.

So, we can conclude that she can build enough ship for the 2100 sailors.

Read more about

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Answer:

280 tons

Step-by-step explanation:

:)

Answer:

[tex] 23x - 10 [/tex]

Step-by-step explanation:

To the find the equivalent of [tex] 9(2x - 3) + 5x + 17 [/tex], evaluate the expression. Start by opening the bracket.

[tex] 9*2x - 9*3 + 5x + 17 [/tex]

[tex] 18x - 27 + 5x + 17 [/tex]

Pair like terms

[tex] 18x + 5x - 27 + 17 [/tex]

[tex] 23x - 10 [/tex]

The equivalent of [tex] 9(2x - 3) + 5x + 17 [/tex] is [tex] 23x - 10 [/tex]

Answer:

y = 17.5

Step-by-step explanation:

y = kx

→ Substitute in the values

5 = 2k

→ Divide both sides by 2 to isolate k

k = 2.5

⇒ y = 2.5x

→ Substitute in x = 7

y = 2.5x ⇔ y = 2.5 × 7 ⇔ y = 17.5

Answer:

  6

Step-by-step explanation:

The angle bisector divides the other segments proportionally. There are many ways the proportion can be written. One is ...

  XN/NY = XA/AY

  XN = NY×XA/AY = 4 × 18/12

  XN = 6

   Value of [tex]10^x[/tex] will be between 1 and 10.

 Given in the question,

If we have to find the range of the value of the number, substitute x = 0 and 1

[tex]10^0=1[/tex]

[tex]10^1=10[/tex]

  Therefore, value of [tex]10^x[/tex] will vary between 1 and 10.

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Answer:

11.21157846 =x

Step-by-step explanation:

We know log b (a) = c  can be written as b^c =a

log 3 (x) = 2.2

3^2.2 = x

11.21157846 =x

Answer:

[tex]\large \boxed{\sf \bold{A.} \ x=11.21}[/tex]

Step-by-step explanation:

[tex]\large \sf log_3 (x)=2.2[/tex]

Solve this by converting the logarithmic statement into its equivalent exponential form, using the relationship:

[tex]\large \sf log_b(y)=x[/tex]

[tex]\large{\sf y=b^x}[/tex]

Apply the relationship.

[tex]\large \sf log_3 (x)=2.2[/tex]

[tex]\large \sf x=3^{2.2}[/tex]

[tex]\large \sf x=11.21157845...[/tex]

[tex]\large \sf x \approx 11.21[/tex]

Answer:

The function is y = -6 / x.

Step-by-step explanation:

Since (-2, 3) belongs to the function, we know that x = -2, y = 3 is a solution to the function so when we plug those values in to solve for a, we get:

3 = a / (-2)

3 * (-2) = a / (-2) * (-2)

-6 = a so the function is y = -6 / x.

Answer:

C. 96 pi

Step-by-step explanation:

Formula for volume of cone = 1/3 * h * pi * r^2

1. 1/3 * 18 * 4^2 * pi

2. 96 pi

I hope this helps

Answer:

C. 96π cubic units

Step-by-step explanation:

The volume of a cone can be found using the following formula.

[tex]V=\frac{1}{3} \pi r^2h[/tex]

The radius of the cone is 4 units and the height is 18 units.

r= 4 units

h=18 units

Substitute the values into the formula.

[tex]V=\frac{1}{3} \pi (4units)^2(18 units)[/tex]

First, evaluate the exponent, 4 units^2.

4 units^2= 4 units * 4 units= 16 units^2

[tex]V=\frac{1}{3}\pi(16 units^2)(18 units)[/tex]

Next, multiply 16 units^2 and 18 units

16 units^2*18 units= 288 units^3

[tex]V=\frac{1}{3}\pi(288 units^3)[/tex]

Next, multiply 1/3 and 288 units^3, or divide 288 units^3 by 3.

1/3 * 288 units^3 =96 units^2

288 units^3/3=96 units^3

[tex]V=\pi*96units^3[/tex]

This can be rewritten as:

[tex]V= 96\pi units^3[/tex]

The volume of the cone is 96π cubic units. Therefore, C is the correct answer choice.

Answer:

(x - 1)² + (y + 4)² = 81

Step-by-step explanation:

Circle Formula: (x - h)² + (y - k)² = r²

(h, k) is the center

2r = d

Step 1: Find r

18 = 2r

r = 9

Step 2: Plug known variables into formula

(x - 1)² + (y + 4)² = 9²

Step 3: Evaluate

(x - 1)² + (y + 4)² = 81

Answer:

(x-1)^2 + (y+4)^2 = 81

Step-by-step explanation:

The equation of a circle can be written as

(x-h)^2 + (y-k)^2 = r^2

where ( h,k) is the center and r is the radius

The center is ( 1,-4)

and the radius is d/2 = 18/2 = 9

(x-1)^2 + (y- -4)^2 = 9^2

(x-1)^2 + (y+4)^2 = 81

Answer:

1 and 11/15.

Step-by-step explanation:

To solve, we can separate the integers from the fractions.

(6 - 4) + (2/5 - 2/3)

= 2 + (6/15 - 10/15)

= 2 + (-4/15)

= 1 + 15/15 - 4/15

= 1 + 11/15

= 1 and 11/15

Hope this helps!

Answer:

y=mx+b

y = dependent variable

x = independent variable

m = the slope of the line

b = the y-intercept

This is why they call itI "slope-intercept" because it gives you the SLOPE(m) and the Y-INTERCEPT (b)

Step-by-step explanation:

Answer:

The variable m represents the slope

Step-by-step explanation:

Hey there!

Well slope intercept is,

y = mx + b

The m stands for slope,

b stands for y-intercept

x stands for independent variable

y stands for the dependent variable

Hope this helps :)

Answer:

120c

Step-by-step explanation:

7c(-5c)*(-4+6)

7c+5c*4+6

12c*10

120c

Answer:

the answer can be step by step explanation will be found in the answer was Matilda by 776 7 x 6 then the answer you will you - with the answer dancer used you New divide the answer that answer the simple your answer if we multiply you can contact me and say me in which is correct or wrong and I am a teacher

Answer:

5%

Step-by-step explanation:

Total 'halwa' made = 1

Divided into four equal portion = 1/4

Arrival of an unexpected guest = 1/5

By what percentage has each family member's share been reduced:

Change in the sharing proportion:

Previous share ratio - new sharing ratio

(1/4 - 1/5) = (5 - 4) / 20 = 1/20

That means total reduction in the sharing = 1/ 20

Since each member comes contributed equally:

Reduction in each family member's share ;

(1 / 20) ÷ 4

(1 / 20) * 1/4 = 1/ 80

Percentage reduction:

(Reduction / original share) * 100%

[(1/80) ÷ (1/4)] * 100

(1/80 * 4/1) * 100%

(1/20) * 100%

= 5%

Reduction in each family members share = 5%

Step-by-step explanation:

There are answers to this problem based on how we interpret this question.

If the question is x^2 + x =2

=> x = 1

Since, 1^2 + 1 = 2.

Another way to interpret this question is 2x+ x = 2

=> 3x = 2

=> x= 2/3

The answer differs based on how we interpret this question.

Hope this helps you.

Answer:

-2

Step-by-step explanation:

The EASIEST way to do this is using the laws of the sum and products of roots.

When you multiply two roots together, you simply get c/a

So, let's start:

x^2 + x = 2

subtract the 2 to get a quadratic equation equal to 0

x^2 + x -2 =0

Now,

a=1

b=1

c=-2

plug b and a into c/a

-(2/1)= -(2)   =   -2

The answer is -2.

It's NOT 1. the answer would be 1 IF it was adding the roots.

Answer:

Hey there!

11 meters is about 36 feet tall.

Let me know if this helps :)

Answer:

you answer is :33.8328

Answer:

2' 3"

Step-by-step explanation:

Here 4' 1" − 1' 10" is certainly possible, but to carry out this operation we must borrow 1', or 12", from 4' 1":

4' 1" becomes 3' 13", and so the original problem becomes

3' 13" - 1' 10"

which in turn becomes 2' 3"

Answer:

[tex]\boxed{4 units}[/tex]

Step-by-step explanation:

Hey there!

Well if the base is 4 and we use the formula,

b*h / 2

4*4 = 16

16/2 = 8

So x is 4.

Hope this helps :)

Answer:

Step-by-step explanation:

Area of a triangle is given by

base × height

[tex] A = \frac{1}{2} base × height[/tex]

From the question

Area = 4 units²

height = 4 units

let x represent the base

We have

[tex]4 = \frac{1}{2} \times x \times 4[/tex]

4 = 2x

Divide both sides by 2

Hope this helps you

Answer:

D) 972

Step-by-step explanation:

2160*9/20 = 19440/20

= 972

Answer:

7.125*10⁻⁹ = 0.000000007125

Step-by-step explanation:

7.125*10⁻⁹ = 0.000000007125

Answer:

B

Step-by-step explanation:

area of the full piece of pie. π(8)²*60/360 (we know 60°, because it's an equilateral triangle)

32π/3

now subtract the area of the triangle

1/2(8)(4√3) = 16√3

32π/3 - 16√3

Answer: P≈2.4×10 power5

Step-by-step Explanation: P=4a=4·60025=2.401×10 power5

Answer:

[tex]\huge \boxed{\mathrm{980 \ m}}[/tex]

Step-by-step explanation:

The formula for the area of a square is:

[tex]A=s^2[/tex]

The area is given as 60025 m².

We need to find the length of each side.

[tex]60025=s^2[/tex]

Take the square root of both sides.

[tex]s=245[/tex]

The side length is 245 m.

The formula for the perimeter of a square is:

[tex]P=4s[/tex]

Plug in the value for the side length.

[tex]P=4(245)[/tex]

[tex]P=980[/tex]

The perimeter of the field is 980 m.

Answer:

The third one

Step-by-step explanation:

Translation is when it moves

Answer:

r = 0.5 or 1/2

Step-by-step explanation:

Simple Interest Rate Formula: A = P(1 + r)^t

Simply plug in our known variables:

2700 = 800(1 + r)³

Now we solve for r:

Divide both sides by 800

27/8 = (1 + r)³

Take the cube root on both sides

∛27/8 = ∛(1 + r)³

Simplify

3/2 = 1 + r

Subtract 1 on both sides

r = 1/2

r = 0.5

Answer:

For compound interest, 50%.

Step-by-step explanation:

(I'm assuming this question is asking for the compound interest):

The formula for compound interest is given by:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Plug in the values we know. We can use 1 for n:

[tex]2700=800(1+r)^3\\27/8=(1+r)^3\\1+r=\sqrt[3]{27/8}\\r=3/2-1\\r=1/2=.5[/tex]

So, the interest rate is 50%.

Step-by-step explanation:

That is $250-$50=$200

why because he plans to

save $50 per month and

he already has$250to begin

so that explains what i did