Two straight roads meet at right angles at an intersection. A car is traveling due
south towards the intersection at a constant speed of 60 miles per hour. A second
car is traveling due west towards the same intersection at a constant speed of 70
miles per hour. How fast is the distance between the cars changing at the instant
when the southbound car is 30 miles from the intersection and the westbound car
is 40 miles from the intersection?

Answer:

33.3 % of the dodgeball team consist of boys.

Step-by-step explanation:

Hope that helps!

Answer:

Then he should have 524,296 books left

Answer:

True

Step-by-step explanation:

Because -5 x -5 = -25

Answer:D

Step-by-step explanation: answer D. 1/4x-1

slope = 1/4 so the coefficent (number attatched to x) is going to be 1/4

y=-1 when x=0

A. =-1/4

B= -1 but the coefficent is not 1/4

C=1

D=-1

D is the correct answer

Answer:

-7

Step-by-step explanation:

-9 - (-2)

If there is a negative sign in front of a negative number in parenthesis, then that makes it a positive number.

-9 + 2 = -7

Given parameters:

Bearing of the tree from the house  = 295°

Unknown:

Bearing of the house from the tree = ?

Solution:

This is whole circle bearing problem(wcb). There are different ways of representing directions from one place to another. In whole circle bearing, the value of the bearing varies from 0° to 360° in the clockwise direction.

To find the back bearing in this regard, simple deduct the forward bearing from 360°;

    Backward bearing  = 360° -295°

                                    = 65°

The bearing from house to the tree is 65°

Using the z-distribution, as we are working with a proportion, it is found that samples of 937 should be taken.

A confidence interval of proportions is given by:

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

In which:

The margin of error is given by:

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

In this problem, we have that:

Then, we solve for n to find the minimum sample size.

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

[tex]0.03 = 1.96\sqrt{\frac{0.675(0.325)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.675(0.325)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.675(0.325)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.675(0.325)}}{0.03}\right)^2[/tex]

[tex]n = 936.4[/tex]

Rounding up, it is found that samples of 937 should be taken.

More can be learned about the z-distribution at https://brainly.com/question/25890103

Answer:

8 cookies

Step-by-step explanation:

64*1.25 = 80 to find how much cookies noah made

if 90%(0.9) were sold, we will find 80(0.1) to find whats left, which is 8

Work Shown:

C = 2*pi*r

6.28 = 2*3.14*r

6.28 = 6.28r

6.28r = 6.28

r = (6.28)/(6.28)

r = 1

The radius of the circle is 1 yard.

A = pi*r^2

A = 3.14*1^2

A = 3.14

The area is roughly 3.14 square yards.

The area of the trampoline  is mathematically given as

a = 3.14

Question Parameters:

You found one online that has a circumference of 6.28 yards

Generally, the equation for the Circumference   is mathematically given as

C = 2*pi*r

Thererfore

6.28 = 2*3.14*r

r = (6.28)/(6.28)

r = 1

In conclusion, where radius is

[tex]a= pi*r^2[/tex]

a = 3.14*1^2

a = 3.14

Read more about  Arithmetic

https://brainly.com/question/22568180

Answer:

Step-by-step explanation:

let the amount spent on popcorn be x and amount spent on drinks be y

If the total bill paid is  $17.94, then x+y =  $17.94

If she spend twice as much on popcorn as on drinks, then y = 2x

Substitute y = 2x into the original equation

x+y =  $17.94

x + 2x =  $17.94

3x =  $17.94

x =  $17.94/3

x = $5.98

Since y = 2x

y = 2($5.98)

y = $11.96

Therefore she spent  $5.98 on popcorn and $11.96 on drinks

9514 1404 393

Answer:

  {1, 5, 7}

Step-by-step explanation:

For x=0, y = 2·0 +1 = 1

For x=2, y = 2·2 +1 = 5

For x=3, y = 2·3 +1 = 7

The range is the list of y-values, so is {1, 5, 7}.

Answer:

wheres the graph.

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

On edg

Answer:

1.63

Step-by-step explanation:

-31 + 7 = -24

[tex]\sqrt{-24}[/tex]  = 4.9

4.9/3 = 1.63 (rounded down from 1.6333333)

Answer:

[tex]x = 2 \sqrt{2} i \: or \: x = - 2 \sqrt{2} i[/tex]

Step-by-step explanation:

• Add 7 to both sides.

[tex]3x {}^{2} - 7 + 7 = - 31 + 7[/tex]

• Simplify

[tex]3x {}^{2} = - 24[/tex]

• Divide both sides by 3

[tex] \frac{3x {}^{2} }{3} = \frac{ - 24}{3} [/tex]

• Simplify

[tex]x {}^{2} = - 8[/tex]

• Find the solution

[tex]x = \sqrt{ - 8} \: and \: x = - \sqrt{ - 8} [/tex]

• Simplify

[tex] \sqrt{ - 8} = 2 \sqrt{2i} [/tex]

[tex] - \sqrt{ - 8} = - 2 \sqrt{2i} [/tex]

ANSWER:

[tex]x = 2 \sqrt{2} i \: and \: x = - 2 \sqrt{2} i[/tex]

Answer:

[tex]\sqrt{6} -3\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{150} -\sqrt{96} -\sqrt{162} +\sqrt{72}[/tex]

[tex]=\sqrt{25\cdot6} -\sqrt{16\cdot6} -\sqrt{81\cdot2} +\sqrt{36\cdot2}[/tex]

[tex]=\sqrt{25}\sqrt{6} -\sqrt{16}\sqrt{6} -\sqrt{81}\sqrt{2} +\sqrt{36}\sqrt{2}[/tex]

[tex]=5\sqrt{6} -4\sqrt{6} -9\sqrt{2} +6\sqrt{2}[/tex]

[tex]=\sqrt{6} -3\sqrt{2}[/tex]

Answer:

See below.

Step-by-step explanation:

a) √2 + √50 + √98

= √2 + 5√2 + 7√2

= 13√2

c) 5√7 + 2√5 - 3√28

= 5√7 + 2√5 - 6√7

= 2√5 - √7

e) √150 - √96 - √162 + √72

= 5√6 - 4√6 - 9√2 + 6√2

= √6 - 3√2

g) 7√3 - 2√8 + √12 + 3√8

= 7√3 - 4√2 + 2√3 + 6√2

= 9√3 + 2√2

i) 3√49 + 2√288 - √144 - 2√18

= 21 + 24√2 - 12 - 6√2

= 9 + 18√2

= 9(1+ √2)

Answer:

185

Step-by-step explanation:

Total area is 27 x 10= 270

unshaded are is 17x5= 85

270 - 85 = 185 (total shade area)

Answer: its A

Step-by-step explanation:

Answer:

Check your mathematics Text book...Then you can see heading True conditional statement..Check the example question then i am sure you will get the correct answer...

Answer: 2.44 miles.

Step-by-step explanation:Answer:

2.44 miles

Step-by-step explanation:

Give the following :

Average miles to school = 12 miles per hour

Average Miles from school = 15 miles per hour

Total ride time : ( time to school + time from school) = 22 minutes = (22/60) = 0.3667

Recall:

Speed = distance / Time

Time = distance / speed

Let distance = d

For the scenario described :

d/12 + d/15 = 0.3667

(5d + 4d) / 60 = 0.3667

5d + 4d = 22

9d = 22

d = 22/9

d = 2.44 miles

Answer:

3x^2-12x-63, 7x^2-28x-147

Step-by-step explanation:

I think this problem has two answers.

3(x+3)(x-7), 7(x+3)(x-7)

Answer: D) The linear model shows a strong fit to the data

The actual strength of the relationship is unknown unless we have the actual values of each data point (so we can compute the correlation coefficient r), but the residuals are randomly scattered about both above and below the horizontal axis. This means we have a fairly good linear fit. If all of the points were above the line, or all below the line, or all residuals fit a certain pattern (eg: parabola), then it wouldn't be a good linear fit.

Answer:

The volume of a prism is given by ...

 V = Bh

Step-by-step explanation:

Here, the base is an equilateral triangle with side length 3 in. The area of such a triangle is given by

 A = (√3)4*s²

where s is the side length.

Your triangular prism has a base area of ...

 B = (√3)/4*(3 in)² = (9/4)√3 in²

so the volume is

 V = ((9/4)√3 in²)(6 in)

 V = (27/2)√3 in³

 V ≈ 23.383 in³

:)

Answer:

61.54

Step-by-step explanation:

The decimal is .36 + .18 which is .54 and 17 + 44 is 61 so 61 + .54 is 61.54

Answer:

$24

Step-by-step explanation:

1. MULTIPLY: 3 x 56 = 168

2. DIVIDE: 168 / 7 = $24

I hope this helps!

Based on multiplication we have found that 3/7 of $56 is equal to $24.

We are given that the expression 3/7 of $56

To determine 3/7 of $56, we can multiply 3/7 by $56.

Multiply 3/7 by $56:

(3/7) x $56 = (3 x $56) / 7

Calculate the numerator:

3 x $56 = $168

Divide the numerator by the denominator:

$168 / 7 = $24

Therefore, 3/7 of $56 is equal to $24.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ6

Answer:

slope

Step-by-step explanation:

Answer:

Step-by-step explanation:

use the formula: y = mx + b

where:

y = how far up the line goes

m = slope or gradient

x = how far along

b = Y-intercept

Answer:

61

Step-by-step explanation:

Complementary angles have sum 90°

[tex]\\ \rm\Rrightarrow 5x+7x-6=90[/tex]

[tex]\\ \rm\Rrightarrow 12x-6=90[/tex]

[tex]\\ \rm\Rrightarrow 12x=96[/tex]

[tex]\\ \rm\Rrightarrow x=8[/tex]

Answer:

x = 8

Step-by-step explanation:

Complementary angles are two angles with measures that sum to 90°

Given:

⇒ m∠C + m∠D = 90°

⇒ 5x + 7x - 6 = 90

⇒ 12x - 6 = 90

⇒ 12x = 96

⇒ x = 8

Answer:

6

Step-by-step explanation:

I hope this helps!

Answer:

92%

Step-by-step explanation:

368+32=40

368*100=36800 36800/400=92

Answer:

40

Step-by-step explanation:

The value of a right angle is 90° and <SQR is a fraction of <PQR.

Hence,  <PQS, which is the other fraction of <PQR, equals 90-50 and 90-50 is 40.

Or we can do it like this;

⇒ 180-90-50

⇒ 90 - 50

⇒ 40

Thus, Answer is 40.

[RevyBreeze]

Answer:

  3.9

Step-by-step explanation:

The right triangle is marked with the sides adjacent and opposite the angle. That suggests the relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(52°) = 5/x

  x = 5/tan(52°) ≈ 3.9