What is the product?

Answer:

The car was moving approximately at a speed of 37.74 miles per hour.

Step-by-step explanation:

We are given the following in the question:

The stopping distance of a car is given by

[tex]d = 0.05r(r + 2)[/tex]

where d is the stopping distance in feet and r is speed of the car in miles per hour.

The stopping distance is 75 feet, we have to find the speed of the car,

Putting d = 75 in the equation, we get,

[tex]75 = 0.05r(r + 2)\\r^2 + 2r = 1500\\r^2 + 2r-1500 = 0\\\\r =\dfrac{-2\pm \sqrt{4-(4)(1)(-1500)}}{2}\\\\r\approx -39.74,37.74[/tex]

Thus, the car was moving approximately at a speed of 37.74 miles per hour.

Find the volume of the candle using the formula for volume of a cylinder:

V = PI x r^2 x h = 3.14 x 3.4^2 x 6 = 217.79 cubic cm. Round to 217.8

Find the volume of the block: V = l x w x h = 15 x 12 x 18 = 3,240 cubic cm.

Now divide the volume of the block by the volume of a candle:

3240 / 217.8 = 14.88

Round to the nearest tenth = 14.9 candles.

Number of cylindrical candles after melting the rectangular block  is 14.9.

" Cylinder is a three dimensional surface formed by two parallel lines and two parallel circular base."

" Volume is the total amount of space occupied by any 3 dimensional body."

Formula used

Volume of a cylinder = π r²h

Volume of a rectangular block = length × width ×height

According to the question,

Height of a cylinder = 6cm

radius of cylinder = 3.4cm

Length of a block = 15cm

width of a block = 12cm

height of a block = 18cm

Volume of a cylinder = [tex]3.14[/tex]× [tex](3.4)^{2}[/tex]×[tex]6[/tex]

                                  =217.8 cubic cm

Volume of rectangular block = [tex]15[/tex] × [tex]12[/tex] × [tex]18[/tex]

                                                 = 3240 cubic cm

Number of candles = Volume of rectangular block / volume of cylinder

                                 = [tex]\frac{3240}{217.8}[/tex]

                                 = 14.88

                                 = 14.9 (nearest tenth)

Hence the Number of cylindrical candles after melting the rectangular block  is 14.9.

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Answer:

Step-by-step explanation:

the second option

Answer:

1/2 bh

Step-by-step explanation:

Multiply the base by the height then multiply by 1/2, or divide by 2

Answer:

A=hbb

2            

Step-by-step explanation:

Answer:

4x+1

Step-by-step explanation:

Please see attached image.

Answer:

n=7/3

Step-by-step explanation:

1 (n – 4) – 3 = 3 - (2n+3)

1. distribute the 1 on the left side and distribute the -1 on the right side

1n-4-3=3-2n-3

2. add like terms

1n-7=-2n

3. move n to one side and by itself

-7=-3n

4. divide -3 to get n alone. Both negatives cancel out each other

7/3=n

Step-by-step explanation:

[tex]1(n-4)-3=3-(2n+3)[/tex]

[tex]n-4-3=3-2n-3\\n+2n=3-3+3+4\\3n=7\\n=\frac{7}{3}[/tex]

Proof

[tex]1(n-4)-3=3-(2n+3)[/tex]

[tex]1(\frac{7}{3} -4)-3=3-[2(\frac{7}{3}) +3]\\1(\frac{7-12}{3} )-3=3-(\frac{14}{3} +3)\\1(\frac{-5}{3} )-3=3-(\frac{14+9}{3})\\\frac{-5}{3} -3=3-(\frac{23}{3})[/tex]

[tex]\frac{-5-9}{3} =\frac{9-23}{3} \\\frac{-14}{3} =\frac{-14}{3}[/tex]

Answer: you would expect it to flip about 150 times heads.

Step-by-step explanation: A coin has two sides. There's an equal chance for each side. So 50-50 chance.

300 divided by 2 is 150

(Sorry if it's not the best mathematical way to say it)

Answer:

90°

Step-by-step explanation:

By inscribed angle theorem:

[tex]m\angle STU = \frac{1}{2} \times 180 \degree = 90 \degree[/tex]

Step-by-step explanation:

40° + 90° + 90° + angle ACB = 360°

220° + angle ACB = 360°

angle ACB = 360° - 220°

Therefore angle ACB = 140°

Hope it will help :)

Final answer:

To find angle ACB, determine angle AOB by subtracting the tangents' right angles and angle APB from 360 degrees, which results in 140 degrees. Then, using the Inscribed Angle Theorem, angle ACB is half the measure of angle AOB, yielding 70 degrees.

Explanation:

The student is asking how to find the angle ACB when given that PA and PB are tangents to a circle with centre O, and angle APB is 40 degrees. To find angle ACB, which is the angle at the circle subtended by the chord AB, we first determine the measure of angle AOB, which is central and subtended by AB as well. Since the tangents from a point outside a circle form a right angle with the radius at the point of contact, we have two right triangles OAP and OBP, each with an angle of 90 degrees. These right angles add to the given angle APB to form a full angle around point P which is 360 degrees. Knowing angle APB is 40 degrees, we can find angle AOB by subtracting the sum of the two right angles and angle APB from 360 degrees.

Angle AOB = 360 degrees - (90 degrees + 90 degrees + 40 degrees) = 360 degrees - 220 degrees = 140 degrees

Finally, since angle ACB is inscribed and angle AOB is central, both subtended by the same chord AB, angle ACB is half the measure of angle AOB by the Inscribed Angle Theorem. Therefore, angle ACB is 70 degrees.

Angle ACB = ½ * Angle AOB = ½ * 140 degrees = 70 degrees

Answer:

20

Step-by-step explanation:

Because it is a square table, that means all the sides are even. And to find the area, we do Height * Base. But again, because they're even, we would just need to find 2 numbers that multiply to be 400. And that number, is 20. 20 * 20 = 400. So the length of one side is 20.

Answer:

2

Step-by-step explanation:

There are 120 different ways to assign 6 weapons to 3 soldiers, each receiving one weapon, calculated using permutations.

Calculating Permutations for Weapons Assignment

To determine how many different ways 3 soldiers can be assigned weapons from a selection of 6, we need to calculate the permutations of 6 objects taken 3 at a time. We use the permutation formula, which is expressed as P(n, k) = n! / (n-k)!, where n is the total number of items, and k is the number of items to choose. In this case, n is 6 (the total number of weapons), and k is 3 (the total number of soldiers).

We calculate the permutations as follows:

6! / (6-3)! = (6  * 5 * 4) / (3 * 2 * 1) = 120 ways.

Therefore, there are 120 different ways to assign the weapons to the soldiers, with each soldier getting one weapon.

Answer:

[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]

[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]

[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]

Step-by-step explanation:

The point is in the 3rd Quadrant of the Cartesian Plane. Therefore, angle must be between 180° and 270° with respect to the horizontal.

The angle is:

[tex]\theta = 180^{\textdegree}+\tan^{-1}\left(\frac{24}{7} \right)[/tex]

[tex]\theta \approx 253.740^{\textdegree}[/tex]

The values of the trigonometrical functions are computed below:

[tex]\sin 253.740^{\textdegree} = -\frac{24}{25} = -0.960[/tex]

[tex]\cos 253.740^{\textdegree} = -\frac{7}{25} = -0.280[/tex]

[tex]\tan 253.340^{\textdegree} = \frac{24}{7} = 3.429[/tex]

Answer:

The speed of 65 ​mph is an outlier in the distribution of the​ player's serve​ speeds

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100 mph

Standard Deviation, σ = 10 mph

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

Outlier on basis of z-score:

Calculation of z-score:

[tex]x = 65\Rightarrow z = \dfrac{65-100}{10} = -3.5\\\\x = 110\Rightarrow z = \dfrac{110-100}{10} = 1\\\\x = 120\Rightarrow z = \dfrac{120-100}{10} = 2[/tex]

Thus, the speed of 65 ​mph is an outlier in the distribution of the​ player's serve​ speeds as the corresponding z-score is less than -3.

Graph the integer 6 and its opposite

Plot -6 and 6 <- the opposite of 6 is -6

Graph the integer 0 and its opposite on the number line

0 and 0 <- The opposite of 0 is itself as it has no negative value

Step-by-step explanation:

Graph the integers between 2 and 6 on a number line

5 + 3 + 2 = 10 total marbles.

Steve picking a yellow one would be 3/10 (3 yellow / 10 total)

The marble is put back, so there will still be 7 marbles in the bag.

Sam picking a yellow one would then be the same as Steve: 3/10

The probability of them both picking yellow would be 3/10 x 3/10 = 9/100

Answer:

0.09

Step-by-step explanation:

Total: 5+3+2 = 10

3/10 × 3/10

9/100

0.09

Answer:

1) (a/3) - (b/2)

2) (m/3) + (5n/12)

3) (-5m/3) + (4x/3)

4) (4x/9) + (8y/9) - (z/3)

5) (-5a/8) + (-3b/8) + (-3c/2)

Step-by-step explanation:

1) 2a-3b divided by 6

(2a-3b)/6 = (2a/6) - (3b)/6 = (a/3) - (b/2)

2) 4m+5n divided by 12

(4m+5n)/12 = (4m/12) + (5n/12) = (m/3) + (5n/12)

3) 5m-4x divided by -3

(5m-4x)/(-3) = (-5m/3) + (4x/3)

4) 4x+8y-3z divided by 9

(4x+8y-3z)/9 = (4x/9) + (8y/9) - (3z/9) = (4x/9) + (8y/9) - (z/3)

5) 5a+3b+12c divided by -8

(5a+3b+12c)/(-8) = (-5a/8) + (-3b/8) + (-12c/8) = (-5a/8) + (-3b/8) + (-3c/2)

Answer:

See below.

Step-by-step explanation:

The 3 angles in a triangle add up to 180 degrees, so the sum of the other 2 angles is 180 - 35 = 145 degrees.

So, for example the other 2 angles could be 60 and 85 degrees.

Answer:

75° and 70°

25° and 120°

90° and 55°

Step-by-step explanation:

I got it right

Answer:

x =(-4-√96)/10=(-2-2√ 6 )/5= -1.380

x =(-4+√96)/10=(-2+2√ 6 )/5= 0.580

Step-by-step explanation:

Answer: cccccccccccccc

Step-by-step explanation: <3

Answer:

rate of motorboat: b

rate of current: c

So the rate the boat travels upstream is $b - c$, and the rate it travels downstream is $b + c$

Step-by-step explanation:

d = rt

200 = (b - c)\cdot 5

200 = (b + c)\cdot 4

b - c = 40

b + c = 50

Adding these equations, we get:

2b = 90

b = 45

So

c = 50 - 45 = 5

Therefore the rate of the boat is 45kph, and the rate of the current is 5kph

Hope this helps :)

Final answer:

The boat has a speed of 45 mph in still water, and the current runs at 5 mph. By using the given times and distances for upstream and downstream travel, we can set up equations to solve for the boat's speed and the current's speed.

Explanation:

To find the rate of the boat in still water and the rate of the current, let's denote the boat's speed in still water as b and the speed of the current as c. When the boat goes upstream, its effective speed is b - c, and when it goes downstream, its effective speed is b + c. We can translate this into two equations based on the information given:

(b - c) × 5 hours = 200 miles (upstream)

(b + c) × 4 hours = 200 miles (downstream)

By dividing the distance by the time, we can solve for the effective speeds upstream and downstream.

b - c = 200 miles / 5 hours = 40 mph

b + c = 200 miles / 4 hours = 50 mph

Add these two equations:

2b = 90 mph

b = 45 mph (boat's speed in still water)

Next, subtract the first equation from the second:

2c = 10 mph

c = 5 mph (current's speed)

So, the boat has a speed of 45 mph in still water, and the current has a speed of 5 mph.

Answer:

-18

Step-by-step explanation:

b is where the line crosses the y-axis, or where x=0. Since it starts at -18, then that would be the b.

Answer:

1/6

Step-by-step explanation:

[tex]\frac{5}{4} x\frac{2}{15}[/tex] multiply the top number and the bottom to get [tex]\frac{10}{60} = \frac{1}{6}[/tex]

Answer:

5 apples

Step-by-step explanation:

brainliest?

5 Apples Are Left

Simply subtract the initial total and the apples given away.

10 - 5 = 5 left

Answer:

a = 13

Step-by-step explanation:

The three angles of any triangle MUST add up to 180°.  Thus, 3a + 8a + 37 = 180, and 11a = 180 - 37 = 143.

If 11a = 143, then a = 143/11 = 13

a = 13

Answer:

a = 13

Step-by-step explanation:

8a + 3a + 37° = 180°

11a + 37° = 180°

11a = 180° - 37°

11a = 143°

a = 143/11

a = 13

Answer:

15 m

Step-by-step explanation:

25² = 20² + b²

625 = 400 + b²

b² = 225

b = 15

it is 15 hope this helped and good luck...

Answer:

Hawkins's Store = 60 ounces for 6.50

Don's Store = 54 ounces for 5.50

Allen's Market = 48 ounces for 5.61

Value Market = 40 ounces for 4.50

6.50/60=.10833333

5.50/54=.10185       smallest decimal

5.61/48 = .116875

4.50/40=.1125

Step-by-step explanation:

the answer is Don's Store

hope this helps(:

The store Don's has the lowest price per ounce is $0.10.

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

Here,

In Hawkin's Store:

The cost of 1 ounce is 6.50/60

= $0.11

In Don's Store:

The cost of 1 ounce is 5.50/54

= $0.10

In Allen's Market

The cost of 1 ounce is 5.61/48

= $0.12

In Value Market:

The cost of 1 ounce is 4.50/40

= $0.1125

Therefore, the store Don's has the lowest price per ounce is $0.10.

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To find the speed of the truck, start by assigning the speed of the train as 'x', then the truck's speed is 'x + 20'. Set up an equation based on the principle of time = distance/speed, make them equal to each other then solve for 'x'. The truck's speed will be 'x + 20'.

Let's call the speed of the freight train 'x' (in mph). We know from the question, that the loaded truck is traveling 20 mph faster than the train, so the truck's speed is 'x + 20' mph.

Given that the time it takes for the train to travel 160 miles is the same time it takes the truck to travel 240 miles, we can write an equation based on the principle that time equals distance divided by speed.

For the train, time = 160/x and for the truck, time = 240/(x+20). As both times are equal, we can write the equation as:

160/x = 240/(x + 20).

Solving this equation for 'x' will give us the speed of the freight train in mph. Then, by adding 20 to 'x', we can find the speed of the truck.

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Answer: [tex]5.05[/tex]

Flip

Keep: 1.8

Change: - into +

Change: -3.25 into 3.25

Your new problem

[tex]1.8+3.25[/tex]

Add

[tex]1.8+3.25=5.05[/tex]

The expression 1.8 minus negative 3.25 simplifies to 1.8 plus 3.25, which equals 5.05.

The question asks you to calculate the result of the expression 1.8 minus negative 3.25. When you have a minus sign followed by a negative sign, they cancel each other out and it becomes an addition problem. Therefore, the expression simplifies to 1.8 + 3.25.

To calculate this, you add the two numbers:

Adding these numbers together gives you 5.05. So, 1.8 - (-3.25) equals 5.05.

Answer:G

Step-by-step explanation:I HAVE NO IDEA