The clocks radius is 10m. What is the circumference of the clock

Final answer:

The quadratic equation x²-5x-31=5 is solved by factoring to (x - 9)(x + 4) = 0, giving the solutions x = 9 and x = -4.

Explanation:

To solve the quadratic equation x²-5x-31=5 by factoring, we first move all terms to one side to get it into standard form:

x² - 5x - 36 = 0

Next, we look for two numbers that multiply to -36 and add up to -5. These numbers are -9 and 4. So, we can write:

(x - 9)(x + 4) = 0

Now, we have two possible solutions for x:

Therefore, the solutions to the equation are x = 9 and x = -4.

Answer:

cylinder

Step-by-step explanation:

Answer:

y= 1/5 (fraction)

x=−3

Step-by-step explanation:

Let's solve for x.

x−5y=15

Step 1: Add 5y to both sides.

x−5y+5y=15+5y

x=5y+15

Let's solve for y.

x−5y=15

Step 1: Add -x to both sides.

x−5y+−x=15+−x

−5y=−x+15

Step 2: Divide both sides by -5.

−5y

−5

=

−x+15

−5

Answer:

b

Step-by-step explanation:

The table could show the relationship between the number of toppings and the cost of a medium pizza is table B.

We divide the change in y (output) by the change in x to determine the average rate of change (input).

The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.

In table 1, when the topic goes from 4 to 5 then the price increase by $2 which is not convenient here.

In table 2, when the topic goes from 4 to 5 then the price increase by $1 which is not convenient here.

In table 3, when the topic goes from 4 to 5 then the price increase by $2 which is convenient here.

In table 4, when the topic goes from 4 to 5 then the price increase by $2 which is not convenient here.

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Answer: 10:55

Step-by-step explanation:

Taking statement at face value and the simplest scenario that commencing from 08:00am the buses take a route from depot that returns bus A to depot at 25min intervals while Bus B returns at 35min intervals.

The time the buses will be back at the depot simultaneously will be when:

N(a) * 25mins = N(b) * 35mins

Therefore, when N(b) * 35 is divisible by 25 where N(a) and N(b) are integers.

Multiples of 25 (Bus A) = 25, 50, 75, 100, 125, 150, 175, 200 etc

Multiples of 35 (Bus B) = 35, 70, 105, 140, 175, 210, 245 etc

This shows that after 7 circuits by BUS A and 5 circuits by Bus B, there will be an equal number which is 175 minutes.

So both buses are next at Depot together after 175minutes (2hr 55min) on the clock that is

at 08:00 + 2:55 = 10:55

Answer: 7.32 inches

Step-by-step explanation: We can set up an equation to solve: y = 0.61x where y is the total amount of rain in inches and x is how many days it rained.

Multiply 0.61 by 12 to get how many inches total it rained: y = 0.61(12)

y = 7.32 inches

Answer: 4 Tons

Step-by-step explanation:

Simply just add and subtract

Answer:

C

Step-by-step explanation:

V(t) = [x(t)]³

A(t) = 6[x(t)]²

dV/dt = k × 6[x(t)]²

Where k < 0

From the options,

taking k = -0.2

dV/dt = -1.2[x(t)]²

The correct answer is A) dV/dt=-1.2x^2, which represents a rate of volume decrease directly proportional to the cube's surface area.

The question involves finding a differential equation that describes the rate at which the volume of a cube decreases when the rate is proportional to the cube's surface area. Since the surface area of a cube is 6x(t)^2 and the volume is x(t)^3, the rate of decrease in volume, dV/dt, is proportional to the surface area.

The correct differential equation would show this relationship by having the change in volume be proportional to the square of the edge length, so dV/dt = -kx^2 for some constant k, which means the valid option is A) dV/dt=-1.2x^2.

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Answer:

Step-by-step explanation:

Answer:

r= -6

Step-by-step explanation:

Here's why:

6 r = 6 + 7r

Subtract 7r from each side:

-r = 6

Divide by each side -1 to get the answer of:

r=-6

Answer:

z=3.8196

Step-by-step explanation:

-We notice that this is a normal distribution problem.

-Given the mean is $8500, standard deviation is $1200 , and n=350, the critical z-value using alpha=0.05 is calculated as:

[tex]z=\frac{x-\mu_o}{\sigma/\sqrt{n}}\\\\=\frac{8745-8500}{1200\sqrt{350}}\\\\\\=3.8196[/tex]

Hence, the test statitic is z=3.8196

Answer:

2/5

Step-by-step explanation:

6+7+2=15

6 out of the 15 are bananas

you can simply and reduce this fraction from 6/15 to 2/5

Answer:

An exponential equation is when we let the the independent variable become the exponent.

Answer:C. 1.4 10-11 N up

step-by-step explanation:

Explanation:

The magnetic force, F on a charge q moving with velocity v in a magnetic field B at an angle θ is given by:

F = q v B sin θ

Charge of proton, q = 1.6 × 10⁻¹⁹ C

Strength of magnetic field, B = 3.4 T pointing outwards

velocity of the proton, v = 2.5 × 10⁷ m/s towards left

Magnetic force is given by:

F =  1.6 × 10⁻¹⁹ C× 2.5 × 10⁷ m/s ×3.4 T× sin 90 = 13.6 × 10⁻¹² N = 1.4 × 10⁻¹¹ N up

The direction of the force is given by Lorentz Right hand rule. The fingers point magnetic field, the thumb points towards velocity, then the force on the proton is given by the direction perpendicular to the palm.  

The magnetic field acts outwards with velocity of the proton towards left. The force would act perpendicular to the two -upwards.

The magnetic force on the proton, moving to the left at 2.5 x [tex]10^6[/tex] m/s in a 3.4 Tesla magnetic field directed toward you, is approximately 1.36 x [tex]10^{-12}[/tex] Newtons.

To calculate the magnetic force acting on the proton in this scenario, we'll use the formula F = q × v × B × sin(θ), where:

F is the magnetic force,

q is the charge of the proton (1.6 x [tex]10^{-19}[/tex] C),

v is the velocity of the proton (2.5 x [tex]10^6[/tex] m/s),

B is the magnetic field strength (3.4 Tesla), and

θ is the angle between the proton's velocity vector and the direction of the magnetic field.

In this case, since the proton is moving to the left and the magnetic field is directed toward you, the angle θ is 90 degrees because they are perpendicular to each other.

Now, plug the values into the formula:

F = (1.6 x  C) × (2.5 x [tex]10^6[/tex] m/s) × (3.4 Tesla) × sin(90°)

sin(90°) is equal to 1, so:

F = (1.6 x [tex]10^{-19}[/tex] C) × (2.5 x [tex]10^6[/tex] m/s) × (3.4 Tesla) × 1

F ≈ 1.36 x [tex]10^{-12}[/tex] N

So, the magnetic force acting on the proton is approximately 1.36 x [tex]10^{-12}[/tex] Newtons. This force causes the proton to experience a curved path due to the interaction between its velocity and the magnetic field.

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Complete question below:

"What is the magnetic force acting on a proton moving at a velocity of 2.5 x [tex]10^6[/tex] m/s to the left when it enters a magnetic field with a strength of 3.4 Tesla, directed toward you? The charge of a proton is 1.6 x [tex]10^{-19}[/tex] C. Calculate the magnetic force using the formula F = q × v × B × sin(θ)."

To apply two coats of paint on all the walls, you will need to buy 4 quarts of paint.

To find out how many quarts of paint you need to buy to apply two coats of paint on all the walls, we need to calculate the total area that needs to be painted.

If 2 quarts cover 175 square feet, then 1 quart covers 175/2 = 87.5 square feet.

Since you need to apply two coats of paint, the total area that needs to be painted is 175 square feet x 2 = 350 square feet.

To find out how many quarts you need, divide the total area by the area covered by 1 quart: 350 square feet / 87.5 square feet/quart = 4 quarts.

You will need to buy 4 quarts of paint to complete the job.

Answer:

No

Step-by-step explanation:

If GH is tangent to circle F, then it forms a right angle with FG.  Therefore, triangle FGH would be a right triangle and would satisfy Pythagorean theorem.

34² + 256² = 288²

66692 = 82944

The sides are not a Pythagorean triple, so GH is not tangent to the circle.

Answer:

Yes  because  it fits the Pythagorean Theorem

Step-by-step explanation:

see:   5 ^2 = 25

and   3^2 + 4^2 =  9 + 16 = 25

25 = 25

so it is

The number 31 was increased to 44 by approximately 41.9%.

To calculate the percentage increase, you can use the formula:

[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 \][/tex]

In this case, the original value is 31, and the new value is 44. Plug these values into the formula:

[tex]\[ \text{Percentage Increase} = \left( \frac{44 - 31}{31} \right) \times 100 \][/tex]

[tex]\[ \text{Percentage Increase} = \left( \frac{13}{31} \right) \times 100 \][/tex]

Now, calculate the percentage increase:

[tex]\[ \text{Percentage Increase} \approx 41.9\% \][/tex]

So, the number 31 was increased to 44 by approximately 41.9%.

The number 31 was increased by approximately [tex]\( \boed{41.9\%} \)[/tex] to become 44.

Step 1

To find the percentage increase from 31 to 44, we can use the formula for percentage increase:

[tex]\[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100\% \][/tex]

Step 2

Given:

- Old value (31)

- New value (44)

[tex]\[ \text{Percentage Increase} = \left( \frac{44 - 31}{31} \right) \times 100\% \]\[ \text{Percentage Increase} = \left( \frac{13}{31} \right) \times 100\% \]\[ \text{Percentage Increase} \approx 0.419 \times 100\% \]\[ \text{Percentage Increase} \approx 41.9\% \][/tex]

So, the number 31 was increased by approximately [tex]\( \boed{41.9\%} \)[/tex] to become 44.

Answer:

Use the 45-45-90 rule.

Step-by-step explanation:

Based on angle A being 45 and angle B looking like its 90 degrees, angle C will be 45 degrees and so you'd use the 45-45-90 rule, which is a special right triangle. The 45 degrees sides are x and the hypotenuse is x[tex]\sqrt{2}[/tex]. It will be easier if you look it up to see a graphic of it, but I'm pretty sure that both sides CB and AB are 6 based on this rule.

Answer:

2/3

Step-by-step explanation:

Answer: the answer is d.2/3 just took the test!!

Step-by-step explanation:

Answer:

[tex]\frac{13}{60}[/tex]

Step-by-step explanation:

18 people preferred MILK

29 preferred COFFEE

13 preferred JUICE

We want probability that a person preferred JUICE. For that, we need number of people who preferred juice and total number of people.

Lets find total:

18 + 29 + 13 = 60 total people

Total people who preferred JUICE is:

13

Probability (preferred JUICE) = 13/60

The answer is  [tex]\frac{13}{60}[/tex]

Answer:

a.The expected value of the game to the player is -$0.2105

b. The player should expect to lose $210.50¢ if he/she places the bet or plays the game 1,000 times

Step-by-step explanation:

Please kindly check the attached files for explanation.

The total number of pieces of fruit that they bought should be 72.

Here we assume 3 bags of apples with 4 apples in each bag  [tex](3 \times 4 = 12)[/tex]

And, 3 bunches of bananas with 4 bananas in each bunch  [tex](3 \times 4 = 12)[/tex]

Now  

= 12 + 12

= 24 pieces of fruit

Since

4 + 4 + 4  (12)  apples   +   4 = 4 + 4  (12)  bananas

So,

= 12 + 12

= 24  

here we need to multiplied by 3

So,  [tex]= 24 \times 3[/tex]

= 72

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Answer:

x = 3.75 inches

Step-by-step explanation:

We have,

Perimeter of a rectangle, P = 21 inches

Its length is 3 inches greater than its width. Let width is x. So, length of rectangle is l = 3+x

The perimeter of a rectangle is :

[tex]P=2(l+b)[/tex]

l is length and b is breadth

Here, l = 3+x, b = x

Perimeter :

[tex]P=2(3+x+x)\\\\21=2(3+2x)[/tex]

[tex]21=6+4x\\\\15=4x\\\\x=3.75\ \text{inches}[/tex]

So, the width is 3.75 inches.

Final answer:

To find the width of the rectangle, create an equation using the perimeter formula P = 2l + 2w. By substituting the known perimeter and the relationship between length and width, solve for w, resulting in a width of 3.75 inches.

Explanation:

The student is tasked with finding the width of a rectangle when the perimeter is known to be 21 inches and the length is 3 inches greater than the width. To solve this, we set up an equation representing the perimeter of a rectangle: P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

Let w represent the width of the rectangle. The length is then w + 3 inches. Substituting these values into the perimeter formula, we get: 21 = 2(w + 3) + 2w. Simplifying this, we get 21 = 2w + 6 + 2w or 21 = 4w + 6. Solving for w, we subtract 6 from both sides to get 15 = 4w, and then divide both sides by 4 to get w = 3.75 inches. This means the width of the rectangle is 3.75 inches.

Answer:

1.)angle 0 = 62 degrees,  

2.) angle 0 = 90 - y degrees.

Step-by-step explanation:

1). Sin(0) = cos (28)

angle 0 would be  arcsin (cos (28)) =  62 degrees.

2). Cos(y) = sin (0)

angle 0 = arcsin ( cos (y) ) = 90 - y

To solve the equations involving trigonometric functions Sin(0) = cos(28) and Cos(y) = sin(0), use co-function identities to find 0 equals 62 degrees or (90° - 28°), and y could be 28 degrees or (360° - 28°) due to cosine's periodic nature.

To solve the set of equations Sin(0) = cos (28) and Cos(y) = sin (0), we need to apply trigonometric identities and the given constraints.

Firstly, we can use the co-function identities which state that sin(90° - x) = cos(x), and similarly, cos(90° - x) = sin(x). Therefore, for the first equation, we can express 0 in terms of 28°:

sin(0) = cos(28°) implies 0 = 90° - 28° or 0 = 62°.

For the second equation, we replace 0 with 62°:

cos(y) = sin(62°)

We know that sin(62°) equates to the same value as cos(28°) from the first equation.

Therefore, cos(y) = cos(28°), which means y = 28° or y = 360° - 28° due to the periodic nature of cosine.

Answer:

25% Decrease

Step-by-step explanation:

15/20 is 75%. 100-75 (since they read less) is 25%

Answer:

25% decrease

Step-by-step explanation:

25% of 20 is 5. Because 0.25*20=5.

And because they read 15 book next month, if was 5 bookks less, which was 25% less.

Very choppy answer. But I hope that helped

Answer:

The parent graph of (x-2)^4+1               shifts 2   units to the right and one unit up.

The parent graph of 3x^4-6            is stretched vertically by a factor of 3   and then shifted 6   units down.

The parent graph of 2(x+3)^4+10                 is shifted 3   units to the left, stretched vertically by a factor of 2   and shifted 10    units up.

The parent graph of 1/4(6x-1)^4                 is shifted one unit to the right, compressed horizontally by a factor of 1/6     , and compressed vertically by a factor of  1/4.

Step-by-step explanation:

Answer:

6051

Step-by-step explanation:

fo sho

Answer:The value of X is 7.

Step-by-step explanation: It's counting up starting at 3 so the 4..5..6..7 so, then the 6 is right one the invisible line with X

Answer:

x =2

Step-by-step explanation:

Similar triangles:-

   Given diagram ΔABC  AND ΔDBE are similar triangles.

    [tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]

  [tex]\frac{x+x+1}{x+1} = \frac{6+4}{6}[/tex]

on simplification , we get

[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]

cross multiplication , we get

12x+6 =10x +10

12x-10x = 10 -6

 2x =4

  x =2

Therefore the value of x =2

verification:-

[tex]\frac{BC}{BE} = \frac{AB}{BD}[/tex]

[tex]\frac{2x+1}{x+1} = \frac{6+4}{6}[/tex]

put x=2

[tex]\frac{2(2)+1}{2+1} = \frac{6+4}{6}[/tex]

[tex]\frac{5}{3} = \frac{6+4}{6}[/tex]

[tex]\frac{5}{3} = \frac{5}{3}[/tex]

both sides are equal

Therefore x value is 2