What is the measure of the angle formed by the minute hand and the hour hand of a clock when the clock shows 4:00?

Answer:

Step-by-step explanation:

The answer is 2.5%

The probability of rolling a number with exactly two prime factors on a six-sided die is 1/3, as there are two outcomes (4 and 6) with exactly two prime factors and six possible outcomes in total.

The student is asking about the probability of an event in a probability experiment involving rolling a single six-sided die. The specific event of interest is rolling a number with exactly two, not necessarily unique, prime factors. On a standard six-sided die, the faces are labeled with the numbers 1 through 6. When considering the numbers on a die with two prime factors, we must first identify which of these numbers have exactly two prime factors. The numbers are:

The other numbers (1, 2, 3, and 5) have fewer than two prime factors. Since 4 and 6 are the only outcomes with exactly two prime factors, we have two favorable outcomes out of six possible outcomes on a six-sided die.

Thus, the probability of rolling a number with exactly two prime factors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 2 / 6 = 1 / 3

Therefore, the probability of the event is 1/3, or approximately 0.3333 (repeating).

To find f(1/4) when f(x)=2x^2+9x-7, substitute x=1/4 into the function and simplify.

To find f(1/4) when f(x) = 2x² + 9x - 7, we substitute x = 1/4 into the function.

Plugging in the value of x, we have f(1/4) = 2(1/4)² + 9(1/4) - 7.

Simplifying the expression, we get f(1/4) = 2/16 + 9/4 - 7. Evaluating the fractions and subtracting, we find that f(1/4) = -45/16.

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The inverse of a function is its opposite

The values of the unknown are: b = 1, c = 81 and d = 9

The function is given as:

[tex]y = x^2 - 18x[/tex]

Rewrite the equation in vertex form as:

[tex]y = (x - 9)^2 - 81[/tex]

Swap the positions of x and y

[tex]x = (y - 9)^2 - 81[/tex]

Add 81 to both sides

[tex](y - 9)^2 = x + 81[/tex]

take the square roots of both sides

[tex]y - 9 = \pm\sqrt{x + 81}[/tex]

Add 9 to both sides

[tex]y = \pm\sqrt{x + 81} + 9[/tex]

By comparison, the values of the unknown are:

b = 1, c = 81 and d = 9

Read more about inverse functions at:

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Answer: It took Sean 55 seconds to drink all the slushy

Solution:

Original Volume: Vo=275 milliliters

After t1=13 seconds, 210 milliliters remained: V1=210 milliliters

He drank the slushy at a constant rate: r

Sean drank V=Vo-V1=275 milliliters-210 milliliters→V=65 milliliters

r=V/t1

r=65 milliliters / 13 seconds

r=5 milliliters/second

Sean will drink the remained volumen in a time t2:

t2=V1/r

t2=210 milliliters / (5 milliliters/second)

t2=42 seconds

Total time to drink: t

t=t1+t2

t=13 seconds + 42 seconds

t=55 seconds

Answer:

Sean drank at a rate of 5 milliliters per second.

It took Sean 55 seconds to drink all the slushy.

Step-by-step explanation:

Hope it helps in the picture below.

Answer:  [tex]\frac{8}{17}[/tex] or 8:17

Step-by-step explanation:

For any angle x (other than right angle) in a right triangle ,the trigonometric ratio of sin x is given by :-

[tex]\sin x=\frac{\text{side opposite to x}}{\text{Hypotenuse}}[/tex]

Given: A right triangle with hypotenuse = 68 units

The side adjacent to S =  60

Let h be the side opposite to S, then using Pythagoras in the given right triangle, we get

[tex](68)^2=60^2+h^2\\\\\Rightarrow\ h^2=68^2-60^2\\\\\Rightarrow\ h^2=1024\\\\\Rightarrow\ h=\sqrt{1024}=32[/tex]

Thus, the side opposite to S = 32 units

Now,  the trigonometric ratio for sin S is given by :-

[tex]\sin S=\frac{\text{side opposite to S}}{\text{Hypotenuse}}\\\\\Rightarrow\sin S=\frac{32}{68}=\frac{8}{17}[/tex]

Hence, the  trigonometric ratio for sin S =[tex]\frac{8}{17}[/tex] or 8:17

Answer:

D

Step-by-step explanation:

Answer:

Cam has [tex]b-7[/tex] dollars.

Step-by-step explanation:

Here b represents the number of dollars Ben has,

Given,

Cam has 7 fewer dollars than Ben,

So, the number of dollars cam has = The number of Ben's dollar - 7

[tex]=b-7[/tex]

Hence, the expression that represents cam's dollar is,

[tex]' b-7 '[/tex]

the answer is three square units

The radius of the circle with an area of 324π sq cm is  18 cm.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

We know, The area of a circle is πr².

So, We can equate the given area with the general formula,

324π = πr².

r² = 324.

r = 18 cm.

A clock can be thought of as a circle having 12 steps and we know that circle is 360°,

So, the measure of each integer step of a clock is 30°.

Also, If we want to find some portion(arc) of the circumference we use the formula, s = rФ.

learn more about circles here :

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The frequency of Dexter's fourth group (35-39) in his frequency distribution is 2. This was determined by counting the numbers within the 35-39 range from the provided data set.

Calculating the Frequency of the Fourth Group:

To calculate the frequency of the fourth group in Dexter's frequency distribution, let's first establish the groups.

Next, we'll count how many data points fall within each range:

Thus, there are 2 data points in the fourth group (35-39).

Answer:

There are 144 inches in 12 feet.

Answer:

From the given problem statement of the this question,the amount of the gift is 1 dollar and sixty cents

x=60*B

Yes is it possible to have 60 pennies in $1.87