Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6 rolls of quarters containing 40 coins each. How much money does she have?

A. $106.20
B. $17.50
C. $8.00
D. $94.50

To find the value of cos θ when sin θ = 1/4 and tan θ > 0, use the Pythagorean identity. As the angle is in the first quadrant, cos θ is positive and equals the square root of 15/16 or √15/4.

If sin θ = 1/4 and tan θ > 0, we need to determine the value of cos θ. When the sine of an angle is positive and the tangent is positive, we know the angle must be in the first quadrant, where all trigonometric functions are positive. To find cos θ, we utilize the Pythagorean identity sin2 θ + cos2 θ = 1. Rewriting this identity for cos θ, we get cos2 θ = 1 - sin2 θ.

Substituting the given value of sin θ, we have:

cos2 θ = 1 - (1/4)2
cos2 θ = 1 - 1/16
cos2 θ = 15/16

Since θ is in the first quadrant, and cos θ is positive, the value of cos θ is the positive square root of 15/16:

cos θ = √(15/16)
cos θ = √15/4 or approximately 0.9682

Step 2 can be justified using the Multiplication Property of Equality. This property states that if we multiply or divide both sides of an inequality by the same number, the inequality will still hold true.

Step 2 can be justified using the Multiplication Property of Equality. This property states that if we multiply or divide both sides of an inequality by the same number, the inequality will still hold true.

In this case, Jax divided both sides of the inequality by 3. This is a valid step because dividing both sides of the inequality by a positive number does not change the inequality. So, by dividing both sides by 3, Jax found that x > -1.

Answer:

(The other answer has missing a number.)

The full answer is: $22.85

Answer:

1. always

2. sometimes

Step-by-step explanation:

Two lines are coplanar if they lie in the same plane or in parallel planes. There is  ALWAYS a plane which contains two parallel lines (see first attached image for details).

Two lines that lie in parallel planes are sometimes parallel. For example, see at second image. Planes [tex]\alpha[/tex] and [tex]\beta[/tex] are parallel. Consider pair of lines [tex]a[/tex] and [tex]a_1[/tex] - they are parallel, but if you consider the pair of lines [tex]a[/tex] and [tex]b_1[/tex], you can see they are not parallel.

Answer:

always

sometimes

Step-by-step explanation:

By definition parallel lines are lines in a plane which do not meet, that means, they have to be coplanar. Coplanar means they are included in the same plane. Then, two parallel lines are always coplanar (imagine two parallel lines in a 3d space, there is always a plane that can contain them).

Two lines that lie in parallel planes are sometimes parallel. As stated before, if there is a third plane which contains the two lines, they can be parallel or cannot, but if there is no plane which contains them, they are not parallel.

To find the unit rate in cost per hour, you will write the amount of money over the total time for each class. Then divide the cost by the time to find the unit rate.

New Steps: $7.50/1.5 hours = $5 per hour

Stepping High: $6.50/1.25 hours = $5.20 per hour

Answer:

To find the unit rate in cost per hour, you will write the amount of money over the total time for each class. Then divide the cost by the time to find the unit rate.

New Steps: $7.50/1.5 hours = $5 per hour

Stepping High: $6.50/1.25 hours = $5.20 per hour

Answer: [tex]\dfrac{3}{5}[/tex]

Step-by-step explanation:

The slope of a line passing through two points X(a,b) and Y(c,d) is given by :-

[tex]m=\dfrac{d-b}{c-a}[/tex]

Given points : C(3, 8) and  D(-2, 5)

Then , the  slope of a line passing through two points C(3, 8) and  D(-2, 5) is given by :-

[tex]m=\dfrac{5-8}{-2-3}=\dfrac{-3}{-5}=\dfrac{3}{5}[/tex]

Hence, the  slope of the line that contains the points C(3, 8) and  D(-2, 5) is [tex]\dfrac{3}{5}[/tex]

.

Hence, the probability that he will receive job is:

                                   1/6

It is given that:

chance of passing a qualifying examination is 2/3=P

and chance of being appointed if he does pass is 1/4=P'

Now, we are asked to find the probability that he will receive the job.

We are asked to find the probability that he will receive the job.

The probability is calculated as:

Probability that he qualify exam×Probability that he is being appointed.

=P×P'

=(2/3)×(1/4)

=1/6

The probability of selecting a chocolate at random that is either white chocolate with cream filling or dark chocolate with no filling is [tex]\frac{8}{30}[/tex].

Probability is the chance of happening an event or incident.

Given, the box contains 30 chocolates.

The number of chocolates that are white chocolate with cream filling is 5.

Therefore, the probability of selecting a chocolate at random that is white chocolate with cream filling is [tex]= \frac{5}{30}[/tex].

The number of chocolates that are dark chocolate with no filling is 3.

Therefore, the probability of selecting a chocolate at random that is dark chocolate with no filling is [tex]= \frac{3}{30}[/tex].

Now, the probability of selecting a chocolate at random that is either white chocolate with cream filling or dark chocolate with no filling is

[tex]= \frac{5}{30} + \frac{3}{30} \\= \frac{8}{30}[/tex]

Learn more about probability here: https://brainly.com/question/28001361

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Answer:

y = sin(4x) + 3

Step-by-step explanation:

Answer:  The correct option is

(A) 4 m/s.

Step-by-step explanation:  We are given that a force of 60 N is exerted on a 15 kg object.

We are to calculate the acceleration that the object undergoes.

From Newton's second law of motion, we have

[tex]F=ma,[/tex] where m is the mass of the object, a is the acceleration and F is the force exerted.

For the given object, we have

F = 60 N  and  m = 15 kg.

So, we get

[tex]F=ma\\\\\Rightarrow 60=15\times a\\\\\Rightarrow a=\dfrac{60}{15}\\\\\Rightarrow a=4.[/tex]

Thus, the required acceleration that the object undergoes is 4 m/sec.

Option (A) is CORRECT.

The term describing what a manufacturer spends for goods or services is cost. Cost is the expenses incurred by the manufacturer as a result of his business or undertaking. There are two types of cost of a manufacturer. The cost of goods sold and the operating expenses. The cost of goods sold are those cost incurred directly as a result of manufacturing. The operating expenses are those other expenses not indirectly involved with the manufacture of goods or services.

Answer:

Its FALSE on odyssey

The lim t>infinity P(t) is 5,000, which is the carrying capacity of the species.

The logistic differential equation dP/dt = P(2-(P/5000)) models the population growth of a species. To find the lim t>infinity P(t), we need to find the stable population when t becomes very large. In this equation, the population growth rate is initially exponential, but as the population approaches its carrying capacity (Q), the growth rate slows down and levels off to zero.

Solving the differential equation, we find that the equation represents logistic growth. The solution to the equation is P(t) = Q / (1 + (Q/Po)e^(-rt)), where Po is the initial population, Q is the carrying capacity, and r is the growth rate.

In this case, the initial population is given as 3,000. To find the carrying capacity (Q), we set dP/dt = 0 and solve for P. Substituting the values into the equation, we find Q = 5,000.

As t becomes very large, e^(-rt) approaches 0, and the equation simplifies to P(t) = Q. Therefore, the lim t>infinity P(t) is 5,000, which is the carrying capacity of the species.