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1 year ago

tim estimates that 60÷5.7 is about 10. Will the actual quotient be greater then or less than 10? explain

1 answer:

7 0

The actual quotient will be greater than 10 because 60 divided by 5 is 12, so the answer will be between 10 and 12, so it will be greater than 10

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Represent 23/-4 on number line

Dmitrij [34]

$\frac{23}{-4}=-5\frac{3}{4}$

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2 years ago

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An item regularly priced at $80 is on sale for 20% off. There is a 3% sales tax.

Katena32 [7]

Answer:$14.08 and the discount is $16

Step-by-step explanation:first you find 20% of 80 which is 16 and you subtract it from 80 which gives you 64 then you have to find 3% of 64 which is 1.92 and you add it to 64 which is 65.92 then to find how much you are saving you subtract 65.92 from 80 which is 14.08

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2 years ago

Two sides of a triangle have lengths 12 m and 14 m. The angle between them is increasing at a rate of 2°/min. How fast is the le

Dvinal [7]

Answer:

1.692 m/min

Step-by-step explanation:

Let $\theta$ be the angle between the two sides and x be the length of the third side. By cosine rule,

$x^2 = 12^2+14^2-2\times12\times14\cos\theta = 340 - 336\cos\theta$

$x= \sqrt{340 - 336\cos\theta}$

We differentiate x with respect to $\theta$ by applying chain rule.

$\dfrac{dx}{d\theta} = \dfrac{336\sin\theta}{2\sqrt{340 - 336\cos\theta}} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}}$

Rate of change of $\theta$ is 2

$\dfrac{\theta}{dt} = 2$

Rate of change of x is

$\dfrac{dx}{dt} = \dfrac{dx}{d\theta}\times\dfrac{d\theta}{dt}$

$\dfrac{dx}{dt} = \dfrac{168\sin\theta}{\sqrt{340 - 336\cos\theta}} \times2=\dfrac{336\sin\theta}{\sqrt{340 - 336\cos\theta}}$

At 60°,

$\dfrac{dx}{dt} = \dfrac{336\sin60}{\sqrt{340 - 336\cos60}} = 1.692 \text{ m/min}$

4 0

2 years ago

For which discriminant is the graph possible b2-4ac=0 b2-4ac=-1 b2-4ac=4

VARVARA [1.3K]

Answer:

The graph is possible for $b^2-4ac=4$

Step-by-step explanation:

we know that

The discriminant of a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$D=b^2-4ac$

If D=0 the quadratic equation has only one real solution

If D>0 the quadratic equation has two real solutions

If D<0 the quadratic equation has no real solution (complex solutions)

In this problem , looking at the graph, the quadratic equation has two real solutions (the solutions are the x-intercepts)

$b^2-4ac > 0$

therefore

The graph is possible for $b^2-4ac=4$

4 0

1 year ago

A manager records the number of hours, X, each employee works on his or her shift and develops the probability distribution belo

Reika [66]

Answer:

c. 2

Step-by-step explanation:

Given : X = No. of hours worked

No. of people work for the manager = 50

X = 3, 4 , 5 , 6 , 7, 8

P(X) = 0.1 , ? , 0.14 , 0.3 , 0.36 , 0.06

To Find : No. of people work for four hours

Solution : First understand the fact that sum of all probabilities is equal to 1

So, sum of all values of P(X) = 1

⇒ $0.1+?+0.14+0.3+0.36+0.06 = 1$

⇒ $0.96+? = 1$

⇒ $?= 1-0.96$

⇒ $? = 0.04$

So, the probability of no. of people worked for 4 hours is 0.04.

⇒P(4)=0.04

Thus , To calculate no. of people work for four hours :

$0.04\times 50$

⇒ 2 no. of people work for four hours per shift .

5 0

2 years ago

Read 2 more answers