All categories

3 years ago

20 points up for the answer

Mathematics

1 answer:

lyudmila [28]3 years ago

6 0

$\dfrac ab=\dfrac38\implies a=\dfrac38b$
$\dfrac bc=\dfrac6{11}\implies c=\dfrac{11}6b$

$\implies a+b+c=\left(\dfrac38+1+\dfrac{11}6\right)b=\dfrac{77}{24}b$

Since each of $a,b,c$ are integers, so must be $a+b+c=\dfrac{77}{24}b$ . The only way for this to be the case is if $b$ is a multiple of 24 because 77 and 24 share no common divisors. The smallest multiple would be $b=24$ . So the smallest value of $a+b+c$ is 77.

You might be interested in

When we test Upper H 0: muequals0 against Upper H Subscript a: mugreater than0, we get a P-value of 0.03. a. What would the

Anastasy [175]

Answer:

(a) The null hypothesis will be rejected.

(b) Type I error

Step-by-step explanation:

The hypothesis provided is:

$H_{0}: \mu = 0\\ H_{a} : \mu > 0$

The p-value of the test obtained is 0.03

(a)

Decision rule for hypothesis testing, based on p-value, states that if the p-value is less than the significance level (α) then the null hypothesis is rejected and vice versa.

The significance level is α = 0.10

Then,

$p-value = 0.03 < \alpha = 0.10$

Thus, the null hypothesis will be rejected.

Conclusion:

The null hypothesis is rejected stating that the value of μ is more than 0.

(b)

If the decision in (a) is an error, i.e. the null hypothesis is rejected when in fact it is true, this type of error is known as type I error.

(c)

The significance level is α = 0.01

Then,

$p-value = 0.03 > \alpha = 0.01$

Thus, the null hypothesis will not be rejected.

Conclusion:

The null hypothesis was not rejected stating that the value of μ is 0.

If this decision is an error, i.e. the null hypothesis was not rejected when in fact it is false, this type of error is known as type II error.

3 0

3 years ago

You are jumping off the 12 foot diving board at the municipal pool. You bounce up at 6 feet per second and drop to the water you

NARA [144]

Answer:

When do you hit the water?

1.075 seconds after you jump.

What is your maximum height?

the maximum height is 12.5626 ft

Step-by-step explanation:

The equation:

h(t) = -16*t^2 + 6*t + 12

Is the height as a function of time.

We know that the initial height is the height when t = 0s

h(0s) = 12

and we know that the diving board is 12 foot tall.

Then the zero in h(t)

h(t) = 0

Represents the surface of the water.

When do you hit the water?

Here we just need to find the value of t such that:

h(t) = 0 = -16*t^2 + 6*t + 12

Using the Bhaskara's formula, we get:

$t = \frac{-6 \pm \sqrt{6^2 - 4*(-16)*12} }{2*(-16)} = \frac{-6 \pm 28.4}{-32}$

Then we have two solutions, and we only care for the positive solution (because the negative time happens before the jump, so that solution can be discarded)

The positive solution is:

t = (-6 - 28.4)/-32 = 1.075

So you hit the water 1.075 seconds after you jump.

What is your maximum height?

The height equation is a quadratic equation with a negative leading coefficient, then the maximum of this parabola is at the vertex.

We know that the vertex of a general quadratic:

a*x^2 + b*x + c

is at

x = -b/2a

Then in the case of our equation:

h(t) = -16*t^2 + 6*t + 12

The vertex is at:

t = -6/(2*-16) = 6/32 = 0.1875

Evaluating the height equation in that time will give us the maximum height, which is:

h(0.1875) = -16*(0.1875 )^2 + 6*(0.1875) + 12 = 12.5626

And the height is in feet, then the maximum height is 12.5626 ft

6 0

3 years ago

Sally can detail a car in 50 minutes. Manny does the same job in 35 minutes. How long will it take them to detail a car working

Debora [2.8K]

<u>Answer:</u>

Both Sally ans Manny can detail a car in 20.6 min.

<u>Solution: </u>

Let us assume that together they will take total x minutes to detail the car.

Sally detail the car in 50 min.

So in 1 min sally can detail \left(\frac{1}{50}\right) of the car.

Hence in x min sally can detail \left(\frac{x}{50}\right) of the car.

Manny can detail a car in 35 min.

So in 1 min many can detail \left(\frac{1}{35}\right) of the car.

Hence in x min Manny can detail \left(\frac{x}{35}\right) of the car.

So we can say,

\left(\frac{x}{50}\right)+\left(\frac{x}{35}\right)=1

x\left(\frac{1}{50}+\frac{1}{35}\right)=1

x\left(\frac{7+10}{350}\right)=1

\left(\frac{17 x}{350}\right)=1

$17 x=350$

x=\left(\frac{350}{17}\right)=20.5 8 $\approx$ 20.6

So, both of them can detail a car in 20.6 min.

3 0

3 years ago

What is the area of the composite figure in problem 3?

suter [353]

Answer:

trapazoid

Step-by-step explanation:

5 0

2 years ago

What does m represent in the equation y=mx+b? Please I need help with this

artcher [175]

Slope

Step-by-step explanation:

y=mx+b

y=slope+ y-intercept

8 0

2 years ago