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3 years ago

The function with a rate of change of 3/2 whose graph passes through the point (4,10.5)

Mathematics

1 answer:

tamaranim1 [39]3 years ago

4 0

Answer:

y = 1.5x+4.5

Step-by-step explanation:

Let's try to fit this into slope-intercept form, which is y=mx+b, where m=slope and b=y-intercept.

Rate of change means slope, so m=3/2 = 1.5.

y = 3/2x+b

We can plug in the given point, remembering that it's in the form (x,y), so x=4, y=10.5.

y = 3/2x+b

10.5 = 3/2*4 + b

4.5 = b

Plug b back in.

y = 1.5x+4.5

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A teacher wants to estimate the mean time (in minutes) that students take to go from one classroom to the next. His research ass

PilotLPTM [1.2K]

Answer:

a: We can't determine this from the given information

b: 98%

Step-by-step explanation:

For a:

n = 42

The confidence interval has equal time on each side of µ, so we can add the two end points and divide them by 2 to find the middle of the interaval:

7.4 + 8.6 = 16

16/2 = 8

Now subtract 7.4 from 8 to find the distance from the mean to the end of the interval

8 - 7.4 = 0.6

So the sample mean, plus the calculated error was 0.6 minutes.

We don't have a way of calculating the sample mean with the given information. We could only find the sample standard deviation and the variance.

For b:

We have:

E = 0.6

s = 1.606

n = 42

See attached photo for the calculation of this value

The value is 2.421.

Using a sample size of 42, our degrees of freedom are 41. Use the t-distribution chart to see which level of confidence has 2.421 under it.

The level of confidence is: 98%

We need 41 degrees of freedom, but the chart has only 40, then 45. We can see that 40 has 2.423, and the values go down as the degrees of freedom go up, so 41 will correlate to 2.421

6 0

4 years ago

If f(x) = 3x2 − 8x, 0 ≤ x ≤ 3, evaluate the Riemann sum with n = 6, taking the sample points to be right endpoints.

denis23 [38]

Split up the interval [0, 3] into 6 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], [3/2, 2], [2, 5/2], [5/2, 3]

The right endpoints are given by the arithmetic sequence,

$r_i=0+\dfrac i2=\dfrac i2$

with $1\le i\le6$ .

We approximate the integral of $f(x)$ on the interval [0, 3] by the Riemann sum,

$\displaystyle\int_0^3f(x)\,\mathrm dx=\sum_{i=1}^6f(r_i)\Delta x_i$

$\displaystyle=\frac{3-0}6\sum_{i=1}^6\left(3{r_i}^2-8r_i\right)$

$\displaystyle=\frac12\sum_{i=1}^6\left(\frac{3i^2}4-4i\right)$

$\displaystyle=\frac38\sum_{i=1}^6i^2-2\sum_{i=1}^6i$

Recall the formulas,

$\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2$

$\displaystyle\sum_{i=1}^ni^2=\frac{n(n+1)(2n+1)}6$

Then the value of the integral is approximately

$\displaystyle=\frac38\cdot\frac{6\cdot7\cdot13}6-2\cdot\frac{6\cdot7}2=\boxed{-\frac{63}8}=-7.875$

Compare to the exact value of the integral, -9.

7 0

3 years ago

The base of a triangle is 5 meters greater than the height. If the area of the triangle is 102 m2, which are the dimensions of t

kakasveta [241]

Answer: The base is 17 meters long, and the height is 12 meters.

Step-by-step explanation:

The area of a triangle is:

A = b*h/2

where:

b = base

h = height.

For this particular triangle, we have that:

b = 5m + h

A = 102 m^2 = b*h/2

We can replace the first equation into the second one:

b*h/2 = 102 m^2

(5m + h)*h/2 = 102 m^2

(5m + h)*h = 2*102 m^2 = 204m^2

5m*h + h^2 = 204m^2

We can rewrite this as a quadratic equation:

h^2 + 5m*h - 204m^2 = 0

The solutions are given by the Bhaskara formula, the solutions are:

$h = \frac{-5m +- \sqrt{(+5m)^2 -4*1*(-204m^2)} }{2*1} = \frac{-5m+-29m}{2}$

Then the two solutions are:

h = (-5m - 29m)/2 = -17 m

This is a negative height, that is not really defined, so this will be discarded.

The other solution is:

h = (-5m + 29m)/2 = 12m

This is positive, so this is the option we will use.

Knowing h, we can find the value of b.

b = 5m + h = 5m + 12m = 17m

Then the area is:

A = 12m*17m/2 = 102m^2

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3 years ago

I will give you Brainiest if you are right.

olganol [36]

Answer:

F. 4d + h + 2f

Step-by-step explanation:

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3 years ago

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rewona [7]

Answer:

1 (7/45)

Step-by-step explanation:

you'll see how many 45 can go into 52. Only 1 45 can fit into 52 with some leftover.

so to find the left over numbers you'll subtract 45 from 52= 7

so 7/45 is left over

5 0

3 years ago

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