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4 years ago

(-4y^3-5y+16)+(4y^2-y+9)

Mathematics

1 answer:

cricket20 [7]4 years ago

6 0

Answer:

$-4y^3 + 4y^2 -6y + 25$

Step-by-step explanation:

Combine like terms.

$(-4y^3-5y+16)$

+ $(4y^2 - y +9)$

----------------------------

$-4y^3 + 4y^2 -6y + 25$

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Final numeric grades in a certain course are normally distributed with a mean of 72.3 and a standard deviation of 6.4. The profe

Dimas [21]

Answer:

The minumum numeric grade you have to earn to obtain an A is 81.29.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 72.3, \sigma = 6.4$

The professor curves the grades so that the top 8% of students will receive an A. What is the minumum numeric grade you have to earn to obtain an A?

The minimum numeric value is the value of X when Z has a pvalue of 1-0.08 = 0.92. So it is X when Z = 1.405.

$Z = \frac{X - \mu}{\sigma}$

$1.405 = \frac{X - 72.3}{6.4}$

$X - 72.3 = 1.405*6.4$

$X = 81.29$

The minumum numeric grade you have to earn to obtain an A is 81.29.

6 0

3 years ago

The city park is 9 and 2/5 km from Roland Public School. The city library is 3 and 3/10 km from the same school. How much farthe

Marina86 [1]

Answer:

6 1/10

Step-by-step explanation:

Convert the mixed numbers into improper fractions (denominator × whole number + numerator / denominator):

9 2/5 = 47/5

3 3/10 = 33/10

Convert improper fractions to have the same denominator:

47/5 × 2/2 = 94/10

Find the difference by subtracting the numerators:

94/10 - 33/10 = 61/10

Convert the answer into a mixed number:

61/10 = 6 1/10

8 0

3 years ago

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circu

Marina CMI [18]

Answer:

E = 3072i - 5904ohms

Step-by-step explanation:

From ohms law recalled that E = IR given already

E = voltage (volts)

I = Current (amps)

R = resistance (ohms)

Therefore, by substitution

I = 16i and R = (2+4)ohms(32+66i)

= 6(32+66i) ohms

= (192+396i)ohms

E = (16i)×(192+396i)

E = 3072i + 5904i²

Recall that i² = -1 from complex number

E = 3072i +5904(-1)

E = 3072i - 5904ohms

5 0

3 years ago

Help answer and EXPLAIN STEP BY STEP

pychu [463]

15. $(-k^{3} -5k^{2} + 1) - (6k^{3}-k^{2} -2)$

Step 1: Distribute the subtraction sign to all the numbers in the second set of parentheses...

$(-k^{3} -5k^{2} + 1) - (6k^{3}-k^{2} -2)$

$-k^{3} -5k^{2} +1 - 6k^{3} +k^{2} +2$

Step 2: Combine like terms ( $k^{2}$ 's go with $k^{2}$ 's)

$-k^{3} -5k^{2} + 1 - 6k^{3}+k^{2} +2$

$-5k^{2} +k^{2}$

$-4k^{2}$

$-k^{3} -4k^{2} + 1 - 6k^{3}+2$

Step 3: Combine like terms ( $k^{3}$ 's go with $k^{3}$ 's)

$-k^{3} -4k^{2} + 1 - 6k^{3}+2$

$-k^{3} + (- 6k^{3})$

$-7k^{3}$

$-7k^{3} -4k^{2} + 1 +2$

Step 4: Combine like terms (normal numbers go with normal numbers)

$-7k^{3} -4k^{2} + 1 +2$

1 + 2

$-7k^{3} -4k^{2} + 3$

You were correct!

16. $49m^2 - 84mn + 36n^2$

I don't really know how to explain this one but I got: (7m-6n)(7m-6n)

7 0

4 years ago

A monument in the shape of a right triangle sits on a rectangular pedestal that is 5 meters high by 11 meters long. The longest

Vladimir [108]

Based on the information given, there are 2 possibilities:
1) the hypotenuse is the base of the triangles, sitting on the rectangular pedestal
2) the right angle touches the pedestal, with the base equalling the pedestal length

In 1) it is pretty straightforward, because the right angle is the apex (top). The base is 61m, because the longest side in a right is always the hypotenuse.
So now we need the height (h), which will split the triangle into two 45-45-90 triangles with base and h = 30.5 (1/2 the initial base)
This will make the height off the ground = 30.5+5 = 35.5 m

2) with right angle touching the pedestal, we can only assume that the base equals the pedestal length, 11. Then we need the missing side (h), which we can derive from Pythagorean Theorem:
${h}^{2} = {61}^{2} - {11}^{2} \\ \sqrt{({h}^{2})} = \sqrt{({61}^{2} - {11}^{2})} \\ h = \sqrt{({61}^{2} - {11}^{2})} = \sqrt{(3721- 121)} \\ h= \sqrt{3600} = 60$
So in this triangle the height off ground would be 60+5 = 65 m

6 0

4 years ago