Write an equation of the line and interpret the slope:

The matrices shows the number of dance students enrolled in each type of class for two different years.

Scorpion4ik [409]

Answer:

n54

Step-by-step explanation:

3 0

3 years ago

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Given the following sets.

laila [671]

B = {a, b, c, d}

C = {0, a, 2, b}

B ∪ C = {a, b, c, d, 0, 2}

<h3>Answer: E)</h3>

Everything from the set B and everything from the set C give to one set. Duplicated elements are written only once.

8 0

3 years ago

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Elena is buying cups and plates for her party. Cups are sold in packs of 8 and plates are sold in packs of 6. She wants to have

Svet_ta [14]

Answer:

For 80 people, Elena would need

14 packs of plates and 10 packs of cups

She would have at least 80 of each.

I am not completely sure of this, sorry if wrong.

Step-by-step explanation:

80 people

8 cups per pack

6 plates per pack

8, 16, 24, 32, 40, 48, 56, 64, 72, 80

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84

LCM (least common multiple) = 24

8 0

2 years ago

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Find the 44th percentile, P44, from the following data! pls help

irina [24]

Answer:

$P_{44} = 29.9$

Step-by-step Explanation:

The 44th percentile, $P_{44}$ , of the given data can be calculated using the kth formula for percentile given as:

$i = \frac{k}{100}(n + 1)$

where,

i = the ranking or the position of the percentile = ?

k = the percentile = 44

n = total number of the given data values = 23

Plug in the values into the formula to find "i"

$i = \frac{44}{100}(23 + 1)$

$i = \frac{44}{100}(24)$

$i = \frac{1,056}{100}$

$i = 10.56$

Since "I", 10.56, is not an integer, round the number down, and round it up to the nearest integer, then look for the position each occupy in the ordered data set, and find their average.

Thus,

$i_{down} = 10.56 = 10$

$i_{up} = 10.56 = 11$

The data occupying the 10th position on the data set = 28.7

11th = 31.1

$P_{44} = \frac{28.7 + 31.1}{2} = \frac{59.8}{2}$

$P_{44} = 29.9$

6 0

3 years ago

Help evaluating the indefinite integral

Dafna11 [192]

Answer:

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$

General Formulas and Concepts:
Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]:
$\displaystyle (cu)' = cu'$

Derivative Property [Addition/Subtraction]:
$\displaystyle (u + v)' = u' + v'$
Derivative Rule [Basic Power Rule]:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integration

Integrals

Integration Rule [Reverse Power Rule]:
$\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Property [Multiplied Constant]:
$\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Methods: U-Substitution and U-Solve

Step-by-step explanation:

Step 1: Define

Identify given.

$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution/u-solve.

Set u:
$\displaystyle u = 4 - x^2$
[u] Differentiate [Derivative Rules and Properties]:
$\displaystyle du = -2x \ dx$
[du] Rewrite [U-Solve]:
$\displaystyle dx = \frac{-1}{2x} \ du$

Step 3: Integrate Pt. 2

[Integral] Apply U-Solve:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-x}{2x\sqrt{u}}} \, du$
[Integrand] Simplify:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \int {\frac{-1}{2\sqrt{u}}} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \frac{-1}{2} \int {\frac{1}{\sqrt{u}}} \, du$
[Integral] Apply Integration Rule [Reverse Power Rule]:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = -\sqrt{u} + C$
[u] Back-substitute:
$\displaystyle \int {\frac{x}{\sqrt{4 - x^2}}} \, dx = \boxed{ -\sqrt{4 - x^2} + C }$