The president of the student council wants to survey the student population. She decides to take a random sample of

What is the answer of 3[4(2³)-5²+7(8+4²)-16]?

Montano1993 [528]

3[4(23)-52+7(8+42)-16]

3 x (4 x 8 - 52 + 7 x (8 + 42) - 16)

3 x (32 - 52 + 7 x (8 + 42) - 16)

3 x (16 – 52 + 7 x (8 + 42))

3 x (16 - 25 + 7 x (8 + 42))

3 x (-9 + 7 x (8 + 42))

3 x (-9 +7 x (8 + 16))

3 x (-9 + 7 x 24)

3 x (-9 + 168)

3 x 159

477

8 0

2 years ago

Whats the length in meters of CD?

Gnesinka [82]

Answer:

The length of DC in meters is $\frac{60}{13}$ ⇒ A

Step-by-step explanation:

In the circle O

∵ AB passing through O

∴ AB is a diameter

∵ D is on the circle

∴ ∠ADB is an inscribed angle subtended by arc AB

∵ Arc AB is half the circle

→ That means its measure is 180°

∴ m∠ADB = $\frac{1}{2}$ × 180° = 90°

In ΔADB

∵ m∠ADB = 90°

∵ AD = 5 m

∵ BD = 12 m

→ By using Pythagorase Theorem

∵ (AB)² = (AD)² + (DB)²

∴ (AB)² = (5)² + (12)²

∴ (AB)² = 25 + 144 = 169

→ Take square root for both sides

∴ AB = 13 m

∵ ∠ADB is a right angle

∵ DC ⊥ AB

∴ DC × AB = AD × DB

→ Substitute the lengths of AB, AD, and DB

∵ DC × 13 = 5 × 12

∴ 13 DC = 60

→ Divide both sides by 13

∴ DC = $\frac{60}{13}$ m

∴ The length of DC in meters is $\frac{60}{13}$

6 0

2 years ago

Figure ABCD is reflected over the x-axis to create figure PQRS. What are the coordinates of point Q?

Mekhanik [1.2K]

Answer:

Q = (1, -5)

Step-by-step explanation:

Reflection over x-axis (x,y) → (x,-y)

B = (1,5)

Q = (1,-5)

4 0

2 years ago

John made 3 out of 12 attempted baskets in the game. What percentage of the shots did he make?

erik [133]

Answer:25 percent

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

astraxan [27]

ANSWER

The value of the expression is
$- 1$

EXPLANATION

Method 1: Rewrite as product of
${i}^{2}$

The expression given to us is,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4}$

We use the fact that
${i}^{2} = - 1$
to simplify the above expression.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{1} \times {i}^{3} \times {i}^{2} \times {i}^{4}$

This implies,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2} \times {i}^{2}$

We substitute to obtain,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times - 1 \times - 1 \times - 1\times - 1 \times - 1$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = 1\times 1 \times 1 \times - 1 = - 1$

Method 2: Use indices to solve.

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{0 + 1 + 2 + 3 + 4}$

This implies that,

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = {i}^{10}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( {{i}^{2}} )^{5}$

${i}^{0} \times {i}^{1} \times {i}^{2} \times {i}^{3} \times {i}^{4} = ( - 1 )^{5} = - 1$

8 0

3 years ago

Read 2 more answers