Which phrase describes the volume of a -dimensional figure?

Sanja made a hole-in-one on the sixth hole of miniature golf 8 times and missed it 4 times. If Sanja attempts 24 more holes-in-o

hram777 [196]

Answer:

16 holes in ones

Step-by-step explanation:

I just did the guiz and got that one right

7 0

3 years ago

Read 2 more answers

Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

4 0

3 years ago

A baker is using a cookie recipe that calls for 2 1/4 cups of flower to yield 36 cookies. How many flour will the baker need to

Kryger [21]

90/36 is 2.5, so the Baker needs to make 2.5 batches of cookies

2.5 batches of cookies x 2.25 cups of flour

is 5.625 cups of flour

which is 5 5/8 cups of flour

6 0

3 years ago

1. Write the following in exponential form and as a multiplication sentence using only 10 as a factor

Irina-Kira [14]

Answer:

1. a. 1,000 = 10³ = 10 × 10 × 10

b. 100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10² = 300

b. 2.16 × 10⁴ = 21,600

c. 800 ÷ 10³ = 0.8

d. 754.2 ÷ 10² = 7.542

Step-by-step explanation:

3. a. 1,000

There are 3 zeros in 1000. This is equivalent to 10 raised to the power of 3. Writing this in multiplication sentence using 19 as the only factor, we would have:

1,000 = 10³ = 10 × 10 × 10

b. 100 × 100

Using the same logic as explained in (a) above, we would have:

100 × 100 = 10² × 10² = 10 × 10 × 10 × 10

2. a. 3 × 10²

Convert 10² to 100 and multiply both numbers

3 × 10² = 3 × 10 × 10 = 3 × 100 = 300

b. 2.16 × 10⁴

2.16 × 10 × 10 × 10 × 10 = 2.16 × 10,000

Multiplying both numbers, since we have 4 zeros, move the decimal point 4 places to the right.

2.16 × 10,000 = 21,600

c. 800 ÷ 10³ = 800 ÷ 10 × 10 × 10

800 ÷ 1,000

There are 3 zeros in 1000, since we are dividing, move the decimal point 3 places to the left.

800 ÷ 1,000 = 0.8

d. 754.2 ÷ 10² = 754.2 ÷ 10 × 10

754.2 ÷ 100

Move the decimal point 2 places to the left.

754.2 ÷ 100 = 7.542

5 0

3 years ago

SOS HELPPPP

Hunter-Best [27]

Answer:

18

Step-by-step explanation:

5 0

3 years ago