A metal cube has sides of length 4.5 cm, correct to the nearest 0.5 cm.
The cube is melted down and the metal is used to make small spheres.
Each sphere has a radius of 3 mm, correct to the nearest millimetre.
Work out the greatest number of spheres that could be made from the metal.

Answer:714.1

Step-by-step explanation:

500 times tan(55)

We can use the tangent function from trigonometry to estimate the depth of the crater. The depth is approximately 714.1 meters when the length of the shadow is 500 meters and the angle of sun elevation is 55 degrees.

To solve this problem, we can use trigonometry, specifically the tangent function. The tangent function of an angle in a right triangle is equal to the ratio of the opposite side over the adjacent side. Here, the shadow length of the moon's crater functions as the adjacent side, and the depth of crater is the side opposite to the angle.

So tangent(55°) = depth / 500 meters.

To find the depth, rearrange the equation to multiply both sides by 500: depth = 500 * tangent(55°).

Using a calculator, you'll find that the tangent of 55° is approximately 1.4281. So then your final depth equation would look like: depth = 500 meters * 1.4281. By doing this calculation, we find depth ≈ 714.05 meters, and rounding this to the nearest tenth, we have 714.1 meters. So the estimated depth of the crater is 714.1 meters.

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Answer:

  see attached

  angles: 39.8°, 68.2°; side: 8

Step-by-step explanation:

The triangle and its measurements are shown in the attachment.

_____

If you do this with pencil and paper and protractor, likely your angle measurements will only be to the nearest degree.

Answer:

Step-by-step explanation:

2 out of 4 throws:

Let x more throws is made to achieve 75%

Then the equation would be:

Answer: d.16 days

Step-by-step explanation:

Hi, using  PERT technique we can calculate the mean by applying the next formula:

Mean = (a + 4m + b)/6

Where:

a = optimistic time

m = most likely time

b = pessimistic time

Replacing with the values given:

Mean = (12 +4 (15) + 24)/6

Solving

m = (12+ 60+24)/6

m= 96/6

m = 16 days

Feel free to ask for more if needed or if you did not understand something.

Answer:

The answer is D

Step-by-step explanation:

Surface Area is the outside part of a shape. Opposite of Volume

To find the area of one side its L x H

So 7 x 7 = 49

Since all the sides of the cube are the same you don't need to figure out the area of the other sides

so 49 x 6 sides = 294

Answer:

SA =294 units^2

Step-by-step explanation:

The surface area of a cube is found by the following

SA = 6 s^2 where s is the side length

SA = 6* 7^2

SA = 6*49

SA =294 units^2

Answer:

Step-by-step explanation:

Given that an aquarium has exhibits that feature different marine animals.

Also given that [tex]\frac{5}{8}[/tex] of the staff are male.

[tex]\frac{5}{12}[/tex] of the staff works part time at the aquarium

 Let the entire staff is represented by the fraction [tex]\frac{8}{8}[/tex].

[tex]\frac{8}{8}-\frac{5}{8}[/tex]

[tex]=\frac{8-5}{8}[/tex]

[tex]=\frac{3}{8}[/tex]

Answer:

D) 25.5 cm

Step-by-step explanation:

Circumference = pi × d

20 = 3.14 × d

d = 6.3694267516

Diameter = length of one side

Perimeter of the square = 4s

4(6.3694267516)

25.4777070064 cm

From the options, closest is 25.5

Answer:

$11.57

Step-by-step explanation:

Let's call the price of the coffee two years ago by X.

The price increased 10% per year (that is, the price is multiplied by 1+0.1=1.1) over two years, so the current price is:

X * 1.10 * 1.10 = X * 1.21

If the current price is $14, we have that:

X * 1.21 = 14

X = 14/1.21 =  11.57

The price of the coffee two years ago was $11.57

Answer:

360 combinations

Step-by-step explanation:

To calculate the number of different combinations of 2 different flavors, 1 topping, and 1 cone, we are going to use the rule of multiplication as:

              6          *        5             *            4           *          3             = 360

       1st flavor           2nd flavor              topping              cone

Because first, we have 6 possible options for the flavor, then we only have 5 possible options for the 2nd flavor. Then, we have 4 options for the topping and finally, we have 3 options for the cone.

It means that there are 360 different combinations of two different flavors, one topping, and one cone are possible

Since the odds against choosing the lemon-flavored piece wasn't included, let us now assume that it is 2/5

Answer:

The Probability of choosing a lemon-flavored piece is 5/7

Step-by-step explanation:

Please kindly see the attached files for explanation

N equals 78

The equation: (56+n)/2 - 40=27

Add 40 to 27=67

Multiply everything by 2 leaving you with 56+n=134

Subtract 56 from 134

Leaves you with n=78

If you plug it in you would get 67-40, which equals 27

Complete question is;

In a race that consisted of three parts, the cycling part was 12 1/2 miles long. The running part of the race was 1/4 the distance of the cycling part. The kayaking part of the race was 1/2 the distance of the running part. What was the entire distance, in miles of the race?

Answer:

Total distance of race = 17.1875 miles

Step-by-step explanation:

The 3 parts of the race are; cycling, running and kayaking.

The cycling distance was; 12½ miles

We are told that the running part was ¼ of the cycling distance. Thus;

Running distance = ¼ x 12½ = ¼ x 25/2 = 25/8 miles

Lastly, we are told that the kayaking part was ½ the distance of the running part. Thus;

Kayaking distance = ½ x 25/8 = 25/16

Thus,total distance of race = cycling distance + running distance + kayaking distance = 12½ + 25/8 + 25/16 = 17.1875 miles

Answer: A) organized in similar manner adjacent to each other, and are anatomically similar from one person to the next.

The physical organization of the motor cortex and somatosensory cortex, which are located next to one another, is the same in every individual. Hence, Option A is correct.

The brain's cerebral cortex is located on the outside. It looks wrinkled because of the numerous folds on its surface. Numerous deep grooves, or sulci, and elevated regions, or gyri, make up the folds.

These folds increase the surface area of the cerebral cortex, which enables more nerve cells to handle significant amounts of information. A nerve cell's dendrites are the area where a chemical communication from another cell is received. The mass of the brain is roughly divided in half by the cerebral cortex.

There are between 14 billion and 16 billion nerve cells in each of the six layers that make up the cerebral cortex. The brain's gray matter, which is located in the outer layer, is made up of nerve cell bodies, including dendrites, the end of nerves.

Therefore, Option A is correct.

Learn more about cortex from here:

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Answer:

The 99% confidence interval is (553.7523, 582.2477)

Step-by-step explanation:

The formula for the confidence interval is

[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]

Where:

s = Standard deviation

z = t[tex]_{df}[/tex] since the population variance is unknown

df = Degrees of freedom

n = Sample count

Which gives

[tex]568 \pm t_{79}(0.05\%) \frac{48.28}{\sqrt{80} }[/tex]

= 568 [tex]\pm[/tex] 2.64×5.4

(553.7523, 582.2477)

That is there is a 99% chance that the mean weight of a jar of jelly is

553.75 < μ < 582.25.

Answer:

the answer is 5

Step-by-step explanation:

YW

Answer:

There are 5 faces in a triangular prism

I hope this help. If I'm wrong/made any mistakes please let me know so that I can learn from it!

Answer:

I'm newbie here

Step-by-step explanation:

Elimination Method.

4x + 6/y = 15 → step 1

6x - 8/y = 14 → step 2

so,

4x + 6/y = 15 |×6|

6x - 8/y = 14 |×4|

24x + 6/y(6) = 90

24x - 8/y(4) = 56

24x + 36/y = 90

24x - 32/y = 56

____________ _

68/y = 34

68 = 34y

34y = 68

y = 2

subsitution y = 2 to..

4x + 6/y = 15

4x + 6/2 = 15

4x + 3 = 15

4x = 12

x = 3

So, for x is 3, and for y is 2

Answer:

x = 3, y = 2

Step-by-step explanation:

Multiply equation 1 by -6

-24x - 36/y = -90

Multiply equation 2 by 4

24x - 32/y = 56

Add the two equations:

-36/y - 32/y = -34

-68/y = -34

y = -68/-34

y = 2

4x + 6/2 = 15

4x = 15 - 3

4x = 12

x = 3

Given Information:

Coastline of Canada = 202080 km

Coastline of British Columbia = 2/15 of Coastline of Canada

Required Information:

How long is the coastline of British Columbia = ?

Answer:

Coastline of British Columbia is 26944 km long

Step-by-step explanation:

We are given the length of Coastline of Canada that is 202080 km

We also know that Coastline of British Columbia is 2/15 of the Coastline of Canada.

So,

Coastline of British Columbia = (2/15)*202080

Coastline of British Columbia = 26944 km

Therefore, the Coastline of British Columbia is about 26944 km.

Answer:

He use 120 grams of flour.

Step-by-step explanation:

Given:

Flaky pastry can be made using flour and fat in the ratio 4 : 3. Jake makes some flaky pastry using 90 grams of fat.

Now, to find the weight of flour he use in making flaky pastry.

Let the weight of flour be [tex]x.[/tex]

Weight of fat = 90 grams.

The ratio of flour and fat used in making flaky pastry is 4 : 3.

As, 4 is equivalent to 3.

Thus, [tex]x[/tex] is equivalent to 90.

Now, to solve using cross multiplication method:

[tex]\frac{4}{3} =\frac{x}{90} \\\\By\ cross\ multiplying\ we\ get:\\\\360=3x\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\120=x\\\\x=120\ grams.[/tex]

Therefore, he use 120 grams of flour.

Final answer:

The rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec. The rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.

Explanation:

To solve for the rates at which the tip of the shadow is moving away from the pole and from the person, we can use similar triangles and related rates. Let's solve each part step by step:

a. Rate the tip of the shadow is moving away from the pole:

We have a right triangle formed by the pole, the person, and the tip of the shadow. Let x be the distance between the person and the tip of the shadow.

Since the person is moving away from the pole at a rate of 2 ft/sec, dx/dt = 2 ft/sec.

Using the similar triangles, we have:

(12 ft + 5.5 ft) / x = 12 ft / (x + 25 ft)

Simplifying the equation gives:

17.5x + 437.5 = 12x + 300

5.5x = 137.5

x = 25 ft

Now, let's differentiate both sides of the equation with respect to time t:

17.5 (dx/dt) = 12 (dx/dt) + 0

17.5 (dx/dt) - 12 (dx/dt) = 0

5.5 (dx/dt) = 0

dx/dt = 0 ft/sec

So, the rate at which the tip of the shadow is moving away from the pole when the person is 25 ft from the pole is 0 ft/sec.

b. Rate the tip of the shadow is moving away from the person:

Using the similar triangles, we have:

(12 ft + 5.5 ft) / x = 5.5 ft / 25 ft

Simplifying the equation gives:

17.5x = 137.5

x = 7.857 ft

Now, let's differentiate both sides of the equation with respect to time t:

17.5 (dx/dt) = 5.5 (dx/dt) + d(7.857)/dt

12 (dx/dt) = d(7.857)/dt

dx/dt = (d(7.857)/dt) / 12

dx/dt = (0 ft/sec) / 12

So, the rate at which the tip of the shadow is moving away from the person when the person is 25 ft from the pole is 0 ft/sec.

Answer:

X = 1.183

Step-by-step explanation:

X/6.5=0.1820

Multiply each side by 6.5

X/6.5 * 6.5=0.1820*6.5

X = 1.183

Answer:

the distance travelled in 3 3/4 hours is 37/8 km

Answer:

170°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2)

Here n = 36, thus

sum = 180° × 34 = 6120°

The size of each interior angle = [tex]\frac{6120}{36}[/tex] = 170°

Final answer:

The sum of the measures of each interior angle of a regular 36-gon is 6120 degrees.

Explanation:

For a regular 36-gon, or a polygon with 36 sides, we can calculate the sum of the measures of the interior angles using the formula ((n - 2) × 180°), where n is the number of sides. So for a regular 36-gon:

((36 - 2) × 180°) = (34 × 180°) = 6120°.

Therefore, the sum of the measures of each interior angle of a regular 36-gon is 6120 degrees.

Answer:

18x^2 - 45x + 28 , ( r + 4 )( r + 3 )

Step-by-step explanation:

Heres your answers :)

Answer:

[tex]d = |h - 0\,ft|[/tex], The driver is 350 feet below sea level.

Step-by-step explanation:

The distance of the driver from the sea level is given by the following expression:

[tex]d = |h - 0\,ft|[/tex]

[tex]d = |-350\,ft-0\,ft|[/tex]

[tex]d = |-350\,ft|[/tex]

[tex]d = 350 \,ft[/tex]

The driver is 350 feet below sea level.

Answer:

Driver is 350 Below sea Level

Step-by-step explanation:

Driver has Elevation of -350 meters, negative indicates below sea level.

Therefore it can be inferred that the driver is 350 below sea level.

Answer:

Domain of the function is (inf, -inf)

Step-by-step explanation:

Answer:

(0.55, 0.75)

Step-by-step explanation:

The standard deviation and range are both used to measure the spread of a data set. The number of the range and standard deviation gives us information in its own way how spaced out the data are due to the fact that they are both a measure of variation. However, there is not an explicit relationship between the range and standard deviation, there is a rule of thumb that can be useful to relate these two statistics. This relationship is sometimes referred to as the range rule for standard deviation.

The range is estimated to be 6 standard deviations wide.  Therefore, the standard deviation is:

Standard deviation= maximum sample proportion - minimum sample proportion / 6

σ = (0.72 - 0.42) / 6

σ = 0.05

The margin of error is defined as a statistic showing the amount of random sampling error in the result of a survey. The greater the margin of error, the lesser the confidence that a poll result would reflect the result of a survey of the entire population.

Here, the margin of error is ±2σ, so:

ME = ±0.10

Interval estimation in statistics is the use of sample data to compute an interval of possible values of an unknown population parameter. This is therefore in contrast to point estimation, which gives a single value.

Therefore, the interval estimate is:

(0.65 - 0.10, 0.65 + 0.10)

(0.55, 0.75)



Final answer:

A study by the Annenberg Foundation shows a stark lack of knowledge about the Legislative, Executive, and Judicial branches of the U.S. government. Educational resources can help improve public understanding of these branches, which are pivotal for civic engagement and democratic processes.

Explanation:

The Annenberg Foundation study highlights a concerning lack of knowledge among the U.S. adult population regarding the basic structure of their government. Despite the importance of understanding the three branches of the U.S. government, which include the Legislative, Executive, and Judicial branches, a majority of adults struggle to identify all three.

The Legislative branch is responsible for making laws and is embodied in Congress, which is divided into the House of Representatives and the Senate. The Executive branch, headed by the President, is tasked with implementing and executing the laws passed by Congress. The Judicial branch, represented by the Supreme Court and other federal courts, interprets the laws and adjudicates legal disputes under the law.

Understanding these branches and their functions is critical for civic engagement and informed participation in democratic processes. Educational resources such as videos, games, and government websites can help improve civic knowledge and awareness of the structure and roles of government.

Answer:

i think it is x=5y

Step-by-step explanation:

Answer:

y - 1 = -1/5(x + 5)

y - 1 = -1/5x - 1

y = -1/5x

Step-by-step explanation:

Answer:

[tex]cos(G)=\frac{28}{53}[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle EFG

[tex]cos(G)=\frac{GF}{EG}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(G)=\frac{28}{53}[/tex]