The sum of 5 consecutive integers is 110. What is the fourth number in the sequence?

[tex]10(x-14)=90[/tex]

The volume of a sphere is.

Answer:

C

Step-by-step explanation:

141.9in3

To find the height of the mat off the ground, we can use trigonometry.

To find the height of the mat off the ground, we can use trigonometry. Since the angles of the right triangle formed by the mat are 60° and 30°, we can determine the height using the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.

In this case, the side opposite the 30° angle is the height of the mat, and the hypotenuse is the length of the mat, which is 5 feet. So, we have sin(30°) = height/5. Solving for the height, we get height = 5 * sin(30°) = 5 * 0.5 = 2.5 feet.

Therefore, the mat is 2.5 feet off the ground.

The correct answer is option B. The height of the gymnastics mat off the ground is [tex]\frac{5\sqrt{3}}{3}}[/tex] feet.

Given that the gymnastics mat extends 5 feet across the floor, this length corresponds to the side opposite the 60° angle in the right triangle.

Let's denote the length of the side opposite the 30° angle as [tex]$x$[/tex].

According to the properties of a 30-60-90 triangle, the side opposite the 60° angle is [tex]\sqrt{3}[/tex] times the side opposite the 30° angle, so we have:

[tex]\[ 5 = x\sqrt{3} \][/tex]

To find [tex]$x$[/tex], we divide both sides of the equation by [tex]$\sqrt{3}$[/tex]:

[tex]\[ x = \frac{5}{\sqrt{3}} \][/tex]

To rationalize the denominator, we multiply the numerator and the denominator by [tex]$\sqrt{3}$[/tex]:

[tex]\[ x = \frac{5\sqrt{3}}{3} \][/tex]

The complete question is:

From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?

A. [tex]\frac{5}{2}[/tex] ft.

B. [tex]\frac{5\sqrt{3}}{3}[/tex] ft.

C. [tex]5\sqrt{3}}[/tex] ft.

D. 10 ft.

The total wage for full-time workers is 84000$.

Simplifying a value simply means finding it in its most basic form. To simplify the problem, we use a number of approaches, including PEMDAS and BODMAS. Aside from the value, the variables must also be made simpler.

Given, A factory employs 3 full-time workers and 6 part-time workers; the amount earned by each is $36,000 for the production supervisor; $27,000 for the machine operator; $21,000 for the general assistant; a total of $50,000 for part-time staff.

The Total wage for the full-time staff =  36000 + 27000 + 21000

The total wage for the full-time staff = 84000

Therefore 84000$ was the wage bill for the 3 full-time staff.

Learn more about simplification here:

https://brainly.com/question/746677

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46.08 grams of protine daily

Final answer:

To find the map distance of an 8 km actual distance on a map with a scale of 1:50,000, convert 8 km to meters (8,000 m), and divide by the scale factor (50,000) to get the map distance of 16 centimeters.

Explanation:

To calculate the length of an 8 km distance on a map with a scale of 1:50,000, you can use the formula:
Actual distance (in real life) / Scale = Distance on the map. This can be rearranged to: Distance on the map = Actual distance / Scale. Therefore, 8 km / 1:50,000 conversion would be calculated as follows:

The distance of 8 km is represented as 16 centimeters on a map with a scale of 1:50,000.

The probability of rolling an even number on a fair number cube and drawing a red card from a standard deck of cards is 1/4.

The probability of rolling an even number on a fair number cube is 1/2 because there are three even numbers (2, 4, 6) out of a total of six possible outcomes (1, 2, 3, 4, 5, 6).

The probability of drawing a red card from a standard deck of cards is 26/52, or 1/2, because there are 26 red cards (13 hearts + 13 diamonds) out of a total of 52 cards in the deck.

To find the probability of both events happening, you multiply the probabilities together: (1/2) * (1/2) = 1/4.

The probability of rolling an even number on a six-sided die and drawing a red card from a standard deck of cards is 1/4. P(EM) refers to the probability of rolling a number that is both even and a multiple of three. P(E OR M) represents the probability of rolling a number that is either even or a multiple of three.

The probability of rolling an even number on a fair six-sided die is calculated by counting the even numbers (2, 4, 6) and dividing by the total number of sides, which gives us P(E) = 3/6 = 1/2. For drawing a red card from a standard deck of 52 playing cards, half of the cards are red, so P(Red) = 26/52 = 1/2. To find the combined probability of both independent events occurring, we multiply their respective probabilities: P(Even number and Red card) = P(E) × P(Red) = (1/2) × (1/2) = 1/4.

What does P(EM) mean in words?

P(EM) represents the probability of the intersection of two events, E and M, meaning the probability that the number rolled is both even and a multiple of three.

What does P(E OR M) mean in words?

P(E OR M) signifies the probability of the union of two events, E or M, which is the chance that the number rolled is either even or a multiple of three.

110% =1.10

 multiply the old price by that

2.85 *1.10 = 3.135

 round to 3.14

 new price is $3.14

Answer:

Option D. [tex](\frac{1}{16}) ft^{3}[/tex]

Step-by-step explanation:

Since formula to find volume of a cube is V = (side)³

and one side of the cube is [tex](\frac{1}{4})[/tex] foot

Therefore, volume of the cube will be

V = [tex](\frac{1}{4})[/tex]³

We have to calculate the volume of 4 cubes

4 × V = 4 × [tex](\frac{1}{4})[/tex]³

=  [tex]\frac{4\times 1}{4^{3}}=\frac{1}{4^{2}}=(\frac{1}{16})ft^{3}[/tex]

Option D. [tex](\frac{1}{16}) ft^{3}[/tex] is the answer.

Answer:

Now they have left to decorate 20% cupcakes.

Step-by-step explanation:

Darren and Latisha are decorating cupcakes for a bake sale.

They need to decorate 100 cupcakes.

Each of them has decorated 40% of the cupcakes = 40% + 40% = 80%

Both of them has decorated 80% of the cupcakes.

80% of 100 cupcakes = 80 cupcakes

Now they have left to decorate 100 - 80 = 20

Now they have left to decorate 20% cupcakes.

1 ton = 2000 pounds

4* 2000 = 8000 pounds total

8000 * 0.60 = $4,800.00

it will cost $4,800 to move

Answer:

Step-by-step explanation:

1 ton = 2000 pounds

4* 2000 = 8000 pounds total

8000 * 0.60 = $4,800.00

it will cost $4,800 to move