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Dmitrij [34]
3 years ago
5

A cone has a slant height of 10 centimeters and a lateral area of 60π square centimeters. what is the volume of a sphere with a

radius equal to that of the cone?
Mathematics
1 answer:
morpeh [17]3 years ago
5 0
The surface area of a cone is A= \pi r^{2}+ \pi r \sqrt{ h^{2} + r^{2} }. Lateral area is A= \pi r \sqrt{ r^{2} + h^{2} }. Here \sqrt{ h^{2} + r^{2} } is a slant height. 

Using this information we can write that 60 \pi =10 \pi r and r=6 cm

The volume of the sphere is given by V= \frac{4}{3} \pi r^{3}. If we calculate it, we'll obtain V=288 \pi
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Daniel wanted to know his approximate score on the final exam for his mathematics class. His professor hinted that his score was
Marizza181 [45]

Answer:

The raw score for his exam grade is 99.69.

Step-by-step explanation:

Given : The professor announced that the mean for the class final exam was 88 with a standard deviation of 7. Given Daniel's z score of 1.67.

To find : What is the raw score for his exam grade?

Solution :

The formula use to find the z-score is

z=\dfrac{x-\mu}{\sigma}

Where, z=1.67 is the z-score

\mu=88  is the means

\sigma=7 is the standard deviation

x  is the raw score for his exam grade

Substitute the values,

1.67=\dfrac{x-88}{7}

1.67\times 7=x-88

11.69=x-88

x=88+11.69

x=99.69

Therefore, the raw score for his exam grade is 99.69.

7 0
3 years ago
Michael rented a truck for one day. There was a base fee of $19.99 , and there was an additional charge of 88 cents for each mil
Vsevolod [243]

163 Miles


(163.43-19.99)÷0.88=163

4 0
3 years ago
How many kilograms of a 5% salt solution and how many kilograms of a 15% salt solution must be mixed together to make 45kg of an
JulsSmile [24]

Answer:

31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Step-by-step explanation:

Let us assume that the number of kilograms of a 5% salt solution used be x .

Let us assume that the number of kilograms of a 15% salt solution used be y .

As given

A 5% salt solution and 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Equation becomes

x + y = 45

5% is written in the decimal form .

= \frac{5}{100}

= 0.05

15% is written in the decimal form .

= \frac{15}{100}

= 0.15

8% is written in the decimal form .

= \frac{8}{100}

= 0.08

Thus

Concentration of 5% salt solution × Number of kilograms of 5% salt solution used + Concentration of 15% salt solution × Number of kilograms of  15% solution used = Concentration of 8% salt solution × Number of kilograms of 8% salt solution

Thus

0.05x + 0.15y = 0.08 × 45

Simplify the above

\frac{5x}{100} + \frac{15y}{100} = \frac{8\times 45}{100}

5x + 15y = 360

Thus two equations becomes

x + y = 45

5x + 15y = 360

Multiply x + y = 45 by 5 and subtracted from 5x + 15y = 360 .

5x - 5x + 15y - 5y = 360 - 225

10y = 135

y = \frac{135}{10}

y = 13.5 kilograms

Put value of y in the equation

x + 13.5 = 45

x = 45 - 13.5

x = 31.5 kilograms

Therefore the 31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

5 0
3 years ago
the base of the Eiffel tower has a square with an area of 15625 square feet what is the length of the side of the base​
tigry1 [53]
77374747484847373848484848
6 0
3 years ago
Which of the following is defined by a line parallel to one side of a triangle
Katarina [22]

Answer:

Triangle Proportionality Theorem is  defined by a line parallel to one side of a triangle  divides the other two sides proportionally.

Step-by-step explanation:

Triangular Proportionality Theorem states that:

  • If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.

Let us consider the triangle ΔABC as shown in attached figure.

If

DE║AC

then

\frac{BD}{DA} = \frac{BE}{EC}

Therefore, Triangle Proportionality Theorem is  defined by a line parallel to one side of a triangle  divides the other two sides proportionally.

Keywords: Triangle Proportionality Theorem, triangle, line segment

Learn more about Triangle Proportionality Theorem from brainly.com/question/11827486

#learnwithBrainly

3 0
3 years ago
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