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3 years ago

Please help!! See the attachment, please!

Mathematics

1 answer:

topjm [15]3 years ago

5 0

Answer:

$946$

Step-by-step explanation:

we know that

The formula to find the sum is equal to

$S=(a1+an)n/2$

where

a1 is the first term

an is the last term

n is the number of terms

In this problem we have

$n=11$

$a1=(98-2(1))=96$

$an=(98-2(11))=76$

substitute the values in the formula

$S=(96+76)(11/2)=946$

You might be interested in

What is the equivalent fraction?

Vera_Pavlovna [14]

$0.7 = \dfrac{7}{10} = \dfrac{7 \times 10 }{10 \times 10} = \dfrac{70}{100}$

Answer: 70/100

3 0

3 years ago

Read 2 more answers

Which sentence correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14

denis-greek [22]

Answer:

Option (c) is correct.

68% of the data points lie between 10 and 18.

Step-by-step explanation:

Given : a normal distribution with a standard deviation of 4 and a mean of 14

We have to choose the sentence that correctly describes a data set that follows a normal distribution with a standard deviation of 4 and a mean of 14.

Since, given 68% data.

We know mean of data lies in middle.

And standard deviation is distribute equally about the mean that is 50% of values less than the mean and 50% greater than the mean.

So, 68% of data lies

mean - standard deviation = 14 - 4 = 10

mean + standard deviation = 14 + 4 = 18

So, 68% of the data points lie between 10 and 18.

4 0

3 years ago

Which statements about the cylinder are true? Select two

Rus_ich [418]

Answer:

The radius of the cylinder is (1/2)x units

The area of the cylinder’s base is (1/4)πx2 square units

The height of the cylinder is 4x units

Step-by-step explanation:

The complete question is

A cylinder with a base diameter of x units has a volume of πx3 cubic units.

Which statements about the cylinder are true? Check all that apply.

(1) The radius of the cylinder is (1/2)x units.

(2) The radius of the cylinder is 2x units.

(3) The area of the cylinder’s base is (1/4)πx2 square units.

(4) The area of the cylinder’s base is (1/2)πx2 square units.

(5) The height of the cylinder is 2x units.

(6) The height of the cylinder is 4x units

we know that

The volume of the cylinder is equal to

$V=\pi r^{2}h$

we have

$r=\frac{x}{2}\ units$ ----> the radius is half the diameter

$V=\pi x^{3}\ units^3$

substitute the given values in the formula of volume

$\pi x^3=\pi (\frac{x}{2})^{2}h$

solve for h

simplify

$x=(\frac{1}{4})h$

$h=4x\ units$

Verify each statement

(1) The radius of the cylinder is (1/2)x units

The statement is true

see the explanation

(2) The radius of the cylinder is 2x units.

The statement is false

Because, the radius of the cylinder is x/2 units

(3) The area of the cylinder’s base is (1/4)πx2 square units

The statement is true

Because, the area of the cylinder's base is equal to

$A=\pi r^{2}$

$r=\frac{x}{2}\ units$

substitute

$A=\pi (\frac{x}{2})^{2}$

$A=\frac{\pi x^2}{4}\ units^2$

(4) The area of the cylinder’s base is (1/2)πx2 square units.

The statement is false

Because, the area of the cylinder's base is equal to

$A=\frac{\pi x^2}{4}\ units^2$

see the part (3)

(5) The height of the cylinder is 2x units.

The statement is false

Because, the height of the cylinder is 4x units (see the explanation)

(6) The height of the cylinder is 4x units

The statement is true

see the explanation

7 0

3 years ago

The source of the error when a computer system fails are either the disk drive, the computer memory, or the operating system. Ve

faltersainse [42]

Answer:

The probability of an operating system error given that a failure has ocurred is P(O/E)= 0.19

Step-by-step explanation:

Hello!

There are three different sources of error when a computer system fails:

D: disk drive error. ⇒ P(D)= 0.50

M: computer memory error. ⇒P(M)= 0.20

O: operating systems error. ⇒ P(O)= 0.30

According to the component perdormance standard:

The probability of failure "E", given that there is a disk drive error is P(E/D)= 0.40

The probability of failure "E", given that there is a computer memory error is P(E/M)= 0.6

The probability of failure "E", given that there is a operating system error is P(E/O)= 0.25

You need to calculate the probability of an operating system error given that a failure has ocurred, symbolically:

P(O/E)

$P(O/E)= \frac{P(OnE)}{P(E)}$

To reach the probability of the marginal E you have to add all intersections between the event "E" and the events "D", "M" and "O"

D M O Total

E: P(E∩D); P(E∩M); P(E∩O); P(E)

Using the formula of the conditional probability I'll clear all three intersections using the known probabilities:

General formula: $P(A/B)= \frac{P(AnB)}{P(B)}$ ⇒ $P(AnB)= P(A/B)*P(B)$

P(E∩D)= P(E/D)*P(D)= 0.4*0.5= 0.2

P(E∩M)= P(E/M)*P(M)= 0.6*0.2= 0.12

P(E∩O)= P(E/O)*P(O)= 0.25*0.3= 0.075

P(E)= P(E∩D) + P(E∩M) + P(E∩O)= 0.2+0.12+0.075= 0.395

$P(O/E)= \frac{P(OnE)}{P(E)} = \frac{0.075}{0.395}= 0.189 = 0.19$

I hope it helps!

7 0

3 years ago

Which expression is NOT equivalent to 8 times −5 and 1/4? Drag this expression to the box.

timurjin [86]

The correct answer is 8×(-6) - 8×3/4.

Simplifying this problem is the same as the problem 8× - 6 3/4, not 8× -5 1/4.

6 0

3 years ago

Please help!! See the attachment, please!​

Please help!! See the attachment, please!