How thick is the crust layer of the earth in kilometers?

(1) This series consists of terms of an arithmetic sequence:

179 - 173 = 6

173 - 167 = 6

and so on, so that the n-th term in the series is (for n ≥ 1)

a(n) = 179 - 6 (n - 1) = 185 - 6n

Then the sum of the first 53 terms is

[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\sum_{n=1}^{53}1-6\sum_{n=1}^{53}n[/tex]

[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = 185\times53-6\times\frac{53\times54}2[/tex]

[tex]\displaystyle\sum_{n=1}^{53}(185-6n) = \boxed{1219}[/tex]

(2) This series has terms from a geometric sequence:

-12 / 6 = -2

24/(-12) = -2

-48/24 = -2

and so on. The n-th term is (again, for n ≥ 1)

a(n) = 6 (-2)ⁿ⁻¹

and the sum of the first 19 terms is

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 + (-2) + (-2)^2 + (-2)^3 + \cdots+(-2)^{19}\right)[/tex]

Multiply both sides by -2 :

[tex]\displaystyle-2\sum_{n=1}^{19}6(-2)^{n-1} = 6\left((-2) + (-2)^2 + (-2)^3 + (-2)^4 + \cdots+(-2)^{20}\right)[/tex]

Subtracting this from the first sum gives

[tex]\displaystyle(1-(-2))\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]

and solving for the sum, you get

[tex]\displaystyle3\sum_{n=1}^{19}6(-2)^{n-1} = 6\left(1 -(-2)^{20}\right)[/tex]

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-2)^{20}\right)[/tex]

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -(-1)^{20}2^{20}\right)[/tex]

[tex]\displaystyle\sum_{n=1}^{19}6(-2)^{n-1} = 2\left(1 -2^{20}\right) = 2-2^{21} = \boxed{-2,097,150}[/tex]

Part 1

Let the consecutive multiples be 5x and 5x + 5

ATQ

5x + 5x + 5 = 55

10x = 55 - 5

10x = 50

x = 5

Answer is 25 and 30

Part 2

Let the number be x , x + 1, x + 2

ATQ

x + x + 1 + x + 2 = 93

3x + 3 = 93

3x = 93 - 3

x = 90/3

x = 30

The integers are 30,31 and 32

Part 3

Let the number be x

ATQ

3x - 5 = 10

3x = 10 + 5

x = 15/3

x = 5

The number is 5

Answered by Gauthmath must click thanks and mark brainliest

Answer:

96 yuan

Step-by-step explanation:

We know how much one yuan is, so we can convert that to $1, Then multiply by 600. To find a USD, we need to divide the yuan by the dollar.

[tex]1/6.11=0.16[/tex]

Now we have a full dollar, and we need to multiply the yuan by 600 to get our 600 dollar value.

[tex]0.16*600=96[/tex]

Answer:

128.06

Step-by-step explanation:

think about the diagonal of the field, breaking up a rectangle into 2 right angled triangles. we are already given the legs of the triangle (80, and 100) and now we have to solve for the hypotenuse (or the diagonal). so use pythagorean theorem :

80^2 + 100^2 = c^2

16400 = c^2

c = 128.06

Answer:

Step-by-step explanation:

10 people don’t play volleyball 120-10=110 110 play one or both games 90+72 =162 which is > 110 by 52

There are 52 people who play volleyball as well as football.

Let A, B be two different sets the,

n (A ∪ B) = n (A) + n (B) − n (A ∩ B) .

"A Venn diagram is a diagram that uses overlapping shapes to illustrate the logical relationships between two or more sets."

For given situation:

Let set A: People playing volleyball

set B: People playing football

⇒ n(A) = 90

⇒ n(B) = 72

Given group is of 120 people.

10 people play neither of games.

This means, only 110 people play football or volleyball or both.

⇒ n(A ∪ B) = 110

Using the Inclusion Exclusion Principle,

n (A ∪ B) = n (A) + n (B) − n (A ∩ B)

⇒ 110 = 90 + 72 - n (A ∩ B)

⇒ n(A ∩ B) = 52

Therefore, 52 people play volleyball as well as football.

Venn-diagram for given information is as shown below.

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Answer:

9.75 meters

Step-by-step explanation:

Davis and Catherine are approximately 13.90 meters apart.

To find the distance between Davis and Catherine, we can use the concept of right triangles and apply the Pythagorean theorem.

Let's consider a right triangle where the distance between Davis and Mrs. Kennedy is the base, the distance between Mrs. Kennedy and Catherine is the height, and the distance between Davis and Catherine is the hypotenuse.

According to the given information, Mrs. Kennedy is 7 meters in front of Catherine, and Davis and Mrs. Kennedy are 12 meters apart.

Using the Pythagorean theorem, we have:

(Base)² + (Height)² = (Hypotenuse)²

Substituting the given values:

(12)² + (7)² = (Hypotenuse)²

Simplifying the equation:

144 + 49 = (Hypotenuse)²

193 = (Hypotenuse)²

Taking the square root of both sides:

√193 ≈ 13.89 = 13.90

Therefore, Davis and Catherine are approximately 13.90 meters apart.

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Answer:

A, B, F

Step-by-step explanation:

2/3 - x + 1/6 = 6x

Collect like terms

2/3 + 1/6 = 6x + x

(4+1) / 6 = 7x

5/6 = 7x

x = 5/6 ÷ 7

= 5/6 × 1/7

x = 5/42

a) 4 - 6x + 1 = 36x

4 + 1 = 36x + 6x

5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

b) 5/6 - x = 6x

5/6 = 6x + x

5/6 = 7x

This is equivalent to the third step of the simplification

c) 4 - x + 1 = 6x

4 + 1 = 6x + x

5 = 7x

x = 5/7

Not equivalent to any of the steps in the simplification above

d) 5/6 + x = 6x

5/6 = 6x - x

5/6 = 5x

x = 5/6 ÷ 5

= 5/6 × 1/5

x = 5/30

Not equivalent to any of the steps in the simplification above

e) 5 = 30x

x = 5/30

Not equivalent to any of the steps in the simplification above

f) 5 = 42x

x = 5/42

Equivalent to the last step of the simplification above

Answer:

The graph is shifted 7 units right and 5 units up.

Answer:

1/2.

Step-by-step explanation:

The inclination of the line to the x axis = 1/3*√3

= √3/3.

This is the tangent of the angle.

The sine of the angle =√3/hypotenuse.

The hypotenuse = √( √3)^2 + 3^2)    (By the Pythagoras theorem)

= √12

= 2√3

Therefore the required sine is  √3/  2√3

= 1/2.

I think that's what you want!!

Answer:

30

Step-by-step explanation:

Angle PNM = 180-105

                   = 75

IF PM = PN  then

<PNM = <PMN = 75

<PMN + <PNM + <P = 180 since they form a triangle

75 + 75 + x = 180

150+x = 180

x = 180-150

x = 30

Answer:

Step-by-step explanation:

180° - <PNQ = <PNM ( Angles in a straight line )

180° - 105° = 75°

<PMN = < PNM = 75°

<PMN + <PNM + <MPN = 180°

75 ° + 75° + <MPN = 180°

<MPN = 180° - 150°

<MPN = 30°

Answer:

1/25 of a mile per minute, I think

Step-by-step explanation:

Answer:

1/25

Step-by-step explanation:

V=S:t=1/5÷5=1/5*1/5=1/25

Answer:

-x+5

hope this help!!!

Step-by-step explanation:

Answer:

I am currently taking a unit test and I just got this question. I believe it is the answer but I haven't submitted yet.

Step-by-step explanation:

The answer I chose seems to be the only logical answer.

Answer:

i might be wrong but this is what i put

Step-by-step explanation:

In question 3 it was comparing three triangles where now it is using the triangles to find the area of a square instead of proving that they are the same.

Answer:

GH

Step-by-step explanation:

A secant is a straight line which cuts the circle at 2 points

GH and FE both do this but FE is a special secant, that is the diameter

Then GH is a secant

Answer:

cos x= 11/19

x=54.62

Step-by-step explanation:

use cosine to find the angle

Answer:

-24 x^7

Step-by-step explanation:

(-2x^2)^3 ·3x

(-2x^2) (-2x^2) (-2x^2)*3x

-8 x^6 *3x

-24 x^7

Answer:

(-7, 3)

General Formulas and Concepts:

Algebra I

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify

y - 3 = 4(x + 7)

↓ Compare to Point-Slope Form

Point (-7, 3)

Slope m = 4

Answer:

Step-by-step explanation:

If this is in terms of angles, 4x+6 must be equal to 90 since it is half of the angle produced by a line (180°) So solving for 4x+6=90, x=21

Answer:

3 9/50

Step-by-step explanation:

3.18 is 3 18/100

Simplifying it further you get: 3 9/50

Answer:

OAmalOHopeO

Answer:

The margin of error associated with a 98% confidence interval that estimates the proportion of them that are involved in an after school activity is of 0.1219.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

A simple random sample of 49 8th graders at a large suburban middle school indicated that 84% of them are involved with some type of after school activity.

This means that [tex]n = 49, \pi = 0.84[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].  

Margin of error:

[tex]M = 2.327\sqrt{\frac{0.84*0.16}{49}} = 0.1219[/tex]

The margin of error associated with a 98% confidence interval that estimates the proportion of them that are involved in an after school activity is of 0.1219.

Answer:

I think the answer is C.

Answer:

3 sqrt(3)

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp side / hyp

sin 60 = ZY / 6

6 sin 60 = ZY

6 (sqrt(3) /2) = ZY

3 sqrt(3) = ZY

Step-by-step explanation:

180-46 = 134

180 - 13 = 177

177-134 = 43

? = 43

Answer:

x=5

Step-by-step explanation:

Use the distributive property and the addition and subtraction properties of equality to solve.

3.5+7.56-8.4x=9.38

11.06-8.4x=9.38

-8.4x=-1.68

x=5

Answer:

options:

B,C,D

Step-by-step explanation:

Answer:

The graph solution is defined in the attachment file please find it.

Step-by-step explanation:

The first line equation:

[tex]\to Y= 0.22x + 67.5\\\\[/tex]

The second line equation:

[tex]\to Y= 0.15x + 75.507\\\\[/tex]

Intersection points:

[tex]\to (114.387,92.665)\\\\[/tex]

By adding the value of the first year (1970) into the x-value that is

[tex]\to 114.387+1970=2084.387[/tex]

Answer:

x = 6

Step-by-step explanation:

Since <F = <F, this shows that the triangles are similar. Therefore:

XZ/DF = XY/DE

12/8 = 9/X

Cross multiply

12X = 9*8

12X = 72

X = 72/12

X = 6

Hence the value of x is 6

As the name implies, a two-step equation is an equation that is solved in just two steps. There are several two-step equations; an example that can be set up as a two-step equation is a target savings with an initial amount and a constant rate of savings.

To set up the target savings equation, we consider the following parameters (I will assume values for the parameters).

[tex]Amount = \$1000[/tex]

[tex]Initial\ Capital = \$50[/tex]

[tex]Rate = \$2[/tex]

Let x be the number of savings.

[tex]Initial\ Capital + Rate \times x= Amount[/tex] ----- the equation

Mathematically, we have:

[tex]50 + 2x = 1000[/tex]

The equation is solved as follows:

The first step is to isolate the variable term by subtracting 50 from both sides

So, we have:

[tex]2x = 950[/tex]

The second step is to solve for x by dividing both sides of the equation by 2

[tex]x = 475[/tex]

This means that you have to save $2 in 475 times to reach the target amount

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