What is the sum of the first 7 terms of the series −4+8−16+32−... ?

Answer:

25 cm hope whoever gets to see this has a great day :D

The last two numbers of the given sequence are respectively gotten to be; 83 and 77

From the sequence, we see that;

From 98 to 97, there is a decrease of 1

From 97 to 95, there is a decrease of 2

From 95 to 92, there is a decrease of 3

From 92 to 88, there is a decrease of 4

The sequence pattern of decrease is seen to be: 1, 2, 3, 4

Thus, by inference we can say that the next decrease is 5. Thus,

Next number in sequence = 88 - 5 = 83

The number after that will be; 83 - 6 = 77

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To solve this problem, you can use the principle of addition of rates since the work done (filling the tank) would be equal when the pipes are working together or separately. Therefore, adding the rate of pipe A and B should equal to the rate of them working together.

To solve this problem, we'll use the principle that work done is equal to rate multiplied by time. In this case, the 'work' is filling the tank, and the 'rate' is how quickly each pipe can fill it.

Pipe A, we know, takes 18 hours to fill the tank. Therefore, its rate of work is 1/18 tanks per hour. For both pipes working together, it takes 9.9 hours, so their combined rate is 1/9.9 tanks per hour.

Assuming that the pipes work independently, we can add their rates together to get the combined rate. Let the rate of pipe B be 1/b, then:

(1/18) + (1/b) = 1/9.9

Solving this equation for b, which is the time taken by pipe B alone to fill the tank will give you the answer.

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Answer: 8.62 meters

Step-by-step explanation:

Given: The height of the rock, in meters, is given by the function [tex]f(x)=-4.9x^2+17[/tex] , where x is the number of seconds after Noelle releases her rock.

The height of Cesar’s rock, in meters, is given by the function [tex]g(x)=-4.9x^2+13x[/tex] , where x is the number of seconds after he releases his rock.

The moment when the rocks are at the same height  then f(x)= g(x)

[tex]\Rightarrow-4.9x^2+17=-4.9x^2+13x\\\\\text{Add }-4.9x^2\text{ ion both sides, we get}\\\\\Rightarrow\ 17=13x\\\\\Rightarrow\ x=\frac{17}{13}\\\\\Rightarrow\ x=1.3076[/tex]

To calculate height put x in first equation, we get

[tex]-4.9(1.3076)^2+17=8.62189\approx8.62[/tex]

Hence, the height = 8.62 meters

Answer:

A.X+4

Step-by-step explanation:

3x2 + 18x + 24

A. x + 4

B. x - 4

C. x - 3

D. x + 3

Apex Answers

Answer: a. [tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Given : Events X and Y are independent.

The probability of X occurring is [tex]\dfrac{1}{3}[/tex].

The probability of Y occurring is [tex]\dfrac{1}{2}[/tex].

Since both events are independent, then we have

[tex]\text{P(X and Y)}=\text{P(X)}\times \text{P(Y)}\\\\\Rightarrow\ \text{P(X and Y)}=\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{1}{6}[/tex]

Hence, [tex]\text{P(X and Y)}=\dfrac{1}{6}[/tex]

Thus , (a.) is the correct option.

Answer:

All of them will double at the same time.

Step-by-step explanation:

The rule of 72 wa created to have an estimate of how long will an account that pays interests will take to double its value, in this case, as they all have the same interest rate, and the rule of 72 depends only on the interests that the account pays, there will be no difference between the doubling time of the accounts since eventhough they all have different amounts of money, having the same interest rate, will make them grow at the same rate.

Given the points are A(3, 2) and B(6, 4).

If it is asking about the slope of the line AB, then we can use the slope formula as given by :-

[tex] Slope, \;m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

where (x₁, y₁) = A(3, 2) and (x₂, y₂) = B(6, 4)

[tex] m = \frac{4-2}{6-3} =\frac{2}{3} [/tex]

Hence, m = 2/3 would be slope of the line AB.

If it is asking about the y-intercept of the line AB, then we can use slope-intercept form as given by :-

y = mx + b

where m is the slope and b is the y-intercept.

we can plug the value of m = 2/3 and point A(3, 2) into the equation and solve for b.

[tex] 2=(\frac{2}{3} )(3) +b \\\\
2 = 2 + b \\\\
b = 0 [/tex]

Hence, b = 0 would be y-intercept of the line AB.

If it is asking for the equation of the line AB, then we can use slope-intercept form and put values of m = 2/3 and b = 0.

y = mx + b

[tex] y=\frac{2}{3} x+0 \\\\
y=\frac{2}{3} x \;\;
or\;\; 3y=2x [/tex]

Hence, [tex] y=\frac{2}{3} x \;\; or\;\; 3y=2x [/tex] would be equation of the line AB.

Answer:

3 ways

Explanation:

We know that a parabola has a second degree equation), while a line has a first degree equation.

To get the points of intersection, we will need to solve both simultaneously.

Solving them, we can reach a maximum of two solutions, however, other scenarios are also possible.

Possible scenarios:

1- no intersection occurs as shown in the first attachment

2- one intersection occurs as shown in the second attachment

3- two intersections occur as shown in the third attachment

Based on the above, there are three ways where the line and parabola can intersect

Hope this helps :)

Answer:

0,1,2

Step-by-step explanation:

When both variables are standardized, the correlation coefficient remains the same. Scaling the variable by a constant factor doesn't change the relationship or correlation strength.

When both variables are standardized, the correlation coefficient between the standardized variables will always be the same as the correlation coefficient between the original variables. The standardization process does not change the relationship between the variables, but rather scales them to have a mean of 0 and a standard deviation of 1. Therefore, the correlation coefficient remains unchanged.

If median family income had been measured in thousands of dollars instead of dollars, the correlation would not change. Scaling the variable by a constant factor, such as thousands, would only change the units of measurement, but not the relationship between the variables or the strength of the correlation.

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6/4=b/24

1.5=b/24

24(1.5)=b

36=b

Building is 36 ft tall

Answer:

36 feet

Step-by-step explanation:

Let x be the height of the building,

Given,

Length of the building's shadow = 24 ft,

Height of the person = 6 feet,

Length of person's shadow = 4 feet.

Since, at the same time,

[tex]\frac{\text{Height of the building}}{\text{Length of building's shadow}}=\frac{\text{Height of the person}}{\text{Length of person's shadow}}[/tex]

[tex]\frac{x}{24}=\frac{6}{4}[/tex]

[tex]4x=144[/tex]   ( By cross multiplication )

[tex]\implies x = 36[/tex]

Hence, the height of the building is 36 ft.

Answer:

For scientific notation, we write one number to the left of the decimal point and the other numbers are written as a power of ten.

2.)1,220,000,000

[tex]1.22\times10^{9}[/tex]

3.)0.0287

We can write this in fraction form as:

[tex]\frac{287}{10000}[/tex]

So, when 10000 will go up that is in numerator it will hold a negative power.

So, in scientific notation it will be [tex]2.87\times10^{-2}[/tex]

The length of midsegment DE is going to be 38.

The correct answer is option C.

For a better understanding let us name the triangle as ABC and DE is the midpoint on side AB and Ac respectively.

We need to find the value of DE.

We are given that AD = 45 DB = 45 , AE = 55 EC = 55 DE = 6x + 2 and BC = 2x + 64

We need to find the value of midsegment which means we need to find the value of DE.

In order to find the value of DE we would first need to find the value of x.

So , for finding the value of x we would first use the concept of similarity of triangles.

In triangle ADE and triangle ABC

angleA = angleA ( common)

angleD = angleB ( as DE || BC, so the angles formed by parallel lines are going to be equal)

By AA similarity we can say that triangle ADE similar to triangle ABC.

So , now after proving that both of the triangles are similar we can say that all of the sides of the triangles are going to be equal.

AD/ AB = DE/BC = AE/AC

AD/AB = DE / BC

Substituting the required values in expression above.

45/ AB = 6x + 2/ 2x + 64

45/ 90 = 6x + 2 / 2x +64 (AB = AD + DB = 45 + 45 = 90)

Cross-multiplying :

90x + 2880 = 540x + 180

-450x = -2700

x = 6

So , the value of x is going to be 6.

As we have found the value of x now we can easily find the value of DE by substituing the value of x in expression :

DE = 6x + 2

DE= 6(6) + 2

DE = 36 + 2

DE = 38

So , the length of DE is going to be 38.

Therefore , from the given options the correct one is C.

The question probable may be:

9. Find the length of the midsegment The diagram is not to scale:

A. 18

B. 15.5

C. 38

D. 76

Answer:

'Sometimes' is the correct option

Step-by-step explanation:

We are given the statement,

'A kite is a rhombus'.

We know that,

Rhombus - is a parallelogram whose all four sides are equal and opposite angles are equal.

Kite - is a quadrilateral having two equal length adjacent sides and the angles where the pair of adjacent sides meet are equal.

So, we get that,

Thus, the kite is a rhombus when the all the sides of a kite are equal.

Hence, 'A kite is sometimes a rhombus'.

Answer:

Actually, it's never true.

Step-by-step explanation:

A kite is a quadrilateral defined to have no pairs of parallel sides.

A rhombus is a quadrilateral that has two pairs.

The required solution is 8.

It is required to find the least common denominator.

The smallest common multiple of two or more numbers and the common multiple of lowest degree of two or more polynomials.

Given:

Multiply 4 times 2 to get 8, then multiply 1 times 4 for the numerator of the first fraction .

1/4=1*2/4*2=4/8

5/8=5*1/8*1=5/8

The least common denominator of 1/4 and 5/8 is 8.

Therefore, the required solution is 8.

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