A 33-m tall building casts a shadow. the distance from the top of the building to the tip of the shadow is 34m. Find the length of the shadow. If necessary, round your answer to the nearest tenth.

The explicit formula for the geometric sequence 6, -24, 96, ... is

Every term in a geometric series is obtained by multiplying the term before it by the same number called the common ratio

The common ratio is denoted by the number r. It can be calculated by dividing any term in the sequence by the term before it.

For the given sequence the first term is a = 6

The common ratio is solved as follows

a * r  = second term

6 * r = -24

r = -24/6

r = -4

check

-24 * -4 = 96 correct

The nth term of a geometric sequence

= ar^(n - 1)

= a * -4^(n - 1)

checking for the third term

= a * -4^(n - 1)

= 6 * -4^(3 - 1)

= 6 * -4^(2)

= 6 * 16

= 96

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Answer:x=-2,5, -[tex]i\sqrt{2}[/tex], +[tex]i\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

100°

Step-by-step explanation:

180°- 80°= 100°

The angles are supplementary, meaning that they have to add up to 180.

Hope this helps!!! :)

Answer:  [tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]

Given: [tex]3x + 2y = 5[/tex]

We are needed to find the slope-intercept form.

We know that the slope-intercept form of an equation is given by

[tex]y = mc + c[/tex]

[tex]3x + 2y = 5[/tex]

[tex]2y = 5 -3x[/tex]

[tex]2y = -3x + 5[/tex]

[tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]

Thus, the answer is [tex]y = \frac{-3} {2} x + \frac{5}{2}[/tex]

In the following proportions:-

A. [tex]\frac{2}{8} =\frac{3}{12}[/tex]

C. [tex]\\\\\ \frac{25}{10} =\frac{5}{2}[/tex]

D. [tex]\\\\ \frac{3}{4} =\frac{15}{20}[/tex] Are Equal

What are proportion?

A part, share, or quantity that is compared to a total is referred to as a proportion. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

When two ratios are equal, they are said to be in proportion.For instance, the time it takes a train to go 50 kilometers per hour is equal to the time it needs to travel 250 kilometres in 5 hours. e.g., 250km/5 hours at 50 km/h.

[tex]A) \\\\\frac{2}{8} =\frac{3}{12} =\frac{1}{4}\\\\(B) \\\\\frac{3}{4} \ !=\frac{8}{10}= \frac{4}{5}\\\\\ (C)\\\\\frac{25}{10} =\frac{5}{2}\\\\(D)\\\\ \frac{3}{4} =\frac{15}{20}[/tex]

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The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.

Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.

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Answer:

X=100

Step-by-step explanation:

I assume you want to find the value of x.

3/5x=60

5/3*60=x

x=20*5=100

Answer:

x > 24 goes to the bottom

x < 24 goes to the 3rd slot

x ≤ 24 goes to the 1st slot

x ≥ 24 goes to the 2nd slot

Step-by-step explanation:

Hope this helps.

Answer:

√65

Step-by-step explanation:

Compute the Euclidean distance between the following points:

p_1 = (-2, 3) and p_2 = (5, -1)

The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:

sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)

Substitute (x_1, y_1) = (-2, 3) and (x_2, y_2) = (5, -1):

= sqrt((-2 - 5)^2 + (--1 + 3)^2)

(-1)^2 = 1:

= sqrt((-2 - 5)^2 + (1 + 3)^2)

-2 - 5 = -(2 + 5):

= sqrt((-(2 + 5))^2 + (3 + 1)^2)

2 + 5 = 7:

= sqrt((-7)^2 + (3 + 1)^2)

Multiply each exponent in -7 by 2:

= sqrt((-1)^2×7^2 + (3 + 1)^2)

7^2 = 49:

= sqrt((-1)^2×49 + (3 + 1)^2)

(-1)^2 = 1:

= sqrt(49 + (3 + 1)^2)

3 + 1 = 4:

= sqrt(49 + 4^2)

4^2 = 16:

= sqrt(49 + 16)

| 1 |

| 4 | 9

+ | 1 | 6

| 6 | 5:

Answer: √65

Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line.

A line's slope is determine by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.

Two locations located on a straight line can be used to determine a line's slope. We can use the slope of line formula if we know the two spots' coordinates. These two points' coordinates should be-

P1 = (x1, y1) and P2 = (x2, y2)

Hence, Between (5,10) and (15,70), a line runs. As a result, the slope of the line through the supplied locations is 3.

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The bags of chips sold are 111.

The percentage is the term use to tell the hundredth part of something.

Given that, The snack bar sold 75% of its inventory of bags of chips, and the snack bar still has 37 bags of chips,

Let the original number of bags of the chips be x,

Since, 75% is already sold, so left number of bags are = 100%-75% = 25%

Therefore,

25% of x = 37

x = 37x4

x = 148

The number of bags sold = 75% of 148

= 75x148/100

= 111

Hence, they sold 111 bags of chips.

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Answer: y = 14/19x+15

Step-by-step explanation: using the equation y = mx+b, m is your slope and b is the y-intercept. plug your slope (14/19) and y-intercept (15) into the equation and you’ve got your answer in slope-intercept form

The equation that can be used to find the length of the side of the original square is 4(x+5) = 60. Option A. is the answer

Given that:

When the length of a side of a square is increased by 5, the perimeter of the new square is 60.

Let x represent the length of the side of the original square

when x is increased by 5, you have (x+5)

Perimeter (P) = 4 × length of the side

Thus, 4(x+5) = 60

Therefore,  the equation to find the length of the side is  4(x+5) = 60

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Answer:

  see attached

Step-by-step explanation:

Given the equation for a line, y +3 = (x -6), you want to identify the slope and a point on the line, then graph it.

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

Comparing this to the given equation, you can see ...

This tells you the slope is 1 and a point on the line is (6, -3).

You graph this equation by plotting point (6, -3) and drawing a line through it that goes up 1 unit for each 1 unit to the right. A graph is attached.

__

Additional comment

If you like, you can rearrange the equation to slope-intercept form by subtracting 3:

  y +3 -3 = (x -6) -3

  y = x -9

This tells you another point is -9 on the y-axis.

Answer:

C

Step-by-step explanation:

Because it says -8 x 7, the * is negative and the 7 is positive.

The relation is:

(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)

Is a function, because each element in the domain is mapped to a single element in the range.

A relation maps elements from one set, called the domain, into another set, called the range.

For example, the element x mapped into element y is written as (x, y).

Particularly, a relation is a function if each element from the domain is mapped into only one element of the range.

So, if we had two points like (2, 4) and (2, 5), then the relation is not a function (because the element 2 is mapped into two different elements of the range).

Here the relation is:

(1, 2), (-3, 5), (6, 6), (-2, 0), (1, 2)

So the input x = 1 appears twice, but both times is mapped to the same element, so this relation is a function.

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In 11.56 years the given amount of $ 900 will be double.

The interest charged on a loan or deposit is known as compound interest which depends on both the principal amount and rate of interest.

The formula  used for

where P = Principal amount

r = Rate of interest in decimal

n = Number of compounds per year  

t = Time period  

Here from the given data,

Principal amount, p = $ 900

Rate of interest, r = 6% = 6/100 = 0.06

Number of compounds, n = 12    [ ∵ compounded mothly ]

Here we need to find the time period

Assume that after 'n' years the amount will be doubled i.e $ 1800

From the given problem,

Amount, A = 900(1+0.06/12)¹²ⁿ        

= 900(1+0.06/12)¹²ⁿ

= 900(1 + 0.005)¹²ⁿ

= 900 (1.005)¹²ⁿ  

As we assumed after 'n' years the amount is $ 1800

=> 900 (1.005)¹²ⁿ = 1800  

=> (1.005)¹²ⁿ = 2    

Apply to log on both sides

=> log (1.005)¹²ⁿ = log 2

=> 12n log(1.005) = log 2

=> 12n = log 2/log(1.005)

[ use calculator for log (1.005) and log 2]

=> 12n = 0.301029996/ 0.00216606176  

=> 12n = 138.975722

=>  n =  11.5813102

=>   n = 11.56  

Therefore,

In 11.56 years the given amount of $ 900 will be double.

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If f(x) = 4x - 5 and g(x) = 6 - 3x then f(x) + g(x) = x + 1.

When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).

We know f(x) + g(x) = (f + g)(x).

Given, f(x) = 4x - 5 and g(x) = 6 - 3x.

∴ f(x) + g(x) = (4x - 5) + (6 - 3x).

f(x) + g(x) = 4x - 3x - 5 + 6.

f(x) + g(x) = x + 1.

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Answer: To determine Alejandro's earnings for the first 4 weeks, we first need to calculate his weekly pay. To do this, we divide his annual salary by the number of weeks in a year:

Annual salary / 52 weeks/year = weekly pay

$71,500 / 52 weeks/year = $1,375/week

Next, we need to determine the agency fee that Alejandro will pay each week. The agency fee is equal to 40% of the first 5 weeks' pay, so we multiply Alejandro's weekly pay by 40% to get the agency fee:

Weekly pay * 40% = agency fee

$1,375/week * 40% = $550/week

Finally, to determine Alejandro's earnings for the first 4 weeks, we multiply his weekly earnings by the number of weeks:

Weekly pay * number of weeks = earnings

$1,375/week * 4 weeks = $5,500

So, Alejandro will earn $5,500 during the first 4 weeks of his new job, after paying the agency fee each week.

Answer:

goes from(6,0),(10,1),(14,2) in +ve

Answer:

equal to area of rectangle

Step-by-step explanation:

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Angle θ with 0∘ < θ < 360∘ that has the same: sine as 30°:∅= degrees

cosine as 30°:∅= degrees are 150 and 330 degrees.

What is trigonometric function?

Trigonometric functions are referred to as Circular Functions may be merely outlined because the functions of an angle of a triangle

Main Body:

We have to find an angle θ with 0° < θ < 360° that has the same:

(a) sin(30∘)

We know that sin(θ) is positive in 2nd quadrant and in the 2nd quadrant θ lies between 90∘ and 180∘.

sin(30∘)=sin(180∘−30∘)

[∵sin(180∘−θ)=sin(θ)]=sin(150∘)

Thus:

sin as 30∘:θ=150 degrees

(b) cos(30∘)

We know that cos(θ) is positive in the 4th quadrant and in the 4th quadrant θ lies between 270∘ and 360∘.

cos(30∘)=cos(360∘−30∘)

[∵cos(360∘−θ)=cos(θ)]=cos(330∘)

Thus:cos as 30∘

:θ=330 degrees

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The number of liters in the tank after 109 seconds is 60.5 liters.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

2.5 liters = 1 minute

2.5 liters = 60 seconds

Multiply 109/60 on both sides.

109/60 x 2.5 liters = 109 seconds

4.5 liters = 109 seconds

This means,

4.5 liters is drained after 109 seconds

Now,

The liters of water in the tank.

= 65 - 4.5

= 60.5 liters

Thus,

There are 60.5 liters in the tank.

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Answer:

---------------------------------

Given  number is 71830.

The last part:  830 is same on both lines.

We need to represent 71000 in different way, instead of 7 ten thousands and 1 thousands we have 6 ten thousands then we need:

It is 11 thousands.

Answer:

11,000 (or) 11 thousands

Step-by-step explanation:

Now we have to,

→ find the missing number.

→ Let the number be x.

Forming the equation,

→ 60,000 + x + 800 + 30 = 71,830

Then the value of x will be,

→ 60,000 + x + 800 + 30 = 71,830

→ x + 60,830 = 71,830

→ x = 71,830 - 60,830

→ [ x = 11,000 ]

Hence, the value of x is 11,000.

Answer:

Step-by-step explanation:

Let

n--------> the number

we know that

1) the sentence" Three less than the product of seven and a number"  represent the expression------>  

2) the sentence" is four more than the number"  

represent the expression ------->  

3) the complete sentence" Three less than the product of seven and a number is four more than the number"  represent the expression

represent the expression ------->  

therefore

the answer is

(7n-3) =(n+4)

we want to find the number of hours (or rather days) until only 4.25% of the drives fail.

that means for an exponential distribution we have

P(X < x) = 1 - e^(-Lx)

L = 1/mean = 1/12500

and we need to find x, so that P(X <x) = 0.0425 (that is 4.25% converted into a probability).

so, we get

0.0425 = 1 - e^(-x/12500)

0.0425 - 1 = -e^(-x/12500)

-0.9575 = -e^(-x/12500)

0.9575 = e^(‐x/12500)

ln(0.9575) = -x/12500

-x = ln(0.9575)×12500

x = -ln(0.9575)×12500 = - -0.043429558...×12500 =

= 0.043429558...×12500 = 542.8694741... hours

after 542.8694741... hours = 22.61956142... days

it is expected that 4.25% of the hard drives fail.

you left out to what decimal this should be rounded. and if you need hours or days. in case of doubt use hours (as the only other time information is given in hours).

please round yourself as you need.

The position of the √7 on the number line is slightly right of the 2.6.

What is a number line?

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

Here,

In general conclusion,

√4< √7 < √9

2 < √7 < 3

So, the value of the √6 lies between 2 and 3.

√6 = 2.6457

Hence, the position of the √7 on the number line is slightly right of the 2.6.

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Answer:

y = 3x + 2

y = 1/2 x -1

Step-by-step explanation:

The slope intercept form of a line is

y = mx + b  You substitute in the slope for m and the y intercept for b

Answer:

Step-by-step explanation: 270