A 20-ft flagpole casts a shadow of 12 feet long. How tall is a nearby building that casts a shadow of 20 feet long? Round to one decimal place.

Answer:nothin much

Step-by-step explanation:

Answer:

B) x = √118 mi

Step-by-step explanation:

This is a right triangle, so we can the measure of x using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

Step 1:  Plug in x and √26 for a and b and 12 for c and simplify:

x^2 + (√26)^2 = 12^2

x^2 + 26 = 144

Step 2:  Subtract 26 from both sides to isolate x^2:

(x^2 + 26 = 144) - 26

x^2 = 118

Step 3:  Take the square root of both sides to isolate x:

√(x^2) = √118

x = √118 mi

Answer:

C

Step-by-step explanation:

There is a difference of 16 between consecutive terms, that is

259 - 243 = 275 - 259 = 291 - 275 = 16

This indicates the sequence is arithmetic with nth term

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 243 and d = 16 , then

\(a_{n}\) = 243 + 16(n - 1) = 243 + 16n - 16 = 227 + 16n → C

The value of x is 4 which means that the first digit in the sequence is 4, the second digit is 5, the third digit is 6, and so on.

This problem is asking for the value of x in a sequence of 14 digits where the sum of any three consecutive digits is equal to 15. To solve for x, we can use the information provided and basic algebra.

Let's assign a variable to each of the 14 digits in the sequence. For example, let x be the first digit, (x + 1) be the second digit, (x + 2) be the third digit, and so on. Then, the sum of any three consecutive digits must equal 15:

x + (x + 1) + (x + 2) = 15

Expanding and solving for x, we get:

3x + 3 = 15

3x = 12

x = 4

So, the value of x is 4. This means that the first digit in the sequence is 4, the second digit is 5, the third digit is 6, and so on. By continuing this pattern, we can fill in the entire sequence of 14 digits such that the sum of any three consecutive digits is equal to 15.

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Answer:

Principal amount (P) = $6000

Rate (R) = 12%

Time = 2 years

Simple interest, I = P X R X T / 100

= 6000 X 12 X 2 / 100

= 144000 / 100

= 1440

=> Simple interest, I = $1440

Amount they would owe at the end of 2 years,

= P + I

= 6000 + 1440

= $7440

Answer:

39.99 + 0.45a = 44.99 + 0.40a you're welcome (:

Answer:

Explanation:

Here, we want to get the value of the logarithmic or exponential expression

a)

Thus, the above statement is true

b)

The above is false

c)

This means that the above statement is false

Answer:

1) measure angle T= 72, measure angle U=54

2)measure angle M=76, measure angle N=76

3)EF= 18 inches, measure angle F=134

4)measure angle P,Q,R= 60

Step-by-step explanation:

Answer:

(15 – 22x)/4x(2x – 5)

Step-by-step explanation:

Let us take the numerator first:

(1/2x – 5) – (7/8x – 20) = (1/(2x – 5)) – (7/4(2x –5)) = (8x – 20 – 7(2x – 5))/(4(2x – 5)(2x – 5)

= (8x – 20 – 14x + 35)/4(2x – 5)² = (15 – 22x)/4(2x – 5)²

The denominator is: x/2x – 5

So we now have:

(15 – 22x)/4(2x – 5)² ÷ x/(2x – 5) = (15 – 22x)/4(2x – 5)² x (2x – 5) /X = (15 – 22x)/4x(2x – 5)

Length of tree = 8.57 m.

Let AB represent the length of lower CD represent the length of tree.

Now we use the trigonometric ratios formula

tan = Perpendicular / base.

Now, in triangle AEC

tan 28° = AE / EC = AE / 44

= AE = 44 * Tan 28^.

= AE = 23.39 m

Now, in triangle ABD.

Length of tree = Length of  tower

= Length of tree = 31.97 – 23.39

= Length of tree = 8.57 m.

Pythagoras of Samos became an historic Ionian Greek logician and the eponymous founder of Pythagoreanism. His political and religious teachings were widely recognized in Magna Graecia and motivated the philosophies of Plato, Aristotle, and, through them, the West in preferred. knowledge of his life is clouded with the aid of legend; however, he appears to have been the son of Menarches, a gem-engraver at the island of Samos. cutting-edge students disagree concerning Pythagoras's schooling and influences; however, they do agree that, around 530 BC, he travelled to Croton in southern Italy, wherein he based a school in which initiates have been sworn to secrecy and lived a communal, ascetic lifestyle.

This lifestyle entailed some of dietary prohibitions, historically said to have included vegetarianism, despite the fact that current students doubt that he ever encouraged entire vegetarianism. The coaching most securely recognized with Pythagoras is metempsychosis, or the "transmigration of souls", which holds that every soul is immortal and, upon demise, enters into a new body.

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Answer:

1) 3x+8

2) -2y+3x

Step-by-step explanation:

thats the answer! hope it helps :)

The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

In this question we have been given an expression.

We need to identify the property that is used to multiply two binomials.

(3x+5)(2x+7)=2x(3x+5)+7(3x+5)

Consider two binomials,

(3x+5)(2x+7)

= (2x+7)(3x+5)                     ...............(commutative property)

= 2x(3x+5)+7(3x+5)            ................(distributive property)

Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.

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Answer:

For the coefficients, the prime factorization of 50 is 2 x 5 x 5, and the prime factorization of 125 is 5 x 5 x 5. The common factors are 5 x 5 = 25.

For the variables, we can find the lowest exponent of each variable that appears in both terms.

The variable x appears in both terms, with exponents of 5 and 3. The lowest exponent is 3.

The variable y appears in both terms, with exponents of 2 and 3. The lowest exponent is 2.

The variable z appears in both terms, with exponents of 2 and 1. The lowest exponent is 1.

Therefore, the GCF of 50x^5y^2z^2 and 125x^3y^3z is 25x^3y^2z.

Answer: x^3y^2z

Step-by-step explanation:

To find the GCF (Greatest Common Factor) of the terms 50x^5y^2z^2 and 125x^3y^3z, we need to identify the largest factor that is common to both terms.

First, we can break down each term into its prime factors:

50x^5y^2z^2 = 2 * 5^2 * x^5 * y^2 * z^2

125x^3y^3z = 5^3 * x^3 * y^3 * z

Now we can identify the common factors by looking at the prime factors that are common to both terms:

x^3

y^2

z

The GCF is the product of these common factors:

GCF = x^3 * y^2 * z = x^3y^2z

Therefore, the GCF of 50x^5y^2z^2 and 125x^3y^3z is x^3y^2z.

Answer:

$18.67

Step-by-step explanation:

First, convert the percentage to a decimal.

1.45% = 0.0145

Then, multiply the gross pay by the decimal.

$1287.50 × 0.0145 = $18.67

The Social Security Tax will be $18.67.

Answer:  300 in3

Step-by-step explanation: To find the volume you multiply the base area by the height. 30 x 10 = 300. Did this for my exam and got the question correct.

The volume of the prototype is 300in^3.

Since The designer uses octagons with a base area of 30 in2 and rectangles with a length of 10 in to create a prototype for the new package.

So here the volume is

= 30(10)

= 300

Therefore, The volume of the prototype is 300in^3.

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Answer:

16.9275130641

Step-by-step explanation:

\tan^{-1}\left(\frac{7}{23}\right)

independent event-the occurrence of one event does not affect the probability of the occurrence of another event

compound event-two or more events considered

dependent event-the occurrence of one event affects the probability of the occurrence of another event

a) Compound Event refers to the combination of two or more events considered.

b) Independent Event occurs when one event does not affect the probability of the occurrence of another event.

c) Dependent Event describes a situation where the occurrence of one event affects the probability of the occurrence of another event

a) Compound Event: This refers to the combination of two or more events considered together. It involves analyzing the probability of multiple events occurring in a specific situation or experiment. For example, when rolling a pair of dice, the compound event might be the probability of getting a sum greater than 9.

b) Independent Event: This occurs when the outcome or occurrence of one event has no impact on the probability of the outcome or occurrence of another event. In other words, the events are unrelated and do not influence each other. For example, flipping a coin and rolling a die are independent events since the outcome of the coin flip does not affect the outcome of the die roll.

c) Dependent Event: This describes a situation where the occurrence of one event does affect the probability of the occurrence of another event. In dependent events, the outcome or happening of the first event has an impact on the likelihood of the second event. For instance, drawing cards from a deck without replacement is a dependent event since the probability of drawing a certain card changes after each card is drawn.

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Answer:

r = -1.5

Step-by-step explanation:

recall that ,the recursive formula for a geometric sequence \(a_n\) is :

\(a_{n} = r \times a_{n-1} \ \ \text{where r is the common ratio }\)

therefore

The common ratio of the sequence:

\(a_{n} = -1.5 \times a_{n-1}\)

is r = -1.5

Answer:

answer is A

Step-by-step explanation:

p: shape is a triangle

q: a shape has four sides

The statement that has to be true is p v q.

Logic is a means of expression which involves the use of symbols to represent statements.

Since the shape has to be a rectangle then it follows that the statement that has to be true is p v q.

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Answer:

angle 1: 30

angle 2: 41

angle 3: 96

Step-by-step explanation:

So the angles' sum in one triangle is 180 degrees so you know two of the first triangle's angles so you sum them up and you get: 150 so now you subtract that from 180 and get 30.

Now you can see that if you want to get angle 2 you need to get angle 3 first. so you can see that the 84 degrees is on the same line as angle 3 so, we also know that a line is 180 degrees. so 180-84=96.

Now to get angle 2 we just simply sum up 43 and 96 which is 139, then we subtract that from 180, then we get 41.

A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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Answer:

1.41421

Step-by-step explanation:

Answer:

Hope the picture will help you

Answer:

i. 4 two-point shots

ii. 10 free throws

Step-by-step explanation:

Number of times scored = 14

total points made = 18

let her two-point shot be represented by x, and her free throw by y.

So that;

x + y = 14 .......... 1

But, two points for each two-point shot and one point for each free throw;

2x + y = 18 ......... 2

Subtract equation 2 from 1

2x - x + y - y = 18 - 14

x = 4

substitute the value of x in equation 1

4 + y = 14

y = 14 - 4

y = 10

x= 4, y = 10

Thus, she made 4 two-point shots, and 10 free throws.

Answer:

4 two-pointers and 10 free throws

Step-by-step explanation:

18 - 14 = 4

4 two-pointers = 8

10 free throws = 10 points

Answer:

C; 8x+3y= 45  

Step-by-step explanation:

The process is really long so here we go...

8x+3y=15 is the equation and we want to bring it to slope intercept form so that we can know what the slope is.

(8x+3y=15) -8x = (3y=-8x+15) /3 = y= -8/3x +5

We now know that the slope of the equation is -8/3x, and since we are trying to find out a line parallel to the that equation we can use the same slope in the equation: y+y1=m(x+x1)

Which would be: y-1=-8/3(x+6)

then: y-1=-8/3x-16

then: y= 8/3x+15

We're not done yet because we have to simplify it to standard form so we can subtract 8/3x so that it can join the y's side, and we would have the multiply the whole equation by -3 so that x wouldn't be a fraction, which results it not being in standard form. That leaves the final answer, 8x+3y=45

The equation in standard form of the line that passes through the point (6, -1) and is parallel to the line represented by  8x + 3y = 15 is 8x + 3y = 45

Ax + Bx = C

where

Therefore, using slope intercept form

y = mx + b

where

m = slope

b = y-intercept

8x + 3y = 15

3y = -8x + 15

y = -8 / 3 x + 5

slope = - 8 / 3

It passes through (6, -1)

let's find b

-1 = - 8 / 3 (6) + b

-1 = -48 / 3 + b

-1  = -16 + b

b = -1 + 16

b = 15

Therefore,

y = - 8 / 3 x + 15

8 / 3 x  + y = 15

8x + 3y = 45

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Answer:

Where do you get this soft drink?

The missing values are derived from the graph as follows:

3 ) 7, 14, 21, 28, 35

4) 3, 7, 10, 14, 17

5) 1, 21, 10, 49, 19

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In order to solve for the above values, the best way is to spot the function that exists in the graph which is given as:

F(y) = 3.5x

In the first table, where x = 2

y= 3.5 *2

= 7

This iteration goes on and on and is consistent for all the values.

In the second table,

Where F(y) is known, for example 10.5, then x is derived as:

10.5 = 3.5x (divide both sides by 3.5)

x = 3

This iteration goes on and on and is consistent for all the values.

In the third table, we simply swap the values back and forth using the function F(y) = 3.5x to derive all values.

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