Each picture shows how a mapping, f, maps elements of a domain onto a range.
Which mapping, f, is NOT a function?
Domain
Range
Domain
Range
-6
2.
5
6 00
4
7
7
1
9
8
Domain
Range
Domain
Range
5
4
2
→8
7
2

Each Picture Shows How A Mapping, F, Maps Elements Of A Domain Onto A Range.Which Mapping, F, Is NOT

Answers

Answer 1

Answer:

Top left

Step-by-step explanation:

If an x value (domain) leads to more than one y-value (range), it is not a function. In other words, if each input value leads to only one output value, it is a function. It's still a function if the y-value leads to multiple x-values.


Related Questions

Question 1. Write a function called simulate that generates exactly one simulated value of your test statistic under the null hypothesis. It should take no arguments and simulate 50 area codes under the assumption that the result of each area is sampled from the range 200-999 inclusive with equal probability. Your function should return the number of times you saw the 781 area code in those 50 random spam calls.

Answers

Answer:

The function written in python is as follows:

import random

def simulate():

    count = 0

    for i in range(1,51):

         num = random.randint(200,1000)

         if num == 781:

              count = count + 1

    print(count)

Step-by-step explanation:

This line imports the random library

import random

This line defines the function

def simulate():

This line initializes count to 0

    count = 0

This line iterates from 1 to 50

    for i in range(1,51):

This line generates random number between 200 and 999

         num = random.randint(200,1000)

This line checks if random number is 781

         if num == 781:

If yes, the count variable is incremented by 1

              count = count + 1

This line prints the number of times 781 is generated

    print(count)

Helppp need help (p.s: Zearn

Answers

(50×20) - (1×20)

Step-by-step explanation:

there is 50 twenties (20) so its 50 × 20 and 1 twenty is 20

Which table of values will generate this graph?

On a coordinate plane, points are at (negative 2, 0), (0, 1), (0, negative 4), and (3, 0).

Answers

Answer:

i need help with this to

Step-by-step explanation:

the table of values will be values of x and y respectively.

x= -2,0,0,and 3

y= 0,1,-4 and 0.

Big chickens: The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 192 grams. Use the TI-84 Plus calculator to answer the following. (a) What proportion of broilers weigh between 1150 and 1308 grams? (b) What is the probability that a randomly selected broiler weighs more than 1510 grams? (c) Is it unusual for a broiler to weigh more than 1610 grams? Round the answers to at least four decimal places.

Answers

Answer:

a) 0.2318

b) 0.2609

c) No it is not unusual for a broiler to weigh more than 1610 grams

Step-by-step explanation:

We solve using z score formula

z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

Mean 1387 grams and standard deviation 192 grams. Use the TI-84 Plus calculator to answer the following.

(a) What proportion of broilers weigh between 1150 and 1308 grams?

For 1150 grams

z = 1150 - 1387/192

= -1.23438

Probability value from Z-Table:

P(x = 1150) = 0.10853

For 1308 grams

z = 1308 - 1387/192

= -0.41146

Probability value from Z-Table:

P(x = 1308) = 0.34037

Proportion of broilers weigh between 1150 and 1308 grams is:

P(x = 1308) - P(x = 1150)

0.34037 - 0.10853

= 0.23184

≈ 0.2318

(b) What is the probability that a randomly selected broiler weighs more than 1510 grams?

1510 - 1387/192

= 0.64063

Probabilty value from Z-Table:

P(x<1510) = 0.73912

P(x>1510) = 1 - P(x<1510) = 0.26088

≈ 0.2609

(c) Is it unusual for a broiler to weigh more than 1610 grams?

1610- 1387/192

= 1.16146

Probability value from Z-Table:

P(x<1610) = 0.87727

P(x>1610) = 1 - P(x<1610) = 0.12273

≈ 0.1227

No it is not unusual for a broiler to weigh more than 1610 grams

what is 2(3x+4)=x-7​

Answers

the answer to your question is x=-3

What is the measurement of G?

Answers

Answer:

59 Degrees!!

Step-by-step explanation:

Answer:

59°

Step-by-step explanation:

180 - (57 + 64) =

180 - 121 = 59

logan drew 4 hearts and 40 circles. What is the ratio of hearts to al shapes?

Answers

Answer:

1:11

Step-by-step explanation:

4(hearts):44(all) in simplest form is 1:11 because 4 and 44 are divisible by 4.

Answer:4:40

Step-by-step explanation:

help with math pls pls

Answers

Answer:

62 degrees

Step-by-step explanation:

If 167 degrees is the whole angle measurement, then you take 167-105.

(PLS HELP 50 PTS + BRANLIEST)
A={2, 3, 5, 7, 10} B={1, 4, 6, 8, 9, 10}, C={5, 6, 7}. The universal set U={1, 2, 3, 4, 5, ...10} List the elements of the following:

AUC=
A⋂U=
A⋂Ø=
Ā=
ĀUB=

Answers

Answer:

AUC= {2,3,5,6,7,10}

The second one=A

The third one= empty

I'm sorry. I don't know the others.

An electrican's shop charges $55
service fee plus $50 per hour for labor.
The linear equation that models
C= $50+ $55, where h is the number of labor hours and C is the total cost.
How much would the shop charge a customer for a job that takes 17hrs?

Answers

Answer:

$905

Step-by-step explanation:

$50×h+55=?

h=17 and you pay so $50×h

so $50×h=850

so now that you calculated the cost of the labor add the $55 dollar service fee

850+55=905

Solve graphically, 2x^2+2x-4=0

Answers

The answer is in the picture below !

How much smaller is x−3 than x+4?

Answers

Answer: bsf google

Step-by-step explanation: go to google look it up and find the answer

Answer:

x-3

Step-by-step explanation:

It's x-3 because if you put 12-3 it will be 9 but if you add x+4 it will be 16

A television with a 5:3 screen shows an image with a ratio of 5:4 which creates a letter boxed image. What percent of the screen’s area is occupied by the image?


a)

133%

b)

75%

c)

20%

d)

33%

e)

25%

Answers

Answer:

C

Step-by-step explanation:

#9A
What is a reasonable first step to solve for y?
1/ 4x + 3y = 2z

Answers

Subtract 1/4 x because you wanna isolate y

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the lengths of two different pipes produced by the process. h)What is the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X)

Answers

The probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.

Here,

Since the length of the pipes follows a uniform distribution on the interval [10 feet, 10.57 feet], the probability density function (PDF) for each pipe is:

f(x) = 1 / (10.57 - 10) = 1 / 0.57 ≈ 1.7544 for 10 ≤ x ≤ 10.57

Since the lengths of the pipes are independent, the joint probability density function (PDF) of X and Y is the product of their individual PDFs:

f(x, y) = f(x) * f(y) = 1.7544 * 1.7544 = 3.0805 for 10 ≤ x ≤ 10.57 and 10 ≤ y ≤ 10.57

Now, we want to find the probability that the second pipe (Y) is more than 0.11 feet longer than the first pipe (X).

Mathematically, we want to find P(Y > X + 0.11).

Let's set up the integral to calculate this probability:

P(Y > X + 0.11) = ∬[10 ≤ x ≤ 10.57] [y > x + 0.11] f(x, y) dx dy

We integrate with respect to x first and then with respect to y:

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] ∫[10 ≤ x ≤ y - 0.11] f(x, y) dx dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [∫[10 ≤ x ≤ y - 0.11] 3.0805 dx] dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (x)] from x = 10 to x = y - 0.11 dy

P(Y > X + 0.11) = ∫[10 ≤ y ≤ 10.57] [3.0805 * (y - (10 - 0.11))] dy

P(Y > X + 0.11) = 3.0805 * ∫[10 ≤ y ≤ 10.57] (y - 9.89) dy

P(Y > X + 0.11) = 3.0805 * [(y² / 2) - 9.89y] from y = 10 to y = 10.57

P(Y > X + 0.11) = 3.0805 * [((10.57)² / 2) - 9.89 * 10.57 - (((10)² / 2) - 9.89 * 10)]

P(Y > X + 0.11) = 3.0805 * [((111.7249 / 2) - 104.9135 - (50 / 2 - 98.9)]

P(Y > X + 0.11) = 3.0805 * [(55.86245 - 104.9135 + 49.9)]

P(Y > X + 0.11) = 3.0805 * [0.84895]

P(Y > X + 0.11) ≈ 2.6092

Therefore, the probability that the second pipe (with length Y) is more than 0.11 feet longer than the first pipe (with length X) is approximately 2.6092%.

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Help please
-x^3 = 216
a. +/- 6
B. 6
C. -6 ∛6
D. -6

Answers

Answer:

D. -6

Step-by-step explanation:

SInce x is negative, the - before the six would be cancelled out leaving the equation to be 6^3=216 which is correct

Diana goes on vacation with $260. Each day, she spends the same amount of
money. After 1, 2, 3, and 4 days on vacation, she has $242, $224, $206, and
$188, respectively.
Please help

Answers

She has 860 dollars after vacation

350 - 15x = 200 - 10x
Sam’s Jet Ski rental charges $350 to rent a jetski plus $15 per hour. Brian’s Jet Ski rental charges $200 to rent a jetski plus $10 per hour

Steven has an account with $350 in it and he withdrawals $15 per day. Jessica has an account with $200 and withdrawals $10 per day.

Water tank A has 350 gallons of water and is losing 10 gallons per minute. Water tank B has 200 gallons of water and is losing 15 gallons per minute

Tree A has a height of 350 centimeters and is growing at a rate of 15 cm per day. Tree B has a height of 200 centimeters and is growing at a rate of 10 centimeters per day

Answers

Answer

Steven has an account with $350 in it and he withdrawals $15 per day. Jessica has an account with $200 and withdrawals $10 per day.

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 9 percent, has a YTM of 7 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of 9 percent, and also has 13 years to maturity. The bonds have a $1,000 par value.



What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In three years? In eight years? In 12 years? In 13 years?

Answers

Answer:

Bond X

current market price:

PV of face value = $1,000 / (1 + 3.5%)²⁶ = $

PV of coupon payments = $45 x 16.89035 (PV annuity factor, 3.5%, 26 periods) = $760.07

current market price = $408.84 + $760.07 = $1,168.91

price in 1 year:

PV of face value = $1,000 / (1 + 3.5%)²⁴ = $437.96

PV of coupon payments = $45 x 16.05837 (PV annuity factor, 3.5%, 24 periods) = $722.63

market price = $437.96 + $722.63 = $1,160.59

price in 3 years:

PV of face value = $1,000 / (1 + 3.5%)²⁰ = $502.57

PV of coupon payments = $45 x 14.2124 (PV annuity factor, 3.5%, 20 periods) = $639.56

market price = $502.57+ $639.56 = $1,142.13

price in 8 years:

PV of face value = $1,000 / (1 + 3.5%)¹⁰ = $708.92

PV of coupon payments = $45 x 8.31661 (PV annuity factor, 3.5%, 10 periods) = $374.25

market price = $708.92 + $374.25 = $1,083.17

price in 12 years:

PV of face value = $1,000 / (1 + 3.5%)² = $933.51

PV of coupon payments = $45 x 1.89969 (PV annuity factor, 3.5%, 2 periods) = $85.49

market price = $933.51 + $85.49 = $1,019

price in 13 years:

market price = $1,000 + $45 = $1,045

Bond Y

current market price:

PV of face value = $1,000 / (1 + 4.5%)²⁶ = $318.40

PV of coupon payments = $35 x 15.14661 (PV annuity factor, 4.5%, 26 periods) = $530.13

current market price = $318.40 + $530.13 = $847.53

price in 1 year:

PV of face value = $1,000 / (1 + 4.5%)²⁴ = $347.70

PV of coupon payments = $35 x 14.49548 (PV annuity factor, 4.5%, 24 periods) = $507.34

market price = $347.70 + $507.34 = $855.04

price in 3 years:

PV of face value = $1,000 / (1 + 4.5%)²⁰ = $414.64

PV of coupon payments = $35 x 13.00794 (PV annuity factor, 4.5%, 20 periods) = $455.28

market price = $414.64+ $455.28 = $869.92

price in 8 years:

PV of face value = $1,000 / (1 + 4.5%)¹⁰ = $643.93

PV of coupon payments = $35 x 7.91272 (PV annuity factor, 4.5%, 10 periods) = $276.95

market price = $643.93 + $276.95 = $920.88

price in 12 years:

PV of face value = $1,000 / (1 + 4.5%)² = $915.73

PV of coupon payments = $35 x 1.87267 (PV annuity factor, 4.5%, 2 periods) = $65.54

market price = $915.73 + $65.54 = $981.27

price in 13 years:

market price = $1,000 + $35 = $1,035

Wite the number
in standered form 80+9=

Answers

The number in standard from is 89 :)

Answer:

89

eighty-nine

A chemist is performing an experiment by observing the effects when she combines two solutions. She monitors the temperature of the combined solution over the course of eight hours and records it in this table below.

The chemist can model the temperature with a polynomial function. During these eight hours, over what interval is the temperature decreasing?

A. From hour 0 to hour 8

B. From hour 5 to hour 8

C. From hour 0 to hour 5

D. From hour 2 to hour 6

Answers

Answer:

A. From hour 0 to hour 5

Step-by-step explanation:

For all Plato users

Interval of the temperature decreasing is from hour 0 to hour 5.

What is interval?

an interval is defined as a group of numbers which includes all numbers between the beginning and the end.

According to given data is showing that the temperature decreasing zero hour to 1 hour , then 1 to 2 hour, then 2 to 3 hour, then 3 to 4 hour, then 4 to 5 hour.

So the interval of the temperature decreasing is from hour 0 to hour 5.

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Pls help me plssss. Bella measured the heights of her corn stalks in centimeters. The heights are 81, 88, 69,65, 87.
What is the mean height of Bella's corn stalks? ——————————
O A 69 cm
O B. 75 cm
O C. 78 cm
OD 80 cm
O E 81 cm

Answers

Answer:

the answer is C. 78

Step-by-step explanation:

First, you have to add together 81, 88, 69, 65, and 87; its total is 390. The next step is to see how many numbers there are. In total there are 5 numbers. Lastly, you have to divide 390 by 5 which is 78.

In , the Pew Internet & American Life Project asked teens aged to several questions about their attitudes toward social media. The results showed that say social media makes them feel more connected to what is going on in their friends' lives; say social media helps them interact with a more diverse group of people; and feel pressure to post content that will get a lot of likes and comments.
Round your answers to four decimal places.
a. Develop a point estimate of the proportion of teens aged to who say social media makes them feel more connected to what is going on in their friends' lives.
b. Develop a point estimate of the proportion of teens aged to who say social media helps them interact with a more diverse group of people.
c. Develop a point estimate of the proportion of teens aged to who feel pressure to post content that will get a lot of likes and comments.

Answers

Complete Question

The  complete question is shown on the first uploaded image

Answer:

a

[tex]\^ p_1 =  0.8102 [/tex]

b

[tex]\^ p_2 =  0.6904 [/tex]

c

[tex]\^ p_3 =  0.3701 [/tex]

Step-by-step explanation:

From the question we are told that

   The sample size is  n  =  743

    The number that said social media makes them feel more connected  to what is going on in their friends' lives is  k =  602

   The number that said social  media helps them interact with a more diverse group of people is  y =  513

   The  number that said feel pressure to post content that will get a lot of likes and comments is  c  =  275

Generally a point estimate of the proportion of teens aged 13 to 17  who say social media makes them feel more connected to what is going on in their friends' lives is mathematically represented as

        [tex]\^ p_1 =  \frac{k}{n}[/tex]

=>      [tex]\^ p_1 =  \frac{602}{743 }[/tex]\

=>      [tex]\^ p_1 =  0.8102 [/tex]

Generally a point estimate of the proportion of teens aged 13 to 17  who say social media helps them interact with a more diverse group of people is mathematically represented as

        [tex]\^ p_2 =  \frac{k}{n}[/tex]

=>      [tex]\^ p_2 =  \frac{513}{743 }[/tex]\

=>      [tex]\^ p_2 =  0.6904 [/tex]

Generally a point estimate of the proportion of teens aged 13 to 17   who feel pressure to post content that will get a lot of likes and comments is mathematically represented as

        [tex]\^ p_3 =  \frac{k}{n}[/tex]

=>      [tex]\^ p_3 =  \frac{275}{743 }[/tex]

=>      [tex]\^ p_3 =  0.3701 [/tex]

The point estimate of the teens aged to who say social media makes them feel more connected is 0.8102.

How to calculate the point estimate

The point estimate of the proportion of teens aged to who say social media makes them feel more connected to what is going on in their friends' lives will be:

= Number of teens / Sample size

= 602/743

=™0.8102

The point estimate of the proportion of teens aged to who say social media helps them interact with a more diverse group of people will be:

= 513/743

= 0.6904

The point estimate of the proportion of teens aged to who feel pressure to post content that will get a lot of likes and comments will be:

= 275/743

= 0.3701

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what is the sum a 23 and 4 /4

Answers

Answer:

the anwser is 24 please mark brianliest

Answer:

The answer is 24.

The radius of a semicircle is 2 yards what is the semicircle’s perimeter

Answers

10.28 because you would take your radius times pie and add that to 2tikes your radius

Which equation would you choose in order to most easily identify the vertex?
K
y = 9x4 + 6x2 +1
y = x2 + 6x + 9
y = (x + 6)(x + 9)
y = (x + 6)2 +9
a 5

Answers

Answer:

last

Step-by-step explanation:

Would 3.99. million flies or 47,000,000 ants have a greater mass

Answers

Ants

Step-by-step explanation:

The output from the machine depends on the input to to

A.

B.

C.

D.​

Answers

Answer:

i think its B

Step-by-step explanation:

Solve the inequality. 12x<-144

Answers

Answer:

Step-by-step explanation:

x=-12

Answer:

x= -12

Step-by-step explanation:

The capacity of a dump truck is listed by the manufacturer as 10 yd3 . A construction site requires the removal of of dirt, and the contractor has four identical trucks. How many trips will each need to make

Answers

Question:

The capacity of a dump truck is listed by the manufacturer as 10 yd^3. A construction site requires the removal of 200 m^3 of dirt, and the contractor has three identical trucks. How many trips will each need to make?

Answer:

7 trips

Step-by-step explanation:

Given

[tex]Capacity = 10yd^3[/tex]

[tex]Dirts = 200m^3[/tex]

[tex]Trucks = 4[/tex]

Required

Determine the number of trips of each truck

Divide the volume of dirts by 4 to get the portion of each truck

[tex]Each\ Truck = \frac{200m^3}{4}[/tex]

[tex]Each\ Truck = 50m^3[/tex]

Divide the portion of each truck by capacity of each truck to get the number of trip

[tex]Trip = \frac{50m^3}{10yd^3}[/tex]

Convert m^3 to yd^3

[tex]Trip = \frac{50 * 1.30795yd^3}{10yd^3}[/tex]

[tex]Trip = \frac{65.3975yd^3}{10yd^3}[/tex]

[tex]Trip = \frac{65.3975}{10}[/tex]

[tex]Trip = 6.53975[/tex]

Approximate:

[tex]Trip = 7[/tex]

Other Questions
You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $12 each. You have a budget of $300 for the shirts. The equation $10x+12y=300$ models the total cost, where $x$ is the number of short-sleeved shirts and $y$ is the number of long-sleeved shirts. a. Graph the equation. Interpret the intercepts what are some promo codes First person to answer gets brainly!! Dr. Adams is studying how the quality of breakfast influences academic performance for elementary school children. A sample of 100 children is selected. Fifty children are provided with a nutritious breakfast when they arrive at school each morning. The other 50 children are given a doughnut each morning. After three months, Dr. Adams records the academic achievement level for each child and compares the two groups of scores. In this example, there are __________ levels of the independent variable, and __________ dependent variable(s). 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He then turned to the caregiver who was assisting him, smiled, and said calmly, Go get Michelle.Michelle was scanning boxes of gauze bandages and stacking them onto a shelf in the storeroom when the caregiver came in and announced, Phillips trying to get Erkan to take a shower and he needs your help. Michelle rushed out of the store room and down the hall to Erkans room.This was the last week of Michelles internship. It was her junior year, and the internship was part of her Workplace and Consumer Education class. At first she wanted to intern at her dads gas station, but her teacher told her she needed to branch out and signed Michelle up at the Oakcourt Nursing Home, only 15 minutes away from her house.Wearing a Pittsburgh Steelers sweatshirt and jeans, with dark curls pushed back in a hair clip, Michelle stood out from the crowd of nurses and caregivers in white pants and polo shirts who were standing huddled in the doorway of Erkans room. She moved past them and rushed to Erkans side. As soon as he saw her, Erkans face brightened and he stopped looking like a stricken animal and instead looked like someone who recognized a dear old friend.He cant have them, Michelle. I sold them at the corner, Erkan shouted, pushing his way to Michelle. He stole my guitar, he whispered.I know, Erkan, but he was only trying to help you get some money to pay for your trip. Michelle had been frightened by a lot of the residents of the nursing home when she first started the beginning of the semester. Many of them were incoherent and loud, and some could be very aggressive and scary. Erkan often pushed or kicked and ranted. Michelle had started to regret this internship, and she even avoided going near Erkans room whenever possible. He lives in his own world, Philip, the managing nurse, explained to Michelle after her first encounter with Erkans temper.Still, Michelle had been curious, and she felt sorry that Erkan had a bad reputation among the staff. She too had felt like everyone mistrusted herespecially at the nursing home where she was so much younger than the rest of the staffso she understood how he must feel. Besides, he was the only person in the whole place with skin nearly as dark as hers.Over time, she noticed patterns in Erkans rants: He would sometimes mention his guitar and his father and the city of Diyarbakir, which she learned is in Turkey. So she decided that the next time she brought supplies to his room, instead of avoiding Erkan, she would play along with whatever he said. If he lived in his own world, then she would try to join him there. Bit by bit, she discovered that he had immigrated to the United States from Turkey when he was very young. His father had saved as much money as possible to pay for his journey, but he needed to sell Erkans guitar to help cover the cost. Erkan had moved in with his aunts family in Scranton, Pennsylvania, and finished school there. Eventually he got married, had children of his own, and worked for years signing Turkish singers to a small record label. But hed never quite felt at home in the United States.I know he sold your guitar, but you told me yourself he just wants whats best for you, Michelle said, while Philip and the caregiver looked on in amazement as Erkan settled into an armchair. Now why dont you listen to Philip, take your shoes off, and have a shower?For you, Michelle, Ill do it.You can feel out of place in a country, in the place where you live, or even in your own head, Michelle thought. But if youre lucky, someone will know how to find you and remind you that we all feel that way sometimes.In Out of Place, how has Ekrans relationship with Michelle affected him? Discuss interactions between the two characters and explain how Ekran reacts to these interactions. Use evidence from the text to support your response. Your response should be at least two complete paragraphs.Answer:Type your answer here Jessica completed 20 haircuts in 8 hours. On average how many haircuts per hour did Jessica do? What are the two largest urban centers in the Crossroads region? Shreveport and MonroeAlexandria and PinevilleNew Orleans and Baton RougeLake Charles and Sulphur Part C: Create a graph that represents the solutions to the equation from Part A In "The Ride of His Life," what is the author's viewpoint toward Senkos career?Senko is passionate about working with marine wildlife.Senko is overly protective of sea turtles.Senko is on the cutting edge of modern technology.Senko is an avid fisherman who wants to help save wildlife. What are the 6 types of skill related to physical fitness 8(k - 6) +58 = 2(4k + 5)one solutionno solutionsinfinite solutions what is the answer to 9/11 - 4/11 The Galapagos Islands are part of:PeruColumbiaChileEcuador Which of the following emerged in Western Europe in large part as a reaction to the diplomatic exchanges exemplified in the passage?