What is the image of the point
(
1
,
−
4
)
(1,−4) after a rotation of
18
0
∘
180
∘
counterclockwise about the origin?

The times associated with each speed are:

It is always true that the speed is inversely proportional to time.

In this case we find the situation of bicycle moving at constant speed, where the traveled distance (s), in miles, is equal to the following expression:

s = v · t           (1)

Where:

Now we proceed to calculate time needed for each speed:

t = s / v

Case 1

t = 100 mi / 5 mi / h

t = 20 h

Case 2

t = 100 mi / 10 mi / h

t = 10 h

Case 3

t = 100 mi / 15 mi / h

t = 6.667 h

Case 4

t = 100 mi / 20 mi / h

t = 5 h

Case 5

t = 100 mi / 25 mi / h

t = 4 h

According to the model for rectilinear uniform motion, the speed is inversely proportional to time.

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Step-by-step explanation:

For the value of x = 0 then the f(x) will became f(o) = 0

Answer:

Step-by-step explanation:

You want the ratio of vowels to consonants in each of the words "pineapple" and "strawberry."

To form the reduced ratio vowels:consonants, we need to identify the type of letter each is. Here we use bold to identify the vowels.

  pineapple ⇒ 4:5

  strawberry ⇒ 3:7 . . . . counting "y" as a vowel

Answer:

angle A=125 angle B= 114 angle C= 121

Step-by-step explanation:

first you have to find x so that you can find each angle

the interior angles of a triangle is equal to 360

add the angles together x+x+7+x+11=360

combine like terms 3x+18=360

subtract 18 on both sides 3x=342

divide by 3 on both sides x=114

to find angles:

plug in X to each side

(114)+7 = angle C

(114)+11= angle A

114= angle B

Answer:

Step-by-step explanation:

4 is the maximum number of days.

Using Inequality, the maximum number of days that Lily can rent the car while staying within her budget is 4 days.

The rental car company charges $71.02 per day to rent a car and $0.12 for every mile driven.

Lily wants to rent a car and she plans to drive 475 miles. She has a budget of $390.

Therefore, the maximum number of days that Lily can rent the car while staying within her budget can be calculated as follows:

Using inequality,

total cost = 71.02(x) + 0.12(y)

where

x = number of days

y = number of miles

Therefore,

71.02x + 0.12(475) ≤ 390

71.02x ≤ 390 - 57

71.02x ≤ 333

x ≤ 333 / 71.02

x ≤ 4.68882005069

Therefore,

she can drive maximum of 4 days.

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The value of the composite function f(g(x)) is calculated as f(g(x)) = 65.

Composite functions is one in which one function is placed within another.

For, the given values in the question;

f(x) = 9x+2 and g(x) = x-2

We have to find the value of f(g(x)) for x = 9.

First estimate the value of g(x) by substituting  x = 9 in it.

g(x) = x-2

g(9) = 9-2 = 7

Now,

f(x) = 9x+2 and

f(g(x)) = f(7) = 9x+2, (substitute x = 7)

f(g(x)) = 9×7 + 2

f(g(x)) = 65.

Thus, the value of the composite function f(g(x))  = 65.

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The amount Vicente needs to deposit now in order to have a balance of $20,000 in his savings account after 10 years is $15,384.62

What is simple interest?

The simple interest on the savings is determined as the deposit multiplied by the annual interest rate and the number of years that deposit would last in the account

I=PRT

I=simple interest

P=principal=deposit=unknown

R=annual simple interest=3%

T=number of years=10

A(amount in 10 years)=P+PRT

A=P(1+RT)

$20,000=P(1+3%*10)

$20,000=P*1.30

P=$20,000/1.30

P=$15,384.62

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x+5/-6= -4

multiply each side by -6

x-5/6= -4

*-6 *-6

x+5=24

subtract 5 from each side

x=19

Answer:

-152

Step-by-step explanation:

-152 < 12

-152 is negative, which means it is less than 1.

12 is positive, which means it is greater than 1.

Therefore, -152 is the lesser of the two given numbers.

Have a great rest of your day! :)

Hi!

-152 is less than 12, because:

[tex]\mathbb{NUMBER \ LINE}[/tex]

[tex]_ < \!\!\!\rule{300}{1}\!\!\!_ >[/tex]

     [tex]-152[/tex]                                                                         [tex]12[/tex]

Cheers!

Have a nice day!

I hope this helps!

Marketable securities are 63,360 credits (refer to the table below for journal entries).

So,

The following can be deduced from the information provided in the question:

The purchase price per share will be as follows:

The share price will be as follows:

The following is the loss on the sale of marketable securities:

Then, the journal entries are: (Refer to the table below)

Therefore, marketable securities are 63,360 credits (refer to the table below).

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The correct question is given below:
Wheat Corporation pays $ 528 comma 000 for 100,000 shares to acquire 45​% common stock of Grain​ Investments, Inc. on January​ 5, 2018. Wheat Corporation sells 12 comma 000 shares for $ 54 comma 000 on January​ 6, 2018. What is the correct journal entry for the transaction on January​ 6, 2018?​ (Round any intermediate calculations to two decimal​ places, and your final answer to the nearest​ dollar.)

1) This narrative is an example of a sample survey.

2) This narrative is an example of an experiment.

3) This narrative is an example of an observational study.

There are some common methods of data collection in statistical studies which are sample survey, observational study, experiments e.t.c

A sample survey is a survey that is done by taking a sample of people or items that represent a larger population.

An observational study is a type of study whereby a researcher utilizes observed information to gain more information about a group of individuals.

An experiment is where a researcher purposely applies different treatments to different groups and then does a comparison of  the groups to determine if there is any difference in a specific variable of interest.

1) This narrative is an example of a sample survey because he studied a sample of 50 people who exercise regularly to determine if their blood pressures are low or average.

2) This narrative is an example of an experiment because we see that he studies 20 people who exercise and another 20 who don't exercise and uses the result to generate a conclusion about both groups.

3) This narrative is an example of an observational study because he is using the information he gets from the question he asks every fifth patient to learn about a group of individuals.

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The following statement are true:

It's an easy way to calculate just how long it's going to take for your money to double. Just take the number 72 and divide it by the interest rate you hope to earn. That number gives you the approximate number of years it will take for your investment to double.

Using the formula

time for doubling money= 72/R

So, 72/12 = 6 years

Thus, It will take 6 years to double the investment. This statement is true.

So, 72/18 = 4 years

Thus, It will take 4 years to double the investment. This statement is not true.

so, 72/8= 9 years.

Thus, It will take 9 years to double the investment. This statement is true.

So, interest = PRT/100

I  = (2000 × 0.05 × 20)

I = $2000

Thus, This statement is true.

Interest = ( 700 × 0.06 × 12 ) = $504

Amount after 12 years

=700 + 504

= $1204.

Thus, This statement is not true.

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Step-by-step explanation:

Number of post-it's = 6*100=600+4*10+4+3=647post-its

Answer:

[tex]\dfrac{q^{4} r^8}{p}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{p^{-4}q^5r^6}{p^{-3}qr^{-2}}[/tex]

Separate the variables:

[tex]\implies\dfrac{p^{-4}}{p^{-3}} \times \dfrac{q^5}{q} \times \dfrac{r^6}{r^{-2}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies p^{(-4-(-3)} \times q^{(5-1)} \times r^{(6-(-2)}[/tex]

[tex]\implies p^{(-4+3)} \times q^{(5-1)} \times r^{(6+2)}[/tex]

[tex]\implies p^{-1} \times q^{4} \times r^8[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies \dfrac{1}{p} \times q^{4} \times r^8[/tex]

Simplify:

[tex]\implies \dfrac{q^{4} \times r^8}{p}[/tex]

[tex]\implies \dfrac{q^{4} r^8}{p}[/tex]

The algebraic expression for the given statement is: 2(n - 6).

To translate the statement, "twice the difference of a number and six", follow the steps below:

The two operations we would use are multiplication and subtraction.

The constants are 2 and 6.

Twice is translated as 2  ×, (-) is "difference".

Let the number be "n" .

The difference of a number, n, and 6, would be: n - 6.

Therefore, we would have the following algebraic expression: 2(n - 6).

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there woldbe 96 volume

Step-by-step explanation:

to find the volume you have to multiply width x lenghth x height

so set up your equation like this -

3 x 2 x 2

the times everything by 2 so it will now look like this -

6 x 4 x 4

then solve and get the answer 96

The number of miles that John Smith can travel with his budget if he has ​$500 left in his budget for car rental expenses is 900 miles.

Amount left in the budget = $500

Since he will rent a car that costs $50 per day and $ 0.50per mile, the expression will be:

50 + 0.50m = 500

where m  = number of miles

Collect like terms

0.5m = 500 - 50

0.5m = 450

Divide

m = 450/0.5

m = 900

Therefore, the number of miles that John Smith can travel with his budget is 900 miles.

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Maths:

Round 1

1) Grapes cost £1.50 per kg and carrots cost £1.00 per kg. How much would it costs for 3kg of

grapes and half a kilogram of carrots? £5

2) Jenny decides to share her sweets between herself and her 3 friends. She has 212 green

sweets, 310 blue sweets and 502 yellow sweets. How many sweets will Jenny and her friends

get each? 256

3) Large chocolate bars come with 32 pieces. Medium chocolate bars come with 24 pieces.

Barry buys 8 large bars of chocolate and 6 medium bars. How many pieces of chocolate will he

have altogether? 400

4) A flower shop sells roses for £1.79, carnations for £1.25 and buttercups for £1.30. Holly

decides to buy 3 roses and a buttercup. How much does she spend? £6.67

5) Pencils come in packs of 12 and each pack costs £1.19. Mr Green needs to buy a pencil for

each of the 50 children in his class. How much will he spend on pencils? £5.95

Round 2

1) Mrs Orange decides to share her savings between her six grandchildren. She has £350 in

her savings tin and £1450 in her savings account. How much will each of her grandchildren get?

£300

2) Green lollipops come in packs of 5, yellow lollipops come in packs of 6 and blue lollipops

come in packs of 4. A school buys 32 packs of blue lollipops and 18 packs of green lollipops.

How many lollipops will they buy altogether? 218

3) The baker’s oven can bake 28 loaves of bread at a time. In a day, it can go through 30 full

bakes. How many loaves of bread would be baked after 1 week? 5880

4) Ms Purple sells cars for a living. In one day, she sells 2 blue cars (at £4500 each), 7 yellow

cars (at £6000 each) and 12 black cars (at £8000 each). How much money does she take in car

sales in that one day? £147,000

5) Coaches carry 58 people. A school decides to take its 300 pupils and 38 staff on a visit to the

beach. A single coach costs £128. How much will the total cost of the coaches come to? £768

Topic:

Fruit Veg

Quince

raspberry

Lettuce

garlic

tomato

strawberry

grape

pumpkin

blackberries

nashi

kiwi

chilli

pear

passion fruit

cantaloupe

fig

eggplant/aubergine

cucumber

lemon

peach

lime

watermelon

pineapple

Zucchini/courgette

grapefruit

persimmons

mango

plum

cauliflower

Broccoli

Leeks

Fennel

Carrots

Coriander

Silverbeet

Snow peas

Beans

Celery

Beetroot

Peas

Artichoke

Sweet potato

Considering the definition of combination,  if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.

Combinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.

To calculate the number of combinations, the following expression is applied:

[tex]mCn=\frac{m!}{n!(m-n)!}[/tex]

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

If a family has 5 children, you can know that:

So, you can observe that 5C3 is equal to 5C2. Then:

5C3 = 5C2 = [tex]\frac{5!}{3!2!}[/tex]= 10

Finally, if a family has 5 children, in 10 ways the parents can have 2 boys and 3 girls as children.

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The number of months so that the investment gets double will be 86 months.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on. The amount is given as,

A = P + (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

The principal amount is $450 and if the amount gets doubled, then the value of the amount will be $900. The simple interest rate is 14%. Then the time is given as,

A = P + (PRT)/100

900 = 450 + [450 x 14 x T] / 100

450 = 450 x 14 x T / 100

T = 100 / 14

T = 7.14 years

T = 7.14 x 12

T = 85.7 ≈ 86 months

The number of months so that the investment gets double will be 86 months.

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The original price of the car is $15,000

Let us assume the original price of car be x. So, forming the equation to find the value of x and hence the original price of the car.

Equation -

x - 20% × x = 12000

x - 20/100×x = 12000

Cancelling zero as common in both numerator and denominator, on the left hand side of the equation

x - x/5 = 12000

Taking LCM on Left Hand Side of the equation

(5x - x)/5 = 12000

Rewriting the equation

4x = 12000 × 5

Performing multiplication on Right Hand Side of the equation

4x = 60,000

x = 60,000 ÷ 4

Performing division

x = 15,000

Therefore, the original price of the car is $15,000.

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The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.

Let the point be having coordinates (x,y).

If the point is in first quadrant:

Subcase: Clockwise rotation:

Then (x,y) → (y, -x)

Subcase: Counterclockwise rotation:

Then (x,y) → (-y, x)

We know that the rotation of a point (x,y) about the origin by 90° is (-y,x).

Given vertices of ΔLMN are  L(2,-2), M(7,-3), and N(5,2).

Let consider the rotations of L, M, and N are L', M', and N' respectively.

The rotation of a point L(2,-2)  about the origin by 90° is L'(-2,-2).

The rotation of a point M(7,-3) about the origin by 90° is M'(-7,-3).

The rotation of a point N(5,2) about the origin by 90° is N'(5,2).

Hence, the points  L'(-2, -2), M'(-7, -3), and N'(5, 2) are the rotation of vertices.

Therefore, L, M, and N of ΔLMN about the origin by 90°.

Hence, The rotation of the vertices L(2,-2), M(7,-3), and N(5,2) are L'(-2, -2), M'(-7, -3), and N'(5, 2) respectively.

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Answer:

Option 4

Step-by-step explanation:

This is the same as a rotation of 180° about the origin, which means we can negate the x and y coordinates of the preimage to get the coordinates of the image.

Answer:

A

Step-by-step explanation:

It might be the best one!

The expression that have 2\3 as a product are 4/5 × 5/6  and 6/7 × 7/9 which is option (a) and (e) .

(a) 4/5 × 5/6 = 20/30

                     = 2 /3

(b) 7/8 × 9/10 = 63 / 80

(c) 1/3 × 2/3 = 2 /9

(d)  3/4 × 7/12 = 21 / 48

                       = 7 / 16

(e) 6/7 × 7/9 = 42 /63

                    = 6 / 9

                    = 2 / 3

Only the expression (a) and (e) have  2\3 as a product.

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The complete question is given below :

Choose all the expressions that have 2\3 as a product.

(a) 4/5 × 5/6

(b) 7/8 × 9/10

(c) 1/3 × 2/3

(d) 3/4 × 7/12

(e) 6/7 × 7/9