During a sale atthe book store sold for 3$ and magazinssold for2.50. Jan spent 16$ and bought a total of 6 books and magazines. How many of each did she buy.

Carl's horse traveled approximately 31.4 feet further than Allison's horse in one complete turn of the carousel. The distances were calculated using the circumference formula for each horse based on their distance from the centre of the carousel.

The question involves comparing the distances traveled by horses on a carousel based on their distance from the center of the ride. To find out how much further Carl's horse traveled compared to Allison's, we need to calculate the circumference of the circular paths each horse took during one complete turn of the carousel and then find the difference between these two distances.

To calculate the circumference (C) of a circle, we use the formula C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle, in this case, the distance from the center of the carousel to the horse.

For Carl's horse:
CCarl = 2π(15 feet) ≈ 2π×15 ≈ 94.2 feet

For Allison's horse:
CAllison = 2π(10 feet) ≈ 2π×10 ≈ 62.8 feet

The difference in the distances traveled by the horses in one complete turn is CCarl - CAllison, which is approximately 94.2 feet - 62.8 feet = 31.4 feet. Therefore, Carl's horse travelled about 31.4 feet further than Allison's horse in one complete turn.

Answer:

Saul is incorrect. The proper answer should be 6x^3

Step-by-step explanation:

Think of "x^3" as "x". So we have 2x+4x = 6x. Similarly, 2x^3+4x^3 = 6x^3. The exponents of the like terms do not change.

As a more real world example, let's say that we replace "x^3" with "dogs". Saying "2x^3" could mean "2 dogs". Same goes for "4x^3" meaning "4 dogs". So "2x^3+4x^3" turns into "2 dogs + 4 dogs", and you can see that leading to 6 dogs total. The last step is to replace "dogs" with "x^3" to end up with 6x^3. The x^3 stays the same the whole time in much the same way that "dogs" do not change either.

Answer:

saul is incorrect

2x3 + 4x3 is the same as (2 . x^3) + (4 . x^3)

6x6  is the same as 6x . x. x. x. x. x

2x3 + 4x3 simplifies to 6x^3

Step-by-step explanation:

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ H(\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad K(\stackrel{x_2}{7}~,~\stackrel{y_2}{2}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{7+9}{2}~~,~~\cfrac{2+4}{2} \right)\implies (8,3)[/tex]

Answer:

41

Step-by-step explanation:

We know that complex numbers are a combination of real and imaginary numbers

Real part is x and imaginary part y is multiplied by i, square root of -1

Modulus of x+iy = [tex]\sqrt{x^2+y^2}[/tex]

Here instead of x and y are given 9 and 40

i.e. 9+40i

Hence to find modulus we square the coefficients add them and then find square root

|9+49i| =[tex]\sqrt{9^2+40^2} =\sqrt{1681}[/tex]

By long division method we find that

|9+40i| =41

Answer:  Modulus of |9+40i| =41

Step-by-step explanation:

Since we have given that

[tex]z=\mid9+40i\mid[/tex]

Here,

[tex]z=a+bi\\\\where,\\\\a=\text{real number}=9\\\\b=\text{imaginary number}=40[/tex]

We need to find the modulus of z:

[tex]\mid z\mid=\sqrt{a^2+b^2}[/tex]

[tex]\mid z\mid=\sqrt{9^2+40^2}\\\\\mid z\mid=\sqrt{81+1600}\\\\\mid z\mid=\sqrt{1681}\\\\\mid z\mid=41[/tex]

Hence, Modulus of |9+40i| =41

Answer:

By the looks of it i would assume 3 grams of protein and 12 calories burned but i am not sure either i am stuck on the same question

Step-by-step explanation:

Answer:

7.11 and 9.48

Step-by-step explanation:

.12 is equal to 7.11

with out coupon

.12 is equal to 9.48

with the coupon

a. Isaac's total bill is $84.53

b. Isaac's price after the discount is $63.40

c. The shoe store clerk's commission before the coupon is $9.48 and $7.11  after the coupon

Solution to the first question

Total bill = cost of shoes + tax paid

Tax paid = tax rate + cost of shoes

Cost of shoes = $37.00 + $42.00. = $79

Tax paid = $79 + 0.07 = $5.53

Total bill = $5.53 + $79 = $84.53

Solution to the second question

The discounted price of the shoes can be found by subtracting the value of the discount from the price of the shoes

Discounted price = cost of the shoes = value of the 25% discount

Value of the 5% discount = 0.25 x $79= $19.75

Discounted price = $79 - $19.75 = 59.25

Bill = discounted price x ( 1 + tax rate)

59.25 x 1.07 = $63.40

Solution to the third question

Commission before the coupon

Commission = 12% x price before the coupon

0.12 x $79 = $9.48

Commission after the coupon

Commission = 12% x price after the coupon

0.12 x 59.25 = $7.11

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Answer:

Hence third choice RQ, RP, PQ is correct.

Step-by-step explanation:

We know that if A, B, C are the angles of the triangle and if ∠A > ∠B

a>b   {Where “a” is side created by angle A and “b” is side created by angle B }.

We will use same property to decide which side is bigger.

In triangle PRQ,

∠P = 30 degree

∠R = 85 degree

then ∠P + ∠R + ∠Q = 180 {since sum of all three angle of triangle is 180 degree}

30 + 85 + ∠Q = 180

115 + ∠Q = 180

∠Q = 180 - 115

∠Q = 65

Now we know measure of all angles so we can do comparison using above property.

Smallest angle is ∠P so side RQ will be smallest.

Largest angle is ∠R so side PQ will be largest.

Hence we get RQ < RP < PQ.

Hence third choice RQ, RP, PQ is correct.

Answer: D) 80000; exponential function

Step-by-step explanation:

It would double 3 times in total; first from 10k to 20k, then from 20k to 40k, and finally from 40k to 80k. Hope this helps

Answer:

D)80,000; exponential function

Step-by-step explanation:

We are given that a town with a population of 10,000 doubles every 14 years

So, Initial Population = 10,000

Now we are given that  what will the population be in 42 years

First determine how many times population will double : [tex]\frac{42}{14} = 3[/tex]

So, In 42 years it doubles three times .

Now Linear functions change at a constant rate per unit interval while An exponential function changes by a common ratio over equal intervals.

So, the given situation will be modeled by exponential function

So, Using exponential function : [tex]y=ab^x[/tex]

Where a is Initial Population = 10,000

b is rate of change

x = time = 3 times

So, the population will be in 42 years=[tex]10000 (2)^3[/tex]

                                                             =[tex]80000[/tex]

So, the population will be 80,000 after 42 years.

Thus Option D is correct.

D)80,000; exponential function

Answer:

d.  m = fs/ (a+r)

Step-by-step explanation:

f/ (a+r) = m/s

We want to isolate m, so we will multiply both sides by s

f/ (a+r)  *s= m/s*s

fs/ (a+r) = m

[tex]\dfrac{m}{s}=\dfrac{f}{a+r}\qquad\text{multiply both sides by}\ s\neq0\\\\\boxed{m=\dfrac{fs}{a+r}}[/tex]

Answer:

(-∞,7) U (7,∞)

Step-by-step explanation:

f(x)= x+2

g(x) = x-7

[tex]\frac{f(x)}{g(x)} =\frac{x+2}{x-7}[/tex]

Here we have x-7 in the denominator

To find domain we set the denominator =0  and solve for x

x-7=0

Add 7 on both sides

x=7

x=7 makes the denominator 0 that is undefined

So we ignore 7 for x

Hence domain is

(-∞,7) U (7,∞)

Answer:

The correct answer i believe is A.

Answer: Choice C)

y = (x-2)(x-2)

note: This is the same as y = (x-2)^2

======================================================

The x intercept or root is x = 2, so x-2 is a factor. There is only one root visible, but this is a parabola, so it's technically a double root (it repeats itself). That is why (x-2) shows up twice giving (x-2)(x-2)

If the equation was simply y = x-2, then it would be a linear equation instead of a curved parabola.

Note how plugging in x = 2 leads to the following y value

y = (x-2)(x-2)

y = (2-2)*(2-2)

y = 0*0

y = 0

So (2,0) is the only x intercept.

Answer:

X=3

Step-by-step explanation:

We have two linear functions which intersect at a point. Linear functions are lines which are made of points that satisfy the function or relationship.  This means at the intersection, this point (3,-1), both functions have values. An input of x=3 produces y=-1 in both functions.

Answer:

The correct option is 4.

Step-by-step explanation:

If the graph of a function represent in coordinate plane, then x-axis represents the domain of the function and y-axis represents the range of the function.

We have to find the input value that produces the same output value for the two functions on the graph.

From the given graph it is clear that the intersection point of both functions is at (3,-1).

At x=3 the output value of f(x) is -1.

At x=3 the output value of g(x) is -1.

It means both functions have same output -1 at x=3.

Therefore the correct option is 4.

Answer: 28 and 18

Step-by-step explanation:

I used the guess and test strategy to find that:

28 - 10 = 18

28 + 18 = 46

To find the two numbers, we need to solve a system of equations. By assigning variables to the numbers and setting up equations based on the given information, we can use the method of substitution to find the values of x and y. The two numbers are 28 and 18.

To solve this problem, let's assign variables to the numbers. Let's say the two numbers are x and y. We are given two pieces of information: the sum of the two numbers is 46, so we can write the equation x + y = 46, and the difference between the two numbers is 10, so we can write the equation x - y = 10.

To solve this system of equations, we can use the method of substitution. Rearrange one of the equations to solve for one variable in terms of the other. For example, we can rearrange the first equation to get x = 46 - y. Substitute this expression for x in the second equation:

(46 - y) - y = 10.

Simplify the equation:

46 - 2y = 10. Subtract 46 from both sides:

-2y = -36. Divide both sides by -2 to solve for y:

y = 18. Substitute this value of y back into one of the equations to solve for x:

x + 18 = 46. Subtract 18 from both sides:

x = 28.

So the two numbers are 28 and 18.

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Answer:

(C) 17.15

Step-by-step explanation:

Answer:

9/16

Step-by-step explanation:

(2+1/4)/4=(8/4+1/4)/4=(9/4)(1/4)=9/16

The answer is 26.46. I got it correct on my GoFormative.

The price of shoe store merchandise after markup price will be equal to 26.46.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given data given in the question,

The wholesale price of merchandise = 24.50

Markup percentage on merchandise = 8%

Then, the amount of increment in the price will be,

(24.50 × 8)/100

= 196/100

=1.96

Then, the price of merchandise after markup will be,

= 24.50 + 1.96

= 26.46

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Answer:

v = 15 miles / hour

Step-by-step explanation:

Given:

Distance covered by biker = s=45 miles

time taken by him = t=180 minutes

TO Find:

speed in miles per hour = v = ?

Solution:

As it is given that the distance covered is 45 miles

and time taken by him is 180 minutes

as one hour have 60 minutes

so time taken by rider = t = 180 /60

                                          = 3 hours

this step is done because we have to find speed in miles per hour

Now

The formula for finding the distance is

distance = speed * time

or

s = v * t

we have to find v

so dividing both sides by t

[tex]\frac{s}{t} = \frac{v*t}{t}[/tex]

it becomes

[tex]v = \frac{s}{t}[/tex]

Putting the values

[tex]v = \frac{45}{3}[/tex]

solving it gives

v = 15 miles / hour

which is the required speed

in the given options it is not available

The speed is 15 miles per hour, not matching any of the provided answer choices.

The question asks for the speed of the biker in miles per hour when given the distance rode over a certain amount of time. To find the speed, we can use the formula: Speed = Distance / Time.

In this case, the biker rode 45 miles in 180 minutes. Since there are 60 minutes in an hour, we first convert 180 minutes into hours by dividing by 60: 180 / 60 = 3 hours.

Next, we calculate the speed: Speed = 45 miles \/ 3 hours = 15 miles per hour. But since this isn't one of the options provided, it seems there has been a typo in the answer choices. The correct answer, which should be 15 mph, is missing in the options.

Answer:

Step-by-step explanation:

Shelly's first race time is 43.13 seconds.

Shelly's second race times is 43.1 seconds.

Basically, she improved 0.03 seconds, because 43.13 - 43.1 = 0.03.

If she keeps this patterns that means she will improve 0.03 each race.

So, the third race times is 43.1 - 0.03 = 43.07 seconds.

The fourth race time is 43.07 - 0.03 = 43.04 seconds.

Therefore, the time in the fourth race is 43.04 seconds, because she's improving at a constant rate of 0.03 seconds per race.

Answer:

Total pay = 400+ 1650* 5/100= 482,5 $

Step-by-step explanation:

€9.31

total = price + tax

... tax = 0.19×price . . . . . . . meaning of 19% VAT

... total = price + 0.19×price = 1.19×price

Dividing by 1.19, we can find the price in terms of the total.

... total/1.19 = price

And we can use this to find the tax

... tax = 0.19×price = 0.19×(total/1.19) . . . . . substitute for price

... tax = 0.19/1.19 × total = 19/119 × total . . . . . . simplify

... tax = 19/119 × 58.31  . . . . . . .  put in total amount

... tax = 9.31 . . . . euros

Multiplying by a fraction yields a smaller number if the fraction is less than 1, and a larger number if the fraction is greater than 1.

When multiplying by a fraction, the result depends on the fraction you're multiplying by. If the fraction is less than 1 (or what we refer to as a proper fraction where the numerator is less than the denominator), then the result is a smaller number than the original number you started with. For instance, multiplying 5 by 1/2 (which is a proper fraction) will yield 2.5, which is smaller than 5. However, if you multiply by a fraction greater than 1 (an improper fraction where the numerator is greater than the denominator), such as 5/3, the result will be a larger number. So, multiplying 5 by 5/3 will yield approximately 8.33, which is larger than 5.

Answer:

P(A or B) = 2/3                      

Step-by-step explanation:

Blue Garments = 1 blue shirt, 1 blue hat, 1 blue pair of pants

Total blue garments = 3

Green garments= 1 green shirt, 1 green hat, 1 green pair of pants

Total green garments = 3

Total no. of garments = blue garments +green garments = 6

A = event that Ivan selects a green garment

P(A) = Favourable outcomes/Total no. of outcomes

P(A)    = 3/6

B = event that Ivan chooses a pair of pants

P(B) = 2/6

We need to find P(A or B) = P(A∪B)

By formula, P(A∪B) = P(A)+P(B)-P(A∩B)

P(A∩B) = Probability that a green pair of pant is chosen = 1/6

P(A∪B) = 3/6+2/6-1/6

           = 4/6

           =2/3

Answer:

1/2

Step-by-step explanation:

Answer:

the square root of 2 times the negative square root of 2 would be -2, which is a rational number.

Answer: 4.01% interest rate

This value is approximate. It is rounded to the nearest hundredth of a percent.

============================================

Work Shown:

A = P*e^(r*t)

1833 = 1500*e^(r*5)

1833/1500 = e^(5r)

1.222 = e^(5r)

e^(5r) = 1.222

5r = Ln(1.222)

5r = 0.2004888607494

r = 0.2004888607494/5

r = 0.04009777214989

r = 0.0401

r = 4.01%

Answer: Option A is correct

(-5,3) U (3,6]

Step-by-step explanation:

Domain of a function is the complete set of values that the independent variable can assume.

In the given graphed function we can see that the minimum value of independent variable (x) is -5 and the maximum value is 6, wherein the values -5 and 3 do not belongs to x.

This set of values is represented as

(-5,3) U (3,6]

Hope it helps.

Thank you.

The domain of the graphed function is (-5,3) U (3,6].

The correct option is A.

The domain of a function is the entire range of values that the independent variable can take.

In the given graphed function, we observe that the lowest value of the independent variable (x) is -5, and the highest value is 6.

However, it is the values -5 and 3 are not included in the domain.

So, the set of values is represented as (-5,3) U (3,6].

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Answer: B

Step-by-step explanation:

  x³ - 3x²  + 16x - 48 = 0

→ x²(x - 3)   + 16(x - 3) = 0

→ (x² + 16) (x - 3) = 0

→ (x² - (-16)) (x - 3) = 0

→ (x - 4i)(x + 4i)(x - 3) = 0

→ x - 4i = 0    x + 4i = 0   x - 3 = 0

→  x = 4i          x = -4i        x = 3

2 imaginary roots         and 1 real root

ANSWER:

For the first picture, it is the first answer. This is because of the Exterior Angle Theorem.

For the second picture, use the Exterior Angle Theorem again, but this time, solve for x.

[tex]132 = x + (3x-24)\\132 = 4x - 24\\156=4x\\x=39[/tex]

The m∡B = 39°

What are the answer choices?

To find out what percent of the calories in a candy bar comes from sugar, divide the calories from sugar (132) by the total calories (220) and multiply by 100, resulting in 60% of the calories being from sugar.

To calculate what percent of the calories in the candy bar are from sugar, we can use the formula for percentage: (part / whole) x100. In this case, the part is the number of calories from sugar, and the whole is the total number of calories in the candy bar.
First, let's identify the given values:

Now, let's calculate the percentage:

Calculating this, we find:

Therefore, 60% of the calories in the candy bar are from sugar.