Last year 950 people attended a town's annual parade. This year $1,520 people attended. What was the percent increase in attendance from last year to this year?

[tex]\text{Let}\ f(x)=3x+5\ \text{and}\ g(x)=x^2\\\\\dfrac{f(x)}{g(x)}=\dfrac{3x+5}{x^2}\\\\\text{The domain:}\\\\x^2\neq0\to x\neq0\\\\Answer:\ \boxed{x\in\mathbb{R}-\{0\}}\to\boxed{x\in(-\infty,\ 0)\ \cup\ (0,\ \infty)}\\\\\text{All real numbers except 0.}[/tex]

Answer:

Option A is correct.

d = 50t shows the relationship between d and t

Step-by-step explanation:

Point slope form: For a point [tex](x_1, y_1)[/tex] and a slope m, the equation of the line can be written as

[tex]y-y_1=m(x-x_1)[/tex] ......[1], where m is the slope of the line.

Here, d represents the total distance ( in miles) and t represents the time (in hours).

From the given table:

Consider any two points (1, 50) and (2, 100).

Calculate slope:

Slope(m) =  [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

               = [tex]\frac{100-50}{2-1}=\frac{50}{1} =50[/tex]

⇒[tex]m= 50[/tex]

Now, by point slope intercept form:

Substitute  m= 50 and (1, 50) in [1]

we have;

[tex]y -50 = 50(x-1)[/tex]

Using distributive property: [tex]a\cdot(b+c) = a\cdot b+ a\cdot c[/tex]

y -50 = 50x -50

Add both sides 50 we get;

y -50+ 50= 50x -50 + 50

Simplify:

[tex]y =50x[/tex]

∵y = d represents the distance and x = t represents the time;

then, our equation become:

[tex]d = 50t[/tex]

The equation representing the relationship between the distance covered (d) and time (t) in the given situation is d = 50t. This signifies that the distance covered is equal to 50 times the time.

In the given data, we observe that the total distance (d) travelled by the car in an hour is always 50 miles. This means that every hour, the car covers a distance of 50 miles.

Therefore, the relationship between the distance covered (d) and time (t) can represent this situation is d = 50t.

This signifies that 'd', the distance covered, is equal to 50 times 't', the time in hours. For example, when t=1 hour, d = 50*1 = 50 miles. Similarly, when t=2 hours, d = 50*2 = 100 miles. This continues accordingly.

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Answer:

[tex] b \le -6 [/tex]

Step-by-step explanation:

[tex] -1.2b - 5.3 \ge 1.9 [/tex]

Add 5.3 to both sides of the inequality.

[tex] -1.2b - 5.3 + 5.3 \ge 1.9 + 5.3 [/tex]

[tex] -1.2b \ge 7.2 [/tex]

Divide both sides by -1.2. When you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction. In this case, the "greater than or equal to" sign changes to a "less than or equal to" sign.

[tex] \dfrac{-1.2b}{-1.2} \le \dfrac{7.2}{-1.2} [/tex]

[tex] b \le -6 [/tex]

The solution set of the given inequality is {-6, -7, -8, -9, -10,......}.

The given inequality is -1.2b-5.3≥1.9.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The solution of given inequality can be solved as follows:

Add 5.3 to both side of the inequality, we get

-1.2b-5.3+5.3≥1.9+5.3

⇒ -1.2b≥7.2

Divide -1.2 to both side of the inequality, we get

-1.2b/(-1.2) ≤ 7.2/(-1.2)

⇒ b ≤ -6

So, solution set = {-6, -7, -8, -9, -10,......}

Therefore, the solution set of the given inequality is {-6, -7, -8, -9, -10,......}.

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Answer:

$497.80

Step-by-step explanation:

First, you want to find half of 10.48. This should be 5.24.

So, add 10.48 and 5.24. This gives you 15.72.

Now, you want to multiply that by 5, since 5 hours were overtime.

This gives you 78.60.

Lastly, you want to multiply 10.48 by 40.

This gives you 419.20

Now, add 78.60 and 419.20 together, giving you your answer of $497.80

Sara got $497.80 for the week.

I’m pretty sure you can first do 10% at a time which you can round to 13 which is 3 so 3 plus 3 then add tax

Hi There!

Step-by-step explanation:

20% = 0.2

6.25% = 0.0625

Discount: 12.99 * 0.20 = $2.598

Sale Price: 12.99 - 2.598 = $10.392

Tax: 10.392 * 0.0625 = 0.6495

Price After Tax: 10.392 - 0.6495 = 9.7425

Round: 9.7425 = 9.74

Answer:

$9.74

Hope This Helps :)

ABOUT SLOPE INTERCEPT FORM:

You have to get y by itself:

5x + 8y = 16

-5x          -5x

8y = -5x + 15

8             8

y = -5/8x + 15/8

OR

I you wants to simplify 15/8, it's this:

y = -5/8x +1.875

HI!!! Really really sorry if I'm incorrect...

1. The direction of the vector [tex]\theta[/tex] relative to the positive x-axis satisfies

[tex]\tan\theta=\dfrac35\implies\theta\approx30^\circ[/tex]

2. A vector with magnitude [tex]\|\mathbf v\|[/tex] and direction [tex]\theta[/tex] has component form

[tex]\mathbf v=\langle\|\mathbf v\|\cos\theta,\|\mathbf v\|\sin\theta\rangle[/tex]

We have [tex]\|\mathbf v\|=5[/tex], but "angle of 60 degrees with the negative x-axis" is a bit ambiguous. I would take it to mean "60 degrees counterclockwise relative to the negative x-axis", so that the direction is [tex]\theta=240^\circ[/tex]. Then

[tex]\mathbf v=\langle5\cos240^\circ,4\sin240^\circ\rangle\approx\langle-2.5,-4.3\rangle[/tex]

But this doesn't match any of the options, so more likely it means the angle is 60 degrees clockwise relative to the negative x-axis, in which case [tex]\theta=120^\circ[/tex] and we'd get

[tex]\mathbf v=\langle5\cos120^\circ,4\sin120^\circ\rangle\approx\langle-2.5,4.3\rangle[/tex]

3. Same as question 2, but now we're using [tex]\mathbf i,\mathbf j[/tex] notation. The vector has magnitude [tex]\|\mathbf v\|=14[/tex] and its direction is [tex]\theta=-30^\circ[/tex]. So the vector is

[tex]\mathbf v=14\cos(-30^\circ)\,\mathbf i+14\sin(-30^\circ)\,\mathbf j=12.1\,\mathbf i-7\,\mathbf j[/tex]

4. The velocity of the plane relative to the air, [tex]\mathbf v_{P/A}[/tex] is 175 mph at 40 degrees above the positive x-axis. The velocity of the air relative to the ground, [tex]\mathbf v_{A/G}[/tex], is 35 mph at 60 degrees above the positive x-axis. We want to know the velocity of the plane relative to the ground, [tex]\mathbf v_{P/G}[/tex].

We use the relationship

[tex]\mathbf v_{P/G}=\mathbf v_{P/A}+\mathbf v_{A/G}[/tex]

Translating the known vectors into component form, we have

[tex]\mathbf v_{P/G}=\langle145\cos40^\circ,145\sin40^\circ\rangle+\langle35\cos60^\circ,35\sin60^\circ\rangle\approx\langle152,143\rangle[/tex]

This vector has magnitude and direction

[tex]\|\mathbf v_{P/G}\|\approx\sqrt{152^2+143^2}\approx208\,\mathrm{mph}[/tex]

[tex]\tan\theta\approx\dfrac{143}{152}\implies\theta\approx43^\circ[/tex]

(or 43 degrees NE)

Answer: #3 is v=12.1i-7j

got it right on my test

#4 is C 208 mph and 43 northeast

Step-by-step explanation:

Answer:

≈ 44 cm²

Step-by-step explanation:

the area (A) of the washer is found using A = πr² ( r is the radius )

A = external area - internal area

external radius = [tex]\frac{15}{2}[/tex] = 7.5 cm

internal radius = [tex]\frac{13}{2}[/tex] = 6.5 cm

A = π ( 7.5² - 6.5² ) = π (56.25 - 42.25 ) = 14π ≈ 44 cm²

The area of the washer is calculated by finding the area of the external circle using its radius and then subtracting the area of the internal circle determined by its radius.

To find the area of a washer, we need to calculate the area of the larger outer circle and subtract the area of the smaller inner circle. The formula for the area of a circle is A = πr², where r is the radius of the circle.

Firstly, we calculate the area of the outer circle with a diameter of 15 cm. The radius r is half the diameter, so r = 15cm / 2 = 7.5 cm. The area, A₁, of the outer circle is:

A₁ = π × (7.5 cm)²

Secondly, we calculate the inner circle's area with a diameter of 13 cm. Similarly, its radius r is 13cm / 2 = 6.5 cm. The area, A₂, of the inner circle is:

A₂ = π × (6.5 cm)²

To find the washer's area, we subtract the inner area from the outer area:

Area of Washer = A₁ - A₂ = (π × (7.5 cm)²) - (π × (6.5 cm)²)

The result will be the cross-sectional area of the washer.

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Answer:

36

Step-by-step explanation:

5/6 of x = 30 miles

Multiply each side by 6 to get rid of the fraction

5x = 180

Divide each side by 5

x = 36

Answer: B. X^1/8 Y^8

Step-by-step explanation:

The equivalent expression for (x^1/4 y^16)^1/2 is x^1/8 y^8, using the power of a power rule in properties of exponents.

The expression (x^1/4 y^16)^1/2 can be simplified through the properties of exponents. To simplify, we apply the power of a power rule, which states that (a^m)^n = a^(m*n). Applying this rule:

(x^1/4 y^16)^1/2 = x^(1/4 * 1/2) * y^(16 * 1/2) = x^(1/8) * y^8

Therefore, the equivalent expression is x^1/8 y^8, which corresponds to option B.

Answer:

0,1.5

Step-by-step explanation:

y = 510 - 60x

We want to find the domain or the x values where x represents the time

We need to determine the possible values for x

Y cannot be greater than 510 or less than 0.  510 means they have not started the trip, and 0 means they have arrived

510 = 510 -60x

Subtract 510 from each side

510-510 = 60x

0 = 60x

The smallest value of x can be 0

0 = 510 - 60x

Subtract 510 from each side

-510 = 510-510-60x

-510=-60x

Divide by -60

-510/-60 = -60x/-60

8.5 = x

The maximum value of x is 8.5 hours

So x must be between 0 and 8.5 inclusive.

Answer:

1.5 and 0

Step-by-step explanation:

The domain is the set of all possible x-values that make the function work and generate real y-values.

y = 510 – 60x

y cannot be greater than 510, because that would mean they are not yet at their starting point.

y cannot be less than 0, because that would mean they have passed their destination

We can get an idea of the domain if we solve the function for x. We get

x=(510 – y)/60

If y = 510, x = 0.

If y = 0, x = 510/60 = 8.5.

Thus, the domain is 0 ≤ x ≤ 8.5.

The only numbers in your list that could be in the domain are 1.5 and 0.

10 and 60 are wrong, because they give negative values for y.

-3 is wrong, because it gives y > 510.

Answer:

$150.77

Step-by-step explanation:

The cost of the bike after a 30% markup is equal to $196.  In order for this to happen we have to understand that to mark something up means 100% + 30% in this case.  100% represents the original price of the item and 30% is the markup.  In decimals 100% is = 1 since 100÷100=1 and 30% is 30÷100=0.3, therefore to mark the original item "x" we have to multiply that number by 1.30 and so mathematically speaking:

[tex]x(1.3)=196\\\\x=\frac{196}{1.3}\\\\x=150.77[/tex]

The wholesale price of the bike is $150.77

Answer:

The answer is C (4,-3)

Step-by-step explanation:

When you reflect over the x axis that means you flip the image to the opposite side over the x (horizontal) line. So if the first line is (4,3) then the reflection is (4,-3)

Answer: 2 and 1/3 cans per day

Step-by-step explanation:

Attempt to divide the cans into 3 equal piles. you get 2 cans in each pile and one left over. Divide the last can into three parts.

Multiply by 2:

2=u-2

4=u or u=4.

Answer:

constant = 15

coefficient = 2.5

Step-by-step explanation:

A constant does not change value no matter what, and a constant's derivative is always 0. In this equation, 15 does not change with any variable, therefore it is the constant.

A coefficient is the number that comes before a variable. In the equation, r is a variable, and the number 2.5 comes before it, making it the coefficient.

Answer:

c = (ab -d) /a

Step-by-step explanation:

a(b – c) = d  

Divide each side by a

a/a(b – c) = d  /a

b-c = d/a

Subtract b from each side

b-b-c = d/a -b

-c = d/a -b

Multiply by -1

-1*-c = -1(d/a -b)

c = -d/a +b

c = b - d/a

Get a common denominator

c = b*a/a -d/a

Combine over the common denominator

c = (ab -d) /a

Answer:

$86 is she spending on the party.

Step-by-step explanation:

As per the statement: A company employee is planning a promotion party with her friends. She orders 6 pizzas for $7 each, 2 bowls of mixed salad for $12 each, and 4 cases of assorted soft drinks for $5 each.

⇒ 6 pizzas for $7 each

Total cost for 6 pizzas = [tex]6 \times 7 = \$42[/tex]

2 bowls of mixed salad for $12 each.

Total cost for 2 bowls = [tex]2 \times 12 = \$24[/tex]

and

4 cases of assorted soft drinks for $5 each.

Total cost for 4 cases of assorted soft drinks = [tex]4 \times 5 = \$20[/tex]

She spending on party = Total cost for 6 pizzas + Total cost for 2 bowls + Total cost for 4 cases of assorted soft drinks

Substitute the values we get;

Total cost she spending on party = [tex]\$42 + \$24 + \$20 =\$86[/tex]

Answer:

(x + 6)(x + 8)

Step-by-step explanation:

Multiply x^2 by 48.

48 * x^2 = [tex]48x^2[/tex]

Factor 48.

Find two factors which add to 14.

6 and 8.

Check

6 * 8 = 48

6 + 8 =14

Add x by 6

Add x by 8

Answer

(x + 6)(x + 8)

The factors of the given trinomial are (x+6) & (x+8)

If an algebraic expression has three non-zero terms or monomials, then it is called trinomial.

Example : [tex]x^{2} +x+1[/tex] , where [tex]x^{2} , x, 1[/tex] are three non-zero terms or monomials.

Given trinomial is [tex]x^{2} +14x+48[/tex]

First, we have to factorise 48 & find two factors whose addition is 14.

The factors are 6 & 8, since 6×8=48 & 6+8=14

Rewrite the terms : [tex]x^{2} +6x+8x+48[/tex]

Regroup terms into two proportional parts : [tex](x^{2} +6x)+(8x+48)[/tex]

Taking common from both parts : [tex]x(x+6)+8(x+6)[/tex]

Factor the expression : [tex](x+6)(x+8)[/tex]

∴ The factors are (x+6) & (x+8).

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Answer:

x = 12

Step-by-step explanation:

Remark

These two angles are corresponding angles and as such, they are equal.

Equation

8x+ 36 = 5x + 72

Solution

Subtract 5x from both sides

8x - 5x + 36 = 5x - 5x + 72          Combine like terms.

3x + 36 = 72                                 Subtract 36 from both sides

3x + 36 - 36 = 72 - 36                  Collect like terms

3x = 36                                          Divide by 3

3x/3 = 36/3                                   Divide

x = 12                                             Answer

The area of the rectangle is 60 units²

Since from the graph, we have the vertices of the rectangle at (-1,1), (8, -2), (-3, -5) and (6, -8).

The pair (-1, 1) and (8, -2) represent the coordinates for the length of the rectangle while the pair (-1, 1) and (-3, -5) represent the coordinates for the width of the rectangle.

So, we find the length of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₂, y₂)

So, the length, L = √[(x₂ - x₁)² + (y₂ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₂, y₂) = (8, -2)

So, L = √[(x₂ - x₁)² + (y₂ - y₁)²]

L = √[(8 - (-1))² + (-2 - 1)²]

L = √[(8 + 1))² + (-3)²]

L = √[(9)² + (-3)²]

L = √[81 + 9]

L = √90

L = 3√10 units

Also, we find the width of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₃, y₃)

So, the width, W = √[(x₃ - x₁)² + (y₃ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₃, y₃) = (-3, -5)

So, W = √[(x₃ - x₁)² + (y₃ - y₁)²]

W = √[(-3 - (-1))² + (-5 - 1)²]

W = √[(-3 + 1))² + (-6)²]

W = √[(-2)² + (-6)²]

W = √[4 + 36]

W = √40

W = 2√10 units

Since the area of a rectangle A = LW, we have

A = 3√10 units × 2√10 units

A = 3 × 2 × √10 × √10 units²

A = 3 × 2 × 10 units²

A = 60 units²

So, the area of the rectangle is 60 units²

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The area of the rectangle is 60 units².

To find the area of a rectangle, you need to multiply its length by its width.

Since from the graph, we have the vertices of the rectangle at (-1,1), (8, -2), (-3, -5) and (6, -8).

The pair (-1, 1) and (8, -2) represent the coordinates for the length of the rectangle while the pair (-1, 1) and (-3, -5) represent the coordinates for the width of the rectangle.

So, we find the length of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₂, y₂)

So, the length, L = √[(x₂ - x₁)² + (y₂ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₂, y₂) = (8, -2)

So, L = √[(x₂ - x₁)² + (y₂ - y₁)²]

L = √[(8 - (-1))² + (-2 - 1)²]

L = √[(8 + 1))² + (-3)²]

L = √[(9)² + (-3)²]

L = √[81 + 9]

L = √90

L = 3√10 units

Also, we find the width of the rectangle from the equation for the distance between two points (x₁, y₁) and (x₃, y₃)

So, the width, W = √[(x₃ - x₁)² + (y₃ - y₁)²] where  (x₁, y₁) = (-1, 1) and (x₃, y₃) = (-3, -5)

So, W = √[(x₃ - x₁)² + (y₃ - y₁)²]

W = √[(-3 - (-1))² + (-5 - 1)²]

W = √[(-3 + 1))² + (-6)²]

W = √[(-2)² + (-6)²]

W = √[4 + 36]

W = √40

W = 2√10 units

Since the area of a rectangle A = LW, we have

A = 3√10 units × 2√10 units

A = 3 × 2 × √10 × √10 units²

A = 3 × 2 × 10 units²

A = 60 units²

So the area of the rectangle is 60 units².

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Answer:

C. 6 ⋅ 9 + 1

Step-by-step explanation:

Start with the multiplication:

"one more than the product of six and nine"

6 ⋅ 9

Now take care of the addition by adding 1 to the product.

"one more than the product of six and nine"

6 ⋅ 9 + 1

Answer: C. 6 ⋅ 9 + 1

Answer:

i is equal to the square root of -1, and -1 to any power equals -1

Step-by-step explanation:

[tex]i^18[/tex] must be equal to 1 because [tex]i^4[/tex] is equal to 1, and 18 is a multiple of 4.

The imaginary unit i is defined as the square root of -1. Therefore, by definition, [tex]i^2[/tex] = -1.

Now let's consider higher powers of i:

[tex]- i^3 = i^2 i = -1 i = -i[/tex]

[tex]- i^4 = i^2 = -1 = 1[/tex]

Notice that when we raise i to the fourth power, we get 1. This is a key observation because it means that the powers of i repeat every four powers. This is known as the cyclical nature of the powers of i.

Given that [tex]i^4 = 1[/tex], we can express any power of i that is a multiple of 4 as 1. This is because raising i to any multiple of 4 will result in an even number of -1 factors, which will always multiply to 1.

Now, let's consider [tex]i^18[/tex]:

- Since 18 is divisible by 4 (18 = 4 * 4.5), we can express [tex]i^18 as (i^4)^4.5[/tex].

- We know that [tex]i^4 = 1[/tex], so [tex](i^4)^4.5 = 1^4.5 = 1[/tex].

Therefore, [tex]i^18[/tex] = 1, not -1 as initially stated. The power of i cycles through -1, -i, 1, and i, repeating every four powers. Since 18 is a multiple of 4, i^18 lands on 1 in this cycle.

The answer in fraction form is c = 1/2

The answer in decimal form is c = 0.5

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

Explanation:

Saying "A is 1 less than B" means A = B-1. So whatever B is, subtract 1 from it and you get the value of A.

Replace A with the expression 2(3-5c). Replace B with 4(1-c)

We go from this

A = B - 1

to this

2(3-5c) = 4(1-c) - 1

----------

Let's isolate c

2(3-5c) = 4(1-c) - 1

2(3)+2(-5c) = 4(1)+4(-c) - 1

6-10c = 4 - 4c - 1

6-10c = 3 - 4c

6-3 = -4c+10c

3 = 6c

6c = 3

c = 3/6

c = 1/2

c = 0.5

The value of c in the given expressions is 1.

The value of c when the expression 2(3–5c) is 1 less than the expression 4(1–c) is 1.

First, we set up the equation: 2(3-5c) = 4(1-c) - 1.

Solving this equation step by step will lead us to the value of c.

In this case, the solution is c = 1.

Answer:

0.125

Step-by-step explanation:

you have half of box divide that by 4

Answer:  Explained.

Step-by-step explanation: We are familiar with the theory of probability and the Law of 'Large Numbers'.

According to this law, if same experiment is repeated a large number of times, then the average of the experimental results in each trial shoul be very close to the theoretical probability.

When Jake flipped the magic coin 100 times, the probability of getting hesd was 0.64.

When he flipped 500 times, the probability of getting head was 0.57.

When he flipped 1000 times, the probability of getting head was 0.58

and when he flipped 1500 times, the probability was 0.62.

Also, the theoretical probability of the magic coin coming up head is

[tex]p=\dfrac{1}{2}=0.5.[/tex]

Therefore, we see that as the number of experiments increases, the value becomes closer to the theoretical value which is 0.5.

Answer:

1

Step-by-step explanation:

first of all, use substitution.

3x + - 4x +10 =9

Then move all x's to one side.

10 = 9 + x

Move all normal numbers to one side

1 = x

Answer:

y=6

Step-by-step explanation:

Answer:

30b

Step-by-step explanation:

-6(-5) is 30.

Answer:

x = ± 1/8

Step-by-step explanation:

64 x^2 =1

Divide each side by 64

64 x^2/64 = 1/64

x^2 = 1/64

Take the square root of each side, remembering to take the positive and negative.

sqrt(x^2) = ±sqrt(1/64)

x = ±sqrt(1)/ sqrt(64)

x = ± 1/8