I need help please!!!

Answer:

$47.70

Step-by-step explanation:

45 × 0.06 = $2.70

the tax is $2.70 add tax with price of shoes

45+ 2.7= $47.70

Answer:

the tax is $7.50 :)

Answer:

(y - 2)² = -12(x - 5)

Step-by-step explanation:

A parabola is a locus of points, which are equidistant from the focus and directrix;

Generic cartesian equation of a parabola:

y² = 4ax, where the:

Focus, S, is: (a, 0)

Directrix, d, is: x = -a

a > 0

Put simply, a is the horinzontal difference between the directrix and the vertex or between the vertex and focus;

Always a good idea to do a quick drawing of the graph;

We are the told the focus, F, is: (2, 2) and directrix, d, is: x = 8;

First thing to note, the vertex, or turning point will be in line with the focus vertically, i.e. they will share the same y-coordinate;

Horizonatally, it will be halfway between the focus and the directrix, i.e. halfway between 8 and 2;

Therefore, the vertex will be will be (5, 2);

We can also work out a:

a = 8 - 5 = 5 - 2

a = 3

Substituting this value of a into the generic cartesian equation:

y² = 4(3)x

y² = 12x

The focus and directrix will be:

S: (3, 0)

d: x = -3

Next thing to note, a parabola curves away from the directrix;

In this case, the directrix is x = 8, so the vertex will be the right-most point on the parabola, it will curve off to the left and the focus will also be to the left;

What we want to do is compare with y² = 12x;

This parabola, has a vertex (0, 0), which is the left-most point that curves off to the right and a focus also to the right;

Since we know the formula of this parabola, if we figure out how to transform it into the one in the question, we can find out it's equation;

What we should recognise first is that the parabola in the question is reflected in the y-axis, compared to y² = 12x;

So we apply the transformation that corresponds to this, i.e. use the f(-x) rule:

y² = 12(-x)

y² = -12x

Now the two graphs will have the same shape and orientation;

The focus and directrix will also be affected:

S: (-3, 0)

d: x = 3

Now, the only remaining difference would be the coordinates of the focus and directrix of the two graphs;

The focus of the graph in the question is 5 units to the right and 2 units upwards compared to the focus of y² = -12x;

The directrix is 5 units to the right of that of y² = -12x;

So we apply a translation transformation of 5 units right and 2 units up, like so:

(y - 2)² = -12(x - 5)

Replace y with (y - 2) to translate up 2 units;

Replace x with (x - 5) to translate 5 units right.

We know have a parabola with focus, (2, 2), directrix, x = 8 and vertex, (5, 2), i.e. the parabola in the question;

Hence, the equation of the parabola in the question is:

(y - 2)² = -12(x - 5)

It might seem a bit long and complicated to begin with, but can be done very quickly if you can get used to it.

Answer:

Step-by-step explanation:

Solve the System of Equations

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Point Form:

(−1,7)

Equation Form:

x=−1,y=7

Answer:

The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

For this problem, we have that:

\(n = 603, \pi = \frac{142}{603} = 0.2355\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 - 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2016\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2355 + 1.96\sqrt{\frac{0.2355*0.7645}{603}} = 0.2694\)

The 95% confidence interval for the proportion of all shoppers during the year whose visit was because of a coupon they'd received in the mail is (0.2016, 0.2694)

Answer: 2/3

Step-by-step explanation:

Answer: 2/3

Step-by-step explanation:It can sometimes be difficult to divide fractions, such as 1/4 divided by 3/8. When we divide two fractions, such as 1/4 ÷ 3/8, we flip the second fraction and then we simply multiply the numerators with each other and the denominator with each other.

In accordance with the exponential model, the current forest area is equal to 2801.149 square kilometers after six years.  

According with statement, the forest area decreases exponentially in time. Then, the exponential model is defined by following model:

n(x) = n' · (1 - r)ˣ

Where:

If we know that n' = 4400 km², r = 0.0725 and x = 6 yr, then the current forest area is:

n(6) = 4400 · (1 - 0.0725)⁶

n(6) = 2801.149

To learn more on exponential functions: https://brainly.com/question/30951187

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Answer:

First triangle x=9

Second triangle x=20

Step-by-step explanation:

Using Pythagorean theorem

40^2+x=41^2

1600+x^2=1681

-1600        -1600

x^2=81

To find x we do the opposite of powers and find the squared

x=9

Second triangle

21^2+x^2=29^2

441+x^2=841

-441        -441

x^2=400

x=20

Answer:

q= -40p+c

q= -40p+4,000

Step-by-step explanation:

$5 each for 3800 tye-dye shower curtains

$10 each for 3600 tye-dye shower curtains

Slope of the demand line is

3800-3600/5-10

=200/-5

= -40

Demand function is

q= -40p + c

Where c is a constant

For q=3800 and p=$5

Demand function is

q= -40p + c

3800= -40(5)+c

3800= -200+c

c=3800+200

c=4,000

Linear demand function is

q= -40p+4,000

Answer and Explanation:

See attached image.

Answer:

Step-by-step explanation:

Area is the function of two dimensions.

If each dimension is increased 3 times then the area will increase:

Correct choice is D

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

The correct answer is \(y = \sqrt{x} - 4\)

Step-by-step explanation:

We are given:

\(y = \sqrt{x}\)

The domain of the function is [0, infinity).

In the graph:

The domain(values of x), is still [0, infinity). Thus, there was no change in the domain, which rules out the first and the third option.

Change:

The change in the graph is that the function starts 4 units down(sqrt(0) = 0, in the graph when x = 0, y = -4). That is, 4 is subtracted from the function, and thus the correct answer is \(y = \sqrt{x} - 4\)

Answer:

Its 20

Step-by-step explanation:

The equation of a line that passes through points (2,5) and (4,3) is

y = -x+7.

Finding the equation of a line:

First, we need to find out the slope for the given points.

(X1,Y1) = (2,5)

(X2,Y2) = (4,3)

formula for slope(m) = \(\frac{Y2 - Y1}{X2 - X1}\)

substitute the points in the above formula

\(\frac{3 - 5}{4 - 2}\) = \(\frac{-2}{2}\)

\(\frac{-2}{2}\) = -1

slope for the given points(m) = -1.

m = -1

The equation of a line is y-y1 = m(x-x1), where x and y are variables.

substituting the values in the above equation then :

y-5 = -1(x-2)

y-5 = -x+2

y+x = 2+5

x+y = 7

y = -x+7

Therefore, the equation of the line passing through the points (2,5) and (4,3) is y = -x+7

To solve more problems based on the linear equations:

https://brainly.com/question/9753782

Answer:

cos 30° = 9√3 / d

d = 18 cm

r = d/2 = 18/2 = 9 cm

A = πr² = π•9² = 81π cm² or 254.47 cm²

Answer: 2/8, 3/8, 4/8, 5/8, 7/8

Step-by-step explanation:

     Since they all have a common denominator, we can list them based on their numerator without having to worry about the denominator.

2/8 < 3/8 < 4/8 < 5/8 < 7/8

Answer: 7

Step-by-step explanation:

Since there are 42 tubes and each tray can hold 6 tubes, it will be 42/6 which is 7.

Answer:

400 litres

Step-by-step explanation:

The answer is True.

Since we are talking about the cost of something, and whenever you have a y-intercept, it means the price.

The y-intercept represents the initial cost of the taxi ride then how many miles you ride for, the more you pay plus the initial cost.

Best of Luck!

Answer:

3:25

Step-by-step explanation:

The photo shows how it's solved.

Answer: 3:25

Step-by-step explanation:

Step 1) Convert the decimal number to a fraction by making 0.12 the numerator and 1 the denominator

0.12 = 0.12/1

Step 2) Multiply the numerator and denominator by 100 to eliminate the decimal point.
0.12 x 100

------------ = 12/100
1 x 100

Step 3) Simplify the fraction in the previous step by dividing the numerator and the denominator by the greatest common factor (GCF) of 12 and 100. (The GCF of 12 and 100 is 4.)

12 ÷ 4

---------  = 3/25  

100 ÷ 4

Step 4) Convert the fraction in the previous step to a ratio by replacing the divider line with a colon like this:  

3  

25   =  3:25

Answer:

10

Step-by-step explanation:

Step-by-step explanation:

dividing the figure in triangle and rectangle.

then applying formula.

then adding them.

Answer:

Step-by-step explanation:

Following changes will be there when the figure is transformed by the given rules.

1). Rule for transformation has been given as,

   (x, y) → (x, -y)

   Reflection across x axis.

2). (x, y) → (-x, -y)

   Rotation of 180° about the origin.

3). (x, y) → (x - 4, y)

   Shifted 4 units left horizontally.

4). (x, y) → (x, y + 3)

   Shifted vertically up by 3 units

5). (x, y) → (x - 1, y + 4)

   Shifted 1 units left horizontally and 4 units up vertically.

6). (x, y) → (4x, 4y)

   Dilated by 4 units.

Answer:

1023/4

Step-by-step explanation:

shown in the picture

Answer:

\(\displaystyle A=\frac{20}{3}\)

Step-by-step explanation:

\(\displaystyle A=\int^2_{-2}(|x|-(x^2-2))\,dx\\\\A=2\int^2_0(x-(x^2-2))\,dx\\\\A=2\int^2_0(-x^2+x+2)\,dx\\\\A=2\biggr(-\frac{x^3}{3}+\frac{x^2}{2}+2x\biggr)\biggr|^2_0\\\\A=2\biggr(-\frac{2^3}{3}+\frac{2^2}{2}+2(2)\biggr)\\\\A=2\biggr(-\frac{8}{3}+2+4\biggr)\\\\A=2\biggr(-\frac{8}{3}+6\biggr)\\\\A=2\biggr(\frac{10}{3}\biggr)\\\\A=\frac{20}{3}\)

Bounds depend on whether you use -x or +x instead of |x|, but you double regardless. See the attached graph for a visual.

A probability is given by the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes when a pair of dice is rolled is given by:

6² = 36.

As each throw has six outcomes.

The outcomes with a sum of 5 are given as follows:

(1,4), (2,3), (3,2), (4,1).

Hence 4 outcomes, and the probability that player A wins is of:

p = 4/36 = 1/9.

The outcomes with a sum of 4 are given as follows:

(1,3), (2,2), (3,1).

Hence the probability that B wins is given by:

p = 3/36 = 1/12.

Then the probability that a player wins on each trial is given by:

p = 4/36 + 3/36 = 7/36.

Then the expected number of rolls is given as follows:

E(X) = 1/(7/36) = 36/7 = 5.1 rolls.

More can be learned about probabilities at https://brainly.com/question/14398287

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First we rewrite

\(\dfrac{1 + \cos(4x)}{\cos(x)} = 2\cos^2(2x)\)

then expand the integrand as

\(\displaystyle \ln^2(2) - 2 \ln(2) x^2 + x^4 \\\\ {} + 2\ln(2) \ln(\cos^2(2x)) - 2\ln(2) \ln(\cos(x)) - 2x^2 \ln(\cos^2(2x) + 2x^2 \ln(\cos(2x)) \\\\ {} + \ln^2(\cos^2(2x)) + \ln^2(\cos(x)) - 2 \ln(\cos(x)) \ln(\cos^2(2x))\)

We'll use the following identity:

\(\displaystyle \cos(2kx) = \frac{e^{i2kx} + e^{-i2kx}}2 \\\\ \sum_{k=1}^\infty \frac{\cos(2kx)}k = \frac12 \left(\sum_{k=1}^\infty \frac{(e^{i2x})^k}k + \frac{(e^{-i2x})^k}k\right) \\\\ \sum_{k=1}^\infty \frac{\cos(2kx)}k = -\frac12 \left(\ln(1-e^{i2kx}) + \ln(1 - e^{-i2kx})\right) \\\\ \implies \ln(\sin(x)) = -\ln(2) - \sum_{k=1}^\infty \frac{\cos(2kx)}k\)

as well as the fact that for any integer n,

\(\displaystyle \int_0^{\frac\pi2} \cos(2nx) \, dx = 0\)

Consult the attachments for the integrals of the non-trivial terms.

Putting everything together, the end result is then

\(\displaystyle \int_0^{\frac\pi2} \ln^2\left(\frac{e^{-x^2}}{\cos(x)}(1+\cos(4x))\right) \, dx \\\\ = \boxed{\frac{\pi^5}{160} + \frac{\pi^3}4 - \frac{11\pi}{16} \zeta(3)}\)

x₁ = - 1

x₂ = 2

2²ˣ⁺¹ - 9ₓ2ˣ + 4 = 0

2²ˣₓ2 - 9ₓ2ˣ + 4 = 0

2ˣ = n

2n² - 9n + 4 = 0

2n² - n - 8n + 4 = 0

n(2n - 1) - 4(2n - 1) = 0

(2n - 1)(n -4) = 0

2n - 1 = 0 => n₁ = 1/2

n - 4 = 0 => n₂ = 4

2ˣ = 1/2 => 2ˣ = 2⁻¹ => x₁ = - 1

2ˣ = 4 => 2ˣ = 2² => x₂ = 2