c) The phone case you want to buy is marked down 30%, and you have a 25% off coupon.
You pay $42.00. Can this equation be used to find the original price of the phone case? If so,
what is the original price of the item? Explain. (5 points)
(0.7c) = 42

Answer:

7x is monomial according to question.

Ali's strategy is essentially the same as Mary's strategy. Both strategies estimate the HST as 15% of the price. However, Mary's strategy involves taking half of 10% of the price.

Mary suggests estimating the HST in Ontario as finding 10% of the price, taking half of this answer and adding the two. Ali proposes finding 10% of the price, then 5% of the price and adding the two answers.

Their strategies differ in the way they approach finding the estimate, but both methods can be used to arrive at the same result.

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The HST in Ontario is 13%, which can be estimated using 15%. Mary tells Ali that it can be estimated as: find 10% of the price, take a half of this answer and add the two. Ali tells Mary that he thinks they should find 10% of the price, then 5% of the price and add the two answers. Compare their strategies.

Answer:

f(3) = 1

Step-by-step explanation:

substitute x = 3 into f(x) , that is

f(3) = 3² - 4(3) + 4 = 9 - 12 + 4 = 1

Answer:

1

Step-by-step explanation:

Substitute 3 for x in your equation leaving you with (3)^2-4(3)+4.

9-12+4

-3+4=1

Step-by-step explanation:

there is nothing missing. this is a complete proof.

yes, the various steps are correct.

Answer:

The answer is 42.1 degrees Celsius

The product of given numbers is 384400.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Given that, the moon is in an orbit around the earth, and the length of this

orbit is 3.844×100,000 kilometers.

Here, 3.844 multiplied by 1 we get 3.844

When multiplying decimals by 100000, the digits shift five places to the left.

That is, 384400.0

Therefore, the product of given numbers is 384400.

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Answer:

\(\boxed{\df\ \dfrac{-19}{2}}\)

Step-by-step explanation:

Hi,

x=-2

it gives

9*(-2)-4y=20

<=> -18-4y=20

<=> 18-18-4y=20+18=38

<=> -4y=38

<=> y = -38/4=-19/2

hope this helps

(a) The marginal distribution of X is

Pr(X = x) = ∑ Pr(X = x, Y = y)

… = 0.0625 + 0.0625 + 0.0625 + 0.0625

… = 0.25

That is, the first equality follows from the law of total probability, with the sum taken over y from {0, 5, 10, 15}. Each probability Pr(X = x, Y = y) is given in the table to be 0.0625.

Similarly, the marginal distribution of Y is

Pr(Y = y) = 0.25

(b) Yes, they're independent because

Pr(X = x, Y = y) = 0.0625,

and

Pr(X = x) Pr(Y = y) = 0.25 • 0.25 = 0.0625.

(c) The mean of X is

E[X] = ∑ x Pr(X = x)

… = 0.25 ∑ x

… = 0.25 (0 + 5 + 10 + 15)

… = 7.5

and you would find the same mean for Y,

E[Y] = 7.5

The variance of X is

V[X] = E[X^2] - E[X]^2

… = (∑ x^2 Pr(X = x)) - 7.5^2

… = 0.25 (∑ x^2) - 56.25

… = 0.25 (0^2 + 5^2 + 10^2 + 15^2) - 56.25

… = 31.25

and similarly,

V[Y] = 31.25

(each sum is taken with x and y from {0, 5, 10, 15})

Answer:

Width = 7, Length = 42

Step-by-step explanation:

Length is 6 times its width, means that it's the same number but times 6 so we'll use "x" for both length and width:

6x · x = 294

6x^2 = 294

divide both sides by 6

x^2 = 49

\(\sqrt{x^2}\) = \(\sqrt{49}\)

x = 7, width is 7 and length is 6(7) = 42

The 3 sets of data with the same median but different mean are given as follows:

The mean of a data-set is calculated as the sum of all values in the data-set divided by the number of values in the data-set.

The median of a data-set is the middle value of the data-set, the value which 50% of the data-set is less than and 50% of the data-set is more than.

Hence, for a data-set of five elements, which is an odd cardinality, the median is the third element of the ordered data-set.

Then the three data-sets can be constructed with five elements, in which the third element is the same but the sum of the five elements is different.

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Answer:

1 7/10 miles

Step-by-step explanation:

Answer:

Z = 22.5, Y = 81, X = 26.7

Step-by-step explanation:

Using the lengths you do know compare them to the copy, the only two lengths available that are for the same side length are 33 and 22, divide them together and you get 1.5. Thats the scale factor. Everything else you can figure out by multiplying or dividing by this scale factor.

\(Z = (15)(1.5) = 22.5\\Y = (54)(1.5) = 81\\X = (40)/(1.5) = 26.7\)

Answer: neither

Step-by-step explanation:

To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.

Answer:

\(Distance = 880ft\)

Step-by-step explanation:

Given

\(Speed = 20\frac{miles}{hour}\)

\(Time = 30\ seconds\)

Required

Determine the distance

To answer this question, we make use of speed-distance relationship

\(Speed = \frac{Distance}{Time}\)

Make Distance the subject

\(Distance = Speed * Time\)

\(Distance = 20 miles/hour * 30 seconds\)

Convert seconds to hour

\(Distance = 20 miles/hour * \frac{30}{3600} hour\)

\(Distance = 20 miles * \frac{30}{3600}\)

\(Distance = \frac{20 miles * 30}{3600}\)

\(Distance = \frac{600\ miles}{3600}\)

\(Distance = \frac{1}{6} miles\)

Convert to foot

\(Distance = \frac{1}{6} * 5280\ ft\)

\(Distance = \frac{1* 5280\ ft}{6}\)

\(Distance = \frac{5280\ ft}{6}\)

\(Distance = 880ft\)

The distance from where she entered the water to when she reached her lowest point in the pool is 16 ft

The axis of symmetry is x = 8 ft

We are told that she jumped from the side of the pool and the point at which she made contact with the water to dive under was a distance of 4 ft horizontal from the pool side. Secondly, the point at which she came out of the pool was 12 ft from the pool side.

Thus, since the points where she came out and where she dove into the pool are the x-intercepts, then it means that the factors of the parabola formed are; (x - 4) and (x - 12)

Thus, the quadratic equation formed by the parabola is;

y = (x - 4) * (x - 12)

y = x² - 16x + 48

Now, the coordinates for the vertex will be (h, k).

h = -b/2a

h = -(-16)/(2 * 1)

h = 8

k = 8² - 16(8) + 48

k = -16

Thus, the distance from where she entered the water to when she reached her lowest point in the pool is 16 ft

The axis of symmetry is x = 8 ft

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Answer:

-------------------------

Initial value of the toy is €450.

After 10% increase the value is:

After further 10% decrease the value becomes:

The final value of the toy is €445.50.

Answer:

y = 4x + 1

Step-by-step explanation:

Let's graph it in slope intercept form y = mx + b

m = the slope

b = y-intercept

m = 4

b = 1

So, the equation is y = 4x + 1

Answer:

560 Tickets

Step-by-step explanation:

40 tickets in 30 minutes will become 80 tickets in 60 minutes (an hour)

Multiply 80 by 7 to get 560

The coordinates of point E is (-37/7, 23/7)

The formula for calculating a coordinate points using the points (-1, -1) and point A is located at (-7, 5) in the ratio 2:5 is expressed as:

E (x, y) = {(ax₁+bx₂)/a+b, (ay₁+by₂)/a+b}

Substitute the coordinates and ratios to have;

E (x, y) = {(2(-1)+5(-7))/2+5, (2(-1)+5(5))/2+5}

E(x, y) = {-35-2/7, -2+25/7}

E(x, y) = (-37/7, 23/7)

Hence the coordinates of point E is (-37/7, 23/7)

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

Explanation:

"The ratio of pumpkins to squashes in a garden is 5 to 4". This means that we could have 5 pumpkins and 4 squashes. However, this doesn't match with the fact that "there are 25 pumpkins". Luckily, we can multiply both the "5" and "4" by the value 5 like so

5*5 = 25

5*4 = 20

The ratio "5 to 4" is equivalent to "25 to 20". Now we have 25 pumpkins and 20 squashes. The grand total is 25+20 = 45 which is the final answer.

We know there are more pumpkins than squashes because the "5" in "5 to 4" is the larger value, and also that '5' corresponds to the number of pumpkins in relation to the number of squashes. If we had more squashes, then it would be something like 4 to 5. The order of the values matters.

------------

Here's another way to solve:

x = number of squashes

5/4 = 25/x

5x = 4*25 .... cross multiply

5x = 100

x = 100/5

x = 20

We have 25 pumpkins to go with 20 squashes, so there are 25+20 = 45 vegetables total.

The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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Answer: 44-24 = 20 minutes

Step-by-step explanation:

Time spent going back to the car = 12 minutes .

Since the distance between the car and the bird-watching spot didn't change, this means it must have taken him 12 minutes to get to the specific spot he stood at.

12 minutes (going to spot) + 12 minutes (coming back from spot)
= 24 minutes

44 minutes (bird-watching) - 24 minutes (walking to and from the car)

= 20 minutes longer spent bird-watching than walking back and forth to the car

Answer:

y = (-5x + 12)/-7

Step-by-step explanation:

5x - 7y = 12

-7y = -5x + 12

I now divide both sides by -7.

y = (-5x + 12)/-7

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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Answer:

14

Step-by-step explanation:

14.5 to 1

205/14.5 = 14

Answer:

650,000,000

Step-by-step explanation:

6.5x10^8

First think of what 0.2% is as a fraction,

\(0.2\%=\frac{0.2}{100}=\frac{2\cdot10^{-1}}{10^2}=\frac{2}{10^3}=\frac{2}{1000}\)

Now multiply the fraction by a fifth,

\(\frac{2}{1000}\cdot\frac{1}{5}=\frac{2}{5000}\)

Which then simplifies to,

\(\frac{2}{5000}=\boxed{\frac{1}{2500}}\)

Hope this helps :)

Answer:

(-5, 0)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

4x - 3y = -20

-x - 8y = 5

Step 2: Rewrite Systems

-x - 8y = 5

Step 3: Redefine Systems

4x - 3y = -20

x = -8y - 5

Step 4: Solve for y

Substitution

Step 5: Solve for x

Answer:

x = -5

y = 0

Step-by-step explanation:

4x-3y=-20

-x-8y=5  then x = 8y-5

substitute for x

4(8y-5)-3y = -20

32y-20-3y = -20

29y = 0

y = 0

4x-0 = -20

x = -5