The Torrey family was on vacation. One day, they spent $140 for a motel room, $130 for meals, and $200 at a park. How much money did they spend that day? ​

Step-by-step explanation:

Simple events in probability have a certain chance of happening. For example, a 10% chance of rain today. When two or more probabilities are possible, they are added together to get the total probability. A 10% chance of snow and a 15% chance of hail would mean a 10% + 15% = 25% chance of bad weather. This article will show you how to find the probability of a simple event happening.

For the given sentences, the algebraic expressions are:

a) N = 110*c - 300

b) N = 12*b

For the first statement:

A 3-digit number, where the tens digit is c, can be written as:

N = 100*a + 10*c + b

Then the hundreds digit is a, and here we know that is 3 less than the tens digit, then:

a = c - 3

The ones digit is b, here we know that it is 0, then b = 0.

Replacing that in our number we get:

N = 100*(c - 3) + 10*c = 110*c - 300

N = 110*c - 300

That is the algebraic expression.

b) A two-digit number can be written as:

N = b*10 + a

Where b is the tens digit and a is the ones digit.

Here we know that the units digit is twice as bit as the tens digit, then:

a = 2b

Replacing that we get:

N = b*10 + a = b*10 + 2b = 12*b

N = 12*b

That is the algebraic expression.

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The value of (-12) . 8 is -96 and the value of 14.(-5).(-11) is 770

The question implies that we calculate the expressions in two different ways.

1) (-12).8

Way 1:

We have:

(-12).8

This means

(-12) . 8 = -12 * 8

Evaluate

(-12) . 8 = -96

Way 2

We have:

(-12).8

This means

(-12) . 8 = -12 * 8

Express 8 as 4 + 4

(-12) . 8 = -12 * (4 + 4)

Expand

(-12) . 8 = -12 * 4 -12 * 4

Evaluate the products

(-12) . 8 = -48 - 48

Evaluate the sum

(-12) . 8 = -96

Hence, the value of (-12) . 8 is -96

2) 14.(-5).(-11)

Way 1:

We have:

14.(-5).(-11)

This means

14.(-5).(-11) = 14 * -5 * -11

Evaluate

14.(-5).(-11) = 770

Way 2

We have:

14.(-5).(-11)

This means

14.(-5).(-11) = 14 * -5 * -11

Multiply -5 and -11

14.(-5).(-11) = 14 * 55

Multiply 14 and 55

14.(-5).(-11) = 770

Hence, the value of 14.(-5).(-11) is 770

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The probability that it is a heart = 1/4 or 0.25.

Total standard cards = 52

The probability of choosing a heart from a deck of cards with 13 card values  (Ace, King, Queen, Jack, and 2-10) in each of the four suits (clubs, diamonds, hearts, spades) is given by =

P(Heart) = number of hearts / total number of cards

= 13 / 52

= 1/4 or 0.25

Hence, The probability that it is a heart = 1/4 or 0.25.

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Answer:7m^5 - 3m^3 + 9

Step-by-step explanation: You’d have to remove the brackets, but remember that the second has to have everything multiplied by -1, because there’s a minus sign in front of the second bracket. Then you’d group like terms, then add or subtract. Here’s the step by step

6m^5 + 3 - m^3 - 4m + m^5 - 2m^3 + 4m + 6

2. 6m^5 + m^5 - 2m^3 - m^3 + 4m - 4m + 6 + 3

Subtract or add what’s needed, which would be figures with the same variable and coefficient.

3. 7m^5 - 3m^3 + 9

After this, there’s nothing you can add, since the remaining figures don’t have the same variable.
Hope it’s clear and this wasn’t that long

The smallest possible length of the hypotenuse is 118

The given parameters are:

The non-degenerate implies that the right triangle has a positive area.

Since at least one length is 84, then both lengths can also be 84.

The hypotenuse is then calculated using the following Pythagoras theorem.

h^2 = 84^2 + 84^2

Evaluate the sum

h^2 = 14112

Take the square root of both sides

h = 118.8

Round down

h = 118

Hence, the smallest possible length of the hypotenuse is 118

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Answer: A

Step-by-step explanation:

Let's first review how turning about the origin changes a point's coordinates:

After rotating and translating some points, one can see the following pattern:

Using these patterns will make it much easier to find the correct series of transformations than graphing each one.

A: A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

Using the patterns found above, this set of transformations would make (x,y) move first to (-y, x), then (-y-1, x).

B: A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin

This would make (x,y) move first to (x-1,y), then to (-y, x-1)

C: A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

This would make (x,y) move first to (y, -x), then (y-1, -x)

D: A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin

This would make (x,y) move first to (x-1,y), then (y, -x+1)

Therefore, the answer is A, as only it correctly matches to polygon A'B'D'C'.

4/3 of the area of the larger hexagon to the area of the smaller hexagon

Let the sides of the interior hexagon be 2 cm long, then this hexagon is made up of 6 equilateral triangles of side = 2.

The area of this hexagon = 6 * 1 * sqrt3 = 6 sqrt3 ( as the triangle is made up of 2 60-30-90 triangles)

The exterior hexagon is made up of 6 equilateral triangles with altitude 2 and the area = 6 * 2 * (2 / sqrt3 ) = 24 / sqrt3

area exterior hex / interior hex = 24 / sqrt3 * 1 / 6sqrt3 = 24/18

= 4/3

Required ratio = 4/3 answer

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Answer:

The answer is 74.

Step-by-step explanation:

To find the area, you have to divide the shape into rectangles. To solve, I divided it like the image above. (Sorry if the lines are squiggly I'm trying to do this fast)

So first, now that we've divided it into smaller rectangles, we find the area of the smaller ones. Remember, the area of a rectangle is length * height.

Since the two smaller rectangles are the same, we just need to find one and multiply it by 2.

[tex]3 \times 5=15 \\15\times 2=30[/tex]

So the area of the two smaller ones is 30. Now we need to find the big rectangle and add it together. We know that the length is 11, but we don't know the height. The height of the small rectangles was 5, so the height is 4 since 9 - 5 = 4. So to finish up, we do this:

[tex]11\times4=44 \\ 44 + 30=74[/tex]

So our final answer is 74.

The perimeter of the top of the basket is 20 in.

Perimeter of square is defined as addition the lengths of the  square's four sides.

Diagonal = 6

Let,  side of square = a

a²+a² = 6²

2a² = 36

a² = 18

a = 3√2

Perimeter of the square = 4 × side of square

Perimeter of the square = 4 × 3√2

Perimeter of the square = 12√2 ≈ 20 in

Hence, the perimeter of the top of the basket is 20 in.

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Answer:

77

Step-by-step explanation:

Based on the question, we can deduce the arrangement of the plants is in a form of a square. (Number of rows = Number of Columns).

In that case, the answer is very straightforward, just square root the number of plants to be planted:

[tex]\sqrt{5,929} \\= 77[/tex]

This means there would be 77 rows of 77 plants per row.

Answer:

45

Step-by-step explanation:

the number of ones expected is

probability × number of rolls

= 0.3 × 150

= 45

Answer:

  6 +7x

Step-by-step explanation:

To write an English expression as an algebraic one, you must first understand what the English is telling you. Then the translation is straightforward.

A plus sign (+) signifies addition. Multiplication is signified several different ways. The simplest is writing the factors next to each other.

The objects involved in the addition are 6 and a product:

  6 + product

The product is said to consist of two factors: 7 and "a number". The instructions say to use "x" for "a number", so the product can be written ...

  7x

Then the complete algebraic expression is ...

  6 +7x

The volume of a cuboid implies the product of its length, width, and height. So that the fraction of the original cuboid that would remain is [tex]\frac{7}{15}[/tex].

A cuboid is a solid derived from a rectangle, thus it has rectangular faces. Its volume can be determined by;

volume of a cuboid = length x width x height

In the given question, the volume of the original cuboid can be determined as;

  volume = 3 x 4 x 5

                = 60 Cubic units

Since holes can not be drilled at the intersection of the holes, then the volume of the hole has to be determined.

To determine the volume of the hole drilled, we have:

(6 x 3) + (3 x 2) + (2 x 2) = 28 Cubic units

So that the fraction of the original cuboid that would remain = [tex]\frac{28 cubic units}{60 cubic units}[/tex]

                                                                   = [tex]\frac{7}{15}[/tex]

Therefore,  [tex]\frac{7}{15}[/tex] of the original cuboid would remain.

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Answer: 33/100, 33%

Step-by-step explanation:

I can't choose two answers if you don't give me the possible answers

67 days of homework = 100-67 or 33 days without homework.

33/100 or 33%

Step-by-step explanation:

100% = 100 days

1% = 100%/100 = 100/100 = 1 day

the student does NOT have homework on 100-67 = 33 days.

that is 33 out of 100 days or on 33/100 of days.

33 days are 33×1% = 33%

The bottom triangle is a 30°-60°-90° triangle that has the special property that its hypotenuse is twice the length of the shortest leg, 20√3.

The upper triangle is a 45°-45°-90° triangle, in which the hypotenuse is longer than one of its legs by a factor of √2.

All this to say x = √2 × 20√3 = 20√6 (A).

Answer:

$15

Step-by-step explanation:

Range is the difference of the highest and lowest data.

Based on the given $20 is the highest and $5 is the lowest.

$20 - $5 = $15

Answer:

15

Step-by-step explanation:

you can think of this table as a data set--and you could even write it out

5, 5, 5, 10, ......... 20, 20 {I did not write it out in full of course}

so, when thinking about the range, we can think of it as a range of our data set.

We find the range of a data set by finding the difference between the highest and lowest values

So, we know that our highest data value (amount) is 20, and the lowest is 5:

20 - 5 = 15

meaning that there is a range of $15 in this data set of allowance amounts

hope this helps!! have a lovely day! :)

Answer:

[tex]1[/tex]

Step-by-step explanation:

The gist of modular arithmetic in a nutshell: the numbers [tex]a[/tex] and [tex]b[/tex] are considered to be congruent by their modulus [tex]m[/tex] if [tex]m[/tex] is a divisor of their difference.

In mathematics: [tex]a \equiv_{m} b \Leftrightarrow (a - b) \vdots m[/tex]

Exemplifying this: [tex]6 \equiv_{7} -1[/tex] because [tex]6 - (-1) = 6 + 1 = 7[/tex], [tex]7 \vdots 7[/tex].

Let us have following equivalences: [tex]a \equiv_{m} b[/tex] and [tex]c \equiv_{m} d[/tex], then:  [tex](a - b) \vdots m[/tex] and [tex](c - d) \vdots m[/tex] by definition.

Properties:

1. [tex]a + c \equiv_{m} b + d \Leftrightarrow ((a + c) - (b + d)) \vdots m \Leftrightarrow (a + c - b - d) \vdots m \Leftrightarrow ((a - b) + (c - d)) \vdots m[/tex].

2. [tex]a - c \equiv_{m} b - d \Leftrightarrow ((a - c) - (b - d)) \vdots m \Leftrightarrow (a - c - b + d) \vdots m \Leftrightarrow ((a - b) - (c - d)) \vdots m[/tex].

3. [tex]ac \equiv_{m} bd \Leftrightarrow (ac - bd) \vdots m \Leftrightarrow (ac - bc - bd + bc) \vdots m \Leftrightarrow (c(a - b) + b(c - d)) \vdots m[/tex].

4. What if we have [tex]a \equiv_{m} b[/tex] twice? If we abide by property 3, we can come to the conclusion that [tex]a^2 \equiv_m b^2[/tex]. It is fair enough that there is room for the equivalence [tex]a^n \equiv_{m} b^n[/tex].

[tex]2001 * 2002 * 2003 + 2004^3 = 2002 * (2001 * 2003) + 2004^3 \equiv_{7} 0 * (2001 * 2003) + 2^3 \equiv_{7} 0 + 8 \equiv_{7} 8 \equiv_{7} 1[/tex]

Notice that [tex]2002 \vdots 7[/tex] already. There is no need to consider the rest multipliers because the product is [tex]0[/tex] anyways, we can cut corners in this regard.

We used property 4.

Recapitulating this: our remainder is [tex]1[/tex].

The probability that a person wins the game is 32.1%

Based on the information given, the following can be depicted. It should be noted that there are 6 sides as well as 4 cards.

Therefore, the numbers on the dice i.e from 1 - 6 will be represented 4 times each. This gives a total of (4 × 6) = 24. There are also 4 cards. The total in sample space will now be:

= 24 + 4 = 28

The frequency table will be such that 28 or more have a relative frequency of 9. Therefore, the probability that a person wins the game will be:

= 9/28 = 32.1%

When you win 25% of the time, this illustrates that the number of products picked will be:

= 25% × 28

= 7 products.

The probability of participants achieving a winning score of 36 or higher in four consecutive attempts will be:

= 1/6⁴ = 1/1296

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The equation that best represents the set-up is (d) 9^2 + x^2 = 16^2

The complete question is in the image

The value of x is calculated using the following Pythagoras theorem

16^2 = x^2 + 9^2

Rewrite as:

9^2 + x^2 = 16^2

Hence, the equation that best represents the set-up is (d) 9^2 + x^2 = 16^2

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The area of the composite solid in the image given is: 399.6 m².

The surface are of the composite solid = area of the 3 triangular face of the top solid + area of the triangular base of the bottom solid + 3(area of rectangular face of the bottom solid).

Area of the 3 triangular face of the top solid = 3(1/2bh) = 3(1/2 × 8 × 7) = 84 m²

Area of the triangular base of the bottom solid = 1/2bh = 1/2 × 8 × 6.9 = 27.6 m²

3(area of rectangular face of the bottom solid) = 3(length × width) = 3(12 × 8) = 288 m²

Surface area of the solid = 84 + 27.6 + 288 = 399.6 m²

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Answer:

y = x + 2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m = [tex]\frac{2-0}{0-(-2)}[/tex] = [tex]\frac{2}{0+2}[/tex] = [tex]\frac{2}{2}[/tex] = 1

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = x + 2 ← equation of line

Answer:

answer is A - incenter just did it

Step-by-step explanation:

Answer:

18+[tex]6\sqrt{5}[/tex]

Step-by-step explanation:

Since the helicopter flies east for six miles and north for 12 miles, it flies 18 miles. Then on the way back, it flies an unknown amount of miles. the path the helicopter takes is in the form of a triangle, and the path back is the hypotenuse of the triangle. To find the hypotenuse, we can do [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse. We do

[tex]6^2+12^2=c^2\\36+144=c^2\\180=c^2\\\sqrt{180}=c\\ 6\sqrt{5}=c[/tex]Therefore, the total distance flown by the helicopter is 18+[tex]6\sqrt{5}[/tex].  

Answer:

30$ (the labor charge per hour)

Step-by-step explanation:

The rate of change can be described as the slope, or how much the y-value is going to change as the x-value increases by 1. So the first step would be to understand what is x and what is y in this context. Well usually y is the dependent variable and x is the independent variable, so as x changes y changes as a result. In this case the y would represent the price the repair person charges and the x would represent the amount of hours, since as the amount of hours changes, the price changes. And since the person charges 30$ per hour, that means the rate of change is 30, since as the amount of hours increases by 1, the price or amount charged increases by 30$

Answer: $30

Step-by-step explanation:

The appliance repair person charges $30 per hour, meaning the rate of change is 30

Answer:

3474

Step-by-step explanation:

To determine the difference in the amount sold, take the amount sold today and subtract the amount sold yesterday

46453-42979

3474

The maximum data rate of that modem is doubled if the number of points in its constellation were doubled

According to statement

Modem has a data rate is 14,400 bps

we know that the data rate can be calculated by T=A/S

If a is Doubled then the data rate is also doubled.

Because A is directly proportional to the T and S is inversely proportional to T.

So, The maximum data rate of that modem is doubled if the number of points in its constellation were doubled

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Answer:

Step-by-step explanation: