Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below. 6 x = negative 2 x minus 4.5 What errors did Emma make? Select two options. She should have used division to represent the quotient of six and x. She should not have included an equal sign. She should have used parentheses to show that Negative 2 is multiplied by (x minus 4.5). She should have subtracted the difference (x minus 4.5) from Negative 2. She should have used parentheses to show that Negative 2 is multiplied by (4.5 minus x).

Notice that

5 - 3 = 2

11 - 5 = 6

29 - 11 = 18

and these differences form a geometric sequence,

{2, 6, 18, ...} = {2×3⁰, 2×3, 2×3², ...}

so a reasonable guess for the next number in the sequence might be 2×3³ = 54.

The sequence might be 2×3^3^3 = 54.

We notice that 5 - 3 = 2

11 - 5 = 6

29 - 11 = 18

and these differences form a geometric sequence,

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.

{2, 6, 18, ...} = {2×3^0, 2×3^1, 2×3^3, ...}

So the next number in the sequence might be 2×3^3 = 54.

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Answer: 110

Step-by-step explanation:

<ABC = <DEF

180 - <DEF = 180 - 70

<BED = 110

Answer:

О  x = 10 3/4

[tex]x = 10\frac{3}{4}[/tex]

Step-by-step explanation:

-1/5 ( x + 1 3/4) = -2 1/2

Particularly:

1 3/4 = 1 + 3/4 = 4/4 + 3/4 = 7/4

-2 1/2 = -2 - 1/2 = -4/2 - 1/2 = -5/2

Then:

-1/5 (x + 7/4) = -5/2

(x*-1/5 + 7/4*-1/5) = -5/2

(-x/5 + ((7*-1) / (4*5))) = -5/2

-x/5 + (-7/20) = -5/2

-x/5 - 7/20 = -5/2

-4x/20 - 7/20 = -50/20

-4x - 7 = -50

-4x =  -50  + 7

-4x = -43

x = -43/-4

x = 43/4

43/4 = 40/4 + 3/4 = 10 + 3/4 = 10 3/4

(3,6) (4,6) (5,6) (6,6) (4,5) (5,5)

Each of these pairs is equiprobable and which i will be using throughout the exercise:

[tex]p(pair) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} [/tex]

[tex]p(a) = (\frac{1}{36} \times 2) \times 4 + \frac{1}{36} \times 2 = \frac{5}{18} [/tex]

The 2 (2!) is to account for permutations like ( 3 , 6 ) and ( 6 , 3 ) and the 4 are the different combinations that are composed of different numbers.

The 2 (2!) is to account for permutations like ( 3 , 6 ) and ( 6 , 3 ) and the 4 are the different combinations that are composed of different numbers.Whereas combinations like ( 5 , 5 ) cannot be switched in order, so we do not multiply by 2!

(1,3) (2,2) (2,6) (4,4) (5,3) (6,6) (1,4) (2,3) (5,5) (4,6)

[tex]p(not \: b) = ( \frac{1}{36} \times 2) \times 6 + \frac{1}{36} \times 4 = \frac{4}{9} [/tex]

[tex]p(b) = 1 - p(not \: b) = 1 - \frac{4}{9} = \frac{5}{9} [/tex]

The amount of money invested at 13% was $8111, while $6135 was invested at 12%.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the amount invested at 13% and y represent the amount invested at 12%, hence:

x +  y = 14246   (1)

Also:

0.13x = 0.12y + 318.23  (2)

Hence:

x = 8111, y = 6135

The amount of money invested at 13% was $8111, while $6135 was invested at 12%.

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Answer:

568.3 into the nearest hundred

5.683

Answer:

568

Explanation:

A whole number is a number without any fractional part; in other words, it does not have any non-zero digits after the decimal point.

When you round a number to the nearest whole number, first look at the digit right after the decimal point;

• if the digit is less than 5, then the nearest whole number is the original number, but without any digit after the decimal point. [rounding down]

• if the digit is 5 or greater than 5, then the nearest whole number is the next whole number (i.e., add 1 to the original number and remove the digits after the decimal point). [rounding up]

The coordinates of the mid-point between points B and C is given by:

(-5, -10).

The mid-point between two points is the halfway point between them, and is found using the mean of the coordinates.

The points in this problem are given as follows:

B(-40, -30), C(30, 10)

Hence the coordinates of the mid-point are:

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Answer:

extraneous: 2, 5, 7

not: 1, 3, 4, 6, 8

Step-by-step explanation:

ones that have root of an even number and equal a negative are extraneous

Hello,

What is the explicit formula for this sequence? -7, -3, 1, 5, ... ?

Aₙ₊₁ = Aₙ + 4 and A₀ = -7

⇒ Aₙ = A₀ + nr = -7 + 4n

Answer:

10x² + 8x + 22

Step-by-step explanation:

The perimeter of a rectangle is the measurements of all four side lengths added together

(you can simply multiply both side lengths by 2, because they are the same on both sides--but I'll write them all out for clarity)

side A (top): 5x² + 3x + 7

side B (right): x + 4

side C (bottom): 5x² + 3x + 7

side D (left): x + 4

perimeter = side A + side B + side C + side D

5x² + 3x + 7 + x + 4 + 5x² + 3x + 7 + x + 4

now, as you might have noticed, this is a long equation

so, we must combine like terms:

(this is the problem reordered so like terms are next to each other:)

(5x² + 5x²) + (3x + x + 3x + x) + (7 + 4 + 7 + 4)

10x² + 8x + 22

So, the perimeter of this rectangle is 10x² + 8x + 22

hope this helps! have a lovely day :)

Answer:

p = 2.7x - 20

p(90) = $223

Step-by-step explanation:

revenue → f(x) = 3x  ,where x is the number of downloads.

the statement “Your profit p is $20 less than 90% of the revenue for x downloads”

means

[tex]p=90\% f\left( x\right) -20[/tex]

means

[tex]p=\frac{90}{100} \times f\left( x\right) -20[/tex]

means

[tex]p=\frac{9}{10} \times (3x) -20[/tex]

means

[tex]p=\frac{9}{10} \times (3x) -20[/tex]

means

[tex]p=2.7x -20[/tex]

………………………………

the profit for 90 downloads :

= p(90)

= 2.7×(90) - 20

= $223

Answer:

33, 165, 133

Step-by-step explanation:

Check this file for the solution!

Answer:

33, 165, 133

Step-by-step explanation:

let the first number be n then

second number is 5n

third number is n + 100

sum the 3 numbers and equate to 331

n + 5n + n + 100 = 331 , that is

7n + 100 = 331 ( subtract 100 from both sides )

7n = 231 ( divide both sides by 7 )

n = 33

5n = 5 × 33 = 165

n + 100 = 33 + 100 = 133

the numbers are 33, 165, 133

Answer:

Step-by-step explanation:

we can break up the figure into 2 rectangles by extending the 8m side downward until it meets the bottom (see image)

Area of this rectangle = 10 * 2 =20 sq meters

Area of the other rectangle = 8 *2 = 16 sq meters

Total area = 36 sq meters

The least to greatest slope, the segments are B, C, and A.

We have given that,

The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below.

A graph represents the water level to fill the tank on Y-axis per time on X-axis.

The rate of increase of water level is indicated by the slope of the segment. The slope is the ratio of rise to run, and is related to the angle the segment makes with the +x axis.

Segments that have more rise for the same run have greater slope. Segments that make a larger reference angle with the +x axis have a larger slope.

Here, segment B has the least slope, followed by C, then A, which has the largest slope.

In order, the least to greatest slope, the segments are B, C, and A.

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Answer: bca

Step-by-step explanation:

B C A

Answer:

m = 10/3

(as a decimal: m = 3.333...)

Step-by-step explanation:

5m - 8 = 2m + 2

 5m - 8 = 2m + 2

- 2m       - 2m              (make all "m" on one side to isolate variable)

 3m - 8 = 2    

      + 8 + 8              (get m entirely on 1 side)

3m = 10

÷3      ÷3                         (divide by 3 to get 1m)

m = 10/3

(as a decimal: m = 3.333...)

hope this helps!! have a lovely day :)

The value of Ry= -x (P) is P' = (4, 6)

The point is given as:

P = (-6, 4)

The transformation Ry= -x (P) means tha:

(x, y) = (y, -x)

So, we have:

P' = (4, 6)

Hence, the value of Ry= -x (P) is P' = (4, 6)

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The confounding variable which is controlled by randomly assigning individuals to treatments is: C. the time of day participants drank the beverages.

A confounding variable is also referred to as a confounder and it can be defined as a type of variable that has the ability to influence both the independent and dependent variables.

Also, a confounding variable is usually not accounted for by the researcher and as such it can cause a spurious association between the independent and dependent variables.

In this context, we can infer and logically deduce that the time of day at which participants drank the beverages is a confounding variable which is controlled by randomly assigning individuals to treatments.

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Answer:

Point A

Step-by-step explanation:

Point A is closest to 9

every line counts as 0.1

By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.

Mass of radioactive isotopes (m (t)), in grams, decay exponentially in time according to the following model:

[tex]m(t) = m_{o}\cdot e^{-t/\tau}[/tex]     (1)

Where:

The time constant can be found in terms of half-life:

τ = t'/㏑ 2

If we know that t' = 24100 yr, t = 1000 yr and m(t) = 5.4 g, then the initial mass of the radioactive isotope is:

τ = 24100 yr/㏑ 2

τ ≈ 34768.95 yr

[tex]5.4 = m_{o}\cdot e^{-1000/24100}[/tex]

[tex]m_{o} = 5.629\,g[/tex]

By applying the radioactive simple decay model, we find that the initial quantity of the radioactive isotope is equal to approximately 5.63 grams.

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Answer: A, C, C.

100%

Step-by-step explanation:

The intersection of A and I are {-2, -1, 1}

The sets are given as;

A={−2,−1,0,1,7} I= {−2,−1,1,2,8}

The intersection of A and I are the common elements in both sets

The common elements in both sets -2, -1 and 1

This means that:

A n I = {-2, -1, 1}

Hence, the intersection of A and I are {-2, -1, 1}

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Answer: constant of proportionality = 0.75

How to find constant of proportionality?

Constant of proportionality is the same as the slope of a straight line.

Slope formula is given by:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y}{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

Here take two points: (0, 0), (4, 3)

[tex]So, \sf \ slope : \dfrac{3-0}{4-0} = \dfrac{3}{4} \quad or \quad 0.75[/tex]

Hence, the constant of proportionality is 0.75

Answer:

Constant of proportionality = 0.75

Step-by-step explanation:

To find the constant of proportionality of a graph that goes through the origin:

• First select a point on the graph whose coordinates you can easily read; in this case such a point is already marked (4, 3).

• Next, simply divide the y-value by the x-value of the coordinates to find the constant of proportionality:

Constant of proportionality = y ÷ x

                                             ⇒ 3 ÷ 4

                                             ⇒ 0.75

Hence the value of the expression above are as listed below

f(6+4) = 25

f(6)+f(4) = 20

f(6-4) = 1

f(6)-f(4) = 6

f(6*4) = 67

f(6)*f(4) = 91

Given the expression below f(x) = 3x - 5

f(6+4) = f(10) =3(10) - 5

f(6+4) = 25

f(6) = 3(6) - 5

f(6) = 18 - 5 = 13

f(4) = 3(4) - 5

f(4) = 7

f(6)+f(4) = 13+7

f(6)+f(4) = 20

f(6-4) = f(2) =3(2) - 5

f(6-4) = 1

f(6) = 3(6) - 5

f(6) = 18 - 5 = 13

f(4) = 3(4) - 5

f(4) = 7

f(6)-f(4) = 13-7

f(6)-f(4) = 6

f(6*4) = f(24) =3(24) - 5

f(6*4) = 67

f(6) = 3(6) - 5

f(6) = 18 - 5 = 13

f(4) = 3(4) - 5

f(4) = 7

f(6)*f(4) = 13*7

f(6)*f(4) = 91

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Answer:

x=80

Step-by-step explanation:

x=0.7x+24

We move all terms to the left:

x-(0.7x+24)=0

We get rid of parentheses

x-0.7x-24=0

We add all the numbers together, and all the variables

0.3x-24=0

We move all terms containing x to the left, all other terms to the right

0.3x=24

x=24/0.3

x=80

Answer:

x = 80

Step-by-step explanation:

We are given the following equation.

x = 0.7x + 24

And we want to solve it for x.

For these kinds of equations, the way to solve for x is to isolate x on one side.

Because we have terms with x on both sides of the equation, we need to remove it from one side.

It's a good idea to remove x from the right side, as we also have our numbers on that side. If we move it to the left side, there aren't any numbers there, so we can more easily solve this equation.

Here is our equation again:

x = 0.7x + 24

Subtract 0.7x from both sides.

x = 0.7x + 24

-0.7x -0.7x

______________________

0.3x = 24

Now, we have variables on one side, and numbers on the other, but we aren't done yet.

Remember that we are solving for x, not 0.3x. (When x is written by itself, it is the same as 1x).

So, in order to find the value of 1x, we need to divide both sides by 0.3, as when a number is divided by itself, the value is 1. If there is a variable, the value will be 1*that variable (e.g. 1n, or n)

**Note that we don't divide by 0.3x, as if we did that, the left side would equal just 1, not 1x.

So, let's divide both sides by 0.3.

0.3x = 24

÷0.3   ÷0.3

__________

x = 80

Topic: solving linear equations

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Answer:

i am not sure

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

what 3 logy z^9 means you need to break it into two pieces, one log y z^9 means to find the exponent of y, and you can think z^9 as a number, and then if we multiple it with 3, which means three logs are summed,(the property of multiplication:3*2 means 2+2+2), thus log + log

has the property that the y is same z^9*z^9*z^9=z^(9+9+9)=z^27

Using the arc length formula, the length of the outer curve is approximately 85 feet.

Arc length = ∅/360 × 2πr.

Apply the arc length formula to find the length of the outer curve, given the following:

Plug in the values

Arc length = 70/360 × 2(3.14)(70)

Arc length = 70/360 × 2(3.14)(70) ≈ 85 feet.

The length of the outer curve is approximately 85 feet.

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m=1/4

(or m=0.25)

M= rise/run

= 1/4

Hope this helps!

Using the binomial distribution, it is found that there is a 0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are:

n = 10, p = 0.2.

The probability that at least 3 Canadian are on CERB in the sample is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]

[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]

Then:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778.

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222[/tex]

0.3222 = 32.22% probability that at least 3 Canadian are on CERB in the sample.

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