Given that a= 3, b= -2 and c= -4, evaluate the following expression. 3a-b/2c + 3a-c/c-b

Using the Fundamental Counting Theorem, the number of potential outcomes is given by: [tex]4^5[/tex]

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

There are five decisions, each with four options, hence:

[tex]n_1 = n_2 = n_3 = n_4 = n_5 = 4[/tex]

The number of options is:

[tex]N = 4 \times 4 \times 4 \times 4 \times 4 = 4^5[/tex].

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Answer: Parallel lines have equal slopes

If the slope of line s is -32 or -3/2, then the same applies to line t

Parallel lines have equal slopes but different y intercepts. These lines do not cross or intersect.

Answer:  -32

Step-by-step explanation:

The two lines are parallel which means these two lines have the same slope. Therefore, the slope of line t is -32.

The equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72

Given the equation below as shown;

3/5(30x - 15) = 72

Expand

3/5(30x) - 3/5(15) = 72

90x/5 - 15/5 = 72

3(6x - 3) = 72

Expand

18x - 9 = 72

Hence the equivalent expressions are 3(6x - 3) = 72 and 18x - 9 = 72

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathbf{2(-5x + 4) + 4x - 5 = -3}[/tex]

[tex]\huge\textbf{Solving for it:}[/tex]

[tex]\mathbf{2(-5x) + 2(4) + 4x - 5 = -3}[/tex]

[tex]\mathbf{-10x + 4 + 4x - 5 = -3}[/tex]

[tex]\huge\textbf{Combine the like terms:}[/tex]

[tex]\mathbf{(-10x + 4x) + (8 - 5) = -3}[/tex]

[tex]\mathbf{-10x + 4x + 8 - 5 = -3}[/tex]

[tex]\mathbf{-6x + 3 = -3}[/tex]

[tex]\huge\textbf{Subtract \boxed{\bf 3} to both sides:}[/tex]

[tex]\mathbf{-6x + 3 - 3= -3 - 3}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{-6x = -3 - 3}[/tex]

[tex]\mathbf{-6x = -6}[/tex]

[tex]\huge\textbf{Divide \boxed{\bf -6} to both sides:}[/tex]

[tex]\mathbf{\dfrac{-6x}{-6} = \dfrac{-6}{-6}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathbf{x = \dfrac{-6}{-6}}[/tex]

[tex]\mathbf{x = -6\div-6}[/tex]

[tex]\mathbf{x = 1}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf x =\frak{1}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

A) 384

B) 576

Step-by-step explanation:

the area of a rhombus is

pq/2

First Rhombus

we have p but to find q we can cut the triangle in half to form a right triangle, that allows us to use the Pythagorean theorem

20² = 12² + b²

400 - 144 = b²

b² = 256

b = 16

since the height (b) is half the rhombus, we double it to get q

p = 24

q = 32

a = [tex]\frac{24*32}{2}[/tex]

a = 384

Second Rhombus

Since rhombuses are parallelograms, we can use its area formula  (b)(h)

a = (24)(24)

a = 576

Answer:

Function 2

Step-by-step explanation:

An initial value of a function, aka y-intercept, is obtained by using x=0 and evaluating the function at that point. Evaluating the two functions given:

Function1: y = 2x(1/3)^x|x=0 = 2*0*1=0

with the chart

xy

03

16

2 12

3 24

Function2 has value 3 for x=0

So, Function 2 has a greater initial value

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A normal distribution can be used to approximate a binomial distribution when n* p and n * q are greater than 5.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

A probability bell curve is more properly described as the normal distribution.

The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.

Not all symmetrical distributions are normal, but all normal distributions are symmetrical.

Natural occurrences frequently resemble the usual distribution.

However, most price distributions in finance are not exactly normal distributions.

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The intervals that represent the number line are given as follows:

b. [tex](-\infty, -5] \cup [8, \infty)[/tex]

The first painted interval is of numbers to the left of x = -5(inclusive due to closed circle), hence:

[tex](-\infty, -5][/tex]

The second interval is of numbers to the right of x = 8, also inclusive, hence:

[tex][8, \infty)[/tex]

Hence the union is given by:

[tex](-\infty, -5] \cup [8, \infty)[/tex]

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Answer:

B

Step-by-step explanation:

mark me Brainliest pls

The set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.

Mathematically, the general form of the equation of a circle is given by;

(x - h)² + (y - k)² = r²

Where:

Based on the information provided that the center of the circle lies on the y-axis, we have:

(h, k) = (0, 4)

Radius, r = 3 units.

Substituting the given parameters into the formula, we have;

(x - 0)² + (y - 4)² = 3²

x ² + y² - 8y + 16 = 9

x ² + y² - 8y + 7 = 0.

Therefore, the set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.

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Complete Question:

The general form of the equation of a circle is Ax² + By² + Cx + Dy + E = 0, where A = B. If the circle has a radius of 3 units and the center at (0, 4), which set of values of A, B, C, D, and E correspond to the circle?

Answer: 9 m

Step-by-step explanation:

[tex]75=\frac{1}{3}(25)(h)\\\\h=\frac{75}{25/3}=9[/tex]

Answer:

70

Step-by-step explanation:

10tickets x 8students = 80tickets

150tickets-80tickets=70tickets

The solution to the absolute value inequality is (-3,2).

Absolute Value Inequality is the expression which contains absolute function as well as inequality signs .

The absolute value inequality is represented in the form of  a line

Interval of the function is  -3 to 2

As the intervals are represented by open circles, so  -3 and 2 are exclusive of the values of the inequality.

Therefore the another way to show the solution is

-3 < x < 2

or

(-3,2)

Therefore,  the solution to the absolute value inequality is (-3,2).

The complete question is attached with the answer.

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R, which is the rate is 20%.

Simple interest is the interest on a sum of money invested or borrowed for a specific period of time.

The sum invested is called the principal.

Analysis:

simple interest (I) = PRT/100 = 300

P = principal = 3000

R = rate = ?

T = 0.5 year

300 = 3000 x R x 0.5/100

R = 20%

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Answer: 4:9

Step-by-step explanation:

The ratio of the surface areas is the square of the ratio of the edge lengths.

The height of the pole is 96 feet

In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the legs a, b and the hypotenuse c, often called the Pythagorean equation:[1]

[tex]a^{2}+b^{2}=c^{2},[/tex]

Create a diagram of the scenario first. You would have a right triangle with a hypotenuse (longest side) of h + 4, a longest leg of h - 68, and one leg of length h to represent the pole.

Set up the equation [tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex] using the Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex]).

[tex]h^2 + (h - 68)^2 = (h + 4)^2[/tex]

On simplifying we get

[tex]h^2+h^2-136h+4624 = h^2+8h+16[/tex]

[tex]2h^2-136h+4624=h^2+8h+16[/tex]

[tex]h^2-144h+4608=0[/tex]

Solving using quadratic formula

[tex]h_{1,\:2}=\frac{-\left(-144\right)\pm \sqrt{\left(-144\right)^2-4\cdot \:1\cdot \:4608}}{2\cdot \:1}[/tex]  

[tex]h_1=\frac{-\left(-144\right)+48}{2\cdot \:1},\:h_2=\frac{-\left(-144\right)-48}{2\cdot \:1}[/tex]

h1 = 96 feet , h2 = 48 feet

If height would have been 48 feet then the other side would have a negative value as as 48 - 68 = -20 .

Hence the height of the pole is 96 feet

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Answer:

not enough information given

Step-by-step explanation:

as the rules say, we need at least 3 pieces of information :

2 angles and a side, or 3 angles (or there are other options like 2 sides and one angle or 3 sides).

but here we get 1 side and 1 angle. the shared point does not give us anything in that regard.

so, not enough information.

Answer:

1

Step-by-step explanation:

Knowing that the entire number line equals 7, and that the second line segment RS equals 6, we can subtract the two values to find QR.

[tex]7-6=1[/tex]

Therefore, QR equals 1.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:QR = 1 \:\: unit [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \qquad \tt \rightarrow \: QR + RS = QS[/tex]

Let QR = x

[tex]\qquad \tt \rightarrow \: x + 6 = 7[/tex]

[tex]\qquad \tt \rightarrow \: x = 7 - 6[/tex]

[tex]\qquad \tt \rightarrow \: x = 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

First, 0.0004853 is < 1, so we need to multiply the number by 10 to a negative power if it's greater than 1 (if that makes sense i cant describe it better)

So, b and c is incorrect.

10 to the power of negative 4 = 0.0001, and 4.853 x 0.0001 = 0.0004853 (true), so answer is a

Answer:

a

Step-by-step explanation:

a number expressed in standard form is

a × [tex]10^{n}[/tex]

where 1 ≤ a < 10 and n is an integer

given

0.0004853 ( place the decimal point after the 4 )

= 4.853 × [tex]10^{n}[/tex]

to place the decimal point in its original position we require to shift it 4 places left , denoted by - 4 on the exponent , that is

0.0004853 = 4.853 × [tex]10^{-4}[/tex]

The distance from Mytown to Little Village is 350 miles.

The distance from Capital City to Little Village is 660 miles.

The distance  from Capital City to Mytown is 310 miles,

The distance from Mytown to Yourtown is 200 miles,

and from Yourtown to Little Village is 150 miles.

Assuming all the places are collinear,

The distance from Mytown to Little Village is

200 + 150   = 350 miles

Hence, The Mytown is 350 miles far from the Little Village

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Using a system of equations, it is found that a value of h = 4 will result in an infinite number of solutions.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

If two equations are equal, the system has infinite solutions.

In this problem, the equations are:

4x - 16 = h(x - 4).

Then:

4(x - 4) = h(x - 4).

h = 4.

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The store manager would reach his goal of $20,000 if the sales team sold 80 tables and 10 laptops.

To calculate if the store manager achieves its goal, we must perform the following operations:

According to the above, sales do reach the goal if 80 tablets and 10 laptops are sold.

Note: This question is incomplete because there is some information missing. Here is the missing information:

A computer store sells both tablets and laptops. One brand of tablet costs $200. That same brand of laptop costs $400. The store manager wants to sell enough of this brand of tablets and laptops to reach the sales goal of $20,000.

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Answer:

5x/2

Step-by-step explanation:

Say the mystery number is "x"

5 times that = 5 * x = 5x

Then the quotient (that means the result of division, so divide!) of that and 2 would give you: 5x/2

Step-by-step explanation:

I assume that DF and DQ are tangents to the circle.

angle FGQ = 268°

therefore, angle FQ = 360 - 268 = 92°

b = 1/2 × (angle FGQ - angle FQ) = 1/2×(268 - 92) =

= 1/2 × 176 = 88°

Answer:

3

Step-by-step explanation:

Irregular pentagon since it has 5 sides

Answer:

irregular pentagon

(first option listed)

Step-by-step explanation:

This shape still has five sides--making it a pentagon. Because the angles are not exactly the same, and so the side lengths are also not equal, we name it an "irregular" pentagon.

hope this helps! have a lovely day :)

The percentage of the survey respondents that do not like both hamburgers and burritos is 16.09%.

The percentage of the survey respondents that do not like both hamburgers and burritos will be:

= 33/205 × 100

= 16.09%

The marginal relative frequency of all customers that like hamburgers will be:

= 134/205

= 0.65

The data point that has strongest association of its two factors will be:

Those who like hamburger and burrito = 39/134 = 0.29

Those who like hamburger and not burrito = 95/134 = 0.71

Those who like burrito but not hamburger = 38/71 = 0.53

Those who do not like hamburger or burrito = 33/71 = 0.47.

Therefore, the data point that has strongest association of its two factors will be those who like hamburgers but not burritos.

A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:

Likes hamburgers Does not like hamburgers Total

Likes burritos 38 77

Does not like burritos 95 128

Total 134 71

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Answer: P(A)=4/425≈0,0094.

Step-by-step explanation:

[tex]P(A)=\frac{C_4^1*C_3^1}{C_{51}^2} .[/tex]

The desk has 4 kings.

First card is drawn from a well shuffled deck is a card of king.     ⇒

[tex]C_4^1=\frac{4!}{(4-1)!*1!} =\frac{3!*4}{3!*1}=4.[/tex]

Second card is drawn from a well shuffled deck is a card of king too.    ⇒

[tex]C_{4-1}^1=C_3^1=\frac{3!}{(3-1)!*1!}=\frac{2!*3}{2!*1}=3.\\ The \ desk\ has\ 51\ card.\ \ \ \ \Rightarrow\\C_{51}^2=\frac{51!}{(51-2)*2!}=\frac{49!*50*51}{49!*1*2} =51*25=1275.\\ P(A)=\frac{4*3}{1275} =\frac{4}{425} \approx0,0094.[/tex]

Answer:

Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes. For instance, rolling a die once and landing on a three can be considered one event.

Step-by-step explanation:

for more information check the above attachment

Answer:

z = 30

Step-by-step explanation:

→ 360 ÷ z = 12

→ 360/z = 12

→ 12z = 360

→ z = 360/12

→ [ z = 30 ]

Hence, the value of z is 30.

Answer:you have to isolate z,make z the subject.

Step-by-step explanation: z=360 multiply by 12,

giving us 4320.z=4320,i mean thisis the answer you have to stick with if u want to find a value for z.

step by step;z/360=12

z=360 into 12

z=4320

The probability is 5/343.

Given :8 floors and 4 passengers.

Passengers will be assumed to start on the first floor, where everyone goes up, and each passenger only gets off on the 2nd floor (no one gets off on the 1st floor!)

Now we need to find the number of all ordered lists of four numbers out of seven, eg 2<3<7<8, 3<6<7<8, 4<5<6o<8, etc.

This can be done in 7C4 ways.

The total numbers of ways 4 passengers can get off at 7 floors (starting at the 2nd!) is [tex]7^{4}[/tex].

Therefore the probability is [tex]\frac{7C4}{7^{4} }[/tex] = [tex]\frac{5}{343}[/tex]

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Answer:

The answer is the 3rd option (2)

Step-by-step explanation:

Hope this helped! :D