Sandra saves 12% of her salary for retirement. This year her salary was $3000 more than in the previous year, and she saved $4200. What was her salary in the previous year?

The binomial coefficient

[tex] \displaystyle \binom{4}{2} = \dfrac{4!}{2!(4-2)!} = \dfrac{4\cdot 3}{2} = 2\cdot 3 = 6 [/tex]

Tells you that there are 6 ways of choosing a subset of two letters from the four given letters.

For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)

So, there is a total of 12 combinations of the letters w, x, y, z, taking two at a time.

There are 6 ways of choosing a subset of two letters from the four given letters.

The arrangement of the different things or numbers in a number of ways is called the combination.

For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)

So, there is a total of 6 combinations of the letters w, x, y, z, taking two at a time.

The combination will be calculated as:-

[tex]^4C_2=\dfrac{4!}{2!(4-2)!}[/tex]

[tex]^4C_2=\dfrac{4\times 3}{2}[/tex]

[tex]^4C_2=6[/tex]

Therefore there are 6 ways of choosing a subset of two letters from the four given letters.

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8+4=12

Since we are trying to find out how much was deducted from the wallet, make 12 negative

integer: -$12

45-12=33

$33 left

The integer shows the amount of money in Shaniqua's wallet is -12 and the money left will be $33

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The integer will be calculated as:-

The amount deducted is

8  +  4  =  12

Since we are trying to find out how much was deducted from the wallet, make 12 negative

integer:  -$12

45  -  12  =  $33

Therefore the integer shows the amount of money in Shaniqua's wallet is -12 and the money left will be $33.

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Answer: 576

Step-by-step explanation:

To find the area of a triangle you do base times the height divided by two. Now that you have the area and the base you just have to do the opposite

So you would do 1,440*2 = 2,880

Then you would divide 2,880 from 5. 2,880/5=576

So the answer is 576

Remember to isolate the variable. Subtract 9 from both sides

10 (-9) ≥ 9 (-9) + v

10 - 9 ≥ v

Simplify. Combine like terms

1 ≥ v

1 ≥ v is your answer

hope this helps

Answer:

The minimum value of C is -9

Step-by-step explanation:

we have

[tex]C=-2x+y[/tex]

[tex]x\geq -5[/tex]

[tex]x\leq 4[/tex]

[tex]y\geq -1[/tex]

[tex]y\leq 3[/tex]

using a graphing tool

The solution is the shaded rectangle

see the attached figure

The vertices of the rectangle are the points

[tex](-5,3),(4,3),(4,-1),(-5,-1)[/tex]

To find the the minimum value of C, substitute the value of x and the value of y of each vertex and calculate the value of C, then compare the results

For [tex](-5,3)[/tex]

[tex]C=-2(-5)+3=13[/tex]

For [tex](4,3)[/tex]

[tex]C=-2(4)+3=-5[/tex]

For [tex](4,-1)[/tex]

[tex]C=-2(4)-1=-9[/tex]

For [tex](-5,-1)[/tex]

[tex]C=-2(-5)-1=9[/tex]

therefore

The minimum value of C is -9

Simplify: 12 + 10i +14i = 12 +24i

answer

B) 12 +24i

24i+12 thats pretty basic though

When dealing with a quadratic equation, you usually assign the following name to the coefficients of the variables:

[tex] ax^2+bx+c=0 [/tex]

So, [tex] a [/tex] is the coefficient of [tex] x^2 [/tex], [tex] b [/tex] is the coefficient of [tex] x [/tex] and [tex] c [/tex] is the constant term.

In your case, the coefficient of [tex] x^2 [/tex] is -3, so [tex] a=-3 [/tex]

The coefficient of [tex] x [/tex] is -2, so [tex] b = -2 [/tex]

The constant term is 6, so [tex] c = 6 [/tex]

The complete statement is:

There were 59 bacteria after 5 hours

The initial population of the bacteria is given as:

[tex]a =100[/tex]

The proportion left after each hour is given as:

[tex]b = 90\%[/tex]

An exponential function is represented as:

[tex]f(x) = ab^x[/tex]

Substitute values for (a) and (b)

[tex]f(x) = 100 \times (90\%)^x[/tex]

Express percentage as decimal

[tex]f(x) = 100 \times (0.9)^x[/tex]

After 5 hours, the value of x is 5

i.e. x = 5

So, we have:

[tex]f(x) = 100 \times (0.9)^5[/tex]

Evaluate the exponent

[tex]f(x) = 100 \times 0.59049[/tex]

Multiply

[tex]f(x) = 59.049[/tex]

Approximate

[tex]f(x) = 59[/tex]

Hence, there were 59 bacteria after 5 hours

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12 - x < 8

add x to both sides

12 - x + x < 8 + x

12 < 8 + x

re-write

8 + x > 12

Subtract 8 to both sides

8 + x - 8 > 12 - 8

x > 4

The graph B is matching the answer (x > 4)

So answer is B.

Let's solve your inequality step-by-step.

12−x<8

Step 1: Simplify both sides of the inequality.

−x+12<8

Step 2: Subtract 12 from both sides.

−x+12−12<8−12

−x<−4

Step 3: Divide both sides by -1.

−x

−1

<

−4

−1

x>4

Answer:

x>4

NOTE step 3 i was tryna do a fractions it aint work out so good soo i like added a pic

The percentage decrease in price from $4.59 to $4.09 is 10.9%, while the percentage increase from $4.09 to $4.59 is 12.2%. Therefore, the percentages of change are not the same and the percentage increase is a greater change.

To calculate the percentage decrease in price from $4.59 to $4.09, we subtract $4.09 from $4.59, then divide by the original price of $4.59, and multiply by 100: (($4.59 - $4.09) / $4.59) * 100 = 10.9%. Therefore, the percentage decrease is 10.9%.

For the percentage increase from $4.09 back to $4.59, we similarly subtract $4.09 from $4.59, divide by the 'new' original price of $4.09, and multiply by 100: (($4.59 - $4.09) / $4.09) * 100 = 12.2%. Therefore, the percentage increase is 12.2%.

The resultant decrease and increase percentages are not the same. The percentage increase of 12.2% is a greater change compared to the 10.9% decrease.

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To calculate the median: you want to organize all the numbers in it's data so it should look like this:  2, 5, 5, 8, 10, 12, 18, 20.

Now that it is organized look for the middle number so 9 is our median. I got this by adding 8 + 10 which equals 18 then dividing it by 2. So anytime you have 2 middle numbers add them then divide it by 2 it will always be your median.

To determine the mode: look for the number the occurs the most. I only see two 5's so the answer is 5 for our mode.

To determine the mean: Add all the numbers together then divide it by how many numbers there are so there are 8 numbers divide it by 8 after we add them.

2+5+5+8+10+12+18+20= 80 divide it by 8 and it equals 10. So 10 is the mean.

Answer:

Intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

Step-by-step explanation:

Required vector is consists of the two components

vx= 2+4=6 units  and vy= 1 unit and vx ⊥ vy

We will use Pythagorian theorem to find intensity of the vector v

v∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 units

The angle ∡α between vector and east direction we wil find with tanα

tanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

Good luck!!!

Answer:

The vector that describes their hike from their starting position to their final destination is  < 6, 1 >

Answer: .0000356

Step-by-step explanation:

3.56 x 10⁻⁵

the exponent of 5 tells you to move the decimal 5 places

the negative sign tells you to move the decimal to the left.

Equation Given: 3.56 x 10^-5  

Simple Explanatio: Lets start with this 10^-5 since the exponents is a negative you must subtract the exponent from the base and after you do so this is what your left with -5 and now since we have done the work lets rewrite the answer as 3.56 x 10^-5 the equation may not be changed but that's how i was told to do it and now solve. The decimal in 3.56 will be moved to the left five times because this equation has an negative exponent not a positive so you should end up with the simple answer of 0.0000356

Hopefully this helps  ^0^

Angle created by intersecting lines are 115° and 65°

Given that;

One angle is less than 50°

Find:

Measure of all angles

Computation:

We know that;

Sum of two adjacent angles = 180°

Assume;

One angle = a

So,

Another angle = a - 50

So,

a + (a - 50) = 180

2a - 50 = 180

2a = 230

a = 115°

another angle = 180 - 115

Another angle = 65°

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[tex]x-intercept(\frac{26}{3},0)

y -intercept (0,\frac{13}{2} )[/tex]

y is a lil messed up in term of looks but meh

have a good day breh

Answer:

x = 5/2

Step-by-step explanation:

Isolate x by adding 2x to both sides, obtaining:  5 - 2x + 2x = 2x.  Then 5 = 2x, and dividing both sides by 2 results in x = 5/2.

Answer:

for anyone in the future that needs this the answer is The rule (x,y) ----> (x+2, y-4) represents a translation 2 units RIGHT and 4 units DOWN

Step-by-step explanation:

A translation is a transformation that moves every point in a figure in the same direction by the same amount. The rule (x, y)→(x+2, y−4) represents a translation of 2 units right and 4 units downwards

A translation is a transformation that moves every point in a figure in the same direction by the same amount. It is also a sort of transformation in which each point in a figure is moved the same distance in the same direction resulting in the same figure again.

For any graph, if the value of x is increased it moves in the right direction while it moves in the left direction if the value is decreased.

Similarly, For any graph, if the value of y is increased it moves upwards while it moves in downwards if the value is decreased.

Now, as per the given rule of transformation, (x, y)→(x+2, y−4), the graph will translate 2 units right and 4 units downwards.

Hence, The rule (x, y)→(x+2, y−4) represents a translation 2 units right and 4 units downwards.

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The polynomial 55° + 6st - 85° - 6t has 4 terms and a degree of 10 after it has been fully simplified.

To determine the number of terms in a polynomial, count the separate algebraic expressions that are added or subtracted. In this case, the polynomial is composed of four distinct terms: 55°, 6st, -85°, and -6t.

Next, the degree of a term in a polynomial is the highest power of its variable. Examine each term to identify the variable and its corresponding exponent. The term 55° has a degree of 0 since any nonzero constant raised to the power of 0 is 1. Both 6st and -6t have a degree of 2, as the variables s and t are raised to the power of 1. Lastly, the term -85° has a degree of 1.

To find the overall degree of the polynomial, identify the term with the highest degree. In this case, it is the term 6st, which has a degree of 2. Therefore, the fully simplified polynomial has four terms and a degree of 2, making the correct statement: "It has 4 terms and a degree of 10."

Complete question :-

Which statement is true about the polynomial 55° + 6st-85°-6t after it has been fully simplified?
It has 3 terms and a degree of 9.
It has 3 terms and a degree of 10.
It has 4 terms and a degree of 9.
It has 4 terms and a degree of 10.

"An on-line electronics store must sell at least $5000 worth of computers and printers per day"

The bold faced words tell us greater than or equal to 5000

"The store can ship a maximum of 20 items per day"

The bold faced words tell us less than or equal to 20

We can automatically eliminate A and B since they don't have EQUAL sign in them. From C and D, we choose D because it correctly attaches the price of printers and computers to the respective variables (printers is p & computers is q). Choice C does this wrong!

ANSWER: D

Substitute x = 2 into each of the expressions

left: 6* 8  - 2(2) = 48 - 4 = 44

right: 6(5 +2) = 6(7) = 42

44 > 42

Answer

>

20% = 1/5

20/5 = 4

Sam scored 4 points

Answer:

4

Step-by-step explanation:

20% of 20 points would be 4 you can literally just type it into google

Answer:

It is correct because 8/9x3/4=2/3

Step-by-step explanation:

Call that number x.

Then rewrite as equation:

4x+6=7x

solve for x

6=3x

2=x

So the number is 2.

Check that 2 is the number by following the original wording, mentally.

Hey there!!

Let's take the number as 'x'

4 times the number is 4x

This is increased by 6

We will have to add 6.

... 4x + 6

7 times a number is 7x

... 7x

Both these values are equal.

Hence,

... 4x + 6 = 7x

... 6 = 3x

... x = 2

Hence, the number is 2.

Answer,

Explanation,

All you need to do is simplify,

15 - (-3) -4 = ?

15 - (-3) = 18

18 - 4 = 14

Hope this helps :-)

Domain=all real numbers

Range is x≤4

Hope this helps :)

Answer:

42%

Step-by-step explanation:

We will use the conditional probability in this case

We use conditional probability when two cases occur are dependent.

So by using:

[tex]\frac{P(A\capB)}{P(B)}[/tex]

Here, A is the event of experience needed.

And B is the event of part-time

Substituting the values in the formula we get:

[tex]\frac{6}{14}=.42[/tex]

Intersection of experience needed and part-time is 6

And part-time total is 6+8=14

To get in percent we will multiply it by 100

42% is the required probability.

The given figure is a rectangle.

Given angles are- m∠BDC = 47°, m∠CAB = 52°, and m∠BEC = 99°

The sum of the angles m∠BDC = 47°, m∠CAB = 52° is the measure of  m∠BEC  which is 99°

This is sufficient to prove. Measure of angle A and D are 90 degrees each as they are right angles triangles. So, inner angle A is 90-52 = 38 degrees. Inner angle D will be    90-47  =43 degrees.

Measure of triangle AED = 180 degrees

Let inner E = x

then, 38+43+x=180

x=99 degrees

Outer E and inner are vertical angles and so, they are same.

Moreover, triangles AED and BEC are same so E is 99 degrees

Answer:

-8

Step-by-step explanation:

1 1/2 - 2 5/6  (multiply the denominator by the whole number, then add with the numerator)

3/2 - 17/6  (get the common denominator which is 6 in this situation and multiply that with the numerator)

9/6 - 17/6 = -8