Sandra saves 12% of her salary for retirement. This year her salary was $1,000 more than in the previous
year, and she saved $4,920. What was her salary in the previous year?

The altitude exists 9.500 centimeters and the area exists 88.000 square centimeters is [tex]$ -\frac{9.26316}{4.75d}[/tex].

A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry. The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude exists the point at where the extended base and the height converge.

A triangle's altitude is determined by drawing a perpendicular line from its vertex to its opposite side. The altitude, sometimes referred to as the triangle's height, forms a right-angle triangle with the base.

Let A be the  area of the triangle

h be the altitude

b be the base

The formula that relates the three is the area of a triangle

A = (1/2) bh

Note that anything listed as a "rate" is a derivative value.

dh (rate of change of altitude) = 3.000 cm/min

dA (rate of change of area) = 4 cm²/min

h = 9.500 cm

A = 88.000 cm²

Consider that both b and h are changing in this situation, so we have to treat them both as variables. This means we have to use the product rule, inserting the derivatives where applicable.

dA = (1/2) × db × h + (1/2)b × dh

substitute the values in the above equation, we get

4 = (1/2) × db × 9.5 + (1/2) b × 3.000

88 = (1/2) × b × 9.5

b = 18.52631

Now, looking back at our derivative

4 = (1/2) × db × 9.5 + (1/2) × 18.52631 × 3.000

simplifying the above equation, we get

4 = 4.75 db + 13.26316

b =[tex]$ -\frac{9.26316}{4.75d}[/tex]

To learn more about altitude of a triangle refer to:

https://brainly.com/question/14357999

#SPJ4

If 7 out of every 12 coins are nickles (7/12) and 3 out of every 12 coins are dimes (3/12), there has to be 2 quarters out of every 12 coins (2/12)

Now, the ratio would be:

The result of the expression given as 6x/(-2) is -3x

From the question, the expression is given as

6x/(-2)

The above expression is a quotient expression

So, we start by rewritting it as a product

This is represented as

6x/(-2) = 6x * 1/(-2)

Remove the bracket

So, we have the following equation

6x/(-2) = 6x * 1/-2

Evaluate the product

6x/(-2) = -3x

Hence, the value of the expression is -3x

Read more about expression at

https://brainly.com/question/20662459

#SPJ1

3.5% of all sold units have been returned so far. The probability that at most 6 units were returned out of 200 sold unit records is 0.7323.

Given that,

For an online store, Stephan is evaluating the data on product returns. 3.5% of all sold units have been returned so far.

We have to find what is the probability that at most 6 units were returned out of 200 sold unit records.

From binomial,

Binomial to normal approximations without continuity factor Sample size ,

n = 200

Probability of an event of interest,  

p = 0.035  

P(0<=n<=2)

=0.7323

Therefore, the probability that at most 6 units were returned out of 200 sold unit records is 0.7323.

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ4

Since Carrie wants to make a wallpaper border to go around the top of her room. She wants the border to look something like the illustration below. This is a Reflection

A transformation is an operation that is performed on a picture. Transformations are classified into four types: translations, reflections, dilations, and rotations. In transformations, reflections are achieved by flipping a shape or figure across a line of reflection, a point of reflection, or a plane of reflection.

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure is equidistant from every point in another figure.

Learn more about reflection in:

https://brainly.com/question/1908648

#SPJ1

The percentage of the employed population are people older than 40 who do not work in the hospitality industry is B. 17%.

The city's residents work in the hospitality industry = 28%

The residents that are age 40 or younger, and 15% of residents are people age 40 or younger = 55%

Those who work in the hospitality industry that are younger than 40% = 15%

Therefore, those that don't work in the industry will be:

Percentage of 40 or older - Percentage of those working

= (100 - 55%) - 28%

= 45% - 28%

= 17%

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

Answer:

solve for what? x or y? or anything another

Step-by-step explanation:

if x

1.

[tex] - \sqrt[4]{2} \sqrt[4]{2} [/tex]

2.

[tex]x = (2 \: or \: \infty )[/tex]

so hope it help

The probability of a less-than-ideal day (no free pizza and no sun) is 0.25

Let us define the events from the example.

Let event A: Sunny day for any given day

event B: Getting free pizza for any given day.

Now, we will translate the word problem into our symbols.

The probability of a sunny day is 80% i.e P(A)=0.8

The probability of free getting pizza is 30% i.e. P(B) = 0.3

The probability of free pizza and a sunny day is 35% .i.e P(A∩B) = 0.35

a)Complement means not happening an event i.e. event A’ : No sunny day for any given day event B’: Not getting day free pizza for any given.

Here dash ( ‘ ) complement.

The probability of a less-than-ideal day

(no free pizza and no sun) is

P(A'∩B') = P(A∪B)'... (De Morgan's Jaw)

De Morgan's law: (A∩B)'= A'∪B'

                             (A∪B)’ = A'∩B'

P(A'∩B') = 1-P(A∪B)    (P(A) = 1-P(A)).

= 1-[P(A) + P(B)-P(A∩B)]

= 1-[0.8+0.3-0.35]

P(A'∩B') = 0·25

The probability of a less-than-ideal day (no free pizza and no sun) is 0.25.

b)To check whether free pizza and sun are independent events or not, let us see when two events are said to be independent.

Two events (A & b) are said to be independent if P(A∩B) = P(A)· P(B)

Let us check whether this property satisfies our case or not.

LHS = P(A∩B)=0.35

RHS= P(A) P(B)

= 0.8 x 0.3

RHS = 0.24.

LHS ≠ RHS

P(ANB) ≠ P(A). P(B) in our case.

Two events A and B are not independent in our case

Sun and free pizza are not independent events.

c)Probability of no free pizza on a sunny day is P(A∩B').

P(A∩B') = P(A) - P(A∩B) = 0.8 0.35

P(A∩B') = 0·45

The probability of no free pizza on a sunny day is 0.45

To learn more about Probability click here:

brainly.com/question/11234923

#SPJ4

Answer: yes

Step-by-step explanation: 64 is a factor of 4 because you can multiply it by 16 to get 64. Remember if you divide and get a whole number it is a factor .

Answer:

[tex]45120 in^2[/tex]

Step-by-step explanation:

Area of Taylor's Banner (AT): [tex]A_T = 8*564=4512 in^2[/tex]

Area of Emily's Banner (AE): [tex]A_E=10*A_T[/tex]

Plugging in AT: [tex]A_E = 10 * 4512 = 45120 in^2[/tex]

The Area of Emily's Banner is 45120 inch²

The Area of rectangle is the product of its length to its width.

i.e., Area of rectangle= length x width

Given:

Taylor’s banner : 8 inches tall and 564 inches wide.

Area of Taylor's Banner= l x w

                                       = 8 x 564

                                       = 4512 inch²

and, area of Emily’s banner is 10 times as large as the area of Taylor’s banner.

So, Area of Emil's Banner= 10 x 4512

                                          = 45120 inch²

Learn more about area of rectangle here:

https://brainly.com/question/20693059

#SPJ2

Answer:

9 terms

Step-by-step explanation:

The sequence given is a geometric sequence

In a geometric sequence, the nth term of the sequence can be found by the formula

[tex]a_n = a_1r^{n-1}[/tex]

[tex]\text{where }\\\\ a_n = \text {nth term}\\\\\text{$a_1 = $ first term}\\\\\text{$r = $ common ratio}[/tex]

In the given sequence,

a₁ = 1

r = -4

aₙ = 65536

So we get the relation:
65536 =  1·  (-4)ⁿ⁻¹

65536  = (-4)ⁿ⁻¹

It is clear that n-1 has to be even so that the power of 4  is positive.
Substituting x = n -1 where x is even gives us
4ˣ = 65536

If we take logarithms to the base 4 on both sides we get

=> x = [tex]\log_465536 = 8\\\\[/tex]

Since x = n - 1 and x = 8, n = 9

So the 9th term in the series is 65536

The simplest form of the ratios are:

So, the ratios in the simplest form are:

We can observe that the simplest form of all the ratios is similar which is 3.

Therefore, the simplest form of the ratios are:

Know more about ratios here:

https://brainly.com/question/2328454

#SPJ13

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.

Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.

X has a value of 3. The following is a list of the arguments made for each step.

Adding more line segments

Rule of substitution (b)

c) Simplifying by incorporating related terms

d) Compiling terms for lies

e) Multiplying each side by 8

AB = 2x

BC = 6x + 8

AC = 32

AB plus BC equals AC. (Extension rule)

addition of a line's individual segments

2x + 6x + 8 = 32 (Substitution rule) (Substitution rule)

replacing AB, BC, and AC in the formula AB + BC = AC

8x + 8 = 32 (Simplification) (Simplification)

2x + 6x + 8 = 32, simplified adding comparable terms

8x = 24 (Assembling similar terms)

8x = 32 - 8

8x = 24

x = 3 (Divide both sides by 8) (Divide both sides by 8)

8x / 8 = 24/8

x = 3

To learn more about value refer to:

https://brainly.com/question/843074

#SPJ13

Answer:

The slope is undefined

Step-by-step explanation:

89 degrees

The sum of an angle and its complement is equal to 90 degrees.

Let the measure of the complement be "x"

Given the information below:

Angle = 1 degrees

Taking the sum of the angle and its complement will give:

Subtract 1 from both sides

Therefore the measure of the complement for the angle given is 89 degrees

Let the total number students be s. Then

s = 3 + 5 + 2= 10

x | Number of students(n) | Pr(x) | xPr(x)

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

76 | 3 | 0.3 | 22.8

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

79 | 5 | 0.5 | 39.5

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

175 | 2 | 0.2 | 35

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

Therefore, the expected value of x is 97.3

Answer:

  sum = -15/2

Step-by-step explanation:

Given the formula for the n-th term of a sequence is n(n-8)/√(n+3), you want the sum of the 1st and 6th terms.

The first term is found by substituting 1 for n:

  1(1 -8)/√(1 +3) = 1(-7)/√4 = -7/2

The sixth term is found by substituting 6 for n:

  6(6 -8)/√(6 +3) = 6(-2)/√9 = -12/3 = -4

The sum of the first and sixth terms is ...

  -7/2 +(-4) = -(7/2 +8/2) = -15/2

  sum = -7 1/2

The sampling strategy used in this problem is an example of:

Sampling is when a subset of an entire population is studied, to verify whether characteristics of the sample can be expanded to the entire population.

The sample has to be representative of the population, that is, large enough, hence it should contain all the subsets of the population.;

In the context of this problem, the chain sees about 500 customers a week and they receive the responses from 50 of them. This is a not large enough sample size, hence it could cause biased results, meaning that the perspective of the entire population will not be considered.

In the context of this problem, the survey are anonymous, and the objective of a survey is generally not to reward the participants, hence the last two options are false.

The options are given as follows:

More can be learned about sampling at https://brainly.com/question/9910540

#SPJ1

Answer:

angle 4 and 5 are interior angles, and 3 and 6 as well

We have to calculate the area and perimeter of ABC.

Area:

We can calculate the area by substracting from the area of the big triangle ABD the area of the little triangle BCD. Both are right triangles.

The area of ABD is:

The area of BCD is:

Then, the area of ABC is:

The area of ABC is 90 cm^2.

Perimeter:

We calculate the perimeter by adding the length of the three sides. We know only 2 of the sides, so we have to calculate the other one (BC).

The length of BC can be calculated using Pythagorean theorem for the triangle BCD, so we can write:

Now, we can calculate the perimeter as:

The perimeter is 53 cm.

we have

1/2 +1/3

Remember that

1/2=0.5

1/3=0.33 -----> rounded 0.3

so

0.5+0.3=0.80

Answer: please help

Step-by-step explanation: I don’t know what the answer is I need help

Answer:

Yes 12 is an Integer

Step-by-step explanation:

12 is a whole number that can be written without a fractional component, thus 12 is an integer.

There are 64000 distinct combinations .

The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.

The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.

How many possible three-number combinations are there?

You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.

Learn more about Three-number combination here:

brainly.com/question/27242731

#SPJ1

The amount that Dado will pay for 1 xylobar and 2 yakities is 1.779.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Zimak bought 3 xylobars and 5 from the intergalactic Candy. Let this be:

3x + 5y = 1.75

x = xylobars

y = yackities

Jeejuju paid 1.88 and got 4 xylobars and 1 yackity. Let this be:

4x + y = 1.88

Equate the equations and this will be:

4x + y = 1.88 ....... i

3x + 5y = 1.75 .... ii

From equation i y = 1.88 - 4x

Put this into equation ii

3x + 5y = 1.75

3x + 5(1.88 - 4x) = 1.75

3x + 9.4 - 30x = 1.75

Collect like terms

3x - 30x = 1.75 - 9.4

-27x = -7.65

Divide

x = 7.65 / 27

x = 0.283

xylobars = 0.283

Since 4x + y = 1.88

4(0.283) + y = 1.88

1.132 + y = 1.88

y = 1.88 - 1.132

y = 0.748

The cost for 1 xylobar and 2 yakities will be:

x + 2y

0.283 + 2(0.748)

= 0.283 + 1.496

= 1.779

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

Answer:175/48

Step-by-step explanation:

The length of the arc of the circle is 19.6 inches

We can find the length of the arc using the formula;

where ;

Substituting these values;

ok

apples = a

babanas = b

a = 2b

Answer:

Step-by-step explanation:

A perpendicular line will have a sope that is the negative inverse of the reference line.  The reference line is y = -3 + 4, with a slope of -3.  The negative inverse would be -(-1/3) or (1/3).

The new line will take the form of y = (1/3)x + b, where b is the y-intercept (the value of y when x=0).  We want the new line to go through point (-3,-7).  We;ll need a value of b that will make that happen.  To find b, enter the given data point and solve for b:

y = (1/3)x + b for (-3,-7).

-7 = (1/3)(-3) + b

-7 = -1 + b

b = -6

The new equation is y = (1/3)x - 6

See the attached graph.