an employer agrees to pay $5,000 for medical insurance and contribute an additional 5% of the employees'

Answer:

£824

Step-by-step explanation:

3% of 800 + 800

1% = ÷100

800 ÷ 100 = 8

8×3=3%=24

800 +24 =£824

Answer:

7 7/80 or 7.0875

Step-by-step explanation:

product is the result of multiplication

7/8 * 81/10 = 567/80 = 7 7/80 or 7.0875

The equation to find Shanti's age is y = x - 3 where y is Shanti's age.

Given,

Shanti's sister Uri is Shanti's age plus 3 years.

Uri is 7 years old.

We need to write an equation to find Shanti's age.

We have,

Uri age = Shanti age + 3______(1)

Uri = 7 years old

Putting in (1)

We get,

Uri age = Shanti age + 3

7 = Shanti age + 3

Subtracting 3 on both sides.

7 - 3 = Shanti age + 3 - 3

4 = Shanti age

We see that Shanti's age is 4 years old.

If we have to write an equation then,

Consider Uri's age to be x and Shanti's age to be y.

Now,

Uri age = Shanti age + 3

x = y + 3

Subtracting 3 on both sides

x -3 = y

y = x - 3 is our equation.

Thus the equation to find Shanti's age is y = x - 3.

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On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667

A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.

red die, there are 3 numbers greater than 3 out of 6 numbers

Probability (A) = 3/6 = 1/2.

green die, there are 2 numbers less than 3 out of 6 numbers

Probability (B) = 2/6 = 1/3.

events are independent

P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)

16.67% probability = 0.1667

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Answer:

Perimeter:\(4x+10\) feet
Area:\(x^{2}+5x+6\) feet

Step-by-step explanation:

The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=\(x^{2}+2x+3x+6=x^{2}+5x+6\)

Answer:

f(-8) = -2

Step-by-step explanation:

f(x)=x/4

Let x = -8

f(-8)=-8/4

f(-8) = -2

If a manufacturer manufactures 5,000 dozen of sweaters, and sells 3,000 dozen of them only, then the total profit he/she earns from the these sweaters is [1000(3x - 5y)], assuming that the cost of manufacturing one sweater is "x" and the selling price of that sweater is "y".

As per the question statement, a manufacturer miscalculates the demand of the market and manufactures 5,000 sweaters, but sold only 3000 of them.

We are required to calculate the total profit earned by the manufacturer from the sale of the sweaters.

Since, no data about the manufacturing cost of the sweaters and their selling price is provided in the question statement, let us assume that the cost of manufacturing one sweater is "x" and the selling price of that sweater is "y". Solving with these variables will give us a generalized answer which we can use for any value.

Now, Since assumed that, manufacturing cost of one sweater is "x", then, manufacturing cost of 5000 sweaters will be \((5000*x)=5000x\).

Similarly assumed that, selling cost of one sweater is "y", and then, selling cost of 3000 sweater will be \([(3000*y)=3000y]\).

Now, we know that,

[Profit = (Total Selling Cosy) - (Total Manufacturing Cost)],

Therefore, in this case, total profit from the sale of 3000 sweaters

\(=(3000y-5000x)\\=1000(3y-5x)\).

Now, on using real integers or numbers in place of "x" and "y", if the value of Profit comes negative, it will mean, that for those values of "x" and "y", the manufacturer makes loss, not profit.

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Answer:

A

Step-by-step explanation:

Answer:

200π

Step-by-step explanation:

Surface area is abbreviated to SA

TOTAL SA of cone = Base area + πrl

Base area = πr² = π x 8² = 64π

Curved SA = πrl = π x 8 x l

to work out l, use pythagoras theorem: √(15)² + (8)² = 17

so, curved SA = π x 8 x 17 = 136π

Total SA of cone = 64π + 136π = 200π

Answer:

1366.66 ft³

Step-by-step explanation:

12ft × 8ft × 12ft = 1152 ft³

214.66 ft³ + 1152 ft³

1366.66 ft³

Answer:

The total volume of the trailer is 1366.6 ft^3

Step-by-step explanation:

12 * 8 = 96

96 * 12 = 1152 ft^3

1152ft^2 + 214.66 = 1366.6 ft^3

sorry I was late.

Answer:

okay luego le digo 4yo1 xkw k ​

Step-by-step explanation:

It seems you havent posted a graph

Answer:

x=-1

Step-by-step explanation:

9(x+2) = 5 - 2(x - 1)

9x+18 = 5-2x+2

9x+18 = -2x+7

+2x = +2x +7

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

11x+18 = 7

-18 = -18

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

11x = -11

÷11 = ÷11

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

x = -1

Answer:

x = -1

Step-by-step explanation:

9(x+2) = 5 - 2(x-1)

9(x+2) = 5 - 2(x - 1)

9x+18 = 5-2x+2

9x+18 = -2x+7

+2x        +2x

11x + 18 = 7

      -7     -7

11x + 11 = 0

    -11      -11

11x = -11

x = -1  

Answer:

You answered it

Tally won the dirt throwing game and his score was 1.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information, The score of Tally is,

= 3×2 - 3×3 + 4×1.

= 6 - 9 + 4.

= 1.

The score of Awasin is,

= 4×2 - 4×3 + 2×1.

= 8 - 12 + 2.

= - 2.

So, Tally won the game and his score is 1.

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Answer:

34

Step-by-step explanation:

Given that the ages of a group of lifeguards are listed. 17, 17, 18, 19, 22, 23, 25, 27, 32, 38 If another age of 18 is added to the data, (d) The mean would decrease in value to about 23.3.

The mean is also called as the average or a measure of central tendency.  The mean can be calculated as the sum of observation divided by the number of observation.

Given in the question,

ages of lifeguard : 17, 17, 18, 19, 22, 23, 25, 27, 32, 38

Sum of ages = 238

Number of ages = 10

Mean = \(\frac{Sum\ of \ ages}{Number \ of \ ages } = \frac{238}{10} = 23.8\)

Given that an age of 18 is added to the data,

The sum of ages changes to = 238 + 18 = 256

Number of ages given changes to = 10+1 = 11

Mean becomes = \(\frac{Sum\ of \ ages}{Number \ of \ ages } = \frac{256}{11} = 23.27\)

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\({ \blue{ \tt{option(d)}}} \: { \boxed{ \red{ \sf{181.097}}}}\)

Step-by-step explanation:

\( \: \: \: \: 235.987\)

\( - \: \: \: 54.89\)

_______________

\({ \boxed{ \red{ \sf{= 181.097}}}}\)

The correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

To prove that \(BC^2 = AB^2 + AC^2\), we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

\($\frac{AB}{BC} = \frac{AD}{AB}$\)

Cross-multiplying, we get:

\($AB^2 = BC \cdot AD$\)

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

\($\frac{AC}{BC} = \frac{AD}{AC}$\)

Cross-multiplying, we have:

\($AC^2 = BC \cdot AD$\)

Now, we can substitute the derived expressions into the original equation:

\($BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$\)

It was made possible by cross-product property.

Therefore, the correct step to prove that \(BC^2 = AB^2 + AC^2\) is:

By the cross product property, \(AC^2 = BC \cdot AD\).

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Answer:

f(x) = x⁴-11x³+37x²-29x-78

Step-by-step explanation:

The zeros -1 and 6 are real zeros, so we'll use them directly.

The zero 3-2i is complex, and ALL complex zeros come in pairs. So we use the complex conjugate of 3-2i for the other zero: 3+2i.

Now, set up your factors. There are four zeros, so four factors:

(x- -1)(x-6)(x-(3-2i))(x-(3+2i)) = (x+1)(x-6)(x- 3-2i)(x- 3+2i)

Next, the instructions say "with real coefficients" so we must multiply everything out and combine like terms. I recommend starting with the two real factors: (x+1)(x-6) = x²-5x-6.

then multiply the two complex factors:

    (x- 3-2i)(x- 3+2i) = x²-3x+2ix-3x+9-6i-2ix+6i-4i² [remember that i²=-1!!]

                              = x²-6x+13

and finally multiply the two trinomials that you get; you'll have 9 terms to combine.

The system Y = -2x + 3 is a linear equation that shows how y changes depending on x.

A linear equation is an equation of a straight line written in the form of y = mx + b.

In a linear equation or function, m is the slope, and b is the y-intercept, and it shows how the dependent variable, y, changes as the input (independent variable), x, changes by a constant rate (slope).

When m < 0, the line goes down from left to right. When m = 0, the line is horizontal. A bigger absolute value of the slope, m, increases the steepness of the line.

The y-intercept b determines the value of y when x = 0.

The slope, m = -2

The y-intercept, b = 3

For example, if x = 6, y = -2(6) + 3 = -9.

Thus, the equation y = -2x + 3 is linear.

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What system is Y = -2x + 3?

Answer:

Step-by-step explanation:

a. The number of red roses left t hours before the store opens can be represented by the formula:

N(t) = 400 * (1/2)^(t/2)

Here, we're dividing the number of available roses by 2 every 2 hours, so the exponent t/2 represents the number of 2-hour intervals that have passed since the store opened.

b. The number of box chocolates left t hours after the store opens can be represented by the formula:

M(t) = 200 * (0.85)^t

Here, we're multiplying the number of available boxes by 0.85 every hour, so the exponent t represents the number of hours that have passed since the store opened.

c. We need to find the time t when the number of roses is equal to the number of boxes of chocolates:

400 * (1/2)^(t/2) = 200 * (0.85)^t

Dividing both sides by 200:

2 * (1/2)^(t/2) = 0.85^t

Taking the logarithm of both sides:

log(2) - (t/2) * log(2) = t * log(0.85)

Simplifying:

t * (log(0.85) + (log(2)/2)) = log(2)

t = log(2) / (log(0.85) + (log(2)/2))

Using a calculator, we get:

t ≈ 11.9 hours

Therefore, the number of roses will be equal to the number of boxes of chocolates approximately 11.9 hours before the store opens, or around 9 p.m. on the day before Valentine's Day.

d. To find the number of boxes of chocolate left at 12:30 p.m. (3.5 hours after the store opens), we can use the formula:

M(3.5) = 200 * (0.85)^3.5

M(3.5) ≈ 97.4

Therefore, there are approximately 97 boxes of chocolate left at 12:30 p.m.

e. To buy 36 red roses, we need to find the latest time we can arrive before the store runs out of roses. We can set N(t) equal to 36 and solve for t:

400 * (1/2)^(t/2) = 36

Dividing both sides by 400:

(1/2)^(t/2) = 0.09

Taking the logarithm of both sides:

t/2 * log(1/2) = log(0.09)

Simplifying:

t ≈ 5.2 hours

Therefore, the latest time we can arrive to successfully buy 36 red roses is approximately 5.2 hours before the store opens, or around 3:50 a.m. on the day before Valentine's Day.

Answer: 3 7/14 + 2 12/14 = 5 19/14

Step-by-step explanation:

Find the LCM of the denominator.

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

7 = 7, 14, 21, 28, 35

3 1/2 = 3 7/14

2 6/7 = 2 12/14

3 7/14 + 2 12/14 = 5 19/14

Hope that helped!

Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  \(\boxed{y=\dfrac{-5}{2}x+1}\)

#95141404393

a) C = 14w + 48

b) slope =

Explanation:

A) Let C represent the cost of the waste

w represent the number of kilograms of waste

when cost = $1448, the amount of waste = 100kg

(w, C) = (100, 1448)

when cost = $2498, the amount of waste = 175kg

(w, C) = (175, 2498)

we need to find the slope of the points we were given

Slope formula is given as:

B) slope = 14

Slope = cost/amount of waste

In units, we are dividing the dollar by the kilogram = $/kg

The units of the slope is dollars per kilogram (option D)

C) Vertical intercpet is the y -intercept

From our calculation, y-intercept is = b = 48

Hence, the vertical intercept is 48

The y-intercept is the intial value or initial cost of the waste. This is the cost when the kilogram of waste is zero

C = 14w + 48

w = 0

C = 14(0) + 48

C =48

Since the unit of C is dollars. Then the unit of the intercept will also be in dollars (option D).

By paying off the higher interest card first, we save $1932 - $1579 = $353 in interest charges over the course of 56 months.

The conventional method is to pay off the credit card with the highest interest rate first if we have two credit cards with differing interest rates. We can figure out how much money we save by reworking the issue to pay off the card with the lowest interest rate first.

Consider that we have two credit cards: Card A, which has a $5,000 debt and a 15% interest rate, and Card B, which has a balance of $3,000 and a 10% interest rate. We can save money by lowering the interest paid on Card B while still making minimum payments on Card A if we pay that card off first.

It would take us around 22 months to pay off Card B and 36 months to pay off Card A if we made the minimum payments of $300 on Card B and $150 on Card A each month. We would pay interest on Card A in total of $1932 and Card B in total of $386 throughout this time.

Instead, if we pay off Card A first, we would devote the remaining $300 to Card A until it is completely paid off while continuing to make the minimum payments on Card B. We would need around 24 and 32 months, respectively, to pay off Card A and Card B. We would pay interest on Card A for a total of $1579 and Card B for a total of $282 during this time.

We therefore save $1932 - $1579 = $353 in interest fees over the course of 56 months by paying off the higher rate card sooner.

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Answer:

Hannah is taller because her z-score is higher than Kylie’s z-score.

Step-by-step explanation:

Answer:

The 3.907 is approximate.

====================================

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

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

Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

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

Extra info: