14. A clothing store has a cost of producing t-shirts at $4.50 per unit. The store also has a
monthly rent charge of $500. The store sells each t-shirt for $12.00 each.

Write an equation to model the store's profits each month:

The sides show that we have an equilateral triangle

An equilateral triangle is a triangle in which all three sides are of equal length. Since all three sides are equal, all three angles are also equal and measure 60 degrees each.

We know that;

12x - 22 = 10x - 6

Collect like terms;

12x - 10x = -6 + 22

2x = 16

x = 8

Thus the sides of the triangle are;

12(8) - 22 = 74

10(8) - 6 = 74

7(8) + 18 = 74

In the second triangle;

4x - 25 = x + 14

4x - x= 14 + 25

3x = 39

x = 13

Thus the sides are;

4(13) - 25 = 27

13 + 14 = 27

6(13) - 51 = 27

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Answer:

Step-by-step explanation:
150/2 = 75
500/75 = 6.6666666667 hours

it will take 6.2/3 hours to reach 500 bacteria cells

NOT SURE ABOUT EXPERSION BUT YOU COULD TRY THIS

p = 75t

Given that a culture of bacteria grows at a rate proportional to its size. Where the culture starts with 50 cells, then grows 150 after time, "t" equals 2 hours.

We are asked to:

> (a) Find an expression, P(t), to model the number of cells present after "t" hours.

> (b) Determine the time at which the population is at 500 cells.

For part (a):

Since the culture of bacteria grows at a rate proportional to its size, we can model it as the following differential equation.

[tex]\Rightarrow \frac{dP}{dt}=kP; \ Where \ P =P_0 \ at \ t=0 \ and \ P=3P_0 \ at \ t=2[/tex]

Solve the first-order separable differential equation with the given initial condition.

[tex]\Longrightarrow \frac{dP}{dt}=kP \Longrightarrow \frac{1}{P}dP=kdt \Longrightarrow \int\limits {\frac{1}{P} } \, dP=\int\ {k} \, dt \Longrightarrow ln(P)=kt+c[/tex]

[tex]\Longrightarrow e^{ln(P)}=e^{kt}+e^{c} \Longrightarrow P=ce^{kt}[/tex]

Plug in the initial condition.

[tex]\Longrightarrow P_0=ce^{k(0)} \Longrightarrow P_0=c(1) \Longrightarrow \boxed{c=P_0}[/tex]

[tex]\Longrightarrow P=ce^{kt} \Longrightarrow \boxed{P=P_0e^{kt}}[/tex]

Use the second initial condition to find "k."

[tex]\Longrightarrow 3P_0=P_0e^{k(2)} \Longrightarrow 3=e^{k(2)} \Longrightarrow 3=e^{2k} \Longrightarrow ln(3)=ln(e^{2k})[/tex]

[tex]\Longrightarrow k=\frac{ln(3)}{2} \Longrightarrow \boxed{k \approx 0.5493}[/tex]

Thus, the equation to model the situation is,

[tex]\boxed{\boxed{P(t)=50e^{0.5493t}}} \therefore Sol.[/tex]

For part (b):

[tex]P=10P_0[/tex]

[tex]\Rightarrow 10P_0=P_0e^{0.5493t} \Longrightarrow 10=e^{0.5493t} \Longrightarrow ln(10)=ln(e^{0.5493t})[/tex]

[tex]\Longrightarrow ln(10)=0.5493t \Longrightarrow t=\frac{ln(10)}{0.5493} \Longrightarrow \boxed{t=4.192 \ hrs}[/tex]

Thus, the time it takes the population to reach 500 is approx. 4.192 hours.

Answer:

To find the mean daily passenger count per plane, we need to calculate the average of the passenger counts for the sample.

We can do this by adding up all the passenger counts and dividing by the number of planes in the sample:

(123 + 132 + 158 + 77 + 158 + 123 + 132 + 123 + 158 + 77) / 10

= 1259 / 10

= 125.9

Therefore, the mean daily passenger count per plane is approximately 125.9 passengers.

Step-by-step explanation:

Answer:

[2 -4/ -6 -2]

Step-by-step explanation:

To solve for Y, we need to rearrange the equation X-2Y=Z to isolate Y.

X - 2Y = Z

2Y = X - Z

Y = (X - Z)/2

Now we substitute the given matrices for X and Z, and solve for Y:

X =

[b  a

4  a]

Z =

[a   c

16  b]

X - Z =

[b-a   a-c

-12   a-b]

Y = (X - Z)/2 =

[(b-a)/2  (a-c)/2

-6       (a-b)/2]

So the answer is Y = [ (b-a)/2, (a-c)/2 / -6, (a-b)/2 ].

Therefore, the answer is (a) [2 -4/ -6 -2].

The calculated value of the matrix Y is [tex]Y = \left[\begin{array}{cc}2&-4\\-2&-6&\end{array}\right][/tex]

From the question, we have the following parameters that can be used in our computation:

The matrix definitions

Given that

X - 2Y = Z

So, we have

b - 2c = a

a - 2d = c

4 - 2a = 16

a - 2b = b

So, we have

4 - 2a = 16

-2a = 12

a = -6

Next, we have

a - 2b = b

-6 - 2b = b

3b = -6

b = -2

Next, we have

b - 2c = a

-2 - 2c = -6

-2c = -4

c = 2

Lastly. we have

a - 2d = c

-6 - 2d = 2

-2d = 8

d = -4

The matrix Y is given as

[tex]Y = \left[\begin{array}{cc}c&d\\b&a&\end{array}\right][/tex]

So, we have

[tex]Y = \left[\begin{array}{cc}2&-4\\-2&-6&\end{array}\right][/tex]

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The cumulative probability is

P(at most 2 ) = 0.187560896 [answer]

a)

Note that the probability of x successes out of n trials is

P(n, x) = nCx p^x (1 - p)^(n - x)

where

n = number of trials = 12

p = the probability of a success = 0.33

x = the number of successes = 3

Thus, the probability is

P ( 3 ) = 0.21509867 [answer]

***********

b)

Note that P(at least x) = 1 - P(at most x - 1).

Using a cumulative binomial distribution table or technology, matching

n = number of trials = 12

p = the probability of a success = 0.33

x = our critical value of successes = 4

Then the cumulative probability of P(at most x - 1) from a table/technology is

P(at most 3 ) = 0.402659566

Thus, the probability of at least 4 successes is

P(at least 4 ) = 0.597340434 [answer]

***************

c)

Using a cumulative binomial distribution table or technology, matching

n = number of trials = 12

p = the probability of a success = 0.33

x = the maximum number of successes = 2

Then the cumulative probability is

P(at most 2 ) = 0.187560896 [answer]

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Answer: x is greater than or equal to 5 (I can't put the symbol in)

Step-by-step explanation:

Add 5 to both sides then simplify, which will get you 2x is greater than or equal to 10, then divide by 2.

Answer:

Step-by-step explanation:

3x+10<3

3x<3-10

3x<-7

x<-7/3

2x-5≥5

2x≥5+5

2x≥10

x≥10/2

x≥5

so x<-7/3 or x≥5

The amount of sand in each vase is 2.8 pounds by dividing the total amount by the number of vases.

Given that,

Raj combined white sand with black sand to make 14 pound mixture of sand.

Total amount of sand = 14 pounds

Number of vases to which sand is put = 5 vases

Amount of sand in each vase can be found by dividing the total amount by the number of vases.

Amount of sand in each vase = 14 / 5 = 2 4/5 pounds = 2.8 pounds

Hence the total amount of sand is 2.8 pounds.

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Based on the information, bIda would owe $3700 at the end of 12 months.

Ida would owe $3808 at the end of 12 months.

The formula will be:

I = P * r * t

I = 2500 * 0.04 * 12 = $1200

So, Ida would owe $2500 + $1200 = $3700 at the end of 12 months.

b. For option b, , the monthly interest rate is:

r = 0.01 * 4.33 = 0.0433

Using the same simple interest expression:

I = 2500 * 0.0433 * 12 = $1308

Ida would owe $2500 + $1308 = $3808 at the end of 12 months.

Therefore, option a is the better choice due to the fact she would owe less in total with a simple interest rate of 4% annually.

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Answer: y= 1700 (1- .0325) ^15= 1700(.9675) ^15=1700(.60920660)= 1035.65 km Hope this helps!

Step-by-step explanation:To calculate the area of the forest after 5 years, we need to use the formula:

A = A0 * (1 - r/100)^t

PLEASE MARK BRAINLIST

Answer:

8 over 15 multiplied by 7 over 14 is equal to 56 over 210

8 over 15 plus 7 over 14 is equal to 217 over 210

8 over 15 plus 8 over 15 is equal to 16 over 15

8 over 15 multiplied by 8 over 15 is equal to 64 over 225

She's taking it out and then she replaces it

and so that means the denominator would stay 15 both times

and since it's a white chip in both draws, it would be 8/15 * 8/15

Step-by-step explanation:

Area of a traingle = 1/2 * base * height

   area = 1/2 * 6 * 4 = 12 cm^2

An equation and solution that tells how long it takes the object to reach a height of 96 feet if its initial height is 208 feet is:

D. 96 = 208 - 16t²

    t = √7

Based on the information provided, we can logically deduce that the height (h) in feet, of this object above the​ ground is related to time by the following quadratic function:

h(t) = h₀ - 16t²

When the initial height is 208 feet and final height is 96 feet, the height function becomes;

h(t) = h₀ - 16t²

96 = 208 - 16t²

16t² = 208 - 96

16t² = 112

t² = 112/16

Time, t = √7 seconds.

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Correct option is,

A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.

Since, An independent variable is a variable that represents a quantity that is being controlled  in an experiment.

A dependent variable represents a quantity whose value depends on how the independent variable is controlled.

Now, In the given question;

The number of cars represents the independent variable while money raised represents independent variable .

Domain is the set of values the independent variable can take .

The number of cars 30 to 100 represents the Domain.

The range is corresponding y values .

The charge per car is $20.

Hence, Range = 30 x 20

                       =600

to Range = 100 x 20

              = 2000.

Thus, Correct option is,

A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.

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Complete question is,

The French club is holding a car wash fundraiser. They are going to charge $20 per car, and expect between 30 and 100 cars. Identify the independent and dependent quantity in the situation, and find reasonable domain and range values.

A: number of cars; money raised; 30 to 100 cars; $600 to $2000

B: money raised; number of cars; 30 to 100 cars; $600 to $2000

C: number of cars; money raised; $600 to $2000; 30 to 100 cars

D: money raised; number of cars; $600 to $2000; 30 to 100 cars

Answer:

tennis team

Step-by-step explanation:

because they ran 8 miles is 7 days to get equal amount of days you multiply by 2 on both 8 miles and 7 days so they ran 16 miles in 14 days thats y tennisbteam ran more miles

The height of tree is given as follows:

40 ft.

The height of the tree is obtained applying the proportions in the context of this problem.

The proportions are applied as a rule of three can be formed between the heights and the shadows for both the tree and the person, as follows:

h/30 = 6/4.5

Applying cross multiplication, the value of h is obtained as follows:

4.5h = 30 x 6

4.5h = 180

h = 180/4.5

h = 40 ft.

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Answer: The answer is B and im 100% correct

Step-by-step explanation:

Answers in bold

7.  Not congruent

8.  Congruent by the HL theorem

HL = hypotenuse leg

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

Explanation for problem 7

The tickmarks on segments MA and AT tell us that these segments are congruent. Another pair of congruent segments would be AE = AE by the reflexive property.

Then angle EMA = angle ETA because of the similar arc markings for those angles.

We have these congruence facts:

But recall that the "side side angle" rule isn't a valid congruence theorem. Search out "SSA ambiguous case" for more information.

We cannot use SAS because the angle is not between the sides mentioned.

Therefore, we don't have enough information to determine if the triangles are congruent or not. We can't say they are congruent, so the only thing we can do is say "not congruent" until more info comes along.

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

Explanation for problem 8

We use the HL (hypotenuse leg) theorem. It works for right triangles only.

The congruent legs are segment ON = segment ON because of the reflexive property.

The congruent hypotenuses are MN = RO because of the tickmarks.

In short, the triangles are congruent by the HL theorem.

Answer:

log(10)

Step-by-step explanation:

We can use the product property for logarithms:

log(a)+log(b)=log(ab)

In our case, a=5 and b=2. We can multiply a and b now to get the new number we're taking the logarithm of.

log(2)+log(5)=log(2×5)=log(10)

Answer:

For this question, you can use the simultaneous equation to solve this problem.

Equation 1 reads: x + y = 34. (There are 34 notes in total.)

Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)

To find x in terms of y, we can apply equation 1:

x = 34 - y

When we use this expression to replace x in equation 2, we obtain:

5(34 - y) + 10y = 235

By condensing and figuring out y, we get at:

y = 15

There are 15 $10 bills in the wallet as a result.

Answer:

  (d)  5i -j

Step-by-step explanation:

You want the value of the expression 2u -v where u=3i and v=i+j.

Use the given definitions of u and v, and simplify in the usual way.

  2u -v = 2(3i) -(i+j)

  = 6i -i -j . . . . . . . . . eliminate parentheses

  = 5i -j

__

Additional comment

The unit vectors i and j can be treated as though they were variables. The usual properties of equality and (scalar) arithmetic apply.

Answer:

78

Step-by-step explanation:

(5+8)×12/2=78

(5+8)×12/2=78

Answer:

B

Step-by-step explanation:

When translating in the y-axis, we want to add or subtract our value outside of the function, or in this case, outside of the modulus.

We want to move 3 units down, or 3 units in the negative direction. Therefore, we take 3 away from the function.

Answer B.

The solution of the expression -8+27÷(-3)-(-2)​ is determined by applying the rule of BODMAS as -35.

The solution of the expression is calculated by applying the following formula as shown below;

BODMAS;

Based on the rule of BODMAS, we solve the bracket first, then division, before addition and subtraction.

-8+27÷(-3)-(-2)​ = -8+27÷ -1

-8+27÷ -1 = -8 - 27

-8 - 27 = - 35

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Check the picture below.

so let's recall that the area of a circle is just πr² where r = radius, so since the sizes of each pizza are 10, 14, 18 and 22, that's simply their diameter, so that means they each have a radius half of that, or namely 5, 7, 9 and 11, as you see in the picture, so, hmmm which radius gives us the most area per the fraction provided, namely per slices provided?

[tex]\cfrac{4}{8}\pi 5^2\implies \cfrac{25\pi }{2} ~~ \approx ~~ 39.26~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{3}{8}\pi 7^2\implies \cfrac{147\pi }{8} ~~ \approx ~~ 57.73~in^2 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{2}{8}\pi 9^2\implies \cfrac{81\pi }{4}~~ \approx ~~ 63.62~in^2 ~~ \textit{\LARGE \checkmark} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}\pi 11^2\implies \cfrac{121\pi }{8}~~ \approx ~~ 47.52~in^2[/tex]

Answer: Large

Step-by-step explanation:  Hope it helps Good luck!!!

Based on Joey's debt-to-income ratio, the maximum monthly rent payment he can make and still maintain the DTI ratio would be; b. $898.

WE are given that Joey has a DTI ratio of 36% which means that his maximum debt payment should be 36% of his income.

This amount would be:

= DTI x monthly income

= 36% x 3,600

= $1,296

Maximum monthly rent can be found as:

= Maximum monthly debt payment - Car payment - Credit card payment

= 1,296 - 178 - 220

= $898

In conclusion, option B is correct.

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Answer: 1/2 cup oats 2/3 cup flower

Answer:

Let's use "g" to represent the number of green lollies in the jar.

According to the problem, there are 6 more orange lollies than green ones, so the number of orange lollies is "g + 6".

We also know that there is only one red lolly.

The total number of lollies in the jar is 47, so:

g + (g + 6) + 1 = 47

Simplifying the equation:

2g + 7 = 47

Subtracting 7 from both sides:

2g = 40

Dividing by 2:

g = 20

So there are 20 green lollies in the jar.

And since there are 6 more orange lollies than green ones, there must be:

g + 6 = 20 + 6 = 26 orange lollies in the jar.

Step-by-step explanation: