Write an exponential function that satisfies the given conditions:
- Initial mass: 1.3 g
- doubling every week

Answer:

x = 1, y = 2

Step-by-step explanation:

9x - 4y = 1 -----Equation 1

-8x - 7y = -22 -----Equation 2

-(8x+7y) = -(22) I have inserted an extra equation here so that it is easier to see how I did the next step.

Equation 2 × (-1): 8x+7y = 22 ------Equation 3

When an equation is multiplied by (-1), the -signs can be removed as two - makes one +. This applies to both sides of the equation.

Equation 1 × 22: 198x - 88y = 22 -----Equation 4

Now, Equations 3 and 4 have the same total, that means that they equal to each other.

8x+7y = 198x - 88y

Evaluate by putting the expressions with x on one side and expressions with y on the other side.

7y+88y = 198x-8x

Further evaluate.

95y = 190x

Further simplify by dividing both sides by 95.

y = 2x -----Equation 5

Now we can substitute y = 2x into equation 1.

9x - 4(2x) = 1

Evaluate.

9x - 8x = 1

Further evaluate.

x = 1 -----Equation 6

Substitute x = 1 into equation 5.

y = 2(1)

Evaluate.

y = 2

a) The mean of the sample of size 5 is equals to 103.

b) The mean of the sample of size 12 is equals to 103.3.

c) Median of sample of size 5 is 104.

d) Median sample of size 30 is 105.5.

Mean: Sum of observations is divided by number of observations in the sample is named as mean, which is denoted by X- bar. Moreover, the sample mean signifies the measure of centre of the data.

X-bar = (x₁ + x₂ + --- + xₙ)/n

Median: Median divides the observations into two equal parts. It represents the middle value for a set of observations when they are arranged in order of magnitude. There are two cases arises.

Case (1): Sample size (n) is odd: First, arrange the data in ascending order. Then, the median is the middle value and lies at the position.

Case (2): Sample size (n) is even: First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on either side of the position. Median = ( n/2)ᵗʰ term , n is odd

=[(( n/2)ᵗʰ term + (n/2 + 1)ᵗʰ term]/2, n is even

Now, a) Mean of first sample with sample size, n = 5.

Sum of values = 105 + 111 + 97 + 94 + 108 = 515

So, mean = 515/5 = 103

b) Sample 2, sample size , n = 12

Sum of values = 105 + 111 + 97 + 94 + 108 + 101 + 112 + 114 + 103+ 102+ 91 + 101

= 515 + 724 = 1239

Mean = 1239/12 = 103.25

c) Now, we have to determine median for sample size 5. Here, sample values are odd in number, i.e., 5. So, middle term is median after arranging in order. Ascending order is 94,97, 104, 108, 111 and middle term is 104, so median is 104.

d) Now, we have a sample of size 30, which is an even number. First arrange the numbers in ascending order as 91,92,92,94,95,97,100,101,101,101,101,102,103,105,105,105,106,107,107,108,110,111, 111, 112,113,114,115,115,116,116. So,

Median is [((n/2)th + (n/2 + 1)th ]/2 i.e, [ 30/2)th + 30/2 + 1)th ]/2

=( 15th + 16th)/2 ( observations)

= (105 + 106 )/2 = 211/2 = 105.5

Hence, the median of sample size 30 is 105.5.

To learn more about Median , refer:

https://brainly.com/question/16408033

#SPJ4

Complete question:

See the above figure, each of the following three data sets represents the iq scores of a random sample of adults. iq scores are known to have a mean and median of 100.

a) What is the mean of the sample of size 5? Full data set Sample of Size 108 114 (Type an integer or decimal rounded to one decimal place as needed._ Sample of Size 12

b) What is the mean of the sample of size 12? 114 105 115 (Type an integer or decimal rounded to one decimal place as needed:)

c) What is the median of the sample of size 5? (Type an integer or decimal rounded to one decimal place as needed:)

d) What is the median of the sample of size 30? (Type an integer or decimal rounded to one decimal place as needed:)

Answer:

The answer is below

Step-by-step explanation:

We have a weekly amount of 100 pounds, you ask us if the waste would be 100 pounds in the same way.

We can say that more information is needed to estimate the waste that leaves the house. In the case that 100 pounds would come out, we consider that dry and wet waste have a distribution of 50-50%, 50 pounds of dry waste and 50 pounds of wet waste will leave the house.

If not, we wouldn't know how much could come out. since there are other factors that could influence it to be a greater or lesser quantity, in the case of a greater quantity of waste that is consumed outside the home and in the case of less, it is that the food is not consumed in its entirety.

The answer to this problem is that we cannot determine the distance of beacon light and ship from point A to point B

What is tangent function ?

In trigonometry, tangent is one of the six basic trigonometric functions (along with sine, cosine, cosecant, secant, and cotangent). The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

In other words, if we have a right triangle with one acute angle θ, the tangent of θ is defined as:

tan(θ) = opposite / adjacent

where "opposite" refers to the length of the side opposite the angle θ, and "adjacent" refers to the length of the side adjacent to the angle θ.

According to the question:
From the information given, we can set up two right triangles: one with the boat, point A, and the lighthouse, and another with the boat, point B, and the lighthouse.

In the first triangle, we have:

tan(16°) = h/x

In the second triangle, we have:

tan(21°) = h/y

We want to find y - x, the distance traveled by the boat between the two measurements. We can set up an equation for this by subtracting the first equation from the second:

tan(21°) - tan(16°) = h/y - h/x

We know the height of the lighthouse is 0 feet, so h = 0. We can simplify the equation to:

tan(21°) - tan(16°) = 0/y - 0/x

To solve for y - x, we need to solve for y/x:

tan(21°) - tan(16°) = 0/y - 0/x

tan(21°) - tan(16°) = 0/(y-x)

Since 0/(y-x) = 0, we can simplify the equation to:

tan(21°) - tan(16°) = 0

We can solve this equation for the difference in distance, y - x:

y - x = 0/(tan(21°) - tan(16°))

y - x = 0

This tells us that the boat did not travel any distance between the two measurements. This doesn't make sense, so we must have made a mistake somewhere.

Looking back at the equations, we notice that we made a mistake when we set h = 0. The height of the lighthouse is actually given as "no feet above the water," which means h = 0 feet. We need to go back and redo the calculations with the correct value for h:

tan(16°) = h/x

tan(21°) = h/y

Substituting h = 0 into these equations, we get:

tan(16°) = 0/x

tan(21°) = 0/y

Solving for x and y, we get:

x = infinity (since tan(16°) is positive)

y = infinity (since tan(21°) is positive)

Therefore, the answer to this problem is that we cannot determine the distance from point A to point B.


To know more about tangent function visit:
https://brainly.com/question/29342276
#SPJ1

Answer:

The rate is 5 dollars per student.

Step-by-step explanation:

The rate per student can be found with \(\frac{dollars}{student}\):

\(\frac{150dollars}{30student}=5\frac{dollars}{student}\\\\\frac{350dollars}{70student}=5\frac{dollars}{student}\)

The rate is 5 dollars per student.

The nearest Whole number, the best prediction possible for the number of times you will pick a blue or a green marble out of 75 trials is 34.

The number of times you will pick a blue or a green marble when selecting a marble without looking and then putting it back, we need to consider the probability of selecting a blue or a green marble on each individual trial.  there are four colors of marbles: blue, green, red, and yellow. If we know the relative frequencies or probabilities of each color, we can make a prediction.

For the purpose of this example, let's say there are 20 marbles in total, and the distribution of colors is as follows:

- Blue: 5 marbles

- Green: 4 marbles

- Red: 6 marbles

- Yellow: 5 marbles

To calculate the probability of picking a blue or a green marble on each trial, we add the probabilities of the individual events:

P(blue or green) = P(blue) + P(green) = 5/20 + 4/20 = 9/20

Now, we can use this probability to predict the number of times you will pick a blue or a green marble out of 75 trials:

Predicted number = P(blue or green) * Total number of trials

                  = (9/20) * 75

                  = 33.75

Since we round the number to the nearest whole number. Therefore, the best prediction possible for the number of times you will pick a blue or a green marble out of 75 trials is 34.

To know more about Whole number.

https://brainly.com/question/29640378

#SPJ11

The area of a triangle with side lengths 17, 18, and 19 in simplest radical form is 18√7770

The area of the triangle is calculated using the formula

Area of triangle = √[s(s – a)(s – b)(s – c)]

s = perimeter o the triangle

a, b and c are the lengths of the triangle

s = a + b + c = 17 + 18 + 19 = 54

Area of triangle = √[54 * (54 – 17)(54 – 18)(54 – 19)]

Area of triangle = √[2517480]

Area of triangle = 18√7770

Learn more about area of triangle at:

https://brainly.com/question/21735282

#SPJ1

Answer:

Step-by-step explanation:

37

The extra calories that you are consuming per year is 182,500 calories.

The number of miles that you should walk to burn the extra calories is 1,825 miles.

You are consuming 20 oz of Dr. Pepper each meal. You take Dr. Pepper twice in a day. To determine the total extra calories that is being consumed, multiply the calories consumed per month by the number of times in a day you consume Dr. Pepper and by the number of days in a week.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign used to represent multiplication is ×.

Extra calories consumed in a year = calories per meal x 2 x number of days in a year

250 x 2 x 365 = 182,500 calories

In order to determine the number of miles you have to walk to lose the extra calories, divide the extra calories by the calories lost per mile

Number of miles to walk = 182,500 / 100 = 1825 miles

To learn more about division, please check: https://brainly.com/question/13281206

#SPJ1

Answer:

$ 558k

Step-by-step explanation:

the condition 'the house was sold for 124% of its purchase price' means Initial_price*1.24, where Initial_price is $450k:

$450000*1.24=$558000.

Answer:

Therefore, the solution to the equation -x + 3y = 11 is x = -34/11 and y = 29/11.

Step-by-step explanation:

The given equation is:

-x + 3y = 11

To solve this equation by elimination, we need to add or subtract one or both equations to eliminate one of the variables. In this case, we can eliminate the variable x by adding the equation with another equation that has x with the same coefficient, but opposite sign.

Let's suppose we have another equation with x, for example:

2x + 5y = 7

We can eliminate x by multiplying the first equation by 2 and the second equation by 1, so that the coefficients of x are opposite:

-2x + 6y = 22 (multiply the first equation by -2)

2x + 5y = 7 (the second equation)

Now we can add the two equations to eliminate x:

-2x + 2x + 6y + 5y = 22 + 7

Simplifying the equation, we get:

11y = 29

Dividing both sides by 11, we get:

y = 29/11

Now that we know the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 3y = 11

Substituting y = 29/11, we get:

-x + 3(29/11) = 11

Simplifying the equation, we get:

-x + 87/11 = 11

Subtracting 87/11 from both sides, we get:

-x = 11 - 87/11

Multiplying both sides by -1, we get:

x = 87/11 - 11

Simplifying the equation, we get:

x = (87 - 121)/11

x = -34/11

Answer:

6 m or 3 meters

Step-by-step explanation:

Area formula = w * L

Perimeter formula =2 x (l+w)

So, that is how I found the answer.

Hope this helps!

Answer:

\((11)\ -2x + 5y = 20\)

\((12)\)   \(4x + y= -25\)

\((13)\)   \(3x + 8y = -15\)

\((14)\ -9x + 4y = 2\)

\((15)\ y = - 9\)

Step-by-step explanation:

Required

The line equation

\((11)\ (-5,2); m =\frac{2}{5}\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = \frac{2}{5}(x - (-5)) + 2\)

\(y = \frac{2}{5}(x +5) + 2\)

Open bracket

\(y = \frac{2}{5}x +2 + 2\)

\(y = \frac{2}{5}x +4\)

Multiply through by 5

\(5y = 2x + 20\)

Rewrite as:

\(-2x + 5y = 20\)

\((12)\ (-6, -1);\ m = -4\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = -4(x - -6) - 1\)

\(y = -4(x +6) - 1\)

Open bracket

\(y = -4x -24 - 1\)

\(y = -4x -25\)

Rewrite as:

\(4x + y= -25\)

\((13)\ (3,-3)\ m =-\frac{3}{8}\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = -\frac{3}{8}(x - 3) -3\)

\(y = -\frac{3}{8}x + \frac{9}{8} -3\)

Multiply through by 8

\(8y = -3x + 9 - 24\)

\(8y = -3x -15\)

Rewrite as:

\(3x + 8y = -15\)

\((14)\ (0, \frac{1}{2}); m = \frac{9}{4}\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = \frac{9}{4}(x - 0) + \frac{1}{2}\)

\(y = \frac{9}{4}x + \frac{1}{2}\)

Multiply through by 4

\(4y = 9x + 2\)

Rewrite as:

\(-9x + 4y = 2\)

\((15)\ (\frac{16}{3}, -9); m =0\)

The equation is calculated using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = 0(x - \frac{16}{3}) - 9\)

\(y = 0 - 9\)

\(y = - 9\)

Answer:

Yes it's a right triangle

Step-by-step explanation:

IF it's a right triangle

a² + b² will equal c²

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

25.5² = 650.25

12² + 22.5² = 650.25

Therefor this IS a right triangle

Answer:

2x(5x+1)(2x+3)=0

Step-by-step explanation:

x{20x^2+34x+6}=0

2x(10x^2+17+3)=0

2x(10x^2+15x+2x+3)=0

2x{5x(2x+3)+1(2x+3)}=0

2x(5x+1)(2x+3)=0

Answer:

its 4

Step-by-step explanation:

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

for such more question on cost

https://brainly.com/question/25109150

#SPJ8

Answer:

33°

Step-by-step explanation:

you add the two numbers together and subtract from 180° to get your answer

For Leo conclusion to be valid, he should apply both brand A and B to area receiving same amount of sunlight.

Bias is an error due to sampling or testing by selecting or preferring one outcome over others.

Leo applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial shade. This shows that Leo is bias.

For Leo conclusion to be valid, he should apply both brand A and B to area receiving same amount of sunlight.

Find out more on bias at: https://brainly.com/question/24491228

Answer:

His conclusion is not valid. 

He should have put both tarps over the area of the yard that receives full sunlight. So that the experiment can be valid.

Step-by-step explanation:

Answer:

18 weeks

Step-by-step explanation:

Ethan earns $5.50 per week (5.5w) in an attempt to reach $99 (99)

5.5w=99

divide both sides by 5.5 and you get:

w=18

Therefore, Ethan must work 18 weeks in order to save enough for a $99 pair of AirPods

The given graph representing function is a relation.

For the given question,

For every singles value of 'x' there is value on y. Thus, no domain element is repeating for the graph.

Thus, the graph shows the relation of the function.

To know more about the relation and function, here

https://brainly.com/question/12792558

#SPJ13

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

Learn more about LCM here :

https://brainly.com/question/6756370

#SPJ1

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

We have,

To determine the angle created by the bottom of the ramp and the ground, we can use the trigonometric function of sine.

In the given triangle, the height is 6 ft and the base is 16 ft.

The angle we want to find is opposite the height (let's call it θ).

The sine of an angle is defined as the ratio of the opposite side to the hypotenuse.

sin(θ) = opposite/hypotenuse

sin(θ) = 6/16

sin(θ) = 0.375

To find the angle θ, we can take the inverse sine (also known as arcsine) of 0.375:

θ = arcsin(0.375)

θ ≈ 22.62°

To meet safety regulations, the angle should be no more than 18°. Therefore, the contractor needs to lower the ramp by:

22.62° - 18° ≈ 4.62°

Thus,

The contractor should lower the ramp by approximately 4.62° to meet safety regulations.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Answer:

1.66 is the answer. 166% whole be a whole 1, plus .66

As a result, the set of all [u, w] Rn Rn satisfying the previous equation is the tangent space to F at [v1, v2]  by using preimage theorem.

Let F be the Stiefel manifold of orthonormal 2-frames in Rn to apply the preimage theorem. The collection of all tangent vectors to curves passing through [v1, v2] in F is what is known as the tangent space T[F] at a location [v1, v2]. Let (t) be a straight line in F such that (v1, v2) is a smooth curve. The tangent vector to t at time t = 0 is then given by

γ′(0) = [u, w] ∈ T[F].

We must now determine the requirements that [u, w] must meet in order to be in T[F]. Assume that V is a matrix with columns named v1 and v2. If Q is an orthogonal matrix, then any orthonormal 2-frame [v1′, v2′] in Rn can be represented as VQ. The category to which [v1′, v2′] belong Q is a 2 by 2 matrix with determinant 1, and F is equivalent to Q. Given that Q(0) = I, let Q(t) be a smooth curve in SO(2). Then, there is

γ(t) = VQ(t) (t),

and

γ′(0) = VQ′(0) (0).

We have Q since Q(t) is orthogonal (t)

TQ(t) = I, indicating

Q′(0)T + Q′(0) = 0.

Let [u, w] T[F] now. Once this is the case, a smooth curve Q(t) in SO(2) exists with Q(0) = I and

[u, w] = VQ′(0) (0).

Applying the equation above, we obtain

v1uv2w plus v1wv2u equals 0.

As a result, the set of all [u, w] Rn Rn satisfying the previous equation is the tangent space to F at [v1, v2].

to know more about" theorem" at https://brainly.com/question/343682

#SPJ4

Answer: you will spend 56$

Step-by-step explanation: 20% less is 2$ difference so you buy a medium pizza for 8$ times 7 is 56$

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x

=

103

4160

Decimal Form:

x

=

0.02475961

…

Step-by-step explanation:

a) The Ferris wheel has an angular speed is 12.222 radians per minute.

b) The Ferris wheel makes 116.712 revolutions in an hour.

Kinematics is a branch of mechanical physics that studies the motion of objects without considering its causes. In other words, kinematics studies displacements, velocities and accelerations in translation, rotation and combined motion. In this case we find a Ferris wheel rotating around its axis at constant rate.

a) Then, the angular speed (ω), in radians per minute, is determined by the following product:

ω = v / R

Where:

Please notice that the length of the radius is the half of the length of the diameter.  

If we know that v = 5 mi / h and R = 36 feet, then the angular speed of the wheel is:

ω = [(5 mi / h) · (1 h / 60 min) · (5280 ft / 1 mi)] / [(0.5) · (72 ft)]

ω = 12.222 rad / min

The angular speed is 12.222 radians per minute.

b) A revolution is equal to an angular displacement of 2π radians and an hour is equal to 60 minutes. Then, we can derive the number of revolutions in an hour by dimensional analysis:

n = (12.222 rad / min) · (1 rev / 2π rad) · (60 min / h)

n = 116.712 rev / h

There are 116.712 revolutions in an hour.

To learn more on Ferris wheels: https://brainly.com/question/16396069

#SPJ1