At the beginning of a population study, a city had 240,000 people. Each year since, the population has grown by 6.6%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.

Answer:

1. $950

2. 80

Step-by-step explanation:

Answer:

Step-by-step explanation:

19)

Make the point (-7,2) to (2,-7)

Make point (-1,-2) to (-2,-1)

Make the point (1,4) to (4,1)

20) Make the point (-1,-4) to (-4,-1)

Make the point (-4,-5) to (-5,-4)

Make the point (-7,-6) to (-6,-7)

a) She can make 400 milliliters of the fizzy drink.

b) The change does not affect the greatest amount of drink.

We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.

If we divide the total amount of apple juice in 7 parts, then each part has:

280ml/7 = 40ml

Then we need 3 parts of 40ml of the lemonade, this is:

3*40ml = 120ml

Then the total amounf of drink fizz that she can make is:

280ml + 120ml = 400ml.

b) Now she has  160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.

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Answer:

\(we \: have \: ohms \: law \: h = {i}^{2} rt \\ \frac{h}{t} = {i}^{2} rt \div t = p \\ p = {i}^{2} r....(1) \\ we \: have \: v = ir \\ i = \frac{v}{r} .....(2) \\ put \: (2) \: in \: (1) \\ then \: p = { (\frac{v}{r}) }^{2} r \\ p = \frac{ {v}^{2} }{r} \\ v = \sqrt{pr} = {(pr)}^{ \frac{1}{2} } \\ 2) \\ here \: r = 32 \: and \: p = .5 \\ then \: v = \sqrt{32 \times .5} \\ = \sqrt{16} = 4volt \\ thank \: you\)

Answer:

35.6 m/s

Step-by-step explanation:

P = kS²

1760 = k× 35²

1760=1225k

1760/1225 = k

1.44 = k

P=1.44×S²

1820= 1.44 × s²

1820/1.44 = s²

√1820/1.44 = s

s= 35.6 m/s

The area is given by the integral

\(\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds\)

where C is the curve and \(dS\) is the line element,

\(\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt\)

We have

\(x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1\)

\(y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2\)

\(\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt\)

So the area is

\(\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt\)

Substitute \(u=t^2+2\sqrt2\,t+3\) and \(\mathrm du=(2t+2\sqrt 2)\,\mathrm dt\):

\(\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3\)

Answer:

<N is corresponding to <P   and  <P and <L correspond

Step-by-step explanation:

Corresponding angles: any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

To improve understanding of this topic look up corresponding angles and go to pictures. I believe it shows a more clear example

Hope this helps :D

Answer:

k = -0.1

Step-by-step explanation:

An ordered pair is in the form (x,y)  We can use the x and y from the point (-30,3) to find k

y = kx  We will replace x with -30 and y with 3

3 = (-30)k  divide both sides by -30

-0.1 = k  or \(\frac{-1}{10}\) in the fraction form

Answer:

The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

\(\mu = 68, \sigma = 15\)

Middle 68.26% of the grades:

From the

50 - (68.26/2) = 15.87th percentile

To the

50 + (68.26/2) = 84.13rd percentile.

15.87th percentile:

X when Z has a pvalue of 0.1587. So X when Z = -1.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1 = \frac{X - 68}{15}\)

\(X - 68 = -1*15\)

\(X = 53\)

84.13rd percentile:

X when Z has a pvalue of 0.8413. So X when Z = 1.

\(Z = \frac{X - \mu}{\sigma}\)

\(1 = \frac{X - 68}{15}\)

\(X - 68 = 1*15\)

\(X = 83\)

The range that you would expect 68.26 percent of the grades to fall is between 53 and 83.

Based on the given system of equations, the value of x and y are undefined.

In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:

x = 5 - 2y      .......equation 1.

6y = 5 - 3x            .......equation 2.

By using the substitution method to substitute equation 1 into equation 2, we have the following:

6y = 5 - 3(5 - 2y)

6y = 5 - 15 + 6y

6y = -10 + 6y

6y - 6y = -10 (no solution).

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Answer:

4/15

Step-by-step explanation:

2/5 = 6/15

1/3 = 5/15

6/15 + 5/15 = 11/15

15/15 - 11/15 = 4/15

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Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

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Answer:

to convey the parametric expression to be use the explosions

The x-intercepts are when y=0, so:

\(x^2 + 4x-6=0\\\\x=\frac{-4 \pm \sqrt{4^{2}-4(1)(-6)}}{2}\\\\x=\frac{-4 \pm \sqrt{40}}{2}\\\\x=-2 \pm \sqrt{10}\)

So, the x-intercepts are at \(\boxed{(-2 \pm \sqrt{10}, 0)}\)

The y-intercept is when x=0, so \(y=0^{2}+4(0)-6\), and thus the y-intercept is at (0, -6).

The weight before the party could be any positive number

The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:

x - weight used at the party = 7/8

We know that the weight used at the party is the weight before the party minus the weight after the party.

So we can substitute 3x for the weight before the party:

3x - (7/8) = weight used at the party

We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.

So we can set up another inequality:

weight used at the party ≤ 3x

Putting it all together:

3x - (7/8) ≤ 3x

Simplifying:

-(7/8) ≤ 0

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Step-by-step explanation:

18 ball=3team

18=3x

x=18/3

x=6

the answer is 18:3

if (:) this sigh of urs indicate divide

Commutativity justifies the statement, of If n is a multiple of 8, then n is even. However, n is not even. Therefore, n is not a multiple of 8.

Commutativity is used in Maths equations and describes sums that can be moved around and will still give the same answer.

'Commutative' comes from the word 'commute' which means to move and travel around, so equations that are commutative have numbers that can be moved within the equation.

commutative law, in mathematics, is either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba.

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The misleading about the data shown on the figure is the clas width

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

The histogram

On the histogram, we have the following readings

From the above, we can see that

The above readings are not consistent i.e. the class widths are not equal

Hence, the misleading about the data shown on the figure is the clas width

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Answer:

If you go to desmos.com, select the graphing calculator, and enter in y = 3x you should be able to see how it's graphed! Hope this helps!

Answer:

(0, 0) and (1, 3)

happy to help!

Answer:

You have 164 stamps.

Step-by-step explanation:

Let the no. of my stamps be 'x'

Half of x subtracted by 26 = 56

\(\frac{1}{2} x\) - 26 = 56

\(\frac{1}{2} x\) = 56 + 26 =  82

\(x\) = 82 x 2 =  164

Let's check

\(\frac{164}{2}\) - 26 = 56

\(\frac{164}{2}\) = 56 + 26

164     = 82 x 2

164 = 164!

The answer is correct.

Based on the calculations, the average selling price for these properties is equal to $127,865.

Mathematically, the average selling price for these properties would be calculated by using the following formula:

Average price = [F(x)]/n

Note: The total number of properties is equal to 5.

Substituting the given parameters into the formula, we have;

Average price = [118,450 + 126,500 + 128,000 + 130,425 + 135,950]/5

Average price = 639,325/5

Average price = $127,865.

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Complete Question:

Property taxes are based on the value of the property. city officials use the average selling price of similar properties to estimate the value. the selling prices of similar properties are listed below. $118,450 $126,500 $128,000 $130,425 $135,950. What is the average selling price?

Answer: x = 21/4

First, you want to Add 5 to both sides of the equation:

4x - 5 + 5 = 16 + 5.

Then you want to simplify:

4x = 21.

Divide both sides of the equation by the same term:

4x/4 = 21/4.

Then you want to simplify:

x = 21/4.

The final solution is:

x = 21/4

Exact Form:

x = 21/4

Decimal Form:

x = 5.25

Mixed Number Form:

x = 5 1/4

Step-by-step explanation:

Hope this helps =)

Answer:

Below

Step-by-step explanation:

a) they won 120 games out of 369 played  = 40/23=.325

b) they lost 248 out of 369 played = 248/369 = .672

c) Home games are 185 out of 369 = .501

d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389

Answer: Ima say 6

Explanation: I don't have an explanation

In each diagram, line f is parallel to line g, and line t intersects both lines f and g. The given information suggests the application of certain geometric properties and relationships.

Firstly, when a transversal line (line t) intersects two parallel lines (lines f and g), it creates several pairs of corresponding angles.

Corresponding angles are congruent, meaning they have equal measures. This property can be used to determine the measures of specific angles in the diagram.

Secondly, when a transversal intersects parallel lines, it also creates alternate interior angles and alternate exterior angles.

Alternate interior angles are congruent, as well as alternate exterior angles.

By utilizing these properties and relationships, one can analyze the diagram and determine the measures of various angles.

It is important to measure angles systematically and compare them to find congruent or equal measures.

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Let the two integers be m and n

the sum of the integers is 41 => m + n = 41

the difference between the integers is 7 => m - n = 7

m + n = 41 ---- 1

m - n