in 2010 , a city's population was 55,210 and it was declining at a rate of 1.09% each year. which is the best prediction for when the city's population will first be below 48,000?

51 divided by 3 is k, the value of k is 17.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

51 divided by 3 is k

51/3=k

17=k

Therefore, by algebra the answer will be 17

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The real roots of a function are the rational and the irrational roots of the function

The real roots are: [tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]

The equation is given as:

[tex]\mathbf{ 4x^4+31x^3-4x^2-89x+22=0}[/tex]

Factorize

[tex]\mathbf{(x + 2) (4 x - 1) (x^2 + 6 x - 11) = 0}[/tex]

Split

[tex]\mathbf{x + 2 = 0\ or\ 4 x - 1 = 0 \ or\ x^2 + 6 x - 11 = 0}[/tex]

Solve for x

[tex]\mathbf{x = -2\ or\ x = \frac 14 \ or\ x^2 + 6 x - 11 = 0}[/tex]

Solve

[tex]\mathbf{x^2 + 6 x - 11 = 0}[/tex] using the following quadratic formula:

[tex]\mathbf{x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

So, we have:

[tex]\mathbf{x = \frac{-6 \pm \sqrt{6^2 - 4 \times 1 \times -11}}{2 \times 1}}[/tex]

[tex]\mathbf{x = \frac{-6 \pm \sqrt{80}}{2}}[/tex]

[tex]\mathbf{x = \frac{-6 \pm 4\sqrt{5}}{2}}[/tex]

[tex]\mathbf{x = -3 \pm 2\sqrt{5}}[/tex]

Hence, the real roots are:

[tex]\mathbf{x = -2}[/tex], [tex]\mathbf{x = \frac 14}[/tex], [tex]\mathbf{x = -3 - 2\sqrt{5}}[/tex] and [tex]\mathbf{x = -3 + 2\sqrt{5}}[/tex]

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The height of the building seen by both Jack and Jill is 37m to the nearest whole metre.

Let the distance of Jill from the base of the building be represented with x while the height of the building be y so that by observation we get two right triangles with same opposite sides to the angles formed by Jack and Jill. We can solve for x and y using tangent of the angles as follows:

tan 40 = y/x {opposite/adjacent}

y = xtan40 {cross multiplication}

tan 30 = y/(20 + x)

y = tan30(20 + x)

Thus;

xtan40 = tan30(20 + x)

xtan40 = 20tan30 + xtan30

xtan40 - xtan30 = 20tan30 {collect like terms}

x(tan40 - tan30) = 20tan30

x = 20tan30/(tan40 - tan30)

x = 44.1230m

Putting the 44.1230m for x in y = xtan40 we have;

y = 44.1230m × tan40

y = 37.0236m.

Therefore, the height of the building approximately to the nearest whole metre is 37.

Answer:

In seventh time she ran more than one mile from first time she ran.

Step-by-step explanation:

Given Vicki started jogging. The first time she ran she ran 3/16 mile. The second time, she ran 3/8 Mile, and the third time, she ran 9/16 mile.

We have to find when was the first time she ran more than one mile.

The sequence followed is

[tex]\frac{3}{16}, \frac{6}{16}, \frac{9}{16}, \frac{12}{16}, \frac{15}{16}, \frac{18}{16}, \frac{21}{16}....[/tex]

First time she ran more than 1 mile is [tex]\frac{3}{16}+1=\frac{19}{16}[/tex]

In the seventh time she ran [tex]\frac{21}{16}[/tex] miles which is more than one mile from the first time.

Hence, in seventh time she ran more than one mile from first time she ran.

Final answer:

To make the inequality 43 < y - 30 true, add 30 to both sides to get 73 < y. Any number greater than 73, such as 74, 80, or 90, will satisfy the inequality.

Explanation:

To find values that make the inequality 43 < y - 30 true, you simply need to add 30 to both sides of the inequality. This gives you:

73 < y

This means that any value greater than 73 will make the inequality true. Here are three examples:

You can choose any three numbers greater than 73, and they will satisfy the inequality 43 < y - 30.

In the case above, the standard matrix A for T:

T= [0 1]

    [-1 0]

A linear transformation is known to be a kind of a function that exist from one vector point to another and it is one that often respects the linear) structure of all of vector space.

Note that in the linear transformation;

T: R² R²

T=  (x, y), (-x, y)

Since:

(x,y) - (x,-y) - (y,-x)

A= [-1 0]

   [0 1]

A= [-1 0]    =       A= [-x]

   [0 1]                    [y]

Then [tex]T_{b}[/tex] is the reflection of (x- y); Since;

B = [0 1]

    [1 0]

Then [tex]T_{B} (T_{a}(x) )[/tex]  =  [0 1]        =      A= [-x]

                              [0 1]                     [y]

  = [-x]

    [y]

Then: T: = [0 1]                  [x]

                [0 1]                   [y]

Therefore, In the case above, the standard matrix A for T:

T= [0 1]

    [-1 0]

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In this exercise we have to use the knowledge of vectors to find the dot product between them, in this way we can say that:

[tex]|a|*|b|=42.9[/tex]

Knowing that it was stated by the text that the vectors have the value of :

[tex]a=<4.60,7.20>\\ b=<5.10,2.70> [/tex]

The scalar product, or the inner product, or the dot-product, is by summing the products of the respective directions, will be:

[tex]|a|*|b|=4.6*5.1+7.2*2.7\\ =23.46+19.44\\ =42.9 [/tex]

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Answer: 54

Step-by-step explanation: 43-16=27 times 2 =54

Answer:

Nothing will be left over.

Step-by-step explanation:

You need to multiply the 175 by 14.25 to get his total income each month.

Then you add all of the expenses of 1250, 200, 350, 400, 225, 300.

Huey earns 2,493.75 every month, and his expenses are 2,725.

2,493.75 - 2725 = a negative rational number

I ain't gonna do it, because he ain't got no money in his wallet.

(I don't talk like that above, I'm just pretending to be an official Texan.)

If he has negative money left over, I don't think he would spend some more tbh, so the answer would be nothing would be left over.

Hope this helps someone in the future!

Answer:

the answer is  1,437

Step-by-step explanation:

Answer:

I believe you meant to put " log10 (0.001)= -3

10^-3=0.001

The expression log100.001 = -3 in exponential form is 10^-3 = 0.001. This demonstrates that 10 raised to the power of -3 equals 0.001, showing the inverse relationship between logarithms and exponents.

To express log100.001 = -3 in exponential form, recall that the logarithm is the exponent to which the base, in this case, 10, must be raised to produce the given number. The equation log10(0.001) = -3 tells us that the base 10 raised to the power of -3 equals 0.001.

In exponential form, this can be written as 10-3 = 0.001.The concept of converting a decimal to a negative power of 10 involves moving the decimal point to make the number into a whole number, and the negative exponent indicates how many places the decimal point needs to move to the left. In our case, 10-3 means we move the decimal three places to the left: 1 becomes 0.001.

We can use the z-score formula with the known z-score corresponding to a probability of 0.01 to calculate the exhaust NOx emission level. This gives us approximately 0.001 g/mi.

In this scenario, we're dealing with a normal distribution problem wherein we use the formula for z-score to answer it. The z-score formula is =(−)/(/√), where x is the data point, μ is the population mean, n is the size of the data set, and σ is the standard deviation.

In this case, we want to find x, or the NOx emission level, such that the probability of finding an automobile with a level greater than x is 0.01. So, we need to find the z-score that corresponds to a probability of 0.01 and then use it in our formula to solve for x.

Using standard z-score tables or an online z-score calculator, we find that a probability of 0.01 corresponds to a z-score of approximately -2.33 (p and z have opposite signs). We then substitute this z-score, along with the given mean μ=0.03 and standard deviation σ=0.01 into the z-score formula, solving for x. The value of n is 64 (number of vehicles in the fleet).

Inserting these values into the formula gives us = + z/√ =0.03 + (-2.33)*(0.01/√64), which simplifies to =0.03 - (2.33/80) = 0.03 - 0.029125= 0.000875 g/mi. Therefore, the NOx emission level, such that the probability of finding an automobile with a level greater than it, is 0.01 for this fleet is approximately 0.001 g/mi when rounded to three decimal places.

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To find the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01, we can use the z-score formula and the properties of the normal distribution. The z-score formula allows us to convert a probability into a corresponding value on the distribution. Rearranging the z-score formula, we can find the value of l.

To find the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01, we can use the z-score formula and the properties of the normal distribution. The z-score formula is z = (x - µ) / (σ / √n), where x is the average NOx level, µ is the mean, σ is the standard deviation, and n is the sample size. We want to find the value of l such that the area to the right of l under the normal curve is 0.01.

First, we need to find the z-score corresponding to a right-tail probability of 0.01. This can be done using a z-table or a calculator. In this case, the z-score is approximately 2.326. Now we can use the z-score formula to find the value of l. Rearranging the formula, we have l = µ + (z * σ / √n). Substituting the given values, l = 0.03 + (2.326 * 0.01 / √64). Calculating this, we get l ≈ 0.031.

Therefore, the level l such that the probability that the average NOx level x for the fleet is greater than l is only 0.01 is approximately 0.031 g/mi.

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Answer: There is 15% error for the erasers

Step-by-step explanation:

Since we have given that

Number of folders he predicted = 25

Number of erasers he predicted = 230

Total number of inventories he predicted is given by

[tex]230+25=255[/tex]

Number of erasers he actually sold = 200

Number of folders he actually sold = 30

Total number of inventories he actually sold is given by

[tex]200+30=230[/tex]

Error in estimation is given by

[tex]230-200=30[/tex]

Percentage of error for the erasers only  

[tex]\frac{30}{200}\times 100\\\\=\frac{30}{2}\\\\=15\%[/tex]

Hence, there is 15% error for the erasers.

Answer:

15 %

Step-by-step explanation:

The amount of a chemical solution is measured to be 2 liters. What is the percent error of the measurement?

25%

Answer:

Step-by-step explanation:

common ratio of a Geometric series can be found by dividing the second term by first term of the series .

we are given that first term a1= -125 and second term a2 =-25

so the common ratio must be

[tex]r=\frac{a2}{a1}[/tex]

[tex]r=\frac{-25}{-125}[/tex]

[tex]r= \frac{1}{5}[/tex]

Hence the common ratio is 1/5.