What is the solution to the equation 16^2x-3 . 4^-2x = 4^2

Answer:

4.52 %

Step-by-step explanation:

the percentage increase in height is calculated as

[tex]\frac{increase}{original}[/tex] × 100%

increase in height = 1.62 - 1.55 = 0.07 ,

then

% increase = [tex]\frac{0.07}{1.55}[/tex] × 100% = 0.045.. × 100% ≈ 4.52% ( to 2 decimal places )

Let's represent the number of dimes in the coin purse as d. Then, the number of nickels in the coin purse can be represented as 5d - 2.

The total value of the coins can be expressed as:

0.05 * (5d - 2) + 0.10 * d = 0.95

Expanding and simplifying the equation, we get:

0.05 * 5d - 0.05 * 2 + 0.10 * d = 0.95

0.50d - 0.10 = 0.95

0.50d = 1.05

d = 2.10

Since the number of dimes must be a whole number, we round d down to 2. So, there are 2 dimes in the coin purse and 5 * 2 - 2 = 6 nickels in the coin purse.

The equation which correctly represents the sentence in discuss as required is; n + 328 = 13.

It follows from the task content that the equation which correctly represents the sentence given in the task content is to be determined.

The word phrase; n and 328 more can be represented as; n + 328.

Therefore, n and 328 more is the same as 13 can be represented as; n + 328 = 13.

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The inequality that shows the least amount he needs is  4x + 22 ≥ 85.50 which shows he needs at least $15.875

The Inequality that will represent this problem is 4x + 22 ≥ 85.50, where x is the number of windows Jonathan washes.

To solve the inequality, we'll start by subtracting 22 from both sides:

4x ≥ 63.50

And finally, dividing both sides by 4:

x ≥ 15.875

So, Jonathan needs to wash at least 15 windows in order to save up enough money to buy the boxed set.

b.

The graph on the number line showing x ≥ 15.875 is attached below

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The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

In isosceles trapezoid KRWT, the trianngles are ΔKTW and ΔRWT are formed.

In trianngles ΔKTW and ΔRWT, then we have

KW = TR        {Given}

∠W = ∠T       {Isosceles angles}

WT = WT       {Common side}

Then the trianngles ΔKTW and ΔRWT are congruent to each other.

The angles ∠KTW and ∠RWT are congruent with each other and WK = TR. Then the correct option is C.

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Answer:

The answer is provided in the image below.

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{ 7}(x-\stackrel{x_1}{(-2)}) \implies y +9= 7 (x +2) \\\\\\ y+9=7x+14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]

The PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths, without having any tickets left over.

We need to find a number that is divisible by at least 3, but less than 10.

We can start by listing out the multiples of 3 and see which one is closest to 1,932:

3 × 1 = 3

3 × 2 = 6

3 × 3 = 9

3 × 4 = 12

3 × 5 = 15

3 × 6 = 18

3 × 7 = 21

3 × 8 = 24

3 × 9 = 27

We can see that the closest multiple of 3 to 1,932 is 1,932 ÷ 3 = 644. This means that if the PTO split the tickets into 644-ticket batches, they would have 3 equal booths of 644 tickets each.

We can check whether 644 is also divisible by 4, 5, 6, 7, 8, or 9, as those numbers are less than 10. We can see that 644 is not divisible by 4 or 5, but it is divisible by 6, 7, 8, and 9. This means that the PTO could also split the tickets into 6, 7, 8, or 9 ticket booths, with each booth having an equal number of tickets.

Therefore, the PTO could split the 1,932 tickets into either 3, 6, 7, 8, or 9 ticket booths.

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Answer:

Step-by-step explanation:

To find the solutions of the equation 24x² + 2x - 15 = 0, you can use the quadratic formula.

The quadratic formula states that given a quadratic equation of the form ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0, the solutions are given by:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 24, b = 2, and c = -15, so:

x = (-2 ± √(2² - 4 * 24 * -15)) / 2 * 24

x = (-2 ± √(4 + 1440)) / 48

x = (-2 ± √(1444)) / 48

Taking the square root of both sides, we have:

x = (-2 ± 38.2) / 48

Therefore, the solutions are:

x = (-2 + 38.2) / 48 = 36.2 / 48 = 0.75

x = (-2 - 38.2) / 48 = -40.2 / 48 = -0.84

Since 0.75 > -0.84, the greater of the two solutions is 0.75.

Answer:

the answers are: 36/48

-40/48

Answer:

84

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

We can first convert 96 into a fraction.

Now that we know this, we can solve for the number of shrubs. If we know that at least [tex]\frac{7}{8}[/tex] of the shrubs should survive, we can use an equation that looks like this:

Solving the equation:

Therefore, the minimum number of shrubs that should survive is 84.

In the algebra on of the form of sequence is arithmetic progression or sequence which is described below.

In the arithmetic sequence  the common difference between any two consecutive terms remains constant .

In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any nth term in AP,

T = a + nd

d = T₂-T₁

Where, a is first term , n is nth term and d is common difference

If aₙ = aₙ₋₁  -4

where aₙ is a nth term and aₙ₋₁ is a (n-1)th term

Now,

a + nd  = a + (n-1-1)d - 4

nd   = (n - 2)d - 4

nd = nd -2d - 4

2d = -4

d = -2

So, aₙ = a -2n

aₙ₋₁ = a -2(n - 2)

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The ratio of stars to red stripes is 50 to 7

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

Number of stars = 50

Red stripes = 7

White stripes = 6

Using the above as a guide, we have the following:

Ratio = Stars : Red stripes

substitute the known values in the above equation, so, we have the following representation

Stars : Red stripes = 50 : 7

Hence, the ratio is 50 : 7

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Yes, the data provided is not correct. This can be proven using the principle of inclusion-exclusion.

According to the given data, the total number of students who failed in Math is 750, the total number of students who failed in Accounts is 600, and the total number of students who failed in Costing is 600.

However, if we apply the principle of inclusion-exclusion, the total number of students who failed in at least one of the three subjects should be equal to the sum of the number of students who failed in each subject, minus the number of students who failed in two subjects, plus the number of students who failed in all three subjects.

Therefore, using this principle, we have:

750 + 600 + 600 - 450 - 400 + 75 = 975

This result shows that the number of students who failed in at least one of the three subjects is 975, which is greater than the total number of students who appeared for the examination (1000), which is not possible.

Therefore, the given data is not correct.

The GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.

What is Interest?

Interest is the income that is returned to the holder of capital. Different kinds of interest include gross interest and net interest.

To find GI (Gross Income), we add wages and interest:

GI = Wages + Interest = $145,000 + $2500 = $147,500

To find AGI (Adjusted Gross Income), we subtract the contributions towards retirement from GI:

AGI = GI - Contributions towards Retirement = $147,500 - $3000 = $144,500

To find TI (Taxable Income), we subtract exemptions and deductions from AGI:

TI = AGI - Exemptions - Deductions = $144,500 - $4100 - $2800 = $137,600.

Therefore, the taxable income is $137,600.

Hence, GI (Gross Income) is $147,500, AGI (Adjusted Gross Income) is $144,500, and TI (Taxable Income) is $137,600.

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The initial value of the function is 1.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

A relationship in which one input value exactly equals one output value is known as a function. A function's initial value is a crucial component. A starting value or starting point is exactly what it sounds like: It is an initial value.

The line intersects the y-axis at (0,1).

The initial value of the function is 1.

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Answer:

57

Step-by-step explanation:

To find the ratio of the area of Alaska to the area of Rhode Island, we need to divide the area of Alaska by the area of Rhode Island.

The area of Rhode Island is 1000 square miles and the area of Alaska is 5.7 x 10^5 square miles.

So, the ratio is: 5.7 x 10^5 / 1000 = 57

Therefore, Alaska's area is 57 times the area of Rhode Island.

5.7 x 10^5 divided by 1000 = 57.

Answer:

10x = 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

Step-by-step explanation:

Distributive property of multiplication says every element within every pair of elements is added and multiplied to each other. So the value of 10 times that of 5 is 50.

(a) W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.

(b) W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.

(c) We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5

What is the quadratic equation?

The quadratic equation is a formula used to solve quadratic equations of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable.

(a) To find the locally linear approximation of W at t=3, we first need to find W(3) and W'(3).

We know that at time t=3, the volume of water in the tub is 2.5 cubic feet. Therefore, W(3) = 2.5.

To find W'(3), we need to use the fact that the rate of change of the volume of water in the tub is equal to the rate of water flowing in minus the rate of water leaking out.

So, W'(t) = F(t) - L(t).

At time t=3, we have F(3) = arctan(π/2 - 3/10) ≈ 1.383 cubic feet per minute, and L(3) = 0.03(20*3 - 3² - 75) = 0.9 cubic feet per minute. Therefore, W'(3) = 1.383 - 0.9 = 0.483 cubic feet per minute.

The locally linear approximation of W at t=3 is given by:

W(t) ≈ W(3) + W'(3)(t-3)

W(t) ≈ 2.5 + 0.483(t-3)

To approximate the volume of water in the tub at time t=3.5, we plug in t=3.5 into the above equation:

W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.

(b) To find W''(8), we first need to find an expression for W'(t). We know that:

W'(t) = F(t) - L(t)

Taking the derivative with respect to t:

W''(t) = F'(t) - L'(t)

We know that F(t) = arctan(π/2 - t/10), so F'(t) = -1/(10π/4 - t²/100 + t/5²) * (1/5), where we used the chain rule and the derivative of arctan(x) = 1/(1+x²). Evaluating this expression at t=8, we get F'(8) ≈ -0.0397 cubic feet per minute.

We also know that L(t) = 0.03(20t - t²- 75), so L'(t) = 0.03(20 - 2t). Evaluating this expression at t=8, we get L'(8) = -0.6 cubic feet per minute.

Therefore, W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.

Interpreting the meaning of W''(8), we see that it represents the rate of change of the rate of change of the volume of water in the tub at time t=8. Specifically, W''(8) tells us how quickly the volume of water in the tub is changing with respect to time at time t=8 is changing.

(c) Yes, there is a time t for which the volume of water in the tub is neither increasing nor decreasing. This occurs when the rate of water flowing into the tub is equal to the rate of water leaking out. That is, we need to find a value of t such that F(t) = L(t).

We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5

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Ordinal data can be ordered, as the naming implies. Both have "ord" to help remember the connection. An example of this would be something like small, medium, large. The items do not have to be numeric in nature.

Nominal data is any category or name. Order isn't present here. For example, if a survey asked about a person's favorite color, then there isn't any inherent order here.

Answer:

hi

Step-by-step explanation:

[tex]x {}^{3} - 27 = {x}^{3} - {3}^{3} \\ = (x - 3)( {x}^{2} + 3x + 9) \\ {x}^{3} + 27 = {x}^{3} + {3}^{3} \\ = (x + 3)( {x}^{2} - 3x + 9)[/tex]

The height of tree is 9.9372.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

ΔABC ~  ΔDEF  only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.

Given;

Juanita is 1.82 meters tall

From the tree's base, she walks 12.20 meters along the tree's shadow to a position where the end of her shadow.

She is now 6.10 meters from the end of the shadows.

Now,

Let, h be the height of the tree;

Here, ΔABC ~ ΔADE,

So, DE/BC = AD/AB

h/1.82 = (6.10 + 12.20)/6.10

h/1.82= 18.30/6.10

h=33.306/6.10

h=5.46

h = 1.82*5.46

= 9.9372

Therefore, by congruency of triangle the answer will be 9.9372.

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Answer:

No. The length of the ramp is [tex]\sqrt{226[/tex] The rubber mat will be too short

Step-by-step explanation:

a) P(10.99 ≤ X ≤ 11.01) = 0.9544

b) Probability that the sample mean diameter exceeds 11.01 when n = 25 is 0.0062.

We are given the following in the question:

Mean, μ = 11 cm

Standard Deviation, σ = 0.02 cm

We are given that the distribution of diameter is a bell-shaped distribution that is a normal distribution.

Formula: z = (x - μ)/σ

a) P(10.99 ≤ X ≤ 11.01 when n = 16)

Standard error due to sampling = σ/n = 0.02/√16 = 0.005

P(10.99 ≤ X ≤ 11.01) = P((10.99 - 11)/0.005 ≤ z ≤ (11.01 - 11)/0.005)

                              = P(-2 ≤ z ≤ 2) = 0.9772-0.0228

                              = 0.9544 = 95.44%

b) P(sample mean diameter exceeds 11.01 when n = 25)

Standard error due to sampling =  σ/n = 0.02/√25 = 0.004

P(x > 11.01) = P(z > (11.01 - 11)/0.004) = P(z > 2.5)

                 = 1 - P(z ≤ 1) = 1 - 0.9938 = 0.0062 = 0.62%

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Answer: b

Step-by-step explanation:  ias  chinadu  

B because that's the VA which would be intellectually specialist.

Answer:

x= -5

Step-by-step explanation:

4(x + 3) = -8

4x + 12 = -8

4x = -20

x = -5

The practise of extracting information from data to guide better business decisions is known as data analysis. Five iterative phases typically comprise the data analysis process:

Choose the data you want to examine.

gather the data

Clean up the data before analysis.

Study the information

Interpret the analysis' findings

It is common knowledge that data analysts focus on the sample size in order to

To prevent a few outlier responses from distorting the results

ensuring that the data reflects a variety of viewpoints

to prevent making erroneous conclusions due to a tiny sample size

An analyst of data is who?

An individual involved in the handling of data is referred to by this phrase.

Such a person aids in the analysis, retrieval, and drawing of conclusions from the information at hand.

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The slope of the line on the graph is equal to: A. -1/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (-2, 4).

Points on y-axis = (2, 0).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (0 - 2)/(4 + 2)

Slope, m = -2/6

Slope, m = -1/3.

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Answer:

Step-by-step explanation:

x - 5 = 8 - 4x

rearrange

x - 5 = -4x + 8

x + 4x - 5 = -4x + 4x + 8

5x - 5 = 8

5x - 5 + 5 = 8 + 5

5x = 13

Divide by 5

5x/5 = 13/5

x = 13/5 or 2 [tex]\frac{3}{5}[/tex]

or 2.6 as a decimal