Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire. O14 ft 15 ft 20 ft 29 ft Jason planted and staked a tree . The stakes are 21 ft from the base of the tree . They are connected to wires that attach to the trunk at a height of 20 ft . Find the length of a wire . O14 ft 15 ft 20 ft 29 ft ​

The shaded area under the curve is equal to 0.6826.

From the information provided, we have the following parameters:

Mean, μ = 501

Standard deviation, σ = 55.00

In this exercise, you are required the shaded area under the curve and this can be represented or modeled by this mathematical expression:

446 ≤ x ≤ 556

The lower limit (boundary) is equal to 446 i.e x₁ = 446.

The upper limit (boundary) is equal to 556 i.e x₂ = 556.

Next, we would determine the z-score for both limits as follows:

Z-score = (x₁ - μ)/σ

Z-score = (446 - 501)/55.00

Z-score = -55/55.00

Z-score = -1.00

For the upper limit, we have:

Z-score = (x₂ - μ)/σ

Z-score = (556 - 501)/55.00

Z-score = 55/55.00

Z-score = 1.00

By using a z-score calculator, the area is given by:

P(446 ≤ x ≤ 556) = P(-1.00 ≤ x ≤ 1.00)

P(-1.00 ≤ x ≤ 1.00) = P(x ≤ 1.00) - P(x ≤ -1.00)

P(-1.00 ≤ x ≤ 1.00) = 0.6826.

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So,

We're going to convert the following number in base 2:

To base 8.

Step 1: Write down the binary number

(011011001)2

Group all the digits in sets of three starting from the far right. Add zeros to the left of the last digit if there aren't enough digits to make a set of three. We obtain:

Now, remember the following equivalences:

Bin: 000 001 010 011 100101110111

Octal:01234567

Therefore,

011 011 001 = 331

And finally:

The compound inequality on the number line is shown below.

We have been given a compound inequality. We are asked to graph the given inequality on number line.    

x>8 and x≤3

The solution for the inequality is all values of x less than or equal to 3 and greater than or equal to 8.

We will have solid dots at  x>-8 and x≤-3 .

One arrow of the number line would be from 3 to left of the number line (towards negative infinity). The other arrow will be from 8 to right side of number line towards positive infinity.

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Answer:

v = 196.25

Step-by-step explanation:

v = 3.14*r^2*h

v = 3.14*5^2*2.5

v = 196.25

Based on the attached graph, the y-intercept is 3

The y-intercept of the function is the point or points where the graph of the function crosses the y-axis i.e. the point where the value of x equals 0

The graph that completes the question is added as an attachment

Using the definition above, we understand that

The y-intercept for the graph of the exponential function is the point where x = 0

On the attached graph, we have

y = 3, when x = 0

This means that the y-intercept for the graph of the exponential function is 3

This is so because the graph of the function crosses the y-axis  at y = 3 when x = 0

Hence, the y-intercept of the exponential function is 3

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Answer:

Step-by-step explanation:

No. of White rectangular boxes = 5

No. of Black rectangular boxes = 8

No. of White square boxes = 9

No. of Black square boxes = 4

5x + (-8x) + 9 + (-4)

= - 3x + 5 (Ans) (option D)

Answer:

10

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

This is the graph of y = tan(x) shifted 3 units up.

The graph shown is of tan function where the vertical shift is of 2 units.

The graph of a tan function is shown we have to determine the vertical shift to the graph. As we know that tanx function has its inflection point at the origin, as the graph is already translated we can see that the inflection point of the graph is at x = -π/12. The corresponding value of y is 2

Equation of the given function is given by:

f(x) = tan(x+π/12)+2

Where -π/12 shows the horizontal shift while +2 shows the vertical shift.

Therefore, the required vertical shift is +2 units.

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\( = \frac{2}{3} \div - \frac{5}{7} \\ = \frac{2}{3} \times - \frac{7}{5} \\ = - \frac{14}{15} \)

ATTACHED IS THE SOLUTION.

NOTE WHEN WE ARE DIVIDING WE CHANGE THE DIVISION SIGN TO A MULTIPLICATION SIGN TO AND SWAP THE FOLLOWING FRACTION .

Answer:

-0.019047619

That’s the Answer Hope this helps:)

1. Relation 1 is a function

2. Relation 2 is a function

3. Relation 3 is not a function

4. Relation 4 is a function

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

The relations (1) to (4)

Relation (1)

This relation is a function

This is because each range value point to unique domain values

Relation (2)

This relation is a function

This is because each range value point to unique domain values

Relation (3)

This relation is not a function

This is because domain values w have different range values.

Relation (4)

This relation is a function

This is because each range value point to unique domain values

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Comparing the √17 and 29/7 using <, > or = , we have √17 < 29/7.

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than." Comparing amounts is a technique for figuring out how much to compare units in relation to a different standard or reference unit. A common reference point is necessary for two comparing units to be compared; otherwise, they cannot be compared.

Given,

Comparing the following using <, > or = ,

Numbers:

√17 and 29/7

For √17

Simplifying,

√17 = 4.123

For 29/7

29/7 = 4.14

√17 < 29/7

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Answer:

(x - 5)² + (y + 6)² = 16

Step-by-step explanation:

assuming you require the equation of the circle

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

here (h, k ) = (5, - 6 ) and r = 4 , then

(x - 5)² + (y - (- 6) )² = 4² , that is

(x - 5)² + (y + 6)² = 16

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The algorithm/abstract strategy to justify the fraction 3/5 involves interpreting it as a division, performing the division, and obtaining the decimal representation as the results.

To justify the fraction 3/5, we can use the concept of division and understand it as a ratio or proportion.

Algorithm/Abstract Strategy:

Start with the numerator, which is 3.

Identify the denominator, which is 5.

Interpret the fraction as a ratio or comparison between the numerator and denominator.

Understand that 3/5 represents a division where the numerator (3) is divided by the denominator (5).

Perform the division: 3 ÷ 5.

Simplify the division to its simplest form, if necessary.

The result of the division, in this case, is the decimal representation of the fraction.

If required, convert the decimal representation to a percentage or any other desired form.

For example, if we perform the division 3 ÷ 5, the result is 0.6.

So, 3/5 can be justified as the ratio or proportion where the numerator (3) is divided by the denominator (5) resulting in 0.6.

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Answer:

  f(11) ≈ 52

  f(9.5) ≈ 49

  f(10.25) ≈ 50.5

Step-by-step explanation:

Given a function value (f(10) = 50) and its derivative (f'(10) = 2), you want approximations of nearby points.

The linear approximation of the function near x=10 is given by ...

  f(x) ≈ f(10) +f'(10)(x -10)

  f(x) = 50 +2(x -10) = 30 +2x

  f(11) ≈ 30 +2·11 = 52

  f(9.5) ≈ 30 +2·9.5 = 49

  f(10.25) ≈ 30 +2·10.25 = 50.50

Answer:

Step-by-step explanation:

"y" is geometric mean ⇒ y² = 5 × 12

y = √60 ≈ 7.7

x² = 5² + ( √60 )²

x = √85 ≈ 9.2

Answer:

An equilateral triangle has 3 lines of symmetry

Hope this helps

Step-by-step explanation:

Answer:

12.49 is the constant of proportionality

Step-by-step explanation:

Answer:

q

hey g(x) = x2 + 3x - 3

Step-by-step explanation:

es la respuesta

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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There are 5 nickels, 3 dimes, and 9 pennies.

Let d = The number of dimes

Let n = number of nickels

Let p = The number of pennies

As given, there are two more nickels than dimes and three times as many pennies as dimes:

d+2=n

3d=p

0.10d+0.05n+0.01p=0.64

Plug in the value to find d

\(0.10d+0.05(d+2)+0.01(3d)=0.64\)

\(0.10d+0.05d+0.1+0.03d=0.64\)

\(0.18d=0.64\)

\(d=3\)

The value of p is equal to 3d

p=3(3)=9

n=d+2

n=3+2

n=5

Hence, there are 5 nickels, 3 dimes, and 9 pennies.

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Answer:

It should be 32.

Step-by-step explanation:

The compound interest is larger than the simple interest by $3071.31

Where, simple interest is $3060 and compound interest is $6131.31

Compound interest refers to the method of calculating interest on a principal amount and any accumulated interest that has already been earned. In other words, it is the process of earning interest on interest.

The amount of interest earned using both simple and compound interest over a period of 30 years.

Simple interest formula:

\(SI = P*r*t\)

Using this formula, here, r = \(4\frac{1}{4}\) % = 0.0425

We can calculate the simple interest earned over 30 years,

SI = 2400 * 0.0425 * 30 = $3060

Compound interest formula:

\(A = P(1 + \frac{r}{n} )^{nt}\)

Using this formula, we can calculate the amount of money in the account after 30 years:

\(A=2400(1 + \frac{0.0425}{4} )^{4*30}\) = $8531.31

So, the Compound Interest earned = $8531.31 - $2400 = $6131.31

Therefore, the compound interest is larger than the simple interest by:

$6131.31 - $3060 = $3071.31

This is because compound interest earns interest on the interest that is already earned, resulting in a higher total interest earned over time compared to simple interest, which only earns interest on the initial principal amount.

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By answering the above question, we may infer that The inaccuracy, equation when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The following formula may be used to get the percent error:

percent error is calculated as follows: 100% divided by (actual value - measured value).

Whereas, "|" stands for absolute value.

In this instance, the measured measurement is 8.5 inches, whereas the real value is 9.1. Hence, by entering these values into the formula, we may obtain:

error = |(9.1 - 8.5) / 9.1| x 100% error = 6.59%

The inaccuracy, when rounded to the closest tenth of a percent, is around 6.6%. The measurement's percent error is 6.6% as a result.

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, in the presented question, we can conclude that Interval   \((0, 1): f(0) 5, f(1) -3\), indicating that the function switches signs and has a zero in the interval  \((0, 1).\)

Interval  \((4, 3): f(-4) -41, f(-3) 5,\)therefore, the function reverses its sign and has a zero in the interval  \((-4, -3).\)

Interval  \((3, 2): f(-3) 5, f(-2) -9,\) indicating that the function changes sign and has a zero in the interval  \((-3, -2).\)

Interval \((2, 1): f(-2) -9, f(-1) 1\), therefore the function reverses its sign and has a zero in the interval  \((-€2, -1).\)

Interval \((1, 0): f(-1) 1, f(0) 5\), so the function does not change sign and the interval may or may not contain a zero \((-1, 0).\)

Interval  \((0, 1): f(0) 5, f(1) -3,\) indicating that the function switches signs and has a zero in the interval  \((0, 1).\)

Therefore, in the presented question, we can conclude that Interval   \((0, 1): f(0) 5, f(1) -3\), indicating that the function switches signs and has a zero in the interval  \((0, 1).\)

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Answer:

160....................

Answer:

Step-by-step explanation:

Answer:

no it is not because two different input values have the same output

Step-by-step explanation:

Answer:

Yes it is a function... Because we have output for each input

The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

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

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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Total fencing required to completely surround the triangular garden construct by Claire is equal to 30 ft.

As given in the question,

As shown in the diagram,

Shape of the triangular garden construct by Claire is right triangle.

In given right triangle,

Perpendicular side = 12 ft

Base = 5 ft

Let x be the hypotenuse of the given right triangle

Apply Pythagoras theorem

(Hypotenuse)²= (Perpendicular side)² + (Base)²

⇒x² = 12² +5²

⇒x = 13ft

Perimeter of the triangular garden = 12+13+5

                                                        = 30 ft

Therefore, total fencing required to completely surround the triangular garden construct by Claire is equal to 30 ft.

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According to the unitary method,

A) The time taken for Peter to finish the job alone is 4 hours, 48 minutes.

B) The time taken for Emily and Peter to finish the job together is 2 hours, 36 minutes.

Unitary method:

In math, unitary method refers the process of finding the value of a single unit, and based on this value.

Given,

Emily, Ashley and Peter can clean a warehouse in 2 hours. If Emily does the job alone, she can finish it in 6 hours. If Ashley does the job alone she can finish it in 8 hours.

Here we need to find the following:

A) The time take for Peter to finish the job alone

B) The time taken for Emily and Peter to finish the job together

Let us consider x be the time taken for Peter to finish the job alone.

So, based on the given question we can write it as,

=> 1/6 + 1/8 + 1/x = 1/2

=> (8 + 6)/48 + 1/x = 1/2

=> 14/48 + 1/x = 1/2

=> 7/24 + 1/x = 1/2

=> 1/x = 1/2 - 7/24

=> 1/x = 12 -7/24

=> 1/x = 5/24

=> x = 24/5

=> x = 4.8

So, the time taken for Peter to finish the job alone is 4 hours, 48 minutes.

Then the time taken for Emily and Peter to finish the job together is calculated as,

=> 5/24 + 1/6

=> 5 + 4/ 24

=> 9/24

=> 3/8

Therefore, the time taken for Emily and Peter to finish the job together 2 hours, 36 minutes.

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