a ladder leans against a wall and reaches a point 35 feet up the wall.The base of the ladder is 7 feet from the wall.To the nearest tenth of a foot, what is the length of the ladder

Final answer:

To simplify the fourth root of a non-perfect power, use a calculator to raise the number to the power of 0.25, or calculate the square root twice. For non-integer powers, calculate roots with corresponding fractional exponents. Request assistance from your instructor if necessary.

Explanation:

Simplifying the Fourth Root of Non-Perfect Powers

When simplifying the fourth root of a number that is not a perfect fourth power, you can utilize the power function on a calculator. This involves raising numbers to the power of 0.25, which equates to calculating the fourth root. For example, using the y* button (or equivalent) you can calculate the fourth root of any number by raising it to the power of 0.25. This is analogous to how raising a number to the 0.5 power gives us the square root of that number. If your calculator doesn't have this function, another technique is to calculate the square root of the number twice, since the fourth root is essentially the square root of the square root.

To work through a non-integer power, like 31.7, you can find the tenth-root of 3 by raising it to the power of 0.1 and then raise the result to the 17th power. Similarly, for expressions with fractional exponents like x0.5, you can interpret this as the square root of x. Understanding that fractional powers represent roots can help in simplifying complex expressions without a calculator as well.

If you are dealing with equilibrium problems or other scenarios that require finding roots of numbers, it's crucial to be comfortable with these techniques. If you are unsure about how to perform these operations, don't hesitate to ask for assistance from your instructor. Developing a natural and forgiving relationship with numbers, and only representing precision as needed, is also an important aspect of working with mathematical problems.

Answer:

C

Step-by-step explanation:

did the test

Answer:

c

Step-by-step explanation:

Final answer:

The perimeter problem is solved using two simultaneous equations derived from the given information about the perimeter and sum of sides. The solution reveals that the width (w) of the fence is 30 feet and the length (l) is 40 feet.

Explanation:

We are given that the perimeter of a fence is 140 feet. The perimeter formula for a rectangle is P = 2l + 2w, where l is the length and w is the width of the rectangle.

According to the problem, we also know that 3 times the length plus 2 times the width equals 180 feet (3l + 2w = 180).

Let's assign variables: Let l represent the length and w represent the width of the fence. We can now set up two equations:

We can solve these equations simultaneously to find the values for l and w.

First, simplify the perimeter equation by dividing everything by 2: l + w = 70. Now substitute l from the simplified equation into the given equation to find w:

Now that we have the width, we can find the length using the simplified perimeter equation:

Therefore, the width (w) is 30 feet, and the length (l) is 40 feet.

The length of the fence is 40 feet and the width is 30 feet.

To solve this problem, we can set up a system of equations. Let's denote the length of the fence as 'l' and the width as 'w'. From the given information, we have the following equations:

2l + 2w = 140   (equation 1)

3l + 2w = 180   (equation 2)

We can solve this system of equations by eliminating a variable. Multiply equation 1 by 3 and equation 2 by 2 to eliminate 'w':

6l + 6w = 420   (equation 3)

6l + 4w = 360   (equation 4)

Subtract equation 4 from equation 3 to eliminate 'l':

6w - 4w = 420 - 360

2w = 60

w = 30

Substitute the value of 'w' into equation 1 to solve for 'l':

2l + 2(30) = 140

2l + 60 = 140

2l = 80

l = 40

Therefore, the length of the fence is 40 feet and the width is 30 feet.

The larger the standard deviation, the more dispersed the distribution is, because the standard deviation measures how far each observation is from the mean value of the distribution.

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Answer:

The dot plot representing the calico crayfish has more than one mode.

Step-by-step explanation:

We know that mode of the data is the value corresponding to the highest frequencies.

or we may say the mode of a data set is the number that occurs most frequently.

Clearly from the dot plot we could see that the data representing the calico crayfish have two quantities with four dots ( one is when number of calico crayfish are 5 and the other when number of calico crayfish are 8)

Also by making a frequency table we may check it as:

Number of calico crayfish         frequency

      1                                                    1

      2                                                   0

      3                                                    1

      4                                                    3          

     5                                                    4

      6                                                     1    

      7                                                     2

      8                                                     4  

      9                                                     0  

     10                                                     2

The dot plot shows calico crayfish has more than one mode. In the data set each column of a table represents a specific variable and each row represents a specific record of the data sets.

A data set is a set of information corresponds to one or more database tables in the case of tabular data,

From the table of the calico crayfish, it is observed that the data no 5 on the x-axis the frequency is 4. As well as on data no 8 the frequency is 4.

The dot plot shows calico crayfish has more than one mode. because it shows the same frequency at two other variables;

Hence the dots plot shows calico crayfish has more than one mode.

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The ordered pairs are (0, 1), and (2, -1) which are solutions to the inequality 2x+3y>-1 option first and fifth are correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have an inequality:

2x+3y>-1

The above inequality is a straight line and represents a region.

After plotting the inequality on the graph.

The points are in the region of the inequality:

These points satisfy the inequality.

Thus, the ordered pairs are (0, 1), and (2, -1) which are solutions to the inequality 2x+3y>-1 option first and fifth are correct.

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To find the stadium's profit margin, subtract its expenses from its revenue and divide by the revenue, then multiply by 100 to get the percentage.

In order to find the stadium's current profit margin, we need to subtract its total expenses from its total revenue and then divide the result by the total revenue. The stadium brings in $16.25 million per year and has football-related expenses of $13.5 million and stadium expenses of $2.7 million per year.

To calculate the profit margin, we subtract the total expenses ($13.5 million + $2.7 million) from the total revenue ($16.25 million): $16.25 million - ($13.5 million + $2.7 million) = $16.25 million - $16.2 million = $0.05 million.

Finally, we divide the profit ($0.05 million) by the total revenue ($16.25 million) and multiply by 100 to get the profit margin as a percentage: ($0.05 million / $16.25 million) * 100 = 0.003076923076923 * 100 = 0.3076923076923%.

The volume of the sand in the top portion of the hourglass is calculated using the volume formula for cones. Given the dripping rate, it takes about 115 seconds for all the sand to drip to the bottom.

To determine how many seconds it will take for all the sand to drip to the bottom, we need to find the volume of sand in the top cone.

The total height of sand in the top portion is 54 millimeters, which means the equivalent of three cones of sand (since 54 mm / 18 mm/cone = 3).

Thus, the total volume of sand is 3 x 1206.37 = 3619.11 cubic millimeters.

Given the sand drips at a rate of 10π cubic millimeters per second, we find the total time by dividing the volume by the rate:

Time = Total Volume / Rate = 3619.11 / 10π ≈ 115.13 seconds.

Therefore, it will take approximately 115 seconds for all the sand to drip to the bottom of the hourglass.

Answer:

c on edge

Step-by-step explanation:

took the exam

The expression [tex]\(\frac{7x^4 + x + 14}{x + 2}\)[/tex] is [tex]\(7x^3 - 14x^2 + 28x - 55 + \frac{124}{x + 2}\)[/tex].

To find the correct form of the expression [tex]\(\frac{7x^4 + x + 14}{x + 2}\)[/tex] in the form [tex]\(q(x) + \frac{r(x)}{b(x)}\)[/tex], where [tex]\(q(x)\)[/tex] is the quotient and [tex]\(r(x)\)[/tex] is the remainder, we need to perform polynomial long division. Here, [tex]\(b(x) = x + 2\)[/tex].

Step-by-Step Solution:

1. Setup the Division:

  Divide [tex]\(7x^4 + 0x^3 + 0x^2 + x + 14\)[/tex] by [tex]\(x + 2\)[/tex].

2. First Term:

  - Divide the leading term of the dividend by the leading term of the divisor: [tex]\(\frac{7x^4}{x} = 7x^3\)[/tex].

  - Multiply [tex]\(7x^3\)[/tex] by [tex]\(x + 2\)[/tex]: [tex]\(7x^3 \cdot (x + 2) = 7x^4 + 14x^3\)[/tex].

  - Subtract this from the original polynomial:

    [tex]\[ (7x^4 + 0x^3 + 0x^2 + x + 14) - (7x^4 + 14x^3) = -14x^3 + 0x^2 + x + 14. \][/tex]

3. Second Term:

  - Divide the leading term of the new polynomial by the leading term of the divisor: [tex]\(\frac{-14x^3}{x} = -14x^2\)[/tex].

  - Multiply [tex]\(-14x^2\) by \(x + 2\)[/tex]: [tex]\(-14x^2 \cdot (x + 2) = -14x^3 - 28x^2\)[/tex].

  - Subtract this from the current polynomial:

    [tex]\[ (-14x^3 + 0x^2 + x + 14) - (-14x^3 - 28x^2) = 28x^2 + x + 14. \][/tex]

4. Third Term:

  - Divide the leading term of the new polynomial by the leading term of the divisor: [tex]\(\frac{28x^2}{x} = 28x\)[/tex].

  - Multiply [tex]\(28x\)[/tex] by [tex]\(x + 2\)[/tex]: [tex]\(28x \cdot (x + 2) = 28x^2 + 56x\)[/tex].

  - Subtract this from the current polynomial:

    [tex]\[ (28x^2 + x + 14) - (28x^2 + 56x) = -55x + 14. \][/tex]

5. Fourth Term:

  - Divide the leading term of the new polynomial by the leading term of the divisor: [tex]\(\frac{-55x}{x} = -55\)[/tex].

  - Multiply [tex]\(-55\)[/tex] by [tex]\(x + 2\)[/tex]: [tex]\(-55 \cdot (x + 2) = -55x - 110\)[/tex].

  - Subtract this from the current polynomial:

    [tex]\[ (-55x + 14) - (-55x - 110) = 124. \][/tex]

Final Result:

- Quotient [tex]\(q(x) = 7x^3 - 14x^2 + 28x - 55\)[/tex]

- Remainder [tex]\(r(x) = 124\)[/tex]

Thus, the expression [tex]\(\frac{7x^4 + x + 14}{x + 2}\)[/tex] can be written as:

[tex]\[7x^3 - 14x^2 + 28x - 55 + \frac{124}{x + 2}\][/tex]

This is the required form [tex]\(q(x) + \frac{r(x)}{b(x)}\)[/tex].

The formula that represents the nth term of a arithmetic sequence is given by:

[tex]A(n)=-6+(n-1)(\dfrac{1}{5})[/tex]

Now, we are asked to find the  first, fourth, and tenth terms of the arithmetic sequence.

i.e. we are asked to find the value of A(n) when n=1 ,4 and 10

[tex]A(1)=-6+(1-1)(\dfrac{1}{5})\\\\i.e.\\\\A(1)=-6+0\\\\i.e.\\\\A(1)=-6[/tex]

[tex]A(4)=-6+(4-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(4)=-6+3\times \dfrac{1}{5}\\\\i.e.\\\\A(4)=-6+\dfrac{3}{5}\\\\i.e.\\\\A(4)=\dfrac{-6\times 5+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-30+3}{5}\\\\i.e.\\\\A(4)=\dfrac{-27}{5}[/tex]

[tex]A(10)=-6+(10-1)\times (\dfrac{1}{5})\\\\i.e.\\\\A(10)=-6+9\times \dfrac{1}{5}\\\\i.e.\\\\A(10)=-6+\dfrac{9}{5}\\\\i.e.\\\\A(10)=\dfrac{-6\times 5+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-30+9}{5}\\\\i.e.\\\\A(10)=\dfrac{-21}{5}[/tex]

the answer i got was x = - 9/2

hope this helps

The solution set appears at x ≥ 5 for (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

The symbol ∩ represents an intersection or common between them.

Given, (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).

( x ≥ 5) ∩ ( x ≥ 5).

So, x ≥ 5.

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There are 2,598,960 ways to choose 5 cards out of a 52-card deck.

To determine the number of ways to choose 5 cards out of a deck of 52 cards, we can use the concept of combinations. In this case, order doesn't matter, so we use the formula for combinations. The formula is:

C(n, r) = n! / (r!(n-r)!)

where n is the total number of items to choose from and r is the number of items to be chosen.

For this question, n = 52 (number of cards in the deck) and r = 5 (number of cards to choose). We can plug these values into the formula to calculate the number of ways:

C(52, 5) = 52! / (5!(52-5)!) = 2,598,960

So, there are 2,598,960 ways to choose 5 cards out of a 52-card deck.

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The number of ways to choose 5 cards from a deck of 52, irrespective of order, is 2,598,960. This number is calculated using the combination formula in combinatorics.

This question relates to the field of Mathematics known as combinatorics, specifically the concept of combinations. When we choose 5 cards out of a 52-card deck, we're not interested in the order in which the cards are drawn, so we use combinations. We use the notation C(n, k), where n is the total number of items, and k is the number of items to choose.

The formula for finding combinations is C(n, k) = n! / [k!(n-k)!]. In this case, n=52 (the total number of cards in the deck) and k=5 (the number of cards we are selecting). Plug these values into the formula to get C(52, 5) = 52! / [5!(52-5)!] = 52! / (5!47!) = 2,598,960

So, there are 2,598,960 ways to choose 5 cards out of a 52 card deck. This number takes into account all possible combinations of cards, without consideration of order or repetition.

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Answer:

a. 46.5 mph

b. 32.3 kph

Step-by-step explanation:

If the speed limit is 100 km/hour we and this equals 62 mile per hour we can determine how many kilometers is in miles and vice versa:

WE can do this as:

[tex]62/100=0.62[/tex]

Therefore the 0.62 miles per kilometer

a) For 75 kph we can use the conversion we determine to convert to miles per hour:

[tex]75*0.62=46.5[/tex]

It takes a speed limit of 46.5 mph for a 75 kph limit

b) For 20 mph we can use the conversion we determine to convert to kilometers per hour:

[tex]20/0.62=32.3[/tex]

It takes a speed limit of 32.3 kph for a 20 mph limit

Answer:

x=12

Step-by-step explanation:

if ab =58 find the value of x

The length of AB= 58

Given : AC= 3x-6

CB= 2x+4

[tex]AC + CB=AB[/tex]

Now replace the expressions

[tex]3x-6+2x+4=58[/tex]

now we solve for x, combine like terms

[tex]5x-2=58[/tex]

Add 2 on both sides

[tex]5x=60[/tex]

Divide both sides by 5

x=12

Table 4 represents the linear function that has slope of 5 and a y-intercept of 20.

Further explanation:

The linear equation with slope [tex]m[/tex] and intercept [tex]c[/tex] is given as follows.

[tex]\boxed{y = mx + c}[/tex]

Given:

The y-intercept is [tex]\left( { - 9, - 3} \right).[/tex]

The slope of the linear function is [tex]- 6.[/tex]

Explanation:

The linear function can be expressed as follows,

[tex]y = 5x + 20[/tex]

In table 1,

Substitute [tex]-60[/tex] for [tex]x[/tex] and 8 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function.

[tex]\begin{aligned}8&= 5\left({ - 60} \right) + 20\\8&= - 300 + 20\\8&= - 280\\\end{aligned}[/tex]

Table 1 is not correct.

In table 2,

Substitute 20 for [tex]x[/tex] and [tex]0[/tex] for [tex]y[/tex] in linear function to check whether the point satisfy the linear function

[tex]\begin{aligned}0&= 5\left( {20} \right) + 20\\0&= 100 + 20\\&0\ne120\\\end{aligned}[/tex]

Table 2 is not correct.

In table 3,

Substitute [tex]-20[/tex] for [tex]x[/tex] and 0 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function

[tex]\begin{aligned}- 20&= 5\left( 0 \right) + 20\\- 20 &\ne 20\\\end{aligned}[/tex]

Table 3 is not correct.

In table 4,

Substitute [tex]-4[/tex] for [tex]x[/tex] and 0 for [tex]y[/tex] in linear function to check whether the point satisfy the linear function

[tex]\begin{aligned}0&= 5\left( { - 4} \right) + 20\\0&= - 20 + 20\\0&= 0\\\end{aligned}[/tex]

Table 4 is correct.

Table 4 represents the linear function that has slope of 5 and a y-intercept of 20.

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: linear function,  numbers, slope 5, y-intercept of 20, slope intercept, inequality, equation, linear inequality, shaded region, y-intercept, graph, representation.

You can expect to have approximately $447 in your account after 1.5 years of continuously compounded interest on your $400 investment.

How much will you have in the account after 1.5 years?

To find out how much you'll have in your account after 1.5 years, we can follow these steps:

1. Formula: Use the formula for continuous compounding:

[tex]Final\ amount = Initial\ amount * (1 + annual\ interest\ rate)^{time}\[/tex]

2. Plug in the values: We know:

Initial amount = $400

Annual interest rate = 7.6% (remember to convert it to a decimal by dividing by 100, so 7.6% becomes 0.076)

Time = 1.5 years

3. Calculation: Substitute the values and calculate:

Final amount = $400 * (1 + 0.076)^{1.5}

[tex]Final\ amount = $400 * (1 + 0.076)^{1.5} = 446.5[/tex]

4. Round the answer: Round the final amount to the nearest dollar:

Final amount  = 447