Tim's holds a fishing line at the surface of a lake, and it sinks 10 feet below the surface of the water. Tim then pulls the lure up 4 feet.which of the following statements about this situation are true?select all that apply

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

C. \( (x +2) ^2 +(y+8)^2 =10 \)

Step-by-step explanation:

Center of the circle (h, k) = (-2, - 8)

Radius \( r=\sqrt {10}\)

Equation of circle in center radius form is given as:

\( (x - h) ^2 +(y-k) ^2 =r^2 \)

Plugging the values of h, k and r in the above equation, we find:

\( [x - (- 2)] ^2 +[y-(-8) ]^2 =(\sqrt {10})^2 \)

\( (x +2) ^2 +(y+8)^2 =10 \)

We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Using the triangle inequality theorem, the possible values for the third side of the triangle are: 5 < x < 35.

The Triangle Inequality Theorem asserts that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Stated differently, the difference between the lengths of any two sides must be less than the length of the third side.

Thus, if you have the lengths of two sides of a triangle, as 20 and 15, we have:

20 - 15 < x < 20 + 15

5 < x < 35

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Answer:

4+12+8 = 24

Step-by-step explanation:

4+8=12 + 12 = 24 :)

Answer:

The margin of error M.O.E = 2.5%

Step-by-step explanation:

Given that;

The sample size = 1500

The sample proportion \(\hat p\) = 0.60

Confidencce interval = 0.95

The level of significance ∝ = 1 - C.I

= 1 - 0.95

= 0.05

The critical value:

\(Z_{\alpha/2} = Z_{0.05/2} \\ \\ Z_{0.025} = 1.96\) (From the z tables)

The margin of error is calculated by using the formula:

\(M.O.E = Z_{\alpha/2} \times \sqrt{\dfrac{\hat p(1 -\hat p)}{n}}\)

\(M.O.E = 1.96 \times \sqrt{\dfrac{\hat 0.60(1 -0.60)}{1500}}\)

\(M.O.E = 1.96 \times \sqrt{\dfrac{0.24}{1500}}\)

\(M.O.E = 1.96 \times \sqrt{1.6 \times 10^{-4}}\)

M.O.E = 0.02479

M.O.E ≅ 0.025

The margin of error M.O.E = 2.5%

Answer:

\(1 + 1 = 2 \\ 2 + 2 = 5\)

Step-by-step explanation:

tae plas tae is 1

Answer:

Mel : 50 and 35

Victor : 60 , 4 and 50

Step-by-step explanation:

Edge 2021

Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Answer:

44 m2

Step-by-step explanation:

The area of the rhombus can be divided into 4 equal triangles.

The area of one triangle is A=bh/2

so:

A = 5.5*2

A = 11 squared m

Since there are four (4) triangles in the rhombus we just need to multiply 11 by 4 so:

A = 11 * 4

A = 44 squared m

The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))

To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.

The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.

The total number of possible arrangements is given by the factorial of the total number of letters:

Total arrangements = 10!

However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:

Total arrangements = 10! / (2!)

To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.

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Answer:

  total deposits: $35,100

Step-by-step explanation:

You have the value of an annuity earning 5% with payments of $65 a month for 45 years as $131,718.42. You want to know the total value of payments.

12 payments per year of $65 for 45 years will have a total value of ...

  12·65·45 = 35100

Total deposits will be $35,100.

Hi there! :)

2>-10

This statement is true, because positive numbers are always greater than negative ones.

Therefore, this statement is true.

Hope this helps you.

Please let me know if you have any questions.

~GracefulGirlie

Good luck on your assignment.

The equivalent expression is 14x + 38z = 0.

We have to note that an expression has to do with a mathematical statement. According to the distributive property, we can be able to open up the brackets over the values that we have in the question.

As such we would have;

21x + 39z = (7x + z)

Removing the brackets;

21x + 39z = 7x + z

Then we collect the like terms;

21x - 7x = z - 39z

14x = -38z

14x + 38z = 0

This is the expression that is equivalent to the one given above.

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Answer:

64 cm^2

Step-by-step explanation:

SA = s^2 + 2sl

= 4^2 + 2(4)(6)

= 64 cm^2

Answer:

7 1/8

Step-by-step explanation:

Hope this helps

Answer: 7.1875

Step-by-step explanation:

First you would multiply the two numbers which are 1 1/4 and 5 3/4 then you would simplify that because you would get 115/16 then when you simplify you get 7.1875

Answer:

\( {( \sqrt{ {x}^{ - 3} }) }^{5} = ({( {x}^{ - 3}) }^{ \frac{1}{2} } ) ^{5} \\ \\ = {x}^{ - 3 \times \frac{1}{2} \times 5} = {x}^{ - \frac{15}{2} } = \frac{1}{ {x}^{ \frac{15}{2} } } \)

Or ;

\( {( \sqrt{ {x}^{ - 3} } )}^{5} = {( \sqrt{ \frac{1}{ {x}^{3} }} })^{5} = ( { \frac{ \sqrt{1} }{ \sqrt{ {x}^{3} } } })^{5} \\ \\ = ( { \frac{1}{ \sqrt{x} \sqrt{ {x}^{2} } } })^{5} = ({ \frac{1}{ x\sqrt{x} }})^{5} \\ \\ = ( \frac{ {(1)}^{5} }{ {x}^{5} ( \sqrt{x} )^{5} } ) = \frac{1}{ {x}^{5} \times {x}^{ \frac{1}{2} \times 5 } } \\ \\ = \frac{1}{ {x}^{5} \times {x}^{ \frac{5}{2} } } = \frac{1}{ {x}^{5} \sqrt{ {x}^{5} } } \\ \\ = \frac{1}{ {x}^{5} \sqrt{ {x}^{4} {x}^{1} } } = \frac{1}{ {x}^{5} \sqrt{x} \sqrt{( { {x}^{2} })^{2} } } \\ \\ = \frac{1}{ {x}^{5} {x}^{2} \sqrt{x} } = \frac{1}{ {x}^{7} \sqrt{x} } = \frac{ \sqrt{x} }{ {x}^{8} } \)

The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.

A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.

The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.

To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:

Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:

-3 | 1 8 9 -18 0

Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.

-3 | 1 8 9 -18 0
  -3

Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.

-3 | 1 8 9 -18 0
  -3
 -3

Step 4: Add the result to the 8, and place the new result in the next row.

-3 | 1 8 9 -18 0
  -3
 -3
  5

Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.

-3 | 1 8 9 -18 0
  -3
 -3
  5
 -15
-15
 18

Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0

Answer: 7: 29 stickers for each friend

8: 412 seats in each section

Step-by-step explanation:

We will have to divide 145 (stickers) by 5 (friends) to get 29

We will have to divide 2472 by 6 to get 412

7.) 145 ÷ 5 = 29 → Each friend will get 29 stickers

8.) 2,472 ÷ 6 = 412 → There are 412 seats in each second.

I divided for both problems using the long division method and multiplied which is the inverse operation, to check my work.

Therefore, the longest length of pencil that John can hide in the pencil holder is approximately 127.32 cm (rounded to two decimal places).

Given that John has a 100 cm³ pencil holder, the longest length of pencil he can hide in the pencil holder can be found by using the formula for the volume of a cylinder which is given by: V = πr²h where r is the radius of the cylinder and h is the height of the cylinder.The volume of a cylinder can also be expressed as V = lwh where l is the length of the cylinder, w is the width of the cylinder and h is the height of the cylinder.

If we assume that the pencil is cylindrical in shape, then its volume can be given by V = πr²l where r is the radius of the pencil and l is the length of the pencil.Since the volume of the pencil holder is given to be 100 cm³, then we have:100 = πr²h (Equation 1)

Now, we need to find the value of l that can fit inside the pencil holder. We can use the formula for the volume of the pencil to do this as follows:

V = πr²lLet V = 100 cm³ and

r = 0.5 cm

(since the pencil holder is cylindrical in shape, we can assume that it has a radius of 0.5 cm)Then, we have:100 = π(0.5)²lSolving for l, we get:

l = 100 / (π(0.5)²)

l = 100 / (0.7854)l ≈ 127.32 cm

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Answer:

p=20°

Step-by-step explanation:

(7p+7)°+33°=180°

7p°+7°+33°=180°

Step 1: Simplify both sides of the equation.

7p°+7°+33°=180°

(7p)°+(7+33)°=180°(Combine Like Terms)

7p°+40°=180°

7p°+40°=180°

Step 2: Subtract 40 from both sides.

7p°+40°−40°=180°−40°

7p°=140°

Step 3: Divide both sides by 7.

7p°/7°=140°/7°

p=20°

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=20\\ \theta =65 \end{cases}\implies a=\cfrac{(65)\pi (20)^2}{360} \\\\\\ A=\cfrac{650\pi }{9}\implies A\approx 226.89\)

Answer:

A. the angular speed is 3771.4 rad/min

b. 5921 rpms

Step-by-step explanation: I just got this same question right on a test.

Answer:

I had gotten 26ft to the power of 2 but I'm not fully sure.

Answer:

Step-by-step explanation: formula is (y2 - y1) / (x2 - x1)

so in this case it is: (4-(-4) / (-8 - 2) -> 8/-10 -> -4/5(final solution)

The rate of change of the function h(x) = 2x on the interval 2 ≤ x ≤ 4 is 6.

Step-by-step explanation:

A ratio is a simple way to express the relationship between two quantities (numbers).

A ratio can also show how much greater a quantity is to another.

Express the ratio as 300:250.

This ratio can be simplified by dividing each quantity by 50.

6:5

Given:

Two cards are drawn from a standard deck of 52 cards without replacement.

To find:

The probability that both cards selected for black.

Solution:

We know that,

Total number of cards = 52

Total number of red cards = 26

Total number of black cards = 26

\(\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

Probability of selecting first black card is

\(\text{Probability}=\dfrac{26}{52}\)

\(\text{Probability}=\dfrac{1}{2}\)

Number of remaining total cards = 52-1 = 51

Number of remaining black cards = 26-1 = 25

Probability of selecting second black card is

\(\text{Probability}=\dfrac{25}{51}\)

So, the probability that both cards selected for black is

\(\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}\)

\(\text{Probability}=\dfrac{25}{102}\)

Therefore, the required probability is \(\dfrac{25}{102}\).

Answer: The side of the playground is around 10 meters long

Step-by-step explanation:

use the diagonal as the hypotenuse of a right triangle, where the sides of the square form the legs of said triangle.

Usually

\(a^{2} +b^{2} =c^{2}\)

since we know a and b are the same length (sides of a square are congruent) we would have

\(a^{2} +a^{2} =c^{2} \\2a^{2} =c^{2}\)

We know that c is 14 so

\(2a^{2} =14^{2} \\2a^{2} =196\\a^{2} =98\\a=\sqrt{98} \\a= 9.999\)

Given statement solution is :-  Box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

To construct a box-and-whisker plot using the given data, you first need to find the minimum, maximum, median, and quartiles. Here are the steps to create the box-and-whisker plot for the given data set:

Sort the data in ascending order:

12, 12, 13, 14, 14, 15, 15, 15, 16, 16, 17, 18, 20

Find the median (middle value) of the data set. Since the data set has an odd number of values, the median will be the middle value:

Median = 15

Find the lower quartile (Q1), which is the median of the lower half of the data set.

Counting from the start, the lower half of the data set is:

12, 12, 13, 14, 14

Q1 = 13

Find the upper quartile (Q3), which is the median of the upper half of the data set.

Counting from the end, the upper half of the data set is:

17, 18, 20

Q3 = 18

Find the minimum and maximum values in the data set:

Minimum = 12

Maximum = 20

Now that we have the necessary values, we can construct the box-and-whisker plot:

lua

Copy code

       |                 |

 12  |      -------------|    

 13  |                 |

 14  |              ----  

 15  |           -------

 16  |      -------------|    

 17  |                 |

 18  |              ----  

 20  |                 |

       |_________________|

In this box-and-whisker plot, the box represents the interquartile range (IQR), which is the range between Q1 and Q3 (13 to 18). The line inside the box represents the median (15). The whiskers (lines extending from the box) represent the minimum and maximum values (12 and 20).

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Answer:

See explanation

Step-by-step explanation:

It appears that the second graph is better since it seems to be rather consistent. The graph of the first one seems out of place. Therefore it seems to be confusing and could be misleading.