Find the missing side lengths. Show work.
x=______ y=_____

From the conversation it can be inferred that Paul's approach to getting on the horse is methodical (option c).

A methodical attitude or behavior refers to the preference of people to use an organized method and sequences to perform an activity correctly.

According to the above, it can be inferred that Paul behaves in a methodical manner because he prefers to relate to the horse slowly and in a controlled manner before proceeding to mount it.

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The result of the evaluation of the equation given in the task content is; x =-2.

It follows from the task content that the equation given whose solution is to be determined is;

3[-x + (2 x +1)]=x-1

The equation can be solved as follows;

-3x + 6x +3 = x-1

2x = -4

x = -2

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Answer: 1/5

Step-by-step explanation: You just subtract 4/5 from 1, or 5/5. And BOOM! you get 1/5.

The difference between the tallest and shortest heights is 0.787 × 10

From tallest to shortest:

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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Answer:

Step-by-step explanation:

Find the roots of x^2-25=0 by solving for x.

Add 25 to both sides

x^2=25

Square root both sides

x=-5

x=5

Answer:

x=5;x=-5

Step-by-step explanation:

It was right for me

Answer:

circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

[tex] \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}[/tex]

[tex] \large {\boxed{ \tt{p = 2 \times \pi \times r}}}[/tex]

If the radius is 2 inches and

Use 3,14 for π So:

[tex] \tt{ {A = \pi \times {r}^{2} }}[/tex]

[tex] \tt{A = (3.14 \times 2 \times 2)} [/tex]

[tex] \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}[/tex]

Answer:

$96

Step-by-step explanation:

Answer:

x ≤ 2

Step-by-step explanation:

We are given the inequality:

[tex]\displaystyle{2x-3 \leq \dfrac{x}{2}}[/tex]

First, get rid of the denominator by multiplying both sides by 2:

[tex]\displaystyle{2x\cdot 2-3\cdot 2 \leq \dfrac{x}{2}\cdot 2}\\\\\displaystyle{4x-6 \leq x}[/tex]

Add both sides by 6 then subtract both sides by x:

[tex]\displaystyle{4x-6+6 \leq x+6}\\\\\displaystyle{4x \leq x+6}\\\\\displaystyle{4x-x \leq x+6-x}\\\\\displaystyle{4x-x \leq 6}\\\\\displaystyle{3x \leq 6}[/tex]

Then divide both sides by 3:

[tex]\displaystyle{\dfrac{3x}{3} \leq \dfrac{6}{3}}\\\\\displaystyle{x \leq 2}[/tex]

Therefore, the answer is x ≤ 2

Answer: [tex]x \leq 2[/tex]

Step-by-step explanation: Given [tex]2x - 3 \leq \frac{x}{2}[/tex], we multiply 2 by both sides to cancel out the 2 in the denominator (multiplying by a number in a fraction turns it into 1, and since the denominator is one, it is the same as saying the number [or variable] on the numerator by itself.)

We then get [tex]4x - 6 \leq x[/tex].

Adding 6 to both sides, we get [tex]4x \leq x + 6[/tex].

Subtracting x from both sides, we get [tex]3x \leq 6[/tex]

Dividing by 3 from both sides, we get [tex]x \leq 2[/tex]

Hope this helped!

The Number of teams is  mathematically given as

N= 30100

Generally, the equation for Number of teams is  mathematically given as

X items are selected from n items by [tex]^nC_x[/tex] ways

[tex]^nC_x = \frac{n!}{ [ (n-x)! * x! ]}[/tex]

Number of teams

N= n(1 child and 3 adults) + n(2 child and 2 adults) + n(3 child and 1 adults) + n(4 child)

N= 16C1 * 15C3 + 16C2 * 15C2 + 16C3 * 15C1 + 16C4 * 15C0

N= 16 * 455 + 120 * 105 + 560 * 15 + 1820

N= 30100

In conclusion, the Number of teams

N= 30100

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Answer: Not similar

Step-by-step explanation:

The polygons are not similar because the ratio of the corresponding sides is not equal (30/18 is not equal to 18/8)

Monthly interest payment is $100.

According to the statement

balance in account = $100

APR = 12%

we use the formula Balance formula to solve this problem.

So, BALANCE * [APR / 12 month] to find monthly interest payment

Here balance is the starting amount in the bank account

And APR is the type of interest rate applied on the amount

And 12 month is the time period for which APR is applicable.

So, substitute the values in it then

Monthly interest payment = 100 * [12/12]

After solving the equation become

Monthly interest payment = 100*1

Monthly interest payment = 100$

So, Monthly interest payment is $100.

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440 repeat 11 more times.

400+(400*.1)=440 repeat 11 more times. Remember to use a new value each time.

Vacations can get expensive fast. The average cost per person for a week-long vacation is about $1,200 annually. So, if you've got a family of five, you'll need to sock away at least $6,000 for transportation, hotels, meals, and amusement parks.

Financial experts suggest that the average family vacation costs between 5-10% of your total income. If your family makes $40,000 per year then experts say your yearly family vacation budget should average between $2,000-$4000.

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The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].

First, we need to determine the value of the vector u by subtracting two vectors whose initial points are at the origin:

[tex]\vec u = (19\,\hat{i} - 8\,\hat{j}) - (21\,\hat{i} + 12\,\hat{j})[/tex]

[tex]\vec u = - 2\,\hat{i} - 20\,\hat{j}[/tex]     (1)

According to the statement, vector v is antiparallel to vector u and its magnitude is five times as the magnitude of vector v, which means that (1) must be multiplied by two scalars:

[tex]\vec v = - 1 \,\cdot \, 5\cdot \vec u[/tex]      (2)

Please notice that antiparallelism is represented by the scalar - 1, whereas the dilation is represented by the scalar 5.

[tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex]

The correct form of vector v expressed as a linear combination of the unit vectors i and j is [tex]\vec v = 10\,\hat{i} + 100\,\hat{j}[/tex].

The statement presents typing mistakes, correct form is shown below:

Vector u has initial points at (21, 12) and its terminal point at (19, - 8). Vector v has a direction opposite that of u, whose magnitud is five times the magnitud of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?

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$1799.10

Each year, the amount of money in the account is increased by 8%. This is the same as multiplying by 1.08 each year.

For 10 years, you multiply the original $100,000 by 1.08 a total of 10 times.

This tends to be simplified to:

[tex]100,000 * 1.08^{10}[/tex]

This gives $215892.4997.

This is paid back over 10 years, which is 10 x 12 months, or 120 months.

Divide the $215892.4997 by 120 to get the monthly payment of:

$1799.10 (round to 2 decimal places as it is a currency)

Answer:

1. Becky's rate of sales is 9 cups per hour

2. Mayisha's rate of sales is 10 cups per hour

3. Becky is selling 1 fewer cups per hour than Mayisha

4. Becky started with 2 fewer cups than Mayisha

Step-by-step explanation:

1. 30-12=18 18/2=9

2. 31-21=10 21-11=10

3. 10-9=1

4. 30+9=39 31+10=41 41-39=2

Answer:

Becky's rate of sales is [tex]\boxed{\sf 9}[/tex] cups per hour.

Mayisha's rate of sales is [tex]\boxed{\sf 10}[/tex] cups per hour.

Becky is selling [tex]\boxed{\sf 1\: fewer}[/tex] cup(s) per hour than Mayisha.

Becky started with [tex]\boxed{\sf 2}[/tex] fewer cups than Mayisha.

Step-by-step explanation:

Mayisha

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 31 & 21 & 11\\\cline{1-4} \end{array}[/tex]

Becky

[tex]\begin{array}{|c|c|c|c|}\cline{1-4} \sf Hours\:(x) & 1 & 2 & 3\\\cline{1-4} \sf Cups\: {left}\:(y) & 30 & & 12\\\cline{1-4} \end{array}[/tex]

Selling at a steady rate.

To calculate the rate of sales, use the rate of change formula:

[tex]\sf Rate\:of\:change = \dfrac{change\:in\:y}{change\:in\:x}[/tex]

Therefore:

[tex]\textsf{Becky's rate of sales}=\dfrac{12-30}{3-1}=-9[/tex]

Therefore, as the number of cups reduces by 9 each hour, Becky's rate of sales is 9 cups per hour.

[tex]\textsf{Mayisha's rate of sales}=\dfrac{11-31}{3-1}=-10[/tex]

Therefore, as the number of cups reduces by 10 each hour, Mayisha's rate of sales is 10 cups per hour.

As 9 is one less than 10, Becky is selling 1 fewer cup(s) per hour than Mayisha.

As Becky had 30 cups left after 1 hour, and her rate of sales is 9 cups, then she started with 30 + 9 = 39 cups.

As Mayisha had 31 cups left after 1 hour, and her rate of sales is 10 cups, then she started with 31 + 10 = 41 cups.

As 39 is 2 less than 41, Becky started with 2 fewer cups than Mayisha.

i) The number of students that come to school by motorcycle only = 8

ii) The number of students that did not take all the three types of transportation = 9

iii) Number of students that did not come to school by car = 28

The total number of students = 40

The number of students that come to school by car alone = 9

The number of students that come to school by motorcycle only = 8

The number of students that come to school by car only = 11

The number of students that come to school by both car and motorcycle = 3

Number of students that did not take all the three types of transportation = 40 - (9 + 8 + 3 + 11)

= 40 - 31

Number of students that did not take all the three types of transportation = 9

Total students that come to school by car = 9+3 = 12

The total number of students that did not come to school by car = 40 - 12 = 28

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Answer:

4. b) an angle

5. b) the angles of a triangle

6. b) opposite, hypotenuse and adjacent

Step-by-step explanation:

4. To find sine, cosine, tangent, you use the sin, cos, tan key of the calculator.

If you are given the value of the sin, cos, tan, and you are looking for the angle, then you use the second function of the calculator.

Answer: b) angle

5. angles of a triangle

6. The sides that form the right angle are the legs. In trig, there is an angle of interest, so to distinguish between the legs, one leg is called the adjacent leg, and the other leg is called the opposite leg. The side opposite the right angle is the hypotenuse.

Answer: opposite, hypotenuse and adjacent

Answer:

The answer that you have highlighted is correct.

Step-by-step explanation:

When you are dividing, you divide the exponents

-10 - (-4)

-10 + 4

-6

The maximum height of the ball that is displayed by the graph is: D. 108 feet.

A graph is a statistical diagram that displays the relation between two variables. One of the variables is plotted on the x-axis (horizontal axis) against the other variable on the y-axis (vertical axis).

The variable on the x-axis (horizontal axis) is the input, while the variable on the y-axis (vertical axis) is the output.

Considering the given graph in the image above, we have the following variables:

On the x-axis (horizontal axis): time which is the input

On the y-axis (vertical axis): height of the ball which is the output.

Thus, the peak of the line represents the maximum height the ball reaches. The maximum height which is the peak is approximately 109 feet.

Therefore, the maximum height is: D. 109 feet.

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Answer:

109 feet

Step-by-step explanation:

just took the lesson

In the given figure of circle, if RT = 90, SU = 25, and SO is perpendicular to RT, the length of the radius RO is 53.

In the given figure,

RT = 90

SU = 25

SO is perpendicular to RT.

Here, SO and RO are the radii of the circle and RT is a chord.

The length of the chord, RT is given as,

RT = 2 √(r² - d²)

Here, r is the radius and d is the distance of the chord RT from the center O.

Radius, r = RO and distance, d = OU

∴ RT = 2 √(RO² - OU²)

Substituting RT = 90 in the above equation, we get,

90 = 2 √[(RO)² - (OU)²]

√[RO)² - (OU)²]  = 45

(RO)² - (OU)² = 45²

(RO)² - (OU)² = 2025 ........... (1)

Now, OU = SO - SU   [From the figure]

⇒ OU = SO - 25

Substituting OU = SO - 25 in equation (1), we obtain,

(RO)² - (SO - 25)² = 2025

(RO)²- [(SO)² + (25)² - 2(SO)(25)] = 2025    [ ∵ (a-b)² = a²+b²-2ab ]

(RO)²- (SO)² - (25)² + 50(SO) = 2025 ........... (2)

Since, RO and SO both are the radii of the same circle, we have,

SO = RO

Thus, we can write equation (2), as follows,

⇒ (RO)² - (RO)² - (25)² + 50(RO) = 2025

⇒ -625 + 50RO = 2025

⇒ 50RO = 2025 + 625

⇒ RO = 2650/50

⇒ RO = 53

Hence, the length of the radius RO of the given circle is 53.

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The probability that all three players obtain an odd sum is 3/14.

The probability is the ratio of possible distributions to the total distributions.

I.e.,

Probability = (possible distributions)/(total distributions)

Given that,

There are nine tiles - 1, 2, 3,...9, respectively.

A player must have an odd number of odd tiles to get an odd sum. That means he can either have three odd tiles, or two even tiles and an odd tile.

In the given nine tiles the number of odd tiles = 5 and the number of even tiles = 4.

The only possibility is that one player gets 3 odd tiles and the other two players get 2 even tiles and 1 odd tile.

So,

One player can be selected in [tex]^3C_1[/tex]  ways.

The 3 odd tiles out of 5 can be selected in [tex]^5C_3[/tex] ways.

The remaining 2 odd tiles can be selected and distributed in [tex]^2C_1[/tex] ways.

The remaining 4 even tiles can be equally distributed in [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex] ways.

So, the possible distributions = [tex]^3C_1[/tex] × [tex]^5C_3[/tex] × [tex]^2C_1[/tex] × [tex]\frac{4 ! \cdot 2 !}{(2 !)^{2} \cdot 2 !}[/tex]

⇒ 3 × 10 × 2 × 6 = 360

To find the total distributions,

The first player needs 3 tiles from the 9 tiles in [tex]^9C3=84[/tex] ways

The second player needs 3 tiles from the remaining 6 tiles in [tex]^6C_3=20[/tex] ways

The third player takes the remaining tiles in 1 way.

So, the total distributions = 84 × 20 × 1 = 1680

Therefore, the required probability = (possible distributions)/(total distributions)

⇒ Probability = 360/1680 = 3/14.

So, the required probability for the three players to obtain an odd sum is 3/14.

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[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4x}{y}\right)^{2} \end{gathered}$}[/tex]

To raise 4x/y to a power, raise the numerator and denominator to the power, and then divide.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{(4x)^{2} }{y^{2} } \end{gathered}$}[/tex]

Expand (4x)².

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{4^{2} x^{2} }{y^{2} } \end{gathered}$}[/tex]

Calculates 4 to the power of 2 and gets 16.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{16x^{2} }{y^{2} } \end{gathered}$} }[/tex]

The coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

The functions are given as:

y = x + 1

2x + y = 4

x + y = 5

Next, we plot the graph of the lines (see attachment)

From the attached graph, the coordinates of the vertices are (-1, 6), (1, 2) and (2, 3)

Rewrite the equations in slope intercept form

y = x + 1 ⇒ Slope = 1

y = -2x + 4 ⇒ Slope = -2

y = -x + 5 ⇒ Slope = -1

The equations y = x + 1 and y = -x + 5 have their slopes to be opposite reciprocals

This means that the lines are perpendicular (they form a right angle)

Hence, the triangle is a right triangle

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The value of p(cc and tc) is 0.1173

The distribution of the replies is 0.12, as shown by the two-way table.

We've done that.

520 randomly chosen individuals from the teen, young adult, and adult age groups were asked about their preferred musical genres by the researcher.

The distribution of the answers is shown in the two-way table.

There are 61 teenagers in the country.

seeing as how this is only one of 520,

The probability formula?

P(E) = (Number of favorable outcomes) = Probability of an Event (Sample space).

61/520=0.1173

We calculate 0.1173 by dividing 61 by 520 and rounding to the next hundredth to obtain 0.12.

Thus the value of p(cc and tc) is 0.1173.

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Answer:

x = 5, y = sqrt6, z = 3

Step-by-step explanation:

[tex]\frac{10}{\sqrt{6} } \\\\\frac{(10)(\sqrt{6} )}{(\sqrt{6} )(\sqrt{6}) } \\\\\frac{10\sqrt{6} }{6} \\\\or\\\\\frac{5\sqrt{6} }{3}[/tex]

❄ Hi there,

let us revise the way we rationalize the denominator before we get down to the actual process.

__________

Suppose you had a problem, and you did all the steps, and you arrived at the following answer: [tex]\sf{\dfrac{10}{\sqrt6}}[/tex].

Well, this answer is not in its simplest form, because it has an irrational number in its denominator.

So what we do is we get rid of that irrational number in the denominator  by multiplying the fraction's top & bottom by [tex]\sqrt6[/tex]:

[tex]\sf{\dfrac{10\sqrt6}{\sqrt6\times \sqrt6}}[/tex]

Now we simplify

[tex]\sf{\dfrac{10\sqrt6}{6}}[/tex]

Reduce

[tex]\sf{\dfrac{5\sqrt6}{3}}[/tex]

- - - - -  - - -

Answer:

B. Every integer is also an irrational number.

Answer:

Length= 50

Width=17

Step-by-step explanation:

length= n+8

Since n= 42, Just plug it in. So it would be 42+8 which is 50 for the length

Widith: 1/2n-4

basically since N is given for 42, you do 1/2 multipied by 42 which is 21.

Since you also have to subtract 4 inches it would be 17 for the length

The slope of given data is a -3.

According to the statement

we have given a some data and we have to find the slope of the data.

So, data given is:

x, has the entries, negative 2, negative 1, 0, 1, 2.

y, has the entries, negative 2, 1, 4, 7, 10.

and we have to find the slope of the data

So, we know that it is a data represent in the graph then

We know that a there is a graphical representation of data.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

And when we observe this data then we see that the there is some increase the y axis value as compare to the x axis values.

So,

For each unit of run in the x-values, there is an increase of 3 in the y-values. The slope is rising over Run so 3/1 = 3

So, The slope of given data is a -3.

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Answer: the answer is a -3

Step-by-step explanation:

The lower bound of the 90% confidence interval for the gift basket's average shipping weight is 55.605.

Given mean weight of 57 ounces ,sample size 70 ,confidence level 90% and standard deviation of 7.1 ounces.

We have to find the lower bound of the confidence interval for the gift's basket's avrage shipping weight.

We can easily find the confidence interval and its lower bound through theformula of margin of error.

Margin of error is the difference between real values and calculated values.

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

where z is the critical value of confidence level

σ is standard deviation,

n is the sample size

We have to first find the z value for 90% confidence level which is 1.645.

Margin of error=1.645*7.1/[tex]\sqrt{70}[/tex]

=11.6795/8.3666

=1.395

Lower bound of the confidence interval = Mean - margin of error

=57-1.395

=55.605.

Hence the lower bound of the confidence interval for the gift basket's average shipping weight is 55.605.

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