A right triangle has side lengths 8, 15, and 17 as shown below.
Use these lengths to find sin.X, tanX, and cos.X.

Ricky had 176 cookies initially

Let Ricky has x number of cookies

Cookies left after he ate 1/8 of his cookies and additional 14 cookies:

x - (1/8x + 14)

Cookies left after he ate 3/10 of the remaining cookies and an additional 24 cookies on Saturday:

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24)

Cookies left after he ate 40 more cookies on Sunday

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24) - 40 ------(1)

Cookies left with him at the end = 34

Therefore, equating equation (1) with 34

(7/10)((7x/8) - 14) - 64 = 34

x = 176

Thus Ricky had 176 cookies intially

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10 m/s can be expressed as 36km/h.

Here, we are given an expression for speed, that is: 10 meter per second.

Now, as per the rules of mathematics,

1 kilometer = 1000 meters

⇒ 1 meter = 1/1000 kilometers

or 1 meter = 0.001 kilometers

and also, 1 hour = 60 mins

and 1 min = 60 seconds

⇒ 60 mins = 60 × 60 seconds

= 3600 seconds

Thus, 1 hour = 60 mins = 3600 seconds

⇒ 1 second = 1/3600 hours

Now, we need to convert meter per second into kilometer per hour,

1 meter/ 1 second =  [tex]\frac{0.001}{\frac{1}{3600} }[/tex]

= (0.001 × 3600)/ 1

= 3.6

This 1 meter per second = 3.6 kilometer per hour

⇒ 10 meter per second = 3.6 × 10 = 36 kilometers per hour

Thus, 10 m/s is 36km/h.

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Answer:

43

Step-by-step explanation:

The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.

Therefore, the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.

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Answer:

Step-by-step explanation:

The angles lie on a straight line summing to total 180 degrees.

Form an equation:

m∠1 + m∠2 = 180

2x + x + 72 = 180

and solve:

3x + 72 = 180

3x = 180 - 72

3x = 108

x = 36

Answer:

see below

Step-by-step explanation:

We are here given a straight line which is splitted into two parts by a line , such that it makes two angles.

Also we know that the angle measure of a straight line is 180° . Therefore; here the sum of angles 1 and 2 will be 180° .

So that,

==> angle 1 + angle 2 = 180°

==> 2x + x + 72° = 180°

==> 3x = 180° - 72°

==> 3x = 108°

==> x = 108°/3

==> x = 36° .

The equation which we used to solve the problem is ,

==> Equation = 2x + x + 72° = 180°

For finding the individual angels substitute the value of x into their expressions , as ;

==> angle 1 = 2x = 2(36°) = 72°

==> angle 3 = x + 72° = 36° + 72° = 108° .

And we are done!

Answer:

Piecewise

Step-by-step explanation:

It is basically made up of 2 linear functions

Answer :                                                                                                              500,000                                                                                                                       450,000                                                                                                                        453,000                                                                                                                                       452,900                                                                                                                                         452,910                                                                                                                                                                                                                                                                                step-by-step explanation:

look to the right one digit of the place they are asking to round . if it is either greater than or equal to5, then you round up the place they want. if it is not, then it says the same. then all he number to right of it becomes 0s.

The number can be -3, -2, -1, 0 ,1

Here, we are given that twice a number is increased by three and the result is between negative three and seven.

Let the number be x

Twice of the number = 2x

Four more than twice the number = 2x + 4

This number is between -3, 7

⇒ -3 < 2x +4 < 7

subtracting 4 from both sides we get

-3 -4 < 2x < 7 - 4

-7 < 2x < 3

Dividing both sides by 2 we get

-7/2 < x < 3/2

- 3.5 < x < 1.5

Thus the original number lies between -3.5 and 1.5

This means that it can take 5 values-

-3, -2, -1, 0 ,1

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Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form: 10√21 where t = 10 and u =21

our ordered pair is ( 2 , 1/2).

What is linear equations in two variables?

Let's first move the y's to the left side in the first equation.

4x - y  = 3y + 7

4x - 4y = 7

Dividing both sides by 4,

x - y  = 7/4

Our other equation is

x + 8y = 4

Subtracting the first equation from the second, we get

 9y = 9/4

   y = 1/4

We plug this into one of the equations

  x + 2 = 4

   x =  2

So our ordered pair is ( 2 , 1/2)

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Answer: -15x+30

Step-by-step explanation:

-3(5x-10)=

-3*5x-10(-3)=

-15x-(-30)=-15x+30

Answer:

-15x-30

Step-by-step explanation:

Just multiply -3 by 5 in 5x and get -15 and then put x back with -15. thhen multiply -3 by 10 and get -30

Answer:

(2/3)^4 = 2^4/3^4

(2/3)^1 = 2/3

(-3/4)^0 = 1

(-0.4)^8/(-0.4)^4 = (-0.4)^4

Step-by-step explanation:

(2/3)^4 = 2^4/3^4

(2/3)^1 = 2/3

(-3/4)^0 = 1

(-0.4)^8/(-0.4)^4 = (-0.4)^4

a. The formula solved for t is t = I/Pr

b. The value of t in the table is 3 years

From the question, we are to solve for t in the given formula

The given formula is the formula for simple interest

I = Prt

To solve for t, we will divide both sides of the equation by Pr

That is,

I/Pr = Prt/Pr

I/Pr = t

∴ t = I/Pr

The formula solved for t is t = I/Pr

b. We are to find the value of t when

I = $75

P = $500

r = 5% = 0.05

From

t = I/Pr

t = 75/(500×0.05)

t = 75/25

t = 3 years

Hence, the value of t in the table is 3 years

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Answer:

12, 3/5, 25%, -1/12, -0.17

Step-by-step explanation:

The simplest way to do this is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.

25% is already a percentage

-0.17 = -17%

3/5 = 60%

-1/12 (you can use a calculator to divide and find the percentage here) = -8.33

12 = 1200%

Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):

12, 3/5, 25%, -1/12, -0.17

FINAL ANSWER: 12, 3/5, 25%, -1/12, -0.17

Answer:

x = 27

Step-by-step explanation:

You need to cube each side.

[tex]\sqrt[3]{x} ^{3}[/tex] = [tex]3^{3}[/tex]

x = 27

So the percentage would be 9500/15000 = 63.333333333... = 63.3...%

Answer:

-2(7+2n) +4 = 5

step by step explantation:

-2(7-n) +4

-2×7 =-14

-2x-n = 2n

14+2n = 4

2n = 14 - 4

2n/ 2= 10/2

n= 5

The interquartile range of the players' weights = 48 pounds.

The boxplot attached to this question is missing. It was obtained online and is attached to this solution of the question.

It should be noted that the following is true for a boxplot.

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

So, it is evident that for this question,

First quartile = 174 pounds

Third quartile = 222 pounds

Inter Quartile Range = (Third quartile) - (First quartile)

= 222 - 174

= 48 pounds.

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Answer:

• [tex](f+g) (x)[/tex]  = [tex]9x + \sqrt{x} -2[/tex]

• [tex](f-g)(x)[/tex] = [tex]5x - \sqrt x - 2[/tex]

Step-by-step explanation:

[tex]f(x) = 7x - 2[/tex]

[tex]g(x) = \sqrt{x} + 2x[/tex]

To calculate [tex](f+g) (x)[/tex] and [tex](f-g)(x)[/tex], we have to add and subtract [tex]f(x)[/tex] and [tex]g(x)[/tex] respectively:

• [tex](f+g) (x)[/tex]

⇒ [tex]f(x) + g(x)[/tex]

⇒ [tex]7x - 2 \: + \sqrt{x} + 2x[/tex]

⇒ [tex]9x + \sqrt{x} -2[/tex]

• [tex](f-g)(x)[/tex]

⇒ [tex]7x - 2 - (\sqrt x + 2x)[/tex]

⇒ [tex]7x - 2 - \sqrt x - 2x[/tex]

⇒ [tex]5x - \sqrt x - 2[/tex]

The solution of the given equation are (1/2 , 17/2) and (-3 , 12)

The two equation that we have been given are :

    y = 9 – x            (1)

    y = 2x² + 4x + 6       (2)

We will solve this simultaneously, from equation (1) we will equate the value of y in equation (2) we get

       9 – x = 2x² + 4x + 6

        3 = 2x² + 5x

2x² + 5x – 3 = 0

Now to find the factors of the value x we will use quadratic formula.

   x = (-b±√b² – 4ac)/2a

   x = [ -5 ± √25 + 24 ]/4

   x = [ -5 ± 7 ]/4

x = (-5 + 7)/4              and                 x = (-5 – 7)/4

x = 1/2     and    x= -3

putting the required value of x in equation (1) we get

y = 9 – 1/2            and             y = 9 – (-3)

y = 17/2      and    y = 12

Hence the solution of the equation is (1/2 , 17/2) and (-3 , 12)

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Answer:

I am more on the sure side it's 8

Step-by-step explanation:

And if it isn't im so so sorry

The two vectors and a vector and a scalar which shows that H is not a subspace of [tex]R^2[/tex] are [tex]\bold{\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right]}[/tex] , [tex]\bold{\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right]}[/tex]  and [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] and 6.

Given the set, [tex]H=\{\left[\begin{array}{c}x\\y\end{array}\right] :8x^2+5y^2\leq 1\}[/tex] which represents the set of points on and inside an ellipse in the xy-plane.

We have to show that H is not a subspace.

We can show that this set is not closed under vector addition of two vectors by finding those vectors.

[tex]\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right][/tex] and [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right][/tex] are two vectors in H, since it satisfies the given condition, [tex]8x^2+5y^2\leq 1[/tex].

i.e., [tex]8\times(\frac{1}{5})^2 + 5\times (\frac{1}{4})^2 = 0.6325\leq 1[/tex] and [tex]8\times(\frac{1}{6})^2 + 5\times (\frac{1}{7})^2 = 0.3242\leq 1[/tex]

[tex]\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right][/tex] + [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right][/tex] = [tex]\left[\begin{array}{c}\frac{11}{30} \\\frac{11}{28} \end{array}\right][/tex]

But  [tex]8\times(\frac{11}{30})^2 + 5\times (\frac{11}{28})^2 =1.847 \geq 1[/tex]

So the vector  [tex]\left[\begin{array}{c}\frac{11}{30} \\\frac{11}{28} \end{array}\right][/tex] does not belongs to H.

So It is not closed under addition.

Now we will prove that H is not closed under scalar multiplication of a vector and a scalar either.

[tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] is a vector in H. But [tex]6\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] does not belongs to H, where 6 is a scalar.

This is because [tex]6\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex]  = [tex]\left[\begin{array}{c}1 \\2 \end{array}\right][/tex] and  [tex]8\times1^2 + 5\times 2^2 =28 \geq 1[/tex].

So the two vectors are [tex]\bold{\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right]}[/tex] and [tex]\bold{\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right]}[/tex]  and one vector and a scalar are [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] and 6.

The question is incomplete. Find the complete question below:

Let  [tex]H=\{\left[\begin{array}{c}x\\y\end{array}\right] :8x^2+5y^2\leq 1\}[/tex], which represents the set of points on and inside an in the xy-plane. Find two specific examples two vectors, and a vector and a scalar to show that H is not a subspace of  [tex]R^2[/tex].

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Answer:

91/7=13

so x=11×13

x=143

The amount of fruit in the smoothie will be 3/2 .

It is given in the question that a smoothie calls for 4/6 of a peach, 1/2 of a banana, and 2/6 of a kiwi.

We have to find the amount of fruit in the smoothie.

We know that,

Amount of fruit in the smoothie = Amount of peach in the smoothie +  Amount of banana in the smoothie +  Amount of kiwi in the smoothie

Hence,

Amount of fruit in the smoothie = 4/6 + 1/2 + 2/6

Adding all the fractions, we get,

4/6 + 3/6 + 2/6 = 9/6 = 3/2

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Answer:

173, 339.10

Step-by-step explanation:

Move the decimal from 157,581.00 to the left to give you 10% of 15,758.10.

Add 15,758.10 to 157,581.00 to give you the total from last month.

Or, convert 10% to a decimal.

157,781 x 0.10 = 15,758.10

15,758.10 + 157,581 = 173,339.10

Four more than five times x is the same as x increased by 26. The value of x is  x=5.5

Given information can be written in the form of algebraic equation is :

5x+4=x+26

5x-x=26-4

4x=22

x=5.5

The equal to (=) symbol is used to unite two algebraic expressions to form an algebraic equation. Because polynomials are included on both sides of the equal sign, algebraic equations are sometimes referred to as polynomial equations. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of an algebraic equation.

A mathematical statement with two equal algebraic expressions is called an algebraic equation. When P and Q are polynomials, the usual form of an algebraic equation is P = 0 or P = Q. Equations in algebra with only one variable are referred to as univariate equations, whereas equations with several variables are referred to as multivariate equations. The solution of an algebraic problem is always balanced.

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The population is growing as the births are more than deaths in an year.

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

To find: Is population growing or shrinking?

Finding:

Hence the population is growing as the births are more than deaths in an year.

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Answer: 25=0.011x+13

Answer:

9 books are needed for the plans to cost the same

Step-by-step explanation:

50 = 5 + 5x

45 = 5x

x = 9