Which number sentence represents the Associative Property of Addition?

18 + 7 = 7 + 18
4 + (1 + 11) = (4 + 1) + 11
0 + 90 = 90
22 + 3 = 25

Correct question is;

The terminal side of angle θ intersects the unit circle in the first quadrant at (9/25,y). What are the exact values of sinθ and cosθ?

Answer:

sinθ = (√544)/25) and cosθ = 9/25

Step-by-step explanation:

We are given that (9/25,y) lies on the unit circle. Thus, from general representation of equation of a circle, we can write that;

(9/25)² + y² = 1²

y² = 1 - (9/25)²

y² = (625 - 81)/25²

y² = 544/25²

y = ±(√544)/25

We are told the point is in the first quadrant and so we will choose the positive value of y = (√544)/25.

Therefore, the terminal side of the angle θ intersects the unit circle at [9/25, (√544)/25)]

In unit circle geometry, cosθ = x, while sinθ = y.

Thus; sinθ = (√544)/25) and cosθ = 9/25

The exact value of [tex]sin\theta[/tex] and [tex]cos\theta[/tex] is  [tex]cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex] and this can be determined by forming the equation of circle.

Given :

The terminal side of angle [tex]\theta[/tex] intersect at unit circle ([tex]\frac{9}{25}, y[/tex]).

From general representation of equation of circle , we can write

[tex]x^{2} + y^{2} = a^{2}\\[/tex]

[tex](\frac{9^{2} }{25^{2} })[/tex] + [tex]y^{2} = 1^{2}[/tex]

[tex]y^{2} = 1 - \frac{81}{625}[/tex]

[tex]y^{2} = \frac{625-81}{625}[/tex]

[tex]y^{2}=\frac{544}{625}[/tex]

Taking square root both sides

[tex]y= \frac{\sqrt{544} }{\sqrt{625} }[/tex]

[tex]y = \frac{\sqrt{544} }{25}[/tex]

We are taking only because point  lies in first quadrant.

The terminal side of angel [tex]\theta[/tex] unit circle in first quadrant at [tex](\frac{9}{25} , \frac{\sqrt{544} }{25})[/tex]

In unit circle

[tex]x = cos\theta , y = sin\theta[/tex]

[tex]\rm cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex].

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Answer:

14 f g

Step-by-step explanation:

Multiply  7  by  2 .

Answer:

Piecewise functions are functions that behave differently in different regions of the domain.

One example that you may see in your city is the case of the street illumination, such that can be modeled as:

x = time

Suppose that the lights are turned on at a given hour x0 and then turn off at the hour x1, we can define:

f(x) = 0 if x1 < x < x0

f(x) = 1 if x0 ≤ x ≤ x1

Where f(x) represents the intensity of the light at the time x.

Between x1 and x0, the lights are not working, so the illumination that they provide is zero.

Between x0 and x1 the lights are turned on, so the illumination is 1.

Another example can be the accurate description of the velocity of a car as a function of time.

For some pieces, the car will be stopped (maybe in a red light)

For some pieces, the car will be moving slow (maybe there is a lot of traffic)

For some pieces, the car will be moving fast or accelerating (in an empty street).

So we can define this motion as a piecewise function that obviously will depend on how the car moves.

Answer:

288 Miles

Step-by-step explanation:

Solve for x (speed)

5.5x = 264

Divide by 5.5

x = 48

y = 48x

Subsitute 6 hours in for x

y = 48(6)

y = 288

Answer: Allie went 288 miles in 6 hours.

Step-by-step explanation:

First, you must find out how many miles Allie travled in one hour

= 264/5.5

= 48

Next, multiply the quotient by the number of hours to get the answer.

= 48 x 6

= 288

Simple answer.

You will have to replace a, with the given numbers.

For the 1st one)

70-25² since a=25. 70-625=-55

2nd)

70-1²=70-1=69

3d)

70-10²=70-100=-30

Hope this helped.

Answer:

a=60

b=85

c=35

Step-by-step explanation:

a is shown to be 60 in the text along with c being 85 with its angle so just add 60 and 85 to get 145 and fill in the remaining to get 180 which gives you c as 35

Answer:

a

 [tex]E(Z) =  202 [/tex]  

b

[tex]E(Z) = 198[/tex]

c

[tex]E(Z) = -140  [/tex]

Step-by-step explanation:

From the question we are told that

   The mean of X  is [tex] E(X)  =  20[/tex]

   The standard deviation of X is  [tex]s_1 = 5[/tex]

   The mean of Y  is [tex]\= y  =  40[/tex]

    The standard deviation of Y is  [tex]s_2 = 10[/tex]

Considering question a  

Generally the mean of   Z = 2 + 10X. is mathematically  represented

    [tex]E(Z) = E[2 + 10X ][/tex]

=> [tex]E(Z) =  2 +  10 E(X)[/tex]

=>  [tex]E(Z) =  2 +  10 * 20 [/tex]        

=>  [tex]E(Z) =  202 [/tex]          

Considering question b

Generally the mean of   Z = 10X - 2.. is mathematically  represented  

        [tex]E(Z) = E[10X -2 ][/tex]

   => [tex]E(Z) = 10E(X) - 2[/tex]

  =>  [tex]E(Z) = 10* 20  - 2[/tex]

  =>  [tex]E(Z) = 200  - 2[/tex]

 =>  [tex]E(Z) = 198[/tex]

Considering question c

Generally the mean of   -3X - 2Y is mathematically  represented

     [tex]E(Z) = E[-3X -2Y ][/tex]

     [tex]E(Z) = -3 E(X) -2E(Y) [/tex]

=>   [tex]E(Z) = -3 * 20 -2* 40 [/tex]

=> [tex]E(Z) = -140  [/tex]

Answer:

Rational

Step-by-step explanation:

You are able to put 18.18 in a fraction.

Hope this helped, Have an AMAZING day/night!

Answer:

-1

Step-by-step explanation:

Put these two numbers on a number line with the correct circles. Now choose from any of the between numbers.

Answer: 3x-3 needs to be done first, and then 4x+7, and then multiply and whatever you get will be your answer

Step-by-step explanation:

Answer:

Thank you ☺️

Answer:

One Hundred Sixty

Step-by-step explanation:

Answer:

12 ounces for $1.47.

Step-by-step explanation:

:) ello

Answer:

6

Step-by-step explanation:

A way to answer these questions like I usually do is to subtract the result by the number you already know, like this;    10-4=6, so 6 would be what X equals, or you can just take the long way and keep guessing what the answer would be and keep doing the problems, but that would be very time consuming so I would recommend just doing the subtraction method!

Hope this helps!

Answer:

x = 6

Step-by-step explanation:

x + 4  = 10

=> x = 10 - 4

=> x = 6

Answer:

[tex]5\leq x\leq 40[/tex]

Here, [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far

Step-by-step explanation:

Number of cookies made by Walter so far = 15

He is asked by his coach to make at least 20 cookies but no more than 55.

Let [tex]x[/tex] denotes the additional cookies that need to be made by Walter besides 15 cookies made by him so far.

The inequality is [tex]20\leq x+15\leq 55[/tex]

Now solve this inequality.

[tex]20\leq x+15\leq 55\\20-15\leq x\leq 55-15\\5\leq x\leq 40[/tex]

Answer: a

Step-by-step explanation: because its right

Answer:

The p-value is  [tex]p-value = 0.0039854[/tex]

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1100

   The population proportion is  p = 0.50

  The sample proportion is  [tex]\^ p = 0.54[/tex]

The null hypothesis is  [tex]H_o : p = 0.50[/tex]

The alternative hypothesis is [tex]H_a : p > 0.50[/tex]

 Generally the test statistics is mathematically represented as

     [tex]z = \frac{\^ p - p }{ \sqrt{\frac{ p(1 - p)}{n} } }[/tex]

=>   [tex]z = \frac{ 0.54 - 0.54 }{ \sqrt{\frac{ 0.50 (1 - 0.50)}{1100} } }[/tex]

=>  [tex]z = 2.6533[/tex]

Generally from the z-table the probability of 2.6533 for a right tailed test is  

         [tex]p-value = 0.0039854[/tex]

Answer:

Bar graphs are used with nominal or ordinal scores; histograms are used with interval or ratio scores.

Step-by-step explanation:

Answer:

C. rational numbers and irrational numbers

Step-by-step explanation:

Rational numbers are those numbers that can be used to express the ratio of two whole numbers. An example is the figure 2. It can be expressed as a fraction of another number like when we write 2/8. Both figures are rational. Irrational numbers cannot be used to express the ratio of two whole numbers or integers. An example is a digit like 0.666666... Rational and irrational numbers are real numbers because real numbers encompass all the types of numbers we can think of, positive, negative, decimals, whole, etc.

The density of numbers is seen in the fact that there is no vacuum created between real numbers when plotted on the number line.

Answer:

[tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] is equivalent to  [tex]f = 0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex].

Step-by-step explanation:

Let be [tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex], we transform this into an equivalent expression with sums and differences of logarithms by applying logarithm properties:

1) [tex]\log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] Given.

2) [tex]\log_{4}\left[\left(\frac{m\cdot n}{19} \right)^{0.5}\right][/tex] Definition of square root.

3) [tex]0.5\cdot \log_{4}\left(\frac{m\cdot n}{19} \right)[/tex]   [tex]\log_{a} b^{c} = c\cdot \log_{a} b[/tex]

4) [tex]0.5\cdot (\log_{4}m\cdot n -\log_{4} 19)[/tex]   [tex]\log_{a} \frac{b}{c} = \log_{a} b - \log_{a} c[/tex]

5) [tex]0.5\cdot \log_{4} m\cdot n -0.5\cdot \log_{4} 19[/tex] Distributive property.

6) [tex]0.5\cdot (\log_{4}m + \log_{4}n)-0.5\cdot \log_{4}19[/tex]   [tex]\log_{a} b\cdot c = \log_{a}b +\log_{a} c[/tex]

7) [tex]0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex] Distributive property/Result.

[tex]f = \log_{4}\left(\sqrt{\frac{m\cdot n}{19}}\right)[/tex] is equivalent to  [tex]f = 0.5\cdot \log_{4} m + 0.5\cdot \log_{4}n -0.5\cdot \log_{4}19[/tex].

Answer:

1/2 liters

Step-by-step explanation:

Rosanne makes 1 1/2 liters of strawberry lemonade

She pours 1/4 of the lemonade into a thermos

The quantity left is

= 1 1/2 - 1/4

= 3/2 - 1/4

= 5/4

Her brother drinks 2/5 of the remaining lemonade

Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows

= 2/5 × 5/4

=1/2

Hence the quantity of lemonade that Rosanne brother drinks is 1/2 liters

Answer:

1/2 liters

Step-by-step explanation: Rosanne makes 1 1/2 liters of strawberry lemonade

She pours 1/4 of the lemonade into a thermos

The quantity left is

= 1 1/2 - 1/4

= 3/2 - 1/4

= 5/4

Her brother drinks 2/5 of the remaining lemonade

Therefore the quantity of lemonade that Rosanne brother drinks can be calculated as follows

= 2/5 × 5/4

=1/2

Answer:

We can check this two ways: distributing the -0.5, and plugging in a number for x.

First, we can check this by distributing the -0.5.  Our equation becomes:

-1.5x -2.5 = -1.5x + 2.5

Clearly, this is not true.  We can show this one more time by plugging in a number for x.  I will use 2.

Now, we evaluate both sides and see if they are equal.

-3 - 2.5 = -3 + 2.5

-5.5 = 0.5

Clearly, this is not true.  These expressions are not equivalent.

Step-by-step explanation:

Answer:

Step-by-step explanation:   Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.

Answer:

1 oz

Step-by-step explanation:

Given that:

% solution of super grow fertilizer = 10%

To obtain mixture of 36oz of a 12.5% concentration

Let oz of pure supergrowth to be added = s

(Initial % * (36 - s) + s) / 36 = target concentration

(10% * (36 - s) + s) / 36 = 12.5%

(0.1(36 - s) + s) / 36 = 0.125

Cross multiply:

0.1(36 - s) + s =. 0.125 * 36

3.6 - 0.1s + s = 4.5

3.6 + 0.9s = 4.5

0.9s = 4.5 - 3.6

0.9s = 0.9

s =. 0.9/0.9

s = 1

Hence, 1 oz of pure supergrowth should be added to the 10% solution to get 36 oz of a 12.5% concentration.

Step-by-step explanation:

ADD::If the denominators are not the same, you must find the common denominator by finding the least common multiple of the 2.

SUBTRACT::If the denominators are not the same, you must find the common denominator by finding the least common multiple of the 2.

that's the answer. good luck

Step-by-step explanation:

Hope it helps man .................

Answer:

I want to say 2.5

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

cause 2+2 is 4 and 2x2 is four and since u put - it take it away a then divide 0 by 2 u get 0

Answer:

[tex]Probability = \frac{1}{24}[/tex]

Step-by-step explanation:

Given

[tex]Oranges = 3[/tex]

[tex]Apples = 5[/tex]

[tex]Banana = 2[/tex]

[tex]Total = 10[/tex]

Required

Determine the probability of 1 orange, 1 apple and 1 banana

Since, order is not important:

[tex]Probability = P(Orange) * P(Apple) * P(Banana)[/tex]

[tex]Probability = \frac{3}{10} * \frac{5}{9} * \frac{2}{8}[/tex]

The difference in the numerator is as a result of picking the fruit without replacement

[tex]Probability = \frac{30}{720}[/tex]

[tex]Probability = \frac{1}{24}[/tex]

Probability is simply how likely something is to happen.

The probability of 1 orange, 1 apple, and 1 banana are  [tex]\frac{1}{24}[/tex]

On lunch counter,

Number of oranges = 3

Number of apples = 5

Number of bananas = 2

If 3 piece of fruit is selected then, probability of 1 orange, 1 apple and 1 banana

                          [tex]=\frac{3}{10}*\frac{5}{9} *\frac{2}{8} \\\\=\frac{30}{720}\\\\=\frac{1}{24}[/tex]

Therefore, the probability of  selecting 1 orange, 1 apple, and 1 banana are [tex]\frac{1}{24}[/tex]

Learn more:

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Answer:

1021

Step-by-step explanation:

Answer:

1021 is the answer to this question

Answer:

8

Step-by-step explanation:

Answer:

From the information given, you can write the following system of equations:

x+y+z=16 (1)

5x+4.5y+5.5z=82 (2)

z=x+y (3)

You can replace (3) in (1) and (2):

x+y+x+y=16

2x+2y=16 (4)

5x+4.5y+5.5(x+y)=82

5x+4.5y+5.5x+5.5y=82

10.5x+10y=82 (5)

Now, you have the following equations:

2x+2y=16 (4)

10.5x+10y=82 (5)

You can isolate x in (4):

2x=16-2y

x=8-y (6)

Then, you have to replace (6) in (5):

10.5(8-y)+10y=82

84-10.5y+10y=82

84-82=10.5y-10y

2=0.5y

y=2/0.5

y=4

Now, you can replace the value of y in (6) to find x:

x=8-4

x=4

Finally, you can replace the vaue of x and y in (3) to find z:

z=4+4

z=8

According to this, she should buy 4 apple pies, 4 banana pies and 8 chocolate pies.