Apply the distributive property to factor out the greatest common factor. 56+32=56+32=56, plus, 32, equals

Answer:

C) 24/25

Step-by-step explanation:

did the quiz and got it right

The value of the sine theta in the first quadrant in the diagram given is [tex]\mathbf{\dfrac{24}{25}}[/tex]

The explanation of the trigonometric functions (i.e cosine, sine, tangent) in respect of point coordinates on the unit circle informs us of the signs and meanings of the trigonometric functions for each of the four(4) quadrants, depending on the signs of the x, as well as, y coordinates in each quadrant.

In the first quadrant;

Thus, we have a positive x and y-axis.

Taking the forms x and y, i.e. (x, y) = (cos θ, sin θ)

The value of sine theta in [tex]\mathbf{(\dfrac{7}{25}, \dfrac{24}{25} ) = \dfrac{24}{25} }[/tex]

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Answer: y-2=1/2(x-(-7)) or y-2=1/2(x+7)

Step-by-step explanation:

The point-slope formula is y-y₁=m(x-x₁). Since we are given the point and the slope, we can directly plug them into where it is appropriate. The slope is 1/2. Slope is represented by m. We would plug in 1/2 into m. The point is (x₁,y₁). That format matches (-7,2).

y-2=1/2(x-(-7))

y-2=1/2(x+7)

Answer:

D.

Step-by-step explanation:

Answer:

C h^2  / 680 = x

Step-by-step explanation:

C=680x/h^2

Multiply each side by h^2

C h^2=680x/h^2  * h^2

C h^2=680x

Divide each side by 680

C h^2  / 680=680x/680

C h^2  / 680 = x

Answer:

Step-by-step explanation:

Hello,

Question 15

We can search x such that:

   [tex]x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }[/tex]

There is 1 solution.

Question 16

Again, we search x such that:

  [tex]x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }[/tex]There are two solutions.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

-1 is not in the domain of (f o g)(x)

Step-by-step explanation:

f(x) = sqrt(x - 9)

g(x) = -6x - 3

(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)

(f o g)(x) = sqrt(-6x - 3 - 9)

(f o g)(x) = sqrt(-6x - 12)

Let x = -1:

(f o g)(-1) = sqrt(-6(-1) - 12)

(f o g)(-1) = sqrt(6 - 12)

(f o g)(-1) = sqrt(-6)

Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).

To write an inequality and show on a number line all numbers: greater than (−3) but less than or equal to 3

Let n be the number, then -3 < n ≤3 .

On number line we mark open circle at -3 (since it has a strictly less than sign) and a closed circle at 3  (since it has a less than and equal to sign) .

To the required inequality that shows all the numbers greater than (−3) but less than or equal to 3 : -3 < n ≤3 and the number line is represented below.

Answer:

[tex] A = 50.7 [/tex] (to nearest tenth)

Step-by-step explanation:

Use the Law of Cosines to find the value of angle A as follows:

[tex] cos(A) = \frac{b^2 + c^2 - a^2}{2*b*c} [/tex]

Where,

a = 7 in

b = 5 in

c = 9 in

Plug in the values into the formula

[tex] cos(A) = \frac{5^2 + 9^2 - 7^2}{2*5*9} [/tex]

[tex] cos(A) = \frac{57}{90} [/tex]

[tex] cos(A) = 0.6333 [/tex]

[tex] A = cos^{-1}(0.6333) [/tex]

[tex] A = 50.7 [/tex] (to nearest tenth)

Answer:

a) We reject H₀ we have enough evidence for that

b) 1.-The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)

2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits

Step-by-step explanation:

We have to develop a proportion test. One tail-test

Population proportion mean (national proportion)  p₀  = 72 %

Sample information

sample proportion  271/300         p = 0,90      p = 90 %

We assume Confidence Interval  90 %     then α = 0,1

Test Hypothesis

Null Hypothesis                                 H₀     p   =  p₀

Alternative Hypothesis                       Hₐ    p   >  p₀

As  α = 0,1 and    

We look at z-table for z(c) and find     z(c) = 1,28

And we compute z(s)  as

z(s) = ( p - p₀ ) √  (p₀q₀/n

z(s) =  ( 0,9 - 0,72 ) /√(0,72)*(0,28)/300

z(s) =  0,18 / √0,1296/300

z(s) =  0,18/ 0,026

z(s) =   6,92

z(s) > z(c)      6,92 > 1,28

As z(s) is bigger than z(c), z(s) is in the rejection region, so we reject the null hypothesis. We have enough evidence to claim that the proportion in the district is bigger than the national one.

b)1. The survey was made over a district, results will surely be different if the survey is carried out over a whole state ( considering urban and rural areas)

2.-In a district we find an equalized level of salaries, which could be associated with a similar level of habits

Answer:

37.7

Step-by-step explanation:

Well use the formula for the volume of a cylinder which is,

,[tex]\pi r^2 h[/tex]

So the radius is 2 and the height is 3, so we plug those numbers into the formula,

(pi)(2)^2(3)

2^2 is 4 4*3 is 12

12*pi is about 37.7 rounded to the nearest tenth.

If you would like to check look at the image below.

Answer:

The given data is:

30, 32, 11, 14, 40, 37, 16, 26, 12, 33, 13, 19, 38, 12, 25, 15, 39, 11, 37, 17, 27, 14, 36

We will fill the table with the relevant information:

Question 1: 21 - 25 (because the previous range stops at 20 and the following range starts at 26)

Question 2: III (write 3 as a tally)

Question 3: II (write 2 as a tally)

Question 4: 8 (write the tally as a number)

Question 5: 4 (write IIII as a number)

Answer:

[tex]8cos^4}x = (3 + 4cos2x + cos4x)[/tex]

Step-by-step explanation:

Using the power reduction identity, we have that:

[tex]cos^{2}x = \frac{1}{2}(1 + cos2x)\\ \\cos^{4}x = (cos^{2}x)^2 = (\frac{1}{2}(1 + cos2x))^2\\\\cos^{4}x = \frac{1}{4} (1 + 2cos2x + cos^{2}2x)\\[/tex]

From the first line:

[tex]cos^{2}2x = \frac{1}{2}(1 + cos4x)[/tex]

Therefore:

[tex]cos^{4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2}(1 + cos4x))\\\\cos^4}x = \frac{1}{4} (1 + 2cos2x + \frac{1}{2} + \frac{1}{2} cos4x)\\\\cos^4}x = \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\=> 8cos^4}x = 8 * \frac{1}{4} (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = 2 * (\frac{3}{2} + 2cos2x + \frac{1}{2} cos4x)\\\\8cos^4}x = (3 + 4cos2x + cos4x)[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello,

First of all, we need to find the equation of the line.

It will be something like y = ax + b (we need to find a and b).

Then the graph is the part of the plan which is above this line, so the inequality will be

[tex]\large \boxed{\sf \ \ y\geq ax+b \ \ }[/tex]

There is only one line passing by two different points, right?

We need to find two points of this line, the x-axis gives the x of the point and the y-axis give the y of the point.

We can see on the graph that (-1,-1) and (6,13) are two points of this line.

I attached a graph with the two points A (-1,-1) and B (6,13).

We need to solve y = ax + b to find a and b which means:

(-1) = a(-1 )+ b <=> -1 = -a + b <=> -a + b = -1

(13) = a(6) + b <=> 6a + b = 13

To eliminate b, we can subtract the first equation from the second one.

6a + b -(-a) - b = 13 - (-1) = 13 + 1 = 14

<=> 6a + a = 7a = 14 we can divide by 7 both parts of the equation.

[tex]\large \boxed{\sf \ \ a=\dfrac{14}{7}=2 \ \ }[/tex]

And then, b = -1 + a = -1 + 2 = 1

[tex]\large \boxed{\sf \ \ b=1 \ \ }[/tex]

The equation of the line is then [tex]y=2x+1[/tex]

So, the inequality is:

[tex]\Large \boxed{\sf \ \ y\geq 2x+1 \ \ }[/tex]

And this is the answer of the question 1.

2. First, we find the equation of the line by finding two points on this line. Then, we deduce the inequality from the equality as the graph is all the points above the line (as explained above).

3. A real-life example is the following.

My parents gave $1 to my sister and they will give her $2 every day.

So today at x = 0 she has $1 and her pocket money will be represented by the line. And I told my parents that there were no way I can get less than my little sister. To help them understand what can be an acceptable deal I provided this graph, and I told them to only look for t positive of course.

The label for the x-axis is the time.

The label for the y-axis is the pocket money in $

After one day x = 1 my sister has $3 (point on the line), a possible solution for my pocket money is $6, $14 (two points from the graph) is also a solution of course :-)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

(1.5, -13.5)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Simply plug in our coordinates into the formula:

x = (17 - 14)/2

x = 3/2

y = (-11 - 16)/2

y = -27/2

Answer:

(-1.5, -13.5)

Step-by-step explanation:

To find the x coordinate of the  midpoint, add the x coordinates and divide by 2

( 17+-14)/2 = 3/2 =1.5

To find the y coordinate of the  midpoint, add the x coordinates and divide by 2

( -11+-16)/2 = -27/2= - 13.5

Answer:

the probability that one parachute of the  five parachute is damaged is 0.156

Step-by-step explanation:

From the given information;

Let consider X to be the altitude above the  ground that a parachute opens

Then; we can posit that the probability that the parachute is damaged is:

P(X ≤ 100 )

Given that the population mean μ = 155

the standard deviation σ = 30

Then;

[tex]P(X \leq 100 ) = ( \dfrac{X- \mu}{\sigma} \leq \dfrac{100- \mu}{\sigma})[/tex]

[tex]P(X \leq 100 ) = ( \dfrac{X- 155}{30} \leq \dfrac{100- 155}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq \dfrac{- 55}{30})[/tex]

[tex]P(X \leq 100 ) = (Z \leq -1.8333)[/tex]

[tex]P(X \leq 100 ) = \Phi( -1.8333)[/tex]

From standard normal tables

[tex]P(X \leq 100 ) = 0.0334[/tex]

Hence; the probability of the given parachute damaged is 0.0334

Let consider Q to be the dropped parachute

Given that the number of parachute be n= 5

The probability that the parachute opens in each trail be  p = 0.0334

Now; the random variable Q follows the binomial distribution with parameters n= 5 and p = 0.0334

The probability mass function is:

Q [tex]\sim[/tex] B(5, 0.0334)

Similarly; the event that one parachute is damaged is :

Q ≥ 1

P( Q ≥ 1 ) = 1 - P( Q < 1 )

P( Q ≥ 1 ) = 1 - P( Y = 0 )

P( Q ≥ 1 ) = 1 - b(0;5; 0.0334 )

P( Q ≥ 1 ) = [tex]1 -(^5_0)* (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = [tex]1 -( \dfrac{5!}{(5-0)!}) * (0.0334)^0*(1-0.0334)^5[/tex]

P( Q ≥ 1 ) = 1 -  0.8437891838

P( Q ≥ 1 ) = 0.1562108162

P( Q ≥ 1 ) [tex]\approx[/tex] 0.156

Therefore; the probability that one parachute of the  five parachute is damaged is 0.156

ok its 45.15% trust me

Answer:

Step-by-step explanation:

This curve alone does  not give exact percentages with the exception of P(z=0) = .50 or 50%

A Pictorial where 'some' of the % have been added for helps more...  

However, most often one needs to use a table, calculator, or an Excel function ect to find exact Percentage,

P(x > 4000) = P(z = 0) =  .50  or 50 % |using above pictorial

Using Calculator etc:  Here, am using the Excel NORMSDIST function to find the Percentages:

P(z=3/5 - z=-3/5) =  .7257 - .2742 =.4515 or 45.15%

Answer:

[tex]\boxed{\sf x - 5 = 10}[/tex]

Step-by-step explanation:

Taking away 5 from x ⇒ subtracting 5 from x

[tex]\large {\sf x - 5[/tex]

Gives 10 ⇒ result is 10

[tex]\large {\sf x - 5 = 10[/tex]

Answer:

see explanation

Step-by-step explanation:

The median is the middle value of the data set in ascending order. If there is no exact middle then the median is the average of the values either side of the middle.

Given

3   8   14   19   22   29   33   37   43   49

                            ↑ middle is between 22 and 29

median = [tex]\frac{22+29}{2}[/tex] = [tex]\frac{51}{2}[/tex] = 25.5

The upper quartile [tex]Q_{3}[/tex] is the middle value of the data to the right of the median.

29   33   37   43   49

               ↑

[tex]Q_{3}[/tex] = 37

The lower quartile [tex]Q_{1}[/tex] is the middle value of the data to the left of the median.

3   8   14   19   22

           ↑

[tex]Q_{1}[/tex] = 14

The min is the smallest value in the data set, that is 3

The max is the largest value in the data set, that is 49

The 5 number summary is

3,  14,  25.5,  37,  49

Answer:

decreases.

Step-by-step explanation:

Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.

Answer: 10

Step-by-step explanation:

Given : Total number of coins tossed = 10

Possible outcomes to toss a coin = Head or tail

Number of possible outcomes = [tex]2^{10}=1024[/tex]

Number of ways of obtaining exactly 1 heads = [tex]{10}C_1=\dfrac{10!}{1!9!}[/tex]     [using combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex] ]

=10

Hence, the numbers of ways of obtaining exactly 1 heads= 10

Answer:

D

Step-by-step explanation:

1/3(9x + 27) > x + 33

3x + 9 > x + 33

2x > 24

x > 12

> means open circle

Answer:

The answer is D

Step-by-step explanation:

I took the plato test!

Answer:

[tex] c = 15.5 [/tex]

Step-by-step explanation:

Using the Law of Cosines, c² = a² + b² - 2ab*cos(C), let's find c.

Where,

a = 15 ft

b = 20 ft

C = 50°

Thus:

[tex] c^2 = 15^2 + 20^2 - 2*15*20*cos(50) [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 600*0.6429 [/tex]

[tex] c^2 = 625 - 385.74 [/tex]

[tex] c^2 = 239.26 [/tex]

[tex] c = \sqrt{239.26} [/tex]

[tex] c = 15.5 [/tex] (nearest tenth)

Answer:

c sorry gotta get points.

Step-by-step explanation:

Answer:

0.0414 with an upper tailed test

Step-by-step explanation:

Claim: P1P1 = P2P2

The above is a null hypothesis

The alternative hypothesis for a two-tailed test would be:

P1P1 \=/ P2P2

Where "\=/" represents "not equal to".

Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04

With an upper tailed test, the

2 × [probability that z>2.04] = 2[0.0207] = 0.0414

This is the p-value for the test statistic.

Focus is on the alternative hypothesis.

Answer:

Option D

Step-by-step explanation:

A type I error occurs when you reject the null hypothesis when it is actually true.

The null hypothesis in this case is minimum breaking strength is less than or equal to 0.5.

A type one error would be allowing the production process to continue when the true breaking strength is below specifications.

The formula C = π2r

Is used for the circumference.

We know that the number π is defined as the quotient between the circumference of a circle and its diameter, so we can write:

C/d = π

And remember that the diameter is twice the radius, so we can write:

d = 2r

Then we can rewrite the equation for the circumference as:

C = π2r

Then we conclude that the correct option is B.

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Answer:

200 N/m

Step-by-step explanation:

Rearranging the formula F = kx, you find that k = F/x. For the first spring,

F = 36 N and x = 0.06 m (6 cm). So the spring constant, F/x, is 36N/0.06m = 600 N/m

For the second spring, F = 36 N and x = 0.09 m. F/x = 36N/0.09m = 400 N/m

The difference between these values is 200 N/m, and that's the answer.

Answer:

83.0°

Step-by-step explanation:

Given ∆XYZ, with 3 known sides, to find angle X, apply the Law of Cosines, c² = a² + b² - 2ab*cos(C).

For convenience sake, this formula can be rewritten to make the angle we are looking for the subject of the formula.

Thus, we would have this following:

[tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]

Where,

C = X = ?

a = 8 ft

b = 16 ft

c = 17 ft

Plug in the stated values into the formula and solve for X

[tex] cos(X) = \frac{8^2 + 16^2 - 17^2}{2*8*16} [/tex]

[tex] cos(X) = \frac{320 - 289}{256} [/tex]

[tex] cos(X) = \frac{31}{256} [/tex]

[tex] cos(X) = 0.1211 [/tex]

[tex] X = cos^{-1}(0.1211) [/tex]

[tex] X = 83.0 [/tex] (to nearest tenth)

Answer:

its actually 83 not 83.0

Step-by-step explanation:

im only saying this bc i know people with type 83.0 in the box

Answer:

$4800.25

Step-by-step explanation:

$42603 is a yearly salary.

There are 12 months in 1 year.

Monthly salary:

$42603/12 = $3550.25

Monthly travelling allowance: $1250

Total amount earned in 1 month:

$3550.25 + $1250 = $4800.25

Answer:

47, 40, 33, 26 are the first four terms of the sequence.

Step-by-step explanation:

Expression representing the sequence is,

[tex]a_n=46-7(n-1)[/tex]

where n = number of term in the sequence

For n = 1,

[tex]a_1=47-7(1-1)[/tex]

    = 47

For n = 2,

[tex]a_2=47-7(2-1)[/tex]

    = 47 - 7

    = 40

For n = 3,

[tex]a_3[/tex] = 47 - 7(3 -1)

   = 47 - 14

   = 33

For n = 4,

[tex]a_4=47-7(4-1)[/tex]

    = 47 - 21

    = 26

Therefore, first four terms of the sequence are 47, 40, 33 and 26.

Answer:

3/11

Step-by-step explanation:

There are eleven equal parts.

So the denominator is 11.

He copies 8 parts on Sunday.

11-8=3.

He copied 3 parts on Saturday.

Hope this helps ;) ❤❤❤

Answer:

[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]

Step-by-step explanation:

The area of the shaded region can be calculated as the area of the semicircle less the area of the right triangle.

The area of the right triangle can be calculated as:

[tex]A_t=\frac{b*h}{2} =\frac{LM*MN}{2}[/tex]

Where LM and MN have the same length because the internal angles are L=45°, M=90°, and N=45°. So the area is:

[tex]A_t=\frac{4*4}{2}=8[/tex]

The diameter of the circle can be calculated using the Pythagorean theorem as:

[tex]D=\sqrt{(LM)^2+(MN)^2} =\sqrt{4^2+4^4}=4\sqrt{2}[/tex]

So, the radius is [tex]r=2\sqrt{2}[/tex]

Finally, the area of the semicircle is:

[tex]A_c=\frac{\pi*r^2 }{2}=\frac{\pi*(2\sqrt{2})^2 }{2}=4\pi[/tex]

So, the area of the shaded region is:

[tex]A = A_c-A_t=4\pi -8=4.5664cm^2[/tex]