Need some help with algebra

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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:

ŷ = 7.02895X1 + 12.6959X2 - 170.33728

Since the calculated F=32 falls in the critical region F ≥ 9.55 we reject our null hypothesis and conclude that there is association between at least one of the regressors and the dependent variable.

Step-by-step explanation:

Using stat calculator:

Part A:

x1         x2            y              Predicted Y          Residual

13        11         62.8739       60.693967        2.179933

15        11        76.1328         74.751867          1.380933

13        13        87.4667       86.085767         1.380933

15        13       102.3236      100.143667        2.179933

14         12      76.1872         80.418817         -4.231617

14        12        77.5287        80.418817         -2.890117

mean

14        12       80.418817     80.418817           0            

standard deviation

0.89 0.89      13.2812       12.979739       2.813451        

Calculation

Sum of X1 = 84

Sum of X2 = 72

Sum of Y = 482.5129

Mean X1 = 14

Mean X2 = 12

Mean Y = 80.4188

Sum of squares (SSX1) = 4

Sum of squares (SSX2) = 4

Sum of products (SPX1Y) = 28.1158

Sum of products (SPX2Y) = 50.7836

Sum of products (SPX1X2) = 0

Regression Equation = ŷ = b1X1 + b2X2 + a

b1 = ((SPx1y)*(SSx2)-(SPx1x2)*(SPx2y)) / ((SSx1)*(SSx2)-(SPx1x2)*(SPx1x2)) = 112.46/16 = 7.02895

b2 = ((SPx2y)*(SSx1)-(SPx1x2)*(SPx1y)) / ((SSx1)*(SSx2)-(SPx1x2)*(SPx1x2)) = 203.13/16 = 12.6959

a = MY - b1MX1 - b2MX2 = 80.42 - (7.03*14) - (12.7*12) = -170.33728

ŷ = 7.02895X1 + 12.6959X2 - 170.33728

X1-Mx1         X2-Mx2        Y-My               (X1-Mx1)²            (X2-Mx2)²

-1                     -1                 -17.545               1                       1

1                        -1                -4.286               1                       1

-1                       1                  7.048                1                      1

1                        1                  21.905              1                       1

0                       0                -4.232               0                      0

0                       0                 -2.89                0                     0            

                                                             SSX1: 4       SSX2: 4        

SPx1y            SPx2y         SPx1x2

17.545           17.545            1

-4.286            4.286            -1

-7.048             7.048          - 1

21.905             21.905        1

0                        0                0

0                       0                 0                      

SPX1Y:         SPX2Y:           SPX1X2: =0

= 28.116       =50.784                                    

Part B

Coefficient Table

             Coefficient           SE                     t- stat        

x1           -170.337283      33.519576          -5.081725

x2           7.028950         1.816075            3.870408

b            12.695900        1.816075           6.990847    

Part C:

Test for significance of β1 and β2.

State the null and alternate hypotheses as

H0: β1=β2=0

Ha:  At least one of the β1 and β2 is non zero.

The significance level is set at ∝= 0.05

The test statistic to use is

F= MSR/ MSE= MS regression/ MS Residual

which if H0 is true has F distribution with υ1= 2 and υ2= n- 3= 6-3= 3  degrees of freedom.

To set up the ANOVA table we find the necessary sum of squares .

Regression SS ( between y^ and y`) = SSR= 842.368060

Residual SS ( between yi and y^) = SSE=  39.577526

Total SS  = SSR+ SSE= 842.368060+39.577526= 881.945586

ANOVA table

Source                 DF      Sum of Square     Mean Square    F Statistic

Regression

(b/w ŷi and yi) 2    842.368060 421.184030 31.926000

Residual

(b/w yi and ŷi) 3    39.577526          13.192509                  

Total (b/w yi and yi)5      881.945586 176.389117                              

The critical region is F≥F (0.05) (2,3)=9.55

Conclusion:

Since the calculated F=32 falls in the critical region F ≥ 9.55 we reject our null hypothesis and conclude that there is association between at least one of the regressors and the dependent variable.

Answer:

x = 6

Step-by-step explanation:

Take the statement x varies directly as y and z

This means value of x is directly proportional to the value of y and z  represented as x ∝ yz which can be represented as x = k.y.z where k is a constant known as the constant of proportionality

If x varies inversely as the square  of r  we represent this as x ∝ 1/r² or in equation form x = k/r²

Since the value of x is dependent on the values of y, z and  jointly we have a single equation of proportionality:

\(\bold{x= k\cdot\frac{yz}{r^{2}}}\)

Given the values for x, y, z and r we can compute the proportionality constant and determine the value of x for any value of y, z or r

x = 16 when y = 3, z = 12 and r = 3

\(16 = k\cdot \frac{3\cdot 12}{3^2} \\\\16 = k\cdot \frac{3\cdot 12}{9}\\\\16 = k\cdot4\\\\k = 16/4 = 4\\\)

So the constant of proportionality is k = 4. Us this value in the proportionality equation along with y, z and r to get the value of x

\(x = 4\cdot \frac{5\cdot 30}{10 \cdot 10}\\\\x = 4\cdot\frac{150}{100}\\\\x = \frac{600}{100} = 6\\\\\)

So x = 6 is the answer

Among the given options, 90 degrees (option A) is not a solution to the equation sin(2θ) = 1. The equation sin(2θ) = 1 represents the values of θ for which the sine of twice the angle is equal to 1. To determine which option is not a solution, we need to evaluate each choice.

A) 90 degrees: If we substitute θ = 90 degrees into the equation sin(2θ) = 1, we get sin(180 degrees) = 1. However, sin(180 degrees) is actually 0, not 1. Therefore, 90 degrees is not a solution to the equation sin(2θ) = 1.

B) 45 degrees: Substituting θ = 45 degrees gives sin(90 degrees) = 1, which is true. Therefore, 45 degrees is a solution to the equation sin(2θ) = 1.

C) 225 degrees: When we substitute θ = 225 degrees, we get sin(450 degrees) = 1. However, sin(450 degrees) is also 0, not 1. Thus, 225 degrees is not a solution to sin(2θ) = 1.

D) -135 degrees: Similarly, substituting θ = -135 degrees gives sin(-270 degrees) = 1. However, sin(-270 degrees) is 0, not 1. Hence, -135 degrees is not a solution to the equation sin(2θ) = 1.

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Answer:

30 hours

Step-by-step explanation:

The equation we use is 1/15 + 1/x = 1/10. X being the amount of time it takes Ian alone. X works out to 30 hours which is the answer

Answer:

Answer down below

Step-by-step explanation:

h (3x-4)

= \(\frac{1}{3x-4+2}\)

= \(\frac{1}{3x-2}\)

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer:

\(y=-x+1\)

Step-by-step explanation:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:

\(-7x-7y=7\)

add 7x to both sides:

\(-7y=7x+7\)

Divide both sides by -7

\(y=-x-1\)

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

\(y=-x+b\text{ where b }\ne -1\)

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)

Now we just plug this into the general equation to get: \(y=-x+1\)

Answer:

48×4.3=184 and that is the easy way how to do it

Answer:

range: 8

Step-by-step explanation:

In order to find the range you need the minimum and maximum

minimum: 17

maximum: 25

Subtract

25-17=8

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

Answer:

4/9 = 1/2 x

Step-by-step explanation:  2.84 sands

Answer: x=

7

Step-by-step explanation:

Answer:

Basic facts:

1foot =12 inch

Step-by-step explanation:

Vidal's treehouse was 6 feet which are 72 inches

Mateo's treehouse was 48 inches

72-48=24

24/12=2      

2 feet and 0 inches

First, you eat the 5 types each, which only leaves for 8 more. So the top of the would be (8+5-1), for the choose part that means there 1 less type of pizza to choose from which makes the equation

This means that there are 495 ways you can do this.

Step-by-step explanation:

when we give a function an actual value as argument, we are using the variable(s) in the functional definition as intended : as placeholders for actual values.

so, we only need to replace any occurrence of the variable by the actual value and calculate.

a.

zero items are produced means x = 0.

C(0) = 10×0 + 900 = $900

fixed cost = $900

b.

making 25 items means x = 25.

C(25) = 10×25 + 900 = 250 + 900 = $1,150

c.

the domain is the interval or set of all valid values for x.

the range is the interval or set of all valid values for y (the functional result).

now, the maximum cost allowed is $1900.

how many items are that ?

1900 = 10x + 900

1000 = 10x

x = 100

so, the domain is

0 <= x <= 100

the range is

$900 <= y <= $1900

Answer:

52.5 cubes

Step-by-step explanation:

100-25=75

100%=70

75%=x

75 x 70=5250/100=52.5 cubes

Answer:

Briainliest here

Step-by-step explanation:

there is 70 cubes of sugar

now 25% is sold

70 x 75% = 70 x 0.75 = 52.5

(I did 75% insted of -25% because its and it actualy works!

Oliver's number is bigger than that of Chen.

It is a number equal to 10 times 10.

Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.

Oliver number can be written as follows -

8 x 10 x 10

Chens number can be written as follows -

3 x 10 x 10

It can be concluded that Oliver's number is bigger than that of Chen.

Therefore, Oliver's number is bigger than that of Chen.

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Answer:

a

Step-by-step explanation:

hope this helps

Answer:

-----------------

Find the base area, considering the legs are 3 in and 4 in, since it is a right triangle:

We know the volume is V = Bh.

Substitute the known values and solve for h:

So, the height of the prism is 16 in.

The height of the prism is 8 inches.

To find the height of the prism, we need to use the formula for the volume of a right prism: V = Bh, where B is the area of the base and h is the height.

Since the bases are right triangles with sides of 3, 4, and 5, we can calculate the area of each base using the formula A = 1/2bh, where b and h are the base and height of the triangle, respectively.

So, the area of each base is (1/2)(3)(4) = 6 in². Since the volume of the prism is given as 96 in³, we can substitute the values we have into the formula for the volume: 96 = 6h.

Solving for h, we get h = 16/3, or approximately 5.33 inches. Therefore, the height of the prism is 8 inches.

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9514 1404 393

Answer:

  (√17 -4√595)/102

Step-by-step explanation:

To use the sine of the angle sum formula, we need to know the sine and cosine of each of the angles.

  sin(sin^-1(1/6)) = 1/6 . . . . a first-quadrant angle

  cos(sin^-1(1/6)) = √(1 -(1/6)²) = √(35/36) = (√35)/6

  sin(tan^-1(-4)) = -4/√(1+(-4)²) = -4/√17 . . . . a 4th-quadrant angle

  cos(tan^-1(-4)) = √(1 -(-4/√17)²) = 1/√17

The sum of angles formula is ...

  sin(α+β) = sin(α)cos(β) +cos(α)sin(β)

So, our sine is ...

  \(\sin\left(\sin^{-1}\left(\dfrac{1}{6}\right)+\tan^{-1}(-4)\right)=\dfrac{1}{6}\cdot\dfrac{1}{\sqrt{17}}+\dfrac{\sqrt{35}}{6}\cdot\dfrac{-4}{\sqrt{17}}\\\\=\dfrac{1-4\sqrt{35}}{6\sqrt{17}}=\boxed{\dfrac{\sqrt{17}-4\sqrt{595}}{102}}\)

Answer:

10-16i

Step-by-step explanation:

use distrubutive property and treat i like a variable

Answer:

mn

Step-by-step explanation:jhhh

Answer:

f(x) \(\leq\) 3x + 4

g(x)  ≥ -1/2x - 5

Step-by-step explanation:

Point D is below f(x)  and above g(x)

Helping in the name of Jesus.

Answer:

5pi/12

105 degrees

Step-by-step explanation:

I can help with the first 2 too many answers in one will get my answer deleted

7pi/12  x 180/pi

7x15=105

Hopes this helps please mark brainliest

Answer:

47...

Step-by-step explanation:

the product of 4 and 8 is 32 and added 15 then it is 47.

Answer:

47

Step-by-step explanation:

4*8+15=32+15=47 (by BODMAS rule)

Answer:

the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.