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Vlada [557]
2 years ago
12

A mirror frame in the shape of an oval is shown below. The ends of the frame form semicircles:

Mathematics
1 answer:
Volgvan2 years ago
4 0

Answer:

abcdefghijklmnopqrstuvwxyz

Step-by-step explanation:

You might be interested in
X/a+x/b=1<br>make x the subject of the formular​
monitta

Answer:

x = \frac{ab}{b+a}

Step-by-step explanation:

Given

\frac{x}{a} + \frac{x}{b} = 1

Multiply through by ab to clear the fractions

bx + ax = ab ← factor out x from each term on the left side

x(b + a) = ab ← divide both sides by (b + a)

x = \frac{ab}{b+a}

8 0
3 years ago
In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa
arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

<em>The question is incomplete:</em>

<em>The significance level is 0.05.</em>

<em>The data is:</em>

<em>Brand X: 91, 100, 88, 89</em>

<em>Brand Y: 99, 96, 94, 99</em>

<em>Brand Z: 83, 88, 89, 76</em>

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

H_0:\mu_x=\mu_y=\mu_z

Alternative hypothesis: the means are not equal

H_a: \mu_x\neq\mu_y\neq\mu_z

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33

Then, we calculate the mean standard error (MSE):

MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91

The MSB is then:

s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172

Now we calculate the F statistic as:

F=MSB/MSE=172/23.78=7.23

The degrees of freedom of the numerator are:

dfn=a-1=3-1=2

The degrees of freedom of the denominator are:

dfd=N-a=3*4-3=12-3=9

The P-value of F=7.23, dfn=2 and dfd=9 is:

P-value=P(F>7.23)=0.01342

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

3 0
3 years ago
What are the real and complex solutions of the polynomial equation? x^3-8=0. with imaginary numbers
seraphim [82]

Answer:

Solutions are 2,  -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

or 2,  -1 +  1.58 i  and -1 - 1.58i

(where the last 2 are equal to nearest hundredth).


Step-by-step explanation:

The real solution is x = 2:-

x^3 - 8 = 0

x^3 = 8

x = cube root of 8 = 2

Note that a cubic equation must have  a total of 3 roots ( real and complex in this case).  We can find the 2 complex roots by using the following identity:-

a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Here  a = x and b = 2 so we have

(x - 2)(x^2 + 2x + 4) = 0

To find the complex roots we solve x^2 + 2x + 4 = 0:-

Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2

= -1 +/- (sqrt( -10)) / 2

= -1 +  0.5 sqrt10 i  and -1 - 0.5 sqrt10 i

4 0
2 years ago
Read 2 more answers
Mike says he can find a fraction equivalent to 1/10 even though 1/10 is a unit fraction is Mike correct explain
chubhunter [2.5K]

yes Mike is correct because 1/10 is also be used as a decimal which could be switched into a fraction

8 0
3 years ago
2. Mourette is a member of her high school golf team. She hits a golf ball
Llana [10]

Answer:

a. h = 60t − 4.9t²

b. 12.2 seconds

c. 183.7 meters

Step-by-step explanation:

a. Given:

y₀ = 0 m

v₀ = 60 m/s

a = -9.8 m/s²

y = y₀ + v₀ t + ½ at²

h = 0 m + (60 m/s) t + ½ (-9.8 m/s²) t²

h = 60t − 4.9t²

b. When the ball lands, h = 0.

0 = 60t − 4.9t²

0 = t (60 − 4.9t)

t = 0 or 12.2

The ball lands after 12.2 seconds.

c. The maximum height is at the vertex of the parabola.

t = -b / (2a)

t = -60 / (2 × -4.9)

t = 6.1 seconds

Alternatively, the maximum height is reached at half the time it takes to land.

t = 12.2 / 2

t = 6.1 seconds

After 6.1 seconds, the height reached is:

h = 60 (6.1) − 4.9 (6.1)²

h = 183.7 meters

7 0
3 years ago
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