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2 years ago

Find the area of the irregular figure. 14 cm 12cm 21 cm 14 cm 16 cm

Mathematics

1 answer:

stiv31 [10]2 years ago

8 0

Answer:

Step-by-step explanation:

Find the area of each shape (rectangle and triangle) and then add the areas together.

Area of rectangle:

A = bh

A = 14*12 = 168 cm2

Area of triangle:

A = 1/2*bh

A = 1/2(16)(21 - 12)

A = 1/2(16)(9)

A = 1/2(144)

A = 72 cm2

Add areas together: (area of the whole shape)

168 + 72 = 240 cm2

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Divide x to the 5 eighths power divided by x to the 1 fourth power.

8_murik_8 [283]

$\frac{x^{5/8}}{x^{1/4}} = x^{5/8-1/4}= x^{5/8-2/8}= x^{3/8} or \sqrt[8]{x^3}$

8 0

3 years ago

How would I solve this equation?

Assoli18 [71]

2(7/2)^x = 49/2

Divide both sides by 2:

(7/2)^x = 49/4

I notice that 49/4 can be rewritten as (7/2)^2, so we now have:

(7/2)^x = (7/2)^2

The only way for this to be true is if x = 2. Thus, we are done.

6 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:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

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

MATH.... TRIANGLE JKL HAS VERTICES...

7nadin3 [17]

<h3>Answer: Choice (d)</h3>

Explanation:

To reflect over the y axis, we apply this rule

$(x,y) \to (-x,y)$

which says to flip the sign of the x term but keep the y coordinate the same.

So that means something like J(-2,5) becomes J ' (2, 5). The other points are handled in the same fashion and that leads us to choice (d). Points on the y axis will stay where they are.

6 0

3 years ago

What is the remainder when 16,055 is divided by 16? (Input numeric values only)

Rudik [331]

Answer:56

Step-by-step explanation:

with 16 into 55 do that math then put the number you got then put it into another 16 boom 56

7 0

3 years ago