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aksik [14]
3 years ago
8

Given the figure below, calculate the area

Mathematics
1 answer:
Aleksandr [31]3 years ago
6 0

Answer:

<em>1+√3</em>

Step-by-step explanation:

Area of the triangle = 1/2 * base * height

Area of the triangle = 1/2 * AC * BD

We need to get AC

AC = AD+DC

Get base AD using SOH CAH TOA

tan 45 = 4/AD

AD = 4/tan45

AD = 4/1

AD = 4

Get DC

tan 30 = 4/DC

DC = 4/tan 30

DC = 4/(1/√3)

DC = 4√3

AC = 4 + 4√3

AC = 4(1+√3)

Get the Area of the triangle

<em>Area = 1/2 * 4 *  4(1+√3)</em>

<em>Area of the triangle = 1+√3</em>

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The number a exceeds the number b by 50 percent. By what percent is the number b smaller than the number a?
inna [77]

Answer:

   33 1/3 percent smaller

Step-by-step explanation:


The number a exceeds the number b by 50 percent.

a = b + b*.5

a = b(1.5)

Divide by 1.5

a/1.5 = b

2/3a =b



We want to find (a-b)/a  to find the percent decrease

                           (a-2/3a)/a *100percent

                             (1/3a)/a* 100 percent

                                  1/3 * 100 percent

                                     33 1/3 percent smaller

5 0
3 years ago
Evaluate ^3 sqrt 0.008- need answer asap!!
Ann [662]
∛0.008 = ∛(0.2)^3
= 0.2

hope it helps
7 0
3 years ago
Fizzy Waters has been involved in multiple lawsuits regarding the alkaline substance concentration in their product and getting
ser-zykov [4K]

Answer:

Step-by-step explanation:

For the sample, n = 12

Mean, x = (158.2 + 162.8 + 161.5 + 161.2 + 166.5 + 160.1 + 158.4 + 175.6 + 159.9 + 168.8 + 161.9 + 163.7)/12 = 163.22

Variance, s² = (summation(x - mean)²/n

Summation(x - mean)² = (158.2 - 163.22)^2 + (162.8 - 163.22)^2 + (161.5 - 163.22)^2 + (161.2 - 163.22)^2+ (166.5 - 163.22)^2 + (160.1 - 163.22)^2 + (158.4 - 163.22)^2 + (175.6 - 163.22)^2 + (159.9 - 163.22)^2 + (168.8 - 163.22)^2 + (161.9 - 163.22)^2 + (163.7 - 163.22)^2 = 273.5368

Variance, s² = 273.5368/12 = 22.79

This is a test for a single variance. We would set up the test hypothesis.

For the null hypothesis,

H0: σ² ≥ 25

For the alternative hypothesis,

H1: σ² < 25

The formula for determining the test statistic,x² is

x² = (n - 1)s²/σ²

Where n - 1 is the degree of freedom, df.

df = 12 - 1 = 11

x² = (11 × 22.79)/25 = 10.0276

For a test of 90% reliability, Confidence level = 0.9

Cl = 1 - alpha(level of significance)

alpha = 1 - 0.9 = 0.1

The critical value from the chi-square distribution table is 17.28. Since 17.28 > 10.0276, we would reject the null hypothesis. Therefore, the filling machine does not need repair because the variance of the process is not more than 25 oz.

8 0
3 years ago
Please help with this question asap
stepladder [879]

Pythagoras theorem: leg 1 squared + leg 2 squared = hypotenuse squared

In the diagram, the triangle has angles 90 and 45. So the other angle in the triangle must be 45 degrees as well.  (180 - 90 -45 = 45)

This means it is an isosceles triangle (since two angles are the same), so the two legs have the same length.

So we can say that length of leg1 = x, and the length of leg2 also equals x

Now let's use pythagoras' theorem:

leg1 = x

leg2 = x

hypotenuse = 16

x^2 + x^2 = 16^2

      2x^2 = 16^2

      2x^2  = 256

        x^2 = 128

        x = √(128)

        x = 8√2

3 0
3 years ago
26. -2, 3, 8, 13, 18,...
-Dominant- [34]

Answer:

each number is being added by 5

Step-by-step explanation:

5 0
3 years ago
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