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sweet-ann [11.9K]

4 years ago

5

Draw a isosceles triangle ABC in which AB=AC=6cm and BC=5cm. Construct a triangle PQR similar to triangle ABC in which PQ=8cm. A

lso justify the construction

1 answer:

xenn [34]4 years ago

5 0

Answer:

See the diagram

Step-by-step explanation:

$ABC \cong PQR\\\Rightarrow \frac{PQ}{AB} =\frac{PR}{AC}=\frac{QR}{BC} \\\frac{PQ}{AB}=\frac{PR}{AC}\\ \\Since \ AB=AC\\PQ=PR\\PR=8cm\\\\\frac{PQ}{AB}=\frac{QR}{BC}\\\\QR=\frac{PQ}{AB} \cdot BC\\\\QR=\frac{8}{6} \cdot 5\\\\QR=\frac{20}{3}$

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genetic experiment with peas resulted in one sample of offspring that consisted of green peas and yellow peas. a. Construct a %

Andreas93 [3]

Complete Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 432 green peas and 164 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. b. It was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

Answer:

The 95% confidence interval is $0.2392 < p < 0.3108$

No, the confidence interval includes 0.25, so the true percentage could easily equal 25%

Step-by-step explanation:

From the question we are told that

The total sample size is $n = 432 + 164 =596$

The number of offspring that is yellow peas is $y = 432$

The number of offspring that is green peas is $g = 164$

The sample proportion for offspring that are yellow peas is mathematically evaluated as

$\r p = \frac{ 164 }{596}$

$\r p = 0.275$

Given the the confidence level is 95% then the level of significance is mathematically represented as

$\alpha = (100 - 95)\%$

$\alpha = 5\% = 0.0 5$

The critical value of $\frac{\alpha }{2}$ from the normal distribution table is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1- \r p )}{n} }$

=> $E = 1.96 * \sqrt{\frac{0.275 (1- 0.275 )}{596} }$

=> $E = 0.0358$

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

=> $0.275 - 0.0358 < p < 0.275 + 0.0358$

=> $0.2392 < p < 0.3108$

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3 years ago

A little help with this math problem

laila [671]

Answer:

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Step-by-step explanation:

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3 years ago

How many centimeters is a piece of paper that measures 12 inches? centimeters?

viktelen [127]

Well, there are 2.54 centimeters in an inch, so if you multiply 12 by 2.54, you get 30.48, which would be how many centimeters there are in 12 inches. Hope this helps!

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3 years ago

Lisa has $6450 in her savings account. If the bank pays 3.7% interest per year on savings, how much interest does she earn in on

Marizza181 [45]

Answer:

9.008443

Step-by-step explanation:

6 0

4 years ago

Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ.

miskamm [114]

[w + (h/tan θ)] × h

<h3>Further explanation</h3>

We aim is to find the area of the trapezoidal cross-section of the irrigation canal.

The formula for the area of the trapezoid is $\boxed{\boxed{ \ Area = \frac{1}{2} \times (a + b) \times h \ }}$

a & b = parallel sides
h = height

We assume the lower side is $\boxed{ \ a = w \ }$ and the upper side is b = x + w + x or $\boxed{ \ b = w + 2x \ }$ . See the attached picture.

In the right triangles located on the left and right of the trapezoid, we calculate the value of x based on trigonometric ratios namely tan of theta.

$\boxed{ \ tan \ \theta = \frac{opposite}{adjacent} \ }$

$\boxed{ \ tan \ \theta = \frac{h}{x} \ }$

$\boxed{ \ x = \frac{h}{tan \ \theta} \ }$

Substitute the equation of x to $\boxed{ \ b = w + 2x \ }.$

We get $\boxed{ \ b = w + \frac{2h}{tan \ \theta} \ }$

Finally all components are complete and can be substituted into a formula to calculate the area of a trapezoid.

$\circ \ \boxed{a = w}\\ \circ \ \boxed{ \ b = w + \frac{2h}{tan \ \theta} \ }\\\circ \ and \ h$

$\boxed{ \ Area = \frac{1}{2} \times (w + w + \frac{2h}{tan \ \theta}) \times h \ }$

$\boxed{ \ Area = \frac{1}{2} \times (2w + \frac{2h}{tan \ \theta}) \times h \ }$

$\boxed{ \ Area = \frac{1}{2} \times 2(w + \frac{h}{tan \ \theta}) \times h \ }$

Hence, the area of the trapezoidal cross-section of the irrigation canal is $\boxed{\boxed{ \ Area = (w + \frac{h}{tan \ \theta}) \times h \ }}$

<h3>Learn more</h3>

Find out the area of parallelogram brainly.com/question/4459688
The order of rotational symmetry of rhombus brainly.com/question/4228574
Find out the coordinates of the image of a point after the triangle is rotated 270° about the origin brainly.com/question/7437053

Keywords: the trapezoidal, cross-section of the irrigation canal, the area, the answer will be in terms of h, w, and θ, trigonometric ratios, tan, opposite, adjacent, height, sides

3 0

4 years ago

Read 2 more answers