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3 years ago

The parallelograms below are similar.

Mathematics

2 answers:

artcher [175]3 years ago

4 0

Answer:

30 deg

Step-by-step explanation:

AD/EH = 6/1.5 = 4

Each side in ABCD is 4 times the length of the corresponding side in EFGH.

Since EF = 1, then AB = 4 * 1 = 4

Answer: AB = 4

Angle A and angle E are corresponding angles, so they are congruent.

m<E = m<A = 30 deg

Answer: 30 deg

OLEGan [10]3 years ago

3 0

Answer:

Side AB= 4

Angle E= 30°

Step-by-step explanation:

6÷1.5=4

Scale factor is 4

1×4= 4

angle A = angle E

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A random sample of 700 home owners in a particular city found 112 home owners who had a swimming pool in their backyard. Find a

vekshin1

Answer: $(13.28\%,\ 18.72\%)$

Step-by-step explanation:

Given : A random sample of 700 home owners in a particular city found 112 home owners who had a swimming pool in their backyard.

i.e. n= 700 and x= 112

Sample proportion : $\hat{p}=\dfrac{x}{n}=\dfrac{112}{700}=0.16$

z-value for 95% confidence interval : $z_c=1.960$

Now, the 95% confidence interval for the true percent of home owners in this city who have a swimming pool in their backyard will be :-

$\hat{p}\pm z_c\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$=0.16\pm (1.96)\sqrt{\dfrac{0.16(1-0.16)}{700}}$

$=0.16\pm (1.96)(0.013856)\\\\\approx 0.16\pm0.0272\\\\ =(0.16-0.0272,\ 0.16+0.0272)=(0.1328,\ 0.1872)=(13.28\%,\ 18.72\%)$

Hence, 95% confidence interval for the true percent of home owners in this city who have a swimming pool in their backyard : $(13.28\%,\ 18.72\%)$

6 0

3 years ago

Perform the indicated operation. Be sure the answer is reduced.

avanturin [10]

<h3>Given Equation:-</h3>

$\boxed{ \rm \frac{4x^{2}y^{3}z}{9} \times \frac{45y}{8 {x}^{5} {z}^{5} }}$

<h3>Step by step expansion:</h3>

$\dashrightarrow \sf\dfrac{4x^{2}y^{3}z}{9} \times \dfrac{45y}{8 {x}^{5} {z}^{3} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{ \cancel4x^{2}y^{3}z}{9} \times \dfrac{45y}{ \cancel8 {x}^{5} {z}^{3} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{9} \times \dfrac{45y}{2{x}^{5} {z}^{3} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{ \cancel9} \times \dfrac{ \cancel{45}y}{2{x}^{5} {z}^{3} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{x^{2}y^{3}z}{1} \times \dfrac{5y}{2{x}^{5} {z}^{3} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{x^{0}y^{3}z}{1} \times \dfrac{5y}{2{x}^{5 - 2} {z}^{3} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{y^{3}z}{1} \times \dfrac{5y}{2{x}^{3} {z}^{3} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{y^{3}z {}^{0} }{1} \times \dfrac{5y}{2{x}^{3} {z}^{3 - 1} }$

$\\ \\$

$\dashrightarrow \sf\dfrac{y^{3}}{1} \times \dfrac{5y}{2{x}^{3} {z}^{2} }$

$\\ \\$

$\dashrightarrow \sf \dfrac{5y \times {y}^{3} }{2{x}^{3} {z}^{2} }$

$\\ \\$

$\dashrightarrow \sf \dfrac{5y {}^{0} \times {y}^{3 + 1} }{2{x}^{3} {z}^{2} }$

$\\ \\$

$\dashrightarrow \sf \dfrac{5 \times {y}^{4} }{2{x}^{3} {z}^{2} }$

$\\ \\$

$\dashrightarrow \bf \dfrac{5 {y}^{4} }{2{x}^{3} {z}^{2} }$

$\\ \\$

$\therefore \underline{ \textbf{ \textsf{option \red c \: is \: correct}}}$

8 0

2 years ago

Ben spent 2/3 of his allowance on video games. What is the fraction of his allowance expressed as a decimal?

Law Incorporation [45]

2/3 = 0.6667 round up = 0.7
Answer is B. 0.7 repeating
Hope it helps

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3 years ago

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Two lines, C and D, are represented by the following equations:

Usimov [2.4K]

The second choice is the answer

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4 years ago