All categories

3 years ago

The leg of an isosceles triangle has a length 2x+4 and the base has length 3x. The

Mathematics

1 answer:

ikadub [295]3 years ago

4 0

Answer:

$Base = 57$

Step-by-step explanation:

Given

$Length = 2x + 4$

$Base = 3x$

$Perimeter = 141$

Required

Determine the length of the base

The perimeter of an isosceles triangle is:

$Perimeter = 2*Length + Base$

$141 = 2 (2x + 4) + 3x$

$141 = 4x + 8 + 3x$

Collect Like Terms

$4x + 3x = 141 - 8$

$7x = 133$

Divide both sides by 7

$x = 19$

To get the base, we substitute 19 for x in $Base = 3x$

$Base = 3 * 19$

$Base = 57$

You might be interested in

Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In p

Bingel [31]

Answer:

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is significant difference between in drug resistance between the two states

B)

The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance

Rejected H₀

There is a significant difference in drug resistance between the two states.

P - value = 0.0066

P - value = 0.0066 < 0.02

D)

1) Reject H₀

There is a significant difference in drug resistance between the two states.

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 174

Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant.

First sample proportion

$p_{1} = \frac{x_{1} }{n_{1} } = \frac{11}{174} = 0.0632$

Given second sample size n₂ = 375

Given data Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant

Second sample proportion

$p_{2} = \frac{x_{2} }{n_{2} } = \frac{7}{375} = 0.0186$

Step(ii):-

Null hypothesis:H₀:- There is no significant difference between in drug resistance between the two states

Alternative Hypothesis :H₁:

There is significant difference between in drug resistance between the two states

Test statistic

$Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }$

Where

$P = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} +n_{2} }$

$P = \frac{174 (0.0632) + 375 (0.0186) }{174+375 } = \frac{17.9718}{549} = 0.0327$

Q = 1 - P = 1 - 0.0327 = 0.9673

Step(iii):-

Test statistic

$Z = \frac{p_{1}-p_{2} }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }$

$Z = \frac{0.0632-0.0186 }{\sqrt{0.0327 X 0.9673(\frac{1}{174 }+\frac{1}{375 } ) } }$

Z = 2.7261

Level of significance = 0.02 or 0.98

The z-value = 2.054

The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance

Reject H₀

There is a significant difference in drug resistance between the two states.

P- value

P( Z > 2.7261) = 1 - P( Z < 2.726)

= 1 - ( 0.5 + A (2.72))

= 0.5 - 0.4967

= 0.0033

we will use two tailed test

2 P( Z > 2.7261) = 2 × 0.0033

= 0.0066

P - value = 0.0066 < 0.02

Reject H₀

There is a significant difference in drug resistance between the two states.

8 0

3 years ago

water flows through a pipe at a rate of 7 cubic meters per month. Express this rate of flow in gallons per minute. Round your an

Nezavi [6.7K]

Answer:

0.04

Step-by-step explanation:

4 0

3 years ago

9966 [12]

Answer:

The SAS(Side-Angle-Side) triangle congruency theorem can be used to prove Triangle MNL is congruent to ONP.

Step-by-step explanation:

We would use the side-angle-side theorem because the two triangles both have two equal sides and one angle. For instance, side MN has two lines and so does side ON has two lines. Same goes with sides NL and NP.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

7 0

3 years ago

Read 2 more answers

8. The cone below has a diameter of 8 inches and a height of 20 inches. The

IRINA_888 [86]

Answer: A 2

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

PLEASE HELP 10 POINTS WILL GIVE BRAINLIEST: Which geometric solid is the best model for the head of a human being?

-BARSIC- [3]

Answer:

sphere

Step-by-step explanation:

Human heads are close to circles and sometimes are circles

3 0

3 years ago