1) The math department at Kennedy Middle School is planning to buy some pattern blocks

Paladinen [302]

Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

<h3>What is the Pythagoras Theorem?</h3>

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In △ABD and △ACB,

∠A = ∠A (common)

∠ADB = ∠ABC (both are right angles)

Thus, △ABD ∼ △ACB (by AA similarity criterion)

Similarly, we can prove △BCD ∼ △ACB.

Thus △ABD ∼ △ACB,

Therefore, AD/AB = AB/AC.

We can say that AD × AC = AB².

Similarly, △BCD ∼ △ACB.

Therefore,

CD/BC = BC/AC.

We can also say that

CD × AC = BC².

Adding these 2 equations, we get

AB² + BC² = (AD × AC) + (CD × AC)

AB² + BC² =AC(AD +DC)

AB² + BC² = AC²

Hence proved

Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Learn more about Pythagoras theorem from:

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6 0

2 years ago

The function g(x) is graphed.

sergejj [24]

g(1)=-1 : We need to check values of function for x=1. From the graph, we can see, for x=1 the value of y is 1.

So, g(1)=-1 is false.

g(0)=0 : We need to check values of function for x=0. From the graph, we can see, for x=0 the value of y is 0.

So, g(0) =0 is true.

g(4)=-2 :We need to check values of function for x=4. From the graph, we can see, for x=4 the value of y is going up but it's not equal to -2.

So, g(4)=-2 is false.

g(1)=1 :We need to check values of function for x=1. From the graph, we can see, for x=1 the value of y is 1.

So, g(1) =1 is true.

g(-1)=1 :We need to check values of function for x=-1. From the graph, we can see, for x=-1 the value of y is 1.

So, g(-1)=1 is true.

g(4)=2 :We need to check values of function for x=4. From the graph, we can see, for x=4 the value of y is going up but it's not equal to 2.

So, g(4)=2 is false.

3 0

3 years ago

Find the future value if £7400 is<br> invested for 6 years at 12.8% p.a.<br> Total

Juli2301 [7.4K]

Answer:

the future value is £15,243.56

Step-by-step explanation:

The computation of the future value is shown below:

As we know that

Future value = Present value × (1 + rate of interest)^number of years

= £7400 × (1 + 0.128)^6

= £15,243.56

Hence, the future value is £15,243.56

7 0

3 years ago

The Municipal Transit Authority wants to know if, on weekdays, more passengers ride the northbound blue line train towards the c

Kitty [74]

Answer:

The 90% confidence interval $-49.8$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 < \mu_2$

The distribution test statistics is $t = -3.222$

The rejection region is p-value < $\alpha$

The decision rule is reject the null hypothesis

The conclusion is

There is sufficient evidence to conclude that there are more passengers riding the 8:30 train

The p-value is $p-value =0.000951$

Step-by-step explanation:

From the question we are told that

The first sample size $n_1 = 30$

The first sample mean is $\= x _1 = 323$

The first standard deviation is $s_1 = 41$

The second sample size is $n_2 = 45$

The second sample mean is $\=x_2 = 356$

The second standard deviation is $s_2 = 45$

given that the confidence level is 90% then the level of significance is mathematically represented as

$\alpha = (100 -90)\%$

$\alpha = 0.10$

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

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the pooled variance is mathematically represented as

$s^2 = \frac{(n_1 - 1)s_1^2 + (n_2 -1)s_2^2 }{n_1 + n_2 -2}$

$s^2 = \frac{(30 -1)(41^2) + (45-1)45^2}{30+45 -2}$

$s^2 = 1888.34$

Generally the standard error is mathematically represented as

$SE = \sqrt{\frac{s^2}{n_1} + \frac{s^2}{n_2} }$

=> $SE = \sqrt{\frac{1888.34}{30} + \frac{1888.34}{45} }$

=> $SE = 10.24$

Generally the margin of error is mathematically evaluated as

$E = Z_{\frac{\alpha }{2} } * SE$

$E = 1.645* 10.24$

$E = 16.85$

Generally the 90% confidence interval is mathematically represented as

$\=x_1 -\=x_2 -E < \mu_1 -\mu_2 < \=x_1 -\=x_2 +E$

$323 -356 -16.84$

$-49.8$

The null hypothesis is $H_o : \mu_1 = \mu_2$

The alternative hypothesis $H_a : \mu_1 < \mu_2$

Generally the test statistics is mathematically represented as

$t = \frac{\= x_1 - \=x_2 }{SE}$

=> $t = \frac{323-356}{10.24}$

=> $t = -3.222$

Generally the degree of freedom is mathematically represented as

$df = n_1+n_2 -2$

$df = 30 + 45 -2$

$df = 73$

The p-value is obtained from the student t distribution table at degree of freedom of 73 at 0.05 level of significance

The value is $p-value =0.000951$

Here the level of significance is $\alpha = 5\% = 0.05$

Given that the p-value < $\alpha$ then we reject the null hypothesis

Then the conclusion is

There is sufficient evidence to conclude that there are more passengers riding the 8:30 train

5 0

3 years ago

Marie wants to know the most popular car for parents. She plans to survey the people entering the mall from 10:00 a.m. to 11:00

Andreyy89

Answer:

C. Marie should make sure she surveys both the fathers and mothers.

3 0

2 years ago