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2 years ago

What is the area of this triangle?

Mathematics

1 answer:

Ganezh [65]2 years ago

6 0

Answer:

$\boxed{\bold{120 \ Units^2}}$

Step By Step Explanation:

Area Of Triangle: $\bold{\frac{1}{2}Base \ \cdot \ Height}$

Base: 10

Height: 24 (This triangle has a right angle, so we use the height based off of the 90° angle, which is 24)

Insert Numbers Into Equation

$\bold{\frac{1}{2}10 \ \cdot \ 24}$

$\bold{\frac{1}{2}}$ 10 = 5

$\bold{5 \ \cdot \ 24 \ = \ 120}$

➤ $\boxed{\bold{Mordancy}}$

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Three perfect cube blocks of different volumes were stacked on top of each other. The top block was 64 cubic centimeters, the mi

lesya [120]

We know that

[volume of a cube]=b³---------> b=∛Volume
b------> is the side length of a cube

The top block was 64 cm³------> b1=∛64-------> b1=4 cm
The middle block was 125 cm³------> b2=∛125------> b2=5 cm
The biggest block was 729 cm³------> b3=√729------> b3=9 cm

[the stack of blocks tall]=b1+b2+b3-------> 4+5+9-----> 18 cm

the answer is
the stack of blocks was 18 cm tall

5 0

2 years ago

kiyoko lives 7/8 of a mile from school. if she walks half the distance and runs the other half, both to and from school, how man

love history [14]

If she runs half the distance to school, and runs the same back, this means that she suns 7/8 miles in a day. In 5 days, 5 x 7/8 = 35/8 miles (or 4.375 miles in 5 days).

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2 years ago

The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of th

timama [110]

Answer: (0.076, 0.140)

Step-by-step explanation:

Confidence interval for population proportion (p) is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = sample proportion.

n= sample size.

$\alpha$ = significance level .

$z_{\alpha/2}$ = critical z-value (Two tailed)

As per given , we have

sample size : n= 500

The number of Independents.: x= 54

Sample proportion of Independents $\hat{p}=\dfrac{x}{n}=\dfrac{54}{500}=0.108$

Significance level 98% confidence level : $\alpha=1-0.98=0.02$

By using z-table , Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

The 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters will be :-

$0.108\pm (2.33)\sqrt{\dfrac{0.108(1-0.108)}{500}}\\\\=0.108\pm2.33\times0.013880634\\\\=0.108\pm0.03234187722\\\\\approx0.108\pm0.032=(0.108-0.032,\ 0.108+0.032)=(0.076,\ 0.140)$

Hence, the 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters.= (0.076, 0.140)

8 0

2 years ago

A manufacturer of running shoes knows that the average lifetime for a particular model of shoes is 15 months. Someone in the res

AveGali [126]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the designer's claim of a better shoe is supported by the trial results.

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 15 \ months$

The sample size is n = 25

The sample mean is $\= x = 17 \ months$

The standard deviation is $s = 5.5 \ months$

Let assume the level of significance of this test is $\alpha = 0.05$

The null hypothesis is $H_o : \mu = 15$

The alternative hypothesis is $H_a : \mu > 17$

Generally the degree of freedom is mathematically represented as

$df = n -1$

=> $df = 25 -1$

=> $df = 24$

Generally the test statistics is mathematically represented as

$t = \frac{\= x- \mu }{\frac{s}{\sqrt{n} } }$

=> $t = \frac{ 17 - 15 }{\frac{5.5}{\sqrt{25} } }$

=> $t = 1.8182$

Generally from the student t distribution table the probability of obtaining $t = 1.8182$ to the right of the curve at a degree of freedom of $df = 24$ is

$p-value = P(t > 0.18182 ) = 0.4286$