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3 years ago

What is the value of x?

Mathematics

1 answer:

Phantasy [73]3 years ago

6 0

Answer:

value of x = 5.8 mm

Step-by-step explanation:

We have given,

Two right triangles EDH and EDG.

In right triangle EDH, EH = 56mm , DH = 35 mm

Using Pythagoras theorem we can find ED.

i.e EH² = ED²+DH²

56²=ED²+35²

ED²=56²-35²

ED = √(56²-35²) = 7√39 = 43.71 mm

Now, Consider right triangle EDG

Here, EG=44.8mm , GD = x+4 and ED = 7√39

Again using Pythagoras theorem,

EG² = ED² + DG²

44.8²= (7√39)²+ (x+4)²

(x+4)² = 44.8² - (7√39)²

x+4 = √(44.8² - (7√39)²)

x+4 = 9.8

or x = 9.8 - 4 = 5.8 mm

Hence we got the value of x = 5.8 mm

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Suppose you pick two cards from a deck of 52 playing cards. What is the probability that they are both queens?

photoshop1234 [79]

Answer:

0.45% probability that they are both queens.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes

The combinations formula is important in this problem:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes

You want 2 queens. Four cards are queens. I am going to call then A,B,C,D. A and B is the same outcome as B and A. That is, the order is not important, so this is why we use the combinations formula.

The number of desired outcomes is a combinations of 2 cards from a set of 4(queens). So

$D = C_{4,2} = \frac{4!}{2!(4-2)!} = 6$

Total outcomes

Combinations of 2 from a set of 52(number of playing cards). So

$T = C_{52,2} = \frac{52!}{2!(52-2)!} = 1326$

What is the probability that they are both queens?

$P = \frac{D}{T} = \frac{6}{1326} = 0.0045$

0.45% probability that they are both queens.

4 0

3 years ago

What is the top half of a fraction called

ZanzabumX [31]

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3 years ago

Read 2 more answers

Consider the hypotheses below. Upper H 0: mu equals 50 Upper H 1: mu not equals 50 Given that x overbar equals 60, s equals 1

Neko [114]

Answer:

We conclude that $\mu\neq$ 50.

Step-by-step explanation:

We are given that x bar = 60, s = 12, n = 30, and alpha = 0.10

Also, Null Hypothesis, $H_0$ : $\mu$ = 50

Alternate Hypothesis, $H_1$ : $\mu$ $\neq$ 50

The test statistics we will use here is;

T.S. = $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, X bar = sample mean = 60

s = sample standard deviation = 12

n = sample size = 30

So, Test statistics = $\frac{60-50}{\frac{12}{\sqrt{30} } }$ ~ $t_2_9$

= 4.564

At 10% significance level, t table gives critical value of 1.311 at 29 degree of freedom. Since our test statistics is more than the critical value as 4.564 > 1.311 so we have sufficient evidence to reject null hypothesis as our test statistics will fall in the rejection region.

P-value is given by, P( $t_2_9$ > 4.564) = less than 0.05% {using t table}

Here also, P-value is less than the significance level as 0.05% < 10% , so we will reject null hypothesis.

Therefore, we conclude that $\mu\neq$ 50.

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3 years ago

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snow_tiger [21]

Answer:

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Step-by-step explanation:

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3 years ago