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3 years ago

Need answers ASAP 15 points!

Mathematics

1 answer:

VLD [36.1K]3 years ago

7 0

Answer:

Step-by-step explanation:

Part A: 5/26

Part B: 5/26+ 1/2 which is 18/26 or 9/13

Part C: 5/26 +21/25. 'without replacing' means there is one less option in the bag. So denominator becomes 26-1=25. Numerator is 21 because there are a total of 21 consonants in the alphabet. Since we removed a vowel and not a consonant, it will remain 21.

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A rectangle is formed by placing two identical squares side by side

Agata [3.3K]

The perimeter of one square is 20 cm.

explanation: since the rectangle can be divided into two squares, we can conclude that the area of one square is 25 cm^2 because 50 / 2 = 25. the square root of 25 is 5, so one side length of the square is 5 cm. multiply that by 4 (because there’s 4 sides) and you get 20 cm.

7 0

3 years ago

If the life in years of a television set is normally distributed with a mean of 36 years and a standard deviation of 8 years wha

TiliK225 [7]

Answer:

The company should guarantee a lifetime of less than equal to 20.95 years so that less than 3% of the television sets fail while under warranty.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 36 years

Standard Deviation, σ = 8 years

We are given that the distribution of life of television sets is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

We have to find the value of x such that the probability is 0.03.

$P( X < x) = P( z < \displaystyle\frac{x - 36}{8})=0.03$

Calculation the value from standard normal z table, we have,

$\displaystyle\frac{x - 36}{8} =-1.881\\\\x = 20.952\approx 20.95$

Thus, the company should guarantee a lifetime of less than or equal to 20.95 years so that less than 3% of the television sets fail while under warranty.

3 0

3 years ago

Es of two children are 11 and 8 years.

nikdorinn [45]

Answer:

<em>In 5 years the product of their ages will be 208</em>

Step-by-step explanation:

The age of two children is 11 and 8 years.

Let's call x the number of years ahead.

We need to find when the product of their future ages is 208. The 11 years old child will be 11+x years old and the other child will be 8+x years, thus:

(11+x)(8+x)=208

Operating:

$88+11x+8x+x^2=208$

Simplifying:

$x^2+19x-120=0$

Factoring:

(x-5)(x+24)=0

Solving:

x=5, x=-24

The negative solution is not valid, thus x=5

In 5 years the product of their ages will be 208

3 0

2 years ago

David made a triangle with sides 6 cm, 9cm , 12 cm. George wanted to make a triangle bigger in size but similar to that drawn by

SashulF [63]

Step-by-step explanation:

Given :

\triangle ABC \sim \triangle XYZ .△ABC∼△XYZ.

AB = 6\:cm, \:BC = 9 \:cm, CA = 12 \:cmAB=6cm,BC=9cm,CA=12cm

Let \: XY = 10\:cm, \:YZ = x \:cm, \: XZ = y /:cmLetXY=10cm,YZ=xcm,XZ=y/:cm

\frac{AB}{XY} = \frac{BC}{x} = \frac{CA}{y}XYAB=xBC=yCA

\blue {( The \: lengths \:of \: corresponding }(Thelengthsofcorresponding

\blue {sides \:are \: proportional .)}sidesareproportional.)

\implies \frac{6}{10} = \frac{9}{x} = \frac{12}{y}⟹106=x9=y12

i) \implies \frac{6}{10} = \frac{9}{x}i)⟹106=x9

\implies x = \frac{9 \times 10}{6}⟹x=69×10

\implies x = 15\:cm⟹x=15cm

ii) \implies \frac{6}{10} = \frac{12}{y}ii)⟹106=y12

\implies y = \frac{12 \times 10}{6}⟹y=612×10

\implies y = 20\:cm⟹y=20cm

Therefore.,

\red { Value \:of \:x } \green { = 15\:cm }Valueofx=15cm

\red { Value \:of \:y } \green { = 20\:cm }Valueofy=20cm

•••♪

8 0

3 years ago

A local high school held a two-day fundraiser selling lunches. The equations shown represent the amount of money the school coll

Over [174]

Answer:

Step-by-step explanation:

The two equations appear to be ...

12x +4y = 152
32x +12y = 420

These can be solved for y using Cramer's rule:

y = (152(32) -420(12))/(4(32) -12(12)) = -176/-16 = 11

The cost of the vegetarian lunch is 11.

_____

<em>Comment on Cramer's Rule</em>

For equations ...

ax +by =c

dx +ey = f

The solutions are ...

x = (bf -ey)/(bd -ea)

y = (cd -fa)/(bd -ea) . . . . note the denominators are the same expression

Once you memorize the pattern of products, this can be the simplest way to solve a pair of equations--especially if you only need one of the variable values.

6 0

3 years ago