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3 years ago

"\frac{?}{5} * \frac{10}{8} =1.5\\" alt="\frac{?}{5} * \frac{10}{8} =1.5\\" align="absmiddle" class="latex-formula"> What number would replace the '?'

Mathematics

1 answer:

Serggg [28]3 years ago

4 0

Answer:

$\boxed{\sf \huge \boxed{ \sf ?} = 6}$

Step-by-step explanation:

$\sf Solve \: for \: \boxed{ \sf ?} : \\ \sf \implies \frac{\boxed{ \sf ?}}{5} \times \frac{10}{8} = 1.5 \\ \\ \sf \implies \frac{\boxed{ \sf ?} \times 10}{5 \times 8} = 1.5 \\ \\ \sf \frac{10}{5} = \frac{ \cancel{5} \times 2}{ \cancel{5}} = 2 : \\ \sf \implies \frac{ \boxed{ \sf 2} \times \boxed{ \sf ?} }{8} = 1.5 \\ \\ \sf \frac{2}{8} = \frac{ \cancel{2}}{ \cancel{2} \times 4} = \frac{1}{4} : \\ \sf \implies \frac{\boxed{ \sf ?}}{ \boxed{ \sf 4}} = 1.5 \\ \\ \sf Multiply \: both \: sides \: of \: \frac{\boxed{ \sf ?}}{4} = 1.5 \: by \: 4 : \\ \sf \implies \frac{4 \times \boxed{ \sf ?}}{4} = 4 \times 1.5 \\ \\ \sf \frac{4 \times \boxed{ \sf ?}}{4} = \frac{ \cancel{4}}{ \cancel{4}} \times \boxed{ \sf ?} = \boxed{ \sf ?} : \\ \sf \implies \boxed{\boxed{ \sf ?}} = 4 \times 1.5 \\ \\ \sf 4 \times 1.5 = 6 : \\ \sf \implies \boxed{ \sf ?} = 6$

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1. Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into

Ludmilka [50]

Answer:

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Step-by-step explanation:

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3 years ago

Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

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6 0

3 years ago

VERY URGENT.

NemiM [27]

Answer:

(1)Base Area= 81 square yards.

(2)

3 ft long and 16 ft wide

6 ft long and 8 ft wide
24 ft long and 2 ft wide

(3)Height=12 Units

Step-by-step explanation:

Question 1

Volume of the rectangular prism=2,592 cubic yards.

Height of the rectangular prism=32 yards

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=2592

32lb=2592

lb=2592/32=81

Base Area= 81 square yards.

Question 2

Volume of the rectangular prism=432 cubic feet.

Height of the rectangular prism=9 feet

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=432

9lb=432

lb=432/9=48

Base Area= 48 square yards.

Any dimension whose product is 48 is a possible choice.

They are:

3 ft long and 16 ft wide
6 ft long and 8 ft wide
24 ft long and 2 ft wide

Question 3

Volume of the rectangular prism=960 cubic units.

Base Area of the rectangular prism, lb=80 Square Units

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=960

80h=960

h=960/80=12

Height= 12 units.

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3 years ago

Please help!

AfilCa [17]

Answer:

a.) P(HH|C)=2/5

Explanation:

Given following:

P(HH) = 7

P(C) = 10

P(HH ∩ C) = 4

P(HH ∪ C) = 13

Solving steps:

$\sf P(HH|C) = \dfrac{P(HH \cap C) }{P(C)}$

$\sf P(HH|C) = \dfrac{4 }{10}$

$\sf P(HH|C) = \dfrac{2 }{5}$

8 0

1 year ago

6 times the difference of a number and 4 equals 7

Nonamiya [84]

6( x - 4) = 7
6 x - 24 = 7
6 x = 7 + 24
6 x = 31
x = 31/6

6 ( 31/6 - 4) = 7
186/6 - 24 = 7
186/6 = 144/6 = 7

42/6 = 7
7 = 7

4 0

3 years ago