What is the first step in solving for zin equation 5z

LekaFEV [45]

Step-by-step explanation:

In trapezoid ABCD, it is given that:

AE = BE & DF = CF

Hence, points E and F are the mid points of the sides AB and CD respectively.

We know that:

In a trapezoid length of the line segment joining the mid points of non parallel sides is equal to one half of the sum of lengths of the parallel sides.

$\therefore \: 4x = \frac{1}{2} \{(x + 5) + 44 \} \\ \\ \therefore \: 4x = \frac{1}{2} \{x + 5 + 44 \} \\ \\ \therefore \: 4x \times 2= \{x + 49\} \\ \\ \therefore \: 8x = x + 49 \\ \\ \therefore \: 8x - x = 49 \\ \\ \therefore \: 8x - x = 49 \\ \\ \therefore \:7x = 49 \\ \\ \therefore \:x = \frac{49}{7} \\ \\ \therefore \:x = 7\\ \\ \therefore \:4x = 4\times 7.. (\because EF = 4x)\\ \\ \: \: \: \: \: \huge \red{ \boxed{\therefore \:EF = 28}}$

3 0

4 years ago

A model ship is built to scale of 1:400. If the actual length of the ship is 45 m, the length of the model will be what in centi

jekas [21]

Answer:

11.25 cm

Step-by-step explanation:

Actual ship: 45m → 4500 cm

Model ship: 4500/400 = 11.25 cm

5 0

4 years ago

for the data values below construct a 95 confidence interval if the sample mean is known to be 12898 and the standard deviation

Volgvan

Answer:

A 95% confidence interval for the population mean is [3315.13, 22480.87] .

Step-by-step explanation:

We are given that for quality control purposes, we collect a sample of 200 items and find 24 defective items.

Firstly, the pivotal quantity for finding the 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 proportion of defective items = 12,898

s = sample standard deviation = 7,719

n = sample size = 5

$\mu$ = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.776 < $t_4$ < 2.776) = 0.95 {As the critical value of t at 4 degrees of

freedom are -2.776 & 2.776 with P = 2.5%}

P(-2.776 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.776) = 0.95

P( $-2.776 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.776 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.776 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.776 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.776 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.776 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $12,898-2.776 \times {\frac{7,719}{\sqrt{5} } }$ , $12,898+2.776 \times {\frac{7,719}{\sqrt{5} } }$ ]

= [3315.13, 22480.87]

Therefore, a 95% confidence interval for the population mean is [3315.13, 22480.87] .

5 0

4 years ago

8. What is m<1 77 1 56 A 103° | C 133° C ° D 124° B 47°

saveliy_v [14]

Answer:

Option C

Step-by-step explanation:

Exteriore angle property: Exterior angle equals the sum of opposite interior angles.

∠I = 77° + 56°

= 133°

5 0

3 years ago

Ryan and Marie had some marbles. if Ryan lost `15 marbles, he would have 4 times as many marbles as Marie. If Ryan lost 75 marbl

vaieri [72.5K]

Ryan's marbles = x
Marie has 4 times less marbles then Ryan would have if he lost 15 marbles (it means he would have x-15)
So, Marie marbles = (x-15):4
If Ryan lost 75 marbles (it means he would have x-75), he would have 1 1/2 times as many marbles as Marie.

We got an equation: $x-75=1\frac{1}2\cdot\frac{x-15}{4}$

          $x-75=\frac{3}2\cdot\frac{x-15}{4}$

Multiply both sides by 8:     $8x-8\cdot75=3\cdot(x-15)$

      $8x-600=3x-45$

Add 600 and subtract 3x on both sides:    $5x=555$

Divide both sides by 5:    $x=111$

Answer: Ryan have 111 marbles.

5 0

3 years ago

What is the first step in solving for zin equation 5z - 4 = 26