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3 years ago

4) Here is a multiplication fact.

Mathematics

1 answer:

Fittoniya [83]3 years ago

3 0

Answer:

$= \frac{2}{ 3} \\$

Step-by-step explanation:

$\frac{1}{2} \div \frac{3}{4} \\ \\ = \frac{1}{2} \times \frac{4}{3} \\ \\ = \frac{4}{6} \\ \\ = \frac{2}{3}$

ماهين

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What is the slope of the line connecting (1,5) and (4,14)?

yan [13]

m = change in y over change in x

m = (14-5)/(4-1)

m = 9/3 = 3

m = 3

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3 years ago

-9 + y = 12 <br> How do you solve this?

Goshia [24]

Answer:

-9+y=12

y=12+9

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Ans: y=21

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3 years ago

1/2 : 10 = 2 12 : x<br> What is the value of x

liberstina [14]

I am probably wrong but with the math I do I got 35

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3 years ago

Solve each triangle. Round your answers to the nearest tenth.<br>show work If possible

kvasek [131]

<h2>Answer:</h2>

∠ABC = 76°

BC = 20.1

CA = 28.0

<h2>Step-by-step explanation:</h2>

Solving the triangle means finding all unknown angles and sides of the triangle.

(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating <em>that the sum of angles of a triangle is equal to 180°.</em>

Therefore, the sum of angles of the triangle ABC is 180°. i.e

∠ABC + ∠BCA + ∠CAB = 180°

=> ∠ABC + 60° + 44° = 180°

=> ∠ABC + 104° = 180°

=> ∠ABC = 180° - 104°

=> ∠ABC = 76°

(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;

=> $\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}$

=> $\frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}$

<em>Substitute the necessary values</em>

$\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}$ ---------------------(ii)

(a) To get side BC, use the first two terms of equation (ii)

$\frac{sin60}{25} = \frac{sin44}{BC}$

<em>Cross multiply</em>

BC x sin 60 = 25 x sin 44

BC x 0.8660 = 25 x 0.6947

0.8660 x BC = 17.3675

BC = $\frac{17.3675}{0.8660}$

BC = 20.05

=> BC = 20.1 to the nearest tenth

(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;

$\frac{sin60}{25} = \frac{sin76}{CA}$

<em>Cross multiply</em>

CA x sin 60 = 25 x sin 76

CA x 0.8660 = 25 x 0.9703

0.8660 x CA = 24.2575

CA = $\frac{24.2575}{0.8660}$

CA = 28.01

=> CA = 28.0 to the nearest tenth

5 0

3 years ago

You are trying to determine if you should accept a shipment of eggs for a local grocery store. About 4% of all cartons which are

padilas [110]

Answer:

0.8809

Step-by-step explanation:

Given that:

The population proportion p = 4% = 4/100 = 0.04

Sample mean x = 16

The sample size n = 300

The sample proportion $\hat p =\dfrac{x}{n}$

= 16/300

= 0.0533

∴

$P(\hat p \leq 0.0533) = P\bigg ( \dfrac{\hat p - p}{\sqrt{\dfrac{P(1-P)}{n}}}\leq\dfrac{0.0533 - 0.04}{\sqrt{\dfrac{0.04(1-0.04)}{300}}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{\dfrac{0.04(0.96)}{300}}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{\dfrac{0.0384}{300}}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{1.28 \times 10^{-4}}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{0.0113}}\bigg )$

$P(\hat p \leq 0.0533) = P\bigg ( Z\leq1.18}\bigg )$

From the z tables;

= 0.8809

Let X be the random variation that follows a normal distribution;

Then;

population mean $\mu$ = n × p

population mean $\mu$ = 300 × 0.04

population mean $\mu$ = 12

The standard deviation $\sigma = \sqrt{np(1-p)}$

The standard deviation $\sigma = \sqrt{300 \times 0.04(1-0.04)}$

The standard deviation $\sigma = \sqrt{11.52}$

The standard deviation $\sigma = 3.39$

The z -score can be computed as:

$z = \dfrac{x - \mu}{\sigma}$

$z = \dfrac{16 -12}{3.39}$

$z = \dfrac{4}{3.39}$

z = 1.18

The required probability is:

P(X ≤ 10) = Pr (z ≤ 1.18)

= 0.8809

5 0

3 years ago