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3 years ago

15

A cake recipe calls for 3 grams of salt for every 7 grams of sugar.If we are to use 31 grams of sugar,how much salt should we us

e ?

1 answer:

Zanzabum3 years ago

7 0

Answer:

13.2855 salt

Step-by-step explanation:

31÷7 = 4.4285

4.4285 × 3 = 13.2855 salt

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3 years ago

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Land's Bend sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the intern

Naya [18.7K]

Answer:

80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases ( $\mu_1-\mu_2$ ) is [-9.132 , 23.332].

Step-by-step explanation:

We are given that a random sample of 7 sales receipts for mail-order sales results in a mean sale amount of $81.70 with a standard deviation of $18.75.

A random sample of 11 sales receipts for internet sales results in a mean sale amount of $74.60 with a standard deviation of $28.25.

Firstly, the Pivotal quantity for 80% confidence interval for the difference between population means is given by;

P.Q. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ ~ $t__n__1-_n__2-2$

where, $\bar X_1$ = sample mean sales receipts for mail-order sales = $81.70

$\bar X_2$ = sample mean sales receipts for internet sales = $74.60

$s_1$ = sample standard deviation for mail-order sales = $18.75

$s_2$ = sample standard deviation for internet sales = $28.25

$n_1$ = size of sales receipts for mail-order sales = 7

$n_2$ = size of sales receipts for internet sales = 11

Also, $s_p=\sqrt{\frac{(n_1-1)s_1^{2} +(n_2-1)s_2^{2} }{n_1+n_2-2} }$ = $\sqrt{\frac{(7-1)\times 18.75^{2} +(11-1)\times 28.25^{2} }{7+11-2} }$ = 25.11

<em>Here for constructing 80% confidence interval we have used Two-sample t test statistics as we don't know about population standard deviations.</em>

<em />

So, 80% confidence interval for the difference between population means, ( $\mu_1-\mu_2$ ) is ;

P(-1.337 < $t_1_6$ < 1.337) = 0.80 {As the critical value of t at 16 degree

of freedom are -1.337 & 1.337 with P = 10%}

P(-1.337 < $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ < 1.337) = 0.80

P( $-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ < ${(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}$ < $1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ ) = 0.80

P( $(\bar X_1-\bar X_2)-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ < ( $\mu_1-\mu_2$ ) < $(\bar X_1-\bar X_2)+1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ ) = 0.80

<u>80% confidence interval for</u> ( $\mu_1-\mu_2$ ) =

[ $(\bar X_1-\bar X_2)-1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ , $(\bar X_1-\bar X_2)+1.337 \times {s_p\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } }$ ]

= [ $(81.70-74.60)-1.337 \times {25.11 \times \sqrt{\frac{1}{7} +\frac{1}{11} } }$ , $(81.70-74.60)+1.337 \times {25.11 \times \sqrt{\frac{1}{7} +\frac{1}{11} } }$ ]

= [-9.132 , 23.332]

Therefore, 80% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases ( $\mu_1-\mu_2$ ) is [-9.132 , 23.332].

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3 years ago

Real estate ads suggest that 75 % of homes for sale have garages, 29 % have swimming pools, and 13 % have both features. What

Vedmedyk [2.9K]

Answer: a) 91% b) 9% c) 16%

Step-by-step explanation:

Let A be the event that homes for sale have garages and B be the event that homes for sale have swimming pools.

Now, given : $P(A)=75\%=0.75$

$P(B)=29\%=0.29$

$P(A\cap B)=13\%=0.13$

a) $P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow\ P(A\cup B)=0.75+0.29-0.13=0.91$

Hence, the probability that a home for sale has a pool or a garage is 91%.

b) The probability that a home for sale has neither a pool nor a garage is given by :-

$1-P(A\cup B)=1-0.91=0.09$

Hence, the probability that a home for sale has neither a pool nor a garage is 9%.

c) The probability that a home for sale has a pool but no garage is given by :-

$P(B)-P(A\cap B)=0.29-0.13=0.16$

Hence, the probability that a home for sale has a pool but no garage is 16%.

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3 years ago

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77julia77 [94]

1. 3 x 2 = 6 2/3 x 2 = 4/3 which is 1 whole and 1/3 so the answer is 6 + 1 1/3 = 7 1/3
2. 3 1/2 x 4 1/7 = 58
3. 1/6 x 4 you only times the first number so 4/6 which is simplified is 2/3
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5. 4 -:- 2 = 2 2/7 you only divide the first number (the 2 which makes it 1/7)
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3 years ago

Hamal has a new part time job bagging groceries after school. The equation y=10x+50 show the relationship between his hours of w

Alborosie

Answer: fdbs

Step-by-step explanation:

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3 years ago

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