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2 years ago

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The length of a rectangle is 1 more than 3 times the width. 5 times the length is 45 more than the perimeter. Find the dimension

s.

1 answer:

Murljashka [212]2 years ago

3 0

Answer:

width = w

length= 3w+1

perimeter= 5(3w+1) -45

perimeter = 2(l+b)

5(3w+1) -45 = 2{(3w+1)+w}

15w - 40 = 8w+2

6w = 42

w =7

therefore width = <u>7</u>

length= 3w+1 = <u>22</u>

perimeter= <u>65</u>

Step-by-step explanation:

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To help with thinking about this, we can say that the 6 gallons of 50% acid contains 3 gallons of pure acid and 3 gallons of filler. This would make the concentration 3/6, or 50%. Adding a gallon of pure acid would shift the concentration to 4/7, or 57.1%.

When the relationship becomes 70%, four gallons of pure acid have been added.

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2 years ago

What is less then -1 and greater then -5

FrozenT [24]

Answer:

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Step-by-step explanation:

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3 years ago

Calcium is an essential nutrient for strong bones and for controlling blood pressure and heart beat. Because most of the body’s

irakobra [83]

Answer:

No, because the 95% confidence interval contains the hypothesized value of zero.

Step-by-step explanation:

Hello!

You have the information regarding two calcium supplements.

X₁: Calcium content of supplement 1

n₁= 12

X[bar]₁= 1000mg

S₁= 23 mg

X₂: Calcium content of supplement 2

n₂= 15

X[bar]₂= 1016mg

S₂= 24mg

It is known that X₁~N(μ₁; σ²₁), X₂~N(μ₂;δ²₂) and σ²₁=δ²₂=?

The claim is that both supplements have the same average calcium content:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

α: 0.05

The confidence level and significance level are to be complementary, so if 1 - α: 0.95 then α:0.05

since these are two independent samples from normal populations and the population variances are equal, you have to use a pooled variance t-test to construct the interval:

[(X[bar]₁-X[bar]₂) ± $t_{n_1+n_2-2;1-\alpha /2}$ * $Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} }$ ]

$t_{n_1+n_2-2;1-/2}= t_{25;0.975}= 2.060$

$Sa= \sqrt{\frac{(n_1-1)S^2_1+(n_2-1)S^2_2}{n_1+n_2-2} }= \sqrt{\frac{11*529+14*576}{12+15-2} } = 23.57$

[(1000-1016)±2.060*23.57* $\sqrt{\frac{1}{12} +\frac{1}{15} }$ ]

[-34.80;2.80] mg

The 95% CI contains the value under the null hypothesis: "zero", so the decision is to not reject the null hypothesis. Then using a 5% significance level you can conclude that there is no difference between the average calcium content of supplements 1 and 2.

I hope it helps!

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=16y%20%5E%7B5%7D%20-%2012y%20%5E%7B4%7D%20%2B%204y%20%5C%5C%20%5C%5C%2064%20a%20%5Ctimes%20%5E

Shkiper50 [21]

Answer:

see explanation

Step-by-step explanation:

Assuming you require to factorise the expressions

16 $y^{5}$ - 12 $y^{4}$ + 4y ← factor out 4y from each term

= 4y(4 $y^{4}$ - 3y³ + 1)

--------------------------------

64ax² - 49ay² ← factor out a from each term

= a(64x² - 49y²) ← this is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

64x² - 49y²

= (8x)² - (7y)²

= (8x - 7y)(8x + 7y)

then

64ax² - 49ay² = a(8x - 7y)(8x + 7y)

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1 year ago

You need to purchase supplies for an employee appreciation picnic. Your boss gives you the shopping list below and asks that you

Natalka [10]

To get the units needed, divide the given number of items needed shown in the above portion of table, with the package size given in the below portion. Then multiply with given prices. Round off the numbers to whole numbers.

Now, money needs to be spent in Quality Groceries-

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=$ 168.40

Now, money needs to be spent in Fresh Market-

$(7*12.4)+(3*4.99)+(7*3.55)+(3*2.55)+(2*5.55)+(5*6.99)$

=$ 180.32

So, the answer is option B.

3 0

3 years ago

Read 2 more answers