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4 years ago

For more than three times a number is greater than 22

Mathematics

1 answer:

TiliK225 [7]4 years ago

5 0

Answer:

Four more than three times a number is greater than twenty-two.What is the number?

The number is greater than 6.

Step-by-step explanation:

Given:

Four more than three times a number is twenty-two.

Let the number be 'x'.

Three times of 'x' = '3x'

Four more means further four is added.

So,

The number is $3x+4$

According to the question.

⇒ $3x+4=22$

⇒ $3x+4-4=22-4$ ...Subtracting 4 on both sides

⇒ $3x=18$

⇒ $x=\frac{18}{3}=6$ ...Dividing 6 on both sides

Now if it says that it is greater than 22 then we will use $>$ sign.

So the number is greater than 6 'x' > 6.

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A building inspector believes that the percentage of new construction with serious code violations may be even greater than the

Y_Kistochka [10]

Answer:

The inspector's claim has strong statistical evidence.

Step-by-step explanation:

To answer this we have to perform a hypothesis test.

The inspector claimed that the actual proportion of code violations is greater than 0.07, so the null and alternative hypothesis are:

$H_0: \pi\leq0.07\\\\H_a: \pi>0.07$

We assume a significance level of 0.05.

The sample size is 200 and the proportion of the sample is:

$p=\frac{23}{200}= 0.115$

The standard deviation is

$\sigma=\sqrt{\frac{\pi(1-\pi)}{N} }= \sqrt{\frac{0.07*0.93}{200}}=0.018$

The z-value can be calculated as

$z=\frac{p-\pi-0.5/N}{\sigma} =\frac{0.115-0.07-0.5/200}{0.018} =\frac{0.0425}{0.018}=2.36$

The P-value for this z-value is P=0.00914.

This P-value is smaller than the significance level, so the effect is significant and the null hypothesis is rejected.

The inspector's claim has strong statistical evidence.

7 0

4 years ago

Read 2 more answers

Express the weight of the main axle of the 1893 Ferris wheel in kilograms.

WITCHER [35]

Answer:

40514.837 kg

Step-by-step explanation:

The weight of the main axle of the 1893 ferris wheel built by George Washington Gale Ferris Jr. in Chicago, USA was 89,320 pounds (lb).

1 kg=2.20462 pounds (lb)

$\Rightarrow 1 lb=\frac{1}{2.20426}$

$\Rightarrow 1 lb=0.453592 kg$

$\Rightarrow 89320 lb=89320\times 0.453592$

$\therefore 89320 lb=40514.837 kg$

5 0

4 years ago

The temperature of a chemical solution is originally 21^\circ\text{C}21 ? C21, degree, C. A chemist heats the solution at a cons

Kryger [21]

Answer:

The rate is $4.5\frac{\°C}{min}$

Step-by-step explanation:

we know that

The formula to calculate the rate or slope between two points is equal to $m=\frac{y2-y1}{x2-x1}$

Let

x----> the time in minutes

y-----> the temperature in Celsius degrees

we have

$A(0,21)\ B(12,75)$

Substitute the values

$m=\frac{75-21}{12-0}$

$m=\frac{54}{12}=4.5\frac{\°C}{min}$

5 0

3 years ago

What is the sale price if an item selling for $10 id discounted 20%

lana [24]

Answer:

Step-by-step explanation:

20% of 10 is 2 so 10-2=8

3 0

3 years ago

A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section)

dolphi86 [110]

Answer:

radius r = 47/π in

length l = 23.5 in

Step-by-step explanation:

Let us recall that:

Volume of a cylinder = $\pi r^2 h$ --- (1)

The girth g = $2 \pi r + h$ ----- (2)

Given that:

height (h) + girth (g) = 141

Then g = 141 - h ----- (3)

Equating equation (2) and (3), we have:

141 - h = 2πr + h

2h = 141 - 2πr

h = 70.5 - πr ------ (4)

From, here now, we can now replace the value of h into equation (1)

i.e.

V = πr²(70.5 - πr)

V = 70.5πr² - π²r³

Taking the differential of the above equation with respect to r, we have:

$\dfrac{dv}{dr} = 141 \pi r- 3\pi ^2 r^2$

By further differentiation:

$\dfrac{d^2v}{dr^2} = 141 \pi - 6\pi ^2 r$

Let set $\dfrac{dv}{dr}= 0$ , Then:

141πr - 3π²r² = 0

141πr = 3π²r²

Divide both sides by πr

141 = 3πr

r = 141/3π

r = 47/π in

Replacing the value of r = 47/π into equation (4), we have:

h = 70.5 - πr

h = 70.5 - π(47/π)

h = 70.5 - 47

h = 23.5 in

From equation (3);

h + g = 141

23.5 + g = 141

g = 141 - 23.5

g = 117.5 in

Volume = πr²h

V = π × (47/π )² × 23.5

V = 16523.94 in³

4 0

3 years ago