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avanturin [10]
2 years ago
7

Find three consecutive integers such that the product of the first and third is 5 greater than 5 times the second.

Mathematics
1 answer:
ivolga24 [154]2 years ago
6 0

Answer:

Step-by-step explanation:

3 consecutive integers....

1st integer = x

2nd integer = x + 1

3rd integer = x + 2

the product of 1st and 3rd is 5 greater then 5 times the 2nd...

x(x+2) = 5(x + 1) + 5

x^2 + 2x = 5x + 5 + 5

x^2 + 2x = 5x + 10

x^2 + 2x - 5x - 10 = 0

x^2 - 3x - 10 = 0

(x - 5)(x + 2) = 0

x - 5 = 0             x + 2 = 0

x = 5                   x = -2

so it will be : 5,6,and 7     or -2,-1, and 0

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If there are 42 boys and 54 girls in a room, fill out all of the possible
Setler79 [48]

Answer:

21:27 and 14:18

Step-by-step explanation:

We can solve this by using common factors

one of the common factors of 54 and 42 is 3

42/3=14

54/3=18

so one of the ratios is 14:18

another common factor is 2

42/2=21

54/2=27

so another ratio is 21:27

4 0
3 years ago
Of 136 randomly selected adults, 33 were found to have high blood pressure. Construct a 95% confidence interval for the true of
navik [9.2K]

Answer:

The 95% confidence interval of the proportion of all adults that have high blood pressure is 0.17059 < \hat{p} < 0.314695

Step-by-step explanation:

The confidence interval for a proportion is given by the following formula;

CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}

Where:

x = 33

n = 136

\hat{p} = x/n = 33/136 = 0.243

z value for 95% confidence is 1.96

Plugging in the values, we have;

CI=0.243\pm 1.96\times \sqrt{\frac{0.243(1-0.243)}{136}}

Which gives;

0.17059 < \hat{p} < 0.314695

Hence the 95% confidence interval of the proportion of all adults that have high blood pressure = 0.17059 < \hat{p} < 0.314695

From the above we have;

23.2 < x < 42.798

Since we are dealing with people, we round down as follows;

23 < x < 42.

4 0
2 years ago
What is -2(4n - 1) +15<br> I think that it is -8n - 13 but i am not sure plz help
ANEK [815]

Answer: Your right!

-8n-13

Step-by-step explanation:

-2(4n-1)+15=

-8n+2-15

Combine like terms- 2-5= -13

so -8n-13

8 0
2 years ago
Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with
skad [1K]

Parameterize S by the vector function

\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle

with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.

Compute the outward-pointing normal vector to S :

\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle

The integral of the field over S is then

\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv

\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv

\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}

8 0
2 years ago
Does anyone need help
daser333 [38]
Me please !!!!!! MEEE
7 0
2 years ago
Read 2 more answers
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