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2 years ago

Find the surface area of an open-top box with length 5 cm, width 6 cm, and height 4 cm.

Mathematics

1 answer:

Dimas [21]2 years ago

4 0

Answer: 148 cm²

Step-by-step explanation:

Surface Area will be= [2 x {(5x6)+(6x4)+(5x4)}] = 148 cm²

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Solve 15 < 4x on a number line

prisoha [69]

Answer:

that shall answer 15 < 4x on a number line

Step-by-step explanation:

view image for more clarity

7 0

3 years ago

X-3y=2 what is the slope

Brums [2.3K]

1/3 is the slope.
x-3y=2
-3y=-x+2
y=(1/3)x+2/3

3 0

3 years ago

| x - 1 | = 5x + 10<br> Check for extraneous solutions.

Ronch [10]

[x-1]=5x+10

We have two equations:
1) x-1=5x+10

x-1=5x+10
x-5x=10+1
-4x=11
x=-11/4

2) x-1=-(5x+10)

x-1=-(5x+10)
x-1=-5x-10
x+5x=-10+1
6x=-9
x=-9/6=-3/2

we have two possible solutions:
solution₁; x=-11/4
solution₂: x=-3/2

we check it out:
1) x=-11/4
[x-1]=5x+10
[-11/4 - 1]=5(-11/4)+10
[(-11-4)/4]=-55/4 + 10
[-15/4]=(-55+40) /4
15/4≠-15/4 This solution don´t work.

2) x=-3/2
[x-1]=5x+10
[-3/2 - 1]=5(-3/2)+10
[(-3-2)/2]=-15/2 + 10
[-5/2]=(-15+20)/2
5/2=5/2; this solution works.

Therefore:

Answer: x=-3/2.

8 0

3 years ago

Read 2 more answers

In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0

uysha [10]

Answer:

a) A response of 8.9 represents the 92nd percentile.

b) A response of 6.6 represents the 62nd percentile.

c) A response of 4.4 represents the first quartile.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5.9

Standard Deviation, σ = 2.2

We assume that the distribution of response is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) We have to find the value of x such that the probability is 0.92

P(X < x)

$P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.92$

Calculation the value from standard normal z table, we have,

$P(z$

$\displaystyle\frac{x - 5.9}{2.2} = 1.405\\x = 8.991 \approx 8.9$

A response of 8.9 represents the 92nd percentile.

b) We have to find the value of x such that the probability is 0.62

P(X < x)

$P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.62$

Calculation the value from standard normal z table, we have,

$P(z$

$\displaystyle\frac{x - 5.9}{2.2} = 0.305\\x = 6.571 \approx 6.6$

A response of 6.6 represents the 62nd percentile.

c) We have to find the value of x such that the probability is 0.25

P(X < x)

$P( X < x) = P( z < \displaystyle\frac{x - 5.9}{2.2})=0.25$

Calculation the value from standard normal z table, we have,

$P(z$

$\displaystyle\frac{x - 5.9}{2.2} = -0.674\\x = 4.4172 \approx 4.4$

A response of 4.4 represents the first quartile.

4 0

3 years ago

Find the angle between the vectors u=i-9j and v=8i+5j

Katyanochek1 [597]

Answer: $\cos^{-1} \left(\frac{-37}{\sqrt{7298}} \right) \approx 115.665^{\circ}$

Step-by-step explanation:

$u \cdot v=(1)(8)+(-9)(5)=-37\\\\|u|=\sqrt{1^{2}+(-9)^{2}}=\sqrt{82}\\\\|v|=\sqrt{8^{2}+5^{2}}=\sqrt{89}\\\\\cos \theta=\frac{-37}{\sqrt{82}\sqrt{89}}\\\\\theta=\cos^{-1} \left(\frac{-37}{\sqrt{82}\sqrt{89}} \right)\\\\\theta=\boxed{\cos^{-1} \left(\frac{-37}{\sqrt{7298}} \right) \approx 115.665^{\circ}}$

7 0

2 years ago