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3 years ago

Solve : .5x - 3.5 = 3x + 4.5

Mathematics

1 answer:

umka2103 [35]3 years ago

6 0

Answer:

x = 4.

Step-by-step explanation:

5x - 3.5 = 3x + 4.5

5x - 3x = 4.5 + 3.5

2x = 8

x = 4.

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A scale on a blue print drawing of a house shows that 10 1010 centimeters represents 2 22 meters. What number of actual meters a

Ivenika [448]

Answer:

On Blue print 18 centimeters represents 3.6 meters.

Step-by-step explanation:

Given:

Scale is 10 cm = 2 m

We need to find the number of actual meters are represented by 18 1818 centimeters on the blue print.

Solution:

Now we know that;

10 cm = 2 m

so 1 cm = Number of meters in 1 cm.

By using Unitary method we get;

Number of meters in 1 cm = $\frac{2}{10}=0.2\ m$

Now we know that;

1 cm = 0.2 m

18 cm = Number of meters in 18 cm.

Again by using Unitary method we get;

Number of meters in 18 cm = $0.2\times 18 = 3.6\ m$

Hence On Blue print 18 centimeters represents 3.6 meters.

7 0

3 years ago

The 154 tenth-graders at Wilson High School were polled on whether they enjoyed their algebra or geometry course more. The resul

wolverine [178]

Answer: 80/154

47/87

No, P(male)does not equal P(male | geometry)

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What value is the 9's in 39,990?

Reptile [31]

Thousands of your talking about 9,99O but if it's only one nine it's either tens hundreds or thousand

8 0

4 years ago

Suppose a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg,

lianna [129]

Answer:

(a) Probability that Y falls into the dangerous region is 0.0013.

(b) Probability that the mean Y-bar falls into the dangerous region is 0.00001.

Step-by-step explanation:

We are given that a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg, σ = 1 mg).

A dosage of 13 mg is considered dangerous.

Let Y = dosage of the active ingredient

The z-score probability distribution for normal distribution is given by;

Z = $\frac{ Y-\mu}{\sigma} } }$ ~ N(0,1)

where, $\mu$ = population mean = 10 mg

$\sigma$ = standard deviation = 1 mg

(a) Probability that Y falls into the dangerous region is given by = P(Y $\geq$ 13 mg)

P(Y $\geq$ 13 mg) = P( $\frac{ Y-\mu}{\sigma} } }$ $\geq$ $\frac{ 13-10}{1} } }$ ) = P(Z $\geq$ 3) = 1 - P(Z < 3)

= 1 - 0.9987 = 0.0013

The above probability is calculated by looking at the value of x = 3 in the z table which has an area of 0.9987.

(b) We are given that a dosage of 13 mg is considered dangerous. And we sample 49 capsules at random.

Let $\bar Y$ = sample mean dosage

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar Y-\mu}{\frac{\sigma}{\sqrt{n} } } } }$ ~ N(0,1)

where, $\mu$ = population mean = 10 mg

$\sigma$ = standard deviation = 1 mg

n = sample of capsules = 49

So, Probability that the mean Y-bar falls into the dangerous region is given by = P( $\bar Y$ $\geq$ 13 mg)

P(Y $\geq$ 13 mg) = P( $\frac{\bar Y-\mu}{\frac{\sigma}{\sqrt{n} } } } }$ $\geq$ $\frac{13-10}{\frac{1}{\sqrt{49} } } } }$ ) = P(Z $\geq$ 21) = 1 - P(Z < 21)

= 0.00001

6 0

3 years ago

Translate into an algebraic expression and simplify if possible. C It would take Maya x minutes to rake the leaves and Carla y m

lina2011 [118]

Answer:

in one minute they rake $\frac{y+x}{xy}$ leaves working together.

Step-by-step explanation:

If Maya rakes the leaves in x minutes, then, in one minute she rakes $\frac{1}{x}$ leaves.

In the case of Carla, if she rakes the leaves in y minutes, in one minute she rakes $\frac{1}{y}$ leaves.

Therefore, to know the portion of leaves they can rake in one minute working together, we need to sum up both of the portions each one of them rake in one minute, this gives us: $\frac{1}{x}+ \frac{1}{y}$

Now, to simplify this expression:

$\frac{1}{x}+ \frac{1}{y} =\frac{y+x}{xy}$

Thus, in one minute they rake $\frac{y+x}{xy}$ leaves.

8 0

4 years ago