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3 years ago

0.5 (x-3) = 3x - 2.5 how many solutions

Mathematics

1 answer:

Nimfa-mama [501]3 years ago

4 0

Answer:

There is 1 solution.

Step-by-step explanation:

0.5(x - 3) = 3x - 2.5

0.5x - 1.5 = 3x - 2.5

-2.5x = -1

x = 0.4

There is 1 solution.

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A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.

SVEN [57.7K]

Answer:

0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

A pretzel company calculated that there is a mean of 73.5 broken pretzels in each production run with a standard deviation of 5.1.

This means that $\mu = 73.5, \sigma = 5.1$

Find the probability that there will be fewer than 69 broken pretzels in a run.

This is the p-value of Z when X = 69.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{69 - 73.5}{5.1}$

$Z = -0.88$

$Z = -0.88$ has a p-value of 0.1894

0.1894 = 18.94% probability that there will be fewer than 69 broken pretzels in a run.

3 0

3 years ago

Question mark 1: Match the triangle to correct function and answer

postnew [5]

Answer:

Triangle 1 - $m\angle A = 58^{\circ}$ , hypotenuse = 16

$x \approx 8.479$

Triangle 2 - $m \angle A = 44^{\circ}$ , adjacent leg = 18

$x \approx 17.382$

Triangle 3 - $m\angle A = 49^{\circ}$ , opposite leg = 12

$x \approx 15.900$

Step-by-step explanation:

Each triangle is solved by means of trigonometric relations:

Triangle 1 - $m\angle A = 58^{\circ}$ , hypotenuse = 16

$\cos 58^{\circ} = \frac{x}{16}$

$x = 16\cdot \cos 58^{\circ}$

$x \approx 8.479$

Triangle 2 - $m \angle A = 44^{\circ}$ , adjacent leg = 18

$\tan 44^{\circ} = \frac{x}{18}$

$x = 18\cdot \tan 44^{\circ}$

$x \approx 17.382$

Triangle 3 - $m\angle A = 49^{\circ}$ , opposite leg = 12

$\sin 49^{\circ} = \frac{12}{x}$

$x = \frac{12}{\sin 49^{\circ}}$

$x \approx 15.900$

8 0

3 years ago

Solving equations with Fractions?

Viefleur [7K]

Answer:

basically just multiply the fractions by a common number until you have whole numbers, then solve like normal

Step-by-step explanation:

5 0

4 years ago

What is the quotient? 3806/ 22<br>

OLEGan [10]

Answer:

173

Step-by-step explanation:

Brainliest please

3 0

3 years ago

Read 2 more answers

Halla el área total y el volumen de un prisma triangular de altura 6cm y base un triángulos equilátero de lado 5cm. Redondea el

dangina [55]

Answer:

<h2>The total volume of the prism is 32.49 cubic centimeters.</h2><h2>The total surface area of the figure is 111.66 square centimeters.</h2>

Step-by-step explanation:

This problem is about finding the volume of a prism which base is an equilateral triangle.

The volume of the prism would be defined as

$V_{prism}=\frac{1}{2} B \times h$

Where $B$ is the area of the base and $h$ is the height of the prism.

The area of the equilateral triangle at the base is

$B=\frac{\sqrt{3} }{4} l^{2}$

Where $l= 5 \ cm$

$B=\frac{\sqrt{3} }{4} l^{2}=\frac{\sqrt{3} }{4}(5 \ cm)^{2} \approx 10.83 \ cm^{2}$

Replacing the base area in the volume formula, we have

$V_{prism}=\frac{1}{2} B \times h=\frac{1}{2} (10.83 \ cm^{2} )(6 \ cm)\\V_{prism}=32.49 \ cm^{3}$

Therefore, the total volume of the prism is 32.49 cubic centimeters.

Now, the total surface area would be the sum of three rectangle faces and two triangles faces.

$S_{total}= 3(5 \times 6) + 2(10.83)=90+21.66 = 111.66 \ cm^{2}$

Therefore, the total surface area of the figure is 111.66 square centimeters.

5 0

3 years ago