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2 years ago

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Two parallel lines are crossed by a transversal. Horizontal and parallel lines y and z are cut by transversal x. At the intersec

tion of lines y and x, the top right angle is (2 k + 11) degrees. At the intersection of lines z and x, the bottom left angle is 131 degrees. What is the value of k? k = 9 k = 20 k = 60 k = 71

2 answers:

BigorU [14]2 years ago

7 0

Answer:

60

Step-by-step explanation:

ruslelena [56]2 years ago

3 0

Those two angles have the same measure, so you have

$2k+11=131 \iff 2k=120 \iff k=60$

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What is a factoring Line?

earnstyle [38]

Answer:

A factoring line is a "funding loan"

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2 years ago

Emery looks out their apartment window to the building across the way. The building isknown to be 42 feet tall. The angle of dep

Amanda [17]

Answer:

$x=44.5ft$

Step-by-step explanation:

From the question we are told that:

Height $h=42ft$

Angle of depression $\theta=27\textdegree$

Angle of Elevation $\alpha=23 \textdegree$

Generally the equation for the vertical distance between Emery's distance x and the bottom of the building is mathematically given by

Since the angle of depression and elevation are given as

27 and 23 respectively

Therefore

Emery's view of the 42 ft building is

$\gamma=23+27$

$\gamma=50 \textdegree$

Therefore Emery's distance x to the base of the building h' is

$h'=\frac{27}{50}*42$

$h'=22.68ft$

Generally the Trigonometric equation for Emery's distance x is mathematically given by

$x=\frac{h'}{tan\theta}$

$x=\frac{22.68}{tan 27}$

$x=44.5ft$

6 0

1 year ago

A machine shop produces heavy duty high endurance 20-inch rods that are meant for use in a variety of military grade equipment.

QveST [7]

Answer:

The probability that a defective rod can be salvaged = 0.50

Step-by-step explanation:

Given that:

A machine shop produces heavy duty high endurance 20-inch rods

On occasion, the machine malfunctions and produces a groove or a chisel cut mark somewhere on the rod.

If such defective rods can be cut so that there is at least 15 consecutive inches without a groove.

Then; The defective rod can be salvaged if the groove lies on the rod between 0 and 5 inches i.e ( 20 - 15 )inches

Now:

P(X ≤ 5) = $\dfrac{5}{20}$

= 0.25

P(X ≥ 15) = $\dfrac{5}{20}$

= 0.25

The probability that a defective rod can be salvaged = P(X ≤ 5) + P(X ≥ 15)

= 0.25+0.25

= 0.50

∴ The probability that a defective rod can be salvaged = 0.50

4 0

2 years ago

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 7 minutes and a stand

julsineya [31]

Answer:

There is a 2.28% probability that it takes less than one minute to find a parking space. Since this probability is smaller than 5%, you would be surprised to find a parking space so fast.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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

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

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.

Also, a probability is unusual if it is lesser than 5%. If it is unusual, it is surprising.

In this problem:

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 7 minutes and a standard deviation of 3 minutes, so $\mu = 7, \sigma = 3$ .

We need to find the probability that it takes less than one minute to find a parking space.

So we need to find the pvalue of Z when $X = 1$

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

$Z = \frac{1 - 7}{3}$

$Z = -2$

$Z = -2$ has a pvalue of 0.0228.

There is a 2.28% probability that it takes less than one minute to find a parking space. Since this probability is smaller than 5%, you would be surprised to find a parking space so fast.

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2 years ago

Soup can be packaged in two different containers: a box and a cylinder. The dimensions of the box are 7.5 cm by 4.7 cm by 14.5 c

Brilliant_brown [7]

Answer: Cylinder uses less material to make.

Box holds more soup then cylinder.

Step-by-step explanation:

Total surface area of cuboidal box =2(lw+wh+lh), l= length, w=width, h=height

Total surface area of cylinder = $2\pi r(r+h)$ where r= radius and h is height.

Given , Dimension of box : 7.5 cm by 4.7 cm by 14.5 cm

Dimension of cylinder : radius of 3.3 cm and a height of 10 cm.

Total surface area of box =2((7.5)(4.7)+(4.7)(14.5)+(7.5)(147.5)) sq. cm

= 2(1209.65)

=2419.3 sq. cm

Total surface area of cylinder = $2(3.14)(3.3)(3.3+10)$ $=275.63\ \text{ sq. cm}$

<em>[π=3.14]</em>

(Total surface area of cylinder)<(Total surface area of box )

So, cylinder uses less material to make.

Volume of box = l x w x h

= (7.5)(4.7)(14.5) = 511.13 cubic cm

Volume of cylinder = $\pi r^2h$

$=(3.14)(3.3)^2(10)$

= 341.946 cubic cm

As (Volume of box) > (Volume of cylinder )

So, Box holds more soup then cylinder.

6 0

2 years ago