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3 years ago

Anthony has 4 times the amount of pencils as matthew. Together they have 35 pencils.how many pencils does Anthony have

Mathematics

2 answers:

irakobra [83]3 years ago

8 0

Answer:

Step-by-step explanation:

marin [14]3 years ago

7 0

Answer:

28 pencils

Step-by-step explanation:

Anthony=4x

Matthew=1x

4x+1x=5x

35=5x

x=7

1 unit=7

Matthew=4x

7x4=28

28 pencils

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A truck loaded with 8000 electronic circuit boards has just pulled into a firm’s receiving dock. The supplier claims that no mor

Juliette [100K]

Answer:

The 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

Step-by-step explanation:

Let X = number of boards that fall outside the most rigid level of industry performance specifications.

In a random sample of 300 boards the number of defective boards was 12.

Compute the sample proportion of defective boards as follows:

$\hat p =\frac{12}{300}=0.04$

The (1 - α)% confidence interval for population proportion p is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The critical value of z for 95% confidence level is,

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.04\pm1.96\sqrt{\frac{0.04(1-0.04)}{300}}\\=0.04\pm0.022\\=(0.018, 0.062)\\\approx(1.8\%, 6.2\%)$

Thus, the 95% confidence interval for the proportion of all boards in this shipment that fall outside the specification is (1.8%, 6.2%).

3 0

2 years ago

Two trains 150 miles apart are traveling toward each other along the same track. The first train goes 60 miles per hour; the sec

Nataly_w [17]

Answer:

120 miles

Step-by-step explanation:

Distance = 150 miles

train 1 = 60 mph

train 2 = 90 mph

directions of trains = towards each other

Time to meet = 150/(60+90) = 150 miles / 150 mph = 1 hour

Speed of fly = 120 mph

Since fly has been flying for one hour, it travelled 120 miles.

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2 years ago

Find cos theta if sin theta = 2/3. assume the terminal side of the angel falls in quadrant 2

kow [346]

Well knowing that the terminal arm of the standard position angle is in quadrant 2, we can determine the reference angle, in quadrant 2, by simply taking the difference between 180 and whatever the angle is.

So ø reference = 180 - ø in standard position.

Regardless, the reference angle is in quadrant 2, we need to then label the sides of the reference triangle based on the opposite and hypotenuse.

Solve for adjacent side using Pythagoras theorem.

A^2 = C^2 - B^2
A^2 = 3^2 - 2^2
A^2 = 9 - 4
A^2 =5
A = sq root of 5.

Then write the cos ratio using the new side.

Cos ø =✔️5/3. Place a negative in front of cos ø as cos is negative in second quadrant.

3 0

2 years ago

19. The areas of corresponding faces of two similar hexagonal prisms are 25 cm² and 121 cm². What is the ratios of the correspon

Pie

ANSWER

I) 5:11

ii) 5:11

iii) 125:1331

EXPLANATION

Let the side lengths be in the ratio:

x:y

This implies that the area will be in the ratio:

$\frac{ {x}^{2} }{ {y}^{2} } = \frac{25}{121}$

Take positive square root.

$\frac{x}{y} = \sqrt{ \frac{25}{121} }$

$\frac{x}{y} = \frac{5}{11}$

Hence the sides are in the ratio:

x:y=5:11

The perimeter of the smaller hexagon is 6×5=30

The perimeter of the larger hexagon is 6×11=66

The ratio of the perimeter is

30:66=5:11

The volume will be in the ratio

5³:11³

125:1331

6 0

3 years ago

If the measure of arc XY plus the measure of arc YZX equals 360°, and the arcs do not overlap, then the arcs form a _____. A. po

s344n2d4d5 [400]

I think it is a parallelogram

5 0

3 years ago

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