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3 years ago

The 7th term of an AP is 4 and its common difference is -4. What is the first term?

Mathematics

1 answer:

Dennis_Churaev [7]3 years ago

8 0

Answer: 28

Step-by-step explanation:

The 7th term of an AP is 4 and its common difference is -4. The 7th term of an arithmetic progression is written as:

a + 6d = 4

where,

a = first term

d = common difference= -4

a + 6d = 4

a + 6(-4) = 4

a - 24 = 4

a = 4 + 24

a = 28

The first term is 28.

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Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds out he is off course and 160

elena-14-01-66 [18.8K]

CHECK THE COMPLETE QUESTION BELOW

Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160 miles from island B. What bearing should he turn to, so he is heading straight towards island B?

A. 111.65

B. 119.84

C. 21.65

D. 135.53

Answer:

OPTION A IS CORRECT

A. 111.65

Step-by-step explanation:

This question can be explained using a triangle, let us say triangle ABD

and let us say A and B represent the islands and D is the particular point from where the captain is standing at a distance of 160 miles from B island .

We will be making use of cosines rule to calculate our angles, and we know that from cosine rule

D² = a² + b² -2abCosD

Where, a= 160 b = 260 and d = 250 then we can substitute in order to calculate our angles

250²= 60² + 260² - 2(160*260)Cos(D)

62500= 625600+ 67600- 83200CosD

83200CosD= 25600+ 67600 - 625600

83200CosD= 30700

CosD= 30700/83200

CosD= 0.369

D= cos⁻¹ (0.369)

D=68.35

Therefore, the angle inside the triangle is 68.35°

Now we can now find the bearing the captain supposed to turn , if he is heading to island B which will be the external angle of the triangle, but we know that The external angle =180°(supplimentary angles )

Then the angle he would turn will be external angle of the triangle - 68.35°

= (180 - 68.35)

= 111.65°

Therefore, the bearing the captain should turn is 111.65° for him to be heading straight towards island B.

7 0

3 years ago

Which of the following slopes of a line passes through points (2, 3) and (4,7) ?

serg [7]

Answer:

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (7 - 3)/(4 - 2)

slope = 4/2 = 2

Answer: 2

8 0

3 years ago

A foreman for an injection-molding firm admits that on 55% of his shifts, he forgets to shut off the injection machine on his li

motikmotik

Answer:

0.8594

Step-by-step explanation:

Let a denote the event of forgetting to shut off machine and b be the event of being defective.

-A foreman forgets to shut off machine 55% of the time.

-If he forgets, 15% of molds are defective.

-If he does not, 3% of molds are defective.

#The probability that he forgot to shut off the machine is calculated as:

$P(a \ and \ b)=0.55\times 0.15\\\\=0.0825\\\\$

P(a and ~b)=0.55(1-0.15)=0.4675

P(~a and b) = (1-0.55)*0.03=0.0135

P(~a and ~b) = (1-0.55)*(1-0.03)=0.4365

#Conditional probability is defined as:

$P(a|b)=\frac{P(a \ and\ b)}{P(a)}\\\\=\frac{P(a \ and \ b)}{[(P(a \ and \ b)+P(\~a \ and \ b)}\\\\\\=\frac{0.0825}{0.0825+0.0135}\\\\\\=0.8594$

Hence, the probability that the foreman forgot to shut off the machine the previous night is 0.8594

5 0

3 years ago

Find the midpoint of a segment whose endpoints are (9, –7) and (–3, 5).

suter [353]

For this question, you would have to use the midpoint formula.
(X1 +X2 / 2 , Y1 + Y2 / 2)

In other words,
(9 + -3 / 2 , -7 +5 / 2)
(6 / 2 , -2 / 2)
(3 , -1)

Your midpoint is (3, -1)

7 0

3 years ago

A video game costs $45.99. It is 45% off today at the store. What is the sale price of the video game?

stepan [7]

Answer:

the sale price of the video game after discount is 25.29

hope this helps have a nice day please give me brainliest:)

Step-by-step explanation:

5 0

3 years ago