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Akimi4 [234]
3 years ago
14

(U...

Mathematics
1 answer:
Tresset [83]3 years ago
3 0

Answer:

the 19th term of the arithmetic sequence is 73.

Step-by-step explanation:

Given:

The arithmetic sequence whose common difference is

d=4

And first term is

a=1

Find the 19th term of the arithmetic sequence

n=19

Now we know that,

a_{n}=a+(n-1)d

Put all the value in above AP.

a_{19}= 1+(19-1)4

a_{19}= 1+18\times 4

a_{19}= 1+72

a_{19}= 73

So, 19_{th} term of the sequence is 73.

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A recipe for individual chocolate hazelnut tarts calls for ½ cup of hazelnuts per tart. If 1 cup of hazelnuts weighs 4 ounces, w
DerKrebs [107]

Answer:

The amount is sufficient to make 75 tarts.

Step-by-step explanation:

We have been given that a recipe for individual chocolate hazelnut tarts calls for ½ cup of hazelnuts per tart and 1 cup of hazelnuts weighs 4 ounces.

The half cup of hazelnuts will weigh 2 ounces (\frac{4}{2}=2).

1 kg equals 35.274 ounces.

\text{5 kg}=5\times 35.274\text{ ounces}

\text{5 kg}=176.37\text{ ounces}

Since each tart needs  ½ cup of hazelnuts and half cup of hazelnuts will weigh 2 ounces, so we will divide 176.37 ounces by 2 to find number of tarts.

\frac{176.37}{2}=88.185\approx 88

Since we can make 88 tarts from 5 kg hazelnuts, therefore, the 5-kilogram bag of hazelnuts be sufficient to make 75 tarts.

7 0
3 years ago
Suppose y varies directly with x. Write a direct variation equation that relates x and y. y=7 1/2 when x=3
kolbaska11 [484]

Answer:

y/x = 2.5

Step-by-step explanation:

y ∝ x

change ∝ to = by adding constant k or c

y = kx

Divide both sides by x

y/x = k, also k = y/x

Input the values

k = (7 1/2)/3.  Change 7 1/2 to improper fraction to give 15/2

k = (15/2)/3

k = \frac{15}{2} ÷ 3  

Change the division sign to multiplication which will change 3 to its inverse(1/3)

k = \frac{15}{2} × \frac{1}{3}

k = \frac{15}{6}

Divide the numerator and denominator by 3 to get 5/2

k = 5/2

From y/x = k,input k into the eqn

y/x = 5/2

y/x = 2.5

8 0
3 years ago
Which ordered pair represents the y-intercept of the graph of the equation y = –4x – 7?
Dovator [93]
If <span>y = –4x – 7, the x-intercept is found by setting y=0 and solving for x:

</span><span>0 = –4x – 7  =>  4x = -7, or   x = -7/4       The x-intercept is (-7/4, 0).

</span><span>The y-intercept is found by setting x = 0 and reading off the value of y:

y = –4x – 7  =>  y = 0 - 7, or y = -7.  The y-intercept is (0, -7).</span>
7 0
3 years ago
A=34.5. B=29.04. C= 204.7 D= 18.83
ahrayia [7]

The answer is B.) 29.04

you find c and then add it to a and b

5 0
3 years ago
What is the value of θ for the acute angle in a right triangle?
Murrr4er [49]

Answer:

64 degrees

Step-by-step explanation:

3 0
3 years ago
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