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3 years ago

Help me solve this question please

Mathematics

1 answer:

pychu [463]3 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

there is a difference of - 9 between the 3rd and 4th terms. indicating the sequence could be arithmetic , then

a₂ - a₁ = a₃ - a₂ , that is

k - 17 = - 1 - k ( add k to both sides )

2k - 17 = - 1 ( add 17 to both sides )

2k = 16 ( divide both sides by 2 )

k = 8

The sequence is 17, 8, - 1, - 10

The nth term of an arithmetic sequence is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 17 and d = - 9 , then

$a_{n}$ = 17 - 9(n - 1) = 17 - 9n + 9 = 26 - 9n

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Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) i

Vaselesa [24]

Complete question:

Dr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (V) is the color of the light produced by the lamp (red, orange, yellow, green, or blue) Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?

Answer:

Here,

Independent variable (IV) is: the color of the light produced by the lamp (red, orange, yellow, green, or blue)

We are also told only 10 participants are available.

All 10 participants are being exposed to all five levels of the color variable in the same order.

Counterbalancing is said to be a technique used when establishing task order. It helps prevent introduction if cofounding variables.

Dr. Lyte will need to use counterbalancing technique in this scenario because some of the participants may be unable to understand difference in similar colours. Example some participants may not be able to differentiate between orange and red when the red colour comes after orange.

But using counterbalancing technique, Dr. Lyte can avoid such an error.

6 0

4 years ago

A garden table and a bench cost $653 combined. The garden table cost $97 less than the bench. what is the cost of the bench?

SIZIF [17.4K]

T is the cost of the table. B is the cost of a bench.

b+t=652
b+98=t

t-98+t=652
2t=554
t=277
b=375

Hope this helps!

8 0

3 years ago

Limit definition for slope of the graph, equation of tangent line point for<br> f(x)=2x^2 at x=(-1)

Tems11 [23]

The slope of the tangent line to $f$ at $x=-1$ is given by the derivative of $f$ at that point:

$f'(-1)=\displaystyle\lim_{x\to-1}\frac{f(x)-f(-1)}{x-(-1)}=\lim_{x\to-1}\frac{2x^2-2}{x+1}$

Factorize the numerator:

$2x^2-2=2(x^2-1)=2(x-1)(x+1)$

We have $x$ approaching -1; in particular, this means $x\neq-1$ , so that

$\dfrac{2x^2-2}{x+1}=\dfrac{2(x-1)(x+1)}{x+1}=2(x-1)$

Then

$f'(-1)=\displaystyle\lim_{x\to-1}\frac{2x^2-2}{x+1}=\lim_{x\to-1}2(x-1)=2(-1-1)=-4$

and the tangent line's equation is

$y-f(-1)=f'(-1)(x-(-1))\implies y-4x-2$

6 0

3 years ago

Donnel practiced the piano 3 hours longer than Marcus. Together they practiced the piano for 11 hours. How many hours did each b

andriy [413]

Here is the equation: $x+(x+3)=11$ ⇒ $x+x+3=11$

You need to get "x" by itself so minus 3 from each side

$x+x+3-3=11-3$ ⇒ $x+x=8$ ⇒ $2x=8$

Divide 8 by 2

$8$ ÷ $2=4$

x=4

So each 4 is equivalent to 4

Lets check:

$4+(4+3)=11$ ⇒ $4+4+3=11$ ⇒ $11=11$

So that means that Marcus practiced the piano for 4 hours and Donnel practiced for 7

4 0

3 years ago

Each grape at the supermarket weighs 5 grams. If Eric buys a bag of grapes that weighs 50 grams, how many grapes did he buy?

Usimov [2.4K]

Answer:

10 grapes

Step-by-step explanation:

50 divided by 5 is 10

7 0

3 years ago

Help me solve this question please​

Help me solve this question please