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3 years ago

Seven times a number is less than or equal to a quantity that is 24 less than that same

Mathematics

1 answer:

Ad libitum [116K]3 years ago

6 0

Answer:

$7x\leq x-24$

Here, $x$ denotes the required number.

Step-by-step explanation:

Let $x$ denotes the required number that satisfies the following condition.

''seven times a number is less than or equal to a quantity that is 24 less than that same number''

Seven times a number is equal to $7x$

Quantity that is 24 less than that same number is equal to $x-24$

Now find the inequality.

As seven times a number is less than or equal to a quantity that is 24 less than that same number,

$7x\leq x-24$

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3x3 systems answers 4x + 8y + z = 2 x + 7y - 3z = -14 2x - 3y + 2z = 3

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3 years ago

100 points!!! PLEASE ANSWER IT HOW I HAVE IT IN ORDER!!

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2 years ago

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Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimeters,

tiny-mole [99]

Answer:

Probability that the sample mean would be greater than 141.4 millimetres is 0.3594.

Step-by-step explanation:

We are given that Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 141 millimetres, and a standard deviation of 7.

A random sample of 39 steel bolts is selected.

Let $\bar X$ = sample mean diameter

The z score probability distribution for sample mean is given by;

Z = $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }$ ~ N(0,1)

where, $\mu$ = population mean diameter = 141 millimetres

$\sigma$ = standard deviation = 7 millimetres

n = sample of steel bolts = 39

Now, Percentage the sample mean would be greater than 141.4 millimetres is given by = P( $\bar X$ > 141.4 millimetres)

P( $\bar X$ > 141.4) = P( $\frac{ \bar X-\mu}{\frac{\sigma}{\sqrt{n} } } }$ > $\frac{141.4-141}{\frac{7}{\sqrt{39} } } }$ ) = P(Z > 0.36) = 1 - P(Z $\leq$ 0.36)

= 1 - 0.6406 = 0.3594

The above probability is calculated by looking at the value of x = 0.36 in the z table which has an area of 0.6406.

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3 years ago

If ax^3+9x^2+4x-10 when divided by x-3 leaves the reminder 5,then a=

FinnZ [79.3K]

Let f(x) = ax³ + 9x² + 4x – 10

g(x) = 0⇒x - 3 = 0

⇒ x = 0 + 3

⇒ x = 3

On dividing f(x) by x - 3, it leaves a remainder 5.

Now keeping, f(3) = 5

⇒a(3)³ + 9(3)² + 4(3) - 10 = 5

⇒ a × 27 + 9 × 9 + 4 × 3 - 10 = 5

⇒ 27a + 81 + 12 - 10 = 5

⇒ 81 + 12 - 10 - 5 = 27a

⇒ 81 + 12 - 15 = 27a

⇒ 93 - 15 = 27a

⇒ 78 = 27a

⇒ a = 27/78

⇒ a = 0.3461

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3 years ago

Simplify the function f(x)= 1/2 (27) 2x/3. Then determine the key aspects of the function

jeyben [28]

The given expression is:

$f(x)= \frac{1}{2}(27)^{ \frac{2x}{3} } \\ \\ 
f(x)= \frac{1}{2}((27)^{ \frac{2}{3} })^{x} \\ \\ 
f(x)= \frac{1}{2}(9)^{x}$

From the above equation, we can answer all the 4 questions.

a) Initial value occurs when x = 0

So,

$f(0)= \frac{1}{2}(9)^{0}= \frac{1}{2}$

So, the Initial value of the function is 1/2.

b) Simplified Base:
The base of an exponential function is the term which contains the exponent.
From the simplified equation, we can see that the base has been simplified and is equal to 9.

So, the simplified base is 9

c) Domain:
From the equation we can see that there is no such value which makes the function undefined. So all reall numbers are included in the Domain.

So, Domain is Set of All real numbers.
In Interval notation this can be expressed as: (-∞,∞)

d) Range:
Range is the set of all y values that a function can take. Since the graph is not shifted vertically up or down, the range will be the set of all real numbers greater than zero.

So, Range is equal to All real numbers greater than 0.
In Interval notation, this can be expressed as (0,∞)

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3 years ago

Read 2 more answers