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3 years ago

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The graph of a function, ƒ, is shown here. What is the domain of ƒ? A) (−∞, −3] ∪ (−1, 4) ∪ [5, ∞) B) (−∞, −3] ∪ (−1, 4) ∪ [5, ∞

] C) [−∞, −3] ∪ (−1, 4) ∪ [5, ∞) Eliminate D) [−∞, −3] ∪ (−1, 4) ∪ [5, ∞]

1 answer:

kicyunya [14]3 years ago

7 0

Answer:

the answer is c

Step-by-step explanation:

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It cost Naomi $7.70 to send 154 text messages. How many text messages did she send

s2008m [1.1K]

You have to find the unit rate

SO..

7.70 / 154 = 0.05

So it cost her 0.05 cents for each text.

So then you divide $ 5.25 by the unit rate to get the number of text

5.25 /0.05 = 105

so she sent 105 text

To check it you just multiply the unit rate by the number of text you got and you show come up with $ 5.25

0.05 x 105 = 5.25

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3 years ago

How could you calculate each product? Describe the strategy you would use. Then calculate.

VashaNatasha [74]

Hey there!

1. To solve 9 x 5 , I could add the number 9 five times . . .

9 + 9 + 9 + 9 + 9 = 45

9 x 5 = 45 <----

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Hope this helps you.
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3 years ago

Compute the conditional probabilities from the two-way frequency table.

Natali5045456 [20]

Answer:

The table is show clearly in the figure attached.

P(boy if favourite activity is swimming) = 8/17 = 0.47

P(girl if favourite activity is sport) = 7/27 = 0.26

P(girl if favourite activity is reading) = 4/6 = 0.67

P(boy if favourite activity is sport) = 20/27 = 0.74

P(favourite activity is swimming if a girl) = 9/20 = 0.45

P(favourite activity is reading if a boy) = 2/30 = 0.07

P(favourite activity is swimming if a boy) = 8/30 = 0.27

P(favourite activity is reading if a girl) = 4/20 = 0.2

6 0

3 years ago

What is the next number to follow 17, 18, 22, 31, 47, ?

Minchanka [31]

Answer:

72

Step-by-step explanation:

First differences are ...

18 -17 = 1

22 -18 = 4

31 -22 = 9

47 -31 = 16

We observe that these are square numbers. The next square number is 25, so we expect the next number in sequence to be ...

47 +25 = 72

3 0

3 years ago

For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4

Elina [12.6K]

Answer:

<em>C.</em> $(5-\frac{1}{2})^6$

Step-by-step explanation:

Given

$15(5)^2(-\frac{1}{2})^4$

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

$Sum = 2 + 4$

$Sum = 6$

Each term of a binomial expansion are always of the form:

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

Where n = the sum above

$n = 6$

Compare $15(5)^2(-\frac{1}{2})^4$ to the above general form of binomial expansion

$(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......$

Substitute 6 for n

$(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......$

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

By direct comparison of

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

and

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

We have;

$^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4$

Further comparison gives

$^nC_r = 15$

$a^{n-r} =(5)^{6-4}$

$b^r= (-\frac{1}{2})^4$

[Solving for a]

By direct comparison of $a^{n-r} =(5)^{6-4}$

$a = 5$

$n = 6$

$r = 4$

[Solving for b]

By direct comparison of $b^r= (-\frac{1}{2})^4$

$r = 4$

$b = \frac{-1}{2}$

Substitute values for a, b, n and r in

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

$(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

Solve for $^6C_4$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......$

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em> $(5-\frac{1}{2})^6$ <em />

3 0

3 years ago