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3 years ago

What is the x-intercept of the following function? h(x) = 4x+3 - 2

Mathematics

2 answers:

Firdavs [7]3 years ago

5 0

Answer:

(-2.5,0)

Step-by-step explanation:

$h(x)=4^{x+3}-2$

Since the x intercept of a graph is when the y value is 0:

$0=4^{x+3}-2 \\\\2=4^{x+3} \\\\2=(2^2)^{x+3} \\\\2^1=2^{2x+6} \\\\1=2x+6 \\\\2x=-5 \\\\x=-2.5$

Hope this helps!

ddd [48]3 years ago

4 0

Answer:

Let h(x) = y

y = 4^(x+3) -2

For x intercept let y = 0

2 = 4^(x+3)

2= 2^2(x+3)

1 = 2x +6

2x = -5

Divide by 2

x = -5/2

The x intercept for the function is ( -5/2, 0)

Hope this helps.

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in a party,there is 40 percent more males than females.there are 475 males and females altogether.how many males were at the par

Phantasy [73]

The ratio of males to females is 1.4 : 1, so the fraction of the total that is made up of males is 1.4/(1.4 + 1) = 1.4/2.4 = 7/12.

There were (7/12)*475 ≈ 277 males at the party.

There were 475 - 277 = 198 females at the party.

7 0

3 years ago

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x

Anna11 [10]

Answer:

a) Figure attached

b) $y=1.31 x +98.57$

c) The correlation coefficient would be r =0.47719

d) $y=1.31 x +98.57=1.31*21 + 98.57 =126.08$

Step-by-step explanation:

(a) Draw a scatter diagram for the data.

See the figure attached

(b) Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x =__ y =__ b =__ y =__ + __x

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=6576-\frac{300^2}{14}=147.429$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=38186-\frac{300*1773}{14}=193.143$

And the slope would be:

$m=\frac{193.143}{147.429}=1.31$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{300}{14}=21.429$

$\bar y= \frac{\sum y_i}{n}=\frac{1773}{14}=126.643$

And we can find the intercept using this:

$b=\bar y -m \bar x=126.643-(1.31*21.429)=98.571$

So the line would be given by:

$y=1.31 x +98.57$

(c) Find the sample correlation coefficient r and the coefficient of determination r?2. (Round your answers to three decimal places.)

n=14 $\sum x = 300, \sum y = 1773, \sum xy=38186, \sum x^2 =6576, \sum y^2 =225649$

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

$r=\frac{14(38186)-(300)(1773)}{\sqrt{[14(6576) -(300)^2][14(225649) -(1773)^2]}}=0.9534$

So then the correlation coefficient would be r =0.47719

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

The % of variation is given by the determination coefficient given by $r^2$ and on this case $0.47719^2 =0.2277$ , so then the % of variation explaines is 22.8%.

(d) If a female baby weighs 21 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.) ___ lb

So we can replace in the linear model like this:

$y=1.31 x +98.57=1.31*21 + 98.57 =126.08$

7 0

3 years ago

Which arrangment shows 27/5,5 3/5, and 33/6 in order least to greatest

svetoff [14.1K]

5 3/5, 27/5, 33/6 , hope I helped lmk if I got it right

8 0

2 years ago

The length of a room is 4 feet less than twice its width. The perimeter of

AlladinOne [14]

L=2W-4

PERIMETER=2L+2W

58=2(2W-4)+2W

58=4W-8+2W

58=6W-8

6W=58+8

6W=66

W=66/6

W=11 ANS. FOR THE WIDTH.

L=2*11-4

L=22-4

L=18 ANS. FOR THE LENGTH.

PROOF:

58=2*18=2*11

58=36+22

58=58

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3 years ago

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grigory [225]

Answer:

it a

Step-by-step explanation:

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3 years ago

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