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2 years ago

Which function has a vertex on the y-axis?

Mathematics

1 answer:

VARVARA [1.3K]2 years ago

8 0

Answer:

f(x) = (x - 2)(x + 2)

Step-by-step explanation:

When you expand out the expression, you should get f(x) = x² - 4, where only vertical movement is present. Therefore, the vertex is on the y-int at (0, -4) and your answer is the 3rd choice.

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A sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of th

Kruka [31]

Answer:

95% confidence interval for the true mean score is [4.6 , 6.6].

Step-by-step explanation:

We are given that a sample of 81 tobacco smokers who recently completed a new smoking-cessation program were asked to rate the effectiveness of the program on a scale of 1 to 10.

The average rating was 5.6 and the standard deviation was 4.6.

Firstly, the pivotal quantity for 95% confidence interval for the true mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample average rating = 5.6

s = sample standard deviation = 4.6

n = sample of tobacco smokers = 81

$\mu$ = population mean score

Here for constructing 95% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean score, $\mu$ is ;

P(-1.993 < $t_8_0$ < 1.993) = 0.95 {As the critical value of t at 80 degree of

freedom are -1.993 & 1.993 with P = 2.5%}

P(-1.993 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 1.993) = 0.95

P( $-1.993 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $1.993 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-1.993 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.993 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-1.993 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.993 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $5.6-1.993 \times {\frac{4.6}{\sqrt{81} } }$ , $5.6+1.993 \times {\frac{4.6}{\sqrt{81} } }$ ]

= [4.6 , 6.6]

Therefore, 95% confidence interval for the true mean score is [4.6 , 6.6].

4 0

1 year ago

A bank records deposits as positive numbers and withdrawals as negative numbers. Mike withdrew \$60$60dollar sign, 60 from his b

galina1969 [7]

Answer:

8,000

Step-by-step explanation:

5 0

2 years ago

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is___ units. The point (

Pachacha [2.7K]

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is 5_ units. The points(-7,5) and (-7,-1) lie on this circle.

3 0

2 years ago

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Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equ

irga5000 [103]

I hope the equation will be 2000=16000(1-r)^t because t is missing in the equation which we need to find.

Given rate: r= 35%= 0.35.

So, first step is to plug in 0.35 for r in the given formula to get the value of t.

Hence, the equation will be:

2000=16000(1-0.35)^t

2000=16000(0.65)^t (By subtraction)

2000/16000= 16000(0.65)^t /16000 (Dividing each sides by 16000)

0.125 = 0.65^t (By simplifying).

log 0.125 = log 0.65^t (Taking log each sides to isolate t).

log 0.125 = t log 0.65 (By applying the log property).

$\frac{log 0.125}{log 0.65} =t$ (Dividing each sides by log 0.65)

-0.903/-0.187 =t

t= 4.83

t= 5 ( Rounded to nearest integers)

So, Devon's car is 5 years old.

7 0

2 years ago

The endpoints of JK are J(–25, 10) and K(5, –20). What is the y-coordinate of point L, which divides JK into a 7:3 ratio? a. –16

Andrews [41]

let's say the point dividing JK is say point P, so the JK segment gets split into two pieces, JP and PK

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ J(-25,10)\qquad K(5,-20)\qquad \qquad \stackrel{\textit{ratio from J to K}}{7:3} \\\\\\ \cfrac{J~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} P \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~K} = \cfrac{7}{3}\implies \cfrac{J}{K} = \cfrac{7}{3}\implies3J=7K\implies 3(-25,10)=7(5,-20)\\\\[-0.35em] ~\dotfill$

$\bf P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\cfrac{(3\cdot -25)+(7\cdot 5)}{7+3}\quad ,\quad \stackrel{\textit{y-coordinate}}{\cfrac{(3\cdot 10)+(7\cdot -20)}{7+3}}\right) \\\\\\ P=\left( \qquad ,\quad \cfrac{30-140}{10} \right)\implies P=\left(\qquad ,~~\cfrac{-110}{10} \right)\implies P=(\qquad ,\quad -11)$

8 0

2 years ago

Read 2 more answers