What is the value of ¡97 - i?

Answer:

4

Step-by-step explanation:

2(6x+4)-6+2x=3(4x+3)+1

=14x+2=12x+10

=14x+2-2=12x+10-2

=14x=12x+8

=14x-12x=12x+8-12x

=2x=8

=2x/2=8/2

x=4

Answer:

Half-life of the goo is 49.5 minutes

[tex]G(t)= 300e^{-0.014t}[/tex]

191.7 grams of goo will remain after 32 minutes

Step-by-step explanation:

Let [tex]M_0\,,\,M_f[/tex] denotes initial and final mass.

[tex]M_0=300\,\,grams\,,\,M_f=37.5\,\,grams[/tex]

According to exponential decay,

[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt[/tex]

Here, t denotes time and k denotes decay constant.

[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\\\ln \left ( \frac{37.5}{300} \right )=-k(150)\\-2.079=-k(150)\\k=\frac{2.079}{150}=0.014[/tex]

So, half-life of the goo in minutes is calculated as follows:

[tex]\ln \left ( \frac{50}{100} \right )=-kt\\\ln \left ( \frac{50}{100} \right )=-(0.014)t\\t=\frac{-0.693}{-0.014}=49.5\,\,minutes[/tex]

Half-life of the goo is 49.5 minutes

[tex]\ln \left ( \frac{M_f}{M_0} \right )=-kt\Rightarrow M_f=M_0e^{-kt}[/tex]

So,

[tex]G(t)= M_f=M_0e^{-kt}[/tex]

Put [tex]M_0=300\,\,grams\,,\,k=0.014[/tex]

[tex]G(t)= 300e^{-0.014t}[/tex]

Put t = 32 minutes

[tex]G(32)= 300e^{-0.014(32)}=300e^{-0.448}=191.7\,\,grams[/tex]

Answer: 4 / 663

Step-by-step explanation:

There are 4 queens in a deck of 52 cards.

Probability = 4/52 = 1/13

There are 4 sevens

Probability = 4/51

Total probability = 1/13 x 4/51 = 4 / 663

The probability of drawing a queen first and a seven-second is 3/613.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

There are 4 queens in a standard deck, and once one queen is drawn, there are 51 cards left, including 3 sevens.

So, the probability of drawing a queen first is 4/52 or 1/13, and the probability of drawing a seven-second is 3/51.

By the multiplication rule of probability, multiply the probabilities of each event occurring:

P(Queen and Seven) = P(Queen) × P(Seven after Queen)

P(Queen and Seven) = (1/13) × (3/51)

P(Queen and Seven) = 3/613

Thus, the probability of drawing a queen first and a seven-second is 3/613.

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Answer:

42

Step-by-step explanation:

Mean = Sum of numbers/ Total numbers

Sum of 6 numbers = 32 x 6

= 192

If one number is excluded the mean reduce by 2 . so it becomes 30

Sum of 5 Numbers = 5 x 30

=150

Therefore the excluded number is

= 192 - 150

= 42.

Answer:

y=4x

Step-by-step explanation:

an independent variable is the variable  that is changed or controlled in an experiment or observation to test the effects on the dependent variable

a dependent variable is variable being tested and measured in a scientific experiment

in this case, the number of help desk tickets  closed out is dependent on the number of hours the individual works so y is the number of tickets closed (dependent variable). The number of tickets closed of will be 4 multiplied by the number of hours worked i.e. y=4x

Answer:

x = -8 or x = 3

Step-by-step explanation:

To factor ax² + bx + c, use AC method.

a times c is 1 × -24 = -24.

Factors of ac (-24) that add up to b (5) are 8 and -3.

Divide by a and reduce: 8/1 and -3/1.

Therefore, the factors are x + 8 and x − 3.

x² + 5x − 24 = 0

(x + 8) (x − 3) = 0

x = -8 or 3

Answer:

x=-3

Step-by-step explanation:

The vertex is at x = -3

The axis of symmetry is along the vertex

x=-3

Answer:

x=-3

Step-by-step explanation:

To find the axis of symmetry, you just need to find the x-coordinate of the vertex using this formula: -b/2a=x  

*Only when provided a three variable quadratic equation.

For looking at a graph, you find the center of the parabola in which when you reflect it over itself, it will be symmetrical.

According to the graph, x=-3 is the line which you can draw to fold over to the other side and it can fit perfectly.

Answer: 1/4 of 70,000,000

Step-by-step explanation: 17,500,000 / 70,000,000 = 0.25

Answer:

[tex]25\%[/tex]

Step-by-step explanation:

[tex]\frac{17,500,000}{70,000,000}[/tex]

[tex]\frac{1}{4}=0.25=25/100=25\%[/tex]

Answer:

Step-by-step explanation:

A fluctuating electric current II may be considered a uniformly distributed random variable over the interval (9, 11)

[tex]p_1=\{^{\frac{1}{2}:9\leq i\leq 11}_{0:otherwise[/tex]

Now define

[tex]p = 2I^2[/tex]

[tex]\Rightarrow I^2=(\frac{p}{2} )\\\\\Rightarrow I=(\frac{p}{2} )^{\frac{1}{2} }\\\\\Rightarrow h^{-1}(p)=(\frac{p}{2} )^{\frac{1}{2}}[/tex]

[tex]\frac{dh^{-1}}{dp} =\frac{d[h^{-1}(p)]}{dp} \\\\=\frac{d(p/2)^{\frac{1}{2} }}{dp}[/tex]

[tex]=\frac{1}{2} \times \frac{1}{2} (\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{4}(\frac{p}{2} )^{{\frac{1}{2}-1} }\\\\=\frac{1}{2}(\frac{2}{p} )^{{\frac{1}{2}} }[/tex]

using the transformation method, we get

[tex]f_p(p)=f_1(h^{-1}(p))|\frac{d[h^{-1}(p)]}{dp} |\\\\=\frac{1}{2} \times \frac{1}{4} (\frac{2}{p} )^{\frac{1}{2} }\\\\=\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} }[/tex]

[tex]f_p(p)=\{^{\frac{1}{8} (\frac{2}{p} )^{\frac{1}{2} },162\leqp\leq 242} }_{0,otherwise}[/tex]

Corrected Question

Is the function given by:

[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex] ​

continuous at x=4​? Why or why​ not? Choose the correct answer below.

Answer:

(D) ​Yes, f(x) is continuous at x = 4 because [tex]Lim_{x \to 4}f(x)=f(4)[/tex]

Step-by-step explanation:

Given the function:

[tex]f(x)=\left\{\begin{array}{ccc}\frac{1}{4}x+1 &x\leq 4\\4x-11&x>4\end{array}\right[/tex]

A function to be continuous  at some value c in its domain if the following condition holds:

At x=4

Therefore: [tex]Lim_{x \to 4}f(x)=f(4)=2[/tex]

By the above, the function satisfies the condition for continuity.

The correct option is D.

Answer:

[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-3.33)=0.000434[/tex]  

For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.

Step-by-step explanation:

Information given

[tex]\bar X=20[/tex] represent the sample mean  

[tex]\sigma=9[/tex] represent the population deviation

[tex]n=36[/tex] sample size  

[tex]\mu_o =25[/tex] represent the value to verify

[tex]\alpha=0.1[/tex] represent the significance level

tzwould represent the statistic

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test the hypothesis that the true mean is lower than 25  and the system of hypothesis are:  

Null hypothesis:[tex]\mu \geq 25[/tex]  

Alternative hypothesis:[tex]\mu < 25[/tex]  

The statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info given:

[tex]z=\frac{20-25}{\frac{9}{\sqrt{36}}}=-3.33[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-3.33)=0.000434[/tex]  

For this case the p value is a very low value compared to the significance level of 0.1 so then we can reject the null hypothesis and we can conclude that the true mean is significantly less than 25 at 10% of significance.

Answer:

5.5 hours

Step-by-step explanation:

We have that the distance is given by:

d = v * t = 50 mph * 1/2 h = 25 miles

The relative speed is given by:

 vr = 55 mph - 50 mph = 5 mph

Now the time required to reach

 would come being:

t = t '+ d / vr

we know that t '= 1/2 h, replacing:

t = 1/2 h + 25 mi / 5 mph

t = 1/2 h + 5 h

t = 5.5 h

Therefore, the required time is 5.5 hours.

Answer:

(-1,4)

Step-by-step explanation:

Divide each imput by 4

The required image of the given point (-4, 12) dilation by a scale factor of 1/4 and centered at the origin is (1, -3).

Given that,
To determine the image of  (-4,12) after dilation by a scale factor of 1/4 centered at the origin.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Coordinate, is represented as the values on the x-axis and y-axis of the graph

Here,
For the point, we have a dilation factor of 1/4,
So dilated coordinate,
= (1/4 * - 4 ,   1/4 * 12)
= (-1 , 3)
To form the image across the origin
= - (-1, 3)
= (1, -3)

Thus, the required image of the given point (-4, 12) with a scale factor of 1/4 and centered at the origin is (1, -3).

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Answer:

16

Step-by-step explanation:

The range is the difference between the highest and lowest number of a data set. 22-6=16

Answer:

The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 1000, \pi = \frac{710}{1000} = 0.71[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 - 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.6819[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.71 + 1.96\sqrt{\frac{0.71*0.29}{1000}} = 0.7381[/tex]

The 95% confidence interval for the true population proportion of adults with at least a high school education is (0.6819, 0.7381). This means that we are 95% sure that the true proportion of adults in the entire population surveyed with at least a high school education is (0.6819, 0.7381).

Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...

Answer:

a = 35º

b = 140º

c = 40º

d = 140º

e = 58º

Step-by-step explanation:

Angle A is supplementary to the angle that is 145º, and supplementary angles always add up to 180º. Therefore, 180 - 145 = 35, the measure of angle a. Angle B is supplementary to the 40º angle, so its measure is 140. Angle C is opposite the 40º angle, and opposite angles are congruent, so its measure would also be 40º. Angle D is also 140º because it is opposite of angle B. Angle E is supplementary to the angle that measures 122º, so 180 - 122 = 58. Hope this helped!

Answer:

2,748.5

Step-by-step explanation:

Answer:

thank uuu

Step-by-step explanation:

Answer:

D. It would be less steep.

Step-by-step explanation:

→When the absolute value of the number in front of x is greater than 1, the function on the graph narrows. When the absolute value of the number in front of x is less than 1, the function on the graph widens.

In this case, the number is less than 1, making it grow wider. And as a result of it growing wider, it also becomes less steep.

Answer:

At least 18 of the households have between 2 and 6 televisions.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean = 4

Standard deviation = 1

Percentage of households that have between 2 and 6 televisions.

2 = 4 - 2*1

So 2 is two standard deviations below the mean

6 = 4 + 2*1

So 6 is two standard deviations above the mean

By Chebyshev's Theorem, at least 75% of the measures are within 2 standard deviations of the mean.

Out of 24

0.75*24 = 18

At least 18 of the households have between 2 and 6 televisions.

Answer:

I think its C. All students in each grade

Step-by-step explanation:

because it should be the students choice.

Step-by-step explanation:

9 + 1/6 + 2 1/12

9 + 2.25

11.25

Answer:

C ; A

Step-by-step explanation:

Question 30:

Perimeter is the sum of all sides.

Perimeter for a recatngle can be found with the formula:

2(L+W)

Length is 7

Width is 4

Plug our values in.

2(7+4)

2(11)

22

Answer C

Question 31:

Circumference of a circle can be found with the formula:

πd.

Diameter of the given circle is 6.

Plug it in

6π

Round π to 3.14

6(3.14)

18.84

Answer A

Answer:

[tex]5[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the number of tuba players.

We are given that the number of saxophone players is one less than twice the number of tuba players.

There are 9 saxophone players.

[tex]9 = 2 x-1[/tex]

[tex]9+1=2x[/tex]

[tex]10=2x[/tex]

[tex]10 \div 2=x[/tex]

[tex]5=x[/tex]

For (2,6) the 2 is the x value which is the left/right position and 6 is the y value which is the up/down position.

Moving 2 units to the right, you would add 2 to the x value. Moving 3 units down you would subtract 3 from the y value.

The answer would be (4,3)

Answer:

Step-by-step explanation:

Null hypothesis: u = 10

Alternative hypothesis: u =/ 10

Using the formula: t = (x - u) / (s /√n)

Where x = 12, u = 10, s = 5 and n = 25

t= (12-10) / (5/√25)

t = (2)/(5/5)

t = 2/1= 2

t = 2.0

At a 0.01 level of significance with a degree of freedom of 24, the p-value is 0.0569, which is greater than 0.01 we will fail to reject the null and conclude that parents do not read more than the average number of books to their children

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 238

For the alternative hypothesis,

H1: µ < 238

This is a left tailed test

b) Since the population standard deviation is not given, the distribution is a student's t.

Since n = 100

Degrees of freedom, df = n - 1 = 100 - 1 = 99

t = (x - µ)/(s/√n)

Where

x = sample mean = 231

µ = population mean = 238

s = samples standard deviation = 80

t = (231 - 238)/(80/√100) = - 0.88

We would determine the p value using the t test calculator. It becomes

p = 0.19

c) Since alpha, 0.05 < than the p value, 0.19, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed insignificant evidence that the mean weekly unemployment insurance benefit in Virginia was below the national average.

d) Since α = 0.05, the critical value is determined from the t distribution table. Recall that this is a left tailed test. Therefore, we would find the critical value corresponding to 1 - α and reject the null hypothesis if the test statistic is less than the negative of the table value.

1 - α = 1 - 0.05 = 0.95

The negative critical value is - 1.66

Since - 0.88 is greater than - 1.66, then we would fail to reject the null hypothesis.

Answer:

x = 17 or x = ±7i

Step-by-step explanation:

x³ − 17x² + 49x − 833 = 0

x² (x − 17) + 49 (x − 17) = 0

(x² + 49) (x − 17) = 0

x = 17 or ±7i

Answer:

y = 1/4x + 2

Step-by-step explanation:

Since they gave you point slope form already, all you need to do is convert that into slope-intercept form. Just distribute the parenthesis and move the 4 over. Once you do so, you should get C/3rd option as your answer.

Answer:

The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month. 

Step-by-step explanation:

To answer this item, we let x be the number of hours per month that Mrs. Gleason should work. The total budget is equal to sum of the amount acquired by Mr. Gleason and Mrs. Gleason. The equation that would express this is,

                         4,500 = 900(4) + 9x

The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month. 

I am sorry if you get this wrong.