How do you write 345,000,000,000 in scientific notation

Step-by-step explanation:

Replace x = 3

f(3) = 2(3) - 2

= 6 - 2

= 4

Answer:

f(3) =4

Step-by-step explanation:

f(x) = 2x - 2

Let x=3

f(3) = 2*3 - 2

     = 6-2

     = 4

Answer:

Endangered species

Step-by-step explanation:

An endangered species is a species that is at risk of extinction due to rapid decrease in their population .Their decrease in population might be due to loss of habitat and genetic variation. The loss of habitat might be due to natural factors like the climate change For example animals like dinosaurs during the cretaceous period that experience rapid change in the climate loss their habitat and went extinct.

Human activity can also influence loss of habitat. Development in housing , agriculture and industry can also threaten the habitats of native organisms. The loss of their habitat might cause sudden extinction of these organisms. They might find it hard to adapt to another environment or even procreate.  

Generally,  endangered species are species that are threatened by extinction. Elephants that are in danger of been wiped out is an endangered species.

Answer:

Any values that is greater than 1/2.

Step-by-step explanation:

You have to form an inequality. Given that what values is added to c will satisfy that 3 - 5c is less than 1 - c :

[tex]3 - 5c < 1 - c[/tex]

Next, you have to solve :

[tex] - 5c + c < 1 - 3[/tex]

[tex] - 4c < - 2[/tex]

[tex]c > \frac{ - 2}{ - 4} [/tex]

[tex]c > \frac{1}{2} [/tex]

Answer:

For this case the mean is given by:

[tex] \mu = p =0.46[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] n = 215[/tex] represent the sample size

[tex]p = 0.46[/tex] represent the proportion of business graduate students from private universities had student loans

For this case we want to find the distribution for the sample proportion and we know that this distribution is given by:

[tex] \hat p \sim N (p , \sqrt{\frac{p(1-p)}{n}}) [/tex]

And for this case the mean is given by:

[tex] \mu = p =0.46[/tex]

And the standard deviation would be:

[tex] \sigma = \sqrt{\frac{0.46*(1-0.46)}{215}}= 0.0340[/tex]

Answer:

The mean of this distribution is 0.46 and the standard deviation is 0.034.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sampling distributions of samples of size n of a proportion p, the mean is [tex]\mu = p[/tex] and the standard deviation is [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]n = 215, p = 0.46[/tex]

So

[tex]\mu = 0.46, s = \sqrt{\frac{0.46*0.54}{215}} = 0.0340[/tex]

The mean of this distribution is 0.46 and the standard deviation is 0.034.

Answer:

D. Parabola; 0°

Step-by-step explanation:

Answer:

Null hypothesis: H0 = 0.65

Alternative hypothesis: Ha ≠ 0.65

z = 1.172

P value = P(Z≠1.172) = 0.24

Decision we fail to reject the null hypothesis. That is, there is convincing evidence enough to reject the Null hypothesis.

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 95% confidence interval) ---- reject Null hypothesis

Z score < Z(at 95% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

Given;

n=80 represent the random sample taken

Null hypothesis: H0 = 0.65

Alternative hypothesis: Ha ≠ 0.65

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 80

po = Null hypothesized value = 0.65

p^ = Observed proportion = 57/80 = 0.7125

Substituting the values we have

z = (0.7125-0.65)/√(0.65(1-0.65)/80)

z = 1.17201807734

z = 1.172

To determine the p value (test statistic) at 0.05 significance level, using a two tailed hypothesis.

P value = P(Z≠1.172) = 0.241197 = 0.24

Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = 1.172) which falls within the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.24 which is higher than 0.05. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is valid.

Answer:

[tex] y = -\frac{1}{3}x-2[/tex]

Step-by-step explanation:

From the table it is clear that the line is passing through the points [tex] (0,\: -2)= (x_1, \:y_1) \: \&\: (-6, \:0)=(x_2,\:y_2) [/tex]

(There are many other points in the table and any two of them can chosen as per our convenience)

Equation of line in two point form is given as:

[tex] \frac{y-y_1}{y_1 - y_2} = \frac {x-x_1}{x_1 - x_2} \\\\

\therefore \frac{y-(-2)}{-2 - 0} = \frac {x-0}{0 - (-6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{0+6)} \\\\

\therefore \frac{y+2}{-2} = \frac {x}{6)} \\\\

\therefore 6(y + 2) = - 2(x)\\

\therefore 6y + 12 = - 2x \\

\therefore 6y = - 2x - 12\\\\

\therefore y = -\frac{2}{6}x-\frac{12}{6}\\\\

\huge \red {\boxed {y = -\frac{1}{3}x-2}} \\\\[/tex]

Answer:

(0, 8).

Step-by-step explanation:

The y intercept occurs when  = 0, so we have the equation:

y = -3(0) + 8

y = 0 + 8

y = 8.

The answer is (0, 8).

Answer:

D.

Step-by-step explanation:

Let's solve each choice.

A: 3 divided by 90 is 3/90 and can be simplified to 1/30. So no.

B: 1/5 divided by 6. Recall that when dividing, you multiply the 1st term by the 2nd term's reciprocal. If you do this, you get 1/30. So no.

C: 1/6 divided by 5. Again, multiply 5's reciprocal to 1/6. There you get 1/30. So no.

D: 6 divided by 1/5. Again, multiply 1/5's reciprocal to 6. 1/5's reciprocal is 5. 5*6 = 30. So this is the correct answer.

Answer:

Step-by-step explanation:

the data is skewed left

The data in the given set is skewed towards left because the mean of the data is 7.5 and the data is not distributed symmetrically in the given set. Thus, the correct option is C.

Skewed data is the data which creates an asymmetrical, skewed curve on the graph scale. In statistics, the graph of a data set with normal distribution is symmetrical and has a bell-like shape. However, the skewed data has a tail on either side of the graph as well.

Skewness can be demonstrated on a bell curve when the data points are not distributed symmetrically to the left and right sides of the median on the curve. If the bell curve is shifted to the left or towards the right side, it is said to be skewed curve. The two halves of the distribution are not mirror images in the skewed curve because the data are not distributed equally on both sides of the distribution peak.

Therefore, the correct option is C.

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Answer:

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Step-by-step explanation:

To find the experimental probability of an outcome we divide:

The number of trials in which the desired outcome happened by the total number of trials.

In this question:

Experimental probability of winning this game.

She played the game 11+57 = 68 times. She won 11 times. So the experimental probability of Lee winning is 11/68 = 0.1618 = 16.18%.

Answer:

Option (3)

Step-by-step explanation:

From the figure attached,

AB and CD are two chords intersecting at O.

m∠AOD = 37°

m∠AOC + m∠AOD = 180° [Since these angles are supplementary angles]

m∠AOC = 180° - 37°

              = 143°

By the theorem of intersecting chords,

Measure of angle formed is the half of the sum of measures of the arcs intercepted by the angle and vertical angle.

m∠AOC = [tex]\frac{1}{2}(\widehat{AC}+\widehat{BD})[/tex]

143° = [tex]\frac{1}{2}[(x+5)+(x-5)][/tex]

143° = x

Therefore, Option (3) will be the answer.

Answer: 268 hamburgers

Answer:

24% of those surveyed liked neither

Step-by-step explanation:

Set concepts:

We use set concepts to solve this question.

I am going to say that:

P(A) is the percentage of people that liked to swim.

P(B) is the the percentage of people that liked to run.

The percentage of people that liked at least one of these activities is:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

In which [tex]P(A \cap B)[/tex] is the probability that a person liked both these activities.

The percentage of people that liked neither is:

[tex]P = 1 - P(A \cup B)[/tex]

Of those surveyed, 58% said they liked to swim and 36% said they liked to run.

This means that [tex]P(A) = 0.58, P(B) = 0.36[/tex]

18% said they liked both swimming and running

This means that [tex]P(A \cap B) = 0.18[/tex]

What percent of those surveyed liked neither?

At least one:

[tex]P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76[/tex]

Neither:

[tex]P = 1 - P(A \cup B) = 1 - 0.76 = 0.24[/tex]

24% of those surveyed liked neither

Answer:

Yes. Some examples are √2, √3, √5.

You better believe it !  In fact, if you don't count an infinite number of examples, you'll find that MOST of their square roots are irrational.

Let's examine the smallest 1,000 integers . . .

-- They're all rational numbers, but ...

-- only 31 of them have rational square roots !

Answer:

The correct answers are B, C, D, B

Step-by-step explanation:

These answers complete the statements that show the difference between the mathematical and reasonable ranges. Good luck! :)

B) Rational Numbers

C) 30,800

D) Real Numbers

B) 800

Correct on edge2020!

Answer:

BCDB

Step-by-step explanation:

Answer:

GRAPH OF 3X+2 IS 6

Step-by-step explanation:

Answer:

The graph below

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is

The table below contains the overall miles per gallon (MPG) of a type of vehicle. Complete parts a and b below.

28, 34, 28, 20, 21, 31, 28, 24, 34, 35 , 36, 26, 25, 20

a. Construct a 95% confidence interval estimate for the population mean MPG for this type of vehicle, assuming a normal distribution.

b. Choose the correct answer below.

A. We have 95% confidence that the mean MPG of this type of vehicle for the sample is contained in the interval.

B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval. This is the correct answer.

C.95 % of the sample data fall between the limits of the confidence interval.Your answer is not correct.

D. The mean MPG of this type of vehicle for 95?% of all samples of the same size is contained in the interval.

Solution:

a) Mean = (28 + 34 + 28 + 20 + 21 + 31 + 28 + 24 + 34 + 35 + 36 + 26 + 25 + 20)/14 = 27.86

Standard deviation = √(summation(x - mean)²/n

n = 14

Summation(x - mean)² = (28 - 27.86)^2 + (34 - 27.86)^2 + (28 - 27.86)^2 + (20 - 27.86)^2 + (21 - 27.86)^2+ (31 - 27.86)^2 + (28 - 27.86)^2 + (24 - 27.86)^2 + (34 - 27.86)^2 + (35 - 27.86)^2 + (36 - 27.86)^2 + (26 - 27.86)^2 + (25 - 27.86)^2 + (20 - 27.86)^2 = 399.7144

Standard deviation = √(399.7144/14) = 5.34

Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × s/√n

Where

s = sample standard deviation = 5.34

n = number of samples = 14

From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score

In order to use the t distribution, we would determine the degree of freedom, df for the sample.

df = n - 1 = 14 - 1 = 13

Since confidence level = 95% = 0.95, α = 1 - CL = 1 – 0.95 = 0.05

α/2 = 0.05/2 = 0.025

the area to the right of z0.025 is 0.025 and the area to the left of z0.025 is 1 - 0.025 = 0.975

Looking at the t distribution table,

z = 2.16

Margin of error = 2.16 × 5.34/√14

= 3.08

The confidence interval is 27.86 ± 3.08

b) B. We have 95 ℅ confidence that the population mean MPG of this type of vehicle is contained in the interval.

Answer:

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 66, \sigma = 2, n = 87, s = \frac{2}{\sqrt{87}} = 0.214[/tex]

Find the probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

This probability is 1 subtracted by the pvalue of Z when X = 66.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{66.5 - 66}{0.214}[/tex]

[tex]Z = 2.336[/tex]

[tex]Z = 2.336[/tex] has a pvalue of 0.99.

1 - 0.99 = 0.01

0.01 = 1% probability of finding a random sample of 87 retired people in which the average age of retirement is 66.5 or more.

Answer:

relative maximum: x = 1

relative minimum: x = 7

Step-by-step explanation:

Critical points:

Values of x for which f'(x) = 0.

Second derivative test:

For a critical point, if f''(x) > 0, the critical point is a relative minimum.

Otherwise, if f''(x) < 0, the critical point is a relative maximum.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4ac[/tex]

In this question:

[tex]f(x) = x^{3} - 12x^{2} + 21x - 8[/tex]

Finding the critical points:

[tex]f'(x) = 3x^{2} - 24x + 21[/tex]

[tex]3x^{2} - 24x + 21 = 0[/tex]

Simplifying by 3

[tex]x^{2} - 8x + 7 = 0[/tex]

So [tex]a = 1, b = -8, c = 7[/tex]

[tex]\bigtriangleup = (-8)^{2} - 4*1*7 = 36[/tex]

[tex]x_{1} = \frac{-(-8) + \sqrt{36}}{2} = 7[/tex]

[tex]x_{2} = \frac{-(-8) - \sqrt{36}}{2} = 1[/tex]

Second derivative test:

The critical points are x = 1 and x = 7.

The second derivative is:

[tex]f''(x) = 6x - 24[/tex]

[tex]f''(1) = 6*1 - 24 = -18[/tex]

Since f''(1) < 0, at x = 1 there is a relative maximum.

[tex]f''(7) = 6*7 - 24 = 18[/tex]

Since f''(x) > 0, at x = 7 there is a relative minumum.

Answer:

2.9 per hour

Step-by-step explanation:

Divide 69.9 by 24

Answer:

9 inches

Step-by-step explanation:

For similar problems like this, divide the area by the given length or width. In this case, your equation would be 54/6 = 9.

The width of the rectangle can be found as 9 inch.

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The area and length of rectangle are given as 54 inch² and 6 inches.

Suppose the width of the rectangle be x.

Since, the area of rectangle is given as the product of length and breadth, the following equation can be written as,

6x = 54

⇒ x = 54/6

⇒ x = 9

Hence, the width is given as 9 inch.

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Answer:

-$5.06

Step-by-step explanation:

Given the probability distribution of X where X is the net gain or loss

[tex]\left|\begin{array}{c|c|c}Profit(X)&\$6&-\$8\\P(X)&0.21&0.79\end{array}\right|[/tex]

The expected value of X is defined as follows:

Expected Value of X, [tex]E(X)=\sum_{i=1}^nx_iP(x_i)[/tex]

Therefore, the expected value of the player

E(X)=(6*0.21)+(-8*0.79)

=1.26-6.32

[tex]E(X)=-\$5.06[/tex]

The expected value of each player at the casino is -$5.06.

Answer: 2 ÷ 17

Step-by-step explanation: When you have something in this form, a/b, it means the same thing as a divided by b.

So 2/17 means the same thing as 2 ÷ 17.

Answer:

Lauren is wrong

Step-by-step explanation:

1. Lauren is wrong

2. What’s the cost of the shirts before tax

Each shirt cost $15 and the total = $15 x 3 = $45

3. How much is the sales tax for all shirts

Sale tax for all shirts is $45 x 0.08 = $3.6

4. What is the total cost of the shirts, including tax?

Total cost  = $45 + $3.6 = $48.60

Answer:

Los pinos ocupan [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.

Step-by-step explanation:

Una manera de resolver este problema es la siguiente:

[tex] \\ 1km^{2} = 1km * 1km = 1000m * 1000m = 1000000m^{2}[/tex]

[tex] \\ 2km^{2} = 2km * 1km = 2000m * 1000m = 2000000m^{2} = 2 * 10^{6}m^{2}[/tex]

En palabras, [tex] \\ 2km^{2} = 2000000m^{2}[/tex], o dos kilómetros cuadrados son iguales a 2 millones de metros cuadrados.

Sabemos que:

De esta manera, la parte que ocupan los pinos es el total del bosque menos el área ocupada por las hayas. Por lo tanto, el área ocupada por los pinos es:

[tex] \\ 2000000m^{2} - 380000m^{2}[/tex]

[tex] \\ 1620000m^{2}[/tex]

¿Cuántos metros cuadrados ocupan los pinos?

Los pinos ocupan, entonces, [tex] \\ 1620000m^{2}[/tex] o 1 millón seiscientos veinte mil metros cuadrados.

Step-by-step explanation:

We have,

If a quadratic equation with real coefficients has a discriminant of -36.

The general form of quadratic equation is :

[tex]ax^2+bx+c=0[/tex]

The discriminant of this equation is : [tex]D=b^2-4ac[/tex]

If D=0, it will have 1 real roots

If D>0, it will have 2 real roots

If D<0, it will have no real roots

We have,

D = -36 < 0, so, the quadratic equation will have no real roots.

Answer:

[tex]=13x+5[/tex]

Step-by-step explanation:

[tex]\left(2x+9\right)+\left(11x-4\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=2x+9+11x-4\\\mathrm{Group\:like\:terms}\\=2x+11x+9-4\\\mathrm{Add\:similar\:elements:}\:2x+11x=13x\\=13x+9-4\\\mathrm{Add/Subtract\:the\:numbers:}\:9-4=5\\=13x+5[/tex]

Answer:

(a)77.4bpm

(b)Mean of Sample 1 = 70.3 beats per minute.  

Mean pulse of sample 2 = 70 beats per minute.

(c)

Step-by-step explanation:

(a)Population mean pulse.

The pulse of the nine students which represent the population are:

[tex]\text{Population Mean} =\dfrac{64+77+89+69+89+65+88+69+87}{9} \\=\dfrac{697}{9} \\\\=77.44[/tex]

The population mean pulse is approximately 77.4 beats per minute.

(b)Sample 1: {Janette,Clarice,Megan}

Mean of Sample 1

[tex]\text{Sample 1 Mean} =\dfrac{65+69+77}{3} \\=\dfrac{211}{3} \\\\=70.3[/tex]

Sample 2: {Janette,Clarice,Megan}

Mean of Sample 2

[tex]\text{Sample 2 Mean} =\dfrac{64+69+77}{3} \\=\dfrac{210}{3} \\\\=70[/tex]

The mean pulse of sample 1 is approximately 70.3 beats per minute.  

The mean pulse of sample 2 is approximately 70 beats per minute.

(c)