What is the equation of the line that is perpendicular to
the given line and has an x-inter cept of 6?
O y = x + 8
O y = x + 6
O y = fx-8
O y=x-6

Answer:

The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 62, standard deviation of 8.

What is the approximate percentage of trees planted between 38 and 86?

38 = 62 - 3*8

86 = 62 + 3*8

So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.

Answer:

Step-by-step explanation:

Even function has following property:

It is easy to show this works with the second choice only. All the others don't work:

This is not correct as x - 1 ≠ -x - 1 so as their squares, so g(x) ≠ g(-x)

The last two choices are not even similarly.

Answer:

B. g(x) = 2x2 + 1

Correct on edge

Answer:

The function represents the sequence is - 3 n + 23.

Step-by-step explanation:

20. 17, 14, 11, 8,......

Here, the first term is

a = 20

Common difference, d = -3

Let the nth term is Tn.

Tn = a + (n -1) d

Tn = 20 + (n -1) x (-3)

Tn = 20 - 3 n + 3

Tn = 23 - 3 n = - 3 n + 23

So, the function represents the sequence is - 3 n + 23.

Answer:

Y'all know what it is already, but I want points, so: f(n) = -3n + 23

Answer:

Circumference =10 pi yard

Area =25 pi yard squared

Step-by-step explanation:

C=2*pi*r

Circumfrance =10 pi

A=pi r^2

Area =25 pi

For the estimate just sub in pi on the calculator for pi, then round to the hundreth.

Circumfrence= just the unit

Area= squared

Answer:

900 at 12%

2100 at 10%

Step-by-step explanation:

Let x= amount invested at 12%

let y= amount invested at 10%

with that being said we can write the two equation

Equation 1: x+y=3000

Equation 2: 3000*.106=.12x+.1y

isolte x from equation 1

x= 3000-y

plug this into equation 2

318=.12(3000-y)+.1y

318=360-.12y+.1y

-42= -.02y

y= 2100

Plug this into equation 1

x+2100=3000

x=900

she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

Let's denote the amount of money Hattie invests at 12% as \(x\) dollars, and the amount she invests at 10% as \(\$3000 - x\) dollars.

The formula for calculating interest is: \(\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}\).

For the 12% account:

Interest_12% = \(x \times 0.12 \times 1\) (1 year)

For the 10% account:

Interest_10% = \((3000 - x) \times 0.10 \times 1\) (1 year)

Hattie wants to earn 10.6% interest on the total investment, so we can set up the equation:

\(\text{Total Interest} = \text{Interest}_12% + \text{Interest}_10%\)

\(3000 \times 0.106 = x \times 0.12 + (3000 - x) \times 0.10\)

Now, solve for \(x\):

\(318 = 0.12x + 300 - 0.10x\)

\(318 = 0.02x + 300\)

\(18 = 0.02x\)

\(x = 900\)

Hattie should invest $900 at 12% and \(3000 - 900 = 2100\) at 10%.

Therefore, she should invest $900 into the account earning 12% interest and $2100 into the account earning 10% interest.

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Solution :

The significant figure of a number are defined as the positional notation of that number which are most reliable and are absolutely necessary to represent the quantity of something.

In the context, we have to express the given numbers into three significant figures in the form of scientific notation or in the exponential form :

(i). 5590    -----    [tex]$5.59 \times 10^3$[/tex]

(ii).  0.000498   -----    [tex]$4.98 \times 10^{-4}$[/tex]

(iii) 135000  -----   [tex]$1.35 \times 10^5$[/tex]

(iv) 0.000438   -----  [tex]$4.38 \times 10^{-4}$[/tex]

Answer:

x= - 1

Step-by-step explanation:

Graph B is the best graph that represents the linear equation

Answer:

m=2b=1y=2x+1

just enter it

Answer:

2.409

Step-by-step explanation:

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\ln 200 = log_{e}200[/tex]

[tex]log_{9}200 = \frac{log_{e}200}{log_{e}9}[/tex]

           = [tex]\frac{5.3}{2.2}[/tex]

           = 2.409

The approximate value of log 200 would be; 2.409

When we raise a number with an exponent, there comes a result.

Let's say you get  a^b = c Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows [tex]b = \log_a(c)[/tex]'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We have given the values in 9 = 2.2 and 200 – 5.3

We need to find the approximate value of log, 200.

Therefore,

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\\\ln 200 = log_{e}200[/tex]

Using the logarithm property;

[tex]log_{9}200 = \dfrac{log_{e}200}{log_{e}9}\\ = \dfrac{ln 200}{ln 9}\\ = \dfrac{5.3}{2.2}[/tex]

=  2.409

Hence, the approximate value of log, 200 would be; 2.409

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9514 1404 393

Answer:

  y -9

Step-by-step explanation:

From 4 years ago until 5 years from now, John will age 9 years. That is, his age 4 years ago is 9 years less than it will be in 5 years.

John's age 4 years ago is y-9 years.

[tex]x = \frac{ - b \frac{ + }{} \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

Answer:

F

Step-by-step explanation:

4.85-4.15=0.7 divided by 2 = 0.35+4.15=4.5*25 cause 30-20=10 divided by 2=5+20=25*4.5=112. closest to that is 120

Answer:

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

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 normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean diameter of 144 millimeters, and a variance of 49.

This means that [tex]\mu = 144, \sigma = \sqrt{49} = 7[/tex]

Sample of 46:

This means that [tex]n = 46, s = \frac{7}{\sqrt{46}}[/tex]

Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?

Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.

Probability the sample mean is below 142:

p-value of Z when X = 142, so:

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

By the Central Limit Theorem

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

[tex]Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}[/tex]

[tex]Z = -1.94[/tex]

[tex]Z = -1.94[/tex] has a p-value of 0.0262

2*0.0262 = 0.0524

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Answer:

C.No, the two triangles can only be proven congruent through SSS.

Answer:

True

Step-by-step explanation:

Required

Does dilation preserve angle measure?

When a point, side, line, or angle is dilated; the length of the line will be altered by the ratio or scale of dilation.

However, the measure of angle will remain the same.

Hence, the given statement is true.

Answer:

3 x² y¹

Step-by-step explanation:

15 x²y³ = 3. 5. x². y³

-18x³yz = -2. 3². x³. y¹. z¹

so, the GCF = 3. x². y¹

Answer:

Solution given:

15x²y³=3*5*x*x*y*y*y

-18x³yz=-3*2*3*x*x*x*y*z

over here common is

3*x*x*y

so

greatest common factor is 3x²y¹

Answer:

The answer is [tex]b=3, a=-2[/tex], and [tex]c=3[/tex].

Step-by-step explanation:

To solve this system of equations, start by solving for (a) in the third equation.

To solve for (a) in the third equation, add [tex]3b[/tex] to both sides of the equation, which will look like [tex]2a=-13+3b\\-a+b-c=2\\2a+3b-4c=-7[/tex]. Next, divide each term in [tex]2a=-13+3b[/tex] by 2 and simplify, which will look like [tex]\frac{2a}{2}=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex]   =  [tex]a=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex].

Then, replace all variables of (a) with [tex]-\frac{13}{2} +\frac{3b}{2}[/tex] in each equation and simplify, which will look like [tex]-13+6b-4c=-7\\-\frac{2c-13+b}{2}=2\\a=-\frac{13}{2}+\frac{3b}{2}[/tex].

The next step is to reorder [tex]-\frac{13}{2}[/tex] and [tex]\frac{3b}{2}[/tex], which will look like [tex]\frac{3b}{2}-\frac{13}{2}\\-13+6b-4c=-7\\-\frac{2c-13+b}{2} =2[/tex].

Then, solve for (b) in the second equation. To solve for (b) in the second equation start by moving all terms not containing (b) to the right side of the equation, which will look like [tex]6b=6+4c\\a=\frac{3b}{2}-\frac{13}{2} \\-\frac{2c-13+b}{2} =2[/tex]. Next, divide each term in                ([tex]6b=6+4c[/tex]) and simplify, which will look like [tex]b=1+\frac{2c}{3} \\a=\frac{3b}{2} -\frac{13}{2\\}\\-\frac{2c-13+b}{2} =2[/tex].

Then, replace all variables of (b) with [tex]1+\frac{2c}{3}[/tex] in each equation and simplify, which will look like [tex]-\frac{2(2c-9)}{3}=2\\a=c-5\\b=1+\frac{2c}{3}[/tex].

The next step is to solve for (c) in the first equation. To solve for (c) in the first equation start by multiplying both sides of the equation by [tex]-\frac{3}{2}[/tex] and simplify, which will look like [tex]2c-9=-3\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Then, move all terms not containing (c) to the right side of the equation, which will look like [tex]2c=6\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Next, divide each term in [tex]2c=6[/tex] by 2 and simplify, which will look like [tex]c=3\\a=c-5\\b=1+\frac{2c}{3}[/tex].

Then, replace all variables of (c) with 3 in each equation and simplify, which will look like [tex]b=3\\a=-2\\c=3[/tex]. Finally, the list of all the solutions are [tex]b=3,a=-2[/tex], and [tex]c=3[/tex].

Answer:

A - $214.40

Step-by-step explanation:

Since b is the number of boxes of cards and n is the number of ink colors, and we're given the number of boxes of cards, and number of ink colors, we plug in:

4= b

and

3 = n

into the given equation to solve for C.

Using the order of operations we start inside our parentheses and work from there:

C= $25.60*4 + $14.00*4(3 - 1)

C= $25.60*4 + $14.00*4(2)

C= $102.40 + $112

C= $214.40

Answer:

[tex]241^{257}\ mod\ 12 =1[/tex]

[tex]7 * 20 = 140[/tex]

[tex]\frac{1}{700}[/tex]

Step-by-step explanation:

Solving (a): 241^257 mod 12

To do this, we simply calculate [tex]241\ mod\ 12[/tex]

Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]

The highest number less than or equal to 241 that is divisible by 12 is 240; So:

[tex]241\ mod\ 12 = 241- 240[/tex]

[tex]241\ mod\ 12 =1[/tex]

Hence:

[tex]241^{257}\ mod\ 12 =1[/tex]

Solving (b): 7 * 20

[tex]7 * 20 = 140[/tex]

Solving (c): Multiplicative inverse of 7 in 719

The position of 7 in 719 is 700

So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number

Answer:

7

Step-by-step explanation:

First, add all the cards.

[tex]2 + 5 + 7 + 8 + 9 = 31[/tex]

If we remove one card, the remaining four cards average will be 6, this means that the 4 remaning cards will average total will be at 24 because 6×4=24. So we need to find a value that will equal 24 if we remove that card.

The answer is 7 because

[tex] \frac{2 + 5 + 8 + 9}{4} = 6[/tex]

9514 1404 393

Answer:

  remove 7 to make the total be 6×4 = 24.

Step-by-step explanation:

The description "mean average" is redundant to no apparent purpose. "Mean" and "average" are the same thing: the total divided by the number of contributors.

If the mean of 4 cards is 6, then we require ...

  6 = (total of 4 cards) ÷ 4

  24 = total of 4 cards . . . . . . . multiply both sides of the equation by 4

__

We note that the total of all the cards shown is ...

  2 + 5 + 7 + 8 + 9 = 31

In order to make the total be 24, we need to remove a card that has a value of ...

  31 -24 = 7

Removing 7 will bring the total to 2 + 5 + 8 + 9 = 24, and the average to 24/4 = 6.

_____

Additional comment

It is worthwhile to remember the relationship between the total and the average and the number of contributors. This shows up a lot in problems involving adjusting an average or finding a value to give a certain average.

Answer:

[tex]PQ=6\frac{1}{2} =\frac{13}{2}[/tex]

[tex]|Q-P|=\frac{13}{2}[/tex]

[tex]|Q+4|=\frac{13}{2}[/tex]

[tex]Q+4=+-\frac{13}{2}[/tex]

[tex]Q=-4[/tex] ± [tex]\frac{13}{2}[/tex]

[tex]Q=\frac{21}{2} \times2\frac{1}{2}[/tex]

[tex]Answer: C)~2\frac{1}{2}[/tex]

------------------------

Each shirt = $12.25

so, x = shirts = 12.25 x

cost including shipping= 77.49

So,

12.25 x + 3.99=77.49

Answer: D)

-------------------------

hope it helps...

have a great day!!

Answer:

1384.5

Step-by-step explanation

Diviseion is just the oppisite of multiplication so you can think to yourself that what times two equals 2769. If you multiply 1384.5 on a calculater you get 2769.

Answer:

a. difference of means

Step-by-step explanation:

Given that :

Mean , x = 9.4

Standard deviation, [tex]s.d_1[/tex] = 2.5

Number, [tex]n_1[/tex] = 12

Mean, y = 6.5

standard deviation, [tex]s.d_2[/tex] = 2.4

Number, [tex]n_2[/tex] = 12

The null hypothesis is : [tex]$H_0: \mu_1=\mu_2$[/tex]

The alternate hypothesis is : [tex]$H_1: \mu_1>\mu_2$[/tex]

Level of significance, [tex]\alpha[/tex] = 0.1

From the [tex]\text{standard normal table, right tailed,}[/tex] [tex]$t_{1/2}$[/tex] = 1.363

Since out test is right tailed.

Reject [tex]H_0[/tex], if [tex]$T_0>1.363$[/tex]

We use the test statics,

[tex]$t_0=\frac{(x-y)}{\sqrt{\frac{s.d_1}{n_1}+\frac{s.d_2}{n_2}}}$[/tex]

[tex]$t_0=\frac{(9.4-6.5)}{\sqrt{\frac{6.25}{12}+\frac{5.76}{12}}}$[/tex]

[tex]$t_0=2.899$[/tex]

[tex]$|t_0|=2.899$[/tex]

[tex]\text{Critical value}[/tex]

The value of [tex]$|t_{1/2}|$[/tex] with minimum [tex]$\left(n_1-1,n_2-1)$[/tex] that is 11 df is 1.363

We go [tex]$|t_0|=2.899$[/tex] and [tex]$|t_{1/2}|$[/tex] = 1.363

Decision making:

Since the value of [tex]|t_0|>|t_{1/2}|$[/tex]  and we reject the [tex]H_0[/tex]

The p-value : right tail [tex]H_a:(p>2.8988)[/tex]

                                      = 0.00724

Therefore the value of [tex]$p_{0.1} > 0.00724$[/tex], and so we reject the [tex]H_0[/tex]

Thus we are testing 'the difference of means" in this problem.

9514 1404 393

Answer:

  h = -4.79(t -0.58)^2 +3.26

Step-by-step explanation:

The coordinates (t1, h1) are the time and height at the maximum. Then 'a' can be found from ...

  h = a(t -t1)^2 +h1

  1.65 = a(0 -0.58)^2 +3.26

  -1.61 = 0.3364a . . . . . subtract 3.26

  -4.786 = a . . . . . . . divide by the coefficient of a

The equation is ...

  h = -4.79(t -0.58)^2 +3.26

Answer:

0.2305 = 23.05% probability that exactly 2 workers say yes.

Step-by-step explanation:

For each worker, there are only two possible outcomes. Either they say yes, or they say no. The probability of a worker saying yes is independent of any other worker, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

5% of workers in the US use public transportation to get to work.

This means that [tex]p = 0.05[/tex]

You randomly select 25 workers

This means that [tex]n = 25[/tex]

Find the probability that exactly 2 workers say yes.

This is P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{25,2}.(0.05)^{2}.(0.95)^{23} = 0.2305[/tex]

0.2305 = 23.05% probability that exactly 2 workers say yes.

Answer:

1.74 or [tex]\frac{103}{59}[/tex]

Step-by-step explanation:

3(x-5) = 8 (11-7x)

3x-15=88-56x

59x=103

x = 1.74

Answer:

18

Step-by-step explanation:

3:2 means 3/2 or 3÷2

but its better to leave it as

3/2

Answer:

p = 15/x

x= -3

Step-by-step explanation:

For the first problem, we can expand the equation to 4px+4=64

then simplify it to:

4px=60

then divide 4x from both sides of the equation

p=60/4x

then simplify:

p=15/x

For the second problem:

plug in -5 for p so the equation would look like

4(-5x +1)=64

simplify

-20x=60

x= -3

Given: Given that for 16 brownies we need

Butter- [tex]\frac{2}{3}[/tex] cups

unsweetened chocolate-5 ounces

sugar-1-1/2 cup

vanilla-2 teaspoons

eggs-2

flour- 1 cup

To find: The amount of ingredients to make 6 brownies.

Solution: The amount we need to make 6 brownies is,

Butter

[tex](\frac{2}{3}.16)/6\\=0.25125 cups[/tex]

unsweetened chocolate

[tex]\frac{5.6}{16}\\=\frac{30}{16}[/tex]ounces

sugar-0.5625 cup

vanilla-[tex]\frac{12}{16}[/tex]teaspoons

eggs-[tex]\frac{12}{16}[/tex]

flour- [tex]\frac{6}{16}[/tex] cup