The graph of an exponential function passes through (2,−12) and (3,−24). Find the exponential function that describes the graph.

Answer:

Ignore the A before the ±, it wouldn't let me type it correctly.

[tex]x=\frac{2±\sqrt{7} }{3}[/tex]

Step-by-step explanation:

3x + 4 = 1 ÷ x

3x + 4 - 4 = 1 ÷ x - 4

3x = 1 ÷ x - 4

[tex]3x=\frac{1}{x} +\frac{x(-4)}{x}[/tex]

[tex]3x=\frac{1+x(-4)}{x}[/tex]

[tex]3x=\frac{1-4x}{x}[/tex]

[tex]x(3x)=x(\frac{1-4x}{x})[/tex]

x · 3x = - 4x + 1

3x² = - 4x + 1

3x² - (- 4x + 1) = 0

3x² + 4x - 1 = 0

Ignore the A before the ±, it wouldn't let me type it correctly.

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

a = 3

b = 4

c = - 1

[tex]x=\frac{-4±\sqrt{4^{2}-4((3)(-1)) } }{2(3)}[/tex]

[tex]x=\frac{-4±\sqrt{16-4((3)(-1)) } }{2(3)}[/tex]

[tex]x=\frac{-4±\sqrt{16+12 } }{2(3)}[/tex]

[tex]x=\frac{-4±\sqrt{28 } }{2(3)}[/tex]

[tex]x=\frac{-4±\sqrt{(2)(14) } }{2(3)}[/tex]

[tex]x=\frac{-4±\sqrt{(2)(2)(7) } }{2(3)}[/tex]

[tex]x=\frac{-4±\sqrt{2 } \sqrt{2}\sqrt{7} }{2(3)}[/tex]

[tex]x=\frac{-4±2\sqrt{7} }{2(3)}[/tex]

[tex]x=\frac{-4±2\sqrt{7} }{6}[/tex]

Two separate equations

[tex]x=\frac{-4+2\sqrt{7} }{6}[/tex]

[tex]x=\frac{2+\sqrt{7} }{3}[/tex]

[tex]x=\frac{-4-2\sqrt{7} }{6}[/tex]

[tex]x=\frac{2-\sqrt{7} }{3}[/tex]

Answer: d

Step-by-step explanation:

edge 2020

ok check image file in the image is answers with color code

Step-by-step explanation:

[tex] \frac{2}{3} \times \frac{99}{1} = 66 \: kg[/tex]

12z - 21 = 92

12z - 21 + 21 = 92 + 21

12z = 113

z = 113/12

Answer:

[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]

Step-by-step explanation:

The following formula can be utilized for this question:

[tex]N = N_o (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\\frac{N}{N_o} = (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\[/tex]

where,

[tex]\frac{N}{N_o}[/tex] = ratio of the remaining amount to the original amount = ?

t = tme passed = 6 days

[tex]t_{1/2}[/tex] = half-life = 13 days

Therefore,

[tex]\frac{N}{N_o} = (\frac{1}{2} )^{\frac{6\ days}{13\ days} }\\\\[/tex]

[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]

Answer: 45 pencils were in the box originally

Step-by-step explanation:

Suppose there were x pencils in the box originally. Since 18 pencils is equal to 2/5 of the total number of pencils in the box originally, set 18 equal to 2/5x or

18=2/5x

Now solve

x = 18x5/2 = 45

Answer:

Eighty thousand

Step-by-step explanation:

Look at the place value chart.

Answer:

We do not reject the Null Hypothesis

Step-by-step explanation:

From the question we are told that:

Sample size [tex]n=23[/tex]

Population mean [tex]\mu=9.02cm^3[/tex]

Sample mean [tex]\=x=8.16[/tex]

Standard deviation [tex]\sigma=0.7cm^3[/tex]

Significance level [tex]\alpha =0.01[/tex]

Generally the Null and and alternative Hypothesis are as follows

 [tex]H_0:\mu=9.02cm^3[/tex]

 [tex]H_a:\mu<9.02cm^3[/tex]

Therefore t critical Value is

 [tex]t\ critical\ Value=(\alpha,df)[/tex]

 [tex]t\ critical\ Value=(0.01,22)[/tex]

Where

  [tex]df=n-1\\\\df=23-1=>22[/tex]

Therefore

From t Table

 [tex]t value=-2.8[/tex]

Generally the equation for Z Critical is mathematically given by

 [tex]t=\frac{\=x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]

 [tex]t=\frac{8.16-9.02}{\frac{0.7}{\sqrt{23} } }[/tex]

 [tex]t=-5.89[/tex]

Therefore

Since the t test statistics is greater than the Critical value

Hence,we do not reject the Null Hypothesis

Answer:

CLAE

Step-by-step explanation:

1=43

2=28

3=24

4=83

Answer:

D. 0.85

Step-by-step explanation:

The data points in the scatter plot are closer to each other along the line of best fit, this means that there is a strong positive association between minutes and distance and therefore, the correlation coefficient would be relatively closer to 1.

The correlation is positive since both variables tend to increase together in the same direction.

Therefore, the best estimate of the correlation coefficient out of the given options would be 0.85

Answer:

7w - 14

if w = 9

7(9) - 9

63 - 9

w=57

Answer

19.013.153,42629466 giây

Step-by-step explanati

van toc ánh sán  =299.792.458 m/s

s= v*t

t=s/v

t= 5.699.999.999.999.999/299.792.458= 19.013.153,42629466 giây

Answer:

The probability is:

P = 0.375

Step-by-step explanation:

First, we need to find the total number of four-digit numbers that can be made with the digits 0-8, such that the first digit can not be zero.

To do this, we first need to find the number of selections that we have, in this case, there are 4, one for each digit in our 4-digit number.

Now let's count the number of options that we have for each one of these selections:

first digit: we have 8 options (because the 0 can not be here)

second digit: we have 9 options (because now the zero can be taken)

third digit: we have 9 options

fourth digit: we have 9 options.

The total number of combinations is equal to the product of all the numbers of options, this is:

C = 8*9*9*9 = 5,832

Now we need to find how many of these are less or equal than 4000.

So now let's count the options again:

first digit: 3 options {1, 2, 3}

second digit: 9 options

third digit: 9 option

fourth digit: 9 options

Total number of combinations:

C' = 3*9*9*9 = 2,187

Here we should also count the combination for the number 4000 itself, as it was not counted in our previous calculation, then we have:

C' = 2,187 + 1 = 2,188 combinations.

The probability of randomly choosing a number that is smaller than or equal to 4000 will be equal to the quotient between the number of combinations that are smaller than or equal to 4000 (2,188 combinations) and the total number of combinations (5,832)

this is:

P = 2,188/5,832 = 0.375

Answer:

33.51 cubic inches

Step-by-step explanation:

Formula for volume of a sphere is V= 4 /3 · π · r3

We know the diameter is 4, and the radius is half the diameter, so the radius is 2.

V = 4 /3 · π · [tex]2^{3}[/tex]

≈ 33. 51032

Rounded to the nearest hundreth is 33.51.

Answer: 5,508 m3

Step-by-step explanation:  V= 18 x 17 x 18 = 5,508 m3

Answer:5, 508

Step-by-step explanation:

V 18×18×17=5,508

Answer:

B.

Step-by-step explanation:

The equation of a circle with center at (h, k) and radius r is

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

We have center at (-5, 0). That makes h = -5, and k = 0.

The radius is 3, so r = 3.

[tex] (x - (-5))^2 + (y - 0)^2 = 3^2 [/tex]

[tex] (x + 5)^2 + y^2 = 9 [/tex]

Answer: B.

Answer:

B

Step-by-step explanation:

The equation of a circle has the form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

Where (h, k) is the center of the circle and r is the radius.

From the graph, we can see that the center of the circle is at (-5, 0). So, (h, k) is (-5, 0), where h = -5 and k = 0.

And by counting, we can determine that the radius of the circle is three units. Hence, r = 3.

Substitute the information into the equation:

[tex](x-(-5))^2+(y-(0))^2=(3)^2[/tex]

Simplify. Therefore, our equation is:

[tex](x+5)^2+y^2=9[/tex]

Our answer is B.

Answer:

The lorry travels by 6 mph more than the expected speed.

Step-by-step explanation:

Velocity formula:

Velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

Shortest route:

400 miles in 10 hours, which means that [tex]d = 400, v = 10[/tex]. So

[tex]v = \frac{d}{t} = \frac{400}{10} = 40[/tex]

In mph.

The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 10 hours.

Distance is multiplied by 100% + 15% = 115% = 1.15, so:

[tex]d = 1.15*400 = 460[/tex]

Then

[tex]v = \frac{d}{t} = \frac{460}{10} = 46[/tex]

46 mph

By how many more mph than the expected speed does the lorry travel?

46 - 40 = 6 mph

The lorry travels by 6 mph more than the expected speed.

Answer:

(a):

Dannette                   Alphonso

[tex]\bar x_D = 4.33[/tex]                    [tex]\bar x_A = 5.17[/tex]

[tex]M_D = 2.5[/tex]                    [tex]M_A = 5[/tex]

[tex]\sigma_D = 3.350[/tex]                  [tex]\sigma_A = 1.951[/tex]

[tex]IQR_D = 7[/tex]                  [tex]IQR_A = 1.5[/tex]

(b):

Measure of center: Median

Measure of spread: Interquartile range

(c):

There are no outliers in Dannette's dataset

There are outliers in Alphonso's dataset

Step-by-step explanation:

Given

See attachment for the appropriate data presentation

Solving (a): Mean, Median, Standard deviation and IQR of each

From the attached plots, we have:

IQR_A = 1.5 ---- Dannette

[tex]A = \{3,4,4,4,4,5,5,5,5,6,6,11\}[/tex] ---- Alphonso

n = 12 --- number of dataset

Mean

The mean is calculated

[tex]\bar x = \frac{\sum x}{n}[/tex]

So, we have:

[tex]\bar x_D = \frac{1+1+1+1+2+2+3+7+8+8+9+9}{12}[/tex]

[tex]\bar x_D = \frac{52}{12}[/tex]

[tex]\bar x_D = 4.33[/tex] --- Dannette

[tex]\bar x_A = \frac{3+4+4+4+4+5+5+5+5+6+6+11}{12}[/tex]

[tex]\bar x_A = \frac{62}{12}[/tex]

[tex]\bar x_A = 5.17[/tex]  --- Alphonso

Median

The median is calculated as:

[tex]M = \frac{n + 1}{2}th[/tex]

[tex]M = \frac{12 + 1}{2}th[/tex]

[tex]M = \frac{13}{2}th[/tex]

[tex]M = 6.5th[/tex]

This implies that the median is the mean of the 6th and the 7th item.

So, we have:

[tex]M_D = \frac{2+3}{2}[/tex]

[tex]M_D = \frac{5}{2}[/tex]

[tex]M_D = 2.5[/tex] ---- Dannette

[tex]M_A = \frac{5+5}{2}[/tex]

[tex]M_A = \frac{10}{2}[/tex]

[tex]M_A = 5[/tex]  ---- Alphonso

Standard Deviation

This is calculated as:

[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]

So, we have:

[tex]\sigma_D = \sqrt{\frac{(1 - 4.33)^2 +.............+(9- 4.33)^2}{12}}[/tex]

[tex]\sigma_D = \sqrt{\frac{134.6668}{12}}[/tex]

[tex]\sigma_D = 3.350[/tex] ---- Dannette

[tex]\sigma_A = \sqrt{\frac{(3-5.17)^2+............+(11-5.17)^2}{12}}[/tex]

[tex]\sigma_A = \sqrt{\frac{45.6668}{12}}[/tex]

[tex]\sigma_A = 1.951[/tex] --- Alphonso

The Interquartile Range (IQR)

This is calculated as:

[tex]IQR =Q_3 - Q_1[/tex]

Where

[tex]Q_3 \to[/tex] Upper Quartile       and        [tex]Q_1 \to[/tex] Lower Quartile

[tex]Q_3[/tex] is calculated as:

[tex]Q_3 = \frac{3}{4}*({n + 1})th[/tex]

[tex]Q_3 = \frac{3}{4}*(12 + 1})th[/tex]

[tex]Q_3 = \frac{3}{4}*13th[/tex]

[tex]Q_3 = 9.75th[/tex]

This means that [tex]Q_3[/tex] is the mean of the 9th and 7th item. So, we have:

[tex]Q_3 = \frac{1}{2} * (8+8) = \frac{1}{2} * 16[/tex]           [tex]Q_3 = \frac{1}{2} * (5+6) = \frac{1}{2} * 11[/tex]

[tex]Q_3 = 8[/tex] ---- Dannette                 [tex]Q_3 = 5.5[/tex] --- Alphonso

[tex]Q_1[/tex] is calculated as:

[tex]Q_1 = \frac{1}{4}*({n + 1})th[/tex]

[tex]Q_1 = \frac{1}{4}*({12 + 1})th[/tex]

[tex]Q_1 = \frac{1}{4}*13th[/tex]

[tex]Q_1 = 3.25th[/tex]

This means that [tex]Q_1[/tex] is the mean of the 3rd and 4th item. So, we have:

[tex]Q_1 = \frac{1}{2}(1+1) = \frac{1}{2} * 2[/tex]                  [tex]Q_1 = \frac{1}{2}(4+4) = \frac{1}{2} * 8[/tex]

[tex]Q_1 = 1[/tex] --- Dannette                   [tex]Q_1 = 4[/tex] ---- Alphonso

So, the IQR is:

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR_D = 8 - 1[/tex]                                     [tex]IQR_A = 5.5 - 4[/tex]

[tex]IQR_D = 7[/tex] --- Dannette                      [tex]IQR_A = 1.5[/tex] --- Alphonso

Solving (b): The measures to compare

Measure of  center

By observation, we can see that there are outliers is the plot of Alphonso (because 11 is far from the other dataset) while there are no outliers in Dannette plot (as all data are close).

Since, the above is the case; we simply compare the median of both because it is not affected by outliers

Measure of  spread

Compare the interquartile range of both, as it is arguably the best measure of spread, because it is also not affected by outliers.

Solving (c): Check for outlier

To check for outlier, we make use of the following formulas:

[tex]Lower =Q_1 - 1.5 * IQR[/tex]

[tex]Upper =Q_3 + 1.5 * IQR[/tex]

For Dannette:

[tex]Lower = 1 - 1.5 * 7 = -9.5[/tex]

[tex]Upper = 8 + 1.5 * 7 = 18.5[/tex]

Since, the dataset are all positive, we change the lower outlier to 0.

So, the valid data range are:

[tex]Valid = 0 \to 18.5[/tex]

From the question, the range of Dannette's dataset is: 1 to 9. Hence, there are no outliers in Dannette's dataset

For Alphonso:

[tex]Lower = 4 - 1.5 * 1.5 =1.75[/tex]

[tex]Upper = 5.5 + 1.5 * 1.5 =7.75[/tex]  

So, the valid data range are:

[tex]Valid = 1.75\to 7.75[/tex]

From the question, the range of Alphonso's dataset is: 3 to 11. Hence, there are outliers in Alphonso's dataset

9514 1404 393

Answer:

  d, b, c, a, e

Step-by-step explanation:

The order of the letters in the congruence statement tells you ...

  ΔQOP ≅ ΔABC

  ∠Q ≅ ∠A

  ∠O ≅ ∠B ≅ 115°

  ∠P ≅ ∠C

  QO ≅ AB = 5 m

  OP ≅ BC = 8 m

  PQ ≅ CA

Answer:

2.45.250- 94.750

= 92. 2975. this is the learners who got the admission

Answer:

1,50,500 students

Step-by-step explanation:

Hope this helps... vote as brainliest

Answer:

A U B={1,2,3,4,5,6,7,8,9,10} represents A union B

(includes all the members of set Sand the members of set Bout together, do not repeat anyone that comes twice)

A n B={1,4} represents A interception B( this refers to the members that sets A and B have in common)

Answer:

A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

Step-by-step explanation:

A = { 1 , 3 , 4 , 5 , 7 , 9 }

B = { 1 , 2 , 4 , 6 , 8 , 10 }

A ∪ B = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 }

           It represents the whole numbers between 0 and 11

          [ A ∪ B is the elements of both A and B , without any repetition ]    

A ∩ B = { 1 , 4 }

            It represents the common numbers in both A and B

Answer:

43.5 % decrease

Step-by-step explanation:

Take the original price and subtract the new price

850-480

370

Divide by the original price

370/850

.435294118

Change to percent form by multiplying by 100

43.5294118 % decrease

43.5 % decrease

Answer:

Tuesday's z-score was of -1.325.

The percentile rank of sales for this day was the 9.25th percentile.

Step-by-step explanation:

Z-score:

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.

A department store, on average, has daily sales of $21,000. The standard deviation of sales is $3600.

This means that [tex]\mu = 21000, \sigma = 3600[/tex]

On Tuesday, the store sold $16,230 worth of goods. Find Tuesday's z score.

This is Z when X = 16230. So

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

[tex]Z = \frac{16230 - 21000}{3600}[/tex]

[tex]Z = -1.325[/tex]

Tuesday's z-score was of -1.325.

What is the percentile rank of sales for this day

This is the p-value of Z = -1.325.

Looking at the z-table, this is of 0.0925, and thus:

The percentile rank of sales for this day was the 9.25th percentile.

Answer and Step-by-step explanation:

The answer is the second answer choice. y = 2x + 1

By looking at the graph, we see that there is a y-intercept at (0, 1), and it has a positive slope of 2.

#teamtrees #PAW (Plant and Water)

Answer:

9 + 10 = 21

Step-by-step explanation:

9 + 10 = 21

Factor out 9 and 10

9 = 3 · 3   10 = 2 · 5

Next multiply 3 by 2

3 × 2 = 6

Then multiply 3 by 5

3 · 5 = 15

Finally add the products

15 + 6 = 21

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Interest amount paid on loan = $90

Principal value, amount borrowed = $500

Period, t = 16 days

The equivalent annual interest :

Using the simple interest formula :

simple interest = principal * rate * time

Using, days of year = 365

Plugging in the values into the formula :

90 = 500 * rate * (16/365)

90 = 500 * rate * 0.0438356

90 = 21.917808 * rate

Rate = 90 / 21.917808

Rate = 4.10 = 4.10 * 100% = 410%

If days of year = 360 is used :

90 = 500 * rate * (16/360)

Rate = 90 / 22.222

Rate = 4.05 = 4.105 * 100% = 405%

Answer:

(h o k) (3) = 3

(k o h) (-4b) = -4b

Step-by-step explanation:

An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.

This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.

Answer:

48

Step-by-step explanation:

the answer is 48 I got this answer by multiplying 5 by 10 and subtracting is from 2 which gives me 50 - 2 which is 48

Answer:

48

Step-by-step explanation:

5×10-2=50-2

=48

hope it helps!!