Solving exponential equations with a common base problem in the picture!

the frequency of success is 244.

part b's answer is 240.

A relative frequency distribution shows the proportion of the total number of observations associated with each value or class of values and is related to a probability distribution, which is extensively used in statistics.

Relative frequency can be defined as the number of times an event occurs divided by the total number of events occurring in a given scenario. The relative frequency formula is given as:

Relative Frequency = Subgroup frequency/ Total frequency.

1. Frequency of success

=400 - 96 - 60

=244

relative frequency of fail

=60/400= 0.15

Relative Frequency of success

=1-0.15 - 0.24

=0.61

Learn more about relative frequency here:

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Answer:

c

Step-by-step explanation:

Answer:

Do your classmates prefer warm or cool places to travel for vacation?

Step-by-step explanation:

Answer:

10%

Step-by-step explanation:

Percentage increase for any change is calculated by formula

{(Final value - initial value)/initial value} * 100

Given

population in 2010 = 2 million ----------->initial value

population in 2015 = 2.2 million ----------->Final value

[tex]Percentage \ \ increase = {(2.2 - 2)/2} *100= (0.2/2)*100 = 10%[/tex]

Answer:

10%

Step-by-step explanation:the population in 2010 - 2015 is grown though 10%

as a percent incease the number willl incease in increase will increase and increase until the number can increase to 2.2 million or 2 millions and also the population would probably decrease

Answer:

The standard error (SE) is 0.1847.

The t-statistic for this test is 2.490.

Step-by-step explanation:

We are given that the sample has a mean of [tex]\bar X[/tex] = 101.09 and a standard deviation of s = 0.4887 .

Also, the 7 sample values are also given.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 100.63  

Alternate Hypothesis, [tex]H_1[/tex] : [tex]\mu[/tex] > 100.63  

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

                         T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = 101.09

            s = sample standard deviation = 0.4887

            n = sample values = 7

The Standard Error (SE) is given by =  [tex]\frac{s}{\sqrt{n} }[/tex]  =  [tex]\frac{0.4887}{\sqrt{7} }[/tex] = 0.1847

So, test statistics  =  [tex]\frac{101.09-100.63}{\frac{0.4887}{\sqrt{7} } }[/tex]  ~ [tex]t_6[/tex]

                                =  2.490

The value of t test statistics is 2.490.

The given options are:

Answer:

Step-by-step explanation:

If Elizabeth has a combined total of 20 apps and movies.

Where:

Number of apps=x

Number of Movies =y

Then:

Their total,

If we subtract x from both sides

x+y-x=-x+20

In Option E

8 apps and 12 movies  add up to 20. Therefore, this could also apply.

cones

cylinders

spheres

Step-by-step explanation:

The question was worded incorrectly and instead of giving the options it gave you the answers

Answer:

A, B and F

Step-by-step explanation:

Area of 2 triangles:

2(½ × 6 × 8)

48 in²

Area of 3 rectangles:

3(18 × 6)

324 in²

Total surface area:

324 + 48

372 in²

Answer:

[tex] ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635[/tex]

And the best answer on this case would be:

b) m = 4.635

Step-by-step explanation:

Let X the random variable of interest and we know that the confidence interval for the population mean [tex]\mu[/tex] is given by this formula:

[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}} [/tex]

The confidence level on this case is 0.9 and the significance [tex]\alpha=1-0.9=0.1[/tex]

The confidence interval calculated on this case is [tex]60.128 \leq \mu \leq 69.397[/tex]

The margin of error for this confidence interval is given by:

[tex]ME =t_{\alpha/2} \frac{s}{\sqrt{n}} [/tex]

Since the confidence interval is symmetrical we can estimate the margin of error with the following formula:

[tex] ME = \frac{Upper -Lower}{2}[/tex]

Where Upper and Lower represent the bounds for the confidence interval calculated and replacing we got:

[tex] ME= \frac{69.397-60.128}{2}= 4.6345 \approx 4.635[/tex]

And the best answer on this case would be:

b) m = 4.635

Answer:

235 people

Step-by-step explanation:

Given:

P' = 15% = 0.15

1 - P' = 1 - 0.15 = 0.85

At 99% confidence leve, Z will be:

[tex] \alpha [/tex] = 1 - 99%

= 1 - 0.99 = 0.01

[tex] \alpha /2 = \frac{0.01}{2} = 0.005 [/tex]

[tex] Z\alpha/2 = 0.005 [/tex]

Z0.005 = 2.576

For the minimum number of 25-50 year old people who must be surveyed in order to estimate the proportion of non-grads to within 6%, we have:

Margin of error, E = 6% = 0.06

sample size = n = [tex] (\frac{Z\alpha /2}{E})^2 * P* (1 - P) [/tex]

[tex] = (\frac{2.576}{0.06}) ^2 * 0.15 * 0.85 [/tex]

= 235.02 ≈ 235

A number of 235 people between 25-30 years should be surveyed .

Answer:

n = 236

Step-by-step explanation:

Solution:-

- The proportion of people over the age of 50 who didn't graduate from high school are, p = 0.15 - ( 15 % )

- We are to evaluate the minimum sample size " n " from the age group of 25-50 year in order to estimate the proportion of non-grads within a standard error E = 6% of the true proportion p within 99% confidence.

-  The minimum required sample size " n " for the standard error " E " for the original proportion p relation is given below:

                             [tex]n = \frac{(Z_\alpha_/_2)^2 * p* ( 1 - p )}{E^2}[/tex]

- The critical value of standard normal is a function of significance level ( α ), evaluated as follows:

                            significance level ( α ) = ( 1 - CI/100 )

                                                                 = ( 1 - 99/100 )

                                                                 = 0.01

- The Z-critical value is defined as such:

                           P ( Z < Z-critical ) = α / 2

                           P ( Z < Z-critical ) = 0.01 / 2 = 0.005

                          Z-critical = Z_α/2 = 2.58

- Therefore the required sample size " n " is computed as follows:

                           [tex]n = \frac{(2.58)^2 * 0.15* ( 1 - 0.15 )}{0.06^2}\\\\n = \frac{6.6564 * 0.1275}{0.0036}\\\\n = \frac{0.848691}{0.0036}\\\\n = 235.7475\\[/tex]

Answer: The minimum sample size would be next whole number integer, n = 236.

Answer:

y_g(x) = C1*x^2 + C2*x^-2 +  x^4 / 12

Step-by-step explanation:

Given:-

- The following second order ODE :

                                  x^2y''+xy'-4y=x*(x+x^3)  

Find:-

Find a particular solution of the nonhomogeneous equation    

Solution:-

- First note that the ODE given is a Cauchy Euler ODE. The order of derivative of independent and dependent variables are similar. The general form of Cauchy Euler ODE is:

                           a*x^n y^(n) + b*x^n-1 y^(n-1) + c*x^n-2 y^(n-2) + ... + d*y = f(x)

- We will use the following Auxiliary Equation to find the complementary solutions - Solving Homogeneous part of ODE.

                           am*(m-1) + bm + c = 0

Where, a,b,c are constants such that:

                            x^2y'' + xy' - 4y = 0

                            a = 1 , b = 1 , c = -4

- Solve the Auxiliary equation for (m) as follows:

                            m*(m-1) + m - 4 = 0

                            m^2 - 4 = 0

                            m = +/- 2  ...... ( Real and distinct roots )

- The complementary solutions to the Real and distinct roots from Auxiliary Equation is:

                            yc(x) = y1(x) + y2(x)

                            yc(x) = C1*x^2 + C2*x^-2   .... ( Complementary Solution ).

- Now for the non-homogeneous part of ODE. The function f(x) is defined as:

                            f(x) = x*( x + x^3 ) = x^2 + x^4

- We see that (x^2) term is common to both f(x) and complementary solution yc(x). So when we develop a particular solution, we have to make sure that the solution is independent from complementary solution. If not we multiply the particular solution with (x^n). Where n is the smallest possible integer for which the solution is independent. So in our case ( Using undetermined Coefficient method ) :

                           y_p (x) = A*x^4 + B*x^3 + C*x^2 + D*x + E

- To make the solution independent we multiply y_p by (x^3) where n = 3.

                          y_p (x) = A*x^7 + B*x^6 + C*x^5 + D*x^4 + E*x^3

- Take first and second derivatives of the y_p(x) as follows:

                          y'_p(x) = 7A*x^6 + 6B*x^5 + 5C*x^4 + 4D*x^3 + 3E*x^2

                          y''_p(x) = 42Ax^5 + 30Bx^4 + 20Cx^3 + 12Dx^2 + 6Ex

- Substitute y_p(x) , y'_p(x) and y''_p(x) into the ODE given:

                     42Ax^7 + 30Bx^6 + 20Cx^5 + 12Dx^4 + 6Ex^3

              +       7Ax^7  + 6B*x^6  + 5C*x^5 + 4D*x^4 + 3E*x^3

              -      ( 4Ax^7 +  4B*x^6 +  4C*x^5 +  4D*x^4 + 4E*x^3 )

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

                       45Ax^7  + 32Bx^6 + 21Cx^5 + 12Dx^4 + 5Ex^3  

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

            45Ax^7  + 32Bx^6 + 21Cx^5 + 12Dx^4 + 5Ex^3 = x^2 + x^4

- Compare the coefficients:

                                           A = B = C = E = 0

                                           D = 1 / 12.

The particular solution is:

                                          y_p(x) = x^4 / 12

- The general solution is as follows:

                                     y_g(x) = yc(x) + y_p(x)

                                     y_g(x) = C1*x^2 + C2*x^-2 +  x^4 / 12

Answer:

The particular solution to the differential equation

x²y'' + xy' - 4y = x(x + x³)

is

y_p = (1/12)x^4 - x²/2 - x/3

Step-by-step explanation:

Given the differential equation:

x²y'' + xy' - 4y = x(x + x³)...............(1)

First, we solve the homogeneous part of (1)

x²y'' + xy' - 4y = 0...........................(2)

Let x = e^z

=>z = lnx

Let D = d/dz

dz/dx = (1/x)

dy/dx = (dy/dz).(dz/dx)

= (1/x)(dy/dz)

dy/dz = xdy/dx = xy' = Dy

d²y/dx² = (-1/x²)(dy/dz) + (1/x)(d²y/dx²)(dz/dx)

= (1/x²)(d²y/dx² - dy/dz) = (1/x²)(D² - D)y

Using these, (2) becomes

(D² - D)y + Dy - 4y = 0

(D² - 4)y = 0

The auxiliary equation is

m² - 4 = 0

(m - 2)(m + 2) = 0

m1 = 2, m2 = -2

The complementary function is

y = C1e^(2z) + C2e^(-2z)

But z = lnx

y_c = C1x² + C2/x² ...........................(3)

Now we solve (1) using the method of undetermined coefficients.

The nonhomogeneous part is

x(x + x³) = x² + x^4

So, we assume a particular solution of the form

y_p = Ax^4 + Bx³ + Cx² + Dx + E

y'_p = 4Ax³ + 3Bx² + 2Cx + D

y''_p = 12Ax² + 6Bx + 2C

Using these in (1)

x²y''_p + xy'_p - 4y_p = x²(12Ax² + 6Bx + 2C) + x(4Ax³ + 3Bx² + 2Cx + D) - 4(Ax^4 + Bx³ + Cx² + Dx + E)

= x² + x^4

12Ax^4 + 6Bx³ + 2Cx + 4Ax^4 + 3Bx³ + 2Cx² + Dx - 4Ax^4 - 4Bx³ - 4Cx² - 4Dx - 4E = x² + x^4

Comparing the coefficients of various powers of x, we have

12A + 4A - 4A = 1

12A = 1

=> A = 1/12

6B + 3B - 4B = 0

5B = 0

=> B = 0

2C - 4C = 1

-2C = 1

=> C = -1/2

2C + D - 4D = 0

2C - 3D = 0

2C = 3D

2(-1/2) = 3D

=> D = -1/3

-4E = 0

=> E = 0

(A, B, C, D, E) = (1/12, 0, -1/2, -1/3, 0)

y_p = Ax^4 + Bx³ + Cx² + Dx + E

= (1/12)x^4 - (1/2)x² - (1/3)x

The general solution is

y = y_c + y_p

= C1x² + C2/x² + (1/12)x^4 - x²/2 - x/3

Answer: The owner reaches at Rs. 56438.28 after 30 years.

Step-by-step explanation:

Since we have given that

Sum = Rs. 17000

Rate of compounded daily = 4%

Number of years = 30 years

So, Using "compound interest formula" we get that :

[tex]A=P(1+\dfrac{r}{n})^{nt}\\\\A=17000(1+\dfrac{0.04}{365})^{365\times 30}\\\\A=17000(1.000109589)^{10950}\\\\A=56438.28[/tex]

Hence, The owner reaches at Rs. 56438.28 after 30 years.

Answer:

Step-by-step explanation:

given that Suppose that $2n$ tennis players compete in a round-robin tournament. Every player has exactly one match with every other player during $2n-1$ consecutive days.

this is going to be proved by contradiction

Answer:

Option C) is the correct answer.

Step-by-step explanation:

We are given the following in the question:

Mean = 192

Sample mean, [tex]\bar{x}[/tex] = 212

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 56.5

95% Confidence interval:

[tex]\mu \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]

Putting the values, we get,

[tex]z_{critical}\text{ at}~\alpha_{0.05} = 1.96[/tex]

[tex]192 \pm 1.96(\dfrac{56.5}{\sqrt{40}} ) = 192 \pm 17.5 = (174.5,209.5)[/tex]

Thus, the correction answer is

Option C)

"The interval that contains 95% of the sample means is 174.5 and 209.5 visits. Because the sample mean is not between these two values, we have support for the results of the May 2011 study."

Answer:Triangle A

Step-by-step explanation: It has one right angle.

Answer:

THE ANSWERS A

Step-by-step explanation:

OMG GOOD LUCK!!! BECAUSE IT HAS THE AREA LAYED OUT HAVE A BLESSED DAY!!!

Answer:

The test statistic t = 1.126 <  1.703 of '27' degrees of freedom at 0.05 level of significance.

null hypothesis(H₀ ) is accepted

There is evidence that the average breaking strength is  7.000.

Step-by-step explanation:

Step 1:-

Given random sample size (n) =28 <30

small sample size n= 28

The sample mean (x⁻) = 7.142

sample standard deviation (S) =0.672

Step 2:-

Null hypothesis :- there is evidence that the average breaking strength is  7.000.

H₀ : μ =7

Alternative hypothesis:-there is evidence that the average breaking strength is  7.000.

H₁ : μ ≠7

The test statistic [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

Substitute all values and simplification ,

[tex]t = \frac{7.142 -7}{\frac{0.672}{\sqrt{28} } } = \frac{0.142 }{0.1269}[/tex]

t = 1.126

Calculated value is t = 1.126

The degrees of freedom γ = n-1 = 28-1 =27

The tabulated value t= 1.703 at degrees of freedom at 0.05 level of significance.

since  calculated t < tabulated value 't' value of 27 degrees of freedom at 0.05 level of significance.

null hypothesis(H₀ ) is accepted

There is evidence that the average breaking strength is  7.000.

Answer:

The correct option is;

Callie multiplied incorrectly

Step-by-step explanation:

Here we have 0.42 × 4.73 = 1.9866 then

1.9866 + 29.4 + 168 = 199.3866

Therefore, from the question, we had 0.42 × 4.73 = 1.26 which is incorrect, meaning that Callie multiplied incorrectly

Apparently, Callie multiplied as follows;

0.42 × 3 = 1.26 but what was in the question was

0.42 × 4.73 which is equal to 1.9866.

Answer:

Callie multiplied incorrectly

Step-by-step explanation:

all the credit goes to guy above me

Answer: 4 outcomes

Step-by-step explanation:

For two number cubes, the total possible outcomes are:

6 events for the first and 6 events for the second, then the total number of combinations is 6*6 = 36

If the dice are different, the possible outcomes are:

Dice 1 = 3, Dice 2 = 2

Dice 1 = 2, Dice 2 = 3

Dice 1 = 4, Dice 2 = 1

Dice 1 = 1, Dice 2 = 4

Then we have 4 outcomes in the collection for event E.

Answer:

4

Step-by-step explanation:

I did it on college board

Answer:

  612

Step-by-step explanation:

Both x and y are linear functions of t, so for each increment of t, the x- and y-coordinates will increment by 8 and 15, respectively. The length of a line segment joining points 8 units in the horizontal direction and 15 units in the vertical direction is given by the Pythagorean theorem as ...

  d = √(8² +15²) = 17

From t=4 to t=40, there are 36 increments in t, so the length of the line segment defined by the given functions is ...

  36×17 = 612 . . . units

Answer:

  $2400

Step-by-step explanation:

Let x represent the amount invested at 9%. (3600-x) will be the amount invested at 8%. The total interest earned is then ...

  312 = 0.09x +0.08(3600 -x)

  24 = .01x . . . . subtract 288, simplify

  2400 = x . . . . divide by .01

$2400 was invested in the 9% account.

Answer: 4 litres of air is held in Braydon’s tank.

Step-by-step explanation:

The law relating pressure to volume is the Boyle's law. It states that the volume of a given mass of gas is inversely proportional to its pressure as long as temperature remains constant. It is expressed as

P1V1 = P2V2

Where

P1 and P2 are the initial and final pressures of the gas.

V1 and V2 are the initial and final volumes of the gas.

From the information given,

V1 = 6 litres

P = 220 psi

P2 = 330 psi

Therefore,

6 × 220 = 330V2

V2 = 1320/330 = 4 litres

Answer:

V=1320/p

the tank holds 4 liters

Step-by-step explanation:

Answer:

We need to conduct a hypothesis in order to check if the true mean for sales is significantly higher than 8000, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 8000[/tex]  

Alternative hypothesis:[tex]\mu > 8000[/tex]  

[tex]z=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2[/tex]    

[tex]p_v =P(z>2)=0.0228[/tex]  

Step-by-step explanation:

Data given  

[tex]\bar X=8300[/tex] represent the sample mean  for the sales

[tex]\sigma=1200[/tex] represent the population standard deviation

[tex]n=64[/tex] sample size  

[tex]\mu_o =8000[/tex] represent the value that we want to test

z would represent the statistic (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean for sales is significantly higher than 8000, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 8000[/tex]  

Alternative hypothesis:[tex]\mu > 8000[/tex]  

The statistic to check this hypothesis is given by:

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

Calculate the statistic

[tex]t=\frac{8300-8000}{\frac{1200}{\sqrt{64}}}=2[/tex]    

P-value

Since is a one right tailed test the p value would be:  

[tex]p_v =P(z>2)=0.0228[/tex]  

Answer:

confidence interval using a  two sample t test between percents

Step-by-step explanation:

confidence interval using a  two sample t test between percents This can be used to compare percentages drawn from two independent samples in this case employees. It is used to compare two sub groups from a single sample example the population on the planet

The lower limit of the 95% confidence interval for the difference in mean credit card debt between female and male students can be calculated by formula using sample means, standard deviations, sample sizes, and accounting for the t-value associated with 95% confidence.

To calculate the 95% confidence interval for the difference between the mean credit card debt of female and male StatCrunchU students, we use the given information: µ1 (mean credit card debt of females) = 2577.75, µ2 (mean credit card debt of males) = 3809.42, std. dev. of females = 1916.29, std. dev. of males = 2379.47, number of females = 67, number of males = 33.

To calculate the confidence interval, we will use the t-model formula for confidence intervals for difference in means, which is:

(µ1-µ2) ± t*(sqrt([std. dev.1/sqrt(n1)] + [std. dev.2/sqrt(n2)]))

After plugging in the objective values, we would get the confidence range. The lower limit will be (µ1-µ2) - t*(sqrt([std. dev.1/sqrt(n1)] + [std. dev.2/sqrt(n2)])).

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Answer:

209.467mm³

Step-by-step explanation:

the explanation is in the picture

hope this helps<3

please like and Mark as brainliest

Answer:

Step-by-step explanation:

It’s 1 3,and 4

Answer:

1,3,4

Step-by-step explanation:

Final answer:

The probability that a randomly selected golf ball from the bag is not a type A ball is 11/16, as we calculate this by dividing the number of non-type A balls (11) by the total number of balls (16).

Explanation:

The probability that the golf ball selected at random is not a type A ball can be found by first determining the total number of balls in the golf bag and then subtracting the number of type A balls to obtain the number of non-type A balls. The total number of balls is 5 type A balls + 8 type B balls + 3 type C balls = 16 balls. The number of non-type A balls is 8 type B balls + 3 type C balls = 11 balls.

To find the probability that the selected ball is not a type A ball, we divide the number of non-type A balls by the total number of balls, which gives us a probability of 11/16.

Final answer:

The probability that a randomly selected golf ball from the bag is not a type A ball is 0.6875 or 68.75%.

Explanation:

To find the probability that the golf ball selected at random is not a type A ball, we need to determine the total number of non-type A balls in the golf bag and divide it by the total number of balls in the bag. The golf bag contains 5 type A balls, 8 type B balls, and 3 type C balls, so the total number of balls in the bag is 5 + 8 + 3 = 16. There are 8 + 3 = 11 non-type A balls (type B and type C).

The probability of selecting a non-type A ball is then given by the number of non-type A balls divided by the total number of balls:

Probability = Number of non-type A balls / Total number of balls

We calculate it as:

Probability = 11 / 16 = 0.6875

Thus, the probability that the selected golf ball is not a type A ball is 0.6875 or 68.75%.

Answer:

54689

Step-by-step explanation:

Answer:-18-9=-17

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

Nine less than negative eighteen

[tex] - 18 - 9 = - 27[/tex]

Answer:

-3/2

Step-by-step explanation:

Answer:  x = -2/3 = -0.667

Answer: b. finding all studies published on a topic, calculating the effect size for each of those studies, and averaging the effect sizes together to find the average size of the effect across all studies.

Step-by-step explanation: