U = C(1 + rt) solve for t​

Answer:

The answer is [tex]\frac{25}{4}[/tex]

Step-by-step explanation:

Velocity formula:

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

In which v is the velocity, d is the distance, and t is the time.

A tourist can bicycle 28 miles in the same time as he can walk 8 miles. He can ride 10 mph faster than he can walk:

This means that:

[tex]v = \frac{8}{t}[/tex]

And

[tex]v + 10 = \frac{28}{t}[/tex]

[tex](v + 10)t = 28[/tex]

From the first equation:

[tex]vt = 8[/tex]

So

[tex]vt + 10 = 28[/tex]

[tex]8 + 10t = 28[/tex]

[tex]10t = 20[/tex]

[tex]t = \frac{20}{10}[/tex]

[tex]t = 2[/tex]

He walks 8 miles in two hours, so:

[tex]v = \frac{8}{2} = 4[/tex]

4 miles per hour.

How much time (in hr) should he allow to walk a 25-mile trail?

This is t when [tex]d = 25[/tex]. So

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

[tex]4 = \frac{25}{t}[/tex]

[tex]4t = 25[/tex]

[tex]t = \frac{25}{4}[/tex]

The answer is [tex]\frac{25}{4}[/tex]

Answer:

Base = 6 feet

Step-by-step explanation:

Area of Triangle = [tex]\frac{1}{2} Base*Height[/tex]

For finding Base:

Base = [tex]\frac{2(Area)}{Height}[/tex]

Where Area = 15, Height = 5

Base = [tex]\frac{2(15)}{5}[/tex]

Base = 2*3

Base = 6 feet

Answer:

The base is 6 feet long.,

Step-by-step explanation:

Area of a triangle = 1/2 * base * height so we have

1/2 b h = 15

1/2 b * 5 = 15

2.5 b = 14

b = 15/2.5

b = 6 feet.

Answer:

Weight of Large Box = 18.5 kg

Weight of Large Box = 13.25 kg

Step-by-step explanation:

Given:

There are two types of boxes i.e. Large and Small

Let the weight of Large boxes = L kg

Let the weight of Small boxes = S kg

As per given statement:

Writing equation for above:

[tex]8L + 4S = 201[/tex] ....... (1)

Writing equation for above:

[tex]3L + 2S = 82 ....... (2)[/tex]

Now, by solving the equations (1) and (2), we can get the values of L and S.

Multiplying equation (2) with 2 and subtracting from equation (1):

[tex]8L + 4S = 201[/tex]

-

[tex]2 \times (3L + 2S) = 82 \times 2[/tex]

[tex]8L + 4S = 201[/tex]

-

[tex]6L + 4S = 164[/tex]

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

[tex]2L = 37[/tex]

L = 18.5 Kg

Putting value of L in equation (1):

[tex]8 \times 18.5 + 4S = 201\\\Rightarrow 148 + 4S = 201\\\Rightarrow 4S = 201 - 148\\\Rightarrow 4S = 53\\\Rightarrow S = 13.25\ kg[/tex]

So, the answer is:

Weight of Large Box = 18.5 kg

Weight of Large Box = 13.25 kg

Answer:

$ 2,4

Step-by-step explanation:

135% .............$ 3,24

100% .............$ x

x = 3,24×100/135

= 324/135

= $ 2,4

Answer:

110 feet/sec

Step-by-step explanation:

75 miles x 5280 feet

= 396000

396000/60 min

=6600

6600/60 secs

=110 feet/second

Answer:

3/4

Step-by-step explanation:

There are 3 numbers greater than 1. 2, 3, and 4. Since there are 4 numbers total, we get a 3/4 chance.

Answer:

3/4

Step-by-step explanation:

There are four options and 3 of them =3 or greater than 1

P(3 or greater than 1) = 3/4

Answer:

Event 3 -> Event 1 -> Event 4 -> Event 2

Step-by-step explanation:

The probability of choosing a certain pen is the number of that pen in the box over the total number of pens in the box.

So we have that:

Event 1: We have 4 black pen and 20 total pens, so P = 4 / 20 = 1 / 5

Event 2: All pens are black or orange so the probability is 1.

Event 3: We don't have white pens, so the probability is 0.

Event 4: We have 2 black pen and 5 total pens, so P = 2 / 5

Listing from least likely to most likely, we have:

Event 3 -> Event 1 -> Event 4 -> Event 2

Answer:

80%

Step-by-step explanation:

The probability of getting a four is 1/5

The probability of getting a odd is3/5

So u add them and it gives u 4/5 which in decimal is .8 which in percent is 80%

Hope this helps

Answer:

12

Step-by-step explanation:

For polygons that are similar to each other, the ratio of their corresponding sides are usually equal to each other, as they are proportional.

Therefore, given that ∆DAE is similar to ∆BAC, AD = 6, AB = 6+4 = 10, AE = x, AC = x + 8, therefore:

AD/AB = AE/AC

6/10 = x/(x+8)

Cross multiply

6*(x+8) = x*10

6x + 48 = 10x

Subtract 6x from both sides

48 = 10x - 6x

48 = 4x

Divide both sides by 4

48/4 = x

x = 12

Length of side AE = 12

Answer:

You have to multiply 3 x 6.

Step-by-step explanation:

[tex]3/\frac{1}{6} \\Flip\\3*\frac{6}{1} \\3*6[/tex]

Hope this helped! :)

To find the quotient of 3 divided by one-sixth, multiply 3 by 6

Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division,

An algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/). An example of an algebraic expression is 5x + 6. Here 5 and 6 are fixed numbers and x is a variable.

Given:

3 ÷ 1/6

As, division in fraction is not possible.

So, we will change sign of division into multiplication and reciprocal the number on right of sign.

Thus, 3 ÷1/6

=3*6

=18

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Answer:

Explanation;

Associated line with this equation is:

y=mx+c

when,

X=0

y=-4

so, c=-4

X=1

y=-1

[tex] - 1 = m- 4 \\ - m = - 4 + 1 \\ - m = - 3 \\ m =3 \\ [/tex]

[tex]y = 3x - 4 \\ or \: y + 4 = 3x \\ or \: \frac{y + 4}{3} = x[/tex]

Inequality representated by graph:

[tex]x \geqslant \frac{y + 4}{3} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

4/ (x+3)

Step-by-step explanation:

The sum of x and 3

(x+3)

4 is divided by the above

4/ (x+3)

Answer:

400

Step-by-step explanation:

The manufacturer spends $5 to make each widget and sells them for $8.  This means that each widget gives him a profit of $3.

8 - 5 = 3

You need to figure out how many widgets it will take for the manufacturer to make up for the costs each month ($1200).

3x = 1200

(3x)/3 = 1200/3

x = 400

The manufacturer needs to sell 400 widgets.

Answer:

Step-by-step explanation:

He sells them 8 dollars and uses 5 dollars worth of material.

His profit is 8 - 5 = 3 dollars.

He has to sell enough to overcome the 1200 dollars.

1200 / 3 = 400

He breaks even after selling 400 widgets.

is this what u need.....

Answer:

Parallel

Step-by-step explanation:

Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:

2(12x + 4y = 16)

24x + 8y = 32

This shows that both lines have the same slope, but then you find the y-intercepts, they are different:

1st equation y-int = 4

2nd equation y-int = 9/2 or 4.5

Answer:

[tex]\boxed{ x = 0}[/tex]

Step-by-step explanation:

7x + 24x = 25 x

31 x = 25 x

Subtracting 25x to both sides

31x - 25x = 0

6x = 0

Dividing both sides by 6

=> x = 0

Answer:

x = 0

Step-by-step explanation:

7x + 24x = 25x

Combine like terms.

31x = 25x

Subtract 25x on both sides.

6x = 0

Divide both sides by 6.

x = 0

Answer:

4 and 4

Step-by-step explanation:

We have 2 numbers that will be X and Y

X * Y = 16 => Y = 16 / X

We must minimize the sum, therefore:

S = X + Y

S = X + 16 / X

we derive and equal 0 and we are left with:

dS / dA = 1 - 16 / (X ^ 2) = 0

1 = 16 / X ^ 2

X ^ 2 = 16

X = 4

in the case of Y:

Y = 16/4 = 4

Therefore the numbers are 4 and 4.

The two positive numbers are 4 and 4

Let the two numbers be x and y

If the product of both numbers is 16, hence;

xy = 16 ........................... 1

If the sum will be at the minimum, hence x + y = minimum

From equation1, x = 16/ y

Substitute into the second equation to have;

16/y + y = A(y)

A(y) = 16/y + y

For the expression to be at a minimum, hence dA/dy = 0

dA/dy = -16/y² + 1

0 = -16/y² + 1

0 - 1 =  -16/y²

-y² = -16

y = √16

y = 4

Recall that xy = 16

4x= 16

x = 4

Hence the two positive numbers are 4 and 4

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Answer:

60

Step-by-step explanation:

if ts = 10 and sp = 10, use the formula 1/2 b x h therefore it will be 5 x 12=60, or 10 x 6 = 60. So the answer of the area of triangle tsp is 60.

Answer:

9 ones, 8 tenths, 0 hundredths, 7 thousandths

Step-by-step explanation:

Answer:

9 thousands

8 hundreds

0 tens

7 ones

Step-by-step explanation:

Hope it helped!

Answer:

Experiment 1 and 3 are clear binomial experiments.

Experiment 2 needs tweaking to be a binomial experiment.

Check Explanation.

Step-by-step explanation:

A binomial experiment is one in which

1) The probability of success doesn't change with every run or number of trials.

2) It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure.

3) The outcome of each trial/run of a binomial experiment is independent of one another.

Checking each of the experiments one at a time

- You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.

For this experiment,

1) The probability of success doesn't change with every run or number of trials as it is a 50% chance that each child examined is a boy.

2) It consists of a fixed number of runs (850) with only two possible outcomes, success (if it's a boy) and failure (if it's a girl).

3) The probability of each trial being a boy is independent from all the other trials.

Hence, this experiment is a binomial experiment.

- You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.

For this experiment,

1) If the marbles aren't being replaced after each draw, the probability of success, that is, picking a particular marble colour changes from trial to trial.

2) Although, it consist of a fixed number of runs/trials, there are more than two possible outcomes with 3 types of colours. Unless the experiment focuses on one colour and treats the other two colours as 'others', this condition too isn't satisfied.

3) Without replacement, the probability of success (picking a particular marble colour) in one trial isn't independent of the other trials.

This is not a binomial experiment as it doesn't satisfy all the required conditions to be one.

- Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.

1) The probability of success doesn't change with every run or number of trials as it is the same chance that each person finds the cough suppressant to be effective.

2) It consists of a fixed number of runs (820) with only two possible outcomes, success (cough suppressant is effective) and failure (cough suppressant isn't effective).

3) The probability of each trial being a person that finds the cough suppressant to be effective, is independent from all the other trials.

Hence, this experiment is a binomial experiment.

Hope this Helps!!!

Answer:

a) 104 F=30 C

b) 41 F=5 C

c) 131 F=55

d) 95 F= 35 C

Step-by-step explanation:

Answer:

slope = [tex]\frac{6}{5}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 5) and (x₂, y₂ ) = (7, 1)

m = [tex]\frac{1+5}{7-2}[/tex] = [tex]\frac{6}{5}[/tex]

The required slope of the line passes through the points (2, -5) and (7, 1) is m = 6/5

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

here,

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Let's apply this formula to the given points:

m = (1 - (-5)) / (7 - 2)

m = 6 / 5

Thus, the required slope of the line passes through the points (2, -5) and (7, 1).

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Answer:

75%

Step-by-step explanation:

The numbers that are not 5 are 6, 7, and 8.

3 numbers are not 5 out of 4 total numbers on the spinner.

3/4 = 0.75

= 75%

Answer:

75%

Step-by-step explanation:

Total no.s = 4

Divided in parts = 25%

P(not 5) = 75%

Answer:

b. The null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

c. Student's t distribution, as it is a two-sample test for the difference between means.

d. Test statistic t = 5.42.

P-value = 0

e. They appear to be significantly different, as the sample data gives strong evidence that the difference is greater than 0.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the mean life spans in the county is significantly different for whites and nonwhites.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]

The significance level is 0.05.

The sample 1 (white), of size n1=124 has a mean of 45.3 and a standard deviation of 12.7.

The sample 2 (non-white), of size n2=82 has a mean of 34.1 and a standard deviation of 15.6.

The difference between sample means is Md=11.2.

[tex]M_d=M_1-M_2=45.3-34.1=11.2[/tex]

The estimated standard error of the difference between means is computed using the formula:

[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12.7^2}{124}+\dfrac{15.6^2}{82}}\\\\\\s_{M_d}=\sqrt{1.301+2.968}=\sqrt{4.269}=2.066[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11.2-0}{2.066}=\dfrac{11.2}{2.066}=5.42[/tex]

The degrees of freedom for this test are:

df=n_1+n_2-2=124+82-2=204

This test is a two-tailed test, with 204 degrees of freedom and t=5.42, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=2\cdot P(t>5.42)=0.0000002[/tex]

As the P-value (0.0000002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean life spans in the county is significantly different for whites and nonwhites.

Answer:

I hope this will help you :)

Step-by-step explanation:

6+(-x)+2x(-7)+2x

6-x+2x✖️(-7)+2x

6-x-14+2x

6-14-x+2x

-8+x

Answer:

0.125

Step-by-step explanation:

Smaller Wheel

Total Number of Equal Sectors = 8

The number of Red sectors =3

The probability of obtaining red on the smaller wheel [tex]=\dfrac38[/tex]

Larger Wheel

Total Number of Equal Sectors = 12

The number of Red sectors =4

The probability of obtaining red on the larger wheel [tex]=\dfrac{4}{12}[/tex]

Assuming that the wheels are independent and each outcome is equally​ likely, the probability that we get red on both wheels

[tex]=\dfrac38 \times \dfrac{4}{12}\\\\=\dfrac18\\\\=0.125[/tex]

The probability is: 0.125

Answer:

[tex]X \sim N(\mu, \sigma)[/tex]

And from this case we can see that the deviation is given by:

[tex]\sigma = 3[/tex]

Step-by-step explanation:

For this case we have the following notation given:

[tex] X \sim N (5,3)[/tex]

And from this we know that the distribution for the random variable is normal and we know that in general the normal distribution is given by:

[tex]X \sim N(\mu, \sigma)[/tex]

And from this case we can see that the deviation is given by:

[tex]\sigma = 3[/tex]

You are told up to 40 people are going and that the van holds 12.

40-12 = 28

So up to 28 people will need to buy train tickets.

Let n be the number of people buying train tickets and x is the total number of people going

N <= (x-12)

Answer:

To obtain a stratified sample of 30 participants, we divide the people according to their destination, ending up with four groups(Naples, Liverpool, Barcelona, Paris). Finally, we choose some members each of those groups. Adding the members choosing from all groups, we have 30 members.

Step-by-step explanation:

Samples may be classified as:

Convenient: Sample drawn from a conveniently available pool.

Random: Basically, put all the options into a hat and drawn some of them.

Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.

Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.

Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.

In this question:

A stratified sample divided all the people into groups, and then surveyes some elements(some people) of each group.

Population: 390 people in the terminal.

Groups: 4 groups. Those traveling to Naples, those traveling to Barcelona, those traveling to Paris and those traveling to Liverpool.

Stratified sample of 30:

To obtain a stratified sample of 30 participants, we divide the people according to their destination, ending up with four groups(Naples, Liverpool, Barcelona, Paris). Finally, we choose some members each of those groups. Adding the members choosing from all groups, we have 30 members.

Answer:

Step-by-step explanation:

Part A

Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48

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

n = 6

Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484

Standard deviation = √(0.1484/6

s = 0.16

Standard error = s/√n = 0.16/√6 = 0.065

Part B

Confidence interval is written as sample mean ± margin of error

Margin of error = z × s/√n

Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5

Therefore, z = 3.365

Margin of error = 3.365 × 0.16/√6 = 0.22

Confidence interval is 2.48 ± 0.22

Part C

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 = 2.3

For the alternative hypothesis,

H1: µ > 2.3

This is a right tailed test

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 6

Degrees of freedom, df = n - 1 = 6 - 1 = 5

t = (x - µ)/(s/√n)

Where

x = sample mean = 2.48

µ = population mean = 2.3

s = samples standard deviation = 0.16

t = (2.48 - 2.3)/(0.16/√6) = 2.76

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

p = 0.02

Assuming significance level, alpha = 0.05.

Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.