If a and b are real numbers and a>0 and b>0 , then ab ___0

The system of equations is inconsistent and has no solution.

We have Equations:

1/2x  - 1/3 y = 4

3/2x - y = 0

From Second equation

3/2x - y = 0

3/2x = y

x = (2/3)y

Now, put value of x = (2/3)y into the first equation:

1/2x - 1/3y = 4

1/2(2/3)y - 1/3y = 4

(1/3)y - 1/3y = 4

0 = 4

The equation 0 = 4 is not true, which means the system of equations is inconsistent and has no solution.

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Answer:

x<15

Step-by-step explanation:

Answer:

I'm sorry I don't know

Step-by-step explanation

Pickles are pretty tasty, though!

Answer:

0.0841

Step-by-step explanation:

1. convert 2/7 to a fraction (0.29)

2. 29*29 (841)

3. Since you took out two zeros, (one from 0.29 and one from the other 0.29) you have 2 zeros to put in front of the 841.

Answer: 0.0841

A large mean difference and small sample variances. The correct option is B.

A statistical measure known as the effect size () assesses the magnitude of the link (numerically) between two variables. The difference between the weights of male and female candidates, for instance, is known as the effect size. If we obtain information on the weights of male and female candidates and discover that men are, on average, heavier than women, for example.

The weight difference between men and women will increase as the effect size increases. Statistic effect size aids in determining whether a difference is real or the result of changing variables. Effect size, power, sample size, and critical significance level are all related to hypothesis testing.

Therefore, a large mean difference and small sample variances. The correct option is B.

The complete options are given below:-

a. A small mean difference and small sample variances ​

b. A large mean difference and small sample variances ​

c. A small mean difference and large sample variances ​

d. A large mean difference and large sample variances

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The p-value associated with the test statistic calculated to test the claim that less than 40% of the county residents are protected by earthquake insurance is 0.42

The term p - value is defined as a statistical measurement used to validate a hypothesis against observed data.

Here we have given that a survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance.

Then the Null hypothesis for the given situation is written as,

=> H0 = p => 0.40

And the Alternative hypothesis is written as

=> H1 = p <0 .40

Then the value of za is calculated as,

=> za = 133/137

=> za = 0.39

Now by  using a formula for a binomial proportion one-sample z-test with your data included, we have

=> z = 0.39 - 0.40

Then the test value is calculated as

=> (0.39 - 0.40)/√[(0.40)(0.60)/337]

Therefore, the value of P-value is 0.42.

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Answer:

30 and 9

Step-by-step explanation:

x+y=39 , x-y=21

Solve for x:

x+y=39 , x-y=21

x= 30

Substitute x with 30:

(30)+y=39 , (30)-y=21

Solve for y:

y=9

Answer:

30 and 9

Eeexplination;

The equation is equivalent to the r = d/t.

There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

We have to find which equation is equivalent to the formula d = rt.

Formula given: d = rt

Divide both sides by t

d/t = rt / t

d/t = r

Thus, the equation is equivalent to the r = d/t.

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Answer:

Bank A

Step-by-step explanation:

Answer:

a because its true it is

Step-by-step explanation:

a so a because its true

Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

The given expression is: (a4b-2)-5/(7a3b-1)-2Let's simplify the given expression using the properties of exponents: step 1:

To simplify the given expression, we need to use the rule of exponents which states that for any non-zero number a and any integer m, a⁻ᵐ = 1/am.

For the first term, we have (a⁴b⁻²)⁻⁵Now, (a⁴b⁻²)⁻⁵ = (1/a⁴b⁻²)⁵= (b²/a⁴)⁵= b¹⁰/a²⁰. Similarly, for the second term, we have (7a³b⁻¹)⁻². Now, (7a³b⁻¹)⁻² = (1/7a³b⁻¹)²= 1/49a⁶b⁻²= a⁻²/49b².

Therefore, the given expression (a⁴b⁻²)⁻⁵/(7a³b⁻¹)⁻² = b¹⁰/a²⁰ × a⁻²/49b²= b⁸/a²² × 1/49= b⁸/49a²².

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The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:

Step-by-step explanation:

1 +1/3 = 4/3

2 + 1/2 = 5/2

4/3 feet per hour multiplied by 5/2 hours

\(\frac{4}{3} *\frac{5}{2}\) = 20/6 feet

therefore: 3 1/3 feet

The value that represents the elevation of the hole relative to the ground level after digging for (5/2) hours is \(18\frac{1}{3}\) feet.

The unitary method is a mathematical way of deriving the value of a single unit and then multiplying the given unit with it.

This type of problem can be solved by the unitary method here rate per hour is already given therefore we have to multiply the digging rate per hour by the amount of time.

∴ In \(2\frac{1}{2}\) hours or (5/2) hours Calving can dig (5/2)×(11/3) feet.

= 55/3 or \(18\frac{1}{3}\) feet.

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To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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The required answers are:

a) The probability that a randomly chosen light bulb lasts more than 10,500 hours is approximately 0.9332.

b) The distribution of the mean lifespan of 15 light bulbs is approximately normal with \(\mu\) = 9,000 hours and \(\sigma\) = 258.198 hours.

c) The probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours is approximately 0.0019.

(a) To find the probability that a randomly chosen light bulb lasts more than 10,500 hours, we can use the z-score formula and the standard normal distribution.

First, we calculate the z-score using the formula:

\(z = (x - \mu) / \sigma\)

where x is the value we're interested in (10,500 hours), \(\mu\) is the mean (9,000 hours), and \(\sigma\) is the standard deviation (1,000 hours).

z = (10,500 - 9,000) / 1,000 = 1.5

Next, we can find the probability of z being greater than 1.5 by looking up the z-score in the standard normal distribution table or using a calculator. From the table, the probability corresponding to a z-score of 1.5 is approximately 0.9332.

Therefore, the probability that a randomly chosen light bulb lasts more than 10,500 hours is approximately 0.9332 (rounded to four decimal places).

(b) The distribution of the mean lifespan of 15 light bulbs can be described as approximately normal with a mean (\(\mu\)) equal to the mean of the individual bulbs (9,000 hours) and a standard deviation (\(\sigma\)) equal to the standard deviation of the individual bulbs (1,000 hours) divided by the square root of the sample size (15):

\(\mu\) = 9,000 hours

\(\sigma\) = 1,000 hours / √15

Therefore, the distribution of the mean lifespan of 15 light bulbs is approximately normal with \(\mu\) = 9,000 hours and \(\sigma\) = 258.198 hours.

(c) To find the probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours, we use the same z-score formula but with the new values:

\(z = (x - \mu) / (\sigma / \sqrt{n})\)

where x is the value of interest (10,500 hours), μ is the mean (9,000 hours), σ is the standard deviation (1,000 hours), and n is the sample size (15).

z = (10,500 - 9,000) / (1,000 / \(\sqrt{15}\)) = 2.897

Next, we find the probability of z being greater than 2.897. Using the standard normal distribution table or a calculator, we find that the probability corresponding to a z-score of 2.897 is approximately 0.0019.

Therefore, the probability that the mean lifespan of 15 randomly chosen light bulbs is more than 10,500 hours is approximately 0.0019 (rounded to four decimal places).

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The price difference between the two brands when buying 700 g of hot chocolate is £0.85.

To find the difference in price between the two brands when buying 700 g of hot chocolate, we need to compare the prices per gram of each brand and calculate the total cost for 700 g.

Let's calculate the prices per gram for each brand:

Brand A: £2.65 for 140 g

Price per gram = £2.65 / 140 g = £0.01892857 per gram

Brand B: £3.10 for 175 g

Price per gram = £3.10 / 175 g = £0.01771429 per gram

Now, let's calculate the total cost for 700 g for each brand:

Brand A: £0.01892857 per gram * 700 g = £13.25

Brand B: £0.01771429 per gram * 700 g = £12.40

To find the difference in price, we subtract the cost of Brand B from the cost of Brand A:

£13.25 - £12.40 = £0.85

Therefore, the difference in price between the two brands when buying 700 g of hot chocolate is £0.85.

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Answer:

D

Step-by-step explanation:

Answer:

(2x-3)(x+1)

Step-by-step explanation:

2x²-x-3

(2x-3)(x+1)

Step-by-step explanation:

jdyxgxismsm? Juebzbijbs sbj? {![%°%=%℅%ש™${$[$¢

Jacks meeting lasted for 160 min or 2 hrs 40 min.

Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.

Given is that jacks meeting stared at 2:45 pm and ended at 5:25 pm.

The time for which the meeting lasted can be written as -

{i} = 2:45 pm

{i + 60 minutes} = 3:45 pm

{i + (2 x 60) minutes} = 4:45 pm

{i + (2 x 60 + 40) minutes} = 5:25 pm

{f} = 5 : 25 pm

The meeting lasted for -

2 x 60 + 40

160 minutes

or

2 hours 40 minutes

Therefore, Jacks meeting lasted for 160 min or 2 hrs 40 min.

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Answer:

-1, -1, 1/2, and 2

Step-by-step explanation:

Sorry if I’m wrong

Answer:

It will take 1 hour and 24 minutes.

Step-by-step explanation:

Given that:

Eastbound train travels at a rate of 65 miles per hour and Westbound train travels at a rate of 85 miles per hour

So speed = 65 + 85 = 150 miles per hour

Total distance = 210 miles

We have to find the time, we know that

Distance = time * speed

OR

Time = distance / speed

Time = 210/150

Time = 1.4 hours

Or it can be written as:

Time = 1 hour 24 minutes

Hope this helped :D

Answer:

first step

convert 180m and 1 cm in mm that is 180000mm and 10mm

then

ples mark me brainlist

Answer:

f(x) = 16*(3/2)^(x-1)

Step-by-step explanation:

See attachment.

Answer:

B

Step-by-step explanation:

Answer:

0.86602540

Step-by-step explanation:

Apply the cosine double-angle identity.

cos

(

2

⋅

105

)

Multiply

2

by

105

.

cos

(

210

)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

−

cos

(

30

)

The exact value of

cos

(

30

)

is

√

3

2

.

−

√

3

2

The result can be shown in multiple forms.

Exact Form:

−

√

3

2

Decimal Form:

−

0.86602540

…

Answer:

-√3/2 is the exact form

Answer:

$10.00

Step-by-step explanation:

Expenses

Blanket = $35.78

A flag= $10.25

A glove = $15.75

Total expenses = 35.78+10.25+15.75

Total expenses = $61.78

Let the amount borrows be x

If he paid $60, amount he has left with him will be = $61.78-$60 = $1.78

Amount borrowed will be = amount collected from cashier + amount left with him

Amount borrowed = $8.22 + $1.78

Amount borrowed = $10.00

Answer:

$10

Step-by-step explanation:

Given that:

Cost of all items bought = (35.78 + 10.25 + 15.75) = $61.78

Amount borrowed = change collected ftom cashier + (61.78 - 60)

Amount borrowed = $8.22 + $1.78

Amount borrowed = $10

Answer:

$65.475 ($65.48 rounded)

Step-by-step explanation:

The word "per" is usually a trigger-word for multiplication. So, we multiply.

\(14.55 * 4.5\)

The probability that a student has a cat given that they do not have a dog is 2/29.

Let's call the event of having a cat "C" and the event of having a dog "D". We want to find the probability that a student has a cat given that they do not have a dog, which can be written as P(C | not D).

To find this probability, we first need to calculate the total number of students who do not have a dog. From the table, we can see that 7 students have a dog, so the total number of students who do not have a dog is:

Total number of students who do not have a dog = Total number of students - Number of students who have a dog

= 3 + 7 + 6 + 13

= 29

Next, we need to find the number of students who have a cat but do not have a dog. From the table, we can see that 6 students do not have a cat, so the number of students who have a cat but do not have a dog is:

Number of students who have a cat but do not have a dog = Number of students who have a cat - Number of students who have both a cat and a dog

= 3 - 1

= 2

Finally, we can use Bayes' theorem to calculate the probability of having a cat given that the student does not have a dog:

P(C | not D) = P(C and not D) / P(not D)

= 2 / 29

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