Use the change of base formula to approximate the solution to log0.5 15= 1-2x.

Answer:

The value of t = 18

Step-by-step explanation:

202 = 2t + 5 + t + 3t - 2 + 5t +1  Combine like terms

202 = 11t + 4  Subtract 4 from both sides

198 = 11\(\frac{11x}{11}\)x  Divide both sides by 11

\(\frac{198}{11}\) = 18

Is the question the value of t or the length of each side?

Each side

2t + 5

2(18) + 5

41

T

18

3T - 2

3(18) - 2

52

5T + 1

5(18) + 1

91

91 + 52 + 18 + 41 = 2002

Helping in the name of Jesus.

The value of x can be determined by using the z-score formula and substituting the given z-score into it. For a z-score of -2.25, when x=50 and x=3, the calculated value of x will be around 18.5.

Explanation: A z-score represents the number of standard deviations an x-value is away from the mean of a distribution. To find the corresponding x-value for a given z-score, we can use the formula: x = z * σ + μ, where z is the z-score, σ is the standard deviation, and μ is the mean.

In this case, the z-score is -2.25, but the mean (μ) and standard deviation (σ) are not provided. Therefore, we cannot calculate the exact value of x. However, we can estimate it by comparing the z-scores of the given x-values (50 and 3) with the given z-score (-2.25).

If x=50, the z-score would be (x - μ) / σ. Since the z-score for x=50 is -2.25, we have (-2.25) = (50 - μ) / σ.

Similarly, for x=3, the z-score would be (-2.25) = (3 - μ) / σ.

By comparing these two equations, we can observe that the change in x from 50 to 3 should be approximately equal to the change in z-score from -2.25. Therefore, we can estimate that the value of x, when x=3, would be around 18.5.

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The term that best describes the analysis conducted by the researcher is trend analysis.

We have,

Trend analysis involves studying data over time to identify patterns or trends.

In this case,

The researcher recorded the lengths of fish caught in the lake over several years and observed that the average length has been decreasing by approximately 0.25 inches per year.

By recognizing this consistent decrease over time, the researcher has conducted a trend analysis to understand the long-term pattern in the data.

Thus,

The term that best describes the analysis conducted by the researcher is trend analysis.

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The following are the results obtained using the empirical rule: About 95% of organs will be between 260 and 380 grams. Approximately 99.74% of organs weigh between 230 and 410 grams.

A bell-shaped distribution of data is also known as a normal distribution. A normal distribution is characterized by the mean and standard deviation. The empirical rule, also known as the 68-95-99.7 rule, is used to determine the percentage of data within a certain number of standard deviations from the mean in a normal distribution. The empirical rule is a useful tool for identifying the spread of a dataset. This rule states that approximately 68% of the data will fall within one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will fall within three standard deviations.

The weight of an organ in adult males has a bell-shaped distribution with a mean of 320 grams and a standard deviation of 30 grams. About 95% of organs will be within two standard deviations of the mean. To determine this range, we will add and subtract two standard deviations from the mean.

µ ± 2σ = 320 ± 2(30) = 260 to 380 grams

Therefore, about 95% of organs will be between 260 and 380 grams.

To determine the percentage of organs that weigh between 230 and 410 grams, we need to find the z-scores for each weight. Then, we will use the standard normal distribution table to find the area under the curve between those z-scores. z = (x - µ)/σ z

for 230 grams:

z = (230 - 320)/30 = -3 z

for 410 grams:

z = (410 - 320)/30 = 3

From the standard normal distribution table, the area to the left of -3 is 0.0013, and the area to the left of 3 is 0.9987. The area between z = -3 and z = 3 is the difference between these two areas:

0.9987 - 0.0013 = 0.9974 or approximately 99.74%.

Therefore, approximately 99.74% of organs weigh between 230 and 410 grams

To determine the percentage of organs that weigh less than 230 grams or more than 410 grams, we need to find the areas to the left of -3 and to the right of 3 from the standard normal distribution table.

Area to the left of -3: 0.0013

Area to the right of 3: 0.0013

The percentage of organs that weigh less than 230 grams or more than 410 grams is the sum of these two areas: 0.0013 + 0.0013 = 0.0026 or approximately 0.26%.

Therefore, approximately 0.26% of organs weigh less than 230 grams or more than 410 grams.

To determine the percentage of organs that weigh between 230 and 380 grams, we need to find the z-scores for each weight. Then, we will use the standard normal distribution table to find the area under the curve between those z-scores.

z = (x - µ)/σ

z for 230 grams: z = (230 - 320)/30 = -3

z for 380 grams: z = (380 - 320)/30 = 2

From the standard normal distribution table, the area to the left of -3 is 0.0013, and the area to the left of 2 is 0.9772. The area between z = -3 and z = 2 is the difference between these two areas: 0.9772 - 0.0013 = 0.9759 or approximately 97.59%.

Therefore, approximately 97.59% of organs weigh between 230 and 380 grams.

The following are the results obtained using the empirical rule: (a) About 95% of organs will be between 260 and 380 grams. (b) Approximately 99.74% of organs weigh between 230 and 410 grams. (c) Approximately 0.26% of organs weigh less than 230 grams or more than 410 grams. (d) Approximately 97.59% of organs weigh between 230 and 380 grams.

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Answer:

A cone has a diameter of 8 units and a height of 8 units. Its radius is 4units its volume is 134.04 cubic units. A cylinder with the same height and radius as the cone will have a volume of 402.12 cubic units. If a sphere has the same radius as the cylinder, Its volume is less than the volume of the cylinder​.

radius = diameter / 2 = 8/2 =4units

\(volume \ of \ cone = \pi r^2 \frac{h}{3}\)    =134.04cubic units

\(volume \ of \ cylinder = \pi r^2h\)  = 402.12 cubic units

\(volume \ of \ sphere = \frac{4}{3}\pi r^3\) = 268.08 cubic units

Answer:

\( \: \)

Step-by-step explanation:

Let us assume A, B, C and D are the four angles of the parallelogram. Where, ∠A = 20° and we have to find the measure of ∠B, ∠C and ∠D

So, If ∠A = 20°, then So, also ∠C = 20°.

Therefore,

⠀

And, ∠A and ∠B are adjacent angles. We know,

So,

⇒ ∠A + ∠B = 180°

⇒ 20° + ∠B = 180°

⇒ ∠B = 180° – 20°

⇒ ∠B = 160°

So,

⠀

So, If ∠B = 160°, then So, also ∠D = 160°.

Therefore,

Answer:

A fall breeze and a bowl of soup I might say.

If the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.

Given that the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10.

We are required to find the cost of 1 kg of mushrooms and the cost of 1 kg of turnips.

Cost is basically the expenditure that we do in order to buy or produce a product.

Suppose the cost of 1 kg of mushrooms be x and the cost of 1 kg of turnips be y. The equations will be as under:

2x+2.5y=8.55------1

3x+4y=13.10-------2

Equation1 *3 and Equation2 *2.

6x+7.5y=25.65-----3

6x+8y=26.20-------4

Subtract 4 from 3.

6x+7.5y-6x-8y=25.65-26.20

-0.5y=-0.55

y=1.1

Put the value of y in 1.

2x+2.5*1.1=8.55

2x+2.75=8.55

2x=8.55-2.75

2x=5.80

x=2.9

Hence if the cost of 2 kg of mushrooms and 2.5 kg of turnips is £8.55 and the cost of 3 kg of mushrooms and 4 kg of turnips is £13.10, then cost of 1 kg of turnips is £1.1 and cost of 1 kg of mushrooms is £2.9.

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The probability of getting 2 tails is option (b) 37.5%

The event of "2 tails" can occur in three possible outcomes: {htt, tht, tth}, so the probability of getting 2 tails is the sum of the probabilities of these three outcomes.

Each toss of a fair coin is independent and has a 50% chance of landing tails. Therefore, the probability of each of these three outcomes is:

P(htt) = 1/2 × 1/2 × 1/2 = 1/8

P(tht) = 1/2 × 1/2 × 1/2 = 1/8

P(tth) = 1/2 × 1/2 × 1/2 = 1/8

So, the probability of getting 2 tails is:

P(2 tails) = P(htt) + P(tht) + P(tth) = 1/8 + 1/8 + 1/8 = 3/8

= 0.375

0.375 multiplied by 100% gives:

P(2 tails) = 37.5%

Therefore, the correct option is (b) 37.5%

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Using the together rate, it is found that it takes 144.5 hours to fill the empty pool when only the input pipe is open.

It is the sum of each separate rate.

In this problem:

Hence:

\(\frac{1}{x} + \frac{1}{x - 1} = \frac{1}{72}\)

\(\frac{x - 1 + x}{x(x - 1)} = \frac{1}{72}\)

\(x^2 - x = 144x - 72\)

\(x^2 - 145x + 72 = 0\)

Which is a quadratic equation with coefficients a = 1, b = -145, c = 72, hence:

\(\Delta = b^2 - 4ac = (-145)^2 - 4(1)(72) = 20737\)

\(x_1 = \frac{145 + \sqrt{20737}}{2} = 144.5\)

\(x_2 = \frac{145 - \sqrt{20737}}{2} = -0.5\)

Time is a positive measure, hence, it takes 144.5 hours to fill the empty pool when only the input pipe is open.

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Step-by-step explanation:

the ratio Niam:Owen

2:5

total ratio is 2+5=7

Niam's fraction=2/7*35

= £10

owen's fraction = 5/7*35

=£25

Answer:

21

Step-by-step explanation:

To solve this problem, we need to remember the order of operations. First, you would do 6×6 to get 36, and then 36÷3 to get 12. 9+12 is 21, so the answer is (in words) twenty-one.

Answer:

Twenty-one

Step-by-step explanation:

Follow PEMDAS:

9 + 6^2 / 3

9 + 36 / 3

9 + 12

21

But I put the answer above in standard form…

Hope this helps!

Part a)Given, utility function of the consumer as:U(x1, x2) = log(x1) + log(x2)X1 ≤ 0.5Let p2 = 1 and m = 1, and p1 is unknown. The consumer has a budget constraint as: p1x1 + p2x2 = m = 1Now we have to find the minimal p1 such that the consumer consumes x1 strictly less than 0.5.

We need to find the value of p1 such that the consumer spends the entire budget (m = 1) on the two goods, but purchases only less than 0.5 units of the first good. In other words, the consumer spends all his money on the two goods, but still cannot afford more than 0.5 units of good 1.

Mathematically we can represent this as:

p1x1 + p2x2 = 1......(1)Where, x1 < 0.5, p2 = 1 and m = 1

Substituting the given value of p2 in (1), we get:

p1x1 + x2 = 1x1 = (1 - x2) / p1Given, x1 < 0.5 => (1 - x2) / p1 < 0.5 => 1 - x2 < 0.5p1 => p1 > (1 - x2) / 0.5

Now we know, 0 < x2 < 1.So, we will maximize the expression (1 - x2) / 0.5 for x2 ∈ (0,1) which gives the minimum value of p1 such that x1 < 0.5.On differentiating the expression w.r.t x2, we get:d/dx2 [(1-x2)/0.5] = -1/0.5 = -2

Therefore, (1-x2) / 0.5 is maximum at x2 = 0.

Now, substituting the value of x2 = 0 in the above equation, we get:p1 > 1/0.5 = 2So, the minimal value of p1 is 2.Part b)Now, we have to show mathematically that whether the threshold on p1 found in Part a increases/decreases/stays the same when p2 increases.

That is, if p2 increases then the minimum value of p1 will increase/decrease/stay the same.Since p2 = 1, the consumer’s budget constraint is given by:

p1x1 + x2 = m = 1Suppose that p2 increases to p2′.

The consumer’s new budget constraint is:

p1x1 + p2′x2 = m = 1.

Now we will find the minimal p1 denoted by pi, such that the consumer purchases less than 0.5 units of good 1. This can be expressed as:

p1x1 + p2′x2 = 1Where, x1 < 0.5

The budget constraint is the same as that in Part a, except that p2 has been replaced by p2′. Now, using the same argument as in Part a, the minimum value of p1 is given by:

p1 > (1 - x2) / 0.5.

We need to maximize (1 - x2) / 0.5 w.r.t x2.

As discussed in Part a, this occurs when x2 = 0.Therefore, minimal value of p1 is:

pi > 1/0.5 = 2

This value of pi is independent of the value of p2′.

Hence, the threshold on p1 found in Part a stays the same when p2 increases.

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When a train takes 17 seconds to pass a 206-meter long bridge at normal speed. The length of train is equals to the 227.86 metres.

We have a train with a normal speed. With a normal speed, the length of long bridge covered by train in 17 seconds

= 206 meter

Let the length of train and normal speed of train be 'x meter' and 's m/sec ' respectively. As we know speed of an object ratio of covered distance to the time taken by object to covered the distance

=> s = (206 + x)/ 17 m/sec --(1)

In case second, the speed of same train which covered a length 170 m of bridge in 45 seconds = one-third of the normal speed

=> s/3 = (170 + x) /45 m/sec --(2)

We have to determine the length of train.

Using substitution, substitute value of s in equation(2) from equation (1) ,

=> (206+ x)/17 = (170 + x)/45

Cross multiplication

=> 45( 206 + x) = ( 170 + x) 17

=> 45 x - 17x = 45× 206 - 170 × 17

=> x = 227.86 m

Hence, required value is 227.86 m.

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Answer: 8+7

Step-by-step explanation: 3+5+7 is equivalent to 8+7 because if you add the both of them you’ll get the same exact answer which is 15

Answer:

20

Step-by-step explanation:

Answer:

3626 i hope this is correct sorry if it is not

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

5th term is 6 and the 7th term is 48, we know the nth term for a GP is  arn−1

 so let's substitute the given information in that formula for the nth term

ar3=6

  ar6=48

ar6ar3=486

The  a

and  a

cancelout hence we remain with  r3=8

 take a cube root on both sides and we end up having  r=2

Substitute the value of r in any given equation to get the value of a

ar3=6

a(2)3=6

8a=6

a=34

The formula for the nth term of this GP is given by  34(2n−1)

And when you substitute the value of n in the above formula of nth term you will get the following values; 3/4, 3/2, 3, 6…

The correct value of convolution of x(t) = u(t-1) with h(t) = \(e^(-t)u(t) is y(t) = -e^(-t) + 1.\)

To evaluate the convolution of x(t) = u(t-1) with h(t) = e^(-t)u(t), we can use the formula for convolution:

y(t) = ∫[0 to t] x(t - τ) * h(τ) dτ

Let's substitute the given functions:

x(t - τ) = u(t - τ - 1)

h(τ) = e^(-τ)u(τ)

Now we can compute the convolution:

y(t) = ∫[0 to t] u(t - τ - 1) * e^(-τ)u(τ) dτ

Since u(t - τ - 1) and u(τ) are both step functions, their product will be non-zero only when both functions are non-zero. Therefore, we can rewrite the integral as:

y(t) = ∫[0 to t] e^(-τ) dτ

Integrating this expression gives us:

y(t) = -e^(-t) + 1

So, the convolution of x(t) = u(t-1) with h(t) = \(e^(-t)u(t) is y(t) = -e^(-t) + 1.\)

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Answer:

0.2x+3

Step-by-step explanation:

Answer:

Hope this helps

Step-by-step explanation:

Solving an inequality is using things like <, and >. Equations don’t use things like those

Answer:

Solving an inequality is different from solving an equation because an inequality involves a range of possible solutions, while an equation involves finding a specific value for the variable that makes the equation true.

When solving an equation, the goal is to find the value of the variable that makes the equation true. This is typically done by performing a series of operations on both sides of the equation to isolate the variable on one side of the equation. The solution is a specific number that satisfies the equation.

On the other hand, when solving an inequality, the goal is to find the range of values that make the inequality true. This is typically done by performing a series of operations on both sides of the inequality to isolate the variable on one side of the inequality. However, the solution to an inequality is a range of values, rather than a single value.

For example, if you were solving the equation x + 3 = 7, you would find that the solution is x = 4. This is a specific value that makes the equation true.

If you were solving the inequality x + 3 < 7, you would find that the solution is x < 4. This is a range of values that makes the inequality true, including all values less than 4.

The x value would be 3.

A state with a sales tax is a better option for both individuals and state governments.

WHAT IS SLES TAX?

A state without a sales tax may seem preferable since they do not have to pay additional taxes on purchases. However, in such states, the government often imposes higher income taxes or property taxes to compensate for the lack of sales tax revenue. Therefore, it ultimately depends on the individual's financial situation and spending habits.

From the state government's perspective, having a sales tax is generally more beneficial as it provides a consistent and reliable revenue stream. Sales tax revenue is collected on a regular basis and is not subject to fluctuations in the economy or changes in demographics. Additionally, sales tax revenue is not as heavily reliant on the state's residents and can be partially collected from tourists and visitors who make purchases within the state.

In my opinion, a state with a sales tax is a better option for both individuals and state governments. While paying additional taxes may not seem appealing, it allows the state to fund essential services such as education, healthcare, and infrastructure. Additionally, sales tax revenue is spread across a wider population, making it more equitable and less burdensome on individual taxpayers. Overall, having a sales tax system in place helps to ensure that the state government can continue to provide essential services and maintain a stable economy.

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The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the expression :

Jacob's yearly income :

2000x + 3000 ; x = number of hours worked per week.

Carlos income :

3800x - 40000

Managers prediction = 35

Jacob.: 2000(35) + 3000 = 73000

Carlos : 3800(35) - 40000 = 93000

Carlos will earn more than Jacob given the manager's prediction.

Number of hours required so they can earn the same amount :

2000x + 3000 = 3800x - 40000

3000 + 40000 = 3800x - 2000x

43000 = 1800x

x = 43000/1800

x = 23.88

x = 24 hours

Answer:

B- hope this helps:)

Step-by-step explanation:

The total cost to paint 864.5 square feet of wall is $2,048.87.

It is given that the cost to paint one square foot of wall is $2.37.

We are asked to find the total cost to paint 864.5 square feet of wall.

If we have a number that has a decimal point then we have two parts.

The whole number part and the fractional part.

After the decimal point, we will count the place value as tenths, hundredths, thousandths, and so on.

You can also see the given figure below.

We know that,

One square foot = $2.37.

Remember that Feet is the plural form of the foot.

We can write,

864.5 square feet = 864.5 x  one square foot

Because in 864.5 square feet we have 864.5 one square foot.

And since one square foot cost $2.37.

864.5 square feet will cost 864.5 x 2.37 dollars.

Now,

864.5 x 2.37 = $2048.865.

Rounding to the nearest hundredth.

6 is in the hundredth place so we will round 86 to 87 since the number in the thousandth place is greater than 4.

Thus the total cost to paint a wall of 864.5 square feet is $2,048.87.

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