Could you Show work please

Answer:

Options A, C, and F

Step-by-step explanation:

Answer:

y = 2/3x - 1

Step-by-step explanation:

Find the slope:

2y = 3x - 5

2/2y = 3/2x - 5/2

y = 3/2x - 5/2

Slope is 3/2

In order for a line to be perpendicular the slope in the equation should be flipped. 3/2 becomes 2/3.

Perpendicular equation:

y = 2/3x + b

b is going to be equal to the y intercept of the point they gave us, so -1.

Answer: y = 2/3x - 1

Answer:

\((x + 6)^2 = 49\)

\(x = 1\)    or \(x = -13\)

Step-by-step explanation:

Given

\(12x = 13 - x^2\)

Using Completing the Square

\(12x = 13 - x^2\) ---- Add \(x^2\) to both sides

\(x^2 + 12x = 13 - x^2 + x^2\)

\(x^2 + 12x = 13\)

Divide the coefficient of x by 2; then add the square to both sides

\(x^2 + 12x + 6^2 = 13 + 6^2\)

\(x^2 + 12x + 36 = 13 + 36\)

\(x^2 + 12x + 36 = 49\)

Factorize

\(x^2 + 6x + 6x + 36 = 49\)

\(x(x + 6) + 6(x + 6) = 49\)

\((x + 6)(x + 6) = 49\)

\((x + 6)^2 = 49\)

Hence, the equation is \((x + 6)^2 = 49\)

Solving further

Take square root of both sides

\((x + 6) = \sqrt{49}\)

\(x + 6 = \±7\)

\(x = \±7- 6\)

This implies that

\(x = 7 - 6\)     or \(x = -7 -6\)

\(x = 1\)    or \(x = -13\)

HEnce, the solutions are \(x = 1\)    or \(x = -13\)

Answer:

(x+6)^2=49 and  x=−6±7

Step-by-step explanation:

Answer:

A or \(\frac{\sqrt{6} }{2}\)

Step-by-step explanation:

*note- this method only works because the denominator values are being multiplied, if they were being added then there are extra steps to keep in mind but for now this is simple*

Start by dividing the root 12 in the numerator by the root 2 in the denominator

\(\frac{\sqrt{12} }{\sqrt{2} }=\sqrt{6}\)

Then we simply substitute back in the 2 (from the denominator) that we ignored for a second to get our answer

\(\frac{\sqrt{6} }{2}\)

*note- if you are allowed to use a calculator then you could also plug in your values to check each answer option but since this question isn't too complicated there should be no need to do so unless you forget how to solve it algebraically*

Answer:

\( \huge{ \fbox{ \sf{x = 5}}}\)

Step-by-step explanation:

\( \star{ \sf \: - 8 = 12 - 4x}\)

\( \text{Step \: 1 \: : Swap \: the \: sides \: of \: the \: equation}: \)

\( \mapsto{ \sf{12 - 4x = - 8}}\)

\( \text{Step \: 2 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}\)

\( \mapsto{ \sf{ - 4x = - 8 - 12}}\)

\( \text{Step \: 3 \: : Calculate}\)

\( \text{ \underline{Remember ! }} : \sf{ \: The \: negative \: integers \: are \: always \: added \: but \: posses \: the \: negative \: ( - ) \: sign.}\)

\( \mapsto{ \sf{ - 4x = - 20}}\)

\( \text{Step \: 4 \: : Divide \: \: both \: sides \: by \: 4}\)

\( \mapsto{ \sf{ \frac{ - 4x}{ - 4} = \frac{ - 20}{ - 4}}} \)

\( \text{Step \: 5 \: : Calculate}\)

\( \mapsto{ \sf{x = 5}}\)

Hope I helped!

Best regards! :D

~\( \sf{TheAnimeGirl}\)

The statement 'The mode is the value of the observation that appears most frequently.' is True.

We know that, the mode is the most frequent number.

It is the number that occurs the highest number of times.

The observation occurring the most number of times or which has highest frequency is known as the mode.

For example,  in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 as it occurs most often.

There is no mode when all observed values appear the same number of times in a data set.

Therefore, the statement 'The mode is the value of the observation that appears most frequently.' is True.

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Answer:

Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour(h) he works. And ammount of money can be (m)

considering theres no like first hour pay or something then it would be

Equation: m = 8h

Scenario 2: At a local bakery, one box of doughnuts(b) costs $5(c). Two boxes of doughnuts cost $10.

Equation: c = 5b where b is the ammount of doughnut boxes and c is the cost

Scenario 1a: Jim goes to the gym for 10 hours(h) It costed him $20(c) for those 10 hours.

Equation:  c = 2h

Scenario 1b: Kayla goes to a for a ride on her bike and traveled 15 miles(m) and was out for 30 minutes. (t)

Equation: t = 2m

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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Answer:18

Step-by-step explanation:

Check on a calculation

The height of the kite is given as follows:

43.3 feet.

The three trigonometric ratios are defined as follows:

For the angle of 48º, we have that:

Hence the height of the kite is obtained as follows:

tan(48º) = h/39

h = 39 x tangent of 48 degrees

h = 43.3 feet.

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The diameter of the small volcano 'Pico' would be = 8km

An isoline is defined as the line found on a map that has constant value of either distance, temperature or rainfall.

The isoline that is used in the given map above = 2000m.

The number of lines that surrounds the pico volcano = 4

Therefore the diameter of the volcano = 2000×4 = 8000m

But 1000m = 1km

8000m = 8km

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Answer:

oopppppp yes

Step-by-step explanation:

Answer:

Yes

Good luck, and have the most amazing day!

We can use a normal distribution to model phat and construct a confidence interval. We are 90% confident that 6.85% to 10.15% of first-time site visitors will register using the new design.

(a) The visitors are from a simple random sample, so independence is satisfied. The success/failure condition is also satisfied, with both 64 and 752 − 64 = 688 above 10. Therefore, we can use a normal distribution to model phat and construct a confidence interval.

(b) The sample proportion is phat = 0.085, SE = 0.010

(c) For a 90% confidence interval, use z⋆ = 1.65. The confidence interval is 0.085 ± 1.65 × 0.010 → (0.0685, 0.1015). We are 90% confident that 6.85% to 10.15% of first-time site visitors will register using the new design.

Normal distribution is a statistical concept that describes the probability distribution of a random variable that is continuous and symmetric around its mean. It is also known as Gaussian distribution or bell curve because of its characteristic bell-shaped curve. The normal distribution is important in statistical analysis because it occurs naturally in many real-world situations, such as the distribution of heights, weights, and test scores. It is also used in hypothesis testing and in the construction of confidence intervals.

The normal distribution is characterized by two parameters: the mean, which is the central tendency of the distribution, and the standard deviation, which measures the spread or dispersion of the distribution. The standard deviation determines the width of the bell curve, with a larger standard deviation indicating a wider curve.

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Answer:

  the value of hi changes from 58 to 0:

  h(t) = -4.9t^2 +19.8t

Step-by-step explanation:

If the initial height changes, then the term in the equation that represents that height will change. The initial height term is hi, so it changes from 58 to 0.

  \(h(t)=-4.9t^2+19.8t+0\\\\\boxed{h(t)=-4.9t^2+19.8t}\)

The numerical value of the substitution effect on the consumption of good x is $36, and the numerical value of the income effect on the consumption of good x is -$54.

To find the numerical values of the substitution effect and the income effect on the consumption of good x, we need to analyze the impact of the price change from $4 to $9 on the consumer's utility and consumption choices.

The substitution effect measures the change in consumption of good x due to the change in its relative price while keeping utility constant. In this case, since the utility function is U(x,y) = 2xy, we can set up the equation U(x,y) = U(x', y') where x' and y' represent the new consumption bundle after the price change. Solving for x' in terms of y', we can find the numerical value of the substitution effect, which is $36.

The income effect measures the change in consumption of good x due to the change in purchasing power caused by the change in price. In this case, since the consumer's income is $144, we can calculate the initial budget constraint equation as 4x + y = 144. After the price change, the new budget constraint equation becomes 9x' + y' = 144. By comparing the solutions for x in the initial and new budget constraint equations, we can find the numerical value of the income effect, which is -$54.

Therefore, the numerical value of the substitution effect is $36, indicating an increase in the consumption of good x due to the relative price change. The numerical value of the income effect is -$54, indicating a decrease in the consumption of good x due to the change in purchasing power caused by the price change.

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The work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

To calculate the work required to pump all the water over the edge of the tank, we need to consider the weight of the water in the tank and the height it is lifted.

First, let's find the volume of the water in the tank. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Plugging in the values, we have:

V = (1/3)π(3²)(12)

= (1/3)π(9)(12)

= 36π

Next, we need to find the weight of the water. The weight of an object is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity. The mass of the water can be found by multiplying its volume by the density of water, which is approximately 62.4 pounds per cubic foot:

m = (36π)(62.4)

≈ 22619.47 pounds

Now, we can calculate the work done by multiplying the weight of the water by the height it is lifted. In this case, the height is 12 feet:

W = (22619.47)(12)

≈ 271433.64 foot-pounds

Therefore, the work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

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The work required to pump water out of an inverted conical tank involves calculating the pressure-volume work at infinitesimally small volumes within the tank and integrating this over the entire volume of the tank. This provides an interesting application of integral calculus in Physics.

The question requires the concept of work in Physics applied to a fluid, in this case, water lying within an inverted conical tank. Work is done when force is applied over a distance, as stated by work = force x distance. In the fluid analogy, the 'force' link is the pressure exerted on the water and the distance is the change in volume of the fluid. Therefore, work done (W) = Pressure x Change in Volume (ΔV).

In this scenario, you are required to pump out water from an inverted conical tank, hence, the work you do is against the gravitational force pulling the water downwards. To calculate the total work done, you have to consider the work done at each infinitesimally small (hence, constant pressure) strip of volume and integrate over the entire volume of the tank.

The detail of calculation would require the knowledge of integral calculus and the formula for volume of a cone. I recommend considering this as an interesting application of integrals in Physics. Also remember that the volume of a cone = 1/3πr²h, where 'r' is the radius of base and 'h' is the height of cone.

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Answer:

x - y - 2 ≥ 0

Step-by-step explanation:

Answer:

See below ~

Step-by-step explanation:

Domain = range of x values

Range = range of y-values

\(\huge\red{\boxed{Answer}}\)

Given:

To find:

Solution:

⇛y - 2 = 6

⇛y = 6 +2

⇛y = 8

substitute 8 in place of y

⇛y + 4

⇛8 + 4

⇛12

12 is the answer

.

The average velocity of the first half-second. Calculate the change in displacement and divide it by the change in time to obtain .

By integrating the supplied velocity function throughout the range [0, 0.5], the displacement can be calculated. Now let's figure out the displacement:

∫(6400t^2 - 6505t + 2686) dt

When we combine each term independently, we obtain:

\((6400/3)t3 - (6505/2)t2 + 2686t = (6400t2) dt - (6505t) dt + (2686t)\)

The displacement function will now be assessed at t = 0.5 and t = 0:

Moving at time\(t = 0.5: (6400/3)(0.5)^3 - (6505/2)(0.5)^2 + 2686(0.5)\)

Displacement at time zero: (6505/2)(0) + 2686(0) - (6400/3)(0)

We only need to determine the displacement at t = 0.5 because the displacement at t = 0 is 0 (assuming the bullet is launched from the origin):

Moving at time \(t = 0.5: (6400/3)(0.5)^3 - (6505/2)(0.5)^2 + 2686(0.5)\)

Streamlining .

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Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

722

To find the depth of water in the tank at t = 3 minutes, we need to calculate the volume of water that has been pumped into the tank by that time.

The rate at which water is pumped into the tank is given by r(t) = 100 - 6t ft^3/min.

To find the volume of water pumped into the tank from t = 0 to t = 3, we integrate the rate function over the interval [0, 3]:

V = ∫[0, 3] (100 - 6t) dt

V = [100t - 3t^2/2] evaluated from 0 to 3

V = (100(3) - 3(3)^2/2) - (100(0) - 3(0)^2/2)

V = (300 - 27/2) - 0

V = 300 - 13.5

V = 286.5 ft^3

The volume of water pumped into the tank after 3 minutes is 286.5 ft^3.

To find the depth of water in the tank, we need to divide this volume by the cross-sectional area of the tank.

The tank has a radius of 6 feet, so its cross-sectional area is given by:

A = πr^2

A = π(6)^2

A = 36π ft^2

Now, we can find the depth of water:

depth = V / A

depth = 286.5 / (36π)

depth ≈ 2.53 ft

Therefore, the depth of water in the tank at t = 3 minutes is approximately 2.53 feet.

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Suppose X = the time that elapses between the bell and the end of the lecture and suppose the pdf of X is f(x)= kox, then the pdf of X is f(x) = (1/2)x, for 0 ≤ x ≤ 2.

Given that X represents the time elapsed between the bell and the end of the lecture, and the probability density function (pdf) of X is f(x) = kx, we can analyze the situation within the context of probability distributions.

Since the professor always finishes within 2 minutes after the bell, the range of X is between 0 and 2 minutes (0 ≤ x ≤ 2). To find the value of k, we need to ensure that the pdf integrates to 1 over this range, as required by probability density functions:

∫(from 0 to 2) kx dx = 1

After integrating, we get:

(k/2) * x² |(from 0 to 2) = 1

Evaluating at the limits:

(4k/2) - (0) = 1

Solving for k:

k = 1/2

Therefore, the pdf of X is f(x) = (1/2)x, for 0 ≤ x ≤ 2.

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"Draw a ray with one endpoint" demonstrates the correct first step in copying an angle. This is further explained below.

In general, the distance (which is sometimes stated as a degree) that occurs between two crossing lines or surfaces at or near the point where they meet. This distance might be positive or negative.

The formation of an angle is caused by the conjunction of two rays at a single point in space. The split or 'opening' that can be seen between these two rays is referred to as a 'angle,' and the symbol denotes this particular angle. The degree is the standard unit of measurement for angles, and its values include things like 60 degrees and 90 degrees, amongst other possible combinations.

In conclusion, "Draw a ray with one terminal" illustrates the correct first step in duplicating an angle. This step shows how to replicate an angle.

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Answer:

aww I find this so cutee

Step-by-step explanation:

Merry Christmas :) :) ^ ^

Answer:

its past t but it never too late to celebrate christmas happy christmas past and future

Step-by-step explanation:

The correct answer is (a) The population for the census is all the students in the school.(b) Advantage: Provides a complete representation of all students' opinions. Disadvantage: Time and resource-intensive.

(a) The population for the census in this scenario would be all the students in the school. It includes every student enrolled in the school, regardless of grade level or other criteria.

(b) Advantage:

Comprehensive Representation: By conducting a census, the headteacher ensures that every student's opinion is captured. It provides a complete and accurate picture of what all students think about the school, leaving no room for sampling error or potential bias.

Disadvantage:

Time and Resource Intensive: Conducting a census can be time-consuming and resource-intensive, especially in larger schools with a significant number of students. It requires significant effort to collect data from every student, which may involve distributing and collecting questionnaires, conducting interviews, or using other data collection methods. This can put a strain on resources and may require additional personnel.

It's worth noting that while a census offers a comprehensive understanding of the entire population, it may not always be practical or feasible due to the associated time, cost, and logistical challenges. In many cases, using a well-designed sample can provide reliable insights while being more efficient and cost-effective.

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Answer: Ace

Step-by-step explanation: Since the line rests on y = 100, the range is indeed y= 100.

(note that domain is x while range is y)

Answer: $21000

Step-by-step explanation:

By uwing option A, the salesperson will make (40 × $21) = $840.

Let the amount of sales that is needed for the week to be thesame as option A be x. Therefore,

4% of x = $840

4% × x = $840

0.04x = $840

x = $840/0.04

x= $21000

The salesperson need to sell $21,000 worth of sales