Which table has a constant of proportionality between y and x of 1/4?

Answer:

it's 7

Step-by-step explanation:

the one side is equal to the other side do it's 7

Answer:

3

Step-by-step explanation:

7x12 = 84

252/84 = 3

7x12x3=252

Answer:

yes

P(x) = (x + 2)(2x² + x + 3)

Step-by-step explanation:

see attachment for step by step

Step-by-step explanation:

5x-16 = 3 (10+x)

=> x= 23

Answer:

x=771

Step-by-step explanation:

−771 + x = 0

x − 771 = 0

x − 771 + 771 = 0 + 771

Answer:

14

Step-by-step explanation:

Given that:

Cost of purchase and installation = 5323.50

Cost per window = 230.25

Cost of installation = 2100

Hence,

Total purchase cost of windows alone :

5323.50 - 2100 = 3,223.50

Therefore, the number of windows purchased is :

(Total purchase cost of windows alone / price per window)

(3,223.50 / 230.25)

= 14

Hence, 14 windows was purchased

Answer:(x + 6) + (y + 2)^2 = 13

Step-by-step explanation:

The centre of the circle is halfway along the diameter = (-6, -2)

r^2 = (-4 - -6)^2 + ( 1 - -2)^2 = 2^2 + 3^2 = 13

So circle equation is (x - -6)^2 + (y - -2)^2 = 13

The marginal cost of producing one more unit of the product when x = 100 is $150 per unit. To find the instantaneous rate of change (or the marginal cost) of c with respect to x when x = 100, we need to calculate the derivative of the cost function c(x) with respect to x and evaluate it at x = 100.

Let's assume that we have the cost function c(x) = 0.5x^2 + 50x + 1000, where x is the number of units produced. To find the derivative of this function, we need to use the power rule of differentiation, which states that if f(x) = x^n, then f'(x) = nx^(n-1). Applying this rule to our cost function, we get:

c'(x) = d/dx (0.5x^2 + 50x + 1000)
     = 1x^(2-1) + 50x^(1-1) + 0
     = x + 50

Now, we can evaluate this derivative at x = 100 to find the marginal cost:

c'(100) = 100 + 50
       = 150

Therefore, the marginal cost of producing one more unit of the product when x = 100 is $150 per unit. This means that if the company produces one more unit of the product, it will cost them $150 more than the cost of producing the previous unit. The significance of the marginal cost will be explained in a future chapter, but for now, it is important to understand that it is a crucial concept in economics and business decision-making.

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Answer: 2(n - 12)

n is “the number”

Step-by-step explanation:

Hope that helps :D

Answer:

2(n - 12)

Step-by-step explanation:

An obtuse triangle and right angle triangle can always be used as counter examples to the given statement.

What is acute angle?

An angle which is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle

What is obtuse angle?

An obtuse angle is a type of angle that is always larger than 90° but less than 180°. In other words, it lies between 90° and 180°.

What is right angle?

A right angle is an angle of exactly 90 degrees or \pi /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles..

Hence, an obtuse triangle and right angle triangle can always be used as counterexamples to the given statement " All angles in a triangle are acute".

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a) I∇fpl = ∇f(P) · (9,81) = (162e^648)(9) + (-9e^648)(81) = 0.

b) The rate of change of f in the direction of ∇fp is approximately 1406.57

c)  The rate of change of f in the direction of a vector making an angle of 45° with ∇fp is approximately 6.364

To answer this question, we need to use the concepts of gradient vectors and directional derivatives.

(a) To calculate I∇fpl, we need to find the gradient vector of f at point P and evaluate it at P. The gradient of f is:

∇f = (2xe^x^2-y, -xe^x^2-y)

So, at point P = (9,81), we have:

∇f(P) = (2(9)e^(9^2-81), -(9)e^(9^2-81)) = (162e^648, -9e^648)

Therefore, I∇fpl = ∇f(P) · (9,81) = (162e^648)(9) + (-9e^648)(81) = 0.

(b) The rate of change of f in the direction of ∇fp is given by the directional derivative of f at point P in the direction of the unit vector ∇fp/‖∇fp‖, where ‖∇fp‖ is the magnitude of the gradient vector at P. Since we already know that ∇f(P) = (162e^648, -9e^648), we can find its magnitude:

‖∇f(P)‖ = sqrt((162e^648)^2 + (-9e^648)^2) = 162sqrt(1+81) e^648 ≈ 162*9.055 e^648.

So, the unit vector ∇fp/‖∇fp‖ is:

(∇fp/‖∇fp‖) = (∇f(P)/‖∇f(P)‖) = (1/162sqrt(1+81) e^648)(162e^648, -9e^648) = (sqrt(82)/82, -1/sqrt(82))

The directional derivative of f at point P in the direction of ∇fp/‖∇fp‖ is:

D∇fpf(P) = ∇f(P) · (∇fp/‖∇fp‖) = (162e^648)(sqrt(82)/82) + (-9e^648)(-1/sqrt(82)) ≈ 1406.57.

Therefore, the rate of change of f in the direction of ∇fp is approximately 1406.57.

(c) To find the rate of change of f in the direction of a vector making an angle of 45° with ∇fp, we need to find a unit vector in that direction. Let's call this vector u. Since the angle between u and ∇fp is 45°, we have:

cos(45°) = ∇fp · u/‖∇fp‖‖u‖

Simplifying, we get:

1/sqrt(2) = (∇fp/‖∇fp‖) · u/‖u‖

We can choose ‖u‖ = 1 to make u a unit vector, so we have:

1/sqrt(2) = (∇fp/‖∇fp‖) · u

Therefore, u = (1/sqrt(2)) (∇fp/‖∇fp‖) + v, where v is a vector orthogonal to ∇fp/‖∇fp‖. We can choose v = (-1/sqrt(2)) (∇fp/‖∇fp‖), so that u is orthogonal to ∇fp/‖∇fp‖ and has unit length:

u = (1/sqrt(2)) (∇fp/‖∇fp‖) - (1/sqrt(2)) (∇fp/‖∇fp‖) = (0, -1/sqrt(2))

The directional derivative of f at point P in the direction of u is:

Duf(P) = ∇f(P) · u = (162e^648)(0) + (-9e^648)(-1/sqrt(2)) ≈ 6.364

Therefore, the rate of change of f in the direction of a vector making an angle of 45° with ∇fp is approximately 6.364.

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Answer:

8

-3

___

y

Step-by-step explanation:

Answer:

Here is the sample space:

(1, 1), (1, 2) (1, 3), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3)

Answer:

a=−1/2

Step-by-step explanation:

Answer:

Explanation:

Plato

Answer:  1)5/6

2) each person gets 0.3 of a pizza

3) 1/2

4) 2.4

5) 4/5   5/4   12/30   30/12

Step-by-step explanation:

1) you divide 5 cakes between 6 people which will be viewed as 5/6 because you are dividing the number of cakes by the number of people you have.

2) equation= 3/10+ 0.3 because you are dividing the number of cakes by the number of people you have.

3) 4/8= 1/2

4) you get the answer by dividing 12 by 5.

Statistical power is a measure of the ability to reject the null hypothesis when it is false. It represents the probability of correctly identifying a true effect or relationship in a statistical hypothesis test.

A high statistical power indicates a greater likelihood of detecting a significant result if the null hypothesis is indeed incorrect. The power of a statistical test depends on several factors, including the sample size, the effect size (the magnitude of the true effect or difference), the chosen significance level (often denoted as α), and the variability or noise in the data. Increasing the sample size or effect size generally increases the statistical power, while a lower significance level or higher variability decreases it.

Power analysis is commonly used to determine an appropriate sample size for a study, ensuring that it is adequately powered to detect the desired effect. A higher power is desirable as it reduces the chances of a Type II error (failing to reject the null hypothesis when it is false) and increases the chances of correctly detecting real effects or relationships.

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If joe walks by 21 cats in one week then 7 cats are black.

Percentage can be defined as a ratio that is expressed as fraction of 100.

For Example , 1%= 1/100

Given that Joe's town there are 33 black cats

Total cats = 100.

The percentage of black cats in town =\(\frac{33}{100}\)=33%

Number of cats joe sees in a week =21

Number of black cats joe sees in a week will be = 33% of 21

\(=21*\frac{33}{100} \\ \\ =\frac{693}{100} \\ \\ =6.93\\ \\\)= approx. 7

Therefore , If joe walks by 21 cats in one week then 7 cats are black.

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If the first inequality is written as:

3x ≤ -12

Then the correct option is D.

If it is written as it is in the problem, then neither of the graphs is the correct option.

Here we have the inequalities:

3x ≤ 12

2x + 3 > 11

(notice that in all the options, the first inequality has a negative sign, while in the two given inequalities there are no negative sign. This means that you will never get the correct answer if you use the given information, as the problem is incorrectly written).

First, we need to isolate x on both inequalities, we will get:

3x ≤ 12

x ≤ 12/3

x ≤ 4

(As you can see, because we don't have the negative sign, this inequality is different to all the ones in the options).

And for the other:

2x + 3 > 11

2x > 11 - 3

x > 8/2

x > 4

So neither of the options is actually correct.

If we instead write the first inequality as:

3x ≤ -12

We would solve this as:

x ≤ -4

And in that case, our two inequalities are:

x ≤ -4

x > 4

So the correct graph is graph D.

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The SOH CAO TOA identity is used to determine the acute angles of a right triangles. The terminal point of ø is (-1,0), what is tan ø is 0

Given the terminal point (-1, 0), the value of tanø is expressed as:

tanø = opposite/adjacent

tanø = y/x

From the coordinate given:

x = -1

y = 0

Substitute

tanø = 0/-1
tanø  = 0

Hence the terminal point of ø is (-1,0), what is tan ø is 0

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The confidence interval width for a 99% confidence interval for the mean difference between the two populations is 0.1393 cm.

For the confidence interval width for a 99% confidence interval for the mean difference between the two populations with the pooled sample variance of 0.435 cm, 242 butterflies from sub-population 1 and 159 butterflies from sub-population 2, you can use the following formula:

Confidence Interval Width = t(n₁ + n₂ - 2, 0.005) × Sp × √(1/n₁+ 1/n₂), where t(n₁ + n₂ - 2, 0.005) is the t-value for a two-tailed test with 99% confidence level and n₁ and n₂ are the sample sizes for the two sub-populations respectively.

The pooled standard deviation Sp is calculated as Sp = √(((n1 - 1) * s₁² + (n₂ - 1) * s₂²) / (n₁ + n₂ - 2)),

Where s₁ and s₂ are the sample standard deviations for the two sub-populations respectively.

Substituting the given values in the formula, we have:

Sp = √(((242 - 1) * s₁² + (159 - 1) * s₂²) / (242 + 159 - 2))

= √((241s₁²  + 158s₂²) / 399)

We don't know the sample standard deviations s₁ and s₂, but we can estimate them using the pooled sample variance s₂² = 0.435 cm². Therefore, s₁² = s₂²/2

s₁² = 0.435 / 2

s₁² = 0.2175 cm²

Plugging in the values, we get:

Sp = √((241(0.2175) + 158(0.2175)) / 397)≈ 0.2054 cm

Now we need to find the t-value for a 99% confidence level with 399 degrees of freedom. Using a t-table or a calculator, we get:

t(0.005, 399) ≈ 2.638

The confidence interval width is given by:

Confidence Interval Width = t(n₁ + n₂ - 2, 0.005)× Sp × √(1/n₁ + 1/n₂)

= 2.638 × 0.2054 × √(1/242 + 1/159)≈ 0.1393 cm

Therefore, the confidence interval width for a 99% confidence interval for the mean difference between the two populations is about 0.1393 cm.

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The construction to determine the incenter of a triangle involves drawing the perpendicular bisectors of any two sides of the triangle, finding their intersection point, drawing the bisectors of any two angles of the triangle, finding their intersection point, and drawing perpendiculars from the incenter to each side of the triangle.

The incenter of a triangle is the point where the angle bisectors of each angle of the triangle intersect. It is the center of the circle that is tangent to each side of the triangle. The construction to determine the incenter of a triangle involves several steps.

First, draw any triangle ABC. Then, take any two sides of the triangle, say AB and AC, and draw their perpendicular bisectors. The perpendicular bisector of a line segment is a line that intersects the segment at its midpoint and is perpendicular to it.

Let the perpendicular bisectors of AB and AC intersect at point O. Point O is the circumcenter of triangle ABC, which is the center of the circle that passes through the three vertices of the triangle.

Next, take any two angles of the triangle, say ∠BAC and ∠ABC, and draw their bisectors. The bisector of an angle is a line that divides the angle into two equal parts.

Let the bisectors of ∠BAC and ∠ABC intersect at point I. Point I is the incenter of triangle ABC, which is the center of the circle that is tangent to each side of the triangle.

Finally, draw a line segment from point I to each side of the triangle. Each of these line segments will be perpendicular to its corresponding side of the triangle. The point where all three perpendicular lines intersect is the incenter of the triangle.

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Answer:

3.418 grams

Step-by-step explanation:

please mark me as brainliest

Find attached to this answer, the appropriate diagram that would help us better understand the question

Answer:

10779 feet

Step-by-step explanation:

We would be using the Trigonometric function called Tangent to solve this question.

tan θ = Opposite side / Adjacent side

From the attached diagram,

θ = 33°

Opposite side = 7000 feet

Adjacent side = the distance of bird (B) from the plane (P) = unknown

tan 33° = 7000 feet / Adjacent side

Cross multiply

tan 33° × Adjacent side = 7000 feet

divide both sides by tan 33°

Adjacent side = 7000 feet / tan 33°

Adjacent side = 10779.054747 feet.

Approximately = 10779 feet.

Therefore, the distance of bird (B) from the plane (P) to the nearest whole number is 10779 feet.

An approximate of 4 gaps will be there in one hour that are longer than 6 seconds at the flow rate of 1800 vph.

The flow rate is given to be 1800 vph.

This means that 1800 vehicles pass through the lane every hour.

To determine the number of gaps that are longer than 6 seconds, we need to calculate the time it takes for one vehicle to pass and then subtract it from 60 minutes.

Assuming that the vehicle length is negligible, the gap between two consecutive vehicles is equal to the time taken by one vehicle to pass by completely plus the time taken by the following vehicle to reach the starting position of the preceding vehicle.

Let's say, for example, that the time it takes for one vehicle to pass is 2 seconds.

The gap between two consecutive vehicles would then be 2 + 2 = 4 seconds, meaning that there would be 60/4 = 15 gaps in one minute, or 900 gaps in one hour.  

If we assume that the time it takes for one vehicle to pass is 2 seconds, the total time taken for a vehicle to cover the distance would be 1/1800*60*60= 2 sec.

Hence, 60/2 = 30 vehicles would pass through the lane in one minute.1800 vehicles/60 minutes = 30 vehicles/min

Now, we know that the gap between two consecutive vehicles is 2 seconds, so we can calculate the number of vehicles that pass through the lane in one minute.

30 vehicles/min x 2 sec/vehicle = 60 seconds/min

We can see that there are 60 seconds in a minute.

Thus, the total time taken for a vehicle to pass is 60/1800 = 0.033 minutes.

So, the total number of gaps that are longer than 6 seconds would be:

Number of minutes in an hour = 60.

Number of vehicles that pass through the lane in an hour = 1800.

Time taken for one vehicle to pass = 0.033 minutes.

Therefore, number of gaps = 60 - (1800 x 0.033) / 6 = 4 gaps.

An approximate of 4 gaps will be there in one hour that are longer than 6 seconds.

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Answer:

Given distance=360 km.

Let the speed of the train be x km/hr.

Speed when increased by 5 km/hr =(x+5) km/hr

x

360

−

(x+5)

360

=1

x(x+5)

[360x+1800−360x]

=1

x

2

+5x−1800=0

x

2

+45x−40x−1800=0

x(x+45)−40(x+45)=0

(x−40)(x+45)=0

x=40,−45

The speed of the train is 40 km/hr.

Step-by-step explanation:

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The area of the field is 10,765.44 square meters.

Given that:

Diameter, d = 72 m

Width, W = 72 m

Length, L = 93 m

The area of a two - dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the field is calculated as,

A = (π/4)d² + W·L

A = (3.14 / 4) x 72² + 72 x 93

A = 4,069.44 + 6,696

A = 10,765.44 square meters

The area of the field is 10,765.44 square meters.

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Answer:

x= 5.5      y=2.25

Step-by-step explanation:

5(10 - 2y) -6y=14

50-10y-6y=14

50- 16y=14

-16y=-36

divide by negtivve # to get positive #

y=2.25

substiue

x+ 2(2.25) =10

x+4.5=10

x=5.5