Kennedy's car used 11 gallons to travel 319 miles. How many gallons of gas would she need to travel 406 miles?

Answer:

0 ≤ x ≤ 8/3

Step-by-step explanation:

|x/4 - 1/3| ≤ 1/3

|x/4| ≤ 2/3

|x| ≤ 8/3

0 ≤ x ≤ 8/3

Answer:

r = 2

Step-by-step explanation:

r/18 = 1/9

r = 1 * 18 /9

r = 18/9

r = 2

The required proportional control G(s) = Kp is G(s) = 0.25.

A proportional control that is to be used to control the temperature inside of an oven with plant Gp(s) = (s+10) / (s²+5s+6).

The root locus of the given plant is shown below: From the root locus, we can see that there is a pole at s = -2, which lies on the root locus.

However, there is no zero. Therefore, we can place a zero at s = -2 to cancel out the pole, and this will result in a stable closed-loop system.

This is because the closed-loop poles will move towards the left side of the s-plane as we add a zero.

The value of the proportional gain Kp can be determined from the gain equation, which is given as: K = -1 / Gp(-2) = -1 / (-8/2) = 0.25

Therefore, the required proportional control G(s) = Kp is G(s) = 0.25.

This control will be used to control the temperature inside of an oven with plant Gp(s) = (s+10) / (s²+5s+6).  

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We're using `count` as a helper function to count the number of times the first bag appears in the second.

Multisets, also known as bags, can be represented as a list of pairs (x,n) in which n indicates the number of times x appears in the multiset.

Type bag `a=[(a,Int)]` is a set of this kind.

In the following activities, the bag representation's following characteristics can be considered.

However, your function definitions must maintain these characteristics for any multiset they create! 1.

In the list, each component x appears in at most one pair.

2. Each element that occurs in a pair has a positive counter.

A bag contains a bag b if every element that appears n times in b appears at least n times in

b. This function can be defined as follows:

```subbag:: Eq a => Bag a -> Bag a -> Boolsubbag [] _ = Truesubbag _ [] = Falsesubbag ((a,n):xs) b = if (n > count a b) then False else subbag xs b

where count a [] = 0count a ((b,m):ys) = if (a==b) then m else count a ys```Note:

Here, `subbag` is a recursive function that takes two bags as its input and returns a Boolean value indicating whether or not the first bag is included in the second.

We're using `count` as a helper function to count the number of times the first bag appears in the second.

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1. An integer p >1 is a prime number if and only if its only divisors are 1 and p. Option a is the correct choice.

2.  Two integers are relatively prime if their only common positive integer factor is 1. In other words, they have no other common divisors other than 1. Option a is the correct choice.

3. The greatest common divisor of two numbers is the largest integer that divides both numbers. It is commonly denoted as GCD. Option a is the correct choice.

1. A prime number is a natural number greater than 1 that is not divisible by any number other than itself and 1. A prime number has only two factors: 1 and itself.

In other words, a number that can only be divided by 1 and itself is known as a prime number. The number 2 is the smallest prime number because it can only be divided by itself and 1.

2. If two integers a and b are relatively prime, then their greatest common divisor is 1, and they are said to be coprime.

3. For example, the GCD of 16 and 24 is 8 since 8 divides both 16 and 24 without any remainder. It is also known as the greatest common factor or the highest common factor.

The GCD is calculated using the Euclidean algorithm, which is a method for finding the GCD of two numbers based on the observation that if the remainder of dividing a number a by a number b is r, then the GCD of a and b is the same as the GCD of b and r.

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The answer is $43.75

Answer:

$18.75

Step-by-step explanation:

you have to add it up

The measure of the arc of a circle indicates that the measure of the angle BAP, expressed in relation to the arc \(\widehat{ACB}\) is therefore;

∠BAP = (180° - m\(\widehat{ACB}\))/2

An arc of a circle is a curve joining two points which is a part of the circumference of the circle.

The measure of the angle ∠BAP can be obtained in terms of the measure of the arc \(\widehat{ACB}\) in the circle with center P as follows;

arc \(\widehat{ACB}\) = ∠APB (The angle of an arc is the angle at the center of a circle between the radii subtended by the arc

The triangle formed by the radii AP and BP is an isosceles triangle, therefore; ∠BAP ≅ ∠PBA (The base angles of a triangle are congruent)

Therefore;

∠APB + ∠BAP + ∠PBA = 180° (Angle sum property of a triangle)

∠APB + ∠BAP + ∠PAB = 180° (Substitution property)

∠BAP = (180° - ∠APB)/2

m∠BAP = (180° - ∠APB)/2

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Answer:

B

Step-by-step explanation:

yea

Answer:

a) area

Step-by-step explanation:

well you just need to find the carpet area. carpet is just for the floor, so you don't need the perimeter, volume is for 3D figures, and surface area is for the outside of an object. carpet is a 2D figure, so the answer is a) area :)

hope this helps!

Answer: 10x + 19 = 519              x = 50

Step-by-step explanation:

We are looking for the number of students that rode in each bus, so first lets subtract out those that drove in cars.

519-19=500

So 500 students rode on 10 buses. So now we divide the students onto the buses.

500/10 = 50

Each bus drove 50 students.

An equation to represent the total number of students as a function of those on the buses would be

10x + 19 = 519

x = 50 (the number of students on each bus)

Answer:

1. 4

2. -7

3. 3

4. -7.5

Step-by-step explanation:

They are opposites on a number line thereforeit would be your answer. Hope this helps you :)

option C is the correct answer. sin β = 15 / 17

Given data

Right angled triangle has sides

opposite = 15

adjacent = 8

Hypotenuse = 17

sin β = opposite / hypotenuse

substituting the values gives

sin β = 15 / 17

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On solving the equation Ý = 140 + (-0.0667)X, the value for blood pressure is obtained as 129.328 mm Hg.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The equation is given as Ý = 140 + (-0.0667)X.

An amount of medication of 160 mg is found to result in a blood pressure of 127.74 mm Hg.

Here the value of X is X = 160.

The predicted blood pressure will be -

Ý = 140 + (-0.0667)160

Ý = 140 - 10.672

Ý = 129.328

The predicted blood pressure value is 129.328 mm Hg.

Here the predicted blood pressure value 129.328 mm Hg is greater than the actual blood pressure value 127.74 mm Hg.

Therefore, the observed value will be below the regression line.

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Answer: y=4/3x-4

Step-by-step explanation:

Points given (x,y): (0,-4) (3,0)

y=mx+b

-4=0x+b (0 times anything is 0)

-4=0+b---> b=-4

y=mx+b

0= (m*3)-4

4=3m

m=\(\frac{4}{3}\)

y=mx+b

y=\(\frac{4}{3}\)-4

The value of k from the equation is k = -20

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = kx   be equation (1)

Let the first point be P ( 4 , -80 )

Substituting the values in the equation , we get

-80 = 4k

Divide by 4 on both sides of the equation , we get

k = - ( 80/4 )

On simplifying the equation , we get

k = -20

Hence , the equation is k = -20

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The equation without logs is: K = (P/T) * V^1.

The given equation is: log K = log P - log T + 1.3 log V
To express this without logs, we can use the logarithmic properties to simplify the equation step by step.
Use the properties of logarithms to combine the logs on the right side:
log K = log(P/T) + log(V^1.3)
Combine the logs on the right side using the product rule of logarithms (log a + log b = log ab):
log K = log((P/T) * V^1.3)
Remove the logs by using the property of exponentiation (if log x = y, then x = 10^y):
K = (P/T) * V^1.3
So, the equation without logs is:
K = (P/T) * V^1.3

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The sample size that would be required for the width of 99% is 2653.

The number of subjects involved in a sample size is referred to as the sample size in market research. A set of people chosen from the general community who are thought to be a representative sample size for that particular study is referred to as the sample size.

The following details are given:

Margin of error, E = 0.025; Significance Level, = 0.01

The proportion p is estimated to be p = 0.53.

The significance level with a critical value of 0.01 is 2.58.

The smallest sample size needed to estimate the population proportion p within the necessary margin of error is determined using the formula shown below:

n >= p*(1-p)*(zc/E)2 n = 0.53 *(1 - 0.53*)2 n = 2652.97 *(1-p)*(2.58/0.025)2

As a result, we determine that n = 2653 is the minimal sample size needed to satisfy the criteria that

n >= 2652.97 and that it must be an integer value.

Sample size is 2653.

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Answer:

  D.  less than: 4 < 4.52

Step-by-step explanation:

The area of the circle is found using the given formula:

  A = π(1.2 in)^2 = 1.44π in^2 ≈ 4.52 in^2

The table tells you the area of a 2-inch square is 4 in^2.

Comparing the two areas, we see that ...

  4 < 4.52

The area of the square is less than the area of the circle.

Answer

La letra D es la respuesta. Menos que.

Step-by-step explanation:

A plane is an object goes infinitely in every direction, but it has no thickness whatsoever.

The four primary categories of market segmentation are thought to be geographic, psychographic, behavioral, and demographic; however, there are many other tactics you can employ, as well as countless variants on the four primary types.

A circular segment is a section of a circle that has been split off from the remainder of the circle by a chord or secant. Segments are also the components that the arc of the circle divides into and connects to its endpoints through a chord.

A plane is an object goes infinitely in every direction, but it has no thickness whatsoever.

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A plane is an object goes infinitely in every direction, but it has no thickness whatsoever.

What are four type of segments?

The four primary categories of market segmentation are thought to be geographic, psychographic, behavioral, and demographic; however, there are many other tactics you can employ, as well as countless variants on the four primary types.

How segment is formed?

A circular segment is a section of a circle that has been split off from the remainder of the circle by a chord or secant. Segments are also the components that the arc of the circle divides into and connects to its endpoints through a chord.

A plane is an object goes infinitely in every direction, but it has no thickness whatsoever.

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Answer: a) To find the height of the pyramid, we can use the Pythagorean theorem. Let H be the height of the pyramid, and let M be the midpoint of QR. Then, PM is half of PQ, which is 15 cm. We can use the Pythagorean theorem to find H:

H^2 = PQ^2 - PM^2

H^2 = 30^2 - 15^2

H^2 = 675

H = sqrt(675) = 5 sqrt(3) cm

b) To find the angle that PS makes with the base QRST, we can use trigonometry. Let A be the foot of the perpendicular from P to the base QRST, and let B be the midpoint of PS. Then, we have:

tan(angle PSB) = AB / PB

Since triangle PAB is a right triangle, we can use the Pythagorean theorem to find AB:

AB^2 = AP^2 - PB^2

AB^2 = H^2 + (PQ/2)^2 - PB^2

AB^2 = (5 sqrt(3))^2 + (15/2)^2 - PB^2

AB^2 = 225/4 + 75 - PB^2

AB^2 = 375/4 - PB^2

Since triangle PBS is also a right triangle, we can use the Pythagorean theorem to find PB:

PB^2 = PS^2 - BS^2

PB^2 = (2 H)^2 - (PQ/2)^2

PB^2 = 4 (5 sqrt(3))^2 - (15/2)^2

PB^2 = 500 - 56.25

PB^2 = 443.75

Substituting these values into the equation for tan(angle PSB), we get:

tan(angle PSB) = sqrt(375/4 - 443.75) / sqrt(443.75)

tan(angle PSB) = -0.4385

Since angle PSB is in the second quadrant, we have:

angle PSB = 180 degrees + arctan(-0.4385) = 152.4 degrees (rounded to one decimal place)

c) To find the total surface area of the pyramid, including the base, we can divide the pyramid into four triangular faces and a square base. The area of each triangular face can be found using the formula:

area = (1/2) base * height

where the base is the length of one edge of the square base, and the height is the height of the pyramid. The area of the base is simply the area of the square QRST, which is (20 cm)^2 = 400 cm^2. Therefore, we have:

area of each triangular face = (1/2) (20 cm) (5 sqrt(3) cm) = 50 sqrt(3) cm^2

total surface area = 4 (50 sqrt(3) cm^2) + 400 cm^2 = 200 sqrt(3) cm^2 + 400 cm^2

total surface area = (200 + 200 sqrt(3)) cm^2 ≈ 532.4 cm^2 (rounded to one decimal place)

Step-by-step explanation:

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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Answer:

Slope: y= 4/5x+21/8

The distance is 4 units up and 5 units to the right.

Step-by-step explanation:

Answer:

Chamoy

Step-by-step explanation:

585/9= 65

605/11= 55

Answer:

(4w^2+180w+1800) meters^2

Explanation:

(60+2w) x (30+2w)

1800+120w+4w^2+60w

Combine like terms and rearrange into quadratic equation

4w^2+180w+1800

Don't forget to put your units and since we are talking about area be sure to add your squared symbol

The probability of drawing the first yellow ball on the eighth draw is 1/2772.

The probability of drawing a yellow ball on the eighth draw is the probability of drawing 7 non-yellow balls followed by a yellow ball.

The probability of drawing a non-yellow ball on the first draw is 7/12 since there are 7 non-yellow balls out of a total of 12 balls in the bag. After the first non-yellow ball is drawn, there will be 6 non-yellow balls left out of a total of 11 balls. So the probability of drawing a non-yellow ball on the second draw is 6/11. Continuing in this manner, the probability of drawing 7 non-yellow balls in a row is

(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6)

Now, there are 5 yellow balls left out of a total of 5 + 7 + 3 = 15 balls. So the probability of drawing a yellow ball on the eighth draw is 5/15.

Therefore, the probability of drawing the first yellow ball on the eighth draw is

(7/12) × (6/11) × (5/10) × (4/9) × (3/8) × (2/7) × (1/6) × (5/15)

Simplifying this expression, we get

(7 × 6 × 5 × 4 × 3 × 2 × 1 × 5) / (12 × 11 × 10 × 9 × 8 × 7 × 6 × 15)

which simplifies to:

1/2772

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The given question is incomplete, the complete question is:

A bag contains 3 red balls, 4 green balls, and 5 yellow balls. If balls are drawn one at a time without replacement, what is the probability that the first yellow ball is drawn on the eighth draw?

Answer:What is the slope of the line through (-5,-10)(−5,−10)left parenthesis, minus, 5, comma, minus, 10, right parenthesis and (-1,5)(−1,5)left parenthesis, minus, 1, comma, 5, right parenthesis?

Step-by-step explanation:

Answer:x^2-x-3

Step-by-step explanation:

step 1-find area of rectangular lawn

(2x+1)(x+1)=2x^2+3x+1

step 2-find area of garden

(x+2)(x+2)=x^2+4x+4

step 3- subtract the two

=x^2-x-3

Answer:

m \(\leq\) 2

Step-by-step explanation:

"at most" can translate to "less than or equal to," meaning m is less than or equal to 2.

Answer:

3.5

Step-by-step explanation:

We need to add the first 4 terms of the series in order to find the sum to the indicated accuracy of 0.00005.

The series ∑n=1[infinity]​(−1)n−1n49​ is an alternating series, which means that the terms alternate in sign and decrease in size.

This type of series converges,and the error   in approximating the sum with the first n terms is less than or equal to the absolute value of the (n+1)th term.

In this case, we are given that the desired accuracy is 0.00005.

The (n+1)th   term of the series is (-1)^n / n⁴⁹, so we need to find the smallest n such that (-1)^n / n⁴⁹ <0.00005.

Using a calculator, we can find that n = 4   satisfies this condition. Therefore, we need to add the first 4 terms of the series in order to find the sum to the indicated accuracy.

The first 4 terms of the series are -

1/1⁴⁹ = 1

-1/2⁴⁹ = -1/1610612736

1/3⁹ = -1/29859862048

-1/4⁴⁹ = 1/209227898880

The sum of these 4 terms is 0.12345, which is accurate to within 0.00005

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The domain of the function here is {0 ≤ x ≤ 600}. The first option is the right answer.

The domain of a function is the set of all input values (or independent variables) for which the function is defined and produces a valid output (or dependent variable). It is the set of values that can be plugged into a function and yield a valid result.

The domain of this function in this context is {0 ≤ x ≤ 600}.

This is because x represents the number of t-shirts Henry sells and he has ordered 600 shirts. So, he can only sell a non-negative number of shirts (x ≥ 0) and a maximum of 600 shirts (x ≤ 600). Any values outside this range are not meaningful in this context, hence they are not part of the domain.

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Answer:

9.275 inches or 9 11/40

Step-by-step explanation:

current depth = beginning depth - inches swam up + inches swam down

8 3/4 - 2 3/5 + 3 1/8

\(9\frac{30 - 24 + 5}{40}\) = 9 11/40