For a ride on a rental scooter, david paid a $3 fee to start the scooter plus 11 cents per minute of the ride. the total bill for david's ride was $17.41. for how many minutes did greg ride the scooter

We can be 95% confident that the true proportion of people who select a Pepsi product when purchasing a soft drink in this restaurant is between 0.341 and 0.435.

To find a 95% confidence interval for the proportion of people having a soft drink who select a Pepsi product, we can use the following formula:

CI = p ± Zc * √(P(1-P)/n)

where:

P is the sample proportion of people who selected a Pepsi product

n is the sample size

Zc is the critical value for a 95% confidence interval, which is 1.96 for large samples

From the problem statement, we have:

P = 178/(178+280) = 0.388

n = 178+280 = 458

Zc = 1.96

Substituting these values into the formula, we get:

CI = 0.388 ± 1.96 * √(0.388*(1-0.388)/458)

Simplifying this expression, we get:

CI = 0.388 ± 0.047

Therefore, the 95% confidence interval for the proportion of people having a soft drink who select a Pepsi product is (0.341, 0.435). We can be 95% confident that the true proportion of people who select a Pepsi product when purchasing a soft drink in this restaurant is between 0.341 and 0.435.

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The height of the triangle is approximately 26.67 feet. To find the height of a triangle, we can use the formula for the area of a triangle:

Area = (1/2) * base * height

In this case, we know that the area of the triangular garden can be no more than 160 square feet, and the base of the triangle is 12 feet. We can substitute these values into the formula and solve for the height.

160 = (1/2) * 12 * height

Multiplying both sides of the equation by 2:

320 = 12 * height

Dividing both sides of the equation by 12:

height = 320 / 12

height ≈ 26.67 feet

Therefore, the height of the triangle is approximately 26.67 feet.

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If 2 layers will fill the entire truck then the volume of the truck is 16 cubic meters.

Since the floor of the truck can be completely covered with a layer of 8 boxes, we know that the area of the truck's floor is equal to the total area of 8 boxes.

The volume of each box is one cubic meter, which means each box has a height, length, and width of 1 meter. Therefore, the area of the truck's floor is 8 square meters (8 boxes x 1 square meter per box).

If two layers of boxes will fill the entire truck, we need to multiply the area of the truck's floor by the height of two layers. Since each box has a height of 1 meter, the height of two layers will be 2 meters.

The volume of the truck = Area of the floor x Height

Volume of the truck = 8 square meters x 2 meters

Volume of the truck = 16 cubic meters

Therefore, the volume of the truck is 16 cubic meters.

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Answer: Alex is 15 years

Step-by-step explanation:

Since Alex is w years old and her sister is three years younger than him. The age of his sister will be:

= w - 3.

We will then multiply their ages and equate to 180. This will be:

w × (w - 3) = 180

w² - 3w = 180

w² - 3w - 180 = 0

w² - 15w + 12w - 180 = 0

w(w - 15) + 12(w - 15) = 0

(w + 12)(w - 15)

w - 15 = 0

w = 0 + 15

w = 15 years

Alex is 15 years, her sister is 12 years.

Answer:

24

Step-by-step explanation:

15 =4

15x 6=90

4x6=24

Answer:

15 foot tree = 4 foot shadow

90 foot telephone pole

Setting up a proportion:

15 / 4 = 90 / x

15x = 360

x = 24 feet (telephone pole shadow)

Step-by-step explanation:

Answer:

The correct answer is "rational" . It is not an "integer" because it is a "decimal value". It is not "irrational" because the decimal value terminates and does not repeat.

Option (c) is correct.

If a set of exam scores forms a symmetrical distribution, the most of the students had relatively high scores.

Most of the students had relatively high scores.

Symmetrical distribution is the probability distribution where the probability of the random variable being less than or equal to some value is the same as the probability that it is greater than or equal to some other value.Exam scores can be considered as the data set. If it is forming symmetrical distribution, then we can conclude that the most of the students had relatively high scores.

This means, there will be same number of low score students as the number of high score students. For example, in a normal distribution, we can see that the most of the students will score around the mean value, which is considered as relatively high score.

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If a set of exam scores forms a symmetrical distribution, the most of the students had relatively high scores. The correct option is c. Most of the students had relatively high scores.What is a symmetrical distribution.

A symmetrical distribution is a data distribution that looks the same on both sides when we divide it down the middle. It implies that the data is uniformly distributed around the midpoint.Therefore, if a set of exam scores forms a symmetrical distribution, it indicates that most of the students had relatively high scores. It is important to understand that a symmetrical distribution has equal or nearly equal percentages of scores on both sides of the midpoint.

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The amplitude of a function is determined by analyzing the y-values of the graph and calculating the difference between the highest and lowest points on the graph.

You use y-values to compute the amplitude of a function. The amplitude of a function is the maximum distance between the function's graph and its midline. It is measured by finding the difference between the highest and lowest y-values of the function. By examining the graph of the function and determining the highest and lowest points on the graph, you can find the amplitude.

To find the amplitude, first, identify the maximum and minimum y-values of the function. Then, subtract the minimum value from the maximum value to calculate the amplitude. Keep in mind that the amplitude is always positive and represents the vertical distance between the midline and the peak or trough of the function.

For example, if the highest point on the graph is y = 5 and the lowest point is y = -3, the amplitude would be 5 - (-3) = 8.

In summary, the amplitude of a function is determined by analyzing the y-values of the graph and calculating the difference between the highest and lowest points on the graph.

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The area of the parallelogram with vertices K(1,2,3), L(1,3,6), M(3,8,6), and N(3,7,3) is approximately √265 square units.

To find the area of the parallelogram with the given vertices K(1,2,3), L(1,3,6), M(3,8,6), and N(3,7,3), we can use the cross product of two vectors.

First, let's define vectors KM and KN using the coordinates of the vertices:

Vector KM = (3-1, 8-2, 6-3) = (2, 6, 3)

Vector KN = (3-1, 7-2, 3-3) = (2, 5, 0)

Next, we calculate the cross product of vectors KM and KN to obtain a vector perpendicular to the parallelogram's plane:

KM x KN = ((6)(0) - (3)(5), (3)(2) - (2)(0), (2)(5) - (6)(2)) = (-15, 6, -2)

The magnitude of the cross product vector gives us the area of the parallelogram:

Area = |KM x KN| = √((-15)^2 + 6^2 + (-2)^2) = √(225 + 36 + 4) = √265

Therefore, the area of the parallelogram with vertices K(1,2,3), L(1,3,6), M(3,8,6), and N(3,7,3) is approximately √265 square units.

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Question

How do you find the Area of the Parallelogram with Vertices k(1,2,3), l(1,3,6), m(3,8,6), and n(3,7,3)?

Using completing the square method (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.

Get the intermediate step:

Divide the equation by 3 into both sides:

Adding 1 on both sides to complete the square:

Therefore, (x + 8)2 = +1 is the intermediary step in the equation (x + a)2 = b after the square is complete.

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The area of the triangle is 3 units^2. Since the area is equal to

hside * side/ 2.

Define area.

The measure of a region's size on a plane or curved surface is called area. While surface area refers to the area of an open surface or the boundary of a three-dimensional object, the area of a plane region or plane area refers to the area of a form or planar lamina.

Area is defined as the total amount of space occupied by a flat (2-D) surface or the shape of an object. On a sheet of paper, draw a square with a pencil. It is a two-dimensional figure. The area of a shape on paper is the area it occupies.

Solution Explained:
Given,

Length of Hypotenuse = 3units
One side = 2units

Area = (Length of Hypotenuse X Length one side) / 2
        = (3 X 2) / 2
        = 3units^2 (after calculation)

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Answer: A, C and E.

Step-by-step explanation: To compare the given fractions, we need to convert them to a common denominator and then compare their numerators. In this case, the common denominator is 8, which is the denominator of 5/8.

After converting the fractions to a common denominator, we get:

a) 3/4 = 6/8 = 3/4

b) 5/6 = 10/8 = 5/4

c) 1/2 = 4/8 = 1/2

d) 2/5 = 8/8 = 4/5

e) 1/4 = 2/8 = 1/4

Since 5/8 is the largest fraction, we can compare the other fractions to it by looking at their numerators. In this case, we see that the numerators of 3/4, 1/2, and 1/4 are all less than the numerator of 5/8, which is 5. Therefore, the correct answers are a) 3/4, c) 1/2, and e) 1/4.

Answer:

sjsndbgeehjsscpxhwhdhdhd

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

25-(3-2+(4-1))

25-(1+(3)

25-4

21

Answer: 4x^6

Step-by-step explanation:

Para responder esta pregunta debemos conocer que es un monomio, su grado y el coeficiente.

Un monomio es un polinomio que posee 1 solo termino, el grado se refiera a la potencia a la que esta elevada la variable (en este caso usaremos la letra x)

El coeficiente es el número que está a la izquierda de una variable:

Entonces:

Monomio de grado 6 y coeficiente 4

4x^6

When a specific element c with P(c) true is known, one can infer that xP(x) is true using the rule of inference.

Inference Rules Table

Rule of Inference Title

P∨Q¬P∴Q

Contradictory Syllogism

P→QQ→R∴P→R

Hypothetical Syllogism (P Q R S )P R Q S

Constructive Dilemma: P Q R S Q S P R

Defeasible Predicament.

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Answer:

(x + 7) = 41

Step-by-step explanation:

Let the number of lions in the wildlife reserve = x

Since, 7 lion cubs were born, so the total number of lions in the wildlife reserve will be (x + 7)

Now total number of lions = 41

Therefore, equation representing this situation will be,

(x + 7) = 41

Answer:

the answer is |x-15.3|_<_0.4

14.8 and 15.6 in that order

Step-by-step explanation:

With an allowance of 0.4 the length of the straw will be x > 14.8 and x < 15.6.

The absolute value of equality is expressed as |a| is a = ±a.

The absolute value of inequality can be expressed as |a| < 2 is a<2 and a > -2 in the later case we have multiplied a with negative sign and this switches the inequality after simplification.

According to the given question

The length of a manufactured plastic straw is 15.2cm with an acceptable allowance of 0.4cm.

Here allowance of 0.4cm means ±0.4cm allowance on the specific size that plastic straw manufacturer have fixed.

∴ The equation of this will of two forms

(i) x - 15.2 > -0.4.

(ii) x - 15.2 < 0.4.

Now solving these two equations

 x - 15.2 > - 0.4

 x > 15.2 - 0.4

 x > 14.8.

AND

 x - 15.2 < 0.4

 x < 15.2 + 0.4

x < 15.6.

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We requires a positive volume, we can conclude that there is no minimum volume subject to the given constraint

Let r be the radius of the can, and let h be its height. We want to minimize the volume V = πr^2h subject to the constraint A = 2πrh + 2π\(r^2\) = 54.

We can solve for h in terms of r using the constraint equation:

2πrh + 2π\(r^2\) = 54

h = (54 - 2π\(r^2\)) / (2πr)

Substituting this expression for h into the expression for V, we get:

V = π\(r^2\) [(54 - 2π\(r^2\)) / (2πr)]

V = (27/π) \(r^2\) (54/π - \(r^2\))

To find the minimum value of V, we can differentiate it with respect to r and set the result equal to zero:

dV/dr = (27/π) r (108/π - 3\(r^2\)) = 0

This equation has solutions r = 0 (which corresponds to a minimum volume of 0) and r = sqrt(36/π) = 2.7247 (rounded to four decimal places). To check that this value gives a minimum, we can check the second derivative:

\(d^2V/dr^2\) = (27/π) (108/π - 9r^2)

At r = 2.7247, we have \(d^2V/dr^2\) = -22.37, which is negative, so this is a local maximum. Therefore, the only critical point that gives a minimum is r = 0, which corresponds to a zero volume.

Since the problem requires a positive volume, we can conclude that there is no minimum volume subject to the given constraint.

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Answer:

D. none

Step-by-step explanation:

we only know about the right angle at the bottom right.

that is not enough information.

we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.

like the other answer options would indicate :

SAS : side - angle - side.

2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.

SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.

HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).

since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.

The specific gravity of the combined product is 1.22

Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.

Given,

The total quantity of portion= 50 ml

Specific gravities of the three syrups = 1.10,1.25 and 1.32

Then,

The specific gravity of the combined product= \(\frac{1.10+1.25+1.32}{3}\)

= 1.22

Hence, the specific gravity of the combined product is 1.22.

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Answer: 1.8 L/h

Step-by-step explanation:

To convert the rate of water dripping from a tap from millilitres per second (ml/sec) to litres per hour (L/h), we need to use conversion factors.

Step 1:

First, let's convert the rate from millilitres per second to litres per second.

There are 1000 millilitres in a litre, so we can divide the rate in millilitres per second by 1000 to get the rate in litres per second:

\(\LARGE \boxed{\textsf{0.5 ml/sec $\div$ 1000 = 0.0005 L/sec}}\)

Step 2:

We can convert the rate from litres per second to litres per hour. There are 3600 seconds in an hour, so we can multiply the rate in litres per second by 3600 to get the rate in litres per hour:

\(\LARGE \boxed{\textsf{0.0005 L/sec $\times$ 3600 = 1.8 L/h}}\)

Therefore, the rate of water dripping from the tap is 1.8 L/h.

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The probability that detector B goes off is 0.75

In this question we have been given the security system in a house has two units that set off an alarm when motion is detected.

Here, the probability that detector A will not go off is 0.35

And the probability that A will go off and B will not go off is 0.25

We need to find the probability that B goes off

The probability that detector A will go off would be,

1 - P( detector A will not go off )

= 1 - 0.35

= 0.65

And the probability that both A and B will go off would be,

= P(A will go off) - P( A will go off and B will not go)

= 0.65 - 0.25

= 0.40

Now we find the required probability.

P(B goes off) = P(both A and B will go off) + P(detector A will not go off)

                     = 0.40 + 0.35

                     = 0.75

Therefore, the required probability is 0.75

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Answer:

y = 35- 15x

Step-by-step explanation:

To solve for y, first isolate the term containing y.

1/5y = 7 - 3x

Multiply both sides by 5 to cancel out the fraction.

5(1/5y) = 5(7 - 3x)

This will result in:

y = 35- 15x

Do not forget to distribute the 5 when multiplying.

The equation is now solved for y.

Answer:

Step-by-step explanation:

Measure of an inscribed angle intercepted by an arc is half of the measure of the arc.

From the picture attached,

m(∠A) = \(\frac{1}{2}m(\text{arc BD})\)

           = \(\frac{1}{2}[m(\text{BC})+m(\text{CD}]\)

           = \(\frac{1}{2}[55^{\circ}+145^{\circ}]\)

           = 100°

m(∠C) = \(\frac{1}{2}[(360^{\circ})-m(\text{arc BCD})]\)

           = \(\frac{1}{2}(360^{\circ}-200^{\circ})\)

           = 80°

m(∠B) + m(∠D) = 180° [ABCD is cyclic quadrilateral]

115° + m(∠D) = 180°

m(∠D) = 65°

m(arc AC) = 2[m(∠D)]

m(arc AB) + m(arc BC) = 2(65°) [Since, m(arc AC) = m(arc AB) + m(arc BC)]

m(arc AB) + 55° = 130°

m(arc AB) = 75°

m(arc ADC) = 2(m∠B)

m(arc AD) + m(arc DC) = 2(115°)

m(arc AD) + 145° = 230°

m(arc AD) = 85°

The domain of discourse is the integers is smaller integer

What is Integer?

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

1.(a) ∃x∀y(y > x)

The statement is False

it is impossible to find a single integer x that has the property that all integer y are bigger that it. for any integer x, the integer y =x-1 is smaller

(b) ∀y∃x(y > x)

the statement is true for every integer y, we can find a integer x that is smaller, for example x=y-1

(c) ∃x(x = 0 → x = 1)

The statement is True

there exist x such that (x = 0, x=1). in this statement when we select x =1. this statement is true  regardless of x not equal to 0 therefore this statement is true if x=1 when x=1

2. (a) ∀x∃y(2 < x ≤ y)

we know

∀xP(x)=∃y(P(x))

∃xP(x)=∃y(P(x))

now apply de morgan law

∃x∀(y)=2>x v x>y

(b) ∀y∃x(y > 0 → x ≤ 0)

we know that A-B = A V B

∀y∃x (Y<0 V X< 0)

∀y∃x (Y<0 : X< 0)

3.(a) Given : All people weigh at least 100 pounds.

The negation is : Some people weigh less than 100 pounds. ( All negates to some, at least negates to less than )

(b) The statement is : Somebody did not see any animals in the zoo.

Equivalently : Somebody see no animals in the zoo.

Negation : Everybody saw some animals in the zoo. ( Somebody negates to everybody, No animals negates to some animals )

4. P(x,y): x is friends with y.

Then the given translates to " For all x there is a person y and a person z such that if y and z are not the same people that x and y are friends and x and z are friends."

The given statement is False. For every person x, we can always find two distinct persons y and z such that x is friends with y and y is friends with z. But, we reach a contradiction when we consider the case when x has only one friend. Then for that particular person x, we can find a person y such that P(x,y) but we cannot find a person z such that P(x,z). Hence, in that case, the statement is FALSE.

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Answer:

The answer is (4, 5)

Answer:

D

Step-by-step explanation:

The fruit punch has 2.4 gallons but x %

Apple juice has 5.6 gallons but 100 % or 1

The total mixture would then have 8 gallons and 82 %.

2.4+5.6=8

8×0.82 = 6.56

Then you would do 2.4x + 5.6(1) = 6.56

2.4x + 5.6 = 6.56

2.4x = 0.96

0.96/2.4 = 0.4 = 40%

Therefore, Brand A has 40% fruit juice

Answer: 4

Step-by-step explanation: