Gillian spends a third of her pocket money on snacks and a quarter of it on bus fare. How much money did she remain with?​

In a direct proof of the theorem "if r and s are rational numbers, then the product of r and s is a rational number," the following assumptions or facts are typically used:

Using these facts, a direct proof of the theorem can be constructed by assuming that r and s are rational numbers and then showing that their product is also a rational number. Specifically, we can express r and s as fractions with integer numerators and denominators, multiply their numerators together to obtain the numerator of the product.

Since the numerator and denominator of the product are both integers, and the denominator is nonzero, the product is a rational number.

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Therefore, the correct answer is:   [tex](x+10)^2=82[/tex]. ( right hand side of the equation).

An equation is a mathematical statement that indicates that two expressions are equal. It typically contains variables, which are represented by letters, and may also include constants and operators. The general format of an equation is:

expression = expression

For example, the equation x + 2 = 6 means that the expression x + 2 is equal to the expression 6. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

To solve the quadratic equation by completing the square, Jamie needs to follow the steps:

Move the constant term to the right-hand side of the equation:

[tex]x^2 + 20x = -18[/tex]

Add and subtract the square of half the coefficient of x to the left-hand side of the equation:

[tex]x^2 + 20x + (20/2)^2 - (20/2)^2 = -18[/tex]

[tex](x+10)^2 - 100 = -18[/tex]

Simplify the right-hand side of the equation:

[tex](x+10)^2 = 82[/tex]

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The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches. 0.8 is the probability that a randomly selected cedar tree will grow more than 8 inches in a given year.

The annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.

To find the probability that a randomly selected cedar tree will grow more than 8 inches in a given year, the following steps should be followed:

Calculate the range of increase in height of cedar trees:

The range of increase in height is

(12 - 7) = 5 inches.

Calculate the probability that a cedar tree will grow more than 8 inches:

P(X > 8) = (12 - 8) / 5 = 0.8

where X is the annual increase in height of a cedar tree.

Round the answer to four decimal places:

Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is 0.8000 or 0.8 (rounded to four decimal places).

Probability can be defined as the measure of how likely an event is to occur.

The probability of an event ranges between 0 and 1, where 0 denotes that the event will not occur and 1 denotes that the event will certainly occur.

If a random variable X has a uniform distribution over an interval (a, b), then the probability of X falling between two values c and d is given by:

P(c < X < d) = (d - c) / (b - a)

In this problem, the annual increase in height of cedar trees is believed to be distributed uniformly between seven and twelve inches.

Therefore, the probability that a randomly selected cedar tree will grow more than 8 inches in a given year is: P(X > 8) = (12 - 8) / (12 - 7) = 4 / 5 = 0.8 (rounded to four decimal places).

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Answer:

We have the equation:

-3 + sin(-3x) = -7/2

Adding 3 to both sides gives:

sin(-3x) = -1/2

The solutions for sin(x) = -1/2 are x = 7π/6 and x = 11π/6 in the interval [0, 2π).

We need to find the solutions for -3x in the interval [0, π).

For x = 7π/18, we get -3x = -7π/6, which is not in the given interval.

For x = 5π/18, we get -3x = -5π/2, which is not in the given interval.

For x = π/18, we get -3x = -π/2, which is in the given interval.

Therefore, the solution to the equation in the given interval is:

-3x = -π/2

x = π/6

Step-by-step explanation:

Apply the power rule and multiply the exponents

Answer:B. A horizontal cross section through the center of a cone with a radius of 4 and a height of 4 in.

Step-by-step explanation:

The given probability is 0.37 which is the probability of a supply container dropped from an aircraft by a parachute hitting a target. So the expected number of container drops needed to hit a target is approximately 2.7027.

       To find out the expected number of container drops needed to hit a target, we can use the formula given below;            

                      E(X) = (1/p) E(X)

                             = (1/0.37)E(X)

                             = 2.7027

          Thus, the expected number of container drops needed to hit a target is approximately 2.7027.

An expected value is a statistical concept that represents the theoretical average value of a random variable. It is represented as E(X).

            The expected value is calculated by multiplying each possible value of the random variable by its probability and then adding all of the products.

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a.) The mode for the chart is 24.

b.) The probability that the winning score will be 25 = 7/50

C.)The probability that the winning score will be 23 or more = 37/50.

The number of times the game is played = 50 times

The number of games that showed the score of 25= 7

The probability of winning a score of 25 = 7/50

The scores that are 23 and above; 10+14+7+4+2= 37

The probability of winning a score of 23 and above = 37/50

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For numbers 1-6, using the order of operations to evaluate each expression is given as follows:

[tex](8.15 x 4 + 5) x 3.2 = 120.32\\12 + 5 + 32 x 2.2 = 87.4\\17 + 8 x (2.7 + 6) - 3 = 83.6\\38.9 - 2.3 x 1.5 + 2.6 = 37.05\\0.2 x (5 - 0.7) + 1.8 + 2 = 4.66\\5 + (8.06 - 12.5 + 2) = 4.56[/tex]

A pοlynοmial equatiοn is an equatiοn in which a pοlynοmial expressiοn is set equal tο anοther expressiοn οr tο zerο. It is an algebraic equatiοn that invοlves οne οr mοre terms in which the variables are raised tο a pοsitive integer pοwer and multiplied tοgether. The degree οf the pοlynοmial is the highest pοwer οf the variable in the pοlynοmial equatiοn.

(8.15 x 4/5) x 3.2

= (6.52) x 3.2 (Perfοrming multiplicatiοn befοre divisiοn)

= 20.86

2. 12/5+32 x 2.2

= 2.4 + 70.4 (Perfοrming multiplicatiοn befοre additiοn)

= 72.8

3. 17+8 x (2.7/6)-3

= 17 + 1.2 - 3.0 (Perfοrming divisiοn befοre multiplicatiοn and subtractiοn)

= 15.2

4. 38.9 - 2.3 x 1.5 + 2.6

= 38.9 - 3.45 + 2.6 (Perfοrming multiplicatiοn befοre subtractiοn)

= 37.05

5. 0.2 x (5 - 0.7) + 1.8 / 2

= 0.2 x 4.3 + 0.9 (Perfοrming subtractiοn inside the parentheses)

= 1.12

6. 21.5/5+(8.06-12.5/2)

= 4.3 + 1.53 (Perfοrming divisiοn befοre subtractiοn and additiοn inside the parentheses)

= 5.83

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Answer: the answer is 21 percent

Step-by-step explanation:

when you have 16 of 52 which is all of the colors together then it will give you 21%

Answer:

21% or 4/13

Step-by-step explanation:

when you have 16 of 52 which is all of the colors together, then it will give you 21%

For fractions, you have 16 of 52, then you can simplify the fraction down to 4/13. Giving you the answer of a simplified fraction.

The property of the average of any two odd integers being odd is true for all integers.

This is because the sum of any two odd integers is always an even integer. For example, if we take any two odd integers, say 3 and 7, then the sum of these two is 10, an even integer. Therefore, the average of 3 and 7, which is (3 + 7)/2, is also an even integer, in this case, 5.

Since all even integers are divisible by 2, the average of any two odd integers must be an odd integer.

Therefore, the property is true for all integers.


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Answer:

x = 40

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

65 + 75 + x = 180

140 + x = 180 ( subtract 140 from both sides )

x = 40

Answer: x = 40

Step-by-step explanation:

In a triangle, all the angles add up to 180 degrees.

In this case, 65 + 75 + x = 180.

Add the 65 and 75 together using column addition:

65

+75

-------

140

Now, the equation is 140 + x = 180

Subtract 140 from both sides:

x = 40

Therefore, x is 40.

The axis of symmetry of equation f(x) = x² - x³ - 4 is x = 2/3.

The axis of symmetry is a vertical line that passes through the vertex of a parabolic function, which is the highest or lowest point on the graph depending on the direction of the parabola. The equation f(x) = x² - x³ - 4 is a cubic function that can be written in standard form as:

f(x) = -x³ + x² - 4

To find the axis of symmetry, we need to first find the x-coordinate of the vertex. This can be done by taking the derivative of f(x) and setting it equal to zero:

f'(x) = -3x² + 2x = 0

x(2-3x) = 0

x = 0 or x = 2/3

Since the coefficient of the x³ term is negative, the vertex of the cubic function is a maximum. Therefore, the axis of symmetry is the vertical line passing through the x-coordinate of the vertex, which is x = 2/3.

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The area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence. So the correct answer is d. 7 3/4.

When measuring the area of a shape, we are determining the amount of surface the shape takes up.

To calculate the area enclosed by each fence, we must multiply the length and width of each.

The area enclosed by the wood fence is

6 1/2 x 2 1/4 = 14 7/8 square yards,

and the area enclosed by the metal fence is

2 3/4 x 2 1/2 = 6 7/8 square yards.

To determine how many times greater the area enclosed by the wood fence is than the area enclosed by the metal fence, we must divide the area of the wood fence by the area of the metal fence:

14 7/8 / 6 7/8 = 7 3/4.

This means the area enclosed by the wood fence is 7 3/4 times greater than the area enclosed by the metal fence.

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The given statement "The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of y and the line" is true because it provides the best fit line.

The simple linear regression equation estimates the relationship between two variables - a dependent variable (y) and an independent variable (x) - by fitting a straight line through the data points.

The line is chosen so that the sum of the squared deviations (also known as the sum of squared errors or SSE) between the observed values of y and the predicted values of y on the line is minimized.

In other words, the simple linear regression equation finds the line that is closest to all the data points in terms of the vertical distance between the points and the line.

This line is chosen to minimize the sum of squared deviations because it provides the best estimate of the relationship between x and y, and it allows for the prediction of y values for a given x value.

Thus, minimizing the sum of squared deviations is a crucial aspect of the simple linear regression equation because it ensures that the line of best fit provides the most accurate estimate of the relationship between the variables.

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When the sphere has a radius of 5 feet, the radius is increasing at a very slow rate of 0.018 feet per minute if volume is increasing.

The volume of a sphere formula, V = (4/3)r3, must be used to determine the rate of change of the radius.

Using this formula's derivative with regard to time t, we obtain:

[tex]dV/dt = 4r2(dr/dt)[/tex].

Here, r: radius of the sphere, and we need to determine dr/dt, the rate of change of the radius when r=5. dV/dt is the rate of change of the volume, which is provided as 562 cubic feet per minute.

When we enter the provided values, we obtain:

[tex]562 = 4\pi (17)^2(dr/dt)[/tex]

0.018 feet per minute is equal to[tex]dr/dt = 562 / (4(17)2)[/tex].

As a result, the radius changes at a rate of about 0.018 feet per minute when the radius is 5 feet.

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The line of sight distance using the angle of depression 13° is derived to be 2222.71 m to the nearest hundredth meters.

The angle of depression is an angle formed between the horizontal line and the line of sight when an observer looks downwards.

Considering the right triangle formed by the height of the tower and the complementary angle 77°, we shall represent the line of sight distance for the television camera to the base of the stadium with x so that;

cos 77° = 500/x {adjacent/hypotenuse}

note that 90° - 13° = 77°

x = 500/ cos 77° {cross multiplication}

x = 2,222.7057.

Therefore, the line of sight distance for the television camera to the base of the stadium to the nearest hundredth meters is equal to 2,222.71. Using the trigonometric ratio of cosine for the angle 77° which is complementary to the angle of depression 13°

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We would expect around 3 students to have an IQ of 140 or above at Hogwarts School of Witchcraft and Wizardry.

Based on the given information, we can use the normal distribution formula to calculate the number of students expected to have an IQ of 140 or above.

To explain this, we can use the following steps:

1. Calculate the z-score for an IQ of 140 using the formula: z = (x - μ) / σ where x is the IQ score, μ is the mean IQ score and σ is the standard deviation.

2. Look up the probability of a z-score of 2.67 or above using a standard normal distribution table or calculator. This gives us the proportion of the population with an IQ of 140 or above.

3. Multiply the proportion by the total number of students to get the expected number of students with an IQ of 140 or above.

Since we cannot have a fraction of a student, we can round this to the nearest whole number to get the final answer.

Therefore, we would expect around 3 students to have an IQ of 140 or above at Hogwarts School of Witchcraft and Wizardry.

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An access control list (ACL) specifies which subjects and objects users or groups can access.

An Access Control List (ACL) is a term used to describe a security mechanism that regulates who has access to an object in a computing system. An Access Control List (ACL) is a type of file that contains the names of people or groups of individuals who are allowed or denied access to a system resource.

ACLs are one of the most widely used security measures in computer networks today, and they are used to establish access control policies for network resources such as files, folders, devices, or services. This list is compiled on the basis of the requirements and policies of the security team in place.
The access control list (ACL) is a security feature that allows administrators to define and manage the permissions and rights for different users or groups to access specific resources, such as files, directories, or applications. Implementing an ACL helps to ensure proper security and privacy in a system or network.

The access control list (ACL) is correct in the blanks.

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Answer: Inequality 1

Step-by-step explanation: Let's solve each inequality first.

4(2.8z+175 )>-26.6

let's distribute the 4.

4(2.8z)+4(175)

11.2z+700>-26.6

Now let's isolate the variable by subtracting 700 on each side.

11.2z>-726.6

Now let's divide both sides by 11.2

z>-64.875

Oh? This one already has 5 as a solution as 5 is more than -64.875!

According to the Vertical Angle Theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.

The opposing angles created by the junction of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal. Moreover, a vertical angle and the angle to which it is next are supplementary angles, meaning their sum is 180 degrees.

WH ⊥ VZ at y ,

Y is the midpoint of WX

Now since only one line can pass through W and Y ,

X must lie WH

Either W-Y-X-H of W-Y-H-X.

In any case W, Y, X and H are collinear.

Since, WH ⊥ VZ ⇒ WX ⊥ VZ at Y.

m∠VYW = m∠VYX = 90°

∠VYW ≅ ∠VYX = 90°.

Next,

Y is midpoint of WX

WY = XY

WY ≅ XY

Finally, VZ bisects ∠WYX

m∠WVY = m∠XVY

∠WVY ≅ ∠XVY

Using 1, 2, 3

ΔVWY ≅ ΔVXY by Right Hypotenuse side Congruency,

Alternatively ,

using 2, 3 and

VY ≅ VY

ΔVWY ≅ ΔVXY (by SSS congruence )

Using equations,

ΔVWY ≅ ΔVXY

by SAS congruence,

ΔVEY = ΔVXY by ASA Congruence

ΔVNY ≅ ΔVXY by AAS congruence

ΔVWY ≅ ΔVXY by AAS congruence.

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First one is 6

second one is 12

third one is -8

hope this helps

Answer:

Step-by-step explanation:

x=6

x=12

x=-8

The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.

The largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven. This is because the restaurant only sells nuggets in packs of five and seven. This means that if you wanted to order eleven nuggets, it would not be possible.

To explain this mathematically, eleven can be written as 5+5+1, 7+4, or 3+3+3+2. As none of these can be made with just five and seven packs of chicken nuggets, it is impossible to order eleven.

If the restaurant sold chicken nuggets in packs of three and seven, then it would be possible to order eleven nuggets (3+3+3+2).

In conclusion, the largest number of chicken nuggets that is impossible to order from your neighborhood fast food restaurant is eleven.

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Extrapolation is a useful tool for predicting future values based on past data

Bethany used a method of predicting future values from past values known as extrapolation. Extrapolation is a powerful tool for predicting future values, but it is important to remember that it only works if the underlying trend in the data does not change. In Bethany's case, she is making an assumption that her income over the next 10 years will follow the same trend as it did in the past 5 years.

In extrapolation, the assumption is that the data points that were observed in the past will continue in the same direction and with the same intensity into the future. Therefore, extrapolation can be used to make predictions about future values even when no new data points have been collected. It is important to remember, however, that any predictions made using extrapolation are only estimates and may not be accurate.

Extrapolation is used in many different fields, such as finance, economics, medicine, engineering, and even weather forecasting. For example, stock analysts may use extrapolation to make predictions about future stock prices based on past prices. Similarly, meteorologists may use extrapolation to make predictions about future weather conditions based on historical weather data.

Overall, extrapolation is a useful tool for predicting future values based on past data. However, it is important to remember that it only works when the underlying trend in the data does not change. Additionally, any predictions made using extrapolation are only estimates and may not be accurate.

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The median of 49 is the most accurate to use, since the data is skewed.

Distribution refers to the pattern of variation in a dataset. Specifically, it refers to how the values in the dataset are spread out or clustered together.

The most appropriate measure of center to represent the data depends on the shape of the distribution. In this case, we can see from the histogram that the data is skewed to the right, with a longer tail of higher values.

Therefore, the correct answer is: the median of 49 is the most accurate to use, since the data is skewed. This represents the middle value of the data when it is arranged in order, and is less sensitive to the outliers at the high end of the distribution. Using the median can give a more accurate representation of the typical donations received by the charity.

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The probability that all four cards drawn from a deck are black cards is 1/4165.

There are 26 black cards and 52 cards in a standard deck of cards. Therefore, the probability of drawing a black card from a standard deck of cards is 26/52 or 1/2. In the first draw, there are 26 black cards out of 52 cards, so the probability of drawing a black card is 26/52.

In the second draw, there are 25 black cards left out of 51 cards, so the probability of drawing a black card is 25/51. In the third draw, there are 24 black cards left out of 50 cards, so the probability of drawing a black card is 24/50. In the fourth draw, there are 23 black cards left out of 49 cards, so the probability of drawing a black card is 23/49.

Using the multiplication principle of probability, the probability that all four cards drawn from a deck are black cards is 26/52 × 25/51 × 24/50 × 23/49 = 1/4165.

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Examining the figures of the circles, the values for x is calculated to be

11. x = 8

12. ED = 11

The value of x in the two figure is solved using the relationship between secant and angle measures

11. The formula used here is

(2x + 7) = 0.5 * (78 - 32)

(2x + 7) = 0.5 * (46)

2x + 7 = 23

solving for x

2x = 23 - 7

2x = 16

x = 8

12.

11x - 9 = 0.5 ( (15x-39) - (9x-3) )

11x - 9 = 0.5 ( 15x - 39 - 9x + 3 )

11x - 9 = 0.5 ( 6x - 36 )

11x - 9 = 3x - 18

11x + 3x = -18 + 9

14x = -9

x = 14/9 = 1.56

solving for

ED = 9x - 3 = 9 * 14/9 - 3 = 14 - 3 = 11

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Answer: 290.

Step-by-step explanation:

9,280

How many times can 32 go into 9? no times.

How many times can 32 go into 92? 2 times.

2880 remaining.

How many times can 32 go into 2? no times.

How many times can 32 go into 28? no times.

How many times can 32 go into 288? 9 times.

00 remaining.

Since there is an extra zero, you add a zero to your final answer.

The data set which consists of 900 values that follow a standard normal distribution with a mean of 90 and a standard deviation of 8 has 480 values that lie between 86 and 98.

We need to determine how many values in the data set lie between 86 and 98. The formula for calculating the Z-score is as follows: Z = (X - μ) / σwhereX = the value of interestμ = the meanσ = the standard deviation

Using this formula, we can find the Z-scores for the lower and upper bounds of the range as follows:Z lower = (86 - 90) / 8 = -0.5Z upper = (98 - 90) / 8 = 1.0We can then look up these Z-scores in the standard normal distribution table to find the corresponding probabilities.

Using the table, the probability of a Z-score being less than -0.5 is 0.3085, and the probability of a Z-score being less than 1.0 is 0.8413. Therefore, the probability of a Z-score being between -0.5 and 1.0 is:0.8413 - 0.3085 = 0.5328

Finally, we can convert this probability to the number of values in the data set that lie between 86 and 98 by multiplying it by the total number of values in the data set:900 x 0.5328 = 479.52 values

Therefore, there are approximately 480 values in the data set that lie between 86 and 98.

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The prompt on fractions is given as follows:

1 ) (1/2) ÷ 4 = 1/8
2) ( 1/5) ÷ 2 = 1/10

3) (1/3) ÷ 5 = 1/15

4) (1/4) ÷ 4 = 1/16
5) The solution to the puzzle for (1/2) ÷ 3 is given below.

The calculations are given as follows;

1 )

= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]

= 1/8

2) (1/5) ÷ 2

= (1/5) x (1/2)

= 1/10

3)

(1/3) ÷ 5

= (1/3) x (1/5)

= 1/15

4) (1/4) ÷ 4

= (1/4) x (1/4)

= 1/16

5) Mary had 1/2 of a pie that she wanted to share with 3 of her friends. She decided to divide it equally among them. Each friend got 1/6 of the pie. To check, Mary multiplied 1/6 by 3 and got 1/2. This shows that (1/2)/3 equals 1/6, since dividing by 3 is the same as multiplying by its reciprocal, 1/3.


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