5 Four children all play a computer game on the first day of the year. Then Anne plays every second day, Bernard plays every third day, Charles plays every fourth day and Danielle only plays every fifth day. What is the date when they next all play on the same day? b On how many days of the year do they all play on the same day?

Answer: 0.4337

Step-by-step explanation:

Let X represents the test results for a class that follow a normal distribution .

Given: Mean \(\mu=78\), Standard deviation  \(\sigma=36\)

Then, the probability that it is greater than 84 will be

\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)

Hence, the required probability = 0.4337

Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

Answer:

(a) The average rate of change from 0 to 2 is 6

(b) The average rate of change from 3 to 5 is 24

(c) The average rate of change from -3 to 0 is -9

Step-by-step explanation:

The formula for the average rate of change (AROC) is given by:

\(AROC=\frac{f(b)-f(a)}{b-a}\)

(a):

Finding the AROC from 0 to 2

To find the average rate of change from 0 to 2, we use f(2) and f(0), while we plug in 2 for b and 0 for a:

\(\frac{f(2)-f(0)}{(2-0)}\\ \\\frac{((3(2)^2+4)-(3(0)^2+4))}{(2-0)} \\\\\frac{(16-4)}{(2)}\\ \\\frac{12}{2}\\ \\6\)

Thus, the average rate of change from 0 to 2 is 6.

(b):

Finding the AROC from 3 to 5:

To find the average rate of change from 3 to 5, we use f(5) and f(3), while we plug in 5 for b and 3 for a:

\(\frac{f(5)-f(3)}{(5-3)}\\ \\\frac{((3(5)^2+4)-(3(3)^2+4))}{(2-0)} \\\\\frac{(79-31)}{(2)}\\ \\\frac{48}{2}\\ \\24\)

Thus, the average rate of change from 5 to 3 is 24.

(c):

To find the average rate of change from -3 to 0, we use f(0) and f(-3), while we plug in 0 for b and -3 for a:

\(\frac{f(0)-f(-3)}{(0-(-3))}\\ \\\frac{((3(0)^2+4)-(3(-3)^2+4))}{(0+3)} \\\\\frac{(4-31)}{(3)}\\ \\\frac{-27}{3}\\ \\-9\)

Thus, the average rate of change from -3 to 0 is -9.

Answer:

Lee drank 31/15 qt. of water (2 1/15 qt. as a mixed number, or approximately 20.07 qt. as a decimal).

Step-by-step explanation:

To add and subtract fractions, a least common denominator needs to be found. But first, to make it easier, mixed numbers should be replaced with improper fractions. So, Lee drank 5/3 qt. of water.

Now to find the LCD (least common denominator), the denominators of each fraction should be multiplied by 1, then 2, then 3, etc until a product of one fraction is the same as that of another (as shown):

For 2/5, the denominator is 5, so 5*1 = 5, 5*2 = 10, 5*3 = 15...

For 5/3, the denominator is 3, so 3*1 = 3, 3*2 = 6, 3*3 = 9, 3*3 = 4, 3*5 = 15...

15 is the LCD, since both denominators can be multiplied by a whole number for a product of 15.

Now, each fraction is multiplied by 1, by multiplying each fractions numerators and denominators by the number found previously that causes the denominator to equal 15:

For 2/5, 5*3 = 15, so both 2 and 5 are multiplied by 3

        2* 3 = 6, 5 * 3 = 15, so 2/5 = 6/15

For 5/3, 3*5 = 15, so both 5 and 3 are multiplied by 5

        5* 5 = 25, 3 * 5 = 15, so 5/3 = 25/15

Now these fractions can easily be added or subtracted by performing these operations on their numerators. Sonia drank 6/15 qt. more than Lee, so she drank 6/15 + 25/15 qt. of water, or 31/15 qt.

Step-by-step explanation:

its congruent by HL or RHSaxiom

Answer:

HL

Step-by-step explanation:

\( In\: right \triangle 's DAB \: \&\: CBA\\

\angle DAB \cong \angle CBA... (each 90\degree) \\ hypotenuse \: DB \cong hypotenuse \: CA. (given) \\

side AB \cong side BA.. (common) \\

\therefore \triangle DAB \cong \triangle CBA.. (By \: RHS\: or \: HL \: Postulate) \)

The quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

A division is a process of splitting a specific amount into equal parts.

We have to find 3x³-2x²+7x+9 divided by x²-3x

3x³-2x²+7x+9 is the dividend and x²-3x is the divisor.

The steps to solve this are given below.

Step 1: Take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor.

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

Step 4: Bring down the next digit of the dividend (if present).

Step 5: Repeat the same process.

Hence, the quotient is 3x + 7, and the remainder is (28x + 9) / (x^2 - 3x).

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Type of rotation of Anticlockwise and clockwise .

A point in coordinate geometry can be rotated through 180 degrees around the origin by drawing an arc with a radius equal to the distance between the provided point's coordinates and the origin, and then extending an angle of 180 degrees at the origin.

The point must be rotated around the origin with regard to its location in the cartesian plane. It is nicely explained in the next part of the 180-degree rotation formula.

The formula for 180-degree rotation of a given value is as follows: if R(x, y) is a point that has to be rotated around the origin, then coordinates of R(x, y) .

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Total: 150

Job: 93

Driver's license: 128

Both: 76

We construct the table:

Now, using the fact that the total is 150, from the last row:

And from the last column:

Finally, the complete table is:

Answer:

$180

Step-by-step explanation:

If the perimeter is 30 yards and each yard costs $6 you times 30 and 6 and you get $180

Answer:

? = 92°

Step-by-step explanation:

the chord- chord angle ? is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is

? = \(\frac{1}{2}\) (LM + AK) = \(\frac{1}{2}\) (120 + 64)° = \(\frac{1}{2}\) × 184° = 92°

Heracio used the computer 4 more hours to do homework than shop online.

To find out how many more hours Heracio used the computer to do homework than shop online, we first need to calculate the number of hours he spent on each activity.

Let's start by calculating the number of hours Heracio spent on each activity:

Shopping: 10% of 40 hours = 4 hours

Videos: 15% of 40 hours = 6 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Now, to find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 4 hours (shopping) = 4 hours

Therefore, Heracio used the computer 4 more hours to do homework than shop online.

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The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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The expression 8x + 4y is not equivalent to 4(2x + 1). Therefore, 8x + 4y = 4(2x + y)

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Let's determine whether the expression 8x + 4y is equivalent to 4(2x + 1).

Let's factorise to know whether the expressions are equivalent.

Therefore, using the common factors,

8x + 4y = 4(2x + y)

Hence, the expression are not equivalent .

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Answer:

6 dishes

Step-by-step explanation:

since he made 2 dishes and there is a two in the numerator, all we have to do is multiply by 6 to get 2 by itself

The statement "for every positive rational number x, there exist positive integers n1, ..., nk such that x = n1/n2 + ... + nk/nk" is known as the Egyptian fraction representation theorem and is proved.

Let x be a positive rational number with numerator p and denominator q, where p and q are coprime. Let's assume that x can't be represented as a sum of positive unit fractions (i.e., fractions with numerator 1).

Then, construct a sequence of positive rational numbers x1, x2, ..., xk such that x1 = x and for each i, xi is equal to the difference between xi-1 and the largest unit fraction that is less than or equal to xi-1.

Since x is a positive rational number, it follows that xi is also a positive rational number for all i. Since x can't be represented as a sum of positive unit fractions, it follows that xi can't be represented as a sum of positive unit fractions for all i. Since the sequence x1, x2, ..., xk is constructed as the difference of two positive rational numbers, it follows that xi is a positive rational number for all i.

Since x1 = x, it follows that there exists a positive integer n such that x1 is equal to n/n + 1. But this contradicts our assumption that x can't be represented as a sum of positive unit fractions. Thus, our assumption is false, and it follows that x can be represented as a sum of positive unit fractions.

Therefore, we have proved that for every positive rational number x, there exist positive integers n1, ..., nk such that x = n1/n2 + ... + nk/nk.

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_____The given question is incomplete, the complete question is given below:

prove: let x be a positive rational number, then there exist positive integers n1, ..., nk such that x = n1/n2 + ..... + nk/nk.

To find the inverse of a funciton, you must switch the “x” and the “y” variables. As you said B is not a choice, I will take that out.

In the work below, I will switch f(x) with y, it makes no difference in the equation. But you’ll have to switch back to f(x).

A.

y= 2x+1

Inverse:

x=2y+1

x-1=2y

(x-1)/2= y

y= (x-1)/2

A is not an inverse

C.

y=(x+1)/5

Inverse

x=(y+1)/5

5x=y+1

5x-1=y

y=5x-1

C. Is not an inverse

D.

y=3x+2

Inverse

x=3y+2

x-2=3y

(x/3)-(2/3)=y

y=(x/3)-(2/3)

f(x)=(x/3)-(2/3)

SO D is the answer

Option D is the answer, sorry I have H.W to complete, so no time to explain...

Thank you have a magnificent day ahead...

If possible brainliest please

Answer:

B

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors

The correct answer is \(4\sqrt[3]{6}\) which is option B.

What is radical?

The symbol \(\sqrt[n]{x}\) indicates a root which is called as radical and it is read as x radical n or nth root of x.

Factor the terms of numerator of the given expression.

\(\frac{4\cdot8\sqrt[3]{3\cdot6y} }{8\sqrt[3]{3y} }\)

On dividing the common factors we get,

\(4\sqrt[3]{6}\)

Therefore, the simplified expression for the given expression is  \(4\sqrt[3]{6}\) which is option B.

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A dot plot would show 7 points for numbers greater than 2 and a histogram would have a maximum of 7 bars. Hence, Both statements b and d are true about a graph representing the data.

Statement b: A dot plot would show 7 points for numbers greater than 2. This is true because there are 7 data points (2, 3, 4, 4, 4, 5, 6) in the data set that is greater than 2.

Statement d: A histogram would have a maximum of 7 bars. This is because there are 7 unique values in the data set (0, 1, 2, 3, 4, 5, 6), and each unique value would correspond to a bar in the histogram.

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The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.

The sequence that shows the numbers in order from least to greatest is D. 2.14 < 2.8 < 3.16227766017.What is the meaning of the inequality symbols?The inequality symbols are mathematical symbols that are used to compare two values.

They indicate the relationship between two values that are not equal to each other. Here are the inequality symbols:

< (less than)≤ (less than or equal to)> (greater than)≥ (greater than or equal to)What is the meaning of the sequence?

A sequence is a set of numbers arranged in a particular order. The order of the numbers in a sequence can be from smallest to largest or largest to smallest.

The sequence D. 2.14 < 2.8 < 3.16227766017 is arranged from smallest to largest because the first number in the sequence, 2.14, is the smallest, and the last number in the sequence, 3.16227766017, is the largest.

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Answer:

The equations have one solution at (5, -5).

Step-by-step explanation:

We are given a system of equations:

\(\displaystyle{\left \{ {{-2x+5y=-35} \atop {7x+2y=25}} \right.}\)

This system of equations can be solved in three different ways:

Graphing the Equations

We need to solve each equation and place it in slope-intercept form first. Slope-intercept form is \(\text{y = mx + b}\).

Equation 1 is \(-2x+5y = -35\). We need to isolate y.

\(\displaystyle{-2x + 5y = -35}\\\\5y = 2x - 35\\\\\frac{5y}{5} = \frac{2x - 35}{5}\\\\y = \frac{2}{5}x - 7\)

Equation 1 is now \(y=\frac{2}{5}x-7\).

Equation 2 also needs y to be isolated.

\(\displaystyle{7x+2y=25}\\\\2y=-7x+25\\\\\frac{2y}{2}=\frac{-7x+25}{2}\\\\y = -\frac{7}{2}x + \frac{25}{2}\)

Equation 2 is now \(y=-\frac{7}{2}x+\frac{25}{2}\).

Now, we can graph both of these using a data table and plotting points on the graph. If the two lines intersect at a point, this is a solution for the system of equations.

The table below has unsolved y-values - we need to insert the value of x and solve for y and input these values in the table.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & a \\ \cline{1-2} 1 & b \\ \cline{1-2} 2 & c \\ \cline{1-2} 3 & d \\ \cline{1-2} 4 & e \\ \cline{1-2} 5 & f \\ \cline{1-2} \end{array}\)

\(\bullet \ \text{For x = 0,}\)

\(\displaystyle{y = \frac{2}{5}(0) - 7}\\\\y = 0 - 7\\\\y = -7\)

\(\bullet \ \text{For x = 1,}\)

\(\displaystyle{y=\frac{2}{5}(1)-7}\\\\y=\frac{2}{5}-7\\\\y = -\frac{33}{5}\)

\(\bullet \ \text{For x = 2,}\)

\(\displaystyle{y=\frac{2}{5}(2)-7}\\\\y = \frac{4}{5}-7\\\\y = -\frac{31}{5}\)

\(\bullet \ \text{For x = 3,}\)

\(\displaystyle{y=\frac{2}{5}(3)-7}\\\\y= \frac{6}{5}-7\\\\y=-\frac{29}{5}\)

\(\bullet \ \text{For x = 4,}\)

\(\displaystyle{y=\frac{2}{5}(4)-7}\\\\y = \frac{8}{5}-7\\\\y=-\frac{27}{5}\)

\(\bullet \ \text{For x = 5,}\)

\(\displaystyle{y=\frac{2}{5}(5)-7}\\\\y=2-7\\\\y=-5\)

Now, we can place these values in our table.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)

As we can see in our table, the rate of decrease is \(-\frac{2}{5}\). In case we need to determine more values, we can easily either replace x with a new value in the equation or just subtract \(-\frac{2}{5}\) from the previous value.

For Equation 2, we need to use the same process. Equation 2 has been resolved to be \(y=-\frac{7}{2}x+\frac{25}{2}\). Therefore, we just use the same process as before to solve for the values.

\(\bullet \ \text{For x = 0,}\)

\(\displaystyle{y=-\frac{7}{2}(0)+\frac{25}{2}}\\\\y = 0 + \frac{25}{2}\\\\y = \frac{25}{2}\)

\(\bullet \ \text{For x = 1,}\)

\(\displaystyle{y=-\frac{7}{2}(1)+\frac{25}{2}}\\\\y = -\frac{7}{2} + \frac{25}{2}\\\\y = 9\)

\(\bullet \ \text{For x = 2,}\)

\(\displaystyle{y=-\frac{7}{2}(2)+\frac{25}{2}}\\\\y = -7+\frac{25}{2}\\\\y = \frac{11}{2}\)

\(\bullet \ \text{For x = 3,}\)

\(\displaystyle{y=-\frac{7}{2}(3)+\frac{25}{2}}\\\\y = -\frac{21}{2}+\frac{25}{2}\\\\y = 2\)

\(\bullet \ \text{For x = 4,}\)

\(\displaystyle{y=-\frac{7}{2}(4)+\frac{25}{2}}\\\\y=-14+\frac{25}{2}\\\\y = -\frac{3}{2}\)

\(\bullet \ \text{For x = 5,}\)

\(\displaystyle{y=-\frac{7}{2}(5)+\frac{25}{2}}\\\\y = -\frac{35}{2}+\frac{25}{2}\\\\y = -5\)

And now, we place these values into the table.

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)

When we compare our two tables, we can see that we have one similarity - the points are the same at x = 5.

Equation 1                  Equation 2

\(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & -7 \\ \cline{1-2} 1 & -33/5 \\ \cline{1-2} 2 & -31/5 \\ \cline{1-2} 3 & -29/5 \\ \cline{1-2} 4 & -27/5 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)                 \(\begin{array}{|c|c|} \cline{1-2} \textbf{x} & \textbf{y} \\ \cline{1-2} 0 & 25/2 \\ \cline{1-2} 1 & 9 \\ \cline{1-2} 2 & 11/2 \\ \cline{1-2} 3 & 2 \\ \cline{1-2} 4 & -3/2 \\ \cline{1-2} 5 & -5 \\ \cline{1-2} \end{array}\)

Therefore, using this data, we have one solution at (5, -5).

Answer:

The simplified version of this equation is -3x - 12.

Step-by-step explanation:

To simplify this equation, distribute -3 to both x and 4.

-3(x+4) = -3x -12

Answer:

-3x-12 as an expression

Step-by-step explanation:

To solve this problem, we need to distribute!

Multiply -3 by both the x and the 4

When we do this, we get:

-3x and -12

Note: when you multiply a positive by a negative, you get a negative so it turns into a negative number

Note 2: When you see an x without a number in front of it, it becomes 1x. In this problem, that is why it is a -3x because -3 x 1 is -3

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Answer:

slope = - \(\frac{1}{4}\)

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (3, - 5) and (x₂, y₂ ) = (7, - 6)

m = \(\frac{-6-(-5)}{7-3}\) = \(\frac{-6+5}{4}\) = - \(\frac{1}{4}\)

On looking for a pattern in the given data set, the quadratic model best describes the data.

2nd option is correct.

A data model represents the type of relationship between the variables of a data set.

Data models are of four types, namely, Linear, Cubic, Quadratic and Exponential data models.

Given data is:

Distance Traveled                      Average Speed(miles per hour)

(miles)

1                                                                7

2                                                               6.3

3                                                              5.67

4                                                              5.103

A quadratic model is the best data model for the given data set.

The pattern observed in the given data set observes the properties of a quadratic function.

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Answer:

Exponential is the correct answer.

Step-by-step explanation:

Answer:

so 15 hour for the 100 to become 200 and then it will become 400 in another 15 hours. but we need to find the time for 300 so it will take half of 15 hours

+ 15 hours for it to become 300 cells which is: 7 1/2 + 15 = 22 hours and 30 minutes

Step-by-step explanation:

answer from gauth math

Answer:

22 hours and 30 minutes

Step-by-step explanation:

The number of each type of ad that the department can run each month are:

TV Ads = 32

Radio Ads = 12

News Ads =  20

x = number of tv ads

y = number of radio ads

z = number of news ads

Two formulas are indicated.

x + y + z = 64

1000x + 200y + 600z = 46400

they want as many tv ads as radio and news ads combined.

equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 64

1000 * (y + z) + 200 * y + 600 * z = 46400

combine like terms and simplify to get:

2y + 2z = 64

1000y + 1000z + 200y + 600z = 46400

combine like terms again to get:

2y + 2z = 64

1200y + 1600z = 46400

Solving simultaneously gives:

y = 12

z = 20

Thus:

x = 12 + 20

x = 32

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Step-by-step explanation:

Answer:

2983839i8

468393749493948

Hsjejrhrjjh4u4i84748394

Je83847483

373783838383884

373838383

Jkffffffffffffffffffffffffffffdddfddfffffffddddddddddddddddddfffffffffffffffffffffffffff

Answer:

  see attached

Step-by-step explanation:

You want the graph of the circle defined by the equation ...

  (x-2)^2 + (y-7)^2 = 4.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Comparing this to the given equation, we see ...

  h = 2, k = 7, r² = 4

Then r = √4 = 2.

The circle will have its center at (2, 7) and will have a radius of 2. It is shown in the attached graph.

<95141404393>