bens owns two cars, car 4 and car B. This year, car A is 9 years old and car B is x years old. 5 years ago, the ratio of the age of car 4 to the age of car B was 2:5 Calculate the value of x.​

The diameter of the circle C/13

The formula provides the circumference of a circle.

The circumference of any shape in mathematics designates the path or limit that surrounds the shape. In other words, the circumference, sometimes referred to as the perimeter, aids in figuring out how long the contour of a shape is. The size and perimeter of a circle are, as we all know, its two most important properties.

C = pi * d, where d is the diameter and c is the circumference.

C = pi * 13 gives the diameter as 13.

Subtract 13 from each side, C/13 = d.

Dimensions are C/13.

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Given:

To determine the local maximum and the local minimum of the given equation, we check the graph first as shown below:

We also note that local maximum and minimum points on a function's graph stand out rather noticeably, making them helpful for interpreting the graph's overall shape. The points of the functions that define the maximum and minimum range are local maximum and minimum.

As we can see, the point that has the minimum range is at point (4,-310), while the point that has the maximum range is at point (8,-246).

Therefore, this function has a local minimum point at x=4 with value equal to -310 and a local maximum at x=8 with value equal to -246.

Answer:

Apple Cost: $1.10

Orange Cost: $1.05

Three oranges and two apples cost: $5.35

Step-by-step explanation:

Answer:

35 times, or D

Step-by-step explanation:

A bag contains 5 red marbles, 6 blue marbles, 3 green marbles, 4 black marbles, and 2 yellow marbles. A marble will be drawn from the bag and replaced 100 times. What is a reasonable prediction for the number of times a green or black marble will be drawn?

A quick lesson on probability:

The probability of an event is: (the number of ways what you want can happen) / (total number of outcomes possible). For example, in a coin flip, there is 1 way to get heads, and 2 possible outcomes. Thus, the possiblity  of flipping a coin and getting heads is:

(1 way to get heads) / (2 possible outcomes) = 1/2

Then, if we were to flip the coin 100 times, we would expect about 1/2 of the times to be heads, so we should expect heads 50 times.  

On to the problem.

There are 3 green marbles and 4 black marbles, so there are 7 ways to draw a green or black marble.

Then, there are 5 + 6 + 3 + 4 + 2 = 20 possible outcomes.

Using the formula to find the probability, substitute the values we just found.

(the number of ways what you want can happen) / (total number of outcomes possible) =

(7 ways to draw a green or black marble) / (20 marbles that can be drawn) = 7/20 chance of getting a green or black marble.

Then, because there is a 7/20 chance of getting what we want, and there are 100 draws, we can say that an we should get green or black

7/20 * 100 = 35 times, or D

Feel free to ask any questions! :)

Answer:

The first one

\( log_{11} \: (x)\)

Step-by-step explanation:

f(x) = 11^x

Here are the steps to find the inverse of a function:

1. Let f(x)=y

2. Make x the subject of formula.

3. Replace y by x.

\(11 {}^{x} = y \\ \: log(11 {}^{x} ) = log(y) \\ x log(11) = log(y) \\ x = \frac{ log(y) }{ log(11) } = log_{11}(y) \\ f {}^{ - 1} (x) = log_{11}(x) \)

The pitch of a gear with 44 teeth and a pitch diameter of 12.5714 inches is approximately 3.5 inches.

In gear terminology, the pitch is a measure of the distance between corresponding points on adjacent teeth. It is typically denoted by the symbol P. The pitch can be calculated using the formula P = N / D, where N is the number of teeth on the gear and D is the pitch diameter of the gear.

Given the gear has 44 teeth and a pitch diameter of 12.5714 inches, we can calculate the pitch as follows:

P = N / D

P = 44 / 12.5714

P ≈ 3.5

Therefore, the pitch of the gear is approximately 3.5.

The pitch value indicates that for every revolution of the gear, the distance between corresponding points on adjacent teeth is approximately 3.5 inches. This information is crucial when designing gear systems, as it determines the compatibility and engagement of gears within a system.

The pitch value is an essential parameter in gear design and selection. It allows engineers to ensure proper gear meshing and avoid issues such as gear slipping or misalignment. By matching the pitch values of gears within a system, the rotational motion can be effectively transferred, ensuring smooth and efficient operation.

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Answer:

Step-by-step explanation:

formula of volume of cone is given so u simply substitute the values given and calculate.

Work is done for u .

Hope this helps u

The charted values that originate in a worksheet are called Chart Data Sources.

Charted values that originate in a worksheet are called Chart Data Sources. Chart Data Sources refer to the source data used to construct a chart in a spreadsheet program like Microsoft Excel. This data is usually contained in the worksheet cells and ranges used to plot the chart. The chart will then be updated as the data changes in the spreadsheets. Chart Data Sources can also refer to external data sources like databases, text files, or web services.

Therefore, the charted values that originate in a worksheet are called Chart Data Sources.

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The expression 3 ln x + 5 ln y - 6 ln z can be written as a single logarithm: ln(x^3 y^5/z^6).

Explanation:

Using the logarithmic identity ln(ab) = ln(a) + ln(b), we can combine the terms of the expression:

3 ln x + 5 ln y - 6 ln z = ln(x^3) + ln(y^5) - ln(z^6)

Using another logarithmic identity ln(a/b) = ln(a) - ln(b), we can simplify further:

ln(x^3) + ln(y^5) - ln(z^6) = ln(x^3 y^5/z^6)

Therefore, the expression 3 ln x + 5 ln y - 6 ln z can be written as a single logarithm ln(x^3 y^5/z^6).

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The rate at which the area of the Rectangle is changing at the instant when the other side is 13 cm and increasing at 3 cm per minute is approximately -1.385 cm/min. Note that the negative sign indicates that the width is decreasing

To find how fast the area of the rectangle is changing, we can use the formula for the derivative of the area with respect to time. Let's denote the width of the rectangle as x (in cm) and the length as y (in cm). We are given that x = 6 cm and dy/dt = 3 cm/min. We want to find dx/dt, the rate at which the area is changing.

The area of a rectangle is given by A = x * y. Taking the derivative of both sides with respect to time t, we have:

dA/dt = (d/dt)(x * y)

To solve for dA/dt, we need to express y in terms of x. We know that the length y is increasing at a rate of dy/dt = 3 cm/min. Therefore, we can write:

dy/dt = 3 cm/min

dy = 3 dt

dy/dt = 3

Now, we can differentiate the area equation with respect to time:

dA/dt = x * (dy/dt) + y * (dx/dt)

Substituting the given values:

dA/dt = 6 * 3 + 13 * (dx/dt)

Since we are interested in finding dx/dt, we can rearrange the equation:

dx/dt = (dA/dt - 6 * 3) / 13

Now, let's plug in the given values and calculate the rate at which the area is changing:dx/dt = (dA/dt - 6 * 3) / 13

dx/dt = (0 - 6 * 3) / 13

dx/dt = -18 / 13

Therefore, the rate at which the area of the rectangle is changing at the instant when the other side is 13 cm and increasing at 3 cm per minute is approximately -1.385 cm/min. Note that the negative sign indicates that the width is decreasing

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The area of the rectangle is increasing at a rate of 18 cm^2 per minute when the other side is 13 cm and increasing at 3 cm per minute.

Let's use the formula for the area of a rectangle: A = lw, where A is the area, l is the length, and w is the width.

Since one side of the rectangle is fixed at 6 cm, we can express the area as a function of the other side w: A(w) = 6w.

The rate of change of the area with respect to time is given by the rectangle of A with respect to time t:

dA/dt = d/dt (6w) = 6 dw/dt

We also know that the width is increasing at a rate of 3 cm per minute, so dw/dt = 3 cm/min.

At the instant when the other side is 13 cm, the width of the rectangle is w = 13 cm. Therefore, the rate of change of the area at that instant is:

dA/dt = 6 dw/dt = 6(3) = 18 cm^2/min.

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Answer: B. XIX

Step-by-step explanation: If Sarah is 3 years older than Ben, she is 3 years older than 16. That means she is 19 years old. In Roman numerals, we need to think of it as she is 10+9 years old.

X represents 10.

IX represents 9 Because...

... in order to represent a number less than ten, we need to think about how much less than ten it is. Since 9 is one less than 10, you write it as IX since a smaller numeral in front of X represents subtraction.

So you combine the 10 and 9 to get XIX.

The data set of the sample is

62 82 79 76 73 70 67 64 61 66 66 66 63 63 63 60 60 71 71

we have that

(84.5-59.5)/5=5

therefore

The classes are equal to

N 1) 59.5-64.5 ------> midpoint 62

N2) 64.5-69.5 -----> midpoint 67

N3) 69.5-74.5 -----> midpoint 72

N4) 74.5-79.5 -----> midpoint 77

N5) 79.5-84.5 -----> midpoint 82

Find out the frequency for each class

N 1) 59.5-64.5 ------> 8

N2) 64.5-69.5 ----->4

N3) 69.5-74.5 ----> 4

N4) 74.5-79.5 ------> 2

N5) 79.5-84.5 ----> 1

see the figure below to better understand the problem

Answer:

  6x -18

Step-by-step explanation:

Use the distributive property to eliminate parentheses. Then combine like terms.

  2x -6 +4(x) +4(-3) . . . . distribute the multiplier 4

  2x +4x -6 -12 . . . . . group like terms together

  6x -18

To solve this problem, we have to use the combination formula

Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have

Remember that factorials are solved by multiplying the number in a reversal way, as follows

Answer:

4n^2

Step-by-step explanation:

n to the power of 2 (squared), multiplied by 4

\(4n^{2}\)

An algebraic expression is one that is constructed using integer constants, variables, and algebraic operations.

Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.

Square of \(n=n^{2}\)

Four times the square of \(n^{2}\) is equal to \(4n^{2}\)

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Answer:

2

Step-by-step explanation:

Five and above, round up. Four and below, round down.

Answer:

2

Step-by-step explanation:

anything less then five is rounded down anything above 5 is rounded to the higher number

Answer:

(x + 1)² = 4(y + 10)

Step-by-step explanation:

Equation of parabola:

(x - h)² = 4a(y - k)

with vertex(h, k) and focus (h, k + a)

vertex(h, k) = (-1, -10)

⇒h = -1 and k = -10

focus (h, k + a) = (-1, -9)

⇒ k + a = -9

⇒ -10 + a = -9

⇒ a = 10 - 9

⇒ a = 1

Equation of parabola:

(x - h)² = 4a(y - k):

(x - (-1))² = 4(1)(y - (-1))

= (x + 1)² = 4(y + 10)

there are 128 different bit strings of length 7. To calculate the number of bit strings of length 7, we need to consider that each position in the bit string can either be 0 or 1.

Since there are 7 positions in the string, we have 2 options (0 or 1) for each position. Therefore, the total number of bit strings of length 7 is 2^7 = 128.To calculate the number of bit strings of length 7 that start with 0110, we need to fix the first four positions as 0110. The remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that start with 0110 is 2^3 = 8.

To calculate the number of bit strings of length 7 that contain the string 0000, we need to consider the possible positions for the string 0000. It can occur in five different positions: at the beginning, at the end, or in any of the three middle positions. For each position, the remaining three positions can have either 0 or 1, giving us 2 options for each position. Therefore, the total number of bit strings of length 7 that contain the string 0000 is 5 * 2^3 = 40. However, we need to subtract the cases where the string 0000 occurs in both the beginning and end positions, as they were counted twice. So, the final answer is 40 - 24 = 16.

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Answer:

21

Step-by-step explanation:

Because h(3) times h(7) is equal to 21.

Hope it helps!

The error represented in this scenario is an inappropriate task allocation or a mismatch between job responsibilities and the assigned task during the interview process.

The primary role of a customer service representative is to interact with customers, address their concerns, and log calls professionally and efficiently. In contrast, performing a detailed analysis of call-in data falls under the domain of data analysis or business intelligence roles.

By asking the candidate to perform a task unrelated to their potential job responsibilities, the company may not accurately assess the candidate's aptitude for customer service tasks. This error could lead to selecting a candidate who may excel in data analysis but may not possess the necessary communication and problem-solving skills required for a customer service representative position.

To avoid this error, the company should focus on evaluating candidates based on their skills, experience, and performance in tasks directly relevant to the customer service role.

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Answer:

y=29

x=9

Step-by-step explanation:

plug the first equation into the second one as y

2x+y=47

solve

then plug answer u got in x

y=3(9)+2

solve

Using the system of equation, the unit cost of candy and pretzel are $3 and $4.25 respectively

System of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns.

We can set up two different equations to represent the problem given;

Let candies = x, pretzels = y

3x + 2y = 17.50 ...eq(i)

9x + 4y = 44 ...eq(ii)

Solving for equation (i) and (ii);

The value of x and y are 3 and 4.25 respectively.

The cost of the candy is $3 and pretzel is $4.25

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The correct answer is:

b. Test statistic: t = -1.841

Critical value = ±2.045

Do not reject H0

To conduct the hypothesis test using the pooled t-test, we compare the calculated test statistic to the critical value at a significance level of α = 0.05.

Given the following statistics for two independent samples:

Sample 1: x1 = 11.1, s1 = 4.5, n1 = 14

Sample 2: x2 = 17.2, s2 = 4.9, n2 = 17

The pooled t-test assumes that the population variances are equal. We calculate the pooled standard deviation (sp) using the formula:

sp = sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1 + n2 - 2))

Next, we calculate the test statistic (t) using the formula:

t = (x1 - x2) / (sp * sqrt(1/n1 + 1/n2))

For the given data, the calculated test statistic is t = -3.577.

To determine whether to reject or fail to reject the null hypothesis (H0), we compare the absolute value of the test statistic to the critical value from the t-distribution at a significance level of α = 0.05. In this case, the critical value is ±1.699.

Since the absolute value of the test statistic (-3.577) is greater than the critical value (1.699), we do not reject the null hypothesis (H0). Therefore, the correct answer is c. Test statistic: t = -3.577, Critical value = ±1.699, Do not reject H0.

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Answer:

I think your answer would be B. let me double check

Answer:

(B)

Step-by-step explanation:

Let  us denote rectangular tiles by R and square tile by S, then

According to figure.

3 rectangular tiles +2 square tiles +2 square tiles =2 rectangular tiles +4 square tiles +1 rectangular tiles +4 square tiles

∴3R+2S+2R=2R+4S+R+4S

⇒5R+2S=3R+8S

⇒5R-3R=8S-2S

⇒2R=6S

⇒R=3S

Hence, 0ne rectangle =3 square

Answer:

In analytic geometry, using the common convention that the horizontal axis represents a variable x and the vertical axis represents a variable y, a y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system. As such, these points satisfy x = 0.

Step-by-step explanation:

Answer:

9x - 54 = 18            x = 8

Step-by-step explanation:

54 less than 9 times x is 18

lets work backwards to solve this one.

We know that the entire eqation is equal to 18. We also know that 9 will be multiplied to x and that 54 will be taken from that.

 18   =   9x   -   54

+54               +  54

 72  =  9x

 72/9 = x

   8  =  x

The correct answer is:

c. The z-value for a standard normal distribution can be either positive or negative.

The z-value, also known as the standard score, measures the distance between a data point and the mean of its distribution in units of standard deviation. It is calculated by subtracting the population mean from the data point and then dividing the result by the standard deviation.

Since the mean of a standard normal distribution is zero, the z-value simply represents the number of standard deviations a data point is from the mean. As a result, the z-value can be either positive or negative, depending on whether the data point is above or below the mean, respectively.

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An appropriate statement of the null hypothesis, H₀ is that: A. The proportion of contaminated wrist-watches from medical personnel is the same as the proportion of contaminated wrist-watches from security guards, i.e., H0: p = 46.6%.

In Mathematics, a null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (Ha) and it asserts that two (2) possibilities are the same.

For an experiment to test the contamination of medical personnel wrist-watches at a New York hospital, the appropriate null hypothesis and alternative hypothesis would be given by this mathematical expression:

H₀: p = 10.

Ha: p < 10.

In this context, we can logically that the proportion of contaminated wrist-watches would be the same for both sample proportion i.e., H₀: p = 46.6%.

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Answer:

d. 10

Step-by-step explanation:

trust me its right