If x varies inversely as y and x=16 when y=5, find x when y=20.

Answers

Answer 1

9514 1404 393

Answer:

  x = 4

Step-by-step explanation:

The inverse variation means that when y goes up by a factor of 20/5 = 4, the value of x goes down by the same factor.

  x = 16/4

  x = 4


Related Questions

For the following right triangle, find the side length x , round to the nearest hundredth.

Answers

Answer: 14.9

Step-by-step explanation:

Pythagoras Theorem States that for any right angled triangle.

a ^ 2 + b^2 = c ^2.

a = 10

b = 11

x = unknown

x^2 = a ^ 2 + b^2

x^2 = (10 * 10) + (11 * 11)

x = sqrt(100 + 121)

x = sqrt(221)

x = 14.9

John started a home delivery service from several local restaurants. He charges a $5 tip on the delivery, plus $0.75 for every mile he travels.

Write an equation for the function that relates the total cost of a trip to the distance.

Answers

Answer:

y = total cost

x = mile

y = 5 + 0.75x

Step-by-step explanation:

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Answer: y = 5 + 0.75x

Step-by-step explanation:

How can you find 50% of a number quickly in your head?

Answers

Answer:

Divide by 2

Step-by-step explanation:

Calculate the standard deviation of the following set of numbers. Use the formula for the standard deviation (s) shown, where x represents the values, n is the number of values, and is the summation symbol, which indicates that you should add the values. S = mon-1) (* {x? - (Ex)}) values: Xı = 13,X2 = 16, x3 = 10 Do not round your answers. Step 1. Calculate the square of each data value. Step 2. Determine n times the sum of squares of the three values. 1 Step 3. Calculate the sum of the three values. Step 4. Calculate the square of the sum of the three values. ηΣ x2 = Step 3. Calculate the sum of the three values. Σx= Step 4. Calculate the square of the sum of the three values. Step 5. Calculate the variance. (n-1) (»« - (Ex)")= Step 6. Calculate the standard deviation. 1 nin – 1) (»Ex2 - (2 x)") =

Answers

The standard deviation is 3.

What is standard deviation?

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Given, formula for the standard deviation

s = √[1/n(n-1)](n∑x²-(∑x)²)

values: x₁ = 13, x₂ = 16, x₃ = 10

step1: Calculate the square of each data value.

x₁² = 13² = 169

x₂² = 16² = 256

x₃²= 10² = 100

step2: Determine n times the sum of squares of the three values.

n∑x² = n(x₁²+x₂²+x₃²)

=3(169+256+100) = 1575

step3: Calculate the sum of the three values.

∑x = x₁+x₂+x₃

= 13+16+10 =39

step4: Calculate the square of the sum of the three values.

(∑x)² = 1521

step5: Calculate the variance.

[1/n(n-1)](n∑x²-(∑x)²)

=[1/3(3-1)](1575-1521)

=54/6

=9

step6: Calculate the standard deviation.

√[1/n(n-1)](n∑x²-(∑x)²)

= √9

=3

Hence, The standard deviation using the given formula for x₁=13, x₂=16 and x₃=10 is 3.

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A random sample of 55 standard hotel rooms in the Philadelphia area has a mean nightly cost of $154.17. From previous studies, it has been found that the standard deviation of the price of all hotel rooms in Philadelphia is $38.60. Construct a 99% confidence interval for the population mean cost . Round to the nearest penny. Show work below . (5 points )

Answers

The 99% confidence interval for the population mean cost is 38.37 to 269.97.

What is confidence interval?

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

Given that the standard hotel rooms in the Philadelphia area has a mean nightly cost of $154.17.

The standard deviation of the price of all hotel rooms in Philadelphia is $38.60.

According to the empirical rule,

P(μ - 3σ ≤ X ≤ μ - 3σ) = 99%.

Here μ = 154.17 and σ = 38.60.

Calculating the confidence interval:

154.17 -  (3 × 38.60) ≤ X ≤ 154.17 + (3 × 38.60)

38.37 ≤ X ≤ 269.97

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If a random variable that is normally distributed has a mean of 25 and a standard deviation of
3, convert the given value to a z-score.
a. x = 23
b. x = 33
c. x = 19
d. x = 45

Answers

Answer:

Step-by-step explanation:

To convert a value to a z-score, you need to subtract the mean and divide by the standard deviation. Here is how to convert each value to a z-score:

a. x = 23: (23 - 25) / 3 = -0.67

b. x = 33: (33 - 25) / 3 = 2.33

c. x = 19: (19 - 25) / 3 = -1.67

d. x = 45: (45 - 25) / 3 = 6.67

Therefore, the z-scores are -0.67, 2.33, -1.67, and 6.67 for values a, b, c, and d respectively.

What is the common ratio of the geometric sequence?

Number graph ranging from zero to ten on the x axis and zero to twenty-eight on the y axis. Points are plotted on the graph at (one, eight), (two, twelve), (three, eighteen) and (four, twenty-six point five). The points form a general positive trend.

Answers

A geometric series is one in which there is a constant between two successive numbers in the series.

What is geometric progression?

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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Differentiate with respect to x
a) 2 + sin x​

Answers

Answer:

cos x

Step-by-step explanation:

d( 2 + sin x )/DX

= d( 2 )/dx + d( sin x )/dx

= 0 + cos x

= cos x

Note : -

Differentiation of any number with respect to any variable ( here x ) is 0.Differentiation of sin x is cos x.d/dx is the notation to denote Differentiate with respect to x.

A fisherman is measuring the amount of bait he has remaining, y, in his bucket he puts 20 peices of bait in his bucket at the beginning of his fishing trip and uses 2 pieces every hour, x.

What is the slope for this linear relationship and what does it mean in this situation?

A. -2; the amount of bait decreases by 2 pieces each hour
B. 2; the amount of bait increases by 2 pieces each hour
C. -20; the amount of bait in the bucket when the fishing trip began
D. 20; the amount of bait in the bucket when the fishing trip began​

Answers

Answer:

A

Step-by-step explanation:

bait left = 20 - 2x     where x = hours      slope = -2   answer A

URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!

Answers

The only number set that includes only rational numbers is {-4/5, 0, 0.121314.., 97/3}. All of the other number sets include at least one irrational number.

In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by A. Delta y = f(x_1 + x_1, x_2, ....., x_k) - f(x_1, x_2, ... x_k). B. Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k). C. Delta Y = f(x_1 + Delta x_1, x_2 + Delta x_2, ...., x_k + Delta x_k) - f(x_1, x_2, ...., x_k). D. Delta Y = f(x_1 + x_1, x_1, .... x_k).

Answers

The expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).

Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.

To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.

The cause is the independent variable. Its value is unaffected by the other study variables.

The effect is the dependent variable. Changes in the independent variable affect its value.

A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.

Dependent variables are also referred to as:

.response elements (they respond to a change in another variable)

.outcome factors (they represent the outcome you want to measure)

.Left-side parameters

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The expected change in the dependent variable for a change in one of the explanatory variables in a nonlinear model is given by Delta Y = f(x_1 + Delta x_1, x_2, ...., x_k) - f(x_1, x_2, .... x_k).

Any attribute that can have different values, such as height, age, temperature, or test results, is referred to as a variable in research.

To assess the causality of relationships, researchers frequently modify or measure independent and dependent variables in studies.

The cause is the independent variable. Its value is unaffected by the other study variables.

Effect is the dependent variable. Changes in the independent variable affect its value.

A dependent variable is one that is altered as a result of the modification of an independent variable. Your independent variable "depends" on the outcome you're interested in measuring.

Dependent variables are also referred to as:

.response elements (they respond to a change in another variable)

.outcome factors (they represent the outcome you want to measure)

.Left-side parameters

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Solve: 2x - 3= 2x - 5

A infinitely many solutions
B no solution
C 5/3
D 0
E -2

Answers

When solving you will get -3=-5

Therefore it’s false

Option B [no solution]

Write x² + 10x + 29 in the form (x + c)² + d, where c
and d are numbers.
What are the values of c and d?

Answers

Answer:Write x² + 10x + 29 in the form (x + c)² + d, where c

Step-by-step explanation:

Answer:

(x+5)² + 4, so c is 5 and d is 4

Step-by-step explanation:

x² + 10x + 29 is a quadratic equation which can be witten as x² + bx + c, where b is 10 and c is 29.

We need to complete the square to get it in the form

(x + c)² + d

Completing the square uses the form:

[tex](x + \frac{b}{2} ) {}^{2} - ( \frac{b}{2} ) {}^{2} + c[/tex]

substitute b = 10 and c = 29 in this form:

[tex](x + \frac{10}{2}) {}^{2} - ( \frac{10}{2} ) {}^{2} + 29[/tex]

Simplify further:

[tex](x + 5) {}^{2} - 25 + 29[/tex]

[tex](x + 5) {}^{2} + 4[/tex]

c = 5, d = 4

Answer and explain your answer.

Answers

With the help of Geometry We would make Australia 200 miles more wider.

What is geometry?

Geometry is a branch of mathematics that is concerned with the study of shapes, sizes, and relative positions of figures and the properties of space. It is one of the oldest branches of mathematics that has been around for centuries and is still relevant today. Geometry is used to explain many aspects of our lives, from the size of buildings and bridges to the path of a baseball in flight. It is a powerful tool for problem solving and understanding the world around us. Geometry is based on axioms, or accepted truths, that are used as the basis for forming logical proofs. These proofs are used to develop theorems and formulas which help us to understand and explain our world.

We would make Australia 200 miles more wider too or just give 200 miles long US to some other country to make their sizes equal.

Hence, we would make Australia 200 miles more wider

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NO LINKS!!
You are offered two jobs selling textbooks. One company offers an annual salary of $42000 plus a year-end bonus of 1% of your total sales. The other company offers an annual salary of $30000 plus a year-end bonus of 2.5% of your total sales. How much would you have to sell in a year (in dollars) to make the second offer the better offer?

Total sales would need to be greater than $

Answers

Answer:

At $800,000 of sales the offers are equal.  Anything over 800,000 makes the second deal a better deal.

Step-by-step explanation:

Let y equal the total money earned.

Let x equal the total sales.

y = .01x + 42000

y = .025x + 30000  Set these two equations equal to each other.

.01x + 42000 = .025x + 30000  Subtract .01x  from both sides

.01x -.01x + 42000 = .025x - .01x + 30000

42000 = .015x + 30000   Subtract 30000 from both sides

12000 = .015x   Divide both sides by .015

[tex]\frac{12000}{.015}[/tex] = [tex]\frac{.015x}{.015}[/tex]

800,000 = x

Answer:

job 1 , y = 42 000 + 0.01x

job 2 , y = 30 000 + 0.025x

42 000 + 0.01x < 30 000 + 0.025x

42 000 - 30 000 < 0.025x - 0.01x

12 000 < 0.015x

x < 800 000

You need to make total sales of more than $800 000 to make the second offer better.

example of u get 900 000 total sales

42 000 + 0.01(900 000) < 30 000 + 0.025(900 000)

42 000 + 9000 < 30 000 + 22 250

51 000 < 52 500

Therefore, you need to make a total sales of more than $800 000.

Step-by-step explanation:

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At 2 p.m., two cars leave Eagle River, WI, one headed north and one headed south. If the car headed north averages 45 mph and the car headed south averages 40 mph, when will the cars be 170 miles apart?​

Answers

The time at which the two cars will be 170 miles apart is; 1.619 hours

How to solve Algebra Word Problems?

Let us write an equation for each car as;

d₁ = r₁*t₁ (northbound)

d₂ = r₂*t₂ (southbound)

They both start at the same time, and will stop them both when they are 170 miles apart. Thus;

t = d₁/r₁

t = d₂/r₂

Thus, the equation to find their times is;

d₁/r₁ = d₂/r₂

d₁ = d₂r₁ /r₂

Thus;

d₁ + d₂ = 170

d₁ = 170 - d₂

Similarly, r₁ = 45 mph and r₂ = 40 mph

170 - d₂ = d₂(45/60)

4(170 - d₂) =3d₂

7d₂ = 680

d₂ = 680/7

d₂ = 97.143 miles

d₁ = 170 - 97.143

d₁ = 72.857 miles

t₁ = d₁/r₁ = 72.857/45 = 1.619 hours

This represents the time that they will be 170 miles apart

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Given f(x) = -x - 5 find f (0)

Answers

Answer: f(0)=-5

Step-by-step explanation:

f(0) means that x = 0

sub in 0 into the equation

f(0)=-0-5

f(0)=-5

Answer:

f(0) = -5

Step-by-step explanation:

Given f(x) = -x - 5

In order to find f(0), you need to replace x with 0

so f(0) = -(0) - 5

f(0) = -5

Please show me how to solve this problem?

Answers

Answer:

I think you forgot to show us the problem

Please Help!!

Jamie and Hudson took a road trip to the beach. Their total distance traveled after getting on the highway can be found using the function d(h)=55h+10, where h is the number of hours they have been driving on the highway.

1) Explain why the relationship between total distance and hours is a function.

2) Is this function continuous or discrete? Explain how you know.

3) If the girls can drive a maximum of 8 hours, what is the domain for the function? Explain your answer.

4) If the girls can drive a maximum of 8 hours, what is the range for the function? Explain your answer.

5) Create a graph that models this function. Be sure to include a title and to label your x- and y-axis with the variable names, not just x and y.

6) What is the slope of the function? What does it represent?

7) What is the y-intercept? What does it represent?

Answers

The total distance is an illustration of a linear function.

(1) Why the relationship is a function

The relationship is a function because all input values of h, have exactly one corresponding output value of d

(2) The function type

The function is a discrete function, because the number of hours is an integer, and it cannot take decimal values (in this case)

(3) The domain for a drive of 8 hours

The domain is the set of time the girls drive.

So, the domain is: [0,8]

(4) The range

The function is given as:

d= 55h + 10

When h = 0,

d = 55(0) + 10 = 10

When h = 8,

d =  55(8) + 10 = 450

So, the range is: [10,450]

(5) The graph

Sorry

(6) The slope

A linear function is represented as:

y = mx + c

Where:

m represents the slope.

So, by comparison:

Slope = 55

The slope in this case represents the distance travelled per hour

(7) The y-intercept

In (6) above, c represents the y-intercept.

So, by comparison:

c = 10

The y-intercept in this case represents the initial distance

The trip to Australia is in six months how much does she need to save each month to make her go of $2,370.00?

Answers

Answer:

2 370 / 6 = 395

She need to save $395 per month

Step-by-step explanation:

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A rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. Another agency charges $18 per day plus 8 cents per mile to rent the same car. How many miles will have to be driven for the cost of the car from the first agency to equal the cost of a car from the second agency?

Answers

If a rental car agency charges $15 per day plus 11 cents per mile to rent a certain car. The number of  miles you have to be driven for the cost of the car from the first agency to equal the cost of a car from the second agency is 100 miles.

How to find the number of miles:

First step is to set the equation that will be used to find the number of miles

Equation

15+.11x=18+.08x

So,

Number of miles

15+.11x=18+.08x

Collect like terms

.03x=3

Divide both side by  0.03

x=3/.03

x =100 miles

Therefore we can conclude that the number of miles is 100 miles.

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I do not understand what is going on for this question

Answers

(x,y,z)=(19,14,3)

What is equation matrix and vector?This means that by dividing the inverse of the A matrix by the B matrix, we may calculate the values of x, y, and z (the X matrix).An arrangement of numbers, occasionally expressions and symbols, in rows and columns is called a matrix. Quantum mechanics, optics, mathematics, and other mathematical functions are all solved using matrix formulas.It's not nearly as difficult as it sounds; all you have to do is multiply the rows by the columns and add up the components.In geology, seismic surveys are carried out using matrix technology. They are employed in the production of graphs, statistics, calculations, and scientific investigations and research in a range of fields.A matrix is a collection of numbers, while a vector is a list of numbers that can be in either a row or a column (one or more rows, one or more columns).

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4. The wholesale price of a commodity for seven consecutive days in month is as follows: Days: 2 3 4 5 6 7 1 260 270 245 255 286 264 Commodity Price: 240 Calculate variance and standard deviation. 5. Calculate the standard deviation and variance from the following frequency distribution X: 10 12 14 16 18 20 22 F: 3 5 9 16 8 7 2 6. 6.Calculate Standard Deviation from the following Distribution C.I.: 10-20 20-30 30-40 40-50 50-60 60-70 70-80 8 Freq: 4 8 16 12 6 4

Answers

The variance is 206 and standard deviation is 14.353.

In the given question, we have to find the standard deviation and variance from the following frequency distribution X.

Days:                          1         2         3         4         5         6         7

Commodity Price:    240    260    270    245     255     286    264

x                                (x-X)                             (x-X)^2

240                    (240-260) = -20                   400

260                    (260-260) = 0                        0

270                    (270-260) = 10                      100

245                    (245-260) = -15                     225

255                    (255-260) = -5                      25

286                    (286-260) = 26                     676

264                    (264-260) = 4                        16

Total = 1820                                                    Σ(x-X)^2 = 1442

X = Total of x/total number

X = 1820/7

X = 260

Variance = Σ(x-X)^2/n

Variance = 1442/7

Variance = 206

Standard Deviation = √(Variance)

Standard Deviation = √206

Standard Deviation = 14.353

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Find the measure of triangle ABD from given figure

Answers

You didn’t give a figure ?

-\sqrt(16x^(2)) if x<0

Answers

Therefore ,  [tex]-4|x|[/tex]   is the square root of [tex]-\sqrt{16x^{2} }[/tex]

what is square root?

When a number is multiplied by itself, the result is known as the square root of the number. To represent the square root, use the radical symbol. For illustration, [tex]\sqrt[/tex]16 = 4. Another name for the radical sign is the root symbol or surds.

given

- [tex]\sqrt{16x^{2}[/tex] when [tex]x[/tex] < 0,

In order to solve the given expression we will take the square root of the term inside the root.

Perfect squares (squares of integers) make up the word in the square root, thus we can express it as a square of the numbers.

⇒  [tex]-\sqrt{(4x)^{2} }[/tex]    [ as [tex](4x)^{2}[/tex] = [tex]16x^{2}[/tex]]

On taking square root the square gets removed. So, we have,

[tex]-|4x|[/tex]  =[tex]-4|x|[/tex]

Since , so the value would be negative.

Therefore , [tex]-4|x|[/tex] is the square root of [tex]-\sqrt{16x^{2} }[/tex]

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Write 0.006655 in scientific notation

Answers

Answer: 6.655 * 10^-3

Step-by-step explanation:

0.006655 in scientific notation

6.655 × 10³

What is the product of (-4)(16) (-7)
A-108
B -71
C 57
D 448

Answers

Answer:

D 448

multiply -4×16×-7

= 448

A new cure has been developed for a certain type of cement that should change the mean compressive strength.It is known that a standard deviation is 130 kg/cm2and we may assume normal distribution. 9 pieces of cementhave been tested and the observed sample mean is ¯X= 4970. Find the 95% confidence interval for the mean.
(a) [4858.37,5081.63] (b) [4885.07,5054.93] (c) [4858.37,5054.93]
(d) [4944.52,4995.48] (e) [4858.37,5054.93]

Answers

(a) The 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.

(b) The 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.

a) We have to find the 95% confidence interval for the mean of the compressive strength.

we are given

x = sample mean = 4970

n = sample size = 9

σ = population standard deviation = 130

The 95% confidence interval for population mean is

x - Z​​​​​​a/2*(σ/√n) < μ < x + Z​​​​​​a/2*(σ/√n)

For a = 0.05 Z​​​​​​a/2 = Z​​​​​​0.025 = 1.96

4970 - 1.96*(130/√9) < μ < 4970 + 1.96*(130/√9)

4885.1 < μ < 5054.9

Hence, the 95% confidence interval for the mean of the compressive strength is 4885.1 < μ < 5054.9.

b) We have to find the 95% confidence interval for the mean of the compressive strength.

Since the population's standard deviation is unknown in this instance, the population mean's t confidence interval is used.

From the data n = 9

X = sample mean = 4993.8

s = sample standard deviation = 24.2

For a= 0.05 and degree of freedom = n -1 = 8

t​​​​​​a/2 , n-1 = t​​​​​​0.025,8 = 2.306

x - t​​​​​​a/2*(s/√n) < μ < x + t​​​​​​a/2*(s/√n)

4993.8 - 2.306*(24.2/√9) < μ < 4993.8 + 2.306*(24.2/√9)

4975.2 < μ < 5012.4

Hence, the 95% confidence interval for the mean of compressive strength is 4975.2 < μ < 5012.4.

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The complete question is:

A new cure has been developed for a certain type of cement that should change its mean compressive strength.

a) It is known that the standard deviation of the compressive strength is 130 kg/cm^2 and that we may assume that it follows a normal distribution. 9 chunks of cement have been tested and the observed sample mean is X = 4970. Find the 95% confidence interval for the mean of the compressive strength.

b) Now, assume that we do not know the standard deviation of the normal distribution. 9 chunks of cement have been tested, and the measurements are 5001, 4945, 5008, 5018, 4991, 4990, 4968, 5020, 5003. Find the 95% confidence interval for the mean of the compressive strength.

A dog allergy test for people has a 98% accuracy rate. Only one percent of the population has an allergy to dogs actually it is much smaller than that. Use a group of 100,000 people who have taken the test and the information provided to complete the table and answer the following question if you tested positive what is the probability you have a dog allergy

Answers

The probability that one has a dog allergy when tested positive will be 0.3311.

What do you mean by probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

According to the given question,

We have the given information:

1% of the population has an allergy to dogs.

This will be:

= 1% × 100000

= 1000

So, 1000 people have an allergy to dogs.

The number of people who doesn't have allergy to dogs will be:

= 100000 - 1000

= 99000

Those that have allergies = 2% × 1000 = 20

So, the probability that one has dog allergy will be:

= P(has allergy and test positive)

= (0.01 × 0.98) + (0.098 + 0.0198)

= 0.0098/0.0296

= 0.3311

Therefore, the probability is 0.3311.

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The two graphs shown below detail the results of two independent response polls studying favorite movie genres.
Which genre had the same number of votes in each study?
a. action
b. horror
c. mystery
d. not enough information
Please select the best answer from the choices provided
• A
• B
• C
• D​

Answers

The genre which had the same number of votes in each study is: B. horror.

What are the types of graph?

In Mathematics, there are different types of graph and these include the following:

Box and whisker plotScatter plotBar graphDot graphLine graphHistogramPie chart

What is a pie chart?

A pie chart can be defined as a type of graph that is used for the graphical representation of the proportion relationship between each part or unit to a whole, especially by dividing a circle into various sectors.

From the bar chart, the number of votes for horror movie is equal to 40 votes. Next, we would calculate the number of votes for horror movie in the pie chart as follows;

Number of votes = 16/100 × 250

Number of votes = 0.16 × 250

Number of votes = 40 votes.

In conclusion, we can logically deduce that horror is a movie genre that has the same number of votes in each independent study.

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