The probability of someone randomly selecting a computer that does not have a virus is 0.8.
Total number of computers = 20
Virus affected = 4
Perfect computers = 20 - 4 = 16
The probability of choosing a computer that does not have a virus is equivalent to the number of computers without a virus and divided by the total number of computers in the lab.
The probability of selecting a computer without a virus is:
P(C) = 16/20
Simplifying this fraction, we get:
P(20 - 4 = 16) = 4/5
P(20 - 4 = 16) = 0.8
Therefore we can conclude that the probability of someone randomly selecting a computer that does not have a virus is 0.8.
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Taylor is proving the Pythagorean theorem.
(photo attached)
How could Taylor use the diagram to prove the Pythagorean theorem?
A. Taylor could set the area of a square with side length a + b equal to the sum of the areas of the 4 triangles and the square with side length c.
B. Taylor could set the area of the square with side length c equal to the sum of the areas of the 4 congruent triangles.
C. Taylor could find the ratio of the area of the square with side length a + b to the area of one of the congruent triangles.
D. Taylor could find the ratio of the area of the square with side length a + b to the area of the square with side length c.
If Taylor is proving the Pythagorean theorem. Taylor can use the diagram to prove the Pythagorean theorem by: A. Taylor could set the area of a square with side length a + b equal to the sum of the areas of the 4 triangles and the square with side length c.
How could Taylor use the diagram to prove the Pythagorean theorem?To prove the Pythagorean theorem, we want to show that in a right triangle with legs a and b and hypotenuse c, the square of the hypotenuse c^2 is equal to the sum of the squares of the legs a^2 + b^2.
From the given diagram, we can see that we have a square with side length a+b, which is divided into 4 congruent right triangles and a smaller square with side length c. Each of the 4 triangles has legs a and b, which are also the legs of the right triangle we want to prove the theorem for. The smaller square with side length c has an area equal to c^2, which is the square of the hypotenuse of the right triangle.
The area of the square with side length a+b is (a+b)^2 = a^2 + 2ab + b^2. The area of one of the congruent right triangles is (1/2)ab, so the sum of the areas of the 4 triangles is 2ab. Therefore, the sum of the areas of the 4 triangles and the smaller square is:
a^2 + 2ab + b^2 + c^2
But this is also equal to the area of the larger square with side length a+b, which is (a+b)^2. So we have:
a^2 + 2ab + b^2 + c^2 = (a+b)^2
Expanding the right-hand side gives:
a^2 + 2ab + b^2 + c^2 = a^2 + 2ab + b^2
Canceling the common terms on both sides gives:
c^2 = a^2 + b^2
This is the Pythagorean theorem, which we have proved using the given diagram.
Therefore, option A is the correct answer.
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Natalie gathered a random sample of favorite writing utensils of the students in her class. She calculated data on different variables. For one data that she collected, she constructed a bar graph. Which of the following variables did she use?
O Price of writing utensil
O Type of writing utensil
O The volume of each writing utensil
O Weight of each writing utensil
Natalie used for constructing the bar graph is type of writing utensil.
What is bar graph ?The representation of numerical data using rectangles (or bars) of equal width and varying height is known as a bar graph.
Depending on the distribution and nature of the data, various types of charts or graphs, such as scatter plots, histograms, or box plots, would typically be used to represent the mentioned quantitative variables, such as the price, volume, and weight of each writing utensil.
Natalie probably used the variable "type of writing utensil" for the bar graph based on the information provided. This is due to the fact that a bar graph is a type of chart that uses rectangular bars to represent categorical data. Each bar represents a distinct category or group.
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X2 - 12x + 8 = 0 by completing the square
To solve x^2 - 12x + 8 = 0 by completing the square, we can follow these steps:
Move the constant term to the right side:
x^2 - 12x = -8
Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 - 12x + (-12/2)^2 = -8 + (-12/2)^2
Simplifying the right side:
x^2 - 12x + 36 = -8 + 36
Factor the left side:
(x - 6)^2 = 28
Take the square root of both sides:
x - 6 = ±√28
Add 6 to both sides:
x = 6 ±√28
Simplify the roots:
x = 6 ±2√7
Therefore, the solutions to the equation x^2 - 12x + 8 = 0 by completing the square are x = 6 + 2√7 and x = 6 - 2√7.
Rudy too a job through an employment agency. The job pays $75.9K per year.
He must pay a fee to the employment agency. The fee is 40% of his first 3
week's pay. How much money must Rudy pay the agency, to the nearest cent.
1. $30,360
2. $1,459.62
3. $1,751.54
4. $4,378.85
Answerabout 51/52 weeks in ayear
75,000/52=1459.615385
1459.615385(3)=4378.846155
40% of 4378.846155=1751.538462
$1,751.54
answer is 3
Step-by-step explanation:
to compare the frequency of hypertension in the white and non-white population surveyed, the most appropriate measure is the:
The most appropriate measure to compare the frequency of hypertension in white and non-white populations is the relative risk.
How to find the most appropriate measure?To compare the frequency of hypertension between two populations, the most appropriate measure is the prevalence ratio or prevalence odds ratio. The prevalence ratio is the ratio of the prevalence of hypertension in the exposed group (e.g., non-white population) to the prevalence of hypertension in the unexposed group (e.g., white population). It is a measure of the strength of association between the exposure and the outcome.
The prevalence odds ratio is the ratio of the odds of hypertension in the exposed group to the odds of hypertension in the unexposed group. It is a commonly used measure in epidemiology and can be used to estimate the relative risk of hypertension in the exposed group compared to the unexposed group.
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what is the independent variable? 1 point the variable that you purposely change the variable that is being observed the variable that is not changed
Independent variable is the variable that is being purposely changed by the researcher in an experiment to observe its effect on the dependent variable.
It is the variable that is manipulated or altered to test a hypothesis or research question.
The independent variable is the variable that you purposely change in an experiment to observe the effect it has on the dependent variable.
It is also known as the manipulated variable because it is the one that is manipulated or altered by the researcher in order to study the effect it has on the dependent variable.
Investigate the effect of fertilizer on plant growth, we would manipulate the amount of fertilizer that the plants receive. In this case, the amount of fertilizer would be the independent variable because it is the variable that we are purposely changing.
The dependent variable, in this case, would be the plant growth because it is the variable that we are observing and measuring to see if there is any change.
It is important to note that the independent variable is not always the only variable that can affect the dependent variable.
There may be other variables, known as extraneous variables, that could also have an effect on the dependent variable.
In order to control for these variables, researchers will often use control variables or hold them constant in their experiments.
This allows them to isolate the effect of the independent variable on the dependent variable.
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Determine if I triangle can be constructed with the following sides. Explain
2/3 , 4/5 , 1/2
what value of x would allow a triangle to be constructed with the following measures?
a. 21,8,x
b. 13,7,x
With the image Find x
Yes, a triangle can be constructed with sides of 2/3, 4/5, and 1/2. the value of x is 17.
Since a triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.
To determine if a triangle can be constructed, we need to check if the sum of the two smaller sides is greater than the largest side.
In this case, we can see that
2/3 + 1/2 > 4/5,
2/3 + 4/5 > 1/2,
1/2 + 4/5 > 2/3,
Therefore, a triangle can be formed.
The value of x can be calculated as;
45 + 68 + 3x + 16 = 180
3x = 51
x = 17
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a sample containing years to maturity and yield for 40 corporate bonds is contained in the excel online file below. construct a spreadsheet to answer the following questions. open spreadsheet a. what is the sample mean years to maturity for corporate bonds and what is the sample standard deviation?
Use STDDEV.s function to find standard deviation and AVERAGE function to find mean years of maturity.
To answer this question, you would need to open the provided Excel file and input the data into a spreadsheet. Once the data is inputted, you can use Excel's built-in functions to calculate the mean and standard deviation.
To calculate the mean years to maturity, you would use the AVERAGE function and select the column of years to maturity data. The result will give you the average years to maturity for the sample of 40 corporate bonds.
To calculate the standard deviation, you would use the STDEV.S function and select the column of yield data. This will give you the sample standard deviation for the yield data.
Overall, your spreadsheet should have columns for years to maturity and yield, with 40 rows of data for each bond. The mean years to maturity and sample standard deviation for yield can then be calculated using Excel functions.
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The sample mean years to maturity for corporate bonds:
Type the following formula and press Enter:
=AVERAGE(A1 : A40).
The sample standard deviation:
Press Enter: = STDEV.S(A1 : A40).
To calculate the sample mean and sample standard deviation for years to maturity of the 40 corporate bonds, follow these steps:
Open the Excel online file provided.
Assuming that the years to maturity data is in column A, click on an empty cell (let's say B1) to find the sample mean.
Type the following formula and press Enter:
=AVERAGE(A1 : A40).
This will calculate the mean of the years to maturity for the 40 corporate bonds.
To find the sample standard deviation, click on another empty cell (let's say B2) and type the following formula and press Enter:
=STDEV.S(A1 : A40)
This will calculate the sample standard deviation of the years to maturity for the 40 corporate bonds.
Now, you should have both the sample mean years to maturity and the sample standard deviation in cells B1 and B2 respectively.
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how many people chosen at random are needed to make the probability greater than 12 that there are at least two people born on the same day of the week? rearrange the solution of the above question in correct order.
To make the probability greater than 0.12 that there are at least two people born on the same day of the week, we need at least 21 people chosen at random.
To solve the problem, we can use the concept of the pigeonhole principle.
The probability that no two people share the same birth day of the week is given by:
P(No two people share the same birth day of the week) = 7/7 x 6/7 x 5/7 x … x [(7-(n-1))/7]
Here, n is the number of people chosen at random. The first person can be born on any day of the week. The probability that the second person is born on a different day of the week is 6/7. The probability that the third person is born on a day of the week different from the first two is 5/7, and so on.
The probability that at least two people share the same birth day of the week is
P(At least two people share the same birth day of the week) = 1 - P(No two people share the same birth day of the week)
We want to find the smallest value of n for which P(At least two people share the same birth day of the week) is greater than 0.12.
1 - P(No two people share the same birth day of the week) > 0.12
P(No two people share the same birth day of the week) < 0.88
Using a calculator or a spreadsheet, we can find that n = 21 is the smallest value that satisfies this inequality. Therefore, we need at least 21 people chosen at random to make the probability greater than 0.12 that there are at least two people born on the same day of the week.
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I need help with this ASAP please
Answer:
y- coordinate = 4
Step-by-step explanation:
consider a right triangle formed by the x- axis, the radius (hypotenuse) of 5 and a vertical line drawn to the x- axis from the point ( 3, - )
using Pythagoras' identity in the right triangle
3² + y² = 5²
9 + y² = 25 ( subtract 9 from both sides )
y² = 16 ( take square root of both sides )
y = [tex]\sqrt{16}[/tex] = 4
the y- coordinate of the point is 4 , that is (3, 4 )
Answer:
y= coordinate 4
right triangle formed by the x- axis, the radius (hypotenuse) of 5 and a vertical line drawn to the x- axis from the point ( 3, - )
using Pythagoras' identity in the right triangle
3² + y² = 5²
9 + y² = 25 ( subtract 9 from both sides )
y² = 16 ( take square root of both sides )
y =
16
16
= 4
the y- coordinate of the point is 4 , that is (3, 4 )
Mrs. Hallmark wants to sell a box of two varieties of
birthday cards for $5. 80. The number of 30¢ cards is six
more than one half the number of 35¢ cards. The number
of 35¢ cards is:
According to unitary method, there are 10 30¢ cards and 8 35¢ cards in the box, which adds up to a total of $5.80.
Let's start by defining our units. In this case, our units are the number of 30¢ cards and the number of 35¢ cards. We know that the box of cards is being sold for $5.80, which means the total value of all the cards in the box is $5.80. We can use this information to set up an equation:
0.30x + 0.35y = 5.80
where x is the number of 30¢ cards and y is the number of 35¢ cards.
Next, we are given the information that the number of 30¢ cards is six more than one half the number of 35¢ cards. Using the unitary method, we can set up an equation that relates the number of 30¢ cards to the number of 35¢ cards:
x = 0.5y + 6
Now we can use this equation to eliminate x from our first equation:
0.30(0.5y + 6) + 0.35y = 5.80
Simplifying this equation gives:
0.15y + 1.80 + 0.35y = 5.80
0.50y = 4.00
y = 8
So there are 8 35¢ cards in the box. We can use the unitary method again to find the number of 30¢ cards:
x = 0.5y + 6
x = 0.5(8) + 6
x = 10
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if the number of bacteria in a petri dish culture doubles every 3 hours, and initially there were 2500 bacteria present, in how many hours will there be 100,000 bacteria?
The time required to have number of bacteria to be 100,000 is equal to 15.96 hours.
Let us consider,
N = final number of bacteria
= 100,000 bacteria
N₀ = initial number of bacteria
= 2500 bacteria
t = time elapsed
T = time it takes for the population to double
= 3 hours
Use exponential growth formula to solve this problem,
N = N₀ × 2^(t/T)
Substitute the values in the formula,
⇒ 100,000 = 2500 × 2^(t/3)
Simplify this equation by dividing both sides by 2500,
⇒ 100,000/2500 = 2^(t/3)
⇒ 40 = 2^(t/3)
To solve for t, we can take the logarithm of both sides of the equation,
⇒ log40 = (t/3) log 2
⇒ t/3 = log 40 /log 2
⇒t = 3 × ( log 40 /log 2)
Using a calculator, we can evaluate this expression to get,
t ≈ 15.96 hours
Therefore, it will take approximately 15.96 hours for the number of bacteria to reach 100,000.
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in the chi square test of hypothesis, the null hypothesis states that the variables are select one: a. dependent b. independent c. causally related d. non-random
Option b is correct.
The null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.
What is chi-square test of hypothesis? Explain more indetail?In the chi-square test of hypothesis, the null hypothesis states that the variables under consideration are independent. That is, there is no relationship between the two variables being studied.
The chi-square test is a statistical method used to determine if two categorical variables are associated or independent. Categorical variables are those that take on values that are categories or labels.
For example, gender (male or female) or educational level (high school, college, graduate school) are categorical variables.
The chi-square test determines the expected frequency of each category based on the null hypothesis, which assumes independence between the two variables.
The observed frequency is then compared to the expected frequency, and if the difference is significant enough, it suggests that the null hypothesis should be rejected, and the two variables are considered to be associated or dependent.
Therefore, in summary, the null hypothesis in the chi-square test of hypothesis states that the two categorical variables under consideration are independent of each other, meaning that there is no relationship or association between them.
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Find the three trigonometric ratios. If needed, reduce fractions.
In this instance, the three trigonometric ratios are:
Sinx = 15/17
Cosx = 8/17
Tanx = 15/8
What are trigonometric ratios?Mathematical trigonometric functions connect the angle of a right-angled triangle to the ratios of its two side lengths.
In all areas of study that involve geometry, such as geodesy, solid mechanics, celestial mechanics, and many others, they are widely used.
Review the trigonometric ratios for sine, cosine, tangent, cotangent, secant, and cosecant.
So, the 3 trigonometric ratios in the given situation would be:
Sinx = O/H = 15/17
Cosx = A/H = 8/17
Tanx = O/A = 15/8
Therefore, in this instance, the three trigonometric ratios are:
Sinx = 15/17
Cosx = 8/17
Tanx = 15/8
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Observa la tabla de valores de una función lineal.
x 4 9 14 19 24
y 9 14 19 24 29
¿Cuál es la razón de cambio de y con respecto a x en la función?
The rate of change for the given table is 1.
How to get the rate of change?For a function y = f(x), the rate of change in any interval (a, b) is:
R = (f(b) - f(a))/(b - a)
Here we can use any pair of values in the table, because it clearly is linear, so we can use the first two.
(4, 9) and (9, 14)
The rate of change is:
r = (14 - 9)/(9 - 4) = 5/5 = 1
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2525 students in a high school health class are asked to write down what foods they ate last week. Of the
25
2525 students,
14
1414 write steak,
6
66 write chicken, and
5
55 write both steak and chicken. Using this information, answer each of the following questions.
Let
�
SS be the event that a randomly selected student writes steak and
�
CC be the event that a randomly selected student writes chicken.
What is
�
(
�
)
P(S)P, left parenthesis, S, right parenthesis, the probability that a student writes steak?
What is
�
(
�
)
P(C)P, left parenthesis, C, right parenthesis, the probability that a student writes chicken?
What is
�
(
�
and
�
)
P(S and C)P, left parenthesis, S, start text, space, a, n, d, space, end text, C, right parenthesis, the probability that a student writes steak and chicken?
What is
�
(
�
or
�
)
P(S or C)P, left parenthesis, S, start text, space, o, r, space, end text, C, right parenthesis, the probability that a student writes steak or chicken?
according to the question the probabilities of event can be P(s)= 14/2525, P(C) = 6/2525, P(S and C) = 5/2525, P(S or C) = 3/505
explain probability?Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.
given,
To solve the problem, we can use the formula:
P(A and B) equals P(A) plus P(B) minus P(A or B)
where P(A) is the probability of event A, P(B) is the probability of event B, and P(A or B) is the probability of either A or B occurring (including the case where both A and B occur).
P(S): the probability that a student writes steak is 14/2525.
P(C): the probability that a student writes chicken is 6/2525.
The likelihood that a student would write steak plus chicken equals 5/2525.A or B. P(A and B) Equals P(A) +P(B), which -P(P(S or C))
P(S or C): the probability that a student writes steak or chicken can be calculated as:
P(S or C) = P(S) + P(C) - P(S and C)
= (14/2525) + (6/2525) - (5/2525)
= 15/2525
= 3/505
Therefore, the answers to the questions are:
P(S) = 14/2525
P(C) = 6/2525
P(S and C) = 5/2525
P(S or C) = 3/505
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i cant do this it is hard we did go over it tho so yeah
The position of sea horse after lower & higher elevations with help of representing it as integers is:
a)The total elevation of the sea horse = 24 feet lower
b)The position of the sea horse = on the sea level.(elevation = 0)
In second part of the story, the answer to the elevation woas zero.
What are integers?
The negative numbers as well as all whole numbers are considered integers. Integers are created when we combine negative and full numbers. Integers are represented on a number line with negatives to the left of zero and positives to the right. The entire number, zero, is neither positive nor negative. Every negative number is less than zero, as are all positive numbers.Greater than the farthest-from-zero negative integer is the negative number that is less than zero.
Given that the elevation of sea horse is -12 feet.
a)Initial position of seahorse= 12 feet below sea level
= - 12 feet.
Drift in position due to strong current=12 feet lower in elevation
= -12 feet
Total elevation below sea level = -12 + (-12)
= -12-12
= -24 feet below sea level.
The elevation of the sea horse = 24 feet lower
b)Initial position of seahorse= 12 feet below sea level
= - 12 feet.
Drift in position due to strong current=12 feet higher in elevation
= +12 feet
Total elevation below sea level = -12 + (+12)
= -12 + 12
= 0 feet below sea level.
The position of the sea horse = on the sea level.
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Find the differential of the function. Z = e−4x cos(4πt)
The differential of the function Z is -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ
To find the differential function of Z = e⁻⁴ˣ cos(4πt), we will use the product rule of differentiation. The product rule states that the derivative of the product of two functions is equal to the first function multiplied by the derivative of the second function plus the second function multiplied by the derivative of the first function.
Let's apply the product rule to our function Z:
First, we differentiate the first function e⁻⁴ˣ with respect to x. The derivative of e⁻⁴ˣ is -4e⁻⁴ˣ.
Next, we differentiate the second function cos(4πt) with respect to t. The derivative of cos(4πt) is -4πsin(4πt).
Therefore, the differential function of Z is:
dZ/dt = -4e⁻⁴ˣcos(4πt) - 4πsin(4πt)e⁻⁴ˣ
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3. What is the surface area of this composite solid? Show your work.
The surface area of the composite solid is 162 unit²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The composite solid has 6 faces . The area of each face is calculated as follows;
Face 1
area = 5×7 = 35 units²
face 2
area = 1/2bh + l×b
= 1/2 ×3×4 + 3×4
= 6+12 = 18units²
face 3 = face 2
area = 18units²
face 4
area = 3× 7 = 21units²
face 5
area = 4×7
= 28units²
face 6
area = 3×7 + 3×7
= 21+21 = 42units²
Therefore total surface area = 42+28+21+18+18+35
= 162 units²
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if decision variables for a problem have to be integers then rounding the linear programming optimal solution for that problem will group of answer choices always result in feasible but not optimal solution may result in either a feasible or infeasible solution always result in an optimal solution always result in a feasible and the optimal solution
If the decision variables for a problem have to be integers, rounding the linear programming optimal solution for that problem will always result in a feasible solution.
However, this solution may not always be optimal. It may result in either a feasible or infeasible solution depending on the problem constraints.
Rounding may also result in an optimal solution if the optimal solution happens to already have integer values for the decision variables. Therefore, rounding may result in a feasible and optimal solution or just a feasible solution but not necessarily always optimal.
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find the radius of a circle with the given circumference. 15 ft. r = 7.5 ft. 7.5 ft. 30 ft. 30 ft.
The radius of the circle with a circumference of 15 ft is approximately
7.5 ft.
We have,
The circumference of a circle is the distance around its boundary. It is calculated by multiplying the diameter of the circle by π (pi), which is approximately 3.14159.
The formula for the circumference of a circle is:
Circumference = 2 π radius
To find the radius of a circle, we can rearrange the formula and solve for the radius:
Radius = Circumference / (2 π)
In this case, the given circumference is 15 ft.
Plugging this value into the formula:
Radius = 15 ft / (2 π)
Simplifying further:
Radius ≈ 7.5 ft
Therefore,
The radius of the circle with a circumference of 15 ft is approximately
7.5 ft.
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Claire works at the Sweet Shop, where candy is bagged and sold by its weight. Claire's last 4 sales of gourmet gummy worms are shown in the table.
The cost of the gummy worms is proportional to the amount, in pounds, of gummy worms purchased.
This situation can be represented by an equation in the form y = kx, where k is the constant of proportionality.
Gourmet
Gummy Worms,
x (pounds)
Cost,
y
0.75 $6.30
2.5 $21.00
4 $33.60
7 $58.80
What is the constant of proportionality?
The constant of proportionality is $8.40
What is constant of proportionality?The constant of proportionality is a value that relates two quantities that are proportional to each other. It is represented by the letter k and is found by dividing the dependent variable by the independent variable. In this case, the constant of proportionality is $8.40 for the given data set.
According to the given information:
To find the constant of proportionality, we can use any two data points from the table and plug them into the equation y = kx.
Let's use the first and second data points: (0.75, $6.30) and (2.5, $21.00).
We can set up the equation as:
$6.30 = k(0.75)
Solving for k, we get:
k = $6.30/0.75 = $8.40
Now, we can check our work by using another data point. Let's use the third data point: (4, $33.60).
Plugging in the values, we get:
$33.60 = k(4)
k = $33.60/4 = $8.40
Since we get the same value for k, we can be confident that our answer is correct.
Therefore, the constant of proportionality is $8.40.
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4 √(20) + 6 √(45) - √(80)
Answer:
22√5
Step-by-step explanation:
√20=√4x5 = √4 x √5 = 2√5
√45 = √9 x 5 = √9 x √5 = 3√5
√80 = √16 x 5 = √16 x √5 = 4√5
4√20 = 6 √45 - √80 = 4(2√5) + 6(3√5)- 4√5
8√5 + 18√5 - 4√5 = 22√5
So its 22√5
Answer:
[tex]22 \sqrt{5} [/tex]
Step-by-step explanation:
the explaination is avaliable in the picture i sent you
and please give me branliest
1001(in base 2)-111(in base 2)
313(in base 4)-123(in base 4)
234(in base 5)-12(in base 5)
1. 1001 (in base 2) - 111 (in base 2) = 2 (in base 2).
2. 313 (in base 4) - 123 (in base 4) = 210 (in base 4).
3. 234 (in base 5) - 12 (in base 5) = 222 (in base 5).
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
To perform the subtractions in different bases, we need to convert the numbers to the same base and then subtract them.
1. 1001 (in base 2) - 111 (in base 2):
First, we need to align the two numbers by adding leading zeros to the second number:
1001
0111
0010
Therefore, 1001 (in base 2) - 111 (in base 2) = 2 (in base 2).
2. 313 (in base 4) - 123 (in base 4):
Again, we need to align the two numbers by adding leading zeros to the second number:
313
123
210
Therefore, 313 (in base 4) - 123 (in base 4) = 210 (in base 4).
3. 234 (in base 5) - 12 (in base 5):
Once again, we need to align the two numbers:
234
012
222
Therefore, 234 (in base 5) - 12 (in base 5) = 222 (in base 5).
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you want to rent an unfurnished one-bedroom apartment for next semester. the mean monthy rent for a random sample of 45 apartments advertised in the local newspaper is $775. assume the standard deviation is $110. find a formula used to generate the 98% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.
Formula:
98% Confidence Interval = (Mean - (2*Standard Deviation/√n), Mean + (2*Standard Deviation/√n))
98% Confidence Interval = ($775 - (2*$110/√45), $775 + (2*$110/√45))
98% Confidence Interval = ($735.56, $814.44)
PLEASE SHOW YOUR WORK
PRACTICE : DETERMINE THE PROBABILITY OF EACH DEPENDENT EVENT OCCURRING.
what is the probability of drawing a red 4 in a deck of cards,keeping it,and then picking a queen of diamonds???
As a result of probability, there is a 1/1326 chance of drawing a red 4 and selecting a queen of diamonds.
Describe probability?A measure of an event's likelihood is probability. It is represented by a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty.
For instance, you can get either heads or tails when you flip a coin. Given that there is only one way to receive heads and a total of two outcomes, the chance of receiving heads is half (or 0.5).
Since there are two red fours in a deck of 52 cards, the likelihood of drawing one is one in every 52 draws.
Since there are 51 cards in the deck after drawing the red 4, the likelihood of getting a queen of diamonds is 1/51 if you decide to keep the red 4.
Since the outcomes of these two occurrences are interdependent (the first event's outcome influences the second event's outcome), we may multiply their probabilities to determine the likelihood that both events will occur:
(2/52)× (1/51) = 1/1326
As a result, there is a 1/1326 chance of drawing a red 4 and selecting a queen of diamonds.
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13
A shop sells red paper lanterns for Chinese New Year. The graph below shows the total pr
for different numbers of paper lanterns purchased. The graph can be modeled using the
equation y-5x.
Total Price (S)
35
30
25
5
RED PAPER
LANTERNS
0 1 2 3 4 5 6 7
Number of Lanterns
Which statement describes the relationship between the number of lanterns purchased and
the total price?
A
A 1-unit increase in the independent variable, number of lanterns, means a 5-unit
increase in the dependent variable, total price.
B
A 5-unit increase in the independent variable, total price, means a 1-unit increase in the
dependent variable, number of lanterns.
C
A 1-unit increase in the independent variable, total price, means a 5-unit increase in the
dependent variable, number of lanterns.
D
A 5-unit increase in the independent variable, number of lanterns, means a 1-unit
increase in the dependent variable, total price.
Answer: Option A) A 1-unit increase in the independent variable, number of lanterns, means a 5-unit increase in the dependent variable, total price.
How to determine the statement describes the relationship between the number of lanterns purchased and the total priceThe correct statement that describes the relationship between the number of lanterns purchased and the total price is Option A
A 5-unit increase in the independent variable, number of lanterns, means a 1-unit increase in the dependent variable, total price.
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This is because the graph shows a slope of 5/1, meaning that for every 5 lanterns purchased, the total price increases by 1 unit.
Does anyone know what 3D model this is?-
The given 3D model is a trapezoidal pyramid.
What is pyramid?A pyramid is a 3D polyhedron having three or more triangle-shaped faces that meet above the base and a polygonal base. The point above the base is referred to as the apex, while the three sides are referred to as faces. The base and apex are joined to form a pyramid. To distinguish them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.
Hence, the given 3D model is a trapezoidal pyramid.
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i need help with this question
The solution of the equation log(t - 3) = log(17 - 4t), is 4.
option A.
What is the solution of the equation?To find the solution for the equation log(t - 3) = log(17 - 4t), we can use the properties of logarithms.
Step 1: Remove the logarithms on both sides.
Applying the property of logarithms that states log(a) = log(b) if and only if a = b, we can remove the logarithms from both sides of the equation:
t - 3 = 17 - 4t
Step 2: Add 4t to both sides.
Adding 4t to both sides of the equation to isolate the t term on one side:
t + 4t - 3 = 17
Step 3: Combine like terms.
Combining like terms on the left-hand side:
5t - 3 = 17
Step 4: Add 3 to both sides.
Adding 3 to both sides of the equation to isolate the t term:
5t - 3 + 3 = 17 + 3
5t = 20
Step 5: Divide by 5.
Dividing both sides of the equation by 5 to solve for t:
5t/5 = 20/5
t = 4
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