When a number is decreased by 40% of itself, the result is 54. What is the number?

The solution of the equation which is a vertex, from plot of the equation is

In mathematics, a vertex (plural: vertices) is a point where two or more lines, curves, or edges meet. The term is commonly used in geometry, graph theory, and other areas of mathematics.

In geometry, a vertex is a point where two or more edges of a polygon or a polyhedron meet. For example, a triangle has three vertices, while a cube has eight vertices.

The graph is attached and other vertices shown

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We are 90% confident that the true proportion of surveys returned is between 0.4330 and 0.4882.

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

(a) First, we need to calculate the sample proportion, denoted by $\hat{p}$. The sample proportion is the number of surveys returned divided by the total number of surveys sent:

p = 1111/ 2410 ≈ 0.4606

(b) The standard error of the sample proportion is:

SE = p(1−p)/n = 0.4606(1−0.4606)/2410≈0.0168

(c) To find the margin of error at 90% confidence level, we need to use the z-score associated with a 90% confidence interval, which is 1.645 (obtained from a standard normal table or calculator). The margin of error is:

ME = z∗×SE = 1.645 × 0.0168 ≈ 0.0276

(d) Finally, we can construct the 90% confidence interval for the proportion of returned surveys by subtracting and adding the margin of error to the sample proportion:

p ± ME = 0.4606 ± 0.0276 =(0.4330,0.4882)

Therefore, we are 90% confident that the true proportion of surveys returned is between 0.4330 and 0.4882.

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Answer:

A. 6, 7 , 8, 9 and 15

B. 1, 3, 5, 7 and 19

Step-by-step explanation:

please see the attached I put.

The three options given in the question are not the correct steps to solve the given quadratic equation.

What is quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term that is squared (raised to the power of 2).

The three steps that Inga could use to solve the quadratic equation [tex]2x^2 + 12x - 3 = 0[/tex] are:

1.Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex], where a, b, and c are constants: [tex]2x^2 + 12x - 3 = 0.[/tex]

2.Use the quadratic formula x = [-b ± sqrt([tex]b^2[/tex] - 4ac)]/2a, where a = 2, b = 12, and c = -3, to find the values of x:

x = [-12 ± [tex]\sqrt{(12^2 - 4(2)(-3))[/tex]]/(2*2)

x = [-12 ± [tex]\sqrt{(156)[/tex]]/4

x = (-3 ± [tex]\sqrt{(39)[/tex])/2

3.Simplify the roots if possible:

x = (-3 + [tex]\sqrt{(39)[/tex])/2 or x = (-3 - [tex]\sqrt{(39)[/tex])/2

Therefore, the three options given in the question are not the correct steps to solve the given quadratic equation.

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The functions y(x) = [tex]e^{4x}[/tex] and y(x) = [tex]e^{8x}[/tex] are therefore solutions of the specified differential equation.The values of mi = 4 and 8.

A differential equation is an equation with one or more terms and one or more derivatives of the dependent variable with regard to the independent variable. (i.e., independent variable) dy/dx equals f(x) Here, the independent variable "x" and the dependent variable "y" are both present. So, dy/dx equals 5x, for instance.

We are given with differential equation

[tex]\frac{d^{2}y }{dx^{2} } - 12 \frac{dy}{dx} + 32y = 0[/tex]

We need to find the values of m1 and m2

[tex]y(x) = e^{m1x} and y(x) = e^{m2x}[/tex]are solutions to the differential equation.

First, we solve the differential equation for [tex]y(x) = e^{mx}[/tex]to obtain:

[tex]m^{2} e^{mx} - 12me^{mx} + 32 e^{mx} = 0[/tex]

By factoring out e(mx) from the left side, we obtain

[tex]e^{mx} (e^{mx} - 12m + 32) = 0[/tex]

The number enclosed in parentheses must be equal to zero for e(mx) to be a non-zero solution of the differential equation. To resolve the quadratic problem, we must:

[tex]m^{2} - 12m + 32 = 0[/tex]

The quadratic algorithm yields:

[tex]m = (12 ± √(144 - 4*32))/2\\m = (12 ± \sqrt{\frac{(144 - 4 * 32)}{2} } \\[/tex]

mi = 6 ± 2

Therefore, m1 and m2 have the following values:

m1 = 4

m2 = 8

The functions y(x) = [tex]e^{4x}[/tex]and y(x) = [tex]e^{8x[/tex]are therefore solutions of the specified differential equation.

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Complete question:

The complete question is in the image form.

So, the value of the car after 13 years is approximately $13,330.

In mathematics, an initial value refers to the value of a function or a variable at a specific starting point or initial condition. For example, when solving a differential equation, the initial value is the value of the function at the starting point or initial time.

In the context of calculus, the initial value of a function f(x) at a point x=a is denoted by f(a). In the context of differential equations, the initial value of a function y(x) at a point x=a is denoted by y(a) or y(a) = y0.

he given exponential function can be written as:

[tex]v(t) = 25,900(0.95)^t[/tex]

where t is the age of the car in years.

To find the initial value of the car, we need to evaluate v(0):

[tex]v(0) = 25,900(0.95)^0[/tex]

[tex]v(0) = 25,900(1)[/tex]

[tex]v(0) = 25,900[/tex]

So, the initial value of the car is $25,900.

To find the value of the car after 13 years, we need to evaluate v(13):

[tex]v(13) = 25,900(0.95)^{13}[/tex]

v (13) ≈ 13,330

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a)  Population proportion is the sample proportion: p' = 108/4319 ≈ 0.025. b) 0.007. c) (0.018, 0.032) d) Option A is correct statement.

In statistics, the standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is also called the Z distribution, where Z represents the standard normal variable.

The standard normal distribution is a continuous probability distribution that is symmetric around the mean of 0. The shape of the distribution is bell-shaped, with the majority of the data falling within 3 standard deviations from the mean.

The standard normal distribution is widely used in statistics and probability theory as a benchmark for comparing other normal distributions. It is particularly useful for converting other normal distributions into a standardized form, which allows for easier comparison and analysis.

a) The best point estimate of the population proportion is the sample proportion: p' = 108/4319 ≈ 0.025.

b) The margin of error E is given by E = z* ×√(p'(1-p')/n), where z* is the critical value of the standard normal distribution for a 99% confidence level. Using a table or calculator, we find that z* ≈ 2.576. Substituting the given values, we have E ≈ 0.007.

c) The confidence interval is given by p' ± E, or 0.025 ± 0.007. Using a calculator, we find that the lower bound is approximately 0.018 and the upper bound is approximately 0.032. Therefore, the 99% confidence interval for the proportion of adverse reactions is (0.018, 0.032).

d) A. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

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Expressing the resuIt in οne significant figure, we get: 1x10^22

The number οf digits in a particuIar vaIue οr measurement required tο determine the accuracy and precisiοn οf measurement are knοwn as significant figures (οr significant digits).

The resuIt οf[tex](5.01\times10^{21})* 3[/tex] is [tex]1.50\times10^{22}.[/tex]

Tο express the answer in οne significant figure withοut rοunding, we need tο determine the first significant figure in the resuIt.

In scientific nοtatiοn, the first significant figure is the first nοn-zerο digit. In this case, the first nοn-zerο digit is 1.

Therefοre, expressing the resuIt in οne significant figure, we get:

[tex]1\times10^{22[/tex]

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Answer: w/explanation

To calculate your merit increase, we need to first determine your performance score on a scale of 0 to 100. We can convert your score of 3.4 to this scale by subtracting 2 and multiplying by 25:

performance score = (3.4 - 2) x 25 = 35

Now that we have your performance score, we can use the given merit increase formula to calculate your increase:

Merit increase = (performance score - 26) / 4

Merit increase = (35 - 26) / 4

Merit increase = 2.25%

Therefore, your merit increase is 2.25%.

Answer:

90°

Step-by-step explanation:

Since CD is a tangent to circle B and BA is the circle's radius, the tangent to the radius forms a right angle at the point of contact:

∠BAD = 90°

Therefore, the line Ф = [tex]\frac{\pi }{2}[/tex], but not with respect to the pole, is the answer to the given equation's problem.

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures.

In this case, levelling generates [tex]b+7[/tex] rather than another method that could divide [tex]12[/tex] into two parts, analyse the information provided by [tex]y+7[/tex]and generate [tex]y+7[/tex]

A curve is said to be symmetric with respect to the pole if it does not alter when the pole is reflected across the origin. To test for this symmetry, we replace [tex]r[/tex] with [tex]-r[/tex] and see if the answer is still correct.

∴[tex]r = -3+3cos[/tex]Ф[tex]- r = 3-3(cos[/tex]Ф[tex])[/tex]Ф

Regarding the lineФ[tex]= \frac{\pi }{2}[/tex] there is symmetry. We replace Ф with [tex]\pi[/tex]/Ф and verify to see if the solution holds to see if this symmetry holds.

[tex]r= 3-3cos(\pi -[/tex]Ф[tex])[/tex]

[tex]r= 3-3cos[/tex]Ф

Due to the constant expression, the curve is symmetric with respect to the line Ф = [tex]\pi[/tex]/[tex]2[/tex].

Therefore symmetric with respect to the polar axis and the line Ф = [tex]\pi[/tex]/[tex]2[/tex], but not with respect to the pole.

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Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

a. FPCF for this sample is FPCF = √(199/24) = 2.89.

b. The population cannot be considered effectively infinite, so the answer is no.

When the sample size is significant compared to the size of the community, the Finite Population Correction Factor, also known as the FPC factor, is applied. The population in most cases is so vast that typical sample sizes are insufficient to raise concerns about the need for the FPC.

The recommendation is to use the FPC when the sample size to population size ratio is higher than 5%. The FPCF must be used, for instance, if the population number is 300 and the sample size is 30, which results in a ratio of 10%.

a. To calculate the FPCF (finite population correction factor) for this sample, we can use the formula:

FPCF = √(N/n)

where N is the population size, and n is the sample size.

In this case, N = 199 (the number of blood samples in the racks), and n = 24 (the number of samples selected every seventh blood sample).

FPCF = √(199/24) = 2.89 (rounded to two decimal places)

b. To determine whether the population should be considered effectively infinite, we need to compare the sample size to the population size. A general rule of thumb is that the population can be considered effectively infinite if the sample size is less than 5-10% of the population size.

In this case, the sample size is 24, which is approximately 12% of the population size of 199. Therefore, the population cannot be considered effectively infinite, and the FPCF should be applied to adjust for the finite population size.

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The sample space for rolling a fair 12-sided die is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

Sample space refers to the set of all possible outcomes or events that can occur in an experiment or random process. It is denoted by the symbol "S" and contains all the possible values, results, or states that can be observed or measured. In probability theory, the sample space is used to define the range of possible outcomes that can be observed or measured in a given experiment or event.

Probability is a measure of the likelihood or chance of an event occurring. It quantifies the likelihood of an event happening based on the ratio of the number of favorable outcomes to the total number of possible outcomes. It is expressed as a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

According to the given information:

When you roll a 12-sided dice, number of dots on the uppermost face is called as outcome. Now, whenever a dice is rolled we can get either 1, 2,3,4,5,6,7,8,9,10,11 or 12 dots on the uppermost face that is now outcome.

So experiment here is "Rolling a 12-faced dice" and list of possible outcomes is "{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}".

Sample space by its definition is list of all the possible outcomes of an experiment.

S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

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For given dataset,  the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis.

What exactly is a data set?

A dataset is a collection of data points or observations that are related to each other in some way. Each data point in a dataset represents a single instance or measurement of some variable or phenomenon that is being studied.

A dataset can take many different forms depending on the type of data being collected and the purpose of the study.

Now,

To test the claim that 3% of users develop nausea, we will use a hypothesis test with a significance level of 0.01.

Let p = true proportion of users who develop nausea.

Null Hypothesis: H0: p = 0.03

Alternative Hypothesis: H1: p > 0.03 (one-tailed test)

We will use the normal approximation to the binomial distribution since np and n(1-p) are both greater than 10, where n is the sample size and p is the hypothesized proportion.

The test statistic is calculated as follows:

z = (P - p)/√(p(1-p)/n)

Here P = sample proportion and n = sample size.

The sample proportion is:

P = 160 / 6209 = 0.0258

Substituting the values, we get:

z = (0.0258 - 0.03) / √(0.03 x 0.97 / 6209) = -1.72

Using a z-table or calculator, we find that the p-value for this test is approximately 0.043. Since the p-value is greater than the significance level of 0.01, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to support the claim that more than 3% of users develop nausea. However, we should still be cautious about this adverse reaction and continue monitoring it.

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The composition (f ∘ g)(–2) = 3.

What is Function ?

In mathematics, a function is a relation between two sets of values, where each value in the first set (called the domain) is associated with exactly one value in the second set (called the range). A function can be represented by a formula or an equation, which specifies how the input values are transformed into output values.

To find the composition (f ∘ g)(–2), we need to apply the function g to –2 first, and then apply the function f to the result. Here's how we can do it:

First, we need to find g(–2) by substituting –2 for x in the expression for g(x):

g(–2) = (–2)2 – 3

g(–2) = 4 – 3

g(–2) = 1

Now that we have found g(–2) = 1, we can substitute it for x in the expression for f(x) to find f(g(–2)):

f(g(–2)) = 2(1) + 1

f(g(–2)) = 3

Therefore, the composition (f ∘ g)(–2) = 3.

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The required password for different conditions are 216 and 120.

(a) If a letter can be repeated, then we can use the multiplication principle to determine the number of possible passwords. For each of the three positions in the password, there are six choices of letters. Therefore, the total number of possible passwords is:

[tex]$6^3 = \boxed{216}$[/tex]

(b) If a letter cannot be repeated, then we can use the permutation formula to determine the number of possible passwords.

There are six choices for the first letter, five choices for the second letter (since one letter has already been used), and four choices for the third letter (since two letters have already been used). Therefore, the total number of possible passwords is:

[tex]$P(6,3) = 6 \times 5 \times 4 = \boxed{120}$[/tex]

Thus, required password for different conditions are 216 and 120.

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Exact Form: 131/12

Decimal Form:10.916

Mixed Number Form: 10 11/12

Answer:

131/12 or 10.91666. or  [tex]10\frac{11}{12}[/tex]

Hope this helps!

Step-by-step explanation:

( [tex]\frac{8}{3}[/tex] × [tex]\frac{11}{2}[/tex] ) - [tex]\frac{15}{4}[/tex]

( [tex]\frac{4}{3}[/tex] × [tex]\frac{11}{1}[/tex] ) - [tex]\frac{15}{4}[/tex]

[tex]\frac{44}{3}[/tex] - [tex]\frac{15}{4}[/tex]

[tex]\frac{176}{12}[/tex] - [tex]\frac{45}{12}[/tex]

[tex]\frac{131}{12}[/tex]

Answer:

A .278

Step-by-step explanation:

138 x 14÷28+209 = 1932 ÷28+209=69+209=278

The 2nd graph shows the line of best fit for the data (10, 2) and (6, 4) and (3, 6)

A scatter plot is a type of graph that is used to display the relationship between two sets of data. The data is represented by a collection of points on a two-dimensional plane, with one variable represented on the x-axis and the other variable represented on the y-axis. Each point on the graph represents an individual observation, and the position of the point on the x and y axes represents the values of the two variables for that observation.

Plot the data points on a scatter plot.

Visually identify the overall trend or pattern of the data. Does it appear to be a positive or negative correlation, or is there no correlation at all?

Draw a straight line that appears to fit the trend of the data as closely as possible. This line is your estimate of the line of best fit.

Calculate the equation of the line of best fit using statistical methods such as linear regression. This will give you the most accurate representation of the line of best fit.

Therefore, Plot the line of best fit on the scatter plot to see how well it fits the data.

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Complete question:

Look at the data graphed on the scatter plot below.

(10, 2) and (6, 4) and (3, 6)

Which graph shows the line of best fit for the data?

Without the exact Number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make

Step 1: Identify the number of leftover bread slices.
Unfortunately, the question doesn't provide the exact number of leftover bread slices. Let's assume Rosa and Clarice have "B" bread slices in total.

Step 2: Determine the number of sandwiches needed.
We know that they are making sandwiches for the custodian, librarian, and office staff. We need to know the number of people in each category to calculate the total number of sandwiches required. Since this information is not provided, let's assume there are "C" custodians, "L" librarians, and "O" office staff members.

Step 3: Calculate the number of sandwiches required.
Each sandwich typically requires 2 slices of bread. Therefore, the total number of sandwiches required can be calculated using the following formula:

Total Sandwiches = (C + L + O)

Step 4: Determine if there is enough bread.
We can now compare the total number of sandwiches required with the number of bread slices available. If there are enough bread slices (B >= 2 * Total Sandwiches), Rosa and Clarice can make sandwiches for everyone. Otherwise, they will not be able to make enough sandwiches for everyone.

In conclusion, without the exact number of bread slices and people in each category, we cannot determine the specific number of sandwiches Rosa and Clarice can make. To answer the question accurately, please provide the missing information.

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Graph with Numbers

The coordinate plane is a two-dimensional plane that is divided into four quadrants. The upper-right quadrant is known as quadrant one, and the following quadrants go in counter-clockwise order: quadrant two, quadrant three, quadrant four (see image below). Quadrants are typically labeled using Roman numerals (I, II, III, and IV). The coordinate plane is comprised of two axes that are perpendicular lines, meaning when they are joined together, they create four right angles. The x-axis is the horizontal axis, and the y-axis is the vertical axis. The point where the two axes are joined together is called the origin. The coordinates of the origin are (0, 0). This means that the x-coordinate is 0 and the y-coordinate is 0. Ordered pairs are always written in the format (x, y).

The coordinate plane has four quadrants, a horizontal x-axis and vertical y-axis, and the origin is the point in the center.

The left side of the x-axis contains negative numbers. Traveling to the left on the coordinate plane indicates the x-value is getting smaller. The right side of the x-axis contains positive numbers. Traveling to the right on the coordinate plane indicates the x-value is getting larger. The upper half of the y-axis contains positive numbers. Traveling upward on the coordinate plane indicates the y-value is getting larger. The lower half of the y-axis contains negative numbers. Traveling downward on the coordinate plane indicates the y-value is getting smaller.

In the following image, point A is graphed on the coordinate plane. The coordinates for point A are (3, 2). This means that the x-value is 3 and the y-value is 2. To graph point A on the coordinate plane, start at the origin and go three spaces to the right (because the x-value, 3, is positive) and two spaces upward (because the y-value, 2, is positive). Since the x-value and y-value are both positive, point A will be in quadrant I.

Graphing the point (3, 2)

In order to graph the point (3, 2), move left three spaces and up two spaces on the coordinate plane.

Therefore, the distance from the coal tray is approximately 301.96 inches when the heat intensity is 0.685 and the width of the coal tray is 25 inches.

We can write the following using the formula in the question:

[tex]P = 100/(1 + d^2)[/tex]

where d represents the proportion of the food's distance from the coals to the tray's width.

Substituting d = z/25 results in:

[tex]P = 100/(1 + (z/25)^2)[/tex]

With y = 0.685, we can replace P with P = 0.685 and find z:

[tex]0.685 = 100/(1 + (z/25)^2)[/tex]

By dividing the two sides by [tex](1 + (z/25)^2)[/tex], we get at:

[tex]0.685 + 0.685(z/25)^2 = 100[/tex]

If we simplify, we get:

[tex](z/25)^2 = (100/0.685) - 1(z/25)^2 = 145.9854[/tex]

When we square the two sides, we obtain:

[tex]z/25 = 12.0783z = 25*12.0783z = -25*12.0783[/tex]

Given that z cannot be negative, we decide:

Z=25 * 12.0783 * 301.9575 inches

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Answer: -1 Is the answer.

The equatiοn fοr H, the number οf times Nοah’s beats in m minutes is H = k * m

Expressiοns that perfοrm the same functiοn regardless οf appearance are said tο be equivalent. If twο algebraic expressiοns are equivalent, then they have the same value when the same variable value is used.

Assuming yοu meant "Nοah's heart beats", the equatiοn fοr H, the number οf times Nοah's heart beats in m minutes can be given by:

H = k * m

where k is a cοnstant that represents the number οf heartbeats per minute.

The value οf k may vary depending οn the individual and their physical cοnditiοn.

Hence,  the equatiοn fοr H, the number οf times Nοah’s beats in m minutes

is H = k * m

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Complete Question;

A persons resting heart rate is typically between 60 and 100 beats per minute. Nοah looks at his watch, and counts 8 heartbeats in 10 seconds.

Is his heart rate typical? Explain how you know.

Write an equation for h, the number of times Noahs heart beats (at this rate) in m minutes.

Answer:

the bird will need to fly 4feet closer to the flower

Answer:

Step-by-step explanation:

H(n)=91x(-1/7) n-1

do not know

Hope it helps the answer is the 2nd one have a great day