What single decimal multiplier would you use to decrease by 19% followed by a 17% decrease?

The given expression "the square of a number is 3 less than four times the number" is represented as x² = 3 - 4x and the values of number could be: x1= 0.645 , x2= -4.645

In mathematics, when we refer "square of a number" we mean that the exponent of that number is 2. So we express it mathematically as:

x²

When we express "3 less than" of a number we mean that the number 3 is subtracting that number. So we express it mathematically as: 3 -

x² = 3 -

When we express "four times the number" we mean that the number is exactly 4 times greater than a number or that it contains it 4 times. So we express it mathematically as: 4x

x² = 3 - 4x

Organizing the values, we have a quadratic equation: x² + 4x – 3 = 0

Where:

Solving the quadratic question we get the values for the (x) number

x= {- b ± √ [b² - (4* a*c)]} / (2 *a)

x= {- 4 ± √ [4² - (4* 1*-3)]} / (2 * 1)

x= {- 4 ± √ (16 + 12)} / 2

x= {- 4± √ 28} / 2

x= (- 4 ± 5.29 ) / 2

x1= (- 4 + 5.29 ) / 2

x1= (1,29) / 2

x1= 0.645

x2= (- 4 - 5.29 ) / 2

x2= (9.29) / 2

x2= -4.645

We can check the values, replacing them into the equation:

(x1)² = 3 - 4(x1)

(0.645)² = 3 - 4*(0.645)

0.42 = 0.42

(x2)² = 3 - 4(x2)

(-4.645)² = 3 - 4*(-4.645)

21.58 = 21.58

It is an algebraic equation where the polynomial formed has three terms, one variable has an exponent 2, another in which the variable has exponent 1 and the last term without any variable. Its standard form is:

ax²+ bx + c = 0

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Answer: 6x-8

Step-by-step explanation:

If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.

To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;

C² = a² + b²

where;

a= 80

b= 100

c= ?

That is;

c²= 80²+100²

= 6400+10000

= 16,400

c = √16400

= 128.1m

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a. Tom has the absolute advantage in making sweaters. b. Tom has the absolute advantage in making a pair of pants. c. Tom has the comparative advantage in making sweaters. d. Susan has the comparative advantage in making a pair of pants.

To determine who has absolute and comparative advantage in making sweaters and pants, we compare the production capabilities of Susan and Tom.

a. Absolute advantage in making sweaters:

Susan can make 4 sweaters in one day, while Tom can make 6 sweaters in one day. Therefore, Tom has the absolute advantage in making sweaters.

b. Absolute advantage in making a pair of pants:

Susan can make 6 pairs of pants in one day, while Tom can make 8 pairs of pants in one day. Therefore, Tom has the absolute advantage in making a pair of pants.

c. Comparative advantage in making sweaters:

To determine comparative advantage, we compare the opportunity cost of producing each item. The opportunity cost is the amount of one good that must be given up to produce an additional unit of another good.

For Susan, the opportunity cost of making 1 sweater is 6/4 = 1.5 pairs of pants.

For Tom, the opportunity cost of making 1 sweater is 8/6 = 1.33 pairs of pants.

Since Tom has a lower opportunity cost (1.33 pairs of pants) compared to Susan (1.5 pairs of pants), Tom has the comparative advantage in making sweaters.

d. Comparative advantage in making a pair of pants:

For Susan, the opportunity cost of making 1 pair of pants is 4/6 = 0.67 sweaters.

For Tom, the opportunity cost of making 1 pair of pants is 6/8 = 0.75 sweaters.

Since Susan has a lower opportunity cost (0.67 sweaters) compared to Tom (0.75 sweaters), Susan has the comparative advantage in making a pair of pants.

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Answer:

x=-75/46

Step-by-step explanation:

\(10 - 5 + \frac{x}{3} - 8x + \frac{5}{2} = 20\)

The LCM of the denominator is 6 because both 2 and 3 can go into 6.

\(10 - 5 + \frac{2x}{6} - 8x + \frac{15}{6} = 20\)

Multiply all terms by 6 to drop the fraction. Make sure to multiply both sides of the equation

\(60 - 30 + 2x - 48x + 15 = 120\)

Put all x values on one side

\(2x - 48x = 120 - 60 + 30 - 15\)

\( - 46x = 75\)

\(x = - \frac{75}{46} \)

All of the following are measures of central tendency except the range.

The range is a measure of dispersion, representing the difference between the largest and smallest values in a dataset. It provides information about the spread or variability of the data but does not provide information about the central tendency.

On the other hand, measures of central tendency are statistical measures that aim to summarize the center or typical value of a dataset. They include the mode, median, and mean.

The mode represents the most frequently occurring value(s) in the dataset.

The median is the middle value when the data is arranged in ascending or descending order. It divides the dataset into two equal halves.

The mean is the arithmetic average of all the values in the dataset. It is calculated by summing all the values and dividing by the total number of values.

Therefore, option C, range, is not a measure of central tendency as it focuses on the spread or dispersion of the data rather than summarizing the central or typical value.

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From the present question, let's say that the missing angles are a, b, and c. We know that the sum of the other seven is equal to 1220°. By definition, the sum of the inner angles of any polygon is given by:

In the present case, n = 10. Which means:

From the information given, we are able to say that:

Here we found the first equation. The information about supplementary and complementary angles can be written as:

Now we have the following system of equations:

If we substitute the second equation in the first one, we are able to find the value for c. Performing this calculation, we find the following:

With this value, we are able to substitute the value of c in the third equation, and find the value of b, as follows:

Now, we can substitute the value of b in the second equation of the system, to find the value of a, as follows:

Now, from all the given information, we were able to find that, the three missing angles are:

Because the question did not name the angles, their name and order are not important, just the values.

Answer:

its c

i took the quiz

Step-by-step explanation:

The speed in centimeters per hour is 0.2328 centimeters per hour.

Given,

An object is moving at a speed of 11 yards every 6 months.

We need to find this speed in centimeters per hour.

1 yard = 91.44 centimeters.

We have,

11 yards every 6 months

11 yard = 6 months

1 month = 30 days

1 day = 24 hours

30 days = 30 x 24 hours

30 days = 720 hours

1 month = 720 hours

6 months = 6 x 720 hours

6 months = 4320 hours

11 yards = 4320 hours

1 yard = 91.44 cm

11 x 91.44 cm = 4320 hours

1005.84 cm = 4320 hours

So,

we will find how many cm per hour.

if 1005.84 cm = 4320 hours then,

Dividing both sides by 4320.

1005.84/ 4320 cm = 4320/4320 hours

0.2328 cm = 1 hour

Rounding to the nearest hundredth.

0.23 cm = 1 hour

Thus the speed in centimeters per hour is 0.2328 centimeters per hour.

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The vector parallel to v is approximately (0.7857, 1.5714, 2.3571).

To decompose vector u into a sum of two vectors, one parallel to vector v and one perpendicular to vector v, we can use the projection formula. The part of vector u that is parallel to vector v can be calculated as:

proj_v(u) = (u dot v / ||v||^2) * v

where u dot v is the dot product of vectors u and v, and ||v||^2 is the magnitude of vector v squared.

The part of vector u that is perpendicular to vector v can be calculated as:

u_perp = u - proj_v(u)

Therefore, the vector parallel to vector v is given by proj_v(u). Let's say that u is the vector (-3, 1, 4) and v is the vector (1, 2, 3):

u dot v = (-3)(1) + (1)(2) + (4)(3) = 11

||v||^2 = (1)^2 + (2)^2 + (3)^2 = 14

proj_v(u) = (11 / 14) * (1, 2, 3) = (11/14, 22/14, 33/14) = (0.7857, 1.5714, 2.3571)

Therefore, the vector parallel to v is approximately (0.7857, 1.5714, 2.3571).

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The irrational numbers to children can be explained as the numbers  that can be written as a nonrepeating or nonterminating decimal .

What are Irrational Numbers ?

The real numbers that can be represented as a nonrepeating or a nonterminating decimal but not as a fraction, and the decimal that goes on forever without repeating.

For Example : \(\sqrt{2} , \sqrt{5} , \sqrt{7}\) are few example of irrational numbers .

In simpler words : the irrational number is a number that is not rational. which means It is a number which cannot be written as a ratio of two integers or cannot be written as fraction.

and If a fraction has a 0 in the denominator , it is an irrational number .

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For each given scenario, the uncertainty and percent uncertainty of the dependent quantity can be calculated using error propagation. The uncertainty ΔA and percent uncertainty ΔA% of the dependent quantity A, in terms of the measured quantities and their uncertainties, can be determined using the provided formulas.

1. For the scenario where z = me^y, with y being the measured quantity with uncertainty Δy and m as a constant, the uncertainty ΔA and percent uncertainty ΔA% of A can be calculated using the formula provided: ΔA = (∂x/∂A)^2(Δx)^3 + (∂y/∂A)^2(Δy)^2 + (∂z/∂A)^2(Δz)^2 + ...

2. In the case of P = 4L + 3W*L, where L and W are measured quantities with uncertainties ΔL and ΔW respectively, the uncertainty ΔA and percent uncertainty ΔA% of A can be determined using the same error propagation formula, considering the partial derivatives (∂x/∂A, ∂y/∂A, ∂z/∂A, ...) based on the given equation.

3. Similarly, for the equation z = 3x - 5y*x, with Δx and Δy being the uncertainties associated with x and y respectively, the uncertainty ΔA and percent uncertainty ΔA% of A can be calculated using error propagation.

4. In the scenario I = A/r^2, where r is a measured quantity with uncertainty Δr and A is a constant, the uncertainty ΔA and percent uncertainty ΔA% of A can be determined using the given error propagation formula.

5. Finally, for N = 0.5rpR^4h, with R and h being measured quantities, the uncertainty ΔA and percent uncertainty ΔA% of A can be calculated using error propagation, taking into account the partial derivatives (∂x/∂A, ∂y/∂A, ∂z/∂A, ...) specific to this equation.

By applying the error propagation formula in each case, the uncertainty and percent uncertainty of the dependent quantity A can be calculated based on the given measured quantities and their respective uncertainties.

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The equation which represents the price of the ticket after the discount is y = 0.25x.

A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that the movie theatre is giving a discount of 75% the original cost of the ticket is x and discounted cost is represented by the variable y.

The equation for the cost of the ticket will be written as,

y = x - 0.75x

y = 0.25x

The graph of the linear equation is attached with the answer below.

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Answer:

3 Blouses cost $450

Step-by-step explanation:

1,200 ÷ 8 = 150

150 x 3 = 450

Answer: $450

Step-by-step explanation:

First divide 1,200 by 8 (150) Then times that by 3 to get the answer

The predicted college GPA for a student with a high school GPA of 3.3 and an ACT score of 31 is approximately 2.747 on a four-point scale.

To compare the models based on goodness of fit, we need to look at the adjusted R-squared values. The adjusted R-squared adjusts for the number of predictors in the model and provides a measure of how well the model fits the data while considering the degrees of freedom.

Comparing the models:

Model A: Adjusted R-squared = 0.74

Model B: Adjusted R-squared = 0.73

Model C: Adjusted R-squared = 0.72

Model D: Adjusted R-squared = 0.75

Based on the adjusted R-squared values, we can see that Model D has the highest value (0.75), indicating the best goodness of fit among the four models. Model A has the second-highest value (0.74), followed by Model B (0.73), and Model C (0.72).

Therefore, the correct answer is:

d. D>A>B>C

Now, let's move on to the second part of your question regarding predicting the college GPA of a student.

The estimated model is:

colGPA = β1 + β2 hsGPA + β3 ACT + ω1

Given:

β1 = 0.6

β2 = 0.35

β3 = 0.032

hsGPA = 3.3

ACT = 31

To predict the college GPA of a student, we substitute the values into the equation:

colGPA = 0.6 + (0.35 * 3.3) + (0.032 * 31)

= 0.6 + 1.155 + 0.992

= 2.747

Therefore, the predicted college GPA for a student with a high school GPA of 3.3 and an ACT score of 31 is approximately 2.747 on a four-point scale.

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Answer:

y = 9.1

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

\(\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}\)

\(\frac{\text{SinW}}{\text{w}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinX}}{\text{x}}\)

Since m∠W + m∠X + m∠Y = 180°

m∠W + 58° + 106° = 180°

m∠W = 180° - 164°

m∠W = 16°

\(\frac{\text{Sin16}}{\text{w}}=\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}\)

\(\frac{\text{Sin106}}{\text{y}}=\frac{\text{Sin58}}{\text{8}}\)

y = \(\frac{8\times (\text{Sin106})}{\text{SIn58}}\)

y = 9.068

y ≈ 9.1

The first part of the function is a constant function, so its Fourier Transform is zero. The second part of the function is a linear function, so its Fourier Transform is a constant times

the Fourier Transform of the given function:

F(w) = where and is the Heaviside step function.

To find the Fourier Transform of the given function, we can use the following steps:

Start with the definition of the Fourier Transform:

F(w) = ∫ f(x) e^(-iwx) dx

Substitute the given function into the formula:

F(w) = ∫ 1 - x/2 0 -1 otherwise e^(-iwx) dx

Split the integral into two parts:

F(w) = ∫ 1 e^(-iwx) dx + ∫ -x/2 e^(-iwx) dx

Evaluate the first integral:

∫ 1 e^(-iwx) dx = -i/w

Evaluate the second integral:

∫ -x/2 e^(-iwx) dx = i/(2w) (e^(-iwx) - e^(iwx))

Add the two integrals to get the final answer:

F(w) =

The given function is a piecewise function, so we need to use the Heaviside step function to evaluate the Fourier Transform. The Heaviside step function is defined as follows:

H(x) = where is a real number.

In this case, the Heaviside step function is used to represent the two parts of the given function. The first part of the function is zero for

and one for. The second part of the function is zero for and

The Fourier Transform of a piecewise function can be found using the following steps:

For each part of the function, find the Fourier Transform of the function.

Add the Fourier Transforms of each part to get the final answer.

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He has eaten \(\frac{5}{8}\) pizza altogether.The total pieces of pizza was 8.Marco ate 3 for lunch and 2 for dinner.So, he ate 5 pieces of pizza out of 8.

What is fraction?

A fraction is a numerical value that is a part of whole number.In this numerator divided by denominator .In simple term both are integers.The word fraction means to break.

there are many types of fraction.Proper fraction, improper fraction,mixed fraction,whole fraction, like fraction, unlike fraction and unit fraction.

Total pieces of pizza =8

Marco ate for lunch =3

He ate for dinner =2

Total he ate =3+2

                     =5

Now remaining pieces of pizza=8-5

                       =3

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Answer:

5/8

Step-by-step explanation:

The equation of the line of best fit is given as y = -11.2X + 1585

The slope indicates that the number of student would decrease by 11.2

To the nearest thousandth, The value of R is -0.9842. This shows that there is a strong negative correlation.

The x and the y values would be inputted . The output is as shown on the image. Then the negative value of the slope tells us that there is a decrease in the number of students

From the attached solution, the graph shows the slope is given as  y = -11.2X + 1585

The negative value shows that there is a decrease in the number of students. That is shown in the slope of -11.2

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The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

Answer:

subu muna titi ko

Step-by-step explanation:

(=ﾟДﾟ=)

Answer:

Step-by-step explanation:

ISSA PARADE INSIDE MY CITY YEAHHHHH

Answer:

3:4 is the answer by dividing 15 and 20

Answer:

3:4

Step-by-step explanation:

15/20 reduced as much as possible is 3:4

Answer:

dilation is size

Step-by-step explanation:

A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value

We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.

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The singular points of a differential equation are the points where the coefficients of the highest and/or second-highest order derivative are zero.

These singular points usually play a vital role in the analysis of the behavior of solutions around them.

Now, let's solve the given differential equations one by one:

1. The given differential equation is `(t² - t - 30)x'' + (t + 5)x' - (t - 6)x = 0`.

We can write the equation in the form of a polynomial as follows: p(t)x'' + q(t)x' + r(t)x = 0,

`where `p(t) = t² - t - 30`, `q(t) = t + 5`, and `r(t) = -(t - 6)`.

The singular points are the values of `t` that make `p(t) = 0`.We can factorize `p(t)` as follows: `p(t) = (t - 6)(t + 5)`.

Therefore, the singular points are `t = 6` and `t = -5`.

So, the answer is "The singular points are t = 6,-5.

2. The given differential equation is `ln(x – 6) y' + sin(6x)y - ey = 0`.

We can write the equation in the form of a polynomial as follows: `p(x)y' + q(x)y = r(x)`where `p(x) = ln(x - 6)`, `q(x) = sin(6x)`, and `r(x) = e^(y)`.

The singular points are the values of `x` that make `p(x) = 0`.For `ln(x - 6) = 0`, we get `x = 7`.

So, the singular point is `x = 7`.

Therefore, the answer is "The singular points are x = 7."

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From of the pool to her friend's house, Andaya could bicycle in a straight line for a distance of 6.4 units.

The marked coordinates are:

A(1,2), (6,5), C(5,7)

AC is the distance between her friend's house and pool.

Using distance formula:

AC = √(x2 - x1)² + (y2 - y1)²

AC = √(5 - 1)² + (7 - 2)²

AC = √16 + 25

AC = √41

AC = 6.403

AC = 6.4 units

Thus, From of the pool to her friend's house, Andaya could bicycle in a straight line for a distance of 6.4 units .

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To find the angle that maximizes the range of the projectile, we can differentiate the x-coordinate equation with respect to θ, set it equal to zero, and solve for θ. This will give us the critical angle that yields the maximum range. We can then substitute this angle back into the x-coordinate equation to find the maximum range.

To find the angle that maximizes the arc length of the trajectory, we can use the arc length formula for parametric curves. The arc length formula for a parametric curve given by x = f(t) and y = g(t) is given by ∫[a,b] √[f'(t)² + g'(t)²] dt. By differentiating this arc length equation with respect to θ and setting it equal to zero, we can find the critical angle that maximizes the arc length. We can then substitute this angle into the x and y coordinate equations to find the coordinates of the point on the trajectory that corresponds to the maximum arc length.

Please note that the exact stepwise solution with specific numbers will depend on the given values of θ and the range of integration for the arc length calculation.

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