Dave ate 3 bags of potato chips each having 5/6 pound of chips. How many pounds of potato chips did Dave eat in all?

Step-by-step explanation:

By Sine rule,

5/(x + 5) = 7/(y + 7) = 8/10.

Therefore x + 5 = 6.25 and y + 7 = 8.75.

=> x = 1.25 and y = 1.75.

The given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3.

What is the linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

We have,

The equation 4x=3y-7

So, here we can solve this equation for the x as well as y equals,

Firstly we will solve for x:

4x = 3y - 7

dividing the whole equation by 4 we get,

4x/4 = (3y - 7)/4

x = (3y - 7)/4

Similarly, we will solve for y:

4x = 3y - 7

3y = 4x + 7

dividing the whole equation by 3 we get,

3y/3 = (4x + 7)/3

y = (4x + 7)/3

Hence, the given equation can be solved for the value of x and y

i.e. x = (3y - 7)/4 & y = (4x + 7)/3

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To determine the constant amount that can be withdrawn each year for 20 years, we need to calculate the annuity payment using the present value of an annuity formula.

Inherited amount: RM300,000

Interest rate: 7% per year

Number of years: 20

Using the present value of an annuity formula:

PV = P * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present value (inherited amount)

P = Annuity payment (constant amount to be withdrawn each year)

r = Interest rate per period (7% or 0.07)

n = Number of periods (20 years)

Plugging in the values:

300,000 = P * [(1 - (1 + 0.07)^(-20)) / 0.07]

Solving this equation, we find that the constant amount that can be withdrawn each year is approximately RM15,000.

Therefore, the correct answer is A. RM15,000.

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Answer: 38

Step-by-step explanation:

3.8=19/5

u have to flip the reciprocal to divide by fraction so 1/10 will be just 10

Then u get 19/5 x 10

You can reduce the GCF so it would be 19 x 2

19 x 2 = 38

Or you can plug it into your calculator (3.8 x .1)

If an independent event has four uncertain outcomes, their probabilities are 20%, 45%, 15%, and C: 20%.

In probability, the sum of the probabilities of all possible outcomes must equal 100%. In this case, the probabilities of the four uncertain outcomes are given as 20%, 45%, 15%, and 20%. This means that each of these outcomes has a chance of occurring equal to the given percentage, and the total probability of all four outcomes is 20% + 45% + 15% + 20% = 100%.

It is important to note that when calculating probabilities, the percentages must add up to 100% to ensure that the total chance of all possible outcomes occurring is equal to 1 or 100%.

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Answer:

Rounding the adjusted forecast to two decimal places, the adjusted forecast in year 2022 for Period-2 is 12136.37.

Step-by-step explanation:

To find the adjusted forecast in 2022 for Period-2, we'll need to use the given seasonality index and the trend line equation.

The trend line equation is:

Fₜ = 179 + 4t

First, we need to determine the value of 't' for 2022 Period-2. Since Period-1 corresponds to 2021, and each period represents a year, we can calculate the value of 't' for 2022 Period-2 as follows:

2022 Period-2 = 2022 + 1 = 2023

Now, we can substitute the value of 't' into the trend line equation:

Fₜ = 179 + 4t

Fₜ = 179 + 4 * 2023

Fₜ = 179 + 8092

Fₜ = 8271

The unadjusted forecast for 2022 Period-2 is 8271.

To adjust the forecast, we multiply it by the seasonality index for Period-2, which is given as 1.47:

Adjusted Forecast = Unadjusted Forecast * Seasonality Index

Adjusted Forecast = 8271 * 1.47

Adjusted Forecast = 12136.37

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Answer:

John would be 69 in.

Step-by-step explanation:

Answer:

ookk

so what is it

Step-by-step explanation:

Answer:

E (5, 5), C (10, 4), D (10, -5). Those are the new points for each of them, since you said no files. (x, y)

Step-by-step explanation:

The line is provided for you in your file, and all you need to do is reflect the triangle from one side to the other.

Answer:

-243

Step-by-step explanation:

Since your finding the 36th term and you know the equation plugin 36(as n) into the arithmetic sequence.

-7(36)+9 = -243

The curves intersect at two points and their angle of intersection is approximately 125.1° and 62.7°.

To find the point of intersection between two curves, we need to solve the system of equations:

t = 3 - s

1 - t = s - 2

3 + t² = s²

Simplifying the second equation, we get:

t + s = 3

Substituting t = 3 - s in the third equation, we get:

s⁴ - 6s³ + 17s² - 24s + 10 = 0

This quartic equation can be solved using numerical methods or factored using the rational root theorem. However, the solutions are rather messy and not easy to obtain by hand. So we'll use a graphing calculator to find the approximate values of s:

s ≈ 2.399, 0.313

Substituting each value of s back into the first equation, we get the corresponding values of t:

When s ≈ 2.399, t ≈ 0.601

When s ≈ 0.313, t ≈ 2.687

So the two curves intersect at approximately two points: (0.601, 0.399, 4.360) and (2.687, -1.687, 0.534).

To find the angle of intersection, we can use the dot product formula:

cosθ = (F'(t) · ū'(s)) / (|F'(t)| |ū'(s)|)

where F'(t) and ū'(s) are the derivatives of the respective curves, and |F'(t)| and |ū'(s)| are their magnitudes.

Differentiating the first curve, we get:

F'(t) = (1, -1, 2t)

Differentiating the second curve, we get:

ū'(s) = (-1, 1, 2s)

So the dot product is:

F'(t) · ū'(s) = -1 - 1 + 4ts

The magnitudes of the derivatives are:

|F'(t)| = √(1 + 1 + 4t²)

|ū'(s)| = √(1 + 1 + 4s²)

Substituting the values of t and s for each point of intersection, we get:

At (0.601, 0.399, 4.360):

cosθ ≈ (-2.398) / (2.440 * 2.248) ≈ -0.527

θ ≈ 125.1°

At (2.687, -1.687, 0.534):

cosθ ≈ (8.542) / (6.144 * 2.784) ≈ 0.459

θ ≈ 62.7°

Therefore, the curves intersect at two points and their angle of intersection is approximately 125.1° and 62.7°.

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Answer:(-4,3)

Step-by-step explanation:

Here, Every equation has same slope (-4) and same y-intercept (3), so we don't need to calculate those.

Now, as coordinates are in left-portion, and also touches the line, it would be: y ≥ -4x + 3

Answer:

9800 ml

Please mark as Brainliest!

Answer:

Step-by-step explanation:

So im gonna be using the substitution method because its easier

We divide the equations into two and solve for y

-6x+y=20

We add 6x to both sides

-6x+y+6x=20+6x

y=6x+20

Now we plug in 6x+20 for y into the other equation

2x+3y=10

2x+3(6x+20)=10 We can simplify now

20x+60=10

20x=-50

take 20 from both sides so its gonna be a fraction

-5/2

We plug in -5/2 for x

y=6(-5/2)+20

y=5

]so therefore x is -5/2 and y is 5

珠ɪᴢᴜᴍɪᴿᴬᴳᴱ

The equality of the expression after removing y by substituting y is 2x + 21 = 10 - 6x + 7 = 20.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

More than one variable may be present inside a linear equation. An equation is said to be linear if the maximum power of the variable is consistently unity.

A formula known as an equation uses the same sign to denote the equality of two expressions.

In another word, the equation must be constrained with some constraints.

Given the expression,

2x + 3y = 10 -6x + y = 20

So,

2x + 3y = 20 and  10 - 6x + y = 20

To remove y we need to find y and substitute.

So by substituting,

10 - 6(20 - 3y)/2 + y = 20

y = 7

So,

2x + 21 = 10 - 6x + 7 = 20

Hence "The equality of the expression after removing y by substituting y is 2x + 21 = 10 - 6x + 7 = 20".

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The given question is in the Spanish language in English it is ;

{2x + 3y = 10 -6x + y = 20 if it is solved by the equalization method, what is the equality that results if the variable y is cleared from both equations?

To find the critical value that corresponds to a confidence level of 95% for estimating a population mean, we can use the t-distribution since the sample size is small (n = 4) and the population is assumed to have a normal distribution.

The critical value is obtained by considering the desired confidence level and the degrees of freedom, which is equal to the sample size minus 1 (df = n - 1 = 4 - 1 = 3). Since we are looking for a 95% confidence level, the remaining 5% is divided equally into two tails (2.5% in each tail). Therefore, we need to find the critical value that leaves 2.5% in the upper tail. Using a t-distribution table or statistical software, the critical value for a confidence level of 95% and 3 degrees of freedom is approximately 3.182.

Therefore, the critical value that corresponds to a confidence level of 95% for estimating a population mean with a sample size of 4 is approximately 3.182.

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Using the concept of proportional, it is found that the value of x  for the given similar triangles is 2.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

Since two triangles ΔACD and ΔABE are similar triangles, then their corresponding sides will be proportional.

Therefore, AC/ AB = AD / AE

By substituting the measures of the sides here;

AC/ AB = AD / AE

(x + 10) / 10 = (15 +3) / 15

15(x + 10) = 180

x + 10 = 12

x = 12 - 10

x = 2

Therefore, the value of x  for the given similar triangles is 2.

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Answer:

Square root 18 (3rd option)

Step-by-step explanation:

Irrational = can’t be expressed in a fraction or decimal/whole number

Answer: r - 5 = 8

Step-by-step explanation:

From the question, we are informed that Skye ran r laps today at soccer practice while Nadine ran five fewer laps than Skye.

If Nadine ran eight laps at practice, the equation that can be used to find how many laps Skye ran will be:

r - 5 = 8

This means Skye ran 13 laps

Answer:

a: $49

b: $91

Explaination:

a: 35% of 140 = 49

b: 140 - 49 = 91

You're welcome! <3

The amount of discount is $49 and  the sale price of the dress is $91 and this can be determined by using the unitary method.

Given :

Elise bought a dress that was discounted 35% off of  the original price of $140.

a) The unitary method can be used in order to determine the amount of discount. If the original price is $140 then the discounted price is given by:

\(=\dfrac{35}{100}\times 140\)

Simplify the above expression.

= $49

b) The unitary method can be used in order to determine the sale price of the dress. If the original price is $140 then the selling price is given by:

\(=\dfrac{65}{100}\times 140\)

Simplify the above expression.

= $91

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Answer: I think it’s a or c

Step-by-step explanation:

(a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, (d) boxplot is attached, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

(a) The mean = sum of all values divided by the number of values

μ = (x1 + x2 + ..... + xn)/n

n = 20

μ = (0.0395 + 0.0443+ 0.0450 + ... + 0.0550 + 0.0571)/20

μ = 0.9878/20

μ = 0.0494

(b) Variance = sum of squared deviations from the mean divided by n-1

s² = {(x1-μ)² + (x2-μ)² + .... (xn - μ)²)/(n-1)

s² = {(0.0395-0.0494)² + (0.0443-0.0494)² + .... +(0.0571-0.0494)²}/19

s² = 0.000016

(b) The minimum is 0.0395 and the maximum is 0.0571.

since the number of data is even, the median will be the average of two middle values.

M = Q2 = (0.0496+0.0499)/2 = 0.04975

Now, the first quartile is the median of the data values below the median

so Q1 = (0.0470+0.0485)/2 = 0.04775

And third quartile will be the median of the data values above the median

Q3 = (0.0504+0.0516)/2 = 0.0510

(c) Since we know that the number of data values is even, the median will be the average of the two middle values of the data set

so M = (0.0496+0.0499)/2

or M = 0.04975

(d) The boxplot is at maximum and minimum values. It will start in Q1 and end in Q3 and has a vertical line at the median or Q2.

The boxplot is attached.

(e) The 5th percentile means 0.05(n+1)th data value

or = 0.05(20+1) = 1.05th data value

5th percentile = 0.0550 + 0.05(0.0443-0.0395) = 0.03974

similarly,

95th percentile = 0.0550 + 0.95(0.0571-0.0550) = 0.056995

Therefore, (a) the sample mean is 0.0494 and the sample variance is 0.000016, (b) the upper quartile is 0.04775, and the lower quartile is 0.0510, (c) the sample median is 0.04975, and (e) the 5th and 95th percentiles of the inside diameter are 0.03974 and 0.056995 respectively.

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The principal should then survey the selected students to gather their opinions on the new dress code.

To answer your question, the principal should choose a sample of students that is both representative and random. This will ensure that the opinions gathered are an accurate reflection of the entire high school population.

How the principal can achieve this:
Determine the sample size:

The principal should decide on a suitable sample size based on the total number of students in the high school.

A larger sample size will yield more accurate results, but it may not be feasible to survey too many students.

To ensure representativeness, the principal should divide the high school population into different strata, such as grade levels or other relevant demographic categories.

This will help ensure that the sample includes a balanced mix of students from different backgrounds and groups.
Select a random sample:

Within each stratum, the principal should choose a random sample of students.

The principal should then survey the selected students to gather their opinions on the new dress code.
By following these steps, the principal can select an appropriate sample of students that will provide an accurate representation of the high school's overall opinion on the new dress code.

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1) \(\overline{WX} \cong \overline{UY}\), \(\angle YXZ \cong \angle XYZ\) (given)

2) \(\overline{XY} \perp \overline{XY}\) (reflexive property)

3) \(\triangle WXY \cong \triangle UYX\) (SAS)

4) \(\overline{WY} \perp\overline{ UX}\) (CPCTC)

The division of the polynomial x^2 + 2*x - 6 by (x + 1), using the long division method of dividing polynomials is x + 1 - 7/(x + 1)

The long division method allows the division of large numbers (which is the dividend) into the number of groups of the divisor and a remainder which is a value less than the expressed value of the divisor.

The expression \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 can be presented as follows;

The long division showing the steps can be obtained using code found online as follows;

\(\begin{array}{*1r {\arraycolsep}{\arraycolsep} *{11}l} & && x + 1 \\\cline{4-3}& &x+1& \longdiv {) x^2 +2\cdot x - 6& & & & & \\ & & & x^2 +x \\\cline{4-} && &\ \ \ x -6& \\ & & \ \ \ & \ \ \ x +1 \\\cline{4-} & & & \ \ \ \ \ \ \ -7 & \\ \cline{4-} \end{array}\)

The remainder of the long division is -7, therefore, we get;

\(\dfrac{x^2+2\cdot x-6}{x + 1} = x + 1 - \dfrac{7}{x+1}\)

The value of the expression, \_f_rac{x}{y} x^2 + 2*x - 6/x + 1 following the long division is; x + 1 - 7/(x + 1)

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In general, for a set A with n elements, the number of distinct pairs of disjoint non-empty subsets of A, whose union is all of A, is given by \(2^{(n-1)} - 1.\)

The number of distinct pairs of disjoint non-empty subsets of set A, whose union is all of set A, can be calculated as \(2^{(n-1)} - 1\). where n is the number of elements in set A.

To understand why this formula holds, let's consider an example:

Suppose set A has 3 elements: {a, b, c}.

The possible non-empty subsets of set A are:

{a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}.

Among these subsets, we need to find pairs of disjoint subsets whose union is all of A. Disjoint subsets are subsets that have no elements in common.

The pairs of disjoint subsets whose union is all of A are:

({a}, {b, c}), ({b}, {a, c}), ({c}, {a, b}).

So in this case, there are 3 such pairs.

Using the formula \(2^{(n-1)} - 1\):

n = 3 (number of elements in set A)

\(2^{(3-1)} - 1\) = 4 - 1

= 3

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The time constant of the 1 mm diameter copper thermocouple bead is approximately 0.0031 seconds.

To calculate the time constant of a thermocouple bead, we need to know the thermal conductivity (k) of the material. Since the thermal conductivity of copper is approximately 400 W/m·K, we can use this value for our calculation.

The time constant (τ) is given by the equation:

τ = (ρ * Cp * V) / (h * A)

where:

ρ is the density of the material,

Cp is the specific heat capacity of the material,

V is the volume of the thermocouple bead,

h is the convective heat transfer coefficient,

A is the surface area of the bead.

To find the time constant, we need to determine the density and specific heat capacity of copper. The density of copper is about 8,960 kg/m³, and the specific heat capacity is about 385 J/kg·K.

Now, let's calculate the time constant:

First, we need to determine the volume of the thermocouple bead. Since the diameter is 1 mm, the radius (r) is 0.5 mm or 0.0005 m.

The volume (V) of a sphere is given by V = (4/3) * π * r^3. Plugging in the values:

V = (4/3) * π * (0.0005)^3 ≈ 5.24 x 10^-10 m³.

Next, we calculate the surface area (A) of the bead. The surface area of a sphere is given by A = 4 * π * r^2:

A = 4 * π * (0.0005)^2 ≈ 3.14 x 10^-6 m².

Now we can calculate the time constant:

τ = (ρ * Cp * V) / (h * A) = (8,960 * 385 * 5.24 x 10^-10) / (5 * 3.14 x 10^-6) ≈ 0.0031 seconds.

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In the context of Range Safety and Risk Mitigation, the ability to detect, assess, and respond to potential hazards is essential.

Range safety and risk mitigation involve identifying and minimizing potential hazards associated with range operations, such as the launch or test of rockets, missiles, or unmanned aerial vehicles. To ensure safety, it is critical to have the ability to detect and assess potential hazards, such as debris, vehicle or equipment malfunctions, and human error. Once hazards have been identified and assessed, the next step is to develop and implement appropriate safety measures to mitigate the risk associated with those hazards. These measures may include the use of safety protocols, engineering controls, or administrative procedures to ensure that all personnel and equipment are protected. In summary, the ability to detect, assess, and respond to potential hazards is critical for effective range safety and risk mitigation. By implementing appropriate safety measures and protocols, the risks associated with range operations can be minimized, ensuring the safety of personnel and equipment.

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Answer:

y=50x+120

Step-by-step explanation:

y is the ending altitude

x is the number of hours the climber has climbed

put 50 before x because that how fast the climber is climbing

then 120 is your y intercept  

Answer:

Step-by-step explanation:

The Luminosity of a star is proportional to its Effective Temperature to the 4th power and its Radius squared." Example 1: Two stars are the same size, (RA=RB), but star A is 2x hotter than star B (TA=2TB): Therefore: Star A is 24 or 16x brighter than Star B.