Lucy spent $3.60 for stamps to mail packages. Some were 30¢ stamps and the rest were 20¢ stamps. The number of 20¢ stamps was 2 less than the number of 30¢ stamps. How many stamps of each kind did Lucy buy?

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.

(a) For the series 1+2+3+4+...+392:

Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.

(b) For the series 1+2+3+4...x:

To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).

(c) For the series 546 + 547 + 548 + 549:

Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.

The final answer for each part is:

(a) The sum of the series 1+2+3+4+...+392 is 77,028.

(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).

(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.

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Answer:

the intersection point is ( -5/4, -5/4, -9/8)

Step-by-step explanation:

F(x,y,z) = x² +y² -z= 0

Then find differential of each terms then we have

∀f(x)=2x

∀f(y)=2y

∀f(z)=-1

The partial differential which is the director vector is at F(x,y,z)= (1,1,2)

Vf(1,1,2) = (2,2,-1)

But the given point is ( 1.1,2)

Then the parametric equation of normal line will be

x= 1+2t

y= 1+2t

z= 2 -t

The parametric equation can be formed as

(1+2t)² + (1+2t)² - (2-t)= 0

If we expand the expression above we have,

2(1+4t+4t²) - 2+t= 0

0= 8t² + 9t

t= 0 or t= -9/8

Substitute the value of t into the parametric equation above

At t=0

x= 1+2t; x= 1+2(0)=1

y= 1+2t; y= 1+2(0)=1

z=2 -t ; z= 2-(0)= 2

At =0 , we have (1,1,2)

At t= -9/8

x= 1+2t; x= 1+2(-9/8)=-5/4

y= 1+2t; y= 1+2(-9/8)=-5/4

z=2 -t ; z= 2-(-9/8)= -9/8

Therefore, the intersection point is ( -5/4, -5/4, -9/8)

The normal intersects the paraboloid at \((-\frac{5}{4},-\frac{5}{4},\frac{25}{8} )\)

A surface all of whose intersections by planes are either parabolas and ellipses or parabolas and hyperbolas.

Given function is,

\(z = x^2 + y^2\)

We can write the given function as,

\(F(x,y,z)=x^2+y^2-z\)

Compute the gradient  \(F\) by using the formula,

\(\nabla F(x,y,z)=\left\langle 2x,2y,-1\right\rangle\)

At (1,1,2) we get,

\(\nabla F(x,y,z)=\left\langle 2,2,-1\right\rangle\)

The equation of the tangent plane at (1,1,2) is,

\(2(x-1)+2(y-1)-(z-2)=0\\2x+2y-z-2=0\\\frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{-1}=t\\ x=2t+1,y=2t+1,z=-t+2\)

Replace the values of \(x,y,z\) in \(z = x^2 + y^2\) and then solve for \(t\) then,

\(-t+2=(2t+1)^2+(2t+1)^2\\8t^2+9t=0\\t=0,-\frac{9}{8}\)

Substituting the value into the parametric equations,

\(x=2(-\frac{9}{8} )+1,y=2(-\frac{9}{8} )+1,\ and \ z=-(-\frac{9}{8} )+2\\x=-\frac{5}{4}, \ y= -\frac{5}{4} ,z=\frac{25}{8}\)

Therefore, the normal intersects the paraboloid at \((-\frac{5}{4},-\frac{5}{4},\frac{25}{8} )\)

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Given:

To find:

The height from the ground to the base of the window.

Explanation:

Since the triangles XWY and XVZ are similar by AA similarity.

So we can write,

The true equations are x²- 4 = 0 and 4x² = 16. the correct options are A and C.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The two equations that are true for x = -2 and x = 2 are:

x²- 4 = 0 (true for x = -2 and x = 2)

4x² = 16 (true for x = -2 and x = 2)

To check this, we can substitute -2 and 2 into each equation and see if they are equal to 0:

(-2)² - 4 = 0, 2² - 4 = 0 (true for x = -2 and x = 2)

4(-2)²= 16, 4(2)² = 16 (true for x = -2 and x = 2)

The other three equations, x² = -4, 3x2 + 12 = 0, and 2(x - 2)²= 0, are not true for either x = -2 or x = 2.

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Answer:

Slope is 1

Step-by-step explanation:

From the general linear equation:

\({ \rm{y = mx + c}}\)

m is the slope

Comparing with the equation given:

\({ \rm{y = { \green{1}}x - 3}}\)

Step-by-step explanation:

a= c-b pls let me know if it is correct or not

Answer:

8m=10m

Step-by-step explanation:

Answer:

C. 32,500

Step-by-step explanation:

the pattern is adding by 4.

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

Answer:

Given, the sides of a triangle are 5cm,12cm and 13cm

semi−perimeter = a+b+c/2

s= (5+12+13)/2

s= 30/2

s=15cm

Area of the triangle (according to the Heron's Formula)

= s(s−a)(s−b)(s−c)

= 15(15−5)(15−12)(15−13)

= 15(10)(3)(2)

= 900

=30cm ^2 .

Step-by-step explanation:

Hope it is helpful....

Given: a tabletop that is a rectangle 24 in long and 18 in wide.

Find: (a) the area of the tabletop in square centimeters

(b) The designer wants to cover the tabletop with tiles. She doesn't have any to begin with and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm². number of bags of tiles does the designer need to buy to completely cover the tabletop

(c)If each bag of tiles costs $3.76, how much will she need to spend on tiles.

Explanation: (a)

so the length of the tabletop in cm will be

and the breadth of the tabletop in cm will be

the area of the tabletop will be

(b) The designer wants to cover the tabletop with tiles and she can't buy partial bags of tiles. Each bag of tiles covers 260 cm² so the numbe rof bags designer needs to buy to cover the tabletop is

it means that designer needs to buy 11 bags of tiles to cover the tabletop.

(c) If each bag of tiles costs $3.76.the the total cost will be equal to

The average absolute deviation, which tells you how much the values in the data set vary from the mean on average.

Deviation is a statistical measure that indicates how much a set of data varies from its average or expected value. It is calculated by finding the difference between each data point and the mean value of the data set.

Absolute deviation is a measure of how far apart a set of numbers is from their average, or mean, value. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences.

Here are the basic steps to find the absolute deviation:

1) Find the mean of the data set by adding up all the numbers and dividing by the total number of values.

2) For each value in the data set, subtract the mean from the value to find the difference.

3) Take the absolute value of each difference (ignore the positive or negative sign) by simply dropping the minus sign if there is one.

4) Add up all the absolute differences found in step 3.

5) Subtract the total number of values in the data set from the sum of the absolute differences.

The result is the average absolute deviation, which tells you how much the values in the data set vary from the mean on average.

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Answer:

what's the question?

Step-by-step explanation:

..

A small aircraft takes off from the ground. The height of the aircraft increases by 1,000 feet for every minute that has passed since the aircraft left the ground.

Which function best represents the height of the aircraft in feet, as a function of time in minutes?

___________________________________________

f(x ) = 1000x

y= mx+b

b= 0

The slope m (feet for every minute) (y/x) (variation of y with respect to x)

After finishing the craft, you remain with \(25/6\) feet of rope. The simplest version of this is \(4\) & \(1/6\) feet long rope.

Both British imperial and American customary methods of measurement both use the unit of length known as the foot (plural: feet), denoted by the standard sign ft. An other sign that is frequently used is the prime symbol, ′. One foot equals 12 inches in both customary & imperial measures, and one yard equals three feet.

In both the Imperial and American customary systems of measurement, the foot serves as a unit of length. It is equivalent to a yard and a third, or 12 inches.

The mixed numbers must first be transformed into improper fractions:

\(4\) and \(2/3 = (4 * 3 + 2) / 3 = 14/3\)

\(3\) and \(1/6 = (3 * 6 + 1) / 6 = 19/6\)

Next, we add the two fractions to get the total amount of rope needed:

\(14/3 + 19/6 = (28/6) + (19/6) = 47/6\)

Now we can subtract this total from the amount of rope you started with:

\(12 - 47/6\)

To simplify this subtraction, we need a common denominator of \(6\):

\(72/6 - 47/6 = 25/6\)

Therefore, you will have \(25/6\) feet of rope left after working on the project. This can be simplified to \(4\) and \(1/6\) feet of rope.

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Answer:

Adeniyi   = (2/7)

Akintola  = (4/7)

Bello     =   (1/7)

Step-by-step explanation:

Let x stand for the money that Adeniyi recieves for her share.  We can then write expressions for all the lucky recipients:

Adeniyi = x

Akintola = 2x  [Akintola gets twice as much as Adeniyi]

Bello = (1/2)x  [Bello gets half of Adeniyi's share]

The original amount is the sum of all three shares:

Total = x + 2x + (1/2)x

Total = (3+(1/2))x  or = (7/2)x

The proportions for each can be set as the ratio of the individual's amount to the total of (7/2)x.

Adeniyi = x/((7/2)x)       = (2/7)

Akintola = 2x/((7/2)x)    = (4/7)

Bello = (1/2)x/((7/2)x)    =  (1/7)

Total  =                             (7/7)

Answer:

In mathematics, the extrema of a function refer to the maximum and minimum values that the function can take on. These values can be local extrema, which occur within a certain range of the function, or global extrema, which are the maximum and minimum values over the entire domain of the function.

To find the extrema of a function, one can use a variety of techniques, such as taking the derivative of the function and setting it equal to zero to find the points of stationary values, or using the second derivative test to determine whether a stationary point is a local maximum or minimum.

Interpreting the extrema of a function can provide valuable information about the behavior of the function. For example, the global maximum of a function might represent the highest possible value that the function can attain, while the global minimum might represent the lowest possible value. Local extrema can also be important, as they can indicate changes in the slope or concavity of the function, which can have important implications for applications such as optimization or modeling real-world phenomena.

Answer:

D, and C sorry if I'm wrong

Answer:

They won't

Step-by-step explanation:

Benjamin makes 50 per week, and Bill spends 25 per week, here's a table with each week for 10 weeks.

Step-by-step explanation:

1.solution

=2a+5a

=7a

2.solution

=12x-3x

=9x

3.solution

=3p+2p-p

=5p-p

=4p

Hope it helps you.

Hey there!

1. “2a + 5a”

COMBINE your LIKE TERMS

2 + 5 = 7

So this means that: 2a + 5a has to equal 7a

Answer: 7a ☑️

2. “12x – 3x”

COMBINE your LIKE TERMS

12 – 3 = 9

So that means 12x – 3x has to equal 9x

Answer: 9x ☑️

3. “3p + 2p – p”

Side note: “P” by itself is understood as 1

Equation: 3p + 2p – 1p

COMBINE your LIKE TERMS

3p + 2p – 1p

3 + 2 = 5

Which makes 3p + 2p have to equal to 5p

5 – 1 = 4

So this means that 5p – 1p has to equal to 4p

Answer: 4p ☑️

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

It is true that when difference on dependent variable is attributed to effect of that variable through statistical hypothesis testing then it is unlikely that the difference would occur by chance alone

A formal assertion about the nature of a phenomenon made within the constraints of a statistical model is known as a statistical hypothesis.

Statistical hypothesis is a description of the makeup of a population. A population parameter is frequently used to express it.

There are two statistical hypotheses used in hypothesis testing. The above-described null hypothesis (H0) is the first.

If it turns out that the null hypothesis is statistically invalid, an alternative hypothesis (Ha) for each H0 will be given preference. Depending on the research hypothesis, the Ha may be directed or nondirectional.

About the statement in the question,

It is improbable that an observed difference between two groups on the dependent variable would occur by chance alone when the difference is explained by the effect of the dependent variable through statistical hypothesis testing.

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As per the concept of hypothesis, the value of p is 0.47 the value of the static hypothesis is 4.3893 and the statistical division when the alpha = 0.05 is 0.1085.

What is meant by hypotheses?

in math, hypotheses refers a an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

Here we have given that, a movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a 2nd time. The target is to have 40 million viewers and they want more than 40% of the viewers to return to see the movie again.

And they show the movie to a test audience of 140 people.

Of the test audience, 66 people said they would see it again.

And we have to determine, the p-value is, the p-value for the test statistic.

And the statistical division when the alpha = 0.05 and explain the managerial conclusion for this situation.

Based on the question, the null hypothesis is,

H0: P = 3

H1: P > 0.03

Here we know that they show the movie to a test audience of 140 people.

So, n = 140

Here the test audience, 66 people said they would see it again.

So, x = 66

Therefore, the value of p is,

=> 66/140 = 0.47

Then the test hypothesis is,

=> Z = (0.47 - 0.3) / √[(0.3(1 - 0.3))/140]

When we simplify this one, then we get,

=> Z = 4.3893

Therefore, value of the static hypothesis is 4.3893.

Then the p-value = 0.1085 at 5% level of significance.

Here, 0.1085 <  4.3893,

Therefore, the null hypothesis is not rejected.

Therefore, p-value  = 0.1085, and we will not reject the null hypothesis.

So, the value of the static hypothesis is greater than the null hypothesis and the value of p so the value of not rejects the null hypothesis.

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X = 30°

The triangle in the circle as one angle of the main triangle and it is equilateral indicated by the slashes meaning all angles are 60°. (Every triangle has a total of 180°) the next angle is made from a tangential line the forms a 90° right angle with one of the radii in the circle meaning the main triangle has 1 angle of 60°, 1 angle of 90°, and that means that angle X is 30°.

Answer:

triangle ABD is a equilateral triangle.

so each angle is 60°

<ADB=60°

<BAD=60°

again

we have

CD is perpendicular to AD[tangent on the arc is perpendicular to the radius]

:. ADC=90°

°

again

In triangle ADC

<A+<B+<C=180°[sum of a interior angle of a traingle is 180°]

60°+90°+x=180°

x=180°-150°

x=30°

is a right answer.

(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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Answer:

it'll cost about $4.13

Step-by-step explanation:

Answer:

(−∞,∞)

Step-by-step explanation:

Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.

All real numbers

So, the answer is (−∞,∞)

Answer:

Can you format this a little better?

The value of the probability P (Sheep | Male) is 2/7

From the question, we have the following parameters that can be used in our computation:

Sheep = 4 and 3

Male = 1, 4, 2, 2 and 5

The probability P (Sheep | Male) is then calculated as

P(Sheep | Male) = (Sheep and Male)/Male

Substitute the known values in the above equation, so, we have the following representation

P(Sheep | Male) = 4/(1 + 4 + 2 + 2 + 5)

So, we have

P(Sheep | Male) = 4/14

Simplify

P(Sheep | Male) = 2/7

Hence, the probability is 2/7

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