For the period 1995-2002, the total personal expenditures (in billions of dollars) in the United States for food, f(x), and for housing, h(x), can be described by the equations shown below, where x is the number of years past 1995.†
f(x) = 40.74x + 742.65 and h(x) = 47.93x + 725
Find the year in which these expenditures were equal and the amount spent on each. (Round the year up. Give the amount correct to the nearest whole billion.)
year______
amount ______

The system of equations are solved

a) y = 2x + 3

b) y = 3x

c) f = p + 3/2

d) y = 3x

e) The number of dogs Becca walks at the end of third month is y = 9 dogs

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

a)

The initial number of cards Stacy has = 3 cards

The number of cards she gets per week = 2 cards

So , the total number of cards after x weeks = 2x cards

And , the total number of cards = initial number of cards + number of cards after x weeks

Substituting the values in the equation , we get

y = 2x + 3

b)

The first point is P ( 3 , 9 )

The second point is Q ( -3 , -9 )

So , the equation of line is y = 3x

when x = 3 , y = 9

c)

f = p + 3/2   be equation (1)

when p = 1

f = 1 + 3/2

f = 5/2

when p = 2

f = 2 + 3/2

f = 7/2

when p = 3

f = 3 + 3/2

f = 9/2

d)

The equation of line is y = 3x and the graph is plotted with the points P ( 1 , 3 ) and Q ( 2 , 6 )

e)

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 0 , 1 )

Let the second point be Q ( 2 , 5 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 5 - 1 ) / 2

Slope m = 2

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 1 = 2 ( x - 0 )

y - 1 = 2x

Adding 1 on both sides of the equation , we get

y = 2x + 1

Now , when the number of years = 4

y = 2 ( 4 ) + 1

y = 9 dogs

Hence , the equation is solved

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Answer:

The answers are x=-37 and x=3

Step-by-step explanation:

The solution set for the equation (7x+3)(2x-6)=0 is {−37,3}. To solve for x, one can use the distributive property to expand the equation and then solve for x. For example, 7x² - 3x - 12x - 18 = 0 can be rearranged to 7x² - 15x - 18 = 0 and then solved using the quadratic formula.

Answer: After 39 minutes, both pools will have the same amount of water.

Step-by-step explanation:

Let's call the number of minutes elapsed t. Then the amount of water in Destiny's pool after t minutes is 800 + 25t gallons, and the amount of water in Jabez's pool after t minutes is 20 + 45t gallons.

We want to find the time t at which the two pools have the same amount of water, so we set their amounts equal:

800 + 25t = 20 + 45t

Subtracting 20 from both sides of the equation:

780 + 25t = 45t

Subtracting 25t from both sides of the equation:

780 = 20t

Dividing both sides of the equation by 20:

39 = t

So, after 39 minutes, both pools will have the same amount of water.

Answer: To calculate the total, we need to first calculate the discount and then the tip.

First, calculate the discount: $21.50 x 10% = $2.15

Then, subtract the discount from the subtotal: $21.50 - $2.15 = $19.35

Next, calculate the tip: $19.35 x 20% = $3.87

Finally, add the tip to the subtotal after the discount to find the total: $19.35 + $3.87 = $23.22

Therefore, Abdiel's total would be $23.22 if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount.

Step-by-step explanation:

Answer:

6 GB

Step-by-step explanation:

First find the rate per day. You can do that by dividing 4GB by 20 days.

4/20 = 1/5 = 0.2GB per day

Then, just multiply 30 days by the rate of 0.2GB/day.

30 x 0.2 = 6

The number of phones and accessories sold are 8 and 24 respectively.

Indigo works as a salesperson at an electronics store and sells phones and phone accessories. Indigo earns a $8 commission for every phone she sells and a $4 commission for every accessory she sells. On a given day, Indigo made a total of $160 in commission from all accessory and phone sales and she sold 3 times as many accessories as phones.

Therefore, the number of phones and accessories she sold can be calculated as follows:

Using equation,

let

x = number of phone sold

y = number of accessories sold.

Therefore,

8x + 4y = 160

y = 3x

Therefore,

8x + 4(3x) = 160

8x + 12x = 160

20x = 160

x = 160 / 20

x = 8

Hence,

y = 3(8) = 24

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Family's fuel efficiency is 32.67 miles per gallon.

Unit conversion is the conversion between different units and measurements of the same quantity done by the division or multiplication.

Mitchell family's fuel efficiency in km/l =[tex]\frac{750}{54}[/tex]

                                                               =13.89 km/l

The fuel efficiency in miles per gallon = 13.89*2.35

                                                               = 32.67 m/g

(1 kilometer per liter = 2.35 miles per gallon)

Hence, mitchell family's fuel efficiency is 32.67 miles per gallon.

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The number of people in Indiana residents is given by the equation

A = 5,750,000 or 5.75 million

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of people in Indiana residents aged 5 years and older be A

Now , the equation will be

Substituting the values in the equation , we get

The percentage of population residents aged 5 years and older = 5.6 %

The number of residents aged 5 years and older = 322,000

So , the total population A is calculated as

( 5.6 % ) of A = 322,000

On simplifying the equation , we get

( 5.6 / 100 ) A = 322,000

Divide by 6.6 on both sides of the equation , we get

A / 100 = 57,500

Multiply by 100 on both sides of the equation , we get

A = 5,750,000

A = 5.75 million

Hence , the population of Indiana is A = 5,750,000 or 5.75 million

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It is true that both triangles meet the prerequisites listed before. FGH and JKL are then consistent.

Expected to give that it has three sections and three vertices, a triangle qualifies as a rectangle. It belongs to the core geometric shapes. Triangle ABC is the term utilized to refer to a triangle only with vertices A, B, and C. When the three principles are not collinear, a unique rectangle and square in Geometry and trigonometry are discovered. Triangles are polygons because they have sides and three corners. The points at which three sides of the triangle coincide are referred to as the triangle's edges. Three triangle angles are multiplied to generate 180 degrees.

given

FGH and JKL in the specified right angle

GF ≅ KJ ( one side of both right angle triangles) ( one side of both right angle triangles)

∠F≅ ∠J (right angle) (right angle)

FH ≅ JL (opposite side of both right angle triangles ) (other side of both right angle triangles )

Then ,

We can conclude that GH KL (hypotenuse of both right angle triangles)

In two right triangles, if the hypotenuse and one side of one triangle are identical to the hypotenuse and one side of the other triangle, then the two triangles are congruent according to the RHS congruence rule.

It is true that both triangles meet the prerequisites listed before. FGH and JKL are then consistent.

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Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Here,

Given :

customer uses 390 minutes , the monthly cost will be $178.

customer uses 940 minutes, the monthly cost will be $398.

To find an equation ,

where x is number of monthly minutes

and y is total monthly of splint plan.

So , equation is :

=> y =mx +b

For first case :

=> 178 = 390x + b

Second case :

=> 398 = 940x + b

Solve for x:

=> 178 - 390x = 398 - 940x

=> -200x = - 550

=> x = 550/200

=>x = 55/20

=>x = 11/4

=> x = 2.75

For value of b

=>  178 = 390(2.75) + b

=> 178 - 1072.5 = b

=> -894.5 = b

B)

=> y = 866(2.75) - 894.5

=> y = 2381.5 - 894.5

=> y = 1487

Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.

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Answer:

A regular prism with 10 faces and 12 vertices has 6 sides. This is because the number of faces and vertices are related by the equation F+2 = E+2V, where F is the number of faces, E is the number of edges, and V is the number of vertices. In this case, 10+2 = 12+2V, so V = 6 and the number of sides of the prism is also 6

Step-by-step explanation:

1. A regular prism has 10 faces and 12 vertices.

2. The number of faces and vertices is related by the equation F+2 = E+2V.

3. Where F is the number of faces, E is the number of edges, and V is the number of vertices.

4. In this case, 10+2 = 12+2V, so V = 6.

5. Therefore, the number of sides of the prism is also 6.

Answer:

Angular velocity = 93.33 radians/second

Revolutions per minute = 1,782.51 revolutions per minute

Step-by-step explanation:

The relation between angular velocity, ω and linear velocity, v is given by the equation
[tex]\omega = \dfrac{v}{r}[/tex]

where ω is in radians per second

v = m/s

and r is the radius (m) of the circular motion, in this case, the radius of the tire

Given v = 28 m/s and r = 0.300 m

we get

[tex]\omega = \dfrac{28 \;m/s}{0.3\;m} = 93.33 \;radians/second[/tex]

Since 2π radians make a full revolution, 93.33 radians/sec = 93.33 ÷ 2π = 29.708 revolutions per second

To get the revolutions per minute, multiply this by 60 since there are 60 seconds to a minute:

29.708 x 60 = 1,782.51 revolutions per minute

The ranges of each equation for the domain {-2,0,2} are given as follows:

The domain is the set of input values for each equation, hence the range will be the set of output values for the given domain.

For the equation y = -x, the range is obtained as follows:

Hence the range is:

{-2, 0, 2}.

The same procedure is applied to the other equations, the range is the set containing the numeric value of the function for each input value.

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Answer:

======================================================

Reason:

The number of weeks can be any number from the set {0,1,2,3,...} so we say that this value is independent. It does not depend on the number of stickers.

But the number of stickers does depend on the number of weeks. As w changes, so does the value of 's'.

The equation would be:  s = 2w+12

And so on. Each time 'w' goes up by 1, 's' goes up by 2.

In isosceles triangle ΔABE, the correct option is option D. which proves that BC ≅ ED.

What is the isosceles triangle?

An isosceles triangle is a triangle having any two sides equal in length. The third side is called the base of the isosceles triangle. In an isosceles triangle, the angles opposite to equal sides are equal in measure.

1.∠ABC ≅ ∠AED (Given)

2.  Isosc. △ABE, base BE (Given)

3.  AB ≅ BE (Def. of Isosc. △)

4.  ∠A ≅ ∠A (Reflex. Prop. of ≅)

5.  △ABC ≅ △AED (ASA Steps 1, 3, 4)

6.  BC ≅ ED (CPCTC)

option 1 is wrong in that the step 3. AB is not congurent with BE,

option 3 is wrong in that step 5.   △ABC≅△AED  should be prove by BD ≅ CE, ∠A BE ≅ ∠AEB, BE  ≅ BE

hence, in isosceles triangle ΔABE, the correct option is option D. which proves that BC ≅ ED.

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Answer:First, we can calculate how many bottles of wine can be made per pound of grapes:

14 bottles / 80 pounds = 0.175 bottles / pound

Next, we can multiply this number by the number of pounds of grapes the wine maker has to find the total number of bottles of wine that can be made:

0.175 bottles / pound * 625 pounds = 110.31 bottles

Rounding to the nearest whole bottle, we find that the wine maker can make 110 bottles of wine with 625 pounds of grapes.

Step-by-step explanation:

The total spent in 2006 is nearly 28  billion dollars.

A logarithmic function is a function of the form. which is read “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1. There are no restrictions on y.

here, we have,

The total spent on research and development by the federal government in the United States given by function,

S(t) = 3.1 ln(t) + 22

To find total spent in 2006.

We have to substitute t=6 in given function.

S(6) = 3.1 ln(6) + 22

      = 5.5 +  22  

      =27.5

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Answer: The formula for continuously compounded interest is given by:

A = P * e^(rt)

Where:

A = the final account balance

P = the initial investment (principal)

r = the annual growth rate as a decimal

t = the number of years the investment is held

In this case, P = 540, r = 0.091 and t = t years.

So, the function showing the value of the account after t years is:

A = 540 * e^(0.091t)

To find the percentage of growth per year (APY), we can use the formula:

APY = (e^r - 1) * 100

Substituting r = 0.091, we find:

APY = (e^0.091 - 1) * 100 = 9.56%

So, the APY is approximately 9.56%, to the nearest hundredth of a percent.

Step-by-step explanation:

Here are some examples of quantitative survey or simulation questions:

On a scale of 1 to 5, how likely are you to recommend our product to a friend or colleague?

1 (Not at all likely)

2

3

4

5 (Extremely likely)

How often do you use our app?

Daily

3-4 times a week

Once a week

Once every two weeks

Rarely

How much time do you spend using our app in an average day?

Less than 30 minutes

30 minutes to 1 hour

1 to 2 hours

More than 2 hours

How satisfied are you with the overall performance of our app?

Very dissatisfied

Dissatisfied

Neutral

Satisfied

Very satisfied

How do you rate the usability of our app?

Poor

Fair

Good

Very good

Excellent

A quantitative survey uses statistics to gather facts and figures. It's most frequently utilized to support or refute a conclusion you may have reached after conducting qualitative research.

A survey may be qualitative, quantitative, or a combination of the two. A quantitative survey is one that uses a questionnaire with scaleable responses. If your survey has descriptive questions with in-depth answers then it is a qualitative survey. Your survey is a mixed-method survey if it uses both of them.

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Answer:

234 miles

Step-by-step explanation:

Lets set the variable 'n' as the number of miles driven. We can set up the following equation:

18.95 + 0.83n = 213.17

Now, all we have to do is solve it. We can get 0.83n = 194.22, so n = 194.22/0.83 = 234 miles

Answer: 96 m.

Step-by-step explanation: Let's call the length of the rectangular field "L".

We know the perimeter of the field is equal to the sum of all its sides, so:

350 = 2L + 2 * 79

Expanding the right side, we have:

350 = 2L + 158

Subtracting 158 from both sides:

192 = 2L

Dividing both sides by 2:

L = 96 m

So the length of the rectangular field is 96 m.

(a)Contrapositive: If an object does not have a border, then it is not red.

Converse: If an object has a border, then it is red.

Inverse: If an object is not red, then it does not have a border.

(b)Contrapositive: If an object is not red or does not have a border, then it is not a rectangle.

Converse: If an object is a rectangle, then it is red and has a border.

Inverse: If an object is not red or does not have a border, then it is not a rectangle.

(c)Contrapositive: If an object does not have a border, then it is not red or blue.

Converse: If an object is red or blue, then it has a border.

Inverse: If an object does not have a border, then it is not red or blue.

a) Original Conditional Statement (P - Q): If an object is red, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red.

Converse (Q - P) If an object has a border then it is red.

Inverse (not p → not q) If an object is not red then it does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may have a border but not be red.

b) Original Conditional Statement (P - Q): If an object is a rectangle, then it is red and has a border.

Contrapositive (not Q - not P): If an object is not red and does not have a border, then it is not a rectangle.

Converse (Q - P) If an object is red and has a border, then it is a rectangle.

Inverse (not p → not q) If an object is not a rectangle then it is not red or does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may be red and have a border but not be a rectangle.

c) Original Conditional Statement (P - Q): If an object is red or blue, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red or blue.

Converse (Q - P) If an object has a border then it is red or blue.

Inverse (not p → not q) If an object is not red or blue then it does not have a border.

The contrapositive and converse are true, while the inverse is false. For example, object H may have a border but not be red or blue.

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The average daily balance of the credit card for the January 1 - January 31 billing period is $1283.87.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

The average daily balance can be determined by dividing the total daily balances for January by the number of days in January.

The average daily balance = Total balance / Total number of days in January.

Total balance = (800 x 1 days) + (1000 x10 days) + (1250 x 10 days) + (1650 x 10 days)

Total balance = 800 + 10,000 + 12,500 + 16,500 = 39800

The average daily balance = 39800/31 = $1283.87

Therefore, the average daily balance of the credit card for the January 1 - January 31 billing period is $1283.87.

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The derivative of the given function is  23t^22 ln |t| +  t^22

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The product rule  will be most helpful in beginning this problem.

S = t^23 ln|t|

Differentiate with respect to t

D(s) = ds/dt = D( t^23 ln|t| )

Apply the rule :

D(uv) = u'v+uv'

u' =du/dt , v'=dv/dt

D(s) = 23t^22 ln |t| +  t^23 (1/t)

D(s) = 23t^22 ln |t| +  t^22

The derivative of the given function is  23t^22 ln |t| +  t^22

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The derivative of the given function is  23t²² ln |t| +  t²².

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The product rule will be most helpful in beginning this problem.

S = t²³ ln |t|

Differentiate with respect to t

D(s) = ds/dt = D( t²³ln|t| )

Apply the rule :

D(uv) = u'v+uv'

u' =du/dt , v'=dv/dt

D(s) = 23t²² ln |t| +  t²³ (1/t)

D(s) = 23t²² ln |t| +  t²²

The derivative of the given function is  23t²² ln |t| +  t²²

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Answer:

[tex](10 {}^{2}) + (9 {}^{2}) = 181[/tex]

[tex]181 + 15 = 196[/tex]

[tex] \sqrt{196} = 14[/tex]

Hope that helps

Answer:

15

Step-by-step explanation:

15 must be added to the sum of squares of 9 to 10 gives a perfect square.

Answer:

Step-by-step explanation:

48 miles = 1 hour

??           = 4.5hr

=> cross multiplicationt

4.5/1 *48Miles

= 216Miles

Answer:

h=V/πr2

Step-by-step explanation:

Rewrite the equation as π r 2 h = V . π r 2 h = V

Divide each term in π r 2 h = V by π r 2 and simplify.