Solve this problem in your notebook using all four steps. Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the ages of Harvey and Jane. Jane is a0 years old. Harvey is a1 years old.

Answer:

C = $100+$35x

Step-by-step explanation:

Given :

A company spends $100 per day on fixed expenses such as electricity, rent, and the like.

It also spends $35 per day on each employee working that day.

To Find : a linear equation relating the total daily cost, C, with the number of employees working on any particular day, x.

Solution :

A company spend  $100 per day on fixed expenses

No. of employees working on a particular day = x

Company spend on each employee  per day = $35

It spends on x employee = $35x

Since total daily cost = C

Thus C = $100+$35x

Hence , a linear equation relating the total daily cost, C, with the number of employees working on any particular day, x. :  C = $100+$35x

Answer:

The total cost charged by the two companies will be the same for 10 square yards of carpeting .

Step-by-step explanation:

Let us assume that the number of square yards for carpeting  used be x.

Let us assume that the total cost of the  charged by the companies be y.

As given

Country Carpets charges $22 per square yard for carpeting, and an additional installation fee of $100.

Than the equation becomes

y = 22x + 100

As given

City Carpets charges $25 per square yard for the same carpeting, and an additional installation fee of $70.

Than the equation becomes

y = 25x + 70

Than the two equations are

y = 22x + 100 and y = 25x + 70

Than compare the two equations are

22x + 100 = 25x + 70  

25x - 22x = 100 - 70

3x = 30

[tex]x = \frac{30}{3}[/tex]

x = 10 square yards .

Therefore the total cost charged by the two companies will be the same for 10 square yards of carpeting .

Answer:

42° and 48°

Step-by-step explanation:

Complementary angles sum to 90°, hence

x + 10 + x + 4 = 90

2x + 14 = 90 ( subtract 14 from both sides )

2x = 76 ( divide both sides by 2 )

x = 38

x + 10 = 38 + 10 = 48° and x + 4 = 38 + 4 = 42°

Answer:

2

Step-by-step explanation:

let the number be n then

[tex]\frac{n}{2}[/tex] = 2n - 3 ( myltiply both sides by 2 )

n = 4n - 6 ( subtract 4n from both sides )

- 3n = - 6 ( divide both sides by - 3 )

n = 2

check

[tex]\frac{2}{2}[/tex] = 1 and (2 × 2 ) - 3 = 4 - 3 =1

Lets hope i'm right.

Triangle formula: 1 / 2 b x h

y:

Half one of them. Lets do 4 since 5 would result in a decimal.

(4) = 2 x 5 = 10.

y (10) + 1 = 11

x:

Half one.

(2) = 1 x 3 = 3

Answers:

y = 11

x = 3

Hope this helps! Wait for another answer to make sure i'm right. ;) ~Pooch ♥

Final answer:

After subtracting the cost of a haircut ($32) and a manicure ($26) from Samantha's spa day budget of $75, she would have a maximum of $17 left over.

Explanation:

If Samantha has at most $75 for her day at the spa and she plans to spend $32 on a haircut and $26 on a manicure, we can calculate the maximum amount she would have left over by subtracting the cost of the haircut and manicure from her total budget. The equation we use for this calculation is:

Total Budget - (Cost of Haircut + Cost of Manicure) = Money Left Over

Let's do the math:

$75 - ($32 + $26) = $75 - $58 = $17

So, Samantha will have a maximum of $17 left after she pays for her haircut and manicure.

Answer:     Arithmetic , Divergent

Step-by-step explanation:

Given sequence is  

{aₙ} =  {  4 , 10/3  , 8/ 3 , 2 , . . .   }

To check whether the sequence is geometric or not , we divide second term by first term  to find the common ratio . Then we again divide third term by second term to get common ratio .

The common ratio we get would same , then it is geometric .

         10/3               10            5

r₁  =  -----------  =     ------    =   ------

             4                12             6

        8/3                8                  3                4

r₂=   ----------   =  ----------  *   ------------   =     -----

           10/ 3             3              10                  5

Thus the common ratio are not same . So the sequence is not geometric .

Now we check for arithmetic .

We take difference of second and first term and then difference of third and second term . If it will be same then it is arithmetic . This is called common difference , d .

             10                       -  2

d₁   =    ------     - 4   =       -------

              3                          3

                8            10             - 2

d₂   =    ------    -   --------    =   ---------

               3             3                 3

Thus the common difference is same .

So the given sequence is arithmetic .

To find whether it is convergent or divergent , we need to write sum of n terms first .

Formula for finding sum of n terms of arithmetic sequence is

            n

sₙ =     -----  [ 2a + ( n - 1 ) d]

             2

We have a = 4 , d = - 2/3 .

Plug  in this formula we get

              n                                                    n                2             2

sₙ  =     ------- [ 2 * 4 + ( n - 1 ) ( -2/3) ]  =     ------ [  8 -   -----  n  +   ------  ]

              2                                                    2                3               3

           n          26              2

sₙ  =   ------  [    ------    -    ------- n  ]

           2           3                3

To check whether it is convergent or divergent , we take limit sₙ approaches to infinity .

                               n       26       2

lim   sₙ   =     lim    { ---   [  ---  -  ------ n ] } =     - ∞

n → ∞           n→∞      2        3       3

As the sequence diverge , thus the series is divergent .

Thus given series is arithmetic , divergent .

Second is the  correct option .

Answer: width = 4 ft, length = 8 ft, height = 4 ft

Step-by-step explanation:

width (w): w

length (L): 2w

height (h): w

Volume (V) = w * L * h

128 = w(2w)(w)

128 = 2w³

64 = w³

∛64 = ∛w³

4 = w

width (w): w = 4

length (L): 2w = 2(4) = 8

height (h): w = 4

Answer:

35

Step-by-step explanation:

It’s a 90 degree angle. 3x35=105 and 105-15=90

Answer:

x = 35

Step-by-step explanation:

Angle JML is 90 degrees

3x-15 = 90

Add 15 to each side

3x-15+15 = 90+15

3x = 105

Divide each side by 3

3x/3 =105/3

x = 35

Answer:

Step-by-step explanation:

Introduction:

Mixtures are not unique to chemistry; we encounter them on a daily basis. The food and drinks

we consume, the fuel we use in our vehicles, building materials, soil, air, and ordinary water are

all mixtures. In fact, very few common materials in the world are pure. Any material made up

of two or more substances that are not chemically combined is a mixture. It is not difficult to

separate the components of a mixture if you take advantage of differences in physical properties

of the components.

1. Sublimation. Some substances change directly from a solid to a gas when they

are heated. The reverse process, when the vapor goes back to the solid phase

without a liquid state in between, is called deposition. Some solids which sublime

are iodine, caffeine, and paradichlorobenzene (mothballs). Dry ice sublimes also.

2 Extraction. This uses a solvent to selectively dissolve one component of the

solid mixture. With this technique, a soluble substance can be separated from an

insoluble substance.

3. Decantation. This separates a liquid from insoluble solid sediment by carefully

pouring the liquid from the solid without disturbing the solid.

4. Filtration. This separates a solid from a liquid through the use of a porous

material as a filter. Paper, charcoal, or sand can serve as a filter. These materials

trap the solid but let the liquid pass through (see diagram in Procedure section).

5. Evaporation. This is the process of heating a mixture in order to remove a

liquid that evaporates easily, leaving a dry residue.  

Pure substances are further broken down into elements and compounds. Mixtures are physically combined structures that can be separated into their original components. A chemical substance is composed of one type of atom or molecule.

The correct answer is A.

Hope this helps,

Davinia.

The inverse of the function g(x)=-4/3x+2 is

[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]

The given function is:

[tex]g(x) = -\frac{4}{3}x + 2[/tex]

To find the inverse of the function g(x), follow the steps below

Make x the subject of the formula

[tex]g(x) = -\frac{4}{3}x+2\\\\ -\frac{4}{3}x = g(x) - 2\\\\-4x=3g(x)-6\\\\x = -\frac{3}{4}g(x)+\frac{6}{4} \\\\x = -\frac{3}{4}g(x)+\frac{3}{2}[/tex]

Replace x by [tex]g^{-1}(x)[/tex] and replace g(x) by x

The inverse function therefore becomes:

[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]

The inverse of the function g(x)=-4/3x+2 is [tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]

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Answer:

They have 1,690 miles left.

Step-by-step explanation:

12 x 30 = 360 miles

2050 - 360 = 1690 miles

Answer:

[tex]12.5x-285[/tex].

Step-by-step explanation:

We are told that a man drove x miles per hour for 3 hours, so he traveled 3x miles in three hours.

We are also told that he drove (2x-60) miles per hour for the next 4.75 hours. So The distance traveled by in next 4.75 hours will be:

[tex]4.75\cdot (2x-60)=9.5x-285[/tex]  

To find the total distance traveled by man we will add distances traveled by him in first 3 hours and next 4.75 hours.

[tex]\text{The total distance traveled}=3x+9.5x-285[/tex]

Upon combining like terms we will get,

[tex]\text{The total distance traveled}=(3+9.5)x-285[/tex]

[tex]\text{The total distance traveled}=12.5x-285[/tex]

Therefore, the total distance traveled in terms of x will be [tex]12.5x-285[/tex].

The total distance traveled in terms of x is the sum of the distances for each part of the trip: 3x miles for the first part and 9.5x - 285 miles for the second part, equating to a total distance of 12.5x - 285 miles.

To express the total distance traveled in terms of x, we need to use the distance formula d = vt, which states that distance (d) is equal to velocity (v) multiplied by time (t).

For the first part of the trip, the man drove at x miles per hour for 3 hours. Therefore, the distance for this part is:

d1 = x miles/hour * 3 hours = 3x miles

For the second part of the trip, he drove at (2x-60) miles per hour for 4.75 hours. So, the distance for this part is:

d2 = (2x-60 miles/hour) * 4.75 hours = 9.5x - 285 miles

To find the total distance traveled, we add the two distances together:

Total Distance = d1 + d2 = 3x miles + 9.5x - 285 miles = 12.5x - 285 miles

Answer:

3 and 4

Step-by-step explanation:

We apply 2 transformations here.

f(x)  ----> f(x + a) - this is  a shift of a units to the left.

f(x) ---- > f(x) + a - this is a shift of a units vertically up.

x - 1  ----> x + 2  shifts  it 3 units to the left.

3 ---->5  shifts it 2 units up.

Answer:

Options 3 & 4

Step-by-step explanation:

Recall, an exponential function has the basic form  

[tex]y=ab^{x+h}+k[/tex].

Thus [tex]f(x)=2^{x-1} +3[/tex] is shifted to the right 1 unit and up 3 units.\\

This means that [tex]g(x)=2^{x+2}+5[/tex] is shifted to the left 2 units and up five units.

Remember it had already been shifted up 3 so, moving up to 5 is a movement of 2 units. Option 3 is correct.

Also, remember the function started 1 unit to the right and then shifted left to 2. This would be 1--2=3 units in total were shift from f(x) to g(x). This makes Option 4 correct too.

Answer:

To convert 1 meter into yards

Using the given facts : 100 centimeters in a meter, 2.54 centimeters in an inch, 12 inches in a foot, and 3 feet in a yard.

we can write these as;

[tex]1 m = 100 cm[/tex]

[tex]1 inches = 2.54 cm[/tex]

[tex]1 ft = 12 inches[/tex] and

[tex]1 yard = 3 ft[/tex]

1 ft = 12 inches

3 ft = [tex]3 \times 12 = 36 inches[/tex]

Since,

1 inches  = 2.54 cm

36 inches = 91.44 cm

Also,

1 m = 100 cm

or

1 cm = [tex]\frac{1}{100} m[/tex]

then;

91.44 cm = [tex]\frac{91.44}{100} =0.9144 m[/tex]

⇒ 1 yards = 0.9144 m

Divide both sides by 0.9144 we get;

1 meter = [tex]\frac{1}{0.9144} = 1.0936133[/tex] yards.

Therefore, the answer is, 1 m =  1.1 yards (nearest to tenth)

Answer:

All i want the 5 stars. Answer is down below.

Step-by-step explanation:

To convert 1 meter into yards

Using the given facts : 100 centimeters in a meter, 2.54 centimeters in an inch, 12 inches in a foot, and 3 feet in a yard.

we can write these as;

and

1 ft = 12 inches

3 ft =

Since,

1 inches  = 2.54 cm

36 inches = 91.44 cm

Also,

1 m = 100 cm

or

1 cm =

then;

91.44 cm =

⇒ 1 yards = 0.9144 m

Divide both sides by 0.9144 we get;

1 meter =  yards.

Therefore, the answer is, 1 m =  1.1 yards (nearest to tenth)

Answers:

a) Choice D -- Graph is discrete due to b only taking on whole number values (b = 0, b = 1, b = 2, etc)

see the attached image below for the graph

---------

b) She bought 9 basketballs

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

Explanation for part A

To make a table, we simply replace every copy of 'b' with a positive whole number. So for instance, replace b with 0 and we get

a = 18*b = 18*0 = 0

Therefore b = 0 leads to a = 0 meaning buying 0 basketballs cost the coach $0

If b = 1, then a = 18 because

a = 18*b = 18*1 = 18

So 1 basketball costs $18 as expected

2 basketballs cost a total of $36 and we see that as shown below

a = 18*b = 18*2 = 36

This pattern continues however long as you need. Each row of the table represents an ordered pair of (b,a) values. Unfortunately your teacher made 'b' the independent variable meaning that it must come first even if the temptation is to put 'a' first in the ordered pair due to alphabetical order.

To graph this function, we just plot the points from the table. Each row is an ordered pair so it represents 1 point. We do NOT connect the dots with a straight line. Why not? Because we can't buy half a basketball, so the point with b = 1/2 = 0.5 wouldn't make any sense, so it's no use to us. The fact we have disconnected points as the graph shows visually tells us that we have a discrete graph. Connecting the dots would make the graph continuous.

Once again, have a look at the image attached below for the table and graph.

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

Explanation for part B

The equation in part A helps us find the pre-tax total cost. If that cost is $162, then a = 162 and b is...

a = 18*b

162 = 18*b

18*b = 162

18*b/18 = 162/18

b = 9

So she bought 9 basketballs

This is represented as point J(9,162) on the graph below.

Answer:

it is a fifty fifty chance

Step-by-step explanation:

if they are the same number it is always a fifty fifty chance

Answer

Given the statement: In parallelogram ABCD, diagonals AC and BD intersects at point E.

Given that ABCD is a parallelogram.  

As, we know that in a parallelogram diagonals bisect each other.

Since AC and BD intersect at E, and we get E is the mid point of both diagonals AC and BD.

⇒ BE = DE                  .....[1]

Substitute the given values of [tex]BE = 2x^2 -3x[/tex] and [tex]DE = x^2+10[/tex] in [1] we have;

[tex]2x^2-3x = x^2+10[/tex]

Subtract [tex]x^2[/tex] on both sides we get;

[tex]2x^2-3x-x^2 = x^2+10-x^2[/tex]

Simplify:

[tex]x^2-3x =10[/tex]

Subtract 10 on both sides we get;

[tex]x^2-3x-10 =0[/tex]

or

[tex]x^2-5x+2x-10 =0[/tex]

[tex]x(x-5)+2(x-5)=0[/tex]

[tex](x-5)(x+2)=0[/tex]

equate these factors equal to zero we get;

(x-5) = 0  and (x+2) = 0

we have;

x = 5 and x = -2

Since, x cannot be negative.

So, x =5

[tex]BE = DE = x^2+10 = (5)^2+10 = 25+10 = 35 units[/tex]

Diagonals BD = BE + DE = 35 + 35 =70 units.

Therefore, the value of BD = 70 units.

Answer:

2, and 10

Step-by-step explanation:

Let's work through each one.

First, plug -10 into the equation:

-10² + 20 = 12 x -10?

-10² = 100

100 + 20 = 120

12 x -10 = -120

120 = -120?    False!

But, using these same calculations, we can see that 10 is a correct answer.

Because everything's the same up to 12 x 10 = 120.

120 = 120

Same with 2 and -2

-2 does not work, but 2 does.

2² + 20 = 12 x 2?

4 + 20 = 24?

24 = 24?    True!

The solution of the given quadratic equation is x = 2 and x = 10.

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

Given a quadratic equation, x²+20 = -12x

x²-12x+20 = 0

On factorizing the equation,

x²-10x-2x+20 = 0

x(x-10)-2(x-10) = 0

(x-10)(x-2) = 0

x = 10 or x = 2

Hence, the solution of the given quadratic equation is x = 2 and x = 10.

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Answer:

C - If Jason's monthly payment were $130, the amount of the loan that he is considering taking out would be less than $21,037.05.

Step-by-step explanation:

The EMI formula is :

[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

here r = 5.1/12/100=0.00425

p = 21037.05

and n = 20*12 = 240

Putting the values in formula we get

[tex]\frac{21037.05*0.00425*(1.00425)^{240} }{(1.00425)^{240}-1 }[/tex]

= (21037.05*0.00425*2.767)/1.767 = $140.00

Hence, for an amount of $21,037.05, the monthly payment becomes $140. So, if Jason is paying $130, he must have taken less loan than $21037.05.

So, option C is correct.

If you want to calculate, lets take p = x and emi = 130 and put the values in above formula. (r and n are same)

130=(x*0.00425*2.767)/1.767

130= 0.0066x

x = $19696.96(approx) (This shows that the loan will be less than $21037.05)

Answer:

45 %

Step-by-step explanation:

Time left until Christmas = 2 weeks

                                         = 2 * 7 days                [since 1 week = 7 days]

                                         = 14 days

Number of days in December = 31

Percentage of the month left before Christmas = [tex]\frac{Time left until Christmas}{Number of days in December} * 100[/tex]

= [tex]\frac{14}{31} * 100[/tex]

= 0.45 * 100

= 45 %

Answer:

what the other person said.

Step-by-step explanation:

Answer:

0.0611

Step-by-step explanation:

Answer:

B. 0.0611

Step-by-step explanation:

We have been given that a data set which follows a nonstandard normal distribution curve and mean of data set is 715 and standard deviation is 24.

To find the probability that a randomly selected value will be between 660 and 680 we will use probability formula to find the values between two z-scores.

First of all let us find z-score for our given values using z-score formula.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]z=\text{ z-score}[/tex],

[tex]x=\text{Random sample score}[/tex],

[tex]\mu=\text{ Mean}[/tex],

[tex]\sigma=\text{ Standard deviation}[/tex].

Let us find z-score for random score 660.

[tex]z=\frac{660-715}{24}[/tex]

[tex]z=\frac{-55}{24}[/tex]

[tex]z=-2.29[/tex]

Let us find z-score for random score 680.

[tex]z=\frac{680-715}{24}[/tex]

[tex]z=\frac{-35}{24}[/tex]

[tex]z=-1.458\approx -1.46[/tex]

We will use formula [tex]P(a<z<b)=P(z<b)-P(z<a)[/tex] to find the probability between our given values.

Upon substituting our given values in above formula we will get,

[tex]P(-2.29<z<-1.46)=P(z<-1.45)-P(z<-2.29)[/tex]

Using normal distribution table we will get,

[tex]P(-2.29<z<-1.46)=0.07215-0.01101[/tex]

[tex]P(-2.29<z<-1.46)=0.06114[/tex]

Therefore, the probability that a randomly selected value will be between 660 and 680 is 0.0611 and option B is the correct choice.

Answer:

Given the coordinates of rectangle ABCD are;

A = (3, 5)

B = (5,5)

C = (5, 1) and

D = (3, 1)

The rule of rotation 90 degree counter-clockwise around the origin is given by;

[tex](x, y) \rightarrow (-y, x)[/tex]

Now, the coordinates of each vertex when rectangle ABCD is rotated 90 degree counter-clockwise around the origin are;

[tex]A(3, 5) \rightarrow A'(-5, 3)[/tex]

[tex]B(5, 5) \rightarrow B'(-5, 5)[/tex]

[tex]C(5, 1) \rightarrow C'(-1, 5)[/tex]

[tex]D(3, 1) \rightarrow D'(-1, 3)[/tex]

m∠BCA = 57 degrees.

The sum of the exterior angles of a triangle is 360 degrees.

So,

[tex](5x+12)+(9x+1)+(10x-37)=360\\24x-24=360\\24x=384\\x=16[/tex]

So the exterior angle corresponds to ∠BCA is = 10x - 37 = 10(16) - 37 = 123.

So the interior angle ∠BCA is = 180 - 123 = 57 degrees.

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Answer:

Option d is correct.

Both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.

Step-by-step explanation:

The rule of 180 degree rotation about the origin is:

[tex](x, y) \rightarrow (-x , -y)[/tex]

Since a Rotation of a point through 180°, about the origin when a point a(h, k)  is rotated about the origin through 180° in anticlockwise or clockwise direction.

then, By the rule of 180 degree rotation;

[tex]a(h, k) \rightarrow a'(-h , -k)[/tex]

so, it takes the new position i.e, [tex]a'(-h , -k)[/tex]

Therefore, both the x and y coordinates of the point on δa'b'c' have opposite signs from the corresponding points on δabc.

The cost of one gallon of gas is $3.50 (calculated by dividing $10.50 by 3). Therefore, to find out the budget needed for the one-way trip to border=0 cell spacing=0 cellpadding=0 the grandmother's house, multiply the cost per gallon by the number of gallons needed, getting: 20 gallons * $3.50/gallon = $70.

The first step is to identify the cost per gallon of gas. From the problem, we know that three gallons of gas cost $10.50. So, we can find out how much one gallon of gas costs by dividing $10.50 by 3, which is $3.50 per gallon.
To find out how much it would cost Melissa's family to make the one-way trip to her grandmother's house, we need to multiply the cost per gallon by the number of gallons it takes to get there.
So, the family needs to budget 20 gallons * $3.50/gallon = $70 for the one-way trip.
Therefore, Melissa's family should budget $70 to be able to make the one-way trip to her grandmothers house.

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