An equation for the line graphed is
A) y =
3
2
x + 3
B) y =
1
2
x + 3
C) y = -
3
2
x + 3
D) y = -
1
2
x + 3

Answer:

The radii of the circles are 12 cm and 7cm.

Step-by-step explanation:

Let the radii of the circles be [tex]r_{1}\ and\ r_{2}[/tex]

Given:

Sum of circumference of two circles= 38π cm

Formula for circumference of a circle with radius r = 2πr

[tex]2\pi r_{1}+2\pi r_{2}=38\pi \\r_{1}+r_{2}=19[/tex]------------1

Sum of areas of two circles= 193π cm²

Area of circle with radius r = πr²

[tex]\pi r_{1}^{2}+\pi r_{2}^{2}=193\pi \\r_{1}^{2}+r_{2}^{2}=193[/tex]-------2

Substituting r2 = 19 - r1 in equation 2 we get:

[tex]r_{1}^{2}+(19-r_{1})^{2}=193\\2r_{1}^{2}-38r_{1}+168=0\\r_{1}^{2}-19r_{1}+84=0\\(r_{1}-12)(r_{1}-7)=0\\r_{1}=12\ or\ 7[/tex]

Then r2 = 19 - r1

[tex]r_{2}=12\ or\ 7[/tex]

Answer: the employee worked for 41 hours

Step-by-step explanation:

Let x represent the total number of hours that the employee worked. An employee earns $7.00 an hour for the first 35 hours worked in a week and $10.50 for any hour over 35. Let y represent the amount earned for x hours. Therefore

y = 7×35 + 10.5(x - 35)

y = 245 + 10.5x - 367.5

One week's paycheck (before deduction) was for $308.00. This means that y = $308.00. Therefore,

308 =245 + 10.5x - 367.5

308 = 10.5x - 122.5

10.5x = 308 + 122.5 = 430.5

x = 430.5/10.5

x = 41

Answer: The value of 528 would change by 40 if 6 replaced 2

Step-by-step explanation:

The given number is 528. If we replace 2 by 6, the new number becomes 568. This is greater than the previous number. The difference between the new number and the previous number would be

568 - 528 = 40

Answer:

y + b > 15

Step-by-step explanation:

given data

positive integers = x, y, a, b

x divided by y then remainder = 6

a divided by b then remainder = 9

to find out

possible value for y + b

solution

we know that here when  x divided by y then remainder is 6

its mean y is greater than 6 and when a divided by b then remainder is 9

so its mean b is greater than 9

and we know remainder is less than divisor

so here y + b must be greater than = 6 + 9

y + b > 15

Answer:

The money Rachael plan to collect for the shelter is $350.

Step-by-step explanation:

Given:

Rachel is collecting donations for the local animal shelter.

So far she has collected $245, which is 70% of what she hopes to collect.

Now, to find the money Rachael plan to collect for the shelter.

Let the total amount Rachael plan to collect be [tex]x[/tex].

Amount she collected = $245.

Percentage of amount she collected = 70%.

Now, to get the amount Rachael plan to collect we put an equation:

[tex]70\%\ of\ x=\$245.[/tex]

⇒ [tex]\frac{70}{100} \times x=245[/tex]

⇒ [tex]0.70\times x=245[/tex]

⇒ [tex]0.70x=245[/tex]

Dividing both sides by 0.70 we get:

⇒ [tex]x=\$350.[/tex]

Therefore, the money Rachael plan to collect for the shelter is $350.

Answer:

Step-by-step explanation:

Suppose the time required for an auto shop to do a tune-up is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - u)/s

Where

x = points scored by students

u = mean time

s = standard deviation

From the information given,

u = 102 minutes

s = 18 minutes

1) We want to find the probability that a tune-up will take more than 2hrs. It is expressed as

P(x > 120 minutes) = 1 - P(x ≤ 120)

For x = 120

z = (120 - 102)/18 = 1

Looking at the normal distribution table, the probability corresponding to the z score is 0.8413

P(x > 120) = 1 - 0.8413 = 0.1587

2) We want to find the probability that a tune-up will take lesser than 66 minutes. It is expressed as

P(x < 66 minutes)

For x = 66

z = (66 - 102)/18 = - 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

P(x < 66 minutes) = 0.02275

Answer:

k-5

Step-by-step explanation:

"k and 12" : (k + 12)

"17 less than k and 12" : (k + 12) - 17

simplifying:

(k + 12) - 17

= k + 12 - 17

= k-5

Answer:

Option B is right

Step-by-step explanation:

Given that in the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 40 percent of the male and 20 percent of the female students are 25 years old or older.

                      Males              Females

                        48%                    52%

25 or more

age                  40%                     20%

One student in the class is randomly selected,

to find the probability that he or she will be less than 25 years old

= Prob (male and less than 25 years old)+Prob (female and less than 25 years old)

(since mutually exclusive and exhaustive)

= [tex]0.48(1-0.4) + 0.52(1-0.20)\\= 0.288+ 0.416\\= 0.704\\[/tex]

After rounding off to 1 one decimal

we get 0.7

Option B is right

Answer:

30 gallons

Step-by-step explanation:

let x represent the full container, then

[tex]\frac{1}{10}[/tex] x + 21 = [tex]\frac{4}{5}[/tex] x

Multiply through by 10 to clear the fractions

x + 210 = 8x ( subtract x from both sides )

210 = 7x ( divide both sides by 7 )

30 = x

The volume of the container is 30 gallons

Answer: the volume of the container is 30 gallons

Step-by-step explanation:

Let V represent the volume of the container, in gallons.

The initial volume of grains in the container is 1/0 × V = V/10

If 21 additional gallons of grain are added, the container is 4/5 full. This means that 21 gallons of grain + V/10 will occupy 4/5 of the volume of the container. Therefore

4/5 × V = 21 + V/10

4V/5 = 21 + V/10

4V/5 - V/10 = 21

7V/10 = 21

Multiplying the left hand side and right hand side of the equation by 10, it becomes

7V/10 × 5 = 21 × 10 = 210

7V = 210

V = 210/7 = 30

Answer:

  (-10, -6), (4, -6), (-3, -13), (-3, 1)

Step-by-step explanation:

The easiest points to find that have rational coordinates are the ones 7 units up or down, left or right from the given point. Those are listed above.

We used the distance formula to find four points that could serve as the other end of a line segment with one end at (-3, -6) and length of 7 units. The four points are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).

Finding the Other End Point of a Line Segment

To find four points that can serve as the other end point of a line segment with one end point at (-3, -6) and a length of 7 units, we use the distance formula. The distance formula is:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Given, (x₁, y₁) is (-3, -6) and the distance is 7, we need to find (x₂, y₂) such that:

√((x₂ + 3)² + (y₂ + 6)²) = 7

Squaring both sides: (x₂ + 3)² + (y₂ + 6)² = 49

(0 + 3)² + (y₂ + 6)² = 49

9 + (y₂ + 6)² = 49

(y₂ + 6)² = 40

y₂ + 6 = ±√40

y₂ = -6 ± √40

(x₂ + 3)² + (0 + 6)² = 49

(x₂ + 3)² + 36 = 49

(x₂ + 3)² = 13

x₂ + 3 = ±√13

x₂ = -3 ± √13

Thus, the four possible points for the other end point of the line segment are (0, -6 + √40), (0, -6 - √40), (-3 + √13, 0), and (-3 - √13, 0).

Answer:

78/2,652, or 0.0294, or 2.94%.

Answer:

4/33

Step-by-step explanation:

x=0.121212...

100x=12.1212...

100 x-x=12

99 x=12

x=12/99=4/33

Given a decimal number 0.12, we have that its expression as a fraction in its simplest form is mathematically given as x=4/33

A fraction is simply a numerical quantity or use of integers in a form that is not in a whole number form.

Question Parameter(s):

X=0.121212...

Generally, the equation for the statement  is mathematically given as

x=0.121212

Therefore

100x=12.1212...

100 x-x=12

99 x=12

x=12/99

x=4/33

In conclusion, X=0.121212 as a fraction is x=4/33.

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Answer:

Andrew walks more steps than Sarah.

Step-by-step explanation:

The question is incomplete. The complete question is :

Andrew and Sarah are tracking the number of steps they walk. Andrew records that he can walk 6000 steps in 50 minutes. Sarah writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andrew and Sarah each walk for a total of 5 hours. Who walks more steps?

Solution:

Given:

Andrew walks 6000 steps in 50 minutes.

Number of steps Sarah walks is given by the equation :

[tex]y=118x[/tex]

where [tex]y[/tex] is the number of steps and [tex]x[/tex] is the number of minutes she walks.

Finding the number of steps each walks in 5 hours.

Total number of minutes in 5 hours = [tex]5\times 60 = 300\ min[/tex]

For Andrew:

Using unitary method:

If in 50 minutes Andrew walks = 6000 steps.

In 1 minute he will walk = [tex]\frac{6000}{50}[/tex] = 120 steps

In 300 minutes he will walk = [tex]120\times 300 = 36000[/tex] steps

Thus, Andrew will walk 36,000 steps in 5 hours.

For Sarah:

We will plugin [tex]x=300[/tex] in the equation and solve for [tex]y[/tex].

We have:

[tex]y=118(300)[/tex]

∴ [tex]y=35400[/tex]

Thus, Sarah will walk 35,400 steps in 5 hours.

Therefore, Andrew walks more steps than Sarah as [tex]36,000>35,400[/tex].

Answer:the perimeter of the regular pentagon is 5x + 20

Step-by-step explanation:

The perimeter of a plane figure is the distance around the plane figure. The pentagon is a plane figure. It has 5 sides. Since it is a regular Pentagon, it means that all the sides are equal.

From the information given, the length of each side of the regular Pentagon is x + 4

The perimeter of the regular Pentagon would be 5 times the length of each side. It becomes

5(x + 4) = 5x + 20

Answer:

No solution , The line's are parallel

Step-by-step explanation:

Given set of equations are y = 56x + 2 and y = 56x - 2

If we observe carefully these lines are in the form of y=mx+c where m is the slope of the line and c is the y-intercept

Here both the line's have slope m = 56

We also know that two lines are parallel only if their slopes are equal ie m1=m2

Here the two line's have same slope, so the giventwo line's are parallel And they don't have a solution So jane is wrong.

Answer:

- √5

Step-by-step explanation:

Given that, a ray intersects point (negative 3, 6) in quadrant 2 and we are told to find the value of secant theta.

To get the answer to the question,  

The first step is to find the hypotenuse, we have to use the Pythagoras theorem  where, Hypotenuse = opposite raise to power two + adjacent raise to power.  

(I.e. h= O² + A²)

H = 6² + (-3)2

H = 36 + 9

H = 45

We then convert the answer to surds form.  

H = 3√5

The next step is to find the value of secant theta.  

To get the value of secant theta we will have to divide the hypotenuse by adjacent with a negative sign because of the negative sign in the second quadrant  

We have  

Sec ø = - (hypotenuse/adjacent)  

Sec ø = - (3√5/ 3)

Sec ø = - √5

Answer:

-√5

Step-by-step explanation:

Answer:

Therefore the THREE roots are

[tex]x=0\ or\ x=-3\ or x=-4[/tex]

Step-by-step explanation:

Given:

[tex]x^{3}+7x^{2} +12x= 0[/tex]

To Find:

All  the Roots = ?

Solution:

As the degree of the polynomial is THREE then the number of root are also THREE.

[tex]x^{3}+7x^{2} +12x= 0\\\\x(x^{2}+7x +12)= 0\\\\x=0\\or\\x^{2}+7x +12= 0\\[/tex]

Now one root is Zero For other we need to Factorize

So by Splitting the middle term

i.e Factor of 12 such that sum should be 7

i.e 3 × 4 = 12  and 3 + 4 = 7

∴ [tex]x^{2}+7x +12= 0\\x^{2}+3x+4x +12= 0\\x(x+3)+4(x+3)=0\\(x+3)(x+4)=0\\\\x+3=0\ or\ x+4 = 0\\\\\therefore x=-3\ or x=-4\ \textrm{Which are the roots}[/tex]

Therefore the THREE roots are

[tex]x=0\ or\ x=-3\ or x=-4[/tex]

Answer:sdxfrcgtvyhujikokjhgfdsasdfghjknbv 6yujhgtrfgb         srry .\.

Question is Incomplete, Complete question is given below:

In Triangle ABC shown below, side AB is 6 and side AC is 4.

Which statement is needed to prove that segment DE is parallel to segment BC and half its length?

Answer

Segment AD is 3 and segment AE is 2.

Segment AD is 3 and segment AE is 4.

Segment AD is 12 and segment AE is 4.

Segment AD is 12 and segment AE is 8.

Answer:

Segment AD is 3 and segment AE is 2.

Step-by-step explanation:

Given:

side AB = 6

side AC = 4

Now we need to prove  that segment DE is parallel to segment BC and half its length.

Solution:

Now AD + DB = AB also AE + EC = AC

DB = AB - AD also EC = AC - AE

Now we take first option Segment AD is 3 and segment AE is 2.

Substituting we get;

DB = 6-3 = 3 also EC = 4-2 =2

From above we can say that;

AD = DB and EC = AE

So we can say that segment DE bisects Segment AB and AC equally.

Hence From Midpoint theorem which states that;

"The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side."

Hence Proved.

Answer:

The profits for firma A and B will decrease.

Step-by-step explanation:

Oligopoly by definition "is a market structure with a small number of firms, none of which can keep the others from having significant influence. The concentration ratio measures the market share of the largest firms".

If the costs remain the same for both companies and both firms decrease the prices then we will have a decrease of profits, we can see this on the figure attached.

We have an equilibrium price (let's assume X) and when we decrease a price and we have the same level of output the area below the curve would be lower and then we will have less profits for both companies.

Answer:

The shorter piece   x  =  8.4 in

The longer one    y  =  15.6 in

Step-by-step explanation:

If we cut  a string length  L  in to unequal  pieces we get two pieces

first one with length  x  and the other one with length  y

Let call  x  the smaller piece,  then   y = L  -  x will be the longer one

If   x  =  35 %    then

x  =  0,35* L     and

y = L -  x  =  L - 0,35*L      ⇒  y  =  0,65 L     ⇒ y  =  0.65*24

Now if L  =  24  in

x  =  0,35*24          ⇒               x = 8.4 in

and

L  -  x  =  0.65*L      ⇒       L - x  =  0.65*24     y  =  L  -  x  =  15.6 in

as way of verification you can add the length of the two pieces and find:

8.4  +  15.6  = 24 in

Final answer:

The ratio of the length of the small piece to the big piece is found to be 7/13 after calculating the lengths of each piece, with the small piece being 28 inches and the big piece being 52 inches.

Explanation:

Given that the length of the small piece is 35% of the total length L, we can denote the length of the small piece as 0.35L. The big piece is 24 inches longer than the small piece, so the length of the big piece is 0.35L + 24 inches. Since the string is cut into only two pieces, the total length L is the sum of the lengths of the two pieces, which means L = 0.35L + (0.35L + 24).

Simplifying, we have L = 0.7L + 24. Subtracting 0.7L from both sides gives 0.3L = 24 inches. Therefore, the total length of the string is L = 24 / 0.3 = 80 inches. So the small piece is 0.35L = 0.35 * 80 = 28 inches, and the big piece is 28 + 24 = 52 inches.

To find the ratio of the lengths of the small piece to the big piece, we divide the length of the small piece by the length of the big piece: 28/52. Simplifying this ratio by dividing both the numerator and denominator by 4 gives us 7/13. Therefore, the ratio of the length of the small piece to the big piece in its lowest terms is 7/13.

[tex]\fontsize{18}{10}{\textup{\textbf{The number of different combinations is 120.}}}[/tex]

Step-by-step explanation:

A, B and C are integers between 1 and 10  such that A<B<C.

The value of A can be minimum 1 and maximum 8.

If A = 1, B = 2, then C can be one of 3, 4, 5, 6, 7, 8, 9, 10 (8 options).

If A = 1, B = 3, then C has 7 options (4, 5, 6, 7, 8, 9, 10).

If A = 1, B = 4, then C has 6 options (5, 6, 7, 8, 9, 10).

If A = 1, B = 5, then C has 5 options (6, 7, 8, 10).

If A = 1, B = 6, then C has 4 options (7, 8, 9, 10).

If A = 1, B = 7, then C has 3 options (8, 9, 10).

If A = 1, B = 8, then C has 2 options (9, 10).

If A = 1, B = 9, then C has 1 option (10).

So, if A = 1, then the number of combinations is

[tex]n_1=1+2+3+4+5+6+7+8=\dfrac{8(8+1)}{2}=36.[/tex]

Similarly, if A = 2, then the number of combinations is

[tex]n_2=1+2+3+4+5+6+7=\dfrac{7(7+1)}{2}=28.[/tex]

If A = 3, then the number of combinations is

[tex]n_3=1+2+3+4+5+6=\dfrac{6(6+1)}{2}=21.[/tex]

If A = 4, then the number of combinations is

[tex]n_4=1+2+3+4+5=\dfrac{5(5+1)}{2}=15.[/tex]

If A = 5, then the number of combinations is

[tex]n_5=1+2+3+4=\dfrac{4(4+1)}{2}=10.[/tex]

If A = 6, then the number of combinations is

[tex]n_6=1+2+3=\dfrac{3(3+1)}{2}=6.[/tex]

If A = 7, then the number of combinations is

[tex]n_7=1+2=\dfrac{2(2+1)}{2}=3.[/tex]

If A = 3, then the number of combinations is

[tex]n_8=1.[/tex]

Therefore, the total number of combinations is

[tex]n\\\\=n_1+n_2+n_3+n_4+n_5+n_6+n_7+n_8\\\\=36+28+21+15+10+6+3+1\\\\=120.[/tex]

Thus, the required number of different combinations is 120.

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Question : ow many types of zygotic combinations are possible between a cross AaBBCcDd × AAbbCcDD?

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Answer:

The cost of a 12 minute call to France is $ 3.63

Step-by-step explanation:

given:

The cost of 15 minute call to France = $ 4.29

The cost of 10 minute call to France   = $ 3.19

To Find :

The cost of a 12 minute call to France = ?

Solution:

Let the flat fee be X

and the cost per minute be Y

so the  15 minute call to France will be

X + 15(Y) = 4.29---------------------------(1)

the  10 minute call to France will be

X + 10(X) = 3.19----------------------------(2)

Subtracting (2) from (1)

X + 15(Y) = 4.29

X + 10(Y) = 3.19

-      -           -

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

      5Y = 1.10

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

[tex]Y =\frac{1.10}{5}[/tex]

Y = 0.22

So the cost per minute of a call = $0.22

substituting the values in (1)

X + 15(0.22) = 4.29

X + 3.3 = 4.29

X = 4.29 -3.3

X = 0.99

Now the cost of 12 minute call is

=>X + 12(Y)

=> 0.99 + 12(0.22)

=> 0.99 + 2.64

=> 3.63

When considering mortgage payments, homeowners insurance, property tax and maintenance costs over 30 years, the true cost of the $96,000 home is $287,068.80.

The true cost of a home not only includes the original purchase price but also takes into account annual homeowners insurance, property taxes, and maintenance costs. In this case, the purchase price is $96,000, homeowners insurance costs $1012 per year, property taxes are 1.1% of the home price each year, and annual home maintenance is 1% of the home price.

First, calculate the total mortgage payments made over 30 years. The monthly payment is $545.08, so the total mortgage payments are:

30 years * 12 months/year * $545.08/month = $196,228.80

Next, calculate the total cost of homeowners insurance over 30 years:

30 years * $1012/year = $30,360

Then, calculate the total property taxes over 30 years:

30 years * 1.1% of $96,000/year = $31,680

Lastly, calculate the total home maintenance over 30 years:

30 years * 1% of $96,000/year = $28,800

Adding all of these costs together gives the total cost of the home:

$196,228.80 + $30,360 + $31,680 + $28,800 = $287,068.80

So, the correct answer is option C: $287,068.80.

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Answer:

D

Step-by-step explanation:

Remember how absolute values turn everything inside of it into a positive number? Like |-4|=4 and |4|=4 as well.

Well, it works the same for equations.

When you have an absolute value equation like this, you have to split it into two parts.

The positive version

| d-3.5 | ≤ 1.5

and the negative version

|-(d-3.5)| ≤ 1.5

solve for the value of d in both equation.

Remember that you have to flip the inequality sign when dividing or multiplying by a negative number

I assume you know how to graph the inequality once you get the value for d.

d≤5 and d≥2

so

2 ≤ d ≤ 5

meaning d is between 2 and 5.

Answer:her total sales is 25

Step-by-step explanation:

Let x represent her total sales.

Nicole's job pays her salary plus commission. She earns a daily salary of $60 plus 15% commission of her total sales. This means that the amount that she receives for x total sales would be

60 + 15/100× x

= 60 + 0.15x

On Monday, she earned a total of $63.75. This means that

63.75 = 60 + 0.15x

63.75 - 60 = 0.15x

0.15x = 3.75

x = 3.75/0.15 = 25

Lacy would earn a commission of $104.

Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.

Step-by-step explanation:

Given,

Commission earned on phones sales = 6% = [tex]\frac{6}{100}=0.06[/tex]

Commission earned on computer sales = 2% = [tex]\frac{2}{100}=0.02[/tex]

Worth of phones sold = $1100

Commission amount = 0.06*1100 = $66

Worth of computers sold = $1900

Commission amount = 0.02*1900 = $38

Total commission amount = 66+38 = $104

Lacy would earn a commission of $104.

For $x of phones, we will multiply the given amount with commission rate;

Commission amount of $x phones = 0.06*x = 0.06x

For $y computers;

Commission amount of $y computers = 0.02*y = 0.02y

Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.

Keywords: percentage, addition

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Answer: Infrequent decisions and long lasting decisions

Step-by-step explanation:

Infrequent: decisions made infrequently, they are not urgent, and deeper consideration is appropriate (ex., product strategy, international expansion).

Long-lasting: Once made, these decisions are unlikely to change not immediately but at least in the short term (e.g., commitment to a standard technology platform, commitment to organizational realignment around Value Streams)

Answer:

Step-by-step explanation:

Chrissie likes to tip a server in a restaurant a minimum of 25% of her lunch bill. She and her friend have a lunch bill that is $13.78. This means that the amount of tip that she would give to the server would be

25/100 × 13.78 = 0.25 × 13.78 = $3.445

If Chrissie says the tip will be $3.00, he is incorrect because the tip is $3.445 which is higher than $3

If her friend says that the amount is not a minimum of 25% he is correct because a minimum if 25% is $3.445 which is higher than $3

Answer:

Step-by-step explanation:

let length=x

width=y

area A=xy

[tex]\frac{dA}{dt}=x\frac{dy}{dt}+y\frac{dx}{dt}\\ \frac{dx}{dt}=0.5 ~cm/sec\\\frac{dy}{dt}=-0.5~cm/sec\\\frac{dA}{dt}=10*(-0.5)+7(0.5)=-5+3.5=-1.5[/tex]

area is decreasing at the rate of 1.5 cm^2/sec

The rate of change in the area of the rectangle when the length is 10 cm and the width is 7 cm, with their rates of change being 0.5 cm/sec and -0.5 cm/sec respectively, is -1.5 cm²/sec.

To determine the rate of change in the area of a rectangle where the length is increasing at 0.5 cm/sec and the width is decreasing at 0.5 cm/sec, we can use the concept of derivatives from calculus.

Let L be the length and W be the width of the rectangle. The area A of the rectangle is given by A = L * W. Given that the length is increasing at 0.5 cm/sec (dL/dt = 0.5 cm/sec) and the width is decreasing at 0.5 cm/sec (dW/dt = -0.5 cm/sec) the rate of change of the area with respect to time can be found using the product rule for derivatives: dA/dt = (dL/dt) * W + L * (dW/dt).

At the moment when the length L is 10 cm and the width W is 7 cm, we can plug these values into the formula: dA/dt = (0.5 cm/sec) * 7 cm + 10 cm * (-0.5 cm/sec). This simplifies to dA/dt = 3.5 cm2/sec - 5 cm2/sec, giving us the rate of change in the area as dA/dt = -1.5 cm2/sec.