There are 3 girls and 4 boys in the Reese's family. Mr Reese's booth 6 1/2 pounds of candy. How much will each kid get

Greetings!

Answer:

2370 miles can be travelled

Step-by-step explanation:

If 474 miles can be travelled in 1 hour, this means that to find the total amount in 5 hours we can simply multiply this value by 474:

474 * 5 = 2370

So it can travel 2370 miles!

Answer:

13. The slope for a line that is perpendicular to the line y=4x+8 is  -1/4

14. The slope for a line that is perpendicular to the line x=-6 is 0

15. The equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin is y = - (1/2) x

16. The equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10) is y=3x-10

Step-by-step explanation:

13. What is the slope for a line that is perpendicular to the line y=4x+8?

y=mx+b

Comparing with the form slope-intercept, the slope of the given line is the coefficient of x, then the slope of the given line is 4.

A line perpendicular to y=4x+8 must have a slope opposite and inverse, then:

Slope of the perpendicular = - 1/4

14. What is the slope for a line that is perpendicular to the line x=-6?

The line x=-6 is a vertical line. A line perpendicular to the line x=-6 must be a horizontal line (Angle=0°), then:

Slope of the perpendicular = tan Angle = tan 0° = 0

15. Write the equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin.

8x-4y=12

Isolating y: Subtracting 8x both sides of the equation:

8x-4y-8x=12-8x

-4y=-8x+12

Dividing all the terms by -4:

-4y/(-4)= -8x/(-4)+12/(-4)

y=2x-3

The slope of the given line is 2

The slope of the perpendicular is m=-1/2 (opposite and inverse to the slope of the given line)

The perpendicular passes through the origin:

P1=(0,0)=(x1,y1)→x1=0, y1=0

Using the equation point - slope:

y-y1=m(x-x1)

Replacing the known values:

y-0=(-1/2)(x-0)

y=(-1/2)x

16. Write an equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10).

The slope of the given line is -(1/3)

The slope of the perpendicular is m=3/1→m=3 (opposite and inverse to the slope of the given line)

The perpendicular passes through the point:

P1=(0,-10)=(x1,y1)→x1=0, y1=-10

Using the equation point - slope:

y-y1=m(x-x1)

Replacing the known values:

y-(-10)=3(x-0)

y+10=3x

Isolating y: Subtracting 10 both sides of the equation:

y+10-10=3x-10

y=3x-10

[tex]\dfrac{1}{2}h(b_1+b_2)=A\qquad\text{multiply both sides by 2}\\\\h(b_1+b_2)=2A\qquad\text{divide both sides by }\ h\neq0\\\\b_1+b_2=\dfrac{2A}{h}\qquad\text{subtract}\ b_2\ \text{from both sides}\\\\\boxed{b_1=\dfrac{2A}{h}-b_2}\to\boxed{F.}[/tex]

Answer:      " r  =  a  +  b  -  s "  .

_____________________________________________________

Step-by-step explanation:

_____________________________________________________

Given:  

a + b = s + r ;  Solve for:  "r" ;  that is; rewrite the equation in terms of:  " r " .

_____________________________________________________

Subtract "s" from each side of the equation;  

   to isolate "r" on one side of the equation:

_____________________________________________________

    →      a + b - s  =  s + r - s  ;

    →   to get:

   →       a + b - s  =  r  ;

____________________________________________________

 ↔   " r = a + b - s "  .

____________________________________________________

   →  which is the answer.

____________________________________________________

Hope this helps!

 Best wishes to you!

____________________________________________________

Answer:

$573

Step-by-step explanation:

955* 0.60=573

or

10% of 955= 95.5

50% of 955=477.5

477.5=95.5=573

The sale price of the computer is given by the equation A = $ 573

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 sale price of the computer after the price reduction be A

Now , the equation will be

The initial sale price of the computer = $ 955

The price reduction percentage on computer = 40 %

So , the sale price after reduction A = initial sale price of the computer - ( price reduction percentage x initial sale price of the computer )

Substituting the values in the equation , we get

The sale price after reduction A = 955 - ( 40/100 ) x 955

On simplifying the equation , we get

The sale price after reduction A = 955 - 382

The sale price after reduction A = $ 573

Therefore , the value of A is $ 573

Hence , the price of the computer is $ 573

To learn more about equations click :

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Final answer:

Ali's fish weighs 25/6 lb more than Lisa's fish.

Explanation:

To find out how much more Ali's fish weighs compared to Lisa's fish, we need to subtract the weight of Lisa's fish from the weight of Ali's fish.

Ali's fish weighs 9 and 1/2 lb, which can be rewritten as 19/2 lb. Lisa's fish weighs 5 and 1/3 lb, which can be rewritten as 16/3 lb.

Now, subtracting the weight of Lisa's fish from Ali's fish, we have:

Ali's fish weight - Lisa's fish weight = (19/2) lb - (16/3) lb = (57/6) lb - (32/6) lb = 25/6 lb.

Therefore, Ali's fish weighs 25/6 lb more than Lisa's fish.

Answer:

275

Step-by-step explanation:

To find out how many more, we find the difference between the two values. We use the math operation subtraction to find the difference.

Friday had 537 and Saturday had 812. We subtract 812-537= 275.

275 more people attended Saturday than Friday.

Answer:

The correct answer option is: The y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Step-by-step explanation:

We are given a scatter plot with a best fit line as shown on the given graph.

The equation of the best fit line is given by:

y = 0.75x + 5

So with the help of the equation and by looking at the given graph, we can conclude about the representation of the y intercept that the the y-intercept of the line of best fit shows that when time started, the distance was 5 feet.

Since the distance shown on the y axis is already 5 when the time started at 0 minutes.

[tex]t_1=4\\t_n=-3t_{n-1}\\\\t_2=-3\cdot4=-12\\t_3=-3\cdot(-12)=36\\t_4=-3\cdot36=-108[/tex]

Answer:

Correct choice is D

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}4x+y=8\\6x-9y=12\end{array}\right..[/tex]

Fro mthe first equation

[tex]y=8-4x.[/tex]

Substitute into the second equation [tex]8-4x[/tex] instead of y:

[tex]6x-9(8-4x)=12.[/tex]

Note that [tex]8-4x=-4x+8,[/tex] then the second equation will take look

[tex]6x-9(-4x+8)=12.[/tex]

Answer:

S22 for the arithmetic sequence is:

First option: 15.4

Step-by-step explanation:

a12=2.4

d=3.4

S22=?

Sn=(a1+an)n/2

n=22

S22=(a1+a22)22/2

S22=(a1+a22)11

ak=aj+(k-j)d

a12=a1+(12-1)d

2.4=a1+11(3.4)

2.4=a1+37.4

Solving for a1: Subtracting 37.4 both sides of the equation:

2.4-37.4=a1+37.4-37.4

Subtracting:

-35=a1

a1=-35

a22=a12+(22-12)d

a22=2.4+10(3.4)

a22=2.4+34

a22=36.4

S22=(a1+a22)11

S22=(-35+36.4)11

S22=(1.4)11

S22=15.4

Answer:

5, 5/2

Step-by-step explanation:

80, 40, 20, 10, ______,

80/40 = 2

40/20 = 2

We are dividing by 2 each time

10/2 =5  so the next term is 5

5/2 = 5/2

Answer:

C. y=4x+17

Step-by-step explanation:

If we want to find a line parallel to y =4x-1, the slopes will have to be the same because parallel lines have the same slope.  Knowing y= mx+b we know the slope of the  old line is 4, so the slope of the parallel line is 4.

If we know the slope of the line and a point, we can use the point slope form of a line

y-y1 = m(x-x1)

y-5 = 4(x--3)

y-5=4(x+3)

Distribute the 4

y-5 = 4x+12

Add 5 to each side

y-5+5 = 4x+12+5

y = 4x+17

Answer: The answer is C. y=4x+17

Step-by-step explanation:

The other person was correct and i got an A<3

Final answer:

To create a rectangular field with the same perimeter but a smaller area than the original 115 yards by 75 yards field, one could have a field that is 130 yards long and 60 yards wide.

Explanation:

To find the length and width of another rectangular field that has the same perimeter as a 115 yards by 75 yards field but a smaller area, we first calculate the perimeter of the original field:

Perimeter = 2(length + width) = 2(115 yd + 75 yd) = 2(190 yd) = 380 yd

To have a smaller area, the new field cannot be a square (which would maximize the area) and the sides need to have a greater difference in their measurements while still adding up to half of the original perimeter:

Let's assume the new length is 130 yards, to find the new width: 380 yd / 2 - 130 yd = 60 yd

Therefore, a new rectangular field could be 130 yards long and 60 yards wide.

Answer:

In your first picture

7) -40

14) 200

Step-by-step explanation:

The symbol in the picture is asking for multiplication. Typically for these, teachers encourage the use of the multiplication button on a calculator, but otherwise you need to know the basic steps of multiplication.

Answer:

7) -40

14) 200

Step-by-step explanation:

Answer: y-7 = 4(x+3), choice B

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

Point slope form is generally

y-y1 = m(x-x1)

we have m as the slope and (x1,y1) as the point this line goes through. In this case,

m = 4

(x1,y1) = (-3,7) so x1 = -3 and y1 = 7

So,

y-y1 = m(x-x1)

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

y - 7 = 4(x + 3)

which is why choice B is the answer

Point-slope form:

y - y₁ = m(x - x₁)    "m" is the slope

Since you know:

m = 4

(x₁ , y₁) = (-3,7)

You can plug it into the equation

y - y₁ = m(x - x₁)  

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

y - 7 = 4(x + 3)

Your answer is the 2nd choice

Answer:

The growth factor is option c. 1.03 per year

Step-by-step explanation:

Growth rate: r = 3% = 3 / 100 → r = 0.03

Growth factor: b = 1+r

Replacing r by 0.03 in the formula above:

b = 1+0.03

b = 1.03

Answer: The growth factor is 1.03 per year

Answer:

D

Step-by-step explanation:

The domain is the set of all x-values. We know the domain by finding the start and stop point of the function on the x-axis. The domain is all the values in between if the function is continuous without any breaks.

Here the function begins at x=-5 and ends at x=6.

We write the domain as [tex]-5\leq x\leq 6[/tex].

Answer is D.

Answer: False

Step-by-step explanation:

45-45-90 is a special triangle because there is a specific relationship between the legs and the hypotenuse: a - a - a√2

So, If the leg of the 45-45-90 triangle is 12, then the hypotenuse (labeled as x in your drawing) will be 12√2.

By the polynomial remainder theorem, a polynomial [tex]p(x)[/tex] has a factor of [tex]x-c[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]f(x)[/tex] at [tex]x=1,3,-3,5,-5[/tex]. You should get

[tex]f(1)=-96[/tex] (so [tex]x-1[/tex] is NOT a factor)

[tex]f(3)=-96[/tex] (so [tex]x-3[/tex] is NOT a factor)

[tex]f(-3)=f(5)=f(-5)=0[/tex] (so the last three options are factors)

Answer:

the answer is c and yeah

Step-by-step explanation:

Answer:

It does not converge.

Step-by-step explanation:

Given is an infinite geometric series whose first term is a = 4/7 and common ratio is r = 7/6.

The series ∑a·rⁿ converges if we have |r| < 1.

And the series ∑a·rⁿ diverges if we have |r| > 1.

But we can easily check that |r| = 7/6 > 1.

It means the given series diverges, i.e. does not converge.

Hence, option D is correct answer, i.e. It does not converge.

Answer:

D. it does not converge

Answer:

2√17

Step-by-step explanation:

V = (-8, 2)

|v| = √((-8)^2 + 2^2)

= √(64 + 4)

= √68

= √4* √17

= 2√17

Answer:

  = 2 sqrt(17)

Step-by-step explanation:

To find the magnitude of v using the dot product

|v| = sqrt(v1*v1 + v2*v2)

    = sqrt( -8*-8 + 2*2)

    = sqrt(64+ 4)

   = sqrt(68)

   = sqrt(4*17)

  = sqrt(4) sqrt(17)

  = 2 sqrt(17)

Answer: choice A only

(1,-2) is the only solution (from the list of choices)

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

Explanation:

Let's go through each answer choice. We'll plug the coordinates in one at a time.

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

Choice A has the point (1,-2) so x = 1 and y = -2 pair up together

y < -|x|

-2 < -|1|

-2 < -1

This is a true statement as -2 is to the left of -1 on the number line. So (1,-2) is one solution. Let's see if there are others.

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

Choice B) plug in (x,y) = (1,-1)

y < -|x|

-1 < -|1|

-1 < -1

False. A number is not smaller than itself. So we can cross B off the list.

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

Choice C) plug in (x,y) = (1,0)

y < -|x|

0 < -|1|

0 < -1

This is false because -1 is smaller than 0. Cross choice C off the list.

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

Only choice A is a solution point for this inequality. If we were to graph the inequality, we would see only point A is in the shaded region while the other points are outside the shaded region.

The dashed boundary line does not count as the shaded region. This visually confirms why point B does not work.

After evaluating each point against the inequality y < -|x|, only point A (1, -2) satisfies the condition, making it the correct answer.

To determine which point is a solution for the inequality y < -|x|, we need to check if the y-value of each point is less than the negative absolute value of its corresponding x-value.

Therefore, the correct answer is point A (1, -2), as it is the only point where the y-value is less than the negative absolute value of the x-value.

Answer:4.-37 5.-6 6.-33 11.-20 12.-16

13.19

Step-by-step explanation:

Answer:

1. -41

2. -40

3. -4

4. -37

5. -24

6. -33

8. -47

9. 14

10. 59

11. -20

12. -16

13. 19

A value which x represent in the function when determining the population after 6 years is 6.

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]f(x)=a(b)^x[/tex]

Where:

In this context, we can reasonably infer and logically deduce that the variable x in the standard form of the equation of an exponential function represent time, which can either be measure in years, months, days, hours, minutes, or seconds.

In conclusion, x represents 6 in the exponential function when determining the population after 6 years.

Complete Question:

An initial population of 8 wolves increases by 9% each year. The function [tex]f(x) = ab^x[/tex] models this situation. Which value does x represent in the function when determining the population after 6 years?

Let's do the usual thing and make t the years since 1950.   We'll just abbreviate a billion B.

f(1950-1950)=39.4 B

f(2000-1950) =2025.2 B

Our exponential form for f will be

[tex]f = a e^{kt}[/tex]

[tex]39.4 \textrm{ B} = a e^{ 0 k} = a[/tex]

[tex]2025.2 \textrm{ B} = a e^{50 k}[/tex]

Dividing

[tex]\dfrac{2025.2}{39.4} = e^{50 k}[/tex]

[tex]50 k = \ln \dfrac{2025.2}{39.4}[/tex]

[tex]k = \frac 1 {50} \ln \dfrac{2025.2}{39.4} \approx 0.0787932[/tex]

Our function is

[tex]f = 39.4 \textrm{ B } e^{0.0787932 t }[/tex]

Since [tex]e^{0.0787932} \approx 1.08198[/tex]

[tex]f = 39.4 \textrm{B } 1.08198^t }[/tex]

around 8.2 % annualized growth.

Final answer:

An exponential function modeling U.S. federal budget growth between 1950 and 2000 is based on the formula f(t) = a ×[tex]b^t[/tex], where 'a' is the initial value in 1950 ($39.4 billion) and 'b' is the growth factor, calculated from the data in 2000 ($2025.2 billion). Solving the equations gives us the function [tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Explanation:

We can model the growth of the U.S. federal budget using an exponential function, given the data from 1950 and 2000. First, we identify the years as our variable 't' where t=0 corresponds to the year 1950. We'll use the formula for exponential growth, which is f(t) = a × b^t, where 'a' is the initial amount, 'b' is the growth factor, and 't' is the time in years.

From the question, we have two data points: the budget in 1950 (t=0) is $39.4 billion, which gives us our 'a' value. In 2000 (t=50), the budget is $2025.2 billion. Plugging these values into our exponential function, we get two equations:

f(0) = 39.4 = a × [tex]b^0[/tex] which simplifies to a = 39.4.

f(50) = 2025.2 = 39.4 × b^50.

To find the value of 'b', we solve the second equation:

2025.2 = 39.4 ×  [tex]b^{50[/tex]
Divide both sides by 39.4:
51.4 = [tex]b^{50[/tex]
Take the 50th root of both sides:
b =[tex]51.4^(1/50).[/tex]

Now that we know both 'a' and 'b', we can write the exponential function that models the federal budget from 1950 to 2000:

[tex]f(t) = 39.4 * (51.4^{(1/50)})^t.[/tex]

Keep in mind that this model does not account for complexities like inflation or changing economic conditions. It provides a simplified view of the growth of the federal budget over this particular time period.