Mathematics College

Gretchen lives in Florida, for the current temperature 69°F and rising at a rate of 2°F per hour. She's talking on the phone to her friend in Indiana where the temperature is now 84°F and falling at a rate of 3°F per hour.
A.) If the temperature continue changing at the same rates, how many hours would Gretchen and her friend have to talk before the temperature become equal?
B.) What will the temperature be?

Answers

Answer 1
69 + 2h = 84 - 3h
2h + 3h = 84 - 69
5h = 15
h = 15/5
h = 3 <=== the temps will be the same in 3 hrs

69 + 2(3) = 69 + 6 = 75
84 - 3(3) = 84 - 9 = 75

and the temps will both be 75 F <==


Answer 2

Answer:

A) Gretchen and her friend have to talk 3 hours before the temperature become equal.

B) The temperature after 3 hours will be 75°F.

Step-by-step explanation:

Current temperature in Florida = 69°F

Rate at which temperature is rising = 2°F per hour

Current temperature in Indiana = 84°F

Rate at which temperature is falling= 3°F per hour

A) Suppose in x hours both places have same temperature:

[tex] 69^oF +2F^o\times x=84^oF-3^oF\times x[/tex]

[tex]5x=84^oF-69^oF[/tex]

x = 3 hours

Gretchen and her friend have to talk 3 hours before the temperature become equal.

B) The temperature after 3 hours:

x  = 75°F

[tex]69^oF +2F^o\times x=69^oF +2F^o\times 3=75^oF[/tex]

Related Questions

what is the value of the underlined digit? 587

Answers

There is no underlined dogit
If the line is under the 5 it's five hundreds, in the 8 eight hundreds, and the 7 seven ones.

50 POINTS!!! DO NOT ANSWER JUST FOR THE POINTS!!! IF YOU DO, IF YOU DO ALL OF YOUR EARNED POINTS WILL BE TAKEN~~~~~~~~~~~~~~~
Find this a bit complicated. Please explain and show work with steps.

Suppose f(x)=–x²–4x+4. Compute the following:

A. f(–5)+f(5)=

B. f(–5)–f(5)=

Answers

A. f(-5) = -(-5)^2-4(-5)+4 = -1

  f(5) = -(5)^2-4(5)+4 = -41

-1 + -41 = -42

B. -1 - -41 = 40

Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are . If point D divides in the ratio 4 : 5, the coordinates of point D are

Answers

Given:
A has coordinates (-6,5)
C has coordinates (3.6,-0.4).
C divides AB in the ratio 3:2.

Refer to the diagram shown below.
The coordinates of B are determined by
[tex] \frac{3.6-(-6)}{x-(-6)} = \frac{3}{3+2} \\ \frac{9.6}{x+6} = \frac{3}{5} \\ 3(x+6) = 48 \\ 3x +18=48 \\ x=30/3=10[/tex]
Also,
[tex] \frac{5-(-0.4)}{5-y} = \frac{3}{5} \\ 3(5-y) = 27 \\ 15-3y=27 \\ y= \frac{12}{-3} =-4[/tex]

Answer:
The coordinates of B are (10,-4).

Now, we know the coordinates of line segment AB as A (-6, 5) and B (10,-4).
D (x,y) divides AB in the ratio 4:5.
Therefore
[tex] \frac{x-(-6)}{10-(-6)} = \frac{4}{4+5} \\ \frac{x+6}{16} = \frac{4}{9} \\ 9(x+6)=64 \\ 9x+54=64 \\ x=1.11[/tex]
Also,
[tex] \frac{5-y}{5-(-4)} = \frac{4}{9} \\ 5-y = 4 \\ y = 1[/tex]

Answer:
The coordinates of D are (1.11, 1)

Answer:

I just had to do this problem and,

B is (10, -4) and D is (58/9, -2)

Step-by-step explanation:

A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is –16 ft/s2.

Answers

Hello,

g=9.81m/s²= 9.81/0.3048 =32.18.. ft/s² rounded to 32

h=-g/2*t²+vt+h0
if t=0,h=0 ==>h0=0

==>h=-16*t²+vt
50 ft in 2.5s ==> 25 ft in 1.25s

25=-16*1.25²+v*1.25
==>v=50/1.25=40

Equation h=-16t²+40*t

The denominator of a fraction is 1 more than the numerator. If both the numerator and denominator are decreased by 3, the resulting fraction is equal to 4/5. Find the fraction

Answers

Sent a picture of the solution to the problem (s).

What's S divided by 8=2 ?.....Answer needed ASAP.

Answers

16 ÷ 8 = 2
S = 16
Hope it helps :)
S/8 = 2

S/8 * 8 = 2 * 8

S = 2 * 8

S = 16

hope this helps

An urn contains 8 red balls, 8 white balls, and 8 blue balls, and a sample of 5 balls is drawn at random without replacement. Compute the probility that all of the balls in the sample are the same color.

Answers

(8/24)*(7/23)*(6/22)*(5/21)*(4/20)

The motorcycle engine on a kawasaki ninja 1000 has a displacement of 1043 cubic-centimeters (cm3). in order to calculate its engine displacement in cubic-inches (in3) what unit conversion factor would you use to multiply the given displacement

Answers

1 in3 / (2.54)3 cm3      this is the answer

[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]

Further explanation

We will calculate the unit conversion factor used to convert its engine displacement from cubic-centimeters to cubic-inches.

The relationships between inch and cm are as follows:

[tex]\boxed{ \ 1 \ inch = 2.54 \ cm\ }[/tex]

Inches and cm represent units of length.

Made into fractions, 1 inch as the denominator and 2.54 cm as the numerator.

[tex]\boxed{ \ \frac{1 \ inch}{2.54 \ cm} \ }[/tex]

As a unit conversion factor of volume, the numerator and the denominator in cubic.

[tex]\boxed{ \ \frac{(1 \ inch)^3}{(2.54 \ cm)^3} \ }[/tex]

[tex]\boxed{ \ \frac{1 \ inch^3}{16.387 \ cm^3} \ }[/tex]

Thus, we get the unit conversion factor

[tex]\boxed{\boxed{ \ 0.061 \frac{inch^3}{cm^3}\ }}[/tex]

Let's use this unit conversion factor to calculate its engine displacement in new units.

[tex]\boxed{= 1,043 \ cm^3 \times 0.061 \ \frac{inch^3}{cm^3}}[/tex]

Note for cm³ units that have been crossed out.

The conversion result is [tex] \ \boxed{ \ 63.623 \ inch^3\ }[/tex]

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Keywords: the motorcycle engine, Kawasaki Ninja 1000, 1043 cubic-centimeters (cm³), to calculate, its engine displacement, in cubic-inches (in³), what unit conversion factor

Find the area of the rectangle?! Please :)

Answers

Multiply the length and width: 
L*W = 36*(x-3) = 36*x - 36*3 = 36x - 108

The answer is 36x - 108
(the units are "square kilometers" or "sq km" or "km^2")

55% of what number is 22?

Answers

55% = 55/100 = 0.55

22 : 0.55 = 40 

55% of  40 is 22
The number will be represented by the variable x.

Now convert the percent into a decimal by moving the % sign two places to the left and make the % sign into a decimal point.

55% = 0.55

In mathematics, 'of' can sometimes mean multiply.
Likewise, 'is' can sometimes mean equal.

0.55x = 22

Solve for x.

0.55x = 22
x = 40 <-- Divide both sides by 0.55.

So, the answer is 40.

Kendra and her horse completed the barrel racing course in 15.839 seconds. What is this number rounded to the nearest tenth? :explain how you decided

Answers

the answer is 15.84.

To find the nearest tenth, you go to the 3rd place after the decimal and decide: if the value is 5 or greater, go to the second place after the decimal and round up one. If it does not, the value of the second decimal stays the same.
15.839 rounded to the nearest tenth would be 15.8. It would be that because when you look at the number to the right when it is below five you leave the number your rounding alone, but when the number to the right is higher you would add one to the number that you are rounding. Easy. 

Specify 3 fractions with different denominators that have an LCD of 24

Answers

1/3, 1/4, 1/8 The answer given is not the only possible answer. You need to come up with 3 different fractions so that the LCD (least common denominator) So first, determine the prime factors of 24. 24 = 2 * 2 * 2 * 3 Now you want some denominators that will need all of those prime factors. For the above list of 3, 4, 8, only the 3 and 8 are important, since one of them uses the prime factor of 3 and the other uses 3 prime factors of 2, so the LCD for those 2 numbers is 24. The 3rd denominator could be almost anything that uses some combination of prime factors 2,2,2,3 such as 1/2, 1/4, 1/6, 1/12, etc. I just happened to pick 1/4. The only real restriction is that none of the denominators can use any extra prime factors. If they did. then the resulting LCD would not be equal to 24.

Pre cal/cal master needed

F(x)= 2x^2 + 3x-2 and g(x)= x-2

find equation for f(g(x))

My answer : 2x^2 -8 +3x-8

True answer: 2x^2 -5x

How do we get true answer? I plugged in g(x) into the x's of F(x) but got a waaaaaay different answer.

Answers

Take x-2 and insert it into 2x^2 + 3x-2 where the x is located 
2x^2 + 3x-2
2(x-2)^2 + 3(x-2)-2

Now work out 2(x-2)^2 + 3(x-2)-2 also follow PEMDAS
2(x-2)^2 + 3(x-2)-2 
Since (x-2)^2 is an Exponent, lets work with that first and expand (x-2)^2.
(x-2)^2
(x -2)(x-2)
x^2 -4x + 4
Now Multiply that by 2 because we have that in 2(x-2)^2
(x-2)^2  =  x^2 -4x + 4
2(x-2)^2  =  2(x^2 -4x + 4)
2(x^2 -4x + 4) = 2x^2 - 8x + 8
2x^2 - 8x + 8

Now that 2(x-2)^2 is done lets move on to 3(x-2).

Use the distributive property and distribute the 3
3(x-2) = 3x - 6

All that is left is the -2 

Now lets put it all together 
2(x-2)^2 + 3(x-2)-2

2x^2 - 8x + 8 + 3x - 6 - 2

Now combine all our like terms 
2x^2 - 8x + 8 + 3x - 6 - 2
Combine:  2x^2      =  2x^2 
Combine: -8x + 3x  =  -5x
Combine:  8 - 6 - 2 =   0

So all we have left is
2x^2 - 5x





Convert 1.2x10^(-2) into standard form

Answers

Its scientific Notation here's your answer:

1.2×10^-2

Sense its negative you will have to go left.

.0012

So your answer is
.0012

n standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.

We have,

In scientific notation, a number is expressed as the product of a coefficient between 1 and 10 and a power of 10.

Given [tex]1.2\times10^{-2}[/tex],

We can rewrite it by moving the decimal point two places to the left to obtain 0.012.

The coefficient 0.012 is between 0.01 and 0.1, which is equivalent to 1/100 or 1 divided by 10 raised to the power of 2.

Thus, we can write it as 1.2 multiplied by 10 raised to the power of -2.

Thus,

In standard form, we express it without using scientific notation, so [tex]1.2\times10^{-2}[/tex] becomes 0.012.

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93 times the sixth power of ten

Answers

93 x 6^10

93 x 60466176 = 5623354368
hope this helps

Janae bought wallpaper that cost $25.90 for each roll of 14 square feet. Find the unit price.

Answers

Answer:

The unit price is $1.85

Step-by-step explanation:

Janae bought a roll of wallpaper that cost = $25.90

Each roll is of = 14 square feet

Cost per square feet = [tex]\frac{25.90}{14}[/tex] = $1.85

The unit price is $1.85

Solve for x: 1/4(4x+15)=24

Answers

t's solve your equation step-by-step.14(4x+15)=24Step 1: Simplify both sides of the equation.14(4x+15)=24(14)(4x)+(14)(15)=24(Distribute)x+15/4=24Step 2: Subtract 15/4 from both sides.x+15/4−15/4=24−154x=81/4

Find the probability of randomly selecting 4 good quarts of milk in succession from a cooler containing 20 quarts of which 5 have spoiled

Answers

Need 4 good quarts out of 20, of which 5 have spoiled.

=>

Need 4 good quarts out of 15 good quarts out of 20.

Getting

P(G)=15/20
P(GG)=(15/20)(14/19)
P(GGG)=(15/20)(14/19)(13/18)
P(GGGG)=(15/20)(14/19)(13/18)(12/17)
=91/323

(fractions provide exact answers in probability problems.  Decimals are approximate most of the time).
Final answer:

The question asked is related to probability, which is a topic in Mathematics. After calculating the probability of selecting a good quart of milk four times in a row (considering that the quantity decreases each time a good quart is selected), the probability equates approximately to 0.3 or 30%.

Explanation:

The given question is a statistical problem related to probability and involves the concept of independent events. In this case, each quart of milk being good or spoiled is an independent event, meaning the outcome of one event doesn't affect the other.

In the cooler, there are 20 quarts of milk in total, 15 of which are good (20 - 5 spoilt quarts equals 15 good ones). Hence, the probability of selecting a good quart of milk at first is 15/20, or 0.75.

After removing one good quart, there are now 14 good quarts out of 19. Hence, the probability of drawing a second good quart is 14/19. We can calculate the probabilities for the third and fourth quarts in the same way, resulting in 13/18 and 12/17 respectively.

Since these are independent events, the probability of all these events happening is the product of their individual probabilities. Therefore, the answer is 0.75* (14/19)* (13/18)* (12/17), which is approximately 0.3 or 30%.

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Find the true balance:
Check register balance:$463.80
Bank statement balance: $592.53
Outstanding checks: $49.80 and $86.93
Service charge: $8.00

A. $592.53

B. $584.53

C. $327.07

D. $455.80

Answers

Answer:

D. $455.80

Step-by-step explanation:

True Balance = Bank Statement - Outstanding Checks

= $592.53 - ($49.80 + $86.93)

= $455.80

Solve for A. R = x(A + B) A = (R - B)/x A = (B - Rx)/x A = (R - Bx)/x

Answers

R = x(A + B)...distribute
R = Ax + Bx.....subtract Bx
R - Bx = Ax...divide both sides by x
(R - Bx) / x = A <==

In the given equation of the provided problem, the solution for A is A =  [tex]\frac{R - xB}{x}[/tex].

Mathematically, an equation is a statement that asserts the equivalency of two expressions. It consists of two hands, the left-hand side( LHS) and the right-hand side( RHS), separated by an equal sign( =). The LHS and RHS can be numbers, variables, constants, or further complex fine expressions.

To solve for A in each of the given equations, we'll isolate the variable A on one side of the equation. Let's go through each equation:

R = x(A + B)

To solve for A, we'll start by expanding the expression on the right side:

R = xA + xB

R - xB = xA

Divide both sides of the equation by x to solve for A:

A = [tex]\frac{R - xB}{x}[/tex].

Therefore, the solution for A is A =  [tex]\frac{R - xB}{x}[/tex].

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Central Middle School has 2,470 students and the ratio of students to teacher is 26:1. How many new teachers are needed to reduce this ratio to 19:1?

Answers

so, the school has 2470 students, and the ratio from students to teacher is 26:1 currently, so hmmm how many teachers are there with that ratio anyway?

[tex]\bf \cfrac{student}{teacher}\qquad 26:1\implies \cfrac{26}{1}=\cfrac{\stackrel{2470}{students}}{\stackrel{teachers}{t}}\implies \cfrac{26}{1}=\cfrac{2470}{t} \\\\\\ t=\cfrac{1\cdot 2470}{26}\implies \boxed{t=95}[/tex]

hmm alrite... what if the amount of students is kept the same, but more teachers come in, that the ratio changes and is no longer 26:1 but 19:1?

how many teachers will there be then?

[tex]\bf \cfrac{student}{teacher}\qquad 19:1\implies \cfrac{19}{1}=\cfrac{\stackrel{2470}{students}}{\stackrel{teachers}{t}}\implies \cfrac{19}{1}=\cfrac{2470}{t} \\\\\\ t=\cfrac{1\cdot 2470}{19}\implies \boxed{t=130}[/tex]

so, if there are 130 teachers and 2470 students, the ratio is 19:1.

at 26:1 is with 95 teachers.

how many more new teachers are needed? well, surely you'd know that.

1/3 (9x+3)=3x+1 what does x equal

Answers

Distribute on the left
3x+1=3x+1

Since the equations are equivalent, x can be any number and the equation will be true.

Final answer: Infinitely many solutions

chloe is sorting items at a thrift store. She finds a box of tiny blocks that has 1,344 written on the outside. She can see that each layer in the box has 64 blocks. How many layers of blocks are there?

Answers

There is 21 layers in the box.

Answer: There are 21 layers of blocks.

Step-by-step explanation:

Since we have given that

Number of blocks in a box = 1344

Number of blocks in each layer = 64

We need to find the number of layer of blocks.

So, the number of layer of blocks is given by

[tex]\dfrac{1344}{64}\\\\=21[/tex]

Hence, there are 21 layers of blocks.

Point Q is the midpoint of segment PR. If PQ= (15x-2) and QR= (5x+3) find the value of Q.

Answers

is that the measure or linear equation
check the picture below.

so, the distance to Q, or one can say Q's length is the same as PQ's. or QR's for that matter.

Prove that 1=2 with well arranged steps and justify each step

Answers

Justification Step 1: Let a = b. Step 2: Then a^2 = ab , Step 3: a^2 + a^2 = a^2 + ab , Step 4: 2a^2=a^2 + ab, Step 5: 2a^2 - 2ab = a^2 + ab - 2ab, Step 6: and 2a^2 - 2a^b = a^2 + ab - 2ab . Step 7: This can be written as 2(a^2 - ab) = 1(a^2 - ab) , Step 8: and cancelling the (a^2 - ab) from both sides gives 1 = 2.

If Logx (1 / 8) = - 3 / 2, then x is equal to

A. - 4

B. 4

C. 1 / 4

D. 10

Answers

answer is C 1/4

 see attached picture, it is not exact but with rounding it comes out correct.

which is 625 written as a power of 5 (exponets) A. 4*5 B.3*5 C.5*3 D.5*4

Answers

625 written as a power of 5 = 5^4
because
5^4 = (5) * (5) *(5) * (5)  =625

answer is
D.5^4
If 625 is written as a power of 5 the Answer is D. 5*4

Find the numerator of the equivalent fraction with denominator 12 :

1/2

Answers

The answer is 6/12 is 1/2. To figure half of 12 you could've divided it by 2 or .5 because they are the same
Final answer:

The numerator of the equivalent fraction with denominator 12 for 1/2 is 6. This comes from multiplying both the numerator and denominator of 1/2 by the same number (6).

Explanation:

To find the numerator of the equivalent fraction with denominator 12 for 1/2, we simply multiply both parts of the fraction by the same number such that the denominator becomes 12. We know that 2 * 6 equals 12, so we multiply the numerator 1 by 6 as well, which gives us the numerator 6.

Therefore, the fraction 1/2 is equivalent to 6/12.

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Fine the missing coordinate of the ordered pair

Answers

[tex]\bf 6x+7y-6=0\qquad \qquad (\stackrel{x}{-2}~,~\stackrel{y}{?}) \\\\\\ \textit{if x = -2 then }\implies 6(-2)+7y-6=0\implies -12+7y-6=0 \\\\\\ 7y-18=0\implies 7y=18\implies y=\cfrac{18}{7}[/tex]

The temperature in Minneapolis changed from -7°F at 6 AM to 7°F at noon. how much did the temperature increase?

Answers

that would be 7 - (-7)  = 7 + 7 = 14 degrees F
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