7-3=4 feet per hour
50 : 4 = 12,5 hour
The time taken by frog to get out of the well will be equal to [tex]22\frac{6}{7}[/tex] hours.
It is given that a well has a depth of 50 feet and a frog can climb 7 feet/hour but then takes a rest of 1 hour and slips by 3 feet.
We have to find out what time will it take for frog to get out of the well ?
What is the unitary method?
The unitary method is a method in which we find the value of a unit and then the value of the required number of units.
As per the question ;
The frog starts from the bottom of the well.
It is given that the well has a depth of 50 feet.
Frog can climb 7 feet/hour but then takes a rest of 1 hour and slips by 3 feet.
Let's check distance covered by frog in 2 hours ;
1st hour = 7 feet
2nd hour = 7 - 3 = 4 feet
So ,
In 2 hours frog covers a distance of 4 feet.
Hence ,
To climb 44 feet or 4 × 11 feet , the frog will take 2 × 11 or 22 hours
and
To climb rest of 6 feet distance , the frog would take [tex]\frac{6}{7}[/tex] of an hour.
Also ;
It is needed to be mentioned that once the frog reaches at the top of well it won't slip back.
So ,
The total time taken by frog to climb 50 feet deep well will be ;
= [tex]22\frac{6}{7}[/tex] hours
Thus , the time taken by frog to get out of the well will be equal to [tex]22\frac{6}{7}[/tex] hours.
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Amelia’s hourly wage is $3.50 less than double David’s hourly wage. Write an equation to find David’s hourly wage
The equation to find David’s hourly wage is:
David’s hourly wage = [tex]\frac{1}{2}[/tex] x + 1.75, where x represents Amelia’s hourly wage
Step-by-step explanation:
The given is:
Amelia’s hourly wage is $3.50 less than double David’s hourly wage
We need to find an equation to find David’s hourly wage
Assume that:
Amelia's hourly wage is xDavid’s hourly wage is y∵ Amelia’s hourly wage is $3.50 less than double David’s
hourly wage
- That means multiply David’s hourly wage by 2, then
subtract 3.50 from the product to get Amelia’s hourly wage
∴ x = 2y - 3.50
Now let us find y in terms of x
∵ x = 2y - 3.50
- Add 3.5 to both sides
∴ x + 3.50 = 2y
- Divide each term by 2
∴ [tex]\frac{1}{2}[/tex] x + 1.75 = y
- Switch the two sides
∴ y = [tex]\frac{1}{2}[/tex] x + 1.75
∵ y represents David’s hourly wage
∴ David’s hourly wage = [tex]\frac{1}{2}[/tex] x + 1.75, where x represents
Amelia’s hourly wage
The equation to find David’s hourly wage is:
David’s hourly wage = [tex]\frac{1}{2}[/tex] x + 1.75, where x represents Amelia’s hourly wage
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What is the number of possible outcomes if two quarters are tossed at the same time and the numbers of heads and tails are counted?
A) 2
B) 3
C) 4
D) 6
2)
Caroline flips a coin 3 times. According to the tree diagram, how many possible outcomes exist?
A) 2
B) 4
C) 6
D) 8
3)
Kyle is purchasing a refurbished phone. He is looking at the phone models 4, 5, and 6, with a protective case in red (R), blue (B), or camo (C). What are all of the different choices he has?
A) {4, 5, 6}
B) {4R, 5B, 6C}
C) {4R, 4B, 4C, 5R, 5B, 5C}
D) {4R, 4B, 4C, 5R, 5B, 5C, 6R, 6B, 6C}
4)
You are going to roll two dice What are the outcomes in the sample space?
A) {1, 2, 3, 4, 5, 6}
B) {2, 4, 6, 8, 10, 12}
C) {1-1, 2-2, 3-3, 4-4, 5-5, 6-6}
D) {1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 2-2, 2-3, 2-4, 2-5, 2-6, 3-3, 3-4, 3-5, 3-6, 4-4, 4-5, 4-6, 5-5, 5-6, 6-6}
5)
Hannah is getting dressed for a party. She plans to wear either shorts or jeans, a red, blue or green shirt, and flip flops or tennis shoes. According to the tree diagram, how many possible outfits can she make?
A) 8
B) 10
C) 12
D) 14
1st pic is 2nd q and 2nd pic is for 5th q
Answer:
1.) C
2.) C
3.) D
4.) D
5.) C
Step-by-step explanation:
1.) Each coin has two possible outcomes, and they are two coins in total.
2 (outcomes) x 2 (coins) = 4 possible outcomes
*hint: Look at the 1st column of the diagram and count how many branches come from it
*another hint: The branches are equal to the number of H's and T's in the 2 Column (4 branches or 4 possible outcomes)
2.) Each coin has two possible outcomes, and they are three coins in total.
2 (outcomes) x 3 (coins) = 6 possible outcomes
*hint: Look at the number of branches coming from 3 of the H's and T's in the 2nd column. (6 total branches or possible outcomes)
3.) They are 3 different types of phones, and 3 different types of cases.
3 (phones) x 3 (cases) = 9 possible combinations
{4R,4B,4C,5R,5B,5C,6R,6B,6C,}
*hint: Count 3 cases for each phone and add them (9 total)
4.)Each Dice has 6 sides (cube) and there are 2 Dice. But Each side gets paired with another side, so
6 (sides) x 6 (sides) = 36 possible outcomes
A - Shows outcomes for 1 Dice
B - Shows sum for both Dice
C - Shows some possible combinations when they are both the same number
D - Shows some more possible combinations including those when both dice are not the same number
D Appears to be the best answer as it has more details
5.) 2 Types of bottom wear (shorts or jeans), 3 Types of shirts (red, blue, green) and 2 Types of shoes (flip flops or tennis shoes).
2 (bottom) x 3 (top) x 2 (feet) = 12 possible combinations
*hint: For each bottom wear (shorts or jeans) there are 6 possible combinations so multiplying by two will give you the amount for each one.
Answer:
2 is 8 :)
Step-by-step explanation:
That is 30/8 simplified
Answer:
3 3/4
Step-by-step explanation:
Answer:
15/4
in order to simplify you need to find the gcf (greatest common factor) and divide by that number on both numerator and denominator, since two is the gcf, 15/4 is the answer
Question 2
Sarah opens a savings account that has a 2.75% annual interest rate, compounded monthly. She deposits $500 into the
account. How much will be in the account after 15 years?
$500.00
$754.94
$1255.27
$255.27
Therefore $754.94 will be in account after 15 years.
Step-by-step explanation:
Given , Sarah opens a saving account that has a 2.75% annual interest rate , compounded monthly. She deposits $500 into the account.
P = $500, r = 2.75% = 0.0275 , t = 15 years and n= 12
[tex]Amount (A) =P(1+\frac{r}{n})^{nt}[/tex]
[tex]=\$500(1+\frac{0.0275}{12})^{(12\times15)}[/tex]
=$754.94
Therefore $754.94 will be in account after 15 years.
After 15 years with a 2.75% annual interest rate, compounded monthly, an initial deposit of $500 in a savings account will grow to approximately $754.94.
Explanation:The student has asked how much money will be in a savings account after 15 years with an initial deposit of $500 if the account has a 2.75% annual interest rate, compounded monthly. To calculate the future value of this account, we can use the compound interest formula:
A = P (1 + r/n)^(nt)
Where:
Here, P is $500, r is 0.0275 (2.75% expressed as a decimal), n is 12 (since the interest is compounded monthly), and t is 15 years.
So, the calculation is:
A = $500 * (1 + 0.0275/12)^(12*15)
By computing this, we can determine the future value of the savings account after 15 years:
A ≈ $500 * (1 + 0.00229167)^(180)
A ≈ $500 * (1.00229167)^180
A ≈ $500 * 1.510383954
A ≈ $754.94
Therefore, the amount in the savings account after 15 years will be approximately $754.94.
Heather is making a blanket for her baby and is going to put a ribbon border around it. The blanket will be 3 feet by 5 feet. The fabric for the blanket cost $1.25 per square yard and the ribbon costs $.50 per foot. What is the approximate total cost for the blanket? A) $1.75 B) $10.08 C) $20.84 D) $26.75 E) $32.48
Answer:
The approximate total cost for the blanket is $10.08 ⇒ B
Step-by-step explanation:
The formula of the area of a rectangle is A = L × W
The formula of the perimeter of a rectangle is P = 2(L + W)
where:
L is the length of the rectangleW is the width of the rectangle∵ The baby blanket shaped a rectangle
∵ The dimensions of the blanket are 3 feet and 5 feet
- Find the area of the blanket
∵ A = 3 × 5 = 15 feet²
- Change feet to yard because the cost is by square yard
∵ 1 foot = [tex]\frac{1}{3}[/tex] yard
∴ 1 foot² = [tex](\frac{1}{3})^{2}=\frac{1}{9}[/tex] yard²
∴ 15 feet² = 15 × [tex](\frac{1}{9})[/tex] = [tex]\frac{5}{3}[/tex] yards²
∴ The area of the blanket is [tex]\frac{5}{3}[/tex] yards²
∵ The fabric cost of the blanket is $1.25 per square yard
∴ The fabric cost = [tex]\frac{5}{3}[/tex] × 1.25
∴ The fabric cost = 2.08333 dollars
∵ Heather is going to put a ribbon border around it
- The length of the ribbon is equal to the perimeter of the blanket
∵ P = 2(3 + 5) = 16 feet
∴ The length of the ribbon is 16 feet
∵ The cost of the ribbon is $0.5 per foot
∴ The cost of the ribbon = 16 × 0.5
∴ The cost of the ribbon = 8 dollars
Now add the fabric cost to the ribbon cost to find the total cost of the blanket
∵ The total cost = 2.08333 + 8
∴ The total cost = 10.08333
- Round it to the nearest cent
∴ The total cost = 10.08 dollars
The approximate total cost for the blanket is $10.08
What is the solution to the system that is created by the equation y = negative x + 6 and the graph shown below? On a coordinate plane, a line goes through (0, 0) and (4, 2). (–8, –4) (–4, –2) (4, 2) (6, 3)
Answer:
The solution point is (4,2).
Step-by-step explanation:
Equation of straight line passing through the points (0,0) and (4,2) is given by
[tex]\frac{y - 2}{2 - 0} = \frac{x - 4}{4 - 0}[/tex]
⇒ 2y = x ............ (1)
And the other straight line is y = - x + 6 .............. (2)
Now, solving equations (1) and (2) we get, y = - 2y + 6
⇒ 3y = 6
⇒ y = 2
And from equation (1) we get, x = 2y = 4
Therefore, the solution point is (4,2). (Answer)
Answer:
C: (4,2)
Step-by-step explanation:
1 In a test, a hybrid car drove 619 yards on 1 fluid
ounce of gasoline. To the nearest tenth, what is
this rate in miles per gallon?
A. 7.5 mi/gal
B. 15 mi/gal
C. 22.5 mi/gal
D. 45 mi/gal
The rate in miles per gallon will be 45 miles per gallon. Then the correct option is D.
What is conversion?Conversion means to convert the same thing into different units.
In a test, a hybrid car drove 619 yards on 1 fluid ounce of gasoline.
We know that 1 yard = 1/1760 miles. Then we have
619 yards = 619 x 1 / 1760 miles
We know that 1 fluid ounce = 1 / 128 gallons
The rate in miles per gallon will be
R = (619 / 1760) / (1 / 128)
R = 619 x 128 / 1760
R = 45 miles per gallon
The rate in miles per gallon will be 45 miles per gallon. Then the correct option is D.
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5(n + 3) -7n when n = 1/2
Answer:
14
Step-by-step explanation:
Replace n with 1/2
5(1/2 + 3) -7(1/2)
17.5 - 3.5
=14
So, n=14
Answer:
14
Step-by-step explanation:
5(n + 3) -7n
putting value of n
5(1/2 + 3) - 7/2
5(0.5 + 3) - 3.5
5(3.5) - 3.5
17.5 - 3.5
14
Rewrite the equation y=2|x−3|+5 as two linear functions f and g with restricted domains.
Please help
Answer:
f(x) = 2+5
g(x) = 2(-(x−3))+5
Step-by-step explanation:
If you remember, an absolute value can have two different answer, a positive and negative answer because the absolute value symbol makes all values in it positive. Example: |-2|=2 and |2|=2
So if y = 2|x−3|+5
then the two possibilities are
y = 2(x−3)+5 and
y = 2(-)+5
Set one of them equal to f(x) and the other one to g(x)
f(x) = 2(x−3)+5
g(x) = 2(-(x−3))+5
You can also write it as a piecewise function.
[tex]y(x)=$\begin{array}{cc} \{ & \begin{array}{cc} -(x-3) & x<3 \\ 0 & x=3 \\ (x-3) &x>3 \end{array}\end{array}$[/tex]
What fraction is it equivalent to 9/20
Answer: 18/40 and 27/60
Step-by-step explanation:
Multiply the numerator and denominator by whatever number it needs to be multiplied by
9*2 to get 18
20*2 to get 40
9*3 to get 27
20*3 to get 60
Which expression is equivalent to (XY^−6)^2
XY^−36
x^2y^−12
x ^2y^12
xy^36
Answer:
answer is b
Step-by-step explanation:
look at picture shown
the perimeter of a square with 2/3g cm sides without polynomial
Answer:
P = 2.7g/cm
Step-by-step explanation:
Perimeter (P) = 4×number of sides (S)
P = 4S
Where S = 2/3gcm
Therefore, P = 4 × 2/3
P = 8/3gcm or 2.66667~ 2.7g/cm
A box measures 4 inches by 2 inches by 3 inches. Find the volume of the box
in cubic feet. Enter your answer as a fraction. Use the '/' as the fraction bar.
Do not include units in your answer.
Answer:
24/1
Step-by-step explanation:
Anything on this page please! BIG POINTS! Please provide Explanations!
Answer:
Step-by-step explanation:
B. For roses you could sell 84 bunches of 14 roses. For tulips, you could sell 70 bunches of 18 tulips, and for gerberas, you could sell 75 bunches of 18 gerberas.
C. well 8 dollars times 84 is $672. 11 times 70 equals $770, and 9 times 75 is $675. in total $2,117.
D. i - 1176 well to start we add up all the digits to see if its sum is divisible by 9. 1+1+7+6=15. 15 is not a multiple of 9 so its not divisible.
ii. 1260 well to see if 1260 is divisible by 8 is by taking the last 3 digits of the number and dividing it by 8. 260 divided by 8 equals 32.5. since 32.5 is a decimal and 8 can't go into 260 evenly 1260 is not divisible by 8.
If you have any questions feel free to ask in the comments - Mark
Also when you have the chance please mark me brainliest.
also did you know the word divisibility has 5 i's in it? lol also the picture is for number 1 or letter a.
Answer:
what he said :>
Step-by-step explanation:
If an arrow is shot upward on Mars with a speed of 54 m/s, its height in meters t seconds later is given by
y = 54t − 1.86t2.
(Round your answers to two decimal places.)
(a) Find the average speed over the given time intervals.
(i) [1, 2]
m/s
(ii) [1, 1.5]
m/s
(iii) [1, 1.1]
m/s
(iv) [1, 1.01]
m/s
(v) [1, 1.001]
m/s
(b) Estimate the speed when t = 1.
m/s
The average speed calculated over the given time intervals is
48.42 m/s, 49.35 m/s, 50.09 m/s, 50.26 m/s, and 50.29 m/s. The estimated speed when t = 1 is 50.28 m/s.Given formula is y = 54t - 1.86t²
Speed = dy/dt = 54 - 3.72t
a) Average speed over the time intervals given below are:
In [1, 2] time interval, it is [tex]\frac{54t - 1.86t^{2} }{2-1} = \frac{54t - 1.86t^{2} }{1}[/tex] = 48.42 m/sIn [1, 1.5] time interval, it is[tex]\frac{54t - 1.86t^{2} }{1.5-1} = \frac{54t - 1.86t^{2} }{0.5}[/tex] = 49.35 m/sIn [1, 1.1] time interval, it is [tex]\frac{54t - 1.86t^{2} }{1.1-1} = \frac{54t - 1.86t^{2} }{0.1}[/tex] = 50.09 m/sIn [1, 1.01] time interval, it is [tex]\frac{54t - 1.86t^{2} }{1.01-1} = \frac{54t - 1.86t^{2} }{0.01}[/tex] = 50.26 m/sIn [1, 1.001] time interval, it is [tex]\frac{54t - 1.86t^{2} }{1.001-1} = \frac{54t - 1.86t^{2} }{0.001}[/tex]= 50.29 m/sb) When t = 1, the speed is v = 50 - (3.72*1) = 50.28 m/s
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Lacey can type 105 words in 3 minutes. At this rate, how many words can she type in 26 minutes
Vince has a rectangular rug in his room with an area of 10 ft the length of the rug is 18 inches longer than the width what could be the dimensions of the rug?
The length of the rug is 4 ft.
The width of the rug is 2.5 ft.
Explanation:
The area of the rug is 10 ft.
The length of the rug be l.
Let us convert the inches to feet.
Thus, [tex]18 inches = 1.5 ft[/tex]
Thus, the length of the rug is [tex]l=1.5+w[/tex]
Let the width of the rug be w.
Substituting these values in the formula of area of the rectangle, we get,
[tex]A=length\times width[/tex]
[tex]10=(1.5+w)(w)\\10=1.5w+w^2\\w^2+1.5w-10=0[/tex]
Solving the expression using the quadratic formula,
[tex]$w=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]
Substituting the values, we have,
[tex]$w=\frac{-15 \pm \sqrt{15^{2}-4 \cdot 10(-100)}}{2 \cdot 10}\\[/tex]
[tex]$w=\frac{-15 \pm \sqrt{4225}}{20}$[/tex]
[tex]$w=\frac{-15 \pm 65}{2 0}$[/tex]
Thus,
[tex]w=\frac{-15 + 65}{2 0}\\w=\frac{50}{20} \\w=2.5[/tex] and [tex]w=\frac{-15 - 65}{2 0}\\w=\frac{-80}{20} \\w=-4[/tex]
Since, the value of w cannot be negative, the value of w is 2.5ft
Thus, the width of the rug is 2.5ft
Substituting [tex]w=2.5[/tex] in [tex]l=1.5+w[/tex], we get,
[tex]l=1.5+2.5\\l=4[/tex]
Thus, the length of the rug is 4 ft.
It's A
length 4 and width 2.5
When solving graphically ,which system of equations will have exactly one point of intersection
Answer: you still need help? let me know okay UwU
Step-by-step explanation:
When solving graphically ,which system of equations will have exactly one point of intersection.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Let consider an example.
Consider the slope-intercept form of equations: y = -6x+8 and y=-3x-4
Since the slopes are different, the lines must intersect.
Because the lines intersect at a point, there is one solution to the system of equations the lines represent.
Hence, when solving graphically, the linear system of equations will have exactly one point of intersection.
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help me please so confsed
The answers is 2,200
Answer:
2600
Step-by-step explanation:
first you would round them to the nearest hundred. this means that if the figure in the tens column is greater than or equal to 5 you would round up. if it is less than 5 you round down
so 1400+400+800=
then you would add them up
so 1400+400+800=2600
1400+400=1800
1800+800=2600
What could you do to solve the problem below?
When Sabine set off to climb Mt. Marcy, she had 18 gummi bears in her bag.
When she returned to the lodge, she had 6 gummi bears left. How many
gummi bears did she eat during her hike?
A. Subtract 6 from 18
B. Multiply 18 by 6
C. Divide 18 by 6
D. Add 6 to 18
Answer: A. Subtract 6 from 18
The length of the major axis of the ellipse below is 17, and the length of the
red line segment is 6. How long is the blue line segment?
Answer:
Option C. 11
Step-by-step explanation:
If a point P lies on an ellipse, The sum of distances between the point p and the foci will be equal the major axes.
So, applying the previous rule to the problem
The red line + the blue line = major axis
6 + the blue line = 17
So, the blue line = 17 - 6 = 11
The answer is option C. 11
The slope of a line that is perpendicular to a line whose slope is -2/7 is
solve if 2/3 + 1/3x = 2x
Answer:
x = [tex]\frac{2}{5}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{3}[/tex] + [tex]\frac{1}{3}[/tex] x = 2x
Multiply through by 3 to clear the fractions
2 + x = 6x ( subtract x from both sides )
2 = 5x ( divide both sides by 5 )
[tex]\frac{2}{5}[/tex] = x
Answer: x=2/5
Step-by-step explanation:
Trust me
when a=2 b=3 and c=5 what is the value of a(b+c)
solve and show how you got the answer
Answer:
16
Step-by-step explanation:
If we plug in all the variables, we get 2(3+5)
Evalutation: 2(3+5)=2(8)=16
So the value is 16
Hope this helped!
Answer:
16
Step-by-step explanation:
a =2
b = 3
c =5
a(b +c)
2(3+5)
2x3 + 2x5
6 + 10
16
The height of a rectangular prism is 3 in.. The perimeter is 88 in. (4 in. wide and 11 in. long). What is the value of the base?
Step-by-step explanation:
Given,
The height of a rectangular prism(h) = 3 in and
The perimeter of a rectangular prism = 88 in
To find, the base of a rectangular prism(b) = ?
We know that,
The perimeter of a rectangular prism = 2l + 2b or 2b + 2h or 2h + 2l
∴ 2b + 2(3) = 88
⇒ 2b = 88 - 6
⇒ 2b = 82
⇒ b = 41 in
Thus, the base of a rectangular prism(b) = 41 in.
Find the volume
4 3/4 cm
3cm
7 1/5 cm? need help asap
Step-by-step explanation:
hope the answer will helpful
9(6u+5)+2(u-4) need solved
Answer:
Step-by-step explanation:
Subtract
6 u from 2 u .
− 4 u + 9 = 19
Move all terms not containing u to the right side of the equation.
− 4 u = 10
Divide each term by − 4 and simplify.
u = − [tex]\frac{5}{2}[/tex]
The result can be shown in multiple forms.
Exact Form:
u = − [tex]\frac{5}{2}[/tex]
Decimal Form:
u =− 2.5
Mixed Number Form:
u = − 2 [tex]\frac{1}{2}[/tex]
i need help with both of them i will give you 25 points
plz help
Answer:
1)m<DCH =89
2)m<BCD=103
Step-by-step explanation:
1) We have that:
m<EFB=91 degree.
We want to find m<DCH.
By same side interior angle property:
m<DCH +m<EFB=180
m<DCH +91=180
m<DCH=180-91
m<DCH =89
2) Given that: m<HFG=103, we seek to find m<BCD.
By the alternate exterior angle property:
m<HFG=m<BCD
Therefore
m<BCD=103
Dave, Frank, and Kathy can process 1,300 catalog orders per day when all three of them are working. Dave and Frank can do 780 orders per day and Frank and Kathy can do 850 orders per day. How many can each do in a day?
What is one whole and three fourths plus five sixths plus one whole and one fourth
Answer:
First of all cant give u the anssswer i am srry but i can give u a hint u need to find eqivelent fractions for the denominators then u can add them
Step-by-step explanation:
Answer: The answer is Three whole and five sixths (3 5/6)
Step-by-step explanation: One whole and three fourths can be expressed as 1 3/4, and this is added to five sixths, that is, 5/6. therefore these can be expressed as
[1 3/4 + 5/6}
The other part of the questions says one whole and one fourth which can be expressed as 1 1/4.
The entire question can now be written out as
[1 3/4 + 5/6] + [1 1/4]
We would start by solving for the left hand side of the expression
1 3/4 + 5/6
= 7/4 +5/6
By using a common denominator which is 12 (the LCM), the expression now becomes,
[21 + 10]/12
= 31/12
We can now add this to the right hand side of the expression. Thus,
[31/12] + 1 1/4
=31/12 + 5/4
By using a common denominator which is also 12, the expression now becomes,
[31 + 15]/12
= 46/12, By simplifying further we arrive at,
23/6.
Written as a proper fraction, this becomes
3 5/6 (Three whole and five sixths)