Pam bought different drinks for a party she was throwing. After the party, she had the following drink amounts left over.
\dfrac1{2}
2
1
start fraction, 1, divided by, 2, end fraction liter of soda
\dfrac15
5
1
start fraction, 1, divided by, 5, end fraction liter of water
\dfrac8{10}
10
8
start fraction, 8, divided by, 10, end fraction liter of apple juice
Which statement correctly compares the amounts of 2 left over drinks?
Choose 1 answer:
(Choice A)
A
Pam had less water left over than apple juice.
(Choice B)
B
Pam had more soda left over than apple juice.
(Choice C)
C
Pam had less soda left over than water.
Answers
Answer:
A) Pam had less water left over than apple juice.
Step-by-step explanation:
Given amounts of drinks left over:
[tex]\dfrac{1}{2}\; \sf liter \;of \;soda[/tex][tex]\dfrac{1}{5}\; \sf liter \;of \;water[/tex][tex]\dfrac{8}{10}\; \sf liter \;of \;apple\;juice[/tex]To compare the amounts of drinks left over, convert the fractions into equivalent fractions that have the same denominator.
The denominators of the three fractions are 2, 5 and 10.
The lowest common multiple of the denominators is 10.
Therefore, rewrite the first two fractions so that their denominators are also 10.
[tex]\textsf{Soda}: \quad \dfrac{1}{2}=\dfrac{1 \cdot 5}{2 \cdot 5}=\dfrac{5}{10}[/tex]
[tex]\textsf{Water}: \quad \dfrac{1}{5}=\dfrac{1 \cdot 2}{5 \cdot 2}=\dfrac{2}{10}[/tex]
Therefore, as:
[tex]\dfrac{2}{10} < \dfrac{5}{10} < \dfrac{8}{10}[/tex]then:
water < soda < apple juiceTherefore, Pam had less water left over than apple juice.
Answer:
a) Pam had less water than apple juice.
★ Water < Soda < Apple juice
Step-by-step explanation:
Converting the fraction into decimals,
→ Soda left = 1/2 = 0.5 litres
→ Water left = 1/5 = 0.2 litres
→ Apple juice left = 8/10 = 0.8 litres
Let's order them in ascending order,
→ 0.2 < 0.5 < 0.8
→ 1/5 < 1/2 < 8/10
→ Water left < Soda left < Apple juice left
Now the applicable options is,
→ Pam had less water than apple juice.
Hence, option (a) is correct answer.
Related Questions
read the whole question and then answer it!!
Answers
1a. No, the value of 60% of 400 is 240.
1b. No, the value of 60% of 200 is 120.
1c. No, the value of 60% of 120 is 72.
2. The equation the express the relation 60%, x, and 87 is 0.6x = 87. The value of x is 145.
3a.The equation is0.6c = 43.2. The value of c is 72.
3b. The equation is0.38e = 190. The value of e is 500.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
1.a
Compute the vale of 60% of 400.
Using the formula a% = a/100
60% of 400 = 60/100 of 400
Replace of by multiplication:
60% of 400 = (60/100) × 400
60% of 400 = 240.
1b.
Compute the vale of 60% of 200.
Using the formula a% = a/100
60% of 200 = 60/100 of 200
Replace of by multiplication:
60% of 200 = (60/100) ×2 00
60% of 400 = 120.
1c.
Compute the vale of 60% of 120.
Using the formula a% = a/100
60% of 120 = 60/100 of 120
Replace of by multiplication:
60% of 120 = (60/100) × 120
60% of 400 = 72.
2.
Given that 60% of x is 87.
Compute the vale of 60% of x.
Using the formula a% = a/100
60% of x = 60/100 of x
Replace of by multiplication:
60% of x = (60/100) × x
60% of x = 0.6x
Therefore the relationship is 0.6x = 87
Now divide both sides by 0.6:
x = 87/0.6
x = 145.
3a.
Given that 60% of c is 43.2.
Compute the vale of 60% of c.
Using the formula a% = a/100
60% of c = 60/100 of c
Replace of by multiplication:
60% of c = (60/100) × c
60% of c = 0.6c
Therefore the relationship is 0.6c = 43.2
Now divide both sides by 0.6:
c = 43.2/0.6
c =72.
3b.
Given that 38% of e is 190.
Compute the vale of 38% of e.
Using the formula a% = a/100
38% of e = 38/100 of e
Replace of by multiplication:
38% of e = (38/100) × e
38% of e = 0.38e
Therefore the relationship is 0.38e = 190
Now divide both sides by 0.38:
e = 190/0.38
e = 500.
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The graph below shows a transformation of y=2^x .
Write an equation of the form y=A . 2^x+k for the graph above.
y=
Answers
The graph showing the transformation of the function y = 2ˣ, with points (0, -1), and (1, -4), as well as an horizontal asymptote of y = 2, indicates that the equation of the graph in the form y = A·2ˣ + k is; y = -3·2ˣ + 2
What is an asymptote of a graph?The asymptote is a line that can be drawn on the graph such that the curve of the graph approaches the line without touching it as the values of the variables increase.
The required form of the exponential equation is; y = A·2ˣ + k
Where;
k = The horizontal asymptote
The graph included in the question indicates that an horizontal asymptote is indicated by the line y = 2
= 2
Points on the graph of the transformed function are (1, -4), (0, -1)
When x = 0, y = -1, therefore;
-1 = A·2⁰ + 2
A·2⁰ + 2 = -1 - 2 = -3
A = -3
The equation for the graph is therefore;
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A person standing close to the edge on top of a 72-foot building throws a ball vertically upward. The quadratic function h = − 16 t^2 + 84 t + 72 models the ball's height above the ground, h , in feet, t seconds after it was thrown.
a) What is the maximum height of the ball? ____________ feet
b) How many seconds does it take until the ball hits the ground? ____________ seconds
Answers
What is the maximum height of the ball 182.25 feet
How many seconds does it take until the ball hits the ground 6 seconds
How to find the maximum height of the ballThe maximum height will occur at the vertex v(h', k)
h' = -b/2a
From the equation h = − 16 t^2 + 84 t + 72
a = -16
b = 84
h' = -84/(2 * -16)
h' = t = 2.625
k = h = − 16 t^2 + 84 t + 72 at t = 2.625
= − 16 * 2.625^2 + 84 * 2.625 + 72
= 182.25 feet
The ball hits the ground when h = 0
0 = − 16 t^2 + 84 t + 72
solving the quadratic equation gives
t = 6 OR -3/4
Use the positive value
t = 6 seconds
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solution set of a compound inequality
Answers
The solution of a compound inequality is the common region or intersection region of two inequalities.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
A sentence having two inequality statements connected by the words 'or' Or 'and' is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence.
For example, if in a compound inequality we get x > 3 and x > 5 so the final conclusion is x > 5.
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The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
a. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million.
Answers
The population of the state is 23.1 million
The population of the state will reach 28.3 million in 13.5 years
What is population ?
Any whole group that shares at least one trait is referred to be a population. People do not make up all populations. Populations can include, but are not limited to, individuals, animals, organizations, structures, buildings, cars, farms, objects, or occasions.
The population state is:
A = 23.1*e^(0.0153*t)
In millions.
Where t represents the number of years after 2000.
a) For the population at the year 2000, we need to evaluate the function at t = 0 (2000 is 0 years after 2000).
A(0) = 23.1*e^(0.0153*0) = 23.1
The population at year 2000 was 23.1 millions.
b) Now we want to solve:
A(t) = 28.3 = 23.1*e^(0.0153*t)
28.3/23.1 = e^(0.0153*t)
1.23 = e^(0.0153*t)
Now we can apply the natural logarithm to both sides:
ln(1.23) = ln( e^(0.0153*t) )
ln(1.23) = 0.0153*t
ln(1.23)/0.0153 = t = 13.5
So 13.5 years after 2000 the population will be 28.3 million.
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Write an equation and solve for p. Show all work.
Answers
a) The equation is 10p + 80 = 180 and p = 10.
b) The three angles are 90°, 37°, 53°.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given that, the angles of the triangles are 53°, 2p + 17°, and 8p + 10°.
The sum of all angles of a triangle is 53° + 2p + 17° + 8p + 10° = 80 + 10p
The sum of all angles of a triangle is 180°.
Therefore,
80 + 10p = 180
Subtract 80 from both sides:
10p = 100
divide both sides by 10:
p = 10.
Putting p = 10 in 2p + 17°, and 8p + 10°:
2p + 17° = 20° + 17° = 37°
8p + 10° = 80° + 10° = 90°
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fhyyyyyyyyyyyyyyyyyyyyytttttttttttttttttttttttttttttttttttttttttgsdddddddddddddtttttttt
Answers
Answer:
Step-by-step explanation:
there is no answer it just a bunch of f,h,y and t this is not math this is something
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
If x = 13,
(13 - 7)^2 = 6^2 = 36
If x = 1
(1 - 7)^2 = -6^2 = 36
If x = -29
(-29 - 7)^2 = -36^2 = 1296
If x = 42,
(42 - 7)^2 = 35^2 = 1225.
So option A and B are the answer
Find the slope of the line that passes through all of the points on the table.
Answers
Step by step
Slope can be found using two points from the graph and formula y2 - y1 over x2 - x1
(2, 2) (5, -6)
-6 -2 over 5 - 2 = -8/3
Try another set to be sure
(8, -14) (11, -22)
-22 - -14 over 11 - 8 = -8/3
So your slope is -8/3
El primer término en una serie geométrica es 64 y la razón común es 0.75
Answers
Answer:
Si...
En una progresión geométrica se conocen a1 = 64 y r = 0,75
The figure below is reflected over the y-axis. What are the coordinates of the image of point R after this transformation?
Answers
Explanation- if point R is 2 squares away from the y-axis in the third quadrant, you have to count 2 squares away from the y-axis in the fourth quadrant. This gives you the co-ordinates (2,-9).
I don’t understand this any help please answer and explain please
Answers
Answer:
25.5 inches.
Step-by-step explanation:
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we have a right triangle with legs of length 19 inches and 17 inches. The length of the hypotenuse is the square root of the sum of the squares of the other two sides. We can calculate this as follows:
hypotenuse = sqrt(19^2 + 17^2)
hypotenuse = sqrt(361 + 289)
hypotenuse = sqrt(650)
hypotenuse = 25.495097568 inches
Rounding to the nearest tenth, the length of the hypotenuse is 25.5 inches.
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Suppose you have a group of 20 people, 7
are women and the remaining people are
men. What is the probability you select 4
women from the group?
Answers
The probability of select 4 women from the group is, P = 35.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given: You have a group of 20 people, 7 are women and the remaining people are men.
7 are women then 13 are men.
No. of ways in which 4 women can be chosen from 7 women are 7C4.
So, the probability of select 4 women from the group is,
[tex]P = {7_C_4} \\P = \frac{7!}{4!*(7-4)!} \\P=\frac{7!}{4!*3!} \\P = 35[/tex]
Hence, the probability of select 4 women from the group is, P = 35.
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A new gaming chair costs $239.87. You have already saved $106.37 and earn $44.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
44.5w + 106.37 = 239.87; w = 3
44.5w − 106.37 = 239.87; w = 9
44.5w − 239.87 = 106.37; w = 9
44.5 + 106.37w = 239.87; w = 3
Answers
The equation will be 44.50 w + 106.37 = 239.87, and it will take 3 weeks to collect money for gaming chair.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the data provided in the question,
Cost of new gaming chair = $239
Savings for gaming chair = $106.37
Each week earning = $44.50
Then the expression will be,
44.50 w + 106.37 = 239.87
44.50 w = 239.87 - 106.37
w = 133.5/44.50
w = 3
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20 + 4 (3x - 5) + 2x = 28
How can I get the answer and please explain step by step!
Answers
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
Equation
[tex]20 + 4(3x-5)+2x=28[/tex]
Expand the brackets
[tex]20 + 12x- 20 + 2x=28[/tex]
Combine like terms
[tex]14x=28[/tex]
Solve
[tex]x=2[/tex]
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Find the measure of X
Answers
The measure of x = 64°
Vertical opposite angles:The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposed angles. A pair of angles that are vertically opposed to one another are always equal.
Here we have
Three lines are intersected and formed a triangle
Let's assume that the triangle formed is ΔABC
In ΔABC, ∠C = 34°
Since Vertical opposite angles are equal
=> ∠B = 30°
As we know the sum of angles in a triangle = 180°
=> ∠A + ∠B + ∠C = 180°
=> ∠A = 180° - 30° - 34°
=> ∠A = 116
From the line CL [ observe the given picture ]
=> ∠A + x = 180°
=> 116° + x = 180°
=> x = 180° - 116°
=> x = 64°
Therefore,
The measure of x = 64°
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A sample of 200g of an isotope decays to another isotope according to the function A(t)= 200е⁻⁰⁰⁵⁴⁺ ,where t is the time in years
(a) How much of the initial sample will be left in the sample after 25 years?
(b) How long will it take the initial sample to decay to half of its original amount?
(a) After 25 years, about __g of the sample will be left.
(Round to the nearest hundredth as needed.)
Answers
The amount of initial sample will be left in the sample after 25 years is $771.49.
What is isotope decay?
An unstable atomic nucleus loses energy via radiation during the process of radioactive decay. A substance is regarded as radioactive if it has unstable nuclei. The three most frequent types of decay are alpha decay, beta decay, and gamma decay, all of which involve the emission of one or more particles.
Given:
A sample of 200g of an isotope decays to another isotope according to the function [tex]A(t) = 200e^-^0^.^0^5^4^t[/tex],where t is the time in years.
We have to find the amount of initial sample will be left in the sample after 25 years.
Plug t = 25 in the given equation.
[tex]A(25) = 200e^-^0^.^0^5^4^(^2^5^)\\A(25) = 771.4851\\A(25) = 771.49[/tex]
Hence, the amount of initial sample will be left in the sample after 25 years is $771.49.
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√3 + (4 + √x + 3)² / 6 = 3
Answers
Answer: x = 1
Step-by-step explanation:
need help!!! with geometry
Answers
The value of r is 45 and the value of s is 29
Calculating value of missing variablesFrom the question, we are to solve the parallelogram for the missing variables.
The missing variables are r and s
Since opposite angles of a parallelogram are equal, we can write that
(r - 10)° = (3r - 100)°
Solve for r
r - 10 = 3r - 100
-10 + 100 = 3r - r
90 = 2r
r = 90/2
r = 45
Also,
We can write that
(5s)° = (4r - 35)°
Substitute the value of r and solve for s
5s = 4(45) - 35
5s = 180 - 35
5s = 145
s = 145/5
s = 29
Hence, r = 45, s = 29
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Solve for a.
a+(−7)=−17
Answers
Answer: a= (-10)
Step-by-step explanation:
step 1- move the -7 to the other side of the equal sign to combine with -17.
step 2- to do this we need to make -7 positive so instead of (-17) -7, it would be (-17) +7.
step 3- leaving you with
a= (-10) hope this helped :)
The sum of 5 consecutive odd numbers
is 145.
What is the third number in this sequence?
Answers
Hello,
I hope you and your family are doing well!
The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. Since the sum of 5 consecutive odd numbers is 145, we can set up the equation:
(a + (a + 4)) / 2 * 5 = 145
where a is the first term in the sequence.
Solving this equation gives us:
a = -23
The third number in the sequence is the third odd number after a, which is a + 4. Substituting -23 for a gives us:
(-23) + 4 = -19
Therefore, the third number in the sequence is -19.
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Happy Holidays & New Year!
A thermometer shows the temperature in degrees Celsius (°C) and degrees Fahrenheit (°F). One day, it shows 87°F and 31°C. The next day, it shows 94°F and 34°C. Determine if there is a proportional relationship between the temperature in degrees Celsius and the temperature in degrees Fahrenheit.
No, there is not a proportional relationship because 87 over 31 does not equal 94 over 34.
Yes, there is a proportional relationship because 87 over 31 equals 94 over 34.
No, there is not a proportional relationship because degrees Celsius and degrees Fahrenheit are not the same measurement.
Yes, there is a proportional relationship because degrees Celsius and degrees Fahrenheit are the same measurement.
Answers
The values shown by the thermometer of 87 °F and 94 °F which in degrees Celsius are 31 °C and 34 °C indicates that the relationship is not a proportional relationship. The correct option is therefore;
No, there is not a proportional relationship because 87 over 31 does not equal 94 over 34.What is a proportional relationship?A proportional relationship is one in which one variable is a constant multiple of the other, such that the ratio of each data pair is a constant.
The temperature it shows on the first day = 87 °F and 31°CThe temperature it shows on the next day = 94 °F and 34 °CThe ratio of the two temperatures are therefore;
[tex]\dfrac{87}{31}[/tex] and [tex]\dfrac{94}{34}[/tex]
31 is a prime number, therefore'
[tex]\dfrac{87}{31} \neq \dfrac{94}{34}[/tex]
The ratio of the ordered pair of a proportional relationship is constant, the ratio of the specified values is not constant, therefore, the relationship is not a proportional relationship.
The correct option is therefore;
No there is not a proportional relationship because 87 over 31 does not equal 94 over 34
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One angle measures 160°, and another angle measures (3k + 61)°. If the angles are vertical angles, determine the value of k.
k = 14
k = 33
k = 74
k = 160
Answers
Answer:
Therefore, the value of k is 1.
Step-by-step explanation:
Vertical angles are pairs of angles that are opposite each other and are formed by two intersecting lines. If one angle measures 160°, the other angle must measure 180° - 160° = 20°. Therefore, if the other angle measures (3k + 61)°, we can set up the equation 20 = 3k + 61. Solving for k, we get k = -41. However, since the value of k must be a positive integer, the only possible value of k is k = 1. Therefore, the value of k is 1.
Answer:
k = 33
Step-by-step explanation:
You can afford a $1050 per month mortgage payment. You've found a 30 year loan at 7% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
Answers
(a) Loan you can afford is $143097.67. (b) Total money will you pay the loan company is $378000. (c) Interest amount is $234902.33.
What is Loan interest ?Loan interest is the additional cost that a borrower must pay on top of the principal amount of a loan. Interest is typically expressed as a percentage of the principal and is charged over a specific period of time. The rate of interest charged on a loan is determined by a variety of factors, including the borrower's creditworthiness and the type of loan. The purpose of interest is to compensate the lender for the risk and cost of providing the loan.
Given data:
Principal = $1050 per month
Time = 30 year
= 30 × 12
= 360 months
Interest rate = 8%
= 0.08/12
= 0.006667 monthly
(a) We get here first maximum amount of loan by present value of annuity as
Present value of annuity = principal × [tex]\frac{1-(1+rate)^{-t} }{rate}[/tex] .........(1)
Put here value we get
value of annuity = 1050 × [tex]\frac{1-(1+0.006667)^{-360} }{0.006667}[/tex]
value of annuity = $143097.67
(b) Total amount = principal × time period
= $1050 × 360
= $378000
(c) Total amount of interest paid will be
interest amount = total amount paid - loan amount
interest amount = $378000 - $143097.67
interest amount = $234902.33
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2. Sandra gets 2 dollars for every 50 aluminum cans she recycles. What is the ratio of dollars to
cans? How much money does she make per can?
Answers
Answer:
1:25
$0.04 or 4 cents per can
Step-by-step explanation:
The ratio of dollars to can is 2:50 = 1:25.
$1/25 = $0.04
She gets $0.04 or 4 cents per can
Q4 Two consecutive numbers are such that the larger number when
added twice the smaller number gives a sum of 70. Find the two numbers.
Answers
Answer:
The answer is in the picture
Step-by-step explanation:
The explanation is in the picture
Xavier is riding on his bike at a constant speed of 15
miles per hour. What is the closest approximation of
how long it will take Xavier to ride 5 miles?
A. 0.15 hour
B. 0.2 hour
C. 0.33 hour
D. 0.5 hour
Answers
Answer:
C. 0.33 hour
Step-by-step explanation:
15 miles = 1 hr
5 miles = x hr
cross multiply
5 = 15x
x = 5/15
x = 0.333 hr
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Use technology to find the P-value for the hypothesis test described below.
The claim is that for a smartphone carrier's data speeds at airports, the mean is
μ=12.00
Mbps. The sample size is
n=25
and the test statistic is
t=2.376.
Answers
The p-value for the hypothesis test in this problem is given as follows:
0.0258.
How to obtain the p-value of the test?The first step in obtaining the p-value of the test is verifying the hypothesis that are test, to classify the test.
At the null hypothesis, it is tested if the mean carrier data speed is of 12 Mbps, that is:
[tex]H_0: \mu = 12[/tex]
At the alternative hypothesis, it is tested if the mean carrier data speed is different of 12 Mbps, that is:
[tex]H_1: \mu \neq 12[/tex]
Then we have a two-tailed test, as we are testing if the mean is different of a value, and the parameters are given as follows:
25 - 1 = 24 degrees of freedom.Test statistic of t = 2.376.Using a t-distribution calculator with these parameters, the p-value for the test is given as follows:
0.0258.
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R(x) = -40x^2 + 5000x
Determine the prices where the revenue is zero?
For each price where the revenue is zero, explain why the revenue is zero.
Answers
Answer:
The prices where the revenue is zero are $x = 0 and $x = 125.
When x = 0, the revenue is 0 since the function is equal to zero (R(0) = -40(0)^2 + 5000(0) = 0).
When x = 125, the revenue is 0 since the coefficient of the x^2 term is negative and the coefficient of the x term is positive. Since the equation is equal to zero, the two terms must cancel each other out, resulting in zero revenue (R(125) = -40(125)^2 + 5000(125) = 0).
Step-by-step explanation:
PLEASE HELP ME SLOVE FOR X
Answers
Answer:
x = 5
Step-by-step explanation:
Since the lines with red arrows are parallel, we can use the ratios
(28 - 12)/28 = 4x/35
35(16) = 28(4x)
560 = 112x
x = 560/112
x = 5