Answer:
Part A: 32 square yards per gallon
Part B: 13 square feet per gallon difference
Step-by-step explanation:
Part A:
To find how many square yards each gallon covers, you have to divide 42 2/3 by 1 1/3, which equals 32. That means each gallon of paint covers 32 square yards.
Part B:
First, you have to convert how much Angela covered in square yards to square feet. Since one square yard is equal to 9 square feet, we have to multiply 32 by 9, which equals 288. To find the difference, you have to subtract 288 - 275, which equals 13.
Final answer:
Angela's rate of paint coverage in square yards per gallon is 32, and the difference in square feet per gallon between Angela’s rate and the average rate on the paint label is 13 square feet per gallon.
Explanation:
Part A: Calculating Paint Coverage
To find Angela’s rate of paint coverage in square yards per gallon, we would divide the total area painted by the amount of paint used. We have 42 2/3 square yards painted using 1 1/3 gallons of paint. First, it's easier to work with improper fractions, so we convert 42 2/3 to (126/3 + 2/3) = 128/3 square yards, and 1 1/3 to (3/3 + 1/3) = 4/3 gallons. Now, we calculate the rate by dividing the square yards by the gallons:
Rate = (128/3) / (4/3) = (128/3) × (3/4) = 128/4 = 32 square yards per gallon.
Part B: Difference in Square Feet per Gallon
To find the difference in square feet per gallon, we need to compare Angela's rate to the average rate given on the label. Angela's rate is 32 square yards per gallon, and there are 9 square feet in a square yard. So, Angela's rate in square feet would be 32 × 9 = 288 square feet per gallon. The label states an average coverage rate of 275 square feet per gallon. Thus, the difference is:
Difference = Angela’s rate - Label’s rate = 288 - 275 = 13 square feet per gallon difference.
A bag contains 18 small red, 19 small black, 13 large black, and 15 large red T-shirts, and nothing else. What is the least number of T-shirts Alpa must take out of the bag (without looking at them) to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color?
Alpa must take out five T-shirts in order to be absolutely sure of having at least two T-shirts that differ only by size or by color.
Explanation:The subject of this question is a probability problem, which falls under the domain of Mathematics, more specifically combinatorics. In scenarios such as this, we want to ensure we have at least two T-shirts that only differ by size or color. To guarantee this, Alpa must select one T-shirt of each color and size first. That means she must take out four T-shirts: a red small, a red large, a black small, and a black large. For the fifth T-shirt that she takes out, it will either be the same color as one she already has but different in size or it will be the same size as one she already has but a different color. So, the least number of T-shirts Alpa must take out of the bag in order to be absolutely sure of having at least two T-shirts among them that differ only by size or color is five.
Learn more about Probability here:
https://brainly.com/question/22962752
#SPJ3
Triangles A and B are right angled.
a) show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B.
b) explain why the two triangles are congruent.
Answer:
13²-12²
169-144
=25
√25
=5
The 2 shortest sides are 5cm and 12cm
Let the sides of the triangles be a, b and c. According to Pythagoras theorem;
[tex]c^2=a^2+b^2[/tex] where:
a is the hypotenuse (longest side)
For triangle A:
c = 13
b = 12
Get "a"
[tex]13^2=12^2+b^2\\169=144+b^2\\b^2=169-144\\b^2=25\\b=5cm[/tex]
Similarly for triangle B:
[tex]c^2=5^2+12^2\\c^2=25+144\\c^2=169\\c^2=\sqrt{169} \\b=13cm[/tex]
We can see that the two shorter sides have the same length which is 5cm
Since all the sides of the triangle are the same, hence the two triangles are congruent.
Learn more here: https://brainly.com/question/20545047
Help ASAP
Zero product property
1. 100-x²=0
2. 3x²-75=0
3. 0=2x²+20x+50
4. 2x²-5x-12=0
Answer:
1. x=10,-10
2. x = 5
x = -5
3. x=-5
4. x ∈ {4,- 3/2}
Step-by-step explanation:
A bag contains 666 red jelly beans, 444 green jelly beans, and 444 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red?
Answer:
12/91
Step-by-step explanation:
The question is not properly formatted, here is how it should be formatted.
A bag contains 6red jelly beans, 4 green jelly beans, and 4 blue jelly beans. If we choose a jelly bean, then another jelly bean without putting the first one back in the bag, what is the probability that the first jelly bean will be green and the second will be red
Step one
This is selection without replacement.
Sample space
6red jelly beans,
4 green jelly beans, and
4 blue jelly beans.
S= 6+4+4= 14
Probability that the first jelly bean will be green = 4/14= 2/7
Without replacement, Probability that the second jelly bean will be red = 6/13
Hence for the two selections the probability is= 2/7*6/13= 12/91
What kind of salad do snowmen eat? Punchline 73 answer key
Answer:
Coldslaw
Step-by-step explanation:
Two parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles. If angle 1 measures 120 degrees , how does angle 7 compare with angle 1?
A.Angle 7 is supplementary with angle 1
B.Angle 7 and angle 1 are congruent.
C.The angles cannot be compared.
Answer: B.Angle 7 and angle 1 are congruent.
Step-by-step explanation:
Alternate angles means that the angles are formed on the alternating sides of the transversal. The term "exterior" means that the alternate angles are formed outside the parallel lines.
Since the parallel lines are cut by a transversal and angles 1 and 7 are alternate exterior angles, it means that angles 1 and 7 are equal or congruent. This is because of the rule in geometry stating that two alternate exterior angles are congruent. Therefore, the correct option would be
B. Angle 7 and angle 1 are congruent.
Answer: The correct option is B; Angle 7 and angle 1 are congruent
Step-by-step explanation: Please refer to the picture attached for more details. The parallel lines AB and CD have been drawn and a transversal line have also been drawn to cut both lines as shown in the picture.
Since both lines are parallel, the angles formed by the transversal would be equal.
A careful observation would show that the interior angle formed by the transversal (which is the supplement of angle 120), is equal or congruent to the interior angle formed at angle 7. These are commonly referred to as "z angles" by virtue of the shape formed. Angle 1 and angle 7 are the exterior alternate angles formed by the transversal and they are both congruent, that is, they both have the same measurement.
The angles cannot be described as supplementary, because supplementary angles add up to 180 degrees. That is, if angle A plus angle B equals 180, then angles A and B are both supplementary. This does not apply to angle 1 and angle 7.
Please help need it I can really use it!
Answer:
B
Step-by-step explanation:
The highest MOC is 4 in group A but in group B the MOC is 3. So group A has one more dot than group B.
Ana played 4 rounds of golf and then played her lowest round of golf with a score of 80 The scores of the first 4 round and the lowest round start
Answer:
Step-by-step explanation:
6
Answer:
c
Step-by-step explanation:
The data set is a list of the heights of 6th grade basketball players: 60, 62, 66, 70, 66, 68, 67, 64, 64, 63. Find the mean of the set.
Answer:
65
Step-by-step explanation:
The mean is 65 because
Step one- Add up 60, 62, 66, 70, 66, 68, 67, 64, 64, 63 together to get 650.Step two- Next you need to divide. since there are 10 numbers that we added up we have to take 650 and divide it by 10. so 650/10=65Finally your answer is 65Hope this helped :)A baker purchases flour each week from a wholesale warehouse. The chart shows the quantities and prices available this week. If the best deal last week for flour was $1.60 per pound. What is the difference between the unit price for last week's best deal and this week's best deal?
The chart showing the quantities and prices is;
Best Deal 1
Quantity of Flour Price
3 pounds $5.25
5 pounds $9.75
7 pounds $12.60
10 pounds $14.20
12 pounds $18.24
Answer:
difference between last weeks best deal = $0.3
Step-by-step explanation:
Let's calculate the unit price for each of the quantities in the chart.
For quantity of 3 pounds;
We have; unit price = 5.25/3 = $1.75
For 5 pounds;. Unit price = 9.75/5 = $1.95
For 7 pounds; unit price = 12.6/7 = $1.8
For 10 pounds; unit price = 14.2/10 = $1.42
For 12 pounds; unit price = 18.24/14 = $1.3
Thus, last weeks best deal is the lowest = $1.3
Thus; difference between last weeks best deal is given as;
= this weeks best deal - last weeks best deal
This gives;
$1.6 - $1.3 = $0.3
Answer:
0.18
Step-by-step explanation:
The Haskins family spends $600 per month on groceries for their family. If this is 15% of their monthly budget, , then what is their monthly budget?
Hi
15/100 = 600 / X
X = 600 *100 /15 = 4000
monthly budget =4000
Answer:
Their monthly budget is $600
Find the area of a regular octagon (8 sides) that has an apothem of 12.1 meters and a side length of 10 meters.
Encuentra el área de un octágono regular (8 lados) que tiene una apotema de 12.1 metros y una longitud lateral
de 10 metros.
0
m2
1
2
3
0 1
0
4.
5
6
+
7
8
-
a lo
0
.
if the interest earned is $750 and the interest rate is 12.5% and the time is 4 years what is the principal
Answer:
There would be : 750 x (1 + 12.5/100)^4 = 1201.35 dollar after 4 years, with the earning is 750$ and interest rate is 12.5%.
Answer:
$1,500
Step-by-step explanation:
Interest = P × 12.5/100 × 4
750 = P × 0.5
P = 1500
Eric put several CD's in a case. Four CDs are country, six are rap and ten are pop. If Eric picks one CD from the case without looking, what is the probability that he will pick a country CD?
Probability that Eric will pick a country CD is 0.2.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Number of CD's which are country = 4
Number of CD's which are rap = 6
Number of CD's which are pop = 10
Total number of CD's = 4 + 6 + 10 = 20
Probability = Number of likely outcomes / Total number of outcomes3
Probability of getting country CD = 4 / 20
= 1/5
= 0.2
Hence the required probability is 0.2.
To learn more about Probability, click on the link :
https://brainly.com/question/11234923
#SPJ1
Randy has 4 pennies , 3 nickels , and 3 dimes in his pocket if he randomly chooses 2 coins without replacement what is the probility they are both dimes.
[tex]3 \div 10 \times 2 \div 9 = 1 \div 15[/tex]
the probability of drawing one dime is 3/10. if you don't replace the coin, there are only 9 left, 2 of which are dimes. so multiple the to probabilities and there you have it
Answer:
0.09
Step-by-step explanation:
Which graph represents this equation?
Y=3/2x^2-6x
The parabola is passing through (0, 0) and (9, 0). Then the correct option is C.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of the parabola is given below.
y = (3/2)x² - 6x
Then the factor of the equation will be
y = 3x (x / 2 - 3)
Then the zeroes of the function will be
y = 0
x = 0, 9
Then the correct option is C.
The graph is given below.
More about the parabola link is given below.
https://brainly.com/question/8495504
#SPJ2
mia wants to earn 2500 in her job at a bycicle store she is paid 55 for every bycicle she tunes up the minimum number of bycicles mia needs to tune up to reach her goal of 2500
Mia needs to tune up at least 46 bicycles at $55 each to reach her goal of $2500, as she cannot tune up a fraction of a bicycle.
To calculate the minimum number of bicycles Mia needs to tune up to reach her goal of $2500, we must divide her goal amount by the amount she earns per bicycle. Thus, the calculation is as follows:
Number of bicycles = Total goal amount / Earnings per bicycle
Number of bicycles = $2500 / $55
When we divide 2500 by 55, we get approximately 45.4545. Since Mia cannot tune up a fraction of a bicycle, she will need to tune up a whole number of bicycles. Therefore, she needs to tune up at least 46 bicycles to reach or exceed her goal of $2500.
5: Un músico golpea un tambor una vez cada 24 segundos exactamente, mientras que otro lo hace cada 14 segundos. Suponiendo que acaban de golpear ambos a la vez, ¿cuándo volverán a coincidir?
Answer:
168 seconds
Step-by-step explanation:
To find out when they coincide again, the least common multiple between both numbers must be calculated:
24 14 | 2
12 7 | 2
6 7 | 2
3 7 | 3
1 7 | 7
1 1
Therefore the least common multiple is:
2 * 2 * 2 * 3 * 7 = 168
This means that they will coincide again at 168 seconds, when the first musician has struck 7 times (168/24) and the other 12 times (168/14)
Please help me now plz
I will mark you brainliest
Answer:
theta = 24.4 degrees
Step-by-step explanation:
This is a right triangle.
sin theta = opp/ hyp
sin theta = 33/80
Take the inverse of each side
sin^-1 sin(theta) = sin^-1 (33/80)
theta =24.36197794
To the nearest tenth
theta = 24.4 degrees
5. (8 pts) Compute the derivative of h(x) = x^3+x^2/e^3x
and simplify your answer.
Answer:
h'(x) = (-3x^3 +2x)/e^(3x)
Step-by-step explanation:
The formula for the derivative of a quotient is ...
(u/v)' = (vu' -uv')/v²
Using u = (x^3 +x^2) and v = e^(3x), this becomes ...
h'(x) = (e^(3x)(3x^2 +2x) -(x^3 +x^2)(3)(e^(3x))/e^(6x)
h'(x) = (-3x^3 +2x)/e^(3x)
32 slices from 4 cakes = slices from 5 cakes
If 4 cakes make 32 slices, one cake will make [tex]\frac{32}{4}[/tex] = 8 slices. Therefore, 5 cakes will make (8 x 5) = 40 slices.
Answer:
You can get 40 slices from 5 cakes because each cake has 8 slices in it.
Step-by-step explanation:
what is the area of a semicircle with a diameter of 21.5
Area of a circle = PI x R^2
r = 1/2 diameter
r = 21.5/2
r = 10.75
Area of circle = 3.14 x 10.75^2 = 3.14 x 115.5625 = 362.86625 square units.
A semicircle is half a circle:
Area of semicircle = 362.86625 / 2 = 181.433125 square units (round the answer as needed).
The radius of a circle is 15 inches.
Enter the area of the circle, in square inches. Round your answer to the nearest tenth and use 3.14 for pi.
______ square inches
Answer:
706.5
it's saying i need to fill in twenty characters to answer
so here is my twenty characters
Answer:
[tex]706.5 {in}^{2} [/tex]
Step-by-step explanation:
[tex]area \\ = \pi {r}^{2} \\ = 3.14 \times 15 \times 15 \\ = 706.5 {in}^{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Please I need help ASAP!!
Answer:
I think 3%
Step-by-step explanation:
Hope this helps:)
Answer:
33.3%
Step-by-step explanation:
I had answered another question first. This is the answer for this problem. Sorry!
hope this helps :)
Find the volume of the cylinder.
Either enter an exact answer in terms of or use 3.14 for pi. with a radius of 4 and a height of 10
HELP PLEASE!!!!
© 8 t-shirts and a hat costs £42.00
3 t-shirts and a hat costs £17.00.
How much does a t-shirt cost?
How much does a hat cost?
<
t-shirt: £
hat: £
Answer:
t-shirt: £5.00, hat: £2.00
Step-by-step explanation:
You can rewrite them into equations:
8t+h=42.
3t+h=17.
Then subtract the h from both equations using the elimination process.
8t-3t is 5t, and 42-17 is 25. The new equation is 5t=25, thus t=5. If we substitute the 5 into one of the other equations, we get h=2.
Answer:
T-shirt: £5
Hat: £2
Step-by-step explanation:
Use simultaneous equations elimination method for best results.
8t + h= 42
3t + h= 17
Subtract the two equations. h gets cancelled. 8t-3t= 5t. 42-17= 25.
5t= 25
t= 25÷5
t= £5
Substitute the value of t to give h.
8(5) + h=42
40+ h=42
h= 42-40
h= £2
a ladder 13m long is placed on the ground in such a way that it touches the top of a vertical wall 12m high. find the distance of the foot of the ladder from the bottom of the wall
Answer:
by applying Pythagoras theorem;
the ladder(13m) acts as hypotenuse
the wall (12m) acts as height
the distance between the the two is the base
therefore
a² + b² = c²
b²= c²- a²
b²= 169 - 144
b² = 25
√b² = √25
b= 5m
the distance is 5m
Karen is on a game show. She will choose a box to see if she wins a prize. The odds in favor of Karen winning a prize are 5/7. Find the probability of Karen winning a prize
Answer:
0.71
Step-by-step explanation:
P(Karen wins a prize) = 5/7 = 0.71
When April made tortillas for the first time, she used all the dough to make 10 tortillas. After making quesadillas, she decided that the tortillas were not large enough. The next time, using the same amount of dough, she made each tortillas the same thickness for 25% larger. How many tortillas did April make the second time? If the area of each tortilla in the second batch is 201 in2, what was the area of each tortilla in the first batch?
Answer:
Second time: 8 tortillas
Area of tortillas in the first batch: 160.8 in2
Step-by-step explanation:
Let's say that the amount of dough to make a tortilla is x.
So, in the first time, the amount of dough used is 10 * x = 10x
Then, she made the tortillas 25% larger, so the amount of dough used for each tortilla now is 1.25x
So, using the same amount of dough (10x), the amount of tortillas she can make is:
10x / 1.25x = 8 tortillas
If the area of the larger tortilla is 201 in2, and this tortilla is 25% larger than the ones in the first batch, to find the area of the inicial tortillas we just need to divide this new area by 1.25:
Area of first tortillas = 201 / 1.25 = 160.8 in2
The sum of the first
6
66 terms of a geometric series is
15
,
624
15,62415, comma, 624 and the common ratio is
5
55.
What is the first term of the series?
Answer:
The first term of the series is 4
Step-by-step explanation:
The sum of the first 6 terms of a geometric series is 15 , 624 and the common ratio is 5 .
To find the first term, we use the formula for the sum of terms in a geometric series.
Since the common ratio of the series is greater than 1, the sum of [tex]n^{th}[/tex] term of the geometric series is;
[tex]S = \frac{a(r^n - 1)}{r - 1}[/tex]
where r = common ratio
a = first term
When S = 15,624, r = 5 and n = 6, the first term, a, will be:
[tex]15624 = \frac{a(5^6 - 1)}{5 - 1} \\\\15624 = \frac{a(15625 - 1)}{4}\\\\15624 = \frac{a(15624)}{4}\\\\a = \frac{4 * 15624}{15624}[/tex]
a = 4
The first term of the series is 4.