Answer:
C. $2.70
If one pound of apples cost 3 times the amount of a pound of bananas, then a pound of apples costs; $2.70.
The cost per pound of apples will be $2.70, which is the correct answer would be option (C).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the cost per pound of apples be x, and the cost per pound of banana be y
She spent a total of $9.90 on 3 pounds of apples and 2 pounds of bananas.
So, 3x + 2y = 9.90 ....(i)
And the apple cost 3 times as much per pound as bananas.
So, x = 3y
y = x/3 ....(ii)
Substitute the value of y = x/3 in the equation (i), and solve
3x + 2(x/3) = 9.90
3x + 2x/3 = 9.90
11x/3 = 9.90
11x = 2.97
x = 2.97/11
x = 2.70
Thus, the cost per pound of apples will be $2.70.
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Solve the compound inequality.
5 < 2x - 1<9
show your work solving the inequality
Answer:
x> 3 and x <5
OR
3 < x <5
Step-by-step explanation:
To solve the compound inequality, we will follow the steps below:
We will first break it into two inequalities.
That is;
5 < 2x - 1<9
5 < 2x - 1 AND 2x - 1<9
Then we will solve separately
5 < 2x - 1
add 1 to both-side of the equation
5 +1 < 2x - 1 +1
6 < 2x
Divide both-side of the inequality by 2
6 /2 < 2x/2
3 < x
x>3
we will now solve the other inequality
2x - 1<9
add 1 to both-side of the equation
2x - 1+1<9 +1
2x < 10
divide both-side of the inequality by 2
2x /2< 10/2
x < 5
Therefore x> 3 and x <5
or
3 < x <5
Answer:
[tex]x = (5 \: . \: 3)[/tex]
Step-by-step explanation:
To solve a compound inequality, seperate it into two inequalities:
[tex]2x - 1 > 5 \\ 2x - 1 < 9[/tex]
Solve the inequality for x:
[tex]x > 3 \\ 2x - 1 < 9[/tex]
Solve the inequality for x:
[tex]x > 3 \\ x < 5[/tex]
Find the intersection:
[tex]x = (5 \: . \: 3)[/tex]
5n+6+(−7n) answer olz
Answer:
-2n + 6
Step-by-step explanation:
When we simplify the equation, we add like terms. 5n - 7n is 2n and 6 doesn't have anything to add/subtract to, so we have -2n + 6
[tex]\frac{y-95}{4} = 1[/tex]
y = _____
Complete the equation of the line through (-6,-5) (−4,−4) PLZ HELP !!!
Answer: y=1/2x−2
Step-by-step explanation:
A computer randomly generates a 5-digit string using numbers between 0 and 9 inclusive. What is the probability that the first two digits in the string are a 4 and a 2 , in that order?
Answer: 0.01.
Step-by-step explanation:
Given: A computer randomly generates a 5-digit string using numbers between 0 and 9 inclusive.
i.e. each place in 5 digit number has 10 choices.
Total ways to make such a number = [tex]10^5=100000[/tex].
If the first two digits in the string are a 4 and a 2, in that order, then the number of ays to make this kind of number = 1 x 1 x 10 x 10 x 10 = 1000 [as 4 and 2 can be put on first and second place in 1 way ]
Now, the probability that the first two digits in the string are a 4 and a 2 , in that order = [tex]\dfrac{1000}{100000}=\dfrac{1}{100}=0.01[/tex]
Hence, the probability that the first two digits in the string are a 4 and a 2 , in that order = 0.01.
Find the area of the right triangle. If necessary, round to the nearest tenth.
A right triangle with side 15 yards and hypotenuse 25 yards.
a.
20 yd
b.
150 yd
c.
60 yd
d.
300 yd
Answer:
B - 150 yd
Step-by-step explanation:
Obviously the first step is to find the missing measurement. To do this, you use the Pythagorean theorem; a² + b² = c².
In this case, let's label the the missing side A, the height B, and the hypotenuse C.
X² + 15² = 25²
Then you must figure out what 15² and 25².
15² = 225
25² = 625
The next step is to subtract 15² (225) from 25² (625), which will give you the result of X².
625 - 225 = 400.
Now you know X² = 400, you can find the square root of 400 to give you the length of the triangle.
√400 = 20.
The missing length of the triangle is 20 yards.
Now it's just a matter of finding the area by using the formula;
A = [tex]\frac{bh}{2}[/tex]
Or,
(20 × 15) ÷ 2 = 150.
And there's your answer. Don't forget to add the units.
Hope this helped.
A shoe store marks up the wholesale cost of all shoes they sell by 20%. Calvin wants to buy a pair of shoes that has a price tag of $145. What was the wholesale cost of the shoes?
The sell price is the wholesale price plus 20%
Divide the sell price by 1.2 ( 100% + 20%)
145 / 1.2 = 120.83
The wholesale price is $120.83
Answer:
The wholesale price is $120.83
There are only red,blue and green counters in a bag. There are 6 red counters,4 blue counters and 8 green counters. Matt takes a counter from the bag at random a) What is the probability that the counter is red.Give your answer in a fraction. b) What is the probability that the counter is not blue.Give the answer as a fraction. pls help.
Answer:
a) 1/3
b) 7/9
Step-by-step explanation:
The first part asks for the probability that Matt takes the red counter.
There are 6 red counters out of total 6+4+8 = 18 counters.
6/18
Simplify the fraction.
= 1/3
The second part asks for the probability that the counter is not blue.
The counters that are blue are 4. Not blue becomes 18-4 = 14. 14 red or green counters out of total 18.
14/18
= 7/9
Answer:
Total outcome = 6 + 4 + 8 = 18
a) Probablity that the counter is red = 6/18 = 1/3
b) Probablity that the counter is blue = 14/18 = 7/9
Please help ASAP!!!!! I will give extra 20 points please help i really want to go roller blading !!!! The perimeter of a rectangle is dependent on the length of each of its sides. Suppose the base of a rectangle is two more than its height. Complete an input/output table for at least three pairs of inputs and outputs. Make sure to use values that make sense within the context of this situation.
Answer:
See below,
Step-by-step explanation:
Input Output
B H Perimeter (2B + 2H)
3 1 8
5 3 16
14 12 52
I hope this helps.
A jumbo chocolate bar with a rectangular shape measures 13 centimeters in length, 7 centimeters in width, and 2 centimeters in thickness. Due to escalating costs of cocoa, the management has decided to reduce the volume of the bar by 20 %. To accomplish this reduction, management decides that the new bar should have the same 2 centimeter thickness, but the length and width of each should be reduced by an equal number of centimeters. What should be the dimensions of the new candy bar?
Answer:
Reduce every dimension except thickness by 20%.
The requried new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.
To find the dimensions of the new candy bar after reducing the volume by 20%, we need to determine the reduction in length and width.
Let's start by calculating the original volume of the candy bar using the formula: volume = length × width × thickness.
Original volume = 13 cm × 7 cm × 2 cm = 182 cm³
Since the management wants to reduce the volume by 20%, we need to find 20% of the original volume and subtract it from the original volume.
20% of 182 cm³ = 0.2 × 182 cm³ = 36.4 cm³
Reduced volume = 182 cm³ - 36.4 cm³ = 145.6 cm³
Now, we need to determine the new dimensions while maintaining the 2 cm thickness.
Let's assume the reduction in length and width is x cm for both dimensions.
The new volume can be calculated using the formula:
volume = (length - x) × (width - x) × thickness.
Setting this equal to the reduced volume, we have:
(13 - x) × (7 - x) × 2 = 145.6
Simplifying and rearranging the equation, we get:
(91 - 20x + x²) = 72.8
x² - 20x + 18.2 = 0
Using the quadratic formula, we can solve for x:
[tex]x = \dfrac{-(-20)\pm \sqrt{(-20)^2- 4(1)(18.2)}} {2(1)}\\x = \dfrac{20 \pm \sqrt{400 - 72.8}} {2}\\x =\dfrac {20 \pm \sqrt{327.2}} {2}[/tex]
x ≈ (20 ± 18.09) / 2
Taking the positive value, we have:
x ≈ (20 + 18.09) / 2
x ≈ 19.045 / 2
x ≈ 9.5225
Since the dimensions cannot be negative, we discard the negative value.
Therefore, the reduction in length and width is approximately 9.5225 cm.
To find the new dimensions, we subtract this value from the original length and width:
New length = 13 cm - 9.5225 cm ≈ 3.4775 cm
New width = 7 cm - 9.5225 cm ≈ -2.5225 cm (discard as it is negative)
Therefore, the new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.
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A family has two cars. The first car has a fuel efficiency of 30 miles per gallon of gas and the second has a fuel efficiency of 15 miles per gallon of gas. During one particular week, the two cars went a combined total of 1050 miles, for a total gas consumption of 50 gallons. How many gallons were consumed by each of the two cars that week?
Answer:
Car 1 consumes 30 gallons of gas.
Car 2 consumes 20 gallons of gas.
Step-by-step explanation:
what pattern exists in each period of 356,039?
Answer:
1/1
Step-by-step explanation:
because that is it
Answer the question now fast
Answer:
second and third choice
Step-by-step explanation:
supplamentary = add up to be 180
THE IMAGE DOWN BELOW MATH PLEASE HELP ME WITH THIS ALEGEBRA IM CRYING YALL
Answer:
33.33 %
Step-by-step explanation:
Difference:
=> 27 - 18 = 9
%age Increase:
=> [tex]\frac{9}{27} * 100 %[/tex]
=> 33.33 %
Answer:
33.3 %
Step-by-step explanation:
Based on the graph of which statement is true?
A. The inverse of f exists.
B. The inverse of f does not exist.
Answer:
A
Step-by-step explanation:
Image attached: geometry
===================================================
Explanation:
For me, I find it easier to find the exterior angle first. For any convex polygon, the sum of the exterior angles is 360 degrees. When we talk about regular polygons with n sides, each exterior angle is 360/n degrees. In this case, we have a nonagon with 9 sides. So n = 9 is plugged into 360/n to get 360/9 = 40 as the exterior angle measure
exterior angle = 40
We could stop here since we can see the answer must be choice A. But let's keep going. To get the interior angle, we subtract the result we got from 180
interior angle = 180-(exterior angle) = 180-40 = 140
This is because any adjacent pair of interior and exterior angles must form a straight angle of 180 degrees.
--------------------
side note: you could use the formula [tex]i = \frac{180(n-2)}{n}[/tex] to find the measure of the interior angle.
2. Below is a circle with centre C. A, B, D, and E
are points on the circumference. BD is a diameter of
the circle.
Angle CDA is 18° Find the size of angle EDA.
You must show your workings
Answer:
Step-by-step explanation:
45-37
8x17 = 136
Put the following numbers in order from greatest to least 7 030 400, 70 000 200, 78 330, 790 300, 709 400, 70 800
Answer:
70 000 200, 7 030 400, 790 300, 709 400, 78 300, 70 800
Step-by-step explanation:
Greatest is always the number with the most digits.
Answer:
70 000 200, 7 030 400, 790 300, 709 400, 78 330, 70 800
Step-by-step explanation:
To answer this I simply needed to know the orders of numbers from ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, tens of millions, and hundreds of millions. You must also know which digits hold the most value.
[tex]1\\10\\100\\1,000\\10,000\\100,000\\1,000,000\\10,000,000\\100,000,000[/tex]
Consider the quadratic function f(x) =
3x2–5x + 12. Which statements are true about the function and its
graph? Select three options.
Answer:
A, B, D
Step-by-step explanation:
What is the quotient of 6/7 divided by 3/14
Answer:
6/7 ÷ 3/14
= 6/7 × 14/3
= 2/7 × 14 (we cancelled 3 with 6)
= 2×2 (we cancelled 7 with 14)
= 4
hope it helps
Step-by-step explanation:
Answer:
[tex]\frac{6}{7} / \frac{3}{14} = \frac{6}{7} x \frac{14}{3} = (6)(14) / (7)(3) =\frac{84}{21} = 4[/tex]
Step-by-step explanation:
Hope this helps you!! ( BTW this means / Divide ).
heleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeep
Answer:
3.625 is ans
Step-by-step explanation:
4.5+0.25_+1.125=3.625
Step-by-step explanation:
this is your answer sis ...
If F(x) =5x/3 +5
+5, which of the following is the inverse of F(x)?
O A. F'(x) = 5(x+5)
3
O B. F'(x) = 3(x+5)
5
C. F1(x) = 5(x-5)
O D. F'(x) = 3(-5)
Answer:
[tex]f^{-1}(x)=\frac{3(x-5)}{5}[/tex]
Step-by-step explanation:
[tex]f(x)=y=\frac{5x}{3}+5\\y-5=\frac{5x}{3}\\3(y-5)=5x\\x=\frac{3(y-5)}{5}\\ => f^{-1}(x)=\frac{3(x-5)}{5}[/tex]
The inverse of the linear function, f(x), f(x) =5x/3 +5 is f⁻¹(x) = 3 (x -5) / 5. The correct option is f⁻¹(x) = 3 (x -5) / 5
What is the inverse of a function?The inverse of a function is a function that reverses the effect the original function.
Here, we have,
The original function is; f(x) =5x/3 +5
The inverse of f(x) can therefore be found by making x the subject of the equation as follows;
f(x) = 5x/3 +5
f(x) -5 = 5x/3
(f(x) -5) 3 = 5·x
x = (f(x) -5) 3 / 5
x = 3 (f(x) -5) / 5
Plugging in x = f⁻¹(x) and f(x) = x, in the above equation, we get;
f⁻¹(x) = 3 ((x) -5) / 5
f⁻¹(x) = 3 (x -5) / 5
The correct option that is an inverse of f(x) is f⁻¹(x) = 3 (x -5) / 5.
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PLEASE HELP!!!! 5. POINTS EACH.
Answer:
question 3: 1/3 question 4: 5/7 question 5: 2/3
Answer:
1/3
5/7
2/3
Step-by-step explanation:
The numbers greater than 4 on a fair dice are 5 and 6.
2 numbers out of 6 or 2/6
2/6 = 1/3
Total parts = 7 + 12 + 18 + 5 = 42
12 are orange marbles.
42 - 12 = 30
30 marbles are red, yellow, and purple.
30/42 = 15/21 = 5/7
The numbers greater than 2 on a fair dice are 3, 4, 5, and 6.
4 numbers out of 6 total numbers.
4/6 = 2/3
Find the interest on $5,432 at 6% for 2 years.
Answer:
the interest is 5.42
Step-by-step explanation:
Answer:
Interest = 5.42
Step-by-step explanation:
If p(x) = x2 - 1 and 4(x) = 5(x-1), which expression is equivalent to (p - 9)(x)?
5(x - 1) - x2-1
(5x-1) -(x2-1)
(x2 - 1) - 5(x - 1)
(x2-1) - 5x-1
Answer:
x^2 - 10 = (p - 9)(x)
Step-by-step explanation:
Please indicate exponentiation with the symbol " ^ ": p(x) = x^2 - 1.
To obtain (p - 9), start with p(x) = x^2 - 1 and subtract 9:
(p - 9)(x) = x^2 - 1 - 9 = x^2 - 10 = (p - 9)(x)
Ordered pair for this point? (The point is circled in Blue)
Answer:
( -3, 1)
........
Answer:
(-3, 1)
Step-by-step explanation:
The point lies on the line x = -3.
The point lies on the line y = 1.
Where both lines intersect, that is the coordinate.
(x, y)
(-3, 1)
What is the number of possible outcomes for the tree diagram below?
w
w
w
A. 8
B. 6
C. 4
0
D. 2
Answer:
4
Step-by-step explanation:
Please answer I’m not good with math
Answer: A
Step-by-step explanation:
it's easy
Solve for x: –|2x+3|=1
Step-by-step explanation:
-|2x+3|=1
-|2x+3|/-1=1/-1
|2x+3|=-1
2x=-1-3
2x=-4
2x/2=-4/2
x= -2
6. At a bus interchange, a number of passengers boarded a bus. At the first
bus stop, of the passengers alighted the bus and 6 people boarded the
bus. At the 2nd bus stop, of the passengers alighted and 10 passengers
boarded the bus. There were 24 passengers on the bus when it left the
2nd bus stop. How many passengers boarded the bus at the interchange?
Answer:
The answer is given below
Step-by-step explanation:
Let the number of passengers that boarded the bus at the interchange be x.
At the first bus stop, 1/4 of the passengers alighted the bus and 6 people boarded the bus.
Therefore The number of passengers when the bus left the first bus stop = [tex]x-\frac{1}{4}x +6=\frac{3}{4}x+6[/tex]
At the 2nd bus stop, 8/15 of the passengers alighted and 10 passengers boarded the bus.
Therefore The number of passengers when the bus left the second bus stop
[tex]=\frac{3}{4}x+6-\frac{8}{15}( \frac{3}{4}x+6)+10=\frac{3}{4}x+6-\frac{8}{20}x-3.2+10\\\\=\frac{7}{20}x+12.8[/tex]
Given that there were 24 passengers on the bus when it left the 2nd bus stop
[tex]\frac{7}{20}x+12.8=24\\7x+256=480\\7x=480-256\\7x=224\\x=32[/tex]
Therefore 32 passengers boarded the bus at the interchange