A customer pays $3.27 for oranges and $4.76 for pears. How many pounds of fruit does the customer buy?
A total of 7 pounds of fruit does the customer buy.
Given that, a customer pays $3.27 for oranges and $4.76 for pears.
The cost of 1 pound orages=$1.09 and the cost of 1 pound pears=$1.19
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, the number of pounds of oranges =3.27/1.09=3 pounds
The number of pounds of pears =4.76/1.19=4 pounds
Total weight=3+4=7 pounds
Therefore, a total of 7 pounds of fruit does the customer buy.
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The gas tank in the car holds 20 gallons of gasoline. You used up 4 gallons and 1 quart on your trip. How much gasoline is left in the tank?
The correct answer is:
Total capacity of tank in quarts:
20 gallons = 20 × 4 = 80 quarts
Gasoline used in quarts:
4 gallons 1 quart = (4 × 4) + 1 = 17 quarts
Gasoline left in the tank in quarts:
80 − 17 = 63 quarts
Gasoline left in the tank in gallons and quarts:
63 quarts = 63 ÷ 4 = 15 remainder 3 = 15 gallons 3 quarts
a 9 pound bag of sugar is being split into containers that hold 2/3 of a pound. how many containers of sugar will the 9 pound bag create?
Answer:
13 1/2
Step-by-step explanation:
The formula s= sa/6 gives the length of the side, s, of a cube with the surface area, sa. How much longer is the side of the cube with a surface area of 180 square meters than a cube with the surface area of 120 square meters ?
Answer with explanation:
Side of cube = S
Surface Area of Cube = S.A
Relation between Side of a cube and surface area
[tex]S=\frac{S.A}{6}[/tex]
→If surface area of cube =180 Square meters
Side of cube (S)
[tex]S_{1}=\frac{180}{6}\\\\=30[/tex] meters
→ If surface area of cube =120 Square meters
Side of cube (S)
[tex]S_{2}=\frac{120}{6}\\\\=20[/tex] meters
[tex]S_{1}-S_{2}=30 -20=10\\\\S_{1}=S_{2}+10[/tex]
Side of cubic having surface area 180 square meters is greater by 10 meters, than a cube with the surface area of 120 square meters.
Given that P = (-4, 11) and Q = (-5, 8), find the component form and magnitude of vector QP
Answer:
<1, 3>, square root of ten
Step-by-step explanation:
Cody filled a container with 7 3/16 quarts of iced tea. how many 1/4 quart glasses can be served from the container
how to round 254 to the nearest hundred
What percentage of 3000 is 330
Answer:
11
Step-by-step explanation:
Solve the system 2x-2y=10 4x-5y=17
If the circular opening of the pipe has a diameter of 21 inches and the oil was estimated to be flowing at 30 inches/second, how many cubic feet of oil were leaving the pipe each second? Each day?
To find the flow rate of oil, first calculate the cross-sectional area of the pipe using the formula for the area of a circle, A=πr². Then, multiply the area by the given oil speed to find the volume of oil flowing every second. Multiply this by the number of seconds in a day to find the amount of oil leaving the pipe each day, and remember to convert from cubic inches to cubic feet.
Explanation:The question is asking us to find the volume of oil leaving the pipe per second and per day. To calculate the flow rate of oil, we first find the cross-sectional area of the pipe by using the formula for the area of a circle A=πr², where r is the radius of the pipe (half the diameter). Since the diameter given is 21 inches, the radius is 10.5 inches.
Next, use the given flow rate of 30 inches/second to calculate the volume of oil flowing every second. This is done by multiplying the area by the oil speed V = A * oil speed.
To find the amount of oil leaving the pipe each day, we multiply the volume per second by the number of seconds in a day .
Note: To convert cubic inches to cubic feet (since the question asks for cubic feet), remember there are 1728 cubic inches in 1 cubic foot.
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How many kilometers could the red car travel in 12 hours?
Find the area of the following circle. Use = 3.14
r = 5 yd.
Find all points on the circle x 2 + y 2 = 100 where the slope is 3 4
The points on the circle x² + y² = 100 where the slope of the tangent is ¾ are (6, -8) and (-6, 8). This is found by taking the derivative of the circle equation, setting it equal to the slope, solving for y, substituting this into the original circle equation, and solving for x.
Explanation:The equation of the circle is x² + y² = 100. To find the points on this circle where the slope of the tangent is ¾, we need to find the derivative of this equation. The derivative of y with respect to x is dy/dx = -x/y. Set this equal to ¾ and solve for y, which gives y = -4x/3. Substitute this into the original circle equation to solve for x, which yields x = ± 6. Then substitute these x-values back into the equation y = -4x/3 to get y = ± 8. Therefore, the points on the circle where the slope of the tangent is ¾ are (6, -8) and (-6, 8).
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Final answer:
To find points on the circle x² + y² = 100 where the slope is 3/4, differentiate the circle's equation and set the derivative equal to 3/4. Solve the system of equations involving the circle's equation and the line's equation derived from the slope criteria. This process typically yields two points of intersection due to the geometrical properties of circles and lines.
Explanation:
To find all points on the circle x2 + y2 = 100 where the slope is 3/4, we first acknowledge that the given circle is centered at the origin (0,0) with a radius of 10 units. Since the slope of a tangent to the circle at any point can be found using implicit differentiation, let's differentiate the given equation with respect to x. Doing so, we get 2x + 2yy' = 0 where y' denotes the slope of the tangent to the circle at (x,y). Solving for y', we get y' = -x/y. Setting this equal to the given slope of 3/4, we have -x/y = 3/4.
By cross-multiplying and rearranging, we get 4x + 3y = 0. To find the points of intersection between the line and the circle, we substitute x2 + y2 = 100 into this equation. Solving the system of equations will yield the points on the circle where the slope of the tangent is 3/4.
Note: The exact points of intersection would require solving a resulting quadratic equation, which can give two possible points since a line with a given slope (except vertical) will typically intersect a circle at two points.
If m and n are two positive real numbers whose product is 10, what is the minimum value of m + 2n
The minimum value of (m + 2n) is 8.95 and this can be determined by using the arithmetic operations.
Given :
If m and n are two positive real numbers whose product is 10.
Given that m and n are two positive real numbers whose product is 10 that is:
mn = 10
[tex]\rm m= \dfrac{10}{n}[/tex] ---- (1)
The minimum value of (m + 2n) can be determined by using the following calculation.
Put the value of m in the given expression.
[tex]\rm = \dfrac{10}{n}+2n[/tex] ---- (2)
Now for minimum value differentiate the above expression with respect to n.
[tex]\rm =-\dfrac{10}{n^2}+2[/tex]
Now equate the above equation to zero.
[tex]\rm \dfrac{10}{n^2}=2[/tex]
[tex]\rm n = \sqrt{5}[/tex]
Now, put the value of n in equation (2).
[tex]\rm Minimum \;Value = \dfrac{10}{\sqrt{5} }+2\sqrt{5}[/tex]
= 8.95
The minimum value of (m + 2n) is 8.95.
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How much pure acid should be mixed with 6 gallons of a 20% acid solution in order to get a 90% acid solution?
To get a 90% acid solution, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution.
Explanation:To solve this problem, we can use the formula for concentration:
Concentration = (Volume of pure acid) / (Total volume of solution)
Let x represent the volume of pure acid to be added. We know that the total volume of the solution after adding the pure acid is 6 gallons + x gallons. We also know that the concentration of the 20% acid solution is 0.2.
Using the formula, we can set up the equation:
0.9 = x / (6 + x)
Multiplying both sides of the equation by (6 + x), we get:
0.9(6 + x) = x
Simplifying the equation, we have:
5.4 + 0.9x = x
Subtracting 0.9x from both sides of the equation, we get:
5.4 = 0.1x
Dividing both sides of the equation by 0.1, we get:
54 = x
Therefore, you should mix 54 gallons of pure acid with the 6 gallons of the 20% acid solution to get a 90% acid solution.
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if a ball is thrown directly upward with a velocity of 40 ft/s, its height (in feet) after t seconds is represented by 40t-16t^2. what is the maximum height attained by the ball?
The maximum height attained by the ball is 25 feet.
Explanation:The maximum height attained by the ball can be found by determining the vertex of the quadratic equation representing the height of the ball. In the given equation 40t - 16t^2, the coefficient of t^2 is negative, indicating a parabolic shape with a maximum point. The formula for the x-coordinate of the vertex is -b/2a, which in this case is -40/(2*(-16)) = 1.25 seconds. Substituting this value into the equation gives the maximum height: 40(1.25) - 16(1.25^2) = 25 feet.
Carlos has 5/8 pound of pumpkin seeds. He puts the seeds evenly into 20 envelopes. How much pumpkin seed is in each envelope?
Min Jee wants to build a small patio using either brick or paver stones. It will be 70 inches long and 49 inches wide. Each brick covers an area of 3 1/2 inches by 7 1/2 inches, and cost $0.59. Each paver covers an areas 8.4 inches by 8.4 inches and costs $1.88. What would be less expensive to use, and by how much?
Describe or show two ways to find the following product: 1/4 x 2/3.
Solve for x.y = mx+b
Barb’s class has 18 bikes .tim’s class has some rows of bikes with 5 bikes in each row. Tim’s class has more bikes than barb’s class. How many rows of bikes could tim’s class have?
spiders can walk on walls write the statement in if then form
Given the values of the derivative f′(x) in the table and that f(0)=150, find or estimate f(x) for x=0,2,4,6.
To find or estimate f(x) for x=0,2,4,6, integrate the given derivative f'(x) with respect to x to find the constant term. Then, add each value of f'(x) in the table to the constant term to obtain the values of f(x) for x=0,2,4,6.
Explanation:To find or estimate f(x) for x=0,2,4,6, we need to use the values of the derivative f'(x) given in the table. Since f'(x) represents the rate of change of f(x) at different values of x, we can use the derivative to find or estimate the values of f(x). Given that f(0) = 150, we can start by finding the constant term of the function using this initial condition.
To find the constant term, we need to integrate the derivative f'(x) with respect to x. This will give us the original function f(x).Integrating f'(x) gives us f(x) = 150 + C, where C is the constant term we need to find.Next, we can use the given values of f'(x) in the table to find or estimate the corresponding values of f(x) for x=0,2,4,6.Let's assume that the third column in the table represents the values of f'(x) at different values of x. We can add each value to the constant term C to obtain the values of f(x) for x=0,2,4,6.Therefore, by integrating f'(x) and adding the constant term, we can find or estimate the values of f(x) for x=0,2,4,6.
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write all names that apply to each number 121/121
help!! me asap!! please!!
Find the vertex of the parabola whose equation is y = x2 - 4x + 6.
The perimeter of a square is 26.46 inches. What is the side length of the square?
The side length of a square whose perimeter is 26.46 inches can be calculated by dividing the given perimeter by 4 (the number of sides in a square), resulting in a side length of approximately 6.615 inches.
Explanation:The subject of this question is Mathematics, with the specific topic being measurement and geometry. This question is applicable to Middle School grade levels. The student seeks to determine the side length of a square, knowing the perimeter is 26.46 inches.
To find the side length, we need to recall the formula for the perimeter of a square: P = 4s, where P represents the perimeter and s represents the length of a side. The student's square has a perimeter of 26.46 inches, so the equation would be 26.46 = 4s.
To isolate the value of s, we divide both sides of the equation by 4. This gives us: s = 26.46/4. Upon doing the division, we find that each side of the square is approximately 6.615 inches.
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How to find the factor for the expression
4x-6y
There are 24 student's in a science class. Mr. Sato will give each pair of student's 3 magnets. So far, Mr. Sato has given 9 pairs of students their 3 magnets. How many more magnets does Mr. Sato need zo.that each pair of student's habe exactly 3 magnets?
10 x 6 tens-unit form and standard form
Answer:
Standard form: 600
Unit form: 6 hundreds.
Step-by-step explanation:
We have been given a number [tex]10\times 6[/tex]-tens. We are asked to write our given number in unit form and standard form.
To write our given number in standard form, we will expand our given number as shown below:
6-tens [tex]6\times 10=60[/tex]
[tex]10\times 6[/tex]-tens would be [tex]10\times 60=600[/tex]
Therefore, our given number in standard form would be 600.
We know that unit form is writing a number using place value units.
We can see that our given number has 0 ones, 0 tens and 6 hundreds.
Therefore, our given number in unit form would be 6 hundreds.
We have that the Tens unit form of 10 x 6 and Standard form is mathematically
[tex]6*10^1[/tex]
6tens
From the question we are told that
10 x 6
10 x 6=60
Standard form is a number, between 1 and 10 multiplied by a power of 10
Generally the equation for the Standard form is mathematically given as
x*10^y
Therefore
the Standard form of 10 x 6 is mathematically given as
[tex]6*10^1[/tex]
And
Generally the equation for the Tens unit form of 10 x 6 is mathematically given as
x*tens(10)
Tens-unit form is mathematically given as
6tens
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