Final answer:
To obtain a 70% acid solution, mix 4 gallons of pure acid with the existing 6 gallons of 50% acid solution.
Explanation:
To find out how much pure acid should be mixed with 6 gallons of a 50% acid solution to obtain a 70% acid solution, we use the concept of mixtures in percentage problems. Let x be the number of gallons of pure acid to be added.
Firstly, the amount of pure acid in the initial solution is 50% of 6 gallons, which is 3 gallons. When we add x gallons of pure acid, the total volume of the mixture becomes x + 6 gallons, and the total amount of pure acid is x + 3 gallons.
To have a 70% acid solution:
The total amount of pure acid divided by the total volume should equal 70%.
Therefore, the equation is:
(x + 3) / (x + 6) = 0.70
By solving for x:
x + 3 = 0.70(x + 6)
x + 3 = 0.70x + 4.20
x - 0.70x = 4.20 - 3
0.30x = 1.20
x = 1.20 / 0.30
x = 4 gallons
You need to mix 4 gallons of pure acid with the 6 gallons of 50% acid solution to end up with a 70% acid solution.
What is tan (x)?
20/21
20/29
29/21
29/20
How do you find the base of this triangle? (Picture should be able to be seen)
shadesha invests $24,000 at age 27. at the age 31 jerome invests $2000 annually until retirement both invest at 7% compounded annually to plan to retire at 65 who has more money for retirement
The data set represents a month-to-month progression of gasoline prices over the course of several months in an unspecified city. Use a graphing calculator to determine the quadratic regression equation for this data set.
Answer:
The correct option is a.
Step-by-step explanation:
The general form of a quadratic regression equation is
[tex]y=ax^2+bx+c[/tex] ..... (1)
Using graphing calculator we get
[tex]a=-0.143393\approx -0.143[/tex]
[tex]b=0.59525\approx 0.595[/tex]
[tex]c=2.82964\approx 2.830[/tex]
Substitute these values in equation (1) to find the quadratic regression equation for this data set.
[tex]y=-0.143x^2+0.595x+2.830[/tex]
Therefore the correct option is a.
Find the volume of a cylinder that has the following dimensions. Do not round your answer. (Use 3.14 for π.)
CONVERT M INTO CM
The volume of cylinder is 1962.5 [tex]cm^{2}[/tex].
To find the volume of a cylinder.
What is mensuration?The part of geometry concerned with ascertaining lengths, areas, and volumes. Mensuration deals with the size, region, and density of different forms both 2D and 3D.
Given that:
Radius= 5 cm
Height= 0.25 m=25 cm
π=3.14
By the formula of volume of cylinder
Volume=π[tex]r^{2} h[/tex]
TO put the value,
Volume=3.14*5*5*25
Volume=1962.5 [tex]cm^{2}[/tex]
So, the volume of cylinder is 1962.5 [tex]cm^{2}[/tex].
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A bag contains 10 res marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Five marbles are drawn from the bag. what is the approximate probability that exactly two of the five are blue
The equation of a circle is (x+9)2+(y+6)2=225 .
What is the center of the circle?
Enter your answer in the boxes.
(
,
)
Answer:
[tex](-9,-6)[/tex]
Step-by-step explanation:
We have been given an equation of a circle [tex](x+9)^2+(y+6)^2=225[/tex]. We are asked to find the coordinates of the center of the given circle.
We know that center-radius form of a circle is in format: [tex](x-h)^2+(y-k)^2=r^2[/tex], where,
[tex](h,k)=\text{Center of circle}[/tex],
[tex]r=\text{Radius of circle}[/tex]
Upon comparing our given equation with center-radius form of a circle we will get,
[tex](x-(-9))^2+(y-(-6))^2=15^2[/tex]
Therefore, the center of our given circle is at point [tex](-9,-6)[/tex].
A wheelchair ramp has a slope of 1 10 . if its rise is 1 5 2 feet, what is its run?
Which equation shows 2x – y = 6 converted to slope-intercept form? y = x – 3 y = 2x – 6 y = –2x + 6
When you have two shapes to compare on a coordinate plane, you can determine the scale factor, knowing that the transformation was a dilation. Generate instructions you would give another student to determine the scale factor.
Sample Response: Locate two corresponding ordered pairs of the two shapes. Calculate how much the pre-image values were multiplied by to obtain the image values. This is your scale factor. You can calculate this by dividing the coordinates of the mage by the corresponding coordinates of the pre-image.
WILL GIVE BRAINLIEST
solve for x
A. 70/6
B. 60/16
C. 6
D. 11
One ounce is equal to 28.35 grams. convert 16 ounces to grams round your answe to the nearest tenth
The amount 16 ounce into grams using the conversion factor 1 ounce = 28.35 grams is 454.2 grams.
To convert ounces to grams, you can use the conversion factor:
1 ounce = 28.35 grams
Now, to convert 16 ounces to grams:
= 16 ounces * 28.35 grams/ounce
= 454.16 grams
Rounding to the nearest tenth:
454.16 grams rounded to the nearest tenth is 454.2 grams.
Therefore, the required quantity is 454.2 grams.
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To convert 16 ounces to grams, we multiply 16 by the conversion factor of 1 ounce to grams (28.35). This gives us 453.6 grams, when rounded to the nearest tenth.
Explanation:To convert ounces to grams, we use the conversion factor 1 oz = 28.35 g. Given that we are converting 16 ounces to grams, we multiply the number of ounces by the conversion factor.
So, 16 oz * 28.35 g/oz = 453.6 g. Rounding to the nearest tenth, the result is 453.6 g.
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Solve 7 + x - 15 = -2
5 1/3
6 1/3
10 2/3
20 2/3
Since the mod decided to delete my question because of a mistake. Please answer. Need it ASAP
Wright a real world problem that involves classifying a quadrilateral. Then solve the problem.
) the supplement of an angle is thirty more than twice the angle. find the measure of the angle and its supplement. answer
The longest side of an obtuse triangle measure 20 cm. the two shorter sides measure x cm.and 3x sm round to the nearest tenth,what is the greatedt possible value of x
22cm is the greatest
It should be greater than17(20-3)
and smaller than 23(20+3)
Find the volume of the pyramid with height 15 and rectangular base with dimensions 3 and 7.
Deon worked 16 hours last week at the grocery store and earned $124.00. If he continues to earn the same hourly pay, how many additional hours must he work to earn another $186.00? A. 20 hours B. 24 hours C. 32 hours D. 62 hours
The side of a square measures 2x^2y^3 what is the area of the square if x=-2 and y=2
The area of the square is -128.
What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)squared + 4?
Answer:
x = 3/2
Step-by-step explanation:
That is quite long and drawn out, so we have to get it down to a single quadratic equation, set equal to 0.
Begin by expanding the right side to get
[tex]y+3x-6=-3(x^2-4x+4)+4[/tex]
then multiplying in the -3 to get
[tex]y+3x-6=-3x^2+12x-12+4[/tex]
Now we will combine all the like terms and get everything on one side of the equals sign, and set it equal to 0:
[tex]-3x^2+9x-2=0[/tex]
In order to find the equation of the axis of symmetry we have to put it into vertex form, which is accomplished by completing the square on this quadratic.
In order to complete the square, the leading coefficient has to be a +1. Ours is a -3, so we will factor that out. First, though, now that it is set to equal 0, we will move the constant, -2, over to the other side, isolating the x terms.
[tex]-3x^2+9x=2[/tex]
Now we can factor out the -3:
[tex]-3(x^2-3x)=2[/tex]
The rules for completing the square are as follows:
Take half the linear term, square it, and add it to both sides. Our linear term is 3. Half of 3 is 3/2, and squaring that gives you 9/4. We add into the parenthesis on the left a 9/4, but don't forget about that -3 hanging around out front that refuses to be ignored. We didn't add in just a 9/4, we added in (-3)(9/4) = -27/4:
[tex]-3(x^2-3x+\frac{9}{4})=2-\frac{27}{4}[/tex]
In the process of completing the square we created a perfect square binomial on the left. Stating that binomial and simplifying the addition on the right gives us:
[tex]-3(x-\frac{3}{2})^2=-\frac{19}{4}[/tex]
We can determine the axis of symmetry at this point. Because this is a positive x-squared polynomial, the axis of symmetry is in the form of (x = ) and what it equals is the h coordinate of the vertex. Our h coordinate is 3/2; therefore, the axis of symmetry has the equation x = 3/2
Computer amount of interest earned and the following simple interest from a deposit of 5500 at 6% for three years equals?
Factor this expression.
4x – 20
A. 4(x – 16)
B. 4(x – 6)
C. 4(x – 5)
D. 4(x – 10)
What is 12.5(18/6)+5³
Final answer:
To solve the expression 12.5(18/6) + 5³, divide 18 by 6 to get 3. Multiply 12.5 by 3 to get 37.5. Then, calculate 5³, which equals 125. Adding the results, you get 162.5.
Explanation:
To solve the expression 12.5(18/6) + 5³, follow the order of operations (PEMDAS/BODMAS). First, divide 18 by 6, which equals 3. Next, multiply 12.5 by 3, which equals 37.5. Finally, calculate 5³, which equals 125. Adding the results, 37.5 + 125 = 162.5.
How many eggs are needed to make 1 dozen waffles, assuming you have enough of all other ingredients? given: 2 cups flour + 3 eggs + 1 tbs oil → 4 waffles
a. 12
b. 48
c. none of these choices is correct
d. 9
e. 16?
We have been given that
2 cups flour + 3 eggs + 1 tbs oil → 4 waffles
In order to make 4 waffles we need 3 eggs.
Thus, to make 1 waffle we need 3/4 eggs.
Now, in 1 dozen there are 12 waffles. Hence, to make 12 waffles we need
[tex]\frac{3}{4} \times 12\\ \\ =3 \times 3\\ =9[/tex]
Therefore, 9 eggs are needed to make 1 dozen waffles.
D is the correct option.
Final answer:
The correct option is (d) 9. Using the given recipe, we can determine that 9 eggs are needed to make 1 dozen waffles by setting up a proportion and solving for the number of eggs.
Explanation:
The original recipe provided states that 2 cups of flour, 3 eggs, and 1 tablespoon of oil will yield 4 waffles. To find out how many eggs are needed to make 1 dozen (12) waffles, we need to set up a proportion based on the given recipe.
Since 4 waffles require 3 eggs, we can set up the following equation: 4 waffles / 3 eggs = 12 waffles / x eggs. Cross-multiplying gives us 4x = 36, and dividing both sides by 4 gives us x = 9. Therefore, 9 eggs are required to make 1 dozen waffles.
Under the normal curve, approximately what percent of scores fall between and -1 to +1 standard deviations around the mean?
I don't know how to do this question, help!!
Help
How much will $5,000 invested at 6% compounded annually amount to after 10 years?
p(x)= x^3+4x^2-8x-6
a= -2
realtor makes 3% commission. What is the commission on a $200,000 house?
PLEASE HELP !!
2. A cube-shaped aquarium has edges that are 3 ft long. The aquarium is filled with water that has a density of 62 lb/ft³.
(a) Should the aquarium be placed on a table that can support a maximum weight of 200 lb? Explain why or why not.
(b) Would the density of the water change if the aquarium was only half full? Explain.
The weight of the water in the cube-shaped aquarium will be 1674 lb, which is much greater than the table's maximum weight capacity of 200 lb. Therefore, the aquarium should not be placed on the table. The density of the water remains constant at 62 lb/ft³ regardless of how much the aquarium is filled.
To determine if the aquarium can be placed on a table with a weight limit of 200 lb, we must first calculate the weight of the water the aquarium will hold. We calculate the volume of the aquarium, then multiply it by the density of water, as the density is given as weight per unit volume (specifically 62 lb/ft³).
The volume (V) of a cube is given by V = side³, so for our aquarium with 3 ft long edges, V = 3³ = 27 ft³. The weight of the water (W) is therefore W = density x volume = 62 lb/ft³ x 27 ft³ = 1674 lb. Since 1674 lb exceeds the table's maximum weight capacity of 200 lb, the aquarium should not be placed on the table.
As for part (b), the density of the water does not change whether the aquarium is full or half full. Density is an intensive property meaning it's independent of the quantity of the substance present. Therefore, whether the aquarium is filled or only half filled, the density of the water remains at 62 lb/ft³.