We need 30 ml of the 15 percent solution to complete the order.
Here, we are given that we need to prepare 180 mL of a 2.5% solution by diluting a 15% solution with water.
the 180 ml 2.5% solution will contain-
2.5% pf 180 ml acid
= 2.5/100 × 180
= 25/1000 × 180
= 1/40 × 180
= 18/4
= 9/2
= 4.5 ml
Water in the 180 ml solution will be = 180 - 4.5 = 175.5
Now, we have say x ml of 15% solution
It must contain 4.5 ml of acid
Thus-
15% of x = 4.5
15/100 × x = 4.5
x = 4.5 × 100/15
x = 450/15
x = 30
Thus, we need 30 ml of the 15 percent solution, hence, option C.
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For the parallelogram, AB = 12 and BD = 20. Find the length of AC.АThe length of the diagonal AC isBE
The value of line segment AB is given in the problem. Line segment AB is half of the diagonal AC. Hence, if we want to solve for the length of the diagonal AC, we just multiply the length of line segment AB by 2. This is a parallelogram, therefore, we can say that the line segment AB is half of the diagonal AC.
The length of the diagonal AC is therefore 12 x 2 = 24.
Hello is it possible to receive help on this question?
Vertex = (4, 5)
focuse = (7, 5)
The vertex and focus lie on the same horizontal line; y = 5
So we will be applying the equation of horizontal parabola
[tex]\begin{gathered} \text{Equation of the parabola (horizontal):} \\ (y-k)^2=\text{ 4a(}x\text{ - h)} \end{gathered}[/tex]The focus lies on the right of the vertex, parabola opens upward as a result, a = positive
[tex]\begin{gathered} As\text{ the y coordinates are the same, }a\text{ = 7 - 4 } \\ a\text{ = 3} \\ \\ \text{Vertex: h = 4, k = 5} \end{gathered}[/tex]substituting the values:
[tex]\begin{gathered} (y-5)^2\text{ = 4(3)(x - 4)} \\ (y-5)^2\text{ = 12(x - 4)} \end{gathered}[/tex]Necesito la fórmula y una breve explicación
The value of the height of the rectangle is 80 m.
Rectangles
The rectangle is a quadrilateral. The classification for quadrilaterals is given by the length of sides and angles. For a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
A rectangle is a geometric figure that has 4 sides called: length and height. Due to its characteristics, the rectangle presents two length (L) and two heights (H).
The perimeter is the sum of all sides of a geometric figures. For a rectangle, the perimeter is 2L+2H.
The question gives:
length (base) = 20 + H width (height) = H perimeter = 360 mFrom the perimeter, you can find the height, see below.
P=2L+2H
360=2*(20 + H) +2H
360= 40 +2H +2H
360-40 = 4H
320= 4H
320/4 = H
80=H
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In order to graph the inequality using a graphing calculator, tell what function to enter for the boundaryline, whether the graph should be shaded above or below the line, and if the boundary line is included inthe solution.63+7y>xThe boundary line is given by the functionThe graph is shaded _____ the line, and the boundary line ______ included in the solution.
Answer:
• 63+7y=x
,• Above
,• Is not Included
Explanation:
Given the inequality:
[tex]63+7y>x[/tex]To get the boundary line, we replace the inequality sign with an equality sign.
• The boundary line is given by the function 63+7y=x
Since the inequality is greater than:
• The graph is shaded ,above, the line
,• The boundary line ,is not, included in the solution so we use a dotted line.
Solve each system by graphing. If the lines are parallel, write no solution. If the lines coincident, write infinitely many solutions.
Answer:
No Solution
Explanation:
Given the system of equations:
[tex]\begin{gathered} y-2x=4 \\ y=5+2x \end{gathered}[/tex]First, graph each equation using the x and y-intercepts.
Equation 1
[tex]\begin{gathered} y-2x=4 \\ \text{When }x=0,y=4\implies\text{Point (0,4)} \\ \text{When y}=0,x=-2\implies\text{Point (-2,0)} \end{gathered}[/tex]Join the points (0,4) and (-2,0) as done below:
Equation 2
[tex]\begin{gathered} y=5+2x \\ \text{When }x=0,y=5\implies\text{Point (0,5)} \\ \text{When y}=0,x=-2.5\implies\text{Point (-2.5, 0)} \end{gathered}[/tex]Join the points (0,5) and (-2.5, 0) as done below:
We observe that the two lines are parallel.
Therefore, the system of equations has No Solution.
determine the range of y=√x/√x+2
Solution
[tex]y=\frac{\sqrt[]{x}}{\sqrt[]{x+2}}[/tex]For this case we can do the following:
[tex]y=\sqrt[]{\frac{x}{x+2}}[/tex]The minimum value should be 0 for y assuming that x>= 0
Then the range should be:
[tex]0\le y<1[/tex]Simplify(5x-6.9) (2x + 12.2)O10x84.18O 10x² +47.2x-84.187x² + 74.8x + 5.37x² + 5.3
QUESION: Simplify (5x-6.9)(2x + 12.2)
EXPLANATION:
(5x - 6.9)(2x + 12.2)
Let's open the bracket by multiplying:
10x² + 61x - 13.8x - 82.18
Let's collect like terms but adding and subtracting each variable according to its power:
10x² + 47.2x - 82.18
Therefore, the simplified form of (5x-6.9)(2x + 12.2) is 10x² + 47.2x - 82.18.
So, the correct option is the second option which is 10x² + 47.2x - 82.18.
Do all proofs have the same number of steps?
Write an equation for the scenario. Solve the equation to answer the question. Show all steps.
5. Ben is signed up for drivers ed. He will spend 7.5 hours driving with an instructor and will also attend
a 2.5 hour class each week. When Ben completes the 30 total hours of instruction, he will take his
driver's test. How many weeks will he be required to attend class?
He will require 9 weeks to attend class, Based on given condition, 7.5 + 2.5x = 30.
What is Equation?Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the two equations 3x + 5 and 14, which are separated by the 'equal' sign, make up the equation 3x + 5 = 14.
According to question,
The time he spend as instructor is 7.5 and 2.4 hour class.
total hours = 30
7.5 +2.5x = 30
2.5x = 30- 7.5
2.5x = 22.5
x= 22.5/2.5
x = 9
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This month, a vegetarian restaurant used 9,168 ounces of spinach. That is 20% more than last month, when the restaurant had a different menu. How much spinach did the restaurant use last month?
Consider 9,168 ounces of spinach is 20% more than the amount of spinach of the last month. If x is such unknown amount of spinach, you can write:
[tex]x+(\frac{20}{100})x+9,168[/tex]where (2/100)x factor represents the 20% of x.
Simplify the pervious equation and solve for x:
[tex]\begin{gathered} x+0.2x=9,168 \\ 1.2x=9,168 \\ x=\frac{9,168}{1.2} \\ x=7,640 \end{gathered}[/tex]Hence, last month the restaurant used 7,640 amount of spinach.
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 34 meters ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 meter per second, and the adults hobbled after them at a rate of 2 meters per second. Soon they were side-by-side. How long did that take? How far did the adults go?It took ____ seconds for the adults to go ____ meters and catch up to the kids.
From the question,
The equation for the distance covered by the kids is d = 1 t + 34
The equation for the distance covered by the adults is d = 2t
Now, when the adults caught up with the kids was when : 2 t = 1 t + 34
Solving this equation, we have 2 t - 1 t = 34
t = 34
since d= 2 t , when t = 34
d = 2 x 34 = 68
It took ___34_ seconds for the adults to go _68___ meters and catch up to the kids.
B. -3/4x-4=-6C. Is 0 solution to -3/4x-4>-6Select answerYes. No.D. Using interval Notation, solve: -3/4x-4>-6
Explanation:
Part A:
The question is given below as
[tex]\begin{gathered} whenx=0,evaluate \\ -\frac{3}{4}x-4= \end{gathered}[/tex]By putting x=0, we will have that
[tex]\begin{gathered} \begin{equation*} -\frac{3}{4}x-4 \end{equation*} \\ -\frac{3}{4}(0)-4 \\ =-4 \end{gathered}[/tex]Hence,
The final answer for part A is
[tex]\Rightarrow-4[/tex]Part B:
[tex]\begin{gathered} solve, \\ -\frac{3}{4}x-4=-6 \end{gathered}[/tex]add 4 to both sides
[tex]\begin{gathered} -\frac{3}{4}x-4=-6 \\ -\frac{3}{4}x-4+4=-6+4 \\ -\frac{3}{4}x=-2 \\ coess\text{ multiply, we will have} \\ -3x=-2\times4 \\ -3x=-8 \\ divide\text{ both sides by -3} \\ \frac{-3x}{-3}=-\frac{8}{-3} \\ x=\frac{8}{3} \end{gathered}[/tex]Hence,
The final answer for part B is
[tex]\Rightarrow x=\frac{8}{3}[/tex]Part C:
[tex]-\frac{3}{4}x-4>-6[/tex]Add 4 to both sides, we will have
[tex]\begin{gathered} -\frac{3}{4}x-4\gt-6 \\ -\frac{3}{4}x-4+4\gt-6+4 \\ -\frac{3}{4}x>-2 \\ cross\text{ multiply} \\ -3x>-2\times4 \\ -3x>-8 \\ divide\text{ bth sides by -3} \\ \frac{-3x}{-3}>-\frac{8}{-3}(the\text{ sighn will be reversed\rparen} \\ x<\frac{8}{3}(0\text{ is a solution\rparen} \end{gathered}[/tex]Hence,
The final answer for part C is YES
Part D:
[tex]\begin{gathered} -\frac{3}{4}x-4\gt-6 \\ -\frac{3}{4}x-4+4\gt-6+4 \\ -\frac{3}{4}x>-2 \\ cross\text{ multiply} \\ -3x>-2\times4 \\ -3x>-8 \\ divide\text{ bth sides by -3} \\ \frac{-3x}{-3}>-\frac{8}{-3}(the\text{ sighn will be reversed\rparen} \\ x<\frac{8}{3} \\ hence,in\text{ interval notation we will have the final answer be} \\ (-\infty,\frac{8}{3}) \end{gathered}[/tex]Hence,
The final answer for part D is given below as
[tex]\Rightarrow(-\infty,\frac{8}{3})[/tex]
Ash practiced her free throw 900 times. She made 30% of her shots. How many did she make?
Jason and Whitney deposit $700.00 into a savings account which earns 11% interest compounded quarterly. They want to use the money in the account to go on a trip in 3 years. How much will they be able to spend?
To solve this problem we need to use the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where P is the initial deposit:
[tex]P=700[/tex]r is the interest rate in decimal form, since the interest rate is 11%, in the decimal form we have:
[tex]r=0.11[/tex]n is the number of times that the interest is compounded in a year, in this case, it is compounded quarterly, and since there are 3 quarters in a year, the interest will be compounded 3 times per year:
[tex]n=3[/tex]and t is the total time, in this case, 3 years:
[tex]t=3[/tex]Substituting all of these values into the formula to find the Amount "A" they will have after 3 years:
[tex]A=700(1+\frac{0.11}{3})^{3\cdot3}[/tex]Solving the operations:
[tex]A=700(1+0.03666)^9[/tex][tex]A=700(1.03666)^9[/tex][tex]A=700(1.382777)[/tex][tex]A=967.944[/tex]Answer: They will have $967.944 to spend
a number from 15 to 23 is drawn at random p(a number divisable by 3)
Solution:
Given:
[tex]\begin{gathered} Sample\text{ space}=\lbrace15,16,17,18,19,20,21,22,23\rbrace \\ Total\text{ n}umber\text{ of possible outcomes}=9 \\ \\ \\ Numbers\text{ divisible by 3}=\lbrace15,18,21\rbrace \\ Number\text{ of required outcome}=3 \end{gathered}[/tex]Therefore, the probability of picking a number divisible by 3 is;
[tex]\begin{gathered} P(a\text{ number divisible by 3\rparen}=\frac{3}{9} \\ \\ Simplifying\text{ further,} \\ P(a\text{ number divisible by 3\rparen}=\frac{1}{3} \end{gathered}[/tex]Find the maximum value of the objective function and the values of x and y for which it occurs.
F = 2x + y
3x + 5y ≤ 45 x 20 and y20
2x + 4y ≤ 32
In linear equation, value of x and y = ( 10 , 3 ).
What is linear equation with example?
Ax+By=C is the typical form for two-variable linear equations. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).3x + 5y = 45 ............1
2x + 4y =32 .........2
Multiply by 2 in equation 1 and by 3 in 2
6x + 10y = 90
6x + 12y = 96
equation 2 - equation 1
2y = 6
y = 3
put value of y put in equation 1
3x + 5y = 45
3x + 5 * 3 = 45
3x = 45 - 15
3x = 30
x = 10
value of x and y = ( 10 , 3 )
the value of the objective function at each of the vertices to find the maximum.
I'll do one vertex, you do the rest.
(0,8)
F = 2x + y
F = 2 * 0 + 8
F = 8
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A) In how many years will both companies have the same profit ?
B) Approximately what will that profit be ?
C) Which company’s profits are growing more quickly
Answer: 3 years
$60,000
Company B
Step-by-step explanation: Analyze the data on the graph
Help with algebra 2 question.12). In a circle with radius of 18cm, a central angle of 5pi/6 radians intercept an arc. Find length of the arc in cm.
Given:
Radius of circle r is 18 cm.
angle
[tex]\emptyset=\frac{5\pi}{6}=5*\frac{180}{6}=150\degree[/tex]Required:
We need to find the arc length in cm
Explanation:
The formula to find arc length is
[tex]l=2\pi r*\frac{\emptyset}{360}[/tex]Substitute the values in the formula
[tex]l=2*3.14*18*\frac{150}{360}=47.1\text{ cm}[/tex]Final answer:
Arc length of given circle is 47.1 cm
I don’t understand these questions. Could you please help me? I need clearly explain.
We need to sketch the graph of V(t), with V in ml and t in seconds. Notice that:
[tex]V(0)=2200[/tex]because for t = 0, her lungs start with a volume of 2200 ml.
Since the period (of a complete breath) is 4 seconds, and the function is sinusoidal, the graph is:
b. Now, a sinusoidal function has the form:
[tex]V(t)=A\sin \lbrack\frac{2\pi}{T}(t-b)\rbrack+c[/tex]where:
• A is the amplitude (half the difference between the smallest and the largest values of V);
,• T is the period;
,• b is the horizontal shift (the difference between the initial value of t and the value of t for which V(t) has the mean value);
,• c is the vertical shift (the mean value of V(t)).
So, observing the graph, we see that:
[tex]A=\frac{2800-2200}{2}=300[/tex][tex]T=4[/tex][tex]b=1[/tex][tex]c=\frac{2200+2800}{2}=2500[/tex]Therefore, the equation representing the volume V, in ml, after t seconds is:
[tex]\begin{gathered} V(t)=300\sin \lbrack\frac{2\pi}{4}(t-1)\rbrack+2500 \\ \\ V(t)=300\sin \lbrack\frac{\pi}{2}(t-1)\rbrack+2500 \end{gathered}[/tex]c. If Aira breathed more rapidly, the period and the horizontal shift of the function V(t) would be smaller. Thus, the graph would change more rapidly also, i.e., we would see more variations in the 20 seconds.
For example, if she breathed 2 times faster, the period would be 2 instead of 4, and the equation would be:
[tex]\begin{gathered} V(t)=300\sin \lbrack\frac{2\pi}{2}(t-0.5)\rbrack+2500 \\ \\ V(t)=300\sin \lbrack\pi(t-0.5)\rbrack+2500 \end{gathered}[/tex]And the graph would be:
And if Aire took bigger breaths, the amplitude and the vertical shift of the function V(t) would increase. For example, if her lungs could reach the volume of 3000 ml, assuming the same period of 4 seconds, the equation would be:
[tex]V(t)=400\sin \lbrack\frac{\pi}{2}(t-1)\rbrack+2600[/tex]And the graph would be:
Explain what it means to solve a formula for a variable
The meaning of solving a formula for a variable is rewriting the formula in a way that the variable is "isolated" in one side of the formula, that is, one side of the equation has only the variable alone, without coefficients or other expressions.
For example, let's solve the formula below for the variable y:
[tex]\begin{gathered} 2x+3y+4=0\\ \\ 3y=-2x-4\\ \\ y=\frac{-2x-4}{3} \end{gathered}[/tex]We can see that in the formula above, the left side of the equation has only "y", this way it is solved for y.
Prove that if x and y are real numbers, then max(x, y) +
min(x, y) = x + y. [Hint: Use a proof by cases, with
the two cases corresponding to x ≥ y and x
Real numbers contain the number zero and can be either positive or negative.
If x > y, then max (x, y) = x and min (x, y) = y.
So, max (x, y) + min (x, y) = x + y
What is meant by real numbers?Real numbers contain the number zero and can be either positive or negative. Because they exists not imaginary, which exists a separate type of number system, they are directed to as real numbers. Unquantifiable quantities, like the square root of -1, are referred to as imaginary numbers.
A "actual" and practical idea, infinity. Infinity, on the other hand, is not a number on the real number line since it is not a part of the mathematically defined set of "real numbers."
If x > y, then max (x, y) = x and min (x, y) = y.
So, max (x, y) + min (x, y) = x + y
If x ≤ y , then max (x, y) = y and min (x, y) = x.
And we have, max (x, y) + min (x, y) = y + x = x + y
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A cab company charges a $11 boarding fee and a meter rate of $2 per mile. The equation is y = 2x + 11 where x represents the number of miles to your destination. If you traveled 5 miles to your destination, how much would your total cab fee be?
We are given a function, y = 2x + 11, where x is the number of miles driven. If we are told that the cab was driven 5 miles, x = 5. So, substitute 5 for x.
y = 2x + 11
= 2(5) + 11
= 10 + 11
= 21
y = 21
What is 100,000 written as a power of 10 in exponent. Help
If we have the following number:
[tex]100,000[/tex]and we want to write it as a power of 10 in exponent, we just have to count the zeros of the number, in this case there are 5, and that would be our exponent, then, we have:
[tex]100,000=10^5[/tex]EX #5: Based on the definition above, identify the following: A. Relative Maximum is __ where x = __ B. Relative Minimum is __ where x = __ C. Relative Minimum is __ where x = __
Based on the given graph, you can conclude:
A. Relative Maximum is f(x) = 1 where x = 2
(Because the relative maximum of a function is given by a point of the graph with a slope m = 0, but this point is not necessarily the absolute maximum. Furthermore, the concavity of the curve at this point is negative).
B. Relative minimum is f(x) = -8 where x = -3
C. Relative minimum is f(x) = 0 where x = 4
Both relative minima correspond to points in which the slope of the line is 0 and the concavity of the line is positive.
Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures.
m/1 = (5x +15)°, m/4= (30x - 60)°
To identify the answer we will use Angles Theorem which is m∠1 = 150. When the transversal line cuts through the two parallel lines, it creates the alternate exterior angles 1 and 8. Both are consistent with the alternate exterior angles theorem. As a result, m1 = m8 and m1 = (50x)°.
m∠8 = 150
Setting both equal, find x 50x = 150.
50x/50 = 150/50 x = 3 when you divide both sides by 50.
Unknown stance
m∠1 = (50x) = 50*3 = 150°
What exactly is a mathematical postulate?A proposition—also referred to as an axiom—that is accepted as true without evidence. Lemmas and theorems arise from postulates, which is their fundamental structure. Five tenets, referred to as Euclid's postulates, form the foundation of Euclidean geometry as a whole.
An unsupported assertion is referred to as a postulate. A postulate is also referred to as an axiom. For instance, you would believe Pam if she claimed that all of her siblings are at least five foot one tall if you knew that she is five feet tall and that all of her siblings are taller than her.
The fundamental tenet of consumer theory holds that consumers choose the bundle from the available options that provides the greatest level of satisfaction. On the set of bundles, assumptions are made that ensure the existence of a comprehensive, reflexive, and transitive preference order.
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R Clarissa packed books for a garage sale. ● She packed 3 boxes of books each day. Each box had 15 books. If she packed for 4 days, how many books did Clarissa pack R Draw a Picture
Clarissa packed 180 books at the end of day 4
How Many Books Did She PackTo calculate the number of books she carried, we can simply multiply the total number of boxes, the books and the number of days.
What is multiplication or product of two numbers?
In mathematics, a product is the result of multiplication, or an expression that identifies objects to be multiplied, called factors. For example, 30 is the product of 6 and 5
To achieve this, we can write this mathematically as;
[tex]3 * 15 * 4 = 180[/tex]
At the end of the fourth day, Clarissa had carried 180 books.
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What does 2/4 + 3/6=
Answer: 1
Step-by-step explanation: becuase 2/4 + 3/6 = 1
Answer: 6/6 = 1
Step-by-step explanation:
First, if you were to look at both fractions they both equal to 0.5 or one half.
Therefore, 2/4 = 1/2
And, 2/4 = 1/2
1/2 + 1/2 = 1
Select the statement that correctly describes the solution to the system of equations.
To identify the solution of the system, solve for the value of y for each equation.
[tex]\begin{gathered} y=-2x-2 \\ y=-2x \end{gathered}[/tex]Notice that when we subtract the second equation for the first equation, the obtained equation is not true.
[tex]\begin{gathered} y-y=-2x-2-(-2x) \\ 0\neq-2 \end{gathered}[/tex]This means the two equations are parallel. Thus, there should be no solution since the two linear equations will not meet.
I am an odd number. When you multiply me by 6, then
divide the product by 3, the quotient is 10. What number am I?
Answer:
20 hope this is helpful and also enjoy your day
I am 5 when you multiply me by 6, then divide the product by 3, the quotient is 10.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Assuming I am 'n'.
∴ When you multiply me by 6, which is 6n, then divide the product by 3, which is 6n/3 the quotient is 10 which is 6n/3 = 10.
6n/3 = 10.
2n = 10.
n = 5.
So, I am an odd number 5.
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if angle 1 and angle 2 are vertical angles, angle 2 and angle 3 are complementary angles, and the measure of angle 3 = 56, find the measure of angle 1
We know that
[tex]m\angle3=56[/tex]If angle 2 and angle 3 are complementary, then by its definition we can express the following.-
[tex]\begin{gathered} m\angle2+m\angle3=90 \\ m\angle2=90-m\angle3 \\ m\angle2=90-56=34 \end{gathered}[/tex]Then, angle 1 and angle 2 are equal by definition of vertical angles.
[tex]m\angle1=m\angle2=34[/tex]Therefore, angle 1 measures 34°.