We are given the following information:
110 oz of 60% acid solution
We need to find the amount of water needed to dilute it to 45%.
To answer this, let's set up the equation first.
We know that 60% of the 110 oz. is acid. This amount of acid must then be the same amount of acid that makes up 45% of the new solution. So our equation would be:
[tex]60\%\times110=45\%\times N[/tex]Solving for N, we get:
[tex]\begin{gathered} 0.60(110)=0.45N \\ 66=0.45N \\ \frac{66}{0.45}=N \\ \\ N=146.666...\approx146.67 \end{gathered}[/tex]Now we know that the total amount must be 146.67 oz. We already have 110 oz. So we only need 146.67 - 110 = 36.67 oz of water to dilute the solution.
The vertices of a triangle are located at the points A(-2,-1) , B (1,3) and C (2,-4). The triangle is translated 2 units right and 3 units up. What are the coordinates of the vertices of triangle A'B'C'?
Given the coordinates of the parent function
[tex]\begin{gathered} A\rightarrow(-2,-1) \\ B\rightarrow(1,3) \\ C\rightarrow(2,-4) \end{gathered}[/tex]Then, the triangle is translated 2 units right and 3 units up. This will then be
[tex]\begin{gathered} A^{\prime}\rightarrow(-2+2,-1+3)=(0,2) \\ B^{\prime}\rightarrow(1+2,3+3)=(3,6) \\ C^{\prime}\rightarrow(2+2,-4+3)=(4,-1) \end{gathered}[/tex]Hence, the coordinates of the vertices of triangle A'B'C' are
[tex]A^{\prime}(0,2),B^{\prime}(3,6),C^{\prime}(4,-1)[/tex]how many 36-passenger busses will it take to carry 144 people?
Solution
how many 36-passenger busses will it take to carry 144 people?
Step by step explanation:
To solve this divide.
[tex]\frac{144}{36}=4[/tex]144/36
and that =4
So it takes 4 buses.
If a race averages 125 miles per hour for 4 hours, how far does the car travel? Use the number line to help you find the answer.
If the speed is 125 miles per hour and the amount of time is 4 hours, in order to find the distance traveled, we just need to multiply the speed and the time:
[tex]\begin{gathered} \text{distance}=\text{speed}\cdot\text{time} \\ \text{distance}=125\cdot4 \\ \text{distance}=500\text{ miles} \end{gathered}[/tex]Using the number line, we have:
1. A(-9,-12), B(-2,2), C(-1,6), D(-5,-2)Slope ofABSlope ofCDLine Typeparallel,perpendicular,or neither
m ab = 2 , m cd =2, Parallel.
1) Given A(-9,-12), B(-2,2) let's find the slope of AB
2) Given C(-1,6), D(-5,-2) let's find the slope of CD
3) Line type
Since the slope determines whether it is parallel, perpendicular, or neither by checking both slopes. As they are identical, we can state that these lines are parallel to each other.
Use Elimination to solve this problem:-4x+2y=-124x+8y=-24
we add the two equations to eliminate the variable x
[tex]\begin{gathered} -4x+2y=-12 \\ 4x+8y=-24 \\ ----------- \\ 0x+10y=-36 \end{gathered}[/tex]now solve y
[tex]\begin{gathered} 10y=-36 \\ y=-\frac{36}{10} \\ \\ y=-\frac{18}{5} \end{gathered}[/tex]now we can reaplce y on any equation to solve x, i will replace on the first equation
[tex]-4x+2(-\frac{18}{5})=-12[/tex]do the operations on solve for x
[tex]\begin{gathered} -4x-\frac{36}{5}=-12 \\ \\ -4x=-12+\frac{36}{5} \\ \\ -4x=-\frac{24}{5} \\ \\ x=\frac{\frac{24}{5}}{4} \\ \\ x=\frac{6}{5} \end{gathered}[/tex]so, the solution point is
[tex](\frac{6}{5},-\frac{18}{5})[/tex]how much more are us there in the 16inch pizza compared to the 12 inch pizzaI really need help
To find the difference we need to calculate the area of each pizza. The area of a circle is given by:
[tex]A\text{ = }\pi\cdot r^2[/tex]Calculating the area for each pizza we have:
[tex]\begin{gathered} A_1=\pi\cdot(\frac{16}{2})^2 \\ A_1=\pi\cdot(8)^2=64\pi \\ A_2\text{ = }\pi\cdot(\frac{12}{2})^2 \\ A_2\text{ = }\pi\cdot(6)^2\text{ = 36}\pi \end{gathered}[/tex]The difference is the subtraction between them:
[tex]dA\text{ = 64}\pi-36\pi=28\cdot3.14159\text{ = 87}.96[/tex]The difference is 87.96 square inches.
The table shows how much water was in a swimming pool as it was being filled. if you were to use the data to male a graph, what is the slope of the line
To find the slope of the line that passes through the points given in the table, you can use the slope formula, that is:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]In this case, the variable x corresponds to the time in minutes and the variable y corresponds to the amount of water in the swimming pool as time passes.
Then, you can use any two ordered pairs in the table to find the slope of the line.
If for example, you take the ordered pairs (10,40) and (16,64), you have:
[tex]\begin{gathered} (x_1,y_1)=(10,40) \\ (x_2,y_2)=(16,64) \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{64-40}{16-10} \\ m=\frac{24}{6} \\ m=4 \end{gathered}[/tex]Therefore, the slope of the is 4 and the correct answer is c) 4.
Can 44.998 be the probability of an outcome in a sample space yes or no
The value 44.998 is NOT a value for a probability of an outcome in a sample space (all possible outcomes in an experiment).
The values for probability must be a value between 0 and 1 (both inclusive), and we have here a value of 44.998.
The probability is a ratio of favorable cases over the total possible cases (sample space), and it can be represented as a decimal that represents a fraction, a fraction, or a percentage. The number 44.998 cannot be represented as a number between 0 and 1 (both inclusive).
In summary, the answer is NO.
. Simplify;2 - 2+5 - 2 - 8 -8.
The given expression:
[tex]\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8[/tex]To simplify the expression :
Group the similar terms together :
[tex]\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=\frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z+5-8[/tex]
Simplify the similar terms together :
[tex]\begin{gathered} \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=\frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z+5-8 \\ \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=(\frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z)+5-8 \\ LCM\text{ of 9,9,9 is 9 So:} \\ \frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z=\frac{4-3-5}{9}z \\ \frac{4}{9}z-\frac{3}{9}z-\frac{5}{9}z=\frac{-4}{9}z \\ \text{Substitute the value of fraction addition:} \\ \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z+5-8 \\ \text{ Since, 5-8= (-3)} \\ \frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z-3 \end{gathered}[/tex]
So, :
[tex]\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z-3[/tex]
Answer :
[tex]\frac{4}{9}z-\frac{3}{9}z+5-\frac{5}{9}z-8=-\frac{4}{9}z-3[/tex]
Determine the equation of the midline of the following graph.543121527олST11131-2-3- 5
Given the equation of the graph
[tex]y=2\cos (\frac{\pi x}{2})-3[/tex]To obtain the equation of the midline, will be the straight line that divides the trigonometric graph into two halves
The equation of the midline is y = -3
A cereal box has a base that is 3 inches by 8 inches . It is 12 inches tall. How many square inches of cardboard is needed to make the box ?
Given the length of the base of the cereal box is 8 inches and the width of the cereal box is 3 inches. The height of the cereal box is 12 inches.
The cardboard is needed to make the box is equal to the surface area of the box. The surface area of the rectangle is given by
[tex]\begin{gathered} S=2(lw+wh+hl) \\ =2(8\times3+3\times12+12\times8) \\ =2(24+36+96) \\ =2(156) \\ =312 \end{gathered}[/tex]Hence, the cardboard is needed to make the box equal 312 square inches.
Help please ! Charlie is traveling 15 m/s which expression could be used to convert this be km/h
15 m/s
To convert ms to km we have to multiply the expression by 3.6:
15 m/s x 3.6 = 54km/h
(15m /1 sec ) (60 sec/1 min) (60 min /1 hour) (1 km/1000 m)
Hi, I was wondering if anyone would be open to helping me with this. I’ve been stuck on this one for a while and I honestly can’t figure out what to answer.The answer choices are either1, 2, 3, 4, 5, 6, 7, 8 for each box If anyone can help i’d appreciate it so muchOr if you give me a hint
Given:
The instruction to draw equilateral triangle inscribed in a circle.
Required:
Mark instruction as step 1, step 2 in correct order.
Explanation:
So, the order for constructing equilateral triangle is as points are given. We will give each one by one name step 1, step 2, step ,step 4, step 5, step 6, step 7, step 8.
Answer:
1, 2, 3, 4, 5, 6, 7, 8 are the answers of respective boxes.
Find out if these expressions are functions or not then compare
Answer to Question 9
Doman ={ 0, 5, 1, -8 }
Range = {3, 5 -4, 4, 2 }
It is not a function.
Step - by - Step Explanation
What to find?
• Domain
,• Range
Given:
{ (0, 3), (5, 5), (1, -4), (-8, 4), (5, 2) }
The domain of a function (x, y) is the x - value and its range is the y - value.
If a set has one x - value mapped to more than one different y- value, then it is a relation otherwise it is a function.
From the given set, the domain are { 0, 5, 1, -8 }
The range are {3, 5 -4, 4, 2 }
Observe that in the given set, one x - value are mapped to two different y- values i. e The range are {5, 5} and { 5, 2}.
Therefore, it is not a function.
Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation? 2 4x + y = 3 13.5x - 13y = 6 x + y = 4 x - y = 6 4x + 6y = 13 3x + 7y = 13.5 4x - 6y = 13 3x - 7y = 13.5
Explanation
Step 1
let x represents the price of 1 apple
let x represents the price of 1 banana
then
. On Monday she purchased 4 apples and 6 bananas for a total of $13
so ,
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Determine weather each function represents exponential growth or exponential decay function
The exponential function is represented by
[tex]y=ab^x[/tex]if a is positive and b is greater than 1 then it's an exponential growth
But if a is positive and b is less than 0, then is an exponential Decay.
A is DECAY
B is GROWTH
C is GROWTH
D is DECAY
E is DECAY
The advertising agency counted the number of billboards in each city in the state. Number of billboards Number of cities 2 85 2 96 3 125 2 154 1 X is the number of billboards that a randomly chosen city has. What is the expected value of X? Write your answer as a decimal.
In order to calculate the expected value of x, we can just calculate the total number of billboards over the total number of cities. So we have:
[tex]\begin{gathered} E(x)=\frac{2\cdot4+2\cdot85+3\cdot96+2\cdot125+1\cdot154}{2+2+3+2+1} \\ E(x)=\frac{870}{10} \\ E(x)=87 \end{gathered}[/tex]So the expected value of x is 87.
Help please this is timed ! It is an assignment that I have to get done thank u
SOLUTION
This is a right-angled triangle and to solve for the unknown side we will use the Pythagoras theorem.
Given parameters:
Opposite side= 15
Adjacent side = 12
Hypotenuse side = x
Pythagoras theorem:
[tex]\text{hypotenuse}^2=opposite^2+adjacent^2[/tex]Substituting the given parameters into the equation above, we will have:
[tex]\begin{gathered} x^2=15^2+12^2 \\ x^2=225+144 \\ x^2=369 \\ \sqrt[]{x^2}=\sqrt[]{369} \\ x=19.2094 \\ x=19.21(\text{to the nearest hundredth)} \end{gathered}[/tex]Final answer: x = 19.21
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 81 people in the 18-21 age bracket and finds that 69 of them respond and 12 refuse to respond. When 301 people in the 22-29 age bracket are contacted, 282 respond and 19 refuse to respond. Assume that 1 of the 382 people is randomly selected. Find the probability of getting someone in the 18-21 age bracket or someone who agreed to respond.
Answer:
Prob = 95.0%
Explanation:
There are 382 people in total
69 respond and are in the 18-21 age bracket
12 refuse to respond and are in the 18-21 age bracket
282 respond and are in the 22-29 age bracket
19 refuse to respond and are in the 22-29 age bracket
Then, the number of people that are in the 18-21 age bracket or agreed to respond is
69 + 12 + 282 = 363
Therefore, the probability of getting someone in the 18-21 age bracket or someone who agreed to respond is
P = 363/382
P = 0.9502
P = 95.0 %
The lines below are parallel. If the slope of the green line is -3/4 what is the slope of the red line?
Answer:
-3/4
Explanation:
Using the coordinate points (-2, 0) and (0, -1.5)
Slope m = y2-y1/x2-x1
From the coordinates x1 = -2, y1 = 0, x2 = 0 and y2 = -1.5
Slope m = -1.5-0/0-(-2)
Slope m = -1.5/2
Slope m = -15/10 * 1/2
Slope m = -15/20
Slope m = -3/4
Hence the slope of the red line is -3/4
Find the primary solution of tan 0 = 6.88.A.8.3°B. 0.1207°C. 674°D. 81.7°
We will have the following:
[tex]tan(6.88)\approx0.1207[/tex][Option B]
Ron borrowed $30,000 to start up his consulting business. The loan at a simple interest rate of 6.9% for three years. Use the formula l = pet to find the amount of interest he will pay on the loan. I= interest, p = principal, r = rate (expressed as a decimal 0.069), t = time in years. He will pay $ on the loan?
Answer:
He will pay $6,210 on the loan
Explanation:
Given Formula
what's the is the measure of three obtuse angles
anThe measure of any obtuse angle is a range between 90 degrees and 180 degrees
[tex]90Since we need the measure of 3 obtuse angles, multiply each term in the inequality above by 3[tex]\begin{gathered} 3\times90The measure of 3 obtuse angles is a range between 270 degrees and 540 degrees
Find the slope and equation of line through (-2,4) & (2,-4)
Given:
Points (-2,4) and (2,-4)
Using the given two points, find the slope of the line.
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(2,-4) \\ \\ m = \dfrac{y_2 - y_1}{x_2 - x_1} \\ m=\dfrac{-4-4}{2-(-2)} \\ m=\dfrac{-8}{2+2} \\ m=\frac{-8}{4} \\ m=-2 \end{gathered}[/tex]Now that we have the slope, use the slope and any of the two points to solve for the equation of the line using point slope form. In this instance we will use m = -2, and (-2,4).
[tex]\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y - 4 = -2\left(x + 2\right) \\ y-4=-2x-4 \\ y=-2x-4+4 \\ y=-2x\cancel{-4+4} \\ y=-2x \end{gathered}[/tex]Therefore, the slope of the line is m = -2, and the equation of the line is y = -2x.
The perimeter of a triangle is 72 cm. The longest side is 4 cm less than the sum of the other two sides. Twice the shortest side is 8 cm less than the longest side Fi of each side of the triangleThe perimeter of a triangle is 72 cm. The longest side is 4 cm less than the sum of the other two sides. Twice the shortest side is 8 cm less than the longest side. Find th of each side of the triangle
Answer:
13 cm, 25 cm and 34 cm
Step-by-step explanation:
Define the variables:
Let a = shortest side of the triangle.Let c = longest side of the triangle.Let b = other side of the triangle.Given the perimeter of the triangle is 72 cm:
⇒ a + b + c = 72
Given the longest side is 4 cm less than the sum of the other two sides:
⇒ c = a + b - 4
Given twice the shortest side is 8 cm less than the longest side.
⇒ c = 2a + 8
Substitute the third equation into the second equation and solve for b:
⇒ c = a + b - 4
⇒ 2a + 8 = a + b - 4
⇒ a + 8 = b - 4
⇒ b = a + 12
Substitute the found expression for b and the third equation into the first equation and solve for a:
⇒ a + b + c = 72
⇒ a + (a + 12) + (2a + 8) = 72
⇒ 4a +20 = 72
⇒ 4a = 52
⇒ a = 13
Substitute the found value of a into the other expressions to find b and c:
⇒ b = a + 12
⇒ b = 13 + 12
⇒ b = 25
⇒ c = 2a + 8
⇒ c = 2(13) + 8
⇒ c = 26 + 8
⇒ c = 34
Therefore the lengths of the sides of the triangle are:
13 cm25 cm34 cmJoe bought n packs of pencils. Each pack has 10 pencils. Write an equation to represent the total number of penca.D=0.loх
Given:
The number of pencils in each box is 10.
The total number of pencil boxes is n.
To write: The equation that represents the total number of pencils
Explanation:
The total number of pencils is calculated by multiplying the number of boxes by the number of pencils in each box.
So, the equation is written as
[tex]\begin{gathered} \text{Total number of boxes=Total number of boxes}\times Number\text{ of pencils in each box} \\ p=n\times10 \end{gathered}[/tex]Final answer: The equation is,
[tex]p=10n[/tex]Which polynomial is prime? • x^2+7 • x^2-25 • 3x^2-27 • 2x^2-8
Polynomials can be factored using their zeros and leading coefficient like this:
[tex]f(x)=a(x-r_1)(x-r_2)...(x-r_n)[/tex]Where a is the leading coefficient and the r's are the zeros of the
Identify the converse of the statement "A → B: If x = 3, then x + 8 = 11."
Answer: Option A
Explanations :
The converse of the statement would be :
• B→A ;
,• if (x+8 ) = 11, then x = 3
Find the volume of a cylinder that has a diameter of 12 yds and a height of 4 yds.
To find the volume of a cylinder using the following formula:
[tex]V=\pi\cdot r^2\cdot h[/tex]Replace for the given value, remember that the radius is half the diameter.
[tex]\begin{gathered} V=\pi\cdot(\frac{12}{2})^2\cdot4 \\ V=\pi\cdot6^2\cdot4 \\ V=\pi\cdot36\cdot4 \\ V=452.39 \end{gathered}[/tex]The volume of the cylinder is 452.39 cubic yards.
quick answer = best rating
tan(x)=0.3
x=16.7 degrees