The y-intercept is (0,-3) while the x-intercept is (18.75,0)
Here, we want to find the x and y-intercepts of the given line
Firstly, we have to rewrite the equation of the line in the standard form
We have this as;
[tex]\text{y = mx + b}[/tex]m is the slope and b is the y-intercept
Rewriting the given equation, we have this as;
[tex]\begin{gathered} 5y\text{ = 4x-15} \\ y\text{ =}\frac{4}{5}x-\frac{15}{5} \\ \\ y\text{ = }\frac{4}{5}x\text{ - 3} \end{gathered}[/tex]We have the y-intercept as -3
In the coordinate form, this is (0,-3)
To get the x-intercept, we set the y value to zero
We have this as;
[tex]\begin{gathered} 0\text{ = }\frac{4}{5}x-15 \\ 15\text{ = }\frac{4x}{5} \\ \\ 4x\text{ = (15}\times5) \\ 4x\text{ = 75} \\ x\text{ = }\frac{75}{4} \\ x\text{ = 18.75} \end{gathered}[/tex]The x-intercept is 18.75 which in the coordinate form is (18.75,0)
graph the system of linear inequalities.x + 2y ≥ 2-x + y ≤ 0
INFORMATION:
We have the next system of equations
[tex]\begin{gathered} x+2y\ge2 \\ -x+y\leq0 \end{gathered}[/tex]And we must graph it
STEP BY STEP EXPLANATION:
To graph the system, we need to graph first the two inequalities as equations. So, we would have
[tex]\begin{gathered} x+2y=2 \\ -x+y=0 \end{gathered}[/tex]- x + 2y = 2:
To graph it, we can find the x and y intercepts.
x intercept:
To find it, we need to replace y = 0, and solve for x
[tex]\begin{gathered} x+2(0)=2 \\ x=2 \end{gathered}[/tex]y intercept:
To find it, we need to replace x = 0, and solve for y
[tex]\begin{gathered} 0+2y=2 \\ y=1 \end{gathered}[/tex]So, the graph would be a line that passes through the points (2, 0) and (0, 1).
Since the symbol of this inequality is ≥, the graph would be the values that are on the line and above it.
- -x + y = 0:
To graph it, we can rewrite the equation as
[tex]y=x[/tex]And this is the identity line.
So, since the symbol of this inequality is ≤, the graph would be the identity line and the values below it.
Finally, the graph of the system would be the common part of the graph of each inequality
So, the graph of the system is the part colored in red and blue at the same time
ANSWER:
School is making digital backups of old reels of film in its library archives the table shown approximate run Times of the films for a given diameter of film in the reel. Which of the following equations is a good model for the run time, y, as a function of the diameter, X?
One technique that you can apply when solving such a problem is trial and error. We try to use each equation to prove that a given value of x on the table given will correspond to the value of y on the table.
a) Let's try to put x = 3 for the first equation and we must get an answer equal to 2.25.
[tex]y=7.72(3)-29.02=-5.86_{}[/tex]Since the value of y is not equal to 2.25 and the deviation is too large. this equation is not a good model,
b) We put x = 3 on the second equation and solve for y
[tex]y=-7.52(3)^2+0.19(3)+3.26=-63.85[/tex]Since the value of y is not equal to 2.25 and the deviation is too large. this equation is not a good model,
c) We put x = 3 on the third equation and solve for y,
[tex]y=0.4(3)^2+0.79(3)-4.93=1.04[/tex]Again, the value that we get is not equal to 2.25, hence, this equation is not a good model. But since its value is close to 2.25, we try to other values of x. If x = 5, we get
[tex]y=0.4(5)^2+0.79(5)-4.93=9.02[/tex]which has a slight deviation on the given value of y on the table for x = 5. let's try for x = 7. We have
[tex]y=0.4(7)^2+0.79(7)-4.93=20.2[/tex]and the answer has a small deviation compared to the actual value given. The other values of x can again be put on the equation and check their corresponding value of y, and the resulting values are as follows
[tex]\begin{gathered} y=0.4(8)^2+0.79(8)-4.93=26.99 \\ y=0.4(12)^2+0.79(12)-4.93=62.15 \\ y=0.4(14)^2+0.79(14)-4.93=84.53 \end{gathered}[/tex]And as you can see, the deviation of values from the table to calculated becomes smaller. Hence, this is the best model.
d) We put x = 3 on the third equation and solve for y,
[tex]y=4.19(1.02)^3=4.45_{}_{}[/tex]Again, the value that we get is not equal to 2.25, hence, this equation is not a good model. But since its value is close to 2.25, we try to other values of x. If x = 5, we get
[tex]y=4.19(1.02)^5=4.63[/tex]where the answer's deviation is too large compared to the value of y if x = 5 on the table given.
Based on the calculations used above, the best equation that can be a good model is equation 3.
12What mistake did the student make when solvingtheir two-step equation?(a)b) If correctly solved what should the value of be?
Given the equation:
[tex]\frac{x}{6}+3=-18[/tex](a) You can identify that the student applied the Subtraction Property of Equality by subtraction 3 from both sides of the equation:
[tex]\frac{x}{6}+3-(3)=-18-(3)[/tex]However, the student made a mistake when adding the numbers on the right side.
Since you have two numbers with the same sign on the right side of the equation, you must add them, not subtract them and use the same sign in the result. Then, the steps to add them are:
- Add their Absolute values (their values without the negative sign).
- Write the sum with the negative sign.
Then:
[tex]\frac{x}{6}=-21[/tex](b) The correct procedure is:
1. Apply the Subtraction Property of Equality by subtracting 3 from both sides (as you did in the previous part):
[tex]\begin{gathered} \frac{x}{6}+3-(3)=-18-(3) \\ \\ \frac{x}{6}=-21 \end{gathered}[/tex]2. Apply the Multiplication Property of Equality by multiplying both sides of the equation by 6:
[tex]\begin{gathered} (6)(\frac{x}{6})=(-21)(6) \\ \\ x=-126 \end{gathered}[/tex]Hence, the answers are:
(a) The student made a mistake by adding the numbers -18 and -3:
[tex]-18-3=-15\text{ (False)}[/tex](b) The value of "x" should be:
[tex]x=-126[/tex]Suppose an auto racer won a 400 mile race with a time of 1:48:51. At one point the racer was 50 miles closer to the finish than the start. How far had the racer gone at that point?How far from the start was the racer? __ miles
To solve this problem, let's use the variables x and y to represent the distance of the racer to the start and to the finish, respectively.
If the total distance of the race is 400 miles, we have that the distance traveled by the racer until now (x) plus the distance he needs to travel to finish the race (y) is 400:
[tex]x+y=400[/tex]Also, at one point the racer was 50 miles closer to the finish than the start, so at that point we have that he is farther away from the beginning (that is, x is 50 units bigger than y):
[tex]x=y+50[/tex]Now, using this value of x in the first equation, we have:
[tex]\begin{gathered} (y+50)+y=400 \\ 2y+50=400 \\ 2y=350 \\ y=\frac{350}{2}=175 \end{gathered}[/tex]Now, finding the value of x, we have:
[tex]x=y+50\to x=175+50\to x=225[/tex]So the racer was 225 miles far from the start.
995
× 55 ?? What’s the partial product of this?
For a certain kind of plaster work, 1.5 cu yd of sand are needed for every 100 sq yd of surface. How much sand will be needed for 350 sq yd of surface?
We are told that we need 1.5 cu yd of sand for every 100 sq yd of surface, then we can express the ratio of sand to surface like this:
[tex]\text{ratio}=\frac{1.5}{100}[/tex]In order to find how much sand we need for 350 sq yd of surface, we just have to multiply 350 by this ratio, then we get:
[tex]350\times\frac{1.5}{100}=5.25[/tex]Then, we need 5.25 cubic yards of sand.
Select the quadrant or axis where each ordered pair is located on a coordinate plane.(9.5, 0)(-4, 7)(-1, -8)options:Quadrant IQuadrant IIQuadrant IIIQuadrant IV
The points (9.5, 0), (-4, 7), and (-1, -8) are plotted in the coordinate plane below:
Therefore, the quadrants where each point is located are:
• Quadrant I: (9.5, 0)
,• Quadrant III: (-1, -8)
,• Quadrant IV: (-4, 7)
Solve: 6 · x=42What dose x=?
We have to solve this expression.
We can solve it dividing both sides by 6:
[tex]\begin{gathered} 6x=42 \\ \frac{6x}{6}=\frac{42}{6} \\ x=7 \end{gathered}[/tex]Answer: x = 7
Flex Gym charges a membership fee of $150.00 plus $41.00 per month to join the gym. Able gym charges a membership fee of $120.00 plus $46.00 per month. Find the number of months for which you would pay the same total fee to both gyms.
We have to write an equation for each gym of the cost as a function of the months, so:
[tex]\begin{gathered} We\text{ call c=the total cost and m=months.} \\ \text{For Flex Gym:} \\ c_F=41\cdot m+150 \\ \text{For Able Gym}\colon \\ c_A=46\cdot m+120 \end{gathered}[/tex]Now, we want to find the number of months at which the both gym have the same cost, so:
[tex]\begin{gathered} c_F=c_A \\ 41\cdot m+150=46\cdot m+120 \\ 150-120=46\cdot m-41\cdot m \\ 30=5\cdot m \\ m=\frac{30}{5}=6 \end{gathered}[/tex]At 6 months the cost of the both gyms is the same.
7) The point spreads on 12 football games for a season are:1, 3, 14,9,7,3,6, 27, 3, 13, 8, 17.a (3pts) Make a histogram for the data.1-511-1516-2021-2526-30Symmetric6-10b. (2 pts) Describe the distribution of the data, (Circle One)FrequencySkewed RightSkewed Left(2 pts)Which measure of center would be most accurate? (circle one)MeanMedianModeC.d. (2 pts) Which measure of spread would be most accurate? (circle one)RangeInterquartile rangeStandard Deviation
Table of frequencies.
Interval Frequency
1-5 4
6-10 4
11-15 2
16-20 1
21-25 0
26 - 30 1
Therefore the graph would be
B. As we can see from the graph it is skewed left.
C. Since the graph is skewed, the better option would be the median.
D. Since the graph is skewed, the better option would be the interquartile range.
Solve the following equation for "b".b/3 = M
In order to solve an equation for a variable we need to isolate it on the left side. In this case we want to find the value of "b", therefore we must perform operations in such a way that it will be the only thing on the left side of the equation. To do so we need to switch the operation of each term we don't want to be on the left side, this means that if a term is adding it should go to the right side subtracting and if it is multiplying it should go dividing. In this case there is only one term that is dividing "b", so it should go to the right side by multiplying. With this in mind lets solve the problem:
[tex]\begin{gathered} \frac{b}{3}\text{ = M} \\ b\text{ = 3}\cdot M \end{gathered}[/tex]Is an irrational number?
In this case a rational number is a number that could be represented as p/q where q is different to 0 in this case pi can't be represete
how much money will be in Devon's retirement account if she continues to make the same monthly investment for 40 years
Annuities
It refers to a special form to accumulate interest over a regular payment or cash flow (C) per period.
Devon decides to save money for her retirement by depositing C=$524 each month in an account that is expected to earn interest with an APR of r=5.25% compounded monthly.
We will calculate the future value (FV) of her investment over a period of n=40 years.
The future value can be calculated with the formula:
[tex]FV=C\cdot\frac{(1+i)^n-1}{i}[/tex]Where i is the interest rate adjusted for the compounding period. Since there are 12 months in one year:
[tex]i=\frac{r}{12}=\frac{0.0525}{12}=0.004375[/tex]The number of periods is also adjusted for monthly compounding:
n = 40*12 = 480
Now apply the formula:
[tex]FV=524\cdot\frac{(1+0.004375)^{480}-1}{0.004375}[/tex]Calculating:
[tex]\begin{gathered} FV=524\cdot1,629.45 \\ FV=853,832.69 \end{gathered}[/tex]There will be $853,832.69 in Devon's retirement account in 40 years
Margo borrows $1400, agreeing to pay it back with 6% annual interest after 16 months. How much interest will she pay?
Given,
The principal amount is $1400.
The rate of interest is 6%.
The time period is 16 months.
Required
The interest paid by Morrow.
The simple interest is calculated as,
[tex]Simple\text{ interest=}\frac{P\times R\times T}{100}[/tex]Substituting the values then,
[tex]\begin{gathered} S.I=\frac{1400\times6\times16}{100\times12} \\ S.I=14\times2\times4 \\ S.I=56\times2 \\ S.I=112 \end{gathered}[/tex]Hence, the interest she will pay is $112.
if FE measures 20 centimeters, the approximate area of circle B is what
If FE measures 20 cm, then the area is 314 cm², if BE measure 3.5 cm, then the area is 38.5 cm², if AB measures 11 cm, then the area is 380 cm² and is EF measures 12 cm, then the area is 113 cm².
Area of a circle:
A = π r²
r = 1 /2 of diameter.
FE is the diameter
r = 20 / 2
r = 10 cm
Area of circle using FE:
A = π ( 10 )² = π × 100 = 314 cm²
BE is a radius:
Area = π × 3.5² = π × 12.25 = 38.465
A = 38.5 cm²
AB is a radius:
Area = π × 11²
A = π × 121
A = 379.94 = 380 cm²
EF is a diameter:
r = 12 / 2 = 6 cm
Area = π × 6²
A = π × 36
A = 113.04 = 113 cm²
Therefore, if FE measures 20 cm, then the area is 314 cm², if BE measure 3.5 cm, then the area is 38.5 cm², if AB measures 11 cm, then the area is 380 cm² and is EF measures 12 cm, then the area is 113 cm².
Learn more about area here:
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Your question was incomplete, Please refer the content below:
1) if FE measures 20 centimeters, the approximate area of circle B is what?
2) if BE measures 3.5 centimeters, the approximate area of circle B is what?
3) if AB measures eleven centimeters, the approximate area of circle B is what
4) If EF measures twelve centimeters, the approximate area of circle B is what?
What is the length, in whole meters, of the plastic edging that Amy needs to complete this project?
The curved path edges are in a form of two pairs of quadrants. One pair is shown below:
We can find the lengths of the inner and outer arcs using the radii of 4m and 6m respectively.
The formula to find the length of the arc of a quadrant is
[tex]L=\frac{1}{2}\pi r[/tex]Length of inner arc:
[tex]\begin{gathered} l=\frac{1}{2}\times\pi\times4 \\ l=6.3m \end{gathered}[/tex]Length of outer arc:
[tex]\begin{gathered} L=\frac{1}{2}\times\pi\times6 \\ L=9.4m \end{gathered}[/tex]Hence, the length of the pair of arcs is
[tex]6.3+9.4=15.7m[/tex]For the two pairs, we have the length to be
[tex]\begin{gathered} 15.7\times2 \\ =31.4m \end{gathered}[/tex]Hence, it will take approximately 32 meters of plastic edging to complete the project.
In the given diagram, line segment BDbisects angle ABC. Segment BDis extended to E, where line segment ECis parallel to line segment AB.Write a two-column proof to show that AB/AD=BC/DC
Explanation:
From the question , we will utilize the concept of isosceles triangles
Concept:
The isosceles triangle theorem states that the angles opposite to the equal sides of an isosceles triangle are equal in measurement. So, in an isosceles triangle △ABC where AB = AC, we have ∠B = ∠C.
From the steps, we can see that
[tex]\angle2\cong\angle5(substituting\text{ property of congruency\rparen}[/tex]Hence,
We can cconclude that the final answer is
[tex]EC=BC(properties\text{ of isosceles triangles\rparen}[/tex]
OPTION A is the correct answer
Answer:
EC = BC; property of isosceles triangle
Hope this helps!
Step-by-step explanation:
The plot below represents the function f ( x ) : 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Evaluate f ( 3 ) : f ( 3 ) =
Solution
The function represented by the graph is
The root of the equation are -0.5 , 1.5
[tex]\begin{gathered} x=-0.5,x=2.5 \\ (x+0.5)(x-2.5) \\ x^2-2.5x+0.5x-1.25 \\ x^2-2x-1.25 \end{gathered}[/tex]Therefore the function of x =
[tex]\begin{gathered} f(x)=x^2-2x-1.25 \\ f(3)=3^2-2(3)-1.25 \\ f(3)=9-6-1.25 \\ f(3)=1.75 \end{gathered}[/tex]Hence the correct value of f(3) = 1.75
Vector u has initial point at (8, 6) and terminal point at (–6, 12). Which are the magnitude and direction of u?
SOLUTION
Write out the given point
[tex](8,6)\text{ and (-6,12)}[/tex]The magnitude of the vertor u is the distance between the two point.
[tex]\begin{gathered} \text{distance = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{Where } \\ x_2=-6,x_1=8 \\ y_2=12,y_1=6 \end{gathered}[/tex]Substitute into the formula, we have
[tex]\begin{gathered} \mleft\Vert u\mleft\Vert=\sqrt[]{(-6-8)^2+(12-6)^2}\mright?\mright? \\ \mleft\Vert u\mleft\Vert=\sqrt[]{(-14)^2+6^2}\mright?\mright? \\ \mleft\Vert u\mleft\Vert=\sqrt[]{169+36}=\sqrt[]{232}\mright?\mright? \end{gathered}[/tex]Hence
|| u || =15.23
The magnitude of the vector is 15.232
Then the direction is obtain by using the formula
[tex]\begin{gathered} \tan \theta=\frac{y_2-y_1}{x_2-x_1} \\ \text{Then } \\ \tan \theta=\frac{12-6}{-6-8}=\frac{6}{-14}=-0.4286 \end{gathered}[/tex]Then we have
[tex]\tan \theta=-0.4286[/tex]take inverse tan of the equation above, we have
[tex]\begin{gathered} \theta=\tan ^{-1}(-0.4286) \\ \theta=156.801^0 \end{gathered}[/tex]Hence
The direction is of u is 156.801°
Answer: Second Option
In the expansion of (3a + 4b)^8, which of the following are possible variable terms?
Remember the Binomial Theorem:
[tex](a+b)^n\text{ =}\sum_{i\mathop{=}0}^n\begin{bmatrix}{n} & \\ {i} & {}\end{bmatrix}a^{(n\text{ - i})}b^i[/tex]Now, consider the following polynomial:
[tex]\left(3a+4b\right)^8[/tex]Applying the Binomial Theorem, where:
a = 3a
b= 4b
we get:
[tex](3a+4b)^8\text{ =}\sum_{i\mathop{=}0}^8\begin{bmatrix}{8} & \\ {i} & {}\end{bmatrix}3a^{(8\text{ - i})}4b^i[/tex]thus, expanding the sum, we get:
[tex]\begin{gathered} \frac{8!}{0!(8\text{ -0})!}(3a)^8(4b)^0+\frac{8!}{1!(8\text{ -1})!}(3a)^7(4b)^1+\frac{8!}{2!(8\text{-2})!}(3a)^6(4b)^2 \\ +\frac{8!}{3!(8\text{ - 3})!}(3a)^5(4b)^3\text{ + ........+}\frac{8!}{8!(8\text{ -8})!}(3a)^0(4b)^8 \end{gathered}[/tex]Now, simplifying we get:
[tex]\begin{gathered} 6561a^8\text{ + 6998a}^7b\text{ + 326592a}^6b^2+870912a^5b^3+1451520a^4b^4 \\ +1548288a^3b^5+1032192a^2b^6+393216ab^7+65536b^8 \end{gathered}[/tex]then, we can conclude that the correct answer is:
Answer:The variable terms are:
[tex]\begin{gathered} a^8\text{ ,a}^7b\text{ , a}^6b^2,\text{ }a^5b^3,\text{ }a^4b^4 \\ ,\text{ }a^3b^5,\text{ }a^2b^6,\text{ }ab^7\text{ and }b^8 \end{gathered}[/tex]At the Dollar Spot, Carl bought pencils for $3.75, sharpies for $5 69, and glue sticks for ? 1. In the box below type which operation you would use: Division Addition Subtraction Multiplication 2. Why did you pick this operation?
Given that Carl bought pencils for $3.75, sharpies for $5 69, and glue sticks for
Although the question didn't give the value for glue sticks, the operation you would use here is Addition.
Addition symbol: +
2. I picked addition because to find the total amount Carl spent at the Dollar spot, you will need to add the amount he spent on pencils, sharpies and glue together.
Jody invested $4400 less in account paying 4% simple interest than she did in an account paying 3 percent simple interest. At the end of the first year, the total interest from both accounts was $592. find the amount invested in each account
The rule of the simple interest is
[tex]I=P\times R\times T[/tex]P is the initial amount
R is the rate in decimal
T is the time
Assume that she invested $x in the account that paid 3% simple interest
then she invested x - 4400 dollars in the account that paid 4% simple interest
Then let us find each interest, then add them, equate the sum by 592
[tex]\begin{gathered} P1=x-4400 \\ R1=\frac{4}{100}=0.04 \\ T1=1 \\ I1=(x-4400)\times0.04\times1 \end{gathered}[/tex]Let us simplify it
[tex]\begin{gathered} I1=0.04(x)-0.04(4400) \\ I1=0.04x-176 \end{gathered}[/tex][tex]\begin{gathered} P2=x \\ R2=\frac{3}{100}=0.03 \\ T2=1 \\ I2=x\times0.03\times1 \\ I2=0.03x \end{gathered}[/tex]Since the total interest is $592, then
[tex]\begin{gathered} I1+I2=592 \\ 0.04x-176+0.03x=592 \end{gathered}[/tex]Add the like terms on the left side
[tex]\begin{gathered} (0.04x+0.03x)-176=592 \\ 0.07x-176=592 \end{gathered}[/tex]Add 176 to both sides
[tex]\begin{gathered} 0.07x-176+176=592+176 \\ 0.07x=768 \end{gathered}[/tex]Divide both sides by 0.07 to find x
[tex]\begin{gathered} \frac{0.07x}{0.07}=\frac{768}{0.07} \\ x=10971.42857 \end{gathered}[/tex]Then She invested about 10971 dollars in the account of 3%
Since 10971 - 4400 = 6571
Then she invested about
Suppose that only two factories make Playstation machines. Factory 1 produces 70% of the machines and Factory 2 produces the remaining 30%. Of the machines produced in Factory 1, 2% are defective. Of the machines produced in Factory 2, 5% are defective. What proportion of Playstation machines produced by these two factories are defective? Suppose that you purchase a playstation machine and it is defective. What is the probability that it was produced by Factory 1?
Given:
Factory 1 produces 70%
Factor 2 produces 30%
Defective machines in factory 1 = 2%
Defective machines in factory 2 = 5%
Find-:
What is the probability that it was produced by Factory 1?
Explanation-:
Probability of machines produced by factory1
[tex]\begin{gathered} P(F_1)=70\% \\ \\ P(F_1)=\frac{70}{100} \\ \\ P(F_1)=\frac{7}{10} \\ \end{gathered}[/tex]Probability of machines produced by factory 2
[tex]\begin{gathered} P(F_2)=30\% \\ \\ P(F_2)=\frac{30}{100} \\ \\ P(F_2)=\frac{3}{10} \end{gathered}[/tex]Probability of factory 1 produced defective item,
[tex]\begin{gathered} P(\frac{x}{F_1})=2\% \\ \\ P(\frac{x}{F_1})=\frac{2}{100} \\ \\ P(\frac{x}{F_1})=\frac{1}{50} \end{gathered}[/tex]Probability of factory 2 produced defective item,
[tex]\begin{gathered} P(\frac{x}{F_2})=5\% \\ \\ P(\frac{x}{F_2})=\frac{5}{100} \\ \\ P(\frac{x}{F_2})=\frac{1}{20} \end{gathered}[/tex]So, the probability that randomly selected items was form factor 1.
[tex]P(\frac{F_1}{x})\text{ is}[/tex]Now, apply Bayes theorem is:
[tex]P(\frac{F_1}{x})=\frac{P(F_1)P(\frac{x}{F_1})}{P(F_1)P(\frac{x}{F_1})+P(F_2)P(\frac{x}{F_2})}[/tex]So, the value is:
[tex]\begin{gathered} =\frac{\frac{7}{10}\times\frac{1}{50}}{\frac{7}{10}\times\frac{1}{50}+\frac{3}{10}\times\frac{1}{20}} \\ \\ =\frac{\frac{7}{500}}{\frac{7}{500}+\frac{3}{200}} \\ \\ =\frac{\frac{7}{5}}{\frac{7}{5}+\frac{3}{2}} \\ \\ =\frac{\frac{7}{5}}{\frac{14}{10}+\frac{15}{10}} \\ \\ =\frac{\frac{7}{5}}{\frac{14+15}{10}} \\ \\ =\frac{7}{5}\times\frac{10}{29} \\ \\ =\frac{14}{29} \end{gathered}[/tex]So, the probability is 14/29.
Solve the following equation on the interval [0°, 360º). Round answers to the nearest tenth. If there is no solution, indicate "No Solution."2sec^2(x) - 13tan(x) = -13
Given
[tex]2\sec ^2(x)-13\tan (x)=-13[/tex]Add 13 to both sides
[tex]\begin{gathered} 2\sec ^2(x)-13\tan (x)+13=-13+13 \\ 2\sec ^2(x)-13\tan (x)+13=0 \end{gathered}[/tex]We have that
[tex]\sec ^2(x)=1+\tan ^2(x)[/tex]So, substitute in the above equation
[tex]2(1+\tan ^2(x))-13\tan (x)+13=0[/tex]Simplify
[tex]\begin{gathered} 2+2\tan ^2(x)-13\tan (x)+13=0 \\ 15+2\tan ^2(x)-13\tan (x)=0 \end{gathered}[/tex]Reordering the equation
[tex]2\tan ^2(x)-13\tan (x)+15=0[/tex]We get a quadratic equation, then solve by factoring
[tex](2\tan (x)-3)(\tan (x)-5)=0[/tex]Separate the solutions
[tex]\begin{gathered} 2\tan (x)-3=0 \\ 2\tan (x)-3+3=0+3 \\ 2\tan (x)=3 \\ \frac{2\tan (x)}{2}=\frac{3}{2} \\ \tan (x)=\frac{3}{2} \end{gathered}[/tex]And
[tex]\begin{gathered} \tan (x)-5=0 \\ \tan (x)-5+5=0+5 \\ \tan (x)=5 \end{gathered}[/tex]Next, solve for x for each solution
[tex]\begin{gathered} \tan (x)=\frac{3}{2} \\ x=\tan ^{-1}(\frac{3}{2}) \\ x=56.3 \end{gathered}[/tex]And
[tex]\begin{gathered} \tan (x)=5 \\ x=\tan ^{-1}(5) \\ x=78.7 \end{gathered}[/tex]Answer:
x = 56.3° and x = 78.7°
2. The water level in a reservoir is now 52 meters. Which equation can be used to find the initial depth, d, if this is the water level after a 23% increase? * O 0.23. d = 52 O d = 52 · 0.23 O 1.23. d = 52 O d = 52. 1.23
Answer:
1.23d = 52
Explanation:
If 52 meters is the water level after a 23% increase, then we can say that the initial depth d added to the 23% of d is equal to 52 meters. So:
d + 23%d = 52 meters
Since 23% is equivalent to 0.23, we get:
d + 0.23d = 52
Finally, adding the like terms, we get:
(1 + 0.23)d = 52
1.23d = 52
So, the equation is:
1.23d = 52
A doctor conducts an experiment to test new treatments for a medical condition. Out of the 6 volunteers in the experiment, 4 do not receive any treatment. What percent of the volunteers do not receive any treatment?
ANSWER
66.67%
EXPLANATION
We have that there were 6 volunteers in the experiment and 4 do not receive any treatment.
To find the percent of volunteers that do not receive any treatment, we have to divide the number of people that do not receive treatment by the total number of people that were in the experiment and multiply by 100.
That is:
[tex]\frac{4}{6}\cdot\text{ 100 = 66.67\%}[/tex]That is the percent of volunteers that do not receive any treatment.
Write down 2 fractions where the denominator of one is a multiple of the denominator of other
The two fractions are 1/3 and 1/6.
What is a fraction?A fraction has two parts: Numerator and Denominator.
It is in the form of a Numerator / Denominator. A fraction is a numerator divided by the denominator.
We need to write 2 fractions where the denominator of one is a multiple of the denominator of the other.
Let's consider the one fraction as;
1/3
Then another one must be multiple of the denominator of the other.
So, 1/6
We see that "the denominator of one is a multiple of the denominator of other".
Thus the two fractions are 1/3 and 1/6.
Learn more about fractions here:
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A tank has a capacity of 13 gallons. When it is full, it contains 20% alcohol. How many gallons must be replaced with an 70% alcohol solution to give 13 gallons of 30% solution? Round your final answer to 1 decimal place if necessary.
Given:
A tank has a capacity of 13 gallons. When it is full.
The tank contains 20% alcohol.
We will find the number of gallons that must be replaced with a 70% alcohol solution to give 13 gallons of 30% solution
Let the number of gallons that must be replaced = x
so, there are x gallons with a 70% alcohol and (13 -x) with a 20% alcohol.
So, we can write the following equation:
[tex]70x+20(13-x)=30*13[/tex]Solve the equation to find (x):
[tex]\begin{gathered} 70x+20*13-20x=30*13 \\ 50x+260=390 \\ 50x=390-260 \\ 50x=130 \\ x=\frac{130}{50}=2.6\text{ gallons} \end{gathered}[/tex]So, the answer will be 2.6 gallons
One custodian cleans a suite of offices in 8 hours. When a second worker is asked to join the regular custodian, the job takes only 4 hours. How long does it take thesecond worker to do the same job alone?The second worker can do the same job alone in___hours.
Given:
One custodian cleans a suite of offices in 8 hours.
So, the rate of the custodian to clean the office = 1/8
When a second worker is asked to join the regular custodian, the job takes only 4 hours.
So, the rate of both custodians = 1/4
Let the rate of the second custodian = x
So,
[tex]\frac{1}{8}+x=\frac{1}{4}[/tex]Solve for x:
[tex]x=\frac{1}{4}-\frac{1}{8}=\frac{1}{8}[/tex]So, the rate of the second custodian = 1/8
This means he will take 8 hours to clean the office alone
So, the answer will be:
The second worker can do the same job alone in 8 hours.
Lin is solving the inequality 15-x< 14. She knows the solution to the equation 15 - x = 14 is x = 1 How can Lin determine whether x > Torx < 1 is the solution to the inequality?
The inequality we have is:
[tex]15-x<14[/tex]To solve this problem the x has to be positive, for this reason, the first step is to add x to both sides of the inequality:
[tex]15-x+x<14+x[/tex]As you can see, on the left side -x+x is equal to 0. So we have:
[tex]15<14+x[/tex]The next step to solving for x, now that the x is positive, is to leave the term with x alone on one side of the inequality. For this reason, we need to subtract 14 to both sides of the inequality:
[tex]15-14<14-14+x[/tex]On the right side, 14-14 is equal to 0, and thus we will be left only with "x" on that side:
[tex]15-14On the left side, 15-14 is equal to 1:[tex]1This can be read as follows: "x is greater than 1".And we can also write this solution with the x at the beginning:
[tex]x>1[/tex]Answer: x>1