We are being asked to subtract two mixed numbers, 7 2/3 - 3 7/8,
First, we need to convert the mixed numbers to improper fractions:
[tex]7\frac{2}{3}-3\frac{7}{8}=\frac{21+2}{3}-\frac{24+7}{8}=\frac{23}{3}-\frac{31}{8}[/tex]Until now, we have changed to improper fractions, now we can make the difference:
[tex]\frac{23}{3}-\frac{31}{8}=\frac{(23\cdot8)-(3\cdot31)}{24}=\frac{184-93}{24}=\frac{91}{24}[/tex]It takes Nina 6 hours to proof a chapter of Hawkes Learning Systems' College Algebra book and it takes Mandy 2 hours. How long would it take them working together? (Round your answer to two decimal places.)
Time taken by Nina to complete the chapter = was 6 hours.
Amount of chapter completed in 1 hour = 1/6.
[tex]\frac{1}{2}[/tex]Mandy takes the time to complete the chapter = 2 hours.
Amount of chapter completed in 1 hour = 1/2.
Amount of chapters completed by both in 1 hour is calculated as,
[tex]\begin{gathered} For\text{ 1 hour = }\frac{1}{6}+\frac{1}{2} \\ For\text{ 1 hour = }\frac{1}{6}_+\frac{3}{6} \\ For\text{ 1 hour = }\frac{4}{6}\text{ = }\frac{2}{3} \end{gathered}[/tex]Thus the amount of time taken by both of them to complete the chapter is
[tex]\frac{3}{2}\text{ hours or 1.5 hours}[/tex]If the formula R=-0.037t + 50.1 can be used to predict the world record in the 400-meter dash 400-m after 1925, for what years will the world records be 48.6 seconds or less?
Step 01:
Data
R=-0.037t + 50.1
Step 02:
You and your group need to calculate the height of the triangle below to emboss a pennant. Assume that the triangle is isosceles. Assume the angle between the two identical sides is 70 degrees and that the opposite side is 3 metres. Calculate the height of the triangle to the nearest tenth of a cm.
To find the height of a isosceles triangle having the angle between the equal sides and the opposite side of it use the next properties:
The line that describes the height of an isosceles triangle is a bisector of angle between equal sides, and also a bisector of opposite side (different side).
Using the right triangle formed and the next trigonometric ratio find h:
[tex]tan\theta=\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} tan(\frac{70}{2})=\frac{3/2}{h} \\ \\ tan35=\frac{1.5}{h} \end{gathered}[/tex]solve h:
[tex]\begin{gathered} h*tan35=1.5 \\ h=\frac{1.5}{tan35} \\ \\ h=2.14m \end{gathered}[/tex]The height of the given triangle is: 2.1m (tenth of a meter)2. Lori Koetters was looking at different simple discount notes available to her. She found a note that would cost her $125 in interest at 8% for 90 days. What was the face value?
Answer:
$6336.81
Explanation:
Given:
• Expected cost of the simple discount note = $125
,• Rate, r = 8%
,• Time = 90 days = 90/365 year
We want to find the face value (or principal).
Using the simple interest formula:
[tex]\text{ Simple Interest}=\frac{Principal\times Rate\times Time}{100}[/tex]Substitute the given values:
[tex]125=\frac{P\times8\times\frac{90}{365}}{100}[/tex]Then solve for the value of P:
[tex]\begin{gathered} 125=\frac{P\times8\times\frac{90}{365}}{100} \\ \text{Cross multiply} \\ 125\times100=P\times8\times\frac{90}{365} \\ Divide\text{ both sides by }8\times\frac{90}{365} \\ P=\frac{125\times100}{8\times\frac{90}{365}} \\ P=\$6336.81 \end{gathered}[/tex]The face value of the note is $6336.81.
Look at the simultaneous equations below.
x - 9y = 10
3y² = 4x + 7
a) Show that 3y² – 36y – 47 –=0
b) Use part a) to solve the simultaneous equations.
If any of your answers are decimals, give them to 1 d.p.
Two values of y will be y = 4.7 and y = 3.7
a. First we will take equation 1 that is
x - 9y = 10
x = 10 + 9y
from here we get x as 10 + 9y and now we will put it in equation 2 which is
3[tex]y^{2}[/tex] = 4x + 7
3[tex]y^{2}[/tex] = 4 ( 10 + 9y ) + 7
3[tex]y^{2}[/tex] = 40 + 36y + 7
3[tex]y^{2}[/tex] - 36y - 47 = 0
Here we can clearly see that 3[tex]y^{2}[/tex] - 36y - 47 = 0
b. Formula of finding roots of a quadratic equation is
y = ( -b ± [tex]\sqrt{b^{2} - 4ac}[/tex] ) / 2a
Put value of b , a and c in the formula.
b = -3
a = 3
c = -47
y = ( 3 ± [tex]\sqrt{9^{2} - 4 * 3 * 47 }[/tex] ) / 2 * 3
By solving this we get
y = ( 3 + 25.4 ) / 6 and y = ( 3 - 25.4 ) / 6
Therefore two values of y will be y = 4.7 and y = 3.7
To know more about quadratic equations
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Use two points on the line to find the equation
To find the equation of the line, we would use two points (-3,0) and (3,2)
We use the equation of a line in 2 point form;
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]We input the points to obtain;
[tex]\begin{gathered} \frac{y-0}{x+3}=\frac{2-0}{3+3} \\ \frac{y}{x+3}=\frac{2}{6} \\ \text{cross multiply} \\ y=\frac{2}{6}(x+3) \\ y=\frac{2}{6}x+1 \end{gathered}[/tex]Therefore, the equation is standard form is;
[tex]y=\frac{2}{6}x+1[/tex][tex]f(x) = x ^{3} + 6x ^{2} + 8x[/tex]find the zeros. is itx= 0,-2,-4x= 0,2,4x= 2,4x= -2,-4
Given the function:
[tex]f(x)=x^3+6x^2+8x[/tex]Let's find the zeros of the function.
To find the zeros of the function, take the following steps.
Step 1:
Set the function to zero
[tex]x^3+6x^2+8x=0[/tex]Step 2:
Factor the left side of the equation
Factor x out:
[tex]x(x^2+6x+8)=0_{}[/tex]Now factor using the AC method:
[tex]x(x+2)(x+4)=0[/tex]We have the factors:
x, x+2, x+4
Step 3:
Equate the individual factors to zero.
Thus, we have:
[tex]\begin{gathered} x=0 \\ \\ x+2=0 \\ \\ x+4=0 \end{gathered}[/tex]Step 4:
Solve each equation for x to get the zeros
• x = 0
• x + 2 = 0
Subtract 2 from both sides:
x + 2 - 2 = 0 - 2
x = -2
• x + 4 = 0
Subtract 4 from both sides:
x + 4 - 4 = 0 - 4
x = -4
Therefore, the zeros of the function are:
x = 0, -2, -4
ANSWER:
[tex]x=0,-2,-4[/tex]help me with this question
we where given the following
Red = 30
Green = 29
Both Red and Green = 17
if there are 17 of them that likes both kinds of jelly beans, there are 17 of them that like both and those are taken into account for the red and green statistics.
in order to provide a nuber of students that like only red, we must ignore those who like both
so,
Only Red = Red - Both
recall, Red = 30
Both = 17
therefore,
Only Red = 30 -17
Only Red =13
A road rises 6 m over a distance of 80 m. What is the gradient angle of the road?
From the statement, we know that the road:
• rises Δy = 6 m,
,• over a distance Δx = 80 m.
The slope of the road (m) and gradient angle (θ) are given by:
[tex]m=\tan(θ)=\frac{\Delta y}{\Delta x}\Rightarrowθ=\tan^{-1}(\frac{\Delta y}{\Delta x})[/tex]Replacing the data of the problem, we get:
[tex]\theta=\tan^{-1}(\frac{6m}{80m})\cong4.289\degree.[/tex]AnswerThe gradient angle of the road is approximately 4.289°.
need help ! an i need it now litterly
The volume of the new structure is given by:
[tex]\begin{gathered} V3=2(V2) \\ V3=2(27) \\ V3=54in^3 \end{gathered}[/tex]Therefore, the dimensions of block D must be given by:
[tex]06543-64 3-22507Find the slope of the line.Slope = m =Enter your answer as an integer or as a reduced fraction in the form A/B.
The slope equation is given by:
[tex]m=\frac{y_2-y_1}{x_{_2}-x_1}[/tex]To get the slope of the graph, we will pick two points along the line:
Let's pick the first point at (x, y) = (-6, 6)
Let's pick the second point at (x, y) = (0, -2)
We plug this into the slope equation, we have:
[tex]\begin{gathered} m=\frac{-2-6}{0--6}=-\frac{8}{6} \\ m=-\frac{4}{3} \end{gathered}[/tex]The slope (m) = -4/3
you are machinist setting up a part that requires a5/8 inch diameter finished hole.stardart practice is to drill an initial ghole with adiameter that is undersided by 1/32 inch before finishing What should be the diameter inches of the initial hole?
We will have that the initial diameter will be:
[tex]\frac{5}{8}-\frac{1}{32}=\frac{19}{32}=0.59375[/tex]So, the initial diameter has to be 19/32 inches.
how did the equation shift from the parent function?y=f(x-4)the answer choices is A. vertical stretch by 4b. shift right by 4 C. Shift left by 4 D. Shift down by 4 E. horizontal stretch by 4
We can translate a function on its two axis. If we want to translate it on the vertical axis we need to add or subtract the constant that determines the translation by the end of the function, as seen below:
[tex]f(x)+c[/tex]If the constant is positive, then the function will be translated up, if its negative it'll be translated down.
We can also shift the function on its horizontal axis. To do that we have to add a constant in the argument of the function as seen below:
[tex]f(x+c)[/tex]If the constant is negative, the shift will happen on the right direction. If the constant is positve, the shift will be on the left direction.
The function given to us is:
[tex]y=f(x-4)[/tex]This falls on the second type of translation and the constant is negative, therefore there is a shift to the right by 4 units. The correct answer is b.
find the slope from the points (5,-1)and (8,-6)
In order to find the slope of the a line that connects the given points, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are the given points.
Replace the following coordinates in the formula for m:
(x1,y1) = (5,-1)
(x2,y2) = (8,-6)
[tex]m=\frac{-6-(-1)}{8-5}=\frac{-6+1}{3}=\frac{-5}{3}=-\frac{5}{3}[/tex]
Hence, the slope is -5/3
If the expressión 2x(25+50) which expressión for finding the perimetral is Also correct
Answer:
C. (2 x 50) + (2 x 25)
Explanation:
We are asked to give another form of the expression given.
Expanding the expression 2x(25+50) gives
[tex](2\times25)+(2\times50)[/tex]Which matches the expression given in choice C; therefore C is the correct answer.
Suppose that IQ scores have a a bell shaped distribution with a mean of 96 and the standard deviation of 17. Using the empirical rule what percentage of IQ scores are no more than 79 please do not round your answer
GIVEN:
We are given that IQ scores have a bell shaped distribution with a mean of 96 and a standard deviation of 17.
Required;
Using the emperical rule, what percentage of IQ scores are no more than 79?
Step-by-step explanation;
For a bell-shaped distribution, we already know that,
68% of the data set lies within one standard deviation
95% of the data set lies within two standard deviations
99.7% of the data set lies within three standard deviations
The condition given is that the IQ scores are no more than 79, hence;
[tex]\begin{gathered} n=\frac{79-96}{17} \\ \\ n=\frac{-17}{17}=-1 \end{gathered}[/tex]Now we can see that the IQ score of 79 is 1 standard deviation to the left of the mean (that is to the left of 96).
We also take note that 68% of the data set lies within one standard deviation on either side of the mean.
Therefore, for the IQ scores to be 1 standard deviation from the mean, we would have;
[tex]\begin{gathered} \frac{1-68\%}{2}=\frac{1-0.68}{2} \\ \\ =0.16 \end{gathered}[/tex]Expressed as a percentage, we now have
[tex]1.6\%[/tex]ANSWER:
Therefore, 1.6% of IQ scores would be no more than 79.
In school, there are 800 students and 80 faculty members. 500 students and 50faculty members are males. If a person is selected at random, then find theprobability that the selected person is a faculty member or a female.
For non-mutually exclusive events, the probability can be calculated using the formula
[tex]P(A\text{ or B) = P(A) + P(B) - P(A }\cap B)[/tex]Let's take
A = Faculty Member
B = Female
The probability of A will be
[tex]P(A)=\frac{80}{880}[/tex]The probability of B will be
[tex]P(B)=\frac{330}{880}[/tex]The probability of (A n B), that is, the number of faculty members that are females, will be
[tex]P(A\cap B)=\frac{30}{880}[/tex]Therefore, the probability will be calculated as
[tex]\begin{gathered} P(\text{A or B) }=\text{ }\frac{80}{880}+\frac{330}{880}-\frac{30}{880} \\ =\frac{380}{880} \\ =0.432 \end{gathered}[/tex]The probability is 0.43.
Can you please explain to me how this is done
As mentioned in the question, Line a and Line b are parallel to each other and these two lines are cut by the transversal line c.
Since line b is cut by the transversal line c forming the angles measuring 64° and y°, these angles are called linear pairs. The sum of the angles of a linear pair is 180°. Hence, we can say that:
[tex]64\degree+y\degree=180\degree[/tex]From that equation, we can solve for the value of y.
[tex]\begin{gathered} y\degree=180-64 \\ y\degree=116 \end{gathered}[/tex]Therefore, the value of y is 116°.
On the other hand, angle x and angle y are what we call alternating exterior angles. By definition, alternating exterior angles are congruent. Hence, the value of x is also 116°.
Why are x and y alternating exterior angles? X and Y are alternating exterior angles because first, they are angles found outside lines a and b, hence, the word exterior. Also, angles x and y do not lie on the same side of the transversal. Hence, the word alternating.
1. Rationalize the numerator of the expression below and simplify your answer.V3 - 2V12+1A
Answer:
[tex]\frac{-1}{8+5\sqrt{3}}[/tex]The expression we have is:
[tex]\frac{\sqrt{3}-2}{\sqrt{12}+1}[/tex]To rationalize the numerator we must do as follows:
[tex]\frac{\sqrt{3}-2}{\sqrt{12}+1}\cdot\frac{\sqrt{3}+2}{\sqrt{3}+2}[/tex]We multiply the whole expression by the numerator, but we change the sign.
Next, we combine the two fractions:
[tex]\frac{(\sqrt{3}-2)(\sqrt{3}+2)}{(\sqrt{12}+1)(\sqrt{3}+2)}[/tex]Now we use the distributive property to multiply each term (this is to multiply each term in each parenthesis by each term in the other parenthesis besides them).
[tex]\frac{\sqrt{3}\cdot\sqrt{3}+2\sqrt{3}-2\sqrt{3}-2\cdot2}{\sqrt{12}\cdot\sqrt{3}+2\sqrt{12}+1\cdot\sqrt{3}+1\cdot2}[/tex]We simplify the multiplications, and cancel the two middle terms in the numerator:
[tex]\begin{gathered} \frac{\sqrt{3\cdot3}-4}{\sqrt{12\cdot3}+2\sqrt{12}+\sqrt{3}+2} \\ \end{gathered}[/tex]we simplify again:
[tex]\frac{\sqrt{9}-4}{\sqrt{36}+2\sqrt{12}+\sqrt{3}+2}[/tex]We solve the square roots of 9 (which is 3) and 36 (which is 6)
[tex]\frac{3-4}{6+2\sqrt{12}+\sqrt{3}+2}[/tex]Solving the numerator
[tex]\frac{-1}{6+2\sqrt{12}+\sqrt{3}+2}[/tex]And finally what we can do simplify further is to express the square root of 12 as follows:
[tex]\sqrt{12}=\sqrt{4\cdot3}=2\sqrt{3}[/tex]Substituting this into our expression:
[tex]\begin{gathered} \frac{-1}{6+2(2\sqrt{3})+\sqrt{3}+2} \\ \\ \frac{-1}{6+4\sqrt{3}+\sqrt{3}+2} \end{gathered}[/tex]We add 4 and 1 square roots of 3 in the denominar and get 5 square root of 3:
[tex]\frac{-1}{8+5\sqrt{3}}[/tex]also we added 6+2 which is 8.
That is the simplified answer.
how to solve this problem, find the variance. Round your answer to one decimal place. Previous answer: mean = 5.8.
To calculate the variance in this case, we need to use the variance for a discrete variable and its probability.
The equation we need to use in this case is:
[tex]\sigma=\sum ^{}_i(x_i-\mu)^2P(x_i)[/tex]Where x_i is each value in the first row and P(x_i) is each value in the second row.
First, let's calculate each square difference:
[tex]\begin{gathered} (4-5.8)^2=(-1.8)^2=3.24 \\ (5-5.8)^2=(-0.8)^2=0.64 \\ (6-5.8)^2=(0.2)^2=0.04 \\ (7-5.8)^2=(1.2)^2=1.44 \\ (8-5.8)^2=(2.2)^2=4.84 \end{gathered}[/tex]Now, we need to multiply each for its corresponding P(x):
[tex]\begin{gathered} 3.24\cdot0.3=0.972 \\ 0.64\cdot0.2=0.128 \\ 0.04\cdot0.1=0.004 \\ 1.44\cdot0.2=0.288 \\ 4.84\cdot0.2=0.968 \end{gathered}[/tex]Finally, we sum them all to get the variance:
[tex]\sigma=\sum ^{}_i(x_i-\mu)^2P(x_i)=0.972+0.128+0.004+0.288+0.968=2.360\approx2.4[/tex]So, the variance to one decimal place is 2.4.
centered at theWhat is the image of (–12, 4) after a dilation by a scale factor oforigin?
Multiply the coordinate points by the scale factor
-12 x 1/2 = -6
4 x 1/2 = 2
Solution: (-6,2)
Question attached as screenshot below, please help. I am happy to contribute as much as I can.
Given
[tex]f(0)=6[/tex]To find the absolute maximum value of f(x) in the interval [0,3].
Explanation:
It is given that,
[tex]f(0)=6[/tex]That implies,
[tex]\begin{gathered} f(0)=0+6 \\ \therefore f(x)=x+6 \end{gathered}[/tex]Hence, the absolute maximum of f(x) is,
[tex]\begin{gathered} f(2)=2+6 \\ =8 \end{gathered}[/tex]A construction worker needs to put a rectangular window in the side of abuilding. He knows from measuring that the top and bottom of the windowhave a width of 9 feet and the sides have a length of 12 feet. He alsomeasured one diagonal to be 15 feet. What is the length of the otherdiagonal?A. 12 feetB. 15 feetC. 21 feetD. 9 feet
The Solution.
Representing the problem in a diagram, we have
The rectangular window has two diagonals, and both diagonals are equal in length. If the length of one of them is 15 feet (as stated in theHence, the length of the
23. ABCD is a rectangle. If m21-5x and m22 - 8x -1, find x, m<1, and m<2.ABEDm
If ABCD is a rectangle, each of its four angles at the vertex is a right angle.
Then the angle at D is a right angle (measure of 90 degrees).
The right angle is divided in two angles, <1 and <2, by the diagonal, so <1 and <2 are complementary.
Then, we can write:
[tex]\begin{gathered} m\angle D=m\angle1+m\angle2=90\degree \\ (5x)+(8x-1)=90 \\ 13x-1=90 \\ 13x=90+1 \\ 13x=91 \\ x=\frac{91}{13} \\ x=7 \end{gathered}[/tex]Then, with the value of x we can calculate m<1 and m<2:
[tex]\begin{gathered} m\angle1=5x=5\cdot7=35\degree \\ m\angle2=8x-1=8\cdot7-1=56-1=55\degree \end{gathered}[/tex]Answer:
x = 7
m<1 = 35º
m<2 = 55º
What’s is the ratio to t shirts and shorts to sunglasses In the simplest form?
The ratio of t shirts and shorts to sunglasses is, (t-shirts + shorts) : sunglasses
We have 25 t-shirts and 15 shorts, total 40 t-shirts and shorts. And 10 sunglasses.Then the ratio is:
[tex]\frac{25+15}{10}=\frac{40}{10}=\frac{4}{1}[/tex]4 t-shirts and shorts per 1 sunglass
Answer: B. 4 to 1
need to find y hypotunse with 45 45 and 90 degree angles and a side length of 85
85√2.
1) Since we have a right triangle with two congruent angles, then we can find the hypotenuse by using a trigonometric ratio:
[tex]\begin{gathered} \sin (45)=\frac{85}{y} \\ \frac{\sqrt[]{2}}{2}=\frac{85}{y} \\ y\sqrt[]{2}=170 \\ y=\frac{170}{\sqrt[]{2}}\times\frac{\sqrt[]{2}}{\sqrt[]{2}} \\ y=\frac{170\sqrt[]{2}}{2} \\ y=85\sqrt[]{2} \end{gathered}[/tex]2) So the hypotenuse is 85√2
Another way to find that out is considering that the hypotenuse would be the diagonal of a square (since we have two 45º angles and one right angle (90º) and the diagonal of a square is a√2 then 85√2
5) Write and solve an inequality for the following:Six less than the product of -2 and a number is greater than -18.
Solution
- Let the unknown number be x. It is this number we are trying to solve for.
- We are told that "Six less than the product of -2 and a number...".
- The product of -2 and a number can be written as:
[tex]-2\times x=-2x[/tex]- The same statement says that we need to make the product of -2 and a number less by 6. That is, we subtract 6 from the product of -2 and a number.
- Thus, we can say:
[tex]-2x-6[/tex]- The above mathematical statement implies "Six less than the product of -2 and a number...".
- Next, we are told that everything is greater than -18. Thus, we can conclude the inequality as follows:
[tex]-2x-6>-18[/tex]- Now that we have the inequality, we can proceed to solve for the unknown number x as follows;
[tex]\begin{gathered} -2x-6>-18 \\ \text{ Add 6 to both sides} \\ -2x>-18+6 \\ -2x>-12 \\ \text{ Divide both sides by -2} \\ \\ -\frac{2x}{-2}<-\frac{12}{-2} \\ \\ \therefore x<6 \\ \\ (\text{ Notice that the inequality sign changed because we divided both sides by a negative number\rparen} \end{gathered}[/tex]- Thus the solution is x < 6
Write two questions about this data that you can interpret from the distribution. write the solution to you questions.
Problem
Solution
For this case we can create the following two questions:
1) what are the mean, median and mode from the data given?
2) What are the standard deviation and the variance from the data given?
Natasha got a raise on her hourly wage, and the graph shows the amount of money she has made this year since her rate of pay was increased..A. Before her raise, Natasha made $12.50 an hour.B. Before her raise, Natasha made $25.00 an hour. C. After her raise, Natasha makes $12.50 an hour. D. After her raise, Natasha makes $25.00 an hour
order to determine the rate of change of the given function, use the following formula:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are any two points of the line.
Use, for example:
(x1,y1) = (0,250)
(x2,y2) = (20,500)
replace the previous values of the coordinates into the expression for m:
m = (500 - 250)/(20 - 0)
m = 250/20
m = 12.5
Hence, the correctstament is:
C. After her raise, Natasha makes $12.50 an hour.
Apple had their iphones on sale for 20% off during labor day weekend. If iphones originally cost 345.00, how much would you pay during the labor day weekend?
If Apple had their iphones on sale for 20% off during labor day weekend and the original cost of iphone is 345.00, the discount on the price during the labour weeked will be expressed as;
20% of 345
20/100 * 345
2/10 * 345
= 690/10
= 69.00
If there is a discount of 69.00 on the iphone price, the amount you would pay during labor day weekend will be 345.00-69.00 = 276.00
The correct answer is 276.000/100