Explanation
the properties of exponents
[tex]\begin{gathered} \sqrt[n]{a}=a^{\frac{1}{n}} \\ \sqrt[n]{a^{n^{}}b^n}\text{ = ab} \\ \sqrt[]{ab}=\sqrt[]{a}\cdot\sqrt[]{b} \end{gathered}[/tex]Step 1
Zoe believes
[tex]\sqrt[]{2}+\sqrt[]{8\text{ }}=\text{ 2.21}[/tex]Marsden Believes
[tex]\sqrt[]{2}+\sqrt[]{8}=3.21[/tex]Step 2
[tex]\sqrt[]{8}=\sqrt[]{4}\cdot\sqrt[]{2}=\text{ 2}\sqrt[]{2}[/tex]then
[tex]\begin{gathered} \sqrt[]{2}+\sqrt[]{8}=\text{ }\sqrt[]{2}+2\sqrt[]{2}=3\sqrt[]{2} \\ \text{also } \\ \sqrt[]{2}=\text{ 1.4142} \\ so, \\ \sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24 \end{gathered}[/tex]then
[tex]\sqrt[]{2}+\sqrt[]{8}=3\sqrt[]{2}=3\cdot1.4142=4.24[/tex]I hope this helps you
In an Oreo factory, the mean mass of a cookie is given as40 grams with a standard deviation of 2 grams. Whatpercentage of the cookies are between 34 grams and 42grams?
The Solution:
Given:
[tex]\begin{gathered} \bar{x}=mean=40g \\ \sigma=\text{ standard deviation}=2g \end{gathered}[/tex]We are required to find the percentage that is between 34 grams and 42 grams.
By z-score statistic,
The lower limit is:
[tex]Z_1=\frac{x-\mu}{\sigma}=\frac{34-40}{2}=\frac{-6}{2}=-3[/tex]The upper limit is:
[tex]Z_2=\frac{x-\mu}{\sigma}=\frac{42-40}{2}=\frac{2}{2}=1[/tex]The probability is:
[tex]P(Z_1Converting to percent, we multiply by 100:[tex]0.840\times100=84\text{\%}[/tex]Therefore, the correct answer is 84%
Write the fraction as a decimal: 2/9
nearest tenth = 0.2
Explanation:2/9 is in its simplest form.
Hence, we use a calculator to find the fraction in decimal
2/9 = 0.2222 (a repeating decimal)
0.2222 to the nearest tenth = 0.2
Answer:
Step-by-step explanation:
2/9 as a decimal is 0.2222
Evaluate the expression without using a calculator.35!———33! - 2
Answer:
595
Explanation:
The given expression is:
[tex]\frac{35!}{33!\cdot2!}[/tex]First, we can rewrite 35! , so the expression is equal to:
[tex]\frac{35\cdot34\cdot33!}{33!\cdot2!}[/tex]Finally, we can simplify to get:
[tex]\frac{35\cdot34}{2!}=\frac{35\cdot34}{2\cdot1}=\frac{1190}{2}=595[/tex]Therefore, the expression is equal to 595
An orange has about I cup of juice. How many oranges are needed to make 2 cups of juice?
An orange has about 1/4 cup of juice. To find how many oranges are needed to make 2 1/2 cups of juice, we can use the next proportion
[tex]\frac{\frac{1}{4}\text{cup}}{2\frac{1}{2}\text{ cup}}=\frac{1\text{ orange}}{x\text{ oranges}}[/tex]Solving for x:
[tex]undefined[/tex]Find sectheta costheta, and cottheta where theta is the angle show in the figure
We will have the following:
We first determine the missing side of the triangle:
[tex]x=\sqrt{17^2-8{}^2}\Rightarrow x=15[/tex]Now, we determine the expressions:
[tex]\begin{gathered} sec(\theta)=\frac{17}{8} \\ \\ \\ cos(\theta)=\frac{8}{17} \\ \\ \\ cot(\theta)=\frac{8}{15} \end{gathered}[/tex]Formulas, walkthrough, something. I can't figure it out.
Answer:
[-16,16]U[20,+oo)
Step-by-step explanation:
1) x-16 ≥ 0
x ≥ 16
2) x-20 ≥ 0
x ≥ 20
3) x+16 ≥ 0
x ≥ -16
- 16. 16. 20
1) - - +. +
2) - - - +
3) - +. +. +
- +. - +
Solution : -16≤x≤ 16 ∨ x≥20
Find the value of 3127°B5xАC с3x + 6D127°c
From the diagram,
The angles, 127 degrees at arc AB and arc CD shows that the Chords AB and CD are equal
[tex]\begin{gathered} \text{chord AB = chord CD} \\ \text{that is} \\ 5x\text{ = 3x + 6} \\ \text{collect like terms} \\ 5x\text{ - 3x = 6} \\ 2x\text{ = 6} \\ \text{divide both sides by 2} \\ x\text{ = }\frac{6}{2} \\ x\text{ = 3} \end{gathered}[/tex]Therefore, the value of x = 3
what ar the restricted value of ratio expressed in fraction.
The given rational expression is:
[tex]\frac{x^2-9}{x^2-4x}[/tex]To find the restr
1. If a line AB is translated in a plane to form A'B', what is true?AB = BBAA = BBA'A' = B'BAA' = BB'
ANSWER
[tex]AA\text{'}=BB\text{'}[/tex]EXPLANATION
We have that line AB is translated in a plane to form line A'B'.
When a line/figure is translated, its shape and size do not change, which means that the distance between corresponding points on the pre-image and image must remain the same.
In other words, the distance between A and A' must be equal to the distance between B and B'.
Therefore, the correct answer is:
[tex]AA\text{'}=BB\text{'}[/tex]What is the slope-intercept form of the line with the point (0, 3) and a slope = -2?O A. y = 2x + 3O C. y = -2x + 3D. y = -2x - 3B. y = 2x - 3
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
The given equation is
[tex]y=-2x+3[/tex]Compare it with the form above to find m and b
Since the coefficient of x is -2, then
m = -2
Since m is the slope of the line, then
The slope of the line is -2
The answer is B
When the length of each edge of a cube is increased by 1 cm, the volume is increased by 19 cm3.A cube is shown.The length is labeled e.The width is labeled e.The height is labeled e.What is the length (in centimeters) of each edge of the original cube? cm
Solution
solution given;
let length be x
its
volume be x ³
we have when length is increased by 1cm volume increased by 19 cm³ so
(x+1)³=x³+19cm³
x³+1³+3x²+3x=x³+19
3x²+3x-18=0
3(x²+x-6)=0
x²+3x-2x-6=0
x(x+3)-2(x+3)=0
(x+3)(x-2)=0
either
x=-3 rejected
or
x=2cm
Hence the correct answer for the length of each cube = 2cm
Find the missing digit and check calculations.went to the store and bought 18 two-litter bottles of off-brand soda for his Super Bowl party last weekend. His receipt is smuggled, But he can see that the cost of these bottles before tax was 15.#4. how much did each bottle cost?
We have a smuggled total that is 15.#4 after buying 18 bottles.
We can estimate the cost of each bottle as:
[tex]p=\frac{15+0.1\cdot x+0.04}{18}[/tex]where x is the tenths of a dollar, and it will have an integer value between 0 and 9.
If we try the different possible values for x, we get:
[tex]\begin{gathered} x=0\Rightarrow15.04/18=0.835555555555555 \\ x=1\Rightarrow15.14/18=0.841111111111111 \\ x=2\Rightarrow15.24/18=0.846666666666667 \\ x=3\Rightarrow15.34/18=0.852222222222222 \\ x=4\Rightarrow15.44/18=0.857777777777778 \\ x=5\Rightarrow15.54/18=0.863333333333333 \\ x=6\Rightarrow15.64/18=0.868888888888889 \\ x=7\Rightarrow15.74/18=0.874444444444444 \\ x=8\Rightarrow15.84/18=0.88 \\ x=9\Rightarrow15.94/18=0.885555555555556 \end{gathered}[/tex]We can see that the only value that give a unit price in cents is for x = 8, which corresponds to a total price of $15.84 and a unit price of $0.88.
Answer: we can estimate that the unit price is $0.88.
Find the solution of the system by graphing.-x-4y=4y = 1/4x-3Part A: Graph the system on the coordinate plane.
the linear equations are
[tex]\begin{gathered} -x-4y=4 \\ y=\frac{1}{4}x-3 \end{gathered}[/tex]Their graph is:
The solution of the system is the point in which the lines cross in the plane.
We can see that this point is (4,-2).
1) Find the probability of rolling at least one 6 2)Find the probability of rolling exactly one 6
ANSWER:
For item 14: 1/36 (there is only one possible way of having both dice as 3)
For item 15: 1/18 (because there are 2 ways that one is 5 and one is 6 so it is 2/36 or 1/18)
For Item 16: 5/9 (because there 20 ways we can have a 5 or 6. 20/36)
For item 17: 11/36 (because there are 11 ways of having at least one six)
For item 18: 25/36 (because there are 25 ways having numbers other than 6)
For item 19: 5/18 (because there are 10 ways having exactly one six 10/36)
the scatter plot shows the number of years of experience, x, and the hourly pay rate,y, for each of 25 cashier im California. (a) write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fif. (b) using your equation from part (a), predict the hourly pay rate for a cashier with 14 years of experience. Note that you can use the graphing tools to help you approximate the line. (a) write an approximate equation of the line of best fit .y=(b) using your equation from part (a), predict the hourly pay rate for a cashier with 14 years of experience. $=
Input data
Points
(2, 8)
(20, 18)
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{18-8}{20-2} \\ m=\frac{5}{9} \end{gathered}[/tex][tex]\begin{gathered} b=y-mx \\ b=8-\frac{5}{9}2 \\ b=\frac{62}{9} \end{gathered}[/tex]The equation of the line that passes through the points. For this case we can use the linear model given:
[tex]y=0.55x+6.8[/tex]predict the hourly pay rate for a cashier with 14
[tex]\begin{gathered} y=0.55(14)+6.8 \\ y=14.5\text{ dollars per hour} \end{gathered}[/tex](a) y = 0.55x+6.8
(b) 14.5 dollars per hour
Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compoundsmonthly. How much will the CD be worth after 10 years using simple interest?
Nathaniel ate 75% of his chocolate bars. If he startedwith 40 chocolate bars, how many did he eat?
We have that the 40 chocolate bars that Nathaniel had is the 100%. Then, to find out how many chocolate bars he ate, we have to multiply 40 by 75%:
[tex]40\cdot0.75=30[/tex]therefore, Nathaniel ate 30 chocolate bars,
Line Segment WV has an endpoint at (5, -7) and the midpoint is at (-3, 2). What are the coordinates of the other endpoint? Write your answer as an ordered pair: (x, y)
Answer:
Step-by-step explanation: it is that
What is the the quotient of 23.7 and 0.8?
A quotient is the result of the division of two numbers. The given numbers are 23.7 and 0.8. Thus,
Quotient = 23.7/0.8
Quotient = 29.625
. Which of the following points are solutions of 5y – 2x ≤ 9?A. both (–3, 1/5), and (5, –17.6)B. (5, –17.6) onlyC. (–3, 1/5) onlyD. both (0, 2) and (5, –17.6)
we have the inequality
5y – 2x ≤ 9
Remember that
If an ordered pair is a solution to the inequality, then the ordered pair must satisfy the inequality
so
Verify each ordered pair
1) (–3, 1/5)
substitute in the given inequality
5(1/5) – 2(-3)x ≤ 9
1+6 ≤ 9
7 ≤ 9 -----> is true
that means ----> the ordered pair is a solution
2) (5, –17.6)
5(-17.6) – 2(5) ≤ 9
-88-10 ≤ 9 ------> is true
that means ----> the ordered pair is a solution
3) (0, 2)
5(2) – 2(0) ≤ 9
10 ≤ 9 -----> is not true
The ordered pair is not a solution
therefore
The answer is
A. both (–3, 1/5), and (5, –17.6)Solve the Equation: -6x=12Your answer
Answer:
x = -2
Step-by-step explanation:
Divide both sides by the coefficient of x, which is -6
= -6x/-6 = 12/-6
x = -2
Find the geographic mean between each pair of numbers. A. 28 and 14. B. 7 and 36
In order to find the geographic mean between each of this pair of numbers, first we would have to define what is the geographic mean.
The geographic mean is the average of a set of numbers.
Therefore, the geographic mean for A. 28 and 14 would be:
Geographic mean (28,14)= (28*14)^0.5
=(392)^0.5=19.798990
The geographic mean for B. 7 and 36 would be:
Geographic mean (7,36)=(7*36)^0.5
=(252)^0.5=15.874508
So, Geographic mean for (28,14) would be 19.798990 and for (7,36) would be 15.874508
Find a linear equation satisfying the condition, if possible. Passes through (−1,5) and (0,10)
The linear equation has the coordinates (−1,5) and (0,10) ,
[tex]y-5=\frac{10-5}{0+1}(x+1)[/tex][tex]y-5=\frac{5}{1}(x+1)[/tex][tex]y-5=5x+5[/tex][tex]y=5x+10[/tex]Hence , the linear equation is y=5x+10.
4. A farmhouse shelters no more than 12 animals. Some are goats and some are ducks.Altogether there are more than 34 legs. How many of each animal could there be?What are you being asked to find?What are you given?Define your variables.Create & solve a system.Explain your solution(s).
• What are you being asked to find? define your variables
We are being asked to find the number of goats and ducks that there might be in the farmhouse.
• What are you given?
,•
From the information given by the question, we know that there are as many as 12 animals and that they have as many as 34 legs.
• Create & solve a system
from the given information we can write two expressions, one for the total number of animals, which equals 12, and another for the number of legs, let's call x to the number of goats and y to the number of ducks.
We know that there are a total of 12 animals, this is the number of goats plus the number of ducks, then we can write the expression:
goats + ducks = 12
x + y = 12
0.
And we know that there are 34 legs since a duck has 2 legs and a goat has 4, the number of legs of all the ducks would be the number of ducks times 2 and the number of legs of all the goats is 4 times the number of goats, then we can express the equation:
goat's legs + duck's legs = 34
4x + 2y = 34
Then, the system of equations that we have to solve is:
1. x + y = 12
2. 4x + 2y = 34
Now let's solve the system of equations, by following these steps:
Solve for y from the first equation:
x+y=12
x-x+y=12-x
y=12-x
Replace the expression y=12-x into the second equation and find the value of x.
4x + 2y = 34
4x+2(12-x)=34
4x+2*12-2x=34
4x+24-2x=34
2x+24=34
2x+24-24=34-24
2x=10
2x/2=10/2
x=5
Now that we know that x equals 5, let's replace it into the expression y=12-x, to find the value of y:
y=12-x
y=12-5=7
Then, x equals 5 and y equals 7
• Explain your solution
,•
In the farmhouse could there be a total of 5 ducks and 7 goats
This pentagonal prism is cut by the plane shown. The plane is parallel to the base of the pentagonal prism. What is the shape of the cross-section?
If the plane is parallel to the base, then the cross section has the same shape of the base: a penthagon.
Lynn needs a large truck toMove some furniture. She found that the cost C of renting a truck is $20 per day plus $1 per mile mWrite an equation for the cost of one day in terms of the miles drivenGraph the equation for values up to and including 100 milesEstimate the cost of driving 20 miles in one day
We can set the following equation with the information given:
[tex]C=1\cdot m+20[/tex]Notice that it is a linear equation and its graph is as follows:
which corresponds to option A.
The estimated cost of driving 20 miles in one day is:
[tex]\begin{gathered} C=1\cdot20+20 \\ C=40 \end{gathered}[/tex]If C=$25, solving the first equation on the board for m we get:
[tex]\begin{gathered} 25=m+20 \\ m=25-20 \\ m=5 \end{gathered}[/tex]Therefore, the truck was driven 5 miles if the cost for one day is $25.
what are the coordinates of the point on the directed line segment from (2,-1) to (9,6) that partitions the segment into a ratio of 5 to 2
Ok, so:
Let x and y be coordinate of the point C that partitions the segment.
And Let A = ( 2, -1 ) and B = ( 9 , 6 ).
So, given that C partitions the segment into a ratio of 5 to 2, we have:
Total parts of the segment: 5+2 = 7.
So, the point C is 5/7 of way from A to B.
Let me draw the situation:
Now, we know that the right distance is 7 and the upper distance is 7.
Now we multiply 5/7 per both distances.
5/7 * 7 = 5
5/7 * 7= 5
Now, we take the initial point A ( 2, -1 ), and sum 5 to each coordinate.
Then, the point C = ( 7 , 4 )
4(b-1)= -4+4b what is the solution
Starting with the equation:
[tex]4(b-1)=-4+4b[/tex]Use the distributive property to expand the parenthesis in the left hand side of the equation:
[tex]4b-4=-4+4b[/tex]Use the commutative property to rewrite the right hand side of the equation, swapping the terms:
[tex]4b-4=4b-4[/tex]Since both sides of the equation are the same, any value of b is a solution to the equation.
Therefore, all numbers are a solution for the equation 4(b-1)=-4+4b.
A car travels 120 miles on 10 gallons of gas. At this rate, how many gallons will it need to travel 312 miles?
26 gallons
1) We can write this information setting up a proportion
miles gallons
120 10
312 x
2) Assuming the pace hasn't changed, then we can consider that as proportional:
120x = 312 * 10
120x= 3120
x = 3120/120
x =26
3) So 26 gallons are going to be needed for those 312 miles.
3. The height of a projectile object fired into the air can be modeled by h(t) = -16t² + 48t + 3, where his
height, in feet, and t is time, in seconds. What is the maximum height the projectile will reach?
A. 3 feet
B. 35 feet
C. 39 feet
D. 105 feet
Answer:
C. 39 feet
Step-by-step explanation:
[tex]{ \tt{h(t) = - 16 {t}^{2} + 48t + 3 }}[/tex]
- Let us find the limits of the function
[tex] { \tt{ \frac{d \{h(t) \}}{dt} = - 32t + 48 }} \\ [/tex]
- So, let us differentiate for the second time;
[tex]{ \tt{ \frac{d {}^{2} \{h(t) \} }{dt {}^{2} } = - 32}} \\ [/tex]
- So, at maximum height; d{h(t)}/dt is 0;
[tex]{ \tt{ - 32t + 48 = 0}} \\ { \tt{ - 32t = - 48}} \\ { \tt{t = 1.5 \: seconds}}[/tex]
- Therefore; maximum height is;
[tex]{ \tt{h(t) = - {16t}^{2} + 48t + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = - 16(1.5) {}^{2} + 48(1.5) + 3}} \\ { \tt{h(1.5) = - 36 + 72 + 3}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ { \tt{h(1.5) = 39 \: feet}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]