We have to find P and Q first.
P is the largest integer that is less than the square root of 380.
P is 19.
Q is the largest number that is less than the square of 54.
Q is 7.
Then the distance between P and Q is |19-7|=12.
Answer: C. 12
Find the length of AC and the measures of a and 0
ANSWER:
AC = 3√ 17
α = 75.96°
Θ = 14.04°
STEP-BY-STEP EXPLANATION:
We can calculate the length of side AC by means of the Pythagorean theorem, just like this:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{ in this case:} \\ (AC)^2=3^2+12^2 \\ (AC)^2=9+144 \\ AC=\sqrt[]{153} \\ AC=3\sqrt[]{17} \end{gathered}[/tex]We can calculate the angles by applying the following trigonometric ratios:
[tex]\begin{gathered} \sin \alpha=\frac{12}{3\sqrt[]{17}} \\ \alpha=\arcsin \mleft(\frac{12}{3\sqrt{17}}\mright) \\ \alpha=75.96 \\ \\ \sin \theta=\frac{3}{3\sqrt[]{17}} \\ \theta=\arcsin \mleft(\frac{3}{3\sqrt{17}}\mright) \\ \theta=14.04 \end{gathered}[/tex]The Following to wait table shows the number of student of the school who have a cell phone and or part-time job:
Explanation
in the column we have
-have cell phones
-do not have cell phones
-total
and
in the other side.
-have a part time job
-do not have part time job,
so to know the number of students whoh fit both conditions ( have a cell phone and have a part time job) we need to find the cell where both intersect each other
hence, the answer is
[tex]2)40[/tex]I hope this helps you
A tee box is 48 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 32 ft/s, the quadratic equation 0 = -16t^2+ 32t +48 givesthe time t in seconds when a golf ball is at height 0 feet on the fairway.What is the height of the ball at 1 second and is the ball at its maximum height at 1 second (explain)?
Answer:
Step by step explanation:
10) 4 4.5 5 5 5.5 6 Y | 0.5 0.6 0.8 LE 0.9 1.2 Which is most likely the equation of the line of best fit for the data given in the table? DELLE А y=034X=09 B y = 0.25x -0.7 с y =0.45x = 1 y=0.50 x -0.6
y = 0.34x - 0.9 (Option A)
We are given the data and we want to find the line of best fit.
The line of best fit is a line that goes through the data points and it gives the best representation of the spread of the data.
The equation of a line is given as:
y = mx + c
y represents y-values
x represents x-values
m is the slope of the line
c is the y-intercept of the line or where the line crosses the y-axis.
To get this equation for this question, we need to find both m and c.
In order to do this, the formulas are given below:
[tex]\begin{gathered} M=\frac{\sum(x_i-\bar{\bar{X})(y_i-\bar{Y)}}}{\sum(x_i-\bar{X)^2}} \\ \text{where M is slope} \\ x_i=\text{ individual data points of x} \\ X=\operatorname{mean}\text{ of x values} \\ Y=\text{ mean of y values} \end{gathered}[/tex]While for c or the y-intercept, we have:
[tex]\begin{gathered} c=\bar{Y}-m\bar{X} \\ \text{where Y and X retain their same meaning from before} \end{gathered}[/tex]Before we can calculate m and c, we need to calculate the means of both x and y values give to us.
This is done below:
[tex]\begin{gathered} \operatorname{mean}=\frac{\sum x_i}{n} \\ \\ \bar{Y}=\frac{0.5+0.6+0.8+0.9+1.2}{5}=0.8 \\ \bar{X}=\frac{4+4.5+5+5.5+6}{5}=5 \end{gathered}[/tex]Now we can proceed to get the slope m of our line.
In order to be tidy, we shall use a table to solve. This table is shown in the image below:
Thus, we can now calculate our slope m:
[tex]\begin{gathered} M=\frac{\sum(x_i-\bar{\bar{X})(y_i-\bar{Y)}}}{\sum(x_i-\bar{X)^2}} \\ \\ M=\frac{(-1)(-0.3)+(-0.5)(-0.2)+0(0)+(0.5)(0.1)+(1)(0.4)}{1+0.25+0+0.25+1} \\ \\ M=\frac{0.3+0.1+0+0.05+0.4}{2.5}=0.34 \end{gathered}[/tex]Therefore the slope (m) = 0.34
Now to calculate intercept (c)
[tex]\begin{gathered} c=\bar{Y}-m\bar{X} \\ \bar{Y}=0.8\text{ (from previous calculation above)} \\ \bar{X}=5\text{ (from previous calculation above)} \\ \\ c=0.8-0.34\times5 \\ c=0.8-1.7=-0.9 \end{gathered}[/tex]Therefore, the intercept (c) = - 0.9
Bringing it all together, we can write the equation of the line as:
y = 0.34x - 0.9
Therefore the answer is: y = 0.34x - 0.9 (Option A)
determine the solution,if it exists,for each system of linear equation. Verify your solution on the coordinate plane. x + 3 = y 3x + 4y = 7
then
[tex]\begin{gathered} 3\mleft(y-3\mright)+4y=7 \\ 3y-9+4y=7 \\ 7y-9=7 \\ 7y-9+9=7+9 \\ 7y=16 \\ \frac{7y}{7}=\frac{16}{7} \\ y=\frac{16}{7} \end{gathered}[/tex]replacing in x
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Determine whether the statement is true or false, and explain why.
The derivative value f'(a) equals the slope of the tangent line to the graph of y=f(x) at x = a.
Choose the correct answer below.
OA. The statement is true because f'(x) is a function of x.
B. The statement is false because f(a) gives the instantaneous rate of change of f' at x = a.
OC. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
OD. The statement is false because f'(a) gives the average rate of change of f from a to x.
Answer: C. The statement is true because f'(a) gives the instantaneous rate of change of fat x = a.
Suppose a person who jumps on Earth returns to the ground in 0.4 second. On Phobos, the same jumper will take 6.4 minutes to return to the ground. How many times longer would it be on Phobos than on Earth for the jumper to return to the ground? Explain.
The times longer would it be on Phobos than on Earth for the jumper to return to the ground is 16 times.
How to calculate the value?From the information, it was given that the person who jumps on Earth returns to the ground in 0.4 second and that on Phobos, the same jumper will take 6.4 minutes to return to the ground.
The number of times longer will be calculated by dividing the values that are given. This will be:.= Time on Phobos / Time on Earth
= 6.4 minutes / 0.4 minutes
= 16
This shows the concept of division of numbers.
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Two functions are shown. f(x) = 29(0.5)* g(x) = 18x + 14 What is the value of f(2) + g(4)?
Answer:
93.25
Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=29(0.5)^x \\ g(x)=18x+14 \end{gathered}[/tex]To be able to find the value of f(2) + g(4), we have to 1st determine the value of f(2) and f(4) as shown below;
[tex]\begin{gathered} f(2)=29(0.5)^2=29\ast0.25=7.25 \\ g(4)=18(4)+14=72+14=86 \end{gathered}[/tex]Let's go ahead and find the value of f(2) + g(4);
[tex]f(2)+g(4)=7.25+86=93.25[/tex]What transaction occurs when an investor decides to liquidate assets?
A. buy
B. hold
C. sell
D. speculate
Answer:
What transaction occurs when an investor decides to liquidate assets?
A. buy
B. hold
(C. sell)
D. speculate
Step-by-step explanation:
I got a 5/5 on the test and i got the answer from a quizlet (:
Sell is the answer
The correct option is (C).
Given,
In the question:
What transaction occurs when an investor decides to liquidate assets?
Now, According to the question:
when an investor decides to liquidate assets.
when an investor decides to liquidate assets means he or she want to sell the property in the open market, in other words liquidate assets means
converting non- liquid assets into liquid assets.
In investing, liquidation occurs when an investor closes their position in an asset. Liquidating an asset is usually carried out when an investor or portfolio manager needs cash to re-allocate funds or rebalance a portfolio. An asset that is not performing well may also be partially or fully liquidated.
According to the statement
Therefore, Sell is the answer
The correct option is (C).
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a coyote can run a hundred one in 5.3 seconds a jack-rabbit can run 75 m in 4.7 seconds compared their unit speeds to determine which animal is faster round to the nearest whole unit Blank#1 Coyote speedBlank#2 Jack Rabbit speedBlank#3 Which one is faster
Answer
Coyote's speed = 19 m/s
Jack Rabbit's speed = 16 m/s
The Coyote is faster since 19 > 16.
Explanation
To answer this, we need to note that the relationship between speed, distance and time is given as
Speed = (Distance/Time)
For the Coyote,
Distance = 101 m
Time = 5.3 seconds
Speed = (Distance/Time)
Coyote's speed = (101/5.3) = 19 m/s
For the Jack Rabbit,
Distance = 75 m
Time = 4.7 seconds
Speed = (Distance/Time)
Jack Rabbit's speed = (75/4.7) = 16 m/s
Since 19 m/s is evidently greater than 16 m/s, we can conclude that the Coyote is faster than the Jack Rabbit.
Hope this Helps!!!
what is the sum of 141.2-79.83
Given:
141.2 - 79.83
Here, we are to subtract 79.83 from 141.2
Let's evaluate the given expression.
We have:
[tex]\begin{gathered} 141.20 \\ -79.83 \\ _{\text{ \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \\ \text{ 61.37} \end{gathered}[/tex]ANSWER:
61.37
Solve the inequality for x and identify the graph of its solution.|x+ 2] < 2Choose the answer that gives both the correct solution and the correct graph.
| x + 2 | < 2
-2 < x + 2 < 2
-2 - 2 < x + 2 < 2 - 2
-4 < x < 0 This is the inequality
Letter B is the right choice.
The function f(t) = 2(2.25)^t models the growth of bacteria cells, where f(t) is the number of bacteria cells and t is time in days. After 10 days, approximately how many bacteria cells are there?
Step 1
write out the function
[tex]\begin{gathered} f(t)=2(2.25)^t \\ \end{gathered}[/tex]Step 2
for every input, an input produce unique output
t = 10days is the input
Step 3
substitute t = 10 in the function
[tex]\begin{gathered} f(t)=2(2.25)^{10} \\ =\text{ 2 }\times2.25^{10} \\ =\text{ 2 x 3325.25673} \\ =\text{ 6650.51} \\ =\text{ 6651} \end{gathered}[/tex]Whichatest initial value?Use the drop-down menus to show your answer.Function AX026y0515Function Choose...has the greatest initial value.Choose...Functionhas the greatest rate of change.410Function By = 3x - 165432-Function C1 2 3 4 5 6X
Given:
Function A:
Function- B
[tex]y=3x-1[/tex]Function C
Find-:
The function has the greatest initial value
The function has the greatest rate of change
Explanation-:
(A)
The function has the greatest initial value
Check the value at x=0
Value of y is:
For functi
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Evaluate the expression (4x^3y^-2)(3x^-2y^4) for x = –2 and y = –1.
Answer:
3x−2y)(4x+3y)
It can be written as =3x(4x+3y)−2y(4x+3y)
By further calculation =12x
2
+9xy−8xy−6y
2
So we get =12x
2
+xy−6y
2
I’m struggling on this math question and could use some help on it
Let's determine the values of f(-4) and g(6).
For f(-4),
[tex]\text{ f\lparen x\rparen= -2x}^3\text{ - 5}[/tex][tex]\text{ f\lparen-4\rparen= -2\lparen-4\rparen}^3-5\text{ = -2\lparen-64\rparen- 5}[/tex][tex]\text{ f\lparen-4\rparen = 128 - 5}[/tex][tex]\text{ f\lparen-4\rparen = 123}[/tex]Therefore, f(-4) = 123
For g(6),
[tex]\text{ g\lparen x\rparen = -3x - 3}[/tex][tex]\text{ g\lparen6\rparen = -3\lparen6\rparen - 3 = -18 - 3}[/tex][tex]\text{ g\lparen6\rparen = -21}[/tex]Therefore, g(6) = -21
How to draw the graphs of the following non-linear functions?y=x^2 + 1y=3^x + 1
The first step is to substitute values of x into each equation.
For y = x^2 + 1,
if x = - 2, y = (- 2)^2 + 1 = 4 + 1 = 5
if x = - 1, y = (- 1)^2 + 1 = 1 + 1 = 2
if x = 0, y = (0)^2 + 1 = 0 + 1 = 1
if x = 1, y = (1)^2 + 1 = 1 + 1 = 2
if x = 2, y = (2)^2 + 1 = 4 + 1 = 5
We would plot the corresponding values of x and y on the graph as shown below
For y = 3^(x + 1),
if x = - 2, y = 3^(-2 + 1) = 3^-1 = 0.33
if x = - 1, y = 3^(-1 + 1) = 3^0 = 1
if x = 0, y = 3^(0 + 1) = 3^1 = 3
if x = 1, y = 3^(1 + 1) = 3^2 = 9
if x = 2, y = 3^(2 + 1) = 3^3 = 27
We would plot the corresponding values of x and y on the graph as shown below
1. Consider the graph f(x) = 34. Describe how to graph thetransformation f(x – 3) + 2.
If the graph shows a constant function, the value of f(x) will always be the same no matter which value does x take. It means: to graph the transformation of this function do an horizontal translation right 3 units (which would show the same graph, basically) and then do a vertical translation up 2 units
Katie opened a savings account and deposited 1,000.00 as principal the account earns 4% interest compounded quarterly what is the balance after 6 years
P = $1000
r = 4% = 4/100 = 0.04
t = 6 years
Therefore,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=1000(1+\frac{0.04}{4})^{4\times6} \\ A=1000\times1.26973464853 \\ A=1269.73464853 \\ A=\text{ \$1269.73} \end{gathered}[/tex]Solve the following system algebraically. y= x2 - 9x + 18 y = x - 3
we have
y=x^2-9x+18 -----> equation A
y=x-3 ------> equation B
Solve the system of equations
substitute equation B in equation A
x^2-9x+18=x-3
x^2-9x+18-x+3=0
x^2-10x+21=0
Solve the quadratic equation using the formula
[tex]x=\frac{-b\pm\sqrt[\square]{b^2-4ac}}{2a}[/tex]we have
a=1
b=-10
c=21
substitute the given values
[tex]\begin{gathered} x=\frac{-(-10)\pm\sqrt[\square]{(-10)^2-4(1)(21)}}{2(1)} \\ \\ x=\frac{10\pm\sqrt[\square]{100-84}}{2} \\ \\ x=\frac{10\pm\sqrt[\square]{16}}{2} \\ \\ x=\frac{10\pm4}{2} \\ \\ x=7 \\ x=3 \end{gathered}[/tex]Find the value of y for x=7
y=x-3
y=7-3=4
the first solution is (7,4)
Find the value of y for x=3
y=3-3=0
the second solution is (3,0)
therefore
the answer is the first option6-Find the measure of ∠AEB.A. 122°B. 132°C. 142°D. 152°7-Find the measure of ∠BEC.A. 58 °B. 48°C. 38°D. 28°8-Find the measure of ∠CED.A. 52 °B. 48 °C. 42 °D. 32°9-Find the measure of ∠FEB.A. 142°B. 180°C. 90°D. 0°10-Find the measure of ∠FED.A. 0°B. 180°C. 45°D. 90°
The answer for 6 is C. 142°
Explanation
∠AEB = 180 - ∠AEF (Sum of angle on a straight line)
∠AEB = 180 - 38 = 142°
An object is dropped from 27 feet below the tip of the pinnacle atop a 1471-ft tall building. The height h of the object after t seconds is giveh= - 16t^2 + 1444. Find how many seconds pass before the object reaches the ground.How many seconds pass before the object reaches the ground
The Solution:
Given:
[tex]h=-16t^2+1444.[/tex]We are required to find t when h = 0.
[tex]\begin{gathered} -16t^2+1444=0 \\ \\ -16t^2=-1444 \end{gathered}[/tex]Divide both sides by -16.
[tex]t^2=\frac{-1444}{-16}=90.25[/tex][tex]\begin{gathered} t=\sqrt{90.25} \\ \\ t=9.5\text{ or }t=-9.5 \end{gathered}[/tex]Thus, the correct answer is 9.5 seconds.
Find the midpoint of the line segment IJ where I (3,-9) and J (-10,-5)
Answer:
M (-7/2, -7)
Explanation:
Given the coordinates as I(3, - 9) and J(-10, -5), we can go ahead and determine the midpoint of the line segment IJ using the midpoint formula stated below;
[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]So we have that x1 = 3, x2 = -10, y1 = -9, and y2 = -5.
Let's go ahead and substitute the above values into our formula and simplify;
[tex]\begin{gathered} M\lbrack\frac{3+(-10)}{2},\frac{-9+(-5)}{2}\rbrack \\ =M(\frac{3-10}{2},\frac{-9-5}{2}) \\ =M(-\frac{7}{2},\frac{-14}{2}) \\ =M(-\frac{7}{2},-7) \end{gathered}[/tex]Calculate the average rate of change for the function f(x) = 3x4 − 2x3 − 5x2 + x + 5, from x = −1 to x = 1.
a
−5
b
−1
c
1
d
5
Average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from
x =-1 to x=1 is equal to -1.
As given in the question,
Given function :
f(x) = 3x⁴ -2x³ -5x² +x +5
Formula for average rate of change for (a, f(a)) and (b, f(b))
[f(b) -f(a)] / (b-a)
Substitute the value of a=-1 and b=1
f(-1)=3(-1)⁴ -2(-1)³-5(-1)² +(-1) +5
= 3+2-5-1+5
=4
f(1)=3(1)⁴ -2(1)³-5(1)² +(1) +5
= 3-2-5+1+5
= 2
Average rate of change = (2-4)/(1-(-1))
= -2/2
=-1
Therefore, average rate of change for the function f(x) = 3x⁴ -2x³ -5x² +x +5 from x =-1 to x=1 is equal to -1.
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what is the area of a triangle with the legth of 8in,12in,6in
Area is
[tex]A=\frac{1}{2}bh=\frac{1}{2}\times6\times8=\frac{48}{2}=24[/tex]answer: 24 sq in
.Find the area of the sector with radius 4 and central angle, ∅= 45°
Remember that the formula for the area of a sector is:
[tex]A=\frac{\pi\cdot r^2\cdot\theta}{360}[/tex]Where:
• r, is the radius
,• Theta ,is the central angle (in degrees)
Using this formula and the data given,
[tex]\begin{gathered} A=\frac{\pi\cdot4^2\cdot45}{360} \\ \rightarrow A=2\pi \end{gathered}[/tex]Susanna has played the piano for s years. Patrick has played the piano for 4 more than twice the number of years that susanna has been playing the piano. which expression correctly shows the number of years that Patrick has been playing the piano.2s + 44s + 22 (s + 4)(s - 4) ÷ 3none of the above
Given data:
The expression for Patrick paly Piano is,
[tex]P=2s+4[/tex]Thus, the first option is correct.
Sue would like to join a gym. Gym A has a $56 joining fee with $3 per visit. Gym B has a $30 joining fee with a $5 per visit. Let x represent the number of visits. After how many visits would the cost of the two gyms be the same?
Let x represent the number of visits it will take for the cost of the two gyms to be the same.
Gym A has a $56 joining fee with $3 per visit. This means that the cost of x visits of gym A would be
3 * x + 56
= 3x + 56
Gym B has a $30 joining fee with a $5 per visit. This means that the cost of x visits of gym B would be
5 * x + 30
= 5x + 30
For both costs to be the same, it means that
3x + 56 = 5x + 30
5x - 3x = 56 - 30
2x = 26
x = 26/2
x = 13
After 13 visits, the cost of the two gyms would be the same
Which of the following tables represents a function?
Answer:
Table A represents a function
Step-by-step explanation:
Table A represents function because it is the only table that doesn't repeat an output or input number.
Use < or > to write a true sentence. Show your work in the lining up decimals and adding zeroes8.41 8.051
8.41 > 8.051
the digit after the decimal point is greater on 8.41 (4) than on 8.051 (0)