how many real solutions does y = (-x + 4)^2 have?
Answers
1.y = -1
2.y = 4/3 = 1.333
Comment
There are a couple of ways of doing this to show there there is just one solution. The most easily done way is to graph the quadratic. I have done that for you.
Notice that the quadratic touches the x axis, it does not cut it in two places or no places. When a quadratic just touches the x axis, it has only one solution.
Method 2
The quadratic is shown in the vertex form. If there was a number outside he bracket showing squares then you would get
y = (-x + 4)^2 + 4 (drawn in blue)
y = (-x + 4)^2 - 6 (drawn in green)
These two examples show what the vertex form would look like if the axis was cut in 2 places or no places and there would be no solution for the first one and 2 places for the second one.
Related Questions
Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a tota rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for X hours
Answers
In ΔMNP, what is the measure of < N?
20 degrees
46 degrees
64 degrees
76 degrees
Answers
Answer:
76
Step-by-step explanation:
The distance between the y value in the data and the y value predicted from the regression equation is known as the residual. what is the value for the sum of the squared residuals
Answers
B. SS = (1-r²)(SS_x)
C. SS = r²(SS_y)
D. SS= (1-r²)(SS_y)
The residual sum is given in the picture below so it is D which is correct.
The value for the sum of the squared residuals is SS(residuals) = (1 - r²) SS(y).
What is meant by Residual Value?Residual value is defined as the difference of the value that we predicts with that of the observed value.
Given that,
The distance between the y value in the data and the y value predicted from the regression equation is known as the residual.
Sum of the squared residuals is used to measure the variance level in a regression model.
We know that,
r² = 1 - [SS(residuals) / SS(total)]
[SS(residuals) / SS(total)] = 1 - r²
SS(residuals) = (1 - r²) SS(total)
SS(residuals) = (1 - r²) SS(y)
Hence the value is SS(residuals) = (1 - r²) SS(y).
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What is the selling price of an item if the original cost is $784.50 and the mark up on the item is 6.5 percent?
Answers
from my calculations it should be $835.49
Answer:
30
Step-by-step explanation:
Use the distance formula to find the distance between (−8, 2.5) and (0, −4.5). 1. Substitute coordinates: 2. Simplify parentheses: 3. Evaluate powers: 4. Simplify. What is the distance between (–8, 2.5) and (0, –4.5)? Round to the nearest hundredth. d ≈
Answers
We have to use the distance formula to find the distance between (−8, 2.5) and (0, −4.5).
The distance formula states:
" For the given points [tex] A(x_{1},y_{1}) [/tex] and[tex] B(x_{2},y_{2}) [/tex], the distance between A and B is given as:
AB = [tex] \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}} [/tex]
We have to find distance between (−8, 2.5) and (0, −4.5). So, [tex] x_{1}= -8, y_{1}= 2.5 , x_{2}=0 , y_{2}=-4.5 [/tex]
AB = [tex] \sqrt{(0+8)^{2}+(-4.5-2.5)^{2}} [/tex]
AB = [tex] \sqrt{64+49} [/tex]
AB = [tex] \sqrt{113} [/tex]
AB = 10.630 units
By rounding to the nearest hundredth, we get
Distance between A and B = 10.63 units.
Suppose you cut a small square from a square of fabric as shown in the diagram. Write an expression for the remaining shaded area. Factor the expression. Type your answer below.
Answers
1. You have the area of the larger square shown in the figure above, is:
A=x²
2. Then, you have the area of the smaller square shown in the figure above, is:
A=3²
A=9
3. Therefore, the expression for the remaining shaded area is:
A=x²-9
A=(x-3)(x+3)
Anyone know the answer?
Answers
Your test scores in one class are 82 and 88. What possible scores can you earn on your next test to have a test average between 85 and 90, inclusive?
Answers
To have a test average between 85 and 90, inclusive, the scores on the next test should be greater than or equal to 85 and less than or equal to 100.
Explanation:To have a test average between 85 and 90, inclusive, you need to find the possible scores on your next test. Let's assume the score on the next test is x. Then, the average of all three tests can be calculated as (82 + 88 + x) / 3. Now, we can set up an inequality to find the possible values of x:
(82 + 88 + x) / 3 ≥ 85 and (82 + 88 + x) / 3 ≤ 90
Simplifying each inequality, we get:
170 + x ≥ 255 and 170 + x ≤ 270
Subtracting 170 from both sides, we have:
x ≥ 85 and x ≤ 100
Therefore, the possible scores you can earn on your next test to have a test average between 85 and 90, inclusive, are any scores greater than or equal to 85 and less than or equal to 100.
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Each of the walls of a room with square dimensions has been built with two pieces of sheetrock, a smaller one and a larger one. the length of all the smaller ones is the same and is stored in the variable small. similarly, the length of all the larger ones is the same and is stored in the variable large. write a single expression whose value is the total area of this room. do not use the pow function. submit
Answers
1. You have the following information given in the problem above:
- The room has square dimensions and it has been built with two pieces of sheetrock, a smaller one and a larger one.
2. Therefore, let's call
x: the smaller one.
y: the larger one.
3. Then, you have that the lenght of the wall is the sum of the smaller one and the larger one:
x+y
4. So, the area of the room is:
(x+y)(x+y)
(x+y)²
Therefore, the answer is: (x+y)²
Kendra has a painting canvas that is 20 inches wide by 37 inches high. She painted a red rose, which covered 50% of the canvas.
What was the area of the canvas which was covered by the red rose?
Answers
A = (20) * (37)
A = 740 in ^ 2
We can make the following rule of three:
740in ^ 2 -----> 100%
x --------------> 50%
Clearing x we have:
x = (50/100) * (740)
x = 370 in ^ 2
Answer:
the area of the canvas which was covered by the red rose was:
x = 370 in ^ 2
The area of the canvas covered by the red rose is 370 square inches, calculated by multiplying the width and height of the canvas to find the total area and then taking 50% of that area.
The task is to calculate the area of a canvas that was covered by a red rose painting, which took up 50% of the total canvas area. To find the area covered by the red rose, we first need to calculate the total area of the canvas. The total area (A) of a rectangle is calculated by multiplying its width (W) by its height (H), which gives us the formula:
A = W x H
In this case, Kendra's canvas is 20 inches wide and 37 inches high. Using the formula:
A = 20 inches x 37 inches = 740 square inches
Now, since the red rose covers 50% of the canvas, we simply take 50% of the total area to find the area covered by the red rose:
Area covered by the red rose = 50% of 740 square inches = 0.50 x 740 square inches = 370 square inches
Therefore, the area of the canvas covered by the red rose is 370 square inches.
Use logarithms to solve each equation 2x9/8=111
Answers
[tex]2x^{\frac{9}{8}} = 111[/tex]
and we need to find the value of x.
First of all, we multiply the whole equation for 1/2, so our goal is to isolate x, therefore:
[tex]x^{\frac{9}{8}}=\frac{111}{2}[/tex]
Next step we must do is to apply logarithms:
[tex]logx^{\frac{9}{8}} = log(\frac{111}{2})[/tex]
Next, we have to apply identities and then to solve the equation:
[tex] \frac{9}{8}logx = log(\frac{111}{2})[/tex]
[tex]logx = \frac{8}{9}log(\frac{111}{2})[/tex]
[tex]logx = 1.5504[/tex]
[tex]10^{logx} = 10^{1.5504}[/tex]
Finally, we have the value of x which was our goal. This is the answer for the question above:
[tex]x= 35.5140[/tex]
What is the domain of the function
Answers
3√6(-7)+42
3√-42+42
3√0
0
If the number under the square root was negative, then its solutions wouldn't be real numbers. Therefore, x has to be equal to or greater than -7.
Tony makes an hourly salary of 15.40 for 40 Regular hours of work. For any time work beyond 40 hours, he is paid at a rate of time and a half per hour. Last week, Tony worked 46 hours. Find each of the following for this period.
Answers
Part (1):
We know that:For the first 40 hours, Tony is paid $11.5 per hour For additional hours,Tony is paid 1.5 * 11.5 = $17.25 for each hourLast week he worked 46 hours.Therefore:he got the normal payment of $11.5 for the first 40 hourshe got the special payment of $17.25 for the extra 6 hoursThis means that:Total amount he gained = 40(11.5) + 6(17.25) = $563.5This means that, before removing any taxes or insurances, Tony had a payment of $563.5
Part (2):
We are given that the social security tax is 6.2% of the amount he gained.
Therefore:
social security tax = 6.2% * 563.5
social security tax = 0.062 * 563.5
social security tax = $34.937
Part (3):
We are given that the medicare tax is 1.45% of the amount he gained.
Therefore:
medicare tax = 1.45% * 563.5
medicare tax = 0.0145 * 563.5
medicare tax = $8.17075
Part 4):
To get the amount that Tony has after all the taxes are paid, we will simply subtract the amount of taxes from what he originally gained as follows:final amount gained = 563.5 - (34.937+8.17075)final amount gained after taxes = $520.39225
Hope this helps :)
Tony's total earnings for the week are $754.60, which includes his regular pay for 40 hours at an hourly rate of $15.40 and overtime pay for 6 extra hours at a rate of time and a half.
Explanation:The subject of this question is Mathematics, specifically, it involves calculations relating to wage and overtime pay.
Calculating Regular and Overtime Pay
Tony earns an hourly wage of $15.40 for regular hours and is paid at a time and a half rate for any hours worked beyond 40 hours. Since he worked 46 hours last week, we can calculate his earnings as follows:
Calculate regular pay for 40 hours: 40 hours × $15.40 = $616.00.
Calculate the overtime pay rate: $15.40 × 1.5 = $23.10 per hour.
Calculate overtime pay for 6 hours: 6 hours × $23.10 = $138.60.
Add regular pay and overtime pay to get total earnings: $616.00 + $138.60 = $754.60.
Therefore, Tony's total earnings for the week, including overtime, are $754.60.
If the area of a circle below is 18ft, what is the area of the shaded sector?
Answers
Area/4 = Shaded
18/4 = Shaded
4.5 = Shaded
Hope this helps!
Answer: It’s definitely 4.5, so D! Hope this helps someone! :>
Lisa swims laps during swim practice. Her coach tells her to swim a certain number of meters (total) each week. Here's a formula for this scenario:
p= t/n
t= total number of meters
p= length of a lap (in meters)
n= number of laps Lisa swims
Lisa wants to know how many laps she must swim to meet her goal. Rewrite the formula to determine the number of laps (not a multiple choice, you don't have to show work) someone please help!
Answers
p = t / n
Where, the variables are:
t = total number of meters
p = length of a lap (in meters)
n = number of laps Lisa swims
Therefore, by clearing n we have:
n = t / p
Answer:
the formula to determine the number of laps is:
n = t / p
Answer:
formula = n = t / p
Step-by-step explanation:
Find the probability for the experiment of tossing a six-sided die twice. the sum is less than 7
Answers
Answer = 15/36 = 5/12
Final answer:
The probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12. There are 15 possible outcomes where the sum is less than 7 out of 36 total outcomes.
Explanation:
The question asks for the probability that the sum of the numbers shown by rolling a six-sided die twice is less than 7. To find this probability, we need to consider all the possible outcomes of rolling two dice.
Each die has 6 faces, so when you roll two dice, there are a total of 6 x 6 = 36 possible outcomes. To get the sum less than 7, we can have the following combinations:
(1,1) Sum = 2
(1,2) Sum = 3
(2,1) Sum = 3
(1,3) Sum = 4
(2,2) Sum = 4
(3,1) Sum = 4
(1,4) Sum = 5
(2,3) Sum = 5
(3,2) Sum = 5
(4,1) Sum = 5
(1,5) Sum = 6
(2,4) Sum = 6
(3,3) Sum = 6
(4,2) Sum = 6
(5,1) Sum = 6
Adding up the number of outcomes, there are 15 possibilities where the sum is less than 7. Therefore, the probability is 15 out of 36. This simplifies to 5/12 when reduced to its simplest form.
So, the probability of getting a sum less than 7 when rolling a six-sided die twice is 5/12.
If p(x) = 2x^3 - 3x + 5, what is the remainder of p(x) divided by (x - 5)
Answers
The question is
if p(x)= 2x³-3x+5, what is the remainder of p(x) divided by (x-5)
We use the synthetic division to find the remainder,
x-5=0
x=5
Now, write the coefficients of polynomial.
5 | 2 0 -3 5
| ↓ 10 50 235
-------------------------------
2 10 47 | 240→ is the remainder.
Quotient= 2x²+10x+47
Remainder= 240
The remainder of [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] divided by [tex]\left( {x - 5}\right)[/tex] is
Explanation:
If division of a polynomial by a binomial result in a remainder of zero means that the binomial is a factor of polynomial.
The polynomial is [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] and [tex]\left( {x - 5} \right).[/tex]
The numerator of the division is [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] and the denominator is
Solve the given polynomial [tex]P\left( x \right) = 2{x^3} - 3x + 5[/tex] by the use of synthetic division.
Now obtain the value of [tex]x[/tex] from the denominator.
[tex]\begin{aligned}x - 5 &= 0\\x&= 5\\\end{aligned}[/tex]
Divide the coefficients of the polynomial by [tex]5.[/tex]
[tex]\begin{aligned}5\left| \!{\nderline {\,{2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0\,\,\,\,\,\,\,\,\,\,\,\,\, - 3\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,5} \,}} \right. \hfill\\\,\,\,\,\underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,50\,\,\,\,\,\,\,\,\,\,\,\,\,\,235}\hfill\\\,\,\,\,\,2\,\,\,\,\,\,\,\,\,\,\,\,\,10\,\,\,\,\,\,\,\,\,\,\,\,\,47\,\,\,\,\,\,\,\,\,\,\,\,\,\,240\hfill\\\end{aligned}[/tex]
The last entry of the synthetic division tells us about remainder and the last entry of the synthetic division is [tex]240[/tex].Therefore, the remainder of the synthetic division is [tex]240.[/tex]
The remainder of [tex]p\left( x \right) = 2{x^3} - 3x + 5[/tex] divided by [tex]\left( {x - 5}\right)[/tex] is [tex]\boxed{240}.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Synthetic Division
Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree.
2. Find the area of the regular polygon. Give the answer to the nearest tenth. Hexagon with a radius of 5 in.
A. 65.0 in.^2
B. 129.9 in.^2
C. 259.8^2
D. 53.0^2
3. Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 miles. The angle between the sides of the triangle is 35°. To the nearest hundredth, find the search area.
A. 2.08 mi.^2
B. 2.97 mi.^2
C. 1.49 mi.^2
D. 1.04 mi.^2
Answers
[tex]360 \div 6 = 60 \\ 60 \div 2 = 30 \\ \frac{1}{2} (2.5 \sqrt{3} )(5) \\ 6(6.25 \sqrt{3} ) = 65.0[/tex]
Answer for #2 is A
3. D
Answer: The correct options are (2). A, (3). A.
Step-by-step explanation: The calculations are as follows:
(1) We are to given the area of a regular hexagon with radius 5 in.
The AREA of a regular hexagon with side 'a' units is given by
[tex]A=\dfrac{3\sqrt3}{2}a^2.[/tex]
We know that the radius of a regular hexagon is equal to the length of each side, so we have
a = 5 in.
Therefore, the area of the hexagon will be
[tex]A=\dfrac{3\sqrt3}{2}\times 5^2=1.5\times 1.732\times 25=64.95\sim 65~\textup{in}^2.[/tex]
Thus, (A) is the correct option.
(2) Given that two adjacent sides of the triangle measure 1.32 miles and 2.75 miles.
The angle lying between the two sides measure 35°.
we are to find the area of the triangle.
We know that the area of a triangle with two adjacent sides of measure 'a' and 'b' units and 'β' be the measure of the angle lying between them is given by
[tex]A=\dfrac{1}{2}ab\sin \beta.[/tex]
Here, a = 2.75 miles, b = 1.32 miles and β = 35°.
Therefore, the total search area, in the form of triangle is given by
[tex]A=\dfrac{1}{2}\times 2.75\times 1.32\times \sin 35^\circ=1.815\times 0.5735=2.08~\textup{mi}^2.[/tex]
Thus, the correct option is (A) 2.08 mi².
Hence, the correct options are (2). A, (3). A.
A surveying instrument aimed at a location can “shoot” the distance to the location, giving the surveyor a measurement. A surveyor used such an instrument to record the distance to a point on a tree 60 m from his position. After rotating his surveying instrument 57° to the left, he measured the distance from his same position to a fence post 35 m away.
a.) Draw the diagram and label the tree as point T, the surveyor as point S, and the fence post as point F.
b.) Determine the distance between the point on the tree and the fence post. (Show
the appropriate formula, substitutions, and work. Give the distance to the nearest tenth of
a meter.)
c.) Use the Law of Sines to find the measure of T. (Show the appropriate formula, substitutions, and work. Give the measure of T to the nearest degree.)
d.) Find mF
Please Help Me :(
Answers
b. Here we are looking for the distance between the tree (T) and the fence post (F). So we want the length of FT. We have the lengths of two sides and an angle and want the other side. The side we seek is opposite the angle whose measure we know. In this case we can use the law of cosines.
The law of cosines is: [tex] c^{2} = a^{2} + b^{2} -2abcosC[/tex]
I have labeled the side we want FT this c in the diagram. It is opposite the 57 degree angle which we will call C. (Little c is the side and big C is the angle). We call the other two sides of the triangle a and b. It doesn't matter which is which. So we have the following:
a= FS = 35
b= ST = 60
c = FT
angle C = angle S = 57 degrees
We plug the above values into the law of cosines and solve for c as follows:
[tex]c^{2} = a^{2} + b^{2} -2abcosC[/tex]
[tex]c^{2} = 35^{2} + 60^{2} -2(35)(60)cos57[/tex]
[tex]c^{2} = 1225+ 3600-(4200)(.544639)[/tex]
[tex] c^{2} =2537.51606[/tex]
[tex]c=50.3737[/tex]
You are asked to round to the nearest tenth (one decimal place) which gives the answer 50.4 meters
c. You are asked to find the measure of angle T. Further you are asked to do so using the Law of Sines. The law of sines is: [tex] \frac{a}{sinA} = \frac{B}{sinB} = \frac{c}{sinC} [/tex]. Even though there are three fractions set equal to eahc other, when we use the Law of Sines to find an angle (or a side) we need only use two fractions in most cases. Using the labels we used in part B we have the following:
A = T = the angle we are looking for
a = FS = 35 meters
C = S = 57 degrees
c = FT = 50.4 meters
We substitute these into the Law of Sines and solve for A as follows:
[tex] \frac{a}{sinA} = \frac{c}{sinC} [/tex]
[tex] \frac{35}{sinA} = \frac{50.4}{sin57} [/tex]
[tex] \frac{35}{sinA} = \frac{50.4}{.8386705} [/tex]
[tex]50.4sinA=29.353469[/tex]
[tex]sinA=.58241011662[/tex]
Here we use the arc sin (on a calculator it looks like sin to the negative 1 but it's called arcsin)
[tex] sin^{-1}(.58241011662)=A [/tex]
[tex]A=35.62023656[/tex]
You are asked to round this to the nearest degree which means to the nearest whole number. The answer is 36 degrees.
d. You are asked for the measure of angle F. Recall that the sum of the measures of the angles in a triangle is 180 degrees. We know that S = 57 degrees and T = 36 degrees (from part c). So to find the missing angle we add these and subtract their sum from 180.
[tex]F = 180-(36+57)[/tex]
F=180-93
F=87
The measure of angle F is 87 degrees
NOTE: Angles can be measure in degrees and in radians. This problem uses degrees so it is important that your calculator is set to degrees when doing this problem.
Find a polynomial with integer coefficients that satisfies the given conditions degree 3 with roots 9 2 and 0
Answers
We first make x(x-2)(x-9) and then we expand it.
You spin a spinner 48 times. Out of the 48 trials, the pointer lands 6 times on section two. What is the experimental probability of the pointer landing on section two?
1/3
1/27
1/8
1/7
Answers
Answer:
1/8
Step-by-step explanation:
Which expression is equivalent to 17s-10+3(2s+1)?
A.23s-9
B.23s-7
C.11s-7
D.11s-9
Answers
Have a good day!
B ) 23s - 7
Which expression is equivalent to (x2 – 3x)(4x2 + 2x – 9)?
A. x2(4x2 + 2x – 9) – 3x
B. x2(4x2 + 2x – 9) – 3x(4x2 + 2x – 9)
C. x2(4x2 + 2x – 9) + 3x(4x2 + 2x – 9)
D. x2(4x2 + 2x) – 3x(2x – 9)
Answers
Answer:
B. [tex]x^2(4x^2 + 2x -9) -3x(4x^2 + 2x - 9)[/tex]
Step-by-step explanation:
The distributivity establish that in order to multiply these two polynomials, first you have to multiply [tex]x^2[/tex] by every element in [tex]4x^2 + 2x - 9[/tex] and then multiply [tex]-3x[/tex] by every element in [tex]4x^2 + 2x - 9[/tex] as well.
That is exactly what the option B. says, since
in the expresion [tex]x^2(4x^2 + 2x - 9) - 3x(4x^2 + 2x - 9)[/tex] [tex]x^2[/tex] is being multiplied by every element in [tex](4x^2 + 2x - 9)[/tex] and also [tex]-3x[/tex] is being multiplied by every element in [tex](4x^2 + 2x - 9)[/tex].
what expression is equivalent to \root(4)(x^(10))
Answers
The equivalent expression to \(\root(4)(x^{10})\) is \(x^{\frac{5}{2}}\), which is obtained by realizing that the fourth root of a number can be expressed as raising that number to the 1/4 power and then applying exponent multiplication.
Explanation:To find an expression equivalent to \(\root(4)(x^{10})\), we need to apply the laws of exponents for roots and powers. The fourth root of a number is the same as raising that number to the 1/4 power, and we know from the properties of exponents that when we raise a power to another power, we multiply the exponents. Therefore:
\(\root(4)(x^{10}) = x^{\frac{10}{4}} = x^{\frac{5}{2}}\)
Thus, the equivalent expression is \(x^{\frac{5}{2}}\).
What is the equation of a parabola with a focus (-2,4) and directrix y = 0?
Answers
The equation of the parabola with focus (-2,4) and directrix y = 0 is (x + 2) = 8(y - 2). This is derived by finding the vertex and applying the general equation for a vertically oriented parabola.
To find the equation of a parabola with a given focus and directrix, we use the definition that a parabola is the set of all points that are equidistant from the focus and the directrix. In this case, the focus is at (-2,4) and the directrix is y = 0. The vertex of the parabola will thus be halfway between the focus and the directrix, which means it will lie on the line y = 2 (since the focus has a y-coordinate of 4 and the directrix is at y = 0).
The standard form equation of a vertically oriented parabola with its vertex at the origin is x = 4py, where p is the distance from the vertex to the focus (or to the directrix). For a parabola that is shifted to have a vertex not at the origin, the equation is (x-h)² = 4p(y-k) where (h,k) is the vertex.
In this scenario, because the vertex is not at the origin and the parabola opens upwards (since the directrix is below the focus), we'll adjust the standard form equation to take these factors into account. The vertex (h,k) is (-2,2), the focus is (-2,4), thus p = 2. Therefore, the equation is (x + 2)² = 4*2*(y - 2)
True or False ? explain your answer
18.csc^{-1} (csc(-\frac{\pi}{4} )) = -\frac{\pi}{4}
19.sec(sec^{-1} (\sqrt{3} ))=\sqrt{3}
Answers
you can think of such combinations this way like in this example,
sin(90°) = 1, well, then what is sin⁻¹(1)?
well, sin⁻¹(1) is really asking "what is the angle or angles whose sine is 1?"
well, we already know that sin(90°) is 1 thus sin⁻¹( sin(90°) ) = 90°.
Need help on this!!!
Answers
Area of the base of the prism: Ab=Area of the equilateral triangle
Height of the prism: h=6
Ab=A triangle= sqrt(3)/4*s^2
Ab=sqrt(3)/4*3^2
Ab=sqrt(3)/4*9
Ab=9 sqrt(3)/4
V=Ab*h
V=[9 sqrt(3)/4](6)
V=54 sqrt(3) /4
V=27 sqrt(3) / 2
V=27/2 sqrt(3)
Danny decided to invest his $500 tax refund rather than spending it. He found a bank that would pay him 4% interest, compounded quarterly. If he deposits the entire $500 and does not deposit or withdraw any other amount, how long will it take him to double his money in the account? Round your answer to the nearest tenth of a year. It will take Answer years for his investment to double.
Answers
Future value, FV = 2*PV = 2*500 = $1,000
Rate, r = 4% = 0.04
Compounding times in a year, n = 4 (compounded quarterly)
Time, t = ??
The future value expression is stated as:
FV = PV (1+r/n)^nt
Substituting;
1000 = 500 (1+0.04/4)^4t
2 = (1.01)^4t
ln 2 = 4t ln 1.01
0.6931 = 4t* 0.00995
0.6931 = 0.0398t
t = 17.414 years
Time required for the amount to double is 17.41 years.
A ________________ event has a 100% chance of occurring. Example: Picking a red ball from a bag of only red balls.
Answers
We have been given that probability of the even is 100%. In other words we can say that the probability is 1. It means that the event will certainly occur.
Now, we know that the highest value of probability is 1 and lower value is 0.
Mathematically, we can represents it as
[tex]0\leq P(E)\leq 1[/tex]
If the probability is 0 then the event will never occur.
And if the probability is 1 then event will definitely occur.
Therefore, A certain event has a 100% chance of occurring.
Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers shee can drive with 12 liters of fuel. How many kilometers can Pamela drive with 12 liters of fuel?
Answers
Answer:
132 km
Step-by-step explanation:
1. she can drive 99 km (kilometers) with 9 liters of fuel, 99/9 is 11
2. if she wants to find out how many kilometers she can drive with 12 liters of fuel, then just multiply 12x11 which is 132