ANSWER
f(1) = 8
EXPLANATION
In this problem, we have to evaluate the function f(t) in t = 1. To do so, substitute t with 1 in the equation, and solve,
[tex]f(1)=-16\cdot1^2+24\cdot1=-16+24=8[/tex]Hence, f(1) = 8.
You have $500,000 saved for retirement. Your account earns 8% interest. How much will you be able to pullout each month, if you want to be able to take withdrawals for 15 years?$
The rule of the payout annuity is
[tex]P=\frac{d(1-(1+\frac{r}{n})^{-nt})}{\frac{r}{n}}[/tex]P is the initial amount
d is regular withdrawals
r is the annual rate in decimal
n is the number of periods in a year
t is the time
Since you have $500 000 saved, then
P = 500000
Since the interest is 8%, then
r = 8/100 = 0.08
Since the time is 15 years, then
t = 15
Since you want the monthly amount, then
n = 12
Substitute them in the rule to find d
[tex]\begin{gathered} 500000=\frac{d(1-(1+\frac{0.08}{12})^{-12(15)})}{\frac{0.08}{12}} \\ 500000(\frac{0.08}{12})=d(1-(\frac{151}{150})^{-180}) \\ \frac{10000}{3}=d(1-(\frac{151}{150})^{-180}) \\ \frac{\frac{10000}{3}}{(1-(\frac{151}{150})^{-180})}=d \\ 4778.260422=d \end{gathered}[/tex]Then you will be able to pull $4778.260422 each month
6.f(x) = 2x + 3x +1g(x)=7X - 2x+7XFind h(x) = f(x) - gix)A.h(x) = -7% -5€ -5x-1B.h --- 5 -- |318
rearrange the terms and simplify
[tex]\begin{gathered} h(x)=-7x^3-7x^2+2x^2+3x+2x+1 \\ =-7x^3-5x^2+5x+1 \end{gathered}[/tex]The right option is A
1 Evaluate 0.1m + 8 – 12n when m = 30 and n = 1/4.
Answer:
8
Step-by-step explanation:
0.1(30)+8-12(0.25)
3+8-3
=8
I need help to solve this I don't quite understand how to do these
Recall the definition of the sine of an angle in a right triangle:
[tex]\sin (A)=\frac{\text{Side opposite to A}}{\text{ Hypotenuse}}[/tex]In the given diagram, the length of the side opposite to the angle of 53° has a length of 10, while the length of the hypotenuse is x. Then:
[tex]\sin (53)=\frac{10}{x}[/tex]Isolate x from the equation:
[tex]x=\frac{10}{\sin (53)}[/tex]Use a calculator to find the value of the expression for x:
[tex]\begin{gathered} x=12.52135658\ldots \\ \Rightarrow x\approx12.5 \end{gathered}[/tex]22) A game is played using one die. If the die is rolled and shows a 2, the player wins $8. If the die
shows any number other than 2, the player wins nothing. If there is a charge of $1 to play the
game, what is the game's expected value?
A) $0.33
B) $7.00
C)-$0.33
D) -$1
The game's expected value is (A) $0.33
How to determine the expected amount the player wins or lose?From the question, we have the following parameters that can be used in our computation:
Outcome of 2 = Win $8
Other outcomes = Win $0
A die has the following sample space
S = {1, 2, 3, 4, 5, 6}
Using the above sample space, the individual probabilities are:
P(Outcome of 2) = 1/6
P(Others) = 5/6
The expected value is calculated as
Expected value = Sum of the products of the probability and the amount win/lose
So, we have
Expected = 1/6 * 8 + 5/6 * 0
Evaluate the products
Expected = 1.33
The charge is $1
So, we have
Expected = 1.33 - 1
Evaluate
Expected = 0.33
Hence, the expected amount is $0.33
Read more about expected values at
brainly.com/question/15858152
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Convert:47.0 grams Cu = ? moles
In 1 grams of Cu there are 0.015736631731344 moles
So, for 47.0 gram Cu : Multiply 47.0 by 0.015736631731344 :
47.0 gram Cu = 47.0 x 0.015736631731344
47.0 gram Cu = 0.73962 mol
Answer : 0.73962 mol
3 Step Problem: Erik is building a cubby bookshelf, that is, a bookshelf divided into storage holes (cubbies) instead of shelves. He wants the height of the bookshelf to be x^2 - 2x - 3 and the width to be x^2 + 4x + 3. Each cubby hole in the bookshelf will have a height of x + 3 and width of x - 3.STEP 1 of 3: Write a rational expression to determine how many cubbies high the book shelf will be.
Step 1:
In order to determine the number of cubbies high, we just need to divide the total height x² - 2x - 3 by the height of one cubby x + 3:
x² divided by x: x
x multiplied by (x + 3): x² + 3x
x² - 2x - 3 minus x² + 3x: -5x - 3
-5x divided by x: -5
-5 multiplied by (x + 3): -5x - 15
-5x - 3 minus -5x - 15: 12
The division doesn't have remainder 0, so let's write the division as a fraction:
[tex]\text{number of cubbies}=\frac{x^2-2x-3}{x+3}[/tex]Jimmy is working at a factory where they make cars and trucks in the ratio five to four if the factory makes 100 trucks how many cars will it produce
From the basic knowledge of ratio:
cars : trucks
[tex]\begin{gathered} \frac{5}{4}\text{ = }\frac{x}{100} \\ \text{cross}-\text{ multiply,} \\ 4\text{ }\times\text{ x = 5 x 100} \\ 4x\text{ = 500} \\ \text{Divide both sides, we have:} \\ x\text{ =500/4} \\ x\text{ = 125} \end{gathered}[/tex]Multiply4V3 * 10V12 * V6*V2Enter your answer, in simplest radical form, in the box.
Given:
[tex]4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2}[/tex]Simplify the expression.
[tex]\begin{gathered} 4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10\sqrt[]{4\times3}\cdot\sqrt[]{3\times2}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10(\sqrt[]{2^2})\sqrt[]{3}\cdot\sqrt[]{2}\cdot\sqrt[]{3}\cdot\sqrt[]{2} \\ =4\sqrt[]{3}\cdot10(2)\sqrt[]{3}\cdot2\sqrt[]{3} \\ =(4\times20\times2)(\sqrt[]{3})^2\cdot\sqrt[]{3} \\ =480\sqrt[]{3} \end{gathered}[/tex]Answer:
[tex]4\sqrt[]{3}\cdot10\sqrt[]{12}\cdot\sqrt[]{6}\cdot\sqrt[]{2}=480\sqrt[]{3}[/tex]which of the following would be an equivalent ratio to 2:90?
Male teachers = 2
Male students = 180/2 = 90
The ratio of male teachers to male students
2:90
2/90, simplify by 2 = 1/45
Kevala sells sodas and sundaes at his food stand. One week the number of sodas he made was 4 fewer than 5 times the number of sundaes. If he made 96 sodas, how many sundaes did he make?
hello
let sundaes be represented by x and soda by y
on this particular week, we made sodas 4 fewer than 5 times the numbers of sundaes
let's write an equation for this
[tex]y=5x-4[/tex]with this equation, we can know the numbers of sundaes he made
remember that y is representing soda and x is representing sundaes
[tex]\begin{gathered} 96=5x-4 \\ \text{solve for x} \\ \text{collect like terms} \\ 96+4=5x \\ 100=5x \\ \text{divide both sides by the coefficient of x} \\ \frac{100}{5}=\frac{5x}{5} \\ x=20 \end{gathered}[/tex]from the calculations above, Kevala made 20 sundaes and 96 soda
I need help with finding the area as 8.7 as the height and I also need to know how to check the height is 8.7
The given figure is a trapezium as two sides are parallel and two are non parallel.
The parallel sides of the trapezium are a=3 mi and b=11 mi.
The height of the trapezium is h=8.7 mi.
The expression for the area of the trapezium is,
[tex]\text{Area}=\frac{1}{2}(a+b)\times h[/tex]Substituting the known values in the above expression,
[tex]\begin{gathered} \text{Area}=\frac{1}{2}(3\text{ mi+11 mil)}\times8.7\text{ mi} \\ =\frac{14\text{ mi}}{2}\times8.7\text{ mi} \\ =7\text{ mi}\times8.7\text{ mi} \\ =60.9mi^2 \end{gathered}[/tex]Thus, the required area is 60.9 square miles.
Miguel and 3 of his friends went to the movies. They originally had a total of $40.00. Each boy had the same amount of money and spent $7.50 on a ticket. How much money did each boy have left after buying his ticket. Write and solve and equation.
Solution
Miguel and 3 of his friends went to the movies.
They originally had a total of $40.00.
Since each boy have the same amount, let the amount each boy have left after the ticket be m
The amount each boy have left is
[tex]4\times m=4m[/tex]Each boy spent $7.50 on a ticket, i.e
[tex]4\times7.5[/tex]The amount of money that each boy have left can be expressed as
[tex]\begin{gathered} 4m+4(7.5)=40 \\ 4(m+7.5)=40 \end{gathered}[/tex]Solving for m
[tex]\begin{gathered} 4(m+7.5)=40 \\ \text{Divide both sides by 4} \\ \frac{4(m+7.5)}{4}=\frac{40}{4} \\ m+7.5=10 \\ \text{Collect like terms} \\ m=10-7.5 \\ m=\text{ \$2.5} \end{gathered}[/tex]Hence, each boy have $2.5 left after buying his ticket.
Answer: $2.50 would be your answer!
Step-by-step explanation: $7.50 x 4 = 30
40$ - 30 = 10
10 ÷ 4 = 2.50
hope this helps! :)
Joshua is going to invest $9,000 and leave it in an account for 5 years. Assuming theinterest is compounded continuously, what interest rate, to the nearest tenth of apercent, would be required in order for Joshua to end up with $12,500?
Let r be the percent annual interest rate of the account. Since $9000 are left for 5 years, for an outcome of $12,500, then:
[tex]9000\times(1+\frac{r}{100})^5=12,500[/tex]Divide both sides by 9000:
[tex](1+\frac{r}{100})^5=\frac{12500}{9000}=\frac{25}{18}[/tex]Take the 5th root to both sides:
[tex]\begin{gathered} 1+\frac{r}{100}=\sqrt[5]{\frac{25}{18}} \\ \Rightarrow\frac{r}{100}=\sqrt[5]{\frac{25}{18}}-1 \\ \Rightarrow r=100(\sqrt[5]{\frac{25}{18}}-1) \end{gathered}[/tex]Use a calculator to find the decimal expression for r:
[tex]r=6.790716585\ldots[/tex]Therefore, to the nearest tenth:
[tex]r=6.8[/tex]This means that Joshua would need to invest his money on a 6.8% annual interest account.
can you help me with this assignment
The two lines are said to be parallel if thier slopes are equal
where, the slope of a line is express as:
[tex]\begin{gathered} y\text{ =m(x-a)+b} \\ \text{ m is the slope} \end{gathered}[/tex]The given expression of line : y= -2x - 1
On comparing with the general equation of line, slope is
m = (-2)
A) x + 2y =-10
Simplify the general equation of line
x+2y =-10
2y=-10-x
y= -x/2 -5
Here slope is (-1/2)
So, the lines are not parallel
B) 2x-y=4
Simplify in the general equation of line
2x-y=4
y=2x-4
Here slope is 2
So, the lines are not parallel.
C)2y-x=-6
Simplify in the general equation of line
2y - x = -6
2y = x - 6
y = x/2 - 3
Here slope is 1/2
So, the lines are not parallel.
D) 2x + y =-6
Simplify in the general equation of line
2x + y =-6
y = -6 -2x
y = -2x -6
Here slope = (-2)
So, the lines are parallel.
The equation 2x + y =-6 & y= -2x - 1 have slope = (-2)
So, the lines are parallel
Answer : D) 2x + y =-6
Allied Health - A wound was measured to be 0.8 cm in length. Whaat is the greatest possible error of this measurement?
The answer is 0.05cm
Explanation
Precision = 0.1
∴ Greatest Possible Error (GPE) = 0.1/2
GPE = 0.05cm
Hence the greatest possible error of the measurement is 0.05cm
Triangle - Interior Angles Find the measure of the indicated angle in each triangle. 3 27 311>P 26 A ma m2Q= 1 s 스 minta mothed
Answer: We are goinf to sovle triangle Number-03:
[tex]m\angle Q=?[/tex]We know that the sum of angles in a triangle is 180 degrees, therefore we can do the following:
[tex]\begin{gathered} m\angle Q+30+31=180^{\circ} \\ \therefore\rightarrow \\ m\angle Q=180^{\circ}-61=119^{\circ} \\ \therefore\rightarrow \\ m\angle Q=119^{\circ} \end{gathered}[/tex]This is the unknown angle that we were interested in.!
Skip designs tracks for amusement park rides. For a new design, the track will be elliptical. If the ellipse is placed on a large coordinate grid with its center at (0, 0), the equation x^2/2500 + y^2/8100 = 1 models the path of the track. The units are given in yards. How long is the major axis of the track? Explain how you found the distance.show the steps
Step 1
Given:
center (0,0)
the equation given should have been:
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]We need to identify the larger denominator. If it is under x, the ellipse is horizontal. If it is under y, the ellipse is vertical. 8100 is the larger denominator and is under y, therefore, the ellipse is vertical
Step 2
The general equation of an ellipse is given as;
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]h and k are the center values which are both 0.
a = length of the semi-major axis
b = length of the semi-minor axis
The given equation is;
[tex]\frac{x^2}{2500}+\frac{y^2}{8100}=1[/tex]which is equivalent to;
[tex]\frac{x^2}{50^2}+\frac{y^2}{90^2}=1[/tex][tex]\begin{gathered} a^2=90^2 \\ \sqrt[]{a^2}=\sqrt[]{90^2} \\ a=90\text{ yard},\text{ the semi-major ax}is \end{gathered}[/tex]The length of the major axis will thus be; 90x2=180 yards
Answer; 180 yards
Yolanda is preparing a liquid fertilizer that she will use on her lawn. She mixes 4 tablespoons of liquid fertilizer with 6 gallons of water.Using this ratio, how many gallons of water should be mixed with each tablespoon of liquid fertilizer?
Given data:
The given amount of liquid fertilizer is f=4.
The given water is w=6 gallons.
4 tablespoons= 6 gallons of water
1 tablespoon= 1.5 gallons of water.
Thus, 1.5 gallons of water is mix with each tablespoon.
Write the quadratic equation in Vertex form with vertex (4 8) and passing through the origin.
Vertex = (4,8)
Passing through the origin = (0,0)
Vertex form:
y= a (x-h)^2+k
(h,k) is the vertex:
y= a (x-4)^2+8
Replace the (x,y ) by the origin coordinates
Solve for a
0= a (0-4)^2+8
-8 = a(-4)^2
-8 = a 16
-8/16 = a
-1/2 = a
y=-1/2 (x-4)^2+8
3.5 feet3 feet3 feet2 feet4.5 feet
The shape in the image is a trapezium. The area of a trapezium is given by:
[tex]A_{trapezium}=\text{ }\frac{1}{2}\text{ (a + b)h}[/tex]From the image, a= 3.5 feet, b= 4.5 feet and h = 2 feet.
Thus, we have:
[tex]\begin{gathered} A_{trapezium}=\text{ }\frac{1}{2}\text{ ( 3.5 + 4.5) 2} \\ A_{trapezium}=8ft^2 \end{gathered}[/tex]Hence, the area of the figure is 8 square feet
the table below shows the length of time a plumber takes on a job and price he charges. what does the y-intercept represent?
The data that represents the y-intercept in a table is always the output/result. In the given table, it shows the cost that the plumber charges after the given hours of work.
Thus, the y-intercept in the data is the total cost of repairs.
The answer is letter B.
1 point It takes 500 packing peanuts to fill a box that is 3 inches x 4 inches x 5 inches. How many peanuts would it take to fill a box that is 6 inches x 8 inches x 10 inches? 1,000 packing peanuts 2,000 packing peanuts 4,000 packing peanuts 8,000 packing peanuts
Well, this is a volume and ratio problem. In a box the volume is given by width times length times height, so the volume of the first box is 3*4*5=60 cubic inches.
In the second box, the volume is 6*8*10=480 cubic inches.
[tex]\frac{480}{60}=\frac{8}{1}=8[/tex]This means that in the big box you could place 8 peanuts for every peanut placed in the small box. If you need 500 peanuts to fill the small box, then for the big box:
[tex]500\cdot8=4000[/tex]So, you need
1. Find Each Right triangles missing length. If necessary, round to thenearest tenth,5 pointsleg =8 cm, leg= 21 cm
We have a right triangle, for which we know the two legs.
We can calculate the hypotenuse H by applying the Pythagorean theorem:
[tex]\begin{gathered} H^2=L^2_1+L^2_2=8^2+21^2=64+441=505 \\ H=\sqrt[]{505}\approx22.5 \end{gathered}[/tex]The missing length (the hypotenuse) is approximately 22.5 cm.
if ABC is an equilateral triangle and BD = 54 inches. find the value of x round to the nearest tenth
Solution
Step 1
Draw half of the given triangle
Step 2
State a known fact of an equilateral triangle to help with the question
Since the triangle is an equilateral triangle, each angle in triangle ADC = 60 degrees
Because the sum of angles in a triagle = 180 degrees and an equilateral triangle has all sides and angles equal
Therefore each angle = 180/3 = 60 degrees
so in the triangle ABD,
Step 3
Find the value of x using a trigonometric ratio
To find the length of x, we will use the trig ratio SOH(sine, opposite, hypothenuse)
[tex]\begin{gathered} \text{Sine 60 = }\frac{opposite}{\text{hypothenuse}} \\ \text{opposite}=\text{ 54inches} \\ \text{hypothenuse = x inches} \end{gathered}[/tex]
After substitution we will have that
[tex]\begin{gathered} \sin e\text{ 60 = }\frac{54}{x} \\ \text{but sine 60 = }\frac{\sqrt[]{3}}{2} \\ \frac{\sqrt[]{3}}{2}=\frac{54}{x} \\ \sqrt[]{3}x=108 \\ x\text{ =}\frac{108}{\sqrt[]{3}} \\ x\text{ =36}\sqrt[]{3} \\ x\text{ }\approx\text{62.4 inches to the nearest tenth} \end{gathered}[/tex]Therefore, x = 62.4 inches to the nearest tenth
Sylvia has 9 nickles. She wants to split the money equally between herself and two friends. How much will each person receive?
Quadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side HI. Round your answer to the nearest tenth if necessary
we have:
[tex]\frac{HI}{DE}=\frac{IF}{EB}[/tex]so
[tex]\begin{gathered} \frac{HI}{23}=\frac{59}{14} \\ 14HI=59\cdot23 \\ 14\cdot HI=1357 \\ HI=\frac{1357}{14} \\ HI=96.9 \end{gathered}[/tex]answer: HI = 96.9
DEF~△VXW.244FED122WXVWhat is the similarity ratio of △DEF to △VXW?Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
We are given two triangles. We notice that each corresponding angle is equal, therefore, by Angle Angle Angle (AAA) theorem the triangles are similar. This means that each corresponding side is at the same ratio. That ratio is called the similarity ratio and it is obtained by finding the quotient between any two corresponding sides, like this:
[tex]r=\frac{DF}{VW}=\frac{DE}{VX}=\frac{FE}{WX}[/tex]Where "r" is the similarity ratio. Now, we substitute the sides:
[tex]r=\frac{4}{2}=\frac{4}{2}=\frac{2}{1}=2[/tex]Therefore, the similarity ratio is 2.
A rectangular paperboard measuring 32 in long and 24 in wide has a semicircle cut out of it, as shown below.Find the area of the paperboard that remains. Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.
We need to subtract the area of the semicircle that was cut out of the paperboard from its original area.
The original area of the paperboard was the area of a rectangle 32in long and 24 in wide:
[tex]32in\cdot24in=768in^{2}[/tex]And the area of the semicircle, noticing that its radius r is 24in/2, is given by:
[tex]\frac{\pi r^2}{2}=\frac{3.14\cdot(12in)^{2}}{2}=\frac{3.14\cdot144in^2}{2}=226.08in^2[/tex]Thus, the area of the paperboard that remains is:
[tex]768in^2-226.08in^2=(768-226.08)in^{2}=541.92in^{2}[/tex]Therefore, the answer is 541.92 in².
You will complete the following question on your own paper. Make sure to show ALL work including a picture you draw. He 2 A point on the ground is 50 feet from my house. The angle of elevation to the top of the house is 48º. Find the height of the house to the nearest tenth. Finis the following template: "Last Name First Name Assignment
ANSWER
The height of the house is 55.5 feet
EXPLANATION
Since this forms a right triangle, we can use the tangent of the elevation angle to the top of the house to find its height - because we know the lenght of the adjacent side and we want to know the lenght of the opposite side:
[tex]\begin{gathered} \tan 48º=\frac{h}{50} \\ h=50\tan 48º \\ h=55.53062574\approx55.5\text{ feet} \end{gathered}[/tex]