The amount of money that must be deposited today is $749 .
In the question ,
it is given that ,
the amount that is need to be made (A) = $2250
time (t) = 20 years
rate percent (r) = 5.5% = 0.055
let the amount that must be deposited today be P .
The amount that is needed to be deposited today at 5.5% compounded continuously can be calculated using the formula .
A = P×[tex]e^{r\times t}[/tex]
Substituting the values , we get
2250 = P × [tex]e^{0.055\times 20}[/tex]
2250 = P × [tex]e^{1.1}[/tex]
P = 2250/ [tex]e^{1.1}[/tex]
P = 748.9599
P ≈ 749
Therefore , The amount of money that must be deposited today is $749 .
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12. What is the sign of the following? Answer "positive," "negative," or "zero." (CONSIDER SLOPE OF TANGENT)
a. f'(2)
c. f'(4)
e. f'(7)
b. f'(x) in the interval (1, 3)
d. f'(x) in the interval (3,6)
f. f'(x) in the interval (6, 9)
g. f'(x) in the interval (9, 12)
Find the interval(s) where the function is increasing and the interval(s) where it is decreasing:
27. h(x):
37. h(x)=
15. f(x) = 3x +5 17. f(x) = 2x²+x+1 21. g(x)= x³ + 3x² +1
1
2x + 3
83. AVERAGE SPEED OF A HIGHWAY VEHICLE The average speed of a vehicle on a stretch of Route 134 between 6 A.M. and 10 A.M. on a
typical weekday is approximated by the function f(t) = 20t-40√t+50 (0 ≤t≤4)
where f(t) is measured in miles per hour and t is measured in hours, with t = 0 corresponding to 6 A.M. Find the interval where fis
increasing and the interval where f is decreasing and interpret your results.
Based on the information, f(t) is increasing on [0,1) and decreasing on (1,4].
How to explain the functionIt should be noted that to find where the function is increasing and decreasing, we need to find the intervals where the derivative is positive or negative, respectively.
a. h'(x) = 3 > 0 for all x, so h(x) is increasing on (-∞, ∞).
b. h'(x) = 4x + 1 > 0 when x > -1/4, so h(x) is increasing on (-1/4, ∞). h'(x) = 4x + 1 < 0 when x < -1/4, so h(x) is decreasing on (-∞, -1/4).
c. f'(x) = 6x > 0 when x > 0, so f(x) is increasing on (0, ∞). f'(x) = 6x < 0 when x < 0, so f(x) is decreasing on (-∞, 0).
a. f(t) = 20t - 40√t + 50, f'(t) = 20 - 20/√t.
f'(t) > 0 when √t < 1, or t < 1. f'(t) < 0 when √t > 1, or t > 1.
Therefore, f(t) is increasing on [0,1) and decreasing on (1,4].
This means that during the first hour (from 6am to 7am), the average speed of the vehicle is increasing, while during the remaining 3 hours (from 7am to 10am), the average speed is decreasing.
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worksheet- triangle sum and exterior angle theorem, help pls!
The value of x in the given triangle is 110°.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given triangle,
∠A=65°, ∠B=90°, ∠C=80°, and ∠D=50°
To find the value of ∠E,
Use triangle ∠ABC, in which eqaute the sum of the angle of a triangle to 180°.
65+90+y=180
y=25
The remaining ∠C =80-25 = 55°
Use exterior angle theorem,
According to this, the sum of two interior angles is equal to an exterior angle.
x=50+55
x=105°
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A giant tortoise can travel 0.15 miles in 1 hour. At this rate, how long would it take the tortoise to travel 1 mile
It would take the tortoise approximately ____
Answer:
6 [tex]\frac{2}{3}[/tex] Hours
Step-by-step explanation:
Distance = rate times time
Let t = time
1 = .15t Divide both sides by .15
6.666... = t The 6 is repeating so as a fraction it would be
6 [tex]\frac{2}{3}[/tex]
Determine between which two consecutive integers does 7√2 lie?
Answer:
9 and 10
Step-by-step explanation:
To three decimal places
[tex]7 \sqrt{2} = 9.899[/tex]
So 7√2 is between 9 and 10 (closer to 10).
write the equation of the line, in standard form, that passes through the point (4, -8) and is parallel to x - 4y=8
Answer: x - 2y = -10.
Step-by-step explanation:
Graph the polygon with the given vertices and its image after the given rotation about point A A(1, 4), B(6, 5), C(8, 2), D(3, 2) ; 90° counterclockwise
Check the picture below.
Carmen is drawing a card from a standard deck of playing cards. Find each probability below.
Answer: How many cards are there tho?
Step-by-step explanation:
Select the function that represents a parabola with vertex at (2,–1) and a point (5,8) on its curve.
A)
ƒ(x) = (x – 2)2 – 1
B)
ƒ(x) = 2(x – 2)2 – 1
C)
ƒ(x) = 2(x + 2)2 – 1
D)
ƒ(x) = (x + 2)2 – 1
The equation of parabola is y = (x - 2)² - 1.
What is Vertex from of Parabola?We know that the standard form of the parabola is y=ax²+bx+c. Thus, the vertex form of a parabola is y = a(x-h)² + k.
Given:
Vertex (2, -1) and point (5, 8)
As, we know the vertex form of a parabola can be written as following
y = a(x - h)² + k ......(1)
Now, We are given that vertex is at (2,-1) and there is a point (5,8) on the curve.
i.e. h = 2 and k = -1,
x = 5 and y = 8
So, to find the value of a
y = a(x - h)² + k
8= a( 5- 2)² - 1
8= 9a - 1
9a= 9
a=1
Now, the equation of Parabola is
y = a(x - h)² + k
y = (x - 2)² - 1
Hence, the equation of parabola is y = (x - 2)² - 1.
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Tell whether the ratios form a proportion 12/22,18/33
The ratios of the given values 12/22,18/33 form a proportion because they all equals to 6/11.
How can we know that the values of 12/22,18/33 form a proportion?The concept that will be used is the concept of proportion. To know that the values whether they form a proportion, then, we will need to express them, in their lowest term.
12/22 can be expressed in its lowest term by dividing the denominator and the numerator by the factor of 2 givings us 6/11.
18/33 can be expressed in its lowest term by dividing the denominator and the numerator by the factor of 3 givings us 6/11.
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What is 2(5+777x60 ÷6[8-9]
Answer:
-15530
Step-by-step explanation:
plug it in to a calculator
why so random numbers
Answer:
Step-by-step explanation:
2(5+777x60/6x(-1))
2(5-7770)
2x(-7765)
-15530
Graph the equation below
Y=1/3x-1
Answer:
Step-by-step explanation:
a(0.2)and b(6.6)are points on a straight line abcd ab=bc=cd work out the coordinates of d
Answer:
i also need help with this because 2,3
Step-by-step explanation: help wich always equals 5,3
Make x the subject of m=n+x/p
The value of x is x=p(m-n).
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Given expression: m=n+(x/p)
To find: Make x the subject.
To make x the subject we have to separate the x to one side.
Expression m=n+(x/p)
Take n to another side,
(x/p)=m-n
Cross multiply,
x=p(m-n)
Therefore, the value of x is x=p(m-n).
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Help Please............
The statement that is true for the function, h is h(2) = 16
It is given that there is a function h
The range of function, h is [tex]1\leq h(x)\leq 25[/tex]
The domain of the function, h is [tex]-3 \leq x\leq 11[/tex]
And it is also given that h(8) = 19 and h(-2) = 2
Now,
The 1st option is h(-3) = -1
But the range of h is between 1 to 25, hence, this option is not true.
The 2nd option is h(8) = 21
But it is already given that h08) = 19, thus this option is not true.
The 3rd option is h(13) = 18
But the domain of h is between -3 and 11, So, this option is not true as well.
The fourth option is h(2) = 16
In this the values of range and domain are correct.
Thus, h(2) = 16.
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Find the integer closest to √42.3
Answer:
42 or 21.15?
not 100% sure but hope this helps
---------------------------------------------
Answer:
7
Step-by-step explanation:
the proper answer is 6.50384501660364
however, this isn't an integer.
to get it to become an integer, we round it up;
6.5 rounded up is 7
and therefore, the answer would be 7
hope this helps
can you find the the mistake
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
consider functions f and g defined by the graph and table
The correct statements regarding the functions are given as follows:
Function g has a greater average rate of change on interval [0,2] than function f.Function g is exponential and eventually exceeds function f, which is linear.Function f has a greater y-intercept than function g.What are the classifications of the functions?Regarding the type of function, we have that:
f(x) is a linear function, as it's graph is a straight line.f(x) is an exponential function, as when x increases by one, y is multiplied by 1.5.The y-intercepts are the values of y for which x = 0, hence they are given as follows:
f(x) = 15.g(x) = 8.Hence function g(x) starts less than f(x), but it eventually exceeds function f(x), as it is exponential, meaning that it has a greater average rate of change.
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Andrew took the midterm exam a second time this week. Andrew earned a score of 72% last week, and calculated the absolute change in the scores to be an increase of 23 percentage points. Calculate Andrew’s score on the midterm this week.
Andrew's score on the midterms this week, based on his scores last week and the absolute change, is 95%.
How to find the midterm score?The Midterm score for this week increased by 23 percentage points over the midterm score for the last week. This increase in the midterm score was an absolute change and not a relative change.
As a result of this being an absolute change, the midterm score for Andrew this week would then be:
= Midterm score last week + absolute change in the score
= 72% + 23 percentage points
= 95%
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1. A cinnamon toast recipe calls for 6 parts sugar to 1 part cinnamon. Place an X to indicate if each set of ingredients is proportional to the recipe. 4.5 tsp sugar and 0.75 cinnamon 9 tsp sugar and 1.5 tsp cinnamon 12 tsp sugar and 2 tsp cinnamon 15 tsp sugar and 3 tsp cinnamon proportional not proportional
Step-by-step explanation:
if they are proportional, then they must keep the original ratio of 6/1 of sugar to cinnamon.
X 4.5/0.75 = 6 = 6/1
X 9/1.5 = 6 = 6/1
X 12/2 = 6 = 6/1
15/3 = 5 and that is NOT 6/1 (not proportional)
a boy ate three fifthof an icicle. he gave away one thirdof it. how much icicle was eaten
In terms of fractions, 2/5 of the icicle was eaten by the boy.
If a boy ate three fifths of an icicle, then he would have two fifths, or two-fifths, left. One third of two-fifths is two-fifths of three, or two-fifths of three fifths, which is two-fifths. Therefore, the boy ate two-fifths of the icicle.In mathematical term:
A boy ate three fifth of an icicle = 3/5
A boy gave = 1/3
So, Icicle eaten by the boy = 3/5 - 1/3
= (9 - 3) / 15
= 6/15
= 2/5
Hence, In terms of fractions 2/5 of the icicle was eaten by the boy.
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A parallelogram has been found to have diagonals which are NOT congruent and slopes which are negative reciprocals.
What kind of quadrilateral is it?
It is a rhombus kind of quadrilateral.
What is quadrilateral?
A quadrilateral has four sides, is two-dimensional (flat), closed (the lines join up), and has straight sides.
A rhombus is a four-sided quadrilateral with all of the features of a parallelogram.
A rhombus has three more characteristics: consecutive sides that are congruent; diagonals that bisect pairs of opposite angles; and diagonals that are perpendicular to one another.
Moving clockwise, beginning at point A in the top left corner of a hypothetical rhombus ABCD, you can see that side AB is congruent to side BC and side CD is congruent to side DA.
Additionally, you can see that diagonals AC and DB are perpendicular to one another and that the rhombus' diagonals split pairs of opposing angles.
Hence, It is a rhombus kind of quadrilateral.
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A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60%pure antifreeze. The company wants to obtain 240 gallons of a mixture that contains 20% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?
The amount of gallons of water is 160 and gallons of the premium antifreeze solution that must be mixed is 80.
How to find the volume of water?Let y represent the volume of water
Hence,
Total volume equation :
x +y = 240 equation 1
Pure antifreeze volume:
0.60 = .20 × 240 gallons equation 2
Hence,
Equation 2
x = .20 × 240 /.60
x = 48 /.60
x = 80 (Pure antifreeze)
So,
y = 240 -80
y = 160 gallons of water
Therefore the volume of water is 160 gallons.
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the mean mass of 5 men is 76kg. the masses of 4 of the men are 72kg, 74kg, 75kg, and 81kg, what is the mass of the 5th? And
Answer:
78kg
Step-by-step explanation:
Let total mass be M.
mean=M÷5=76
M=380kg
mass of 4men is 72+74+75+81=302kg
mass of 5th man=380-302=78kg
Texas Roadhouse Corporate has decided to increase the price of
fried pickles by 15%. What will be the new price of the pickles?
The pickles are $3.99
Answer: The pickles are $3.99
Step-by-step explanation:For percents,this is always done by simply dividing the percent (in this case 15%) by 100%. So, the conversational term "15%" becomes 15% / 100% = 0.15 in terms of a real mathematical number. 0.15 x $152.00=$3.99
Limit x approaches 0 (tan^2x-sin) divide by x4
[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \stackrel{\textit{\Large L'Hopital's rule}}{\lim_{\theta \to 0}\cfrac{\frac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]}{\frac{d}{d\theta }[\theta 4]}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{d}{d\theta }[\tan^2(\theta )-\sin(\theta )]\implies \cfrac{d}{d\theta }[[\tan(\theta )]^2-\sin(\theta )]\implies \stackrel{chain~rule}{2\tan(\theta )\cdot \sec^2(\theta )} ~~ -\cos(\theta ) \\\\\\ 2\tan(\theta )\cdot \cfrac{1}{\cos^2(\theta )}-\cos(\theta )\implies \cfrac{~~ \frac{2\sin(\theta) }{\cos(\theta) } ~~}{\cos^2(\theta )}~~ -\cos(\theta ) \\\\\\ \cfrac{2\sin(\theta) }{\cos^3(\theta) }~~ -\cos(\theta )\implies \cfrac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{d}{d\theta}[4\theta]\implies 4 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\displaystyle \lim_{\theta \to 0}\cfrac{\tan^2(\theta )-\sin(\theta )}{\theta 4}\implies \lim_{\theta \to 0}\cfrac{ ~~ \frac{2\sin(\theta)-\cos^4(\theta)}{\cos^3(\theta)} ~~ }{4}\implies \lim_{\theta \to 0}\cfrac{2\sin(\theta)-\cos^4(\theta)}{4\cos^3(\theta)} \\\\\\ \displaystyle \lim_{\theta \to 0}\cfrac{2\sin(0)-\cos^4(0)}{4\cos^3(0)}\implies \lim_{\theta \to 0}\cfrac{2(0)-1^4}{4(1^3)}\implies {\Large \begin{array}{llll} -\cfrac{1}{4} \end{array}}[/tex]
Which of the following is an example of the associative property of multiplication?
Answer:
The associative property of multiplication states that the product of three or more numbers remains the same regardless of how the numbers are grouped. For example, 3 × (5 × 6) = (3 × 5) × 6.
Step-by-step explanation:
please help
A crate is 24cm by 18cm by 15cm . it is to be packed with boxes that are 8cm by 6cm by 5cm. What is the largest number of boxes that can fit into the crate .
Submit answer and show working out now !11
The largest number of boxes that can fit into the crate is 27.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
From the given data in the question,
The dimension of the crate is: 28 × 18 × 15
Volume of crate = 6480 cm³
And the dimensions of packs = 8 × 6 × 5
the volume of packs = 240 cm³
Then, the number of boxes that fit into the crate = 6480/240
= 27
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What is the factored form of 8x24-27y?
o (8x8-27y2) (2x¹6+xy+3y¹)
○ (2x-3y²) (4x¹6 - 6x³y² +9y4)
16
16
o(2x8-3y2) (4x¹6 +6x8y² +9y4)
O (8x8-27y2) (2x¹6-6xy+3y4)
The factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)
What is a factored form?Equations may be solved and x-intercepts can be found very quickly when a quadratic expression is in factored form and equal to 0. You may also find vertices and maximum and minimum values of the expression.
The four main methods of factoring are the Grouping method, Difference in Two Squares, Sum or Difference in Cubes, and Greatest Common Factor (GCF).
It is referred to as being in factored form when a quadratic expression is represented as the sum of two linear factors plus a constant. Examples of factors include ((5x + 2)(3x-1)) and ((2(x-1)(x+3)).
Given,
8x²⁴-27⁶
=(2x⁸)³-(3y²)³
=(2x⁸-3y²)((2x⁸)²+2x⁸×3y²+(3y²)²
=(2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)
Therefore, the factored form of 8x²⁴-27⁶ is (2x⁸-3y²)(4x¹⁶+6x⁸y²+9y⁴)
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2. When x = 0, y = 3 and z = 5, what is the value
of 3xy³ + 2xy³z + xyz + xz?
The value of 3xy³ + 2xy³z + xyz + xz = 0
Substituting given value in an Equation:
To find the value of a given equation or expression replaces each variable with the given value.
For example, a = 1 and b = 3 then find 3a + 2b.
=> 3(1) + 2(3) = 3 + 6 = 9
Therefore, the value of 3a + 2b = 9
Multiplication with zeroMultiplying any number with zero will give zero i.e 3 × 0 = 0. No matter how large the number is when we multiply it by zero the result will be zero.
Here we have
x = 0, y = 3 and z = 5
We need to find the value of 3xy³ + 2xy³z + xyz + xz
Substitute given values in the given expression
=> 3(0)(y)³ + 2(0)y³z + (0)yz + (0)z [ x × 0 = 0 ]
=> 0 + 0 + 0 + 0
=> 0
Therefore,
The value of 3xy³ + 2xy³z + xyz + xz = 0
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Hot Chocolate Sales and Outside Temperatures
$100 $213 $830 $679 $209 $189 $1,110 $456 $422 $235 $199
Sales ($).
Temperature
(°F)
a) Make a scatterplot of the data above. (2 points)
92° 88° 54° 62° 85° 16°
+
52⁰
65° 68°
89⁰
91°
Hot Chocolate Sales and Outside Temperatures:
(A) The scatter plot is shown below.
(B) The anomaly is located at (189, 16°F).
(C) A negative correlation exists.
(D) Sales are the dependent variable, and temperature is the independent variable.
What is Temperature?
The physical concept of temperature indicates in numerical form how hot or cold something is. A thermometer is used to determine temperature. Thermometers are calibrated using a variety of temperature scales, which historically defined various reference points and thermometric substances.
The following information is provided for hot chocolate sales and outside temperatures:
(Y) Sales Temperature (X)
100 92
213 88
830 54
679 62
209 85
189 16
1110 52
456 65
422 68
235 89
199 91
(A)
Attached below is the scatter plot.
(B)
A cluster is a group of points or values gathered in one location.
A cluster of three values between the temperatures of 80°F and 100°F may be seen on the scatter plot.
A value that differs significantly from the other values in a data set is referred to as an outlier. Either it's too little or it's too big.
In the given data collection, there is an outlier.
The anomalous value is (189, 16°F).
(C)
The scatter plot's points have a decreasing slope.
This suggests that the variables temperature and sales have a bad relationship.
There is a bad association as a result.
(D)
Dependent variables are variables that are being studied, or being kept an eye on for any changes while the other variables in the model are altered.
The variables that are changed to cause the dependent variable to vary proportionately are known as independent variables.
According to the outside temperature, the data in this case shows the sales of hot chocolate.
Sales are therefore the dependent variable, and temperature is the independent variable.
This is due to an increase in hot chocolate sales as the temperature drops.
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