Answer: $7142.86
Step-by-step explanation:
Let the amount to be invested in the bond be represented by y.
Based on this, the amount to be invested in the CD will be: = 50000 - y.
From the information given, yearly interest on bond is 12%, this will be:
= 12% × y = 0.12 × y = 0.12y
Also, interest on CD will be:
= 5% × (50000 - y)
= 0.05(50000 - y)
Then, the equation to get the amount to be invested in bond will be:
0.12y + 0.05(50000 - y) = 3000
0.12y + 2500 - 0.05y = 3000
0.12y - 0.05y = 3000 - 2500
0.07y = 500
y = 500/0.07
y = 7142.8571
y = 7142.86
The amount to be invested in bond will be $7142.86
f(x) = [(9,11),(-11,4),(7,-6),(11,-1), (-6,-15),(-13,-5)].
f^-1(f(93)) = m
(f(7)) = n
Find m and n
Using the inverse functions property:
f⁻¹(f(93)) = m = 93f(7) = n = -6How to find the values of m and n?
Two functions f(x) and f⁻¹(x) are inverses if:
f( f⁻¹(x) ) = x
f⁻¹(f(x)) = x
We want to get:
f⁻¹(f(93)) = m
By using the above definition we get:
f⁻¹(f(93)) = m = 93
Now for the second one we want:
f(7) = n
If you look at the table, you can see that f(x) contains the point (7, -6), then:
f(7) = n = -6
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Why we need the least common denominator to add or subtract ration?
Answer:
It is necesary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator
Step-by-step explanation:
f(x)
X
(b)
Use the graph to determine the limit visually (if it exists). (If an answer does not exist, enter DNE.)
(a)
lim f(x)
X--1
-2
lim f(x)
x 0
Write a simpler function that agrees with the given function at all but one point.
q(x) =
a) Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
b) The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
How to determine whether a limit exists or not
According to theory of limits, a function f(x) exists for x = a if and only if [tex]\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)[/tex]. This criterion is commonly used to prove continuity of functions.
Rational functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following lateral limits:
[tex]\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty[/tex]
[tex]\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty[/tex]
Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
In addition, we can simplify the function by algebra properties:
[tex]\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}[/tex]
[tex]g(x) = \frac{1}{x + 1}[/tex]
The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
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Melissa bought 42 pine seedlings and 30 juniper seedlings
to plant in rows on her tree farm. She wants each row to
have the same number of seedlings. She wants only one
type of seedling in each row. What is the greatest number of
seedlings she can plant in each row? How many rows of each
type
of tree will there be?
Answer:
See below
Step-by-step explanation:
GCF (greatest common factor ) of 42 and 30 is 6
each row will have 6 seedlings
there will be ( 42+30) / 6 = 12 rows
7 pine rows 5 juniper rows
If one three-digit number (0 cannot be a left digit) is chosen at random from all those that can be made from the following set of digits, find the probability that the one chosen is not a multiple of 5.
(0, 1, 2, 3, 4,5)
Answer:
5/25
Step-by-step explanation:
A set of 3 pens costs $1.68. At that unit price, how much would one pen cost?
Answer:
$.56
Step-by-step explanation:
To find the cost of one pen, take the total cost and divide by the number of pens
$1.68/ 3
$.56 per pen
find the surface area of the triangular prism.
The surface area of the triangular prism is 93 squared feet.
What is the surface area of the triangular prism?
The surface area of triangular prism is expressed as;
S.A = bh + ( s₁ + s₂ + s₃ )H
From the diagram;
h = 2ftb or s₁ = 3fts₂ = 3fts₃ = 3ftH = 10ftWe substitute our given values into the equation above.
S.A = bh + ( s₁ + s₂ + s₃ )H
S.A = (3ft × 2ft) + ( 3ft + 3ft + 3ft )10ft
S.A = 3ft² + ( 9ft )10ft
S.A = 3ft² + 90ft²
S.A = 93ft²
The surface area of the triangular prism is 93 squared feet.
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If f(x)f(x) is an exponential function where f(3.5)=12f(3.5)=12 and f(9)=75f(9)=75, then find the value of f(7.5)f(7.5), to the nearest hundredth.
Using an exponential function, it is found that f(7.5) = 45.5.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.For this problem, we have that f(3.5) = 12, then:
[tex]y = ab^x[/tex]
[tex]12 = ab^{3.5}[/tex]
[tex]a = \frac{12}{b^{3.5}}[/tex]
We also have that f(9) = 75, then:
[tex]y = ab^x[/tex]
[tex]75 = ab^9[/tex]
Since [tex]a = \frac{12}{b^{3.5}}[/tex]:
[tex]75 = \frac{12}{b^{3.5}} \times b^9[/tex]
[tex]b^{5.5} = \frac{75}{12}[/tex]
[tex]\sqrt[5.5]{b^{5.5}} = \sqrt[5.5]{\frac{75}{12}}[/tex]
[tex]b = \left(\frac{75}{12}\right)^{\frac{1}{5.5}[/tex]
b = 1.39542165
Then:
[tex]75 = ab^9[/tex]
[tex]a = \frac{75}{1.39542165^9}[/tex]
a = 3.7386
Hence:
[tex]y = 3.7386(1.39542165)^x[/tex]
When x = 7.5, we have that:
[tex]y = 3.7386(1.39542165)^{7.5} = 45.5[/tex]
Hence f(7.5) = 45.5.
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The inside dimensions of a box are 12 inches long, 5 inches wide, and 2 inches deep.
How many cubic inches does it contain?
60
110
120
240
none of these
Select the correct answer. What are the solutions to this equation? 16x2 + 9 = 25
The solutions to the given quadratic equations are x = -25/16 and x = 1
Quadratic equationsFrom the question, we are to determine the solutions to the given quadratic equation
The given quadratic equation is
16x² + 9 = 25
The equation can be solved as follows
16x² + 9 = 25
16x² + 9 - 25 = 0
16x² -16x +25x -25 = 0
16x(x -1) +25(x -1) = 0
(16x +25)(x -1) = 0
16x + 25 = 0 OR x - 1 = 0
16x = -25 OR x = 1
x = -25/16 OR x = 1
Hence, the solutions to the given quadratic equations are x = -25/16 and x = 1
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The surface areas of two similar rectangular prisms Are 361m squared And 441m squared. What is the scale factor Of the larger prism to the smaller prism
The scale factor Of the larger prism to the smaller prism is 0.9
How to determine the scale factor?The given parameters are
Large area = 441
Small area = 361
Divide the small area by the large area
Small/Large = 361/441
Take the square root to determine the scale factor k
[tex]k = \sqrt{\frac{361}{441}[/tex]
Evaluate
k = 0.9
Hence, the scale factor Of the larger prism to the smaller prism is 0.9
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For which interval is the function constant? (−4,0) begin ordered pair negative 4 comma 0 end ordered pair (4,∞) left parenthesis 4 comma infinity right parenthesis (0,4) begin ordered pair 0 comma 4 end ordered pair (−∞,−4)
Answer: (-4, 0)
Step-by-step explanation: I just took the quiz and got it correct!
The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval.
To determine the interval in which the function is constant, we need to examine the given ordered pairs (x, y) and check if the function's output (y-values) remains the same within that interval.
Let's analyze each interval:
1. (-4, 0): This interval represents all x-values greater than -4 and less than 0. In this interval, the function takes the value 0 for all x-values in the interval. Therefore, the function is constant (equal to 0) within this interval.
2. (4, ∞): This interval represents all x-values greater than 4. In this interval, the function's output is given as "∞" (infinity) for all x-values in the interval. The function is constant (equal to infinity) within this interval.
3. (0, 4): This interval represents all x-values greater than 0 and less than 4. In this interval, the function takes the value 4 for all x-values in the interval. Therefore, the function is constant (equal to 4) within this interval.
4. (-∞, -4): This interval represents all x-values less than -4. In this interval, the function's output is not specified or may not be constant. The information provided does not give us the exact function to determine the output for all x-values in this interval.
The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval. However, we don't have enough information to determine if the function is constant on the interval (-∞, -4).
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PLS HELPPPPP ASAPPP OR IMAAA FAIL HELPPPPPPPPPPPPPPPPPPPPPPPPPPPp
Answer:
Step-by-step explanation:
(a). A = 5x( 7x - 2 ) - 3x( 2x + 4 )
(b). A = 35x² - 10x - 6x² - 12x = 29x² - 22x
A = 29x² - 22x
19. Solve each equation by graphing. Round to the nearest tenth.
6x² +18x=0
3,6
0, -3
-3, -6
-1,6
Math 2
Answer:
0, -3
Step-by-step explanation:
Attachment.
In short, it is way easier to not graph it, however, if you really need to graph it, change it to the correct form, then do some plug and chug if the equation is not so friendly.
Evaluate the expression. 2+6+ – 4 4 /5 ÷ – 3 Write your answer as a fraction or as a whole or mixed number.
Answer:
9 3/5
Step-by-step explanation:
2+6+-4 4/5 ÷ -3
PEMDAS! First is multiplicationSo, solve the bold
2+6+ -4 4/5 ÷ -3
So,
2+6+ 1 3/5
Next is Addition(IN ORDER OF THE EQUATION), So solve the bold,
2+6+ 1 3/5
So, the answer is
9 3/5
The acute angle between the lines x – 3y – 6 = 0 and y = 2x + 5 is
Answer:
Step-by-step explanation:
eq. of line x-3y-6=0
3y=x-6
y=1/3 x-6/3
or
y=1/3 x-2
its slope m1=1/3
y=2x+5
slope m2=2
if α is the angle between the lines then
[tex]tan~\alpha =|\frac{m1-m2}{1+m1m2} |=|\frac{\frac{1}{3} -2}{1+1/3\times 2}| =|\frac{1-3\times2}{3+2}| =5/5=1=tan 45\\\alpha =45^\circ\\[/tex]
When a function is evaluated with a zero, it represents:
-the initial amount or starting point before a certain time.
-the initial amount or starting point.
-the initial amount or starting pint after a certain time
Answer: the initial amount or starting point.
Step-by-step explanation:
Use the following regression equation regarding airline tickets to answer the question.
Price = 49 + 0.137 · (Distance)
Note that Distance is the amount of kilometres between the departure and arrival cities, and Price is the cost of an airline
ticket.
Interpret the slope of the regression equation in the context of the data.
The interpretation of the slope is the price of an airline ticker per kilometer is 0.137
How to interpret the slope?The regression equation is given as:
Price = 49 + 0.137 · (Distance)
A regression equation is represented as
y = b + mx
Where m represents the slope
By comparison, we have
m = 0.137
Slopes are used to represent average rates
This means that the interpretation of the slope is the price of an airline ticker per kilometer is 0.137
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What is the additive inverse of the number given below?
6
Answer:
-6 is the answer for instance 6=-6 or +(-6)
Ram bough some pen for Rs 90. If he paid Rs 1 less for each he would have 3 more pens. How many pens did he buy?
Based on the fact that Ram bought some pens and they cost Rs.90 but if he had paid Rs.1 less for each he would have 3 more pens, the number of pens he bought is 6 pens.
What number of pens did Ram buy?This can be represented as:
(x + 3) (y - 3) = 90
Where xy = 90
xy - 3x + 3y - 9 = xy
3y - 3x - 9 = 0
y - x - 3 = 0
x - y + 3 = 0
Solving further gives:
x - 90/ x + 3 = 0
x² + 3x - 90 = 0
Remembering that:
90 = 9 x 10
= 3 x 3 x 2 x 5
= 15 x -6
Going back to the formula:
x (x + 15) - 6 (x + 15)
(x + 15) (x - 6) = 0
x - 6 = 0
x = 6 pens
In conclusion, the number of pens bought was 6 pens.
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In Hawaii”s Kona iron man competition, Gretchen swims the first 7/8 of a mile in 70 minutes. At this pace, how many minutes will it take for Gretchen to swim the entire 2 2/5 mile course
It would Gretchen 192 minutes to swim the entire 2 2/5 mile course.
What is speed?
Speed is distance divided by the time taken to cover the distance.
In this case, we can determine distance covered in a minute by dividing the speed by the distance, which is distance of 7/8 mile(i.e. 0.825 mile) over the time take to cover the distance.
speed per minute=0.825/70
speed per minute=0.0125 mile/minute
With this, we can determine the time in minutes it would take to cover 2.4 miles(2/5=0.4)
0.0125=2.4/time
0.0125*time=2.4
time=2.4/0.0125
time=192 minutes
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Graph the line. y = -1/5x-5 Both points y and x
Answer:
connect the dots (0, -5) and (5, -10).
5-43-2
O (6,4)
-
O (3/2, 1)
2
3
Do,2 of Y is:
O (5, 4)
45
S
73
4
(3.2)
y
12 34
2
N
(4,0) X
(2,-2)
Answer:
(6, 4)
{second option given}
Step-by-step explanation:
we know that point y is (3, 2)
If we dilate this point by a factor of 2, we will get (6, 4)
why?
when we "dilate" something, we multiply both numbers of that point by a scale factor, we can see that this factor is 2--so we can multiply both 3
(3 ·2 = 6) and 2 (2 · 2 = 4) to get our new point, (6, 4)
hope this helps! have a lovely day :)
Q1. A man wants to paint his house in 3 colors. If he can choose 3 colors out of 6 colors, how many
different color settings can he make?
(A) 216 (B) 20 (C) 18 (D) 120
The number of color settings he can make is 20
How to determine the number of color setting?The given parameters are
Colors, n = 6
Selected color, r = 3
The number of color setting is calculated as:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
This gives
[tex]^6C_3 = \frac{6!}{3!3!}[/tex]
Evaluate the expression
[tex]^6C_3 = 20[/tex]
Hence, the number of color settings he can make is 20
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To find the driver's initial speed
The speed of the driver is 200km/hr.
How to calculate the speed?The information is incomplete and an overview will be given since the complete information wasn't found online.
It should be noted that speed is calculated as:
= Distance / Time
Let distance = 2000km
Let time = 10 hours.
Speed = Distance/Time
Speed = 2000/10
Speed = 200km/hr
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say true false .
empty set is the subset of any set
Answer:
True. empty set is the subset of any set
Zendaya runs a farm stand that sells blueberries and grapes. Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25. Zendaya made $55 from selling a total of 33 pounds of blueberries and grapes. Write a system of equations that could be used to determine the number of pounds of blueberries sold and the number of pounds of grapes sold. Define the variables that you use to write the system.
The number of pounds of blueberries and grapes sold are 11 and 22.
According to the statement
we have given that the:
Each pound of blueberries sells for $2.50 and each pound of grapes sells for $1.25.
And total money collected by selling pounds is $55
And total number of pounds sells = 33
And we have to find the Number of pounds of blueberries and grapes.
Let the number of pounds of blueberries is X
And Let the number of pounds of grapes is Y
So,
The equation becomes is:
X + Y = 33 -(1)
2.50X + 1.25Y = 55 -(2)
Now, From substitution method
From (1) equation
Y = 33 - X
put these in equation (2) then
2.50X + 1.25(33 - X ) = 55
2.50X + 41.25 - 1.25X = 55
1.25X = 13.75
X = 11
and the the value of Y becomes
Y = 33 - X
Y = 33 - 11
Y = 22.
So, The number of pounds of blueberries and grapes sold are 11 and 22.
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Find f(-3) for f(x) = 4(2)^x.
Answer:
1/2
Step-by-step explanation:
[tex]f( - 3) = 4 {(2)}^{ - 3} = \frac{1}{2} [/tex]
In the diagram above, angle 1=40. Find the measure of angle 4
Answer:
40
Step-by-step explanation:
angle 1 and 4 are vertical angles therefore they have the same measure of 40 degrees
how many pairs of each type of angles do two lines and a transversal form? vertical angles
The number of pairs of angles formed are about 7 types.
What are the Pairs of Angles Formed by a Transversal and Two Lines?In the image given, when transversal t crosses the two lines, a and b, 8 angles are formed.
The pairs of angles formed are:
Vertical angles, for example, angles 2 and 4.Linear pair angle, for example angles 1 and 2.Corresponding angles, for example angles 1 and 5.Alternate interior angles, for example angles 4 and 5.Alternate exterior angles, for example angles 1 and 8.Same-side interior angles, for example angles 3 and 5.Same-side exterior angles, for example angles 2 and 8.Therefore, there are about 7 types of pairs of each type of angles formed.
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