The amount of money invested at 12% was $4327 while $1442 was invested at 7%.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount invested at 12% and y represent the amount invested at 7%, hence:
x + y = 5679 (1)
Also:
0.12x = 0.07y + 407.5 (2)
From both equations:
x = 4327, y = 1442
The amount of money invested at 12% was $4327 while $1442 was invested at 7%.
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Pls help! Geometry
Calculate square footage and current market value.
Part 1
Each floor is [tex](28)(56)=1568[/tex] square feet. Since there are 2 floors, the total square footage is [tex]2(1568)=3136[/tex] square feet.
Part 2
[tex](3136)(93)=\$291648[/tex]
Fastttt helppppp
Which transformation is not an isometry
Answer:
Third option(double circle)
Step-by-step explanation:
Isometry (iso meaning same and metry meaning measure)
preserves the length and overall mass/size of a shape during a transformation. The 3rd option is the only shape that changes size in the examples, making it a non isometric transformation.
Julián just retired, and has $800,000 to invest. A very safe Certificate of Deposit (CD) account pays 2.5%, while a riskier bond fund pays 5% in interest. Julián figures he needs $36,000 a year in interest to live on. How much should he invest in each account to make enough interest while minimizing his risk?
An equation is formed of two equal expressions. Julian should invest $160,000 in CD and $640,000 in Bond.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the amount invested in CD be represented by x, while the amount invested in bond be represented by y. The total amount that Julian had is,
x + y = 800,000
x = 800,000 - y
The interest that Julian needs in a year is $36,000. Therefore, the total interest should be,
0.025x + 0.05y = 36000
0.025(800,000 - y) + 0.05y = 36000
20,000 - 0.025y + 0.05y =36,000
0.025y = 16,000
y = $640,000
Substitute the value of y
x + y = 800,000
x = $160,000
Hence, Julian should invest $160,000 in CD and $640,000 in Bond.
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given the function f(x) shown, sketch the graph of f(x-2)
Step-by-step explanation:
substitute different values of x inorder to get values of y. so since the value of y will have 2 units substracted from the original function leaving us with shifting. but the graph would be parabolic or slightly curved than my graph.
GIVE EXAMPLE OF ACTION PLAN THAT SHOWS A CONTEXTUALIZED LEARNING PROGRAM
An example of contextualization in teaching is when writing skills are taught with reference to topics.
How to illustrate the information?It should be noted that the contextualization of basic skills is the instructional approach that gives connections in teaching.
In this case, an example of contextualization in teaching is when writing skills are taught with reference to topics.
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A line passes through the point (-2,7) and has a slope of -5. What is the value of a if the point (a,2) is also on the line?
Answer:
a = -1
Step-by-step explanation:
The slope, m from point -2,7 to a,2 has to be -5
m = (y1-y2)/(x1-x2)
-5 = ( 7-2)/(-2 -a) solve for 'a'......cross multiply
10+ 5a = 5
5a = -5
a = -1
What is the solution to the system of equations?
O (5, 0)
O (0,5)
O (0-5)
O (-5, 0)
Answer: (0, -5) which is choice C
Explanation:
The solution is where the lines cross or intersect. This point is on both lines at the same time to make both equations true.
use the Pythagorean identity with X=8 and Y=5 to generate a Pythagorean triple
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming the formula:}[/tex]
[tex]\mathbf{a^2 + b^2 = c^2}[/tex]
[tex]\huge\textbf{If so:}[/tex]
[tex]\mathbf{x^2 + y^2 = c^2}[/tex]
[tex]\mathbf{8^2 + 5^2 = c^2}[/tex]
[tex]\mathbf{8\times 8 + 5 \times 5 = c^2}[/tex]
[tex]\mathbf{64 + 25 = c^2}[/tex]
[tex]\mathbf{89 = c^2}[/tex]
[tex]\huge\textbf{Subtract \boxed{\rm{\bf c^2}} to both sides:}[/tex]
[tex]\mathbf{89 - c^2 = c^2 - c^2}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathbf{-c^2 + 89 = 0}[/tex]
[tex]\huge\textbf{Subtract \boxed{\bf 89} to both sides:}[/tex]
[tex]\mathbf{-c^2 + 89 - 89 = 0 - 89}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{-c^2 = -89}[/tex]
[tex]\huge\textbf{Divide \boxed{\bf{-1}} to both sides:}[/tex]
[tex]\mathbf{\dfrac{-c^2}{-1} = \dfrac{-89}{-1}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathbf{-c^2 = -89}[/tex]
[tex]\huge\textbf{Take the square root of the number:}[/tex]
[tex]\mathbf{c = \pm \sqrt{89}}[/tex]
[tex]\huge\textbf{Thus, this possibly means:}[/tex]
[tex]\mathbf{c = \sqrt{89} \ or\ c = -\sqrt{89}}[/tex]
[tex]\huge\textbf{Thus, your answer possibly is:}[/tex]
[tex]\huge\boxed{\mathsf{c = \sqrt{89} \ or\ c = -\sqrt{89}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Simple interest on a bank loan can be calculated by multiplying the principal times the interest rate times the time. In the formula I = p r t, what does I stand for? a. time c. principal b. interest rate d. simple interest Please select the best answer from the choices provided
Answer:
simple interest
Step-by-step explanation:
this is because r is interest rate, p is principal, and t is time
Answer:
simple interest
Step-by-step explanation:
Simple interest rate is defined as: I = p * r * t. So you're taking the principle amount (initial amount loaned) and multiply it by the interest rate. This gives you the interest rate in a year (usually, depends on time unit of t). Generally speaking, it gives you the interest over a specific amount of time. Now multiply it by the amount of time that's passed. So you're just calculating the total amount of interest. So the I stands for the simple interest.
Last answers 5
Let me know the answer fast
The model for the height of the balloon captured from the ground with a balloon launcher can be represented by the function… how long will it take for the balloon to hit the ground after it’s launched?
Answer:
2 seconds
Step-by-step explanation:
To find the time it takes for the balloon to reach the ground, you need to set the equation equal to 0. This is because the ground technically has a height of 0.
h(t) = -16² + 128t <----- Original expression
0 = -16² + 128t <----- Plug 0 in for h(t)
16² = 128t <----- Add 16² to both sides
256 = 128t <----- Solve 16²
2 = t <----- Divide both sides by 128
Therefore, if t = 2, it will take the balloon 2 seconds to reach the ground.
==========================================================
Explanation:
The balloon is on the ground when the height is zero.
Replace h with 0 and solve for t.
[tex]h(t) = -16t^2 + 128t\\\\0 = -16t^2 + 128t\\\\-16t^2 + 128t = 0\\\\-16t(t - 8) = 0\\\\-16t = 0 \ \text{ or } \ t-8 = 0\\\\t = 0/(-16) \ \text{ or } \ t = 0+8\\\\t = 0 \ \text{ or } \ t = 8\\\\[/tex]
Ignore t = 0 because this is when the balloon is initially on the ground. In other words, the balloon starts on the ground, so it makes sense that t = 0 leads to h = 0.
The other solution t = 8 is what we're after. The balloon touches the ground again at the 8 second mark. This is the length of time the balloon is in the air.
A quick way to determine and confirm the answer is to use graphing software. Check out the diagram below. We have a parabola with x intercepts of 0 and 8.
In two or more complete sentences, describe why the following question is a combination.
In how many ways can five students in a class of 30 be chosen for a committee?
142,506 different five-member committees can be made.
In how many ways can the five students be chosen?If we have a set of N elements, the number of different subsets of K elements that we can make out of these N elements is:
[tex]C(N, K) = \frac{N!}{K!*(N - K)!}[/tex]
In this particular case, the set has 30 elements which are the students. And the committee has 5 members, so K = 5 and N = 30, then we get:
[tex]C(30, 5) = \frac{30!}{(30 - 4)!*5!} = \frac{30*29*28*27*26}{5*4*3*2*1} = 142,506[/tex]
This means that 142,506 different five-member committees can be made.
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PLEASE FIGURE THIS OUT!
Figure M and it’s congruent image, figure N, are graphed on the coordinate plane below.
Describe a sequence of transformations that will take figure M onto its congruent image, figure N.
Answer:
Vertical shift up 2, horizontal shift left 2 reflection over x-axis then reflection over the y-axis.
Step-by-step explanation:
Which of these is the absolute value parent function?
O A. f(x) = Ixl
OB. f(x) = 13x1
O C. f(x) = x-− 1|
OD. f(x)=x+2
Answer: A
Step-by-step explanation:
This is a fact.
The absolute value parent or modulus function is f ( x ) = | x |
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = | x |
The absolute value parent function is f(x) = |x|, which represents the absolute value of x.
Option B, f(x) = 13x1, does not represent the absolute value function, as it has a coefficient of 13, which scales the function vertically.
Option C, f(x) = x-− 1|, represents a translation of the absolute value function. The "-1" shifts the function one unit to the right, and the vertical bar denotes the absolute value of the expression within the bar. While it is related to the absolute value function, it is not the parent function itself.
Option D, f(x) = x+2, represents a linear function with a slope of 1, which is not the absolute value function.
Hence , the absolute value parent function is f ( x ) = | x |
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5q²-2/3(6q²-6q-3)+3q
Answer:
[tex]q^2+7q+2[/tex]
Step-by-step explanation:
Check the attachment I added, hope it helps!
Identify the graph and describe the solution set of this system of inequalities.
y<-x-10
y>-x-2
Answer:
-x-2<y<-x-10
Step-by-step explanation:
Need help with the question
Answer:
x = 0 or x = 1
Step-by-step explanation:
f(x) = |x| - 4
g(x) = x³ - 4
f(x) = g(x)
|x| - 4 = x³ - 4
Add 4 to both sides.
|x| = x³
x = x³ or -x = x³
x³ - x = 0 or x³ + x = 0
x(x² - 1) = or x(x² + 1) = 0
x = 0 or x + 1 = 0 or x - 1 = 0
x = 0 or x = -1 or x = 1
x = -1 does not work, so we discard that solution.
Answer: x = 0 or x = 1
Answer:
values of x: x = 1 and x = 0
Step-by-step explanation:
Given:
f(x)= |x| - 4g(x) = x³ - 4Want: x - values when f(x) = g(x)
f(x) = g(x) → |x| - 4 = x³ - 4positive interval x ≥ 0negative interval x < 0|x| - 4 = x³ - 4, the 4 cancel out on both sides
|x| = x³
|x| - x³ = x³ - x³
|x| - x³ = 0, x ≥ 0
-x - x³ = 0, x < 0
x = 0
x = -1, x ≥ 0
x = 1
x = 0, x < 0
The intersections are x = 0 and x = 1 and no solution
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What is 3/16 of 200 written as a percentage
The expression 3/16 of 200 expression as a percentage is; 6.25%.
What is the value of 3/16 of 200 written as a percentage?The value of the expression given in the task content can be evaluated as follows;
3/16 × 200 = 12.5
Hence, the value 12.5 expressed as a percentage of 200 is;
(12.5/200) × 100%.
= 6.25%.
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Casper has some whipping cream that is 18\%18%18, percent butterfat and some milk that is 4\%4%4, percent butterfat. He wants to make a 500\,\text{mL}500mL500, start text, m, L, end text mixture of them that is 12\%12%12, percent butterfat.
Answer:
CORRECT (SELECTED)
The mixture has less than the intended volume and has more than the intended percent of butterfat.
Explanation: Point LLL is above line aaa, so it represents a scenario where the mixture has more than 12\%12%12, percent butterfat. Also, point LLL is below line bbb, so it represents a scenario where the mixture has a volume of less than 500 \,\text{mL}500mL500, start text, m, L, end text.
Option B. The correct answer to this question is that The mixture has less than the intended volume and has more than the intended percent of butterfat.
How to interpret the graphFrom the graph that we have here, the point L is under the blue line of the graph.
x + y = 500
From here we have
0.18x + 0.04y = 500(0.12)
Continuing on trhe graph the solution is given as x = 285.7 and y = 214.3
From the explanation here we can conclude that option B is correct.
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Answer:
The mixture has the intended volume and has more than the intended percent of butterfat.
Step-by-step explanation:
five people arrived at the check _ out counter of a hotel at the same time, in how many different ways can the people line up?
There are 120 different ways the people can line up
How to determine the number of ways?The number of people that arrived is:
n = 5
Take the factorial to calculate the number of ways they can line up
n! = 5!
Expand
n! = 5* 4 * 3 * 2 * 1
Evaluate
n! = 120
Hence, there are 120 different ways the people can line up
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The base and height of a right triangle are 20 inches and 15 inches. Find the length of the hypotenuse.
Answer:
25
Step-by-step explanation:
its both numbers squared and added, then square root the result
36 is what percent of 48?
Q(3x)=12x+2 then what is Q(x-2)
Answer:
it's ax+b form answer is Q(x-2)=4x-6
Step-by-step explanation:
ax+b=Q(x),Q(x-2)=a(x-2)+2
Q(3x)=a(3x)+b=12x+2, 3a=12 =>a=4,b=2
the original q of x is 4x+2
Q of x-2 =4(x-2)+2=4x-8+2=4x-6
These points are linear.
Find the slope.
x-3-2-10/1/2
y-8 0 8 162432
slope = [?]
Enter
The slope of the given line according to the table is -8
How to calculate the slope of a functionThe slope of a function is also defined as the rate of change of the function.
Using the coordinate points (-3, 8) and (-2, 0) from the table
Slope = 0-8/-2-(-3)
Slope = -8/-2+3
Slope = -8/1
Slope = -8
Hence the slope of the given line according to the table is -8
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A bag of tokens contains
8
8 red,
7
7 green, and
9
9 blue tokens. What is the probability that a randomly selected token is purple? Enter your answer as a fraction.
Answer:
As the bag doesnt conatain any purple token;
purple token = 0
number of total tokens in bag = 24
therefore, the probability of choosing a purple token = 0/24
Hope it helps
How do you Identify and contrast the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets.
One can Identify the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets by?
Observing the trends in prices.Observing Demand and supply curve.Contrast the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets.The difference that exist between a rise in price due to the inflation and a rise in price due to microeconomic markets is based on the price changes that has occurred in terms of demand and supply model.
Note that this is said to be the price in a given market but the price rise as a result of to inflation tells that the price rise is one that reaches a lot of markets and not only just one market.
Hence, One can Identify the differences between the rise in prices due to inflation and the rise in prices in microeconomic markets by?
Observing the trends in prices.Observing Demand and supply curve.Learn more about inflation from
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Use the Law of sines or trigonometric ratios to find each length. Round your answer to 1 decimal place.
a. The length of the zip line
b. The height of the point on the tree where the top of the ladder rests against it.
c. The distance between the base of the ladder and the base of the tree.
d. The distance between the base of the tree and the spot where the zip line is anchored in the ground.
Using the trigonometric ratios, the measures are:
a. z = 222.5 ft
b. h = 38.6 ft.
c. b = 10.4 ft
d. B = 219.1 ft.
What are the Trigonometric Ratios?The ratios of trigonometry that can be used to solve a right triangle are:
sin ∅ = opp/hyp
cos ∅ = adj/hyp
tan ∅ = opp/adj.
a. Find h using the sin ∅ = opp/hyp:
sin 75 = opp/hyp = h/40
h = (sin 75)(40) = 38.6
Find z using the sin ∅ = opp/hyp
sin 10 = opp/hyp = 38.6/z
z = 38.6/sin 10
z = 222.5 ft. (length of the zip line)
b. Height of the tree = h = 38.6 ft.
c. Using sin ∅ = opp/hyp, find b (distance between the base of the ladder and the base of the tree):
sin 15 = b/40
b = (sin 15)(40)
b = 10.4 ft
d. Using sin ∅ = opp/hyp, find B as shown in the image:
sin 80 = opp/hyp = B/222.5
B = (sin 80)(222.5)
B = 219.1 ft.
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Choose the correct simplification of 8x2(4x 2x2 − 1). (5 points) group of answer choices 32x4 − 16x3 8x2 32x4 16x3 − 8x2 16x4 − 10x3 8x2 16x4 32x3 − 8x2
The second option is the correct answer
[tex]16x^{4}+40x^{3} -24x^{2}[/tex]
The expression given to us is:
[tex]8x^{2} (5x+2x^{2}-3 )[/tex]
Herein, we can simplify it by opening up the bracket and multiplying each term inside the bracket by the term which is outside the bracket.
Thus, we get:
[tex]8x^{2} (5x+2x^{2}-3 )=8*5x^{2+1} +8*2x^{2+2}-8*3x^{2}[/tex]
[tex]40x^{3} +16x^{4}-24x^{2}[/tex]
Rearranging the above expression in descending order of power we get:
[tex]16x^{4}+40x^{3} -24x^{2}[/tex]
From the given options we can see this is the second option. Hence the second option is the correct answer.
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A real estate agent is showing homes to a prospective buyer. There are 10 homes in the desired price range listed in the area. The buyer wants to visit only 3 of them. a. In how many ways could the 3 homes be chosen if the order of visiting is considered? b. In how many ways could the 3 homes be chosen if the order of visiting is not important?
There are 720 ways that the 3 homes could be chosen if the order of visiting is considered. There are 120 ways that the 3 homes could be chosen if the order of visiting is not important.
What is permutation?A permutation is the arrangement or ordering of a finite set of an element.
From the information given:
If there are 10 homes in the desired price range listed in the area:
Then:
n = 10 and r = 3So, the number of ways of choosing 3 out of 10 (without replacement) and arranging is:
[tex]\mathbf{^nP_r= \dfrac{n!}{(n-r)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10!}{(10-3)!}}[/tex]
[tex]\mathbf{^nP_r= \dfrac{10\times 9\times 8 \times 7!}{(7)!}}[/tex]
= 720 ways
Now, the number of ways of choosing 3 out of 10 if the order of visiting is not important is the combination of the elements and it can be computed as:
[tex]\mathbf{^nC_r= \dfrac{n!}{(n-r)!r!}}[/tex]
[tex]\mathbf{^{10}C_3= \dfrac{10!}{(10-3)!3!}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9 \times 7!}{(7)! \times 3\times 2}}[/tex]
[tex]\mathbf{\implies \dfrac{10\times 8\times 9}{6}}[/tex]
= 120 ways
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Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.
R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
Triangle RST was transformed by using the rule (x,y) → (-x,-y) and the transformation is described by the transformation of 180° rotation about the origin.
Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Here we have transformed the triangle using the rotation method.
Rotation is the geometric transformation that revolves each point in a shape a predetermined number of degrees around that point. When the number of degrees is positive, the shape spins counterclockwise; when the number of degrees is negative, it rotates clockwise. The following is a broad description of how rotation about the origin can be transformed.
(X,Y) to rotate 90° (-y, x)180° rotation (x, y) (-x,-y)To rotate (x,y) 270° (y, -x)Here the points change to R'(-1,-1) , S'(-3,-1) and T'(-1,-6).
A 180° rotation about the origin will be the transformation.
The triangles RST and R'S'T' are first plotted on a graph. The graph is provided for your reference below.
The original triangle RST, which was in quadrant 1, has changed to triangle R'S'T', which is in quadrant 3, as shown in the graph. The rotation around the origin is 180° from quadrant 1 to quadrant 3.
Your question was incomplete. Please check below for full content.
Triangle RST was transformed using the rule (x, y) → (–x, –y). The vertices of the triangles are shown.
R (1, 1)
S (3, 1)
T (1, 6) R' (–1, –1)
S' (–3, –1)
T' (–1, –6)
Which describes the transformation?
The transformation was a 90° rotation about origin.
The transformation was a 180° rotation about origin.
The transformation was a 270° rotation about origin.
The transformation was a 360° rotation about origin.
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