Answer:
Step-by-step explanation:
The 90th term of the arithmetic sequence is 461
a90=a1+(90-1) x d
a90=16+89 x 5
a90=461
Priscilla invested 20,000 at rate of 12% over 5 years. Much to her surprise, her investment paid off, and her account grew by an additional $12,000. What is the principal in this scenario?
The principal in this scenario is $ 8000.
What is simple & compound interest?Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time.
Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time.
It is Given that:
Priscilla invested 20,000 that means the total amount she invested.
Amount= $ 20,000
Rate of interest=12%
Time= 5 year
Interest= $12,000.
By the formula;
Amount = principal + Interest
Principal = Amount - Interest
Principal= $ 20,000- $12,000
Principal=$ 8000
Hence, the principal in this scenario is $ 8000.
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11 less than the quotient of
4
44 and
�
xx.
The expression which is used to represents the statement "one-more than the quotient of a number x" and 4 is "x/4 + 1".
A "Quotient" is the result of a division operation between two numbers, where one number is divided by another. It represents the number of times one number is contained within another number.
An "Expression" is defined as "mathematical-phrase" which contain numbers, variables, and operators such as addition, subtraction, multiplication, and division. It can also contain functions and other mathematical symbols.
The quotient of a number"x" and 4 can be written as x/4.
So, one more than the quotient of a number x and 4 can be represented by the expression:
⇒ x/4 + 1,
Therefore, required mathematical expression is "x/4 + 1".
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The given question is incomplete, the complete question is
Write an expression to represent : One more than the quotient of a number x and 4.
Select the correct answer from each drop-down menu. Each graph shows the results of a transformation applied to function f where f(x) = (1/2)^x.
Complete the statement given that g(x) =f(kx). The graph of function g is graph Because the graph a function g is the result of a  applied to the graph of function F .
Given that g(x) =f(kx). The graph of function g is graph Z Because the graph a function g is the result of a horizontal compression applied to the graph of function F.
What is a graph?A graph can be described as a pictorial representation or a diagram that represents data or values in an organized manner.
The graph of the function g(x) = f(kx) is obtained from the graph of f(x) by a horizontal compression or stretching, depending on the value of k.
In conclusion, If k is greater than 1, then the graph of g(x) is obtained from the graph of f(x) by a horizontal compression.
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what is the product im simplest form for 3/5×2/3
Answer:
0.4
\(\frac{2}{5}\)
Step-by-step explanation:
Estimate the product of 392 and 624
Answer:
just multiply both
Step-by-step explanation:
understand
Answer:
244,608Step-by-step explanation:
product means multiply
so 392 x 624 = 244,608
Please help meee this is due Friday!!! A fully loaded and fueled spacecraft can weigh close to 5.1 million pounds. What is this weight converted to tons?
Answer:
A fully loaded and fueled spacecraft weighing 5.1 million pounds is equivalent to 2550 US tons
Step-by-step explanation:
Which one doesn’t belong and why
The polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.
What shape is different from the others?
In this problem we have three shapes related to circle-like and ellipse-like arcs (circle, semicircle, ellipse) and a regular polygon.
Circles are closed figures created by a arc whose radius of curvature is the same at every point and ellipses are closed figures created by a arc whose radius of curvature varies in the following interval: a ≤ r ≤ b, where a, b are the lengths of the semiaxes.
Polygons are closed figures created by a finite number of line segments and therefore the concept of radius of curvature is not applicable.
Therefore, the polygon does not belong to the group as it is created by a finite number of line segments and the concept of the radius of curvature is not applicable.
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M = I1+I₂ 31 +32 2 Now let's substitute in our given values. (-2 , 2) = ((-5 Find 2 and y2 We will now set up two equations to solve for our two unknowns of x2 and y₂. (-5 X2 (-5+₂) -5+22), (7+)) 2 - +₂)/2 = We will first want to multiply by 2 on both sides and will get −5+₂= -4 Adding 5 to both sides we get = 7 This is the coordinate of point B. Now we will set up the equation to solve for y2 +y2)/2 =
The coordinates of point B are (-3, 17).
The given equation is M = I₁ + I₂ = 31 + 32.
Now let's substitute in our given values:
(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)
We will now set up two equations to solve for our two unknowns, x₂ and y₂:
Equation 1: (-5 + x₂) / 2 = -4
Multiply both sides by 2:
-5 + x₂ = -8
Add 5 to both sides:
x₂ = -3
This gives us the x-coordinate of point B.
Equation 2: (-5 + 2 + y₂) / 2 = 7
Simplify:
(-3 + y₂) / 2 = 7
Multiply both sides by 2:
-3 + y₂ = 14
Add 3 to both sides:
y₂ = 17
This gives us the y-coordinate of point B.
Therefore, the coordinates of point B are (-3, 17).
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Jeanette purchased a concert ticket on a web site. The original price of the ticket was $75. She used a coupon code to receive a 20% discount. The web site applied a 10% service fee to the discounted price. Jeanette’s ticket was less than the original price by what percent?
Caroline's hair is
7 inches long and grows about 1/5 inch each month. Trinity's hair is 10 inches long and
grows about 1/10 inch each month. What inequality can be used to determine How many months will it take for Caroline's hair to be
at least as long as Trinity's hair?*
Variiable______
Expression 1______
Expression 2______
Inequality______
Solve_____
The inequality can be used to determine how many months will it take for Caroline's hair to be at least as long as Trinity's hair is (1/5)x + 7 ≥ (1/10)x + 10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.
Let x represent the number of months.
For Caroline's hair:
Length = (1/5)x + 7
For Trinity's hair:
Length = (1/10)x + 10
For Caroline's hair to be at least as long as Trinity's hair, hence:
(1/5)x + 7 ≥ (1/10)x + 10
The inequality can be used to determine how many months will it take for Caroline's hair to be at least as long as Trinity's hair is (1/5)x + 7 ≥ (1/10)x + 10
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What is the greatest common factor of 24, 32 and 36
Answer:
4
Step-by-step explanation:
Nothing higher than 12 can be a possiblity for 24.
24 1, 2, 3, 4, 6, 8, 12, 24.
32 1, 2, 4, 8, 16
36 1, 2, 3, 4, 6, 9, 12, 18
The one number that shows up the most and at the highest value, is 4. So the GCF is 4
Hello! Can anyone please tell me the measurement of t and v ? Any help is gladly appreciated.
Answer:
v= 80, t=100
Step-by-step explanation:
yea
Please help me with this question
Please find the area
Answer:
the answer is 6cm like its really obvious
What is 120 divided by 55
Answer:
2.2
..................
120/55
Please help me with the problem below thanks
Answer:
I would say get a small ruler thing and measure them off your screen and say (*Measure off my screen*), then say the distance the dots are from the center point is the same because those dots, when connected to the center point, makes the radius, and the radius stays the same around the circle.
In the example below, check all the answers that are TERMS.
8x + 7 - y
y
8x
+
7
Answer: 8x, 7,
Step-by-step explanation: Terms are separated with an addition or subtraction sign.The terms for 8x + 7 - y are:8x, 7, - yHope this helps!
What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.
The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:
Define the formula p(x, y) as x = yo(x).
This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.
Define the set F as {(x, x) (x)}.
This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.
Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.
This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.
The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.
Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.
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True or false terminating decimals are irrational
joaquin has been working on homework for 3 1/2 hours. if each assignment takes him 1/4 of an hour, how many assignments has he completed?
Convert 3 1/2 to a improper fraction:
3 1/2 = 7/2
Divide 7/2 by 1/4:
7/2 ÷ 1/4
7/2 × 4/1
28 / 2
= 14
Joaquin has finished 14 assignments
Answer:
14
Step-by-step explanation:
PLEASE ANSWER ASAP I NEED IT.
Answer:
\(\huge\boxed{\sf 18^{-3}}\)
Step-by-step explanation:
Given expression:\(\displaystyle \frac{18^4}{18^7}\)
According to exponent rule:\(\displaystyle \frac{a^m}{a^n} = a^{m-n}\)So, the expression becomes:
= \(18 ^{4-7}\)
= \(18^{-3}\)
\(\rule[225]{225}{2}\)
Each square in the grid is a 1 x 1 centimeter square.
What is the area of the shape?
8square centimeters
Step-by-step explanation:
1 square is 1cm2. theres 8 squares so 8cm2
Given the polynomial 2xcube + 5xsquare + 3x +4 what is it’s value when x= 10
Answer:
2534
Step-by-step explanation:
2x^3+5x^2+3x+4
x=10, so:
2(10)^3+5(10)^2+3(10)+4
2000+500+30+4
Answer: 2534
Sour
okshe
A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point
having coordinates (2.5, 0.9), where the units are meters, what is the distance of the fly from the corner of the room?
hello how are you? I am fine
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 4 h, and Car B traveled the distance in 4.5 h. Car B traveled 5 mph slower than Car A. (The formula R⋅T=D , where R is the rate of speed, T is the time, and D is the distance can be used.) How fast did Car B travel? Enter your answer in the box.
Car B travelled with the rate of speed of 40mph .
In the question ,
it is given that ,
Car B travelled 5mph slower than Car A .
let the rate of speed at which Car B travelled be x mph.
So , the rate of speed of Car A is = (x+5) mph
Car A travelled the distance in 4 h , with the speed of (x+5) mph ,
the value of T = 4 h and R = (x+5) mph
So, by the formula R*T=D ,
we get ,the distance travelled by Car A = 4(x+5) miles .
Car B travelled the distance in 4.5 h , with the speed of x mph .
the value of T= 4.5h and R = x mph
So, by the formula R*T=D,
we get , the distance travelled by Car B = 4.5*x = (4.5x) miles .
Since , both the cars travelled the equal distance ,
we get ,
4(x+5) = 4.5x
4x+20=4.5x
4.5x-4x = 20
0.5x= 20
x = 40
Therefore , the rate of speed of Car B is 40 mph.
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The longer base of an isosceles trapezoid measures 23 ft. The nonparallel sides measure 9 ft, and the base angles measure 80°. Find the length of a diagonal.A. 17 ftB. 25 ftC. 23 ftD. 20 ft
The diagram below represent the information given in the question
From the diagram
\(\begin{gathered} AD=9ft \\ DC=23ft \\ <\text{ADC}=80^0 \\ AC=d=\text{diagonal} \end{gathered}\)The diagonal of the trapezoid can be calculated using cosine rule as shown below:
\(d^2=AD^2+DC^2-2\times AD\times DC\times\cos D\)\(d^2=9^2+23^2-2\times9\times23\times\cos 80^0\)\(\begin{gathered} d^2=81+529-414\times0.1736 \\ d^2=610-71.80 \\ d^2=538.10965 \end{gathered}\)\(\begin{gathered} d=\sqrt[]{538.10965} \\ d=23.197 \\ d\approx23ft \end{gathered}\)Hence, the length of the diagonal is 23ft, OPTION C
The following figure is made of 2 triangles.
7
А
5
B
4
Find the area of each part of the figure and the whole figure.
The area of each part of the figure is Triangle B = 10 square units and Triangle A = 17.5 square units. The area of the whole figure is 27.5 square units.
What is area?A two-dimensional surface, like the surface of a shape or object, can be measured in terms of area. Usually, it is expressed in square quantities like square metres (m2) or square feet (ft2). By multiplying the length and breadth of a rectangle, or by applying particular formulas for other forms, such as base times height divided by two for a triangle, one can determine the area of a shape.
From the given figure we observe that the base of the slanted figure has true base length of 5 units.
Thus, for triangle B the area is:
Triangle B = 1/2(b)(h)
Triangle B = 1/2(5)(4) = 10 square units.
For triangle A we have:
Triangle A = 1/2(5)(7) = 35/2 = 17.5 square units.
The area of the whole figure is:
A = 10 + 17.5 = 27.5 square units.
Hence, the area of each part of the figure is Triangle B = 10 square units and Triangle A = 17.5 square units. The area of the whole figure is 27.5 square units.
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10. Tell whether the sequence is arithmetic. If it is, what is the common difference? (1 point)
2.7, 13, 20...
A. yes: 5
B. yes; 6
C. yes: 2
D. no
Answer:
No
Step-by-step explanation:
Which values should you plot to show a linear relationship?
Month Population
Log(population)
1
1400
3.146
2
2600
3.415
3
4700
3.672
4
9000
3.954
5
17000
4.230
6
32000
4.505
O A. "Population on the x-axis and "Log(population)" on the y-axis.
O B. "Month" on the x-axis and "Population" on the y-axis.
w
O C. "Month" on the x-axis and "Log(population)" on the y-axis.
O D. "Log(population)" on the x-axis and "Month" on the y-axis.
Answer:“ C ”
“month” on the x axis and “log” on the y axis
This table gives a few (x,y) pairs of a line in the coordinate plane.
x y
48 -30
61 -45
74 -60
What is the x-intercept of the line?
Answer:
22
Step-by-step explanation:
First, find the equation of the line in slope-intercept form, y = mx + b.
Using the coordinates of these two pairs, (48, -30) and (61, -45), the slope (m) can be calculated as follows:
\( m = \frac{y_2 - y_2}{x_2 - x_1} = \frac{-45 -(-30)}{61 - 48} = \frac{-15}{13} \)
\( slope (m) = -\frac{15}{13} \)
Find the y-intercept (b) by substituting x = 48, y = -30, and \( m = -\frac{15}{13} \) into y = mx + b:
\( -30 = -\frac{15}{13}(48) + b \)
Solve for b.
\( -30 = -\frac{720}{13} + b \)
Add \( -\frac{720}{13} \) to both sides
\( -30 + \frac{720}{13} = b \)
\( \frac{-390 + 720}{13} = b \)
\( \frac{330}{13} = b \)
\( b = \frac{330}{13} \)
Substitute \( m = -\frac{15}{13} \) and \( b = \frac{330}{13} \) into y = mx + b
\( y = -\frac{15}{13}x + \frac{330}{13} \)
The x-intercept of the line with the above equation, would be the value of x when y = 0. This is the value of x where the line cuts across the x-axis. To calculate this, substitute y = 0 into \( y = -\frac{15}{13}x + \frac{330}{13} \).
\( 0 = -\frac{15}{13}x + \frac{330}{13} \)
Subtract \( \frac{330}{13} \) from both sides
\( -\frac{330}{13} = -\frac{15}{13}x \)
Divide both sides by \( -\frac{13}{15}x \)
\( \frac{-\frac{330}{13}}{-\frac{13}{15}} = x \)
\( -\frac{330}{13}*-\frac{13}{15} = x \)
\( -\frac{330}{1}*-\frac{1}{15} = x \)
\( \frac{330}{15} = x \)
\( 22 = x \)
The x-intercept = 22
Answer:
(22,0)
Step-by-step explanation: