In The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account, A. The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.
What is the compound interest equation?The general compound interest equation is given as:
Formula:
A = P(1 + r/n)^nt
A = final amount or future value
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
Compounding interest involves computing interest on both the principal and the accumulated interest.
On the other hand, the simple interest method does not compute interest on accumulated interest.
Thus, the correct representation of the value 0.031 is the compound interest rate as 3.1%.
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Is he right explain if no explain as well and this is my last question I need to answer for my test Thank you.
Scott's statement that (13g + 1) + (-2 - 5g) and 8/3(3g + 9/8) are equivalent is wrong
How to determine if he is right or notFrom the question, we have the following parameters that can be used in our computation:
(13g + 1) + (-2 - 5g)
Remove the brackets
So, we have
13g + 1 - 2 - 5g
Evaluate the like terms
8g - 1
When factorized, we have
8/3(3g - 3/8)
This is not the same as Scott's expression
Hence, Scott is incorrect
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Ted made a nut mixture that contains 52%
peanuts by mixing together 9 kg of mixed
nuts that contain 20% peanuts and 16 kg
of a different brand of mixed nuts. The
second brand of mixed nuts contained
what percent peanuts?
Let's call the added amount of kg of mixed nuts that contain
40
%
peanuts
m
a
d
d
e
d
. If the new mixture contains
34
%
peanuts, then:
m
peanuts
m
total
=
0.34
The bag of
6
kg
already contained
0.3
⋅
6
=
1.8
kg
of peanuts. Furthermore,
40
%
of
m
added
will be peanuts. This means that:
m
peanuts
=
0.4
m
added
+
1.8
The total mass will be the original
6
kg
plus the added mass, so
m
total
=
m
added
+
6
.
This gives us the following equation.
0.4
m
added
+
1.8
m
added
+
6
=
0.34
Multiply both sides with
m
added
+
6
.
0.4
m
added
+
1.8
=
0.34
(
m
added
+
6
)
Multiply out the brackets.
0.4
m
added
+
1.8
=
0.34
m
added
+
2.04
Subtract
0.34
m
added
from both sides.
0.04
m
added
+
1.8
=
2.04
Subtract
1.8
from both sides.
0.06
m
added
=
0.24
Divide both sides by
0.06
.
m
added
=
4
Therefore, Jenny must add
4
kg
.
I need help on this please
The values a and b should be replaced to rewrite the given expression as (x + a)(x - b).
What is a quadratic function?Generally speaking, the standard form of a quadratic function is given by this mathematical expression;
ax² + bx + c = 0
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
c represents the constant.
Next, we would solve the above quadratic function by using the factorization method;
x² + x - 72 = 0
x² - 8x + 9x - 72 = 0
x(x - 8) + 9(x - 8) = 0
(x + 9)(x - 8) = 0
(x + 9)(x - 8) = (x + a)(x - b).
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Rina spins the spinner below 30 times. A success occurs when the spinner lands on a number that is greater than 6.
A spinner is divided into 8 equals sections and the sections are labeled 1 through 8.
What is the probability of a success and a failure for this experiment?
P (success) = one-fourth; P (failure) = Seven-eighths
P (success) = one-fourth; P (failure) = Three-fourths
P (success) = three-fourths; P (failure) = one-fourth
P (success) = seven-eighths; P (failure) = One-eighth
The probability of an event can not be more than the number 1.
The probability of success is 1/4.The probability of failure is 3/4.What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1.
Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event. As,
[tex]Probability[/tex] [tex]of[/tex] [tex]faliure=1-[/tex] [tex]Probability[/tex] [tex]of[/tex] [tex]success[/tex]
Given information-Rina spins the spinner less than the 30 times.
A success occurs when the spinner lands on a number that is greater than 6.
A spinner is divided into 8 equals sections and the sections are labeled 1 through 8.
As the probability of success occurs when the spinner lands on a number that is greater than 6, thus the number should grater than six.
This number should be less than 30 as the spinner spins less than the 30 times.
Thus the total number of outcome of this event is,
[tex]=30-6[/tex]
[tex]=24[/tex]
Thus the probability of success is,
[tex]P=\frac{6}{24}[/tex]
[tex]P=\frac{1}{4}[/tex]
Hence the probability of success is 1/4.
As the probability of failure of a event is equal to the difference of the 1 to the success of the event.
Thus the probability of failure is,
[tex]P^-=1-P[/tex]
[tex]P^-=1-\frac{1}{4}[/tex]
[tex]P^-=\frac{4-1}{4}[/tex]
[tex]P^-=\frac{3}{4}[/tex]
The probability of failure is 3/4.
Hence,
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answer:
A. 2 + x = 5
B x + 1 = 4
E -5 + x = -2
Step-by-step explanation:
2 + 3 = 5
3 + 1 + 4
-5 + 3 + -2
if this correct mark me as brainliest please
If the tire height is 5.2 in. and the rim diameter is 17 in., what is the tire diameter?
Answer:
Circumference = (3.14)(15) = 47.1 in
Step-by-step explanation:
drop-down menu.
An experiment is conducted in which a bead is randomly drawn from a bag, the color is recorded, and then the bead is replaced.
The results of the experiment are given in the table below.
Color
Red
Orange
Yellow
Green
Blue
Purple
Frequency
17
12
10
13
8
5
Which of the following lists would most likely have produced the given experimental results?
Color
List A
List B
Red
33
31
Orange
27
24
Yellow
22
18
Green
30
34
Blue
18
19
Purple
12
5
For the list selected above, what is the theoretical probability of selecting a red bead?
Using the experimental results, if 156 beads are drawn from a bag and returned, which color would have a frequency closest
to 24?
The theoretical probability of selecting a red bead is 0.28.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that,
Color Frequency
Red 17
Orange 12
Yellow 10
Green 9
Blue 8
Purple 5
Color List A List B
Red 33 31
Orange 27 24
Yellow 22 18
Green 30 34
Blue 18 19
Purple 12 5
Probability of selecting a red bead = 17/61
= 0.28
Orange color would have a frequency closest to 24.
Therefore, the theoretical probability of selecting a red bead is 0.28.
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If a vertex of a triangle is (7,-2) and the midpoints of two
sides are (3.5, -0.5) and. (3,1) find the other vertices of
the triangle.
The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).
What is a triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
Let's call the vertex we know A, and the midpoints of the other two sides B and C, respectively.
Using the midpoint formula, we can find the coordinates of the other two vertices, which are the endpoints of the sides that have B and C as midpoints
Coordinates of B:
x-coordinate: (7 + 3.5)/2 = 5.25
y-coordinate: (-2 - 0.5)/2 = -1.25
So, B is (5.25, -1.25)
Coordinates of C:
x-coordinate: (7 + 3) / 2 = 5
y-coordinate: (-2 + 1)/2 = -0.5
So, C is (5, -0.5)
Therefore, The triangle has vertices A(7,-2), B(5.25, -1.25), and C(5, -0.5).
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Please help. what is an equation of the line best fit. This is urgent
a. The line of the best fit is ŷ = -8.55485X + 118.39451.
b. The value of the correlation coefficient is -0.8619.
What is the line of best fit?A straight line that minimizes the gap between it and certain data is called a line of best fit. In a scatter plot containing several data points, a relationship is expressed using the line of best fit. It is a result of regression analysis and a tool for forecasting indicators and price changes.
Sum of X = 117.4
Sum of Y = 298
Mean X = 10.6727
Mean Y = 27.0909
The sum of squares (SSX) = 0.8618
The sum of products (SP) = -7.3727
Regression Equation = ŷ = bX + a
b = SP/SSX = -7.37/0.86 = -8.55485
a = MY - bMX = 27.09 - (-8.55*10.67) = 118.39451
ŷ = -8.55485X + 118.39451
X Values
∑ = 117.4
Mean = 10.673
∑(X - Mx)² = SSx = 0.862
Y Values
∑ = 298
Mean = 27.091
∑(Y - My)² = SSy = 84.909
X and Y Combined
N = 11
∑(X - Mx)(Y - My) = -7.373
R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -7.373 / √((0.862)(84.909)) = -0.8619
Therefore, the line of the best fit is ŷ = -8.55485X + 118.39451
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The diameter of a circle is 18 millimeters. What is the circle's circumference?
Answer:
he circumference of the circle is approximately 56.52 millimeters.
Step-by-step explanation:
The circumference of a circle is given by the formula:
C = πd
where C is the circumference, d is the diameter, and π is a mathematical constant approximately equal to 3.14.
Substituting the given value of the diameter, we get:
C = πd = π(18) = 56.52 mm (rounded to two decimal places)
Therefore, the circumference of the circle is approximately 56.52 millimeters.
9. Liam ran 12 miles total over the weekend. He
ran 5.5 miles on Saturday. Which equation can
be used to find m, the number of miles he ran
on Sunday?
A. 12 + 5.5 = m
B. 5.5m= 12
C. m-5.5 = 12
D. 5.5+ m = 12
Answer:
x=6.5
Step-by-step explanation:
I'm not sure if it's correct
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
The focus of a parabola is (0,-2). The directrix is the line y = 0. What is the equation of the parabola in vertex form?
in the equation y= 1/4p(x-k)² +h, the value of p is______.
The vertex of the parabola is the point (___,___)
The equation of this parabola in vertex form is y =_____2²-1
The equation of this parabola in vertex form is y = 1/4x^2 - 1.
Describe Parabola?A parabola is a type of curve that occurs in nature, science, and mathematics. It is a symmetrical, U-shaped curve that is created by the intersection of a plane and a right circular cone. The shape of the curve is defined by its equation, which can be expressed in standard form as y = ax^2 + bx + c. In this equation, the coefficient a determines the shape of the parabola, with a positive value creating an upward-opening parabola and a negative value creating a downward-opening parabola.
The focus of a parabola is (0,-2). The directrix is the line y = 0. What is the equation of the parabola in vertex form?The vertex of a parabola is equidistant from the focus and the directrix. Since the directrix is the line y = 0, which is the x-axis, the vertex is halfway between the focus and the x-axis, at (0, -1).
The distance from the vertex to the focus is p, which is also the distance from the vertex to the directrix. Since the directrix is the line y = 0, the distance from the vertex to the directrix is simply the y-coordinate of the vertex, which is 1.
Therefore, p = 1, and the equation of the parabola in vertex form is:
y = 1/4p(x - h)^2 + k = 1/4(1)(x - 0)^2 - 1 = 1/4x^2 - 1
in the equation y= 1/4p(x-k)² +h, the value of p is 1.
The vertex of the parabola is the point (0, -1).
The equation of this parabola in vertex form is y = 1/4x^2 - 1.
To solve 2²-1:
2² - 1 = 4 - 1 = 3.
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Answer:
The guy above is somewhat right.
Hope this helps!
Step-by-step explanation:
Which statement is true about this equation??
y = 2^x + 4
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents a function only.
D.
It represents both a relation and a function.
Answer: The correct answer is C. It represents a function only.
A function is a special type of relation where each input value is associated with only one output value. In other words, for every x in the domain of the function, there is only one corresponding y in the range.
In this equation, y = 2^x + 4, for every value of x, there is a unique corresponding value of y. So, it satisfies the requirement of a function and represents a function only.
Step-by-step explanation:
Answer:
D. It represents both a relation and a function
Hope this helps!
Step-by-step explanation:
All functions are relations, but not all relations are functions. The equation given is an Exponential function.
based on the data in the table, what is the probability that a randomly selected persons favorite restaurant is a deli?
Answer choices
8/25
2/5
1/10
9/50
The probability that a randomly selected persons favorite restaurant is a deli is 9/50
How to determine the probabilityFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
Total = 100
Deli = 18
So, the probability is
P = Deli/Total
Substitute the known values in the above equation, so, we have the following representation
P = 18/100
Simplify
P = 9/50
Hence, the probability is (d) 9/50
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For the points P and Q do the following.
(a) Find the distance d(P,Q).
(b) Find the coordinates of the midpoint M of the segment PQ.
P (3√2,5√3), Q(√2,-√3)
The solution is, the distance = √116.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
here, we have,
given that,
P (3√2,5√3), Q(√2,-√3)
so, the distance d(P,Q).
by using the formula we get,
the distance = √108 + 8
= √116
Hence, The solution is, the distance = √116.
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You start driving west for 3 miles, turn right, and drive north for another 2 miles. At the end of driving, what is your straight line distance from your starting point?
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
[tex]L^{2}[/tex]=[tex]3^{2}[/tex]+[tex]2^{2}[/tex]=9+4=13
L=[tex]\sqrt{13}[/tex]
Write an equation in slope-intercept form for the line that passes through each pair of points.
(-7, -3) (-3, 5)
The equation of line passes through the points (- 7, -3) and (-3, 5) will be;
⇒ y = 2x + 11
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (- 7, -3) and (-3, 5).
Now,
Since, The equation of line passes through the points (- 7, -3) and (-3, 5).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (5 - (-3)) / (-3 - (-7))
m = 8 / 4
m = 2
Thus, The equation of line with slope 2 is,
⇒ y - (-3) = 2 (x - (-7))
⇒ y + 3 = 2 (x + 7)
⇒ y + 3 = 2x + 14
⇒ y = 2x + 14 - 3
⇒ y = 2x + 11
Therefore, The equation of line passes through the points (- 7, -3) and
(-3, 5) will be;
⇒ y = 2x + 11
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Need help???!!!! Please
Answer:
+5&-2
Step-by-step explanation:
The function is used to model the height of an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. What are the domain and range? round to the nearest hundredth. Domain: [0, 12. 76] range: [1. 80, 590. 90] domain: range: [1. 80, 590. 90] domain: range: [0, 590. 90] domain: [0, 12. 76] range: [0, 590. 90].
For the function f(t) the domain and range is [0, 12.76] and [1.80, 590.90] respectively.
A function is a mathematical tool used to associate one value with another.
In this case, the function models the height of an object being tossed from a tall building. The height of the object is given by the function h(t), where h represents the height in meters and t represents the time in seconds.
The domain and range of a function describe the set of all possible input values (domain) and the set of all possible output values (range) of a function. The domain and range of the function h(t) are as follows:
The domain of the function h(t) is the set of all possible values of t for which the function h(t) is defined. In this case, the domain of the function h(t) is [0, 12.76], which means that the function h(t) is only defined for time values between 0 and 12.76 seconds.
The range of the function h(t) is the set of all possible values of h(t) that the function can produce. In this case, the range of the function h(t) is [1.80, 590.90], which means that the height of the object can only be between 1.80 meters and 590.90 meters.
Therefore, the correct option is (a).
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The sides of a triangle measure 32 inches, 22 inches, and 19 inches. What is the area of the triangle? Round intermediate results to 3 decimal places and the final answer to 1 decimal place. The area of the triangle is?
The area of the given triangle is approximately 204.2 square inches.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles.
To calculate the area of a triangle with given side lengths, we can use Heron's formula:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle (half of the perimeter), and a, b, and c are the lengths of the sides.
In this case, the lengths of the sides are a=32, b=22, and c=19. Therefore, the semi-perimeter is:
s = (a + b + c) / 2 = (32 + 22 + 19) / 2 = 36.5
Now we can plug in these values into the formula and simplify:
Area = √(36.5(36.5-32)(36.5-22)(36.5-19)) ≈ 204.16
Rounding this to 1 decimal place, the area of the triangle is approximately 204.2 square inches.
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d) The cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. Was the distance traveled during the first 8 minutes 1.75 times greater than the distance traveled during the second 8 minutes
The distance traveled in the first 8 minutes is 1.75 d2
What is speed?Speed is the rate of change of distance with time. it is a scalar quantity and it is measured in meter per second.
speed = distance /time
time = distance /speed
total time = 16
represent u by the first 8minutes and v by the second 8 minutes
u = 1.75v
8 = d1/1.75v
8 = d2/v
d1/1.75v = d2/v
d1 ×v = 1.75v × d2
d1 = 1.75d2
therefore ;
d1 = 1.75d2
where d1 and d2 are the distances for the first 8 minutes and second 8minutes respectively.
therefore the distance in the first 8minutes is 1.75 times greater than the second 8 minutes
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what function is equivalent to y = 3x(x+2)^2+7?
The function equivalent to y = [tex]3x(x+2)^2+7[/tex] is [tex]y = 3x^3[/tex]+[tex]12x^2[/tex] + 12x + 7.
Which function is equivalent functionally?Functionally equivalent refers to when a design, material, practice, method, technique, procedure, or component serves the same purpose and offers the same or better utility as is needed by the rule.
When we add the parenthesis to the expression, we get:
[tex]y = 3x(x^2 + 4x + 4) + 7[/tex]
If we simplify, we get:
[tex]y = 3x^3 + 12x^2 + 12x + 7[/tex]
As a result, y = 3x(x+2)2+7 is identical to y = 3x3 + 12x2 + 12x + 7.
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Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6,
2√10 ÷ 5 and √14
can anyone help me with this answer please.
The order from least to greatest would be as follows:
√3 - 1 < 2√10 ÷ 5 < √14 < 3√2 < √19 + 1 < 6
How did we get the value?To order the numbers, we need to first simplify and evaluate each expression.
1. √3 - 1 = 1.73205080757 - 1 = 0.73205080757
2. 2√10 ÷ 5 = 1.265
3. √14 = 3.74166
4. 3√2 = 4.243
5. √19 + 1 = 5.359
6. 6 is simply 6
Therefore, the correct answer is as given above. It could then be concluded that the order from least to greatest is:
0.73205080757 < 1.265 < 3.74166 < 4.243 < 5.359 < 6
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In the figure, QR≅ST. What is the length of QR ?
There are 2 chords inside the circle parallel to each other on opposite sides of the circle. Chord QR=7x+3 and Chord ST=5x+25
I NEED HELP ON THIS ASAP!!
The solution of both inequalities is (-1, 2).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have the inequalities
x+ y >1.........(1)
-x+ y <3.........(2)
The graph for x+ y >1 is shown by the red shaded region.
and, the graph for -x+ y <3 is shown by the blue shaded region.
Also , the Inequality intersect at (-1, 2) which shows the solution of both inequalities.
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Please help please now help ASAP
Answer:
2
Step-by-step explanation:
The fourth term in an arithmetic sequence is 3 and the tenth term is 18. If the first term is a1, which is an equation for the nth term of this sequence?
The equation for the nth term of this sequence is an = -4.5 + 2.5(n - 1)
How to determine the equation for the nth term of this sequence?From the question, we have the following parameters that can be used in our computation:
a4 = 3
a10 = 18
An arithmetic sequence is represented as
an = a + (n - 1)d
Using the above as a guide, we have the following:
a + 3d = 3
a + 9d = 18
Subtract the equations
So, we have
6d = 15
Divide
d = 2.5
So, we have
a + 3 * 2.5 = 3
This gives
a = -4.5
So, the sequence is -4.5 + 2.5(n - 1)
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An August 2022 report from The College Board states that, among all test takers who graduated high school in 2022 , the average SAT score was 1050 points, with a standard deviation of 216 points. The SAT score distribution can be assumed to follow a normal distribution. Question 3 Subquestions 3.a 1 point(s) Let a test taker who scores more than 1320 points be considered a top performer. What proportion of test takers are considered top perfors?
0.8400
0.1600
0.1056
0.8944
0.6800
3.b 1 nnint(s) What is approximately the minimum SAT score needed for a test taker to be in the top
20%
of the distribution? If a test taker has scored in the top
20%
of the distribution, what is the likelihood that the test taker is a top performer? Recall that a test taker who scores more than 1320 points is considered a top performer.
0.124
0.352
0.727
0.627
0.704
0.528
The proportion of test takers that are considered top performers is given as follows:
0.1056.
The minimum SAT score needed for a test taker to be in the top 20% is given as follows:
1231.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of SAT scores are given as follows:
[tex]\mu = 1050, \sigma = 216[/tex]
The proportion of scores above 1320 points is one subtracted by the p-value of Z when X = 1320, hence:
Z = (1320 - 1050)/216
Z = 1.25
Z = 1.25 has a p-value of 0.8944
1 - 0.8944 = 0.1056.
The minimum SAT score needed for a test taker to be in the top 20% is the 80th percentile, which is X when Z = 0.84, hence:
0.84 = (X - 1050)/216
X - 1050 = 216 x 0.84
X = 1231.
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Copy each statement. Insert , -, x, + or division symbol to make each statement true.
27 3 5 2 = 19
81 11 8 4 1 = 60
The Complete statement are:
1. 27/3 + 5 x 2
2. 81 + 1 - 8 x 4 x 1 = 60
What are Arithmetic Operations?Combining operands with a single arithmetic operator specifies an arithmetic operation. The ADD, SUBTRACT, DIVIDE, and MULTIPLY can also be used to specify arithmetic operations.
Given:
we have to apply the operation to make
27 3 5 2 = 19
81 11 8 4 1 = 60
so, first 27 3 5 2 = 19
1. 27/ 3 = 9
2. 5 x 2= 10
3. 9+ 10 = 19
For second,
1.81 + 11 = 92
2. 8 x 4 x 1 = 32
3. 92-32 = 60
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if line 1= y=-1/2x-4 and line 2= x+2y=-8 how many soloutions are there and what is the coordinate.
Answer:
No solutions
Step-by-step explanation:
I graphed the equations and the lines overlap, so no solution.
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