Answers
Answer:
Number three is D.
Step-by-step explanation:
Related Questions
Factor each polynomial using difference of squares. Check for common factors first.
a) x² – 36
b) 3x² - 12
Factor the following using the trinomial method. Check for common factor first.
a) x² + 6x + 9
b) 4x² - 8x - 60
PLS HELP!!!!! I ONLY HAVE 2 HOURS!!!
Answers
The results of factoring the polynomials are (x - 6)(x + 6), 3(x - 2)(x + 2), (x + 3)² and 4(x + 3)(x - 5)
Factoring using difference of squaresFirst, we have
x² – 36
Applying the property of difference of squares, we have
(x - 6)(x + 6)
Next, we have
3x² - 12
Factor out 3
3(x² - 4)
Applying the property of difference of squares, we have
3(x - 2)(x + 2)
Factoring the following using the trinomial methodFirst, we have
x² + 6x + 9
Expand and factorize
x² + 6x + 9 = x² + 3x + 3x + 9 = (x + 3)²
Next, we have
4x² - 8x - 60
Expand and factorize
4x² - 8x - 60 = 4(x² - 2x - 15) = 4(x + 3)(x - 5)
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The volume of the triangular pyramid below is 210 units³. Find the value of x.
Answers
The value of x as shown in the triangular prism is 14 unit.
What is traingular pyramid?Triangular pyramids are formed solely from triangles. The 3 triangular sides slant upwards to form the triangular base.
To calculate the value of x of the rectangular pyramid, we use the formula below
Formula:
V = bhH/6............................. Equation 1Where:
V = volume of the Pyramidb = Base of the triangleh = Height of the triangleH = Height of the pyramidFrom the diagram and the question,
Given:
V = 210 unit³b = 10h = 9 H = xSubstitute these values into equation 1 and solve for x
210 = (10×9×x)/6210 = 15xx = 210/15x = 14 unitHence, the value of x is 14 unit.
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The pairs of polygons below are similar. Give the scale factor, perimeter ratio, and area ratio of Figure A to Figure B
Answers
1.) The scale factor = 4
The perimeter ratio = 1:3
The area ratio = 1:16
How to calculate the scale factor of the given shapes?To calculate the scale factor of the given shapes, the formula that should be used would be ;
Scale factor = Bigger dimensions/ Smaller dimensions
Length of the bigger rectangle (B) = 16
Length of the smaller rectangle (A) = 4
The scale factor = 16/4 = 4
The perimeter = 2(l+w)
length B = 16
width B = 8
perimeter B = 2(16+8)
= 2(24) = 48
Length A = 4
width A = 2
perimeter A =2(4+2)
= 16
The perimeter ratio = A:B = 16:48 = 1:3
Area = length×width
length A = 4
width A = 2
Area A = 4×2 = 8
length B = 16
width B = 8
area B = 8×16= 128
Area ratio of A:B = 8:128 = 1:16
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cos xº [Hint: Change degree into radian] find the derivative from definition
Answers
The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)
Finding the derivative of the functionFrom the question, we have the following function definition that can be used in our computation:
cos(xº)
Changing the degree into radian, we have
cos(xπ/180)
Express as a function
So, we have
y = cos(xπ/180)
When the cosine function is differentiated, we have
y' = -sin(xπ/180)
Hence, the differentiated function is y' = -sin(xπ/180)
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Ravi is saving money to buy a game. The game costs $12, and so far he has saved one-fourth of this cost. How much money has Ravi saved?
Answers
Answer:
$3
Step-by-step explanation:
since $12 is 4/4 and he save 1/4 its 12÷4
Answer:
$3
Step-by-step explanation:
12 divided by 4 is 3
(3+3)+(3+3)
6+6
= 12
A car is driving away from El Paso with constant velocity. At 1 p.m., it is 145 miles away from El Paso. At 3 p.m., it is 275 miles away from El Paso.
Part A: Write a linear function that describes the distance (in miles) the car is from El Paso in terms of time (in hours after 12:00 p.m.).
Answers
The linear function that describes the distance (in miles) is therefore y = 65x + 80
How to solve for the linear functionWe have to find the slope and the intercept in other to get the linear function
The data points are:
(1, 145) and (3, 275).
m = (y2 - y1) / (x2 - x1)
fixing the data points we have
m = (275 - 145) / (3 - 1)
= 130 / 2
= 65
y = mx + b
(1, 145):
145 = 65(1) + b
b = 145 - 65
= 80
y intercept is 80
The linear function is therefore y = 65x + 80
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Can someone help me please????????????????????????????????????
Answers
The percentage error for each of the given situations are:
1) 23%
2) 21%
3) 11%
4) 16.67%
5) 43%
How to find the percent error?The formula for percent error is:
Percentage Error = ((Actual Number – Estimated Number)/ Estimated number) * 100%
1) Estimated Number = 2310
Actual Number = 3000
Thus:
Percent Error = (3000 - 2310)/3000 * 100%
Percent error = 23%
2) Estimated Number = 17600
Actual Number = 21300
Thus:
Percent Error = (21300 - 17600)/17600 * 100%
= 21%
3) Estimated Number = 4.5
Actual Number = 4
Thus:
Percent Error = (4 - 4.5)/4.5 * 100%
= 11%
4) Estimated Number = 15000
Actual Number = 12500
Thus:
Percent Error = (12500 - 15000)/15000 * 100%
= 16.67%
5) Estimated Number = 350
Actual Number = 200
Thus:
Percent Error = (200 - 350)/350 * 100%
= 43%
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X
-3
-1
1
-1
y
5
2
-1
4
The table above:
Answers
The task here is to determined where the table given is a function. Thus we can state that the above table is NOT a function. This is called Non-Function Relation.
What is the reason for the above assertion?The table given above is suggestive of the relationship between the values of x and y given.
It may be inferred that x values are the input values while the y values are the output.
So the criteria for the values on the table to constitute a function is that each input value (x) must be associated with only one value of y.
From the table, it is clear to see that this rule if violated. You have the x value (-1) being associated with the y values of 2 and 4 respectively, hence, it is proper to conclude that the table is NOT a function.
This is called a Non-Function Relation.
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PLEASE HELP I DON'T UNDERSTAND THIS!!!!!
Answers
Answer:
C. (4, 0)
Step-by-step explanation:
(x, y)
a. (4, 3)
y = 12 - 3x
3 = 12 - 3(4)
3 = 12 - 12
3 = 0 false
b. (-4, 4)
y = 12 - 3x
4 = 12 - 3(-4)
4 = 12 + 12
4 = 24 false
c. (4, 0)
y = 12 - 3x
0 = 12 - 3(4)
0 = 12 - 12
0 = 0 true
d. (0, 4)
y = 12 - 3x
4 = 12 - 3(0)
4 = 12 - 0
4 = 12 false.
Answer: C (4, 0)
Step-by-step explanation:
your function y = 12 - 3x
They are asking which of those points are on the line
(x, y) this is a format of a point where you can plug in x for x and y for y.
a. (4, 3) x=4 y=3 substitute and see if your answer is true
3 = 12 -3(4)
3 = 0 this is not true so (4, 3) is not a solution
b. (-4,4) x= -4 y=4
4 = 12 - 3(-4)
4 = 24 not true
c. (4, 0) x=4 y=0
0 = 12-3(4)
0 = 0 true (4,0) is a solution
d. (0, 4)
4 = 12 - 3 (0)
4=12
The position (in meters) of a particle per respect to time (in seconds) is defined by the
following functions (t)=t4-16t³+72t² +5. Find the maximal and minimal value for
the speed of the particle for t E [1, 7].
Answers
The maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.
How to calculate the valueIt should be noted that upon deriving v(t), an equation of 12t² - 96t + 144 is produced. Subsequently, v'(t) must be set to zero, resulting in a quadratic equation of 12t² - 96t + 144 = 0, requiring division of both sides by 12 to produce t² - 8t + 12 = 0.
The quadratic can now be factored to obtain (t - 2)(t - 6) = 0, indicating that critical points lie on the values t = 2 and t = 6.
After calculating these values— v(1) = 100 m/s, v(2) = 64 m/s, v(6) = 16 m/s and v(7) = 1159 m/s—it is clear that the maximum of 1,159 m/s occurs when t = 7, and the minimum of 16 m/s occurs when t = 6.
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DE bisects AC at point B. AC=a+23
and AB = 3a + 4. Find BC.
Y
X
13
2
X
(X) XS
X₁
IV
Answers
The values of AB and BC are equal and equal to
13 units.How to find BCInformation given in the problem includes
DE bisects AC at point B
AC = a + 23
AB = 3a + 4
From the definition of a bisector, point B divides AC into two equal sides, this means that
AB = BC = (1/2) * AC
Substituting the value of AC and AB
AB = 3a + 4 = (1/2) * (a + 23)
3a + 4 = (1/2) * (a + 23)
solving for a
2 * (3a + 4) = a + 23
6a + 8 = a + 23
6a - a = 23 - 8
5a = 15
a = 3
Then we have that:
AB = 3a + 4 = 3(3) + 4 = 9 + 4 = 13
and, AB = BC
so BC = 13
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NO LINKS!! URGENT HELP PLEASE!!!
Find the equation of a parabola with a vertex at (-2, 6) and that passes through the (-4, -5)
Answers
Answer:
[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]
Step-by-step explanation:
As we know that
The standard equation of a parabola with vertex at point (h,k) is given by:
[tex]y = a(x-h)^2 + k[/tex]
where (h,k) is the vertex
and "a" is a coefficient that determines the direction and shape of the parabola.
We know that the vertex of our parabola is (-2, 6),
so we can substitute those values into the equation to get:
[tex]y = a(x + 2)^2 + 6[/tex]
Now finding a.
Since the parabola passes through point (-4, -5). Substituting these coordinates into the equation, we get:
-5 = a(-4 + 2)^2 + 6
-5 =a(-2)^2+6
-5=4a +6
-5-6=4a
4a=-11
a =- 11/4
Substituting the value of an equation second, we get
[tex]\frac{-11}{4} (x + 2)^2 + 6.[/tex]
Therefore, the equation of the parabola with a vertex at (-2, 6) and passing through (-4, -5) is y =
[tex] \frac{-11}{4} (x + 2)^2 + 6[/tex]
Answer:
[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]
Step-by-step explanation:
The vertex form of a parabola is:
[tex]\boxed{y=a(x-h)^2+k}[/tex]
where:
(h, k) is the vertex."a" is the leading coefficient.Given the vertex is at (-2, 6), substitute h = -2 and k = 6 into the equation:
[tex]y=a(x-(-2))^2+6[/tex]
[tex]y=a(x+2)^2+6[/tex]
To find the value of a, substitute the point (-4, -5) into the equation and solve for a:
[tex]\begin{aligned}-5&=a(-4+2)^2+6\\-5&=a(-2)^2+6\\-5&=4a+6\\-5-6&=4a+6-6\\-11&=4a\\\dfrac{-11}{4}&=\dfrac{4a}{4}\\-\dfrac{11}{4}&=a\\a&=-\dfrac{11}{4}\end{aligned}[/tex]
Substitute the found value of a back into the equation:
[tex]y=-\dfrac{11}{4}(x+2)^2+6[/tex]
Therefore, the equation of a parabola with a vertex at (-2, 6) and that passes through the point (-4, -5) is:
[tex]\boxed{y=-\dfrac{11}{4}(x+2)^2+6}[/tex]
Pamela paid $8.95 for 5 pounds of bananas. How much will it cost to buy 2 pounds of bananas at the same rate?
Answers
Answer:
$3.58
Step-by-step explanation:
Because we know that the 2 lbs of bananas will be purchased at the same rate, the price per pound for 5 lbs of bananas is proportional to the price per pound for 2 lbs of bananas.
Thus, we can solve for price, p of 2 lbs of bananas by setting up a proportion:
[tex]\frac{8.95}{5}=\frac{p}{2}\\ \\ 17.90=5p\\\\3.58=p[/tex]
At Jamie's bank, 20 bankers manage personal loans and 15 bankers manage business loans. Of those, 3 bankers manage both. If the bank only offers these two types of loans, how many bankers does it employ? A. 17 B. 32 C. 35 D. 38
Answers
The bank employs a total of 32 bankers, and the answer is not listed among the options provided. The correct option is B.
Let's denote the number of bankers who manage only personal loans as P and the number of bankers who manage only business loans as B. Then, we can use the following information to form equations:
There are 20 bankers who manage personal loans, which means P + 3 bankers in total manage personal loans.
There are 25 bankers who manage business loans, which means B + 3 bankers in total manage business loans.
The bank has a total of X bankers.
Using these equations, we can solve for X as follows:
P + 3 = 20 (equation 1)
B + 3 = 25 (equation 2)
P + B + 3 = X (equation 3)
Solving equation 1 for P, we get P = 17.
Solving equation 2 for B, we get B = 12.
Substituting P = 17 and B = 22 into equation 3, we get:
17 + 12 + 3 = X
Simplifying, we get X = 32.
Therefore, the bank employs a total of 32 bankers, and the answer is not listed among the options provided.
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If this figure is cut along the dotted line, what 2 shapes will be made?
Answers
The shapes that would be made if the figure is cut along the dotted line are a right angled- triangle and a semi - circle.
How to find the shapes ?Upon reviewing this shape, we observe that it is comprised of two distinct shapes: a right-angled triangle and a semicircle.
This means that if the figure was cut along the dotted lines that joined them, the shapes that would be made are the same shapes which are a right triangle and a semi - circle.
In conclusion, the shapes would be a semi - circle and right triangle.
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answer this please i need help with this problem
Answers
The value of x in the triangle is 1/√3
We know that tan function is the ratio of opposite side and adjacent side
In triangle, for angle 60 degrees the opposite side is 1 unit
Adjacent side is x units
tan 60 = opposite side/adjacent side
√3= 1/x
We need to find value of x
Apply cross multiplication
x=1/√3
Hence, the value of x in the triangle is 1/√3
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The functions fand g are defined as follows.
f(x)=2x²-3x g(x)=-4x-1
Find f(-4) and g (5).
f(-4) = ?
g (5) = ?
Answers
Answer:
f(- 4) = 44 , g(5) = - 21
Step-by-step explanation:
to evaluate f(- 4) substitute x = - 4 into f(x)
f(- 4) = 2(- 4)² - 3(- 4) = 2(16) + 12 = 32 + 12 = 44
to evaluate g(5) substitute x = 5 into g(x)
g(5) = - 4(5) - 1 = - 20 - 1 = - 21
In circle E, EF = 10 and m
ZFEG = 72°. Find the length of FG.
Express your answer as a fraction times π.
Answer:
Length of FG=
Answers
The length of the arc FG is 12.56 units
What is length of an arc?Length of an arc is the distance that runs through the curved line of the circle making up the arc.
An arc is a cut out section of a circle. The circumference is the whole body of the circle.
The length of an arc is expressed as
(tetha))360 × 2πr
where r is the radius and tetha is the angle between the radii.
l = 72/360 × 2 × 3.14 × 10
l = 4521.6/360
l = 12.56 units
therefore the length of the arc FG is 12.56 units
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A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol. What was the total volume of the original mixture? (Please mention the numeric value.)
Answers
The total volume of the original mixture is 4 liters.
Given that:
A mixture of 50% alcohol and 50% water has 4 liters of water added to it. It is now 25% alcohol.
Let 'x' be the amount of water and alcohol. Then we have
x / (x + x + 4) = 0.25
x/(x + 2) = 0.5
2x = x + 2
x = 2
The total volume of the original mixture is calculated as,
Total volume = x + x
Total volume = 2 + 2
Total volume = 4 liters
The total volume of the original mixture is 4 liters.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
What type of correlation is suggested by the scatter plot?
Positive, weak correlation
Negative, weak correlation
Positive, strong correlation
Negative, strong correlation
No correlation
Answers
A rectangular aquarium measures 21 inches long by 11 inches wide by 18 inches tall. If the aquarium is filled to the 15 inch mark, what is the volume of the water in the aquarium?
Answers
The volume of water in the aquarium up to the 15 inch mark is 3465 cubic inches.
What is the volume of the water in the aquarium?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
The volume of water in the aquarium up to the 15 inch mark will be equal to the volume of a rectangular prism with a length of 21 inches, a width of 11 inches, and a height of 15 inches.
This is because the water level is 15 inches from the bottom of the aquarium.
Hence, the volume of water in the aquarium up to the 15 inch mark is:
V = l × w × h
V = 21 × 11 × 15
V = 3465 cubic inches
Therefore, the volume of water in the aquarium is 3465 cubic inches.
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Donovahn made two bracelets for a friend. Each bracelet is made of 36 beads. Bracelet A contains 12 letter beads Bracelet B contains 20 letter beads. Which statement is true?
Answers
Based on the conditions, the correct statements are,
⇒ Bracelet B has 8 more letter beads than Bracelet A.
We have to given that;
Donovahn made two bracelets for a friend.
And, Each bracelet is made of 36 beads. Bracelet A contains 12 letter beads Bracelet B contains 20 letter beads.
Hence, We have;
Based on the information provided, we can say that Bracelet B contains more letter beads than Bracelet A.
Specifically, Bracelet B has 8 more letter beads than Bracelet A.
Thus, Based on the conditions, the correct statements are,
⇒ Bracelet B has 8 more letter beads than Bracelet A.
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Number 1 please help
Answers
Answer:
x^2y^4
Step-by-step explanation:
b because u have to add the exponents of the like variable. x^4 and x^-2 are the like terms in this equations so 4+(-2) so its basically flipping the signs plus and the negative sign so it's just -2
Select the correct answer. Which graph represents the given exponential function? f(x)=5(3)x-1
A.
B.
C.
D.
Answers
The graph of the function f(x) = 5(3)ˣ - 1 is represented as the diagram given in option C.
To find the main points of the function f(x) = 5(3)ˣ - 1, we can identify its key features such as the y-intercept, x-intercept, and any asymptotes.
Y-intercept:
To find the y-intercept, we set x = 0 and evaluate the function:
f(0) = 5(3)⁰ - 1 = 4
Therefore, the y-intercept is (0,4).
Asymptotes:
There are no vertical asymptotes for this function since the base of the exponential function, 3, is positive.
The graph of the function is given in the attached image.
Therefore, the correct option is C.
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Find a linear inequality with the following solution set. Each grid line represents one unit.
[asy]
size(200);
fill((2,-5)--(-5,-5)--(-5,5)--(5,5)--(5,-2)--cycle,yellow);
real ticklen=3;
real tickspace=2;
real ticklength=0.1cm;
real axisarrowsize=0.14cm;
pen axispen=black+1.3bp;
real vectorarrowsize=0.2cm;
real tickdown=-0.5;
real tickdownlength=-0.15inch;
real tickdownbase=0.3;
real wholetickdown=tickdown;
void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) {
import graph;
real i;
if(complexplane) {
label("$\textnormal{Re}$",(xright,0),SE);
label("$\textnormal{Im}$",(0,ytop),NW);
} else {
label("$x$",(xright+0.4,-0.5));
label("$y$",(-0.5,ytop+0.2));
}
ylimits(ybottom,ytop);
xlimits( xleft, xright);
real[] TicksArrx,TicksArry;
for(i=xleft+xstep; i 0.1) {
TicksArrx.push(i);
}
}
for(i=ybottom+ystep; i 0.1) {
TicksArry.push(i);
}
}
if(usegrid) {
xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.1),extend=true),p=invisible);//,above=true);
yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.1),extend=true), p=invisible);//,Arrows);
}
if(useticks) {
xequals(0, ymin=ybottom, ymax=ytop, p=black, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=black, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize));
} else {
xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize));
yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize));
}
};
draw((5,-2)--(2,-5),dashed+red, Arrows(size=axisarrowsize));
rr_cartesian_axes(-5,5,-5,5);
for( int i = -4; i <= 4; ++i) {
draw((i,-5)--(i,5));
draw((-5,i)--(5,i));
}
[/asy]
(Give your answer in "standard form" $ax+by+c>0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater that 1)
I’ve looked at other people’s answers but my website keeps saying im wrong. If anyone knows how to register this answer to aops, please tell me how
Answers
The linear inequality with the solution set (2,-5), (-5,-5), (-5,5), (5,5), (5,-2) are x ≤ 5 and y ≤ 5
Finding a linear inequality with the solution setThe solution set is given as
(2,-5), (-5,-5), (-5,5), (5,5), (5,-2)
We can see that the highest y value in the above ordered pairs is 5
So, we have
y ≤ 5
Also, we can see that the highest x value in the above ordered pairs is 5
So, we have
x ≤ 5
Hence, the linear inequality with the solution set is x ≤ 5 or y ≤ 5
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A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
Answers
Answer:
A. 45(x+3)=60x
Step-by-step explanation:
Nicole‘s mother put tiles on a section of the kitchen floor. The section included 5 rows with 13 tiles in each row. Each tile cost $2. How much money did Nicole’s mother spend on the tiles?
Answers
If each tile cost $2 then the amount spend by Nicole’s mother on tiles is $130
Given that Nicole‘s mother put tiles on a section of the kitchen floor.
The section included 5 rows with 13 tiles in each row
Each tile cost $2.
To find the total amount spend by Nicolas mother on tiles we have to find the number of tiles
Number of tiles =5×13
=65 tiles
Now let us find the amount
Total amount on tiles = 2×65
=$130
Hence, if each tile cost $2 then the amount spend by Nicole’s mother on tiles is $130
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A baker produces 400 brownies a day at a cost of 25 cents per brownie. If all the brownies are sold each day, what is the minimum selling price per brownie to make a daily profit of at least $420?
Answers
The minimum selling price per brownie to make a daily profit of at least $420 is $1.30.
What is the minimum selling price per brownie to make a daily profit of at least $420?Given that: A baker produces 400 brownies a day at a cost of 25 cents per brownie.
Let's begin by calculating the total cost of producing 400 brownies a day:
Cost per brownie = 25 cents = 0.25 dollars
Total cost = 400 × 0.25 = 100 dollars
To make a daily profit of at least $420, the total revenue should be:
Total revenue = Total cost + Minimum profit
Total revenue = 100 + 420 = 520 dollars
The minimum selling price per brownie to achieve this revenue can be calculated as:
Selling price per brownie = Total revenue / Number of brownies produced
Selling price per brownie = 520 / 400
Selling price per brownie = 1.3 dollars
Therefore, the minimum selling price is $1.30 per brownies.
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The half-life of a certain element is 5 days. If you started with 948 grams of this element, how much remains after 30 days?
Answers
After 1 half-life, the amount of the element remaining is half of the original amount. After 2 half-lives, the amount remaining is half of the remaining amount after the first half-life. We can continue this pattern until we get to 30 days.
The number of half-lives in 30 days is 30/5 = 6.
So, after 1 half-life, the amount remaining is 948/2 = 474 grams.
After 2 half-lives, the amount remaining is 474/2 = 237 grams.
After 3 half-lives, the amount remaining is 237/2 = 118.5 grams.
After 4 half-lives, the amount remaining is 118.5/2 = 59.25 grams.
After 5 half-lives, the amount remaining is 59.25/2 = 29.625 grams.
After 6 half-lives, the amount remaining is 29.625/2 = 14.8125 grams.
Therefore, after 30 days, 14.8125 grams of the element remains
UCM college administrators claim that the average freshman enrollment over the last 10 years meets the university's capacity of 6,500 students. You believe hypothesize this is inaccurate and believe that UCM is underestimating the number of college freshman. Using a sample of 500
students, you determine a sample mean of 6,600 freshman. Assume o = 1,000 and a = .05.
Answers
The t-statistic value of the hypothesis is 2.236
The population mean is equal to 6,500 (H0: μ = 6500)
Alternative hypothesis:
The population mean is greater than 6,500 (Ha: μ > 6500)
We are given the sample mean (x) = 6,600, sample size (n) = 500, population standard deviation (σ) = 1,000, and level of significance (α) = 0.05.
First, we need to calculate the t-statistic using the formula:
t = (X - μ) / (σ / √n)
where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values, we get:
t = (6,600 - 6,500) / (1,000 / √500)
= 2.236
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