Answer:
The number of doughnuts left over are 8 doughnuts
Step-by-step explanation:
The information given are;
The number of doughnuts fried per batch = 20 doughnuts
The number of doughnuts contained in a pack = 13 doughnuts
The number of doughnut batches just fried = 20 batches
The number of packs filled = 44 packs
The number of packs filled with the fried = 44 packs
The number of doughnuts per pack = 13 doughnuts
The number of doughnuts in the pack = The number of packs filled with the fried × The number of doughnuts per pack
The number of doughnuts in the pack = 44 × 13 = 572 doughnuts
Given that the number of batches of doughnuts fried = X batches and the amount of left over = Y doughnuts, where each batch contains 20 doughnuts, we have;
Number of doughnuts fried = Number of batches of doughnuts fried × Number of doughnuts per batch
Number of doughnuts fried = X × 20 =20×X doughnuts
Therefore we have;
Number of doughnuts fried = The number of doughnuts in the pack + The number of doughnuts left over
Which gives;
20×X = 572 + Y where Y < 20
Checking we have multiples of 20 are 560, 580
Given that 520 is the next multiple of 20 after 572, we have;
The number of doughnuts fried = 580 and the number of left over = 580 - 572 = 8 doughnuts.
Jack had 4 hours of school. He spent 45 minutes in the library and 12 hour on a science lecture and had a lunch break of 25 minutes. How much time is left for the school to get over? (Write the answer as a fraction.)
Answer:
[tex]\dfrac{10}{4} \ hour[/tex]
Step-by-step explanation:
Given that :
Jack had 4 hours of school.
He spent 45 minutes in the library
1/2 hour on a science lecture and;
had a lunch break of 25 minutes
The objective is to determine how much time is left for the school to get over and we are to write the answer as a fraction.
In order to do that, we will have to convert the minutes into hours,
we all know that; 60 minutes = 1 hour.
Then,
45 minutes = (45/60)hour = 3/4 hour
25/60 minutes = 1/4 hour
Therefore, the amount of time left for the school to get over is:
= [tex]4 - (\dfrac{3}{4}+\dfrac{1}{2}+ \dfrac{1}{4})[/tex]
= [tex]\dfrac{16-(3+2+1)}{4}[/tex]
= [tex]\dfrac{16-6}{4}[/tex]
= [tex]\dfrac{10}{4} \ hour[/tex]
Kelly is a waitress and her average tip rate is 18%. After taking a sample of her tips from a week, she thinks her tip rate is actually higher. The data below is the tip rate for 15 randomly chosen checks (the numbers represent percentage). Assume that tip rates are normally distributed.
18.5 18.2 20 21.3 17.9 17.9 18.1 17.5 20 18
a) Express the null and alternative hypotheses in symbolic form for this claim.
H0 : Select an answer
Ha: Select an answer
b) What is the test statistic. Round to 2 decimals.
c) What is the p-value. Round to 4 decimals p-value =
Answer:
Step-by-step explanation:
From the given information:
the null and alternative hypotheses in symbolic form for this claim can be computed as:
[tex]H_o:\mu = 18 \\ \\ H_a : \mu > 18[/tex]
Mean = [tex]\dfrac{18.5+18.2+20+21.3+17.9+17.9+18.1+17.5+20+18}{10}[/tex]
Mean = 18.74
Standard deviation [tex]\sigma = \sqrt{\dfrac{\sum(x_i - \mu)^2}{N}}[/tex]
Standard deviation [tex]\sigma = \sqrt{\dfrac{(18.5 - 18.74)^2+(18.2 - 18.74)^2+(20 - 18.74)^2+...+(18 - 18.74)^2}{10}}[/tex]
Standard deviation [tex]\sigma[/tex] = 1.18
The test statistics can be computed as follows:
[tex]Z= \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z= \dfrac{18.6- 18}{\dfrac{1.18}{\sqrt{10}}}[/tex]
[tex]Z= \dfrac{0.6}{\dfrac{1.18}{3.162}}[/tex]
Z = 1.6078
Z = 1.61
Degree of freedom = n -1
Degree of freedom = 10 -1
Degree of freedom = 9
Using t - calculator at Z = 1.6078 and df = 9
The P - value = 0.0712
The length of a rectangle is 7 meters longer than its width. What is the width of this rectangle if its perimeter is equal to 86 meters?
Answer:
18 meters
Step-by-step explanation:
If the width is w, the length is w + 7.
Perimeter = 2(width + length), therefore:
86 = 2(w + w + 7)
86 = 2(2w + 7)
43 = 2w + 7
36 = 2w
w = 18
Answer:
18 metersStep-by-step explanation:
Given,
Let length of a rectangle be ' x + 7 ' meters
Let width of a rectangle be ' x ' meters
Perimeter = 86 meters
Now, let's find the width of the rectangle:
Perimeter of rectangle = [tex]2(l + b)[/tex]
plug the values
[tex]86 = 2(x + 7 + x)[/tex]
Collect like terms
[tex]86 = 2(2x + 7)[/tex]
Distribute 2 through the parentheses
[tex]86 = 4x + 14[/tex]
Move constant to R.H.S and change its sign
[tex]86 - 14 = 4x[/tex]
Calculate the difference
[tex]72 = 4x[/tex]
Swipe the sides of the equation
[tex]4x = 72[/tex]
Divide both sides of the equation by 4
[tex] \frac{4x}{4} = \frac{72}{4} [/tex]
Calculate
[tex]x = 18[/tex] meters
Hope this helps..
Best regards!!
Pam works as an office administrator. She spends $7500 of her income on personal expenses each year. If this represents 18% of her salary, how much money does Pam earn in one year? Round your answer to the nearest whole dollar.
Answer:
Her annual salary is approximately $41,667
Step-by-step explanation:
Hello,
This question deals with percentage of a number and it's very easy :)
First of all, get the data and understand what's required of us.
Pam spends $7500 yearly on expenses
But this amount represents 18% of her annual income.
Let her annual income be represented by x
18% = 7500 / x
18÷100 = 7500÷x
cross multiply and solve for x
18 × x = 7500 × 100
18x = 750,000
divide both sides by 18
18x / 18 = 750,000 / 18
x = $41,666.67
x = $41,667
Her annual salary is approximately $41,667
Para ingresar a la Universidad del Chocó se aplica una prueba de razonamiento que consta de 30 preguntas. Por cada respuesta correcta se asignan 5 puntos y por cada incorrecta (o no contestada) se restan 2 puntos. Si un participante obtuvo un puntaje de 94 puntos, ¿cuántas preguntas
Complete question:
Para ingresar a la Universidad del Chocó se aplica una prueba de razonamiento que consta de 30 preguntas. Por cada respuesta correcta se asignan 5 puntos y por cada incorrecta (o no contestada) se restan 2 puntos. Si un participante obtuvo un puntaje de 94 puntos, ¿cuantas preguntas respondió bien?
Responder:
número de respuestas correctas = 22
Explicación paso a paso:
Dado lo siguiente:
Número total de preguntas = 30
Deje respuestas correctas = y; Respuestas incorrectas = n
Marca otorgada por y = 5
Marca deducida por n = 2
Si el total de preguntas = 30; luego
y + n = 30 - - - - (1)
Puntuación total obtenida = 94; luego
5y - 2n = 94 - - - (2)
De 1),
y + n = 30
y = 30 - n
Sustituya y = 30 - n en equ (2)
5 (30 - n) - 2n = 94
150 - 5n - 2n = 94
150 - 7n = 94
-7n = 94-150
-7n = - 56
n = 56/7
n = 8
Sustituir n = 8 en (1)
y + n = 30
y + 8 = 30
y = 30 - 8
y = 22
y = número de respuestas correctas = 22
n = número de respuestas incorrectas = 8
Usando un sistema de ecuaciones, se encuentra que el participante obtuve 22 respuestas correctas.
En el sistema, x es el número de respuestas correctas, con y siendo el número de respuestas incorrectas.
Total de 30 preguntas, o sea:
[tex]x + y = 30 \rightarrow y = 30 - x[/tex]
5 puntos asignados por cada respuesta correcta, 2 restados por cada respuesta incorrecta. Puntaje de 94 puntos, o sea:
[tex]5x - 2y = 94[/tex]
Considerando [tex]y = 30 - x[/tex]
[tex]5x - 60 + 2x = 94[/tex]
[tex]7x = 154[/tex]
[tex]x = \frac{154}{7}[/tex]
[tex]x = 22[/tex]
El participante obtuve 22 respuestas correctas.
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What type of linear system is shown below?
A inconsistent
B. consistent and independent
C. consistent and dependent
D. inconsistent and dependent
Graph is attached , please help
Answer:
The linear system shown on the graph is consistent and independent
Step-by-step explanation:
The linear system shown on the graph is consistent because it has at least one solution which satisfy both linear graphs. The solution is at the point of interception of the two line graphs.
The linear system shown on the graph is independent because the two line graphs are distinct and not parallel or dependent on one another.
Therefore, The linear system shown on the graph is consistent and independent
Which of the following sets contains all roots of the polynomial f(x)=2x^3+3x^2-3x-2?
Answer:
C
Step-by-step explanation:
Given
f(x) = 2x³ + 3x² - 3x - 2
Note that
f(1) = 2 + 3 - 3 - 2 = 0 , thus
(x - 1) is a factor
Dividing f(x) by (x - 1) gives
f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)
To find the roots equate f(x) to zero, that is
(x - 1)(x + 2)(2x + 1) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x + 2 = 0 ⇒ x = - 2
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]
The solution set is therefore
{ - 2, - [tex]\frac{1}{2}[/tex], 1 } → C
Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.
Answer:
Step-by-step explanation:
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
Hope this helps
The zeroes of the function are -4, 0 and 2.
The intervals where the function is positive is [tex]-4 < x < 2, \ \ x >2[/tex].
The intervals where the function is negative is [tex]x < -4[/tex].
The given parameters:
f(x) = x³ + 2x² - 8xWhat is zeroes of a function?The zeroes of a function is the possible values of the unknown that makes the entire function to be zero.
The zeroes of the cubic equation is calculated as follows;
f(x) = 0
x³ + 2x² - 8x
factorize as follows;
[tex]x(x^2 + 2x -8) = 0\\\\x(x^2 + 4x - 2x -8) = 0\\\\x[x (x + 4 )-2(x + 4)]= 0\\\\x(x + 4)(x -2)=0\\\\x = 0, \ \ x = -4 \ \ x = 2[/tex]
The intervals where the function is positive and negative is determined as follows;
[tex]x(x + 4) (x - 2)\\\\[/tex]
[tex]when, \ x = -5, \ f(x) = -ve\\\\when, \ x = -4, \ f(x) =0\\\\when , \ x = -3, \ f(x) = +ve[/tex]
The intervals where the function is positive is determined as;
[tex]-4 < x < 2, \ \ x >2[/tex]
The intervals where the function is negative is determined as;
[tex]x < -4[/tex]
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Solve the inequality.
9p+23<41
Answer:
p < 2
Step-by-step explanation:
9p + 23 < 41
p < 2
Answer:
p < 2
Step-by-step explanation:
9p + 23 < 41
9p < 18
p < 2
I don't understand this question. Could someone please help me?
Answer:
its answer is a not b
As in Formula
A=3.14*r^2
A =144pift^2
Answer:
144π square feet
Step-by-step explanation:
The garden is shaped like a circle.
To find the area of it we can use the formula of area of a circle.
The formula for area of a circle is:
πr^2
Plug our values in.
π(12)^2
144π
The area of the garden is 144πft^2
Help it’s urgent please
Answer:
[tex] \frac{5 {x}^{2} + 20xy + 20 {y}^{2} }{x ^{2} - xy - {6y}^{2} } [/tex]
To simplify first factorize both the numerator and the denominator
For the numerator
5x² + 20xy + 20y²
Factor 5 out
5 ( x² + 4xy + 4y²)
Using a² + 2ab + b² = ( a + b)²
The numerator is
5( x + 2y)²
For the denominator
x² - xy - 6y²
Rewrite -xy as a difference
x² + 2xy - 3xy - 6y²
Factorize
We have the denominator as
( x + 2y)( x - 3y)
So we now have
[tex] \frac{5(x + 2y)(x + 2y)}{(x + 2y)(x - 3y)} [/tex]Simplify
[tex] \frac{5(x + 2y)}{x - 3y} [/tex]We have the final answer as
[tex] \frac{5x + 10y}{x - 3y} [/tex]Hope this helps you
Which of the following Functions is NOT Linear? A:f(x)=x+0.5 B:F(x)=-x+0.5 C: F(x)=x^2-0.5 D: f(x)=0.5x
Answer:
C: F(x)=x^2-0.5
Step-by-step explanation:
When the x is squared it's a parabola. A linear graph is shaped like a straight line, while a parabola is curved inward. I have included a graph of what that function would look like (tap/click on it to see the full graph.)
Answer:
C: f(x) = x² - 0.5Step-by-step explanation:
The grsaph of the linear function is a straight line.
The equation of a line in the slope-intercept fomr is:
y = mx + b
where
m - slope
b - y-intercept
We have:
A: f(x) = x + 0.5
it's a linear function: m = 1, b = 0.5
B: f(x) = -x + 0.5
it's a linear function: m = -1, b = 0.5
C: f(x) = x² - 0.5
it's not a linear function because in the equation is square of x (x²).
The graph of this function is a parabola.
D: f(x) = 0.5x
it's a linear function: m = 0.5, b = 0
In a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%. What’s the probability of the student being a male, if you know the student studies Spanish
Answer:
27.8%
Step-by-step explanation:
P(male | Spanish) = P(male and Spanish) / P(Spanish)
P(male | Spanish) = 0.05 / 0.18
P(male | Spanish) = 0.278
The probability of the student being a male is 27.8%
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that in a certain group of students, the probability of a randomly-chosen student being male is 40%, the probability of the student studying Spanish is 18%, and the probability of the student being a male who studies Spanish is 5%.
The probability of the student being a male will be calculated as below:-
P(male | Spanish) = P(male and Spanish) / P(Spanish)
P(male | Spanish) = 0.05 / 0.18
P(male | Spanish) = 0.278
Therefore, the probability of the student being a male is 27.8%
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Samin can run 5 kilometers in 30 minutes. Assuming she keeps a constant pace, how many kilometers can she run in 45 minutes? URGENT ANSWERS PLEASE!
Answer:
7.5kilometer
Step-by-step explanation:
for 30mins semin runs 5kilometer
then for 1min: (1min×5kilometer)÷30mins,
therefore, for 45mins: (45mins×5kilometer)÷30mins=7.5kilometer
From the given information:
We are being informed that Samin can run for 5 kilometers in 30 minutes;
If Samin can run such a kilometer in 30 minutes;
5 kilometers = 30 minutes
∴
In x kilometers = 45 minutes
By cross multiplying;
(x × 30 minutes) = 5 kilometers × 45 minutes
30x = 225 kilometer/minutes
[tex]x = \dfrac{225 \ kilometer/minutes}{30 minutes}[/tex]
[tex]\mathbf{x = 7.5 \ kilometers}[/tex]
Therefore, we can conclude that the Samin can run 7.5 kilometers in 45 minutes.
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A box contains 6 red, 3 white, 2 green, and 1 black (total 12) identical balls. What is the least number of balls necessary to take out randomly (without looking) to be sure of getting at least two white balls?
Answer:
10
Step-by-step explanation:
12 total and 3 whites
there is 10 11 and 12.
Find the value.
X3-4 when x=3
PLEASE HELP!!! ASAP!!!
Answer:
23
Step-by-step explanation:
Raise 3 to the power of 3
27 - 4
Subtract 4 from 27
23
Hope this was correct
Answer:
23
Explanation:
step 1 - rewrite the expression with the value of x
[tex]x^3 - 4[/tex]
[tex](3)^3 - 4[/tex]
step 2 - solve the exponent
[tex](3)^3 - 4[/tex]
[tex]27 - 4[/tex]
step 3 - subtract
[tex]27 - 4[/tex]
[tex]23[/tex]
therefore, the value of the expression is 23.
find the value of x and y if the distance of the point (x,y) from (-2,0) and (2,0) are both 14 units.
Answer:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex] are both 14 units from points (-2, 0) and (2, 0).
Step-by-step explanation:
distance formula
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
We want the distance, d, from points (-2, 0) and (2, 0) to be 14.
Point (-2, 0):
[tex] 14 = \sqrt{(x - (-2))^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
Point (2, 0):
[tex] 14 = \sqrt{(x - 2)^2 + (y - 0)^2} [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
We have a system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(x - 2)^2 + y^2} = 14 [/tex]
Since the right sides of both equations are equal, we set the left sides equal.
[tex] \sqrt{(x + 2)^2 + y^2} = \sqrt{(x - 2)^2 + y^2} [/tex]
Square both sides:
[tex] (x + 2)^2 + y^2 = (x - 2)^2 + y^2 [/tex]
Square the binomials and combine like terms.
[tex] x^2 + 4x + 4 + y^2 = x^2 - 4x + 4 + y^2 [/tex]
[tex] 4x = -4x [/tex]
[tex] 8x = 0 [/tex]
[tex] x = 0 [/tex]
Now we substitute x = 0 in the first equation of the system of equations:
[tex] \sqrt{(x + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{(0 + 2)^2 + y^2} = 14 [/tex]
[tex] \sqrt{4 + y^2} = 14 [/tex]
Square both sides.
[tex] y^2 + 4 = 196 [/tex]
[tex] y^2 = 192 [/tex]
[tex] y = \pm \sqrt{192} [/tex]
[tex] y = \pm \sqrt{64 \times 3} [/tex]
[tex] y = \pm 8\sqrt{3} [/tex]
The points are:
[tex] (0, 8\sqrt{3}) [/tex] and [tex] (0, -8\sqrt{3}) [/tex]
Please can someone help
Answer:
a) 0
b) 1
c) 0
Step-by-step explanation:
These are common values from the unit circle but you could also just check with your calculator. Just be sure to set it to degree mode and not radian mode.
One liter of paint is needed to cover all 6 sides of a cubical block. How many liters will be needed to cover all 6 sides of a second cubical block whose edge is twice as long as an edge on the first block?
Will mark brainlist
Answer:
4 liters
Step-by-step explanation:
Let's assume that the side lengths of the cubical block are 2 inches.
This means that one of the sides area is 4 in².
Multiplying this by 6 (for there are 6 sides) gets us 24 in².
So one liter of paint covers 24 in².
Now if the side lengths (edge) of the second block is doubled, that means that the side lengths are [tex]2\cdot2 = 4[/tex] inches.
So the area of one side is 16 in².
Multiplying this by 6 (as there are 6 sides) gets us 96 in².
To find how many liters of paint this will take, we divide 96 by 24.
[tex]96\div24=4[/tex]
So 4 liters of paint will be needed for the second cubical block.
Hope this helped!
why the system of si unit is developed
Step-by-step explanation:
Hi, there!!!!
The main purpose of developing si unit is to have standard unit of measurements and to bring uniformity in whole world in terms of measurements.
I hope it helps you...
f(x) = x^2 - 4x + 3 f(x) = 1/2x + p The system of equations above, when graphed in the xy-coordinate plane, intersects at the point (4, q). What is p?
Answer:
p = 1
Step-by-step explanation:
Given that the system intersect at (4, q) then this point satisfies both equations, that is
q = 4² - 4(4) + 3
q = [tex]\frac{1}{2}[/tex] (4) + p
Equating both gives
16 - 16 + 3 = 2 + p, that is
3 = 2 + p ( subtract 2 from both sides )
p = 1
Find the measure of one exterior angle in each regular polygon.
Answer:
72° and 45°
Step-by-step explanation:
The sum of the exterior angles of a polygon = 360°
Since the given polygons are regular, then
Pentagon (5 sides ) has
exterior angle = 360° ÷ 5 = 72°
Octagon ( 8 sides ) has
exterior angle = 360° ÷ 8 = 45°
Step-by-step explanation:
The exterior angle of a polygon is given by
360/n
where n is the number of sides
First figure
For the first shape it has five sides
That's it's a pentagon
The measure of one exterior angle of the shape is
360 / 5
= 72°
Second figure
For the second shape it has 8 sides that's it's an octagon
So the measure of one exterior angle of the shape is
360 / 8
= 45°
Hope this helps you
Find the midpoint of the segment between the points (−5,13) and (6,4)
Answer:
(0.5, 8.5)
Step-by-step explanation:
use this formula ((x1+x2/2), (y1+y2/2)) if you use desmos graphing calculator and you type this formula in, all you have to do it put in the correct numbers and you get your midpoint.
Hope this helped :)
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
We have given that, the points (−5,13) and (6,4)
We have to determine the midpoints
What is the formula for the midpoint?((x1+x2/2), (y1+y2/2))
x1=-5,x2=6,y1=13 and y2=4
-5+6/2=1/2=0.5
and next is,
13+4/2=17/2=8.5
The midpoint of the segment between the points (−5,13) and (6,4) are (0.5 and 8.5)
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A point H is 20m away from the foot of a tower on the same horizontal ground. From the point H, the angle of elevation of the point (P) on the tower and the top(T) of the tower are 30° and 50° respectively.
( a) draw a diagram to illustrate the information above.
(b) calculate correct to 3 s.f,
( I) /PT/
(ii) the distance between H and the too of the tower.
(III) the position of H if the angle of depression of H from the too of the tower is to be 40°
Answer:
a. See Attachment 1
b. [tex]PT = 12.3\ m[/tex]
c. [tex]HT = 31.1\ m[/tex]
d. [tex]OH = 28.4\ m[/tex]
Step-by-step explanation:
Calculating PT
To calculate PT, we need to get distance OT and OP
Calculating OT;
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OT}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan50 = \frac{OT}{20} * 20[/tex]
[tex]20 * tan50 = OT[/tex]
[tex]20 * 1.1918 = OT[/tex]
[tex]23.836 = OT[/tex]
[tex]OT = 23.836[/tex]
Calculating OP;
We have to consider angle 30, distance OH and distance OP
The relationship between these parameters is;
[tex]tan30 = \frac{OP}{20}[/tex]
Multiply both sides by 20
[tex]20 * tan30 = \frac{OP}{20} * 20[/tex]
[tex]20 * tan30 = OP[/tex]
[tex]20 * 0.5774= OP[/tex]
[tex]11.548 = OP[/tex]
[tex]OP = 11.548[/tex]
[tex]PT = OT - OP[/tex]
[tex]PT = 23.836 - 11.548[/tex]
[tex]PT = 12.288[/tex]
[tex]PT = 12.3\ m[/tex] (Approximated)
--------------------------------------------------------
Calculating the distance between H and the top of the tower
This is represented by HT
HT can be calculated using Pythagoras theorem
[tex]HT^2 = OT^2 + OH^2[/tex]
Substitute 20 for OH and [tex]OT = 23.836[/tex]
[tex]HT^2 = 20^2 + 23.836^2[/tex]
[tex]HT^2 = 400 + 568.154896[/tex]
[tex]HT^2 = 968.154896[/tex]
Take Square Root of both sides
[tex]HT = \sqrt{968.154896}[/tex]
[tex]HT = 31.1\ m[/tex] (Approximated)
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Calculating the position of H
This is represented by OH
See Attachment 2
We have to consider angle 50, distance OH and distance OT
The relationship between these parameters is;
[tex]tan50 = \frac{OH}{OT}[/tex]
Multiply both sides by OT
[tex]OT * tan50 = \frac{OH}{OT} * OT[/tex]
[tex]OT * tan50 = {OH[/tex]
[tex]OT * 1.1918 = OH[/tex]
Substitute [tex]OT = 23.836[/tex]
[tex]23.836 * 1.1918 = OH[/tex]
[tex]28.4= OH[/tex]
[tex]OH = 28.4\ m[/tex] (Approximated)
4^6 • 4^-8 pls answer
Answer:
[tex]\boxed{4^{-2}}[/tex]
Step-by-step explanation:
[tex]4^6 \times 4^{-8}[/tex]
When bases are same for exponents and it is multiplication, then add the exponents.
[tex]4^{6+-8}[/tex]
[tex]4^{-2}[/tex]
Explanation: Since these two powers have the same base of 4, you can multiply them together by simply adding their exponents to get 4⁻².
When applying your exponent rules, the bases don't change!
The logistic growth function f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t EndFraction describes the population of a species of butterflies t months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 20 months? Round to nearest whole number.
Answer:
8685 butterflies
Step-by-step explanation:
Given the logistics growth function expressed as f(t)equals440 Over 1 plus 13.7 e Superscript negative 0.28 t which describes the population of a species of butterflies t months after they are introduced to a non threatening habitat, to know the number of butterflies expected butterflies are expected in the habitat after 20 months, we will substitute t = 20 into the function.
f(20) = 440/1+13.7exp-(0.28×20)
f(20) = 440/1+13.7exp-(5.60)
f(20) = 440/1+(13.7× 0.003698)
f(20) = 440/1+0.05066
f(20) = 440/1.05066
f(20) = 8684.9
This means there will be approximately 8685 butterflies in the habitat after 20months.
Please help Asap!!!Math question
Answer:
first one
Step-by-step explanation:
Can you translate a mathematical expression into a verbal expression?
Step-by-step explanation:
An example of a mathematical expression with a variable is 2x + 3. All variables must have a coefficient, a number that is multiplied by the variable. In the expression 2x + 3, the coefficient of x is the number 2, and it means 2 times x plus 3. ... For example, 2x + 3 could also be expressed as 2(x) + 3 or 2 * x + 3. are you talking about this
A lead ball weighs 326 grams. Find the radius of the ball to the nearest tenth of a
centimeter.
Answer:
1.9cm
Step-by-step explanation:
The density d of a material is related to its mass m and volume V as follows;
d = [tex]\frac{m}{V}[/tex] ------------------(i)
The material in question here is the lead ball.
Now, from known experiment;
the density of lead is 11.34g/cm³
From the question, the weight/mass of the lead ball is 326g
Substitute these values into equation (i) as follows;
11.34 = [tex]\frac{326}{V}[/tex]
V = [tex]\frac{326}{11.34}[/tex]
V = 28.75cm³
Now, since the ball is of course spherical, we can get the radius by using the following relation from the volume of a sphere;
V = [tex]\frac{4}{3} \pi r^3[/tex] [V = volume, r = radius]
V = 28.75cm³
=> 28.75 = [tex]\frac{4}{3} \pi r^3[/tex]
=> 3 x 28.75 = 4 π r³
=> 86.25 = 4 π r³
=> 21.5625 = π r³ [Take π = 3.142]
=> 21.5625 = (3.142) r³ [divide both sides by 3.142]
=> 6.86 = r³ [Take the cube root of both sides]
=> ∛6.86 = ∛r³
=> 1.90 = r
Therefore, the radius is 1.9cm to the nearest tenth
Simplify the polynomial expressions by combining like terms, and then multiply the resulting
binomial expressions to find their product.
(6x - 9 - 2x)(8 + 5x - 5)
Answer:
The simplified expression is
20x^2 - 33x - 27
Step-by-step explanation:
(6x - 9 - 2x)(8 + 5x - 5)
We must first rewrite the expression as a product of two binomials.
This can be done by adding like terms
(6x - 9 - 2x)(8 + 5x - 5)
We have,
(4x-9)(5x+3)
Multiplying the resulting binomial expression
(4x-9)(5x+3)
(20x^2+12x-45x-27)
Add the like terms
20x^2-33x-27
The simplified expression is
20x^2 - 33x - 27
Twenty x squared minus thirty-three x minus twenty-seven
Answer:
20x^2 - 33x - 27
Step-by-step explanation: