Step-by-step explanation:
we assume day and night are equally long.
and the mouse will start at night of day 1.
then, on day 2, it will first retreat 2 meters (during daylight) and then advance 14 meters (at night).
so, on every full day, the mouse will effectively advance 12 meters (-2 + 14 = 12).
with a starting value of 14 (the first night).
so, we are getting an arithmetic sequence
an = an-1 + c
c = 12 in our case.
a1 = 14
a2 = a1 + 12 = 14+12 = 26
a3 = a2 + 12 = a1 + 12 + 12 = 14 + 2×12 = 38
an = a1 + (n-1)×12 = 14 + 12(n-1)
at what n will it reach 86 ?
86 = 14 + 12(n-1) = 14 + 12n - 12 = 2 + 12n
84 = 12n
n = 7
so, on the 7th day the mouse will reach the surface (if we truly count the first starting night day 1 - this is up to your teacher, but I would).
What is the value of the expression 30-(-6)?
0 -180
O -5
O 5
O 24
Answer:
36? its not on there but that is it.
The pole casts a 12-foot shadow when the sun is at a 40° angle of elevation. Which equation could Kim use to find x, the length of the pole?
Answer: Therefore the length of the pole in 10.1 foot (approx) .
Step-by-step explanation:
To proof
As given
The pole casts a 12-foot shadow when the sun is at a 40° angle of elevation.
x represented the length of pole .
As shown in the diagram
By using the trignometric identity
tan40° = 0.839099631 ( approx )
Put in the above
x = 12 × 0.839099631
x = 10.1 foot (approx)
Therefore the length of the pole in 10.1 foot (approx) .
x⁴-12x²+8=0
(find value of x)
Alejandro was picked by this teacher to find the integer that has the square root closest to 7, without going over. he wrote 52 on the bored. was he correct? explain your reasoning.
Considering that the square root of 49 is 7, and 52 > 49, Alejandro was not correct, as the correct integer is of 48.
What is the integer that has the square root closest to n, without going over?The integer that has square root n is given by:
S(n) = n².
Hence the closest is given by:
C(n) = n² - 1.
In this problem, we have n = 7, hence:
C(7) = 7² - 1 = 48.
Which means that Alejandro was not correct.
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The midpoint of overline AB is M(2, -2) If the coordinates of A are (-2, 1), what are the coordinates of B?
Answer:
(6, -5)
Step-by-step explanation:
Midpoint :
(2, -2) = (x - 2 / 2, y + 1 / 2)Equations formed :
x - 2 / 2 = 2x - 2 = 4x = 62. y + 1 / 2 = -2
y + 1 = -4y = -5Coordinates of B : (x, y)
(6, -5)Um Help please
Long time of Due[31st June]
Answer:
12
Step-by-step explanation:
This a Venn Diagram.....the shaded overlapping area is common to both sets.... it must be a multiple of 3 AND a multiple of 4
12 would work....Right?
Answer:
B. 12.
Step-by-step explanation:
The numbers that will go into the shaded area are those who are divisible by 3 and 4.
12 = (3*4)is the only one in the list.
A teacher administers three different versions of a test to his students. The two-way table shows the results. Find each probability.
Part A. P(pass | Test A)
The probability is ___%
Part B. P(pass | Test A)
The probability is ___%
SHOW ALL WORK
The P(pass | Test A) is 31.81%, P(pass | Test B) is 29.87%, and P(pass | Test C) is 22.07%
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
Part A:
Total number of students = 154
Total number of students passed the test = 49
The probability:
P(pass | Test A) = 49/154 = 31.81%
Part B:
Total number of students = 154
Total number of students passed the test = 46
The probability:
P(pass | Test B) = 46/154 = 29.87%
Similarly, for the probability:
P(pass | Test C) = 34/154 = 22.07%
Thus, the P(pass | Test A) is 31.81%, P(pass | Test B) is 29.87%, and P(pass | Test C) is 22.07%
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For any positive numbers a,b, and d, with b=1, logb a+logb d=
Answer the right answer is a
A taxi charges an airport pickup fee of $3 plus $1.50 for each mile traveled. If a taxi ride cost John $36, how many miles did John travel in the taxi?
31 miles
21 miles
22 miles
32 miles
Answer:
Step-by-step explanation:
36-3=33
33 divided by 1.5 equals 22
answer is 22 miles
Answer:
Step-by-step explanation:
1.5x + 3 = 36
1.5x = 33
x = 22 miles
What is the value of s to the nearest whole number? 10 12 13 14
The value of s to the nearest whole number is 14. The correct option is the last option 14
TrigonometryFrom the question, we are to determine the value of s
Using the laws of cosines
a² = b² + c² -2bc Cos A
Then,
s² = 8² + 9² -2(8)(9) cos111°
s² = 64 + 81 - 144 cos111°
s² = 145 - (-51.605)
s² = 145 + 51.605
s² = √196.605
s = 14.0216
s ≅ 14
Hence, the value of s to the nearest whole number is 14. The correct option is the last option 14
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The coach has $400 to spend on the end of season party. She
purchases awards for $80 and decorations for $35. She will use the
remaining money to order pizza. If pizzas cost $12 each, what is the
most pizzas can she buy?
Which is an equation of a direct proportion?
y= 1/2x – 2
y=3/x
y = -3x +4
y = -3x
Answer:
y = - 3x
Step-by-step explanation:
an equation involving direct proportion has the form
y = kx ← k is the constant of proportion
the only equation in this form is
y = - 3x ( with k = - 3 )
Label the X-axis and yaxis
Answer:
The y axis is the vertical line which goes up and down the x axis is the horizantal line which goes side to side or straight across
Step-by-step explanation:
find the unit vector in the direction of v= 2i+ j + k
I need help on thiss
Factor −4 out of −24a−44.
Answer:
6a+11
Step-by-step explanation:
-24a-44/-4
=
6a+11
have a wonderful day :))
Answer:
-4(6a + 11)
-Step-by-step explanation:
−24a − 44 if −4 is factored out than...
-4 times ____ = -24a
-4x = -24 → divided both sides by -4
-4x / -4 = -24 / -4 → x = 6
-4 times 6 = -24a
-4 times ____ = -44
-4x = -44 → divided both sides by -4
-4x / -4 = -44 / -4 → x = 11
-4 times 11 = -44
combine: -4 x 6a - 4 x 11
Jocelyn decides to research the relationship between the length in inches and the weight of a certain species of catfish. She measures the length and weight of a number of specimens she catches, then throws back into the water. After plotting all her data, she draws a line of best fit. Based on the line of best fit, how much would you predict a catfish with a length of 32 inches would weigh?
The amount I can predict a catfish with a length of 32 inches would weigh is 28in.
What is the catfish measurement about?Let say the fraction is = yx + b
m = [tex]\frac{20-4}{23-20}[/tex]
= 6/3
=2
Note also that 4= 2 x 20 x b
Make b the subject of the formula and it will be=
B= -36
Therefore, the function will be:
Y= 2x - 36
If x = 32
Then y = 2. 32 - 36
=28
Therefore, the amount I can predict a catfish with a length of 32 inches would weigh is 28in.
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Hi I really need help with this one
Answer:
GCF: 3 , While answer to addition problem is 36.
Step-by-step explanation:
* Help me with mine please thanks*
[tex]12\frac{1}{2}[/tex]% as a simple fraction is:
a)[tex]\frac{12}{100}[/tex]
b)[tex]\frac{1}{8}[/tex]
c)[tex]\frac{3}{25}[/tex]
d) 0.125
e) 12.5
Answer:
E. 12.5
Step-by-step explanation:
[tex](12 \times 2) + 1 = 25 \\ \frac{25}{2} [/tex]
Answer:
B
Step-by-step explanation:
25/2 = 12.5
so, 12.5 /100
= 1/8
Therefore b is the correcrt answer
What is the scale factor of (-2,6) and (-10,30) After dilation
Answer: 5
Step-by-step explanation: -2 * 5 = -10 6 * 5 = 30
Answer: [tex]The ~scale~ factor~ is~ 5[/tex]
Step-by-step explanation:
[tex]-2*5 ~is~=-10[/tex]
[tex]6*5=30[/tex]
[tex]We~use~the~distance~formula~to ~determine~the~distance~between ~two ~points.[/tex]
[tex]8\sqrt{10}[/tex]
The radius of a circle is 1 in. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer:
The circumference is 6.3 in
The circumference of the circle is given by the equation C = 6.3 inches
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the circumference of the circle be represented as C
Now , the equation will be
Let the radius of the circle be r = 1 inch
Now , circumference of circle = 2πr
Substituting the values in the equation , we get
The circumference of the circle C = 2 ( 3.14159 ) x 1
On simplifying the equation , we get
The circumference of the circle C = 6.3 inches
Hence , the circumference of the circle is 6.3 inches
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PLEASE HELP WILL GIVE BRAINLEST!
Answer:
5[tex]\pi[/tex]/12 rad
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
75(π/180) = 5π/12 radians
arc length = central angle (2πr)
360
measure of the inscribed angle = 75º
measure of the central angle = 150º
arc length = 150 (2π1000)
360
arc length = (5/12)
Combine the like terms to create an equivalent expression.
2q+2+92
Answer:
2q + 94
Step-by-step explanation:
2q + 2 + 92 ← collect like terms
= 2q + (2 + 92)
= 2q + 94
Answer:
2q + 94Step-by-step explanation:
2q + 2 + 92
Reorder and group
2q + (2 + 92)
Caculate
2q + 94
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At the city museum, child admission is $5.20 and adult admission is $9.50. On Monday, 167 tickets were sold for a total sales of $1,255.40. How many child tickets were sold that day?
Answer: 77 children tickets were sold that day
Step-by-step explanation:
5.20x+9.50y=1255.40
x+y=167
5.20x+9.50(167-x)=1255.40
x+y=167 5.20x+1586.50-9.50x=1255.40
-x -x -4.30x+1586.50=1255.40
y=167-x -1586.50 -1586.50
-4.30x=-331.1
-4.30 -4.30
x=77
Jorge earns $12 an hour. deductions
for taxes and insurance take 25% of
his earnings. which equation could be
solved to find jorge's take-home pay, p,
after h hours of work?
Answer:
%25 of $12 an hour = 3
find the area of the nearest hundredth use 3.14 for π
Answer:
254.34
Step-by-step explanation:
3.14 x 9^2
or
3.14(9 x 9)
hope this helps
have a good day
Guys Please Help me Fast!!
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
multiply numerator and denominator of [tex]\frac{1}{4}[/tex] by 3
[tex]\frac{1}{4}[/tex] = [tex]\frac{3(1)}{3(4)}[/tex] = [tex]\frac{3}{12}[/tex]
the 2 fractions now have a common denominator of 12 and can be added
[tex]\frac{1}{4}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{3}{12}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex]
If Sam can read 20 pages in 30 minutes, how many hours will it take Sam to read 200 pages?
Whats is the answer with procedure. n=18, n=9 or n= 3
Answer:
n = 3
Step-by-step explanation:
Isosceles means that the left and right sides (non-parallel sides) are equal to each other and so the base angles are also equal to each other. Then you can make an equation with the 8n^2-11 set equal to the 2n^2+7.
see image.
To solve it you have to set everything equal to zero (get all terms on one side of the equation) FACTOR (you end up with the difference of two squares) and solve, using zero product property. See image.
will give brainliest!!! Help pls!
Answer:
I notice that square 3 plus square 2 equals square 1, the biggest square. That must mean that the third square, squared, plus the second square, squared, equals the biggest square, squared, which is square c.