Answer:
[tex] \dfrac{1}{125x^3} [/tex]
Step-by-step explanation:
[tex] (5x)^{-3} = \dfrac{1}{(5x)^3} = \dfrac{1}{5^3x^3} = \dfrac{1}{125x^3} [/tex]
find the volume of the rectangle prism
Answer:176
Step-by-step explanation:
8 x 2 x 11
A baseball is thrown into the air from a height of 5 feet. the ball reaches a maximum height of 43.5 feet and spends a total of 3.2 seconds in the air. which equation models the height of the baseball? assume that acceleration due to gravity is –16 ft/s2. h(t) = 16t2 49.64t 5 h(t) = -16t2 5t 49.64 h(t) = -16t2 49.64t 5 h(t) = 16t2 5t 49.64
The equation that models the height of the baseball is determined as H(t) = 5 + 49.64t -16(t)².
Maximum height reached by the base ball
The maximum height reached by the baseball is calculated as follows;
H = y₀ + v₀yt + ¹/₂gt²
Assuming negative direction for upward motion
H = y₀ + v₀yt - ¹/₂gt²
0 = y₀ + vt -16(t)²
0 = 5 + 3.2v - 16(3.2)²
0 = 5 + 3.2v - 163.84
3.2v = 158.84
v = 158.84/3.2
v = 49.64
Required equation modelH(t) = 5 + 49.64t -16(t)²
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Answer:C?
Step-by-step explanation:
edge
A researcher wishes her patients to try a new medicine for depression. how many different ways can she select 5 patients from 50 patients?
There are 2118760 ways to select 5 patients from 50 patients.
What is Combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.
Here, Total patients= 50
Number of selection is to made = 5
So, total ways of selection = ⁵⁰C₅
= (50X49X48X47X46) / (5X4X3X2X1)
= 2118760 ways
Thus, There are 2118760 ways to select 5 patients from 50 patients.
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Answer:
2118760
Step-by-step explanation:
She can select 5 patients from 50 patients in :
[tex]50c_{5}[/tex]
= [tex]\frac{50!}{5! (50-5)!}[/tex]
= [tex]\frac{50!}{5! 45!}[/tex]
= 50 x 49 x48 x47 x46 x45!
= 2118760
A dune buggy rental company charges $35.50 plus 9¢ per mile
for each mile you drive. You are charged $60.25 for the rental.
You want to know the number of miles you drove.
Represent the situation with an equation and solve the
equation using any of the methods you learned in the last
topic.
The number of miles he drove for a cost of $30.50 is 275 miles.
How to find the number of miles using linear equation?Using linear equation,
y = mx + b
where
m = slopeb = y-interceptTherefore,
9 cents = $0.09
y = 35.50 + 0.09x
where
x = number of miles drove
y = total cost
Therefore,
60.25 = 35.50 + 0.09x
60.25 - 35.50 = 0.09x
24.75 = 0.09x
x = 24.75 / 0.09
x = 275 miles
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Don’t know how to solve
Answer:
Θ ≈11.31°
Step-by-step explanation:
the model is a right triangle with side opposite being the height and side adjacent the horizontal length , in relation to angle Θ , then
using the tangent ration
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{4}{20}[/tex] , then
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{4}{20}[/tex] ) ≈ 11.31° ( to 2 dec. places )
I need help please answer fast!!!
Answer:
2 and -4 :) because -2×4=-8, and 4+(-2)=2. Solve x-2=0 and x+4=0, you get the answer I previously mentioned!
Hello i need help ASAP i cant figure this out its just like part A
and i i have 1 hour
Number of unmarked wolves: 928 - 232 = 696
probability of next wolf being unmarked = 696 / 928 = 0.75
0.75 x 100 = 75%
Answer: 75%
The number scale used on this map is 1:10 000 000 explain what this scale means?
Answer:
1 unit on the map is equivalent to 10 000 on the ground or reality
Construction This section of a concrete skateboard ramp has the shape of a triangular prism. Find the volume
of the triangular prism. Find the value of the concrete used in the ramp if the cost of concrete is $4.00 per cubic
foot.
Answer:
volume = 73.3ft³
value = $194.4
Step-by-step explanation:
volume of prism = (½bh)l
=(½×4×4)×9.2
=73.6ft³
value of concrete
1ft³ : $4.00
73 .6ft³ : X
X : (73.6ft³ × $4.00) ÷ 1ft³
X : $294.4
If a line has a slope of 2 and contains the point (-2, 1), what is its equation in
point-slope form?
A. y +2=-2(x-1)
B. y-2 =-2(x-1)
C. y-1=2(x-2)
D. y- 1 = 2(x+ 2)
Answer:
D
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = 2 and (a, b ) = (- 2, 1 ) , then
y - 1 = 2(x - (- 2)) , that is
y - 1 = 2(x + 2)
you deposit a check for $254.67 into your savings account. Your account has a balance of $419.33 after the deposit. Find the balance of your savings account before the deposit.
Answer:
$164.66
Step-by-step explanation:
Just subtract them from each other
The Question is in the picture because I could not type it out correctly for some reason.
Step-by-step explanation:
the circumference of a complete circle (360°) is
2×pi×r
in our case
2×pi×3 = 6pi (= 18.84955592... ft)
5 ft is now what fraction of the whole circumference ?
because the corresponding arc angle is the same fraction of 360°.
5 ft are 5/(6pi) of the whole circumference.
so, the arc angle AB is
5/(6pi) × 360 = 5×60/pi = 300/pi = 95.49296586...°
but maybe you need the angle in radians instead of degrees ?
then remember, 360° = 2pi radians.
and then the arc angle AB is
5/(6pi) × 2pi = 10/6 = 5/3 = 1.666666... radians.
the prom committee is made up of 8 boys and girls. If there are 12 boys and 15 girls in the group to pick the committee from, how many ways can the committee be organized?
1). 1860 ways
2). 3185325 ways
3). 2220075 ways
4). 675675 ways
Thanks guys!!
The number of ways can the committee be organized will be 2220075. Then the correct option is 3.
What are permutation and combination?A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.
The prom committee is made up of 8 boys and girls.
If there are 12 boys and 15 girls in the group to pick the committee from.
Then the number of ways can the committee be organized will be
Then the number of ways is given by the combination formula. Then we have
Number of ways = ¹²C₀ x ¹⁵C₈ + ¹²C₁ x ¹⁵C₇ + ¹²C₂ x ¹⁵C₆ + ¹²C₃ x ¹⁵C₅ + ¹²C₄ x ¹⁵C₄ + ¹²C₅ x ¹⁵C₃ + ¹²C₆ x ¹⁵C₂ + ¹²C₇ x ¹⁵C₁ +¹²C₈ x ¹⁵C₀
Number of ways = 6435 + 77220 + 330330 + 660660 + 675675 + 360360 + 97020 + 11880 + 495
Number of ways = 2220075
Thus, the correct option is 3.
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7. The perimeter of a circle of diameter 10 cm is-
(a) 30.4 cm. (b) 30.14 cm
(c) 31.4 cm. (d) 30.01 cm.
(Take π = 3.14)
[tex]\qquad\qquad\qquad\boxed{\bf\:\:{(c) \: 31.4 \: cm \: ans \: }}[/tex]
Explanation -:
The diameter is = 10 cm
( Take π = 3.14 )
[tex] \\ \: \tt :\implies \: 10 \: \times 3.14 \\ \\ 31.4 \: ans[/tex]
More Information -:
Area of circle= πr² Circumference= 2 πr π = 22/7 or 3.14 ( approx )Annulas = π(R² - r ²)The nth term of a different sequence is 2^n+5 show that 36 is not part of the sequence
Answer:
It is not a term of the sequence
Step-by-step explanation:
See attached image
What are two possible measures of the angle below?
If you wanted to make the graph of y=3x+1 steeper which equation could you use
Answer:
Increase the slope
Step-by-step explanation:
The slope of this line is '3' ......a steeper line has a higher number than '3' in front of the 'x' like y = 4x+3 or y = 7x + 12
Does the table below represent a function? Why or Why Not?
Answer:
A.
Step-by-step explanation:
For the x value (6) there are two different output values(y) 5 and 6.
If it's a function then there must be one output value for every input.
In a lab, a substance was cooled by 6 degrees celsius each hour for 12 hours.
The total change in temperature was what?
Answer:
72 degrees 72° Celsius. It changed by 72 degrees.
Step-by-step explanation:
6 * 12 because it changed 6 degrees each hour for 12 hours
6 *
12
—-
72
Answer:
72 degree Celsius
Step-by-step explanation:
Since every hour the temperature is cooled by 6⁰C and the total time spent was 12 hour we can do a simple multiplication shown:
6 * 12 = 72
A school had a lot of problems with
student absences and wanted to try a
intervention program to see if it
encouraged students to come to school
more often. As a trial, 20 students were
split into two equal size groups. Group 1
would get the new intervention and
Group 2 got no intervention. The mean-
number of absences was calculated after
one month for each group, as shown in
the table below. What inference can be
made about the results?
The inference is that the results of the study are statistically significant.
How to make the inference about the results?For group 1, we have:
Mean = 1.7
For group 2, we have:
Mean = 3.3
The mean of group 2 is greater than group 1, and the mean difference is:
Difference = 3.3 - 1.7
Evaluate
Difference = 1.6
Based on the sample values, the mean difference of 1.6 is significant.
Hence, the inference is that the results of the study are statistically significant.
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Rachel rides her bike due east at 9 miles per hour. Amos rides his bicycle due north at 12 miles per hour. If they left from the same point at the same time, how far apart will they be in 1 hour? Geometry and measurement :))) help please.
They will be 15 miles apart after one hour if they left the same point at the same time.
How do we measure and calculate the distance in Geometry?The distance between two points in geometry can be calculated by using the Pythagoras theorem.
Mathematically, the Pythagoras theorem can be expressed as:
[tex]\mathbf{d = \sqrt{x^2 +y^2}}[/tex]
where;
x and y are opposite and adjacent sides respectively.[tex]\mathbf{d = \sqrt{(9)^2 +(12)^2}}[/tex]
[tex]\mathbf{d = \sqrt{81+144}}[/tex]
[tex]\mathbf{d = \sqrt{225}}[/tex]
d = 15 miles
Therefore, we can conclude that they will be 15 miles apart after one hour if they left the same point at the same time.
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use decomposition to find the area of the figure
In a city, the distance between the library and the police station is 3 miles less than twice the distance between the
police station and the fire station. The distance between the library and the police station is 5 miles. How far apart
are the police station and the fire station?
O 1 mile
O 3 miles
O4 miles
O6 miles
Answer:
C. 4 milesStep-by-step explanation:
Let the distance between police station and the fire station be x.
According to question we have:
the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station,the distance between the library and the police station is 5 miles.It can be expressed as:
5 = 2x - 3Solve the equation for x:
2x = 5 + 32x = 8x = 4Correct choice is C
(Refer to the attached image)
===========================================
Work Shown:
side a = 8side b = 5angle C = 88 degreesApplying the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = 8^2 + 5^2 - 2*8*5*cos(88)
c^2 = 64 + 25 - 80*cos(88)
c^2 = 86.2080403
c = sqrt(86.2080403)
c = 9.2848285
c = 9
Technically he needs 10 meters of rope because of the extra 0.28 portion, but I'll stick with 9 meters since your teacher said to round to the nearest whole number.
Question 21 of 25
f(x) = 3x + 2
What is f(5)?
OA. 17
OB. 15
OC. 10
01
Answer:
A. 17
Step-by-step explanation:
f(x) = 3x + 2
f(5) = 3(5) + 2
= 15 +2
= 17
i like cheese burger do u liek cheese burgers 2+2+12-21+492
It cost Makayla $2.80 to send 28 text messages. How much would it cost to send 163 text messages?
Answer:
$16.30
Step-by-step explanation:
Hope this helps! Have a great day!!
The cost of 163 text messages is $16.3
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Steps to Use Unitary Method
First, let us make a note of the information we have. There are 5 ice-creams. 5 ice-creams cost $125.
Let's start with finding the price of one ice cream. Divide the entire cost of ice cream by the total number of ice creams to get at that. A single ice cream will cost you 125 divided by the amount of ice creams, or 25 cents. Consequently, 1 ice cream costs $25.Step 2: To calculate the price of three ice creams, multiply the price of one ice cream by the quantity. Cost of 1 ice cream x number of ice creams = 25 x 3 = $75 is the price of 3 ice creams. The final cost is $75, which is the price of three ice creams.Given:
price for 28 text messages = 2.80
So, price for 1 text messages = 2.80/ 28
= $ 0.1
Now, the price for 163 messages = 163 * 0.1
= $16.3
Hence, the price for 163 text messages be $16.30.
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A die has six sides, with the numbers 1, 2, 3, 4, 5, and 6. What is the probability of rolling a number greater than 2?
Answer:
1/2
Step-by-step explanation:
There are 3 numbers greater than 2: 3, 4, 5, and 6. There are 6 numbers, so it is 3/6=1/2.
As air is moved through a duct by a fan, friction between the air molecules and the sides of the duct creates a resistance to movement. Friction loss charts are available to determine the friction loss for a given quantity of air passing through a given size of duct, per 100 feet of duct. You know that a section of exhaust duct is 64 meters long, but you cannot determine the friction loss unless the duct length is in feet. You know that one meter is equal to 3.28 feet. How long is the 64-meter section of duct in feet? Round your answer to a whole number.
The length of the 64 meters section in feet is 210 feet
How to determine the length of the section of duct in feet?The given parameters are:
Length = 64 meters1 meter = 3.28 feetMultiply both sides of 1 meter = 3.28 feet by 64
64 * 1 meter = 3.28 feet * 64
Evaluate
64 meters = 209.92 feet
Approximate
64 meters = 210 feet
Substitute 64 meters = 210 feet in Length = 64 meters
Length = 210 feet
Hence, the length of the section in feet is 210 feet
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4.
In the diagram of AABC below, DE || BC,
AD= 3, DB=2, and DE = 6.m
6
E
2
B
What is the length of BC?
1) 12
2) 10
3) 8
4) 4
C