Answer:
q = 9
Step-by-step explanation:
the key thing to understand in this problem is the distributive property. which basically means we can muliply what's on the interior of the parenthestes ( in this case q-5) by what's on the outside (4).
so 4 will distrubute to both the q and the -5
4q - 20 = 16
add 20 to both sides
4q = 36
divide both sides by 4
q = 9
A cone has a radius of 5 ft and a height of 15 ft. It is empty and is being filled with water at a constant rate of 15 15 ft 3 ft3 / sec sec . Find the rate of change of the radius of the surface of the water when the radius of the surface of the water is 2 2 ft. (You must also include the units)
Answer:
[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]
Step-by-step explanation:
From the question we are told that:
Radius [tex]r=5ft[/tex]
Height [tex]H=15ft[/tex]
Rate [tex]R=15ft/3sec =5ft/s[/tex]
Surface Radius [tex]R_{surf}=2.2ft[/tex]
Generally the equation for Volume is mathematically given by
[tex]V=\frac{1}{3}\pi*r^2h[/tex]
Since radius to height ratio gives
[tex]\frac{r}{h}=\frac{5}{15}[/tex]
[tex]\frac{r}{h}=\frac{1}{3}[/tex]
[tex]h=3r[/tex]
Therefore
[tex]V=\frac{1}{3}\pi*r^2(3r)[/tex]
[tex]V=\pi r^3[/tex]
Generally the equation for Change of Volume is mathematically given by
[tex]\frac{dv}{dt}=\pi \frac{d}{dt}(r^3)[/tex]
[tex]\frac{dv}{dt}=\pi 3*r^2 \frac{dr}{dt}[/tex]
[tex]\frac{dv}{dt}=\pi 3*(2.2)^2 \frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=\frac{5}{45.62}[/tex]
[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]
prove that; tan20+4sin20= square root of3
tan( 20 ) + 4 Sin( 20 ) =
( Sin( 20 ) / Cos( 20 ) ) + 4 Sin( 20 ) =
Sin( 20 ) + 4 Sin( 20 ).Cos( 20 ) / Cos( 20 ) =
Sin( 20 ) + 2 × 2 Sin(20).Cos(20)/ Cos(20) =
Sin( 20 ) + 2 × Sin( 40 ) / Cos( 20 ) =
Sin( 20 ) + 2Sin( 40 ) / Cos( 20 ) =
Sin( 20 ) + 2Cos( 50 ) / Cos ( 20 ) =
Sin( 20 ) + 2Cos( 20 + 30 ) / Cos( 20 ) =
________________________________
2 × Cos( 30 + 20 ) =
2 × [ Cos(30).Cos(20) - Sin(30).Sin(20) ] =
2 × [ √3/2 × Cos(20) - 1/2 × Sin(20) ] =
√3 Cos(20) - Sin(20)
_________________________________
Sin( 20 ) + 2Cos ( 20 + 30 ) / Cos( 20 ) =
Sin( 20 ) + √3 Cos(20) - Sin(20) / Cos(20) =
Sin(20) - Sin(20) + √3 Cos(20) / Cos(20) =
0 + √3 Cos(20) / Cos(20) =
√3 Cos(20) / Cos(20) =
Cos(20) simplifies from the numerator and denominator of fraction
√3 × 1 / 1 =
√3
And we're done ....
Use the graph of the logarithmic function f(x) to answer the question.
What is the x- intercept?
Answer:
(0,-2)
Step-by-step explanation:
Assets Liabilities
Checking and Savings $275
Owe $415 on graduation items
Rare Baseball Cards $210 Borrowed $50 from mom
Check for work done for a neighbor $19
This is a list of Karen's assets and liabilities.
What is her net worth?
$1
$39
$275
$294
Answer:
Step-by-step explanation:
$39
The net worth should be considered as the $39.
Calculation of the net worth;We know that
Net worth = Total assets - total liabilities
here,
total assets = checking & savings + baseball card + check for work done
= $275 + $210 + $19
= $504
And, the total liabilities = owe + borrowed
= $415 + $50
= $465
So, the net worth be
= $504 - $465
= $39
Learn more about assets here: https://brainly.com/question/4029603
Helaine graphed the equation 12x−4y=3. What was the slope of Helaine’s line?
Answer:
The slope is 3
Step-by-step explanation:
12x−4y=3
Solve for y
Subtract 12x from each side
-12x +12x−4y=-12x+3
-4y = 12x+3
Divide each side by -4
-4y/-4 = -12x / -4 +3/-4
y = 3x -3/4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 3
Answer:
The slope is 3
Step-by-step explanation:
12x−4y=3
Solve for y
Subtract 12x from each side
-12x +12x−4y=-12x+3
-4y = 12x+3
Divide each side by -4
-4y/-4 = -12x / -4 +3/-4
y = 3x -3/4
This is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 3
What is the explicit rule for the geometric sequence? 25.5, 5.1, 1.02, 0.204, ... an=25.5(15)n an=25.5(15)n−1 an=25.5(15)n+1 an=25.5(15)n+2
Given:
The geometric sequence is:
25.5, 5.1, 1.02, 0.204, ...
To find:
The explicit rule for the given geometric sequence.
Solution:
We have,
25.5, 5.1, 1.02, 0.204, ...
Here, the first term is 25.5 and the common ratio is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{5.1}{25.5}[/tex]
[tex]r=\dfrac{1}{5}[/tex]
The explicit rule for a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]a=25.5,\ r=\dfrac{1}{5}[/tex] in the above formula, we get
[tex]a_n=25.5(\dfrac{1}{5})^{n-1}[/tex]
Therefore, the correct option is B.
Write the equation of the line that passes through (-7,-4) and (-6,-2) in slope intercept form
Answer:
y = mx + b
m =(-2--4)/(-6--7)
m = 2
-2 = 2(-6) +b
b = 10
y= 2x + 10
Tuan is an artist. He is painting on a large canvas which is 40 inches wide. The height of the canvas is 6 inches less than the width. What is the area of Tuan's canvas?
Answer:
1360 inches.
Step-by-step explanation:
Equation: 40 × (40-6) Since 40 inches is the width :)
40-6= 34
34*40=1360
Taun's canvas is 1360 inches :)
Match the volume of a prism to the correct dimensions of a rectangular prism
Volume of Rectangular Prism
Dimensions of Rectangular Prism
31.3ft:51
6 ft. 2 ft. 4
7.2 ft. 21
6.5 ft. 2 st
48 cubic feet
60 cubic feet
45 cubic feet
28 cubic feet
Answer:
3 ft, 3ft, 5ft => 45 cubic feet
6 ft, 2 ft, 4 ft => 48 cubic feet
7 ft, 2 ft, 2 ft => 28 cubic feet
6 ft, 5 ft, 2 ft => 60 cubic feet
Step-by-step explanation:
Recall: formula for volume of a rectangular prism is given as, V = L × W × H
✔️Volume of rectangular prism with the following dimensions:
L = 3 ft
W = 3 ft
H = 5 ft
V = 3 × 3 × 5
V = 45 cubic feet
✔️Volume of rectangular prism with the following dimensions:
L = 6 ft
W = 2 ft
H = 4 ft
V = 6 × 2 × 4
V = 48 cubic feet
✔️Volume of rectangular prism with the following dimensions:
L = 7 ft
W = 2 ft
H = 2 ft
V = 7 × 2 × 2
V = 28 cubic feet
✔️Volume of rectangular prism with the following dimensions:
L = 6 ft
W = 5 ft
H = 2 ft
V = 6 × 5 × 2
V = 60 cubic feet
2) Use the law of sines to find the length of SR
sin(A)/a=sin(B)/b=sin(C)/c
Answer:
take 28 degree as reference angle
using sine angle
sin28=p/h
0.46=10/h
0.46h=10
h=10/0.46
h=21.73
therefore hypotenuse =21.73
again using sine rule
take 25 degree as reference angle
sin 25=p/h
0.42=SR/21.73
0.42*21.73=SR
9.12=SR
9.1=SR
Step-by-step explanation:
15 points
Right triangle trigonometry
Answer:
Step-by-step explanation:
take theta as reference angle
tan theta=opposite/adjacent
=15/8
Answer:
option B
Step-by-step explanation:
First find opposite side using Pythagoras theorem:
[tex]17^2 = 8^2 + opposite^2 \\\\opposite^2 = 289 - 64 = 225\\\\opposite = 15[/tex]
Therefore,
[tex]tan \theta = \frac{opposite}{adjacent} = \frac{15}{8}[/tex]
Cedar Point has 17 roller coasters. If you want to ride at least 15 of them, how many different combinations of roller coasters can you ride? NO LINKS!!!
================================================
Explanation:
I'll be using the formula
[tex]_n C _r = \frac{n!}{r!*(n-r)!}[/tex]
which is the nCr combination formula. We use nCr instead of nPr because the order of coasters doesn't matter. The whole time, the value of n stays fixed at n = 17 which is the total number of coasters to pick from.
While n is constant, the value of r will vary. It ranges from r = 15 to r = 17 inclusive of both endpoints. In other words, r will take on values from the set {15,16,17}. So we have three cases to consider. The r value is how many coasters we select. This is due to the "at least 15" which means "15 or more".
-----------------------
If you ride r = 15 coasters, then we have the following number of combinations
[tex]_n C _r = \frac{n!}{r!*(n-r)!}\\\\_{17} C _{15} = \frac{17!}{15!*(17-15)!}\\\\_{17} C _{15} = \frac{17!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16*15!}{15!*2!}\\\\_{17} C _{15} = \frac{17*16}{2!}\\\\_{17} C _{15} = \frac{17*16}{2*1}\\\\_{17} C _{15} = \frac{272}{2}\\\\_{17} C _{15} = 136\\\\[/tex]
There are 136 ways to ride exactly 15 coasters (when selecting from a pool of 17 total). The order doesn't matter.
We'll use this result later, so let x = 136.
-----------------------
If r = 16, then we follow the same steps as above. You should get 17C16 = 17
There are 17 ways to ride 16 coasters where order doesn't matter. Effectively this is the same as saying "there are 17 ways of picking a coaster that you won't ride"
Let y = 17 so we can use it later
-----------------------
Lastly, if r = 17, then nCr = 17C17 = 1 represents one way to ride all 17 coasters where order doesn't matter.
Let z = 1
-----------------------
Add up the values of x, y, and z to get the final answer
x+y+z = 136+17+1 = 154
Tickets to the theater cost $8.00 for adults and $3.00 for children. A group of 2
total people showed up to the theater. They spent $93.00 total on tickets. How
many adults and children were in the group?
Answer: 9 adults 7 children
Step-by-step explanation:
Please help me answer the question
Find the sum of the first five terms of the geometric series 50 + 25 + 12.5 +
The sequence is geometric with first term
a
1
=
100
and common ratio
r
=
0.5
Explanation:
a
1
=
100
,
a
2
=
50
,
a
3
=
25
,
a
4
=
25
2
,
a
5
=
25
4
...
50
100
=
0.5
,
25
50
=
0.5
,
25
2
25
=
0.5
,
25
4
25
2
=
0.5
∴
a
2
a
1
=
a
3
a
2
=
a
4
a
3
=
a
5
a
4
=
0.5
The ratio of successive term and preceeding term is constant
(
r
=
0.5
)
. Therefore the sequence is geometric whose first
term is
a
1
=
100
and common ratio is
r
=
0.5
[Ans]
Work Time Lost due to Accidents At a large company, the Director of Research found that the average work time lost by employees due to accidents was hours per year. She used a random sample of employees. The standard deviation of the sample was hours. Estimate the population mean for the number of hours lost due to accidents for the company, using a confidence interval. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.
Answer:
(95.215 ; 100.785)
(95 ; 101) (nearest whole number)
Step-by-step explanation:
To obtain the confidence interval :
Mean ± margin of error
Mean = 98 hours
Margin of Error = Tcritical * (s/√n)
samole standard deviation, s = 5.6 hours
df = n - 1 = 18 - 1 = 17
Tcritical at (0.05, df = 17) = 2.110
Hence ;
Margin of Error = 2.110 * (5.6/√18) = 2.785
Confidence interval :
98 ± 2.785
Lower boundary = 98 - 2.785 = 95.215
Upper boundary = 98 + 2.785 = 100.785
(95.215 ; 100.785)
help asap will be marked BRAINIEST
Answer:
∠BAC = 75°
Step-by-step explanation:
just subtract angle BAD from angle CAD
If a population is
a sample of the population could be
O A. ninth-graders at Peak School; all students at Peak School
B. math teachers; the entire school faculty
O C. people who purchased shoes; all customers
O D. all citizens; registered voters
Answer:
Step-by-step explanation:
D.all citizens; registered voters
You answered 85% of the questions on the quiz correctly. What fraction of
the questions did you answer correctly?
Answer:
A percentage is out of 100.
85/100
in lowest terms this is
17/20
Hope this helps :)
Step-by-step explanation:
Consider the following statements about the effect of different values of a on the function y = ab^x. Which one of the statements, if any, is incorrect?
A. Values of a such that |a| > 1 will vertically stretch the graph of y = b^x.
B. Values of a such that 0 < |a| < 1 will vertically compress the graph of y = b^x.
C. Negative values of a will reflect y = b^x across the y-axis.
D. All of the above statements are correct.
No, There is no any sentences are incorrect.
Hence, All sentences are correct.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Consider the following statements about the effect of different values of a on the function,
⇒ y = a bˣ
Now, We know that;
For the value of a such that |a| > 1
The graph of y = bˣ is vertically stretch.
And, For the values of a such that 0 < |a| < 1;
The graph of y = bˣ is vertically compress.
And, When we take negative value of a.
Then, Function reflect y = bˣ across the y-axis.
Thus, There is no any sentences are incorrect.
Hence, All sentences are correct.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ3
Value of x ?
A 70
B 60
C 50
D 40
please ignore the 90
Answer:
A 70°
Step-by-step explanation:
Angle of the triangle
=180-60-60
=60°
x= 180-60-50
=120-50
=70°
POSSIBLE POINTS 50
Mr Franklin needs to pay for his three kids to go to college. He figured out that college will cost an average of
$50,000 per year per child when they are ready to go to college. To pay for this, Mr. Franklin bought a cylindrical
gas truck, The truck is 40 feet long and the radius of the base is 60 inches, Gas has a density of five pounds per
cubic foot. Mr. Franklin makes $2.50 per pound of gas when he sends a delivery. How many trips of full tanks of
gas will Mr. Franklin have to send to pay for his three kids to go to four years of college each?
Be sure to label each step and show all work. Don't forget units.
a) Find the volume of the cylinder
b) Find the mass of the gas in one truckload by using the density formula
c) Find the amount of money one truckload will generate.
d) Find the amount of money four years of college will cost for Mr. Franklin's three children.
e) Find the amount of trips it will take Mr. Franklin to make enough money to pay for college,
5
x Clear
Und
Answer:
2500
Step-by-step explanation:
What is the probability that both spinners will land on 2?
1/12. 1/6. 1/4. 1/3
Answer:
1/4 bczz its not saying about the highest its about average and the average is 1/4
Can someone help me please?
Answer:
.08
Step-by-step explanation:
Answer:
Hi, there your answer is 0.08
Step-by-step explanation:
Plz help me well mark brainliest!!
Answer:
735 mm³
Step-by-step explanation:
49 x 15 = 735
Answer:
735mm
Step-by-step explanation:
Are these answers all correct?
Answer:
Yes they are all right
Step-by-step explanation:
Answer:
Step-by-step explanation:
Give m = -1/2 and n = -1/3 which statement is true?
Answer:
n
Step-by-step explanation:
angle DAC= angle BAD
what is the length of side bd round to one decimal place
Answer:
BD ≈ 2.8 units
Step-by-step explanation:
By angle bisector theorem,
"If a segment bisects an angle of a triangle, then it divides the opposite side into the segments which are proportional to the other two sides"
Here, AD is the bisector of the ∠BAC,
[tex]\frac{BD}{CD}=\frac{AB}{AC}[/tex]
[tex]\frac{8.1}{5.9}= \frac{BD}{2}[/tex]
BD = [tex]\frac{2\times 8.1}{5.9}[/tex]
BD = 2.75
BD ≈ 2.8 units
Need help Math Question Multiple Choice!
Given :
A function f(x) for different range of x.
To Find :
The value of f( -3 ) .
Solution :
We have to find the value of function at x = -3.
Now, in the given figure -3 lies in range x ≤ -2 and definition of function at that range is :
[tex]f(x) = \dfrac{2}{x}[/tex]
So, putting value of x = -3 in above equation, we get :
[tex]f(-3) = \dfrac{2}{-3} \\\\f(-3) = \dfrac{-2}{3}[/tex]
Hence, this is the required solution.
plz plz plz plz help me plz it is due in 1 hour and no links plz and I needed to be a decimal
Answer:
Solution given:
Area of parking space [parallelogram]=290ft²
base*height=290
base=290/29
base:10ft
Area of rectangular dimensions=11*7.4=81.4ft²
yes
The truck can not fit in the space because the length and breadth is less than that of the parallelogram parking area.
Area of truck bid 81.4ft².