Answer:
q = -p-6
Step-by-step explanation:
=> 5q+2p+4 = 3q-8
(Combining like terms)
=>5q-3q = -2p-8-4
=> 2q = -2p -12
=> 2q = 2(-p-6)
Dividing both sides by 2
=> q = -p-6
[tex]q = - p - 6[/tex]
[tex]5q + 2p + 4 - 3q = - 8 \\ 2q + 2p + 4 = - 8 \\ 2q + 4 = - 8 - 2p \\ 2q = - 8 - 2p - 4 \\ 2q = - 12 - 2p \\ \frac{2q}{2} = \frac{ - 2p - 12}{2} \\ q = \frac{ - 2p - 12}{2} \\ q = - p - 6[/tex]
What is the greastest number of acute angles that a triangle can contain?
Answer:
3 acute angles.
Step-by-step explanation:
Triangles have three angles. If any one angle is obtuse or right-angle, then the remaining two angles must be acute. Or else, all the 3 angles can be acute.
An example can be an equilateral triangle because it has 3 acute angles. Each angle is 60 degrees.
A line is defined by the equation y = negative x + 3. Which shows the graph of this line?
Answer: The answer would be A.
The coordinates of the line are (0, 3) and (3, 0) hence, the line will pass through these points so, option A is correct.
What is graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given:
y = negative x + 3
The above phrase can be written as,
y = -x + 3
Calculate the slope as shown below,
Slope = -1
The x-intercept can be calculated as,
0 = -x + 3 (y is zero at the x-axis)
x = 3
The x-intercept can be calculated as,
y = 0 + 3 (y is zero at the x-axis)
y = 3
Mark the coordinates (0, 3) and (3, 0) on the graph and join the points you will get the graph.
The graph is attached below.
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Peggy has four times as many quarters as nickels she had $2.10 in all how many nickels and how many quarters did she have
Answer:
There are 8 quarters and 2 nickels
Step-by-step explanation:
4 quarters for every 1 nickel
This means that for every 1 dollar, there are 5 cents
Double the statement above
1.05 x 2 = 2.10
There are 8 quarters and 2 nickels
Calculate the mean and standard deviation of the data set ...
Answer:
Mean: 12.9
Standard deviation: 14.8
Step-by-step explanation:
The mean is calculated adding all of the values and dividing by the number of elements:
[tex]m=\frac{2+3+7+12+1+4+27+49+11}{9}=\frac{116}{9}=12.9[/tex]
to find the standard deviation, we first find the variance (which is defined as the sum of all the elements subtracting the mean and squared and then dividing by the total amount of elements):
[tex]v=\frac{(2-12.9)^2+(3-12.9)^2+(7-12.9)^2+(12-12.9)^2+(1-12.9)^2+(4-12.9)^2+(27-12.9)^2+(49-12.9)^2+(11-12.9)^2}{9}\\[/tex]
[tex]v=\frac{1978.89}{9}\\[/tex]
[tex]v=219.88[/tex]
Noe that we have the variance, we can calculate the standard deviation.
The stardard deviation is defined as the squared root of the variance:
[tex]standardDeviation=\sqrt{v}[/tex]
we substitute the variance:
[tex]standardDeviation=\sqrt{219.88} \\standardDeviation=14.8[/tex]
Thus, the answer is:
Mean: 12.9
Standard deviation: 14.8
At the beach, 20% of people have white towels and 58% have blue towels. If
the rest have red, what percentage of the people at the beach have red
towels?
Answer: 22%
Step-by-step explanation: First, you have to add the percetages of the white and blue towels.
20+58=78
Now, you can simply subtract 78% from 100% to get your answer, 22%
Brainliest??? Which inequality is represented by this graph.
Answer:
Step-by-step explanation:
D is the answer
Brainliest please help! A storage bin is a rectangular prism. Its volume is 300 cm cubed.
The width of the prism is one-third its length.
its height is two-thirds its length.
Determine the dimensions of the bin.
Answer:
∛50 cm, 2∛50 cm, 3∛50 cm
Step-by-step explanation:
V= wlh
V=300 cm³
w= 1/3l
h= 2/3l
---------
l*1/3l*2/3l=3002/9l³=300l³= 1350l= ∛1350= 3∛50 cmw= 1/3*3∛50= ∛50 cmh= 2/3*3∛50= 2∛50 cmAnswer:
Length is 11.052cm
Width is 3.684cm
Height is 7.386cm
Step-by-step explanation:
Let length be x, width y and height Z
Width (y) = X/3 , height (z) = 2x /3
volume =xyz
volume = x(x/3)(2/3)x
Volume = (2/9)x³
But Volume =300
300= (2/9)x³
300/(2/9) = x³ (make x³ the subject to find x )
1350 = x³
x=3√(1350)
x=11.052cm
Length is 11.052cm
Width = x/3 =11.052 /3
= 3.684cm
Height = 2x/3 = 2(11.052) /3
= 7.368cm
You can check it by multiplying LWH to see if you get 300 (the volume)
A coin in flipped 4000 times What is the probability that d will land I N tails
Answer:
250
Step-by-step explanation:
1000/4000
The missing term in the following polynomial has a degree of 5 and a coefficient of 16. Which statement best describes the polynomial? It is not in standard form because the degree of the first term is not greater than six. It is not in standard form because the degree of the first term should be equal to zero. It is in standard form because the exponents are in order from highest to lowest. It is in standard form because the coefficients are in order from highest to lowest.
Answer:
A.) It is not in standard form because the degree of the first term is not greater than six.
Step-by-step explanation:
Match the measureable quantity given by its formula with the appropriate unit(s).
speed = distance/time
square meters
area = (length)(width)
meters per second
volume = (length) (width)(height)
UUOO
meters
perimeter = 2 (length) + 2 (width)
cubic centimeters
Intro
rity
Done
Answer: i hope this helps (answer is down below)
Step-by-step explanation:
Area goes to square meters
speed goes to meters per second
volume goes to cubic centimetres
perimeter goes to meters
A principal of $2000 is placed in a savings account at 3% per annum compounded annually. How much is in the account after one year, two years and three years?
Answer:
Step-by-step explanation:
After one year
A=p(1+r/n)^nt
=2000(1+0.03/12)^12*1
=2000(1+0.0025)^12
=2000(1.0025)^12
=2000(1.0304)
=$2060.8
After two-years
A=p(1+r/n)^nt
=2060.8(1+0.03/12)^12*2
=2060.8(1+0.0025)^24
=2060.8(1.0025)^24
=2060.8(1.0618)
=$2188.157
After three years
A=p(1+r/n)^nt
=2188.157(1+0.03/12)^12*3
=2188.157(1+0.0025)^36
=2188.157(1.0025)^36
=2188.157(1.0941)
=$2394.063
Amount in account after one year, two and three years are respectively $2,060 , $2,121.8 and $2,185.45
Given:
Principal amount = $2,000
Rate of interest = 3% = 0.03
Amount in account after one year
A = P(1+r)ⁿ
A = 2,000(1+0.03)¹
A = 2,000(1.03)¹
A = 2,000(1.03)
A = $2,060
Amount in account after two year
A = P(1+r)ⁿ
A = 2,000(1+0.03)²
A = 2,000(1.03)²
A = 2,000(1.0609)
A = $2,121.8
Amount in account after three year
A = P(1+r)ⁿ
A = 2,000(1+0.03)³
A = 2,000(1.03)³
A = 2,000(1.092727)
A = $2,185.45
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PLEASE HELP ASAP WILL GIVE BRAINLIEST IF CORRECT
what is 15x + 21x/2??
Answer:
25.5x
Step-by-step explanation:
Simply convert the fraction into a decimal and add.
21/2x = 10.5x
10.5x + 15x = 25.5x
If you want to keep it in fraction form, 15 is 30/2, so,
30x/2 + 21x/2 = 51x/2
Answer:
51x/2
Step-by-step explanation:
Add it like a normal fraction equation
Have them both with the same denominator of 2
30/2 + 21/2
Add the numerators
51/2
Now put the x into the numerator since it started as in the numerator
Answer: 51x/2
Hope this helps!
2/3y + 15 = 9
What are the steps for this question
Answer:
see below
Step-by-step explanation:
2/3y + 15 = 9
Subtract 15 from each side
2/3y + 15-15 = 9-15
2/3y = -6
Multiply each side by 3/2 to isolate y
3/2 * 2/3y = -6 *3/2
y = -9
Answer:
y = - 9
Step-by-step explanation:
2/3y + 15 = 9
Subtract 15 on both sides.
2/3y = 9 - 15
2/3y = - 6
Multiply both sides by 3/2.
y = - 6 × 3/2
y = -18/2
y = -9
A small plane and a large plane are 6.8km from each other, at the same altitude (height). From an observation tower, the two airplanes are separated by an angle of 58°. The large plane is 5.2km from the observation tower. a. Draw a diagram to represent this situation. b. How far is the small plane from the observation tower, to the nearest tenth of a kilometer?
Answer:
7.9km
Step-by-step explanation:
(a)See attached for the diagram representing this situation.
(b)
In Triangle ABC
[tex]\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ[/tex]
Next, we determine the value of Angle B.
[tex]\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ[/tex]
Finally, we find b.
[tex]\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)[/tex]
The distance between the small plane and the observation tower is 7.9km.
ASAp !!!!!!!!!!! Brenton’s weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800
The set the describes the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}
How to determine the domain?In this case, the domain represents the set of hours he is permitted to work
From the question, we understand that he cannot work more than 60 hours
This means that, the least number of hours to work is 0, and the highest is 60
So, the domain is 0 to 60
When represented properly, the domain of P(h) is (b) {h| 0 ≤ h ≤ 60}
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0.45?
How much do this equal
Answer:
.45
$0.45
45%
45/100
Step-by-step explanation:
The cost of a diamond varies as the square of its weight. A diamond weighing 20 decigrams costs Rs. 4,800. Find the cost of a diamond of the same kind weighing 8 decigrams.
Answer:
768
Step-by-step explanation:
let C represent cost and w weight, then the equation relating them is
C = kw² ← k is the constant of variation
To find k use the condition w = 20, C = 4800, that is
4800 = k × 20² = 400k ( divide both sides by 400 )
12 = k
C = 12w² ← equation of variation
When w = 8, then
C = 12 × 8² = 12 × 64 = 768
if tom spins the spinner 80 times work out an estimate for the number of times the spinner will land on 3 please help me
Answer:
The estimated number of times the spinner will land on 3 is 20.
Step-by-step explanation:
The complete question is:
A four-sided spinner is provided. If Tom spins the spinner 80 times then work out an estimate for the number of times the spinner will land on 3.
Solution:
Assume that the four-sided spinner is unbiased.
That is all the four outcomes are equally likely to be selected.
The probability that the spinner lands on any of the four numbers is:
P(1) = P (2) = P (3) = P (4) = 0.25
It is provided that Tom spins the spinner n = 80 times.
The spinner can land on any of the four numbers independently.
The random variable X, defined as the number of times the spinner lands on 3, follows a Binomial distribution with parameters n = 80 and p = 0.25.
The expected value of X is:
[tex]E(X)=np[/tex]
[tex]=80\times 0.25\\=20[/tex]
Thus, the estimated number of times the spinner will land on 3 is 20.
answer to this please!
Answer:
-2²
Explanation:
Doing -k² is the same thing as -(k²), so the answer will be negative. However, (-k)² will still be positive. -2² will equal -4.
There are 135 people in a sport centre. 73 people use the gym. 73 people use the swimming pool. 67 people use the track. 36 people use the gym and the pool. 35 people use the pool and the track. 32 people use the gym and the track. 14 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility?
Answer:
P = 11/135 = 0.0815
Step-by-step explanation:
we can said that:
14 people use all three facilities18 people use just gym and track (32 people use the gym and the track less the 14 people that use all three facilities)21 people use just pool and track (35 people use the pool and the track less the 14 people that use all three facilities)22 people use just gym and pool (36 people use the gym and the pool less the 14 people that use all three facilities)14 people use just the track (67 people use the track less the 18 people that use just the gym and the track, the 21 people that use just the pool and the track and 14 people that use all three facilities)16 people use just the pool (73 people use the swimming pool less the the 21 people that use just the pool and the track, the 22 people that use just the gym and the pool and 14 people that use all three facilities)19 people use just the gym (73 people use the gym less the 18 people that use just the gym and the track, the 22 people that use just the gym and the pool and 14 people that use all three facilities)So, there are 124 people that use the gym, the pool or the track. This is calculated using the information above as:
14 + 18 + 21 + 22 + 14 + 16 + 19 = 124
Finally, there are 11 ( 135 - 124 = 11 ) people that don't use any facility, so the probability that a person doesn't use any facility is:
P = 11/135 = 0.0815
Answer:
0.0815
Step-by-step explanation:
A given line has the equation .
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?
Answer:
y-6x = 9Step-by-step explanation:
The question is incomplete. Here is the complete answer.
A given line has the equation 2x + 12y = −1.
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?
General formula of equation of a line is exspressed as y = mx+c
m = gradient or slope
c = intercept
Step 1: we need to first get the slope of the given equation of a line by rewriting the equation in standard form y = mx+c
2x + 12y = −1
12y = -1-2x
y = -1/12-2x/12
y = -1/6 x - 1/12
From the equation above, it can be seen that the slope (m) of tghe line is -1/6.
Since both lines are perpendicular, the slope of the unknown line will be;
M = -1/m
M = -1/(-1/6)
M = 6
Step 2: We will find the intercept c by substituting the point (0,9) and the slope into the equation y = mx+c
9 = 6(0)+ c
c = 9
Stwp 3: We will find the equation of the line perpendicular to the given line by substituting the value of m and c into the equation y = mx+c
y = 6x+9
y-6x = 9
The equation in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9) is y-6x = 9
Answer:
y-6x=9
Step-by-step explanation:
Simplify 16-3(8-3)^2÷5
Answer:
1
Step-by-step explanation:
PODMAS:-
16-3(8-3)²/5
=16-3(5)²/5
=16-3(25)/5
=16-3(5)
=16-15
= 1
Answer:
65
Step-by-step explanation:
=> [tex]\frac{16-3(8-3)^2}{5}[/tex]
=> [tex]\frac{13(5)^2}{5}[/tex]
=> [tex]\frac{13(25)}{5}[/tex]
=> 13 × 5
=> 65
Divide the following amounts to the given ratio. A.)28kg in the ratio 2:5=. B.)1km in the room 19:1 =. C.)100 in the ratio 2:3:5 =.
Which of the following is false about investing with borrowed money? (5 points)
heeeeeeeeeeeeeeeeelp
Answer:
230 cm squared
Step-by-step explanation:
Split the shape into a triangle and a rectangle
The area of a triangle is base x height / 2
20 x 9= 180/2= 90 (9 because you do 16-7 to find height of triangle)
Find the area of the rectangle=
7 x 20= 140
Add them up
140+90= 230cm squared
I hope this helped :)
Answer:
230 cm squared
Step-by-step explanation:
Fund the degree of the followung polynomials.
1. 5xyz
Answer:
3
Step-by-step explanation:
=> 5xyz
Degree of polynomial is summing up the powers of the variable, so it will give you the degree of polynomial
=> Degree of this polynomial = 1+1+1
=> 3
Here are Xavier's bowling scores:
135, 140, 130, 190, 112, 200, 185, 172, 163, 151,
149
What is the variance rounded to the nearest tenth?
Answer:
The variance rounded to the nearest tenth is 691.8
Step-by-step explanation:
Xavier's bowling scores:
135, 140, 130, 190, 112, 200, 185, 172, 163, 151, 149
No. of observations n = 11
[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{135+140+130+190+112+200+185+172+ 163+ 151+149}{11}\\Mean =157[/tex]
Formula of variance : [tex]\sigma^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex]
[tex]\sigma^2=\frac{(135-157)^2+(140-157)^2+(130-157)^2+(190-157)^2+(112-157)^2+(200-157)^2+(185-157)^2+(172-157)^2+(163-157)^2+(151-157)^2+(149-157)^2}{11}[/tex]
[tex]\sigma^2=\frac{7610}{11}[/tex]
[tex]\sigma^2=691.81[/tex]
Hence the variance rounded to the nearest tenth is 691.8
Please help me I posted this 10 times and no one helped me they were saying how I was so dumb
Answer:
Just count the unit squares
Step-by-step explanation:
If you learn this they may call u dumb but if your beginner then count the squares
Need help ASAP please
Answer:
-6,6
Step-by-step explanation:
x^2=36
6*6=36
-6*-6=36
does anyone know how to solve
this problem? any help would be amazing please!!
Answer:
x = 60 and y = 100
Step-by-step explanation:
As shown in the table, you have: x + y = 160
Otherwise, you have x:y = 3:5 or x = 3y/5
=> 3y/5 + y = 160
or 8y/5 = 160
or y/5 = 20
or y = 20*5 = 100
=> x = 160 - y = 160 - 100 = 60
=> x = 60 and y = 100