Answer:
3x−4y=9 −3x+2y=9
Add these equations to eliminate x: −2y=18
Then solve−2y=18
for y: −2y=18 −2y −2 = 18 −2 (Divide both sides by -2)
y=−9
Now that we've found y let's plug it back in to solve for x.
Write down an original equation: 3x−4y=9
Substitute−9for y in 3x−4y=9: 3x−(4)(−9)=9
3x+36=9(Simplify both sides of the equation)
3x+36+−36=9+−36(Add -36 to both sides)
3x=−27 3x 3 = −27 3 (Divide both sides by 3) x=−9
Answer: x=−9 and y=−9
Hope This Helps!!!
To make a salad dressing you mix vinegar and olive oil in the ratio 2:5 how much olive oil is needed with 20 ml of vinegar
Answer:
Step-by-step explanation:
Set this up as a proportion with the ratios being
[tex]\frac{vinegar}{oil}[/tex] If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:
[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:
[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.
2x = 100 so
x = 50 ml of oil
what is the complete factorization of 8x^2-8x+2
Answer:
2x(4x-4+1)
Step-by-step explanation:
i hope it will help you
Answer:
x=1/2
Step-by-step explanation:
press the calculator
8x²-8x+2=0
x=1/2
min,x=1/2
min,y=0
The x intercepts of the function f(x) = 2x(x-5)^2(x+4)^3
are…
Answer:
[tex]\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}[/tex]
Step-by-step explanation:
A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,
[tex]\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3 [/tex]
For finding the x intercept , equate the given function with 0, we have ;
[tex]\sf \implies 2x ( x - 5 )^2(x+4)^3= 0 [/tex]
Equate each factor with 0 ,
[tex]\sf \implies 2x = 0[/tex]
Divide both sides by 2 ,
[tex]\sf \implies\bf x = 0[/tex]
Again ,
[tex]\sf \implies ( x - 5)^2=0 [/tex]
Taking squareroot on both sides,
[tex]\sf \implies x - 5 = 0 [/tex]
Add 5 to both sides,
[tex]\sf \implies \bf x = 5[/tex]
Similarly ,
[tex]\sf \implies \bf x = -4 [/tex]
Hence the x Intercepts are -4 , 0 and 5 .
{ See attachment also for graph } .
Which of the following is the intersection of the line AD and line DE?
Answer:
Point D
Step-by-step explanation:
The intersection(s) of lines represents where they cross or intersect. We can see that lines AD and DE cross or intersect as Point D, hence the answer being Point D.
Answer: Point D
Step-by-step explanation: The intersection of two figures is the set of points that is contained in both figures. In the diagram shown, D is the intersection of lines AD and DE because D is the point contained by both line AD and DE.
g ) If it is raining, a home security system detects an intruder with probability 0.70. If it is NOT raining, the probability becomes 0.92. The probability of rain on any 2 given day is 0.25. To test the system on a randomly chosen day, the system technician pretends to be an intruder. Given that the technician will NOT be detected, what is the probability that it is NOT raining
Answer:
0.4444 = 44.44% probability that it is NOT raining
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Technician not detected.
Event B: Not raining.
Probability the technician is not detected:
0.3 of 0.25(raining).
0.08 of 0.75(not raining). So
[tex]P(A) = 0.3*0.25 + 0.08*0.75 = 0.135[/tex]
Probability the technician is not detected and it is not raining:
0.08 of 0.75. So
[tex]P(A \cap B) = 0.08*0.75 = 0.06[/tex]
Given that the technician will NOT be detected, what is the probability that it is NOT raining?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.135} = 0.4444[/tex]
0.4444 = 44.44% probability that it is NOT raining
A researcher wishes to conduct a study of the color preferences of new car buyers. Suppose that 50% of this population prefers the color green. If 14 buyers are randomly selected, what is the probability that exactly 12 buyers would prefer green
Answer:
The probability that exactly 12 buyers would prefer green
=0.00555
Step-by-step explanation:
We are given that
p=50%=50/100=0.50
n=14
We have to find the probability that exactly 12 buyers would prefer green.
q=1-p
q=1-0.50=0.50
Using binomial distribution formula
[tex]P(X=x)=nC_r p^r q^{n-r}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^{14-12}[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{12}(0.50)^2[/tex]
[tex]P(x=12)=14C_{12}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14!}{12!2!}(0.50)^{14}[/tex]
[tex]P(x=12)=\frac{14\times 13\times 12!}{12!2\times 1}(0.50)^{14}[/tex]
[tex]P(x=12)=91\cdot (0.50)^{14}[/tex]
[tex]P(x=12)=0.00555[/tex]
Hence, the probability that exactly 12 buyers would prefer green
=0.00555
Find x so that B = 3x i +5j is perpendicular to is perpendicular to A=2i - 6j
Answer:
5
Step-by-step explanation:
I'm going to call x, x1 because I want to use x as a variable.
So we have a ray with points (0,0) and (3x1,5) on it. This equation for this ray would be y=5/(3x1)×x.
We have another ray with points (0,0) and (2,-6). This equation for this ray would be y=-6/2×x or y=-3x.
We want these two lines' slopes to be opposite reciprocals. The opposite reciprocal of -3 is 1/3.
So we want to find x1 such that 5/(3x1)=1/3.
Cross multiply: 15=3x1
Divide both sides by 3: 5=x1
We want x1 to be 5 so that 5/(3×5) and -3 are opposite reciprocals which they are.
Another way:
If two vectors are perpendicular, then their dot product is 0.
The dot product of <3x,5> and <2,-6> is 3x(2)+5(-6).
Let's simplify:
6x-30.
We want this to be 0.
6x-30=0
Add 30 on both sides:
6x=30
Divide both sides by 6:
x=5
For each of the following variables, identify the type of variable (categorical vs. numeric). (1) Temperature (in Fahrenheit) of an office building (11) Traffic congestion (e.g. light, medium, heavy)
1) (1) Numeric, and (II) Categorical
2) (1) Numeric, and (II) Numeric
3) (1) Categorical, and (II) Numeric
4) There is no correct match.
5) (1) Categorical, and (11) Categorical
Answer:
(a) Temperature: Numerical
(b) Traffic congestion: Categorical
Step-by-step explanation:
Required
Determine the variable type
(a) Temperature
Temperatures are measured in numeric values e.g. 22 degree Fahrenheit, etc.
Hence, the variable is numerical
(b) Traffic congestion
From the question, we understand that the traffic congestion are divided into three categories i.e. light, medium....
Hence, the variable is categorical
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches greater than the box he originally planned to build?
Answer:
The new volume is 3n^2+2n inches greater.
Step-by-step explanation:
Volume of a cube = s^3 where s is side of cube
Original volume = n^3
Volume of a Rectangular Prism = LBH
New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n
DIfference = New- original = 3n^2+2n
when a force of 400N is applied on a body at angle of 60 degree to the horizontal displacement,the body covers a distance of 8m.what is the work done?
Answer:
1600N
Step-by-step explanation:
Force = 400 N
Angle with horizontal = 60°
Displacement in horizontal direction = 8 m
work done formula when angle is included: Force * distance * cos(angle)
400 * 8 * cos(60)
= 400 * 8 * 1/2
= 1600N
exponential function in the form y=ab^xy=ab
x
that goes through points (0, 13)(0,13) and (5, 416)(5,416).
Hello!
[tex]\large\boxed{y = 13(2)^x}}[/tex]
y = abˣ
We know that at x = 0, b = 1 because any number to the power of 0 = 1.
Therefore:
13 = a(1)
13 = a
Now, plug in this value to solve for b:
y = 13bˣ
Substitute in the next point:
416 = 13(b)⁵
Divide both sides by 13:
32 = b⁵
Take the 5th root of both sides:
2 = b
Rewrite:
y = 13(2)ˣ
Verify that the equation is an identity.
Step-by-step explanation:
We need to prove that ,
cot x / csc x - csc x / cot x = - tan x sec x .
LHS :-
> cot x / csc x - csc x / cot x
> cos x / sin x ÷ csc x - sin x × csc x / cos x
> cosx - 1/ cos x
> cos² x - 1 / cos x
> - sin²x / cosx
> -sin x / cos x × sin x
> -tan x sin x
= RHS
Hence Proved !
Instructions: Solve the following linear
equation
4(n + 5) – 2(5 + 7n) = -70
n =
Answer:
Step-by-step explanation:
4*(n +5) - 2*(5 + 7n) = -70
4*n + 4*5 + 5*(-2) + 7n*(-2) = -70
4n + 20 - 10 - 14n = -70
4n - 14n + 20 - 10 = -70
- 10n + 10 = -70
Subtract 10 from both sides
-10n = -70 - 10
-10n = -80
Divide both sides by (-10)
n = -80/-10
n = 8
Step-by-step explanation:
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A sprinkler releases water st a rate of 150 liters per hour. If the sprinkler operated for 80 minutes how many liters of water will be released
The amount of water released from the sprinkler for 80 minutes is 200 L
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of water from the sprinkler for 80 minutes be = A
Now , the value of A is given by the equation
A sprinkler releases water st a rate of 150 liters per hour
So , 60 minutes = 150 Liters of water
80 minutes = 1/60 hours
80 minutes = 1.333 hours
The amount of water released for 1.333 hours A = 150 x 1.333
On simplifying the equation , we get
The amount of water released for 1.333 hours A = 200 L
Therefore , the value of A is 200 L
To learn more about equations click :
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How to answer this question
Answer:
(0.3049 ; 0.3751)
Step-by-step explanation:
The confidence interval for proportion can be obtained using the relation :
Phat ± Zcritical * [√phat(1-phat) / n]
phat = x / n
Sample size, n = 700
x = 238
phat = 238/700 = 0.34
Zcritical at 95% = 1.96
C.I = 0.34 ± 1.96 * [√0.34(1-0.34) / 700]
C.I = 0.34 ± 1.96 * 0.0179045
C. I = 0.34 ± 0.0350928
Lower boundary = 0.34 - 0.0350928 = 0.3049
Upper boundary = 0.34 + 0.0350928 = 0.37509
(0.3049 ; 0.3751)
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean of 1262 and a standard deviation of 118. Determine the 26th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
a) 1186
b) Between 1031 and 1493.
c) 160
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 1262 and a standard deviation of 118.
This means that [tex]\mu = 1262, \sigma = 118[/tex]
a) Determine the 26th percentile for the number of chocolate chips in a bag.
This is X when Z has a p-value of 0.26, so X when Z = -0.643.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.643 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.643*118[/tex]
[tex]X = 1186[/tex]
(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.
Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a p-value of 0.025, so X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -1.96*118[/tex]
[tex]X = 1031[/tex]
97.5th percentile:
X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 1.96*118[/tex]
[tex]X = 1493[/tex]
Between 1031 and 1493.
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Difference between the 75th percentile and the 25th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.675*118[/tex]
[tex]X = 1182[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 0.675*118[/tex]
[tex]X = 1342[/tex]
IQR:
1342 - 1182 = 160
Simplify the given expression below:
(4 + 21) – (1 – 71)
Hey there!
(4 + 21) - (1 - 71)
4 + 21 = 25
= 25 - (1 - 71)
1 - 71 = -70
= 25 - (-70)
= 25 + 70
= 95
Answer: 95
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
What is the correct equation for the graph?
tan graph and its tax because tax=0
Consider this linear function:
y = 1/2x + 1
Plot all ordered pairs for the values in the domain.
D: {-8, -4,0, 2, 6)
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The attachment shows the ordered pairs (x, f(x)) and their graph.
Two cell phone companies charge a flat fee plus an added cost for each minute or part of a minute used. The cost is represented by C and the number of minutes is represented by t.
Call-More: C = 0.40t + 25 Talk-Now: C = 0.15t + 40
Answer:
The call more is cheaper than talk-now.
Step-by-step explanation:
The companies charge a flat fee plus an added cost for each minute or part of a minute used for two companies are as follows :
Call-More: C = 0.40t + 25 Talk-Now: C = 0.15t + 40
We need to find which company is cheaper if a customer talks for 50 minutes.
For call more,
C = 0.40(50) + 25 = 45 units
For talk-now,
C = 0.15(50) + 40 = 47.5 units
So, it can be seen that call more is cheaper than talk-now.
An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?
A. 8
B. 9
C. 10
D.11
Answer:
option B
Step-by-step explanation:
Sum of interior angles of a polygon with n sides:
[tex]= (n - 2 )\times 180[/tex]
[tex]Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180[/tex]
[tex]Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ[/tex]
[tex][ \ because \ straight \ line \ angle = 180^\circ \ ][/tex]
That is ,
[tex]Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9[/tex]
OR
Sum of exterior angles of a regular polygon = 360
Given 1 exterior angle of the regular polygon is 40
Therefore ,
[tex]n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9[/tex]
Answer:
9
Step-by-step explanation:
solve for s 9s+20=−16
Answer:
s = -4
Step-by-step explanation:
Your goal is to manipulate the equation so you can isolate s
9s + 20 = -16
Subtract 20 from both sides to get:
9s = -36
Divide both sides by 9 so s is alone
you end up with s = -4
Answer:
s = -4
Step-by-step explanation:
9s+20=−16
Subtract 20 from each side
9s +20 -20 = -16 -20
9s = -36
Divide by 9
9s/9 = -36/9
s = -4
Tyler and Elena are on the cross country team. Tyler’s distances and times for a training run are shown on the graph. Elenas distances and times for a training run are given by the equation y=8.5x, calculate Tyler’s pace per minute
Answer:
8.2 miles per minute
Step-by-step explanation:
Given
See attachment for graph
Required
The rate of Tyler's graph
This means that we calculate the slope (m) of the graph using:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
So, we have:
[tex](x_1 ,y_1) = (0,0)[/tex]
[tex](x_1 ,y_1) = (1,8.2)[/tex]
So, we have:
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{0 - 8.2}{0 - 1}[/tex]
[tex]m = \frac{-8.2}{- 1}[/tex]
[tex]m = 8.2}[/tex]
Find m∠GHIm∠GHI if m∠GHI=14x+6m∠GHI=14x+6, m∠QHI=130∘m∠QHI=130∘, and m∠GHQ=3x−3m∠GHQ=3x−3.
Answer:
m∠GHI = 160
Step-by-step explanation:
From the question given above, the following data were obtained:
m∠GHI = 14x + 6
m∠QHI = 130°
m∠GHQ = 3x – 3
m∠GHI =?
Next, we shall determine the value of x. This can be obtained as follow:
m∠GHI = m∠QHI + m∠GHQ
14x + 6 = 130 + (3x – 3)
14x + 6 = 130 + 3x – 3
Collect like terms
14x – 3x = 130 – 3 – 6
11x = 121
Divide both side by 11
x = 121 / 11
x = 11
Finally, we shall determine the value m∠GHI. This can be obtained as follow:
m∠GHI = 14x + 6
x = 11
m∠GHI = 14(11) + 6
m∠GHI = 154 + 6
m∠GHI = 160
If 19,200 cm2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
Step-by-step explanation:
√19200cm²
=138.56cm
then the highest possible volume
=(138.56)³
=2660195.926cm³
The largest possible volume of the box is; V = 25600 cm³
Let us denote the following of the square box;
Length = x
Width = y
height = h
Formula for volume of a box is;
V = length * width * height
Thus; V = xyh
but we are dealing with a square box and as such, the base sides are all equal and so; x = y. Thus;
V = x²h
The box has an open top and as such, the surface are of the box is;
S = x² + 4xh
We are given S = 19200 cm². Thus;
19200 = x² + 4xh
h = (19200 - x²)/4x
Put (19200 - x²)/4x for h in volume equation to get;
V = x²(19200 - x²)/4x
V = 4800x - 0.25x³
To get largest possible volume, it will be dimensions when dV/dx = 0. Thus;
dV/dx = 4800 - 0.75x²
At dV/dx = 0, we have;
4800 - 0.75x² = 0
0.75x² = 4800
x² = 4800/0.75
x² = 6400
x = √6400
x = 80 cm
From h = (19200 - x²)/4x;
h = (19200 - 80²)/(4 × 80)
h = (19200 - 6400)/3200
h = 4 cm
Largest possible volume = 80² × 4
Largest possible volume = 25600 cm³
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What is the solution set for |z+4|> 15
Answer:
I think that answer would be B.
Step-by-step explanation:
Match the y coordinate with coo responding pairs of x
Which point is part of the solution of the inequality y ≤ |x + 4| − 3?
Answer:
Step-by-step explanation:
show that 43\2^4×5^3 will terminate after how many places of the decimal
Answer:
4 places after the decimal.
the result is 0.0215
Step-by-step explanation:
I assume the expression is really
43 / (2⁴ × 5³)
this is the same as
(((((((43 / 2) / 2) / 2) / 2) / 5) / 5) / 5)
since the starting value is an odd number, the first division by 2 creates a first position after the decimal point, and it must be a 5, as the result is xx.5
the second division by 2 splits again the uneven end .5 in half, creating a second position after the decimal point again ending in 5, as the result is now xx.x5
the third division by 2 does the same thing with that last 5 and creates a third position after the decimal point ending again in 5, as the result is now xx.xx5
the fourth division by 2 does again the same thing, a fourth position after the decimal point is created ending in 5. now xx.xxx5
in essence, every division of the 0.5 part by 2 is the same as a multiplication by 0.5, which squares 0.5 leading to 0.5². the next division did the same thing leading to 0.5³.
and finally the fourth division to 0.5⁴.
0.5⁴ = (5/10)⁴ = 5⁴/10⁴
so, now we start to divide this result by 5. since the positions after the decimal point are divisible by 5 without remainder, as we have 5⁴ to work with.
every divisible by 5 takes one of these powers away.
so, we go from 5⁴/10⁴ to 5³/10⁴ to 5²/10⁴ to 5/10⁴.
all the time we maintain the 10⁴ in the denominator of the fraction. and that determines the positions after the decimal point.
so, after all the individual divisions we come to and end and are still limited to the 4 positions after the decimal point.
The number of measles cases decreased by 7% to 606 cases this year. What was the number of cases prior to the increase? Express your answer rounded correctly to the nearest whole number.
Answer:
652 cases
Step-by-step explanation:
The formula for percentage increase is 100 times the final-initial/final value. If we plug the numbers in and calculate, we get 652 cases. Have a great day!
