Answer:
264 degree angle
Step-by-step explanation:
Which describes the graph in words?
A. All numbers less than -10 and less than or equal to 8.
B. All numbers greater than -10 and less than 8
C. All numbers greater than or equal to -10 and less than or equal to 8
D. All numbers greater than -10 and less than or equal to 8.
D. All numbers greater than -10 and less than or equal to 8
The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points does the image cross the x-axis?
Answer:
[tex]\large \boxed{\sf \ \ \ (-8,0) \ \text{ and } \ (4,0) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
from the expression of f(x) we can say that there are two zeroes, -8 with a multiplicity of 1 and 4 with a multiplicity of 1.
So the image of the parabolic lens crosses the x-axis at two points:
(-8,0)
and
(4,0)
For information, I attached the graph of the function.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Ashley has 500 songs in his music player. Every week he adds 10 songs to his collection. How many songs will he have in his music player after 20 weeks ?
At the end of n weeks, the number of songs is given by the function
f(n) =500 +10n
Or
f(n) = 10 +20b
The output of the function is 700
or
600
when the input is 20.
Answer:
700
Step-by-step explanation:
500+10*20=700
it's f(n) = 500+10n
Find the length of AG
Answer:
[tex]AG=22[/tex]
Step-by-step explanation:
Follow the next steps:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]
Let:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]
Now:
[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]
Hence:
[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]
Finally:
[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]
[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]
Hence:
[tex]x=1\\x=-1[/tex]
Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]
Therefore:
[tex]AG=22[/tex]
Select the correct answer. Consider matrices A, B, and C:
Answer:
i think it is c. i may be incorrect, i am sorry!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I did the math
One number is 6 more than another. Their product is -9. Need help fast
Answer: the numbers are 3 and -3
Step-by-step explanation:
let the unknown number be x
The first UNKNOWN NUMBER = X
The second unknown number is = 6 + x
Their product = -9
(X)(6 + X) = -9
6x +[tex]x^{2}[/tex]=-9
[tex]x^{2}[/tex] +6x +9=0
we multiply the coefficient of x which is 1 with 9
now, we look for two numbers that when multiplied will give us 9 and when added will give 6 and that is 3 and 3
[tex]x^{2}[/tex] +3x+3x +9 = 0
x(x+3) +3(x+3) = 0
(x +3 ) = 0
or (x +3)=0
x +3 =0
x=0 -3
x =-3
x +3=0
x =0-3
x =-3
since the numbers are the same ,we pick one
therefore,the first number =x =-3
the second number is 6 + x=6 + (-3)
6-3=3
A compressive uniform stress distributed on a rectangular areas of sides. located on the two opposite vertical/radial faces of step. If Force = 1.87kN and stress = 0.987MPa calculate the h * t in m^2
Answer:
Area = 0.019 m²
Step-by-step explanation:
stess = applied Force over Area
since stress = 0.987 MPa
and the force = 1.87 Kn
then Area = h * t
Q = F / (h * t)
0.987 mPa = 1.87 kN / (h* t)
since h * t = Area then 1.87 / 0.987
Area = 1.89 x 0.01 =
Area = 0.019 m²
A loudspeaker converts electrical energy into the kinetic energy of the speaker. This kinetic energy is transferred to air, and the motion of the air is the sound that people hear. An illustration of speaker with a wide arrow away from it labeled electrical energy 100 J and it splits into 3 arrows labeled sound energy 80 J, thermal energy ? J, and friction 5 J. How much thermal energy is put out by the speaker? 5 J 15 J 80 J 100 J
Answer:
15 J
Step-by-step explanation:
There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.
1. Set up the equation
80 + x + 5 = 100
2. Simplify
x + 85 = 100
3. Solve for x by subtracting 85 from both sides
x = 15
Answer:
The correct answer is 15J which is B.
Let T:V→W be a linear transformation from a vector space V into a vector space W. Prove that the range of T is a subspace of W.
Answer:
The range of T is a subspace of W.
Step-by-step explanation:
we have T:V→W
This is a linear transformation from V to W
we are required to prove that the range of T is a subspace of W
0 is a vector in range , u and v are two vectors in range T
T = T(V) = {T(v)║v∈V}
{w∈W≡v∈V such that T(w) = V}
T(0) = T(0ⁿ)
0 is Zero in V
0ⁿ is zero vector in W
T(V) is not an empty subset of W
w₁, w₂ ∈ T(v)
(v₁, v₂ ∈V)
from here we have that
T(v₁) = w₁
T(v₂) = w₂
t(v₁) + t(v₂) = w₁+w₂
v₁,v₂∈V
v₁+v₂∈V
with a scalar ∝
T(∝v) = ∝T(v)
such that
T(∝v) ∈T(v)
so we have that T(v) is a subspace of W. The range of T is a subspace of W.
5/9 + (1/9 + 4/5)=×
Answer:
22/15I hope it helps :)Step-by-step explanation:
[tex]\frac{5}{9}+\left(\frac{1}{9}+\frac{4}{5}\right)=x\\x=\frac{5}{9}+\left(\frac{1}{9}+\frac{4}{5}\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\x=\frac{5}{9}+\frac{1}{9}+\frac{4}{5}\\\mathrm{Compute\:a\:number\:comprised\:of\:factors\\\:that\:appear\:in\:at\:least\:one\:of\:the\:following:}\\9,\:9,\:5\\=3\times \:3\times\:5\\\mathrm{Multiply\:the\:numbers:}\:3\times \:3\times \:5=45\\\frac{5}{9}=\frac{5\times \:5}{9\times \:5}=\frac{25}{45}\\[/tex]
[tex]\frac{1}{9}=\frac{1\times \:5}{9\times \:5}=\frac{5}{45}\\\\\frac{4}{5}=\frac{4\times \:9}{5\times \:9}=\frac{36}{45}\\\\x=\frac{25}{45}+\frac{5}{45}+\frac{36}{45}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\x=\frac{25+5+36}{45}\\\\x=\frac{66}{45}\\\\x=\frac{22}{15}[/tex]
What is the value of x plz help
Solve for one half on the triangle with height 6 and base would be 4/2 = 2
Use the Pythagorean theorem:
X = sqrt( 6^2 + 2^2)
X = sqrt( 36 + 4)
X = sqrt(40)
The answer is D
The gas mileage for a certain vehicle can be approximated by m=−0.05x2+3.5x−49, where x is the speed of the vehicle in mph. Determine the speed(s) at which the car gets 9 mpg. Round to the nearest mph.
Answer:
14mphStep-by-step explanation:
Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;
m = −0.05x²+3.5x−49
when m= 9
9 = −0.05x²+3.5x−49
−0.05x²+3.5x−49 = 9
0.05x²-3.5x+49 = -9
Multiplying through by 100
5x²+350x−4900 = 900
Dividing through by 5;
x²+70x−980 = 180
x²+70x−980 - 180 = 0
x²+70x−1160 = 0
Using the general formula to get x;
a = 1, b = 70, c = -1160
x = -70±√70²-4(1)(-1160)/2
x = -70±√4900+4640)/2
x = -70±(√4900+4640)/2
x = -70±√9540/2
x = -70±97.7/2
x = -70+97.7/2
x = 27.7/2
x = 13.85mph
x ≈ 14 mph
Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph
For the functions f(x)=8 x 2 +7x and g(x)= x 2 +2x , find (f+g)(x) and (f+g)(3)
Answer:
(f+g)(x)= 9x² + 9x
(f+g)(3) = 108
Step-by-step explanation:
f(x)=8x² +7x
g(x)= x² +2x
(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x
(f+g)(x)= 9x² + 9x
(f+g)(3)= 9*3² + 9*3 = 108
How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? Which of the following represents a function
Answer: The required number of heads = 30
Step-by-step explanation:
Given, Total tosses = 50
The theoretical probability of getting head = [tex]\dfrac{1}{2}[/tex]
As per given,
Experimental probability = Theoretical probability + 20% of Theoretical probability
= [tex]\dfrac{1}{2}+\dfrac{20}{100}\times\dfrac{1}{2}[/tex]
= [tex]\dfrac{1}{2}+\dfrac{1}{10}=0.5+0.1=0.6[/tex]
Required number of heads = (Experimental probability) x (Total tosses )
= 0.6 x 50
= 30
Hence, the required number of heads = 30
A relation is said to be a function if each input value corresponds to a unique output value.For example: {(1,2), (3,4), (2,3), (4,1))}
Answer:
35 is the Answer
The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 5.9 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a right-tailed test left-tailed test two-tailed test Calculate the p-value. What is the decision? We reject the claim that the average time on death row is 15 years We fail to reject the claim that the average time on death row is 15 years
Answer:
a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
b) The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Step-by-step explanation:
Step(i):-
Sample size 'n' =75
Mean of the sample x⁻ = 17.8
standard deviation of the sample (S) = 5.9
Mean of the Population = 15
Null hypothesis:H₀:μ = 15 years
Alternative Hypothesis :H₁:μ≠15 years
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]
t = 4.111
Degrees of freedom
ν = n-1 = 75-1=74
t₀.₀₂₅ = 1.9925
The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
P-value:-
The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
A P E X!!!! URGENT :The annual interest rate of Belinda's savings account is 8.6% and simple interest is calculated quarterly. What is the periodic interest rate of Belinda's account?
Answer:
The answer is 2.15%
Step-by-step explanatio
Please help with this
Answer: B
Step-by-step explanation:
Because of Supplementary Angles, we know that the two angles in the right side of the equation add up to 90.
Hope it helps <3
A bus company has contracted with a local high school to carry 450 students on a field trip. The company has 18 large buses which can carry up to 30 students and 19 small buses which can carry up to 15 students. There are only 20 drivers available on the day of the field trip.
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
Answer:
The answer is below
Step-by-step explanation:
Let x represent the big buses and y represent small buses. The large buses can carry 30 students and the small buses can carry 15 students. The total number of students are 450, this can be represented by the inequality:
30x + 15y ≤ 450
They are only 20 drivers, therefore only 20 buses can be used. It is represented by:
x + y ≤ 20
They are only 19 small buses and 18 large buses:
x ≤ 18
y ≤ 19
After plotting the graph, the minimum solution to the graph are at:
A (15,0), B(18,0), C(10, 10), D(18, 2).
The cost function is given as:
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
F(x, y) = 225x + 100y
At point A:
F(x, y) = 225(15) + 100(0) = $3375
At point B:
F(x, y) = 225(18) + 100(0) = $4050
At point C:
F(x, y) = 225(10) + 100(10) = $3250
At point D:
F(x, y) = 225(18) + 100(2) = $4250
The minimum cost is at point C(10, 10) which is $3250
6x²-7x=20 solve the following quadratic equation
Answer:
x = -4/3 and x = 5/2.
Step-by-step explanation:
6x² - 7x = 20
6x² - 7x - 20 = 0
To solve this, we can use the quadratic formula to solve this.
[please ignore the A-hat; that is a bug]
[tex]\frac{-b±\sqrt{b^2 - 4ac} }{2a}[/tex]
In this case, a = 6, b = -7, and c = -20.
[tex]\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}[/tex]
= [tex]\frac{7±\sqrt{49 + 80 * 6} }{12}[/tex]
= [tex]\frac{7±\sqrt{49 + 480} }{12}[/tex]
= [tex]\frac{7±\sqrt{529} }{12}[/tex]
= [tex]\frac{7±23 }{12}[/tex]
[tex]\frac{7 - 23 }{12}[/tex] = [tex]\frac{-16 }{12}[/tex] = -8 / 6 = -4 / 3
[tex]\frac{7 + 23 }{12}[/tex] = [tex]\frac{30}{12}[/tex] = 15 / 6 = 5 / 2
So, x = -4/3 and x = 5/2.
Hope this helps!
Answer:
[tex]x1 = - \frac{4}{3} [/tex][tex]x2 = \frac{5}{2} [/tex]Step-by-step explanation:
[tex]6 {x}^{2} - 7x = 20[/tex]
Move constant to the left and change its sign
[tex] {6x}^{2} - 7x - 20 = 0[/tex]
Write -7x as a difference
[tex]6 {x}^{2} + 8x - 15x - 20 = 0[/tex]
Factor out 2x from the expression
[tex]2x(3x + 4) - 15x - 20 = 0[/tex]
Factor out -5 from the expression
[tex]2x(3x + 4) - 5(3x + 4) = 0[/tex]
Factor out 3x + 4 from the expression
[tex](3x + 4)(2x - 5) = 0[/tex]
When the product of factors equals 0 , at least one factor is 0
[tex]3x + 4 = 0[/tex]
[tex]2x - 5 = 0[/tex]
Solve the equation for X1
[tex]3x + 4 = 0[/tex]
Move constant to right side and change its sign
[tex] 3x = 0 - 4[/tex]
Calculate the difference
[tex]3x = - 4[/tex]
Divide both sides of the equation by 3
[tex] \frac{3x}{3} = \frac{ - 4}{3} [/tex]
Calculate
[tex]x = - \frac{4}{3} [/tex]
Again,
Solve for x2
[tex]2x - 5 = 0[/tex]
Move constant to right side and change its sign
[tex]2x = 0 + 5[/tex]
Calculate the sum
[tex]2x = 5[/tex]
Divide both sides of the equation by 2
[tex] \frac{2x}{2} = \frac{5}{2} [/tex]
Calculate
[tex]x = \frac{5}{2} [/tex]
[tex]x1 = - \frac{4}{3} [/tex]
[tex]x2 = \frac{5}{2} [/tex]
Hope this helps...
Best regards!!
Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
work is shown and pictured
Answer:
2/3
Step-by-step explanation:
got right n edg 2021
Graph parallelogram ABCD on the graph
below with vertices A(2,0), B(7,0), C(10,3),
D (5,3). What is the area of parallelogram
ABCD?
Answer: 25 square units
Step-by-step explanation:
We mark the points, A(2,0), B(7,0), C(10,3), D (5,3). on a graph and then joined them to make parallelogram ABCD as provided in the attachment.
Area of parallelogram = Base x corresponding height
From the figure, base AB = 7 - 2 units = 5 units
corresponding height: h= 5 units
Now , Area of parallelogram ABCD = base AB x corresponding height
= 5 x 5 square units
= 25 square units
Hence, the area of parallelogram ABCD is 25 square units .
When testing the claim that p 1p1equals=p 2p2, a test statistic of zequals=2.04 is obtained. Find the p-value obtained from this test statistic.
Answer:
0.0414 with an upper tailed test
Step-by-step explanation:
Claim: P1P1 = P2P2
The above is a null hypothesis
The alternative hypothesis for a two-tailed test would be:
P1P1 \=/ P2P2
Where "\=/" represents "not equal to".
Using a z-table or z-calculator, we derive the p-value (probability value) for the z-score 2.04
With an upper tailed test, the
2 × [probability that z>2.04] = 2[0.0207] = 0.0414
This is the p-value for the test statistic.
Focus is on the alternative hypothesis.
The volume of wine in liters produced by a parcel of vineyard every year is modeled by a Gaussian distribution with an average of 100 and a variance of 9. Find the probability that this year it will produce 115 liters of wine
Answer:
0.99865
Step-by-step explanation:
The question above is modelled by gaussian distribution. Gaussian distribution is also known as Normal distribution.
To solve the above question, we would be using the z score formula
The formula for calculating a z-score
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
In the above question,
x is 115 liters
μ is 100
σ is the population standard deviation is unknown. But we were given variance in the question.
Standard deviation = √Variance
Variance = 9
Hence, Standard deviation = √9 = 3
We go ahead to calculate our z score
z = (x-μ)/σ
z = (115 - 100) / 3
z = 15/ 3
z score = 5
Using the z score table of normal distribution to find the Probability of having a z score of 5
P(x = 115) = P(z = 5) =
0.99865
Therefore the probability that this year it will produce 115 liters of wine = 0.99865
Evaluate 2x^+2x+8 when x=4
Which is the solution to this question 4X equals 32
Answer:
8
Step-by-step explanation:
you would just divide 32 by 4
4x = 32
x = 32/4
x=8
Answer:
[tex]\large\boxed{\sf \ \ \ x=8 \ \ \ }[/tex]
Step-by-step explanation:
Hello
4x=32 we can divide both parts by 4 so
[tex]\dfrac{4x}{4}=\dfrac{32}{4}\\\\<=> x = 8[/tex]
Hope this helps
when Charles eats Oreos , he likes to dunk 2 out of every 5 cookies in a cold glass of milk. if he eats a total of 15 Oreos , how many will he dunk ? how many will ge eat without dunking?
Answer: 6 with milk, 9 without
Step-by-step explanation:
2/5 of the cookies he eats are dunked. Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.
Hope it helps <3
1. What are the formulas that help determine the equation of a circle? 2. How are the center, radius and a point on the circle expressed algebraically? 3. What do you need to know in order to use the ellipse equation formulas?
Answer: see below
Step-by-step explanation:
1) The equation of a circle is: (x - h)² + (y - k)² = r² where
(h, k) represents the center of the circler represents the radius of the circle.2) If you are given a point on the circle and the center (h, k)
you can input those points into the equation of a circle to find r².
Then input (h, k) and r² to identify the equation of that particular circle.
3) If you divide each term in the equation of a circle by r², you will get:
[tex]\dfrac{(x-h)^2}{r^2}+\dfrac{(y-k)^2}{r^2}=1[/tex]
(h, k) is the center of the circler is the x-radius and y-radiusThe difference between a circle and an ellipse is that an ellipse is in the shape of an oval. In other words, the x-radius and y-radius are different.
The equation of an ellipse is:
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
(h, k) is the center of the ellipsea is the x-radiusb is the y-radiusThe marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation. C'(x)=x^-3/4 Find the cost of printing 142 more posters when 18 have already been printed.
The cost of printing 142 more posters when 18 have already been printed is $________.
(Round to the nearest cent as needed.)
Answer:
The cost of printing 142 more posters when 18 has already been printed is $5.57.
Step-by-step explanation:
We are given that the marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation C'(x)=x^-3/4.
The given equation is: [tex]C'(x) = x^{\frac{-3}{4} }[/tex]
The cost of printing 142 more posters when 18 have already been printed is given by;
Integrating both sides of the equation and using the limits we get;
[tex]\int_{a}^{b} C'(x) dx=\int_{18}^{142} x^{\frac{-3}{4}}dx[/tex]
As we know that [tex]\int\limits {x}^{n} \, dx = \frac{x^{n+1} }{n+1}[/tex] , so;
= [tex]\frac{x^{\frac{-3}{4}+1 } }{\frac{-3}{4}+1 } ]^{142} __1_8[/tex]
= [tex]\frac{x^{\frac{1}{4} } }{\frac{1}{4} } ]^{142} __1_8[/tex]
= [tex]4[x^{\frac{1}{4} } } ]^{142} __1_8[/tex]
= [tex]4[(142)^{\frac{1}{4} }- (18)^{\frac{1}{4} }} ][/tex]
= $5.57
Hence, the cost of printing 142 more posters when 18 has already been printed is $5.57.
Copy the problem, mark the givens in the diagram, and write a Statement/Reason proof. Given: MN ≅ MA ME ≅ MR Prove: ∠E ≅ ∠R
Answer:
Step-by-step explanation:
Given: MN ≅ MA
ME ≅ MR
Prove: ∠E ≅ ∠R
From the given diagram,
YN ≅ YA
EY ≅ RY
<EMA = <RMN (right angle property)
EA = EY + YA (addition property of a line)
NR = YN + RY (addition property of a line)
EA ≅ NR (congruent property)
ΔEMA ≅ ΔRMN (Side-Side-Side, SSS, congruence property)
<MNR ≅ MAE (angle property of congruent triangles)
Therefore,
<E ≅ <R (angle property of congruent triangles)
Consider this quote: "In a recent survey, 65 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries. If there is no difference in the proportions who prefer each type in the population, the chance of such extreme results in a sample of this size is about .03. Because .03 is less than .05, we can conclude that there is a statistically significant difference in preference." Give a numerical value for each of the following.
a. The p-value.
b. The level of significance, α.
c. The sample proportion.
d. The sample size.
e. The null value.
Answer:
Step-by-step explanation:
The p value (probability of obtaining results as extreme the z score if null is true) is usually the value derived to make a conclusion and in this case the p value is 0.03
The level of significance is the value usually compared with the p value which is 0.05
The sample promotion is 65 out of 100 = 65/100 = 0.65
The sample size is the total number of consumers which is 100
The null value is usually the default value. The null value would assume that there is no difference in the proportions who prefer each type in the population. There are two preferences: 100/2 = 50- 0.5 for each preference.