Answer:3.46$
Step-by-step explanation:
Probability distribution:
[tex]\to x \ \ \ \ \ \ \ -\$5 \ \ \ \ \ \ \ \$0 \ \ \ \ \ \ \ \$5\\\\\to P(x) \ \ \ \ \ \ \ 0.36 \ \ \ \ \ \ \ 0.48 \ \ \ \ \ \ \ 0.16\\\\[/tex]
[tex]\to \mu_{x}= Mean\ (X)= E(X) \ = - \$ 1\\\\\to \sigma^{2}_{x}= \Sigma_{x} x^2 p(x)- (\mu_{x})^2\\\\[/tex]
[tex]=(-5)^2 \times 0.36 + 0+ (5)^2 \times 0.16 - (-1)^2\\\\=25 \times 0.36 + 0+ 25 \times 0.16 - 1\\\\=9 + 0+ 4 - 1\\\\= 13-1\\\\=12\\\\[/tex]
Therefore,
[tex]\to \sigma_{x}=\sqrt{12}= \$ 3.464[/tex]
Therefore, the final answer is "3.464".
Learn more about the probability distribution:
brainly.com/question/22631589
The temperature is 71 °F at 2:00 in the afternoon. If the temperature drops 8 °F every hour after that, what is the temperature at 6:00 in the evening?
Answer = _____ F
Answer:
The answer is 39 degrees by 6:00 in the evening.
Step-by-step explanation:
Since it is 2:00 in the afternoon and there is 4 hours, with 8 degrees dropping every hour, 8 times 4 equals 32, so 71 degrees minus 32 degrees is 39 degrees.
Answer: the temperature at 6:00 in the evening is 39°F
Step-by-step explanation:
If the temperature drops 8 °F every hour after that, then the rate is linear and the rate at which the temperature is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = 71 °F
d = - 8 °F (since it is decreasing)
n = 5 (2pm to 6pm)
We want to determine the value of the 5th term, T5. Therefore,
T5 = 71 - 8(5 - 1)
T5 = 71 - 32 = 39
Let V be a vector space and assume that T, U, W are sub spaces of V. Show that if T cup U W is a sub space of V, then two of these subspaces must be contained in the other one?
Answer: T⊂U⊂W are subspaces of V
Step-by-step explanation:
Proof: This is the easier direction.
If T⊂U⊂W or W⊂U⊂T then we have U⊂T⊂W = T or T⊂U⊂W = U
orT⊂U⊂W=W respectively.
SoT⊂U⊂W is a subspace as T, U and W are subspaces.
1st case :T⊂U⊂W is true Then the disjunction W⊂U⊂T or U⊂T⊂W is trivially true.
Let x∈W1 and y∈W2−W1.
By the definition of the union, we have x∈W∪T∪C and y∈T⊂U⊂W
As T∪U∪W is a subspace, x+y∈T∪C∪W which, again by the definition of the union, means that x+y∈W∪T∪C
V∈W∪T∪C
As V was arbitrary, as desired.
Final answer:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one.
Explanation:
If T ∪ U ∪ W is a subspace of V, then two of the subspaces must be contained in the other one. We can prove this by contradiction. Assume that none of the subspaces is contained in the other. This means that there is an element in T that is not in U ∪ W, an element in U that is not in T ∪ W, and an element in W that is not in T ∪ U. If we take any two of these elements, one from each subspace, and add them together, the result will not be in T ∪ U ∪ W, which contradicts the assumption.
Therefore, two of the subspaces must be contained in the other one.
Janay is constructing a triangle using wire an art project.She has 3 inches of purple wire and 7 inches of pink wire.Janay is going to buy some blue wire for the third side of her triangle
For Janay's art project, the blue wire must be longer than 4 inches and shorter than 10 inches to create a triangle. This is based on the Triangle Inequality Theorem, which states that the length of any side of a triangle should be less than the sum of the lengths of the other two sides, but more than the difference of the two sides' lengths.
Explanation:To determine how long the blue wire should be for Janay's art project, we need to understand a rule in geometry related to triangles, specifically the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle must be less than the sum of the lengths of the other two sides.
Here, we have side lengths of 3 inches (purple wire) and 7 inches (pink wire), so the blue wire can be any length that is less than 3+7=10 inches, and more than |7-3|=4 inches. So the blue wire should be more than 4 inches and less than 10 inches to form a triangle.
This ensures that Janay will be able to form a valid triangle for her art project. If the length of the blue wire is less than 4 inches or greater than 10 inches, a triangle cannot be formed.
Learn more about Triangle Inequality Theorem here:https://brainly.com/question/1163433
#SPJ12
58x176 equals what.... will make brainliest
Answer:
10208
Step-by-step explanation:
just 58x176
The area of the base of the prism is 360 square centimetres and the height of the prism 19 centimeters what is the volume in cubic centimeters of the rectangular
Answer:
6,840cm³
Step-by-step explanation:
V = 360 * 19
V = 6,840cm³
A 1500 kg hippo is completely submerged, standing on the bottom of a lake. What is the approximate value of the upward normal force on the hippo?
Answer:
About 428 N
Step-by-step explanation:
Weight = 1,500 * 9.8 = 14,700 N
Density = Mass ÷ Volume
1,030 = 1,500 ÷ V
V = 1,500 ÷ 1,030 = 1.46 m^3.
Buoyant force = Density * g * V
Buoyant force = 1,000 * 9.8 * (1,500 ÷ 1,030)
Buoyant force = 9,800 * (1,500 ÷ 1,030) = 14,272 N.
Net force = 14,700 – [(9,800 * (1,500 ÷ 1,030)]
The upward normal force on a 1500 kg submerged hippo is approximately equal to its weight, calculated as its mass times the acceleration due to gravity (1500 kg × 9.81 m/s²), resulting in a force of 14715 N.
Explanation:The question is asking about the upward normal force on a submerged hippo in a lake. To find this force, we must understand that the upward normal force that the ground (or in this case, the lake bed) exerts on the hippo is equal to the weight of the hippo, which is the product of the hippo's mass (m) and the acceleration due to gravity (g).
In equation form: Normal Force = m × g. Plugging in the values, we have a 1500 kg hippo and the acceleration due to gravity is approximately 9.81 m/s². Therefore, the upward normal force is:
Normal Force = 1500 kg × 9.81 m/s² = 14715 N.
This is the approximate value of the upward normal force exerted on the hippo standing on the bottom of the lake.
Learn more about normal force here:https://brainly.com/question/18799790
#SPJ3
Write the function as a set of ordered pairs.
Give the domain and range of f.
f(1)=10, f(2)=-3, f(3)=3
Answer:
1. (1,10) 2. (2,-3) 3. (3,3)
The reequired ordered pair of the given function is (1, 10), (2, -3), and (3, 3).
Given that,
To determine the function as a set of ordered pairs.
f(1)=10, f(2)=-3, f(3)=3
Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.
Here,
Since order pair of function f(x) = y is given as (x, y)
Similarly ordered pair of the function given is,
f(1) = 10
ordered pair = (1, 10)
f(2) = 3
ordered pair = (2, -3)
f(3) = 3
ordered pair = (3, 3)
Thus, the reequired ordered pair of the given function is (1, 10), (2, -3), and (3, 3).
learn more about function here:
brainly.com/question/21145944
#SPJ2
Need help ASAP
Simplify using only positive exponents
1.) 3^2•3^4
2.) (2x^2)^-4
3.) 2x^4y^-4z^-3
————————-
3x^2y^-3z^4
Part (1) : The solution is [tex]729[/tex]
Part (2): The solution is [tex]$\frac{1}{16 x^{8}}$[/tex]
Part (3): The solution is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Explanation:
Part (1): The expression is [tex]3^{2} \cdot3^{4}[/tex]
Applying the exponent rule, [tex]$a^{b} \cdot a^{c}=a^{b+c}$[/tex], we get,
[tex]$3^{2} \cdot 3^{4}=3^{2+4}$[/tex]
Adding the exponent, we get,
[tex]3^{2} \cdot3^{4}=3^6=729[/tex]
Thus, the simplified value of the expression is [tex]729[/tex]
Part (2): The expression is [tex]$\left(2 x^{2}\right)^{-4}$[/tex]
Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,
[tex]$\left(2 x^{2}\right)^{-4}=\frac{1}{\left(2 x^{2}\right)^{4}}$[/tex]
Simplifying the expression, we have,
[tex]\frac{1}{2^4x^8}[/tex]
Thus, we have,
[tex]$\frac{1}{16 x^{8}}$[/tex]
Thus, the value of the expression is [tex]$\frac{1}{16 x^{8}}$[/tex]
Part (3): The expression is [tex]$\frac{2 x^{4} y^{-4} z^{-3}}{3 x^{2} y^{-3} z^{4}}$[/tex]
Applying the exponent rule, [tex]$\frac{x^{a}}{x^{b}}=x^{a-b}$[/tex], we have,
[tex]\frac{2x^{4-2}y^{-4+3}z^{-3-4}}{3}[/tex]
Adding the powers, we get,
[tex]\frac{2x^{2}y^{-1}z^{-7}}{3}[/tex]
Applying the exponent rule, [tex]$a^{-b}=\frac{1}{a^{b}}$[/tex], we have,
[tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Thus, the value of the expression is [tex]$\frac{2 x^{2}}{3 y z^{7}}$[/tex]
Lisa picked some berries. She used 2/8 of the berries to make a pie she gave 5/7 of the berries to her friend. What fraction of the berries did she give her friend?
Answer:
15/28
Step-by-step explanation:
Let the number of berries Lisa picked be y
Number of berries she used to make pie = 2y/8 = y/4
Number of berries left = y - y/4 = 3y/4
Number of berries she gave her friend = 5/7 × 3y/4 = 15y/28
Fraction of the berries she gave her friend = 15/28
In a lilac paint mixture 40% of the mixture is white paint 20% is blue and the rest is red there are four cups of blue paint used in a batch of lilac paint how many cups of white paint is used
Answer: 8 cups of white paint is used.
Step-by-step explanation:
In a lilac paint mixture 40% of the mixture is white paint 20% is blue and the rest is red. This means that the percentage of red paint in the mixture is 100 - (40 + 20) = 40%
There are four cups of blue paint used in a batch of lilac paint. This means that 20% of the total number of cups of paint used in a batch of lilac paint is 4.
Assuming that the total number of cups of paint in the mixture is x, then,
20/100 × x = 4
0.2x = 4
x = 4/0.2 = 20
Therefore, the number of cups of white paint used is
40/100 × 20 = 0.4 × 20
= 8 cups
Final answer:
In the lilac paint mixture, for every 4 cups of blue paint, which accounts for 20% of the mixture, there are 8 cups of white paint, corresponding to 40% of the mixture.
Explanation:
The question involves determining the amount of white paint used in a batch of lilac paint given that 40% of the paint mixture is white, 20% is blue, and the remainder is red. We're told that 4 cups of blue paint are used. Since blue paint represents 20% of the mixture, we can use this information to find out the total amount of the paint mixture and then calculate the amount of white paint needed.
First, find the total amount of the paint mixture by calculating the full 100% that the 4 cups of blue paint (20%) contribute to. This calculation is as follows:
Total Paint = 4 cups (20%) / 0.20Total Paint = 20 cupsNow that we know the total paint mixture is 20 cups, we can determine the amount of white paint, which is 40% of the total mixture:
White Paint = Total Paint x 40%White Paint = 20 cups x 0.40White Paint = 8 cupsTherefore, 8 cups of white paint are used in the mixture.
A cube of mass m 1 = 7.0 kg is sitting on top of a second cube of the same size and mass m 2 = 0.7 kg while both are in free fall. Ignoring any air resistance, what is the magnitude of the normal force with which the bottom cube is acting on the top cube?
Answer:
0 N
Step-by-step explanation:
We are given that
[tex]m_1=7 kg[/tex]
[tex]m_2=0.7 kg[/tex]
Total mass =[tex]m_1+m_2=7+0.7=7.7 Kg[/tex]
We have to find the magnitude of the normal force with which the bottom cube is acting on the top cube.
When both cube are fall freely then
g=[tex]0m/s^2[/tex]
Then, the weight=[tex]mg=7.7\times 0=0 N[/tex]
The direction of weight is downward.
We know that
Normal force is equal to weight and act in opposite direction of weight.
When the weight is zero N then
The magnitude of the normal force with which the bottom cube is acting on the top cube=0 N
Diane received 300 votes in the election for student council president. That was 60% of the students who voted election. How many students voted in the election?
Answer:
500
Step-by-step explanation:
The problem statement tells you ...
300 = 0.60×voters
Dividing by the coefficient of the variable gives ...
300/0.60 = voters = 500
500 students voted in the election.
Answer:
500
Step-by-step explanation:
Kerry's saving account has balance of $372 for grandmother is going to give her a birthday check was 1/4 of her savings parents are they going to give her a check or 33% of her new savings account balance would you have enough money to buy a plane ticket to alaska the cost $600
Answer:
Step-by-step explanation:
372 + 1/4*372 = $465
$465 is her new savings and 33% of it is $153.45
$465 + $153.45 = $618.45
So yes she would have enough money to buy a plane ticket to alaska the cost $600
26,) If y varies inversely as x, and y = 5 as x = 6, find y for the x-value of 10.
Answer:
3
Step-by-step explanation:
the initial statement is
y ∝ 1 /x
to convert to an equation multiply by k the constant
of variation
y = k × 1 /x = k /x
to find k use the given condition
y = 5 when x = 6
y = k/ x ⇒ k = y x = 5 × 6 = 30
y = 30 /x
when
x = 10
then
y = 30 /10 = 3
Answer: y = 3
Step-by-step explanation:
In inverse variation, as one variable increases, the other variable decreases and as one variable decreases, the other increases.
We would introduce a constant of proportionality, k. Therefore,
y = k/x
When y = 5 , x = 6
Therefore,
5 = k/6
Cross multiplying by 6, it becomes
k = 6 × 5 = 30
The expression becomes
y = 30/x
Therefore, when x is 10,
y = 30/10
y = 3
The radius of the earth is 4000 miles. How fast is someone on the equator moving compared to someone at the north pole due to daily rotation of the Earth (in miles per hour)?
Answer: speed at the equator =
1047.33 miles per hour
Step-by-step explanation:
The radius of earth is 4000miles
The earth rotates on its axis, hence we calculate the circumference at the equator
Circumference, C = 2 π R
C = 2 x 3.142 x 4000miles
C = 25,136 miles
Since the total time of one complete rotation about it's axis is 24hours
Hence, the speed at the equator is
speed = 25,136/24 = 1047.33 miles per hour
The speed of the person on the equator due to daily rotation of the earth is;
Speed = 1047.221 miles per hour
We are told that the radius of the earth is; R = 4000 miles.Formula for circumference is;
C = 2πR
Thus;
C = 2 × π × 4000miles
C = 25,132.74 miles
C ≈ 25133 miles
Now, the time it takes for the earth to complete one full rotation about it's axis is 24 hours.
We know that formula for speed is;
speed = distance/time
Thus;
Speed on the equator is;
speed = 25133/24 = 1047.221 mph
Read more at; https://brainly.com/question/13478542
For which problem do you need to regroup 1 ten as 10 ones? Fill in the bubble next to the correct answer. Subtract 16 from 38, subtract 27 from 85, subtract 51 from 72
Answer:
subtract 27 from 85
Step-by-step explanation:
85
-27
———
58
7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracted from 15 and then the 8 tens becomes 7 tens so 7-2=5
58+27=85 to check your work
We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85
What is a numerical expression?A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
Given that regroup 1 ten as 10 one
85 -27 = 58
Since 7 cannot be subtracted from 5 so borrow a 10 to make it 7 subtracbecomem 15 and then the 8 tens becomes 7 tens thus, 7-2=5
Therefore,
58 + 27 = 85
We need to regroup 1 ten as 10 ones by the problem; subtract 27 from 85
Learn more about a number pattern:
brainly.com/question/14471389
#SPJ5
Identify the triangle that contains an acute angle for which the sine and cosine ratios are equal. 1. Triangle A B C has angle measures 50 degrees, 40 degrees, and 90 degrees. 2. Triangle A B C has angle measures 45 degrees, 45 degrees, 90 degrees. 3. The lengths of sides A C and C B are congruent. 4. Triangle A B C has angle measures 68 degrees, 22 degrees, and 90 degrees. 5. Triangle A B C has angle measures 60 degrees, 30 degrees, and 90 degrees.
Answer:
The correct option: (2) Triangle ABC that has angle measures 45°, 45° and 90°.
Step-by-step explanation:
It is provided that a triangle ABC has an acute angle for which the sine and cosine ratios are equal to 1.
Let the acute angle be m∠A.
For the sine and cosine ratio of m∠A to be equal to 1, the value of Sine of m∠A should be same as value of Cosine of m∠A.
The above predicament is possible for only one acute angle, i.e. 45°, since the value of Sin 45° and Cos 45° is,
[tex]Sin\ 45^{o} =Cos\ 45^{o} = \frac{1}{\sqrt{2} }[/tex]
So for acute angle 45° the ratio of Sin 45° and Cos 45° is:
[tex]\frac{Sin\ 45^{o}}{Cos\ 45^{o}} = \frac{\frac{1}{\sqrt{2} } }{\frac{1}{\sqrt{2} } } = 1[/tex]
Hence one of the angles of a triangle is, m∠A = 45°.
Comparing with the options provided the triangle is,
Triangle ABC that has angle measures 45°, 45° and 90°.
Thus, the provided triangle is a right angled isosceles triangle, since it has two similar angles.
Answer:
IT'S the second option
Step-by-step explanation:
Select TWO equivalent expression to the function 3x^2−12x−36.
Question 1 options:
3(x+6)(x−2)
3(x−6)(x+2)
(3x+6)(x−6)
(3x−6)(x+6)
Answer:
3(x-6)(x+2) and (3x+6)(x-6)
Step-by-step explanation:
The other two answers are wrong because the value for their x will be positive.
A local Walmart sells sweatpants ($7) and jackets ($14). If total sales were $6,160 and customers bought 8 times as many sweatpants as jackets, what would be the number of jackets sold?
A. 880
B. 8
C. 88
D. 8,880
E. None of these
Answer:
Option C) 88
Step-by-step explanation:
We are given the following in the question:
Unit cost of sweatpants = $7
Unit cost of jackets = $14
Let x be the number of sweatpants sold and y be the number of jackets sold.
Customers bought 8 times as many sweatpants as jackets
Then, we can write,
[tex]x = 8y[/tex]
Total sales = $6,160
[tex]7x + 14y = 6160[/tex]
Substituting the values, we get,
[tex]7(8y) + 14y = 6160\\70y = 6160\\y = 88\\x = 704[/tex]
Thus, 88 jackets were sold.
Option C) 88
what are the values of c and d in the matrix [[6,8],[-11,15]]-[[c+2,3],[-5,d-4]]=[[22,5],[-6,17]]
Answer:
c = -18
d = 2
Step-by-step explanation:
[[6,8],[-11,15]]-[[c+2,3],[-5,d-4]]=[[22,5],[-6,17]]
First we arrange the subtraction to clear the unknowns
- [[c+2,3],[-5,d-4]] = [[22,5],[-6,17]] - [[6,8],[-11,15]]
[[c+2,3],[-5,d-4]] = [[6,8],[-11,15]] - [[22,5],[-6,17]]
Now we solve what can be done
[[c+2,3],[-5,d-4]] = [[6-22 , 8-5],[-11+6 , 15-17]]
[[c+2,3],[-5,d-4]] = [[-16 , 3] , [-5 , -2]
we match each term with its corresponding one and we will obtain
c + 2 = -16 d - 4 = -2
c = -16 - 2 d = -2 + 4
c = -18 d = 2
Two pools are being drained. To start, the first pool had 3700 liters of water and the second pool had 4228 liters of water. Water is being drained from the first pool at a rate of 31 liters per minute. Water is being drained from the second pool at a rate of 42 liters per minute.
This is a comparison problem involving rates. We multiply the rate of draining by the time and subtract the result from the initial amount, which gives us the amount of water after that time.
Explanation:This problem is considerate a comparison problem that involves rates of draining water from two pools. In these cases, it's crucial to keep the rates and the initial amounts separate to correctly solve the problem.
The first pool is initialy with 3700 liters of water and the draining rate is 31 liters per minute. The second pool from the start has 4228 liters and is being drained at a rate of 42 liters per minute.
To know the amount of water in each pool after any given time in minutes, we would multiply the rate by that time, and subtract the result from the initial amount of water.
For example, if we wanted to find out how much water was left after 10 minutes, we would do the following calculations:
For the first pool: 3700 - (31 * 10) = 3400 liters remained.For the second pool: 4228 - (42 * 10) = 3828 liters remained.Therefore, after 10 minutes, the first pool had 3700 liters and the second one had 3828 liters of water.
Learn more about Comparison problem here:
https://brainly.com/question/33509333
#SPJ3
The cylinder coffee cup has a radius of 1.8 inches and a height of 4 inches. Find the surface area of the coffee cup, not including the handle. Round to the nearest tenth
Answer:
Step-by-step explanation:
The formula for determining the total surface area of a cylinder is expressed as
Total surface area = 2πr² + 2πrh
Where
r represents the radius of the cylinder.
h represents the height of the cylinder.
π is a constant whose value is 3.14
Assuming that the cylindrical cup is open at the top, the formula becomes
Area = πr² + 2πrh
From the information given,
Radius = 1.8 inches
Height = 4 inches
Therefore, the surface area of the coffee cup is
(3.14 × 1.8²) + (2 × 3.14 × 1.8 × 4)
= 10.1736 + 45.216
= 55.4 inches² to the nearest tenth.
Answer:
55.4 :))
Step-by-step explanation:
Which of the following functions are solutions of the differential equation y'' + y = sin(x)?a) y= sinx
b) y= cosx
c) y=1/2sinx
d) -1/2xcosx
Answer:
Option (d)
Step-by-step explanation:
Given,
y" +y=sin x ...........(1)
The particular solution
[tex]y_p=A x sinx +Bx cosx[/tex]
[tex]y'_p=Axcosx+Asinx+B cosx-Bxsinx[/tex]
[tex]y"_p=Acosx-Axsinx+Acosx-Bsinx-Bsinx-Bxcosx[/tex]
[tex]y"_p=2Acosx-Axsinx-2Bsinx-Bxcosx[/tex]
Putting the value of y" and y in equation (1)
[tex]2Acosx-Axsinx-2Bsinx-Bxcosx+Axsinx+Bxcosx = sinx[/tex]
[tex]\Rightarrow 2Acosx-2Bsinx=sinx[/tex]
Therefore 2A =0 -2B=1
⇒A=0 [tex]\rightarrow B=-\frac{1}{2}[/tex]
Therefore [tex]y_p=-\frac{1}{2} x cosx[/tex]
The solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).
Explanation:To determine which of the given functions are solutions of the differential equation y'' + y = sin(x), we can substitute each function into the equation and check if it satisfies the equation. Let's go through each option:
Substituting y = sin(x) into the equation, we get -sin(x) + sin(x) = sin(x), which is not true. So, y = sin(x) is not a solution.Therefore, the solutions of the differential equation y'' + y = sin(x) are y = cos(x), y = (1/2)sin(x), and y = -(1/2)xcos(x).
Learn more about Solutions of a differential equation here:https://brainly.com/question/33719537
#SPJ3
Use the graph that shows the solution to
f(x)=g(x) .
f(x)=−3/4x^2+3x+1
g(x)=2x
Graph A is the correct representation, as it aligns with the functions f(x) and g(x), resulting in the accurate intersection point (2, 4). Graph B does not accurately represent the functions based on the reported intersection point (4, 1).
The correct graph can be determined by analyzing the given functions and the specified intersection points. The functions are f(x) = -3/4 * x^2 + 3x + 1 and g(x) = 2x, and the reported intersection points are (2, 4) for graph A and (4, 1) for graph B.
To verify the accuracy, substitute the x-values into both functions:
Graph A (Intersection at (2, 4)):
f(2) = -3/4 * (2)^2 + 3 * 2 + 1 = 4
g(2) = 2 * 2 = 4
Both functions align, confirming the correctness of the reported intersection point.
Graph B (Intersection at (4, 1)):
f(4) = -3/4 * (4)^2 + 3 * 4 + 1 = 1
g(4) = 2 * 4 = 8
There is a discrepancy here, as the y-values do not match. Therefore, graph B does not accurately represent the functions f(x) and g(x).
In conclusion, graph A is correct since it accurately reflects the given functions and results in the reported intersection point (2, 4).
Some of helen's plants need water every day,some need water every other day,and others need water every third day.If she waters them all today,how many days will it be before she waters them all again?
Answer: Waters on 7th day
Step-by-step explanation:
If she waters everyday then days= 1,2,3,4,5,6,7,8,9
If she waters every other day= 1,3,5,7,9
If she waters every third day= 1,4,7,10,13
So the common day to all is either 1st day or 7th day.
which of the following terms is not a monomial a)6x b)1/3x^2 c)13 d) 3x^-3
Answer:
The answer is D.
Step-by-step explanation: A monomial is an algebraic expression that consists of one term. D consists of 2 terms and is considered a binomial.
The sun subtend an angle at 35degree from the centre of the earth whose distant from the centre of the earth is 382,100km. Find the diameter of the sun
Study the figure attached below:
Answer:
240951.33km
Step-by-step explanation:
For this type of question first we need to draw the figure as shown in the attached file (Figure.1).
Looking at the figure, we can see that triangle ABC is formed by bisecting the angle 35 degree (i.e. if the angle is bisected, it will divide into two equal parts, so 35 degree will divide into two equal parts of 17.5 degree).
As the triangle ABC is a right triangle, so we can use the trigonometric ratios to find the diameter of the sun.
[tex]tan(\theta )= \frac{perpendicular}{Base}[/tex]
In the triangle ABC, perpendicular (opposite side to [tex]\theta[/tex] ) is BC and base (Adjacent side) is AC
[tex]tan(\theta)=\frac{BC}{AC}[/tex]
[tex]\theta[/tex]=17.5 degree
AC=382100km
Putting the values, we get
[tex]tan(17.5)=\frac{BC}{382100}\\ \\BC=tan(17.5)*382100km\\\\BC=0.315*382100km\\\\BC=120475.66km[/tex]
Diameter=d=2*Radius
As BC is the distance from center of the sun, it is the radius, so we can find the diameter if we multiply it by 2.
Diameter of the sun=d=2*120475.66km
[tex]The\ diameter\ of\ the\ sun\ = 240951.33km[/tex]
Final answer:
To find the diameter of the Sun based on its angular diameter and distance from Earth, use the trigonometric function tan to calculate the true diameter, resulting in an approximate value of 865,373 miles.
Explanation:
To find the diameter of the Sun:
Given: Angular diameter = 0.5°, Distance from Earth = 93,000,000 milesCalculate the true diameter using the formula: True Diameter = 2 * Distance * tan(Angular diameter)Plug in the values: True Diameter = 2 * 93,000,000 * tan(0.5°)After calculation, the diameter of the Sun is approximately 865,373 miles.The golden state bridge is 8980 feet long .For a science project , garbriel built a scale model of the bridge . How long is the model if he used the scale.1 millimeters equals 20 feet/
Answer:
449 millimeters.
Step-by-step explanation:
Each millimeter corresponds to 20 feet.
Therefore the length of the model = 8980 / 20 = 449 millimeters.
Answer:
HI! I'VE DONE THIS B4, IT IS 449 MILLIMETERS. DOES ANYONE KNOW HOW TO TURN THE CAPS BUTTON OFF? ANYWAYS, PLZ MARK BRAINLIEST
Step-by-step explanation:
Peter answered 15 questions on a quiz and obtained 29 points. If 3 points were given for each correct answer and one point deducted for each wrong answer, how many questions did Peter answer correctly?
Final answer:
By setting up an equation with x representing the number of correct answers, we find that Peter answered 11 questions correctly on his quiz.
Explanation:
To determine how many questions Peter answered correctly on his quiz, we first need to set up an equation to represent the situation. Let's let x be the number of questions Peter got right, and since he answered 15 questions in total, it means he got (15 - x) questions wrong. Since he gets 3 points for each correct answer and loses 1 point for each wrong answer, we can write the equation as:
3x - (15 - x) = 29
Now, we will solve for x:
3x - 15 + x = 29
4x - 15 = 29
4x = 29 + 15
4x = 44
x = 44 / 4
x = 11
So, Peter answered 11 questions correctly.
Leah gets to paint her room since she bought a new bedspread set. Two gallons of paint covers 800 square feet. How many gallons of paint will Leah need to paint her entire room, which is 1,200 square feet?
Answer:
3 gallons
Step-by-step explanation:
If two gallons of paint covers 800 square feet, 'x' gallons of paints will cover 1200square feet room where x is the number of gallons needed to paint the 1200 square feet room.
Mathematically,
2 gallons = 800sq.ft
x gallons = 1,200sq.ft
x × 800 = 2 × 1200
x = 2 × 1200/800
x = 3 gallons
Therefore Leah will need 3gallons of paint for 1200sq.ft room