The equation to determine the lengths of Zach's and Ginny's cars is Z + G = 30, where Z represents the length of Zach's car and G represents the length of Ginny's car.
In this problem, we are given information about the lengths of model cars being built by Zach and Ginny. We need to determine the lengths of their cars using an equation. Let's break down the problem and establish the equation step by step.
Step 1: Assign variables:
Let's assign variables to represent the lengths of Zach's and Ginny's cars. We can use "Z" for Zach's car and "G" for Ginny's car.
Step 2: Translate the given information into mathematical terms:
We are told that Ginny's car is 2 more than 3 times the length of Zach's car. This can be expressed as:
G = 3Z + 2
Step 3: Formulate the equation using the sum of the lengths:
The problem states that the sum of the lengths of both cars is 30 inches. We can write this as an equation:
Z + G = 30
Step 4: Substitute the value of G from the previous equation:
Using the equation G = 3Z + 2, we can substitute this expression for G in the equation Z + G = 30:
Z + (3Z + 2) = 30
Step 5: Solve the equation:
Now we can solve the equation to find the value of Z. Combining like terms, we have:
4Z + 2 = 30
Next, we can isolate Z by subtracting 2 from both sides:
4Z = 30 - 2
4Z = 28
Finally, divide both sides by 4 to solve for Z:
Z = 28/4
Z = 7
Step 6: Determine Ginny's car length:
To find the length of Ginny's car, we can substitute the value of Z back into the equation G = 3Z + 2:
G = 3(7) + 2
G = 21 + 2
G = 23
Step 7: Verify the solution:
To verify our solution, we can check if the sum of the lengths of Zach's and Ginny's cars is indeed 30. Let's substitute the values we found into the equation Z + G = 30:
7 + 23 = 30
30 = 30
Since the equation is true, our solution is correct.
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Expand and simplity-(x-5)-(2x+7)
Answer:
-3x - 2
Step-by-step explanation:
-(x - 5) ⇒ -x + 5
-(2x + 7) ⇒ -2x - 7
-x + 5 - 2x - 7 ⇒ -3x - 2
multiply by sign:-x+5-2x-7
collect like term:-x-2x+5-7
simplify:-3x-2
so finally the answer is -3x-2Consider an election with three candidates with the following results:
(ACB) (BAC) (CBA) (CAB)
2
5
4
2
a. Is there a majority winner? If not, who is the plurality winner?
b. Who wins the election using the Borda count method? c. Who wins if he or she first eliminates the one with the most last-place votes and then has a runoff
between the other two?
Please help me with this homework
Answer:
$3.09
Step-by-step explanation:
You go to the restaurant and order $137.00 worth of food. You decided to tip the waiter 18%. You also have to pay tax of 6.5% on the original bill. What is the final cost of the meal?
Answer: $1, 615
Step-by-step explanation:
You earn $8.50 per hour and work 30 hours this week. What is the straight time pay?
Answer:
255
Step-by-step explanation:
help me pleaseeeeeee
The slope between (2, 5) and (-3, 4)
Answer:1/5
Step-by-step explanation:
Erin gets her exercise by running. The graph shows the distances she covers in a given amount of time. How many hours does it take for Erin to run 25 miles?
Answer:
C because 25miles is in between 2and 3 hours
(2+3)/2=2.5Two friends, Nayeli and Aiden, had just bought their first cars. The equation y=22.8xy=22.8x represents the number of miles, yy, that Nayeli can drive her car for every xx gallons of gas. Aiden uses 5 gallons of gas to drive 210 miles in his car.
How many miles less does Nayeli's car travel on one gallon of gas than Aiden's car?
Answer:
Step-by-step explanation:
Use the form
a
cos
(
b
x
−
c
)
+
d
to find the amplitude, period, phase shift, and vertical shift.
find the volume of the region bounded above by the paraboloid z=4x^2 3y^2
Therefore, The volume of the region bounded above by the paraboloid z=4x^2+3y^2 is 8π/3. This is obtained by evaluating the double integral using polar coordinates.
Explanation: To find the volume of the region bounded above by the paraboloid z=4x^2+3y^2, we need to integrate the double integral of the function z over the region. The region is defined by the paraboloid z=4x^2+3y^2 and the xy-plane. We can write the double integral as ∬R 4x^2+3y^2 dA, where R is the region in the xy-plane. To evaluate this integral, we need to determine the limits of integration for x and y. The region R is a circle with a radius 1, centered at the origin. Therefore, we can use polar coordinates to evaluate the integral. The limits for r are 0 to 1, and the limits for θ are 0 to 2π. After evaluating the integral, we get the volume of the region to be 8π/3.
Therefore, The volume of the region bounded above by the paraboloid z=4x^2+3y^2 is 8π/3. This is obtained by evaluating the double integral using polar coordinates.
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Each of your eight friends owes you 10$. use integer multiplaction to represent the total amount your friends owe you
Answer:
$80 bucks
Step-by-step explanation:
.......................
Answer:
Width: \(10y^6\)
Length: 7y² + 3
Step-by-step explanation:
Step 1: Factor out 10
\(10(7y^8+3y^6)\)
Step 2: Factor out \(y^6\)
\(10y^6(7y^2+3)\)
According to the question, the width is the monomial (1 term), so that is equal to \(10y^6\). That means the distributed part would be the length (7y² + 3).
Jesse and Janie are playing a game. On the table in front of them, there are 50 coints. They take turns removing some of these coins from the table. At each turn, the person moving can remove either 1,2,3,4,5 or 6 coins (they cannot remove 0 or 7 etc). The person to remove the last coin wins. Suppose Janie is the first player to have a turn. 1) In the subgame perfect equilibrium, Janie begins by taking ______coins.
In the subgame perfect equilibrium, Janie should begin by taking three coins.
To determine Janie's optimal move, we need to work backwards from the end of the game. If there is only one coin left on the table, the next player (Jesse) will have to take it and Janie wins. Therefore, Janie's goal is to force the game to end with only one coin remaining.
If Janie takes one or two coins at the beginning, Jesse can always mirror her move and take the remaining coins on his turn, leaving one coin for Janie and guaranteeing his victory. If Janie takes four, five, or six coins, Jesse can simply mirror her move and force Janie to be the one left with one coin.
Janie should take three coins initially. This move forces Jesse into a losing position since he can only take between one and six coins. No matter how many coins Jesse takes, Janie can mirror his move and leave him with one coin on his turn, ensuring her victory in the subgame perfect equilibrium.
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The mean percent of childhood asthma prevalence in 43 cities is %. A random sample of of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than %? interpret this probability. Assume that %.
In 13.567% of the 30 cities, the mean prevalence of childhood asthma will be higher than 2.5%.
Given that:
X: childhood asthma prevalence
With mean u = 2.22%
and standard deviation σ= 1.39%
To find : Determine the probability that the average prevalence of childhood asthma in a sample of n cities is higher than 2.5%.
Although we are unsure about the distribution of the variable, keep in mind that from n ≥ 30, the sampling distribution can be roughly compared to the normal distribution according to the central limit theorem:
X≈N(μ;σ²/n)
Additionally, compute the requested probability using the standard normal distribution:
P(X>2.5)= 1 - P(X≤2.5)
Determine the Z value given the X value:
Z = (X - u)/ (σ/√n)
Z = (2.5-2.2)/(1.39/√30)
Z = 1.10
Using the Z-tables you have to look for the value of
P(Z≤1.10)= 0.86433
1 - 0.86433= 0.13567
Then P(X>2.5)= 1 - P(X≤2.5)= 1 - P(Z≤1.10)= 1 - 0.86433= 0.13567
So, 13.567% of the 30 cities will have a mean childhood asthma prevalence greater than 2.5%
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round up 28.046 to the nearest hundredth
Answer:
28.05
Step-by-step explanation:
i dont get the question someone help please
Answer: Would love to help,but you did not add a question.
Step-by-step explanation:
when students are tested and the test results are used to place them in a certain category of classes (remedial, advanced, college prep, etc.), this process is called:
Tracking is the practice of testing students and using the results to place them in specific classes (such as remedial, advanced, college prep, etc.).
What is tracking?Tracking in mathematics has become a hot topic in many school systems. By definition, tracking means that students are separated into different levels of courses due to their. mathematical ability and prior performance.The term "tracking" refers to a strategy many secondary schools employ to classify students based on their perceived aptitude, IQ, or levels of achievement. In an effort to match the curriculum and instruction to the students' needs, they are divided into high, middle, and low tracks.Tracking is the most commonly used term for ability grouping, the practice of lumping children together according to their talents in the classroom. On the elementary level, the divisions sound harmless enough: Kids are divided into the Bluebirds and Redbirds.hence,Tracking is the practice of testing students and using the results to place them in specific classes (such as remedial, advanced, college prep, etc.).
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The graph of a function is shown below. What is its range?
O (1, 2, 4)
O (1, 2, 3, 5)
O All real numbers.
O (1, 2, 3, 4)
(1,2,4)
Step-by-step explanation:Range describes the y-values of a graph.
Range
Range is the y-values that a graph covers. Remember that the y-values are found on the vertical axis. If the graph is not continuous, then the values between the points are not included in the range. Similar to the range, the domain of a graph is the x-values that a graph covers. If there is a coordinate point with a y-value, then that y-value should be included in the range.
Finding Range
In order to find the range, we need to find all the unique y-values of the graph. Additionally, the range is given in numerical order. This means starting from the least value and going up to the greatest. The lowest y-value is 1, then 2, and finally 4. Even though there are two points where y = 2, we are only looking for unique values. This means that the range is (1,2,4).
5. calculating the phi-coefficient suppose a researcher is interested in examining the relationship between a person’s gender and whether he or she likes the taste of vegemite (a dark-brown food paste, made from yeast, that is popular in australia). she collects a sample of n
The value of phi-coefficient is -0.2 negative association correlation.
Given that the researcher's data that is shown in attached images.
The completed table is shown below:
Gender Likes the taste of vegemite
0=male 0=no
1=female 1=yes
0 0
0 0
0 1
0 1
0 1
1 0
1 0
1 0
1 1
1 1
Here, the code '0' means 'male' and '1' means 'female'. Also, code '0' means 'Does not like the taste of vegemite' and code '1' means 'likes the taste of vegemite'.
Phi-correlation is the most appropriate correlation here because we are dealing with binary variables in this study.
Phi-correlation coefficient is given by
Ф=(AD-BC)/√((A+B)(C+D)(A+C)(B+D))
Here, by the given informtion A=2, B=3, C=3, D=2
Ф=(2(2)-3(3))/√((2+3)(3+2)(2+3)(3+2))
Ф=(4-9)/√(5×5×5×5)
Ф=-5/√625
Ф=-5/25
Ф=-1/5
Ф=-0.2
Hence, the value of phi-coefficient for the researcher's data that is shown in attached images is -0.2.
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Which proportion could be used to find the length of side b?
A
9
64°
85
9.3
A.
B.
sin 31
9.3
sin 31
9.3
8
Csin 64
b
11
D. Sin 64
9.3
sin 85
b
sin 64
b
sin 85
a
sin 85
b
D sin 85 sin 31
---------- = ----------
b 9.3
How to solve thisWe can use the law of sins
sin B sin A sin C
--------- = ----------- = ----------
b a c
We do not know angle C, but we can calculate it
The angles of a triangle add to 180
A + B + C = 180
64+ 85 + C = 180
149 + C = 180
C = 180-149
C =31
sin B sin C
--------- = ----------
b c
We know B = 85, C = 31, b = unknown and c = 9.3
sin 85 sin 31
---------- = ----------
b 9.3
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a bicycle has 26 inch diameter wheels, the front chain drive with the pedals has a radius of 2.2 inches, and the back dive on the wheel has a radius of 3 inches. how far does the bicycle travel for every rotation of the front chain drive? round to one decimal place.
For every rotation of the front chain drive, the bicycle travels a distance equal to the circumference of the back wheel. To find the distance the bicycle travels for every rotation of the front chain drive, we need to consider the gear ratio and the wheel circumference.
1. Calculate the gear ratio:
Gear ratio = (Radius of front chain drive) / (Radius of back chain drive)
Gear ratio = 2.2 inches / 3 inches
Gear ratio ≈ 0.7333
2. Calculate the wheel circumference:
Circumference = π × Diameter
Circumference = π × 26 inches
Circumference ≈ 81.68 inches
3. Calculate the distance traveled per rotation of the front chain drive:
Distance traveled = Gear ratio × Wheel circumference
Distance traveled = 0.7333 × 81.68 inches
Distance traveled ≈ 59.9 inches
Therefore, the bicycle travels approximately 59.9 inches for every rotation of the front chain drive, rounded to one decimal place.
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if f(x) = 1/2 * x - 1 what is f(- 2x + 1) equal to?
Answer:
f(-2x+1)=-x -1/2
Step-by-step explanation:
f(-2x+1)= 1/2 * ( -2x + 1 ) - 1
f(-2x+1)=-x + 1/2 - 1
f(-2x+1)=-x -1/2
9) You are a contractor and charge $55 for a site visit plus an additional $25 per hour for each hour you spend
working at the site, Write and solve an equation to determine how many total hours you have to work to earn
$555 working at a site.
Okay
The contractor would have to work for 20 hours on the site to earn $555 total pay
What is total cost function?
Total cost function is the sum of the fixed charge, which is fixed cost to the person paying the contractor when the contractor visits the site and charge per hour multiplied by the number of hours spent working
TC=a+bX
TC=total cost=$555
a=fixed charged=$55
b=charge per hour=variable element of contractor's pay=$25
X=number of hours spent working=unknown
$555=$55+$25X
$555-$55=$25X
$500=$25*X
X=$500/$25
X=20
The contractor needs to work for 20 hours in order to earn a total pay of $555
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A tank of water in the shape of a cone is being filled with water at a rate of 12 m/sec. The base radius of the tank is 26 meters, and the height of the tank is 18 meters. At what rate is the depth of
The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.
To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.
To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).
By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.
Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.
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10 fewer than the difference of 8 and w? PLEASE HELP GETS BRAINLY 5 STARS AND A LIKEEEE!!!!!!!!!
Answer:
(8-w)-10
so -w-2
if w is a variable... sorry this answer is just for reference
Step-by-step explanation:
a simple electrical motor has three components: windings, armature, and housing. the three components have reliabilities of 0.9998, 0.9992, and 0.9999. there is no possibility of redundant parts. what is the reliability of the motor? round your answer to four decimal places.
The reliability of a simple electrical motor with three components (windings, armature, and housing) is :
0.9989.
To find the reliability of a simple electrical motor with three components (windings, armature, and housing), we need to multiply the reliabilities of each component. The given reliabilities are 0.9998, 0.9992, and 0.9999.
Multiply the reliabilities of the three components.
Reliability = Windings reliability * Armature reliability * Housing reliability
Reliability = 0.9998 * 0.9992 * 0.9999
Calculate the product.
Reliability ≈ 0.99889988
Round the answer to four decimal places.
Reliability ≈ 0.9989
So, the reliability of the motor is approximately 0.9989.
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(05.02)
Solve the following system of equations: (1 point)
x − 2y = 14
x + 3y = 9
Group of answer choices
(1, 12)
(−1, −12)
(12, −1)
(12, 1)
Can you help me with this question
The value of angle G in the quadrilateral is 98⁰.
What is the measure of angle G in the quadrilateral?
In a quadrilateral, opposite angles are the angles that are opposite to each other when the two diagonals are drawn. Adjacent angles are angles that are next to each other.
One special property of opposite angles of a quadrilateral is that they are equal in measure. This property is known as the "opposite angles of a quadrilateral are equal" theorem.
The value of angle G is calculated as follows;
based on the given shape, angle I is equal to angle G.
m∠I = m∠G = x
x + x + 92 + 72 = 360 ( sum of angles in a quadrilateral)
2x + 164 = 360
2x = 196
x = 196 / 2
x = 98⁰
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In the reading, it states: F∝ r 2
1
What is the interpretation of this equation? A. Gravity is a force that acts as a directly proportional square law with respect to distance. B. Gravity is a force that acts as an inversely proportional law with respect to distance. c. Gravity is a force that acts as an inversely proportional square law with respect to distance. D. Gravity is a force that acts as an directly proportional law with respect to distance. QUESTION 2 What is currently used to test how the constant G has changed over the evolution of the Universe? A. atoms B. type la supernovae c. black holes D. comets QUESTION 3 By the same token as this excerpt, the gravity of the Sun is directed and A. upwards; towards the center of the Sun B. downwards; towards the surface of the Sun c. upwards; towards the surface of the Sun D. downwards; towards the center of the Sun
1. C. Gravity is a force that acts as an inversely proportional square law with respect to distance.
2. B. Type Ia supernovae
3. D. Downwards; towards the center of the Sun
The interpretation of the equations and the correct options for the given questions are as follows:
Question 1:
The equation interpretation is related to gravity. The equation states a relationship between gravity and distance. The correct option is:
C. Gravity is a force that acts as an inversely proportional square law with respect to distance.
Question 2:
To test how the constant G (gravitational constant) has changed over the evolution of the Universe, certain phenomena or objects are used. The correct option is:
B. Type Ia supernovae
Question 3:
Based on the excerpt, the direction of gravity from the Sun is described. The correct option is:
D. Downwards; towards the center of the Sun
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proof by contradiction every integer greater than 11 is a sum of two composite numbers
Proof by contradiction: Every integer greater than 11 is a sum of two composite numbers.
Step 1: Assume the negation of the statement, which is "There exists an integer greater than 11 that cannot be written as a sum of two composite numbers."
Step 2: Let n be the smallest integer greater than 11 that cannot be written as a sum of two composite numbers. This means that all integers greater than n can be written as a sum of two composite numbers.
Step 3: Since n is not composite, it is either prime or 1. If n is prime, then it cannot be written as a sum of two composite numbers because the sum of two composite numbers is composite. If n is 1, then it cannot be written as a sum of two composite numbers because 1 is not composite.
Step 4: Therefore, n cannot be prime or 1. This means that n must be composite. Since n is composite, it can be written as the product of two numbers a and b, where a and b are greater than 1.
Step 5: Since a and b are greater than 1, they must be composite. Therefore, n can be written as the sum of two composite numbers, a and b. This contradicts the assumption that n cannot be written as a sum of two composite numbers.
Step 6: Therefore, the assumption that there exists an integer greater than 11 that cannot be written as a sum of two composite numbers is false. In other words, every integer greater than 11 can be written as a sum of two composite numbers.
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