The required linear function is
f(x) = -2x+ 7
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Let the linear function f(x) = ax + b
f(0) = 7
a [tex]\times[/tex] 0 + b = 7
b =7
f(x) = ax + 7
f(3) = 1
3a + 7 = 1
3a = 1 - 7
3a = -6
a = [tex]-\frac{6}{3}[/tex]
a = -2
The given linear function is
f(x) = -2x+ 7
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Adnan bought
pounds of apples for $0.72 per pound and
pounds of bananas for $1.60 per pound.
a%2Bb=12 [1]
.75a%2B1.05b=10.20 [2]
Use elimination: multiply the first equation by .75 and then compare the two equations (i.e., subtract one equation from the other):
.75a%2B.75b=9
.75a%2B1.05b=10.2
.3b=1.2
3b=12
b=4
ANSWER: He bought 4 pounds of bananas, which means 8 pounds of apples.
CHECK: 8($.75)+4($1.05) = $6+$4.20 = $10.20
If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, what is the statistic said to be?.
The statistic said to be Unbiased Estimator If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated.
What is statistic?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States. On the other hand, a sample statistic is the average income for a sample taken from the United States. Although both figures correspond to the mean income, only one is a statistic.
Here,
The reported statistic is Independent Estimator If the mean of the sampling distribution for a statistic used to estimate a parameter matches the actual value of the parameter being estimated.
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rate?
2) James Bond took 4.5 minutes to complete a Grand Prix circuit when driving at an average speed.
97 mph. How long would it take to complete one circuit driving at a speed of 112 mph.
Answer: 30 meters
Step-by-step explanation:
A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second.
A train takes 16 hours to travel a distance of 35,376 km. Find the distance travelled in one hour if it covers the same distance every hour
Question What is the decibel level of the noise from a motorcycle with intensity 10-2 watts per square inch? Use a logarithmic model to solve. Provide your answer below: 100 dB
The decibel level of the noise from a motorcycle with intensity 10⁻² watts per square inch (W/in²) is equal to 50 dB.
What is sound intensity?In Science, sound intensity can be defined as a measure of the power of a sound wave per unit area. This ultimately implies that, sound intensity is a quantity that is typically be used for measuring the energy of sound and its unit of measurement is Watts per square meter (W/m²) or .
How to calculate the sound intensity level?Mathematically, sound intensity level or decibel level can be calculated by using this formula:
[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]
Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² watts per square inch (W/in²).
Since the intensity of the noise from this motorcycle is 10⁻² W/in², the decibel level (in dB) would be calculated as follows:
Decibel level, β = 10 × log(10⁻²/10⁻¹²)
Decibel level, β = 10 × log(10¹⁰)
Decibel level, β = 10 × 10
Decibel level, β = 100 dB.
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Are the two functions inverse of one another ?
When Alvin woke up in the morning, it was –
9°F. By the afternoon, the temperature had risen to –
2°F.
There is a 7°F difference in temperature between the morning and the afternoon.
What causes the temperature change?A body's level of heat might alter as a result of a temperature shift.To calculate the difference, subtract the final temperature from the initial temperature.Change in temperature now equals -2-(-9) = -2+9=7.As a result, there is a 7°F difference in temperature from morning to afternoon.Alvin awoke in the morning to a temperature of -9°F. The afternoon saw a rise in temperature to -2°F.We need to figure out why the temperature changed from the morning to the afternoon.To learn more about change in temperature refer to:
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Pleas help me find the equation for this chart please
Answer: y = 1/12x
Step-by-step explanation:
(24, 2)
(12, 1)
find slope (y2 - y1) / (x2 - x1)
2 - 1 / 24 - 12
1 / 12
find y intercept
y = mx + b
1 = 1/12(12) + b
1 = 1 + b
b = 0
y = 1/12x + 0
y = 1/12x
A total of 1,043 players signed up for a citywide soccer league. Each team in the league can have up to 18 members. How many teams will be needed?
Answer:
58 teams
Step-by-step explanation:
This is a division problem. There are a total of 1043 players and there is a max number of 18 members per team. 1043 divided by 18 = 57 and a remainder. Because there is a remainder you add one more team for the remaining members.
Answer: 57.9
Step-by-step explanation:
Based on the given conditions, formulate: 1043 / 18
Evaluate the equation/expression: 57.9444
get the result: 57.9444
After rounding: 57.9
Answer: 57.9
A competition mark is worked out by doubling the sum of the middle four scores, then adding the average of the top and bottom scores.
Martha scores: 7 7 6 8 5 9
What is her competition mark?
The required competition mark is given as 60, as of the given condition.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60
Thus, the competition mark is 60.
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please answer the problem in the image :)
question: "The lengths of the three sides of a triangle (in centimeters) are consecutive odd integers. If the perimeter is 45 centimeters, find the value of the shortest of the three side lengths."
The value of the shortest of the three sides of the triangle is 13 cm.
How to find the length of a triangle?A triangle is a polygon with threes sides. The perimeter of a triangle is the sum of the whole three sides.
The lengths of the three sides of a triangle (in centimetres) are consecutive odd integers. The perimeter is 45 cm.
The shortest side of the three sides can be calculated as follows:
let
the first side = x
second side = x + 2
third side = x + 4
Hence,
perimeter = x + x + 2 + x + 4
45 = 3x + 6
45 - 6 = 3x
3x = 39
divide both sides by 3
x = 39 / 3
x = 13
Therefore,
shortest side = 13 cm
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what is m% of n? HII PLS HELP! :0
Answer:SLOPE
Step-by-step explanation:M in a equation is slope
A movie streaming service charges a set fee for
membership each month, plus an additional fee
for the number of movies streamed each
month. If 2 movies are streamed, the cost is
$14 per month, however if 6 movies are
streamed, the cost is $20. Write an equation to
model the cost, y, based on the number of
movies streamed x.
The equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.
What is a linear equation in one variable?
The linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
For the first case:
If 2 movies are streamed, the cost is $14 per month
So the cost = number of movies * cost per movie
y = 2*x
14 = 2x
For the second case:
If 6 movies are streamed, the cost is $20 per month
So the cost = number of movies * cost per movie
y = 6*x
20 = 6x
Hence the equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.
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PLEASE HELP SOON I NEED TO LEAVE TO MY LAB
Answer: 10: 6 is
ration add them 16
Step-by-step explanation:
Find all of the prime numbers between 10 and 20
Answer:
11, 13, 17, and 19!
Step-by-step explanation:
Answer:
11, 13,17 and 19
Step-by-step explanation:
prome numbers are natural numbers that are greater than 1 and not a product of two natural numbers eg 2×5 =10 so it's not a prime number 2×6 or 3×4 =12 it's not also a prime number e.t.c
What is the minimum temperature?
STEM AND LEAF
I will appreciate your help cause my grade is going down :(
7) The minimum temperature is 31⁰F. So, the answer is option B.
What is stem and leaf plot?The frequency of various types of values can be easily observed using a stem and leaf plot, also known as a stem and leaf diagram. This graph displays numerical data that is arranged in chronological order. There is a stem and a leaf for each piece of data.
Each first or second digit of the data value is divided into a stem, and the last digit is represented by a leaf, in a stem and leaf plot, which is represented by a particular table. The stem and leaf plot key is the "|" symbol that is used to indicate the values of the stem and the leaf. In the case of 46, the stem is 4 and the leaf is 6.
7) The minimum value in the stem is 3
And the minimum value in the leaf is 1
So, according to the given key 4|3=43°F
Here | denotes the key symbol.
So, in this solution the minimum value of stem is 3 and the minimum value of leaf is 1
Therefore, it must be 3|1
Hence, from the given key
This can be written as 31⁰F
Therefore, the answer is option B.
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A basketball coach recorded how many shots each of the 30 players at tryouts made in a set of 6
attempts. Here are the results:
The median would lie in the mean of the 15th and the 16th position.
What is median?The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.
The mean (average), mode, and standard deviation are some other descriptive statistics that are frequently contrasted with the median.
Given, the total number of basketball players present (n) = 30
Total number of attempts made = 6
Since there are even number of players present, 30, the location of the median would be n/2 and n/2 + 1 positions.
For 30, the positions would be
= 30/2 and 30/2 + 1
= 15 and 16th position
Hence, the median would lie in the mean of the 15th and the 16th position.
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Mariya is solving the quadratic equation by completing the square.
4x2-20x+3=0
4x2-20x=-3
A(x2-5x)=-3
What is the value of A?
Answer:
A = 4
Step-by-step explanation:
4x2-20x=-3 and A(x2-5x)=-3
Hence:
4x2-20x = A(x2-5x)
4x^2 - 20x = A(x^2 - 5x)
Divide both sides by (x^2 - 5x) to isolate A:
(4x^2 - 20x)/(x^2 - 5x) = (x^2 - 5x) * A/(x^2 - 5x)
A = (4x^2 - 20x)/(x^2 - 5x)
A = (4x(x - 5)) / (x(x - 5)) ==> factor each polynomial
A = (4x) / (x) * (x - 5)/(x - 5)
A = (4x) / (x) * 1 ==> (x-5)/(x-5) = 1
A = (4x) / (x)
A = 4x/x ==> simplify
A = 4
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For a ride on a rental scooter, Kevin paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Kevin's ride was $19.64. For how
many minutes did Kevin ride the scooter?
minutes
Answer:
1 minute, Because per minute is $2, 12 cents
Find the range of the function f(x)=x^2- 6x if the domain is (-7,-2, 1)
The range of the function will be;
⇒ Range = (91, 16, - 5)
What is Domain?The set of all inputs of the function is called Domain of set.
Given that;
The function is,
⇒ f (x) = x² - 6x
And, The domain = (- 7, - 2, 1)
Now,
Since, The function is,
⇒ f (x) = x² - 6x
We know that;
The range of the function gives the value of y.
Here, The domain (x) = (- 7, - 2, 1)
Put x = - 7;
⇒ f (-7 ) = (-7)² - 6 × - 7
= 49 + 42
= 91
Put x = - 2;
⇒ f (- 2) = (-2)² - 6 × - 2
= 4 + 12
= 16
Put x = 1;
⇒ f (1) = (1)² - 6 × 1
= 1 - 6
= - 5
Thus, The range = (91, 16, - 5)
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which graph represents the solution to this system of inequalities? y < -x - 3 y > 2x - 4
The intersection region of every solution in the system of inequalities is the system's solution. Inequality y≤x2 should be graphed first. y=x2 serves as the related equation.
Which point is a solution to the system of inequalities?Get y alone on one side of a two-variable linear inequality (like x and y) before graphing it. Once the inequality sign has been replaced with an equality sign, take into consideration the relevant equation that results. This equation's graph is a straight line.Create a comparable graph for every systemic inequality. The intersection region of every solution in the system of inequalities is the system's solution.Example
Graph the inequalities and solve the system:
y≤x−2y>−3x+5
Inequality yx2 should be graphed first. y=x2 serves as the related equation.
The border line is solid due to the inequality's, which is not a rigid one.
The inequality yx2 should be substituted in for a point that is not on the line, such as (0,0).
0≤0−20≤−2
It's untrue. The point (0,0) is therefore not part of the solution. Subtract from the line's lower half.
To do the same for the second inequality's related equation, y>3x+5, which has a rigorous inequality, draw a dashed line. The half that does not contain the point (0,0) should be shaded because it does not satisfy the inequality at that location.
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A large tree casts a shadow that is 51 feet long. A 6-foot-tall person standing next to the tree casts a shadow that is 4.5 feet long. How tall is the tree?
Answer:
68 feet tall
Step-by-step explanation:
Imagine the shadows for both the tree and the person are set up like right triangles. The length of their shadows are the bases of the triangles, while the actual heights of the tree and person are the heights of the triangle. We can set up proportions since "height of the person" divided by " their shadow's length" should equal "height of tree" divided by "tree shadow length".
Set up a proportion of the person's high height relative to their shadow's length (which is 6/4.5). Set this equation equal to the tree's proportion (which is x/51).
Solve for x.
[tex]\frac{6}{4.5} = \frac{x}{51}\\Isolate x by multiply 51 to both sides\\\\(306/4.5)=x\\68=x[/tex]
The proportion is solved and the height of the tree is A = 68 feet
What is Proportion?The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
Now , we can set up the following proportion:
Height of tree / length of tree's shadow = height of person / length of person's shadow
On simplifying , we get
A / 51 = 6 / 4.5
Now we can solve for A by cross-multiplying and simplifying:
A = 51 x 6 / 4.5
A = 68 feet
Therefore, the tree is 68 feet tall
Hence , the proportion is solved
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Select the correct text.
A spherical ball for a machine was made with a radius of 2 centimeters.
If the ball has a mass of 278.1 grams, which material was used to make the ball?
Copper-8.3 g/cm³
Brass -8.6 g/cm³ Iron - 7.8 g/cm³
The mass of the ball is 278.1 g, the material used to make the ball must be brass which having density of 8.6 g/cm³.
How to find mass of the ball ?To determine the material used to make the ball, we need to first calculate the volume of the ball.
The volume of a sphere with radius r is given by:
V = (4/3) * π * r^3
Plugging in the given values, we get:
V = (4/3) * π * (2 cm)^3
= (4/3) * π * 8 cm^3
= (4/3) * 8π cm^3
= 32π cm^3
We can then use the density of each material (given in g/cm³) to calculate the mass of the ball if it were made of that material:
Copper: 8.3 g/cm³ * 32π cm³ = 266.4 g
Brass: 8.6 g/cm³ * 32π cm³ = 275.2 g
Iron: 7.8 g/cm³ * 32π cm³ = 250.4 g
Since the mass of the ball is 278.1 g, the material used to make the ball must be brass.
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Andre wanted to measure the width of a creek by his camp but cannot get to the other side of the creek. Andre decided to construct two triangles to determine the width of the creek indirectly. Sighting the position of a tree on the opposite bank of the creek and placing 4 wooden pegs at point N, O, P, and Q as shown in the figure, such that MN is perpendicular to NP, NP is perpendicular to PQ, and O is the midpoint of NP. Andre claims that triangle MNO and triangle QPO are congruent.
Part A: Provide a valid argument, using geometry theorems or postulates, to validate
Andre's claim that AMNO and APQO are congruent.
Part B: Which segment should Andre measure to determine the width of the creek? Explain why.
Use the space below to answer Parts A and B of the question above. Use the CER (Claim, Evidence, Reasoning) method as a guide to your response. You may also upload a screenshot of your work
Triangles MNO and QPO are congruent.
What is congruent triangle?When two triangles are congruent, their three sides and their three angles match precisely.If there is a turn or a flip, the equal sides and angles might not be in the same place, but they are still present.Formally speaking, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions like translation, rotation, and reflection. Therefore, if two separate plane figures on a piece of paper can be cut out and then perfectly fitted up, they are congruent.It is given that
O is the midpoint of NP,
NP is perpendicular to MN, and
NP is perpendicular to PQ.
When two lines intersect at a specific point, the opposite angles formed in this situation are equal.Then ∠MNP =∠QPO=90°∠MON=∠QOP∠MOP=∠QONTherefore, Triangles MNO and QPO are congruent.
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Help pls explain!!!!!!!!!!!!
The exact value of the logarithmic expression 12 · ㏒₃ [z⁷ / (y⁵ · t²)] is equivalent by logarithm properties to -711 / 5.
How to determine the result of logarithmic expression by logarithmic properties
In this question we must determine the exact value of a logarithmic expression by means of logarithm properties, which are described below:
Logarithm of a product
㏒ (a · b) = ㏒ a + ㏒ b
Logarithm of a division
㏒ (a / b) = ㏒ a - ㏒ b
Logarithm of a power
㏒ aⁿ = n · ㏒ a
Now we proceed to determine the exact value of the expression:
12 · ㏒₃ [z⁷ / (y⁵ · t²)]
12 · [㏒₃ z⁷ - ㏒₃ (y⁵ · t²)]
12 · (㏒₃ z⁷ - ㏒₃ y⁵ - ㏒₃ t²)
12 · (7 · ㏒₃ z - 5 · ㏒₃ y - 2 · ㏒₃ t)
12 · (7 · 7.74 - 5 · 11.03 - 2 · 5.44)
-711 / 5
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Ruby and her children went into a movie theater and she bought $42 worth of bags of popcorn and drinks. Each bag of popcorn costs $6 and each drink costs $4. She bought a total of 8 bags of popcorn and drinks altogether. Determine the number of bags of popcorn and the number of drinks that Ruby bought.
Answer:
5 bags of popcorn
3 drinks
Step-by-step explanation:
Let's set up a system of equations!
Let p equal the number of bags of popcorn and d be the number of drinks.
We know Ruby bought 8 total, so we know [tex]p + d = 8[/tex]. We also know that she spent $42 total, so we can multiply their respective costs by the number to set up another equation: [tex]6p+4d=42[/tex]. We have our system of equations now!
Let's use substitution to solve this. From the first equation, subtracting p from both sides gives us that [tex]d=8-p[/tex]. We can plug this into our second equation to solve for p. Plugging in this for d gives us [tex]6p+4(8-p)=42[/tex]. Multiplying through and then combining like terms results in [tex]32+2p=42[/tex]. We then can subtract 32 from both sides and divide us by 2, which gives us that p = 5.
Now we solve for d! We can plug in the value of p into the equation [tex]p+d=8[/tex], to get that d = 3. To check our work, we can plug these values into the other equation, which gives us [tex]6*5 + 4*3 = 42[/tex]. This is true, so our values are correct!
Thank you! Feel free to contact me with any questions about my answer. I hope this helps!
Adam currently run about 20 mile per week, and he want to increae hi weekly mileage by 10%. How many mile will Adam run per week? He will run mile per week
The sum of two numbers is 33. One number is 2 times as large as the other. What are the numbers?
six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. of the six countries, if country a sent the second greatest number of representatives, did country a send at least 10 representatives?
One of the six countries sent 41 representatives to the congress.
What, in the simplest words, is the Congress?
The Congress is our country's legislative body, which drafts our laws. The United States Senate and the United States House of Representatives are the two branches of Congress.
Each state has two U.S. Senators and a minimum of one U.S. Representative; the number of U.S. Representatives that can be elected depends on the number of citizens in the state.
(1) One of the six countries sent 41 representatives to the congress
(2) Country A sent fewer than 12 representatives to the congress
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Solve each system by elimination: 4x-7y=10 3x+2y=-7
Using the elimination method, the solution to the system of equations is as follows:
x = 19 / 13 and y = - 74 / 13
How to solve system of equation?System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.
Let's use the elimination method to solve the system of equations as follows:
The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Therefore,
4x - 7y = 10
3x + 2y = -7
multiply equation(ii) by 3.5
4x - 7y = 10
10.5x - 7y = 24.5
subtract equation(i) from equation(ii)
6.5x = 14.5
x = 14.5 / 6.5
x = 145 / 65
x = 19 / 13
Let's find y
3(19 / 13) + 2y = -7
57 / 13 + 2y = -7
2y = - 7 - 57 / 13
2y = -91 - 57 / 13
2y = - 148 / 13
cross multiply
26y = - 148
y = - 148 / 26
y = - 74 / 13
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