[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{7}}} \implies \cfrac{ -4 }{ -4 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{ 1}(x-\stackrel{x_1}{7}) \\\\\\ y-18=x-7\implies {\Large \begin{array}{llll} y=x+11 \end{array}}[/tex]
You are running a fuel economy study. One of the cars you find is blue. It can travel 44 1/2 miles on 1 1/4 gallons of gasoline. Another car is red. It can travel 28 4/5 miles on 4/5 gallon of gasoline. What is the unit rate or miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
The unit rate or miles per gallon for Blue car is 35.6 miles and for Red car is 36 miles. Red car could travel the greater distance on 1 gallon of gasoline.
44 1/2 = 44 + 1/2
= (88+1)/2
= 89/2
1 1/4 = 1 + 1/4
= (4+1)/5
= 5/4
28 4/5 = 28 + 4/5
= (140+4)/5
= 144/5
Distance blue car covers in 5/4 gallons of fuel = 89/2
Distance blue car covers in 1 gallon of fuel = (89/2) / (5/4)
= (89*4)/(2*5)
= 178/5
= 35.6
Distance red car covers in 4/5 gallons of fuel = 144/5
Distance red car covers in 1 gallon of fuel = (144/5) / (4/5)
= (144*5)/(4*5)
= 144/5
= 36
Hence, Red car could travel the greater distance on 1 gallon of gasoline by 0.4 miles.
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Beth tells her math teacher that the following set of ordered pairs IS a function. Is Beth correct?
Why or why not?
(2,3) (3,8) (2,4) (5,7)
Answer:
No, Beth is not correct. One of the x-values, 2, corresponds to two y-values.
If The Area Of The Smaller Pentagon Is 36, What Is The Area Of The Larger Pentagon?
A) 27
B) 52
C) 64
D) 144
pls help ty :')
Answer:
64
Step-by-step explanation:
16 ÷ 12 = 1.33 (rounded to 2 decimal places)
1.33 = scale factor
1.33² = area scale factor
1.33² × 36 = 64 (rounded to a whole number)
the table shows the heights of players in a basket ball team. work out the mean height of the team round your answer to 1 decimal place. new player joins the team and raises the mean average height to 201 cm. work out the height of this new player (height) 198,199,200,201,202) (frequency) (1,3,2,5,2)
The mean height of the team rounded to 1 decimal place is 200.0.
The height of this new player is 206.
What is mean Average?
The mean average, of a data set is the sum of all the numbers divided by the total number of values.
Formular for calculating mean Average:
Mean Average = {Sum of all the values} ÷ {Total numbers of values}
From the question the height of the players are as follows:
(height) 198,199,200,201,202)
a) Mean Average =(198 +199 +200 +201 +202)
5
=1000
5
=200.0
b) The new player joins the team to make the Mean Average 201. hence the height of the new player will be calculated using:
Mean Average = {Sum of all the values} ÷ {Total numbers of values}
201 =(198 +199 +200 +201 +202 + x )
6
201 = 1000+ x
6
crossmultiply to solve for X:
201 *6 =1000+ x
1,206 = 1000+ x
making x subject of the formular we have:
x = 1,206 - 1000
x = 206
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10x^2y divided by 5xy
The value of Indices 10x^2y÷ 5xy is 2x^(2y-1)×y^-1
What is Indices?An index is a small number that tells us how many times a term has been multiplied by itself. The plural of index is indices. Below is an example of a term written in index form: 4^3. 4 is the base and 3 is the index.
10x^2y = 10x^2(y)
dividing 5xy with 10x^2y
the coefficient 5 will divide 10 to give 2
therefore the value is
2x^2y÷ xy
using law of INDICIES
the value will be 2x^(2y-1)×y^-1
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what type of statistics has been used in the following: descriptive or inferential the national center for health statistics, part of the centers for disease control and prevention has reported about 60 births per every 1,000 women ages 15 to 44 years.
In the situation, 60 births per every 1,000 women ages 15 to 44 years, the statistics used is descriptive statistics.
What is descriptive statistics?
Suppose there is a population and suppose there is a sample of the population. If the inference is made on the sample alone and not on the whole population, the statistics used is called descriptive statistics.
Here, the sample is 60 births per every 1,000 women ages 15 to 44 years.
And the inference is made only about those 60 births per every 1,000 women ages 15 to 44 years, and not on the whole population of women aged between 15 to 44 years. So the statistics used in this case is descriptive statistics.
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When baking bread using yeast, the typical recipe suggests 8 grams of yeast for every 500 grams of flour. What is the constant of proportionality for this relationship that is greater than 1? What is the constant of proportionality for this relationship that is less than 1?
Solving the Question
To find the constant of proportionality of a given relationship, divide the given ratios:
8 grams of yeast for every 500 grams of flour
⇒ 8/500
⇒ 0.016
We can find the constant that is greater than 1 by reversing the values:
500 grams of flour for every 8 grams of yeast
⇒ 500/8
⇒ 62.5
AnswerGreater than 1: 62.5
Less than 1: 0.016
Exam-style P is the point with coordinates (5, 7). Q is the point with coordinates (x, 15).
The gradient of line PQ is 2. Work out the value of x.
By using the formula for the gradient, we can solve a simple equation to find that the value of x is 9.
How to find the value of x?For a segment whose endpoints are:
P = (x₁, y₁) and Q = (x₂, y₂)
The gradient of the line PQ is:
G = (y₂ - y₁)/(x₂ - x₁)
So it is like the slope of a linear equation.
In this case, the endpoints are:
P = (5, 7)
Q = (x, 15)
And the gradient is equal to 2, so we have G = 2, then we can write the equation:
2 = (15 - 7)/(x - 5)
We can solve this to get:
2*(x - 5) = (15 - 7)
2x - 10 = 8
2x = 10 + 8
2x = 18
x = 18/2 = 9
The value of x is 9.
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12. 9/11 = ?/22
OA. 18
OB. 4
OC. 9
OD. 12
Answer:
18
Step-by-step explanation:
to make the 11 denominator turn into 22 they had to multiply by 2
So we multiply the numerator by 2 too
9x2=18
Hopes this helps please mark brainliest
Answer:
If you would like to solve the equation 9/11 = x/22, you can calculate this using the following steps:
Steps to find ?
9/11 = x/22 /*22
x = 9/11 * 22
x = 18
The correct answer should be 18 through my calculations
Each truck holds 22. 5 cubic yards of gravel one cubic yard of gravel weighs 1.48 tons. Gravel will be placed in containers that hold 11. 1 tons of gravel. How many containers are these sides are needed to hold all grandma for one truck?
The number of containers that are needed to hold all the gravel in one truck is 3.
How many containers are needed?The first step is to convert the capacity of the truck from cubic yards to tons. In order to do this multiply the unit of conversion by the capacity of the truck in cubic yards.
Multiplication is the mathematical process used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.
1 cubic yards = 1.48 tons
1.48 x 22.5 = 33.3 tons
The next step is to determine the number of containers that can be on the truck. To do this, divide the converted capacity of the truck by the capacity of each container.
Division is the mathematical operation that is used to determine the quotient of two or more numbers. The sign that is used to represent division is ÷.
Number of containers = total capacity of the truck in tons / capacity of one container
Number of containers = 33.3 / 11.1 = 3 containers
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Cube A has a mass of 81 g.
Cube B has a mass of 128 g.
Work out
the density of cube A: the density of cube B
Give your answer in the form a: b, where a and b are integers.
The ratio of the density of cube A to the density of cube B as required in the task content is; 81 : 128.
What is the ratio of the density of cube A to the density of cube B?It follows from the task content that the ratio of the density of cube A to cube B is to be determined.
Recall that the density of an object is given as its mass to volume ratio.
Therefore, given that the volumes are equal; it can be inferred that the density and mass are directly proportional.
Ultimately, the required density ratio can be estimated from the given masses as;
Density of A : Density of B = 81 : 128.
Consequently, the required ratio is; 81 : 128.
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a pharmaceutical company is interested in comparing four brands of sleep medication to see which brand is best at relieving sleep pattern symptoms, primarily insomnia. the participants are 80 people with sleep pattern symptoms. they are randomly assigned to four groups of 20 participants. each group receives one of the four brands of sleep medication. the improvement in the sleep pattern of the 80 participants is recorded 6 weeks after taking the medication and the average improvement is compared among the four treatment groups. what are the factor(s) and level(s) of this scenario? the factor is the . the levels are the
Answer:
The factor is the sleep medication
The levels are the 4 different treatments, or medications
Step-by-step explanation:
The half-life of a radioactive iotope i the time it take for a quantity of the iotope to be reduced to half it initial ma. Starting with 115 gram of a radioactive iotope, how much will be left after 3 half-live?
14.375 grams of the radioactive isotope will be left after 3 half-lives.
The initial mass of the isotope = 115 gm
after each half-life, the amount of the isotope is reduced to half
therefore,
after the first half-life, the mass of the isotope will become = 115/2
= 57.5 gram
now after the second half live, the mass will again be reduced to half of the previous mass = 57.5/2
= 28.75 gram
similarly, after the third half-life, the mass will be half of the previous mass = 28.75/ 2
= 14.375 gram
OR
simply we can write that
weight after 3 half-lives will be = 115/ 2³
= 115 / 8
= 14.375 grams.
So the mass after 3 half-lives is 14.375 grams.
A risky form of a chemical element that releases radiation as it breaks down and will become extra stable. Radioisotopes may additionally arise in nature or be made in a laboratory. In medication, they may be used in imaging exams and in treatment. additionally known as a radionuclide.
Atoms of equal detail with extraordinary numbers of neutrons are known as isotopes. Many elements have one or extra isotopes which might be radioactive. Their nuclei are risky, so they destroy down, decay, and emit radiation.
whilst utilized in cautiously controlled clinical programs, radioactive isotopes are safe and no longer almost as frightening as we first imagined. The radiation from those isotopes has a quick half of lifestyles and handiest give off low stages of radiation. Radioactive isotopes are not constantly risky, though. a few most effective ones supply tiny amounts of radiation. There are radioactive isotopes in nature all around us. maximum of them cause us very little damage.
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if the numbers in the brackets go together in a certain way, find the missing number.
(1,2) (2,5) (3,10) (?,362)
a. 4
b. 10
c. 15
d. 19
e. none of these
The missing number in the bracket is 19. The correct option is d. 19
Determining the missing numberFrom the question, we are to determine the missing number in the bracket.
The given sequence is
(1,2) (2,5) (3,10) (?,362)
Now, to determine the missing number, we will study the given sequence.
Let the missing number be x
From the sequence, we can observe that
1² + 1 = 2
2² + 1 = 5
3² + 1 = 10
and
x² + 1 = 362
Now, we will solve the equation for x
x² + 1 = 362
Subtract 1 from both sides of the equation
x² + 1 - 1 = 362 - 1
x² = 361
Therefore,
x = √361
x = 19
Hence, the missing number is 19
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The balance in an interest-bearing account is modeled with a continuous function over time.
Which of the domain choices is a possibility?
A. Real numbers greater than 0
C. Integers
Whole numbers
D. Natural numbers
The domain choice that is a possibility is A. A. Real numbers greater than 0.
What is a continuous function?A continuous function in mathematics is one in which a continuous variation of the argument causes a continuous variation of the function's value. This means that there are no abrupt changes in value, which are referred to as discontinuities.
Option A: Real numbers greater than zero:
Because real numbers are continuous functions, the greater than zero part of them can be used to represent the balance sheet.
Option B: Use only whole numbers: It is not possible.
Whole numbers are discrete, not continuous, and thus cannot represent decimal points.
Option C: Integers: Invalid
Because integers are discrete rather than continuous, they cannot represent decimal points.
Natural numbers are not an option.
Natural numbers, like whole numbers, are discrete rather than continuous and cannot represent decimal points.
In conclusion, the correct option is A.
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Mason was recently hired for a job with an annual income of $18,000. Using the federal income rate of 15%, what amount should Mason expect to pay in federal income tax?
Answer:
$2,700
Step-by-step explanation:
15% of $18,000 = 0.15 × $18,000 = $2,700
(10x-27)=7x
find b
i need help
Answer:
x = 9
Step-by-step explanation:
Apparently, you want the solution to (10x -27) = 7x.
SolutionSubtract 7x from both sides to get ...
3x -27 = 0
Divide by 3, and you have ...
x -9 = 0
Add 9 to show the value of x:
x = 9
The solution to the given equation is x=9.
__
Additional comment
There is no information here that relates the given equation to b, so we cannot help you find b.
Alang and his children went into a grocery store that sells apples for $2 each and peaches for $0.50 each. Alang has $20 to spend and must buy a minimum of 16 apples and peaches altogether. If xx represents the number of apples purchased and yy represents the number of peaches purchased, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities has been solved graphically and one possible solution is buying 4 apples and 12 peaches.
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of apples purchased and number of peaches purchased by Alang and his children, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of apples purchased.Let the variable y represent the number of peaches purchased.Since apples for $2 each and peaches for $0.50 each, the cost of fruits is given by:
2x + 0.5y ≤ 20
Also, they must buy a minimum of 16 apples and peaches altogether:
x + y ≥ 16
Therefore, a possible solution when x = 4 is given by:
x + y ≥ 16
4 + y ≥ 16
y ≥ 16 - 4
y ≥ 12
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Find the value of each variable. a,b,c,d,e
Answer:
a - 67
b - 58
c - 125
d - 23
e - 90
Step-by-step explanation:
Solve for b first
90 - 32 = 58
Then you can solve for a
180 - 58 - 55 = 67
Now solve for c
180 - 55 = 125
Now you can solve for d
180 - 125 - 32 = 23
e is equal to 32 + b, so it is 90.
Geometry Homework Question
According to the given triangle, ΔBCE ≅ ΔCBD is proved.
Triangle:
The three-sided polygon that consists of three edges and three vertices is know as triangle.
Given,
Here we have the triangle and we need to prove the ΔBCE ≅ ΔCBD.
Let us consider ABC be the triangle with sides BC, AC, AB add the opposite angles A, B, C being in length equal to a, b, c respectively.
Here they draw a perpendiculars AD, BE and CF from A, B, C to opposite sides meeting sides BC, AC and AB at D, E, F respectively.
So, here we take the ΔCBD and ΔBCE,
Then the
∠D = ∠E = 90°
So, the Side BC = Side BC and the Side BD = Side CE.
From this relation, and based one the concept of RHS Congruence Criterion
We have identify that, the Corresponding Angle Congruence Test
∠DCB = ∠EBC
Therefore, the ΔBCE ≅ ΔCBD is proved
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Jina will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $49.98 and costs an additional $0.15 per mile drive
The second plan has an initial fee of $43.98 and costs an additional $0.19 per mile driven. How many miles would Jina need to drive for the two plans to cost the same?
Answer:
150 miles
Step-by-step explanation:
Jina wants to know the number of miles driven that would make the cost of two rental plans the same. One costs $0.15 per mile plus $49.98; the other costs $0.19 per mile plus $43.98.
Difference in costsThe difference in cost between the to plans for m miles driven is zero when ...
(0.15m +49.98) -(0.19m +43.98) = 0
-0.04m +6.00 = 0 . . . . . . . . simplify
m -150 = 0 . . . . . . . . . . . . divide by -0.04
m = 150 . . . . . . . . . . . . . add 150
Jina would need to drive 150 miles for the two plans to cost the same.
how many triangles can be constructed with the side lengths of 5 inches, 8 inches, and 20 inches
Answer:
60
Step-by-step explanation:
5 x8 = 40 40 + 20 = 60
50 PTS!!!!! NEED ANSWER WITHIN 5 MINS!!!!!!
Select the correct answer.
y - 6 = 4(x - 4)
Which of the following shows a graph of the equation above?
The graph of the linear function y - 6 = 4(x - 4) is the bottom right graph.
What is a linear function?The point-slope representation of a linear function is given as follows:
y - y* = m(x - x*).
In which the coefficients of the equation are defined as follows:
m is the slope of the linear function, determining the rate of change of the output variable y relative to the input variable x.(x*, y*) are the coordinates of the point of the function.In this problem, the equation is:
y - 6 = 4(x - 4).
From this equation, the slope is of:
m = 4.
This means that the linear function is increasing, and thus, both the left graphs are not correct.
The coordinates of the point that the function passes through are given as follows:
(4, 6).
The only function that passes through this point is the bottom right function, hence it is the correct graph of y - 6 = 4(x - 4).
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Find the surface area and volume of each triangular prism (base is a right triangle).
triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft
The surface area of the triangular prism be 108 ft²
The volume of the triangular prism be 48 ft³.
Given, a triangular prism (base is a right triangle).
Triangle legs are 3 ft and 4 ft, hypotenuse is 5 ft, height of prism is 8 ft.
Now, the surface area of the triangular prism is,
Surface Area = 2×Area of the base triangle + Side rectangle 1 +Side rectangle 2 + Side rectangle 3
Surface Area = 2×(1/2×3×4) + 5×8 + 3×8 + 4×8
Surface Area = 12 + 40 + 24 + 32
Surface Area = 108 ft²
Now, Volume of the triangular prism be,
Volume = Area of the base triangle × height
Volume = 1/2×3×4×8
Volume = 48 ft³
Hence, the surface area of the triangular prism be 108 ft²
and the volume of the triangular prism be 48 ft³.
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Derive the sampling distribution for the sample variance using the distribution above: 0.5 K 0.12 Question 10: Find the value of J (probability of the sample mean when $2 = 0) 0.12 0.5 0.38 0.24 ) Question 11 1 pts Derive the sampling distribution for the sample variance using the distribution above. 0.5 K 0.12 Question 11: Find the value of K (probability of the sample mean when g2 0.5) 0.12 0.5
J and K have values of 0.38 and 0.50, respectively with sampling distribution for the sample variance.
Given data;
The sampling distribution for the sample variance using the distribution;
(I) To find the value of J,
(II) To find the value of K,
We know;
⇒ ∑P(s²) = 1
⇒ J + K + 0.12 = 1
J + K = 0.88
K = 0.88 - K
Now K = 0.5;
J = 0.88 - 0.5
= 0.38
Therefore, the values of J and K are 0.38 and 0.50 respectively.
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Need help asap. Simplify the expression 6/c+4/c^2 show work
By taking a common denominator, we can find out that the simplified expression of the given expression is [tex]\frac{6c+4}{c^{2} }[/tex] .
The given expression is -
[tex]\frac{6}{c}+\frac{4}{c^{2} }[/tex] ---- (1)
We have to simplify the expression.
From equation (1), we have the given expression as -
[tex]\frac{6}{c}+\frac{4}{c^{2} }[/tex]
Establishing common denominator [tex]c^{2}[/tex], we have
[tex]\frac{6c}{c^{2} }+\frac{4}{c^{2}}[/tex]
Combining the numerator and common denominator, we have
[tex]\frac{6c+4}{c^{2} }[/tex]
Thus, the simplified expression of the given expression is [tex]\frac{6c+4}{c^{2} }[/tex] which is obtained by taking a common denominator.
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When an object (with negligible wind resistance) is dropped, its height, h, in feet at a certain
time is given by the model h = - 16t+s where s is the height from which the object was dropped and t
is the number of seconds it has fallen. Find the number of seconds it takes for such an object to fall to the
ground (height = 0) from a height of 800 feet.
The number of seconds it takes for such an object to fall to the
ground from a height of 800 feet is 50 seconds
According to the question,
When an object (with negligible wind resistance) is dropped, its height, h, in feet at a certain time is given by the model
h = - 16t+s
where s is the height from which the object was dropped
t is the number of seconds it has fallen
We have to find the number of second it takes to reach ground when fall from height 800 feet
given,
s = 800
h = 0 (ground height = 0)
using the model h = - 16t+s
0 = -16t + 800
800 = 16t
t = 800/16
t = 50 seconds
Hence, the object will take 50 seconds to reach ground when drop from 800 feet
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the great pyramid of cheapos is a square based pyramid
The height of the pyramid is 99.1875 meters when the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.
Given that,
The Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.
We have to find what would the height be if you gave the base sides of 280m using the same material.
We know that,
Volume of Great Pyramid of Cheops = Volume of the pyramid with the base sides of 280m
Volume of Great Pyramid of Cheops is 1/3×(side of the base)²×(height of the pyramid)
Side of the base is 230 meters.
Height of the pyramid is 147 meters.
Volume of the pyramid with the base sides of 280m is 1/3×(side of the base)²×(height of the pyramid)
Side of the base is 280 meters.
Height of the pyramid is h meters.
Volume of Great Pyramid of Cheops = Volume of the pyramid with the base sides of 280m
1/3×(230)²×(147)=1/3×(280)²×h
h = 99.1875 meters.
Therefore, the height of the pyramid is 99.1875 meters while the Great Pyramid of Cheops has a square base, 230-meter-long sides, and a height of 147 meters.
The complete question is:
The Great Pyramid of Cheops is a square-based pyramid, the base has sides of 230m, and the height is 147m.
Using the same material, what would the height be if you give the base sides of 280m.
Please give the answer to the nearest meter.
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Name the object below.
Answer:
Answer option C
Step-by-step explanation:
it is a line that ends so it’s C
*NEED ANSWER ASAP* A bicycle store costs $1950 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $90. How many bicycles must the store sell each month to break even?
At a profit of $30 per bike and $1950 operating cost per month the store needs to sell 65 bikes to break even.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The store pays an average of $60 per bike. The average selling price of each bicycle is $90.
∴ The profit per bike the bicycle store make is $(90 - 60) = $30.
Also, the bicycle store costs $1950 per month to operate,
Assuming no. of bikes the store needs to sell to break even is x.
∴ 30x = 1950.
x = 195/3.
x = 65.
The store needs to sell 65 bikes to break even the cost.
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