Considering the expression of a line, the slope intercept form is y= -x+2.
What is a linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.This is known as the slope-intercept form. This form is one of the most common forms used to represent the equation of a line and can be used to find the equation of a line when given the slope of the straight line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis).
Slope intercept form in this caseIn this case, the line is x+y=2. Expressed in the form y = mx + b, you get:
y= 2 -x or y= -x +2
Finally, x+y=2 in slope intercept form is y= -x+2.
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the radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60, how many centimeters does it move? express your answer in terms of pand then round to two decimal places.
The radius of a wheel rolling on the ground is 80 centimeters. if the wheel rotates through an angle of 60. Therefore, It move to 84 cm.
Circumference Of Circle:
The total length of the circle boundary. The circumference of a circle is the product of the constant π and the diameter of the circle. A person walking across a circular park or a circular table needs this measure of circumference. The circumference is a length value and its units are the same as the length units. A circle is a round closed figure with all endpoints equidistant from a fixed point called the center.
The formula for the circumference of a circle is expressed using the values of the circle's radius 'r' and 'pi'. It is represented by the equation of circumference = 2πr. Using this perimeter formula, if you don't have a value for the radius, you can use the diameter to find it. To calculate the circumference is to use the formula circumference = π × diameter.
If you need to calculate the radius or diameter, consider the circumference of a circle and use the following formula:
Radius = circumference/2π
Now,
According to the Question:
If the radius is 80cm
and, the circumference is 2×π×80cm.
If the wheel rotates by 60° then a fraction 60/360 (= 1/6) of the circumference moves over the ground.
Therefore, the distance moved is
[tex]\frac{2*\pi*80 }{6}[/tex]
= 83.77580
≈ 84 cm.
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a roast removed from an oven has an internal temperature of 160f and it is left to sit at room temperature, which is 72f. after 8 minutes the internal temperature of the roast has dropped to 155f. the roast is ready to eat when its temperature has dropped 150f. how long does the roast need to sit before it is ready to be eaten?
The roast needs to sit 116 minutes before it is ready to be eaten.
Let T(t) = temperature after t minutes
By Newton's Law of Cooling, T(t) = 75 + (185-75)e^kt = 75 + 110e^kt
Newton's law of cooling states that the rate of change of temperature of an object is directly proportional to the difference in temperature between the object and its surroundings. Mathematically, it can be expressed as:
dT/dt = k(T - T0)
Where:
dT/dt is the rate of change of temperature (in degrees per time unit, such as degrees per second)
k is the cooling constant (in units of 1/time), which is a measure of how quickly an object cools down and depends on the properties of the object and its surroundings
T is the current temperature of the object (in degrees)
(a). T(30) = 75 + 110e^30k = 150
⇒110e^30k = 75
⇒e^30k = 0.681818
⇒30k = ln(0.681818)
⇒k = -0.0127664
We know, T(t) = 75 + 110e^-0.0127664t
So, T(45) = 75 + 110e^-0.0127664(45) ≈ 137°
(b). T(t) = 100 when 75 + 110e^-0.0127664t = 100
⇒ e^-0.0127664t = 0.2272727
⇒-0.0127664t = ln(0.2272727)
⇒t ≈ 116 minutes
Therefore, The roast needs to sit 116 minutes before it is ready to be eaten.
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How do you calculate the longest side of a triangle?
The longest side of the given triangle can be calculated by using the cosine rule: b² = a² + c² - 2(ca)(cos B) where 'b' represents the longest side of the triangle opposite to largest angle B.
As given in the question,
Let us consider a triangle ABC,
Side opposite to ∠A = a
Side opposite to ∠B = b
Side opposite to ∠C = c
By calculating the measure of the angles of the triangle using given measures.Identify the measure of the largest angle.Side opposite to the largest angle is longest side.Let angle B be the largest angle then 'b' is the longest side.
To calculate the measure of the longest side using given measure apply :cosine rule :
b² = a² + c² - 2(ca)(cos B)
Therefore, to get the measure of the longest of a triangle apply cosine rule : b² = a² + c² - 2(ca)(cos B) where 'b' represents the longest side.
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. what is the probability that the clock stops exactly 5 hours from the start of the 24 hour period? b. what is the probability that the clock stops within the 24 hour period? c. what is the probability the clock stops somewhere between 6 and 12 hours from the start of the 24 hour period? d. what is the probability the clock stops somewhere between 20 and 24 hours from the start of the 24 hour period?
On solving the provided question, we can say that the, probability P( 24 period hour) = 5/24
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
here,
E1 = stops at 5 clock
E2 = start at 24 hours
P( 24 period hour) = 5/24
the, probability P( 24 period hour) = 5/24
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CLASS 10 CBSE
PLS ANSWER ASAP
from a solid cylinder whose height is 15 cm and the diameter is 16 cm a conical cavity of the same height and same diameter is hollowed ou
t find the total surface area of remaining solid
The total surface area of the remaining solid is 443.14cm2
What drives your use of surface area?A three-dimensional object's surface area is the sum of all of its faces. Real- world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.
Here,
Given:
h = 15, r = 8cm
Slant height of cone
1 = r2+h2 = (8)2 + (15)2 = 17
Total Surface Area = Curved Surface area of Cylinder + Curved Surface area of Conical Part + Area of Circular
=2arh+arl+πr2
=2(3.14)(8) (1.5) + (3.14) (8) (17) + (3.14)(17)2 =443.14cm2
Therefore , the solution of the given problem of surface area comes out to be 443.14cm2.
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work out the area of this shape
Answer:
80
Step-by-step explanation:
96-16
we have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this?
126 number of ways we can arrange the men, women in order to committee with 2 women and 2 men ,the combination is explained below as
We can use the combination formula to find out the number of ways to choose 2 women and 2 men from a group of 4 women and 5 men.
as we know the formula for combination as :
C(n ,k) = n! / (k!(n-k)!)
where n is the total number of people, k is the number of people we want to choose, and ! denotes factorial to find the number of combinations (i.e. the product of all integers up to that number, e.g. 4! = 432*1 = 24).
In this case, to choose the number of individuals as = 4 + 5 = 9 and k = 2 + 2 = 4. So, the number of ways to choose the committee is:
C(9,4) = 9! / (4!(9-4)!) = 126 ways
Hence the number of ways to choose committee is 126 ways.
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our water polo team has 15 members. i want to choose a starting team consisting of 7 players, one of whom will be the goalie (the other six positions are interchangeable, so the order in which they are chosen doesn't matter). in how many ways can i choose my starting team?
you can choose my starting team in equation of 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7 x 5 x 4 x 3 x 2 = 2520 ways.
7 x 6 (choose 7 players from 15) x 5 x 4 x 3 x 2 x 1 (7 players in any order) = 7 x 5 x 4 x 3 x 2 (7 players in any order, ignoring the goalie)
= 2520 ways.
In order to figure out how many ways I can choose my starting team, I can use a combination equation. Start by taking the number of players (15) and subtracting the number of players I need for the starting team (7). This gives me 8 players who will not be chosen. Now, I can calculate the number of ways I can choose the 7 players from the 15 available players. This is equal to 15 x 14 x 13 x 12 x 11 x 10 x 9. This is the same as 7 x 6. Now, I need to account for the order in which I choose the players. Since the 6 players other than the goalie can be interchangeable, I can use the equation 7 x 6 x 5 x 4 x 3 x 2 x 1. This gives me 2520 ways to choose my starting team. To simplify this, I can factor out the 7 and the 1, leaving me with 7 x 5 x 4 x 3 x 2, which is still equal to 2520. Therefore, I can choose my starting team in 2520 ways.
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sarah can bicycle a loop around the north part of lake washington in 2 hours and 40 minutes. if she could increase her average speed by 1 km/hr, it would reduce her time around the loop by 6 minutes. how many kilometers long is the loop? (round your answer to two decimal places.)
The loop is 4112.16 kilometers long.
To solve this problem, we can set up the following equation:
distance = speed x time
We know that Sarah's current speed is s km/hr, and that the loop is d kilometers long. We also know that her current time is 2 hours and 40 minutes, or 160 minutes.
From the information given, we know that if Sarah increases her speed by 1 km/hr, her time around the loop would be reduced by 6 minutes. Therefore, we can set up the following equation:
d = (s + 1)(160 - 6) = (s + 1)154
We also know that Sarah's current speed is s km/hr, and that the loop is d kilometers long and the time she takes is 160 minutes. Therefore, we can set up the following equation:
d = s * 160
We can now solve for s by substituting the first equation into the second equation:
d = s * 160
d = (s+1)154
s160 = (s+1)*154
We can now solve for s
s = 154/6 = 25.66 km/hr
Now we can plug in s into the first equation we have:
d = s * 160
d = 25.66 * 160
d = 4112.16 km
The loop is 4112.16 kilometers long.
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a curve passes through the point (4,2) and has the property that the slope of the curve at every point p is three times the y-coordinate p. what is the equation of the curve?:
The slope of the curve at a point (x,y) is given as 3y. This means that the equation of the curve is in the form of y = mx + b, where m is the slope of the curve and b is the y-intercept.
Since the curve passes through the point (4,2), we can use this point to find the value of b:
y = mx + b
2 = 3(4) + b
b = -10
So the curve's equation is: y = 3x - 10
You can confirm this by plugging in the point (4,2) into the equation.
2 = 3(4) - 10
2 = 12 - 10
2 = 2
You purchae a computer for $1999. 99 plu 7% ale tax. The electronic tore offer an intallment loan that allow you to pay for the computer by making 12 equal monthly payment of $203. 30. What i the cot of credit, in dollar, for thi loan?
The cost of credit, in dollars, for this loan is 299.6107 dollars.
Let's recall the total cost of the computer with tax C. Then,
C = 1999.99 + 0.07 × 1999.99 = 1999.99 + 139.9993 = 2139.9893.
Since the loan allows you to pay for the computer in 12 equal payments of $203.30, the total cost of the loan is 12 × 203.30 = 2439.60.
The cost of credit is then the difference between the total cost of the computer with tax and the total cost of the loan: 2439.60 - 2139.9893 = 299.6107.
So the cost of credit is 299.6103 dollars.
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1) Pastor and Mrs. Gentle visited ten more church members this week than the number they visited last week divided by four. If they visited sixteen members this week, how many did they visit last week?
Answer:
24
Step-by-step explanation:
Let the number of members they visit last week be x.
Then, they visit x/4 + 10 this week
x/4 + 10 = 16
x = 4 x 6
x = 24
Pls mark as brainliest if possible. Don't know why i need it, but i do. Cheers
A botanist is studying the growth of the sequoia tree. He selects one sequoia tree and records it’s hight each year. What is the equation of the line in slope-intercept form? Define your variables. Show your work
Answer: h= 4/5yr+ 5
Step-by-step explanation: by looking at the graph the slope is 4/5 and it intercepts the graph at 5 so y=4/5x + 5, then I plugged in the variables on the graph to get yr for year and h for height
Can some one do one two and four
Algebra 2 I am really lost on this topic
2) The standard definition of function f(x) is given as follows: A. F(x) = ax³ + bx² + cx + d.
4) The solution to the system of equations v(x) = b(x) is given as follows:
A. (-3.43, 6.30).
How to define the cube function?The standard definition of a cube function is given as follows:
y = ax³ + bx² + cx + d.
As all the coefficients are positive, the definition is this one.
The system of equations for this problem is defined as follows:
v(x) = x³ + 2x² - 5x + 6.b(x) = -3x - 4.The solution for the system of equations in this problem is approximated graphically.
The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.
From the graph given at the end of the answer, the coordinates of the point of intersection are given as follows:
(-3.432, 6.296).
Meaning that the solution to the system of equations is approximated by option A.
Missing InformationItem 2 asks for the standard cube function, with positive coefficients.
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One of the solutions to the equation 5x^2+bx+12=0 is -4/5. Find the value of b.
Answer:
19
Step-by-step explanation:
Substitute x = -4/5 and solve for b.
5x² + bx + 12 = 0
5(-4/5)² + b(-4/5) + 12 = 0
16/5 − 4/5 b + 12 = 0
16 − 4b + 60 = 0
4b = 76
b = 19
Answer:
Step-by-step explanation:
Round each angle to the nearest degree and round each Side to the nearest hundredth. Do not use rounded answers in your calculations to find missing measures.
Length of AB = c = 7.12
Measures of angles:
A = 56°
B = 34°
What is Pythagoras theorem?The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
AB² = AC² + BC²
Given in the figure,
AC = 3.96
BC = 5.96
AB = ?
A = ?
B = ?
By Pythagoras theorem
AB² = AC² + BC²
AB² = 3.96² + 5.96²
AB² = 15.6816 + 35.5216
AB² = 51.2032
AB = √51.2032
AB = 7.1156
Rounded to nearest hundredth
AB = 7.12
Now, tan B = AC/BC
tan B = 3.96/5.96
tan B = 0.6644
B = tan⁻¹ (0.6644)
B = 33.6°
Sum of Interior angles of a triangle = 180°
A + B + C = 180°
A + 33.6° + 90° = 180°
A + 123.6° = 180°
A = 180° - 123.6°
A = 56.4°
Rounded to nearest degree,
A = 56°
B = 34°
Hence, 7.12 is the measure of AB, 56° and 34° are the measures of angles A and B respectively.
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In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403. What is the first term
In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.
Let a1 be the first term....then the successive terms are
3a1 + 4, 9a1 + 16, 27a1 + 52, 81a1 + 160
So 81a1 + 160 = 403 subtract 160 from each side
81a1 = 243 divide both sides by 81
a1 = 3
in other word
403 - 4 = 399/3 = 133
133 - 4 = 129/3 = 43
43 - 4 = 39/3 = 13
13 - 4 = 9/3 = 3
So, first term = 3
In a sequence, each term after the first is four more than three times the previous term. The fifth term is 403.then First term is 3.
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Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
9
5
÷
6
5
Answer:
[tex]\frac{19}{13}[/tex]
Step-by-step explanation:
expressing 9.5 ÷ 6.5 as a fraction , that is
[tex]\frac{9.5}{6.5}[/tex] ( multiply numerator and denominator by 2 for whole numbers )
= [tex]\frac{9.5(2)}{6.5(2)\\}[/tex]
= [tex]\frac{19}{13}[/tex] ← in simplest form
a fraction is in simplest form when no other value but 1 will divide into the numerator and denominator.
if a regression model is estimated using observations on each of these variables, what are the degrees of freedom (df) for the regression sum of squares, error sum of squares, and total sum of squares?
The degrees of freedom for the regression sum of squares in a regression model is determined by the number of variables that are being used to make predictions. For example, if you have three independent variables in your model, the degrees of freedom for the regression sum of squares would be 3.
The degrees of freedom for the error sum of squares is the total number of observations in your dataset, minus the number of independent variables used in the model.
The total sum of squares is the sum of the squared differences between each observation and the overall mean of the variable being predicted. This has the same number of degree of freedom as the error sum of squares, which is total number of observations -1.
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what sample size would be required to reduce the standard deviation of the sam- pling distribution to one-third the value you found in exercise 36(b)? justify your answer.
Multiplying the sample size by 4 reduces the standard deviation to half of the previous value, so a sample size of 30(4) = 120 would reduce the standard deviation of the sampling distribution to one-half of the value found in 35(b).
Now, According to the question:
Let's Know:
What is Standard Deviation?
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Multiplying the sample size by 4 reduces the standard deviation to half of the previous value, so a sample size of 30(4) = 120 would reduce the standard deviation of the sampling distribution to one-half of the value found in 35(b).
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Flavia bought a pair of roller blades. the regular price was 129.50. they were bought for 40% off and the sales tax was 15%. determine each of these amounts:
On solving the provided question, we can say that equation of cost of the roller blades is $ 89.66
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Let the total cost = A
initial cost = $ 129.50
he discount percentage = 40 %
So , the equation will be
= 129.50 - ( 40/100 ) x 129.50
= 129.50 - 51.8
= $ 77.7
sales tax percentage = 15 %
So , the equation will be
= 77.7 + ( 15/100 ) x 77.7
= 77.7 + 11.655
= $ 89.655
final cost is A = $ 89.66
final cost of the roller blades is $ 89.66
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Use the distributive property to find the product of 9 and 23.
Answer:
Step-by-step explanation:
187
153
197
207
5 gallons to 6 quarts in simplest ratio
The simplest ratio between 5 gallons and 6 quarts is 10:3.
To convert 5 gallons to quarts, we can use the conversion factor that 1 gallon is equal to 4 quarts.
Therefore, 5 gallons is equal to 5 x 4 = 20 quarts.
Now we need to express this ratio in its simplest form.
To simplify the ratio, we can divide both the number of quarts and the number of gallons by their greatest common divisor (GCD).
The GCD of 20 and 6 is 2. So, dividing both numbers by 2, we get:
20 ÷ 2 = 10
6 ÷ 2 = 3
Therefore, the simplest ratio between 5 gallons and 6 quarts is 10:3.
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a scientist suggests keeping indoor air relatively clean as follows: provide two or three pots of flowers for every 100 sq ft of floor space under a ceiling of 8 ft. if your classroom has an 8-ft ceiling and measures 35 ft by 40 ft, how many pots should it have? a. 37-56 pots c. 28-42 pots b. 26-39 pots d. 27-36 pots
The classroom should have 28-42 pots.
To find the number of pots needed for a classroom, you first need to determine the total floor space in square feet. If the classroom has a length of 35 feet and a width of 40 feet, the total floor surface area is 35 feet * 40 feet = 1400 sq ft.
The scientist suggests providing two or three pots of flowers for every 100 sq ft of floor space. To find the number of pots needed for 1400 sq ft of floor space, you can divide 1400 sq ft by 100 sq ft/pot.
So 1400 sq ft / 100 sq ft/pot = 14 pots
The researcher suggests a minimum of 2 pots per 100 sq ft of floor space, therefore, the classroom needs at least 2 pots. The researcher also suggested a maximum of 3 pots per 100 sq ft of floor space,
Therefore, the classroom should have between 2 and 3 pots of flowers per 100 sq ft of floor space, which means that the classroom should have between 28 and 42 pots of flowers.
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0
с
z←
85⁰
D
Work out the three-figure bearing of D from C.
Answer:
095
Step-by-step explanation:
You want the bearing from C to D, given that the bearing from D to C is 85° west of north.
BearingThe bearing from C to D will be the opposite of the bearing from D to C.
Bearing is measured clockwise from north, so the bearing shown from D to C is -85°. Its opposite is found by adding 180°.
180° +(-85°) = 95°
The 3-digit bearing of D from C is 095.
Human body temperatures have a mean of 98. 20° F and a standard deviation of 0. 62°. Sally's temperature can be described by z = 1. 4. What is her temperature? Round your answer to the nearest hundredth. 99. 07°F 97. 33°F 99. 60°F 100. 45°F
Sally's temperature is 99.07°F if human body temperatures have a mean of 98. 20° F and a standard deviation of 0. 62° F and her temperature can be described by z = 1.4.
Therefore the answer is 99.07°F.
To get this answer, you need to know how to convert standard scores (z-scores) back into original units.
As z = (x - μ)/ σ
Formula to convert z-score to original units is:
x = μ + (z × σ)
where x is the original value, μ is the mean, z is the standard score, and σ is the standard deviation.
Plugging in the given values we get
x = 98.2 + (1.4 × 0.62)
x = 98.2 + 0.868
x = 99.068
which round off to 99.07°F
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This pentagonal right pyramid has a base area of 30 m. 5 m 7 m 8 m What is the volume of the figure?
The volume of the pentagonal right pyramid with base area 30 square metres and height 5 metre is 50 m³.
Therefore the answer is 50 m³.
To find the volume of a pentagonal pyramid, we can use the formula:
V = (Bh)/3
where V is the volume, B is the area of the base and h is the height.
Area of the base is given, B = 30 m². From figure it is evident that the height of the pentagonal right pyramid is 5m. Therefore the volume of the figure is
V = 30 × 5/ 3
V = 50 m³
--The question is incomplete, answering to the question below--
"This pentagonal right pyramid has a base area of 30 m². What is the volume of the figure?"
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37) Kelly opened a bank account that earns 1.2% simple interest each year. After 7 years, Kelly will earn $126 in
interest. How much did Kelly deposit when she opened the account? _
Answer:
13.4 dollars
Step-by-step explanation:
13.4 dollars is how much kelly deposit
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
The results of a confidence interval and significance test should agree as long as:
the significance test is two-sided
both are conducted on the same data set
we are making inferences about means
we are making inferences about proportions
The right answer involves doing both studies with the identical data set, drawing conclusions regarding means, and using a two-sided significance test.
What exactly are ratios?An algorithm which it sets two ratios to the same value is called a fraction. You might, for instance, write its ratio as follows: 1: 3 in the case of 1 male & Three girls (for every one boy there are 3 girls) There are 3 out of 4 females and 1 out of 4 guys. 0,25 are men (by dividing 1 by 4)
What's an illustration of proportion?A ratio that connects a part to yet another is a percentage. For instance, there are 100 students in the class containing 20 men or 80 women. The percentage of males is 20/100, or 20%. 80 out of 100, or 80%, are women.
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