Answer:
[tex]Rate = 2[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2 + 3[/tex]
Required
Determine the average rate of change from -2 to 4
This is calculated using:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
In this case:
[tex]a = -2[/tex]
[tex]b = 4[/tex]
So, we have:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
[tex]Rate = \frac{f(4) - f(-2)}{4 - (-2)}[/tex]
[tex]Rate = \frac{f(4) - f(-2)}{4 +2}[/tex]
[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]
Calculate f(4):
[tex]f(x) = x^2 + 3[/tex]
[tex]f(4) = 4^2 + 3[/tex]
[tex]f(4) = 19[/tex]
Calculate f(-2)
[tex]f(x) = x^2 + 3[/tex]
[tex]f(-2) = (-2)^2 + 3[/tex]
[tex]f(-2) = 7[/tex]
So:
[tex]Rate = \frac{f(4) - f(-2)}{6}[/tex]
[tex]Rate = \frac{19-7}{6}[/tex]
[tex]Rate = \frac{12}{6}[/tex]
[tex]Rate = 2[/tex]
The average rate of change is 2.
Due to expected droughts, the farmer will only be planting crops on 3/ 4 of this area. How would you correctly calculate the size of this new area? A. the total area multiplied by 4 divided by 3 B. the total area divided by 3 C. the total area divided by 4 D. the total area multiplied by 3 divided by 4 math
Answer:your answer is D.
Step-by-step explanation:
When dividing fractions you must flip the numerator and denominator so that would leave you with 6/1 divided by 3/4, solve this and then you have an improper fraction so after you multiply by 3 you must divide because of the improper fraction and you will divide by 4.
Answer:
d .the total area multiplied by 3 divided by 4
Step-by-step explanation:
.
the total area multiplied by 3 divided by 4
A line with a slope of 8 and includes the points (8,-10) and (10,w).What is the value of k?
Answer:
w = 6
Step-by-step explanation:
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]
[tex]\frac{w-[-10]}{10-8}=8\\\\\frac{w+10}{2}=8\\\\w+10= 8*2\\[/tex]
w +10 = 16
w = 16 - 10
w = 6
The measure of an angle is 166º. What is the measure of its supplementary angle?
HELP PLZZ
Answer:
14
Step-by-step explanation:
To make 166 a supplementary angle you should add 14 because supplementary angles equal 180.
Answer:
14
Step-by-step explanation:
Supplementary angles add to 180 degrees.
Let x be the unknown supplement
x+166 = 180
x+166-166 = 180-166
x =14
The unknown supplement is 14
An experiment was conducted that recorded the weight of a new bar of soap after each use. The line of best fit for the data collected is
y = -5.6x + 123, where y is the weight of the bar of soap, in grams, and x is the number of times that the bar was used.
Which statement describes the meaning of the y-intercept for the line of best fit equation?
Answer:
The initial weight of the bar soap is 123g
Step-by-step explanation:
No options but the question can still be solved.
Given
[tex]y = -5.6x + 123[/tex]
Required
What does the y intercept mean
Start by calculating the y intercept (i.e. when x = 0)
The equation becomes
[tex]y = -5.6*0 + 123[/tex]
[tex]y = 0 + 123[/tex]
[tex]y = 123[/tex]
This means that the initial weight of the bar soap is 123g
Among fatal plane crashes that occurred during the past 55 years, 347 were due to pilot error, 83 were due to other human error, 596 were due to weather, 374 were due mechanical problems, and 114 were due to sabotage. Construct the relative frequency distribution.
Required:
What is the most serious threat to aviation safety, and can anything be done about it?
Answer:
Pilot error = 347 / 1487 = 0.233 = 23.3%
Other human error = 83 / 1514 = 0.055 = 5.6%
Weather = 596 / 1487 = 0.401 = 40.1%
Mechanical problem = 374 / 1487 = 0.233 = 23.3%
Sabotage = 114 / 1487 = 0.077 = 7.7%
Step-by-step explanation:
Given the data :
Pilot error = 347
Other human error = 83
Weather = 596
Mechanical problem = 374
Sabotage = 114
Cummlative sum = (347 + 83 + 596 + 374 + 114) = 1487
Relative frequency :
Pilot error = 347 / 1487 = 0.233 = 23.3%
Other human error = 83 / 1514 = 0.055 = 5.6%
Weather = 596 / 1487 = 0.401 = 40.1%
Mechanical problem = 374 / 1487 = 0.233 = 23.3%
Sabotage = 114 / 1487 = 0.077 = 7.7%
Based on the relative frequency estimate, Weather is the most serious threat to aviation safety.
Deployment of more weather monitoring technologies
Find the difference 0.2−0.05. Show your reasoning.
The difference 0.2−0.05 is equal to 0.15.
To find the difference between 0.2 and 0.05.
The larger number is 0.2.
The smaller number is 0.05.
When you subtract 0.05 from 0.2, you align the decimal points and subtract each digit accordingly:
[tex]0.2 - 0.05[/tex]
[tex]= 0.15[/tex]
So, the difference between 0.2 and 0.05 is 0.15.
To learn more on Equation:
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A number is greater than 8. The same number is less than 10. The inequalities x > 8 and x < 10 represent the situation.
Which best explains the number of possible solutions to the inequality?
O There is one solution because 9 is the only number between 8 and 10.
There are a three solutions because 8, 9, and 10 are possible solutions.
There are a few solutions because there are some fractions and decimals between 8 and 10.
There are infinite solutions because there is always another number between any two numbers.
Mark this and retum
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Answer:
There are infinite solutions because there is always another number between any two numbers.
Step-by-step explanation:
Pick any number (including decimal) add an extra decimal after the smallest one and then you have a number between them. E.g.
1.234 and 2.987
1.2341, 1.2342, 1.2343, ... are all between them
Answer:
D
Step-by-step explanation:
What is the number of the parking space covered by the car?
Ralph Chase plans to sell a piece of property for $150000. He wants the money to be paid off in two ways a - short-term note at 11% interest and a long-term note at 8% interest. Find the amount of each note if the total annual interest paid is $15200
.
Answer:
Amount on 11% note = $106,666.67
Amount on 8% note = $43,333.33
Step-by-step explanation:
Let the amount for the short-term note at 11% interest be x.
Thus, the amount for the short-term note at 8% interest will be (150000 - x)
Now we are told that the total interest paid is $15,200.
Thus;
0.11x + 0.08(150000 - x) = 15200
0.11x + 12000 - 0.08x = 15200
Rearranging gives;
0.03x = 15200 - 12000
0.03x = 3200
x = 3200/0.03
x = $106666.67
Thus, amount for 8% note = $150000 - $106666.67 = $43,333.33
How are these three numbers related. 50 1/2, 1/4, 202
Answer: If you divide 202/4=50.5 or 50 1/2
Step-by-step explanation:
Calculate and give your answer
its simplest form.
8 /7
X
7/8
Your answer
Answer:
1 I believe if your asking in in simplified form and if 8/7 and 7/8 are multiplied
Step-by-step explanation:
Determine the equation of straight line which passes through the point (a, b)and perpendicular to ax+by=5
Answer:
[tex]y=\frac{b}{a} x.[/tex]
Step-by-step explanation:
1) if the required straight line is 'l', the given point is A(a;b), then the required equation of line can be written in form:
[tex]\frac{x-a}{x_1-a} =\frac{y-b}{y_1-b},[/tex]
where (x₁;y₁) is other point B, which belongs to the 'l';
2) from the equation it is possible to detect the coordinates of the perpendicular, they are (x₁-a;y₁-b);
3) if the given perpendicular is ax+by=5, then the coordinates of the vector (a;b) are coordinates of the vector, which belongs to the required line 'l', and then: x₁-a=a and y₁-b=b;
4) if to substitute the a=x₁-a and b=y₁-b into the required equation of line 'l', then:
[tex]\frac{x-a}{a} =\frac{y-b}{b};[/tex]
5) finally, the equation is: ay=bx, or y=b/a *x (slope-interception form).
note: the suggested solution is not the only way.
What is 18 % of 120?
O 2. 160
O 666
0 21.6
0 15
Multiply 120 by 18%
Change 18% to a decimal: 0.18
120 x 0.18 = 21.6
Answer: 21.6
Help me write an explanation
Answer:
9.375 grams
Step-by-step explanation:
30 days = 3(10 days)
m = 75·0.5³ = 9.375 grams
A soft drink-dispensing machine uses paper cups that hold a maximum of 12 ounces. The machine is set to dispense a mean of 10 ounces of the drink. Because of an imprecise process, the amount dispensed actually varies; it is normally distributed with a standard deviation of 1 ounce. If we simulated the filling process, and had the random number .564, how many ounces would the cup contain? Give your answer to 3 decimal places.
Answer:
The cup would contain 10.16 ounces.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Mean of 10 ounces, standard deviation of 1 ounce:
This means that [tex]\mu = 10, \sigma = 1[/tex]
If we simulated the filling process, and had the random number .564, how many ounces would the cup contain?
This means that we have to find X when Z has a pvalue of 0.564. So X when Z = 0.16. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.16 = \frac{X - 10}{1}[/tex]
[tex]X - 10 = 0.16*1[/tex]
[tex]X = 10.16[/tex]
The cup would contain 10.16 ounces.
the equations are
A. y=5/3 x -5
B. y=3/5 x -5
C. y=5/3 x +5
D. y=3/5 x +5
Answer:
A
Step-by-step explanation:
The map of a town is placed on a coordinate grid. Use the map to find
the distance between the post office and the lake.
4. A rectangular strip of aluminum, 30 cm long and 10 cm wide, is rolled into the form of a cylinder.
Which would have the greater volume, a cylinder 10 cm high with circumference of 30 cîn or a cylinder
30 cm high with circumference of 10 cm?
Answer:
A cylinder 10 cm high with a circumference of 30 cm would have a greater volume
Step-by-step explanation:
Volume of a Cylinder
Given a cylinder of radius r and height h, the volume is calculated as:
[tex]V=\pi r^2h[/tex]
It's given a rectangular strip of aluminum 30 cm long and 10 cm wide. If we roll it to form a cylinder we can do it in two ways.
Rolling it across its length will make the cylinder have a height of h=10 cm and the circumference of the base equal to 30 cm.
The circumference of a circle of radius r is:
[tex]C=2\pi r[/tex]
Thus the radius is:
[tex]\displaystyle r=\frac{C}{2\pi}[/tex]
[tex]\displaystyle r=\frac{30}{2\pi}=\frac{15}{\pi}[/tex]
Thus the volume of the cylinder is:
[tex]V=\pi ( \frac{15}{\pi})^2*10[/tex]
[tex]V=\pi ( \frac{225}{\pi^2})*10[/tex]
[tex]V= \frac{2250}{\pi}[/tex]
If we rolled the strip across its width, then the height will be h=30 cm and the circumference C=10 cm, thus the radius is:
[tex]\displaystyle r=\frac{10}{2\pi}=\frac{5}{\pi}[/tex]
And the volume is:
[tex]V'=\pi ( \frac{5}{\pi})^2*30[/tex]
[tex]V'=\pi ( \frac{25}{\pi^2})*30[/tex]
[tex]V'= \frac{750}{\pi}[/tex]
Dividing V/V' = 3. The first volume it 3 times as much as the second volume.
A cylinder 10 cm high with a circumference of 30 cm would have a greater volume
How many solutions does the system of equations have?
Answer:
The system has just one solution, it is (1,4).
Step-by-step explanation:
When we have a system of linear equations, the solution is given by the intersection point of the two lines.
So if we see the graph, the intersect point is at (1,4). Therefore, the system has a unique solution.
I hope it helps you!
Question 7 (1 point)
The angle of elevation from point P to the top of the pole is 65°. Point Pis 21 feet from the base of the flagpole. To
the nearest tenth, what is the height of the pole?
65°
21 ft.
Plz help
Answer:
h = 452.5 ft
Step-by-step explanation:
Angle of elevation from P to top of the pole = 65°
Horizontal distance between the pole and point P = 21 ft
By Applying tan rule in the given triangle ABP,
tan(∠APB) = [tex]\frac{AB}{PB}[/tex]
tan(65°) = [tex]\frac{h}{21}[/tex]
h = 21[tan(65°)]
h = 452.491
h ≈ 452.5 ft
Therefore, height of the pole is 452.5 ft.
Ten 4th grade girls and ten 7th grade girls were randomly selected. Their heights, in inches, are recorded below:
4th Grade
44, 48, 48, 51, 52, 52, 54, 54, 57, 60
7th Grade
52, 55, 57, 57, 58, 60, 60, 62, 64, 65
On average, 7th grade girls tend to be about (these are your answer options for your answer put one of these numbers and tell me which grade) 6,7,5,8 inches taller than 4th grade girls, and ( Answer choices ) there is more variability in the height of 4th grade girls or there is more variability in the height of 7th grade girls.
Answer:
7
Step-by-step explanation:
average of 7th grade - average of 8th grade = 7
average of 7th = (52+55+57+57+58+60+60+62+64+65)/10
= 590/10
= 59
average of 4th = 44+48+48+51+52+52+54+54+57+60
= 520/10
= 52
59 - 52 = 7
please give me brainliest if it is helpful for you
Answer: Hoped I help
7 and there is more variability in the height of 7th grade girls
Step-by-step explanation:
4th grade
44+48+48+51+52+52+54+54+57+60
found the median which is 52 and 52 but you add them and divide them by 2 to get the median which is 104/2= 52
7th grade
52+55+57+57+58+60+60+62+64+65
median is 60 + 58=118/2= 59
59-52= 7
and
there is more variabilty in the hieght f 7th grade girls. because 4th grade has a lot of modes already while 7th grade has only like two so 7th grade will have more variability.
Which student solved the equation 107 d = 1,733.4 correctly?
Gianna's work: 107 d = 1,733.4. 1,733.4 times 107 = 185,473.8.
Teddy's work: 107 d = 1,733.4. 1,733.4 minus 107 = 1,626.4.
Sid's work: 107 d = 1,733.4. 1,733.4 + 107 = 1,880.4.
Sammi's work: 107 d = 1,733.4. 1,733.4 divided by 107 = 16.2.
Answer:
It's D, Sammi's work. Hope it helps! Remember your perfect, your awesome, your worth it, just the way you are, you deserve this world! Have an amazing day!
Step-by-step explanation:
Answer:
The person above me is correct.
Are the hypontuse and the height of this triangle the same?
Answer:th hypotenuse and the height can’t possibly be the same size because the Pythagorean theorem is a^2 +b^2=c^2
Step-by-step explanation:
Answer:
hypotenuse is equal to side of this square.
but hypotenuse is never be equal to hieght of the triangle.
3.X + 20 = 120
Hey I need this done by 9pm tonight, I know that we have to switch the expression to multiplication but then after that one step I don’t get it can someone pls help me
3x+20=100
Now you would need to move the constant to the right side and change within it’s sign
3x=100-20
Now you would subtract the numbers so for 100-20 would give you 80
So now you then do 3x=80
But if you want to divide the equation, divide it by both sides by 3
Which would give you x=80/3, x=26.6 or x=26 2/3
The length of the base of an isosceles triangle is x. The length of a leg is 4x - 2. The perimeter of the triangle is 95. Find x.
Answer:
x = 11
Step-by-step explanation:
sides of triangle measure: 'x', '4x-2' and '4x-2' since isosceles means both legs are equal
perimeter is the sum of all sides, so set up equation:
95 = 4x - 2 + 4x - 2 + x
95 = 8x - 4 + x
95 = 9x - 4
99 = 9x
x = 11
Please help and how do you know this answer
Answer:
21
Step-by-step explanation:
Answer:
1.67
Step-by-step explanation:
25/15 = 1.67
The mean is estimated by dividing the total of the values by the range of values.
Tell whether the ordered pair is a solution to the system of linear equations. 1 point
63 + 3y = 12
(5.-6):
4x + y = 14
Yes
No
Maybe
Next
Page 1 of 3
Forms
Tell whether the ordered pair is a solution to the system of linear equations
Yes
No
Maybe
Answer:
(5,-6) is a solution
Step-by-step explanation:
Given
[tex]6x + 3y = 12[/tex]
[tex]4x + y = 14[/tex]
Required
Tell whether (5,-6) is a solution
In (5,-6): x = 5 and y = -6.
Substitute these values in the given equations
[tex]6x + 3y = 12[/tex] becomes
[tex]6 * 5 + 3 * -6 = 12[/tex]
[tex]30-18 = 12[/tex]
[tex]12 = 12[/tex]
[tex]4x + y = 14[/tex] becomes
[tex]4 * 5 - 6 = 14[/tex]
[tex]20 - 6 = 14[/tex]
[tex]14 = 14[/tex]
Because both solutions are true, then (5,-6) is a solution
Move values to the lines to complete each equation.
|8| =
|-8| =
-|8| =
-|-8| =
Answer:
I think this is what you meant not sure tho
Step-by-step explanation:
|8| = correct as it is
|-8| = correct as it is
-|8| = |-8|
-|-8| = |8|
Look at the following number sequence.
6, 9, 12, 15, . . .
Based on the pattern, what are the next two terms?
Answer:
18, 21
Step-by-step explanation:
By finding the difference between each term, you can find the pattern. 9-6=3, 12-9=3, 15-12=3, so we know that each term is 3 more than the last.
Therefore, by following the pattern of +3, the next term is 15+3=18 and the one after that is 18+3 = 21
Answer:
the next two terms would be 18 and 21
The height h(n) of a bouncing ball is an exponential function of the number n of bounces.
One ball is dropped and on the first bounce reaches a height of 6 feet. On the second
bounce it reaches a height of 4 feet.
PLEASE HURRY
Answer:
The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].
Step-by-step explanation:
According to this statement, we need to derive the expression of the height of a bouncing ball, that is, a function of the number of bounces. The exponential expression of the bouncing ball is of the form:
[tex]h = h_{o}\cdot r^{n-1}[/tex], [tex]n \in \mathbb{N}[/tex], [tex]0 < r < 1[/tex] (1)
Where:
[tex]h_{o}[/tex] - Height reached by the ball on the first bounce, measured in feet.
[tex]r[/tex] - Decrease rate, no unit.
[tex]n[/tex] - Number of bounces, no unit.
[tex]h[/tex] - Height reached by the ball on the n-th bounce, measured in feet.
The decrease rate is the ratio between heights of two consecutive bounces, that is:
[tex]r = \frac{h_{1}}{h_{o}}[/tex] (2)
Where [tex]h_{1}[/tex] is the height reached by the ball on the second bounce, measured in feet.
If we know that [tex]h_{o} = 6\,ft[/tex] and [tex]h_{1} = 4\,ft[/tex], then the expression for the height of the bouncing ball is:
[tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex]
The height of a bouncing ball is defined by [tex]h(n) = 6\cdot \left(\frac{4}{6} \right)^{n-1}[/tex].
Answer:
9 (2/3) ² but insted of 2 its n
Step-by-step explanation: