The rate of change for the given table is 1.
How to get the rate of change?For a function y = f(x), the rate of change in any interval (a, b) is:
R = (f(b) - f(a))/(b - a)
Here we can use any pair of values in the table, because it clearly is linear, so we can use the first two.
(4, 9) and (9, 14)
The rate of change is:
r = (14 - 9)/(9 - 4) = 5/5 = 1
Learn more about rate of change at:
https://brainly.com/question/8728504
#SPJ1
Find the three trigonometric ratios. If needed, reduce fractions.
Two friends, Julieta and Camila, had just bought their first cars. The equation
y = 38.8x represents the number of
miles, y, that Camila can drive her car for every a gallons of gas. Julieta uses 10 gallons of gas to drive 333 miles in her
car.
We can use the equation y = 38.8x to find how many miles Camila can drive her car for each gallon of gas, and then use that information to find how many gallons of gas she would need to drive the same distance as Julieta.
Julieta drives 333 miles using 10 gallons of gas, so her car can travel 333/10 = 33.3 miles per gallon.
To find how many miles Camila's car can travel per gallon, we can use the equation y = 38.8x, where x is the number of gallons of gas. If Camila uses 1 gallon of gas, then y = 38.8(1) = 38.8 miles. Therefore, Camila's car can travel 38.8 miles per gallon.
To travel 333 miles like Julieta, Camila would need to use:
333 miles / 38.8 miles per gallon = 8.58 gallons of gas
Therefore, Camila would need to use 8.58 gallons of gas to travel the same distance as Julieta.
solve
2r - 22 = 4(r-3)
Answer:r= -5
Step-by-step explanation:
Answer:
r=-5
Step-by-step explanation:
2r-22=4(r-3)
first expand brackets
2r-22=4r-12
then take away the least amount of r's from one side
-22=2r-12
add 12 to each side
-10=2r
divide by 2 to get r by itself
-5=r
RSM 174f) absolute value of x+1 plus absolute value of x-2 is equal to 3
The absolute value of x + 1 is added to the absolute value of x - 2 is equal to 3. So the value of x is equal to -1, 0 and 2.
To solve the equation | x + 1 | + | x - 2 | = 3. We need to find out the possible cases based on the signs of x + 1 and x - 2. In case of x is less than or equal to -1, both expressions inside the absolute value signs are negative.
f(x ≤ - 1) = | -1 + 1 | + | -1 - 2 | = 3
f(x ≤ - 1) = 0 + 3 = 3
So x can be less than or equal to be -1.
In case, when x = 0, expressions inside the absolute value bars will be positive & negative, so we can rewrite the equation as 0 + 1 + 0 + 2 = 3, which simplifies to x = 0
f(x = 0) = |0 + 1 | + | 0 - 2 | = 3
f(x = 0) = 1 + 2 = 3
so x can be equal to 0.
When x ≥ 2, both expressions inside the absolute value bars will be positive, so we can rewrite the equation as x + 1 + x - 2 = 3, which simplifies to 2x = 4, or x = 2.
f(x ≥ 2) = | 2 + 1 | + | 2 - 2 | = 3
f(x ≥ 2) = 3 + 0 = 3
so x can be greater than or equal to 2.
Therefore, the solutions to the equation |x + 1| + |x - 2| = 3 are x = - 1, x = 0 and x = 2.
Learn more about Absolute Value:
https://brainly.com/question/12928519
#SPJ4
Find the scale factor of a prism with the surface area of 81m^2 to a similar prism with the surface area of 361m^2
The scale factor of the first prism to the second prism is approximately 2.11.
If two prisms are similar, their corresponding linear dimensions are in proportion, which means that their surface areas are in proportion to the square of the scale factor.
Let x be the scale factor of the first prism to the second prism. Then we have,
(surface area of second prism) / (surface area of first prism) = (scale factor)^2
Plugging in the given values, we get,
361/81 = x^2
Simplifying this equation,
x^2 = 4.45679...
Taking the square root of both sides, we get,
x ≈ 2.11
To learn more about prism here:
https://brainly.com/question/29722724
#SPJ4
what fraction of a day is 8 hours 20minute
Answer:
So after dividing 8 by 20 your answer will come out to be 1 by 3. So the time is 1/3.
8 hours and 20 minutes is equivalent to 8.3333... hours, or approximately 8 hours and 20 minutes, or 0.35 of a day.
Helppp please!!!'!!!!!!!!!!
Answer:
The domain is {-1, 3, 5}, so D is correct.
The prism below is made of cubes which measure of a centimeter on one side.
Which of the following represents the volume of the prism?
There are multiple answers.
3/2 cubic cm
1/216 cubic cm x 24
4/3 cubic cm
1/18 cubic cm x 24
1/9 cubic cm
(4 x 1/6cm) + (2 x 1/6cm) + (3 x 1/6cm)
(4 x 1/6cm) X (2 x 1/6cm) X (3 x 1/6cm)
NO LINKS NO FILES
The prism has an 8/27 cubic centimetre volume.
What is the volume of a cube?The following formula determines a cube's volume:
V = s³
where V is the volume of the cube and s is the length of one of its sides.
In other words, to find the volume of a cube, you simply need to raise the length of one of its sides to the third power (cube it).
The volume of a cube = s³
Given that the prism is composed of cubes with a one-third-centimeter side measurement.
Volume of a cube = (1/3)³ = 1/27
There are 8 cubes in the prism.
Therefore, the volume of the prism is;
=8(1/27)
= 8/27 cubic centimeter.
To know more about prism visit:
https://brainly.com/question/21839328
#SPJ1
The complete question is:
The prism below is made of cubes which measure of a centimeter on one side. What is the volume?
Note: Figure is not drawn to scale.
The prism below is made of cubes which measure 1/3 of a centimeter on one side. What is the volume?
Image is attached below.
Given that £1 = $1.62
a) How much is £650 in $?
b) How much is $405 in £?
Answer:
a 1053
b 250
multiply 650 by 1.62 for part a.
for part b divide by 1.62 since pound is less than dollar
hope this helps :)
The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? Round to the nearest tenth.
1. 460.1 ft
2. 301.9 ft
3. 262.4 ft
4. 459.3 ft
The height of the hill in the triangle is approximately 460.1 feet, which corresponds to option 1.
What is angle of elevation?Angles are used to define how an object is situated in respect to an observer. These angles include the angle of elevation and the angle of depression. The angle of elevation is the angle formed between the horizontal and a line connecting an item above eye level and the observer. In other words, it is the angle created while gazing up at an item from the ground. On the other hand, the angle of depression is the angle formed by the horizontal and a line drawn from the observer to an object that is below their level.
For the given triangle, applying the trigonometric function we have:
tan(49°) = h / 400
h = 400 * tan(49°) ≈ 460.1 ft
Hence, the height of the hill is approximately 460.1 feet, which corresponds to option 1.
Learn more about angle of elevation here:
https://brainly.com/question/16716174
#SPJ1
a road perpendicular to a highway leads to a farmhouse located 1 1 mile away. an automobile traveling on the highway passes through this intersection at a speed of 45mph. 45 mph . how fast is the distance between the automobile and the farmhouse increasing when the automobile is 9 9 miles past the intersection of the highway and the road? the distance between the automobile and the farmhouse is increasing at a rate of miles per hour.
The distance traveling between them is increasing at a rate of miles per hour = 45 m/h.
The distance between the automobile and the farmhouse is increasing by 45 mph, since the automobile is traveling at this speed.
When the automobile is 9 miles past the intersection of the highway and the road, the distance between the automobile and the farmhouse is increasing at a rate of 45 mph, due to the automobile traveling at this speed.
When the automobile is 9 miles past the intersection of the highway and the road, the distance between the automobile and the farmhouse is increasing at a rate.
So,
The rate at which the distance between the automobile and the farmhouse is increasing when the automobile is 9 miles past the intersection is 45 mph.
For similar question on distance traveling:
brainly.com/question/509450
#SPJ11
Find the three trigonometric ratios . If needed, reduce fractions.
The trigonometric ratios with respect to the angle C are:
sin(C) = 15/17, cos(C) = 8/17, tan(C) = 15/8, cosec(C) = 17/15, sec(C) = 17/8, cot(C) = 8/15
What is trigonometric ratios?Trigonometric ratios are ratios of the sides of a right triangle used to calculate angles and side lengths.
The three main ratios are sine, cosine, and tangent, which are defined as the ratios of the opposite, adjacent, and hypotenuse sides.
Using the right triangle ABC, we can find the trigonometric ratios with respect to angle C:
sin(C) = opposite/hypotenuse = AB/AC = 15/17
cos(C) = adjacent/hypotenuse = BC/AC = 8/17
tan(C) = opposite/adjacent = AB/BC = 15/8
cosec(C) = 1/sin(C) = AC/AB = 17/15
sec(C) = 1/cos(C) = AC/BC = 17/8
cot(C) = 1/tan(C) = BC/AB = 8/15
To know more about right triangle visit:
https://brainly.com/question/15101552
#SPJ1
assume that for some statistic 1000 tests were performed. to avoid the situation of the incorrectly found significance, bonferroni correction was applied. the resulting p-value is 0.00013. what significance level was chosen for the tests? the significance level was:
The significance level chosen for the tests with total number of test performed as 1000 for given p-value is equal to 0.87 or 87%.
Total number of test performed = 1000
p-value is equal to 0.00013
The Bonferroni correction involves ,
Adjusting the significance level for multiple comparisons by dividing it by the number of comparisons performed.
Here, 1000 tests were performed and the resulting p-value is 0.00013.
The significance level that was chosen for the tests,
Reverse the Bonferroni correction by multiplying the p-value by the number of comparisons,
adjusted p-value = p-value / number of comparisons
number of comparisons = 1000
adjusted p-value = 0.00013
p-value = adjusted p-value x number of comparisons
⇒p-value = 0.00013 x 1000
⇒p-value = 0.13
So the original p-value before the Bonferroni correction was 0.13.
The significance level, we subtract the p-value from 1,
significance level = 1 - p-value
⇒significance level = 1 - 0.13
⇒significance level = 0.87
Therefore, the significance level chosen for the tests was 0.87 or 87%
learn more about significance level here
brainly.com/question/3487014
#SPJ4
find the equation of the line passing through point (-4,-5) and is parallel to the line 7x-5y=-6
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]7x-5y=-6\implies -5y=-7x-6\implies y=\cfrac{-7x-6}{-5} \\\\\\ y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{7}{5}}x+\cfrac{6}{5}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 7/5 and it passes through (-4 , -5)
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{7}{5} \\\\\\ \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}{(-5)}=\stackrel{m}{ \cfrac{7}{5}}(x-\stackrel{x_1}{(-4)}) \implies y +5 = \cfrac{7}{5} ( x +4) \\\\\\ y+5=\cfrac{7}{5}x+\cfrac{28}{5}\implies y=\cfrac{7}{5}x+\cfrac{28}{5}-5\implies {\Large \begin{array}{llll} y=\cfrac{7}{5}x+\cfrac{3}{5} \end{array}}[/tex]
Which answer choice best describes the domain and range of the function for this
situation?
A.
Domain: All real numbers greater than or equal to 0 and less than or equal
to 100
Range: All real numbers greater than or equal to 0 and less than or equal
to 50
B.
Domain: (-2)
Range: (100)
Domain: All real numbers greater than or equal to 0 and less than or equal
to 50
Range: All real numbers greater than or equal to 0 and less than or equal
to 100
D.
Domain: (100)
Range:{-2)
D for balls
Step-by-step explanation:
trust the process
If X has the hypergeometric distribution, what is the minimum value that X can take?
N – K
N
K
n
0
If X has the hypergeometric distribution, the minimum value that X can take is option (e) 0
The hypergeometric distribution models the probability of getting a certain number of successes in a fixed-size sample drawn without replacement from a finite population containing a known number of successes and failures.
The minimum value that X can take depends on the specific parameters of the distribution.
If the population size is N, the number of successes in the population is K, and the sample size is n, then the minimum value that X can take is max(0, n - (N - K)).
This is because the sample can contain at most n items, and if all of them are failures (i.e., none of them are successes), then X would be 0. On the other hand, if there are fewer than n failures in the population, then the sample can contain at most n - (N - K) successes. If n - (N - K) is negative, then there are more successes than failures in the population, and X can take any value between 0 and n, inclusive.
Therefore, the correct option is (e) 0
Learn more about hypergeometric distribution here
brainly.com/question/30911049
#SPJ4
A school has members of 6000 out of which 1200 are girls find the probability of people who are boys
Answer: 80% are boys and 20% are girls
Step-by-step explanation: Take 1200 ÷ 6000 = 0.2 , to find the percentage multipy 0.2 x 100 = 20%, then subtract 20% from 100 giving you 80%. This means 80% of the members are boys.
Can someone help me asap? It’s due today. Select all that apply.
I will give brainliest if it’s all correct!!
Answer:
3 & 4
Step-by-step explanation:
Since you have 3 choice, you want to pick the options that can represent 3 options.
1. False, since a coin only has 2 sides.
2. False, black and red is two halves of a deck, meaning you only have 2 options.
3. True, 6 is divisible by three, so it can be used. Assuming each choice is represented by two number.
4. True, 3 choices is evenly represented by 3 sections
Dan did 3/11 a load of laundry on Saturday 3/4 on Wednesday and 3/10 on Sunday the first load was 2/5 colored clothes How many loads of laundry did Dan do in total.
Dan did a total of 27/20 loads of laundry.
What is fraction?
A fraction is a numerical representation of a part of a whole or a ratio between two numbers, expressed as one number divided by another number and typically written with a horizontal line between the numerator and the denominator. The numerator represents the number of parts being considered, while the denominator represents the total number of equal parts that make up the whole or the total number of items being compared.
From the information given, we know that Dan did three loads of laundry on different days, with the following breakdown of the first load: 2/5 colored clothes.
To find out how many loads of laundry Dan did in total, we need to add up the number of loads he did on each day,
3/11 + 3/4 + 3/10
To add these fractions, we need to find a common denominator. In this case, the lowest common denominator is 220,
3/11 = 60/220
3/4 = 165/220
3/10 = 66/220
Now we can add the fractions,
60/220 + 165/220 + 66/220 = 291/220
This means that Dan did a total of 291/220 loads of laundry. However, this is not a practical or meaningful way to express the answer. We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 11,
291/220 = (291 ÷ 11) / (220 ÷ 11) = 27/20
Therefore, Dan did a total of 27/20 loads of laundry.
Learn more about fraction here,
https://brainly.com/question/78672
#SPJ1
Which of the following functions is graphed below?
Note that the function that is graphed below is y = x + 7.
What is the explanation for the above response?The equation y = x + 7 represents a linear function, where x is the independent variable and y is the dependent variable.
It has a slope of 1, which means that for every unit increase in x, y increases by 1. The y-intercept is 7, which is the value of y when x is zero. This equation can be graphed as a straight line on a coordinate plane, with a positive slope and y-intercept of (0, 7).
Learn more about graph at:
https://brainly.com/question/17267403
#SPJ1
A metronoe uses an invented pendulum rod to control tempo. A weight can be slid up the pendulum rod to decrease tempo, or down the pendulum rod to increase tempo. A second fixed weight is hidden inside the mettronome at the base of the pendulum. The longer the distance between the two weights, the slower the tempo. The equation is used to calculate the frequency of the metronome pendulum: f=square of g/L / 2x f= frequency (number of back and forth cyles in 1 second) measured in hertz g=the acceleration due to gravity;9. 8m/s^2 L=length of the rod- in this case, the length of the rid between the two weights- measured in meters. Part 1 Each time the metronome's pendulum completes one back and forth cycle, it produces two ticks or beats. To calibrate the metronome for beats per minute (bpm), the manufacturer needs to know the length of the pendulum for various tempos. Solve f=square root of g/L /2x for L. Part 2 If f=1. 6 then there are 2 beats a second, or 192 beats per minute (bpm) What is the length of the rod between the two weights at that tempo? Use you equation from Part 1 to solve for L
The length of the pendulum rod (L) can be calculated using the formula L = g/(4π²f²) and the length of the rod between the two weights at a tempo of 192 bpm is approximately 0.101 meters.
Starting with the equation
f = √(g/L)/(2π)
Squaring both sides, we get
f² = g/L(4π²)
Rearranging, we get
L = g/(4π²f²) ------ (1)
Therefore, the length of the pendulum rod (L) can be calculated using the formula L = g/(4π²f²).
Given, f = 1.6 Hz, which means there are 2 beats per second or 120 beats per minute (bpm).
Using the formula in equation (1)
L = g/(4π²f²)
L = 9.8/(4π²(1.6)²)
L = 0.101 meters (rounded to three decimal places)
Therefore, the length of the rod between the two weights at a tempo of 192 bpm is approximately 0.101 meters.
To know more about length here
https://brainly.com/question/9112078
#SPJ4
i don’t understand how to do this helpppp
The total area of the figure with of the semicircle and triangle is 12.27 sq. ft.
What is semicircle?Half of a circle is known as a semicircle, and the diameter of the circle is equal to the length of the semicircle's straight edge. A sector of a circle is a section of a circle that is bounded by an arc, two radii, and both. A semicircle is always half of a circle and has a constant central angle of 180 degrees, but a sector can be any part of a circle and has a central angle that can vary from 0 to 360 degrees. This is the major distinction between the two.
Given, the diameter of the semicircle is 3 ft, so its radius is 1.5 ft.
Now, area of the semicircle is given as:
A = 1/2 * pi * (1.5)² = 1.77 sq ft
The area of the triangle is:
A = 1/2 * 3 ft * 7 ft = 10.5 sq ft
Adding the areas we have the total area of the figure:
1.77 sq ft + 10.5 sq ft = 12.27 sq ft
Hence, the total area of the figure is 12.27 sq. ft.
Learn more about area of semicircle here:
https://brainly.com/question/16952186
#SPJ1
Can someone help me in this?
Answer:
18
Step-by-step explanation:
Since it is an equilateral triangle AB=AC=5
If I sum up all sides u will get 18. How this helps.
Please help,, my teacher didnt show me how to do ths
Answer:
sorry did not mean to answer this
Step-by-step explanation:
Answer:
Domain: (0, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
Domain solution: x > 0
Range solution: -∞ < f(x) < ∞
Hope this helps.
help please? I just need an answer. A clear explanation earns brainliest.
Answer:
9. You don't need to take action because the denominator is the same. You only operate on the numerator.
10. Use equivalent fractions that do have a shared denominator if the denominators are not the same. To accomplish this, you must identify the two denominators' least common multiples (LCM). Rename the fractions having a common denominator before adding those with different denominators.
Step-by-step explanation:
9. You don't need to take action because the denominator is the same. You only operate on the numerator.
10. Use equivalent fractions that do have a shared denominator if the denominators are not the same. To accomplish this, you must identify the two denominators' least common multiples (LCM). Rename the fractions having a common denominator before adding those with different denominators.
the manager of a gas station has observed that the times required by drivers to fill their car's tank and pay are quite variable. in fact, the times are exponentially distributed with a mean of 6 minutes. what is the probability that a car can complete the transaction in less than 5 minutes?
The probability that a car can complete the transaction in less than 5 minutes is approximately 0.578 or 57.8%.
Since the times required by drivers to fill their car's tank and pay are exponentially distributed with a mean of 6 minutes, we can use the exponential distribution formula to find the probability that a car can complete the transaction in less than 5 minutes:
P(X < 5)
where X is the time required for a car to complete the transaction.
To find P(X < 5), we can use the cumulative distribution function (CDF) of the exponential distribution, which is:
F(x) = 1 - e^(-λx)
where λ is the rate parameter of the distribution. For an exponential distribution with mean μ, the rate parameter λ is equal to 1/μ.
So, in our case, λ = 1/6 and we can calculate P(X < 5) as:
P(X < 5) = F(5) = 1 - e^(-1/6 × 5) ≈ 0.578
In other words, there is a 57.8% chance that a car will finish filling its tank and paying within 5 minutes at this gas station.
To learn more about probability click on,
https://brainly.com/question/29221515
#SPJ4
help! i need help best answer gets brainly ! thank you
The measure of angle ∠1 in the figure is 28 degrees.
What is the measure of angle 1 in the figure?Vertical angles are simply angles that are opposite of each other when two lines cross.
They are congruent, meaning that they have the same angle measure.
Angle 140° and angle ( 112° + ∠1 ) are vertical angles since they are opposite of each other as two lines cross.
Since vertical angles are congruent, Angle 140° and angle ( 112° + ∠1 ) are equal.
Hence;
Angle 140° equals angle ( 112° + ∠1 )
140 = 112 + ∠1
Solve for ∠1
∠1 = 140 - 112
∠1 = 28°
Therefore, angle 1 measures 28 degrees.
Learn more about vertical angle here: https://brainly.com/question/24460838
#SPJ1
Jenny and Hong each opened a savings account today. Jenny opened her account with a starting amount of $160, and she is going to put in $50 per month.
Hong opened his account with no starting amount, and he is going to put in $90 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in
the account after x months.
Amount of money in Jenny's account (in dollars) =
Amount of money in Hong's account (in dollars) =
(b) Write an equation to show when the two accounts have the same
the fol
amount of money?
Answer:
a)
jenny - $160 + $50X = total
hong - $90X = total
b)
$160 + $50X = $90X
Step-by-step explanation:
a)
jenny starts with $160 so that is the flat rate, does not depend on X. the $50 does depend on X. add these together and you get the total amount on money in x amount of monthshong starts with $0 dollars, and because it doesnt depend on x, it does not need to be in the equation. $90 does depend on x. so it's just 90X = totalb)
all you need to combine these is put an equal sign between the two equations.mateo has drawn a line to represent the parallel cross-section of the triangular prism. is he correct? explain. riangular prism lying on a rectangular face and a line drawn along the length of a rectangular face
Based on the information provided, Mateo has drawn a line to represent the parallel cross-section of the triangular prism. Is he correct? Yes, he is correct. Here's an explanation:
A triangular prism has two triangular bases and three rectangular faces. When a triangular prism is lying on a rectangular face, it means that one of its rectangular faces is on the bottom. If Mateo draws a line along the length of this rectangular face, he is creating a parallel cross-section of the triangular prism.
This is because the line he drew is parallel to the triangular base of the prism, and the two bases are also parallel to each other. A parallel cross-section is created when a plane cuts through a solid parallel to its base, and in this case, Mateo's line fulfills this condition.
Therefore, Mateo is correct in representing the parallel cross-section of the triangular prism by drawing a line along the length of a rectangular face.
Learn more about prism at https://brainly.com/question/31315453
#SPJ11
The function h(t) = −16t2 + 48t + 36 models the height of a ball, in feet, at t seconds after being thrown into the air.
Part A
What feature of the function represents the highest point of the ball?
A. end behavior
B. symmetry
C. vertex
D. zero
Part B
What is the highest point of the ball, in feet?
