The required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
3 1/2+(-7 1/5) = 3+(-7) + 2/5 + (-1/5)
7/2 - 34/5 = -4 + 2/5 + -1/5
-33/10 = -4 + 1/5
-33/10 ≠ -19/5
Thus, the required simplified solution of the given expression is LHS is not equal to RHS as -33/10 ≠ -19/5.
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For this exponential function,
what is the output value (y),
when the input value (x) is O?
y = 2.3x
(0, [?])
Answer:
When the input value (x) is 0, the output value (y) is also 0. In this exponential function, any value raised to the power of 0 equals 1, and 2.3 raised to the power of 0 equals 1, so 2.3x (0) = 2.3 * 1 = 2.3, and the output value is 0.
find the 12 term of the geometric sequence 10 -20 40
Answer:
the answer is 9.6
Step-by-step explanation:
Suppose you choose at random a number from the interval
[8,32]
with the following density function:
f(x)= 32256
3
⋅x 2
,8≤x≤32
The probability of the event
E=[10,23]
is
P(E)=
The probability of selecting a number from the interval [10,23] is 3/32256 × (23^2 - 10^2) = 0.7122. Probability of selecting number [10,23] is 0.7122, integrating density function.
The probability of selecting a number from the interval [8,32] is given by the density function f(x)= 3/32256⋅x^2, where 8 ≤ x ≤ 32. We can calculate the probability of the event E=[10,23] by integrating the density function over the interval, i.e. P(E)=∫1023f(x)dx. This can be simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. Therefore, the probability of selecting a number from the interval [10,23] is 0.7122. To calculate this, we first determined the probability density function f(x) by noting that the probability of selecting a number between 8 and 32 is 1. We then divided this probability by the size of the interval, giving us the probability density f(x)= 3/32256⋅x^2. This was used to calculate the probability of the event E=[10,23] by integrating the density function over the interval. The integral was simplified to P(E)=3/32256 × (23^2 - 10^2), which equals 0.7122. This is the probability of selecting a number from the interval [10,23].
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In an isosceles triangle, the two equal sides are
called the
Select one:
O a. altitudes
O b. legs
O c. medians
O d. bases
Answer: B. Legs
Step-by-step explanation: The sides of the triangle are called legs because the actual name of the triangle, isosceles, comes from the greek word Iso meaning same, and the greek word Skelos, meaning leg.
how many yards in a foot
A yard is 36 inches or three feet long. The yard is a common way to express distance. A yard measures 3 feet.
Is a yard exactly 3 feet?36 inches or three feet make up a yard. Distances are frequently expressed using the yard. 3 feet make up a yard.
The length is determined by the yard and feet. In both the imperial and US customary systems of measuring, both units are utilized. Three feet make up one yard. The length of three feet is equal to one yard.
The yard to foot conversion factor makes 1 yard equivalent to 3 feet. Use the converter below to change the value of a yard to a foot.
The yard is an English unit of length that is equivalent to 3 feet, or 36 inches, in both the British imperial and US customary systems of measurement. It has been precisely standardized as 0.9144 meters by international agreement since 1959.
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can someone help please and I will give brainliest :))
Answer: The car is driving 374 meters in 17 seconds, so the car is driving 22 meters in 1 second. The Bus is drving 414 meters in 23 seconds, so the bus is driving 18 meters in 1 second. The car is traveling faster. It is traveling faster by 22 - 18 = 4 meters per second.
Step-by-step explanation:
374/17 = 22.
414/23 = 18.
22-18 = 4.
Pls help me i’ll give brainliest
Answer:
Step-by-step explanation:
root 14= 3.7
root 15= 3.9
24/7= 3.4
so the numbers will be placed in its location accordingly
A construction company completes two projects. The first project has $3,000 in labor expenses for 60 hours worked, while the second project has $2,100 in labor expenses for 42 hours worked. The relationship between the company’s labor expenses and hours worked is linear. Which of the following would correctly calculate the y-intercept of the linear equation? Select all that apply. 3,000 = 50(60) + b 3,000 = 0.02(60) + b 60 = 50(3,000) + b 2,100 = 0.02(42) + b 2,100 = 50(42) + b 42 = 50(2,100) + b
The equation that correctly calculate the y-intercept of the linear equation would be;
3,000 = 50(60) + b
2,100 = 50(42) + b
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given that The first project has $3,000 in labor expenses for 60 hours worked, while the second project has $2,100 in labor expenses for 42 hours worked.
Then the relationship between the company’s labor expenses and hours worked is linear.
So, the required equation are;
3,000 = 50(60) + b
2,100 = 50(42) + b
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Divide using long division . -4x^2+12x^3-7x+2 by 2x^2 +1
The quotient is -2x2 + 8x3 - 7x + 2 and indeed the remainder is 0, according to the question.
What is an example of long division?We can put the division symbol "" between two integers to indicate that they have been split. As an illustration, we may write 36 6 to represent the division of 36 by 6. Additionally, we may represent it as the fraction 366.
To divide[tex]-4x^2 + 12x^3 - 7x + 2[/tex] by [tex]2x^2 + 1[/tex]using long division, we write out the division in the form:
[tex]2x^2 + 1[/tex]
[tex]-4x^2 + 12x^3 - 7x + 2[/tex]
Step 1: Divide the first term of the dividend ([tex]-4x^2[/tex]) by the first term of the divisor (2x^2). We get -2x^2.
Step 2: Multiply the entire divisor ([tex]2x^2 + 1[/tex]) by [tex]-2x^2.[/tex] This gives us[tex]-4x^4 + -2x^2.[/tex]
Step 3: Subtract this result from the dividend, updating the dividend to [tex]8x^3 - 7x + 2.[/tex]
Step 4: Repeat the process until the degree of the remainder is less than the degree of the divisor. In this case, the final remainder is non-zero, so we have:
[tex]2x^2 + 1[/tex]
[tex]-4x^2 + 12x^3 - 7x + 2[/tex]
[tex]-2x^2[/tex]
[tex]8x^3 - 7x + 2[/tex]
[tex]8x^3 - 7x + 2[/tex]
So the quotient is [tex]-2x^2 + 8x^3 - 7x + 2[/tex] and the remainder is 0.
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h = 17 + x/6 find the output h when the input is -18
Answer:
x = 6h-102
Step-by-step explanation:
multiply both sides
move the terms
change the signs
reorder the terms
let be a random variable with pdf where is a constant. find the variance of (write it up to first decimal place).
The variance of the random variable X is 0.
To find the variance of the random variable X, we need to compute its mean (μ) and then calculate the expected value of the squared deviations from the mean.
The variance (σ²) is the average of these squared deviations.
First, let's find the mean (μ):
μ = ∫[x × f(x)]dx
Considering the piecewise function, we can split the integral into two parts:
For -3 < x < 0:
∫[-cx × (-cx)]dx = c² × ∫[x²]dx
= c² × [x³ / 3] between -3 and 0
= c² × (0 - (-3)³ / 3)
= c² × (0 - (-27) / 3)
= c² × (-9)
For 0 ≤ x < 3:
∫[cx × (cx)]dx = c² × ∫[x²]dx
= c² × [x³ / 3] between 0 and 3
= c² × (3³ / 3 - 0)
= c² × (27 / 3)
= c² × 9
Therefore, the mean (μ) is given by:
μ = (-9c² + 9c²) / 6
= 0
Now, let's calculate the expected value of the squared deviations from the mean:
E[(X - μ)²] = ∫[(x - μ)² × f(x)]dx
For -3 < x < 0:
∫[(x - 0)² × (-cx)]dx = c × ∫[x²]dx
= c × [x³ / 3] between -3 and 0
= c × (0 - (-3)³ / 3)
= c × (-27 / 3)
= -9c
For 0 ≤ x < 3:
∫[(x - 0)² × cx]dx = c × ∫[x²]dx
= c × [x³ / 3] between 0 and 3
= c × (3³ / 3 - 0)
= c × (27 / 3)
= 9c
Therefore, the expected value of the squared deviations from the mean is:
E[(X - μ)²] = (-9c + 9c) / 6
= 0
Finally, the variance (σ²) is the average of the squared deviations:
σ² = E[(X - μ)²]
= 0
Hence, the variance of the random variable X is 0.
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How do you determine the equation of a circle in center-radius form whose center is (4,-3) and passes through the point (6,0)?
Using the formula (x - a) 2 + (y - b) 2 = r 2 and knowing the circle's radius and center, you can determine the circle's equation. Here, stands for the circle's center, and is the radius.
How to Find the equation of a circle using the centre and radius?A circle's center and radius can be used to get its equation. The discriminant can identify the type of intersections between two circles or a circle and a line to demonstrate tangency.
Utilize the equation (x - a2 + (y - b)2 = r 2 to determine a circle's equation when you are aware of its radius and center. Here, (a,b) stands for the circle's center and is its radius.
It's merely spelled differently, but this equation is the same as the basic equation of a circle.
Example
A circle with a center at (2,-3) and a radius of √7 has an equation that you must find.
(x - 2 )² + (y - (-3))² = (√7)²
(x - 2 )² + (y + 3 )² = 7
You can add more to this if it's necessary for more labor to provide:
x² - 4x + 4 + y² + 6y + 9 - 7 = 0
x² + y² -4x + 6y + 6 =0.
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$75 invested for 6 months yield simple interest of $2.00. what was the of interest ?
The rate of interest was 5.33%
What Is Simple Interest?Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.
Given here: The amount invested was $75 for 6 months and S.I =$2.0
We know S.I= P×R×T / 100
2.0 =75×r×1/2 /100
r=2×100×2/75
r=400/75
r=5.33%
Hence, The rate of interest was 5.33%
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shawn and brittney rode bikes for the same amount of time. shawn traveled at 10.2 mph and brittney at 13.7 mph. if brittney traveled 8.75 miles further than shawn, how long were they both riding bikes for?
Shawn and Brittney both were riding bikes for 2.5 hours.
As per the given data, Shawn traveled at 10.2 mph and Britney traveled at 13.7 mph.
They traveled for the same amount of time.
Britney traveled 8.75 miles further than Shawn.
Let, Shawn and Britney both traveled for t hours.
Shawn traveled at 10.2 miles per hour.
Therefore for t hours, Shawn traveled is [tex]$(10.2 \times \mathrm{t})$[/tex] miles [tex]$=10.2 \mathrm{t}$[/tex] miles.
Britney traveled at 13.7 miles per hour.
Therefore for t hours, Britney traveled [tex]$(13.7 \times \mathrm{t})$[/tex] miles [tex]$=13.7 \mathrm{t}$[/tex] miles.
Brittney traveled 8.75 miles more than Shawn.
That means the distance between both of them after t hours is 8.75.
Therefore We can write,
13.7 t - 10.2 t = 8.75
3.5 t =8.75
t = [tex]$\frac{8.75}{3.5} \\[/tex]
t = 25
So we have got that they are riding the bikes for 25 hours.
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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4
Answer:
Option A and Option D have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p. The equation can be rewritten as 2.3p – 14.1 = 6.4p – 4 by combining the constants and subtracting 0.01p from both sides.
russell is a history teacher who recently held an exam in his class. the mean score result is 65, while the standard deviation was 20. assume that the scores are normally distributed. if a student's z-score was 1.5, how many points did he score on the exam?
If a student's z-score was 1.5, then 95 points he scored on the exam.
The mean score result is 65.
The standard deviation was 20.
A student's z-score was 1.5.
The average of a set of data is known as the set's mean. Each item of data has a z-score that indicates how far it deviates from the mean, whereas the standard deviation of a set of data reveals how dispersed the data is.
We can relate a piece of data using a formula that uses the mean, standard deviation, and z-score to identify various pieces of information in a certain situation.
The formula of z-score is:
Z = (X - Mean)/Standard Deviation
Now putting the value
1.5 = (X - 65)/20
Multiply by 20 on both side, we get
30 = X - 65
Add 65 on both side, we get
X = 95
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Jan spends part of her year as a member of a gym. She then finds a better deal at another gym, so she
cancels her membership with the first gym and spends the rest of the year with the second gym. The
membership to the first gym costs $80 per month, while the membership for the second gym costs $45 per
month. If she ends up spending a total of $645 over the course of the year, how much time did she spend at
each gym?
Answer:
Jan spent $240 at the first gym and $405 at the second gym.
Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of inequalities.
y\leqx2 , z\leq0
x\geqz2 , -5\leqy\leq0
The set of points is a pyramid-shaped region in space with a base of the xz-plane between x = z2 and x = 0, extending to a height of y = 0 at its peak. The region is bounded by the planes y = x2, z = 0, and y = -5.
The set of points is bounded by the four planes: y = x2, z = 0, x = z2, and y = -5. The two inequalities, y <= x2 and z <= 0, imply that the region is limited to the space below the plane y = x2 and behind the plane z = 0. The other two inequalities, x >= z2 and -5 <= y <= 0, indicate that the region is limited to the space in front of the plane x = z2 and between the planes y = -5 and y = 0. This forms a pyramid-shaped region with a base at the xz-plane between x = z2 and x = 0, extending to a height of y = 0 at its peak.
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I need help PLEASE SOMEONE!!!!!
Answer:
Square
4,4,4
Step-by-step explanation:
A restaurant sells Thai iced teas and flatbread called roti. The scatter plot shows the relationship between the number of Thai iced teas and the number of roti sold each day for two weeks. Which line best fits the data?
A linear trend line is best fits the data.
Which line best fits the data?The theory used in this question is linear regression, which is used to identify the linear relationship between two variables.
By plotting the points from the scatter plot and fitting a line to the data, we can determine the linear trend of the data.
1. Look at the scatter plot and identify the type of data.
In this case, the data is numeric, showing the relationship between two variables: the number of Thai iced teas and the number of roti sold each day.
2. Determine the type of line that best describes the data.
A linear trend line is best for this type of data, as it shows the relationship between the two variables in a straight line.
3. Draw the line. Using the data points from the scatter plot, draw a straight line that passes through as many of the points as possible.
This line is the linear trend line.
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A conveyor belt carries bales of hay from the ground to the barn loft 24 ft above the ground. The belt makes a 60 degree angle with the ground. How far does a bale
of hay travel from one end of the conveyor belt to the other. Round your answer to the nearest foot.
Answer = 24 ÷ sin 60 = 27.71281 = 28 ft
Tyrants his own landscaping business he earns $30 per hour pulling weeds 25 per our raking leaves and $20 per hour cutting the grass ty want to know how much he earns each week
Tyrant earns a total of $800 per week from his landscaping business.
What is amount?Amount the term used to describe a quantity or size of something will stop it is used to refer to a number of objects items or people as well as the measure of money time distance.
He earns $600 from pulling weeds ($30 per hour for 20 hours), $250 from raking leaves ($25 per hour for 10 hours) and $150 from cutting the grass ($20 per hour for 10 hours). This adds up to a total of $800 per week. By working this amount of hours, Tyrant can make a decent amount of money and still have time to enjoy his life.
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PLEASE Help I will Mark Brainlist thanks so much :D
Answer:
x = a, p
Step-by-step explanation:
the solution is at the points of intersection of the parabola and the straight line.
the points of intersection of the two graphs are (a, b ) and (p, q )
with x = a and x = p
thus x = a , p are the values of x that make the statement true
Where do i put the dots on the graph? Screenshot*
Swathi purchased a bed for $219 and a mattress for $359. How much did she spend on these items in total?
$
Answer:578
Step-by-step explanation:
219+359=578
a disk 2 inches in diameter is thrown at random on a tiled floor, where each tile is a square with sides 4 inches in length. let c be the event that the disk will land entirely on one tile. in order to assign a value to p(c), consider the center of the disk. in what region must the center lie to ensure that the disk lies entirely on one tile?
The probability that the disk will land entirely on one tile is 1/4.
For, this question I have attached an image which shows that the inner red square is the area of a tile in which the centre of the disk could land and the disk would be contained entirely within the tile while the grey area is the area in which the centre of the disk would land and the disk would not be entirely contained within the tile.
Now, The area of a square is the square of side length. The inner square has an area of 2² = 4 and the entire square (red and grey regions combined) has an area of 4² = 16.
Hence, the probability that the disk's centre lands in the red zone is the area of the red zone, divided by the total area, which is
4/16 = 1/4
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Miguel bought 8 equally priced pens for $3.84
How much will 15 pens cost?
if she uses 486.7 cm2 of the paper to cover the lateral surface area of the cylinder, what is the diameter of the cylinder?
The diameter of the required cylinder is a function dependent on h given as 155/h
What is the area and volume of a right circular cylinder?The volume of a Right Circular Cylinder. In general, the volume of a right cylinder is the area of the base times the height of the cylinder. The area of the circular base is given by the formula A = πr2. Substitute to get V = πr2h.
Given here: The lateral surface Area of the cylinder as 486.7 cm²
Let the radius of the cylinder be r then we have
2πrh=486.7
D=486.7/π×h ( where D=2r)
D=155/h
Where h is the height of the cylinder.
Hence, The diameter of the required cylinder is a function dependent on h given as 155/h
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Find the average rate of change of the function over the given intervals.
f(x) = 10x^3 + 10; a) [1,3] b) [-6,6]
a) The average rate of change of the function f(x) = 10x^3 + 10 over the interval [1,3] is ______ (Simply your answer)
The average rate of change of the function f(x) = 10x³ + 10 over the interval [1,3] is 130, and The average rate of change of the function f(x) = 10x³ + 10 over the interval [-6,6] is 360.
The average rate of change of function f over the interval a≤x≤b is given by the expression:
f(b)−f(a)/b−a
It is a calculation of how much the function changed per unit, on average, over that interval.
It is derived from the straight-line slope connecting the interval's endpoints on the function's graph.
a) [1,3]
Here, a = 1, b = 3
⇒f(3)−f(1)/3−1
⇒[10(3)³ + 10] - [10(1)³ + 10]/2
⇒(270 + 10 - 10 - 10)/2
⇒260/2
⇒130
b) [-6,6]
Here, a = -6, b = 6
⇒f(6)−f(-6)/6+6
⇒[10(6)³ + 10] - [10(-6)³ + 10]/12
⇒(2160 + 10 + 2160 - 10)/12
⇒4320/12
⇒360
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Based on these formulas, which scenario would not have been possible?
Following the volumes a cone formula, one can determine a cone's volume given the necessary inputs. When the basis radius or even the see that, height, and slanted height of the cone are determined, the further stages can be carried out.
What is the cone's volume formula?V=1/3hπr²
Cone volume is calculated using the method V=1/3hr2. Learn how to solve a sample problem using this formula.
Step 1: Write down the given parameters, "r" denoting the radius of the cone's base, "d" denoting its diameter, "L" denoting its slant height, and "h" denoting its height.
Step 2: Apply the calculation to determine the cone's volume.
Cone volume using the base radius: V = 1/(r2h) or 1/(r2) (L2 - r2)
Cone volume using the formula V = (1/12)d2h = (1/12)d2 (L2 - r2)
Determine the volume of the a cone with a 3 inch radius and a 7 inch height. (Use π = 22/7).
Solution: We are aware of the volume
As we already know, the cone's volume is (1/3)r2h.
Taking into account that r = 3 inches, h = 7 inches, and = 22/7
So, the volume of the cone is V = (1/3)r2h V = (1/3) × (22/7) × (3)2 × (7) = 22 × 3 = 66 in3
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