Answer:
24 inches squared
Step-by-step explanation:
That is a triangle, and the area of a triangle is 1/2(b)(h), which is one half times the base times the height. Let's identify those things.
1/2: the area of a rectangle can be calculated base times the height, and a triangle is half of that rectangle, hence the 1/2
(b) or base: base is usually identified as the horizontal line in the triangle, which is 6 inches in this case.
(h) or height: height is usually the vertical line, and in this case, the vertical line is 8 inches.
Now time for the math:
1/2(6)(8) = 24 inches squared
Can someone help me with this question
Thank you!
Answer:
-10x^2+4x-8 im 75% sure
Step-by-step explanation:
box contains 3 red pencils, 5 blue pencils, 4 black pencils, and 2 green pencils.
The best description of the likelihood of selecting a green pencil at random from the box is , 1 of 1.
Select Choice
.
The likelihood of selecting a green pencil at random from the box is the probability of randomly selecting a green pencil which is equal to 1/7
What is probabilityThe probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
The total possible outcome = 14
the event of selecting a green pencil = 2
probability of selecting a green pencil = 2/14
by simplification;
probability of selecting a green pencil = 1/7
Therefore, likelihood of selecting a green pencil at random from the box is the probability of randomly selecting a green pencil which is equal to 1/7.
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Evaluate each expression for t = 0, x = 1.5, y = 6, and z = 23
1. y + 5 = ??
2. z - 2x = ??
3. 2z - 2y = ??
4. 2.6y - 2x =??
5. 4(y - x) = ??
6. 4(2 + z) + 5 = ??
Answer:
1. 11
2. 20
3. 34
4. 12.6
5. 18
6. 105
Step-by-step explanation:
We are told that ---> t = 0, x = 1.5, y = 6, and z = 23
1. y + 5
= 6 + 5
= 11
2. z - 2x
= 23 - 2(1.5)
= 23 - 3
= 20
3. 2z - 2y
= 2(23) - 2(6)
= 46 - 12
= 34
4. 2.6y - 2x
= 2.6(6) - 2(1.5)
= 15.6 - 3
= 12.6
5. 4(y - x)
= 4(6 - 1.5)
= 24 - 6
= 18
6. 4(2 + z) + 5
= 4(2 + 23) + 5
= 8 + 92 + 5
= 105
What is the LCM of 72, 96and 160
Two numbers each with two decimd
places round to 312 to one decima
place. The total of the numbers is
62.4, What could the numbers be?
You need to be clear on their understands
of rounding and what it means when f
Says two numbers each with two
decimal places, for example, they may
choose 3121+ 3419 both of which
round
to 31.2 when rounded to
I decimal place.
Fows on knowing that when rounding.
it is
Can they find all of these using
Systematic approach.
It is not possible to find two numbers with two decimal places that round to 312 when rounded to one decimal place and have a total of 62.4.
To solve this problem systematically, we can break it down into smaller steps:
Let's assume the two numbers are x and y, both with two decimal places.
We can represent them as x = a.b and y = c.d, where a, b, c, and d are digits.
Rounding x and y to one decimal place gives us the following equations:
Round(x) = a.b ≈ 312
Round(y) = c.d ≈ 312
Since the total of the numbers is 62.4, we have the equation:
x + y = a.b + c.d
= 62.4
From Step 2, we know that both a.b and c.d are approximately equal to 312.
So, we can write:
a.b ≈ 312
c.d ≈ 312
Since a.b and c.d are rounded to one decimal place, we can rewrite them as:
a.b = 312 + p
c.d = 312 + q
p and q are the decimal parts that were rounded.
Substituting the new representations of a.b and c.d into the equation from Step 3, we get:
(312 + p) + (312 + q) = 62.4
Simplifying the equation gives us:
624 + (p + q) = 62.4
Solving for (p + q), we have:
p + q = 62.4 - 624
= -561.6
Since p and q are decimal parts, they must be between 0 and 1. -561.6 is outside this range, which means there are no values for p and q that satisfy the given conditions.
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A line passes (-8,-2) and has a slope of 5/4. Write an equation in Ax + By=C
Answer:
5x-4y = -32
Step-by-step explanation:
First write the equation in point slope form
y-y1 = m(x-x1)
y - -2 = 5/4 ( x- -8)
y+2 = 5/4 (x+8)
Multiply each side by 4 to clear the fraction
4( y+2 )= 4*5/4 (x+8)
4y +8 = 5(x+8)
4y+8 = 5x+40
Subtract 4y from each side
8 = 5x-4y +40
Subtract 40 from each side
-32 = 5x-4y
5x-4y = -32
Answer:
The answer is
5x - 4y = -32Step-by-step explanation:
To write an equation of a line given a point and slope use the formula
y - y1 = m( x - x1)
where
m is the slope
( x1 , y1) is the point
From the question
slope = 5/4
point (-8 , -2)
So the equation of the line is
\(y + 2 = \frac{5}{4} (x + 8)\)Multiply through by 4
4y + 8 = 5( x + 8)
4y + 8 = 5x + 40
5x - 4y = 8 - 40
We have the final answer as
5x - 4y = -32Hope this helps you
The utility function is u(x1,x2)=ax1+bx2, with a>0,b>0. The budge set (constraint) is p1x1+x2=w where the price of good 2 is normalized to 1 , and w is consumer's total wealth. Find the optimal consumption bundle (x1∗,x2∗) as a function of w and p1 ? Note that this is similar to the perfect substitute case shown in lecture notes 2 , so you need to use a graph to consider 3 difference cases.
The optimal consumption bundle (x1*, x2*) can be determined by solving the consumer's utility maximization problem subject to the budget constraint. Given the utility function u(x1, x2) = ax1 + bx2, where a > 0 and b > 0, and the budget constraint p1x1 + x2 = w, we need to find the values of x1* and x2* that maximize the utility function while satisfying the budget constraint.
To analyze the problem graphically, we can plot the budget constraint on a two-dimensional graph with x1 on the horizontal axis and x2 on the vertical axis. The slope of the budget constraint is -p1, indicating the rate at which the consumer can trade x1 for x2. The budget constraint represents all the possible combinations of x1 and x2 that the consumer can afford given their wealth (w) and the price of good 1 (p1).
By drawing indifference curves for different levels of utility, which are downward-sloping straight lines in this case due to the linear utility function, we can identify the optimal consumption bundle. In this particular case, since the utility function represents perfect substitutes, the indifference curves are parallel straight lines with a slope of -a/b. The consumer maximizes utility by choosing the consumption bundle that lies on the highest possible indifference curve and is tangent to the budget constraint.
Now, let's consider three different cases:
Case 1: When w/p1 < a/b, the consumer's wealth is not sufficient to reach the highest indifference curve. In this case, the consumer's optimal consumption bundle will be at the corner point of the budget constraint where x1 = w/p1 and x2 = 0.
Case 2: When w/p1 > a/b, the consumer's wealth is more than enough to reach the highest indifference curve. In this case, the consumer's optimal consumption bundle will be at the point where the budget constraint is tangent to the highest indifference curve, which will be at x1 > 0 and x2 > 0.
Case 3: When w/p1 = a/b, the consumer's wealth is exactly enough to reach the highest indifference curve. In this case, the consumer can choose any consumption bundle along the budget constraint.
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Using the data in the scatter plot what is a reasonable slope of a model that fits this data
We can conclude that the reasonable slope of a model that fits the given data is: C. 1.
What is the Slope on a Scatter Plot?Slope = change in y/change in x.
To find the slope of that fits the data, pick any two points on the scatter plot, say, (12, 1985) and (16, 1988)
Slope = (1988 - 1985)/(16 - 12) = 0.75 ≈ 1.
Therefore, we can conclude that the reasonable slope of a model that fits the given data is: C. 1.
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Write out pi in fraction form. lolol
Answer:
the answer to your question is 157/50 which would be 3 7/50
can u find the suface area of the figure below
The surface area of the given prism is 230 in².
Given is a net of triangular prism, we need to find the surface area of the prism,
The surface area of a triangular prism = perimeter × length + base area
= (5 + 5 + 8) × 10 + 5 × 10
= 18 × 10 + 50
= 180 + 50
= 230 in²
Hence the surface area of the given prism is 230 in².
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Hi, could you please help me with the following? i appreciate it!!
Sketch the graph of the given priecewise-defined function. Find any x- and y-intercepts of the graph. Give any numbers at which the graph is discontinuous.
y= -2 + |x+1|
thank you!!
A graph that represents the absolute function y = -2 + |x + 1| is shown on the coordinate plane attached below.
The x- and y-intercepts are:
x-intercepts = (-3, 0) and (1, 0).y-intercept = (0, -1).What is an absolute value function?In Mathematics and Geometry, an absolute value function is a type of function that contains an expression, which is placed within absolute value symbols.
By critically observing the transformed absolute value function y = -2 + |x + 1|, we can logically deduce that the parent absolute value function y = |x| was vertically shifted downward by 2 units and horizontally shifted (translated) to the left by 1 units. Also, the graph is continuous over all the intervals and the x-intercepts and y-intercepts are:
x-intercepts = (-3, 0) and (1, 0).
y-intercept = (0, -1).
In conclusion, we would use an online graphing tool to plot the given absolute value function y = -2 + |x + 1| as shown in the graph attached below.
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If point E is the midpoint of segment available and point d is the midpoint of segment bf which expression represents the value of S?
On solving the question, The expression that most effectively represents u's value would be: u = 2s
What does segment mean?A area that is formed by a secant or chord and the matching arc of the circle is referred to as a segment of a circle. The major section is the one that shows a greater region, while the minor segment is the one that shows a smaller area.
We have
In ΔABC,
E is the midpoint in the segment AC,
While D is the midpoint of BC,
As different letters are provided equivalent to different segments. For example; Segment ED = s ; Segment CE = p ; Segment EA = r
\(Segment CD = q ; \\Segment DB = t ; \\Segment ED = s ; \\Segment AB = u\)
As,
CE = 0.5 × AC(midpoint)
CD = 0.5 × CB (midpoint)
Thus,
\(\frac{CE}{AC} = \frac{CD}{CB} = \frac{ED}{AB} = \frac{1}{2}\) (Through side angle side similarity)
Since ED = s and AB = u
Therefore,
u = 2s (using midpoint theorem)
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Find the Value of X!!! Geometry!! Pls helppp!! I will mark brainlest. Thank you!! :)
-2/5y = -22 equation
ps. I think this one a two step equation
A. 75
B. 55
C. -55
D. -75
Answer:
55
Step-by-step explanation:
multiply both sides by -5/2
Answer:
B. 55
Step-by-step explanation:
-2/5y = -22
y = -22 : -2/5
y = -22 x 5/-2
y = 11 x 5/1
y = 11 x 5
y = 55
that doesn't give the answer
Answer:
what doesnt give the answer??
Step-by-step explanation:
Write the slope-intercept form of the
equation of a line with a slope of −2/5 that passes through the point (15, −9/2).
The equation in slope-intercept form is y = (-2/5)x - 9/2.
What is slope-intercept?Slope-intercept form is an equation of a line that is written in the form of y=mx+b, where m is the slope of the line and b is the y-intercept. The slope-intercept form makes it easy to identify the slope and y-intercept of a line from an equation.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Therefore, for a line with a slope of −2/5 that passes through the point (15, −9/2), we can solve for b using the point-slope formula.
Point-slope formula: y - y1 = m(x - x1)
Plugging in the given information, we get:
-9/2 - (-9/2) = (-2/5) (15 - 15)
Solving this equation yields b = -9/2.
Therefore, The equation in slope-intercept form is y = (-2/5)x - 9/2.
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Find the probability, expressed to the nearest percent, that a variable has a z-score less than 0.42. 65% 6690 6798 689
Explanation:
The probability that a variable has a z-score less than a number - let's call this number 'a'- is represented on a z-score table. Each number in the table represents the area under the curve on to the left of 'a':
In other words, the numbers in the table are the probability of the variable being less than a:
\(P(Z\(P(Z<0.42)=0.6628\)If we multiply by 100 we have the probability expressed as a percent: 66.28%.
Answer:
Rounded to the nearest percent, P( Z < 0.42) = 66%
I NEED HELP! simplify expression
Answer:
I think it would be (25) + 27
Step-by-step explanation:
im srry if its wrong im bad at math but i hope this helped!
I really need help with this
Answer:
Step-by-step explanation:
thhh
Which equation best represents the line graphed above?
Answer: x=2 because for any y value the x value is always 2.
Can someone help me solve this ???
Answer:
y = 4 x = 12
Step-by-step explanation:
The blue square I started on my own and ended with a calculator
URGENT!!! I ONLY HAVE A SPECIFIC AMOUNT OF TIME! PLEASE DON'T SKIP!!!
BRAINLIEST + EXTRA POINTS!!
Answer:
x=5
Step-by-step explanation:
25x+30+5x=180 <----- do this (dont feel like showing my work)
USE SYMBOLAB I LITERALLY USE IT ALL THE TIME!!
Find the area of this parallelogram.
Step by step explanation :
❃ \( \underline{ \underline{ \sf{Given} }}: \)
Base length ( b ) = 21 cmVertical height ( h ) = 9 cm Slant height = 12 cm { Ignore the slant height as it is not required while finding the area }❃ \( \underline{ \underline{ \sf{To \: find}} }: \)
Area of the given parallelogram✑ \( \bold{ \red{ \boxed{ \sf{Area \: of \: a \: parallelogram \: = bh}}}}\)
Substitute the known values :
⇝ \( \sf{21 cm \times 9 \: cm}\)
⇝ \( \boxed{ \bold{ \sf{189 \: {cm}^{2} }}}\)
☥ \( \boxed{ \boxed{ \tt{Our \: final \: answer : \bold{ 189 \: {cm}^{2} }}}}\)
Hope I helped ! ♡
Have a wonderful day / night ツ
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Please help,
A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
Determine the distance between the Woozy Wheel and the Roller Rail.
A. 119 units
B. 11 units
C. 169 units
D. 13 units
Answer:
D. 13 units
Step-by-step explanation:
Woozy Wheel: (-14, 1)
Roller Rail: (-2, -4)
\( \sqrt{ { - 14 - ( - 2))}^{2} + {(1 - ( - 4))}^{2} } \)
\( \sqrt{ {( - 12)}^{2} + {5}^{2} } \)
\( \sqrt{144 + 25} = \sqrt{169} = 13\)
The distance between the Woozy Wheel and the Roller Rail is D. 13 units
What is the distance formula between two points?The distance formula between two points (x₁, y₁) and (x₂, y₂) is
D = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Given, A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
The point at which Woozy Wheel is (-14, 1) and the point at which Roller Rail
is (-2, - 4).
∴ The distance between the Woozy Wheel and the Roller Rail is,
D = \(\sqrt{(-2 + 14)^2 + (-4 - 1)^2}\) units.
D = \(\sqrt{(12)^2 + (-5)^2}\) units.
D = \(\sqrt{144 + 25}\) units.
D = \(\sqrt{169}\) units.
D = 13 units.
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An automaker has introduced a new midsize model and wishes to estimate the mean EPA combined city and highway mileage, u. that would be obtained by all cars of this type. In order to estimate the u, the automaker has conducted EPA mileage tests on a random sample of 35 of its new midsize cars and has obtained the sample of mileages. 71 = 35 x = 24 population = 1.2 Calculate the 70% confidence interval. (round to the second decimal point) Lower bound of 70% confidence interval= Upper bound of 70% confidence interval=
To estimate the mean EPA combined city and highway mileage, the automaker conducted EPA mileage tests on a random sample of 35 midsize cars. The sample mean is 24, and the population standard deviation is 1.2. The task is to calculate the 70% confidence interval for the population mean.
To calculate the confidence interval, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))
First, we need to determine the critical value associated with a 70% confidence level. The critical value can be found using a standard normal distribution or a t-distribution, depending on the sample size and whether the population standard deviation is known.
Since the sample size is relatively large (n = 35), we can use the standard normal distribution. The critical value for a 70% confidence level corresponds to a z-score of ±1.036.
Next, we calculate the margin of error:
Margin of Error = (Critical Value) * (Standard Deviation / √(Sample Size)) = 1.036 * (1.2 / √35) ≈ 0.380
Finally, we can calculate the lower and upper bounds of the confidence interval:
Lower Bound = Sample Mean - Margin of Error = 24 - 0.380 ≈ 23.62
Upper Bound = Sample Mean + Margin of Error = 24 + 0.380 ≈ 24.38
Therefore, the 70% confidence interval for the mean EPA combined city and highway mileage is approximately 23.62 to 24.38.
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ELISE BOUGHT A VIDEO GAME FOR 85:00. IF THE STORE CHARGES 170 PERCENT OOF ITS COST FOR THE GAME. HOW MUCH IS THE STORES PROFIT?
The store is making a profit of $59.5 on the game whose original price is $85.
Given, Elise bought a video game for $85.
The store charges 170% of its cost for the game.
we have to find the profit that the store is making on the game.
As, according to the question it is clear that the store is charging 70% more than the original price of the game.
So, the profit of the store is 70% of the original price of the game i.e.
Profit = 70/100×85
Profit = 59.5
So, the store is making a profit of $59.5 on the game.
Hence, the store is making a profit of $59.5 on the game whose original price is $85.
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Question 2(Multiple Choice Worth 1 points)
(02.05 MC)
Given f(x) = 3x - 4 and g(x) = f(2x), which table represents g(x)?
x g(x)
1-2
24
3 10
x g(x)
1-1
20
35
O
x g(x)
12
24
36
The table that represents g(x) is
x g(x)
1 1
2 5
3 9
The correct option (4)
A function is defined as a relationship between a collection of inputs with one output each. In simple terms, a function is a relationship between inputs, with each input corresponding to exactly one output. Every function has a domain and a codomain or range. A function is commonly denoted by f(x), where x is the input.
From the given information, we have that
f(x) = 3x - 4 and
g(x) = f(2x)
Then,
g(x) = f(2x) becomes
g(x) = f(2x) = 3(2x) -4
g(x) = 6x - 4
Now, we'll plug x numbers ranging from 1 to 3 into the equation.
When x = 1
g(x) = 6x - 4 becomes
g(x) = 6(1) - 4
g(x) = 6 - 4
g(x) = 2
When x = 2
g(x) = 6x - 4 becomes
g(x) = 6(2) - 4
g(x) = 12 - 4
g(x) = 8
When x = 3
g(x) = 6x - 4 becomes
g(x) = 6(3) - 4
g(x) = 18 - 4
g(x) = 14
Hence, the table that represents g(x) is
x g(x)
1 2
2 8
3 14
Therefore option (4) is correct.
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Gary drops a pair of gloves off of a balcony that is 64 feet high down to his friend on
the ground. How long does it take the pair of gloves to hit the ground?
It takes the pair of gloves approximately 2 seconds to hit the ground.
To find the time it takes for the gloves to hit the ground, we can use the free fall equation, which is d = 1/2 * g * t^2, where d is the distance (64 feet), g is the acceleration due to gravity (approximately 32 ft/s^2), and t is the time in seconds.
1. Rearrange the equation to solve for t: t^2 = 2d/g
2. Plug in the given values: t^2 = 2(64 ft) / 32 ft/s^2
3. Calculate the result: t^2 = 4
4. Find the square root to get the time: t = √4 = 2 seconds
Summary: When Gary drops the pair of gloves from a 64-foot-high balcony, it takes about 2 seconds for them to hit the ground.
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A bookstore owner has 15 different books to arrange on the shelves in a display case. Each shelf can display 3 books.In how many different ways can the owner arrange 3 books on the top shelf of the display case
There are 15 different books and 3 each can be arranged on a shelf i.e., there are 15/3 i.e., 5 shelves to arrange the book in the the display case.
How many different ways can you arrange3 books on a shelf?different bundles of novels, and we have to put this bundle and other 3 books onto the shelf. So the total number of ways is 3! × (3 + 1)! = 144.How many ways can you arrange 3 books on a shelf from a group of 7?= 5040 arrangements. Three books that we want together have 3!Therefore, the number of ways in which the 3 letters can be arranged, taken all a time, is 3! = 3*2*1 = 6 ways.A trilogy is a set of three distinct works that are connected and can be seen either as a single work or as three individual works. They are commonly found in literature, film, and video games.When using three shelves, place the middle shelf higher or lower than the one on either side. Five shelves can be staggered with two or three higher than the others, alternating every other shelf for a horizontal groupingTo learn more about arrange3 books on a shelf refers to:
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Use the Integrating Factor Method to solve the following differential equations: x⁴ dy/dx + 2x⁴y = x⁴e⁻ˣ
a) Rewrite the equation in Standard Form. b) Identify P(x). c) Identify Q(x). d) Evaluate Integrating Factor. e) Solve for the general solution.
The equation in Standard Form. b) Identify P(x). c) Identify Q(x). d) Evaluate Integrating Factor. e) Solve for the general solution are given below:
a) Rewrite the equation in Standard Form:
To rewrite the equation in standard form, divide the entire equation by x⁴:
dy/dx + 2y = e^(-x)
b) Identify P(x):
In standard form, the coefficient of the y term is 2, which is the function P(x). So, P(x) = 2.
c) Identify Q(x):
In standard form, the right-hand side of the equation is e^(-x), which is the function Q(x). So, Q(x) = e^(-x).
d) Evaluate the Integrating Factor:
The integrating factor (IF) is given by the exponential of the integral of P(x) with respect to x. In this case, the integrating factor is:
IF = e^(∫P(x)dx) = e^(∫2dx) = e^(2x)
e) Solve for the general solution:
Multiply the entire equation by the integrating factor (IF = e^(2x)):
e^(2x) * (dy/dx + 2y) = e^(2x) * e^(-x)
Simplify the left side by applying the product rule of exponents:
(e^(2x) * dy/dx) + 2y * e^(2x) = e^(x)
Notice that the left side is now in the form (f(x)g(x))' = f'(x)g(x) + f(x)g'(x), where f(x) = y and g(x) = e^(2x). Apply the product rule and simplify further:
(d/dx)(y * e^(2x)) = e^(x)
Integrate both sides with respect to x:
∫(d/dx)(y * e^(2x)) dx = ∫e^(x) dx
Integrating the left side gives:
y * e^(2x) = ∫e^(x) dx = e^(x) + C₁, where C₁ is the constant of integration.
Finally, solve for y by dividing both sides by e^(2x):
y = (e^(x) + C₁) / e^(2x)
This is the general solution to the given differential equation using the Integrating Factor Method.
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