The statements about Alina's and Cesar’s estimates should be completed as follows:
Alina is 5 miles off the actual mileage of 50 miles. That is a percent error of 10%. Cesar is 10 miles off the actual mileage of 200 miles. That is a percent error of 5%. Because Alina's mileage is lesser than Cesar's mileage, each mile of error results in a greater percent error.What is percentage error?Percentage error is also referred to as percent error and it can be defined as a measure of the extent to which an experimental numerical value differs from the actual (theoretical) numerical value.
Mathematically, percentage error can be calculated by using this expression;
[tex]Percent\; error = \frac{Actual\;value - Experimental\;value}{Experimental\;value} \times 100[/tex]
For the Alina's result, we have:
Difference = Actual mileage - Estimated mileage
Difference = 50 miles - 45 miles
Difference = 5 miles.
Next, we would determine Alina's percentage error as follows:
Percentage error = 5/50 × 100
Percentage error = 500/50
Percentage error = 10%.
For the Cesar's result, we have:
Difference = Actual mileage - Estimated mileage
Difference = 200 miles - 190 miles
Difference = 10 miles.
Next, we would determine Cesar's percentage error as follows:
Percentage error = 10/200 × 100
Percentage error = 1000/200
Percentage error = 5%.
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Complete Question:
Alina and Cesar estimated the number of miles they drove during a trip. Alina estimated the number of miles they drove in the morning. Cesar estimated the number of miles they drove in the afternoon. Use the drop-down menus to complete the statements about Alina's and Cesar’s estimates.
Alina's Estimate Actual Mileage
45 miles 50 miles
Cesar's Estimate Actual Mileage
190 miles 200 miles
Alina is ___ miles off the actual mileage of 50 miles. That is a percent error of %.
Cesar is ___ miles off the actual mileage of 200 miles. That is a percent error of %.
Because Alina's mileage is _____ than Cesar's mileage, each mile of error results in a ____ percent error.
A box contains 5 reams of paper. How could you estimate the thickness of 2 sheets of paper. One ream is 500 sheets.
Answer:
If one ream is 500 sheets, then that would mean that two reams combined are 1,000 sheets, and the fact that there are 5 reams is just a random number meant to throw you off.
Ben's monthly housing costs for his new home will be $2100 per month. What
must his monthly net income be to keep housing as 30% of his budget?
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The monthly net income to keep housing a 30% of his budget is $7000.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Cost of monthly housing per month = $2100
$2100 = 30%
Monthly income = 100%
30% = 2100
Multiply 100/30 on both sides.
100/30 x 30% = 100/30 x 2100
100% = 7000
Thus,
The monthly net income to keep housing a 30% of his budget is $7000.
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one number is 9 more than 3 times another. Their product is 9 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two integers first
Let x and y be the two numbers we are trying to find.
'One number is 9 more 3 times another' is equivalent to x=9+3y
'Their product is 9 more than 3 times their sum' is equivalent to xy=9+3(x+y)
We have two equations and two unknowns; therefore, we can solve the problem
[tex]\begin{cases}x=9+3y \\ xy=9+3(x+y)\end{cases}[/tex]Solve it as shown below
[tex]\begin{gathered} x=9+3y \\ \Rightarrow xy=(9+3y)y=9y+3y^2 \\ \text{and} \\ 9+3(x+y)=9+3(9+3y+y)=9+3(9+4y)=9+27+12y=36+12y \\ \Rightarrow9y+3y^2=36+12y \\ \Rightarrow3y^2-3y-36=0 \\ \Rightarrow y^2-y-12=0 \end{gathered}[/tex]Solve the quadratic equation
[tex]\begin{gathered} y^2-y-12=0 \\ \Leftrightarrow(y-4)(y+3)=0 \\ \Rightarrow y=4,y=-3 \end{gathered}[/tex]Finally,
[tex]\begin{gathered} y=4 \\ \Rightarrow x=9+3(4)=21 \\ \Rightarrow(21,4) \\ y=-3 \\ \Rightarrow x=9+3(-3)=0 \\ \Rightarrow(0,-3) \end{gathered}[/tex]The solutions are (21,4) and (0,-3)
2. You are riding your bicycle. It takes you 20 minutes to go 5 miles.
a. Find your average speed per minute.
b.
How long would it take you to cycle 12 miles?
Answer:
a= one mile in 4 minutes
b =48 minutes
Step-by-step explanation:
A
t = 20 minutes
d = 5 miles
Average speed = distance ÷ time
5 miles÷ 20 minutes
= 1 mile in 4 minutes
= 0.25 miles in 1 minute
B
0.25 miles in 1 minute
12 miles in g minutes
12 miles in 48 minutes
we get this answer because 0.25 in one minute is 1 ÷4
12÷ 12 × 4
12÷ 48
= 12 miles In 48 minutes
An empty swimming pool is shaped like a rectangular prism with a length of 18 feet and a width of 9 feet. once water begins to be pumped into the pool, the depth of the water increases at a rate of 0.5 foot per hour.
Answer:
volume=length×width×depth
Step-by-step explanation:
Is it possible to have a series of true conditional statements that lead to a false
conclusion? Explain.
It is possible to have a series of true conditional statements that lead to a false conclusion.
How to illustrate the information?Making decisions based on particular situations is made easier with conditional statements.
A conditional statement's truth value can be either true or false. Simply demonstrate that the conclusion is true whenever the hypothesis is true to establish the truth of a conditional.
Simply demonstrating that the conclusion is wrong each time the hypothesis is true suffices to demonstrate that a conditional is untrue.
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Suppose a projectile is fired from a cannon with velocity v0 and angle of elevation θ. The horizontal distance Rθ it travels (in feet) is given by the following. R(θ)=(v0)²sin2θ/32 If v0=80ft/s, what angle θ (in radians) should be used to hit a target on the ground 129 feet in front of the cannon? Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a radian. (If there is more than one answer, enter additional answers with the "or" button.)
The angle at which the projectile should be launched to hit the target which is 129 feet away is 7/100π.
The projectile fires with a velocity V₀ and angle of elevation θ, then the horizontal distance is given by the R(θ),
R(θ) = V₀²sin2θ/32
The given function in dependent on theta θ,
The angle at which the projectile must be fired so that it reaches the horizontal distance of 129 feet in front of the cannon,
R(θ) = V₀²sin2θ/32
putting R(θ) equal to 129, V₀ = 80ft/s,
129 = (80)²sin2θ/32
sin2θ = (129 x 32)/(80 x 80)
sin2θ = 0.645
Hence,
θ = 7/100π
so, the projectile should be launched at angle of 7/100π.
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NEED HELP ASAP - 100 Points (Operations with Polynomials)
In multiple sentences, create your own real-world application problem for either adding or subtracting polynomials. Include a description of how the problem can be solved.
Answer: Well we can look at whether or not cubes may or may not equal the same by using volume and surface area, where the volume can be used as x^3 and the surface area x^2, but the reason why polynomials can help us a great deal in world problems is whether or not measurements are accurate, or just in general for solving big math equations. Hope this helps.
Calculate the surface area of the can. Area of a circle =
Height = 10cm
Diameter = 7 cm
Please help me thank you!
What is the surface area of the circle?
The surface area of the can is 220cm².
The height of the can is 10cm, and the diameter is 7cm.
height (h) = 10cm
radius(r) = 7/2 cm
The formula to find the surface area of the can = 2πrh
= 2 × 22/7 × 7/2 × 10
= 220cm²
Therefore the surface area of the can is 220cm².
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Based on triangle inequality theorem, what are the restrictions on the values of y
The restriction on the the values of y of the triangle is 4 < y < 16
How to find the side of a triangle using the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle.
According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side.
Therefore, a triangle x, y and z have the following rule:
x < y + z
y < x + z
z < x + y
Hence, the restriction of the on the values of y, third side of the triangle is as follows:
6 < 10 + y
10 < 6 + y
y < 10 + 6, y < 16
Therefore, the restriction is y > 4 and y < 16.
Hence,
4 < y < 16
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Characterize the slope of the line in the graph,
A. Positive
B. Negative
C. Zero
D. Undefined
Answer:
D. Undefined
Step-by-step explanation:
[tex]m=[/tex] ∞
Hope this helps
PLS HELO IM MARKING BRAINLEIST!!
∠O ≅ ∠U is third statement which is congruent .
What is congruent triangle?
Two figures are said to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to having precisely the same form and size.If all three sides of two triangles are the same, they are said to be congruent. If we have a side, an angle between the sides, and then a second side that is congruent, we know they are congruent. In other words, side, angle, side.ΔONP and ΔUTV are congruent .
By using ASA Theorem ,
NP ≅ TV
∠P ≅ ∠V
∠O ≅ ∠U
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Answer:
∠O ≅ ∠U is third statement which is congruent .
Step-by-step explanation:
What is congruent triangle?
Two figures are said to be "congruent" if they can be placed perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other.
Congruent refers to having precisely the same form and size.
If all three sides of two triangles are the same, they are said to be congruent.
If we have a side, an angle between the sides, and then a second side that is congruent, we know they are congruent. In other words, side, angle, side.
ΔONP and ΔUTV are congruent .
By using ASA Theorem ,
NP ≅ TV
∠P ≅ ∠V
∠O ≅ ∠U
BRAINLIST??
BRAINLIEST will be given to the answer
Write in the form (x + p)^2 + q
x^2 - 5x + 3
Answer:[tex][x{-\frac{5}{2}] ^{2} +\frac{-12}{25}[/tex] is in the form [tex][x+p]^{2} +q[/tex]
Step-by-step explanation:
Here given is [tex]x^{2} -5x+3[/tex].................................eq [1]
now we know that [tex][x-\frac{5}{2}] ^{2}[/tex]= [tex]x^{2} -5x+\frac{25}{4}[/tex]............eq [2]
now add and subtract [tex]\frac{25}{4}[/tex] in eq 1
[tex]x^{2} -5x+3+\frac{25}{4} -\frac{25}{4}[/tex]
[tex]x^{2} -5x+\frac{25}{4}+3-\frac{25}{4}[/tex]
[tex][x-\frac{5}{2} ]^{2} +\frac{3*4-25}{4}[/tex]................................from eq[2]
[tex][x{-\frac{5}{2}] ^{2} +\frac{-12}{25}[/tex]
so comparing with the given form [tex][x+p]^{2} +q[/tex]
where p=[tex]\frac{5}{2\\}[/tex] and q=[tex]\frac{-12}{5}[/tex]
a) How much time do people in Bhutan spend watching TV each night?
Answer:
about 2 hours
Step-by-step explanation:
it is the reported average
50 POINTS
What system of linear inequalities is shown in the graph? Enter your answers in the boxes.
enter your answers in the boxes
□
□
Answer:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
Step-by-step explanation:
Find the equations of the two lines by substituting two points on each line into the slope formula to find the slope, then substituting the found slope and one of the points into the point-slope formula.
Equation of Line 1
Points on the line: (0, 2) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{2-0}=-\dfrac{1}{2}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]
[tex]\implies y=-\dfrac{1}{2}x+2[/tex]
Equation of Line 2
Points on the line: (0, -3) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-3)}{2-0}=-\dfrac{4}{2}=2[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-3)=2(x-0)[/tex]
[tex]\implies y=2x-3[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.As the line for equation 1 is solid and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y \geq -\dfrac{1}{2}x+2}[/tex]
As the line for equation 2 is dashed and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y > 2x-3}[/tex]
Therefore, the system of linear inequalities shown in the graph is:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
how would i solve this?
FIRST FIND THE EQUATION OF THE LINE
I WILL USE THE POINTS (-94,24) AND (-54,12)
TO FIND THE GRADIENT
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{12 - 24}{ - 54 - ( - 94)} \\ m = \frac{ - 24}{ - 54 + 94} \\ m = \frac{ - 24}{40} \\ m = \frac{ - 3}{5} [/tex]
THE m ABOVE IS THE GRADIENT.
I WILL USE THE POINT (-74,18) TO GET THE VALUE OF C IN THE EQUATION Y=MX+C
[tex]15 = \frac{ - 3}{5} ( - 74) + c \\ 15 = \frac{222}{5} + c \\ c = 15 - \frac{222}{5} \\ c = \frac{ - 147}{5} [/tex]
THEREFORE THE EQUATION NOW IS
[tex]y = \frac{ - 3}{5} x - \frac{147}{5} \\
FOR THE X-INTERCEPT Y=0 SINCE IN THR X-AXIS Y=0..PLUG IN 0 IN THE PLACE OF Y TO GET X-INTERCEPT.
[tex] \frac{ - 3}{5} x - \frac{147}{5} = 0 \\ \frac{ - 3}{5} x = \frac{147}{5} \\ x = \frac{147}{5} \div \frac{ - 3}{5} \\ x = - 49[/tex]
(-49,0)
If a biker travels 380 meters in 20 seconds at that rate how far could he travel in 3 seconds
I think its 57 meters.
Convert the following repeating decimal to a fraction in simplest form. .07
12x + 5y = -24 13x - 5y = 14 Linear Equations By Elimination
Let,
[tex]\begin{gathered} 12x+5y=-24\ldots(1) \\ 13x-5y=14\ldots(2) \end{gathered}[/tex]Perform the operation (1)+(2),
[tex]\begin{gathered} 12x+5y+(13x-5y)=-24+(14) \\ 12x+13x+5y-5y=-10 \\ 25x+0y=-10 \\ 25x=-10 \\ x=\frac{-10}{25} \\ x=\frac{-2}{5} \end{gathered}[/tex]Substitute the value of x=-2/5 in the expression (1).
[tex]\begin{gathered} 12\times\frac{-2}{5}+5y=-24 \\ 5y=-24+\frac{24}{5} \\ 5y=\frac{-96}{5} \\ y=\frac{-96}{5\times5} \\ y=\frac{-96}{25} \end{gathered}[/tex]Thus, the value of x is -2/5 and value of y is -96/25.
(-5 -5) (10 4), point-slope
The slope is 5/3, and the point-slope is y = 5(x+2)/3.
Describe point slope.
A linear equation has the general form y-y1=m (x-x1). It highlights the line's slope as well as one of the line's points (that is not the y-intercept).
The formula provided is to find slope, i.e.
m = (y2 - y1) / (x2 - x1) (x2 - x1)
where (-5, -5) for (x1, Y1) and (x2, Y2) (10, 4)
m = (10 + 5) / (4 + 5)
= 15 / 9
= 5 / 3
Now that we have the slope value, we can easily enter it into the supplied equation.
y - y1 = m(x - x1) (x - x1)
y + 5 = 5/3(x + 5)
Upon resolution, we obtain
y = 5x/3 + 10/3
or, y = 5(x + 2)/3
As a result, the slope is 5/3 and the point-slope is y = 5(x+2)/3.
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Given: 4+x=16
What is the value of x?
Need this answered ASAP
Answer:
To get the answer for X we have to subtract 16 from 4 which gives us 12
X=12
Hope this helps.
Answer:
4+X= 16
X=16-4
X=12
*To find X , you need to minus 16 by four. That is because you have to move (+4) to the other side (change sides,change signs). So (+4) becomes (-4) so 16-4 =12
Which ordered pairs are on the graph of 7x−y=2?
Select ALL that applies.
A. >>(−3,−19)open paren negative 3 comma negative 19 close paren
B. (−1,−9)open paren negative 1 comma negative 9 close paren
C. (0,−2)open paren 0 comma negative 2 close paren
D. (1, 9)(1, 9)
(3, 23)(3, 23)
The ordered pairs which are on the graph of 7x - y = 2 as required in the task content are; Choices B and C; (-1, -9) and (0, -2).
Which ordered pairs are on the graph of 7x - y = 2 as required in the task content?It follows from the task content that the ordered pairs which are on the graph of 7x - y = 2 be determined.
Hence, by testing each pair as follows; we have;
For (-3, -19); we have; 7(-3) - (-19) = 2; -21 + 19 = 2; -2 ≠ 2. Hence, FALSE.For (-1, -9); we have; 7(-1) - (-9) = 2; -7 + 9 = 2; 2 = 2. Hence, TRUE.For (0, -2); we have; 7(0) - (-2) = 2; 0 + 2 = 2; 2 = 2. Hence, TRUE.For (1, 9); we have; 7(1) - (9) = 2; 7 - 9 = 2; -2 ≠ 2. Hence, FALSE.For (3, 23); we have; 7(3) - (23) = 2; 21 - 23 = 2; -2 ≠ 2. Hence, FALSE.Ultimately, the required ordered pairs are; (-1, -9) and (0, -2).
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Damon drew a scale drawing of a swimming pool. The scale he used was 1 inch : 9 feet. The diving board is 2 inches long in the drawing. How long is the actual diving board?
Since the scale utilized in the draw is 1 inch : 9 feet and the diving board is 2 inches, we need to multiply the 2 inches by the scale:
[tex]2\cdot9ft=18ft[/tex]The actual diving board is 18ft long
What is 0.044444... as a fraction?
Answer:
0.044444 = 11111/250000
Step-by-step explanation:
[tex]=\frac{44444}{1000000} =\frac{22222}{500000} =\frac{11111}{250000}[/tex]
Hope this helps
mr jeneski is preparing for a half marathon. He runs a total of 60 miles per week. Five of those miles are ran on saturday, and he takes sunday off. How many miles does he run per day, Monday-Friday
11 miles he run per day, Monday-Friday.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total distance travelled = 60 miles.
On Saturday= 5 miles
Sunday was off
So, from Monday to Friday he travelled
=60 - 5
= 55 miles.
and, per day he run
= 55/5
= 11 miles
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HELP PLEASE I GIVE BRAINY IF U ANSWER RIGHT AND IF I CANT READ THAT THERE IS MORE THEN ONE ANSWER U WONT GET ANYTHING
ANSWER BOTH QUESTIONS PLEASE IF U DON'T I WONT GIVE U A THING
Question 1
Which ordered pairs lie on the graph of the exponential equation
f(x) = 25(2.2)^x ?
Select EACH correct answer.
A. (0, 0)
B. (0.5, 37.08)
C. (1, 55)
D. (2, 121)
THE FIRST PICTURE GOES WITH QUESTION 2 ONLY
Question 2
The function f(x) = (3/8)^x is shown on the coordinate plane.
Determine which expressions describe the end behaviors of the function.
Select EACH correct answer.
A. As x increases without bound, the graph of f(x) decreases without bound.
B. As x increases without bound, the graph of f(x) approaches y = 1.
C. As x decreases without bound, the graph of f(x) increases without bound.
D. As x decreases without bound, the graph of f(x) approaches y = 0.
The ordered pairs lie on the graph of the exponential equation is
(0.5, 37.08) (1, 55) (2, 121)What is exponential equation?Exponents are used in exponential functions, as the name indicates. But take note that an exponential function does not have a constant as its base and a variable as its exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). One of the following forms can be used for an exponential function.
According to its definition, a fundamental exponential function has the formula f(x) = [tex]b^x[/tex], where b is a constant and x is a variable. The exponential function f(x) = [tex]e^x[/tex], where "e" is "Euler's number," and e = 2.718, is one of the most well-known ones. An exponential function may incorporate a constant if we expand the potential of various exponential functions.
Given function:
f(x) = 25 [tex](2.2)^x[/tex]
Now, taking x=0
y = f(x) = 25
and, x=0.5
y= f(x) = 37.08
and, x = 1
y = 55
and, x=2
y = 121
So, the ordered pairs lie on the graph of the exponential equation is
(0.5, 37.08) (1, 55) (2, 121)2. The given function is [tex]f(x)= (3/8)^x[/tex]
Now, as per the graph As x decreases without bound, the graph of f(x) approaches y = 1.
Or, As x decreases without bound, the graph of f(x) increases without bound.
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What is the slope line that passes through the points (-6,4) and (-15,4)?
Answer: the slope=0
Step-by-step explanation:
[tex]\displaystyle\\(-6,4)\ \ \ \ \ (-15,4)\\\\\boxed {The\ slope=\frac{y_2-y_1}{x_2-y_1} }\\\\The\ slope=\frac{4-4}{-15-(-6)} \\The\ slope=\frac{0}{-15+6} \\\\The\ slope=0[/tex]
Ron's youth group commits to making a certain number of sandwiches for a local soup
kitchen. They make 132 sandwiches, but then they run out of peanut butter. The group still
has 110 sandwiches left to make to meet their commitment.
Use an equation to find the total number of sandwiches the youth group commits to making.
sandwiches
Answer:
242 sandwiches
Step-by-step explanation:
The group wants to make x number of sandwiches.
They have already made 132 sandwiches and still have 110 sandwiches to make.
To find the total, you can add these numbers up, because:
132 + 110 = total sandwiches
This way, you get 242 sandwiches
how to find the edge of a cube with the volume of 125 inches
Answer:
5 inches
Step-by-step explanation:
Hello!
The volume of a cube is simply the side length cubed, or the side lengthed multiplied by itself 3 times.
So, to find the edge, we can find the cube root of 125 to find that measure.
Find the Side Lengthx³ = 125x = ∛125x = 5The edge is 5 inches.
help me 20 points please
Answer:
Step-by-step explanation:
the one on top is simple it's 120