Answer:
To solve this problem, we will use the following steps:
Step 1: We know that the amount of time it takes Susan to get from her residence to class averages 50 minutes, with a standard deviation of 5 minutes. So we can use this information to calculate the proportion of Susan's trips to class that would take less than 40 minutes.
Step 2: To calculate the proportion of Susan's trips to class that would take less than 40 minutes, we need to find the z-score for the value of 40 minutes. We can use the following formula to find the z-score:
z = (x - μ) / σ
Where x is the value we are interested in (40 minutes), μ is the mean (50 minutes), and σ is the standard deviation (5 minutes).
z = (40 - 50) / 5 = -2
Step 3: We can use a standard normal table or a calculator to find the proportion of Susan's trips to class that would take less than 40 minutes.
The proportion of Susan's trips to class that would take less than 40 minutes is 0.0228 or 2.28%.
Step 4: To calculate the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes, we need to find the proportion of Susan's trips to class that would take more than 50 minutes and add it to the proportion of Susan's trips to class that would take less than 40 minutes.
Step 5: To find the proportion of Susan's trips to class that would take more than 50 minutes, we need to find the z-score for the value of 50 minutes.
z = (50 - 50) / 5 = 0
Using a standard normal table or a calculator, the proportion of Susan's trips to class that would take more than 50 minutes is 0.5 or 50%.
Step 6: Finally, we can add the proportion of Susan's trips to class that would take more than 50 minutes and the proportion of Susan's trips to class that would take less than 40 minutes to find the proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes.
0.50 + 0.0228 = 0.5228 or 52.28%
Final Answer: The proportion of Susan's trips to class that would take more than 50 minutes or less than 40 minutes is 0.5228 or 52.28%.
Help me I need help on how to do this I will upload 13 questions this is number 1
The value of x is 85°
What is angle of a sector?A circular sector, also known as circle sector or disk sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector
A sector is a region bounded by two radii of a circle and the intercepted arc of the circle. The angle formed by the two radii is called a central angle. A sector with a central angle less than 180° is called a minor sector. A sector with a central angle greater than 180° is called a major sector.
The sector where x is the minor sector
The angular distance is x and it is measured in degrees (°)
Therefore the value of x is 85°
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3/5 + 5/7 = ____
6/12 + 9/12 ____
1/4 + 4/4 = ____
2/3 + 5/3 = ____
(fractions please explain step by step how u got your answer)
The answers are 46/35 ,5/4, 5/4, 7/3
What is a fraction in math?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given here: 3/5 + 5/7 = 46/35
6/12 + 9/12=5/4
1/4 + 4/4 = 5/4
2/3 + 5/3 = 7/3
Hence, The answers are 46/35 ,5/4, 5/4, 7/3
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I need help with the following questions please!!!!!!
Step-by-step explanation:
f(-1) = (1/8)^-1 = 1/(1/8) = 8
f(0) = (1/8)⁰ = 1 (a⁰ = 1 for any a)
f(1) = (1/8)¹ = 1/8 = 0.125
f(2) = (1/8)² = 1/64 = 0.015625
f(3) = (1/8)³ = 1/512 = 0.001953125
remember
(a/b)ⁿ = aⁿ / bⁿ
in the same way as
(a×b)ⁿ = aⁿ×bⁿ
Indicate if each equation in the table has no solutions, one solution, or
infinitely many solutions.
Questions
} (8 – 24x) =12
6x
OA
O C
-
Answer
Choices
A. No Solution
B. One Solution
C. Infinitely many
solutions
The correct option is A, the linear equation has no solutions.
How many solutions does the equation has?Here we want to see how many solutions do the equation below has:
(1/4)*(8 - 24x) = 12 - 6x
Now let's try to solve that linear equation, we can start by simplifying the left side:
(1/4)*(8 - 24x) = 12 - 6x
8/4 - 24x/4 = 12 - 6x
2 - 6x = 12 - 6x
Now we can add 6x in both sides, so we will get:
2 - 6x + 6x = 12 - 6x + 6x
2 = 12
That is a false equation, thus, the equation has no solutions.
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The graph shows the depth in feet of snow after each two-hour period during a snowstorm. Find the slope of the line. Enter your answer an an integer or decimal.
Answer:
.5 or 1/2
Step-by-step explanation:
1-.5 .5
------=------- simplify= .5 slope is in fractions 1/2
2-1 1
A television station claims that the amount of advertising per hour of broadcast time has an average of 17 minutes and a standard deviation equal to 2.3 minutes. You watch the station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 5 minutes. Calculate the z-score for this amount of advertising time.
The z-score for this amount of advertising time will be -5.217.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
A TV slot guarantees how much promotion each hour of transmission time has a normal of 17 minutes and a standard deviation equivalent to 2.3 minutes.
The amount of advertising time is equal to 5 minutes. Then the z-score is calculated as,
z = (5 - 17) / 2.3
z = -12/ 2.3
z = -5.217
The z-score for this amount of advertising time will be -5.217.
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act math scores are approximately normally distributed, with a mean of 21 and a standard deviation of 5.4. if eli decides to take the act exam, what would he need to score in order to be in the 85th percentile?
In order to be in the 85th percentile Eli would need to score 26.62.
What is called percentile?In statistics, a score below which a certain percentage of scores (k) in a frequency distribution falls is known as a k-th percentile, whereas a score at or below which a given percentage falls is known as a k-th centile.
Given that act math scores are approximately normally distributed,
mean (μ) = 21 and a standard deviation (σ) = 5.4
percentile P(X>x) = 85 =0.85
P(z<x) = 0.85
z = 1.04
y the formula
z = (x - μ)/ σ
⇒ 1.04 = (x - 21)/5.4
⇒ 1.04*5.4 = x - 21
⇒ 5.616 = x - 21
⇒ x = 5.616 + 21
⇒ x = 26.62
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291 is the same as 359 increased by the product of 125 and m
The equation 291 = 359 + 125m represents the given phrase, and the required value of m is 2.33
What is Algebra?Algebra is a discipline of mathematics that deals with symbols and the rules that govern their use. These symbols, known as variables in elementary algebra, indicate quantities with no set values. Equations in mathematics express relationships between variables in the same way that sentences indicate relationships between specific words.
The equation 291 = 359 + 125m can be solved for m by subtracting 359 from both sides, resulting in:
291 - 359 = 125m - 359
-68 = 125m - 359
Adding 359 to both sides gives:
-68 + 359 = 125m
291 = 125m
Dividing both sides by 125 gives the solution for m:
291 / 125 = 125m / 125
2.33 = m
So, m is equal to 2.33.
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The question seems incomplete, the completed question would be as:
If 291 is the same as 359 increased by the product of 125 and m. what is the value of f?
given the function defined in the table below,find the average rate of change,in simplest form,of the function over the interval 12
Answer: The average rate of change over the interval 12 < x < 30 is -4/3
Step-by-step explanation:
The average rate of change over an interval is defined as the change in the output (f(x)) divided by the change in the input (x) over that interval. In this case, the interval is 12 < x < 30. To find the average rate of change, we need to evaluate the function at the endpoints of the interval and subtract the value at the start point from the value at the end point, and divide that by the change in x.
Given the table:
f(30) = 16 and f(12) = 40
The average rate of change over the interval 12 < x < 30 is:
(f(30) - f(12)) / (30 - 12) = (16 - 40) / 18 = -24/18 = -4/3
So the average rate of change over the interval 12 < x < 30 is -4/3
It's worth noting that this is only the average rate of change, and the function may have different rates of change at different points within the interval 12 < x < 30.
if r(x) = 3x – 1 and s(x) = 2x + 1, which expression is equivalent to ?
a. 3 (6)-1/2(6) +1
b. (6)/ 2(6)+1
c. 36-1/26+1
d. (6)-1/(6)+1
If the expression [tex]r(x) = 3x - 1[/tex] and the expression [tex]s(x) = 2x + 1[/tex] , then the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is (a) [tex]\frac{3(6)-1}{2(6) +1}[/tex] .
What are Algebraic Expression ?
The algebraic Expression are defined as the expressions that are written with the combination of variables and constants joined by mathematical operators , For Example : [tex]3x+7[/tex] .
Here the two expressions are given as [tex]r(x) = 3x - 1[/tex] and [tex]s(x) = 2x + 1[/tex] ;
we have to find equivalent expression for [tex]\frac{r}{s} (6)[/tex] ;
By the Division Property of Algebraic Expression ;
it can be written as : [tex]\frac{r(6)}{s(6)}[/tex] ;
So , Substituting [tex]x=6[/tex] , in r(x) ,
we get ; [tex]r(6) = 3(6) - 1[/tex] , ......equation(1)
On Substituting [tex]x=6[/tex] , in s(x) ,
we get ; [tex]s(6) = 2(6)+1[/tex] , ....equation(2) ;
Substituting the values of r(6) and s(6) from equation(1) and equation(2) in [tex]\frac{r(6)}{s(6)}[/tex] ;
we get ;
⇒ [tex]\frac{r(6)}{s(6)} = \frac{3(6)-1}{2(6) +1}[/tex] ;
Therefore , the expression equivalent to [tex]\frac{r}{s} (6)[/tex] is [tex]\frac{3(6)-1}{2(6) +1}[/tex] .
The given question is incomplete , the complete question is
If r(x) = 3x - 1 and s(x) = 2x + 1, which expression is equivalent to r/s(6) ?
(a) [tex]\frac{3(6)-1}{2(6) +1}[/tex]
(b) [tex]\frac{(6)}{2(6)+1}[/tex]
(c) [tex]\frac{36-1}{26+1}[/tex]
(d) [tex]\frac{(6)-1}{(6)+1}[/tex]
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Can someone help me with this? I need an equation and the cup of nuts. It’s due tmr
Answer:
Step-by-step explanation:
I assume that the amount of peanut butter chips in original recipe is [tex]1\frac{1}{2}[/tex] c (the picture isn't clear!)
2( [tex]1\frac{1}{2}[/tex] + x ) = [tex]4\frac{1}{2}[/tex]
[tex]1\frac{1}{2}[/tex] + x = [tex]4\frac{1}{2}[/tex] ÷ 2
[tex]1\frac{1}{2}[/tex] + x = [tex]2\frac{1}{4}[/tex]
x = [tex]2\frac{1}{4}[/tex] - [tex]1\frac{1}{2}[/tex] = [tex]1\frac{5}{4}[/tex] - [tex]1\frac{2}{4}[/tex] = [tex]\frac{3}{4}[/tex]
There is [tex]\frac{3}{4}[/tex] of a cup of nuts in original recipe.
steve and elsie are camping in the desert, but have decided to part ways. steve heads north, at 7 am, and walks steadily at 3 miles per hour. elsie sleeps in, and starts walking west at 3.5 miles per hour starting at 10 am. when will the distance between them be 35 miles? (round your answer to the nearest minute.)
At 2.57 hours distance between them is 35 miles
(2t)2 + (2.5(t - 2))2 = 302
4t2 + (2.5t - 5)2 = 900
4t2 + 6.25t2 - 25t + 25 = 900
2.25t2 - 25t - 875 = 0
Let t (hours) be the amount of time Elsie needs to travel in order to reach a distance of 35 miles. Steve travels t + 2 miles to the north in the time it takes him since he is 2 hours early.
Solve for t, then add to 7:00 for your time.
which will give you 2.57 hours.
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The correct question will be
Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 7 AM, and walks steadily at 3 miles per hour. Elsie sleeps in and starts walking west at 2.5 miles per hour starting at 9 AM.
When will the distance between them be 35 miles?
Which graph shows the solution to the system of linear equations? y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2
Answer:
a line
Step-by-step explanation:
y equals one half times x x + 2y = 8 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 5 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 3 and another line that passes through the points 0 comma 0 and 2 comma 1 coordinate plane with one line that passes through the points negative 1 comma 2 and 0 comma 4 and another line that passes through the points 0 comma 0 and 1 comma 2 coordinate plane with one line that passes through the points 0 comma 4 and 2 comma 0 and another line that passes through the points 0 comma 0 and 1 comma 2
Answer:
B) A coordinate plane with one line that passes through the points (0, 4) and (2, 3) and another line that passes through the points (0, 0) and (2, 1)
Step-by-step explanation:
Given system of linear equations:
[tex]\begin{cases}y=\frac{1}{2}x\\x+2y=8\end{cases}[/tex]
Substitute the first equation into the second equation and solve for x:
[tex]\implies x+2\left(\dfrac{1}{2}x\right)=8[/tex]
[tex]\implies x+x=8[/tex]
[tex]\implies 2x=8[/tex]
[tex]\implies x=4[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=\dfrac{1}{2}(4)[/tex]
[tex]\implies y=2[/tex]
Therefore, the solution to the given system of linear equations is:
(4, 2)The point of intersection is the solution to a graphed system of linear equations.
Therefore, the graph that shows the solution to the given system of linear equations is the graph where the point of intersection of the two lines is (4, 2).
junior secondary Use elimination method to solve the following simultaneous equations: 10m-7n=26
7m+7n=42
Using Elimination method the simultaneous equations is -16/3.
How can a three-step elimination equation be solved?Elimination is a mathematical technique that can be used to solve a system of three equations with three variables.
In standard form, without any fractions or decimals, write all the equations. Decide which one of the three variables you want to eliminate, then pick any two of the equations to do so.
The term "simultaneous equations" refers to two or more algebraic equations that share the same unknown variables and have the same answer. This suggests that the simultaneous equations have a single, solvable problem. For instance, 2x - 4y = 4, 5x + 8y = 3, are instances of simultaneous equations.
10m-7n=26
- 7m+7n=42
3m = -16
m = -16/3
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explain how to use arrays or area models to find factor pairs
Answer: An array is a visual representation of a multiplication problem, and an area model is a way to represent a multiplication problem using rectangles. Both arrays and area models can be used to find factor pairs of a number.
Here's an example of how to use an array to find the factor pairs of 12:
Draw a rectangle that represents 12.
Divide the rectangle into smaller rectangles by drawing rows and columns.
Fill in the rectangles with the numbers 1 through 12.
Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.
The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.
Here's an example of how to use an area model to find the factor pairs of 12:
Draw a rectangle that represents 12.
Divide the rectangle into smaller rectangles by drawing rows and columns.
Label the rectangles with the factors of 12, which are 1, 2, 3, 4, 6 and 12.
Find the factor pairs by looking for the rectangles that have the same area as the original rectangle, 12.
The factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.
Both arrays and area models are an effective way of finding the factor pairs of a number because they help you to visualize the multiplication problem and to see the relationship between the factors and the product.
Step-by-step explanation:
nd the local maximum and minimum values and saddle point(s) of the function. you are encouraged to use a calculator or computer to graph the function with a domain and viewpoint that reveals all the important aspects of the function. (enter your answers as comma-separated lists. if an answer does not exist, enter dne.) f(x, y)
Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.
saddle point : a point on a curved surface at which the curvatures in two mutually perpendicular planes are of opposite signs
The function :
f(x , y) = x³ = y³ = - 3x² - 3y² - 9x
The first partial derivative with respect to x is:
f' x = 3x²-6x-9
And the partial derivative with respect to y is:
f' y = 3y²-6y
Now equate the above derivatives to zero, to obtain the system of equation:
3x²-6x-9 = 0
3y²-6y = 0
On solving the two equations:
The critical points are : A(-1,0), B(-1,-2), C(3,0) and D(3,2)
Now calculate the discriminant
D = f xx(x , y)f y(x , y)-f xy(x , y)²
Here,
f xx = 6x-6
f yy = 6y-6
f xy = 0
On putting the above values we get:
D = (6x-6)(6y-6)
At, A(-1,0)
D = -18<0
Hence , A(-1,0) is a local maximum point.
At, B(-1,2)
D = -72<0
Hence B(-1,2) is saddle point.
At, C(3,0)
D = -72
Hence C(3,0) is also a saddle point
At, D(3,2)
D = 12>0
Hence , D(3,2) is the minimum point.
Answers : A(-1,0) is a local maximum point, B(-1,2) is saddle point, C(3,0) is also a saddle point, D(3,2) is the minimum point.
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Find the area of the shaded triangle
The area of shaded triangle is 20 square feet
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.
Area of triangle = 0.5*base*height
Area of whole triangle = 0.5*8*10 = 40 square feet
Area of unshaded triangle = 0.5*4*10 = 20 square feet
Area of shaded triangle
= Area of whole triangle - Area of unshaded triangle
= 40 - 20
= 20 square feet
Thus, the area of shaded triangle is 20 square feet
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How do I do this step by step
Answer:
84
Step-by-step explanation:
this is an isosceles triangle so the base angles are equal meaning <BAC= <BCA =48°
48° +48° =96°
180°- 96° = 84°
<ABC = 84°
What is the volume of a hemisphere with a radius of 44. 9 m, rounded to the nearest tenth of a cubic meter?.
The volume of a hemisphere with a radius of 44.9 m is approximately 189582.2 cubic meters, rounded to the nearest tenth.
To calculate the volume of a hemisphere, you can use the formula
V = (2/3)πr^3
where V is the volume, π is pi (approximately 3.14), and r is the radius. In this case, r = 44.9 m.
So, (2/3)π(44.9)^3 = 189582.234 cubic meters.
This is the exact volume, but since the question asked for the volume rounded to the nearest tenth, the final answer would be 189582.234 cubic meters. It's worth mentioning that a hemisphere is half of a sphere, thus, the volume of a full sphere with a radius of 44.9 m would be double of this value.
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Hannah has two bags of sweets.
In the first bag there are 5 red sweets and 7 green sweets.
In the second bag there are 7 red sweets and 4 green sweets.
Harmah takes at random a sweet from the first bag.
She then takes at random a sweet from the second bag.
(a) Complete the probability tree diagram.
first bag
red
green
11
second bag
red
(b) Work out the probability that Hannah takes two green sweets.
green
. red.
green
(2)
28
The size of each interior angle of an
Work out how many sides the poly
Answer:
(a) Refer below for the Probability tree diagram
(b) [tex]\frac{7}{33}[/tex]
Step-by-step explanation:
(a) Probability tree diagram:
First bag: Second bag
Red: [tex]\frac{7}{7 + 4}[/tex] = [tex]\frac{7}{11}[/tex]
Red: [tex]\frac{5}{12}[/tex]
Green:[tex]\frac{4}{7 + 4}[/tex] = [tex]\frac{4}{11}[/tex]
Red: [tex]\frac{7}{11}[/tex]
Green [tex]\frac{7}{12}[/tex]
Green: [tex]\frac{4}{11}[/tex]
(b) Probability that Hannah takes two green sweets:
Green sweet from first bag AND green sweet from second bag
= [tex](\frac{7}{12}).(\frac{4}{11} )[/tex]
= [tex](\frac{28}{132})[/tex]
Divide the numerator and denominator by the highest common factor (i.e 4)
= [tex]\frac{7}{33}[/tex]
Evaluate the line integral, where
C
is the given curve.
∫ xyds,C:x2,y=2t,0≤t≤2
C
According to the given information the line integral is 8(1+125[tex]\sqrt{110}[/tex]) / 15 .
What distinguishes a line integral from a definite integral?
Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.
[tex]\int\limits_c {xy} \, ds[/tex], C : x = t^2 , y = 2t, 0 ≤ t ≤ 3
x' = 2t , y' = 2
ds = [tex]\sqrt{(x')^2 + (y')^2}[/tex]
[tex]\sqrt{4(t)^2 + 4}[/tex]
[tex]\int\limits C {xy} \, ds[/tex] = [tex]\int\limits^3_0 {2.2t.2\sqrt{1+t^2}} \, dt[/tex]
t = tanθ
dt = (1+[tex]tan^{2}[/tex]θ)dθ = ([tex]sec^{2}[/tex]θ)dθ
= [tex]\int\limits^3_0 {4t^3\sqrt{1+t^2} } \, dt[/tex]
= 8(1+125[tex]\sqrt{110}[/tex]) / 15
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Select the expressions that are equivalent to 5(4u).
20u - u+20 - u+9 - 5(u+3u)
The expressions that are equivalent to 5(4u) will be 20 u and 5(u + 3u).
How to calculate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The expression that is equivalent to 5(4u) will be:
= 20 u
and
5(u + 3u)
= 20u
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Can someone please please help mke i was suppose to finnish this at least 2 weeks ago please can someone answer these 3 question for at leat 150 or 200 points.
The ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the equivalent ratio 20 : 1/6.
What is equivalent ratio?By dividing both the antecedent and consequent values by a similar fraction, equivalent ratios can be reduced to the same value. In other words, two ratios are deemed equivalent if the bigger one in value can be expressed as a multiple of the other.
Therefore, we only need to multiply the two amounts by the same number to obtain the equivalent ratio of another ratio. Equivalent ratios and equivalent fractions both have similar ideas. Examples of equivalent ratios include 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.
20 : 1/6
Multiply both by 6
120 : 1
Thus, 120 × 2/3 : 1 × 2/3
80 : 2/3
multiply by 3
80 × 3 : 2/3 × 3
240 : 2
120 : 2
When ratio is 120 : 1
divide both by 120
120/120 : 1/120
1 : 1/120
1 × 10 : 1/120 × 10
10 : 1/12
multiply by 12
120 : 1
1 × 90 : 1/120 × 90
90 : 3/4
multiply by 4
90 × 4 : 3/4 × 4
360 : 3
120 : 1
Thus, the ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the proportion 20 : 1/6.
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A cereal box has dimensions of 12 inches, 7~
4
inches, and 2 inches. A pastry box
has dimensions of 3.
} inches, 3.
¿ inches, and 2¾ inches, Whatis the difference
in volume, in cubic inches, between the two boxes?
Answer:
To find the volume of the cereal box, we multiply the length, width, and height:
12 inches * 7 and 3/4 inches * 2 inches = 96 inches * 7.75 inches * 2 inches = 1458 cubic inches
To find the volume of the pastry box, we multiply the length, width, and height:
3 and 2/3 inches * 3 and 1/2 inches * 2 and 1/3 inches = 3.666 inches * 3.5 inches * 2.333 inches = 25.158 cubic inches
To find the difference in volume between the two boxes, we subtract the volume of the pastry box from the volume of the cereal box:
1458 cubic inches - 25.158 cubic inches = 1432.842 cubic inches
So the difference in volume between the two boxes is 1432.842 cubic inches.
Answer:1432.842 cubic inches
Step-by-step explanation:
The diameter of the Sun is 1.4 x 10 9 m and that of the Earth is 1.2756 x 10 7
m. Approximately how many times is the diameter of the sun greater as compared
to that of the earth ?
Answer:
The Sun has 1.0975 x 10^2 times the diameter of Earth
Step-by-step explanation:
Diameter of Sun = 1.4 x 10^9 m
Diameter of Earth = 1.2756 x 10^7 m
ratio between Diameter of Sun and Earth :-
Diameter of Sun/Diameter of Earth = 1.4 x 10^9/ 1.2756 x 10^7
= 1.0975 x 10^2
In the figure below, which term best describes point W?
A. Incenter
B. Centroid
C. Orthocenter
D. Circumcenter
Orthocenter is the best term to describes point R in the triangle UVW.
What is orthocenter?
" Orthocenter is defined as intersecting point of the altitudes of the sides of the acute angle triangle."
According to the given figure,
In triangle UVW,
Ray VR perpendicular to UW
Ray UR perpendicular to VW
Ray WR perpendicular to UV
Altitudes of side ( UV , VW, and WU) of triangle UVW intersect at
point R.
As per the definition of orthocenter , point R represents orthocenter.
Hence, orthocenter is the best term to describes point R in the triangle UVW.
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Masha is three times as old as Pete. Their age difference is
10 years. How old is Pete?
Pete is
years old.
Answer:
Pete is 5
Step-by-step explanation:
Let Pete's age be x
Therefore Masha is 3x
since their age difference is 10,
3x - x = 10
2x = 10
x = 5
check:
3x = 15
x = 5
15 - 5 = 10
now using the right side of each slice as the height, sketch in 4 rectangles on your graph. find the area of these rectangles and add them up. this is your second approximation of the area under the curve, and hence ln(2). what is your answer (as a decimal with at least four digits of precision)? is this an over-estimate or an under-estimate
The area of the resulting two-dimensional cross-section of the pyramid geometry will be 5 square inches.
What is Geometry?
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
What is an area in math definition
Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. Take a pencil and draw a square on a piece of paper. It is a 2-D figure. The space the shape takes up on the paper is called its Area. Now, imagine your square is made up of smaller unit squares
A slice is made parallel to the base of a right rectangular pyramid, as shown.
Then the area of the resulting two-dimensional cross-section will be
Area = 2 in × 2.5 in
Area = 5 in²
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Graph the image of the given triangle after the transformation with the rule (x, y)→(−x, y).
Select the "Polygon" button from the toolbar to plot your triangle. You may use the "Move" button to move the triangle after it is created.
A graph of the image of the triangle with vertices (4, 7), (3, 4), and (8, 2) after a transformation with the rule (x, y) → (−x, y) is shown in the image attached below.
What is a reflection?In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
By applying a reflection over the y-axis to the coordinates of this triangle the image coordinates include the following:
(x, y) → (-x, y)
Coordinate A = (4, 7) → Coordinate A' = (-(4), 7) = (-4, 7).
Coordinate B = (3, 4) → Coordinate B' = (-(3), 4) = (-3, 4).
Coordinate C = (8, 2) → Coordinate C' = (-(8), 2) = (-8, 2).
Next, we would use an online graphing calculator to plot the coordinates of the image as shown in the image attached below.
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The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The two companies, Shirt Box and Just Tees, are represented by this system of equations where x is the number of T-shirts and y is the total cost of the T-shirts. y
Therefore , the solution of the given problem of linear equation comes out to be $105 is the total cost
The definition of a linear equation.A linear regression model is one that uses the equation y=mx+b. The slope is B, and the y-intercept is m. The preceding sentence is commonly referred to as a "math equation with two variables," despite the fact that both y and x are separate factors. The only variables in bivariate linear equations are two. In all circumstances, the solutions to linear equations' application domains are zero. Y=mx+b is the formula for a single linear equation.
Here,
The first company's equation is y = 10.5x.
Additionally, the second company's equation is y = 7.5x + 30.
Where
number of T-shirts equals x.
y = overall cost
For the overall cost to be the same for both businesses, we have to:
=> 10.5x = 7.5x + 30
=> 10.5 x - 7.5 x = 30
=> 3 x = 30
=> x = 30/3
=> x = 10
To make the T-shirts' prices equal, the volleyball team must purchase 10 from each vendor.
Total for each business:
=> 10.5x = 10.5 (10) = $ 105
OR
Totals for each company are calculated as follows:
=> 7.5x + 30 = 7.5(10) + 30 = 75 + 30
=> $105
Therefore , the solution of the given problem of linear equation comes out to be $105 is the total cost.
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