The assumption Ethan made was correct
What is Fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Ethan said that the result of 10 and 4.07 is 40.7, thus we must verify that his computation is accurate.
In order to do such, we must multiply 10 by 4.07 as illustrated below:
= 10 x 4.07
= 10 x 407/100
= 4070/100
= 40.70
Since the outcome matches Ethan's hypothesis,
The conclusion is valid.
Hence, The result of Ethan is correct
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4. Tyrell bought 4 pizzas and 5 subs and his bill was $56.25. Annabel bought 3 pizzas and 7 subs and her bill was $59.25. How much does each item cost?
let p represent pizza
let s represent subs
when he bought 4 pizza and 5 subs bill is $56.25
[tex]4p\text{ + 5s = 56.25 --------1}[/tex]when he bought 3 pizzas and 7 subs his bill is $59.25
[tex]3p\text{ + 7s = 59.25}--------2[/tex]solving the two equations simultaneosly
[tex]\begin{gathered} 4p\text{ + 5s = 56.25 x 3 (multiply equation 1 by coefficient of p in equation 2 i.e 3)} \\ 3p\text{ + 7s = 59.25 x 4 ( multiply equation 2 by coefficient of p in eqaution 1 i.e 4)} \\ \text{these multiplications gives equation 3 and 4 below} \end{gathered}[/tex][tex]\begin{gathered} 12p\text{ + 15s = 168.75 -------3} \\ 12p\text{ + 28s = 237}--------4 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{subtracting equation 3 from 4, p is eliminated and the equation below is obtained} \\ 13s\text{ = 68.25} \\ (i\mathrm{}e\text{ 12p - 12p) + (28s-15s) = 237-168.75)} \end{gathered}[/tex]divide both side by 13
[tex]\begin{gathered} \frac{13s}{13}=\frac{68.25}{13} \\ s\text{ = 5.25} \end{gathered}[/tex]substitute s= 5.25 in equation 1
4p + 5(5.25) = 56.25
4p + 26.25 = 56.25
4p = 56.25 - 26.25
4p = 30
divide both side by 4
[tex]\begin{gathered} \frac{4p}{4}=\text{ }\frac{30}{4} \\ p=7.5 \end{gathered}[/tex]each pizza cost $7.5
each sub cost $5.25
Order of operations was it evaluated correctly? 5^(2) + 1^(2) = 6(2) = 36EXPLAIN your reasoning. Thank you
The answer to the operation is as follows:
5^(2) + 1^(2) = 5*5 + 1*1 = 25 + 1 = 26.
Here, we have to remember PEMDAS. First, we solve parentheses, then exponents (or exponentiation operations); then, multiplications, divisions, and, after all this, addition and subtractions.
In the above operation, we solve first the raising of 5 to 2, then 1 raised to 2. We sum the result of both operations. So the value of 36 is not correct. The correct value is 26.
Block of iron mass 40kg is sitting on an incline that has an angle of 28degrees above horizontal, what is the normal force of the block of iron
The normal force of the block of iron is mathematically given as
N=1412.64 N
This is further explained below.
What is normal force?Generally, the Mass of an iron block of m=40kg sitting on an incline
That has an angle of 28 degrees above horizontal
as-block is sitting on an incline hence Net force acting perpendicular to the incline will be zero
Then [tex]N-M g \cos 28^{\circ}=0[/tex]
N-Mgcos 28=0
[tex]$$\begin{aligned}&N=M g \cos 28^{\circ} \\&N=40 \times 40 \times 0.8829\\& \end{aligned}$$[/tex]
N=1412.64 N
In conclusion, the normal force on the block is N=86.6 Newton
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By using free body diagrams and trigonometric relations, the normal force of the block of iron has a magnitude of 352.579 newtons.
What is the normal force of the block of iron?
In accordance with the third Newton's law, normal forces (N), in newtons, are reactive forces as the result of the contact of the iron mass with the ground of the incline, that is to say, the normal force is the reaction of the weight of the iron mass (W), in newtons. If the iron mass is at rest, then we find the following free body diagram of the ground-mass system and its related geometric system.
Since the free body diagram represents a three force system, then the magnitude of the normal force is found by trigonometric relations:
N = W · cos 26°
N = (40 kg) · (9.807 m / s²) · cos 26°
N = 352.579 N
The normal force of the block of iron has a magnitude of 352.579 newtons.
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Ken is building a deck. He determined that he needs 25 blocks that cost $7.97 each and 48 deck boards that cost $14.00 each. How much will Ken pay for these items?
Ken will pay $ 871.25 for these items
Explanation
to find the total cost we need add the cost of the blocks to the cost of the total boards, so
Step 1
find the total cost of the blocks
a) when having the cost per unit and the amount, we just need to do a multiplication, so
[tex]\begin{gathered} total\text{ cost= rate*amount} \\ replace \\ tota\text{l cost of the blocks= 7.97}\frac{\text{ \$}}{block}*25\text{ Blocks} \\ tota\text{l cost of the blocks= \$ 199.25} \end{gathered}[/tex]Step 2
now, the total cost of the boards:
[tex]\begin{gathered} total\text{ cost= rate*amount} \\ replace \\ tota\text{l cost of the boards= 14}\frac{\text{ \$}}{board}*4\text{8 boards} \\ tota\text{l cost of the boards= \$ 672} \end{gathered}[/tex]Step 3
finally, add the costs to find the total
[tex]\begin{gathered} total\text{ cost= \$199.25+672} \\ total\text{ cost= 871.25} \end{gathered}[/tex]therefore, Ken will pay $ 871.25 for these items
I hope this helps you
find the value of x for which m parallels nthe value of x for which m paralles n is......
If m and n are parallel, then: 4x - 33 = 3x + 8
Soving for x:
4x - 33 = 3x + 8
4x - 3x = 8 + 33 = 41
x = 41
Answer:
41
the dimensions of the rectangular prism shown are given in centimeters
The volume of the prism = Length x breadth x height
= 4cm x 1.4cm x 3cm = 16.8 cm^3
library has a fund to buy 500 books that cost N$ 20 each. How many books costing N$ 25 each could be bought instead?
Answer:
20 books
Step-by-step explanation:
can u help me with my math question please
In an inverse variation, y = 1 when x = 4. Write an inverse variation equation that showsthe relationship between x and y.
In an inverse variation as one quantity increases the other decreases. For example, if x increases, y decreases
We can write it as:
x=k/y
where k is a constant.
or
x*y = k
replacing the values:
4*1=k
4=k
x*y=4
Can someone please help me with this( there is a part two)
Part A:
We will have that the inequality that represents the scenario is:
[tex]1.75x\le35[/tex]Where x is the number of horses.
Part B:
The solution of the inequality is:
[tex]x\le\frac{35}{1.75}\Rightarrow x\le20[/tex]This means that Sunshine Acre Farm can support at most 20 horses.
Find 15.4% of 360°. (Round your answer to the nearest whole degree.)
We need to find 15.4% of 360º.
Notice that:
[tex]15.4\%=\frac{15.4}{100}=\frac{154}{1000}[/tex]Also, 15.4% of 360º corresponds to the product:
[tex]15.4\%\cdot360\degree[/tex]Thus, we have:
[tex]15.4\%\text{ of }360\degree=\frac{154}{1000}\cdot360\degree=\frac{154\cdot360}{1000}=\frac{154\cdot36}{100}=\frac{5544}{100}=55.44\degree[/tex]Since 0.44 < 0.50, rounding to the nearest whole degree, we obtain:
Answer
55º
-2×+5y=-13×+2y=11[tex] - 2 \times + 5y = - 1[/tex]
nealmiyasmith20, this is the solution:
-2× + 5y= -1
3× + 2y= 11
___________
Step 1: Isolating x on the first equation:
-2× + 5y= -1
-2x = - 1 - 5y
Dividing by -2 at both sides:
-2x/-2 = -1/-2 - 5y/-2
x = 1/2 + 5y/2
______________________
Step 2: Substituting x and solving for y on the second equation:
3× + 2y = 11
3 ( 1/2 + 5y/2) + 2y = 11
3/2 + 15y/2 + 2y = 11
19y/2 = 11 -3/2
19y/2 = 19/2
Multiplying by 2/19 at boths sides:
19y/2 *2/19 = 19/2 * 2/19
y = 1
___________________
Step 3: Substituting y and solving for x on the first equation:
-2× + 5y = -1
-2x + 5 * 1 = -1
-2x + 5 = -1
-2x = -1 - 5
-2x = -6
Dividing by -2 at both sides:
-2x/-2 = -6/-2
x = 3
Step 4: Proving that x = 3 and y = 1 are correct on the second equation:
3× + 2y = 11
3 * 3 + 2 * 1 = 11
9 + 2 = 11
11 = 11
We proved that x = 3 and y = 1 are correct
I attached a picture of the graphIn which interval is the median age?Choose 1 answer:A.) 0 - 5B.) 5 - 10 C.) 10 - 15 D.) 15 - 20 E.) 20 - 25
We have the following:
The median is the value of the half, therefore
[tex]M=\frac{25+0}{2}=12.5[/tex]Therefore the answer is C) 10 - 15
Answer:
dbxbdghdhdvddhbdhddu
suppose you spend 35% of your monthly budget on food and 14% on the bus fare food and bus fares total to 12.50/month what is your monthly budget 
Let the monthly budget be 100
35% of it was spent on food i.e 35/100×100= 35
14% of it was spent on bus fare i.e. 14/100×100= 14
Total 49% is spent on food and bus fare, when total budget is 100
∴ 1% is spent when budget is 100/49
12.5 is spent when budget = 100/49×12.5
=25.5
∵ The monthly budget is 25.5
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My child ask for help on this I don’t know how to help
Them
Please see attached photo
After 6 months he spents $228.5 on cable and for 10 months he could have cable service for $344.5
What is the expression?An expression is a set of numbers or variables combined using the operations + , – , × or ÷ . Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.
Given:
c(x)=29x+54.5
a) At x=6
c(6) = 29*6 + 54.5
c(6) = $ 228.5
b) c(x) = 344.5
344.5 = 29x+54.5
x = 10 months
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Determine which set of side measurements could be used to form a triangle.
13, 19, 7
25, 12, 13
18, 2, 24
3, 1, 5
Answer:
ima go with (A: 13, 19, 1)
Step-by-step explanation:
formula:
a+b>c = 13+19>7
a+c>b = 13+7>19
b+c>a = 7+9>13
The set 13, 19, 7 can be used to form a triangle.
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
A triangle is formed when one side of triangle is greater than the difference of the two remaining sides, less than the sum of the two remaining sides.
If a, b and c are the sides of triangle,
Then
|a - b| < c < |a + b|
To find the set of measurement that could be used to form a triangle,
Use the options,
(a)
The given set is,
13, 19, 7
19 - 13 < 7 < 19 + 30
6 < 7 < 49
This set follows the condition of a triangle.
Therefore, this set can be used to form a triangle.
(b)
The given set is,
25, 12 , 13
25 - 12 < 13 < 25 + 12
13 < 13 < 37
This set does not follow the condition of a triangle.
(c)
The given set is,
18, 2, 24
18 - 2 < 24 < 18 + 2
16 < 24 < 20
This set does not follow the condition of a triangle.
Solve for option (D) also.
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x(4b-a)² + y(4b - a)²
factor the binomial out of each polynomial.
please explain how you got the answer i am deeply confused.
Answer:
(4b - a)²(x + y)
Step-by-step explanation:
x(4b - a)² + y(4b - a)² ← factor out (4b - a)² from each term
= (4b - a)²(x + y)
Use the graph at the top of the page for 22 and 23. A) 8/3 B) 8 C) - 1/8 D) -3/8 22) Write the slope of the line that would be parallel to h(x)23) Write the slope of the line that would be perpendicular to h(x)
Given the line h(x), it can be observed that two points with coordinate below can be located
[tex]\begin{gathered} (-4,0),\text{point where h(x) cut the x-axis} \\ (4,-1),\text{point where h(x) and m(x) cross each other} \end{gathered}[/tex]The slope,s, of a line given coordinates of two points can be found using the formula below:
[tex]\begin{gathered} s=\frac{y_2-y_1}{x_2-x_1} \\ \text{points} \\ (x_1,y_1),(x_2,y_2) \end{gathered}[/tex]The slope of the line h(x) with the coordinates of the two points gotten can be gotten as shown below
[tex]\begin{gathered} (-4,0),(4,-1) \\ s_{h(x)}=\frac{-1-0}{4--4} \\ s_{h(x)}=\frac{-1}{4+4} \\ s_{h(x)}=-\frac{1}{8} \end{gathered}[/tex]It should be noted that two parallel lines have the same slope, while the slope of two perpendicular lines can be found to be negative inverse of their slopes
For example, if m1 is the slope of a line, the slope of its parallel line would be m1. But the slope of the perpendicular line would be -1/m1
The slope of the line that would be parallel to h(x) is the same as the slope of h(x)
The slope of the line that would be perpendicular to h(x) would be negative inverse of the slope of line h(x)
[tex]\begin{gathered} s_{\text{parallel}}=-\frac{1}{8} \\ s_{\text{perpendicular}}=\frac{-1}{-\frac{1}{8}}=-1\times\frac{-8}{1}=8 \end{gathered}[/tex]Hence, The slope of the line that would be parallel to h(x) is -1/8, while the slope of the line that would be perpendicular to h(x) is 8
I
3. How many pictures would you draw for biking if
each = 5 students?
Answer:
You can draw a car for five students
A. The graph of g(x) is horizontally compressed by a factor of 4.B. The graph of g(x) is shifted 4 units to the right.C. The graph of g(x) is horizontally stretched by a factor of 4.D. The graph of g(x) is vertically compressed by a factor of 4.
Give:
There are given the function:
[tex]f(x)=x^2,g(x)=(\frac{1}{4}x)\placeholder{⬚}^2[/tex]Now,
The transformation of the graph g(x) is shown below.
The,
Transformation is:
[tex][/tex]24.) In the figure below, Z1 is supplementary to z3 under which of the followingconditions?F Line a is parallel to line bG Line a is parallel to line c.H Line a is perpendicular to line c.J Line b is perpendicular to line c.the
For this statement to be true, the only condition that is necessary is that Line a is parallel to Line b. The right answer is the first one.
Please help with the question below (please try to answer in max 10/15 minutes).Jasmine can run 4 5/6 miles in 2/3 of an Hour. How many miles can she run in 1 hour?Simplify completely
Explanation
We are given the following:
[tex]Jasmine\text{ }can\text{ }run\text{ }4\frac{5}{6}\text{ }miles\text{ }in\text{ }\frac{2}{3}\text{ }of\text{ }an\text{ }hour[/tex]We are required to determine how many miles she can run in 1 hour.
This is achieved thus:
[tex]\begin{gathered} 4\frac{5}{6}miles\Rightarrow\frac{2}{3}hour \\ \therefore1hour\Rightarrow4\frac{5}{6}\div\frac{2}{3} \\ =\frac{29}{6}\div\frac{2}{3} \\ =\frac{29}{6}\times\frac{3}{2} \\ =\frac{29}{2}\times\frac{1}{2} \\ =\frac{29}{4} \\ =7\frac{1}{4} \end{gathered}[/tex]Hence, the answer is:
[tex]7\frac{1}{4}\text{ }miles[/tex]To start solving the system, Elena wrote:4x + y = 14x + 8y = 36And then she wrote:4x + y =14x + 8y = 36 --7y=-351. What were Elena's first two moves? What might be possible reasons for those moves?
Looking at the equations after Elena started solving the system, we can see that the second equation is different.
Each coefficient is 4 times greater the old coefficiets. That means equation B was multiplied by 4. She did this step to make both equations have the term 4x.
Then, in the next step, she subtracted the equations. Since both equations have 4x, subtracting the equations would cancel this term, then she can solve the result for y.
Therefore, in this step, she Subtracted the equations, this way she can cancel out the variable x.
Graph to find an ordered pair and where they intersect.y=-x+2y=-1/4x-1
Given:
The equations are,
[tex]\begin{gathered} y=-x+2 \\ y=-\frac{1}{4}x-1 \end{gathered}[/tex]To draw the lines on the graph first find the points on the graph,
[tex]\begin{gathered} y=-x+2 \\ x=0,y=2 \\ x=1,y=-1+2=1 \\ x=2,y=-2+2=0 \\ x=-1,y=1+2=3 \end{gathered}[/tex]And,
[tex]\begin{gathered} y=-\frac{1}{4}x-1 \\ x=0,y=-1 \\ x=2,y=-\frac{1}{2}-1=-1.5 \\ x=-2,y=\frac{1}{2}-1=\frac{1}{2}=0.5 \\ x=1,y=-\frac{1}{4}-1=-1.25 \end{gathered}[/tex]Plot the points on the graph.
From the graph, the lines intersect at the point (4,-2).
There is a game where the outcome is a random integer from 1 to 50. If the outcome is odd, you wi $26. If the outcome is even, you win nothing. If you play the game, what is the expected payoff?
We have a game like the one described in the question and we have to calculate the expected payoff, which is equal to the sum of the possible outcomes weighted by the probability of that outcome.
In this case we have two outcomes:
1) We get an odd number and we win $26 (W=26).
2) We get an even number and we get $0 (W=0).
To calculate the probabilities of each oucome we have to know the proportion of odd an even numbers in the list of 1 to 50. We have a total of 50 numbers, rom which 25 are odd numbers and 25 are even numbers, so the probability of each outcome can be calculated as the relative frequency of each category:
[tex]\begin{gathered} P_1=\text{ number of odds / total numbers}=\frac{25}{50}=0.5 \\ P_2=\text{ number of evens / total numbers}=\frac{25}{50}=0.5 \end{gathered}[/tex]Then, we can calculate the expected payoff as:
[tex]E=\sum ^n_{i=1}p_iW_i=p_1W_1+p_2W_2=0.5\cdot26+0.5\cdot0=13+0=13[/tex]p_i: probability of outcome i.
W_i: prize when outcome i happens.
Then, the expected payoff for this game is $13.
Answer: the expected payoff for this game is $13.
Solve each expression by completing the square. x^2+6x=9
x^2+6x=9
To create a trinomial square on the left side of the equation, you have to find a value that is equal to the square of half of 9.
(9/2)^2=(3)^2
Then, add this therm to each side of the equation.
x^2+6x+(3)^2=9+(3)^2
Simplifying that equation:
x^2+6x+9=18
Factor the perfect trinomial square into (x+3)^2
(x+3)^2=18
To solve the equation for x, you have to take the square root of each side of the equation:
(x+3)^(2*1/2)=18^1/2
Joseph and his children went into a movie theater where they sell bags of popcorn for $7.50 each and pretzels for $4.75 each. Joseph has 595 to spend and must buy no less than 16 bags of popcorn and pretzels altogether. If z represents the number of bags of popcorn purchased and y represents the number of pretzels purchased, write and solve a sstem of inequalities graphically and determine one possible solution.
We will have the following system of inequalities:
[tex]\begin{cases}z+y\ge16 \\ 7.50z+4.75y\le595\end{cases}[/tex]This graphically is:
So, the solutions will be located at the intersection of both graphs. So, one possible solution is:
5 bags of popcorn and 15 bags of pretzels. This solution can be seen in the following graph:
A recipe book shows measurement conversions for pints to cups. It shows that 1.5 pints equals 3 cups and 2.5 pints equals 5 cups.
Write an equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups.
p equals 3 over 1.5 times n
n equals 1.5 over 3 times p
p = 0.5n
n = 0.5p
The equation that shows the proportional relationship between pints and cups where p represents pints and n represents cups is p = 0.5n
How to calculate the value?From the information, the recipe book shows measurement conversions for pints to cups. It shows that 1.5 pints equals 3 cups and 2.5 pints equals 5 cups.
p = pints
n = cups.
Therefore, the equation will be illustrated as
1.5 = 3k
where k = constant of proportionality
Divide
k = 1.5/3
k = 0.5
Therefore, the equation is p = 0.5n.
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Choose the graph of the linear equation 24x + 64y = 384?
On a coordinate plane, a line goes through points (0, 6) and (16, 0).
On a coordinate plane, a line goes through points (0, 8) and (12, 0).
On a coordinate plane, a line goes through points (0, 16) and (6, 0).
The graph that represents the linear equation, 24x + 64y = 384 is shown in the diagram.
How to Determine the Graph of a Linear Equation?A linear equation can be expressed as y = mx + b, which is the slope-intercept form where the slope is represented as m and the y-intercept is represented by b. This y-intercept is the point where the line intercepts the y-axis when x is equal to zero.
Given the linear equation, 24x + 64y = 384, rewrite in slope-intercept form to easily figure out the slope:
24x + 64y = 384
64y = -24x + 384
y = -24x/64 + 384/64
y = -6/16x + 6
This shows that the graph would have a y-coordinate, b = 6, while the slope is -6/16. The graph would be the one shown below in the diagram.
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Answer:
A
Step-by-step explanation:
Need x please?????????I’m looking to find x. The line inside is just to know where x is.Round to the nearest tenth.
The triangle given in the exercise is a Right Triangle because the square inside it indicates that it has an angle that measures 90 degrees.
Then, you can use the following Trigonometric Function:
[tex]\sin \alpha=\frac{opposite}{hypotenuse}[/tex]In this case:
[tex]\begin{gathered} \alpha=31\degree_{} \\ opposite=11 \\ hypotenuse=x \end{gathered}[/tex]Then, by substituting values and solving for "x", you get:
[tex]\begin{gathered} \sin (31\degree)=\frac{11}{x} \\ \\ x\cdot\sin (31\degree)=11 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{11}{\sin (31\degree)} \\ \\ x\approx21.4 \end{gathered}[/tex]Therefore, the answer is:
[tex]x\approx21.4[/tex]what are all the possible rational roots of x^2+x-6
The root of x^2 + x - 6 is the values of x when y = 0
x^2 + x - 6 = 0
Factorize it into two factors
Since the last sign is (-), so the brackets of the factors have different sign
Wr need two numbers their product = 6 and their
