Answer:
yes
Step-by-step explanation:
[tex]\frac{16}{84}[/tex] ( divide numerator and denominator by 4 )
= [tex]\frac{4}{21}[/tex]
they represent the same proportion
Question 1-1
The Jansen family has an SUV that gets 25 miles per gallon and a sedan that gets 32 miles per gallon. They plan to go on a 125-
mile car trip and know that gas costs $4 per gallon. The relationship between miles and gallons is proportional, as is the
relationship between gas price and gallons.
How much money will they save if they take the sedan instead of the SUV? Round to the nearest cent if needed.
O $1.75
O $7.00
O $1.09
O $4.38
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Answer: 4.38
Step-by-step explanation:
Firstly to answer this question we need to take a look at both of the mpg for each of them. We already know that the SUV has 25 mpg and the Sedan has 32 mpg, to figure this out we need to get the answer to $4 x 25 and $4 x 32.
The answer to that is $100 for the SUV and $128 for the Sedan. Next, we need to figure out the mile difference between to 2 vehicles.
100 x 2 = 200
128 x 2 = 256
knowing those numbers overall we can conclude that the sedan will cost $4.38 less than the Suv
Can someone answer these please?
Answer:
Step-by-step explanation:
1. -17x+1
2. -5/6a-1/2
3.-2/3x+2/5
4.-6(2x+3y+0.6)
5.2/3(x+6)
The Triple L investment club is considering purchasing a certain stock. After considerable research, the club members determine that there is a 50% chance of making $12,000, a 20% chance of breaking even, and a 30% chance of losing$6,600. Find the expectation of this purchase.
We would apply the formula for calculating the expectation of the mean or expected value which is expressed as
Ex = ΣxP(x)
In this scenario, from the information given,
12000 is profit at 50%
Breakeven mean = 0 because there is no profit or loss' at 20%
loss = - 6600 at 30 %
Thus,
Expectation = 50/100 * 12000 + 20/100 * 0 + 30/100 * 6600
Expectation = 6000 + 0 + 1980
Expectation = 7980
the expectation of this purchase is $7980
D
If the conditional statement "If I use my cell phone too much, my bill will be expensive," is true, which other statement must also be true?
If I do not use my cell phone too much, my bill will not be expensive.
O None must be true.
Of my bill is expensive, I used iny cell phone too much.
If my bill is not expensive. I did not use my cell phone too much
4
Answer: "If my bill is not expensive. I did not use my cell phone too much"
Reason:
The original statement is of the form "If P, then Q"
P = "I use my cell phone too much"
Q = "my bill will be expensive"
An equivalent form to the original condition is known as the contrapositive of the form "If not Q, then not P". We swap the positions of P and Q. We also negate each part. You can use a logical truth table to verify that the conditional and contrapositive have equivalent truth values, which means they are effectively equivalent statements.
Answer:
If my bill is not expensive. I did not use my cell phone too much
Step-by-step explanation:
I need help to Find the missing percentages and what is the independent and dependent variable.
Solution:
From the given table;
Where, the November values is used as 100 percent;
To find the missing percentages of Elm leaves
For the month of May
[tex]\begin{gathered} For\text{ the month of November: 3481} \\ For\text{ the month of May;} \\ =\frac{1739}{3481}\times100\%=49.95690\approx50.0\%\text{ \lparen1 decimal place\rparen} \\ For\text{ the month of August} \\ =\frac{35}{3481}\times100\%=1.00545\approx1.0\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]To find the missing percentages of Hazel leaves
[tex]\begin{gathered} For\text{ the month of November:}1723 \\ For\text{ the month of May;} \\ =\frac{501}{1723}\times100=\:29.07719\approx29.1\%\text{ \lparen1 decimal place\rparen} \\ For\text{ the month of August;} \\ =\frac{62}{1723}\times100\%=3.59837\approx3.6\%\text{ \lparen1 decimal place\rparen} \end{gathered}[/tex]What is the independent and dependent variable?
An independent variable is a variable that does not depend on any other variable.
For example,
[tex]3y=4x+1[/tex]x is an independent variable because for every value of x, there is a different value of y
A dependent variable is a variable whose value depends upon an independent variable.
For example;
[tex]y=5x[/tex]From the expression above, the value of y depends on the value of x
what do we do with 3 1/3 in the problem and also i need the answer to all of it
The answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.
Given:
x = 3 , y = 1/3 and z = 5 and expression 12x - 3y / 4x - z.
substitute the x,y,z values in expression.
= 12(3)-3(1/3) / 4(3)-5
= 36 - 3/3 / 12 - 5
= 36 - 1 / 7
= 35/7
= 5.
Therefore the answer after solving the expression 12x - 3y / 4x - z with x = 3,y=1/3 and z = 5 is 5.
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4 Friends shot free throws for a charity event. Adam scored 8 more points than cheryl. Laura scored twice as many points as Adam. Tom scored 10 points less than Laura. Together the four friends scored a total of 66 points.Cheryl's Expression = Adam's Expression = Laura's Expression = Tom's Expression =State each person's points :Cheryl's points = Adam's points = Laura's points = Tom's points =
Let cheryl score "c", Adam score "a", Laura score "l" and Tom score "t", points.
Now, let's write equations for statements given.
Adam scores 8 more than Cheryl, so:
a = c + 8
or
c = a - 8
Laura scored twice as Adam, so:
l = 2a
Tom scores 10 less than Laura:
t = l - 10
or
t = 2a - 10
Altogether, they scored 66, so:
c + a + l + t = 66
Putting the 3 bold equations in the last one, we can solve for "a" first. Shown below:
[tex]\begin{gathered} c+a+l+t=66 \\ a-8+a+2a+2a-10=66 \\ 6a-18=66 \\ 6a=66+18 \\ 6a=84 \\ a=\frac{84}{6} \\ a=14 \end{gathered}[/tex]So,
c = a - 8
c = 14 - 8
c = 6
l = 2a
l = 2(14)
l = 28
t = 2a - 10
t = 2(14) - 10
t = 28 - 10
t = 18
So,
Adam = 14 points
Cheryl = 6 points
Laura = 28 points
Tom = 18 points
here is the 5th one to do.
Answer:
a is not equivalent to b and c.
Step-by-step explanation:
a.
[tex]50( {2}^{x + 2} ) = 25 \times 2( {2}^{x + 2} ) = 25( {2}^{x + 3} )[/tex]
b.
[tex]25( {2}^{2x + 1} ) [/tex]
c.
[tex]50( {4}^{x} ) = 50( { {2}^{x} )}^{2} = 50( {2}^{2x} ) = 25 \times 2( {2}^{2x} ) = 25( {2}^{2x + 1} )[/tex]
Angles abc and bcj are alternate interior angles. use a transformation that takes angle abc to angle bcj to prove that alternate interior angles are congruent
Angle two and angle six line up with one another. Angle three would consequently be consistent with angle six. Angles two and three are congruent because they both have vertical angles.
What are the alternate interior angles?Alternate internal angles are the pair of angles formed on the inner side of the parallel lines and on the opposing sides of the transversal when two parallel lines are intersected by a transversal. These angles are all equal. There is an alternative perspective on this. The parallelism or non-parallelism of the provided lines can be determined by the alternative inner angles. If these angles are equivalent, the given lines that a transversal crosses are said to as being parallel.
To see the many internal angles, look at the following diagram. Here, a transversal divides AB and CD, two parallel lines.
Alternate Interior Angles Theorem's opposite, then?The two lines are said to be parallel if a transversal intersects them such that their alternate interior angles are equal, according to the converse of the alternate interior angles theorem.
Let's examine the following diagram to better comprehend this: 1 = 5 (matching angles), 3 = 5 (vertically opposite angles). Thus, ∠1 = ∠3. The same goes for the demonstration of 2 = 4. This demonstrates that the two supplied lines are parallel to one another since their alternate inner angles are equal.
Example: Two lines are parallel to one another if the alternate interior angles created by the transversal line on two coplanar are congruent. As a result, we can write that 2 and 5 are corresponding angles.
Transformations would show that the accompanying exterior angles EBI and BCJ are congruent, proving that an is parallel to a pair of alternate exterior angles with measurements of 130° and 50°.
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Based on the diagram below, we can say that the two triangles ___.
Solution
Step1
The AA criterion for triangle similarity states that if two triangles have two pairs of congruent angles, then the triangles are similar.
Step2
Two pairs angles are equal, hence they are similar
Answer
Are similar by AA
each day for three weeks, keisha recods the number of eggs her chickens lay. The frequency table shows her data. which statement describes the data distribution
The greatest number of eggs laid by the chicken any day is 7
What is frequency table?A frequency table is a table that lists items and shows the number of times the items occur.Frequency refers to the number of times an event or a value occurs.
A frequency table lists a set of values and how often each one appears.
The frequency table above shows the number of eggs laid for 3weeks.
From the table, the least number of egg laid in anyday is 3 and the greatest number of egg laid in a day is 7.
Therefore the greatest number of egg that can be laid by the chickens in anyday is 7
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Answer:
The distribution is spread from 3 eggs to 7 eggs.
Solve the following inequality and select all possible solutions.
please help with circles
Answer:
≈ 466 cm
Step-by-step explanation:
the total length of wire required is
outside sides of square + 4 straight pieces + circumference of circle
= (4 × 70) + (4 × 15) + (π d ← d is the diameter )
= 280 + 60 + 40π
= 340 + 125.66
= 465.66
≈ 466 cm ( to the nearest cm )
We need to find out the total length of wire needed to make this design. We can do this by finding out the perimeter of square and Circle and finally adding the lengths of the four 15cm wire used .
Given data:-
length of side of square= 70cmdiameter of Circle= 40cm , r = 20cm 15cm four wiresPerimeter of the square:-
[tex]\longrightarrow p_s = 4(side) \\ [/tex]
[tex]\longrightarrow p_s = 4(70cm) \\ [/tex]
[tex]\longrightarrow p_s = 280cm \\ [/tex]
Perimeter/circumference of the circle:-
[tex]\longrightarrow p_c = 2\pi r \\ [/tex]
[tex]\longrightarrow p_c = 2(3.14)(20cm) \\ [/tex]
[tex]\longrightarrow p_c = 125.71 cm \\ [/tex]
Additionally length of four wires would be 15cm*4 = 60cm .
So , total length of the wire required,
[tex]\longrightarrow l =( 125.71 + 280+60)cm \approx \boxed{466\ cm}\\ [/tex]
and we are done!
Literal equation
6 = 2(m-b)/m+b
for b.
Answer:
b= −1/2m
Step-by-step explanation:
Step 1: Multiply both sides by b+m.
6b+6m=−2b+2m
Step 2: Add 2b to both sides.
6b+6m+2b=−2b+2m+2b
8b+6m=2m
Step 3: Add -6m to both sides.
8b+6m+−6m=2m+−6m
8b=−4m
Step 4: Divide both sides by 8.
Divide each amount in the ratio given. $84in the ratio 2:1
The ratio shows how many times one value is contained in another value.
1 part = $28
2 parts = $56
3 parts = $84
The amount 84 in the ratio 2:1 is 56:28.
What is a ratio?
The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Amount = $84.
We will divide the amount into 2:1
This means,
There are 3 parts.
2 + 1 = 3
The amount for each part.
= 84/3
= 28
Now,
1 parts = $28
2 parts = 2 x $28
2 parts = $56
The ratio 2:1 of 84 is 56:28
Thus,
The amount 84 in the ratio 2:1 is 56:28.
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Select the correct answer.
Consider the graph of function g.
A parabola labeled lowercase g declines through the points (negative 4, 4), (negative 3, 2 point 2), (negative 2, 1), (0, 0), (2, 1) and (3 point 5, 3) on the x y coordinate plane.
If f(x) = x2, which equation represents function g?
A. g(x) = f(2x)
B. g(x) = f(4x)
C. g(x) = 2 f(x)
D. g(x) = f(1/2x)
The correct option is B that is g(x)=f(4x) as the condition says, "A parabola labeled lowercase g declines through the points (negative 4, 4), (negative 3, 2 point 2), (negative 2, 1), (0, 0), (2, 1) and (3 point 5, 3) on the x y coordinate plane".
What is parabola?A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side intersect. Ideally, a projectile traveling under the pull of gravity will travel along a curve similar to this one. A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.
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PLSsSsSsSsSssSsSSSsSS HeEeEeEeeEeLPpPpPPp!!!!!!!
Answer:
Function 1 is increasing bcz the slope is positive since it is observed that the values of the abscissa (X) increase as well as the values of the ordinate (Y), while function 2 is decreasing, bcz it has a negative slope since it is observed that as the values of the abscissa (X) increase, the values of the ordinate (Y) decrease
what is y+2=-6(x-3) in standard form?
Answer: 6x + y = 16
Step-by-step explanation:
How many ways can the letters in the word PARALLEL be arranged?
Answer:
3,360 ways.
Explanation:
In the word PARALLEL
• Number of letters = 8
,• Number of Ls = 3
,• Number of As = 2
Since no other restriction is given, the number of ways in which the letters can be arranged is:
[tex]\frac{8!}{3!\times2!}[/tex]We solve to obtain our result.
[tex]\begin{gathered} \frac{8!}{3!\times2!}=\frac{8\times7\times6\times5\times4\times3!}{3!\times2!} \\ =\frac{8\times7\times6\times5\times4}{2!} \\ =8\times7\times6\times5\times2 \\ =3360\text{ ways} \end{gathered}[/tex]The word can be arranged in 3,360 ways.
What is the cube root of 3 and 512
Answer:
1.4422
Step-by-step explanation:
Depends what they are asking for in some cases they will want you to simplify it to 1.4 or
[tex]\sqrt[n]{x}[/tex] It might also look like this with a 3 on top and bottom
sry if this is confusing
If you have any questions just ask : )
Objective function Z=3x+6yFind the value at each corner of the graph
Given: An objective function
[tex]z=3x+6y[/tex]with constraints-
[tex]\begin{gathered} \\ \begin{cases}{x\ge0,y\ge0} \\ {2x+y\leq12} \\ {x+y\ge6}\end{cases} \end{gathered}[/tex]Required: To graph the linear inequalities representing the constraints and determine the objective function's value at each corner.
Explanation: The inequalities can be graphed by considering them as equations and then determining the shaded region by less than or greater than symbol.
The equation for the first inequality is-
[tex]2x+y=12[/tex]This represents a straight line passing through points (6,0) and (0,12).
The shaded region will be below this line as the inequality is-
[tex]2x+y\leq12[/tex]Similarly, the inequality-
[tex]x+y\ge6[/tex]Represents a shaded region above the line x+y=6.
The inequalities-
[tex]x\ge0,y\ge0[/tex]Represents the positive values of x and y. Hence we need to determine the graph in the first quadrant.
The graph of the inequalities is-
The graph in blue represents the inequality-
[tex]2x+y\leq12[/tex]While the graph in green represents the inequality-
[tex]x+y\ge6[/tex]The corner points of the common shaded area are A(0,6), B(0,12), and C(6,0).
Now the value of the objective function at these points is-
a) At A(0,6)
[tex]\begin{gathered} z=3(0)+6(6) \\ =36 \end{gathered}[/tex]b) At B(0,12)
[tex]\begin{gathered} z=3(0)+6(12) \\ =72 \end{gathered}[/tex]c) At C(6,0)
[tex]\begin{gathered} z=3(6)+6(0) \\ =18 \end{gathered}[/tex]Final Answer: a) The graph is drawn.
b) 36,72,18
When spinning a wheel with 1 red, 2 blue, and 3 green spaces, what
is the probability that you will not spin a red?
Step-by-step explanation:
so, we have 1 + 2 + 3 = 6 total spaces.
a probability is always the ratio
desired cases / totally possible cases
the probability to spin red is therefore
1 desired case
6 total possible cases
1/6 = 0.166666666...
a probability of 1 means a sure result = anyone of the totally possible cases.
so, 6/6 = 1 in our case.
if the desired cases are everything but red, we need to eliminate the possible red results (1) from the amount of our desired cases : 6 - 1 = 5
so the probability of not spinning a red is
5/6 = 0.833333333...
formally we can also say this is the sure thing minus the opposite of what we want to have. the opposite of not spinning a red is spinning a red (1/6) :
1 - 1/6 = 5/6 = 0.833333333...
For t(x) = 3x - 5, find the value of x
for which /(x) = 4.
Answer:7
Step-by-step explanation:
3x-5
replace x for 4
3(4)-5
=12-5
=7
A 6 inch personal pizza has 620 calories, with 240 of those fromfat. A 16 inch pizza is cut into 8 slices. Estimate the number ofcalories in one slice of a 16 inch pizza.calories
Given:
A 6-inch personal pizza has 620 calories, with 240 of those from fat.
A 16-inch pizza is cut into 8 slices.
So, the total number of calories in a 16-inch pizza will be calculated using the ratio and the proportions:
A 6-inch pizza : A 16-inch pizza
6 : 16
620 : x
Using the cross product:
[tex]x=\frac{16\cdot620}{6}=1653.33[/tex]A 16-inch pizza is cut into 8 slices.
So, the number of calories in one slice =
[tex]\frac{1653.33}{8}\approx206.67[/tex]So, the answer will be:
The number of calories in one slice = 206.67 calories
Which function is best represented by this graph?
Responses
A
y = - 2 x + 2
5y = - 2 x + 2 5
B
y = - 5 x + 5
2y = - 5 x + 5 2
C
y = - 5 x + 2
2y = - 5 x + 2 2
D
y = 2 x + 2
5
The function best represented by the graph is y = - 5 x + 5 2y = - 5 x + 5². Option B.
Use the vertical line test to determine if a graph represents a function. A graph is a function if a vertical line moves across it and touches it only at one point at a time. If a vertical line touches a graph at multiple points, the graph is not a function.
Calculation:-
X intercept = 2
y intercept = 5
slopt = y/x
= 5/2
= 2.5
For the line to be perpendicular to each other angle must be 90⁰.
Hence option B.
B.y = - 5 x + 5
2y = - 5 x + 5 2
slope m = 5/2
2.5.
A function is defined as a relation between a set of inputs each with an output. Simply put, a function is a relationship between inputs, each associated with exactly one output. Each function has a domain and a codomain or scope. The graph of a quadratic function is called a parabola and has a curved shape. One of the main points of the parabola is the vertex.
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Translate the following phrase into an algebraic expression. Do not simplify. Use the variable names "x" or "y" to describe the unknowns.6 divided by the sum of 4 and a number
Let:
x = Unknown number
[tex]\frac{6}{x+4}\equiv6_{\text{ }}divided_{\text{ }}by_{\text{ }}the_{\text{ }}sum_{\text{ }}of_{\text{ }}4_{\text{ }}and_{\text{ }}a_{\text{ }}number[/tex]A knitter is planning to knit a blanket and refers to a chart showing the size of blanket that can be knited based on the amount of yarn available.Which statement is true?A.The dependent variable is the amount of yarn because that is the input and the independent variable is the size of the blanket because that is the output B. The dependent variable is the size of the blanket because that is the input and the independent variable is the amount of yarn became that's is the output C. The Independent variable is the amount of yarn because that is the input, and the dependent variable is the size of the blanket became is the output D.The independent variable is the size of the blanket because that is the input, and the dependent variable is the amount of yarn became that is the output for
Since the amount of yarn available is what defines the size of the blanket, the amount of yarn is the independent variable, and it is the input for the table or equation.
The size of the blanket depends on the amount of yarn, so the size of the blanket is the dependent variable, and it is the output of the table or equation.
Therefore the option that shows the true statement is C.
Solve - 8x = 56 for x.
Nobody is answering mathematics anymore so it doesn't matter just pls answer
Answer:
7/20 of the laundry still needs to be washedStep-by-step explanation:
Laundry washed:
2/5 and 1/4 of totalWho washed more?
Compare the fractions by bringing them to common denominator:
2/5 = (2*4)/(5*4) = 8/20,1/4 = (1*5)/(4*5) = 5/20.Compare the numerators:
8 > 5,It means Mrs. Stem washed more than laundry her son.
Total portion of laundry washed:
8/20 + 5/20 = 13/20Laundry left to wash is the difference of full and the fraction of washed laundry:
1 - 13/20 = 20/20 - 13/20 =(20 - 13)/20 = 7/20Answer:
7/20 of laundry is still pending.
Step-by-step explanation:
Now the both washed is,
→ (2/5) + (1/4)
→ ((2 × 4)/(5 × 4)) + ((1 × 5)/(4 × 5))
→ (8/20) + (5/20)
→ 13/20
Forming the equation,
→ (13/20) + x = 1
Then required value of x will be,
→ (13/20) + x = 1
→ x = 1 - (13/20)
→ x = (20/20) - (13/20)
→ x = (20 - 13)/20
→ [ x = 7/20 ]
Hence, 7/20 of laundry is pending.
Match the Parallel line of y=-1/2x-2
The family of all linear equations that are parallel to y=-1/2x-2 is defined as:
y = (-1/2)*x + b
Such that b ≠ -2.
Which lines are parallel to the given one?We know that a general linear equation is written in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
We know that two linear equations are parallel if and only if the lines have the same slope and a different y-intercept.
So the family of lines parallel to:
y = (-1/2)*x - 2
Are of the form:
y = (-1/2)*x + b
Where b ≠ -2.
All these lines are parallel to the given ones.
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