Solution:
Let b represent the cost of 1 banana
Let p represent the cost of 1 pear
From the first statement, The cost of 4 bananas and 6 pears is $1.68
4b + 6p = 1.68 ----------------------------equation (1)
From the second statement, Nine bananas and 2 pears cost $1.48
9b + 2p = 1.48 -----------------------------equation (2)
Solve both equations simultaneously
4b + 6p = 1.68 ----------------------------equation (1)
9b + 2p = 1.48 -----------------------------equation (2)
Multiply equation (2) by 3 to eliminate p
27b + 6p = 4.44
4b + 6p = 1.68
Subtract both equatuions above
23b = 2.76
b = 2.76/23
b= 0.12
Substitute b = 0.12 into equation (1)
9b + 2p = 1.48
9(0.12) + 2p = 1.48
1.08 + 2p = 1.48
2p = 1.48 - 1.08
2p = 0.4
p = 0.4/2
p = 0.2
Hence, the cost of each banana is $0.12 while the cost of each pear is $0.2
Choose the scenarios that demonstrate a proportional relationship for each person's income.
Millie works at a car wash and earns $17.00 per car she washes.
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
Carla makes sandwiches at her job and earns $7.85 per hour.
Tino is a waiter and makes $3.98 per hour plus tips.
The scenarios that demonstrate a proportional relationship for each person's income are :
Millie works at a car wash and earns $17.00 per car she washes.Carla makes sandwiches at her job and earns $7.85 per hour.Consider the income as y in each scenario
Scenario 1
Millie works at a car wash and earns $17.00 per car she washes.
Consider the number of car she washes as x
y = 17x
y ∝ x
This is a proportional relationship
Scenario 2
Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.
The relationship will be
y = 25 +12.50x
where x is the number of hours
This is not a proportional relationship
Scenario 3
Carla makes sandwiches at her job and earns $7.85 per hour.
The relationship will be
y = 7.85x
y ∝ x
Where x is the number of hours
This is a proportional relationship
Scenario 4
Tino is a waiter and makes $3.98 per hour plus tips.
The relationship will be
y = 3.98x + tips
Where x is the number of hours
This is not a proportional relationship
Hence, the scenarios that demonstrate a proportional relationship for each person's income are
Millie works at a car wash and earns $17.00 per car she washes.Carla makes sandwiches at her job and earns $7.85 per hour.Learn more about proportional relationship here
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How many times larger is 3 x 10⁹ than 3 x 10⁷ ?
Answer:
100 times
Step-by-step explanation:
[tex]\frac{10^{9} }{10^{7} }[/tex] = [tex]10^{2}[/tex] = 100
When you are dividing exponents with the same bases, you subtract the exponents.
Answer:
3 x 10^9 is larger than 3 x 10^7 by 2,970,000,000
Step-by-step explanation:
Neegan paddles a kayak 21 miles upstream in 4.2 hours. The return trip downstream takes him 3 hours. What isthe rate that Neegan paddles in still water? What is the rate of the current?
System of Equations
When Neegan paddles the kayak upstream, the real rate (speed) is the difference between the rate that Neegan paddles in still water and the rate of the water against his paddling.
When he goes downstream, the real rate is the sum of the rates because the water and Neegan push in the same direction.
He takes 4.2 hours to paddle for 21 miles against the current, so the real rate is 21/4.2 = 5 mi/h
He takes only 3 hours to return, so the real speed is 21 / 3 = 7 mi/h.
Let:
x = rate at which Neegan paddles in still water
y = rate of the current.
We set the system of equations:
x - y = 5
x + y = 7
Adding both equations:
2x = 12
Divide by 2:
x = 6
Substituting in the second equation:
6 + y = 7
Subtracting 6:
y = 1
Neegan paddles at 6 mi/h in still water. The rate of the current is 1 mi/h
(Third choice)
I need help with this question involving the Cartesian plane will post pic
The graph of f(x) is a parabola with "arms up"
The vertex of the parabola is (0,-3)
Then we can know all the problem ask us:
increasing: (-3, infinity)
decreasing: (minus infinty, -3)
DNE maximum, beacuase it's arbitrarily large.
The minimum is the vertex: minimum of -3 at x = 0
The domain is all real numbers
The range is [-3, infinity)
-------------------------------------------------------------------------------------------------------------------------------------------------------------
To know the shape of a parabola you want to look 2 things. The standar formula of a parabola is:
[tex]f(x)=ax^2+b[/tex]We focus on a and b. Always will be a squared x, but a and b vary. a lot
A tell us if the parabola has it's arms up or down. If is positive, has arms up. If it's negative, arms down.
Also, this isn't something "strictly mathematical" but can tel you is the parabola is thin or fat.
Now b tells us what happends when x=0. If b is positive, the vertex will be "rised up". If b is negative, the vertex will be "pulled down"
When you get relatively confident, you can watch a and b, and based on their sign and how big they are, you can make a really good idea how the graphic is.
All the information the problem ask, you can get it by those numbers.
To know how wide is a parabola, you need to look at a. Let's supose a = 100. This is a very big number, si if I plug in an x, the function will square it and multiply it by 100 right? Then the function will be very thin. For an x very low, the function will be very great. Example: f(x)=100x^2 if I put x = 1 then I have to square it, and multipli it by 100: 1^2*100=100
Now let's copare this with an smaller a. Suppose a =2. Then if I plug x = 1 I get:
[tex]2x^2\text{ at x =1 }\Rightarrow f(1)=2\cdot1^2=2[/tex]For the same value of x, the first function is 100 and the second 2
Given g=(1+2a)/a, solve for the variable a.
We are given the equality
[tex]g=\frac{1+2a}{a}[/tex]and told to solve for a. That is, we should apply mathematical operations on both sides of the equality so we "isolate" variable a on one side of the equality. We start by multiplying both sides by a, so we get
[tex]a\cdot g=1+2a[/tex]Now, we subtract 2a from both sides. We get
[tex]a\cdot g-2a=1[/tex]We can factor on the left side a as a common factor, so we get
[tex]a\cdot(g-2)=1[/tex]Finally, we divide by (g-2) on both sides, so we get
[tex]a=\frac{1}{g-2}[/tex]Please help me. Will mark most brainliest.
Matthew's Maths mark increased by a factor of 3/2 this term. His new mark is 75%. Use an equation to calculate Matthew's mark last term.
We need to know about scale factor to solve the problem. Matthew's mark last term was 50%.
It is given that Matthew's marks increased by a factor of 3/2 this term. This means that whatever marks Matthew had received in his previous term, it was increased by 3/2 this term. If we consider his original marks to be x, then we can get the increased marks by multiplying x by 3/2. We know that the new marks is 75%, we need to find the value of x.
3x/2=75
x=75x2/3=25x2=50
Therefore the marks Matthew received in the previous term is 50%.
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Ben works at a mobile phone store, where he earns a flat $80 for each 8-hour shift. He also earns a commission of $20 for each phone that he sells. If e stands for Ben's earnings and m is the number of mobile phones he sells, which of the following equations describes the amount of money that he earns in one shift?Question 5 options:A) e = m + 80B) e = m + 100C) e = –20m + 80D) e = 20m + 80
fixed earnings = $80 ( for 8 hour shift)
Number of mobile phones he sells = m
Commision for each mobile phone sold = $20
Amount he earns in 1 shift (e) = flat + number of phones* commision
e = 80 + 20m
e= 20m + 80 (D)
HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
the rational number :
-1 ³/₄ is located as point 1
14/8 is located as point 5
1.125 is located as point 6
-0.875 is located as point 4
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
Here,
the rational number -1 ³/₄ is located as point 1, as -1 ³/₄ is greater then -1 and less then -2 on number line and is 3/4 of the gap between -1 and -2.
the rational number 14/8 is located as point 5, as 14/8 is greater then 0 and less then 1 on number line and is 3/4 of the gap between 0 and 1.
the rational number 1.125 is located as point 6, as 1.125 is greater then 1 and less then 2 on number line and is 1/8th of the gap between 1 and 2.
the rational number -0.875 is located as point 4, as -0.875 is greater then 0 and less then -1 on number line and is 1/8 th of the gap between -1 and 0.
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45. For customers generating their own solar power, ZG&E charges them $3 per month per kilowatt (kWh) for excess electricity they export to the grid. Ready Edison charges customers a flat rate of $20 per month and credits them $0.06 per kWh for excess electricity they export to the grid. Determine the monthly bills for customers of both companies for each of the following:(A) Customer owns a 3-kW system and exports 120 kWh monthly to the grid.(B) Customer owns a 5-kW system and export 300 kWh monthly to the grid.
(A) The customer that owns a 3-kW system exports 120 kWh monthly to the grid will have the following bills for both companies:
For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be
[tex]120kWh\times\frac{\$3}{1kWh}=\$360[/tex]For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be
[tex]\$20+(120kWh\times\frac{\$0.06}{1kWh})=\$27.2[/tex](B) The customer that owns a 5-kW system exports 300 kWh monthly to the grid will have the following bills for both companies:
For ZG&E that collects $3 per kWh on a monthly basis, the monthly bill will be
[tex]300kWh\times\frac{\$3}{1kWh}=\$900[/tex]For Ready Edison that collects $0.06 per kWh exported energy monthly, the computation of bill will be
[tex]\$20+(300kWh\times\frac{\$0.06}{1kWh})=\$38[/tex]Find an equation of line L. Write your answer using fractions or integers.The equation of line L is y =
Find slope m, in equation y= mx + b
m = Y/X =( y - y')/ (x - x')
m= (5 - -5 )/ (-3 -3) = 10/-6 = -5/3
Now find b
b = y - mx
= 5 - (-5/3)•-3
. = 5 - 5 = 0
b = 0
Then answer is, equation is
y = (-5/3)x
Show exact steps to solve and show the image!Don't mind the pink writing
1)To construct the line parallel to given line passing through given point, first take a point on the line.
2)Here in the problem that point is Q.
3)Join PQ.
4)After joining PQ, copy the angle made by PQ by constructing the arc MN with steel point of compass on Q. Keep same disttance and get arc M'N' by keeping steel point on P. Then measure length MN on the angle PQR and cut arc by placing steel point on M' and cutting the arc to get point N'.
5) Join PN' and extend till point S.
6) PS is parallel to QR.
What is the factorization of496^4-9
The given expression is
[tex]496^4-9[/tex]To factorize this, we find the square root of each term.
[tex]\begin{gathered} \sqrt[]{496^4}=496^2 \\ \sqrt[]{9}=3 \end{gathered}[/tex]Then, we use the difference of perfect square which states
[tex]a^2-b^2=(a+b)(a-b)[/tex]So, we have
[tex]496^4-9=(496^2+3)(496^2-3)[/tex]In a scale drawing of a rectangularswimming pool, the scale is 2 inch: 4feet. Find the perimeter and area ofthe swimming pool.15 in.3.5 in.
The given scale is
[tex]2in\colon4ft[/tex]This means each two inches of the scale represents 4 feet of the actual size (or each inch is equivalent to two feet).
So, if the dimensions of the scale are 15 inches by 3.5 inches, then the actual dimensions would be 30 feet by 7 feet.
The perimeter would be
[tex]P=2(w+l)=2(30+7)=2(37)=74ft[/tex]The area would be
[tex]A=w\cdot l=30.7=210ft^2[/tex]Therefore, the perimeter is 74 feet, and the area is 210 square feet.Solve the missing angles by using trig function Answer Choices: A. 57.4B. 53.1
We can relate an angle x to its opposite leg and its adjacent leg, by means of the trigonometric function tangent of x, like this:
[tex]\tan (x)=\frac{\text{opposite}}{\text{adjacent}}[/tex]Then we can find the value of the angle by applying the inverse function of tangent, like this:
[tex]x=\tan ^{-1}(\frac{opposite}{adjacent})[/tex]Let's replace the values from the figure into this equation to find x, like this:
[tex]\begin{gathered} x=\tan ^{-1}(\frac{25}{16}) \\ x\approx57.4 \end{gathered}[/tex]Then, x equals 57.4°
one inlet pipe can fill an empty pool in 6 hours and a drain can empty the pool in 15 hours. how long will it take the pipe to fill the pool if the drains left open
The time that it will take the pipe to fill the pool if the drains left open is 10 hours.
How to calculate the value?From the information, one inlet pipe can fill an empty pool in 6 hours and a drain can empty the pool in 15 hours.
The information illustrated that the input pipe gills 1/6 if the pool and the drain empties 1/15 in the pool every hour
The required time taken will be:
= 1/6 - 1/15
= 5/30 - 2/30
= 3/30
= 1/10
Therefore, the time taken is 10 hours.
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A rectangular sheet of metal is 40 inches wide and 100 inches long. What is its perimeter?
Explanation
We are given the following:
[tex]Rectangle\begin{cases}width={\text{ }40inches} \\ length={\text{ }100inches}\end{cases}[/tex]We are required to determine the perimeter of the rectangular sheet.
This is achieved thus:
We know that the perimeter of a rectangle is given as:
[tex]P=2(l+w)[/tex]Therefore, we have:
[tex]\begin{gathered} P=2(100+40) \\ P=2(140) \\ P=280inches \end{gathered}[/tex]Hence, the answer is:
[tex]280inches[/tex]Which statement best describes the growth rates of the functions below?
ANSWER:
D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4
STEP-BY-STEP EXPLANATION:
We can see from the graphs that the growth is the same from 0 to 2 and then the exponential function grows faster, therefore, strictly speaking, the correct answer is D. the exponential function grows faster than the quadratic function over two intervals; 2 < x ≤ 4
which statement is true?
This is the graph of the function
The answer is (8,0)
Hi, can you help me answer this question please, thank you!
1. Test statistic:
To find the test statistic, we use the formula:
[tex]\begin{gathered} Z=\frac{\bar{X_d}-\mu_d}{\frac{s_d}{\sqrt[]{n}}} \\ \text{where,} \\ \bar{X}_d=sample\text{ difference} \\ \mu_d=\text{population difference} \\ s_d=\text{standard deviation of the differences } \\ n=\text{ number of people in the survey.} \\ \\ \text{ We use Z statistic because the number of people are more than 30} \end{gathered}[/tex]Solving for Z, we have:
[tex]\begin{gathered} \bar{X}-\mu_d=3.1\text{ (Average difference given in the question)} \\ \\ \therefore Z=\frac{3.1}{\frac{13.8}{\sqrt[]{40}}}=1.4207\approx1.421\text{ (To 3 decimal places} \end{gathered}[/tex]Thus, the test statistic is 1.421
2. P-value:
To find the p-value, we check the Z-distribution table.
The value for the p-value is
[tex]2\times0.077658=0.15532\approx0.1553\text{ (To 4 decimal places)}[/tex](We multiply by 2 because it is a two-tailed test.
3. Comparison:
The alpha level is 0.001.
Thus, the p-value is greater than the alpha level
evaluate the function found in the previous step at x= 1
Given:
[tex]y+\sqrt[]{x}=-3x+(x-6)^2[/tex]To evaluate the function at x=1, we simplify the given relation first:
[tex]\begin{gathered} y+\sqrt[]{x}=-3x+(x-6)^2 \\ Rearrange \\ y=-\sqrt[]{x}-3x+(x-6)^2 \end{gathered}[/tex]We let:
y=f(x)
[tex]f(x)=-\sqrt[]{x}-3x+(x-6)^2[/tex]We plug in x=1 into the above function:
[tex]\begin{gathered} f(x)=-\sqrt[]{x}-3x+(x-6)^2 \\ f(1)=-\sqrt[]{1}-3(1)+(1-6)^2 \\ \text{Simplify} \\ f(1)=-1-3_{}+25 \\ f(1)=21 \end{gathered}[/tex]Therefore,
[tex]f(1)=21[/tex]Bryce drew a rectangle and labeled five of the angles, as shown. He knew these factsWHOabout the angles:• The measurements of angles 1 and 3 are the same.The measurement of angle 2 equals 110°.• The measurements of angles 3 and 5 are the same.Part A Based on these facts, what is the sum of the measurements of angle 1and angle 2? Show your work or explain your answer.Part B What is the measurement of angle 4? Show your work or explain your answer.
The given figure is;
It is given that :
The measurements of angles 1 and 3 are the same.
The measurement of angle 2 equals 110°.
PART A:
Since, angle 1 , 2 and 3 are lie at the same point on the same line
Thus, from the property of angle on a line
Sum of all angles on a strainght line at a point is equal to 180 degree
thus;
Angle1 + Angle2 + Angle 3 = 180
Angle 1 + Angle 2 + Angle1 = 180 {Angle1 = Angle 3, given}
2(Angle 1) + Angle 2 = 180
2 (angle 1) + 110 = 180 {Angle 2 = 110, given}
2(Angle 1) = 180 -110
2(Angle 1) = 70
Angle 1 = 70/2
Angle 1 = 35
Since, angle 2 = 110
The sum of angle 1 and 2 is 110 + 35
Sum of angle 1 and 2 = 145
PART B:
From the properties of the rectangle;
All the angles of a rectangle are 90°
In the given rectangle;
Thus, in the triangle form by the angle3, 4 and the right angle
Sum of all angles in a triangle is equal to 180
Angle 3 + Angle 4 + 90 = 180
35 + Angle 4 + 90 = 180
Angle 4 + 125 = 180
Angle 4 = 180 - 125
Angle 4 = 55
.....
Canvas that costs 3/4 cents/in squared is used to make golf bags. Find the cost (in dollars) of 200 rectangular pieces of canvas, each 6.0 in. by 4.0 in.
The cost of 200 rectangular pieces of canvas given its dimensions is $36.
What is the cost?The first step is to determine the area of one of the rectangular pieces. A rectangle is a two-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
6 X 4 = 24 in²
The next step is to determine the area of the 200 rectangular pieces.
Area of the 200 rectangular pieces = 200 x 24in² = 4,800 in²
The last step is to determine the cost of the 200 rectangular pieces.
Total cost = total area x cost per squared inches
3 / 4 x 4800 = 3600 cents = $36
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Ex5: The half-life of a certain radioactive isotope is 1430 years. If 24 grams are present now, howmuch will be present in 500 years?
For the given situation:
[tex]\begin{gathered} A_0=24g \\ h=1430 \\ t=500 \\ \\ A=24(\frac{1}{2})^{\frac{500}{1430}} \\ \\ A=24(\frac{1}{2})^{\frac{50}{143}} \\ \\ A\approx18.83g \end{gathered}[/tex]Then, after 500 years there will be approxiomately 18.83 grams of the radioactive isotopeHow can a greatest common factor be separated from an expression
Answer: divide each term from the original expression (3x3+27x2+9x ) by the GCF (3x), then write it in the parenthesis
Step-by-step explanation:
Answer:
You take it out and place it as a multiple.
Step-by-step explanation:
5x+15
GCF = 5
5(x+3)
Hope that helps
Determine if u is a solution to 1 - 9u = 19u= -2, 7, 0, 6
-2
Replace u by -2, and check if the equality remains
1-9u = 19
1-9(-2) = 19
1-(-18)=19
1+18 = 19
19=19
-2 YES
7
1- 9(7) = 19
1-63 = 19
-62=19
NO
0
1-9(0) = 19
1= 19
NO
6
1-9(6) = 19
1-54=19
-53=19
NO
identifies the kind of symmetry the figure has below if any.
We are asked to identify the types of symmetries found in the given geometrical figure. Let's remember that asymmetry is a transformation that maps the figure onto itself. In this case the object has symmetry under reflections, also has symmetry under rotations around its center
Find the equation of the line with the given properties. Express the equation in general form or slope-intercept form.
To asnwer this questions we need to remember that two lines are perpendicular if and only if their slopes fullfil:
[tex]m_1m_2=-1[/tex]Now to find the slope of the line
[tex]-7x+y=43[/tex]we write it in slope-intercept form y=mx+b:
[tex]\begin{gathered} -7x+y=43 \\ y=7x+43 \end{gathered}[/tex]from this form we conclude that this line has slope 7.
Now we plug this value in the condition of perpendicularity and solve for the slope of the line we are looking for:
[tex]\begin{gathered} 7m=-1 \\ m=-\frac{1}{7} \end{gathered}[/tex]Once we hace the slope of the line we are looking for we plug it in the equation of a line that passes through the point (x1,y1) and has slope m:
[tex]y-y_1=m(x-x_1)[/tex]Plugging the values we know we have that:
[tex]\begin{gathered} y-(-7)=-\frac{1}{7}(x-(-7)) \\ y+7=-\frac{1}{7}(x+7) \\ y+7=-\frac{1}{7}x-1 \\ y=-\frac{1}{7}x-8 \end{gathered}[/tex]Therefore the equation of the line is:
[tex]y=-\frac{1}{7}x-8[/tex]Can you please help me
we have that
the area of parallelogram is equal to
A=b*h
we have
b=14 mm
Find the value of h
tan(60)=h/7 -----> by opposite side divided by the adjacent side
Remember that
[tex]\tan (60^o)=\sqrt[]{3}[/tex]so
h=7√3 mm
substitute
A=14(7√3 )
A=98√3 mm2use accounting principles to find the number of outcomes: How many ways can Mark create a 4-digitcode for his garage door opener?
To creat a 4 - digit code, we need to consider that for each digit we have 10 options:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -----> 10 options for each digit.
Next, we multiply the number of options we have for each digit. In this case, since we need the code to have 4 digits:
[tex]10\times10\times10\times10[/tex]We multiply 4 times 10.
And the result is:
[tex]10\times10\times10\times10=10,000[/tex]He has 10,000 ways to create a 4-digit code.
Mai made $192 for 12 hours of work at the same rate how many hours would she have to work to make $128? Please help
We were told that Mai made $192 for 12 hours of work. This means that the amount that she made per hour is
192/12 = $16
Given that her constant rate is $16 per hour,
let x = the number of hours would she have to work to make $128. Then, we have the following equations
1 = 16
x = 128
By crossmultiplying, we have
16x = 128
x = 128/16
x = 8
She has to work for 8 hours