Answers
Answer:
39 ft²
Step-by-step explanation:
11 ft × 3 ft = 33 ft²
2 ft × 3 ft = 6 ft²
33 ft² + 6 ft² = 39 ft²
Related Questions
The table shows the proportional relationship between the number of tickets required per game at a carnival.
Games 3 8 13
Tickets 9 24 39
Determine the constant of proportionality.
18
6
5
3
PLS HELP
Answers
Answer:
constant of proportionality = 3Step-by-step explanation:
You want to find the number of tickets required per game, given that the relationship is proportional and 9 tickets are required for 3 games.
ProportionThe equation of a proportional relationship can be written as ...
y = kx
where k is the constant of proportionality.
ConstantSolving for k, we have ...
k = y/x
Using a given ordered pair, we find ...
k = 9/3 = 3
The constant of proportionality is 3 (tickets per game).
__
Additional comment
Since the relationship is given as being proportional, we only need one (x, y) pair to find the constant of proportionality.
Write the equation of the piecewise function whose graph is shown
Please help will give brainlist only if correct!
Answers
Answer:
C.
Step-by-step explanation:
Also what you picked
The question is in the image. Please go through the image.
The best answer will be marked brainliest.
I hope you will explain nicely and step wise.
Answers
Step-by-step explanation:
when defined like this, we remember that when the right-angled triangular is inscribed into a circle, sine of an angle is the length of the opposite side of the angle divided by the radius. while cosine of the same angle is the adjacent side divided by the radius.
so, sin(angle) = 12/13 makes us imagine a circle of radius 13, and the side (or leg) opposite of the angle is 12.
now, Pythagoras tells us
c² = a² + b²
c being the Hypotenuse (which is the radius in our scenario), a and b are the legs.
13² = 12² + second leg²
169 = 144 + second leg²
second leg² = 25
second leg = 5
so,
cos(theta) = 5/13
tan(theta) = sin(theta) / cos(theta) =
= 12/13 / 5/13 = (12×13)/(5×13) = 12/5
sin²(theta) + cos²(theta) = (12/13)² + (5/13)² =
= 144/169 + 25/169 =
= 169/169 = 1
sec²(theta) - tan²(theta) =
= (1/cos(theta))² - (12/5)² =
= (1 / 5/13)² - 144/25 = (13/5)² - 144/25 =
= 169/25 - 144/25 = 25/25 = 1
Sebastian has $600 saved for a trip.
He buys an airline ticket for $120 and reserves a hotel room for $55 each night for 4 nights. He wants to use the same amount of spending money each day. If his trip lasts for 5 days, how much mone can he spend each day?
Answers
Answer:
$52
Step-by-step explanation:
Sebastian spent $120 on the airline ticket and $55 * 4 = $<<55*4=220>>220 on the hotel.
So, he spent a total of $120 + $220 = $<<120+220=340>>340 on the airline ticket and hotel.
He has $600 - $340 = $<<600-340=260>>260 left to spend.
He plans to be on the trip for 5 days, so he can spend $260 / 5 = $<<260/5=52>>52 per day.
Two beetles sit at the top edge of a house roof. The roof has two faces. The first face is such that the horizontal shift by 3cm along this face means 2cm shift vertically. Simultaneously, the beetles start moving downwards, the first beetle by the first face, the second - by the second face of the roof. First beetle moves twice as fast as the second beetle. Find the altitude of the first beetle above the second beetle when they will be 72 cm apart horizontally, if the second face of the roof
has the same incline as the first face or is perpendicular to the base
Answers
Answer:
16
mark me brainliest
Step-by-step explanation:
Jerry flew a total of 4,320 miles over 3 months.
• He flew 6 flights each month.
• He flew the same distance each flight.
How many miles was each of Jerry’s flights?
Answers
The number of miles was each of Jerry’s flights travel is 240 miles.
Explain distance in miles.A mile is characterized as the unit of length, which is precisely equivalent to 5280 feet, or 1760 yards, and normalized as precisely 1609.344 meters by the Peaceful accord in 1959. The biggest unit is generally used to quantify the distance between places that are not even close to one another.
According to question:Jerry flew 6 flights each month.
Total flights in 3 months = 3(6) = 18 flights
Let distance traveled in each flight be x
Then,
18x = 4320 miles
x = 4320/18
x = 240 miles
Thus, each flight flow 240 miles.
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Could someone help me with this trig question?
Answers
k= 5.
Step-by-step explanation:1. Write the expression.[tex]ksin^{2} (x)+kcos^{2} (x)=5[/tex]
2. Factorize k.[tex]k(sin^{2} (x)+cos^{2} (x))=5[/tex]
3. Simplify using pythagorean identities.Check attached image 1.
[tex]k(1)=5\\ \\k=5[/tex]
4. Verify.Let's graph the function to see if it's true that it equals 5 for any value of x and k=5.
Check attached image 2.
As we can see in the graph, for any value of x the function returns 5. Hence, the answer is correct.
how many shapes are drawn based on the code below? def drawshapes(centerx, centery, radius, points, color): star(centerx, centery, radius, points, fill
Answers
6 shapes can be drawn by the given code.
Describe shapes.Shapes in mathematics specify an object's boundaries or contour. Depending on their characteristics, the forms can be divided into many types. The shapes are typically enclosed by an outline or boundary that is composed of points, lines, curves, etc. Geometric figures and figures composed of fixed lines or curves are other names for forms. There are two types of shapes: closed shapes and open shapes. Examples of shapes in daily life are the Sun, Earth, Doors, Windows, Watches, Wall Clocks, and so forth.
Given
Codes are def draw shapes( centerx , centery, radius, points, color): star(centerx, centery, radius, points, fill.
6 shapes can be drawn by the given code.
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During a mathematics test, 18 students answered question 1 correctly, 23 students answered question 2 correctly, 8 students got them both correct and 11 students answered incorrectly on both questions. How many students took the test?(A) 41 (B) 44 (C) 49 (D) 52 (E) 60
Answers
Answer:
(D) 52
Step-by-step explanation:
sum up correct answers from questions 1, 2 and both 1 and 2 incorrect this time therefore we have --> 18+23+11=52 students
You could also do a Venn diagram to understand this better with 8 being the intersection of students who goth both 1 and 2 correct and 11 being left out as the number of students who got both questions incorrectly.
Russell is going to hire a makeup artist for a fashion show and is comparing prices. Martha charges $10 as a booking fee and an additional $40 per hour. Jackie charges $35 per hour, plus a booking fee of $20. Depending on the length of the show, the cost could end up being the same for either artist. Write the system of equations for this scenario and define the variables.
Answers
After solving the equation, the number of hours obtained is that after 2 hours, the cost ends up being the same for either artist.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Booking fee of Martha = $10
Additional hourly charge of Martha = $40
Then, the equation will be,
y = $10 + $40x (i)
Here, y is the total cost and x is the number of hours.
Booking fee of Jackie = $20
Additional hourly charge of Jackie = $35
Then, the equation for this will be,
y = $20 + $35x (ii)
Here, y is the total cost and x is the number of hours.
Then, depending on the length of the show, the cost could end up being the same for either artist.
So,
From equations (i) and (ii)
$20 + $35x = $10 + $40x
20 - 10 = 40x - 35x
5x = 10
x = 2 hours
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Is there a transformation that maps shape I onto shape IV? Explain your answer.
Answers
Yes, there is a transformation that maps shape I onto shape IV. If the figure I is reflected over the x-axis, we get figure IV.
What is a transformation in math?In mathematics, a transformation is a function or a mapping that takes a set of inputs and produces a new set of outputs.
Transformations can be applied to geometric shapes, functions, and other mathematical objects to change their properties or positions.
There are various types of transformations that can be performed in mathematics, including translation, rotation, reflection, dilation, and more. Each type of transformation has its own specific rules and properties that dictate how it affects the original object.
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Full Question:
See the attached Image
The table shows the transportation method of employees at a certain company. What percent of the employees walk to work?
A. 0.5 %
B. 1 %
C. 5 %
D. 7 %
Answers
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100. 0.5% of employees walk to work.
What percent of the employees walk to work?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.
Given,Employees who use;
Car: 758
Bus: 530
Walk: 7
Other: 105
Total = 758+530+7+105 = 1400
Employees percentage who walk to work
=No of employees who walk /Total number*100
Percentage =700/1400 =0.5%
0.5% of employees walk to work.
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A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the standard deviation of the sampling distribution of p hat ? Enter your answer as a decimal rounded to the hundredths place. The standard deviation of the sampling distribution of p hat is
Answers
The shape of the sampling distribution of p hat is approximately Normal, because we would expect at least 10 success and 10 failures
What is meant by sampling distribution ?The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.
approximately Normal, because we would expect at least 10 success and 10 failures. because they are dividing three times a week
A typical probability distribution in the natural world is the normal distribution, sometimes known as the bell curve. When the sample size is high enough, scientists often assume that a sequence of measurements obtained from a population would be regularly distributed.
The complete question is : A large university with over 40,000 students recently took a survey in which 31% of the students claimed to exercise at least 3 times a week. A simple random sample of 250 students was selected. Let p hat = the proportion of students in the sample who claimed to work out at least 3 times a week. What is the shape of the sampling distribution of p hat and why?
A. approximately Normal, because all sampling distributions are approximately Normal
B. approximately Normal, because we would expect at least 10 success and 10 failures
C. skewed to the right, because 0.31 is lower than 0.5
D. skewed to the left, because 0.31 is lower than 0.5
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What is equivalent to 1:9
Answers
Answer:
2 : 18
Step-by-step explanation:
to find equivalent ratios , multiply or divide each part of the ratio by the same numeric value.
1 : 9 ( multiply both parts by 2 )
= 2 : 18
or
1 : 9 ( multiply both parts by 3 )
= 3 : 27
and so on...
Circles P and Q are externally tangent to each other and have radii 18 meters
and 32 meters, respectively. As shown, circles P and Q are externally tangent
to a line segment at points X and Y, respectively. What is XY?
Answers
Answer:
48 m
Step-by-step explanation:
You want to know the distance XY between tangent points on a segment tangent to two circles that are externally tangent to each other. The circles have radii 18 m and 32 m.
Pythagorean theoremAs shown in the attachment, a segment parallel to XY joining segments PX and QY can form a right triangle whose hypotenuse is the sum of the radii, and whose short leg is the difference of the two radii. The length of XY is the unknown leg of the right triangle, and can be found using the Pythagorean theorem.
a² +b² = c²
14² +b² = 50²
b² = 50² -14² = 2304
b = √2304 = 48
The length of XY is 48 meters.
__
Additional comment
In this geometry, the length XY is twice the geometric mean of the two radii. XY = 2√(18·32) = 48.
Given the function f(x) = −5x2 + 2x + 9, find f(1) and f(2). Choose the statement that is true concerning these two values
Answers
We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.
What do you mean by Polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. A function that can be expressed as a polynomial is referred to as a polynomial function. A polynomial equation's definition can be used to derive the definition. A polynomial is typically denoted by P. (x). The degree of the variable in P(x) is its maximum power. The degree of a polynomial function is crucial because it reveals how the function P(x) will behave when x is very large. Whole real numbers make up a polynomial function's domain (R).
CalculationGiven f(x)=-5x2 + 2x + 9
f(1)=-5(1)2+2(1)+9
∴f(1)=6
f(2)=-5(2)2+2(2)+9
∴f(2)=-7
We can solve the question using the concept Polynomial functions. The value of f(1) is 6 and f(2) is -7.
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Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Answers
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
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People at an airport can pass through security on one of two levels: level A or level B. Suppose that, on average, it takes people
22
2222 minutes to pass through security on level A with a standard deviation of
7
77 minutes. On level B, the mean and standard deviation are
20
2020 and
6
66 minutes, respectively.
Every day, the airport looks at an SRS of
100
100100 people who use level A, and an independent SRS of
150
150150 people who use level B. They calculate the mean time for each sample, then look at the difference
(
A
−
B
)
(A−B)left parenthesis, start text, A, end text, minus, start text, B, end text, right parenthesis between the sample means.
What are the mean and standard deviation (in minutes) of the sampling distribution of the difference in sample means?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
250
7
2
+6
2
(Choice B)
B
μ
x
ˉ
A
−
x
ˉ
B
=
2
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=2
=
100
7
2
+
150
6
2
(Choice C)
C
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
+
6
2
250
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
250
7
2
+6
2
(Choice D)
D
μ
x
ˉ
A
−
x
ˉ
B
=
21
σ
x
ˉ
A
−
x
ˉ
B
=
7
2
100
+
6
2
150
μ
x
ˉ
A
−
x
ˉ
B
σ
x
ˉ
A
−
x
ˉ
B
=21
=
100
7
2
+
150
6
2
Answers
The mean and standard deviation (in ) of the sampling distribution of the difference in sample means [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex] = (7)² ÷100+ 6² /150.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
Level A:
S.D. = 7
Level B: Mean = 20
S.D. = 6
So, [tex]\nu_1[/tex] = 22
[tex]\nu_2[/tex] = 20
Then, [tex]\nu_1[/tex] - [tex]\nu_2[/tex] = 22-20=2
and, [tex]\sigma_1[/tex] - [tex]\sigma_2[/tex]
= (7)² ÷100+ 6² /150
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NO LINKS!!
Find the binomial coefficient
( 11)
(6)
Evaluate using Pascal's Triangle
4_C_1
Answers
Answer:
462; 4------------------------------
The binomial coefficients can be found using Pascal's triangle.
Remember the rows are numbered starting from the second one on the top, and the first element is skipped in every row.
For the first one, follow the 11th row and 6th column, it is number 462, and for the second one follow the 4th row and 1st column, this is number 4, see the attached for both.
Calculation of the binomial coefficient is as follows:
[tex]\[ \binom{11}{6} = _{11}C_6=\cfrac{11!}{6!(11-6)!}=\cfrac{6!*11*10*9*8*7}{6!5!} =\cfrac{11*10*9*8*7}{5*4*3*2} =462[/tex][tex]\[ \binom{4}{1} = _4C_1=\cfrac{4!}{1!(4-1)!} =\cfrac{4!}{3!} =\cfrac{3!*4}{3!} =4[/tex]What fraction is equal to 75% of 1/2
Answers
Answer:
3/8
Step-by-step explanation:
75% of 1/2
3/4 of 1/2
3/4x1/2
3/8
3/4•1/2
3/8
2. In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers, 25 have both pensils and pens, 30 have both pencils and rulers while 47 have both pens and rulers, each pupil has at least one of the items. a). write the set notation. b) Draw a Venn diagram to illustrate this information c).How many pupils have pencils only
Answers
a) The set notation is shown below.
b) 27 pupil have pencils only.
What is Venn Diagram?A Venn diagram depicts the logical relationships between two or more sets of items by using overlapping circles or other shapes. They frequently serve to graphically organise things, demonstrating how similar and dissimilar the pieces are.
Given:
In a school of 160 pupils, 75 have pencils, 87 have pens and 93 have rulers.
25 have both pencils and pens,
30 have both pencils and rulers while 47 have both pens and rulers.
a) The set notation is
n(p)= 75
n(Pens)= 87
n(R)= 93.
n (p∩ pens) = 25
n (p∩ R) = 30
n (pens ∩ R) = 47
n (p∩ R ∩ pens) = x
c) Number of Pupil that have only pencils
= 75- [(30-7) + 25-7 +7]
=75-(23+18+7)
= 75-48
=27
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The data below are the temperatures on randomly chosen days during a summer class and the number of absences on those days: Temperature, x | 72 85 91 90 88 98 75 100 80 No. of absences, y | 3 7 10 10 8 15 4 15 5 a) Find the equation of the regression line for the data. b) Assuming that the variables x and y have a significant correlation, what is the predicted number of absences when the temperature is 91? c) Calculate the correlation coefficient. d) Calculate the standard error for the model.
Answers
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
See table for sum of values.
The regression equation is:
y=α+βx
β = [tex]\frac{Sxx}{Syy}[/tex]=6995-97799779[tex]\frac{6995-9\times\frac{779}{9}\times\frac{77}{9}}{68613-9(\frac{779}{9} )2}[/tex]= 0.449
α=y-βx= 779-(0.449)7799 = =-30.27
The equation is y=-30.27+0.449x
Where y = predicted variable; x = independent variable = 0.449; - 30.27 = intercept/ slope
Constructing a 91% prediction interval for y:
x = 910
Inputting x = 91 into the regression equation : y = 0.449(91) - 30.27
y = 40.859 - 30.27 = 10.589
Prediction interval = y pm error margin
To save computing time, error margin (E) can be obtained using the online error margin calculator.
Obtained error margin (E) value = 2.3398
(10.589- 2.3398, 10.589+ 2.3398)
(8.2492, 12.9288)
(8, 13)
The equation of the regression line is y=-30.27+0.449x and predicted number of absences when the temperature is 910= 10.589
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The edge of a cube has length 10 inches with a possible error of 1%. The possible error, in cubic inches, in the volume of the cube is: a) 3 b) 1 c) 10 d) 30 e) all of these
Answers
Answer:
d) 30
Step-by-step explanation:
1% of 10 inch is 0.1 inch
10 inch + 0.1 inch = 10.1 inch
10 inch - 0.1 inch = 9.9 inch
V = s³
For s = 9.9 in., V = (9.9 in.)³ = 970.299 in.³
For s = 10.1 in., V = (10.1 in.)³ = 1030.301 in.³
For 10 in., V = (10 in.)³ = 1000 in.³
|1000 in.³ - 970.299 in.³| = 29.701 in.³
|1000 in.³ - 1030.301 in.³| = 30.301 in.³
The error is 30 in.³.
The diagram below shows a cylinder with diameter 6 cm and height 20 cm. The
Volume, in cm³, of the cylinder is
-6 cm
20 cm
Answers
The volume of the cylinder is 180π cm³.
What is volume ?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
Volume is a measurement of three-dimensional space that is occupied. Numerous imperial or US customary units, as well as SI-derived units (such the cubic meter and liter), are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship.
As diameter = 6cm
We know that radius is half of diameter
∴ radius = 3 cm
height = 20 cm
Volume = π r² h
= π (3)²×20
= π × 9 × 20
= 180 π cm³
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HELP ASAP!! READ CAREFULLY
Answers
Answer:
not true:
3. AD = DC
4. YZ = XW
explanation:
lower base is only congruent to upper base.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-when the admission price for a conference is $400, 1000 people will attend. for each $5 reduction in price, an additional 20 peopel will attend. let x be the number of 5 dollar reductions. determine the number of people that will attend as a function of x.
Answers
Let y be the number of people that will attend the conference as a function of x. The given information tells us that when x = 0 (the admission price is $400), y = 1000. Additionally, for each $5 reduction in price, an additional 20 people will attend.
We can express this relationship as a function as follows:
y = 1000 + 20xThis function tells us that the number of people that will attend the conference is equal to 1000, plus an additional 20 people for each $5 reduction in price (represented by the variable x).
For example, if the admission price is reduced by $10 (x = 2), the number of people that will attend the conference is given by:
y = 1000 + 20(2)
y = 1000 + 40
y = 1040
So, if the admission price is reduced by $10, 1040 people will attend the conference.
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When 2x^2/y=w+2/4 is solved for w, one equation is w =8x^2/7 -2 Which of the following is an equivalent equation to find w?
w = StartFraction 8 x squared + 2 y Over y EndFraction
w = StartFraction 8 x squared minus 2 y Over y EndFraction
w = 8 x squared minus 3 y
w = 8 x squared minus y
Answers
Step-by-step explanation:
To solve an equation for a variable, you can isolate the variable by performing operations that eliminate all other terms.
In this case, the given equation is 2x^2/y = w + 2/4. To solve for w, you can first eliminate the 2/4 term on the right-hand side by multiplying both sides of the equation by 4/2:
4 * (2x^2/y) = 4 * (w + 2/4)
4 * 2x^2/y = 4w + 4 * 2/4
8x^2/y = 4w + 2
Then, you can subtract 2 from both sides to eliminate the 2 on the right-hand side:
8x^2/y - 2 = 4w + 2 - 2
8x^2/y - 2 = 4w
Finally, you can divide both sides of the equation by 4 to eliminate the 4 on the right-hand side:
(8x^2/y - 2) / 4 = (4w) / 4
w = 8x^2/7 - 2
Therefore, the correct answer is w = 8 x squared minus 2 y Over y. This is an equivalent equation to find w, as it gives the same value for w as the original equation when the same values are used for x and y.
The other equations given are not equivalent to the original equation for finding w.
Jessica earns 35 for 7 hours of babysitting she is saving to buy a 160 radio how many hours will Jessica have to buysit to have enough money to buy the radio
Answers
To have enough money to buy the radio, Jessica will have to babysit for 32 hours
How to determine the number of hours Jessica will have to babysit?From the question, we have the following parameters that can be used in our computation:
Earnings = $35 for 7 hours
This means that the hourly rate can be calculated as
Hourly rate = $35/7 hours
Using the above as a guide, we have the following:
Evaluate the quotients
Hourly rate = $5 per hour
The number of hours Jessica will have to babysit is calculated as
Number of hours = 160/Hourly rate
Substitute the known values in the above equation, so, we have the following representation
Number of hours = 160/5
Evaluate
Number of hours = 32
Hence, the number of hours is 32
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A drama club earns $1040 from a production. It sells a total of 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket.
a. Write a system of linear equations that represents this situation. Let x represent the cost of an adult ticket and y represent the cost of a student ticket.
System of equations: x=
x+
y=1040
Question 2
b. What is the cost of each ticket?
The cost of an adult ticket is $
.
The cost of a student ticket is $
.
Answers
The system of linear equations, that models the problem is represented as x = 2 and 64x + 132y = 1040 while the cost of adult and student tickets is $8 and $4 respectively.
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
Let;
x = cost of adult tickety = cost of student ticketa)
x = 2y ...eq(i)
64x + 132y = 1040 ...eq(ii)
b)
From equation (i)
64(2y) + 132y = 1040
y = 4
Put y = 4 into equation (i)
x = 2(4)
x = 8
The cost of adult ticket is $8 and student ticket is $4
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Use the properties of exponents to determine which functions (if any) are the same.
f(x)= 3^x + 11
g(x) = 2^(3x+5)
h(x)= 32(8^x)
a. f(x) = g(x)
b. f(x) = h(x)
c. g(x)=h(x)
d. All three functions are equal
e. None of the functions are equal
Answers
Answer:
c. g(x) = h(x)
Step-by-step explanation:
Given functions:
[tex]f(x) = 3^x+11[/tex]
[tex]g(x)=2^{3x+5}[/tex]
[tex]h(x)=32(8^x)[/tex]
Rewrite function g(x) using exponent rules.
[tex]\textsf{Apply exponent rule} \quad a^{b+c}=a^b \cdot a^c:[/tex]
[tex]\implies g(x)=2^{3x} \cdot 2^5[/tex]
[tex]\implies g(x)=2^{3x} \cdot 32[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies g(x)=(2^3)^{x} \cdot 32[/tex]
[tex]\implies g(x)=8^{x} \cdot 32[/tex]
[tex]\implies g(x)=32(8^{x})[/tex]
Therefore, g(x) = h(x).