Answer:
x = 3.5 hours
y = 1.5 hours
Step-by-step explanation:
There are two unknowns, x and y, both in umits of hours. We need at least two equations before we start trying to solve this with substitution. Looking at the information, this should be possible.
First, we know that Speed x Time = Distance.
The distance covered by the cyclyst would be the sum of (12km/h)*x and (16km/h)*y, where x is the time, in hours, for the slower speed and y for the faster. Together, the student travels 66 km.
The total distance of 66 km would be comprised of the two distances 12x and 16y:
12x + 16y = 66 km
For the second equation, we know that the total time is 5 hours. That would be the sum of x and y:
x + y = 5 hours
We now have 2 equations, so we stand a good chance of finding the answer. Pick one of the equations and isolate one of the variables to one side. Let's choose x + y = 5 hours, since that is easy to rearrange:
x = 5-y
Now take the first equation and substitute the definition of x from above (5-y):
12x + 16y = 66
12(5-y) + 16y = 66
60-12y + 16y = 66
4y = 66-60
4y = 6
y = (6/4) or 1.5 h
The time spent at 16 km/h was 1.5 hours.
Use this value of y in either equation to find x. Let's use x+y=5, since that will be easier:
x+y = 5 for y = 1.5
x+1.5 = 5
x = 3.5h
The time spent at 12 km/h was 3.5 hours
How many complete centerpieces can she make? Find the exact answer.
The number of centerpieces that she can make, using proportions, is of:
25.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem, and basic arithmetic operations, especially multiplication or division, to find the desired amounts in the same context of this problem.
In the context of this problem, the number of centerpieces is given by the division of the the total number of flowers by the number of flowers in each centerpiece.
The amounts are given as follows:
Flowers: 430.Flowers per centerpiece: 17.Hence the division giving the number of flowers per centerpiece is:
n = 430/17 = 25.2.
The amount is rounded down to 25, as for 26 centerpieces, more flowers would be needed.
Missing InformationHailey is making floral centerpieces for a wedding. Each centerpiece has 17 flowers. She has 430 flowers for the project.
How many complete centerpieces can she make? Find the exact answer.
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fill in the blank 96 inches = blank feet
Answer:
8 feet
Step-by-step explanation:
there's 12 inches in 1 foot so 12 x 8 = 96
Amy’s restaurant has budgeted at most $60 to spend this month on gourmet coffee. All international blends cost
$8.50 per package and all house blends cost $6.00 per package. She would like to purchase some international
blends and at least 3 packages of the house blends. Write a system of linear inequalities that describes this
situation. Graph the system. Give a possible solution and describe what it means
Answer:
8.50x + 6.00y < 60 and y > 3.
Please consider the complete question.
Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee. All international blends cost $8.50 per package and all house blends cost $6.00 per package. She would like to purchase some global combinations and at least 3 boxes of the house blends. Write a system of linear inequalities that describes this situation.
Let x represent the number of international blends and y represent the number of house blends.
The cost of x international blends would be and the cost of y house blends would be.
Since Amy's restaurant has a budget of at most $60 to spend this month on gourmet coffee, so the cost of x international blends and y house blends should be less than or equal to 60.
We can represent this information in an inequality as:
Since Amelia wants to purchase at least 3 packages of the house blends, so y should be greater than or equal to 3. We can represent this information in an inequality as:
Therefore, our required system of inequalities would be 8.50x + 6.00y < 60 and y > 3.
Step-by-step explanation:
TWO trains leave the station at the same time, one heading west and the other east. The westbound train travels at 85 miles per hour. The eastbound train
travels at 95 miles per hour. How long will It take for the two trains to be 396 miles apart?
Do not do any rounding.
Solve the equation by completing the square. x2 + 6x = 9
4. If the landing angle at an airport is 4° and you are two miles out and ½ mile high, are you safe to land?
Yes, you are safe to land, If the landing angle at an airport is 4° and you are two miles out and ½ mile high.
Define the final approach.The final approach, also known as the final leg or final approach leg, is the last leg of an aircraft's approach to landing in aviation. During this leg, the aircraft is aligned with the runway and descending for a landing. In aircraft radio lingo, it is frequently abbreviated to "final".
Given,
If the landing angle at an airport is 4° and you are two miles out and ½ mile high,
Yes, you are safe to land.
A normal airport landing pattern calls for aircraft to turn from the base leg to the final within 0.5 to 2 miles of the airport when visual meteorological conditions (VMC) are present. A "straight-in" final approach, when all other legs are skipped, is frequently employed for instrument approaches as well as VFR approaches onto controlled airfields. At American non-towered airports, straight-in approaches are discouraged.
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Lucia makes braided key chains out of cotton cord. For every 8 feet of cotton cord she has, she can make 3 braided key chains. Use a model to represent the relationship between the feet of cotton cord and the number of key chains.
(NEED HELP ASAP PLEASE)
A model for representing the relationship between the number of key chains and the number of feet of cotton cord is: 8x - 3y = 0.
Define the term linear equation?Linear equations are first-order equations. Lines with in coordinate system are determined by linear equations. When the equation contains a degree 1 homogeneous variableSince Lucia creates braided key chains from out cotton cord and can create 3 braided key chains per each 8 feet of cotton cord she does have, the following equations must be performed via cross multiplication to symbolize the relationship between both the feet of cotton cord as well as the number of key chains but also obtain the number of cotton cord Lucia requires to achieve 5 key chains:
8 cotton cords = 3 key chains
Let the total length in feet of cotton cords be x.
And the total number of key chain made be y.
Then, the linear equation formed as;
8x = 3 y
8x - 3y = 0
Thus, a model for representing the relationship between the number of key chains and the number of feet of cotton cord is: 8x - 3y = 0.
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What is the value of log10 1000000000
Answer:
9 i think
Step-by-step explanation:
work out the circumferecnce of this cricle take π to be 3.142 and write down all the digits given by your calculator 16.8cm
The circumference of the circle with a radius of 16.8 cm is 105.504 cm
How to calculate the circumference?The given parameters are
Radius = 16.8 cm
As a general rule, radius are represented by the variable r
So, we have the following representation equation
r = 16.8 cm
The circumference of the circle is then calculated as
C = 2πr
Next, we substitute the value of the variable r in the above equation
i.e. r = 16.8 cm
So, we have the following equation
C = 2π * 16.8 cm
From the question, we have
π = 3.14
So, we have the following equation
C = 2 * 3.14 *16.8 cm
Evaluate the products
So, we have the following equation
C = 6.28 *16.8 cm
Evaluate the products
C = 105.504 cm
Hence, the circumference is 105.504 cm
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Find the geometric mean between ab³ and a³b?
[tex]{ \green{ \sf{G = \sqrt{ ab}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ (ab³)(a³b)}}}}[/tex]
[tex]{ \green{ \sf{G = \sqrt{ a⁴b⁴}}}}[/tex]
[tex]{ \red{ \boxed{ \pink{ \sf{G = \sqrt{ a².b²}}}}}}[/tex]
the mean cost of domestic airfares in the united states rose to an all-time high of $385 per ticket. airfares were based on the total ticket value, which consisted of the price charged by the airline plus any additional taxes and fees. assume domestic airfares are normally distributed with a standard deviation of $110. answer to four decimals. what is the probability domestic airfare is $250 or less.
The probability 11.1% of domestic airfares within the United States are $250 or less.
Define the term standard deviation?A square root of variance is used to calculate the standard deviation, a statistic that illustrates how distributed widely a dataset is in relation to its mean. By evaluating the deviation of each data point from the mean, the standard deviation may be approximated as the square root of variance.The formula for the z score is -
z = (x - μ)/σ
In which,
μ = mean = $385 per ticketσ = standard deviation = $110x = sample value = $250 or less.Substitute the value in formula.
P(x ≤ 250) = (250 - 385)/100
P(x ≤ 250) = -1.22
Select the p value from negative z score table;
P(x ≤ 250) = 0.111
P(x ≤ 250) = 11.1%
Thus, 11.1% of domestic flights within the United States are $250 or less.
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if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?
The number of points that are expected to lie inside the circle is 785.
A circle is a closed two-dimensional figure. In a circle, all points are equidistant from the centre.
As per the given question, the circle is inscribed in a square,
The radius of the circle ( r ) = 1 The side length of the square ( s ) = 2⇒ The area of the circle = π × r × r
= π × 1 × 1
∴ The area of the circle = π
⇒ The area of the square = s × s
= 2 × 2
∴The area of the square = 4
The probability that a randomly selected point inside the square will lie inside the circle,
p = π / 4
The probability that a randomly selected point inside the square will lie outside the circle,
q = 1 - p
q = 1 - ( π / 4 )
⇒ Binomial trial with n = 1000 and p = π / 4,
Number of points expected to lie inside the circle(N) = n × p
= 1000 × ( π / 4 )
= 1000 × ( 3.14 / 4 )
= 1000 × ( 0.785 )
N = 785
Therefore, 785 expected points lie inside the circle.
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The complete question is
Answer: 56 square
Step-by-step explanation:
At a carnival game, it cost Noah $12 to toss 30 rings. Fill out a table of equivalent ratios and plot the points on the coordinate axes provided.
The equivalent ratios table is:
Toss Dollars
5 2
30 12
45 18
See the diagram in the attachment that shows the plotted points.
What are Equivalent Ratios?Equivalent ratios are ratios that have the same value when they are compared together.
For example, 4/6 = 2/3, therefore, the equivalent ratios are 2:3 and 4:6.
Create an equation that models equivalent ratios that can be used to complete the table if:
x = toss
y = dollars
Therefore, given that 30 toss equals $12,
Constant of proportionality, k = y/x = 12/30
k = 2/5.
Plug in the value of k into y = kx:
y = 2/5x.
Therefore:
2 dollars (y = 2), will give:
2 = 2/5(x)
x = 10/2
x = 5 toss
45 tosses (x = 45) will need:
y = 2/5(45)
y = 18 dollars
The equivalent ratios table would be:
Toss | Dollars
5 2
30 12
45 18
The graph below shows the points, (5, 2), (30, 12), and (45, 18), where y = dollars, and x = toss.
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Express your answer as a polynomial in standard form.
f(x)=
f(x)=
\,\,-3x+5
−3x+5
g(x)=
g(x)=
\,\,x^2+2x+15
x
2
+2x+15
\text{Find: }(g\circ f)(x)
Find: (g∘f)(x)
The function (g∘f)(x) expressed as a polynomial in standard form is 9x² - 36x + 40
What is a function?A function can be defined as an equation, a rule or a law that shows or rather explain the relationship between two variables in an equation.
The variables are known as;
The independent variableThe dependent variableWe have the function given;
fx) = - 3x + 5g(x) = x² + 2x + 15To determine the composite function (g ∘f)(x), we have to substitute the value of x as fx) in the function g(x), we have;
(g∘f)(x) = (- 3x + 5)² + 2( -3x + 5) + 5
expand the bracket
(g∘f)(x) = 9x² - 15x - 15x + 25 - 6x + 10 + 5
Now, collect like terms, we get;
(g∘f)(x) = 9x² - 15x - 15x - 6x + 25 + 10 + 5
Add or subtract the like terms, we get;
(g∘f)(x) = 9x² - 36x + 40
The polynomial is written as; 9x² - 36x + 40
Hence, the value is 9x² - 36x + 40
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the graph of y=f(x) is shown below. find the value of f(5)
Answer:
f(5) = -5
Step-by-step explanation:
To find the value of f(5), find the value of y when x = 5.
To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line.
Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.
Therefore, the value of f(5) is -5.
See attachment.
Answer:
f(5) = - 5
Step-by-step explanation:
Given the graph of the function f(x).
In order to find the value of f for any value of x on the graph, find the point x on the x-axis, then add a vertical line from this point to the graph. The y-coordinate of the intersection is the value of the function at given x-coordinate.
We are asked to find the value of f(5).
This is f(5) = - 5 as per above explanation.
See the attached for better understanding.
how many cards must be selected from the standard 52 deck to guarantee that at least 3 cards of the same suit are chosen
Nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
What is the pigeon-hole approach?
According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m. For instance, if one possesses three gloves but none of them are ambidextrous or reversible, then there must be at least two right-handed gloves or at least two left-handed gloves since there are three items but only two categories of handedness. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.
The standard 52 deck has 4 suits of 13 cards each, thus as per n pigeons need to be extracted from p = 4 pigeon-holes; as per established literature above.
∴ [(n - 1) / p] + 1 = 3 ⇒ [(n - 1) / 4] + 1 = 3 ⇒ n - 1 = 8 ⇒ n = 8 + 1 ⇒ n = 9
Therefore, nine (9) cards must be selected from the standard 52 deck to guarantee that at least three cards are chosen from the same suit.
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The function g(x) is continuous on the closed interval [8, 10] and differentiable on the open interval
(8, 10). The value x = 8.5 satisfies the conditions of the Mean Value Theorem on the interval [8, 10].
What is g(10) given g'(8.5) = -9 and g(8) = 6?
Answer:
g(10) = -12
Step-by-step explanation:
Mean Value Theorem
If f is continuous on [a, b] and differentiable on (a, b), then there is a number c such that a < c < b and:
[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]
We are told that the function g(x) is continuous on the closed interval [8, 10] and differentiable on the open interval (8, 10).
Therefore:
a = 8b = 10Given:
g'(8.5) = -9g(8) = 6As 8 < 8.5 < 10 then c = 8.5:
[tex]\begin{aligned} \implies g'(8.5)=\dfrac{g(10)-g(8)}{10-8}&=-9\\\\\dfrac{g(10)-6}{2}&=-9\\\\g(10)-6&=-18\\\\g(10)&=-12\end{aligned}[/tex]
Four congruent parallelograms are joined to make the shape below.
24 cm
The total shaded area is 192 cm²
Work out the value of x.
x cm
5 cm
For the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
As given in the question,
Given four congruent parallelograms
Shaded area of the parallelogram is 192cm²
As four parallelograms are congruent
Let the area of each parallelogram is A
4A = 192
⇒A = 48cm²
For two parallelogram base length = 24cm
Base length of each parallelogram = 12cm
Area of parallelogram = base × height
48 = 12 × height
⇒ height = 4cm
Value of x = 2 times of height
= 2 (4)
= 8cm
Therefore, for the given four congruent parallelograms and the shaded area of 192cm² then value of x is equal to 8cm.
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divide 50x4-50x3+12x2+10x-2 by 5x-3
Dividing 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 with the long division method will result to a quotient of 10x³ - 4x² + 2 and a remainder of 1.
Long division methodThe method of long division involves the following steps:
Divide.Multiply.Subtract.Bring down the next number and Repeat the process to end at zero or arrive at a remainder.We sall divide the 50x⁴ - 50x³ + 12x² + 10x - 2 by 5x - 3 by applying the long division method as follows;
50x⁴ divided by 5x equals 10x³
5x - 3 multiplied by 10x³ equals 50x⁴ - 30x³
subtract 50x⁴ - 30x³ from 50x⁴ - 50x³ + 12x² + 10x - 2 will result to -20x³ + 12x² + 10x - 2.
This process is repeated until we have a remainder of 1.
Therefore, by the long division method, we have quotient of 10x³ - 4x² + 2 and a remainder of 1.
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1/4(8x+12)=-15 ''solve''
After solving the value of x in the equation is x [tex]=[/tex] -9 .
In the question ,
it is given that ,
the equation is 1/4(8x+12) = -15
Applying the associative property of multiplication ,
we get ,
8x/4 + 12/4 = -15
cancelling out the common factor 2 from numerator and denominator ,
we get ,
2x + 3 = -15
Subtracting the number 3 from both sides of the equation ,
we get ,
2x = -15 - 3
2x = -18
Dividing both sides of the equation above by the number 2 ,
we get ,
x = -18/2
x = -9
Therefore , After solving the value of x in the equation is x [tex]=[/tex] -9 .
The given question is incomplete , the complete question is
Solve the given equation for x ?
1/4(8x+12)= -15
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Vertex of f(x) = |2x + 3
The vertex of the equation given as .f(x) = |2x + 3| is (-3, 0)
What is the vertex?The vertex of a function or an equation is the minimum or the maximum point on the function
How to determine the vertex of the graph?From the question, we have the equation of the function to be
f(x) = |2x + 3|
The above function is an absolute value function
An absolute value function is represented as
f(x) = a|x - h| + k
Where the vertex is represented as
Vertex = (h, k)
By definition, a graph that has a vertex would have an obvious maximum or minimum point on it
By comparing the equations f(x) = a|x - h| + k and f(x) = |2x + 3| to determine the vertex, we have
(h, k) = (-3, 0)
This means that
Vertex = (-3, 0)
Hence, the vertex of the equation is (-3, 0)
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which of the following is a linear equation
The option that is a a linear equation is B. 4x - 2 = 20.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign
This is illustrated as 4x - 2 = 20
4x = 20 + 2
4x = 22
x = 22/4 = 5.5
This illustrates an equation.
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After 3 new kids came to the park, a total of 18 kids played at the park. Write an equation that could be used to find x, the number of kids at the park before the 3 new kids came.
Please help, please
Answer:
x + 3 = 18
Step-by-step explanation:
original number of kids: x
additional kids: 3
new total number of kids: x + 3
actual total number of kids: 18
Equation: x + 3 = 18
one year, the scores on the test were approximately normally distributed with a mean of 420 and a standard deviation of 70. the 81st percentile for this test was . . .
81 percentile of the given test is 482
The square root of the means of the squared deviations from the arithmetic mean is known as the standard deviation. Standard deviation is used in finance to quantify the risks associated with an investment instrument.
Given that the Marble Academy of Whoville conducts an annual test for all high school juniors one year, the scores on the test were approximately normally distributed with a mean of 420 and a standard deviation of 70
Here mean μ = 420 and Standard deviation σ = 70
We have find 81 percentile of this test = ?
The z score corresponding to the area 0.81 is
Z = 0.88 By standard normal table
X = μ + z σ
X = 420 + 0.88 x 70
= 420 + 62
= 482
Therefore 81 percentile of this test is 482
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a person has a 5% chance of winning a free ticket in a state lottery. she plays the game 12 times. what is the probability she will win two or more tickets? round your answers to three decimal places.
The probability to win two or more tickets in the lottery is 0.118
It is given that there is a 5% chance to win a lottery ticket.
Therefore, the probability to win a lottery ticket is
0.05
The girl here plays the game 12 times. The above distribution is clearly a Binomial Distribution
ⁿCₓ X pˣ X (1 - p)ⁿ⁻ˣ
We need to calculate the probability to win 2 or more tickets
= 1 - the probability to win at least one ticket
= 1 - P(X = 0) + P(X = 1)
here,
p = 0.05
1 - p = 0.95
n = 12
P(X = 0)
= ¹²C₀ X 0.05⁰ X 0.95¹²
= 0.54036
P(X = 1)
= ¹²C₁ X 0.05¹ X 0.95¹¹
= 0.34128
Hence we get
P(X ≥ 2) = 1 - 0.54036 - 0.34128
= 0.118
Therefore, we get the probability that the person will win 2 or more tickets to be 0.118
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Suppose that A and B are points on the number line.
If AB=5 and B lies at 12, where could A be located?
If there is more than one location, separate them with commas.
:0
Location(s) of A :
0.0....
X
Answer:
locations of A are 7, 17
Step-by-step explanation:
since B is positioned at 12 and AB = 5 , then
A = 12 - 5 or 12 + 5 = 7 , 17
you want to determine whether a new medication affects children's test scores. you have 10 sets of identical twins as your sample. one twin in each set takes the medication, while the other doesn't. you will compare the test scores of the medicated twins to the test scores of the unmedicated twins. the null hypothesis is that there will be no difference in test scores between the medicated and unmedicated twins. which tool within data analysis will you use?
T-test paired two samples for means should be used .
What does test score mean?
A test score is a numeric piece of information that describes how well a test-taker performed. It is described in one formal definition as "a summary of the evidence contained in an examinee's responses to the items of a test that are related to the construct or constructs being measured."here the samples are dependent, the score of one twins is compared with the score of any another from the same pair .
Hence, T-test paired two samples for means should be used
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A sample of gas is enclosed in a container of fixed volume. Identify which of the following statements are true. Check all that apply. If the container is heated, the gas particles will lose kinetic energy and temperature will increase. If the container is cooled, the gas particles will lose kinetic energy and temperature will decrease. If the gas particles move more quickly, they will collide more frequently with the walls of the container and pressure will increase. If the gas particles move more quickly, they will lose energy more rapidly and collide with the walls of the container less often, and pressure will decrease. If the gas particles move more quickly, they will collide with the walls of the container more often and with more force, and pressure will increase.
The true statement about the sentence 'sample of gas is enclosed in a container of fixed volume' are:
If the container is cooled, the gas particles will lose kinetic energy and temperature will decrease. If the gas particles move more quickly, they will collide more frequently with the walls of the container and pressure will increase.What will happen to 'sample of gas is enclosed in a container of fixed volume?When a sample of gas is been enclosed in a container of fixed volume then then if the container temperature is been reduced then the kinetic energy of the gas will reduce.
Therefore the first and the third option are correct.
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Dina pours 16-ounce containers of juice into a dispenser with a capacity of 960 ounces. The function y = 16x models this situation. What is the range of the function?
The range of the function is [0, 960]
How to determine the range of the function?From the question, we have the equation of the function to be
f(x) = 16x
Where
The size of the container is 16 ouncesThe capacity of the dispenser is 960 ouncesWhen the dispenser is empty, it means that f(x) = 0
When the dispenser is full, it means that f(x) = 960
When these values are combined, they represent the range
In other words, the range is 0 to 960
This can be rewritten as [0, 960]
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Answer:
big black men
Step-by-step explanation:
(i have your search history)
1. Perform Gauss-Jordan elimination on the augmented matrix shown.
O
-261
3
A. 0 1 -7
00 0
3
B. 0 -1 7
0
[102]
C.0 17
001
2370
[100]
D. 0 1 0
00
Answer:
Step-by-step explanation:
Isabella, do you know how to do the "elementary row operations"?
Also, when did they begin teaching linear algebra in H.S. :DDD nice work getting there.
Gauss Jordan, just mean get your matrix in RREF (Reduced Row Echelon Form)
I suggest using Matlab to do this. it's got the "RREF(x) function to do this exact thing.
Your teacher probably wants you to do this by hand. thou, huh. :/
here is my Matlab code and the answer
clc
close all
clear
format compact
A=[3 -4 2;0 -1 7]
mymatx=rref(A)
A =
3 -4 2
0 -1 7
mymatx =
1.0000 0 -8.6667
0 1.0000 -7.0000
Yes, maybe it's totally cheating, but it seems fair nowadays to use technology that is commonly available. :)
So answer A) looks right