Answer:
3 out of 4
Step-by-step explanation:
the denominator represent the whole number and numerator represent the amount
Owen spent $10 on 4 pieces of toast and 7 pieces of bacon. James spent $4 on 1 piece of toast and 1 piece of bacon. Which systems of equations models the situation given b for bacon and t for toast?
The system of equations that models the situation and can be used to get the prices is:
4*t + 7*b = $10
t + b = $4
Which system of equations models the situation?We know that the variables that we will be using are:
b = cost of a piece of bacon.t = cost of a piece of toast.First, we know that Owen spent $10 on 4 pieces of toast and 7 pieces of bacon, so we can write the equation:
4*t + 7*b = $10
And James spent $4 on 1 piece of each, then the other equation is:
t + b = $4
Then the system of equations that models this situation is the one we can make with these two equations:
4*t + 7*b = $10
t + b = $4
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20 pts. Find the inverse
The inverse of the given statement is if x does not equal 4 then 4x - 5 doesn't equal 11. Option C is the correct option.
What is a statement?
A statement in mathematics is a declarative utterance that can only be either true or false. A proposal is another name for a statement. It's important that there be no ambiguity. A sentence can only be true or untrue and not both for it to be a statement.
The given statement is if x equals 4, then 4x - 5 equals 11.
Each of the original statements' inverses is presumptive in the inverse statement.
The inverse statement of the given statement is if x does not equal 4 then 4x - 5 doesn't equal 11.
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Which statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407?
Statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407 are number 4 is in 10th place, and number 4 is in the 100th place respectively.
What are numbers?
A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them.
In mathematics, the first ten numbers are referred to as the fundamental numbers. These fundamental numbers are listed beginning at 0 and ending at 9. Basic numbers include 0 through 9 are 0, 1, 2, 3, 4, 5, 6, 7, and 8.
The given numbers are 3245 and 8407.
We have to find the place of 4 in the given numbers.
Consider, the number 3245.
In this number 4 is in 10th place.
Consider, the second number 8407.
In this number 4 is in the 100th place.
Hence, statement correctly compares the values of the digit 4 in the numbers 3,245 and 8,407 are number 4 is in 10th place, and number 4 is in the 100th place respectively.
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3 The length of a mobile phone is twice the width.
There is a border around the screen.
The border is 1.5cm wide at the top and bottom.
The border is 0.25 cm wide at the sides.
The perimeter of the screen is 32 cm.
Let the width of the phone be.xcm.
(a) Form an equation in x.
(b) Hence find the area of the screen in cm².
On solving the provided question we can say that - the linear equation of .25x + 3y = 1 +3 = 4
What is a linear equation?The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.
here, x= 4 and = 1
.25x + 3y
= 1 +3
= 4
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-10 in simplest radical form.
Answer:
The square root of -10 is already in the simplest radical form. Therefore, the answer is:
√10
-10 in simplest radical form is written as -√10.
Daren can run 8.55 kilometers in one hour. Umberto can run 9.5 kilometers in one hour. If Daren plans to run for 3.5 hours and Umberto plans to run for 3 hours who will run more kilometers assuming their running pace stays the same for the entire time? How do you know?
The total distance travelled covered by the Daren is greater than that of Umberto.
What is distance travelled in Kinematics?Distance travelled is the product of speed of the body and the time for which it moved. Mathematically -
Distance = Speed x Time
Given is that Daren can run 8.55 kilometers in one hour. Umberto can run 9.5 kilometers in one hour. Now, Daren plans to run for 3.5 hours and Umberto plans to run for 3 hours.
Total distance travelled by Daren is -
d₁ = 8.55 x 3.5
d₁ = 29.925 Km
Total distance travelled by Umberto is -
d₂ = 9.5 x 3
d₂ = 28.5 Km
It can be seen that -
d₁ > d₂
Therefore, the total distance travelled covered by the Daren is greater than that of Umberto.
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jennifer is on a trip and travels a distance of 150 miles. she spends some of her time walking, and some of her time travelling by train. if she spends w hours walking and t hours travelling by train, what is the meaning of 3w in the equation below? 50t 3w
Answer:
it means 3 weeks and time traveled
A special membership card allows you to get 5% off all purchases. Your purchases total $125.95 before the discount. What would you pay once the discount is applied?
Answer: 103.96
Step-by-step explanation:
A swimming coach needs to choose a team for a relay race. The coach must select 444 of 666 available swimmers and put them in a strategic sequence. How many unique ways are there to arrange 444 of the 666 swimmers?.
When a swimming coach needs to choose a team for a relay race then the number of ways they can arrange 444 of the 666 swimmers is 3.53×[tex]10^{1735}[/tex]
There are a total of 444[tex]C_{444}[/tex] (or 6.64 x [tex]10^{847}[/tex]) ways to select 444 swimmers from the pool of 666.
Once the swimmers have been chosen, they need to be arranged in a strategic sequence.
This can be done in 444! (or 5.34 x [tex]10^{906}[/tex]) ways.
Therefore, the total number of unique ways to arrange 444 of the 666 swimmers is
6.64 x [tex]10^{847}[/tex] x 5.34 x [tex]10^{906}[/tex]
3.53 x [tex]10^{1735}[/tex]
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On a school trip, a class travels 471.459 kilometers by train and 2.66 kilometers by bus. How far did the class travel?
Answer:
474.119 kilometers
Step-by-step explanation:
The class traveled 474.119 kilometers in total. You can find this by adding the distance traveled by train (471.459 km) to the distance traveled by bus (2.66 km).
471.459 + 2.66 = 474.119
What is an example of a complex number in standard form?
An example of a complex number in standard form is (5 + 4i), where i is the imaginary unit.
example to solve (x + 5i)(2x - 3i):
Step 1: Multiply the real numbers together:
x × 2x = 2x²
Step 2: Multiply the imaginary numbers together:
5i × -3i = -15i²
Step 3: Multiply the real and imaginary parts together:
x × -3i = -3ix and 2x × 5i = 10xi
Step 4: Add all the terms together:
2x² - 15i² + -3ix + 10xi = 2x² - 15i² - 3ix + 10xi
Step 5: Simplify the terms:
2x² - 15i² - 3ix + 10xi = 2x² - 18ix - 15i²
The product of two complex numbers (x + 5i)(2x - 3i) can be found by multiplying the real numbers together, the imaginary numbers together, and the real and imaginary parts together, then adding all of the terms together and simplifying.
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Please help as fast as you can
I think it is W(week)...........
A city doubles its size every 41 years. If the population is currently 700,000, what will the population be in 123 years?
The population in 123 years will be 5600000.
How to calculate the population?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. in this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, the city doubles its size every 41 years. If the population is currently 700,000. After 123 years, it'll have doubled 3 times.
The population will be:
= 700000 × 2³
= 5600000
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Answer: 5600000
Step-by-step explanation: I got it right on my ixl
9/10 x 5/7 fraction form
Answer:
9/
Step-by-step explanation:
As we have to multiply the fraction so we will multiply numerator with numerator and denominator with denominator we get 45/70. As we know both 45 and 70 are divisible by 5 and the simplest form answer we get will be 9/ 14
check all that apply to the differential equation dydx+sin2(x)y=cos2(x)y A. homogeneous B. ODE C. PDE D. first order E. second order F. third order G. linear H. a candidate for integrating factors I. separable J. autonomous
All properties that apply to the differential equation dy/dx+sin²(x)y = cos²(x)y are following
(A) homogeneous
(B) ODE
(D) first order
(G) linear
(I) separable
Ordinary Differential equation: A differential equation consisting an unknown function and its derivatives with respect to a single independent variable.
Partial Differential equation: A differential equation consisting an unknown function and its partial derivatives with respect to a two or more independent variables.
First order Linear differential equation: The standard form of first order Linear differential equation is dy/dx + p(x)y = q(x)
and if q(x)=0, then this linear differential equation is homogeneous.
Separable Differential equation: A differential equation, y′ = f(x,y)
is said to be in separable form if the function f(x,y) can be written as
fx,y) = g(x)h(y). Now, we have an equation
dy/dx+sin²(x)y=cos²(x)y --(1)
As we see differential equation (1) contains derivative with respect to a single independent variable, x only, therefore this is an Ordinary differential equation. Also, the order of the differential equation (1) is one, i.e. first order differential equation. Now the given differential equation can be written as
dy/dx + ysin² x - ycos²x = 0
=> dy/dx − y(sin²x−cos²x) = 0
This is the standard form of first order Linear differential equation with q(x) = 0 . Therefore, there is not a candidate for integrating factors. The right side function is zero, therefore the the differential equation is homogeneous and dy/dx = y(sin²x−cos²x) = f(x,y)
= g(y) h(x) , so, it is a separable one . Hence, we check all properties for equation (1) .
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£1=€1.45 if a graph was on the axes below to show the relationship between pounds and euros, he points (0,a) and (1,b) would be on the line work out the values of a and b
Based on the graph which shows the relationship between pounds and euros, the value of a is €0 and the value of b is €1.45.
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
x represents pounds (£).y represents euros (€).k represents the constant of proportionality.In order to have a proportional relationship and equivalent ratios, the relationship between pounds (£) and euros (€) must have the same constant of proportionality.
Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 1.45/1
Constant of proportionality (k) = 1.45.
When x = 0, the value of a is given by:
y = a = 1.45x
a = 1.45(0)
a = €0.
When x = 1, the value of b is given by:
y = a = 1.45x
b = 1.45(1)
b = €1.45.
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What is the factor of x³ 5x² 2x 24?
The factor of x3 5x2 2x 24 is (x - 4)(x + 2)(x + 6), which can be expanded as x3 + 2x2 - 4x2 + 6x - 8x - 24.
1. Factor out the greatest common factor (GCF) from the coefficients of the terms.
x3 5x2 2x 24
2. Factor out the GCF from each term:
x3 = x•x•x
5x2 = 5•x•x
2x = 2•x
24 = 24
3. Our factors are now:
x•x•x 5•x•x 2•x 24
4. Group the terms with common factors:
(x•x•x) (5•x•x) (2•x) (24)
5. Factor out the common factor from each group:
x•x (x•5) (2•x) (24)
6. Our factors are now:
x (x•5) (2•x) (24)
7. Factor out the common factor from each group:
x (x•5) (2•x) (24)
8. Our factors are now:
x (x + 2)(x + 6) (24)
9. Our final answer is:
(x - 4)(x + 2)(x + 6)
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two payment options to rent a car you can pay $20 a day plus 25 cents a mile (option a) or pay $10 a day plus 50 cents a mile (option b) for what amount of daily miles will option a be the cheaper plan?
Answer:
Option A will be the cheaper plan for any daily mileage over 80 miles.
Step-by-step explanation:
The sum of 9 consecutive positive integers is 99. What is the largest of these Intigers?
Answer: 15
Step-by-step explanation:
Let x be the first of the consecutive integers.
So, the consecutive integer after x would be x+1. The one after this one would be x+2. Continue this until there are nine consecutive integers.
x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) = 99
Simplify:
9x + 36 = 99
9x = 63
x = 7
The largest of these consecutive integers is the last one, x+8. Plug in x to this expression:
(7) + 8 = 15
The largest of these consecutive integers is 15.
Problem 1.4 A submarine starts at 0 units and has groups of 3 floats and groups of
4 anchors attached. Using these groups of floats and anchors, write as many different expressions as you can that would make the submarine's final position -5 units.
Please help giving out 20pt for this question please help ASAp
The submarine's final positions expressions are
3F + 4A = -5 units 3F - 4A = -5 units F + 2A = -5 units 5F - A = -5 units What is the expression?Generally, An expression is a finite combination of symbols that is well-formed according to principles that rely on the context in which it is used. In mathematics, an expression is also known as a mathematical expression.
3F + 4A = -5 units
Working:
3 floats * -1 unit/float + 4 anchors * -1 unit/anchor
= -3 units + -4 units
= -7 units
3F - 4A = -5 units
Working:
3 floats * -1 unit/float - 4 anchors * 1 unit/anchor = -3 units - 4 units
= -7 units
F + 2A = -5 units
Working:
1 float * -1 unit/float + 2 anchors * -1 unit/anchor
= -1 units + -2 units
= -3 units
5F - A = -5 units
Working: 5 floats * -1 unit/float - 1 anchors * 1 unit/anchor
= -5 units - 1 unit = -6 units
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What are the slope and y-intercept of the line 4y = -x - 32?
Answer:
slope = - [tex]\frac{1}{4}[/tex] , y- intercept = - 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
4y = - x - 32 ( divide through by 4 )
y = - [tex]\frac{1}{4}[/tex] x - 8 ← in slope- intercept form
with slope m = - [tex]\frac{1}{4}[/tex] and y- intercept c = - 8
A winch at the top of a 12-meter building pulls a pipe of the same length to a vertical position, as shown in the figure. The winch pulls in rope at a rate of
−0.7
meter per second
(ds/dt = −0.7 m/sec)
. Find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 2. (Round your answers to three decimal places.)
The rate of vertical change is -0.4 m/s and the rate of horizontal change is -0.7 m/s.
THE RATE OF VERTICAL AND HORIZONTAL CHANGETo find the rate of vertical change and the rate of horizontal change at the end of the pipe when y = 2, we need to use the chain rule of Calculus.The chain rule states that if we have a function f(g(x)) and we know the derivative of f and the derivative of g, we can find the derivative of f(g(x)) by multiplying the derivative of f by the derivative of g. In this case, y is a function of x and x is a function of t. So we have:dy/dt = dy/dx * dx/dt
To find dx/dt, we can use the fact that the pipe is being pulled in at a rate of -0.7 m/s. So dx/dt = -0.7 m/s.To find dy/dx, we can use the equation for the pipe, which is:y = 12 - √(12² - x²)
Taking the derivative of this equation with respect to x, we get:dy/dx = x/(√(12² - x²))
Now that we have both dx/dt and dy/dx, we can use them in the chain rule to find dy/dt:dy/dt = x/(√(12² - x²)) * (-0.7 m/s)
To find the rate of vertical change, we need to find dy/dt at the point where y = 2. We know that x = sqrt(12² - 2²) = √(144-4) = √(140) = 2√(35). So we can substitute this value of x into the equation for dy/dt and find the rate of vertical change:dy/dt = 2√(35)/√(140) * (-0.7 m/s) = -0.4 m/s
To find the rate of horizontal change, we know that dx/dt = -0.7 m/s, so the rate of horizontal change is:dx/dt = -0.7 m/s
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Which of the following is the best model to use to document the inputs and the outputs to a system?a. State chart diagram c. Activity diagramb. Fully developed use case description d. System sequence diagram
System sequence diagram is the best model to use to document the inputs and the outputs to a system.
In the realm of software engineering, a sequence diagram, also known as a system sequence diagram (SSD), depicts process interactions grouped in chronological order. It illustrates the processes involved and the order in which messages must be exchanged for the processes to provide the functionality. In the 4+1 architectural perspective model of the system under development, sequence diagrams are often connected to use case realizations. Event diagrams and event scenarios are other names for sequence diagrams.
The diagrams display the events that external actors produce, their order, and any potential inter-system events for a given scenario of a use case. [1] The diagram emphasizes events that cross the system boundary from actors to systems and treats all systems as black boxes. The main success scenario of the use case, as well as frequent or complex alternate situations, should be represented using a system sequence diagram.
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Examine the figure of two parallel lines cut by a transversal.
(2x + 10)°
What is the value of x?
(2x-30)
©2017 StrongMind. Created using GeoGebra
The value of x will be;
⇒ x = 50
What are Parallel lines?Parallel lines are those lines that are equidistance from each other and never intersect each other.
Given that;
Two parallel lines cut by a transversal.
Now,
Since, Two parallel lines cut by a transversal.
Hence, By definition of co-interior angle, we get;
The sum of co-interior angle in supplementary.
Hence, We get;
⇒ (2x + 10)° + (2x - 30)° = 180°
⇒ 4x - 20 = 180
⇒ 4x = 180 + 20
⇒ 4x = 200
⇒ x = 200/4
⇒ x = 50
Thus, The value of x = 50
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If the range of X is the set {0,1,2,3,4,5,6,7,8} and P(X=x) as defined in the following table:
x 0 1 2 3 4 5 6 7 8
P(X=x) 0.06528 0.3870 0.03062 0.0968 0.06913 0.0968 0.04846 0.01252 0.1935
Determine the mean and variance of the random variable.
(a) mean
(b) variance
Mean and Variance of the given table are 3.43672 and 7.837755 respectively.
What is probability ?
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
a)E(x) = ∑ xᵢp(xᵢ)
∑ xᵢp(xᵢ) = 1(0.3870) + 2(0.038062) + 3(0.0968) + 4(0.06913) + 5(0.0968) + 6(0.04846) + 7(0.01252) + 8(0.1935)
∑ xᵢp(xᵢ) = 3.43672
Mean = 3.43672
b) Variance = E(x²) - [E(x)]²
E(x²) = ∑ x²ᵢp(xᵢ)
∑ x²ᵢp(xᵢ) = 1²(0.3870) + 2²(0.038062) + 3²(0.0968) + 4²(0.06913) + 5²(0.0968) + 6²(0.04846) + 7²(0.01252) + 8²(0.1935)
∑ x²ᵢp(xᵢ) = 19.6488
∴ Variance = 19.6488 - (3.43672)² = 7.837755
Hence , Mean and Variance of the given table are 3.43672 and 7.837755 respectively.
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Miss Weaver makes jewelry. A necklace costs $6 while a bracelet
costs $3.50. Last week, she sold 18 items of jewelry for a total cost
of $88. How many bracelets did she sell?
Answer:
She sold 8 bracelets
Step-by-step explanation:
I knew the number of bracelets would have to be an even number otherwise the total cost would have a decimal. Then I just went down the list doing 3.5*16 + 6*2, etc. until I got the answer (she sold 10 necklaces btw)
Which equation in slope-intercept form represents a line that passes through the point (2,3) and is parallel to the line y−9=23(x+7)?
Answer:
y = 23x - 43
Step-by-step explanation:
y - 9 = 23 (x + 7)
y - 9 = 23x + 161
y = 23x + 170
y = 23x + b
3 = 23(2) + b
3 = 46 + b
y = -43
y = 23x - 43
There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 reds?
The probability of getting 2 red marbles will be 0.298.
How to calculate the probability?Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.
In this case, there is a bag filled with 5 blue and 6 red marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced.
The probability of getting 2 reds will be;
= 6/11 × 6/11
= 0.298
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How many 4 digit numbers greater than 4000 can be formed?
The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.
We are having digits 2,3,4,5 and 6. Numbers greater than 4000 are to be formed using these digits without repetition.
The number can have 4 digits but greater than 4000 or can have 5 digits.
The total number of 4 digits number greater than 4000 is => 3*4P3 = 3*24 = 72.
Total number of 5 digits numbers = 5P5=5!=120
So, the Total number of required numbers =120+72=192
Hence, The number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition is 192.
Complete question: Find the number of numbers that are greater than 4000 which can be formed using the digit 2,3,4,5,6 without repetition.
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According to the combination method, the number of formation using the digit 4 is 192
The term combination in math is called as the mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
While we looking into the four-digit has 4 digits and the first digit is the thousands place. Then the digits 2 and 3 are less than 4, here we know that they can't take the thousands place. Here we also know that the digit 4, 5, and 6 can take this place.
Here we have the remaining 4 numbers and the remaining three digits can be taken by any of them to form a number greater than 4000.
Then the number of ways is calculated as
=> 3×4×3×2 = 72
Then the number of 5 digit numbers greater than 4000.
Here we have to observe that all five-digit numbers are greater than 4000. And here we have 5 digits and hence the number of five-digit numbers is written as
=> 5×4×3×2×1 = 120
Then the total number of ways is calculated as
=> 72 + 120 = 192
Therefore the number of numbers that are greater than 4000 which can be formed using the digits 2, 3, 4, 5, 6 without repetition is 192.
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Find the 50th term of the following arithmetic sequence.
14, 17, 20, 23,
...
Answer: 161
Step-by-step explanation: 23 + 3 times 46 (since the first 4 numbers are already there) is 161
