Answer:
22.48 km/h
Step-by-step explanation:
it took James 45 minutes to cycle 15 km, sInce he was traveling at 20 km/h, which was worked out by dividing 50 by 2.5.
since Peter left 5 minutes later, it took 5 minutes less, so 40 minutes. 40 minutes as a fraction is 0.667.
15 divided by 0.667 is 22.48 km/h
Answer:22
Step-by-step explanation:
what the guy before said
Olivia is a stockbroker. She makes 4% of her sales in commission. Last week,she sold $7,200 worth of stocks. How much commission did she make last week?
Commission (Related to business mathematics) made by selling $7200 worth of stock is $288.
What is business mathematics ?
Business Math always deals with profit or loss. The cost of a product is fixed by taking into consideration it’s profit, margin, cash discount, trade discount, etc. Business mathematics is used by commercial companies to record and manage business works. Commercial businesses use math in departments of accounting, inventory management, marketing, sales forecasting and financial analysis.
The most important topics covered in Business Mathematics are:
Profit and LossStatisticsSimple and Compound InterestInterest RatesLoansMarkups and markdownsTaxes and Tax LawsDiscount FactorAnnuitiesInsuranceCreditDepreciationFuture and Present ValuesFinancial StatementsNow,
Sales made= $7200
Commission=4%
Commission earned= 7200*4/100
=72*4
Commission earned = $288
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The volume of a right cone is 8647 units³. If its circumference measures 187 units,
find its height.
Answer:
9.323 units
Step-by-step explanation:
radius = 29.76
https://www,omnicalculator,com/math/height-of-cone
The image shows quadrilateral ABCD. Find the perimeter of ABCD. Explain or show your reasoning.
(The reasoning is really what I need. Thank you :))
Answer:12.64
Step-by-step explanation: Using the pythagorean therum, we can see that each side of ABCD is part of a triangle whose other legs are 4 and 1. This means that each side of ABCD squared is equal to 3 squared + 1 squared which means that each side squared is 10. So each side is equal to the square root of 10 which means each side is around 3.16. So the perimenter is around 3.16x4 = 12.64
Ted and Truman held a contest to see who could collect more free baseball caps. Ted collected three caps in April, four in May, none in June, eight in July, three in August, and four in September. Truman collected one in April, seven in May, three in June, none in July, four in August, and three in September. How many caps did each boy collect? math
22 caps were collected by Ted and 18 caps were collected by Truman.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Ted collected three caps in April'
For Ted, In April the number of caps collected = 3
In May the number of caps collected = 4
In June the number of caps collected = 0
In July the number of caps collected = 8
In August the number of caps collected = 3
In September the number of caps collected = 4
The total number of caps collected by Ted=3+4+8+3+4
=22 caps.
For Truman, In April the number of caps collected = 1
In May the number of caps collected = 7
In June the number of caps collected = 3
In July the number of caps collected = 0
In August the number of caps collected = 4
In September the number of caps collected = 3
The total number of caps collected by Truman = 1+7+3+4+3
=18
Hence, 22 caps were collected by Ted and 18 caps were collected by Truman.
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Greta rolls a pair of 6- sided dice. If she gets two of a kind, she scores the sum of the 2 dice. Otherwise, she gets 0 points. What is the expected value of the number of points she scores on a toss of the 2 dice?
The expected value of the number of points she scores on a toss of the 2 dice is 7.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, Greta rolls a pair of 6- sided dice.
If she gets two of a kind she scores the sum of the 2 dice.
The number of sample space N(S) of rolling two dice is 36.
The number of events for getting same number on both dice are,
(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) = 6.
Therefore, The probability of getting the same numbers on both dice is,
= 6/36.
= 1/6.
The total score is,
= 2 + 4 + 6 + 8 + 10 + 12.
= 42.
We know The expected value, also known as the expectation, average, is a generalization of the weighted average in the field of probability theory. Informally, the anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
Therefore, The expected value of the number of points she scores on a toss of the 2 dice is,
= (1/6)×42.
= 7.
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Can a system of linear equations have zero solutions?
f a₁/a₂ = b₁/b₂ = c₁/c₂ this system of linear equations have zero solutions.
Multiple equations in algebra are known as simultaneous equations or systems of equations, and they must be solved simultaneously (i.e., the answer must satisfy every equation in the system). For a system to have a singular solution, the number of equations and unknowns must be equal.
Systems of equations are used to solve problems when there are multiple unknowns and enough data to construct equations in those unknowns. In general, when there are n unknowns, we need enough knowledge to create an equation for each unknown.
We are aware that the equations,
a₁x + b₁y = c₁
a₂x + b₂y = c₂
if the equation a1/a2 = b1/b2 = c1/c2 is unsolvable.
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Find X!!! Thank you so much
The possible values of x are; 8 > x
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
The given diagram is a triangle. From the diagram we can see that;
2x + 8 > 3x (according to the length)
Solve the resulting inequality;
2x + 8 > 3x
8 > 3x - 2x
8 > x
x> 0.5
Hence the possible values of x are 8 > x
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Select the correct answer. Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(0) = 2 C. g(7) = -1 D. g(-4) = -11
Since function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, the statement that could be true for g is: A. g(-13) = 20.
How to determine the true statement for function g?Based on the information provided in this scenario, the domain and range of this function g(x) in interval notation are as follows:
Domain = -20 ≤ x ≤ 5 or [-20, 5]
Range = -5 ≤ g(x) ≤ 45 or [-5, 45]
Function g(0) = 2 is simply a false statement because it was explicitly stated that g(0) = -2. Additionally, g(-4) = -11 is a false statement because it is outside the scope of the given range for this function.
Furthermore, the function g(7) = -1 is a false statement because it is not within the domain for the given function. However, we can logically deduce that the function g(-13) = 20 is a true statement because it is within the domain for the given function and it would produce an output that is within the scope of the given range for this function.
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what happens when you multiply a negative by a positive?
Answer:
you get a negative answer.
Which of the following rational functions is graphed below?
A. F(x)=2/x
B. F(x)=1/x-2
C. F(x)=1/2x
D. F(x)=1/x+2
Find the values at which the rational function is undefined before you can graph it.Any values that would result in a denominator of zero for a function are undefined.
Which of the rational functions listed below is represented by a graph? Find the values at which the rational function is undefined before you can graph it.Any values that would result in a denominator of zero for a function are undefined.If a value's rational function is undefinable, a dotted line is put on the graph to represent that value.The term "vertical asymptote lines" refers to these lines.If a polynomial can be expressed as a polynomial divided by a polynomial, that function is deemed rational.A rational function's domain is the collection of all numbers except the zeros in the denominator since polynomials are defined everywhere.f(x) Equals x in Example 1. (x - 3).
The graph of the function.
From the given graph , the vertical asymptote is at x=2
Lets find out the vertical asymptote of each function
To find out vertical asymptote we set the denominator =0
f(x) = 1/2x
2x = 0
x= 0
The second function has vertical asymptote at x=2
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What is the quotient of 45 and 3?
Answer: 15
Step-by-step explanation:
Quotient- the result of the division equation.
45/3=15
solve the system of equations.
Therefore, the system of equations with the elimination approach has a solution of (5, -2) for the equations 6x + 10y = 10 and -6x - 24y = 18.
what is equations ?An equation is a mathematical formula that joins two statements and uses the equal symbol (=) to indicate equivalence. For instance, in the equation 3x + 5 = 14, the equal sign divides the variables 3x + 5 and 14. The relationship between the two sentences on either side of a letter is explained by a mathematical formula. There is frequently only one variable, which also serves as the symbol. for instance, 2x - 4 = 2.
given
6x + 10y = 10
-6x - 24y = 18
-14y = 28
y = -2
so x = 6x -20 = 10
= 6x= 30
x = 5
Therefore, the system of equations with the elimination approach has a solution of (5, -2) for the equations 6x + 10y = 10 and -6x - 24y = 18.
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or Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Olivia owns a cake shop and she is working on two wedding cakes this week. The first cake consists of 3 small tiers and 2 large tiers, which will serve a total of 144 guests. The second one includes 3 small tiers and 1 large tier, which is enough servings for 102 guests. How many guests does each size of tier serve?
Answer:
small tier serves 20; large tier serve 42
Step-by-step explanation:
s = # guests a small tier serves
l = # guests a large tier serves
1) 3s + 2l = 144
2) 3s + 1 = 102 subtract equation (2) from equation (1)
0 + l = 42
l = 42 plug this into equation (2) to solve for s
3s + 42 = 102
3s = 60
s = 20
The number of people served by the small tier is 20.
The number of people served by the large tier is 42.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 9 is an equation.
We have,
Small tier = S
Large tier = L
The first cake consists of 3 small tiers and 2 large tiers, which will serve a total of 144 guests.
This means,
3S + 2L = 144 ____(1)
The second one includes 3 small tiers and 1 large tier, which is enough servings for 102 guests.
This means,
3S + 1L = 102 _____(2)
Solve (1) and (2)
Using the elimination method.
3S + 2L = 144
3S + L = 102
(-) (-) (-)
L = 144 - 102
L = 42
Now,
L = 42 in (1)
3S + 2L = 144
3S + 2 x 42 = 144
3S + 84 = 144
3S = 144 - 84
3S = 60
S = 20
Thus,
The small tier serves 20 people.
The large tier serves 42 people.
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Factor the quadratic expression completely. -3x^2+17x-20=−3x 2 +17x−20=minus, 3, x, squared, plus, 17, x, minus, 20, equals
The quadratic equation -3x^2 + 17x - 20 can be factorized to get:
y = -3*(x - 4)*(x - 5/3)
How to factorize the quadratic equation?Here we want to factorize the quadratic equation:
-3x^2 + 17x - 20
If the two roots are x = h and x = k, then we can rewrite that quadratic as:
-3*(x - h)*(x - k)
So we need to find the two roots for the quadratic equation, using the quadratic formula we will get:
[tex]x = \frac{-17 \pm \sqrt{17^2 - 4*(-3)*(-20)} }{2*-3} \\\\x = \frac{-17 \pm 7 }{-6} \\\\[/tex]
Then the two roots are:
x = (-17 - 7)/-6 = -24/-6 = 4
x = (-17 + 7)/-6 = -10/-6 = 5/3
Then the quadratic equation can be written as:
y = -3*(x - 4)*(x - 5/3)
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Answer:
−(3x−5)(x−4)
Step-by-step explanation:
Correct on Khan
Adele's parents bought her a used car for her 18th birthday, but she has to pay the car
insurance. After one month, she had spent $183 on car insurance. After 4 months, she'd
spent a total of $732 on car insurance; and after a full year, she'd spent a total of $2,196 on
car insurance. Is the relationship between the number of months since Adele got her car and
the total amount of money she had spent on car insurance a linear relationship?
yes
no
Now, justify your answer.
A. The total amount spent on car insurance increased
by a greater amount each month.
B.The total amount spent on car insurance increased
by the same amount each month.
C. The total amount spent on car insurance didn't
increase by a constant amount each month.
D.The total amount spent on car insurance had no
relation to the number of months.
Answer:
C
Step-by-step explanation:
The answer is C. The total amount spent on car insurance didn't increase by a constant amount each month.
A linear relationship means that the relationship between two variables can be described by a straight line, with the rate of change being constant. In this case, the relationship between the number of months since Adele got her car and the total amount of money she had spent on car insurance is not linear. If the relationship was linear, we would expect the rate of increase to be constant, but in this case, the rate of increase is not constant. The car insurance cost 183 in the first month, 732 in 4 months, and 2196 in a year. That means 183 in 1 month, 549 in 4 months, and 1464 in a year. As we see, the rate of increase is not constant.
Rodrigo is organizing his CD collection. He has 5 pop CDs and 85 other CDs. If Rodrigo randomly selects one of his CDs, what is the probability that it will be a pop CD?
If Rodrigo randomly selects one of his CDs, then the probability that it will be a pop CD is 1/18.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Rodrigo is organizing his CD collection.
The number of pop CDs are 5
The number of other CDs are 85.
If Rodrigo randomly selects one of his CDs we have to find the probability that it will be a pop CD
The total number of cd are 90.
The the probability that it will be a pop CD is 5/90 which is 1/18.
Hence, If Rodrigo randomly selects one of his CDs, then the probability that it will be a pop CD is 1/18.
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y - 4 - 3x divide by x - 5
By calculating , with the subject of x we get x = 4 + 5y / y + 3 as a final resultant .
What is subject of a formula?
Making x the subject of a formula means rearranging the formula so that we have a single x variable equal to the rest of it.
Making x subject of the formula is as follows:
x = 4 + 5y / y + 3
y = 4 - 3x ÷ x - 5
cross multiply
y(x - 5) = 4 - 3x
distribute the values on the left side
yx - 5y = 4 - 3x
add 3x to both sides of the equation
yx + 3x - 5y = 4 - 3x + 3x
yx + 3x - 5y = 4
add 5y to both sides
yx + 3x - 5y + 5y = 4 + 5y
yx + 3x = 4 + 5y
factorise the left hand side
x(y + 3) = 4 + 5y
divide both sides by (y + 3)
Therefore,
x = 4 + 5y / y + 3
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Graph the following system of equations. y = 3x + 9 6x − 2y = 6 What is the solution to the system?
Step-by-step explanation:
The solution to the system can be found by graphing the equations and finding the point of intersection of the two lines. The point of intersection is the point (x,y) that satisfies both equations. In this case, the point of intersection is (2,15) which means that at x=2 and y=15 the system of equations is satisfied.
Here is a diagram and it’s corresponding equation.Find a solution to the equation and explain your reasoning.
The solution of the equation is 5/3.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that,
The equation is,
⇒ 6x + 11 = 21
Now, Solving for x as;
6x + 11 = 21
6x = 10
x = 5/3
Hence, The value of x is 5/3.
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3. Here is a hanger:
a. Write an equation to represent the hanger.
b. Draw more hangers to show each step you would take to find x. Explain your
reasoning.
c. Write an equation to describe each hanger you drew. Describe how each equation
matches its hanger.
The equation that describes the hanger is y = x + 1.b-This line will represent the equation y = x + 1.c. The equation for the first hanger is y = x + 1.
What is equation?Equation is a mathematical statement that expresses the equality of two expressions by using symbols. It typically consists of an equals sign (=) and two expressions that are related by the equals sign. Equations are used to describe the relationship between different variables, such as the area of a circle or the speed of a moving object. Equations are also used to solve problems, to make predictions, or to reveal patterns or trends.
a. The equation that describes the hanger is y = x + 1. This equation states that the y-coordinate (height of the hanger) is always 1 unit greater than the x-coordinate (width of the hanger).
b. To find x, I will draw more hangers to represent each step of the process. For the first hanger, I will draw a line with a y-intercept of 1 and a slope of 1. This line will represent the equation y = x + 1.
For the second hanger, I will draw a line with a y-intercept of 1 and a slope of 2. This line will represent the equation y = 2x + 1.
For the third hanger, I will draw a line with a y-intercept of 1 and a slope of 3. This line will represent the equation y = 3x + 1.
The reason I chose to draw each hanger with a y-intercept of 1 is to represent the constant value of 1 in each equation. The slope of each hanger is increased by 1 from the previous hanger to represent the coefficient of x in each equation.
c. The equation for the first hanger is y = x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 1.
The equation for the second hanger is y = 2x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 2.
The equation for the third hanger is y = 3x + 1. This equation matches the hanger because the y-intercept is 1 and the slope is 3.
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I need help please!!!
On solving the provided question, we can say that this function f(x) = 2x - 4 => f(x) = 18 - 4 = 14
what is function?The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.
f(x) = 2x - 4
here, in this function f(x)
x = 9
so, f(9) = 2*9 - 4
f(x) = 18 - 4 = 14
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2=2/3x what is the value of x
Solve for X, Leave in simplest radical form. (Help please)
The required value of the x for the given right angle triangle is x = 4.
What are trigonometric equations?These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
here,
For the given right-angle triangle,
cosФ = base/hypoentuse
cos60 = 2/x
1 / 2 = 2/x
x = 4
Thus, the required value of the x for the given right angle triangle is x = 4.
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Work for 3,565 X 232. It’s 827,080
Answer:
827080
Step-by-step explanation:
caculator
Answer:
Answer in image
Step-by-step explanation:
Follow steps in image
-Hope this helped
What is the domain?
ху
1
1
32
5 3
73
22
O {1, 2, 3, 4, 5, 6, 7}
O {1,2,3,5,7)
O {1,3,5,7)
O {1,2,3}
the domain is the x intercept
{1,2,3,5,7}
Together, teammates Pedro and Ricky got 2683 base hits last season. Pedro had 277 more hits than Ricky. How many hits did each player have?
The Pedro contains 1483 hits. and Ricky contains 1199 hits.
What is meant by equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.
Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.
Pedro had 284 more hits than Ricky.
Let Ricky had 'x' hits.
So, Pedro had x + 284 hits
Together Pedro and Ricky got 2682 base hits.
This can be modeled as:
[tex]$$\begin{aligned}& x+x+284=2682 \\& 2 x+284=2682 \\& 2 x=2682-284=2398 \\& \text { So, } x=2398 / 2=1199\end{aligned}$$[/tex]
Therefore, Ricky contains 1199 hits.
Pedro has = 1199 + 284 = 1483 hits.
Therefore, the Pedro contains 1483 hits.
The complete question is;
Together, teammates Pedro and Ricky got 2682 base hits last season. Pedro had 284 more hits than Ricky. How many hits did each player have?
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What is the factored form of 27x3 64?
After taking the common, the factored form of [tex]27x^3+64[/tex] is [tex](3x+4)(9x^2-12x+16)[/tex].
In the given question, we have to find the factored form of [tex]27x^3+64[/tex].
The following is how we factor the GCF out of a polynomial:
(1) Find the expression's numbers' greatest common factor before analyzing each variable or expression separately to identify the GCF. Factor out the least power that arises if the variable or expression appears in every term.
(2) Write the GCF outside the parentheses and divide each term by the GCF inside the parentheses to factor out a GCF.
To solve this question we use the formula [tex](a^3+b^3) = (a+b)(a^2-ab+b^2)[/tex]
We can write [tex]27x^3+64[/tex] as
[tex]27x^3+64[/tex] = [tex](3x)^3-(4)^3[/tex]
[tex]27x^3+64[/tex] = [tex](3x+4)((3x)^2-3x\cdot4+(4)^2)[/tex]
[tex]27x^3+64[/tex] = [tex](3x+4)(9x^2-12x+16)[/tex]
Hence, the factor form of [tex]27x^3+64[/tex] is [tex](3x+4)(9x^2-12x+16)[/tex].
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The complete question is:
What is the factored form of [tex]27x^3-64[/tex]?
Someone pls help with this onee pleaseee im desperate ill give you branilest
Answer:
1+6x
Step-by-step explanation:
Sum means addition and product means multiply
The only expression that has both is
1+ 6*x
1+6x
Answer:
2nd answer
Step-by-step explanation:
Before finding answer let us get to know about the meanings of words.
sum --> Addition
product --> Multiplication
Accordingly, we have to find the answer with addition & multiplication.
So, the only answer with these two characteristics is 2nd answer.
That is,
1 + 6x
Here, there is a sum between 1 and 6.
And there is a product between 6 and x.
A rectangular prism is packed with cubes that have a side length of 0. 7 inches if a total of 60 cubes is used what will be the volume of the rectangular prism
The right rectangular prism's volume is equal to 123.48 cubic inches.
In the presented problem, a right rectangular prism is filled with cubes that are 0.7 inch in side length.
If a rectangular prism has 60 cubes along its length, 3 cubes along its width, and 2 cubes along its height, we must determine the volume of the prism.
The rectangular prism's length would be,
l = 60 × 0.7
L=42 inches.
The rectangular prism's width would be,
w = 3 × 0.7
w = 2.1 in.
The rectangular prism's height would be,
h = 2 × 0.7
h=1.4 of an inch
Consequently, the rectangular prism's volume would be,
V = l × w × h
V = 42 × 2.1 × 1.4
123.48 cubic inches equals V.
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Note: The correct question would be as follow,
A rectangular prism is packed with cubes that have a side length of 0. 7 inches if a total of 60 cubes is used 3 cubes along the width, and 2 cubes along the height, what is the volume of the prism?
how many numbers among the second one thousand natural numbers are not multiples of any of the first three odd prime number
The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.
A natural number is not a multiple of the first three odd prime numbers (3, 5, 7) if and only if it is not divisible by any of them. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 3. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 5. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 7. However, if a number is divisible by 3 and 5, it is also divisible by 15 and we have counted it twice. Similarly, if a number is divisible by 3 and 7, or 5 and 7, or all three, we have counted it thrice, twice and thrice respectively. Hence, the total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.
Therefore, The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.
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The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.
A natural number is not a multiple of the first three odd prime numbers (3, 5, 7) if and only if it is not divisible by any of them. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 3. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 5. There are 1000-999=1 number among the second one thousand natural numbers that is not divisible by 7. However, if a number is divisible by 3 and 5, it is also divisible by 15 and we have counted it twice. Similarly, if a number is divisible by 3 and 7, or 5 and 7, or all three, we have counted it thrice, twice and thrice respectively. Hence, the total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.
Therefore, The total number of numbers among the second one thousand natural numbers that are not multiples of any of the first three odd prime number is 1 + 1 + 1 - 1 - 1 + 1 = 2.
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