Explanation
Let the cost of the drink be x.
Therefore;
[tex]\begin{gathered} cost\text{ of dish+cost of drinks =total cost} \\ 11.99+x=14.48 \\ x=14.48-11.99 \\ x=2.49 \end{gathered}[/tex]Answer: 2.49 dollars
| Log Out Which function has a y-intercept that is equivalent to the y intercept of 3x - 4y = 16? A y = 4x + 1 B y = - 4x + 16 © y = 3x + 4 D y = 2x - 4
The slope-intercept form of a line is given by:
y = mx + b
where:
m = slope
b = y-intercept
From:
[tex]\begin{gathered} 3x-4y=16 \\ 4y=3x-16 \\ y=\frac{3}{4}x-4 \end{gathered}[/tex]Therefore, the y-intercept of this line is -4.
Hence, the correct option is:
[tex]y=2x-4[/tex] A = {2, 3, 4, 5, 6, 7}
B = {2, 4, 7, 8)
C = {2,4}.
Which of the following mathematical statements is true?
The mathematical statement is as follows:
(a) B ⊄ A
(b) C ⊂ A
(c) B ⊄ C
(d) ∅ ⊂ B
(e) C ⊂ C
(f) C ⊂ B
What is meant by sets?A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
The way that sets are represented by a person is always the same: as a group of clearly defined objects or elements. A capital letter designates a set. The cardinal number of a set is the number of elements in the finite set.
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) and C = {2, 4}.
The mathematical statement is as follows:
(a) B ⊄ A
(b) C ⊂ A
(c) B ⊄ C
(d) ∅ ⊂ B
(e) C ⊂ C
(f) C ⊂ B
belongs to ⊂ sign is used if an element belongs to the given set and vice versa.
The complete question is:
Let A = {2, 3, 4, 5, 6, 7} B = {2, 4, 7, 8) C = {2, 4}. Fill in the blanks by ⊂ or ⊄ to make the resulting statements true.
(a) B __ A
(b) C __ A
(c) B __ C
(d) ∅ __ B
(e) C __ C
(f) C __ B
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anne took a test in chemistry she scored 20 markes out of 50 work out her percentge mark
Answer:
40%
Step-by-step explanation:
to change a fraction to a percentage multiply by 100% , that is
[tex]\frac{20}{50}[/tex] × 100% = 0.4 × 100% = 40%
Answer:
40%
Step-by-step explanation:
Total Mark = 50Mark obtained = 20Percentage = (Mark obtained/Total mark) x 100(20/50) x 100(2/5) x 1002 x 2040%3(x + 2) = 3x + 2
Show your work
i need help with this please check work when you finish answering
ANSWER :
The answer is A. 2π
EXPLANATION :
Period can be determine by getting the measurement of one complete cycle.
From the graph.
One complete cycle is the blue mark.
Therefore, the period is 2π
a committee on community relations in a college town plans to survey local businesses about the importance
The most appropriate choice for population and sample will be given by-
Second option is correct
44% is the percentage of non response
What is population and sample?
Population is the entire set of items from where the data is drawn for statistical study
A random selection of members of the population is known as sample.
Here
Number of business chosen at random = 50
Number of questionnaire returned by mail = 28
Number of non responses = 50 - 28
= 22
Since the committee plans to survey local businesses about the importance of students as customers, the population is all about local business.
Since the specific group from the population are 50 local businesses chosen by the committee, sample is the 50 to whom the questionnaire was sent
Percentage of non response = [tex]\frac{22}{50} \times 100[/tex]
= [tex]44[/tex] %
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Complete Question
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 50 businesses at random. Of these, 28 return the questionnaire mailed by the committee.
Identify the population and the sample for this study.
a)The population is all students in the college town and the sample is the 50 local businesses to whom the questionnaire was sent.
b)The population is all local businesses and the sample is the 50 to whom the questionnaire was sent.
c) The population is the 28 businesses who responded to the questionnaire and the sample is all local businesses.
d)The population is the 50 local businesses to whom the questionnaire was sent and the sample is the 28 who responded.
What is the rate (percent) of nonresponse?
(Use decimal notation. Give your answer as an exact number.)
A) list roots and multiplicity.B) domain and range C) degree : 4 D) equation (show work by solving for a)
ANSWER :
A. (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain : (-∞, ∞)
C. Range : (-16, ∞)
D. Degree : 4
E. f(x) = (x + 3)(x + 1)(x - 1)(x - 3)
EXPLANATION :
From the problem, we have a graph in the illustration.
A. Roots are the points in which the graph intersects the x-axis.
Multiplicity means how many times the graph intersects at the specific point.
Roots :
The graph intersects at (-3, 0) multiplicity 1, (-1, 0) multiplicity 1, (1, 0) multiplicity 1 and (3, 0) multiplicity 1.
B. Domain and Range.
Domain is the set of x-values in the graph.
Range is the set of y-values in the graph.
From the graph,
Domain :
x values are all real numbers. (-∞, ∞)
Range :
y values are from y = -16 to the positive infinity. That will be (-16, ∞)
C. Degree : 4
D. The equation of a function with a degree of 4 is given by :
[tex]f(x)=a(x-b)(x-c)(x-d)(x-e)[/tex]where a = coefficient
b, c, d and e are the roots of the function.
Since we already solved for the roots, that will be :
b = -3, c = -1, d = 1 and e = 3
The equation will be :
[tex]f(x)=a(x+3)(x+1)(x-1)(x-3)[/tex]Plug in the given point (0, 9) then solve for the value of "a"
[tex]\begin{gathered} 9=a(0+3)(0+1)(0-1)(0-3) \\ 9=a(3)(1)(-1)(-3) \\ 9=9a \\ a=\frac{9}{9} \\ a=1 \end{gathered}[/tex]The equation will be :
[tex]f(x)=(x+3)(x+1)(x-1)(x-3)[/tex]Zan took her dog, Simba, to the dog park on Saturday afternoon. There were more than 20 dogs running around the park when they arrived. Determine which inequality describes the dogs at the park. d < 20 d > 20 d ≥ 20 d ≤ 20
Answer:
Number 2 is the answer to this question.
The inequality to represent the given scenario is d>20. Therefore, option B is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, there were more than 20 dogs running around the park when they arrived.
Let the number of dogs be d.
So, the inequality is d>20
Therefore, option B is the correct answer.
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What is the value of 6x² - 4 when x = 5?
146
Step-by-step explanation:= 6x^2 - 4
= x = 5
= 6 x 5^2 - 4
= 5^2 = 25
= 6 x 25 - 4
= 150 - 4
= 146
Answer:
[tex]\underline{146}[/tex]Step-by-step explanation:
Plug in the value of x into the expression [tex]6x^2-4[/tex].
- You will obtain this: [tex]6(5)^2-4[/tex].
Then all you need to do is use the correct Order of operations to evaluate.
- For example, you need to square 5 first: [tex]6\cdot25-4[/tex].
Then, you need to multiply: [tex]150-4[/tex].
Then, you should subtract: [tex]146[/tex]
↣ I hope I could help!
- RosaliaA circle in the xy-plane has a center at G 3 1 42 3 and a radius that is units long. Which of the 15 following is an equation of the circle?
We are asked to find the equation of a circle on the xy-plane, with center (3/4 , 1/2) and a radius of 3/5 units. For doing so, we remember the general equation of a circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h,k) represents the center of the circunference, and r its radius.
In our example, we obtain that,
[tex]\text{Center}=(\frac{3}{4},\frac{1}{2})[/tex]And so,
[tex]\begin{gathered} h=\frac{3}{4},k=\frac{1}{2} \\ r=\frac{3}{5} \end{gathered}[/tex]Applying the above formula, we get that the equation of the circle will be:
[tex](x-\frac{3}{4})^2+(y-\frac{1}{2})^2=(\frac{3}{5})^2[/tex]This is:
[tex]\mleft(x-\frac{3}{4}\mright)^2+\mleft(y-\frac{1}{2}\mright)^2=\frac{9}{25}[/tex]What is the range of this data set?{5, 12, 15, 11, 15, 7, 15, 10, 13}8101215
We are asked to find the range of the following data
{5, 12, 15, 11, 15, 7, 15, 10, 13}
First, we need to sort the data in ascending order (least to greatest)
{5, 7, 10, 11, 12, 13, 15, 15, 15}
The range is given by
[tex]Range=\max -\min [/tex]The maximum value in the data set is 15
The minimum value in the data set is 5
So, the range is
[tex]\begin{gathered} Range=\max -\min \\ Range=15-5 \\ Range=10 \end{gathered}[/tex]Therefore, the range of the given data set is 10
POSSIBLE PC14. A bag contains:5 red marbles6 blue marbles3 green marbles4 black marbles2 yellow marblesA marble will be drawn from the bag and replaced 100 times.What is a reasonable prediction for the number of times agreen or black marble will be drawn?P (green or black)P=/100P=(write the whole ratio)P(green and red) without replacement
Solution
We have
5 red marbles
6 blue marbles
3 green marbles
4 black marbles
2 yellow marbles
For a total of 5+6+3+4+2 = 20 marbles
And we want to find the following probability:
p(green or black) = P(green) + P(black) - P(green and black) = 3/20 + 4/20 - 0/20 = 7/20
Equivalent to : 7/20 * 5/5 = 35/100
p(green and red) without replacement = 0/100
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
[tex]\textsf{Let $\boxed{x}=\boxed{\textsf{The total dollar amount of all phone sales}}$}\:.[/tex]
[tex]\textsf{Let $\boxed{y}=\boxed{\textsf{The total dollar amount of all computer sales}}$}\:.[/tex]
System of Equations
[tex]\boxed{x + y = 3600}[/tex]
[tex]\boxed{0.04x + 0.06y = 178}[/tex]
Step-by-step explanation:
Given information:
4% commission on the total dollar amount of all phone sales.6% commission on all computer sales.Total sales = $3600Total commission = $178Define the variables:
Let x = The total dollar amount of all phone sales.Let y = The total dollar amount of all computer sales.Convert the percentages into decimal form:
[tex]\implies \sf 4\%=\dfrac{4}{100}=0.04[/tex]
[tex]\implies \sf 6\%=\dfrac{6}{100}=0.06[/tex]
Therefore, the system of equations that could be used to determine the dollar amount of phone sales and computer sales is:
[tex]\begin{cases}x + y = 3600\\0.04x + 0.06y = 178\end{cases}[/tex]
Solving the system of equations
Rewrite the first equation to isolate y:
[tex]\implies x=3600-y[/tex]
Substitute the expression for x into the second equation and solve for y:
[tex]\implies 0.04(3600-y)+0.06y=178[/tex]
[tex]\implies 144-0.04y+0.06y=178[/tex]
[tex]\implies 144+0.02y=178[/tex]
[tex]\implies 0.02y=34[/tex]
[tex]\implies y=1700[/tex]
Therefore, Cameron made $1,700 of computer sales.
Substitute the found value of y into the first equation and solve for x:
[tex]\implies x+1700=3600[/tex]
[tex]\implies x=1900[/tex]
Therefore, Cameron made $1,900 of phone sales.
. G(x) is the function defined by the following graph. The graph window is: [-3,5,1] by [-60,80,10]
We are given a function and we are asked the following questions:
Part 1. Evaluate G(-1). The value of G(-1) is the value of the independent variable, that is the vertical axis when the dependent variable is -1, that is the horizontal axis. To find the value we draw a vertical line perpendicular to the horizontal at the value -1, until we intercept the graph, from there we draw a vertical line until we intercept the vertical axis. From the graph we see that:
[tex]G(-1)=20[/tex]Part 2. Evaluate G(2). This is the value of the independent variable when the dependent variable is 2. From the graph we see:
[tex]G(2)=-10[/tex]Part 3. Determine:
[tex]\frac{G(-1)^3-G(2)^2+4G(-1)}{10}[/tex]Replacing the known values:
[tex]\frac{(20)^3-(-10)^2+4(20)}{10}[/tex]Solving the operations:
[tex]\frac{8000-100+80}{10}=\frac{7980}{10}=798[/tex]. BUILD PERSEVERANCE Factor the algebraic
expression 7.2x²y-0.9xy².
3. Jamie's grade has increased 42 points over the last 6 weeks because he
has turned in homework and done a few retakes. If his grade increased the
same amount each week, what integer represents his change in grade?
Answer:
7
Step-by-step explanation:
(x = increase each week)
(6=weeks)
(42= total Grade Change)
Linear equation:
42=6x
Solved:
x=7
Consider the function given by the graph. What are
these values?
f(-2)=
f(0) =
f(4) =
The values of the function given by the graph are:
f(-2 ) = 2
f(0) = 3
f(4) = -1
The graph depicts an inequality equation with discontinuities. Points of discontinuity are breaks in the graph caused by an undefined point when the f(x) function is substituted with an x point that is not part of the solution. Looking at the graph of the provided function f(x), we can clearly see that the function f(x) increases in the interval (-∞ ,0] and subsequently decreases in the interval (0,∞).Furthermore, the function terminates at x=0.
(Because there is a gap in the graph and the function's left and right-hand limits are not equal at x=0)
So from the graph, we can determine the values of the functions as,
f(-2 ) =2
f(0) = 3
f(4) = -1
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Answer:
f(–2 ) = 2
f(0) = 3
f(4) = -1
Step-by-step explanation: i hope this helps :)
Research one of the methods listed above or another method of your choice for factoring trinomials of the form ax² + bx + c.State the method you are using and explain the process of factoring a trinomial in words, modeling the process by using examples that contain all the steps to factor the trinomial
The grouping (a · c) method is another method for factoring trinomials of the form ax² + bx + c.
The process of factoring a trinomial using the grouping method is,
First, find a GCF and then factor it out.The coefficient of the leading phrase an is then multiplied by the constant term c. List the elements of this product (a · c) to discover the pair of factors, f1, and f2, that add to b, the middle-term coefficient. When c is positive, the sign of the components of (a · c) is the same - Find the pair of factors that adds to b if the middle-term bx is positive. If the middle-term bx is negative, both factors are negative. When c is negative, the elements of (a · c) have the inverse sign - Find the pair of factors that subtracts to b. The largest of these factors has the same sign as the middle term.Rewrite the middle term bx with the components f1 and f2 from Step 2. The phrase currently has four terms: ax² + bx + c = ax² + f1x + f2x + cThen, as illustrated, group the expression's terms into binomial pairs: (ax² + f1x) + (f2x + c) Then, for each pair, factor out a GCF The terms will have a common binomial factor if the equation can be factored by grouping. To write the factorization, subtract the common binomial factor.Finally, double the result to confirm.Learn more about factoring trinomials at
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I'll give brainliest!
Answer:
The side length, s, of the square is 18
Step-by-step explanation:
The sides can be found by taking the square root of the area.
(Area)^1/2=s, where s = side.
(324)^1/2=18
what is 3 +(-4) on a number line
please helppppppppppppppppppppppppppppppp!
Answer:
(9 x 27) x 5
Step-by-step explanation:
First we have to figure out the powers. 3 To the power of 2 is 9 and 3 to the power of 3 is 27 so we first multiply that and later multiply 5
PLEASE HURRY ASAP
Which of the following could be an algebraic expression for the total cost of dinner, less a $10 coupon, divided by 4 people?
(x − 10) ÷ 4
4x − 10
10 − 4x
4x(10)
Answer:
(x − 10) ÷ 4
Step-by-step explanation:
So, the equation is trying to figure out how much each person is paying. x = the whole dinner. Then, you take away $10 from the total cost. Then, with that discounted cost, you're dividing by 4 people to figure out how much each person is paying.
Please help ASAP
Question is attached below
Answer:
√30/4
I Hope that This Helped!
sixty and four hundredths in decimal form
60 + 0.04 = 60.04
The answer is 60.04
In the the diagram to the right, sphere O with radius 5 cm is intersected by a plane 4 cm from center O. Find the radiusof the cross section O A
Since a right triangle is formed, the radius of the cross-section is the missing side of the triangle.
Apply the Pythagorean theorem:
C^2 = a^2 + b^2
Where:
c = hypotenuse = 5
a & b = the other 2 legs of the triangle = 4 and x
Replacing:
5^2 = 4^2 + x^2
solve for x ( radius of the cross-section)
25 = 16 + x^2
25-16 = x^2
9 = x^2
√9 = x
x = 3 cm
Find the volume of the cylinder. Either enter an exact answer in terms of or use 3.14 for 4 units 3 Stuck? Watch a video or use a hint.
the volume of a cilinder is:
[tex]V=\pi r^2h[/tex]So we can replace the radius and the high so:
[tex]\begin{gathered} V=\pi6^24 \\ V=36\cdot4\cdot\pi \\ V=144\pi \end{gathered}[/tex]Now we can replace pi by 3.14 so:
[tex]undefined[/tex]A clerk spent his 35-hour workweek as follows: 1/5 of his time in sorting mail; 1/2 of his time in filing letters; and 1/7 of his time in reception work. The rest of his time was devoted to messenger work. The percentage of time spent on messenger work by the clerk during the week was most nearly:
A 6%
B 14%
C 10%
D 16%
So , the percentage of time spent on messenger work by the clerk during the week was most nearly is 16%.
How to find percentage?From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.
35 h * 1 / 5 = 7 h
35 h * 1 / 2 = 17.5 h
35 h * 1 / 7 = 5 h
7 h + 17.5 h + 5 h
= 29.5 h
The rest of his time = 35 - 29.5
= 5.5 h
5.5 / 35 = 0.15714
= 15 .714 %
Approx. 16 %
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Solve the following formula for t.
Q=M + Mrt
t= (Simplify your answer.)
Mathematical objects other than numbers can be used in operations. Here, t can be expressed as [tex]\frac{Q-M}{r}[/tex].
What are mathematical operations?Binary and unary operations are the two most popular forms of operations. Trigonometric functions and negation are examples of unary operations that use only one value. Contrarily, binary operations, which include addition, subtraction, multiplication, division, and exponentiation, only accept two values.
Mathematical objects other than numbers can be used in operations. Logic operations like and, or, and not can be used to combine the logical values true and false. It is possible to add and subtract vectors. Utilizing the function composition operation, it is possible to combine rotations by first performing the first rotation and then the second. The binary operations union and intersection as well as the unary operation of complementation are operations on sets. Composition and convolution are two operations on functions.
Solving for t,
Q = M + Mrt
t = [tex]\frac{Q-M}{r}[/tex]
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Nicholas earned $2,000.00 working over the summer and wants to put the money into a savings account. A savings account at bank A earns 5% simple interest and a savings account at bank B earns 4% interest compounded quarterly. If Nicholas plans to deposit the $2,000.00 and leave it in the account for 4 years, at which bank would he earn more interest? A. The interest earned cannot be calculated from the given information. B. The interest earned at both banks will be the same. C. bank A D. bank B
Answer:
Choice C
==> Bank A
Step-by-step explanation:
Principal P = $2000
Bank A calculation
Simple Interest at 5% for 4 years = Prt = 2000 x 5/100 x 4 = $400
Bank B Calculation
At 4% interest compounded quarterly, the accrued value(Principal + Interest) is given by the formula:
[tex]A = P(1 + r/n)^{nt}[/tex]
where
P = principal
r = annual interest rate as percentage
n = number of compounding per year
t = number of years
We have r = 4/ 100 = 0.04
n = 4 since interest is computed quarterly or 4 times a year
t = 4 years
[tex]A = 2000 ( 1 + 0.04/4)^{(4) \cdot (4)}\\\\A = 2000 (1.01)^{16} = \$2,345.16\\\\\text{Interest } = 2345.16 - 2000 = $345.16[/tex]
Since interest earned at bank A (400) > interest earned at bank B(345.16), the answer would be C. ==> Bank A
yes I am having problems learning about equations
If we have a function [Equation] it would look something like this:
3x+y=4
In order to solve for both values and graph it [If that's what you are trying to do], you solve for y and then replace values [Of your own choosing, or they are given to be studyed] in x, after we replace the values in x, we are going to have the respective value of y.
From our previous example, it would be:
y = -3x+4
So, when we start replacing the values of X, we will get the respective values for Y, let's try doing it from -3 to 3.
x = -3 => y = -3(-3)+4 => y = 13
x = -2 => y = -3(-2)+4 => y = 10
x = -1 => y = -3(-1)+4 ) => y = 7
x = 0 => y = -3(0)+4 => y = 4
x = 1 => y = -3(1)+4 => y = 1
x = 2 => y = -3(2)+4 => y = -2
x = 2 => y = -3(3)+4 => y = -5
From this, we would end up with the following points:
(-3, 13)
(-2, 10)
(-1, 7)
(0, 4)
(1, 1)
(2,