The number of days it would take if both Sonia and Jennifer work together on the job is 1 7/8 or 1.875 days.
How long would it take them working together?Let the amount of time (in days) that it would take both Sonia and Jennifer working together to paint Sonia's room be t. Additionally, the amount of work done by both Sonia and Jennifer to paint her room in 1 day is given by:
The amount of work done by Sonia in 1 day is 1/x or 1/3.
The amount of work done by Jennifer in 1 day is 1/y or 1/5.
Therefore, the amount of work done by both Sonia and Jennifer working together to paint Sonia's room in 1 day is given by this mathematical expression:
Combined work done = 1/x + 1/y
Combined work done = 1/3 + 1/5
Combined work done = 8/15
Next, we would calculate the combined time as follows:
8/15 × t = 1
Combined time, t = 15/8
Combined time, t = 1 7/8 or 1.875 days.
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Which expression is equivalent to (3 5i)2? –16 30i 6 34i –16 – 34i 16 30i
As per the concept of complex number, the equivalent expression to the given complex number is: –16 + 30i.
In math, the term complex number is defined as the following form:
=> a+bi,
where a and b are real numbers.
where the variables: a is the real part and bi imaginary part.
Here we have given that the complex expression: (3+5i)²
And we need to find the equivalent expression for this one.
Here we know that the same properties used for real numbers can be applied to complex numbers.
According to this rule, we have to solve the operations math with these numbers, it is important to know that i²= -1.
As we know that the algebraic expressions are considered equivalent when they are equal.
Therefore, for solving this question, you should:
We have to apply the power rules and then select the option that is equal to the result found.
= > (3+5i)²
Now it can be expanded like the following,
=> 9+30i+25i²
Apply the rule,
=> 9+30i+25*(-1)
=> 9+30i-25
=> -16 + 30i
Therefore, option (a) is correct.
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Find the indicated side of the triangle?
What does A equal to?
What is included in the triangle:
A, B,7,30
Also please show your work?
The ratio of any two right-angled triangle sides may be used to compute trigonometric ratios.
How is trigonometric ratio rule calculated ?You may determine trigonometric ratios by either utilising the provided acute angle or by figuring out the ratios of the right-angled triangle's sides. The formulae for trigonometric ratios are sin = Perpendicular/Hypotenuse and cos = Base/Hypotenuse.Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. The sin, cos, and tan functions may be used to obtain the other significant trig ratios, cosec, sec, and cot.The ratio of any two right-angled triangle sides may be used to compute trigonometric ratios. The Pythagorean theorem may be used to evaluate the third side.Given details :
The measurement of the given angle is 30 degree.
Here we use trigonometric ratio rule which is sin theta= opposite/hypotenuse
Here theta = 30 degree, opposite =7 and hypotenuse =a
So we get
sin 30 = 7/a
a= 7/sin 30
And value of sin 30 = 0.5
So we get , a = 7/0.5 = 14
So the value of a is 14 .
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The purpose of a interview
Answer:
To make sure who ever want the job is reliable and suitable for it.
Step-by-step explanation:
Cassie drive 165 miles in 3 hours. Circled the numbers that make the rates below equivalent to the rate 165 miles in 3 hours.
Answer: I Do not know specifically but If we are talking about rates/per hour the answer is 55 Per hour
Step-by-step explanation:
165 miles ÷ 3 hours because It may be talking about rates. Per "HOUR"
It costs £5.33 for 650g of beef steak. What is the price per kg?
Answer: 8.20
Step-by-step explanation:
1kg = 1000g
take 650 divided by 1000 = 0.65kg
Then take 5.33 divided by 0.65 = 8.20
Rewrite the following equation in slope-intercept form. y − 9 = –10(x − 10)
Answer:
y = -10x + 109
Step-by-step explanation:
Given equation,
→ y - 9 = -10(x - 10)
The slope-intercept form is,
→ y = mx + b
Rewrite in slope-intercept form,
→ y = mx + b
→ y - 9 = -10(x - 10)
→ y - 9 = -10x + 100
→ y = -10x + 100 + 9
→ [ y = -10x + 109 ]
Hence, answer is y = -10x + 109.
A project calls for a 50 in. long board to be cut into three pieces. The first piece must be twice the length of the second piece. The third piece is 10 in. shorter than the second piece. How long must each piece be?
Answer:
Step-by-step explanation:
la première planche = 2x
la deuxième = x
la troisième = x-10
1ere planche + 2eme planche + 3eme planche = 50 pouces
donc :
(2x) + x + (x-10) =50
4x-10 = 50
4x-10+10 = 50 +10
4x = 60
4x diviser par 4 = 60 diviser par 4
x=15
la première planche = 30
la deuxième = 15
la troisième = 5
30+15+5=50
let $p$ be a prime number between 40 and 60. what is the probability that $p 12$ is also a prime number? express your answer as a common fraction.
The probability is: 3/5
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
There are : 41 | 43 | 47 | 53 | 59 (5 primes) Between 40 and 60.
41 + 12 =53 is a prime
43 + 12 =55 Not a prime
47 + 12 =59 is a prime
53 + 12 =65 Not a prime
59 + 12 =71 is a prime
Therefore, the probability is: 3/5
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can someone help me with these questions only five of them.
Answer:
Step-by-step explanation:
For number 1, It is $52.4
Divide the cost by the number f days to get your constant
for number 2, It is 2
Just format it to y=mx+b
I do not know the answer to the third one
And the fourth one it is true with a 1/25 fraction
a quadratic equation can be written in vertex form or in standard form sometimes one form is more beneficial than the other Identify which form would be more helpful if you needed to do each task listed below and explain why. A .factor the equation. B graph the parabola.C identify the vertex minimum or maximum of the parabola D and solve the equation using the quadratic formula
a. In order to factor the equation, the vertex form needs to be expanded to the standard form first, to obtain the factors of the equation
b. The parabola is easily graphed with the information on the vertex given in the vertex form of the quadratic equation
c. The vertex, minimum or maximum of the parabola are easily obtained in the vertex form of the quadratic equation
d. The quadratic formula is defined based on the standard form of the quadratic equation
Answer:
[tex]\huge{\boxed{\text{A) Standard form}}}\\\huge{\boxed{\text{B) Vertex Form}}}\\\huge{\boxed{\text{C) Vertex Form}}}\\\huge{\boxed{\text{D) Standard Form}}}\\[/tex]
Step-by-step explanation:
Vertex form is represented as: [tex]f(x) = a(x-h)^2+k[/tex], where the vertex of the parabola is (h, k).
Standard form is represented as [tex]f(x) = ax^2+bx+c[/tex], where a, b, and c are constants.
A) When factoring an equation, the sum of the roots is equal to b and the sum of the roots is equal to c, meaning standard form is the beneficial.
B) When graphing a parabola, vertex form is extremely beneficial, as it provides the vertex of the parabola, and the direction in which it opens. If "a" is positive, the vertex opens upward, while when "a" is negative, the vertex opens downward. As such, graphing is greatly eased with this information.
C) As is evident from the name, vertex form is the best for identifying the vertex of a parabola, as it is explicitly shown via the constants h and k.
D) The quadratic formula directly uses the constants a, b, and c, so working in standard form is more beneficial, as it removes the effort of solving for each constant.
Hope it helps :) and let me know if you want me to elaborate.
2(a+c) =5(a-b) make c the subject
Please someone help me I need help
Answer:
Yes
Step-by-step explanation:
Since the point is in the intersection area (purple) of the lines it is a solution.
Solve for x ?????????????????
Answer:
x = 7
Step-by-step explanation:
Compare the ratios of the longer side length to the shorter side length:
8 : 10 = (3x - 9) : 15
8*(3/2) : 15 = (3x - 9) : 15
Then, form an equation.
8 * (3/2) = 3x - 9
12 = 3x - 9
21 = 3x
7 = x
45 points pls help
In the equation y=mx +b
What is the meaning of the M and the b. Explain in your own words what kind of thinking are you engaged in
In the equation y = mx + b, the meaning of the m and the b is
m is the slopeb is the y interceptWhat is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + b
How to determine the meaning of m and bInformation gotten from the question include
In the equation y = mx + b
m = ? and b = ?
y = mx + b
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
b = y intercept
therefore m and b are the slope and y intercept respectively
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y is greater than negative 4 over 3x plus 2
In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .
What is Standard Form of a Equation ?
Ax+By=C
The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).
The standard form of a linear equation is helpful for determining the x and y-intercepts of a graphed equation. It also helps you understand the concept of least common denominators, which is finding the lowest number to multiply and thus convert two fractions into whole numbers.
Given Equation :[tex]y = -\frac{4x}{3} + 2\\[/tex]
To convert it into Standard form , Multiply both sides with 3
[tex]3y = 3(\frac{-4x}{3} +2)[/tex]
[tex]3y = -4x + 6\\4x + 3y = 6[/tex]
Hence , In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .
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The vertex is always the highest point of a function.
True false question.
True
False
Answer:
False!
Step-by-step explanation:
See picture for examples.
[tex]x^{2} +11x +24[/tex]
The factored form of the equation x² + 11x + 24 is (x + 3)(x + 8).
How to factor quadratic equation?A quadratic equation is an algebraic equation of the second degree in x. Quadratic equation can be represented in standard form as follows:
ax² + bx + c
where
a, b and c are constantFactoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.
Therefore, let's factor the equation x² + 11x + 24 as follows:
x² + 11x + 24
The two numbers we can add to get 11 and multiply to get 24 are 3 and 8.
Therefore,
x² + 3x + 8x + 24
x(x + 3) + 8(x + 3)
Hence, the factored form is (x + 3)(x + 8)
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a sports analyst claims that the mean batting average for teams in the american league is not equal to the mean batting average for teams in the national league because a pitcher does not bat in the american league. what hypothesis test would be used to test that batting average for teams in the american league is not equal to the batting average in the national league?
Hypothesis test used to test the batting average of the two given team national league and American league is given z-test.
As given in the question,
Given : Mean batting for American league is not equal to Mean batting for National league.
Here two teams are given representing sample size of the population.Hypothesis tests help us to make decisions or conclusion about the value of the given parameters, such as the population mean. Based on it two approaches are used for conducting a hypothesis test one is the critical value and the P-value test.If in the given data population standard deviation (σ) can be calculated, a hypothesis test used for one population mean is z-test. A z-test represents the hypothesis test which is used to test a population mean, μ, against a considered population mean, μ₀.Therefore, hypothesis test used to test the batting average of the national league and American league is given z-test.
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Last night, the two dinner specials at Dwayne's favorite restaurant were salmon filet and steak. The restaurant served 25 specials in all, 24% of which were salmon filets. How many salmon filets did the restaurant serve?
HELPP
Last night, the two dinner specials at Dwayne's favorite restaurant were salmon filet and steak. The restaurant served 25 specials in all, 24 percent of which were salmon filets 6 salmon filets did the restaurant serve.
What exactly do percentages mean?10%, a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.
How do you calculate a percentage of a number?A percentage in mathematics is a figure or ratio that may be stated as a fraction of 100. If we need to determine a percentage of a number, we should divide it by 100 and multiply the result.
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A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?
A rectangle is transformed according to the rule R0, 90º.
What does parallelogram mean ?
A quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size.
Additionally, the internal angles on the same transverse side are supplementary. 360 degrees is the sum of all interior angles.
We are given that the rotation is
(x,y) --------> (x,y)
This means that the point is rotated back into its original position.
This means that full rotation occurred.
Since the full rotation is 360°,
For the other options:
Rotation 90° gives:
(x,y) ----------> (-y,x)
Rotation 180° gives:
(x,y) ----------> (-x,-y)
Rotation 270° gives:
(x,y) ---------> (y,-x)
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a satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. each unit contains the same number of non-upgraded sensors. if the number of non-upgraded sensors on one unit is 15 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
Fraction of the sensors on the given satellite which have been upgraded is equal to option D. 1/7.
As given in the question,
Total number of modular units = 30
Let 'n' be the total number of upgraded sensors available on the entire satellite
Number of non-upgraded sensors available on one unit = ( 1/5)n
= x/5
Number of non-upgraded sensors available on 30 modular unit
= 30n /5
= 6n
Total number of non- upgraded and upgraded sensors makes one unit
⇒n + 6n = 1
⇒7n = 1
Fraction of upgraded sensors are:
⇒ n = 1/7
Therefore, the fraction of the sensors available on the satellite and are upgraded is equal to option D. 1/7.
The above question is incomplete , the complete question is:
A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
A. 5/6 B. 1/5 C. 1/6 D. 1/7 E. 1/24
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Write a y=mx+b equation that has a slope of -1/7. Passes through the point (-2, 4)
Answer:y=-1/7x+26/7
Step-by-step explanation: y=mx+b substitute m=-1/7
y=-1/7x+b
The line passes through the point (-2,4)
This means x=-2 and y=4 must be substituted in the above equation
4=-1/7*-2+b
4=2/7+b
Solve for b
To get b on its own we need take 2/7 from both sides
4-2/7=2/7-2/7+b
26/7=b
Need to solve 4/1-2/7
Must make denominators the same
Multiply top and bottom by 7
4*7/1*7-2/7
28/7-2/7=26/7
In a survey conducted on an SRS of 200 American adults, 72% of them said they believed in aliens Give a 95% confidence interval for percent of American adults who believe in aliens 6. Section 7.2; Problem 6: Have the assumptions been met? A. Yes. Values of 72 and 28. B. Yes. Values of 144 and 56. C. Yes. Values of 14400 and 5600. D. No. Values of 0.72 and 0.28. E. No. Values of 14.4 and 516
The assumptions been met (0.6581,0.7819).
What is American adults?
In 2020, the U.S. Census Bureau counted 331.4 million people living in the United States; more than three-quarters (77.9%) or 258.3 million were adults, 18 years or older — a 10.1% increase from 234.6 million in 2010.
Given that.
[tex]$$\begin{aligned}& p=0.72 .(1-p)=1-0.72=0.28 \\& n=200 .\end{aligned}$$[/tex]
At [tex]$95 \%$[/tex] confidence level x value is 1.96
z=1.96
So r
A 95 % confidence interval bor percent of American adults who beleive in Aliens is,
[tex]$$\begin{gathered}p \pm 2 \sqrt{\frac{p \times q}{n}} \\\therefore 0.72+1.96 \sqrt{\frac{0.72 \times 0.28}{200}} \\\therefore 0.72 \pm 1.96 \sqrt{0.0010} \\0.72 \pm 0.0619 \\\therefore \quad(0.6581,0.7819)\end{gathered}$$[/tex]
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Decide whether each equation is true for all, one, or no values of x.
The description of each equation in comparison with its' right hand side is;
A) True for all values of x.
B) True for no values of x.
C) True for no values of x.
D) True for no values of x.
E) True for all values of x.
F) True for no values of x.
G) True for no values of x.
H) True for all values of x.
How to solve Linear equations?
A) We are given the equation;
7x - 5
This can also be written as; -5 + 7x and so the right hand side is true.
B) We are given the equation as 5x - 7.
There is no 4 in the equation and so the right hand side is wrong.
C) We are given the equation as -3x + 5.
The coefficient of x is -3 and not -4 and so the right hand side is wrong.
D) We are given the equation as;
3x - 32 + 4(4x - 2463)
By basic inspection, the right hand side cannot be true because we can see a very huge value in this bracket.
E) We are given the equation as 7x - 9 + 3(6x + 3)
Expanding the bracket gives;
7x - 9 + 18x + 9 = 25x
Thus, the right hand side is correct.
F) We are given the equation as 3x + 9
The equation does not contain -4 and 20 and so the right hand side is wrong.
G) We are given the equation as 10(2x - 3)
Multiplying the bracket gives 20x - 30. Thus, the right hand side is wrong
H) We are given the equation as 4(4x + 3) - 3x
Multiplying out the bracket gives us;
16x + 12 - 3x = 13x + 12
Thus, the right hand side is correct.
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The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 600 people. By selling tickets, the members would like to raise $3,300 every night to cover all expenses. Let d represent the number of adult tickets sold at $7.50. Let s represent the number of student tickets sold at $4.50 each. If all 600 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly $3,300? At one performance there were two times as many student tickets sold as adult tickets. If there were 360 tickets sold at that performance, how much below the goal of $3,300 did ticket sales fall??
By using simultaneous linear equation, it can be calculated that-
200 adult tickets and 400 student tickets were sold
In another performance, ticket sale falls $1320 below the goal of $3300
What is simultaneous linear equation?
At first it is important to know about linear equation
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a simultaneous linear equation needs to be solved
Here, d represents the number of adult tickets and s represents the number of student tickets
Their auditorium holds 600 people
d + s = 600 ..... (1)
Price of adult ticket = $7.50
Price of student ticket = $4.50
Total price = $(7.50d + 4.50s)
By the problem,
7.50d + 4.50s = 3300
5d + 3s = 2200 ..... (2)
Multiplying (1) by 3
3d + 3s = 1800.... (3)
Subtracting (3) from (2)
2d = 400
[tex]d = \frac{400}{2}[/tex]
d = 200
Putting the value of d in (1)
200 + s = 600
s = 600 - 200
s = 400
Now,
At one performance there were two times as many student tickets sold as adult tickets.
Total tickets sold = d + 2d = 3d
By the problem-
3d = 360
d = [tex]\frac{360}{3}[/tex]
d = 120
s = 2 [tex]\times[/tex] 120 = 240
Number of student ticket sold = 240
Number of adult ticket sold = 120
Total cost = 240 [tex]\times[/tex] 4.50 + 120 [tex]\times[/tex] 7.50
= $1980
Fall in ticket sale = $(3300 - 1980) = $1320
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I need help on this question.
Answer:
x=43
Step-by-step explanation:
Since the two interior angles of a triangle always add up to the exterior angle (d=a+b btw if u dont understand what i mean), x+90=133
x=133-90
x=43
Work out the value of (6. 31 * 10 ^ 5) + (2. 6 * 10 ^ 4) give your answer in standard form.
The standard form of (6.31×10⁵ ) + (2.6×10⁴) is 65.7 × 10⁴.
What is a simplification of an expression?
Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
As given,
(6.31×10⁵ ) + (2.6×10⁴) = ( 6.31× 10⁴ ×10 ) + (2.6 × 10⁴ )
= ( 6.31 × 10 + 2.6 )
= ( 63.1 + 2.6 )
= ( 65.7 )
= 65.7 × 10⁴
Hence, the standard form of ( 6.31× 10⁵) + (2.6 × 10⁴) = 65.7 × 10⁴.
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Which expression represents the correct form for the quotient and remainder, written as partial fractions, of startfraction 8 x cubed minus 2 x squared minus 67 x minus 24 over 2 x squared minus x minus 21 endfraction?.
The remainder and quotient are written as the following partial fractions:
Quotient: [tex]4x + 1[/tex]
Reminder: [tex](18x - 3)[/tex]
Divide the leading term of the numerator by the leading term of the denominator to obtain the first term of the quotient:
[tex]\dfrac{8x^3} { 2x^2} = 4x[/tex]
Multiply the entire denominator by the first term of the quotient, then subtract it from the numerator:
[tex](4x)(2x^2 - x - 21) = 8x^3 - 4x^2 - 84x\\\\(8x^3 - 2x^2 - 67x - 24) - (8x^3 - 4x^2 - 84x) = 2x^2 + 17x - 24[/tex]
With the new numerator, repeat steps 1 and 2 [tex](2x^2 + 17x - 24)[/tex] and the original denominator [tex](2x^2 - x - 21)[/tex]:
[tex]\dfrac{2x^2} { 2x^2} = 1\\(1)(2x^2 - x - 21) = 2x^2 - x - 21\\(2x^2 + 17x - 24) - (2x^2 - x - 21) = 18x - 3[/tex]
The resulting numerator [tex](18x - 3)[/tex] is the remainder.
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Find the point where the line x = t, y = 1 + t, z = 1 − t intersects the plane 13x + 11y + 20z = 39
The plane 13x + 11y + 20z = 39 is where the line x = t, y = 1 + t, and z = 1 t cross (2,3,-1).
What is plane?A plane is an infinitely long, Euclidean, two-dimensional surface in mathematics. A plane is a point, a line, and three-dimensional space's equivalent in two dimensions. In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used.
Here,
13t+11(1+t)+20(1-t)=39
13t+11+11t+20-20t=39
4t+31=39
4t=8
t=2
x=2, y=3, z=-1
The line x = t, y = 1 + t, z = 1 − t intersects the plane 13x + 11y + 20z = 39 at (2,3,-1).
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bro i need help on this thing please help
The value of x is 21.
What are similar figures?If the ratios of the lengths of the respective sides of two figures are the same and their corresponding angles are congruent, then the figures are said to be similar.
Given that, the corresponding angles of the two trapezoids are equal, therefore, the trapezoids are similar.
Since the trapezoids are similar, the ratio of their corresponding sides are in proportional:
14/18 = x/27
x = 27× (14/18)
x = 21
Hence, the value of x is 21.
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