Answer:
672
Step-by-step explanation:
If we call the number of non-fiction books as x, the number of fiction books would be 3x. Therefore: we can write the following equation:
3x - 120 = 2(x - 24) ← the 3x - 120 and x - 24 represents the new number of books
3x - 120 = 2x - 48
x - 120 = 48
x = 168 which means 3x = 3 * 168 = 504, therefore the total number of books is 168 + 504 = 672.
Shawna spent half of her weekly allowance playing arcade games. To earn more money her parents let her clean the windows in the house for $4.37. What is her weekly allowance if she ended with $11.18?
Answer:
$13.62
Step-by-step explanation:
By working backward we can see that before she cleaned the windows she had $6.81.
We know that she spent half her allowance on the arcade and the $6.81 she had before cleaning the windows is the other half.
So, if you multiply by 2 you get that here weekly allowance is $13.62.
Answer:
$13.62
Step-by-step explanation:there
The admission fee at an amusement park is $1.50 for children and S4 for adults. On a certain day, 289 people entered the park, and the admission fees collected totaled 746.00 dollars. How many children and
how many adults were admitted?
number of children equals
number of adults equals?
Set up two equations:
Let a = adults and c = child:
a + c = 289 ( rewrite as a = 289 - c)
1.50c + 4a = 746
Replace a with the rewritten formula:
1.50c + 4(289-c) = 746
SImplify:
1.50c + 1156 - 4c = 746
Combine like terms:
-2.50c + 1156 = 746
Subtract 1156 from both sides:
-2.50c = -410
Divide both sides by -2.50
c = -410 / -2.50 = 164
Number of children = 164
Number of adults = 289 - 164 = 125
Answer:
[tex] x+y = 289[/tex] (1) total people entered
[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected
From the first equation we can solve for x and we got:
[tex] x = 289-y[/tex] (3)
Replacing (3) into (2) we got:
[tex] 1.5(289-y) +4y = 746[/tex]
And solving for y we got:
[tex] 433.5 -1.5 y +4y = 746[/tex]
[tex] 2.5 y= 312.5[/tex]
[tex]y=\frac{312.5}{2.5}= 125[/tex]
And then using (3) we can solve for x and we got:
[tex] x= 289-125= 164[/tex]
So then we have:
number of children = 164
number of adults = 125
Step-by-step explanation:
Let x the number of children and y the number of adults. From the info given we can set up the following equations:
[tex] x+y = 289[/tex] (1) total people entered
[tex] 1.50 x +4 y = 746[/tex] (2) total amount collected
From the first equation we can solve for x and we got:
[tex] x = 289-y[/tex] (3)
Replacing (3) into (2) we got:
[tex] 1.5(289-y) +4y = 746[/tex]
And solving for y we got:
[tex] 433.5 -1.5 y +4y = 746[/tex]
[tex] 2.5 y= 312.5[/tex]
[tex]y=\frac{312.5}{2.5}= 125[/tex]
And then using (3) we can solve for x and we got:
[tex] x= 289-125= 164[/tex]
So then we have:
number of children = 164
number of adults = 125
The amount of time (t) in minutes it takes to make a coffee at Starbucks is related to (n) the number of coffees they purchase. The equation is t =2n-3. How long does it take if a customer buys 5 coffees ?
Answer:
7 minutesStep-by-step explanation:
Given the expression for time
[tex]t =2n-3[/tex]
say a customer buys 5 coffees, hence n=5
substituting n=5 into the function time it takes to prepare a coffee we have the time it will take to prepare 5 coffees
[tex]t= 2(5)-3\\t=10-3\\t=7[/tex]
Hence it will take 7 minutes to prepare 5 coffees
Which parent function is represented by the graph?
A. The quadratic parent function
B. The absolute value parent function
C. An exponential parent function
D. The linear parent function
Answer:
D. The linear parent function
Step-by-step explanation:
Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.
Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;
m= gradient of the straight line graph
x= the independent variable
y= the dependent variable
c= the vertical intercept
Answer:
The linear parent function :)
Step-by-step explanation:
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for
itself since the time it takes to produce the product using the new machine is significantly less than the
production time using the old machine. To test the claim, independent random samples were taken from
both machines. You are given the following results.
New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain your
Answer:
Step-by-step explanation:
We will develop a test to compare the mean of two population
Population 1.
population mean μ₀₁ = 25 ; Sample variance 27 ; and sample size n = 45
Population 2.
population mean μ₀₂ = 23 ; Sample variance 7,56; and sample size n = 36
As our major interest is to investigate if the new machine uses less time for the same production, the test will be a one tail test ( left test)
Test Hypothesis
Null Hypothesis H₀ ⇒ μ₀₂ - μ₀₁ = 0
Alternative Hypothesis Hₐ ⇒ μ₀₂ - μ₀₁ < 0
We will use confidence of 90 %, therefore α = 10 % α = 0,1
α = 0,1
We get z score of z = 1,28 or z = - 1,28 ( left tail)
And compute z(s) = ( μ₀₂ - μ₀₁ ) /√ (s₁)²/n₁ + (s₂)²/n₂
z(s) = - 2 / √(729/45) + (57,15/36)
z(s) = - 2 / √16,2 + 1,59
z(s) = - 2 / 4,2178
z(s) = - 0,4742
As |z(s)| < |z(c)|
We are in the acceptance region. If we lok at 90 % as Confidencial Interval α = 0,1 and α/2 = 0,05 in this case
₀,₉CI ( μ₀₂ - μ₀₁) = [ -2 ± z(0,05)√ (s₁)²/n₁ + (s₂)²/n₂ )
From z Table z ( 0,05 ) ⇒ z score z = 1,64
And √ (s₁)²/n₁ + (s₂)²/n₂ ) = √(729/45) + (57,15/36) = 4,2178
₀,₉CI ( μ₀₂ - μ₀₁) = [ -2 ± 1,64 *4,2178]
₀,₉CI ( μ₀₂ - μ₀₁) = ( - 8,917 ; 4,917 )
We can see that 0 is a possible value in the ₀,₉CI ( μ₀₂ - μ₀₁) so again we cannot reject H₀. Then as we are not quite sure about the strengths of the new machine over the old one we should not recomend to purchase the new machine
In an ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even. (Round your answer to four decimal places.) (a) What is the probability that a subject would guess exactly 18 correct in a series of 36 trials
Answer: The answer is 0.1350
Step-by-step explanation:
Given data
n=36
p=1/2
q=1/2
X=18
O=3
U = 18
a. With n = 36 and p = q = 1/2, you may use the normal approximation with µ = 18 and o = 3. X = 18 has real limits of 17.5 and 18.5 corresponding to z = -0.17 and z = +0.17. p = 0.1350.
The probability that a subject would guess exactly 18 correct in a series of 36 trials is 0.1350.
Given that,
ESP experiment subjects must predict whether a number randomly generated by a computer will be odd or even.
We have to determine,
What is the probability that a subject would guess exactly 18 correct in a series of 36 trials?
According to the question,
Number of trials n = 36
The probability must per whether a number randomly generated by a computer will be odd is 1/2 or even is 1/2.
By using the normal approximation,
[tex]\mu = 18 \ and \ \sigma = 3[/tex]
Therefore,
X = 18 has real limits of 17.5 and 18.5 corresponding to z = -0.17 and z = +0.17.
p = 0.1350
Hence, the probability that a subject would guess exactly 18 correct in a series of 36 trials is 0.1350.
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Examine the system of equations. y = 3 2 x − 6, y = −9 2 x + 21 Use substitution to solve the system of equations. What is the value of y? y =
Answer:
its 3/4
Step-by-step explanation: i got it right trust me
The solution to the system of equations will be x= 9 / 2 and y= 3 / 4.
What is a system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given equations are y=(3/ 2 )x-6 and y=(-9/2)x+21 to calculate the values of x and y using the substitution method.
Since both equations are equated to y, you just need to use substitution to create the equation below:
(3/ 2 )x-6 =(-9/2)x+21
Solve the equation for x:
(3/ 2 )x + (9/2)x = 27
x = 27 / 6 = 9 / 2
Plug x into any one of the given equations to find the value of y:
y=(3/ 2 )x-6
Solve for the value of y.
y=(3/2) x (9 / 2)-6
y = ( 27 / 4 ) - 6
y = ( 27 - 24 ) / 4
y = 3 / 4
Hence, the solution for the equation will be x = 9 / 2 and y = 3 / 4.
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Please answer this correctly without making mistakes
What is the correct answer library or theater
Answer:
theater
pls mark me as BRAINLIEST
Select the correct answer. Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing diameters of the circle. He labels the ends the diameters A, B, C, D, E, and F, and he uses a straightedge to draw the chords that form a hexagon. Which statement is true? A. Vincent’s construction method produces a hexagon that must be regular. B. Vincent’s construction method produces a hexagon that must be equilateral but may not be equiangular. C. Vincent’s construction method produces a hexagon that must be equiangular but may not be equilateral. D. Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
Answer:
B.
Step-by-step explanation:
Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular. The correct option is D.
What is a regular polygon?A regular polygon is a polygon that is equiangular and equilateral. Therefore, the measure of all the internal angles and the measure of all the sides of the polygon are equal to each other.
Given that Vincent wants to construct a regular hexagon inscribed in a circle. He draws a circle on a piece of paper. He then folds the paper circle three times to create three folds representing the diameters of the circle.
Now as it can be seen as the paper is folded as shown in the below image but it does not create a hexagon that is equilateral and equiangular.
Hence, Vincent’s construction method produces a hexagon that may not be equilateral and may not be equiangular.
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A 4 foot wide painting should be centered on a 10 foot wide wall. How many feet (x) should be on each side of the painting?
Answer:
3 feet
Step-by-step explanation:
To find x, we can write the following equation:
x + 4 + x = 10
2x + 4 = 10
2x = 6
x = 3 feet
Find The measure of the unknown angle.
1. Add the two known angles:___+___=___
2. Subtract the sum from 180°: 180-___=___
3. The measure of the unknown angle is:____
Answer:
L = 45°
Step-by-step explanation:
1. 82° + 53° = 135°
2. 180° - 135° = 45°
3. Angle L is 45°
I hope this helps.
How does a reflection across the y-axis change the coordinates of a shape?
Answer:
When you reflect a shape avross the y-axis, the y-coordinates stay the same, but the x-coordinates turn into its opposites.
Step-by-step explanation:
EXAMPLES:
(3,6)---(reflected over y-axis)--> (-3,6)
(9,2)---(reflected over y-axis)--> (-9,2)
Hope this helped! Brainliest would be really appreciated :)
What equation results from completing the square and then factoring? x^2+22x=31 A.(x+22)^2=53 B.(x+22)^2=152 C.(x+11)^2=152 D.(x+11)^2=53
Answer:
[tex]\boxed{\mathrm{Option \ C}}[/tex]
Step-by-step explanation:
=> [tex]x^2+22x = 31[/tex]
=> [tex](x)^2+2(x)(11) = 31[/tex]
Since b = 11 , So [tex](11)^2[/tex] needs to be added to both sides
Adding [tex](11)^2[/tex] to both sides
=> [tex](x)^2+2(x)(11)+(11)^2 = 31+(11)^2[/tex]
Completing the square
=> [tex](x+11)^2 = 31+121[/tex]
=> [tex](x+11)^2 = 152[/tex]
At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM
Answer:
The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.
Step-by-step explanation:
Vectorially speaking, let assume that ship A is located at the origin and the relative distance of ship B with regard to ship A at noon is:
[tex]\vec r_{B/A} = \vec r_{B} - \vec r_{A}[/tex]
Where [tex]\vec r_{A}[/tex] and [tex]\vec r_{B}[/tex] are the distances of ships A and B with respect to origin.
By supposing that both ships are travelling at constant speed. The equations of absolute position are described below:
[tex]\vec r_{A} = \left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i[/tex]
[tex]\vec r_{B} = \left(170\,km\right)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j[/tex]
Then,
[tex]\vec r_{B/A} = (170\,km)\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j-\left[\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i[/tex]
[tex]\vec r_{B/A} = \left[170\,km-\left(40\,\frac{km}{h} \right)\cdot t\right]\cdot i +\left[\left(15\,\frac{km}{h} \right)\cdot t\right]\cdot j[/tex]
The rate of change of the distance between the ship is constructed by deriving the previous expression:
[tex]\vec v_{B/A} = -\left(40\,\frac{km}{h} \right)\cdot i + \left(15\,\frac{km}{h} \right)\cdot j[/tex]
Its magnitude is determined by means of the Pythagorean Theorem:
[tex]\|\vec v_{B/A}\| = \sqrt{\left(-40\,\frac{km}{h} \right)^{2}+\left(15\,\frac{km}{h} \right)^{2}}[/tex]
[tex]\|\vec r_{B/A}\| \approx 42.720\,\frac{km}{h}[/tex]
The distance between the ships is changing at 42.720 kilometers per hour at 4:00 PM.
Simplify (4x)². Rewrite the expression in the form k ⋅ xⁿ
Answer:
16x²
Step-by-step explanation:
(4x)²4² *x²16*x² 16x²After Keith picked 9 lemons, he wanted to share them with his fellow classmates. If Keith wants to give 1 1/8 lemons to each of his classmates, then how many classmates will get some lemon?
Answer:
8 classmates
Step-by-step explanation:
[tex]9/1\frac{1}{8}=\\9/\frac{9}{8}=\\9*\frac{8}{9}=\\\frac{72}{9}=\\8[/tex]
Below are some of the scores on a math quiz given last week,
{82, 73, 74, 78, 46, 73}
What will happen to the mean of the quiz scores if the outlier is removed?
A
The mean will decrease.
OB
The mean will increase
C
There is not enough information given.
OD
The mean will not change.
Answer:
B: The mean will increase
Step-by-step explanation: The outlier is 46, which is way below all the other numbers, which is the definition of an outlier. If we remove a really low number from the set, then the mean(average) will increase.
subtract 2-3/4-1 1/10=
Answer:
23/20
Step by step Explanation
Answer:
3/20Step-by-step explanation:
[tex]2-\frac{3}{4}-1\frac{1}{10}=x\\x=2-\frac{3}{4}-\frac{11}{10}\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\x=\frac{2}{1}-\frac{3}{4}-\frac{11}{10}\\1,\:4,\:10\\\mathrm{Prime\:factorization\:of\:} ;\\1=1\\4=2\times \:2\\10=2\cdot \:5\\\mathrm{Multiply\:the\:numbers:}\:2\times \:2\times \:5=20\\Adjust\: fractions\: based\: on\: their\: LCM ;\\\frac{2}{1}=\frac{2\times \:20}{1\times \:20}=\frac{40}{20}\\\\\frac{3}{4}=\frac{3\times \:5}{4\times \:5}=\frac{15}{20}\\[/tex]
[tex]\frac{11}{10}=\frac{11\times \:2}{10\times \:2}=\frac{22}{20}\\\mathrm{Since\:the\:denominators\:are\:equal,\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\\mathrm{Subtract\:the\:numbers:}\:40-15-22=3\\\\x=\frac{3}{20}[/tex]
Dan's mean average on 5 exams is 86 determine the sum of his score
Answer: 430
Step-by-step explanation:
An average of 5 scores can be found via: (the sum of the scores)*5. Thus, simply multiply 86*5 to get that the sum of his scores is 430
Hope it helps <3
The length of a rectangle is six times its width. The area of the
rectangle is 294 square centimeters. Find the dimensions of the
rectangle.
Answer:
length= 42
width = 7
Step-by-step explanation:
Given: F={(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4,7), (5, 8), (6,9). (7.5))
(F. G) (2) =
10
O 20
O 40
Answer:
(F·G)(2) = 20
Step-by-step explanation:
We assume you want (F·G)(2).
(F·G)(2) = F(2)·G(2)
F(2) = 4 . . . . from the ordered pair (2, 4)
G(2) = 5 . . . .from the ordered pair (2, 5)
So your product is ...
F(2)·G(2) = 4·5 = 20
(F·G)(2) = 20
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 22 days and a standard deviation of 6 days. 72% of all of these types of trials are completed within how many days
Answer:
25.5 days
Step-by-step explanation:
Mean number of days (μ) = 22 days
Standard deviation (σ) = 6 days
Z-score for the 72nd percentile (according to tabulated values) = 0.583
The z-score for any number of days, X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
The value of X that is greater than 72% of the trial times is:
[tex]0.583=\frac{X-22}{6}\\ X=25.5\ days[/tex]
Therefore, 72% of all of these types of trials are completed within 25.5 days.
ASAP!!! NEED HELP!!!! Max is stacking logs at his campground for firewood. After his first load of logs, he has 8 logs on the stack. After his seventh load of logs, he has 62 logs on the stack. Use sequence notation to represent the arithmetic function. ANSWER CHOICES: A. an = 8 + 6(n − 1) B. an = 62 + 6(n − 1) C. an = 8 + 9(n − 1) D. an = 62 + 9(n − 1)
Answer: Choice C. an = 8 + 9(n-1)
===========================================
Work Shown:
a1 = 8 is the first term
a7 = 62 is the seventh term
an = a1+d(n-1) = nth term of arithmetic sequence
a7 = a1+d(7-1) ... plug in n = 7; solve for d
62 = 8+d(6)
62 = 6d+8
6d+8 = 62
6d = 62-8
6d = 54
d = 54/6
d = 9 is the common difference
an = a1 + d(n-1)
an = 8 + 9(n-1) is the nth term of this arithmetic sequence
Answer:
Choice C. an = 8 + 9(n-1)
Step-by-step explanation:
I just took the test
Type the slope-intercept equation
of the line that passes through
the points (-1,3) and (2,-3).
y = [? ]x + [ ]
Answer:
y= -2x +1
Step-by-step explanation:
slope- intercept form:
y= mx +c, where m us the gradient and c is the y-intercept.
Let's find the value of m first using the gradient formula.
Gradient= [tex] \frac{y1 - y2}{x1 - x2} [/tex]
[tex]m = \frac{ - 3 - 3}{2 - ( - 1)} \\ m = \frac{ - 6}{2 + 1} \\ m = \frac{ - 6}{3} \\ m = - 2[/tex]
y= -2x +c
To find the value of c, substitute a pair of coordinates.
When x= -1, y=3,
3= -2(-1) +c
3= 2 +c
c= 3 -2
c= 1
Thus the equation of the line is y= -2x +1.
Translate the phrase into a variable expression. Use the letter sto name the
variable. If necessary, use the asterisk (*) for multiplication and the slash
(1) for division.
the product of 60 and the number of seconds...
Answer:
The statement
the product of 60 and the number of seconds is written as
60 * s
Hope this helps you
Help ASAP!!!!
Find the cos(A). Reduce the ratio if necessary.
Answer:
[tex]\boxed{Cos A = 3/5}[/tex]
Step-by-step explanation:
Cos A = Adjacent/Hypotenuse
Where Adjacent = 30 and Hypotenuse = 50
Cos A = 30/50
Cos A = 3/5
Answer:
[tex]\boxed{\mathrm{cos(A) = \frac{3}{5} }}[/tex]
Step-by-step explanation:
[tex]\displaystyle \mathrm{cos(\theta) = \frac{adjacent}{hypotenuse} }[/tex]
The adjacent side to angle A is 30 units. The length of the hypotenuse of the triangle is 50 units.
[tex]\displaystyle \mathrm{cos(A) = \frac{30}{50} }[/tex]
The fraction can be simplified.
What is the answer need answer now !!!
Step-by-step explanation:
RD=BL
RE=BU
ED=UL
Please mark brainliest!!!
Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green and 2 red marbles. Find probability that both marbles are white. Round to nearest thousandth
solve the nonlinear system of equations. State the number of solutions.
Answer:
Step-by-step explanation:
Hello,
Question 15
We can search x such that:
[tex]x^2-4x+4=2x-5\\\\\text{*** subtract 2x-5 from both sides ***}\\ \\x^2-4x-2x+4+5=0\\ \\\text{*** simplify ***}\\ \\x^2-6x+9=0 \\ \\\text{*** we can notice a perfect square ***}\\ \\x^2 -2\cdot x \cdot 3 + 3^2=(x-3)^2=0\\\\\text{*** taking the root ***}\\\\x-3=0\\\\\large \boxed{\sf \ \ x=3 \ \ }[/tex]
There is 1 solution.
Question 16
Again, we search x such that:
[tex]x^2-8x+15=2x-6\\\\\text{*** subtract 2x-6 from both sides ***}\\\\x^2-8x-2x+15+6=0\\\\\text{*** simplify ***}\\\\x^2-10x+21=0 \\ \\\text{*** we are looking for two roots where the sum is 10 and the product is 21 = 7 x 3 ***} \\\\x^2-7x-3x+21=x(x-7)-3(x-7)=(x-3)(x-7)=0\\\\\large \boxed{\sf \ \ x= 3 \ or \ x =7 \ \ }[/tex]There are two solutions.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages
Answer:
Brian is 6 years old, John is 9 years old
Step-by-step explanation:
i.
J = 3 + B
J x B = 54
ii.
(3 + B) x B = 54
B² + 3B = 54
iii.
(B + 9)(B - 6) = 0
B = -9 or 6 -- -9 is irrational as one cannot be negative years old
Brian = 6 years old; therefore, John = 9 years old