Answer:
2,180 people
Step-by-step explanation:
Let
x-----> number of people at the book fair
we know that
1) 1/4 of the people bought 1 book each
(1/4)x=(5/20)x
2) 3/5 of the remaining people bought 2 books each
The remaining people is (3/4)x
so
(3/5)(3/4)x=(9/20)x
3) the rest of the people bought 3 books each
The rest of the people is x-(5/20)x-(9/20)x=(6/20)x
The linear equation that represent this situation is
(1)*(5/20)x+(2)*(9/20)x+(3)*(6/20)x=4,469
(5/20)x+(18/20)x+(18/20)x=4,469
(41/20)x=4,469
x=4,469*20/41
x=2,180 people
Factorise completely 9a^2-1
Answer:
(3a-1)(3a+1)
Step-by-step explanation:
We can quickly see with this problem that it is the difference of two squares as 9a^2 is (3a)^2 and 1 is 1^2 and therefore can factorise quickly using this rule.
x^2-y^2 = (x-y)(x+y) where x = 3a and y = 1
ANSWER
[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]
EXPLANATION
We want to simplify completely:
[tex]9 {a}^{2} - 1[/tex]
We express the two terms as difference of two squares;
[tex] {(3 {a})^{2} } - {1}^{2} [/tex]
Recall and apply the following identity;
[tex]{x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]
We apply this identity to obtain:
[tex]{(3 {a})^{2} } - {1}^{2} = (3a + 1)(3a - 1)[/tex]
What are the factor of 8x^3 - 27?..
Answer:
(x - 3)(4x² + 6x + 9)
Step-by-step explanation:
This is a difference of cubes which factors in general as
a³ - b³ = (a - b)(a² + ab + b²)
8x³ = (2x)³ ⇒ a = 2x
27 = 3³ ⇒ b = 3
Hence
8x³ - 27
= (2x)³ - 3³
= (2x - 3)( (2x)² + (2x × 3) + 3²)
= (2x - 3)(4x² + 6x + 9)
Can someone help me please
Answer: W = 700 divided by a+18
Step-by-step explanation:
a) We can plug in $358 into A(w), since A(w) represents the amount of money Dale needs. So,
358 = 700 - 18w
Subtract: -342 = -18w
Divide: w = 19 weeks
b) We can plug in 6 into w, since w represents the number of weeks Dale saves money. So,
A(w) = 700 - 18(6)
Multiply: A(w) = 700 - 108
Subtract: A(w) = $592
Jenna's family is going on a trip * after driving 72 miles they used 3.2 gallons of gas * After driving 72 miles, they used 3.2 gallons of gas *Her family has 850 miles remaining on their road trip *The gas tank holds 15 gallons They filled the gas tank at the start of the road trip. They plan to only stop to fill up when their gas tank nears empty. There are plenty along the route. HOW MANY ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION? explain your answer using numbers words and/or pictures
Answer:
2
Step-by-step explanation:
Given Data:
total distance= 850 miles
gas tank holds gas= 15 gallons
mileage = 72/3.2 miles/gallon
if
72 miles uses= 3.2 gallon
then
850 miles uses= x gallons
by cross-multiplication we get
72x=3.2(850)
x=37.778
i.e. 850 miles will use 37.7778 gallon of gas
Asgas tank holds 15 gallons
number of times gas tank is used up= 37.3/15
= 2.518
rounding off
number of times gas tank is used up=3
As they filled the gas tank at the start of the road trip, hence 3-1=2
ADDITIONAL STOPS FOR GAS WILL THEY NEED TO MAKE TO GET TO THEIR DESTINATION =2 !
Solve using the following quadratic equation for all values of x in simplest form !! Please answer this !!
Answer:
No solution
Step-by-step explanation:
Rearrange into quadratic form: 3x² + 0x - 3 = 0
Quadratic formula: when ax² + bx + c = 0: x = (-b ± √(b² - 4ac))/2a
Plug in: x = 0 ± √(0 - 4*3*3))/2a
From this, we can conclude that this equation has no solution, as 0 - 4*3*3 will definitely be negative, and a negative number can not be square rooted.
In the rhombus, m angle 1 =40. Find m angle 2
ANSWER
40°
EXPLANATION
The opposite sides of a rhombus are parallel.
This implies that, the diagonal is a transversal.
This means that,
m<1 and m<2 are alternate interior angles.
Since alternate interior angles congruent,
m<1 =m<2=40°
The correct choice is C.
An arithmetic sequence has this reclusive formula.
Answer:
D
Step-by-step explanation:
The n th term ( explicit formula ) of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
The recursive formula allows us to find the next term from the previous term by adding d to it
Given
[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 3 ⇒ d = - 3
Hence
[tex]a_{n}[/tex] = 9 + (n - 1)(- 3) ← explicit formula → D
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The general formula is a_n = a_1 + (n-1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference.
Explanation:An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. The general formula for an arithmetic sequence is an = a1 + (n-1)d, where an is the nth term, a1 is the first term, and d is the common difference.
For example, in the given sequence 1, 3, 5, 7, 9, the first term a1 is 1, and the common difference d is 2. Using the formula, we can find the nth term by replacing n with the position of the term we want to find. For instance, to find the 5th term, we substitute n = 5:
a5 = 1 + (5-1)2 = 1 + 8 = 9
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How does the greenhouse effect keep the Earth warm? The atmosphere
O
A. causes the winds moving down from the
poles to bend away from the equator
B. contains strong winds that move from west
to east between hot and cold air
O
c. allows uneven heating of the Earth so that
winds blow from high to low pressure
O
D. contains gases that allow light to pass
through, but trap heat
Answer:
D
Step-by-step explanation:
Answer: D
Step-by-step explanation:
ten people were asked if they have a brother or sister. this venn diagram shows the results. a person is randomly chosen from those shown in the venn diagram.
let event A = the person has a sister
let event B = the person has a brother
What does P(B| A) = 0.50 mean in terms of the venn diagram ?
Answer:
out of the 4 people who had a sister, 2 also had a brother
Step-by-step explanation:
a pex
The P(B| A) = 0.50 mean in terms of the Venn diagram is of the 4 people who have a brother, 2 of them also have a sister.
What is the experimental probability?Experimental probability is a probability that is determined on the basis of a series of experiments.
Events are defined as follows.
Event A: The selected person has a sister
Event B: The selected person has a brother
The conditional probability of A given B is the probability that the selected person also has a sister since he has a brother.
[tex]\rm P(A|B)=\dfrac{P(A\ and \ B)}{P(B)}[/tex]
P(B) is the probability that the selected person has a brother. Notice that there are 4 people who have a brother.
P(A and B) is the probability that the selected person has a brother and also a sister. Notice that there are 2 people who have a brother and a sister.
So P(A| B) = 0.5 means that of the 4 people who have a brother, 2 of them also have a sister.
Hence, the P(B| A) = 0.50 mean in terms of the Venn diagram is of the 4 people who have a brother, 2 of them also have a sister.
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a pet store buys bags of dog food for 30.00 dollars per bag and sells them for 54.00 dollars per bag. What is the percent markup?
Answer:
80%
Step-by-step explanation:
(54-30)/30 *100 = 80%
jim can paint a house in 12 hours. alex can paint the same house in 8 hours. Enter an equation that can be used to find the time in hours, t, it would take alex and jim to paint the house together assuming they both work at the wages they work when working alone
Answer:
4.8 hr, or 4 hr 48 min
Step-by-step explanation:
Let '1' represent 'the whole house-painting job.'
Then perform a dimensional analysis:
1 whole house job
-------------------------------- = 12 hours. →This restates the obvious: Jim can
1 job/ 12 hrs paint a house in 12 hours.
Now if both people work together, the total time required to paint the house is:
1 house job 1 house job
----------------------------------------- = ------------------------------ = t for whole job
1 job 1 job 8 job-hr + 12 job-hr with both people
------------ + ------------ ----------------------------- working
12 hours 8 hours 96 hr
This turns out to be:
1
-------------------------- = 96/20 hr = 4.8 hr, or 4 hr 48 min
20/96
It would take Jim and Alex 4.8 hours to paint the house together if they both work at their individual rates.
Now, Let's start by finding the individual rates of Jim and Alex in terms of the fraction of the house they can paint per hour.
Jim can paint a house in 12 hours, so his rate is 1/12 of the house per hour.
Similarly, Alex can paint the same house in 8 hours, so his rate is 1/8 of the house per hour.
Now, let's suppose they work together for t hours to complete the job.
During this time, Jim will be able to paint t/12 of the house and Alex will be able to paint t/8 of the house.
The sum of their individual rates is equal to the combined rate at which they can paint the house together.
So we can set up the following equation:
t/12 + t/8 = 1
Solving for t, we get:
t = 4.8 hours
Therefore, it would take Jim and Alex 4.8 hours to paint the house together if they both work at their individual rates.
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Which is the most likely to be the actual proportion of defective toys in the population?
The mean, or average, of the data set is 3 defective toys per sample group. Therefore set 0.3 and 0.5 are the most accurate representations.
Option C) 0.3
find the slope of the line (-4,-4) and (4,3)
Answer:
The slope is 7/8
Step-by-step explanation:
Use the equation: (Y2 - Y1) / (X2 - X1)
[3 - (-4)] / [4 - (-4) = 7/8
The slope is 7/8
it's important that you should remember this formula, so you know the slope of the line:
slope formula: [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
usually i would label the points, like the picture shown below
then, you plug in the points into the equation:
m = [tex]\frac{3 - (-4)}{4 - (-4)}[/tex]
m = [tex]\frac{7}{8}[/tex]
hope this helps!
Martin has 48 blue balloons and 36 orange balloons he separates the balloons into mixed groups of blue and orange there are the same number of blue balloons in each group and the same number of orange balloons I'm each group.what is the leat total number of balloons that could be in each group?
A.)4
B.)7
C.)9
D.)21
Answer: A
48+ 36 = 84
84/4 = 21 groups
there are 21 groups of 4 balloons
The mass of a box with 6 tennis balls is 2 kg 40 g The same box with
10 tennis balls is 3 kg 160g. What is the mass of the empty box!
Answer:
maybe you add then all up
recall that the difference between a country's exports and imports is called the country's trade balance. suppose last year the United states had $968 billion in exports and $1658 billion in imports. what would be the u.s. trade balance for that year?
Let's call trade balance b, exports e and imports i.
We now construct formula.
[tex]b=\Delta{ei}=e-i[/tex]
Put in the data from last year.
[tex]b=968-1658=\boxed{-690}[/tex]
U.S trade balance for that year is -690 billion dollars.
If you are finding the area of a triangle and there are three sides
Answer:
If you're asking for the formula to find the area of a triangle, its:
1/2bh
b = base
h = height
Calculate the product matrix for the following matrix multiplication.
Answer:
[tex]\large\boxed{\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right] }[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}8&3\\-7&2\end{array}\right] \cdot\left[\begin{array}{ccc}8&3\\-7&-6\end{array}\right] \\\\=\left[\begin{array}{ccc}(8)(8)+(3)(-7)&(8)(3)+(3)(-6)\\(-7)(8)+(2)(-7)&(-7)(3)+(2)(-6)\end{array}\right] \\\\=\left[\begin{array}{ccc}43&6\\-70&-33\end{array}\right][/tex]
Answer:
D
Step-by-step explanation:
43, 6
-70, -33
A small 17 kilogram canoe is floating downriver at a speed of 2 m/s. What is the
canoe's kinetic energy?
Your Answer:
Answer:
units:
The answer is:
Answer: 34
Units: Joules
[tex]KE=34J[/tex]
Why?The kinetic energy is the work needed to accelerate an object to a determined speed.
The kinetic energy can be calculated using the following equation:
[tex]KE=\frac{1}{2}mv^{2}[/tex]
Where,
m, is the mass of the object.
v, is the speed of the object.
So, we are given the information:
[tex]mass=17kg\\\\v=\frac{2m}{s}[/tex]
Then, substituting and calculating we have:
[tex]KE=\frac{1}{2}mv^{2}[/tex]
[tex]KE=\frac{1}{2}*17kg*(\frac{2m}{s})^{2}[/tex]
[tex]KE=8.5kg*(\frac{4m^{2}}{s^{2}})[/tex]
[tex]KE=34\frac{kg.m^{2}}{s^{2}}=34J[/tex]
Have a nice day!
PLLLLEEEAAAASSSSSEEEE HELP!
Answer:
see explanation
Step-by-step explanation:
The length of the arc is calculated as
arc = circumference of circle × fraction of circle
= 2πr × [tex]\frac{90}{360}[/tex] ← r = 1
= 2π × [tex]\frac{1}{4}[/tex] = [tex]\frac{\pi }{2}[/tex] ≈ [tex]\frac{3.14}{2}[/tex] = 1.57
Help me, please easy Geometry question
A
Step-by-step explanation:
A is a midpoint and so is O, giving reason to why the distances are the same
What function represented by graph? Answer choices
y=tan 2 theta
y=tan 1/2 theta
y=tan theta
y=tan 1/4 theta
Answer:
[tex]y=\tan \frac{1}{2} \pi[/tex]
Step-by-step explanation:
The given graph has a period of [tex]2\pi[/tex], because the graph repeats after every [tex]2\pi[/tex] units.
The formula for finding the period of a tangent function is
[tex]T=\frac{\pi}{b}[/tex]
We substitute the period to get;
[tex]2\pi=\frac{\pi}{b}[/tex]
This implies that;
[tex]b=\frac{\pi}{2\pi}[/tex]
Therefore[tex]b=\frac{1}{2}[/tex]
Hence the function represented by the graph is
[tex]y=\tan \frac{1}{2} \pi[/tex]
Mr. Case is placing boxes along one of the walls in his attic. If the wall is 11 1⁄3 feet long and each box is 2 1⁄2 feet long, how many boxes can he fit along the attic wall?
He can fit 4 boxes along the wall
Which of the numbers in each pair is farther to the left on the number line?
a. 305 and 17
b. 187 and 900
c. 16 and 46
d. 157,019 and 149,984
Answer:
16 and 46
Step-by-step explanation:
Lowest number = left of the number line
1 , 2 , 3 , 4 , 5 , 6 , 7
Answer:
Step-by-step explanation:
a) 17 is further to the left on the number line than 305.
b) 187 .... than 900.
c) 16 ... than 46.
d) 149,984 is further to the left than 157,019.
50 POINTS! WILL MARK BRAINLIEST, THANK, AND RATE! The volume of a right rectangular prism can be determined by multiplying the base area of the figure by the height. The volume of a right rectangular prism with a base area of 8 square inches is more than 64 cubic inches. The inequality 8h > 64 can be used to model the situation, where h represents the height of the figure. Which is a possible value of h?
A. 2
B. 4
C. 8
D. 12
Answer:
D. 12
Step-by-step explanation:
Answer:
D 12
Step-by-step explanation:
8h > 64
Divide each side by 8
8h/8 > 64/8
h > 8
H must be greater than 8
The only value in your list greater than 8 is 12
PLEASE HELP!!
A cat is watching a bird in a tree nearby. The tree is approximately 20 ft from the cat (ground distance). If the cat’s line of sight makes a 25° with the ground when he has his eye on the bird, how high up is the bird in the tree?
A. Draw a picture
B. Solve the problem, Solve to the nearest ft.
Answer:
The bird is approximately 9 ft high up in the tree
Explanation:
The required diagram is shown in the attached image
Note that the tree, the cat and the ground form a right-angled triangle
Therefore, we can apply special trigonometric functions
These functions are as follows:
[tex]sin(\alpha)=\frac{opposite}{hypotenuse} \\ \\ cos(\alpha)=\frac{adjacent}{hypotenuse} \\ \\tan(\alpha)=\frac{opposite}{adjacent}[/tex]
Now, taking a look at our diagram, we can note the following:
α = 25°
The opposite side is the required height (x)
The adjacent side is the distance between the cat and the tree = 20 ft
Therefore, we can use the tan function
This is done as follows:
[tex]tan(\alpha)=\frac{opposite}{adjacent}\\ \\ tan(25)=\frac{x}{20}\\ \\x=20tan(25) = 9. 32 ft[/tex] which is 9 ft approximated to the nearest ft
Hope this helps :)
Please please help it’s my last question! :) thankyou
Answer:
(-2.65, 3) and (0, -4) and (2.65, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}x^2+y^2=16&(1)\\y+4=x^2&(2)\end{array}\right\qquad\text{substitute (2) to (1)}\\\\(y+4)+y^2=16\\y^2+y+4=16\qquad\text{subtract 16 from both sides}\\y^2+y-12=0\\y^2+4y-3y-12=0\\y(y+4)-3(y+4)=0\\(y+4)(y-3)=0\iff y+4=0\ \vee\ y-3=0\\\\y+4=0\qquad\text{subtract 4 from both sides}\\\boxed{y=-4}\\\\y-3=0\qquad\text{add 3 to both sides}\\\boxed{y=3}[/tex]
[tex]\text{Put the values of y to (2)}:\\\\\text{for}\ y=-4\\x^2=-4+4\\x^2=0\to x=\sqrt0\to\boxed{x=0}\\\\\text{for}\ y=3\\x^2=3+4\\x^2=7\to x=\pm\sqrt{7}\\\boxed{x=-\sqrt7\approx-2.65}\ \vee\ \boxed{x=\sqrt7\approx2.65}[/tex]
Which equation represents the hyperbola (y -2)^2/4 - (x-2)^2/9=1
in general form?
Answer:
[tex]9y^2-4x^2-36y+16x-16=0[/tex]
Step-by-step explanation:
The given hyperbola has equation:
[tex]\frac{(y-2)^2}{4}-\frac{(x-2)^2}{9}=1[/tex]
We multiply through by 36 to get:
[tex]9(y-2)^2-4(x-2)^2=36[/tex]
We expand to get:
[tex]9(y^2-4y+4)-4(x^2-4x+4)=36[/tex]
[tex]9y^2-36y+36-4x^2+16x-16=36[/tex]
[tex]9y^2-36y-4x^2+16x-16=0[/tex]
The equation of the hyperbola in general form is:
[tex]9y^2-4x^2-36y+16x-16=0[/tex]
The options for this are :
8 millimeters
9 millimeters
10 millimeters
12 millimeters
if segments OX = OC and perpendicular to those chords, then AB = YZ, the chords are also equal.
What is the perimeter and area of a triangle?
J(-5,6). K(3,4) L(-2,1)
Answer:
Perimeter of triangle JKL: [tex]2 \sqrt{17} + 2\sqrt{34}[/tex].
Area of triangle JKL: 17.
Step-by-step explanation:
None of the three sides of triangle JKL is parallel to either the x-axis or the y-axis. Apply the Pythagorean Theorem to find the length of each side.
[tex]\rm JK = \sqrt{(3 - (-5))^{2} + (4- 6)^{2}} = \sqrt{8^{2} + (-2)^{2}} = \sqrt{68} = 2\sqrt{17}[/tex].
[tex]\rm JL = \sqrt{(-2 - (-5))^{2} + (1- 6)^{2}} = \sqrt{3^{2} + (-5)^{2}} = \sqrt{34}[/tex].
[tex]\rm KL = \sqrt{(-2 - 3)^{2} + (1-4)^{2}} = \sqrt{(-5)^{2} + (-3)^{2}} = \sqrt{34}[/tex].
The perimeter of triangle JKL will be:
[tex]\rm JK + JL + KL = 2\sqrt{17} + \sqrt{34} + \sqrt{34} = 2 \sqrt{17} + 2\sqrt{34}[/tex].
Finding the Area of JKL:Method OneIn case you realized that [tex]\rm JK : JL : KL = \sqrt{2} : 1 : 1[/tex], which makes JKL an isosceles right triangle:
Area of a right triangle:
[tex]\begin{aligned}\displaystyle \rm Area &= \frac{1}{2} \times \text{First Leg} \times \text{Second Leg}\\ &=\frac{1}{2} \times \sqrt{34}\times\sqrt{34}\\&= 17\end{aligned}[/tex].
Method TwoAlternatively, apply the Law of Cosines to find the cosine of any of the three internal angles. This method works even if the triangle does not contain a right angle.
Taking the cosine of angle K as an example:
[tex]\displaystyle\begin{aligned}\rm \cos{K}&=\frac{(\text{First Adjacent Side})^{2} + (\text{Second Adjacent Side})^{2}-(\text{Opposite Side})^{2}}{2\times (\text{First Adjacent Side})\times(\text{Second Adjacent Side})}\\&\rm =\frac{(JK)^{2} + (JL)^{2} -(KL)^{2}}{2\times JK \times JL}\\&=\frac{(2\sqrt{17})^{2}+(\sqrt{34})^{2}-(\sqrt{34})^{2}}{2\times\sqrt{34} \times(2\sqrt{17})}\\ &=\frac{2^{2}\times 17}{2\times \sqrt{2}\times\sqrt{17}\times 2\times \sqrt{17}}\\&=\frac{1}{\sqrt{2}}\end{aligned}[/tex].
Apply the Pythagorean Theorem to find the sine of angle K:
[tex]\displaystyle \rm \sin{K} = \sqrt{1 - (\cos{K})^{2}} = \sqrt{1 - \left(\frac{1}{\sqrt{2}}\right)^{2} } = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}[/tex].
The height of JKL on the side JK will be:
[tex]\displaystyle \rm KL \cdot \sin{K} = \sqrt{34} \times \frac{\sqrt{2}}{2} = \frac{\sqrt{68}}{2} = \frac{2\sqrt{17}}{2} = \sqrt{17}[/tex].
What will be the area of JKL given its height [tex]\sqrt{17}[/tex] on a base of length [tex]2\sqrt{17}[/tex]?
[tex]\displaystyle \rm Area = \frac{1}{2} \times Base\times Height = \frac{1}{2}\times (2\sqrt{17})\times \sqrt{17} = 17[/tex].