The system of equation are:
[tex]\begin{gathered} 3x+2y=17 \\ 4x+6y=26 \end{gathered}[/tex]to solve this problem we can solve the second equation for x so:
[tex]\begin{gathered} 4x=26-6y \\ x=6.5-1.5y \end{gathered}[/tex]Now we can replace x in the firt equation so:
[tex]3(6.5-1.5y)+2y=17[/tex]and we can solve for y so:
[tex]\begin{gathered} 19.5-4.5y+2y=17 \\ 19.5-17=2.5y \\ 2.5=2.5y \\ \frac{2.5}{2.5}=1=y \end{gathered}[/tex]Now we replace the value of y in the secon equation so:
[tex]\begin{gathered} x=6.5-1.5(1) \\ x=5 \end{gathered}[/tex]So the solution as a ordered pair is:
[tex](x,y)\to(5,1)[/tex]3. You draw one card from a standard deck.(a) What is the probability of selecting a king or a queen? (b) What is the probability of selecting a face card or a 10? (c) What is the probability of selecting a spade or a heart? (d) What is the probability of selecting a red card or a black card?
Given:
The objective is to find,
a) The probability of selecting a king or a queen.
b) The probability of selecting a face card or a 10.
Explanation:
The total number of cards in a deck is, N = 52 cards.
a)
Out of 52 cards, the number of king cards is,
[tex]n(k)=4[/tex]Similarly, out of 52 cards, the number of queen cards is,
[tex]n(q)=4[/tex]Then, the probability of drawing one out of 4 king cards or one out of 4 queen cards can be calculated as,
[tex]\begin{gathered} P(E)=P(k)+P(q) \\ =\frac{n(k)}{N}+\frac{n(q)}{N} \\ =\frac{4}{52}+\frac{4}{52} \\ =\frac{8}{52} \end{gathered}[/tex]Hence, the probsability of selecting a king or a queen is (8/52).
b)
Out of 52 cards, the number of face cards is 12.
[tex]n(f)=12[/tex]Similarly, out of 52 cards, the number of 10 is,
[tex]n(10)=4[/tex]Then, the probability of drawing one out of 12 face cards or one out of 4 ten cards can be calculated as,
[tex]\begin{gathered} P(E)=P(f)+P(10) \\ =\frac{12}{52}+\frac{4}{52} \\ =\frac{12+4}{52} \\ =\frac{16}{52} \end{gathered}[/tex]Hence, the probability of selecting a face card or a 10 is (16/52).
c)
Out of 52 cards, the number of spade cards is 13.
[tex]n(s)=13[/tex]Similarly, out of 52 cards, the number of heart cards is 13.
[tex]n(h)=13[/tex]Then, the probability of drawing one out of 13 spade cards or one out of 13 heart cards can be calculated as,
[tex]\begin{gathered} P(E)=P(s)+P(h) \\ =\frac{n(s)}{N}+\frac{n(h)}{N} \\ =\frac{13}{52}+\frac{13}{52} \\ =\frac{26}{52} \end{gathered}[/tex]Hence, the probability of selecting a spade or a heart is 26/52.
d)
Out of 52 cards, the number of red cards is,
[tex]n(r)=26[/tex]Out of 52 cards, the number of black cards is,
[tex]n(b)=26[/tex]Then, the probability of drawing one out of 26 red cards or one out of 26 black cards is,
[tex]\begin{gathered} P(E)=P(r)+P(b) \\ =\frac{n(r)}{N}+\frac{n(b)}{N} \\ =\frac{26}{52}+\frac{26}{52} \\ =\frac{52}{52} \\ =1 \end{gathered}[/tex]Hence, the probability of selecting a red card or a black card is 1.
Geometry Problem - Given: segment AB is congruent to segment AD and segment FC is perpendicular to segment BD. Conclusion: Triangle AEG is isosceles. (Reference diagram in picture)
As the triangle AEF has 2 angles with the same measure, triangle AEF is isosceles.
A website recorded the number y of referrals it received from social media websites over a 10-year period. The results can be modeled by y = 2500(1.50), where t is the year and 0 ≤ t ≤9.Interpret the values of a and b in this situation.O a represents the number of referrals after 9 years; b represents the growth factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the decay factor of the number of referralseach year.O a represents the number of referrals after 9 years; b represents the decay factor of the number of referrals each year.a represents the number of referrals it received at the start of the model; b represents the growth factor of the number ofreferrals each year.What is the annual percent increase?The annual percent increase is%.
In this problem
we have an exponential growth function
[tex]y=2500(1.50)^t[/tex]where
a=2500 ----> initial value of the number of referrals at the start of the model
b=1.50 ---> the base of the exponential function (growth factor of the number of referrals each year
therefore
The answer Part 1 is the last option
Part 2
Find out the annual percent increase
we know that
b=1+r
b=1.50
1.50=1+r
r=1.50-1
r=0.50
therefore
r=50%
The annual percent increase is 50%Evaluate when n=5 4n
We are given an expression "4n"
The question says to evaluate this expression when n = 5
Here, evaluation simply means, finding the value of "4n" when n = 5. This is a simple problem of substitution. By substitution I mean replacing every occurence of n in the given expression by 5. This would be done as follows:
Given expression = 4n
Note that here 4 is being multiplied to n.
Replacing n by 5, we get the result as:
[tex]4\text{ }\times\text{ 5 = 20 }[/tex]From here, we can conclude that the value of expression "4n" for n = 5 will be 20.
the circumference of a circle is 18pi ft. what is the area in square feet.
We have first the formula of the circumference of a circle
[tex]C=2\pi r[/tex]In order to know the area we need to know the radius of the circle, it can be obtained using the formula above and the next information.
C=18pi
r is the radius
[tex]18\pi=2\pi r[/tex]then we isolate the r
[tex]\begin{gathered} r=\frac{18\pi}{2\pi} \\ r=9 \end{gathered}[/tex]the radius is 9 ft
then we can calculate the area using the next formula
[tex]A=\pi r^2[/tex]we substitute the value of the radius
[tex]\begin{gathered} A=\pi(9)^2 \\ A=81\pi ft^2 \\ A=254.47ft^2 \end{gathered}[/tex]Break apart ones to add 18+5=
Answer: 23
Step-by-step explanation:
You have 1 ten and 8 ones + 5 ones. First, add the ones to get 13 ones. Then, split the ones into tens and ones to get 2 tens and 3 ones which is 23.
On Friday, you and your friends took a 140 mile road trip to go to a concert.On Sunday you returned home and calculated that the round trip was 7 hours.What was your average speed?Your answer
20 miles per hour
1) Gathering the data from the question:
S=140 miles
Time spent =7 hours
Average speed=?
2) The average speed is calculated using a ratio:
[tex]A\text{ =}\frac{140}{7}=\text{ 20}[/tex]Since the units are in a standard usual way, we don't need to do any conversion so, the answer is
20 miles per hour
Una clase tiene 42 alumnos. Se puede determinar que 3/9 son niños y 4 6 son niñas, ¿Cuántos niños y cuantas niñas hay en la clase?
The number of boys and girls that are in this class is equal to 28 students and 14 students respectively.
How to determine the number of boys?In order to determine the number of boys that are in this class with a total population of 42 students, we would have to multiply the total number of students by the fraction representing only the number of boys as follows:
Number of boys, B = 4/6 × Total number of students
Substituting the given parameters into the formula, we have;
Number of boys, B = 4/6 × 42
Number of boys, B = 4 × 7
Number of boys, B = 28 students.
Similarly, we we would have to multiply the total number of students by the fraction representing only the number of girls as follows:
Number of girls, G = 3/9 × Total number of students
Number of girls, G = 3/9 × 42
Number of girls, G = 1/3 × 42
Number of girls, G = 42/3
Number of girls, G = 14 students.
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Complete Question:
A class has 42 students. It can be determined that 3/9 are boys and 4/6 are girls, how many boys and girls are there in the class?
You use a garden hose to fill a wading pool. If the water level rises 17 centimeters every 4 minutes and you record the data point of (12,y), what is the value of y? Use slope to justify your answer
Answer:
51
Step-by-step explanation:
so we can use the variable x for minutes & y for water level. (4,17) is what we start with. its asking after 12 minutes what is the water level, 4 x 3 is 12 so we would multiply 17 x 3 as well which is 51.
Ashley pounds 98 pounds one year ago .If she weight 112 pounds what is the percent increase in her weight ?
Answer:
The increase to the nearest percent is 14%
Step-by-step explanation:
[tex]\frac{112 - 98}{98}[/tex] The percent of increase is the weight change over the original amount
.14285714285 To change a decimal to a percent, move the decimal two places to the right.
Rounded to the nearest percent is
14%
Find d the side length of a square given the area of the square
Area of a square = side length ^2
Given: A= 20.25
Replacing:
20.25 = s^2
√20.25 = s
s = 4.5 m
A psychology test has personality questions numbered 1, 2, 3, intelligence questions numbered 1, 2, 3, 4, and attitudequestions numbered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?
Answer:
7/9.
Step-by-step explanation?
Total number of questions: 3 + 4 + 2 = 9.
Number of Intelligence questions: 4
Number of questions that have an odd number: 5
The probability of a question is Intelligence questions = 4/9
The probability a question has an odd number = 5/9
The probability a question is Intelligence questions and has an odd number = 2/9
The probability a question is Intelligence question OR has an odd number is:
4/9 + 5/9 - 2/9 = 7/9.
Make a table for the graph labeled hours studies average grade
We can easily create a table with the first column labeled "hours studied" and second column labeled "average grade".
The hours studied are:
0, 1, 2, 3, and 4
The respective average grades are:
56, 75, 85, 90, 100
The table can look like this:
Answer:
To make the table, you must correlate the average test grade with the hours spent studying.
The graph shows the idea that the more we learn, the higher will be our test grades.
The table is attached.
After knee surgery, your trainer tells you to return to your jogging program slowly. He suggests you start by jogging for 14 minutes each day. Each week after, he suggests that you increase your daily jogging time by 7 minutes. How many weeks before you are up to jogging 70 minutes?
Given that initial time for jogging is,
[tex]a_{_1}=14[/tex]After each week the time is increased by
[tex]d=7[/tex]This gives an arithmetic sequence.
To find n such that,
[tex]a_n=70[/tex]Therefore,
[tex]\begin{gathered} a_n=a_1+(n-1)d \\ n=\frac{a_n-a_1}{d}+1 \end{gathered}[/tex]So,
[tex]\begin{gathered} n=\frac{70-14}{7}+1 \\ =\frac{56}{7}+1 \\ =8+1 \\ =9 \end{gathered}[/tex]Therefore, 9 weeks before you are up to jogging 70 minutes.
Nathan and some friends are going to the movies. At the theater, they sell a bag of popcorn for $6 and a drink for $4. How much would it cost if they bought 5 bags of popcorn and 7 drinks? How much would it cost if they bought pp bags of popcorn and dd drinks?Total cost, 5 bags of popcorn, and 7 drinks: Total cost, p bags of popcorn and d drinks:
a) Since the cost of a bag of popcorn is $6 and the cost of a drink is $4,
[tex]\begin{gathered} T=6\cdot5+7\cdot4 \\ \Rightarrow T=30+28=58 \\ \Rightarrow T=58 \end{gathered}[/tex]Therefore, the answer to the first question is $58.
b) Substitute 5 for p and 7 for d in the expression above; therefore,
[tex]T=6p+4d[/tex]The total cost is given by the equation T=6p+4d, where T is in dollars, p is the number of bags of popcorn and d is the number of drinks.
select the reason that best supports statement 6 in the given proof please help me image attached
Answer:
B. Distributive Property
Step-by-step explanation:
You want to know the reason in the proof that best supports the transition from 5. 99-3x = 12(x+2) to 6. 99-3x = 12x+24.
TransformationYou will notice that in the transition from
5. 99-3x = 12(x+2)
to
6. 99-3x = 12x+24
the expression 12(x+2) has been replaced by the expression 12x+24.
Distributive propertyThe property of addition and multiplication that makes it true that ...
12(x +2) = 12x +24
is the distributive property of multiplication over addition. That property tells you that parentheses can be eliminated by multiplying each of the terms inside by the factor outside.
A normal distribution has a mean of 101 and a standard Deviation of 12. find the probability that a value selected at random is in the following interval.at most 13
Answer:
84.134%
Explanation:
First, determine the value of the z-score.
[tex]\begin{gathered} Z=\frac{X-\mu}{\sigma} \\ =\frac{113-101}{12} \\ =\frac{12}{12} \\ z-score=1 \end{gathered}[/tex]Next, we determine the probability that a value selected at random is at most 113:
[tex]\begin{gathered} P(X\le113)=P(x\le1)_{} \\ =0.84134 \\ =84.134\% \end{gathered}[/tex]Thus, the probability that a value selected at random is in the given interval is 84.134%.
Which of the following statements is not true based on the given graph?abd0OlbicasbCO
The Solution.
From the given number line graph, we can see clearly that the following option are true.
[tex]undefined[/tex]The only option that is not true is
[tex]undefined[/tex]Write a proportional that relates the corresponding sides. You must use all of the sides for both triangles in your statement.
Given
Answer
[tex]\Delta HGF\approx\Delta HKL[/tex]GF is proportional to KL
HG is proportional to HK
HF is proportional to HL
Given l//m//n find the value of x (5x)° (6x-13)°
The line l and the transversal line are intersecting each other.
So, from the theorem of Vertically Opposite angle
A pair of vertically opposite angles are always equal to each other.
thus, 5x = 6x - 13
Simplify the expression :
5x = 6x -13
6x-5x =13
x = 13
Answer : x = 13
Kindly assist in answering these questions
The point of origin on the graph is (0,0) and the constant of proportionality is equal to 3.
Equation of LineThe equation of a straight line is y=mx + c. y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system. The numerous points which together form a line in the coordinate axis are represented as a set of variables x, y to form an algebraic equation, which is referred to as an equation of a line.
In the given question, we are asked to find several values relating to the graph attached.
5) The point of origin on the graph is at (0,0) because the graph passes through the center along the straight line.
6) The constant of proportionality (k) is the value before the variable x.
The equation of the line is y = 3x.
The constant of proportionality of the equation is equal to 3.
7) The value of the ratio k is given as y/x
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3. Identify the solution to the system of equations by graphing:(2x+3y=12y=1/3 x+1)
Given equations are
[tex]2x+3y=12[/tex][tex]y=\frac{1}{3}x+1[/tex]The graph of the equations is
Red line represents the equation 2x=3y=12 and the blue line represents the equation y=1/3 x=1.
Using this picture, describe what we are doing with the factored form of p(x) shown in the image in order to create a sketch of the function.
Given:
[tex]p(x)=(x-1)(x+1)(x-4)^2[/tex]Sol:
[tex]\begin{gathered} p(x)=(x-1)(x+1)(x-4)^2 \\ \\ p(0)=(0-1)(0+1)(0-4)^2 \\ \\ p(0)=-16 \end{gathered}[/tex]X-intercept is at p(x) = 0 then,
[tex]\begin{gathered} p(x)=0 \\ \\ p(x)=(x-1)(x+1)(x-4)^2 \\ \\ 0=(x-1)(x+1)(x-4)^2 \\ \\ x=-1,1,4 \end{gathered}[/tex]At y- intercept the value of x is zero and at x = 0 function value is:
[tex]\begin{gathered} y=-16 \\ \\ \text{ The point is:} \\ (0,-16) \end{gathered}[/tex]At x-intercept y value is zero and x-intercept is -1,1,4 is:
[tex]\begin{gathered} \text{ At }x=-1 \\ \\ the\text{ value of }y=0 \\ \\ (-1,0) \\ \\ At\text{ }x=1 \\ \\ \text{ The value of }y=0 \\ \\ (1,0) \\ \\ \text{ At }x=4 \\ \\ \text{ The value of }y=0 \\ \\ (4,0) \end{gathered}[/tex]So all point is (-1,0) ,(1,0) and (4,0)
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x2 + 3x - 2
F(a) =
For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4
Given,
The function f(x) = x² + 3x - 2
We have to find f(a) and domain f(x - 1)
Here,
f(x) = x² + 3x - 2
Then,
f(a) = a² + 3a - 2
Now,
f(x - 1) = (x - 1)² + 3(x - 1) - 2
f(x - 1) = x² - 2x + 1 + 3x - 3 - 2
f(x - 1) = x² + x - 4
That is,
For a given function f(x) = x² + 3x - 2, f(a) is a² + 3a - 2 and f(x - 1) = x² + x - 4
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Determine the functions value when x= -1?a. g(-1) = -3b. g(-1) = 0c. g(-1) = 1d. g(-1) = 27
Problem
Determine the functions value when x= -1?
a. g(-1) = -3
b. g(-1) = 0
c. g(-1) = 1
d. g(-1) = 27
Solution
For this case we just need to find the value of g when x= -1 and if we look at the table we got:
g(-1)= (-1)^3 + 6(-1)^2 +12(-1) +8
g(-1)= -1 +6 -12+8 = 5-12+8= 1
And then the solution for this case would be:
c. g(-1) = 1
BK has endpoints B(1,4) and K(4, -3). Rotate BK clockwise 270 degrees about the ongin. Part A: Write an algebraic description of the transformation of BK. Part B: What are the endpoints of the new line segmente
B ( 1, 4)
K (4, -3)
We plot the points and after that, calculate their angles, then we measure 270 clockwise to calculate the new points.
The endpoints of the new segment are
B' = (-4.5, 1)
K' = (3, 4)
These are the points of the new segment
XYZ is a right-angled triangle. A is a point on line XZ and B is a point on line XY. XA = XB What is the size of angle XAB? xzy= 34 degrees
A. Monkey man
Step-by-step explanation:
M+o+n+k+e
find the zeros algebraically: f(x)=x^4-8x^3+5x^2+14x
The given equation is:
x^4-8x^3+5x^2+14x
In this question, we have to find the zeros algebraically. Hence, we need to find the values of x that satisfy the equation.
Note: The roots (values of x) are equal to the power of the equation. Therefore, the given equation will have 4 roots
Therefore,
x^4-8x^3+5x^2+14x = 0
or
x(x^3-8x^2+5x+14) = 0
=> x = 0 and x^3-8x^2+5x+14 = 0
Therefore, the first root is x = 0.
Now,
x^3-8x^2+5x+14 = 0
To simplify that, try putting different values of x (starting from 1 and -1). The value that makes both sides equal to zero would be the solution.
Let's start with (1):
For x = 1
(1)^3 - 8(1)^2 + 5(1) + 14 = 0
1 -8(1) + 5 + 14 = 0
-1 -8 +5 + 14 = 0
- 9 + 19 = 0
10 = 0
It is false, therefore, x = 1 is not the solution.
For x = -1
(-1)^3 - 8(-1)^2 + 5(-1) + 14 = 0
-1 -8(1) - 5 + 14 = 0
-1 -8 -5 + 14 = 0
- 14 + 14 = 0
0 = 0
hence, x = -1 is the second solution.
If x = -1 is the solution, (x + 1) should be the factor of x^3-8x^2+5x+14. Therefore, the whole equation can be divided by factor
x^3-8x^2+5x+14 / (x+1). = x^2 - 9x + 14. (using division)
Now, let's find the roots of x^2 - 9x + 14
x^2 - 9x + 14 = 0
x^2 - 7x - 2x + 14 = 0
x(x - 7) - 2 (x - 7) = 0
(x - 7) (x - 2) = 0
or
x - 7 = 0. and x - 2 = 0
x = 7 and x = 2
Therefore, the zeros of the given equation are, 0, -1, 2 and 7.
$3.44 at the Farmers market at a grocery store the same oranges cost $8.40 for a bag of 20 find the better deal by calculating the unit rate for both locations how much would be saved per orange by purchasing oranges at the locations with the better deal solve the word problemFarmers market unit rate --------------grocery store unit rate ------------------better deal -------------how much is saved ------------A $0.01/ orangeslB $0.41 / orangeC grocery storeD Farmers marketE $0.43 / orangeF $0.40 / OrangeG $0.10 / Orange
Given :
At the farmer market : a bag of 8 oranges cost $3.44
At the grocery store : a bag of 20 oranges cost $8.4
So, the unit rate at the farmer market = 3.44/8 = $0.43/ orange
And the unit rate at the grocery store = 8.4/20 = $0.42/ orange
So, the better deal is the grocery store
how much is saved ?
the saving = 0.43 - 0.42 = $0.01/ orange
An equation that can be used to determine the total
The equation that we have to build has the following form:
[tex]y=mx+b[/tex]• The fixed cost of the phone is $88, which will be represented by ,b,.
,• The variable cost per month is $116.43, which will be represented by ,m,.
,• y ,is the dependent variable that we want to know (, C(t) ,)
,• x ,is the independent variable, in our case, ,t,.
Replacing the values given in the problem we get:
[tex]C(t)=116.93t+88[/tex]The cost for 22 months will be:
[tex]C(22)=116.93\cdot22+88[/tex][tex]C(22)=2660.46[/tex]Answer:
• Equation
[tex]C(t)=116.93t+88[/tex]• Cost in 22 months: $2660.46
