Input data
Points
(2, 8)
(20, 18)
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{18-8}{20-2} \\ m=\frac{5}{9} \end{gathered}[/tex][tex]\begin{gathered} b=y-mx \\ b=8-\frac{5}{9}2 \\ b=\frac{62}{9} \end{gathered}[/tex]The equation of the line that passes through the points. For this case we can use the linear model given:
[tex]y=0.55x+6.8[/tex]predict the hourly pay rate for a cashier with 14
[tex]\begin{gathered} y=0.55(14)+6.8 \\ y=14.5\text{ dollars per hour} \end{gathered}[/tex](a) y = 0.55x+6.8
(b) 14.5 dollars per hour
Describe the transformation from triangle DEF to triangle D′E′F′ in the figure.Question options:A) Rotation 90° clockwise about the originB) Reflection about the originC) Rotation 90° counterclockwise about the originD) Transformation down 8 units and right 6 units
The transformation from triangle DEF to triangle D'E'F' is a reflection about the origin.
since,The corrdinates of the traingle DEF is,
point D is (-5,6) , E is (-1,5) , F (-4,2) and The corrdinates of the traingle D'E'F' is,
D' (5,-6) , E' (1,-5) and F' (4,-2).
place the letter of the angle relationship that beat represents the given angle pair in the box.
Angle relationship that best represents the given angle
Considering the angles in the attached diagram above
<6 and <13 has no relationship because they are not parallel
Hence NO relationship between <6 and <13
Hi! I've tried this problem a couple times but am still stumped :( Can you help?!
ANSWER:
[tex]X\text{ = }\begin{bmatrix}{12} & {-4} & {-2} \\ {-8} & {-13} & {8} \\ {8} & {15} & {18}\end{bmatrix}[/tex]EXPLANATION:
Given:
[tex]U\text{ = }\begin{bmatrix}{1} & {3} & {-5} \\ {2} & {14} & {11} \\ {-8} & {0} & {5}\end{bmatrix}\text{ V =}\begin{bmatrix}{13} & {1} & {-7} \\ {-6} & {1} & {9} \\ {0} & {15} & {23}\end{bmatrix}[/tex]Since U and V are Matrices with equal dimensions(3 x 3 matrix), and
X + U = V.
To solve for X, we have:
X = V - U
[tex]\begin{gathered} X\text{ = V - U} \\ X\text{ = }\begin{bmatrix}{13-1} & {-1-3} & {-7-(-5)} \\ {-6-2} & {1-14} & {19-11} \\ {0-(-8)} & {15-0} & {23-5}\end{bmatrix}=\text{ }\begin{bmatrix}{12} & {-4} & {-2} \\ {-8} & {-13} & {8} \\ {8} & {15} & {18}\end{bmatrix} \end{gathered}[/tex][tex]X\text{ = }\begin{bmatrix}{12} & {-4} & {-2} \\ {-8} & {-13} & {8} \\ {8} & {15} & {18}\end{bmatrix}[/tex]does the point (2,0) satisfy the equation y=9×
No, it does not.
[tex]0\ne18[/tex]A supermarket is holding a raffle for a new wrist watch. Out of the 500 tickets sold, David buys ticketsnumbered 5, 6, 7, and 8. What are the odds in favor of David's winning the raffle?O 1:500O 500:1O 1:124O124:1
Explanation:
Total tickets = 500
Tickets number bought by David = 5, 6, 7 and 8
Number of tickets bought by David = 4
Remaining ticket = 500 - Number of tickets bought by David
Remaining ticket = 500 - 4
Remaining ticket = 496
Odds in favour of an event = success for the event/ failures for the event
success for winning the raffle = Number of tickets bought by David = 4
failures for winning the raffle = Remaining ticket = 496
[tex]\begin{gathered} \text{odds in favour of David winning = }\frac{4}{496} \\ \text{odds in favour of David winning = }\frac{1}{124} \\ \\ \text{odds in favour of David winning = }1\text{ : 124 (option C)} \end{gathered}[/tex]Write an equation to represent the sum modeled in the following number line. H H H -4 -3 -2 -1 0 1 2 3 4
The number line shows numbers graded into three parts each such that each point between numbers represent 0.33 units.
This means the red line moving towards the left is a negative because it falls to the left of point 0, where the division between positive and negative numbers take place.
Hence the red line indicates -3.33
The blue line is movin towards the right which means its a positive value. Note that it begins from -3.33 and ends at -1.33. Hence the blue line is a positive value and it covers two units.
The equation that models this number line can be written out as
[tex]x=-3.33+2[/tex]Determine the measures of the unknown angle.
To find the measure of the unknown angle we can use the triangle sum theorem that states that the sum of the measures of the interior angle of a triangle is 180°. We know the measure of two of the interior angles of the triangle that are 50° and 88°, and we can use this information to find the unknown one:
[tex]\begin{gathered} 50+88+\measuredangle3=180 \\ 138+\measuredangle3=180 \\ \measuredangle3=180-138 \\ \measuredangle3=42 \end{gathered}[/tex]The correct answer is C. 42°.
Hello I need help on question number 12 and number 14 if possible please
N 12
Remember that
In any triangle, the sum of the interior angles must be equal to 180 degrees
so
In the triangle EBF
mso
mm
step 2
we have that
m by form a linear pair
substitute given values
52+mmm
Heart Rates For a certain group of individuals, the average heart rate is 74 beats per minute. Assume the variable is normally distributed and the standarddeviation is 2 beats per minute. If a subject is selected at random, find the probability that the person has the following heart rate. Use a graphing calculator.Round the answers to four decimal places.Higher than 73 beats per minute,P (x> 73) =
we need to determine P (x> 73)
when
mean: μ = 74 beats/min
standard deviation: σ = 2 beats/min
First we need to use the following formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]where
x = 73
μ = 74
σ = 2
and
Z is the z-score
... therefore
[tex]z=\frac{73-74}{2}=-\frac{1}{2}=-0.5[/tex]If we check a table of z scores, we will find that when z = -0.5, then P = 0.3085
Now, since we need P(x>73)
therefore
[tex]P=1-0.3085=0.6915[/tex]P(x>73) = 0.6915
the table below shoes the number of white and yellow flowers Cara used in five different arrangements.a. Are the numbers of white and yellow flowers in Cara's arrangements proportional?b. If it is a proportional relationship, which equations related the number of white flowers, x, to the number of yellow flowers, y?
to find if it is proportional all the data must fulfill the constant of proportionality.
in this case we can see a pattern in which the yellow flowers tend to be the double of the white flowers.
however this is not fulfilled when there are 7 white flowers, indicating that the arragements are not proportional
[tex]y=kx[/tex][tex]\begin{gathered} 6=k\cdot(3) \\ \frac{6}{3}=k \\ 2=k \end{gathered}[/tex]the constant of proportionality is 2
[tex]\begin{gathered} 12=k\cdot7 \\ k=\frac{12}{7} \end{gathered}[/tex]Which of the following statements about the graph of f (x)=(0.5)^x shown above are true? Select all that apply.
From the graph, the following are true
[tex]1)Thefunctionf(x)=(0.5)^xis\text{ a decay function.}[/tex][tex]2)\text{The range of the function is the set of all real numbers }>0[/tex][tex]3)\text{ The graph of the function intersects the x-axis at x = 5}[/tex]Given is a parallelogram ABCD. Verify each measure is correct. AE = 10EC = 10 DE = 10EB = 10
AE = 10 and EC = 10
1) Let's find out the measure of each section of those diagonals. Since in a parallelogram their diagonals are bisected. So we can write:
2y = y+5 Subtract y from both sides
2y -y = 5
y= 5
x+1 = 3x -13
x-3x = -13 -1
-2x =-14
2x = 14
x = 7
2) As we now know the measure of each half of those diagonals we can write:
AE = 2y
AE = 2(5)
AE = 10
EC = y+5,
EC =10
DE = x +1
DE = 8
EB = 3(7) -13 = 8
3) Hence, the correct measures are AE = 10 and EC = 10
I need help with this please, I know that the opposite of 4.6 is -4.6 but I don’t know how to explain it.
Answer:
As a rational number is a fraction we had to convert our number to a fraction, and as the opposite number is the number with the same magnitude but a different sign, we had to change the sign.
[tex]-4\cdot\frac{3}{5}[/tex]
Explanation
• Rational numbers are the numbers that can be written as the fraction of two integers.
,• Additionally, opposite numbers are numbers with the same magnitude but different signs.
Thus, based on these definitions, we have to change the sign and search for a fraction.
Steps:
0. From 4.6 we go to -4.6.
,1. We convert -4.6 to a fraction: -4 is the whole number and we are left with -0.6, which is 6/10 (as it is in the tenth's place).
,2. Simplifying 6/10 to 3/5 dividing both numbers by 2.
The triangular faces of the prism shown are equilateral triangles with perimeter 30 cm. Use a net to find the surface area of the prism.
Explanation:
[tex]\begin{gathered} The\text{ surface area is made up of the two equilateral triangles shown above as well as the three rectangles.} \\ Area\text{ of Triangles = 2\lparen}\frac{1}{2}b*h) \\ If\text{ the perimeter of the triangle is 30cm, the length of one side = 30/3 = 10 = base} \\ Area\text{ = 2\lparen}\frac{1}{2}*10*8.7) \\ \text{ =87} \\ Area\text{ of the three rectangles = 3\lparen length*width\rparen } \\ \text{ =3\lparen10*12\rparen} \\ \text{ =360} \\ Total\text{ Surface Area = 360 + 87 = 447} \end{gathered}[/tex]Surface Area of the two triangles in the net = 2*(0.5*b*h)
= 2*(0.5*10*8.7)
=87
Surface Area of three rectangles in the net = 3(l*b)
= 3*12*10
=360
Answer: Total Surface area = 360 + 87 = 447
Additional and SubtractionAnswers should have only three significant figures.Question a) 86.5-0.07 ?Question b) 30.61-87.3-42.109 ?
a. 86.5-0.07
The result of the subtraction is:
[tex]\begin{gathered} 86.50 \\ -0.07 \\ ----- \\ 86.43 \end{gathered}[/tex]As the answer should have only three significant figures then, the result is: 86.4
b. 30.61-87.3-42.109
The subtraction is:
[tex]\begin{gathered} 30.61 \\ -87.30 \\ ----- \\ -56.690 \\ -42.109 \\ ------ \\ -98.799 \end{gathered}[/tex]As the answer should have only 3 significant figures, then the result is -98.8
If you bought 12 gallons of gas for $26.00, how much did you pay per gallon?
To get pay per gallon, we divide the total payment by the total amount of gallons.
So,
Total Cost = 26
Total Gallons = 24
Pay Per Gallon = 26/24 = $1.08 per gallon
y = 2x – 2 y = -x + 7
Given the system of equations:
[tex]\begin{gathered} y=2x-2 \\ y=-x+7 \end{gathered}[/tex]We will find the solution of the system by the graph
To draw each line, we need to know 2 points
So, we will substitute with 2 values of x and calculate the corresponding value of y
For the first equation: y = 2x - 2
[tex]\begin{gathered} x=0\rightarrow y=2\cdot0-2=-2 \\ x=2\rightarrow y\rightarrow=2\cdot2-2=2 \end{gathered}[/tex]So, the line passes through the points ( 0, -2 ) and ( 2, 2)
For the second line: y = -x + 7
[tex]\begin{gathered} x=0\rightarrow y=0+7=7 \\ x=2\rightarrow y=-2+7=5 \end{gathered}[/tex]so, the line passes through the points ( 0, 7) and ( 2, 5)
The graph of the system will be as shown in the following figure:
As shown in the figure:
Equation 1 is the blue line
Equation 2 is the red line
The point of intersection = ( 3, 4)
So, the answer is the solution of the system = ( 3, 4 )
13. Rose's probability of successfully shooting a basketball is 2/5. What is the probability of hershooting in at least 1 if she makes 4 shots?
Answer:
0.8704
Explanation:
The probability of successfully shooting a basketball is 2/5, so the probability t3/o fail will be equal to:
[tex]P=1-\frac{2}{5}=\frac{3}{5}[/tex]Then, we will calculate the probability of failing the 4 shots. So, we need to multiply 3/5 by itself 4 times.
[tex]P(\text{fail all times) = }\frac{3}{5}\times\frac{3}{5}\times\frac{3}{5}\times\frac{3}{5}=0.1296[/tex]Finally, the probability of her shooting in at least 1 if the complement of the probability to fail all times, so, the answer is:
[tex]P(at\text{ least 1) = 1 - 0.1296 = 0.8704}[/tex]Therefore, the answer is 0.8704
15. Deanna started a savings
account for her
when she was bom. She put
$1,500 in an account with a
simple 3.25% interest rate. What
will be the total amount in the
account after 18 years?
granddaughter
$23,775.00 will be the total amount in the account after 18 years, Formula of simple interest = A = P(1 + rt).
What is simple interest?
The straightforward interest formula makes figuring out how much interest will be applied to a loan quick and simple. Multiply the principle, this same number of days between payments, as well as the daily interest rate to determine simple interest.
Although this method of calculation is used in some mortgages, this type of interest is typically associated with auto loans as well as short-term loans.
Simple interest is calculated by multiplying the principle by the daily interest rate and number of days among payments.Simple interest rewards borrowers for making on-time or early monthly payments on their loans.Auto loans as well as short-term personal loans are two common uses for simple interest loans.A represents the total amount of accrued interest and principal.
P is the principal amount.
The interest rate is I.
The annual percentage real interest rate, abbreviated as r, is 1/10.
R is the interest rate in annual percentage terms; R = r * 100 t is the time period in months or years.
In light of the query
P=$1500
r=3.25%
=0.0325
t=18 years
simple interest = 1500(1+ 0.0325 x 18)
=$(1500+877.5)
=$ 23,775
Thus the simple interest is $23,775
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Can you help me with this math question? it says "A cell phone plan costs $200 to start. Then there is a $50 charge each month, Write an expression that shows the total cost for x months on this plan" Is there a proportional relationship between time and cost of the cell phone plan?
Cost = 200 + 50x
The relationship between time and cost of the plan is not proportional. By definition, proportional ;relationships between two variables have equivalent ratio; one variable is always a constant value times the other which in this case is not .
To illustrate,
Month 1 Cost = 200 + 50(1) = 250 Ratio ( time:cost) = 1:250
Month2 Cost = 200 + 50(2) = 300 Ratio ( time:cost) = 2:300 = 1:150
Month 3 Cost = 200 + 50(3) = 350 Ratio ( time:cost) = 3:350
Month 4 Cost = 200 + 50(4)= 400 Ratio ( time:cost) = 4 :400 = 1:100
The ratios are not equivalent,thus the relationship is not proportional.
In which type of composition does a soloist or a small group of instruments interact wi
dance suite
sonata
concerto
chamber music
Step-by-step explanation:
Hey! The correct answer is Chamber Music.
The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3628 grams and a variance of 408,321. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be greater than 4330 grams. Round your answer to four decimal places.
Answer:
0.13597 = 0.136
Step-by-step explanation:
using normal cd in calculator
Lower- 4330 (since we want weight above this)
Upper- 100000 (any large number will still be valid)
std deviation- [tex]\sqrt{408,321}[/tex]
mean- 3628
p- 0.13597
Hope this helps!
Some of the tallest crystals in a cave in Mexico are 85 feet tall. Lin is 6 feet tall. About how many times as tall as Lin are the tallest crystals?
What is 85 / 6
/= divided by
14.16 ≈ 14 times as tall as Lin are the tallest crystals.
Given:
Some of the tallest crystals in a cave in Mexico are 85 feet tall.
Lin is 6 feet tall.
Number of times = tallest crystals height / lin height.
= 85 feet / 6 feet
= 14. 16 ≈ 14 times
14.16 is not represented in times so we take the nearest number which is 14.
Therefore 14 times as tall as Lin are the tallest crystals.
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a spinner with 10 equally sized slices has four yellow slices, three red slices, and three blue slices. Martina spun the dial 500 times and got the following results. (refer to pic)answer the following. Round your answers to the nearest thousand.a) from Martinas results, compute the experimental probability of landing on red.b) assuming that the spinner is fair, compute the theoretical probability of landing on red.c) assuming that the spinner is fair, choose the statement below that is true. 1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 2. the smaller the number spins, the greater the likelihood that the experimental probability will be close to the theoretical probability. 3. the experimental probability will never be close to the theoretical probability, no matter the number of spins.
Given the experimental results of spinning the spinner:
Yellow: 212
Red: 144
Blue: 144
The sum of times = 500
a) from Martina's results, compute the experimental probability of landing on red.
So, the answer will be probability = 144/500 = 0.288
b) assuming that the spinner is fair, compute the theoretical probability of landing on red.
As shown: the spinner has 10 equally sized slices.
The number of red slices = 3
So, the probability of red = 3/10 = 0.3
c) assuming that the spinner is fair, choose the statement below that is true.
The true statement will be:
1. the larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
10 pointsThe cafeteria manager at a middleschool asked 90 randomly selectedstudents to name their favorite schooldessert. The table below shows theresults of the manager's survey.Favorite School DessertDessertFrequencyCakeTHL THE 1941CookiesTULMAL 18 41Ice Cream MIL MHL MSL 1971CobblerTHEMAFruitPHI HI |||Based on the results of the survey,how many of the school's 1,200students would the manager expoato choose fruit as their favorite schooldessert?A 120C 300B 240D600
From the table , we can see that:
Cake ------------ -16
cookies - 20
Ice cream - 26
Cobbler - 10
Fruit - 18
Total - 90
Out of 1900 students, the manager is expected to choose fruits as their favourite school desert?
Ice cream - 26/90 x 1900 = 548 .89 = 600 ------- option D
3. Write the tangent of angle Mas a fraction. Then write it as a decimal rounded to the nearest hundredth. tan M=
solution
For this case we can do the following:
[tex]\tan M=\frac{\sin M}{\cos M}=\frac{\text{opposite}}{\text{adjacent}}[/tex]For this case the opposite side is 8 and the adjacent is 6 so we got:
[tex]\tan M=\frac{8}{6}=\frac{4}{3}[/tex]Please help me I don’t know if I’m right or missing any other to select.
The given equations are
[tex]-x+4y=7[/tex][tex]6x-3y=42[/tex]To find the answer we need to cancel out x or y.
so we have to find the LCM of the coefficients of the corresponding variable.
consider the coefficients of x is -1 in the first equation and 6 in the second equation .
Lcm of -1 and 6 is 6.
Multiplying the first equation by 6.
consider the coefficients of y is 4 in the first equation and -3 in the second equation .
Lcm of 4 and 3 is 12
Multiplying the first equation by 3 and the second equation by 4.
Either one of these is the first step to eliminate variables.
Amswer os
The graph shows the number of gallons of white paint that were mixed with gallons of blue paint in various diffrent ratios:
From the graph, we can note that the points are in a line.
Hence, we must find the line equation for these points.
The general form of the straigh line equation is
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept. The slope can be computed as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where,
[tex]\begin{gathered} (x_1,y_1)=(2,4) \\ (x_2,y_2)=(6,12) \end{gathered}[/tex]By substituying these values into m, we have
[tex]m=\frac{12-4}{6-2}[/tex]hence,
[tex]\begin{gathered} m=\frac{8}{4} \\ m=2 \end{gathered}[/tex]the form of the line equation is
[tex]y=2x+b[/tex]where x is the blue paint and y the white paint.
In order to find b, we can substitute one point into the above equation. For instance, the point
(2,4):
[tex]\begin{gathered} 4=2(2)+b \\ 4=4+b \\ b=0 \end{gathered}[/tex]Thefore, the line equation is
[tex]y=2x[/tex]Hence, the number of galons when we mix 1 gallon of blue pain is
[tex]\begin{gathered} y=2(1) \\ y=2 \end{gathered}[/tex]in other words, for 1 gallon of blue paint we must have 2 gallons of white paint
Mason calculated the sales tax on his clothing purchase to be $5.57375. Round to the nearest hundredth. ANS $ __________
As per given by the question,
There are given that the sales tax is $5.57375.
Now,
For find the value nearest hundredth,
Nearest hundredth is the second digit after the decimal point.
That means,
If there is given that the value , x.yzw
Then, the nearest hundredth number is x.yz.
So,
From the given value.
The nearest hundredth value is, secon digit after the decima.
Here, second digit after the decimal is 57.
Then,
The nearest value of hundredth is 5.57.
Hence, the value is $5.57
NO LINKS!! Use the method of to solve the system. (if there's no solution, enter no solution). Part 2z
Answer:
smaller x-value: (-4, 18)
larger x-value: (3, 11)
Step-by-step explanation:
Solving for x:
y = x^2 + 2
x + y = 14 ---> y = 14 - x
14 - x = x^2 + 2
0 = x^2 + x - 12
0 = (x + 4)(x - 3)
x = -4 or 3
Solving for y:
If x = -4
y = 14 + 4
y = 18
if x = 3
y = 14 - 3
y = 11
Answer:
[tex](x,y)=\left(\; \boxed{-4,18} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{3,11} \; \right)\quad \textsf{(larger $x$-value)}[/tex]
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}\phantom{bbbb}y=x^2+2\\x+y=14\end{cases}[/tex]
To solve by the method of substitution, rearrange the second equation to make y the subject:
[tex]\implies y=14-x[/tex]
Substitute the found expression for y into the first equation and rearrange so that the equation equals zero:
[tex]\begin{aligned}y=14-x \implies 14-x&=x^2+2\\x^2+2&=14-x\\x^2+2+x&=14\\x^2+x-12&=0\end{aligned}[/tex]
Factor the quadratic:
[tex]\begin{aligned}x^2+x-12&=0\\x^2+4x-3x-12&=0\\x(x+4)-3(x+4)&=0\\(x-3)(x+4)&=0\end{aligned}[/tex]
Apply the zero-product property and solve for x:
[tex]\implies x-3=0 \implies x=3[/tex]
[tex]\implies x+4=0 \implies x=-4[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]\begin{aligned}x=3 \implies 3+y&=14\\y&=14-3\\y&=11\end{aligned}[/tex]
[tex]\begin{aligned}x=-4 \implies -4+y&=14\\y&=14+4\\y&=18\end{aligned}[/tex]
Therefore, the solutions are:
[tex](x,y)=\left(\; \boxed{-4,18} \; \right)\quad \textsf{(smaller $x$-value)}[/tex]
[tex](x,y)=\left(\; \boxed{3,11} \; \right)\quad \textsf{(larger $x$-value)}[/tex]