Work Shown:
y = (4/5)x + 3
5y = 4x + 15 ... multiply all terms by 5 to clear out the fraction
0 = 4x + 15 - 5y ... subtract 5y from both sides
4x-5y+15 = 0 .... rearrange terms
The equation is in standard form Ax+By+C = 0 where A = 4, B = -5, C = 15.
Some books use Ax+By = C to represent standard form. It's effectively the same thing just with C on the other side.
26. A positive whole number is called stable if at least one of its digits has the same value
as its position in the number. For example, 78247 is stable because a
the 4th position. How many stable 3-digit numbers are there?
appears in
Answer:
OneStep-by-step explanation:
Given the value 78247 a s a stable number because at least one of its digits has the same value as its position in the number. The 4th number in the value is 4, this makes the number a stable number.
The following are the 3-digits stable numbers that appears in 78247
The first number is 824. This digits are stable numbers because 2 as a number is situated in the same place as the number (2nd position).
Hence, there are only 1 stable 3-digit numbers in the value 78247 since only a value exists as 2 in the value and there is no 1 and 3 in the value.
Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M. Which angle is an adjacent interior angle to ∠JKM? ∠JKL ∠MKL ∠KLM ∠LMK
Answer:
The correct option is;
∠MKL
Step-by-step explanation:
From the construction of the line LKJ to form the exterior angle ∠JKM, we have that the segment MK of triangle KML forms two adjacent angles on JKL which are ∠JKM and ∠MKL, therefore, the adjacent interior angle to angle ∠JKM is angle ∠MKL
PLease find attach The drawing of triangle KML showing the extended point J
Answer:
B) ∠MKL
Step-by-step explanation:
Took the quiz on edge
Zahara asked the students of her class their gymnastic scores and recorded the scores in the table shown below: Gymnastic Scores Score Number of Students 0 1 1 1 2 2 3 6 4 4 5 3 6 2 Based on the table, what is the mean gymnastic score? 2.5 3.5 5.2 9.4
Answer:
3.5
Step-by-step explanation:
I did the test, also, take the people multiply by score, u get 66 total, divided by 19=number of students, is 3.5-ish
The mean for gymnastic score is, 3.5
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
Zahara asked the students of her class their gymnastic scores and recorded the scores in the table shown in table.
Now, We get;
The mean for gymnastic score is,
= ((1×0)+(1×1)+(2×2)+(6×3)+(4×4)+(3×5)+(2×6)) / 19
= 3.47
= 3.5
Thus, The mean for gymnastic score is, 3.5
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A middle school took all of its 6th grade students on a field trip to see a play at a theatre that has 2000 seats. The students filled 65% of the seats in the theatre. How many 6th graders went on the trip?
Answer: 1,300 students went on the trip
Step-by-step explanation: So we know that 65% filled the seats so let's turn that into a fraction. [tex]\frac{65}{100}[/tex] . Now we know that there are 2,000 seats in total so let's put that into a fraction. [tex]\frac{x}{2,000}[/tex] The x represents the students that went on the trip.
[tex]\frac{65}{100} = \frac{x}{2,000}[/tex] we have to cross multiply
65(2,000) = 100 (x)
130,000 = 100 (x)
130,000 ÷ 100
1,300 = x So now we know that 1,300 went to the trip students
Find the solution of y= 4x+ 2 for x = -5.
Answer:
[tex]y=-18[/tex]
Step-by-step explanation:
[tex]y=4x+2[/tex] for [tex]x=-5[/tex]
[tex]y=4(-5)+2\\y=-20+2\\y=-18[/tex]
Answer:
y = -18
Step-by-step explanation:
y = 4x+2
Let x = -5
y = 4(-5) +2
y = -20 +2
y = -18
Solve –|2x+3|=1 for x it might have more than one answer
Express 15 degrees in Radian measure.
Answer:
Formula 15° × π/180 = 0.2618rad
0.261799
Step-by-step explanation:
Answer:
1 /12 pi
Step-by-step explanation:
To convert degrees to radians, multiply by pi/ 180
15 * pi/ 180
1 /12 pi
Consider the following 8 numbers, where one labelled x is unknown. 4, 32, 6, x , 10, 3, 35, 37 Given that the range of the numbers is 64, work out 2 values of x
Answer:
[tex]\boxed{x=-27, \: x=67}[/tex]
Step-by-step explanation:
There can be two values of x.
The range is largest no. - smallest no.
Range = 64
Let x be the smallest no.
largest no. from the list is 37
37 - x = 64
-x = 64 - 37
x = -27
Let x be the largest no.
smallest no. from the list is 3
x - 3 = 64
x = 64 + 3
x = 67
The needed two values of x are: 67 and -27.
Given sequence of 8 numbers as:
[tex]4, 32, 6, x, 10, 3, 35, 37[/tex]
Given range of above sequence: 64
The range of a sequence is defined as the difference between the maximum and minimum value of the sequence.
Since the value x can assume any value, it have option to be minimum value in the sequence or maximum value in the sequence such that the range remains at 64.
Case 1: x as minimum value of given sequence:
If so, then the maximum value is 37. Then-
[tex]range = maximum \:value - minimum \:value\\or\\64 = 37-x\\or\\x = -27\\[/tex]
Case 2: x as maximum value of the given sequence:
If so, then the minimum value of the sequence is 3. Then-
[tex]range = maximum \:value - minimum \:value\\or\\64 = x - 3\\or\\x = 67\\[/tex]
Thus the needed two values of x are: 67 and -27.
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At Camp Sunshine, 4 kids went home sick. Of the remaining campers, 18 kids went hiking and the other 41 kids spent the day swimming. How many kids started the day at Camp Sunshine?
Answer:
63 kids
Step-by-step explanation:
We can add up the number of students who went home sick, hiked, and swam to find the total amount of people.
[tex]4+18+41 = 63[/tex]
Therefore, 63 kids started their day at Camp Sunshine.
I get that feeling I oversimplified this one, let me know if I did. I'm not sure if this is right.
Answer:
63 kids
Step-by-step explanation:
We know that there are some kids who went home sick, some went hiking and some went swimming.
The total number of kids that started the day at Camp Sunshine can be found by adding the number who went home sick, went hiking and went swimming.
sick + hiking + swimming
4 went home sick, 18 went hiking and 41 went swimming.
4+ 18 + 41
Add the numbers together
22+ 41
63
63 kids started the day at Camp Sunshine.
The smaller the cookies the more I can fit in a container. Which graph models this situation?
A)А
B)B
C)C
D)D
Answer:
C: as the size increases the amount decreases. this means as the x-value increases, the y-value decreases, which is shown by graph C.
Answer:
your answer is c )c and where are you live
Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 200 voters finds that 94 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
Answer:
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
Step-by-step explanation:
From the information given :
An exit poll of 200 voters finds that 94 voted for the referendum.
How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.52? Based on your result, comment on the dangers of using exit polling to call elections.
This implies that ;
the Sample size n = 200
the probability p = 0.52
Let X be the random variable
So; the Binomial expression can be represented as:
X [tex]\sim[/tex] Binomial ( n = 200, p = 0.52)
Mean [tex]\mu[/tex] = np
Mean [tex]\mu[/tex] = 200 × 0.52
Mean [tex]\mu[/tex] = 104
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{np(1-p)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(1-0.52)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{200 \times 0.52(0.48)}[/tex]
The standard deviation [tex]\sigma[/tex] = [tex]\sqrt{49.92}[/tex]
The standard deviation [tex]\sigma[/tex] = 7.065
However;
P(X ≤ 94) because the discrete distribution by the continuous normal distribution values lies in the region of 93.5 and 94.5 .
The less than or equal to sign therefore relates to the continuous normal distribution of X < 94.5
Now;
x = 94.5
Therefore;
[tex]z = \dfrac{x- \mu}{\sigma}[/tex]
[tex]z = \dfrac{94.5 - 104}{7.065}[/tex]
[tex]z = \dfrac{-9.5}{7.065}[/tex]
z = −1.345
P(X< 94.5) = P(Z < - 1.345)
From the z- table
P(X ≤ 94) = 0.09012
From what we observe; There is a probability of less than 94 people who voted for the referendum is 0.09012
Comment:
The result is unusual because the probability that p is equal to or more extreme than the sample proportion is greater than 5%. Thus, it is not unusual for a wrong call to be made in an election if the exit polling alone is considered.
A student stands 20 m away from the footof a tree and observes that the angle of elevation of the top of the tree, measured from a table 1.5 m above the ground, is 34°28'. Calculate the height of the tree tothe nearest metre.
Answer:
6 to the north
Step-by-step explanation:
mark as brainliest
Solve this one 0.2=x/5-1.4
Answer:
x = 8[tex]0.2 = \frac{x}{5} - 1.4[/tex]
Move 1.4 to the left side of the equation
That's
[tex]0.2 + 1.4 = \frac{x}{5} \\ \\ \frac{x}{5} = 1.6[/tex]
Convert the decimal to fraction
That's
1.6 = 8/5
[tex] \frac{x}{5} = \frac{8}{5} [/tex]
Multiply through by 5
We have
[tex] \frac{x}{5} \times 5 = \frac{8}{5} \times 5 \\ \\ \\ x = 8[/tex]
Hope this helps you
Suppose $600 is compounded yearly for 20 years. If no other deposits are made, what rate is needed for the balance to triple in that time? Round your answer to the nearest hundredth of a percent.
Answer:
5.65%
Step-by-step explanation:
Principal=$600
Time=20 years
FV=600*3=$1800
n=1
r=?
r= n[(A/P)^1/nt - 1]
=1{(1800/600)^ 1/1*20 - 1}
={(3)^1/20-1}
=3^0.05-1
=1.0565-1
=0.0565
rate=0.0565*100
=5.65% to the nearest hundredth percent
Find the volume of the cone shown below.T
15
12
A. 9727 units
B. 972 units
C. 3247 units
D. 324 units
The answer is- D. 324 pi units squared
The volume of the cone is 324π cubic units, option C is correct.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of cone whose height is 12 units, radius is 9 units
Volume = πr²h/3
Now let us plug in values of r and h which are radius and height respectively
Volume of cone = π × 9² ×12 /3
= π × 81×4
=324π cubic units
Hence, the volume of the cone is 324π cubic units, option C is correct.
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PLEASE HELP ASAP ON ALL THE PARTS!!! suppose there is a card game where you are dealt a hand of three cards. you have already learned that the total number of three card hands that can be dealt from a deck of 52 cards is:
Answer:
A. The total number of three-card hands (permutations) that can be made with two aces is 576
B. The actual number of two-ace hands (combinations) you can get from a deck of 52 cards is 288
C. The probability of drawing a three-card hand that includes two aces from a deck of 52 cards is 0.0130
Step-by-step explanation:
A. In order to calculate the total number of three-card hands (permutations) that can be made with two aces we would have to make the following calculation:
total number of three-card hands (permutations) that can be made with two aces=4*3*52
total number of three-card hands (permutations) that can be made with two aces=576.
B. In order to calculate the actual number of two-ace hands (combinations) you can get from a deck of 52 cards we would have to make the following calculation:
actual number of two-ace hands (combinations) you can get from a deck of 52 cards=4C2*48
4C2=4!/2!2!
C2=6
Therefore, actual number of two-ace hands (combinations) you can get from a deck of 52 cards=6*48=288
C. In order to calculate the probability of drawing a three-card hand that includes two aces from a deck of 52 cards we would have to make the following calculation:
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=actual number of two-ace hands (combinations) you can get from a deck of 52 cards/52C3
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=288/22,100
probability of drawing a three-card hand that includes two aces from a deck of 52 cards=0.0130
A tomato is cut into 8 slices. If each slice contains 0.12 grams of fiber, how can rounding be used to estimate the amount of fiber in the entire tomato?
Answer:
The amount of fiber in the entire tomato is approximately 1 g
Step-by-step explanation:
A tomato is cut into 8 slices.
1 slice contains 012 g of fiber
8 slices will contain;
[tex]\frac{8 * 0.12}{1}[/tex] g = 0.96g which equals to 1 g when rounded up nearest gram.
So the amount of fiber in the entire tomato is 0.96g ≈ 1g
Will there be more than one relay exchange between 2 consecutive tenths of a mile?
Answer:
No
Step-by-step explanation:
data provided in the question
Long = 2 miles
distance = [tex]\frac{2}{11}[/tex]
based on the above information,
We can conclude that
there is not more than one relay as if we divide the 2 by 11 so it comes 0.18 which is greater than 0.1
i.e
0.18 > 0.1
So there is no need for more than one relay i.e to be exchanged between two consecutive mile
The cylinder shown has a volume of 150 cubic inches and its height is equal to its radius. The cylinder and the sphere shown have the same radius. What is the volume of the sphere?
Answer:
V = 200
Step-by-step explanation:
Cylinder
V = pi r^2 h
150 = pi r^2 h
We know that h = r
150 = pi r^2 r
150 = pi r^3
Divide each side by pi
150 /pi = r^3
Take the cube root of each side
( 150 / pi ) ^ 1/3 = r
3.627831679 = r
Rounding to 3.63
Now find the volume of the sphere
V = 4/3 pi r^3
Replacing r^3 with 150 /pi
V = 4/3 * pi ( 150/pi)
V = 4*150 /3
V = 200
Which statement(s) is(are) true about cones? Statement 1: A cone has a triangular base. Statement 2: A cone is 3 times larger than a cylinder with the same height and radius. Statement 3: A cone is one-third the size of a cylinder with the same height and radius. Statement 4: A cone has a circular base.
Answer:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
Step-by-step explanation:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
The true statement is:
Statement 3: A cone is one-third the size of a cylinder with the same height and radius.
Statement 4: A cone has a circular base.
What is Cone?A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top . A cone has one face . There are no edges for a cone.
Properties of Cone
A cone is a shape that has a curved surface and a circular base. The following properties of a cone help us identify it easily. They are as follows.A base of a cone is circular.There is one face, one vertices, and no edges for a cone.The slant height of a cone is the length of the line segment joining the of the cone to any point on the circumference of the base of the cone.A cone have circular base at a perpendicular distance is called a right circular cone.A cone have circular base is an oblique cone.As, from the properties of cone we can say that.
A cone is one-third the size of a cylinder with the same height and radius. and, : A cone has a circular base..
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What the correct answer now
Answer:
388.6 yd²
Step-by-step explanation:
the missing angle in triangle is 180 - 32 - 38 = 110
Law of sines: 31/sin 38 = VT/sin 32
VT = 26.68
area = 1/2ab sinC
A = 1/2 (31)(26.68) sin 110
388.6 yd²
The legs of a right triangle are 3 units and 8 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth.
8.54 units
9.54 units
11.00 units
24.00 units
Answer:
8.54 unitsStep-by-step explanation:
Given,
Perpendicular ( p ) = 8 units
Base ( b ) = 3 units
Hypotenuse ( h ) = ?
Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
plug the values
[tex] {h}^{2} = {8}^{2} + {3}^{2} [/tex]
Evaluate the power
[tex] {h}^{2} = 64 + 9[/tex]
Calculate the sum
[tex] {h}^{2} = 73[/tex]
Squaring on both sides
[tex]h = \sqrt{73} [/tex]
Calculate
[tex]h = 8.54[/tex] units
Hope this helps..
Best regards!
Answer:
TEST ANSWER: q1:C q2:a q3:b q4:c
Step-by-step explanation:
i got it right on the test 100%
What is the equation of a line, in general form, that passes through points (-1, 2) and (5, 2)? A. y - 2 = 0 B. y - x - 2 = 0 C. x - 2 = 0
Answer:
y=2 or y-2=0
Step-by-step explanation:
to find the equation first find the slope m points (-1,2) and (5,2)
m=y2-y1/x2-x1 =2-2/5-(-1)=0/6=0
y=mx+b the slope is zero then y=b=2
NEED HELP ASAP!!!! RIGHT NOW
Answer:
120 degrees
Step-by-step explanation:
Answer:
120
Step-by-step explanation:
Add all the number then subtract it with 360.
A baby is 19 inches long at birth. After 14 months, the baby is 30 inches long. What is the rate of change?
pls help me (i got this from khan academy) f(x)=(5x+1)(4x−8)(x+6)f, left parenthesis, x, right parenthesis, equals, left parenthesis, 5, x, plus, 1, right parenthesis, left parenthesis, 4, x, minus, 8, right parenthesis, left parenthesis, x, plus, 6, right parenthesis has zeros at x = − 6 x=−6x, equals, minus, 6, x = − 1 5 x=− 5 1 x, equals, minus, start fraction, 1, divided by, 5, end fraction, and x = 2 x=2x, equals, 2. What is the sign of f ff on the interval − 1 5 < x < 2 − 5 1
Answer: Negative
Step-by-step explanation:
f(x) = (5x + 1)(4x - 8)(x + 6)
x = -1/5 x = 2 x = -6
Zeros (in order): -6, -1/5, 2
Now, let's look at the End Behavior of the function.
The leading coefficient is positive (5x)(4x)(x) = +20x³ so the right side of the graph goes toward positive infinity.
The Degree is odd (degree = 3) so the left side is opposite of the right side which means it goes toward negative infinity.
------o-------------o--------------o------
-6 -1/5 2
-- + -- +
y-values for -1/5 < x < 2 is NEGATIVE
The sign of the function f(x) = (5x + 1)(4x − 8)(x + 6) in the interval of -1/5 to 2 will be negative.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function.
The function is given below.
f(x) = (5x + 1)(4x − 8)(x + 6)
The x-intercept of the function will be
(-6, 0), (-1/5, 0), (2, 0)
Then the sign of the function in the interval of -1/5 to 2 will be
Find the value of the function at x = 0, we have
f(x) = (5*0 + 1)(4*0 − 8)(*0 + 6)
f(x) = 1 x (-8) x 6
f(x) = -48
Thus, the value of the function at x = 0, is negative.
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17.A company produces three sizes of a dog
25 house: small, medium, and large. The
small dog house sells for $80, the
medium size for $110, and the large for
$140. The small dog houses cost $50
each to make, medium $70 each, and
large $79 each. Let s represent the
number of small size dog houses, m
represent the number of medium size
dog houses and L represent the number
of large size dog houses. Write an
expression in simplest form for the net
profit.
Answer:
10s+40m+61l=net profit
Step-by-step explanation:
subtract the value you pay from the value you charge
of the CP of 15 articles equals to the SP of 12 articles, find the gain percent.
an
ple 4:
Question
If the CP of 15 articles equals to the SP of 12 articles, find the gain percent.
Answer:
gain percent = 25%
Step-by-step explanation:
To solve the question given, we will follow the steps below:
gain% = [tex]\frac{s.p - c.p}{c.p}[/tex] × 100%
But from the question;
"CP of 15 articles equals to the SP of 12 articles", this implies that
15 c.p = 12 s.p
s.p = 15c.p / 12
s.p = [tex]\frac{15 c.p}{12}[/tex] = [tex]\frac{5c.p}{4}[/tex]
s.p = [tex]\frac{5c.p}{4}[/tex]
substitute s.p = [tex]\frac{5c.p}{4}[/tex] into the formula
gain% = [tex]\frac{s.p - c.p}{c.p}[/tex] × 100%
=[tex]\frac{\frac{5c.p}{4} - c.p }{c.p}[/tex] × 100%
= [tex]\frac{\frac{5c.p - 4c.p}{4} }{c.p}[/tex] × 100%
= [tex]\frac{c.p}{4}[/tex] ÷ c.p × 100%
= [tex]\frac{c.p}{4}[/tex] × [tex]\frac{1}{c.p}[/tex] × 100%
= [tex]\frac{1}{4}[/tex] × 100%
= 25 %
At a pond, there were 24 ducks swimming. The ratio of ducklings to adult ducks is 5:1. How many ducklings were swimming at the pond?
Answer:
Hey there!
The ratio of ducklings to adult ducks is 5:1.
This means for every six ducks, five are ducklings and one is an adult.
If there are 24 ducks, then 5 times 4 = 20 ducklings and 4 adults.
Thus, there are 20 ducklings.
Hope this helps :)
Answer:
20 ducklings.
Step-by-step explanation:
Solve the equation for x.
Answer:
x = 27
Step-by-step explanation:
2/3x - 1/9x + 5 = 20
Subtract 5 from each side
2/3x - 1/9x + 5 -5= 20-5
2/3x - 1/9x = 15
Get a common denominator on the left side
2/3 *3/3 x - 1/9x = 15
6/9x - 1/9x = 15
5/9 x = 15
Multiply each side by 9/5
9/5 * 5/9x = 15 * 9/5
x = 15/5 *9
x = 3*9
x = 27
Answer:
x=27
Step-by-step explanation:
2/3 x -1/9 x+5=20
2/3x -1/9 x=20-5 common denominator
(6x-1x)/9=15 multiply each side by 9
(5x)=135
5x=135
x=135/5=27
x=27