Answer:
Step-by-step explanation:
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is:((x1 + x2)/2, (y1 + y2)/2)Substituting the coordinates of points P and Q into the formula, we get:((2 + (-7))/2, (4 + (-2))/2) = (-2.5, 1)The coordinates of the midpoint of segment PQ are (-2.5, 1).To verify that this point is on the line through P and Q, we can find the slope of the line using the coordinates of points P and Q:slope = (y2 - y1)/(x2 - x1) = (-2 - 4)/(-7 - 2) = -6/-9 = 2/3We can then use the point-slope form of a linear equation to write the equation of the line through points P and Q:y - y1 = m(x - x1)
y - 4 = (2/3)(x - 2)We can substitute the coordinates of the midpoint (-2.5, 1) into this equation to see if it is a solution:1 - 4 = (2/3)(-2.5 - 2)
-3 = -10/3The equation is true, so the midpoint (-2.5, 1) is on the line through points P and Q.To show that this point is just as far from P as it is from Q, we can use the distance formula to find the distance from the midpoint to points P and Q:distance = √((x2 - x1)^2 + (y2 - y1)^2)distance from (-2.5, 1) to (2, 4) = √((2 - (-2.5))^2 + (4 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4distance from (-2.5, 1) to (-7, -2) = √((-7 - (-2.5))^2 + (-2 - 1)^2) = √(4.5^2 + 3^2) = √(20.25 + 9) = √(29.25) = 5.4. Since the distance from the midpoint to points P and Q is the same, the midpoint is just as far from P as it is from Q.
line L has y- intercept at (0,4) and an x- intercept at (10,0)
Answer:
y = -2/5 x + 4
Step-by-step explanation:
slope = (0-4)/(10-0)
-4/10
-2/5
y intercept = 4
y = -2/5 x + 4
I have 2/3 L (litre) of liquid detergent. I ued 3/4 of thi to wah my heet on the weekend. How much liquid detergent do I have left?
Liquid detergent do I have left is 8/9.
What is detergent ?
When washing items like clothing or dishes, detergent is a chemical compound that is often in the form of a powder or liquid. Alternatives include washing liquid, soap powder, and cleaner. More detergent synonyms. More detergent synonyms.
I have 2/3 L (litre) of liquid detergent. I ued 3/4 of thi to wah my heet on the weekend.
[tex]\frac{\frac{2}{3}}{\frac{3}{4}}$$[/tex]
Apply the fraction rule: [tex]$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a \cdot d}{b \cdot c}$[/tex]
[tex]=\frac{2 \cdot 4}{3 \cdot 3}$$[/tex]
Multiply the numbers: 2-4=8
[tex]=\frac{8}{3 \cdot 3}$$[/tex]
Multiply the numbers: 3-3=9
[tex]=\frac{8}{9}$$[/tex]
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a trucker driver can expect to make $us55,065 per year in the us. assuming that this driver works 70 hours per week and 52 weeks per year, what is the equivalent salary in canadian dollars per hour?
The equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
To convert the annual salary of a truck driver in the US from US dollars to Canadian dollars, you can use the current exchange rate between the two currencies. The exchange rate fluctuates constantly, so you will need to use the most current rate.
Assuming the current exchange rate is 1 US dollar to 1.26 Canadian dollars, the annual salary of a truck driver in the US, $55,065, is equivalent to 71,040.90 Canadian dollars. If the truck driver works 70 hours per week and 52 weeks per year, their hourly wage in Canadian dollars would be $28.13.
Here's the calculation:
Annual salary in Canadian dollars = $55,065 * 1.26 = $71,040.90
Hourly wage in Canadian dollars = $71,040.90 / (70 hours/week * 52 weeks/year) = $28.13/hour
Keep in mind that this is just a rough estimate, as the exchange rate can change over time, and the actual wage may vary depending on the driver's experience, location, and other factors.
So, the equivalent salary in Canadian dollars per hour of the driver is $28.13/hour.
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the tens digit of a two-digit number exceeds the units digit by 1. if the number is divided by the sum of its digits, the quotient is 6. what is the number?
The reqiured two digit number is 54
Let, a two-digit number be n
the digit at tens place as x and the digit at unit place be y
The tens digit of a two-digit number exceeds the units digit by 1.
x = y + 1 .............(1)
if the number is divided by the sum of its digits, the quotient is 6.
(10x + y)/(x + y) = 6
Substitute above value of x in this equation.
(10(y + 1) + y) = 6(y + 1 + y)
10y + 10 + y = 6(2y + 1)
11y + 10 = 12y + 6
y = 4
Substitute above value of y in equation (1),
x = 4 + 1
x = 5
So, the number would be, 10x + y = 50 + 4
= 54
Therefore, the number is 54
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Helen thinks of two numbers. The highest common factor of her two numbers is 5. The lowest common multiple of her two numbers is a multiple of 12. Write down two possible numbers that Helen could be thinking of.
It is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.
Explain the term LCM and HCF?The entire form of the Least Common Multiple in mathematics is LCM, whereas the official name of the Highest Common Factor is HCF. The L.C.M. indicates the least number that is precisely divisible by 2 or more numbers, while the H.C.F. describes the biggest factor existing between any given pair of 2 or more numbers.The given condition are-
Helen considers two numbers that fit the following criteria:
Five is the two integers' largest common factor.Twelve is the least frequent multiple of a two numbers.The steps to solve the condition are-
1. It is assumed that when Helen considers of two numbers, they have corresponding HCF and LCM values of 5 and 12.
2. A smallest common multiple shared by two numbers is referred to as the least common number.
LCM of 4 with 6 is 12, for instance.
3. The highest number which divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.
HCF of 6 and 8 is 2, for instance.
4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are indeed the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.
5. The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values apart from 5. 60 and 120 have an HCF of 60, but not 5.
6. As a result, it is evident from the steps above that it is impossible to be have two numbers with the same LCM and HCF as 12 and 5, respectively.
Therefore, the aforementioned criteria cannot exist mathematically.
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A store sells new video games for $45 each and used video games for $14 each. Jerry is buying 3 new video games and xused video games?
forty-five times three equals one-hundred-thirty-five
45x3=135
Leslie creates designer bracelets with gemstones. Her most recent order included a total of 7 bracelets. It takes 14 stones to make one bracelet. Write and solve an equation that represents how many stones were used for the order.
7s = 14; s = 2 stones
s/14 = 7 ; s = 98 stones
s + 7 = 14; s = 7 stones
s − 7 = 14; s = 21 stones
An expression that represents the number of bracelet Leslie designs is
s/14 = 7 ; s = 98 stonesHow to find the number of stones used for the orderInformation from the question include
Her most recent order included a total of 7 bracelets
It takes 14 stones to make one bracelet
let s represent stone
It takes 14 stones to make one bracelet means that one bracelet = 14 s
hence if 1 bracelet is 14 stones then 7 bracelet will be
1 bracelet = 14 s
7 bracelet = ?
cross multiplying
1 * ? = 7 * 14
? = 98 stones
the equation is written as
s/14 = 7 ; s = 98 stones
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An elevator started on the first floor and went up 18 floors. It then came down (11 floors,
and went back up 16. At what floor did the elevator stop?
An elevator stop for 23 floor.
it went up so +18
it came down so -11
again it went upward +16
so... 18-11+16
=18+16-11
=34-11
=23
An elevator or lift is a cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or decks of a building, vessel, or other structure. They are typically powered by electric motors that drive traction cables and counterweight systems such as a hoist, although some pump hydraulic fluid to raise a cylindrical piston like a jack.
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Answer:
24th floor
Step-by-step explanation:
You want to know where an elevator stopped if it started at the first floor, went up 18, down 11, and back up 16.
Floor numberIf it started at the first floor and went up 1, it would be at the 2nd floor. Starting from the first floor and going up 18, it would be at the 19th floor.
Down 11 floors from there is the 8th floor. Back up 16 floors from the 8th floor puts the elevator at the 24th floor.
The elevator stopped at the 24th floor.
__
Additional comment
If there is no 13th floor, then it may have stopped at the 25th floor.
assume a single spin of the roulette wheel is made. find the probability of the marble landing on a 00 or even slot.
By applying this theory, it is discovered that there is an 0.5 = 50% chance that the marble will land on a 00 or even slot.
What is the definition of the term probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.A probability is calculated by dividing the entire number of possible outcomes by the desired outcomes.
In this issue:
There are thus 38 positions; T =3818 of them are even, plus 00, so D = 19The preferred likelihood is:
P = D/T
P = 19/38 = 0.5
Thus, the probability that the marble will land on a 00 or even slot is 50%, or 0.5.
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The complete question is-
When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a 00 or even slot.
using the graph, determine the question of the axis of symmetry
The required equation is y = -(x + 1)² + 9.
What is parabola ?Parabola is a curve like shape, in which any point is equal distance from a fix point.
The standard equation of parabola,
y = a(x-h)² + k.
Here, h = horizontal coordinate of the vertex,
k = vertical coordinate of the vertex.
In the given graph, the vertical coordinate of the vertex k = 9,
The horizontal coordinate of the vertex h = -1.
And the focus of the parabola = -1,
The required equation,
y = -1(x - (-1))² + 9
y = -(x + 1)² + 9
The required equation of the given graph is y = -(x + 1)² + 9.
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1-a)divide both sides by 2 and then subtract 1.1
b)divide both sides by 2 and then add 1.1
C)multiply both sides by 2 and then subtract 1.1
d)multiply both sides by 2 and then add 1.1
3-a)add or b)subtract
4-a) multiply b) divide
One way to solve 2(a - 1.1) = 5.8 is divide both sides by 2 and then add 1.1 on both sides to find a = 4.
To solve 5/2 b - 2 3/4= 7 1/4, add 2 3/4 on both sides, and then multiply both sides by 2/5 to find b = 4.4
In the equation a and b divide the same value.
What is an equation?
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
Given equation is
2(a - 1.1) = 5.8
divide both sides by 2
a - 1.1 = 5.8/2
a - 1.1 = 2.9
Add 1.1 on both sides:
a - 1.1 + 1.1 = 2.9 + 1.1
a = 4.
Another equation is
5/2 b - 2 3/4= 7 1/4
add 2 3/4 on both sides:
5/2 b= 7 1/4 + 2 3/4
Convert the mixed fraction to improper fraction:
5/2 b = 29/4 + 15/4
5/2 b = 44/4
Multiply both sides by 2/5:
b = (44/4) × (2/5)
b = 11× (2/5)
b = 22/5
b = 4.4
Both number 4 a and 4.4 is divisible by 4.
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Find the rate of change shown in the table. X 1 2 3 4 Y -3 -q -15 -21
Answer:
q = -9
Step-by-step explanation:
(3, -15), (4, -21)
(-21 + 15)/(4 - 3) = -6/1 = -6
y + 15 = -6(x - 3)
y + 15 = -6x + 18
y = -6x + 3
q = -6(2) + 3 = -12 + 3 = -9
Jorge has a box with different colors of tubes of paint. In the box, there are 7 tubes of blue paint, 4 tubes of red paint, 3 tubes of yellow paint and 6 tubes of green paint. Jorge selects a tube of paint at random. Which is more likely: selecting a tube of blue or yellow paint, OR selecting a tube of green or red paint?
The probability that is more likely between selecting a tube of blue or yellow paint, OR selecting a tube of green or red paint id; Both are equally lilkely.
What is the probability of selection?We are given;
Number of blue tubes = 7
Number of red tubes = 4
Number of yellow tubes = 3
Number of green tubes = 6
Thus;
Total number of painted tubes = 7 + 4 + 3 + 6 = 20
Probability of selecting a blue tube = 7/20
Probability of selecting a red tube = 4/20
Probability of selecting a yellow tube = 3/20
Probability of selecting a green tube = 6/20
Thus;
P(selecting a tube of blue or yellow paint) = (7/20) + (3/20) = 10/20
P(selecting a tube of green or red paint) = (6/20) + (4/20) = 10/20
Thus, they are equally likely.
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due today pls help me :c
1. (x + 2)(2x + 3) =
???? Help lol
Answer:
[tex]2x^2+7x+6[/tex]
Step-by-step explanation:
Use the FOIL method to multiply these two expressions:
[tex](x+2)(2x+3)\\x(2x)+2(2x)+3(x)+2(3)\\2x^2+4x+3x+6\\2x^2+7x+6[/tex]
Line c has an equation of y= 1 /5 x–3. Line d, which is parallel to line c, includes the point (– 1,1). What is the equation of line d?
Answer:
[tex]y=\frac{1}{5}x+\frac{6}{5}[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of line [tex]d[/tex] is [tex]1/5[/tex].
So, the equation of line [tex]d[/tex] is:
[tex]y-1=\frac{1}{5}(x+1) \\ \\ y-1=\frac{1}{5}x+\frac{1}{5} \\ \\ y=\frac{1}{5}x+\frac{6}{5}[/tex]
The function `P` gives the number of people, in millions,
who own a smartphone, `t` years after year 2000. could t be 4 ?
The interpretations of the equations are
(a) P(17) = 2320: There are 2320 million people in 2017(b) P(-10) = 0: There are 0 million people in 1990How to interpret the equationsFrom the question, we have the following parameters that can be used in our computation:
The function `P` gives the number of people, in millions,
Years = t
The function P(17) = 2320
Recall that, we have
P(t) = the number of people, in millions,
This means that the year is
Year = 2000 + 17
Year = 2017
So, the interpretation is there are 2320 million people in 2017
The function P(-10) = 0
So, we have
Year = t + 2000
Substitute the known values in the above equation, so, we have the following representation
Year = -10 + 2000
Evaluate
Year = 1990
So, the interpretation is there are 0 million people in 1990
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Complete question
The function gives the number of people , in millions. who own smarphone t years alter the year 2000
What does each equaton tell us about smartphone ownership?
(a) P(17) = 2320
(b) P(-10) = 0
The sales tax is $53 on the purchase of a dining room set for $1060. Find the sales tax rate.
Answer: Sale tax rate is 5%
Step-by-step explanation:
Take $53 divided by $1060, then time 100% = 5%
suppose the lifetime of a particular brand of tire for cars is approximately normally distributed with a mean of 48,000 miles and standard deviation of 3,000 miles. step 1 of 2: what is the probability that a single tire randomly selected from the population will have a lifetime between 46,800 and 49,200 miles? round your answer to 4 decimal places if necessary.
0.3108 is the probability that a single tire randomly selected from the population will have a lifetime between 46,800 and 49,200 miles
What is probability?Probability is a mathematical discipline that concerns with numerical figures of how probable an occurrence is to occur or how probably a statement is to be true. A number between 0 and 1 is the probability of an occurrence, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
X ~ N ( µ = 48000 , σ = 3000 )
As we know, P ( 46800 < X < 49200 )
Standardizing the value, we get -
Z = ( X - µ ) / σ
Z = ( 46800 - 48000 ) / 3000
Z = -0.4
Z = ( 49200 - 48000 ) / 3000
Z = 0.4
Also,
P ( -0.4 < Z < 0.4 )
P ( 46800 < X < 49200 ) = P ( Z < 0.4 ) - P ( Z < -0.4 )
P ( 46800 < X < 49200 ) = 0.6554 - 0.3446 (Probability calculated from Z table)
P ( 46800 < X < 49200 ) = 0.3108
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Mr. Dyson works at a music camp. he has $90 to spend on guitar strings for his students. a pack of bronze strings cost $6. A pack of nickel strings cost $4.50. The equation 6x + 4.5y = 90 represents the situation. how many packs of nickel strings does he buy if he only buys nickel strings and no bronze strings.
By evaluating the linear equation, we will see that Mr. Dyson will buy 20 packs of nickel strings.
How many packs of nickel strings does he buy?We know that the linear equation:
6x + 4.5*y = 90
Represents the given situation, where the variable x is the number of bronze strings and y is the number of nickel strings.
We want to find the number of packs of nickel strings that he will buy if he does not buy any bronze strings, so we need to evaluate in x = 0.
We will get:
6*0 + 4.5*y = 90
4.5*y = 90
y = 90/4.5 = 20
He will buy 20 packs of nickel strings.
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Find the additive inverse of -[tex]\frac{1}{2}[/tex]
Answer: 1/2
Step-by-step explanation:
Let N be any number and M be the additive inverse of N
N + M = 0 = M + N
that additive inverse of N is - N
x + ( - 1/2 ) = 0
x - 1/2 = 0
x = 1/2
the additive inverse of -1/2 is 1/2
Suppose that scores on the mathematics part of the National Assessment of Educational
Progress (NAEP) test for high school seniors follow a normal distribution with mean 240 and standard deviation 27. In a random sample of 49 students, find the probability that their average score is between 200 and 250.
The probability that their average score is between 200 and 250 is 42.49%.
What is z- score?The Z-score quantifies the discrepancy between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree
Given:
Mean = 240
and standard deviation = 27
So, P( 200 < x < 250) = P( (x- [tex]\mu[/tex])/ [tex]\sigma[/tex] < x < x- [tex]\mu[/tex])/ [tex]\sigma[/tex])
= P (200- 240 / 27 < x < 250- 240 /27)
= P( -1.481 < x < 0.370)
= 0.42499
Hence, the probability that their average score is between 200 and 250 is 42.49%.
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a box of frozen vegetables weighing 144kg 780g was delivered at a grocery shop. If there were 15 packets of equal inside the box, what was the weight of each bag?
Answer:
9.652 kg
Step-by-step explanation:
144 kg 780 g = 144.78 kg
if there are 15 packets in the box then:
144.78 ÷ 15 = x
x = 9.652 kg
Therefore the weight of each bag is 9.652 kg
Jada sold 9 stuffed animals last year, which was 36 % of her collection. How many stuffed animals did she start the year with?
Answer:
25
Step-by-step explanation:
9/x = 36/100
9 x 4 = 36
? x 4 = 100
100 ÷ 4 = 25
Will give thanks 5 stars and brainliest if work shown
Answer:
152°
Step-by-step explanation:
Circle Theorem vocabulary
Secant: a straight line that intersects a circle at two points.
Arc: the curve between two points on the circumference of a circle
Intercepted arc: the curve between the two points where two chords or line segments (that meet at one point on the other side of the circle) intercept the circumference of a circle.
Angles of Intersecting Secants Theorem
If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.
[tex]\implies m \angle PRD=\dfrac{1}{2}\left(m\overset{\frown}{PD}-m\overset{\frown}{QS} \right)[/tex]
From inspection of the given diagram:
[tex]m \angle PRD=50^{\circ}[/tex][tex]m\overset{\frown}{PD}=(12x+8)^{\circ}[/tex][tex]m\overset{\frown}{QS}=(4x+4)^{\circ}[/tex]Substitute these into the formula and solve for x:
[tex]\implies 50^{\circ}=\dfrac{1}{2}\left((12x+8)-(4x+4)\right)^{\circ}[/tex]
[tex]\implies 50^{\circ}=\dfrac{1}{2}\left(8x+4\right)^{\circ}[/tex]
[tex]\implies 100^{\circ}=(8x+4)^{\circ}[/tex]
[tex]\implies 96^{\circ}=8x^{\circ}[/tex]
[tex]\implies x=12[/tex]
Substitute the found value of x into the expression for arc PD:
[tex]\implies m\overset{\frown}{PD}=(12x+8)^{\circ}[/tex]
[tex]\implies m\overset{\frown}{PD}=(12 \cdot 12+8)^{\circ}[/tex]
[tex]\implies m\overset{\frown}{PD}=(144+8)^{\circ}[/tex]
[tex]\implies m\overset{\frown}{PD}=152^{\circ}[/tex]
Therefore, the measure of arc PD is 152°.
HELP ASAP DUE TODAY
!
Answer:
Step-by-step explanation:
2x - 3y = 6
-3y = -2x + 6
y = 2/3x - 2
correct answer is A
5.
The population of arctic foxes in Yukon can be modelled by the following equation:
P = 400 cos(30t - 180) + 1100
Where 't' represents the number of years since 1992.
a.
What was the population of arctic foxes in Yukon in 1992?
b. What are the maximum and minimum number of arctic foxes?
C. Sketch a graph that represents how the population of artic foxes changes over time (since 1992).
D. What will be the population of arctic foxes in 2030?
E. When was the first time the population of arctic foxes reached 1300 (since 1992)?
Answer:
Step-by-step explanation:
[tex]P(t)=400cos(30t-180)+1100[/tex]
a. What was the population of arctic foxes in Yukon in 1992?
t' represents the number of years since 1992. So plugging in 0 gives the population in 1992.
[tex]P(0)=400cos(30*0-180)+1100[/tex]
Subtract 180 from 0.
[tex]P(0)=400cos(-180)+1100[/tex]
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
[tex]P(0)=400(-cos(0))+1100[/tex]
The exact value of cos (0) is 1.
[tex]P(0)=400(-1*1)+1100[/tex]
[tex]P(0)=400*-1+1100[/tex]
Multiply 400 by −1. Then add −400 and 1100.
[tex]P(0)=700[/tex]
D. What will be the population of arctic foxes in 2030?
[tex]P(38)=400cos(30(38)-180)+1100[/tex]
[tex]P(38)=900[/tex]
Find the value of b.
Give reasons.
Answer:
b = 72
Step-by-step explanation:
Since AB and AC are congruent then Δ ABC is isosceles with base angles also congruent, that is
∠ ACB = ∠ ABC = b
the sum of the 3 angles in the triangle is 180° , then
b + b + 36 = 180
2b + 36 = 180 ( subtract 36 from both sides )
2b = 144 ( divide both sides by 2 )
b = 72
Israel and Kylie plan a fundraiser for a running club. They begin with a balance of $-80 because of expenses. In the first hour of the fundraiser, they collect equal donations from 9 family members, which brings their balance to $-44. How much did each parent give?
Explain.
Answer: $4
Step-by-step explanation: To find how much each family paid, we must do this:
80-44
That gets us to 36. Now, we do 36 / 9, and get 4!
TIP: Don't worry about the negative signs, It won't be used in this. I hope this helped!
A cla ha 12 boy and 18 girl. The cla a a whole ha a GPA (grade point average) of 2. 88, and the boy have a GPA of 2. 52. What i the GPA of the girl? (Round your anwer to two decimal place. )
The GPA of the girls is 3.12
In this question, we have been given a class has 12 boys and 18 girls.
The class as a whole has a GPA (grade point average) of 2.88, and the boys have a GPA of 2.52
We need to find the GPA of girls.
Let m be the GPA of girls.
The weighted average GPA would be,
(12(2.52) + 18m)/ (12+18) = 2.88
We solve above equation to find the value of m
30.24 + 18m = 30 * 2.88
18m = 86.4 - 30.24
18m = 56.16
m = 3.12
Therefore, the GPA of the girls in the class is 3.12
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