Answer: 6
Step-by-step explanation:
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
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
*NOT A QUIZ QUESTION JUST REGULAR HOMEWORK*
Two figures are similar when they have some common properties. The value of PQ as required is 28 units.
Similar triangles are two or more which have a series of common properties. This may be in relations to the length of their sides or measure of their angles.
In the given triangle PQR,
ΔPQS ll ΔSTR
Given that PS = RS, and QT = RT.
Then we can say that;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{PQ}{PQ}[/tex]
But, PR = 2RS;
[tex]\frac{RS}{ST}[/tex] = [tex]\frac{2RS}{PQ}[/tex]
[tex]\frac{1}{ST}[/tex] = [tex]\frac{2}{PQ}[/tex]
2ST = PQ
2(-22 + 9x) = 9x - 8
-44 + 18x = 9x - 8
18x - 9x = -8 + 44
9x = 36
x = 4
So that,
PQ = 9x - 8
= 9(4) - 8
PQ = 36 - 8
= 28
Thus, the length of PQ is 28 units.
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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°.
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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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%
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.
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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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
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
Help me with ixl please
A straight line = 180°. You have: 58° , 40°, and q so:
q = 180° - (58° + 40°)
q = 82°
Answer:
82
Step-by-step explanation:
180 i s the line length so
180-40=140
140-58=82
A truth erum ha the property that 90% of the guilty upect are properly judged while, of coure, 10% of the guilty upect are improperly found inno cent. On the other hand, innocent upect are mi judged 1% of the time. If the upect wa elected from a group of upect of which only 5% have ever committed a crime, and the erum indicate that he i guilty, what i the probability that he i innocent
Therefore in this question the probability that he is innocent is 0.1743
What is probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Here,
In this case, let G represent the state of guilt and H represent the state of innocence.
and Let K stand for the situation where the truth serum shows that someone is guilty.
We are aware that 90% of the guilty suspects receive just verdicts, i.e. P(K|G)=0.9.
Additionally, we know that innocent suspects are mistakenly identified 1% of the time, or P(K|H)=0.01.
When a suspect is chosen from a group of suspects, of whom 5% committed a crime, and the serum suggests that the suspect is guilty, we must determine the likelihood that the suspect is innocent.
We must therefore determine the probability P(H|K).
A group of people was chosen for the suspect, of which 5% were criminals.
so the probability that selected person is guilty is
P(G) = 0.05
Therefore, the probability that selected person is not guilty is
P(H) = 1 – P(G) = 1 – 0.05 = 0.95
Then,
Using Bayes' Theorem, we get
P(H|K) =[tex]\frac{P(H)P(K|H)}{P(H)P(K|H) + P(G)P(K|G)}[/tex]
= [tex]\frac{0.95*0.01}{0.95*0.01 + 0.05*0.9}[/tex] =0.1743
Therefore in this question the probability that he is innocent is 0.1743
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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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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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The figure is made up of 10 identical squares. The perimeter is y cm. What is the side
of each square in terms of y?
(answer in cm)
The side of each square in terms of y is y/16.
What is a perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges.
Here, we have
The figure is made up of 10 identical squares. The perimeter is y cm.
The number of outer sides is 16
Let the side be x
then
16x = y
x = y/16
Hence, the side of each square in terms of y is y/16.
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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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Hello, can someone help me out with this question please!?!?!
Answer: C
Step-by-step explanation:
Distributive property 2. combine like terms 3. subtraction proerty of equality 4 division of equality.
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]
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
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]
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average peed of 52 km/h. A) Find the time at which the lorry the time taken arrive at it detination. B) on the return journey, the lorry leave at 14 55 and arrive at the factory at 18 15. Calculatge the time taken and the average peed of the lorry on the return journey
The time at which the lorry the time taken arrive at it destination is 12.20.
Given :
A lorry leave a factory on a journey of 195km at 08 45 , travelling at an average speed of 52 km/h.
here,
Distance = 195 km
Speed = 52 km/h
we know that ,
speed = distance / time
on cross muliplicating
speed * time = distance
time = distance / speed
substitute the values
time = 195 / 52
= 3.75 hours
destination time = 8.45 + 3.75
= 12.20
Therefore the time at which the lorry the time taken arrive at it destination is 12.20
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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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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
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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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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Whitch one is correct a b c or d
Answer:
Step-by-step explanation:
u got it right the first time it is D
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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What is the 9th term of the sequence 2,8,32,128
Answer: 131072
Step-by-step explanation:
Basically the sequence is just being multiplied by 4, like 2(4)=8 and 8 is the next number in the sequence or 32(4)=128 which then again is the next number in the sequence.
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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