Jessica's speed is 4 mph and Janine's speed is 8 mph
Let us assume that x represents Jessica's speed.
Janine bikes 4 mph faster than her sister, Jessica.
So, Janine's speed would be (x + 4) mph
We know that the formula for the speed is: speed = distance/time
Here, Janine can ride 24 mi in 3 hr less time than Jessica can ride the same distance.
24/(x+4) = (24/x) - 3
24/(x+4) = (24 - 3x)/x
24x = (24 - 3x)(x + 4)
24x = 24x + 96 - 3x² - 12x
3x² + 12x - 96= 0
After solving above quadratic equation we get.
(x - 4) (x + 8) = 0
x = -8 speed is not possible.
So, x = 4 mph
And x + 4 = 8 mph
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a jet travels 2964 miles against the wind in 4 hours and 3564 miles with the wind in the same amount of time. what is the rate of the jet in still air and what is the rate of the wind?
The rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.
What is rate ?
A rate is a ratio of two quantities, typically a change in one quantity over a corresponding change in another quantity, often over a specific time period. For example, the interest rate on a loan is the ratio of the interest paid to the amount of the loan. A speed is a rate at which an object covers distance, velocity is a rate of change of position, etc.
To find the rate of the jet in still air:
Rate = Distance / Time
The distance is 2964 miles, and the time is 4 hours. So the rate of the jet in still air is:
Rate = 2964 / 4 = 741 mph
To find the rate of the wind, you can use the formula:
Wind Rate = (Distance with wind - Distance against wind) / Time
The distance with the wind is 3564 miles, the distance against the wind is 2964 miles, and the time is 4 hours. So the rate of the wind is:
Wind Rate = (3564 - 2964) / 4 = 600 / 4 = 150 mph
So the rate of the jet in still air is 741 mph, and the rate of the wind is 150 mph.
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There are 10 girls and 16 boys in a class. The teacher has sticks with each student's name on them in a bag. What is the probability of selecting sticks with a boy's
name and then a girl's name if the first stick is not replaced?
40
A
169
(B)
16
65
45
128
26
51
The probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.
Now, According to the question:
Formula to find the probability of an event:
"P(A) = n(A) / n(S)
where, n(A) is the number of favorable outcomes of an event A
n(S) is the total number of outcomes for an experiment"
"Information available from the question"
Total number of students are,
n(S) = 10 + 16
n(S) = 26
Let event A: selecting first stick with a boy name
n(A) = 16
So, the probability of a boy is,
P(A) = n(A)/n(S)
P(A) = 16/26
P(A) = 8/13
if the first stick is not replaced, then n(S) would be,
26 - 1 = 25
Let event A: selecting first stick with a boy name
n(B) = 10
So, the probability of a boy is,
P(B) = n(B)/n(S)
P(B) = 10/25
P(B) = 2/5
Therefore, the probability of selecting sticks with a boy's name is 8/13 and the probability of selecting sticks with a girl's name is 2/5.
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For every mile of highway on land, the city needs two truckloads of asphalt and one gallon of paint. For every mile of highway on bridges, the city needs one truckload of asphalt and three gallons of paint. The city has 50 truckloads of asphalt and 80 gallons of paint.
(a)What is the largest total number of miles of highway the city can build?
(b)Suppose the city is on an island and must build at least 25 miles of highway on bridges to reach other islands. Now what is the largest total number of miles of highway the city can build?
A Are they are limited to the amount of paint they have? 80g / 1 g/mile = 80 miles using all of the paint
50 trucks /2 trucks/mile = 25 miles using all of the trucks of asphalt
B 25 miles of bridge = = 25 trucks leaving 25 trucks of asphalt 25 trucks/2 trucks/mile = 12.5 miles of land highway possible
25 miles of bridge = 25 miles x 3 gal/mile = 75 gallons of paint leaving only 5 gallons of paint for 5 add'l land miles
25 miles of bridge + 5 land miles = 30 miles total highway .
An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is x. Another side is 11 more than four times the length of the bottom of the triangle. The last side is 11 more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle. Help please i'm not smart-
The expression for the perimeter of the triangle will be 6x + 22.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The perimeter of the triangle is determined by adding together all of its sides.
A workmanship class is making a painting for their school which has a triangle attracted the center. The length of the lower part of the triangle is x. Another side is 11 a larger number of than 4 times the length of the lower part of the triangle. The last side is 11 a greater number of than the lower part of the triangle.
Then the dimension of the triangle will be x, 4x + 11, and x + 11. Then the perimeter isgiven as,
P = x + 4x + 11 + x + 11
P = 6x + 22
The expression for the perimeter of the triangle will be 6x + 22.
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which of the following is not true of a good hypothesis? a) it includes a null hypothesis b) it is experimentally testable c) it is phrased as an if, then statement d) it must contradict previous theories e) it could explain an unexpected observation.
False claims do not have to engage with previous theories in order to be effective. So it must contradict previous theories. So the option d is correct.
A tentative, verifiable explanation for a natural world phenomenon is what is known as a scientific hypothesis. The scientific method's foundational element is it.
It's sometimes referred to as a "informed guess" that was made using past knowledge and observation. Despite the fact that this is true, a hypothesis is a better guess.
Creating a hypothesis calls for active observation and background research, in contrast to making a "informed guess," which implies a random prediction based on one's expertise. A hypothesis is predicated on the fundamental tenet that no outcome is predetermined.
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12. Estimate the average rate of change of p between peak, p(8), and closing, p(14). What is
the meaning of the rate of change in the context of this problem? Show all work.
The rate of change in this context refers to the change in the value of p, specifically between the peak and closing.This allows us to understand how much p changes on average between these two points in time.
What is the meaning of the rate of change in the context of this problem?It is a measure of how quickly or slowly the value of p is changing over time.
By calculating the average rate of change, we can understand the overall trend of the value of p and whether it is increasing or decreasing at a steady rate or if there are fluctuations.
This information can be useful for understanding the performance of a stock or investment, as well as predicting future trends.
Additionally, the rate of change can also help to identify any potential issues or opportunities within the market.
Overall, the rate of change provides a clear picture of the stock's performance over a certain period of time.
To calculate the average rate of change of p between peak and closing, we need to find the difference in p values (p(14) - p(8)) and divide that by the difference in time (14 - 8).
p(14) - p(8) = ? - ? = ?
(14 - 8) = ?
The average rate of change of p is ?/6.
The meaning of the rate of change in the context of this problem is the average change in the value of p per unit of time.
In this case, we are looking at the average change in p between the peak and closing, and expressing that change as a ratio of p(14) - p(8) to (14 - 8). This allows us to understand how much p changes on average between these two points in time.
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John goes to a restaurant and has a bill of 32.57. He uses a 10% off coupon on the cost of the meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied. how much does he spend?
The total amount spent by John is $37.78.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that John goes to a restaurant and has a bill of 32.57. He uses a 10% off coupon on the cost of the meal. The tax is 8%. He leaves a tip of 18% on the amount before the coupon or tax is applied.
Amount left as a tip -
{t} = 18% of 32.57
{t} = 18/100 x 32.57
{t} = 5.87
Amount included in tax -
8% of 32.57
8/100 x 32.57
2.61
Billed amount after coupan is applied -
10% of 32.57
10/100 x 32.57
$3.26
Amount spend -
(32.56 - 3.26) + 2.61 + 5.87
$37.78
Therefore, the total amount spent by John is $37.78.
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Bicycles in the late 1800s looked very different than they do today.
60ft 9ft
a. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.
Note that where the diameter of the bicycles are 60 inches and 9 inches respectively, the rotation of each tire after traveling 600 feet would be:
Small Tire (9in Diameter ) = 188.4 Rotations.
Big Tire (60 in Diameter) = 3.2 rotations
Note that the above were arrived at using the knowledge of Circumference.
What is the circumference of a circle?Note that the circumference in geometry is the perimeter of a circle or ellipse.
This is calculated using the formula:
C = 2πr
or
C = πD
Where C = Circumference
R = radius
D = Diameter which is 2r
π = 3.14
To arrive at how many rotations each tire did, we'd have to divide the distance traveled by the circumference of each tire.
For the Small Tire, the diameter is 9 feet.
Thus, the circumference of Small Tire = 3.14 * 9
= 28.26 feet
Thus, the rotations by the small tire is:
600/28.26
= 21.2314225053
[tex]\approx[/tex] 21.2feet
Applying the same process to the big tire, we have:
C = 3.14 * 60
C = 188.4
The rotations by the big tire =
600/188.4
= 3.1847133758
[tex]\approx[/tex] 3.2 feet.
Thus, the rotations by each tire over 600ft is given as:
Big Tire = 3.2
Small Tire = 188.4 .
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Full Question:
See attached image.
in government data a household consists of all ocupants
American household size According to government statistics, a family is defined as two or more people who live together and are related by blood or marriage, whereas a household is defined as all the residents of a dwelling unit.
What do we mean by dwelling unit?A housing unit, also known as a dwelling unit or a housing unit, is a building, a portion of a building, or a space that is used as a home, a place to live, or a place to sleep by one or more people who maintain a common household.
Size of American households In contrast to a household, which is defined as all the occupants of a dwelling unit, a family is defined as two or more people who live together and are related by blood or marriage.
As a result, although all families are part of households, some households do not.
Therefore, American household size According to government statistics, a family is defined as two or more people who live together and are related by blood or marriage, whereas a household is defined as all the residents of a dwelling unit.
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1
2
2
y=1/30
y=3(4)
d
(3) *
LO
Which function is graphed below?
5
6
6
.CO...
8
X
7
8
9
10
TIME REMAIN
45:49
In a connection that is represented by an exponential function, the independent variable's proportional change is unchanged with a constant change in the independent variable.
Explain about the exponential function?Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.
When the input variable x appears as an exponent in the formula f(x) = axe, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x.
After x hours, you will have twice as much germs if you start with one and it doubles every hour. F(x) = 2x can be used to express this.
The fundamental exponential function generally has the shape,
y = nakx-------
(0,3) is the function's y intercept.
This location has to satisfy the equation (1). So let's substitute in order to get,
3 = na k(0)
⇒ 3 = n x a 0
⇒ 3 = n x 1
⇒ n = 3
Our equation 1 now changes.
y = nakx-------
Noting that the graph crosses through,(1 ,1) it must also satisfy its equation because it does so. Equation (2) can be solved by substituting this point, giving us
1 = 3ak (1)
⇒ 1/3 = ak
Now let's enter the value of ak = 1/3 into equation (3) to get,
y = 3(1/3)x
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EASY STATISTICS QUESTION--- PLEASE HELP!!!
The required mean of the table is 32.71.
How can I calculate the probability distribution's mean and standard deviation?Mean: The formula is E(X)=μ=∑xP(x). where x represents the value of the random variable X, P(x) represents the corresponding probability, and the symbol Σ represents the sum of all products xP(x). Here we use the symbol μ for mean, since it is a parameter. Represents the population mean.
Mean=Total of household/Total number of dogs
⇒ [tex]\frac{(323+176+87+51+32+8+10)}{(0+1+2+3+4+5+6)}[/tex]=[tex]\frac{687}{21}[/tex]=32.71
Standard Deviation: Standard deviation is calculated as the square root of variance by determining the deviation of each data point from the mean. If the data points are far from the mean, there will be more variation within the data set. Therefore, the wider the data, the higher the standard deviation.
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y=6 in graph form please!!!
Answer:
It will be straight line on x equal zero and y equal 6 horizontal straight line
Given that B is between A and C,
find the value of x and the measure
of BC.
AB = 3x, BC = 5x, and AC = 8.
The numerical value of x and the measure of segment BC are 1 and 5 respectively.
What is the numerical value of and the measure of BC?Given that; B is a point between A and C.
Segment AB = 3xSegment BC = 5xSegment AC = 8Since B is between A and C
AC = AB + BC
8 = 3x + 5x
Solve for x
8 = 8x
8x = 8
x = 8/8
x = 1
Next, determine the measure of BC,
BC = 5x
Plug in x = 1
BC = 5( 1 )
BC = 5
Therefore, x equal 1 and the measure of BC is 5.
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(Simple)......Classify the transformation pls
The transformation represented by the figure is (a) reflection
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
On the figure, we can
An arc and its mirrored image
When a shape is mirrored to form another, then the transformation is a reflection
Hence, the transformation is reflection
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(WILL MARK BRAINLIEST)
John plans to practice piano at least 2 1/2 hours this weekend.
If he practices 1 1/6 hours on Saturday and 1 1/4 hours on Sunday, will he meet his goal?
John will be able to meet the goal of practicing piano for mentioned time on Saturday and Sunday.
Required amount of practice = [tex]2 \frac{1}{2} [/tex] hours
Required amount of practice = (2×2)+1/2
Required amount of practice = 5/2 hours
Required amount of practice = 2.5 hours
Practice performed on Saturday = [tex]1 \frac{1}{6} [/tex]
Practice performed on Saturday = (6×1)+1/6
Practice performed on Saturday = 7/6 hours
Practice performed on Sunday = [tex]1 \frac{1}{4} [/tex]
Practice performed on Sunday = (4×1)+1/4
Practice performed on Sunday = 5/4 hours
Combined practice performed = 7/6 + 5/4
Combined practice performed = 1.2 + 1.3
Performing addition
Combined practice performed = 2.5 hours
The performed practice is equal to the goal and hence he will meet the goal.
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Which lines are perpendicular to 3x – y = 10? Select all that apply.
A. y = 3x + 5
B. y = –1/3x + 17
C. x + 3y = 27
D. y – 2 = 1/3 (3x + 36)
The lines that are perpendicular to 3x – y = 10, are y = –1/3x + 17 and x + 3y = 27.
The correct option is B and C.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
We have a linear equation,
3x – y = 10.
Arranging to the slope-intercept form.
y = 3x - 10.
The slope of the lines that are perpendicular to line y = 3x - 10,
= negative reciprocal of 3
= -1/3
Therefore, the required lines are y = –1/3x + 17 and x + 3y = 27.
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Which answer choice correctly shows 6 x 6 in exponential notation?
The expression that correctly shows 6 x 6 in exponential notation is 6²
How to determine the expression in exponential notationFrom the question, we have the following parameters that can be used in our computation:
6 * 6
Next, we apply the law of indices/exponent
So, we have the following representation
6¹⁺¹
Evaluate the sum
6²
Hence, the correct expression of 6 * 6 is 6²
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Let us assume that you started a job on 08/21/2019. You graduated on 05/20/2022. How many days have you been working at the job as a student?
Group of answer choices
a. 1215
b. 1287
c. 905
d. 1003
I have been working 1004 days at the job as a student
They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, and division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:Start = 08/21/2019Graduated = 05/20/2022Days =?Calculate the days from 08/21/2019 to 08/21/2022, we get:
Days 1 = (08/21/2022 - 08/21/2019) * (365 days/1 year)
Days 1 = 3 years * (365 days/1 year)
Days 1 = 1095 days
Calculate the days from 05/21/2019 to 08/21/2019, we get:
Days 2 = (08/21/2019 - 05/21/2019) * (30 days / 1 month)
Days 2 = 3 months * (30 days / 1 month)
Days 2 = 90 days
Calculating the days from 05/20/2019 to 05/21/2019, we get:
Days 3 = 05/21/2019 - 05/20/2019
Days 3 = 1 day
Calculate the total days from 08/21/2019 to 05/20/2022, we get:
Total days = Days 1 - days 2 - days 3
Total days = 1095 days - 90 days - 1 day
Total days = 1004 days
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Use the table, which shows the number of monthly users, in millions, for the 10
most used mobile gaming apps. Let the 10 mobile gaming apps be the universal
set. Use the list to determine the following set in roster form.
The set of mobile gaming apps in which the number of monthly users was greater
than 12 million.
Select the correct choice below and, if necessary, fill in the answer box within your
choice.
O A.
(Use a comma to separate answers as needed.)
OB. Ø
…
Mobile
Gaming App
A
B
CTIOπποο
D
Mobile
(in mill
23
5
6
6
13
9
12
11
11
10
The set of mobile gaming apps in which the number of monthly users was greater than 12 million is {A, B}
How to find the set of mobile gaming apps with monthly users greater than 12 million?A set is a collection of distinct objects, called elements or members, that are brought together by a common property or rule.
Sets can be represented using set notation, which uses curly brackets {} to enclose the elements of the set. For example, the set of natural numbers less than 5 can be represented as {1, 2, 3, 4}.
The set of mobile gaming apps in which the number of monthly users was greater than 12 million can be determined by checking given the table for mobile gaming apps with value greater than 12 million.
You will notice that only A and B have values greater than 12 million. That is 23 million and 13 million for A and B respectively.
Thus, the set will be {A, B}
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in a sample of 2000 people, 430 people have their ears pierced. two unrelated people are selected at random without replacement, find the probability that at least one of the people selected have their ears pierced.
How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out
How are probabilities calculated?The probability of anything occurring is known as probability. To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur.There is a 50% chance that the outcome will be heads, thus 50 heads are to be expected. When we really attempt it, though, we might instead get 48 heads, 55 heads, or anything else at all, but in most situations, it will be a figure close to 50.How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability.To learn more about probability refer to:
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A 5kg bag of peas cost $17.91 at the same rate what amount money would a 9kg bag of peas cost
Find the lateral surface area of the cylinder. Round your answer to the nearest tenth.
i think it is 326.7 but i really not sure
a bagel factory produced 90 bags of bagels. there were 10 bagels in each bag. how many bagels did the factory produce?
Answer:
900
Step-by-step explanation:
90 x 10
bryce and alejandro hiked miles. In one day, dominic hiked times as far as bryce and alejandro hiked. How far did he hike?
We can write the expression as →
{z} = n{x + y}
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that Bryce, Alejandro and Dominic went for hiking.
Assume that Bryce and Alejandro travelled {x} and {y} miles respectively.
Assume that Dominic hiked {z} miles and {n} times as far as Bryce and
Alejandro hiked.
We can write the expression as -
z = n{x + y}
Therefore, we can write the expression as →
{z} = n{x + y}
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jamal plans to buy a new laptop which is currently priced at $859. ON saturday the store is giving a 25% discount off all laptops =. he will need to pay 8.5% sales tax on the final purchase. how much will the final cost of the laptop be if jamal buys it on saturday.
The final cost of the laptop be if jamal buys it on saturday is $695.79
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
Given;
The new laptop is currently priced at $859
On saturday the store is giving a 25% discount off all laptops
Sales tax on final purchase=8.5%
Now, the final value on saturday be x
x*100/859=25
x=25*859/100
x=214.75
The value will be 859-214.75=644.25
8% of 644.25
x*100/644.25=8
x=8*644.25/100
x=51.54
Final cost= 644.25+51.54
=695.79
Therefore, the final cost after 8 percent sales tax will be $695.79
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Determine whether the variable is qualitative or quantitative Weight Is the variable qualitative or quantitative? A. The variable is qualitative because it is a numerical measure B. The variable is quantitative because it is an attribute characteristic. C. The variable is quantitative because it is a numerical measure. D. The variable is qualitative because it is an attribute characteristic.
A. The variable is qualitative because it is a numerical measure is correct answer.
Any variable that isn't numerical is referred to as a qualitative variable or a category variable. It describes information that falls into a category. for instance: Eye color (variables include: blue, green, brown, hazel).
In statistics, qualitative variables are given nominal scales since they cannot be ordered on a numerical scale. Qualitative variables are exactly what the word "nominal" means: names. No ordering is either conceivable or inferred on a nominal scale (except for alphabetical ordering like New York, Washington, West Virginia or Chelsea, Edinburgh, London). In other words, data are classified according to a category on the nominal scale.
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In ΔXYZ, y = 500 inches, m∠Y=117° and m∠Z=10°. Find the length of z, to the nearest inch.
Answer:
97 inches
Step-by-step explanation:
Using law of sines, we know that y/sin∠Y = z/sin∠Z.
Solve:
[tex]\frac{500}{sin117}[/tex] = [tex]\frac{z}{sin10}[/tex]
Therefore, z = (500/sin117)(sin10)
Enter this into a calculator to get:
z = 97.44495296, which rounds to 97 inches.
I hope this helps! :D
Part of the population of 6,000 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 7 of them are infected. How many elk are likely to be infected?
Answer: The number of elk that are likely to be infected can be estimated using the sample proportion of infected elk. The sample proportion is the ratio of the number of infected elk in the sample to the total number of elk in the sample.
In this case, the sample proportion is:
7/50 = 0.14
This proportion can be used to estimate the proportion of the entire population of elk that is infected. To do this, we can multiply the sample proportion by the total population of elk and round to the nearest whole number.
0.14 * 6,000 = 840
So, it's likely that 840 elk are infected.
Please note that this is an estimate and the actual number of infected elk could be different. Additionally, this estimation is based on a random sample, so it can have a margin of error.
Step-by-step explanation:
whats the parallel equation and perpendicular?
The equations of the lines are
Parallel lines: y = 4/3x + 2 and y = 4/3x - 2Perpendicular line: y = -0.75x + 8.5How to determine the equationsThe parallel lines
We have the points to be
(3, 6) and (0, 2)
A linear equation is represented as
y = mx + c
Where
c = y when x = 0
So, we have
y = mx + 2
Using the points, we have
6 = 3m + 2
So, we have
3m = 4
Divide
m = 4/3
So, the equation is
y = 4/3x + 2
For the other parallel line, we have
y = 4/3x - 2
Perpendicular line
The slopes of parallel and perpendicular lines are opposite reciprocals
So, we have
m = -3/4
This gives
y = -3/4x + c
We have the point to be (0, 8.5)
So, we have
y = -3/4x + 8.5
y = -0.75x + 8.5
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Which is a correct solution for the following system of Inequalities
The correct solution for the following system of Inequalities is (-1, 1) because it is on the darker region.
What is an equation?An equation is an expression that shows the relationship between numbers and variables.
Inequalities is used for the non equal comparison of these numbers and variables.
Let x represent the x axis and let y represent the y axis.
The solution to the system of linear equalities is the intersection of both inequalities which is the darker region.
The point that satisfies both inequalities as shown on the graph is (-1, 1) because it is on the darker region.
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