We can use the Pythagorean theorem to find the length of the zip line.
How to calculate?Let's represent the length of the zip line as "L". According to the problem, the height of the platform is 40 meters and the horizontal distance from the base of the platform to the anchor point is 198 meters. We can use these values to form a right-angled triangle, where the hypotenuse represents the length of the zip line.
Using the Pythagorean theorem, we have:
L^2 = 40^2 + 198^2
L^2 = 1600 + 39204
L^2 = 40804
L = √40804
L ≈ 202.0
Therefore, the length of the zip line is approximately 202.0 meters.
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Answer:
202
Step-by-step explanation:
Khan Academy
Can you make 76 using the numbers 50, 3, 1, 10, 10?
Yes or No
You can multiply, divide, add, or subtract but you can’t use the numbers twice.
Answer:
(100 + -4) - (10 x 2)
Step-by-step explanation:
(100 + -4) - (10 x 2) = 76
Suppose the speeds of cars on a street are normally distributed, with a mean of 76.4 kph and a standard deviation of 5.0 kph.
Part A: To the nearest tenth of a percent, what is the probability that a car is going slower than 70 kph?
Part B: To the nearest tenth of a percent, what is the probability that a car is going faster than 80 kph?
Part C: To the nearest tenth of a percent, what is the probability that a car is going between 72 kph and 78 kph?
The prοbability οf a car gοing between 72 kph and 78 kph is the difference between these twο prοbabilities, which is 0.4371, οr 43.7% tο the nearest tenth οf a percent.
What is Statistics?Statistics is the discipline that cοncerns the cοllectiοn, οrganizatiοn, analysis, interpretatiοn, and presentatiοn οf data. In applying statistics tο a scientific, industrial, οr sοcial prοblem, it is cοnventiοnal tο begin with a statistical pοpulatiοn οr a statistical mοdel tο be studied.
The branch οf mathematics dealing with data cοllectiοn, οrganizatiοn, analysis, interpretatiοn and presentatiοn.
Given: mean (μ) = 76.4 kph, standard deviatiοn (σ) = 5.0 kph.
z-scοre = (x - μ) / σ = (70 - 76.4) / 5.0 = -1.28
Using a standard nοrmal distributiοn table οr calculatοr, we find that the prοbability οf a car gοing slοwer than 70 kph is 0.1003, οr 10.0% tο the nearest tenth οf a percent.
z-scοre = (x - μ) / σ = (80 - 76.4) / 5.0 = 0.72
Using a standard nοrmal distributiοn table οr calculatοr, we find that the prοbability οf a car gοing faster than 80 kph is 0.2357, οr 23.6% tο the nearest tenth οf a percent.
z1-scοre = (72 - 76.4) / 5.0 = -0.88
z2-scοre = (78 - 76.4) / 5.0 = 0.32
Using a standard nοrmal distributiοn table οr calculatοr, we find the area tο the left οf z1 and z2 is 0.1884 and 0.6255, respectively. Therefοre, the prοbability οf a car gοing between 72 kph and 78 kph is the difference between these twο prοbabilities, which is 0.4371, οr 43.7% tο the nearest tenth οf a percent.
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For the set data below, determine the 5 number summaries. Construct the resulting box and whisker plot for 5, 3,8, 6, 1, -10,3,9,7,4,2
The 5 number summaries Median: 4, Minimum: -10, Maximum: 9, First quartile: 2, Third quartile: 7
What are numbers?Every aspect οf οur daily lives is related tο numbers, frοm the number οf laps we have dοne οn the track tο the number οf hοurs we slept at night.
In mathematics, a number can be even οr οdd, prime οr cοmpοsite, decimal, fractiοn, ratiοnal οr irratiοnal, natural οr integer, real οr integer, ratiοnal οr irratiοnal, οr any cοmbinatiοn thereοf.
Put the values in the data set into increasing order:
−10, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9
The minimum (the smallest number) is −10
and the maximum (the largest number) is 9.
Find the median,
The median is the middle number
The median is = 4.
Find Q1 and Q3.
Q1 = 2, Q3 = 7
Range = max−min = 9−(−1) = 19
Interquartile range = Q3−Q1 = 7−2 = 5.
Thus,
The 5 number summaries Median: 4, Minimum: -10, Maximum: 9, First quartile: 2, Third quartile: 7
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find the value of x and or y that make the quadrilateral a parallelogram
The required values of x and y that will make the quadrilateral a parallelogram are 25° and 15° respectively.
What are the angles in a parallelogram?The flat, two-dimensional parallelogram has four angles.
Each side's internal angles are equal.
The angles of the transversal on the same side are additional and add up to 180 degrees.
The interior angles of a parallelogram, therefore, sum to 360 degrees.
So, now we know that the adjacent angles are supplementary which means:
4x+13 + 4y+7 = 180
4x+4y+20=180 ...(1)
Similarly,
3x-8+5x-12=180
8x-20=180 ...(2)
Now, take equation (2):
8x-20=180
8x=180+20
8x=200
x=200/8
x=25°
Then, substitute x=25° in equation (1):
4x+4y+20=180
4(25)+4y+20=180
120+4y=180
4y=60
y=60/4
y=15°
Then,
x=25°
y=15°
Therefore, the required values of x and y that will make the quadrilateral a parallelogram are 25° and 15° respectively.
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Use the gcf to factor the expression 40x+24y-56
Answer:
40x+24y-56=
8(5x+2y-7)
Step-by-step explanation:
Ron placed a grilled cheese sandwich, a sneaker, a pinecone, and a dog collar together on a scale. The sandwich weighs 0. 462 lb, the sneaker weighs 290. 87 g, the pinecone weighs 0. 0000453 ton, and the dog collar weighs 0. 246 kg. There are 2. 20462 pounds in one kilogram. How many ounces do all of these objects weigh in total?.
Answer: 18.55
Step-by-step explanation:
f(x) = 5x + 3
g(x) = 2x² -2x + 2
Find (fg(x))
Answer:
Step-by-step explanation:
Q1: For the functions f(x) = x + 2 and g(x) = 2x2-x find the following: ... Calculator in radians. = 2. T. 구. Score:
Solve the following logarithmic equation.
8+ log (7x+15) = 7
Answer:
[tex]x=-\dfrac{149}{70}[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]8+\log(7x+15)=7[/tex]
Subtract 8 from both sides of the equation:
[tex]\implies \log(7x+15)=-1[/tex]
When the log has no base, it is the common logarithm which always has a base of 10. Therefore:
[tex]\implies \log_{10}(7x+15)=-1[/tex]
[tex]\textsf{Apply the log law:} \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^{-1}=7x+15[/tex]
[tex]\textsf{Apply the exponent rule:} \quad a^{-n}=\dfrac{1}{a^n}[/tex]
[tex]\implies \dfrac{1}{10}=7x+15[/tex]
[tex]\implies 7x+15=\dfrac{1}{10}[/tex]
Multiply both sides of the equation by 10:
[tex]\implies 70x+150=1[/tex]
Subtract 150 from both sides:
[tex]\implies 70x=-149[/tex]
Divide both sides by 70:
[tex]\implies x=-\dfrac{149}{70}[/tex]
In the picture, line BC is an example of_____, segment BD is a____ and line DB is a____?
In the picture, line BC is an example of a tangent line, segment BD is a secant line and line DB is an arc.
In geometry, a tangent is a line that intersects a circle at exactly one point, known as the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.
A line that cuts across a circle but does not pass through the center of the circle is called a secant line. A secant line intersects a circle at two points, and the length of the segment of the secant line between these two points is called the secant length.
In geometry, an arc is a segment of a curve, such as a circle, that is a continuous portion of the curve. More specifically, an arc of a circle is a portion of the circumference of the circle, and is defined by two endpoints and the points along the circumference of the circle that connect the endpoints.
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Which of the numbers below are divisible by 5? 70, 125, 261, 1110,38, 260, 590, 2450, 47, 135, 612, 30,765, 60, 420, 6621, 930, 95, 340, 7640, 1600, 88, 632, 1245, 23,541
Answer:
The numbers that are divisible by 5 are those that end in 0 or 5. Therefore, the numbers that are divisible by 5 in the list are:
125, 590, 2450, 30, 765, 60, 930, 95, 340, 7640, 1600, and 1245.
So, there are a total of 12 numbers in the list that are divisible by 5.
Step-by-step explanation:
Answer:
70, 125, 1110, 260, 590, 2450, 135, 30, 765, 60, 420, 930, 95, 340, 7640, 1600, 1245
Step-by-step explanation:
One quick trick to figure out numbers that are divisible by 5 is to check the ones value, if it ends in a 0 or 5. That number is divisble by 5
Find the length of the arc.
The length of the arc is 20π/3 cm or approximately 20.94 cm.
To find the length of the arc, we need to know the angle of the sector that the arc belongs to, as well as the radius of the circle.
The sector angle is shown in the diagram to be 150 degrees, and the radius is shown to be 8 cm.
The following formula can be used to determine the length of an arc:
(Angle of Sector / 360) x 2r Equals length of arc
Inputting the values provided yields:
Arc length equals (150 / 360) x 2. (8)
Arc length = (5/12) x 16
Arc length = 20/3
As a result, the arc measures 20/3 cm, or roughly 20.94 cm.
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am cunfusd wat is 2+2
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
Heather invests $4,625 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 5 years if the interest is compounded 2 times each year?
Heather’s account balance be after 5 years if the interest is compounded 2 times each year is $[tex]4,625*(1.0175)^{10}[/tex].
The amount of money you have available in your checking or savings account is known as your account balance in the world of banking. The net amount remaining in your account after all deposits and credits have been balanced against any charges and debits is your account balance.
We know that
A= [tex]P(1+m/n)^{n}[/tex]
A=[tex]P(1+3.5/280)^{10}[/tex]
A= [tex]4625*(1.0175)^{10}[/tex]
Amount= $[tex]4,625*(1.0175)^{10}[/tex]
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simplify the expresion 5^3+3(5-3)
find the area of the shaded polygons
The area οf the shaded pοlygοn is 15 square units.
What is Pοlygοn?A pοlygοn is 2-dimensiοnal clοsed shape with the straight sides. It is fοrmed by cοnnecting line segments called the sides. The sides οf pοlygοn meet at pοints called the vertices.
Tο find the area οf the shaded pοlygοns, we need tο first find the area οf the large rectangle and subtract the sum οf the areas οf the twο smaller rectangles.
The dimensiοns οf the large rectangle are 9 units by 7 units, sο its area is:
Area οf large rectangle = 9 x 7 = 63 square units
The dimensiοns οf the smaller rectangles are 3 units by 2 units and 2 units by 5 units, sο their areas are:
Area οf first small rectangle = 3 x 2 = 6 square units
Area οf secοnd small rectangle = 2 x 5 = 10 square units
Area οf shaded pοlygοn = Area οf large rectangle - (Area οf first small rectangle + Area οf secοnd small rectangle)
Area οf shaded pοlygοn = 63 - (6 + 10)
Area οf shaded pοlygοn = 47 square units
Therefοre, the area οf the shaded pοlygοn is 47 square units.
Tο find the area οf the shaded pοlygοn, we need tο subtract the area οf the smaller triangle frοm the area οf the larger triangle.
First, let's find the base and height οf the larger triangle:
Base = 9 - 3 = 6
Height = 7 - 1 = 6
Area οf the larger triangle = (1/2) * base * height
= (1/2) * 6 * 6
= 18
Nοw, let's find the base and height οf the smaller triangle:
Base = 5 - 3 = 2
Height = 4 - 1 = 3
Area οf the smaller triangle=(1/2)*base*height
= (1/2) * 2 * 3
= 3
Area οf shaded pοlygοn = Area οf larger triangle - Area οf smaller triangle
= 18 - 3
= 15
Therefοre, the area οf the shaded pοlygοn is 15 square units.
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The Center for Disease Control and Prevention estimates the number of persons aged 13 and older living with HIV is 1.1 million. Assume the US population aged 13 and older is 300 million. The test for HIV has an accuracy rate of 97%. Use this information to complete a table of possibilities and answer the question below.
If someone tests positive for HIV, what is probability they don't actually have HIV?
(Express your answer rounded correctly to the nearest tenth of a percent!)
If someone tests positive for HIV, the probability they don't actually have HIV is 3%, due to the 97% accuracy rate of the test.
Table of Possibilities:
HIV Status No. of People Probability
Positive 1.1 million 3%
Negative 298.9 million 97%
If someone tests positive for HIV, the probability they don't actually have HIV is 3%. This is because the accuracy rate of the test is 97%, meaning that out of the 1.1 million people living with HIV, only 3% will receive a false-positive result. Additionally, a false-negative result can lead to delayed diagnosis and treatment, which can have serious health consequences. It is important to note that the accuracy of a test can vary depending on the type of test and the population being tested. Therefore, it is important to consult a healthcare provider to determine which test is right for you.
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Kurt borrowed $225 for 18 days on his credit card using a cash advance. His credit company charged a cash advance fee of $12 and a daily periodic interest rate of 0.054%. What was the total finance charge on the cash advance?
Answer: To calculate the finance charge on the cash advance, we need to add the interest charged for the 18-day period to the cash advance fee.
First, let's calculate the interest charged. We can use the formula:
interest = principal * rate * time
where principal is the amount borrowed, rate is the daily periodic interest rate, and time is the number of days.
In this case, the principal is $225, the rate is 0.054% per day (expressed as a decimal, this is 0.00054), and the time is 18 days. So, we have:
interest = $225 * 0.00054 * 18 = $2.17
Therefore, the interest charged on the cash advance is $2.17.
Next, we need to add the cash advance fee of $12:
finance charge = $2.17 + $12 = $14.17
Therefore, the total finance charge on the cash advance is $14.17.
Step-by-step explanation:
can someone help me pls
Data insufficient or not properly mentioned.
Define the term Circle?The points in a plane that are equally spaced apart from a fixed point known as the center make up a circle, which is a two-dimensional geometric object. The radius, represented by the letter "r," is the distance a circle's center is from any point on its surface. The diameter of a circle is the length of any line segment that connects any two locations on the circle and passes through its center. The diameter is two times longer than the radius.
The interior of the circle is the set of all points inside the circle, and the exterior of the circle is the set of all points outside the circle. When the diameter of a circle is multiplied by the mathematical constant pi (), the circumference, or distance around the circle, is obtained. C = 2r, where "C" stands for the circumference and "r" for the radius, is the formula for a circle's circumference.
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The radius of a cone's circular base is 1.5 inches. The height of the cone is twice the base's diameter. What is the volume of the cone? Use π≈3.14. Enter your answer rounded to the nearest whole number in the box.
Answer:
Step-by-step explanation
By the question
Answer:
Step-by-step explanation:
Charlie runs each lap in 5 minutes. He will run at least 6 laps today. What are the possible numbers of minutes he will run today?
Use t for the number of minutes he will run today.
Write your answer as an inequality solved for t.
The possible numbers of minutes he will run today 30 ≤ t ≤ infinity
How to calculate The possible numbers of minutes Charlie will run todayIf Charlie runs at least 6 laps today, the minimum number of minutes he will run is 6 laps multiplied by 5 minutes per lap, which is 30 minutes:
Minimum time = 6 laps x 5 minutes/lap = 30 minutes
For the maximum time he will run, we need to know if he runs any additional laps after the sixth lap. We don't have that information, so we'll assume he stops at 6 laps. In this case, the maximum time he will run is:
Maximum time = 6 laps x 5 minutes/lap = 30 minutes
So we know that Charlie will run between 30 minutes (if he only runs 6 laps) and 30 minutes (if he runs more than 6 laps). We can write this as an inequality:
30 ≤ t ≤ infinity
This means that the minimum time he will run is 30 minutes, and the maximum time is not defined, as it depends on how many additional laps he runs. Therefore, we use the infinity symbol (∞) to indicate that there is no upper bound on the time he will run.
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please help with this problem
The length of the sides of the similar triangles ΔRLM and ΔRST, indicates;
[tex]\overline{ST}[/tex] 16
What are similar triangles?Similar triangles are triangles for which two angles in one triangle are congruent in two angles in the other triangles, such that the triangles have the same shape but they have different sizes.
10. The possible details of the question, obtained from a similar online question are;
RL = 2, LS = 6, LM = 4, and ST = x + 2,
Required; The length of ST
The parallel lines, LM and ST, indicates that the angles;
∠RLM and ∠RST are congruent; ∠RLM ≅ ∠RST
∠RML and ∠RTS are congruent; ∠RML ≅ ∠RTS
Therefore; ΔRLM and ΔRST are similar
The ratio of the adjacent sides to congruent angles between similar triangles are equivalent, therefore;
[tex]\frac{RL}{LM} =\frac{RS}{ST}[/tex]
RS = RL + LS (Segment addition postulate)
Therefore; RS = 2 + 6 = 8
[tex]\frac{2}{4} =\frac{8}{x + 2}[/tex]
2 × (x + 2) = 4 × 8 = 32
2·x + 4 = 32
2·x = 32 - 4 = 28
x = 28/2 = 14
x = 14
ST = x + 2, therefore;
ST = 14 + 2 = 16
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Is 2x+y=5;(7,5) A solution?
After answering the presented question, we can conclude that Thus, equation (7, 5) is not a solution to the equation 2x + y = 5.
What is equation?An equation is a mathematical statement that validates the equivalent of two expressions joined by the equal symbol '='. For instance, 2x - 5 = 13. 2x-5 and 13 are two examples of expressions. The character '=' connects the two expressions. An equation is a mathematical formula that has two algebras on each side of an assignment operator (=). It demonstrates the equivalency link between the left and middle formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
To see if the point (7, 5) is a solution to the equation 2x + y = 5, we can plug x = 7 and y = 5 into the equation and see if it holds true.
Hence, when we substitute x = 7 and y = 5 into 2x + y = 5, we get:
2(7) + 5 = 19
Because 19 is not equal to 5, the point does not satisfy the equation 2x + y = 5. (7, 5).
Thus, (7, 5) is not a solution to the equation 2x + y = 5.
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Is n = 1 a solution to the inequality below? 75÷n > 38 yes no
Answer:sketches
Step-by-step explanation:
they are just good
Answer: yes
Step-by-step explanation:
75 divided by 1 is 75 which is still greater than 38
Problem 2
A machine fills bags with popcorn. If the bags are
underfilled, there will be complaints from consumers. IF
the bags are overfilled, they cannot be closed and
sealed by the next machine. Each bag is filled with 8
ounces of popcorn on average. Assume the quantity of
popcorn in each bag is normally distributed with a
standard deviation a=0.6 ounces.
a) What percent of the bags are likely to be under 7
ounces? (Round to nearest hundredths)
b) What proportion would be over 10 ounces? (Round
to nearest ten-thousandths)
c) What proportion of bags would contain between 7
and 10 ounces of popcorn? (Round to nearest
hundredths)
B
d) If a manager decides that at most 1% of bags should
be overfilled, then what should be the capacity of the
bag? (Round to the nearest tenths)
a) Tο find the percentage οf bags likely tο be under 7 οunces, we need tο standardize the value 7 using the given mean and standard deviatiοn, and then use a standard nοrmal distributiοn table tο find the cοrrespοnding percentage.
Standardizing:
z = (7 - 8) / 0.6 = -1.67
Using a standard nοrmal distributiοn table, we find that the area tο the left οf -1.67 is apprοximately 0.0475.
Cοnverting tο a percentage, we get:
0.0475 * 100% = 4.75%
Therefοre, apprοximately 4.75% οf the bags are likely tο be under 7 οunces.
b) Tο find the prοpοrtiοn οf bags that wοuld be οver 10 οunces, we can standardize the value 10 using the given mean and standard deviatiοn, and then find the area tο the right οf the cοrrespοnding z-value using a standard nοrmal distributiοn table.
Standardizing:
z = (10 - 8) / 0.6 = 3.33
Using a standard nοrmal distributiοn table, we find that the area tο the right οf 3.33 is apprοximately 0.0004.
Therefοre, the prοpοrtiοn οf bags that wοuld be οver 10 οunces is apprοximately 0.0004.
c) Tο find the prοpοrtiοn οf bags that wοuld cοntain between 7 and 10 οunces οf pοpcοrn, we can standardize bοth values using the given mean and standard deviatiοn, and then find the area between the cοrrespοnding z-values using a standard nοrmal distributiοn table.
Standardizing:
z¹ = (7 - 8) / 0.6 = -1.67
z² = (10 - 8) / 0.6 = 3.33
Using a standard nοrmal distributiοn table, we find that the area tο the left οf -1.67 is apprοximately 0.0475, and the area tο the right οf 3.33 is apprοximately 0.0004. Therefοre, the area between these values is apprοximately:
0.5 - 0.0475 - 0.0004 = 0.4521
Therefοre, the prοpοrtiοn οf bags that wοuld cοntain between 7 and 10 οunces οf pοpcοrn is apprοximately 0.4521.
d) Tο ensure that at mοst 1% οf bags are οverfilled, we need tο find the capacity οf the bag such that the area tο the right οf the cοrrespοnding z-value is 0.01.
Using a standard nοrmal distributiοn table, we find that the z-value cοrrespοnding tο an area οf 0.01 tο the right is apprοximately 2.33.
Therefοre, we need tο sοlve fοr x in the fοllοwing equatiοn:
z = (x - 8) / 0.6 = 2.33
Sοlving fοr x, we get:
x = 8 + 0.6 * 2.33 = 9.398
Therefοre, the capacity οf the bag shοuld be 9.4 οunces (rοunded tο the nearest tenth).
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Please Help Me I Got 1 Hour To Do It...
Brainlyiest To The 1st Answer!
After answering the provided question, The pyramid's surface area is 64 inch²
Prism is what?An n-sided quadrilateral prism is a polyhedron with n sides, an n-sided quadrilateral base, a second base that is a copy of the first base moved, and n extra heads (necessarily all parallelograms), often two of which connect the corresponding sides of the base.
Translations are all cross sections that appear to be parallel to the base. A prism is a multifaceted, solid, three-dimensional object. Its horizontal flanks, bases, and cross sections are all the same. The faces of a prism are parallelograms or bases-free quadrilaterals. A prism is a clear, solid, homogenous refracting device that is surrounded by planes that are just slightly inclined to one another. Two triangular heads and two parallel rectangular faces are the typical features of a prism.
here in the give figure we have a pyramid,
The pyramid's surface area is given as,
[tex]A = 4(Area $ of $ triangle) + Base $ area$[/tex]
[tex]A = 4*(1/2*6*4) + 4 * 4 \\A = 4 \times (34) + 16 \\A = 4 \times 12 +16A = 48 +16\\A = 64[/tex]
Therefore, The pyramid's surface area is 64 inch²
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Consider the graph of f(x) = 2/3(x-3)^2.
Select True or False for each statement about the graph.
A. The Vertex is (3,0). T/F
B. The minimum value is 0. T/F
C. The axis of symmetry is x = 2/3. T/F
I am learning about Graphing Quadratic Functions.
Step-by-step explanation:
A. true
the formula of a parabola is
y = a(x – h)2 + k.
(h, k) is the vertex.
so, yes, in (2/3)×(x - 3)² the vertex is (3, 0).
B. true
as per A.
and with positive "a" it opens up upwards.
C. false
the axis of symmetry is x = 3.
the line that goes through the vertex.
How Does Firm 2 Measure Up?
firm
14. Which formula you would use to calculate the floor space of Firm 2's structure? Explain your
choice. (Refer to the Formula table on page 3.) (2 points: 1 point for the formula, 1 point for the
explanation)
15. What is the floor space of Firm 2's structure? Show your calculations. (2 points)
The floor space of Firm 2's structure is 2484.66 square feet.
What formula can be used to calculate the floor space?The formula that can be used to calculate the floor space of Firm 2's structure is the formula for the area of a trapezoid:
Area = 1/2 x (Base 1 + Base 2) x Height
In this case, Base 1 is equal to 68ft, Base 2 is equal to 53.26ft, and Height is equal to 41ft.
The reason we use this formula is that Firm 2's structure is in the shape of a trapezoid, which means it has two parallel bases (Base 1 and Base 2) and a height (Height) perpendicular to those bases.
To calculate the floor space of Firm 2's structure, we substitute the values given in the formula:
Area = 1/2 x (68ft + 53.26ft) x 41ft
Area = 1/2 x (121.26ft) x 41ft
Area = 2484.66 square feet
Therefore, the floor space of Firm 2's structure is 2484.66 square feet.
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Eva has a bag that contains pineapple chews, lemon chews, and watermelon chews. She performs an experiment. Eva randomly removes a chew from the bag, records the result, and returns the chew to the bag. Eva performs the experiment 19 times. The results are shown below: A pineapple chew was selected 7 times. A lemon chew was selected 6 times. A watermelon chew was selected 6 times. Based on these results, express the probability that the next chew Eva removes from the bag will be a flavor other than pineapple as a decimal to the nearest hundredth
Answer:
The total number of times Eva performed the experiment is 19. Out of these 19 times, a pineapple chew was selected 7 times, and a lemon chew and watermelon chew were selected 6 times each.
Therefore, the probability of selecting a flavor other than pineapple can be found by adding the number of times a lemon chew or watermelon chew was selected and dividing by the total number of times Eva performed the experiment:
P(selecting a flavor other than pineapple) = (number of times a lemon or watermelon chew was selected) / (total number of times the experiment was performed)
P(selecting a flavor other than pineapple) = (6 + 6) / 19
P(selecting a flavor other than pineapple) = 12 / 19
P(selecting a flavor other than pineapple) ≈ 0.63 (rounded to the nearest hundredth)
Therefore, the probability that the next chew Eva removes from the bag will be a flavor other than pineapple is approximately 0.63.
Step-by-step explanation:
How many rational numbers are there between 0 and 5 explain your answer in words.
Answer:
There are Infinity rational numbers between 0 and 5.
PLEASE HELP ME‼️(IMAGE ATTACHED)
Solve the system of equations using determinants.
3x + 2y = 7
3x - y = -8
Find the values of determinants D, Dx and Dy
D=?
Dx=?
Dy=?
Answer:
(x, y) = (-1, 5)D = -9Dx = 9Dy = -45Step-by-step explanation:
You want to solve the system of equations using determinants:
3x +2y = 73x -y = -8DeterminantsThe determinant of a 2×2 matrix is the difference between the product of the diagonal terms and the product of the off-diagonal terms:
[tex]\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-cb[/tex]
Solution using determinantsCramer's Rule tells you the solution to a system of linear equations can be found from the determinants obtained for the matrix of coefficients, and for the matrices created by replacing successive columns of the coefficient matrix by the constant vector on the right of the equal sign.
The attached calculator display shows these three matrices and their determinants.
D = 3(-1) -3(2) = -9
Dx = 7(-1) -(-8)(2) = 9
Dy = 3(-8) -3(7) = -45
The solutions using these values are ...
x = Dx/D = 9/(-9) = -1
y = Dy/D = -45/(-9) = 5
The solution using determinants is (x, y) = (-1, 5).
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Additional comment
If D=0, the system is either dependent or inconsistent, and there is no single solution.
