1.The following is the 90% confidence interval for the mean difference between the park's tree heights in 2009 and 2019:
(11.59, 14.21)
2. The conditions for the confidence interval are of:
A. Large samples and no extreme outliers.
D. Independently sampled pairs.
Given,
What is a confidence interval for the t-distribution?
When the population's standard deviation is unknown, the t-distribution is utilized, and the boundaries of the confidence interval are provided using the following formula:
x ± t s/√n
When the equation's variables are laid down as follows:
The sample mean = x
The critical value = t
The sample size = n
The standard deviation for the sample = s
Using a t-distribution calculator, the critical value is t = 1.6766 for a two-tailed 90% confidence interval with 50 - 1 = 49 df.
The remaining parameters are given as follows:
x = 12.9, s = 5.52, n = 50
Then the lower bound of the interval is of:
12.9 - 1.6766 x 5.52/sqrt(50) = 11.59.
The upper bound of the interval is of:
12.9 + 1.6766 x 5.52/sqrt(50) = 14.21.
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Question is incomplete. Completed question is given below;
Forest rangers wanted to better understand the rate of growth for younger trees in the park. They took measurements of a random sample of 50 young trees in 2009 and again measured those same trees in 2019. The data below summarize their measurements, where the heights are in feet.
Year Mean SD n
2009 11.4 3.6 50
2019 24.3 8.8 50
Difference 12.9 5.52 50
Round all calculated values to 4 decimal places as appropriate.
1. Construct a 90 confidence interval for the mean difference between the height of trees in the park in 2009 and in 2019.
2. What conditions must be met if we want to perform a hypothesis test and answer the question of the management? Select all that apply:
A. Large samples and no extreme outliers.
B. There must be at least 3 levels of the categorical variable.
C. np^≥10 and n(1−p^)≥10
D. Independently sampled pairs.
a cowboy agreed to work for one year for $\$19{,}200$ plus a horse. he quit after 7 months and was paid $\$10{,}450$ plus a horse. how many dollars was the horse worth, if the paid salary reflects the fair proportion of his yearly salary?
The horse was worth it for $1800.
What is proportion?
A mathematical comparison of two numbers is called a proportion. Ratios and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion. In this case, a and b can be any two integers.
Based on the given question condition, where, 'h' denotes the amount for the horse in dollars, the proportion can be defined as:
or, [tex]\frac{19200 + h}{12} = \frac{10450+h}{7}[/tex]
or, (19200 + h)7 = (10450 + h)12
or, 134400 + 7h = 125400 + 12h
or, 12h - 7h = 134400 - 125400
or, 5h = 9000
or, h = 9000/5 = 1800
Hence, the horse was worth $1800.
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Evaluate:
please help fast
Answer: 256
Step-by-step explanation:
8^8/3 is the same as an 8 square root! We have to factor out and I get 2^8 after finish factor the smallest number and get 256!
Find the digits in the ones,tens,and thousandth place
603.2798
Answer:
3 is in the ones place
0 is in the tens place
9 is in the thousandths place
Step-by-step explanation:
thousands, hundreds, tens, ones (DECIMAL) tenths, hundredths, thousandths
Adrian took out a students' loan that charges 10% annual simple interest. If Adrian paid back a total of $1200 in interest alone during the first four years , how much was Adrian's original loan, in dollars?
$1,000
$3,000
$4,000
$ 6,000
$12,000
The required simple interest of 10% of four year on principle amount is $857.
What is simple interest?Simple interest depends on the chief measure of a credit or the first store in quite a while account. Straightforward interest doesn't build, and that implies a loan boss will just compensation interest on the chief sum and a borrower couldn't have ever to pay more interest on the recently gathered interest.
According to question:We have,
Amount of four year = $1200
simple interest = 10%
Let loaned amount is x
Then,
interest of four year =×4 x×10/100 = 4x/10
According,
x + 4x/10 = $1200
14x/10 = $1200
x = $12000/14
X = $857 (appox)
Thus, the required loaned amount is $857.
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The radius of a circle is 10 feet. What is the area of a sector bounded by a 180° arc?
Answer:
50π feet^2
Step-by-step explanation:
area of the circle = 10^2 π = 100π feet^2
A of the sector = 100π/2 = 50π feet^2
Which figure is
misleading?
1) Figure A
2) Figure B
Answer:
Figure B.
Step-by-step explanation:
Figure A uses what is visually similar in size cylinders to give a detailed image of the amount of money (assumingly as profit). Each given cylinder that is in similar size represents $200, and so it is easy to figure out how the amount of money per store.
In the case of Figure A,
Save Store = $400
Leff's Store = $800
Low Pricer = $1200
In the case of Figure B, however, while it gives a legend for price per cylinder of that proportion, it does not make use of the legend, and does not give a adequate legend to decipher the Figure. In essence, the data given in Figure B is useless as it makes no use of its legend.
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(71+9+3)-(9-11+2) I really need help
Answer: The correct answer is 83
Step-by-step explanation:
Complete the equations within each set of brackets
(71+9+3)-(9-11+2)
71+9+3 = 83
9-11+2 = 0
Subtract the results
83 - 0 = 83
the actual answer pleaseee hellpp asapp
Answer:
∠BEC is supplementary to ∠AEB
∠AED and ∠BEC are a pair of vertical angles
g what is the probability of flipping at least 3 heads in 4 flips of 2 fair coin given that the first flip is heads?
The probability is 0.25.
What is probability?
Probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To determine how likely an event is to occur, mathematics has created the concept of probability.
Given there are 2 coins flipped 4 times, we get the following sample space
S = {HHHH, HHHT, HHTH, HHTT, HTHH, HTHT, HTTH, HTTT, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}
Now, A = event of having at least 3 heads.
A= {HHHH, HHHT, HHTH, HTHH, THHH}
The number of events having the first flip heads is 4.
Therefore, the probability is:
P(A) =
[tex]=\frac{successful \space\ events}{total\space\ sample\space\ events}\\=\frac{4}{16}\\=0.25[/tex]
Therefore, the probability of flipping at least 3 heads in 4 flips of 2 fair coins given that the first flip is heads is 0.25.
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Chris earns $7.00 per hour working on the weekends
He needs at least 210.00 for a new cell phone
Just look at the picture and help please
american express executives hypothesize that 40% of college students own an american express credit card. testing this hypothesis is an example of
Testing the hypothesis "Americans express executives hypothesize that 40% of college students own an Americans express credit card." is an example of generalizing.
What is hypothesis?A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge. A straightforward hypothesis only hypothesizes the relationship between two independent and dependent variables.
An example of testing a generalization is "American Express executives' hypothesis that 40% of college students own an American Express credit card."
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in the xy-plane, the line x y k , where k is a constant, is tangent to the graph of 2 y x x 3 1. what is the value of k?
The value of k is -3.
What is a tangent line?
The straight line that "just touches" the curve at a given location is referred to as the tangent line to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are endlessly close to one another.
Here, we have
Given
x + y = k
y = x² + 3x
slope of tangent line = dy/dx = 2x+3
k is y-intercept of the tangent line
2x+3 = -1
x = -2
y = (-2)^2+3(-2)+1 = -1
The tangent line passes through the point (-2,-1)
k = x+y
k = -2 -1
k = -3
Hence, the value of k is -3.
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which expression is equivalent to (1 tanθ)tan(2θ) for all values of θ for which (1 tanθ)tan(2θ) is defined?
The given expression of trigonometry is equivalent to cos(2θ).
What is trigonometric function ?trigonometry capability, in math, one of six capabilities (sine [sin], cosine [cos], digression [tan], cotangent [cot], secant [sec], and co-secant [csc]) that address proportions of sides of right triangles. These six geometrical capabilities comparable to a right triangle.
According to question:We have,
1 - tan^2(θ)/1 + tan^2(θ)
Use 1 + tan^2(θ) = sec^2(θ)
1 - tan^2(θ)/ sec^2(θ)
1/ sec^2(θ) - tan^2(θ)/sec^2(θ)
Use tan(θ) = sin(θ)/cos(θ)
cos^2(θ) - sin^2(θ)×cos^2(θ)/cos^2(θ)
cos^2(θ) - sin^2(θ)
Using sin^(θ) + cos^2(θ) = 1
cos^2(θ) - (1 - cos^2(θ))
2cos^2(θ) - 1
Here we have 2cos^2(θ) - 1 = cos(2θ)
Then, simplification of given expression is cos(2θ).
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Correct question:
which expression is equivalent to 1 - tan^2(θ)/1 + tan^2(θ) for all values of θ for which 1 - tan^2(θ)/1 + tan^2(θ) is defined?
the surface area of a rectangular box is given by the polynomial 2hl 2lw 2hw and is measured in square units. a rectangular box is to be constructed for shipping materials. the box is to have dimensions of 5 inches by 3 inches by 7 inches. find the surface area of the box.
Surface area of the box measuring 5 inches by 3 inches by 7 inches is 142 square inches.
What is surface area ?The surface area of the object that refers to the overall space that is filled by its surfaces. Different 3D shapes in the geometry have various surface areas, which can be quickly estimated using the formulas. Two categories are used to classify the surface area:
Curved surface area or Lateral surface area
Surface area in total
Surface area of rectangle = 2 ( lb + bh + hl )
Dimensions of box = 5 inches by 3 inches by 7 inches
Hence,
Length = 5 inches
Breadth = 3 inches
Height = 7 inches
By putting it in formula of surface area of rectangle
= 2 ( lb + bh + hl )
= 2 ( 5*3 + 3*7 + 7*5 )
= 2 ( 15 + 21 + 35 )
= 2 * 71
= 142 square inches
Hence, the total surface area of the box is 142 square inches.
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a lottery offers one $1000 prize, one $500 prize, and eight $100 prizes. one thousand tickets are sold at $4.00 each. find the expectation if a person buys five tickets.
Answer:
he would have a 50% chance of getting one of the 10 prizes
Problem 9. Find the perimeter of quadrilateral PORS with the vertices P(-2-2), Q(-1,3), R(5,3), and S(4,-2)
Answer:
Perimeter is 12+2√26
Step-by-step explanation:
Question:
The perimeter of quadrilateral PQRS with the vertices
P(-2, -2), Q(-1, 3), R(5, 3), and S(4, -2)
Find distances PS and QR:
Notice the y-coordinates are the same for 2 pairs of points
P(-2, -2), S(4, -2) and Q(-1, 3), R(5, 3)
So the distance PS = |-2|+4= 6 and QR = |-1|+5 = 6
Find the distances PQ and SR:
Use the distance formula:
[tex]d= \sqrt{(x_{2}-x_{1} ) ^{2} + (y_{2}-y_{1} ) ^{2} }[/tex]
P([tex]x_{1}[/tex] = -2, [tex]y_{1}[/tex] = -2), Q( [tex]x_{2}[/tex] = -1, [tex]y_{2}[/tex] = 3)
PQ = [tex]\sqrt{(-1--2)^{2} +(3- -2)^{2} } = \sqrt{1^{2} +5^{2} } = \sqrt{26}[/tex]
SR = [tex]\sqrt{26}[/tex], because of PQ and SR are equal.
Find the perimeter of quadrilateral PQRS:
The perimeter is equal to the sum of all sides of the quadrilateral.
P= PS + QR + PQ + SR = 6+6+ √26 +√26 = 12+2√26
Sarah can make 4 cards in 60 minutes. At this rate, how many cards will she make in
300 minutes?
Answer: 20 cards.
Step-by-step explanation: If Sarah can make 4 cards in 60 minutes, then she can make 1 card in 60/4 = 15 minutes.
Therefore, in 300 minutes, she can make 300/15 = <<300/15=20>>20 cards.
s It is required to set a stake to mark a grade of 45.49 ft. The Hl of the level is 53.56 ft and the rod on stake reads 4.32 ft. Determine the amount of cut (C) or fill(F) to be marked on the stake. cut 8.07 ft O fill 8.07 ft cut 3.75 Ft fill 3.75 Ft
The correct option is option C i.e. the amount of cut (C) to be marked on the stake is equivalent to 3.75 Ft.
Given that:
It is required to set a stake to mark a grade of 45.49 ft.
i.e. required grade = 45.49 ft
The Hl of the level is 53.56 ft
i.e. HI = 53.56 ft
the rod on the stake reads 4.32 ft.
i.e. Stake reading = 4.32 ft
We know that,
The formula for cut/fill is:
Cut/Fill = HI – Stake reading – required grade
Cut/Fill = 53.56 ft - 4.32 ft - 45.49 ft
Cut/Fill = 53.56 ft - 49.81 ft
Cut/Fill = 3.75 ft
As the value is positive therefore this amount is for cut and not the amount of fill.
The amount of cut (C) to be marked on the stake is 3.75 Ft.
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47. refer to exercise 46. suppose the distribution is normal (the cited article makes that assumption and even includes the corresponding normal density curve). a. how likely is it that the sample mean diameter exceeds 71 when n
The probability that the sample mean diameter surpasses 71 when n = 30 is 0.5 if the distribution is normal (the quoted article makes this assumption and even gives the related normal density curve).
The likelihood that the sample mean diameter exceeds 71 when n = 30 is 0.5, since the normal distribution is symmetric around the mean. This means that there is a 50% probability of the sample mean diameter being above the mean, and a 50% probability that it is below the mean.
The correct question is : suppose the distribution is normal (the cited article makes that assumption and even includes the corresponding normal density curve). a. how likely is it that the sample mean diameter exceeds 71 when n = 30
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Monique and Tara each make an ice-cream undae. Monique get 2 coop of Cherry ice-cream and 1 coop of Mint Chocolate Chunk ice-cream for a total of 60g of fat. Tara ha 1 coop of Cherry and 2 coop of Mint Chocolate Chunk for a total of 87g of fat. How many gram of fat doe 1 coop of each type of ice cream have?
The factors in the word problem for the amount of fat in the ice cream
combination are given by the fat in each constituent.
The amount of fat in Cherry ice-cream is 11 grams.
The amount of fat in the Mint Chocolate Chunk ice-cream is 16 grams.
Reasons:
The given parameters are;
Let C represent the amount of fat in Cherry ice-cream, and let M represent
the amount of fat in Mint Chocolate Chunk ice-cream, we get;
4·C + M = 60...(1)
C + 4·M = 75...(2)
Multiplying equation (1) by 4 and then subtracting equation (2) from the
result gives;
4 × (4·C + M) = 4 × 60
16·C + 4·M = 240...(3)
(16·C + 4·M) - (C + 4·M) = 240 - 75
15·C = 165
The amount of fat in Cherry ice-cream C = 11 grams
4 × 11 + M = 60
M = 60 - 4 × 11 = 16
The amount of fat in the Mint Chocolate Chunk ice-cream, M = 16 grams
Secretary of State Roxana Tillerson is worried about malpractice at the 4 processing centers for Green Cards in the country. Green Card applications are given a grade g on a scale 0-100. They are assigned randomly to different centers and thus Tillerson expects all centers to have similar mean scores. She collects the data in the table. #applications g 8g 9360 67.50 14.85 9870 67.17 15.10 0 1 2 3 7020 67.28 14.79 5040 66.77 15.16 4 rows x 3 columns At this point she just wants to decide whether or not to initiate a deeper investigation into malpractice at all sites. Does she have sufficient evidence for this, at 9% significance? SSTr number (rtol=0.01, atol=0.0001) SSE number (rtol=0.01, atol=0.0001) Fx number (rtol=0.01, atol=0.0001) P-val number (rtol=0.01, atol=0.0001) (a) Yes, she has enough evidence (b) No, she cannot make a conclusion Select the key assumptions in the test you used. (a) All the sampled data come from a uniform distribution. (b) The populations are independent and therefore their covariances are one. (c) All the sampled data come from a normal distribution. (d) The populations are independent and therefore their covariances are zero. (e) All sample sizes are equal ? ? ?
The p-value is 0.0388 at 9% significance, so (a) Yes, she has enough evidence with assumptions used in the test is (c) all the sampled data come from a normal distribution and (d) the populations are independent and therefore their covariances are zero.
How to determine whether the evidence is sufficient or not?All data in attached table
First, we must calculate the grand mean. So,
Grand mean ([tex]\bar{\bar{g}}[/tex]) = [tex]\frac{\bar{g_{1}} + \bar{g_{2}} + \bar{g_{3}} + \bar{g_{4}}}{k}[/tex]
= (67.5 + 67.17 + 67.28 + 66.77) / 4
= 67.18
Next, we calculate SSTr
SSTr = [tex]\sum n_i(\bar{g_{i}} - \bar{\bar{g}})^2[/tex]
= 9360(67.5-67.18)^2 + 9870(67.17-67.18)^2 + 7020(67.28-67.18)^2 + 5040(66.77-67.18)^2
= 1,876.875
Then, we calculate SSE
SSE = [tex]\sum(n_i-1)Sg_i^2[/tex]
= (9360-1)(14.85^2) + (9870-1)(15.1^2) + (7020-1)(14.79^2) + (5040-1)(15.16^2)
= 7,007,556.804
Before we calculate F test, we first calculate the N value with this formula,
N = [tex]\sum n_i[/tex]
= 9360 + 9870 + 7020 + 5040
= 31,290
Then, for F test use this formula,
F = [tex]\frac{SSTr/(k-1)}{SSE/(N-k)}[/tex]
= [tex]\frac{1876.875/(4-1)}{7007556.804/(31290-4)}[/tex]
= 2.793
Next, for p-value we use p value calculator for f test with following data,
F-ratio value = 2.793
DF-numerator = k - 1 = 4 - 1 = 3
DF-denominator = N - k = 31290 - 4 = 31286
and we get the p-value is 0.0388
Since, 0.0388 < 9% of significance, so she has enough evidence to initiate a deeper investigation.
Thus, assumptions used in the test is all the sampled data is normal distribution and the population are independent with covariances are zero and the result is yes, she has sufficient evidence.
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a 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft . find the side length of the original cube. round your answer to two decimal places.
The side length of the original cube is, 8.60 feet.
What is volume?
The amount of three-dimensional space that is occupied is measured by volume. It is frequently expressed quantitatively using SI-derived units, other imperial units, or US customary units. Volume and the notion of length are connected.
Given:
A 8ft thick slice is cut off the top of a cube, resulting in a rectangular box that has volume 44ft^3.
Let x = the side of the cube then
x^3 = original volume of the cube and
8x^2 = volume of the 8 feet slice
Therefore,
x^3 - 8x^2 = 44
Subtract 44 on both sides,
x^3 - 8x^2 - 44 = 44 - 44
x^3 - 8x^2 - 44 = 0
After solving x ≈ 8.59553
⇒ x = 8.60
Hence, the side length of the original cube is 8.60 feet.
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The points given in the table lie on a line. Find the slope of the line.
Answer:
-4/3
Step-by-step explanation:
We can find the slope of the line using
m = ( y2-y1)/(x2-x1)
m = ( -9 -3)/( 8 - -1)
= ( -9-3)/( 8+1)
= -12 / 9
= -4/3
Answer:
[tex]\sf m=-\frac{4}{3}[/tex]
Step-by-step explanation:
First, select any two coordinates of the line.
( -1, 3 ) ⇒ ( x₁ , y₁ )
( 2, -1 ) ⇒ ( x₂ , y₂ )
And now let us use the below formula to find the slope of the line.
[tex]\sf m= \frac{y_1-y_2}{x_1-x_2} \\[/tex]
Let us find the slope now.
[tex]\sf m= \frac{y_1-y_2}{x_1-x_2} \\\\\sf m= \frac{3-(-1)}{-1-2} \\\\\sf m= \frac{4}{-3}\\\\\sf m=-\frac{4}{3}[/tex]
HELPPP PLEASE ASAP!!!!!!!!
Answer:
x=6
Step-by-step explanation:
i assume these are similar triangles so we can set them up as fractions
x/9=4/x
cross multiply
9(4)=x(x)
36=x^2
√. √
6=x
and now we can check if each have the same ratio
6/9= 4/6
2/3=2/3
hopes this helps please mark brainliest
mr. smith has a maximum of $50 to spend at a museum. a ticket to the museum costs $7. he can spend p dollars to buy other things at the museum. write the inequality that can be used to find the values for p and solve for p.
The inequality that can be used to find the values for p is p + 7 ≤ 50.
Given the information,
Mr. Smith can only spend up to $50 at a museum. The museum admission ticket is $7. He can use his P dollars to purchase other items from the museum.
The total budget is $50.
The cost per ticket is $7
⇒ Total spent ≤ Total Budget
⇒ p + 7 ≤ 50
⇒ p ≤ 43
Therefore, p + 7 ≤ 50 will be the inequality that aids in determining the range of values for p.
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4 a. Graph the following system of equations.
y = -3x
y = x + 4
b. what does the graph show to be the solution of the system?
5 DeAndre and Leah are making origami cranes. their goal is to complete 1,000 cranes by the end of the summer.
- DeAndre already has 30 cranes and makes 5 more each day.
- Leah already has 10 cranes and makes 15 more each day.
The graph shows how many cranes, c, each person has made after d days.
a. what does the graph show to be the solution of the system?
b. what does the solution mean in this context?
4. a. The graph of the system is attached below.
b. The solution is: (-1, 3).
5. a. (2, 40) is the solution as shown by the graph.
b. (2, 40) means that both will complete 40 cranes after 2 days
How to Graph a System of Equation?On a graph, when two lines are plotted for different equations, the solution is the coordinates of the point where both lines intersect.
4. a. The graph of y = -3x is the red line in the image attached below, while that of y = x + 4 is the blue line. They both intersect each other at (-1. 3).
b. The solution of the system is therefore, (-1, 3).
5. a. Using the graph given that shows the lines of the equations of DeAndre and Leah, both lines intersect at (2, 40).
We can therefore state that the solution to the system as shown in the graph is: (2, 40).
b. In the context of the scenario given, the solution (2, 40) means that both will have completed equal amounts of 40 cranes after 2 days.
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Jar A contains 4 red marbles and 6 blue marbles. Jar B contains 8 red marbles and 2 blue marbles. (20 points) (a) How many ways are there to choose a marble from Jar A or Jar B? (b) How many ways are there to choose a marble from Jar A and Jar B? (C) How many ways are there to choose a red marble from Jar A and Jar B? (d) If you choose marbles from Jar A and Jar B at random, what is the probability that they are both red?
The probability of randomly getting the red marbles from both Jar A and Jar B is 8/25.
What do we mean by probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, the probability that both marbles will be red is:
Probability formula: P(E) = Favourable events/Total events
We know that:
Jar A: 4 red marbles and 6 blue marbles
The probability of randomly choosing red marble is:
P(E) = Favourable events/Total events
P(E) = 4/10
P(E) = 2/5
Jar B: 8 red marbles and 2 blue marbles
The probability of randomly choosing red marble is:
P(E) = Favourable events/Total events
P(E) = 8/10
P(E) = 4/5
So, the total probability will be:
2/5 * 4/5
8/25
Therefore, the probability of randomly getting the red marbles from both Jar A and Jar B is 8/25.
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Correct question:
Jar A contains 4 red marbles and 6 blue marbles. Jar B contains 8 red marbles and 2 blue marbles. (20 points) If you choose marbles from Jar A and Jar B at random, what is the probability that they are both red?
Plot the points (0, 6) and (3, 0). What is the slope?
6/-3
O 1/2
-1/2
6/3
Slope is "change in y over change in x".
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using those two points, you'd have
[tex]m=\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{0-6}{3-0}=\dfrac{-6}{3}=-2[/tex]
Notice that doesn't match any of the listed answers. The reason is that two of those answers aren't reduced.
If you reduce the first answer of [tex]\dfrac{6}{-3}[/tex], you have [tex]\dfrac{6}{-3}=-2[/tex]. So that first answer is equivalent to the calculation above.
The answer from your list is the first one.
one number added to three times another number is 24 five times the number added to three times the other number is 36 find the numbers
The required numbers for the given case are 3 and 7 respectively.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
As per the given data the problem can be solved as follows,
Suppose the first number be x and the second be y.
Now, the equations can be formed as,
x + 3y = 24 (1)
5x + 3y = 36 (2)
Solve these equations by multiplying equation (1) by 5 and then subtract from (2) as below,
5x + 3y - 5(x + 3y) = 36 - 5 × 24
3y - 15y = -84
=> -12y = -84
=> y = 7
Substitute y = 7 in equation (1) to get,
x + 3 × 7 = 24
=> x = 3
Hence, the numbers for the given problem are 3 and 7 respectively.
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Find:
11/3÷2/3
the question is five and
Answer:
[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]
Step-by-step explanation:
Division of fractions can be represented as multiplication by one of the fractions' reciprocal. (Skip, Flip, and Multiply)
So,
[tex]\dfrac{11}{3} \div \dfrac{2}{3} = \dfrac{11}{3} \times \dfrac{3}{2}[/tex]
And we can simplify this to:
[tex]\dfrac{11}{2}[/tex] or [tex]5 \, \dfrac{1}{2}[/tex]