Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000, select the correct answer. Note that the profit is distributed proportionally based on the respective amount each invested. A. The ratio of the investment of Bob, Paula and Sam is 11:15:10. B. The ratio of the investment of Bob, Paula and Sam is 12:17:21. C. The ratio of the investment of Bob, Paula and Sam is 12:5:4. D. The profit of Paula was $23,800
Answer:
D
Step-by-step explanation:
since sam invest the least, let a be the amount invested by sam
sam = a
paul = a + 5000
bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
a = 12000
thus sam is 12000, paul is 17000 and Bob is 21000
therefore the ratio of B:P:S is 21:17:12
profit by paula is 17/50 x 70000 = 23800
The profit by Paula is 17/50 x 70000 = 23800.
We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000
Since sam invest the least, let a be the amount invested by sam
Therefore we get,
sam = a
What is the investment of Paul?
The investment of Paul = a + 5000
Bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
divide both sides by 3 so we get,
a=36000/3
a = 12000
Therefore, sam is 12000,
paul =5000+12000=17000 and
Bob =12000+9000= 21000
Therefore the ratio of B:P:S is 21:17:12
The profit by Paula is 17/50 x 70000 = 23800.
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Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. Livia may eat only part of a cheese stick, so x may not always be a whole number.
Step-by-step explanation:
C
Answer:
The answer is C
Step-by-step explanation:
I took the test and got it right :)
hopefully this helps you :)
pls mark brainlest ;)
word problem of addition or subtraction
Answer:
subtraction
Step-by-step explanation:
In order to find out how many more flowers you need, you need to subtract both of the numbers to get the difference.
Answer:19
Step-by-step explanation:subtract 27 from 8.
Carla Ridley is a high school algebra teacher. Her annual salary is $38,625.00. If she receives a pay check every month of the year, what is her monthly salary?
Answer:
3218.75 a month
Step-by-step explanation:
For the data 20, 40, 50, 20, 10, 70. What is there mean absolute deviation?
Answer:
18.333
Step-by-step explanation:
Suppose you had to
guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25
Answer:
For 0 correct answer [tex]^4c_0p^0q^{4-0}[/tex]
For 1 correct answer [tex]^4c_1p^1q^{4-1}[/tex]
For 2 correct answer [tex]^4c_2p^0q^{4-2}[/tex]
For 3 correct answer [tex]^4c_3p^1q^{4-3}[/tex]
For 4 correct answer [tex]^4c_4p^1q^{4-4}[/tex]
Step-by-step explanation:
It is given that there are 4 questions n = 4
Number of choices is 4
So probability of getting correct answer [tex]=\frac{1}{4}[/tex]
Probability of getting incorrect answer [tex]=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability distribution is given by [tex]^nc_rp^rq^{n-r}[/tex]
Therefore probability distribution of 0 correct answer
[tex]^4c_0p^0q^{4-0}[/tex]
Therefore probability distribution of 1 correct answer
[tex]^4c_1p^1q^{4-1}[/tex]
Therefore probability distribution of 2 correct answer
[tex]^4c_2p^0q^{4-2}[/tex]
Therefore probability distribution of 3 correct answer.
[tex]^4c_3p^1q^{4-3}[/tex]
Therefore probability distribution of 4 correct answer.
[tex]^4c_4p^1q^{4-4}[/tex]
In the right triangle shown DF=EF=3. How long is DE?
Answer:
4.24
Step-by-step explanation:
To solve this, use the Pythagorean therom. A^2 + b^2 = C^2
in this case a = 3 and b = 3
so 9 + 9 = sqrt 18
4.24
Answer:3√(2)
Step-by-step explanation:
DF=3
EF=3
DE=√(3^2 + 3^2)
DE=√(3x3 + 3x3)
DE=√(9+9)
DE=√(18)
DE=√(2 x 9)
DE=√(2) x √(9)
DE=√(2) x 3
DE=3√(2)
Find the area of the shape
Hotel 3 provides a 6 hour booking for 120 delegates in one room (including tea and lunch).how much would this cost?
Answer:
$3840
Step-by-step explanation:
The total cost is ...
(6 hr)(cost per hr) +(120 persons)(food cost per person)
= 6($190) +120($15 +7.50)
= $3840
The booking at Hotel 3 would cost $3840.
According to a Pew Research Center report from 2012, the average commute time to work in California is 27.5 minutes. To investigate whether the small city she lives in has a different average, a California high school student surveys 45 people she knows (her teachers, her parents, and their friends and co-workers) and finds the average commute time for this sample to be 24.33 minutes with a standard deviation of 9.53 minutes. The data are not too skewed. The null and alternative hypotheses of her study are: H0 : µ = 27.5 versus Ha : µ 6= 27.5
Required:
a. Identify the observational units for this study.
b. Identify the variable of interest and state whether it is categorical or quantitative.
c. Identify (in words and using an appropriate symbol) the parameter of interest
d. Use the 2SD approach to find a 95% confidence interval for the parameter.
e. Interpret the interval from part d. in context.
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. It can be described with the equation -4h=-14. What value of h makes the equation true?
The equation is -4h = -14
To find h, divide both sides of the equation by -4:
H = -14 / -4
H = 3.5 hours.
5×60=5×___tens
=_____tens
=______
Answer:
300
Step-by-step explanation:
5x60=5x6 tens it equal to 30 tens. 30 tens equals 300
Answer:
see below
Step-by-step explanation:
there are 6 tens in 60!
5x60 = 5 x 6 tens
= 30 tens
= 300
If the base-ten blocks shown are to be divided into 5 equal groups, what should be done first?
Answer:
2 divided
Step-by-step explanation:
Simplify the expression below.
14a8y3 - 7 Ay5 + 28a12y2
7aty
A.
OB.
2a²y3 - ay5 + 4a3y2
2a4y? - JA + 428 y
2a4y3 – 5 + 428 y?
D. 2012,4 - 2876 +4215,3
C.
Answer:
14a8y3 - 7 Ay5 + 28a12y2- 7ay2 • (4a11 + 2a7y - y3)
Step-by-step explanation:
Equation at the end of step 1 :
(((14•(a8))•(y3))-(7a•(y5)))+((22•7a12)•y2)
Step 2 :
Equation at the end of step 2 :
(((14•(a8))•(y3))-7ay5)+(22•7a12y2)
Step 3 :
Equation at the end of step 3 :
(((2•7a8) • y3) - 7ay5) + (22•7a12y2)
Pull out like factors
Answer: 7ay2 • (4a11 + 2a7y - y3)
Hope this helps.
Solve 20x = 10 for x. A. x = 1/2 B. x = 1.5 C. x = 2 D. x = 10
Answer:
A. 1/2
Step-by-step explanation:
20x=10
Divide 20 on both sides of the equation to get x by itself
20x=10
___. __
20. 20
x =1/2
Answer:
A) x= 1/2
Step-by-step explanation:
20x= 10 we then divide 10 by 20 to get x= 10/20 or if we simplify x= 1/2. Thus answer choice A) is correct!
How does Harrison Bergeron's physical description help to create satire?
Answer:
The absurdity of Harrison's exaggerated handicaps ridicules society's obsession with equality.Step-by-step explanation:
Answer:
Step-by-step explanation:
In the year 2081, the 211th, 212th, and 213th amendments to the Constitution dictate that all Americans are fully equal and not allowed to be smarter, better-looking, or more physically able than anyone else. The Handicapper General's agents enforce the equality laws, forcing citizens to wear "handicaps": masks for those who are too beautiful, loud radios that disrupt thoughts inside the ears of intelligent people, and heavy weights for the strong or athletic.
One April, 14-year-old Harrison Bergeron, an intelligent, athletic, and good-looking teenager, is taken away from his parents, George and Hazel Bergeron, by the government. They are barely aware of the tragedy, as Hazel has "average" intelligence (a euphemism for stupidity), and George has a handicap radio installed by the government to regulate his above-average intelligence.
Hazel and George watch ballet on television.They comment on the dancers, who are weighed down to counteract their gracefulness and masked to hide their attractiveness. George's thoughts are continually interrupted by the different noises emitted by his handicap radio, which piques Hazel's curiosity and imagination regarding handicaps. Noticing his exhaustion, Hazel urges George to lie down and rest his "handicap bag", 47 pounds (21 kg) of weights locked around George's neck. She suggests taking a few of the weights out of the bag, but George resists, aware of the illegality of such an action.
On television, a news reporter struggles to read the bulletin and hands it to the ballerina wearing the most grotesque mask and heaviest weights. She begins reading in her unacceptably natural, beautiful voice, then apologizes before switching to a more unpleasant voice. Harrison's escape from prison is announced, and a full-body photograph of Harrison is shown, indicating that he is seven feet (2.1 m) tall and burdened by three hundred pounds (140 kg) of handicaps.
George recognizes his son for a moment, before having the thought eliminated by his radio. Harrison himself then storms the television studio in an attempt to overthrow the government. He calls himself the Emperor and rips off all of his handicaps, along with the handicaps of a ballerina, whom he proclaims his "Empress". He orders the musicians to play, promising them nobility if they do their best. Unhappy with their initial attempt, Harrison takes control for a short while, and the music improves. After listening and being moved by the music, Harrison and his Empress dance while flying to the ceiling, then pause in mid-air to kiss.
Diana Moon Glampers, the Handicapper General, enters the studio and kills Harrison and the Empress with a ten-gauge double-barreled shotgun. She forces the musicians to put on their handicaps, and the television goes dark. George, unaware of the televised incident, returns from the kitchen and asks Hazel why she was crying, to which she replies that something sad happened on television that she cannot remember. He comforts her and they return to their average lives.
In ΔXYZ, the measure of ∠Z=90°, the measure of ∠X=57°, and XY = 8 feet. Find the length of YZ to the nearest tenth of a foot.
Answer:
21
Step-by-step explanation:
Answer:
6.7
Step-by-step explanation:
A teacher of statistics wants to know if a new teaching methodology that includes IT is efficient in terms of increased average score. He took a class with old methodology and a class with new methodology for samples and gave a same test. Open the file by clicking the file name above. Once you open the file and run Excel, you need not open it again. What is Ha? Find it from Excel output that you generate.
a) 0.62.
b) 0.5.
c) 0.31.
d) -0.5.
Answer:
The answer is 0.31
Step-by-step explanation:
Old Method New Method .
Mean 73.5625 Mean 75.70588
Standard Error 3.143736 Standard Error 2.923994
Median 72 Median 75
Mode 90 Mode 64
Standard deviation 12.57494 Standard deviation 12.05594
Sample Variance 158.1292 Sample Variance 145.3456
Kurtosis -1.14544 Kurtosis -0.76646
Skewness 0.171025 Skewness 0.091008
Range 39 Range 41
Minimum 55 Minimum 56
Maximum 94 Maximum 97
Sum 1177 Sum 1287
Count 16 Count 17
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: μNew< μOld
Alternative hypothesis: μNew > μOld
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
[tex]SE=\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } \\\\SE=4.29[/tex]
DF = 31
[tex]t = \frac{(x_1-x_2)-d}{SE} \\\\t = - 0.4997[/tex]
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of - 0.499. We use the t Distribution Calculator to find P(t < - 0.499) = 0.311
Therefore, the P-value in this analysis is 0.311.
Interpret results. Since the P-value (0.311) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do have sufficient evidence in the favor of the claim that new method is efficient than the old method.
A tire manufacturer has 1000 units of raw rubber to use in producing radial tires for passenger cars and tractor tires. Each radial tire requires 5 units of rubber; each tractor tire requires 20 units. Labor costs are $80 for a radial tire and $120 for a tractor tire. Suppose the manufacturer does not wish to pay more than $15,000 in labor costs and wishes to make a profit of $100 per radial tire and $250 per tractor tire. How many of each kind of tire should be made in order to maximize profit
Answer:
180 Passenger Car Tires and 5 Tractor Tires should be produced in order to maximize profit.
Step-by-step explanation:
Here, we can form two equations from the given situation.
First, we are given that the total raw tube units are 1000. And 5 units are required for passenger car tire, while 20 units are required for tractor tire. So, the equation becomes:
5 x + 20 y = 1000 -------- eqn (1)
where,
x = no. of passenger car tires produced
y = no. of tractor tires produced
Another condition is given that, maximum labor cost should be $ 15,000. Since, the labor cost is $80 for a passenger tire and $120 for a tractor tie. Thus, the equation becomes:
80 x + 120 y = 15000 -------- eqn (2)
Solving eqn (1) and eqn (2), simultaneously, we get:
x = 180
y = 5
Therefore,
No. of Passenger Car Tires Produced = x = 180
No. of Tractor Tires Produced = y = 5
A ladder is leaning against a building. Match the values with their descriptions.
(K is up Above the G )
Answer:
The height of the building: g
Distance from the building to the base of the ladder: 57
The length of the ladder: m
Angle the ladder makes with the building: k
Angle the ladder makes with the ground: 55
Step-by-step explanation:
Based off the location of the variables and numbers, the descriptions match where they are.
Hope that helps!
will mark the branliest to first one who answers
Answer:
3 1/4
Step-by-step explanation:
3/4 + (1/3 ÷1/6) - (-1/2)
Subtracting a negative is adding
3/4 + (1/3 ÷1/6) +1/2
Parentheses first
Copy dot flip
3/4 + (1/3 * 6/1) +1/2
3/4 + 2 + 1/2
Get a common denominator
3/4 + 2 + 2/4
2 + 5/4
2 + 4/4 +1/4
2+1 + 1/4
3 1/4
Which equation represents the hyperbola shown in the
graph?
10
8
(x - 2)2
(y + 3)
25
(-2,5) 6
(-7,3)
(1-21)
4-12-10 -8 -6 4-2
(3,3)
(x + 2)2
(y = 3) = 1
4
2 4 6
(x + 2)2
25
(y - 3)2
4
1
(232) - (7,31 = 1
(x - 2)2
25
Answer:
Step-by-step explanation:
A general equation of a hyperbola is
x^2 y^2
-------- - ------- = 1 (This applies only when the center of the hyperbola
a^2 b^2 is at (0, 0) ).
You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.
The equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
What is a hyperbola?A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
Given that, a graph, showing hyperbola, we need to find the equation,
We have the general equation for up - down facing hyperbola as
(y - k)² / b²- (x - h)² / a² = 1.
Let's start listing the properties of this graph -
Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).
Therefore, (h, k) = (- 4,1).
This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.
Therefore, a = 3.
That gives asymptotes. Now remember that it will be in the form
y = ± b / a.
We already know a = 3, so we have to find b.
Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).
Calculating the slope of the dotted line would be as follows,
Given: (- 4,1) and (- 2, - 2)
Slope = - 2 + 4 / - 2 - 1 = 2 / 3
We have the equation y = 2 / 3x.
Therefore, b = 2.
Let's substitute to equation...
h = - 4, k = 1, b = 2, a = 3
(y - 1)² / (3)²- (x + 4)² / (2)² = 1
(y - 1)² / 9 - (x + 4)² / 4 = 1
Hence, the equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
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The complete question is attached
The operations manager at a compact fluorescent light bulb (CFL) factory needs to estimate the mean life of a large shipment of CFLs. The manufacturer’s specifications are that the population standard deviation is 1,000 hours. A random sample of 64 CFLs indicated a sample mean life of 7,500 hours.
Construct a 95% confidence interval estimate for the popu- lation mean life of compact fluorescent light bulbs in this shipment.
Answer:
The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.95[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1000}{\sqrt{64}} = 245[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 7500 - 245 = 7255 hours.
The upper end of the interval is the sample mean added to M. So it is 7500 + 245 = 7745 hours.
The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.
A means of the estimate numerical, the variation in that estimate is referred to as the confidence interval, therefore its value is "[tex][7255, 7745][/tex]".
Confidence interval:[tex]95\%[/tex] C.I. for a mean lifetime is given by
[tex]= [ \overline{X} - \tau_{0.975} \frac{\sigma}{\sqrt{n}} , \overline{X} + \tau_{0.975} \frac{\sigma}{\sqrt{n}} ][/tex], where
[tex]\bar{X}[/tex] (sample mean) [tex]= 7500[/tex]
[tex]\sigma[/tex] (standard deviation)[tex]= 1000[/tex]
[tex]n = 64[/tex]
by putting the value into the above-given formula we get the value that is [tex]= [7255, 7745].[/tex]
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Find the mean, median, mode and range for each set of data. Calculator usage is encouraged!
1. 23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26 Please help thank you!
Answer:
mean: 46.63636
median: 34
mode: 87
range:95
How To:
Step 1 : To find Mean
Average = ( 1 + 5 + 5 + 7 + 8 + 10 ) / 6
=36 / 6
Mean = 6
Step 2 : To find Median
Middle value = ( 5 + 7 ) / 2
= 12 / 2
Median = 6
Step 3 : To find Mode
Mode = 5 (The number with more repetition, here 5 is repeated two times)
Step 4 : To find Range
Range = Largest number - Smallest number
= 10-1
= 9
Range = 9
Answer:
Mean: 46.6
Mode: 87
Median: 34
Range: 95
Step-by-step explanation:
Mean: (finding the average)
Median: (the middle number of the data set)
Mode: (the most number repeated from the data set)
Range: (is the difference between the highest value and the lowest value)
first arrange the following data set.
23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26
so:
5, 14, 19, 23, 26, 34, 37, 81, 87, 87, 100
Lets us first find the mean by adding up all the numbers and dividing it by the amount of numbers in the data set.
Mean: 5 + 14 + 19 + 23 + 26 + 34 + 37 + 81 + 87 + 87 + 100 = 513/11 = 46.6
Mode: 87
Median: 34
Range: 100 - 5 = 95
To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3,500, and the commission for each new account opened is $5,000. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.
(a) Determine the equation for computing Gustin's profit per seminar, given values of the relevant parameters. Profit = (New Accounts Opened × ) –
(b) What type of random variable is the number of new accounts opened? (Hint: Review Appendix 11.1 for descriptions of various types of probability distributions.)
(c) Choose the appropriate spreadsheet simulation model to analyze the profitability of Gustin's seminars. (I) (II) (III) (IV) Would you recommend that Gustin continue running the seminars?
(d) How many attendees (in a multiple of five, i.e., 25, 30, 35, . . .) does Gustin need before a seminar's average expected profit is greater than zero?
Answer:
a) profit = (new account opened x 5000) -3500
b) Opening account is binomial distribution with n =25 and p = 0.01
c) Probability of loss is 0.77781 --I don't recommend the company that it running the seminar
d) n ≅ 71
Step-by-step explanation:
See attached image
The quarterback Tom Brady completes 60% of his passes. To simulate the outcome of a single pass we use the digits 0, 1, 2, 3, 4, and 5 to represent the outcome "the pass is completed" and the digits 6, 7, 8, and 9 to represent the outcome "the pass is not completed." To be confident that our simulation is accurate, one needs to :
A. Repeat the simulation several more times
B. Assign new digits to represent outcomes
C. Take the average of the results of Line 134 and Line 101
Answer:
A. Repeat the simulation several more times
Step-by-step explanation:
The purpose of the simulation model is to represent the effectivity of the passes.
The proportion of successful passes is 60%.
As we have 10 digits available, 6 (digits from 0 to 5) are used for the outcome "the pass is completed" and 4 (digits 6, 7, 8, and 9) to represent the outcome "the pass is not completed". This is correct, as it represents a probability of 60% of having a successful pass.
But to have a representative distribution of the possible and probable results, the simulation have to run enough times to have a stable distribution of the results.
. The pet store salesman told Evan to feed his dog 8 ounces of food per day. The food is sold in pounds. How many pounds does Evan need to buy for 2 weeks of feeding his dog? (16 ounces = 1 pound)?
A store sells gift cards in preset amounts. You can purchase gift cards for $20 or $30. You have spent $680 on gift cards. Write an equation in standard form to represent this situation. What are three combinations of gift cards you could have purchased?
Let x be the number of gift cards for $20, and let y be the number of gift cards for $30. Write an equation in standard form to represent this situation
Answer:
20x + 30y = 680
Step-by-step explanation:
Give me a good rating please!
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Number of gift cards for $20 = x
Number of gift cards for $30 = y
Total amount spend on gift card = $680
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
Thus,
The equation represents the number of $20 and $30 gift cards bought.
20x + 30y = 680
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7.6 cm
3.7 cm
Find the area of the parallelogram.
Answer:
7cm²
Step-by-step explanation:
اذا كانت س زاويه حاده و كان جاس= ٣/٥ فان ظا س=؟؟
