90./04/ (C) 98.7877 TD) (D) 98.7777 12. If two perpendicular sides of a right-angled triangle are 5 cm and 12 cm, its perimeter is: (A) 13 cm (B) 17 cm (C) 27 cm (D) 30 cm 3. An article is purchased for 7,500 and sold for 8,400. The profit percent is : (A) 8% (B) 10%
Answers
Answer:
1) D - 30 cm 2) 12 percents
Step-by-step explanation:
The first question was If two perpendicular sides of a right-angled triangle are 5 cm and 12 cm, its perimeter is: (A) 13 cm (B) 17 cm (C) 27 cm (D) 30 cm
two perpendicular sides are legs, find the hipotenuse of the triangle
It is equal to sqrt(5^2+12^2)= sqrt169=13
5+12+13=30 - D - the perimeter
The second question
7500 -100 percents
8400- x
7500/8400=100/x
75/84=100/x
(25/28)*x=100
(1/28)*x=4
x=4/(1/28)= 4*28= 112 percents
The profit is 12 percents
2) Option D is correct. If two perpendicular sides of a right-angled triangle are 5 cm and 12 cm, its perimeter will be 30cm.
3) None of the given options are correct. If an article is purchased for 7,500 and sold for 8,400, the profit percentage will be 12%
2) A right-angled triangle is a triangle with three sides and one of its angles is 90degrees. Find the image of a right-angled triangle attached below.
The triangle consists of 3 sides which are:
The opposite sideThe adjacent sideThe hypotenuse sideBefore we can get the perimeter of the right triangle, we need to get the third side first (the hypotenuse side) using the Pythagoras theorem. According to the theorem:
[tex]c^2=a^2+b^2[/tex]
Given
a = 5 cm
b =12 cm
[tex]c^2=5^2+12^2\\c^2=25+144\\c^2=169\\c=\sqrt{169}\\c=13 cm[/tex]
Perimeter of the right triangle = a + b + c
Perimeter of the right triangle = 5 cm + 12 cm + 13 cm
Perimeter of the right triangle = 30 cm
Hence the perimeter of the right triangle is 30 cm.
3) If an article is purchased for 7,500, then;
Cost price (C.P) = 7,500If the same article is sold for 8,400, then:
Selling price (S.P) = 8,400[tex]\% profit=\frac{SP-CP}{CP} \times 100[/tex]
Substitute the given parameters
[tex]\% profit=\frac{8400-7500}{7500} \times 100\\\%profit=\frac{900}{7500} \times 100 \\\%profit=\frac{900}{75}\\\% profit = 12 \%[/tex]
This shows that the profit percent is 12%
Learn more on perimeter and percentage profit here: https://brainly.com/question/23264165
https://brainly.com/question/22104935
Related Questions
in figure , EF=1 and FC=2 What is the length of AC?
Answers
Step-by-step explanation:
ae=ec
ec=1+2=3
then ae=3
Answer:
6-most likely (AC=6)
Step-by-step explanation:
Because the 2 sides, AE and EC *look the same. Also you can look at the opposite sides.
*This is what I think
Look at the pattern below. If the
pattern continues, what will be
the tenth number?
3. 11, 9, 17, 15, 23, 21...
Answers
Answer:
35
Step-by-step explanation:
We are adding 8 and then subtracting 2
3, 11, 9, 17, 15, 23, 21
The 8th number is 21+8 = 29
The 9th number
Subtract 2
29-2 = 27
10th number
Add 8
27+8 = 35
First is adding 8 to get the next number then subtract 2 to get the number after.
21 is the 7th number.
8th number = 21 + 8 = 29
9th number = 29-2 = 27
10th number = 27 + 8 = 35
Answer: 35
Consider a credit card with a balance of $7000 and an APR of 16.5 %. If you want to make monthly payments in order to pay off the balance in 1 year, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.
Answers
9514 1404 393
Answer:
$7641.24
Step-by-step explanation:
The amortization formula tells the payment amount.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where principal P is paid off in t years with n payments per year at interest rat r.
Using the given values, we find ...
A = $7000(0.165/12)/(1 -(1 +0.165/12)^-12) = $7000×0.01375/(1 -1.01375^-12)
A = $636.77
The total of 12 such payments is ...
$636.77 × 12 = $7641.24
You will pay a total of about $7641.24.
_____
Additional comment
Since the payment amount is rounded down, the actual payoff will be slightly more. Usually, the lender will round interest and principal to the nearest cent on each monthly statement. The final payment will likely be a few cents more than the monthly payment shown here.
find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x-2y=10
Answers
Answer:
(14,2) and (-6/5,-28/5)
Step-by-step explanation:
The distance, d, from two points (x,y) and another point (a,b) can be calculated using
d=sqrt((x-a)^2+(y-b)^2).
Our point (a,b) is (2,7) and d=13.
Making substitutions:
13=sqrt((x-2)^2+(y-7)^2)
We are also given the relation between x and y is given as x-2y=10.
Adding 2y to both sides gives: x=10+2y
Make this insertion into our equation:
13=sqrt((10+2y-2)^2+(y-7)^2)
Simplify inside:
13=sqrt((8+2y)^2+(y-7)^2)
Square both sides:
169=(8+2y)^2+(y-7)^2
Expand binomial squares:
169=64+32y+4y^2+y^2-14y+49
Combine like terms:
169=5y^2+18y+113
Subtract 169 on both sides:
0=5y^2+18y-56
We could try to factor
0=(5y+28)(y-2)
So y=2 or y=-28/5
Recall x=10+2y
So if y=2, then x=10+2(2)=10+4=14.
So if y=-28/5, then x=10+2(-28/5)=10+(-56/5)
=50/5 +-56/5
=-6/5.
So two points satisfying given criteria is
(14,2) and (-6/5,-28/5).
John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John
buys a new cylindrical propane tank that is twice as wide and half as tall as his
current tank, how much larger will the volume of the new tank be?
Answers
Answer:
2 times as large
Step-by-step explanation:
For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128
For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus
V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256
To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in
π * 256 / (π *128) = 2
△DOG ~△?
Complete the similarity statement and select the theorem that justifies your answer.
**If they are not similar, select "none" for both parts
Answers
9514 1404 393
Answer:
nonenoneStep-by-step explanation:
The reduced side ratios, shortest to longest are ...
AC : AT : CT = 8 : 9 : 15
OD : OG : DG = 5 : 6 : 10
These are different ratios, so the triangles are not similar.
round 32.68 to the nearest hundredth
Answers
Answer:
32.70
Step-by-step explanation:
round up
Twelve residents from the city of Rocklin were randomly selected and asked "How many TVs are in your household?". The following data were obtained: 2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, and 3.
According to Nielsen Media Research the national average is 2.7 TVs per household. Is this sufficient sample evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average of 2.7 TVs per household? Use ! = 5% and assume that the number of TVs in Rocklin households is normally distributed.
Answers
Answer:
There isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average .
Step-by-step explanation:
This is a one sample mean test ;
H0 : μ = 2.7
H1 : μ > 2.7
Given the data :
2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3
Sample size, n = 12
The sample mean, xbar = ΣX / n = 33/12 = 2.75
The sample standard deviation, s = 1.215 ( from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.75 - 2.7) ÷ (1.215/√(12))
T = 0.05 / 0.3507402
T = 0.1426
The critical value from Tscore ;
df = 12 - 1 = 11
Critical value = 1.796
Since ; Test statistic < Critical value ;WE fail to reject the Null and conclude that there isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average
Mr. Cole packed 20 pounds into a suitcase, and Mrs. Cole packed 23 pounds into the same suitcase. They then had to remove 8 pounds because it was too heavy. How many pounds was their suitcase after making it lighter?
Answers
Answer:
35 lbs is the final weight
Step-by-step explanation:
20 +23 = 43 lbs
Then they had to remove 8 lbs
43 - 8 =35
35 lbs is the final weight
[tex]4 + \frac{4}{4 } \: = [/tex]
what is answer
Answers
Answer:
5Step-by-step explanation:
[tex]4 + \frac{4}{4} [/tex]
= 4 + 1
= 5 (Ans)
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink what fraction of the bouquet is pink? There are 12 roses in a dozen.
A. 5/12
B. 7/12
C. 5/7
D. 7/5
Answers
Answer:
7/12
Step-by-step explanation:
There are 12 roses - 5 white = 7 pink
7 pink / 12 total
Help me Please I need this
Answers
there are 7 vertices in this shape
Answer:
7.
Step-by-step explanation:
The vertices are the points where the lines meet.
the ratio of sadia's age to her father's age is 3:6. The sum of their age is 96 .What is sadia's age
Answers
We have,
[tex]a:b=3:6,a+b=96[/tex]
Introduce variable [tex]x[/tex] such that [tex]a=3x,b=6x[/tex]
The sum [tex]a+b=96[/tex] is therefore [tex]9x=96\implies x=10.\overline{6}[/tex]
So,
[tex]a=3\cdot10.\overline{6}=\boxed{32}[/tex] (sadia's age)
[tex]b=6\cdot10.\overline{6}=\boxed{64}[/tex] (father's age)
Hope this helps :)
Why wouldn't you use division to find an equivalent fraction for 7/15
Answers
Answer:
This depends whether you want to make the fraction bigger or smaller.
Step-by-step explanation:
If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.
However, if you want to make the fraction bigger, then you would multiply.
Hope this helps! :)
Answer:
Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.
Step-by-step explanation:
How many minutes will the bus take to complete the trip If a bus completes half a trip at 40 km per hour and the other half at 50 20. if the whole trip was 60 k.m. ?
Answers
Answer:
The bus will take 81 minutes to complete the trip.
Step-by-step explanation:
To determine how many minutes will the bus take to complete the trip if a bus completes half a trip at 40 km per hour and the other half at 50 km per hour, and the whole trip was 60 km, the following calculation must be performed:
60/2 = 30
30/40 = 3/4 of an hour = 45 minutes
30/50 = 3/5 of an hour = 36 minutes
45 + 36 = 81
Therefore, the bus will take 81 minutes to complete the trip.
Help me with this please.
Answers
Answer:
the answer should be B
Step-by-step explanation:
take the total of people who got the flu(63) and the amount of them who were vaccinated(35) and write it as a fraction. 35/63 in its simplest form is 5/9
The product of two rational numbers is 47/42 and one of them is -11/21, find the other number
Answers
answer:
another number is -47/22
explanation:
let one number be x and the other be y
-11/21 × y = 47/42
y = -47/22
Answer:
- [tex]\frac{47}{22}[/tex]
Step-by-step explanation:
let n be the other number , then
- [tex]\frac{11}{21}[/tex] × n = [tex]\frac{47}{42}[/tex] ( divide both sides by - [tex]\frac{11}{21}[/tex] )
n = [tex]\frac{\frac{47}{42} }{-\frac{11}{21} }[/tex]
= [tex]\frac{47}{42}[/tex] × - [tex]\frac{21}{11}[/tex] ( cancel 21 and 42 )
= [tex]\frac{47}{2}[/tex] × - [tex]\frac{1}{11}[/tex]
= - [tex]\frac{47}{22}[/tex]
The mean output of a certain type of amplifier is 102102 watts with a standard deviation of 1212 watts. If 6363 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 3.43.4 watts
Answers
Answer:
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 102, standard deviation of 12:
This means that [tex]\mu = 102, \sigma = 12[/tex]
Sample of 63:
This means that [tex]n = 63, s = \frac{12}{\sqrt{63}}[/tex]
What is the probability that the mean of the sample would differ from the population mean by greater than 3.4 watts?
Below 102 - 3.4 = 98.6 or above 102 + 3.4 = 105.4. Since the normal distribution is symmetric, these probabilities are equal, and thus, we find one of them and multiply by two.
Probability the mean is below 98.6.
p-value of Z when X = 98.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{98.6 - 102}{\frac{12}{\sqrt{63}}}[/tex]
[tex]Z = -2.25[/tex]
[tex]Z = -2.25[/tex] has a p-value of 0.0122.
2*0.0122 = 0.0244
0.0244 = 2.44% probability that the mean of the sample would differ from the population mean by greater than 3.4 watts.
In a mixture 60 liters, the ratio of milk and water 2:1.If this ratio is to be 1:2, then what is the quantity of water to be further added?
Answers
Answer:
Hello,
60L
Step-by-step explanation:
Quantity of water /Quantity of milk =2/1
Quantity of mixture= Quantity of water +Quantity of milk =60L
Quantity of milk =40 L
Quantity of water =20 L
Let say x the quantity of water to be added
New ratio =1/2=40/(20+x)
20+x=80 (cross products)
x=60 (L)
*20 points*
how do you get the weighted average from this table?
Answers
Answer:
it is
[(2+3+4+6)-2*4]:4=1.75
I THINK
Step-by-step explanation:
Wesley is making a patio from stones of two sizes, 5 inch wide and 10 inch wide. He wants to begin and end his pattern with a 10 inch stone so there will be one more of the 10 inch stones than of 5inch stones. His patio will be 130 inches wide.
How many 10 inch stones will Wesley need for one row?
Answers
9514 1404 393
Answer:
9
Step-by-step explanation:
If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...
10x +5(x-1) = 130
15x -5 = 130 . . . . . . . eliminate parentheses
15x = 135 . . . . . . add 5
x = 9 . . . . . . . divide by 15
Wesley will need 9 10-inch stones for one row.
look at the image below urgent plz over 100 points
Answers
Answer: 1,526.04 yd³ (this is what i got on my calculator others may vary use any rounding you need)
VOLUME of CONE is: V= Pir² h / 3
Pi= 3.14
r= 9
h= 18
V= (3.14) x (9)² x (18)
9²= 81
3.14 x 81= 254.34 x 18= 4,578.12
4,578.12 / 3= 1,526.04 <-- answer
10. In a group of 50 people, there are two types of professionals, engineers and managers. If 36 of them are engineers and 24 of them are managers, how many persons are both managers and engineers?
Answers
Step-by-step explanation:
The photo above is the Venn diagram
Now, the number of persons that are both managers and engineers= n
Since, Total number of persons is 50
Therefore, 50= M+n+E
M only = 36-n
E only = 24-n
Therefore, 50= 36 - n + n + 24 - n
50 = 36+24-n
50 = 60 - n
60 - n = 50
-n = 50 - 60
-n = - 10
Therefore, n = 10
Therefore, the number of persons that are both Managers and Engineers is 10persons.
Part C
Based on feedback from an independent research firm, the flashlight manufacturer has decided to change the design of the flashlight. The reflector now needs to extend 4 centimeters past the center of the bulb, as shown in the diagram. In the new design, how wide will the reflector (CD) be at its widest point? Show your work.
Answers
Answer:
The answer is "18".
Step-by-step explanation:
In the given graph by concluding we observe that on the x-axis, one step is 2 units, and when we half each of the steps it will= 1 unit
[tex]\therefore\\\\CD = distance\ from\ -(8+1)\ to\ (8+1)\ = \text{distance between} -9 \ to\ 9\ = 18[/tex]
Area of a circle whose circumference is 100ft
Answers
Answer:
A≈795.77ft²
Step-by-step explanation:
C=100ft
Area of circle=C^2/4pie
100/4×22/7≈795.77472ft²
In the following problem, the ratios are directly proportional. Find the missing variable.
If y1 = 4, x2 = 6, and y2 = 8, what is the value of x1?
Answers
Answer:
x1 = 3
Step-by-step explanation:
first set up the proportion (write as fractions):
(y1/x1) = (y2/x2)
then fill in the variables:
4/x1 = 8/6
now cross multiply:
8 • x1 = 6 • 4
simple algebra:
8 • x1 = 24
x1 = 24/8
x1 = 3
If y1 = 4, x2 = 6, and y2 = 8, then the value of x1 is 3 which we can solve using ratios.
In a directly proportional relationship, the ratios between the corresponding values of two variables remain constant. This constant ratio is often referred to as the "proportionality constant."
In this problem, you have two pairs of values: (x1, y1) and (x2, y2). We're given that the ratios are directly proportional, which means:
x1 / y1 = x2 / y2
Plugging in the given values:
x1 / 4 = 6 / 8
Now, cross-multiply to solve for x1:
x1 * 8 = 4 * 6
x1 = 24 / 8
x1 = 3
Therefore, the value of x1 is 3.
Learn more about ratios here:
https://brainly.com/question/32531170?
#SPJ3
please help
Question: 6b = 18
Answer: ?
Answers
Answer:
6b=18
b=18/6
b=3
.
.
.
.
.
.
Answer:
6b=18
b=18/6
b=3
.
Step-by-step explanation:
Wyatt is making a salad using tomatoes, cucumbers, and carrots. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Wyatt uses:
Ingredient Price per kilogram Amount
Tomatoes 3.30dollars per kilogram 0.3
Cucumbers x dollars per kilogram y kilograms
Carrots z dollars per kilogram 0.20
The total amount Wyatt spends on ingredients is C dollars.
Write an equation that relates x, y, z, and C.
Answers
According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:
[tex]C = 0.99 + xy + 0.2z[/tex]
Cost:
0.3 kilograms of tomatoes, at 3.30 dollars per kilogram.
Thus, the cost starts at:
[tex]C = 0.3*3.3 = 0.99[/tex]
y kilograms of cucumbers, at x dollars per kilogram.
Considering this, the cost will now be of:
[tex]C = 0.99 + xy[/tex]
0.2 kilograms of carrots, at z dollars per kilogram:
Now, we have to consider this for the cost, so:
[tex]C = 0.99 + xy + 0.2z[/tex]
A similar example is given at https://brainly.com/question/14544759
Help me plz 20 points to who ever gets it right
Answers
Step-by-step explanation:
2., 3., 4., 5.
yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.
you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).
2.
(-4, 6) to (10, -10)
in x the distance is 10 - -4 = 14. half is 7.
in y the distance is |-10 - 6| = |-16| = 16. half is 8.
so the midpoint is
(-4 + 7, 6 - 8) = (3, -2)
remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).
3.
(-3, -8) to (-6.5, -4.5)
in x distance : -3 - -6.5 = 3.5. half is 1.75
in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75
midpoint is
(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)
4.
(3, 7) to (-8, -10)
x : 3 - -8 = 11. half is 5.5
y : 7 - -10 = 17. half is 8.5
midpoint is
(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)
5.
(-6, -13) to (-6.4, -3.8)
x : -6 - -6.4 = 0.4. half is 0.2
y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6
midpoint is
(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)
6.
(-1, 7) to (5, 1)
x : -1 - 5 = |-6| = 6. 1/3 is 2.
y : 7 - 1 = 6. 1/3 is 2.
1/3 from C to D
(-1 + 2, 7 - 2) = (1, 5)
7.
2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).
again
(1, 5)
8.
2/3 of the way from C to D.
so, we need to double what we added in 6.
(-1 + 4, 7 - 4) = (3, 3)
9.
1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).
again
(3, 3)
10.
exactly. Pythagoras.
the square root of the sum of the squares of the coordinate differences.
distance = sqrt((x1 - x2)² + (y1 - y2)²)
11.
(6, 8) to (-1, 8)
distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7
12.
(5, -6) to (5, 6)
sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12
13.
(-2, 0) to (11, 0)
sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13
14.
(1, -5) to (9, 1)
sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10
15.
ST and MT are basically the same equation.
MT is half of ST.
ST equation based on 2 points :
y – yS={(yT – yS)/(xT – xS)}(x – xS)
M = (xS + (xT - xS)/2, yS +(yT - yS)/2)
so, let's put that into the general equation :
y - yM={(yT - yM)/(xT - xM)}(x - xM)
y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))
16.
the two corners farthest away are (5, 10) and (9, 6).
what distance from (0, 0) is now bigger ?
since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.
5² + 10² = 125
9² + 6² = 117
so, the corner (5, 10) is the farthest away.
Not sure how to do this
