Answer:
45
------
75
Step-by-step explanation:
Let x be the value of the numerator and x+30 be the value of the denominator
This is equal to 3/5
x 3
-------- = -------
x+30 5
Using cross products
5x = 3(x+30)
Distribute
5x = 3x+90
Subtract 3x from each side
2x = 90
Divide by 2
x = 45
The fraction is
45
-----
30+45
45
------
75
[tex]\dfrac{x}{x+30}=\dfrac{3}{5}\\\\5x=3(x+30)\\5x=3x+90\\2x=90\\x=45\\\\\dfrac{x}{x+30}=\dfrac{45}{45+30}=\dfrac{45}{75}[/tex]
g If the events A and B are independent with P( A) = 0.35 and P( B) = 0.45, then the probability that both events will occur simultaneously is:
Answer:
0.1575.
Step-by-step explanation:
Here, as they are independent, we multiply the probabilities:
P( A and B) = 0.35*0.45
= 0.1575.
The probability that both events will occur simultaneously is 0.1575.
Given that, the events A and B are independent with P( A) = 0.35 and P( B) = 0.45.
What is independent probability?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
Since, the events A and B are independent
We have P(A and B)
= P(A) × P(B)
= 0.35 × 0.45
= 0.1575
Hence, the probability that both events will occur simultaneously is 0.1575.
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How many dimensions does an angle have?
Answer:
the length has dimension 1, the area has the dimension 2, the volume has dimension 3, etc. And the angle has dimension 0.
Step-by-step explanation:
10 points plssssss!!!
Answer:
A. rectangle
B. any of triangle, quadrilateral, pentagon, hexagon
Step-by-step explanation:
A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.
__
B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...
trianglequadrilateralpentagonhexagonwhich terms are like terms in the following expression ? 6x + 8xy - 3x + 9y + 4x^2
Answer:
[tex]\Large \boxed{{6x \ \mathrm{and} \ -3x}}[/tex]
Step-by-step explanation:
Like terms have identical variables and exponents, the coefficients don’t have to be the same.
The like terms from the expression are 6x and -3x.
Step-by-step explanation:
Hey, there!!
6x and -3x are like terms.
Like terms in algebraic terms are those terms which has same variable or exponents. In This expression "6x+8xy-3x+9y4x^2"
6x and -3x has "x" common in them so, The answer is 6x and -3x.
Hope it helps..
3.85∙47.3+52.7∙3.85 PLSSSSS HELP
Answer:
385
Step-by-step explanation:
In an examination, 40% of the candidates failed. The number candidates who failed was 160. How many candidates passed the examination?
Answer:
240 candidates
Step-by-step explanation:
40% candidates failed, i. e. out of every 100 candidates 40 failed.
40 failed ----------------------------- 100 total students
1 failed --------------------------------100/40 total students, given 160 failed therefore
160 failed ----------------------------(100/40) x 160 total students
Total students = (100/40) x 160 = 400
Number of candidates passed = (total candidates) - (total candidates failed)
= 400 - 160 = 240 candidates
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find y! Round to the nearest tenth!!
Answer:
y = 178.3 ftStep-by-step explanation:
Since the above figure is a right angled triangle we can use trigonometric ratios to find y
To find y we use tan
tan∅ = opposite/ adjacent
From the question
the opposite is y
the adjacent is 350 ft
Substitute the values into the above formula
That's
[tex] \tan(27) = \frac{y}{350} [/tex]
y = 350 tan 27
y = 178.3339
We have the final answer as
y = 178.3 ft to the nearest tenthHope this helps you
square root of 49/64 answered as a fraction
Answer:
Hey there!
That would be 7/8
Let me know if this helps :)
Which one is correct? in need of large help
Answer:
Option C. x + 12 ≤ 2(x – 3)
Step-by-step explanation:
From the question, we obtained the following information:
x + 12 ≤ 5 – y .......(1)
5 – y ≤ 2(x – 3) ....... (2)
To know which option is correct, do the following:
From equation 2,
5 – y ≤ 2(x – 3)
Thus, we can say
5 – y = 2(x – 3)
Now, we shall substitute the value of 5 – y into equation 1 as shown below:
x + 12 ≤ 5 – y
5 – y = 2(x – 3)
x + 12 ≤ 2(x – 3)
From the above illustration, we can see that if x + 12 ≤ 5 – y and 5 – y ≤ 2(x – 3), then x + 12 ≤ 2(x – 3) must be true.
Option C gives the correct answer.
Find an equation of the plane through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1). Do this problem in the standard way.
Answer:
x+5y+z = 25Step-by-step explanation:
Given a plane passing through the point(1, 5,-1) and perpendicular to the vector (1, 5, 1), the equation of the plane can be expressed generally as;
a(x-x₀)+b(y-y₀)+c(z-z₀) = 0 where (x₀, y₀, z₀) is the point on the plane and (a, b,c) is the normal vector perpendicular to the plane i.e (1,5,1)
Given the point P (1, 5, -1) and the normal vector n(1, 5, 1)
x₀ = 1, y₀ =5, z₀ = -1, a = 1, b = 5 and c = 1
Substituting this point in the formula we will have;
a(x-x₀)+b(y-y₀)+c(z-z₀) = 0
1(x-1)+5(y-5)+1(z-(-1)) = 0
(x-1)+5(y-5)+(z+1) = 0
x-1+5y-25+z+1 = 0
x+5y+z-1-25+1 = 0
x+5y+z-25 = 0
x+5y+z = 25
The final expression gives the equation of the plane.
A class with n kids lines up for recess. The order in which the kids line up is random with eachordering being equally likely. There are three kids in the class named John, Betty, and Mary. The useof the word "or" in the description of the events, should be interpreted as the inclusive or. That is"A or B" means thatAis true,Bis true, or bothAandBare true.Give an expression for each of the probabilities below as a function ofn. Simplify your final expressionas much as possible so that your answer does not include any expressions of the form (a/b).Requried:a. What is the probability that Betty is first in line or Mary is last in line? b. Explain the method used to calculate probability.
Answer:
A) P(Betty is first in line and mary is last) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
B) The method used is Relative frequency approach.
Step-by-step explanation:
From the question, we are told a sample of n kids line up for recess.
Now, the order in which they line up is random with each ordering being equally likely. Thus, this means that the probability of each kid to take a position is n(total of kids/positions).
Since we are being asked about 3 kids from the class, let's assign a letter to each kid:
J: John
B: Betty
M: Mary
A) Now, we want to find the probability that Betty is first in line or Mary is last in line.
In this case, the events are not mutually exclusive, since it's possible that "Betty is first but Mary is not last" or "Mary is last but Betty is not first" or "Betty is the first in line and Mary is last". Thus, there is an intersection between them and the probability is symbolized as;
P(B₁ ∪ Mₙ) = P(B₁) + P (Mₙ) - P(B₁ ∩ Mₙ) = P(B₁) + P(Mₙ) - (P(B₁) × P(Mₙ/B₁))
Where;
The suffix 1 refers to the first position while the suffix n refers to the last position.
Also, P(B₁ ∩ Mₙ) = P(B₁) × P(Mₙ/B₁)
This is because the events "Betty" and "Mary" are not independent since every time a kid takes his place the probability of the next one is affected.
B) The method used is Relative frequency approach.
In this method, the probabilities are usually assigned on the basis of experimentation or historical data.
For example, If A is an event we are considering, and we assume that we have performed the same experiment n times so that n is the number of times A could have occurred.
Also, let n_A be the number of times that A did occur.
Now, the relative frequency would be written as (n_A)/n.
Thus, in this method, we will define P(A) as:
P(A) = lim:n→∞[(n_A)/n]
Given this pair of probabilities, the probability that Mary is the first is n(A) = n-1!, while the probability that Betty is last is n(A) = n-1!
There are n! ways of making this arrangement
We have probability of A: Betty is the first person in this line
Probability of B: Mary is the last person
A U B = p(A) + p(B) - p(A ∩ B)
n(A) = n-1 that is given that Betty is the first person on the line.
then n(A) = n-1!
As the last person on the line P(B) = n-1!
Probability of (A∩B) =( n-2)! this has Mary as the first and Betty as the last person.
Remaining students that would have to be on this line are n-2
Prob(A∪B) = n(A ∪ B)/n!
= 2(n-2)/n(n-1)
What is the probability theory in Mathematics?This is the theory that talks about the chances or the likelihood of an event occuring in a pair of events.
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What is seven to the fifth power equal to
Answer:
16,807
Step-by-step explanation:
Write it out: [tex]7^{5}[/tex] [tex]7^{5}[/tex] = 7 × 7 × 7 × 7 × 77 × 7 = 4949 × 7 = 343343 × 7 = 24012401 × 7 = 16,8072/5(10c -35) (the 35 is negative)
Answer:
The simplified form is 2 (c - 7).
Step-by-step explanation:
The expression to be solved is:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
Simplify the expression as follows:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
[tex]=[\frac{2}{5}\times 10c]-[\frac{2}{5}\times 35]\\\\=[2\times 2c]-[2\times 7]\\\\=4c-14\\\\=2(c-7)[/tex]
Thus, the simplified form is 2 (c - 7).
A department store offers two promotions. Promotion A says, "Buy one pair of shoes, get the second pair for half the price." Promotion B says, "Buy one pair of shoes, get $10 off the second pair." Jane wants to buy two pairs of shoes that cost $30 each. She can only use one of the promotions, A or B. Jane decides to use the promotion that will save her the most money. How many dollars does Jane save by picking one promotion over the other? (For example, if Jane spends $150 on her purchase by using one promotion and $100 on her purchase by using the other promotion, she saves $150-100=50$ dollars by using the second promotion over the first.)
Answer:
$5
Step-by-step explanation:
Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.
Candice spent 5 1/4 hours doing her homework. Her brother, Ronald, spent 1/2 that number of hours doing his homework. How many hours did Ronald spend on his homework?
Answer:
Step-by-step explanation:
½ of 5¼
½×(21/4)
=21/8
=2⅝ hours
Answer:
2 5/8
Step-by-step explanation:
you would divide 5 1/4 by 2 :
5 divided by 2 =2 1/2
1/4 divided by 2=1/8
then make the numbers have the same denomanator
1/2, 2/4, 4/8
1/8,
then you add
2 4/8+1/8=2 5/8
football team, won 35 out of 39 games over a period of 4 years. if they keep winning pace, predict how many games you would expect them to win over the next 78 football games
Answer:
70
Step-by-step explanation:
If the team continues with same pace, they expected wins as per previous ratio:
35/39*78 = 70Expected wins 70 out of 78 games
Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Accounting 83 Management 68 Marketing 85 Economics 64 Total 300 Has there been any significant change in the number of students in each major between the last school year and this school year?
Answer:
There has been no significant change in the number of students in each major between the last school year and this school year.
Step-by-step explanation:
A Chi-square test for goodness of fit will be used in this case.
The hypothesis can be defined as:
H₀: There has been no change in the number of students.
Hₐ: There has been a significant change in the number of students.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
Here,
[tex]O_{i}[/tex] = Observed frequencies
[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.
The chi-square test statistic value is, 1.662.
The degrees of freedom is:
df = 4 - 1 = 4 - 1 = 3
Compute the p-value as follows:
[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]
*Use a Chi-square table.
The p-value is 0.645.
The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.
Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.
Megan’s room is expanded so the width is 150% of 3 meters. What is the new width?
Work Shown:
The keyword "of" means "multiply".
150% = 150/100 = 1.5
150% of 3 = 1.5*3 = 4.5
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
100% = 3 meters
150% = 4.5 meters
The new width is 4.5 meters.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Megan’s room is expanded so the width is 150% of 3 meters.
This means,
100% = 3 meters
Multiply 150/100 on both sides.
150% = 150/100 x 3
150% = 4.5 meters
Thus,
The new width is 4.5 meters.
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5(y–3.8)=4.7(y–4) help help
Answer:
y = 2/3 or 0.667Step-by-step explanation:
5(y–3.8)=4.7(y–4)
Expand the terms in the bracket
That's
5y - 19 = 4.7y - 18.8
Group like terms
5y - 4.7y = 19 - 18.8
0.3y = 0.2
Divide both sides by 0.3
We have the final answer as
y = 2/3 or 0.667Hope this helps you
A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table. A 2-column table has 5 rows. The first column is labeled Color with entries blue, green, red, orange, yellow. The second column is labeled Number with entries 1, 2, 0, 4, 3. Which statements are true about Yuri’s experiment? Select three options. The theoretical probability of spinning any one of the five colors is 20%. The experimental probability of spinning blue is One-fifth. The theoretical probability of spinning green is equal to the experimental probability of spinning green. The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
Answer:
A. The theoretical probability of spinning any one of the five colors is 20%.
C. The theoretical probability of spinning green is equal to the experimental probability of spinning green.
E. If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
These are the answers on edg 2020, just took the test.
Step-by-step explanation:
Answer:
a, c, e,
Step-by-step explanation:
:)
Find the measure of F. A. 44 B. 88 C. 90 D. 46
Answer:
A. 44º
Step-by-step explanation:
The sum of internal angles in a triangle is equal to 180 degrees, whereas the sum for a square is equal to 360 degrees. Given that three triangles depicted on figure constructs a square, it is to conclude that each is an isosceles triangle. The following relations are presented:
1) [tex]e + 92^{\circ} = 180^{\circ}[/tex] Given
2) [tex]a = b[/tex], [tex]c = d[/tex] Given
3) [tex]a + b + 92^{\circ} = 180^{\circ}[/tex] Given.
4) [tex]c + d + e = 180^{\circ}[/tex] Given.
5) [tex]b + c = 90^{\circ}[/tex] Given.
6) [tex]2\cdot a + 92^{\circ} = 180^{\circ}[/tex] 2) in 3)
7) [tex]a = 44^{\circ}[/tex] Algebra
8) [tex]b = 44^{\circ}[/tex] By 2)
9) [tex]b= f[/tex] Alternate internior angles.
10) [tex]f = 44^{\circ}[/tex] By 8). Result
Hence, the answer is A.
)Patrick buys some bananas for 35%. He sells all the bananas for $40.60. Calculate profit
percentage. Show your working.
Answer:
40.60-35=5.6
Step-by-step explanation:
Profit is cost minus the amount you sold it for
At a store An orange costs 18 cents A pineapple costs 27 cents An apple costs 15 cents How much does a strawberry cost??
Answer:
A strawberry cost 30 cents
Step-by-step explanation:
Given:
Orange= 18 cents
Pineapple = 27 cents
Apple = 15 cents
Strawberry = ?
From the given:
Orange has 6 letters multiplied by 3
=6 * 3
=18 cents
Pineapple has 9 letters multiplied by 3
=9 * 3
=27 cents
Apple has 5 letters multiplied by 3
= 5 * 3
= 15 cents
Therefore, cost of the strawberry=
Strawberry has 10 letters. Multiply the 10 letters by 3
That is,
10 × 3
= 30 cents
Simplify 70 +(-30)+2+(-9)+0.3+(-0.1)=[70+(-30)] +[2+(-9)]+[0.3+(-0.1)]
Answer:
Step-by-step explanation:
When you add the left side of the equation, you get 33.2 because 70-30 is 40, 40+2 is 42, 42-9 is 33, 33+0.3 is 33.03, 33.3-0.1 is 33.2.
When you add the right side of the equation, you get 33.2, because they are the same problem but on side has brackets.
Hope this helps you.
Part 3: Choose a proof method
Answer: see proof below
Step-by-step explanation:
Statement Reason
1. ∠WZX ≅ ∠YZX 1. Given
2. ZW ≅ ZY 2. Given
3. ZX = ZX 3. Reflexive Property
4. ΔWZX ≅ ΔYZX 4. SAS Congruency Theorem
5. WX = YX 5. CPCTC
6. ∠WXZ = 90° 6. bisector of isosceles ΔWZY
∠YXZ = 90°
7. ZX is perpendicular bisector of WY 7. Definition of perpendicular bisector
Step-by-step explanation:
In this question we have to prove that zx = wy
the question is proved in the above attachment
and as we know that the straight line is of 180 degree and Ab is the bisector of line so the angles are also equally divided it means angle zxw= 90 and zxy = 90
Hope it helps you mate
50q + 43 > −11q + 70
Answer:
q > 27/61
Step-by-step explanation:
50q + 43 > −11q + 70
Add 11 q to each side
50q+11q + 43 > −11q+11q + 70
61q+43> 70
Subtract 43 from each side
61q> 27
Divide each side by 61
61q/61> 27/61
q > 27/61
Select the correct answer from each drop-down menu. The gasoline prices in seven states are $1.96, $2.09, $1.79, $1.61, $1.75, $2.11, and $1.84. The median gasoline price is _____. The difference of the first and third quartiles in this set of gas prices is ______ .
Answer:
The median is 1.84 and the difference between the first and third quartile is 0.34
Step-by-step explanation:
When you write them out 1.84 is the median (middle number). To find the difference I just subtracted the third quartile (2.09) by the first quartile (1.75)
========================================================
Explanation:
Original data set = {1.96, 2.09, 1.79, 1.61, 1.75, 2.11, 1.84}
Sorted data set = {1.61, 1.75, 1.79, 1.84, 1.96, 2.09, 2.11}
Notice that 1.84 is in the middle of the sorted set. Three values are smaller than it, and three values are larger than it.
Therefore, 1.84 is the median.
The values {1.61, 1.75, 1.79} are smaller than the median. We'll call this set L for lower set.
The values {1.96, 2.09, 2.11} are larger than the median. We'll call this set U for upper set.
From set L = {1.61, 1.75, 1.79}, the median here is 1.75. This is the value of the first quartile Q1
The value of Q3 is 2.09 as it is in the direct middle of set U = {1.96, 2.09, 2.11}
The interquartile range (IQR) is the difference of Q3 and Q1
IQR = Q3 - Q1
IQR = 2.09 - 1.75
IQR = 0.34
What is the equation of the following line? Be sure to scroll down first to see all answer options.
A.
y = - 1/2x
B.
y = 1/2x
C.
y = 2x
D.
y = -6x
E.
y = 6x
F.
y = 3x
Answer:
y=-6x
Step-by-step explanation:
It keeps saying my answer is wrong after i identified the GCF as 3 but maybe I typed it wrong.
Answer:
3(9t^5-7p^4)(9t^5+7p^4)
Step-by-step explanation:
243 t^10 - 147 p^8
3 ( 81 t^10-49 p^8 )
Then we need to factor what is in the parentheses
3 ( ( 9t^5) ^2 - ( 7p^4) ^2)
This is the difference of squares ( a^2 -b^2) = ( a-b) (a+b)
3(9t^5-7p^4)(9t^5+7p^4)
Topic: Linear functions and their inverses Carlos and Clarita have a pet sitting business. When they were trying to decide how many each of dogs and cats they could fit into their yard, they made a table based on the following information. Cat pens require 6 ft2 of space, while dog runs require 24 ft2 . Carlos and Clarita have up to 360 ft2 available in the storage shed for pens and runs, while still leaving enough room to move around the cages. They made a table of all of the combinations of cats and dogs they could use to fill the space. They quickly realized that they could fit in 4 cats in the same space as one dog. cats 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 dogs 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 8. Use the information in the table to write 5 ordered pairs that have cats as the input value and dogs as the output value. 9. Write an explicit equation that shows how many dogs they can accommodate based on how many cats they have. (The number of dogs "d" will be a function of the number of cats "c" or 10. Use the information in the table to write 5 ordered pairs that have dogs as the input value and cats as the output value. 11. Write an explicit equation that shows how many cats they can accommodate based on how many dogs they have. (The number of cats "c" will be a function of the number of dogs "d" or c = g(d).) Base your answers in #12 and #13 on the table at the top of the page. 12. Look back at problem 8 and problem 10. Describe how the ordered pairs are different.
