Final answer:
To find the three consecutive odd integers whose sum is between 27 and 51, set up an inequality with n representing the smallest integer. Solve the inequality to find the possible values for n, which are then used to derive the consecutive integers.
Explanation:
To find three consecutive odd integers whose sum lies between 27 and 51, we need to establish variables for the integers and then solve for them. Let's call the smallest integer n, the next integer will then be n+2 (since odd numbers are two units apart), and the largest integer will be n+4. The equation will be n + (n+2) + (n+4), which simplifies to 3n + 6.
Since their sum must be between 27 and 51, our inequalities are:
27 < 3n + 6 < 51
Subtract 6 from all parts of the inequality:
21 < 3n < 45
Now, divide everything by 3:
7 < n < 15
Since n must be an odd integer, we have the options 9, 11, or 13 for n. Therefore, our sets of three consecutive odd integers could be:
(9, 11, 13), (11, 13, 15), or (13, 15, 17).
X and Y are two mutually exclusive events. P(X)= 0.55 and P(X or Y)=0.7. Work out P(not Y) (2 marks)
To find the probability of not Y occurring when events X and Y are mutually exclusive, we subtract P(X) from P(X or Y) to get P(Y) and then subtract P(Y) from 1 to get P(not Y), resulting in a probability of 0.85.
The question asks us to find the probability of not event Y occurring, given that X and Y are mutually exclusive events, and we're provided with P(X) and P(X or Y). Since X and Y are mutually exclusive, the sum rule of probability states that P(X or Y) = P(X) + P(Y). Using the given values, we can express P(Y) as P(X or Y) - P(X), which is 0.7 - 0.55 = 0.15. Since the probability of an event and its complement sum to 1, P(not Y) is 1 - P(Y), which gives us 1 - 0.15 = 0.85.
Therefore, the probability of not Y is 0.85.
Figure ABCD is a square. Prove BD ≅ AC. Statements Reasons 1. ABCD is a square 1. given 2. ∠DAB, ∠ABC, ∠BCD, and ∠CDA are right angles 2. definition of a square 3. ∠DAB ≅ ∠ABC ≅ ∠BCD ≅ ∠CDA 3. right angles are congruent 4. AB ≅ BC ≅ CD ≅ DA 4. ? 5. △BAD ≅ △ABC 5. SAS 6. BD ≅ AC 6. CPCTC What is the missing reason in the proof?
The missing reason for statement 4 in the given proof is: all sides are congruent.
What are Congruent Sides?Congruent sides are corresponding sides of corresponding figures that are congruent to each other. This means, they have the same measure of length.
In the proof given, statement 4 states that: AB ≅ BC ≅ CD ≅ DA. This implies equal lengths of sides AB, BC, CD, and DA.
Therefore, the missing reason in the proof is: all sides are congruent.
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What is n. S=180n-360
which equation could used to solve : 3 less than 5 time a number is 22?
Which of the following is a true statement a.5/6>10/12
B.6/9=1./3
C.13/15>4/5
D.1/4>1/3
The true statements among the given statement by converting them as like fractions is equal to option c. 13/15 > 4/5.
To compare fractions, it's helpful to have them with the same denominator.
Let's convert each fraction to a common denominator, and then we can compare them:
a. 5/6 > 10/12
Common denominator for 6 and 12 is 12:
5/6 = 10/12
So, a is not true.
b. 6/9 = 1/3
Both fractions are simplified and convert to have same denominator (9),
6/9 and 3/9
6/9 > 3/9
so b is not true.
c. 13/15 > 4/5
Both fractions are simplified and convert to have the same denominator (15),
4/5 = 12/15
13/15 > 12/15
and we can see that 13/15 is greater than 4/5, so c is true.
d. 1/4 > 1/3
To compare these fractions, we need a common denominator, which is 12:
1/4 = 3/12
1/3 = 4/12
Now we can see that 1/3 is greater than 1/4, so d is not true.
Therefore, the true statements is option c. 13/15 > 4/5.
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If EF =9x+17 , FG = 35 , and EG=196 , find the value of x
The required simplified value fo x is 16 in the expression of the line segment.
Given that,
If EF =9x+17 , FG = 35 , and EG=196 , find the value of x is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here
EG = 196
EF + FG = 196
9x + 17 + 35 = 196
9x + 52 = 196
9x = 196 - 52
9x = 144
x = 144/ 9
x = 16
Thus, the required simplified value fo x is 16 in the expression of the line segment.
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2.05 MC) Triangles ABC and DEF. Coordinates for A are 0, 2, for B 2, 4, and for C 1, negative 2. Given: ΔABC ≅ ΔEFD What is the length of Segment line FE rounded to the nearest tenth? (4 points) 2.8 3.4 4.1 6.1
Answer:
2.8
Step-by-step explanation:
From the congruence statement, we see that AB corresponds with EF; this means they will be congruent.
To find the measure of FE, we will find the distance between points A and B using the distance formula:
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Using our coordinates for A and B, we have
[tex]A(0,2)\text{and }B(2, 4)\\\\d=\sqrt{(4-2)^2+(2-0)^2}=\sqrt{2^2+2^2}\\\\=\sqrt{4+4}=\sqrt{8}=2.828427\approx 2.8[/tex]
A psychology class consists of 14 males and 36 females. if the professor selects names from the class list using random sampling, what is the probability that the first student selected will be a female? if a random sample of n = 3 students is selected and the first two are both females, what is the probability that the third student selected will be a male?
Final answer:
The probability of selecting a female first from a class with 14 males and 36 females is 0.72. If the first two students selected are females, the probability that the third student will be a male is approximately 0.292.
Explanation:
The subject of this question is Mathematics, specifically dealing with the concept of probability in a high school level. We are to determine two probabilities: the chance of selecting a female student first from a class, and the likelihood of selecting a male student third given that the first two selected were females.
To find the probability of selecting a female first, we need to consider the total number of students and the number of females. The class has 14 males and 36 females, so the total number of students is-
14 + 36 = 50
The probability of selecting a female first is therefore the number of females divided by the total number of students, which is-
36/50 or 0.72
For the second probability, since the first two students selected are females, we now have a reduced pool of 34 females and 14 males, with a new total of 48. The probability of the third student being a male is then 14/48, which simplifies to 0.292 approximately.
molly has 1 3/8 cups of strawberries she needs 3/8 cups of strawberries to make one batch of muffins how many batches did molly make?
How can you use a number line to add and subtract like fractions?
a museum has a wax sculpture of a historical village. The scale is 1.5 : 8. If the height of a hut in the sculpture is 5 feet how tall is the original hut to the nearest whole foot?
Answer:
Step-by-step explanation:
The directions say...Use dimensional analysis to convert the measurements.
The question is...Convert 950 US dollars to British pound sterling. Use 1 US dollar = 0.62 British pound sterling.
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evalute the numerical expression
{[(3x4)+18]+[(6x7)-27]}divided by 5
please help me with this math question i'm not good at math and i don't understand this well
9/2x+4 = 6/x+4
9x+36 = 12x+24
3x=12
x = 4
4+4 = 8
ED = 8
The temperature outside is dropping at 3°/h. Given that the temperature at noon was 0°, what would the temperature at 1 PM at 2 PM at 3 PM and 6 PM what was the temperature T hours afternoon
Which lines are parallel in the square pyramid?
Select each correct answer.
BC←→ and DE←→
CD←→ and BE←→
AD←→ and BC←→
AB←→ and AD←→
A square pyramid is a pyramid with a square base. In this problem, this base is formed by the points B, C, D and E as illustrated in the Figure above. So, the correct answers are:
First. (BC←→ and DE←→)
This is indicated in Figure 1. As you can see, the red lines are parallel, that is:
[tex]\overline{BC} \ is \ parallel \ to \ \overline{DE}[/tex]
Recall that two lines are parallel if they are always the same distant apart in which case they are equidistant, that is, they never meet.
Second. (CD←→ and BE←→)
This is indicated in Figure 2. As you can see, the green lines are parallel, that is:
[tex]\overline{CD} \ is \ parallel \ to \ \overline{BE}[/tex]
Answer: The correct options are
(A) BC←→ and DE←→
(B) CD←→ and BE←→
Step-by-step explanation: We are given to select each pair of sides that are parallel to each other in the square pyramid.
We know that
the base of a square pyramid is a square. And the opposite sides of a square are parallel to each other.
So, in the given square pyramid ABCDE, the base is a square BCDE.
Therefore, the pair of parallel sides are
BC and DE ; CD and BE.
This implies that option (A) and (B) are correct.
Thus, the correct options are (A) and (B).
A line blank has endpoints
Answer: A line never has endpoints .
Step-by-step explanation:
In geometry , a line is a straight one-dimensional undefined figure which extends infinitely in both directions.
Thus , a line contains no endpoints because it is extending infinitely in both the directions.
If a line has one end point then we call it a ray and if it has both endpoints then we call it line-segment.
Therefore , the complete sentence will be : A line never has endpoints
Marcel is designing a circular necklace that will consist of 4 sections, each with a different color of plastic. Determine how he needs to cut the plastic by finding the measures of the angles.
Answer:
measure of angle 1 is 83 and measure of angle 2 is 97
Step-by-step explanation:
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Marcel needs to cut the plastic to create four equal angles of 90 degrees each for his circular necklace since a circle has a total of 360 degrees.
Explanation:The student is being asked to calculate the measures of the angles in a circular necklace that is divided into four equal sections. Since a circle has 360 degrees, and the necklace is divided into four sections, each section must be an equal fraction of the total degrees in a circle. To find the measure of each angle, we divide the total degrees in a circle (360) by the number of sections (4).
Step-by-step calculation:
Identify the total degrees in a circle: 360 degrees. Divide this number by the number of sections: 360 ÷ 4. Calculate the result: each section has an angle of 90 degrees.
Therefore, Marcel needs to cut each angle at 90 degrees to create four sections of the circular necklace.
Perform the indicated operation. 13/16 – 3/8
7/16
5/8
1 3/16
13/16 - 3/8
convert 3/8 to 16ths
3/8 = 6/16
13/16 - 6/16 =
13/6 =7
7/16 is the answer
Answer:
The correct option is 1.
Step-by-step explanation:
The given expression is
[tex]\frac{13}{16}-\frac{3}{8}[/tex]
We need to perform the indicated operation.
Make denominator common.
[tex]\frac{13}{16}-\frac{3\times 2}{8\times 2}[/tex]
[tex]\frac{13}{16}-\frac{6}{16}[/tex]
It can be written as
[tex]\frac{13-6}{16}[/tex]
[tex]\frac{7}{16}[/tex]
The value of given expression is [tex]\frac{7}{16}[/tex].
Therefore the correct option is 1.
Evaluate. (14)−2−(50⋅2)⋅1−1
A farmer owns a total of 8 acres of land. The land is separated into 313 equally sized sections. How many acres are in each section?
solve the equation x-4-3x=-2x-3-1
Answer:
the equation is true for any value of x
Step-by-step explanation:
The equation simplifies to ...
-2x -4 = -2x -4
This is true for any value of x. There are an infinite number of solutions.
Luis needs to run no less than 120 miles in order to go with the cross country team to a summer training camp. He has thirty days to pre-train for the camp. Which inequality can be used to find how many miles Luis must run each day to meet this goal?
30 days to run at least 120 miles
120/30 = 4
let x = number of days
he needs to run at least 4 miles per day
so x≥4 ( do any of your choices look like this?)
The rest of the numbers are cut offf
225
250
270
there are 8 sides so the angles are 360/8 = 45
the answer is 45 degrees
Under which condition does a country with a small GDP have a large per capita income?
Answer:
Small population
Step-by-step explanation:
GDP is defined as the Gross domestic product of a country. It is the amount of money made in the country at a specific period of time. It measures the economic state and progress of the country.
Per capital income is the average income citizens earn in a country.
However a country with a small GDP will have a large per capital income only if the population size of the country is small. This small population size will make it possible for less competition and more money going round for the citizens.
If p(x) = x2 – 1 and ,q(x)=5(x-1) which expression is equivalent to (p – q)(x)?
Answer:
C ) ( x² - 1 ) - 5 ( x - 1 )
Step-by-step explanation:
Andy used 1/6 of a can of paint to cover 1/2 of a wall. How much of the can of paint did Andy use to paint the whole wall? Express your answer in simplest form. help ill mark brainliest
MATH PLEASE HELP!!! loolissy
The equation of line q is 5y - 4x = 10. Write the standard form of the equation of the line that fits the following description: parallel to q and passes through the point at (-15, 8)
Answer:
y = [tex](\frac{4}{5})[/tex]x + 20
Step-by-step explanation:
The equation of line q is 5y - 4x = 10
5y = 4x + 10
y = [tex]\frac{4}{5}x+2[/tex]
If a line is parallel to this line the slope of the line will be the same as the given line = [tex](\frac{4}{5})[/tex]
Let the parallel line is y = mx + c
where m = slope
and c = y-intercept
equation will be y = [tex]\frac{4}{5}x+c[/tex]
This line passes through (-15, 8)
so 8 = (-15) [tex](\frac{4}{5})[/tex] + c
8 = -12 + c
c = 12 + 8
c = 20
Now the equation of the parallel line will be y = [tex](\frac{4}{5})[/tex]x + 20
Complete the equations to prove that vertical angles always have equal measure. In terms of b and a numberin degrees, \purple c=c=start color purple, c, end color purple, equals In terms of b and a numberin degrees, \pink a=a=start color pink, a, end color pink, equals Combining these equations to get a in terms of c, \pink a=a=start color pink, a, end color pink, equals
180-b
180-b
c
Step-by-step explanation: