Answer:
1. 17/8 2. 89/24 3. 47/12 4. 9/7
Answer:
1) 29
2) 57
3) 91
4) 15
Step-by-step explanation:
1) 7/8 + 11/4
find lcm
lcm=8
multiply through by 8
8×7/8+8×11/4
Gives: 7 + 22
=29
2) 12/6+ 11/4
lcm=12
multiply through by 12
12× 12/6 + 12× 11/4
24 + 33
=57
3) 23/4 + 11/6
lcm=12
multiply through by 12
12× 23/4 + 12× 11/6
=69 +22
=91
4) 22/7 - 1
lcm=7
multiply through by 7
7 ×22/7 - 7 ×1
22-7
=15
9. In a certain school, of the students had over 80%
in math. If 465 students had 80% or less, how many
had over 80%?
Answer:
4 students
Step-by-step explanation:
Let's call the total number of students in the school "x". We know that a certain percentage of them had over 80% in math, and the rest (100% - that percentage) had 80% or less.
Let's call the percentage of students who had over 80% "p". Then, we can set up the following equation:
p% of x + (100% - p%) of x = x
We can simplify this to:
p/100 * x + (100 - p)/100 * x = x
Multiplying both sides by 100 to get rid of the denominators, we get:
px + (100 - p)x = 100x
Simplifying further:
px + 100x - px = 100x
100x = 465
x = 465/100 = 4.65 (rounded to two decimal places)
So the total number of students in the school is approximately 4.65. However, we can't have a fraction of a student, so let's round up to the nearest whole number and assume there are 5 students in the school.
Now we can use the information given to find the number of students who had over 80%:
"of the students had over 80% in math"
implies that
p% of x = number of students who had over 80%
So if we plug in the values we have:
p% of 5 = number of students who had over 80%
Simplifying:
0.01p * 5 = number of students who had over 80%
0.05p = number of students who had over 80%
We don't know the value of p, but we can solve for the number of students who had over 80% for different values of p. For example:
If p = 90, then:
0.05(90) = 4.5
So 4.5 students had over 80%. Since we can't have half a student, we can assume that 4 students had over 80%.
Alternatively, we can solve for p using the information given:
"of the students had over 80% in math"
implies that
p% of x = number of students who had over 80%
So:
p% of x = number of students who had over 80%
p% of 5 = number of students who had over 80%
0.01p * 5 = number of students who had over 80%
0.05p = number of students who had over 80%
We know that the number of students who had over 80% is some integer value between 0 and 5, inclusive. We can test different values of p within this range to see if they give us an integer solution:
If p = 90, then:
0.05(90) = 4.5
This is not an integer solution, so p = 90 is not the correct answer.
If p = 80, then:
0.05(80) = 4
This is an integer solution, so p = 80 is the correct answer. Therefore, 4 students had over 80%.
Find the solution to the systems \frac{m}{5}+\frac{n}{3}=0,\frac{m}{10}-\frac{7n}{6}=4
The two points on the line are (5, -9/5) and (-5/3, 3).
The other point on the line is (0, -12/7).
What is system of equations?The equation [tex]\frac{m}{5} +\frac{n}{3} =0[/tex] can be rewritten as:
3m + 5n = 0
When m=5:
3m + 5n = 0
3(5) + 5n = 0
n = -9/5
Simplify the above equation,
When n=3:
3m + 5n = 0
3m + 5(3) = 0
m = -5/3
the two points on the line are (5, -9/5) and (-5/3, 3)
The equation [tex]\frac{m}{10} -\frac{7n}{6} =4[/tex] can be simplified as follows:
m/10 - 7n/6 = 4
m/10 = 7n/6 + 4
m = 70n/6 + 40
m = 35n/3 + 20
When n=0:
m = 35n/3 + 20
m = 20
So, the point on the line is (20, 0).
When m=0:
35n/3 + 20 = 0
35n/3 = -20
n = -12/7
So, the other point on the line is (0, -12/7).
To know more about equation, visit:
https://brainly.com/question/29174899
#SPJ1
At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 2.5%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
Quadrilateral JKZM will be reflected over the x-axis to create its image, quadrilateral JKZ'M What will be the r-coordinate of vertex K*?
53'5 San
I can assist you in determining the r-coordinate of vertex K* following the reflection if you provide me the coordinates of vertex K in the original quadrilateral.
what is expression ?It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.
I can assist you in determining the r-coordinate of vertex K* following the reflection if you provide me the coordinates of vertex K in the original quadrilateral.
To know more about expressions visit :-
https://brainly.com/question/14083225
#SPJ1
HELP PLSZZZZSZZZZZZZZZZ need asap
Answer:
please insert question
Step-by-step explanation:
Find the perimeter and area of a square if the length of its diagonal is 16 mm. Round your answers to the nearest tenth. (Hint: Draw and label the square)
The solution is : the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².
Here, we have,
Use the basic 45-45-90 triangle with side length 1 as the building block here. If the length of one side is 1, then the perimeter is 1 + 1 + 1 + 1, or 4, and the length of the diagonal is √2.
We are told that the length of the diagonal of the given square is 16 m.
Determine the length of one side of this square, using an equation of proportions:
16 x
------ = -------
√2 1
16
Then (√2)x = 16, and x = -----------
√2
The perimeter of the given square (with diagonal 16 mm) is 4 times the side length found above, or:
16 16
4 ---------- = (2)(2) ----------- = (2)(√2)(16) = 32√2 (all measurements in mm)
√2 √2
This perimeter, rounded to the nearest tenth, is 45.3 mm.
so, area of the square is:
(16/√2)² = 512mm².
Hence, The solution is : the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².
To learn more on Area click:
brainly.com/question/20693059
#SPJ1
Please help me with this math question
The first three terms of the expression (2 · x + 1 / x)¹² are 4096 · x¹², 24576 · x¹⁰ and 67584 · x⁸, respectively.
How to determine the first three terms of the power of a binomial
In this problem we find the case of a expression of the form (a + b)ⁿ, where any term of the expression can be found by binomial theorem:
[tex](a + b)^{n} = \sum\limits_{k = 0}^{n} \frac {n!}{k! \cdot (n - k)!}\cdot a^{n - k}\cdot b^{k}[/tex]
Where:
a, b - Coefficients of the binomial.n - Power of the binomial. k - Index of the term of the expanded form of the binomial.If we know that a = 2 · x, b = 1 / x and 12, then the first three terms of the power of the binomial are, respectively:
n = 0
[tex]C_{0} = \frac{12!}{0! \cdot (12 - 0)!}\cdot (2\cdot x)^{12 - 0} \cdot (\frac {1}{x})^{0}[/tex]
C₀ = 4096 · x¹²
n = 1
[tex]C_{1} = \frac{12!}{1! \cdot (12 - 1)!}\cdot (2\cdot x)^{12 - 1} \cdot (\frac {1}{x})^{1}[/tex]
C₁ = 12 · (2048 · x¹¹) · (1 / x)
C₁ = 24576 · x¹⁰
n = 2
[tex]C_{2} = \frac{12!}{2! \cdot (12 - 2)!}\cdot (2\cdot x)^{12 - 2} \cdot (\frac {1}{x})^{2}[/tex]
C₂ = 66 · (1024 · x¹⁰) · ( 1 / x²)
C₂ = 67584 · x⁸
To learn more on binomial theorem: https://brainly.com/question/30100273
#SPJ1
A baseball player threw a baseball from the top of a stadium 48
feet above the ground, with an upward velocity of 32
feet per second. To find the time, t
, that it took for the ball to land on the ground, Greg solved the equation 0=−16t2+32t+48
. Using Greg's work, which choice is the correct time, t
, that it took for the ball to hit the ground?
0=−16t2+32t+48
0=16(−t2+2t+3)
0=−t2+2t+3
0=(−t+3)(t+1)
As per the given equation the correct time, t, that it took for the ball to hit the ground is t = 3 seconds.
What is an equation?An equation is a mathematical statement that expresses the equality between two expressions. Equations typically include variables, which are symbols that represent unknown or varying quantities, and constants, which are known values.
An equation can be written in various forms, depending on the type of equation and the context in which it is used. Some common forms of equations include linear equations, quadratic equations, and polynomial equations.
For example, the equation x + 5 = 10 is a linear equation that has one variable, x. It can be solved by subtracting 5 from both sides of the equation to get x = 5.
A quadratic equation, such as x² + 2x + 1 = 0, has a variable raised to the second power. It can be solved using the quadratic formula or by factoring.
According to the given informationTo solve the equation 0=−16t²+32t+48, Greg factored out a common factor of -16 from all three terms to get:
0 = -16(t² - 2t - 3)
Then, he factored the quadratic expression inside the parentheses as:
0 = -16(t - 3)(t + 1)
This gives us two solutions for t: t = 3 and t = -1.
However, we can discard the solution t = -1, since time cannot be negative in this context. Therefore, the correct time, t, that it took for the ball to hit the ground is t = 3 seconds.
To know more about the equations visit:
brainly.com/question/12788590
#SPJ1
Find a.the mean b. the median mass of the fish
Answer: Mean = 1.15 Median = 1
Step-by-step explanation: add all numbers up and then divide it by 4 which will give you the mean.
Median: 0.9 and 1.1 are the 2 middle numbers in which you will add together then divide by 2 to get the exact middle value which is 1 exactly.
Write the coordinates for
each given point on the
coordinate plane below.
1. Point A
2. Point B
3. Point C
4. Point D
Answer:
Point A (-3,3)
Point B about (3,-2.75)
Point C (-4,-4)
Point D (1,0)
Step-by-step explanation:
Numbers in the octal number system are numbered from 0 to 7. Based on the numbering pattern in the decimal number system, list the next 20 octal numbers
The next 20 octal numbers after 7 are: 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33
How to determine the next 20 octal numbersIn the decimal system, we count from 0 to 9 before moving to the next place value. In the octal system, we count from 0 to 7 before moving to the next place value. Therefore, the next 20 octal numbers after 7 are:
10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33
To understand how this pattern works, consider the decimal number 32. To convert it to octal, we can repeatedly divide it by 8 and record the remainders:
32 ÷ 8 = 4 with remainder 0
4 ÷ 8 = 0 with remainder 4
So the octal representation of 32 is 40. Similarly, we can convert any decimal number to octal by repeatedly dividing by 8 and recording the remainders.
Learn more about number system at https://brainly.com/question/17200227
#SPJ1
The net income of the Apex Company was $110 million in 1995 and has been increasing by $30 million per year since. Over the same period, the net income of its
chief competitor, the Best Corporation, has been growing by $20 million per year, starting with $170 million in 1995. Which company earned more in 2004?
Apex Company
Best Corporation
In what year did/will Apex surpass Best?
Answer:
Step-by-step explanation:
In 2004, the net income of the Apex Company would be $110 million + ($30 million x 9 years) = $380 million.
The net income of the Best Corporation in 2004 would be $170 million + ($20 million x 9 years) = $350 million.
Therefore, Apex Company earned more in 2004.
To find the year when Apex surpassed Best, we need to set their net incomes equal and solve for time:
110 + 30t = 170 + 20t
10t = 60
t = 6
Therefore, Apex surpassed Best in the year 1995 + 6 = 2001.
What is the length of side c? (Hint: There are 2 angles and 2 sides)
The length of side c is approximately 4.62 units.
How to solveCalculating the value of side c can be done by applying the Law of Sines on two angles and two sides.
Initially, determining angle C is necessary:
The corresponding formula for Angle C: 180° - (Angle A + Angle B) evaluates to 90° after substituting in reference values; 60°, and 30° respectively.
Implementing the Law of Sines culminates in this expression:
a/sin(A) = b/sin(B) = c/sin(C)
Replace with known angles and evaluate as follows:
Since the measures are known;
c/sin(C) = a/sin(A).
Subsequently,
by simple algebra c= a * sin(C) / sin(A) leads to desired outcome.
Putting relevant points into the equation above gives:
c = 4 * sin(90°) / sin(60°)
By using sine values from a calculator:
the preceding expression becomes,
c = 4 * 1 / (sqrt(3)/2)
After solving for c:
c = 8 / sqrt(3)
Using square root's rationalization: multiply numerator, and denominator by √3 resulting in
c = (8 * sqrt(3)) / 3
The length of side c is approximately 4.62 units.
Read more about triangles here:
https://brainly.com/question/1058720
#SPJ1
Let's assume we have a triangle with angles A and B and sides a and b, where angle A is opposite to side a, and angle B is opposite to side b. Given angle A = 60°, angle B = 30°, side a = 4 units, and side b = 2 units, find the length of side c.
If the length of BE is 3x-11 and the length of CD is 9x - 43, what is the length of CD?
The value of line CD is 20
How to determine the valueFrom the diagram shown, we have that;
Line BE = 3x - 11
Line CD = 9x - 43
Note that the length of line BE is half the length of line CD
this is represented as;
2BE = CD
Now, substitute the values
2(3x - 11) = 9x - 43
expand the bracket
6x - 22 = 9x - 43
collect the lie terms
6x - 9x = -43 + 22
-3x = -21
Make 'x' the subject
x = 7
Then, CD = 9(7) - 43 = 20
Learn more about line segments at: https://brainly.com/question/17374569
#SPJ1
joseph is baking brownies. the recipe calls for 3 1/2 pounds of flour for every 3/4 cup of sugar how many pounds of flour should joseph use for 1 cup of sugar?
If the recipe requires 3(1/2) pounds of flour for every (3/4) cups of sugar, then for 1 cup of sugar , Joseph should use 4.67 pounds of flour.
A "Proportion" is defined as a statement that two fractions are equal. It expresses the relationship between two quantities that are in the same ratio.
To solve the problem, we set up a proportion to relate the amount of flour to the amount of sugar:
We know that, recipe requires 3(1/2) pounds of flour for every (3/4) cups of sugar,
Which means,
⇒ (3.5 pounds of flour)/(0.75 cups of sugar) = (x pounds of flour)/(1 cup of sugar),
where x is = amount of flour needed for 1 cup of sugar.
We "cross-multiply" and simplify;
⇒ 3.5 × 1 = 0.75 × "x" pounds of flour,
⇒ 3.5/0.75 = x,
⇒ x ≈ 4.67 pounds of flour,
Therefore, Joseph should use 4.67 pounds of flour for 1 cup of sugar.
Learn more about Proportion here
https://brainly.com/question/10644018
#SPJ1
- Higher Order Thinking A sporting goods store manager was selling
a kayak set for a certain price. The manager offered the markdowns
shown on the right, making the one-day sale price of the kayak set $328.
Find the original selling price of the kayak set.
KANN &
SET
10%
OFF
TRRAY
EXTRA
30%
OFF
The original selling price of the kayak set, given the discounts, would be $ 520. 63
How to find the original selling price ?The kayak is being sold such that a discount was offered of 10 % and then an additional discount was offered for 30 %.
The first step to the original price is:
= 328 / ( 1 - 30 %)
= 328 / 0. 70
= $ 468. 57
Then, the original price, would then account for the original discount of 10 % to become:
= 468. 57 / ( 1 - 10 %)
= 468. 57 / 0. 90
= $ 520. 63
Find out more on original price at https://brainly.com/question/28914479
#SPJ1
All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having the letter C written on it?
The odds against the paper having the letter C written on it is 10 : 11
What are the odds against the paper having the letter C written on it?From the question, we have the following parameters that can be used in our computation:
MATHEMATICS
In the above word, we have
Letter C = 1
letters = 11
So, the probability of C is
Probability = 1/11
When converted to odds we have
Odds = Letter - Letter C : Letters
Substitute the known values in the above equation, so, we have the following representation
Odds = 11 - 1 : 11
Evaluate
Odds = 10 : 11
Hence, the odds is 10 : 11
Read more about probability
https://brainly.com/question/24756209
#SPJ1
Shen bought a desk on sale for $218.40. This price was 72% less than the original price. What was the original price?
Answer:
780
Step-by-step explanation:
In this example we will call Original Price = y
72%=0.72
218.40=0.72*y
1-0.72=0.28
218.4÷0.28=780
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one
baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has
no effect, so the probability of a girl is 0.5. Assume that the groups consist of 45 couples. Complete parts (a) through (c)
below.
a) The value of the mean is μ = 22.5
The value of the standard deviation is σ = 3.5
b) The Value of 15 girls or fewer is significantly low.
The value of 30 girls or more is significantly high.
c) The result 36 is significantly high because 36 is greater than 30 girls. A result of 36 girls is not necessarily definitive proof of the method's effectiveness.
What is the standard deviation?The standard deviation is a measure of the amount of variability or dispersion in a set of data values. It is a statistical measure that tells you how much, on average, the values in a dataset deviate from the mean or average value.
According to the given informationa) Since the probability of having a girl for each couple is 0.5, the number of girls each couple will have can be modeled as a binomial distribution with parameters n=1 and p=0.5.
Let X be the random variable denoting the number of girls in 45 couples. Then, X follows a binomial distribution with parameters n=45 and p=0.5.
The mean of a binomial distribution is given by μ = np, so in this case, the mean number of girls in a group of 45 couples is:
μ = np = 45 x 0.5 = 22.5
Therefore, we expect to see around 22-23 girls in a group of 45 couples.
The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, the standard deviation of the number of girls in a group of 45 couples is:
σ = √(np(1-p)) = √(45 x 0.5 x 0.5) = 3.535
Therefore, we can expect the number of girls in a group of 45 couples to have a standard deviation of around 3.5.
b) In this case, we can assume that the number of girls in a group of 45 couples follows a normal distribution due to the Central Limit Theorem.
Using the standard deviation we found in the previous answer (σ = 3.535), we can calculate the values that separate the results that are significantly high and significantly low.
Significantly high:
Mean + 2σ = 22.5 + 2(3.535) = 29.57
Significantly low:
Mean - 2σ = 22.5 - 2(3.535) = 15.43
c) To determine if the result of 36 girls is significantly high, we need to compare it to the values we calculated in the previous answer.
Mean + 2σ = 22.5 + 2(3.535) = 29.57
Since 36 is greater than 29.57, we can conclude that the result of 36 girls is significantly high.
This suggests that the method of gender selection may be having an effect on the probability of having a girl. However, we cannot conclusively say this without conducting further analysis or testing.
It is also important to note that the result of 36 girls is not necessarily definitive proof of the method's effectiveness.
To know more about the standard deviation visit:
brainly.com/question/13905583
#SPJ1
If you know 4 parts (angles and sides) of one triangle are congruent to the
corresponding 4 parts of another triangle, are the triangles congruent? Why?
Answer: Yes, the triangles are congruent.
Step-by-step explanation:
According to the Side-Angle-Side (SAS) congruence theorem, if two triangles have two pairs of corresponding sides that are congruent and the included angle between those sides is also congruent, then the triangles are congruent.
In this case, we know that four parts (angles and sides) of one triangle are congruent to the corresponding four parts of another triangle. This means that two pairs of corresponding sides are congruent (since corresponding sides are equal) and the included angles between those sides are also congruent (since corresponding angles are equal). Therefore, the triangles satisfy the conditions of the SAS congruence theorem and are congruent.
It's important to note that this applies only to two triangles with exactly the same four congruent parts. If there is even one part that is not congruent between the two triangles, they cannot be proven to be congruent just by these means alone.
Answer:
If you know that 4 parts (angles and sides) of one triangle are congruent to the corresponding 4 parts of another triangle, then the triangles are congruent by the Side-Angle-Side (SAS) Congruence Postulate. This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
The SAS postulate is one of five ways to prove that two triangles are congruent. The other four ways are Angle-Side-Angle (ASA), Side-Side-Side (SSS), Hypotenuse-Leg (HL), and Reflexive Property of Congruence.
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answer:
B
Step-by-step explanation:
163 money t for time 2 for 2hours
If you multiply or divide both sides of an inequality by a negative number you must_______ the inequality sign
Answer:
reverse or flip
Which of the following is not a benefit of just-in-time processing?
O Control of significant inventory balances
O Production cost savings
O Reduction of rework costs
O Enhanced product quality
Step-by-step explanation:
The answer is:
- Control of significant inventory balances
This is because just-in-time processing is a system that emphasizes on producing goods or services at the exact time they are needed, without accumulating inventory. Therefore, it does not prioritize the control of significant inventory balances. The other options are benefits of just-in-time processing.
Compare the three decimals in each column. Circle the decimal that is greatest, and underline the decimal that is least. (4) 13.655 13.565 13.65 .
The side measures of a rectangular prism are tripled. What is the relationship between the surface area of the original prism and the surface area of the new prism?
Answer:
The new prism has 9 times the surface area of the original prism
Step-by-step explanation:
There are three ways in which you can answer this question.
The hard way:
The surface area of a rectangular prism is given by
A = 2(LW+ LH+ WH)
where L= length, W= width and H = height)
If we were to triple the sides we would get the new side measures as
3L, 3W, 3H
New surface area becomes:
A' = 2 (3L · 3W + 3L · 3H · 3W· 3H)
A' = 2(9LW + 9 LH + 9 WH)
Factoring out 9 from the brackets we get
A' = 2 · 9 (LW+ LH+ WH)
A'/A = 2 · 9 (LW+ LH+ WH) /2(LW+ LH+ WH)
The common term 2(LW+ LH+ WH) cancels out from numerator and denominator leaving 9 as the answer
A smarter and easy way of doing this
A cube is nothing but a rectangular prism with all sides equal. Let a be the length of a side of the cube
A cube has 6 sides. The surface area of each side = a x a = a²
So total surface area A = 6a²
If each side is tripled, each side becomes 3a.
New surface area A' = 6 (3a)² = 6 (9a²)
A'/A = 6 (9a²)/6(a²) = 9
An even easier way
Again we take a cube. But instead of using a variable, let's assign the side of the cube a length of 1 unit
Surface area A = 6 · 1² = 6
After tripling each side becomes 3 units long
New surface area A' = 6 · 3² = 6.9 = 54
A'/A = 54/6 = 9
Choose whichever method you feel comfortable with
$500 is deposited in an account with 7%
interest rate, compounded continuously.
What is the balance after 10 years?
7
F = $[?]
The required balance after 10 years with continuous compounding at a 7% interest rate would be approximately $1007.
To calculate the balance after 10 years with a continuous compounding interest rate of 7%, we can use the formula for continuous compound interest:
[tex]F = P * e^{rt}[/tex]
Where:
F is the future balance or the final amount
P is the principal amount (initial deposit)
e is the base of the natural logarithm (approximately 2.71828)
r is the interest rate (expressed as a decimal)
t is the time in years
In this case, the initial deposit (principal) is $500, the interest rate is 7% (0.07 as a decimal), and the time is 10 years. Plugging these values into the formula, we get:
[tex]F = 500 * e^{0.07 * 10}[/tex]
Using a calculator, we can evaluate e^(0.07 * 10) ≈ 1.96728. Multiplying this by 500 gives us:
[tex]F=500 * 1.96728[/tex]
F = $1007
Therefore, the balance after 10 years with continuous compounding at a 7% interest rate would be approximately $1007.
Learn more about continuous compounding here:
https://brainly.com/question/30460031
#SPJ1
Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
OA. None of these
B. What may be false
C. What may be true
D. What must be true
R
SUBMIT
Answer: D
Step-by-step explanation:
When using deduction and starting from a given set of rules and conditions, you can determine what must be true. Therefore, the correct answer is:
D. What must be true
At the beach, Trevor and his sister both built sandcastles and then measured their heights. Trevor's sandcastle was 1/2 of a foot tall and his sister's was 1/5 of a foot tall. How much taller was Trevor's sandcastle than his sister's?
The height of Trevor's sandcastle is 3/10 foot taller than his sister's.
Given that, Trevor's sandcastle was 1/2 of a foot tall and his sister's was 1/5 of a foot tall.
Difference in the height of sandcastles = 1/2 - 1/5
= 5/10 - 2/10
= (5-2)/10
= 3/10
So, the difference in heights = 3/10 foot
Therefore, the height of Trevor's sandcastle is 3/10 foot taller than his sister's.
To learn more about the subtraction of fractions visit:
https://brainly.com/question/5220474.
#SPJ1
Determine the function is positive, negative, increasing, or decreasing. Then describe the end behavior of the function.
The graph is positive and increases as the value of x increases.
What is the behavior of graph of y = √(4x)?
The behavior of the graph of y = √(4x) is determined by substituting some value of x into the function and check the corresponding value of y.
When x = 0, the value of y is calculated as;
y = √(4(0))
y = 0
When x = 1, the value of y is calculated as;
y = √(4(1))
y = 2
When x = 4, the value of y is calculated as;
y = √(4(4))
y = 4
When x = 9, the value of y is calculated as;
y = √(4(9))
y = 6
From the data above, the value of y increases as x increases, although not at equal increment.
Learn more about behavior of graphs here: https://brainly.com/question/29366585
#SPJ1
1. Each person in a random sample of 1.026 adults in the United States was asked the following question "Based on what you know about the Social Security System today, what would you like Congress and the President to do during this next year? The response choice and the percentages selecting them are shown below
Completely overhaul the system 19%
Make some major changes 39%
Make some minor adjustments 30%
Leave the system the way it is now
No opinion 1%
Find a 95% confidence interval for the proportion of all United States adults who would respond "Make some major changes to the question
a. Identify the variables needed to solve the problem.
b. Can a normal distribution be used to approximate this data Justify your evidence. c. Find the standard deviation
d. Calculate the point estimate and margin of error
e. calculate the confidence interval
Answer:
Step-by-step explanation:
a. Variables needed to solve the problem:
Sample size: n = 1,026
Proportion of the sample that responded "Make some major changes": p = 0.39
Confidence level: 95%
b. To determine if a normal distribution can be used to approximate the data, we need to check if the sample size is large enough to meet the requirements for a normal approximation. The sample size should be at least 10 times larger than the number of successes (np) and 10 times larger than the number of failures (n(1-p)). In this case, we have:
np = 1026 x 0.39 = 399.14
n(1-p) = 1026 x 0.61 = 626.86
Both np and n(1-p) are greater than 10, so we can assume that a normal distribution can be used to approximate the data.
c. The standard deviation of the proportion can be calculated using the following formula:
standard deviation = sqrt(p(1-p) / n)
standard deviation = sqrt(0.39 x 0.61 / 1026) = 0.024
d. The point estimate of the proportion of all United States adults who would respond "Make some major changes" is simply the sample proportion, which is p = 0.39. The margin of error can be calculated using the following formula:
margin of error = z* * standard deviation
where z* is the z-score associated with the 95% confidence level. Using a standard normal distribution table or a calculator, we find that the z-score for a 95% confidence level is approximately 1.96. Therefore:
margin of error = 1.96 * 0.024 = 0.047
e. The confidence interval can be calculated using the following formula:
confidence interval = point estimate ± margin of error
confidence interval = 0.39 ± 0.047
confidence interval = (0.343, 0.437)
Therefore, we are 95% confident that the proportion of all United States adults who would respond "Make some major changes" is between 0.343 and 0.437.