The simplest direct ratio of boys to girls in the room is 3:4, which means for every 3 boys, there are 4 girls. This is determined by finding the greatest common divisor of the two quantities. Other possible ratios such as 6:8, 9:12, 12:16, and 15:20 are multiples of this base ratio.
Explanation:The question is asking for us to form all the possible ratios of boys to girls in the given situation. We are given that there are 42 boys and 56 girls. The simplest ratio of boys to girls can be determined by finding the greatest common divisor (GCD) of both numbers and then dividing both numbers by it. The GCD of 42 and 56 is 14, so if we divide both numbers by the GCD, we get the ratio of 3:4. This implies that for every 3 boys, there are 4 girls. However, other possible ratios could use multiple of these numbers. Therefore, the possible ratios of boys to girls in this scenario also include 6:8, 9:12, 12:16, 15:20, and so on.
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Someone help me please
Answer:
P = 48A = 144Step-by-step explanation:
The formula of regular polygon with n sides of length b and apothem a:
[tex]A=\dfrac{nba}{2}[/tex]
We have:
n = 6
b = 8
a = 6
Substitute:
[tex]A=\dfrac{(6)(8)(6)}{2}=144[/tex]
The perimeter:
[tex]P=6b\to P=(6)(8)=48[/tex]
Which of the following is the correct radical form of this expression
ANSWER
The correct answer is A.
EXPLANATION
The given expression is
[tex]( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) ^{ \frac{5}{6} } [/tex]
Recall that:
[tex] {a}^{ \frac{m}{n} } = (\sqrt[n]{a} ) ^{m} [/tex]
For the given expression,
[tex]m = 5[/tex]
[tex]n = 6[/tex]
and
[tex]a = \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} [/tex]
We substitute all these values to obtain the radical form:
[tex]( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) ^{ \frac{5}{6} } = ( \sqrt[6]{( \frac{ {p}^{12} {q}^{ \frac{3}{2} } }{64} ) })^{5} [/tex]
The correct choice is A.
south korea’s leadership arrested and killed thousands of
Answer:
4. South Korea’s leadership arrested and killed thousands of
✔ alleged North Korean agents.
Step-by-step explanation:
got it right on edge 2021
Answer:
alleged North Korean agents.
Step-by-step explanation:
Edge 2022
plz help me
WILL GIVE BRAINLIEST
Answer:
2 and -1
Step-by-step explanation:
y = x^2 -x-2
To find the x intercept, set y = 0
0 = x^2 -x-2
Factor
What 2 numbers multiply to -2 and add to -1
-2*1 = -2
-2 +1 = -1
0 = (x-2) (x+1)
Using the zero product product property
x-2 = 0 x+1 =0
x=2 x=-1
Do you think that a 270° clockwise rotation is the same as a 90° counterclockwise rotation? Explain why or why not.
Answer: This would equal the same distance
Explanation: Think of a clock if it rotates 90 degrees counter clockwise it would stop at the number 9. If it rotates 90 clockwise it would stop at 3, then rotate that hand clockwise by 90 degrees one more time it will stop at 6, then 9 at 270 degrees.
Answer:
sorry if im late but this is the answer:
Step-by-step explanation:
Yes, I think they are the same. One revolution is 360 degrees. A 180-degree clockwise rotation is the same as a 180-degree counterclockwise rotation. The sum of the measures is 360. So, moving in a clockwise direction for 270 degrees would end at the same place as moving 90 degrees in a counterclockwise direction.
Stretch your thinking.Rewrite this using the word fewer.Carey reads 10 more pages than lucey
Answer:
Lucy reads 10 fewer pages that Carey
Step-by-step explanation:
The first sentence reads as Carey having more, so Lucy has fewer,
Rewriting it using fewer means that Lucy will be the main subject of the sentence, so Lucy reads 10 fewer pages that Carey is the sentence you want
Jason is cutting a roll of sausage into pieces that are 1/2 inches thifk if the roll is 6 inchew long how many pieces of sausage can he. Cut use tiles to hlep to solve
Final answer:
Jason can cut 12 pieces of sausage from the 6-inch roll, since dividing the roll's length by the thickness of each piece (6 inches ÷ 1/2 inch) yields 12 pieces.
Explanation:
To determine how many pieces of sausage Jason can cut from a roll that is 6 inches long, where each piece is 1/2 inches thick, one would perform a simple division.
The length of the sausage roll (6 inches) is divided by the thickness of each piece (1/2 inch) to find out how many pieces can be cut.
This is a basic fraction division problem that we solve by multiplying the length of the roll by the reciprocal of the thickness of the pieces to be cut.
Calculation
To calculate:
6 inches × 2/1 (which is the reciprocal of 1/2) equals 12.
So, Jason can cut 12 half-inch-thick pieces from the 6-inch roll.
16...06...68...88...?...98
What is the missing number??
Answer:
L8
Step-by-step explanation:
We turn that upside-down
86 '? '88 '89 '90 '9I
Then obviously we can tell that ? is to be replaced by 87
86 '87 '88 '89 '90 '9I
Then we turn it back right-side up again, and we have:
I6, 06, 68, 88, L8, 98
Answer: L8
Hope this helps ;)
The missing number in the sequence 16...06...68...88...?...98 is 78
How to determine the missing number in the sequenceFrom the question, we have the following parameters that can be used in our computation:
16...06...68...88...?...98
When the number are flipped upside down, we have
91....90....89.....88......?.......86
In the above sequence, we can see that -2 is added to the previous term to get the new term
This means that the complete sequence is
91....90....89.....88......87.......86
When flipped, we have
16...06...68...88...78...98
Hence, the missing number is 78
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Evaluate lim x → 0+ x ln(x3). solution the given limit is indeterminate because, as x → 0+, the first factor (x) approaches 0 correct: your answer is correct. while the second factor ln(x3) approaches −∞. writing x = 1/(1/x), we have 1/x → ∞ as x → 0+, so l'hospital's rule gives lim x → 0+ x ln(x3) = lim x → 0+ ln(x3) 1/x = lim x → 0+ 3/x −1/x2 = lim x → 0+ incorrect: your answer is incorrect. = .
[tex]\displaystyle\lim_{x\to0^+}x\ln x^3=\lim_{x\to\infty}\frac{\ln\frac1{x^3}}x=-3\lim_{x\to\infty}\frac{\ln x}x=\frac\infty\infty[/tex]
L'Hopital's rule tells us the limit is equal to
[tex]-3\displaystyle\lim_{x\to\infty}\frac{\frac1x}1=0[/tex]
Evaluate the log without a calculator ( Show your work )
[tex]log_{2} \sqrt[5]{16}[/tex]
Answer: x = 1/5
//Hope it helps.
Answer:
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}[/tex]
Step-by-step explanation:
The given logarithmic expression is:
[tex]\log_2(\sqrt[5]{16} )[/tex]
We rewrite the radical as an exponent to obtain;
[tex]\log_2(\sqrt[5]{16} )=\log_2(16^{\frac{1}{5}} )[/tex]
Recall and use the power rule; [tex]\log_a(M^n)=n\log_a(M)[/tex]
[tex]\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(16 )[/tex]
We write 16 as an index number to base 2.
[tex]\log_2(\sqrt[5]{16} )=\frac{1}{5}\log_2(2^4)[/tex]
We apply the power rule again;
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}\log_2(2)[/tex]
We simplify to get;
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}(1)[/tex]
[tex]\log_2(\sqrt[5]{16} )=\frac{4}{5}[/tex]
What is the probability of getting a head with the flip of a coin?
A) 0/2
B)1/4
C)1/2
D)2/2
Answer:
Answer is C (1/2)
Step-by-step explanation:
WHICH OF THE FOLLOWING DESCRIBES THE FUNCTION -X^4+1?
Answer:
B
Step-by-step explanation:
The function -x^4 + 1 is a polynomial graph. As such it has specific characteristics or behavior you can expect to see:
It's leading coefficient is -1. This means the graph changes direction. Both ends of this graph face down into negative infinity.Its degree is 4 meaning it is an even graph. This means both ends end the same way and NOT opposite directions.In conclusion, this graphs has ends which end the same direction and both face down.
Simplify −2√45+3√3+2√3 Question 4 options: A.−6√5+6√3 B.−2√5+6√3 C.−6√5+5√3 D.−18√5+5√3
Answer:
C
Step-by-step explanation:
You're probably stuck by this problem. Let's rewrite the problem.
-2√45 + 3√3 + 2√3The first part of simplifying the expression is to simply the radicals. Since 45 has a factor which is a square, let's simplify.
-2√45 = -2√5 × 9 = (-2 × 3)√5 = -6√5Let's just continue simplifying and dissect the 3√3 + 2√3.3√3 + 2√3 = 5√3...The answer is...5√3 - 6√5 or -6√5 + 5√3, Csolve for x
2x+3+5x=24
what is x?
Answer:
x=3
Step-by-step explanation:
[tex]2x+3+5x=24\\7x+3=24\\7x=21\\x=3[/tex]
There are 10 cards. Each card has one number between 1 and 10, so that every number from 1 to 10 appears once. In which distributions does the variable X have a binomial distribution? Select each correct answer. When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen. When a card is chosen at random without replacement three times, X is the number of times an even number is chosen. When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen. When a card is chosen at random with replacement multiple times, X is the number of times a card is chosen until a 5 is chosen.
Answer:
When a card is chosen at random with replacement five times, X is the number of times a prime number is chosen; When a card is chosen at random with replacement six times, X is the number of times a 3 is chosen.
Step-by-step explanation:
In a binomial distribution, there are only two outcomes, or outcomes that can be reduced to 2. In the first choice, we either draw a prime number or do not draw a prime number. In the third choice, we either draw a 3 or do not draw a 3.
There must be a fixed number of trials. In the first choice, we have 5 trials; in the third option, we have 6 trials.
The trials must be independent of each other. Since the cards in the first and third options are drawn with replacement, the outcome of one trial does not influence the probability of the next trial.
The probability must be the same for every trial. This is true of the first and third options.
Answer:
Prime And 3 is choosen
Step-by-step explanation:
Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)
Answer:
(sin^2 w + 1) / cos w.
Step-by-step explanation:
Note: sec w = 1 / cos w and csc w = 1/ sin w.
So we have:
(sec w(1 + csc^2 w)) / (csc^2 w)
= 1/cos w ( 1 + 1/ sin^2 w) / (1 / sin^2 w)
= ( 1/ cos w + 1 / sin^2 w cos w) * sin^2 w
= sin^2 w/ cos w + sin^2 w / (sin^2 w cos w)
= sin^2 w / cos w + 1 / cos w
= (sin^2 w + 1) / cos w.
I will give BRAINLY im bad at math
Answer:
[tex]an = 2.5 + (n - 1)(-5)[/tex]
Step-by-step explanation:
we know that
The explicit formula for the nth term of an arithmetic sequence is given by the formula
[tex]an = a1 + (n - 1)r[/tex]
where
a1 is the first term
n is the term number
r is the common difference
In this problem we have
[tex]a1=2.5, r=-5[/tex]
substitute
[tex]an = 2.5 + (n - 1)(-5)[/tex]
Solve for x.
x2−9=16
Enter the solutions for the equation in the boxes.
x = ___ or x = ___
The answer will be
x=5 or x=-5
hope this help
Jody practiced a piano piece for 500 seconds bill practiced a piano piece for 8 minutes who practiced longer explain
Answer:
Jody
Step-by-step explanation:
You can either convert 500 seconds to minutes or 8 minutes to seconds to compare. I'll do both.
There is 60 seconds in a minute. To find the total minutes of 500 seconds, divide 500 by 60 → 8.3, which means that Jody practiced for 8.3 minutes.
To find the total seconds of 8 minutes, multiply 60 seconds per minute by 8 minutes → 60 * 8 = 480 seconds which means that Bill practiced for 480 seconds.
Now you can compare. Jody practiced for 500 seconds, or 8.3 minutes. Bill practiced for 480 seconds, or 8 minutes. Jody practiced longer.
Please answer this question, only if you know the answer! Will give brainliest!
Answer:
Because point P is not the midpoint of OQ.
Step-by-step explanation:
The circle center is found at the intersection of the perpendicular bisectors of any two chords. Segment PC is perpendicular to OQ, but does not bisect it. Hence, point C cannot be the circle center.
Find all solutions of the given equation. (enter your answers as a comma-separated list. let k be any integer. round terms to two decimal places where appropriate.) cos θ + 1 = 0
Answer:
θ = 6.28k +3.14
Step-by-step explanation:
cos(θ) is -1 for θ = π and multiples of 2π added to that.
___
The answer above rounds π and 2π as requested by the problem statement. Those values are only valid for small values of k. (I suppose it might be reasonable to argue that no rounding is appropriate.)
Please help me quickly!
Select all of the following true statements if R = real numbers, Z = rational numbers, and W = {0, 1, 2, ...}.
WZ
RZ
-1 W
R
{0, 1, 2, ...} W
0 Z
Answer:
We can start solving this problem by first identifying what the elements of the sets really are.
R is composed of real numbers. This means that all numbers, whether rational or not, are included in this set.
Z is composed of integers. Integers include all negative and positive numbers as well as zero (it is essentially a set of whole numbers as well as their negated values).
W on the other hand has 0,1,2, and onward as its elements. These numbers are known as whole numbers.
W ⊂ Z: TRUE. As mentioned earlier, Z includes all whole numbers thus W is a subset of it.
R ⊂ W: FALSE. Not all real numbers are whole numbers. Whole numbers must be rational and expressed without fractions. Some real numbers do not meet this criteria.
0 ∈ Z: TRUE. Zero is indeed an integer thus it is an element of Z.
∅ ⊂ R: TRUE. A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition (since NONE of its elements are not an element of R).
{0,1,2,...} ⊆ W: TRUE. The set on the left is exactly what is defined on the problem statement for W. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be equal to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).
-2 ∈ W: FALSE. W is just composed of whole numbers and not of its negated counterparts.
Step-by-step explanation:
Certain elements and sets are examined for their relationships with the sets of real numbers, integers, and whole numbers; identifying which elements belong to which sets and if one set is a subset of another.
When comparing different sets of numbers, we analyze whether one set is a subset of another and whether certain elements belong to specific sets. The given question involves the sets R (real numbers), Z (integers), and W = {0, 1, 2, ...}, also known as the set of whole numbers or non-negative integers.
→ W ⊂ Z: This is true because all elements of W are non-negative integers, which are a subset of Z, the set of all integers including negative, zero and positive whole numbers.
→ R ⊂ W: This is false because the set of real numbers includes irrational numbers as well as negative numbers, which are not included in W.
→ 0 ∈ Z: This is true because zero is an integer and, therefore, is an element of Z.
→ ∅ ⊂ R: This is true because the empty set is a subset of all sets, including the set of real numbers.
→ {0, 1, 2, ...} ⊆ W: This is true because this set is exactly W itself, and a set is always a subset of itself.
→ -2 ∈ W: This is false because W contains only non-negative integers, and -2 is a negative number.
Walt has a box of 80 postage stamps. The box contains 16 stamps featuring the Bald Eagle and 40 stamps featuring the Stars and Stripes. If Walt randomly chooses a stamp to paste on an envelope, what is the probability that the stamp features the Bald Eagle or the Stars and Stripes?
Answer:
C) 0.70
Explanation:
:))
A recipe calls for 4 cups of strawberries for every 6 cups of whipped topping. If gary uses 54 cups of whipped topping how many cups of strawberries does he need?
Answer:
36 cups
Step-by-step explanation:
If you notice, 6 times 9 is 54. So, 4 times 9 is 36. You need 36 cups of strawberries!
For 1 and 2, state whether the numbers are parameters or statistics, and use the appropriate notation to describe each number. 1. a random sample of female college students has a mean height of 64.5 inches, which is greater than the 63-inch mean height of all adult american women.
Answer:
x-bar 64.5 is a statistic because it describes a sample.
Mu 63 is a parameter because it describes a population.
The symbol for mu is a Greek m
Step-by-step explanation:
Final answer:
A random sample mean, like the 64.5 inches height for female college students, is a statistic denoted as \( \bar{x} \), while the mean height of all adult American women is a parameter denoted as \( \mu \). Determining whether a number is a parameter or statistic informs how it is used in hypothesis testing and confidence interval construction.
Explanation:
When identifying whether the numbers are parameters or statistics, it's important to distinguish between data collected from a population or a sample. In the scenarios mentioned, such as when a random sample of female college students has a mean height of 64.5 inches, we are dealing with a statistic. This is because it is a measure obtained from a sample. The appropriate notation for this sample mean would be \( \bar{x} \). This contrasts with the information such as the mean height of all adult American women, which is a parameter because it relates to the entire population. The notation for a population mean is \( \mu \). Considering other examples provided, when we calculate a p-value or when we undertake a study and calculate the difference in mean heights between groups, we are dealing with statistics.
In practice, the difference between statistics and parameters is essential for hypothesis testing, constructing confidence intervals, and making inferences about the population based on sample data. For example, if the p-value is close to zero in a test related to the mean height of high school basketball players, it suggests that there is strong evidence against the null hypothesis \( H_0 \), which posits no effect or no difference. The alternative hypothesis \( H_1 \) would be that there is a significant difference.
Selena walks from home to school each morning and back each afternoon altogether she walks 2/3 mile each day how far does Selena live from school
Answer:
Selena lives 1/3 of a mile away from her school.
Step-by-step explanation: If the walk to her school AND back is 2/3 of a mile, then all you have to do is split 2/3 in half. Which is 1/3 of a mile.
Answer:
1/3 miles. 2/3 divided by 2 = 1/3.
Step-by-step explanation:
HELP! ASAP
Find the area of the shaded region.
Step 1) Find the area of the bigger rectangle.
Step 2) Find the area of the smaller rectangle.
Step 3) Subtract the 2 polynomials.
Answer:
Tthe area of the shaded region is [tex](x^{2}-3x+36)\ unit^{2}[/tex]
Step-by-step explanation:
we know that
To find the area of the shaded region (blue region), subtract the area of the smaller rectangle from the area of the larger square
so
Find the area of the larger square
[tex]A=(x+1)^{2}=(x^{2}+2x+1)\ unit^{2}[/tex]
Find the area of the smaller rectangle
[tex]A=5(x-7)=(5x-35)\ unit^{2}[/tex]
Subtract the polynomials
[tex](x^{2}+2x+1)-(5x-35)=(x^{2}-3x+36)\ unit^{2}[/tex]
Thirty Mercedes and Audi participated in a 30 mile race. The average driving speed of the Mercedes and Audi were recorded. A random sample (Sample 1) of the Mercedes's average driving speed (km/h) is: 120, 142, 142, 165, 132, 130, 156, 136, 167, 139, 144. A random sample (Sample 2) of the Audi's average driving speed (km/h) is: 112, 145, 146, 165, 163, 141, 112, 134, 113, 114, 125. What is the median of Sample 1? What is the median of Sample 2?
Answer:
Median for sample 1 = 142
Median for sample 2 = 134
Step-by-step explanation:
For Sample 1:
For finding median, the data is first arranged into ascending or descending order. We are arranging the data in ascending order.
120, 130, 132, 136, 139, 142, 142, 144, 156, 165, 167
The formula for calculating the term which will be median is:
Median= ((n+1)/2)
Here in sample 1, n=11
So, putting n=11 in the formula
= ((11+1)/2)
= (12/2)
=6th term
The sixth term is 142, so
Median of sample 1=142
For Sample 2:
For finding median, the data is first arranged into ascending or descending order. We are arranging the data in ascending order.
112, 112, 113, 114, 125, 134, 141, 145, 146, 163, 165
The formula for calculating the term which will be median is:
Median= ((n+1)/2)
Here in sample 2, n=11
So, putting n=11 in the formula
=((11+1)/2)
=(12/2)
=6th term
The sixth term is 134, so
Median of sample 2=134
Alex doesn't remember what the Zero Product Property is used for. Explain to Alex what the property is and how it is used.
The Zero Product Property in mathematics states that if the product of two numbers is zero, then at least one of the numbers must be zero. You typically use this property when solving quadratic equations by setting each factored term equal to zero and then solving for every variable.
Explanation:The Zero Product Property is an essential concept in algebra, particularly when it comes to solving quadratic equations. The Zero Product Property states that if the product of two numbers, terms, or factors is zero, then at least one of the factors must be zero. In simple terms, if a * b = 0, then a has to be zero, or b has to be zero, or both.
To use the Zero Product Property, you usually start by setting an equation equal to zero. For example, let's solve the quadratic equation x^2 - 5x = 0. First, you would factor the equation to (x)(x-5) = 0. Now, using the Zero Product Property, we can set each factor equal to zero and solve for x. This gives us x = 0 and x = 5.
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The sum of two integers is 23 and the positive difference of the same two integers is 13. What is the product of these two integers?
A) 90 B) 75
C) 46 D) 299
Answer:
A) 90
Step-by-step explanation:
"The sum of two integers is 23" becomes
a + b = 23
"the positive difference of the same two integers is 13" becomes
a - b = 13 (difference means subtract)
Now solve the system..
a + b = 23
a - b = 13 *use addition or elimination method, since b has opposite coefficients...
2a = 36 ( we add the two equations together)
a = 18 (divide by 2 on both sides)
Since a = 18, 18 + b = 23, gives us b = 5. (18 + 5 = 23)
ab = (18)(5) = 90
Answer: A) 90
Let one integer is = x.
Sum of them is 23. So the other integer is (23 - x).
Given: Difference = 13.
So,
[tex]x-(23-x)=13\\ x-23+x=13\\ 2x=36\\ x=18[/tex]
So the other number is = 23 - x = 23 - 18 = 5.
So the product = 18*5=90
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