We find that there are 24 girls and 40 boys, leading to a total of 64 people in the group.
To solve for the total number of people in the group given the ratio of boys to girls and the information that there are 16 more boys than girls, we can set up a proportion based on the ratio 5:3. Let the number of girls be represented by x and the number of boys be represented by x + 16, as there are 16 more boys than girls. From the ratio 5:3, we know that for every 8 parts (5+3), there are 5 parts boys and 3 parts girls. This gives us two equations: 5/8 of the total is boys, and 3/8 of the total is girls.
From the information given:
(x + 16) / x = 5 / 3
Cross-multiplying gives us:
3(x + 16) = 5x
3x + 48 = 5x
48 = 5x - 3x
48 = 2x
x = 24
This means there are 24 girls. Since there are 16 more boys, this means there are 24 + 16 = 40 boys. Adding up the boys and girls gives us the total number of people in the group:
40 boys + 24 girls = 64 people in total.
The scores on a standardized test are normally distributed with a mean of 500 and a standard deviation of 60. Jake scored 520 on the test. What percent of students scored below Jake? Include a step by step description of the process you used to find that percentage. (Round your answer to the nearest whole number.)
Answer:
63 percent student scored below Jake.
Step-by-step explanation:
For finding the percentile
Step 1: Subtracting mean from Jake’s score
=520-500
=20
Step 2: Calculating z-score
The z-Score is found by dividing the difference obtained in step 1 by SD of the data
z-score= 20/60
z-score=0.333
Step 3: Converting the z-score to percentile
The z-score will be converted to percentile using the z-score to percentile conversion table, the value of percentile for 0.3333 is 63rd .
So, 63 percent students scored below Jake.
What is the value of X in the triangle below to the nearest degree? The triangle is not drawn to scale. I selected an answer but I’m not sure about it
Answer:
x = 25
Step-by-step explanation:
To find the value of x we use the formula:
tan x° = opposite side /adjacent side
Opposite Side = 8
Adjacent Side = 17
tan x° = 8/17
tan x° = 0.4705882352941
[tex]Tan^{-1}[/tex] of [tex]0.4705882352941[/tex]
x° = 25
35 POINTS HELP PLEASE! RUNNING OUT OF TIME!
Answer:
[tex]\large\boxed{9x^8,\ 25x^{12},\ 36x^{16}}[/tex]
Step-by-step explanation:
[tex]Use\\(\sqrt{s})^2=s\ for\ s\geq0\\(a^n)^m=a^{nm}\\(ab)^n=a^nb^n\\a^n\cdot a^m=a^{n+m}\\===========================\\6x^2=(\sqrt6)^2x^2=(x\sqrt6)^2\to\boxed{NOT}\\\\9x^8=3^2x^{4\cdot2}=3^2(x^4)^2=(3x^4)^2\to\boxed{YES}\\\\16x^9=4^2x^{8+1}=4^2x^{4\cdot2}\cdot x=4^2(x^4)^2x=(4x^4)^2x\to\boxed{NOT}\\\\25x^{12}=5^2x^{6\cdot2}=5^2(x^6)^2=(5x^6)^2\to\boxed{YES}\\\\36x^{16}=6^2x^{8\cdot2}=6^2(x^8)^2=(6x^8)^2\to\boxed{YES}[/tex]
Answer:
[verb] to allow someone to do; to allow something; to acquiesce on something; to concede something.
Which choice is equivalent to the product below? Square root Of 8 Times Square root 3
Answer:
The answer would be around 3.7
Step-by-step explanation:
Complete the statements describing investments by filling in the correct words. Different investments have different levels of and offer different rates of return. For example, investing in property than investing in bonds.
Answer:
Risk
More risky
Step-by-step explanation:
Got it right on edmunto
Different investments have different levels of - RISKS and offer different rates of return. For example, investing in property is MORE RISKY than investing in bonds.
The property rates can change drastically within a short period of time, while bonds are static in income. This is why investing in property is riskier than investing in bonds.
Which expression best represents the product of two consecutive integers? CLEAR CHECK x?(2+x) x?(x+1) 2?(x+1) 2x+2
Answer:
The product of two consecutive integers:x · (x+1) = x(x + 1)Step-by-step explanation:
Consecutive integer:
... -2, -1, 0, 1, 2, 3, ...
Difference between two consecutive integers is equal to 1.
Therefore two consecutive integers is x and x + 1.
HELP PLEASE LAST QUESTION I NEED!!!!!!!!!!!!!!!!!
The question is a little blurry. I can't read it.
Answer:
I believe the answer is c.
Step-by-step explanation:
Ernestine deposited $6800 into a savings account that earns 3.5% simple interest each year calculate annually what is the future value of understands account to 16 years
Answer:
[tex]\$10,608[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=16\ years\\ P=\$6,800\\r=0.035[/tex]
substitute in the formula above
[tex]A=\$6,800(1+0.035*16)=\$10,608[/tex]
State the domain and range of the graph in interval notation.
Answer:
The domain is the interval [tex][-6,6][/tex]
The range is the interval [tex][-2,2][/tex]
Step-by-step explanation:
we know that
Observing the graph
The domain is the interval [tex][-6,6][/tex]
All real numbers greater than or equal to -6 and less than or equal to 6
The range is the interval [tex][-2,2][/tex]
All real numbers greater than or equal to -2 and less than or equal to 2
The graph's domain spans from -6 to 6, and the range extends from -2 to 2. In summary, the domain is [-6, 6], and the range is [-2, 2].
In the given graph, the domain represents all possible input values, and it spans from -6 to 6, inclusive. This is because the graph includes every real number greater than or equal to -6 and less than or equal to 6 along the horizontal axis.
The range, on the other hand, corresponds to the output values of the function and extends from -2 to 2, inclusive. This is derived from the observation that the graph encompasses all real numbers greater than or equal to -2 and less than or equal to 2 along the vertical axis.
The domain is [-6, 6], indicating all real numbers between -6 and 6, and the range is [-2, 2], signifying all real numbers between -2 and 2. The graph visually illustrates these intervals as the inclusive bounds for both domain and range.
To learn more about domain
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Each bottle of lemonade costs the local soccer team $0.75 they have $437.25 in their treasury to buy as many bottles of lemonade as possible to sell for a profit at their soccer games. How many bottles can they afford to buy.
$437.25 ÷ $0.75 = 583 bottles of lemonade
Hope this helps :)
In 2000 there were approximately 27 million people 18-24 years old in the United States.
Myra invested $10,000 in an account earning a nominal 8% per year compounded continuously. How much was in the account at the end of one year? Round the answer to nearest dollar.
Answer:
[tex]\$10,833[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=1\ years\\ P=\$10,000\\ r=0.08[/tex]
substitute in the formula above
[tex]A=\$10,000(e)^{0.08*1}=\$10,833[/tex]
Compound interest computed continuously after one year on a principal sum of $10,000 with an 8% interest rate will yield $10,833, rounded to the nearest dollar.
Explanation:Your question relates to the mathematics topic of compound interest. When interest is compounded continuously, we use the formula A = P * e^(rt), where A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money), r is the annual interest rate (in decimal form), and t is the time in years.
In your case, you are looking to find how much $10,000, invested at a nominal 8% per year compounded continuously, would amount to at the end of one year. Substituting the given values into the formula, we have:
A = $10,000 * e^(0.08*1).
The value of 'e' is approximately 2.71828. Therefore, we calculate:
A = $10,000 * 2.71828^0.08 = $10,833.
So, the amount in the account at the end of one year, rounded to the nearest dollar, would be $10,833.
Learn more about Compound Interest here:https://brainly.com/question/14295570
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What is the surface area of a box that is 237.7 in squared if it is scaled up by 10
1.) 2x + y = 3 2.) x - 2y = -1 If equation 1 is multiplied by 2 and then the equations are added, the result is
Which expressions are equivalent to 5x-15?Check all that apply
5(x+15)
5(x-3)
4x+3y-15-3y+x
-7y-6x-8y+x
-20-3x+5+8x
Answer:
Step-by-step explanation:
4×+3Y-15-3y+×
The equivalent expressions to 5x-15 are 5(x-3), 4x+3y-15-3y+x, and -20-3x+5+8x. These simplify to 5x-15 when combining like terms and distributing, matching the original expression.
The student is asking which expressions are equivalent to 5x-15. To find the equivalent expressions, we need to check each option to see if they simplify to the same form.
5(x+15) is not equivalent because when you distribute the 5, you get 5x + 75, which is not the same as 5x - 15.5(x-3) is equivalent because when you distribute the 5, you get 5x - 15, which matches the original expression exactly.4x+3y-15-3y+x is equivalent because when you combine like terms (4x + x and 3y - 3y), you get 5x - 15.-7y-6x-8y+x is not equivalent because even if you combine like terms, the x terms do not add up to 5x, nor do the constants add up to -15.-20-3x+5+8x is equivalent because when you combine like terms (-3x + 8x), you get 5x, and when combining constants (-20 + 5), you get -15; hence, it simplifies to 5x - 15.Therefore, the expressions 5(x-3), 4x+3y-15-3y+x, and -20-3x+5+8x are equivalent to 5x - 15.
How do the expressions 72 / 9 and -72/ (-9) compare when they are evaluated?
A. They have different values and are different signs.
B. They have different values but are the same sign.
C. They have the same value but are different signs.
D. They have the same value and the same sign.
Answer:
D. They have the same value and the same sign.
Step-by-step explanation:
72 / 9 and -72/ (-9)
Answer:
D
Step-by-step explanation:
just took the test
20 POINTS!!!!!!!!!
Which data sets could be used to create the box plot below?
4, 11, 8, 12, 1, 6, 14
10, 6, 9, 14, 1, 6, 12, 7
14, 10, 6, 9, 11, 8, 1
6, 8, 11, 1, 7, 14, 10
7, 9, 11, 1, 6, 7, 14, 8
Select more than one answer
4,12,16,22,32,45648383929282
Answer:
B.) 10, 6, 9, 14, 1, 6, 12, 7
&
D.) 6, 8, 11, 1, 7, 14, 10
Step-by-step explanation:
i got it right
Please help me out if possible. :)
Answer:
R(c - a, b)Step-by-step explanation:
Look at the picture.
R(x, y)
y - is the same as second coordinate of the point Q → y = b
x - is first coordinate of the point S reduced by distance a → x = c - a