Erin loves to play sports! She has earned 333 tennis trophies, 444 basketball trophies, 777 soccer trophies, and 111 volleyball trophy.
What is the ratio of Erin's tennis trophies to soccer trophies?
The ratio of Erin's tennis trophies to soccer trophies is 3/7.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
As per the given,
She has earned 333 tennis trophies, 444 basketball trophies, 777 soccer trophies, and 111 volleyball trophies.
The ratio of tennis trophies to soccer = 333/777
3/7(111/111) = 3/7
Hence "The ratio of Erin's tennis trophies to soccer trophies is 3/7".
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(5 x 2) + (5 x 4) = 5 x (2 + 4)
Which picture represents this equation?
A) A
B) B
C) C
D) D
Answer:
Step-by-step explanation:
Wheres the picture?
The equation (5 x 2) + (5 x 4) = 5 x (2 + 4) showcases the distributive property in mathematics where two different expressions yield the same result.
The equation (5 x 2) + (5 x 4) = 5 x (2 + 4) is a demonstration of the distributive property in mathematics.
(5 x 2) + (5 x 4) can be simplified as 10 + 20 = 30.
5 x (2 + 4) can be simplified as 5 x 6 = 30.
Hence, both sides of the equation result in the same value, displaying the equality of the expression.
Match each scientific notation with the appropriate number
Answer:
wheres the answer choices
the difference between the measures of two supplementary is 42. Find both angles.
Answer:
111 deg and 69 deg
Step-by-step explanation:
let the angles be x and y
given:
x - y = 42 degrees -------> eq 1
also given that they are supplemantry,
i.e x + y = 180 degrees ----------> eq 2
by elimination,
eq 1 + eq 2
(x-y) + (x+ y) = 42 + 180
2x = 222
x = 111 degrees (substitute back into eq 2)
111 + y = 180
y = 180 - 111
y = 69 deg
The length of a rectangle is 3 cm greater than its width. the area of the rectangle is 180 cm². find the length and the width.
Answer:
L=15 W=12 15*12 = 180
Step-by-step explanation:
W*L = area
W*(W+3) = 180
Do the distributive
W^+3 W-180=0
Find 2 numbers that when multiplied ,the result is -180
and when added the result is 3
- 12* 15 = -180
-12 +15 = 3
In a video game green gems are worth 5 points and blue gems are worth 10 points. Eric collects 25 gems and earned 160?points form his gems. Find how many green gems and how many blue gems Eric collected.
Eric collected 18 green gems and 7 blue gems.
Step-by-step explanation:
Let,
Green gems = x
Blue gems = y
One green gem = 5 points
One blue gem = 10 points
According to given statement;
x+y=25 Eqn 1
5x+10y=160 Eqn 2
Multiplying Eqn 1 by 5;
[tex]5(x+y=25)\\5x+5y=125\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 3 from Eqn 2;
[tex](5x+10y)-(5x-5y)=160-125\\5x+10y-5x-5y=35\\5y=35[/tex]
Dividing both sides by 5;
[tex]\frac{5y}{5}=\frac{35}{5}\\y=7[/tex]
Putting y=7 in Eqn 1;
[tex]x+7=25\\x=25-7\\x=18[/tex]
Eric collected 18 green gems and 7 blue gems.
Keywords: linear equations, subtraction
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Eric collected 18 green gems and 7 blue gems. This conclusion is reached by forming and solving a system of linear equations based on the problem's conditions related to the total number of gems and their respective point values.
Explanation:This question deals with a system of equations, defined by the value of the gems and the total number of gems. Here, let's represent green gems as 'g' and blue gems as 'b'.
The two equations formed from the problem are as follows: g + b = 25 (since Eric collected 25 gems) and 5g + 10b = 160 (since green gems are worth 5 points each and blue ones 10, yielding a total score of 160).
To solve it, we need to isolate one of the variables: first, multiply the first equation by 5: 5g + 5b = 125. Then subtract this equation from the second equation, so we get 5b = 35, which simplifies to b = 7.
Substitute b = 7 into the first equation to get g = 25 - 7 = 18. Therefore, Eric collected 18 green gems and 7 blue gems.
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I need help!! Can you please make t the subject
Answer:
t=3
Step-by-step explanation:
What are the next two terms in the sequence?
2, 14, 26, 38, ...
Answer:
50, 62
The drawing will help
Answer:
50, 62Step-by-step explanation:
[tex]a(1)=2\\\\a(2)=a(1)+12=2+12=14\\\\a(3)=a(2)+12=14+12=26\\\\a(4)=a(3)+12=26+12=38\\\\a(5)=a(4)+12=38+12=50\\\\a(5)=a(5)+12=50+12=62[/tex]
If you want the formula.
It's an arithmetic sequence with the first term 2 and common difference 12.
The explicit formula of an arithmetic sequence:
[tex]a(n)=a(1)+(n-1)d[/tex]
d - common difference
Substitute:
[tex]a(n)=2+(n-1)(12)[/tex] use the distributive property
[tex]a(n)=2+12n-12[/tex]
[tex]a(n)=12n-10[/tex]
write down in terms of n an expression for the nth term -7,-12,-17,-22,-27
The expression for the nth term of the given sequence -7, -12, -17, -22, -27 is -7 - 5(n-1).
Explanation:The given sequence is -7, -12, -17, -22, -27. In this sequence, each term is obtained by subtracting 5 from the previous term. So, we can write the expression for the nth term as:
-7 - 5(n-1)
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find the product of the following expression (x-15) (x-3)
Answer:
x²-18x+45
Step-by-step explanation:
(x-15)(x-3)
Product of the first terms is x² [x times x] F
Product of the outer term is -3x [x times -3] O
Product of the inner term is -15x [-15 times x] I
Product of the last term is 45 [-15 x -3] L
Combine like terms and you'll get x²-18x+45
Clare wants to mail a package that weighs 4 1/2 ponds what could be its volume in liters
Answer:
The volume in liters is 2.041165665 liter.
Step-by-step explanation:
Given : Clare wants to mail a package that weighs [tex]4\frac{1}{2}[/tex] pounds.
To find : What could be its volume in liters ?
Solution :
We know that,
Pound (lb) is a unit of Weight used in Standard system.
Liter (l) is a unit of Volume used in Metric system.
To convert 1 pound into liter is
1 pound (lb) = 0.45359237 liter (l)
[tex]4\frac{1}{2}[/tex] pounds in simpler fraction is [tex]\frac{9}{2}[/tex]
Converting into liter,
[tex]\frac{9}{2}[/tex] pound (lb)=[tex]\frac{9}{2}\times 0.45359237[/tex] liter (l)
[tex]\frac{9}{2}[/tex] pound (lb) = 2.041165665 liter (l).
Therefore, the volume in liters is 2.041165665 liter.
3 pounds of bananas cost 1.5. what is the constant of proportionality that relates the cost in dollars ,y, to the number of pounds of bananas ASAP
Answer:
$0.5
Step-by-step explanation:
formula ; y = kx
where ; y = $1.5
x = 3 pounds of bananas
k = constant of proportionality
Step 1. Do the equation based on the data given
y = kx
$1.5 = k3
Step 2. Compute the mathematical equation. Divide both sides by the coefficient of 3.
$1.5 = k3
3 3
k = .5
Answer; $0.5 is the constant of proportionality cost in dollars per pound of banana.
Answer:
0.25
Step-by-step explanation:
Have a nice day <3
A small business owner wants to compare how much she spent with how much money she earned. The table shows her expenses and income.
If the expenses and income form a proportional relationship, what was the amount of income when she spent $300? pst the answer is d
A. $400
B. $600
C. $900
D. $1,200
Answer:?=x
100.800=200.400
200.x=300.800
200.x=240000
X=1200
Good luck!
Step-by-step explanation:
Answer:
D) $1,200
Step-by-step explanation:
300*4=1200
Which of the following linear equations matches the graph?
y = 1/x
y = 1/3 x
y = 3x
y = -x
y = x
Answer:
y=x
Step-by-step explanation:
Answer:
y = x
because it's at 1y axsis, and 1x axsis
7th grade math help thxs
Answer:
a is 7.5
b is 67.5
c is 100
d is let me think on d
Answer:
a is 7.5
b is 67.5
c is 100
d is for every 7.5
Find the annual rate of interest. Principal = 4600 rupees, Period = 5 years, Total amount = 6440 rupees, Annual rate of interest = __%
The annual rate of interest per year is 8%
Solution:
Given:- Principal (p) = 4600 rupees, Time –Period (t) = 5 years, Total amount(A) = 6440 rupees
First we will calculate the Interest and then using formula of simple interest we will calculate the rate of interest
Interest = Amount – Principal
Interest = 6440 – 4600 = 1840
Now using the formula of simple Interest and on putting values we get,
[tex]\text {Simple Interest }=\frac{P \times R \times T}{100}[/tex]
Where "P" is the principal and "R" is the rate of interest per annum and "T" is the time period
[tex]1840=\frac{4600 \times R \times 5}{100}[/tex]
[tex]\begin{aligned} \mathrm{R} &=\frac{1840 \times 100}{4600 \times 5} \\\\ \mathrm{R} &=\frac{1840}{230} \\\\ \mathrm{R} &=8 \% \end{aligned}[/tex]
Hence, the required rate of interest per year is 8%
Answer:
The annual rate of interest per year is 8%
Solution:
Given:- Principal (p) = 4600 rupees, Time –Period (t) = 5 years, Total amount(A) = 6440 rupees
First we will calculate the Interest and then using formula of simple interest we will calculate the rate of interest
Interest = Amount – Principal
Interest = 6440 – 4600 = 1840
Now using the formula of simple Interest and on putting values we get,
Where "P" is the principal and "R" is the rate of interest per annum and "T" is the time period
Hence, the required rate of interest per year is 8%
Let me know if it is correct! Thank you. :)
Step-by-step explanation:
Death Valley, located in California, is the lowest place in North America. It is 282 feet below sea level, or -282 feet. Mount McKinley in Colorado is the highest place in North America. Its elevation is approximately -71.76 times the elevation of Death Valley. What is the approximate elevation of the Mount McKinley?
-20,236.32 feet
20,236.32 feet
-3.93 feet
3.93 feet
Answer:
20,236.32
Step-by-step explanation:
because (-282) * (-71.76) = 20,236.32
Answer:
20236.32 feet
Step-by-step explanation:
-282*-71.76=20236.32
Solve for x
-16 = 8x/5
x=-25 3/5
x=10
x=-10
Answer:
x = -10
Step-by-step explanation:
-16 = 8x/5
-80 = 8x
x = -10
If you could marry, anyone in the world. Who would it be?
Answer:
I would marry Ino from Naruto
Step-by-step explanation:
Plz mark brainliest
Answer:
my bestfriend jaheim
Step-by-step explanation:
Last month, when Joe took his puppy to the veterinarian, the puppy weighed 5.3 pounds. This month, the puppy weighed 8.48 pounds. What is the percentage increase of the weight of the puppy?Last month, when Joe took his puppy to the veterinarian, the puppy weighed 5.3 pounds. This month, the puppy weighed 8.48 pounds. What is the percentage increase of the weight of the puppy?
A. 63%
B. 3%
C.60%
D. 37%
The puppy's weight increased by 60%.
Answer:
Step-by-step explanation:
60
Can someone help me answer this?
Given the function f(x)= x^2+7x+10 / x^2+9x+20
Describe where the function has a hole and how you found your answer.
We need to simplify the function by factoring the numerator and the denominator. Plug the excluded values into the simplified function to find the hole.
Answer:
The function f(x) has a hole at point x = - 5.
Step-by-step explanation:
We are given a function as
[tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]
Now, we have to describe where the function has a hole.
Now, [tex]f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}[/tex]
⇒ [tex]f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}[/tex]
Therefore, the common factor of the numerator and denominator is (x + 5).
Now, (x + 5) = 0
⇒ x = - 5
Therefore, the function f(x) has a hole at point x = - 5. (Answer)
By factoring and simplifying the function f(x)=(x^2+7x+10)/(x^2+9x+20), we find a hole at x=-5. This is because -5 was an excluded value in the original function, but does not cause the denominator to be zero in the simplified function.
Explanation:The given function is f(x) = (x^2+7x+10) / (x^2+9x+20). To find where the function has a hole, we need to factor both the numerator and the denominator. We also must exclude any values of x that would cause the denominator to be zero as these are undefined in the function.
The numerator factors into (x+2)(x+5), and the denominator into (x+4)(x+5). If we simplify, the x+5 term will cancel out, leaving us with f(x) = (x+2)/(x+4).
Originally, x could not be equal to -4 or -5, as these would make the denominator zero. In the simplified function, only x=-4 causes the denominator to be zero. But since x=-5 was an excluded value in the original function, that indicates there is a 'hole' at x=-5 on the function.
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find last years salary if, after 6 percent raise, this years salary is $33,920
Last year's salary is $32000
Step-by-step explanation:
We will use the linear equations to solve the given problem
Let x be the last years salary
then
0.06x will be the raise in the salary
This year's salary is $33920
So,
[tex]x+0.06x=33920\\1.06x=33920[/tex]
Dividing both sides by 1.06
[tex]\frac{1.06x}{1.06}=\frac{33920}{1.06}\\=32000[/tex]
Hence,
Last year's salary is $32000
Keywords: Percentage, Linear equations
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harvey the wonder hamster can run 3 1/6 km in 1/4 hour. harvey runs at a constant rate.
find his average speed in kilometers per hour.
___ kilometers per hour
please help lol.
Answer:
38/3 km per hour
Step-by-step explanation:
3 1/6=19/6
1/4=0.25
(19/6)*4=38/3
Which fuction is positive for the entire interval [-3, -2 ]
Answer:
f(x) = |x| or f(x) = x² etc.
Step-by-step explanation:
There are several functions that gives positive value for entire interval [-3,-2].
Like the function, y = |x| , where if you put any negative value of x, the resulting output of the value of y is always positive. Therefore, for domain of [-3,-2] the range of the function will be [3,2]
Again, the function y = x², where if you put any negative number as a value of x, the corresponding value of y will be always positive.
Therefore, for domain of [-3,-2] the range of the function will be [9,4] (Answer)
olivia has read 143 pages of a 220 -pages novel find the percent
Answer:
65%
Step-by-step explanation:
Cross, multiply and divide method has saved my life with these problems, heres how to do it.
Set up like this:
143 x
------- = -------
220 100
Multiply 143 by 100, then divide that by 220.
x= 65, so she has read 65%
Final answer:
Olivia has read approximately 65% of her 220-page novel by reading 143 pages.
Explanation:
To calculate the percent of the novel that Olivia has read, we use the formula: (number of pages read ÷ total number of pages) × 100%. Olivia has read 143 pages of a 220-page novel. Therefore, the calculation is (143 ÷ 220) × 100%, which simplifies to approximately 65%.
The steps to solve the problem are given below:
Step 1: 143 / 220 = 0.65
Step 2: 0.65 x 100 = 65%
So, Olivia has read about 65% of the novel.
What is the inverse of the function h(x) = 5/2x + 4
[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]
Step-by-step explanation:
Given function is:
[tex]h(x) = \frac{5}{2}x+4[/tex]
In order to find the inverse:
Replacing h(x) with y
[tex]y = \frac{5}{2}x+4[/tex]
Replacing x with y and y with x
[tex]x = \frac{5}{2}y+4[/tex]
Solving for y
[tex]x = \frac{5}{2}y+4\\x - 4 = \frac{5}{2}y+4-4\\x-4 = \frac{5}{2}y\\y = \frac{2}{5}(x-4)\\y = \frac{2x-8}{5}[/tex]
Replace y with h^(-1)(x)
[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]
Hence,
[tex]h^{-1}(x) = \frac{2x-8}{5}[/tex]
Keywords: Inverse, Functions
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visa usa stated that over the last year, the number of friday and saturday sales transactions increased 16% to $38.8 million. what were the total sales transactions at this time lasy year?
Answer:
$33.45 million
Step-by-step explanation:
The transaction increased by 16% between last year and this year.This mean that [tex]S_1=S_0\times{(1+16\%)=S_0\times{1.16}[/tex] ([tex]S_0[/tex] are last year sales and [tex]S_1[/tex] are this year sales. This means that, today's sales are greater than last year sales by a 16%.Then, [tex]S_0=\frac{S_1}{1.16} =33.45[/tex].Answer:
Last year’s sales transaction was $33.448 million
Explanation:
Consider the last year’s total sales transaction be x
According to question,
Sales were increased by 16% to 38.8 million
Then, according to question,
x + 16% of x = 38.8 million
Solving for x,
[tex]x + (\frac{16}{100})x[/tex] = 38.8 million
[tex]\frac{116}{100}x[/tex]= 38.8 million
x = [tex]\frac{(38.8 million \times 100)}{116}[/tex]
x = 33.448 million
Therefore, last year’s sales transaction was $33.448 million
Samantha deposit 300 in an account that earns an annual interest rate of 2.5 after nine months she computes the simple interest. What mistakes did Samantha make?
Answer:
She is doing a mistake of calculating interest after 9 months in place of after 12 months.
Step-by-step explanation:
Samantha deposit $300 in an account that earns an annual interest rate of 2.5%.
Now, Samantha after nine months of deposit computes the simple interest.
She is doing a mistake of calculating interest after 9 months in place of after 12 months.
The calculation of interest should be on a yearly basis (i.e. 12 months) as the interest rate is 2.5% per year. (Answer)
Find the slope of the line that contains (3, -4) and (7, -2).
Answer:
The slope is 1/2.
Step-by-step explanation:
m=(-2-(-4))/(7-3)=(-2+4)/4=1/2
Given that sin=2/5 and cos<0. Find the rest of the trigonometric functions
Answer:
[tex]\cos x=-\dfrac{\sqrt{21}}{5}\\ \\\tan x =-\dfrac{2}{\sqrt{21}}\\ \\\cot x=-\dfrac{\sqrt{21}}{2}[/tex]
Step-by-step explanation:
Given
[tex]\sin x=\dfrac{2}{5}\\ \\\cos x<0[/tex]
Use formula:
[tex]\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left(\dfrac{2}{5}\right)^2=1\\ \\\cos^2x=1-\dfrac{4}{25}\\ \\cos^2x=\dfrac{21}{25}\\ \\\cos x=\pm \dfrac{\sqrt{21}}{5}[/tex]
Since [tex]\cos x<0,[/tex] then
[tex]\cos x=-\dfrac{\sqrt{21}}{5}[/tex]
By definition,
[tex]\tan x =\dfrac{\sin x}{\cos x}=\dfrac{\frac{2}{5}}{-\frac{\sqrt{21}}{5}}=-\dfrac{2}{\sqrt{21}}\\ \\ \\\cot x=\dfrac{1}{\tan x}=\dfrac{1}{-\frac{2}{\sqrt{21}}}=-\dfrac{\sqrt{21}}{2}[/tex]