At the 6th grade school dance, there are 130 boys, 100 girls, and 20 adults. Write the ratio of the number of girls to the number of adults.
The ratio of the number of girls to the number of adults is 5 : 1.
What is the ratio?Ratio is used to compare two or more values together. Ratio shows the frequency of one number compared to the frequency of another number. The sign that is used to represent ratio is :.
The ratio of the number of girls to the number of adults = number of girls : number of adults
number of girls = 100
number of adults = 20
The ratio of the number of girls to the number of adults = 100 : 20
Express the ratio in its simplest form. To do this, divide both numbers by the greatest common factor of 100 and 20. The greatest common factor of 100 and 20 is 20.
The ratio of the number of girls to the number of adults = 5 : 1
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Fun times Amusement Park Charges a $7 admission fee plus $1.75 per ride. What is the equation, in intercept form for calculating the total cost, C, of going to the park and riding r rides?1. C = 1.75 + 7r2. C = 1.75r3. C = 7r4. C = 7 + 1.75r
The general form of an equation in intercetp form is:
[tex]y=mx+b[/tex]Where m is the change of y in function of x and b is the value of b when x is 0
In this situation you have:
y=C
x=r
m= 1.75 ( C increase 1.75 each r)
b= 7 (When there is not ride r=0 the admission fee is 7)
Then, you have the equation:[tex]C=1.75r+7[/tex]or C = 7 + 1.75rDrag each label to the correct location on the table. Match each equation with its number of unique solutions. y = -52 – 41 +7 y = –202 + 91 - 11 y = 3.12 – 61 + 3 Two Real Solutions One Real Solution One Complex Solution Two Complex Solutions Reset Next reserved
When b²−4ac=0 there is one real root.
When b²−4ac>0 there are two real roots.
When b²−4ac<0 no real roots or two complex roots
First equation
-x²-4x+7
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-4\mright)^2-4\mleft(-1\mright)\cdot\: 7 \\ 16+28=44 \end{gathered}[/tex]b²−4ac>0, then equation -x²-4x+7 has two real roots.
Second equation
-2x²+9x-11
[tex]\begin{gathered} b^{2}-4ac \\ 9^2-4\mleft(-2\mright)\mleft(-11\mright) \\ 81-88=-7 \end{gathered}[/tex]b²−4ac<0, then equation -2x²+9x-11 has two complex roots.
[tex]x1=\frac{9}{4}-i\frac{\sqrt{7}}{4},\: x2=\frac{9}{4}+i\frac{\sqrt{7}}{4}[/tex]Third equation
3x²-6x+3
[tex]\begin{gathered} b^{2}-4ac \\ \mleft(-6\mright)^2-4\cdot\: \: 3\cdot\: \: 3 \\ 36-36=0 \end{gathered}[/tex]b²−4ac=0, then equation 3x²-6x+3 has one root.
At his comic book store, Korey's Comics, Korey sells approximately $3,250 in comic books each month.
But as a comic book dealer, Korey only pays $1,285 for these comic books. Korey's monthly operating expenses, including labor, are $875. Calculate Korey's monthly net income.
Answer:
Korey's monthly net income is $1090Step-by-step explanation:
The spending is the cost plus expenses:
1285 + 875 = 2160Net income is the difference of money made and spent:
3250 - 2160 = 1090if the ratio of similarity of the figures above is 2/3, then what is the ratio of the perimeters of the two figures?
Perimeter = side 1 + side 2 ´+ side 3.
Triangle 1
Perimeter = 6 + 8 + 10
= 24
Triangle 2
Perimeter = 9 + 12 + 15
= 36
Ratio
24/36 = 2/3
The ratio of the perimeters is also 2/3
On the scale drawing of a small town, 1 inch equals 15 feet. On this scale drawing, a parking lot measures 4 2/5 in. by 8 3/5 in.
What is the area of the actual parking lot?
_________ square feet.
Answer:
Step-by-step explanation:
4 and 2/5 inches by 8 and 3/5 inches.
60 and 6 feet by 120 and 9 feet.
66 by 129 feet
8514 feet squared
Sal elrove 3000 miles in 75 hours. At this rate how long will it take to drive 4000 miles
Answer:
Step-by-step explanation:
First, we need to find the rate. miles/hours. 3000/75 = 40mph (miles per hour). to find the answer we need to divide the rate by the distance they want us to find. to see a deeper explanation of why scroll past the answer. 4000/40 = 100 hours.
deeper explanation:
we can set the numbers given to us equal to what we are looking for.
miles/hour
3000/75 = 4000/x x being the time we are looking for
cross multiply 3000x=300000
divide by 3000 x=100 hours
In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between f = 1/4 * c + 40 , chirps and outdoor temperature is where c is the number of chirps per minute and ƒ is the temperature in degrees Fahrenheit. a. Suppose 110 chirps are heard in a minute. According to this model, what is the outdoor temperature? b. If it is 75 deg * F outside, about how many chirps can we expect to hear in one minute? c. The equation is only a good model of the relationship when the outdoor temperature is at least 55 deg * F (Below that temperature, crickets aren't around or inclined to chirp.) How many chirps can we expect to hear in a minute at that temperature?
HELPPPP ME PLEASEEEEEEE
a. Using the equation of the relationship, the temperature outdoor would be 67.5 °F.
b. 140 chirps in a minute.
c. 60 chirps at that temperature is expected.
d. The graph for the relationship is given below.
e. 1/4 is the unit rate or slope = in 1/4°F per chirp.
f. 40 represents the starting or initial temperature.
What is the Graph of a Linear Equation?The graph of a linear equation, y = mx + b, will have a slope value of m, and an initial value or y-intercept of b, which is the point on the y-axis that the line intercepts.
Given the equation, f = ¼c + 40, where:
f = temperature in degrees Fahrenheit
c = number of chirps
1/4 represents the temperature in °F per chirp
40 represents the initial temperature
a. Substitute c = 110 into the equation, f = ¼c + 40:
f = ¼(110) + 40
f = 67.5
The outdoor temperature is predicted to be 67.5 °F.
b. Substitute f = 75 into the equation, f = ¼c + 40:
75 = ¼c + 40
75 - 40 = ¼c
35 = 1/4c
4(35) = c
c = 140
140 chirps would be heard in a minute.
c. Substitute f = 55 into the equation, f = ¼c + 40:
55 = ¼c + 40
55 - 40 = ¼c
15 = c/4
4(15) = c
c = 60
Expect to hear 60 chirps at that temperature.
d. The graph for f = ¼c + 40 is in the attachment.
e. 1/4 is the unit rate or slope, which is the temperature in °F per chirp.
f. 40 tells us about the equation of the relationship that the initial temperature where we can start expecting the crickets to chirp starts from 40 °F.
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Y varies 1/x², when X=2, Y=1. Find the values of X when Y=4/9.
Answer:
x = ± 3
Step-by-step explanation:
given y varies as [tex]\frac{1}{x^2}[/tex] , then
y = k × [tex]\frac{1}{x^2}[/tex] = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k use the condition x = 2 , y = 1
1 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
4 = k
y = [tex]\frac{4}{x^2}[/tex] ← equation of variation
when y = [tex]\frac{4}{9}[/tex] , then
[tex]\frac{4}{9}[/tex] = [tex]\frac{4}{x^2}[/tex] ( cross- multiply )
4x² = 36 ( divide both sides by 4 )
x² = 9 ( take square root of both sides )
x = ± [tex]\sqrt{9}[/tex] = ± 3
Can you please help me out with a question
Formular for total surface area of a cylinder
[tex]TSAofacylinder=2nr^2\text{ + 2nrh}[/tex][tex]\begin{gathered} T\mathrm{}S\mathrm{}A\text{ = 2 }\times\text{ }\pi\text{ }\times7^2\text{ + 2 }\times\pi\times7\times21ft^2^{} \\ \text{ = 307.876 + }923.628 \\ \text{ = 1231.504 ft}^2 \\ =1231.5ft^2\text{ (nearest tenth)} \end{gathered}[/tex]S = 1231.5 sq ft
Valeria created a triangular pyramid as part of her science fair project. The triangular base has a height of 8 cm and a length of 6 cm. The height of the pyramid is 12 cm. Determine the volume of Valeria's pyramid.A. 192 cm B. 288 cmC. 96 cmD. 576 cm
Given:
Height of triangular base = 8 cm
Length of traingular base = 6cm
Height of pyramid = 12 cm
Let's determine the volume of Valeria's pyramid.
To find the volume of the triangular pyramid, apply the formula:
[tex]V=\frac{1}{3}(A\ast h)[/tex]Where A is the area of the triangular base and h is the height of the pyramid
To find the area of the triangular base, apply the area of a triangle formula:
[tex]\begin{gathered} A=\frac{b\ast h}{2} \\ \\ A=\frac{6\ast8^{}}{2}=\frac{48}{2}=24cm^2 \end{gathered}[/tex]To find the volume of the pyramid, substitute 24 for A and 12 for h in the formula above.
Thus, we have:
[tex]\begin{gathered} V=\frac{1}{3}(A\ast h) \\ \\ V=\frac{1}{3}(24\ast12) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} V=\frac{1}{3}(288) \\ \\ V=\frac{288}{3} \\ \\ \text{ V = 96 cm}^3 \end{gathered}[/tex]Therefore, the volume of Valeria's pyramid is 96 cubic centimeters.
ANSWER:
[tex]\text{ C. 96 cm}^3[/tex]pleas help quick
What is the value of the expression
PLUG IN THE VALUES IN THE RIGHT POSITIONS AND SIMPLIFY.
[tex] = 2( \frac{1}{2} + \frac{3}{4} ) + 6 \\ = 2( \frac{5}{4} ) + 6 \\ = \frac{10}{4} + 6 \\ = \frac{5}{2} + 6 \\ = \frac{17}{2} [/tex]
THE ANSWER IS OPTION C.
Three t-shirts for $10. find the unit rate
Answer:
Step-by-step explanation:I don’t know
Hey need help with this problem! Will give brainliest if right
Answer: 899.998434785 times more than the loser.
Trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5),
and U(-13,-9); scale factor: k = 1/4,
center of dilation: (-5, 3)
The coordinates of the trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5), and U(-13,-9) after dilation with scale factor of k= 1/4 are
R' (-7, -2) S' (-4, -2) T' (-4, -2.5)U' (-7, -6) How to determine the coordinates of the image after dilationData gotten from the question
Trapezoid RSTU with vertices R(-13, 7), S(-1, 7), T(-1, -5) U(-13,-9)scale factor: k = 1/4center of dilation: (-5, 3)Dilation refers to an increment or reduction in dimension and location of a preimage to get a new image
The coordinate of the image of dilation is gotten using the formula
x₂ = kx₁ - x₀(k - 1) for x coordinate
y₂ = ky₁ - y₀(k - 1) for y coordinate
definition of terms
terms with subscript 2 is corresponding to the image
terms with subscript 1 is corresponding to the preimage
terms with subscript 0 is corresponding to the center of dilation
\k = scale factor
R(-13, 7) ⇒ R'(-7, -2)
x₂ = 1/4 * -13 - -5(1/4 - 1) = -7
y₂ = 1/4 * 7 - -5(1/4 - 1) = -2
S(-1, 7) ⇒ S' (-4, -2)
x₂ = 1/4 * -1 - -5(1/4 - 1) = -4
y₂ = 1/4 * 7 - -5(1/4 - 1) = -2
T(-1, -5) ⇒ T' (-4, -2.5)
x₂ = 1/4 * -1 - -5(1/4 - 1) = -4
y₂ = 1/4 * -5 - -5(1/4 - 1) = -2.5
U(-13,-9) ⇒ U' (-7, -6)
x₂ = 1/4 * -13 - -5(1/4 - 1) = -7
y₂ = 1/4 * -9 - -5(1/4 - 1) = -6
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PLEASE help thank you!
Answer:
70
Step-by-step explanation:
So 175% of 40 is the amount in april so we can split it up into 2 problems
100% of 40? 40
75% of 40? 30
Then you add the 2 to get 175% of 40 which will be 70!
Is 5^x a polynomial?
yes, 5^x a polynomial. a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
What is Polynomial?a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables.
In the given expression 5^x x is a variable and 5 is a real number.
5^x is a finite polynomial or infinite polynomial. It depends upon the value of x. If x is finite then 5^x is a finite polynomial and if x is infinite then 5^x is a infinite polynomial.
Hence If x is finite then 5^x is a finite polynomial and if x is infinite then 5^x is a infinite polynomial.
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cuáles son las raíces de la ecuación x²-6x-7=0
Answer Las raíces de la ecuación x2 − 6x + 7 = 0 son α y β. Encuentra la ecuación con raíces α + 1 β y β + 1 α. Deduzco que α + β = − b a = 6 1 = 6 y que αβ = c a = 7 1 = 7.
Step-by-step explanation:
I have no clue what to do so pls include an explination
[tex]10=\frac{z}{2} +7[/tex]
The solution for the given linear equation is z = 6
How to solve the linear equation?
Here we have the following linear equation:
10 = z/2 + 7
To solve it, we need to isolate the variable in one of the sides of the equation.
First, we can subtract 7 in both sides:
10 - 7 = z/2 + 7 - 7
3 = z/2
Now we can multiply both sides by 2 to get:
2*3 = 2*(z/2)
6 = z
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What is the slope of the line that passes through the points (-2, 2) and (-4, -1)?
Write your answer in simplest form.
The slope of line through points (-2, 2) and (-4, -1) is 3/2 by using the slope-point formula that tells that change in y divided by change in x.
What is slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
What is point?A point is a basic concept in classical Euclidean geometry that represents an exact location in space and has no length, width, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.
Here,
The points are (-2, 2) and (-4, -1)
m=(y2-y1)/(x2-x1)
m=Δy/Δx
m=(-1-2)/(-4+2)
m=3/2
By dividing the change in y by the change in x, the slope of the line passing through the points (-2, 2) and (-4, -1) is 3/2.
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When the internet first launched, it was slow, clogged up phone lines and was most certainly not cheap. In fact, most Internet service providers (ISP) charged a flat rate access fee that included 20 hours a month of internet time. After twenty-hours of use, the ISP’s charged an additional per-hour fee. Suppose in 1995, Charter charged a flat rate of $39.95 for the first twenty hours of service and an additional per-hour charge of $5.99.a. How much would a Charter bill for 18 hours of internet used be in 1995? b. How much would a Charter bill for 28 hours of internet used be in 1995?
from the question, we were told in 1995, Charter charged a flat rate of
$39.95 for the first twenty hours.
and an additional per hour charge of $5.99
if,
for 20 hours = 39.95
therefore for 1 hour = 39.95/20
so for 18 hours = 39.95/20 X 18.95/20
so for 18 hours = 9
so,
to get the amount Charter bill for 18 hours in 1995 is,
39.95 x 18/20
= 39.95 x 0.9
= $35.955
so Charter bill for 18 hours of internet used in 1995 is $35.955
ould bill for 28 hours is
so, what Charter would
Find A (please help)
Answer:
a=1
Step-by-step explanation:
Rewrite one fourteenth times x cubed times y plus three fourteenths times x times y squared using a common factor.
The expression which can be rewritten using a common factor is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].
According to the question,
We have the following information:
One fourteenth times x cubed times y plus three fourteenths times x times y squared.
(We know that 'times' has to be replaced with multiplication.)
Now, we will change this into mathematical expression:
[tex]\frac{x^{3} y}{14} +\frac{3xy^{2} }{14}[/tex]
Now, from these two terms, the common factor can be [tex]\frac{xy}{14}[/tex].
(Common factor means that the number and the variables taken as a common factor should be able to completely divide the terms given any expression.)
Now, taking it as a common factor, we have the following expression:
[tex]\frac{xy}{14} (x^{2} +3y)[/tex]
Hence, the required expression is [tex]\frac{xy}{14} (x^{2} +3y)[/tex].
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quick sell outlet sold a total of 40 televisions, each of which was either a model p television or a model q television. each model p television sold for $p and each model q television sold for $q. the average (arithmetic mean) selling price of the 40 televisions was $141. how many of the 40 televisions were model p televisions? (1) the model p televisions sold for $30 less than the model q televisions. (2) either p
Model P televisions made up 12 of the 40 televisions when Quick Sell outlet sold a total of 40 television, each of which was either a model P television or a model Q television.
Price plus quantity equals revenue.
Let x be the quantity of sold TVs of model p.
40 - x units of the model q TV would have been sold.
Profits from model p TV sales are
px
Sales of the type q TV bring in money.
(40 - x)q
Total income equals px plus (40 - x)q
The average price calculation formula is written as
Total revenue / total number of TVs sold equals average price.
The 40 televisions sold for an average (arithmetic mean) price of $141. It follows that
141 = (px + (40 - x)q)/40
141 × 40 = px + (40 - x)q
5640 = px + (40 - x)q
p = q - 30
5640 = x(q - 30) + (40 - x) (40 - x)
q
30x + 40q - xq = 5640
5640 = - 30x + 40q
Since q = 120,
5640 = - 30x + 40 × 120
5640 = - 30x + 4800
5640 - 4800 = - 30x
840 = - 30x
x = 840/- 30 = - 28
Q cannot equal 120 since x cannot be negative.
Again,
5640 = px + (40 - x)q
If q = 30 + p, then
5640 = px + (40 - x)(30 + p)
5640 = px + 1200 + 40p - 30x - px
5640 = 1200 + 40p - 30x
Therefore,
If p = 120, then
5640 = 1200 + 40 × 120 - 30x
5640 = 6000 - 30x
30x = 6000 - 5640
30x = 360
x = 360/30
x = 12
Therefore, out of 40 televisions 12 tv are of model p
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9x+3y=-6 rewrite this equation in slope intercept form (y=Mx+b)
Given the 2 statements: "If you study for your test, then you will pass
your test," and "If you passed your test, then you studied for your
test." the biconditional is:
The biconditional statement is "You study for your test if and only if you passed".
What is biconditional statement?
A biconditional statement combines a conditional statement with its opposite expressed in the form of "if and only if."
The given statements are,
"If you study for your test, then you will pass your test" and "you passed your test then you studied for your test".
The biconditional statement is: "You study for your test if and only if you passed".
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Help!!, its a math question... it TIMED! The question is in the pic...
I think
Answer:
23
Step-by-step explanation:
Isolate the variable. Divide each variable
a container full of marbles has a ratio of orange marbles to black marbles of 5 : 12. a what does this ratio mean . b . if a container held 72 black marbles, how many oranges are in the container?
The ratio 5:12 means that we have 5 orange marbles for 12 black marbles (5 to 12) and the orange marbles will be 30 if the container has 72 black marbles.
According to the question,
We have the following information:
A container full of marbles has a ratio of orange marbles to black marbles of 5:12.
It means that we have 5 orange marbles when the number of black marbles is 12.
Now, let's take the number of orange marbles to be 5x and the number of black marbles to be 12x.
Now, we have the number of black marbles as 72.
So ,we have:
12x = 72
x = 72/12
x = 6
Now, we will put the value of x in 5x to find the number of orange marbles:
5x
5*6
30
Hence, the number of orange marbles in the container when it has 72 black marbles is 30.
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What is the value of x+ y in the system of equations below?
8x + 9y = 4.92
9x + 14y = 6.93
The value of x + y in the system of equations is 0.82125.
Given system of equations:-
8x + 9y = 4.92 ...(1)
9x + 14y = 6.93 ...(2)
We have to find the value of x + y in the system of equations.
Multiplying (1) by 9 and (2) by 8, we get,
72x + 81y = 44.28 ...(3)
72x + 112y = 55.44 ...(4)
(4) - (3), we get,
0x + 31y = 11.16
31y = 11.16
y = 11.16/31
y = 0.36
Putting the value of y in (1), we get
8x + 9*(0.36) = 6.93
8x + 3.24 = 6.93
8x = 6.93 - 3.24
8x = 3.69
x = 0.46125
Hence,
x + y = 0.46125 + 0.36 = 0.82125
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Find the value of x for which the lines p and q are parallel.
Question 17 options:
A) 6
B) 8
C) 9
D) 7
Answer:
D
Step-by-step explanation:
(14x + 18) and 116 are corresponding angles and are congruent, then
14x + 18 = 116 ( subtract 18 from both sides )
14x = 98 ( divide both sides by 14 )
x = 7