She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade.
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.
Given that,
To make the recipe,
3/4 quart of lemonade and 3 cups of cranberry juice
The ratio of cranberry juice to a quart of lemonade
⇒ 3/(3/4) = 4
To make the same recipe with 1(2/5) quarts of lemonade the ratio of cranberry juice to a quart of lemonade must be maintained.
So,
4 = cranberry juice / 1(2/5)
(5/7) × cranberry juice = 4
Cranberry juice = 28/5 ⇒ 5 (3/5).
Hence "She will need 5 3/5 cups of cranberry juice to make a punch for the school if Molly uses 1 2/5 quarts of lemonade".
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Let f(x)=x-4 and g(x)=x²-16 . Perform each function operation and then find the domain. f(x)+g(x)
The domain for g (x) + f (x) = x² + x - 20 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
We are given the two functions as:
f (x) = x - 4
g (x) = x² - 16
Now, first, we need to add f (x) from g (x).
So, we get that:
g (x) + f (x) = x² - 16 + (x - 4)
g (x) + f (x) = x² - 16 + x - 4
g (x) + f (x) = x² + x - 20
Now, the domain of the function will be all real numbers as it will be defined for all the real numbers.
Therefore, we get that the domain for g (x) + f (x) = x² + x - 20 will be all real numbers when f (x) = x - 4 and g (x) = x² - 16.
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Use v=-0.0098 t+c ln R , where v is the velocity of the rocket, t is the firing time, c is the velocity of the exhaust, and R is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. Find the velocity of a spacecraft whose booster rocket has a mass ratio of 20 , an exhaust velocity of 2.7km/s, and a firing time of 30 s . Can the spacecraft achieve a stable orbit 300km above Earth?
The velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.
What is mass ratio of a rocket?An indicator of a rocket's effectiveness is its mass ratio.It describes the ratio of the rocket's wet mass to its dry mass, or how much more massive the vehicle is with propellant than without.Given:
v = - 0.0098(t) + c (ln (R) ), where:v = maximum shuttle velocityt = firing timec = velocity of exhaustR = mass ratioTo find: Velocity of the spacecraft (v) = ?
Finding:
Here, c = 2.7 km/s, t = 30s, R = 20
On substituting the values of 'R', 't', 'v', we get:
v = -0.0098 ( 30) + 2.7 ( ln (20))
=> v = - 0.294 + 2.7 (2.995)
=> v = 7.7025 km/s
Hence, the velocity of the spacecraft is 7.7025 km/s as calculated with the help of mass ratio.
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Estimate 3 √ 70 to the nearest integer.
The value of the expression 3√70 to the nearest integer will be 25.10.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ 3√70
We know that the value of √70 will be 8.3666. Then the value of the expression will be given as,
⇒ 3√70
⇒ 3 x 8.3666
⇒ 25.0998 ≈ 25.10
The value of the expression 3√70 to the nearest integer will be 25.10.
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Open-Ended Write a problem that could be modeled with y=20(1.1) x
The problem that can be defined by the function is:
A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount and x is the number of time periods.
Consider the modeled function y = 20(1.1)ˣ.
Now, y = 20 × ( 1 + r)ˣ
f(x) = 20 × ( 1 + r)ˣ
Comparing the above equation with A(x) = a( 1 + r)ˣ
The initial amount is 20 and it increases 1 + r = 1.1.
Therefore, r = 0.1 = 10 %
Let's say we are starting a cat breeding company. Initially, we have 20 cats.
So, the problem for the function is:
A cat breeding company has 20 cats initially. The number of cats increases by 10% each year. Write a function for the exponential growth of the number of cats over the years. How many cats will the company have after 10 years?
So, a = 20, x = 10, and r = 10% = 0.1
Therefore,
A(x) = a( 1 + r)ˣ
y = a( 1 + r)ˣ
y = 20( 1 + 0.1 )ˣ
y = 20( 1.1)¹⁰
y = 20 × 2.594
y = 52
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Evaluate each function at the specified value
f(x)=7x-5;x=6
You use 130 feet of fencing to go around a rectangular pool and patio. The length of the area is 9 more than the width. What are the dimensions of the fence?
The dimensions of the fencing is 28 ft and 37 ft respectively.
How to find the dimension of the rectangular fence?He use 130 feet of fencing to go around a rectangular pool and patio.
The length of the area is 9 more than the width.
The dimension of the fence can be found as follows:
Therefore,
perimeter of the rectangular fence = 2(l + w)
where
l = lengthw = widthHence,
l = 9 + w
perimeter of the rectangular fence = 2(w + 9 + w)
perimeter of the rectangular fence = 2(2w + 9)
130 = 4w + 18
130 - 18 = 4w
112 = 4w
w = 112 / 4
w = 28 ft
l = 9 + 28 = 37 ft
Therefore, the width and length of the fencing is 28 ft and 37 ft respectively.
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Suppose that (x₁, y₁) and (x₂, y₂) are values from an inverse variation. Show that x₁/x₂=y₂/y₁.
It can be proved using the method of inverse variation.
What is inverse variation?
In mathematics, inverse variation refers to the relationships between variables expressed as y = k/x, where x and y are two variables and k is a constant. According to this statement, if the value of one item rises, the value of the other quantity falls.
Given,
(x₁, y₁) and (x₂, y₂) are values from an inverse variation.
inverse function of x and y will be -
y1 = k. 1 / x1
k = y1 / x1 ....(1)
y2 = k. 1 / x2
k = y2 / x2 ....(2)
from (1) , (2)
we can say that,
y1 / x1 = y2 / x2
⇒ y2 / y1 = x1 / x2
Hence proved.
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If f(x) = 1 -x, which value is equivalent to f(1)|?
The value corresponding to |f(i)| is √2.
The given function is f(x)=1-x.
Given f(x) = 1 - x
To find the value of |f(i)| we have to substitute x=i.
After substituting this, we get
f(i) = 1 - i
As we all know that, this is an imaginary even function in the form a + ib
The modulus of the imaginary function can be represented as √(a²+b²)
Here a = 1 and b = -1
Now, we will substitute this value in the above formula, we get
|f(i)| = √(1² + (-1)²)
|f(i)| = √(1+1)
|f(i)| = √2
Hence, the value of the given function f(x)=1-x which is equivalent to |f(i)| corresponding value is √2.
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2.39 repeating as a mixed number
which of the following is equal to 16%
Answer:0.16=16%
Step-by-step explanation: [tex]\frac{0.16}{100}[/tex]
the 100 is directly under the point so the zero will cancel out leaving= [tex]\frac{16}{100}[/tex]
And [tex]\frac{16}{100}[/tex] equals to 16%
if we had a value "z", and we'd like to know how much is 16% of "z", well
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of z}}{\left( \cfrac{16}{100} \right)z}\implies 0.16z[/tex]
so we can use the "factor" of 0.16, to get the 16% of any value,
since 0.16 is the decimal representation of the percentage of 16.
hmmm what is 16% of 50 anyway?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 50}}{\left( \cfrac{16}{100} \right)50}\implies 8[/tex]8 out of 50
how much is 16% of 25 anyway?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of 25}}{\left( \cfrac{16}{100} \right)25}\implies 4[/tex]4 out of 25
Let P=(-2,2), Q=(3,4), R=(-2,5) , and S=(2,-8) . What are the component forms of the following vectors? PQ
The components of PQ are given by {5; 2}
The components of a vector in a two-dimensional coordinate system are usually thought of as the x and y components. This can be expressed as V = (vx, vy), where V is a vector. These are part of the vectors generated along the axis.
Suppose an angle θ is formed between the vector V and the x component of the vector. A vector V and its x component (vx) form a right triangle if you draw a line parallel to the y component (vy).
Due to the trigonometric relationship:
cos θ = adjacent side/hypotenuse = vx/V
sin θ = opposite side/hypotenuse = vy/V
where V is the magnitude of vector V.
So, the Component of PQ is Given by
PQ = {Bx - Ax; By - Ay} = {3 - (-2); 4 - 2} = {5; 2}
PQ= {5; 2}
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which is greater 5/2 or 7/4?
Answer:
Comparamos los dos números decimales anteriores, y podemos ver que 2.5 es mayor que 1.75. Por lo tanto, 5/2 es mayor que 7/4
Step-by-step explanation:
Answer:
7/4 because if you divide them both, 7/4's decimal will be greater
4^3+/(3+1)x2 please solve 15 points dude
question is in the picture
The solution to the system of equations using substitution is: x = 3 and y = -4.
How to Solve a System of Equations Using Substitution?Given the system of equations:
-7x - 2y = -13 -----> equation 1
x - 2y = 11 -----> equation 2
Rewrite equation 2
x - 2y = 11
x = 11 + 2y
Substitute x = (11 + 2y) into equation 1
-7(11 + 2y) - 2y = -13
-77 - 14y - 2y = -13
-77 - 16y = -13
-16y = -13 + 77
-16y = 64
y = -4
Substitute y = -4 into equation 2
x - 2(-4) = 11
x + 8 = 11
x = 11 - 8
x = 3
Therefore, the solution to the system of equations using substitution is: x = 3 and y = -4.
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Jenna works for the Parks Department and just completed some maintenance work at the baseball fields in Memorial Park. She needs to drive to the playground at Veteran’s Park next. In which general direction will she drive?
a map of a town showing two parks
A.
southwest
B.
northwest
C.
southeast
D.
northeast
Answer:North west, the roads should have stopped this answer but north alone wasn’t an option so just pretend Jenna is a lawless maniac ig♂️
Step-by-step explanation:
What is the inverse of y=4 x²+5 ? Is the inverse a function?
The inverse of the function y=4 x²+5 is y = √((x-5)/4).
What exactly is a function's inverse?Inverse functions are those that cancel one another out. In other words, if g(x) is f's inverse, then f(g(x)) = g(f(x)) = x. (x). Given an equation for which we want the inverse, we have a fantastic method we can utilize to do this.
Not every function has a counterpart. If f(x) has an inverse, it is clear to see that it will never again have the same value. We give this resource a special name.
A function (f(x)) is said to be one-to-one if each member of the range corresponds to exactly one element of the domain.
Given,
We have a function,
y=4 x²+5
subtracting 5 from each side.
⇒ y - 5 = 4 x²
Divide by 4 and then either
⇒ x² = (y - 5) / 4
⇒ x = √((y-5)/4)
Just change the labels now, x to y.
⇒ y = √((x-5)/4)
So, the inverse of given function is y = √((x-5)/4)
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A teacher wishes to know whether the males in his/her class have more conservative attitudes than the females. a questionnaire is distributed assessing attitudes.
a. is this a sampling or a census?
b. is this an observational study or an experiment?
c. are there any possible sources of bias in this study?
Descriptive statistics is the correct answer.
Descriptive statistics are numbers that are used to summarize and describe data. The word "data" refers to the information that has been collected from an experiment, a survey, a historical record, etc. (By the way, "data" is plural. One piece of information is called a "datum.") If we are analyzing birth certificates, for example, a descriptive statistic might be the percentage of certificates issued in New York State or the average age of the mother. Any other number we choose to compute also counts as a descriptive statistic for the data from which the statistic is computed. Several descriptive statistics are often used at one time to give a full picture of the data.
Descriptive statistics are just descriptive. They do not involve generalizing beyond the data at hand. Generalizing from our data to another set of cases is the business of inferential statistics, which you'll be studying in another section. Here we focus on (mere) descriptive statistics.
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Graph the piecewise-defined function. What are the domain and range? Over what intervals is the function increasing or decreasing?
2x + 5, -6 ≤ x ≤ -2 2x²-7, -2 < x < 1 1 ≤ x ≤ 3
a. f(x) = H - 4 - X, 1. -8 8 4 -4 O -4 H -8 4 X 1.00 8
Answer:
X" (and any subsequent words) was ignored because we limit queries to 32 words.
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Pakistan
Calculate the volume of the cylinder below
Use natural logarithms to solve each equation. e x=18
2.89 is the value of x in equation [tex]e^x[/tex] = 18 solved by using natural logarithms.
We have been asked to find x in [tex]e^x[/tex] = 18 using natural logarithms
⇒ [tex]e^x[/tex] = 18
⇒ x = ㏑ (18)
⇒ x = 2.89
What is a natural logarithm?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.
The power to which e would need to be raised in order to equal x is the natural logarithm of x.
For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.
Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.
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Correct questionUse natural logarithms to solve each equation.
[tex]e^x[/tex] = 18
I need help can someone help me.
10 order of small popcorn Should be made to keep the cost same at both the theaters
The theater P charges Admission fee of $10 and small popcorn order of $4.55
The theater Q charges Admission fee of $8 and small popcorn order of $4.75
We need to find the number of order of small popcorn so that the cost remain same
Let the number of small popcorn order be x
Then we can form the algebraic equation as
10 + 4.55x = 8 + 4.75x
now we should simplify the equation
10- 8 = 4.75x-4.55x
2= .2x
x = 2/0.2
x = 10
Hence , 10 order of small popcorn Should be made to keep the cost same at both the theaters
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What is the value of the expression 38x − 17 if x is equal to −5?
Answer:
-207
Step-by-step explanation:
38x - 17
38(-5) - 17
-190 - 17
-207
*Please mark brainliest answer
Answer:-173
Step-by-step explanation:
38x - -17
38 multiplied by -5 equals -190
-190 - -17 equals -173
20 POINTS! Can someone help me? The question is located below!
A. 12cm x 8cm
B. 12cm x 9cm
C. 13cm x 8cm
D. 13cm x 9cm
The dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.
What are Whole Numbers?Whole numbers are numbers that do not have any fractional part and represents a whole quantity.
What are Mixed Numbers?A mixed number consist of an whole number and a proper fraction or fractional part.
How to Convert Mixed Numbers to Improper Fractions?Given the dimensions of the rectangular photo as, 12 11/16 cm by 8 3/4cm, convert each dimension to improper fractions:
12 11/16 would be converted to 203/16
8 3/4 would be converted to 35/4
203/16 = 12.6875 ≈ 13 [nearest whole number of cm]
35/4 = 8.75 ≈ 9 [nearest whole number of cm]
Therefore, the dimensions of the rectangular photo frame, rounded to the nearest whole number of centimeters are: D. 13cm x 9cm.
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d.
Rule: Output =
Input
-2
0
3
4
8
er
Process
Ox
3x
4x
8+
Output
-15
-5
10
15
35
Answer:
20000fish deeen of fatherlaal yyyeeeeepee classes link hahahaha nnooooo bb bot play fff 15 sec wait ok now ans free fire max ok u noobbot
15 A railway station has two platforms. Trains stop at the northbound platform every 10 minutes. Trains stop at the southbound platform every 18 minutes Two trains stopped together at 1512 (a) Work out the next time two trains stop together at this station.
The answer is 190m.
The faster train is 160 m long and crosses a lamp post in 12 seconds.
The speed of the faster train = 16012 = 403 m/s
Given that, the speed of the other train is 6 km/hr (53 m/s) less than the faster one. [we can convert speeds from km/h to m/s by multiplying with 5/18]
The speed of the slower train = 353 m/s.
Given that, the two trains cross each other in 14 seconds when running in opposite directions along parallel tracks.
tracks.
Relative speed = total length of two trains time taken to cross each other
25m/s = 160+ length of second train 14
Length of the second train = 190m.
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What is the coordinate of G' if triangle E'F'G' is created by dilating EFG with factor of 4 about the origin?
Answer:
G' (8, - 8 )
Step-by-step explanation:
since the dilatation is centred at the origin then multiply each of the coordinates by the scale factor of 4
G (2, - 2 ) → G' (4(2), 4(- 2)) → G' (8, - 8 )
Solve each equation.
3x =9
Solution of this polynomial equation is x = 3
What are polynomial equations ?In mathematics, polynomial equation can be defined as the equation which consist of coefficient, variables and exponents. A polynomial equation has positive numbers as their exponent which is also known as its degree. All the equations such as quadratic equation, cubic equation which has non negative number as their powers are part of polynomial equation.
Types of polynomial equations :
Monomial equationBinomial equationCubic EquationsLinear Polynomial Quadratic PolynomialSome examples of polynomial equation are :
2x+53x = 93x² + 5x+19(x-3)³According to question,
3x = 9
=> 3x / 3 = 9 /3
=> x = 3
Thus solution for given equation is x = 3.
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Will mark branilest
The function f(x) = ( x + 7)³ - 8 will shift left 7 units along x axis and will shift down 8 units along y axis to its parent function g(x) = x³.
What is translation?By translation, we can stretch, shrink and shift graphs along the x-y coordinate.
We know a parent function is a function that is in its simplest form without any translation.
Given f(x) = (x + 7)³ - 8 and its parent function is g(x) = x³.
Now let us break this function f(x),
f(x) = ( x+ 7)³ implies x + 7 = 0 ⇒ x = -7.
So, x will shift 7 units to the left along the x-axis.
f(x) = ( x + 7)³ - 8, This will shift the function down 8 units along y-axis.
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How many pieces of string each measuring 10cm can be cut from a length measuring 2.5metres
I need this with overtime pay.
Kerry worked 46 hours last week. His hourly rate is $9.60. He has the following deductions taken from his pay: federal income tax at the rate of 10 percent, Social Security tax at the rate of 6.2 percent, Medicare tax at the rate of 1.45 percent, health insurance premiums of $12.20, and union dues of $9.50. Kerry’s net pay for last week was $. Hide Feedback Incorrect Check My Work Feedback Gross pay includes regular hours times regular pay, plus overtime hours times overtime pay. The overtime pay rate is 1½ times the regular rate of pay. Deductions—both required and voluntary—are subtracted from gross pay to compute net pay. (Round to the nearest cent for all calculations.)
Answer:
here to try to help!
Step-by-step explanation:
346.96 why? Kerry was not payed at the overtime for extra hours hope it helped!