Y is 2.25 when x is 9.
What is direct proportional?The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolized by the proportional sign (). According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant. The generic form of the direct proportion equation is also y = kx. where k is the proportionality constant.
Given Data
If x and y vary directly and y is 24 when x is 6, find y when x is 9.
It is direct proportional
So,
y = kx
To find constant,
k = [tex]\frac{y}{x}[/tex]
x = 6 and y = 24
k = [tex]\frac{6}{24}[/tex]
k = [tex]\frac{1}{4}[/tex]
When x = 9,
k = [tex]\frac{1}{4}[/tex]
y = kx
y = [tex]\frac{1}{4}[/tex](9)
y = [tex]\frac{9}{4}[/tex]
y = 2.25
Y is 2.25 when x is 9.
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WS bisects ∠BWV. m∡BWS = 36°. What is m∡BWV?
a. 72
b. 16
c. 54
d. 144
WS bisects angle BWV, m ∠BWS = 36° , then the measure of angle
m ∠BWV is equal to 72°.
As given in the question,
Measure of given angle :
m ∠BWS =36° ____(1)
let 'x' be the measure of angle BWV
WS bisects angle BWV.
⇒ m ∠BWS= m ∠SWV
⇒ m ∠SWV=36° ____(2)
Also , m ∠BWV is equal to the sum of the measure of ∠ BWS and ∠SWV.
⇒ m ∠BWV =m ∠BWS + m ∠SWV
Substitute the value of m∠ BWS and m ∠SWV from (1) and (2),
⇒ m ∠BWV=36° + 36°
⇒m ∠BWV=72°
Therefore, WS bisects angle BWV, m ∠BWS=36° , then the measure of angle m ∠BWV is equal to 72°.
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Jasmine drives every morning to her office that is 12 miles from her home.
Suppose Jasmine drives from home to the office in 20 minutes. Use this information and part (b) to write an equation
100 points please answer!!!!!!!!!
help
Answer:
16
Step-by-step explanation:
gof(-6) means g(f(-6))
f(-6)=-(-6)-2
=6-2=4
g(4)=4^2=16
Joshua is driving to the store
solve the equation for x pls
Answer:
-0.54, 5.54
Step-by-step explanation:
[tex]x^2-5x-3=0 \\ \\ x=\frac{5 \pm \sqrt{25+12}}{2} \\ \\ x=\frac{5}{2} \pm \frac{\sqrt{37}}{2} \\ \\ x \approx -0.54, 5.54[/tex]
The two rectangles shown are congruent.
What transformation for Rectangle A would result in Rectangle B?
A
reflection across the x-axis
B
reflection across the y-axis
C
translation, 4 units up
D
translation, 2 units down
The transformation for Rectangle A which would result in Rectangle B is: A. reflection across the x-axis.
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Mathematics, a reflection over the x-axis would maintain the same x-coordinate (10 → 10) while the sign of the y-coordinate changes from positive to negative (4 → -4) . Therefore, a reflection over the x-axis is given by this rule:
(x, y) → (x, -y) = (10, 4) → (10, -4).
In conclusion, a reflection across the x-axis would transform Rectangle A to Rectangle B.
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Which expression has a value of 74?
Responses
(75−5)×(1+4)
open parenthesis 75 minus 5 close parenthesis times open parenthesis 1 plus 4 close parenthesis
75−5×(1+4)
75 minus 5 times open parenthesis 1 plus 4 close parenthesis
(75−5)×1+4
open parenthesis 75 minus 5 close parenthesis times 1 plus 4
75−(5×1+4)
The expression that will give a value of 74 is C. (75 - 5) × 1 + 4.
What is an expression?It should be noted that an expression is used to how the relationship between the variables that are expressed in the data or information given.
In this case, we want to find the expression that will give a value of 74. This will be :
= (75 - 5) × 1 + 4
= 70 × 1 + 4
= 70 + 4
= 74
The correct option is C.
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Answer: yes then no
Step-by-step explanation:
0.80divide by 50.i need help
The correct answer to the task 0.80 divided by 50 given above is 0.016
Division of numbersWhen we are trying to find the number of times a number can be obtained in another number, we use the term "division" to describe the mathematical expression. The division can be represented as ÷
For instance, the division of 0.80 by 50 is represented and solved below:
0.80 ÷ 50 = 0.016
It can also be represented like this:
0.80 / 50 = 0.016.
Another example of division of numbers is:
8/4 = 2
10 ÷ 2 = 5
So therefore, from the explanation given above we can confirm that when 0.80 ÷ 50, the answer is 0.016.
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you are the newly appointed assistant administrator at a local hospital, and your first project is to investigate the quality of the patient meals put out by the food-service department. you conducted a 10-day survey by submitting a simple questionnaire to the 400 patients with each meal, asking that they simply check off that the meal was either satisfactory or unsatisfactory. for simplicity in this problem, assume that the response was 1,000 returned questionnaires from the 1,200 meals each day. the results are as follows:
Using the z-distribution, the 95% confidence interval for the proportion of unsatisfactory meals is given by:
(0.0553, 0.0647).
What is a confidence interval of proportions?A confidence interval of proportions is given by the following rule:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The estimate and the sample size of the interval are given as follows:
[tex]\pi = \frac{600}{10000} = 0.06, n = 10000[/tex]
The lower bound of the interval is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.06 - 1.96\sqrt{\frac{0.06(0.94)}{10000}} = 0.0553[/tex]
The upper bound of the interval is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.06 + 1.96\sqrt{\frac{0.06(0.94)}{10000}} = 0.0647[/tex]
Hence the interval in (LCL, UCL) format is:
(0.0553, 0.0647).
What is the missing information?The problems asks for the 95% confidence interval of unsatisfactory meals, considering that, out of 10000 meals, 600 were unsatisfactory.
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what 3 numbers can equal 20 and 300 in multiplication trying to help sister
Answer:
Here are all 3 number combinations that you can multiply to get 300: 300 × 1 × 1 = 300 150 × 2 × 1 = 300 150 × 1 × 2 = 300 100 × 3 × 1 = 300:
a^4 b^2 c^3 d by acbd
show with steps
pls tell fast i will mark you brainlist.
The simplified form of the given expression ( a⁴b²c³d ) / acbd is equal to (a³bc² ) .
As given in the question,
Given expression :
( a⁴b²c³d ) / acbd
Simplified form of the given expression using rules of power and exponents:
Since this is division of algebraic fractions, the index (power or exponent) of the like literals in the numerator and denominator are to be subtracted. Thus index of variable a reduces from 4 to 1. Similarly index of variable b reduces from 2 to 1 and that of c reduces from 3 to 2. Lastly variable d remains in the denominator as there is no corresponding factor in the numerator.
( a⁴b²c³d ) / acbd
= (a⁴⁻¹ )(b²⁻¹ )(c³⁻¹ )(d¹⁻¹)
= a³ bc²d⁰
= a³bc²
Therefore, the simplified form of the given expression ( a⁴b²c³d ) / acbd is equal to (a³bc² ) .
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14. Matthew bought 2 movie tickets for $11, and Rosa
bought 7 movie tickets for $38.50. What is the
constant of proportionality?
When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.
Here x be the proportionality constant its value 5.5.
What is meant by proportionality constant ?The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. Constant ratio, constant rate, unit rate, constant of variation, and even rate of change are other names for the constant of proportionality.When two amounts are proportionate, they fluctuate at the same rate, maintaining the constancy of their relationship.In mathematics, we use the constant of proportionality to compute the rate of change and identify whether we are working with direct variation or inverse variation.Matthew bought 2 movie tickets for $11,
Rosa bought 7 movie tickets for $38.50.
let the value of per ticket is x
2x = 11 and 7x = 38.5
7x- 2x = 38.5 -11
x = 5.5
here x be the proportionality constant its value 5.5.
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find x : 5( x + 4 ) - 3^2 = 2^4
Answer:x=1
Step-by-step explanation:
you would have to distribute the 5 into the (x+4)
then it would be
5x+20-3^2=2^4
then do the exponents
5x+20-9+16
then add 9 by both sides
5x+20=25
then subtract 20 on both sides
5x=5
then divide 5 on both sides
x=1
then check your work by putting 1 for x and you get 2^4=16
Answer:
x = 1Step-by-step explanation:
find x :
5( x + 4 ) - 3^2 = 2^4
5x + 20 - 9 = 16
5x = 16 - 20 + 9
5x = 5
x = 5 : 5
x = 1
----------------
check
5(1 + 4) - 3^2 = 2 ^4
25 - 9 = 16
16 = 16
the answer is good
In the diagram below, the man on the diving board is 6 ft. tall and the angle of elevation from the man in the water (angle 4) to the man on the diving board is 40. How far apart are the two men? Round your answer to the nearest tenth.
a a a a a a a a a a a a a a a aa a a
Convert 62 miles/hour to feet/second (5280ft-1 mile)
In mathematics, an operation is a function that transforms 0-n operands or parameters into a known output value. The number of operands affects how complicated the operation is. 90.95 feet per second equates to 62 miles per hour.
What is mathematical operation?An operation in mathematics is the function that converts 0–n parameters or operands into definite output value. The complexity of operation depends on how many operands there are.
The operations that are the most frequently studied are binary operations (i.e., operations of the arity 2), which include addition and multiplication, and the unary operations (i.e., operations of the arity 1), which include additive inverse and the multiplicative inverse. A zero-arity operation, also known as nullary operation, is a constant. An illustration of ternary operation, also known as an operation of arity 3, is the mixed product.
Usually, it is considered that arity is constrained. Even so, the infinitary operations are occasionally considered, in which case "normal" finite dimensionality operations are referred to as finiteary operations.
A partial operation is described as being similar to operation but using a partial function in place of a function.
1miles/hour= 1.467feet/second
62 miles/ hours= 62*1.467feet/second
= 90.95 feet/second
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1 plus 2 = ?
2 plus 3= ?
3 plus 4=?
4 plus 5=?
5 plus 6=?
Answer:
1 + 2 = 3
2 + 3 = 5
3 + 4 = 7
4 + 5 = 9
5 + 6 = 11
Step-by-step explanation:
Linear or nonlinear?innedd it
The given function y = x³ is not a linear function but a cubic function.
What is defined as the linear function?A straight line just on coordinate plane is represented by a linear function. A linear function has the equation f(x) = mx + b, where m and b are real numbers.'m' represents the slope of the line, 'b' represents the y-intercept of the line, and 'x' represents the independent variable.The dependent variable is 'y' (or f(x)). The graph of the a linear function f(x) = mx + b is shown below.when m > 0, its increasing linea decreasing line when m < 0, and a horizontal line when m = 0.For the given function;
y = x.x.x
This, can be written, after adding the power of x as;
y = x³
Now, put x = 1; y = 1
Put x = 2; y = 8
Put x = 3; y = 27
This will not form a straight line but a cubical curve.
As, the function is not changing linearly but cubical.
Thus, the function is not linear function.
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a special deck of cards has 10 cards. four are green, three are blue, and three are red. when a card is picked, the color of it is recorded. an experiment consists of first picking a card and then tossing a coin.a. how many elements are there in the sample space?
The number of elements that are there in the sample space is 6.
What is sample space?It should be noted that sample space simply means the collection or the set of possible outcomes that are in the random experiment.
From the information, in the special deck of cards has 10 cards. four are green, three are blue, and three are red.
Therefore, the sample space will be:
S = GH, GT, BH, BT, RH, RT
It should be noted that H and T represents the head and tail.
Therefore, there are 6 elements.
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3. On a flash drive, 800 megabytes out of 1000 megabytes are used. Write the
amount occupied as a percent.
Answer:
80%
Step-by-step explanation:
you're occupying 800 out of 1000
the way to write this mathematically is to write: 800/1000,
which equals 0.8
then to make this a percentage you x100
and your answer is 80%
Multiply (3-i) (7+2i)
Answer:
23-i
Step-by-step explanation:
Multiply using the FOIL method and after that combine the real and imaginary parts of the expression.
Line ℓ has equation y=7. Find the distance between ℓ and the point j (-5,-1)
The Distance between line ℓ and the point j (-5,-1) is 8units.
The distance between a point PP and a line LL is the shortest distance between PP and LL; it is the minimum length required to move from point PP to a point on LL. In fact, this path of minimum length can be shown to be a line segment perpendicular to LL. The distance d can then be defined as the length of the line segment that has PP as an endpoint and is perpendicular to LL.
We know that the distance d between a point (x1,y1) and a line having equation in form of ax+by+c=0 can be expressed as,
[tex]d = \frac{|ax1+by1+c|}{\sqrt{(a^2+b^2)} }[/tex]
So, we have given that equation of line
y = 7
y-7=0
Point j = (-5,-1)
So, Distance between point j and line = d
d = [tex]\frac{|0(-5)+1(-1)-7|}{\sqrt{(0^2+1^2)} }[/tex]
d = [tex]\frac{8}{\sqrt{1} }[/tex]
d = 8 units
Therefore, The point j is at a distance of 8 units from the line ℓ.
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i need help on this, thanks
Answer: m<1 = 151 m<2 = 29 m<3 = 151
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:\angle1 = 151° [/tex]
[tex]\qquad \tt \rightarrow \: \angle2 = 29 \degree[/tex]
[tex]\qquad \tt \rightarrow \: \angle3 = 151 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We can use angle pairs of intersecting lines to find the remaining angles :
[tex]\qquad \tt \rightarrow \: \angle4 + \angle1 = 180 \degree[/tex]
[ linear pair ]
[tex]\qquad \tt \rightarrow \: 29 \degree + \angle1 = 180 \degree[/tex]
[tex]\qquad \tt \rightarrow \: \angle1 = (180 - 29) \degree[/tex]
[tex]\qquad \tt \rightarrow \: \angle1 = 151\degree[/tex]
next,
[tex]\qquad \tt \rightarrow \: \angle2 = \angle4[/tex]
[ by vertical opposite angles ]
[tex]\qquad \tt \rightarrow \: \angle2 = 29 \degree[/tex]
and,
[tex]\qquad \tt \rightarrow \: \angle3 = \angle1[/tex]
[ by vertical opposite angles ]
[tex]\qquad \tt \rightarrow \: \angle3 = 151 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
what is the cost of buying 4kg of potatoes at 50k per kg
Answer:
200k
Step-by-step explanation:
4x50=200
The cost of buying 4 kg of potatoes at 50k per kg is 200k.
To calculate the cost of buying 4 kg of potatoes at 50k per kg, you can simply multiply the weight (4 kg) by the price per kilogram (50k).
Cost = 4 kg * 50k per kg
Now, perform the calculation:
Cost = 200k
So, the cost of buying 4 kg of potatoes at 50k per kg is 200k.
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8x-5>=6x-1 or 4+4x<=3x-3
Interval Notation and Graph
(-7,∞) & (−∞, 1/2] are the interval notation.
What is interval notation in math?
Continuous sets of real numbers can be represented by the integers that bound them using interval notation. When written, intervals resemble ordered pairs in several ways. They don't necessarily indicate a particular point, though. They are intended to serve as a shortened manner of expressing an inequality or system of inequalities.8x-5>=6x-1 or 4+4x<=3x-3
8x-5 ≥6x-1
8x - 5 ≥ 6x - 1
8x - 6x ≥ 5 - 1
2x ≥ 1
x ≥ 1/2
Therefore, x could be any number less than or equal to 1/2. In interval notation, this looks like
(−∞, 1/2]
4+4x ≤ 3x-3
4 + 4x ≤ 3x - 3
4x - 3x ≤ -3 - 4
x ≤ -7
Therefore, x could be any number less than -7 , but x couldn't be -7, since that would make the two sides of the inequality equal. In interval notation, this looks like:
(-7,∞)
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a) Work out (8 × 10³) × (2 x 10¹)
Give your answer in standard form.
Answer:
8000 times 2x times 1
Step-by-step explanation:
(8 times 10^3) (2xtimes 10^1)
8 times 10^3=8000
= 8000 times 2x times 1
= 160000x
could i get a hand here please
Answer:
4 inches
Step-by-step explanation:
the cube has a volume (V) calculated as
V = s³ ( s is the side length )
given V = 64 , then
s³ = 64 ( take the cube root of both sides )
s = [tex]\sqrt[3]{64}[/tex] = 4
side length is then 4 inches
The mean number of people per day visiting a museum in July was 160. If 20
more people each day visited the museum in August, what was the mean
number of people per day visiting in August?
• A. 640
• B. 160
• C. 620
• D. 180
The mean number of people per day visiting in August will be equal to option (D) 180.
Mean number of students in July = 160
20 more people visited the people each day in the month of August.
As, there is a constant increase in the number of who are visiting the museum in August each day that is 20 people, the mean will also increase by the same number that is 20 and will be:
Mean number of people per day visiting in August = 160 + 20
Mean number of people per day visiting in August = 180
Therefore, we get that, the mean number of people per day visiting in August will be equal to option (D) 180.
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A car drives 283.5 miles in 4.5 hours. Assuming that the distance traveled directly with the time traveld
Answer:
I'm guessing the whole question is: "A car drives 283.5 miles in 4.5 hours. Assuming that the distance traveled directly with the time traveled, how far will the car travel in 7 hours?"
Step-by-step explanation:
If so, here's the answer:
441 miles will be traveled in 7 hours
You could find the speed in mph
To do that, divide 283.5 by 4.5 which gives us 63
because [tex]\frac{283.5 miles}{4.5 hours}[/tex] divide to get the 4.5 hours into 1 hour so, [tex]\frac{283.5/4.5}{1}[/tex]
63 mph times 7 hours = 441
10. A theme park has a ride that is located in half a sphere. The ride goes around the widest part of the sphere, which has a circumference of 514.96 yards. What is the surface area of the sphere? Estimate to the nearest hundredth using 3.14 for pie
The surface area of the sphere is 84453.44 yards².
We are given that:
the ride goes around the widest circle of the sphere whose circumference is = 514.96 yard.
The widest circle of the sphere is the plane contains the sphere's center
The circumference of the widest circle is:
C = 2 π r
where r is radius of the sphere.
The surface area of the sphere is defined as:
A = 4 π r²
where r is radius of the sphere.
So, we get that:
514.96 =2 π r
514.96= 2 × 3.14 × r
r = 514.96 ÷ (2 × 3.14)
r = 514.96 ÷ 6.28
Surface Area A = 4 π r²
A = 4 × 3.14 × (514.96 ÷ 6.28) × (514.96÷ 6.28)
A = 84453.44 yards²
Therefore, we get that, the surface area of the sphere is 84453.44 yards².
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Find the difference and quotient of 8 and 4
FINDING THE DIFFERENCE WE SUBRACT
[tex]8 - 4 \\ = 4[/tex]
FINDING THE QUOTIENT WE DIVIDE
[tex]8 \div 4 \\ = 2[/tex]
HOPE THIS HELPS