Answer:
If you have a 77.2% and you got 34% on a test and it’s worth 60% of your grade, your percentage grade would be 63.2%.
Together, the areas of the rectangles sum to 30 square centimeters.
Solution
Area of the rectangle = length x breadth
A. Write an equation to showing relationship between x and y:
[tex]\begin{gathered} \text{Area = length x breadth} \\ A=l\text{ x b} \\ A_1=3x \\ A_2=2y \end{gathered}[/tex][tex]\begin{gathered} A_1+A_2=30_{} \\ 3x+2y=30 \end{gathered}[/tex]The equation for the relationship between x and y is
3x + 2y = 30
Rewrite the following rectangular equation in polar form assuming a is a real constant.x2 + y2 = 11a=
Answer:
The polar form is
r = √11a
Explanation:
The given equation is
x^2 + y^2 = 11a
Recall,
x = rcosθ
y = rsinθ
By substituting these values into the equation, we have
(rcosθ )^2 + ( rsinθ)^2 = 11a
r^2cos^2θ + r^2sin^2θ = 11a
r^2cos^2θ + r^2sin^2θ - 11a = 0
By factorizing r^2, we have
r^2(cos^2θ + sin^2θ) = 11a
Recall, cos^2θ + sin^2θ = 1
Thus, we have
r^2 = 11a
Taking the square root of both sides,
r = √11a
The polar form is
r = √11a
Lines AB and CD are straight lines. Find x and y. Picture attached/
By using properties of angles, it is obtained that
x = 18.5°, y = 37°
Angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.
Here,
[tex]\angle COF = 90^{\circ}\\[/tex]
By the problem,
4x + 90 + 16 = 180 [Angle on a straight line]
4x + 106 = 180
4x = 180 - 106
4x = 74
[tex]\\x = \frac{74}{4}\\x = 18.5^{\circ}[/tex]
AB and CD are straight lines
[tex]\angle DOB = 16^{\circ}[/tex] [Vertically opposite angle]
By the problem,
90 + 2y + 16 = 180 [ Angle on a straight line]
2y + 106 = 180
2y = 180 - 106
2y = 74
[tex]y = \frac{74}{2}\\y = 37^{\circ}[/tex]
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Question content area top
Part 1
A ramp forms the angles shown to the right. What are the values of a and b?
Answer:
A=151
B= 29
Step-by-step explanation:
Find the area of the polygon. (hint: you need to solve for missing apothem or sides).Also round the area to the nearest whole number
Solution
The hexagon given is a regular hexagon. With apothem of 15 in
Area of a hexagon =
[tex]\begin{gathered} =\frac{1}{2}\times a\times P \\ \text{where a = apothem} \\ p=\text{perimeter of the hexagon} \end{gathered}[/tex]Let us calculate the perimeter of the hexagon
From the triangle above,
[tex]\begin{gathered} \text{tan 60=}\frac{15}{x} \\ x\text{ tan 60 = 15} \\ x=\frac{15}{\tan 60} \\ x=5\sqrt[]{3} \end{gathered}[/tex][tex]\text{The side length of the hexagon = 2x = 2(5}\sqrt[]{3})\text{ = 10}\sqrt[]{3}\text{ in}[/tex][tex]\text{The perimeter of the hexagon = 6 x 10}\sqrt[]{3}\text{ = 60}\sqrt[]{3}\text{ in}[/tex][tex]\begin{gathered} \text{Area of the hexagon = }\frac{1}{2}\times a\times P \\ =\frac{1}{2}\text{ x 15 x 60}\sqrt[]{3} \\ =779.42in^2 \\ \\ Hence,\text{ the area of the polygon is }779in^2\text{ (to nearest wholw number)} \end{gathered}[/tex]A car is traveling at a steady speed. It travels 2 1/3 miles in 3 1/2 minutes. How far will it travel in 49 minutes? In one hour?
In 49 minutes the car will travel 2/147 miles
In 60 minutes the car will travel 1/90 miles
How to determine how far the car will travel in 49 minutesThe concept of average speed is used here. The formula is
= distance covered / time
= 2 1/3 / 3 1/2
= 2.3333 / 3.5
= 2/3
= 0.6667 miles per minutes
In 49 minutes
2/3 = distance / 49
distance = 2/3 / 49
distance = 2/147
= 0.0136 miles
In one hour = 60 minutes
distance = 2/3 / 60
distance = 1/90
= 0.0111 miles
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In 2005, 10.9 out of every 50 employees at a company were women. If there are 41,646 total company employees, estimate the number of women.
Number of women's are 9,078.83.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
In 2005, 10.9 out of every 50 employees at a company were women.
Now,
Since, In 2005, 10.9 out of every 50 employees at a company were women.
Let number of women's in 41,646 total company employees = x
So, We can formulate by the definition of proportion as;
⇒ 10.9 / 50 = x / 41,646
Solve for x as;
⇒ 10.9 × 41,646 / 50 = x
⇒ x = 9,078.83
Thus, Number of women's are 9,078.83.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
based on historical data, your manager believes that 35% of the company's orders come from first-time customers. a random sample of 62 orders will be used to estimate the proportion of first-time-customers. what is the probability that the sample proportion is less than 0.28?
The probability of the company's order from first-time customers with the sample proportion less than 0.28 will be 0.6103.
Total percent of company’s orders from first-time customers are 35%
Probability of the company's orders from first-time customers are 35/100 = 0.35.
Total number of customers in the random sample is 62.
Minimum given probability of company’s order from first time customers is 0.28
And the minimum probability of company’s order not from first time customers will be 1 - 0.28 = 0.72
Therefore,
As per the given question, Let P(z<0.28) is the required probability, where
Z = (0.28 - 0.35)/sqrt(0.28x0.72/62)
= (0.28 - 0.35)/sqrt(0.28x0.0112)
=(0.28 - 0.35)sqrt(0.003250)
= (-0.07)/sqrt(0.003250)
= -0.07/0.057
= -1.228
From the z-score, we can get P( z<0.28 ) = 0.6103 ( From standard normal table )
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Write each equation in slope intercept form.
12x + 4y = 8
This is a way we can organize a linear equation:
[tex]y=mx+b[/tex]
m = slopeb = y-interceptSolving the QuestionWe're given:
[tex]12x + 4y = 8[/tex]
To organize this equation in slope-intercept form, we have to focus on isolating y:
[tex]12x + 4y = 8\\4y = - 12x +8\\y = - 3x +2[/tex]
Answer[tex]y = - 3x +2[/tex]
The answer is y= negative 3 plus 2
Answer these two questions
For PART A: the height of the pole in the right angle triangle is 30 ft and the correct option is C
For PART B: the lenght of wire 1 in the right angle triangle is 45 ft and the right option is D
What is a right angle triangle?A right-angled triangle is a polygon of three sides having one angle as 90 degrees(right angle).
Part A
To calculate the height of the pole in the right angle triangle, we use the formula below.
Formula:
tan∅ = opposite/adjacentFrom the diagram,
Given:
∅ = 41°Opposite = Height of the pole = PAdjacent = 34 ftSubstitute these values into equation 1 and solve for P
tan41° = P/34P = 34×tan41°P = 29.55P ≈ 30 ftPart B
Similarly, fine the length of wire 1, we use the formula below.
Formula:
cos∅ = Adjacent/Hypotenus.......... Equation 2From the diagram,
Given:
Hypotenus = Wire 1 = x∅ = 41°Adjacent = 34 ftSubstitute these values into equation 2 and solve for x
cos41° = 34/xx = 34/cos41°x = 45.05x ≈ 45 ftHence, the height of the pole is 30 ft and the lenght of wire 1 is 45 ft.
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Use the future value formula to find the indicated value.FV = $3648, n = 22; i = 0.08; PMT = ?PMT =?(Round to the nearest cent.)
To calculate the periodic payment (PMT) we use the following formula:
[tex]\text{PMT}=\frac{FV\times i}{(1+i)^n-1}[/tex]Where "FV" is the Future Value, "i" is the interest rate, and "n" is the number of periods. Replacing the known values we get:
[tex]\text{PMT}=\frac{3648\times0.08}{(1+0.08)^{22}-1}[/tex]Solving the operations:
[tex]\text{PMT}=52.68[/tex]In ️FGH, f=65 inches, g=48 inches and h=70 inches. find the measure of
Let's take a look at our triangle:
Using the law of cosines, we'll get that:
[tex]G^2=F^2+H^2-2FH\cos \angle G[/tex]Solving for angle G, we'll get:
[tex]\begin{gathered} G^2=F^2+H^2-2FH\cos \angle G \\ \rightarrow2FH\cos \angle G^{}=F^2+H^2-G^2 \\ \rightarrow\cos \angle G=\frac{F^2+H^2-G^2}{2FH} \\ \\ \rightarrow\angle G=\cos ^{-1}\frac{F^2+H^2-G^2}{2FH} \end{gathered}[/tex]This way,
[tex]\begin{gathered} \angle G=\cos ^{-1}\frac{65^2+70^2-48^2}{2(65)(70)} \\ \\ \Rightarrow\angle G=41 \end{gathered}[/tex]PLEASE I NEED HELP RIGHT AWAY
What is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1) ?
Responses
y+4=11/6(x+1)
=
y+1=6/11(x+4)
y−1=6/11(x−4)
y+1=6/7(x+4)
y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The given two points are (7, 5) and (−4, −1)
m=-1-5/-4-7
=-6/-11
=6/11
The point slope intercept form is y- y₁=m(x-x₁) through (-4,-1)
y-(-1)=6/11(x-(-4))
y+1=6/11(x+4)
Hence, y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).
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The table compares the time at which Layne got on the bus to school (in minutes after 8am) and the duration of the ride(in minutes after 8 am) and the duration of the ride(in minutes), for several days.Can the duration of the ride be represented as a function of the time layne got on the bus?
ANSWER
Yes, it can.
EXPLANATION
First of all, let us sort the data according to increasing value:
Time (minutes) 18 20 20 22 22 23 25 30
Duration (minutes) 38 40 42 41 42 44 47 52
As we can already see, the duration of the ride seems to increase as the amount of time after 8 am that she got on the bus.
This means that the Duration of the ride and the time Layne got on the bus have a linear relationship and so, YES, the duration of the ride can be represented as a function of the time Layne got on the bus.
What is the value of the missing exponent in the equation 652 : 10- = 0.652?
Given the following expression:
[tex]\frac{652}{10^{^-}}=0.652[/tex]notice that the right side of the equation has a decimal number that goes up to the thousandth, therefore, the missing exponent in the equation is 3, since:
[tex]\frac{652}{10^3}=\frac{652}{1000}=0.652[/tex]Milo can run 12 miles in 60 minutes. He needs to reduce his time by 19%. Approximately how many minutes does he have to take off his time? Round to the nearest whole number.
Milo needs to cover 12 miles in 48.6 minutes, as the percentage.
What is percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
Milo can run 12 miles in 60 minutes.
She needs to reduce the time by 19%
So we have to calculate the 19%of 60
= 19/100* 60
=57/5 minutes
= 11.4
So the time he needs to achieve will be 60-11.4 = 48.6 minutes.
Hence, he needs to cover 12 miles in 48.6 minutes.
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2. Identify the vertex from the quadratic function y=-5(x-6)^2+8 *
The given function is
[tex]y=-5(x-6)^2+8[/tex]This equation represents a parabola which is expressed in its vertex form
[tex]y=a(x-h)^2+k[/tex]Where (h,k) is the vertex. Using this rule, the vertex of the given parabola would be (6,8).
Therefore, the answer is (6,8).Annie wants to arrange several plates of fruit so that each plate
has the same number of apples and the same number of apricots.
What is the greatest number of plates Annie can arrange if she
plans to use 8 apples and 20 apricots? How many apples and
how many apricots will be on each plate?
The greatest number of plates Annie can arrange if she plans to use 8 apples and 20 apricots is 4 plates.
The number of apples Annie can arrange on each plate is 2The number of apricots Annie can arrange on each plates is 5What is the greatest number of plates Annie can arrange?Number of apples = 8Number of apricots = 20To find the greatest number of plates Annie can arrange, find the greatest common factor of and 20;
8 = 1, 2, 4, and 8
20 = 1, 2, 4, 5, 10, and 20
The greatest common factor of 8 and 20 is 4
Number of apples on each plate = 8/4
= 2
Number of apricots on each plate = 20/4
= 5
In conclusion, the greatest number of plates is 4 consisting of 2 apples and 5 apricots each.
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Answer:
Step-by-step explanation:
i am also confused with this one so...
hehe
hehe
hehe
I need help again, please.
Answer:
:-f(x)=x²-2x-24
Step-by-step explanation:
according to the rules of polynomial
f(-4) is the same thing as (x+4)
f(6) is the same thing as (x-6)
how?
x+4=0; x=-4
x-6=0; x=6
(x+4)(x-6)
x²-6x+4x-24
x²-2x-24
:-f(x)=x²-2x-24
award me
What is a proportional relationship in YOUR OWN WORDS
If all of the ratios of the variables are equal, then there is a proportional link between the two variables.
Explain about the proportional relationship?One variable is usually a constant value multiplied by the other in proportional interactions. The proportionality constant is the name given to the constant value.
A set of equal ratios connected to one another by a constant of proportionality make up a proportional relationship between two quantities. Different, related representations of proportional connections include tables, equations, graphs, and written descriptions.
We'll now look at a real-world illustration of a proportionate relationship: There is a correlation between the quantity of fuel we put in our car's tank and the price we will have to pay when we fill it up. In other words, we will pay more money the more gas we put in.
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Enter your answer and show all the steps that you use to solve this problem in the space provided. Convert the map scale to a unit rate. How many inches represent one mile? Show your work. Interpret the meaning of the unit rate. 3/ 10 in . = 7 /8 mi . please fast i dont have much time
The map, every 1-inch drawing represents 2.917 miles in reality, using conversation.
What is conversation ?
A unit's use depends on the context; for example, a room's area is expressed in metres, yet a pencil's length and thickness are expressed in centimetres and millimetres, respectively.
Therefore, converting one unit to another is necessary. We must first understand the link between units in order to comprehend the concept of unit conversion.
When addressing many problems in mathematics, unit conversion is necessary. Mathematical conversions are necessary to perform the necessary calculations.
In the map, every 1 inch drawing represents 2.917 miles in reality.
the meaning of the unit rate. 3/ 10 in. = 7 /8 mi
1 in = (7/8) mi ÷ (3/10)
= 7/8 * (10/3) = 70/24
1 in = (70/24) mi
Hence the map, every 1-inch drawing represents 2.917 miles in reality.
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FIND THE MISSING EXPONENT
x^ • x^3 = 1/x^2
Step-by-step explanation:
x^y × x^3 = 1/(x^2) = x^(-2)
that means
y + 3 = -2
y = -5
the missing exponent is -5
x^(-5) × x^3 = 1/(x^2)
Answer:
Step-by-step explanation:
Hi Ashley, this looks harder than it really is :)
recall your powers rules
so [tex]x^{2}[/tex] * [tex]x^{2}[/tex] = [tex]x^{2+2}[/tex]=[tex]x^{4}[/tex]
knowing that you can probably figure this out. But I'll help anyway
[tex]x^{?+3}[/tex] = 1 / [tex]x^{2}[/tex]
now flip over the fraction to make this even easier
[tex]x^{?+3}[/tex] = [tex]x^{-2}[/tex]
ohhhh I bet you can see it now, huh
we just need 3 plus something to equal -2
that's negative 5 , right???
[tex]x^{-5+3}[/tex] = [tex]x^{-2}[/tex]
ahh, nice , now just break it back up
[tex]x^{-5}[/tex] * [tex]x^{3}[/tex] = 1 / [tex]x^{2}[/tex]
got it???
help fast!
make up a word problem that can be represented with y=3.5x
The equation can be used for "the total cost of buying x chocolate bars, such that each one costs $3.50"
How to make a word problem that can be represented by that equation?Here we have the linear equation:
y = 3.5*x
And we want to make a word problem that can be represented by this.
The simplest example would be something like "the total cost of buying x items of a cost equal to the constant of proportionality"
So let's suppose that there is a chocolate bar in a given store that costs $3.50 per unit.
So, if you buy x of these, the total cost will be modeled (in dollars) by the equation:
y = 3.50*x
Which is the same equation that we have above:
y = 3.5*x
Where the second 0 on the constant factor is trivial and can not be written.
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A person is riding a 14 kg bike at velocity of 18m/s. The mass of the person is 60kg. What is the momentum of the person and the bike?
The momentum of the person is zero and the momentum of the bike is 1332.
A person is riding a 14 kg bike at velocity of 18m/s
The momentum of bike = mass x velocity
p = (14 + 60) 18
= 1332
The velocity of the person with respect to the bike is 0
p = mv
p = 60 x 0
p = 0
Therefore, the momentum of the person is zero and the momentum of the bike is 1332.
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[tex]g(x) = 3 log(x + 7) - 8[/tex]is this function increasing or decreasing?
Given function : g(x)=3log(x+7) -8
A function is said to be increasing if the derivative of the function is greater than 0,
and it said to be decreasing tof the derivative of the function is less than 0,
Differentiate the given function with respect to x,
[tex]\begin{gathered} g(x)=3\log (x+7)-8 \\ \frac{dg(x)}{dx}=\frac{d(3\log (x+7)-8)}{dx} \\ g^{\prime}(x)=3\frac{d\log (x+7)}{dx}-\frac{d(8)}{dx} \\ g^{\prime}(x)=\frac{3}{x+7}-0 \\ g^{\prime}(x)=\frac{3}{x+7} \\ \text{ since if x}>7\text{ then the function will be negative, } \\ g^{\prime}(x)<0, \\ \text{thus function at }7Answer :at x >7 , the function g(x) will be decreasing
at x <7 the function g(x) will be increasing.
Which relation is NOT a function?*I am going to send you my answer choices *
th first pic is not a function because a function dont have to values for the same x
the second pic is a function because each value of x has a different result
the third pic is a function because each value of x has a different result
so the first relation is not a function
Please i need your help! What is the slope of each line segment of QRS
Answer:ez 90 degrees
Step-by-step explanation:
Graph the linear inequality & find the coordinates 2x-y<2
Answer:
(1,0) (0,-2)
Step-by-step explanation:
A line segment is graphed on the coordinate plane. What point divides this segment in the ratio 2:3 ?
we have the points
A (1,-2) and B(5,3)
Find out the point (x,y) that divide the segment AB in a ratio 2:3
that means
AX/XB=2/3
step 1
Find out the horizontal distance AB
ABx=5-1=4 units
Find out the vertical distance AB
ABy=3-(-2)=5 units
step 2
we have that
the horizontal distance between A and x is
AX/XB=2/3
AX=(2/3)XB -----> equation 1
AX+XB=4 -----> equation 2
substitute equation 1 in equation 2
(2/3)XB+XB=4
(5/3)XB=4
XB=12/5
XB=2.4
the x-coordinate of X is
x=5-2.4=2.6
Find out the y-cpoordinate
AX=(2/3)XB -----> equation 1
AX+XB=5 ------> equation 2
substitute equation 1 in equation 2
(2/3)XB+XB=5
5/3(XB)=5
XB=3
the y-coordinate of X is
y=3-3=0
answer is
the coordinate of the point is (2.6,0)
answer is option A