The diagram given is a sector, and from the diagram
Radius(r) = 9 in
[tex]\theta=120^{\cdot}[/tex][tex]\begin{gathered} \text{Area of a sector = }\frac{\theta}{360}\times\pi r^2 \\ \\ \text{Area of a sector = }\frac{120}{360}\times\frac{22}{7}\times9^2 \\ \text{Area of a sector =}\frac{19440}{2520}=7.71in^2 \end{gathered}[/tex]The sum of 3 consecutive evennumbers add up to 1002. Find the threenumbers.
Let the three consecutive even number be,
x, x+2, x+4
Sum of the numbers is 1002.
[tex]\begin{gathered} x+x+2+x+4=1002 \\ 3x+6=1002 \\ 3x=996 \\ x=332 \end{gathered}[/tex]Hence, the numbers are,
332, 332+2, 332+4
Hence, the answer is 332, 334, 336.
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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1.5x - 0.25y + 3.5x - 0.75y
Answer:
5x-1y
Step-by-step explanation:
Answer:
Step-by-step explanation:
1. (1.5x+3.5x)-(0.25y+0.75y)
2. 5x-y
3. The answer is 5x-y.
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]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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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 AWhat 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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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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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
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).[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.
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???
A right circular cone with a radius of 3 cm has a slant height of 5 cm. A right cylinder with a radius of 4 cm has a height of 6 cm. What is the number of full cones of water needed to completely fill the cylinder with water?.
About 3 full cones of water are needed to be added to the cylinder to completely fill it.
The radius of the right circular cone is 3cm and the slant height is 5 cm.
The height of the cone can be found as,
H = √(5)²- (3)²
H = 4cm
The volume of the cone is given by,
V = πR²H/3
R is the radius and H is the height of the cone,
Putting values,
v = π x 5 x 5 x 4/3
v = 104.71 cm³
Now, the height h of cylinder is given to be 6 cm and the radius r of the cylinder is 4cm.
The volume of the cylinder is given as,
V = πr²h
V = π x 4 x 4 x 6
V = 301.59
Let us assume that we have to add n full cones of water to completely fill the cylinder, so, we can write,
nv = V
Putting values,
n104.71 = 301.59
n = 2.85
So, we have to add roughly three full cones of water to completely fill the cylinder.
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Please can someone answer this question it would be much appreciated
Thanks so much :)
Answer:
Step-by-step explanation:
(08.01 LC)Describe the process for calculating the volume of a cylinder. Usecomplete sentences. (10 points)
Volume of the cylinder = πr²h
see explanation below
Explanation:A cylinder comprises of two circles and a curved part.
To get the volume, we would multiply the area of the circle with the height of the cylinder
The height of the cylinder is the distance between the two circular ends
Area of a cirlce is pi multiplied by radius squared
Area of circle = π×r² = πr²
where r = radius
h = height of the cylinder
Volume of the cylinder becomes = πr² × h
Volume of the cylinder = πr²h
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
Round 7605 to the nearest hundred.
Answer:
Your answer would be 7,600.
Step-by-step explanation:
7,605 rounded to the nearest hundred would be 7,600 because:
The 7 is the thousands.
The 6 is the hundreds.
The 0 is the tens
The 5 is the ones.
So, we need to find which number makes sense to round. Is 605 closer to 600 or 700? 600. So, we have: 7,600
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
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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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]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:
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
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.
These two lines are parallel. Write an equation for each.
Answer:
Top: y = x
Bottom: y = 0.8x - 3.2
Step-by-step explanation:
I can see the question is asking to write the equation in Slope-Intercept form.
Slope-Intercept Form:
y = mx+b
M is the slope or how much the y value increases every time the x value increases by one. b is the y-intercept or when x=0.
Because these lines are parallel, we know they have the same form.
Lets look at the top line. When x increases by one, how much does y increase by?
1
What is the y value of when the line's x-value is 0?
0
Now, we have,
y = 1x + 0
Because adding 0 keeps the equation the same, we can remove it.
y = 1x
Because multiplying a term by 1 leaves it the same, we can remove one.
y = x
Now, for the bottom line.
How much does y increase by when x increases by 1? Because the slope will be a fraction and is not easy to see, I will use the slope formula.
Slope Formula:
[tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
To find the slope, take any pair of points on the line and plug them in.
I'll use:
(0,-3.2)
(4,0)
Plug the y-values (the latter number, or the height of the point) into the formula. Do the same with the x-values. keep in mind it does not matter what y-value you plug in. For example, for [tex]y_2[/tex] and [tex]y_1[/tex] you can plug in -3.2 and 0 or vice versa. If you make [tex]y_2[/tex] -3.2, then make [tex]x_{2}[/tex] 0.
[tex]\frac{-3.2-0}{0-4}[/tex]
Simplify.
[tex]\frac{-3.2}{-4}[/tex]
Because a negative number multiplied or divided by another negative number is always a positive number, remove the negative signs.
[tex]\frac{3.2}{4}[/tex]
Divide.
3.2/4 = 0.8
Now we have m, the slope on the 2nd line, 0.8
y = 0.8x + b
What is the y-value of the line when the line has the x-value of 0? On the graph, it says -3.2.
y = 0.8x - 3.2
CHECK YOUR UNDERSTANDING
Nick writes a check to his friend James Sloan on May 11 for $150.32.
What should he write in the check register and what should the new
balance be?
Nick will write
Date i.e. 11/5/20XX, Description i.e. Pay James, Check Number i.e. 123, Debit i.e. $150.32, Balance i.e. $X - $150.32.
The New balance will be $X - $150.32, where $X is the previous balance.
Given, that Nick writes a check to his friend James Sloan for $150.32 on May 11.
Let suppose Nick had an 'X' amount in his bank account.
He will fill the check register like this
Date Description Check Number Debit Credit Balance
11/5/20XX $X
11/5/20XX Pay James 123 $150.32 $X-$150.32
Hence, Nick will write
Date i.e. 11/5/20XX
Description i.e. Pay James
Check Number i.e. 123
Debit i.e. $150.32
Balance i.e. $X - $150.32
The New balance will be $X - $150.32 i.e. $150.32 subtracted from the previous balance.
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100 POINTS FOR THIS!!!
Answer: $5 for each vinyl,$4 for each CD,and $1 for each electronic download
Step-by-step explanation:
Answer:
$5 vinyl
$4 CD
$1 every electronic download
Step-by-step explanation:
good luck
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]Suppose that you borrow $15,000 for 4 years at 5% toward the purchase of your car. use pmt to find the monthly payments and the total interest for the loan
The formula for the monthly loan payment is given as
[tex]A\text{ = }P(\frac{r(1+r)^n}{(1+r)^n-1})[/tex]Where
P = loan amount ( initial principal) = $15000
A= Payment amount per period = ?
r = interest rate per period = (5/12) x (1/100) =0.0041667
n = total number of payments or periods = 4 years = 4 x 12 = 48 months
Substituting all these into the above equation gives
[tex]A\text{ =15000( }\frac{0.0041667(1+0.0041667)^{48}}{(1+0.0041667)^{48}-1})[/tex][tex]A\text{ = 15000(}\frac{0.0041667(1.0041667)^{48}}{(1.0041667)^{48}-1})[/tex][tex]\begin{gathered} A\text{ = }15000(\frac{0.0041667\text{ }\times1.2208973}{1.2208973\text{ - 1}}) \\ A=\text{ 15000(}\frac{0.005087112781}{0.2208973}) \end{gathered}[/tex][tex]\begin{gathered} A=15000(0.023029311) \\ A=\text{ \$345.4396759} \end{gathered}[/tex]So each month he pays $345.44 to the nearest cent
B)
The total interest for the loan is given by
Total amount paid over the total period of time - Original amount borrowed
Total amount paid over the total period of time = 345.44 x 48 months = $16581.12
The total interest of the loan hence = $16,581.12 - $15,000 = $1,581.12
The total loan interest to the nearest cent = $1,581.12
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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How do you answer this? I am so confused! Please help me
The coordinates of a slope triangle that could be on the line shown include
8) (10, 13), 15. 1) and (5, 4)C) (5, 4), (10, 4), and (10, 7)What is slope triangle?A slope triangle is a hypothetical triangle that aids in determining a line's or line segment's slope.
The line whose slope you are interested in learning is the triangle's hypotenuse (the diagonal). The slope formula's "rise" and "run" values are the two "legs" of the triangle.
With this idea, the slope triangle is drawn and the image is attached.
The coordinates should be able to form a right triangle which is used in slope calculation
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Solve the following equationX-3(x+2)=4 X - 3 ( x + 2 ) = 4
Given: X-3(x+2)=4X-3(x+2)=4
Find: the solution of the given equation
Explanation:
[tex]\begin{gathered} X-3(x+2)=4 \\ X-3x-6=4 \\ X-3x=10......................(1) \\ 4X-3(x+2)=4 \\ 4X-3x-6=4 \\ 4X-3x=10...........................(2)\text{ } \end{gathered}[/tex]on solving equation (1) and (2) , we get
Answer:
x = -5
Step-by-step explanation:
Solve for 'x':x - 3(x + 2)= 4
x - 3x - 3*2 = 4 {Distributive property}
x - 3x - 6 = 4
Combine like terms in LHS,
-2x - 6 = 4
Add 6 to both sides,
-2x = 4 + 6
-2x = 10
Divide both sides by (-2)
x = 10 ÷ (-2)
[tex]\sf \boxed{x= -5}[/tex]