To draw a 50 degree angle with a protactor, proceed as follows :
Draw a straight line (i.e. an arm of the angle).Place a dot at one end of the arm. This dot represents the vertex of the angle.Place the centre of the protractor at the vertex dot and the baseline of the protractor along the arm of the angle.Find 50 degree angle on the scale and then mark a small dot at the edge of the protractor.Join the small dot to the vertex with a ruler to form the second arm of the angle.Label the angle with capital letters.Remember that 50 degree angle cannot be constructed using compass.
When rolling a pair of die, what is the probability of rolling the sum of 12 OR less than 5? P(sum of 12 OR <5)
Please answer this asap
The probability of rolling a sum of 12 or smaller than 5 is:
P = 7/36 = 0.194
How to find the probability?Each dice has a total of 6 outcomes. Then for rolling two die, the total number of outcomes is:
6*6 = 36
The probability of rolling a sum of 12 or smaller than 5, is equal to the quotient between the number of outcomes that meet the above condition and the total number of outcomes.
There is only one outcome that adds up to 12.
And by looking at the table, we can see that there are 6 outcomes that add up to numbers smaller than 5.
So 7 outcomes meet the condition.
Then the probability is:
P(sum of 12 or <5) = 7/36 = 0.194
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Calculator
What is the length
YX₂
Enter your answer as a decimal in the box. Round your final
answer to the nearest hundredth.
m
of
9m
19 m
A•
X
N
Answer:
1. You can solve this problem by applying the Tangent Secant Theorem. Then, you have:
YX²=(YZ)(YV)
YX=√(YZ)(YV)
YZ=9+19
YV=9
2. When you substitute the values of YZ and YV into YX=√(YZ)(YV), you obtain:
YX=√(YZ)(YV)
YX=√(9+19)(9)
YX=√(28)(9)
YX=√252
YX=15.87
What is the length of YX?
The answer is: The lenght of YX is 15.87
A bunny is released from a cage and hops away along a straight path. Each hop covers a horizontal distance of about 1 meter and a vertical distance of about
0.4 meters.
Which of the following graphs could model the situation if x represents the bunny's horizontal distance from the cage and y represents the bunny's height above ground?
Answer:
D
Step-by-step explanation:
because Y has to be about 0.4 meters high and the X value has to be 1 meter wide
Graph the circle with center (−3, −3) that passes through (2, −3). Find the area in terms of π and to the nearest tenth. Use 3.14 for π.
[tex]\fcolorbox{red}{blue}{Answer}[/tex]
78.5 units²
Step-by-step explanation:
[tex] \textsf{\large{\underline{To find :-}}}[/tex]
The area of circle on graph
[tex] \textsf{\large{\underline{Given :-}}}[/tex]
[tex] \sf (x_1,y_1) = (-3,-3) \\ \sf (x_2,y_2) = (2,-3)[/tex]
[tex] \textsf{ \huge{\underline{\underline{Solution :-}}}}[/tex]
We can see in the above question that we have been provided the center of thee circle and line of the circle passes through a point.
So to find the radius we have to find the distance between center of circle and the point from which line passes.
[tex] \sf \blue{ Distance = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } }[/tex]
Now substituting the required values
[tex] \sf \implies\sqrt{ { \{2 - ( - 3) \}}^{2} + { \{ - 3 - ( - 3) \}}^{2} } \\ \\ \sf \implies \sqrt{ {(2 + 3)}^{2} + {( - 3 + 3)}^{2} } \\ \\ \sf \implies \sqrt{ {5}^{2} + {0}^{2} } \\ \\ \sf \implies \sqrt{25} \\ \\ \sf \implies 5 \: units[/tex]
So the radius will be 5 units
Now we will simply formula for area of circle
[tex] \sf \green{ Area \: of \: circle = \pi {r}^{2} }[/tex]
Now substituting the required values
[tex] \sf \hookrightarrow Area = 3.14 \times {5}^{2} \\ \\ \sf \hookrightarrow Area = 3.14 \times 25 \\ \\ \red{\boxed {\hookrightarrow \frak{78.5 \: {units}^{2} } }}[/tex]
The graph of the circle is plotted with clarity and the area is obtained as 78.5 square units.
How to graph a circle?The graph of a circle can be plotted by knowing its centre and radius.
If radius is not given, then it can be found by knowing the coordinate of any point lying on it.
The radius can be calculated by the distance formula.
The centre of the given circle is at (-3, -3) and it passes through (2, -3).
Now, radius is the distance between the centre and a point lying on circle.
The radius can be calculated by distance formula as below,
√((-3 - 2)² + (-3 - (-3))²) = 5
The graph of the given circle can be drawn as follows,
Now, the area of the circle is πr² = 3.14 × 5² = 78.5
Hence, the graph of the circle is drawn properly and the area is given as 78.5 square units.
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Due to its weakening steel industry, Clay County has been experiencing population decline of 3% every year. The current population is 10,300 people. Assuming the trend continues, what will the population be in 10 years?
Using an exponential function, it is found that the population of Clay County will be of $13,482.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem, the current population is 10,300 people, with a growth rate of 3%, hence A(0) = 10,300 and r = 0.03.
The equation is given by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 10300(1 + 0.03)^t[/tex]
[tex]A(t) = 10300(1.03)^t[/tex]
Hence, in 10 years, the population will be given by:
[tex]A(10) = 10300(1.03)^{10} = 13842[/tex]
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Answer: 7,595
Step-by-step explanation:
ixl
What is the median in the box plot?
Answer:
The answer is 76.
Step-by-step explanation:
The median would be the middle number in a box and whisker plot.
What is the volume of a cylindrical flower vase with a radius of 10cm and a height of 50cm?
In the question, it is given that a flower vase has a radius of 10 cm and a height of 50 cm , we have to find the volume .
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
To Find the volume of the cylindrical flower vase , we must know this formula :
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \Longrightarrow\underline{\boxed{ \color{lime}{V=πr^2h}}}[/tex]
Now, we will substitute the values in the formula:
[tex]\Longrightarrow\sf{V=3.14*10^2*50}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{V=3.14*100*50}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{V=314*50}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex]\Longrightarrow\sf{V=15700}[/tex]
The volume of the flower vase (cylinder).
Solution:[tex]\boxed{\sf{Formula: V = \pi {r}^{2} h}}[/tex]
[tex]V = \pi \times {10}^{2} \times 50[/tex]
[tex]V = 15707.96327 \: {cm}^{3} [/tex]
[tex]\large\boxed{\sf{V = 15707.96 \: {cm}^{3} }}[/tex]
Hence, the volume of the flower vase (cylinder) is 15707.96 cubic centimeters.
A family of 2 adults and 3 children went out to dinner. The total bill was $42. Each child's dinner cost $4. How much did each adult's dinner cost?
Answer: Each adult’s meal costed $15
Step-by-step explanation:
This situation can be modeled by the following equation:
2a + 3c = 42, where a = the cost of an adult’s meal, and c = the cost of a child’s meal
Since we know from the problem that a child’s meal costs $4, we know c:
2a + 3(4) = 42
At this point, we can just solve the resulting equation for a:
2a + 3(4) = 42
= 2a + 12 = 42 (simplify 3(4))
= 2a = 30 (subtract 12 from both sides)
= a = 15 (divide both sides by 2)
So, the cost of each adult’s meal was $15.
Write the quadratic equation whose roots are 4 and -2 and whose leading coffecient is 2
Answer:
[tex]y=2x^2-4x-16[/tex]
Step-by-step explanation:
Factored form of a quadratic equation:
[tex]y=a(x-r_1)(x-r_2)[/tex]
where:
a is the leading coefficient[tex]r_1[/tex] and [tex]r_2[/tex] are the rootsGiven:
[tex]a = 2[/tex][tex]r_1=4[/tex][tex]r_2=-2[/tex]Substitute the given values into the formula and expand:
[tex]\implies y=2(x-4)(x-(-2))[/tex]
[tex]\implies y=2(x-4)(x+2)[/tex]
[tex]\implies y=2(x^2+2x-4x-8)[/tex]
[tex]\implies y=2x^2-4x-16[/tex]
An office supply store sells boxes of pencils.each box contains 160 pencils. write an equation that represents the total number of pencils,y, in x boxes.
Answer:
160 times X
Step-by-step explanation:
160 is the number of pencils in each box.
And
X is how many boxes there are.
If 1 box contains 160 pencils then the equation which represents the total number of pencils is y=160x.
What is equation?An equation is a relationship between two or more variables where variables represent some quantity . It is mostly found in equal to form. It is equated to find the value of variables.
Equation form :y=a+bx
How to form equation?There are 160 pencils in one box and x represents the number of boxes. So the equation that represents the total number of pencils can be found by product of x and 160.
Equation will be x*160=160x.
Hence the equation which represents the total number of pencils is y=160x.
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Solve log (5x+7)=log(8x-2)
QUESTION 10 SOMEONE HELP ME
i cannot understand this AT ALL (would be glad to have an explanation)
hmmm well, don't be so hmmm off due to it, the wording in the exercise sux0rs bad, is very poorly worded and laid out.
if X and Y are numbers, hmmm say let's give them hmmm ohhh X = 7 and Y = 13.
And X and Y are also complete cubes, well, let's make them so, X = 7³ and Y = 13³.
which of those expressions are complete cubes, or namely, something that we can write as a number with a "3" in the exponent, let's check each one.
[tex]\begin{array}{ll|l|l|lllll} 8X&\implies 8\cdot 7^3& 2^3\cdot 7^3& (2\cdot 7)^3& 14^3 ~~ \checkmark\\&&&&\\ X,Y&\implies 7^3,13^3 ~~ \checkmark&&\\&&&&\\ -X&\implies -7^3~~ \checkmark&&\\&&&&\\ 27XY&\implies 27\cdot 7^3\cdot 13^3& 3^3\cdot 7^3\cdot 13^3& (3\cdot 7\cdot 13)^3& 273^3~~ \checkmark\\&&&&\\ XY+27&\implies 7^3\cdot 13^3+27&(7\cdot 13)^3 + 3^3&&91^3+3^3 ~~ \bigotimes \end{array}[/tex]
what's wrong with the last one? well, if we were to add 91³ + 3³ = 753598. Now, is 753598 a complete cube? well, only if we could write it as a whole number with a "3" above, can we? nope.
we can simply check that by getting the 3rd root of that value,
[tex]\sqrt[3]{753598}\approx 91.00108681228277\impliedby \textit{not a complete cube}[/tex]
help pleaseeeeeee. i don’t onowww
in an exponential expression, the rate of change is usually the parenthesized expression, namely on y = a(b)ˣ, the rate will be "b", so in this case the rate is just ∛24
[tex]\sqrt[3]{24} ~~ \begin{cases} 24=2\cdot 2\cdot 2\cdot 3\\ \qquad 2^3\cdot 3 \end{cases}\implies \sqrt[3]{2^3 \cdot 3}\implies 2\sqrt[3]{3}[/tex]
The exchange rate of mexican pesos for u.s. dollars is approximately 10 pesos for 1 dollar. if lynn exchanged 4,000 pesos for u.s dollars, what was the approximate value in u.s.dollars
400 dollars
4000/10=400 dollars
help me with this question please! it’s VERY URGENT and i dont know where to begin with❗️
Answer:
[tex] |x|1 | \: 2 | \: 3 | \: 4 | \: 5 | \\ |y| 5| \: 4 \: | 3 \: | 2 | 1| [/tex]
Step-by-step explaination:
We were told that:
[tex] x + y = 6 [/tex]
therefore to see if it is correct you can just input the values for x and y and see if they add up to 6 (add the vertical values). For example;when x = 1, y = 5 or when x = 2, y = 4
0.025 / 0.08 how do you do it so can you explain the steps
Answer:
5 / 16
Step-by-step explanation:
For a question such as this, we most often simply use a calculator. However, I suppose that to do this by hand you would do as follows:
0.025 / 0.080
= 0.005 / 0.016
= 100 * (0.005 / 0.016)
= 5 / 16
The first step is a simplification. Both the numerator and denominator are divisible by 0.005. In the next step, we can multiply the numerator and denominator both by 100 to get whole numbers. Because we multiply each by the same number, we have not changed the value of the original fraction. This leaves us with 5 / 16.
Done
In circle R, RS = 12 and m/SRT = 90°. Find the length of ST. Express your
answer as a fraction times 7.
R
T
S
Answer:
[tex]l(\widehat {ST})=6\pi [/tex]
Step-by-step explanation:
Radius (r)= RS = 12 (Given)[tex] Central\: angle \:(\theta) = m\angle SRT =90\degree[/tex] (Given)To find: [tex]l(\widehat {ST})[/tex]Formula for finding the length of arc is given as:[tex]l(\widehat {ST})=\frac{\theta}{360\degree}\times 2\pi r[/tex][tex]l(\widehat {ST})=\frac{90\degree}{360\degree}\times 2\pi (12)[/tex][tex]l(\widehat {ST})=\frac{1}{4}\times 24\pi [/tex][tex]l(\widehat {ST})=6\pi [/tex]The required length of an arc ST is 6π units which is subtended by an angle.
What is an arc?The arc is a portion of the circumference of a circle.
The formula for calculating the arc states that:
Arc length = 2πr (θ/360)
Where r = the radius of the circle,
θ = the angle (in degrees) subtended by an arc at the center of the circle.
As per the question, we have:
θ = 90° and r = 12 units
Substitute the given values in the formula,
Arc length = 2π(12) (90/360)
Arc length = 6π
Therefore, the required length of an arc ST is 6π units.
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Tegan is checking her tax bill for the last year
the tax rates were as follows:
•no tax on the first £11000 of earnings
•earnings in excess of £11000 and up to £43000 taxed at a rate of 20%
•earnings in excess of £43000 and up to £150000 taxed at the rate of 40%
last year Tegan earned £48300 before tax
how much did she pay in total?
Multiplication is the process of multiplying. The total tax of Tegan's earnings will be £8,520(£6,400+£1,200).
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Since there is no tax for the first £11,000, therefore, the earnings upto £11,000 will be tax-free.
The amount of tax for the income of £11,000 to £43,000, will be,
20% of (£11,000 to £43,000)
= 20% × (£43,000 - £11,000)
= £6,400
The amount of tax for the income of £11,000 to £150,000, will be,
40% of (£43,000 to £48,300)
= 40% × (£5,300)
= £2,120
Hence, the total tax of Tegan's earnings will be £8,520(£6,400+£1,200).
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Answer:
£8520
Step-by-step explanation:
is 1.010010001 rational
Answer:
Yes, 1.010010001 is rational
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Answer:
yes, 1.010010001 is rationalStep-by-step explanation:
A rational number has the form p q, where p and q are integers, q* 0 otherwise it is an irrational number.
Line A is represented by the equation given below: x + y = 4 What is most likely the equation for line B, so that the set of equations has infinitely many solutions? (1 point) Group of answer choices 4x + 4y = 4 4x + y = 4 2x + 2y = 8 x + y = 8
Answer:
2x+2y = 8
Step-by-step explanation:
Simply multiply the first equation x + y=4 by 2:
x + y=4
*2 *2
(x + y)2 = 8
2x+2y = 8
x + y = 4 and 2x+2y = 8 are the same equation. You can't solve x+y = 4, there's infinite number of solutions, just like how you can't solve 2x+2y = 8
cos(19pi/3)=?
Pls help me :(
Answer:
Step-by-step explanation:
Remove full rotations of [tex]2\pi[/tex] until the angle is between 0 and [tex]2\pi[/tex].
[tex]cos(\frac{\pi }{3} )[/tex]
The exact value of [tex]cos(\frac{\pi }{3})[/tex] is [tex]\frac{1}{2}[/tex].
[tex]\frac{1}{2}[/tex]
The result can be shown in multiple forms.
Exact Form:
[tex]\frac{1}{2}[/tex]
Decimal Form:
[tex]0.5[/tex]
Vocabulary:
Rotation
A transformation in which a figure is rotated through a given angle, about a point.
Angle
The union of two rays with a common endpoint, called the vertex.
PLS HELP PLS
How many days were less than 84°?
Answer:
D
Step-by-step explanation:
the number of days for 80 - 82 is 7 and the number of days for 82-84 is 9. Those are the only temperatures below 84 degrees, so you add them and get 16 :)
Simplify these four questions
Answer:
a. 5a + 3b-5
b. 4e^2 + f^2 + f
c. 42xy(z)^2
d. 7x(y)^2
Step-by-step explanation:
I added/subtracted/multiplied/divided like terms.
Solve:
2x-1/x+4 is greater than or equal to 0
The solution range of the given inequality is (-∞, -4.121) and (0.121,∞)
How to solve the inequality?
Here we want to solve:
[tex]2x - 1/(x + 4) \geq 0[/tex]
To solve this, we multiply both sides by (x + 4) so we get:
[tex]2x*(x + 4) - 1 \geq 0\\\\2x^2 + 8x - 1 \geq 0[/tex]
Now we can solve it graphically, below we have:
There we can see that the solution range is (-∞, -4.121) and (0.121,∞), the regions where the graph is equal or above the horizontal axis.
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Given function g(x) = 3/x, and composite function gh(x) = 64, find h(x)
The key to this problem is to identify the functions; isolate the functions dependent on only x; and define each function in terms of x. Once every function is in terms of x then we can apply them to the equation that needs to be solved. Identify the functions: Here we are given four functions f(x); g(x); h(x); and i(x) so anytime we see these letters appear in an equation is where we would substitute the function. Isolate the functions dependent on only x: At a glance we can tell that only g(x) is purely in terms of x, every other function contains another function within their equations.
Define each function in terms of x: Since g(x) is in terms of x and i(x) contains g(x) then we can substitute 3x+4 for g(x) making i(x)=(x-2)*(3x+4) which then simplifies to i(x)=3x2-2x-8
Since h(x) contains i(x) then we can substitute the i(x) we made in 3a to get h(x)=3x2-11-(3x2-2x-8) which then simplifies to h(x)=2x-3
Since f(x) contains g(x) and h(x) then we can substitute those equations to get f(x)=2(3x+4)-(2x-3) which then simplifies to f(x)=4x+11
Now we apply our defined equations to the equation in question. There are two ways to do this, we can either apply our x values to each individual equation first or make the equation in question in terms of x. In this case I will make the equation in terms of x first. The first part of this process is understanding that the ° symbol does not represent degrees in this case, it represents the substitution of a function into another function. For example, if you saw (f°g)(x) then you would take the equation for g(x) and substitute it for every x value in the f(x) equation. Based on the process around ° it would be best to start from i(x) and work backwards to f(x) then h(x). So 2i=2(i(x))=2(3x2-2x-8)=6x2-4x-16 Ignoring the 3 we then evaluate f°2i=f(2(i(x)))=4(6x2-4x-16)+11=24x2-16x-64. Then we multiply the 3 to get 3f°2i=3(24x2-16x-64)=72x2-48x-192
Then we get to h°3f°2i=2(72x2-48x-192)-3=144x2-96x-384 which can simplify to 48(3x2-2x-8) or 48(3x+4)(x-2).
Finally we can divide g(x) making (h°3f°2i÷g)(x)=(48(3x+4)(x-2))/(3x+4)=48(x-2)
With the final equation in terms of only x we can finally solve by substituting each x value, giving us -288 when x=-4; -240 when x=-3; and 0 when x=2.
#18. estimate the perimeter and the area of the shaded figure to the nearest tenth
Answer:
Area = 22.3 m^2
Perimeter 27.4 m^2
Step-by-step explanation:
Perimeter = __ m
Area __ m^2
The area of the triangle is about 4.2,
The area of the square is 4,
The area of the semicircle is 14.1,
14.1 + 4.2 + 4 = 22.3
Area = 22.3 m^2
9.4 + 6 + 4 + 4 + 4 = 27.4
Perimeter = 27.4 m^2
Therefore the area of the shape is about 22.3 m^2 and the perimeter is about 27.4 m^2.
Alfred is building a slide for a new park. He wants the height of the slide to be 8 feet, and he wants the horizontal distance along the ground to measure 10 feet.
After building the slide, Alfred decides the slide needs a vertical safety support and wants to use a 4-foot piece of wood to build the support. How far from the point where the base of the slide meets the ground should Alfred place the vertical support?
A: 20 Feet
B: 1.3 Feet
C: 5 Feet
D: 4 Feet
Answer:
5ft
Step-by-step explanation:
8/10=0.8
4/0.8=5
Need help with geometry circles problem
Answer:
Step-by-step explanation:
Which function rule represents the best line of fit for the data in the plot?
Answer:
f(x) = -1/2x + 8
or
The first one
Step-by-step explanation:
hope this helps
have a good day