SOLUTION:
Step 1:
In this question, we are given the following:
A circular pool with a radius of 3 m sits in a rectangular yard that is 14 m by 8 m. What area of the yard is NOT covered by the pool?
Step 2:
The area of the yard that is NOT covered by the pool is given as :
[tex]\text{Area of the Rectangular yard - Area of the circular pool}[/tex][tex]\text{( Length }X\text{ Breadth ) - ( }\pi r^2\text{ )}[/tex][tex]\begin{gathered} (\text{ 14 X 8 ) - (}\frac{22}{7}X\text{ 3 X 3 )} \\ =\text{ 112 - (}\frac{198}{7}) \\ =\text{ 112 - 28.28571429} \\ =\text{ 83.71428571} \\ \approx83.71m^2\text{ ( 2 decimal places)} \end{gathered}[/tex]CONCLUSION:
The area of the yard NOT covered by the pool is:
[tex]83.71m^2\text{ ( 2 decimaal places)}[/tex]uve a counterexample. That is, find two lines that do not have a point of intersection and explainhow you know3-36. Write and solve an equation for the following problem.In the last election, candidate C received 15,000 fewer votes than candidate B. If a total of 109,000votes were cast, how many votes did candidate B receive?
If candidate C received 15,000 FEWER votes than candidate B, and the total was 109,000 votes, then :
C + B = 109000
and
C = B - 15000
Then we replace C by (B - 15000) in the first equation:
(B - 15000) + B = 109000
combine like terms on the left
2 B - 15000 = 109000
add 15000 to both sides
2 B = 109000 + 15000
2 B = 124000
divide bothe sides by 2:
B = 124000 / 2
B = 62000
Then, candidate B received 62000 votes.
#9 - A card is drawn from a standard deck of playing cards. Find the probability that youdraw an ace.O 7.7%O 6.8%O 5.5%O 6.2%
Answer:
7.7%.
Explanation:
The number of cards in a standard deck, n(S)= 52
The number of aces in a standard deck, n(A) = 4 i.e 1 per suit.
Therefore, the probability that you draw an ace:
[tex]\begin{gathered} P(A)=\frac{n(A)}{n(S)} \\ =\frac{4}{52} \\ \approx0.0769 \\ \approx7.7\% \end{gathered}[/tex]The probability that you draw an ace is 7.7%.
Aaaaaaaaaaaaaaaaaaaaaaa
To be Liam's puzzle true, then the numbers must be one positive and one negative, that way their products will always be less than the numbers.
Hence, the answer is D.the statue of liberty is approximately 305 feet tall. if the angle of elevation of a ship to the top of the statue is 20.5°, how far, to the nearest foot, is the ship from the statue's base?
The situation forms a right triangle:
Since it's a right triangle, we can apply the trigonometric function:
Tan α = opposite side / adjacent side
Replacing:
Tan 20.5= 305/x
Solve for x:
x = 305/tan 20.5
x= 816 ft
I will show you the question
The given system is
[tex]\begin{cases}3x+6y=12 \\ x+2y=4\end{cases}[/tex]First, we multiply the second equation by -3.
[tex]\begin{cases}3x+6y=12 \\ -3x-6y=-12\end{cases}[/tex]Then, we combine the equations
[tex]\begin{gathered} 3x-3x+6y-6y=12-12 \\ 0=0 \end{gathered}[/tex]This means the system has infinitely many solutions.
Hence, the answer is D.A rectangular room is 2 times as long as it is wide, and its perimeter is 48 meters. Find the dimension of the room.
Answer:
=16cm
Step-by-step explanation:
Let's read the problem carefully:
it says that one side of the rectangular room (let's call it b) is twice as long as the other (let's call it a), which in mathematical terms would be b = 2*a
It also says that the perimeter of the room is 48 meters, which means that (a + b)*2 = 48 => a + 2*a = 48/2 =>
3*a = 24 => a = 8, b = 16
Which graph represents y as a function of x? please help!! im sorry if not all photos show up
The graph does not represent a function between y and x.
How to check if the graph is a function?A function is a relation that maps inputs x into outputs y, such that each input is mapped into at most one output.
To check if a graph belongs to a function, we need to do the vertical line test, this means that if we draw a vertical line on the coordinate axis where we have the graph, and that vertical line touches the graph at more than one point, then the graph does not represent a function.
In this case, if we draw a line at x = 1 we will intersect the graph twice, then it is not a function.
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Let f(x) = 6.4 sin(x) + 5.9 cos(x). What is the maximum and minimum value of thisfunction?
SOLUTION
From f(x) = 6.4 sin(x) + 5.9 cos(x)
[tex]\begin{gathered} \text{The maximum value occurs at where }\frac{d\text{ y}}{d\text{ x}}\text{ = 0 } \\ \end{gathered}[/tex]So we will differentiate the function f(x) = 6.4 sin(x) + 5.9 cos(x)
f(x) = 6.4 sin(x) + 5.9 cos(x)
f'(x) = 6.4 cos(x) - 5.9 sin(x)
6.4 cosx - 5.9 sinx = 0
Squaring both sides we have
[tex]\begin{gathered} 6.4\cos x\text{ + 5.9sinx = 0 } \\ \text{recall that cos x = }\sqrt[]{1-sin^2x} \\ 6.4\text{ }\sqrt[]{1-sin^2x}\text{ + 5.9sinx = 0 } \\ 6.4\text{ }\sqrt[]{1-sin^2x}=\text{ -5.9sinx} \\ \text{square both sides } \\ 40.96(1-sin^2x)=34.81sin^2x \\ 40.96-40.96sin^2x\text{ = }34.81sin^2x \\ 40.96=75.77sin^2x \\ \sin ^2x\text{ = 0.541 taking squaroot} \\ \text{sinx = }\sqrt[]{0.541} \\ \sin x\text{ = 0.735} \\ x\text{ = }\sin ^{-1}0.735 \\ x\text{ = 47.35} \end{gathered}[/tex]We have gotten the value for x, now let's find our maximum and minimum values
[tex]\begin{gathered} f(x)\text{ = 6.4sin(47.35) + 5.9cos(47.35)} \\ =\text{ 4.707 + 3.997} \\ =\text{ 8.70}4 \end{gathered}[/tex]Therefore, the maximum value is 8.704 and the minimum value is -8.707
Note that maximum value is just the direct opposite of minimum value
Use angle relationships (complementary, supplementary, vertical, or adjacent) to find the measure of angle b.
Answer:
vertical, b = 46
Explanation:
Two angles are vertical if they are formed by intersection of two lines.
For examole, the follwing angles are vertical.
The angles b and 46 are vertical, and therefore, their measures are the same.
Therefore,
[tex]b=46^o[/tex]Acellus Find the area of the shaded region. 60° 5 cm A = [?] cm2 Enter a decimal rounded to the nearest tenth.
hello
to solve this question, we simply need to apply the formula of area of a segment
the formula is given as
[tex]A_{\text{segment}}=\frac{1}{2}\times(\theta-\sin \theta)\times r^2[/tex]let's write out the variables given in the question
[tex]\begin{gathered} \theta=60^0 \\ r=5\operatorname{cm} \end{gathered}[/tex]we can now input those values into the equation
[tex]\begin{gathered} A_{\text{segment}}=\frac{1}{2}\times(\theta-\sin \theta)\times r^2 \\ A_{\text{segment}}=\frac{1}{2}\times(60-\sin 60)\times5^2 \\ A_{\text{segment}}=\frac{1}{2}\times(60-0.8660)\times25 \\ A_{\text{segment}}=\frac{1}{2}\times1478.35 \\ A_{\text{segement}}=739.175\operatorname{cm}^2 \end{gathered}[/tex]to get the value of the area of the shaded region,
[tex]\text{area of shaded region=area of circle - area of segment}[/tex]let's calculate the area of the circle
[tex]undefined[/tex]Distributive Property: -3 1/2 divided by 1/2
ANSWER
-7
EXPLANATION
We want to solve the given fractional division by using the distributive property.
Basically, we are going to split the numerator into smaller pieces to make the division simpler.
That is:
[tex]\begin{gathered} \frac{-3\frac{1}{2}}{\frac{1}{2}} \\ =\text{ }\frac{\frac{-7}{2}}{\frac{1}{2}} \\ =\text{ }\frac{(\frac{-6}{2}\text{ - }\frac{1}{2})}{\frac{1}{2}} \\ =\frac{(-3\text{ - }\frac{1}{2})}{\frac{1}{2}} \\ =\frac{-3}{\frac{1}{2}}\text{ - }\frac{\frac{1}{2}}{\frac{1}{2}} \\ =\text{ -6 - 1} \\ =\text{ -7} \end{gathered}[/tex]Can you please help me out with a question
Tangents to a circle that intersects at a point are equal in length.
Therefore,
|AB| = |AC|
Where
|AC| is the length of line AC
and
|AB| is the length of line AB
Hence,
[tex]\begin{gathered} 4x+2=2x+8 \\ \text{this implies that} \\ 4x-2x=8-2 \\ 2x=6 \\ \text{Dividing both sides by 2, we have} \\ \frac{2x}{2}=\frac{6}{2} \\ \text{thus} \\ x=3 \end{gathered}[/tex]x = 3 units
Find the area of the rhombus9 in12 inA = [ ? ] in2?=Enter
The formula for calculating the area of a rhombus is expressed as
Area = d1d2/2
where
d1 is the length of one diagonal
d2 is the length of the other diagonal
From the information given,
length of one diagonal = 12 + 12 = 24
length of other diagonal = 9 + 9 = 18
By substituting these values into the formula,
Area = 1/2 x 24 x 18
Area = 216 in^2
you are machinist setting up a part that requires a5/8 inch diameter finished hole.stardart practice is to drill an initial g hole with a diameter that is undersided by 1/32 inch before finishing What should be the diameter inches of the initial hole?
We will have that the initial size of the hole should be:
[tex]\frac{5}{8}-\frac{1}{32}=\frac{19}{32}[/tex]So, the diameter of the initial hole should be 19/32 inches.
Find the solution set of the quadratic inequalities3x^2 - 15x - 18 > 0
Given -
3x²- 15x - 18 > 0
To Find -
The solution set of the quadratic inequalities =?
Step-by-Step Explanation -
Firstly, We will find the solution to the quadratic equation.
3x²- 15x - 18 = 0
[tex][/tex]find the grade-point average. assume A=4,B=3,C=2,D=1 and F=0
Average is define as the ratio of sum of all the data to the total number of data
[tex]\text{Average=}\frac{Sum\text{ of all the data}}{Total\text{ number of data}}[/tex]In the given question , we hvae five grades
[tex]\begin{gathered} A=4 \\ B=3 \\ C=2 \\ D=1 \\ F=0 \end{gathered}[/tex]Total number of data=5
Use the expression of average to find the average of grade point
[tex]\begin{gathered} \text{Average}=\frac{4+3+2+1+0}{5} \\ \text{Average}=\frac{10}{5} \\ \text{Average}=2 \end{gathered}[/tex]The average of the grade-point is 2.
scores on a test are normally distributed with a mean of 81 and a standard deviation of 8. Find the probability that a randomly chosen score will be between 70 and 93.
Answer:
0.8486
Explanation:
To find the probability that a score will be between 70 and 93, we first need to standardize these values, so we will use the following
[tex]z=\frac{value-mean}{standard\text{ deviation}}[/tex]Therefore, for 70 and 93, we get
[tex]\begin{gathered} z=\frac{70-81}{8}=-1.375 \\ \\ z=\frac{93-81}{8}=1.5 \end{gathered}[/tex]Then, we need to find the following probability
P(-1.375 < z < 1.5)
This probability can be calculate using a standard normal table, so
P(-1.375 < z < 1.5) = P(z < 1.5) - P(z < -1.375)
P(-1.375 < z < 1.5) = 0.9332 - 0.0846
P(-1.375 < z < 1.5) = 0.8486
Therefore, the probability is 0.8486
The width of a picture frame is 16 3/5 centimeters. It’s length is 4 4/5 centimeters longer than the width . Find the length and the perimeter of the picture frame. Write the answer in simplest form.
ANSWER:
[tex]\begin{gathered} \text{Length = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Perimeter = 76 centimeters} \end{gathered}[/tex]EXPLANATION:
Since the length is 4⅘ longer than the width, the length will be:
Length = 4⅘ + 16⅗
[tex]\begin{gathered} W\text{ = 16}\frac{3}{5}\text{ centimeters} \\ Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5} \end{gathered}[/tex]Let's solve for length:
[tex]\begin{gathered} Length\text{ = 4}\frac{4}{5}\text{ }_{}+\text{ 16 }\frac{3}{5}\text{ = }\frac{24}{5}\text{ + }\frac{83}{5}\text{ = }\frac{107}{5}\text{ = 21}\frac{2}{5}\text{ centimeters} \\ \\ \text{Length = 21}\frac{2}{5}\text{ centimeters} \end{gathered}[/tex]From the given dimensions, it shows the picture frame is a rectangle.
To find the perimeter, use the perimeter of a rectangle formula:
Perimeter of a rectangle = 2(Length + Width)
[tex]\begin{gathered} \text{Perimeter = 2(}\frac{107}{5}+\frac{83}{5}) \\ \\ \text{ = 2(}\frac{190}{5}) \\ \\ \text{ = }2(38) \\ \\ \text{ = 76 centimeters} \end{gathered}[/tex]I need help I think I’m supposed to multiply straight across
To find the whole answer, let's look at each multiplication:
[tex]\frac{5280ft}{1\text{ mile}}\cdot\frac{30\text{ miles}}{1\text{ hour}}=\frac{5280ft\cdot30\text{miles}}{miles\cdot hour}=\frac{158400ft}{\text{hour}}[/tex]Now, it changes from hours to minutes:
Use, 1hour = 60 minutes
[tex]\frac{158400\text{ ft}}{1\text{ hour}}\cdot\frac{1\text{ hour}}{60\text{ minutes}}=\frac{158400\text{ ft}\cdot\text{hour}}{\text{hour}\cdot\text{ 60 minutes }}=\frac{158400ft}{60\text{ minutes}}[/tex]Then, it changes from minutes to seconds:
Use, 1 minute = 60 seconds
[tex]\frac{158400\text{ ft}}{60\text{ minutes}}\cdot\frac{1\text{ minute}}{60\text{ seconds}}=\frac{158400\text{ ft}\cdot1\text{ minute}}{60minutes\cdot60\text{seconds}}=\frac{158400\text{ ft}}{3600\text{ seconds}}[/tex]Then:
[tex]\frac{158400\text{ ft}}{3600\text{ second}}=44\text{ f}eet\text{ per second}[/tex]Find the area 21 m 7 m 21 m O A. 1543.5 m2 O B. 220.5 m2 OC. 294 m2 OD. 588 m2
EXPLANATION
Given the sides: 21m , 7m and 21 m
The Area is equal to:
Are
Isabella painted a water colour design on gridpaper. Some of the points were at A (-4, 8),B (-2, 8), C(-1,6), D (-2, 4), E (-4, 4), andF (-5, 6). She folded the paper along y = 3 toreflect the design. The image points are A', B',C', D', E', and F.a) Draw the line y = 3. (Hint: The x-axisis the line y = 0. For which line is they-coordinate 3 for every point?)b) Determine the coordinates of A', B',C.D', E', and F'.c) Draw the image, and label A', B', C',D', E', and F'.y8-7-€6-4.32-5•1 C
EXPLANATION
Drawing the line y=3 give us the following graph:
Reflecting over the axis y=3 give us the following image points:
A' = (-4,2)
B' = (-2,-2)
C' = (-1,0)
D' = (-2,2)
E' = (-4,2)
F'= (-5,0)
Drawing the points in the graph calculator:
The coordinates of quadrilateral ABCD are A(3,4), B(2,7), C(2,8), and D(5,3). Do thediagonals bisect each other?
The image below shoes the given quadrilateral.
An important fact we need to know is that diagonals bisect when we have a symmetrical quadrilateral. As you can see in the image above, the quadrilateral is not symmetrical, it's not square like nor rectangle like.
Therefore, its diagonals don't intersect.Help me solve this hw problem pls formula for getting g(x)
Answer:
Explanation:
Given:
A graph of f(x) in red and a graph of g(x) in blue
To find:
the formula for getting g(x)
First, we need to determine the function for f(x) from the graph
The roots of the function for f(x) are -4, 0, 4
The line crosses the x axis at x = -4, x = 0 and x = 4
x + 4 = 0, x - 0 = 0, x - 4 = 0
The factors: (x + 4)(x - 0)(x - 4)
[tex]\begin{gathered} f(x)\text{ = \lparen x + 4\rparen\lparen x\rparen\lparen x - 4\rparen} \\ Expanding\text{ the function:} \\ f(x)\text{ = \lparen x}^2\text{ + 4x\rparen\lparen x - 4\rparen} \\ f(x)\text{ = x}^2(x\text{ - 4\rparen + 4x\lparen x - 4\rparen} \\ f(x)\text{ = x}^3\text{ - 4x}^2\text{ + 4x}^2\text{ - 16x} \\ f(x)\text{ = x}^3\text{ - 16x} \end{gathered}[/tex]Comparing the coordinates of f(x) and g(x):
[tex]\begin{gathered} From\text{ the graph of g\lparen x\rparen in blue} \\ when\text{ x = -4, y = 3, g\lparen x\rparen} \\ \text{ when x = 0, y = 0 f\lparen x\rparen} \\ \\ when\text{ x = 2, y = 2 g\lparen x\rparen} \\ when\text{ x = 2, y = -4 f\lparen x\rparen} \\ \\ when\text{ x = 4, y = 0 f\lparen x\rparen} \\ when\text{ x= 4, y = 3 g\lparen x\rparen} \end{gathered}[/tex]
There are 100 jelly beans in a jar, 15 are black. 20 are red, 25 are yellow and 30 are green and the are orange. Write a fraction in the simplest form of the number of jelly beans that are orange Explain your reasoning for your answer.
Answer:
The fraction of the number of jelly beans that are orange is;
[tex]\frac{1}{10}[/tex]Explanation:
Given that;
There is a total of 100 jelly beans in the jar.
Of the total;
15 are black
20 are red
25 are yellow
30 are green
And the rest are orange.
The number of orange jelly beans can be calculated by deducting the number of black,red,yellow,and green jelly beans from the total.
[tex]\begin{gathered} n=100-(15+20+25+30) \\ n=100-90 \\ n=10 \end{gathered}[/tex]So, there are 10 orange jelly beans in the jar.
We now need to write a fraction of the number of jelly beans that are orange;
[tex]\begin{gathered} f_o=\frac{\text{ number of orange jelly beans }}{\text{Total number of jelly beans}} \\ f_o=\frac{10}{100} \\ f_o=\frac{1}{10} \end{gathered}[/tex]Therefore, the fraction of the number of jelly beans that are orange is;
[tex]\frac{1}{10}[/tex]
What do you notice and /or wonder about the second graph in the image above
The second graph A'B'C' is the result of a reflection over x axis of the figure ABC; You can see that because the coordinates of the points follow the next rule:
[tex]P(x,y)\rightarrow P^{\prime}(x,-y)[/tex]Point A: (-2,1) becomes A'(-2,-1)
Point B: (1,4) becomes B'(1,-4)
Point C: (3,2) becomes C'(3,-2)
A tract of land, indicated by Quadrilateral MNPQ, is shown on this grid where one square unit represents 50 square feet.What is the area, in square feet, of the tract of land?
We have to find the area of the quadrilateral MNPQ.
We can divide it in two right triangles and then calculate the area as the sum of the area of the two triangles. To do that we would have to calculate the distances between N and P and M and N, as this are the legs of the upper triangle.
We can simplify it by making three right triangles by adding one vertex R(1,0):
Now, the length of the legs of the triangles are easier to find.
We then can calculate the area of the quadrilateral (A) as:
[tex]\begin{gathered} A=A_{\text{MRN}}+A_{\text{PRN}}+A_{\text{MPQ}} \\ A=\frac{(MR)\cdot(RN)}{2}+\frac{(PR)\cdot(RN)}{2}+\frac{(MP)(PQ)}{2} \\ A=\frac{1}{2}(9\cdot6+4\cdot6+13\cdot8) \\ A=\frac{1}{2}(54+24+104) \\ A=\frac{1}{2}\cdot182 \\ A=91 \end{gathered}[/tex]The area covers 91 square units.
As each unit represents 50 square feet, we can calculate the area in feet as:
[tex]A=91\text{ sq. units}\cdot\frac{50\text{ sq. ft.}}{1\text{ sq. unit}}=4550\text{ sq. ft.}[/tex]Answer: the land's area is 4550 square feet.
would adam snitch agree that gross domestic product is the best way to measure
GDP measures our ability to obtain many of the inputs into a worthwhile existence but does not directly measure the things that make life valuable.
What is meant by GDP?GDP accounts for both total income and total expenditure on goods and services in the economy. Thus, GDP per person tells us about the average person's income and expenditure in the economy. Because most people would prefer to have a higher income and spend more money, The average person's GDP per person appears to be a straightforward indicator of their financial security.
People want to know whether an economy's total output of goods and services is increasing or decreasing. However, because GDP is collected at current, or nominal, prices, it is impossible to compare two periods without accounting for inflation.
To calculate "real" GDP, the nominal value must be adjusted to account for price changes, allowing us to see whether the value of output has increased because more is produced or simply because prices have risen.
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car is coasting backwards downhill at a speed of 2.9 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 4.8 m/s. Assuming that the uphill is the positive direction, what is the car's average acceleration? m/s2
The average acceleration of the car is 3.08 m/s² .
The speed of the car down hill = - 2.9m/s
The speed of the car uphill = 4.8 m/s
An object's average acceleration over time is determined by dividing the change in velocity, Δv, by the duration of the period, Δt.
Average acceleration = Δv ÷ Δt
Now the change in velocity ΔV = 4.8 - (-2.9) = 7.7 m/s
Change is time Δt = 2.5 seconds
Average acceleration of the car = 7.7 / 2.5 m/s² = 3.08 m/s²
In mechanics, the acceleration is the change is speed that refers to the exact rate at which the object's velocity varies with respect to time varies. Acceleration is a vector quantity since it has both a magnitude and a direction. The direction of an object's acceleration is determined by the direction of the net force acting on it.
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f (x) = x² + x - 1 F (X + 2)
need help asappppppp
To find a, we will use the Pythagoras theorem,
adjacent² + opposite² = hypotenuse²
From the diagram, opposite = 5 adjacent = a hypotenuse =13
substitute the values into the formula and evaluate
a² + 5² = 13²
a² + 25 =169
subtract 25 from both-side of the equation
a² = 169 - 25
a² =144
Take the square root of both-side
a = 12