Answer:
$49.50
Step-by-step explanation:
First, let's find how much total interest was made
For every year, 2.5% interest was made
Since we're finding the total for 4 years
It will be 4 x 2.5 = 10% total interest
Now let's find 10% of 45
45 x .1 = 4.5
This means we made $4.5 in those 4 years
Now we just add it to our starting amount
45 + 4.5 = 49.5
Consider an experiment in which a marble is tossed into a box whose base is shown in the figure. The probability that the marble will come to rest in the shaded portion of the box is equal to the ratio of the shaded area to the total area of the figure. If the probability is equal to 3/10, find the positive value of x.
Answer:
x = 2
Step-by-step explanation:
Probability that the marble comes to rest in the shaded region is equal to the ratio of the shaded area to the total area.
Probability 'P' = [tex]\frac{A'}{A}[/tex]
Area of the shaded region (A')= (x + 1)(x + 2)
Total area of the figure (A) = (2x + 1)(3x + 2)
P = [tex]\frac{(x+1)(x+2)}{(2x+1)(3x+2)}=\frac{3}{10}[/tex]
10(x + 1)(x + 2) = 3(2x + 1)(3x + 2)
10(x² + 3x + 2) = 3(6x² + 7x + 2)
10x² + 30x + 20 = 18x² + 21x + 6
(18x² - 10x²) + (21x - 30x) + (6 - 20) = 0
8x² - 9x - 14 = 0
x = [tex]\frac{9\pm\sqrt{(-9)^2-4(8)(-14)} }{2(8)}[/tex]
x = [tex]\frac{9\pm \sqrt{81+448}}{16}[/tex]
x = [tex]\frac{9\pm 23}{16}[/tex]
x = -[tex]\frac{7}{8}, 2[/tex]
Therefore, positive value of x = 2 will be the answer.
(Prove) The angle subtended by an arc at the center is double the angle subtended by it at any
point on the remaining part of the circle.
Answer:
The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.
Step-by-step explanation:
Let us consider the image attached.
Center of circle be O.
Arc AB subtends the angle [tex]\angle APB[/tex] on the circle and [tex]\angle AOB[/tex] on the center of the circle.
To prove:
[tex]\angle AOB = 2 \times \angle APB[/tex]
Proof:
In [tex]\triangle PAO[/tex]: AO and PO are radius of the circles so AO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PAO = \angle OPA[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle AOQ = \angle PAO + \angle OPA=2 \times \angle APO .... (1)[/tex]
Similarly,
In [tex]\triangle PBO[/tex]: BO and PO are radius of the circles so BO = PO
And angles opposite to equal sides of a triangle are also equal in a triangle.
So, [tex]\angle PBO = \angle OPB[/tex]
Using external angle property, that external angle is equal to sum of two opposite internal angles of a triangle.
[tex]\angle BOQ = \angle PBO + \angle OPB=2 \times \angle BPO .... (2)[/tex]
Now, we can see that:
[tex]\angle AOB = \angle AOQ+\angle BOQ[/tex]
Using equations (1) and (2):
[tex]\angle AOB = 2\angle APO+2\angle BPO\\\angle AOB = 2(\angle APO+\angle BPO)\\\bold{\angle AOB = 2(\angle APB)}[/tex]
Hence, proved.
Hope you could understand.
If you have any query, feel free to ask.
Every time Liliana bakes a batch of brownies, she uses 34 cup of chocolate. If she has 128 cup(s) of chocolate remaining, how many batches of brownies can Liliana make? Input your answer as a whole number.
Answer:
3
MARK BRAINLIEST IF THIS HELPED!
i hope u have a great day.
Solve the equation for x
Answer:
x = 33
Step 1:
First, let's add the values together from both parentheses.
2x + x = 3x
1 + (-10) = -9
Now we are left with:
3x - 9 = 90.
Step 2:
Add 9 on the left side to cancel out the 9. Add it to the right side.
3x = 99
Finally, divide both sides by 3 to get our answer.
3x / 3 = x
99 / 3 = 33
x = 33
1/sec-1 + 1/sec+1 = 2cotcosec
Solution :
LHS = 1/(secA -1) + 1/(secA+1)
= [secA+1+secA-1]/[(secA-1)(secA+1)]
= (2secA)/[sec²A-1]
=(2secA)/tan²A
= (2/cosA)/(sin²A/cos²A)
= ( 2cosA)/sin²A
= 2(1/sinA)(cosA/sinA)
= 2cosecAcotA
= RHS
••••
A watermelon weighs 6.45 kilograms. How many grams does the watermelon weigh?
Answer:
6450g
Step-by-step explanation:
1kg = 1000g
6.45kg = 6450
The watermelon weighs 6450 grams.
Given that a watermelon weighs 6.45 kilograms.
We need to convert its unit into grams.
To convert kilograms to grams, you need to multiply the weight in kilograms by 1000, as there are 1000 grams in 1 kilogram.
The watermelon weighs 6.45 kilograms, you can use the following formula to convert it to grams:
Weight in grams = Weight in kilograms × 1000
Let's do the math:
Weight in grams = 6.45 kilograms × 1000 = 6450 grams
So, the watermelon weighs 6450 grams.
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What is the volume of the rectangular prism in simplest terms?
Answer:
V=w*h*l
Step-by-step explanation:
w=width
h=height
l=length
volume = w*h*l
volume = w*h*l
volume = w*h*l
A prepaid phone card has a balance of $22.40 remaining. If calls are $0.035 per minute, which equation represents the number of minutes, m, you may talk using the card?
m/.035 = 22.40
22.40m = 0.035
m/22.40 = 0.035
0.035m = 22.40
Answer:
0.035m = 22.40
Find the value of x in the given
right triangle.
Enter your answer as a decimal rounded to the
nearest tenth.
Answer:
x = 12.5Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use cosine
cos∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 10
Substitute these values into the above formula and solve for x
That's
[tex] \cos(37) = \frac{10}{x} [/tex][tex]x \cos(37) = 10[/tex]Divide both sides by cos 37
[tex]x = \frac{10}{ \cos(37) } [/tex]x = 12.52135
We have the final answer as
x = 12.5 to the nearest tenthHope this helps you
Answer:
probably 16.5
Step-by-step explanation:
I had $20.00 My Mom gave me $10.00. My Dad Gave me $50.00 My Aunt & Uncle gave me $100.00. I had another $5.00. How much did I have? I had $20.00 My Mom gave me $10.00. My Dad Gave me $50.00 My Aunt & Uncle gave me $100.00. I had another $5.00. How much did I have?
Answer:
you have $185 in total unless the aunt and uncle gave you 100 each, then your answer would be $285
Step-by-step explanation:
Answer:
0$
Step-by-step explanation:
simple
SOMEONE HELP ME!!!! I WILL GIVE BRAINLIEST!!!
Answer:
B
Step-by-step explanation:
well if we draw the graph we have the following image, and the only one that applies is
B
because 4>3
help..lol i dont need help just to lazy
Answer:
C. -2(-2)
Step-by-step explanation:
A. -2(-1/5) = 1
B. -2(1/2)=1
C. -2(-2)=4
D. -2(2)=-4
Please answer this question now
Answer:
76 degrees.
Step-by-step explanation:
Let as consider O is the center of the circle . So from the figure it is clear that
[tex]\angle AOB=44^{\circ}[/tex]
[tex]\angle COD=118^{\circ}[/tex]
By central angle theorem, central angle subtended by an arc is twice of inscribed angle of the same arc.
We know that, [tex]\angle BAD=97^{\circ}[/tex] and angle BOD is the central angle subtended by arc BD.
[tex]\angle BOD=2\times \angle BAD[/tex]
[tex]\angle BOD=2\times 97^{\circ}[/tex]
[tex]\angle BOD=194^{\circ}[/tex]
Now,
[tex]\angle BOD=\angle BOC+\angle COD[/tex]
[tex]194^{\circ}=\angle BOC+118^{\circ}[/tex]
[tex]194^{\circ}-118^{\circ}=\angle BOC[/tex]
[tex]76^{\circ}=\angle BOC[/tex]
[tex]m(arc(BC))=76^{\circ}[/tex]
Therefore, the measure of arc BC is 76 degrees.
Select the correct answer.
What is the value of x in the figure?
X
400
700
A. 40°
B. 70°
C.80°
D. 120°
E. 150°
Answer: x = 150
Step-by-step explanation:
See the liner pair of angle 70 will be 110 degrees.
Then using angle sum property third angle will be
Third angle = 180 - 150
Third angle of the triangle = 30
Now linear pair of the 30 degree angle
30+x = 180
x = 180-30
x = 150
Therefore answer is option e x = 150.
please click thanks and mark brainliest if you like :)
The measure of the value of angle x is 150°, and the correct option is E
What is the linear pair of angles?Linear pair of angles are formed when two lines intersect each other at a single point.
The angles are said to be linear if they are adjacent to each other after the intersection of the two lines.
BY applying linear pair angles;
[tex]\rm \angle 1+\angle 2=180\\\\70 +\angle 2=180\\\\ \angle 2=180-70\\\\ \angle 2=110\\\\[/tex]
The sum of the three angles is 180.
[tex]\rm \angle 1+\angle 2+ \angle 3=180\\\\ 110+40 +\angle 3=180\\\\150+\angle 3= 180\\\\\angle 3=180-130\\\\\angle 3=30[/tex]
The measure of the value of angle x is;
[tex]\rm 30+x = 180\\\\x = 180-30\\\\x = 150[/tex]
Hence, the measure of the value of angle x is 150°, and the correct option is E.
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Please help...Will give brainiest
Answer:
19.45
Step-by-step explanation:
The median is the middle number. Put the data in order from smallest to largest
16.3, 17.8,17.8 ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4
There are 12 pieces of data,
16.3, 17.8,17.8 ,18.0, 18.7,19.3, 19.6,20.1,20.5, 21.9, 25.2 ,25.4
The median lies between the 6th and 7th piece
Add the 6th and 7th together and divide by 2
(19.3+19.6)/2 =19.45
Answer:
[tex]\large \boxed{\mathrm{19.45}}[/tex]
Step-by-step explanation:
Median of a data set is the middle value.
The data is to be arranged from smallest to largest.
16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4
Find the middle value.
16.3, 17.8, 17.8, 18.0, 18.7, 19.3, 19.6, 20.1, 20.5, 21.9, 25.2, 25.4
Average the two middle numbers.
(19.3+19.6)/2 = 19.45
The median of the data set is 19.45.
Express 0.504 as a fraction in its lowest term
Answer:
63/125
Step-by-step explanation:
Turn the decimal .504
=> 504/1000
=> 504/1000 = 252/500
=> 252/500 = 126/250
=> 126/250 = 63/125
=> 63/125 cannot be simplified anymore.
So, 63/125 is the simplified fraction of .504
Farmer McDonald raises ducks and cows. His animals have a total of 20 heads and
64 legs. How many ducks and how many cows does Mr. McDonald have?
Answer:
8 ducks, 12 cows
Step-by-step explanation:
Let the ducks be x in number and cows be y in number
ATQ, x+y=20 and 2x+4y=64, solving we get y=12 and x=8.
If farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs. Mr. McDonald has 8 ducks and 12 cows.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, Farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs.
Suppose the number of head and legs be x and y respectively.
If His animals have a total of 20 heads and 64 legs,
x+y=20
2x+4y=64,
Solving the above equations we get y=12 and x=8.
Thus, if a farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs. Mr. McDonald has 8 ducks and 12 cows.
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A man makes a profit of 15%6y selling an article for Rs 2500. For what price should he sellituto make a profit of 38%
Find the price before the 15% profit:
2500 / 1.15 = 2173.91
Now multiply the original cost by 1 + 38%:
2173.91 x 1.38 = 2999.99
Answer: 2.999.99 ( may need to round to 3,000)
what is x if y is 50, it is equivalent to 9/150. the first peep gets brainliest
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 3
▹ Step-by-Step Explanation
[tex]\frac{9}{150} \\\\150/3 = 50\\9/3 = 3\\\\x = 3[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
what is the no solution, the one solution, and the infinitely many solution of 2x+5+2x+3x
Answer:
This problem shows an expression, not an equation.
It cannot be solved.
An equation needs an equal sign.
X = [?]°
Dr.
X Х
As
140°
B
C
Answer:
40°
Step-by-step explanation:
x+140=180°(angle on a straight line)
x=180-140
x=40°
∠DBA and ∠DBC are making linear pair.
Linear pair of angles are formed when two lines intersect each other at a single point.
The sum of angles of a linear pair is always equal to 180°[tex] \rm \large\longrightarrow \: \: x \: + \: 140 \degree \: = \: 180 \degree[/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 140 \degree \: [/tex]
[tex]\rm \large\longrightarrow \: \: x \: = \: 40 \degree[/tex]
Is the statement [x]=[x+1] true for all real numbers
Answer:not true
Step-by-step explanation:
To say not true we need only one example so we can take x as -5
[-5]= [-5+1]
5 not equal with 4
what is the same number like 0.07
Answer:
we need more information
Step-by-step explanation:
Find the volume of this cone.
Use 3 for T.
3ft
17 ft.
V = Tr2h
3
V
V ~ [?]ft?
Enter
your answer in decimal form.
Answer:
15.75 ft^3
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h where r is the radius and h is the height
We know the diameter is 3 so the radius is 1/2 the diameter or 3/2
The height is 7 and we will use 3 for pi
V = 1/3 (3) (3/2)^2 *7
V = 15.75 ft^3
Solve the inequality for x.
7 > 2x+9
Answer:
x<-1Step-by-step explanation:
[tex]7 > 2x+9\\\\\mathrm{Switch\:sides}\\\\\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\2x+9-9<7-9\\\\2x<-2\\\\\frac{2x}{2}<\frac{-2}{2}\\\\x<-1[/tex]
-4(-w-10)=
i need help don’t know what the answer is
Answer:
[tex]\boxed{4w+40}[/tex]
Step-by-step explanation:
Use the distributive property to evaluate the equation.
-4(-w - 10)
4w + 40
-4 * -w = 4w because two negatives cancel to make a positive value.
-4 * -10 = 40 for the same reason.
I need help on this question please.
Answer:
27π inch^3
Step-by-step explanation:
Which technique is vital for giving an effective presentation?
A.
Focus on the audience’s opinions of your topic.
B.
Use eye contact and speak clearly and deliberately.
C.
Reference only your own thoughts and opinions about the topic.
D.
Use technical terms when speaking to an informal audience.
E.
Analyze the audience right before delivering your speech.
Reset
Answer:
B.
Use eye contact and speak clearly and deliberately.
Step-by-step explanation:
let me know if you have any questions
Answer:
b
Step-by-step explanation:
because
FOR BRAINLIEST!!!!ASAP
19) One number is 9 more than another. Their product is 11 more than five times their sum.
Find the numbers.
Answer:
-7 and 2 or 8 and 17
Step-by-step explanation:
If we let the numbers be [tex]x[/tex] and [tex]x+9[/tex], the equation to solve this problem will be as follows:
[tex]x(x+9)=5(x+x+9)+11[/tex]
Solving the equation for [tex]x[/tex], we get:
[tex]x(x+9)=5(x+x+9)+11[/tex]
[tex]x(x+9)=5(2x+9)+11[/tex] (Combine like terms)
[tex]x^{2} +9x=10x+45+11[/tex] (Use the Distributive Property of Multiplication to multiply expressions)
[tex]x^{2} +9x=10x+56[/tex] (Combine like terms)
[tex]x^{2} -x-56=0[/tex] (Subtract [tex]10x[/tex] and [tex]56[/tex] from both sides of the equation)
[tex]x^{2} -8x+7x-56[/tex] (Split [tex]-x[/tex])
[tex]x(x-8)+7(x-8)=0[/tex] (Factor by taking a common term out)
[tex](x-8)(x+7)=0[/tex] (Factor by taking a common term out)
[tex]x-8=0[/tex] or [tex]x+7=0[/tex] (Use the Zero Product Property)
[tex]x=8[/tex] or [tex]x=-7[/tex]
Therefore, the first number could be either -7 or 8, and the second number could be -7 + 9 = 2 or 8 + 9 = 17, respectively. Hope this helps!
Create a figure with half the perimeter of a given figure.
you don't have to actually make a shape, can someone explain how to do this pls
Step-by-step explanation:
First you have to add up all of the numbers that make up the perimeter of this arrow.
3+3+1+.5+.5+1.8+1.8=11.6
You than want to divide this number by 2 to find the half perimeter you have to work with, which is 5.8.
A simple shape you can make is a square, with each side being 1.45 m.