[tex]\huge{\boxed{25}}[/tex]
The radius is the distance from the center of the circle to its edge.
The diameter is the distance from one point on the edge to the opposite point on the edge, so it is twice as much as the radius.
This means we just need to multiply the radius by two to get the diameter. [tex]2r=d[/tex]
[tex]2(12.5)=d[/tex]
[tex]\boxed{25}=d[/tex]
What is the domain of y=4sin(x)?
Answer:
( − ∞ , ∞ ) { x | x ∈ R }
Step-by-step explanation:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
soccer practice ended at 7:00 the team stretched for 10 minutes and practice for 40 minutes. then they played a game for 35 minutes. what time did the soccer practice start
Gram is planning a party he for his younger sister he has 36 prizes and 24 Blynn's how many children can he have at the party's of each child gets an equal number of prizes and and an equal number of balloons
Answer:
12 children
Step-by-step explanation:
you would just find the GCF (greatest common factor) of these 2 numbers, which is 12
so each child would get 3 prizes and 2 balloons
Prasant wants to write a statement that can be represented by the inequality h>4.5 Which describes the correct method to write a statement to match this inequality?
Answer:
Prasant needs more than 4.5 bags of candy to hand out during Halloween.
Step-by-step explanation:
The correct method to write a statement that matches the inequality [tex]\( h > 4.5 \)[/tex] is to express that the value of [tex]\( h \)[/tex] is greater than 4.5. This can be done by stating that [tex]\( h \)[/tex] must be some quantity more than 4.5, without specifying the exact amount by which [tex]\( h \)[/tex]exceeds 4.5.
For example, one could write the statement as:
The value of [tex]\( h \)[/tex] is more than 4.5 units.
This statement correctly conveys that [tex]\( h \)[/tex] is not equal to 4.5 and is somewhere on the number line to the right of 4.5, with no upper limit specified. It is important to note that the inequality [tex]\( h > 4.5 \)[/tex] does not include the value 4.5 itself; [tex]\( h \)[/tex] must be strictly greater than 4.5.
In summary, the statement should indicate that \( h \) is any number that is greater than 4.5, and the value of [tex]\( h \)[/tex] can be infinitely close to 4.5 but never equal to or less than it.
The chord XY is a diameter of of O. True or false?
Answer:
False
Step-by-step explanation:
XY is the diameter of the circle with the centre of this circle being O.
But O on it's own is just a coordinate, and not the circle.
Answer:
False, XY is not a diameter
Step-by-step explanation:
To be a diameter, it must go through the center of the circle, which is point O
The chord XY does not pass through the point O, so XY cannot be a diameter
A minivan is purchased for $29,248. The value of the vehicle depreciates over time. Describe the advantages and disadvantages of using a linear function to represent the depreciation of the car over time. Describe the advantages and disadvantages of using an exponential function to represent the depreciation of the car over time. The minivan depreciates $3,000 in the first year. Write either a linear or exponential function to represent the value of the car x years after it was sold.
Answer:
Advantage: If a car is losing value at a constant rate, then the linear function represents accurately the depreciation of the car.
Disadvantage: If the car is not losing value at a constante rate, then when we calculate the value of the car 'x' years after it was sold, we won't get an accurate result.
If the minivan is purchased for $29,248 and the first year it depreciates $3000. Then, the linear function that represents the value of the car is:
y = $29,248 - $3000x
Where 'y' represents the value of the car, and 'x' represents the number of years.
Let us explain this with an example. After 6 years, the price will be:
y = $29,248 - $3000(6) = $11,248
The advantages of using a linear function to represent the depreciation of a car are simplicity and ease of calculation, but it assumes constant depreciation rate. On the other hand, an exponential function can account for varying depreciation rates, but can be more complex. The linear function to represent the value of the minivan after x years is V(x) = 29,248 - 3,000x.
Explanation:When representing the depreciation of a car over time, using a linear function has advantages and disadvantages. The advantages are that it provides a simple and straightforward representation of the depreciation, and it is easy to calculate and understand. However, a linear function assumes that the car depreciates at a constant rate over time, which may not always be accurate.
On the other hand, using an exponential function to represent the depreciation of the car has advantages and disadvantages as well. The advantage is that it can account for different rates of depreciation over time, which may be more realistic. However, exponential functions can be more complex to calculate and understand.
In the case of the minivan that depreciates $3,000 in the first year, a linear function can be used to represent the value of the car x years after it was sold. The linear function would be V(x) = 29,248 - 3,000x, where V(x) is the value of the car x years after it was sold.
The square or a number exceeds that number by 12. What are the two possible solutions.
I'm going to assume that you meant to write: The square of a number exceeds that number by 12. What are the two possible solutions.
In other words x² = x + 12
4² is 16.
4 + 12 = 16
(-3)² is 9
-3 + 12 = 9
Hope this helped!
~Just a girl in love with Shawn Mendes
There are 15 research doctors participating in the study and the research board needs to be established with the offices of director, assistant director, quality control analyst, and correspondent. (Doctors can only hold one office on the research board.) Determine how many ways this research board can be chosen and explain your process.
Answer:
32760
Step-by-step explanation:
There are 4 positions on the board. There are 15 possible candidates for the first position. That leaves 14 candidates for the second position. Which leaves 13 for the third position, and 12 for the fourth position.
15 × 14 × 13 × 12 = 32760
Answer: There are 32,760 ways that research board can be chosen.
Step-by-step explanation:
Since we have given that
Number of research doctors participating in the study = 15
the research board requires to be established with offices of director, Assistant director, Quality control analyst, and Correspondent.
Since there are 15 choices for the Offices of director,
There are 14 choices for the Assistant director,
There are 13 choices for Quality control analyst,
There are 12 choices for Correspondent.
So, by applying "Fundamental theorem of counting", we get that
Number of ways that research board can be chosen is given by
[tex]15\times 14\times 13\times 12\\\\=32,760[/tex]
Hence, there are 32,760 ways that research board can be chosen.
For f(x)=2x+1 and g(x)=x+14, find (g o f)(x).
A) 2x^2-6
B) 4x^2+4x-6
C) 2x+15
D) 2x^2-13
Answer:
C) 2x + 15Step-by-step explanation:
[tex](g\circ f)(x)=g\bigg(f(x)\bigg)\\\\f(x)=2x+1,\ g(x)=x+14\\\\\text{Exchange}\ x\ \text{in}\ g(x)\ \text{to}\ (2x+1):\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)=g(2x+1)=(2x+1)+14=2x+15[/tex]
Find the slope of the linear function graphed below.
A. m=-4/3 B. m=4/3 C. m=3/4 D. m=-3/4
Answer:
0
Step-by-step explanation:
use the slope formula y^2-y^1
x^2-x^1
Add 7.8*10^5+2.4*10^5
Answer:
1020000
Step-by-step explanation:
Step 1 : Use BODMAS (Bracket Open Divide Multiply Add Subtract)
Step 2 : Take the common term
7.8*10^5+2.4*10^5
10^5(7.8 + 2.4)
Step 3 : Solve
10^5(7.8 + 2.4)
100,000(10.2)
=1020000
!!
Answer:
1.02 × 106
Step-by-step explanation:
1.02 × 106
PLEASE HELP!!!!!!!!!!!!!!!!!!!
SOON
Answer:
1. so the total people including the teacher is 24. 12 and 8 are both factors of 24. 12x2 equals 24 and 8x3 equals 24 so if they get 2 packs of hot dogs and 3 pack of buns everyone can get 1 hot dog and 1 bun
Step-by-step explanation:
24 factors: 1, 2, 3,4 ,6,8,12 ,24
8×3=24
12×2=24
get 2 packs of sausages and 3 packs of buns
each person gets 1 hotdog and 1 bun
The quotient of (x4 + 5x3 – 3x – 15) and a polynomial is (x3 – 3). What is the polynomial?
Answer:
x+5
Step-by-step explanation:
Given:
Dividend= x4 + 5x3 – 3x – 15
Quotient=(x3-3)
As per the rule of division of polynomial:
Dividend = Divisor × Quotient + Remainder
Divisor= required polynomial p(x)
remainder=0
x4 + 5x3 – 3x – 15= p(x) *(x3-3) + 0
p(x)=x4 + 5x3 – 3x – 15/x3-3
By long division we get
p(x)= x+5 !
Answer:
The polynomial is x+5.
Step-by-step explanation:
Here we need to recall the algorithm of the division for polynomials, which is very similar to the one for integers. Given polynomials P(x) and Q(x), there always exist polynomials S(x) and R(x) such that
P(x) = Q(x)S(x) + R(x)
where
R(x) is the remainder,S(x) is the quotient,Q(x) is the divisor,P(x) is the dividend.In this particular case,
P(x) = x⁴+5x³-3x-15,S(x) = x³-3R(x) = 0Q(x), is what we are looking for.Then, x⁴+5x³-3x-15 = (x³-3)Q(x). In order to find Q(x) we must complete the division x⁴+5x³-3x-15/x³-3. This gives us that Q(x)=x+5.
A triangle ABC is dilated by a scale factor of 3 to form another triangle, LMN.
Find the measure of the sides of the triangle LMN.
Answer:
Choice B
Step-by-step explanation:
A dilation factor of three means you multiply each side bye three. The order of the letters of the triangle also matter. Since it is triangle LMN and ABC this means that A corresponds with L, B corresponds with M and C corresponds with N.
162*0.967=what? {this is multiplication}
Answer:
156.654
Step-by-step explanation:
162*.967=156.654
To multiply 162 by 0.967, use a calculator or perform the multiplication manually to get approximately 156.654.
The product of 162 and 0.967, you can multiply these two numbers together. When you multiply a whole number by a decimal, you're essentially combining that many groups of the decimal number. In this case, you are combining 162 groups of 0.967.
Here is the step-by-step calculation:
Write down the numbers: 162 and 0.967.
Multiply the whole number by the decimal: 162 * 0.967.
Use a calculator or long multiplication to find the product.
If you use a calculator, the answer you would get is approximately 156.654.
If 47400 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $
(b) Semiannual: $
(c) Monthly: $
(d) Daily: $
Using the formula for compound interest, you can calculate the future value of an investment for different compounding methods. These values turned out to be $66299.84 for annual compounding, $66933.56 for semi-annual compounding, $67183.56 for monthly compounding and $67239.46 for daily compounding.
Explanation:To solve this problem, you need to understand the compound interest formula: A = P(1 + r/n)^(nt).
Where:
A = the future value of the investment/loan, including interestP = principal investment amount (initial deposit)r = annual interest rate (in decimal form)n = number of times interest is compounded per yeart = time the money is invested for, in years(a) For annual compounding (n=1): A = 47400*(1 + 0.07/1)^(1*5) = $66299.84
(b) For semi-annual compounding (n=2): A = 47400*(1 + 0.07/2)^(2*5) = $66933.56
(c) For monthly compounding (n=12): A = 47400*(1 + 0.07/12)^(12*5) = $67183.56
(d) For daily compounding (n=365): A = 47400*(1 + 0.07/365)^(365*5) = $67239.46
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Final answer:
Calculate the value of the investment after 5 years using different compounding methods.
Explanation:
The value of the investment at the end of 5 years:
Annual: $61,571.76
Semiannual: $62,041.46
Monthly: $62,263.11
Daily: $62,334.74
help please. i suck at math
For this case we must convert the given expression to degrees:
[tex]\frac {3 \pi} {8}[/tex]
By definition we have that [tex]\pi = 180[/tex] degrees, then:
[tex]\frac {3 \pi} {8} * \frac {180} {\pi} = \frac {180 * 3} {8} = \frac {540} {8} = 67.5[/tex]
Thus, we have [tex]\frac {3 \pi} {8}[/tex] is equal to 67.5 degrees.
Answer:
67.5 degrees
4. June Elloy makes a 22 percent down payment on a home in Rockford,
Illinois. What is the purchase price of the home assuming her down
payment is $35,200?
Answer:
the price is $160000
Step-by-step explanation:
0.22x = 35200
x=160000
Is M a midpoint of line AB= ? AB= 27 and MB =14
A maybe
B can’t be
C no
D yes
if 1 liter cost $12 how much does 2.5 L cost
Answer:
$30
Step-by-step explanation:
because we know that "1 liter cost(s) $12" we can multiply 12 by 2.5 (the amount we need to know) to get $30
Answer:
$30.0
Step-by-step explanation:
What you'll need to do is multiply 12 by 2.5.
[tex]12.5x2.5=300\\\\$30.0[/tex]
What is the difference of the rational expressions below?
3x/x-5 -4/x
Answer:
3x^2-4x+20/x^2-5x .
Step-by-step explanation:
The given rational expression is:
3x/x-5 - 4/x
Hence to find the difference of the rational numbers we have to take the L.C.M of the denominators:
Thus the L.C.M of x-5 and x is (x-5)(x) and then solve for the numerator:
x(3x) - 4(x-5)/(x-5)(x)
Now solve the numerator and denominator:
3x^2-4x+20/x^2-5x
Thus the answer is 3x^2-4x+20/x^2-5x ....
Answer:
3x^2-4x+20
-----------------
x(x-5)
Step-by-step explanation:
The tail of an airplane is 62 feet, 10 inches tall. How many inches tall is the tail
Answer:
754 inches
Step-by-step explanation:
you have to convert the 62 feet into inches which will be 62*12=744. You then add 10 to it to get 754 as your answer.
How would you answer this math question please this is my last question
Answer:
Shorter sides: 270 feet.
Larger side: 540 feet.
Greatest possible area: 145800 square feet.
Step-by-step explanation:
So we need fencing around the garden except along the river.
The opposite sides of a rectangular are congruent.
So the sides perpendicular to the river in the picture are both of the same length, let's call it x. The length opposite the river is y.
So the perimeter excluding the side along the river is
x+x+y or 2x+y or 1080 is how much fencing we want.
So we have the equation:
2x+y=1080
The area of rectangle can be found by multiplying it's dimensions:
xy=A
We want to find the dimensions that provide us with the maximum area.
This is our area function so for:
A=xy
We need the area to be in terms of one variable.
Let's use our condition that 2x+y=1080.
2x+y=1080
Subtract 2x on both sides:
y=1080-2x
or
y=-2x+1080
We are going to plug this into:
[tex]A=xy[/tex]
[tex]A=x(-2x+1080)[/tex] : I replaced y with -2x+1080 since y=-2x+1080.
[tex]A=-2x^2+1080x[/tex] : I distribute.
Let's find the x-coordinate of the vertex.
To do this we need to determine [tex]a[/tex] and [tex]b[/tex] in the comparison of
[tex]A=ax^2+bx+c[/tex].
[tex]a=-2[/tex]
[tex]b=1080[/tex]
[tex]c=0[/tex]
The formula for the x-coordinate of the vertex is [tex]\frac{-b}{2a}[/tex].
[tex]\frac{-b}{2a}=\frac{-1080}{2(-2)}=\frac{1080}{4}=270[/tex]
We could plug this into our area Area function in terms of to find maximum area.
We could also wait til later. I think I will do both for a later check.
[tex]A=-2x^2+1080x[/tex] with [tex]x=270[/tex]
[tex]A=-2(270)^2+1080(270)[/tex]
[tex]A=145800[/tex]
So we one dimension of the rectangle so for which is 270 feet.
We have the maximum area which is 145800 square feet.
Now recall y=-2x+1080.
y=-2x+1080 with x=270
y=-2(270)+1080
y=540
So we have one dimension of the rectangle is 270 feet.
Another dimension is 540 feet.
And the area of the rectangle is 145800 square feet.
Does 270(540) equal 145800? 270(540)=145800 so yes.
Let's check to see if we have 1080 feet of fencing.
So we have 2 small sides of 270 and 270 feet.
We have a larger side which is 540 feet.
270+270+540=10180 so everything checks out.
Do you prefer to express solutions to inequalities using interval notation or as an inequality ? Do you think it’s important to know both formats ? How could each be used ?
Answer:
I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.
For example, if you have the following inequation:
x-2> 1
x>3
Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U (3, inf) instead of 'x>3 or x<-3' which is more confusing.
A salad dressing is made by combining 2 part vinegar 5 part oil. How much ounces of oil should be mixed with 9 ounces of vinegar?
[tex]\bf \begin{array}{ccll} vinegar&oil\\ \cline{1-2} 2&5\\ 9&x \end{array}\implies \cfrac{2}{9}=\cfrac{5}{x}\implies 2x=45\implies x=\cfrac{45}{2}\implies x=22\frac{1}{2}[/tex]
22.5 ounces of oil should be mixed with 9 ounces of vinegar
EquationAn equation is an expression that shows the relationship between two or more variables and numbers.
Given that:
2 part vinegar 5 part oil.
Let y represent the amount of oil to be mixed with 9 ounces of vinegar.
y = (5/2) * 9 = 22.5 ounces
22.5 ounces of oil should be mixed with 9 ounces of vinegar
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Given the functions f(x) = 10x + 25 and g(x) = x+8, which of the following functions represents f(g(x)] correctly?
Answer:
g(x + 8) = 10x + 105 wherever you see it among your answers.
Step-by-step explanation:
I think I have enough here that I can answer the question, but you should always put in your givens.
f(x) = 10x + 25 Put g(x) where you see x in f(x)
f(g(x)) = 10(g(x) + 25 Put the value for g(x) where you see g(x)
f(x+8) = 10(x + 8) + 25 This might be the answer
From here it is a guess.
f(x+8) = 10x + 80 + 25 Combine the like terms
f(x+8) = 10x + 105
Answer:
on flvs its option C
Step-by-step explanation:
David opened a coffee shop and sold 60 mochas the first day at $2 per cup. He wants to increase the price per cup to increase his revenue. He found out that for every $0.25 increase, x, in the price per cup, the number of cups he sold decreased by 2 per day. How can David find the equation which represents his daily revenue, in dollars, from mocha sales when the price is increased x times?
Answer: Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120
We know that David wants to increase the price per cup to increase his revenue. He found out that for every $0.25 grows( increase), x, in the price for each cup.
In the event of a price increase, 2 cups remain unsold, and doubling the cups is still not sold. Then the numbers are sold (60-2x). Depending on the choice:
Revenue= (60 -2x)(2 +0.25x)
60·2 +60·0.25x -2x·2 -2x·0.25x
= -0.5x² +11x +120
Answer:
Multiply (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x2 + 11x + 120
Step-by-step explanation:
Here, x represents the times at which the price is increased,
Since, the original price of one cup = $ 2,
So, after increasing x times of $ 0.25, the new price of each cup = 2 + 0.25x,
Also, the original number of mochas = 60,
Given,
With increasing the price $ 0.25, x times, the number of cup is decreased by 2 times of x,
That is, the new number of mochas = 60 - 2x
Hence, the total revenue would be,
y = new price of each cup × new number of mochas
⇒ y = (2 + 0.25x)(60 - 2x)
⇒ y = 120 - 4x + 15x - 0.5x²
⇒ y = -0.5x² + 11x + 120
He can find find the equation which represents his daily revenue, by Multiplying (60 − 2x) and (2 + 0.25x) to create the equation y = -0.5x² + 11x + 120
What is the scale factor of this dilation?
a) 1/5
b) 1/2
c) 1
d) 2
2 because everything is multiplied by 2 so the scale factor is two
What is the quotient?
9
Answer:
Step-by-step explanation:
Dividing one number by another yields a quotient. The quotient of 9 divided by 15 can be expressed as a decimal or a fraction. Any time you divide a number by a larger number, the answer will always be less than one.
Answer:
C
Step-by-step explanation:
1/9
Point Q is on line segment PR. Given QR=11 and PQ=3, determine the length PR.
.
Final answer:
The length of line segment PR is the sum of the lengths of PQ and QR, which is 14 units.
Explanation:
The question asks us to determine the length of line segment PR given that point Q is on line segment PR, QR=11 units, and PQ=3 units. To find the length of PR, we simply add the lengths of PQ and QR together, since Q lies on line segment PR meaning PQ and QR are consecutive segments.
Therefore, the length of PR is PQ + QR = 3 + 11, which equals 14 units.