Answer:
125
Step-by-step explanation:
500 ÷ 4 = 125
I think this is the right answer. sorry if I'm wrong.
Answer:
x=5 assuming that x is the radius.
x is the radius?
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3[/tex] is the volume of a sphere.
We are given [tex]V=\frac{500}{3} \pi[/tex] cubic units.
We are asked to find the value of x. If x is not the radius, please correct me:
[tex]V=\frac{4}{3}\pi r^3[/tex] with [tex]V=\frac{500}{3} \pi[/tex] and the assumption that x is r.
[tex]\frac{500}{3}\pi=\frac{4}{3}\pi x^3[/tex]
If you multiply both sides by 3, then you would have:
[tex]500 \pi=4 \pi x^3[/tex]
If you divide both sides by [tex]\pi[/tex] you will have:
[tex]500=4x^3[/tex]
If you divide both sides by 4, you will have:
[tex]125=x^3[/tex]
The last step would be to take the cube root of both sides:
[tex]\sqrt[3]{125}=x[/tex]
[tex]5=x[/tex]
[tex]x=5[/tex]
Use the formula P=21+2w to find the width of a rectangle when the length is 18cm and perimeter is 48 ..
Answer:
w=6
Step-by-step explanation:
P=2(L)+2(w)
48= 2(18)+2w
48=36+2w
12=2w
w=6
checking;
48= 2(18)+2(6)
48= 36+12
48= 48
What is the area of ABC? Helppppp
Answer:
6 square units (rounded to nearest whole number)
Step-by-step explanation:
Area of triangle is found by the formula 1/2 * base * height
But we can't easily figure this out using this formula, instead we use another formula for area of a triangle:
[tex]A=\frac{1}{2}abSinC[/tex]
Where
A is the area
a and b are the two side given (3 and 5 in our case)
C is the angle between a and b (53 degrees given)
We can substitute into the formula and figure out:
[tex]A=\frac{1}{2}abSinC\\A=\frac{1}{2}(3)(5)Sin53\\A=5.99[/tex]
The area is 5.99, to the nearest whole number, the area is 6
A retail store pays a price of $6.25 per toy. It prices the toy at $k so that at a 25%- of sale, the store still makes a profit of 20%. Compute K
The store wants to make a 20% profit:
Multiply the cost of the toy by 1.20 ( cost plus 20%).
6.25 x 1.20 = $7.50
This means when the toy is sold at 25% off, it needs to be $7.50 to make the 20% profit.
When the item is 25% off, that means it would sell for 75% of the original price.
Now to find what the price needs to be before the 25% off divide the profit price by 75%
7.50 / 0.75 = $10
K = $10
Final answer:
To find the price at which the toy should be sold to maintain a 20% profit after a 25% discount, use the cost price and profit margin to calculate the selling price.
Explanation:
To compute the price at which the toy should be priced at a 25% discount and still make a profit of 20%, follow these steps:
Calculate the cost price after a 20% profit margin: $6.25 + 0.20 * $6.25 = $7.50
Set up the equation: $7.50 = (100% - 25%) * $k
Solve for k: $k = $7.50 / 0.75 = $10
help plz
question 1:
a.)8
b.)-8
c.)32.5
d.)-32.5
question 2:
a.)+8
b.)-8
c.)+32.5
d.)-32.5
Answer:
Question 1: 8
Question 2: -32.5
Step-by-step explanation:
Laura gets paid 8 dollars an hour to baby sit
8x represents how much Laura gets paid by the hour.
Laura owes her friend 32.50
-32.50 represents the amount she owes her friend
Combine
y = 8x - 32.50
Answer
Question 1: 8
Question 2: -32.5
Answer:
y = 8x-32.50
Step-by-step explanation:
She makes 8 dollars an hour babysitting. She will work x hours
She makes 8x
She owes 32.50 to her friend. This will be subtracted because she owes it
The amount of money she has at the end, y, is given by
y =8x-32.50
Expand. Your answer should be a polynomial in standard form. (b^2+5)(−b^2+7)=
(b^2+5)(−b^2+7)
Use the FOIL METHOD to expand.
-b^4 + 7b^2 - 5b^2 + 35
-b^4 + 2b^2 + 35
Did you follow?
Standard form (b^2+5)(−b^2+7) polynomial is = -b⁴+2b²+35
What are polynomials?A polynomial expression is an expression that can be built from constants and symbols.Polynomials are algebraic expressions that comprise exponents which can be added, subtracted, or multiplied. Polynomials are of different types. Monomial- Linear equations (A monomial is a polynomial with one term)Binomia l- quadratic equation (A binomial is a polynomial with two, unlike terms).
Using FOIL METHOD to expand.
(b²+5)(−b²+7)
=(b²+5)(7-b²)
=7b²-b⁴+35-5b²
=2b²-b⁴+35
= -b⁴+2b²+35
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What is 51/7 by 31/9 in simplest form
Answer:
51/7 = [tex]\frac7 {2}{7}[/tex] 31/9 = [tex]\frac3{4}{9}[/tex]
Step-by-step explanation: I hope this helps you!
Answer:
Step-by-step explanation:
51/7 = 7 2/7
31/9 = 3 4/9
Hope this helps!
Answer the equation below:
16-2t=5t+9
Answer:
t = 1
Step-by-step explanation:
Given
16 - 2t = 5t + 9 ( subtract 5t from both sides )
16 - 7t = 9 ( subtract 16 from both sides )
- 7t = - 7 ( divide both sides by - 7 )
t = 1
Answer:
2.43
Step-by-step explanation:
16-2t=5t+2t
16-9=5t+2t
17÷7=7t
t=2.43
h(x) = x2 + 1 k(x) = x – 2 (h + k)(2) =
Answer:
5
Step-by-step explanation:
Evaluate (h + k)(x) then substitute x = 2 into the result
(h + k)(x) = h(x) + k(x)
h(x) + k(x) = x² + 1 + x - 2 = x² + x - 1, thus
(h + k)(2) = 2² + 2 - 1 = 4 + 2 - 1 = 5
To find the value of (h + k)(2), substitute x = 2 into h(x) and k(x) and then add the results. The result is 5.
Explanation:To find the value of (h + k)(2), we first need to find the values of h(2) and k(2). To find h(2), we substitute x = 2 into the function h(x) = x² + 1. h(2) = (2)² + 1 = 4 + 1 = 5. Next, to find k(2), we substitute x = 2 into the function k(x) = x - 2. k(2) = 2 - 2 = 0. Now, we can find (h + k)(2) by adding the values of h(2) and k(2). (h + k)(2) = h(2) + k(2) = 5 + 0 = 5.
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This table shows how many sophomores and juniors attended two school events. What is the probability that the student attended the volleyball game, given that the student is a sophomore
A
B
C
or D
Answer:
B 0.55
Step-by-step explanation:
the student is a sophomore - so youre looking at the sophomore row, 77 sophomores total
the student attended the volleyball game - 42 sophomores attended the game
42 / 77 students total = about 0.55
Option: B is the correct answer.
B. 0.55
Step-by-step explanation:Let A denote the event that the student is a sophomore.
and B denote the event that the student attend the volleyball game.
and A∩B denote the event that the student is a sophomore and attend volleyball game.
Let P denote the probability of an event.
We are asked to find the probability : P(B|A)
We know that:
[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]
Based on the table provided to us we have:
[tex]P(A)=\dfrac{77}{137}[/tex]
and
[tex]P(A\bigcap B)=\dfrac{42}{137}[/tex]
Hence, we have:
[tex]P(B|A)=\dfrac{\dfrac{42}{137}}{\dfrac{77}{137}}[/tex]
i.e.
[tex]P(B|A)=\dfrac{42}{77}=0.55[/tex]
Using the diagram as marked, find the length
of HE if GE is the perpendicular bisector of HF.
HE = ??
HELP PLEASE!!
just a quick note, that triangle is misleading some, since the HG side of 6 units, shows longer than GE which is 8, and of course 8 > 6.
Since GE is a perpendicular bisector, that means the angle at G is 90°.
Check the picture below.
To find the length of HE, we utilize the properties of a perpendicular bisector and trigonometry. Knowing that GE halves HF into two equal parts, we calculate HF using trigonometric concepts, then halve it to find HE.
Explanation:In the question, it's mentioned that GE is a perpendicular bisector of HF. This means that GE bisects HF into two equal lengths. Therefore, the length of HE will be equivalent to half of the length of HF.
Since, HF can be calculated using trigonometry as mentioned. By definition, cose = x/h, so if we know the height 'h' and the angle, we can find 'x' which in this case would be HF, and subsequently HE would be HF/2.
Moreover, in trigonometry, the length of side opposite to the right angle in a right-angled triangle is calculated by the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We use this to find out HF if other two sides are known.
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Please answer, will mark brainliest :)
Daniel has $500 in his school lunch account at the beginning of the school year.
By the end of the year he needs at least $100 in the account to roll into the next school year. Each week during the school year, he spends $15 on lunches. Write an inequality that represents the amount of money that Daniel will have to have in his account.
Answer:
100>=500-15x
Step-by-step explanation:
He needs at least 100, so it's greater than OR equal to 100. He starts with 500 and goes down 15 each week. The x stands for the amount of weeks that are in the school year. Sorry for the terrible formatting on the greater than or equal to.
To write an inequality representing Daniel's lunch account scenario, where he begins with $500 and must have at least $100 by year-end despite spending $15 weekly, the inequality would be: 500 - 15x >= 100.
The question involves writing an inequality to represent the condition where Daniel must have at least $100 in his school lunch account by the end of the school year, given he starts with $500 and spends $15 each week on lunches. To frame the inequality, let's denote the number of weeks Daniel buys lunch as x. Given he spends $15 per week, the total expenditure over x weeks will be $15x. Initially having $500 and requiring at least $100 by the end of the school year, the inequality will be:
500 - 15x ≥ 100.
This inequality states that even after spending $15 each week for x weeks, Daniel must have at least $100 remaining in his account. To find how many weeks he can afford to buy lunch while meeting this requirement, one would solve for x in the inequality.
what is another way to write the function f(x) = 5^x. The choices are
f(x)=(625^x)1/125
f(x) = 1/125(625^x)
f(x) = (625^x)^1/4
f(x) = 1/4(6256x)
Answer:
Correct answer is f(x) = (625^x)^1/4
Step-by-step explanation:
We know that
625 = 5^4
This means
f(x) = (625^x)^1/4
f(x) = (5^(4x))^1/4
But we know this is equivalent to
f(x) = (5^(4x*(1/4))) =
= 5^(x)
Correct answer is f(x) = (625^x)^1/4
This graph represents the function (see picture) a= ___ b= ___
Answer:
a=1, b=-12
Step-by-step explanation:
This is a rational function with a hole at x=3 and a vertical asymptote at x=-4.
The denominator of this rational function must be:
[tex](x - 3)(x + 4)[/tex]
When we expand using the distributive property, we get:
[tex] {x}^{2} + 4x -3 x - 12[/tex]
This simplifies to
[tex] {x}^{2} + x - 12[/tex]
Therefore the graphed rational function is:
[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} + x - 12 } [/tex]
Comparing this to
[tex]f(x) = \frac{ {x}^{2} - 4x + 3 }{ {x}^{2} +a x + b} [/tex]
We have
[tex]a = 1[/tex]
and
[tex]b = - 12[/tex]
The next model of a sports car will cost 14.6% less than the current model. The current model costs $38,000 . How much will the price decrease in dollars? What will be the price of the next model?
Answer:
Part 1) The price will decrease $5,548
Part 2) The price of the next model is $32,452
Step-by-step explanation:
Let
x ----> the price of the next model
we know that
The current model costs $38,000 -----> represent the 100%
step 1
To find the price decrease in dollars multiply the current model price by 14.6%
14.6%=14.6/100=0.146
so
0.146*($38,000)= $5,548
step 2
Find the price of the next model
To find the price of the next model subtract the price decrease from the price of the current model
so
x=$38,000-$5,548=$32,452
Triangle ABC has vertices A(0,0) B(6,8) and C(8,4). Which equation represents the perpendicular bisected of BC?
Answer:
[tex]y = \frac{1}{2}x+\frac{5}{2}[/tex]
Step-by-step explanation:
The perpendicular bisector of a line passes through the mid-point of the line and the product of slopes of the line and perpendicular bisector will be -1.
So,
[tex]Mid-point\ of\ BC = (\frac{6+8}{2}, \frac{8+4}{2})\\= (\frac{14}{2}, \frac{12}{2})\\= (7,6)[/tex]
The line will pass through (7,6)
Now,
[tex]Slope\ of\ BC = m_1 = \frac{y_2-y_1}{x_2-x_1} \\=\frac{4-8}{8-6}\\= \frac{-4}{2}\\= -2[/tex]
Let
m_2 be the slope of perpendicular bisector
So,
m_1*m_2 = -1
-2 * m_2 = -1
m_2 = -1/-2 = 1/2
The standard equation of line is:
y=mx+b
Where m is slope
So putting the value of slope and point to find the value of b
[tex]6 = \frac{1}{2}*7 +b\\ 6 = \frac{7}{2} + b\\b = 6 - \frac{7}{2}\\ b = \frac{12-7}{2}\\b = \frac{5}{2}\\So,\ the\ equation\ of\ perpendcular\ bisector\ of\ BC\ is:\\y = \frac{1}{2}x+\frac{5}{2}[/tex]
..
Emma burns 350 calories per hour biking. This can be represented with the function c(h) = 350h, where h is the number of hours spent biking. Her mother asked her to tow her little sister in the bike trailer, which causes her to burn twice as many calories. This can be represented by the function t(c) = 2c, where c is the number of calories burned per hour. Write a function that will help Emma calculate the number of calories she will burn per hour while biking with her sister in the bike trailer.
c[t(c)] = 175c
t[c(h)] = 175h
c[t(c)] = 700c
t[c(h)] = 700h
Answer:
t[c(h)] = 700h
Step-by-step explanation:
Got it wrong, and it told me what was right lol
The function is given by:
t[c(h)] = 700h
Step-by-step explanation:Emma burns 350 calories per hour biking.
The function is given by:
c(h) = 350h.
Also, when her little sister tow in the bike then the she burn twice as many calories.
This could be represented by the function:
t(c) = 2c
where c is the number of calories burned per hour.
Now, we are asked to find the function that calculate he number of calories she will burn per hour while biking with her sister in the bike trailer i.e. we are asked to find the composition function:
[tex]t(c(h))[/tex]
Hence, we have:
[tex]t(c(h))=t(350h)\\\\i.e.\\\\t(c(h))=2(350h)\\\\i.e.\\\\t(c(h))=700h[/tex]
An important property of every line is its steepness, or____
Answer:
An important property of every line is its steepness, or slope.
The important property of every line is its steepness, or slope.
Steepness or Slope:In terms of mathematics, the slope or gradient of a line represent the number that explained both the direction and the steepness of the line.
The steepness, incline, or grade of a line should be determined by the absolute value of the slope. A slope should have a greater absolute value indicates a steeper line.
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Find the leg of each isosceles right triangle when the hypotenuse is of the given measure. Given = 6√2
Answer:
The answer would be 6.
- An experiment consists of rolling two fair
number cubes. What is the probability
that the sum of the two numbers will be
47 Express your answer as a fraction in
simplest form.
Answer:
0
Step-by-step explanation:
Each time two cubes are rolled, the sum can be a number from 2 (rolling 1 and 1) to 12 (rolling 6 and 6). It is impossible to get a sum of more than 12, so there is zero probability of getting a sum of 47.
Answer: 0
what is the solution to the system of equations y= -3x+6 y=9
A (-21,9)
B (9,-21)
C (-1,9)
D (9,-1)
Answer:
C. (-1, 9)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y=-3x+6\\y=9\end{array}\right\ \text{put the value of}\ y\ \text{to the first equation}\\\\9=-3x+6\qquad\text{subtract 6 from both sides}\\3=-3x\qquad\text{divide both sides by (-3)}\\-1=x\to x=-1[/tex]
Quick!! I need help!! For math class
Answer:
x=(2/5) or x=0.4
Step-by-step explanation:
3x+5=7-2x
3x=2-2x
5x=2
x=(2/5) or x=0.4
A line has a slope of –3 and a y-intercept of 3.
Answer:
y = - 3x + 3
Step-by-step explanation:
Assuming you require the equation of the line
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - 3 and c = 3, hence
y = - 3x + 3 ← equation of line
Hey there!
What I am assuming you are looking to do is convert this into a linear equation. I will guide you on how to do just that.
The linear equation form is:
y = mx + b
Note in particular m represents the slope and b represents the y-intercept.
Our answer would be y = -3x + 3
What is the probability
Answer: Last Option
[tex]P=0.4125[/tex]
Step-by-step explanation:
In this case we have a uniform probability. In the graph the horizontal axis represents the possible values of the variable x and the vertical axis represents the probability P(x).
To calculate the probability that x is between 4.71 and 7.4 we calculate the area under the curve.
The horizontal length between 4.71 and 7.4 is:
[tex]7.4-4.1 = 3.3[/tex].
Then notice that the vertical length in this interval is 0.125.
Then the area of a rectangle is:
[tex]A = lw[/tex]
Where l is the length and w is the width.
In this case we have to:
[tex]l = 3.3[/tex]
[tex]w = 0.125[/tex]
So
[tex]P = A = 3.3 * 0.125[/tex]
[tex]P=0.4125[/tex]
Find all complex numbers z satisfying the equation {z+1}/{z-1} = i.
9 points and brainiest: please answer!
Answer:
Step-by-step explanation:
{z+1}/{z-1} = i.
z+1 = i (z-1)
z+1 =iz -i
z - iz = -1 -i
z ( 1 -i) = - 1 -i
z = (- 1 - i ) /(1-i) = - (1+i)/(1-i)
z = - (1+i)(1+i)/(1-i)(1+i)
z = - (1+2i +i²)/ ( 1²-i²).........i² = -1
z =-2i/2
z = - i (one solution)
All the complex numbers z satisfying the equation {z+1}/{z-1} = i is z = -i.
What are Complex Numbers?Complex numbers are numbers which are of the form [tex]a + ib[/tex], where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^2[/tex]= -1.
Given equation is,
(z + 1) / (z - 1) = i
Multiplying both sides by (z - 1),
z + 1 = i (z - 1)
Let z = (a + bi)
Substituting,
(a + bi + 1) = i (a + bi - 1)
(a + bi + 1) - i (a + bi - 1) = 0
a + bi + 1 - (ai + b(i)² - i) = 0
a + bi + 1 - ai - b(i)² + i = 0
Now i² = -1
a + bi + 1 - ai + b + i = 0
Combining the like terms,
(bi - ai + i) + (a + 1 + b) = 0
i (b - a + 1) + (a + b + 1) = 0
Left hand side is a complex number.
A complex number is a + bi = 0, when a = 0 and b = 0.
So, we get,
(b - a + 1) = 0 and (a + b + 1) = 0
b - a = -1 and a + b = -1
So, combining,
a + b = b - a
a + a = b - b
2a = 0
a = 0
Substituting,
b = -1
So the complex number, z = a + bi = -i
Hence the complex number z = -i.
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What is the distance between zero and -53 on the number line?
Hello There!
the distance between 0 and -53 on a number line would be 53 spaces. This is because they are exactly 53 spaces away from each other.
What is the range of the function y=3/x+8?
The range of the function y=3/x+8 is all real numbers except 8, since the function approaches 8 but never reaches it due to the vertical asymptote at x=0.
The range of the function y=3/x+8 refers to all possible output values (y-values) that the function can produce. To find the range, it is essential to consider the values that x can take. Since x is in the denominator, x cannot be 0, as division by zero is undefined. Therefore, the function has a vertical asymptote at x=0.
As x approaches both positive and negative infinity, y approaches the constant 8, because the term 3/x approaches 0. Thus, the function can get close to, but never equal, the value of 8. Also, since 3/x can take any value except 0, the range of the function is all real numbers, excluding 8.
The final range of the function y=3/x+8 is therefore: {y | y ≠ 8}, meaning all real numbers that are not equal to 8.
Convert the radian measure to degrees. (Round to the nearest hundredth when necessary): 7π/3
Answer:
420°
Step-by-step explanation:
To convert from radian to degree measure
degree measure = radian measure × [tex]\frac{180}{\pi }[/tex]
Hence
degree = [tex]\frac{7\pi }{3}[/tex] × [tex]\frac{180}{\pi }[/tex]
Cancel π on numerator/ denominator
= [tex]\frac{7(180)}{3}[/tex] = 420°
To convert 7π/3 radians to degrees, multiply by the conversion factor 180°/π to get 420°.
Explanation:To convert the radian measure to degrees, we can use the conversion factor that 1 radian is equivalent to 57.3°.
Given the radian measure 7π/3, we multiply this by the conversion factor to find the degree measure.
The conversion is as follows:
7π/3 radians × (180°/π) = 7×180°/3 = 420°.
Therefore, 7π/3 radians is equivalent to 420° when converted to degrees.
A alone can complete a work in 16 days and B alone can complete the work in 12 days. How many days will it take to complete the work if they work on alternate days starting from A.
Answer:
14 days
Step-by-step explanation:
1. Convert the amount of work person A and B can do respectively in one day into fractions.
A = 1/16 B = 1/12
2. Get both fractions to a common denominator using the least common multiple. This is 48.
1/16 × 3 = 3/48 1/12 × 4 = 4/48
3. Add both fractions to find out how much work will be done in two days. We are doing this because we are working in a pattern, and this will allow us to multiply, which is more time efficient than repeatedly adding 3 and then 4.
3/48 + 4/48 = 7/48
4. Figure out how many sets of two days work (7/48) will get them to 48/48 (100% done) or closest to it without being under. This would be 7 sets.
7/48 × 7 = 49/48
5. Multiply 7 by 2. We are doing this because we worked in sets of two days to account for A working and then B, since they are taking turns.
7 × 2 = 14
6. It will take them 14 days.
[tex]( - 7x + 1) - (4x + 5)[/tex]
Answer:
-11x-4 is the answer if the expression to simplify is (-7x+1)-(4x+5).
Step-by-step explanation:
We are first going to distribute to get rid of the ( ):
-7x+1-4x-5
Pair up like terms:
-7x-4x+1-5
Combine the like terms:
-11x-4
the mathematical name of this quadrilateral
Answer:
Its a kite
Step-by-step explanation:
Answer:
kite
Step-by-step explanation:
try not to get it confused with a rhombus