The mean age (nearest year) of all the people in the office is 22.4.
How to find the mean age?Age for women
Age = 12 women × 22 years old / 12
Age = 264 /12
Age = 22
Age for men
Age = 3 men × 24 years old / 3
Age = 72/3
Age = 24
Now let find the mean age
Mean age = Sum of men and women age / Number of men and women
Mean age = 264 + 72 / 12 +3
Mean age = 336 /15
Mean age = 22.4
Therefore the mean age is 22.4.
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The simple interest on a sum of money invested 6 months at 5% per annum is $1680. Determine the amount of money invested.
Answer:
9514 1404 393
Answer:
$67,200
Step-by-step explanation:
The amount if interest is given by the formula ...
I = Prt
where P is the amount invested, r is the annual rate, and t is the number of years. Here, we want to find P when r = 0.05 and t = 1/2 such that I = 1680.
P = I/(rt) = $1680/(0.05·0.5) = $1680/0.025
P = $67,200
The amount invested was $67,200.
Step-by-step explanation:
A rock falls from a tower that is 360 feet high. As it is falling, its height is given by the formula ℎ= 200 −162. How many seconds will it take for the rock to hit the ground (h=0)? Round to the nearest tenth of a second.
The time it will takes for the rock to hit the ground (h=0) given the height of 360 feet high is 3.53 seconds.
What is the time of falling?The concept that will be used in the calculation is the concept of height and time .
The formular for the expression is given as ℎ= 200 −16t^2
Then the height of the tower is been given as 360 feet high
ℎ= 200 −16t^2
then
t^2=200/16
t^2=12.5
t=3.53 seconds
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If the 21st and 22nd terms in the expansion of(1+x)⁴⁴ are equal find the value of x
Answer:
21st 22nd are equal so ×=0
Need help with question
se the distributive property to find an expression that is equivalent to 42x + 12 .
The equivalent expression using the distributive property is 6(7x + 2)
How to determine the equivalent of the expressions?From the question, we have the following expression
42x + 12
Rewrite the given expression as follows
This is represented using
(42x + 12)
Factor out 2 from the expression
So, we have the following representation
42x + 12 = 2(21x + 6)
Factor out 3 from the expression
So, we have the following representation
42x + 12 = 2 * 3(7x + 2)
Evaluate the products
42x + 12 = 6(7x + 2)
The above represents the equivalent expression
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-1.25 + 2 1/5 + (-3.5)
Answer: -2.55
Step-by-step explanation:
Answer:
-2.55
Step-by-step explanation:
-1.25 + 2 1/5 + (-3.5) =
= -1.25 + 2.2 - 3.5
= 0.95 - 3.5
= -2.55
-5/6 times 1/8 please help
Answer:
(-5/48)
Step-by-step explanation:
-5 × 1 -5
------- × ------- = -------
6 × 8 48
Multiply the numerators together (top numbers) to get the new numerator
Multiply the denominators together (bottom numbers) to get the denominator.
I hope this helps!
The equation y=2x represents a proportional relationship.
Select the true statement.
The graph is a curve
The y-intercept is 2
The slope is 2
The slope is 0
The slope of the line is 2 whose equation is given by y = 2x.
The given equation is y = 2x
The general equation of the line is given by
y = mx +c where m is the slope and c is the intercept of the line.
The slope of line a line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run."
The intercept of the line is a point on the y-axis known as an intercept is where the line's slope passes.
On Comparing the given equation with the general equation, we have:
m = slope = 2
Thus the slope of the line is 2.
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Which parts of the triangles are congruent in the image?
Answer:
B, C, E
Step-by-step explanation:
B is correct because it is written to the side and also because of the Definition of midpoint.
C is correct because HL and KI H and I are congruent just like L and K because of alternate interior angles.
E is correct because of the verticle angle theorum.
The following data are for Jay Robert Company. Breakeven sales revenue $250,000 Fixed costs $150,000 Calculate the sales revenue necessary to generate net income of $100,000. $618,667 $533,333 $625,000 $400,000 $416,667
The sales revenue necessary to generate net income of $100,000 is: $416,667.
How to find the sales revenue?Using this formula to find the sales revenue
Sales revenue = Sales revenue + (Sales revenue × Net income / Fixed costs)
Let plug in the formula
Sales revenue = $250,000 + ($250,000 × $100,000 /$150,000)
Sales revenue = $250,000 + ($250,000 ×0.6666666)
Sales revenue = $250,000 + $166,666.65
Sales revenue = $416,666.65
Sales revenue = $416,667 (Approximately)
Therefore the correct option is E.
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What is the slope of a line perpendicular to the line whose equation is 5x-y=-7. Fully simplify your answer.
Answer:
-1/5
Step-b-1/5y-step explanation:
The rule for a perpendicular slope of a line is -1/s
In this case, we find the slope of the line first.
5x - y = -7
-y = -5x - 7
y = 5x + 7
The slope is 5, so -1/(5) is the slope of the perpendicular line.
Kaitlyn has a least five purses (how to i solve that with signs and number?)
The solution when Kaitlyn has at least five purses using signs and number is N ≥ 5
How to write expressions with inequalities?Equations and inequalities are both mathematical sentences formed by relating two expressions to each other.
When two expressions are equal, we use the equal sign ( = ). But when we are trying to compare two values or expressions, we use the inequality signs like greater than (>), less than (<), greater than or equal to ( ≥ ) and less than or equal to (≤)
Given that: Kaitlyn has at least five purses
In order to solve this problem with signs and number, you will make use of the inequality that explains the situation:
Let the number of purses be N
Kaitlyn having at least five purses means she has 5 purses or more. Using inequality, the number of purses is greater than or equal to 5. Thus:
N ≥ 5
Therefore, the solution using signs and number is N ≥ 5
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please help it is urgent
[tex]\frac{6x + 1}{6x - 4} - \frac{47 - 27 {x}^{2} }{5 {x}^{2} - 24} = \frac{5}{6} [/tex]
solve x
Answer:
Soultion\left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right)\quad :\quad x=-\frac{7+\sqrt{253}}{6},\:x=\frac{\sqrt{253}-7}{6} steps \left(x^2+\frac{7}{3}x-\frac{17}{3}\right)=3\left(x^2+\frac{7}{3}x+\frac{49}{36}-\frac{49}{36}-\frac{17}{3}\right) simplify -2x^2-\frac{14x}{3}+\frac{34}{3}=0.
Step-by-step explanation:
I got you my boy.
Tara ran to the park and then walked to the store. She ran 4 times as long as she walked. The total time spent walking and running was 25 minutes. Write an equation that can be used to solve for how long it took Tara to walk from the park to the store?
A= x + 4 = 25
B= 1/4x = 25
C= 1/4x + x = 25
D= x + 4x = 25
The equation of the time that it took Tara to get to the store is; x + 4x = 25
What is the time taken?We know that in this case, the task that we have is to form an equation that would reflect the total time that Tara took in moving to the store. We have to factor in that the variable here is the time.
We are told that she ran 4 times as long as she walked and the total time spent walking and running was 25 minutes. Let us designate the time taken to walk as x. This implies that the time that she ran is 4x.
The equation would now be; x + 4x = 25
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juan thinks the answer is between 5 and 6 melanie says the answer is between 3 and 4 who is correct [tex]\sqrt[3]{28}[/tex]
Answer:
28
Step-by-step explanation:
4,8,12,16,20,24,28. +4 every time
Perform the following operation. Write the answer in scientific notation.
0.008/40,000
(Use the multiplication symbol in the math palette as needed.)
Answer:
8.0 × 10^-3 ÷ 4.0 × 10^4
= 2.0 × 10^-3-4
= 2.0 × 10^-7
or 0.0000002
Please help I was sick and missed out on class.Thank you
Answer: [tex]\frac{0}{24}[/tex]
Step-by-step explanation:
The slope is [tex]\frac{y_{1}-y_{2}}{x_{1}-x_{2}}[/tex], or reverse: [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
If we substitute, we get that [tex]\frac{2-2}{6-(-18)}[/tex].
Simplify to get [tex]\frac{0}{24}[/tex].
Solve each equation below. Show each step and check your work.
a) 56a – 178 = 98 – 248
b) 640 + 70 = 69y + 20
Answer:
A) 0.5
B) 10
Step-by-step explanation:
A) First, you need to Combine Like Terms on the right side of the =
98-248 = -150
Now, you need to Isolate the variable by getting rid of the -178. What you do to one side, you must do the the other.
56a-178(+178) = -150(+178)
56a = 28
Finally, you must remove that 56 on the a. Since it stands for 56 x a, you must do the same you did with the -178 except with Division.
56a/56 = 28/56
a = 0.5
B) Combine Like terms
640+70 = 710
Isolate the variable
710(-20) = 69y+20(=20)
690 = 69y
Remove the 69 with division
690/69 = 69y/69
10 = y
Ira invests $4000 into an account that earns 0.6% simple interest annually. Which statement best describes the relationship between the number of years Ira has his money invested and the balance in any year
The Amount of money that she received at the end of the read is $4024, the relationship between the number of years Ira has his money invested and the balance in any year differs by $24 which is the simple interest.
Amount invested by Ira = P = $4000
The rate of Interest (r) = 0.6 %
Time period (t) = 1 year.
The simple interest is given by,
[tex]S.I. = \frac{P*r*t}{100}[/tex]
Now, putting the values in the formula, we get:
[tex]S.I. = \frac{4000*0.6*1}{100} =24[/tex]
Hence, the simple interest will be $24
Now, the Amount/balance that she received in the year is A = P +S.I
A = P+S.I.
A = 4000 +24 = $4024
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Answer:
The relationship is linear. His account increases each year by a constant value of $24.
Step-by-step explanation:
took the test
8. In the following diagram, the diameter of the circle is 15m. What is the distance between the chord and the edge of the circle?
Answer:
7
Step-by-step explanation:
15-8
Can you help me please and explain I don’t get this. *slope*
Answer:-5/1
Step-by-step explanation:
down 5 and over 1
to get the slope, find a spot on the graph and then go 1 to the right and read how much the graph went up or down.
on 5) you see it did neither, so m=0
when the graph goes up, m is positive, when it goes down, m is negative.
so on graph 1, you have 2 dots.
you go 2 right, and 4 down. when the dots are not 1 apart (counting going right) then divide by the steps you went right.
4 divided by 2 is 2.
-> graph went down, slope for 1) is m = -2
graph 2) you go 2 right and 2 up, 2/2 = 1. you went up, so m is positive and m = 1 for this graph.
3) is undefined because it doesn't go anywhere when you go right, it's 100% vertical
4) m = -5 because you went 1 right and 5 down
5) you go 6 right between the dots and 4 down. m is negative because it went down, not up. so m = -(4/6)
A 35-tooth gear on a motor shaft drives a larger gear having 63 teeth. If the motor shaft rotated at 900 rpm, what is the speed of the larger gear
If the motor shaft rotated at 900 rpm, the speed of the larger gear will be 100 rpm.
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
it is given that, A 35-tooth gear on a motor shaft drives a larger gear having 63 teeth and the motor shaft rotated at 900 rpm.
The number of teeth on the smaller gear,n₂ = 35
The number of teeth on the larger gear,n₁ = 63
The gear ratio is obtained as,
n₁/n₂=63/35
n₁/n₂=9:5
If the motor shaft rotated at 900 rpm, The speed of the larger gear is,
=900 rpm / 9
=100 rpm
Thus, if the motor shaft rotated at 900 rpm, the speed of the larger gear will be 100 rpm.
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Where does 1/6 land on a number line
Answer:
On a number line, 1/6 would land in the exact middle between 0 and 2/6
Step-by-step explanation:
Not too sure what your question meant, but I hope my answer helped!
If it wasn't what you were looking for, please let me know and elaborate on your question and I'll be happy to help out! :)
Write an equation for the line parallel to the line 3/2x= -6 through the point (-6, 5).
The equation of the line parallel to the line, [tex]y=\frac{3}{2} x-6[/tex] through the point (-6,5) is [tex]3x-2y+28=0[/tex]
What are Parallel Lines?
Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Parallel lines have the same slope.What is Point-Slope Equation of Line?
The Point-Slope Equation of a straight line is given as, [tex]y-y_{1}=m(x- x_{1})[/tex].This method is useful in determining the equation of a straight line when the slope (m) of the line and a point [tex](x_{1}, y_{1})[/tex] are known.Here, it is given that the equation of the line parallel to the given straight line is [tex]y=\frac{3}{2} x-6[/tex] ----(1)
We know that the slope of parallel lines is equal.
So, the slope of (1) will be equal to the given line.
Writing (1) in the form of [tex]y=mx+c[/tex], we get
Slope, [tex]m=\frac{3}{2}[/tex]
Using the Point-Slope Equation of the line, we have
[tex]y-y_{1}=m(x- x_{1})[/tex]
Now, substituting the point (-6,5) in the place of [tex](x_{1}, y_{1})[/tex], we get
[tex]y-5=\frac{3}{2} (x- (-6))\\\implies 2(y-5)=3(x+6)\\\implies 2y-10=3x+18[/tex]
Simplifying, we get
[tex]3x-2y+18+10=0\\\implies 3x-2y+28=0[/tex]
Therefore, the equation of the given line is [tex]3x-2y+28=0[/tex]
Correct Question: Write an equation for the line parallel to the line y=3/2x-6 through the point (-6, 5).
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Select two numbers that multiply together to make 1 million.
40 A
2,000 B
5,000 C
25,000 D
Answer: A and D
Step-by-step explanation: 40 x 25,000 = 1,000,000
Answer: A and C
Step-by-step explanation:
Because 40x25000 equals 1 million
Write an equation that has the given solutions. 1, -1
Answer:
(x+1)(x-1)
Step-by-step explanation:
The solutions 1 and - 1 is given when
x = 1 or x = - 1
hence; (x - 1) = 0 or (x + 1) = 0
(x - 1)(x + 1) = 0
x² -1 = 0
Mark as brainliest answer please. Thanks
What is the equation of the line?
y=-3x
y=3x
y=3x+1
y=4x
The equation of the given straight line is y = 3x.
We are given a graph. The graph shows a straight line. Several points are marked on the line in the graph. The coordinates of two such points are (1, 3) and (2, 6). We need to find the equation of the straight line.
The equation of the straight line can be found using the two-point form of a line. The equation is solved below.
(y - y1) = [(y2 - y1)/(x2 - x1)]×(x - x1)
(y - 3) = [(6 - 3)/(2 - 1)]×(x - 1)
y - 3 = 3(x - 1)
y = 3x - 3 + 3
y = 3x
Hence, the equation of the line shown in the graph is y = 3x.
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CAN SOMEONE HELP WITH THIS QUESTION?✨
Answer:
24.359
Step-by-step explanation:
The height is opposite of the 77 so we are using sin. The length of the ladder is the hypotenuse.
sin(77°)=height/25 Set up equation sin=height/hypotenuse
25*sin(77°)=height Multiply both sides by 25
25*.96437=height
height=24.359
Simplify this equation:
[tex] {7}^{8} \times {7}^{3} \times {7}^{4} \div {7}^{9} \times {7}^{5} [/tex]
Answer:
7
Step-by-step explanation:
Exponent law:
[tex]\sf a^m * a^n = a^{m+n}\\\\\dfrac{a^m}{a^n}=a^{m-n}[/tex]
In exponents multiplication, when bases are same add the powers.
In exponents division, if bases are same subtract the powers.
[tex]\sf \dfrac{7^8*7^3*7^4}{7^9*7^5}=\dfrac{7^{8+3+4}}{7^{9+5}}[/tex]
[tex]\sf =\dfrac{7^{15}}{7^{14}}\\\\=7^{15-14}\\\\=7^1\\\\=7[/tex]
The curved surface area, A of a cone of height h and base radius r is π√h²+r².
Make h the subject of the formula.
Find the height of a cone of area 550 cm² and base radius 7 cm
The height of the cone is 580.36 cm.
The curved surface area of the cone is given by,
[tex]A = \pi \sqrt{h^{2} +r^{2} }[/tex]
Squaring both sides, we get :
[tex]A^{2} =\pi ^{2} (h^{2} +r^{2} )[/tex]
Now, it is given that the height of the cone is h,
The area of the cone = 550 [tex]cm^{2}[/tex]
And the radius of the cone = 7cm,
Putting these values in the given formula, we get,
[tex]A^{2} =\pi ^{2} (h^{2} +r^{2} )[/tex]
[tex]550^{2} = \pi ^{2} * ( h^{2} +7^{2} )\\[/tex]
3,36,875 = [tex]h^{2}+49[/tex]
[tex]h^{2}[/tex] = 3,36,875 - 49 = 3,36,826
h = 580.36 cm
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