Answer:
4096/15,625
Step-by-step explanation:
The reason is because the power is distributed individually within the fraction. Since the fraction is already fully simplified, 4096/15625 multiplied by itself is also simplified.
Thus the answer is 4096/15,625 = (4^6)/(5^6)
Workers in an office of 40 staff were asked their favourite type of take-away. Pizza 9 Curry 6 Fish & chips 11 Kebab 10 Other 4 How many degrees represent 1 person?
Answer:
Hey there!
In total, there are 360 degrees. If there are 40 staff members, then each member has 360/40=9 degrees.
Hope this helps :)
Answer:
9 degrees
Step-by-step explanation:
There are 360 degrees in a circle
There are 40 people
360 / 40 = 9
Each person gets 9 degrees
What equation represents the slope intercept from the line below y intercept ( 0, 2) slope -3/7 ( PLEASE HELP FAST TOP ANSWER GETS BRAINLIEST!!)
Answer:
[tex]\boxed{Option \ A}[/tex]
Step-by-step explanation:
y-intercept = b = 2 [y-intercept is when x = 0]
Slope = m = -3/7
Putting this in slope-intercept equation
=> [tex]y = mx+b[/tex]
=> [tex]y = -\frac{3}{7}x + 2[/tex]
Answer:
a
Step-by-step explanation:
How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution
Answer:
One
Step-by-step explanation:
y = 3 x - 5.
y = -x + 4.
x=9/4 and y=7/4
1 solution (9/4 , 7/4)
For a system of the equation to be an Independent Consistent System, the system must have one unique solution. The system of the equation has only one solution. Thus, the correct option is A.
What is a System of equations?
Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
Given the two equations y=3x -5 and y=-x+4. If the two of the equations are plotted on the graph. Then it can be observed from the graph that there is only one intersection between the two lines.
Hence, the system of the equation has only one solution. Thus, the correct option is A.
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Enter the coordinates of the vertex of the graph of y=2(x+5)^2
Answer:
The vertex is ( -5,0)
Step-by-step explanation:
The vertex form of a parabola is
y = a( x-h) ^2 +k
where ( h,k) is the vertex
y=2(x+5)^2
y=2(x - -5)^2 +0
The vertex is ( -5,0)
Answer:
vertex = (- 5, 0 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
y = 2(x + 5)² , that is y = 2(x + 5)² + 0 ← is in vertex form
with (h, k) = (- 5, 0 )
Suppose the probability that a randomly selected man, aged 55 - 59, will die of cancer during the course of the year is StartFraction 300 Over 100 comma 000 EndFraction . How would you find the probability that a man in this age category does NOT die of cancer during the course of the year?
Answer:
The probability that a man in this age category does NOT die of cancer during the course of the year is 0.997.
Step-by-step explanation:
Suppose the probability of an event occurring is [tex]P_{i}[/tex].
The probability of the given event not taking place is known as the complement of that event.
The probability of the complement of the given event will be,
[tex]1 - P_{i}[/tex]
In this case an events X is defined as a man, aged 55 - 59, will die of cancer during the course of the year.
The probability of the random variable X is:
[tex]P (X) = \frac{300}{100000}=0.003[/tex]
Then the event of a man in this age category not dying of cancer during the course of the year will be complement of event X, denoted by X'.
The probability of the complement of event X will be:
[tex]P(X')=1-P(X)[/tex]
[tex]=1-0.003\\=0.997[/tex]
Thus, the probability that a man in this age category does NOT die of cancer during the course of the year is 0.997.
The sum of ages Afful and Naomi is 34. In 5 years time , Afful will be 2 times the age on Naomi now. How old are they now.
Answer:
Afful is 21 and Naomi is 13.
Step-by-step explanation:
Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.
The sum of their ages is 34. In other words:
[tex]A+N=34[/tex]
In 5 years time, Afful will be two times the age of Naomi now. In other words:
[tex]A+5=2N[/tex]
Solve for the system. Substitute.
[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]
Afful is currently 21 and Noami is currently 13.
Answer:
Naomi=x
Afful=2x
In 5 years time= +5
So Naomi=x+5
and and Afful=2x+5
=x+5+2x+5=34
=3x+10=34
Subtract 10 on both sides
3x=24
Divide 3 on both sides
X=8
Check:
X=8
Naomi=16
In 5 years
=16+5=21
Naomi=8+5=13
13+21=34
Hope this helps
Step-by-step explanation:
Helpp pleaseeeeeeeeeeee
Work Shown:
sin(angle) = opposite/hypotenuse
sin(40) = 24/x
x*sin(40) = 24
x = 24/sin(40)
x = 37.33737184465
x = 37.3
When you use your calculator, make sure it is in degree mode. One way to check is to compute something like sin(30) and you should get 0.5
Answer:
x = 37.3
Step-by-step explanation:
for the specified angle, the ratio of the length of the side that is opposite that angle to the length of the longest side (hypotenuse) of the triangle, it is sine.
[tex]\sin40^o=0.6428[/tex]
From triangle [tex]\sin40^o=\dfrac{24}x[/tex]
so:
[tex]0.6428=\dfrac{24}x\\\\0.6428\,x=24\\\\x=24\div0.6428=37.336652....\approx37.3[/tex]
PLEASE HELP!!!
These dot plots show the ages in years) for a sample of two types of fish.
Explanation:
The median is the center of the distribution. We see that the center of the shark's distribution is to the left compared to the koi's center. Therefore, the shark's median age is smaller. Choice A is one of the answers.
The spread is exactly what it sounds like: how spread out the data is. Mathematically we use the standard deviation, or sometimes the range, to find out how spread out things are. The koi distribution is more spread out. The shark's data is more clumped together. This is why choice B is the other answer.
Center: Sharks have lower median age than Koi.
Spreads: The ages of koi are more spread out.
What is dot plot?A dot plot is a standardized way of displaying the distribution of data based on a five number summary.
What is the median in a dot plot?The center line in the dot plot shows the median for the data .
What is the spread of data?Spread of data is measured in terms how far the data differs from the mean.
According to the given question
We have a dot plots for the two fishes sharks and Koi.
According to the given dot plot
Most ages of the sharks is lower than the koi.
⇒ Sharks are lower than koi.
So, the center: Sharks have lower median age than Koi.
Also, the ages of Koi are wide spreading.
⇒ The ages of koi are more spread out
Therefore, Spreads: The ages of koi are more spread out.
Hence, option A and B are correct.
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The mean and variance are known as the _____
of a distribution.
Answer:
The mean and variance are known as the parameters of a distribution.
Step-by-step explanation:
The mean and the variance are parameters of a distribution. Parameters are constantly estimated in Statistics using samples of values of a population because they are often unknown.
They characterize a quantitative aspect of a probability distribution, and completely determined the distribution. For example, in the normal distribution, the mean, [tex] \\ \mu[/tex], and the variance, [tex] \\ \sigma^{2}[/tex], determined this distribution.
Most of the time, the standard deviation, [tex] \\ \sigma[/tex], is more used than the variance because is in the same units that the mean.
In this way, we can say that these parameters "tell us" where the central point of the distribution is (this is the case for the mean), and also, how spread the values of a probability distribution are (the case for variance or the standard deviation).
Given that
[tex]v = \pi {r}^{2} h[/tex]
Make h the subject of the formula. Evaluate h when
[tex]\pi = 22 \div 7[/tex]
[tex]r = 7[/tex]
[tex]v = 616[/tex]
Answer:
h = 4Step-by-step explanation:
v = πr²h
To make h the subject divide both sides by πr²
So we have
[tex]h = \frac{v}{\pi {r}^{2} } [/tex]
when
π = 22/7
r = 7
v = 616
We have h as
[tex]h = \frac{616}{ \frac{22}{7} \times {7}^{2} } = \frac{616}{ \frac{22}{7} \times 49} [/tex]
[tex]h = \frac{616}{22 \times 7} = \frac{616}{154} [/tex]
h = 4Hope this helps you
Please answer question now what the answer
Answer:
100 degrees
Step-by-step explanation:
360-260=100
Answer:
x=100
Step-by-step explanation:
130+130+x=360
260+x=360
x=100
Have a great and magnificent day
The area of a rectangular community garden is 200 square feet. The length of a rectangular garden is twice it’s width. Find the length and width of the garden.
PLEASE HELP!!!
Answer:
The length is 20 ft, and the width is 10 ft.
Step-by-step explanation:
area = length * width
Let the width = w
length = 2w
A = LW
A = 2w * w = 200
2w^2 = 200
w^2 = 100
w = 10
L = 2w = 20
The length is 20 ft, and the width is 10 ft.
On August 8, 1981, American Savings offered an insured tax-free account paying 23.24% compounded monthly. If you had invested $90,000 at that time, how much would you have on August 8, 2014, assuming that you could have locked the interest rate at the time of deposit? Someone please help me!!
Answer:
$181,432,754
Step-by-step explanation:
We use the formula for compound interest here, to determine the amount
Mathematically, that would be;
A =I (1 + r/n)^nt
where A is the amount which we want to calculate
I is the initial amount which is $90,000
r is the rate = 23.24% = 23.24/100 = 0.2324
n is the number of times per year the interest is compounded = 12 (compounded monthly)
t is the number of years = 2014 - 1981 = 33
Substituting these values, we have;
A = 90,000(1 + 0.2324/12)^(33 * 12)
A = 90,000(1 + 0.0194)^396
A = 90,000(1.0194)^396
A = 181,432,754.27210504
Which is approximately $181,432,754 to the nearest whole dollars
A plot of land is represented on a map whose scale is 1:10000.On the map perimeter of the plot is 24.8cm.Calculate,in km ,the actual perimeter of the plot
Answer:
24.8 km
Step-by-step explanation
To do this we would just multiply 24.8 by 10,000 which is 248000 and if we divide that by 10000 (to get km) we would get 24.8km
Choose the kind(s) of symmetry for the letter(D). Select all that apply Point Line Plane None
Answer:
The only way is across.
whats the equation for this
Answer:
[tex]x^2 + y^2 + 4x + 4y = -119/16[/tex]
Step-by-step explanation:
The axes x and y are calibrated in 0.25
If the circle is carefully considered, the radius r of the circle is:
r = -1.25 - (-2)
r = 0.75 units
The equation of a circle is given by:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
The center of the circle (a, b) = (-2, -2)
Substituting (a, b) = (-2, -2) and r = 0.75 into the given equation:
[tex](x - (-2))^2 + (y - (-2))^2 = (3/4)^2\\\\(x + 2)^2 + (y + 2)^2 = (3/4)^2\\\\x^2 + 4x + 4 + y^2 + 4y + 4 = 9/16\\\\x^2 + y^2 + 4x + 4y + 8 = 9/16\\\\16x^2 + 16y^2 + 64x + 64y + 128 = 9\\\\16x^2 + 16y^2 + 64x + 64y = -119\\\\x^2 + y^2 + 4x + 4y = -119/16\\[/tex]
HELP Classify the following: 3 + 9 + 27 + ... arithmetic sequence arithmetic series geometric sequence geometric series
Answer:
Geometric sequence
Step-by-step explanation:
Because this is not adding or subtraction, but multiplication, this would be a geometric sequence.
Find the slope and y-intercept of each line:
a. (x+2)(x+3)=(x-2)(x-3)+y
b. x=my+b
Please show workings, and I won't accept nonsense answers! Don't answer the question if you don't know what it means!!
Answer:
See below
Step-by-step explanation:
Part A:
[tex](x+2)(x+3) = (x+2)(x-3) + y[/tex]
Resolving Parenthesis
[tex]x^2+3x+2x+6=x^2-3x-2x+6+y\\x^2+5x+6 = x^2-5x+6+y[/tex]
Subtracting [tex]x^2[/tex] and 6 to both sides
[tex]5x= -5x+y[/tex]
Adding 5x to both sides
[tex]y = 5x+5x\\y = 10x[/tex]
Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept
So,
Slope = m = 10
Y-intercept = b = 0
Part B:
[tex]x = my+b[/tex]
Subtracting b to both sides
[tex]my = x-b[/tex]
Dividing both sides by m
[tex]y = \frac{x-b}{m}\\ y = \frac{x}{m} - \frac{b}{m}[/tex]
Comparing it with [tex]y = mx+b[/tex] where m is the slope while b is the y-intercept
So,
Slope = m = [tex]\frac{1}{m}[/tex]
Y-intercept = b = [tex]-\frac{b}{m}[/tex]
At the souvenir shop. Theo buys k key chains and p photo frames
where each chain and frame costs $2.49. He also buys a T-shirt for
$5.99. What is the total cost of Theo's purchases in terms of k and p?
Answer:
Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99
Step-by-step explanation:
Cost of k key chain=$2.49
Cost of p photo frames=$2.49
Cost of a T-shirt=$5.99
Total cost of all items=cost of k key chain + cost of p photo frame + cost of The shirt
=2.49k + 2.49p + 5.99
Factorise
2.49 is common to both k and p
=2.49(k + p) + 5.99
Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99
CAN ANYONE HELP IM VERY CLUELESS
Answer:
51°
Step-by-step explanation:
A circle has a total of 360 degrees. So,
360 = 62 + 66 + x + 73 + x + 57
Next, combine like terms:
360 = 2x + 258
Next, isolate your variable by subtracting 258 from both sides:
102 = 2x
Finally, divide both sides by 2 to get x:
x = 51
Answer:
x = 51
Step-by-step explanation:
x + 73 + x + 57 + 62 + 66 = 360
2x + 258 = 360
2x = 360 - 258
2x = 102
[tex]\frac{x}{2} =\frac{102}{2}[/tex]
x = 51
Ahmed wants to get a loan from his credit union for $20,000 to buy a new car. He can get an interest rate of 5% and can pay off the loan in 5 years. How much will Ahmed pay each month?, How much will Ahmed pay in interest?
Answer:
Step-by-step explanation:
The cost of the new car is $20,000.
We would apply the periodic interest rate formula which is expressed as
P = a/[{(1+r)^n]-1}/{r(1+r)^n}]
Where
P represents the monthly payments.
a represents the amount of the loan
r represents the annual rate.
n represents number of monthly payments. Therefore
a = $20000
r = 0.05/12 = 0.0042
n = 12 × 5 = 60
Therefore,
P = 20000/[{(1+0.0042)^60]-1}/{0.0042(1+0.0042)^60}]
20000/[{(1.0042)^60]-1}/{0.0042(1.0042)^60}]
P = 20000/{1.286 -1}/[0.0042(1.286)]
P = 20000/(0.286/0.0054012)
P = 20000/52.95
P = $378
Ahmed will pay $378 each month
The total payment is
378 × 60 = $22680
The amount that Ahmed will pay in interest is
22680 - 20000 = $2680
If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 2), (negative 1, 2). (–4, –7) (–4, 2) (2, –7) (2, 11)
Answer:
A ( -4, -7)
Step-by-step explanation:
if you translate -1, three units to the left u get -4 and then when u go nine units down u get -7 do it on a grid and u will see wut im talkin about : )
Answer:
A.
Step-by-step explanation:
A rectangular sheet of paper was folded in half 6 times. In the middle of this folded sheet, two holes were drilled. Then, the sheet of paper was unfolded back to its original shape. How many holes are there?
Answer:
There will be 128 holes
Step-by-step explanation:
Simply think of each fold as doubling the number of holes. So since we have 6 folds, that will be 2^6 and then we have 2 holes in those folds, which makes 2*2^6 == 2^7 == 128 holes. Cheers.
Folding of the paper is an illustration of a geometric sequence
The number of holes in the rectangular paper is 128
The given parameters are:
[tex]\mathbf{h = 2}[/tex] --- holes
[tex]\mathbf{t = 6}[/tex] --- number of times
The sheet was folded in halves i.e. in 2's.
So, the amount of each time is:
[tex]\mathbf{f(t) = 2 \times h^t}[/tex]
Substitute values for h and t
[tex]\mathbf{f(6) = 2 \times 2^6}[/tex]
Evaluate the exponent
[tex]\mathbf{f(6) = 2 \times 64}[/tex]
Multiply
[tex]\mathbf{f(6) = 128}[/tex]
Hence, the number of holes in the rectangular paper is 128
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In △ABC, m∠A=45°, c=17, and m∠B=25°. Find a to the nearest tenth.
Answer:
12.8
Step-by-step explanation:
you have to use the law of sines to calculate it. the measure of angle c is 110 and you have to do
Sin(110)x=17sin(45)
and then it turns into 17sin(45)/sin(110)
then put it into desmos with it being in degrees mode
How many minutes are in 324 hours?
Answer: 19440 minutes
Step-by-step explanation:
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------
Answer: There are 19440 minutes in 324 hours.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Since there are 60 minutes in each hour, we need to multiply the time value by 60. Like this:
324 x 60 = 19440.
4/6, 5/6, 2/6 how do you put it least to greatest?
Answer:
2/6 < 4/6 < 5/6
Step-by-step explanation:
2 < 4 => 2/6 < 4/6
4 < 5 => 4/6 < 5/6
=> 2/6 < 4/6 < 5/6
Answer:
2/6, 4/6 5/6
Step-by-step explanation:
These box plots show the prices for two different brands of shoes.
Answer: I’m pretty sure is letter A
If you had a cube with a side length of 4, how can your write the calculations in exponential form? What are 2 other ways to read the exponent verbally?
Answer: 4^3
(Four cubed or Four to the power of 3)
Step-by-step explanation:
please solve the volume of the triangular prism
Answer:
V = 225 cm²
Step-by-step explanation:
The volume of a prism is the product of the base's area and the height
the base of this prism is triangular
the area of a triangle is given by the formula :
A = [tex]\frac{b*h}{2}[/tex]b is the base(6cm) and h the height (5cm)
A = [tex]\frac{5*6}{2}[/tex] A = 15 cm²So the volume is
V = 15*A V = 15*15 V = 225 cm²Answer:
225 cm³
Step-by-step explanation:
Area of cross-section × length = Volume of a triangular prism
Area of cross-section is the area of the triangle section.
Area of cross section:
5 × 6 × 0.5
30 × 0.5
= 15
Calculate volume:
15 × length
15 × 15
= 225
A box contains 10 red marbles and 10 green marbles. Sampling at random from this box five times without replacement, you have drawn a red marble all five times. Without replacing any of the marbles, what is the probability of drawing a red marble the 6th time?
Answer:
5/15 is the probability of choosing a red marble from the box.
Step-by-step explanation:
We know that,
There are 5 red marbles and 10 green marbles in the box.
Divide the number of events by the number of possible outcomes. This will give us the probability.
P(red marble) = P(5)
Possible outcomes
5 red, 10 green -> 15 possibilities
Probability = [tex]\frac{5}{15}[/tex]
Please leave a 'thanks' if this helped!
The required probability of drawing a red marble the 6th time is 1/2.
Given that,
A box contains 10 red marbles and 10 green marbles.
Sampling at random from this box five times without replacement, you have drawn a red marble all five times.
Without replacing any of the marbles.
We have to determine,
What is the probability of drawing a red marble the 6th time?
According to the question,
There are 10 red marbles and 10 green marbles,
The initial condition is to the same state at every step, so the probability to get a red marble is the same in each sampling and is equal to the ratio of the number of red marbles to the total number of samples.
Therefore,
The probability of drawing a red marble the 6th time is,
[tex]P = \dfrac{10}{10+10}\\\\P = \dfrac{10}{20}\\\\P = \dfrac{1}{2}[/tex]
Hence, The required probability of drawing a red marble the 6th time is 1/2.
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