Ruddy has x dollars in his account. He spends $34.56 to buy medicines for his grandmother. If the balance in his account is $265.34, what was the amount in his account before purchase?
Answer:
$299.90
Step-by-step explanation:
Add the $34.56 back to the $265.34
Modern whales appreared 5-10 million years ago. The vertebrae off a whale discovered by paleontologists contain roughly 0.25% as much carbon-14 as they would have contained when the whale was alive. How long ago did the whale die? Use k=0.00012
Answer: 49929 years ago
Step-by-step explanation:
Radiocarbon dating is a method that provides objective age estimates for carbon-based materials that originated from living organisms
To calculate the time, we will use exponential formula
R% = e^ -kt
Where t = number of years
0.25/100 = e^- 0.00012t
Log both sides with natural logarithm
Ln0.0025 = lne^-0.00012t
-5.9915 = -0.00012t
t = 5.9915/0.00012
t = 49928.9 years
Approximately t = 49929 years
The whale died approximately 49,929 years ago.
To determine how long ago the whale died, we use the fact that its vertebrae contain roughly 0.25% as much carbon-14 as they originally did when the whale was alive. This suggests the carbon-14 has decayed, following its known decay rate.
The carbon-14 decay formula is:
N(t) = N0 × [tex]e^{-kt}[/tex]
where:
N(t) is the remaining quantity of carbon-14.N0 is the initial quantity of carbon-14.k is the decay constant (given as 0.00012).t is the time in years.Given that N(t)/N0 = 0.0025, we solve for t:
1. Divide both sides by N0:
0.0025 = [tex]e^{(-0.00012 * t)}[/tex]
2. Take the natural logarithm of both sides:
ln(0.0025) = -0.00012 × t
3. Solve for t:
t = ln(0.0025) / -0.00012
t = −5.991464547/−0.00012
Calculating this, we get:
t ≈ 49928.87 ≈ 49,929 years
Therefore, the whale died approximately 49,929 years ago.
a wise man once said, “200 reduced by 3 times my age is 29.” What’s is his age?
The man's age is 57 years old.
To find this answer follow the steps below:
1. Subtract 29 from 200 to get 171.
2. Divide 171 by 3 to get 57.
To check this, use the equation 200 - (57 x 3) = 29.
1. 57 x 3 = 171. 200 - 171 = 29
2. 200 - 171 = 29. 29 = 29.
Thus meaning the man is 57 years old. I hope this helps!
Answer:
57
Step-by-step explanation:
x=age
200-3x=29
x=57
What is the distance between (3,5.25 and (3,-8.75)
Answer:
Step-by-step explanation:
hello :
the distance between (3,5.25 and (3,-8.75) is :
√((3-3)²+(5.25+8.75)²) ......continu
Find the length of RS.
Given:
The length of arc TS = 40 in
To find:
The length of arc RS.
Solution:
Length of TS = 40 in
θ = 80°
Using arc length formula:
[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]
[tex]$40=2 \times 3.14 \times {r}\left(\frac{80}{360}\right)[/tex]
[tex]$40=6.28 \times {r}\left(\frac{2}{9}\right)[/tex]
[tex]$40=1.39\times r[/tex]
Divide by 1.39 on both sides, we get
[tex]28.7=r[/tex]
Radius = 28.7
Complete angle of circle = 360°
Angle measure of RS = 360° - 60° - 120° - 80°
Angle measure of RS = 100°
Arc length of RS:
[tex]$\text { Arc length }=2 \pi {r}\left(\frac{\theta}{360}\right)[/tex]
Substitute θ = 100° and r = 28.7
[tex]$=2 \times 3.14 \times 28.7 \left(\frac{100}{360}\right)[/tex]
= 50 inch
The length of arc Rs is 50 inches.
Find the requested value.
f(-6) for f(x) =
Select one:
A. 12
B. -12
C. 3
D. -9
Answer:
C
Step-by-step explanation:
A cylinder has a diameter of 10 inches and a height of 8 inches. What is the volume of the cylinder?
Final answer:
To find the volume of a cylinder with a diameter of 10 inches and height of 8 inches, calculate the radius, then apply the volume formula V = πr²h. In this case, the volume is 628.32 cubic inches.
Explanation:
The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height of the cylinder.
First, find the radius by dividing the diameter by 2: radius = diameter / 2 = 10 inches / 2 = 5 inches.
Next, substitute the values into the formula: V = 3.142 × (5 inches)² × 8 inches = 628.32 cubic inches.
Question 5 options: A high school principal wishes to estimate how well his students are doing in math. Using 40 randomly chosen tests, he finds that 77% of them received a passing grade. Create a 99% confidence interval for the population proportion of passing test scores.
Answer:
We are 99% confident interval for the population proportion of passing test scores between ( 0.5987 and 0.9413 )
Step-by-step explanation:
Given -
n = 40
Population proportion = [tex]\widehat{(p)}[/tex] = [tex]77\%[/tex] = .77
1 - [tex]\widehat{(p)}[/tex] = 1 - .77 =.23
[tex]\alpha[/tex] = 1 - confidence interval = 1 - .99 = .01
[tex]z_{\frac{\alpha}{2}}[/tex] = [tex]z_{\frac{.01}{2}}[/tex] = 2.58
99% confidence interval for the population proportion of passing test scores=
[tex]\widehat{(p)}\pm z_{\frac{\alpha}{2}} \sqrt{\frac{\widehat{(p)} (1 - \widehat{p})}{n}}[/tex]
= [tex].77\pm z_{\frac{.01}{2}} \sqrt{\frac{{(.77)} (.23)}{40}}[/tex]
= [tex].77\pm 0.1713[/tex]
= [tex](.77 + 0.1713 , .77 - 0.1713)[/tex]
= ( 0.5987 , 0.9413 )
9. Simplify k ^ 0 * k ^ - 3 . Write the expression using only positive exponents.
Answer:
Step-by-step explanation:
Purplemath
To simplify with exponents, don't feel like you have to work only with, or straight from, the rules for exponents. It is often simpler to work directly from the definition and meaning of exponents. For instance:
Simplify a6 × a5
The rules tell me to add the exponents. But I when I started algebra, I had trouble keeping the rules straight, so I just thought about what exponents mean. The " a6 " means "six copies of a multiplied together", and the " a5 " means "five copies of a multiplied together". So if I multiply those two expressions together, I will get eleven copies of a multiplied together. That is:
MathHelp.com
Simplifying Expressions on MathHelp.com
Simplifying Expressions
a6 × a5 = (a6)(a5)
= (aaaaaa)(aaaaa)
= aaaaaaaaaaa
= a11
Thus:
a6 × a5 = a11
Simplify the following expression:
\mathbf{\color{green}{\dfrac{6^8}{6^5}}}
6
5
6
8
The exponent rules tell me to subtract the exponents. But let's suppose that I've forgotten the rules again. The " 68 " means I have eight copies of 6 on top; the " 65 " means I have five copies of 6 underneath.
\dfrac{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}{6 \cdot 6 \cdot 6 \cdot 6 \cdot 6}
6⋅6⋅6⋅6⋅6
6⋅6⋅6⋅6⋅6⋅6
How many extra 6's do I have, and where are they? I have three extra 6's, and they're on top. Then:
= \dfrac{6 \cdot 6 \cdot 6}{1} = \mathbf{\color{purple}{6^3}}=
1
6⋅6⋅6
=6
3
Unless the instructions also tell you to "evaluate", you're probably expected to leave numerical exponent problems like this in exponent form. If you're not sure, though, feel free to add "= 216", just to be on the safe side.
Simplify the following expression:
\mathbf{\color{green}{\dfrac{\mathit{t}^{10}}{\mathit{t}^8}}}
t
8
t
10
How many extra copies of t do I have, and where are they? I have two extra copies, on top:
\dfrac{t^{10}}{t^8} = \dfrac{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}{t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t \cdot t}
t
8
t
10
=
t⋅t⋅t⋅t⋅t⋅t⋅t⋅t
t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t⋅t
= \dfrac{t \cdot t}{1} = \mathbf{\color{purple}{\mathit{t}^2}}=
1
t⋅t
=t
2
Once you become comfortable with the "how many extras do I have, and where are they?" reasoning, you'll find yourself not needing to write things out and cancel off the duplicate factors. The answers will start feeling fairly obvious to you.
Content Continues Below
Simplify the following expression:
\mathbf{\color{green}{\dfrac{5^3}{5^9}}}
5
9
5
3
This question is a bit different, because the larger exponent is on the term in the denominator. But the basic reasoning is the same.
How many extra copies of 5 do I have, and where are they? I have six extra copies, and they're underneath:
\dfrac{5^3}{5^9} = \dfrac{5 \cdot 5 \cdot 5}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5}
5
9
5
3
=
5⋅5⋅5⋅5⋅5⋅5⋅5⋅5⋅5
5⋅5⋅5
= \dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5} = \mathbf{\color{purple}{\dfrac{1}{5^6}}}=
5⋅5⋅5⋅5⋅5⋅5
1
=
5
6
1
Note: If you apply the subtraction rule, you'll end up with 53–9 = 5–6, which is mathematically correct, but is almost certainly not the answer they're looking for.
Whether or not you've been taught about negative exponents, when they say "simplify", they mean "simplify the expression so it doesn't have any negative or zero powers". Some students will try to get around this minus-sign problem by arbitrarily switching the sign to magically get " 56 " on top (rather than below a "1"), but this is incorrect.
Let's move on to expressions that are a bit more complex.
Simplify the following expression:
\mathbf{\color{green}{\dfrac{5\mathit{x}^5}{3\mathit{x}^3}}}
3x
3
5x
5
I mustn't forget that the "5" and the "3" are just numbers. Since 3 doesn't go evenly into 5, I can't cancel the numbers.
And I mustn't try to subtract the numbers, because the 5 and the 3 in the fraction "\frac{5}{3}
3
5
" are not at all the same as the 5 and the 3 in rational expression "\frac{x^5}{x^3}
x
3
x
5
". The numerical portion \frac{5}{3}
3
5
stays as it is.
For the variables, I have two extra copies of x on top, so the answer is:
\dfrac{5x^5}{3x^3} = \dfrac{5 \cdot x \cdot x \cdot x \cdot x \cdot x}{3 \cdot x \cdot x \cdot x}
3x
3
5x
5
=
3⋅x⋅x⋅x
5⋅x⋅x⋅x⋅x⋅x
= \dfrac{5 \cdot x \cdot x}{3}=
3
5⋅x⋅x
= \mathbf{\color{purple}{\dfrac{5\mathit{x}^2}{3} = \dfrac{5}{3}\mathit{x}^2}}=
3
5x
2
=
3
5
x
2
Either of the purple highlighted answers should be acceptable: the only difference is in the formatting; they mean the same thing.
Simplify (–46x2y3z)0
This is simple enough: anything to the zero power is just 1.
(–46x2y3z)0 = 1
Simplify –(46x2y3z)0
The parenthetical portion still simplifies to 1, but this time the "minus" is out in front of the parentheses; that is, it's out from under the power, so the exponent doesn't touch it. So the answer in this case is:
–(46x2y3z)0 = –1
Final answer:
The expression using only positive exponents is [tex]1/k^3[/tex].
Explanation:
To simplify the expression [tex]k^0 * k^-3[/tex] and write it using , we need to apply the laws of exponents.
The expression can be broken down into two parts.
Therefore,
[tex]k^0 = 1[/tex] (anything raised to the power of 0 is 1).
[tex]k^-3 = 1/k^3[/tex] (negative exponent indicates reciprocal).
Therefore,
[tex]k^0 * k^-3[/tex] [tex]= 1 * 1/k^3[/tex]
[tex]= 1/k^3.[/tex]
Why do we subtract the y-values and subtract the x-values to find the slope?
Answer:
You mean that if we have two pairs of points, (x1, y1) and (x2, y2)
we can find the slope of the line that conects those two points as:
a = (y2 - y1)/(x2 - x1)
remember that a linear equation has the shape:
y(x) = a*x + b
Now let's prove it:
for our case we have that
y1 = a*x1 + b
y2 = a*x2 + b
we can isolate be in both equtaions and get:
b = y1 - a*x1
b = y2 - a*x2
this means that:
y1 - a*x1 = y2 - a*x2
then:
a*x2 - a*x1 = y2 - y1
a*(x2 - x1) = y2 - y1
a = (y2 - y1)/(x2 - x1)
Which is the thing we wanted to get.
The subtraction of y-values and x-values to find the slope of a line is based on measuring the rate of change of y (rise) per unit change in x (run). This concept is fundamental in determining and understanding the steepness of a line on a graph.
Explanation:To understand why we subtract y-values and x-values to find the slope, let's look at the formula for the slope of a line, m = (y2 - y1) / (x2 - x1). Here, 'm' represents the slope of the line, the y values (y2 and y1) represent points on the vertical axis, and the x values (x2 and x1) represent points on the horizontal axis.
When we say 'slope', we mean how steep a line is. That steepness is determined by how much y changes (the rise) for a certain amount of change in x (the run). By subtracting y-values and x-values from each other, we are able to accurately measure this change, and therefore calculate the slope of the line.
Graphically, if we consider two points on a straight line, the slope of the line (m) can be seen as how much the line rises (the difference in y-values) for each unit it runs horizontally (the difference in x-values).
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Find the sum of a geometric series.
20 - 5 + 5/4 - 5/16 + ...
A) 220/7
B) 16
C) 286/13
D) 66
Answer:
Option B.
Step-by-step explanation:
Consider the given geometric series is
[tex]S=20-5+\dfrac{5}{4}-\dfrac{5}{16}+...[/tex]
We need to find the sum of given series.
Here, first term is a=20 and common ratio is
[tex]r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex]
The sum of infinite GP is
[tex]S=\dfrac{a}{1-r}[/tex]
Substitute [tex]a=20\text{ and }r=\dfrac{-5}{20}=-\dfrac{1}{4}[/tex].
[tex]S=\dfrac{20}{1-(-\dfrac{1}{4})}[/tex]
[tex]S=\dfrac{20}{\dfrac{5}{4}}[/tex]
[tex]S=\dfrac{20\times 4}{5}[/tex]
[tex]S=16[/tex]
Therefore, the correct option is B.
Answer:
B edge
Step-by-step explanation:
Solve using the quadratic formula x^2+4x-40=-8
The solution to the Quadratic equation [tex]x^2+4x-40=-8[/tex] is -8 & 4. correct option is C.
To solve the quadratic equation x^2+4x-40=-8 using the quadratic formula, we first need to rearrange the equation so that it is in the form [tex]ax^2+bx+c=0.[/tex]
So, the equation becomes [tex]x^2+4x-32=0.[/tex]
Now, we can identify the values of a, b, and c.
In this case, a=1, b=4, and c=-32.
Next, we can substitute these values into the quadratic formula: x = (-b±√([tex]b^2-4ac[/tex]))/(2a).
Using the formula, we can calculate the solutions for x.
After performing the calculations, we find that the solutions are x = -8 and x = 4.
Therefore, the correct answer is option c) -8 & 4.
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Marvin earns $7.25 per hour at his summer job. He wants to buy a video game system that costs $166.75. Enter an equation to model the relationship between the number of hours worked h and the amount earned e
Answer:
7.25h = e
If e = $166.75, h = 23 hours
Step-by-step explanation:
7.25h = e
However many hours he works, he'll earn 7.25 times that number.
If he wants to know how many hours he must work to get the video game system where e = 166.75, we model this with
7.25h = e
7.25h = 166.75
Divide both sides by 7.25.
h = 23 hours
Final answer:
Explanation of the equation relating hours worked to earnings and interpretation of variables.
Explanation:
Equation: e = 7.25h - 166.75
Explanation: The equation that models the relationship between the number of hours worked h and the amount earned e can be represented as e = 7.25h - 166.75. This equation captures the idea that Marvin earns $7.25 per hour and wants to buy a video game system costing $166.75.
Independent and dependent variables: Hours worked (h) is the independent variable, and the amount earned (e) is the dependent variable. The y-intercept is -166.75, and the slope is 7.25, indicating that for each additional hour worked, Marvin earns $7.25.
At a school play, there is a spotlight Above the center of the floor that covers a lightend area with a radius of 7 feet. What is the area covered by the spotlight
Answer:
The are of the spotlight is 14.4m
Step-by-step explanation:
Step one :
To find the area of the spotlight
First let us understand that the shape is a circle since it's a spotlight
Hence we will use the formula for area of a circle which is
A=πr²
Step two :
Given r= 7feet - - - >metre =2.14m
i.e
1foot =0.305m
7feet =xm
Crosss multiplying we have
X=7*0.305=2.14m
π= 3.142
Step three :
Substituting into the formula we have
A=3.412*2.14²
A=3.142*4.58
A=14.4m
Answer:
154 square feet
Step-by-step explanation:
Extracting the key information from the question:-
*** At school play, there's spotlight above centre of floor.
*** This covers a light end area with radius 7 feet.
*** We are required to calculate the area covered by the spotlight.
In other words, we are basically required to calculate the area of a circle because it is almost certain that the area it covers will be a perfect circle. So all we need to do is to put down the formula for calculating the area of a circle.
We already know that the radius here is 7 feet. We will now simply draft this into the formula and we are good to go.
Formula for area of a circle = πr^2. π = 22/7, r = radius = 7 feet.
Then 22/7 × 7 × 7
= 154 feet^2. The area that is covered by the spotlight which is a perfect circle = 154ft^2
A newborn who weighs 2,500 g or less has a low birth weight. Use the information on the right to find the z-score of a 2,500 g baby. In the United notes, birth weights of newborn babies are approximately normally distributed with a mean of mu = 3,600 grams and a standard deviation of sigma = 500 grams. Z = StartFraction x minus mu Over sigma EndFraction
Answer:
[tex]Z = -2.2[/tex]
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 3600, \sigma = 500[/tex]
Use the information on the right to find the z-score of a 2,500 g baby.
This is Z when X = 2500. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2500 - 3600}{500}[/tex]
[tex]Z = -2.2[/tex]
Answer:
Step-by-step explanation:
-2
ur welcome ;)
What single transformation was applied to quadrilateral A to get quadrilateral B?
Choose 1 answer:
Answer:
It is translation
3
-5
in brackets
Type this number in decimal form. (6×1000)+(2×100)+(1×10)+(7×1)+(8×110)+(5×1100)
Answer:
979, 717
Step-by-step explanation:
Angle A and angle B are complementary
The measure of angle A is (5x + 15)°
• The measure of angle B is 30°
What is the value of x?
Answer:
Step-by-step explanation:
∠A + ∠B = 90° {given they are complementary}
5x+ 15 + 30 = 90
5x + 45 = 90
5x = 90 - 45
5x = 45
x = 45/5
x = 9
The reciprocal of 11/7
[tex]\Huge{\underline{\underline{\tt{\orange{Answer:}}}}}[/tex]
Reciprocal of 11/7 is 7/11.Reason :
Reciprocal is also known as multiplicative inverse which means the number is to be multiplied with the given number to give the result 1.If we flip 11/7 , it becomes 7/11 , and if 7/11 is multiplied with 11/7 ,the result is 1.Usage :Reciprocal is generally used for division in which the second number is reciprocated and the division sign is converted into the multiplication sign. Then the number is simplified and we obtain our answer.__________________________________________
The reciprocal of the given fraction 11/7 is 7/11.
What is the reciprocal property?The reciprocal of any quantity is, one divided by that quantity. For any number ‘a’, the reciprocal will be 1/a. If the given number is multiplied by its reciprocal, we get the value 1.
The given fraction is 11/7.
The reciprocal of the given fraction is the fraction that results from switching or reversing the numerator and denominator.
The reciprocal of the fraction is 7/11.
Therefore, the reciprocal of the fraction is 7/11.
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two numbers have these properties both numbers are greater than 8 their highest common factor is 8 their lowest common multiple is 40 find the two numbers
Answer:
8 and 40
Step-by-step explanation:
Both area multiples of 8:
8, 16, 24, 32, 40
40 = 8 × 5
Since 5 is prime, it can only be:
8 and 40
Ellie baked a round cookie cake for her sister's birthday. The radius of the cookie cake was 6 inches. If Ellie ate 1/4 of the cookie cake, about how many square inches did she eat?
Answer:
28.26
Step-by-step explanation:
If you find the area by using the eqaution A=pi*raduis*2 you can then divide it by 4
What is the difference between a full warranty and a limited warranty?
a.
A full warranty is a guarantee to replace a faulty product, while a limited warranty is a guarantee to repair a faulty product.
b.
A full warranty will pay for repairs any number of times that the product breaks, but a limited warranty will only pay a certain number of times.
c.
A limited warranty is only good for a certain length of time, but a full warranty is good forever.
d.
A full warranty will cover any repairs or replacement that the product needs, while a limited warranty will only pay for certain repairs.
The people i got the answer from was wrong so heres the right answer for people who might need it: D
d.
A full warranty will cover any repairs or replacement that the product needs, while a limited warranty will only pay for certain repairs.
A full warranty will cover all necessary repairs or replacements, whereas a limited warranty will only cover specific services. Option D is correct.
What is full warranty?A full warranty guarantees the replacement of a damaged product. A comprehensive warranty will cover repairs no matter how many times the product breaks.
The difference between a full warranty and a limited warranty is that a full warranty will cover any repairs or replacements required by the product, but a limited warranty would only cover specified repairs.
Hence, option D is correct.
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find the angle in standard position whose cosine is 1/2
A 5π/3
B π/3
C π/3 and 5π/3
D 4π/3 and 2π/3
Answer:
C is the correct answer
Step-by-step explanation:
In this question, we are tasked with calculating the angle at standard position which has a cosine value of 1/2
With reference to the cartesian coordinates, there are only two quadrants which has positive valued for Cosine. These are the first quadrant and the last or 4th quadrant. While the first quadrant has angles in the range of 0-90 the fourth quadrant has an angle range from 270-360
Now back to the angle. In the first quadrant, the angle that has cosine value equal to 30 is cos 60. This is same as pi/3 radians
Now the general form of the angle on the fourth quadrant is 360-theta
Thus, since our theta is pi/3, which is 60, that angle on the fourth quadrant having same value as 1/2 is 360-60 = 300
This is same as 5pi/3 radians
So our answers are pi/3 radians and 5pi/3 radians where pi radians is same as 180 degrees
Finish the work to solve the equation and find the value for p. 2.5(–3p – 8) + 5p = 4(2.25p + 5.5) + 15.5 1.Use the distributive property: –7.5p – 20 + 5p = 9p + 22 + 15.5 2.Combine like terms on each side: –2.5p – 20 = 9p + 37.5 Use the properties of equality to finish solving the equation. What is the value for p? p =
Answer:
-5
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
wHy aM i hErE?!?!
You roll a 6-sided die. What is the probability of rolling a 4? Write it as a fraction. P(4)=
Answer:
P(4)= 1/6
Step-by-step explanation:
Lots of Love!! <3
Stay Safe! Stay at Home!! =)
Answer:
Step-by-step explanation:
no of sample space, n(s) = 6
no of favorable cases , n(e) = 1
Probability of getting 4,
P(e) = n(e) / n(s)
= 1 / 6
There are 10 people on a basketball team, and the coach needs to choose 5 to put into a game. How many different possible ways can the coach choose a team of 5 if each person has an equal chance of being selected?
To find out how many different possible ways the coach can choose 5 players from a team of 10, we calculate the combinations using the formula C(10, 5) which results in 252 different possible ways.
Explanation:To find out how many different possible ways the coach can choose a team of 5 from 10 players, we use combinations. In mathematics, a combination is a selection of items from a larger set, where the order of selection does not matter. This is often denoted as C(n, k) or sometimes nCk, where n represents the total number of items to choose from, in this case, 10 players, and k is the number of items to choose, which here is 5 players.
The formula for a combination is:
C(n, k) = n! / (k!(n-k)!)
where ! denotes factorial, which is the product of all positive integers up to that number.
So for our specific question:
C(10, 5) = 10! / (5!(10-5)!) = 10! / (5!*5!) = (10*9*8*7*6) / (5*4*3*2*1) = 252
Therefore, there are 252 different possible ways the coach can choose a team of 5 players from a pool of 10.
Please help, I have to find the missing coordinate
Answer:
(14, 6)
Step-by-step explanation:
If you plug in 6 for y you get:
6 = x/2 - 1
Add 1 to both sides:
7 = x/2
Multiply 2 on both sides:
14 = x
The answer is (14, 6)
There are only chickens and pigs in Henry's Barn Henry counted a total of Sixteen animal heads and a total of 50 animal feet.How many pigs does Henry have?
Answer:
9 pigs
Step-by-step explanation:
We have the following numbers of heads:
pigs (p) + chickens (c) = 16 animal heads (1)
And the following numbers of feet:
4p + 2c = 50 animal feet (2)
From equation (1):
p = 16 - c (3)
By entering equation (3) into (2) we have:
4(16 - c) + 2c = 50
64 - 4c + 2c = 50
c = 7
Now, entering the value of c into equation (3) we have the next value of p:
p = 16 - c
p = 16 - 7
p = 9
Therefore, the number of pigs that Henry has is 9.
I hope it helps you!
Please help! Some math questions. I have to submit it in 6 minutessss
Answer:
90 euros more
Step-by-step explanation:
Let the number be x
Then,let Ivan's share be 4x and Tanya's share be x
From the given scenario, the equation to represent this would be
4x+x=150 euros
Combine the like terms so that
5x=150 euros
Divide both sides by 5 and simplify
5x/5 and 150/5
so x=30
Ivan's share is 4 times the amount of Tanya's so
4*30=120 euros
So Tanya's share is x=30 euros
Therefore, Ivan gets 90 euros more than Tanya
Sometimes one action has an effect on another action. The cause is the reason something happens. The effect is the result. Sam wanted to print a digital photo that is 5 inches wide and 7 inches long. Sam can make a table to understand cause and effect.
What if Sam accidentally printed a photo that is 6 inches wide and 8 inches long?
Cause Effect
The wrong size photo was printed. Each side of the photo is a length.
Use the information and the strategy to complete the answers to the problems.
What effect did the mistake have on the perimeter of the photo?
The perimeter by
inches.
What effect did the mistake have on the area of the photo?
The area by
square inches.
Answer: The mistake caused the perimeter to increase by 4 inches
The mistake caused the area to increase by 13 square inches
Step-by-step explanation: The original dimensions have been given as 5 inches by 7 inches. If this measurement had been correctly used, the perimeter was supposed to be;
Perimeter = 2(L + W)
Perimeter = 2(5 + 7)
Perimeter = 2(12)
Perimeter = 24 inches
Also the area was supposed to be;
Area = L x W
Area = 5 x 7
Area = 35 square inches
However, Sam accidentally printed a photo that is 6 inches by 8 inches, therefore the effect would be as follows;
Perimeter = 2(L + W)
Perimeter = 2(6 + 8)
Perimeter = 2(14)
Perimeter = 28 inches
And the Area would be
Area = L x W
Area = 6 x 8
Area = 48 square inches
From the calculations so far, the mistake would cause the perimeter to increase by 4 inches (28 inches - 24 inches).
Also the area would likewise increase by 13 inches (48 inches - 35 inches).