Answer:
what do yuo mean by adding and subtracting mixed fractions
What is the probability of Andre choosing a greater number than five?
Answer:
It is 1/2
Probability is (No of favourable outcomes/ No. of possible outcomes )
or 4/8 = 1/2
Answer:
1/2
Step-by-step explanation:
hope this helps.
a shipping service restricts the dimensions of the boxes it will ship for a certain type of service. the restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130130130 inches. the perimeter of the base is determined using the width and length of the box. if a box has a height of 606060 inches and its length is 2.52.52, point, 5 times the width, which inequality shows the allowable width xxx, in inches, of the box?
The inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service, given that the box has a height of 60 inches and a length of 2.5 times the width.
1. Let x = the width of the box, in inches.
2. The perimeter of the base of the box is calculated by the following formula: Perimeter = 2(Width) + 2(Length)
3. Therefore, the equation is: 60 + 5x + 2(2.5x) = 130
4. Simplify the equation by expanding the parentheses and combining like terms: 60 + 5x + 5x = 130
5. Solve for x: 5x = 130 - 60
6. Simplify: 5x = 70
7. Divide both sides by 5 to find x: x = 70/5
8. Simplify: x = 14
9. Therefore, the inequality 60 + 5x ≤ 130 shows the maximum width, in inches, of the box that meets the restrictions of the shipping service is 14 inches
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Which of the following scatterplots is most likely to have a line of best fit represented by the equation below?y = -5x + 2
A scatterplot that shows a negative linear association.
A scatterplot that is most likely to have a line of best fit represented by the equation y = -5x + 2 is the one where the data points have a strong negative linear association. This means that as the x-values increase, the y-values decrease. The slope of the line is -5, which is negative, indicating a negative association. The y-intercept of the line is 2, which represents the point where the line crosses the y-axis.
A scatterplot that shows a negative linear association would have its points distributed in a downward direction from left to right, with a slope of -5.
Therefore, A scatterplot shows a negative linear association will most likely have a line of best fit
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A teacher would like to estimate the true mean amount of time her students spend completing a particular homework assignment. The day the homework is due, the teacher selects a random sample of 30 of her 75 students and records the amount of time that each of them spent completing the assignment. Are the conditions for constructing a t confidence interval met
The conditions for constructing a t-confidence interval are met.
In order to construct a t-confidence interval for the mean amount of time the students spend completing the homework assignment, the following conditions must be met:
The data must be a random sample from the population of interest
The sample size must be sufficiently large (typically, n > 30)
The data should be approximately normally distributed
The population standard deviation or variance must be unknown
From the information provided it can be inferred that the data is a random sample (30 students out of 75 students) and that the population standard deviation or variance is unknown. If the sample size is greater than 30, and the data is approximately normal or the sample size is large, then the conditions for constructing a t-confidence interval are met.
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teri finds a pile of money with at least $\$600$. if she puts $\$200$ of the pile in her left pocket, gives away $\frac45$ of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away $\$600$ of the original pile and kept the rest. what are the possible values of the number of dollars in the original pile of money? (give your answer as an interval.)
600 ≤ X < 950 are the possible values of the number of dollars in the original pile of money.
What is range?The difference between the highest and lowest values in statistics for a particular data collection is called the range. As an illustration, if the data set contains 1, 5, 8, 12, 3, the range will be 12 - 1 = 11. The difference between the greatest and lowest observation might thus also be used to determine the range.
We need to first put the data in ascending order before we can determine the range of a particular set of observations. To determine the range, calculate the difference between the highest and minimum values afterwards.
Let X be the amount in the pile.
What is left after putting $200 in the pile = X - $200
4/5 = 0.8
What she gives away = 0.8 (X - 200)
The remaining is : 0.2 (X - 200) what she puts in her right pocket.
200 + 0.2(X - 200) > X - 600
200 - 0.2X - 40 > X - 600
Solving the inequality we have :
= 160 + 0.2x > X - 600
= 760 > X - 0.2X
= 760 > 0.8X
= 950 > X
This implies : X < 950
It is said : X ≥ 600
The possible range of X is thus : 600 ≤ X < 950
thus, 600 ≤ X < 950 are the possible values of the number of dollars in the original pile of money.
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Find the logarithmic function f(x)=log a (x-h) that describes each graph.
PLEASE HELP 100 POINTS+BRAINLIEST
just an addition to the decent reply above
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we will be using this rule}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]f(x)=\log_a(x-h) \\\\[-0.35em] ~\dotfill\\\\ 1=\log_a(\frac{3}{2}-h)\implies a^1=a^{\log_a(\frac{3}{2}-h)}\implies a^1=\cfrac{3}{2}-h\implies a=\cfrac{3}{2}-h \\\\[-0.35em] ~\dotfill\\\\ -1=\log_a(3-h)\implies a^{-1}=a^{\log_a(3-h)}\implies a^{-1}=3-h\implies \cfrac{1}{a}=3-h \\\\\\ 1=(3-h)a\implies 1=(3-h)\left( \cfrac{3}{2}-h \right)\implies 1=(3-h)\left( \cfrac{3-2h}{2} \right) \\\\\\ 2=(3-h)(3-2h)\implies 2=9-9h+2h^2\implies 0=2h^2-9h+7[/tex]
[tex]0=(h-1)(2h-7)\implies \boxed{h= \begin{cases} 1\\\\ \frac{7}{2} \end{cases}}\hspace{5em}a=\cfrac{3}{2}-h\implies \boxed{a= \begin{cases} \frac{1}{2} ~~ ~~ \checkmark\\\\ -2 ~~ \bigotimes \end{cases}} \\\\\\ ~\hfill {\Large \begin{array}{llll} f(x)=\log_{\frac{1}{2}}(x-1) \end{array}} ~\hfill[/tex]
now, why we didn't use the negative value for the base "a"?
from the standpoint of a negative value raised to some exponent, is perfectly fine, however if we plug that in the change of base rule, we run into a really hot pickle.
Answer:
[tex]f(x)=\log_{\frac{1}{2}}(x-1)[/tex]
Step-by-step explanation:
Use the given points to assist in determining the logarithmic function of the given graph in the form:
[tex]f(x)=\log_a(x-h)[/tex]Substitute the given points (³/₂, 1) and (3, -1) into the formula to create two equations:
[tex]\log_a\left(\dfrac{3}{2}-h\right)=1[/tex]
[tex]\log_a\left(3-h\right)=-1[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Low law}\\\\$\log_ab=c \iff a^c=b$\\ \end{minipage}}[/tex]
Apply the log law and rearrange each equation to isolate a:
Equation 1
[tex]\begin{aligned}\log_a\left(\dfrac{3}{2}-h\right)&=1\\\\\implies a^1&=\dfrac{3}{2}-h\\\\ a&= \dfrac{3}{2}-h\end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}\log_a\left(3-h\right)&=-1\\\\\implies a^{-1}&=3-h\\\\ \dfrac{1}{a}&=3-h\\\\a&=\dfrac{1}{3-h}\end{aligned}[/tex]
Substitute the first equation into the second to eliminate a:
[tex]\dfrac{3}{2}-h=\dfrac{1}{3-h}[/tex]
Solve for h:
[tex]\implies \dfrac{3}{2}-h=\dfrac{1}{3-h}[/tex]
[tex]\implies \dfrac{3-2h}{2}=\dfrac{1}{3-h}[/tex]
[tex]\implies (3-h)(3-2h)=2[/tex]
[tex]\implies 9-9h+2h^2=2[/tex]
[tex]\implies 2h^2-9h+7=0[/tex]
[tex]\implies 2h^2-2h-7h+7=0[/tex]
[tex]\implies 2h(h-1)-7(h-1)=0[/tex]
[tex]\implies (2h-7)(h-1)=0[/tex]
[tex]\implies h=\dfrac{7}{2},\;1[/tex]
Substitute both values of h into the equations for a:
[tex]h=\dfrac{7}{2}\implies a=\dfrac{3}{2}-\dfrac{7}{2}=-2[/tex]
[tex]h=\dfrac{7}{2}\implies a=\dfrac{1}{3-\dfrac{7}{2}}=-2[/tex]
[tex]h=1\implies a=\dfrac{3}{2}-1=\dfrac{1}{2}[/tex]
[tex]h=1\implies a=\dfrac{1}{3-1}=\dfrac{1}{2}[/tex]
Therefore, the two values of h given is two possible values of a. Since a is the base of the function, and the bases of logarithmic function cannot be negative, the value of a cannot be -2. Therefore, the only valid value of a is ¹/₂.
Similarly, logs of negative numbers are undefined, therefore the value of h cannot be ⁷/₂ since this would make the argument negative for the points given. Therefore, the only valid value of h is 1.
Inputting the found values of a and h into the given formula, the logarithmic function of the given graph is:
[tex]f(x)=\log_{\frac{1}{2}}(x-1)[/tex]Use the histogram to answer the following questions.
1.
what does each axis indicate?
9
8
2.
how is the horizontal axis organized?
7
frequency
3.
how many bowlers competed?
2
describe the general shape of the distribution.
1) The bowler's scores are shown on the horizontal axis, while the frequency is shown on the vertical axis.
2) Groups of 20 points are assigned to the scoring.
3) There are 30 bowlers competing.
4) The distribution is skewed towards the left.
A histogram is a bar graph that shows data that has been divided into equal intervals in terms of frequency. The bars must touch but not overlap, and they must be of equal width.
1) A histogram shows the type of data being measured on the horizontal axis and the number of observations in each bin on the vertical axis.
Here, the horizontal axis displays the bowlers' scores, and the vertical axis displays the frequency at each interval.
2) The categories or bins of the data are listed on the horizontal axis of a histogram. The height of the columns, which represents the frequency or quantity of the occurrences, is listed on the vertical axis.
Here, the scores are arranged into 20-point groups.
3) From the histogram, it is interpreted that:
Bowlers = 2 + 4 + 6 + 8 + 9 + 1 = 30
Therefore, 30 bowlers compete
4) The distribution is skewed left. A distribution is said to be "skewed left" if the tail is to the left. The procedure of determining a "typical value" for the distribution is philosophically more challenging when the distribution is skewed.
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D) 3-2 (s-1) = 13+6s
Answer: -1
E) 2 (n+9) = -6 (2n-5) +8
Answer: 10/7
F) 5 (4k-3) -5k = 10+2 (3k+1)
Answer: 3
The solution for the variable of each expression is given as follows:
D) 3 - 2(s - 1) = 13 + 6s: s = -1.
E) 2(n + 9) = -6(2n - 5) + 8: n = 10/7.
F) 5(4k - 3) - 5k = 10 + 2(3k + 1): k = 3.
How to solve the expressions?The expressions are solved applying the distributive property when needed, then combining the like terms, and finally isolating the variable.
The expression for item d is given as follows:
3 - 2(s - 1) = 13 + 6s
Hence:
3 - 2s + 2 = 13 + 6s -> Distributive property.
8s = 5 - 13 -> Combine the like terms.
8s = -8
s = -8/8
s = -1.
The expression for item e is given as follows:
2(n + 9) = -6(2n - 5) + 8
2n + 18 = -12n + 30 + 8 -> Distributive property.
14n = 20 -> Combine the like terms.
n = 20/14
n = 10/7.
The expression for item f is given as follows:
5(4k - 3) - 5k = 10 + 2(3k + 1)
20k - 15 - 5k = 10 + 6k + 2
15k - 15 = 12 + 6k
9k = 27
k = 27/9
k = 3.
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WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!
What is the area of ΔABC given m∠B = 95°, a = 22 feet, and c = 17 feet?
34.23 feet2
128.54 feet2
188.29 feet2
34680.46 feet2
Answer:
Given m∠B = 95°, a = 22 feet, and c = 17 feet, we can use the Law of Cosines to find the value of b and then use Heron's formula to find the area of ΔABC.
The Law of Cosines states:
c^2 = a^2 + b^2 - 2ab * cos(C)
Since ∠B = 95° , angle C = 180 - 95 = 85
Therefore,
c^2 = a^2 + b^2 - 2ab * cos(85)
so,
b = sqrt(c^2 - a^2 + 2ab * cos(85))
We can substitute the given values of a and c to find b:
b = sqrt(17^2 - 22^2 + 2 * 22 * 17 * cos(85))
Once we have the value of b, we can use Heron's formula to find the area of the triangle:
Area = sqrt(p*(p-a)(p-b)(p-c))
where p is the semiperimeter of the triangle: p = (a + b + c) / 2
Area = sqrt(((22 + b + 17) / 2)((22 + b + 17) / 2 - 22)((22 + b + 17) / 2 - b)*((22 + b + 17) / 2 - 17))
The only option that matches this area is 128.54 feet^2, so the area of ΔABC is 128.54 feet^2.
Find The Range of y-x=3
how to multiply matrices with different dimensions
The number of columns in the first matrix must equal the number of rows in the second matrix in order to multiply matrices with different dimensions.
First, jot down each matrix's dimensions. Let's imagine, for illustration, that we have a matrix A that is 2 by 3 and a matrix B that is 3 by 4. Create a new matrix C with the dimensions 2x4 in step 2. This is what the multiplication will ultimately produce.3. Determine the dot product of the corresponding row in matrix A and the corresponding column in matrix B for each element in matrix C.
4: The final response is matrix C, which is the union of the 2x3 matrix A and the 3x4 matrix B.
Therefore, the result is a 2x4 matrix, which is produced by taking the dot product of the rows and columns of matrix A and matrix B.
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How do you explain what half is?
Answer:
Say you take a pizza and cut it perfectly down the middle so there are two slices. Each slice is a half or 1/2 of the pizza.
x - 10 = √9x show steps
The solution of the equation is as follows;
x = -5How to solve equation?Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
The equation can be solved as follows:
x - 10 = √9x
subtract x from both sides of the equation
x - x - 10 = √9x - x
-10 = √9 x - x
-10 = 3x - x
-10 = 2x
divide both sides by 2
x = -10 / 2
x = -5
Therefore,
x = -5
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For each problem, find the equation of the line tangent to the function at the given point. Your answer should be in slope-intercept form.
the equation of the line tangent to the function at (3, 6) is y = 11x - 21.
1. f(x) = x^2 + 5x - 6, at (3, 6)
Answer: y = 8x - 21
f'(x) = 2x + 5
f'(3) = 2(3) + 5 = 11
The equation of the line tangent to the function at (3, 6) is y = 11x - b.
Substitute 6 for y and 3 for x to get 6 = 11(3) - b
Solve for b to get b = 21
Therefore, the equation of the line tangent to the function at (3, 6) is y = 11x - 21.
The equation of the line tangent to the function at (3, 6) is y = 8x - 21. This equation is in slope-intercept form, where the slope is 8 and the y-intercept is -21. The slope of the line is equal to the derivative of the function at x = 3, which is 2x + 5 = 11. Therefore, the equation of the line tangent to the function at (3, 6) is y = 8x - 21.
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-3(y + 2) = 2(y + 6) + 7
Answer:
y = -5
Step-by-step explanation:
-3(y+2) = 2(y+6)+ seven
-3y-6 = 2y+12+
-3y-6 = 2y + 19
-2 -2
-5y - 6 = 19
+6 +6
-5y 25
-5 -5
y = -5
[amazon - medium] how many cards would you expect to draw from a standard deck before seeing the first ace?
Answer:
You would get your first ace at card 10.6 or about card 11.
Solve this 30-60-90 Triangles
Draw the triangle if necessary
Answer:
y=11.547004; x= 23.094008.
Step-by-step explanation:
Since 20 = y*sqrt*3; y=11.547004; x= 23.094008.
Solve the differential equation by variation of parameters. y" + y = CSC X y(x) =sin(x)ln(|sin(x)|) + C2cos(x) + C1sin(x) + xcos(x)
To solve the differential equation y" + y = csc(x) using variation of parameters, we first need to find a particular solution.
Since the non-homogeneous term is csc(x), we can try a particular solution of the form yp = u(x) csc(x), where u(x) is a function to be determined.
Substituting yp into the differential equation:
u''(x)csc(x) + u(x)csc(x) = csc(x)
To find u(x), we can multiply both sides by csc(x) and integrate with respect to x:
∫u''(x)csc(x) dx + ∫u(x)csc^2(x) dx = ∫csc(x) dx
Integrating the first term by parts:
u'(x) = ∫csc(x) dx = ln|cot(x/2)| + C1
Integrating the second term by parts:
u(x) = -∫csc(x)cot(x) dx = -ln|sin(x)| + C2
So, the particular solution for yp is:
yp = u(x)csc(x) = -ln|sin(x)|csc(x) + C1csc(x) + C2
Now we need to find the general solution y = yc + yp
where yc is the general solution for the complementary homogeneous equation y" + y = 0
yc = C1cos(x) + C2sin(x)
Now we can use the method of variation of parameters to find the general solution for the non-homogeneous equation
By this method, we need to find two functions v1(x) and v2(x) such that W(yc, yp) = v1(x)cos(x) + v2(x)sin(x)
W(yc, yp) = (yc * yp') - (yp * yc')
W(yc, yp) = (C1cos(x) + C2sin(x)) * (-cot(x)csc(x) + C1) - (-ln|sin(x)|csc(x) + C1csc(x) + C2) * (-sin(x)cos(x) + cos(x)sin(x))
W(yc, yp) = -C1cot(x)csc(x) + C1^2 + C2csc(x)
As W(yc, yp) is not identically zero, we can proceed to find v1(x) and v2(x)
v1'(x) = -cot(x)csc(x) + C1
v2'(x) = csc(x)
Integrating both sides by parts:
v1(x) = ln|cot(x/2)| - cot(x) + C3
v2(x) = -cot(x) + C4
The general solution for the non-homogeneous equation y" + y = csc(x) is:
y = yc + yp = (C1cos(x) + C2sin(x)) + (sin(x)ln|sin(x)|
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Type the correct answer in each box. Write your answers as fractions, using / as the fraction bar, and write the greater value first.if log3 (8x-3)-log 4 = 2, the value of x is
The value of x 1/2 or 3/2.
The logarithm of any number N if interpreted as an exponential form, is the exponent to which the base of the logarithm should be raised, to obtain the number N. Here we shall aim at knowing more about logarithmic functions, types of logarithms, the graph of the logarithmic function, and the properties of logarithms.
The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic function properties are helpful to work across complex log functions. All the general arithmetic operations across numbers are transformed into a different set of operations within logarithms. The product of two numbers, when taken within the logarithmic functions is equal to the sum of the logarithmic values of the two functions. Similarly, the operations of division are transformed into the difference of the logarithms of the two numbers.
Here, we use:
1) loga/b = log a - log b
2) logba = (logc a)/(logc b)
Given logarithmic equation:
logₓ(8x-3) - logₓ4 = 2
logₓ (8x-3/4) = 2
(8x-3/4) = x²
8x - 3 = 4x²
4x² - 8x + 3 = 0
x = 1/2 or 3/2
Thus, the value of x 1/2 or 3/2.
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Kristin spent $25 on a magazine and some notepads. If the magazine cost $5 and each notepad cost $4, then how many notepads did she buy?
Answer:
5 notepads
Step-by-step explanation:
We know
Kristin spent $25 on a magazine and some notepads
1 magazine = $5
1 notepad = $4
$25 - $5 = $20
How many notepads did she buy?
We take
$20 divided by $4 = 5 notepads
So, she bought 5 notepads
Answer:
5 notepads
Step-by-step explanation:
25=4x+5
subract 5 from 25 and cancel out old 5
20=4x
divide by 4
20/4 = 5
An elephant weighs 1.1 * 10 to the 4th power pounds a giraffe weighs 2.1 * 10 to the third power pounds how much more does the elephant weigh than the giraffe
The elephant weighs 8.9 × 10³ pounds more than the giraffe.
What is weight?Weight is the gravitational pull of a large second object, like the Moon or the Earth, on a first object. Weight is a result of the universal law of gravitation, according to which any two objects will gravitationally attract one another with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Because of this, larger objects naturally weigh more when placed in the same location; however, the farther an object is from the Earth, the less weight it has.
Given that
Elephant weighs 1.1 × 10⁴ pounds
Giraffe weighs 2.2 × 10³ pounds
To find how much more elephant weighs than giraffe, we need to find the difference of their weights. i.e
1.1 × 10⁴ - 2.1 × 10³
= 11000 - 2100
= 8900
= 8.9 × 10³ pounds
Thus, the elephant weighs 8.9 × 10³ pounds more than the giraffe.
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in the geometric sequence with a first term of $6$ and a second term of $-6$, what is the $205^{th}$ term?
The 205th term of the given geometric sequence is given by 6
What is a Geometric Sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
Given here: The first term of a given geometric sequence as 6 and second term -6.
Thus clearly we can deduce that the common ratio of the sequence is given by -1
Therefore the geometric sequence has two elements that are alternating sequence of the form 6,-6,6,-6,6.........
Therefore the 205th term of the sequence will be given by
T₂₀₅=6×-1²⁰⁵⁻¹
=6×1
=6
Hence, The 205th term of the given geometric sequence is given by 6
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How much Vanilla extract Will be needed to make 2 dozen cookies?
As you answer the following questions, write explanations for why your current answer is correct
The amount of vanilla extract that will be needed to be able to make 2 dozen cookies is 2 teaspoons of vanilla extract
How to find the amount of vanilla extract ?The recipe given will be able to yield 1 . 5 dozen of Oatmeal Raisin Cookies which means that the 1 . 5 teaspoons of vanilla extract will be needed for 1. 5 dozens of Oatmeal Raisin Cookies.
If you are to make 2 dozen cookies therefore, it means that the recipe would require a higher amount of vanilla extract which can be found by the formula:
= ( Dozen cookies needed x teaspoons in 1 .5 dozen ) / 1 . 5 dozen
= ( 2 x 1 . 5 ) / 1 . 5
= 2 teaspoons of vanilla extract
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Find the measures of the angles of a right triangle with one angle measuring 45 . I need three measures
Answer:
Your three angle measurements are 45, 45, and 90
Step-by-step explanation:
Since we know that all the measures of a triangle add up to 180, we have:
45 + b + c = 180
Then, since it is a right triangle, we know one of the sides is 90 degrees, giving us:
45 + 90 + c = 180
Then subtract 135 from both sides:
c = 45
So, your three angle measurements are 45, 45, and 90.
Hope this helped!
Steadman Bailey's bank account shows a previous balance of $65.00. He
made $756.00 in deposits. He wrote $44.10 in checks. He had a service
charge of $4.90 and earned $10.00 in interest. What is his present
balance?
VEGHER
PEREKONNAN
FRECEN
CAFETERA
FREETING
Answer:
present balance=782
Step-by-step explanation:
65+756=821
now has 821 in account
821-44.10=776.9
now has 776.9
776.9-4.90=772
now has 772 in account
772+10=782
he now has 782 in his account
Hunter is 1. 75 meters tall. At 12 noon, he measures the length of a tree's shadow to be 30. 85 meters. He stands 26. 8 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter
The height of the tree to the nearest hundredth of a meter is 29.1m.
We can use the concept of similar triangles to find the height of the tree. The ratio of the height of the tree to the length of its shadow is the same as the ratio of Hunter's height to the length of his shadow.
Let h be the height of the tree.
Hunter's height : h = 1.75m : x (where x is the height of the tree)
Hunter's shadow : Tree's shadow = 1.75m : 30.85m
We know that Hunter is 26.8 meters away from the tree, and the tip of his shadow meets the tip of the tree's shadow.
Hunter's shadow = Hunter's height + Tree's shadow
1.75 + x = 30.85
x = 29.1m
Therefore, the height of the tree to the nearest hundredth of a meter is 29.1m.
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Please help ASAP i will give brainliest if they answer all the questions "100 points"
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g we have 4 women and 5 men and want to create a committee with 2 women and 2 men. in how many ways we can do this?
The required number of ways in which we can create a committee with 2 women and 2 men is 60.
What are Combinations?Combinations are selections that are made by choosing some or all of a group of objects, regardless of how they are arranged.Utilizing the combinations formula, it is simple to determine how many distinct groups of r objects each may be created from the provided n unique objects. The factorial of n divided by the product of the factorial of r and the factorial of the difference between n and r, respectively, is the formula for combinations.Given:
We have 4 women and 5 men.
The required number of ways in which we can create a committee with 2 women and 2 men can be calculated as:
= 4C2 × 5C2
= 4!/(2!)(2!) × 5!/(2!)(3!)
= 6 × 10
= 60
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postus has four 1-cent stamps, three 5-cent stamps, and three 25-cent stamps. how many different postage amount of at least one cent can postus make?
Portus has four 1-cent stamps, three 5-cent stamps, and three 25-cent stamps. 79 different postage amount of at least one cent can postbus make.
We can get the sums of 1 cent, 2 cents, 3 cents and 4 cents by combining one 1-cent coin, two 1-cent coins, three 1-cent coins and four 1-cent coins, respectively. i.e., 4 different sums.
We can get three sums of 5 cents, 10 cents, and 15 cents by combining mean five-cent coins., i.e. 3 different sums.
we can get three sums of 25 cents, 50 cents, and 75 cents by combining means twenty-five-cent coins. i.e,3 different sums.
Now,
4*3 = 12 different sums by combining 4 one-cent coins with 3 five-cent coins.
Again,
4*3 = 12 different sums by combining 4 one-cent coins with 3 twenty-five-cent coins. 3*3 = 9 different sums by combining 3 five-cent coins with 3 twenty-five-cent coins.4*3*3 = 36 different sums by combining 3 five-cent coins with 3 five-cent coins and 3 twenty-five-cent coins.Now,
add all these combinations:
4 + 3 + 3 + 12 + 12 + 9 + 36 = 79.
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Determine the volume of a sphere with a great circle of radius 12 cm. Question 7 options:A) 7,238.2 cm3 B) 3,216.9 cm3 C) 1,024 cm3 D) 21,714.7 cm3
The volume of the sphere with a great circle of radius 12 cm is 7238.2 cm³. The correct option is A) 7,238.2 cm3
Calculating the volume of a sphereFrom the question, we are to calculate the volume of the sphere with the given radius.
From the formula for calculating the volume of a sphere, we have that
V = 4/3πr³
Where V is the volume
and r is the radius
From the given information,
The sphere has a great circle of radius 12 cm
Thus,
r = 12 cm
Substitute the value of r into the equation,
V = 4/3πr³
That is,
V = 4/3 × π × 12³
V = 4/3 × π × 1728
V = 4 × π × 576
V = 4 × 576 × π
V = 2304π
V = 7238.2 cm³
Hence, the volume is 7238.2 cm³
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