Probability of at least one boy and one girl = [tex]\frac{3}{4}[/tex]
The probability of no of boys = 1/2 ×1/2×1/2= 1/8
The probability of no of girls = 1/2×1/2×1/2= 1/8
Now we have to find the probability of at least one girls
Probability of one boy and one girl = 1 - (1/8 + 1/8)
= 1 - 1/4
= 3/4
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Example 1:
If f(x) = 3x-4, find each value. Show all work.
a) ƒ(4)
b) f(-5)
c) f(2-x)
Answer: f(4) = 8, f(-5) = -19, f(2-x) = -3x+2
Step-by-step explanation:
Let's start by analyzing what we are given:
f(x)=3x-4
In this equation, f is the name of the function.
The number in the parentheses represents x.
The 3x-4 tells us what the equation does. In this instance, we multiply x by 3 and then subtract 4.
Let's start with (a).
f(4)
Since we have established that the number in the parentheses is x, we can plug 4 in for x into the equation f. We must abide by the order of operations. Therefore, we can obtain the following:
f(4) = 3(4) -4
f(4) = 12 -4
f(4) = 8
We can continue this for part (b).
f(-5) = 3(-5) -4
f(-5) = -15-4
f(-5) = -19
Part (c) is slightly different, but applies the same principles we established previously. On this part, we must recall the distributive property. The 3 multiples the 2 and the x. We must also remember to combine like terms.
f(2-x) = 3(2-x) -4
f(2-x) = 6 - 3x -4
f(2-x) = -3x +2
8.
Calculate the midpoint of the line segment
formed with the endpoints shown.
Show your work.
(2, 4) and (5, -1)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 5 +2}{2}~~~ ,~~~ \cfrac{ -1 +4}{2} \right) \implies \left(\cfrac{ 7 }{2}~~~ ,~~~ \cfrac{ 3 }{2} \right)\implies \left(3\frac{1}{2}~~,~~1\frac{1}{2} \right)[/tex]
Alice, Billy, and Anna are spending the weekend baking cookies for
winter holiday gifts. For each batch of cookies, they’ll need 21
/2 cups of
flour and 11
/4 cups of butter. Each person contributed supplies from
their mothers’ kitchens and met at Anna’s house.
The fraction that Alice, Billy, and Anna should bring when they are spending the weekend baking cookies for winter holiday is 11/12 cups.
How to calculate the value?It should be noted that based on the information, for each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter.
In this case, it should be noted that there are 3 people.
The fraction will be:
= (2 1/2 + 1 1/4) / 3
= 3 3/4 ÷ 3
= 11/12
Therefore, the fraction will be 11/12 cups for each person.
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Alice, Billy, and Anna are spending the weekend baking cookies for.winter holiday gifts. For each batch of cookies, they’ll need 2 1/2 cups of flour and 1 1/4 cups of butter. Each person contributed supplies from their mothers’ kitchens and met at Anna’s house. What fraction should each person bring?
2x² + 5x-11
+3x² -11x +2
please solve thankyou!!
Answer:
5x^2 - 6x -9
Step-by-step explanation:
Find the inverse of each function.
y=log (x-6)
The inverse of the function y = log(x ₋ 6) is y = 10ˣ + 6.
Given the function is :y = log₁₀ (x ₋ 6)
we are asked to find the inverse of the function.
steps to find inverse function are:
Change f(x) to y to get y = ax + b for the provided function f(x) = ax + b.To get x = ay + b from the equation y = ax + b, replace x with y and y with x.
Here, find y and solve for x = ay + b.
Then we get :
y = (x - b/a).
Finally, we can substitute y = f⁻¹(x) with f⁻¹(x) = (x - b)/a.
now interchange the positions of x and y in the function.x = log₁₀(y ₋ 6)
the next step is to isolate the dependent variables.
y = 10ˣ + 6
hence we get the inverse of the function y = log₁₀ (x ₋ 6) as y = 10ˣ + 6.
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Steve is going to prom with a group of friends. steve's group of friends decide to rent a limo. a local company is willing to rent a limo for $130 an hour. the limo can hold up to six people. steve and his five friends decide to split the cost of the limo evenly. if they rent the limo for four hours, how much will steve and his friends expect to pay? (round up to the nearest dollar amount)
$ 86.67 , Steve and his five friends has to pay $86.67 each to rent limo for four hours.
According to the question,
rent of limo for five hours = $130
now by multiplication ,
rent of limo for four hours = $130 * 4
= $520
now we know that there are six people including Steve hence we divide this $520 by 6 to get the share of each individual,
by division ,
hence the amount for each = $520 / 6
= 86.666666
amount round up to the nearest dollar is $86.67
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The scatter plot and a line of best fit show the relationship between the hours spent sleeping and the hours spent watching TV.
Which statement describes the relationship between the hours spent sleeping and the hours spent watching TV?
For every hour spent watching television, the amount of time spent sleeping drops by an Graph hour.
Graph: A graph is a visual representation, such as a picture or diagram, that shows information or values in a structured way.
The relationships between two or more items are frequently represented by the points on a graph.
Various Graph Types
Pictograph
The term "pictograph" refers to the visual depiction of information. Each graphic represents a specified number of objects.
Line Graph:
In a line graph, dots are connected by lines to depict changes over time.
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Which expression is NOT equivalent to 6√81x⁴y⁸ ?
(f) (3 x y²)²/₃ (g) (3 x)²/₃ y⁴/₃ (h) (3 x²y²)¹/₃ (i) ∛9 x² y⁴
None of the given option is equivalent to 6 [tex]\sqrt81x^{4}y^{8}[/tex].
What are square and square roots?squares are the products of numbers which comes out when the no. is multiplied by itself twice .
and square root helps to find the no. which is multiplied twice to get that no. inside the root.
CALCULATION6 [tex]\sqrt81x^{4}y^{8}[/tex]
= 6 * 9 [tex]x^{2} y^{4}[/tex]
= 54 [tex]x^{2} y^{4}[/tex]
Since from the given option none of the option is equivalent to 6 [tex]\sqrt81x^{4}y^{8}[/tex]
because you can see that all of the option are given in cube roots but the question is in square root .
so , there are two possibilities that maybe the question is typed wrong or the options are incorrect . But if everything present in the question is correct then none of the given values are equivalent to the given expression.
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Forty two billion, three hundred and seven million, one hundred and Two thousand, three hundred and fourteen in number. Please help me
Answer:
42,307,0102,014 is the number form
I need this answered please
Answer: 1. x-8
2. x/8
3. x squared
4. 4x
When they say "a number" that just means "x".
Factor each expression.
x²+x-6
After solving, the factors of equation x²+x-6 are:
(x-2) and (x+3)What is an equation, clearly?A mathematical statement made up of two characterizations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We get the value for the variable x as x = 7 after solving this equation.So,
Given the equation: x²+x-6
Then,
x²+x-6x²+x( - )-6x²+x(3-2)-6x²+3x-2x-6x(x+3)-2(x+3)Factors are: (x+3) and (x-2)
Therefore, after solving, the factors of equation x²+x-6 are:
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A data set related to finding a job contains many variables. Some of the varia
job title, starting salary (in dollars), education required (number of years posts
experience, and location. Classify each variable as categorical or quantitative
column
Categorical variable: job titles, location
Quantitative variable: starting salary, number of years post-experience
Categorical variables represent many data kinds that can be grouped. Race, sex, age, and educational level are a few examples of categorical variables.
In addition, categorical variables are any variables where the data represent groups, as opposed to quantitative variables, which are any variables where the data indicate amounts, such as height, weight, or age.
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Joseph removes 5/8 gallons of white paint from a can. Then he adds 5/8 gallons of blue paint to the can.
Write and then evaluate a subtraction expression to find the overall increase or decrease in the amount of paint in the can.
Answer: Change = - 2.8 gallons
Step-by-step explanation:
Let X be the starting amount of paint in the can, in gallons.
"Removes 5/8 gallon" can be written -(5/8)gal
"Adds 3/8 gallon" becomes +(3/8)gal
The result is : X - (5/8)gal + (3/8)gal = Remaining Paint (gallons)
Consolidating: Remaining (gallons) = X - (2/8)gal
If we want the overall increase/decrease, subtract the initial volume:
Initial - Remaining = Change in amount of paint in can
Change = (X-(2/8)gal) - X = - (2/8) gallons
A recipe requires 3/4 cups if milk.Paula is making 1/2 of the recipe .How many cups of Milk will Paula use?
The answer to this question is:
No. of cups of milk will Paula use = 3/8
Given that recipe requires 3/4 cups of milk.
Paula is making half (1/2) of the recipe.
And we are asked to find that No. of cups of milk will Paula use.
To solve this question, we have to multiply the quantity of milk required by the quantity she is going to make.
The quantity of milk required * the quantity she is going to make
= 3/4 * 1/2
= 3/8
Therefore, No. of cups of milk will Paula use = 3/8
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Find the average rate of change for the following functions over the interval.
Given the function and interval, the average rate of change of the function over the given interval is 1.
What is the average rate of change of the function over the given interval?The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.
r = ( f(1) - f(0) / ( (1) - (0) )
Given the data in the question;
f(x) = 2x² - x - 2
Intervals: [0, 1]
Plug the given values into the average rate of change formula and simplify.
r = ( f(1) - f(0) / ( (1) - (0) )
r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )
r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0
r = ( (-1) - (-2 )) / 1r = ( -1 - (-2 ) / 1
r = ( -1 + 2 ) / 1
r = 1/1
r = 1
Therefore, the average rate of change of the function over the given interval is 1.
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The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.
What is the average rate of change of the function over the given interval?The average rate of change of a function is calculated by dividing the change in y-values over the change in x-values of the two point.
AVR = ( f(1) - f(0) / ( (1) - (0) )
Given the data in the question;
f(x) = 2x² - x - 2Intervals: [0, 1]Plug the given values into the average rate of change formula and simplify.
r = ( f(1) - f(0) / ( (1) - (0) )
r = ( (2(1)² - (1) - 2) - ( 2(0)² - (0) - 2 )) / ( (1) - (0) )
r = ( (2 - 1 - 2) - ( 0 - 0 - 2 )) / 1 -0
r = ( (-1) - (-2 )) / 1
r = ( -1 - (-2 ) / 1
r = ( -1 + 2 ) / 1
r = 1/1
r = 1
The average rate of change of the function f(x) = 2x² - x - 2 over the intervals of 0 to 1 is 1.
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I would really appreciate some help. I am confused with this problem..it says Solve for
Duo makes 65 percent of his dumplings with vegetarian fillings.
What fraction of Duo's dumplings have vegetarian fillings?
The fraction 13/20 of Duo's dumplings have vegetarian fillings.
What is fraction?
A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
Duo makes 65 percent of his dumplings with vegetarian fillings.
According to given question we have
A percentage is a number or ratio expressed as a fraction of 100.
65 percent
=65 %
=65/100
Simplify fraction into simpler fraction,
⇒13/20
Therefore, the fraction 13/20 of Duo's dumplings have vegetarian fillings.
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(-3 1/3 n +1/6) + (1 3/6n - 3/12 )
- 2/6n-1/12
-29/6 n + 1/12
-11/6n - 1/12
- 11/6n+5/12
(-3 1/4d +3/5) -2 7/8 d +7 /10
Answer:
[tex]\frac{4080n+1585d-188}{240}[/tex]
Step-by-step explanation:
I simplified it to the best possible state
9)
Find the length of
the hypotenuse of
the right triangle.
6 ft
6 ft
The hypotenuse of the right triangle is found to be 6√2 ft.
What is defined as the Pythagorean theorem?A right triangle contains a single 90 angle within it, which is known as a right angle.The hypotenuse is really the side straight from the right angle in a right triangle. It is the only side of a triangle that does not form a right angle.The Pythagorean Theorem describes the relationship between the sides of a right triangle, where c represents the hypotenuse and a and b represent the sides that form the right angle.The formula is as follows:
H² = B² + P²
where, H is the hypotenuse.
B is the base
P is the perpendicular.
In the given question, hypotenuse is to be calculated.
Lets, base B = 6 ft and
Perpendicular P = 6 ft.
Thus, put the values in the formula;
H² = 6² + 6²
H² = 2×6²
Taking square root on both sides.
H = 6√2
Thus, the value of the hypotenuse if the right angled triangle is found as 6√2 ft.
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Simplify each radical expression. Use absolute value symbols when needed. 4√16 x¹²
The simplified value of radical expression 4√16 x¹² is 2x^3.
By considering the given expression
4√16 x¹²
=(16x^12)^1/4
=(2^4)^1/4( x^12)^1/4
=2x^3.
An expression with a square root is referred to as a radical expression. Radicand: A value or phrase contained within the radical symbol. Equation with radical expressions and variables as radicands is referred to as a radical equation.
The 'V'-shaped portion of the radical symbol will have a superscript number when it is used to represent any root other than a square root. For instance, the expression 3(8) denotes the cube root of 8.
The radical symbol, which resembles a check mark, the index, a small number written outside the radical symbol, and the radicand, a quantity written beneath the horizontal bar of the radical symbol, are the three main components of the radical expression ab.
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Translate each of the following verbal descriptions into an algebraic rule.The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p.
The algebraic expression which correctly represents the verbal description; The total cost of the order, t, is 11 dollars multiplied by the number of pizzas ordered, p is; t = 11p.
Which algebraic expression correctly represents the verbal description as in the task content?It follows from the task content that the expression which correctly represents the verbal description be determined.
On this note, since total cost is; t and the number of pizzas ordered is; p.
The required expression is therefore;
t = 11 × p
t = 11p.
Ultimately, the verbal representation of the algebraic expression where total cost of the order, t, is 11 dollars and number of pizzas ordered, is p is given by t = 11p.
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i need help with this
Answer:of not
Step-by-step explanation: ops
What is the value of x+26
The value of x can not be told as there is no answer to the question "x+26".
Hence, can not be solved and it is left as 'x+26'
Find the midpoint of the segment with the following endpoints.
(9, 6) and (5, 2)
The midpoint of the segment is (7, 4).
According to the section formula-
If a point (x , y) divides a line in the ratio of m : n, where the two endpoints of the line are (x1, y1) and (x2, y2), then-
x = (nx1 + mx2)/ (m + n)
and y = (ny1 + my2)/ (m + n)
Here, we are given two points- (9, 6) and (5, 2)
Therefore,
x1 = 9, y1 = 6
x2 = 5, y2 = 2
Since, midpoint divides a line segment into two equal halves, m : n = 1 : 1
Now, substituting the values in the section formula we get-
x = (9 + 5)/2
x = 14/2
x = 7
and y = (6 + 2)/2
y = 8/2
y = 4
Thus, the midpoint of the segment is (7, 4).
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What is the slope of a line perpendicular to the line whose equation is 3x+y=8. Fully simplify your answer.
Christopher is the oldest of three siblings whose ages are consecutive odd integers. If the sum of their ages is 6363, find Christopher's age.
Christopher's age given the sum of the ages of the three siblings is 23.
What is Christopher's age?An odd number is a number that is not perfectly divisible by 2. An odd number can be a positive number or a negative number. An example of an odd number is 3 and 7.
Consecutive odd integers are odd integers that follow each other on the number line. Consecutive odd integers increase by a value of (x + 2). Examples of consecutive odd integers are 11, 13, 15.
Let x represent the youngest sibling's age
Second sibling's age : x + 2
Christopher's age : x + 4
x + x + 2 + x + 4 = 63
3x + 6 = 63
3x = 63 - 6
3x = 57
x = 57 / 3
x = 19
Christopher's age : x + 4 : 19 + 4 = 23
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Solve each equation.
ln (x+2)- ln 4=3
After solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
What exactly is an equation?An equation is a mathematical statement made up of two expressions joined by an equal sign.An example of an equation is 3x - 5 = 16.After solving this equation, we obtain the value of the variable x as x = 7.So,
Given equation: ln(x+2)-ln4=3Then,
ln(x+2)-ln4 = 3log(e)(x+2)-In4 = 3log(e)(x+2)-4In = 3[tex]x=e^{4 \ln +3}-2[/tex]Therefore, after solving the given equation ln(x+2)-ln4=3, the value of [tex]x=e^{4 \ln +3}-2[/tex].
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Describe the difference between an equation and an expression. Give an example!
The primary difference between expression and equation has an equal sign. An equation has a left side , a right side and an equal symbol separating the sides. But an expression by contrast does not have any sides and equal symbol.
What is Expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.) Expressions can be thought of as similar to phrases.
The primary difference between expression and equation is an equal sign. An equation has a left side , a right side and an equal symbol separating the sides. But an expression by contrast does not have any sides and equal symbol.
For example
ax2+by+c is an expression.
4x+3y+8=5 is an equation.
Therefore expression and equation both are different.
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Work out ( 3 × 10 − 3 ) − ( 6 × 10 − 5 ) Give your answer in standard form.
Answer:
-28
Step-by-step explanation:
Simplify those in parenthesis first.
( 30 - 3) - (60 - 5)
27 - 55
= -28
an oil tank is being filled at a constant rate of .2 feet per minute. After 15 minutes the tank is 6 feet deep. Write an equation that can be used to determine the amount of oil in the tank at any time.
The equation that represent amount of oil in the tank at x minutes is
6- 0.2t
What is an equation?A mathematical statement that shows that two mathematical expressions are equal.
Given:
rate of filling the tank = 0.2 feet/ minute
After 15 minutes,
height = 6 feet
let the time take be x minutes
So, the equation that represent amount of oil in the tank at x minutes.
=6- 0.2t
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