7776
ExplanationThe size of the sample space is the total number of possible outcomes.for example, for a dice, the possible outcomes are 1, 2,3 4, 5 or 6, when rolling a dice five times we have:
Each time you roll the dice there are 6 possible outcomes. (1 of 6)
[tex]6[/tex]now, you have to roll the dice five times
then
[tex]\text{sample space=6}^5=6\cdot6\cdot6\cdot6\cdot6=7776[/tex]I hope this helps you
how are rational munbers written as decimalsfYI:I was listening but I just don't understand
We have 4 rational numbers which we are asked to express in decimal numbers.
To do this, we divide the numerator of each rational number by its denominator, when we do that, we get the following results:
[tex]undefined[/tex]Please help me with this geometry problem. i don’t understand.
Tangent theorem states that when two tangents intersect out a circle they are said to be equal
Therefore,
Tangent 2x+13 is equal to tangent 4x-8
[tex]\begin{gathered} 4x-8=2x+13_{} \\ by\text{ collecting like terms we will have that,} \\ 4x-2x=13+8 \\ 2x=21 \\ to\text{ find x we will dive both sides by the coefficent of x which is 2} \\ \frac{2x}{2}=\frac{21}{2} \\ x=10\frac{1}{2} \\ x=10.5 \end{gathered}[/tex]Hence,
The value of x =10.5
3. Determine the missing length in the following triangle. Round to thenearest tenth. (2 points: 1 point for correct answer, 1 point for showingyour work) *1214Your answer
7.2
1) Examining the picture, we can assume this is a Right Triangle, and then use the Pythagorean Theorem
a²=b² +c²
14² = 12² +c² The hypotenuse is the larger side a
196=144 +c²
196-144 = c²
52 =c²
√52 =√c²
c= √52
2) Rounding off to the nearest tenth we can write
c= √52 is approximately 7.2
Find the area of each. 'Use your calculator's value of r. Round your answer to the nearest tenth.
To find the area of a circle given the radius;
[tex]undefined[/tex]In your own words describe an exponential function. Are there restrictions on the domain why or why not? Are exponential and logarithmic function inverse. why or why not?(this is all one question, from the same page i just am on my laptop so cant provide picture)
Answer:
An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations, and so on. In this article, you will learn about exponential function formulas, rules, properties, graphs, derivatives, exponential series, and examples.
An example of an exponential formula is given below as
[tex]y=ab^x[/tex]The following figure represents the graph of exponents of x. It can be seen that as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, for x > 1, the value of y = fn(x) increases for increasing values of (n).
Are there restrictions on the domain why or why not?
For any exponential function, f(x) = ab^x, the domain is the set of all real numbers. For any exponential function, f(x) = ab^x, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.
Hence,
The domain of exponential functions is equal to all real numbers since we have no restrictions with the values that x can take.
Are exponential and logarithmic function inverse. why or why not?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function y = logx base a is defined to be equivalent to the exponential equation x = a^y
Hence,
Exponential functions and logarithmic functions are inverses of each other
What is the image of (−9,−12) after a dilation by a scale factor of 1/3
centered at the origin?
By dilation with a scale factor of 1 / 3 centered at the origin, the image of the resulting point is (- 3, - 4).
How to determine the location of the image of a point by using a dilation formula
In this problem we find the coordinates of a point set on Cartesian plane, whose image is the result of using a dilation centered at the origin, whose definition is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Scale factorIf we know that O(x, y) = (0, 0), k = 1 / 3 and P(x, y) = (- 9, - 12), then the image of the original point is:
P'(x, y) = (0, 0) + (1 / 3) · [(- 9, - 12) - (0, 0)]
P'(x, y) = (- 3, - 4)
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Given the system below. What is the x value of the solution? 3x + 5y = 8 y = x + 8
We are given the following system of equations:
3 x + 5 y = 8
y = x + 8
So we can use the "substitution method" to solve it, since the second equation is already giving us a possible substitution to make:
Replace y with x + 8 in the other equation.
We proceed as shown below:
3 x + 5 y = 8
3 x + 5 (x + 8) = 8
Use distributivr property to remove the parenthesis:
3 x + 5 x + 40 = 8
8 x + 40 = 8
subtract 40 from both sides to isolate the term in "x"
8 x = 8 - 40
8 x = - 32
divide both sides by 8 to isolate "x"
x = - 32 / 8
x = - 4
We found the requested x value
We are also asked to find y , so we use the value for x in the substitution equation:
y = x + 8
y = -4 + 8 = 4
Then y = 4
The pair that satisfies this system is x = -4 and y = 4 or in pair form: (-4, 4)
Evaluate the expression xy - 3x when x = 4 and y = 5
Answer:
xy - 3x = 8
when x = 4 and y = 5
Explanation:
Given the expression
xy - 3x
When x = 4 and y = 5, the equation becomes
(4)(5) - 3(4)
= 20 - 12
= 8
A math teacher said that 18 out of 25 students passed the test. What percent of the students did NOT pass the test?can you please show me the work for this?
Given:
A math teacher said that 18 out of 25 students passed the test.
So,
Total number of students = 25 student
Number of students who passed the test = 18
Number of students who did not pass the test = 25 - 18 = 7
So, the percent of the students who did NOT pass the test =
[tex]\frac{7}{25}\times100=28\%[/tex]So, the answer will be 28%
)) Rick has decided to examine his checking account statements. The account balance was $2,010 last month, and 50% less this month. What is the account balance this month?
The account balance this month is $4020
Let the account balance this month = x
From the question, we have
The account balance was $2,010 last month.
∴x* 50%= $2,010
⇒x* 50/100= $2,010
⇒x* 1/2= $2,010
⇒x = $4020
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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a. A random sample of 43 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.58 per car. The population standard deviation is $6.22. Estimate the mean bill for all cars from the drive-thru with 97% confidence. Round intermediate and final answers to two decimal places.
Given
[tex]\begin{gathered} n=43 \\ Mean\text{ = \$18.58} \\ \sigma=\text{ \$6.22} \end{gathered}[/tex]Solution
Formula
[tex]\text{Confident interval =M }\pm\frac{Z\sigma}{\sqrt[]{n}}[/tex]where
[tex]\begin{gathered} M=\text{ mean or Average} \\ Z-score=Z_{97}=2.17 \\ n=43 \end{gathered}[/tex]Substitute the parameters into the Confident Interval formula
[tex]\text{Confident interval =18.58}\pm\frac{2.17\times6.22}{\sqrt[]{43}}[/tex]Then we calculate the Addition and subtraction
First the Addition
[tex]\begin{gathered} \text{Confident interval =18.58+}\frac{2.17\times6.22}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58+}\frac{13.4974}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58+}\frac{13.4974}{6.5574} \\ \text{Confident interval =18.58+}2.05833 \\ \text{Confident interval =}20.63833342 \\ \\ \text{Confident interval =}20.64\text{ two decimal places} \end{gathered}[/tex]Then now for subtraction
[tex]\begin{gathered} \text{Confident interval =18.58-}\frac{2.17\times6.22}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58-}\frac{13.4974}{\sqrt[]{43}} \\ \\ \text{Confident interval =18.58-}\frac{13.4974}{6.5574} \\ \text{Confident interval =18.58-}2.05833 \\ \text{Confident interval =}16.5216658 \\ \\ \text{Confident interval =16.52 two decimal places} \end{gathered}[/tex]The final answer
[tex](16.52,\text{ 20.64)}[/tex]what is the value of the square root of -25+10
Celeste, this is the solution to the exercise:
Let's recall that √-1 = i, therefore:
The first term of the sum is √-25 = √25 * -1 = 5i
The second term remains the same. + 10
Thus, the correct answer is D. 5i + 10
Is A= {9000, 5, 8, 119} a finite set?
ANSWER
Yes, it is.
EXPLANATION
A finite set is a set that contains a finite number of elements. That is, the number of elements in a finite set are countable.
The set given is:
A = {9000, 5, 8, 119}
There are 4 elements in this set and hence, it is countable.
According to the definition of a finite set, this set is a finite set.
if x-1/x = 20, then x =
Given
[tex]\frac{x-1}{x}=20[/tex]Solution
[tex]\begin{gathered} \frac{x-1}{x}=\frac{20}{1} \\ \text{cross multiply} \\ 1(x-1)=20(x)_{} \\ we\text{ have} \\ x-1=20x \\ \text{collect the like terms} \\ -1=20x-x \\ -1=19x \\ \text{rewrite} \\ 19x=-1 \\ \text{Divide both sides by 19} \\ \frac{19x}{19}=-\frac{1}{19} \\ \\ x=-\frac{1}{19} \end{gathered}[/tex]The final answer
[tex]x=-\frac{1}{19}[/tex]Solve the inequality -2d < 5
Answer:
d> -5/2
Step-by-step explanation:
-2d<5
divide both sides by -2
d>-5/2
Answer:
d > - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
- 2d < 5
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
d > [tex]\frac{5}{2}[/tex] or d > 2.5
Which x value is in the domain of the function f(x)=2cot(3x)+4?A. pi/4B. pi/3C. piD. 2pi
Solution:
Given:
[tex]f(x)=2cot(3x)+4[/tex]The domain of the function is;
[tex]\frac{\pi }{3}nHence, the x-value that is in the domain of the function is;[tex]\begin{gathered} any\text{ value that is not a multiple of }\frac{\pi}{3} \\ \\ Hence,\text{ } \\ \frac{\pi}{3},\pi,2\pi\text{ will be multiples of 3x and will make the function undefined.} \\ \\ Therefore,\text{ the x-value in the domain is }\frac{\pi}{4}\text{ because putting x = }\frac{\pi}{4}\text{ makes the function defined} \end{gathered}[/tex]Therefore, OPTION A is correct.
I need help with the third question where it says segment addition
ANSWER
EXPLANATION
We have that the line EG = 71.
We are given that
EF = 8x - 17
and
FG = 5x - 3
We see from the diagram that:
EF + FG
what is the equation in point slope form of the line that passes through the point (5, 0) and has a slope of 1.2?
To see the equation we know that the general equation of a line is:
[tex]y=mx+b[/tex]Where m is the slope. So you know that the slope is 1.2, then you have an equation like this:
[tex]y=1.2x+b[/tex]Since b is just a number we can say that this is also equal to:
[tex]y=1.2(x+c)[/tex]We'll write it this way so it's similar to the options.
Then you know that the line pases through point (5,0). To find the value of constant c we replace the value of x and y from this point (x = 5 and y=0):
[tex]0=1.2(5+c)[/tex]And clear c from this expression
[tex]0=5+c\Rightarrow c=-5[/tex]So the answer is:
[tex]y-0=1.2(x-5)[/tex]The price to mail a letter at the post office is $0.51 for the first ounce, and $0.20 for each additional ounce. Stephanie paid $1.31 to mail her letter. How much did the letter weigh?A. 7 ounces B.6 ouncesC.4 ounces D.5 ounces
The cost of sending mail is given as $0.51 for the first ounce and then every ounce after that costs $0.20.
For each letter, the cost would be expressed as;
[tex]\begin{gathered} C=0.51+0.20x \\ \text{Where x is the weight in ounces} \\ \text{For Stephanie's letter,} \\ 1.31=0.51+0.20x \\ \text{Subtract 0.51 from both sides} \\ 1.31-0.51=0.51-0.51+0.20x \\ 0.8=0.20x \\ \text{Divide both sides by 0.20} \\ \frac{0.8}{0.2}=x \\ 4=x \\ \text{Note that she paid \$0.51 for the first ounce} \\ \text{This means she paid for 1 ounce plus another 4 ounces} \\ \text{Stephanie's letter weighs 5 ounces} \end{gathered}[/tex]Therefore, Stephanie's letter weighs 5 ounces.
The correct answer is option D
Which equation represents a line which is perpendicular to the line y =- +522x - 5y = -302x + 5y = 152y-53 = 10O 5x + 2y 12
Answer:
The equation that represents the perpendicular line is;
[tex]2y-5x=-10[/tex]Explanation:
We want to find the equation of a line perpendicular to the line;
[tex]y=-\frac{2}{5}x+5[/tex]Recall that for two lines to be perpendicular to each other, their slope must be a negative reciprocal of one another.
[tex]m_1.m_2=-1_{}_{}[/tex]so;
[tex]m_2=-\frac{1}{m_1}[/tex]For the given equation, the slope of the given line is;
[tex]m_1=-\frac{2}{5}[/tex]To get the slope of the perpendicular line, let us substitute m1 to the equation above;
[tex]\begin{gathered} m_2=-\frac{1}{m_1} \\ m_2=-\frac{1}{(-\frac{2}{5})_{}} \\ m_2=\frac{5}{2_{}} \end{gathered}[/tex]So, the equation of the perpendicular line would be of the form;
[tex]\begin{gathered} y=m_2x+c \\ y=\frac{5}{2}x+c \\ mu\text{ltiply through by 2} \\ 2y=5x+c \\ 2y-5x=c \end{gathered}[/tex]The equation of the perpendicular line will be of the form;
[tex]2y-5x=c[/tex]Where c is a constant;
From the options, the only equation that is similar to the derived equation is;
[tex]2y-5x=-10[/tex]Therefore, the equation of the perpendicular line is;
[tex]2y-5x=-10[/tex]A teacher bought 28 books for her class. She spent a total of $112.00. What is the price, p, for each book? Let p = price for each book
What are 2 numbers that are exactly the same are said to be?
When two numbers are exactly the same, we say that they're equal. Is denoted by the sign '='
If reciangle ABCD is in quadrant II, and rotated 270 degrees counterciockwise around the origin, then what quadrant will rectangle A'B'C'D' be in ? Quadrant l Quadrant II Quadrant lll Quadrant IV
Quadrant IV.
1) Let's Draw this to give us a better idea.
In a 270º CCW Rotation, the rule is every coordinate to be translated
(x.y) ---(y,-x)
2) Let's give to our quadrilateral
A(-2,3) ---- A'(3,2)
B(-4, 3) -----B'(3,4)
C(-6, 4) -----C' (4,6)
D( -8, 4) ---- D' (4, 8)
And so forth
So Quadrant IV is the answer.
The equation of the line is y=_. The slope indicates that the temperature decreases by 3.5 F for each 1000 foot increase in altitude
The slope of the function is m = -3.5, which indicates that the temperature decreases by 3.5 degrees for each 1000 feet increase in elevation.
The temperature at Sea level is 87 °F
What is the slope of a function?The slope of a straight line function is the ratio of the rise to the run of the function.
Parts of the question that appear missing includes; The slope and the temperature at Sea level is required.
A point on the table of the graph is that at 4 feet, the temperature is 73 °F
The rate at which the the temperature changes = -3.5 °F per 1,000 feet
The slope of the equation is therefore;
y - 73 = -3.5·(x - 4)
y = -3.5·x + 14 + 73 = -3.5·x + 87
y = -3.5·x + 87
The equation of the the line of the temperature above Sea level is an equation of a straight line, which is of the form; y = m·x + c
Where;
m = The slope of the function
By comparison, the slope of the equation of the line the function is; m = -3.5
The temperature at Sea level, which is the y-intercept is found at the point where x = 0, which gives;
y = -3.5 × 0 + 87 = 87
The temperature at Sea level is 87 °F
The slope of line of the graph of the function, m = -3.5
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Work out the lenght off x
Using the Pythagorean theorem, the length of the side x is √147.
What is the Pythagorean theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.So, the formula of the Pythagorean theorem:
H² = l² + w², where H is the hypotenuse.Now, substitute the values and calculate as follows:
14² = 7² + x²x² = 14² - 7²x² = 196 - 49x² = 147x = √147Therefore, using the Pythagorean theorem, the length of the side x is √147.
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What steps should be followed to solve the following equation for x: -3x - 8 1 point= 4*Add 8 to both sides, then divide by 3Divide by -3, then add 8 to both sidesAdd 8 to both sides, then divide by -3Add 8 to both sides, then add 3 to both sides
1) Evaluating
-3x -8= 4 Adding 8 to both sides
-3x -8 +8=4+8
-3x = 12 Dividing both sides by 3
x=-4
2) Examining the options then
C Add 8 to both sides then divide both sides by 3
a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion
If two fractions are in proportion, their inverse ratio are also in proportion.
Proportion:
Proportion means an equation in which two ratios are set equal to each other.
Given,
a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion.
Here we need to fill the blank with the correct answer.
According to Invertendo Property,
For the four numbers a, b, c, d,
Consider if a : b = c : d, then b : a = d : c; which means
if two ratios are equal, then their inverse ratios are also equal.
It can be written as,
If a : b :: c : d then b : a :: d : c.
Then it can be written as,
=> a : b :: c : d
⟹ a/b= c/d
When take the inverse, then we get,
⟹ b/a= d/c
Which implies the following,
⟹ b : a :: d : c
Therefore, the answer is inverse ratio.
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Evaluate the left hand side to find the value of aa in the equation in simplest form. 4
Given
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}[/tex]Solution
Apply exponent rule
[tex]\begin{gathered} x^{\frac{1}{2}-\frac{1}{6}}=x^{\frac{3-1}{6}} \\ \\ \\ x^{\frac{2}{6}}=x^{\frac{1}{3}} \end{gathered}[/tex][tex]a=\frac{1}{3}[/tex]We have
[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{6}}}=x^{\frac{1}{3}}[/tex]Writing an equation in slope intercept form for the line passing through each pair of point . (0, 3) and ( 1, -2)
Data:
• Point ,A( 0, 3 )
,• Point ,B( 1, -2 )
,• Equation in slope-intercept form:
[tex]y=mx+b[/tex]Procedure:
0. Finding the slope ( ,m ,):
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-3}{1-0}=\frac{-5}{1}[/tex][tex]m=-5[/tex]2. Finding the intersection with y-axis ( b ) using point A:
[tex]\begin{gathered} y=mx+b \\ 3=(-5)\cdot0+b \\ b=3 \end{gathered}[/tex]Answer:
[tex]y=-5x+3[/tex]Summary:
0. We found the slope of the equation ( ,m ,)
,1. We found the intersection with the ,y-axis ,( ,b ,)
,2. We displayed the values in the correct position of the equation.
What is the slope and y intercept of the line whose equation is y = -4x + 2?b =m=
To find the slope and the intercept of the line
y = -4x + 2
y = mx + b
so in this case the m = -4, because is the coefficient on x rigth over there
and b is going to be the constant term
b = 2