If two numbers have the same base ( the number below the exponent) then the multiplication of the two of them is the number with the same base but with the sum of its exponents (rule of exponents)
[tex]x^{-11}\cdot x^7=x^{-11+7}=x^{-4}[/tex]On the other hand, if a number is to the power a negative number, it means that it is the reciprocal elevated to the number, in this case
[tex]x^{-4}=(\frac{1}{x})^4[/tex]Number of Hours13.5Total Cost$2.00$6.50$7.00$9.00$12.507.59Identify the domain and range. Select the two correct answers.АDomain: {1, 2.00}BDomain: (1.3.5, 5, 7.5,9)CDomain: 2. 6.50, 7.9. 12.50)DRange: 19. 12.50)ERange: (1,3,5,5, 7.5.9}F.Range: (2,6 50, 7, 9, 12.50)
Domain is the set of x values, or the inputs.
Range is the set of y values, or the outputs.
They are unique.
Looking at the table,
the number of hours is the input on which we have the cost, the output.
So,
We get domain from number of hours
We get range from total cost
1, 3.5, 5, 7.5, and 9 ---- hours (domain)
B is right.
Now,
Range would be the total costs, which are:
2, 6.5, 7, 9, 12.5
F is right.
Correct answers are B and F
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
step 1
Find z score
z=(92-80)/15
z=0.8
step 2
using the z-score table
For z=0.8
P=0.7881
therefore
answer is
P=0.7881Convert 57•F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas.C=5/9 (F-32)F= 9/5 C+32
ANSWER
[tex]13.9°C[/tex]EXPLANATION
We want to convert 57°F to degrees Celsius.
To do this, apply the formula:
[tex]C=\frac{5}{9}(F-32)[/tex]where F = temperature in Fahrenheit
Therefore, 57°F to degrees Celsius is:
[tex]\begin{gathered} C=\frac{5}{9}(57-32) \\ \\ C=\frac{5}{9}*25 \\ \\ C=13.9°C \end{gathered}[/tex]That is the answer.
(linear approximation calc !) The radius of a disc is 24 cm if the radius has a maximum error of 0.2 cm. estimate the relative percentage air in the calculated area the area of a circle = pi r ^2
Given:
The radius of the circular disk is 24cm.
The radius has a maximum error of 0.2 cm.
To find:
The area
Explanation:
Using the area of the circle,
[tex]A=\pi r^2[/tex]The area of the disk is,
[tex]\begin{gathered} A=\pi\times24^2 \\ =576\pi cm^2 \end{gathered}[/tex]If the radius is increased from 24 by 0.02, then the radius becomes, r = 0.02
The change in the calculated area will be,
[tex]\begin{gathered} \Delta A=Area\text{ of the cirlce with radius of 24.02-Area of the circle with radius of 24} \\ =\pi\times24.02^2-\pi\times24^2 \\ =576.96\pi-576\pi \\ =0.96\pi cm^2 \end{gathered}[/tex]The relative percentage of area is,
[tex]\begin{gathered} \frac{\Delta A}{A}\times100=\frac{0.96\pi}{576\pi}\times100 \\ =0.0017\times100 \\ =0.17\text{ \%} \end{gathered}[/tex]Final answer:
The maximum error in area is,
[tex]0.96\pi cm^2[/tex]The relative percentage error in the area is 0.17%.
I do not understand the problem on how to to write an equation.
Given a line passes through the point (-4,6) and has a slope of 3
We will write the equation of the line in point-slope from
The formula of the point-slope form will be as follows:
[tex]y-k=m(x-h)[/tex]Where (h, k) is the point that lies on the line and (m) is the slope
From the given:
m = 3
h = -4
k = 6
Substitute into the formula
so, the answer will be:
[tex]y-6=3(x+4)[/tex]Hi, simplify the following rational expression, if possible: x + 2/ x^2 = 4x + 4
Given:
[tex]\frac{x+2}{x^2-4x+4}[/tex]To simplify the given rational expression, we first factor x^2-4x+4 by applying Perfect Square Formula as shown below:
[tex]\begin{gathered} a^2-2ab+b^2=(a-b)^2 \\ \end{gathered}[/tex]Hence,
[tex]x^2-4x+4=x^2-2x(2)+2^2=(x-2)^2[/tex]Now, we simplify the given expression:
[tex]\frac{x+2}{x^{2}-4x+4}=\frac{x+2}{(x-2)^2}[/tex]Therefore, the answer is:
[tex]\frac{x+2}{(x-2)^{2}}[/tex]what expression is equivalent to 2y+7
The expression which is equivalent to the given expression (3y - 4) (2y + 7) + 11y - 9 is 6 y²+ 24y- 37
Define an expression.A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.
A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.
Presented expression = (3y - 4) (2y + 7) + 11y - 9
Solving the expression we get= 6y²+21y-8y-28+11y-9
= 6y²+24y-37
There for the correct response is that the given expression is equivalent to = 6y²+24y-37
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use the functions f (×) and g (×) to complete the comparison statements using <,>,or =.F(x)= -×-5
First Question:
f(3) = (-3)-5 (Replacing x in the equation)
f(3) = -8 (Operating integers)
From the table we see that g(3) = 8, therefore, f(3)< g(3)
Second Question:
The slope of f is the coefficient of x in the equation, so, the slope of f is -1.
Using the slope formula for g(x) with points (0,2) and (3,8) we find that:
[tex]m=\frac{y2-y1}{x2-x1}=\frac{8-2}{3-0}=\frac{6}{3}=2[/tex]The slope of g is 2.
Therefore, the slope of f is less (<) than the slope of g
Third Question:
The y-intercept of f is the value next to the term -x, so, it is equal to -5
The y-intercept of g can be found with the point (0,2), when x=0, y is equal to 2, then the y-intercept is 2.
Therefore, the y-intercept of f is less(<) than the y-intercept of g.
Please help me quickly I don’t need the explanation I just need the answer I’m sorry I just need a fast
Notice that the area is equivalent to the area of the complete rectangle minus the area of the 3km x 4km rectangle.
[tex]A=TA-AS\text{.}[/tex]Now, the area of a rectangle is given by the following formula:
[tex]A=\text{width}\cdot\text{lenght.}[/tex]Therefore:
[tex]A=9km\cdot16km-3km\cdot4km\text{.}[/tex]Simplifying the above result, we get:
[tex]A=(144-12)km^2=132km^2.[/tex]Answer:
[tex]132km^2.[/tex]Solve this problem, please and thank you. Picture included. Algebra 2.
How much interest is earned on an initial investment of $700 with a 5% annual rate for 2 years? A $700B $350C $70D $35
Let's calculate the 5% of $700 using a rule of three:
This way,
[tex]\begin{gathered} x=\frac{700\cdot5}{100} \\ \Rightarrow x=35 \end{gathered}[/tex]$35 is earned each year, For two years, the earnings would be $70
Answer: C. $70
I need help just a understanding. And show how to get the answer.
An angle is formed when two lines meet. The angle is named with the lines that forms it. Looking at the diagram, the angle 2 is formed at B by lines CB and DB. The correct name for angle 2 is angle CBD
The last option is correct
solve for C -3 (C + 5)- (c-3)=32
Given the equation:
[tex]-3(c+5)-(c-3)=32[/tex]To find the value of 'c', the first step to do is to get rid of the parenthesis. We can do this using the distributive property on both cases:
[tex]\begin{gathered} -3(c+5)-(c-3)=32 \\ \Rightarrow-3\cdot c+(-3)\cdot5-c-(-3)=32 \\ \Rightarrow-3c-15-c+3=32 \end{gathered}[/tex]Now that we don't have any parenthesis in our equation, we start moving similar terms: we leave on the left the terms with the variable 'c' and we move the rest of the terms to the right side with it's sign changed:
[tex]\begin{gathered} -3c-15-c+3=32 \\ \Rightarrow-3c-c=32+15-3 \end{gathered}[/tex]We can make the operations on each side since now we have the similar terms apart:
[tex]\begin{gathered} -3c-c=32+15-3 \\ \Rightarrow-4c=47-3=44 \\ -4c=44 \end{gathered}[/tex]Finally, we move the -4 that is multiplying the 'c' to the other side doing its opposite operation:
[tex]\begin{gathered} -4c=44 \\ \Rightarrow c=\frac{44}{-4}=-11 \\ c=-11 \end{gathered}[/tex]therefore, c=-11
An open box is made from a 30cm by 40cm piece of tin by cutting
s represents the square
[tex]\begin{gathered} s_{1,\: 2}=\frac{-\left(-35\right)\pm\sqrt{\left(-35\right)^2-4\cdot\:1\cdot\:34}}{2\cdot\:1} \\ s_{1,\: 2}=\frac{-\left(-35\right)\pm\:33}{2\cdot\:1} \\ s_1=\frac{-\left(-35\right)+33}{2\cdot\:1}=\frac{35+33}{2}=\frac{68}{2}=34 \\ s_2=\frac{-\left(-35\right)-33}{2\cdot\:1}=\frac{35-33}{2}=\frac{2}{2}=1 \end{gathered}[/tex]The length of the sides of the square is 1 cm
Persuade Mr. Zion whether the numbers 12,16,and 20 make a right triangle or not. Make sure to state reasons for and against your belief
we can corrobarate this using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where:} \\ c>a,c>b \end{gathered}[/tex]Let:
[tex]\begin{gathered} a=12 \\ b=16 \\ c=20 \\ 20^2=12^2+16^2? \\ 400=144+256 \\ 400=400 \\ \end{gathered}[/tex]since the equality is satisfied, we can conclude that it is possible to make a right triangle using those numbers
indicate whether (2, 7) is a solution of the given system.y is greater than or = -x+1Y is less than 4x+2
In order to determine if the point (2, 7) is a solution to the given system of inequalities we just have to replace 7 for y and 2 for x and see if the two inequalities are met, like this:
For y ≥ -x + 17 ≥ -2 + 1
7 ≥ -1
As you can see, 7 is greater than -1 then the first inequality is met.
For y < 4x + 27 < 4(2) + 2
7 < 8 + 2
7 < 10
As you can see, the second inequality is also met, then (2, 7) is a solution for the system of inequalities.
Eric needs to manufacture a turntable with a circumference of `140pi` centimeters. If the allowed error tolerance in the circumference is `+-5` centimeters, how close to the ideal radius must he control the radius of the turntable?
A. `10/pi`
B. `2/pi`
C. 5/(2pi)`
D. `5/(4pi)`
Answer: is C. `5/(2pi)`
The correct option is C 5/(2π) . The ideal radius must he control the radius of the turntable will be 5/(2π) .
What is meant by circumference?circle's circumference 22 inches around make up the circle. Periphery from the center to the sphere's circumference: 2: an object or figure's external boundary or surface The circumference, which in geometry refers to a circle or ellipse's perimeter, is derived from the Latin circumferens, which means "carrying around." In other words, the circumference would be the length of the circle's arc if it were opened out and straightened out to a line segment. Any great circle's circumference, or the distance between any two planes that cross a sphere's center, is measured in meters. Any large circle that traverses a pole-designated point is known as a meridian. The shortest path between any two locations on a sphere is referred to as a geodesic.
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Find the probability of the event.If a single die is tossed once, find the probability of the following event. Rollinga 3 or a 5
ANSWER
1/3
EXPLANATION
If we have a fair die, the probability of rolling any of the numbers is the same. In this case, we want to know the probability of rolling a 3 or a 5, which is the sum of the probabilities of rolling each of these values,
[tex]P(3)=P(5)=\frac{1}{6}[/tex]So,
[tex]P(3or5)=P(3)+P(5)=\frac{1}{6}+\frac{1}{6}=\frac{2}{6}=\frac{1}{3}[/tex]Hence, the probability of rolling a 3 or a 5 is 1/3
I need to know which point is the solution and I need a check for it to make sure it’s correct and the line on the graph
The system of equations are given as
[tex]\begin{gathered} y-2x=-4 \\ y=-x-1 \end{gathered}[/tex]The graph of the system of equations is
The point which is the solution is
[tex](1,-2)[/tex]can you please help me with the work sheet and get all the answers and thank you
ANSWER
[tex](x+2)(x-4)[/tex]EXPLANATION
7) Given;
[tex]f(x)=x^2-2x-8[/tex]Using factors of 2 and -4;
[tex]\begin{gathered} \lparen x^2+2x-4x-8) \\ \left(x^2+2x\right)+\left(-4x-8\right) \\ \end{gathered}[/tex]Factorise;
[tex]\begin{gathered} x\left(x+2\right)-4\left(x+2\right) \\ \end{gathered}[/tex]Factor out the common term;
[tex]\begin{gathered} x(x+2)-4(x+2) \\ (x+2)(x-4) \end{gathered}[/tex]The graphical solution is attached.
Dilate the figure by the scale factor. Then enterthe new coordinates.A(-1,1)B(4,0)K=5A'( [?],[])B'( 1 )C'([ ],[]).C(1,-3)EnterAnswer
A dilation is a proportional stretch or shrink of an image based on a scale factor. It is represented by:
[tex](x,y)\rightarrow(K\cdot x,\text{ K}\cdot y)[/tex]Then, for the figure on the question tab and scale factor of 5:
[tex]A(-1,1)\rightarrow A^{\prime}(-1\cdot5,1\cdot5)=A^{\prime}(-5,\text{ 5)}[/tex][tex]B(4,0)\rightarrow B^{\prime}(4\cdot5,0\cdot5)=B^{\prime}(20,0)[/tex][tex]C(1,-3)\rightarrow C^{\prime}(1\cdot5,-3\cdot5)=C^{\prime}(5,-15)[/tex]Which expression represents the distance between point (0, a) and point (a,0) on a coordinate grid?
2a
Ο Ο Ο Ο
2a
O
Answer:
Explanation:
To determine the distance between two points on a coordinate grid, use the formula below:
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Use the Distributive Property
solve the equation.
- 6(x + 3) = 30
Answer: X = -2
Step-by-step explanation:
-6 time x is -6x and -6 times 3 is -18
Now you have -6x + -18 = 30
Add the now add 18 to both the -18 and 30 now your left with -6x = 12
And at last divide both -6 and 12 to -6
And you have X = -2
Answer: -8
Step-by-step explanation:
-6(x + 3) =30
-Distribute -6 and x = -6x
-Distribute -6 and 3 = -18
-6x -18 = 30
+18 +18. Take away 18 on both sides of the equation
_________
-6 / -6x = 48/-6 Divide -6 on both sides to get x by itself
X = -8
Final Answer : -8
Simplify: 7a + 2a - a + 6b - 5b
We must simplify the following expression:
[tex]7a+2a-a+6b-5b[/tex]From the expression, we see that we have terms with variable a and terms with variable b. In order to simplify the expression, we add the terms with a together (which sums up 8a), and we do the same for the terms with b (which sums up 1b):
[tex]\begin{gathered} 7a+2a-a+6b-5b \\ =(7a+2a-a)+(6b-5b) \\ =8a+b \end{gathered}[/tex]The solution is: 8a+b
Factor 64x3 + 27.(4x – 3)(16x2 – 12x + 9)(4x + 3)(16x2 - 12x + 9)(4x + 3)(16x2 + 12x + 9)(4x - 3)(16x2 + 12x + 9)
Answer
Option B is correct.
64x³ + 27 = (4x + 3) (16x² - 12x + 9)
Explanation
We are told to factorize
64x³ + 27
To do this, we use the factorization of (x³ + y³) as a guide. First of,
(x + y)³ = (x + y) (x + y)² = (x + y) (x² + 2xy + y²)
(x + y)³ = x³ + y³ + 3x²y + 3xy²
So, we can write
x³ + y³ = (x + y)³ - 3x²y - 3xy² = (x + y)³ - 3xy(x + y)
= (x + y) [(x + y)² - 3xy]
= (x + y) (x² + y² + 2xy - 3xy)
= (x + y) (x² - xy + y²)
So, comparing (64x³ + 27) with (x³ + y³), we can see that
64x³ = (4x)³
27 = (3)³
(64x³ + 27) = (4x)³ + 3³
x³ + y³ = (x + y) (x² - xy + y²)
(4x)³ + 3³ = (4x + 3) [(4x)² - (4x × 3) + 3²]
= (4x + 3) (16x² - 12x + 9)
Hope this Helps!!!
Measure the dimensions of all the walls of the bedroom in your home, in feet. Find the dimensions of any windows or doorways as well.
Explanation
we can fill up the dimensions as follow
Evaluate 10y-15 for y=5
10 y - 15
y = 5
We replace 5 in the expression
10 * 5 - 15 =
50 - 15 = 35
____________________
Answer
35
Fibonacci, Pythagoras and Descartes went out for breakfast. The total bill was $38.50. The tax rate was 7% and they left a 20% tip. Determine the total bill. Round to the nearest hundredth.so how much will each person pay if the bill was equally divided?
Given:
• Total bill = $38.50
,• Tax rate = 7% = 0.07
,• Tip = 20% = 0.20
Let's find the total bill after tax and tip.
Now, to find the total bill we have:
Total bill = bill + tax amount + tip amount
Where:
[tex]\begin{gathered} \text{ tax amount = 0.07}\times38.50=2.695 \\ \\ Tip\text{ amount = 0.20 }\times38.50=7.7 \end{gathered}[/tex]The tax amount is $2.695
The tip amount is $7.70
Now, to find the total bill, we have:
Total bill = $38.50 + $2.695 + $7.7 = $48.895 ≈ $48.90
Therefore, the total bill rounded to the nearest hundredth is $48.90
Part B.
To find the amount each person will pay if the bill was equally divided, let's divide the total bill by the number of people.
Where:
Number of people = 3
Hence, we have:
[tex]\frac{48.90}{3}=\text{ 16.30}[/tex]Therefore, the amount each person will pay is $16.30
ANSWER:
(a). $48.90
(b). $16.30
A card is chosen at random from a deck of 28 cards. The deck contains red, 12 black 7 blue, and 2 green cards. Thend the card is returned to the deck and New card is cosen. the table below shows the results of choosing 14 cards. for which color of card is the experimental probability the same as the theoretical probabicaras.Results red= 10 black=2 blue=1green=1
From the question, we can find that we have 7 red cards
so, the probability of chosen at random a card is
p(red)= 7/28
p(black)= 12/28
p(blue) = 7/28
p(green)=2/28
As after picking a card we return the card to the deck, and given that we chose 14 cards, our theoretical number of chosen cards should be around
p(red) = (7/28)x14 = 3.5
p(black) = (12/28)x14 = 6
p(blue) = (7/28)x14 = 3.5
p(green)= (2/28)x14=1
so the color that the experimental probability is the same as the theoretical probability is green
This is non graded algebra 1 I need help on question 10
An exponential decay function can be generically written as:
[tex]y=a\cdot b^x[/tex]The conditions for this function are:
1) The y-intercept is 4.
2) The values of y decrease by a factor of one half as x increases by 1.
The y-intercept corresponds to the value of y when x = 0, so we can express it as:
[tex]\begin{gathered} y=a\cdot b^x \\ 4=a\cdot b^0 \\ 4=a\cdot1 \\ a=4 \end{gathered}[/tex]This condition let us find the value of a.
The next condition will be used to find the value of b.
As x increases by 1, y decreases by one half.
We can write this as a quotient between consecutive values of y:
[tex]\begin{gathered} \frac{y(x+1)}{y(x)}=\frac{1}{2} \\ \frac{4\cdot b^{x+1}}{4\cdot b^x}=\frac{1}{2} \\ b^{x+1-x}=\frac{1}{2} \\ b^1=\frac{1}{2} \\ b=\frac{1}{2} \end{gathered}[/tex]Then, we can write the function as:
[tex]y=4\cdot(\frac{1}{2})^x[/tex]Answer: y = 4*(1/2)^x