SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]4^2\ast4^3[/tex]STEP 2: Simplify the expression using the law of indices
[tex]\begin{gathered} \mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c} \\ 4^2\cdot \:4^3=4^{2+3} \\ =4^{\left\{2+3\right\}} \\ =4^5=1024 \end{gathered}[/tex]Hence, the evaluation gives:
[tex]1024[/tex]f(x) = 2x - 1 g(x) = 3x h(x) = x^2 + 1Find f(g(x))
Given the following functions:
f(x) = 2x - 1
g(x) = 3x
h(x) = x2 + 1
f(g(x)) means that we will be substituting the function of g(x) as x of the f(x) function.
We get,
[tex]f\mleft(g\mleft(x\mright)\mright)\text{ }\rightarrow\text{ f(x) = 2x - 1 }\rightarrow\text{ }f(g(x))=\text{ 2(3x) - 1}[/tex][tex]f(g(x))=\text{ 6x - 1}[/tex]1. (01.01 )At a local restaurant, Enrique is paid $4.55 per hour and earns an average of $19 tips on all food sales. Identify the algebraic expression that could be used to represent Enrique's gross pey (4 points)O 455() +1.90455() +0.19004550) - 1.900O 455-0.1960
Data
• $4.55 per hour
,• Earns an average of 19 tips (assuming that the tips are in dollars).
Procedure
To identify the algebraic expression, we have to identify the variable earn (the quantity that depends on something) and the fixed (the one that is mostly constant).
Based on the information given, we can assume that the variable quantity is $4.55, as it depends on the time, and the fixed is $19. Thus, the algebraic expression can be written as follows:
[tex]E=4.55t+19[/tex]where E represents the earnings and t represents the time.
Answer:
[tex]E=4.55t+19[/tex]how do we know that 1+1=2?
Method 1
By observation
1 cat and another 1 cat makes 2 cats
Method 1
1 boo
using demos find the line of best fit to compare fat (x) and the calories(y) from the table pictured. round to the nearest hundredth (2 decimal places if needed
Find line of aproximation to data
the regression data line gives as result
y = ax + b
a= 11.73
b= 193.85
11> _ <49 how do I solve this?
The question is asking for a number less or equal than 11 and less or equal to 49, then by the options we have, the number would be:
[tex]11\ge8\leq49[/tex]For the following figure, complete the statement for the specified points.RPoints R, S, and Tareneither collinear nor coplanarboth collinear and coplanarcollinearcoplanar
First we need to define what collinear and coplaner means.
It is said that 3 or more points are collinear if they all lie on the same line.
From the diagram, point R, S, T do not lie on the same line.
Hence point R, S and T are not collinear
For a point or line to be coplaner, it must line in the same plane
Also looking at the diagram, points R, S, T do not lie in the same plane.
Hence
10x 10 0 y Match the function with the graph 1 b
To answer this kind of questions, we need to take attention to the original function. In this case, the function is y = 1/x.
We can see from the graph that this function if we multiply this function by -1, the function takes the form of the graph. But we need to add to this function two units in the y-axis direction to obtain the function represented in the graph.
Therefore, the function that matches the one in the graph is y = -1/x +2 (option a).
I need help with a math question i linked the picture below with the questions the question is also a multiple question but i have to answer one question first to get to the next question
The coefficient is the number in front of a variable
EX: 9x, 3y, -4z
9, 3, and -4 are coefficients
Constant is the numerical term
EX: 3x + 2
3 is a coefficient of x and 2 is the constant
The given expression is
[tex]m+9+6n[/tex]We have 2 variables m and n, and 1 numerical term 9, then
The coefficients are the numbers of m and n
Since the number of m is 1 and the number of n is 6, then
The coefficients are 1 and 6
The constant is the numerical term, then
The constant is 9
The error that Sara made is she did not mention the coefficient of m
3/4 + 7/10Write your answer as a fraction in simplest form.
action
Given
[tex]\frac{3}{4}+\frac{7}{10}[/tex]Solution
First, find the LCM which is 20 and write as common denominator
[tex]\frac{15}{20}+\frac{14}{20}[/tex]Add the fraction
[tex]\frac{15}{20}+\frac{14}{20}=\frac{29}{20}[/tex]Now to the simplest form
[tex]\frac{29}{20}=1\frac{9}{20}[/tex]The final answer
[tex]1\frac{9}{20}[/tex]x^2 +2= 0I need help with solving this quadratic equation.
The given quadratic equation is:
[tex]x^2+2=0[/tex]Subtract 2 from both sides
[tex]\begin{gathered} x^2+2-2=0-2 \\ x^2=\text{ -2} \end{gathered}[/tex]Find the square root of both sides
[tex]\begin{gathered} \sqrt[]{x^2}=\text{ }\sqrt[]{-2} \\ x=\sqrt[]{-2} \\ x=\pm\sqrt[]{2}\times\sqrt[]{-1} \\ x\text{ =}\pm\text{ }\sqrt[]{2}i \\ x\text{ = }\pm i\sqrt[]{2} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = }-i\sqrt[]{2}\text{ or i}\sqrt[]{2} \\ \end{gathered}[/tex]Using the graph, determine the coordinates of the x-intercepts of the parabola.10984-10-98-7 -6-5-427 8 9103 410-8-10
The x-intercepts are the points where the parabola crosses the x-axis,
Also, the y coordinate is always zero,
By looking at the graph we can see that the parabola crosses the x-axis at x = 4 and x= 6
X-intercepts = (4,0) and (6,0)
Find and simplify the difference quotient for the following function
Therefore:
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{-4x^2-8xh-h^2+7x+7h+4-(-4x^2+7x+4)}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{7h-8xh-h^2}{h} \\ \frac{f(x+h)-f(x)}{h}=\frac{h(7-8x-h)}{h} \\ \frac{f(x+h)-f(x)}{h}=7-8x-h \end{gathered}[/tex]Analyze the diagram below and complete the instructions that follow./Find the value of x.A.4B.5C.6D.9Please select the best answer from the choices providedABCD
ANSWER
EXPLANATION;
Apply Pythagora's rule to find the value of x
[tex]\begin{gathered} \text{ Pythagora's rule} \\ \text{ Hypotenuse}^2\text{ = opposite}^2\text{ + adjacent}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{ Hypotenuse = }\sqrt{117} \\ \text{ Opposite = x} \\ \text{ Adjacent = \lparen x + 3\rparen} \end{gathered}[/tex][tex][/tex]Can you help me answer a, b and c please?
Answer:
Explanation:
x-5=11;x=5Determine if the value of x is a solution to the equation
Given data:
The given expression is x-5=11.
Substitute 5 for x in the above expression.
5-5=11
0=11
As LHS is not equal to RHS so x=5 is not the solution of the given exprression.
Thus, x=5 is not the solution.
This Venn diagram shows sports played by 10 students.PLAYSBASKETBALLMaiPLAYSSOCCERMickeyMarcusFranEllalanKarlJadaGabbyJuanLet event A = The student plays basketball.Let event B = The student plays soccer.What is PAB)?O A.A. «0.17B. 1=0.1010
ANSWER
[tex]P(A|B)=\frac{1}{3}\approx0.333[/tex]EXPLANATION
We want to find the probability P(A|B).
This is a conditional probability and its formula is:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]where P(A n B) is the probability that the student plays basketball and soccer and P(B) is the probability that the student plays soccer.
We have that:
[tex]P(A\cap B)=\frac{1}{10}[/tex]and
[tex]P(B)=\frac{3}{10}[/tex]Therefore, we have that:
[tex]\begin{gathered} P(A|B)=\frac{1}{10}\div\frac{3}{10} \\ P(A|B)=\frac{1}{10}\cdot\frac{10}{3} \\ P(A|B)=\frac{1}{3}\approx0.333 \end{gathered}[/tex]That is the answer.
Venus' orbital speed is approximately 210 kilometers in 6 seconds. Earth's orbital speed is approximately 270 kilometers in 9 seconds. Which planet travels at a faster speed per second?
We know that
• Venus' orbital speed is 210 kilometers in 6 seconds.
,• Earth's orbital speed is 270 kilometers in 9 seconds.
First, we have to divide the numbers to find the ratio
[tex]\begin{gathered} \frac{210}{6}=35 \\ \frac{270}{9}=30 \end{gathered}[/tex]As you can observe, Venus has greater speed because it's 35 kilometers per second.
Hence, the answer is Venus.Is it possible for a standard deviation to be equal to zero ?
Given:
The objective is to explain whether it is possible for a standard deviation to be equal to zero.
Explanation:
A standard deviation can be zero when all the data are equal.
In general the value of standard deviation will decrease while approaching close to the mean value. Similarly, the standard deviation will increase if data points are away from the mean value.
Hence, standard deviation can be zero if all the obtained/provided data contains equal value.
Look at this diagram:If CE and FH are parallel lines and m
If CE and FH are parallel lines and angle EDG is 42 degree, then angle CDB is also 42 degree
If CE and FH are parallel lines and the line BI is the transversal
angle EDG = angle DGF (interior alternate angles)
(when two lines are parallel and is cut by a transversal, the interior alternate angles are equal)
So. angle DGF = 42 degree
angle CDB = angle DGF (corresponding angles)
(when two lines are parallel and is cut by a transversal, the corresponding angles are equal)
angle CDB = 42 degree
Therefore, if CE and FH are parallel lines and angle EDG is 42 degree, then angle CDB is also 42 degree
To learn more about parallel lines refer here
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which property of equality should you apply to keep the equation 22*a= 242in balance when solving?
The property of division is apply to keep the equation 22a = 242 in balance.
What is division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Consider, the given equation
22 a = 242
The property of equality should you apply to keep the equation 22*a= 242in balance means we have to use an arithmetic operation (multiplication, addition, and subtraction) and find the value of a.
On the left side, "a" is multiplied to 22.
So, divide both sides by "a", we get
[tex]\frac{22a}{22} = \frac{242}{22}\\ a = 11[/tex]
Hence, we use the division property to keep an equation in balance.
To know more about the division, click on the link
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Answer:
The property of division is apply to keep the equation 22a = 242 in balance.
What is division?
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
Consider, the given equation
22 a = 242
The property of equality should you apply to keep the equation 22*a= 242in balance means we have to use an arithmetic operation (multiplication, addition, and subtraction) and find the value of a.
On the left side, "a" is multiplied to 22.
So, divide both sides by "a", we get
[tex] \frac{22a }{22} = \frac{242}{22 } \\ a = 11[/tex]
Hence, we use the division property to keep an equation in balance.
To know more about the division, click on the link
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Using the rule of significant figures!*Please help this one is tricky
Answer: 2
Step-by-step explanation:
223.4: 4 significant figures
7.5: 2 significant figures
when we multiply numbers with sifnificant figures, the answer will have the same number of significant figures as the measurement with the lowest number of significant figure.
In this exercise, since we have a measurent with 2 significant figures and another measurement with 4 significant figures, the result will have 2 significant figures.
what is the volume of the following rectangular prism?3 1/31 2/5
The volume (V) of the given prism will be equal to the area of the green zone times the lenght of 1 2/5 units, that is,
[tex]\begin{gathered} V=\text{ gre}en\text{ zone area }\times\text{ lenght} \\ V=3\frac{1}{3}\times1\frac{2}{5}units^3 \end{gathered}[/tex]In order to make the product of the mixed fractions, we need to convert them into simple fraction form, that is,
[tex]\begin{gathered} 3\frac{1}{3}=\frac{3\times3+1}{3}=\frac{10}{3} \\ 1\frac{2}{5}=\frac{5\times1+2}{5}=\frac{7}{5} \end{gathered}[/tex]Then, the volume is given as
[tex]\begin{gathered} V=\frac{10}{3}\times\frac{7}{5} \\ V=\frac{10\times7}{3\times5} \\ V=\frac{70}{15} \\ V=\frac{14}{3} \end{gathered}[/tex]Then, the volume expressed in simple fraction form is:
[tex]V=\frac{14}{3}\text{ cubic u nits}[/tex]In order to convert this result into mixed form, we need to find the following division:
Then, the answer in mixed form is:
[tex]V=4\frac{2}{5}\text{ cubic units}[/tex]20. Find the volume of the following figure.a. 448.4 cm3b. 149.5 cmC. 896.7 cm3d. 21.4 cm3
Volume of an hexagonal prism (v ): (3√3/2)a^2h
Where:
a = side base = 7cm
h= height = 7 cm
Replacing:
V = (3√3/2)7^2(7) = 891.14 cm3
Find the volume of a cube if an edge has length 2r st units.Volume =cubic unitsQuestion Help: Message instructorCheck Answer
You have a cube with side 2 rst units.
In order to calculate the volume of the given cube, you use the following formula:
V = a³
where a is the length of cube sides.
By replacing the value of a into V formula you obtain:
V = (2 srt)³ units³
V = 8 r³s³t³
where you have used tha fact 2³=8 and that variables r,s and t power to 3 are equal to r³s³t³.
Hence, the volume of the given cube is V = 8 r³s³t³ units³
which of the following relate the side of the triangle shown
The angle facing side b is 90 degrees
The angle facing side a is 75 degrees
Since the side facing angle b is greater than the angle facing angle a, therefore side b will be greater than side a.
This makes the correct option to be b>a
The first option is the correct option
34. A school admissions office accepts 2 out of every 7 applicants. Given that the school accepted 630 students, how many applicants were NOT accepted? F. 140 180 490 J. 1,260 K. 1,575
We were told that the school admissions office accepts 2 out of every 7 applicants. Thus, the probability that the school accepts an applicant is 2/7
There are only two outcomes. It is either the school accepts an applicant or it doesn't. If the school accepts 630 students, It means that 2/7 of the total number of applicants were accepted
Assuming the totla number of applicants is x, it means that
2/7 * x = 630
2x = 630 * 7 = 4410
x = 4410/2
x = 2205
The total number of applicants is 2205
The number of applicants that were not accepted is
2205 - 630 = 1575
1575 applicants were not accepted
31/32 - > Identify the ordered pairs in the graph. Then identify the domain and range. Is this a function? 7) 8) Domain: Domain: Range: that Range: Function? Function? O Type here to search gi 3
7)
The ordered pairs are:
(-4, -2), (-2, 1), (0, -1), (-3, 0), and (-3,2)
Domain = {-4, -3, -2, 0}
Range = {-2, -1, 0, 1, 2}
A function must map every element of the domain to a unique number in the range
But here -3 is mapped to 0 and 2.
Hence it is not a function
8)
The ordered pairs are:
(-2, 3), (-1,-1), (0,-1), (1,-3), (3, 1)
Domain = {-2, -1, 0, 1, 3}
Range = {-3, -1, 1, 3}
In this case, every element of the domain is mapped to a unique
ut -The ordered pairs are:
Two common names for streets are Fourth Street and Main Street, with 14,593 streets bearing one of these names.There are 443 more streets named Fourth Street than Main Street. How many streets bear each name?
Let
x ----> number of streets that bear Fourth Street
y ----> number of streets that bear Main Street
we know that
x+y =14,593 --------> x=14,593-y -----> equation 1
and
x=y+443 ------> equation 2
Solve the system of equations
Equate both equations
14,593-y=y+443
solve for y
2y=14,593-443
2y=14,150
y=7,075
Find out the value of x
x=y+443 ---------> x=7,075+443=7,518
therefore
Fourth Street: 7,518 streetsMain Street: 7,075 streetsThe boxplot below shows salaries for Construction workers and Teachers.
First, let's identify each element in a box plot:
Looking at the first box plot (Construction, Jennie), the first quartile is 30, and looking at the second box plot (Teacher, Markos), the first quartile is 25.
Since the first quartile represents the salary, that means Jennie makes more money, and the amount she does more is $5000.
(The graph shows the money in thousands)
The following summarizes the number of fiction read last summers by a sample of 28 students.
SOLUTION:
The mean is given by the formula;
[tex]\frac{\sum_^fx}{\sum_^x}[/tex]We calculate this as;
[tex]\frac{2(3)+3(10)+4(15)}{3+10+15}=3.4[/tex]Therefore, the mean is 3.4