What is 5,435,778 expressed in scientific notation?A.5.435778 x 10*7B.5.435778 x 10*3C.5.435778 x 10*6D.5.435778 x 10*5
Answers
Given the number
[tex]5,435,778[/tex]We can express it in scientific notation below;
Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.
Therefore, in the given question, we will have;
[tex]5,435,778=5.435778\times10^6[/tex]Answer: Option C
Related Questions
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.A) Create an equation to represent their total earnings in each situation. Explain what each of the variables represent.
Answers
Given:-
Matt and Amy each had summer jobs. Matt worked at a restaurant as a bus boy. He earned $10 per hour, plus tips. Amy worked as a dog-groomer. She earned $8 per hour, plus tips.
To find:-
An equation to represent their total earnings in each situation.
I need help with my math assignment thank you :)
Answers
Okay, here we have this:
Considering the provided information, we are going to match the situations to their corresponding functions, so we obtain the following:
1: The total pages a person reads in x days, if the person reads 6 pages a day: f(x)=6x.
2: The cost of x boxes of mangoes, if 1 box cost $6 and the shipping charge is $6 per order: f(x)=6x+6 -> f(x)=6(x+1)
3: The total cost of x notebooks, if one notebook cost $6 and students receive a discount of $1 off their bill: f(x)=6x-1
4: The total cost of x novels and a pocket dictionary if you buy a novels each at $6 and get a pocket dictionary at $1: f(x)=6x+1
Which function rule would help you find the values in the table?J K2 -124 -246 -368 -48A k=-12jB k=-6jC k=j - 12D k=j - 6
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Solution
As seen from the table
For each values of the table
We define the variation from K to J
[tex]\begin{gathered} K\propto J \\ K=cJ\text{ (where c is constant of proportionality)} \end{gathered}[/tex]When J = 2, K = -12
[tex]\begin{gathered} K=cJ \\ -12=c(2) \\ 2c=-12 \\ c=-\frac{12}{2} \\ c=-6 \end{gathered}[/tex]Therefore, the formula connecting them will be
[tex]k=-6j[/tex]Option B
A triangle has squares on its three sides as shown below. What is the value of x? 4 centimeters 7 centimeters 5 centimeters 3 centimeters
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What is the average rate of change of the function f(x) = 2x^2 + 4 over the interval (-4,-1] ?
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The average rate of change is:
[tex]\frac{f(-1)-f(-4)}{-1+4}=\frac{f(-1)-f(-4)}{3}[/tex][tex]f(-1)=2(-1^2)+4=6[/tex][tex]f(-4)=2(-4^2)+4=2(16)+4=36[/tex]then computing the first formula, the average rate of change of f(x) is
[tex]\frac{6-36}{3}=-10[/tex]In solving for the inverse function for y = sqrt(3x + 2) - 1 , which of the following represents the first step?
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we know that
The first step to find out the inverse of the function is to exchange the variables (x for y and y for x)
therefore
the answer is the second optionFind the measure of x.26x = [?Round to the nearest hundredth.X78°
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To answer this question we will use the trigonometric function cosine.
Recall that in a right triangle:
[tex]\cos\theta=\frac{AdjacentLeg}{Hypotenuse}.[/tex]Using the given diagram we get that:
[tex]\cos78^{\circ}=\frac{x}{26}.[/tex]Multiplying the above result by 26 we get:
[tex]\begin{gathered} 26\times\cos78^{\circ}=26\times\frac{x}{26}, \\ 26\cos78^{\circ}=x. \end{gathered}[/tex]Therefore:
[tex]x\approx5.41.[/tex]Answer:
[tex]x=5.41.[/tex]
8.Find the range,A. (-0,00)B. (-0,0)C. (- 0, 1)D. Cannot be determined4/5
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From the graph, the range of the graph, the y values range from zero down; so the range is given by;
[tex](-\infty,0\rbrack[/tex]Option
2 dot plots. Both number lines go from 0 to 10. Plot 1 is titled fifth grade. There are 2 dots above 1, 3 above 2, 1 above 3, 4 above 4, 5 above 5, 5 above 6, 2 above 7, 2 above 8, 0 above 9, 0 above 10. Plot 2 is titled seventh grade. There are 2 dots above 0, 2 above 1, 3 above 2, 5 above 3, 5 above 4, 3 above 5, 3 above 6, 1 above 7, and 0 above 8, 9, and 10.
The dot plot shows the number of hours, to the nearest hour, that a sample of 5th graders and 7th graders spend watching television each week. What are the mean and median?
The 5th-grade mean is
.
The 7th-grade mean is
.
The 5th-grade median is
.
The 7th-grade median is
.
Answers
The mean and the median for each data-set are given as follows:
5-th grade students:
Mean: 4.67Median: 5 hours.7-th grade students:
Mean: 3.46 hours.Median: 4 hours.Dot plotA dot plot shows the number of times that each observation appears on a data-set.
Hence the hours of the 5th-graders are as follows:
1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8
The mean is the sum of all the numbers of hours divided by the number of students, hence:
Mean = (2 x 1 + 3 x 2 + 1 x 3 + 4 x 4 + 5 x 5 + 5 x 6 + 2 x 7 + 2 x 8)/(2 + 3 + 1 + 4 + 5 + 5 + 2 + 2) = 4.67.
There are 24 elements in the data-set, hence the median is the mean of the 12th and the 13th element, as follows:
Median = (5 + 5)/2 = 5.
Hence the hours of the 7th-graders are as follows:
0,0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7.
Hence the mean is:
Mean = (2 x 0 + 2 x 1 + 3 x 2 + 5 x 3 + 5 x 4 + 3 x 5 + 3 x 6 + 1 x 7)/24 = 3.46.
The 12th element is of 3, the 13th of 5, hence the median is:
Median = (3 + 5)/2 = 4.
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Inequality-x less than or equal to 18
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Answer: x[tex]\leq[/tex]18
Order the numbers from least (1) to greatest (10).ITEM BANK-Move to Battom3.564.034.212V12mor
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To order these numbers, we begin with the whole part of each number. In the case of having two numbers with equal whole part, we look for the greatest tenth. So, the order would be
[tex]3.56;4.03;4.2;12[/tex]Notice that, 4.03 is less than 4.2, because its tenth is less.
Samantha received a loan from the bank for $4,500. She plans on payinyoff the loan in 4 years. At the end of 4 years, Samantha will have paid$900 in interest. What is the simple interest rate on the bank loan?
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The simple interest rate formular is;
I = A - P
A= I + P
A = P ( 1 + rt )
A is the amount after t years
P is the initial amount = $4,500
r is the rate in percent = ?
t is the time in years = 4
A = $4,500 + $900 = $5,400
Therefore to obtain the rate (r)
5400 = 4500 (1 + r x 4 )
1 + 4r = 5400/4500
1 + 4r = 1.2
4r = 1.2 - 1
4r = 0.2
r = 0.2/4 = 0.05
In percentage;
r = 0.05 x 100 = 5%
Thus, the simple interest rate is 5%
152. ) Find all real x such that square root x + 1 = x - Square root x - 1.
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Given the equation:
[tex]\sqrt[]{x}+1=x-\sqrt[]{x}-1[/tex]Solving for x:
[tex]\begin{gathered} \sqrt[]{x}+\sqrt[]{x}=x-1-1 \\ 2\sqrt[]{x}=x-2 \end{gathered}[/tex]Now, we take the square on both sides of the equation:
[tex]\begin{gathered} 4x=x^2-4x+4 \\ 0=x^2-8x+4 \end{gathered}[/tex]Now, using the general solution of quadratic equations:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=1 \\ b=-8 \\ c=4 \end{gathered}[/tex]Then, the solutions are:
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot1\cdot4}}{2\cdot1}=\frac{8\pm\sqrt[]{64-16}}{2} \\ x=\frac{8\pm4\sqrt[]{3}}{2}=4\pm2\sqrt[]{3} \end{gathered}[/tex]But the original equation √(x), so x can not be negative if we want a real equation. Then, the only real solution of the equation is:
[tex]x=4+2\sqrt[]{3}[/tex]A museum curator counted the number of paintings in each exhibit at the art museum. Number of paintings Number of exhibits 9 2 21 1 40 1 1 46 3 52 1 67 2 X is the number of paintings that a randomly chosen exhibit has. What is the expected value of x Write your answer as a decimal.
Answers
Answer
Expected number of paintings that a randomly chosen exhibit has = 40.3
Explanation
The expected value of any distribution is calculated as the mean of that distribution.
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = (9 × 2) + (21 × 1) + (40 × 1) + (46 × 3) + (52 × 1) + (67 × 2)
Σx = 18 + 21 + 40 + 138 + 52 + 134
Σx = 403
N = 2 + 1 + 1 + 3 + 1 + 2 = 10
Mean = (Σx)/N
Mean = (403/10) = 40.3
Hope this Helps!!!
What’s the correct answer answer asap for brainlist
Answers
Answer: serbia
Step-by-step explanation:
RATIOS/UNIT RATESRead and answer the question.Jessica sold 4 out of 32 boxes of the cookies her Girl Scout troop sold onSaturday. Select ALL the choices that display an equivalent ratio to thenumber of boxes Jessica sold to the total boxes sold.8 to 641:80 11O 21602:15
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Hello,Can you help me with the following word problem?A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?This might be using the nCr formula
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Solution:
Given that a medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, this implies that
[tex]\begin{gathered} total\text{ number of options in the set = 13} \\ number\text{ of oprions to be chosen = 6} \end{gathered}[/tex]To evaluate the number of people that can be selected, we use the combination formula expressed as
In this case,
[tex]\begin{gathered} n=13 \\ r=6 \end{gathered}[/tex]Thus, the question involves combination.
How do you solve the system of equations by graphing? y=-3x/2 + 6y=5x - 7
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The given system of equations are
y=-3x/2 + 6
y=5x - 7
We would substitute values for x into the equations and find the corresponding y values. These values would be plotted on a graph. Where the lines of both equations meet would represent the solution of the system of equations.
For the first equation,
y = - 3x/2 + 6
if x = 0, y = 3 * 0/2 + 6 = 6
If x = 1, y = - 3 * 1/2 + 6 = 4.5
if x = 2, y = - 3 * 2/2 + 6 = 3
We would plot these values on the graph
For the second equation,
y = 5x - 7
if x = 0, y = 5 * 0 - 7 = - 7
If x = 1, y = 5 * 1 - 7 = - 2
if x = 2, y = 5 * 2 - 7 = 3
We would plot these values on the graph
The diagram of the graph is shown below
Looking at the graph, at the point where both lines meet,
x = 2, y = 3
Thus, the solution is (2,3)
Identify the augmented matrix for the system of equations and the solution using row operations.
Answers
Given:
The system of equation is given as,
[tex]\begin{gathered} 7x-4y=28 \\ 5x-2y=17 \end{gathered}[/tex]The objective is identify the augmented matrix for the system of equations and the solution using row operations.
Explanation:
The required augmented matrix will be,
Performing the Gauss-Jordan elimination with the following operation,
[tex]R_2=R_2-\frac{5R_1}{7}[/tex]By applying the operation to the augmented matrix,
To find y :
On equating the second row of the matrix,
[tex]\begin{gathered} \frac{6y}{7}=-3 \\ y=\frac{-3}{\frac{6}{7}} \\ y=\frac{-3\times7}{6} \\ y=\frac{-7}{2} \end{gathered}[/tex]To find x :
On equating the first row of the matrix,
[tex]\begin{gathered} 7x-4y=28 \\ 7x=28+4y \\ x=\frac{28+4y}{7} \end{gathered}[/tex]Substitute the value of y in the above equation.
[tex]\begin{gathered} x=\frac{28+4(\frac{-7}{2})}{7} \\ x=\frac{28-14}{7} \\ x=\frac{14}{7} \\ x=2 \end{gathered}[/tex]Thus the value of solutions are,
[tex]\begin{gathered} x=2 \\ y=-\frac{7}{2}=-3.5 \end{gathered}[/tex]Hence, option (3) is the correct answer.
The expression below is scientificnotation for what number? 4.58 • 10^-2
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We are given the number in scientific notation:
[tex]4.58\times10^{-2}[/tex]To convert it to decimal format, we need to move the decimal point two spaces to the left.
Since we don't have enough digits before the decimal point, we add two zeros before the 4:
[tex]004.58\times10^{-2}[/tex]Now we move the point as required:
[tex]004.58\times10^{-2}=0.0458[/tex]The required number is 0.0458
Quadrilateral HGEF is a scaled copy of quadrilateral DCAB. What is themeasurement of lin EG?
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Answer:
14 units
Explanation:
If quadrilaterals HGEF and DCAB are similar, then the ratio of some corresponding sides is:
[tex]\frac{FH}{BD}=\frac{EG}{AC}[/tex]Substitute the given side lengths:
[tex]\begin{gathered} \frac{6}{3}=\frac{EG}{7} \\ 2=\frac{EG}{7} \\ \implies EG=2\times7 \\ EG=14 \end{gathered}[/tex]The measurement of line EG is 14 units.
The scatter plot shows the number of CDs in millions that were sold from 1999 to 2005. Use the points (1999,940) and (2002,805) to find a line of fit for the data. Then use the line of fit to estimate the number of CDs that were sold in 2008
Answers
Based on the given points from the scatter plot on the number of CDs sold in millions, the line of best fit for the data is y = -45x + 90,895
The estimated number of CDs sold in 2008 was 535 CDs.
How to find the line of best fit?The line of best fit will take the form:
y = Slope(x) + y intercept
The value of x will be assumed to be the number of years since 1999.
The slope is:
= Change in y / Change in x
= (805 - 940) / (2002 - 1999)
= -45
The y intercept is:
940 = -45(3) + y
y = 90,895
The line of best fit is:
y = -45x + 90,895
This means that the number of CDs sold in 2008:
= -45(2008) + 90,895
= 535 CDs
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The Max or Min can be found by using the line of symmetry. That line of symmetry can be found by finding the midpoint of the two x-intercepts.Since the line of symmetry is x =-1 Write the function rule to find the coordinate to the minimum of this parabola.[tex]f (x) = (x - 2)(x + 4)[/tex]your answer should be in the form (_,_)
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We know that, for a parabola, the minimum, or the maximum, is given by the vertex of the parabola. The formula for the vertex of the parabola is given by:
[tex]x_v=-\frac{b}{2a},y_v=c-\frac{b^2}{4a}[/tex]And we have the coordinates for x and y for the vertex.
We can see that the line of symmetry is x = -1, and this is the same value for the value of the vertex for x-coordinate, that is, the x-coordinate is equal to x = -1.
With this value for x, we can find the y-coordinate using the given equation of the parabola:
[tex]f(x)=(x-2)\cdot(x+4)\Rightarrow f(-1)=(-1-2)\cdot(-1+4)\Rightarrow f(-1)=(-3)\cdot(3)[/tex]We can also expand these two factors, and we will get the same result:
[tex]f(x)=(x-2)\cdot(x+4)=x^2+2x-8=(-1)^2+2\cdot(-1)-8=1-2-8=-1-8=-9[/tex]Therefore, the value for the y-coordinate (the value for the y-coordinate of the parabola, which is, at the same time, the minimum point for y of the parabola) is:
[tex]f(-1)=(-3)\cdot(3)\Rightarrow f(-1)=-9[/tex]The minimum point of the parabola is (-1, -9) (answer), and we used the given function (rule) to find the value of the y-coordinate.
We can check these two values using the formula for the vertex of the parabola as follows:
[tex]f(x)=(x-2)\cdot(x+4)=x^2+2x-8[/tex]Then, a = 1 (it is positive so the parabola has a minimum), b = 2, and c = -8.
Hence, we have (for the value of the x-coordinate, which is, at the same time, the value for the axis of symmetry in this case):
[tex]x_v=-\frac{2}{2\cdot1}\Rightarrow x_v=-1[/tex]And for the value of the y-coordinate, we have:
[tex]y_v=c-\frac{b^2}{4a}\Rightarrow y_v=-8-\frac{2^2}{4\cdot1}=-8-\frac{4}{4}=-8-1\Rightarrow y_v=-9[/tex]
help meeeeeeeeeeee pleaseee
Answers
Equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
What exactly are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal.An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.Such as 3x + 5 = 15 as an example.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, (f∙g)(x) and (g∙f)(x):
Where, f(x) = 5x + 1 and g(x) = x - 4:(f∙g)(x):
5x(x - 4) + 1(x - 4)5x² - 20x + x - 45x² - 19x - 4(g∙f)(x):
x(5x + 1) - 4(5x + 1)5x² + x - 20x - 45x² - 19x - 4Therefore, equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
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a 14-member board used for admitted
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Using the Borda's method, when one person is ranked as 1st, he/she gets 3 points, if he/she is ranked 2nd, get 2 points, also, if he/she is ranked as 3rd get 1 point, and finally, 0 points if she/he is ranked as 4th
so, let's detemine how many points got each one
Cardona: Was selected 1st by 6 people, 2nd by 2 people, 3rd by 4 people and 4th by 2 people
[tex]C=3*6+2*2+1*4=26[/tex]So, that's a total of 26 points
Pitts-Jones: Was selected as: #1 by 4 people, #2 by 3 people, #3 by 6 people and 4th by 1 person
[tex]P=3*4+2*3+1*6=24[/tex]So, that's 24 points for Pitts-Jones,
De Plata: Was ranked #1 by 2 people, #2 by 8 people, #3 by 1 person and #4 by 3 people
[tex]D=3*2+2*8+1*1=23[/tex]That's 23 points for De Plata
Vincent: Was ranked as #1 by 2 people, #2 by 1 person, #3 by 3 people and #4 by 8 people
[tex]V=3*2+2*1+1*3=11[/tex]that's 11 points for Vincent,
Answer: From the above, we can conclude that the winner using Borda's method is Cardona
help me pleaseeeeeeeee
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The value of the car after 5 years is $13,500 and the value of the car after 9 years is $10,500.
According to the question,
We have the following information:
The value of the car is given by V(x) where x is the number of years.
V(x) = -1500x + 21,000
(a) Now, to find the value of car after 5 years, we will put 5 in place of x in the given expression:
V(5) = -1500*5+21000
V(5) = -7500+21000
V(5) = $13,500
(b) Now, to find the value of car after 9 years, we will put 9 in place of x in the given expression:
V(9) = -1500*9+21000
V(9) = -10500+21000
V(9) = $10,500
(c) When V(12) = 3000 then it means that the value of the car after 12 years is $3000.
Hence, the value of car after 5 years and 9 years is $13,500 and $10,500 respectively.
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identify the slope: 6x - 2y = -6
Answers
The slope = 3
Explanations:Note that:
The slope - Intercept form of the equation of a line takes the form y = mx + c
where m is the slope and
c is the intercept
The given equation is:
6x - 2y = -6
The equation can be re-written as:
2y = 6x + 6
2y / 2 = 6x/2 + 6/2
y = 3x + 3
The slope, m = 3
The intercept, c = 3
Y intercept=3
Find the volume of the figure. 6 cm. 6 cm. 1 8 cm. 10 cm. Volume of the prism cm3
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The volume of the pyramid is 144 cm³
Explanations:The volume of a prism is given by the formula:
V = BH
where B is the base area
and H is the height
The base of the the pyramid is the lateral triangle, and the area is given by the formula:
B = 0.5 x b x h
b = 8 cm
h = 6 cm
B = 0.5 x 8 x 6
B = 24 cm²
The volume is then:
V = BH, where H = 6 cm
V = 24 x 6
V = 144 cm³
Given these points please solve this problme.
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The point that belongs to the solution set is A( 4, 4)
What are inequalities?Inequalities are defined as mathematical relations involving an unequal comparison between two numbers, elements or other arithmetic expressions.
They are mostly used to compare two numbers on the number line on the basis of their sizes.
Given the inequalities;
x + y > 63x - 5y ≤ 2Make 'x' the subject from equation 1, we have;
x > 6 - y
substitute the value into equation 2, we have;
3( 6 - y) - 5y ≤ 2
expand the bracket
18 - 3y - 5y ≤ 2
collect like terms
- 8y ≤ 2 - 18
- 8y ≤ -16
Make 'y' the subject of formula
y ≤ 2
Substitute the value in equation 3
x > 6 - 2
x > 4
Hence, the point is A( 4, 4)
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1 Ms. Signer has to buy pencils for her class. She goes to CVS and buys 15 pencils for $2.50. How much did she spend per pencil?*
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She bought pencils for her class. She bought 25 pencils for $2.50 . The amount for each pencil can be computed below
[tex]\begin{gathered} 25\text{ pencils = \$2.50} \\ 1\text{ pencil = ?} \\ \text{cross multiply} \\ \cos t\text{ of each pencil=}\frac{2.50}{25} \\ \text{ cost of each pencil = \$}0.1 \end{gathered}[/tex]