The expression in scientific notation is given as follows:
3.5 x 10³.
What is scientific notation?A number in scientific notation is given by:
[tex]a \times 10^b[/tex]
With the base being [tex]a \in [1, 10)[/tex].
For this problem, the expression is given by:
[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3}[/tex]
When two factors of a multiplication have the same base and different exponent, we keep the base and add the exponents, hence:
[tex]10^2 \times 10^4 = 10^6[/tex]
5 x 4.2 = 21, hence the expression is:
[tex]\frac{5 \times 10^2 \times 4.2 \times 10^4}{6 \times 10^3} = \frac{21 \times 10^6}{6 \times 10^3}[/tex]
When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:
[tex]\frac{21 \times 10^6}{6 \times 10^3} = 3.5 \times 10^3[/tex]
Which is the simplified expression.
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Create a polynomial that has 4 term, a degree of 6, a leading coefficient of -1 and a
Constant term of -5.5
Answer: Theorems About Roots of Polynomial Equations
Step-by-step explanation:
Theorems About Roots of Polynomial Equations
In the given case we can conclude that the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
To create a polynomial with 4 terms, a degree of 6, a leading coefficient of -1, and a constant term of -5.5, we can use the general form of a polynomial:
A "polynomial" is a mathematical expression consisting of variables (or indeterminates) raised to non-negative integer powers, combined using addition and multiplication. Polynomials are fundamental objects in algebra and are used to represent a wide range of mathematical relationships, including functions, curves, and various mathematical concepts.
P(x) = [tex]ax^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx + g[/tex]
Plugging in the given values, we have:
P(x) = [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5[/tex]
Remember that the degree of a polynomial is determined by the highest exponent of x.
In this case, the degree is 6.
The leading coefficient is the coefficient of the term with the highest degree, which is -1. The constant term is -5.5.
So, the polynomial is [tex]-x^6 + bx^5 + cx^4 + dx^3 + ex^2 + fx - 5.5.[/tex]
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IM GIVING 100 PTS TO WHOEVER ANSWERS THE FASTEST
Jayden went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 200 mg of sodium and each frozen dinner has 650 mg of sodium. Jayden purchased a total of 13 cans of soup and frozen dinners which collectively contain 4400 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.
A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is;
c + f = 13
200c + 650f = 4400
where; c is the number of cans of soup and f is the number of frozen dinners.
How to create a system of equations?Let us denote c as the number of cans of soup and f is the number of frozen dinners.
The total number of items is 13 and so, we can write;
c + f = 13
The total amount of sodium is 4400 mg. Each can of soup has 200 mg, and each frozen dinner has 650 mg.
200c + 650f = 4400
We can use substitution or elimination to solve the equation for c and f but we are not asked to find it. Thus, we will conclude that;
A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is;
c + f = 13
200c + 650f = 4400
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Answer:
Step-by-step explanation:
11970658976
what is the lcm of 12,27,30
Answer:
The least common multiple of 12, 27 and 30 is 540.
Please mark as brainliest
Solve the simultaneous equation
-4x+3y=1
6x-y=2
Step-by-step explanation:
multiply 6x - y = 2 by 3 and subtract the first equation from the second
18x-3y=6 - (-4x+3y=2
3y is cancelled and after the others are subtracted the equation becomes
22x = 4
x = 2/11
Answer:
The value of x = 1/2
The value of y = 1
Step-by-step explanation:
Let's change the equation,
→ 6x - y = 2
→ y = 6x - 2
Then the value of x will be,
→ -4x + 3y = 1
→ -4x + 3(6x - 2) = 1
→ -4x + 18x - 6 = 1
→ 14x = 1 + 6
→ x = 7/14
→ [ x = 1/2 ]
Hence, the value of x is 1/2 (or) 0.5.
Now the value of y will be,
→ y = 6x - 2
→ y = 6(1/2) - 2
→ y = 3 - 2
→ [ y = 1 ]
Hence, the value of y is 1.
Any tips for doing complicated order of operation problems. Algebra 2
13. Which function includes the data set below?
{(2, -2), (6, 10), (13, 31)) (Lesson 2-1)
A. f(x)=2x-3
B. f(x) = -2x + 2
C. f(x) = 3x8
D. f(x) = 4x 10.
-
Answer:
C. 3x-8
Step-by-step explanation:
To solve this, we put the x values into the functions and calculate the y values.
A
y = (1/2)x - 3
test for (2, -2)
-2 = 1/2 × 2 - 3 = 1 - 3 = -2 correct
test for (6, 10)
10 = 1/2 × 6 - 3 = 3 - 3 = 0 wrong
so, A cannot be right.
B
y = -2x + 2
test for (2, -2)
-2 = -2×2 + 2 = -4 + 2 = -2 correct
test for (6, 10)
10 = -2×6 + 2 = -12 + 2 = -10 wrong
so, B cannot be right.
C
y = 3x - 8
test for (2, -2)
-2 = 3×2 - 8 = 6 - 8 = -2 correct
test for (6, 10)
10 = 3×6 - 8 = 18 - 8 = 10 correct
test for (13, 31)
31 = 3×13 - 8 = 39 - 8 = 31 correct
so, C is a right answer.
D
y = 4x - 10
test for (2, -2)
-2 = 4×2 - 10 = 8 - 10 = -2 correct
test for (6, 10)
10 = 4×6 - 10 = 24 - 10 = 14 wrong
so, D cannot be right.
I hope this helped! Have a good day! :D
use the diagram to find bc.
Answer:
BC = 12
Step-by-step explanation:
from the diagram
AB + BC = AC , that is
18 + BC = 30 ( subtract 18 from both sides )
BC = 12
I need Help please :(
Step-by-step explanation: See attached step by step
Please help :(
Use PEMDAS to find the surface area.
81 + 72(4) =
157 km²
369 km²
612 km²
Correlational research results depicting a correlation coefficient of 0. 5 means that the associated variables demonstrate a __________ relationship.
Results of correlational analysis showing a correlation coefficient of 0.5 indicate that the related variables show a moderately positive relationship.
The correct option is B.
Briefing:The strength of the relationship can be quantified by researchers using this coefficient, which is frequently used to determine the relationship between two or more objects.
The coefficient value will range from -1 to +1, where a value of 0.5 indicates that the variables show a moderately positive relationship.
What exactly does it mean to have a moderate correlation?Variables that are thought to be highly correlated have correlation coefficients with magnitudes between 0.7 and 0.9. Variables that are moderately correlated are indicated by correlation coefficients with magnitudes between 0.5 and 0.7.
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I understand that the question you are looking for is:
Correlational research results depicting a correlation coefficient of 0.5 means that the associated variables demonstrate a __________ relationship.
a. weak negative
b. moderately positive
c. weak positive
d. strong positive
Please answer this !!!!!! will give brainliest !on first down, the vultures lost 6 yd. on second down, they lost 5yd. on third down, they lost 8 yd. use an integer to express their overall change in position as a result of the three plays.
As per given condition first they lost 5yd , second lost 6yd , third lost 8 yd ,so change in position shows lost 19 yd.
As given,
Let x be the total number of yards in the beginning
First down they lost 5 yards, second 6 yd and third 8 yd.
Required equation,
x-5-6-8
= x-19
Negative sign represent the lost of 19 yads.
Therefore, as per given condition first they lost 5yd , second lost 6yd , third lost 8 yd ,so change in position shows lost 19 yd.
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the ratio of wins to losses to ties for yan's soccer team at was 3:2:1. if the team played 18 games, how many games did they win? Show your work.
Answer:
9
Step-by-step explanation:
Let the ratio's unit be x. We have:
3x:2x:x. We add these up to get 6x. 6x=18, so x=3. 3*3 (since the wins is 3 in the ratio 3:2:1) is 9, so there's your answer! We can double check because 3*2 = 6 losses, and 3*1 = 3 draws, and 9:6:3=3:2:1, and 9+6+3=18!
Your hourly wage is $10.05 per hr when you work during the day and $12.01 per hr when you work the night shift .what is your gross pay for one week if you worked 24 hrs at night and 16 hrs during the day.
The gross income over the whole week upon working during the day and at night is; $449.04.
What is the gross pay for one week if you worked 24 hrs at night and 16 hrs during the day?Since, the pay rates during the day and night according to the task content are; $10.05 per hour and $12.01 per hr respectively.
It then means that the total gross total income can be calculated as follows;
(10.05 × 16) + (12.01 × 24)
= 160.8 + 288.24
= $449.04.
Therefore, the gross income over the whole week upon working during the day and at night is; $449.04.
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What is the difference quotient of the function, g (x) = startroot x endroot, x greater-than-or-equal-to 0?
The difference quotient of the function g(x) = √x is [√(x+h) -√x]/h
Difference quotient of the function:
Difference quotient of the function means a measure of the average rate of change of the function over an interval.
The difference quotient formula of a function y = f(x) is,
[ f(x + h) - f(x) ] / h
where
f (x + h) is obtained by replacing x by x + h in f(x)
f(x) is the actual function
Given,
Function g(x) = √x where x≥0.
Here we need to find the difference of the quotient of the function.
For that,
First we have to calculate the value of g(x + h),
By simply replacing the value of x as x + h,
So,
g(x + h) = √(x+h)
Now apply the values on the formula in order to solve it,
=> [√(x+h) -√x]/h
We can't simplify it further.
So, the difference quotient of function is,
=> [√(x+h) -√x]/h
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Answer: D
Step-by-step explanation:
took one for the team
Geometry -Triangle
Screenie attached
Answer:102
Step-by-step explanation:
The interior angles of a triangle have to measure 180 degrees, which is an isosceles triangle, and 39+39=78.
180-78=102.Therefore the answer is 102
I need some help please
Step-by-step explanation:
[tex] = \frac{ {2}^{4} }{ {2}^{7} } [/tex]
[tex] = {2}^{4 - 7} [/tex]
[tex] = {2}^{ - 3} [/tex]
[tex] = \frac{1}{ {2}^{3} } [/tex]
[tex] = \frac{1}{2 \times 2 \times 2} [/tex]
[tex] = \frac{1}{8} [/tex]
The answer is not 8, but 1/8.
Solve the system of inequalities by graphing.
3x + 4y ≥ 16
-4x+6y < 30
x= -0.706, y= 4.529
The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
3x+4y z 16
-4x+6y< 30
Solving the two equations we get,
x=-0.706, Y= 4.529
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What is the answer for this question
The values for the net change and average change is given as-
7. Net change = 2 , Average change = 2/3.
8. Net change = -2, Average change = -1/2.
9. Net change = -4, Average change = 4/5.
10. Net change = 4, Average change = 2/3.
What is defined as the net change and the average change?Given two points on the graph of f(x), (a,f(a)) and (b,f(b)), the net change would be the contrast between the different f(x) values.
So, net change is estimated by f(b)−f(a).The ratio of the net change to a change between the 2 input values is equal to the average net change and average rate of change. Taking the same two points, the following formula can be used to calculate the average rate of change: [f(b)−f(a)]/(b - a)In other words, the average rate of change is the slope of the line connecting any two points.Part 7:
The points on x axis are;
a = 1 and b = 4
f(b) = f(4) = 5
f(a) = f(1) = 3
Thus, net change is; f(b)−f(a)
= f(4) - f(1)
= 5 - 3
net change = 2
The average change;
= [f(b)−f(a)]/(b - a)
= [f(4) - f(1)]/(4 - 1)
net change = 2/3.
Part 8:
The points on x axis are;
a = 1 and b = 5
f(b) = f(5) = 2
f(a) = f(1) = 4
Thus, net change is; f(b)−f(a)
= f(5) - f(1)
= 2 - 4
net change = -2
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(1)]/(5 - 1)
net change = -2/4 = -1/2
Part 9:
The points on x axis are;
a = 0 and b = 5
f(b) = f(5) = 2
f(a) = f(0) = 6
Thus, net change is; f(b)−f(a)
= f(5) - f(0)
= 2 - 6
net change = -4
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(0)]/(0 - 5)
net change = -4/-5 = 4/5
Part 10:
The points on x axis are;
a = -1 and b = 5
f(b) = f(5) = 4
f(a) = f(-1) = 0
Thus, net change is; f(b)−f(a)
= f(5) - f(-1)
= 4 - 0
net change = 4
The average change;
= [f(b)−f(a)]/(b - a)
= [f(5) - f(-1)]/(5 + 1)
net change = 4/6 = 2/3
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Cindy and Richard leave their dorm in Charleston
at the same time. Cindy rides her bicycle north at a
speed of 18 miles per hour. Richard rides his bicycle
south at a speed of 14 miles per hour. How long will it
take them to be 96 miles apart?
Answer:
Hello,
Step-by-step explanation:
Let's suppose
t the time of the travel
d1 the distance rided by Cindy in miles
d2 the distance rided by Richard in miles
d1+d2=96
18*t+14*t=96
32*t=96
t=3 (hours)
If the odds against debroah's winning first prize are 3 to 5, what is the probability that she will win 1st prize?
Answer:
See below
Step-by-step explanation:
Odds AGAINST are 3 to5 then odds FOR are 2 to 5
2/5 = .4 = 40% chance of winning
what is the reference angle for 202 degrees
Answer: 22 degrees
Step-by-step explanation:
Since the angle 180° is in the third quadrant, subtract 180° from 202°.
I need help fast please and thank you
Answer:
its the second option
Step-by-step explanation:
u can search for the formula for a right trapezoid and then solve it
A rate is a type of ratio. It uses quantities that are not measured the same way,
like miles and hours. In a unit rate, the number in the denominator is 1. For
example, a speed of 60 miles per hour is written as number of miles traveled
thr
Express 55 miles per hour as a unit rate.
ог
55
55
60 mi
1 hr??
The 55 miles can be written as 24.4m/s.
A Rate is a special kind of ratio that is used to show the comparison of two different units of measurments. a ratio compares the same units
A rate is a ratio because it compares two numbers yet a ratio cannot be a rate because it only compares the same unit.
one common type of rate is per unit time
1 mile has 1600 meters.
distance= 55×1600= 88000m
Time= 1 hour= 3600 second.
speed is euqal to distance upon time.
88000÷ 3600 = 24.4m/s
so the 55 miles can be written as 24.4m/s.
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find the midpoint of the line segment with the given points.
Answer:
[tex]\displaystyle (-\frac{5}{2}, 4)[/tex]
Step-by-step explanation:
We will use the midpoint formula to solve.
[tex]\displaystyle (\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2} )[/tex]
[tex]\displaystyle (\frac{0+-5 }{2}, \frac{3+5}{2} )[/tex]
[tex]\displaystyle (\frac{-5 }{2}, \frac{8}{2} )[/tex]
[tex]\displaystyle (-\frac{5}{2}, 4)[/tex]
The maximum of a function is the highest point on a graph (identified as an ordered pair). For the function below, what is the x-value of its maximum.
For the graphed parabola we can see that the maximum is at (3, 2), then the x-value is x = 3.
What is the x-value of the maximum?For a function f(x), we define the maximum as a value y = f(x₀), such that:
f(x₀) ≥ f(x) for every value in the domain.
In the case of the graph is really easy to identify the maximum, in this case, it is in the vertex of the parabola.
We can see that the maximum is on the point (3, 2)
Then it is at x = 3, y = 2, from that, we can see that the x-value of the graphed function is x = 3.
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Use substitution to solve the system.
y = 2x+14
3x+2y = -7
Answer: x=-5, y=4 (-5,4)
Step-by-step explanation:
To pay for a home improvement project that totals $9,000, Genesis is choosing between taking out a simple interest bank loan at 9% for 3 years or paying with a credit card that compounds monthly at an annual rate of 18% for 7 years. Which plan would give Genesis the lowest monthly payment? The monthly credit card payment would be $295, which is lower than the monthly payment on the bank loan. The monthly payment on a bank loan would be $272.50, which is lower than the monthly credit card payment. The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment. The monthly credit card payment would be $374.21, which is lower than the monthly payment on the bank loan.
A plan which would give Genesis the lowest monthly payment is: C. The monthly payment on a bank loan would be $317.50, which is lower than the monthly credit card payment.
How to determine the plan with the lowest monthly payment?In order to determine the plan which would give Genesis the lowest monthly payment, we would calculate the simple interest earned over each of the time period.
Mathematically, the simple interest earned can be calculated by using this formula:
A = P(1 + rt)
Where:
A represents the future value.P represents the principal or original value.r represents the interest rate.t represents the time.Substituting the given parameters into the formula, we have;
A = 9000[1 + (0.09 × 3)]
A = 9000[1 + 0.27]
A = 9000 × 1.27
Future value, A = $11,430.
Next, we would calculate the monthly payment over a period of 36 months as follows:
Monthly payment = Future value/Time
Monthly payment = 11,430/36
Monthly payment = $317.50.
Similarly, we would calculate the compound interest earned on the credit card by using this formula:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
A = 9000[1 + (0.18/12)]⁽¹² ˣ ⁷⁾
A = 9000[1 + 0.015]⁸⁴
A = 9000 × 1.015⁸⁴
A = 9000 × 3.49258954
Future value, A = $31,433.31.
Next, we would calculate the monthly payment over a period of 84 months as follows:
Monthly payment = Future value/Time
Monthly payment = 31,433.31/84
Monthly payment = $372.21.
In this context, we can reasonably infer and logically deduce that the plan which would give Genesis the lowest monthly payment is the monthly payment on a bank loan.
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Answer:
C
Step-by-step explanation:
got 100% on exam
B. locate and plot (square root of)15 on a number line. find a better approximation using decimals.
The number line for √15 is shown in the figure and the value of √15 is approximately 3.87298.
Number line:
Number line used for visual representation of numbers on a straight line.
Given:
Here we need to locate and plot √15 on a number line.
Steps for the construction:
Step 1) Draw a line AB that is 15 in length, and then add 1 to C so that the distance from A to C is 16.
Step 2) From the midpoint of A C on the line, use your compass and make a half circle from A to C.
Step 3) Draw a vertical line up from B until it touches the red half circle you made in Step 2.
Step 4) From B on the number line, use your compass and make a quarter circle from D to E.
The square root of 15 is the distance from B to E. To make things clearer, we have also created the illustration below showing where B, E, and the square root of 15 are located on the number line, labeled with numbers instead of the half circle, quarter circle and vertical line.
Based on the steps the number line is looks like,
Therefore, The square root of 15 (√15) is approximately 3.87298.
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Find the equation of the line shown.
Answer:
y = -2x + 9
Step-by-step explanation:
The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
The line intersects the y-axis at 9, thus b = 9.
The slope formula is rise/run. The line falls 2 and runs 1, thus m = -2/1, or -2.
y = -2x + 9
Your friend eats 25 strawberries less than 5 times the
amount of strawberries you do. If you eat 10 strawberries,
find out how much your friend eats?
Answer:
25
Step-by-step explanation:
The required amount of strawberries eaten by the friend is given as 25 strawberries.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the number of strawberries he eat be x,
According to the question,
Strawberries that his friend eat = 5x - 25
Put x = 10
Strawberries that his friend eat = 50 - 25 = 25
Thus, the required amount of strawberries eaten by the friend is given as 25 strawberries.
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