Answer: 1/7
Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.
As drug A gets absorbed into the body, less and less of it remains. A scatterplot of data showed a curved relationship between hours since drug A was administered (x) and the number of milligrams of drug A remaining in the body (y). Taking the logarithm of the milligrams of drug A remaining obtains a linear pattern on a scatterplot, and creates the following printout from a statistical software package:
Predictor Coef SE Coef t-ratio P
Constant 3. 00 0. 401 7. 481 0. 000
Time -0. 0737 0. 005 -14. 74 0. 000
s= 0. 014 R-sq= 98. 5% R-Sq(Adj)= 99. 0%
Required:
Write down the correct equation that follows from this output?
The equation is
log ( milligrams of drug A ) =3 - 0.0737 ( Time)
As per the details stated above,
Curved relationship between the number of milligrams of drug A is (x) still in the body and the number of hours since drug A was delivered (y)
The co-efficient of the constant is 3.00
the co-efficient of the time is -0.0737
the SE co-efficient of the constant is 0.4017
the SE co-efficient of the time is 0.005
the t-ratio of the constant is 7.481
the t-ratio of the time is -14.74
now the equation formed is
logarithm of drug A in milligrams is (The co-efficient of the constant - the co-efficient of the time )
that is log ( milligrams of drug A ) =3 - 0.0737 ( Time).
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The table shows a linear function. What is the rate of change?
Hours
Pay
1
18
1.5
23
2
28
2.5
33
3
38
Using the regression concept to find the equation and applying derivative, The rate of change is 10.
What do you mean by regression?Regression analysis is a group of statistical procedures used in statistical modeling to determine the associations between a dependent variable and one or more independent variables. The dependant variable's predicted value in basic linear regression is given by the equation = b0 + b1x. In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b0 + b1X.
What do you mean by derivative?The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
from the given data,
y= a + bx is our regression line.
a=8 and b =10
y=8+10x is the line.
derivate the line , we get,
[tex]\frac {dy}{dx} = 10[/tex]
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5. There are 42 teachers who work in a school. On Monday, 29 teachers were present. What percentage of the teachers showed up for work?
Answer:
69%
Step-by-step explanation:
There are 42 teachers who work in a school. On Monday, 29 teachers were present. The percentage of the teachers that showed up for work will be:
= 29 / 42 × 100
= 69%
Answer:
Step-by-step explanation:
In any case where you're asked, "what percentage of A is B?" you can simply divide the number B by the A. The decimal you get is the answer. for example, if you're being asked what percentage 12 is of 25, you just divide 12 by 25 to get 0.48, which translates to 48 percent. in your case, 29/42 is 0.69 (rounded down from 0.6904761905) which equals 69%.
In a case where B is larger than A, you still do the same, only with the addition of the whole number. Ex: what percentage of 25 is 86?
86/25 is 3.44, so your answer is 344%.
Hope this helped :)
HELP ASAP , im stuck on what one which of the following points represents the complex number 6-3xi ?
Answer:
awser is D. I did the text
PLEASE HELP ME
6.
Dom is selling pizza at Hoopfest to help him raise money to go on a road trip. He wants each topping to increase the total price at a rate of $1.25. When someone ordered a 3-topping pizza the price was $16.25. Write an equation to represent this data.
Answer : if each topping is 1.25 then multiply that by 3 because there's 3 toppings on the pizza and if the total was 16.25 the original price of the pizza is 12.5. I hope this was the answer you were looking for a good luck :)
Step-by-step explanation:
The sales tax in one town is 8%.So, the total cost of an item can be written as c=0.08cents .what is the total cost of an that sells for $12 ?its due tmrr asap
Answer: 12.96
Step-by-step explanation: you should multiply 12 * 0.08 = 0.96
then just add 0.96 + 12 = 12.96
What will be the coefficient of XYZ in the product of 2xy 3zx and Y 2z )?
The coefficient of XYZ in the product of 2xy 3zx and Y 2z is 0.
The formula for coefficient is C = a*b, where a and b are the coefficients of the terms being multiplied.
In the given example, the coefficients for the terms being multiplied are 2 for 2xy, 3 for 3zx, and 0 for Y 2z. Since 0 multiplied by any number is 0, the coefficient of XYZ in the product is 0.
Mathematically, this can be expressed as:
C = 2*3*0 = 0
Therefore, the coefficient of XYZ in the product of 2xy 3zx and Y 2z is 0.
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please awnser the question below
The various statements regarding the given scatter plot is checked and found to be true or false.
What is a scatter plot?
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.
1)The equation of the line is y = 2500x - 125.
From the graph we can take two points on the line,
( 2,2250) and ( 10,1250)
Standard equation of line is y = mx + b
where b is y - intercept and m is slope
m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125
From graph, b = 2500
Equation of line is
y = -125x + 2500
Therefore the given equation is false.
2) The group of hikers descends about 250 feet every minute.
From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.
So the hikers descend 250 feet every minute.
Therefore the given statement is true.
3) The hikers began at the elevation of 2500 feet.
The x-intercept of the graph is 2500 feet.
So the beginning elevation is 2500 feet.
Therefore the statement is true.
4) The graph shows a negative association.
Since the line in the graph is going down and the slope is negative, the graph shows a negative association.
Therefore the statement is true.
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Find a basis for the eigenspace corresponding to each listed eigenvalue of A below.
A = 4 0 -1 14 5 -10 2 0 1 λ=5,2,3
A basis for the eigenspace corresponding to λ = 5 is { }. (Use a comma to separate answers as needed.) A basis for the eigenspace corresponding to λ = 2 is { }. (Use a comma to separate answers as needed.) A basis for the eigenspace corresponding to λ = 3 is . { }. (Use a comma to separate answers as needed.)
The basis for the eigenspace corresponding to lambda=5,1,4 are None,[tex]\left[\begin{array}{c}-1 \\\frac{1}{2} \\0\end{array}\right][/tex] and [tex]$\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]$[/tex]
[tex]$$A=\left[\begin{array}{ccc}5 & -12 & 10 \\0 & 7 & -3 \\0 & 6 & -2\end{array}\right]$$[/tex]
Eigenspace corresponding to lambda=5,1,4
The eigenspace E_lambda corresponding to the eigenvalue lambda is the null space of the matrix a [tex]\mathrm{A}-(\lambda) \mathrm{I}"[/tex]
for lambda=5
[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-5 \mathrm{I})$$[/tex]
Reducing the matrix A-5I by elementary row operations
[tex]$$\begin{aligned}A-5 I & =\left[\begin{array}{ccc}5-5 & -12 & 10 \\0 & 7-5 & -3 \\0 & 6 & -2-5\end{array}\right] \\& =\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 2 & -3 \\0 & 6 & -7\end{array}\right] \\& \sim\left[\begin{array}{ccc}0 & -12 & 10 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_2 \rightarrow \frac{R_2}{2} \\& \sim\left[\begin{array}{ccc}1 & 0 & -8 \\0 & 1 & -\frac{3}{2} \\0 & 6 & -7\end{array}\right] R_1 \rightarrow R_1+2 R_2\end{aligned}$$[/tex]
[tex]\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 2\end{array}\right] R_3 \rightarrow R_3-6 R_2$$\\\sim\left[\begin{array}{ccc}1 & 0 & -8 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] R_3 \rightarrow \frac{\mathrm{R}_3}{2}$$\\\sim\left[\begin{array}{ccc}1 & 0 & 0 \\ 0 & 1 & -\frac{3}{2} \\ 0 & 0 & 1\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+8 \mathrm{R}_3$[/tex]
[tex]$\sim\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right] R_2 \rightarrow R_2+\frac{2 R_3}{2}$[/tex]
The solutions x of A-5I=0 satisfy x_1=x_2=x_3=0 that is, the null space solves the matrix
[tex]$$\left[\begin{array}{lll}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]
Hence The null space is [tex]\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right] E_5[/tex] has no basis
[tex]$$\begin{aligned}& \text { case: } 2 \\& \text { for } \lambda=1 \\& \mathrm{E}_5=\mathrm{N}(\mathrm{A}-(1) \mathrm{I})\end{aligned}$$[/tex]
we reduce the matrix A-I by elementary row operations as follows.
[tex]$$\begin{aligned}A-1 & =\left[\begin{array}{ccc}5-1 & -12 & 10 \\0 & 7-1 & -3 \\0 & 6 & -2-1\end{array}\right] \\& =\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 6 & -3 \\0 & 6 & -3\end{array}\right] R_1 \rightarrow \frac{R_1}{4} \\& \sim\left[\begin{array}{ccc}1 & -3 & \frac{5}{2} \\0 & 1 & -\frac{1}{2} \\0 & 6 & -3\end{array}\right] R_2 \rightarrow \frac{R_2}{6}\end{aligned}[/tex]
[tex]$$$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 6 & -3\end{array}\right] R_1 \rightarrow R_1+3 R_2$\\$\sim\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right] R_3 \rightarrow R_3-6 R_2$[/tex]
Thus, the solutions x of (A-I) X=0 satisfy
[tex]$\left[\begin{array}{ccc}1 & 0 & 1 \\ 0 & 1 & -\frac{1}{2} \\ 0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\ x_2 \\ x_3\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$[/tex]
x_3=t
[tex]$\Rightarrow \mathrm{x}_1=-\mathrm{t}, \mathrm{x}_2=\frac{\mathrm{t}}{2}$[/tex]
[tex]$\vec{x}=\left[\begin{array}{c}-t \\ \frac{t}{2} \\ t\end{array}\right]=\left[\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right] t$[/tex]
The Basis for the nullspace A-I will be: [tex]$\left.\left(\begin{array}{c}-1 \\ \frac{1}{2} \\ 1\end{array}\right]\right)$[/tex]
case:3
lambda=4
[tex]$$\mathrm{E}_5=\mathrm{N}(\mathrm{A}-(4) \mathrm{I})$$[/tex]
we reduce the matrix A-4I by elementary row operations as follows.
[tex]$\begin{aligned} A-4 \mid & =\left[\begin{array}{ccc}5-4 & -12 & 10 \\ 0 & 7-4 & -3 \\ 0 & 6 & -2-4\end{array}\right] \\ & =\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 3 & -3 \\ 0 & 6 & -6\end{array}\right] \\ & \sim\left[\begin{array}{ccc}1 & -12 & 10 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] R_2 \rightarrow \frac{R_2}{3}\end{aligned}$[/tex]
[tex]$\begin{aligned} & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 6 & -6\end{array}\right] \mathrm{R}_1 \rightarrow \mathrm{R}_1+12 \mathrm{R}_2 \\ & \sim\left[\begin{array}{ccc}1 & 0 & -2 \\ 0 & 1 & -1 \\ 0 & 0 & 0\end{array}\right] \mathrm{R}_3 \rightarrow \mathrm{R}_3-6 \mathrm{R}_2\end{aligned}$[/tex]
Thus, the solutions x of (A-4IX)=0 satisfy
[tex]$$\left[\begin{array}{ccc}1 & 0 & -2 \\0 & 1 & -1 \\0 & 0 & 0\end{array}\right]\left[\begin{array}{l}x_1 \\x_2 \\x_3\end{array}\right]=\left[\begin{array}{l}0 \\0 \\0\end{array}\right]$$[/tex]
x_3=t
[tex]$\Rightarrow \mathrm{x}_1=2 \mathrm{t}, \mathrm{x}_2=\mathrm{t}$[/tex]
[tex]$$\vec{x}=\left[\begin{array}{c}2 t \\t \\t\end{array}\right]=\left[\begin{array}{l}2 \\1 \\1\end{array}\right] t$$[/tex]
The Basis for the nullspace A-4 I will be [tex]\left(\left[\begin{array}{l}2 \\ 1 \\ 1\end{array}\right]\right)[/tex]
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The ages of four children are 14, 12, 15, and 17
Work out the range of the ages of the four
children.
Step-by-step explanation: 12 - 14 is 2 years
14 - 15 is 1 year
15 - 17 is 3 years
I would say the rang is 1 -3 years apart
Hope this helps any
What is the value of aaa when we rewrite 6^{x}6 x 6, start superscript, x, end superscript as ax4 ?
The equation can be rewritten as: [tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6) \ and\ x=2[/tex]
What is logarithm?A logarithm is a mathematical function that describes the relationship between a number and its exponent. It is the inverse operation of exponentiation. Logarithms are typically written as log base b, where b is the base of the logarithm and is a positive number.
The logarithm of a number x to base b is denoted as [tex]logb(x)[/tex] and it is the exponent to which we need to raise the base b in order to get the number x.
For example, if we are given [tex]log10(100) = 2[/tex], this means that [tex]10^2 = 100[/tex].
The equation [tex]6^x * 6 * 6[/tex] can be rewritten as [tex]6^x * 6^2[/tex].
To convert 6^x to ax form, we need to take the logarithm of both sides of the equation:
[tex]log(6^x) = log(6^2)[/tex]
And we can simplify the equation as:
[tex]xlog(6) = 2log(6)[/tex]
So, the value of a is log(6) and the value of x is 2.
Therefore, the equation can be rewritten as:
[tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6)\ and\ x=2[/tex]
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elsa received a $80 dollar gift card for a coffee store. she used it in buying some coffee that cost $7.52 per pound. after buying the coffee, she had $34.88 left on her card. how many pounds of coffee did she buy?
Elsa purchased 6 pounds of coffee.
What is product pricing?The process of figuring out a product's quantitative worth based on both internal and external elements is called product pricing. Product price directly affects your company's entire success, including cash flow, profit margins, and client demand.
Here is an easy example of value-based pricing. When you bring a young child to a petting zoo, she expresses a desire to feed the goats. The goat food dispenser is topped off with a quarter. From a financial standpoint, there is the price of the goat food, which is around two cents.
Calculate the total cost of all the items you bought. To calculate the cost price, divide the total cost by the quantity of units purchased. To determine the ultimate price, use the selling price formula: Cost price plus profit margin equals selling price.
Since she started with $80 and ended with with $34,88, we can find the total amount she spent by subtracting these amounts:
$80 - $34.88 = $45.12
This means that she spent $45.12 on coffee. If each pound cost $7.52, we can divide $45.12 by $752 to see how many pounds she bought (ignoring tax):
45.12 / 7.52 = 6 pounds of coffee purchased
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can someone help me with this but please with details on how u got the answer:
The function’s average rate of change over the interval from x: 1 to x:2 is:
The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
We have the interval from x = 1 to x = 2.
To find the function’s average rate of change over the interval from x = 1 to x = 2 is:
We interpreted the interval in the coordinate form.
The curve from (1, 2) to (2, 0) is a straight line.
And the slope of the line is the average rate of change of the function.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (0-2) / (2-1)
m = -2/1
m = -2
Therefore, the average rate of change is -2.
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You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2?
In scenerio 1, the money in the retirement account at 62 years old is $1,267,250.76
In scenerio 2, the money in the retirement account at 62 years old is $ 633,625.38.
How do we calculate future value of an ordinary annuity?Scenerio 1:
a) 6% of salary = Salary * 6% = $6,100 * 6% = $366
b) Total amount the company paid monthly = 6% of salary = Salary * 6% = $6,100 * 6% = $366
c) The money in the retirement account at 62 years old can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where:
FV = Future value = Money in the retirement account at 62 years old = ?
M = Monthly payment = Contribution you + Contribution by the employer = $366 + $366 = $732
r = Monthly interest rate = Annual interest rate / 12 = 6.28% / 12 = 0.0628 / 12 = 0.0052
n = number of months = Number years * Number of months in a year = (Retirement age – Age when hired) * 12 = (62 - 25) * 12 = 37 * 12 = 444
Substituting all the values into equation (1), we have:
FV = $732 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $1,267,250.76
d) Amount of money you put into the account = 6% of salary * number of months = $366 * 444 = $162,504
e) Amount of money your employer put into your account = Amount of money you put into the account = $162,504
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $1,267,250.76 – ($162,504 + $162,504) = $942,242.76
Scenario 2:
a) 3% of salary = Salary * 3% = $6,100 * 3% = $183
b) Total amount the company paid monthly = 3% of salary = Salary * 3% = $6,100 * 3% = $183
c) Using equation (1), we have:
M = Monthly payment = Contribution you + Contribution by the employer = $183 + $183 = $366
Substituting all the values into equation (1), we have:
FV = $366 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $633,625.38
d) Amount of money you put into the account = 3% of salary * number of months = $183 * 444 = $81,252.00
e) Amount of money your employer put into your account = Amount of money you put into the account = $81,252
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $633,625.38 – ($81,252 + $81,252) = $471,121.38
The difference in the amount of money at age 62 between scenarios 1 and 2 = Money in the retirement account at 62 years old in scenarios 1 + Money in the retirement account at 62 years old in scenarios 2 = $1,267,250.76 - $633,625.38 = $633,625.38
Difference in the amounts of money you put into retirement between scenarios 1 and 2 = $366 - $183 = $183
Amount got from your employer in scenario 1 than 2 = $366 - $183 = $183
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A pizza delivery driver must make three stops on her route. She will leave the restaurant and travel 4 miles north to the first house. The next house is 6 miles away in the direction of east. She delivers the last pizza to the third stop, which is 5 miles south of the restaurant before she returns to the restaurant to pick up more pizza. What is her displacment for the entire trip
The displacement of the pizza delivery driver for the full journey is therefore 6.08 miles.
The pizza delivery driver's displacement for the entire trip is the total distance and direction that she travels from the restaurant to her last delivery and back.
To find her displacement, we can use the Pythagorean theorem to find the total distance from the start to the endpoint.
The displacement is the distance between the start and end point and the direction of the trip. Here we can see that she traveled 4 miles north, 6 miles east, and 5 miles south,
To find the displacement we will use the Pythagorean theorem (ax2 + bx2 = cx2)
where c is the displacement and a and b are the east-west and north-south distances respectively.
so, a = 6 miles (east-west)
b = (4 miles - 5 miles) = -1 miles (north-south)
so, c = √(ax2 + bx2)
c = √(6x2 + (-1)x2)
c = √(36 + 1)
c = √(37)
c = 6.08 miles
So the pizza delivery driver's displacement for the entire trip is 6.08 miles.
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Please help me find the circumference of the circle!
Answer:
[tex]C=59.6902604182[/tex]
Step-by-step explanation:
The formula to calculate the circumference of a circle given the diameter is:
[tex]C=\pi d[/tex]
Substitute and solve:
[tex]C=\pi \times19=59.6902604182[/tex]
[tex]C=59.6902604182[/tex]
Since the question doesn't say to round your answer is "59.6902604182."
Hope this helps.
Create a word problem for 4 x 8 = ?
and solve it using a bar model?
Answer:
Jackie has been assigned to hand out papers to all the students in her class. Each student gets 4 pieces of paper, and there are 8 total students. How many papers total does Jackie need to get?
(I cannot show a picture of a bar model, apologies)
A construction worker is tasked with tiling two square rooms, room A and room B. Room B has side lengths that are double the side lengths of room A. The construction worker uses one box of tiles to complete the flooring of room A.
How many boxes of tiles will they need to complete the flooring of room B? Assume the boxes of tiles are identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
Define Volume and Area.The area is the volume a flat, two-dimensional item occupies in a plane. The space occupied by a three-dimensional object is referred to as its volume. Area is measured in square units. Volume is measured in cubic units.
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
Since the side lengths of room B are double the side lengths of room A, the area of room B is four times the area of room A.
The number of tiles needed to cover a floor is equal to the area of the floor divided by the area of each tile.
Since the boxes of tiles are identical, the number of tiles in each box must also be identical.
Therefore, since the area of room B is four times the area of room A, four boxes of tiles will be needed to complete the flooring of room B.
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Write an equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5).
y =
The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.
The slope of the line through the given points :
m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2
Then, The slope of the required bisector: m = -1/(1/2) = -2
The midpoint of the given segment:
((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)
Then the point-slope form of the equation of the bisector:
y -y1 = m(x -x1)
y -2 = -2(x -(-2))
y = -2x -4 +2
y = -2x -2 . . . . . . . slope-intercept form equation
2x +y = -2 . . . . . . .standard form equation
Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
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A saw mill cuts boards that are 16 ft long. After they are cut, the boards are inspected and
rejected if the length has a percent error of 1. 5% or more. The saw mill also cuts boards that are 10, 12, and 14 feet long. An inspector rejects a board that
was 2. 3 inches too long. What was the intended length of the board?
Some acceptable board lengths are: 15.8 ft, 16.20 ft and 16.10 feet
Some board lengths to reject are: 14.8 ft, 17.20 ft and 12.10 feetThe intended lengths are 10.19, 12.19 and 14.19 feetNow, According to the question:
Board lengths that should be accepted
From the question, we have the following parameters that can be used in our computation:
Length = 16 ft
Percent error = 1.5%
This means that the acceptable lengths are
Acceptable = Length ± Percent error * Length
Substitute the known values in the above equation, so, we have the following representation
Acceptable = 16 ± 1.5% * 16
So, we have
Acceptable = 16 ± 0.24
Evaluate
Acceptable = 15.76 to 16.24
Some board lengths that should be accepted are 15.8 ft, 16.20 ft and 16.10 feet
Board lengths that should be rejected
In (a), we have
Acceptable = 15.76 to 16.24
Some board lengths that should be rejected are 14.8 ft, 17.20 ft and 12.10 feet
The intended lengths of the boards
Here, we have
Lengths = 10, 12 and 14 feet
Length too long = 2.3 inches
Convert to inches
Length too long = 0.19
So, we have
Intended lengths = (10, 12 and 14 feet) + 0.19
Evaluate
Intended lengths = 10.19, 12.19 and 14.19 feet
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6. Jenna wants to hang outdoor stringed lights on her house along the roof line
and horizontally across, connecting the ends of the roof line to create a triangle.
What is the approximate length, in feet, of lights that she needs to create one
triangle?
A. 48
B. 64
C. 80
D. 98
The approximate length, in feet, of lights that she needs to create one triangle is 64
This is an approximate estimate as the exact length would depend on the specific measurements of the roof line. However, if the roof line is a typical house roof and the string lights are hung horizontally across to connect the ends of the roof line, creating a triangle, the approximate length of lights needed would be the hypotenuse of the triangle (the longest side) which is equal to the square root of (leg 1^2 + leg 2^2).
A typical house roof is approximately 40 feet wide and 20 feet tall, which creates a right triangle with legs of 40 and 20. The hypotenuse of this triangle (the length of lights needed) would be approximately 64 feet (the square root of (40^2 + 20^2) = 64).
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A baby manatee weighs 58 kilograms. At birth the manatee weighed 30 kilograms. What is the percent increase in the manatee's weight rounded to the nearest whole number?
Answer:
93.3% i hope this is right
Step-by-step explanation:
percentage increase= final-original/originalx100
58-30/30x100=93.3333%
What is the slope of the line? (30 points)
Answer:
Slope = -1 or (-1/1)
Step-by-step explanation:
slope = m
Point 1: (0, 2); Point 2: (2, 0)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 0 - 2 -2
m = ----------- = ---------- = ------- = -1 or (-1/1)
x₂ - x₁ 2 - 0 2
I hope this helps!
Can someone help me!!!!!!
The y - intercept of the graph, given the formula of 2 y - 5x = 16, is y - intercept : ( 0, 8)
How to find the y - intercept ?To find the y - intercept, use the slope - intercept form of the equation of a line which is:
y = mx + b
m = slope
b = y - intercept
So first rewrite the formula given to look like the slope - intercept :
2 y - 5x = 16
2 y = 5x + 16
( 2 y = 5x + 16 ) / 2
y = 5/ 2 x + 8
The y- intercept is therefore 8. As a point on the graph, this is ( 0, 8 )
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3) Breanna thought of a number, subtracted 4 from it, and then multiplied her answer by 3. She got
a final number of 24. What was her starting number?
What is the slope of this line? (5 points)
Show all work.
to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below.
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{3 +4}{4 +2} \implies {\large \begin{array}{llll} \cfrac{7 }{ 6 } \end{array}}[/tex]
Arya has 5 cupcakes and wants to
share them with 8 friends equally.
How many cupcakes will each frien
receive?
Each friend of Arya will receive 0.625 cupcakes.
To divide 5 cupcakes equally among 8 friends, we can use simple division. We would divide the total number of cupcakes (5) by the total number of friends (8) to find the number of cupcakes each friend would receive. In this case, 5 divided by 8 is equal to 0.625. This means that each friend will receive 0.625 cupcakes. However, since cupcakes are not divisible it is not possible to divide 5 cupcakes equally among 8 friends. In this case, either Arya will have to make more cupcakes or they will have to decide on a different way to divide the cupcakes.
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John and Wesley both work for telephone companies installing internet connections into new homes, but they do not work for the same company. John's paycheck at the end of the month includes his base pay of $2,000 and his commission of $65. 25 for each installation he makes that month. Wesley is paid $380 plus a commission of $105. 75 for each installation he makes each month. In September of last year, they both made the same number of installations and they both earned the same amount of money
The number of installations in September were forty that lead to John and Wesley earning same amount of money.
Let the number of installations be x. The equation of be formed for each paycheck will be -
Total paycheck = base pay + number of installations × comission on each installation
The total paycheck and number of installations is same. So equating the equations by keeping x.
2000 + 65.25x = 380 + 105.75x
Rewriting the equation -
105.75x - 65.25x = 2000 - 380
Performing subtraction on each side of the equation
40.5x = 1620
x = 1620/40.5
Performing division on Right Hand Side of the equation
x = 40
There were 40 installations.
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Rewrite 16r²s² as a power of a product.
The solution is
[tex]16r^2s^2[/tex] as the product of power is written as [tex](4rs)^2[/tex]
How would you characterize a product's strength?The power of a product rule states that [tex](a^m)(a^n) = a^(m+n)[/tex], where "a" is the base, "m" is the exponent of the first term, and "n" is the exponent of the second term. This rule allows us to simplify expressions where multiple variables are being raised to a power and multiplied together by adding the exponents.
For example, [tex](a^2)(a^3) = a^(2+3) = a^5[/tex].
It is also important to remember that when we are using the power of a product rule, the bases must be the same. If we have different bases, we cannot use this rule.
For example, [tex](a^2)(b^3) = a^2 * b^3, not a^(2+3) = a^5[/tex].
Rewritten as power of product:
[tex]16r^2 s^2= 4*4*r*r*s*s\\16r^2s^2= 4^2*r^2*s^2\\16r^2s^2=(4rs)^2[/tex]
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The figure shows two circles, with centers A and B, externally tangent at point C. The common tangents to the two circles meet at point P and AP = 30. If the radius of the circle with center A is 10, what is the length of BP?
The length of the line segment BP = 15 using the trigonometric ratio of sine for the angle P.
What are trigonometric ratiosThe trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.
Considering the right triangles formed by points at P, A and the tangent to the bigger circle with its radius as base;
radius r = 10 and hypotenuse AP = 30
sinP = 10/30 {opposite/hypotenuse}
sinP = 1/3
Also for the smaller circle, with right triangle formed by points at P, B and the tangent to the smaller circle with its radius as base;
radius r and hypotenuse BP = 20 - r
sinP = r/(20 - r)
1/3 = r/(20 - r)
3r = 20 - r {cross multiply}
3r + r = 20 {collect like terms}
4r = 20
r = 20/4 {divide through by 4}
r = 5
BP = 20 - 5
BP = 15
Therefore, length of the line segment BP is derived using the trigonometric ratio of sine as 15.
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