Simplify the expression
3[2(x-3) + 2] + 5(x-3)
Answer: 11x-27
Step-by-step explanation:
1- 3[2x-6+2] + 5(x-3)
2- 3[2x-4] + 5x-15
3- 6x-12+5x-15
4- 11x-27
a tumor is injected with 0.2 grams of iodine-125, which has a decay rate of 1.15% per day. write an exponential model representing the number of grams f of iodine-125 remaining in the tumor after t days.
If a tumor is injected with 0.2 grams of iodine-125, which has a decay rate of 1.15% per day. The exponential model representing the number of grams f of iodine-125 remaining in the tumor after t days is: m = m0e^kt.
Exponential modelFirst is to use this formula to find the t day
t = - ln (2) / k
Where,
k = decay rate = 1.15% or 0.0115
Let plug in the formula
t = - In (2) / - 0.0115
t = 60.27
t = 60 (Approximately)
Now let make use of the exponential model to find the gram
m = m0e^kt
where,
m0 =0.2 initial mass
t = 60 time in days
k = -1.15 / 100 = -0.0115 (continuous growth rate)
m0e^kt = 0.2×e^[-0.0115×60]
= 0.2×e^(-0.69)
= 0.100g
Therefore the exponential model is m = m0e^kt.
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What’s the answer plss
Answer:
d. 3.8 m
Step-by-step explanation:
The figure is omitted.
tan(70°) = h/1.4
h = 1.4 tan(70°) = 3.8
You can confirm this by drawing and labeling a right triangle.
Additionally, make sure your calculator is in degree mode.
help me pls asap!! it’s pass due!
Simplify the expression and rationalize the denominator.
Answer: C
Step-by-step explanation:
First, take the square root of both the numerator and denominator. The numerator would then be equal to 6 a^4 b^2 and the bottom would just be sqrt7c. Since you still have a sqrt in the denominator, rationalize the fraction by multiplying sqrt7c to both the numerator and denominator to get rid of the sqrt. This would leave you with answer choice C.
Answer:
[tex]\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]
Step-by-step explanation:
You can distribute radicals across division such that: [tex]\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}[/tex]
So you get the expression: [tex]\frac{\sqrt{36a^8b^4}}{\sqrt{7c}}[/tex]
Similarly with division, you can distribute radicals across multiplication such that: [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex], and you can do this multiple times
So our expression on top becomes: [tex]\frac{\sqrt{36}*\sqrt{a^8}*\sqrt{b^4}}{\sqrt{7c}}[/tex]
Whenever we take the square root of a base to an exponent, we simply divide the exponent by two. In general if you take the "nth" root of any base to an exponent, you divide the exponent by n, since: [tex](x^a)^b=x^{a*b}[/tex] and radicals such as: [tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex], so you're just multiplying the two, which results in a division of "n" which in this case is 2.
So the square root of a^8 simplifies to a^4 after dividing the exponent by 2, which makes since: [tex]a^4*a^4=a^{4+4}=a^8[/tex] which exemplifies the very definition of a square root.
Applying this same logic to b^4 and just simplifying sqrt(36) regularly we get the following expression:
[tex]\frac{6a^4b^2}{\sqrt{7c}}[/tex]
We generally don't want square roots in the denominator, so we rationalize it by multiplying by the sqrt(7c)/sqrt(7c) which just simplifies to one, so we're not actually changing the value but it removes the sqrt(7c) from the denominator
[tex]\frac{6a^4b^2}{\sqrt{7c}} *\frac{\sqrt{7c}}{\sqrt{7c}}\\\\\frac{6a^4b^2\sqrt{7c}}{7c}[/tex]
and this turns out to be our solution!
help needed will give 10 points
Answer:
Step-by-step explanation: 10rh squared
what formula is used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by a and f respectively?
RMSE = (nΣt=1 (At-Ft)²/n is the formula .
What is Root Mean Square Error (RMSE)?
Root mean square error, also known to as root mean square deviation, is one of the techniques more frequently used to evaluate the accuracy of forecasts. It demonstrates the Geometric separation between forecasts and observed true values.What makes a good RMSE?
A general rule of thumb states that the model can reasonably predict the data consistently when the RMSE value is between 0.2 and 0.5. A score of Adjusted R-squared more than 0.75 is also highly effective for proving accuracy. An adjusted R-squared of 0.4 or higher is also acceptable in some situations.Identify the formula used to calculate the root mean square error over a range of forecasted values, if the actual value of the time series at time t and the forecast value for time t are denoted by A t and F t respectively.
RMSE = [ (nΣt=1 (At-Ft)2) / n ]0.5
MSE = (nΣt=1 (At-Ft)²/n
RMSE = Root of MSE
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rectangle QRST has coordinates Q(-8,5), R(-8,7), S(-5,7), and T(-5,5). dilate the rectangle by a scale factor of 4 with a center of dilation at the origin. write a rule to describe this transformation and use the rule to determine the coordinates of rectangle Q'R'S'T
plsssss help !!!!
To describe the transformation, dilation by a scale factor of 4 with center of dilation at origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .
In the question ,
the coordinates of the rectangle QRST are given as Q(-8,5), R(-8,7), S(-5,7), and T(-5,5) .
we have to to dilate the rectangle by a scale factor of 4 with center of dilation at the origin.
So , to dilate the rectangle by a scale factor of 4 with center of dilation at the origin we multiply coordinates of the original shape with the dilation factor .
So , the rule of transformation becomes
(x,y)→(4x,4y)
Using the above rule to find the coordinates of the rectangle Q'R'S'T' .
given Q = (-8,5)
So, Q' = (4*(-8),4*5)
Q' = (-32,20)
Given R = (-8,7)
So, R' = (4*(-8),4*7)
R' = (-32,28)
Given S = (-5,7)
So, S' = (4*(-5),4*7)
S' = (-20,28)
Given T= (-5,5)
So, T' = (4*(-5),4*5)
T' = (-20,20)
hence , the rectangle Q'R'S'T' coordinates are Q' = (-32,20) , R' = (-32,28) , S' = (-20,28) , T' = (-20,20) .
Therefore , to describe the transformation, dilation by a scale factor of 4 with center of dilation at origin the rule is (x,y)→(4x,4y) and , the coordinates of rectangle Q'R'S'T will be Q'(-32,20) , R'(-32,28) , S'(-20,28) , T'(-20,20) .
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Thomas wants to display leaf specimens for a science fair. thomas has 98 leaves, which is 3 fewer than the total needed. will the science display have a total of 111 leaves, 102 leaves, 101 leaves, or 95 leaves?
The total number of leaves that the science display have is 101 leaves.
As per the question, Thomas wants to display leaf specimens for a science fair. Thomas has 98 leaves.
Total number of leaves Thomas have = 98
Thomas has 98 leaves, which is 3 fewer than the total needed. To calculate the total number of leaves Thomas need in the science display , we need to add 3 leaves in the total number of leaves Thomas have. So, we can write this mathematically as,
Total number of leaves that the science display have = Total number of leaves Thomas have + 3
Total number of leaves that the science display have = 98 + 3 = 101
So, the science display have a total of 101 leaves.
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If the lengths of the sides of triangle abc are 4, 5, and 7 feet, what is the perimeter in feet of similar triangle def whose shortest side is 12 feet?
Given,
ΔABC and ΔDEF are similar triangles.
AB = 6 feet, BC = 4 feet, AC = 7 feet
Let the shortest side of ΔDEF be EF = 12 feet.
Let DE = x and DF = y
Since, ΔABC and ΔDEF are similar,
[tex]\frac{BC}{EF}[/tex] = [tex]\frac{AB}{DE} = \frac{AC}{DF}[/tex]
⇒ [tex]\frac{4}{12} = \frac{6}{x} =\frac{5}{y}[/tex]
On Solving,
x = 18 feet and y = 15 feet
We know,
Perimeter of a triangle = sum of all three sides
Hence, perimeter of ΔDEF = DE + EF + DF = 18 + 15 + 12 = 45 feet.
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9. (01.05 MC) The figure below shows the quotient of fraction 5 over 7 Division sign fraction 2 over 7 using a rectangle model. Rectangle divided into seven equal parts indicating five-sevenths and two-sevenths, where the first two parts are shaded dark, the next three parts are shaded light, and the last two parts are not shaded. What is the quotient? (5 points) Fraction 2 and 3 over 5 Fraction 2 and 1 over 2 Fraction 2 and 1 over 3 Fraction 2 and 1 over 7
The quotient is Fraction 2 and 1 over 2.
A quotient is the value obtained by dividing one particular quantity by another. We can find the quotient when we are solving a division problem by multiplying the first term with the reciprocal of the second term. Reciprocal is the exchange between the numerator value and the denominator value.
(5/7) / (2/7)= (5/7) x (7/2)
= 35/14
14 will go into 35 twice = 28
35-28= 7
27/14 = 2 and 1/2
Therefore, we conclude that the quotient of fraction 5 over 7 Division sign fraction 2 over 7 using a rectangle model is 2 and 1/2.
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1/5 x 3/8 x (-5) "Write your answer in simplest form
Answer:
-3/8
Step-by-step explanation:
Multiply the expression(PEMDAS).
Answer: -3/8
Step-by-step explanation: First you do 1/5 times 3/8 which is 3/40 and then you do 3/40 times -5 which would be -3/8.
Hope this helped!!!!
Harmonie bought four packages of school supply kits. Each kit had school supplies and a backpack. The school supplies in each kit cost $18. She spent a total of $130 for all four kits. How much did each backpack cost?
Linear equations - each backpack costs $14 and 5 cents .
What are linear equations with one variable?
A linear equation is a one-variable equation of a straight line. The variable only has one power, which is 1. Simple algebraic operations are used to solve linear equations in one variable, which can have the form ax+b=0.
First, we categorise one-variable linear equations into one of three categories: identity, conditional, or inconsistent. The variable's identity equation holds true for all possible values.
let us assume that the backpack costs $x.
We are informed that each kit included a backpack and school supplies totaling $18.
there are 4 school supply kits in total,
according to the above conditions we have,
4(18+x)
we are also given that she spent a total of $130, thus,
4 (18+x) = 130
72 + 4x = 130
4x = 130 - 72
4x = 58
dividing both the sides with 4,
x = 58/4
thus, x = 14.5
therefore each backpack costs $14 and 5 cents
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Mrs. Lahti bought a pair of shoes for $50.80 and used a coupon for 20% off. What was her discount?
In a case whereby Mrs. Lahti bought a pair of shoes for $50.80 and used a coupon for 20% off then her discount will be $12.7.
What is a discount?A discount can be described as as the decreases in price of a product which can be given to the consumer from the seller.
The given discount given in the question is 20%
Then the price she bought the pair of shoe is $50.80
then the market price will be 100/80 * 50.80 = $63.5
Then the discount she got is ( $63.5 - $50.80) = $12.7
Therefore, discount she got is $12.7
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Her wages vary directly as the time she works. If her wages for 20 hours are $150, what are her wages for 38 hours
Answer:
285
Step-by-step explanation:
i'm stuck pls help me
4/4
Answer: The answer 1/2(p+24)=21
Step-by-step explanation:
The answer could be found by solving each of the equations but that would have been time consuming so it is better to fine the answer through the word problem.
the sunglasses and flip flops were bought at a half-off sale, which means that each of their prices were reduced by 1/2. So the new price was 1/2 of the original price for each of the items. $21 was spent by adding the new price of both the items.
let, 1/2 of original price of sunglasses = p
therefore we get the equation,
new price for sunglasses = 1/2p
therefore
1/2p + 1/2(24) = 21
if we take 1/2 common,
1/2(p+24)=21
54 of the 72 coffee mugs at Ariana's Pancake House are dirty. What percentage of the coffee mugs at the pancake house are dirty? Write your answer using a percent sign (%).
Please answer it with WORKING
Answer:
5 bottles of hand sanitizer
2 thermometers
4 packets of masks
Step-by-step explanation:
We start by factoring each of the numbers to find the common factor which will give us the number of bags used to distribute.
1155 = 5 x 231
462 = 2 x 231
924 = 4 x 231
We see that 231 is the common factor for all 3 numbers. It is also the greatest common factor.
Therefore the greatest number of bags that can be packed = 231
Each bag will contain:
5 bottles of hand sanitizer
2 thermometers
4 packets of masks
A job pays an annual salary of $33,150, which includes
a holiday bonus of $750. If paychecks are issued twice a
month, what is the gross amount for each paycheck?
$47,000 invested for 50 years at 10% compounded annually $47,000 invested for 50 years at 5% compounded monthly
Answer: $47,000 at 10% annually is ≈ $77,297.70 and $47,000 at 5% monthly is ≈ $569,611.01
Step-by-step explanation:
Use the compound interest formula. A=P(1+r/n)^nt
A server earns a dollars per hour at a restaurant in addition to tips. If during a 6-
hour shift, the server earns $164.50 in tips, what is the minimum amount the
must earn per hour to make at least $184 total during the shift, in dollars and cents?
server
Answer: $3.25 an hour.
Step-by-step explanation: If the server wants to make 184 dollars and they already made 164.50, you subtract 184 by 164.50. 184-164.50= 19.50
That is how much the server made without tips over the course of 6 hours, and we want the amount they made in 1 hour. So we now divide 19.50 by 6. 19.50/6=3.25
The school that Pranav goes to is selling tickets to the annual talent show. On the first day of
ticket sales the school sold 10 senior citizen tickets and 3 student tickets for a total of $142. The
school took in $224 on the second day by selling 14 senior citizen tickets and 6 student tickets.
Find the price of a senior citizen ticket and the price of a student ticket.
By solving a system of equations, we conclude that the cost of a senior citizen ticket is $10, and the cost of a student ticket is $14.
How to find the price of each ticket?Let's define the variables:
x = price of a senior citizen ticket.
y = price of a student ticket.
With the given information we can write a system of equations:
10*x + 3*y = 142
14*x + 6*y = 224
To solve if we subtract twice the first equation from the second equation, we get:
(14*x + 6*y) - 2*(10*x + 3*y) = 224 - 2*142
14x + 6y - 20x - 6y = -60
-6x = -60
x = -60/-6 = 10
So each senior citizen ticket costs 10 dollars.
Now that we know the value of x, we can find the value of y:
10*x + 3*y = 142
10*10 + 3*y = 142
3*y = 142 - 100 = 42
y = 42/3 = 14
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2,3,1,4,0 solution i need this sequence please?
Answer:
01234
Step-by-step explanation:
Sequence is smallest to largest therefore the sequence is 01234
Answer:01234
Step-by-step explanation:
Hope this helps.
The number of seconds that it takes for a kettle to boil, n, is
inversely proportional to its power in kilowatts, p.
The equation of proportionality is n
280
p
Work out the power of the kettle if it takes 70 seconds to boil.
If your answer is a decimal, give it to 1 d.p.
The power of the kettle if it takes 70 seconds to boil is 4 kilowatts.
It is given in the question that the number of seconds that it takes for a kettle to boil, n, is inversely proportional to its power in kilowatts, p.
Also, The equation of proportionality is n = 280/p.
We have to find the power of the kettle if it takes 70 seconds to boil.
According to the data given in the question, we can write,
n ∝ 1/p
n = k/p
Where k is the constant of proportionality.
Hence, k = 280
n = 280/p
Putting n = 70 seconds in the equation, we get,
70 = 280/p
p = 280/70
p = 4 kilowatts.
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y is inversely proportional to x².
When x = 2, y = 8.
Find y in terms of x.
Answer: y=32/x^2
Step-by-step explanation: Please mark brainilest. Since y and x^2 are inversely proportional, x^2(y)=k. K is some constant. Since they gave us an example of x and y, we can calculate k as 4*8=32. So our updated equation is y(x^2)=32. Dividing both sides by x^2 we get y=32/x^2, so we have y in terms of x
Answer:
y = 32x
Step-by-step explanation:
y = k/x^2
8 = k/2^2
8 = k/4
8×4 = 32
k = 32
y = 32x
Car A—450 miles for 15 gallons
Car B—651 miles for 21 gallons
Car C—598 miles for 23 gallons
Which car has the best rate of miles per gallon?
Answer:
Car B
Step-by-step explanation:
Car A 450/15 = 30 gallons per mile
Car B 651/21 = 31 gallons per mile
Car C 598/23 = 26 gallons per mile
9x^2-(x^2-4)^2
4+3x-x^2
Multiplying the expression 9x² - (x² - 4)² . 4 + 3x - x² will give -4x⁴ + 40x² + 3x - 64
How to illustrate the information?From the information given, we want to multiply the expression 9x² - (x² - 4)² . 4 + 3x - x². This will be illustrated thus:
Distribute
9x² - (x² - 4)² . 4 + 3x - x².
9x² - (x² - 4)(x² - 4) . 4 + 3x - x².
Now we can open the parentheses. This will be illustrated as:
9x² - 2(x⁴ - 4x² - 4(x² - 4) . 4 + 3x - x³
= -4x⁴ + 40x² + 3x - 64
The value of the expression is -4x⁴ + 40x² + 3x - 64.
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Multiply the expression 9x² - (x² - 4)² . 4 + 3x - x²
9m + 2i= 30
8m -3i= -2
Answer:-60
Step-by-step explanation:
Find a point-slope form for the line that satisfies the stated conditions
Slope 7, passing through (- 6,2)
The equation of the line in point-slope form is……
Answer:
y-2=7(x+6)
Step-by-step explanation:
point slope form
Answer:
me + you = forevea
Step-by-step explanation:
you and me make sum good chemistry too bad were talkin ab math
Answer the question in the photo for a brainliest!
Answer:
image has six circles
∴ A complete circle has 360°
360/6= 60 degrees
Plsss mark as brainliest
Answer:
90 degrees.
Step-by-step explanation:
90 degrees because if you take a right angle and add 90 more then you have half a circle then add 90 2 more times then you have a full circle since this is a circle is like right angles if you add 90 it is the same.
NO NEED TO MARK BRAINLEIST IT IS UP TO YOU.
Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f (x) = 4(3) to predict the population growth.
which rule can also model the function?
The rule that can also model the function is f(x)= 4 + 3x.
How to illustrate the information?The initial population of fruit flies = 4 and the population of fruit flies triple every week
Let x represent number of weeks
Therefore function can be modelled as:
f(x)= 4 + 3x
Now assume population grows for two weeks, using the function:
f(x)= 4 + 3x
f(2)= 4+3×2
f(2)= 10
Therefore population grows to 10 fruit flies in 2 weeks based on our function
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Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f(x)=4(3)x to predict the population growth. Which rule can also model the function?