The value of the quantity after 420 minutes is 1.739
How to calculate the amount of the quantity?
In mathematics, the amount of the quantity can be measured with the help of the exponential function by using its standard equation. But the measured quantity should grow continuously.
According to the question, the growth of the quantity is growing continuously which illustrate the exponential function.
The given parameters are:
Initial value, a = 200; Rate, r = 55%
An exponential growth function is represented as:
y = a(1 + r)^x
Substitute the value in the equation
y = 200(1 + 55%)^x
After 1.55 minutes, x = 7 * 60
So, we have:
y = 200(1 + 55%)^(7 * 60)
Evaluate the expression
y = 1.739
Hence, the value of the quantity after 420 minutes is 1.739
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The answer to this hegarty maths question
The expression written as a single power(exponent) is 9⁶ .
Exponentiation, abbreviated as bⁿ, is a mathematical process that involves the base number (b) and the exponent (or power) number (n). The word is pronounced "b (elevated) to the (power of) n."
When n is a positive integer, exponentiation corresponds to repeated base multiplication because bn is the result of multiplying n bases. Normally, the exponent is shown as a subscript to the right of the base. The term "b raised to the nth power," "b (raised) to the power of n," "the nth power of b," "b to the nth power," or, most simply, "b to the nth," is used to describe bⁿ.the given expression is of the form:
9⁶÷9³
Which is equivalent to:
9⁶⁻³ (properties of exponents)
this is equal to 9⁶ .
The value of the expression is 9⁶ .
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EspanolA lamp has the shape of a parabola when viewed from the side. The light source (which is at the focus) is 3 centimetersfrom the bottom of the lamp and the lamp is 12 centimeters deep. How wide is the lamp?? cm? cma(-a, 12)ca. 12)B12 cm| (0.3)13 cmLightsource(0,0)3 cm12 cmcmCheckSave For LaterSubmit Assignment
It is important to know that the definition of the parabola is
[tex]x^2=4py[/tex]Where p represents the focus coordinate, so p = 3. Also, we know that y = 12, let's find x
[tex]\begin{gathered} x^2=4\cdot3\cdot12 \\ x=\sqrt[]{144} \\ x=12 \end{gathered}[/tex]But, the wide of the lamp is 2x, so
[tex]2x=2\cdot12=24[/tex]Hence, the wide of the lamp is 24 cm.(3x+5)*
/
Y
X(2x-5)*
X
Z
Solve for X. note: A straight angle is exactly 180°.
Answer:
36
Step-by-step explanation:
3x+5+2x-5 = 180 ( being linear pair)
5x = 180
x= 36
Write the expression in simplest form:
The product of 4 and the sum of 10 and a number x.
ILL GIVE BRAINIEST I NEED IT NOW
Answer:
40x
Step-by-step explanation:
4x10x
=
40x
Answer:4x+50?
Step-by-step explanation:
4(10+x)
Simplified into 50+4x
So basically 4x+50
CAN SOMEONE PLEASE ANSWERT THIS?
Answer:
?
Step-by-step explanation:
what are the steps and I can help you
Please help me with this question asap the test is about to close in 20 minutes
Number of cubic feet water is passing through dam in 3 second = 4 cubic ft
Therefore, amount of water passes through dam in 1 seconds
= \frac{\text{Amount of water passing through dam}}{\text{Duration}}
Duration
Amount of water passing through dam
= \frac{4}{3}
3
4
cubic feet per seconds
Heather is building a fence around her garden. For every 2 feet of fencing, the cost is $18.
Complete the table below showing the length of the fence and the cost.
Length of fencing (feet)
Cost ($)
2
18
45
7
72
10
X
S
The length of the fence that corresponds to the cost of fencing respectively is =
Length of fencing (ft): 2, 8, 5, 7, 10
Cost of fencing ($): 18, 72, 45, 63, 90.
What is Length?Length is defined as the measurement of how long a figure or structure is which is usually measured meters, centimetres or feets.
The cost of every 2 feets of the fence Heather is building is = $18
Cost for 8ft = $72, thus;If 2ft = 18
8ft = ×
Make X the subject of formula,
X = 8 × 18/2
X= 4×18 = $72
Cost for 5ft = $45, thus;If 2ft = 18
5ft = ×
Make X the subject of formula,
X = 5 ×18/2
X = 5×9
X = $45
Cost for 7ft = $63, thus;If 2ft = 18
7 ft = ×
Make X the subject of formula,
X = 7× 18/2
X = 7× 9=$ 63
Cost for 10ft = $90, thus;If 2ft = 18
10ft = X
Make X the subject of formula,
X = 10 × 18/2
X= 10× 9
X = $90
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Can you guys please help me with this? This question is worth 40 points for my grade!!
A cardboard box in the shape of cube has volume of 400 cubic inches, then the length of one side box is 7.36806 inches, and the nearest length is 7.4 inches.
Based on the given conditions,
A cardboard box in the shape of cube has volume of 400 cubic inches.
One side of the box = s inches
Given expression,
[tex]s^{3}[/tex] = 400
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
So,
We can write,
[tex]s^{3}[/tex] = 400
s = [tex]\sqrt[3]{400}[/tex]
We can express 400 as 2 × 2 × 2 × 2 × 5 × 5
That is,
[tex]\sqrt[3]{400}[/tex] = [tex]\sqrt[3]{2*2*2*2*5*5}[/tex]
[tex]\sqrt[3]{400}[/tex] = [tex]\sqrt[3]{(2*2*2)*2*5*5}[/tex]
[tex]\sqrt[3]{400}[/tex] = [tex]2*\sqrt[3]{50}[/tex]
[tex]\sqrt[3]{400}[/tex] = 7.36806.
[tex]\sqrt[3]{400}[/tex] ≅ 7.4
Hence,
The value of the cube root of 400 is 7.36806 inches
Therefore,
The length of one side box is 7.36806 inches, and the nearest length is 7.4 inches.
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Change the same radical and simplify the radicand 3√x³
By using exponent properties, we will see that the simplification is the following:
∛x³ = x
How to simplify the expression?Here we have the algebraic expression:
∛x³
And we want to simplify this, there are two things you need to remember before doing this, these are the exponent properties:
(xᵃ)ᵇ = xᵃ*ᵇ
and:
ⁿ√x = x¹/ⁿ
Then we can rewrite:
[tex]\sqrt[3]{x^3} = (x^3)^{1/3}[/tex]
Using the first property now we can write:
[tex](x^3)^{1/3} = x^{3*1/3} = x^1 = x[/tex]
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What function translates the function f(x) = |x| to the right 2 units and up 10 units?
g(x) = |_| +__
Answer:
[tex]g(x)=|x-2|+10[/tex]
Step-by-step explanation:
Translations
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
Given absolute value function:
[tex]f(x)=|x|[/tex]
To translate the given function 2 units to the right, subtract 2 from the x-value:
[tex]\implies f(x-2)=|x-2|[/tex]
Then to translate the given function 10 units up, add 10 to the function:
[tex]\implies f(x-2)+10=|x-2|+10[/tex]
Therefore, the function that translates the function f(x) = |x| to the right 2 units and up 10 units is:
[tex]\large\boxed{g(x)=|x-2|+10}[/tex]
The function p(t)=4+2(t−1) represents the number of people who can be seated at an event. The total of t tables are arranged in a certain way.
Select EACH correct statement about the scenario
The function p(t)=4+2(t−1) represents the number of people who can be seated at an event. Then the correct statements are
The function is an arithmetic sequenceThe number 2 is the number of tables added when t increases by 1.The number 4 represents the number of people that can be seated at an event if only 1 table is available.The function is
p(t)=4+2(t−1)
We know the nth term of the arithmetic sequence is
an = a + (n-1)d
By comparing the nth term of the arithmetic sequence and the given function
The first term a = 4
The common difference d = 2
The value of n = t
Hence, the function p(t)=4+2(t−1) represents the number of people who can be seated at an event. Then the correct statements are
The function is an arithmetic sequenceThe number 2 is the number of tables added when t increases by 1.The number 4 represents the number of people that can be seated at an event if only 1 table is available.The complete question is :
The function The function p(t)=4+2(t−1) represents the number of people who can be seated at an event. The total of t tables are arranged in a certain way.
Select EACH correct statement about the scenario.
The function is an arithmetic sequence.The number 2 is the beginning number of tables.The number 2 is the number of tables added when t increases by 1.The number 4 represents the number of people that can be seated at an event if only 1 table is available.Learn more about arithmetic sequence here
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pls help will mark brainliest
Ax + By = C is the standard form of the line equation, where A and B are constants.
What exactly is a line equation?A straight line is a mathematical equation which explains the connection between the straight line's coordinates.It can be written in a variety of ways and represents a line's slope, x-intercept, and y-intercept.The most common straight line equation forms are y = mx + c and ax + by = c.A straight line is an image created by connecting the two points A (x1, y1) and B (x2, y2) as closely as possible as well as extending both ends to infinity.As a result, a linear equation with x and y variables has the standard form: Ax + By = C, in which A, C and B are constant.
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how do I find which two further transformations will carry rectangle P'Q'R'S back onto rectangle PQRS
Reflection across the x axis involve negating the value of the y axis but the value of the x axis remain the same. Reflection across the y axis negate the x coordinates but the y values remains the same. When you reflect across the line y=x the coordinate and the y coordinates change places. Whe it rotate 180 degree around the origin the x and y values are negated. The transformation is interpreted as follows.
The answer is C which is reflection across the y axis followed by a 180 degree rotation around the origin.
The logic here is that PQRS is first reflected across the x axis which makes the y values negative. Then it reflect across the y axis which makes the value of x negative. So both x and y values are negative at this point. The rotation of 180 degree around the origin negates both the x and y values to make it all positive like the initial values of PQRS.
solve each compound inequality. drag the correct solution and graph next to the inequality
A compound inequality is created by joining two or more inequalities together using or or and (also known as a combined inequality). For a value to be the answer to an or inequality, it simply needs to make one part of the inequality true. To be effective, a solution to an inequality must make both sides true. Examples are x3 or x>2.
Explain about the compound inequality?
A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect.
Divide a compound inequality into two independent ones before attempting to solve it. Choose either a union of sets ("or") and an intersection of sets as the appropriate response ("and"). Then, resolve the graph and all inequalities.
The values that belong to both graphs—where the graphs overlap—are found by first examining the graphs of each individual inequality in order to obtain the answer to a "and" compound inequality. We graph each inequality for the compound inequality x>3 and x2. Next, we search for areas where the graphs "overlap."
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How are the functions y=x and y=x-3 related? How are their graphs related?
Functions y=x and y=x-3 are related in a way that each output for y=x–3 is 3 units more than the corresponding output for y=x.
Their graphs are related in a way that the graph of y=x–3 is the graph of y=x translated down 3 units
A function will defines one variable in terms of the other. Functions y=x means that y will vary directly to whatever value x takes.
When the graph of function y=x is drawn, then it is a straight line through the origin.
Now, functions y=x and y=x-3 are closely related. The graphs of the two are almost the same, the only difference is that every point on function y=x has been lowered by 3 to be function y=x-3.
Hence, the output for y=x-3 is 3 units more than the output of y=x, and the graph of function y=x is translated down by 3 units to get function y=x-3
The graphs for functions y=x and y=x-3 are shown below:
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what is the equation of a line that is parallel to the line y=2x+1 and passes through the point (4,6).
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{2}x+1\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line that has a slope of 2 and it passes thourhg (4 , 6)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 2}(x-\stackrel{x_1}{4}) \\\\\\ y-6=2x-8\implies {\Large \begin{array}{llll} y=2x-2 \end{array}}[/tex]
HURRY!!!
what is negative 24 times positive 24
-24 x 24
Answer:
The answer is -576
Step-by-step explanation:
-24×+24
–×+= –
-24×24= -576
-Name The Slope
-Name The Starting Value
-How many blocks would be in figure 100
A line's slope is a measurement of how steep a line is. Slope is calculated by dividing the change in y values by the change in x values.
In math, what is a slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
Slope is a measure of the steepness of a line.
Slope = rise / run = Δy / Δx.
Slope= Δx /Δy = 4−0 /2−5 = 4 / −3
Slope from two points, for instance
We are informed that there are two possible solutions to a particular linear equation:
Solution: x = 11.4, y = 11.5, x = 11.4, y = 11.5, space, space, space, y = 11.
Answer: x=12.7 y=15.4 x=12.7 y=15.4
Slope=
Δx / Δy = 12.7−11.4 /15.4−11.5
= 1.3 /3.9
= 13 /39
=3.
The line has a 333 slope.
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Mandy bought 3 boxes of cupcakes to share with friends at work. Each box has 6 cupcakes inside.
The letter c stands for the total number of cupcakes. Which equation can you use to find c? Please answer quickly I need it for math. I'll give 20 points.
Answer:
c=3*6
Step-by-step explanation:
c=3 boxes * 6 cupcakes per box
Expand The expression -1/4(8r+12y) to write an equivalent expression. Use as few terms as possible.
Runners at a cross-country meet run 6 miles east and then 2 miles south from the starting line. Determine the shortest straight path they must run to get back to the starting line.
square root of 40 miles
square root of 32 miles
square root of 8 miles
8 miles
help pls i dont have much time!!
The shortest straights path for run to get back to the starting line will be;
⇒ √40
What is square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
Runners at cross country meet run 6 miles east and again 2 miles south from the starting line.
Now,
We can apply the Pythagoras theorem to find the shortest straights path.
Hence,
Shortest straights path. = √6² + 2²
= √36 + 4
= √40
Thus, The shortest straights path for run to get back to the starting line will be;
⇒ √40
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Answer: square root of 40
Step-by-step explanation:
did the quiz!
Base on the scatter diagram, would you estimate the correlation coefficient to be positive, close to zero, or negative? Explain your answer.
Answer:
Positive
Step-by-step explanation:
I would estimate the correlation coefficient to be positive, because the slope is up and to the right, with both the x- and y- values becoming larger and larger which indicates that the correlation is positive.
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Adding mixed numbersFind each sum. Write in simplest form6 2/5 + 3 2/5 =
ANSWER :
The answer is :
[tex]9\frac{4}{5}[/tex]EXPLANATION :
From the problem, we have :
[tex]6\frac{2}{5}+3\frac{2}{5}[/tex]The whole numbers will be added directly.
For the fraction part, the numerator is added and the denominator will stay the same.
That will be :
[tex](6+3)+(\frac{2}{5}+\frac{2}{5})=9\frac{4}{5}[/tex]Which expression is equivalent to (4.3x + 4)(−1.8x)?
The expression which is equivalent to the given expression is -7.74x² - 7.2x.
The given expression is (4.3x + 4)(−1.8x).
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Now, the given expression can be solved as follows:
(4.3x + 4)(−1.8x)
Using distributive property
4.3x × (−1.8x) + 4 × (−1.8x)
= -7.74x² - 7.2x
Therefore, the expression which is equivalent to the given expression is -7.74x² - 7.2x.
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Find the surface area of the rectangular prism.
8 in
6 in
3 in
Answer: 180
Step-by-step explanation: You first have to find the surface area of each face of the rectangular prism. So, we can multiply 8 and 6 to find the largest face, 8 and 3 to find the second largest face, and 6 and 3 to find the smallest face. We also know that there are two of each face.
8*6=48
8*3=24
6*3=18
Now we can either double everything now or add everything and then double it.
48*2=96
24*2=48
18*2=32
96+48+32=180
or we can do it this way:
48+24+18=90
90*2=180
Please help! Two stores are having sales on cameras.
Store Z is offering a 17% off sale
Store B is offering all cameras on sale for 1/6 of their original price
Which store has the better sale price for a camera with an original price of $90?
A- Store Z because the sale price would be $74.70
B- Store B because the sale price would be $75
C- Store Z because the sale price would be $15.30
D- Store B because the sale price would be $15
Please help ASAP, will mark brainliest!
m
y = [?]
The value of y = 12.
Given,
m ∠ABC = 40° and BD is the angle bisector of ∠ABC.
To find the value of y=?
Now, According to the figure,
For value x, (Adjacent angles)
3x - 1 = 34 - 2x
3x + 2x = 34 +1
5x = 35
x = 7
And, For value of y ,
A and C are altitude
3y +6 = 5y - 18
3y - 5y = -18 - 6
-2y = -24
y = 12
Hence, The value of y = 12.
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I am a factor of 40
When you pair me with 15 we have an LCM of 15
I am not one
The number that is a factor of 40 and when you pair it with 15 you have an LCM of 15 is; 5
What is the LCM of the numbers?LCM in mathematics simply means Least Common Multiple which is defined as the least common multiple of two numbers is the very lowest possible number that is divisible by both numbers.
Now, we are told that it is a factor of 40. Let us first list the factors of 40.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Now, since you will pair it with 15, the number also has to be a factor of 15 because only a number that is a factor of 15 can have 15 as a multiple.
Factors of 15 are; 1, 3, 5, 15
Now, the only number that is common to both 40 and 15 are 1 and 5. However we are told that it is not 1. Thus, the number is 5.
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3) Lacie decides to start a small business making monogrammed towels. She can set aside $3,020 for monthly costs. Fixed costs are $1,850 per month and variable costs are $1 per set of towels. How many sets of towels can she afford to make per month?
Answer: 1170 towels
Step-by-step explanation:
Let x be the no. of towels that can be made in a month
The equation for total cost then becomes,
3020 = 1850 + 1x
1170 = 1x
x = 1170 towels
alonzo, bob, and casper work bussing tables at a restaurant. alonzo has a 55% chance, bob has a 15% chance, and casper has a 30% chance of bussing tables in the middle area of the restaurant. if alonzo is bussing tables, he has a 5% chance of breaking a dish. if bob is bussing tables, he has a 2% chance of breaking a dish. finally, if casper is bussing tables, he has a 3% chance of breaking a dish. if there is a broken dish in the middle of the restaurant, what is the probability it was broken by casper?
There is 0.009% probability that Casper broke the dish.
Firstly we will calculate the probability of bussing the table by each person.
Probability of bussing tables by Alonzo = 55%
Probability = 0.55
Probability of bussing tables by Bob = 15%
Probability = 0.15
Probability of bussing tables by Casper = 30%
Probability = 0.3
Now calculating the probability of breaking the dish by each person
Probability of breaking dish by Alonzo = 5%
Probability = 0.05
Probability of breaking dish by Bob = 2%
Probability = 0.02
Probability of breaking dish by Casper = 3%
Probability = 0.03
The phenomenon of bussing of tables and breaking the dish is independent. So, probability will be calculated by the formula -
P (A and B) = P (A) × P (B)
P (Casper of bussing the table and breaking the dish) = Probability of bussing tables by Casper × Probability of breaking dish by Casper
Keep the values
P (Casper of bussing the table and breaking the dish) = 0.3 × 0.03
Performing multiplication
P (Casper of bussing the table and breaking the dish) = 0.009
Hence, probability is 0.009%.
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