Answer: 45x + 75y < 2000
Step-by-step explanation:
x = # of desks
45 = cost/desk
y = # of tables
75 = cost/table
2000 = maximum dollar amount that can be spent
inequality:
45x + 75y < 2000
Write 180 as a product of primes. Use index notation when giving your answer.
Answer: 5x2x2x3x3 is the answer to your question
Nathaniel invested $2,900 in an account paying an interest rate of 5.4% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 11 years?
Answer:
$5252.53============================
GivenInvested amount P = $2900,Annual interest rate r = 5.4% = 0.054,Time t = 11 years,Compound number = continuous.Find the balance after 11 yearsUse equation for continuous compound:
[tex]P(t) = P_0e^{tr}[/tex],where P(t) - final amount, P₀ - initial amount, t - time, r - interest ratePlug in the values and calculate:
[tex]P(11) = 2900e^{11*0.054}=5252.53 \ rounded[/tex]Answer:
$5,252.53 (nearest cent)
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amount.P = Principal amount.e = Euler's number (constant).r = Annual interest rate (in decimal form).t = Time (in years).Given values:
P = $2,900r = 5.4% = 0.054t = 11 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=2900 \cdot e^{(0.054 \cdot 11)}[/tex]
[tex]\implies \sf A=2900 \cdot e^{0.594}[/tex]
[tex]\implies \sf A=2900 \cdot 1.81121882[/tex]
[tex]\implies \sf A=5252.53457...[/tex]
Therefore, assuming no deposits or withdrawals are made, the amount of money in the account after 11 years would be $5,252.53 (nearest cent).
What is the first step to find the volume of the solid?
Answer: c
Step-by-step explanation:
Evaluate the expression −(4)power2− (−2)power4
Answer:
-32
Step-by-step explanation:
-(4)^2 - -2^4 = -16 - 16 = -32
In the equation, what is the value of s?
3(s + 1) − 8 = 6s(2 − 4)
Answer:
[tex]\boxed{\boxed{\sf s=\frac{1}{3}}\sf \:or\:\boxed{\sf s=0.33...}}[/tex]
Step-by-step explanation:
[tex]\sf 3\left(s+1\right)-8=6s\left(2-4\right)[/tex]
Expand ( Apply the Distributive Property):-
[tex]\sf 3s-5=-12s[/tex]
Add 5 to both sides:-
[tex]\sf 3s-5+5=-12s+5[/tex]
Simplify:-
[tex]\sf 3s=-12s+5[/tex]
Add 12s to both sides:-
[tex]\sf 3s+12s=-12s+5+12s[/tex]
Simplify:-
[tex]\sf 15s=5[/tex]
Divide both sides by 15:-
[tex]\sf \cfrac{15s}{15}=\cfrac{5}{15}[/tex]
Simplify:-
[tex]\sf s=\cfrac{1}{3}[/tex]
___________________
Hope this helps!
Have a great day! :)
Body-mass index, or BMI, takes both weight and height into account when assessing whether an individual IS
underweight or overweight. BMI varies directly as one's weight, in pounds, and inversely as the square of one's height,
in inches. In adults, normal values for the BMI are between 20 and 25, inclusive. Values below 20 indicate that an
individual is
underweight and values above 25 indicate that an individual is overweight. A person who weighs 180
pounds and is 5 feet, or 60 inches, tall has a BMI of 35.15. Use the four-step procedure for solving variations to
determine what the BMI is, to the nearest tenth, for a 210-pound person who is 5 feet 9 inches tall. Is this person
underweight, normal, or overweight?
The person is overwieght as his BMI is 31.00 (approx)
What is Proportion?
In general, proportion refers to a part, share, or quantity assessed in comparison to a total. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios or fractions are equivalent.
Solution:
Since, BMI is directly proportionate with weight and indirectly proportionate with square of height, we need to use a constant to make proportion to an equation.
According to the question,
BMI of a person who weighs 180 pounds and is 5 feet tall is 35.15.[tex]BMI = k*weight/height^{2}[/tex]
here, k is any constant value
35.15 = k*180/(60*60)
(35.15 * 3600)/180 = k
k = 703
Calculating BMI of a person weighing 210 pound and is 5 feet 9 inch tall.
First of all we need to convert 5 feet 9 inches into inches
5 feet = 60 inches
so, 5 feet 9 inch means 69 inches
BMI = 210*703/(69*69)
BMI = 31.00 (after rounding off)
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Draw a square and it diagonals. Guess the measures of these angles.
All angles of a square are 90° regardless of the length of its sides. However, all sides must be the same length.
What is a square?A square is a term to refer to a geometric figure that is characterized by the following characteristics:
Has four sidesIt has four 90° anglesAll its sides have the same lengthOne key to identifying a square and the value of its angles is to add them together. The sum of the angles of any geometric figure must result in 360°.
90° + 90° + 90° + 90° = 360°Additionally, if we mark the diagonals of a square we must take into account that these angles will have a different value. To find this value we must divide the angle in half, because these diagonals divide the figure into two parts.
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In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 3 with center (0, 3). What are the slope and y-intercept of line r?.
In the given coordinate plane, based on the given dilation the line r has slope 8 and coordinate (0,8)
Dilation:
Dilation refers the ratio of the given line to line by the scale factor.
Given
In the coordinate plane, line p has slope 8 and y-intercept (0, 5). Line r is the result of dilating line p by a factor of 3 with center (0, 3).
Here we need to find the the slope and y-intercept of line r.
Here we know that scale factor is 3.
Let us consider the slope of the line r will not change and the intercept is the addition of their ordinate will be.
So, it can be written as,
=> Intercept = 5 + 3
=> Intercept = 8
Therefore, the line r has slope 8 and coordinate (0.8).
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Which of the following is equal to ?
The given expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex].
What are Exponents?
The exponent of a number indicates how many times to multiply the number.For example, three to the power of two is represented as, [tex]3^{2}[/tex]. Here, 3 is the base number and 2 is the exponent. Also, [tex]3^{2} =3 \times 3[/tex].What are the Laws of Exponents?
There are major seven Laws of Exponents as follows:
Product Rule of Exponents: [tex]a^{m} \times a^{n} =a^{m+n}[/tex]Quotient Rule of Exponents: [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex]Power of a Power Rule: [tex](a^{m} )^{n} =a^{m \times n}[/tex]Product of a Power Rule: [tex]a^{m} \times b^{m} =(ab)^{m}[/tex]Power of a Quotient Rule: [tex]\frac{a^{m} }{b^{m} } =(\frac{a}{b})^{m}[/tex]Zero Power Rule: [tex]a^{0} =1[/tex]Negative Exponent Rule: [tex]a^{-m} =\frac{1}{a^{m}}[/tex]From the given question, we have the expression, [tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}[/tex] -----(1)
Here, we can use the power of a power rule to simplify the expression.
The power of a power rule is of the form, [tex](a^{m} )^{n} =a^{m \times n}[/tex]
Solving expression (1) using the power of a power rule, we get
[tex][\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-2 \times 3} }{(x^{6} y^{3} z)^{2 \times 3} }\\\implies [\frac{(x^{2} y^{3})^{-2} }{(x^{6} y^{3} z)^{2} } ]^{3}=\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]
Therefore, the given expression is equal to [tex]\frac{(x^{2} y^{3})^{-6} }{(x^{6} y^{3} z)^{6} }[/tex]
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Arnulfo deposited $55 into a savings account. According to the rule of 72, what interest rate will cause his money to double in approximately 23 years?.
Interest rate will cause his money to double in approximately 23 years is 3.13%.
Given:
Arnulfo deposited $55 into a savings account and interest is in semi annually.
For 23 years the interest payments will be = 23*2
= 46
Interest rate = 2*72 / 46
= 144/46
= 72/23
= 3.13%
Therefore Interest rate will cause his money to double in approximately 23 years is 3.13%.
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If f(x) = -8m + 3 and g(x) = -8m^2 + m - 5, what is (f times g)x?
A.) 64m^3 - 16m^2 + 43m - 15
B.) 64m^3 +43m - 15
C.) 64m^3 - 32m^2 + 43m - 15
D.) -16m^2 + 43m - 15
Answer: Choice C
[tex]64m^3-32m^2+43m-15[/tex]
==================================================
Explanation:
Multiply out the expressions using the distribution rule as shown below.
[tex](-8m+3)(-8m^2+m-5)\\\\n(-8m^2+m-5) \ \ \text{ ... see note1}\\\\-8m^2n+mn-5n\\\\-8m^2( n )+m( n )-5( n )\\\\-8m^2( -8m+3 )+m( -8m+3 )-5( -8m+3 ) \ \ \text{ ... see note2}\\\\( 64m^3-24m^2 )+( -8m^2+3m )+( 40m-15 )\\\\64m^3+(-24m^2-8m^2)+(3m+40m)-15 \\\\64m^3-32m^2+43m-15 \\\\[/tex]
I used the tool WolframAlpha to confirm the answer is correct. GeoGebra is another free tool that offers similar capabilities.
Footnotes:
Note1: I let n = -8m+3, and replaced -8m+3 with n. That way the distribution on the next step could happen.Note2: I plugged in n = -8m+3. After which distribution happens 3 more times.I will mark brainliest!! help much needed >_<
Find the missing value so that the line passing through the 2 points has the given slope.
(-20, y) and (-11, 15); slope: 0
a. 15
b. -13
c. 11
The missing value of that makes the line that passes the given points have a slope of 0 is determined as: a. 15.
What is the Slope of a Line?The slope (m) is defined as the rise of a line over its run. The formula for finding the slope (m) of a line is given as:
Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Given the points (-20, y) and (-11, 15) has a slope (m) of 0. Therefore, let:
(-20, y) = [tex](x_1, y_1)[/tex]
(-11, 15) = [tex](x_2, y_2)[/tex]
m = 0
Substitute the values into the slope formula:
0 = (15 - y) / (-11 -(-20))
0 = (15 - y) / 9
Multiply both sides by 9
0 = 15 - y
0 + y = 15 - y + y
y = 15
The answer is: a. 15.
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What type of angles are < 3 and < 6
Answer:
Obtuse Angles
Step-by-step explanation:
Both < 3 and < 6 are visibly over 90° and less than 180°, so both are obtuse.
HELP!!!!!!! LOTS OF POINTS
Answer:
1) 1 A. Yes B. Because the change in x and y is constant
2) 2 A. No B. Although the change in y is
constant, the change in x is not
3) 5. A. No B.Because the change in y is not constant
4) 4,5 A. yes B.Because the change in x and constant
Step-by-step explanation:
Luke claims two circles are always isometric because the shape never changes. Is he correct?
Group of answer choices
Yes - an isometry preserves shape.
Yes - all circles are similar.
No - the center may be located on a difference coordinate.
No - an isometry preserves both size and shape.
Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.
Given that,
Luke asserts that since the shape is constant, two circles are always isometric.
We have to say is he accurate.
The answer is
No, an isometry keeps the size and shape intact.
Because a shape-preserving transformation (movement) in the plane or in space is called an isometric transformation (or isometry). The isometric transformations include translation, rotation, and combinations thereof, such as the glide, which combines a translation with a reflection.
Therefore, Luke asserts that since the shape is constant, two circles are always isometric. he is wrong. No, an isometry keeps the size and shape intact.
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h - 2 > 10; h = 12
is that true?
Answer:
no, h=anything greater than 12
Step-by-step explanation
Answer:
No. It is false.
Step-by-step explanation:
h - 2 > 10; h = 12
Substitute 12 in place of h.
12 - 2 >? 10
Simplify.
10 >? 10
10 is NOT > 10
10 is not greater than 10. 10 is equal to 10. If the symbol had the "or equal to" underline under it, then it would be true. See image.
b) Simplify 18x³y³ + 2x³y
The GCF: 2x³y
answer: 2x³y2x³y(9y³+1)
(Simplify your answer.)Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other. x-8 f(x) = 4x + 8 and g(x) = 4
Answer:
x, x, yes==========================
Givenf(x) = 4x + 8,g(x) = (x - 8)/4.To find f(g(x)), g(f(x)),Determine if f and g are inverse functions.Solutionf(g(x)) = 4(x - 8)/4 + 8 = x - 8 + 8 = xg(f(x)) = (4x - 8 + 8)/4 = 4x/4 = xSince both composite functions result in same value of x, they are inverses of each other.Marie ran 842.4 meters in 12
minutes. How many
did she run?
A. 70.2
B. 70
C. 60.2
D. 72
meters/minute
Answer:
A. 70.2
Step-by-step explanation:
solve your equation step-by-step.
842.412=x1
Step 1: Cross-multiply.
842.412=x1
(842.4)*(1)=x*(12)
842.4=12x
Step 2: Flip the equation.
12x=842.4
Step 3: Divide both sides by 12.
12x12=842.412
x=70.2
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19) For which value of s is the value of the expression s + 6 ÷s greatest?
A. 1
B. 2
C. 3
D. 4
The correct option A. 1, is the value of the variable 's' for which the solution of the expression is greatest .
Define the meaning of the greatest value?whenever one value exceeds another. We employ the "greater than" symbol. as in: 9 > 6.For the given question,
The expression is-
(s + 6) ÷ s
Use the options;
A : s = 1
= (s + 6) ÷ s
= (1 + 6) ÷ 1
= 7
B : s = 2
= (s + 6) ÷ s
= (2 + 6) ÷ 2
= 4
C : s = 3
= (s + 6) ÷ s
= (3 + 6) ÷ 3
= 3
D : s = 4
= (s + 6) ÷ 4
= (4 + 6) ÷ 4
= 2.5
Thus, the value of the variable 's' for which the solution of the expression is greatest is 1.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is placed. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Write the expression in exponential form.
log₆ M = y
Gordon is 5 years older than Krutika. David is 6 years younger than Krutika. If the total of their ages is 86, how old is the eldest of them?
Answer:
Step-by-step explanation:
Well let Krutica’s age = x
K = x, G = x+5, D = x-6
K+G+D = 86
x + x+5 + x-6 = 86
3x = 87
x = 29
Gordon is the eldest of the few:
29 or x+5=
34 years old
Answer: Gordon is 34 years old
9y + 4.1 -6y someone help me on this question
Answer:
3y + 4.1
Step-by-step explanation:
You can't add unlike terms, so you collect like terms:
9y - 6y + 4.1
= 3y + 4.1
A regular hexagon with a perimeter of 45 meters is dilated by a scale factor of 4/3 to create a new hexagon. What is the perimeter of the new hexagon?
The perimeter of the resulting hexagon is 60 meters.
What is the perimeter of the image of a hexagon as a result of a dilation?
In this problem we find the perimeter of a regular hexagon, which is dilated around its center. Regular hexagons are polygons with six sides of equal length. Dilations are rigid operations of the form:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilation.k - Scale factorP(x, y) - Original pointP'(x, y) - Resulting pointThe perimeter is the sum of the side lengths of the hexagon and by dilation we find the following relationship between original and resulting perimeters (p, p'):
p' = k · p
If we know that p = 45 and k = 4 / 3, then the resulting perimeter is:
p' = (4 / 3) · (45)
p' = 60
The resulting hexagon has a perimeter of 60 meters.
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please help with the geometry homework
The triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.
First, let us understand the SAS congruency theorem:
This one denotes Side - Angle - Side and it means that if 2 sides and one angle of a triangle are equal to the corresponding 2 sides and one angle of another triangle, then they are both congruent.
We are given:
SR and ST are straight lines.
side SX ≅ side SY
side XR ≅ side YT
So,
side SR ≅ side ST
In triangle RSY and triangle TSX;
side SR ≅ side ST (above proved)
∠RSY ≅ ∠TSX (Common)
side SY ≅ side SX (Given)
So, triangle RSY ≅ triangle TSX by SAS congruency theorem.
Thus, the triangle RSY is congruent to triangle TSX which is triangle RSY ≅ triangle TSX as side SX ≅ side SY and side XR ≅ side YT.
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21a5b³-14a³b² +63a²b
———————————-
7ab
Answer:
[tex]3a^4b^2-2a^2b+9a[/tex]
Step-by-step explanation:
Because multiplication is the inverse of division, we're able to split this fraction into three separate fractions, which will simplify nicely at the end:
[tex]\frac{21a^5b^3}{7ab}; \frac{-14a^3b^2}{7ab}; \frac{63a^2b}{7ab}[/tex]
We can start by simplifying each fraction since 21, -14, and 63 are all divisible by 7:
[tex]\frac{3a^5b^3}{ab}; \frac{-2a^3b^2}{ab}; \frac{63a^2b}{ab}[/tex]
Finally, when dividing quotients with exponents, we subtract the exponents and we put all of our answers back together since everything was multiplied by each other at the beginning of the problem:
[tex]3a^4b^2-2a^2b+9a[/tex]
The graph represents the number y of computers infected by a virus after x hours. Find the number of computers infected after 90 minutes and after 6 hours.
Examining the given graph the number of computers infected in
90 minutes = 8 computers6 hours = 4096 computersHow to find the number of computers infectedThe graph shows that the function is an exponential function
represented as
The starting term of the function f(x) = 4^t is 1, and base is 4
f(x) = number of computer infected
t = time in hours
90 minutes in hours
90 / 60 = 1.5 hours
for t = 1.5 hours
f(x) = 4^1.5
f(x) = 8
for t = 6 hours
f(x) = 4^6
f(x) = 4096
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A 3 gallon bucket of paint costs $116.64. What is the price per cup?
Answer:
Step-by-step explanation:
You can use proportions to solve this.
You are paying $116.64 for 3 gallons of paint, so you could write this as:
\frac{116.64}{3}
Since the question is asking for price PER CUP, you want to convert 3 gallons to cups. 3 gallons = 48 cups. So now you can rewrite this as:
\frac{116.64}{48 cups}
In order to find the cost per cup, you can set up a proportion that solves for the price, x
\frac{116.64}{48 cups} = \frac{x}{1 cup}
Solve for x by cross multiplying:
48x = 116.64
x = $2.43
It costs $2.43 per cup of paint
The ratio of green M & M's to yellow is 2:5
a. If there are only green and yellow M & M's in the bag, what is the smallest number of M & M's possible?
b. If there are 84 total green and yellow M & M's in the bag, how many are green?
c. If red M & M's were added to the bag in part b to get a total of 100, what is the ratio of green to yellow to red in simplest form? (enter ratio as green:yellow:red)
:
:
a. The smallest number of M & M's possible is 14.
b. The number of green is 24.
c. The ratio of green to yellow to red in 6: 15: 25.
How to calculate the value?a. When there are only green and yellow M & M's in the bag, the smallest number of M & M's possible will be:
= (2 × 2) + (2 × 5)
= 4 + 10
= 14
b. If there are 84 total green and yellow M & M's in the bag, the number of green will be:
= 2 / (2 + 5) × 84
= 2/7 × 84
= 24 green
c. If red M & M's were added to the bag in part b to get a total of 100, the ratio of green to yellow to red in simplest form will be:
= Green : Yello : Red
= 24 : 60 : 100
= 6 : 15 : 25
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Are the lines parallel? y=-3x+2 and 3x+y=6
A. Yes, they have the same slope and a different y intercept
B. No they are not parallell
Answer:
A. Yes, they have the same slope and a different y-intercept.
Step-by-step explanation:
Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.
Rearrange 3x + y = 6 to y = mx + c form.
y = -3x + 6
Parallel lines have the same slope.
Since slope of both lines is -3, the lines are parallel.