Answer:
0.9, 0.6 7/10, 11/100, 0.21, 0.35
Step-by-step explanation:
solve step by step:
3x - 2y = -22
2x + y = -3
the answer is -13. And this is why, because the negative sign is bigger so same sign add keep the same sign that’s why I got -13
Find the surface area of the cylinder. Use 3.14 for pi.
Answer:
527.52 ft²
Step-by-step explanation:
The surface area of a cylinder is:
[tex]\displaystyle{2\pi r^2 + 2\pi r h}[/tex]
where r is radius and h is height.
From the attachment, we know that the radius (r) is 7 ft and the height is 5 ft. Therefore:
[tex]\displaystyle{\text{Surface Area} = 2 \cdot 3.14 \cdot (7)^2 + 2\cdot 3.14 \cdot 7 \cdot 5}\\\\\displaystyle{\text{Surface Area} = 6.28 \cdot 49 + 6.28 \cdot 35}\\\\\displaystyle{\text{Surface Area} = 307.72 + 219.80}\\\\\displaystyle{\text{Surface Area} = 527.52 \ \: \text{ft}^2}[/tex]
Therefore, the surface area of the cylinder is 527.52 ft²
Draw a model for each of the following multiplication problems: A. 4 x 2/3 B. 3 x 2/5
The total number of shaded squares will be equal to the product of 4 x 2/3.
How draw a model?A. For the problem 4 x 2/3, you can draw a model using rectangular arrays or area models. Draw four columns, each representing one of the four groups, and two rows to represent the two-thirds. Shade in two-thirds of the first column, then repeat for the next three columns. The total number of shaded squares will be equal to the product of 4 x 2/3.
B. For the problem 3 x 2/5, you can also draw a model using rectangular arrays or area models. Draw three columns, each representing one of the three groups, and two rows to represent the two-fifths. Shade in two-fifths of the first column, then repeat for the next two columns. The total number of shaded squares will be equal to the product of 3 x 2/5.
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In May 2003, JP Gas Co. had the following rate schedule for natural gas usage in single-family residences. Gas is
measured in units called therms. All customers pay a monthly charge. They also pay a distribution charge based on
the amount of gas they use and a supply charge that is also based on the amount of gas they use. The fees are as
follows:
Monthly Customer Charge $6.45
Distribution Charge
1st 20 therms $0.20/therm
Next 30 therms $0.11/therm
Over 50 therms $0.04/therm
Gas supply charge $0.73/therm
a) What is the charge for using 40 therms?
b) What is the charge for using 202 therms?
c) Construct a function that gives the monthly charge C for the x therms of gas.
Answer:
a) $40.05
b) $161.99
c) C(x) = 6.45 + 0.93x, if x ≤ 20
C(x) = 6.45 + 0.84x, if x > 20 and x ≤ 50
C(x) = 6.45 + 0.77x if x > 50
Does 4/2750 reduce into a smaller fraction
Examine the triangle below, find the mZD =
[Select]
7.
V
[Select]
V
,m
, m/M = 66.6
The measure of angle D, m∠D, found using the specified lengths of the three sides of the triangle and the law of cosines is; m∠D = 75.7°
What is the law of cosines?The law of cosines specifies the relationship between the measures of an angle, and the lengths of the three sides of a triangle. Specifically, the law of cosines states that the square of the length of a (reference) side of a triangle, is equivalent to the sum of the squares of the lengths of the other two sides, less the product of 2, the lengths of the other two sides and the cosine of the angle opposite to the reference side.
Mathematically, the law of cosines can be presented as follows;
a² = b² + c² - 2·b·c·cos(A)Where;
a, b, and c are the lengths of the three sides of the triangle
Angle A, ∠A, is the opposite angle to side a.
Therefore, according to the law of cosines, we get;
38² = 36² + 24² - 2 × 36 × 24 × cos(∠D)
2 × 36 × 24 × cos(∠D) = 36² + 24² - 38² = 428
2 × 36 × 24 × cos(∠D) = 428
cos(∠D) = 428/(2 × 36 × 24) = 428/1728 = 107/432
cos(∠D) = 107/432
m∠D = arccos(107/432) ≈ 75.7°
The measure of angle D, m∠D ≈ 75.7°
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A bicycle manufacturer currently produces 256,000 units a year and expects output levels to remain steady in the future. It buys chains from an outside supplier at a price of $1.80 a chain. The plant manager believes that it would be cheaper to make these chains rather than buy them. Direct in-house production costs are estimated to be only $1.50 per chain. The necessary machinery would cost $206,000 and would be obsolete after 10 years. This investment could be depreciated to zero for tax purposes using a 10-year straight-line depreciation schedule. The plant manager estimates that the operation would require $51,000 of inventory and other working capital upfront (year 0), but argues that this sum can be ignored since it is recoverable at the end of the 10 years. Expected proceeds from scrapping the machinery after 10 years are $15,450. If the company pays tax at a rate of 35% and the opportunity cost of capital is 15%, what is the net present value of the decision to produce the chains in-house instead of purchasing them from the supplier?
Answer:
NPV = -$57,937
Step-by-step explanation:
NPV = ($1.50 - $1.80) * 256,000 - $206,000 - $51,000 + $15,450 / (1 + 0.15)^10 - ($206,000 + $51,000) * 0.35
Please help me answer this 20 POINTS!!!
36 x 5 +59 x(234)(51)
the simplified Answer to the given expression 36 x 5 +59 x(234)(51) will be 7,04,286.
What is simplification?Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.
Given, an expression 36 x 5 +59 x(234)(51)
Simplifying using PEMDAS
=> 36 x 5 +59 x(234)(51)
First, we will open a bracket
=> 36 * 5 + 59 * 11934
Now multiple of the given terms:
=> 180 + 704106
Addition of the last two-term
=> 7,04,286
Therefore, the simplified Answer to the given expression will be 7,04,286.
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PLEASE HELP!!
the variables x and y have a proportional relationship and y=40 when x=30 what is the value of x when y=50
Refer to the given image
Kevin was solving for the area of the triangle below. 8 in: 5 in The formula for area of a triangle is A = =bh. Kevin's answer for the area of this triangle was 40 inches?. Is Kevin's solution correct? Why or why not? If not, what was his mistake? If not, what is the correct solution for the area of this triangle?
Kevin's solution is incorrect because he used wrong formula.
Correct area of triangle = 20 square inches.
What is area of triangle?The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height,
i.e. A = 1/2 × b × h
Given,
Height of triangle h = 8 inches
Base of the triangle b = 5 inches
Formula for area of triangle A = 1/2(b h)
A = 1/2 (8 × 5)
A = 40/2
A = 20 square inches.
Area by given formula for area of the triangle A = b h
A = 8 × 5
A = 40
Since actual area of the triangle is 20 square inch, Kevin found the area with wrong formula.
Actual area of triangle is 20 square inches.
Hence, Kevin's solution is incorrect, as the formula used is wrong.
20 square inches is correct area of the triangle.
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1. X2 +6x +3=0
2.5^2726-6=0
3.12-8+-5:0
4.X(X+8)=-20
5.x- +4x-2=0
Help solve with explaining
1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.
what is equation ?The statistic is said to be in its simplest form is divided into its smallest equivalent fraction. What to do to find the most basic form. Look for common factors in the denominator and numerators. Confirm a fractional integer to verify if it qualifies as a prime number. A statement having two equal sides and an equaled sign in the middle is called an equation in mathematics. The general form of any equation contains the diplomas of all the variables in descending order. The conventional form of an equation is an x + b = 0. The general form of a linear function with two variables is an x + b y + c = 0. (or something similar). An identification holds true no matter what value is given to the variables.
given
equation 1 ) X2 +6x +3=0
by discriminant method
x =(6+√48)/2
=3+2√ 3
= 6.464.
equation 2) 5^2 + 2s - 6 = 0
= 25 + 2s - 6 = 0
= 19 = - 2s
s = 9.5
1) X2 + 6x + 3 = 0. is resolved using the discriminant technique, and the value of s for the second equation, 52 + 2s - 6 = 0, is 9.5.
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Use the definition of continuity and the properties of limits to show that the function
g(x) = (x2 - 3x - 10)(x2 + 2x2 - 5x + 4) is continuous at x = -1.
The given function
g(x) = [x² - 3x -10][x²+ 2x² -5x +4 ]
is continuous at x = -1,
What is continuity ?In mathematics, The function is called as continuous at the particular value of x, if right hand limit, left hand limit and the value of function at x all are equal.
RHL = LHL = F(x)
Limit exist and continuous
Given that,
F(x) = [x² - 3x -10][x²+ 2x² -5x +4 ]
To check whether it is continuous at x = -2
First taking LHL,
[tex]\lim_{h \to \00}[/tex] [(-1-h)² - 3(-1-h) -10][(-1-h)²+ 2(-1-h)² -5(-1-h) +4 ]
[tex]\lim_{h \to \00}[/tex] [(-1-0)² - 3(-1-0) -10][(-1-0)²+ 2(-1-0)² -5(-1-0) +4 ]
⇒ -6 x 12
⇒ -72
Now, taking RHL
[tex]\lim_{h \to \00}[/tex] [(-1+h)² - 3(-1+h) -10][(-1+h)²+ 2(-1+h)² -5(-1+h) +4 ]
[tex]\lim_{h \to \00}[/tex] [(-1+0)² - 3(-1+0) -10][(-1+0)²+ 2(-1+0)² -5(-1+0) +4 ]
⇒ -6 x 12
⇒ -72
The value at x = -1
F(-1) = [(-1)² - 3(-1) -10][(-1)²+ 2(-1)² -5(-1) +4 ]
⇒ -6 x 12
⇒ -72
RHL = LHL = F(-1)
Hence Proved, the function is continuous at x = -1
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Suppose you deposit $1000 in a college fund that pays 7.2% interest compounded annually. Find the account balance after 5 years.
Answer:
To find the account balance after 5 years, we need to calculate the compound interest earned during this period. The formula for compound interest is:
A = P × (1 + r/n)^(nt)
where:
A = the final amount of the investment
P = the principal investment amount ($1000)
r = the annual interest rate (7.2%)
n = the number of times that interest is compounded per year (1)
t = the number of years the investment is held (5)
So, plugging in the values into the formula, we get:
A = 1000 * (1 + 0.072/1)^(1 * 5)
A = 1000 * (1.072)^5
A = 1000 * 1.44444444
A = $1444.44
So, the account balance after 5 years would be $1444.44.
Answer:
Step-by-step explanation: I could mostly say $36,000. How I did it was:
1000x7.2x5=36,000
Could you find this helpful???
If x and y are in direct proportion and y is 6 when x is 12, find y when x is 2.
The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If x and y are in direct proportion. Then the equation is given as,
y ∝ = x
y = kx
At x = 12 and y = 6, then the value of 'k' is given as,
6 = 12k
k = 1/2
Then the equation is given as,
y = (1/2)x
If the value of the variable 'x' is 2. Then the value of y is given as,
y = (1/2) 2
y = 1
The relationship between x and y is y = (1/2)x. When x is 2, then the value of 'y' is 1.
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7. Write and graph an exponential function frepresented by the table
Then compare the graph to the graph of the parent function.
Answer:
f(x) = 2[tex](\frac{1}{2}) ^{x}[/tex]
Step-by-step explanation:
The y intercept is 2 where in the parent function it is 1. In the parent function, as x is increasing y is increasing. In this function as the x is increasing the y is decreasing.
Help
__________________
The minimum = (-11, -2)
And the maximum = (2, 5).
What is differentiation?Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.
Given:
The function,
f(x) = ∛(x + 3).
The graph of the function is given in the attached image.
f'(x) = d/dx{∛(x + 3)}
= 1/{3(x + 3[tex])^{2/3}[/tex]}
The critical point = (-3, 0)
The minimum = (-11, -2)
And the maximum = (2, 5).
Therefore, all the required values are given above.
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Bisecting Bakery sells cylindrical round cakes. The most popular cake at the bakery is the red velvet cake. It has a radius of 13 centimeters and a height of 15 centimeters.
If everything but the circular bottom of the cake was iced, how many square centimeters of icing is needed for one cake? Use 3.14 for π and round to the nearest square centimeter.
A. 531 cm2
B. 612 cm2
C. 1,755 cm2
D. 2,286 cm2
The number of square centimeters of icing that would be needed for one cake is equal to: C. 1,755 cm².
How to determine the surface area of the cylindrical round cakes?Since everything but the circular bottom of the cake was iced, the number of square centimeters of icing that would be needed for one cake can be calculated by using this mathematical expression:
Total surface area of cake = Curved surface area of cake + area of the top
Total surface area of cake = 2πrh + πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the total surface area of cake formula, we have;
Total surface area of cake = (2 × 3.14 × 13 × 15) + (3.14 × 13²)
Total surface area of cake = 1224.6 + 530.66
Total surface area of cake = 1755.26 ≈ 1755 square centimeter.
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Answer: C. 1,755 cm2
Hope this helps
The mass of a radioactive substance follows a continuous exponential decay model, with the decay rate parameter 4% per day. A sample of this radioactive substance has an initial mass of 2.05 kg. Find the mass of the sample after four days. Round your answer to two decimal places.
The mass of the sample after 4 days is 1.54 kg.
What is exponential decay?Exponential decay can be defined as the process in which a quantity decreases over time with the rate of decrease becoming proportionally smaller as the quantity gets smaller.
The formula for exponential decay is given by:
m(t) = m0 * e^(-kt)
where m(t) is the mass of the substance after time t
M0 is the initial mass
k is the decay rate parameter
E is the base of natural logarithms
Plugging in the values:
m(4) = 2.05 * e^(-0.04 * 4)
m(4) = 1.54 kg
Therefore, The mass of the sample after 4 days is 1.54 kg.
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In the given diagram TP and TR are tangents. IfZPTR = 40°, find the value of ZPQR.
Note that the angle labeled ∠PQR is given as 70°
First, note that the Lengths of tangents drawn from external points to a circle are equal in length. This means that:
Length of PT = Lenght of TR
This makes Δ TPR and Isosceles Triangle.
This also makes ∠P = ∠R..............................1
Thus:
∠P + ∠R + ∠T = 180°
Given expression 1 above,
we can say:
x + x + 38° = 180°
Thatis 2x = 180 - 40
2x = 140°
x = 140/2
x = 70°
Note that Line TP is parallel to Line QR and Line PQ is a transversal line. Thus, ∠P and ∠Q are co-interior angles. This means that:
∠P + ∠Q = 180°
Recall that:
70 + 40 + ∠Q = 180°
∠Q = 180 -70 -40
∠Q = 70°
Thus: ∠ PQR = 70°
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Full Question:
See attached image.
0
9
You deposit $200 each month into an account earning 7% interest compounded monthly.
a) How much will you have in the account in 35 years?
https://ohm.lumenlearning.com/assess2/?cid=69660&aid=51 5/#/skip/
b) How much total money will you put into the account?
$
c) How much total interest will you earn?
$
Question Help: Video 1 Video 2
Answer:
Step-by-step explanation:
The monthly compound interest formula.
Future Value = monthly deposit x (1 + r) - 1/r
r = .07/12 = .00583
n = total number of time for compound = 35 years x 12 months/1 year = 420 months
PMT = monthly deposit = $200
Future Value = $200 x (1 + .00583)⁴²⁰ - 1/.00583
Future Value = $394,001.64 in 35 years
Total money you put into the account.
$200 x 420 months = $84,000
Total interest earned.
$394,001.64 - $84,000 = $310,001.64
Sebastian is preheating his oven before using it to bake. The initial temperature of the oven is 75° and the temperature will increase at a rate of 25° per minute after being turned on. What is the temperature of the oven 17 minutes after being turned on? What is the temperature of the oven
t minutes after being turned on?
Temp after 17 minutes:
Temp after t minutes:
Answer: The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven is 75° and it will increase at a rate of 25° per minute after being turned on.
The equation to model the temperature of the oven t minutes after being turned on is:
Temp = 75 + 25t
Where Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.
For example, if we want to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:
Temp = 75 + 25 * 17 = 75 + 425 = 500°
So, the temperature of the oven 17 minutes after being turned on is 500°.
In general, the temperature of the oven t minutes after being turned on can be found by substituting the value of t into the equation:
Temp = 75 + 25t.
Step-by-step explanation:
The temperature of an oven can be modeled by a linear equation. In this case, the initial temperature of the oven will be; 75° and it will increase at a rate of 25° per minute after being turned on.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation to model the temperature of the oven t minutes is:
Temp = 75 + 25t
Where, Temp is the temperature of the oven in degrees and t is the number of minutes after being turned on.
For example, if we need to find the temperature of the oven 17 minutes after being turned on, we can substitute t = 17 into the equation:
Temp = 75 + 25 * 17 = 75 + 425
Temp = 500°
Thus, the temperature of the oven 17 minutes after being turned on is 500°.
In general, the temperature of the oven t minutes after being turned on can be find by substituting the value of t into the equation:
Temp = 75 + 25t.
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pedro is selling apples ata farmers market he starts with 35 1/2 pounds of apple he sells half of them in the morning 8/9 of what is left in the afternoon and 3/4 of whats left in the evening how many pounds of apple id pedro not sell what fraction of the total amount of the apples did he not sell
please make it right for a 100 points
PLEASE HELP!!!!!!!!
TW=12, VW=8, What is the length of UW?
Answers:
A UW=8
B UW=12
C UW=4
D UW=18
The length of the UW of the triangle is 18. The correct option is D.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
The length UW will b calculated as:-
First, in ΔTWU apply the Pythagorean theorem,
TU² = UW² + 12²
TU² = UW² + 144
In ΔTWV apply the Pythagorean theorem,
VT² = 12² + 8²
VT² = 208
Apply Pythagorean theorem in ΔVTU,
( 8 + UW)² = VT² + TU²
Substitute the value of TU² in the above equation,
( 8 + UW)² = 208 + UW² + 144
UW² + 16UW + 64 = UW² + 208 + 144
16UW = 288
UW = 288 / 16 = 18
Therefore, the length of UW is 18.
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This graph shows the function f (x) = 6x -12 and g(x)=(1/2)x -4
What are the solutions of the equation -6x -12= (1/2)x -4?
The solution of the system of equations -6x -12= (1/2)x -4 include the following: D. x = -4 and x = -2.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-axis, which is given by x = -4 and x = -2.
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Select the correct answer from each drop-down menu. The number - 7/5 is
We can conclude, the number -7/5 is less than the number 1 1/5.
How to know whether a fraction is greater or less than other?One of the ways to know how a fraction compares to another is by simplifying the fraction, which can be done by dividing the numerator by the denominator.
Let's simplify the fractions given:
-7/5 = -1.4
-1 1/5 = 1 + 0.2 = -1.2
Moreover, in the case of negative numbers those that are closer to 0 are greater. Based on this, -1.2 is greater than -1.4, which means -7/5 is less than the number 1 1/5.
Note: This question is incomplete; here is the missing section:
The number -7/5 is less or greater than the number 1 1/5.
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A fair spinner contains the numbers 1, 2, 3, 4, and 5. For an experiment, the spinner will be spun 5 times. If Event A = the spinner lands on numbers all less than 3, what is an outcome of Event A?
Any sequence of five spins that consists only of numbers 1 and 2 would be an outcome of Event A.
What is an outcome of Event A?From the question, we have the following parameters that can be used in our computation:
Event A = the spinner lands on numbers all less than 3
An outcome of Event A would be a sequence of five spins on the spinner that result in numbers all less than 3,
For example: 1, 2, 1, 2, 1.
See that each number in the above sequence is less than 3
Hence, the event A represents outcomes less than 3
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Jill and Matt plan to get their homework finished within one hour. Matt
completes his Math homework in 3/5 hour. Jill completes her Math
homework in 5/6 hour remaining. Who completes the homework faster,
and by how many minutes?
Answer: Matt completes his homework faster than Jill by 14 minutes
Step-by-step explanation:
5*12= 60 so if I multiply 3 by 12 I get how many minutes it took Matt to finish her homework. (which was 36 minutes)
6*10=60 so if I multiply 5 by 10 I get how many minutes it took Jill to finish her homework (which was 50 minutes)
50 minus 36 is a difference of 14
Mayra's brother is driving back from college to visit. His college is 330 miles away. After an hour of
driving, he still has 275 miles to go. If the roads are clear, he'll be able to keep up that pace for the
whole drive. Write a linear function to model how much further he'll have to go over time.
He has 5hrs to drive and 275 miles to drive to cover to arrive at the university.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
His college is 330 miles away.
After an hour of driving, he still has 275 miles to go.
If the roads are clear, he'll be able to keep up that pace for the whole drive.
If he drives 55 miles in 1 hr
he would drive 330 miles in
=6hrs.
his total travel time is 6 hr
He has 5hrs to drive and 275 miles to drive.
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