Answer:
a) Rate of change of amount
[tex]A'(t) =110e^{0.055t}[/tex]
b) &170.79
c) 0.21
Step-by-step explanation:
We are given the following in the question:
The balance is given by the equation:
[tex]A(t) =- 2000e^{0.055t}[/tex]
where t is the time in years and the initial investment is $2000 when compounded continuously.
a) Rate of change of amount
[tex]\dfrac{d(A(t))}{dt} = \dfrac{d}{dt}(2000e^{0.055t})\\\\\dfrac{d(A(t))}{dt} = 2000e^{0.055t}\times 0.055\\\\\dfrac{d(A(t))}{dt} =110e^{0.055t}[/tex]
b) We have to find the value of A'(8)
[tex]A'(t) =110e^{0.055t}\\A'(8) = 110e^{0.055(8)} = 170.79[/tex]
Interpretation:
The future value of 9 year investment of $2000 will be $170.79 more than the future value of 8 year investment.
c) Comparison
Approximation = $171
Actual change = $170.79
Difference =
[tex]\text{Approximation - Actual change}\\=171 - 170.79\\=0.21[/tex]
Thus, the error is 0.21
The formula for dA/dt is 2000(0.055)e^(0.055t). A'(8) is found by substituting t=8 into dA/dt. To compare the approximation of $171 to the actual change, subtract the initial investment from the new balance after 8 years.
Explanation:a. To find the formula for dA/dt, we differentiate the equation A(t) = 2000e^(0.055t) with respect to t. Using the chain rule, we have dA/dt = 2000(0.055)e^(0.055t).
b. To find A'(8), we substitute t = 8 into the expression for dA/dt. Plugging in the values, we get A'(8) = 2000(0.055)e^(0.055(8)). This will give us the rate of change of the balance after 8 years.
c. To compare the approximation of $171 to the actual change, we subtract the initial investment of $2000 from the new balance after 8 years. The approximation is $171, so the actual change is A(8) - 2000. Plugging in the values, we get A(8) - 2000 = 2000e^(0.055(8)) - 2000.
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Simplify. Identify any x-values for which the expression is undefined. HELP ASAP!!
The required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression.
= x ² + 8x + 12 / x² - 2x -8
= (x + 6)(x + 2) / (x + 2)(x - 4)
Since, if we put x = -2 and x = 4, the expression will we undefined.
And,
= x + 6 / x -4
Thus, the required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.
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StatTutor: Independence and the multiplication rule A bent coin has probability 0.55 of landing heads up. What is the probability that five tosses of the coin will result in at least one heads? Use four decimal places in your answer.
Answer:
0.9815
Step-by-step explanation:
P(head) = 0.55
P(tail) = 1 - 0.55 = 0.45
P(Atleast one head)
= 1 - P(all tails)
= 1 - 0.45⁵
= 0.9815471875
= 0.9815
In probability, the complementary event of 'at least one heads' is 'getting no heads'. Calculate the probability of the complement (getting tails five times) and subtract it from 1. The result is 0.8155.
Explanation:This type of problem deals with
probability
. The best way to approach it is to consider the complementary event. In this case, the complementary event to getting 'at least one heads' is 'getting no heads'. The probability of getting heads is 0.55, so the probability of getting tails is 1 - 0.55 = 0.45. This is because the sum of the probabilities of all possible outcomes (heads or tails) equals 1. So, the probability of getting tails on all five tosses is (0.45)^5 = 0.1845. Now, we subtract this from 1 to get the probability of the desired event, 'at least one heads': 1 - 0.1845 = 0.8155. Therefore, the probability of getting at least one heads in five coin tosses is 0.8155.
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A watercolor painting is 20 inches long by 9 inches wide. Raymond makes a border around the watercolor painting by making a mat that adds 3 inches to each side of the length and the width. What is the area of the mat
The mat adds 3 inches to each side, so the length would be 3+20 = 23 inches. The width would become 3 + 9 = 12 inches.Area = Length x width:
23 x 12 = 276 square inches
DONT SKIP HELP PLZZZZZZZZZZZZZ
Using the distance formula, d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (-5, -2) and point (8, -3) rounded to the nearest tenth?
10.3 units
12.6 units
1 unit
13 units
Option D: The distance between the two points is 13 units
Explanation:
It is given that the two points are [tex](-5,-2)[/tex] and [tex](8,-3)[/tex]
We need to determine the distance between the two points.
It is also given that the distance between the two points can be determined using the formula,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substituting the points [tex](-5,-2)[/tex] and [tex](8,-3)[/tex] for the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Thus, we get,
[tex]d=\sqrt{(8-(-5))^2+(-3-(-2))^2}[/tex]
Simplifying, we have,
[tex]d=\sqrt{(8+5)^2+(-3+2)^2}[/tex]
Adding the terms, we get,
[tex]d=\sqrt{(13)^2+(-1)^2}[/tex]
Squaring the terms, we have,
[tex]d=\sqrt{169+1}[/tex]
Adding the terms, we get,
[tex]d=\sqrt{170}[/tex]
Simplifying and rounding off the value to the nearest tenth, we have,
[tex]d=13.0 \ units[/tex]
Hence, the distance between the two points is 13 units.
Therefore, Option D is the correct answer.
The variable z is directly proportional to x. When x is 10, z has the value 140.
What is the value of z when x = 20?
Answer: z = 280
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable causes an increase in the value of the other variable. Also, a decrease in the value of one variable causes an decrease in the value of the other variable.
The variable z is directly proportional to x. If we introduce a constant of variation, the expression would be
z = kx
When x is 10, z has the value 140. It means that
140 = 10k
k = 140/10
k = 14
The equation becomes
z = 14x
the value of z when x = 20 is
z = 14 × 20
z = 280
Match the answers on the left with their properly rounded answers.a. 264.34928 rounded to the nearest tenth b. 264.34928 rounded to the nearest thousandth c. 265.34928 rounded to the nearest one d. 264.34928 rounded to the nearest hundreds e. 265.34928 rounded to the nearest tens f. 264.34928 rounded to the nearest hundredths
Answer: a) 264.3, b) 264.349, c) 265, d) 300, e) 260, f) 264.35.
Step-by-step explanation:
Since we have given that
264.34928 rounded to the nearest tenth.
So, it becomes [tex]264.3[/tex]
264.34928 rounded to the nearest thousandths.
So, it becomes [tex]264.349[/tex]
264.34928 rounded to the nearest one.
So, it becomes [tex]265[/tex]
264.34928 rounded to the nearest hundreds.
So, it becomes [tex]300[/tex]
264.34928 rounded to the nearest tens.
So,it becomes [tex]260[/tex]
264.34928 rounded to the nearest hundredths.
So, it becomes [tex]264.35[/tex]
Hence, a) 264.3, b) 264.349, c) 265, d) 300, e) 260, f) 264.35.
a. 264.34928 rounded to the nearest tenth = 264.3
b. 264.34928 rounded to the nearest thousandth = 264.349
c. 265.34928 rounded to the nearest one = 265
d. 264.34928 rounded to the nearest hundred = 264.35
e. 265.34928 rounded to the nearest ten = 265.3
f. 264.34928 rounded to the nearest hundredth = 264.35
Here are the answers matched with their properly rounded values along with explanations:
a. 264.34928 rounded to the nearest tenth: 264.3
Explanation: The tenths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.3.
b. 264.34928 rounded to the nearest thousandth: 264.349
Explanation: The thousandths digit is 9, which is greater than or equal to 5. So, you round up to 264.349.
c. 265.34928 rounded to the nearest one: 265
Explanation: The nearest one for 265.34928 is simply 265 because it is already a whole number.
d. 264.34928 rounded to the nearest hundred: 264.35
Explanation: The hundredths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.35.
e. 265.34928 rounded to the nearest tens: 270
Explanation: The tens digit is 6, and the digit immediately to the right of it is 5 or greater. So, you round up to 270.
f. 264.34928 rounded to the nearest hundredth: 264.35
Explanation: The hundredths digit is 4, and the digit immediately to the right of it is 9, which is greater than or equal to 5. So, you round up to 264.35.
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What is the missing reason for the seventh statement?
a. CPCTC
b. AA postulate
c. All right triangles are similar.
d. Transitive property of similarity.
Answer:
b. AA postulate
Step-by-step explanation:
In a certain data distribution, 85 is 0.25 standard deviation above the mean and 50 is 1.5 standard deviations below the mean. What value is 0.75 standard deviation below the mean
Answer:
The mean is 80 and the standard deviation is 20. Therefore we have
65 is 0.75 standard deviation below the mean.
Step-by-step explanation:
z = [tex]\frac{x-\mu}{\sigma}[/tex]
Since 85 is 0.25 standard deviations above the mean we have
[tex]0.25 = \frac{85-\mu}{\sigma}[/tex] or 0.25·σ = 85 - μ......1
1.5 = [tex]\frac{\mu-50}{\sigma}[/tex] or 1.5·σ = μ - 50..............2
From 1 we have σ = 340 - 4·μ substituting into 2 gives
1.5·(340 - 4·μ) = μ - 50 ⇒ 510 - 6·μ = μ - 50
7·μ = 560 or μ = 80
Therefore σ = 340 - 4·μ = 340 - 4·80 = 20
A value, x, 0.75 standard deviation below the mean is given by
0.75 = [tex]\frac{80-x}{20}[/tex] which gives 15 = 80 - x or
x = 65.
can someone explain this to me please
the answer is 2023 but idk how u get to that
btw the equation for the population of the rabbits was
[tex]r = 50 {e}^{0.5t} [/tex]
for the year 2016
Step-by-step explanation:
Start by finding when the populations become equal.
C = R
1000e^(0.1t) = 50e^(0.5t)
Divide both sides by 50.
20e^(0.1t) = e^(0.5t)
Divide both sides by e^(0.1t).
20 = e^(0.4t)
Take natural log of both sides.
ln 20 = 0.4t
Multiply both sides by 2.5
t = 2.5 ln 20
t ≈ 7.5
The population of rabbits first exceeds the population of crickets in the middle of the 7th year after 2016, or 2023.
Answer:
8th year
Step-by-step explanation:
r > C
50(e^0.5t) > 1000(e^0.1t)
(e^0.5t)/(e^0.1t) > 20
e^(0.5t-0.1t) > 20
e^0.4t > 20
ln(e^0.4t) > ln20
0.4t × lne > ln20
t > ln(20)/0.4
t > 7.489330685
Population of rabbits first exceeds the population of crickets during the 8th year
simplify by like combining terms: 5+m+m+8m+12-9-4m
Answer: 6m+8
m+m+8m-4m = 6m
5+12-9=8
Answer your following questions based on the quadrilateral is given. You must show all your work and
indicate the property you use to find the answers
The rectangle is given below. Find the measurements of 21, 22 and 23.
The measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.
Solution:
By the property of rectangle,
Opposite sides of rectangle are parallel.
By another property of parallel lines,
If two parallel lines cut by a transversal (diagonal) then alternate interior angles are congruent.
60° and ∠1 are alternate interior angles.
Hence m∠1 = 60°.
In rectangle, all the angles are right angle.
m∠1 + m∠2 = 90°
60° + m∠2 = 90°
Subtract 60° from both sides of the equation.
m∠2 = 30°
In rectangle, all the angles are right angle.
m∠3 = 90°
Hence the measurements of ∠1 = 60°, ∠2 = 30° and ∠3 = 90°.
Directions: Using the digits 0 – 9, no more than one time each,
place a digit in each box to create an equation with a solution x=-1/2
.
Create three such equations.
Three equations with a solution of x = -1/2:
(2x - 1) = 0
(-x + 3) = 1
(4x + 2) = -3
Here are three equations, each created using the digits 0 – 9, with a solution of x = -1/2:
(2x - 1) = 0
Solution: When you solve for x, you get x = -1/2.
(-x + 3) = 1
Solution: Solving for x, you find x = -1/2.
(4x + 2) = -3
Solution: Upon solving for x, the result is x = -1/2.
In each of these equations, the placement of the digits ensures that when you calculate the value of x, it equals -1/2. This demonstrates that it's possible to use the digits 0 – 9 once to form equations with the specified solution.
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Complete question below :
Using the digits 0 – 9, no more than one time each, place a digit in each box to create three equations with a solution x = -1/2.
Which construction of parallel lines is justified by the theorem "when two lines are intersected by a transversal and the corresponding angles are congruent the lines are parallel?"
Answer:
c
Step-by-step explanation:
I think you missed attaching the photo, please see my attachment.
And the correct answer is C,
When you look at where the arc meets the parallel lines, if you create a seam between two points, you get a straight line parallel to the horizontal lines so it makes the corresponding angles are congruent.
The theorem stating that when two lines are intersected by a transversal and the corresponding angles are congruent means the lines are parallel, guides a specific construction method in geometry. This method involves using a transversal to determine if the intersected lines are parallel by comparing corresponding angles.
The theorem 'when two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel' justifies a particular construction of parallel lines in geometry.
This principle is a fundamental aspect of geometric theorems on parallel lines and angles created by a transversal. To construct parallel lines using this theorem, one might follow these steps:
Identify or draw a transversal that intersects two lines.
Measure the corresponding angles created by the intersection of the transversal with these lines.
If the corresponding angles are congruent, then by this theorem, the two lines are determined to be parallel.
This concept is essential in understanding the relationships between angles and lines in a plane, providing a cornerstone for proofs and constructions within geometry.
The tallest living man at one time had a height of 259 cm. The shortest living man at that time had a height of 65.6 cm. Heights of men at that time had a mean of 172.27 cm and a standard deviation of 8.82 cm. Which of these two men had the height that was more extreme?
Answer:
Therefore the shortest man of 65.6 cm was more extreme.
Step-by-step explanation:
A z-test is a statistic test. It is used to determine whether two population mean are different when the variances of the population are known and the sample size large.
[tex]z=\frac{x- \mu}{\sigma}[/tex]
z= the standarized z score
x = the height of sample
μ = mean = 172.27 cm
σ = standard deviation = 8.82 cm
For tallest
x = 259
[tex]z= \frac{259-172.27}{8.82}[/tex]
≈9.83
For shortest
x= 65.6
[tex]z= \frac{65.6-172.27}{8.82}[/tex]
≈ - 12.09
The most extreme value has a z score that the furthest from 0.
Since -12.09 is further from 0 than 9.83.
Therefore the shortest man of 65.6 cm was more extreme.
ALGEBRA 2 HELP!
Find all the zeros
f(x)=[tex]x^{3}+64[/tex]
To find the zeros we have to put:
[tex]f(x)=0[/tex]
Now we have:
[tex]x^3+64=0[/tex]
[tex]x^3=-64[/tex]
[tex]x=\sqrt[3]{-64}[/tex]
[tex]x=-4[/tex]
So, the only zero is x=-4
An airplane pilot fell 370 m after jumping without his parachute opening. He landed in a snowbank, creating a crater 1.5 m deep, but survived with only minor injuries. Assume that the pilot's mass was 84 kg and his terminal velocity was 50 m/s.estimate
Answer:
he ded
Step-by-step explanation:
\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \tohe no alive because ⇆ω⇆π⊂∴∨α∈\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to[tex]\neq \lim_{n \to \infty} a_n \pi \left \{ {{y=2} \atop {x=2}} \right. \leq \neq \beta \beta \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \int\limits^a_b {x} \, dx \geq \geq \leq \leq \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{y=2} \atop {x=2}} \right. \lim_{n \to \infty} a_n \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \beta x_{12 \lim_{n \to[/tex]
George is a fast worker. He can mop 50 ft2 in 1 minute. The court is shaped like a rectangle. It is 95 ft long by 50 ft wide. How many minutes will it take George to mop the gym floor?
a.) 95 minutes
b.) 3958.3 minutes
c.) 4,750 minutes
d.) 190 minutes
A. 95 95x50=4750 then you divide 4750 by 50 and you get your answer
To find how long George will take to mop the floor, calculate the area of the court (95 ft x 50 ft = 4,750 ft²) and divide it by his mopping rate (50 ft²/min). The calculation shows it will take George 95 minutes to mop the floor.
Explanation:To determine how long it will take George to mop the gym floor, we first calculate the area of the rectangular court.
Multiplying the length by the width gives us the total area that needs to be mopped:
Area = length × widthArea = 95 ft × 50 ftArea = 4,750 ft²Now, since George can mop 50 ft² in 1 minute, we divide the total area by the rate at which George can mop:
Time = total area / mopping rateTime = 4,750 ft² / 50 ft² per minuteTime = 95 minutesTherefore, it will take George 95 minutes to mop the gym floor, which corresponds to option (a).
Hannah is making calzones to sell her restaurant she starts with nine cans of tomato sauce and then use is 9/10 of the cans for her first batch of calzones how many cans of tomato sauce does Hannah use for the first batch of calzones
Answer:
About 8 cans.
Step-by-step explanation:
Given:
She starts with nine cans of tomato sauce.
Then use is 9/10 of the cans for her first batch of calzones
To find:
How many cans of tomato sauce does Hannah use for the first batch of calzones ?
Solution:
She starts with number of cans = 9
Then use is [tex]\frac{9}{10}[/tex] of the cans.
Now, we will find number of cans used for the first batch of calzones by multiplying number of cans she starts with by fraction of cans she used for the first batch of calzones .
[tex]\frac{9}{10} of 9 cans = \frac{9}{10} \times9\\\frac{81}{10} = 8.1[/tex]
Therefore, number of cans used for the first batch of calzones is about 8 cans.
The output of a plant is 4335 pounds of ball bearings per week (five days). If each ball bearing weighs 0.0113 g, how many ball bearings does the plant make in a single day
Answer:
The plant makes 34,802,178 ball bearings in a single day
Step-by-step explanation:
The total output of a plant in a 5-day week is 4335 pounds
Each ball bearing weighs 0.0113g
We are to calculate the number of ball bearings made per day
First, we ensure both mass are in the same unit
Now 1 pound =453.5924 grams
4335 pounds=453.5924 X 4335 =1966323.054 grams
Number of bearings made in a week therefore
= 1966323.054 /0.0113=174010889.7
≈174010890 (to the nearest whole number)
Since there are 5 days in a week of production,
Daily Production=174010890/5
=34802178
The plant makes 34,802,178 ball bearings in a single da
30 60 90 triangles (quick answers please)
1) EF = 2 and DF = 4
2) KL = 4√3 and JL = 8
3) ST = 6 and RS = 6√3
4) PQ = 4.5√3 and RQ = 4.5
Step-by-step explanation:
Rules for special triangles 30°,60°,90° :
The length of the side opposite to 30° is a.The length of the side opposite to 60° is a√3.The length of the side opposite to 90° is 2a.1) DE = 2√3 is opposite to 60°
⇒ 2√3 = a√3
⇒ a = 2
EF = a which is opposite to 30°.
⇒ EF = 2
DF = 2a which is opposite to 90°.
⇒ DF = 4
2) KJ = 4 is opposite to 30°
⇒ a = 4
KL = a√3 which is opposite to 60°.
⇒ KL = 4√3
JL = 2a which is opposite to 90°.
⇒ JL = 8
3) RT = 12 is opposite to 90°
⇒ 2a = 12
⇒ a = 6
ST = a which is opposite to 30°.
⇒ ST = 6
RS = a√3 which is opposite to 60°.
⇒ RS = 6√3
4) PR = 9 is opposite to 90°
⇒ 2a = 9
⇒ a = 4.5
PQ = a√3 which is opposite to 60°.
⇒ PQ = 4.5√3
RQ = a which is opposite to 30°.
⇒ RQ = 4.5
What is an equation of the line that passes through the points (−5,−7) and (5,1)?
Answer:
y = [tex]\frac{4}{5}[/tex] x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 5, - 7) and (x₂, y₂ ) = (5, 1)
m = [tex]\frac{1+7}{5+5}[/tex] = [tex]\frac{8}{10}[/tex] = [tex]\frac{4}{5}[/tex], thus
y = [tex]\frac{4}{5}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (5, 1), then
1 = 4 + c ⇒ c = 1 - 4 = - 3
y = [tex]\frac{4}{5}[/tex] x - 3 ← equation of line
Chuy wants to buy a new television. The television costs $1,350. Chuy decides to save the same amount of money each week, for 27 weeks. After 8 weeks Chuy saved $440. Which of the following conclusions can you make about Chuy's plan? A. Chuy has a good plan and will have exactly $1,350 saved at the end of 27 weeks. B. Chuy must increase the amount he saves each week in order to meet his goal at the end of 27 weeks. C. Chuy will save more than he needs and will meet his goal in less than 27 weeks.
Answer: option C is the correct answer.
Step-by-step explanation:
The television costs $1,350. Chuy decides to save the same amount of money each week, for 27 weeks. After 8 weeks Chuy saved $440. This means that the amount that she saved per week is
440/8 = $55
If she saves $55 in 8 weeks, the number of weeks left is
27 - 8 = 19 week
Amount that she would save in 19 weeks is
19 × 55 = 1045
Total amount saved in 27 weeks is
1045 + 440 = $1485
Therefore, the conclusion that you can make about Chuy's plan is
C. Chuy will save more than he needs and will meet his goal in less than 27 weeks.
Answer:
c
Step-by-step explanation:
Which statements are true about the ordered pair (10, 5) and the system of equations? {2x−5y=−5 x+2y=11 Select each correct answer. The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true. The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true. The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair (10, 5) is a solution to the system because it makes both equations true.
Answer:
The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.
Step-by-step explanation:
2x−5y=−5
x+2y=11
In equation (1), substitution of (10,5)
2x−5y=2(10)-5(5)=20-25=-5
However in equation (2), on substitution of (10,5)
x+2y=10+2(5)=10+10=20 ≠11.
However, the solutions of the simultaneous equations
2x−5y=−5
x+2y=11
are (5,3)
The ordered pair (10, 5) is a solution to the first equation of the system but not the second, which means it is not a solution to the entire system of equations.
Explanation:To determine if the ordered pair (10, 5) is a solution to the given system of equations, we need to substitute x with 10 and y with 5 into each equation and see if the equations hold true:
First equation: 2x - 5y = -5 becomes 2(10) - 5(5) = -5 which simplifies to 20 - 25 = -5. This is true, so (10, 5) is a solution to the first equation.Second equation: x + 2y = 11 becomes 10 + 2(5) = 11 which simplifies to 10 + 10 = 11. This is false, so (10, 5) is not a solution to the second equation.Since the ordered pair does not satisfy both equations, it is not a solution to the system of equations. Therefore, the correct statements are:
The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true.The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.
Find 6/7 of £60 to the nearest penny.
6/7th of £60 to the nearest penny is £51. 43 penny
Step-by-step explanation:
The amount = £60
The fraction that needs to be decided= 6/7th part
For solving the problem, we need to find out the 6/7th part of £60 and then round off the answer to the nearest 2 digits after decimals.
Thus the amount to the nearest penny= (6/7) *60
Amount= £51.42857714285
When the above amount is rounded off to the nearest penny than the amount becomes= £51.43 meaning 51 pounds and 43 pennies.
Find the probability of winning a lottery in which you win when the six numbers on yourticket must match the six unique numbers selected from a set of positive integers not ex-ceeding 30. The order of the numbers on your ticket, do not matter as in order to win, allyou must do is match all the numbers.
Answer:
0.00016841%
Step-by-step explanation:
The winning group of numbers consist of 6 unique number inside a pool of 30 numbers. To calculate the number of groups of 6 that can be done in a pool of 30 numbers, we do a combination of 30 chosen 6 (groups of 6 numbers in 30 numbers).
The formula of combination is:
C(n,p) = n![p!*(n-p)!]
In our case, n=30 and p=6, so we have
C(30,6)=30!/(6!24!) = 30*29*28*27*26*25/(6*5*4*3*2) = 593775
As we have 593775 numbers of different possibilities of winning ticket, the probability of winning one over this value:
p = 1/593775 = 0.0000016841 = 0.00016841%
Other way to do this question is:
We have to match all 6 numbers. The first number to match have a chance of 6 over 30 to be guessed right, as there are 6 winning number in a pool of 30.
The second number to match have a chance of 5 over 29, as we already picked one winning number, and have only 29 choices left.
Then, following this logic, we have the other 4 numbers with chance 4/28, 3/27, 2/26 and 1/25.
Multiplying all these chances, we have:
p = (6*5*4*3*2*1)/(30*29*28*27*26*25) = 0.0000016841 = 0.00016841%
Vicky has 2 jobs offers for teaching. She just finished her Master’s Degree in mathematics education.
A. She can work at Southside High School as a teacher with a base salary of $43,600 per year. She will also coach JV softball which will add another $900 to her annual salary. The contract suggests the school will be expecting her 190 days but she will be provided with 10 sick days. So, she must actually work a minimum of 180 days (any less and her salary will be reduced). Each day will consist of 8 working hours. With this school she will be provided with free life insurance for $15,000 of coverage. Her health & dental or medical premiums are $78/month. Finally, the school system would require her to automatically invest 5% of his her monthly income for retirement.
B. She can work at Central Tech College as a math instructor. She will be paid $900 for each credit hour she teaches. During the course of her first year of teaching, she would teach a total of 50 credit hours. The college expects she will work a minimum of 170 days (any less and the salary would be reduced) and 8 hours each day. At the college she will have to pay $3 per month for a life insurance policy of $25,000. Her health & dental or medical premiums are $85 per month. Finally, the company would require her to automatically invest $200 per month for retirement.
What is Vicky's Gross Monthly Income for the job at Southside High School?
Answer:
I have a feeling its B
Step-by-step explanation:
Vicky's Gross Monthly Income for the job at Southside High School is $3708.33.
What is Gross Income?Gross income of an individual is the income he/she receives before deduction and taxes.
Given that,
Base salary per year = $43,600
Income for coaching JC softball = $900
Free life insurance coverage = $15,000
Health & dental or medical premiums = $78/month
Gross income is the income an employee receives before all the deductions.
Insurance premiums are deducted from the base salary. So it is not included in gross income.
Annual Gross income = $43,600 + $900 = $44,500
Monthly Gross Income = $44,500 / 12 = $3708.33
Hence the monthly gross income is $3708.33.
Learn more about Gross Income here :
https://brainly.com/question/547727
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4. Explain the meaning of a level of significance of 5%. Why is a level of
significance needed for every hypothesis test?
Answer:
5% significance level indicates the level of risk, error or exactness. It guides our conclusion on which hypothesis a data supports
Level of significance defined as the possibility, probability or chances of rejecting a null hypothesis when it's results is valid.
For every statistical hypothesis, the result has propency or likeliness to be exact or not. That is, it has chances of containing a type of error referred to as level of significance.
Now, a 5% significance level implies that, the statistical results or analysis has 95% reliability or confidence level.
In other words, a 5% significance level indicates that a result has 0.05 RISK level.
The level of significance is needed for every hypothetical test because it indicates validity of each hypothesis data. It gives confidence such that one is at peace to know the hypothesis a particular data supports
Please I am really Confused If you can help that would be great!
Answer:
The answer to your question is Ariel is correct, x = 27 ft
Step-by-step explanation:
Data
angle = Ф = 47°
Adjacent side = 25
Opposite side = x
Process
1.- To solve this problem, we must use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is tangent.
tan Ф = Opposite side / Adjacent side
- Solve for Opposite side
Opposite side (x) = Adjacent side x tan Ф
-Substitution
x = 25 tan 47
x = 25 (1.0724)
-Result
x = 26.8 ≈ 27 ft
Ariel is correct
Answer:
Incorrect angle; 23 feet
Step-by-step explanation:
She has marked the angle incorrectly
Angle of depression is marked between the line of sight and the hypotenuse
The angle she should use is:
90 - 47 = 43
tan(43) = x/25
x = 25tan(43)
x = 23.31287715
REN fine six peanuts, four raisins, 3 cranberries, and 5 chocolate chips in a handful of trail mix. For every 9 pieces in Ren's handful of trail mix there are 2
Answer:
2 raisins.
Step-by-step explanation:
Let x represent total number of required ingredient.
We have been given that Ren finds 6 peanuts, 4 raisins, 3 cranberries, and 5 chocolate chips in a handful of trail mix. We are asked to find of which ingredient Ren will have 2 pieces for a total of 9 pieces.
First of all, we will find total number of ingredients by adding each ingredient as:
[tex]\text{Total number of ingredients}=6+4+3+5[/tex]
[tex]\text{Total number of ingredients}=18[/tex]
Now, we will use ratio to solve for our given problem as:
[tex]\frac{\text{Required ingredient}}{\text{Total ingredient}}=\frac{2}{9}[/tex]
[tex]\frac{x}{18}=\frac{2}{9}[/tex]
[tex]\frac{x}{18}\cdot 18=\frac{2}{9}\cdot 18[/tex]
[tex]x=\frac{2}{1}\cdot 2[/tex]
[tex]x=4[/tex]
Since there are 4 raisins, therefore, for every 9 pieces in Ren's handful of trail mix there are 2 raisins.
12. What three things should you be sure to do before signing a contract?
Answer: 1. Pay clear attention to details of the contract
2. Negotiate
3. Hire a lawyer
Step-by-step explanation:
Pay clear attention by reading the contract agreement over and over again to be sure you are clear with terms and conditions stated.
Negotiate if need be, such that the terms are jointly agreed upon. It is essential to negotiate on the relevant terms and come to a mutual agreement so that there is no misunderstanding after the contract has been signed.
In hiring a lawyer, it is important to note that contract documentation often contains legal term that requires deep analysis. It is better to be clear and take precautions before a deal is concluded.