Answer:
Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.
Step-by-step explanation:
To solve this problem, we can use trigonometry. The angle of climb is 15 degrees, which means that the ratio of the change in altitude to the horizontal distance traveled is the tangent of 15 degrees:
tan(15°) = change in altitude / horizontal distance
We can rearrange this equation to solve for the change in altitude:
change in altitude = horizontal distance x tan(15°)
Substituting the given values, we get:
change in altitude = 2 miles x tan(15°)
We can convert the distance to feet by multiplying by 5280:
change in altitude = 2 miles x 5280 feet/mile x tan(15°)
Using a calculator, we get:
change in altitude ≈ 514.77 feet
Rounding to the nearest hundredth of a foot, the change in altitude is approximately 514.77 feet.
An interior angle of a regular polygon measures 140 degrees how many sides does the polygon have
 In a triangle, the second angle measures two times the first. The measure of the third angle is 170° more than the measure of the second. Find the measures of the three angles
Answer: Let's call the first angle "x".
From the problem statement, we know that the second angle is two times the first, so:
Second angle = 2x
We also know that the third angle is 170° more than the second angle, so:
Third angle = Second angle + 170°
Third angle = 2x + 170°
We know that the sum of the three angles in a triangle is 180°, so we can set up an equation:
x + 2x + (2x + 170°) = 180°
Simplifying and solving for x:
5x + 170° = 180°
5x = 10°
x = 2°
So the first angle is 2°. Using this value, we can find the other two angles:
Second angle = 2x = 2(2°) = 4°
Third angle = 2x + 170° = 2(2°) + 170° = 174°
Therefore, the three angles in the triangle measure 2°, 4°, and 174°.
Step-by-step explanation:
I will give brainliest to whoever answers this correctly, Answer is not x=0.1
The value of x in the infinite geometric series, x = (7 ± i√107) / 26.
What is the value of xWe can start by simplifying the left-hand side of the equation:
-1 + 1/x + x + x² + ...+ xⁿ + ...
= -1 + (1/x) * (1/(1 - x))
Using the formula for the sum of an infinite geometric series:
1 + r + r² + ... = 1/(1 - r) for |r| < 1
We can simplify the left-hand side further:
= -1 + (1/x) * (1/(1 - x))
= -1 + (1/(x - x²))
Now we have:
-1 + (1/(x - x²)) = 10/3
Multiplying both sides by 3(x - x²), we get:
-3(x - x²) + 3 = 10(x - x²)
Simplifying, we get:
13x² - 7x + 3 = 0
Using the quadratic formula, we can solve for x:
x = (7 ± √(7² - 4133)) / (2*13)
x = (7 ± i√(107)) / 26
Since the expression is defined only for |x| < 1, we can discard the solution with the plus sign, leaving:
x = (7 - √(-143)) / 26
x = (7 - 3i√13) / 26
Therefore, the solution for x is x = (7 ± i√107) / 26.
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Help, please? lol its for like homework or whatev. helpppp!!
Jason wants to buy a new HD television but he thinks that if he waits, the quality of HD televisions will improve. The television he wants to buy costs $2500 now, and based on pricing trends, Jason thinks that the price will increase by 4% each year. (SHOW ALL WORK)
a. Write an exponential growth equation to represent the price y of a new HD television t years from now.
b. Use the equation to predict when a new HD television will cost $3000.
c. Jason decides to wait to buy a new television and saves his money. He puts $2200 in a savings account with 4.7% annual interest compounded continuously. Determine when the amount in his savings will exceed the cost of a new television.
the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
a. The exponential growth equation to represent the price y of a new HD television t years from now is:
y = $2500[tex](1 + 0.04)^t[/tex]
where t is the number of years from now.
b. To predict when a new HD television will cost $3000, we can set y = $3000 and solve for t:
$3000 = $2500[tex](1 + 0.04)^t[/tex]
1.2 = [tex]1.04^t[/tex]
ln(1.2) = t ln(1.04)
t = ln(1.2) / ln(1.04)
t ≈ 3.97
Therefore, a new HD television will cost $3000 approximately 4 years from now.
c. To determine when the amount in Jason's savings will exceed the cost of a new television, we can use the formula for continuous compound interest:
A = [tex]Pe^(rt)[/tex]
where A is the amount in savings after t years, P is the principal amount, e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate expressed as a decimal, and t is the time in years.
In this case, P = $2200, r = 0.047 (since the annual interest rate is 4.7%), and we want to find the time t when A = $2500. Plugging these values into the formula, we get:
$2500 = $2200[tex]e^(0.047t)1.13636 = e^(0.047t)[/tex]
ln(1.13636) = 0.047t
t = ln(1.13636) / 0.047
t ≈ 7.22
Therefore, the amount in Jason's savings will exceed the cost of a new television approximately 7.22 years from now.
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Need help on multiple choice question
please answer the question
a.) The area covered by algae for 10 days after it was spotted would be = 35.7 m²
How to calculate the area covered by the algae after 10 days?The area covered by the algae when it was first spotted = 12.5 m²
For every week(7 days) = 2(12.5)
But 10 days = x
Make X the subject of formula;
X = 10× 2(12.5)/7
X = 250/7
X = 35.7 m²
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a six sided cube with the letters s,o,l,v,e,d is rolled twice. what is the probability of rolling two consonants? express as a fraction in simplest form.
There are 6 possible outcomes for each roll of the cube, since there are 6 letters on the cube. Out of the 6 letters, there are 3 consonants (S, L, V) and 3 vowels (O, E, D).
To find the probability of rolling two consonants, we need to multiply the probability of rolling a consonant on the first roll (3/6) by the probability of rolling a consonant on the second roll (also 3/6), since the rolls are independent events.
(3/6) * (3/6) = 9/36 = 1/4
Therefore, the probability of rolling two consonants is 1/4, which can also be expressed as 25%.
l-80-20l – 100 + l-100l = ???
Step-by-step explanation:
We can simplify the given expression using the rules of absolute values:
l-80-20l – 100 + l-100l
= -(20l + 80) - 100 + 100 (since |x| = -x when x is negative)
= -20l - 80
= -20(l + 4)
Therefore, the simplified expression is -20(l + 4).
Answer:
100
Step-by-step explanation:
[tex] | - 80 - 20| - 100 + | - 100| \\ = | - 100| - 100 + | - 100| \\ = 100 - 100 + | - 100| \\ = | - 100| \\ = \boxed{100}[/tex]
____________
hope it helps!
You participate in a 5K competitive race. Which Z-score would you prefer to have compared to your competitors for the time it took you to complete the race?
The z-scοre is prefer tο have cοmpared tο yοur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race is -2.50.
What is z-scοre?When a value is given a Z-scοre, it shοws hοw far οff frοm the standard deviatiοn it is. The amοunt οf standard deviatiοns a given data pοint is abοve οr belοw the mean is represented by the Z-scοre, alsο knοwn as the standard scοre. The level οf variability within a particular data cοllectiοn is effectively reflected in the standard deviatiοn.
We knοw that ,
=> z=(x-µ)/σ
If we have z scοre less it means we cοmplete the race in less time as cοmpare tο οthers.
Sο, z scοre -2.50 is least as per given all the οptiοns. sο ,we wοuld yοu prefer -2.50 cοmpared tο οur cοmpetitοrs fοr the time it tοοk yοu tο cοmplete the race.
Hence the z-scοre is -2.50.
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Write two numbers that multiply to the value on top and add to the value on bottom.
Submit Answer
42
-13
Answer:
-6 and -7
Step-by-step explanation:
-6 + -7 = -13
-6 * -7 = 42
a car travels x km in 3 hours how far will it travel in 9 hours?
Answer:
distance traveled in 1 hour = x/3
To find the distance traveled in 9 hours, we can multiply the distance traveled in 1 hour by 9:
distance traveled in 9 hours = (x/3) * 9
Simplifying this expression gives:
distance traveled in 9 hours = 3x
Therefore, the car will travel 3 times the distance it travels in 3 hours when it travels for 9 hours.
4. A certain radioactive material is known to decay at a rate proportional to the amount present. A block of this material originally having a mass of Qograms is observed, after 24hrs, to have experienced a reduction in mass of 10%. Find an expression for the mass of the block at any time.
Therefore , the solution of the given problem of expressions comes out to be Q = Q0 e(ln(0.9)/24)t this is the formula for the block's mass at any moment t.
Explain expression.Calculations such as joining, random subdivision, variable multiplier, and elimination are required. They would accomplish the following if they were united: An algorithm, some information, and a mathematical equation. Numerical information, formulas, elements, and arithmetic operations like additions, erasures, errors, and categories are all included in a declaration of truth. Words and phrases can be evaluated and analysed.
Here,
Let's write Q for the radioactive material's mass at any moment t. (t). We can write: Because the substance decays at a rate proportional to its mass.
=> -kQ = dQ/dt
where k is a measure of ratio. This first-order differential equation can be solved by separating the variables, and it is separable:
=>-k dt Equals dQ/Q
By combining both parts, we obtain:
=>Q = -kt + C, where
where C is the integration constant. We can use the original assumption that the material has a mass of Q grammes at time t = 0 to determine C:
=> ln(Q) = C
When we add this to the prior solution, we obtain:
=> Q = -kt + ln, where (Q0)
where Q0 is the starting mass of the material.
=> 0.9Q0 = Q(24) = Q0 e^(-k*24)
After finding k, we obtain:
=> k = ln(0.9)/(-24) (-24)
Using this value of k as a substitute in the preceding equation, we obtain:
=> (ln(0.9)/24)t - ln(Q) + ln (Q0)
If we simplify, we get:
=> Q = Q0 e(ln(0.9)/24)t
This is the formula for the block's mass at any moment t.
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Need help asap!
Solve the following system of equations and show all work. y = −x2 + 4 y = 2x + 1
Answer:
The solutions to the given system of equations are:
x = 1, y = 3x = -3, y = -5Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=-x^2+4\\y=2x+1\end{cases}[/tex]
To solve the given system of equations, substitute the second equation into the first equation:
[tex]\implies 2x+1=-x^2+4[/tex]
Add x² to both sides:
[tex]\implies x^2+2x+1=4[/tex]
Subtract 4 from both sides:
[tex]\implies x^2+2x-3=0[/tex]
Factor the quadratic equation:
[tex]\implies x^2+3x-x-3=0[/tex]
[tex]\implies x(x+3)-1(x+3)=0[/tex]
[tex]\implies (x-1)(x+3)=0[/tex]
Apply the zero product property:
[tex](x-1)=0 \implies x=1[/tex]
[tex](x+3)=0 \implies x=-3[/tex]
Substitute the found values of x into the second equation and solve for y:
[tex]x=1 \implies y=2(1)+1=3[/tex]
[tex]x=-3 \implies y=2(-3)+1=-5[/tex]
Therefore, the solutions to the given system of equations are:
x = 1, y = 3x = -3, y = -5which of the following statements are not true? check all that apply.
Answer:
A
b
D
Step-by-step explanation:
The sun revolves around the Earth." Statements 1 and 4 are true.
As the question asks for statements that are not true, I will go through each statement and determine if it is true or false. Statement 1: "Water boils at 100 degrees Celsius."
This statement is true. Water boils at 100 degrees Celsius at sea level under normal atmospheric conditions.
Statement 2: "The moon is made of cheese." This statement is not true. The moon is not made of cheese. It is primarily composed of rock and does not contain any dairy products.
Statement 3: "The sun revolves around the Earth." This statement is not true.
The Earth revolves around the sun in an elliptical orbit. The concept that the Earth is at the center of the solar system and the sun revolves around it was disproven by the heliocentric model proposed by Nicolaus Copernicus in the 16th century.
Statement 4: "Gravity only exists on Earth." This statement is not true. Gravity exists everywhere in the universe. It is a fundamental force that attracts objects with mass towards each other.
While the strength of gravity may vary depending on the mass of the objects and their distance apart, it is present throughout the universe.
To summarize, the statements that are not true are: 2. "The moon is made of cheese." 3. "The sun revolves around the Earth." Statements 1 and 4 are true.
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1. What is a reasonable distance between two cities? (1 point) 200 km 200 m 200 cm 200 mm
Answer:
200km
Step-by-step explanation:
Well.. if 2 cities were 200m apart, 200 cm apart, or 200 mm apart, they would be considered one city. The only logical choice is 200km.
Answer:
a
Step-by-step explanation:
(1x10⁶) - (8x10⁴) I'm scientific notation
Answer: 9.2 x 105
Step-by-step explanation:
someone please help :,)) (picture attached) click question to see photo
Answer:180 square inches
Step-by-step explanation:
18*6+9*8=180
There are 3 teaspoons in a tablespoon. There are 10 16 times more teaspoons in a cup. How many teaspoons are in a cup?
Which of the following is the same as 8(9+2)?
8*9+8
8*9+2
8*9+8*2
9(8+2)
2(8+9)
Answer:
The third one
Step-by-step explanation:
if you look at it, and actually solve it its 88.
I'LL MARK THE BRAINLIEST
What is the exact circumference of the circle?
Answer: c=2πr
Step-by-step explanation:
because im just that guy
Answer:
c=62.8
Step-by-step explanation:
diameter=20
radius=10
c=2πr
c=2×22/7×10
c=62.8
I REALLY REALLY REALLY NEED HELP PLS
The answer of the given question based on Statistics to find minimum monthly premium payments is option D) Plan 2, since it has lower monthly premium payments.
What is Probability?Probability is measure of likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 indicates an impossible event and 1 indicates certain event
Assuming that the coverage details are similar, we can compare the monthly premium payments for each plan based on the different categories of coverage:
Individual: Plan 1 has a monthly premium of $87.32, while Plan 2 has a monthly premium of $11.77. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Spouse: Plan 2 has a monthly premium of $735.00, while Plan 1 has a monthly premium of $890.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Child: Plan 2 has a monthly premium of $606.00, while Plan 1 has a monthly premium of $750.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Individual+Family: Plan 2 has a monthly premium of $1,400.00, while Plan 1 has a monthly premium of $1,600.00. Therefore, Plan 2 has the lower monthly premium for this category of coverage.
Based on these comparisons, we can see that Plan 2 has a lower monthly premium for all categories of coverage. Therefore, the answer is option D: Plan 2, since it has lower monthly premium payments.
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How do I correctly simplify the expression and where did the student go wrong?
Part A: The student that simplified the give trigonometrical identity expression incorrectly is student B.
Part B: The correct complete solution is shown below
Simplifying Trigonometrical identities expressionsFrom the question, we are to determine the student that simplified the expression incorrectly.
Part A:
The student that simplified the expression incorrectly is student B.
The student is went wrong in step 3.
From step 2, the student divided (1 + tan²θ) by (tanθ/cotθ). The student is supposed to divide [(1 + tan²θ)/tanθ] by cotθ
Part B:
The correct solution is shown below
[(1 + tan²θ)/tanθ] ÷ cotθ
(sec²θ/tanθ) ÷ cotθ
Which can be written as:
(sec²θ/tanθ) ÷ 1/tanθ
Then,
(sec²θ/tanθ) × tanθ/1
= sec²θ/1
= sec²θ
Hence, the correct simplified expression is sec²θ
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ASAP HELP!! I REALLY NEED HELP
Answer:
X = 18
Step-by-step explanation:
7x is the opposite angle if 3x, so 10x= 180 180÷10 = 18
NEED HELP!!
Select which points are solutions to this inequality.
y ≥ 5x - 7
(-5, -3)
(-4, 2)
(1, -2)
(-1, 0)
(3, 0)
(4, 1)
Inequality y 5x - 7 has solutions (-5, -3), (-4, 2), and (-1, 0).
What are the three potential remedies for the inequality?In order to address an inequality • You can multiply or divide each side by the same positive amount; • You can add the same amount to each side; • You can take the same amount away from each side. If you multiply or divide each side by a negative value, the inequality sign must be reversed.
Let's examine each point individually:
(-5, -3)
y ≥ 5x - 7
-3 ≥ 5(-5) - 7
-3 ≥ -32
The inequality is true, so (-5, -3) is a solution.
(-4, 2)
y ≥ 5x - 7
2 ≥ 5(-4) - 7
2 ≥ -27
The inequality is true, so (-4, 2) is a solution.
(1, -2)
y ≥ 5x - 7
-2 ≥ 5(1) - 7
-2 ≥ -2
The inequality is not true, so (1, -2) is not a solution.
(-1, 0)
y ≥ 5x - 7
0 ≥ 5(-1) - 7
0 ≥ -12
The inequality is true, so (-1, 0) is a solution.
(3, 0)
y ≥ 5x - 7
0 ≥ 5(3) - 7
0 ≥ 8
The inequality is not true, so (3, 0) is not a solution.
(4, 1)
y ≥ 5x - 7
1 ≥ 5(4) - 7
1 ≥ 13
The inequality is not true, so (4, 1) is not a solution.
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Draw a circle with radius 4cm.
What is the length of the diameter of the circle?
How many sectors of 90° will fit inside the circle?
Draw five radii inside your circle that are equally spaced out around the circumference. Join up the ends of the radii to create a shape inside your circle.
What is the name of the shape that you have created inside your circle?
How long are the chords that are joining the radii together?
How big is the angle of each sector?
If you did the same as above with sectors of 45°, what shape would you create inside your circle?
The length of the diameter of the circle of the radius 4 cm is 8 cm and other solutions are added below
A circle with radius 4cm.See attachment for the circle
The length of the diameter of the circleThis is calculated as
Diameter (d) = 2 * Radius (r)
So, we have
d = 2 * 4 cm
d = 8 cm
Number of sectors of 90°The number of 90° sectors that will fit inside the circle is
Sectors = (360°/90°)
Sectors = 4
Five radii inside the circle equally spacedSee attachment for the circle
The name of the shape in the circleThe shape created inside the circle by joining the ends of five equally spaced radii is a regular pentagon.
Length of the chords joining the radii togetherThe length (L) of one chord is
L = 2 × r × sin(c/2)
For 6 chords created by the 5 radii, we have
Total length = 6 × 2 × r × sin(c/2)
Where
c = 360/6 = 60
So, we have
Total length = 6 × 2 × 4 × sin(60/2)
Evaluate
Total length = 24 cm
How big is the angle of each sector?Each sector of 90° in a circle has an angle of
Angle = (360/6)°
Angle = 60°
What shape would you create inside your circle?If sectors of 45° were used, the shape created inside the circle by joining the ends of the radii would be a nonagon
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Ivan bought a desk on sale for $179.20. This price was 32% of the original price.
Answer:
Below
Step-by-step explanation:
I suppose you are looking for the ORIGINAL price
x = original
32% is .32 in decimal
so .32 * x = $ 179.20
x = 179.20/.32 = $ 560.
Work 1.1.8 The president of South Africa, Mr Cyril Ramaphosa, announced that there will be an inflow of R10 billion investment in South Africa in the following year. Use the multiplier formula to calculate the eventual change in aggregate expenditure due to this R10 billion injection. The marginal propensity to save (mps) is 0,4. Remember to show all formulas and calculations!
Using the multiplier formula, the eventual change in aggregate expenditure due to the inflow of R10 billion into South Africa and using the marginal propensity to consume (MPC) is R6 billion.
What is the multiplier formula?The multiplier formula is used to compute the amount of new income generated from the flow of extra income.
The multiplier formula uses the MPS (marginal propensity to save) to compute the multiplier as follows:
M = 1 / MPS
The marginal propensity to save gives the proportion of income that will be saved.
The marginal propensity to save (MPS) = 0.4
M = 1 / MPS
M = 1/0.4)
= 2.5
Change in aggregate expenditure = R25 billion (2.5 x R10 billion)
Thus, we expect the aggregate expenditure in South Africa to increase by R25 billion following the inflow of R10 billion investment.
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The following table represents measurement of the height of a bean sprout:
Days after sprout
was planted 7 9 11 13
Height of sprout
in inches 3 4.5 6 7.5
Create a linear equation to represent this situation. According to your equation, how tall will the sprout
be after 14 days?
The linear equation representing the situation is y = 0.75x - 2.25, and according to this equation, the height of the sprout after 14 days would be 8.25 inches.
To create a linear equation that represents the relationship between the height of the bean sprout and the number of days after planting.
Therefore, the slope of the line is:
slope = change in height / change in days = (7.5 - 3) / (13 - 7) = 1.5
The intercept of the line can be found by substituting one of the data points into the point-slope form of a line:
y - y1 = m(x - x1)
where m is the slope, x1 and y1 are the coordinates of one of the data points. We choose the first data point (7, 3):
y - 3 = 1.5(x - 7)
y - 3 = 1.5x - 10.5
y = 1.5x - 7.5
Therefore, the linear equation that represents the relationship between the height of the bean sprout (y) and the number of days after planting (x) is:
y = 1.5x - 7.5
To find the height of the sprout after 14 days, we substitute x = 14 into the equation:
y = 1.5(14) - 7.5
y = 10.5
Therefore, the height of the sprout after 14 days is predicted to be 10.5 inches.
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1. Write the equation of the circle, (x-2)²+(y-5)²=7² in general form.
Answer:
The equation in general form is x² + y² - 4x - 10y - 20 = 0
Answer:
x² + y² - 4x - 10y - 20 = 0
Step-by-step explanation:
The general equation of circle is
x² + y² + ax + by + c = 0
where a, b and c are constants
To convert the standard form of the equation (x - 2)² + (y - 5)² = 7² into general form, expand the squares and the constant on the right side and adjust the terms to have 0 on the right side
(x - 2)² = x² - 4x + 4
(y - 5)² = y² - 10y + 25
7² = 49
(x - 2)² + (y - 5)² = 7²
= x² - 4x + 4 + y² - 10y + 25 = 49
Subtract 49 from each side to get 0 on the right:
x² - 4x + 4 + y² - 10y + 25 - 49 = 0
Simplify the constant terms
4 + 25 - 49 = 29 - 49 = -20
Required equation is
x² + y² - 4x - 10y - 20 = 0