Answer: 7,210,000
Step-by-step explanation:
If cos A =
of sin A?
Square root of 5 divided by
3
and tan A < 0, what is the value of Sin A?
Answer: [tex]\tt{a.\fra{2}{3}}[/tex]
Step-by-step explanation:
If cos A = sqrt(5)/3 and tan A < 0, we can use the fact that:
sin^2 A + cos^2 A = 1
to find the value of sin A. First, we can square both sides of the equation cos A = sqrt(5)/3 to get:
cos^2 A = 5/9
Then, we can use the identity sin^2 A = 1 - cos^2 A to get:
sin^2 A = 1 - cos^2 A
sin^2 A = 1 - 5/9
sin^2 A = 4/9
Taking the square root of both sides gives us:
sin A = +/- 2/3
However, we know that tan A < 0, which means that the sine and cosine functions have opposite signs in the quadrant where angle A lies. Since cosine is positive (given by cos A = sqrt(5)/3), angle A must lie in either the first or fourth quadrant, where sine is positive or negative, respectively. Therefore, we can eliminate the negative solution and conclude that:
sin A = 2/3
The variables x and y vary inversely. Use x=−3 and y=4 to write an equation relating x and y. Then find y when x=6 .
Step-by-step explanation:
If x and y vary inversely, we can write the equation:
xy = k
where k is a constant of proportionality. To solve for k, we can use the values x = -3 and y = 4:
(-3)(4) = k
-12 = k
So the equation relating x and y is:
xy = -12
To find y when x = 6, we can plug in these values and solve for y:
(6)y = -12
y = -2
So when x = 6, y = -2.
Ocean waves move in parallel lines toward the shore. The figure shows the path that a windsurfer takes across several waves. For this exercise, think of the windsurfer's wake as a line. If m∠1 = (8x + 5y)° and m∠2 = (8x + y)°, find x and y.
78°
Answer:
x = 9.75 and y = 0
Step-by-step explanation:
Since the path of the windsurfer crosses both angles, we can use the fact that the sum of the angles around a point is 180 degrees to set up an equation:
m∠1 + m∠2 + m∠3 = 180°
We know that m∠1 = (8x + 5y)° and m∠2 = (8x + y)°. We can also see from the diagram that m∠3 = 180° - 78° = 102°. Substituting these values into the equation, we get:
(8x + 5y)° + (8x + y)° + 102° = 180°
Simplifying and solving for x and y, we get:
16x + 6y = 78°
8x = 78° - 6y
x = (78° - 6y)/8
We can substitute this expression for x into one of the earlier equations to solve for y:
8[(78° - 6y)/8] + y = 78°
78° - 6y + y = 78°
-5y = 0
y = 0
Now that we know y = 0, we can substitute this value into the equation we found for x:
x = (78° - 6(0))/8 = 9.75
Which is an example of a periodic event?
O A. The average human body temperature slowly rises and falls every day.
O B. The average person gradually loses bone mass as they age.
OC. The average child grows in bursts throughout childhood.
OD. A resting pulse stays steady for several hours.
What is 6 [4(-5)^n-1] n=1 equal to
The value of 6 [4(-5)^n-1] when n is 1 is 24
What is substitution of variable?This simply means replacing a known value for an unknown value in an expression.
For example, 5x²+2 , the value of the expression when x is -2 is solved by substituting -2 for x in the expression.
5x²+2 = 5(-2)² +2
= 5×4 +2
= 20+2
= 22
Similarly, the value of 6 [4(-5)^n-1] when n= 1 can be calculated by substituting 1 for n in the expression.
6 [4(-5)^n-1] = 6(4(-5)^1-1)
= 6(4(5)^0)
= 6 × 4 × 1
= 24
Therefore the value of 6 [4(-5)^n-1] when n= 1 is 24
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Could anyone help? Thanks
Answer:
Step-by-step explanation:
The formula for a function is in vertex form is
y=a(x-h)²+k
(h,k) is vertex
a is stretch
if it were facing down there would be a - in front
You question:
(-4,1) is vertex
it's facing up and there is no stretch
y=(x+4)+1 you can expand
y=x²+8x+17
Convert each unit. Enter your answers in the boxes.
32
yards =
feet
1
-
4
foot =
inches
3
miles =
yards
Answer:
32 yards = 96 feet (1 yard = 3 feet, so 32 yards x 3 feet/yard = 96 feet)
1 foot = 12 inches, so 4 feet = 48 inches
3 miles = 5,280 yards (1 mile = 1,760 yards, so 3 miles x 1,760 yards/mile = 5,280 yards)
Therefore, the conversions are:
32 yards = 96 feet4 feet = 48 inches3 miles = 5,280 yardsA square pyramid has a base length of 6 inches and a height of 8 inches.
What is the volume of this pyramid?
Enter your answer in the box.
The volume of the pyramid will be equal to 96 in^3.
We are given that square pyramid has a base length of 6 inches and a height of 8 inches.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex] is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, thus its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Therefore, the volume of the pyramid;
V = 1/3 a^2 h
V = 1/3(6^2)(8)
V = 1/3(36)(8)
V = 96 in^3
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suppose x~n(8,1). what value of x has a z-score of -2.25?
The value of x corresponding to a z-score of -2.25 is 5.75.
What is z-score ?
A z-score is a standardized score that expresses the distance of a data point from the mean in terms of the number of standard deviations. It indicates how many standard deviations a data point is above or below the mean of the distribution.
Given that x follows a normal distribution with mean μ = 8 and standard deviation σ = 1, we can find the z-score corresponding to a given value of x using the formula:
z = (x - μ) / σ
To find the value of x corresponding to a z-score of -2.25, we can rearrange the above formula as follows:
x = μ + z * σ
= 8 + (-2.25) * 1
= 8 - 2.25
= 5.75
Therefore, the value of x corresponding to a z-score of -2.25 is 5.75.
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The lower a person's income, the less tax they must pay. People therefore try to lower their taxable income by claiming allowable tax deductions.
Work-related expenses such as uniforms, stationery and job-related travel expenses are all examples of allowable deductions. The income tax is therefore calculated on what we call a person's taxable income.
Taxable income =gross income − allowable tax deductions
Use the tax table below to compare the following jobs in Questions a and b
Taxable income
Tax on this income
$0−$18200
Nil
$18201−$37000
19c for each $1 over $18200
$37001−$80000
$3572 plus 32.5c for each $1 over $37000
$80001−$180000
$17547 plus 37c for each $1 over $80000
$180001+
$54547 plus 45c for each $1 over $180000
a An young accountant earns $3120 a fortnight, with no allowable tax deductions
i. What is the accountant’s taxable income?
ii. How much tax does the accountant owe in a year?
iii. What is the accountant’s annual net pay?
iv. What is the accountant’s fortnightly net pay?
Taxable income = $81,120,Total tax owed = $4,732.50 + $414.40 = $5,146.90 per year,Annual net pay = $81,120 - $5,146.90 = $75,973.10,Fortnightly net pay = $75,973.10 / 26 = $2,922.81
What does taxation mean?An amount of money that a government asks people to pay based on their income, property value, etc., and is used to pay for things that the government does.
The accountant's gross income for two weeks is $3,120, so his gross income for the year is:
3120 x 26 = $81,120
Since they are not allowed to deduct tax, their taxable income equals their gross income:
Taxable income = $81,120
ii. Using the presented tax table, we can determine the accountant's tax liability:
Taxable income = $81,120
Income tax over $80,000 = (81,120 - $80,000) x 0.37 = $414.40
Income tax over $37,000 = ($37,000 - $18,200) x 0.325 = $4,732.50
Total tax liability = $4,732.50 + 414.40 = $5,146.90 per year
iii. An accountant's annual net salary is his gross income minus tax liability:
Annual net salary = $81,120 - $5,146.90 = $75,973.10
iv. The accountant's semi-monthly net salary is the annual net salary divided by 26:
Net salary for two weeks = $75,973.10 / 26 = $2,922.81
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A normal distribution has a mean of 55 and a standard deviation of 3. Find the -score corresponding an -value of 64. Is this score considered to be statistically significant or statistically insignificant? Explain.
The z-score corresponding an x-value of 64 is 3
Finding the z-score corresponding an x-value of 64From the question, we have the following parameters that can be used in our computation:
x = 64
Mean = 55
Standard deviation = 3
using the above as a guide, we have the following:
z = (x - mean)/Standard deviation
Substitute the known values in the above equation, so, we have the following representation
z = (64 - 55)/3
Evaluate
z = 3
This score may or may not be considered to be statistically significant or statistically insignificant
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If the mass of a solid is 25 g and its volume is 50 cm³, what is its density?
Answer:
0.2 because Density = Mass / Volume
Density = 25 / 50
Density= 0.2 g/cubic cm
find other end point of mid point 3,1 and end point -2,5
The coordinate of the other endpoint (x₂, y₂) of the line segment will be (8, -3).
Given that:
Midpoint, (x, y) = (3, 1)
First endpoint, (x₁, y₁) = (-2, 5)
The coordinate of the other endpoint of the line segment is calculated as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
(3, 1) = [(-2 + x₂) / 2, (5 + y₂) / 2]
(6, 2) = [(-2 + x₂), (5 + y₂)]
(x₂, y₂) = (6 + 2, - 5 + 2)
(x₂, y₂) = (8, -3)
The coordinate of the other endpoint (x₂, y₂) of the line segment will be (8, -3).
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A movie critic, rate movies on a scale of four stars to WinStar, a summary of her ratings for 20 movies as shown in the table at the critic rates a total of 100 movies where is the best prediction for the number of movies she gives exactly 3 stars.
A 47B 50 C 35D 27
Answer:
Step-by-step explanation:
you rigt
Question 10 of 25
Suppose g(x) = f(x-1)-5. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is shifted 1 unit left and 5 units down.
B. The graph of g(x) is shifted 1 unit left and 5 units up.
C. The graph of g(x) is shifted 1 unit right and 5 units down.
D. The graph of g(x) is shifted 1 unit right and 5 units up.
SUBMI
The graph of g(x) = f(x - 1) - 5 is: C: The graph of g(x) is shifted 1 unit right and 5 units down.
How to Interpret Transformed Functions?Some of the terminologies in shifting of functions are:
1. Shift graph functions y = f(x) to the left: This means that we will be adding inside the function.
y= f(x + b) , where b is constant
2. Shift graph function y = f(x) to the right means that we will be subtracting inside the function
y = f(x - b)
3. To shift graph function y = f(x) up by b units means that we would be adding outside the function:
y = f(x) + b
4. To shift graph down by b units means that we would be subtracting outside the function:
y = f(x) - b
Therefore, by the definition we can say that the graph of g(x) = f(x-1)-5 is the graph of f(x) 1 units to the right and 5 units down.
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Use decomposition to find the area of the figure.
10 yd
8 yd
The area is
13 yd
square yards.
Answer:
The area is 92 square yards.
Step-by-step explanation:
We can decompose this figure into a rectangle and a triangle.
First, we can find the area of the rectangle.
A(rect) = length × width
A(rect) = 10 × 8
A(rect) = 80 yd²
Next, we can find the area of the triangle.
A(triangle) = (1/2) × base × height
[tex]A(\text{triangle}) = \dfrac{1}{2} \, (13 - 10) \times 8[/tex]
[tex]A(\text{triangle}) = \dfrac{3}{2} \times 8[/tex]
[tex]A(\text{triangle}) = 12 \text{ yd}^2[/tex]
Finally, we can add the two shapes' areas to get the area of the entire figure.
A = A(rect) + A(triangle)
A = 80 yd² + 12 yd²
A = 92 yd²
Answer: 92 yd²
Step-by-step explanation:
Decomposition means to break the shape into parts, but it's not necessary to break apart.
This is a trapezoid turned sideways A=1/2(b1+b1)h
b1=10
b2=13
h=8
A=1/2(10+13)8 =92 yd²
if you decompose, you can make the top a triangle and bottom a rectangle.
A(triangle) = 1/2(b)(h) b=3 h=8
1/2(b)(h)
= 12
A(rectangle)=bh b=10 h=8
=10*8
=80
Add the 2 and you get 92 again
In AKLM, m = 63 inches, m/K=24° and m/L=42°. Find the length of 1, to
the nearest inch.
The length of side l of the triangle using sine rule is: 46 inches
How to use sine rule?Sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:
a/sinA = b/sinB = c/sinC
Where A, B, C are the angles and a, b and c are the opposite sides to the angles.
Thus:
63/sin 114 = l/sin 42
(63 * sin 42)/sin 114 = 46 inches
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2.1 The following task is given to Grade 8 learners:
Lerato spends 2/5 of her money and loses 1/3 of what is left. She still has
R6 left. How much money did she have to begin with?
Fath
2.1.1 Solve the problem using an illustration.
(5)
If Lerato spends ²/₅ of her money, loses ¹/₃ of what is left, and still has R6 left, the amount of money she had to begin with was R15.
How is the beginning amount determined?The beginning amount that Lerato had can be determined using fractional addition and subtraction.
Fractional addition and subtraction involve the addition and subtraction of fractional or proportional values.
The amount of money Lerato spend = ²/₅
The amount left = ³/₅ (1 - ²/₅)
The amount lost = ¹/₃ x ³/₅
= ¹/₅
The total amount spent and lost = ³/₅ (²/₅ + ¹/₅)
The amount of money left after spending and losing ³/₅ = R6
R6 = ²/₅
Proportionately, ²/₅ = R6, ⁵/₅ = R15 (R6 x ⁵/₂).
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shawn deposits $100 every year into a savings account that pays interest at a rate of 3.5% per year, compounded annually. How much money will there be in his account at the end of 4 years
A-214.25
B-210.62
C-207
D-270
The amount of money that should be in the account at the end of 4 years of investment would be = $114.
How to calculate the amount of money in a given account?To calculate the total amount of money that will be in an account at the end of a given time can be calculated using the given formula below;
Simple interest = principal× time×rate/100
where;
principal = $100
rate = 3.5%
time = 4 years
simple interest = 100×3.5×4/100
= 14
Therefore the total amount of money that will be in the account at the end of 4 years = 100+14 = $114.
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Find the volume of a right circular cone that has a height of 15.1 ft and a base with a radius of 10.7 ft. Round your answer to the nearest tenth of a cubic foot.
Determine if the following is traversable. Then trace the object. If the network is not traversable, say why.
In the realm of computer networking, a traversable network is a structure in which any message or packet can be efficiently transmitted from one node to another without impediment.
What is the traversable network?Essentially, this implies that all nodes within the network are interconnected, devoid of any isolated segments that could impede data transmissions.
It should be noted that to ensure a network's traversability, several paths may be established between two given nodes or it might connect each node to a key switch or hub for communication purposes. Designing a topology with reliability and expedience at the core is essential for facilitating successful functioning, as traversable networks allow for information and resources to be sent swiftly - and without potential delay or loss. An overview was given based on the information.
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HELP ASAP PLEASE! Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent.
After considering all the given options we conclude that the probability of selecting a point inside the rectangle randomly falls outside the triangle, which is Option B.
The probability regarding a point selected randomly within the rectangle is in the square is given by the ratio of the area of the square to the area of the rectangle.
The evaluated area regarding the given square is
4² = 16 sq units.
The area of the rectangle is 12 x 8 = 96 sq units. Then , after evaluation the probability regarding a specified point taken randomly inside the rectangle is in the square is
16/96
= 1/6
= 0.1667 or 16.7%
The probability concerning a point taken randomly within the rectangle is outside the triangle is given by subtracting the area of the triangle from the area of the rectangle and then dividing by the area of the rectangle.
The area of the triangle is
(1/2) x base x height
= (1/2) x 4 x 5
= 10 sq units.
Then, the probability that a point chosen randomly inside the rectangle is outside the triangle is
(12 x 8 - 10)/(12 x 8)
= 94/96
= 0.9792 or 97.9%
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A soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
28.26 gallons
113.04 gallons
211.38 gallons
845.54 gallons
Therefore, after the water cooler is fully filled, there will be about 211.38 gallons of water inside.
What is a gallon?Eight pints or 4.564 liters make up a gallon, a unit of liquid or dry capacity.
The cylinder's diameter is specified as 3 feet, so its radius must be half that, or 1.5 feet. The cylinder is described as having a height of 4 feet.
When we enter these values into the formula, we obtain:
V is equal to (1.5)2(4) = 28.26 cubic feet.
We are aware that one cubic foot contains about 7.48 gallons of water. Therefore, we need to multiply the volume of the cylinder by 7.48 to get how many gallons of water are in the water cooler when it is fully filled.
The result of multiplying 28.26 by 7.48 is:
211.38 liters
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What ratio do the triangles to rectangles show in this illustration? 100 points.
please answer i dont have much time left?
Answer: Its 5/2 or 2/5 but I think the right one is 5/2.
The answer is 5/2.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
I will answer more of your questions.
(Expert Answered)
HELPPPPPPPPPPPP and give me an accurate answer too K12 btw thanks
with geico you get a discount for being a good driver of 10% you have a six month policy for 1,025. if you pay it in full, you get another 10% discount how much would you pay per month if you choose not to pay in full?
round your answer to the nearest and do not put a dollar sign.
The monthly cost would be $138 if choose not to pay in full.
If you get a discount of 10% for being a good driver, then the cost of the policy before the full payment discount is:
1,025 × 0.9 = 922.50
If you pay the policy in full, you get an additional discount of 10%, so the cost of the policy after both discounts is:
922.50 × 0.9 = 830.25
If you choose not to pay in full, then you will not get the additional discount.
The policy cost is spread over 6 months, so the monthly cost would be:
= 830.25 / 6
= 138.38
Rounding this to the nearest dollar,
= 138
Thus, the monthly cost would be $138.
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A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 90% confidence if (a) she uses a previous estimate of 0.58? (b) she does not use any prior estimates? refer to picture to view the table of critical values. (a) n = ? (Round up to the nearest integer.). b.) n=?
If she uses a previous estimate of 0.58, n = 733
If she does not use any prior estimates, n = 752
How to solve for the estimatesHere, E is given as 0.03
For 90% confidence level, Z* = 1.645
Using formula for margin of error we have
0.03 = 1.645 x (√0.58(1 - 0.58) / n)
n = 733
without prior estimates the value of p = 0.5
Then we have
0.03 = 1.645 x (√0.5(1 - 0.5) / n)
n = 752
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In triangle ABC, m∠B = (15x − 19)° and the measure of the exterior angle to ∠B is (9x − 17)°. Find m∠B.
116°
71°
64°
9°
Angle B, in the triangle ABC is solved to be 116 degrees
How to find angle BAngle B is solved using the concept of triangles and exterior angle relationship. This helps to know that addition of exterior angle to ∠B to angle B results to 180 degrees. Hence we have that:
exterior angle to ∠B + ∠B = 180
given data:
∠B = (15x − 19)°
exterior angle to ∠B is (9x − 17)°
plugging in gives
9x − 17 + 15x − 19 = 180
9x + 15x = 180 + 19 + 17
24x = 216
x = 9
For m∠B = (15x − 19)°
= 15 * 9 - 19
= 116 degrees
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answer this question
Answer:
The smallest angle in this quadrilateral is 36°.
Step-by-step explanation:
[tex]x + 2x + 3x + 4x = 360[/tex]
[tex]10x = 360[/tex]
[tex]x = 36[/tex]
So x, the smallest angle in this quadrilateral, is 36°.
Destiny has $500 in her bank account . Each month. she adds 100 more
Answer:
Within one year, she'll have:
500 + 100 × 12 which is $1,700.
Quite unsure as the question seems incomplete. But based on the given details, here's your answer..
A day is equivalent to 8.64 x 104 seconds. What is this time in standard form? OA. 8,640 seconds OB. 864,000 seconds OC. 86,400 seconds OD. 864 seconds
