-480 ÷ 8 = -60
2x = -120
-20 × 3 = -60
(2 × 3) × (-5 × 2) = -60
Establish the identity.
(csc 0+1)(csc 0-1) = cot 0
a. Multiply and write the left side expression as the difference of two squares: ?
b. The expression from the previous step is equivalent to cot 0 using what?
OA. Cancellation Property
OB. Quotient Identity
OC. Pythagorean Identity
OD. Reciprocal Identity
OE. Even-Odd Identity
pls help asap i can’t pass this class without passing this test
To establish the given identity, we need to first multiply the left side of the equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.
The left side of the given equation can be written as:
(csc0+1)(csc0-1)
We can then apply the difference of squares formula to this expression to get:
(csc0+1)(csc0-1) = (csc0+1)(csc0-1)
Now, we can see that this expression is equivalent to cot 0 using the Pythagorean Identity. This identity states that the sum of the squares of the cosecant and cotangent of an angle is equal to 1. In this case, since (csc0+1)(csc0-1) = cot 0, we can use the Pythagorean Identity to rewrite the left side of the equation as (csc0^2 + cot0^2) = 1, which is equivalent to cot 0.
Therefore, the given identity is established using the Pythagorean Identity. This means that the correct answer is C. Pythagorean Identity.
Please Help!! I'm super confused!
(2x ⋅ -3/y)^-3 ⋅ (-5x/y)^2
Answer: -25y/216x
Step-by-step explanation: - 25y / 216x
Answer:
(-30x^2/y^2)^5
Step-by-step explanation:
First, we can simplify the exponent in the first term by using the property that (a^m)^n = a^(m⋅n). This property tells us that we can calculate the exponent of the first term by multiplying the exponent of the base by the exponent of the power, which gives us (-3)⋅(-3) = 9. This means that the first term can be rewritten as (2x ⋅ -3/y)^9.
Next, we can simplify the second term by calculating its exponent in the same way, which gives us (-2)⋅(2) = -4. This means that the second term can be rewritten as (-5x/y)^-4.
We can then combine the two terms by using the property that (a^m)⋅(b^n) = (a⋅b)^(m+n). This property tells us that we can calculate the exponent of the combined terms by adding the exponents of the individual terms, which gives us 9 + (-4) = 5. This means that the entire expression can be rewritten as (2x ⋅ -3/y)^9 ⋅ (-5x/y)^-4 = (2x⋅-3/y⋅-5x/y)^5.
Finally, we can simplify the base of the combined terms by multiplying the factors together, which gives us (2x⋅-3/y⋅-5x/y) = -30x^2/y^2. This means that the entire expression can be rewritten as (-30x^2/y^2)^5.
Marcus invested $5000 in a bank at an interest rate of 2.5% compounded annually. (a) Find the total amount he had at the end of second year. At the end of second year, Marcus withdrew all the money in the bank and invested it into another bank which offered simple interest rate of 8% per annum. (b) Find the minimum number of years he had to leave the money in the bank in order for it to be more than $10 000.
1. The total amount (future value) Marcus had at the end of the second year of investing $5,000 at 2.5% compounded annually was $5,253.13.
2. The minimum number of years Marcus must leave the $5,253.13 to be more than $10,000 is 11.3 years.
What is the future value?The future value is the compounded present value at an interest rate.
The future value can be derived from an online finance calculator as follows:
With the future value so determined, we can then compute the minimum time in years required for it to reach more than $10,000 at the simple interest rate.
Initial investment = $5,000
Interest rate = 2.5% compounded annually
Investment period = 2 years
Future Value at Compound Interest:N (# of periods) = 2
I/Y (Interest per year) = 2.5%
PV (Present Value) = $5,000
PMT (Periodic Payment) = $0
Results:
FV = $5,253.13
Total Interest = $253.13
Simple Interest Investment:Principal = $5,253.13
Interest rate = 8% per annum
Future amount = $10,000
Time to reach the future amount = (Future Value/Principal - 1) ÷ Interest rate
= ($10,000/$5,253.13 - 1) ÷ 0.08
= 11.3 years
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when jim cleaned out the fountain at the library, he found a total of 20 nickels and quarters. the collection of nickels and quarters totaled $2.60. how many quarters did jim find?
When jim cleaned out the fountain at the library, he found a total of 20 nickels and quarters , the collection of nickels and quarters totaled $2.60 then he find eight quarters.
Given that:
Let N be the number of nickels.
Q be the number of quarters.
The value of one nickels N is 0.05N
The value of quarters Q = 0.25Q
Sum of total quarters is $ 2.60
Total number of coins
N + Q = 20 , N = 20 - Q
0.05 N + 0.25 Q = 2.60
substitute n = 20 - Q , we get
0.05 (20 - Q) + 0.25 Q = 2.60
1 - 0.05 Q + 0.25 Q = 2.60
1 + 0.2Q = 2.60
0.2 Q = 1.6
Q = 1.6 / 0.2
Q = 8
Therefore , Jim finds 8 quarters
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You have a meeting with a potential client for your printing business. To demonstrate your
professionalism, you should arrive for the appointment:
A) Right on time.
B) A few minutes early to ensure that you can find the office and be well prepared for the
meeting.
C) An hour early so that the potential client will know you are eager to get their business.
D) Within a few minutes before or after the arranged time.
The correct option for given situation is,
⇒ To demonstrate your professionalism, you should arrive for the appointment ''Right on time''.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
You have a meeting with a potential client for your printing business.
And, To demonstrate your professionalism, you should arrive for the appointment.
Now, We know that;
The rule of business is,
To demonstrate your professionalism, you should arrive for the appointment on the right time.
Therefore, The correct option for given situation is,
⇒ Right on time
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A ring-shaped region is shown below. Its inner radius is 15 yd. The width of the ring is 3 yd. Find the area of the shaded region. Use 3.14 for π. Do not round your answer.
Answer:
612.3 in.²
Step-by-step explanation:
Inner circle diameter = 34 in.
Inner circle radius = r = 17 in.
Outer circle diameter = 34 in. + 5 in. + 5 in. = 44 in.
Outer circle radius = R = 22 in.
The are of the ring is the area of the outer circle minus the area of the inner circle.
A = πR² - πr²
A = π(R² - r²)
A = 3.14[(22 in.)² - (17 in.)²]
A = 612.3 in.²
an equation for a tangent to the graph of y=arcsin(x/2) at the origin is
y=x/2 is equation for a tangent to the graph of y=arcsin(x/2) at the origin.
In order to fing the equation of tangent of any graph we need 2 things
i . A point on the graph
ii . Slope a line on that point
Given y=[tex]sin^-^1(\frac{x}{2} )[/tex]
put x=0
y = [tex]sin^-^1[/tex] (0)
=> y =0
so the graph passes through point (0,0)
now we have to find slope of the graph
slope = [tex]y^'[/tex] = [tex]\frac{d(y)}{dx}[/tex]
=> [tex]\frac{1}{\sqrt{4-x^2} }[/tex]
slope of line at point (0,0) is 1/2
so equation of line is y-0=1/2(x-0)
so the equation of tangent to the given graph is y=x/2
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Jason was riding his bicycle, making deliveries on his newspaper route. He had no less than 12 newspapers left to deliver.
Which number line represents this scenario?
number line with closed circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the left
number line with open circle at point 12, shaded to the right
number line with closed circle at point 12, shaded to the right
The number line to represent the given scenario is number line with close circle at point 12 and shaded to the right. The correct option is (D).
What is a number line?A number line is the pictorial representation of numbers on a graph. The reference point on the number line is known as origin and all the numbers right to the origin are taken as positive and those left to it are negative numbers.
The number of newspapers to be delivered is not less than 20.
Suppose the number of newspaper left at any time be x.
Then, the inequality for the given situation can be written as,
x ≥ 12
This implies all the whole numbers greater than and including 12 on the number line.
Hence, the solution can be represented as all numbers greater than and equal to 12.
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What is 6 x 2 / 4 / 3?
/=divide
Answer:1
Step-by-step explanation: 6x2= 12. 12/4=3. 3/3 is 1.
Answer:
1
Step-by-step explanation:
We can see only multiply and divide here so we go from left to right
6x2/4/3
= 12/4/3
= 3/3
= 1
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each equation with the correct solution. 20 POINTS!!!
What is G2? answer quick peasee
both must be true for a person to ride: (1) at least 5 years old, (2) taller than 36 inches. which expression evaluates to true if a person can ride?
Both conditions must be met in order to ride: being at least five years old and being at least 36 inches tall. expression evaluates to true if a person can ride - (Age >= 5) && (Height > 36)
In order for a person to ride, two conditions must be true: they must be at least 5 years old and taller than 36 inches. In order to evaluate whether a person can ride, we can use the expression (Age >= 5) && (Height > 36). This expression evaluates to true if both conditions are true; if either one is false, then the expression will evaluate to false. For example, if a person is 4 years old and 40 inches tall, then the expression will evaluate to false because the first condition is false. On the other hand, if a person is 5 years old and 40 inches tall, then the expression will evaluate to true because both conditions are true.
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What is the degree of 5x³+3x²-4x+1?
03
04
05
06
Answer:
03
Step-by-step explanation:
it is 03. in a polynomial the hightest power of varibale shows the degree of it.
Recall that two angle are complementary if the um of their meaure i 90 degree°. Find the meaure of two complementary angle if one angle i 20 degree° more than forty four time the other angle
The measure of one angle is 1.56° and another angle is 88.64°.
Complementary angles are two angles whose combined angle is 90 degrees.
Let's consider the smaller angle as A and the larger angle as B.
Given that the two angles are complementary, then their sum is A+B = 90°.
The angle B is 20° more than and 44 times angle A. Then B = 44A+20°. Substituting this equation in the A+B = 90° equation, we get,
A+44A+20° = 90°
45A = 90°-20°
A = 70°/45
A = 1.56°
Substitute A = 1.56°in B = 44A+20°, we get,
B = 44(1.56°)+20°
B = 88.64°
The answers are 1.56° and 88.64°. The sum of these two angles gives 90.2°. By rounding off, we will get 90°.
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Salma made $378 for 18 hours of work.
At the same rate, how many hours would she have to work to make $147?
hours
Answer:
7 hours
every hour she makes $21
Step-by-step explanation:
378÷18=21
147÷21=7
7 hours
378÷18=21$/h in ONE hour Salma makes 21$ so you have to do 147÷21=7h
Yaqub ha a bag of green and yellow pin. 3/7 of the pin are green
He pick out a green pin from hi bag and give it to hi iter
2/5 of the remaining pin in hi bag are green
how many of the remaining pin in hi bag are green and how many are yellow?
The number of remaining green and yellow pins is 14 pins and 21 pins.
A proportion is a mathematical calculation that compares two numbers. According to proportion, two sets of given numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
The fraction of green pins present in the bag is 3/7. Then, the fraction of yellow pins present in the bag is 4/7.
When Yaqub picks up the green pin and gives it to his sister, the new fraction of green and yellow pins are 2/5 and 3/5.
Let x be the number of pins remaining in the bag after 1 pin less. This is written as,
[tex]\begin{aligned}\frac{3}{7}x-1 &= \frac{2}{5}x\\\frac{3}{7}x-\frac{2}{5}x&=1\\x&=35\end{aligned}[/tex]
There are about 35 pins remaining in the bag.
Then, the number of green pins remaining is (2/5) × 35 = 14 pins.
The number of yellow pins remaining is (3/5) × 35 = 21 pins.
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g if we randomly selected 3 people born in 1988, what's the probability that they all have different birthdays
The probability that they all have different birthdays is 0.903 or 90.3%.
1. Calculate the number of days in a year.
There are 365 days in a year.
2. Calculate the number of possible combinations for 3 people.
There are 365 x 365 x 365 = 4,738,625 possible combinations for 3 people.
3. Calculate the number of combinations where all 3 people have different birthdays.
There are 365 x 364 x 363 = 4,324,320 combinations where all 3 people have different birthdays.
4. Calculate the probability.
The probability that they all have different birthdays is 4,324,320 / 4,738,625 = 0.903 or 90.3%.
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a researcher wishes to test whether the mean of a normally distributed population is greater than 1.06 at the 5% significance level. based upon 22 independent observations, she observes a sample mean of 1.77 and a sample standard deviation of 0.84 . determine the observed value of student's t statistic rounded to the nearest hundredth. (rounding counts!)
The observed value of student's t statistic rounded to the nearest hundredth is 1.72.
Explain the term significance level?The likelihood that an event (like a statistical test) may have happened by chance is the significance level of the occurrence. When the level, or the possibility of the occurrence occurring by chance, is quite low, the event is considered noteworthy.The stated data is-
Sample size n = 22Significance level = 5%Thus,
Degree of freedom = n -1
Df = 22-1
Df = 21
As, the significance level is 5% then test is right tailed.
So,
Alpha value = 0.05
Now,
For alpha value = 0.05 and degree of freedom = 21.
t- critical value = 1.721 (from the t-statiscts table).
Thus, the observed value of student's t statistic rounded to the nearest hundredth is 1.72.
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at a 95% level of confidence we want to estimate the population mean for a quantitative varible that is normally distributed in the population there a 10 individuals in the random sample what is the value of
As per the given confidence interval, the value of the mean is 1.96
The term confidence interval means a range of numbers constructed around a point estimate such as a sample mean or sample proportion.
Here we need to find at a 95% level of confidence we want to estimate the population mean for a quantitative variable that is normally distributed in the population there a 10 individuals in the random sample what is the value of mean.
While In the large-sample case, a 95% confidence interval estimate for the population mean is given by
=> x ± 1.96σ/√n.
Where the population standard deviation is denoted as σ, is unknown, And the the sample standard deviation is used to estimate σ in the confidence interval formula.
Here by the quantity 1.96σ/√n is often called the margin of error for the estimate.
Then the quantity σ/√n is the standard error, and 1.96 is the number of standard errors from the mean necessary to include 95% of the values in a normal distribution.
Therefore, the interpretation of a 95% confidence interval is that 95% of the intervals constructed in this manner will contain the population mean.
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Water is dripping from an inverted cone with a diameter of 12 cm 12cm and a height of 12 cm 12cm at a rate of 1 cm 3 / sec 1cm3/sec. At what rate is the water level decreasing when the radius of the water's surface is r
The rate is the water level decreasing when the radius of the water's surface is r = 2cm is 0.08 cm/sec or dh/dt = - 0.08 cm/sec.
We have given that,
Water is dripping from an inverted cone.
height , h = 12 cm
diameter , d = 12 cm
so, radius, r = 6 cm
rate , dV/dt = - 1 cm³/sec
At any point, the portion of the cone that is filled will have the ratio of radius/height = 6/12 = 1/2. Put another way, h = 2r.
we have to calculate the rate is the water level decreasing , dh/dt when radius of the water's surface is r = 2 cm .
Volume of cone , V = 1/3 π (r)²h = 1/3π (h/2)²h
plugging all known values,
V = 1/3 ( h³/4)π
differentiating with respect to h we get,
dV/dh = 1/3(3h²)π/4 , h = 12
= 1/12(3× 4r²)π ( from r = 2 cm)
= 4π cm²
but we have required, dh/dt = dV/dt × dh/dV
= - 1 cm³/sec × 1/4π cm²
= - 1/4π cm/sec
= - 0.0792 ~ 0.08 cm/sec
Hence, the required value is - 0.08 cm/sec.
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Complete question:
Water is dripping from an inverted cone with a diameter of 12 cm and a height of 12 cm at a rate of 1 cm3 /sec. At what rate is the water level decreasing when the radius of the water's surface is r = 2 cm?"
given that a = b/(1+b) , express b in terms of a.
[tex]a = \frac{b}{1 + b} [/tex]
Answer:
b = - [tex]\frac{a}{a-1}[/tex]
Step-by-step explanation:
a = [tex]\frac{b}{1+b}[/tex] ( multiply both sides by 1 + b to clear the fraction )
a(1 + b) = b ← distribute parenthesis on left side
a + ab = b ( subtract b from both sides )
a + ab - b = 0 ( subtract a from both sides )
ab - b = - a ← factor out b from each term on left side
b(a - 1) = - a ( divide both sides by a - 1 )
b = - [tex]\frac{a}{a-1}[/tex]
Solve for the value of x
A. 20
B. 10
C. 45
D. 3
Answer:
10
Step-by-step explanation:
[tex]x + 5 = 15 \\ x + 5 - 5 = 15 - 5 \\ x = 10 [/tex]
Algebra 2 Questions that i need help with
The graph has a horizontal intercept at (1, 0)
The line x = 0 (the y-axis) is a vertical asymptote; as x→0+,y→∞
The graph is decreasing if 0 < b < 1.
The domain of the function is x > 0, or (0, ∞)
The range of the function is all real numbers, or (−∞,∞)
What is function?
A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The set of all positive real numbers serves as the function's domain. Assume that base 10 is written when no base is specified for the log. The equation y=logb(x+h)+k shifts the logarithmic function, y=logb(x), by k units vertically and h units horizontally. The graph would be moved upward if k>0.
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2(x+1.25) =3.5 without distributive property
Answer:
x = 0.5
Step-by-step explanation:
2 (x+1.25) = 3.5
Divide by 2 on both sides.
x + 1.25 = 1.75
Subtract 1.25 on both sides.
x = 0.5
Answer:
x = 0.5
Step-by-step explanation:
2(x+1.25) =3.5
Divide both sides by 2.
x+1.25 = 3.5/2
x + 1.25 = 1.75
Subtract 1.25 from both sides.
x = 0.5
Which choice is equivalent to the product below?
sqrt45 ×sqrt10
Answer:
Below
Step-by-step explanation:
= sqt (45*10) = sqrt (450) = 15 sqrt 2
The expression √45 × √10 is simplified using the property of square roots to give an equivalent choice of 15√2
How to simplify the expression with square rootsThe product √45 × √10 can be simplified by using the property of square roots that states √(a × b) = √a × √b.
By application of this property, we have that:
√45 × √10 = √(45 × 10).
To simplify further, we find that 45 and 10 have a common factor of 5, and thus,
45 × 10 = 5 × (9 × 10)
45 × 10 = 5 × 90.
Now, we can rewrite √(45 × 10) as √(5 × 90).
Using the same property again, we obtain √5 × √90. Finally, we recognize that 90 can be factored into 9 × 10.
Thus;
√45 × √10 = √(2 × 9 × 25)
√45 × √10 = √2 × √225
√45 × √10 = √2 × 15
√45 × √10 = 15√2
Therefore, the expression√45 × √10 have an equivalent of 15√2
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Could someone help me with this it would be appreciated
Answer:
0.65
Step-by-step explanation:
The probability that we would get tails is 0.35
so the probability we will get heads is
1 – 0.35 = 0.65
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Question 7
GEOMETRY The perimeter of a square is four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the
square is 4 centimeters. Write an equation in point-slope form to find the perimeter y of a square with side length x.
Answer:
y= 4x + 0
Step-by-step explanation:
The perimeter y of a square with side length x can be described by the equation y = 4x + 0.
The perimeter of a square is equal to four times the length of one side. If the side length of a square is 1 centimeter, then the perimeter of the square is 4 centimeters. We can use this information to write an equation in point-slope form to describe the relationship between the side length of a square and its perimeter.
Point-slope form is a way of writing the equation of a line when we know the slope of the line and the coordinates of a point on the line. In this case, the slope of the line is 4, since the perimeter of a square is four times the length of one side. The coordinates of a point on the line are (1, 4), since the side length of a square is 1 centimeter and the perimeter of the square is 4 centimeters.
We can use this information to write the equation of the line in point-slope form. The equation of a line in point-slope form is given by the following equation:
y - y1 = m(x - x1)
where y is the y-coordinate of a point on the line, y1 is the y-coordinate of a known point on the line, m is the slope of the line, and x is the x-coordinate of a point on the line.
In this case, we can substitute the values we know into the equation above to get:
y - 4 = 4(x - 1)
This simplifies to:
y = 4x + 0
Therefore, the equation in point-slope form that describes the relationship between the side length x of a square and its perimeter y is y = 4x + 0.
This equation tells us that for any square, the perimeter is four times the side length plus zero. For example, if the side length of a square is 5 centimeters, then the perimeter is 4 x 5 + 0 = 20 centimeters. If the side length of a square is 10 centimeters, then the perimeter is 4 x 10 + 0 = 40 centimeters.
In summary, the perimeter y of a square with side length x can be described by the equation y = 4x + 0.
Shade 2 circles. Shade 7/4 more
Answer:
The answer is 3 3/4
Step-by-step explanation:
2 7/4 = 15/4 = 3 3/4
f(x) =2/x^2 and g(x) = 4x^3 find fg(1)
Answer:
Functions
Step-by-step explanation:
ok so you gotta substitute x into the original then expand simplify collect like terms then your done
what equation passes (-4,-1) and is parallel to y=2x+14?
Answer:
y = 2x + 7.
Step-by-step explanation:
An equation that passes through the point (-4,-1) and is parallel to the line y = 2x + 14 is of the form y = 2x + b, where b is the y-intercept of the line. Since the line passes through the point (-4,-1), we can use this point to solve for b:
-1 = 2 * (-4) + b
-1 = -8 + b
b = 7
Therefore, an equation that passes through (-4,-1) and is parallel to y = 2x + 14 is y = 2x + 7.
Answer:
y = 2x + 7
Step-by-step explanation:
parallel = same slope
y-(-1) = 2(x-(-4)
y+1 = 2(x+4)
y+1 = 2x + 8
y = 2x + 8 - 1
y = 2x + 7