Answer:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]
Step-by-step explanation:
The equation needs to be rearranged in terms of one trigonometric function:
[tex]5\cdot \sin 2\theta - 9\cdot \cos 2\theta = 0[/tex]
[tex]5\cdot \tan 2\theta - 9 = 0[/tex]
[tex]5\cdot \tan 2\theta = 9[/tex]
[tex]\tan 2\theta = \frac{9}{5}[/tex]
[tex]\theta = \frac{1}{2}\cdot \tan^{-1} \left(\frac{9}{5} \right)[/tex]
The tangent function has positive values in the 1st and 3rd Quadrants. Then, the solutions are:
[tex]\theta_{1} \approx 30.473^{\textdegree}[/tex]
[tex]\theta_{2} \approx 120.473^{\textdegree}[/tex]
[tex]\theta_{3} \approx 210.473^{\textdegree}[/tex]
[tex]\theta_{4}\approx 300.473^{\textdegree}[/tex]
Which of the following are Pythagorean Triples?
Answer:
6, 8, 10
8, 15, 17
3, 4, 5
5, 12, 13
are the right answers
Step-by-step explanation:
The point (4,10) is in each scatterplot. In which one is it an outlier?
Answer:
A
Step-by-step explanation:
yy chi u yfgbngny NYC tnfnbfrbcsdv
Answer:
A
Step-by-step explanation:
A small accounting firm has 4 accountants who each earn a different salary between 50,000 and 60,000 and a 5th accountant who works part-time for tax season and earns 10,000
The firm decides to get rid of the part-time accountant and keep the other 4 salaries the same
How will getting rid of the part-time accountant affect the mean and median
Answer: B
Step-by-step explanation:
Both the mean and the median will decrease, but the mean will decrease by more than the median.
Answer:
Both the mean and the median will decrease, but the mean will decrease by more than the median.
Step-by-step explanation:
Pls give brainliest I never get them, I beg of u pleaseeeeeeeeeeeee, i am poor
find the value of x in the given right triangle
Step-by-step explanation:
It is a right angled triangle so with reference angle 37°
hypotenuse (b) = 10
perpendicular (p) = x
So
tan 37° = p/ b
0.75 = x / 10
x= 0.75/10
Therefore x = 0.075
Hope it will help you :))
Heather wants to buy new carpet for her living room floor. The floor is in the shape of a rectangle. Its length is 17feet and its width is13 feet. Suppose carpet costs 11
for each square foot. How much will carpet cost for the floor?
Answer:
$2431
Step-by-step explanation:
First we need to find the area
A = l*w
A = 13*17
A =221 ft^2
It cost 11 dollars per square foot so multiply the price times the number of square ft
221*11 =2431
The total cost will be 2431
Final answer:
Heather's new carpet for her rectangular living room floor will cost $2431. This is obtained by calculating the area of the room (221 square feet) and multiplying it by the cost per square foot ($11).
Explanation:
Heather wants to buy new carpet for her living room floor, which is a rectangle with a length of 17 feet and a width of 13 feet. To find out how much the carpet will cost, we need to calculate the area of the floor and then multiply it by the cost per square foot.
First, calculate the area of the floor by multiplying the length by the width:
Area = Length × Width
Area = 17 feet × 13 feet
Area = 221 square feet
Next, multiply the area by the cost of carpet per square foot:
Total cost = Area × Cost per square foot
Total cost = 221 square feet × $11/square foot
Total cost = $2431
Therefore, the carpet will cost Heather $2431 for her living room floor.
You mix the letters A, C, Q, U, A, I, N, T, A, N, C, and E thoroughly. Without looking, you select one letter. Find P(Q or C) as a fraction, a decimal, and a percent.
Answer:
P(Q or C) = 0.25
Step-by-step explanation:
We are given the following in the question:
Letters:
A, C, Q, U, A, I, N, T, A, N, C, E
Total number of observations, n = 12
We have to find the probability that a randomly selected letter is Q or C.
Formula:
[tex]\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}[/tex]
P(Q or C) =
[tex]=\dfrac{\text{n(Q or C)}}{n} = \dfrac{3}{12} =0.25 = 25\%[/tex]
Thus,
P(Q or C) = 0.25
One and one half pounds of chocolate are eaten by 5 people . If each person eats the same amount ,find the unite rate in pounds of chocolate per person
Final answer:
To calculate the chocolate per person, divide 1.5 pounds by 5 people, resulting in 0.3 pounds of chocolate per person.
Explanation:
To find the unit rate of chocolate per person, we divide the total amount of chocolate by the number of people:
Start with 1 and 1/2 (or 1.5) pounds of chocolate for 5 people.
Divide 1.5 pounds by 5 people to find the amount each person eats.
1.5 pounds ÷ 5 people = 0.3 pounds per person.
So, each person eats 0.3 pounds of chocolate.
Find the area of the shape below
Answer:
A =32 units^2
Step-by-step explanation:
This figure is a trapezoid
We can find the area from
A = 1/2(b1+b2)h where b1 and b2 are the base length and h is the height
A = 1/2(4+12) *4
A = 1/2 (16)*4
A =32 units^2
Smart takes the bus to work. Unfortunately, he forgets
his lunch at home. Clever grabs the lunch and drives
after the bus. The bus has a 15-minute head start and
is traveling at an average rate of 40 mph. Clever is
traveling at an average rate of 60 mph. How long does
Clever take to catch up to the bus? Draw a diagram to
solve the problem.
Answer:
Speed = Distance / Time
Distance = Speed x Time
Bus: 15 x 40 = 600 m
Clever: 600 / 60 = 10 minutes
Answer = 10 mins
Step-by-step explanation:
hope it helps:) brainlest?!
PLEASE HELP!!
IF REAL ANSWER IS PUT, I WILL MARK YOU BRAINLIEST!
Answer:
B
Step-by-step explanation:
It's a trapezoid. The top and bottom sides sum is 18+12 which is 30. the height is 10 and the equation would be 30 times 10 times 1/2. The answer would then be 150.
Answer:
b
Step-by-step explanation:
What is the midpoint of the straight line segment joining the points (-2, 9) and (3, -2)?
Answer:
x2-x1/y2-y1
-2--2/3-9=-2+2/3-9
=0/-3
What is the value of x in the equation 13 x minus 2 (8 + 5 x) = 12 minus 11 x?
a.Negative StartFraction 4 Over 7 EndFraction
b.StartFraction 28 Over 29 EndFraction
c.2
d.4
The value of n in given proportion is 16
Solution:
We have to find the value of "n" in the proportion
Given proportion is:
[tex]\frac{n}{28} = \frac{4}{7}[/tex]
We can solve the above proportion by cross-multiplying
Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction
Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction
Set the two products equal to each other
Solve for the variable
[tex]->\frac{n}{28} = \frac{4}{7}[/tex]
[tex]-> 7 * n = 4 * 28[/tex]
[tex]-> n = \frac{4 * 28}{7}[/tex]
[tex]-> n = 4 * 4 = 16[/tex]
Thus the value of n in given proportion is 16
Answer:
the value of n in given proportion is 16
Step-by-step explanation:
To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?
Answer:
Step-by-step explanation:
Let the number of allowable guess be x.
The difference between allowable guess and 645 must not exceed 20.
So, either,
|645 - x| ≤ 20
Or
|x - 645| ≤ 20
where that sign represents the absolute sign.
Hope this Helps!!!
Answer:
| x - 645 | = 20
665
Step-by-step explanation:
We have to guess the amount of beans in a jar to be within 20 of the actual number.
Therefore, the total has to be equal to 20.
We know that the equation required to calculate the minimum and maximum quantity of beans that will win the contest will be:
| x - 645 | = 20
But as we want is the maximum, we break the absolute value and assume "+"
Thus:
x - 645 = 20
fixed for x:
x = 20 + 645
x = 665
The maximum guess you could win is 665
1 + 4x = -5 + 7x
Help plz
Answer:
x=2
Step-by-step explanation:
1 + 4x = -5 + 7x
Subtract 4x from each side
1 + 4x-4x = -5 + 7x-4x
1 = -5+3x
Add 5 to each side
1+5 = -5+5+3x
6 = 3x
Divide each side by 3
6/3 = 3x/3
2 =x
a music company offers a loan to buy a drum set for 1500 dollars. what is the monthly payment. 11.8 simple interest equal monthly payment for 2 years
Answer:
I = Prt
I = 1500(.118)(2) = 354
Total amount to pay = $1854
Monthly payment = $77.25
Step-by-step explanation:
pls mark me brainliest
What information would most likely be presented in graph form?
Answer:
How Fast something is going say like a car or a chart that tell how much the people you live around like that surtitle thing
Step-by-step explanation:
Which equation can be used to find the unknown length, a, in this triangle?
A right triangle has a side with length 15 meters and hypotenuse with length 17 meters. The other side is labeled a.
A. a squared + 15 squared = 17 squared
B. 15 squared + 17 squared = a squared
C. a squared + 15 = 17 squared
D. a + 15 squared = 17 squared
Answer:
It is A.
Look at the attachment down below:
Step-by-step explanation:
The equation is used to find the unknown length (a) will be 17² =15² + a². Then the correct option is A.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A right triangle has a side with length 15 meters and a hypotenuse with length 17 meters.
The other side is labeled a.
17² =15² + a²
Then the correct option is A.
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A waterfall has a hit of 1500 ft. A pebble is thrown upward at the velocity of 24ft per second. The hot, h, of the pebble after t seconds is given by the equation h=-16t+24t+1500. How long after the pebble is thrown will it hit the ground.
Answer:
A waterfall has a height of 1500 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 24 feet per second. The height, h, of the pebble after t seconds is given by the equation h =−16t^2+24t+1500. How long after the pebble is thrown will it hit the ground?
Pebble will hit the ground after 10.46 seconds.
Step-by-step explanation:
Given:
The height, "h" of the pebble after t seconds, "h" = −16t^2+24t+1500
We have to find the time it will take to hit the ground.
For this we have to put h = 0 and solve the quadratic.
Quadratic formula:
⇒ Standard equation : [tex]ax^2+bx+c=0[/tex]
⇒ [tex]x =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]
Now,
Solving the above equation with quadratic formula after comparing its values with the standard equation.
⇒ [tex]a=-16,\ b=24,\ c=1500[/tex]
⇒ [tex]t =\frac{-b\pm \sqrt{(b)^2-4ac} }{2a}[/tex]
⇒ [tex]t =\frac{-24\pm \sqrt{(24)^2-4(-16)(1500)} }{2(-16)}[/tex]
⇒ [tex]t =\frac{-24\pm \sqrt{576+96,000} }{-32}[/tex]
⇒ [tex]t =\frac{-24\pm(310.76)}{-32}[/tex]
⇒ [tex]t =\frac{-24+(310.76)}{-32}[/tex] ⇒ [tex]t =\frac{-24-(310.76)}{-32}[/tex]
⇒ [tex]t =-\frac{286.76}{32}[/tex] ⇒ [tex]t =\frac{334.76}{32}[/tex]
⇒ [tex]t=-8.96\ sec[/tex] ⇒ [tex]t=10.46\ sec[/tex]
Discarding the negative values.
The pebble will hit the ground after 10.46 seconds.
The number of times per minute that a hummingbird's wings flap is normally distributed with a mean of 145 and a standard deviation of 2. Part A: What is the probability that a randomly selected hummingbird flaps its wings more than 151 times a minute? Part B: What percentage of hummingbirds flap their wings between 141 and 149 times per minute? Part C: A hummingbird that flaps its wings 147 times a minute is in the _______________ percentile.
The probability of a hummingbird flapping its wings more than 151 times per minute is close to 0, the percentage of hummingbirds flapping between 141 and 149 times per minute can be found using the standard normal distribution table or calculator and a hummingbird flapping its wings 147 times per minute is in the 84th percentile.
To solve these problems, we'll use the properties of the normal distribution.
Part A:
We'll standardize the value of 151 using the formula for z-score:
[tex]\( z = \frac{{X - \mu}}{{\sigma}} \)[/tex]
[tex]\( z = \frac{{151 - 145}}{{2}} = \frac{6}{2} = 3 \)[/tex]
Now, we find the probability corresponding to z = 3 using a standard normal distribution table or calculator. The probability of a value being more than 3 standard deviations above the mean is very low, close to 0.
Part B:
We standardize 141 and 149 similarly:
[tex]\( z_{141} = \frac{{141 - 145}}{{2}} = -2 \)[/tex]
[tex]\( z_{149} = \frac{{149 - 145}}{{2}} = 2 \)[/tex]
Then, we find the area between these two z-scores using the standard normal distribution table or calculator. It represents the percentage of hummingbirds flapping between 141 and 149 times per minute.
Part C:
To find the percentile for 147 flaps per minute, we standardize it:
[tex]\( z = \frac{{147 - 145}}{{2}} = 1 \)[/tex]
Then, we find the area to the left of z = 1 using the standard normal distribution table or calculator. This area represents the percentile.
Find the missing factor BBB that makes the equality true.
21y^4=(B)(7y^3)21y
4
=(B)(7y
3
)
Answer:21y^4= B*7y^3
B=(21y^4)/(7y^3)
B=3y
i think this is correct
Sandy and Alex are married, with no dependents. They wish to file a joint tax return. Both of them work, but their combined salaries only put them at a slightly above-average income. They would also like to deduct interest paid on their student loans. Recommend an appropriate 1040 form for Sandy and Alex to fill out.
Answer: 1040-A
Step-by-step explanation:
Tax form 1040 is an Internal Revenue Service form that an individual is required to file for a federal income tax return.
One of the shortened form of Tax form 1040 is the 1040-A.
1040-A form enables one to claim some adjustment. This include filing as an household head instead of a single person, claiming dependent and retirement savings, tax deductions, earned income, education, etc.
Form 1040-A is appropriate for the couple as it would allow them have a joint tax return and make tax deductions on their student loans.
Answer:
the other person was correct
The answer is D on edg2020
What are the solution(s) of the quadratic equation 98 – x2 = 0?
x = Plus or minus 2 StartRoot 7 EndRoot
x = Plus or minus 6 StartRoot 3 EndRoot
x = Plus or minus 7 StartRoot 2 EndRoot
no real solution
Answer:
c on ed
Step-by-step explanation:
just took the unit test
Answer:
The answer is c
Step-by-step explanation:
98 - x² = 0
x² = 98
x = ±√98
Lets factor 98
98 | 2
49 | 7
7 | 7
1
So, 98 = 2 . 7 . 7 = 2 . 7²
x = ±√2.7²
x = ±7√2
Hope this helps!!!
Angle x is coterminal with angle y. If the measure of angle x is greater than the measure of angle y, which statement is true
regarding the values of x and y?
©
X = y - 180n for any positive integer n
X-y-360n for any integer n
X = y + 360n for any positive integer n
x = y + 180n for any integern
The statement which is true regarding the values of x and y is option C; x=y+360n , for any positive integer n.
What are Coterminal angles?The algebraic sum of Coterminal angles at a point is 360°.
From the given information;
Angle x is coterminal with angle y.
If the measure of angle x is greater than the measure of angle y.
Then, the statement which is correct is will be as;
x = y + 360n , for any positive integer n.
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What is the center of the circle with the equation: X2 + y2 +18x + 14y + 105 = 0
Answer:
(9, -7)
Step-by-step explanation:
[tex]x^2+y^2+18x+14y+105=0\\[/tex]
Rearrange like x and y terms next to each other, then complete the square on both.
[tex](x-9)^2-361 + (y+7)^2 - 49 + 105 = 0[/tex]
The negative of the # numbers instead the brackets give you the centre of the circle.
The given equation does not represent a circle because the radius is an imaginary number.
Explanation:The given equation represents a circle in the Cartesian coordinate plane. The general form of a circle equation is (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r is the radius. By rearranging the equation, we can find the centre by completing the square for both x and y.
For the given equation, x² + y² + 18x + 14y + 105 = 0, we complete the square for x by adding (18/2)² = 81 to both sides of the equation and for y by adding (14/2)² = 49 to both sides of the equation. This gives us:
(x² + 18x + 81) + (y² + 14y + 49) + 105 - 81 - 49 = 0
(x + 9)² + (y + 7)² = -175
The equation (x + 9)² + (y + 7)² = -175 does not represent a circle because the radius, which is the square root of -175, is an imaginary number. Therefore, the given equation does not have a real centre or radius.
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Item 5 A spotlight on the ground shines a beam of light to the top of a tree that is 12 m tall. The beam of light makes an angle of 40° with the ground. What is the distance from the spotlight to the base of the tree, rounded to the nearest meter? 10 m 14 m 16 m 19 m PreviousFinish
Answer:
14 m
Step-by-step explanation:
We are given that
Height of tree=AB=12 m
[tex]\theta=40^{\circ}[/tex]
We have to find the distance from the spotlight to the base of the tree.
We know that
[tex]tan\theta=\frac{perpendicular\;side}{base}[/tex]
[tex]\frac{AB}{BC}=tan40[/tex]
[tex]\frac{12}{BC}=tan40[/tex]
[tex]BC=\frac{12}{tan40}=14.3\approx 14[/tex]
Hence, the distance from the spotlight to the base of the tree=14 m
Quart cartons of milk should contain at least 32 ounces. A sample of 22 cartons was taken and amount of milk in ounces was recorded. We would like to determine if there is sufficient evidence exist to conclude the mean amount of milk in cartons is less than 32 ounces?
If the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.
To determine if there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces, we would conduct a hypothesis test. The null hypothesis (H0) would state that the mean amount of milk in cartons is at least 32 ounces, while the alternative hypothesis (Ha) would state that the mean amount is less than 32 ounces.
The null hypothesis: [tex]\( H_0: \mu \geq 32 \)[/tex]
The alternative hypothesis: [tex]\( H_a: \mu < 32 \)[/tex]
Here is the step-by-step process to conduct the hypothesis test:
1. **Identify the sample mean [tex](\( \bar{x} \))[/tex] and the sample standard deviation (s).** These values would be calculated from the sample of 22 cartons.
2. **Calculate the test statistic (t-score).** The formula for the t-score in a one-sample t-test is:
[tex]\[ t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}} \][/tex]
where [tex]\( \mu_0 \)[/tex] is the hypothesized mean (32 ounces in this case), [tex]\( \bar{x} \)[/tex] is the sample mean, [tex]\( s \)[/tex] is the sample standard deviation, and [tex]\( n \)[/tex] is the sample size.
3. **Determine the degrees of freedom (df).** For a one-sample t-test, the degrees of freedom are [tex]\( n - 1 \)[/tex], where [tex]\( n \)[/tex] is the sample size. In this case, [tex]\( df = 22 - 1 = 21 \)[/tex].
4. **Find the critical t-value or p-value.** Using the degrees of freedom, we can find the critical t-value from a t-distribution table or calculate the p-value. The significance level (α) is typically set at 0.05 for such tests.
5. **Make a decision.** If the test statistic is less than the critical t-value or if the p-value is less than α, we reject the null hypothesis in favor of the alternative hypothesis. This would mean there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces.
6. **Calculate the p-value.** The p-value is the probability of observing a sample mean at least as extreme as the one observed, assuming the null hypothesis is true. It can be calculated using statistical software or a t-distribution table.
7. **Report the results.** If the p-value is less than α, we report that there is sufficient evidence to conclude that the mean amount of milk in cartons is less than 32 ounces. If the p-value is greater than α, we report that there is not enough evidence to conclude that the mean amount is less than 32 ounces.
Without the actual sample data (sample mean and sample standard deviation), we cannot perform the calculations or make a conclusion. However, if the sample mean is substantially less than 32 ounces and the sample standard deviation is small, it is more likely that we will reject the null hypothesis. Conversely, if the sample mean is close to 32 ounces or the sample standard deviation is large, it is less likely that we will reject the null hypothesis.
Which statements best describe displacement? Check all that apply.
Displacement is measured along the path an object travels.
Displacement is a measurement that includes direction.
Displacement is the difference between a starting point and an ending point.
Displacement is how far an object travels from starting point to ending point.
Displacement is measured as a straight line between a starting point and an ending point.
Answer: displacement is a measure that includes direction
Displacement is the difference between a starting point and a ending point
Displacement is measured as a straight line between a starting point and an ending point
Step-by-step explanation:
Alex, a manager at Symbic Inc., plotted the company's total energy costs of 1 billion dollars over the past 10 years on a chart. The chart suggested that the energy costs appear to be increasing in a fairly predictable linear fashion and that the energy costs are related to time by a linear function Y t =3+5t, where Y trepresents the estimate of the energy cost in year t. Given the equation, which of the following is the value of the intercept of the straight line that best fits the time series?
A. 1
B. 3
C. 5
D. 10
What is the approximate volume of the cylinder of 4cm and 9cm? Use 3.14 for π.
The volume of the cylinder is 452.16 cubic centimeter
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
We have to find the volume of cylinder
Radius of cylinder is 4cm and height is 9cm
The formula for volume of cylinder = πr²h
Plug in the values of r and h
Volume = π(4)²(9)
= π×16×9
=3.14×16×9
=452.16 cubic centimeter
Hence, the volume of the cylinder is 452.16 cubic centimeter
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The approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm is 452.16 cm³, using the formula V = πr²h with π approximated as 3.14.
Calculating the Volume of a Cylinder
To find the approximate volume of a cylinder with a radius of 4 cm and a height of 9 cm using 3.14 for π, you can use the formula for the volume of a cylinder, which is V = πr²h. In this case, V = 3.14 × (4 cm)² × 9 cm.
First, calculate the area of the base (which is a circle) by squaring the radius and multiplying by π: Area = π × r² = 3.14 × 4² = 3.14 × 16 = 50.24 cm². Next, multiply the area of the base by the height of the cylinder to get the volume: Volume = Area × Height = 50.24 cm² × 9 cm = 452.16 cm³.
Therefore, the approximate volume of the cylinder is 452.16 cm³.
starting in the year 1800 the population of the untied states recored until the year 2000
Final answer:
The population of the United States grew from around 5 million in 1800 to approximately 281 million in 2000, with growth rates declining over time due to lower birth rates and increasing reliance on immigration.
Explanation:
The population growth of the United States from 1800 to 2000 showcases remarkable changes over two centuries. Starting with the beginning of the 19th century, the US population was around 5 million and by the year 2000, it had grown to approximately 281 million according to the decennial census data. This substantial increase can be attributed to various factors including immigration, natural growth, and economic prosperity.
During the early 1800s, the population saw a significant surge, increasing by 38% between 1800 and 1810. However, as time progressed, the growth rate began to slow down. Between 1900 and 1910, the growth rate was at 21%, and it further reduced to 10% between 2000 and 2010. The declining growth rates in the later years are linked to a decrease in the total fertility rate (TFR), which at 1.9, is below the replacement rate of 2.1. The nation's population started to rely more on immigration for its growth as the birth rates declined.
In terms of economic impact, the period between 1850 and 1860 is noted for its astounding economic growth despite political tensions, where the nation's wealth and various economic indicators such as farm value and product manufacturing saw increases surpassing 100%.