Find the values of m and n. Give the answer in simplest radical form.
PLS HELP ASAPP!!!!!!
Answers
The values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine
What is trigonometric ratios?The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.
The basic trigonometric ratios includes;
sine, cosine and tangent.
recall that sin60° = √3/2 and sin30° = 1/2
sin 60° = m/(24√3) {opposite/hypotenuse}
√3/2 = m/(24√3)
m = (24√3 × √3)/2 {cross multiplication}
m = 12 × 3
m = 36
sin 30° = n/(24√3)
1/2 = n/(24√3)
n = 24√3/2 {cross multiplication}
n = 12√3
Therefore, the values of the side m and n for the right triangle are 36 and 12√3 respectively using the trigonometric ratio of sine
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Related Questions
What is the rate of change for the interval between 0 and
2 for the quadratic equation as f(x) = 2x² + x - 3
represented in the table?
O
23/1/2
04
05
O 10
Answers
\(\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= 2x^2 + x -3 \qquad \begin{cases} x_1=0\\ x_2=2 \end{cases}\implies \cfrac{f(2)-f(0)}{2 - 0} \\\\\\ \cfrac{[2(2)^2 + (2) -3]~~ - ~~[2(0)^2 +(0) -3]}{2}\implies \cfrac{7-(-3)}{2}\implies \cfrac{7+3}{2}\implies \text{\LARGE 5}\)
The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.
What is the average rate change?It is the average amount by which the function varied per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph depicting the function.
Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]
The function is given below.
f(x) = 2x² + x - 3
The rate of change of the function for the interval between 0 to 2 is calculated as,
Average rate = [f(2) - f(0)] / [2 - 0]
Average rate = [(2(2)² + 2 - 3) - (2(0)² + 0 - 3)] / 2
Average rate = 10 / 2
Average rate = 5
The rate of change for the interval between 0 and 2 for the quadratic equation will be 5. Then the correct option is C.
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Determine the endpoints of the midsegment connecting side YX and side YZ. Question options: A) (4, 3) and (8, 0) B) (9, –4) and (7, 4) C) (4, 3) and (5, –1) D) (1, 2) and (7, 4)
Answers
Answer:c) (4,3) and (5.-1)
Step-by-step explanation:
The endpoints of the midsegment connecting side YX and side YZ
(4, 3) and (-3/2, 11/2).
What is a midpoint of a line segment?The midpoint of a line segment is given as,
x = (a + c)/2
y = (b + d) / 2
Where (x, y) is the midpoint and (a, b) and (c, d) are the two endpoints.
We have,
X = (7, 4)
Y = (1, 2)
Z = (-4, 9)
The midpoint of YX is (4, 3).
i.e
x = (1 + 7)/2 = 4 and y = (2 + 4)/2 = 3
The midpoint of YZ is (-3/2, 11/2).
i.e
x = (-4 + 1)/2 = -3/2 and y = (9 + 2)/2 = 11/2
Thus,
The endpoints of the midsegments are
(4, 3) and (-3/2, 11/2).
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Suppose Derrick is an insect enthusiast who measured the body length and weight of three insects in his backyard. His data are shown in the table.
Answers
Answer:
Step-by-step explanation:
HURRY IM ON A TIME LIMIT!!!
What is the measure of DEF?
E
28
135
F
[Not drawn to scale)
452
739
1079
1179
Answers
Answer:
I think it is 107
Step-by-step explanation:
Its too wide for it to be 73 but too short to be 117
the measure of def is 107
Evaluate a³ - b + 7, if a = 3 and b
=4
Answers
⇒Plug in the given values of the variables in order and then simplify the expression
Given that a= 3 and b=4
⇒\(=(3)^{3} -(4)+7\\=27-4+7\\=23+7\\=30\)
⇒The expression evaluated at the given known variables gives 30.
In Ivy’s neighborhood, 40% of the homes have a swimming pool. If there are 80 homes in the neighborhood, then how many have a swimming pool?
Answers
Answer:
32 homes
Step-by-step explanation:
To get the amount of homes with a pool, simply do
HOMES * 0.40
So 80x0.4 = 32 homes with a pool
f(x) = 6^2+12x -7
please answer and explainnnn!
Answers
Answer:
A) \(x=-1\pm\sqrt{\frac{13}{6}}\)
Step-by-step explanation:
\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)
A-6=13 answer........
Answers
Answer:
A = 19
Step-by-step explanation:
A - 6 = 13
19 - 6 = 13
A = 19
I hope this helps!
Answer:
19
Step-by-step explanation:
13 + 6 = 19
19 - 6 = 13
What is the sum of 6 cups and 4 pints?
Answers
Answer:
14 us cups
Step-by-step explanation:
1. Define, compare and contrast common stock and preferred stock.
2. Define, compare and contrast dividends and dividends in arrears.
3. Define, compare and contrast bond premium and discount.
4. What are the 3 main fee structures of mutual funds?
5. What is NAV and how is it calculated?
Answers
Common Stock:
- Represents ownership in a company and a claim on a portion of the company's assets and earnings.- Has voting rights, allowing shareholders to participate in corporate decision-making.- Dividends are not guaranteed and can fluctuate.- In the event of liquidation, common stockholders are paid after preferred stockholders.Preferred Stock:
- Represents partial ownership in a company but typically does not carry voting rights.- Typically has a fixed dividend rate, which is paid before dividends to common stockholders.- In the event of liquidation, preferred stockholders have priority over common stockholders.- Can be converted to common stock or have a callable feature, allowing the company to redeem shares at a predetermined price.Comparison:
- Common stockholders have voting rights, while preferred stockholders generally do not.- Preferred stock usually has a fixed dividend rate, while common stock dividends can fluctuate.- Preferred stockholders have priority in receiving dividends and in the event of liquidation.2. Dividends vs Dividends in Arrears:Dividends:
- Payments made by a corporation to its shareholders, usually in the form of cash or additional shares.- Typically paid from a company's profits or retained earnings.- Can be regular (e.g., quarterly) or special (one-time) dividends.Dividends in Arrears:
- Unpaid dividends owed to preferred stockholders.- Occur when a company does not pay the full dividend amount it has committed to for preferred stockholders.- Must be paid before any dividends can be paid to common stockholders.Comparison:
- Dividends are regular or special payments to shareholders, while dividends in arrears are unpaid dividends owed to preferred stockholders.- Dividends in arrears must be paid before any dividends can be paid to common stockholders.3. Bond Premium vs Bond Discount:Bond Premium:
- Occurs when a bond's market price is higher than its face value.- Usually results from a decrease in market interest rates, making the bond's fixed interest payments more attractive to investors.- Bond premium is amortized over the life of the bond, reducing the bond's book value.Bond Discount:
- Occurs when a bond's market price is lower than its face value.- Usually results from an increase in market interest rates, making the bond's fixed interest payments less attractive to investors.- Bond discount is amortized over the life of the bond, increasing the bond's book value.Comparison:
- A bond premium represents a bond selling for more than its face value, while a bond discount represents a bond selling for less than its face value.- Bond premiums typically occur when market interest rates decrease, while bond discounts occur when market interest rates increase.4. 3 Main Fee Structures of Mutual Funds:1. Sales Loads: Fees paid when buying or selling shares of a mutual fund. They can be front-end loads (charged when buying shares) or back-end loads (charged when selling shares).
2. Expense Ratio: The annual fee that covers the fund's operating expenses, including management fees, administrative fees, and other costs. It is expressed as a percentage of the fund's average net assets.
3. 12b-1 Fees: Annual fees charged by some mutual funds to cover marketing and distribution expenses. These fees are included in the fund's expense ratio.
5. NAV (Net Asset Value):- NAV represents the per-share value of a mutual fund, calculated by dividing the fund's total net assets by the number of outstanding shares.- Total net assets are calculated by subtracting the fund's liabilities from its total assets.- NAV is typically calculated at the end of each trading day and is the price at which investors can buy or sell shares of the mutual fund.A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings - - - Sauce (cups) - - - Oregano (tsp)
- - - 3- - - - - - - - - - - 6 - - - - - - - - - - - - - -1 & 1/2
8---
At this rate, how much sauce and oregano will be needed to make 8 servings?
A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.
B) The recipe will need 16 cups of sauce and 4 teaspoons of oregano for 8 servings.
C) The recipe will need 14 cups of sauce and 4 teaspoons of oregano for 8 servings.
D) The recipe will need 14 cups of sauce and three and a half teaspoons of oregano for 8 servings.
Answers
The correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.
To determine the amount of sauce and oregano needed to make 8 servings, we can use the ratio of sauce to oregano from the table.
According to the table, for 3 servings, 6 cups of sauce are used along with 1 & 1/2 teaspoons of oregano. We need to find the ratio of sauce to oregano to scale it up for 8 servings.
Ratio of sauce to oregano:
6 cups of sauce / 1 & 1/2 teaspoons of oregano = 6/1.5 = 4 cups of sauce per teaspoon of oregano
Now, for 8 servings, we need to multiply the ratio by the number of teaspoons of oregano required:
8 servings * 1 teaspoon of oregano = 8 teaspoons of oregano
Therefore, for 8 servings, we would need:
8 teaspoons of oregano * 4 cups of sauce per teaspoon of oregano = 32 cups of sauce
Therefore, the correct answer is A) The recipe will need 16 cups of sauce and three and a half teaspoons of oregano for 8 servings.
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g(0)=-4x^2-3x+2
g(2)=-4^2-3x+2
Answers
The simplified value for the function at g(0) and g(2) are 2 and -20 respectively.
What is simplification?To simplify is to make something simpler. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. The issue is made simpler by calculations and problem-solving strategies. We can simplify fractions by removing all common elements from the numerator and denominator and putting the fraction in its simplest/lowest form.
Given a function g(x) = -4x² - 3x + 2
to find the values of g(0)
and g(2)
for g(0)
substitute x = 0 in the equation,
g(x) = -4x² - 3x + 2
g(0) = -4(0)² - 3(0) + 2
g(0) = 2
for g(2), substitute x = 2 in the equation,
g(x) = -4x² - 3x + 2
g(2) = -4(2)² -3(2) + 2
g(2) = -4(4) - 6 + 2
g(2) = -16 - 6 +2
g(2) = -20
Hence the values for g(0) is 2 and for g(2) is -20.
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In a manufacturing process, the assembly line speed (feet per minute) is believed to affect the number of defective parts found during the inspection process. Data (File 3) are collected on the number of defective parts for a variety of line speeds. Develop a linear regression equation that can be used to predict the number of defective parts given the line speed.
Line Speed Number of Defective Parts Found
20 21
20 19
40 15
30 16
60 14
40 17
Required:
a. Develop a scatter chart with line speed as the independent variable. What does the chart indicate about the relationship between line speed and the number of defective parts found?
b. Use the data to develop an estimated regression equation that could be used to predict the number of defective parts found, given the line speed. What is the estimated regression model?
c. Test whether each of the regression parameters βo and β1 is equal to zero at 0.01 level of significance. What are the correct interpretations of the estimated regression parameters?
d. How much of the variation in the number of defective parts found for the sample data does the model you estimated in part (b) explain?
Answers
Answer:
Jaime foxcgvxccvyyvytctvtvffddrgfgqvrctcrgctgtgtgygyg goku is the site
A certain type of kickboard scooter comes in silver, red, 2
or purple with wheel sizes of 125 millimeters or 180
millimeters. Determine the total number of color-wheel size combinations.
(This is probability and I’m having such a hell of a time figuring it out pls help)
Answers
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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In which of these situations do the quantities combine to make 0? 4 of 5 QUESTIONS A player in a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive. OA bird flies 25 feet up in the air. It then flies 25 feet across to its nest. Veronica receives $21 for babysitting. She then spends $21 on a new shirt. SUBMIT
Answers
The situation Veronica receives $21 for babysitting, and then spends the same amount, $21, on a new shirt quantities combine to make 0.The correct answer is option C.
When we add +21 (the money she receives) and subtract -21 (the money she spends), the result is 0. This means that the net change in Veronica's money is zero, indicating that the quantities combine to make 0.
In situations A, B, and D, the quantities do not combine to make 0. In situation A, the player earns 4 points for getting an answer right and then earns an additional 4 points for making it around the board.
The total points earned in this situation would be 8, which is not equal to 0.
In situation B, the car is initially filled with 10 gallons of gas, but then half of that, which is 5 gallons, is used on a day's drive. The remaining fuel in the car would be 5 gallons, which is also not equal to 0.
In situation D, the bird flies 25 feet up in the air and then 25 feet across to its nest. The total distance traveled by the bird would be 50 feet, which is not equal to 0.
Therefore, only in situation C, where Veronica receives and spends the same amount of money, do the quantities combine to make 0.
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The probable question may be:
In which of these situations do the quantities combine to make 0?
A. A player a game earns 4 points for getting an answer right. She then earns 4 points for making it around the board.
B. A car is filled with 10 gallons of gas. Half of the 10 gallons are then used on a day's drive.
C. Veronica receives $21 for babysitting. She then spends $21 on a new shirt.
D. A bird flies 25 feet up in the air. It then flies 25 feet across to its nest.
calculate the mean deviation of the following numbers 8,5,7,10,3,4,31,12.
Answers
Answer:
5.75.
Step-by-step explanation:
The mean = (8+5+7+10+3+4+31+12)/ 8
= 80/8
= 10.
Now we calculate the difference of each value from the mean We take the absolute ( positive) differences
10 - 8 = 2
10 - 5 = 5
10 - 7 = 3
10 - 10 = 0
10-3 = 7
10 = 4 = 6
10 - 31 = 21
10 - 12 = 2
Sum of the differences = 46
and the mean deviation is 46/8 = 5.75.
a-3xb if a = 20 and b= 5
Answers
Answer:
5
Step-by-step explanation:
3x5 = 15
20-15 = 5
Answer:
5
Step-by-step explanation:
20-3x5=
3x5=15
20-15=5
hope this helps!!
Mr. Tanner bought some boxes of markers with 18 markers in each box. He kept 2 markers and gave the rest to his students. Use the equation below to calculate the number of boxes (b) he bought. 18b – 2 = 214
Answers
Answer: 18b-2+2=214 +2
Step-by-step explanation:Add 2 both sides of the equation
Answer:
b = 12; he bought 12 boxes.
Step-by-step explanation:
18b - 2 = 214 (subtract 2 on both sides)
18b = 216 ( divide 18 on both sides to get 'b' alone)
b = 12
x(x+3)(x+3)=0 Plz I need this fast!
Answers
Answer:
x=0,-3
Step-by-step explanation:
x(x+3)(x+3)=0
Using the zero product property
x=0 x+3=0 x+3 =0
x=0 x=-3 x=-3
tia equally shares 8 cookies among herself and 4 friends which fraction shows how many cookies each person gets?
answers:
8/4
8/5
5/8
4/8
Answers
Answer: The answer is 8/5
Answer:
Each person gets 8/5 part of cookie
Write the equation of a line that is parallel to x=−5 and that passes through the point (1, 4)
Answers
Answer:
x = 1
Step-by-step explanation:
The equation x = -5 is a vertical line through point (-5, 0) on the x-axis.
For a line to be parallel to the line x = -5, it must be a vertical line.
Since the vertical line must include the point (1, 4), then the x-coordinate of every point on that line must be 1.
The equation is x = 1.
PLS HELP The histogram displays donations in dollars to a charity. A histogram titled Donations to Charity In Dollars with the x-axis labeled Donations. The x-axis has intervals of 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Number of Donations and starts at 0 with tick marks every one unit up to 5. There is a shaded bar above 10 to 19 that stops at 4, above 20 to 29 that stops at 3, above 30 to 39 that stops at 1, and above 50 to 59 that stops at 1. There is no shaded bar for 40 to 49. Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 49. This might happen if the charity suggested donation minimum of $35 and donors followed that.
The data is skewed, with a maximum range of 49. This might happen if the donations were only allowed in cash and many donors did not have much cash on them.
The data is bimodal, with a maximum range of 49. This might mean that the most popular amounts to donate were between 10 and 19 and 51 and 59 dollars.
The data is symmetric, with a maximum range of 59. This might happen if everyone donated a percent of their salaries.
Answers
Based on the given histogram, the data is skewed with a maximum range of 49.
This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.
One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.
Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.
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Trong không gian với hệ tọa độ Oxyz cho điểm A( 1;2;1) , mặt phẳng ( ) : 4 0 x y z và
mặt cầu ( ) : 1 1 4 36 S x y z 2 2 2 . Gọi (P) là mặt phẳng đi qua A , vuông góc với ( ) và
đồng thời (P) cắt mặt cầu (S) theo giao tuyến là một đường tròn có bán kính nhỏ nhất. Biết rằng phương
trình của mặt phẳng (P) khi đó là ax by cz a b c 1 0 ( , , ) . Tính giá trị biểu thức T a b c 2 .
A. T 5
.
B. T 3
.
C. T 10
.
D. T 1
.
Answers
Answer:
lỗi text rồi. ko đọc dc :))
Keiko is going for a walk.she takes 3 hours to walk 7.5 miles.what is her speed
Answers
Answer:
2.5 mph
Step-by-step explanation:
Select the sets that are not functions.
O E = ((6. 2). (7. 3). (6, -1). (5. 4)]
O A = {(1, 2), (2, 3), (3, 4). (4. 5)}
O C = [(-1, 3), (0.3), (1, 3), (2, 3)}
OB = {(1, 2), (2, 1), (3, 0), (4, -1)]
OD = {(1, 1), (1, 2), (1, 3), (1. 4)}
Answers
Nicks lunch cost $14.75 tax was 1.03 and he left a tip of 2.50 how much did he pay for his lunch
Answers
Answer:
$18.28
Step-by-step explanation:
To complete this problem is a straightforward answer:
First, you add 14.75 + 1.03 which equals $15.78 then, you'll want to add 2.50 to 15.78 and there you have your answer!!
Please help me solve these 3 math problems
Answers
The domain of the rational function h(x) = (x - 3)/(x² - 4) is equal to (-∞, -2) ∪ (-2, 2) ∪ (2, ∞).
The possible points that would lie on h(x) = x² - x + 1 are (3, 7).
True: (1, -1) is a point of the graph of f(x) = -2(x + 1)² + 7.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
From the graph of h(x) = (x - 3)/(x² - 4), the domain in interval notation and set builder notation is as follows;
Domain = (-∞, -2) ∪ (-2, 2) ∪ (2, ∞)
Domain = {x|x ≠ 2, -2}.
Next, we would determine possible x-value for the given quadratic function as follows;
h(x) = x² - x + 1
7 = x² - x + 1
7 - 1 = x² - x
6 = x² - x
x² - x - 6 = 0.
x² - 3x + 2x - 6 = 0.
x(x - 3) + 2(x - 3) = 0
(x + 2)(x - 3) = 0
x = 3 or x = -2.
For second quadratic function f(x) = -2(x + 1)² + 7, we have:
f(x) = -2(x + 1)² + 7
-1 = -2(1 + 1)² + 7
-1 = -2(2)² + 7
-1 = -8 + 7
-1 = -1 (True).
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3. What is the slope of a line perpendicular to the line y =-2/3
x+12
Answers
Answer:
Slope of line (i) = 1.5
Step-by-step explanation:
Line (i) is perpendicular to;Line (ii) whose equation is y = \(-\frac{2}{3} x + 12\)The slope of line (ii) = \(-\frac{2}{3}\)
* Mathematics rule: The product of slopes of two perpendicular lines = -1
∴ The slope of line (i) = -1 ÷ \(-\frac{2}{3}\) = 3/2 = 1.5
A child is standing across the street from his apartment. His mother is on their balcony. The angle of elevation between the child's eyes and his mother's eyes is 28°. If the distance between their eyes is 35 ft, how far is the child standing from his apartment building? Round to the nearest foot.
Answers
whitch figure is showig a ray
Answers
Answer: D.
Step-by-step explanation: It is a figure with no height or length, and it has indefinite length. Two rays are needed to make an angle.