Answer:
1.2.05 2.0.919 3 sf
Step-by-step explanation:
1. cos 70=x/6
6 cos 70=x
x=2.05
2.cos 45=x/1.3
1.3 cos 45=x
x=0.919
3.cant see ;-;
HELP!!!!!!!!!!!!!!!!!!
Answer:
D 0.89275
Step-by-step explanation:
An investment account earns 4% the first year, 5% the second year, and X% the third year. Find X if the three year average interest rate is 10%.
Answer:
The answer is 1 percent because if you add the 5% and 4% you get 9% and all there is left of the average interest 10 and get 1
Step-by-step explanation:
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Can I please get some help I’ve been stuck on this question for a while!
Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes
How many minutes of the ride are spent higher than 28 meters above the ground?The radius of the Ferris wheel is 30 / 2 = 15 meters.
The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.
The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.
The angle between these two positions is 180 degrees.
The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.
Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.
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help. use the figure shown to the right to find the value of x
Answer:
\(\begin{aligned}x &= 16\sqrt3 \\ &\approx 27.7\end{aligned}\)
Step-by-step explanation:
We can see that the longer leg (a) of a right triangle is half of the circle's radius. Since we are given the other two sides of the triangle (shorter leg and hypotenuse), we can solve for the length of the longer leg using the Pythagorean Theorem:
\(a^2 + b^2 = c^2\)
↓ plugging in the given values
\(a^2 + 2^2 = 14^2\)
↓ subtracting 2² from both sides
\(a^2 = 14^2 - 2^2\)
\(a^2 = 196 - 4\)
\(a^2 = 192\)
↓ taking the square root of both sides
\(a = \sqrt{192\)
↓ simplifying the square root
\(a = \sqrt{2^6 \cdot 3\)
\(a = 2^{\, 6 / 2} \cdot \sqrt3\)
\(a = 2^3\sqrt3\)
\(a = 8\sqrt3\)
Now, we can solve for the radius (x) using the fact that the longer leg of the triangle is half of it.
\(a = \dfrac{1}{2}x\)
↓ plugging in the a-value we solved for
\(8\sqrt3 = \dfrac{1}2x\)
↓ multiplying both sides by 2
\(\boxed{x = 16\sqrt3}\)
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Find the amount in a continuously compounded account for the following condition.
Principal, $2000; Annual interest rate, 5.1%; time, 3 years
Whats the balance after 3 years?
Answer:
The balance in the account after 3 years is approximately $2313.94.
Step-by-step explanation:
The formula for calculating the balance in a continuously compounded account is:
B = Pe^(rt)
Where:
B = balance
P = principal
e = Euler's number (approximately 2.71828)
r = annual interest rate (as a decimal)
t = time in years
Using the given values, we have:
P = $2000
r = 0.051 (5.1% expressed as a decimal)
t = 3
Plugging these values into the formula, we get:
B = 2000e^(0.051*3)
B = 2000e^(0.153)
B = $2313.94 (rounded to the nearest cent)
Therefore, the balance in the account after 3 years is approximately $2313.94.
4. Which equation is true?
O A, 4+ (-2) = (-5) - 7
O B.11 – 4 = 8 - (-
O c.5+ 3 = (-1)-(-9)
OD (-6) + (-1) = 2 - (-5)
Please answer quickly
Answer:
C
Step-by-step explanation:
5+3 = (-1)-(-9)
5+3 =(-1)+9
8 = 8
Copper costs £5 per kilogram.
Zinc costs £3.20 per kilogram.
Copper and zinc are mixed in the ratio 4:1 to make brass.
Work out the cost of 7 kilograms of brass
Answer:
4x(5)+1×(3.20)= 20+3.20=23.20
Step-by-step explanation:
The cost of 7kg of brass is £32.48.
What is ratio?
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
According to the given question.
Cost of one kg of copper = £5
Cost of one kg of zinc = £3.20
Also, copper and zinc are mixed in the ratio 4:1.
Let the quantity of copper be 4x and the quantity of zinc 1x.
Weight of brass = 7kg
⇒ 4x + 1x = 7
⇒ 5x = 7
⇒ x = \(\frac{7}{5}\)
⇒ x = 1.4
Weight of copper, 4x = (1.4)(4) = 5.6kg
Weight of zinc, 1x = (1) ×(1.4) = 1.4kg
Therefore,
The cost of 7kg of brass
= (5.6)×(£5) + (1.4)(£3.20)
= 28 + 4.48
= £ 32.48
Therefore, the cost of 7kg of brass is £32.48
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Which is the graph of g(x)=[x+3
The graph of the function g(x) = x + 3 is a straight line that passes through the point (0, 3) on the y-axis and has a slope of 1.
To understand how to plot the graph, let's consider a few points on the line.
We can choose any values for x and calculate the corresponding values for g(x).
Let's start with x = 0.
Substituting this value into the function, we get g(0) = 0 + 3 = 3.
So, the point (0, 3) is on the graph.
Next, let's choose x = 1.
Substituting this value into the function, we get g(1) = 1 + 3 = 4.
This gives us another point on the line, (1, 4).
Similarly, we can choose more values for x and calculate the corresponding values for g(x).
For example, if we let x = -1, we get g(-1) = -1 + 3 = 2, giving us the point (-1, 2).
By connecting these points and extending the line in both directions, we obtain a straight line that represents the graph of g(x) = x + 3.
The line has a positive slope of 1, which means it rises by 1 unit vertically for every 1 unit it moves horizontally.
Overall, the graph of g(x) = x + 3 is a straight line that passes through the point (0, 3) and has a slope of 1.
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the equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940. In this equation, a represents the average age and x represents the years since 1940. Estimate the year in which the average age of brides was the youngest
Answer:
Please help me important question in image
Step-by-step explanation:Please help me important question in image
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Answer:
The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.
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A high school baseball player has a 0.269 batting average. In one game, he gets 8 at bat. What is the probability he will get at least 3 hits in the game? Round your answer to four places.
So, the probability that the player will get at least 3 hits in the game is 0.3991, rounded to four decimal places.
What is Probability?Probability is a measure of the likelihood or chance that a particular event or outcome will occur, expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur. It is a branch of mathematics that deals with the study of random events and the laws governing them. Probability theory is used to analyze and quantify uncertainty and to make predictions about the likelihood of future events based on past observations and data. It is widely used in fields such as statistics, economics, physics, engineering, and finance to model and understand the behavior of complex systems that involve random variables.
Given by the question.
We can use the binomial distribution to model the number of hits the player gets in the game. Let X be the number of hits in the game, then X follows a binomial distribution with parameters n=8 (number of at-bats) and p=0.269 (probability of a hit).
The probability of getting at least 3 hits can be calculated as:
P (X >= 3) = 1 - P (X < 3)
where P (X < 3) is the cumulative probability of getting 0, 1, or 2 hits.
Using the binomial distribution formula, we can calculate P (X < 3) as follows:
P (X < 3) = P (X = 0) + P (X = 1) + P (X = 2)
P (X < 3) = (8 choose 0) * \((0.269)^{0}\) * \((1-0.269)^{8}\) + (8 choose 1) * \((0.269)^{1}\) *\((1-0.269)^{7}\) + (8 choose 2) * \((0.269)^{2}\) * \((1-0.269)^{6}\)
P (X < 3) = 0.6009
Therefore,
P (X >= 3) = 1 - P (X < 3) = 1 - 0.6009 = 0.3991
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Heights of men aged 25 to 34 have a standard deviation of 2.9. Use a 0.05 significance level to test the claim that the heights of women aged 25 to 34 have a different standard deviation. The heights (in inces) of 16 randomly selected women aged 25 to 34 are listed below.
62.13 65.09 64.18 66.72 61.15 67.50 64.65 63.09
63.80 64.21 60.17 68.28 66.49 62.10 65.73 64.72
Select the correct conclusion based on the null hypothesis and final conclusion
Answer:
Based on the given data, there is no evidence to support the claim that the standard deviation of the heights of women aged 25 to 34 have a different standard deviation from men aged 25 to 34
Step-by-step explanation:
The standard deviation for the heights of men aged 25 to 34, σ₀ = 2.9
The population variance, σ₀ = 2.9² = 8.41
The significance level of the test = 0.05
The number of randomly selected women in the sample, n = 16
The given heights of the 16 randomly selected women are listed as follows;
62.13, 65.09, 64.18, 66.72, 61.15, 67.50, 64.65, 63.09, 63.80, 64.21, 60.17, 68.28, 66.49, 62.10, 65.73, 64.72
By using the Mean (Average) and standard deviation of a sample formula from Microsoft Excel, we have;
The mean height of the women, \(\overline x\) = 63.37563
The standard deviation of the variance, s₂ = 2.2 78511
The null hypothesis, H₀; σ = 2.9
The alternative hypothesis, H₀; σ ≠ 2.9
The chi-square test is given as follows;
T = (N - 1)(s/σ₀)²
Therefore, we have;
T = (16 - 1)(2.278511/2.9)² ≈ 9.2597
The critical value for the lower tail = 6.908
The critical value for the upper tail = 28.845
For the critical region, we have;
Reject H₀ if T <6.908 or T > 28.845
Therefore, given that the critical T is larger than 6.908 and less than 28.845, we fail to reject the null hypothesis, and there is not enough statistical evidence to prove that there is a difference in the standard deviation of the heights of men and women aged 25 to 34
help with this please i dont understand
Answer:
A
Step-by-step explanation:
D to E is 6 units apart
Colton measured the high school and made a scale drawing. The scale he used was 1 centimeter : 2 meters. The parking lot is 88 meters long in real life. How long is the parking lot in the drawing?
centimeters
The length of the parking lot in the drawing is 44 centimeters.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.
Since the scale Colton used is 1 centimeter : 2 meters, this means that for every 2 meters in real life, he drew 1 centimeter in his scale drawing.
To find the length of the parking lot in the drawing, we can set up a proportion:
1 cm / 2 m = x cm / 88 m
where x is the length of the parking lot in the drawing in centimeters.
We can solve for x by cross-multiplying:
1 cm * 88 m = 2 m * x cm
88 cm = 2x
x = 44 cm
Therefore, the length of the parking lot in the drawing is 44 centimeters.
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Use the following sets to answer the question.
A={1,2,3,4,5}
B={5,6,7,8}
Which answer shows the union of sets A
and B?
{5}
{1,2,3,4,6,7,8,9}
{1,2,3,4,5,6,7,8}
{2,4,8}
The union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}.
The union of two sets A and B is the set of all elements that are in A, or B, or both. In this case, the elements in set A are {1, 2, 3, 4, 5} and the elements in set B are {5, 6, 7, 8}.
To find the union of these sets, we simply combine all the elements from both sets but remove any duplicates.
Therefore, the answer that shows the union of sets A and B is {1, 2, 3, 4, 5, 6, 7, 8}, since it contains all the elements from both sets without any duplicates.
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Fact families for 4 3 and 12
Answer:
i have 5 sisters my dad and mom are still married and im the youngest
PLEASE HELP!!!! (geometry)
In your own words, what is the main difference between one-way analysis of variance and two-way analysis of variance?
The main difference between one-way ANOVA and two-way ANOVA is that one-way ANOVA compares the means of two or more independent groups based on one factor, while two-way ANOVA compares the means of a dependent variable across two independent variables.
What is an ANOVA?ANOVA is a statistical technique used to determine if there is a significant difference between the means of two or more groups.
We have,
One-way analysis of variance (ANOVA).
It is a statistical test used to compare the means of two or more groups that are independent of each other.
It is called "one-way" because it involves only one independent variable.
This factor can have two or more levels or categories, and the test is used to determine if there is a significant difference in the means of the dependent variable across these levels.
Two-way analysis of variance ANOVA.
It is also a statistical test used to determine the effects of two independent variables on a single dependent variable.
The two variables can be categorical or continuous.
The test is used to determine if there is a significant interaction between the dependent variable.
Thus,
The main difference between one-way ANOVA and two-way ANOVA is that one-way ANOVA compares the means of two or more independent groups based on one factor, while two-way ANOVA compares the means of a dependent variable across two independent variables.
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A media personality argues that global temperatures are not rising because every year an increase is reported such as 0.09 degrees Celsius. The difference from the previous year is less than the margin of error of about 0.13 degrees C, so that difference should be ignored. What is the best counterargument?
The media personality's argument is flawed because they are basing their conclusion on a single year's data and ignoring the overall trend of increasing global temperatures. To counter this argument, one can make the following points:
1. While it is true that the annual increase in temperature may be less than the margin of error, the trend of increasing temperatures over several decades cannot be ignored. The margin of error is a statistical concept that takes into account the uncertainty in the measurement, but it does not negate the overall trend.
2. Global temperature records show that the Earth's temperature has been steadily rising over the past century, with the 10 warmest years on record occurring since 2005. This trend cannot be explained by natural variability alone and is consistent with the effects of human-caused climate change.
3. The consequences of rising global temperatures, such as melting glaciers, rising sea levels, and more frequent extreme weather events, are already being felt around the world. Ignoring this trend could have devastating consequences for future generations.
In summary, the media personality's argument is based on a flawed understanding of statistics and ignores the overall trend of increasing global temperatures. The best counterargument is to highlight the overwhelming evidence of climate change and its potential consequences.
You have to read 36 pages for your history class tonight. If you read 1 page every two minutes, how long will it take you to read the assigned pages?
Answer:
72 minutes or 1 hour and 12 minutes
Step-by-step explanation:
36(2)=72
Question 4
Which term in the sequence given by n th term formula 7n - 50 has a value of 41?
th term
Answer:
13th term
Step-by-step explanation:
41 = 7n - 50
41 + 50 = 7n
91 = 7n
7n = 91
n = 91/7
n = 13
13th term has value 41
Answer:
n = 13
Step-by-step explanation:
7n - 50 = 41
Add 50 to both sides
7n = 41 + 50
7n = 91
Divide both sides by 7
n = 91/7
n = 13
12. If f"(x) = x(x + 1)(x - 2)2, then the graph of f has inflection points when x =
A.-1only
B. 2only
C.-1 and 0only
D.-1 and 2 only
E. -1,0 and 2 only
Answer:
C. - 1 and 0 only
Step-by-step explanation:
(x + 1) / x = 0, - 1, 2
inflection points / when sign Changes
+ / - / + / +
"- 1 " "0" 2
^ ^
"Hope this helps"
The graph of f has inflection points when x = 0 and -1.
Given that,
If graph = f"(x) = x(x + 1)(x - 2)^2
We have to determine,
The graph of f has inflection point when x is.
According to the question,
Inflection point is the point in which the rate of slope changes in increasing to decreasing order or vice versa.
These points are generally not local maxima or minima but stationary points.
\(f''(x) = 0\)
Therefore,
The graph of f has inflection point at,
\(f''(x) = x (x+1) (x-2)^{2} = 0\\\\x = 0 \ and \ x+1 = 0 \ \ = x = -1\\\\ or \ x-2 = 0 , \\\ \ \ = x =2\)
On taking intersection of these points,
The graph has inflection points at x = 0 and -1.
Hence, The graph of f has inflection points when x = 0 and -1.
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7/4x+3 name using degree?
The polynomial 7/4x + 3 is a linear polynomial as its degree is 1
Degree is known as the highest power of the variable x in a given polynomial.
According to the degree,
If degree is 1 then the polynomial is called linear polynomial.
If degree is 2 the it is called quadratic polynomial.
If degree is 3 then it is called cubic polynomial and so on
In the given question the polynomial is 7/4x + 3. Here the degree of the polynomial is 1 that is the highest power of the variable x. Thus the polynomial will be linear polynomial.
Hence the polynomial 7/4x + 3 is linear polynomial.
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A baseball player had 4 hits in 8 games. At this rate, how many hits will the baseball player have in the next 28 games?
O 14
O24
28
O 56
Answer:
14
Step-by-step explanation:
If a baseball player records 4 hits in 8 games, then the player records 1 hit every 2 games. Therefore, the player will have 14 more hits in the next 28 games.
For breakfast, Mr. Hill bought a cup of coffee for $1.39 and a bagel for $1.85. What was his total cost?
Answer:
$3.24
Step-by-step explanation:
Cost for the coffee + Cost for the bagel
$1.39 + $1.85
$3.24
Please really need answer would greatly be appreciated and mark brainliest.
Answer:
8ft of ground is covered, 8ft of metal and about 2 feet wide, it can hold 10ft of water i think
Answer:
Step-by-step explanation:
8 feet
ABCD is a trapezium in which AB= (3x + 2) cm, DC = (x + 3) cm and AD = (x - 1) cm.
(a) Given that the area of the trapezium is 10 cm², show that 4x²+x-25 = 0.
(b) Solve this equation and hence calculate the length of AB, giving your answer in centimetres correct to 2 significant figures.
(a) The area of a trapezium is given by the formula:
Area = (1/2) × sum of parallel sides × distance between them
Substituting the given values, we get:
10 = (1/2) × (AB + DC) × h
where h is the perpendicular distance between AB and DC.
We can express h in terms of AB and DC using the Pythagorean theorem, since AD is the height of the right triangle ACD:
AD² + h² = DC²
(x - 1)² + h² = (x + 3)²
x² - 2x + 1 + h² = x² + 6x + 9
h² = 8x + 8
Substituting this value of h² in the equation for the area, we get:
10 = (1/2) × (AB + DC) × (sqrt(8x + 8) / sqrt(1))
10 = (1/2) × (AB + DC) × sqrt(8x + 8)
Substituting the given values of AB and DC in terms of x, we get:
10 = (1/2) × ((3x + 2) + (x + 3)) × sqrt(8x + 8)
10 = (2x + 5) × sqrt(8x + 8)
(2x + 5)² × (8x + 8) = 100
(2x + 5)² × 2(x + 1) = 25
4x² + 4x + 25 = 25
4x² + x - 25 = 0
(b) We can solve the quadratic equation 4x² + x - 25 = 0 using the quadratic formula:
x = [-b ± sqrt(b² - 4ac)] / 2a
where a = 4, b = 1, and c = -25.
Substituting the values, we get:
x = [-1 ± sqrt(1² - 4(4)(-25))] / 2(4)
x = [-1 ± sqrt(401)] / 8
x = (-1 ± 20.025) / 8
x = -3.128 or x = 1.628
Since the length of a side cannot be negative, we reject the negative value of x and take x = 1.628.
Substituting this value of x in the expression for AB, we get:
AB = 3x + 2 = 3(1.628) + 2 = 7.884 ≈ 7.88 cm
Therefore, the length of AB is approximately 7.88 cm, correct to 2 significant figures.
please help me this question
Answer:
x-5y
Step-by-step explanation:
6x-5x=x
-8y+3y=-5y
The coordinates of a triangle are (1, 4), (3,5), and (0,8). The coordinates of the translated triangle are (3,5), (5, 6), and (2, 9). Find the translation vector.
Since the coordinates of the translated triangle are (3,5), (5, 6), and (2, 9), the translation vector is (x, y) → (x + 2, y + 1).
What is a translation?In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of this triangle vertically upward by 1 unit and horizontally right by 2 units, the coordinates of the image include the following:
(x, y) → (x + 2, y + 1)
(1, 4) → (1 + 2, 4 + 1) = (3, 5).
(3, 5) → (3 + 2, 5 + 1) = (5, 6).
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A firm makes two products X and Y, and has a total production capacity of 9 tones per day, X and Y requiring the same production capacity. The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company. Each tone of X requires 20 machine hours of production time and each tone of Y requires 50 machine hours of production time. The daily maximum possible number of machine hour is 360. All the firm’s output can be sold, and the profit made is birr 80 per tone of X and birr 20 per tone of Y. it is required to determine the production schedule for maximum profit.
The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960
How to solve Linear Programming problems?We are told that two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity
The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.
Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;
x + y ≤ 9
x ≥ 2
y ≥ 3
Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;
20x + 50y ≤ 360
Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;
Z = 80x + 120y maximize
The solution from the graph attached is;
x = 3, y = 6
Thus, the maximum profit is;
Z = 80(3) + 120(6)
Z = 960
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The Gordon family plans to buy a TV. One TV has a purchase price of $330 and an estimated yearly operating cost of $14. The other has a purchase price of $369 and an estimated yearly operating cost of $9. Which TV should the Gordons buy if they plan to keep it for 8 years