Answer:
x = 6/7, y = 33/7
Step-by-step explanation:
y = 2x + 3 ----eq(1)
3x + 2y = 12 ----eq(2)
Substituting value of "y" from eq(1) into eq(2)
3x + 2(2x + 3) = 12
3x + 4x + 6 = 12
7x = 12-6
x = 6/7 ---eq(3)
Substituting value of x or eq(3) into eq (1)
y = 2(6/7) +3
y = 12/7 + 3
y= 12 + 21/7
y= 33/7
Therefore, x = 6/7 and y = 33/7
im having trouble on with question. if you can help thank you
A quadratic equation in standard form to represent the data in the table is as follows;
y = 0.5x² - 4x + 9
How to determine an equation of the line of best fit for the data?In order to determine a quadratic equation in standard form for the line of best fit that models the data points described above, we would use a scatter plot (graphing calculator).
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display a quadratic equation for the line of best fit (trend line) on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the data set, a quadratic equation for the line of best fit is given by:
y = 0.5x² - 4x + 9
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Please help due in 25 minutes Im in needdddd
The graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.
Cost Comparison of Book Printing Bids: Bid 7 vs Bid 8To graph the linear equations, we will use the values in the table to plot points on the coordinate plane, and then connect the points to form lines.
For Bid 7:
X y
0 5
3 50
5 80
7 110
10 155
For Bid 8:
X y
0 40
3 70
5 90
7 110
10 140
We can now plot these points on the coordinate plane and connect them to form two lines. Hence we obtain Graph of Bid 7 and Bid 8
The x-axis represents the number of books, and the y-axis represents the cost. The title of the graph is "Comparison of Bids for Book Printing Services." We can see that Bid 7 is represented by the blue line, while Bid 8 is represented by the orange line.
To create the legend, we can add a key that explains which line represents which bid. For example, we could add a note at the bottom of the graph that says "Blue line: Bid 7, Orange line: Bid 8."
Overall, the graph provides a visual representation of the cost of book printing services for each bid, allowing Bruno to easily compare the two options.
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The probability density of a random variable X is given in the figure below:
From this density, the probability that X>1.6 or X<0.36 is:
From density, the probability that X>1.6 or X<0.36 is 1 - (0.36 + 0.64) = 0.00.
What is density?Density in mathematics is a measure of how much of a certain quantity is contained within a given area or volume. It is defined as the ratio of the mass of the object to the volume of the object.
For example, the density of water is 1 gram per cubic centimeter (1 g/cm3). Density can be used to measure the concentration of a substance in a given area, such as the amount of salt in a given volume of water. Density can also help to identify different substances, such as air, oil, and water. It is an important concept in physics, chemistry, and engineering.
The probability that X>1.6 or X<0.36 is 0.00 because the density function is 0 for values outside the range from 0.36 to 1.6. The density function is a measure of how likely it is for a value of X to be within a certain range, and since the density of X is 0 for values outside the range, the probability of X being outside that range is also 0.
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from a random sample of 185 children from school g, 108 indicated they wanted to study science in college. from a different random sample of 165 children from school h, 92 indicated they wanted to study science in college. assuming all conditions for inference are met, which of the following is closest to the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college?
The difference in population proportions of students who wish to study science in college between the two schools has a standard error for a confidence interval of about 0.0165.
What is Standard Error ?One of the mathematical methods used in statistics to calculate variability is the standard error. It is referred to as SE. The standard deviation of a sample distribution serves as the standard error of a statistic or estimate of a parameter. It can be characterized as a projection of that standard deviation.
The standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college can be calculated as:
SE = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }
where p1 and p2 are the sample proportions, and n1 and n2 are the sample sizes.
For School G, p1 = 108/185 = 0.5838, and n1 = 185.
For School H, p2 = 92/165 = 0.5576, and n2 = 165.
Substituting these values into the formula, we get:
SE = sqrt{ [0.5838(1-0.5838)/185] + [0.5576(1-0.5576)/165] }
SE = sqrt{ [0.2365/185] + [0.2436/165] }
SE = sqrt{ 0.000125 + 0.000147 }
SE = sqrt{ 0.000272 }
SE = 0.0165
Therefore, the standard error for a confidence interval for the difference in population proportions between the two schools of children who want to study science in college is approximately 0.0165.
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A rock climber climbs at a rate of 720 feet per hour. Write and solve an equation to find the number of minutes $m$ it takes for the rock climber to climb 288 feet.
An equation that represents this situation is
.
It takes 24
minutes for the rock climber to climb 288 feet. I got the minutes but I need the equation. THE y=12x IS INCORRECT! I HAVE ONE CHECK LEFT!!! PLEASE HELP!!!
it takes 24 minutes for the rock climber to climb 288 feet.
How to determine?
The correct equation to represent this situation is:
$$\frac{720}{60}m=288$$
Here, we first convert the rate from feet per hour to feet per minute by dividing by 60. Then, we set up the equation where the product of the rate and the time in minutes equals the distance climbed.
Simplifying this equation, we get:
$$12m=288$$
Dividing both sides by 12, we get:
$$m=24$$
Therefore, it takes 24 minutes for the rock climber to climb 288 feet.
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When the new or compared value is P% is more than the reference value, how do you calculate the
reference value? What about less than?
Answer: If the new or compared value is P% more than the reference value, you can calculate the reference value as follows:
Reference value = New or compared value / (1 + P/100)
For example, if the new value is 120% of the reference value, then P = 20 and the reference value can be calculated as:
Reference value = New value / (1 + 20/100) = New value / 1.2
If the new or compared value is P% less than the reference value, you can calculate the reference value as follows:
Reference value = New or compared value / (1 - P/100)
For example, if the new value is 80% of the reference value, then P = 20 and the reference value can be calculated as:
Reference value = New value / (1 - 20/100) = New value / 0.8
Step-by-step explanation:
25. In a company, 40% of the employees are women. The ratio of the number of single women to the number of married women is 2:5. If there are 30 married women how many employees are there in this company?
(Only accurate answers)
Answer:
Step-by-step explanation:
Let's start by finding the total number of women in the company. We know that 40% of the employees are women, so if we let x be the total number of employees, we can write:
Number of women = 40% of x = 0.4x
Let's then use the given ratio to determine the number of single women in the company. If the ratio of single women to married women is 2:5, we can write:
Number of single women = (2/7) * Number of women = (2/7) * 0.4x = 0.114x
We are also given that there are 30 married women. Since the total number of women is 0.4x, we can write:
Number of married women = 30
0.6x = 30
x = 50
Therefore, there are a total of 50 employees in this company.
If a rock is thrown upward on an exoplanet of a nearby star with initial velocity of 20 m/s , its height in meters t seconds later is given by y = 20t - 1.87t².
The rock has an instantaneous velocity of 16 meters per second.
How to determine the average velocity and instantaneous velocity of a rock thrown upward
In this problem we need to determine the average velocity of the rock, represented by a secant line, and estimate its instantaneous velocity, represented by a tangent line. The average speed is defined by the following expression:
u = [y(t + Δt) - y(t)] / Δt
Where:
y(t) - Initial position, in meters. y(t + Δt) - Final position, in meters. Δt - Time interval, in seconds. u - Average speed, in meters per second.The instantaneous speed is the average speed when Δt ⇒ 0.
Part A
Case I
y(1) = 20 · 1 - 1.87 · 1²
y(1) = 20 - 1.87
y(1) = 18.13 m
y(2) = 20 · 2 - 1.87 · 2²
y(2) = 40 - 7.48
y(2) = 32.52 m
u = (32.52 m - 18.13 m) / 1 s
u = 14.39 m / s
Case II
y(1.1) = 20 · 1.1 - 1.87 · 1.1²
y(1.1) = 19.737 m
u = (19.737 m - 18.13 m) / 0.1 s
u = 16.07 m / s
Case III
y(1.01) = 20 · 1.01 - 1.87 · 1.01²
y(1.01) = 18.292 m
u = (18.292 m - 18.13 m) / 0.01 s
u = 16.2 m / s
Case IV
y(1.001) = 20 · 1.001 - 1.87 · 1.001²
y(1.001) = 18.146 m
u = (18.146 m - 18.13 m) / 0.001 s
u = 16 m / s
And the instantaneous velocity of the rock is approximately 16 meters per second.
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Assume the demand curve for bonds in the market for one-year zero-coupon bonds with a face value of $1000 is given by P=1000-0.5Q and the supply curve is given by P=450+5Q. What is the equilibrium interest rate? 5.3% 15.0% Not enough information to calculate.
So, in response to the above question, we can state thatThe equilibrium interest rate is 5.0% as a result (determined by equation adding $50 in interest to a $1000 bond over a year). The right response is thus 5.3%.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
We must locate the point at which the supply and demand for bonds are equal in order to determine the equilibrium interest rate. To do this, we may solve for Q by setting the demand and supply equations to equal values.
1000 - 0.5Q = 450 + 5Q
5.5Q = 550
Q = 100
We can calculate the equilibrium price (interest rate) by putting Q=100 into either the demand or supply equations now that we are aware of the quantities that are requested and supplied at equilibrium:
P = 1000 - 0.5Q = 1000 - 0.5(100) = $950
The equilibrium interest rate is 5.0% as a result (determined by adding $50 in interest to a $1000 bond over a year).
The right response is thus 5.3%.
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8 + v = 26 v = ?
pllljj 3hhyyhtvggvtgv4tr bg gbbrgvrtgtvgvtvt5b5tgvt5btbt
Answer:
v=0.32
Step-by-step explanation:
Please help me. This is homework and I dont understand how to solve this...
The solution of the system x + y ≥ 75 and 2.5x + 10.5y ≤ 800 of the equation is
C. (250, 10)How to find the solution of the equationThe system of equation x + y ≥ 75 and 2.5x + 10.5y ≤ 800 will have a solution that is as written in the equation.
This is done by substituting each value
Using (250, 10)
250 + 10 ≥ 75
260 ≥ 75 correct
2.5x + 10.5y ≤ 800
2.5 * 250 + 10.5 * 10 ≤ 800
730 ≤ 800 correct
since the the values are correct for the equations, (250, 10) is the solution
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In a Pew Research Poll, 287 out of 522 randomly selected US men were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected US women were asked, 233 were able to do so. Construct a 98% confidence interval for the true proportion of US men and US women (m-w) who can identify Egypt on a map.
answer choices
(0.0384, 0.1650)
(0.0301, 0.1733)
(0.0413, 0.1621)
(0.0510, 0.1524)
Answer:
(0.0301, 0.1733)
Step-by-step explanation:
[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_{98\%}=\biggr(\frac{287}{522}-\frac{233}{520}\biggr)\pm 2.326\sqrt{\frac{\frac{287}{522}(1-\frac{287}{522})}{522}+\frac{\frac{233}{520}(1-\frac{233}{520})}{520}}\\\\\\CI_{98\%}\approx\{0.0300,0.1734\}[/tex]
Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733
Question 43 Tim's age was three-quarters of Mary's age 5 years ago. If Tim will be five-sixth of Mary's age in 3 years, what is the sum of their ages right now? Available Options A.28 B.35 C.38 D.41 E.none
Answer:
E. none
Step-by-step explanation:
Let's use algebra to solve the problem:
Let's start by defining some variables. We'll use T for Tim's current age, and M for Mary's current age.
According to the first sentence of the problem, "Tim's age was three-quarters of Mary's age 5 years ago." In other words, we can write:
T - 5 = (3/4)(M - 5)
We can simplify and rearrange this equation to get:
4T - 20 = 3M - 15
4T = 3M + 5
According to the second sentence of the problem, "Tim will be five-sixth of Mary's age in 3 years." In other words, we can write:
T + 3 = (5/6)(M + 3)
Again, we can simplify and rearrange this equation to get:
6T + 18 = 5M + 15
6T = 5M - 3
Now we have two equations with two variables (4T = 3M + 5 and 6T = 5M - 3). We can use these equations to solve for T and M.
Multiplying the first equation by 2, we get:
8T = 6M + 10
Multiplying the second equation by 3, we get:
18T = 15M - 9
We can now solve for M by subtracting the first equation from the second:
10T = 21
T = 2.1
Substituting this value of T into one of the equations (e.g. 4T = 3M + 5), we can solve for M:
4(2.1) = 3M + 5
M = 8.3
Therefore, Tim's current age is 2.1 years and Mary's current age is 8.3 years.
The sum of their ages right now is T + M = 2.1 + 8.3 = 10.4 years.
So the sum of Tim and Mary's ages right now is 10.4 years.
a. y = 2x+5
"Move the function 4 to the right"
Pls I want it with the transition equation and the answers
And graphing if you can
Thanks
Be fast
The solution is, y = 2x + 5+4 when graph would shift by 4 unit.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Given : y = 2x + 5 .
To find :
If you wanted to shift the graph up what would be equation .
Solution : We have given that y = 2x + 5 .
BY the transformation rule ;
if f(x) +k then graph would shift up by k units .
Then to shift the graph of y = 2x + 5 up we need to add something in 5
Like y = 2x + 5+4
Then graph would shift by 4 unit.
Therefore, y = 2x + 5+4 graph would shift by 4 unit.
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P= pay rate (regular)
Alex works 40 hours. When he works overtime, he gets 50% more than his usual pay. Alex worked 6 hours overtime.
What is an expression that can be made with this information?
Let's start by finding the amount that Alex earns per hour before overtime. We know that he works 40 hours, so if we let his hourly pay be x, then his total pay before overtime can be expressed as 40x.
Since Alex gets 50% more than his usual pay for overtime, his overtime pay per hour would be 1.5x, or his usual pay plus 50% of his usual pay. This means that for the 6 hours of overtime he worked, he would earn a total of 6 * 1.5x = 9x.
Now we can write an expression for Alex's total pay, including overtime:
Total pay = 40x + 9x
Simplifying this expression, we get:
Total pay = 49x
So Alex's total pay, including overtime, is 49 times his hourly pay.
Seven friends are seated around a circular table at a wedding reception. In how many ways can they be arranged
Answer:
there are 720 ways to arrange the 7 friends around the circular table at the wedding reception
Step-by-step explanation:
The number of ways to arrange n distinct objects in a circle is (n-1)!, since there are n ways to choose the starting point, and then (n-1)! ways to arrange the remaining objects in a circle.
In this case, we have 7 friends seated around a circular table, so the number of ways to arrange them is:
(7-1)! = 6! = 720
Therefore, there are 720 ways to arrange the 7 friends around the circular table at the wedding reception.
Answer:
720
Step-by-step explanation:
(7-1)! = 6! = 720
A rectangle has a width of 5 inches and a length of 9 inches. What will be the new dimensions of the rectangle after it is dilated by a scale factor of 3?
The dimensions of the rectangle after dilation by a sclae factor of 3 is,
Length = 15 inches
Breadth = 27 inches.
What is Dilation ?A dilation is a transformation that produces an image of a different size but with a similar overall shape to the original.
A dilation that enlarges an image is called an enlargement, and a dilation that shrinks an image is called a reduction.
Scale Factor :The scale factor, which is employed to enlarge a mathematical entity, will determine the size of the image (compared to the original object). When the absolute value of the scaling factor is greater than 1, an expansion occurs.
The given rectangle dimension is :
width= 5 inches and
length= 9 inches.
When the sides of a rectangle are multiplied by a scale factor of 3, the rectangle is said to be dilated by that factor.
So, the width of rectangle is after dilation is 5×3 = 15 inches
So, the length of rectangle is after dilation is 9×3 = 27 inches
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Can someone help me please? I'm really struggling :(
$5
$5 is the y intercept, so that would be the delivery fee. Also, each pizza costs $10
3. If a segment of the Mid-Atlantic Ridge spreads 927 km over a span of 71 million years, what
is the rate of the spreading in one year? (Round it to the nearest hundredth.)
The rate of spreading in one year is approximately 0.00001 km/year.
How The answer was obtainedTo find the rate of spreading in one year, we need to divide the total distance of 927 km by the time it took to spread, which is 71 million years. However, it's important to convert the time unit from million years to years:
71 million years = 71,000,000 years
So, the rate of spreading in one year is:
927 km ÷ 71,000,000 years ≈ 0.00001307 km/year
Rounding to the nearest hundredth, we get:
0.00001307 km/year ≈ 0.00001 km/year
Therefore, the rate of spreading in one year is approximately 0.00001 km/year.
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f(x)=3(x+1)^2 -27 what two equations represent function f?
The given function can also be represented as,
[tex]f(x) =3x^2+6x-24[/tex]
and
[tex]f(x) =3(x+4)(x-2)[/tex]
What is a function ?A relationship between several inputs and outputs is called a function. Simply described, a function is a relation between inputs in which each input is coupled to exactly one output. There is a range, codomain, and domain for each function. A function is usually referred to as f(x), where x is the input . Typically, a function is written as y = f. (x).
Given function is ,
[tex]f(x) =3(x+1)^2-27[/tex]
This function can also be expressed as,
[tex]f(x) =3(x+1)^2-27\\\\f(x) =3(x^2+1+2x)-27\\\\f(x) =3x^2+3+6x-27\\\\f(x) =3x^2+6x-24\\\\f(x) =3(x^2+2x-8)\\\\f(x) =3(x^2+(4-2)x-8)\\\\f(x) =3(x^2+4x-2x-8)\\\\f(x) =3(x+4)(x-2)[/tex]
So, the given function can also be stated as,
[tex]f(x) =3x^2+6x-24[/tex]
and
[tex]f(x) =3(x+4)(x-2)[/tex]
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A rabbit starts at 0 along a number line and then makes three jumps. First the rabbit jumps 4 units, then 2 units, and finally makes a jump of 1 unit. We do not know the direction of any jump. Where on the number line can this rabbit be now?
The rabbit could be at any of these 8 points: 3, 5, 7, 9, 11, 13, 15, or 17.
What is number line?A number line is a pictorial representation of numbers on a straight line. In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
here, we have,
to get the possible positions of the rabbit
The rabbit could be numerous positions, given that each jump can be either positive or negative.
The possible positions are solved as follows
The rabbit is at 10 + 4 + 2 + 1 = 17
The rabbit is at 10 + 4 - 2 + 1 = 13
The rabbit is at 10 - 4 + 2 + 1 = 9
The rabbit is at 10 - 4 - 2 + 1 = 5
The rabbit is at 10 + 4 + 2 - 1 = 15
The rabbit is at 10 + 4 - 2 - 1 = 11
The rabbit is at 10 - 4 + 2 - 1 = 7
The rabbit is at 10 - 4 - 2 - 1 = 3
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Gary buys a barbecue grill online for $617.48. if shipping and handling are an additional 25% of the price how much shipping and handling will Gary pay? PLS HELP I NEED IT ASAP!!!
Answer:
$154.37
Step-by-step explanation:
$617.48 * 0.25 = $154.37
The price of shipping and handling is $154.37.
The graph below is the function f(x)
We can write the given limits as -
[tex]$ \lim_{x \to 2^{-} } f(x)[/tex] = 0[tex]$ \lim_{x \to 2^{+} } f(x)[/tex] = -1[tex]$ \lim_{x \to 2 } f(x)[/tex] = -1What is algebraic expression?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
3x + y
Given is the graph of the function f(x) as shown in the image.
We can write the limits as -
{ 1 } -
[tex]$ \lim_{x \to 2^{-} } f(x)[/tex] = 0
{ 2 } -
[tex]$ \lim_{x \to 2^{+} } f(x)[/tex] = -1
{ 3 } -
[tex]$ \lim_{x \to 2 } f(x)[/tex] = -1
Therefore, we can write the given limits as -
[tex]$ \lim_{x \to 2^{-} } f(x)[/tex] = 0[tex]$ \lim_{x \to 2^{+} } f(x)[/tex] = -1[tex]$ \lim_{x \to 2 } f(x)[/tex] = -1To solve more questions on limits, visit the link below
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Can somebody please help me
find the value of x
15
4 points
16. ALMN has the following angle measures:
mzL=4x-16,
m2M=9x-26,
m2N = 2x + 12.
Find the value of x and each angle measure. Then classify ALMN by sides and angles.
Show Your Work.
The value of x is given as follows:
The angle measures are given as follows:
m < L = 30º.m < M = 100º.m < N = 40º.How to obtain the measures?First we obtain the value of x, considering that the sum of the measures of the internal angles of a triangle is of 180º, hence:
4x - 16 + 9x - 26 + 2x + 12 = 180
15x = 210
x = 210/15
x = 14.
Hence the angle measures are given as follows:
m < L = 4(14) - 16 = 30º.m < M = 9(14) - 26 = 100º.m < N = 2(14) + 12 = 40º.More can be learned about angle measures at https://brainly.com/question/30755286
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a researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. the researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. let p represent the proportion of all households in the city that gave a charitable donation in the past year. which of the following are appropriate hypotheses for the researcher?
The appropriate hypotheses for the researcher are: Null hypothesis: p <= 0.5 and Alternative hypothesis: p > 0.5.
What is hypotheses?In statistics, a hypothesis is an assumption or proposition about a population parameter, based on sample data. A hypothesis is a statement that is tested to determine whether it is true or false. It is an important component of statistical inference, which involves drawing conclusions about a population based on a sample of data. There are two types of hypotheses in statistics: the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis that is tested against the alternative hypothesis. It is usually a statement of "no effect" or "no difference" between two groups or conditions. The alternative hypothesis is the hypothesis that is accepted if the null hypothesis is rejected. It is usually a statement of an effect or difference between two groups or conditions.
Here,
The null hypothesis states that the proportion of households in the city that gave a charitable donation in the past year is less than or equal to 50 percent. The alternative hypothesis states that the proportion of households that gave a charitable donation is greater than 50 percent. The researcher will test these hypotheses using the sample data to determine whether there is convincing statistical evidence to support the alternative hypothesis.
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find the sine angle of ø in the triangle below 
30/34
16/34
15/17
8/15
8/17
SINE OF A TRIANGLE
16/34
The sine of an angle is the opposite divided by the hypotenuse,
In the given triangle, the opposite is the side facing the longest side(hypotenuse)
This will give us the answer 16/34
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I NEED HELP PLEASE ITS URGENT
Answer:
In the given triangle.
Base= 3
Perpendicular=4
Hypotenuse=5
Step-by-step explanation:
CosB = B/H
=3/5
Sin B = P/H
= 4/5
Tan B = P/B
= 4/3
what is the probability of rolling a 4 on a cube and pulling a red marble out of a bag that contains 3 red, 2 black, and 5 yellow marbles?
Therefore, there is a 1/20 chance of getting a red marble out of a container containing 3 red, 2 black, and 5 yellow marbles when rolling a 4 on a cube.
What is probability example?By reducing the number of positive outcomes even by total number of potential outcomes, probability—the chance that a will occur—is determined. The most basic illustration is a coin toss. There are simply two results when users flip a coin: either it shows up heads or tails.
Given that there is only one possible method to roll a 4 out of six equally probable outcomes, the chance of rolling a 4 on a standard six-sided die is 1/6. (rolling a 1, 2, 3, 4, 5, or 6).
The following formula can be used to determine the likelihood of drawing a red marble from a container containing 3 red, 2 black, and 5 yellow marbles:
P(red) = number of red marbles / total number of marbles
So in this case:
P(red) = 3 / (3 + 2 + 5) = 3/10
To find the probability of both events occurring (rolling a 4 and pulling a red marble), we can multiply the probabilities of each event:
P(rolling a 4 and pulling a red marble) = P(rolling a 4) * P(red)
P(rolling a 4 and pulling a red marble) = (1/6) * (3/10)
P(rolling a 4 and pulling a red marble) = 1/20
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Find the perimeter of the triangle whose vertices are (−4,−2)
, (2,−2)
, and (2,6)
. Write the exact answer. Do not round.
The perimeter of the triangle is 24 units.
what is perimeter ?
Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.
Given by the question:
To find the perimeter of the triangle, we need to find the distance between each pair of vertices and then add them up.
Distance between (-4, -2) and (2, -2):
[tex]d = sqrt[(2-(-4))^2 + (-2-(-2))^2] = sqrt[6^2 + 0^2] = 6[/tex]
Distance between (2, -2) and (2, 6):
[tex]d = sqrt[(6-(-2))^2 + (2-2)^2] = sqrt[8^2] = 8[/tex]
Distance between (2, 6) and (-4, -2):
[tex]d = sqrt[(-4-2)^2 + (-2-6)^2] = sqrt[(-6)^2 + (-8)^2] = sqrt[36 + 64] = sqrt[100][/tex]= 10
Now we add up the distances:
Perimeter = 6 + 8 + 10 = 24
Therefore, the perimeter of the triangle is 24.
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