A jogger goes 1.2 mi west then turns south. If the jogger finishes 1.3 mi from the starting point, how far south did the jogger go?
0.5 miles
The jogger's movement can be represented as a right-angled triangle, where the legs of the triangle represent the distances traveled west and south, and the hypotenuse is the direct distance from the starting point to the finishing point. To solve for the distance the jogger traveled south, we need to use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is expressed as c2 = a2 + b2.
Using the Pythagorean theorem:
1.32 = 1.22 + b2
Therefore:
b2 = 1.32 - 1.22
b2 = 1.69 - 1.44
b2 = 0.25
b = [tex]\sqrt{0.25}[/tex]
b = 0.5 mi
So, the jogger traveled 0.5 miles south.
Brady has collected the following data. 11, 15, 15, h, 11. If the range of Brady's data is 9, what is the value of h?
To solve this question, let's start by understanding what the range of a data set means. The range is the difference between the highest value and the lowest value in the set.
Given that the range of Brady's data is 9, and we have the following data points: 11, 15, 15, h, 11, we can use this information to determine the value of h.
1. Identify the smallest value in the data set (without considering h for now). The smallest value given is 11.
2. Identify the largest value in the data set (without considering h for now). The largest value given is 15.
3. Since the range of the data is 9, we can calculate what the new highest and lowest value could be if h were to be the extremum.
If h were the largest value, then:
h - smallest value = 9
h - 11 = 9
h = 9 + 11
h = 20
If h were the smallest value, then:
largest value - h = 9
15 - h = 9
h = 15 - 9
h = 6
4. Now that we have two potential values for h (20 if it’s the maximum, and 6 if it’s the minimum), we have to decide which value is correct. Remember that the range is the difference between the largest and smallest values, so whichever potential value of h does not coincide with a number already in the data set is likely the correct value.
Since the current largest value in the data set without h is 15, and the current smallest value is 11, using h = 20 would yield a new range greater than 9 (20-11 = 9), and using h = 6 would also yield a range greater than 9 (15-6 = 9). But we are only looking for an existing range of 9. Thus, we must consider whether 20 or 6 would form a range of exactly 9 with the current set of numbers.
- If h = 20, it would become the new largest number and the range would be simply h - smallest value, which is 20 - 11 = 9, which is correct.
- If h = 6, it would become the new smallest number and the range would be largest value - h, which would be 15 - 6 = 9, which is also correct.
In this case, both h = 20 and h = 6 satisfy the condition for the range to be 9. However, we should look at the data set to see which data point (h) is not already present because the range should be the difference of two distinct (unique) data points.
In examining the given data set, we see that we already have a smallest value of 11 and a largest value of 15.
To maintain the range of 9 with the given data (without h), h could take on either the value which provides a max-min of 9 and is not already in the data set. In this scenario, both potential values 6 and 20 meet the criteria, since neither is present in the original data set.
Therefore, Brady’s h can be either 6 or 20 and still satisfy the given conditions.
For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?
Answer: The graph of y=mx^2-5x-2 have no x-intercepts for m<-25/8
Solution:
y=mx^2-5x-2
To find x-intercepts we must equal y to zero:
y=0→mx^2-5x-2=0
This is a quadratic equation, and we can solve it using the quadratic formula:
ax^2+bx+c=0; a=m, b=-5, c=-2
x=[-b +- sqrt( b^2-4ac) ] / (2a)
x=[-(-5) +- sqrt( (-5)^2-4(m)(-2) ) ] / (2(m))
x=[5 +- sqrt(25+8m)] / (2m)
This equation doesn't have solution (no x-intercepts) if:
25+8m<0
This is an inequality. Solving for m: Subtracting 25 both sides of the inequality:
25+8m-25<0-25
8m<-25
Dividing both sides of the inequality by 8:
(8m) / 8 < (-25) / 8
m<-25/8
Answer: The graph of y=mx^2-5x-2 heve no x-intercepts for m<-25/8
Rachel says that Graph R has a greater constant of variation that Graph S. Which statement explains whether Rachel is correct?
For this case we have that by definition the constant of variation of a line is given by the slope m, of said line.
Where:
[tex]m = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
To find the slope of a line it is necessary to find two points through which the line passes.
To solve the given problem, we find the slopes of the lines shown in the graphics R and S:
Graphic R:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (2,1)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {R} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {R} = \frac {1-0} {2-0}[/tex]
[tex]m_ {R} = \frac {1} {2}[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {R} = \frac {1} {2}[/tex]
Graphic S:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (1,2)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {S} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {S} = \frac {2-0} {1-0}[/tex]
[tex]m_ {S} = \frac {2} {1}[/tex]
[tex]m_ {S} = 2[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {S} = 2[/tex]
[tex]m_ {S}> m_ {R}[/tex]
then, the graph S has a variation constant greater than the graph R.
Answer:
The graph S has a variation constant greater than the graph R.
Rachel's idea is wrong
Answer:
It’s D
Step-by-step explanation:
hello can you please help me posted picture of question
An oil company is considering 2 sites on which to drill, described as follows:
Site A: profit of oil is found: $60 million
Loss if no oil is found: $5 million
Probability of finding oil: 0.2
Site B: profit of oil is found: $90 million
Loss of no oil is found: 0.1
A: Which site has the larger expected profit?
B: if the expected profit for both sites is not the same, by how much is the expected profit larger?
for every 5 serves Gabby makes tanning makes 3 at volleyball practice Tammy makes 21 serves how many serves did Gabby make show your answer will mark brainiest
The price of a dozen roses in the united states is $30. if $0.3472 can purchase 1.00 turkish lira, how much does the same dozen roses cost in turkey if purchasing power parity holds
well $30 is 185.02 in turkish lira.
SOMEONE PLEASE HELP ASAP
Which of the following are examples of exponential decay?
Answer: B,C,D
Step-by-step explanation:
Simplify (x − 4)(x2 − 2x − 3).
The sales of lawn mowers t years after a particular model is introduced is given by the function y = 5500 In(9t+4), where y is the number of lawn mowers sold. How many mowers will be sold 4.5 years after a model is introduced? Round your answer to the nearest whole number. Show your work to find the number of mowers for credit.
You earn $20.00 per hour at your job. If you get a 10% raise at the end of each year, what will your hourly rate, h, be after 8 years? Use the equation h=C(l+r)^t, where C is the beginning hourly rate, r is the growth rate, and t is time in years. A. $36.00 B. $22.00 C. $47.27 D. $42.87
What is the mode of the following numbers? 8,10,10,10,6,7,8
The mode is the number that appears most frequently in a data set.
In the data set shown here, 10 appears more time than any other number which means that 10 is the mode.
Therefore, the mode of the data set shown here is 10.
Decide whether to reject h 0 for the level of significance ΅ . right - tailed test z = 1.43 ΅ = 0.05 22) the p - value for a hypothesis test is p = 0.006. do you reject or fail to reject h 0 when the level of significance is ΅ = 0.01? 23) find the p - value for the hypothesis test with the standardized test statistic z. decide whether to reject
To decide whether to reject H0 for the level of significance ΅ in a right-tailed test, we compare the p-value to the level of significance. In this case, the p-value for the hypothesis test is 0.006 and the level of significance is 0.01. Since the p-value (0.006) is less than the level of significance (0.01), we reject H0.
Explanation:To decide whether to reject H0 for the level of significance ΅ in a right-tailed test, we compare the p-value to the level of significance. In this case, the p-value for the hypothesis test is 0.006 and the level of significance is 0.01. Since the p-value (0.006) is less than the level of significance (0.01), we reject H0.
For the second question, the p-value is not provided, so we cannot make a decision based on the information given.
The equation sin(40o) = can be used to determine the length of line segment AC. What is the length of ? Round to the nearest tenth._____cm
Answer:
12.9 centimetersStep-by-step explanation:
The given equation is
[tex]sin(40\°)=\frac{b}{20}[/tex]
Where [tex]b[/tex] represents the length of the segment AC, according to the given graph.
To find [tex]b[/tex] we just need to isolate it in the given equation,
[tex]b=20sin(40\°)[/tex]
Then, we know that [tex]sin(40\°) \approx 0.64[/tex], so
[tex]b=20(0.64)=12.9cm[/tex]
Therefore, the length of segment AC is 12.9 centimeters, rounded to the nearest tenth.
Answer:
B
Step-by-step explanation:
edge 2021
Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why. a. Factor the equation. b. Graph the parabola. c. Identify the vertex, minimum, or maximum of the parabola. d. Solve the equation using the quadratic formula.
If a circle has a circumference of 10 pi inches, then what is the area of the same circle in square inches?
To find the area of the circle, use the formula A = πr² and solve for the radius with the equation C = 2πr. Then, substitute the radius value into the area formula to find the area.
Explanation:In order to find the area of the circle, we need to use the formula A = πr², where A is the area and r is the radius of the circle. In this case, we are given that the circumference of the circle is 10π inches.
We know that the formula for circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We can set up an equation to solve for the radius:
10π = 2πrr = 10/2r = 5 inchesNow that we know the radius is 5 inches, we can use the formula A = πr² to find the area:
A = π(5)²A = 25π square inchesSo, the area of the circle is 25π square inches.
The area of the circle is [tex]\( 25\pi \)[/tex] square inches.
To find the area of the circle, we first need to determine the radius of the circle. The circumference [tex]C[/tex] of a circle is given by the formula [tex]\( C = 2\pi r \),[/tex] where [tex]r[/tex] is the radius. Given that the circumference is [tex]\( 10\pi \)[/tex] inches, we can solve for the radius:
[tex]\[ 10\pi = 2\pi r \][/tex]
[tex]\[ r = \frac{10\pi}{2\pi} \][/tex]
[tex]\[ r = 5 \][/tex]
Now that we have the radius, we can find the area [tex]\( A \)[/tex] of the circle using the formula [tex]\( A = \pi r^2 \):[/tex]
[tex]\[ A = \pi (5)^2 \][/tex]
[tex]\[ A = 25\pi \][/tex]
Therefore, the area of the circle is [tex]\( 25\pi \)[/tex] square inches.
Please help with the question,
To form a quadratic equation, let α and β be the two roots.
Let us assume that the required equation be ax22 + bx + c = 0 (a ≠ 0).
According to the problem, roots of this equation are α and β.
Therefore,
α + β = - baba and αβ = caca.
Now, ax22 + bx + c = 0
⇒ x22 + babax + caca = 0 (Since, a ≠ 0)
⇒ x22 - (α + β)x + αβ = 0, [Since, α + β = -baba and αβ = caca]
⇒ x22 - (sum of the roots)x + product of the roots = 0
⇒ x22 - Sx + P = 0, where S = sum of the roots and P = product of the roots ............... (i)
Formula (i) is used for the formation of a quadratic equation when its roots are given.
Given the roots: (-1+-i)
where; i=sqrt(-1)
Thus, the answer is (2x)
You can also do checking to verify if x^2+2x+2 will have roots equal to (-1+-i)
Gabriel determined that his total cost would be represented by 2.5x + 2y – 2. His sister states that the expression should be x + x + 0.5x + y + y – 2. Who is correct? Explain.
Gabriel and his sister's expression mean the same; However, the information available is not sufficient to determine if they are correct or not.
According to the question;
Gabriel representation is; 2.5x + 2y – 2.His sister's expression is; x + x + 0.5x + y + y – 2.Upon computation; we find out that the expressions supplied by Gabriel and his sister are the same.
However, we must note that the information available is not sufficient to determine if both parties are correct or not.
Ultimately, if Gabriel is correct, then his sister is too and if otherwise, she is not correct too.
Read more:
https://brainly.com/question/9253705
At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations?
[tex]SE=\sqrt{p(1-p)\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}[/tex]
where p is the pooled sample proportion, [tex]n_1[/tex] is the size of sample 1, and [tex]n_2[/tex] is the size of sample 2.What is the simplified form of 1 over x minus 2 over x squared plus x ?
Step-by-step explanation:
Given expression [tex]\frac{1}{x} -\frac{2}{x^2+x}[/tex].
Let is factor second denominator [tex]x^2+x[/tex] first.
Factoring out GCF x we get
[tex]x^2+x= x(x+1)[/tex]
Rewriting the equation
[tex]\frac{1}{x} -\frac{2}{x^2+x} = \frac{1}{x} - \frac{2}{x(x+1)}[/tex]
Now, we need to find the lowest common denominator of x and x(x+1).
The lowest common denominator of x and x(x+1) is x(x+1).
So, we need to multiply first fraction by (x+1) in top and bottom to get lowest common denominator x(x+1) under first fraction.
[tex]\frac{1}{x} - \frac{2}{x(x+1)} = \frac{1(x+1)}{x(x+1)} - \frac{2}{x(x+1)}[/tex]
[tex]= \frac{x+1}{x(x+1)} - \frac{2}{x(x+1)}[/tex]
We got denominators same.
Therefore, subtracting numerators, we get
[tex]=\frac{x+1-2}{x(x+1)}[/tex]
[tex]\frac{x-1}{x(x+1)}[/tex].
Therefore, simplified form is [tex]\frac{x-1}{x(x+1)}[/tex].
Which of these is a point-slope equation of the line that is perpendicular to y-25=2(x-10) and passes through (-3,7)
Answer: y - 7= -1/2 (x+3)
Step-by-step explanation:
Steve puts only dimes and quarters into his piggy bank. Right now he has five more dimes than quarters there, and they make exactly $74! How many quarters and how many dimes are there in Steve’s piggy bank?
Answer:
215 dimes and 210 quarters
Step-by-step explanation:
Quarters are x
dimes are x+5
.25x+.10(x+5)=74
.25x+.10x+.5=74
.35x=73.5
x=210 quarters or $52.50
x+5=215 dimes or $21.50
Add to $74.
The pyramid shown has a square base that is 14 centimeters on each side. The slant height is 15 centimeters. What is the surface area of the pyramid?
HELP!!! First gets Top Answer!!!
See image for more details
- Use your calculator and hit the "2nd" button and then the log button which should be the 10x function. Your answer should be 0.00355.
The concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).
The process you described is correct for finding the concentration of hydrogen ions ([H+]) from a given pH value using the formula [H+] = 10^(-pH).
Here's how you would calculate the [H+] concentration for a solution with a pH of 2.45:
a) Take the negative of the pH value:
-log(2.45) = -0.389
b) Now, use your calculator and calculate 10 raised to the power of the negative pH value:
10^(-0.389) ≈ 0.00355
So, the concentration of hydrogen ions ([H+]) in the solution with a pH of 2.45 is approximately 0.00355 moles per liter (M).
for such more question on hydrogen ions
https://brainly.com/question/28444954
#SPJ12
Consider the graphs f(x) = log10x and g(x) = a · log10x.
What happens to the graph of g(x) = a · log10x if a is –7? Check all that apply.
a.The graph is stretched vertically.
b.The graph will shift a units to the right.
c.The graph is compressed.
d.The graph is reflected across the x-axis.
e.The graph will shift a units to the left.
GETS BRAINLIEST AND 50 PTS!
The seventh-grade class is building target areas for a PE activity. The bases for the game will be in a circular shape. The diameter of each circle is 3 feet. Approximately, how many square feet of the turf needs to be painted for a base circle? Use 3.14 for π and round your answer to the nearest tenth. 7.1 square feet 9.4 square feet 18.8 square feet 28.3 square feet
Find the value of x.
Pls help
when Derek planted a tree it was 36 inches tall the tree grew one and one fourth inches per year the tree is now forty four and three fourths how many years ago did Derek plant the tree
Answer:
7
Step-by-step explanation:
Figure out all the fractions in decimal form
44 3/4= 44.75
1 1/4= 1.25
Subtract:
44.75- 36= 8.75
Divide:
8.75/1.25= 7
The answer therefore is 7!
Hope this helps!!!