A camper attaches a rope to the top of her tent to give it more support. She stakes the rope, which is 8 ft long, to the ground at a distance of 6 feet from the middle of her tent. About how tall is her tent? An image shows the tent, the staked rope, and the measurements as a right triangle. The height of the triangle is unknown. The base of the triangle is 6 feet. The hypotenuse is 8 feet.
Answers
The support given to the tent forms a right triangle.
The height of the tent is 5.3 ft
The given parameters are:
[tex]\mathbf{Base = 6}[/tex]
[tex]\mathbf{Hypotenuse= 8}[/tex]
The height is calculated as follows:
[tex]\mathbf{Hypotenuse^2 = Base^2 + Height^2}[/tex]
Substitute known values
[tex]\mathbf{8^2 = 6^2 + Height^2}[/tex]
This gives
[tex]\mathbf{64 = 36 + Height^2}[/tex]
Collect like terms
[tex]\mathbf{Height^2 = 64 - 36 }[/tex]
[tex]\mathbf{Height^2 = 28 }[/tex]
Take square roots
[tex]\mathbf{Height = 5.3 }[/tex]
Hence, the height of the tent is 5.3 ft
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Related Questions
Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.
q + d = 19
0.25q + 0.1d = 4
How many quarters does she have?
4
5
14
15
Answers
To find the number of quarters, solve the system of equations. Kat has 14 quarters.
Explanation:To find the number of quarters Kat has, we can solve the system of equations given. The first equation states that the number of quarters (q) and the number of dimes (d) add up to 19.
The second equation represents the total value of the coins, where each quarter is worth $0.25 and each dime is worth $0.10.
By solving this system of equations, we can determine the value of q, which represents the number of quarters.
Using the first equation, we can solve for d by subtracting q from both sides: d = 19 - q.
Substituting this value of d into the second equation, we get: 0.25q + 0.1(19 - q) = 4.
Solving this equation, we find q = 14. Therefore, Kat has 14 quarters.
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What is the equation of the line that contains the points (3, –6) and (–3, 0)?
A.
y = x – 3
B.
y = –x – 3
C.
y = –x + 3
D.
y = x + 3
Answers
Common equation for the line is 'y=kx+b', where k&b - numbers, x&y - coordinates.
1) using the points it's possible to make up the system of equations:
[tex] \left \{ {{-6=3k+b} \atop {0=-3k+b}} \right. \ =\ \textgreater \ \ \left \{ {{3k+b=-6} \atop {-3k+b=0}} \right. [/tex]
b=-3 and k=-1
2) y=-x-3
Answer: B.
To determine the equation of a line given two points, calculate the slope and then use one point to write the equation in slope-intercept form. The equation of the line through (3, -6) and (-3, 0) is B. y = -x - 3.
To find the equation of the line that contains the points (3,
-6) and (
-3, 0), we need to calculate the slope (m) of the line using the slope formula:
m = (y2 - y1) / (x2 - x1).
Plugging in the given points:
m = (0 - (-6)) / (-3 - 3)
m = 6 / -6
m = -1.
With the slope now known, we can use one of the points and the slope to write the equation of the line in point-slope form (y - y1) = m(x - x1) and then convert it to slope-intercept form (y = mx + b). Let's use the point (-3, 0):
y - 0 = -1(x + 3)
y = -1x - 3.
Therefore, the correct equation of the line is B. y =
-x - 3.
what is the measure of C?
Answers
If its an equilateral all angles are equal
Which statements are true?
Choose all answers that are correct.
A.
All quadrilaterals can be classified as either parallelograms or trapezoids.
B.
All rhombuses are parallelograms.
C.
Some trapezoids are parallelograms.
D.
Some parallelograms are squares.
Answers
Answer:
Step-by-step explanation:
B, C and D
what is the least common denominator of the rational expressions below?
6/x^2+7x - 8/x^2+10x+21
a. x(x+7)(x+3)
b. x+7
c. x(x+7)^2(x+3)
d. x(x+3)
Answers
Notice that in the denominator of the first rational expression we have a common factor [tex]x[/tex], so we can factor x out:
[tex] x^{2} +7x=x(x+7)[/tex]
Now, the denominator of the second rational expression is a quadratic polynomial, we can factor it by finding tow numbers whose product will 21 and its sum will be 10. Those numbers are 7 and 3, (7x3=21 and 7+3=10):
[tex] x^{2} +10x+21=(x+7)(x+3)[/tex]
Lets rewrite our rational expression with our factored denominators:
[tex] \frac{6}{ x(x+7)} - \frac{8}{(x+7)(x+3)} [/tex]
Now, to find the least common denominator we are going to take one of the common factors (x+7) and all the non-common factors: x and (x+3):
[tex]x(x+7)(x+3)[/tex]
We can conclude that the correct answer is a. x(x+7)(x+3)
Explanation of finding the least common denominator of rational expressions.
The least common denominator of the rational expressions provided is option (d): x(x+3).
To find the LCD, first factor each denominator completely. Then, identify the unique factors and their highest powers. The LCD will be the product of these unique factors raised to their highest powers.
If male and female college students work an average of 15 hours per week during the school year and the standard deviation is 5.4 for male students and 2.3 for female students, what may we conclude?
Answers
Answer: the male sample is more spread than the female sample
Step-by-step explanation:
The mean is the same for both genres, but the standard deviation form males is bigger than the one for females.
This means that the data of the male students is more spread than the female data (so there are more male students that study more hours, but there also are more male students that study less hours).
So the general conclusion is that the male sample is more spread than the female sample
Express the complex number in trigonometric form. 3
Answers
The complex number 3, in trig form, would be 3 cos 0 degrees. This is a ray from the center, right, along the x-axis, for a distance of 3 units.
Answer:
Step-by-step explanation:
3(cos(0)+isin(0))
What is the diameter of a circle that has an area of 452.16 mm 2? 144 mm 12 mm 24 mm 6 mm
Answers
now, that's the radius of the circle, recall that the diameter is twice the radius.
Answer:
the diameter is 24
Step-by-step explanation:
Ivan was given two data sets, one without an outlier and one with an outlier.
Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61
How is the median affected by the outlier?
Answers
Answer:
Median is decreased by the outlier or Outlier made median lower.
Step-by-step explanation:
First we calculate median of the data without an outlier:
Data in Ascending or increasing order ,
105 , 108 , 109 , 113 , 118 , 121 , 124
Now there are 7 terms so
Median = [tex]\frac{7+1}{2}^{th}\:term[/tex] = 4th term = 113
Now we find median of the data with outlier:
Data in ascending or descending order,
61 , 105 , 108 , 109 , 113 , 118 , 121 , 124
here no of terms are 8.
So, Median = [tex]\frac{(\frac{8}{2})^{th}+(\frac{8}{2}+1)^{th}}{2}[/tex]
= [tex]\frac{4^{th}+5^{th}}{2}=\frac{109+113}{2}[/tex]
= 111
So, Median is decreased by the outlier or Outlier made median lower.
The ice rink sold 95 tickets for the afternoon skating session, for a total of $828. General admission tickets cost $10 each and youth tickets cost $8 each. How many general admission tickets and how many youth tickets were sold?
Answers
Youth=Y=8 dollars
GA+Y=95
GA=95-Y
10GA+8Y=828
10(95-Y)+8Y=828
950-10y+8Y=828
-2Y=-122 multiply by (-1)
2Y=122
Y=61
GA=34
There were sold 61 youth tickets and 34 general admission
By solving the system of linear equations formed from the scenario given, we find that the ice rink sold 34 general admission tickets and 61 youth tickets during the afternoon skating session.
Explanation:This problem is a simple linear algebra problem. We can represent the total number of tickets with the variable x (for the general admission tickets) and y (for the youth tickets). The scenario provides us with two equations:
The total number of tickets sold is 95, so x + y = 95.The total amount of money collected is $828, so 10x + 8y = 828.To solve the system of equations, we can multiply the first equation by 8 to have both equations involving '8y', which gives us 8x + 8y = 760.
Subtracting the first modified equation from the second gives: 2x = 68. Therefore, solving for x gives us x = 34. That means, there were 34 general admission tickets sold.
Substitute x=34 into x + y = 95, we get 34 + y = 95, which simplifies to, y = 61. That means, there were 61 youth tickets sold.
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Divide 3x^2 -2x^2 -61x -20 by x -5
Answers
.. (3x^3 -2x^2 -61x -20)/(x -5) = 3x^2 +13x +4
What are the zeros of the polynomial function f(x) = x3 – 4x2 – 12x
Answers
f=x2−4x−12
x(x² - 4x - 12)
x(x - 6)(x + 2)
x = 0
x = 6
x = -2
The zeros are 0, 6, and -2
Find a ⋅ b. a = 4i - 4j, b = 4i + 5j
Answers
b=<4,5>
a.b =4*4-4*5=16-20=-4
For this case we have the following vectors:
[tex]a = 4i - 4j\\b = 4i + 5j[/tex]
We must find the product point of both vectors.
To do this, we multiply component by component and add the results.
We have then:
[tex]a.b = (4) (4) + (-4) (5)\\a.b = 16 -20\\a.b = -4[/tex]
Answer:
The point product of both vectors is given by:
[tex]a.b = -4[/tex]
Annie's cafe borrows $6100 at 6% for 290 days. Find the total amount that must be repaid after 290 days. (Use a 365 day year.)
Answers
General Idea:
The formula to find the Amount 'A' that need to be paid after ' t ' years for a Principal ' P ' with a annual rate of interest ' r ' is given below:
[tex] A= P(1+r \cdot t) [/tex]
Applying the concept:
Annie's cafe borrows $6100 at 6% for 290 days.
From the above statement we can conclude,...
[tex] P= \$6100\\ \\ r=6\%\\ \\ t=\frac{260}{365} [/tex]
Substituting the values of P, r and t in the formula, we get...
[tex] A=6100 \cdot (1+6 \% \cdot \frac{260}{365} )\\ \\ A=6100(1+\frac{6}{100} \cdot \frac{260}{365} )=6100(1+\frac{1560}{36500} ) \approx 6361 [/tex]
Conclusion:
The total amount that must be repaid after 290 days is approximately [tex] \$6361 [/tex]
Crystal charges a flat fee of $10 plus an additional $5 per hour to babysit given the situation what is the range
Answers
Answer:
perhaps $10 to $10,810
Step-by-step explanation:
We assume Crystal may be willing to babysit for a period of up to 3 months (90 days), so 90×24 = 2160 hours. Her hourly fee for that period will be ...
... (2160 hours) × ($5/hour) = $10,800
That amount added her $10 initial charge may represent the upper limit of her pay. The lower limit will be the $10 initial charge.
_____
Comment on the question
Since no upper limit on hours is given, we conclude the problem is not well-specified.
We can make a variety of different assumptions regarding the upper limit of babysitting time.
We might choose to consider this a daily charge, so the upper limit is $130 per day. We might consider that Crystal is willing to babysit while the child's parents are on a 2-week vacation. We might consider that Crystal is willing to babysit for the duration of her summer vacation from school (about 3 months). This is the assumption we use here.the number 0.4 can be written as 4/10 so it is a rational number
Answers
Answer: yes it's correct
Step-by-step explanation: yes it's correct
A repairman charged $93.06. the price included 2 hours of labor and a $40 serive charge how much does the repaiman charge per hour for labor?
Answers
53.06 / 2 = 26.53 per hour
53.06/2 = 26.53
The answer should be $26.53 per hour of labor
Of the members of a student choir, 60% are boys. If there are 21 boys in the choir, how many members does the choir have in total?
Answers
Suppose there are x number of members in all.
Now we are given that 60% of these are boys.
So number of members who are boys = 0.6x
We are also given that there are 21 boys in the choir.
So making an equation ,
[tex] 0.6x =21 [/tex]
dividing both sides by 0.6,
x= 35
So there are total 35 members in the choir.
how many prime numbers are there between 0 and 25
Answers
hope this helps<3
The prime numbers between 0 and 25 are:
2
3
5
7
11
13
17
19
23.
This are 9 numbers, so the answer is 9.
Solve the equation x2 = 10.
Answers
Answer:
[tex]\large\boxed{x=-\sqrt{10}\ or\ x=\sqrt{10}}[/tex]
Step-by-step explanation:
[tex]x^2=10\iff x=\pm\sqrt{10}[/tex]
The solution of the equation is x = ±3. 162.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Parts of an Equation
There are different parts of an equation which include coefficients, variables, operators, constants, terms, expressions, and an equal to sign. When we write an equation, it is mandatory to have an "=" sign, and terms on both sides. Both sides should be equal to each other. An equation doesn't need to have multiple terms on either of the sides, having variables, and operators.
An equation can be formed without these as well, for example, 5 + 10 = 15. This is an arithmetic equation with no variables.
Given:
x² = 10
Now to solve the above equation we have to take the square root on both side, we get
√x² = √10
x= ±√10
x= ±3. 162 ( because root provides two values one is positive and other is negative)
Hence, the value of x is ±3. 162.
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A line and a plane are considered parallel if they have no points in common. True or False?
Answers
Find an equation for the nth term of the arithmetic sequence.
9, 11, 13, 15, ...
Answer Choices
A) an = 9 + 2(n - 1)
B) an = 9 + 2(n + 1)
C) an = 9 + 2
D) an = 9 + 2(n)
Answers
an = a1 + d(n-1)
Substituting the values above, you have ...
A) an = 9 + 2(n - 1)
Can anyone please help me I will give you 13 points and make your answer the brainliest.Please help.
Answers
The true statements are ...
2. All squares are rectangles.
3. Not all parallelograms are rectangles.
_____
The attached diagram shows the relationships between various quadrilataral types. The line connecting a lower box to a higher box means "all of the lower box is a higher box." For example, all square are rectangles, and all rectangles are parallelograms.
However, it is typical for a higher box to have several different lower boxes. That is "a higher box may be any of the list of lower boxes or none of them" For example, a parallelogram may be a rhombus or a rectangle or neither.
A company has determined that the number of items it sells varies inversely as the price of the item. If 20,000 items can be sold if the price is $9.50, how many items can be sold of the price is $8.75? Round your answer to the nearest whole number.
Answers
Since the variation is inverse, then the relation between N and p is:
[tex]N=k\dfrac{1}{p}[/tex]
For N=20000 and p = $9.5, we get the formula:
[tex]20000=k\dfrac{1}{9.5}\\p=20000\times9.5=190000[/tex]
If p = 8.75, then the number of items sold can be computed using the formula:
[tex]N= 190000\dfrac{1}{8.75}=21714 \text{ total items}[/tex]
Solve each equation f over 28=24
Answers
How long will it take for a sum of money, invested at 5% compounded annually, to double in value?
Answers
2x=x(1+0.05)^n
(1.05)^n=2
=>
n=log(2)/log(1.05)=14.21 years
Note: This problem can also be solved in the head using the rule of 72.
Since the amount is doubled at an interest rate of 5%, the time needed is 72/5=14 years, approximately.
To determine the time needed for an investment to double at a 5% compounded annual rate, apply the Rule of 72 by dividing 72 by the interest rate, resulting in approximately 14.4 years.
The question pertains to the time it takes for an investment to double in value with compound interest. To calculate this, we can use the Rule of 72. This rule states that you can approximate the number of years it'll take for an investment to double by dividing 72 by the annual interest rate. In this case, with a 5% interest rate, it would be calculated as 72 \/ 5, which equals approximately 14.4 years.
Here's a step-by-step explanation:
Apply the Rule of 72 by dividing 72 by the interest rate: 72 ÷ 5 = 14.4.
Therefore, it will take roughly 14.4 years for the sum of money to double at an annual compounded interest rate of 5%.
This is a quick and efficient way to estimate the power of compound interest and make informed investment decisions.
Which of the following are the coordinates of the vertex of y=-x^2+2x+1
Answers
way 1:
common equation of parabola is y=ax²+bx+c.
rule: x₀=-b/(2a), y₀=-D/(4a), where x₀ and y₀ are coordinates of the vertex.
According to the described rule above x₀=(-2)/(-2)=1, y₀=8/4=2.
The vertex is (1;2).
way 2:
re-write the given equation into the form y=(x+m)²+n.
y=-(x-1)²+2.
Rule: point (-m;n) is vertex of the parabola.
According to the described rule the vertex is (1;2).
Find the probability when a couple has 6 children at at least one of them is a boy
Answers
1. Probability (P): 1-[probability_all_the_girls]
2. P=1- 1/2⁶=1- 1/64=63/64≈0.984375.
Note: P_all_the_g=[needed_cases]/[all_possible_cases], where needed cases=1 (all the girls means 'gggggg'), and all possible cases=2⁶=64 (all possible cases means 'gggggg';'bbbbbb';gbbbbb';'ggbbbb';'gggbbb';'ggggbb';gggggb';'bggggg', etc. Total 64 combinations.)
The probability when a couple has 6 children at at least one of them is a boy is 63/64
First step
Probability of all 6 girls=(1/2)^6
Probability of all 6 girls = 1/64
Second step is to determine the probability at least one of them is a boy
Let at least one boy means not all girls
Hence:
P(all girls)+P(not all girls)=1
P(at least 1 boy)=1-P(all girls)
P(at least 1 boy)=1-1/64
P(at least 1 boy)=63/64
Inconclusion The probability when a couple has 6 children at at least one of them is a boy is 63/64
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A box contains 3 cherry frozen treats and 2 grape frozen treats. Maggie takes a treat from the box without looking, gives it to her brother, and then selects another treat. What is the probability that her brother gets a grape treat and she gets a cherry treat?
Answers
Answer:
6/20 = 3/10
Step-by-step explanation:
Her brother gets the first treat. There are 2 grape treats out of 3+2 = 5 total; this is a probability of 2/5.
Maggie gets the second treat. There will still be 3 cherry treats left, but only 5-1 = 4 treats remaining; this is a probability of 3/4.
Together this gives us 2/5(3/4) = (2*3)/(5*4) = 6/20 = 3/10
Answer:
3/10 or 6/20
Step-by-step explanation:
Could you please help me out ?
Answers
m∠K= 180º-58º-38º
m∠K= 84º
2. If we draw a perpendicular segment from "K" to "k", we will obtain two right triangles and we can find the value of "k".
3. Let's find the heigh ot these two triangles (The perpendicular segment from "K" to "k", which we will call "y"):
Sen(α)=Opposite leg/Hypotenuse
Sen(58º)=y/2.3
y=2.3xSen(58º)
y=1.95 units
4. Now we must find the adjacent leg of the triangle on the left:
Cos(α)=Adjacent leg/Hypotenuse
Cos(58º)=Adjacent leg/2.3
Adjacent leg=1.21 units
5. Let's find the adjacent leg of the other triangle:
Tan(38º)=Opposite leg/Adjacent leg
Adjacent leg=2.49 units
6. The lenght of "k" is:
k=2.49 units+1.21 units
k=3.7 units
7. The length KL is:
Cos(38º)=Adjacent leg/Hypotenuse
Cos(38º)=2.49/KL
KL=2.49/Cos(38º)
KL=3.15 units
KL≈3.2 units