THE TOP OF A 20 FT. WATERSLIDEIS 16 FT. ABOVE THE GROUND.HOW FAR FROM THE BASE OF THESTEPS WILL THE GUESTS BE SHOTINTO THE WATER?
Answers
Using the given information, we form the following diagram.
To find x we use Pythagorean's Theorem.
[tex]20^2=16^2+x^2[/tex]Then, we solve for x.
[tex]\begin{gathered} 400-256=x^2 \\ x=\sqrt[]{144} \\ x=12 \end{gathered}[/tex]Therefore, the answer is 12 feet.
Related Questions
Compare each pair of rationals using a <, >, or =. 7. 3/4 ____ 7/10 8. -1.6 ____ 0.3 9. 2.8 ____ 5/2
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EXPLANATION:
To know when a fraction is greater than another, the following procedure must be done, they must be multiplied by a cross and the result in whole number will determine which of the two is greater.
[tex]\begin{gathered} 7.\frac{3}{4}\text{ }>\frac{7}{10}=(3\times10)=30(4\times7)=28 \\ \\ \end{gathered}[/tex]7.You must first cross multiply the denominator of the first fraction with the number of the second fraction, then multiply the denominator of the second fraction with the numerator of the first fraction,So you will have the exact answer of which is the greatest.
[tex]8.\text{ -1.6 }<0.3[/tex]8.Every negative number that moves away from zero is always less than zero.
9.To compare or know which is greater if a decimal or a fraction we must divide the fraction between itself and this will give me a decimal, now if I can compare;
[tex]\begin{gathered} \frac{5}{2}=2.5_{} \\ \text{Now }compare\text{ the two decimals:} \\ 2.8>2.5; \end{gathered}[/tex]that is, 2.8 is greater than the fraction 5/2
Find the unit price in cents per diaper for each of the brands shown below. Round to the nearest tenth of a cent.Brand A: 36 Diapers, $ 11.99 ? : ¢ per diaper Brand B: 50 Diapers, $11.49? : ¢ per diaper Note: Rounding to the nearest tenth of a cent is the same as rounding to the nearest thousandth of a dollar.Which is the better buy?
Answers
It is required that you find the unit price in cents per diaper.
To do this, convert the prices in dollars to cents by multiplying by 100.
[tex]\begin{gathered} \$11.99=11.99\times100\text{ cents} \\ =1199¢ \end{gathered}[/tex][tex]\begin{gathered} \$11.49=11.49\times100\text{ cents} \\ =1149¢ \end{gathered}[/tex]Next, divide the respective prices in cents by the corresponding number of diapers:
For brand A:
[tex]\frac{1199}{36}\approx33.3¢\text{ per diaper}[/tex]For brand B:
[tex]\frac{1149}{50}=22.98\approx23.0¢\text{ per diaper}[/tex]Next, notice that Brand B has a lower unit price. Hence, it is the better buy.
Brand B is the better buy,
9. A gallon of lemonade calls for 2 scoops of sugar. If you want to make 5 gallons, how much sugar should you put in? (2 pts)
Answers
Answer:10
Step-by-step explanation: if you need 2 for 1 gallon multiply it by 5
you have 1 gallon with 2 scoops
2 for 5 gallons gives you 10 scoops total for 5 gallons
John cleans 3 apartments in a weekend.The apartment have 6,5 and 7 rooms .If he earns $425 for the weekend,how much does she earn per room?
Answers
Given:
The number of departments =3.
The number of rooms is 6,5 and 7.
The total number of rooms = 6+5+7 =18 rooms.
The earning amount = $ 425.
The earing amount per room is
[tex]\frac{425}{18}=\text{23}.611[/tex]The earing amount per room is $23.61.
find the real solution(s), if any, of the system by examining the graph
Answers
Given:
[tex]\begin{gathered} -6x-3y=18\ldots\ldots\ldots(1) \\ \frac{x^{2}}{9}+\frac{y^{2}}{36}=1\ldots\ldots\ldots\ldots(2) \end{gathered}[/tex]Let us consider the equation (1),
[tex]\begin{gathered} -6x-3y=18 \\ -2x-y=6 \\ -y=2x+6 \\ y=-(2x+6)\ldots\ldots\ldots(3) \end{gathered}[/tex]Substitute equation (3) in (2), we get
[tex]\begin{gathered} \frac{x^2}{9}+\frac{(-(2x+6))^2_{}}{36}=1 \\ \frac{4x^2}{36}+\frac{4x^2+36+24x}{36}=1 \\ \frac{4x^2+4x^2+36+24x}{36}=1 \\ 8x^2+36+24x=36 \\ 8x^2+24x=0 \\ 8x(x+3)=0 \\ x=0,x=-3 \end{gathered}[/tex]Substitute x=0 and x=-3 in equation (3) we get,
[tex]\begin{gathered} y=-(2(0)+6) \\ =-6 \\ y=-(2(-3)+6) \\ =0 \end{gathered}[/tex]Hence, the solutions are, (0,-6) and (-3,0).
Let us verify this, by substituting (0,-6) and (-3,0) in equation (1), we get
For (0, -6),
[tex]\begin{gathered} -6(0)-3(-6)=18 \\ 18=18 \end{gathered}[/tex]For (-3, 0)
[tex]\begin{gathered} -6(-3)-3(0)=18 \\ 18=18 \end{gathered}[/tex]Hence, it is verified.
I need help on number 10, the faster u do it the more stars I’ll give u!
Answers
Given the equation;
[tex]P=(l+w)[/tex]At;
[tex]\begin{gathered} l=14ft \\ w=9ft \end{gathered}[/tex]substituting the given values;
[tex]undefined[/tex]-56/6+10x1
please answer it is for a test
Answers
Answer:
-0.6 repeating
Step-by-step explanation:
-56/6 + 10 x 1
-56/6 + 10
-9.3 repeating + 10
-0.6 repeating
Answer:
i think 0.666666667
Step-by-step explanation:
a circle with radius 12 mm is rotated around a diameter what is the volume of the solid formed
Answers
We know that the radius of the sphere will be equal to the radius of the circle:
Since the equation for the volume of the sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]where r is the radius
r = 12 mm
and
π = 3.1416
We can replace it:
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ \downarrow \\ V=\frac{4}{3}\pi\cdot(12\operatorname{mm})^3 \\ \downarrow\text{ since}(12\operatorname{mm})^3=1728\operatorname{mm}^3 \\ V=\frac{4}{3}\pi\cdot1728\operatorname{mm}^3 \\ \downarrow\text{ since }\frac{4}{3}\cdot1728=2304 \\ V=2304\pi\operatorname{mm}^3 \\ \downarrow\text{ since }\pi=3.1416 \\ V=7238.2\operatorname{mm}^3 \end{gathered}[/tex]AnswerThen, the volume is given by
2304π mm³
or
7238.2 mm³
16. - 2y +5=-1Is 3 the solution?17. 1.3m -5.6 = -3Is-2 the solution?
Answers
To find out if a certain value of the variable is the solution of the equation we plug this value into the equation:
[tex]\begin{gathered} 1.3(-2)-5.6=-3 \\ -2.6-5.6=-3 \\ -8.2=-3 \end{gathered}[/tex]Since the last line is not true, then we conclude that -2 IS NOT the solution.
2 A cognitive psychologist conducted a study of whether familiarity of words (X) predicts the time it takes (in seconds) to press a button indicating whether the word is singular or plural (I), with all participants being given the same words. Familiarity with these words was rated at a later time on a 7-point scale (with higher numbers indicating more farniliarity). The participants' scores were 6 2 5 3 7 Y 0.3 1.5 0.8 1.4 0.1 a Figure the Pearson correlation coefficient (25 pts.).
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We will have the following:
*Firts: We have that the correlation coefficient is given by:
[tex]r=\frac{\sum ^n_{i=1}X_iY_i-\frac{1}{n}(\sum ^n_{i=1}X_i)(\sum ^n_{i=1}Y_i)}{\sqrt[]{\sum^n_{i=1}X^2_i-\frac{1}{n}(\sum^n_{i=1}X_i)^2}\sqrt[]{\sum ^n_{i=1}Y^2_i-\frac{1}{n}(\sum ^n_{i=1}Y_i)^2}}[/tex]*Second: We calculate the means, that is:
[tex]x_m=4.6[/tex]&
[tex]y_m=\text{0}.82[/tex]*Third: We calculate the sums:
[tex]\sum ^n_{i=1}X^2_i-\frac{1}{n}(\sum ^n_{i=1}X_i)^2=123-\frac{23^2}{5}=17.2[/tex][tex]\sum ^n_{i=1}Y^2_i-\frac{1}{n}(\sum ^n_{i=1}Y_i)^2=4.95-\frac{4.1^2}{5}=1.588[/tex][tex]\sum ^n_{i=1}X_iY_i-\frac{1}{n}(\sum ^n_{i=1}X_i)(\sum ^n_{i=1}Y_i)=13.7-\frac{23\cdot4.1}{5}=-5.16[/tex]Fourth: We replace the data:
[tex]r=\frac{-5.16}{\sqrt[]{17.2\cdot1.588}}\Rightarrow r=-0.987[/tex]Thus making the coefficient r = -0.987.
And this would be the scatterplot:
Gabriella is a 11 years younger than Mikal the sum of their ages is 51 what is mikhails age
Answers
Answer:
30
Step-by-step explanation:
11 plus 30 is 51 therefor your sum is 30
Determine the area of the shaded sector. Use 3.14 for 7. Round your answer to the nearest tenth.
Answers
If the diameter is 26, the radius is 26/2 = 13
The area of a circle is (pi)(radius)^2 = 3.14(13)^2 = 3.14(169) = 530.66
A complete circle has 360 degrees
Half a circle is 180 degrees
So the shaded area is (360 - 180 - 120)/360 of the complete circle
Doing the operations: (360 - 180 - 120)/360 = 60/360 = 1/6 of the complete circle
If the complete circle area is 530.66, the shaded area is (1/6)(530.66) = 88.443
They ask for the result to be rounded to the nearest tenth, so the result would be 88.4
Answer: 88.4
Last season, your favorite basketball teamwon 60 games. So far this season, yourfavorite basketball team has won 72 games.What is the percent change in the numberof games that your favorite team won fromlast season to this season?
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In order to determine the percent change in the number of games, you first calculate the difference between the number of games won last season and current season.
current season = 70 games won
last season = 60 games won
70 - 60 = 10
next, you determine what is the associated percent of 10 games to 60 games from the last season. You proceed as follow:
(10/60)(100) = 16.66
that is, you calculate the quotient between increase of games won, the number of games won last season, and to the result you multiply by 100.
Hence, the increase in the percent of games won is of 16.66%
A school band has 75 members. The band enters a band competiton at a rival school.1.there are $200 entrance fee each band pluse a $25 entrance fee for each drill team. The competion. has a total of 32 bands and 25 drill teams. write and evaluate an expresion for the total amount of money collected from entrance fees.
Answers
The expression that would describe the problem is
200x +25y = M
where x is the number of band
y is the number of drill teams and
M is the total money collected.
If there are 32 bands and 25 drill team, the total money collected ,M woul d be:
M = 200x + 25 y
M = 200 (32) + 25 (25)
M= 6400 + 625
M = $7025
ANSWER:
M = 200x + 25y
M = $ 7025
Use the following information to fill out the entire two-way table.At PRHS, there are 450 students in the 9th and 10th grade taking geometry, and one third ofthem are 9th graders. The students were surveyed on which unit from quarter 4 they liked best.65 students said that unit 5 was their favorite, but only 25 of them were 9th graders. Unit 8 wasthe most popular for 9th graders, with 50 of them saying it was their favorite. Unit 7 was themost popular with 10th graders, with 100 of them saying it was their favorite. Unit 6 and Unit 8were equally popular for 10th grade students. A total of 125 students sald that Unit 6 was theirfavorite.Answer ALL 3 of the following questions.1. What is the probability that a randomly selected student will be a 9th grade student OR astudent that preferred unit 7? Show your work or explain how you know. Leave it insimplified fraction form.2. What is the probability that a randomly selected student will be a 10th grade student whoalso prefers unit 8? Show your work or explain how you know. Leave it in simplifiedfraction form.3. Given the student prefers Unit 5, what is the probability the student is in the 10th grade?Show your work and explain how you know. Leave it in simplified fraction form.
Answers
Here, we want to calculate probabilities;
We have this as follows;
1) We want to calculate the probability that a randomly selected student is a 9th grader or a student that preferred unit 7
From here, we need the number of students who are 9th graders and students that prefer unit 7
From the question, we have it that 1/3 of the total students are 9th graders
So, for a total of 450, the number of 9th graders will be 1/3 * 450 = 150 students
Secondly we need the number of students that prefers unit 7
Let us try and complete the table as follows;
From the completed table, the numbers that like unit 7 are 130
So the probability we want to calculate is the sum of the two divided by 450
We have this as;
[tex]\frac{130+150}{450}\text{ = }\frac{280}{450}\text{ = }\frac{28}{45}[/tex]2) Here, we want to calculate the probability that a randomly selected student is a 10th grader who also prefers unit 8
From the table, we can see that the number of students who are 10th graders and also prefer unit 8 is 80
So, we have the probability as;
[tex]\frac{80}{450}\text{ = }\frac{8}{45}[/tex]3) Here, we want to calculate the probability that given that a student prefers unit 5, what is the probability that he is a 10th grader
We use the conditional probability value here
Where event A is the probability that student is a 10th grader, while event B is the probability that a student prefers unit 5
We have the probability as;
[tex]\begin{gathered} P(A|B)\text{ = }\frac{P(AnB)}{P(B)} \\ \\ P(\text{AnB) = }\frac{40}{450};\text{ P(B) = }\frac{65}{450} \\ \\ P(A|B)\text{ = }\frac{40}{65} \end{gathered}[/tex]solve the system of linear equations by substitution x+4y=-1 and -3x-14=y
Answers
Explanation
We are given the equations below:
[tex]\begin{gathered} x+4y=-1(equation\text{ }1) \\ -3x-14=y(equation\text{ }2) \end{gathered}[/tex]We are required to solve the equations above simultaneously using substitution. Thus, we have:
[tex]\begin{gathered} From\text{ }equation\text{ }1, \\ x+4y=-1 \\ Make\text{ }x\text{ }the\text{ }subject \\ x=-1-4y(equation\text{ }3) \\ Substitute\text{ }for\text{ }x\text{ }into\text{ }equation\text{ }2 \\ Equation\text{ }2:-3x-14=y \\ \Rightarrow-3(-1-4y)-14=y \\ 3+12y-14=y \\ 12y-11=y \\ Collect\text{ }like\text{ }terms \\ -11=y-12y \\ -11=-11y \\ \frac{-11}{-11}=\frac{-11y}{-11} \\ y=1 \end{gathered}[/tex][tex]\begin{gathered} From\text{ }equation\text{ }3, \\ x=-1-4y \\ Substitute\text{ }the\text{ }value\text{ }of\text{ }y \\ x=-1-4(1) \\ x=-1-4 \\ x=-5 \end{gathered}[/tex]Hence, the answer is:
[tex]x=-5;y=1[/tex]Can you please help me with the following equation
a(1.50) + b(0.50) = $7.00
Answers
Answer:
1.50a+0.50b=7.00
2.00ab=7.00
ab=3.1
Will anyone be willing to help me with this? i’ll give 10 points
Answers
Only first table correctly represents y as a function of x where each value of x is mapped to a unique value of y.
What is a function?A function is defined from a set x to a set y where each element of x receives exactly one element of y. The set x is referred to as the function's domain, while the set y is referred to as the codomain of the function. A popular representation of this connection is y = f(x), which is pronounced "f of x."
Consider the first table:
Any value of x is mapped to a single value of y. Therefore first table represents a function.
Consider the second table:
For x = -50, there are 2 different values of y which are 50 and -50. Therefore second table does not represent a function.
Consider the third table:
For x = 21, there are 4 different values of y. Therefore third table does not represent a function.
Consider the fourth table:
For x = -25, there are 2 different values of y which are 30 and 20. Therefore fourth table does not represent a function.
To learn more about functions visit the below link:
https://brainly.com/question/22340031
#SPJ13
X + 5y = 8, -x + 2y = -1
Answers
x+5y=8
-x+2y=-1 => x=2y+1
(2y+1)+5y=8 => 7y=7 => y=1 => x=3
The answer is x=3 and y=1
Solve the equation 4x= 36
Answers
We are given the following equation
[tex]4x=36[/tex]Let us solve the equation for x
Divide both sides of the equation by 4 (this operation will cancel out the 4 on the left side)
[tex]\begin{gathered} 4x=36 \\ \frac{4x}{4}=\frac{36}{4} \\ x=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Therefore, the value of x is 9
Answer: x = 9
Step-by-step explanation: 4 x 9 = 36
y=0.5x+3; what is the slope?
Answers
The given equation,
[tex]y=0.5x+3[/tex]Comparing it with the slope intercept equation
[tex]y=mx+c[/tex]where m is the slope.
Thus the slope is m=0.5.
Which matrix represents the system of equations below? -12x-13y +132 = 15 7x-10 y– 3z = 11 7x+14y +5z =-5
Answers
The system of equations we have is:
[tex]\begin{gathered} -12x-13y+13z=15 \\ 7x-10y-3z=11 \\ 7x+14y+5x=-5 \end{gathered}[/tex]To write the matrix for the system of equations, we need to write only the coefficients of each variable in the matrix. Also, each column will belong to the coefficients of one variable, and each line will belong to each equation (the first line of the matrix will be for equation one, the second line for the second equation, and so on)
We start by writing the first equation into the matrix:
[tex]\begin{bmatrix}{-12} & {-13} & {13\text{ |15}} \\ {\square} & {\square} & \\ {\square} & {\square} & {\square}\end{bmatrix}[/tex]We write the coefficients of each variable x, y, and z, and then in the final column, we write the number that is after the equal symbol in this case 15 (also note that we put a line before 15 to separate the coefficients of the variables from the result of the equation).
Now we take the second equation of the system: 7x-10y-3z=11, and we write the coefficient number in the second line of the matrix:
[tex]\begin{bmatrix}{-12} & {-13} & {13\text{ |15}} \\ {7} & {-10} & {-3\text{ |11}} \\ {\square} & {\square} & {\square}\end{bmatrix}[/tex]And finally, we do the same with the third equation: 7x+14y+5z=-5, and we put the coefficients in order:
[tex]\begin{bmatrix}{-12} & {-13} & {13\text{ |15}} \\ {7} & {-10} & {-3\text{ |11}} \\ {7} & {14} & {5\text{ |-5}}\end{bmatrix}[/tex]If two lines intersect and one angle measures 25°, what are the measures of the other angles?1. 1252. 1553. 754. 25
Answers
When two lines intersect, four angles are created. Opposite angles are equal, therefore, we have two sets of angles with the same measure. Adjacent angles are supplementary.
By definition, supplementary angles add up to 180º. Since in our intersection we have an angle of 25º, the adjacent angles will be 180º minus 25º.
[tex]180-25=155[/tex]The measure of the other angles are 155º.
I’m not sure why I keep getting this question wrong?
Answers
The value of (3x + 27)/8x when x = 3 is $1.50. That is it costs $1.50 to make 3 dozens cookies (option C)
Explanation:[tex]\begin{gathered} \text{The cost model for making x dozens of cookies:} \\ \frac{3x\text{ + 27}}{8x} \end{gathered}[/tex][tex]\begin{gathered} \text{when x = 3, we substitute x with 3} \\ \frac{3x\text{ + 27}}{8x}\text{ = }\frac{3(3)\text{ + 27}}{8(3)} \\ =\text{ }\frac{\text{9 + 27}}{24} \\ =\text{ }\frac{36}{24}=\frac{3}{2} \\ =\text{ }1.50 \end{gathered}[/tex]Since the cost we got is for 3 dozens of cookies, we say the cost for making 3 dozens of cookies is $1.50
The value of (3x + 27)/8x when x = 3 is $1.50. That is it costs $1.50 to make 3 dozens cookies (option C)
A line passes through the point (4,7) and has slope of 5/4. Write an equation in slope intercept form for this line.
Answers
Given the point (4,7) and the slope 5/4, we can use the line equation in the form slope-point to get the following:
[tex]\begin{gathered} (x_0,y_0)=(4,7) \\ m=\frac{5}{4} \\ y-y_0=m(x-x_0) \\ \Rightarrow y-7=\frac{5}{4}(x-4)=\frac{5}{4}x-\frac{5\cdot4}{4}=\frac{5}{4}x-5 \\ \Rightarrow y=\frac{5}{4}x-5+7=\frac{5}{4}x+2 \\ y=\frac{5}{4}x+2 \end{gathered}[/tex]therefore, the equation in slope intercept form is y = 5/4x + 2
A tire company wants to determine if tires made with a new type of tread will last longer than the tires made with the original type of tread. The company has access to 24 different vehicles. The vehicles will be driven for one year and the depth of the remaining tread will be measured. The average depth for the new type of tread will be compared to the average depth of the original type of tread.Which of the following describes a matched pairs design for this experiment?A. Each of the 24 vehicles is numbered 1–24. These numbers are put into a random number generator. The first 12 unique numbers generated will represent the vehicles that will receive the tires with the new tread. The remaining 12 vehicles will receive the tires with the original tread.B. There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. For each type, the vehicles will be numbered 1–6, and a random number generator will be used to pick three unique numbers. These three vehicles will receive tires with the new tread and the other three vehicles in the group will receive tires with the original tread.c. There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. Each vehicle type is numbered 1–4, and these numbers are entered into a random number generator. The first two unique numbers selected will represent the group of vehicles that will receive tires with the new type of tread. The remaining two groups will receive tires with the original type of tread.D. The vehicles will be put into groups of two based on the size of the vehicle, with the largest two put together, the next largest two, etc. For each of the 12 groups of two, one of the vehicles is selected and a coin will be flipped. If it is heads, this car will receive tires with the new tread and the other vehicle will receive tires with the original tread. If it is tails, then the opposite will be done.
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A matched pairs design is a special case of a randomized block design. It can be used when the experiment has only two treatment conditions; and subjects can be grouped into pairs, based on some blocking variable. Then, within each pair, subjects are randomly assigned to different treatments.
Based in the definition above, the correct answer is D.
Two-Variable inequalities from their graph. (0,0) and (4,3)
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Points (0,0) (4,3)
Find slope m of line y= mx + b
m = 4/3. Positive
b= 0
Then equation is
y = (4/3)x
Now find inequality
y ≤ (4/3)x
Blue zone represents inequality searched
Answer is y≤ (4/3)x
2x+6y=-12Find the y and x
Answers
we have the follwing:
[tex]2x+6y=-12[/tex]solving for y:
[tex]\begin{gathered} 2x+6y=-12 \\ 6y=-12-2x \\ y=\frac{-12-2x}{6} \end{gathered}[/tex]Answer:
[tex]\begin{gathered} y=\frac{-12}{6}-\frac{2}{6}x \\ y=-0.33x-2 \end{gathered}[/tex]Four different stores have the same digital camera on sale. The original price and discounts offered by each store are listed below. Rank the stores from the cheapest to most expensive sale price of the camera.
Store A: price $99.99 and discount of 15%
Store B: price $95.99 and discount of 12%
Store C: price $90.99 and discount of 10%
Store D: price $89.99 and successive discounts of 5% and 5%
Answers
Answer:
Step-by-step explanation:
store A $99.99 x 0.15= 14.9985
99.99-14.9985 = 84.99
store B $95.99 X 0.12= 11.5188
95.99 - 11.5188= 84.47
store C $90.99 x 0.10= 9.099
90.99-9.099= 81.891
store D = $89.99 x 0.05=4.4995
89.99- 4.4995= 85.4905 x 0.05= 4.27
85.4905- 4.27= 81.22
STORE D
STORE C
STORE B
STORE A
Find the volume of the solid. Use 22/7 for II
Answers
We have a rectangular solid prism. The formula to find the volume of this prism is as follows:
[tex]V=\text{lwh}[/tex]Where:
• l = length,. In this case, we have that ,l = 6cm,.
,• w = width,. In this case, we have that ,w = 5cm,.
,• h = height,. In this case, ,h = 1cm,.
Then, we have:
[tex]V=6\operatorname{cm}\cdot5\operatorname{cm}\cdot1\operatorname{cm}=30\text{cubic cm.}[/tex]Therefore, the value for the volume of the rectangular prism is equal to 30 cubic centimeters (30cm³) (30 cubic cm) (last option).