Answers
The answers are:
First image:
The answer is the second option, the angles is [tex]53\°[/tex]
Second image:
The answer is the third option:
[tex]\frac{5}{13}[/tex]
Third image:
The length of the adjacent leg is the first option:
[tex]8\sqrt{2}units[/tex]
Fourth image:
The answer is the fourth option, [tex]72\°[/tex]
Fifth image:
The answer is the fourth option, DF (hypothenuse) is equal to 25 units.
Why?To solve these problems, we need to use the following trigonometric identities and the Pythagorean Theorem, since we are working with right triangles.
[tex]Tan(\alpha)=\frac{y}{x}\\\\(Tan(\alpha))^{-1} =(\frac{y}{x})^{-1}\\\\\alpha =Arctan(\frac{y}{x})[/tex]
[tex]Sin(\alpha)=\frac{opposite}{hypothenuse}[/tex]
Pythagorean Theorem:
[tex]c^{2}=a^{2} +b^{2}[/tex]
So, solving we have:
First image:
We are given a right triangle that has the following lengths:
[tex]base=x=6units\\height=y=8units\\hypothenuse=10units[/tex]
Then, calculating we have:
[tex]\alpha =Arctan(\frac{y}{x})\\\\\alpha =Arctan(\frac{8}{6})\\\\\alpha =Arctan(1.33)\\\\\alpha =53\°[/tex]
Hence, the answer is the second option, the angles is [tex]53\°[/tex]
Second image:
We are given a right triangle that has the following lengths:
[tex]base=x=12units\\height=y=5units\\hypothenuse=13units[/tex]
Then calculating the sin ratio, we have:
[tex]Sin(\alpha)=\frac{opposite}{hypothenuse}[/tex]
[tex]Sin(\alpha)=\frac{5}{13}[/tex]
Thence, the answer is the third option:
[tex]\frac{5}{13}[/tex]
Third Image:
We are given the following information:
[tex]hypothenuse=16units\\\\\alpha =45\°[/tex]
Then, calculating one of the angle legs, since both will have the same length, using the sine trigonometric identity, we have:
[tex]Sin(\alpha)=\frac{Opposite}{Hypothenuse}\\ \\Sin(45\°)=\frac{Opposite}{16}\\\\Opposite=Sin(45\°)*16\\\\Opposite=\frac{\sqrt{2} }{2}*16=8\sqrt{2}[/tex]
Hence, the answer is the first option the length of the adjacent leg is
[tex]Opposite=\frac{\sqrt{2} }{2}*16=8\sqrt{2}units[/tex]
Fourth image:
We are given the following information:
[tex]base=x=9units\\height=y=3units[/tex]
To calculate the angle at the B vertex, first, we need to calculate the angle at the C vertex, and then, calculate the B vertex by the following way:
Since the sum of all the interior angles of a triangle are equal to 180°, we have that:
[tex]180\°=Angle_{B}+Angle{C}+90\°[/tex]
[tex]Angle_{B}=180\° -90\°-Angle_{C}[/tex]
So, calculating the angle at the C vertex, we have:
[tex]\alpha =Arctan(\frac{y}{x})[/tex]
[tex]\alpha =Arctan(\frac{3}{9})[/tex]
[tex]\alpha =Arctan(0.33)=18.26\°[/tex]
Then, calculating the angle at the B vertex, we have:
[tex]Angle_{B}=180\° -90\°-18.26\°=71.74\°=71.8\°=72\°[/tex]
Hence, the answer is the fourth option, [tex]72\°[/tex]
Fifth image:
We are given the following information:
[tex]base=x=24units\\height=y=7units[/tex]
Now, to calculate the distance DF (hypothenuse) we need to use the Pythagorean Theorem:
[tex]c^{2}=a^{2} +b^{2} \\\\hypothenuse^{2}=adjacent^{2}+opposite^{2}\\\\\sqrt{hypothenuse^{2}}=\sqrt{adjacent^{2}+opposite^{2}}\\\\hypothenuse=\sqrt{adjacent^{2}+opposite^{2}}[/tex]
Then, substituting we have:
[tex]hypothenuse=\sqrt{24^{2}+(7)^{2}}[/tex]
[tex]hypothenuse=\sqrt{576+49}=\sqrt{625}[/tex]
[tex]hypothenuse=\sqrt{625}[/tex]
[tex]hypothenuse=25units[/tex]
Hence, the answer is the fourth option, DF (hypothenuse) is equal to 25 units.
Have a nice day!
Related Questions
Use the ratio table to solve the percent problem what percent is 8 out of 40
Answers
Answer:
20%
Step-by-step explanation:
So, 40 is the dependent and 8 is the independent
40% divided by 8% equals 5%
100% divided by 20% equals 5%
-1/5(x-4) =-2 what is the answer for x
Answers
Answer: x=14
Step-by-step explanation:
1. Simplify 1/5(x−4) to (x−4)/5.
(−x−4)/5=−2
2. Multiply both sides by 5.
−x+4=−2×5
3. Simplify 2×5 to 10.
−x+4=−10
4. Regroup terms.
4−x=−10
5. Subtract 4 from both sides.
−x=−10−4
6. Simplify −10−4 to −14.
−x=−14
7. Multiply both sides by −1.
x=14
which of the following is not a unit of volume
Answers
Answer:
square inch — is a unit of area, not volume
Step-by-step explanation:
Some volume measures have their own unit, like liters, cups, pints, quarts, gallons, bushels, or barrels.
Other volume units are the cube of a linear measure, such as cubic centimeters, cubic inches, cubic feet, or cubic meters.
Still other volume units are a hybrid of an area measure and a linear measure, such as acre-feet.
A measure that is the square of a linear unit is an area measure, not a volume measure.
Answer:
Step-by-step explanation:
"square inch" is a unit of area, not of volume.
Water flows at a rate of 7500 cubic inches per minute into a cylindrical tank. The tank has a diameter of 196 inches and a height of 72 inches. What is the height, in inches, of the water in the tank after 10 minutes? Round your answer to the nearest tenth.
Answers
Answer:
2.5 inches in height
Step-by-step explanation:
Givens
water flowing = 7500 in^3 / minute
water flowing = 75000 in^3 / minute * 10 minutes
Tank diameter = 196 inches
Tank radius = 196 inches /2
Tank radius = 98 inches
h_10 minutes = ??
Formula
V = pi r^2 h
Solution
75000 = 3.14 * 98^2 * h
75000 = 3.14 * 9604 * h
75000 = 30156.56 * h
h = 75000 / 30156.56
h = 2.487 which rounded to the nearest 1/10 is
h = 2.5 inches. Seems awfully small doesn't it, considering the volume flowing in.
By United States cultural standards, it has been determined that 6 people live comfortably in 1500 square feet of living space. Based on this standard, how many square feet would be needed to comfortably house 200 people? Enter the number only.
Answers
Answer:
50,000
Step-by-step explanation:
Set up a proportion:
6/1500 = 200/x
Cross multiply and solve for x:
200x1500 = 6x
300000 = 6x
50000 = x
Answer:
50000
Step-by-step explanation:
Find the "unit rate" for occupancy:
1500 ft²
------------- = 250 ft²/person
6 people
Now multiply this unit rate by 200 people. "people" drops out, and you are left with
250 ft²
--------------- * 200 people = 50,000 ft²
1 person
Enter 50000. 200 people will need 50000 ft² of housing.
What is the product of 5/6 and 2/3?
Answers
Answer:
The product of [tex]\frac{5}{6}[/tex] and [tex]\frac{2}{3}[/tex] is [tex]\frac{5}{9}[/tex] .
Step-by-step explanation:
Multiply both numerators and denominators.
[tex]\frac{5*2}{6*3}[/tex]
[tex]\frac{10}{18}[/tex]
Simplify this by dividing both the numerator and denominator by 2.
[tex]\frac{10/2}{18/2}[/tex]
[tex]\frac{5}{9}[/tex]
[tex]\text{Hey there!}[/tex]
[tex]\text{The word product means multiply}[/tex]
[tex]\dfrac{5}{6}\times\dfrac{2}{3}=\ ?\\\\\\\dfrac{5(2)}{6(3)}=\dfrac{5\times2}{6\times3}\\\\\bf{5\times2=10}\\\\\bf{6\times3=18}\\\\\\=\dfrac{10}{18}\\\\\\\text{Both numbers foes into two so we can DIIVIDE it by two}\\\\\\\dfrac{10\div2}{18\div2}=?[/tex]
[tex]10\div2=5\\\\\18\div2= 9\\\\\\\boxed{\boxed{\bf{Answer:\dfrac{5}{9}}}}\checkmark[/tex]
[tex]\text{Good luck on your asignment and enjoy your day!}\\\\\\\frak{LoveYourselfFirst:)}[/tex]
The temperature one winter morning is –8°F. Define a variable and write an expression to find the temperature after the change below. Then evaluate your expression for the change. a rise of 19°F
Answers
Answer:
Step-by-step explanation:
if the temp is -8°F and you add 19 your new temp is 11°F
Final answer:
To find the final temperature after a rise of 19°F from -8°F, define the variable T as the final temperature, and use the expression T = initial temperature + temperature change, which evaluates to T = 11°F.
Explanation:
The student is asked to determine the temperature after a rise of 19°F from an initial temperature of -8°F. To solve this, let's define the variable T to represent the final temperature. The expression to find the final temperature after the rise would be:
T = initial temperature + temperature change
In this case, the initial temperature is -8°F and the temperature change is a rise of 19°F, so the expression becomes:
T = -8°F + 19°F
When we evaluate this expression:
T = 11°F
Therefore, the temperature after a rise of 19°F from -8°F is 11°F.
What is the simplified form of 4z^2-16z+15/ 2z^2-11z+15
Answers
[tex]\frac{4z^2-16z+15}{2z^2-11z+15}[/tex] Factor the numerator and the denominator
[ax² + bx + c]
4z² - 16z + 15 Since a > 1, multiply a and c together, then find the factors of (a·c), that adds or subtracts to = b.
(a·c) --> (4 · 15) = 60
Factors of 60:
1 · 60, 2 · 30, 3 · 30, 4 · 15, 5 · 12, 6 · 10
[The only factor is 6 and 10, (-6) + (-10) = -16] So you substitute -6z - 10z for -16z
4z² - 6z - 10z + 15 Factor out 2z from 4z² - 6z, and factor out -5 from -10z + 15
2z(2z - 3) - 5(2z - 3) Factor out (2z - 3) and your left with:
(2z - 3)(2z - 5)
Do the same for the denominator, and you should get (z - 3)(2z - 5)
Now you have:
[tex]\frac{(2z - 3)(2z-5)}{(z-3)(2z - 5)}[/tex] You can cancel out (2z - 5)
[tex]\frac{2z - 3}{z-3}[/tex]
ANSWER
[tex]\frac{(2z-3)}{(z-3)} [/tex]
EXPLANATION
The given expression is:
[tex] \frac{4z^2-16z+15}{2z^2-11z+15} [/tex]
Let us split the middle terms to get,
[tex]\frac{4z^2-6z - 10z+15}{2z^2-6z - 5z+15} [/tex]
Factor by grouping:
[tex]\frac{2z(2z-3) - 5(2z - 3)}{2z(z-3) - 5(z - 3)} [/tex]
Factor further:
[tex]\frac{(2z - 5)(2z-3)}{(2z - 5)(z-3)} [/tex]
We cancel the common factors,
[tex]\frac{(2z-3)}{(z-3)} [/tex]
where
[tex]z \ne \frac{5}{2} \: or \: z \ne3[/tex]
let f(x)=x^2-6x+13. what is the vertex form of f(x)? what is the minimum value of f(x)?
Answers
Answer:
The vertex form of a quadratic equation is:
[tex]f(x) = (x-3)^2+4[/tex]
the minimum value of f(x) is [tex]y=4[/tex]
Step-by-step explanation:
Given a quadratic equation of the form [tex]f (x) = ax ^ 2 + bx + c[/tex] then the x coordinate of the vertex is
[tex]x=-\frac{b}{2a}[/tex]
So for [tex]f(x)=x^2-6x+13[/tex]
[tex]a=1\\b=-6\\c=13\\[/tex]
Therefore
The x coordinate of the vertex is:
[tex]x=-\frac{(-6)}{2(1)}[/tex]
[tex]x=3[/tex]
The y coordinate of the vertex is:
[tex]f(3)=(3)^2-6(3)+13[/tex]
[tex]y=f(3)=4[/tex]
By definition the minimum value of the quadratic function is the same as the coordinate of y of its vertex
So the minimum value is [tex]y=4[/tex]
The vertex form of a quadratic equation is:
[tex]f(x) = a(x-h)^2+k[/tex]
Where
a is the main coefficient. [tex]a=1[/tex]
h is the x coordinate of the vertex. [tex]h=3[/tex]
k is the y coordinate of the vertex. [tex]k=4[/tex]
So the vertex form of a quadratic equation is:
[tex]f(x) = (x-3)^2+4[/tex]
Answer:
a. [tex]f(x)=(x-3)^2+4[/tex]
b. The minimum value is 4
Step-by-step explanation:
The given function is: [tex]f(x)=x^2-6x+13[/tex]
We add and subtract half the square of the coefficient of x.
[tex]f(x)=x^2-6x+3^2-3^2+13[/tex]
This becomes: [tex]f(x)=x^2-6x+9-9+13[/tex]
The first three terms form a perfect square trinomial.
[tex]f(x)=(x-3)^2+4[/tex]
The function is now in the form: [tex]f(x)=a(x-h)^2+k[/tex], where V(h,k) is the vertex.
Therefore the vertex is (3,4).
The minimum value is the y-value of the vertex, which is 4.
Show the Standard form of this problem
Answers
the answer is C. move the decimal place to the left 4 times since it is positive to the 4th power
Using paper folding to construct a line perpendicular to a given line through a point
Answers
Answer: upon itself
Step-by-step explanation: apex
Find the area of a regular hexagon with a side length of 6 cm and an apothem of approximately 5.2
Answers
Answer:
93.6 inch^2
Step-by-step explanation:
sides=6 side-length=6 inches Apothem= 5.2 inches Area= 6*(1/2)(6)(5.2)
The area of the regular hexagon is 93.6 square centimeter.
What is Area?Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write area as -
V = ∫∫F(x, y) dx dy
Given is a regular hexagon with a side length of 6 cm and an apothem of approximately 5.2.
We can write the area of the regular hexagon as -
A = {3√3}/2 x a²
A = {3√3}/2 x 6 x 6
A = 93.6 square centimeter
Therefore, the area of the regular hexagon is 93.6 square centimeter.
To solve more questions on areas, visit the link-
https://brainly.com/question/29213222
#SPJ7
If possible, could someone assist me by showing me how to get the plausible answer as I was absent while my professer went over this topic.
Answers
Answer:
[tex]7.5m^2[/tex]
Step-by-step explanation:
Divide the composite shape into two shapes, a rectangle and a triangle.
We can see that the rectangle has dimensions of 3 x 2.
We can use the area formula.
[tex]A=b*h[/tex]
[tex]A=3*2[/tex]
[tex]A=6[/tex]
We can also see that the triangle has a height of 3 and a base of 1 (3 - 2).
We can use the area formula.
[tex]A=\frac{1}{2}(b*h)[/tex]
[tex]A=\frac{1}{2}(3)[/tex]
[tex]A=1.5[/tex]
Now we can add these areas together.
[tex]1.5 +6=7.5[/tex]
Can anyone help me on this problem? Please it doesn’t make sense to me...
Answers
Answer:
6
Step-by-step explanation:
Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:
120/(n+24) = (120/n) -16
Multiplying by n(n+24) gives ...
120n = 120(n+24) -16(n)(n+24)
0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms
n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller
(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic
The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.
The woman bought 6 items.
_____
Check
When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.
Please help question about currency exchange rate....
If 55LRD=1USD and 100LRD=1CHD
how much does ?CHD=1USD?
Answers
Answer:
Step-by-step explanation:
55 LRD = 1 USD
100 LRD = 1 CHD
[tex]1 LRD = \frac{1}{55} USD\\\\100 LRD = \frac{100}{55} USD = 1\frac{45}{55} USD=1\frac{9}{11} USD\\1 CHD = \frac{100}{55} USD\\1 USD = \frac{55}{100} CHD = 0.55CHD[/tex]
y intercept,slope,and linear equation=
Answers
ANSWER
Y-intercept: 3000
Slope:-275
Linear equation:y=-275x+3000
EXPLANATION
The straight line touches the y-axis at
(0,3000).
The y-intercept is b=3000
The line also passes through (2,2450).
The slope is calculated using the formula,
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
[tex] = \frac{3000 - 2450}{0 - 2} [/tex]
[tex] = \frac{550}{ - 2} = - 275[/tex]
The slope is -275.
The linear equation is given by:
[tex]y = mx + b[/tex]
[tex]y = - 275x + 3000[/tex]
Determine whether each ordered pair is a solution of the given linear equation.
4x+3y=11; (2,1),(6,0),(0,1)
is (2,1) a solution to the given linear equation? yes or no?
is (6,0) a solution to the given linear equation? yes or no?
is (0,1) a solution to the given linear equation? yes or no?
Please help me.
Answers
Answer:
(2,1) is the only solution to the linear equation
Step-by-step explanation:
to solve, just plug in the values given into the orignal expression. remember, the answer on the left has to be equal to the answer on the right.
(2,1)
4(2) + 3(1) = 11 --> 8 + 3 = 11 --> 11 = 11 (2,1) is a solution to the linear equation
(6,0)
4(6) + 3(0) = 11 --> 24 + 0 = 11 --> 24 ≠ 11 (6,0) is not a solution to the linear equation
(0,1)
4(0) + 3(1) = 11 --> 0 + 3 = 11 --> 3 ≠ 11 (0,1) is not a solution to the linear equation
PLZ HELP I BEG YOU 20 POINTS!!!!
Answers
Answer:
[tex]b=\frac{g}{x} + \frac{5}{x^{3} } +\frac{1}{x^{2} }[/tex]
Step-by-step explanation:
[tex]10=\frac{5}{-2}-b(-2)^{2} +1\\\\\\9=\frac{5}{-2} -b(4)\\\\-18=5-b(4)\\\\-23=-b(4)\\\\\frac{-23}{4} =-b\\\\\frac{23}{4}=b\\\\\\b=\frac{23}{4}[/tex]
Triangle ABC = triangle blank
Answers
Answer:
QPR
Step-by-step explanation:
It is triangle QPR because of the order of corresponding angles.
If the second term of an arithmic progression is -3 and the fourth term is 5, find the ninth term
Answers
Answer:
25
Step-by-step explanation:
You can get that the common difference for all of the terms if four by finding the difference between -3 and 5, which gives us four. Using this, we can calculate the last term by doing 5+4*5 which is 25.
How many 4-digit multiples of 2 are there?
Answers
there are 4,500 of 4 digit multiples of 2
Answer:
4500
Step-by-step explanation:
please help
Find the x-intercepts for the parabola defined by the equation below.
y = 2x2 + 2x - 4
A.
(-4, 0) and (2, 0)
B.
(-2, 0) and (1, 0)
C.
(0, -2) and (0, 1)
D.
(0, -4) and (0, 2)
Answers
Answer:
B. (-2, 0) and (1, 0)
Step-by-step explanation:
The equation can be factored as ...
y = 2(x^2 +x -2) = 2(x +2)(x -1)
The x-intercepts are the values of x where y=0, so will be the values of x that make one or the other of the binomial factors zero:
x = -2
x = 1
Then the intercept points are (-2, 0) and (1, 0). . . . . . . . . matches choice B
Which statements are true about the median of a data set?
Check all that apply.
The median isn’t affected much by one outlier.
The median is always affected by one outlier.
The median is the number in the middle on an ordered set of data.
To find the median, find the difference between the highest and lowest numbers.
To find the median of an even data set, find the average of the two middle numbers.
Answers
Answer: Third and fifth option
3) The median is the number in the middle on an ordered set of data.
5) To find the middle of an even data set, find the average of the two middle numbers.
Step-by-step explanation:
Given a set of data ordered from lowest to highest, the median of the data is the number that is in the middle. In other words, it is a number x for which it is true that 50% of the data is greater than x and the other 50% of the data is less than x.
For example, for the following set of 7 data:
2, 3, [5], 8, 13
the median is 5.
If the data number is even, for example 10 data:
3, 5, 9, 12, [19, 21], 33, 35, 40, 69
The median is the average between the two data that are in the middle
[tex]\frac{19 +21}{2} = \frac{40}{2} = 20[/tex]
Note that the median only represents a partition of the ordered data set. Therefore, it is not affected by outlier. For example
2, 4, 4.5, 4.8, 5 Median = 4.5
2, 4, 4.5, 67, 1506 Median = 4.5
The median does not represent the difference between the highest and the lowest data.
Therefore the correct affirmations are:
3) The median is the number in the middle on an ordered set of data.
5) To find the middle of an even data set, find the average of the two middle numbers.
The perimeter of a quarter circle is 7.14 feet. What is the quarter circles radius
Answers
if the perimeter of 1/4 of the circle is 7.14, then the full circle is 4(7.14) = 28.56.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} C=28.56 \end{cases}\implies 28.56=2\pi r \\\\\\ \cfrac{28.56}{2\pi }=r\implies 4.55\approx r[/tex]
and the radius is the same on any location of the circle.
A quarter of a circle having a perimeter 7.14 feet has a radius of 4.55 feet.
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
If a complete circle has a perimeter of 2πr, the quarter of a circle should have (2πr/4) = (1/2)πr.
Given, The perimeter of a quarter circle is 7.14 feet.
Therefore,
(1/2)πr = 7.14.
πr = 14.28.
r = 14.28/3.14.
r = 4.55 feet.
learn more about circles here :
https://brainly.com/question/29142813
#SPJ2
according to the line plot what is the total distance that was run by Runners who each ran for 1/3 of a mile
Answers
So you would do 1/3 times 4 so that is 1 and 1/3
The total distance that was run by Runners who each ran for 1/3 of a mile will be 4/3.
What is distance?
The distance is defined as the length of the space between the two points separated from each other.
From the graph, the distance of 1/3 miles is covered by 4 runners so the total distance will be calculated as:-
Distance = 1/3 x 4
Distance = 4/3 miles
Hence the total distance that was run by Runners who each ran for 1/3 of a mile will be 4/3.
To know more about distance follow
https://brainly.com/question/2854969
#SPJ2
A bookcase has a mass of 30 kilograms. A book in the bookcase has a mass of 400 grams. How many books of the same mass would it take to equal the mass of the bookcase? A. 75 books B. 120 books C. 750 books D. 1,200 books
Answers
Answer: OPTION A
Step-by-step explanation:
You can convert 30 kilograms to grams ([tex]1\ kilogram= 1,000\ grams[/tex]), then:
[tex](30\ kilograms)(\frac{1,000\ grams}{1\ kilogram})=30,000\ grams[/tex]
Then, if a book in the bookcase has a mass of 400 grams and you need to find the number of books of the same mass that would take to equal the mass of the bookcase, you can divide the weight of the bookcase (in grams) by the weigth of one of these books.
Therefore:
[tex]books=\frac{30,000\ grams}{400\ grams}\\\\books=75[/tex]
A student scores 56 on a geography test and 285 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 10. If the data for both tests are normally distributed, on which test did the student score better relative to the other students in each class? Justify your answer
Answers
Final answer:
The student performed relatively better on the Geography test than on the Mathematics test, with z-scores of -1.2 and -1.5 respectively, because a higher z-score indicates a performance closer to the mean.
Explanation:
To determine on which test the student scored better relative to the other students, we must calculate the z-scores for each test.
The z-score formula is:
Z = (X - μ) /σ
Where X is the student's score, μ is the mean, and σ is the standard deviation.
For the Geography test:
Z = (56 - 80) / 20
Z = -24 / 20
Z = -1.2
For the Mathematics test:
Z = (285 - 300) / 10
Z = -15 / 10
Z = -1.5
A z-score tells us how many standard deviations an element is from the mean. The student had a z-score of -1.2 in Geography and -1.5 in Mathematics. Since a higher z-score reflects a performance that is closer to the mean, the student performed relatively better on the Geography test compared to the Mathematics test.
You have 6 reindeer, Rudy, Jebediah, Ezekiel, Lancer, Gloopin, and Balthazar, and you want to have 5 fly your sleigh. You always have your reindeer fly in a single-file line.
How many different ways can you arrange your reindeer?
Answers
Answer:
Step-by-step Answer:
6 reindeer, from which we fly 5, in N1 ways.
Each of the five must be arranged in N2 ways.
The total number of arrangements is therefore N1*N2 arranglements.
Note: C(n,r) = n!/((r!(n-r)!)
N1 = 6 choose 5 = C(6,5) = 6!/(5!/1!) = 6 ways
(same as number of ways to choose 1 reindeer to be left out).
N2 = 5! ways (5 choices for the first, 4 choices for the second, 3 for the third, and 2 for the fourth, and 1 for the last) = 5*4*3*2*1 = 120 ways.
So total number of arrangements
= N1 * N2 = 6 * 120 = 720 ways.
Alternatively, you can line up the 5 vacant spaces and choose the first among 6 reindeer, second among 5, third among 4, fourth among 3, and the last one among 2 for a total of
6*5*4*3*2 = 720 arrangements.
ind the volume of the pyramid, if the base is a square with the side 3.5 cm and height of the pyramid is 1.5 cm
Answers
Answer:
The volume of the pyramid is [tex]6.125\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the pyramid is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the base of the pyramid
h is the height of the pyramid
Find the area of the base B
[tex]B=3.5^{2}= 12.25\ cm^{2}[/tex]
we have
[tex]h=1.5\ cm[/tex]
substitute
[tex]V=\frac{1}{3}(12.25)(1.5)[/tex]
[tex]V=6.125\ cm^{3}[/tex]
Please help me!!!!!!!
Answers
Answer:
B(5,2)
Explanation:
AC=8 units
AB must equal 2 units.
If line AC is y=x-3, and x values are -1<x<7 in AC, then B is located in x= 5. Plug x in equation.
y=5-3
y=2
B(5,2)