d = 17.3 m
Step-by-step explanation:
We can extend Pythagorean theorem to 3 dimensions by writing
[tex] {d}^{2} = {x}^{2} + {y}^{2} + {z}^{2} [/tex]
or
[tex]d = \sqrt{ {x}^{2} + {y}^{2} + {z}^{2} } [/tex]
Since we are dealing with a cube of side 10 m, then
x = y = z = 10 m
so we get
[tex]d = \sqrt{ {10}^{2} + {10}^{2} + {10}^{2} } [/tex]
or
[tex]d = \sqrt{3 \times {10}^{2} } = 10 \sqrt{3} \: m[/tex]
This becomes
d = 17.3 m
If using the method of completing the square to solve the quadratic equation
x^2– 10x + 21 = 0, which number would have to be added to "complete the
square"?
Answer: 25
Step-by-step explanation: The number that is added to both sides is the number that is needed to create a perfect square trinomial.
The question is, what is that number?
Well, it comes from a formula. The number that is added to both sides always comes from half the coefficient of the middle term squared.
So half of -10 squared or -5 squared which is 25.
So 25 is added to both sides.
What are the values of m and in the diagram below?
a mailbox is 55 inches tall and casts a shadow that is 70 inches long. a nearby flagpole casts a shadow that is 196 inches long. how tall is the flagpole?
Answer:
154 inches tall.
Step-by-step explanation:
In this scenario, the sun's angle is the same for both objects. Since we have three values and 1 variable (height of the pole) we can use the Rule of Three to solve this. In this, we simply multiply the diagonal values of the ratios and divide by the third value to get the value of the variable like so...
55 in. <=====> 70 in.
x <=========> 196 in.
(55 * 196) / 70 = x
10,780 / 70 = x
154 in. = x
Finally, we can see that the flagpole is 154 inches tall.
What is the average rate of change of f over the interval [3,4]?
Answer:
4
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 3, 4 ] , then
f(b) = f(4) = - 1 ← from table
f(a) = f(3) = - 5 ← from table , then
average rate of change = [tex]\frac{-1-(-5)}{4-3}[/tex] = [tex]\frac{-1+5}{1}[/tex] = 4
What is the slope of the line? Khan academy
simplify by adding like terms 3xy+2m+9-xy+3m-4
Answer:
Step-by-step explanation:
3xy +2m +9 -xy +3m -4
add and subtract like terms
=3xy-xy+2m+3m+9-4
=2xy+5m+5
Answer:
2xy+5m+5
Step-by-step explanation:
3xy+2m+9-xy+3m-4=(3xy-xy)+(2m+3m)+(9-4) =2xy+5m+5
can a theorem easily be proved by using corollary
Answer:
Yes, of course
Step-by-step explanation:
Corollary simply means the similar case or alike. So we can apply same theorem. Although it may be lengthy and bit tricky but its easy to prove.
Imagine that the intelligence test score (M=100, SD =15) is perfectly correlated with SAT score. Your Z score on SAT is +1.0, your intelligence test score is likely to be:
Answer:
115
Step-by-step explanation:
Given :
Mean of intelligence score = 100
Standard deviation of intelligence score = 15
Since both are perfectly correlated,
The Zscore ON SAT = +1.0
Using the standard normal interpretation, Xcore on SAT of +1.0 means 1 standard deviation to the right
This means :
Mean + 1 standard deviation
100 + 1*15
= 115
We could use the Zscore formula directly too:
Zscore = (x - mean) / standard deviation
Zscore = +1 ; x = score
Hence, we have
1 = (x - 100) / 15
1 * 15 = x - 100
15 = x- 100
x = 15 + 100
x = 115
Engineers speculate that W, the amount of weight (in units of 1000 pounds) that a certain span of a bridge can withstand without structural damage resulting, is normally distributed with mean 400 and standard deviation 40. Suppose that the weight (again, in units of 1000 pounds) of a car is a random variable with mean 3 and standard deviation.3. Approximately how many cars would have to be on the bridge span for the probability of structural damage to exceed .1?
A. 106
B. 123
C. 120
D. 115
E. 117
Answer:
n = 116.2 ≈ 117
Option E) 117 is the correct answer.
Step-by-step explanation:
Given the data in the question;
Exceed = 0.1
{ 1 - 0.1 = 0.9 }
normal table value at 0.9 = - 1.285
Normal table;
hence
( y - 400 ) / 40 = -1.285
y - 400 = -51.4
y = 400 - 51.4
y = 348.6
so,
348.6 = ∈(y) = ∈[ ⁿ∑[tex]_{i=1[/tex] X[tex]_i[/tex] ]
348.6 = n.∈( X[tex]_i[/tex] )
we substitute
348.6 = n × 3
n = 348.6 / 3
n = 116.2 ≈ 117 { roundup since we talking of number of cars i.e sample size }
Option E) 117 is the correct answer.
Find the area VALUE of each figure below with the following measurements
Answer:
the answer is 180cm for the rectangle
the answer is 126cm for the triangle.
the answer is 880ml for the rectangle.
Step-by-step explanation:
first diagram (rectangle)
area=l×b
15×12
180cm
second diagram(triangle)
area =
[tex] \frac{1}{2} \times l \times b \\ \frac{1}{2} \times 14 \times 18 \\ = 7 \times 18 \\ 126cm[/tex]
third diagram( rectangle)
area=
[tex]l \times b \\ \\ 44 \times 20 \\ 880ml[/tex]
Juan has 2 1/4 L of fruit purée Juan uses 3/8 leader from pier to make once movie which expression can be used to find the number of movies you can make
Answer:
See explanation
Step-by-step explanation:
Total fruit purée = 2 1/4 L
purée for One movie = 3/8 L
which expression can be used to find the number of movies you can make
Number of movies you can make = Total fruit purée ÷ purée for One movie
= 2 1/4 ÷ 3/8
= 9/4 ÷ 3/8
= 9/4 × 8/3
= (9*8) / (4*3)
= 72 ÷ 12
= 6
Number of movies you can make = 6
Can someone help me complete this worksheet please and thank you it’s all multiple choice
Answer:
1. D 12.8 cm
2. B 4.2 m
3. A 9.59
4. A 6.95
5. B 17.5 cm
Four students equally shared 1/2 pan of brownies. What fraction of the whole pan of brownies did each brother get
2 pan......................
.................
Answer:
1/8 of the whole pan
Step-by-step explanation:
Multiply the brothers by 2 to get 8 brothers for 1 whole pan of brownies now what fraction of the pan does each brother get. This method will get the answer 1/8.
A. 24
B. 12
C. 14
D. 16
Answer:
I believe it is C, 14. sorry if its wrong! ^^"
Step-by-step explanation:
Answer:
D. 16
Step-by-step explanation:
the scale factor says it all
PR = 15 PQ = 8 AC = 30
meaning each side length from the bigger triangle is twice as larger than the other triangle
Find the final price of a $849.99
laptop with 6% sales tax.
Answer:
$900.9
Step-by-step explanation:
Find the final price of a $849.99
laptop with 6% sales tax.
Given data
Price= $849.99
Tax = 6%
Let us find the amount of the tax
=6/100*849.99
=0.06*849.99
=$50.9994
Now the final price is
=50.9994+849.99
=$900.9
What are the answers to this someone please help.
1234567890233572o7o5y345uo22u.3936584643728284/43794729237932972478864966666666666666666666666666666666663870434573428734907 goood luck!
If two heterozygous individuals are crossed, what
percent of their offspring are also expected to be
heterozygous?
Complete the punnet square plssssss
Answer:
50%
Step-by-step explanation:
Example of Aa crossed with Aa (both hetero).
Outcomes are:
AA (homo)
Aa (hetero)
aA (hetero)
aa (homo)
So the ratio of hetero to all outcomes = 2:4 = 50%
Math help please and thank you
Answer:
Both m^2 and cm^2 are given below. Take your pick.
Step-by-step explanation:
Area = L * W
L = 1.57 m * 100 cm / 1 meter = 157 cm
W = 45 cm
Area = 157 cm * 45 cm = 7065 cm^2
In meters, the width would be 45 cm * 1 m / 100 cm = 0.45 m
Area = L * W
L = 1.57 m
W = 0.45 M
Area = 1.57 * 0.45
Area = 0.7065 m^2
Find the volume of the triangular prism as pictured below with a = 7 cm, b = 4
cm, c = 3 cm, and d = 8 cm. Do not include units in your answer.
Answer:
48
Step-by-step explanation:
Volume of triangular prism = Base Area × length of prism
Base area = ½*base*height
base = c = 3 cm
height = b = 4 cm
Base area = ½*3*4 = 6 cm²
Length of prism = d = 8 cm
Therefore,
Volume = 6 × 8 = 48 cm³
Carson invested $80,000 in an account paying an
interest rate of 5% compounded continuously.
Makayla invested $80,000 in an account paying an
interest rate of 4% compounded daily. To the
nearest dollar, how much money would Carson have
in his account when Makayla's money has tripled in
value?
Answer:
315881.53
Step-by-step explanation:
We first need to figure out how long it takes for the money to triple
let x= number of years it takes for the money to tirple
[tex]3=(1+\frac{.04}{365})^{365x}\\log_{1.0001}3=365x\\10025.38644=365x\\27.46681216=x[/tex]
Now plug that value into the continously compounding formula
[tex]80000*e^{27.4668*.05}=315881.5314[/tex]
Which rounds to
315881.53
Find the image of the given point under the given translation. P(-7, 1) T(x, y) = (x + 9, y-3) P' = ([?], []). Enter the number that belongs in the green box Enter
Answer:
P’ is (2,-2)
Step-by-step explanation:
For us to get the appropriate translation, we have to add 9 to the x-coordinate value and subtract 3 from the y-coordinate value
so, we have the transformation as follows;
(-7+9, 1-3)
= (2,-2)
Check the functions whose inverses are also functions.
On a coordinate plane, an absolute value function opens down.
On a coordinate plane, an exponential functions increases from quadrant 2 into quadrant 1.
On a coordinate plane, a cubic function has an x-intercept of (0, 0).
Answer:
b and c
Step-by-step explanation:
Answer:
Hands down c and b
Step-by-step explanation:
Which of the following is a logical conclusion based on the two statements below? If Jake forgets his snack, then he will be hungry at school. Jake forgot his snack. A. Jake was not hungry at school. B. Jake ate his snack. C. Jake also missed breakfast. D. Jake was hungry at school.
Answer:
I believe that the answer is either C or D
Step-by-step explanation:
Jake forgot his snack, which could mean that he was hungry at school. But it could be logical to assume that he forgot his breakfast. I may be wrong in both cases, but these are my best guesses!
Four students share 7 feet of ribbon equally. How many feet of ribbon does each student get? 7 ÷ 4 = 7 4 = 4 Each student's share is 4 feet of ribbon.
Answer:
Each student gets 1.75 ft of ribbon
Step-by-step explanation:
r × 4 = 7
First, divide the given factor by itself in order to get the variable by itself.
4 ÷ 4
Next, divide the product by the given factor bc what you do to the left, you must do to other side.
7 ÷ 4
Last, right down your new equation and find you solution.
New Equation: r = 1.75
Answer:
Step-by-step explanation:
Fine the area of a circle with radius 8 in.
Answer:
around 200.96
Step-by-step explanation:
circle area = pir^2
pi*8^2
pi*64
=around 200.96
The browns are moving across the counrty. Mr. Brown leaves 2.5 hours before Mrs. Brown, if he averages 75 mph and she averages 85 mph, how many hours will it take Mrs. Brown to catch up to Mr. Brown?
Answer:
the time taken by Mrs Brown to catch up is 18.75 hours
Step-by-step explanation:
Given;
average speed of Mr Brown = 75 mph
average speed of Mrs Brown, = 85 mph
time first traveled by Mr Brown = 2.5 hours
The distance traveled by Mr Brown before Mrs Brown start her own Journey;
D = speed x time
D = 75 mph x 2.5 h
D = 187.5 miles
Let the time taken by Mrs Brown to catch up = t
(85 - 75)t = 187.5
10t = 187.5
t = 18.75 hours
Check:
after 18.75 hours: Mrs Brown will travel ⇒ 18.75 x 85 = 1593.75 miles
after (2.5 h + 18.75h) : Mr Brown will travel ⇒ 21.25 x 75 = 1593.75 miles
What number is three times larger than 3×10 exponent
4 on top of the ten
Your throw your ball into a air from height of 4.2
solving system by substitution Help ASAP
Answer:
c is 3
d is 10
Step-by-step explanation:
see photo :)
Answer:
Hello answer:
c = 3
d = 10
Step-by-step explanation:
2 × c = 6 6 + 4 = 10
10 × 3 = 30 c × 2 = 6 30 + 6 = 36
Which equation represents a line that passes through (-9, -3) and has a slope of -6?
Answer:
below
Step-by-step explanation:
that is the procedure above