Answer:
Mean = 43.969
Standard deviation = 12.341
Step-by-step explanation:
Given the data :
36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, 50.06
The sample mean :
Σx / n = 351.75 / 8 = 43.969
Sample standard deviation :
√Σ(x - mean)²/n-1
√[(36.45-43.969)² + (67.90-43.969)² + (38.77-43.969)² + (42.18-43.969)² + (26.72-43.969)² + (50.77-43.969)² + (38.9-43.969)² + (50.06-43.969)² ] / ((8 - 1)
Standard deviation = 12.341
The distance traveled (in meters) by an insect is modeled by the equation d=0.3t where d is the distance traveled in meters and t is the time in minutes. Find the distance traveled in 26.3 minutes. A. 0.789 meters B. 87.67 meters C. 26 meters D. 7.89 meters
Answer:
D. 7.89 meters
Step-by-step explanation:
Given,
d = 0.3t
Here,
t = 26.3
Therefore,
d = 0.3*26.3
= 7.89m
Jon recently drove to visit his parents who live 270 270 miles away. On his way there his average speed was 24 24 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 12 12 hours driving, find the two rates.
Answer:
He drove there at 60 mph, and he drove back at 36 mph.
Step-by-step explanation:
one way distance = d = 270 miles
average speed on way back = s
average speed on the way there = s + 24
time driving there = t
time driving back = 12 - t
average speed = distance/time
distance = speed * time
going there:
270 = (s + 24)t
270 = st + 24t
going back
270 = s(12 - t)
270 = 12s - st
We have a system of equations:
270 = st + 24t
270 = 12s - st
Solve the first equation for t.
t(s + 24) = 270
t = 270/(s + 24)
Substitute in the second equation.
270 = 12s - s[270/(s + 24)]
270 = 12s - 270s/(s + 24)
Multiply both sides by s + 24.
270s + 6480 = 12s^2 + 288s - 270s
12s^2 - 252s - 6480 = 0
Divide both sides by 12.
s^2 - 21s - 540 = 0
(s - 36)(s + 15) = 0
s = 36 or s = -15
The average speed cannot be negative, so we discard the solution s = -15.
s = 36
s + 24 = 60
Answer: He drove there at 60 mph, and he drove back at 36 mph.
Which division problem does the number line below best illustrate?
0 1 2 3 4 5 6 7 8 9 10 11 12 13
O 12-3-4
O 9-3-3
O 12-2-6
o 16-4-4
Answer:
12/3=4 ..............
Una torre de 28.2 m de altura esta situada a la orilla de un rio, desde lo alto del edificio el ángulo de depresión a la orilla opuesta es de 25.2°. Calcular el ancho del río
Answer:
El ancho del río es 59.9 metros.
Step-by-step explanation:
El ancho del río lo podemos calcular con la siguiente relación trigonométrica asumiendo que la torre forma un triángulo rectángulo con el río:
[tex]tan(\theta) = \frac{CO}{CA}[/tex]
En donde:
CA: es el cateto adyacente = Altura de la torre = 28.2 m
CO: es el cateto opuesto = ancho del río =?
θ: es el ángulo adyacente a CA
Dado que el ángulo de depresión (25.2°) está ubicado fuera de la parte superior de la hipotenusa del triángulo que forma la torre con la orilla opuesta del río, debemos calcular el ángulo interno (θ) como sigue:
[tex]\theta = (90 - 25.2)^{\circ} = 64.8 ^{\circ}[/tex]
Ahora, el ancho del río es:
[tex]CO = tan(\alpha)*CA = tan(64.8)*28.2 = 59.9 m[/tex]
Por lo tanto, el ancho del río es 59.9 metros.
Espero que te sea de utilidad!
if a third plane could be drawn which contains both lines a and b .
Answer:
must be parallel
Step-by-step explanation:
They must be parallel.
pls help- the question kept cutting off before:
If cos(πr) = 2 cos(πr) and 0 < r < 3, what is one possible value of r?
Answer:
r can be 0.5
Step-by-step explanation:
Here, we want to get a possible value of r
From the question, the value of r is between 0 and 3
Mathematically, we know that in degrees pi is the same as 180 degrees
In a case where we have r = 1/2
we have it that;
cos(pi/2) = 2 cos (pi/2)
Since pi/2 is 90 and cos 90 is zero; then we have it that the two sides of the equation is the same and r can be 1/2
I got c which is 100 but I don’t know how jerry got A
Choice C is the correct answer because
[tex]\frac{(6+2)^3-12}{5}\\\\\frac{(8)^3-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100\\\\[/tex]
So in short, [tex]\frac{(6+2)^3-12}{5}=100\\\\[/tex]
------------------------------------------
The mistake Jerry likely made was that he only cubed the 2 and didn't realize the 6 was part of that cubing process. It seems he didn't add first and decided to cube before adding.
This is probably what steps Jerry did
[tex]\frac{6+2^3-12}{5}\\\\\frac{6+8-12}{5}\\\\\frac{14-12}{5}\\\\\frac{2}{5}\\\\[/tex]
But as mentioned, those steps are incorrect because the 6 is part of the cubing operation. In other words, Jerry should have added the 6+2 first before cubing afterward (due to PEMDAS determining the order of operations).
Or you could think of it like this
[tex]\frac{(6+2)^3-12}{5}\\\\\frac{(6+2)(6+2)(6+2)-12}{5}\\\\\frac{(8)(8)(8)-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100[/tex]
Two spheres have are such that the radius of the bigger sphere is 3 times bigger than the smaller. What is the ratio of the area?
Answer:
1 : 27
Step-by-step explanation:
Radius of sphere one = r₁ = x units
Radius of sphere 2 = r₂ = 3*x = 3x units
Ratio of area of two sphere's = r₁³ : r₂³
= x³ : (3x)³
[tex]= \frac{x^{3}}{3^{3}*x^{3}}\\\\= \frac{1}{3^{3}}\\\\= \frac{1}{27}[/tex]
= 1 : 27
What is the value of x?
[tex] \frac{4}{5} x - \frac{1}{10} = \frac{3}{10} [/tex]
Answer:
x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{4}{5}[/tex] x - [tex]\frac{1}{10}[/tex] = [tex]\frac{3}{10}[/tex]
Multiply through by 10 ( the LCM of 5 and 10 ) to clear the fractions
8x - 1 = 3 ( add 1 to both sides )
8x = 4 ( divide both sides by 8 )
x = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
what is the measure of the angle formed by a side of the given angle and the given angle's bisector:27?
Answer:
Step-by-step explanation:
An angle is cut in half by the bisector.
Since the given angle is 172, its bisector creates 2 equal angles.
2x = 172 Divide both sides by 2
x = 172/2
x = 86
Research suggests improvements in human capital explains what percentage of the growth in U.S. Productivity from 1950 to the early 2000s?
Answer: 20%
Step-by-step explanation:
Human capital refers to the expertise that people gain as a result of working. This includes skills they gain from training and actually working. For instance, the skills a Brainly website designer gets from working on Brainly.
Research suggests that this human capital has led to about a 20% growth in U.S. productivity from the year 1950 to the year 2007 which means that it is a very significant factor in the growth of the country.
please I need answer right now pleasssseee
only C
C. -3×(-2/3)²
Answer:
-4/3
Step-by-step explanation:
-3 x (-2/3)²
= -3 x (4/9)
= -4/3
14,523 to 16,489.
What is the percent increase in the town's population? Finish the division and round to the nearest percent.
Answer:
≈ 14%
Step-by-step explanation:
percent increase is calculated as
[tex]\frac{increase}{original}[/tex] × 100%
Increase = 16489 - 14523 = 1966 , then
percent increase = [tex]\frac{1966}{14523}[/tex] × 100% = [tex]\frac{1966(100)}{14523}[/tex] ≈ 14% ( to nearest percent )
Answer:
14% :)
Step-by-step explanation:
Write an
equivalent expression by distributing the "_" sign outside the parentheses:
-(2h + 9.6k) + 1
Answer:
On distributing the - sign outside the parenthesis we get,
-2h - 9.6k + 1
Someone help me please if you don’t mind
Answer:
Multiply to -63
and add to -2
Step-by-step explanation:
I'm a genius.
Answer:
(x - 9)(x + 7)
Step-by-step explanation:
Given
x² - 2x - 63
Consider the factors of the constant term (- 63) which sum to give the coefficient of the x- term, that is
numbers that multiply to give - 63 and add to give - 2
The factors are - 9 and + 7 , since
- 9 × 7 = - 63 and - 9 + 7 = - 2 , then
x² - 2x - 63 = (x - 9)(x + 7) ← in factored form
Pls ans this question step by step not only ans if it will help me than I will thanks uu comment uu pls ansme
Answer:
-2x+7
Step-by-step explanation:
The sum of the measures of two of the angles formed by the intersection of two lines is 114 degrees. Find the measures of all angles. (There are 4 boxes to fill out for the answer)
Answer:
57°,123°,57°,123°
Step-by-step explanation:
as vertical angles are equal
so one angle=114/2=57°
other angle=180-57=123°
Answer:
pic pls
Step-by-step explanation:
Simplify the expression. x^4/ x^7
a x-11
b x-3
c x11
b x3
Answer:
b
Step-by-step explanation:
[tex]\frac{x^4}{x^7} =x^4 \times x^{-7} =x^{4-7} =x^{-3}[/tex]
Find the measure of DA
Answer:
15
Step-by-step explanation:
First, find x
set your formula up as 3x+5=6x-10, since AB and DC are the same length.
This means x = 5
Now substitute 5 for x in the line DA
4x-5
4 * 5 - 5 = 15
Explain how the quotient of powers was used to simplify this expression
Answer:
See explanation
Step-by-step explanation:
Given:
5⁴/25 = 5²
25 = 5²
Then,
5⁴ / 25
= 5⁴/5²
Note:
• multiplication sign means addition in indices
• Division sign means subtraction in indices
Both numerator and denominator have the same base, so you'll pick one of the bases and subtract the powers
So,
5⁴/5²
= 5^(4 - 2)
= 5^(2)
= 5²
Therefore,
5⁴ / 25 = 5²
Helppppppp and explain pls and thankyouuu
Answer:
so the correct asnwer is c
Answer:
Step-by-step explanation:
Grace earned £32,000 last year. She worked for 35 hours a week for 50 weeks. Calculate her pay per hour. Give your answer to 2 decimal places.
Answer:
18.29
Step-by-step explanation:
32000 ÷ 35 ÷ 50 = 18.2857143
Solve the equation sin(x - 20°) = cos(42º) for x, where 0
Answer:
[tex]x = 68[/tex]
Step-by-step explanation:
Sine are Cosine are Complementary Angles.
We can use this formula
[tex] \sin(x) = \cos(y) [/tex]
when x+y=90.
Add the expressions in the parentents to 90 and solve for x.
[tex]x - 20 + 42 = 90[/tex]
[tex]x + 22 = 90[/tex]
[tex]x = 68[/tex]
The answer is
[tex]x = 68[/tex]
Two data sets are represented by the graphs below.
A.)Smaller range
B.) Lager median
C.)Larger mean
D.)Smaller standard deviation
Stephanie found a sweater on sale for $12.88. The original price of the sweater was $44.95. About how much did she save on the sweater?
rounding
Answer:
$32.07
ROUNDING ANSWER : $32
Step-by-step explanation:
you would subtract $44.95 -$12.88 which would give you $32.07
since you are rounding your answer would be $32
Hope this helps
Answer:
Stephanie saved about $32 on her new sweater.
$44.95 - $12.88 = $32.07
$32.07 rounds down to $32
Step-by-step explanation:
Have the same assignment. Hope this helps!
Find the volume.
Use = 3.14
cone
h = 14 in.
r = 9.9 in.
in 3
h
Type the correct answer rounded to two
decimal places, pls help it would be so appreciated
Answer:
Volume of the cone given rounded to two decimal places is 1415.65in
Explanation:
Volume of a cone
[tex] = \pi {r}^{2} \frac{h}{3} [/tex]
[tex] = (3.14)( {9.9}^{2} )( \frac{14}{3} )[/tex]
[tex] = 3.14 \: \times \: 98.01 \: \times \: 4.6[/tex]
[tex] = 1415.65644[/tex]
Rab has trouble remembering the difference between addition of a positive and
negative number and multiplication of a positive and negative number. Explain how
you could clarify the concepts for him. Use an example to back up your explanation.
Addition of a positive and negative number always means that you are going to subtract the number e. g. 4+-1 = 3. However, multiplication of a positive and negative number means the answer is always negative e. g. 5 x - 3 = - 15.
The addition of positive and negative number will always subtract with sign of maximum value.
The multiplication of positive and negative number will have a negative sign always.
AdditionConcept for the addition of positive and negative numberWhen two numbers which have different sign are added, they will always be subtracted from each other. The sign will vary accordingly.
with negative sign: when two numbers are added such that the number with negative sign has the larger value, then both numbers will get subtracted but with negative sign.Example: Consider two number -5 and 4
= -5 + 4
= -1
Here, 5 is the larger value. So, the sign comes is negative.
with positive sign: when two numbers are added such that the number with positive sign has the larger value, then both numbers will get subtracted but with positive sign.Example: consider two number 5 and -4.
= 5 + (-4)
= 1
Here, 5 is the large number. So, the sign comes is positive.
MultiplicationConcept for the multiplication of positive and negative number:When two numbers with opposite signs are multiplied, the answer is always a negative number.
Example; Consider two numbers 4 and -5.
On multiplication,
4×(-5) = -20
Thus, the multiplication of two numbers with different signs will always give a negative number.
To know more about rational and irrational numbers, here
https://brainly.com/question/5796983
#SPJ2
What is the equation of the following line written in general form? (The y-intercept is -1.)
Answer:
2x-y-1=0
Step-by-step explanation:
.
Subtract
[tex] - 3[/tex]
[tex] - {2y}^{3} [/tex]
[tex] - y[/tex]
[tex] - {5y}^{2} [/tex]
from
[tex] - {2y}^{3} [/tex]
[tex] + 4[/tex]
Answer:
Step-by-step explanation:
-2y³ + 4 - (-3 - 2y³ - y - 5y²) = -2y³ + 4 + 3 + 2y³ + y + 5y²
= -2y³ + 2y³ +5y² + y + 4 + 3 {combine like terms}
= 5y² +y + 7
Help me please guys
Answer:
1st box is -4
2nd box is -4
3rd box is 3
4th box is -1
Answer: 15x squared -4x-3
rewrite the expression
15x squared + 5x-9x-3
factor the expressions
5x × (3x+1)-3(3x+1)
factor the expression
solution
(3x + 1) × (5x - 3)