Step-by-step explanation:
An=A1+(n-1)d
A30=10+(30-1)3
A30=10+(29)3
A30= 10+87
A30=97
it takes me a centuary to type
Verify that the vector X is a solution of the given homogeneous system. X' = −1 1 25 1 −1 X; X = −1 5 e−6t/5 For X = −1 5 e−6t/5, one has
Answer: Find answer in the attached file
A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,correct to 2 significant figure
(a) the new angle which the ladder makes with the ground
(b) the distance the ladder slipped back on the ground from it's original position
Answer to part (a) is: 33 degrees
Answer to part (b) is: 5 meters
=============================================
Explanation:
Check out the diagram below.
For now, focus only on triangle ABC. The ladder is segment AC = 10. We first need to find the length of [tex]AB = h_1[/tex] which is the initial height of the ladder.
sin(angle) = opposite/hypotenuse
sin(70) = h/10
h = 10*sin(70)
h = 9.396926 approximately
Subtract off 4 since the ladder slips 4 meters down the wall
h-4 = 9.396926-4
h-4 = 5.396926
which is the new height the ladder reaches. The hypotenuse stays the same
sin(angle) = opposite/hypotenuse
sin(theta) = 5.396926/10
theta = arcsin(5.396926/10)
theta = 32.662715
theta = 33 degrees when rounding to 2 significant figures
This is the value of [tex]\theta_2[/tex] in the diagram below.
---------------------------------
We'll use the cosine rule with the old theta value [tex]\theta_1[/tex]
cos(angle) = adjacent/hypotenuse
cos(70) = x/10
x = 10*cos(70)
x = 3.420201 is the approximate distance the foot of the ladder is from the wall. This is before the ladder slips.
After the ladder slips, we use the new angle value [tex]\theta_2[/tex]
cos(angle) = adjacent/hypotenuse
cos(32.662715) = x/10
x = 10*cos(32.662715)
x = 8.418622
Subtract the two x values
8.418622-3.420201 = 4.998421
which gives the approximate distance the foot of the ladder moved (the distance from point C to point E in the diagram)
This rounds to 5.0 or simply 5 when rounding to 2 significant figures.
Solve for c
C – 7 = -9
Answer: -2
Step-by-step explanation:
-2 - 7 = -9
Answer:
[tex]\Huge \boxed{c=-2}[/tex]
Step-by-step explanation:
[tex]c-7=-9[/tex]
We need to isolate the [tex]c[/tex] variable on one side of the equation.
Adding 7 to both sides of the equation.
[tex]c-7+7=-9+7[/tex]
Simplifying the equation.
[tex]c=-2[/tex]
What is the slope of the line that contains these points? (39,36) (40,29) (41,22) (42,15)
Answer:
-7
Step-by-step explanation:
As x increases by 1, y decreases by 7, so the "rise"/"run" is ...
slope = rise/run = -7/1 = -7
During a festival, the number of visitors tripled each day.
If the festival opened on a Thursday with 300 visitors, what
was the attendance on Sunday?
Answer:
24,300
Step-by-step explanation:
So on Thursday you have 300 next day it's 900 bc 300x3=900
Friday: 900x3=2,700
Saturday: 2,700x3=8,100
Sunday: 8,100x3=24,300
Which of the following circumstances would likely make factoring the best method for solving a quadratic equation?
Question 3 options:
A quadratic that is prime
The leading coefficient is zero
The leading coefficient is not 1 and the constant is a large number
The difference of 2 perfect squares
Answer:
Option D.
Step-by-step explanation:
We need to find the circumstances that would likely make factoring the best method for solving a quadratic equation.
A quadratic equation is prime if its factors can not possible. So, option A is incorrect.
In a quadratic equation leading coefficient can not be zero. So, option B is incorrect.
For large numbers (coefficient or constant), quadratic formula is best method. So, option C is incorrect.
The difference of 2 perfect squares is:
[tex]x^2-a^2=(x-a)(x+a)[/tex]
In this case factoring is the best method.
Therefore, the correct option is D.
Find the value of x. A. 5√2/2 B. 5 C. 10 D. 10√2
Answer:
C
Step-by-step explanation:
Note that the right triangle has two tick marks.
This means that the sides are equivalent.
Therefore, this is a 45-45-90 triangle.
In a 45-45-90 triangle, the side lengths are n, and the hypotenuse is n√2
Since n is 5√2, then the hypotenuse x is n√2. Thus:
[tex]x=n\sqrt2\\x=(5\sqrt2)\sqrt2[/tex]
Simplify:
[tex]x=5(2)=10[/tex]
The answer is C :)
Suppose a prediction equation was built on training data yielding:
y_hat = 145.5 -5.5*x
Given this small set of test data, calculate the RMSE.
x у
1 10.36 87.87
2 9.96 89.83
3 12.50 71.61
a. 1.98.
b. 3.04.
c. 9.21.
d. 5.37.
Answer:
3.04
Step-by-step explanation:
Given the prediction equation:
y_hat = 145.5 -5.5*x
- - - - x - - - - - - - - - у
1 - - 10.36 - - - - 87.87
2 - - 9.96 - - - - 89.83
3 - - 12.50 - - - - 71.61
1) y_hat = 145.5 -5.5*(10.36)
y_hat = 145.5 - 56.98 = 88.58
2) y_hat = 145.5 -5.5*(9.96)
y_hat = 145.5 - 54.78 = 90.72
3) y_hat = 145.5 -5.5*(12.50)
y_hat = 145.5 - 68.75 = 76.75
Root mean squared error (RMSE) :
Number of observations (n) = 3
√(Σ(y_hat - y)^2) / n
y_hat = predicted value
y = actual value
Σ[(88.58-87.87)^2+(90.72-89.83)^2+(76.75-71.61)]
Σ(0.71^2) + (0.89^2) + (5.14^2)
27.7158 / 3 = 9.2386
√9.2386
= 3.0395065
= 3.04
simplify (1-√3)(⅓+√3) leaving your answer in the form p+q√3
Answer:
[tex]\frac{-8 +2\sqrt{3} }{3}[/tex]
Step-by-step explanation:
When working with surds we need to take note of the roots present there.
To expand this equation we can do it the following way noting that √3 X √3 = 3
Expanding (1-√3)(⅓+√3)
1 X 1/3 = 1/3
1 X √3 = √3
-√3 X 1/3 =-√3/3
√3 X √3 = 3
hence, expanding the equation, we have
1/3 + √3 -√3/3 + 3
We can simply group the like terms and add them up.
[1/3 +3] +[√3-√3/3]
10/3 + [tex]\frac{2\sqrt{3} }{3}[/tex]
= [tex]\frac{-8 +2\sqrt{3} }{3}[/tex]
Write the sentence as an equation.
61 is equal to 268 added to y
Type a slash ( 7 ) if you want to use a division sign
Answer:
y= -207
Step-by-step explanation:
61 = 268 + y
Collect like terms
y= 61 - 268
Simplify
= -207
y= -207
Alternatively,
61 = 268 + y
Subtract 268 from both sides
61 - 268 = 268 + y - 268
-207 = y
Therefore,
y= -207
Will mark the brainliest for correct answer!!!
Answer:
hexagon; not regular
Step-by-step explanation:
hope this helps
reduce the following fractions to their lowest terms: a. 6/8. b. 8/12c. 15/20 d. 9/18 e. 24/30 f. 25/40
Answer:
That's my slovings for your question
What is 10% of 800Hhhhhhhhhhhh
A 35 foot tree casts a 13 foot shadow. What is the degree of elevation for the sun?
Answer:
tan (thita) = 35/13
Step-by-step explanation:
Tan( angle) = opposite/ adjacent
Tan( angle) = 35/13
Angle = arc tan 35/13
Angle = 69.624 degrees
Round the answer as needed.
please help me with this question
Answer:
[tex] {\sqrt[ 3 ]{x^{2} } }•{ \sqrt[4] {{y}^{3}} }[/tex]
Explanation-
As,
[tex]a^{\frac{1}{n} } = \sqrt[n]{a} [/tex]
and
[tex]a^{-n}=1/a^n[/tex]
Does anyone know this?
Answer:
first option is right
Step-by-step explanation:
Write the equation of the line that passes through (3, -2) and has a slope of 4 in point slope form
Answer:
The answer is
y + 2 = 4( x - 3)Step-by-step explanation:
To find an equation of a line given a point and slope we use the formula
y - y1 = m(x - x1)
where
m is the slope
(x1 , y1) is the point
From the question
slope = 4
point = ( 3 , - 2)
Substitute the values into the above formula
We have
y + 2 = 4( x - 3)Hope this helps you
Answer:
y+
Step-by-step explanation:
Point-Slope form- (y − y 1) = m ⋅ (x − x 1)
Slope: m = 4
Point: (x1, y1) = (3, -2)
Answer: y + 2 = 4 ⋅ (x - 3)
Wich expression is equivalent to h+0.48h+0.58?
A.0.06h
B.0.58 + 1.48h
C.h + 1.06
D.2.06h
Answer:
B. 0.58 + 1.48h
Step-by-step explanation:
h+0.48h+0.58
=(1h+0.48h)+0.58
=1.48h +0.58
the question is below
Answer:
RU = 9
ST = 3
Step-by-step explanation:
RT = 6
RS = ST = (1/2)RT = (1/2)(6) = 3
ST = 3
RU = 3ST = 3 * 3 = 9
if m<2, then m<1 is...
Answer:
45
Step-by-step explanation:
m<1 and m<2 are complementary angles because the sum of two angles = 90° and since m<1 = m<2
90 ÷ 2 = 45
190 = 200^b, make b the subject
Answer:
b = [tex]\frac{ln190}{ln200}[/tex]
Step-by-step explanation:
Using the rule of logarithms
log [tex]x^{n}[/tex] ⇔ nlogx
Given
190 = [tex]200^{b}[/tex] ( take the natural log ln of both sides )
ln190 = ln[tex]200^{b}[/tex] = bln200 ( divide both sides by ln200 )
[tex]\frac{ln190}{ln200}[/tex] = b
Adam tabulated the values for the average speed on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. If Adam wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be?
Answer:
7
Step-by-step explanation:
Given the following data:
Average speed : 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4
To construct a one-sample t - statistic, the value of the degree of freedom will be ;
In a one sample test of known mean, if the number of observations are 4, one can choose to vary at most three of the observations and still obtain the mean, that is the 4th observation must remain fixed.
Degree of freedom = Number of observations (n) - 1. This is the maximum number of independent variables which can be varied.
Nunber of observations or sample size in the data above is 8
Hence,
Degree of freedom = (8 - 1) = 7
Answer:the anwser is 7
Step-by-step explanation:
Please Answer Both Questions
Answer:
c. 48 packages
d. Possibilities:
1 x 28 = 28
2 x 14 = 28
4 x 7 = 28
7 x 4 = 28
14 x 2 = 28
28 x 1 = 28
Possible combinations:
17, 1, 28
17, 2, 14
17, 4, 7
17, 7, 4
17, 14, 2
17, 28, 1
Step-by-step explanation:
c. 127 employees get 3 uniforms each, meaning a total of 127 * 3 = 381 uniforms
The uniforms come in packs of 8, so dividing 381 by 8, we get:
381/8 = 47.625
However, you probably can't order a portion of a package, so you must round up to 48 packages. There will be 3 uniforms left over.
d. The divisors of 28 are 1, 2, 4, 7, 14, and 28. All I did was enumerate the six possibilities.
Which equation shows a slope of 3 and a y-intercept of (0,7) ?
Answer: y = 3x + 7
Step-by-step explanation:
Since we are given the slope and y intercept we could write the equation in slope intercept form as y=mx +b .Only m and b are needed to write the equation.M is the slope and B is the y intercept.
Answer:
y=3x+7
Step-by-step explanation:
The equation of a line in slope-intercept form is:
y=mx+b
where m is the slope and b is the y-intercept.
We know the slope is 3, so we can substitute 3 in for m.
y=3x+b
We also know the y-intercept is (0,7). When writing the equation of a line in this form, we can ignore the x-coordinate of 0. Therefore, the y-intercept is also just 7. Substitute 7 in for b.
y=3x+7
The equation of a line with a slope of 3 and a y-intercept of (0,7) is y=3x+7
Making a certain shade of paint requires mixing 3 parts silver with 4 parts green. Meg uses this data to start this table of equivalent ratios.
Answer:
6:8 and 9:12
Step-by-step explanation:
The equivalent ratios of the given quantity of silver parts of paint to green which is 3:4 are: 6:8 and 9:12.
What are Equivalent Ratios?When compared to one another, equivalent ratios are defined as having the same values.
For example, 8/16, 4/8 and 1/2 re equivalent ratios because:
Given:
The table that shows the ratio of the number of parts silver to number of parts green as 3 parts silver to 4 parts green, then
ratio = 3:4.
This means that for 3 parts of silver paint, we would require 4 parts of green paint to give the shade of paint that is needed.
so,
6/8 = 3/4
9/12 = 3/4
Thus, 6/8 = 9/12 = 3/4, which is equivalent.
Hence, the ratios that are equivalent to 3 parts silver paint to 4 parts green paint are: 6:8 and 9:12.
Learn more about equivalent ratios here:
brainly.com/question/13513438
#SPJ2
LSAT test scores are normally distributed with a mean of 152 and a standard deviation of 10. Find the probability that a randomly chosen test-taker will score 142 or lower. (Round your answer to four decimal places.)
Answer:
the probability that a randomly chosen test-taker will score 142 or lower = 0.8643
Step-by-step explanation:
We are given;
Data point; x = 142
Mean; μ = 153
Standard deviation; σ = 10
So,let's find the z-score using;
z = (x - μ)/σ
z = (142 - 153)/10
z = -1.1
From the z-distribution table attached, the probability is;
P(z < -1.1) = 1 - 0.13567 ≈ 0.8643
Find the annual percentage yield for an account with an APR of 13.75% compounded continuously. Round your percentage to two places after the decimal point.
Answer:
14.74%
Step-by-step explanation:
The formula for ANNUAL PERCENTAGE YIELD (APY) for an account that is COMPOUNDED CONTINUOUSLY is given as
APY = Pe^rt - 1
Where P = Principal
e = exponential
r = rate
t = time
Since Principal and Time was not given in the question,
APY = e^r - 1
r = 13.75% = 0.1375
APY = e^0.1375 - 1
APY = 1.147401706 - 1
APY = 0.147401706
Converting to percentage
= 0.147401706 × 100
= 14.7401706%
Approximately to 2 decimal places: 14.74%
Therefore, the annual percentage yield is 14.74%
which statement is true about the value of |-5|
Does anyone know how to solve this? I tried moving the 3 back to make it log 2 (x^3) but for the second one it would be (5x)^2 and I get stuck there
Answer:
x = 100
Step-by-step explanation:
All you need is contained in the sheet attached
Answer:
x = 100
Step-by-step explanation:
3 log2(x) - 2 log2(5x) = 2
We know that a log(c) = log c^a
log2(x)^3 - log2(5x)^2 = 2
log2(x^3) - log2(25x^2) = 2
We know that log a - log b = log a/b
log2(x^3 /25x^2) = 2
Simplify
log2(x /25) = 2
Raise each side to base 2
2^log2(x /25) = 2^2
x/25 = 4
Multiply each side by 25
x = 4*25
x = 100
-7 - (-8) + (-3) + 6 - 2=
Answer:
2
Step-by-step explanation:
-7 - (-8) = 1
1 + (-3) = -2
-2 + 6 = 4
4 - 2 = 2
Answer:
2
Step-by-step explanation:
Start by removing the parentheses appropriately:
-(-8) = +8, and
+(-3) = -3
Then
-7 - (-8) + (-3) + 6 - 2 = -7 + 8 - 3 + 6 - 2
Now, working from left to right, we perform the indicated operations:
-7 + 8 comes out to 1, and so we have 1 - 3 + 6 - 2.
Continuing, we get -2 + 6 - 2, or 4 - 2, or 2