The critical value for the given confidence level, c = 0.90 and n = 21 is [tex]t_c=1.725[/tex].
How to calculate the critical value for t-distribution?The critical value is calculated as follows:
For the given sample size n, find the degree of freedom (d.f)Where d.f = n - 1Using the t-distribution table, the critical value is obtained for the obtained d.f and the confidence level.Calculation:It is given that,
confidence level c = 0.90
sample size n = 21
Then,
degree of freedom,
(d.f) = n - 1 = 21 - 1 = 20
So, from the t-distribution table,
at d.f = 20 and the confidence level 0.90, the critical value is 1.725.
I.e., [tex]t_c[/tex] = 1.725
For this, α = (1 - 0.90)/2 = 0.05
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please help jajajajaja
(06.04 MC)
If [tex]\int\limits^3_ {-2} \, [2f(x)+2]dx=18[/tex] and [tex]\int\limits^1_ {-2} \, f(x)dx =8[/tex], then [tex]\int\limits^3_ {1} \, f(x)dx[/tex] is equal to which of the following?
4
0
−2
−4
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
◉ [tex]\large\bm{ -4}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Before performing any calculation it's good to recall a few properties of integrals:
[tex]\small\longrightarrow \sf{\int_{a}^b(nf(x) + m)dx = n \int^b _{a}f(x)dx + \int_{a}^bmdx}[/tex]
[tex]\small\sf{\longrightarrow If \: a \angle c \angle b \Longrightarrow \int^{b} _a f(x)dx= \int^c _a f(x)dx+ \int^{b} _c f(x)dx }[/tex]
So we apply the first property in the first expression given by the question:
[tex]\small \sf{\longrightarrow\int ^3_{-2} [2f(x) +2]dx= 2 \int ^3 _{-2} f(x) dx+ \int f^3 _{2} 2dx=18}[/tex]
And we solve the second integral:
[tex]\small\sf{\longrightarrow2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot(3 - ( - 2)) }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} 2dx = 2 \int ^3_{-2} f(x)dx + 2 \cdot5 = 2 \int^3_{-2} f(x)dx10 = }[/tex]
Then we take the last equation and we subtract 10 from both sides:
[tex]\sf{{\longrightarrow 2 \int ^3_{-2} f(x)dx} + 10 - 10 = 18 - 10}[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 8}[/tex]
And we divide both sides by 2:
[tex]\small\longrightarrow \sf{\dfrac{2 { \int}^{3} _{2} }{2} = \dfrac{8}{2} }[/tex]
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx=4}[/tex]
Then we apply the second property to this integral:
[tex]\small \sf{\longrightarrow 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
Then we use the other equality in the question and we get:
[tex]\small\sf{\longrightarrow 2 \int ^3_{-2} f(x)dx = 2 \int ^3_{-2} f(x)dx = 8 + 2 \int ^3_{-2} f(x)dx = 4}[/tex]
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =4}[/tex]
We substract 8 from both sides:
[tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx -8=4}[/tex]
• [tex]\small\longrightarrow \sf{2 \int ^3_{-2} f(x)dx =-4}[/tex]
Poormina spends all of her money on comic books and mandarins. in 2013, she earn $12 per hour, the price of a comic book was six dollars, and the price of a mansion was one dollar
The price of a mansion is $1.00 in 2013.
What is difference between a nominal and real variable?
Nominal variables are expressed in money or dollar terms, whereas the real variable compares the wage earned per hour to the basket of goods or services that it can purchase.
In comparing the wage earned per hour to 2 comic books, since the two would cost $12,that explains real variable, which is not required in this case.
However, comparing the the wage of $12 per hour to the price of mansion, which is $1 per one, indicates nominal variable.
In essence, the correct option in this case is that price of a mansion is $1.00 in the year 2013.
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what is the length of the interval of solutions to the inequality 1≤3-4x≤9?
Answer: -3 ≤ x ≤ -1
Step-by-step explanation:
1 ≤ 3 - 4x ≤ 9
1 + 3 ≤ - 4x ≤ 9 + 3; Add 3 on all sides
4 ≤ -4x ≤ 12
1 ≤ -x ≤ 3; Divide 4 on all sides
-1 ≥ x ≥ -3; Multiply -1 on all sides(FYI: When multiplying or dividing negative numbers in inequalities, make sure to reverse the signs as well)
Answer:
2
Step-by-step explanation:
1≤3-4x≤9
subtract 3
1-3≤3-4x-3≤9-3
-2≤-4x≤6
divide by 2
-1≤-2x≤3
multiply by -1
1≥2x≥-3
or
-3≤2x≤1
divide by 2
[tex]-\frac{3}{2} \leq \frac{2x}{2} \leq \frac{1}{2} \\-\frac{3}{2} \leq x\leq \frac{1}{2} \\[/tex]
length of interval
[tex]=\frac{1}{2} -(\frac{-3}{2} )\\=\frac{1}{2} +\frac{3}{2} \\=\frac{1+3}{2} \\=\frac{4}{2} \\=2[/tex]
Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x-30 > 30
Answer:
[tex]x > 60[/tex]
Step-by-step explanation:
[tex]x-30 > 30[/tex]
[tex]x > 60[/tex] (add 30 onto both sides of the inequality)
1/2-1/6
Jzjzhhzhzhzhhz
Answer:
ummm the answer is very simple
The answer is 0/6
Step-by-step explanation:
[tex] \frac{1}{2 \times 3} - \frac{1}{6} [/tex]
[tex] \frac{1}{6} - \frac{1}{6} [/tex]
[tex]1 - 1 = \frac{0}{6} [/tex]
Roberto has 5 more than twice the number of tee shirts that Brisa has. Roberto has 19 tee shirts. How many tee shirts does Brisa have?
Answer:
Step-by-step explanation:
THOMAS OSLER IS BUYING A TOWNHOUSE SELLING FOR $175,000. HIS BANK IS
OFFERING A 30-YEAR FIXED RATE MORTGAGE AT 5.5% WITH A MINIMUM 20% DOWN
PAYMENT. DETERMINE THE AMOUNT OF THE DOWN PAYMENT AND THE MONTHLY PAYMENT
The amount of the down payment and the fixed rate mortgage is $35000 and $9625.
According to the statement
We have given that the
Thomas osler is buying a house selling for $175,000 And we have to find the amount of the down payment and the monthly payment.
So, The down payment is :
percentage of the down payment is 20%
So,
Amount = 20/100*175000
Amount = 35,000$
And the percentage of the fixed rate mortgage with 5.5%
So,
Amount = 5.5/100*175000
Amount = $9625.
This the amount of the down payment with the given percentage and with the fixed rate mortgage.
So, The amount of the down payment and the fixed rate mortgage is $35000 and $9625.
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24 is what percent of 480?
Answer:
5%.
Step-by-step explanation:
That is
(24/480 * 100
Now 480 / 24 = 20 so we have
(1/20) * 100
= 100/20
= 5%.
Answer:
24 is 5% of 480
Step-by-step explanation:
24 / 480 = 0.05
Percent is "for each 100"
Then:
0.05 * 100 = 5%
If
f(x) = 2x2 − 7,
0 ≤ x ≤ 3,
evaluate the Riemann sum with
n = 6,
taking the sample points to be midpoints.
What does the Riemann sum represent? Illustrate with a diagram.
The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
What is Riemann sum?
Formula for midpoints is given as;
M = ∑0^n-1f((xk + xk + 1)/2) × Δx;
From the information given, we have the following parameters
x0 = 0 n = 6 xn = 3Let' s find the parameters
Δx = (3 - 0)/6 = 0.5
xk = x0 + kΔx = 0.5k
xk+1 = x0 + (k +1)Δx
Substitute the values
= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2
We then have;
= (0.5k + 0.5k + 05.)/2
= 0.5k + 0.25.
Now f(x) = 2x^2 - 7
Let's find f((xk + xk+1)/2)
Substitute the value of (xk + xk+1)/2)
= f(0.5k+ 0.25)
= 2(0.5k + 0.25)2 - 7
Put values into formula for midpoint
M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.
To evaluate this sum, use command SUM(SEQ) from List menu.
M = - 12.0625
A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.
Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
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Explain how to modify the graphs of f(x) and G(x) to graph the solution set to the following system of inequalities. How can at least solution set be identified?
Give f(x) a dotted boundary and shade it above.
Give g(x) a solid boundary and shade it above.
The solution set is the region that is in the shaded region of both graphs.
Evaluate the expression if a=2,b=-3,C=-1, and D=4
-2(b^2-5c)
Answer:
Your answer is - 28
Step-by-step explanation:
Given,
a = 2
b = - 3
c = - 1
d = 4
Now,
- 2 ( b² - 5 c )
= - 2 ( -3² - 5 ( - 1 ) )
= - 2 ( 9 + 5 )
= - 2 × 14
= - 28 ans….
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Jasmine got a new puppy for her birthday. He's full of energy, so she takes him for a walk along a 1.2-mile loop in a nearby park. If they walked a total of 3.6 miles, how many loops did they do?
Answer: 3 loops
Step-by-step explanation: The loop is 1.2 miles, and the total walk is 3.6 miles. You want to find out how many laps are in the 3.6 miles. This can be found using division. 3.6/1.2= the number of 1.2 mile laps inside the 3.6 mile walk, which is 3 laps. hope this helped!
Two copies of the same Rational Function are shown below.
On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
The equation for the horizontal asymptote will be y = -2.
How to illustrate the information?Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:
y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)
= y = -2/1
= y = -2
The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0
= x + 3 = 0
= x = -3
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. Find the perimeter of a regular pentagon with each side measuring 4.5 inches.
Answer: 22.5 inches
Step-by-step explanation:
the general formula for finding perimeter is [tex]p=s+s+s...[/tex]a pentagon contains 5 sides[tex]p=s+s+s+s+s[/tex]
note that this is a regular pentagon so it must contain 5 congruent sideseach side will be 4.5 inchesthe formula can be changed to [tex]5(s)[/tex] and solved:[tex]5(4.5 in)=p[/tex]
∴ 22.5 inches = perimeter of the pentagon
I ordered a shoe a few days ago and the seller provided me with the tracking number for the hoodie but through Grailed but USPS has been stuck on "We are preparing your order for shipment" and "Delivery information will be available once the carrier has the updates." What does this mean? Also when I put my tracking number in USPS's Package Tracker, the number doesn't exist in its system. Does anyone know whats going on? Thanks!
The average THC content of marijuana sold on the street is 10.5%. Suppose the THC content is normally distributed with standard deviation of 2%. Let X be the THC content for a randomly selected bag of marijuana that is sold on the street. Round all answers to 4 decimal places where possible,
a. What is the distribution of X? X ~ N(
,
)
b. Find the probability that a randomly selected bag of marijuana sold on the street will have a THC content greater than 8.9.
c. Find the 76th percentile for this distribution.
%
a. This information is given to you.
b. We want to find
[tex]\mathrm{Pr}\{X > 8.9\}[/tex]
so we first transform [tex]X[/tex] to the standard normal random variable [tex]Z[/tex] with mean 0 and s.d. 1 using
[tex]X = \mu + \sigma Z[/tex]
where [tex]\mu,\sigma[/tex] are the mean/s.d. of [tex]X[/tex]. Now,
[tex]\mathrm{Pr}\left\{\dfrac{X - 10.5}2 > \dfrac{8.9 - 10.5}2\right\} = \mathrm{Pr}\{Z > -0.8\} \\\\~~~~~~~~= 1 - \mathrm{Pr}\{Z\le-0.8\} \\\\ ~~~~~~~~ = 1 - \Phi(-0.8) \approx \boxed{0.7881}[/tex]
where [tex]\Phi(z)[/tex] is the CDF for [tex]Z[/tex].
c. The 76th percentile is the value of [tex]X=x_{76}[/tex] such that
[tex]\mathrm{Pr}\{X \le x_{76}\} = 0.76[/tex]
Transform [tex]X[/tex] to [tex]Z[/tex] and apply the inverse CDF of [tex]Z[/tex].
[tex]\mathrm{Pr}\left\{Z \le \dfrac{x_{76} - 10.5}2\right\} = 0.76[/tex]
[tex]\dfrac{x_{76} - 10.5}2 = \Phi^{-1}(0.76)[/tex]
[tex]\dfrac{x_{76} - 10.5}2 \approx 0.7063[/tex]
[tex]x_{76} - 10.5 \approx 1.4126[/tex]
[tex]x_{76} \approx \boxed{11.9126}[/tex]
Which of the following best reflects a theme of art influenced by the teachings of Sigmund Freud?
a.
images with antiwar themes
b.
a dream-like image
c.
ready-mades
d.
none of the above
Please select the best answer from the choices provided
A
B
C
D
Answer:
B
Step-by-step explanation:
a dream like imageeeeee
Multiply each of the following(2x - 3y) and (x + 5y)
Answer:
[tex]2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]
Step-by-step explanation:
We can use the rainbow expansion method to find the expression.
[tex](2x - 3y)(x + 5y) \\ = 2 {x}^{2} + 10xy - 3xy - 15 {y}^{2} \\ = 2 {x}^{2} + 7xy - 15 {y}^{2} [/tex]
For the rhombus, what are the slopes of the two diagonals? DO NOT introduce any new variables.
The slopes of the two diagonals of the rhombus are: A. b - f/a - e and -a + e/b - f.
What is the Slope of a Line Segment?To find the slope, the formula used is: change in y/change in x.
If two lines are perpendicular to each other, their slope values will be negative reciprocals.
What is the Diagonals of a Rhombus?In a rhombus, the two diagonals in the rhombus bisects each other at angle 90 degrees. This means that the two diagonals of a rhombus are perpendicular to each other. Therefore, the slope of the diagonals of any rhombus would be negative reciprocals.
The slope of the diagonals of the rhombus given would therefore be negative reciprocals to each other.
Given two endpoints of one of the diagonals as:
(a, b) = (x1, y1)
(e, f) = (x2, y2)
Slope (m) = change in y / change in x = b - f/a - e
The negative reciprocal of b - f/a - e is -a + e/b - f.
Therefore, the slopes of the two diagonals are: A. b - f/a - e and -a + e/b - f.
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√3018+√36+√169 can you solve this for me please
Answer:
55
Step-by-step explanation:
[tex]\sqrt{3018+\sqrt{36+\sqrt{169} } }[/tex]
= [tex]\sqrt{3018+\sqrt{36+13} }[/tex]
= [tex]\sqrt{3018+\sqrt{49} }[/tex]
= [tex]\sqrt{3018+7}[/tex]
= [tex]\sqrt{3025}[/tex]
= 55
A recipe calls for 3/4 cups of water, 2/3 cups of flour, and 1/6 cups of sugar. What is the ratio of water: flour: sugar? Express your answer reduced to the lowest terms
Answer:
9:8:2
Step-by-step explanation:
3/4 : 2/3 : 1/6 Multiply by 12.
9 : 8 : 2
What is 500$ invested at 8% for 6 and a half years?
Answer:
$824.56
Step-by-step explanation:
Use the compound interest formula which is A = P(1+r/n)^nt
1st using the given information we are going to find out values:
P is our initial amount of $500
r is the annual rate of interest (expressed as a decimal) 8% becomes 0.08.
n is how many times interest is compounded per year, in this case since its not stated we are going to assume its annually, so n is 1
t is how long the money is deposited (in years) so t is 6.5
A is our final amount
2nd plug in our values into the equation
Plugging all these values we get A = 500 (1 +0.08/1)^(0.08)(6.5)
A = $824.56
Add the following polynomials, then place the answer in the proper location on the grid. Write your answer in descending powers of x.
x 4 -3x + 1, 4x 2 - 2x + 8, and x 3 - 9
The addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
Polynomialx⁴ - 3x + 14x² - 2x + 8x³ - 9Adding the polynomial
(x⁴ - 3x + 1) + (4x² - 2x + 8) + (x³ - 9)
Open parenthesis= x⁴ - 3x + 1 + 4x² - 2x + 8 + x³ - 9
Collect like terms in descending powers= x⁴ + x³ + 4x² - 3x - 2x + 1 + 8 - 9
= x⁴ + x³ + 4x² - 5x
Therefore, the addition of the polynomials x⁴ - 3x + 1, 4x² - 2x + 8, x³ - 9 in descending powers of x is x⁴ + x³ + 4x² - 5x.
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Please help me with this question!!!!,
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
The contrapositive of the statement is False.
Because we already know, Cube is a 3 - dimensional shape with 6 faces, all its sides are equal and all faces are congruent.
But the contrapositive of the statement is not true, because not only cube has six faces.
There are other 3 - D shapes that have 6 faces.
[tex] \qquad \large \sf {Conclusion} : [/tex]
The contrapositive of the statement is false.
Question
Find the point-slope form of the equation of the line satisfying the given conditions and use this to write the slope-intercept form of the equation.
x-intercept - 5 and y-intercept = 4
Answer:
y=(−2)x−-6
Step-by-step explanation:
Use the slope −2 and the point (−5,4) to find the y-intercept.
y=mx+b
⇒4=(−2×−5)+b
⇒−4=10+b
⇒b=−6
Write the equation in slope intercept form as:
y=mx+b
⇒y=(−2)x−-6
HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND:
A) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100?
B) ONLY ODD DIGITS CAN BE USED?
C) THE FIRST 3 DIGITS ARE 277?
Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:
a) 900,000.
b) 78,125.
c) 10,000.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:
[tex]n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1[/tex]
Hence the number is:
N = 9 x 10^5 = 900,000.
For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5[/tex]
Hence the number is:
N = 5^7 = 78,125.
For item c, if the first 3 digits are 277, the parameters are:
[tex]n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10[/tex]
Hence the number is:
N = 10^4 = 10,000.
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Is TriangleMNL ≅ TriangleQNL? Why or why not?
Yes, they are congruent by either ASA or AAS.
Yes, they are both right triangles.
No, AngleM is not congruent to AngleNLQ.
No, there are no congruent sides.
Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
What are congruent triangles?A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and right angle triangle. Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other.
From triangle MNL and triangle QNL, in triangle MNL:
∠M + ∠N + ∠L = 180° (sum of angles in a triangle)
90 + 58 + ∠L = 180
∠L = 32°
Hence Triangle MNL and triangle QNL are congruent to each other based on by either ASA or AAS.
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Can segments with lengths of 6, 7, and 9 form a triangle? Why or why not
Answer:
Yes
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side or largest side. So, 7+6 = 13 which is greater than 9
Answer:
Yes, triangle with sides 6, 7 ,9 can be formed.
Step-by-step explanation:
The sum of any two sides of the triangle should be greater than the third side. If so, triangle can be formed.
6 + 7 = 13 > 9
7+ 9 = 16 > 6
6 +9 = 15 > 7
Which of the following statements is false?
A. The parallel sides of an isosceles trapezoid are congruent.
B. Opposite sides of a parallelogram are congruent.
C. The diagonals of a rhombus are perpendicular and bisect each other.
D. The base angles of an isosceles trapezoid are congruent.
The statement which is false among the answer choices as indicated in the task content is; Choice A; The parallel sides of an isosceles trapezoid are congruent.
Which of the statements indicated in the answer choice is correct?It follows from the answer choice A that The parallel sides of an isosceles trapezoid are congruent.
However, it follows from the study of isosceles trapezoids that the base angles of such trapezoids are congruent and their measures are equal, consequently, the isosceles sides have equal length measures.
On this note, the other two sides are parallel but cannot be concluded as congruent.
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