Answer:
Y = 2.843+ 0.037 X
Step-by-step explanation:
Let the equation of the straight line to be fitted to the data , be Y = a+b X where a and b are to be evaluated. The normal equations fro determining a and b are
∑Y = na +b ∑X
∑XY = a∑X + b∑X²
We now calculate ∑X, ∑Y , ∑X², and ∑XY
X Y XY X²
5 4 20 25
7 3 21 49
6 2 12 36
2 5 10 4
1 1 1 1
21 15 64 115
Thus the normal equation becomes
5a + 21b =15
21a +115b = 64
Solving these two equations simultaneously we get
105 a + 441b = 315
105a + 575b = 320
134b= 5
b= 0.037 , a= 2.843
Hence the equation for the required straight line is
Y = 2.843+ 0.037 X
is [tex]\sqrt[4]{5x^{5} }[/tex] equal [tex](\sqrt[4]{5x} )^{5}[/tex] ?
Suppose a triangle has two sides of length 33 amd 37, and that the angle between these two sides is 120°. What is the length of the third side of the triangle
Answer:
c = 60.65 cm
Step-by-step explanation:
Given that,
The two sides of a triangle are 33 cm and 37 cm.
The angle between these two sides is 120°.
We need to find the length of the third side of the triangle. Let c is the third side. Using cosine rule,
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
a = 33 cm, b = 37 cm and C is 120°
So,
[tex]c^2=(33)^2+(37)^2-2\times 33\times 37\cos (120)\\\\c=60.65\ cm[/tex]
So, the length of the third side of the triangle is 60.65 cm.
If you invest $ 30 , 700 with an annual interest rate of 8.9 % , compounded daily, how much would you have at the end of 4 years?
Answer: $43,823.37
Step-by-step explanation:
Formula to calculate the accumulated amount earned on principal (P) at rate of interest (r) compounded daily after t years :
[tex]A=P(1+\dfrac{r}{365})^{365t}[/tex]
As per given , we have
P= $ 30,700
r= 8.9 % = 0.089
t= 4 years
[tex]A=30700(1+\dfrac{0.089}{365})^{365(4)}\\\\=30700(1+0.0002438)^{365(4)}\\\\=30700(1.0002438)^{1460}\\\\=30700(1.42747138525)\\\\=43823.3715272\approx43823.37[/tex]
Hence, the amount at the end of 4 years would be $43,823.37 .
Please answer ASAP PLEASE!
Answer/Step-by-step explanation:
The inequality, x ≤ 7, has solutions that includes values that is equal to 1 or less than 7.
This can be represented on a number line as shown in the number line graphed in the attachment below.
A full circle or shaded "o" indicates that the number 7 is included in the solution.
The arrow points from 7 to the left, telling us that the value of x are all numbers from 7 and below.
If all angles are 90 degrees, and the crystal has a square base with a height that is larger than one of the square sides, what type of unit cell is it
Answer:
Tetragonal unit cell.
Step-by-step explanation:
A unit cell is the smallest part of a material which is formed by a well arranged lattice points. Some common types are; face centered, body center, tetragonal, cubic etc
Tetragonal unit cell has a square top and base, with rectangular sides. The internal angles are [tex]90^{0}[/tex] each, and consists of molecules, atoms, or ions (lattice points) arranged at each corners of the unit cell.
The crystal as described in the given question is a tetragonal unit cell.
What information do you need in order to determine the total distance Sam drives versus the actual displacement between his starting and ending points?
Answer:
his path
Step-by-step explanation:
In order to determine the total distance driven from one place to another, you need to know the path taken.
a milha eh uma unidade usada para medir distancias. ela equivale a cerca de 1,6 quilometros. se cada carro percorrer 240 quilometros, quantas milhas tera percorrido? urgente
Classica aplicação de regra de 3:
é dito que: 1 milha = 1,6km
Logo, eis a regra de 3:
milha km
1 -------- 1,6
X -------- 240
1,6X = 240.1
X = 240/1,6
X = 150milhasLogo 240km equivalem a 150milhas
Find and interpret a 95% confidence interval to estimate the average number of bolts per box for all boxes in the population. Round to 3 decimal places.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is [tex]49.85 < \mu < 54.15[/tex]
This means that there is 95% chance that the true population mean is within this interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\= x = 52[/tex]
The population standard deviation is [tex]\sigma = 6[/tex]
Given that the confidence level is 95% then the level of confidence is evaluate as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]
[tex]E = 2.147[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]52 - 2.147 < \mu < 52 + 2.147[/tex]
[tex]49.85 < \mu < 54.15[/tex]
What is the period of the function shown in the graph?
At origin, the value of the function is [tex]0[/tex]
and then it again becomes zero for the first time is at $2$
but the function isn't repeating itself (it's going downwards)
at $x=4$, it's exactly same, hence the period is $4$
A chemical company makes two brands
of antifreeze. The first brand is 30% pure
antifreeze, and the second brand i$ 80% pure
antifreeze. In order to obtain 80 gallons of a
mixture that contains 70o£ pure antifreeze, hov
mabry gallons of each band ot antifneze must
bo used?
Answer:
16 bags for the first(30% pure) and 64 bags of the second(80% pure)
Step-by-step explanation:
If they are mixed in a ratio of x bags to y bags
(0.3x+0.8y)/(x+y) = 0.7
0.3x + 0.8y = 0.7(x+y)
Multiply both sides with 10
3x + 8y = 7(x+y)
4x = y ——(1)
x + y = 80 ——(2)
Solve simultaneously
x + 4x = 80
5x = 80
x = 16 bags
y = 4x = 64 bags
Let A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%. Lauren says that both events are independent because P(A) + P(B) = P(A and B) Shawn says that both events are not independent because P(A)P(B) ≠ P(A and B) Which statement is an accurate statement? Lauren is incorrect because the sum of the two events is not equal to the probability of both events occurring. Shawn is incorrect because the product of the two events is equal to the probability of both events occurring. Lauren is correct because two events are independent if the probability of both occurring is equal to the sum of the probabilities of the two events. Shawn is correct because two events are independent if the probability of both occurring is not equal to the product of the probabilities of the two events.
Answer:
Shawn is correct because two events are independent if the probability of both occurring is equal to the product of the probabilities of the two events.
Step-by-step explanation:
We are given that A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%.
Now, it is stated that the two events are independent only if the product of the probability of the happening of each event is equal to the probability of occurring of both events.
This means that the two events A and B are independent if;
P(A) [tex]\times[/tex] P(B) = P(A and B)
Here, P(A) = 0.58, P(B) = 0.36, and P(A and B) = 0.94
So, P(A) [tex]\times[/tex] P(B) [tex]\neq[/tex] P(A and B)
0.58 [tex]\times[/tex] 0.36 [tex]\neq[/tex] 0.94
This shows that event a and event B are not independent.
So, the Shawn statement that both events are not independent because P(A)P(B) ≠ P(A and B) is correct.
Answer:
Shawn is correct
Step-by-step explanation:
25. After a horizontal reflection across the y-axis, f(x) is: options: f(–x) f(x – 1) –f(–x) –f(x)
Answer:
A, f(–x)
Step-by-step explanation:
Reflection about the y-axis is defined as:
f(x) = - f(-x)
So the correct answer is
A, f(–x)
21
22
C
Because of President Clinton's stand on Haiti,
O President Aristide was assassinated.
O President Aristide fled to Somalia.
O Haitian military powers agreed to step aside.
O Haitian rulers threatened to invade the United States.
Mark this and return
Save and Exit
sont vodo)
Answer:
Haitian military powers agreed to step aside.
Step-by-step explanation:
How did President Clinton react when military leaders in Haiti overthrew Aristide? He threatened to invade Haiti if Aristide wasn't returned to power. ... Because of President Clinton's stand on Aristide's oust from power in Haiti, Haitian military powers agreed to step aside.
C. Haitian military powers agreed to step aside.
edge 2021
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass? F = 16.1m F = F equals StartFraction 16.1 Over m squared EndFraction. F = 32.2m F = F equals StartFraction 32.2 Over m squared EndFraction.
Answer:
F = 32.2mStep-by-step explanation:
According to newton second law, the force of gravity on an object varies directly with its mass and it is expressed mathematically as Fαm i.e
F = mg where;
F is the force of gravity
m is the mass of the body
g is the proportionality constant known as the acceleration due to gravity.
If the constant of variation due to gravity is 32.2ft/s², the equation that represents F, the force on an object due to gravity according to m, the object’s mass can be gotten by substituting g = 32.2 into the formula above according to the law as shown;
F = m*32.2
F =32.2m
Hence the required equation is F = 32.2m
 evaluate the expression for c=-10, d=9 and f=-1
Answer:
99
Step-by-step explanation:
(-10)(9)(-1) + 9 =
90 + 9 = 99
A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17 x + 2y + 3z = 33 y – x = 3
Answer:
No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4
Step-by-step explanation:
Equations : x + y + z = 17 [ Total times taken to score ]
1x + 2y + 3z = 33 [ Total Score ]
Also, y = x + 3
Putting the value of 'y' in both equations :
x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14 (i)
1x + 2 (x + 3) + 3z = 33 → x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)
Solving these equations :
From (i), z = 14 - 2x
Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27
42 - 3x = 27 → 3x = 15 → x = 5
y = x + 3 = 5 + 3 → y = 8
z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4
Answer:
4
Step-by-step explanation:
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
The parent function of the function represented in the table is
.
If function f was translated down 4 units, the
-values would be
.
A point in the table for the transformed function would be
.
Answer:
3^x9, 15, 33, 87, 249(4, 87) for exampleStep-by-step explanation:
a) First differences of the f(x) values in the table are ...
19 -13 = 6, 37 -19 = 18, 91 -37 = 54, 253 -91 = 162
The second differences are not constant:
18 -6 = 12, 54 -18 = 36, 162 -54 = 108
But, we notice that both the first and second differences have a common ratio. This is characteristic of an exponential function. The common ratio is 18/6 = 3, so the parent function is 3^x.
__
b) Translating a function down 4 units subtracts 4 from each y-value. The values of f(x) in the table would be ...
9, 15, 33, 87, 249
__
c) The x-values of the function stay the same for a vertical translation, so the points in the table of the transformed function are ...
(x, f(x)) = (1, 9), (2, 15), (3, 33), (4, 87), (5, 249)
Answer: I think this is it:
The parent function of the function represented in the table is exponential. If function f was translated down 4 units, the f(x)-values would be decreased by 4. A point in the table for the transformed function would be (4,87)
Step-by-step explanation: I got it right on Edmentum!
a golfer hits the golf ball. the quadratic y = -14x^2+84x gives the time x seconds when the golf ball is at height 0 feet. In total, how long is the golf ball in the air?
Answer: 6 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)
0 = -14x² + 84x
0 = -14x(x - 6)
0 = -14x 0 = x - 6
0 = x 6 = x
x = 0 seconds is when the ball was hit
x = 6 seconds is when the ball landed on the ground
If there are 25 students in a class in which 5 of the 11 guys wear glasses and 6 out of the 14 girls wear glasses- what is the probability that one of the students in the class is a guy that he wears glasses?
Answer:
6 out of 25
Step-by-step explanation:
Helppppp thxxxxxxxxxx
Answer:
F. [tex] \frac{3}{2} [/tex]
Step-by-step explanation:
[tex] \frac{a + 2b}{b} = \frac{7}{2} [/tex]
Cross multiply:
7b= 2(a +2b)
Expand:
7b= 2a +4b
Bring all common variables to 1 side:
7b -4b= 2a
3b= 2a
divide by 2 on both sides:
[tex] \frac{3}{2} b = a[/tex]
divide by b on both sides:
[tex] \frac{3}{2} = \frac{a}{b} \\ \frac{a}{b} = \frac{3}{2} [/tex]
Suppose that a polynomial function of degree 4 with rational coefficients has 6, 4, 6i as zeros. Find the other zero
Answer:
-6i
Step-by-step explanation:
Complex roots have to come in conjugate pairs
So if we have 6i as a root, we must have -6i as a root
Answer:
-6i
Step-by-step explanation:
Hello, because this polynomial function has real coefficients and 6i is a zero, the conjugate of 6i is a zero as well. It means -6i is a zero.
The degree is 4 the number of zeroes is less or equal to 4 and we have already, 6, 4, 6i and -6i. So we have all the zeroes.
Thank you
is perpendicular to . How many 90° angles are formed by the intersection?
Answer:
if a is perpendicular to b then four 90 degree angles are formed
Step-by-step explanation:
if a line is perpendicular to another that means that it forms a 90 degree angle on all of the angles
Answer:
Four
That is the right answer for Edmentum and Plato users
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Find the most general antiderivative of the function. (Use C for the constant of the antiderivative).
f(x) = 6x5 − 7x4 − 9x2
F(x) = ?
Answer:
[tex]x^6 - \frac{7x^5}{5} - 3x^3 + C[/tex]
0.25÷3=x÷1 1/2 That fraction is one and a half.
Answer:
x = 1/8Step-by-step explanation:
Given the expression 0.25÷3=x÷1 1/2, we are to look for the value of x from the given equation. Rewriting the equation we will have;
[tex]\dfrac{0.25}{3} = \dfrac{x}{1\frac{1}{2} }[/tex]
On simplification;
[tex]0.25 * \frac{1}{3} = x * \frac{2}{3} \\ \\ \frac{25}{100}*\frac{1}{3} =\frac{2x}{3}\\\\ \frac{1}{4} * \frac{1}{3} = \frac{2x}{3}\\\\ \frac{1}{12} = \frac{2x}{3}\\\\cross \ multiply\\\\2x * 12 = 3\\\\24x = 3\\\\Divide \ both \ sides \ by \ 24\\\\24x/24 = 3/24\\\\x = 1/8[/tex]
Hence the value of x in the expression is 1/8
Find the value of angle X. x = 40 x = 55 x = 109 x = 130 I will mark as Brainliest
Answer:
130 degree
Step-by-step explanation:
Interior angles of the triangle:
81, 49, (180-x)
and by sum of all angles of triangle is 180 degree,
therefore,
81 + 49 + 180 - x = 180
x = 130 degree
Assume a random sample of size n is from a normal population. Assume a single sample t test is used to for hypothesis testing. The null hypothesis is that the population mean is zero versus the alternative hypothesis that it is not zero. If the sample size is decreased, and the Type I error rate is unchanged, then the Type II error rate will increase.a. Trueb. False
Answer:
true
Step-by-step explanation:
type 1 and type 2 are not independent of each other - as one increases, the other decreases
NEED HELP ASAP
Which point represents the center of the circle shown below?
Answer:
Point O represents the center of the circle
Step-by-step explanation:
HOPE IT HELPS. PLEASE MARK IT AS BRAINLIEST
What is the lateral surface area of a right hexagonal prism whose base is a regular hexagon with sides measuring 8 inches long and altitude measuring 6 inches tall?
Answer:
288 square inches
Step-by-step explanation:
Assuming your "altitude" is the height of the prism--the distance between bases, the lateral area is the sum of the areas of the six rectangular faces. Each of those has an area of ...
(8 in)(6 in) = 48 in^2
so the 6 of them will have an area of ...
lateral area = 6×48 in^2 = 288 in^2
_____
Comment on nomenclature
'Altitude' is usually associated with the height of a triangle. In the case of a regular polygon, the 'altitude' of a triangular section of the polygon is called the 'apothem', and is often designated using the letter 'a'. If the polygon is regular, the apothem can be calculated from the side length and the number of sides, but it is often given in problems involving area, perimeter, and/or volume.
The distance between the parallel bases of a prism is often referred to as the prism height or length. The use of the word 'altitude' is confusing in this case.
Since the lateral area is the product of the perimeter of the base and the distance between bases, we have to assume that your 'altitude' refers to the distance between bases. Otherwise, there is not sufficient information to work the problem.
Caleb made 6 quarts of trail mix for his camping trip. Each week,he ate 4 pints of the trail mix. How many weeks did Caleb have trail mix?
Sry if this is too much
Answer:
3 weeks
Step-by-step explanation:
6 quarts = 12 pints
12 divided by 3 = 4
Step-by-step explanation:
1 quart = 2 pints
6 quarts = 2 x 6 = 12 pints
12 ÷ 4 = 3
He can have 3 weeks
(Algebra)
Plz help me ASAP!! I’ll be so grateful!
Answer:
y > 1
Step-by-step explanation:
-2(7 + y) > -8(y + 1)
-14 -2y > -8y -8
-2y +8y > -8 +14
6y > 6
6y/6 > 6/6
y > 1
