Answer:
Step-by-step explanation:
Hello!
X: content of sugar of a sample of cereal.
Data set:
0.03, 0.24, 0.30, 0.47, 0.43, 0.07, 0.47, 0.13, 0.44, 0.39, 0.48, 0.17, 0.13, 0.09, 0.45, 0.43
n= 16
[tex]\frac{}{X}[/tex]= 0.295g
S= 0.17g
You have to test if the mean sugar content is less than 0.3g
H₀: μ ≥ 0.3
H₁: μ < 0.3
α: 0.05
Assuming that the variable has a normal distribution, you have to conduct a t test:
[tex]t= \frac{\frac{}{X}-Mu }{\frac{S}{\sqrt{n} } } ~~t_{n-1}[/tex]
[tex]t_{H_0}= \frac{0.295-0.30}{\frac{0.17}{\sqrt{16} } } = -0.12[/tex]
p-value: 0.4533
The p-value is greater than α, the decision is to not reject the null hypothesis.
At a 5% significance level the decision is to not reject the null hypothesis. You can conclude that the average sugar content of the cereal is equal or greater than 0.3g of sugar per gram of cereal.
I hope this helps!
The quadratic 3x^2-24x+72 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?
Answer:
7
Step-by-step explanation:
Quadratic Equation: 3x² - 24x + 72
The form we are to convert the equation to:
3x² - 24x + 72
a(x + b)² + 72
3(x² - 8x + 24)
Step 1
Make the Quadratic equation (x² - 8x) in the bracket factorisable using completing the square method
3( x² - 8x +(- 8/2)²) + 24
3( x² - 8x + 16 = -24 + 16
3( x² - 8x + 16 + 8 = 0)
3( x² - 8x + 16) + 8
3( x² - 4x + 4x + 16) + 8
3( x(x - 4) -4(x - 4) + 8
3((x - 4)(x - 4) )+ 8
3( (x - 4)² + 8
Using this form
a(x + b)² + c
a = 3
b = -4
c = 8
We were asked to add up constants a, b, c
Therefore,
3 +(-4) + 8
= 7
A+B=C? I don't get the formula...
Answer:
Read this for more help!
Step-by-step explanation:
That is okay if you do not understand the formula. We all have troubles with math in one spot or in another. With the a²+b²=c², we would have to go really slowly. Just for you!
Let´s do an example. Say we have a triangle, and for this we need to know our square roots! Say we have this triangle, and it has both a 3 and a 4 on its sides. Now a triangle had 3 sides. 2 sides are smaller, and then it would have a larger side, which is called the hypotenuse! That is the side we would need to figure out, because the hypotenuse is the largest side of the triangle, and we only have the smaller sides(3 and 4).
So we need to work with the formula.
So let us plug the example into the formula.
There is no specific order to how we would be putting the sides in. 3 could be b or it could be a. Same goes for the 4. It really does not matter because you would be getting the same answer no matter what.
a²+b²=c²
3²+4²=c²
3²=9
4²=16
We need to add the two of those numbers, both 9 and 16 and we get 25. That is c². But we need c, because the hypotenuse is only c. So we need to take the square root of 25. And we get 5!
I will show you the equation again with 3 and 4 reversed.
4²+3²=c²
4²=16
3²=9
Like what we did above, we would get 25. And then take the square root! Same answer, so it really doesn't matter!
If you still do not understand this topic, you can always ask someone else who does, or go on khan academy, or search for more topics like this on BRAINLY! I hope this helped!
Help please!! Thank you
Answer:
25 ( A)
pls mark me as BRAINLIEST
stay at home stay safe
and keep rocking
Answer:
A
Step-by-step explanation:
The first ten primes are
2,3,5,7,11,13,17,19,23,27
so the number is
2*3*5*7*11*13*17*23*27
so
2*11 is 22, so 22 divides the number
2*3 is 6, so 6 divides the number
2 is there so 2 divides the number
So the only one is 25.
i have tried everything At Central Online High School, 45100 of the students have a dog, 30100 of the students have a cat, and 18100 of the students have both a dog and a cat. What is the probability that students who have a cat also have a dog?
Work Shown:
Let's say this school has 100 people total. We know that 30 of the people have a cat since 30/100 is the fractional portion of cat owners. Similarly, 18 have both a cat and a dog.
The probability of selecting someone who has both pets, given we know they are a cat owner, is 18/30 = 3/5
To reduce the fraction, divide both parts by the GCF 6.
Note: we don't use 45/100 because we know that whoever selected wasn't solely a dog owner.
Answer:
at the rate of 100000.
u t cute
Find the length of the unknown side. Round your answer to the nearest whole number.
7 m
7 m
07 meters
09 meters
10 meters
12 meters
Answer:
10 meters
Step-by-step explanation:
From your question, it seems we are dealing with a triangle and we are given the two legs of the triangle.
The given dimensions are:
7 meters and 7 meters.
Required:
Here, we are required to find the third side of the triangle which is the hypotenus.
Using Pythagoras theorem:
a² + b² = c²
Where a = 7 & b = 7
Thus, we have:
7² + 7² = c²
c² = 49 + 49
c² = 98
Take the root of both sides
√c² = √98
c = √98
c = 9.899
c ≈ 10 meters
Therefore the length of the unknown side is approximately 10 meters
A fruit bowl contains apples and bananas in the ratio 4 : 5. Two apples are removed changing the ratio to 2 : 3. Work out the total number of fruit that remain in the bowl.
Answer:
25
Step-by-step explanation:
Given that the ratio is 4 : 5 = 4x : 5x ( x is a multiplier ), then
4x - 2 : 5x = 2 : 3
Expressing the ratio in fractional form
[tex]\frac{4x-2}{5x}[/tex] = [tex]\frac{2}{3}[/tex] ( cross- multiply )
3(4x - 2) = 10x , distribute left side
12x - 6 = 10x ( subtract 10x from both sides )
2x - 6 = 0 ( add 6 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Thus initially there were
4x + 5x = 9x = 9(3) = 27 pieces of fruit
2 apples were removed, leaving 25
Answer:
25
Step-by-step explanation:
4 : 5. is ratio before two apples were removed.
2 : 3. is ratio after two apples were removed.
combing the two statements will give you the following mathematical statement:
4x-2:5x=2:3 solve for x
3(4x-2)=5x*2
12x - 6=
2x=6
x=3
then 4x + 5x = total ñô fruit
4(3) + 5(3) = total ñô fruit
27= total ñô fruit
remaining fruit=total ñô fruit - 2
remaining fruit=27-2
remaining fruit=25
Which transformation(s) can map ABCD onto AWXY?
rotation only
reflection only
O translation, then rotation
O translation, then reflection
Answer:
Translation, then rotation.Step-by-step explanation:
If you translate the triangle BCD in such a way that vertex B maps onto vertex W, you'll realize that with rotation, you'll map the whole BCD triangle onto triangle WXY.
On the other hand, reflections can't be used here, because the sides of both triangles are not in opposite positions.
Therefore, the right answer is the third choice.
Hey, can anyone help me out plz?
Answer:
Hey there!
That would be the SAS postulate.
This states that one angle is congruent and between two congruent sides.
Hope this helps :)
Find the mean and standard deviation. Show all work. 1. X 0 1 2 3 4 P(x) .07 .38 .22 .13
Answer:
Mean = 2.14
Standard deviation = 2.40
Step-by-step explanation:
The calculation of mean and standard deviation is shown below:-
[tex]X = .07\times0 + 0.20\times 1 + 0.38\times 2 + 0.22\times 3 + 0.13\times 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52[/tex]
= 2.14
So, the mean is 2.14
Now, For computing the standard deviation first we need to find out the variance which is shown below:-
Variance is
[tex]Var(X) = P(X^2) - [P(X)]^2\\\\ P(X^2) = .07\times (0^2) + .20\times (0^1) + .38\times (0^2) + .22\times (0^3) +0.13\times (0^4)[/tex]
After solving the above equation we will get
= 5.78
Now, the standard deviation is [tex]= \sqrt{Variance}[/tex]
[tex]= \sqrt{5.78}[/tex]
= 2.404163056
or
= 2.40
The average age of 15 students is 16 years. If teacher’s age is included the average increases
by 1. Find teacher’s age
31
because 15 +16 :31
[tex]. = y1 = \times [/tex]
Instructions: Find FS if BS=16.
Answer:
48
Step-by-step explanation:
FB:BS=2:1
[tex]\frac{FB}{BS} =\frac{2}{1} \\add~1~to~both~sides\\\frac{FB}{BS} +1=\frac{2}{1} +1=3\\\frac{FB+BS}{BS} =3\\\frac{FS}{BS} =3\\FS=3 \times~BS\\FS=3 \times~16=48[/tex]
Answer:
48
Step-by-step explanation:
Use the screen shot to find the x
Answer:
69
Step-by-step explanation:
A triangle has a 180 degree angle so you do 180-111=69
Answer: x=24
Step-by-step explanation:
lets say 94 is ∠ a
41 is ∠ b
___ ∠ c
111∠ d
x ∠ e
so with that you will figure out that ∠ c is to find X
108-94-41= 45
so ∠ c is 45
now you can ∠a ∠ b∠ c
with that yo take
108-111-45=24
So X=24
Which relation is a function?
The relation { (3,4), (-3, 8), (6,8) } is a function.
====================================================
Explanation:
Choice A can be ruled out because we have x = -3 repeat itself for different y values. For any x input, there must be exactly one y output. This is assuming the x value is in the domain of course.
Choice C can be ruled out for similar reasoning. This time x = 3 repeats.
Choice D is the same story, but we go back to x = -3 showing up twice.
Choice B is the only thing left. Each x value is unique or only written one time. This graph passes the vertical line test. The other graphs fail the vertical line test (it is possible to draw a vertical line through more than one point).
Katie has 8 black marbles, 12 clear marbles, and 14 blue marbles in a bag. If she picks one at random, what is the probability that she will pick a black marble? (Enter your answer as a fraction in its reduced form.) a 4/17 b 7/34 c 6/17 d 12/34
Answer:
a 4/17
Step-by-step explanation:
if you add them all up, you get 34. 8 out of 34 reduced is 4/17
Answer:
4/17
Step-by-step explanation:
8 black marbles, 12 clear marbles, and 14 blue marbles = 34 marbles
P( black) = number of black/ total
= 8/34
=4/17
Which of the following equations have no solutions?
Choose all answers that apply:
-602 + 32 = –60r – 32
-60.X + 32 = 32.r – 60
-60r = 32 — 322 – 60
-602 + 32 = -60r - 60
Answer:
-60.X + 32 = 32.r – 60
Because we only have one equation for 2 unknowns.
Step-by-step explanation:
All the equations have solution for r but the one that has 2 unknowns (r and X).
That is because we only have one equation and 2 unknowns.
Then, we only can express one unknown in function of the other and have an indeterminate solution.
A triangle has three sides of the following side lengths: 7, 10, and x^2. What are all of the positive integer values of x such that the triangle exists? Separate your answers using commas and express them in increasing order.
Answer:
x = {2,3,4} (if x can only be positive whole numbers)
Step-by-step explanation:
For a triangle exists, the side lengths of the triangle must be such that the sum of the two shorter sides must be greater than the third side.
This also is equivalent to any two sides must have a sum greater than the third side.
So
7+10 > x^2, => x^2 < 17 => x < sqrt(17) (maximum)
7+x^2 > 10, => x^2 >3 => x > sqrt(3)
Therefore
sqrt(3) < x < sqrt(17)
If x must be an integer,
2< x < 4, or x = {2,3,4}
What is the first step to circumscribe a circle around a triangle? a Find the diameter b Find the angle bisectors c Find the perpendicular bisectors d Draw the circle
Answer:
Step 1-Construct the perpendicular bisector of one side of the triangle.
Step 2-Construct the angle bisector of another side of the triangle.
Explanation:
A circumscribed circle is the circle that passes through all three vertices of the triangle. The center of the circumscribed circle is the circumcenter of the triangle, the point where the perpendicular bisectors of the sides meet
The product of two numbers is 32. The first number, x, is one-half of the second number, y. Which system of equations can be used to find the two numbers? A system of equations. x y equals 32. x equals StartFraction one-half EndFraction y. A system of equations. x y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals y minus StartFraction one-half EndFraction. A system of equations. x plus y equals 32. x equals StartFraction one-half EndFraction y.
Answer:
xy = 32
x = 1/2y.
Step-by-step explanation:
Let's say the two numbers are x and y.
The product of them is 32, so x times y is 32.
xy = 32.
x is 1/2 of y. So...
x = 1/2y
Your two systems are xy = 32 and x = 1/2y.
Hope this helps!
Answer:
The answer is A on edg 2021
What the correct answer fast
Answer:
[tex] s = 5.8 [/tex]
Step-by-step Explanation:
Given:
∆RST,
m < T = 17°
t = RS = 5
m < S = 20°
s = RT = ?
Apply the Law of Sines to find s
[tex] \frac{s}{sin(S)} = \frac{t}{sin(T)} [/tex]
[tex] \frac{s}{sin(20)} = \frac{5}{sin(17)} [/tex]
Multiply both sides by sin(20) to make s the subject of formula.
[tex] \frac{s}{sin(20)}*sin(20) = \frac{5}{sin(17)}*sin(20) [/tex]
[tex] s = \frac{5*sin(20)}{sin(17)} [/tex]
[tex] s = 5.8 [/tex] (to nearest tenth)
ABC is a triangle in which DE ∥BC. Find ∠A
Answer:
∠A = 35°
Step-by-step explanation:
From the question above,
Sum of Angles on a straight line = 180°
180° = ∠BDE + ∠ADE
∠BDE = 105°
∠ADE = 180° - 105°
∠ADE = 75°
To find Angle ∠EBC and ∠DEB are alternate angles, this means that they are equal to each other
Hence, ∠EBC = ∠DEB
30° = 30°
Sum of Angles on a straight line = 180°
180° = ∠DEB + ∠BEC + ∠DEA
180° = 30° + 80° + ∠DEA
∠DEA = 180° -(30+ 80)°
∠DEA = 180° - 110°
∠DEA = 70°
It is important to note that the sum of Angles in a triangle = 180°
180° = ∠ADE + ∠DEA + ∠A
∠ADE = 75°
∠DEA = 70°
180° = 75° + 70° + ∠A
∠A = 180° - (75° + 70°)
∠A = 180° - 145°
∠A = 35°
HELP ASAPPP ITS TIMED
Given that sin thata= 21/29, what is the value of cos thata, for 0°<thata<90°?
a- sqrt 20/29
b -20/29
c 20/20
d sqrt 20/29
Answer:
The value of cos theta for 0° < theta < 90° will be 20 / 29
Step-by-step explanation:
To solve this problem we can express three trig functions as ratios involving the sides of a right-angle triangle, the adjacent side, the opposite side and the hypotenuse. In this case sin θ = a / c, such that a = 21 and c = 29.
By Pythagorean Theorem,
[tex]b = \sqrt{c^2-a^2} = \sqrt{29^2-21^2} = \sqrt{841-441} = \sqrt{400} = 20[/tex]
Therefore cos θ = b / c = 20 / 29. This is the cosine ration of the adjacent side over the hypotenuse.
how do you solve this y= 6x - 3 y= -3 i need to graph so if you can show how to graph it also
Answer:
:)
Step-by-step explanation:
y=6x-3
y=-3
-3=6x-3
-3=6x-3
+3 +3
=6x
Answer:
Step-by-step explanation:
y=6x-3
y=-3
6x-3=-3
6x=-3+3
6x=0,
x=0
y=-3
so solution is point (0,-3)
Multiply using distributive property.
(2x-5)(4x2-3x+1)
PLEASE HELP!!! ASAP!!!
Answer:
33x-6x(square)-45
Step-by-step explanation:
(2x-5)(9-3x)
= 2x(9-3x) + -5(9-3x)
= 18x-6x(square) - 45+15x
= 33x-6x(square)-45
Answer:
8x^3 - 26x^2 + 17x - 5.
Step-by-step explanation:
(2x - 5)(4x^2 - 3x + 1)
= (2x * 4x^2) + (-5 * 4x^2) + (2x * -3x) + (-5 * -3x) + (2x * 1) + (-5 * 1)
= 8x^3 + (-20x^2) + (-6x^2) + 15x + 2x - 5
= 8x^3 - 26x^2 + 17x - 5.
Hope this helps!
a:b=7.2
How many times larger is a than b?
Does anyone understand this?
PLEASE HELP ASAP
Answer:
3.5 times as large
Step-by-step explanation:
The ratio can be written using a colon or a fraction bar. In the latter case, simplifying the fraction gives you your answer:
a : b = 7 : 2 = 7/2
'a' is 7/2 = 3.5 times as large as 'b'
Helppppp pleaseeeeee
Answer:
(2, 2), (5, 3), (9, 4), and (13, 5).
Step-by-step explanation:
The inverse of a function makes it so that the x-values become y-values, and y-values become x-values.
The current coordinates are (2, 2), (3, 5), (4, 9), and (5, 13).
If the function were inversed, the coordinates would be (2, 2), (5, 3), (9, 4), and (13, 5).
Hope this helps!
The mean annual tuition and fees for a sample of 11 private colleges was $26,500 with a standard deviation of $6,000. A dotplot shows that it is reasonable to assume that the population is approximately normal. You wish to test whether the mean tuition and fees for private colleges is different from $31,000.
i). State the null and alternate hypotheses.
ii). Compute the value of the test statistic and state the number of degrees of freedom.
iii). State a conclusion regarding H. Use the a = 0.05 level of significance.
Answer:
Step-by-step explanation:
Given that:
Sample size n = 11
Sample Mean X = 26500
standard deviation = 6000
Population mean [tex]\mu[/tex] = 31000
the null and alternate hypotheses are being stated as follows:
[tex]H_o : \mu = 31000[/tex]
[tex]H_1 : \mu \neq 31000[/tex]
The value of the test statistic can be computed as:
[tex]Z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{26500 - 31000}{\dfrac{6000}{\sqrt{11}}}[/tex]
[tex]Z = \dfrac{-4500}{\dfrac{6000}{3.3166}}[/tex]
Z = −2.4875
Z = −2.49
The degree of freedom df = n- 1
The degree of freedom df = 11 - 1
The degree of freedom df = 10
At the level of significance ∝ = 0.05
[tex]t_{\alpha/2}[/tex] = 0.025
From the t distribution table at [tex]t_{\alpha/2, 10}[/tex] and critical value = -2.49;
The p-value = 0.0320
Decision Rule: Reject null hypothesis if p -value is lesser than the level of significance
Conclusion:We reject the null hypothesis , therefore, we conclude that there is no sufficient information to that the mean tuition and fees for private colleges is different from $31,000
i cant see the answers anyone else has the problem
Answer: im having the same problem
Step-by-step explanation:
PLEASE help me solve this question! I really need to solve this question ASAP! No nonsense answers, and please attach the solution.
Answer:
{-0.5, 0.1}
Step-by-step explanation:
multiply the 8 on the left with x/x so you can write left hand as [tex]\frac{1-8x}{x}[/tex]cross multiply to get rid of the fractions: [tex]5x = (1-8x)(5x+2)[/tex]simplify into a regular quadratic equation: [tex]-20x^2 - 8x +1 =0[/tex]use the quadratic formula to get the answers:[tex]x = \frac{8 \pm \sqrt{(-8)^2 - 4 \cdot -20 \cdot 1}}{-40} = \frac{8 \pm 12}{-40}[/tex]
so x is 20/-40 = -0.5 or x = -4/-40 = 0.1
points Q and R are midpoints of the sides of triangle ABC. Triangle A B C is cut by line segment Q R. Point Q is the midpoint of side A B and point R is the midpoint of side A C. The lengths of A Q and Q B are 4 p, the length of Q R is 2 p + 3, and the length of C B is 6 p minus 4. The lengths of A R and R C are congruent. What is AQ? 10 units 14 units 20 units 32 units
Answer:
AQ = 20 units
Step-by-step explanation:
I tried figuring in the pic below..
Similar triangles are triangles whose corresponding measures are proportional. All of their corresponding angles are also congruent. There are theorems and postulates that prove triangle similarity. Usually they requrie at least three parts of each triangle. The symbol for similarity is ~.
We have two triangles in the figure. ΔAQR and ΔABC. We will prove first that they are similar.
Answer:
20
Step-by-step explanation:
RQ is 1/2 of CB, so 2(2p+3)=6p-4. This would make p=5. Then, 5*4=20.
(also it is right on edgenuity)
For a class, Mrs. Hawk brought
in 7 different packages of
colored pens. The teacher
randomly selects 2 packages.
How many different
combinations are there?
Answer:
14
Step-by-step explanation:
7x2=14