The correct statement regarding when the events will be independent is given as follows:
B. The probability of getting a red convertible is 0.06.
What are independent events?Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem, the probabilities are given as follows:
P(A) = 0.2.P(B) = 0.3.The events will be independent if:
[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]
The intersection of events A and B is a red convertible car, hence the correct option is:
B. The probability of getting a red convertible is 0.06.
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A graduate student believes that people consider faces with more contrast between eye color and skin tone as more feminine. She identifies the null and alternative hypotheses as:
H₀: The level of contrast between eye color and skin tone does not affect how feminine a face is considered.
H₁: The level of contrast between eye color and skin tone affects how feminine a face is considered.
She chooses a significance level of 0.01. After she collects the data and computes the sample statistics, it is time for her to make a decision about H₀.
Check the two possible decisions that the graduate student can make given her choices of H₀ and H₁. Check all that apply.
There is not enough evidence to reject the hypothesis that the contrast between eye color and skin tone affects how feminine a face is considered.
There is not enough evidence to reject the hypothesis that the contrast between eye color and skin tone does not affect how feminine a face is considered.
There is enough evidence to reject the hypothesis that the contrast between eye color and skin tone affects how feminine a face is considered.
There is enough evidence to reject the hypothesis that the contrast between eye color and skin tone does not affect how feminine a face is considered.
What decision should the graduate student make if the test statistic is not inside the critical region?
A. The graduate student should reject the alternative hypothesis.
B. The graduate student should reject the null hypothesis.
C. The graduate student cannot reject the null hypothesis.
Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is ____ the critical region. Therefore, the graduate student _____ reject the null hypothesis, and she _____ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.
The two possible decisions that the graduate student is that:
There is not enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.There is enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.What decision should the graduate student make if the test statistic is not inside the critical region?If the test is not inside the critical region, the graduate student cannot reject the null hypothesis.
Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is outside the critical region. So:
The test statistic is not in the critical region.
2. Therefore, the graduate student cannot reject the null hyopthesis,
3. and she cannot conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.
Note that a failure to reject the null hypothesis in any kind of significance test does not imply that the null hypothesis holds true. It only imply that the person was not able to give enough evidence for the alternative hypothesis.
See options for the last question
Options for the last section...
1. The test statistic is ____not in/in_____ the critical region.
2. Therefore, the graduate student _____can/cannot_____ reject the null hyopthesis,
3. and she ______can/cannot_______ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered
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What is the greatest common factor of 44, 40, and 50?
Answer:
2
Step-by-step explanation:
44 = 2² × 11
40 = 2³ × 5
50 = 2 × 5²
GCF = product of common factors with lower exponent
GCF = 2
The greatest common factor of 44, 40, and 50 will be;
⇒ 2
What is Greatest common factors?
The highest number that divides exactly into two more numbers, is called Greatest common factors.
Given that;
The numbers are,
⇒ 44, 40 and 50.
Now,
The factors are find as;
⇒ 44 = 2 × 2 × 11
⇒ 40 = 2 × 2 × 2 × 5
⇒ 50 = 2 × 5 × 5
Hence, The greatest common factor of 44, 40, and 50 will be;
⇒ 2
Thus, The greatest common factor of 44, 40, and 50 will be;
⇒ 2
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Write 7/24 as an equivalent fraction with a denominator of 96
Answer: [tex]\frac{28}{96}[/tex]
Step-by-step explanation:
We will figure out what needs to happen to the denominator to get to 96, then we will do the same to the numerator.
[tex]\displaystyle \frac{7}{24}=\frac{?*x}{24*x=96} =\frac{7*4}{24*4}=\frac{28}{96}\\\\ \\\text \\\;\;\;\;\;\; \frac{28}{96}[/tex]
Answer:
28/96
Step-by-step explanation:
Equalize the equivalent fractions according to the desired denominator and solve for the numerator "x"
[tex]\frac{7}{24} =\frac{x}{96}[/tex]
[tex]x=\frac{(96)(7)}{24} =\frac{672}{24} =28[/tex]
The equivalent fraction is
[tex]\frac{28}{96}[/tex]
Hope this helps
The graph of the function f(x) = (x-4)(x + 1) is shown
below.
4-2
64
Mark this and return
6
2
T
6
2
6
X
Which statement about the function is true?
The function is increasing for all real values of x
where
x<0.
O The function is increasing for all real values of x
where
x < -1 and where x > 4.
O The function is decreasing for all real values of x
where
-1 < x < 4.
O The function is decreasing for all real values of x
where
x < 1.5.
Answer: The function is decreasing for all real values of x where x < 1.5.
Step-by-step explanation:
The axis of symmetry is [tex]x=\frac{4-1}{2}=1.5[/tex]
Since the coefficient of [tex]x^2[/tex] is positive, the graph opens upwards.
So, the function is decreasing for all real values of x where x < 1.5.
A small startup company wishes to know how many hours, per week, that it's employees spend commuting to and from work. The number of hours for each employee are shown below. Construct a frequency table for grouped data using four classes.
1,2,18,4,13,18,12,3,17,10,3,12,15,2 15,8,5,17,18,18
The frequency table for grouped data using four classes is shown in the picture.
What are statistics?Statistics is a mathematical tool defined as the study of collecting data, analysis, understanding, representation, and organization. Statistics is described as the procedure of collecting data, classifying it, displaying that in a way that makes it easy to understand, and analyzing it even further.
We have:
A small startup company wishes to know how many hours, per week.
The number of hours for each employee are shown below:
1,2,18,4,13,18,12,3,17,10,3,12,15,2 15,8,5,17,18,18
Make the group of 1-5, 6-10, 11-15, and 16-20
And count the numbers lies between the interval.
Thus, the frequency table for grouped data using four classes is shown in the picture.
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Pls help! Geometry
What is the perimeter and area of the shape above?
Perimeter of the shape = 27.15 units.
Area = 32.3 units²
How to Find the Perimeter and Area of a Composite Shape?The Perimeter of the shape = 1/2(perimeter of circle) + hypotenuse and height of the triangle
Perimeter = = 1/2(2π(5/2)) + [√(9² + 5²)] + 9 = 7.85 + 10.3 + 9 = 27.15 units.
Area = 1/2(area of circle) + area of triangle = 1/2(πr²) + 1/2(bh)
Area = 1/2(π2.5²) + 1/2(5)(9)
Area = 9.8 + 22.5
Area = 32.3 units²
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What is the measure of z?
4
y
N
9
z = 3√ [?]
3₁
Answer:
z = 3[tex]\sqrt{13}[/tex]
Step-by-step explanation:
According to Euclidian theorem we can find the measure of z using the following equation:
z^2 = 9*(9+4)
z^2 = 9*13 multiply
z^2 = 117 find the root of both sides
z = 3[tex]\sqrt{13}[/tex]
given g(x)=3x+6 on what interval is the function negative
Step-by-step explanation:
A number that is negative is less than 0, so
[tex]3x + 6 < 0[/tex]
[tex]3x < - 6[/tex]
[tex]x < - 2[/tex]
So this function is negative, when x is less than -2
Hi !
[tex]3x+6\leq 0\\3x\leq -6\\x\leq \frac{-6}{3} =-2[/tex]
g(x)≤0 for x∈ ]-∞;-2]
Have a nice day
find x and y.
pls pls help
Answer:
x = 65 , y = 64
Step-by-step explanation:
y - 16 and 2y + 4 are same- side interior angles and sum to 180° , that is
y - 16 + 2y + 4 = 180
3y - 12 = 180 ( add 12 to both sides )
3y = 192 ( divide both sides by 3 )
y = 64
then
2y + 4 = 2(64) + 4 = 128 + 4 = 132
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
2y + 4 is an exterior angle of the triangle , then
x + 67 = 132 ( subtract 67 from both sides )
x = 65
find x and y !!!!
pls pls help
Answer:
x = 59°, y = 31°
Explanation:
Angles (x) and (x - 28) sum ups to 90° on a straight line.
→ x + (x - 28) = 90
→ 2x - 28 = 90
→ 2x = 90 + 28
→ 2x = 118
→ x = 59°
Then find value of y
Angle y, x, 90° lies on a straight line which sum ups to 180°
→ x + y + 90° = 180°
→ 59 + y + 90° = 180°
→ y = 180° - 149°
→ y = 31°
10) Bill found a pair of running shoes for $57. The regular price was $68.99. He also found a sweat suit that was
originally $37.80. It was marked down 25%. Find his total SAVINGS.
Oa.) $20.46
Ob.) $21.84
Oc.) $20.45
Od.) $21.44
Answer:
$21.44 or answer D
Step-by-step explanation:
68.99-57=11.99
37.80 x 25/100=9.45
9.45+11.99=21.44
hope this helps you
Part III: Find the unknown side lengths, AB and BC. HINT: Use either the Pythagorean Theorem or special right triangle properties.
The measurement of sides AB, BC, and AC will be 3 units,3 units, and 3√2 units respectively.
What is a right-angle triangle?If any of its inner angles is 90 degrees, the triangle is said to be right-angled. Another term for this triangle is the right triangle or 90-degree triangle.
From the given triangle, it is observed that one of the angles is 90°, showing the given triangle is a right-angle triangle.
From the Δ ABC we found;
tan 45° = AB/BC
1=AB/BC
AB=BC
sin 45° = AB/AC
(1/√2)=AB/AC
AC = √2 AB
From the graph, it is observed that
AB=BC =3 units
AC= √2 AB
AC = 3√2 units
Hence, the measurement of sides AB, BC, and AC will be 3 units,3 units, and 3√2 units respectively.
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To mix weed killer with water correctly, it is necessary to mix 30 teaspoons of weed killer with 5 gallons of water. Find how many gallons of water are needed to mix
with the entire box if it contains 36 teaspoons of weed killer.
gallons of water are needed to mix with the entire box of weed killer.
Three times a number, x, increased by four is equal to five times the number, x. Which equation can be used to sol
for x?
3x+5x-4
3x+4-5x
3x-4+5x
O3x-4-5x
Answer: 3x+4-5x
Step-by-step explanation:
3x+4=5x
3x+4-5x=0
(Help asap!!!, will give brainlyest to first answer)
Rearrange the equation below to solve for x.
3kx+2kx=10
Answer:
B
Step-by-step explanation:
3kx + 2kx = 10 ← collect like terms on left side
5kx = 10 ( isolate x by dividing both sides by 5k )
[tex]\frac{5kx}{5k}[/tex] = [tex]\frac{10}{5k}[/tex]
x = [tex]\frac{2}{k}[/tex]
A restaurant records the number of tables served each night, and the results have the values: minimum = 3, lowe
quartile = 14, median = 23, upper quartile = 29, and maximum = 40.
Which box plot represents the data?
The box plot that represents the data is the first box plot.
What is a box plot?A box plot is graph that is used to study the distribution and level of a set of scores. The box plot consists of two whiskers and a box. The end of the first whisker represents the minimum number and the end of the second whisker represents the maximum number. The difference between the values of the whiskers gives the range of the dataset.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile. The difference between the upper quartile and the lower quartile is the interquartile range.
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Answer:
The box plot that represents the data is the first box plot.
Step-by-step explanation:
What is the value of p if the two side are 140 and 90
The value of P is 50 degree , Option D is the correct answer.
What is the property of Exterior Angle of a Triangle ?According to the exterior angle property the measure of exterior angle is equal to the sum of opposite interior angles.
In the given figure it can be seen that one of the exterior angle is 90 degree ,
which is making a supplementary angle with the interior angle corresponding to it , angle B in the figure
Therefore the interior angle B is 90 degree ,
The value of angle C = p degree
To determine the value of angle C
The exterior angle next to angle A = 140 degree
By the exterior angle property
140 = 90 +p
p = 50 degree
The value of P is 50 degree , Option D is the correct answer.
The complete question is attached as a image
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A bike store marks up the wholesale cost of all bikes they sell by 30%. Calvin wants to buy a bike that has a price tag of 123.50. What was the wholesale cost of this bike?
You roll a fair six-sided die twice. Find the probability of rolling a 2 the first time and a number greater than 4 the second time.
Answer:
1/18
Step-by-step explanation:
So to find the probability of two independent events, you simply multiply the two probabilities. So the probability of rolling any individual number is 1/6 because there's 6 possibilities, and there are no duplicate numbers. So the probability of rolling a 2 the first time is 1/6. The probability of rolling a number greater than 4 has a probability of 2/6, since the numbers 5 and 6 are both greater than 4. This can be further simplified to 1/3. Multiplying these two probabilities gives you 1/18
Please see attached photo please
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{-b + 8c}[/tex]
[tex]\huge\textbf{Simplifying: }[/tex]
[tex]\mathsf{-b + 8c}[/tex]
[tex]\mathsf{= -2 + 8(-2)}[/tex]
[tex]\mathsf{= -2 - 16}[/tex]
[tex]\mathsf{= -18}[/tex]
[tex]\huge\textbf{Therefore, the answer should be: }[/tex]
[tex]\huge\boxed{\frak{-18}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
5. The graph of F(x), shown below, resembles the graph of G(x)=x2, but it has been
flipped over the x-axis, stretched vertically by a factor of 3, shifted down 4 units, and
left 1 unit.
-6
F(X)
Part I: Write the equation of F(x).
Using translation concepts, the equation of F(x) is given as follows:
-3(x + 1)² - 4.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The effect of the transformations on G(x) = x² is given as follows:
Reflection over the x-axis: F(x) = -G(x) = -x².Vertical stretch by a factor of 3: F(x) = -3G(x) = -3x².Shift down of 4 units: F(x) = -3G(x) - 4 = -3x² - 4.Shift left of 1 units: F(x) = -3G(x + 1) - 4 = -3(x + 1)² - 4.More can be learned about translation concepts at https://brainly.com/question/4521517
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Which expression represents a rational number?
StartFraction 5 Over 9 EndFraction + StartRoot 18 EndRoot
Pi + StartRoot 16 EndRoot
StartFraction 2 Over 7 EndFraction + StartRoot 121 EndRoot
StartFraction 3 Over 10 EndFraction + StartRoot 11 EndRoot
The rational number among all the answer choices is; Pi + √16.
What is a Rational number?A rational number by definition, is one that can be represented as the quotient a/b of two integers in which case b ≠ 0.
On this note, it follows that since the constant pi is; 22/7, the number pi + √16 can be represented as a rational number as follows;
22/7 + 4 = 50/7.
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Answer:
The answer is b.
Step-by-step explanation:
goodluck
Question 7(Multiple Choice Worth 1 points)
(02.05 MC)
Write the equation of a function whose parent function, f(x) = x + 6, is shifted 4 units to the right.
Og(x)=x-10
Og(x)=x-4
Og(x)=x+2
g(x) = x + 10
Question 8(Multiple Choice Worth 1 points)
100.05
7
2
Answer:
g(x) = x + 2 ⇒ 3rd answer
Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel, given the following points. Show all work!!! HELP PLEASEE
The prove that the angle ABCD is said to be a parallelogram that shows both pairs of opposite sides as parallel figure is given below.
What is the parallelogram about?The four points in the shape above are : A, B, C, D.
Where
A = (-2,-4)
B = (1,2)
C = (2,10)
D = (-1,4)
We place or sit vector AB with vector DC and vector AD with vector BC
and so we find and place their coordinates.
vector AB (1-(-2), 2-(-4))
vector DC (2-(-1),10-4)
vector AD (-1-(-2), 4-(-4))
vector BC (2-1,10-2)
So we obtained:
vector AB (3,6)
vector DC (3,6)
vector AD (1,8)
vector BC (1,8)
Next step is to calculate for the lengths :
AB= [tex]\sqrt{3^{2} + 6^{2} }[/tex] DC= [tex]\sqrt{3^{2} + 6^{2} }[/tex]
Thus, AB = DC
AD = [tex]\sqrt{1^{2} + 8^{2} }[/tex] BC =[tex]\sqrt{1^{2} + 8^{2} }[/tex]
Hence one can say that AD is equal to BC.
Therefore, angle ABCD IS known to be a parallelogram .
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what is the value of F(6) in the functions below
F(x)-2^x
The value of the exponential function when x = 2 is 64
Exponential functionsThe standard form of exponential equation is expressed as y = ab^x
Given the exponential function expressed as:
f(x) = 2^x
For the value f(6)
f(6) = 2^x
f(6) = 2^6
f(6) = 64
Hence the value of the exponential function when x = 2 is 64
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Find a formula for the general term an of the sequence assuming the pattern of the first few terms continues.
{[tex]\frac{-10}{4}[/tex], [tex]\frac{12}{16}[/tex], [tex]\frac{-14}{64}[/tex], [tex]\frac{16}{256}[/tex],...}
Thank you
Answer:
ans : general term = (2n +8)/(4^n) * (-1)^n
find the measure of the indicated angle to the neareat degree. show your equation, use proper trig function, and clearly mark your answer.
Step-by-step explanation:
for 1st triangle on the left
sin(x) = 24/38
x = inverse sin(24/38)
x = 39.1667 deg
for triangle 2
cos(x) = 20/52
x = inverse cos (20/52)
x = 67.38 deg
Simplify the following by removing parentheses and combining terms
-(2q+6)+3(2q+4)-2q
Answer:
2q+6
Step-by-step explanation:
So basically, you would do this.
-2q-6+6q+12-2q
Next
-4q+6q = 2q
12-6=6
2q+6
Answer:
2q + 6
Step-by-step explanation:
To simplify, we will use the distributive property.
-(2q + 6) simplifies to -2q - 6 (In this case we are distributing the - sign or -1)
3(2q + 4) simplifies to 6q + 12
So if we recombine: -2q - 6 + 6q + 12 - 2q
Let's combine like terms (q's with q's, numbers with numbers)
-2q + -2q + 6q = 2q
-6 + 12 = 6
So if we recombine: 2q + 6
Find the domain and range of the following function.
Answer:
Domain : [-5,5]
Range : [-3,4}
Step-by-step explanation:
By definition:
Domain is the set of all inputs for which the given function is defined
Graphically we can visualize it as the shadow of the graph on the x axis, and the shadow is formed above and below the x axis.In this graph, the shadow starts at -5 and ends at 5 , hence domain is [-5,5]Range is the set of all outputs
Graphically it is the shadow of the graph on the y axis from both sidesIn this graph, the shadow on y axis starts at -3 and ends at 4, hence range is [-3,4}IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
Answer:
.
Step-by-step explanation: