Answer:
4/15
Step-by-step explanation:
Probability is the ratio of the number of possible outcome to the number of total outcome.
Given that the bag contains 2 yellow and 4 orange marbles, the probability of picking a
Yellow marble = 2/(2+4) = 2/6
Orange marble = 4/(2+4) = 4/6
The probability of picking a yellow marble and an orange marble without replacement
= 2/6 * 4/5
= 8/30
= 4/15
Mean of Frequency Tables
1. At a party, thirty people have an age of 30, forty have an age of 40 and fifty an age of fifty. What is their average age?
2. In a hardware shop, there are 30 spanners costing £6, 55 hacksaws costings £9 and 10 soldering irons costings £20. What is the average cost per item?
3. Using this frequency table, find the average height of a turnip.
Height (to nearest cm)
6cm 7cm 8cm 9cm 10cm
Frequency:
3 8 12 4 1
Answer: 1. 41.67years
2. £9.21
3. 7.75cm
Step-by-step explanation:
1. At a party, thirty people have an age of 30, forty have an age of 40 and fifty an age of fifty. What is their average age?
Total ages = (30 × 30) + (40 × 40) + (50 × 50) = 900 + 1600 + 2500 = 5000
Total number of people = 30 + 40 + 50 = 120
Average age = Total ages / Total number of people
= 5000/120
= 41.67 years
2. In a hardware shop, there are 30 spanners costing £6, 55 hacksaws costings £9 and 10 soldering irons costings £20. What is the average cost per item?
Total cost of items = (30 × £6) + (55 × £9) + (10 × £20) = £180 + £495 + £200 = £875
Total number of items = 30 + 55 + 10 = 95
Average cost per item = £875/95 = £9.21
3. Using this frequency table, find the average height of a turnip.
Height (to nearest cm)
6cm 7cm 8cm 9cm 10cm
Frequency: 3 8 12 4 1
Total height = (3 × 6cm) + (8 × 7cm) + (12 × 8cm) + (4 × 9cm) + (1 × 10cm) = 18cm + 57cm + 96cm + 36cm + 10cm = 217cm
Total number of turnips = 3 + 8 + 12 + 4 + 1 = 28
Average height = 217cm/28 = 7.75cm
Write the equation of the sinusoidal function shown.
Answer: A
It looks at though the graph moved down a unit, so definitely a (-1) at the end of the function. If you move the graph up a unit, you will notice that the y = cos x format, therefore, it's not C or D.The amplitude of the function is 1. So B and D are out because their amplitudes are 2.Therefore, the answer is A.
Through (-1,2) parallel to the line x=5. Find an equation of a line that satisfies the given conditions.
Answer:
x= -1
Step-by-step explanation:
Since x= 5 is a vertical line, the unknown line would also be a vertical line with an equation of x=___ as they are parallel to each other.
Given that the line passes through (-1, 2), the equation of the line is x= -1.
Parallel lines have the same slope and will never meet.
Which expression is equivalent to 10k + 17 - 7j - 18 - 11k? A. -8jk - 1 B. -7j - k - 1 C. -7j+k+1 D. -8j - k
Answer:
B
Step-by-step explanation:
10k + 17 - 7j - 18 - 11k
-k - 7j - 1
A car travels a distance of 800m in 40s find its speed
Answer:
the answer is 20m/s
Step-by-step explanation:
speed = distance/time which equals to speed = 800/40, so the answer is 20m/s
Answer:
20m /s
Step-by-step explanation:
Speed = [tex]\frac{Distance}{time}[/tex]
[tex]= \frac{800}{40}=\frac{80}{4}= 20[/tex]
2. Write down the supplementary angle of each of the following angles are 105 degree.
Answer:
75
Step-by-step explanation:
Answer:
75°Step-by-step explanation:
Supplementary angles add up to 180°.
The angle x, supplementary with 105°:
x + 105° = 180°x = 180° - 105°x = 75°Can you answer this, please?
Answer:
-x² + 13x + 2
Step-by-step explanation:
you are on ambitious level, and you cannot answer that yourself ? that is trivial. truly. no hidden traps, just straight forward adding and simplifying. what is the problem, please ?
-7x² + 6x² = -x²
5x + 8x = 13x
-1 + 3 = 2
Answer:
3rd option
Step-by-step explanation:
Given
(- 7x² + 5x - 1) + (6x² + 8x + 3) ← remove parenthesis
= - 7x² + 5x - 1 + 6x² + 8x + 3 ← collect like terms
= - x² + 13x + 2
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute. On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute. Test at 5% significance level on the typist’s claim.
According to the typist claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, reaching a conclusion that:
The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.
-------------------------------------------------------------
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute.
At the null hypothesis, we test if the mean is of at least 45, that is:
[tex]H_0: \mu \geq 45[/tex]
At the alternative hypothesis, we test if the mean is of less than 45, that is:
[tex]H_1: \mu < 45[/tex]
-------------------------------------------------------------
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
-------------------------------------------------------------
45 is tested at the null hypothesis:
This means that [tex]\mu = 45[/tex]
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
This means that [tex]n = 70, X = 43, s = 15[/tex]
Value of the test statistic:
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{43 - 45}{\frac{15}{\sqrt{70}}}[/tex]
[tex]t = -1.12[/tex]
-------------------------------------------------------------
P-value of the test and decision:
The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with 70 - 1 = 69 degrees of freedom and t = -1.12.
Using a t-distribution calculator, the p-value is of 0.1333.
The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.
A similar problem can be found at https://brainly.com/question/24241851
7) 5(r + 2) = 8 + 57
Step-by-step explanation:
5r + 10 = 65
5r =65 - 10
r = 55/5
r = 11
Answer:
r=11
Step-by-step explanation:
you first have to work with the brackets and then group the like terms
5(r+2)=8+57
5r+10=65
5r/5=65-10
5r/5=55/5
r=11
I hope this helps
Estimate the correlation coefficient that would best describe the data below.
Answer:
Last option
....... -0.4
Aaron, Blaine, and Cruz are solving the equation 4 7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7 4 . Blaine started by using the distributive property to multiply 4 7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4 7 .
Answer:
D. All three chose a valid first step toward solving the equation.
Step-by-step explanation:
Aaron, Blaine, and Cruz are solving the equation 4/7 (7 − n) = −1. Aaron started his solution by multiplying both sides of the equation by 7/4 . Blaine started by using the distributive property to multiply 4/7 by both 7 and −n. Cruz started by dividing both sides of the equation by 4/7 .
Which of the following is true?
A. Blaine and Cruz made an error in picking their first steps.
B. Cruz made an error in picking his first step.
C. All three made an error because the right side equals -1.
D. All three chose a valid first step toward solving the equation.
Given:
4/7(7 - n) = -1
Aaron:
4/7(7 - n) = -1
Multiple both sides by 7/4
4/7(7 - n) * 7/4 = -1 * 7/4
7 - n = -7/4
- n = -7/4 - 7
- n = (-7-28)/4
- n = -35/4
n = 35/4
Blaine:
4/7(7 - n) = -1
4/7(7 - n) × 7 = -1 × 7
4(7 - n) = -7
28 - 4n = -7
-4n = -7 - 28
- 4n = - 35
n = -35/-4
n = 35/4
Cruz:
4/7(7 - n) = -1
Divide both sides by 4/7
4/7(7 - n) ÷ 4/7 = -1 ÷ 4/7
4/7(7 - n) × 7/4 = -1 × 7/4
7 - n = -7/4
- n = (-7-28)/4
- n = -35/4
n = 35/4
D. All three chose a valid first step toward solving the equation.
Answer:
D-All three chose a valid first step toward solving the equation.
Step-by-step explanation:
Hope I Helped
Diseases I and II are prevalent among people in a certain population. It is assumed that 11% of the population will contract disease I sometime during their lifetime, 16% will contract disease II eventually, and 2% will contract both diseases. (a) Find the probability that a randomly chosen person from this population will contract at least one disease. .25 Correct: Your answer is correct. (b) Find the conditional probability that a randomly chosen person from this population will contract both diseases, given that he or she has contracted at least one disease. (Round your answer to four decimal places.)
Answer:
a) [tex]P(A \cup B)=0.23[/tex]
b) [tex]P(X)=0.87[/tex]
Step-by-step explanation:
From the question we are told that:
Probability of contacting disease 1 [tex]P(1)=0.11[/tex]
Probability of contacting disease 2 [tex]P(2)=0.16[/tex]
Probability of contacting both disease [tex]P(1\& 2)=0.2[/tex]
a)
Generally the equation for a Random contact is mathematically given by
[tex]P(A \cup B)=P(1)+P(2)-P(A \cap B)[/tex]
[tex]P(A \cup B)=\frac{11}{100}+\frac{16}{100}-\frac{4}{100}[/tex]
[tex]P(A \cup B)=\frac{11+16-4}{100}[/tex]
[tex]P(A \cup B)=0.23[/tex]
b)
Generally the equation for Probability of contacting both after having contacted one is mathematically given by
[tex]P(X)=\frac{P(1\& 2)}{P(A \cup B)}[/tex]
Therefore
[tex]P(X)=\frac{0.2}{0.23}[/tex]
[tex]P(X)=0.87[/tex]
using trig to solve for the missing angle
Step-by-step explanation:
Since there is a 45 and 90 degree angle, this is a 45-45-90 triangle. The legs are equal in a 45-45-90 ttiangle. The hypotenuse sqr root of 2 times more than the legs. So this means the hypotenuse measure is
[tex]18 \sqrt{2} [/tex]
So we can set up a equation.
[tex] {18}^{2} + {x}^{2} = ({18 \sqrt{2}) }^{2} [/tex]
[tex]x = 18[/tex]
So the missing side is 18
What is the recursive rule for this geometric sequence? 7, 21, 63, 189,…
1. a1 = 7;an = 3 • an - 1
2. a1 = 7;an = 1/3 • an - 1
3. a1 = 3;an = 7 • an - 1
4. a1 = 21;an = 7 • an - 1
Answer:
The top choice is the answer. a1=7; an= 3*a_(n-1)
Step-by-step explanation:
Begin by finding out what the terms are multiplied by. It is a geometric sequence so multiplication is involved.
Take the 3rd term (63) and divide it by the second term.
63/21 = 3
What this means is that each term in the sequence is multiplied by 3 to get to the next term.
The first term is 7
So the answer is an = 3* a_n-1
The answer must be the top one. See if it works.
a2 = 3*a_(2 -1 )
a2 = 3 * a1
a2 = 3 * 7
a2 = 21 which it does.
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
1.-4,-1,1,6
2.by substituting the values given, we get
32-|15+8|
32-|23|
32-23=9
3.-15+7=8
4..27-(-12)=27+12=39
5.-6.05+(-2.1)
-6.05-2.1=-8.15
6.-3/4-(-2/5)
-3/4+2/5
=-7/20
7.-9(-12)
=108
8.(3.8)(-4.1)
-15.58
9.(-8x)(-2y)+(-3y)(z)
(16xy)+(-3zy)
(16xy)-(3zy)
10.by substituting the value given,we get
2.5*(-3.2)+5
-8+5
-3
so here are the answers,mark as brainliest if u find it useful
thank you
What is the degree of this polynomial?
5 + 2s
=====================================================
Explanation:
We can rewrite 5 as 5s^0, since s^0 = 1 where s is nonzero.
Think of 2s as 2s^1
With those ideas in mind, the original polynomial turns into 5s^0 + 2s^1
Sorting the terms so that the largest exponent is first gets us the standard form 2s^1 + 5s^0
The largest exponent is the degree, so the degree is 1.
Side note: This trick only works for single variable polynomials.
what would the equation, slope, and point be for this graph?
Answer:
slope is Δy/Δx =
-5/1 = -5
the B intercept is 4
y = -5x + 4
Step-by-step explanation:
Graph the line that passes through (5, 5), and is perpendicular to a line whose slope is –2.
Answer:
y = 1/2x + 5/2
Step-by-step explanation:
y = 1/2x + b
5 = 1/2(5) + b
5 = 5/2 + b
5/2 = b
Please solve these radical equations and show the steps so that I can understand them. In my notes, it says the steps are to Isolate the radical, square both sides, solve for the variable, and check for the extraneous solutions so if this is what you are supposed to do please show these steps in action. Thank you for your time.
Answer:
1) X = 0
2) X = 0 or X = 1
Step-by-step explanation:
1)
[tex] \sqrt{6x} + 9 + 2 = 11 [/tex]
6x = 0 since root can only be = 0 if radicand is 0
X = 0
2)
[tex] \sqrt{x} - 3 + 3 = x[/tex]
[tex] \sqrt{x} = x[/tex]
X = x^2 ( We are squaring both sides to simplify)
x-x^2 = 0
x (1-x) = 0 (Factor the expression)
X = 0 or
1 -x = 0
X = 1
Answered by Gauthmath
Four friends equally divided a whole pizza for lunch. Binli ate 1 of his 3
share and took the rest of his share home. What fraction of the whole pizza did he eat for lunch?
Please help! Will give brainiest!!!
Answer:
He ate 1/12 of the pizza
Step-by-step explanation:
Divide the pizza by 4 to get the share each friend got
1/4
Then Binli ate 1/3 of his share
1/4 * 1/3 = 1/12
He ate 1/12 of the pizza
9. Find the zero of the polynomial in each of the following
i)f(x) = 3x- 5
Answer:
[tex]f(x) = 3x - 5[/tex]
For a zero, f(x) = 0:
[tex]{ \tt{0 = 3x - 5}} \\ { \tt{x = \frac{5}{3} }}[/tex]
Please answer this!!!
Answer:
12/13
Step-by-step explanation:
we know this is a right triangle, and we know that the hypotenuse is the longest side. so we can already say that the hypotenuse of the triangle is DF or 78.
when you draw it out, you find that the shortest leg is 30 and the second is 72 and the hypotenuse is 78. we also know that cosine is adjacent/hypotenuse. once you draw the triangle and notice which side is adjacent to angle F, just fit it into the formula and you get:
cos F = 72/78
cos F = 12/13
Answer: Choice C. [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
It helps to draw a right triangle with hypotenuse DF=78, and adjacent EF=72.Plug in cosine adjacent over hypotenuse and simplify.plz help quick
Find the area of the circle.
Use 3.14 for n. Do not round your answer.
Hint: A = hr2
Area = [?] inches
6 inches
Enter the number that
belongs in the green box.
Answer:
28.26 in ^2
Step-by-step explanation:
The diameter is 6 inches
The radius is 1/2 of the diameter
r = 1/d = 1/2(6) = 3 inches
A = pi r^2 = 3.14( 3)^2 = 3.14 (9) =28.26 in ^2
Help plz Algebra 1
Simplify numbers 10 and 13 <3
Answer:
10t+2
Step-by-step explanation:
2-5t+8+5t-8
10t+2
Jack painted 5 8 part of a wall and Sam painted 7 12 part of another wall of the same size. Who painted a larger part of the wall?
Answer:
Jack
Step-by-step explanation:
convert the fractions to decimals to determine the person that painted the larger part of the wall
5/8 = 0.625
7/12 = 0.583
the fraction Jack painted is larger.
Cos 600 degrees solved by double angle formula (20 points)
show work please :)))
Answer:
[tex] \rm\cos({600}^{ \circ} ) =-1/2 [/tex]
Step-by-step explanation:
we would like to solve the following using double-angle formula:
[tex] \displaystyle \cos( {600}^{ \circ} ) [/tex]
there're 4 double Angle formulas of cos function which are given by:
[tex] \displaystyle \cos(2 \theta) = \begin{cases} i)\cos^{2} ( \theta) - { \sin}^{2}( \theta) \\ii) 2 { \cos}^{2}( \theta) - 1 \\iii) 1 - { \sin}^{2} \theta \\ iv)\dfrac{1 - { \tan}^{2} \theta}{1 + { \tan}^{2} \theta } \end{cases}[/tex]
since the question doesn't allude which one we need to utilize utilize so I would like to apply the second one, therefore
step-1: assign variables
to do so rewrite the given function:
[tex] \displaystyle \cos( {2(300)}^{ \circ} ) [/tex]
so,
[tex] \theta = {300}^{ \circ} [/tex]Step-2: substitute:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \cos ^{2} {300}^{ \circ} - 1[/tex]
recall unit circle thus cos300 is ½:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2 \left( \dfrac{1}{2} \right)^2 - 1[/tex]
simplify square:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = 2\cdot \dfrac{1}{4} - 1[/tex]
reduce fraction:
[tex] \rm\cos(2 \cdot {300}^{ \circ} ) = \dfrac{1}{2} - 1[/tex]
simplify substraction and hence,
[tex] \rm\cos({600}^{ \circ} ) = \boxed{-\frac{1}{2}}[/tex]
Which term of the AP. 8 , -4 , -16 , -28 ,......... is -880 ?
Answer: 75th term
Step-by-step explanation:
If you look at the first terms, you can see that we're subtracting 12 from the previous term to get the number. Knowing this, we can write an expression for the nth term. The expression would be -12n + 20. Since this specific term has value of -880, we set -880 equal to the value of -12n+20. By setting your equation like this -12n + 20 = -880 and solving, you get n = 75, which means the 75th term has a value of -880.
make a the subject of the relation p=2(a+b)
Answer:
a = (p - 2b)/2Step-by-step explanation:
Solve for a:
p = 2(a + b)p = 2a + 2b2a = p - 2ba = (p - 2b)/212 identical coins are placed in the cells on a chess board with 4 rows and 4 columns. If coins are not
allowed to be placed in the same cell, how many ways are there so that there are 3 coins in every rows
and columns?
Answer:
24 waysStep-by-step explanation:
If the coins are identical and not numbered, we need to find the number of patterns.
There are 4 rows and 4 columns. One cell remains empty in each row.
There are 4 options for the first row, 3 options for the second row, 2 options for the third row and 1 option for the fourth row.
The number of options reduces to avoid more than 1 empty cell in each row or column.
Number of options is:
4*3*2*1 = 24_________
[tex] \: [/tex]
4rows, and 4columns.
Soo :
= 4!
= 4 × (4 - 1) × (4 - 2) × (4 - 3)
= 4 × 3 × 2 × 1
= 24
Find the measure of b.
Answer:
b = 55°
Step-by-step explanation:
The angle at the centre is twice the angle on the circle subtended by the same arc, then
a = 0.5 × 110° = 55°
Angles on the circumference subtended by the same arc are congruent, so
b = a = 55°
