Answer:
18
Step-by-step explanation:
Using Zero Product Property, we can split this equation into two separate equations by setting each factor to 0. The equations are:
10x + 33 = 0 or 11x + 60 = 0
10x = -33 or 11x = -60
x = -33/10 or x = -60/11
Multiplying the two solutions together, we get -33/10 * -60/11 = 1980 / 110 = 18.
A sample of 31 observations is selected from a normal population. The sample mean is 11, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 10 H1: μ > 10 Is this a one- or two-tailed test?
Answer:
The test is a two -tailed test
Step-by-step explanation:
From the question we are told that
The sample size is n = 31
The sample mean is [tex]\= x =11[/tex]
The sample standard deviation is [tex]\sigma = 3[/tex]
The null hypothesis is [tex]H_o: \mu \le 10[/tex]
The alternative hypothesis is [tex]H_1 : \mu > 10[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 11 - 10 }{ \frac{3}{\sqrt{ 31} } }[/tex]
[tex]t = 1.85[/tex]
The p- value is mathematically represented as
[tex]p-value = p( t > 1.856) = 0.0317[/tex]
Looking at the value of [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis
Given the that the p value is less than 0.05 it mean the this is a two-tailed test
PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
1)
1/5 of the students earned a C
2)
3% more students earned an A then B
3)
20% of the students earned a D
4)
1/4 of the class earned a B
Answer:
Option (3)
Step-by-step explanation:
From the picture attached,
Bar graph sketched shows the grades earned by the students in an exam.
Number of students who achieved the grade A = 17
Number of students who achieved grade B = 14
Number of students with grade C = 5
Number of students with grade D = 9
Total students who took the exam = 17 + 14 + 5 + 9 = 45
Option (1)
"[tex]\frac{1}{5}[/tex] of the students earned a C"
Fraction of students who earned C = [tex]\frac{\text{Students who earned C}}{\text{Total students}}[/tex]
= [tex]\frac{5}{45}[/tex]
= [tex]\frac{1}{9}[/tex]
Therefore, this option is incorrect.
Option (2)
"3% more students earned an A then B"
Percentage of students who earned A = [tex]\frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{17}{45}\times 100[/tex]
= 37.78%
Percentage of students who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{14}{45}\times 100[/tex]
= 31.11%
Difference in percentage = 37.78 - 31.11
= 6.67%
Therefore, this option is not correct.
Option (3)
"20% of the students earned a D"
Percentage of students who earned D = [tex]\frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{9}{45}\times 100[/tex]
= 20%
Option (3) is the correct option.
Option (4)
" [tex]\frac{1}{4}[/tex] of the class earned a B"
Fraction of class who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}[/tex]
= [tex]\frac{14}{45}[/tex]
Therefore, Option (4) is not correct.
The report "Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel" summarizes data from a survey of a representative sample of 800 teens between the ages of 12 and 17. The following statements were made on the basis of the resulting data.
- 75% of all American teens own a cellphone
- 66% of all American teens use a cellphone to send a receive text messages
- 26% of American teens age 16-17 have used a cellphone to text while driving
Required:
a. Is the inference made one that involves estimation or one that involved hypothesis testing?
b. What is the population of interest? American teenagers? American teenagers between ages 12-17? Americans? Teenagers?
Answer:
"Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel"
a. The inference made involves estimation. The question provided that the statements were made on the basis of the resulting data and not on the basis of some hypothesis testing.
This implies that some statistics were calculated from sample data to approximate the population parameter, as shown in the statements. The statements were not an attempt to establish the statistical significance of some claims.
b. The population of interest is American teenagers between 12-17.
Step-by-step explanation:
An inference from data is a statistical estimation by which some statistics are calculated based on the sample data of 800 teens between the ages of 12 and 17. The statistics serve as an approximation to the population parameter.
Inference based on hypothesis testing establishes if a claim has statistical significance by providing statistical evidence in favor of the claim or against it.
Let T (x, y) = (x + 1, y + 1) and S (x, y) = (x + 5, y + 4). In what
quadrant is S (T (P)) when P(-7, 1)?
Answer:
quadrant 2
Step-by-step explanation:
One number is 4 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 370, find the numbers.
The three numbers are
(Use a comma to separate answers as needed.)
Answer:
45, 180, 145
Step-by-step explanation:
Let n represent the first number. Then "one number" is 4n, and the third number is n+100. The sum of the three numbers is ...
n + 4n + (n+100) = 370
6n = 270
n = 45
4n = 180
n+100 = 145
The three numbers are 45, 180, 145.
70% of what number is 56
Answer:
the number is 80
Step-by-step explanation:
let x be an unknown number so from the above question we deduce that
(70/100)*x=56
70x/100=56
70x=56*100
70x=5600
70x/70=5600/70
x=80
What's the solution of the following linear system? 5x + 2y = 9 –5x – 2y = 3
━━━━━━━☆☆━━━━━━━
▹ Answer
(-39/35, 9/7)
▹ Step-by-Step Explanation
5y + 2y = 9
-5x - 2y = 3
Solve the equation:
y = 9/7
-5x - 2y = 3
Substitute the value of y:
-5x - 2 * 9/7 = 3
x = -39/35
(x, y) = (-39/35, 9/7)
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
To solve this system by addition, we start by adding both of our equations together but notice that the x terms and the y terms cancel out.
This leaves us with 0 on the left side and on the right side,
9 + 13 = 12 so we are left with the equation 0 = 12.
Since 0 = 12 is a false statement, this means that
there is no solution to our system of equations.
A restaurant hands out a scratch-off game ticket with prizes being worth purchases at the restaurant. The back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100. What are the odds that the ticket is worth at least $25?
Answer: 0.05412
Step-by-step explanation:
Formula : Odds of having an event is given by [tex]o=\dfrac{p}{1-p}[/tex], where p = probability that event happens.
In terms to find p , we use [tex]p=\dfrac{o}{1+o}[/tex]
Given, he back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100.
Let X be the worth of ticket.
Then, the probability that the ticket is worth at least $25 =
[tex]P(X\geq 25)=P(X=25)+P(X=50)+P(X=100)[/tex]
[tex]=\dfrac{0.04}{1+0.04}+\dfrac{0.01}{1+0.01}+\dfrac{0.003}{1+0.003}\\\\=0.05135[/tex]
The odds that the ticket is worth at least $25 = [tex]\dfrac{0.05135}{1-0.05135}[/tex]
=0.05412
hence, the odds that the ticket is worth at least $25 is 0.05412 .
10 - 2x, when x = 3
Answer:
4
Step-by-step explanation:
Plug in 3 as x in the expression:
10 - 2x
10 - 2(3)
10 - 6
= 4
Answer:
4
Step-by-step explanation:
10 - 2x
Let x =3
10 -2(3)
10 -6
4
given the vector with a manitude of 9m at an angle a of -80 degrees, decompose this vector into two vector components oarallel to the x axis with a slope of
Answer:
We have the magnitude, M, and the angle A.
(The angle is always measured from the +x-axis)
Then we have that:
x = M*cos(A)
y = M*sin(A)
in this case:
M = 9m
A = -80°
x = 9m*cos(-80°) = 1.562
y = 9m*sin(-80) = -8.86m
Now, the component parallel to the x axis is:
x = 9m*cos(-80°) = 1.562 m
And the slope of something parallel to the x-axis is always zero, as this is a constant line.
A refrigeration system at your company uses temperature sensors fixed to read Celsius (0C) values, but the system operators in your control room understand only the Fahrenheit scale. You have been asked to make a Fahrenheit (°F) label for the high temperature alarm, which is set to ring whenever the system temperature rises above -10°C. What Fahrenheit value should you write on the label?
Answer:
14 °F
Step-by-step explanation:
To answer this problem, we will use the known celsius to fahrenheit conversion formula.
[Celsius * (9/5)] + 32 = Fahrenheit
Now we just plug in the value of celsius:
[-10 * (9/5)] + 32 = Fahrenheit
[ -2 * 9 ] + 32 = Fahrenheit
[ -18 ] + 32 = Fahrenheit
14 = Fahrenheit
So you should right 14(°F) on the label.
Cheers.
Select the correct answer from each drop-down menu.
Nirja has 24 marbles. The number of marbles Nirja has is 6 more than the number of marbles Tim has.
If Tim has x marbles, the equation that represents the situation is
The value of x that makes the equation true is
Reset
Next
Answer:
24 = x+6
x = 18
Step-by-step explanation:
N = 24
T = x
N = x+6
24 = x+6
Subtract 6 from each side
24-6 = x+6-6
18 = x
Time has 6 marbles
Nirja has 6 more than Tim,
So you can subtract 6 from 24 to find x:
24-6 = x
Or you can add 6 to x to equal 24:
x + 6 = 24
You don't list the choices but it should be one of these.
Solve:
24 - 6 = x
x = 18
-3(-5x-2u+1) use the distributive property to remove the parentheses
Answer:
15x+6u−3
Step-by-step explanation:
This means -3 times -5x, -3 times -2u, and -3 times 1.
Do this and you have, 15x+6u-3.
John receives a perpetuity paying 2 at the end of year 4, 4 at the end of year 6, 6 at the end of year 8, etc. The present value of this perpetuity at an annual effective rate of 10% equals X. Calculate X
Answer:
45.35
Step-by-step explanation:
From the above question, we are told that the annual effective rate = 10% = 0.10
Note also that payment is been made every 2 years
Hence , we apply the formula of effective interest rate for a period of 2 years.
Effective Interest rate(j) = (1 + r)² - 1
= (1 + 0.10)² - 1
= 1.10² - 1
= 1.21
= 0.21
Present value of perpetuality = t/[j × j/(1 + r)²]
Where t = time in years = 2
r = 0.10
= 2/ [0.21 × 0.21/(1 + 0.10)²
= 54.87528
Present value at time t = 0
= 54.87528(1 + r)^-2
= 54.87528(1 + 0.10) ^-2
= 54.87528(1.10)^-2
= 45.35
Therefore, the present value at time (t) is 0 = 45.35
The average of 4 numbers is 15 , the sum of 3 numbers is 14 what is the fourth number
Answer:
46
Step-by-step explanation:
(14+x)/4 = 15
14 + x = 60
x = 46
Answer:
46
Step-by-step explanation:
Let a to d be number 1 to 4 respectively.
15 = (a + b + c + d) / 4
(a + b + c + d) = 60 ------> total sum of the 4 numbers
Since the sum of 3 numbers (assuming a to c) is 14,
Fourth number (d) = 60 - 14
= 46
That's how I would do it, hope this helps :)
What is the area of the region bounded by the three lines with equations $2x+y = 8$, $2x-5y = 20$ and $x+y = 10$?
Answer:
42
Step-by-step explanation:
A graphing tool is useful for finding the points of intersection of these lines. If the equations are numbered 1, 2, 3 in the order given, we can find the points of intersection to be ...
equations 1, 2: A(5, -2)
equations 2, 3: B(10, 0)
equations (3, 1): C(-2, 12)
Then the area can be found from the coordinates using the formula ...
A = (1/2)|x1(y2-y3) +x2(y3-y1) +x3(y1-y2)|
= (1/2)|5(0-12) +10(12-(-2)) -2(-2-0))| = (1/2)|-60 +140 +4|
A = 42
The area of the triangular region is 42 square units.
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
Which is the exponential form of log9 5 = y
Answer:
Step-by-step explanation:
[tex]\log _9\left(5\right)=y\\y=\log _9\left(5\right)[/tex]
How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 147 153 170 172 185 181 182 185 181 170 181 167 153 145
Answer:
Mean: 169.4
Median: 171
Mode: 181
Step-by-step explanation:
I first sorted the numbers by value, least to greatest.
145 147 153 153 167 170 170 172 181 181 181 182 185 185
We can see that 181 occurs the most, 3 times, so it's the mode.
The median of this set will be the middle number(s).
When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.
We can add all the numbers and divide by 14 to get the mean.
[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]
Hope this helped!
I NEED FULL EXPLANATION
(4 - 3i) ^2
Answer:
Rewrite
( 4 − 3 i ) 2 as ( 4 − 3 i )( 4 − 3 i ) . ( 4 − 3 i) ( 4 − 3 i ) Expand ( 4 − 3 i ) ( 4 − 3 i )
using the FOIL Method.
4 ⋅ 4 + 4 ( -3 i ) − 3 i ⋅ 4 − 3 i ( − 3 i )
Simplify and combine like terms.
7 − 24 i
Step-by-step explanation:
Answer:
7 -24i
Step-by-step explanation:
(4 - 3i) ^2
(4-3i) * (4-3i)
FOIL
first 4*4 = 16
outer 4 * -3i = -12i
inner -3i *4 = -12i
last -3i*-3i = 9i^2 = 9 (-1) = -9
Add together
16 -12i-12i -9
Combine like terms
7 -24i
Scores on a University exam are normally distributed with a mean of 68 and a standard deviation of 9. Using the 68-95-99.7 rule, what percentage of students score above 77?
Answer:
0.1585, or 15.85%
Step-by-step explanation:
On a standard bell curve, the area from 77 to 100 falls within the 95.45 to 99.73 range.
99.73 - 68.27 = 31.46
31.46 / 2 =15.73
99.7 - 68 = 31.7
31.7 / 2 = 15.85
CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
announced that when he slices the cake, your slice will have a perimeter of 16 inches, because you're his favorite friend, and
that's his favorite number. Since you're helping his mom with the baking, what diameter cake will you recommend she makes
so that you end up with the most possible cake at weird Spud's party? (Hint: you can ignore the thickness df the cake, since
this will be the same, regardless of its diameter.)
10.1
in
Answer:
15.7 in
Step-by-step explanation:
A slice of a round pie is a sector of a circle.
The perimeter of a slice is the arc length s plus twice the radius r.
P = s + 2r
s = rθ = r(16/360) = r/22.5. So,
16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5
16 × 22.5 = 46r
360 = 46r
r = 7.826
D = 2r = 2 × 7.826 = 15.7 in
The diameter of the cake should be 15.7 in.
Check:
[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]
It checks.
A TV studio has brought in 8 boy kittens and 9 girl kittens for a cat food commercial. The director is going to choose 11 of these kittens at random to be in the commercial. What is the probability that the director chooses 4 boy kittens and 7 girl kittens? Round your answer to three decimal places.
Answer:
0.204
Step-by-step explanation:
The formula to use to solve this is the combination formula.
Combination formula =
C(n, r) = nCr = n!/r! (n - r)!
Total number of kittens = 8 boy kittens + 9 girl kittens
= 17 kittens
Step 1
We find the probability of choosing 4 boy kittens out of 8 boy kittens
= 8C4 = 8!/4! × (8 - 4)!
= 8C4 = 8! / 4! × 4!
= 8C4 = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (4 × 3 × 2 × 1) × (4 × 3 × 2 × 1)
8C4 = 70
Step 2
We find the probability of choosing 7 girl kittens out of 9 girl kittens
9C7 = 9!/7! × (9 - 7)!
= 9C7 = 9! / 7! × 2!
= 9C7 = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (7 × 6 × 5 × 4 × 3 × 2 × 1) × (2 × 1)
9C7 = 36
Step 3
Find the probability of Picking 11 kittens out of 17 kittens
17C11 = 17!/11! × (17 - 11)!
= 17C11 = 17! / 11! × 6!
= 17C11 = 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/ (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) × (6 × 5 × 4 × 3 × 2 × 1)
17C11 = 12,376
Step 4
The final step
The probability that the director chooses 4 boy kittens and 7 girl kittens
= 8C4 × 9C7/ 17C11
= 70 × 36/12376
= 2520/12376
= 0.2036199095
Approximately to 3 decimal places = 0.204
Therefore, the probability that the director chooses 4 boy kittens and 7 girl kittens is 0.204
on tuesday, david picked a apples each hour for 5 hours, and elanor picked b apples each hour for 8 hours. which of the following represents the total number of apples picked by david and elanor on tuesday? a) 13ab b) 40ab c) 5a + 8b d) 8a + 5b
Answer:
c) 5a + 8bStep-by-step explanation:
[tex]a \: apples = 1 \: hours\\x \: apples = 5 \: hours\\x = 5a\\Total \:no \:of \:apples \:picked\\\:by \:david \:= 5a\\\\\\b \:apples = 1 \:hour\\x \:apples = 8 hours\\x = 8b\\Total \:no \:of \:apples \:picked\\ \:by \:elanor = 8b\\\\Total \:no \:of \:Apples =5a+8b[/tex]
In this triangle, which of the following is true?
We know that this is a right triangle, so one of the sides has to be 90 (indicated by the square on the corner) The angles of all triangles must add to exactly 180. Subtract 90 and 35 from 180
If we do that, we get 55. We know that the unknown angle is 55 now. Now, it asks us for b. We can pythagoras theorem which states that (a^2 + b^2 = c^2) We already know c (c is 20) It does not tell us 2 of the sides but we do know that the answer is either B or D.
The side opposite of 90* should be the largest. The size opposite of 55 would be the second largest one. The side opposite of 35 would be the smallest one. Using pythagoras theorem again, I can try plugging in both 11.47 and 16.38 with c^2 - b^2 = a^2
11.47:
400 - 132 =268 (sq root now = 16.37) this would mean that A is larger than B. B should be larger than A. Try the other one
16.37:
400 -268 = 132 (sq root = 16.37) this would mean that B is larger than A which is what we want.
Thus, 16.37 = B and the last option would be correct (D)
Hope this helps, give an honest rating for me please
Noel pays $1.54 in sales tax.The sales tax rate is 5.5%,what the original price
Step-by-step explanation:
Hi, there!!!
Let's simply work with it,
Here,
tax=$1.54
rate of tax= 5.5%
now, let the original price be x.
so, 5.5% of x= $1.54 { tax amount = tax% of original price}.
or, 5.5/100 × x= $1.54
or, 5.5x = $1.54×100
or, x= $28.
Therefore, the original price was $28.
Hope it helps...
3 ratios that are equivalent to 6:12
Answer:
1:3
2:4
3:6
Step-by-step explanation:
we can divide both sides by 6 and get 1:2
we can divide both sides by 3 and get 2:4
we can divide both sides by 2 and get 3:6
Answer:
12:24, 3:6, 2:4
Step-by-step explanation:
What we are looking for here is a ratio that, when you divide/multiply the same constant on both parts of the ratio, you get 6:12.
6:12 is the same thing as 1:2, so we can find ratios equivalent to 1:2 (the first value will be half the second).
Hope this helped!
help please precalc will give brainliest
In part (D), we found
[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]
so the phase [tex]\phi[/tex] is [tex]\tan^{-1}\left(\frac52\right)\approx1.19\,\rm rad[/tex], which falls between 0 and [tex]\frac\pi2[/tex]. This means the weight is somewhere between the maximum positive position (where [tex]\phi[/tex] would be 0) and the equilibrium position (where [tex]\phi[/tex] would be [tex]\frac\pi2[/tex]), and would be traveling in the negative direction.
A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below.
Age (in years) Height (inches)
7 47.3
8 48.8
5 41.3
8 50.4
8 51
7 47.1
7 46.9
7 48
9 51.2
8 51.2
5 40.3
8 48.9
6 45.2
5 41.9
8 49.6
Requried:
a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?
b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?
c. How much of the variation in the sample values of height does the model estimated in part (b) explain?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Age(x)
7
8
5
8
8
7
7
7
9
8
5
8
6
5
8
Height (Y)
47.3
48.8
41.3
50.4
51
47.1
46.9
48
51.2
51.2
40.3
48.9
45.2
41.9
49.6
The estimated regression equation:
ŷ = 2.73953X + 27.91395
Where ;
X = independent variable
ŷ = predicted or dependent variable
27.91395 = intercept
C.) To obtain the variation in sample values of height estimated by the model, we obtain the Coefficient of correlation:
Using the online pearson correlation Coefficient calculator :
The correlation Coefficient is 0.9696.
which means that the regression model estimated in part (b) explains approximately (0.9696 * 100) = 96.96% = 97% of the variation in the height in the sample.
Evan’s dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work!
Answer:
ok as we know 15 is a whole number by itself and 3/8 is the decimal part
so we know it is 15. something
that something is 3/8 to find decimal you do 3/8
3/8 is = .375
so 15.375 is the answer
hope it helps
brainliest give me pls
