Answer:
x = -8 or x = 3
Step-by-step explanation:
To factor ax² + bx + c, use AC method.
a times c is 1 × -24 = -24.
Factors of ac (-24) that add up to b (5) are 8 and -3.
Divide by a and reduce: 8/1 and -3/1.
Therefore, the factors are x + 8 and x − 3.
x² + 5x − 24 = 0
(x + 8) (x − 3) = 0
x = -8 or 3
Debby is working on her typing.
• At first, Debby typed at a rate of 80 words per minute
After she took a typing class, she could type 300 more words per hour than she could before the typing class.
How many words per minute could Debby type after taking the typing class?
85
130
220
e
300
Answer:
300/60=5 more words per minute
80+5 = 85 words per minute
or
80 x 60 = 4800 + 300 = 5100
5100 / 60 = 85 words per minute
Hope this helps
Step-by-step explanation:
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/10
There are 42 red marbles in the bag and each is equally likely to be chosen.
How many marbles in total must there be?
Answer:
There are 60 marbles in the bag
Step-by-step explanation:
The total number of marbles times the probability of red marbles = number of red marbles
total * 7/10 = 42
Multiply each side by 10/7
total * 7/10 * 10/7 = 42*10/7
total
60
There are 60 marbles in the bag
An animal shelter has a 65% adoption rate for puppies. Of all puppies in the shelter, 75% live to be 7 years or older. Of the puppies who are adopted, 80% live to be 7 years or older. What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
Answer:
52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: A puppy is adopted.
Event B: The puppy lives 7 or more years.
An animal shelter has a 65% adoption rate for puppies
This means that [tex]P(A) = 0.65[/tex]
Of the puppies who are adopted, 80% live to be 7 years or older.
This means that [tex]P(B|A) = 0.8[/tex]
What is the probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
[tex]P(A \cap B) = P(A)*P(B|A)[/tex]
[tex]P(A \cap B) = 0.65*0.8[/tex]
[tex]P(A \cap B) = 0.52[/tex]
52% probability that a randomly selected puppy in the shelter will get adopted and live 7 or more years
if jm = 5x - 8 and lm = 2x - 6, which expression represents jl
Answer:
7x -14 = jl
Step-by-step explanation:
Assuming a straight line
jm+ ml = jl
5x-8 + 2x-6 = jl
Combine like terms
7x -14 = jl
g Using a calculator, find the actual error in measuring volume if the radius was really 6.5 cm instead of 6 cm, and find the actual error if the radius was actually 5.5 cm instead of 6 cm. Compare these errors to the answer you got using differentials
Answer:
The answer is "[tex]58.625 cm^3[/tex]"
Step-by-step explanation:
Consider the cube volume of x =6 cm.
Substitute x = 6 cm in the volume
[tex]V= x^3\\\\ V = (6)^3\\\\ V = 216[/tex]
Therefore, whenever the cube volume
[tex]x=6 \ cm \ is \ V= 216 \ cm^3[/tex]
Then consider the cube's volume
x = 6.5 cm.
Substitute x = 6.5 cm in the volume
[tex]V_1 = x^3\\V_1 = (6.5)^3\\V_1 = 274.625 \\[/tex] by using the calculator.
Therefore, when another cube volume
[tex]x = 6.5 cm \\\\ V_1 = 274.625 cm^3.[/tex]
The real volume error x = 6.5 cm instead of x = 6 cm is calculated as,
[tex]dV= V_1-V\\[/tex]
[tex]=274.625-216\\=58.625\\[/tex]
Hence, the actual error in the volume when x = 6.5 cm instead of x = 6 cm is [tex]58.625 \ cm^3.[/tex]
DuraBurn claims that the mean lifetime of its SuperGlo light bulbs is 904 hours. A researcher wants to perform a hypothesis test to determine whether the mean lifetime is actually less than this. A random sample of 10 DuraBurn SuperGlo bulbs exhibited an average lifetime x-805 hours with a standard deviation s 158 hours. Using the hypotheses H0: μ = 904 vs Ha: μ < 904, find the P-value and state your conclusion. Use a significance level of 0.05.
1. P-value 0.039, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours
2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
3. P-value 0.079, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
4. P-value0.079, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: μ = 904
For the alternative hypothesis,
Ha: μ < 904
This is a left tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 10,
Degrees of freedom, df = n - 1 = 10 - 1 = 9
t = (x - µ)/(s/√n)
Where
x = sample mean = 805
µ = population mean = 904
s = samples standard deviation = 158
t = (805 - 904)/(158/√10) = - 1.98
We would determine the p value using the t test calculator. It becomes
p = 0.039
Since alpha, 0.05 > than the p value, 0.03953, then we would reject the null hypothesis. Therefore, the correct option is:
2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
Can anyone help me with my homework ?
2x+3y=20
7x+2y=53
Answer:
x=7, y=2
Step-by-step explanation:
Solve2x+3y=20for x:
2x+3y=20
2x+3y+−3y=20+−3y
2x=−3y+20
2x/2=-3y+20/2
x= -3/2 y
The strength of paper used in the manufacturing of cardboard boxes (y) is related to percentage of hardwood concentration in the original pulp (x). Under controlled conditions, a pilot plant manufactures 16 samples, each from differential batch of pulp, and measures the tensile strength. Determine if there is significance relationship between x and y.
y = 101, 117, 117, 106, 132, 147, 147, 134, 111, 123, 125, 145, 134, 145, 144, 146.9
x = 1.0, 1.5, 1.5, 1.5, 2.0, 2.0, 2.2, 2.4, 2.5, 2.5, 2.8, 2.8, 3.0, 3.0, 3.2, 3.3
Answer:
At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.
P-value = 0.003.
Step-by-step explanation:
If we perform a regression analysis relating x and y, we get the best fitting line with equation:
[tex]y=15.82x+92.9[/tex]
and a correlation coefficient r:
[tex]r=0.693[/tex]
We have to test the hypothesis, where the alternative hypothesis claims that there is a relationship between these two variables, and the null hypothesis claiming there is no relationship (meaning that the correlation is not significantly different from 0).
This can be written as:
[tex]H_0: \rho=0\\\\H_a:\rho\neq0[/tex]
where ρ is the population correlation coefficient for x and y.
The significance level is assumed to be 0.05.
The sample size is n=16.
The degrees of freedom are df=14.
[tex]df=n-2=16-2=14[/tex]
The test statistic can be calculated as:
[tex]t=\dfrac{r\sqrt{n-2}}{\sqrt{1-r^2}}=\dfrac{0.693\sqrt{14}}{\sqrt{1-(0.693)^2}}=\dfrac{2.593}{0.721}=3.597[/tex]
For a test statistic t=2.05 and 14 degrees of freedom, the P-value is calculated as:
[tex]\text{P-value}=2\cdot P(t>3.597)=0.003[/tex]
The P-value (0.003) is smaller than the significance level (0.05), so the effect is significant enough.
The null hypothesis is rejected.
At a significance level of 0.05, there is enough evidence to claim that there is a significant relationship between x and y.
Having integrated with respect to ϕ and θ, you now have the constant 4π in front of the integral and are left to deal with ∫[infinity]0A21(e−r/a)2r2dr=A21∫[infinity]0r2(e−r/a)2dr.
What is the value of A21∫[infinity]0r2(e−r/a)2dr?Express your answer in terms of A1 and a.
Find the unique positive value of A1.
Express your answer in terms of a and π.
Answer:
Step-by-step explanation:
[tex]\int\limits^{\infty}_0 {A^2_1} (e^{-r/a})r^2dr= {A^2_1}\int\limits^{\infty}_0r^2(e^{-r/a})^2\, dr)[/tex]
[tex]=A_1^2\int\limits^{\infty}_0 r^2e^{-2r/a}\ dr[/tex]
[tex]=A_1^2[\frac{r^2e^{2r/a}}{-2/a} |_0^{\infty}-\int\limits^{\infty}_0 2r\frac{e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A^2_1[0+\int\limits^{\infty}_0 a\ r\ e^{-2r/a}\ dr][/tex]
[tex]=A^2_1[\frac{a \ r \ e^{-2r/a}}{-2/a} |^{\infty}_0-\int\limits^{\infty}_0 \frac{a \ e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A_0^2[0-0+\int\limits^{\infty}_0 \frac{a^2}{2} e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} \int\limits^{\infty}_0 e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} [\frac{e^{-2r/a}}{-2/a} ]^{\infty}_0[/tex]
[tex]=\frac{A_1^2a^2}{2} -\frac{a}{2} [ \lim_{r \to \infty} [e^{-2r/a} -e^0]\\\\=\frac{A_1^2a^2}{2} -(\frac{a}{2}) (0-1)[/tex]
[tex]=\frac{A_1^2a^3}{4}[/tex]
[tex]\therefore A_1^2\int\limits^{\infty}_0 r^2(e^{-r/a}) \ dr =\frac{A_1^2a^3}{4}[/tex]
Find the unique positive value of A1
[tex]=4\pi (\frac{A_1^2a^3}{4} )\\\\=A_1^2a^3\pi\\\\A_1^2=\frac{1}{a^3\pi} \\\\A_1=\sqrt{\frac{1}{a^3\pi} }[/tex]
A woman forgot her bank ATM PIN but she was able to recall some of the pin.
1)the 1st digit is half of the 2nd pin
2)the sum of 2nd and 3rd is equal to 10
3)the 4th is equal to the 2nd plus 1
4)the sum of all digits is 23
show workings please
what is the ATM digit?
The PIN is 4829
Step-by-step explanation:
let s take 4 numbers a b c and d
the PIN is abcd
we know that
(1) a = b/2
(2) b+c=10
(3) d=b+1
(4) a+b+c+d=23
from (2) c = 10 - b
from (3) d = b + 1
so (4) gives
b/2 + b + 10 - b + b +1 = 23
so
3/2 b = 23 -11 = 12
b = 12*2/3 = 8
so d = 9
c = 10-8=2
and a = 4
so the PIN is 4829
thank you
Write an
explicit formula for
ans
the nth
term of the sequence 20, -10,5, ....
Answer:an=20(-1/2)^n-1
Step-by-step explanation:
in circle c shown below a tangent has been drawn at point A. if measure angle CBA = 28, then explain why the measure of angle DAB must equal 62 degrees.
Answer:
it is the complement of 28°
Step-by-step explanation:
Angle DAB made by a tangent and a chord to the point of tangency is equivalent to every other inscribed angle that intercepts the same arc. Those angles have half the measure of the central angle ACB intercepting the same arc.
In isosceles triangle ABC the base angles (shown as 28°) are the complement of half the measure of the central angle. Hence angle DAB will be the complement of the angle marked 28°.
angle DAB = 90° -28° = 62°
How long is a average teen suppose to be
Answer:
The way adolescents spend their time can strongly influence their health later in life. For youth to maintain a healthy future, they need plenty of sleep; good nutrition; regular exercise; and time to form relationships with family, friends, and caring adults. Additionally, the time adolescents spend in school and in after-school activities with peers and adults can advance healthy academic, emotional, social, and physical development. The amount of time they spend on screens and in social media may also influence adolescents’ overall well-being.
The American Time Use Survey, collected by the U.S. Bureau of Labor Statistics, contains detailed information about how individuals ages 15 and older use their time and provides a picture of a typical weekday and weekend day for a high school teen during the school year. Here we specifically analyze how adolescents ages 15-19 who are enrolled in high school spend their time.
Step-by-step explanation:
Please help! Which statement is true, about the following of the two triangles? (Refer to image)
A: ΔADC≅Δ ACB, by the SSS congruence postulate.
B: ΔADC≅ΔACB, by the SAS congruence postulate.
C: ΔADC≅ ΔCBA, by the SSS congruence postulate.
D: ΔADC≅ΔCBA, by the SAS congruence postulate.
Answer:
The answer is C because DC = BA and DA = CB (given) and AC = CA (reflexive property).
On day two of a study on body temperatures, 106 temperatures were taken. Suppose that we only have the first 10 temperatures to work with. The mean and standard deviation of these 10 temperatures were 98.44oF and 0.30oF, respectively. Construct a 95% confidence interval for the mean of all body temperatures.
Answer:
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622
The margin of error is:
M = T*s = 2.2622*0.3 = 0.68
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF
The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B. Five percent of all type A goggles are returned within 10 days after the sale, whereas only two percent of type B are returned. If a pair of goggles is returned within the first 10 days after the sale, the probability that the goggles returned are of type B is:
Answer:
The required probability is 0.4828.
Step-by-step explanation:
We are given that a company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B.
Five percent of all type A goggles are returned within 10 days after the sale, whereas only two percent of type B are returned.
Let the probability that production is of Type A = P(A) = 30%
Probability that production is of Type B = P(B) = 1 - P(A) = 1 - 0.30 = 70%
Also, let R = event that pair of goggles are returned
So, the probability that type A goggles are returned within 10 days after the sale = P(R/A) = 5%
Probability that type B goggles are returned within 10 days after the sale = P(R/B) = 2%
Now, given a pair of goggles is returned within the first 10 days after the sale, the probability that the goggles returned are of type B is given by = P(B/R)
We will use the concept of Bayes' Theorem to calculate the above probability.
So, P(B/R) = [tex]\frac{P(B) \times P(R/B)}{P(A) \times P(R/A)+P(B) \times P(R/B)}[/tex]
= [tex]\frac{0.70 \times 0.02}{0.30 \times 0.05+0.70 \times 0.02}[/tex]
= [tex]\frac{0.014}{0.029}[/tex] = 0.4828
Please answer...i always answer... please
Answer:
A) -x + y = 2
B) x + 2y = 4
we add both equations
3 y = 6
y = 2
We put y = 2 into equation B)
x + 2 * 2 = 4
x = 0
***********************************************
A) -2x + y = 6
B) x + y = 0
We multiply B) by 2
B) 2 x + 2 y = 0 then we add A)
A) -2x + y = 6
3y = 6
y = 2
Therefore x = -2
Step-by-step explanation:
If the reciprocal of a number is multiplied by 1 less than the original number, the results exceed 1/2 the reciprocal of the original number by 5/8. Find the number.
Answer:
4
Step-by-step explanation:
Let's try this a different way than perhaps the usual way. Let r represent the reciprocal of the number.
r(1/r -1) -1/2r = 5/8
1 -r -1/2r = 5/8 . . . . . . eliminate parentheses
-3/2r = -3/8 . . . . . . . . collect terms, subtract 1
(-3/2)/(-3/8) = 1/r = 4 . . . . . divide by (-3/8)r because we actually want 1/r
The number is 4.
_____
Check
The reciprocal of the number is 1/4.
1 less than the original number is 4 -1 = 3. The product of these is 3/4.
__
Half the reciprocal of the original number is (1/2)(1/4) = 1/8.
Then the difference between these is ...
3/4 -1/8 = (6 -1)/8 = 5/8 . . . . as required.
I need help this question is kinda confusing
Answer:
Geometric Sequence.
Step-by-step explanation:
Geometric sequence. If you take a close look at the graph, it never touches the x - axis. If you use division in a geometric sequence, you will get a very small number, but you will never touch the axis.
Maria, Daniel, Stephanie, Michael, Elena, Tyler, Sue, and Dimitri have reserved eight seats in a row at the theater, starting at an aisle seat. In how many ways can they arrange themselves if Maria and Daniel are to sit next to each other?
Answer:
1x1x6x5x4x3x2x1 = 720 also they can sit in:
6x1x1x5x4x3x2x1 = 720
6x5x1x1x4x3x2x1 = 720
6x5x4x1x1x3x2x1 = 720
6x5x4x3x1x1x2x1 = 720
6x5x4x3x2x1x1x1 = 720
6x5x4x3x2x1x1x1 = 720 or you could have gone 720 x 7
Outcome
0
1
5
10
1000
Probability
0.33
0.32
0.24
0.10
0.01
Which is the expected value of the random variable with the given probability distribution?
a.
5.65
c.
12.52
b.
100.44
d.
5
Answer:
The expected value of the random variable with the given probability distribution = 12 .52
Step-by-step explanation:
Given data
x : 0 1 5 10 1000
p(x) : 0.33 0.32 0.24 0.10 0.01
The expected value of the given random variable of given probability distribution
E(X) = ∑ x p ( X = x)
E(X) = 0 × 0.33 + 1 × 0.32 + 5 × 0.24 + 10× 0.10 + 1000×0.01
E (X) = 12.52
A student works at an on- campus job Monday through Friday. The student also participates in intramural volleyball on Tuesdays and Thursdays. Given Events A and B, are the two events mutually exclusive? Explain your answer.
Event A: On a random day of the week, the student is working at their on-campus job.
Event B: On a random day of the week, the student is playing intramural volleyball.
Answer:
No, the events are not mutually exclusive because they share the common outcomes of the student working and playing volleyball on certain days.
Step-by-step explanation:
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.
In this case, A and B have outcomes in common since the student both works and plays volleyball on Tuesdays and Thursdays. Thus, the events are not mutually exclusive.
evaluate will give brainlist
Answer:
C. 1/25
Step-by-step explanation:
5^-2=5^(2*-1)
5^2=25
25^-1=1/25
Answer:
It is C 1/25 because it won't be -25 because a negative times a negative is a positive
Step-by-step explanation:
Help??!!??!?!!??anyone
Answer:
A. 32.25
Step-by-step explanation:
Because of the first row, we know that to find the cost, we are multipling the gallons by 2.15.
so [tex]15*2.15=32.25[/tex]
So the answer is A.
Hope this helps!
Plx give brainliest
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
According to theorem, congruent angles has congruent sides opposite to them so,
RS = TU
Now
12x+4 = 11x+15
12x-11x = 15-4
So
x = 11
Now
TU = 11x+15
= 11(11)+15
= 121+15
= 136 units
Mariah spent $9.50 on 9 pounds of limes and pears. Limes cost $0.50 per pound and pears cost $1.50 per pound. Let l be the number of pounds of limes and let p be the number of pounds of pears.
The system of linear equations that models this scenario is:
l + p = 9
0.5l + 1.5p = 9.5
How many pounds of each type of fruit did she buy?
Answer:
4 pounds of lime and 5 pounds of pears
Step-by-step explanation:
I + P = 9
0.5l + 1.5P = 9.5
I = 9 - P
0.5(9 - P) + 1.5P = 9.5
4.5-0.5P + 1.5P = 9.5
4.5 + P (1P) = 9.5
P = 9.5-4.5 = 5
I = 9 - 5 = 4
Answer: 4 pounds of lime and 5 pounds of pears
g A cannonball is shot with an initial speed of 62 meters per second at a launch angle of 25 degrees toward a castle wall that is 260 meters away. If the wall is 20 meters tall, how high off the ground will the cannonball hit
Answer:
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Step-by-step explanation:
Given;
Initial speed v = 62m/s
Angle ∅ = 25°
Horizontal distance d = 260 m
Height of wall y = 20
Resolving the initial speed to vertical and horizontal components;
Horizontal vx = vcos∅ = 62cos25°
Vertical vy = vsin∅ = 62cos25°
The time taken for the cannon ball to reach the wall is;
Time t = horizontal distance/horizontal speed
t = d/vx (since horizontal speed is constant)
t = 260/(62cos25°)
t = 4.627 seconds.
Applying the equation of motion;
The height of the cannonball at time t is;
h = (vy)t - 0.5gt^2
Acceleration due to gravity g = 9.81 m/s
Substituting the given values;
h = 62sin25×4.627 - 0.5×9.81×4.627^2
h = 16.2264134736
h = 16.23 m
The cannonball will hit the wall at 16.23m from the ground.
Use the formula v = u + at to find the velocity when the initial velocity is 3 m/s the acceleration is 1.5 m/s the time is 7 s
[tex]answer \\ 13.5 \: m/s \\ given \\ initial \: velocity(u) = \: 3 \: m/s \\ acceleration(a) = 1.5 \: m/s ^2\\ time(t) = 7 \: second \\ now \\ v = u + at \\ or \: v = 3 + 1.5 \times 7 \\ \: or \: v = 3 + 10.5 \\ v = 13.5 \: m/s \\ hope \: it \: helps[/tex]
MARY PUT IN A TOTAL OF 16-1/2 8 FEET LONG. A NEARBY POLE IS 72 HOURS BABYSITTING DURING 5 DAYS FEET HIGH. HOW LONG IS ITS OF THE PAST WEEK. WHAT WAS HER SHADOW? AVERAGE WORK DAY?
Answer: 3 hours and 18 minutes.
Step-by-step explanation:
A real estate purveyor purchases a 60{,}00060,00060, comma, 000 square foot \left(\text{ft}^2\right)(ft 2 )(, start text, f, t, end text, squared, )warehouse and decides to turn it into a storage facility. The warehouse's width is exactly \dfrac 2 3 3 2 start fraction, 2, divided by, 3, end fraction of its length. What is the warehouse's width? Round your answer to the nearest foot.
Answer:
200 feet
Step-by-step explanation:
Area of the warehouse [tex]=60,000$ ft^2[/tex]
Let the length of the warehouse=l
The warehouse's width is exactly [tex]\dfrac23[/tex] of its length
Therefore: Width of the warehouse[tex]=\dfrac23l[/tex]
Area =Length X Width
Therefore:
[tex]\dfrac23l*l=60000\\$Cross multiply\\2l^2=60000*3\\2l^2=180000\\$Divide both sides by 2\\2l^2 \div 2=180000 \div 2\\l^2=90000\\l^2=300^2\\$Length, l=300 feet\\Recall: Width =\dfrac23l\\$Therefore, Width of the warehouse=\dfrac23*300=200$ feet[/tex]
