Answer:
[tex]x =10[/tex]
Step-by-step explanation:
Given
[tex]AB = 12[/tex]
[tex]BC = 18[/tex]
[tex]AC = 3x[/tex]
Required
Solve for x
Since B is in between both points, then:
[tex]AC = AB + BC[/tex]
This gives
[tex]3x = 12 + 18[/tex]
[tex]3x = 30[/tex]
Divide by 3
[tex]x =10[/tex]
3. Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years. Calculate a 96% CI on the death rate from lung cancer.
Answer:
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Of 1000 randomly selected cases of lung cancer, 450 resulted in death within 5 years.
This means that [tex]n = 1000, \pi = \frac{450}{1000} = 0.45[/tex]
96% confidence level
So [tex]\alpha = 0.04[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.054[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4177[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.054\sqrt{\frac{0.45*0.55}{1000}} = 0.4823[/tex]
The 96% CI on the death rate from lung cancer is (0.4177, 0.4823).
7 is added to the product of 5 and 6
Answer:
37
Step-by-step explanation:
7 + (5×6)
= 7 + 30
= 37
.................
Answer:
37
Step-by-step explanation:
First Step: Multiply
5x6=30
Second Step: Add
30+7=37
Therefore your answer is 37
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
The figure below is a rhombus.
w = [? ]°
Answer:
Step-by-step explanation:
The Sureset Concrete Company produces concrete. Two ingredients in concrete are sand (costs $6 per ton) and gravel (costs $8 per ton). Sand and gravel together must make up exactly 75% of the weight of the concrete. Also, no more than 40% of the concrete can be sand and at least 30% of the concrete be gravel. Each day 2000 tons of concrete are produced. To minimize costs, how many tons of gravel and sand should be purchased each day
Answer:
The Sureset Concrete Company
The tons of gravel and sand that should be purchased each day are:
Sand = 800 tons
Gravel = 700 tons
Step-by-step explanation:
Two ingredients for producing concrete = sand and gravel
Cost of sand per ton = $6
Cost of gravel per ton = $8
Sand and gravel = 75% of the concrete
Therefore 25% (100 - 75%) will be made up of cement and water
Tons of concrete produced each day = 2,000
Sand and gravel = 1,500 (2,000 * 75%)
Sand <= 40% of 2,000 = 800 tons
Gravel => 30% of 2,000 = 700 (1,500 - 800) tons
To minimize costs, 800 tons of gravel and 700 tons of sand should be purchased each day.
Total cost incurred daily for both sand and gravel = $10,400 (800 * $6 + 700 * $8)
All I need is number one
Answer:
a. 7 ÷ 4 yes
b. 4 ÷ 7 no
c. [tex]\frac{7}{4}[/tex] yes
d. [tex]\frac{4}{7}[/tex] no
e. 7 × [tex]\frac{1}{4}[/tex] yes
f. [tex]1\frac{3}{4}[/tex] yes
Step-by-step explanation:
hope this helps ^^
The last dividend paid by Wilden Corporation was $1.55. The dividend growth rate is expected to be constant at 1.5% for 2 years, after which dividends are expected to grow at a rate of 6.0% forever. The firm's required return (rs) is 12.0%. What is the best estimate of the current stock price?
Answer:
Net present value= $25.17
Step-by-step explanation:
We are told that The last dividend paid was $1.55 and that the dividend growth rate is constant at 1.5% for 2 years.
Thus;
1) After 1st year;
1.55 × (1 + 0.015) = 1.57325 Div1
After 2nd year;
1.57325 × (1 + 0.015) = 1.59685 Div2
After that 2 years it grows at 6% Constant rate forever;
1.59685 × (1 + 0.06) = 1.69266 Div3
Let's now use the dividend formula which grows in perpetuity at a rate of "g" since required return is 12%:
Thus;
V = 1.69266/(0.12 - 0.06) = 28.211
Thus; Div2 = 28.211 + 1.59685 ≈ 29.80785
Now, using the financial calculator of the Cash Flow function, we have:
Div0 = 0
Div1 = 1.57325
Div2 = 29.80785
i% = 12
Net present value = (1.57325/(1 + 0.12)) + ((1.59685 + 28.211)/(1 + 0.12)²)
Net present value= $25.17
The strength of one's immune system can be evaluated in several ways. One of the most popular methods involves measuring the concentration of adenosine triphosphate (ATP) in the blood. In women, the mean blood ATP level is 390 ng/mL, and the standard deviation is 115 ng/mL. It has been hypothesized that women with Major Depressive Disorder (MDD) have decreased immune function. A recent study found that a random sample of 30 women with MDD had an average blood ATP level of 355 ng/mL. Using a one-sample z test, what is the p-value of this result? (HINT: This involves a one-tailed hypothesis test).
Answer:
Hence the value of p is 0.04746.
Step-by-step explanation:
The test statistic is
[tex]Z=(\bar x-\mu)/(s/vn)\\\\=(355-390)/(115/ \sqrt(30))\\\\=-1.667[/tex]
The p-value= P(Z<-1.67) =0.04746. (from standard distribution table)
Therefore p-value =0.04746.
chang knows one side of a triangle is 13 cm which set of two sides is possible for the length of the other two sides
5 cm and 8 cm
6cm and 7 cm
7cm and 2 cm
8cm and 9 cm
Answer:
i dont knowwww dhehje ejhdjeke jsienje
Answer:
8cm and 9 cm
Step-by-step explanation:
Sum of sides rule:
The sum of the two smallest sides of a triangle has to be greater than the third side.
5 cm and 8 cm
One side is 5, other 8, 5 + 8 = 13. The sum has to be greater than 13, so this is not possible.
6cm and 7 cm
6 + 7 = 13, same as above, not possible.
7cm and 2 cm
7 + 2 = 9 < 13, so not possible.
8cm and 9 cm
8 + 9 = 17 > 13, so possible, and this is the answer.
Which of the following choices is the average speed of a tourist who traveled for 1 hour on a plane at 400 mph and 4 hours by car at 60 mph?
(average= total miles/total hours)
Answer:
128 mph
Step-by-step explanation:
1 hour = 400
4 hours = 240
240+400= 640
4+1 = 5
640/5=128
What is the solution to the linear equation?
-12 + 3b - 1 = -5 - b
Answer:
b=2
Step-by-step explanation:
simplify 3x⁵y³ ÷2y² step by step
Answer:
3/2 x^5 y
Step-by-step explanation:
3x^5y^3
----------------
2y^2
Simplify the y terms
y^3 / y^2 = y^(3-2) = y
3/2 x^5 y
Answer:
[tex] \frac{3}{2} x {}^{5} y {}^{} [/tex]
Step-by-step explanation:
it's all in the image
if 2 (3x - 4 ) =5, then x =
Answer:
2.167 (rounded to the nearest hundredths).
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, divide 2 from both sides of the equation:
(2(3x - 4))/2 = (5)/2
3x - 4 = 2.5
Next, isolate the variable, x. Add 4 to both sides of the equation:
3x - 4 (+4) = 2.5 (+4)
3x = 2.5 + 4
3x = 6.5
Then, divide 3 from both sides of the equation:
(3x)/3 = (6.5)/3
x = 6.5/3 = 2.167 (rounded).
~
Answer:
We have this equation
2*(3x-4) = 5
We can start solving the parentheses
2*(3x- 4) = 5
6x - 8 = 5
We can add 8 to both sides
6x - 8 + 8 = 5 + 8
6x = 13
And divide by 6
6x/6 = 13/6
x = 13/6
Write an expression for the sequence of operations described below.
divide s by u, add the result to t, then add v to what you have
Do not simplify any part of the expression
Step-by-step explanation:
s+u
Add t: You will need to introduce brackets
(s+u) + t
Add v: Introduce another v
((s/u) + t) + v
SCALCET8 3.9.003. Each side of a square is increasing at a rate of 4 cm/s. At what rate is the area of the square increasing when the area of the square is 9 cm2
Answer: [tex]24\ cm^2/s[/tex]
Step-by-step explanation:
Given
Each side of square is increasing at a rate of 4 cm/s
Side of a square when area is [tex]9\ cm^2[/tex]
Suppose a is side of the square
[tex]\Rightarrow a=\sqrt{9}\\\Rightarrow a=3\ cm[/tex]
Area is given by
[tex]\Rightarrow A=a^2\\\text{Differentiate area w.r.t time}\\\\\Rightarrow \dfrac{dA}{dt}=2a\dfrac{da}{dt}\\\\\Rightarrow \dfrac{dA}{dt}=2\times 3\times 4\\\\\Rightarrow \dfrac{dA}{dt}=24\ cm^2/s[/tex]
Area is increasing at a rate of [tex]24\ cm^2/s[/tex]
Answer:
24cm^2/ s
Step-by-step explanation:
What is the y-intercept of the line given by y=4x - 6
Answer:
y= -6
Step-by-step explanation:
the y-intercept is -6, which corresponds to point (0,-6)
remember that you're using the
y=mx+b format of an equation of a line where b is the y-intercept.
Also, if you make x=0, y will be -6.
Test the claim that the mean GPA of night students is larger than the mean GPA of day students at the 0.10 significance level. The null and alternative hypothesis would be: H 0 : p N ≥ p D H 1 : p N < p D H 0 : p N ≤ p D H 1 : p N > p D H 0 : p N = p D H 1 : p N ≠ p D H 0 : μ N ≤ μ D H 1 : μ N > μ D H 0 : μ N ≥ μ D H 1 : μ N < μ D H 0 : μ N = μ D H 1 : μ N ≠ μ D The test is: two-tailed right-tailed left-tailed The sample consisted of 30 night students, with a sample mean GPA of 3.34 and a standard deviation of 0.02, and 30 day students, with a sample mean GPA of 3.32 and a standard deviation of 0.08. The test statistic is: (to 2 decimals) Use the conservative degree of freedoms. The p-value is: (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
Answer:
H0 : μN ≤ μD
H1 : μN > μD
Right tailed
Test statistic = 1.33
Pvalue = 0.097
Fail to reject the Null
Step-by-step explanation:
H0 : μN ≤ μD
H1 : μN > μD
The test is right tailed ; culled from the direction of the greater than sign ">"
Night students :
n1 =30 x1= 3.34 s1 = 0.02
Day students:
n2 = 30 x2 = 3.32 s2 = 0.08
The test statistic :
(x1 - x2) / √(s1²/n1) + (s2²/n2)
T= (3.34 - 3.32) / √(0.02²/30) + (0.08²/30)
T = 0.02 / 0.0150554
Test statistic = 1.328
Using the conservative approach ;
df = Smaller of n1 - 1 or n2 - 1
df = 30 - 1 = 29
Pvalue(1.328, 29) = 0.097
At α = 0.10
Pvalue < α ; Hence, we reject H0 ; and conclude that there is significant evidence that GPA of night student is greater than GPA of day student
Jack brought a new set of golf clubs of $186.75. The original price was $249. What percent of the original price did he pay?
133.3%
33.3%
25%
75%
Answer: 75%
Step-by-step explanation:
186.75/249 =.75
.75x100
75%
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees. If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample
Answer:
19 beers must be sampled.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The population standard deviation for the temperature of beers found in Scooter's Tavern is 0.26 degrees.
This means that [tex]\sigma = 0.26[/tex]
If we want to be 90% confident that the sample mean beer temperature is within 0.1 degrees of the true mean temperature, how many beers must we sample?
This is n for which M = 0.1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.1 = 1.645\frac{0.26}{\sqrt{n}}[/tex]
[tex]0.1\sqrt{n} = 1.645*0.26[/tex]
[tex]\sqrt{n} = \frac{1.645*0.26}{0.1}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645*0.26}{0.1})^2[/tex]
[tex]n = 18.3[/tex]
Rounding up:
19 beers must be sampled.
One jar holds 20 green marbles and 4 white marbles. A second jar holds 60 black marbles and 20 white marbles. What is the probability that a white marble will be drawn from both jars?
Answer:
[tex]\sf \dfrac{1}{24}=0.0417=4.17\%\:\:(3\:s.f.)[/tex]
Step-by-step explanation:
Given information:
Contents of Jar 1:
20 green marbles4 white marblestotal marbles = 20 + 4 = 24Contents of Jar 2:
60 black marbles20 white marblestotal marbles = 60 + 20 = 80Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
Therefore:
[tex]\sf P(white\:marble\:from\:Jar\:1)=\dfrac{4}{24}=\dfrac{1}{6}[/tex]
[tex]\sf P(white\:marble\:from\:Jar\:2)=\dfrac{20}{80}=\dfrac{1}{4}[/tex]
As the events are independent (i.e. drawing a marble from one jar does not influence or affect drawing a marble from the other jar), we can use the independent probability formula:
[tex]\sf P(A\:and\:B)=P(A) \cdot P(B)[/tex]
Therefore, the probability that a white marble will be drawn from both jars is:
[tex]\sf P(white\:marble\:from\:Jar\:1)\:and\:\sf P(white\:marble\:from\:Jar\:2)=\dfrac{1}{6} \cdot \dfrac{1}{4}=\dfrac{1}{24}[/tex]
#Jar 1
Total marbles =20+4=24
P(w)
4/24=1/6#Jar 2
Total marbles=60+20=80
P(w)
20/801/4P(w in total)
1/4(1/6)1/24which of the following is the median of 19, 31, 15, 50, 20
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\text{19, 31, 15, 50, \& 20}[/tex]
[tex]\large\text{When you see or hear the word \underline{median}, think of the question}\\\large\text{asking you \bf what is the MIDDLE NUMBER.}\large\text{To find the}\\\large\text{middle number you have to put the numbers from descending}\\\large\text{(least/decreasing) or ascending (greatest/increasing) order}[/tex]
[tex]\large\text{15, 19, 20, 31, \& 20}[/tex]
[tex]\large\text{Make sure it is even on BOTH SIDES of the DATA SET}[/tex]
[tex]\large\text{It seems to be even on both sides of the number \bf 20}\large\text{ so \underline{20}}\\\large\text{can be your median/middle number in this given set}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: the median is \bf 20}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]
What is the factored form of x2 − 4x − 5?
(x + 5)(x − 1)
(x + 5)(x + 1)
(x − 5)(x − 1)
(x − 5)(x + 1)
Answer:
x2 - 4x - 5 factored form is (x - 5)(x + 1)
Answer:
(x − 5)(x + 1)
Step-by-step explanation:
The answer above is correct.
Please help
Find the value of x,
m∠5 = x-6, m∠4 = 2x+4, m∠2 = 2x-26
9514 1404 393
Answer:
x = 30 2/3
Step-by-step explanation:
Angles 4 and 5 are complementary, so we have ...
m∠4 +m∠5 = 90°
(2x +4) +(x -6) = 90
3x -2 = 90 . . . . . . . . . collect terms
3x = 92 . . . . . . . . . . add 2; next, divide by 3
x = 92/3 = 30 2/3
Combine these radicals. 8 square root 5 + 2 square root 45
Answer
14√5
Step-by-step explanation:
8√5 + 2√45
= 8√5 + 6√5
= 14√5
Hope this helps
Answer:
[tex]\boxed {\boxed {\sf 14 \sqrt{5}}}[/tex]
Step-by-step explanation:
We are asked to combine the radicals. We have the following expression:
[tex]8 \sqrt{5} + 2 \sqrt{45}[/tex]
Currently, we cannot combine these radicals. The value under the square root is not the same for both terms.
However, we can simplify the radical 2 √45 because the value under the radical is divisible by a perfect square.
45 can be divided by 9 (the perfect square) for a quotient of 5. So, we can simplify the radical using this information.
Break the radical into 2 radicals: 9 and 5.
[tex]8 \sqrt{5}+ 2 \sqrt{9}\sqrt{5}[/tex]
Notice that a perfect square is under the radical. √9 can be simplifed to 3.
[tex]8 \sqrt{5}+ 2 *3 \sqrt{5}[/tex]
Multiply 2 and 3.
[tex]8 \sqrt{3} + 6 \sqrt{5}[/tex]
Now the value under the radical is the same for both terms, and we can add the numbers in front of the radicals.
[tex]14 \sqrt{5}[/tex]
The radicals combined is equal to 14√5
Solve, then check algebraically and graphically. 9x-3=78
Answer:
[tex]9x - 3 = 78 \\ 9x - 3 + 3 = 78 + 3 \\ 9x = 81 \\ \frac{9x}{9} = \frac{81}{9} \\ x = 9[/tex]
Answer:
[tex]9x - 3 = 78 \\9 x = 78 + 3 \\ 9x = 81 \\ x = \frac{81}{9} \\ x = 9[/tex]
If f(1) =160 and f(n+1)=-2f(n),
What is f(4)?
Answer:
f(n+1=-2f(n)
f(x)=-2f(n)
f(4)
f(4)=-2f(4)
Answer:
f(4) = - 1280
Step-by-step explanation:
Using the recursive rule and f(1) = 60 , then
f(2) = - 2f(1) = - 2 × 160 = - 320
f(3) = - 2f(2) = - 2 × - 320 = 640
f(4) = - 2f(3) = - 2 × 640 = - 1280
If 89 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 48 grams
Answer:
0.6836
Step-by-step explanation:
(weight - mean weight) = 48
Variance, s² = 204,304
Sample size, n = 89
We need to obtain the Zscore :
Zscore = (X - mean) / standard Error
Zscore = (weight - mean weight ) / (s/√n)
s = √204304 = 452
The difference from the meanncoukdnbe either to the right or left :
Zscore = - 48 / (452/√89) OR 48 / (452/√89)
Zscore = - 48 / 47.911904 OR - 48 / 47.911904
Zscore = - 1.002 or 1.002
P(Z < - 1.002) = 0.1582 (using Z table)
P(Z < 1.002) = 0.8418
P(Z < 1.002) - P(Z < - 1.002)
0.8418 - 0.1582
= 0.6836
insert a digit in a place of each "..." to make numbers that are divisible by 6 if it is possible: 4...6
Answer:
1 There is no number that make it divisible by 6 with no decimals
2 1,4,7
Step-by-step explanation:
2 23718/6= 3953
23748/6= 3958
23778/6= 3963
Johnny tripled his baseball card collection. Then he added 6 more cards to the collection. Now he has 24 cards. How many cards did he start with?
9514 1404 393
Answer:
6
Step-by-step explanation:
Work backward.
If he has 24 after adding 6, he had 18 before that addition.
If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.
__
Note that this is the same process you would use if you started with an equation.
3c +6 = 24 . . . . where c is the number of cards Johnny started with
3c = 24 -6 = 18 . . . . . subtract 6 from the final number
c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value
Johnny started with 6 cards.
In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the largest circle that passes through A and G. Each of the diameters of the small circles with centers B and F equals the radius of the medium-sized circle with center D. The shaded area is what fraction of the largest circle?Single choice.
9514 1404 393
Answer:
5/8
Step-by-step explanation:
The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.
Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.
The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams
Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]
Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.
Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:
[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:
[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]
Divide both sides by 9:
[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]
By logarithm properties:
[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]
Solve for t:
[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]
So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
