Answer:
Base = 19
Height = 26
Step-by-step explanation:
Given :
Height, h = base, b + 7 feets
The area of triangle, A = 247 ft²
The area of a triangle is given by :
A = 1/2 * base * height
247 = 1/2 * b * (b + 7)
247 = 0.5 * b * (b + 7)
247 = 0.5b² + 3.5b
0.5b² + 3.5b - 247 = 0
Solving the quadratic equation ; using the quadratic equation solver, the roots are :
b = -26 or b = 19
Length of base can't be negative :
Hence,
Base, b = 19
Height, h = base + 7 = 19 + 7 = 26
An unknown radioactive material is measured to have a half life of 3 months. When the material was first found, there was 2000mg. a) Write an equation that models the mass of the material, t months. b) Use your equation to determine the mass of material in 4 year c) Calculate around how many months it will take to have 750 mg left
Answer:
OK!!.
N=N(½)ⁿ
n= Time/half life
N=Remaining Mass
N°=Initial Mass or Mass before decay.
t= time taken to decay(Its in Months in this case)
t½= Half Life of the Material. This is the time taken to decay to half its initial value.
N°= 2000mg
a).Equation that Models this is
since n=t/t½
N=N°(½)ⁿ =
N=N°(½)^t/t¹'². This should be your answer.
b). We're asked to find the remaining mass of substance in 4years.
t= 4years
Our Half life is in Months... So we gotta convert or time t from year to Months too.
4yrs === 4x12 = 48Months.
N° was given as 2000mg
N=N°(½)^t/t½
N= 2000(½)^48/3
N=2000(½)^16
Using your calc to evaluate (½)^16... Then multiply by 2000
N=0.0305mg will remain after 4years.
Or After 16Half Lives since 1 half life is 3months
c). We're looking for t this time
N=N°(½)^t/t½
Since it asked for 750mg to remain ... 750 is now our N --- Remaining Mass
750 = 2000(½)t/3
To Isolate "t" and make it the subject
750/2000 = (½)^t/3
0.375 = (½)^t/3
Taking ln(natural log) of both sides
Ln(0.375) = Ln(0.5)^t/3
From the rule of logarithm...
You can bring the power (I.e t/3) to the front
You'll have
Ln(0.375) = t/3Ln(0.5)
Dividing both sides by Ln(0.5) to isolate t
Ln(0.375)/Ln(0.5) = t/3
t/3 = 1.415
t= 3x1.415
t=4.25months.
Have a great day.
Hope this helps... I'm open to questions if you have any too.
Assume that both populations are normally distributed.
a. Test whether u1≠ u2 at the alpha=0.05 level of signifigance for the given sample data. (u= population mean, sorry couldnt insert the symbol). Determine p value. Should the null hypothesis be rejected?
b. Construct a 95% confidence interval about μ1−μ2. at the alphα=0.05 level of significance for the given sample data.
Population 1 Population 2
n 18 18
x 12.7 14.6
s 3.2 3.8
Answer:
Fail to reject the null hypothesis
[tex]CI = (-4.278, 0.478)[/tex]
Step-by-step explanation:
Given
[tex]n_1=n_2 = 18[/tex]
[tex]\bar x_1 = 12.7[/tex] [tex]\bar x_2 = 14.6[/tex]
[tex]\sigma_1 = 3.2[/tex] [tex]\sigma_2 = 3.8[/tex]
[tex]\alpha = 0.05[/tex]
Solving (a): Test the hypothesis
We have:
[tex]H_o : \mu_1 - \mu_2 = 0[/tex]
[tex]H_a : u1 - u2 \ne 0[/tex]
Calculate the pooled standard deviation
[tex]s_p = \sqrt\frac{(n_1-1)\sigma_1^2 + (n_2-1)\sigma_2^2}{n_1+n_2-2}}[/tex]
[tex]s_p = \sqrt\frac{(18-1)*3.2^2 + (18-1)*3.8^2}{18+18-2}}[/tex]
[tex]s_p = \sqrt\frac{419.56}{34}}[/tex]
[tex]s_p = \sqrt{12.34}[/tex]
[tex]s_p = 3.51[/tex]
Calculate test statistic
[tex]t = \frac{x_1 - x_2}{s_p*\sqrt{1/n_1 + 1/n_2}}[/tex]
[tex]t = \frac{12.7 - 14.6}{3.51 *\sqrt{1/18 + 1/18}}[/tex]
[tex]t = \frac{-1.9}{3.51 *\sqrt{1/9}}[/tex]
[tex]t = \frac{-1.9}{3.51 *1/3}[/tex]
[tex]t = \frac{-1.9}{1.17}[/tex]
[tex]t = -1.62[/tex]
From the t table, the p value is:
[tex]p = 0.114472[/tex]
[tex]p > \alpha[/tex]
i.e.
[tex]0.114472 > 0.05[/tex]
So, the conclusion is that: we fail to reject the null hypothesis.
Solving (b): Construct 95% degree freedom
[tex]\alpha = 0.05[/tex]
Calculate the degree of freedom
[tex]df = n_1 + n_2 - 2[/tex]
[tex]df = 18+18 - 2[/tex]
[tex]df = 34[/tex]
From the student t table, the t value is:
[tex]t = 2.032244[/tex]
The confidence interval is calculated as:
[tex]CI = (x_1 - x_2) \± s_p * t * \sqrt{1/n_1 + 1/n_2}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/18 + 1/18}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * \sqrt{1/9}[/tex]
[tex]CI = (12.7 - 14.6) \± 3.51 * 2.032244 * 1/3[/tex]
[tex]CI = -1.90 \± 2.378[/tex]
Split
[tex]CI = (-1.90 - 2.378, -1.90 + 2.378)[/tex]
[tex]CI = (-4.278, 0.478)[/tex]
Choose the expression that represents “three less than seven times a number
Answer: 3-7x
Step-by-step explanation: x represents the "a number" portion since it is a variable
To compute a student's Grade Point Average (GPA) for a term, the student's grades for each course are weighted by the number of credits for the course. Suppose a student had these grades: 3.7 in a 5 credit Math course 1.8 in a 3 credit Music course 2.8 in a 5 credit Chemistry course 2.8 in a 4 credit Journalism course What is the student's GPA for that term
Answer:
2.89, rounded to the nearest hundredth
Step-by-step explanation:
Given that GPA is weighted by credits, we must first multiply each grade by its credit amount and sum those up to weigh the credits. Then, we divide by the total amount of credits to get the GPA per credit.
So, we start with math,
3.7 *5 + 1.8 *3 + 2.8 * 5 + 2.8 * 4 = 49.1 as the total GPA weighted per credit.
Then, to find the average per credit, we divide by the total amount of credits, which is 5 + 3 + 5 + 4 = 17.
Our answer is 49.1/17 = 2.89, rounded to the nearest hundredth
A cable network offers members a Basic plan for $7.26 per month. For $3.00 more per month, the cable network offers a Standard plan, which includes HD movies. During one week, 310 new subscribers paid a total of $2580.60 for their plans. How many Basic plans and how many Standard plans were purchased?
___Basic plans and ___ Standard plans were purchased
Answer:
110 basic plans and 200 standard plans were purchased.
Step-by-step explanation:
This question is solved using a system of equations.
I am going to say that:
x is the number of basic plans.
y is the number of standard plans.
310 new subscribers
This means that [tex]x + y = 310[/tex], and so, [tex]y = 310 - x[/tex]
A cable network offers members a Basic plan for $7.26 per month. For $3.00 more per month. Total paid of $2580.60.
This means that:
[tex]7.26x + 10.26y = 2580.6[/tex]
Since [tex]y = 310 - x[/tex]
[tex]7.26x + 10.26(310 - x) = 2580.6[/tex]
[tex]7.26x + 3180.6 - 10.26x = 2850.6[/tex]
[tex]3x = 330[/tex]
[tex]x = \frac{330}{3}[/tex]
[tex]x = 110[/tex]
Then
[tex]y = 310 - x = 310 - 110 = 200[/tex]
110 basic plans and 200 standard plans were purchased.
Point A is located at (-23, -2). Point B is located at (-23,23). What is the distance
between point A and point B?
Answer:
25
Step-by-step explanation:
Since the x values are the same
the distaance is simply the difference in the y values
23 - (-2) = 25
Which side lengths form a right triangle?
Answer: A and C
Step-by-step explanation: To see if it can be the side lengths of a right triangle we have to use the Pythagoras Theorem which is [tex]a^2 +b^2 = c^2\\[/tex]
C is always the largest length. Now we can sub the numbers in
[tex]5^2+\sqrt{6} ^2=\sqrt{31} ^2[/tex]
The squares and the square roots cancel each other out so we end up with
25+6=31
this is true so those are possible sides for a right triangle
Now for b:
[tex]\sqrt{5}^2 + \sqrt{5}^2 =50^2[/tex]
Again the squares and square roots cancel each other out
5+5=2500
This isn't true so it isn't the possible sides for a right triangle
Finally option C:
[tex]9^2+12^2=15^2[/tex]
81+144=225
225=225
This is true so it can be the side lengths that form a right triangle
A manufacturer claims that the mean lifetime,u , of its light bulbs is 51 months. The standard deviation of these lifetimes is 7 months. Sixty bulbs are selected at random, and their mean lifetime is found to be 53 months. Can we conclude, at the 0.1 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 51 months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)
the null hypothesis:
The alternative hypotehsis:
The type of test statistic (choose Z, t, Chi-square, or F)
The value of the test statistic (round to at least three decimal places:
Can we conclude that the mean lifetime of the bulbs made by this manufacture differ from 51 months?
Answer:
We reject H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month
Step-by-step explanation:
Manufacturing process under control must produce items that follow a normal distribution.
Manufacturer information:
μ = 51 months mean lifetime
σ = 7 months standard deviation
Sample Information:
x = 51 months
n = 60
Confidence Interval = 90 %
Then significance level α = 10 % α = 0.1 α/2 = 0,05
Since it is a manufacturing process the distribution is a normal distribution, and with n = 60 we should use a Z test on two tails.
Then from z- table z(c) for α = 0,05 is z(c) = 1.64
Hypothesis Test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate z statistics z(s)
z(s) = ( x - μ ) / σ /√n
z(s) = ( 53 - 51 ) / 7 /√60
z(s) = 2 * 7.746 / 7
z(s) = 2.213
Comparing z(s) and z(c)
z(s) > z(c) then z(s) is in the rejection region
We reject H₀, and conclude thet the mean lifetime of the bulbs differ from 51 month
Determine the value of y, if x is 1.
y = |x| +7
Help plsss
Answer:
8
Step-by-step explanation:
The absolute value (the lines both sides of x) simply mean the number in between is positive. Since 1 is already positive, just add it to 7!
I need help comment please
Answer:
41
Step-by-step explanation:
The angle were looking for is on the other side of the figure. It is also on the inside so we would divide 82 in half giving us 41.
Which of the following can be used to describe the following:
-20, – 17, – 14, – 11, ...
Geometric Series
Arithmetic Series
Geometric Sequence
Arithmetic Sequence
Answer: Arithmetic Sequence
Step-by-step explanation: It has a common difference of +3 at a constant rate
Based on the family the graph below belongs to, which equation could represent the graph?
where is the graph????
Step-by-step explanation:
The ration of men to women in a community is 25:12.If there are 240 women..(i) how many men are in the community?..(ii) What is the total number of people in the community?
Answer:
500 men
740 total people in community
Step-by-step explanation:
25:12 ratio
When using a ratio both sides should go up the same amount of times to get the number you are trying to reach. Since the women's amount was 240 we need to find the times it took to get from 12 to 240. You take the 240 and divide by 12. We find that the 12 was multiplied 20 times to get to 240. So you turn to the men's side and find the amount using the 25. We use X to signify the amount we are trying to find and the amount of times that 25 goes into X will be 20 to keep the ratio of men to women as specified. When solving for X you multiply both sides of the equation by 25 to find the amount. X will equal 500 (=20*25).
Then 240 women plus 500 men equals to 740 people in the community.
Women
240/12 = 20
Men
X/25=20
X=20*25
X=500
240 women+500 men=740 people
James made 20 basketball shots in 15 minutes.
What is the number of basketball shots James can make in 45 minutes?
А
60
B
45
С
34
D 7
At the beginning of the year, the odometer on an SUV read 37,532 miles. At the end
of the year, it read 52,412 miles. If the car averaged 24 miles per gallon, how many
gallons of gasoline did it use during the year?
He used 620 gallons of gas
The slope-intercept form of the equation of a line that passes through point (–3, 8) is y = –y minus 3 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 8 right-parenthesis.x + 6. What is the point-slope form of the equation for this line?
y – 3 = –StartFraction 8 Over 5 EndFraction x plus StartFraction 2 Over 3 EndFraction equals StartFraction one-half EndFraction minus StartFraction 1 Over 5 EndFraction x.(x + 8)
y + 3 = –y plus 3 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x minus 8 right-parenthesis.(x – 8)
y + 8 = –y plus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x minus 3 right-parenthesis.(x – 3)
y – 8 = –y minus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)
y – 8 = –y minus 8 equals negative StartFraction 2 Over 3 EndFraction left-parenthesis x plus 3 right-parenthesis.(x + 3)
Step-by-step explanation:
PLZ HELP ME!!!!
how much water must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solultion?
Answer:
16 ounces.
Step-by-step explanation:
An 8% solution is 2 times stronger than a 4% solution.
So in the 8% solution we will have 1/2 of the volume as a 4% , so 1/2 * 32
= 16 ounces of water must be evaporated.
The number 16 ounces of water must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution.
What is a linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
To find the amount of water that must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution:
0.96(32) - x = 0.92(32 - x)
30.72 - x = 29.44 - 0.92x
x - 0.92x = 30.72 - 29.44
0.08x = 1.28
x = 16
Therefore, 16 ounces must be evaporated.
To learn more about the linear equation;
https://brainly.com/question/29739212
#SPJ2
tammy buys candy that cost 5 dollars per pound. she will spend more than 40 dollars on candy. what are the possible numbers of pounds she will buy
Answer:
Step-by-step explanation:
x = number of pounds
5x<30
x<30/5
so she can buy X<6 pounds
If y = 8 cm, what is the area of the blue section of this shape?
Answer:
56 cm squared
Step-by-step explanation:
First things first: Cop one triangle off the rectangle, and attach it to the other one, so the shape looks like a L
Now I can actually solve this:
The left side is 8 cm (because y = 8 cm)
The top is 10 cm
The middle is 6 cm
The inside left is 3 cm
And the very bottom is 2 cm
First, we'll solve for the newly constructed rectangle: 3 x 2. That equals 6.
Next, solve for the longer rectangle: 10 x 5. That's 50.
Now, add the two areas, and we get 56. So the area of the whole thing is 56 cm squared.
(Please keep in mind that I could be wrong, so double check it for me, thanks!)
Write the simplified expression that represents the perimeter of the triangle below.
X - 3
4x + 4
2x + 1
Show Work
Answer:
Just plus everything together
X-3+4X+4+2X+1
Step-by-step explanation:
expand 3e(e+4)
Hhhhhhh
Answer:
[tex]3e^{2} + 12e[/tex]
Step-by-step explanation:
[tex]3ee+3e4[/tex]
[tex]3ee+3 * 4e[/tex]
[tex]3e^{2} + 12e\\[/tex]
[tex]3 \: {e}^{2} + 12 \: e[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]3 \: e \: ( \: e + 4 \: ) \\ \\ = 3 \: e \times \: e + 3 \: e \times 4 \\ \\ = 3 \: {e}^{2} + 12 \: e[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]
It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is −4h.
Explain what the inequality −4h ≤-14 represents.
9514 1404 393
Explanation:
-4h ≤ -14
in this context is a relation that would tell how many hours it would take for the temperature to be at or below -14 degrees.
To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one, two, or three steps. The second procedure requires either one or two steps. Answer the first and second questions using this information.List the experimental outcomes associated with performing the blood analysis. (Hint: The first procedure has three possible outcomes (steps needed), the second procedure has two possible outcomes (steps needed)).
Answer:
____ 1 _____ 2 ____ 3
1 __ 1, 1 ____ 1, 2 __ 1, 3
2 __2, 1 ____2, 2 __ 2, 3
Step-by-step explanation:
Given that :
Steps required for procedure One : Either 1, 2, or 3
Steps required for procedure two : Either 1 or 2
The first procedure has 3 possible steps
The second procedure has 2 possible steps
. The experimental outcome associated with performing the blood analysis is displayed in the table below :
____ 1 _____ 2 ____ 3
1 __ 1, 1 ____ 1, 2 __ 1, 3
2 __2, 1 ____2, 2 __ 2, 3
below is a table showing the investment and the investment period of
Answer:
hey. pls complete your question.
2x + 3y = 34
slove for y
Answer:
34/3, -2/3
Step-by-step explanation:
See image below:)
Step-by-step explanation:
2x + 3y = 34
3y = 34 - 2x
y = 3x - 2x/3
Help please asp. !!!
Answer:
12.86 cm³ of water is saved
Step-by-step explanation:
✔️Since width of new ice ball must be the same as the length of original cube, therefore, diameter of the ice ball = 3 cm
Radius of ice ball = ½(3) = 1.5 cm
Volume of the new sphere ice ball = ⁴/3πr³
Substitute
Volume of new sphere ice ball = ⁴/3 × π × 1.5³ = 14.14 cm³
✔️To find out how much water would be saved using the new sphere ice ball, let's find the volume of the cube then find the difference of both.
Volume of original ice cube with length 3 cm:
Volume of cube = s³
s = 3 cm
Volume of cube = 3³ = 27 cm³
Volume of water saved = 27 cm³ - 14.14 cm³
= 12.86 cm³
fourier { 2 if -2 < x < 0 ; 0 if 0 < x < 2}
The Fourier series expansion of f(x) is
[tex]\displaystyle\frac{a_0}2+\displaystyle\sum_{n=1}^\infty \left(a_n\cos\left(\frac{2\pi nx}P\right)+b_n\sin\left(\frac{2\pi nx}P\right)\right)[/tex]
where P = 4 is the period of f(x), and the coefficients are
[tex]a_0=\displaystyle\frac2P\int_{-2}^2f(x)\,\mathrm dx=2[/tex]
[tex]a_n=\displaystyle\frac2P\int_{-2}^2f(x)\cos\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2\sin(n\pi)}{n\pi}=0[/tex]
[tex]b_n=\displaystyle\frac2P\int_{-2}^2f(x)\sin\left(\frac{2\pi nx}P\right)\,\mathrm dx=\frac{2(\cos(n\pi)-1)}{n\pi}=\begin{cases}0&\text{for }n=2k\\-\frac4{(2k-1)\pi}&\text{for }n=2k-1\end{cases}[/tex]
(where k is a positive integer)
The series for f(x) reduces to
[tex]\displaystyle f(x)=1-\displaystyle\sum_{k=1}^\infty \frac4{(2k-1)\pi}\sin\left(\frac{\pi(2k-1)x}2\right)[/tex]
(I've attached a plot showing the original function in blue and the Fourier expansion with k = 10 terms)
Help please, it’s for average rate of change.
Answer in fraction form = -3/2
Answer in decimal form = -1.5
=========================================
Work Shown:
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(1)-g(-3)}{1-(-3)}\\\\m = \frac{0-6}{1-(-3)}\\\\m = \frac{0-6}{1+3}\\\\m = \frac{-6}{4}\\\\m = -\frac{3}{2}\\\\m = -1.5\\\\[/tex]
Effectively, we're finding the slope through the points (-3, 6) and (1, 0)
The g(b)-g(a) represents how y changes when going from x = a to x = b.
Dhani has 4 cards numbered 1 through 4. He removes 2 cards at random and adds their values.
What is the probability that the sum is less than or equal to 5?
7/12
2/3
3/5
3/4
Answer:
[tex]2/3[/tex]
Step-by-step explanation:
The total number of sums (not distinct) is [tex]4\cdot 3=12[/tex], because we're removing without replacement.
Count the sums that fit the stipulation (sum [tex]\leq[/tex] 5):
[tex]1,2,\\2,1\\1,3\\3,1\\1, 4\\4, 1\\2, 3, \\3,2[/tex]
There are 8 sums that work. Therefore, the desired answer is [tex]\frac{8}{12}=\boxed{\frac{2}{3}}[/tex]
Evaluate:
Σ21(2n + 8) = [?]
HELP ME PLS
Answer:
42n+108
Step-by-step explanation:
21(2n+8)
42n+108