The base of the triangular garden is calculated as 40 ft
The given parameters include:
the area of the triangular garden, A₁ = 200 ft²let the height of the triangular garden = hthe base of the triangular garden, b = 30 ft + hThe area of a triangle is given as;
[tex]Area \ = \frac{1}{2} \times \ base \times \ height\\\\A = \frac{1}{2} bh\\\\2A = bh\\\\b = \frac{2A}{h} \\\\Recall, \ b= 30 + h\ \ \ and \ A = 200\\\\30+ h = \frac{2(200)}{h} \\\\30 \ + h = \frac{400}{h} \\\\30h + h^2 = 400\\\\h^2 + 30h - 400= 0\\\\Factorize \ the \ above \ expression\\\\h^2 + 40h- 10h- 400 = 0\\\\h(h + 40) - 10(h + 40) = 0\\\\(h- 10)(h+40)= 0\\\\h = 10 \ \ or \ \ -40\\\\since\ the \ height \ can't \ b e\ negative\\\\h = 10 \ ft\\\\[/tex]
Now solve for 'b' = 30 ft + 10 ft = 40 ft
Therefore, the base of the garden is 40 ft
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Need help please ^-^
Factored form: (x + 1/5)(x + 1/4)
Foil: x^2 + 1/4x + 1/5x + 1/20
Simplify: x^2 + 9/20x + 1/20
Hope this helps!
The starting line up for a basketball team is to consist of two forwards and three guards. Two brothers are on the team. Matthew is a forward and Tony a guard. There are four forwards and six guards from which to choose the line up. If the starting players are chosen at random, what is the probability that the two brothers will end up in the starting line up
Answer:
0.25 = 25% probability that the two brothers will end up in the starting line up
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the players are chosen is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Desired outcomes:
Matthew plus another forward from a set of 3.
Tony plus another two guards from a set of 5.
So
[tex]D = C_{3,1}C_{5,2} = \frac{3!}{1!2!} \times \frac{5!}{2!3!} = 3*10 = 30[/tex]
Total outcomes:
Two forwards from a set of 4.
Three guards from a set of 6.
So
[tex]T = C_{4,2}C_{6,3} = \frac{4!}{2!2!} \times \frac{6!}{3!3!} = 6*20 = 120[/tex]
What is the probability that the two brothers will end up in the starting line up?
[tex]p = \frac{D}{T} = \frac{30}{120} = 0.25[/tex]
0.25 = 25% probability that the two brothers will end up in the starting line up
Solve For X: 12 * X+3=51
Answer:
x=4
Step-by-step explanation:
12 * X+3=51
Subtract 3 from each side
12x +3-3 = 51-3
12x = 48
Divide by 12
12x/12 = 48/12
x = 4
The manager of a juice bottling factory is considering installing a new juice bottling machine which she hopes will reduce the amount of variation in the volumes of juice dispensed into 8-fluid-ounce bottles. Random samples of 10 bottles filled by the old machine and 9 bottles filled by the new machine yielded the following volumes of juice (in fluid ounces).
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
Required:
Use a 0.05 significance level to test the claim that the volumes of juice filled by the old machine vary more than the volumes of juice filled by the new machine
Answer:
Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine
Step-by-step explanation:
Given the data:
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
To test if volume filled by old machine varies more than volume filled by new machine :
Hypothesis :
H0 : s1² = s2²
H1 : s1² > s2²
Using calculator :
Sample size, n and variance of each machine is :
Old machine :
s1² = 0.37889
n = 10
New machine :
s2² = 0.006111
n = 9
Using the Ftest :
Ftest statistic = larger sample variance / smaller sample variance
Ftest statistic = 0.37889 / 0.006111
Ftest statistic = 62.001
Decision region :
Reject H0 ; If Test statistic > Critical value
The FCritical value at 0.05
DFnumerator = 10 - 1 = 9
DFdenominator = 9 - 1 = 8
Fcritical(0.05, 9, 8) = 3.388
Since 62 > 3.388 ; Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine
In the given figure L1and L2 are two parallel sides . if the area of the rectangle PQRS is 60cm^2 then what is the area of the parallelogram PQRS.
Answer:
Step-by-step explanation:
Believe it or not, the two areas are the same.
The base of the rectangle is PQ
The height of the rectangle is PS
Now look at the parallelogram.
The base is PQ
The height is PS
The area has to be the same in both cases. There is no other way to interpret what is happening.
Frances bought a new dress that was discounted by 24%. she used the following expressions to find the price of the dress after the discount was applied
Answer:
[tex]0.76d[/tex]
Step-by-step explanation:
Given
[tex]Formula = d - (0.24)d[/tex]
Required
Equivalent expression
We have:
[tex]Formula = d - (0.24)d[/tex]
Open bracket
[tex]Formula = d - 0.24d[/tex]
[tex]Formula = 0.76d[/tex]
Out of a total of 10 college textbooks estimate the standard deviation of their ages if the oldest textbook is known to be 7.9 years old and the newest textbook is 1.3 years old.
Answer:
Given that the maximum age of the textbook is 7.9 years and the minimum age of the textbook is 1.3 years.
Using the range rule, the standard deviation is estimated as,
S≈maximum−minimum/4
=7.9−1.3/4
=1.65
The required value of the approximate standard deviation is 1.65.
The standard deviation of the data is 1.65.
What is Standard Deviation?Standard deviation is the measure of the deviation of the data from the mean.
The total college textbooks is 10
The oldest book is 7.9 years old
The newest book is 1.3 years old
The standard deviation of range is equal to one fourth of the difference of maximum to minimum.
The standard deviation = ( 7.9 - 1.3 ) /4 = 1.65
To know more about Standard Deviation
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g(x) = f(x+1) using f(x)= x to the power of 2
Answer:
g(x) = x² + 2x + 1
General Formulas and Concepts:
Algebra I
Terms/Coefficients
ExpandingFunctions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
g(x) = f(x + 1)
f(x) = x²
Step 2: Find
Substitute in x [Function f(x)]: f(x + 1) = (x + 1)²Expand: f(x + 1) = x² + 2x + 1Redefine: g(x) = x² + 2x + 1Which expression is equivalent to the given expression?
Answer:
Option C, a³b
Step-by-step explanation:
(ab²)³/b⁵
= a³b⁶/b⁵
= a³b
Answered by GAUTHMATH
Find the value of x.
Answer:
x=3
Step-by-step explanation:
Find the radius and use Pythagoras on the right side
Write the point-slope form of an equation of the line through the points (-4, 7) and (5, 3).
Answer:
[tex]y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)[/tex]
OR
[tex]y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point that falls on the line
1) Determine the slope (m)
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-4, 7) and (5, 3):
[tex]m=\frac{\displaystyle 3-7}{\displaystyle 5-(-4)}\\\\m=\frac{\displaystyle 3-7}{\displaystyle 5+4}\\\\m=\frac{\displaystyle -4}{\displaystyle 9}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 4}{\displaystyle 9}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex] as [tex]m[/tex]:
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
2) Plug a point into [tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
Because we're given two points, there are two ways we can write this equation:
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x-(-4))\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)[/tex]
OR
[tex]y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)[/tex]
I hope this helps!
Assume the sample is a random sample from a distribution that is reasonably normally distributed and we are doing inference for a sample mean
(a) Find endpoints of a t-distribution with 5 % beyond them in each tail if the sample has size n = 12.
(b) Find endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20.
Answer:
a) Hence the endpoints of a t-distribution with 5% beyond them in each tail if the sample has size n=12 is ± 1.796.
b) Hence the endpoints of a t-distribution with 1% beyond them in each tail if the sample has size n=20 is ± 2.539.
Step-by-step explanation:
Here the answer is given as follows,
Can someone help me find the answer?
Answer: B. This function has no intercept. I think B is the correct answer.
Write 6/7 as a decimal rounded to the nearest hundredth
Answer:
0.01
Step-by-step explanation:
6/7% = 6÷7÷100 = 0.0085714286 round to the nearest hundredth = 0.01
I need help with that, if you can, plz. I ty it I think is a not sure
Answer:
-5≤x <1
Step-by-step explanation:
sqrt( x+5) / sqrt(1-x)
The numerator must be greater than zero since it is a square root
sqrt(x+5) ≥0
Square each side
x+5≥0
x≥-5
The denominator must be greater than zero (the denominator cannot be zero)
sqrt(1-x)> 0
Square each side
1-x > 0
1>x
Putting these together
-5≤x <1
According to Fidelity Investment Vision Magazine, the average weekly allowance of children varies directly as their grade level. In a recent year, the average allowance of a 9th-grade student was 9.66 dollars per week. What was the average weekly allowance of a 5 th-grade student?
The average weekly allowance of a 5th grade student as calculated using direct variation with the information provided by Fidelity Investment Vision Magazine is 5.367 dollars per week.
The question given is a direct variation problem:
Let:
• Average weekly allowance = [tex]a[/tex]
• Grade level = [tex]g[/tex]
If Average weekly allowance varies directly as grade level , then , then the direct variation between the variables can be expressed as :
[tex]a = k * g[/tex]
Where , [tex]k[/tex] = constant of proportionality
We can obtain the value of k from the given values of a and g
[tex]9.66 = k * 9\\9.66 = 9k\\k = 9.66/9[/tex]
Our equation becomes:
[tex]a = (9.66/9) * g[/tex]
[tex]a = (9.66/9) * 5\\a = 5.367[/tex] (rounded to 3 decimal places)
Hence, using proportional relationship, the average weekly allowance for a 5th grade student is [tex]5.367[/tex] per week
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The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard deviation 7.1%. Using the normalcdf function on your graphing calculator, what percentage of students would score 70 or better on this entrance exam?
A. 28.4%
B. 18.9%
C. 24.1%
D. 22.3%
Answer:
The correct answer is - C. 24.1%
Step-by-step explanation:
Given:
mean μ = 65%
standard deviation δ = 7.1 %
solution:
Prob( X>70) = 1 - Prob(x<70)
= P (x-μ/δ ≥ 70 -65/7.1)
= 1 - Prob( (70-65)/7.1)
= 1 - Prob ( z < 0.7042553)
= 0.24065
the percentage of students scoring 70 or more in the exam
= 24.065*100
= 24.1%
If p is true and ~ q is false, then p ~ q is _____ false.
a. sometimes
b. always
c. never
a) __m=10km 25m =___km
b) __m=__km__m=1.5 km
Example :
a) 7250m= 7km 250m = 7.250km
Please help me
Answer:
a) 10,025 m = 10km 25m = 10.025 km
b) 1,500 m = 1 km 500 m = 1.5 km
Answer:
a) 10025m = 10km 25m = 10.025km
b) 1500m = 1km 500m = 1.5km
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit conversion.
Unit conversion is the conversion between different units of measurement for the same quantity.
1 km = 1000 m
Solve:
a)
10km 25m = 10×1000 + 25 = 10025 m10km 25m = 10 + 25/1000 = 10.025 kmb)
1.5km = 1 + 0.5 × 1000 = 1km 500m1.5km = 1.5 × 1000 = 1500mHope this helps!! :)
Please let me know if you have any questions
If you were to place $2,500 in a savings account that pays 3% interest
compounded continuously, how much money will you have after 5 years?
Assume you make no other deposits or withdrawals.
Answer:
$2904.59
Step by Step Explanation:
Find the missing numerator: 3 1/3 = x/6
[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]
[tex]\tt3 \frac{1}{3} = \frac{x}{6} \\ = \tt \frac{10}{3} = \frac{x}{6} \\ = \tt \frac{x}{6} = \frac{10}{3} \\ = \tt6 \frac{x}{6} = 6( \frac{10}{3} ) \\ = \tt\large\boxed{\tt{\color{pink}{x = 20}}}[/tex]
[tex]\color{pink}{==========================}[/tex]
#CarryOnLearning
I need answering ASAP please
Answer:
The choose (D) 1/3
I hope I helped you^_^
The lengths of the parallel sides of
a trapezium are 12cm and 26cm
If Its area is 228cm square Find the
perpendicular distance between the
Parallel sides
Answer:
12 cm
Step-by-step explanation:
12+26/2 ×x =228
19x =228
X=12cm
PLEASE HELP!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answer:
y = 4x - 1.5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x - 1.5
Valerie set out to bicycle from TBLS to the beach, a distance of 10 miles. After going a short while at 15 miles per hour, the bike developed a flat tire, and the trip had to be given up. The walk back to TBLS was made at a dejected 3 miles per hour. The whole episode took 48 minutes. How many miles from TBLS did the flat occur
Answer:
I think it is 3 miles becos the bicycle broke at 15miles per hour and the walk from the current place to the TBLS is 3 miles per hour
An F test for the two coefficients of promotional expenditures and district potential is performed. The hypotheses are H0: 1 = 4 = 0 versus Ha: at least one of the j is not 0. The F statistic for this test is 1.482 with 2 and 21 degrees of freedom. What can we say about the P-value for this test?
Answer:
Pvalue > 0.10
Step-by-step explanation:
Given the hypothesis :
H0 : β1 = β4 = 0
H1 : Atleast one of βj is not 0
F statistic = 1.482 ;
Degree of freedom = 2 and 21 ;
DFnumerator = 2
DFdenominator = 21
Using the Pvalue calculator from Fstatistic ;
Pvalue(1.482, 2, 21) = 0.24999 = 0.25
Hence, Pvalue for the test is 0.25
Pvalue > 0.10
Select the expression that has a value of 13.
9 + 3 x (2 ÷ 3) + 6
(9 + 3) x 2 ÷ 3 + 6
9 − (3 x 2) ÷ 3 + 6
(9 + 3 x 2) ÷ 3 + 6
Answer:
9 − (3 x 2) ÷ 3 + 6 is the answer
PLZ ANSWER QUESTION IN PICTURE
Answer:
X-int = -5 and y-int = 6
Step-by-step explanation:
1.2x+6 = 0
1.2x= -6
X = -6/1.2
X = -5
Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
What is the value of the capacitance of a capacitor that stores 40
μ
C on each plate, when a potential difference of 10 V is applied to it?
We know
[tex]\boxed{\sf Q=CV}[/tex]
[tex]\\ \large\sf\longmapsto C=\dfrac{Q}{V}[/tex]
[tex]\\ \large\sf\longmapsto C=\dfrac{40}{10}[/tex]
[tex]\\ \large\sf\longmapsto C=4\mu F[/tex]
