Hey there!
A right pyramid with a square base just means that it isn't slanted all funny. If you create a triangle with a point on one of the edges of the base, the center of the base, and the top of the pyramid, it would be a right triangle.
To find the volume of a right pyramid, you just take the base area, multiply it by the height, and then divide by three.
However, we are looking for the height. We have been given, so we will just go backwards.
252×3=756 (multiply instead of divide)
6×6=36 (base is a square, so you just square 6. This is our base area)
756/36=21
So, the vertical height of the pyramid is 21 cubic centimeters.
Have a wonderful day! :D
A town recently dismissed 10 employees in order to meet their new budget reductions. The town had 7 employees over 50 years of age and 18 under 50. If the dismissed employees were selected at random, what is the probability that exactly 5 employees were over 50
Answer:
0.055 = 5.5% probability that exactly 5 employees were over 50.
Step-by-step explanation:
The employees are dismissed from the sample without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
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]
In this question:
Total of 7 + 18 = 25 employees, which means that [tex]N = 25[/tex]
7 over 50, which means that [tex]k = 7[/tex]
10 were dismissed, which means that [tex]n = 10[/tex]
What is the probability that exactly 5 employees were over 50?
This is P(X = 5). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 5) = h(5,25,10,7) = \frac{C_{7,5}*C_{18,5}}{C_{25,10}} = 0.055[/tex]
0.055 = 5.5% probability that exactly 5 employees were over 50.
PLEASE HELP AND BE CORRECT BEFORE ANSWERING PLEASE AND THANK YOU
9514 1404 393
Answer:
6 units
Step-by-step explanation:
The dilation factor is 2, so the length of A'B' will be 2 times the length of AB.
AB can be seen to be 3 units, so A'B' will be 2×3 = 6 units.
9. Which is a true statement about the denominator in a fraction?
(Select one answer)
It is always a negative number
It cannot be 0
It has to be an even number
It is always smaller than the numerator
Answer:
It cannot be 0
Step-by-step explanation:
it can also be positive number :2/4
it can be odd number too:3/9
it is bigger than numerator bcoz we have to divide it for numerator
So, 0 number cannot be put as denominator in fraction is true statement
What is the value of cot ø= 2/3 what is the value of csc ø
Answer:
Step-by-step explanation:
cotθ = cosθ/sinθ = 2/3
sinθ = 3/√(2²+3²) = 3/√13
cscθ = 1/sinθ = √13/3
1. In 2020, the populations of City A and City B were equal. From 2015 to 2020, the population of City A increased by 20% and the population of City B decreased by 10%. If the population of City A was 120,000 in 2015, what is the population of City B in 2015?
2. A chef is preparing a sauce for a steak she offers as a key dish in her menu. To prepare the sauce she needs to prepare a mix with 40% butter, with the rest being egg yolk. In the kitchen right now, she only has a sauce that has 20% butter (rest is egg yolk) and a sauce that has 50% butter (rest is egg yolk) in stock. In what ratio should she mix the 20% sauce with the 50% sauce in order to obtain the 40% sauce that she needs to prepare her famous recipe?
3. A book was on sale for 30% off its original price. If the sale price of the book was $28, what was the original price of the book? (Assuming there is no sales tax)
4. At a retail store, they needed to do surveys of 32 stores which equals 40% of all their stores. How many stores does the retailer have in total?*
Answer:
180000 people
1 : 2
$40
80 stores
Step-by-step explanation:
1.)
Population in 2020 are equal : Let population =
City A increased by 20% From 120,000 in 2015
(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000
Hence, city A = 144,000.
Since, city A and B have equal population ; city B also has a population of 144000 in 2020.
Let population in 2015 = x
(1 - 0.2) * x = 144000
0.8x = 144000
x = 144000/0.8
x = 180,000
2.)
Let proportion of 20% butter = x and proportion of 50% butter = 1 - x
0.2x + 0.5(1 - x) = 0.4
0.2x + 0.5 - 0.5x = 0.4
-0.3x + 0.5 = 0.4
-0.3x = 0.4 - 0.5
-0.3x = - 0.1
x = 0.1/0.3
x = 0.3333
(1-x) = 1 - 0.33333 = 0.6666%
0.3333% of 20% butter
0.6666% of 50% butter
Hence ;
0.3333 : 0.6666
1 : 2
3.)
Let original price of book = x
Discount on sale = 30%
Sale price = $28
Sale price = original price * (1 - discount)
$28 = (1 - 0.3) * x
$28 = 0.7x
x = $28/0.7
x = $40
4.)
Let total number of stores = x
Store surveys needed = 32
40% of total stores = 32 stores
0.4x = 32
x = 32 / 0.4
x = 80
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
Which equation could represent a linear combination of the systems?
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Answer:
(b) 0 = -78
Step-by-step explanation:
Subtracting 6 times the first equation from the second will give ...
(4x +15y) -6(2/3x +5/2y) = (12) -6(15)
0 = -78
Answer:
the answer is b
Step-by-step explanation:
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week. a. Give a 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week. b. In the general population, 30% have 5 or more servings of soft drinks a week. Is there evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population
Answer:
a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Step-by-step explanation:
Question a:
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].
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.
This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]
The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
Question b:
30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
a.
What is 46.7% of
4/5?
Answer:
0.3736
Step-by-step explanation:
46.7 percent of [tex]\frac{4}{5}[/tex] is 0.3736.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.What is a fraction?A number is stated as a quotient in mathematics when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.Solution -To find 46.7% of [tex]\frac{4}{5}[/tex].
So,
[tex]\frac{46.7}{100}[/tex] × [tex]\frac{4}{5}[/tex]
[tex]\frac{0.467}{100}[/tex] × [tex]\frac{4}{5}[/tex]
⇒ [tex]0.3736[/tex]
Therefore, 46.7% of [tex]\frac{4}{5}[/tex] is 0.3736.
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❤✔
PLEASE HELP ME MAKE SURE YOUR ANSWER IS RIGHT BEFORE ANSWERING
Answer:
Always. Always.
Step-by-step explanation:
All circles conform to the same equations such as using pie to calculate circumference. Unlike a rectangle, for example, all ratios used in a circle are the same.
Riley wants to buy a car and has a choice between two different banks. One bank is offering a simple interest rate of 4.5% and the other bank is offering a rate of 4.5% compounded annually. Which is the better deal?
Which equation represents the parabola with focus (8, 4) and vertex (8, 2)
Answer:
Step-by-step explanation:
The focus lies above the vertex, so the parabola opens upwards.
A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first term (ii) 6th term of the sequence
Answer:
Step-by-step explanation:
r is the common ratio.
Third term minus first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
Fourth term minus second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
:::::
r²-1 = 48/a₁
a₁ = 6
:::::
a₆ = a₁r⁵ = 1458
(i) The common ratio for the given condition is 3.
ii) The first term of the sequence is 6.
iii) The 6th term of the sequence is 1458.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that a is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.
As the third term minus the first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
The fourth term minus the second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
r²-1 = 48/a₁
a₁ = 6
a₆ = a₁r⁵ = 1458
Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence is 1458.
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Find the equation of line b in slope-intercept form. Line a is parallel to line b. Line a passes through the points (1,8) and (2,-1), line b passes through the point (4,13)
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Answer:
y = -9x +49
Step-by-step explanation:
The slope of line b is the same as the slope of line a. That can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-1 -8)/(2 -1) = -9
The y-intercept can be found from the given point using the formula ...
b = y - mx
b = 13 -(-9)(4) = 13 +36 = 49
Then the slope-intercept equation of line b is ...
y = -9x +49
(12 1/3 * 2) + (10 3/4 * 2)
Answer:
[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]
Any help would be very appreciated
Answer:
21
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = x / 7 sqrt(3)
7 sqrt(3) tan 60 = x
7 sqrt(3) sqrt(3) = x
7*3 = x
21 = x
Peter, Jan, and Maxim are classmates. Their total score for the last test was 269. Peter's score was more than the sum of Jan's and Maxim's scores. What could be Peter's least possible score?
Answer:
135
Step-by-step explanation:
Given that :
Total score obtained by Peter, Jan and Maxim = 269
Let :
Peter's score = x
Jan's score = y
Maxim's score = z
x + y + z = 269
x > (y + z)
For x to be greater Than y + z ;
Then x > (269 / 2) ; x > 134.5
The least possible x score is 135
Hence, Peter's least possible score is 135.
A satellite orbits earth at a speed of 22100 feet per second (ft/s). Use the following facts to convert this speed to miles per hour (mph). 1 mile = 5280 ft 1 min = 60 sec 1 hour = 60 min
15,068 mi/hr
Step-by-step explanation:
[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]
[tex]=15,068\:\text{mi/hr}[/tex]
The speed of 22100 feet per second will be 15068.18 miles per hour.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.
Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,
22100 ft /s = ( 22100 x 3600 ) / 5280
22100 ft/s = 79560000 / 5280
22100 ft/s = 15068.18 miles per hour
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Find the slope, if it exists, of the line containing the points (10,-3) and (10,-8).
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
m=
Answer:
The slope is undefined.
Step-by-step explanation:
The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.
What is the index of the radical below?
√10
A. 5
B. 9
C. 2
D. 10
Does the point (0, 0) satisfy the equation y = x2?
Answer:
The point is a solution
Step-by-step explanation:
y = x^2
Substitute the point into the equation and see if it is true
0 = 0^2
0=0
True
Simplify to the extent possible:
(logx16)(log2 x)
Answer:
Step-by-step explanation:
Use the change-of-base rule.
Find the interest on the loan using the Banker's rule. P= $8550. r=8.8%, t= 105 days The interest on the loan using the Banker's rule is $
In this problem, y = 1/(1 + c1e−x) is a one-parameter family of solutions of the first-order DE y' = y − y2. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(0)=-1/3
If y (0) = -1/3, then
-1/3 = 1 / (1 + C e ⁻⁰)
Solve for C :
-1/3 = 1 / (1 + C )
-3 = 1 + C
C = -4
So the particular solution to the DE that satisfies the given initial condition is
[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]
If f(x) = x
2−3x+1
x−1
find f(-1) and f(-3)
Answer:
f(-1) = 2-3(-1) +1
= 7
f(-3)= 2-3(-3)+1
= 12
f(-1) = -1-1
= -2
f(-3) = -3-1
= -4
Find mBFE, help ASAP!!!
Answer: C
<BFE is 148 degrees
Step-by-step explanation:
We have angles <BFC (57 degrees) and <CFD (34 degrees), but what is <DFE?
1. The angle symbol in the vertexes shows that <BFC is congruent to <DFE, meaning that they are the same
2. Knowing this, we can safely say that <DFE is equal to 57 degrees because <BFC is also 57 degrees.
3. Now, we have all the angles we need to find out <BFE.
4. <BFC+<CFD+<DFE=<BFE
5. Substitute to get
57+34+57=<BFE
91+57=<BFE
148=<BFE
6. Now we know that the answer is 148 degrees.
Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out.
t (h) 0 2 4 6 8 10
r(t) (L/h) 8.8 7.6 6.8 6.2 5.7 5.3
V=_____ upper estimate
V= ______lower estimate
The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,
[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]
Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.
So you have
• upper estimate:
(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)
= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)
= 70.2 L
• lower estimate:
(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)
= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)
= 63.2 L
Determine if the sequence below is arithmetic or
geometric and determine the common difference / ratio in
simplest form.
3, 8, 13, ..
(PLEASE HELPP)
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Answer:
arithmetic; common difference of 5
Step-by-step explanation:
It usually works well to check differences first. Here, they are ...
8 -3 = 5
13 -8 = 5
These are the same value, so the sequence is arithmetic with a common difference of 5.
Find the intersection of the parabola y=-2x^2-4x+2 and the line -6x+y=14
Answer:
(-2,2) and (-3,-4)
Step-by-step explanation:
by graphing the line and parabola, you should get this graph
Martha ran a 3-mile race in 24 minutes. how long does it take her to run 1 mile?
Answer:
8 minuets
Step-by-step explanation:
24min/3miles = 8
Answer:
8 minutes.
Step-by-step explanation:
If we divide 24 minutes by 3 miles, your answer will be 8 minutes.
