Answer:
see below
Step-by-step explanation:
If the original dimensions of the tank are x, y, and z, the mock dimensions will be 1/6x, 1/6y and 1/6z. The volume of the original tank is x * y * z = xyz whereas the volume of the mock-up tank is 1/6x * 1/6y * 1/6z = 1/216 * xyz. Therefore, we know that the volume of the mock-up tank is 1/216 th of the original tank.
Expand ( p + 6 )( p - 3 )
Answer:
[tex]\Large \boxed{p^2 +3p-18}[/tex]
Step-by-step explanation:
[tex]( p + 6 )( p - 3 )[/tex]
Expand brackets.
[tex]p(p-3)+6(p-3)[/tex]
[tex]p^2 -3p+6p-18[/tex]
Combine like terms.
[tex]p^2 +3p-18[/tex]
Answer:
p² + 3p - 18
Step-by-step explanation:
(p + 6) (p-3)
Break it apart to make it easier to see:
p(p-3) = p² - 3p
6(p-3) = 6p - 18
Add both parts together(Combine Like terms):
p² - 3p + 6p - 18 = p² + 3p - 18
7.45 x 10^3 in standard notation
Answer:
7450
Step-by-step explanation:
Move the decimal to the right 3 times.
The standard notation is 7450
What is standard notation?Standard and scientific notation are the ways to represent numbers mathematically. We write numbers in standard and scientific notations using the rules for respective mathematical concepts. Here, 7.56×1011 7.56 × 10 11 is a scientific notation. 756,000,000,000 756 , 000 , 000 , 000 is standard notation.
Given:
7.45 x 10^3
So, when there is multiplication in decimals then the decimal point would shift to the right side.
Then,
7.45* 1000
=7450
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Please answer question now
Answer:
MN = 3
Step-by-step explanation:
The following are congruent to each other as each pair are tangents of a circle drawn from the same external point:
PQ = QJ = 1
JK = KL = 4 - 1 = 3
MN = ML
Thus, ML = KM - KL
ML = 6 - 3 = 3
Therefore, MN = ML = 3 (both are tangents drawn from the same external point, M.
Select the correct answer. This set of ordered pairs defines a function. {(-49,7), (-56,8), (-63,9), (-70,10)} Which table represents the inverse of the function defined by the ordered pairs? A.
In the future, you should post all possible answer choices to have a complete post. However, there's enough information to get the answer.
The original set has points in the form (x,y)
The first point is (x,y) = (-49,7) making x = -49 and y = 7. When we find the inverse, we simply swap the x and y values. The inverse undoes the original function and vice versa. So if (-49, 7) is in the original function, then (7, -49) is in the inverse. The rest of the points follow the same pattern.
We end up with this answer
{ (7, -49), (8, -56), (9, -63), (10, -70) }
42. How many solutions does this system of
equations have?
3x + 4y= 7
-3x – 4y = 7
A) 0
B) 1
C) 2
D) Infinite
Answer:
[tex]\Large \boxed{\mathrm{A) \ 0 }}[/tex]
Step-by-step explanation:
3x + 4y = 7
-3x - 4y = 7
Add both equations.
0x + 0y = 14
0 = 14
There are no solutions.
Answer:
A) 0
Step-by-step explanation:
Adding both equations.
0 + 0 = 14
0 = 14 (no solutions)
AB = 3.2 cm
BC= 8.4 cm
The area of triangle ABC is 10 cm²
Calculate the perimeter of triangle ABC.
Give your answer correct to three significant figures.
Answer:
Therefore, perimeter of the given triangle is 18.300 cm.
Step-by-step explanation:
Area of the triangle ABC = [tex]\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})[/tex]
10 = [tex]\frac{1}{2}(3.2)(8.4)(\text{SinB})[/tex]
Sin(B) = [tex]\frac{10}{3.2\times 4.2}[/tex]
B = [tex]\text{Sin}^{-1}(0.74405)[/tex]
B = 48.08°
By applying Cosine rule in the given triangle,
(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB
(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°
(AC)² = 10.24 + 70.56 - 35.9166
(AC)² = 44.88
AC = [tex]\sqrt{44.8833}[/tex]
AC = 6.6995 cm
Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)
= 3.200 + 8.400 + 6.6995
= 18.2995
≈ 18.300 cm
Therefore, perimeter of the given triangle is 18.300 cm
In politics, marketing, etc. We often want to estimate a percentage or proportion p. One calculation in statistical polling is the margin of error - the largest (reasonble) error that the poll could have. For example, a poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%). In a (made-up) poll, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Describe the conclusion about p using an absolute value inequality.
Answer: |p-72% |≤ 4%
Step-by-step explanation:
Let p be the population proportion.
The absolute inequality about p using an absolute value inequality.:
[tex]|p-\hat{p}| \leq E[/tex] , where E = margin of error, [tex]\hat{p}[/tex] = sample proportion
Given: A poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76% .
|p-72% |≤ 4%
⇒ 72% - 4% ≤ p ≤ 72% +4%
⇒ 68% ≤ p ≤ 76%.
i.e. p is most likely to be between 68% and 76% (.
The conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
What is absolute value inequality?An expression using absolute functions and inequality signs is known as an absolute value inequality.
We know that the absolute value inequality about p using an absolute value inequality is written as,
[tex]|p-\hat p| \leq E[/tex]
where E is the margin of error and [tex]\hat p[/tex] is the sample proportion.
Now, it is given that the poll result of 72% with a margin of error of 4% indicates that p is most likely to be between 68% and 76%. Therefore, p can be written as,
[tex]|p-0.72|\leq 0.04\\\\(0.72-0.04)\leq p \leq (0.72+0.04)\\\\0.68 \leq p\leq 0.76[/tex]
Thus, the p is most likely to be between the range of 68% to 76%.
Similarly, the proportion of people who like dark chocolate more than milk chocolate was 32% with a margin of error of 2.2%. Therefore, p can be written as,
[tex]|p-\hat p|\leq E\\\\|p-0.32|\leq 0.022\\\\(0.32-0.022)\leq p \leq (0.32+0.022)\\\\0.298\leq p\leq 0.342[/tex]
Thus, the p is most likely to be between the range of 29.8% to 34.2%.
Hence, the conclusion about p using an absolute value inequality is in the range of 29.8% to 34.2%.
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Plzz help tysm if you do
Answer:
B
Step-by-step explanation:
it is defined for all values so D=R
also we can get any value
so Range =R
Answer:
B
Step-by-step explanation:
because that's odd power function it can take both, negative and positive values
HAPLLAPLPAL! BRAINLIEST!
Answer:
D. 860 square inches
Answer:
D: 860 square inches
Step 1.
Remember:
w = 8
x = 5
y = 20
z = 11.3
Let's start with the bottom rectangular prism. The front and back of it is x * x
(5 * 5), so the from and back is 25 + 25 = 50.
The three long sides are x * y (5*20), so the three long rectangles are 100 * 3 = 300. The bottom shape is 350 in total.
Step 2.
The top two rectangles are w * y, (8 * 20) so the two top rectangles are 160 * 2 = 320.
The triangles are w * w / 2 (8 * 8/2) (64 / 2) (32), so the two triangles are 64.
We subtract x from z to get 6.3.
Then, we multiply 6.3 by 20. We get 126. Finally, we add all the values together to get our final answer.
350 + 384+126 = 860
Our answer is D: 860.
Jeania's parents have given her a interest-free loan of $100 to buy a new pair of running shoes She has to
pay back the loan with monthly payments of $20 each.
Write a function rule for the balance of the function (p), where p represents the number of
payments Jeania has made.
Answer:
The balance on the loan f(p) = $100 - $20 × p
Step-by-step explanation:
The parameters of the question are;
The loan amount = $100
The amount of monthly payment for the loan = $20
The function rule for the balance of the function f(p) where p is the number of payments is given as follows;
The balance on the loan, f(p) = The loan amount less the total amount paid
The total amount payment Jeania has made = Amount of monthly payment × Number of months paid, p
The total amount payment Jeania has made = $20 × p
∴ The balance on the loan, f(p) = $100 - $20 × p
Which gives;
f(p) = $100 - $20 × p.
SOMEONE HELP PLEASE. Kylie is raising money for a school trip by selling packs of cookies and bags of chips. The price of each pack of cookies is $1 and the price of each bag of chips is $2. Yesterday Kylie made $42 and she sold 3 times as many bags of chips as packs of cookies. Graphically solve a system of equations in order to determine the number of packs of cookies sold, x, and the number of bags of chips sold, y.
Answer:
cookies (x): 6 soldchips (y): 18 soldStep-by-step explanation:
It is convenient to let a graphing calculator draw the graph for you. It can also display the solution: (x, y) = (6, 18).
__
The equations of interest are ...
x + 2y = 42 . . . . . . revenue from sale of x cookies and y chips
y = 3x . . . . . . . . . . 3 times as many chips as cookies
Answer:
\underline{\text{Variable Definitions:}}
Variable Definitions:
x=
x=
\,\,\text{the number of packs of cookies sold}
the number of packs of cookies sold
y=
y=
\,\,\text{the number of bags of chips sold}
the number of bags of chips sold
Each pack of cookies sells for $1, so xx packs of cookies will bring in 1x1x dollars. Each bag of chips sells for $2, so yy bags of chips will bring in 2y2y dollars. Therefore, the total amount 1x+2y1x+2y equals \$42:$42:
1x+2y=42
1x+2y=42
Since Kylie sold 3 times as many bags of chips as packs of cookies, she sold more bags of chips, so if we multiply 3 by the number of packs of cookies sold, we will get the number of bags of chips sold, meaning yy equals 3x.3x.
y=3x
y=3x
\underline{\text{Write System of Equations:}}
Write System of Equations:
1x+2y=
1x+2y=
\,\,42
42
y=
y=
\,\,3x
3x
\underline{\text{Solve for }y\text{ in each equation:}}
Solve for y in each equation:
\begin{aligned}\color{indianred}{1x}+2y = 42\hspace{10px} & \hspace{10px}\color{green}{y}\color{green}{=}\color{green}{3x} \\[10px] 2y = \color{indianred}{-1x}+42\hspace{10px} & \hspace{10px} & \\[10px] \frac{2y}{2} = \frac{-1x+42}{2}\hspace{10px} & \hspace{10px} & \\[10px] \color{blue}{y} \color{blue}{= -\frac{1}{2}x+21}\hspace{10px}\hspace{10px} & \hspace{10px} & \end{aligned}
1x+2y=42
2y=−1x+42
2
2y
=
2
−1x+42
y=−
2
1
x+21
y=3x
Step-by-step explanation:
Carolyn was training for cross-country season on an indoor track. During her workout, she ran 24 laps around a track that measured 110 meters. What was the total distance Carolyn ran in kilometers?
Answer:
2.64 km
Step-by-step explanation:
24*110=2640 meters
2640/1000=2.64 km
Find a49 of the sequence 70,63,56,49,…. A. -63 B. -266 C. -273 D. -243
Answer:
(B) -266
Step-by-step explanation:
The formula to find the nth term in a sequence is:
[tex]x_{n} = a + d(n-1)[/tex], where a is the first term and n is the "difference."
Looking at this equation, we can see that the number decreases by 7 each time and the first term is 70.
So:
[tex]x_n = 70 + -7(n-1)[/tex]
Solve for the equation:
[tex]x_n = 70 + -7n+7\\x_n = -7n+77[/tex]
Since we want to find the 49th term:
[tex]x_9 = -7(49) + 77\\x_9 = -343+77\\x_9 = -266[/tex]
Hope this helped!
So... can someone help
Answer:
18 : 30
Step-by-step explanation:
Our ratio could look like this:
Number of games won : Number of games played
6 : 10
=> .6 : 1
Let's check whether the 1st option is correct.
=> 18 : 20
=> 1 x 20 = 20
=> .6 x 20 = 12
=> 12 : 20 is not equal to 18 : 20
The second option is 100% incorrect because the number of games won is greater than the number of games played.
let's check whether the 3rd option is correct.
=> 18 : 30
=> 1 x 30 = 30
=> .6 x 30 = 18
18 : 30 = 18: 30
So, the 3rd option is correct.
Answer:
18:30
Step-by-step explanation:
The ratio of games is 6 won out of 10 games
The ratio at the bottom that is 6:10 is
18:30
Divide each side by 3
18/3 : 30/3
6:10
1. Suzette ran and biked for a total of 80 miles in 9 hours. Her average running speed was 5 miles per hour (mph) and her average biking speed was 12 mph. Let x = total hours Suzette ran. Let y = total hours Suzette biked. Use substitution to solve for x and y. Show your work. Check your solution. (a) How many hours did Suzette run? (b) How many hours did she bike?
Answer:
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
Step-by-step explanation:
Speed is rate of distance traveled, it is the ratio of distance traveled to time taken. It is given by:
Speed = distance / time
The total distance ran and biked by Suzette (d) = 80 miles, while the total time ran and biked by Suzette (t) = 9 hours.
For running:
Her speed was 5 miles per hour, let the total hours Suzette ran be x and the total distance she ran be p, hence since Speed = distance / time, therefore:
5 = p / x
p = 5x
For biking:
Her speed was 12 miles per hour, let the total hours Suzette ran be y and the total distance she ran be q, hence since Speed = distance / time, therefore:
12 = q / y
q = 12y
The total distance ran and biked by Suzette (d) = Distance biked + distance ran
d = p + q
80 = p + q
80 = 5x + 12y (1)
The total time taken to run and bike by Suzette (t) = time spent to bike + time spent to run
t = x + y
9 = x + y (2)
Solving equation 1 and equation 2, multiply equation 2 by 5 and subtract from equation 1:
7y = 35
y = 35/7
y = 5 hours
Put y = 5 in equation 2:
9 = x + 5
x = 9 -5
x = 4 hours
a) Suzette ran for 4 hours
b) Suzette biked for 5 hours
The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + z2 + z – 24.
The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
How to find product of expressions(4z² + 7z – 8) and (–z + 3)
= -4z³+ 12z² - 7z² + 21z + 8z - 24
collect like terms= -4z³ + 5z² + 29z - 24
Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
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Jenny had a wardrobe full of 35 different shirts. In order to make more space in her closet, she got rid of 9 of them. What is a reasonable
estimate for the percentage of shirts Jenny got rid of?
There is no one set answer because there are many ways to estimate here.
35 rounds to 40
9 rounds to 10
She got rid of 10 shirts out of 40, so 10/40 = 1/4 = 0.25 = 25% is the estimated percentage of shirts she got rid of. This is one possible estimate.
Using a calculator, the actual percentage is 9/35 = 0.2571 = 25.71% approximately. So our estimate isn't too bad. Our estimate is an underestimate.
How do I find perimeter and area
Answer:
To find the perimeter of a rectangle or square you have to add the lengths of all the four sides
The area is measurement of the surface of a shape.
Hope this helps! （づ￣3￣）づ╭❤～
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
#3 would be the first one and #4 would be the third answer.
Step-by-step explanation:
i'm so sorry for the wait
can some1 help me out with this problem
Answer:
see explanation
Step-by-step explanation:
Compare the coordinates of corresponding vertices.
C(7, - 2 ) → C'(- 3, 7 )
x- direction 7 → - 3 , that is - 10 of a shift
y- direction - 2 → 7, that is + 9 of a shift
Thus the translation rule is
(x, y ) → (x - 10, y + 9 )
(07.06A) Which scenario best matches the linear relationship expressed in the equation y = 13.50x + 300? Bobby has $300 in the yearbook fund and spends $13.50 on each yearbook. Bobby has $13.50 in the yearbook fund and spends $300 on each yearbook. Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold. Bobby has $13.50 in the yearbook fund and earns $300 for each yearbook sold.
Answer:
Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.
Step-by-step explanation:
The value of the expression when x is zero is 300. For each increment of 1 in x, the value of the expression increases by 13.50. This best matches the scenario ...
Bobby has $300 in the yearbook fund and earns $13.50 for each yearbook sold.
I REALLY NEED HELLP with these 3 questions PLLZZZZ!!!!
Answer:
Below
Step-by-step explanation:
6)
The sum that we have is 85 +99
We want to express it as the product of a whole number thar is greater than 1 and a sum of two whole numbers.
Notice that: 85 = 84+1
● 85 + 99 = 84 + 1 + 99 = 84 + 100
84 and 100 are even numbers so we can factor using 2.
● 84 + 100 = 2(42 +50)
2 is greater than one and 42+50 is the sum of two whole numbers so all the conditions are satisfied.
■■■■■■■■■■■■■■■■■■■■■■■■■■
7)
Dasha go on business trips every 9 months while Charlie go every 6 months.
They came back at the same time.
So Charlie has to wait 6 months before going and Dasha nine months.
Dasha will be alone home for 3 months so she doesn't need to hire someone.
Here is what happens:
● Both Dasha and Charlie are home.
● After 6 months Charlie go and Dasha is at home
● after 3 months Dasha goes also and Charlie is home
● after 3 months charlie go and Dasha is home
● after 3 months both are home.
● aftet 3 months they both go
So the period is:
● 6+3+3+3+3 = 18
So after 18 months they should hire someone.
The picture below makes the understanding easier. ( x is Charlie and y is Dasha)
■■■■■■■■■■■■■■■■■■■■■■■■■■
8)
Pime factorisation
● 96÷2= 48
● 48÷2= 24
● 24 ÷ 2 = 12
● 12 ÷ 2 = 6
● 6÷2 = 3
● 3÷3 = 1
=> 96 = 2 × 2 ×2×2×2 ×3 =2^5 ×3
● 80÷ 2 = 40
● 40 ÷ 2 = 20
● 20÷2 = 10
● 10÷2 = 5
● 5÷5 = 1
=> 80 = 2×2×2×2×5 = 2^4 × 5
So the GCF is 2^4 wich is 16
He can make 16 party
● 80÷16 = 5
There will be 5 boxes of raisin in each one
● 96÷16 = 6
There will be 6 pencils in each party
If sine theta equals one over three, what are the values of cos θ and tan θ?
Answer:
cos theta = √8/3
tan theta = √8/8
Step-by-step explanation:
sin theta = 1/3
1² + x² = 3²
x = √8
cos theta = √8/3
tan theta = 1/√8 = √8/8
construct a right-angled triangle ABC where angle A =90 degree , BC= 4.5cm and AC= 7cm. please ans fast........ Very urgent. Pls don't give wrong answers
Answer and Step-by-step explanation: The described right triangle is in the attachment.
As it is shown, AC is the hypotenuse and BC and AB are the sides, so use Pytagorean Theorem to find the unknown measure:
AC² = AB² + BC²
[tex]AB^{2} = AC^{2}-BC^{2}[/tex]
[tex]AB =\sqrt{AC^{2}-BC^{2}}[/tex]
[tex]AB =\sqrt{7^{2}-4.5^{2}}[/tex]
[tex]AB =\sqrt{28.75}[/tex]
AB = 5.4
Then, right triangle ABC measures:
AB = 5.4cm
BC = 4.5cm
AC = 7cm
Using properties of sets show that : a) A ∩ (A’ U B) = A ∩ B b) A ∩ (A U B )’ = Ф
Answer:
a) From A ∩ A' = ∅, we have;
A ∩ (A' ∪ B) = A ∩ B
b) From A ∩ (A' ∩ B') = (A ∩ A') ∩ B' and A ∩ A' = ∅, we have;
A ∩ (A ∪ B)' = ∅
Step-by-step explanation:
a) By distributive law of sets, we have;
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
From the complementary law of sets, we have;
A ∩ A' = ∅
Therefore, for A ∩ (A' ∪ B) = A ∩ B, we have
A ∩ (A' ∪ B) = (A ∩ A') ∪ (A ∩ B) (distributive law of sets)
A ∩ A' = ∅ (complementary law of sets)
Therefore;
(A ∩ A') ∪ (A ∩ B) = ∅ ∪ (A ∩ B) = (A ∩ B) (Addition to zero identity property)
∴ A ∩ (A' ∪ B) = A ∩ B
b) By De Morgan's law
(A ∪ B)' = A' ∩ B'
Therefore, A ∩ (A ∪ B)' = A ∩ (A' ∩ B')
By associative law of sets, we have;
A ∩ (A' ∩ B') = (A ∩ A') ∩ B'
A ∩ A' = ∅ (complementary law of sets)
Therefore, (A ∩ A') ∩ B' = ∅ ∩ B' = ∅
Which gives;
A ∩ (A ∪ B)' = ∅.
Calculate the volume of the regular triangular pyramid
with the base edges of length 17 feet and a height of
length 5 feet. (Hint: Remember that the base of a
regular triangular pyramid must be an equilateral triangle, not
necessarily congruent to the sides of the pyramid.)
Answer:
70.83 ft³
Step-by-step explanation:
The volume of a pyramid is:
[tex]\frac{bh}{3}[/tex], where b is the base area and h is the height.
Let's first find the area of the base.
[tex]17\cdot5=85\\85\div2=42.5[/tex]
Multiplying this by 5:
[tex]42.5\cdot5=212.5[/tex]
Dividing by 3:
[tex]212.5\div3=70.83[/tex].
Hope this helped!
pls help. A granola mix sells for $8.99 a pound. Tung wants to buy a bag of granola mix that weighs 7.8 pounds. The bag of granola mix will cost about $16. $17. $63. $72.
Answer:
about 72 dollars
Step-by-step explanation
"about" tells us to round our numbers. Therefore, 7.8 becomes 8. As each pound is $8.99, we multiply the two and get 71.92, which is "about" 72.
Answer:
$72
Step-by-step explanation:
To find the cost, multiply the price per pound by the number of pounds.
8.99(7.8)
= 70.12
This is closest to $72
A function of random variables used to estimate a parameter of a distribution is a/an _____.
A. unbiased estimator
B. statistic
C. predictor
D. sample value
Answer:
A. unbiased estimator.
Step-by-step explanation:
In Statistics, an estimator is a statistical value which is used to estimate a parameter. Parameters are the determinants of the probability distribution. Therefore, to determine a normal distribution we would use the parameters, mean and variance of the population.
A function of random variables used to estimate a parameter of a distribution is an unbiased estimator.
An unbiased estimator is one in which the difference between the estimator and the population parameter grows smaller as the sample size grows larger. This simply means that, an unbiased estimator captures the true population value of the parameter on average, this is because the mean of its sampling distribution is the truth.
Also, we know that the bias of an estimator (b) that estimates a parameter (p) is given by; [tex]E(b) - p[/tex]
Hence, an unbiased estimator is an estimator that has an expected value that is equal to the parameter i.e the value of its bias is equal to zero (0).
Generally, in statistical analysis, sample mean is an unbiased estimator of the population mean while the sample variance is an unbiased estimator of the population variance.
Answer: B statistic
Step-by-step explanation:
it just is trust me
a number when divided by 10 leaves the remainder 5. If the same number is doubled, and divided by 10, the new remainder is _____
Answer:
10
Step-by-step explanation
50 divided by 10 is 5 so
50 times 2 which is 100 divided by 10 is 10
-5r+8r+5 what is the anwser
Answer:
-5r + 8r +5
= (-5+8)r+5 (we can calculate number in same variabe)
= 3r +5
hope it helps ^°^
Answer:
3r + 5.
Step-by-step explanation:
-5r + 8r + 5
= 8r - 5r + 5
= 3r + 5.
Hope this helps!
