The sesame street tube bought by the blue bird costs $177.92 which contained one gallon of toothpaste.
Given,
cost of regular toothpaste = $1.39 for 2.7 ounce tube
But the bird took a tube of toothpaste that contained one gallon of toothpaste.
One gallon = 128 ounces
∴the total price at which the toothpaste is brought = price of normal toothpaste × one gallon(128 ounces)
= 1.39 × 128
=$177.92
Here we can observe that a gallon contains 128 ounces. so we need to multiply to the initial cost of the toothpaste to get the final amount of the toothpaste bought by the bird.
Hence the price at which the bird bought the toothpaste is $177.92
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Suppose 40% of American singers are Grammy award winners. If a random sample of size 743 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%
Using the normal distribution, it is found that there is a 0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion and the sample size are given, respectively, by:
p = 0.4, n = 743
Hence the mean and the standard error are given, respectively, by:
[tex]\mu = p = 0.4[/tex][tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.4(0.6)}{743}} = 0.018[/tex]The probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3% is the p-value of Z when X = 0.43 subtracted by the p-value of Z when X = 0.37, hence:
X = 0.43:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.43 - 0.4}{0.018}[/tex]
Z = 1.67
Z = 1.67 has a p-value of 0.9525.
X = 0.37:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.37 - 0.4}{0.018}[/tex]
Z = -1.67
Z = -1.67 has a p-value of 0.0475.
0.9525 - 0.0475 = 0.905.
0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.
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Can someone please help
Answer:
31,41,51,71
Step-by-step explanation:
Answer:
The answer is: 31,41,51,71
An equilateral triangle with side lengths of 8.7 centimeters is shown. An apothem has a length of a and the radius has a length of 5 centimeters. The apothem and radius form a triangle with a base length of b.
Which statements about finding the area of the equilateral triangle are true? Select three options.
The apothem can be found using the Pythagorean theorem.
The apothem can be found using the tangent ratio.
The perimeter of the equilateral triangle is 15 cm.
The length of the apothem is approximately 2.5 cm.
The area of the equilateral triangle is approximately 65 cm2.
Options A,B and D. The correction about the area of the triangle are
The apothem can be found using the Pythagorean theorem.The apothem can be found using the tangent ratio.The length of the apothem is approximately 2.5 cm.How to solve for the length of the Apothem using the Pythagoras theoremFirstly this is an equilateral triangle
3 of the sides have the length of 8.7cm
b = half of 8.7
= 4.35cm
To get A we have
a² + b² = c²
a² + 4.35² = 5²
When we solve this out we would have
a² = 25 - 18.9225
a ≈ 2.5 cm.
Hence we have proved that the first option is correct.
For B,
In an equilateral triangles, each of the angles = 60 degrees
60/2 = 30 is the angle that is made from the base
using tangent ratiosa / 4.35 = tan 30
then a = 4.35 tan 30
This would also give us an approximate of 2.5
For D
The calculations we have done based on the statements in A and B shows that D is correct as 2.5.
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Select the correct answer. The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number? A. The equation that represents this situation is 10 − x = -18. The second number is 28. B. The equation that represents this situation is 10 + x = -18. The second number is -28. C. The equation that represents this situation is x − 10 = -18. The second number is -8. D. The equation that represents this situation is -10 + x = -18. The second number is -8.
Using a system of equations, the correct statement is given as follows:
B. The equation that represents this situation is 10 + x = -18. The second number is -28.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The numbers are x and y, and their sum is -18, hence:
x + y = -18.
The number y is 10, hence:
x + 10 = -18.
x = -18 - 10 = -28.
Which means that option B is correct.
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What is the midpoint of the segment shown below?
A. (-15, -15)
B. (-15,-15)
c. (-1/5, -15)
D. (-15-15)
The midpoint of the segment is (-15/2, -15/2)
How to determine the midpoint?The complete question is in the attached image
The points are given as:
(-8, -7) and (-7, -8)
The midpoint is calculated as:
(x,y) = 1/2 * (x1 + x2, y1 + y2)
So, we have:
(x,y) = 1/2 * (-8 - 7, -7 - 8)
Evaluate the difference
(x,y) = 1/2 * (-15, -15)
Evaluate the product
(x,y) = (-15/2, -15/2)
Hence, the midpoint of the segment is (-15/2, -15/2)
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Please answer correctly
Answer:
The answer is 6 and -6
Step-by-step explanation:
The given equation is
[tex]x^2 - kx + 9 = 0 ... (1)[/tex]
where a = 1. b = -k, c = a
since the equation (1) has equal roots
[tex]\Rightarrow b^2 - 4ac = 0 \newline\\\Rightarrow (-k)^2 - 4(1)(9) = 0\\ \newline\\\Rightarrow (k)^2 - 36 = 0 \newline\\\Rightarrow k^2 = 36 \newline\\\Rightarrow k = \pm 6[/tex]
Hence volume of k = 6, -6
Solve x2 – 6x + 9 = 0 by completing the square.
A)
x = 3
B)
x = –3
C)
x = 3 and x = –3
D)
x = 1 and x = 9
Answer:
A.) x = 3
Step-by-step explanation:
This equation is an example of a perfect square quadratic. This means that the quadratic can be simplified into two of the same factors.
How can you factor the equation? The simplest way is to ask yourself, which two numbers multiply to 9 while also adding to -6? The two numbers which satisfy this question are -3 and -3. Knowing this, you can construct your factors, simplify, and then solve for "x".
x² - 6x + 9 = 0 <----- Expanded equation
(x - 3)(x - 3) = 0 <----- Factored equation
(x - 3)² = 0 <----- Combine both factors
x - 3 = 0 <----- Take square root of both sides
x = 3 <----- Add 3 to both sides
Given: AB = DC, AC = DB
Prove: AABC= ADCB
Look at the proof. Name the postulate you would use to prove the two triangles are congruent.
Given: AB DC, AC = DB
Prove: AABC= ADCB
AB= DC
Given
AC DB
Given
BC BC
Reflexive Property
of Congruence
AABC ADCB
?
B
D
C
Answer:
by sss
Step-by-step explanation:
Make me a brain-list.The property of congruence:
ΔABC ≅ ΔDCB by the SSS criterion.
The correct option is the SSS postulate.
What is congruent?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.
Given information:
AB ≅ DC and AC ≅ DB.
The proof is given described as:
In triangle ABC and triangle DCB,
The two sides are congruent,
AB ≅ DC and AC ≅ DB ( As per the information provided).
And as per the diagram and reflexive property of congruence,
BC ≅ BC.
Therefore, ΔABC ≅ ΔDCB by the SSS criterion.
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If quadrilateral abcd is an isosceles trapezoid, which statements must be true? select three options bc ∥ ad bd ⊥ ac ba ≅ cd be ≅ ed ∠cba ≅ ∠bcd
The true statements among the given options are written below
bc || ad
ba ≅ cd
∠cba ≅ ∠bcd
In an isosceles trapezoid, there is one pair of legs of equal length and a pair of parallel lines.
Given that quadrilateral abcd is a isosceles trapezoid.
In the given trapezoid abcd
bc || ad ( pair of parallel sides )
So this is correct.
ba ≅ cd ( For an isosceles trapezoid legs are equal)
So this is correct
∠cba ≅ ∠bcd (According to the property of isosceles trapezoid )
So this is correct.
Hence, bc || ad, ba ≅ cd, ∠cba ≅ ∠bcd are correct
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Can someone pls help me?
I'm not sure how to convert a logarithm to natural logarithm.
only (a)
Answer:
[tex] \frac{2 ln(5) }{3 ln(2) } [/tex]
Step-by-step explanation:
[tex] log_{8}(25) = \frac{ ln(25) }{ ln(8) } = \frac{ ln( {5}^{2} ) }{ ln( {2}^{3} ) } = \frac{2 ln(5) }{3 ln(2) } [/tex]
Find a in degrees.
√58
3
7
α
Answer:
23.20
Step-by-step explanation:
join my stream for an explanation
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Answer:
α ≈ 23.20°
Step-by-step explanation:
given all 3 sides of the triangle , then any of the trig ratios may be used, that is sine, cosine or tangent to find α
tanα = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{3}{7}[/tex] , then
α = [tex]tan^{-1}[/tex] ( [tex]\frac{3}{7}[/tex] ) ≈ 23.20° ( to the nearest hundredth )
or
sinα = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{\sqrt{58} }[/tex] , then
α = [tex]sin^{-1}[/tex] ( [tex]\frac{3}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )
or
cosα = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{7}{\sqrt{58} }[/tex] , then
α = [tex]cos^{-1}[/tex] ( [tex]\frac{7}{\sqrt{58} }[/tex] ) ≈ 23.20° ( to the nearest hundredth )
In the diagram, O is the centre of the circle, BD = DC and PAB is a straight line. Prove that AD bisects the angle CAP.
Answer:
BAC=BDC(BDX)=30°
Step-by-step explanation:
We know that BD=OD.
But OD=OB= Radius of the circle.
Therefore
BD=OD=OB
BDO is equilateral triangle.
Angle DBO= 60°
Now let us take the intersecting point of CD and AB as X.
In triangle BDX,
BXD= 90°(BXD+BXC=180°, BXD+90°=180°, BXD=90°)
BXD+DBX+BDX=180°{Angle Sum Property}
90°+60°+BDX= 180°
BDX= 30°
We also know that,
BDC(BDX)= BAC (Angles lie on the same arc{BC} are equal in measure.
Therefore,
BAC=BDC(BDX)=30°
Find the missing lengths in the triangle above
ER=
IE=
Step-by-step explanation:
IR = 9√3
E = 60°
I = 30°
R = 90°
• Find ER.
ER/sin(I) = IR/sin(E)
ER/sin(30°) = 9√3/sin(60°)
ER/(1/2) = 9√3/(1/2 √3)
ER/(1/2) = (9√3 . 2)/√3
ER/(1/2) = 18√3/√3
ER/(1/2) = 18 → IR/sin(E)
ER = 18 . 1/2
ER = 9 is the answer
• Find IE (There are 2 ways).
First, using a Sinus Rule.
IE/sin(R) = IR/sin(E)
IE/sin(90°) = 9√3/sin(60°)
IE/1 = 9√3/(1/2 √3)
IE = (9√3 . 2)/√3
IE = (18√3)/√3
IE = 18 is the answer
Second, using a Pythagoras Theorem.
IE = √(IR² + ER²)
IE = √((9√3)² + 9²)
IE = √(81.3 + 81)
IE = √(243 + 81)
IE = √324
IE = 18 is the answer
What is the solution to the system of equations?
Plug the second equation (the one already solved for y) into the first equation
2x - (2x + 3) = 7
2x - 2x - 3 = 7
-3 = 7
Since the 2x's canceled out and left a false statement, this system of equations has no solution.
Hope this helps!
a water tank contains 200 gallons before water is added at a constant rate for six hours until there is 500 gallons in the tank. the faucet is then turned off and the plug is removed so that the tank loses all of its water in over a 10 hour period. write an absolute value function that models the amount of water in the tank V(t) in terms of elapsed time, (t) then state it’s domain.
Answer:
200+500
Step-by-step explanation:
its wrong i answered the wrong question
In a batch of 8,000 clock radios 4% are defective. A sample of 7 clock radios is randomly selected without replacement from the 8,000 and tested. The entire batch will be rejected if at least one of those tested is defective. What is the probability that the entire batch will be rejected?
Using the hypergeometric distribution, there is a 0.2486 = 24.86% probability that the entire batch will be rejected.
What is the hypergeometric distribution formula?The formula to find the hypergeometric distribution formula is
P(X=x)=P(x, N, n, K)[tex]=\frac{C_{k, x} C_{N-k, n-x} }{C_{N, n} }[/tex]
[tex]C_{n, x} =\frac{n!}{(n-x)!}[/tex]
The parameters are:
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.
For this problem, the values of the parameters are given as follows:
N = 8000, n = 7, k = 0.04 x 8000 = 320
The probability that the entire batch will be rejected is P(x≥1), given as follows: P(x≥1)=1-P(X=0)
In which,
P(X=0)=P(0, 8000, 7, 320)[tex]=\frac{C_{320, 0} C_{7680, 7} }{C_{8000, 320} }=0.7514[/tex]
Now, P(x≥1)=1-0.7514=0.2486
Therefore, 0.2486 = 24.86% probability that the entire batch will be rejected.
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Which ordered pair comes from the table ?
Answer:
B
Step-by-step explanation:
The only x,y pair in the table is 4,2
I will give brainiest to who ever can copy and answer this math problem first : 12342345791 + 3214567349=
Answer:
15556913140
Step-by-step explanation:
convert (-6, pi/2) into rectangular coordinates
The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The conversion from polar to rectangular coordinates is:
x = rcosФ and y = rsinФ
Hence:
x = 6cos(π/2) = 0, y = 6sin(π/2) = 6
The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)
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simplify (x^2+2x+3)-(x^2+3x+2)
Answer:
- x + 1
Step-by-step explanation:
(x² + 2x + 3) - (x² + 3x + 2) ← multiply terms inside parenthesis by - 1
= x² + 2x + 3 - x² - 3x - 2 ← collect like terms
= - x + 1
What would the altimeter read if Janelle were at sea level? What do the positive readings on the altimeter represent? What do the negative readings on the altimeter represent?
.
Step-by-step explanation:
a square has the same perimeter as a 5cm by 7cm rectangle. which of the following area of the square
Answer:
At sea level, the altimeter would read 0 feet. Any positive readings on the altimeter would indicate she is above sea level. Any negative readings on the altimeter would indicate she is below sea level.
Step-by-step explanation: PLATO
If y varies directly with x and
y = 48 when x = 6, find y if x = 3.
First, find the direct variation equation.
y = [? ]x
There are 27000Ib of wheat to be transported, the transport company wants to know how many metric tonnes of wheat they would be transporting.
The quantity of wheat to be transported by the company in metric tonnes is; 1.224 metric tonnes.
How many metric tonnes of wheat is to be transported?Since it follows that 1 metric tonne is equivalent to 2205 lb. It therefore follows that the quantity which is equivalent to 2700lb to be transported is;
= 2700/2205 = 1.224
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What's the range of the graph? I have a menu that I could choose from and this is the option that I have.
Answer:
-∞ < x < 4
Step-by-step explanation:
→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.
Juan, Mary, Celia, and Mark work as information specialists at a high tech company. They each spent a certain amount of time fixing a problem with the database. Out of the total number of hours all the workers spent, what percent of that time is Celia's?
A) 17%
B) 18%
C) 21%
D) 25%
Answer:
B) 18%
Step-by-step explanation:
100% - 36% - 29% - 17% = 18%
Answer:
the answer would be B) 18%
A line has a y-intercept of 0 and a slope of 7. What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y=7x
Step-by-step explanation:
The equation of the with a slope of m and a y-intercept of b is y=mx+b.
The cube of the sum of a number and 5.
Answer:
[tex](x+5)^{3}[/tex]
Step-by-step explanation:
Hope this helps
The expression for the word problem is ( x + 5 )².
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The given word problem is the cube of the sum of a number and 5. The expression will be formed as below:-
Let the unknown number be x.
E = ( x + 5 )²
Therefore, the expression for the word problem is ( x + 5 )².
The complete question is given below:-
The cube of the sum of a number and 5. Write the mathematical expression.
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For what values of x will the function f(x) = 3x² + 13x - 10 equal zero?
Answer:
x = - 5 , x = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
the values of x that make f(x) zero are the zeros
to find the zeros let f(x) = 0 , that is
3x² + 13x - 10 = 0
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 10 = - 30 and sum = + 13
the factors are + 15 and - 2
use these factors to split the x- term
3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )
3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term
(x + 5)(3x - 2) = 0
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]
Two trees are next to each other in a clearing. The first tree is 13 feet tall and casts an 8-foot shadow. The second tree casts a 33-foot shadow. How tall is the second tree to the nearest tenth of afoot?
Bricklayer Ben places 42 bricks per hour. Bricklayer Bob places 36 bricks per hour. Bricklayer Bob worked twice as many hours as Bricklayer Ben, and the two of them placed a total of 1254 bricks. How many bricks did Bricklayer Ben place
Bricklayer Ben placed a total of 462 bricks.
How to use equation to find the number of bricks placed?Bricklayer Ben places 42 bricks per hour.
Bricklayer Bob places 36 bricks per hour.
Let
x = number of hours worked by Bricklayer Bob
y = number of hours worked by Bricklayer Ben
Therefore,
x = 2y
42y + 36x = 1254
42y + 36(2y) = 1254
42y + 72y = 1254
114y = 1254
y = 1254 / 114
y = 11
Hence, Bricklayer Ben placed a total of 42 × 11 = 462 bricks.
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