Answer: The graph is below
Step-by-step explanation:
A vase has the shape of a rectangular prism. The vase has a height of 4 1/2 inches and a
square base with a side length of 4 inches. You want to fill the vase with water. You have a pitcher that holds about 75 cubic inches of water. Is the amount of water in the pitcher not enough, just enough, or more than enough? Explain
Pitcher holds 75 in³ of liquid, more than enough to completely fill a vase with a 72 in³ rectangular prism shape.
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid.
Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.
So, the volume of the rectangular prism is:
V = h*w*l
Now, insert values as follows:
V = h*w*l
V = 4.5*4*4
V = 72 in³
Pitcher has 75 in³ of water which is more than enough to fill the vase.
Therefore, the pitcher holds 75 in³ of liquid, more than enough to completely fill a vase with a 72 in³ rectangular prism shape.
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A scientist has two acid solutions: Artesia, which is a $70\%$ acid solution, and Borromeo, which is a $20\%$ acid solution. (a) Find the amount of Artesia (in mL) that must be added to $500$ mL of Borromeo in order to produce a $60\%$ acid solution. (b) Find the amount of Artesia and Borromeo (in mL) that can be combined in order to form a $100$ mL solution that is $55\%$ acid. (c) Does there exist a combination of Artesia and Borromeo that is $80\%$ acid?
Answer:
(a) 2000 mL
(b) 70 mL, 30 mL
(c) No
Step-by-step explanation:
Given that Artesia is a 70% acid solution, and Borromeo is a 20% acid solution.
(a) Let x mL of Artesia is added to 500 mL of Borromeo to produce a 60% acid solution.
So, 70% of x + 20% of 500 = 60% of (x+500)
\(\Rightarrow 0.7 \times x + 0.2 \times 500 = 0.6 \times (x+500) \\\\\ \Rightarrow 0.7 \times x + 0.2 \times 500 = 0.6 \times x+0.6 \times500\\\\ \Rightarrow 0.7 \times x -0.6 \times x= 0.6 \times500- 0.2 \times 500 \\\\ \Rightarrow (0.7-0.6) \times x = (0.6-0.2) \times500\\\\\Rightarrow 0.1 \times x = 0.4 \times500\\\\\)
\(\Rightarrow x = (0.4 \times500)/0.1=2000\) mL.
(b) Let x mL of Artesia and y mL be combined in order to form a 100 mL solution having 55% acid solution.
So, x+y=100\Rightarrow y= 100-x
And, 70% of x + 20% of y = 55% of (100)\\\\
\(\Rightarrow 0.7 \times x + 0.2 \times (100-x) = 0.55 \times 100\\\\\Rightarrow 0.7 \times x + 0.2 \times 100- 0.2 \times x = 0.55 \times 100\\\\\Rightarrow 0.7 \times x -0.2 \times x= 0.55 \times100- 0.2 \times 100 \\\\\Rightarrow (0.7-0.2) \times x = (0.55-0.2) \times100\\\\\Rightarrow 0.5 \times x = 0.35 \times100\\\\\)
\(\Rightarrow x = (0.35 \times100)/0.5=70\) mL.
and y= 100-x= 100-70=30 mL.
(c) Let x mL of Artesia and y mL of Borromeo be combined in order to make 80% acid solution.
And, 70% of x + 20% of y = 80% of (x+y)
\(\Rightarrow 0.7 \times x + 0.2 \times y= 0.8 \times (x+y)\\\\\Rightarrow 0.7 \times x + 0.2 \times y = 0.8 \times x +0.8 \times y\\\\\Rightarrow (0.7-0.8) \times x = (0.8-0.2) \times y\\\\\Rightarrow -0.1 \times x = 0.6 \times y \\\\\Rightarrow \frac {x}{y} = -6 \\\\\)
As x and y are amount of Artesia and Borromeo, so x>0 and y>0
\(\Rightarrow x/y >0\), so the negative value of x/y is not possible.
Ad the negative value of x/y is not so x/y=-6 is not possible, hence, any combination of Artesia and Borromeo that is 80% acid solution is not possible.
A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Rashaad measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot.
The given question is on trigonometry which requires the application of required function so as to determine the value known. So that the length of the guy wire is 67.0 feet.
Trigonometry is an aspect of mathematics that requires the application of some functions to determine the value of an unknown quantity.
Let the length of the guy wire be represented by l, and the angle that the guy wire makes with the stake be θ. So that applying the appropriate trigonometric function to determine the value of θ, we have:
Tan θ = \(\frac{opposite}{adjacent}\)
= \(\frac{11}{4}\)
Tan θ = 2.75
θ = \(Tan^{-1}\) 2.75
= 70.0169
θ = \(70^{o}\)
Considering triangle formed by the tower and the stake to determine the value of l, we have;
Cos θ = \(\frac{adjacent}{hypotenuse}\)
Cos \(70^{o}\) = \(\frac{23}{l}\)
l = \(\frac{23}{Cos 70^{o} }\)
= \(\frac{23}{0.3420}\)
l = 67.2515
l = 67 feet
The length of the guy wire is 67 feet.
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Subtract these polynomials.
(2x²+2x+3)(x²+2x+1)=
A x² + 4x+2
B. +4
C. x² + 4x+4,
D. x² + 2
Answer:
x²+2
Choice D
Step-by-step explanation:
(2x²+2x+3)(x²+2x+1)
Subtract these, which means
2x²+2x+3-(x²+2x+1)2x²+2x+3-x²-2x-1Bringing like terms,
2x²-x²+2x-2x+3-1x²+0+2x²+2Choice D
Required
1. Gabby won 70 super bouncy balls playing basketball at the county fair. At school she gave one
to every student in her math class. She only has 51 remaining. How many did she give away?
Answer:
19
Step-by-step explanation:
70 - 51 = 19
To check:
19 + 51 = 70
What is the probability of rolling a number greater than 4 on a standard die?
01
Oy
0
the entertainment section of the local magazine needs to know the number of movies showing daily in nearby theaters this box and whisker plots shows the resultsmovies shown daily at theaters
SOLUTION
We want to find the interquartile range of the box and whisker plot in the picture.
Interquartile range is calculated as
\(Q3-Q1\)In the box and whisker plot
\(\begin{gathered} Q1=16 \\ Q3=22 \\ Q3-Q1=22-16=6 \end{gathered}\)Hence the answer is 6
answer and or help would be much appreciated work is due and needs to be submitted
Answer:
1. D
2. C
3. B
4. A
Step-by-step explanation:
just match up the number y is on the right side and x on the left side like this (x,y)
Suppose that the average price for a gallon of gasoline in the Country A is $2.78 and in Country B it is $2.45. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a standard deviation of $0.25 in the Country A and a standard deviation of $0.20 in Country B.(a) What is the probability that a randomly selected gas station in Country A charges less than $2.50 per gallon? (Round your answer to four decimal places.) .1314 (b) What percentage of the gas stations in Country B charge less than $2.50 per gallon? (Round your answer to two decimal places.) .60 X % (c) What is the probability that a randomly selected gas station in Country B charged more than the mean price in the Country A? (Round your answer to four decimal places.) .0495
Answer:
(a) 0.1314(b) 59.87%(c) 0.0495Step-by-step explanation:
Given μA = $2.78, σA = $0.25, μB = $2.45, σB = $0.20, you want ...
p(A < $2.50)p(B < $2.50)p(B > $2.78)ProbabilityThe probabilities of interest are found using the CDF function of a suitable calculator or spreadsheet.
(a) P(A < $2.50) ≈ 0.1314
(b) P(B < $2.50) ≈ 59.87%
(c) P(B > $2.78) ≈ 0.0495
__
Additional comment
We note that you have provided your own answers to these questions. The answer you give for question B is not given as the percentage requested.
<95141404393>
the greek letter used to represent the probability of a type i error is alpha (α). T/F?
True, the Greek letter used to represent the probability of a Type I error is alpha (α).
In hypothesis testing, a Type I error occurs when the null hypothesis is rejected even though it is true. The alpha level, also known as the significance level, is a pre-determined threshold that indicates the probability of making such an error. By setting an appropriate alpha level, researchers can control the risk of incorrectly rejecting the null hypothesis.
Typical alpha levels used in research are 0.05 or 0.01, indicating a 5% or 1% chance of making a Type I error, respectively. It is crucial to consider the consequences of Type I errors when choosing an alpha level, as it affects the overall reliability and validity of the study.
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Which quantity makes the equation true?
x + 3x + _______ = 7x
Answer:
Step-by-step explanation:
C) 3X
Answer: C. 3x
Step-by-step explanation:
Since x and 3x both have x, you can add them together to get 4x (if there is x by itself, it really means that there is one of it, so it would be 1x.)
Then, you subtract 7x by 4x, which gives you the answer, 3x. You could also solving it by asking yourself: What number plus 4x equals 7x, which would give you 3x.
Simplify -7 1/9 - (-9 1/2)
Answer:
Here: 2 7/18
Step-by-step explanation:
Hope this helped and brainlest please!
19/8 or 2 3/8 you choose :)
Jada cuts an 11 inch strip of paper into 5 equal parts, how many inches long is each part?
Answer:
2.2
Step-by-step explanation:
11 / 5 = 2.2 inches
The balance of a certain loan increases at a rate that is proportional at any time to the balance at that time. The loan balance is $1600 initially, and it is $1920 after one year (365 days). What is the balance of the loan after 90 days?
By answering the presented question, we may conclude that As a result, proportionality the loan debt after 90 days is roughly $1713.17.
what is proportionality?Proportionate relationships are those that have the same ratio every time. For example, the average number of apples per tree defines how many trees are in an orchard and how many apples are in an apple harvest. Proportional refers to a linear relationship between two numbers or variables in mathematics. When the first quantity doubles, the second quantity doubles as well. When one of the variables decreases to 1/100th of its previous value, the other falls as well. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two remains constant at all levels. The diameter and circumference of a circle serve as an example.
Let B represent the loan balance at any moment t. (t).
k * B d(B(t))/dt (t)
where k is a proportionality constant.
This differential equation may be solved by separating the variables.
k * dt = d(B(t))/B(t).
When both sides are combined, the following results:
B(t) ln(t) = k*t + C
where C is an integration constant.
ln(B(0)) = k*0 + C
ln(1600) = C
So,
\(k*t + ln(B(t)) = ln(B(t)) (1600)\\= k*1 + ln(B(1)) (1600)\\ln(1920) = k + ln (1600)\\k = ln(1920) - ln (1600)\\k = ln(1.2) (1.2)\)
Therefore,
\(ln(B(t)) = ln(1600) * 1.2 * t\\1600 * 1.2t = ln(B(t))\\B(t) = 1600 * 1.2^t\\\)
To calculate the loan balance after 90 days, enter t=90/365:
\(B(90/365) = 1600 * 1.2^(90/365)\\B(90/365) ≈ $1713.17\\\)
As a result, the loan debt after 90 days is roughly $1713.17.
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The mean of (x + 5), (x + 3), (2x + 1) and (x - 6) is 12. What is the
value of x?
Answer:
x=9
Step-by-step explanation:
answers too short so cigdtusrysyksrytf7hiuf6s4td6figiio
Can someone answer this for e pleaseeeee
Answer: 220
Step-by-step explanation:
Proof of Laws Consider sets A and B, and: 1. Prove the absorption law A U (AnB) = A by universal generalization (applied twice). 2. Prove the associative law An (BnC) = (A n B) n C by membership table.
1.) Proving the absorption law A U (AnB) = A by universal generalization (applied twice).
2.) Proving the associative law An (BnC) = (A n B) n C by membership table.
1.) Let x be an element in An (BnC).
By universal generalization, x is in A or x is in (AnB).
If x is in A, then x is in A U (AnB) by definition of union.
If x is in (AnB), then x is in A and x is in B by definition of intersection.
Since x is in A, x is in A U (AnB) by definition of union.
Therefore, x is in A U (AnB) if and only if x is in A.
By universal generalization, A U (AnB) = A.
2.) Prove the associative law An (BnC) = (A n B) n C by membership table.
Let x be an element in An (BnC).
By definition of intersection, x is in A and x is in (BnC).
By definition of intersection, x is in B and x is in C.
Therefore, x is in A and x is in B and x is in C.
By definition of intersection, x is in (A n B) and x is in C.
By definition of intersection, x is in (A n B) n C.
Therefore, x is in An (BnC) if and only if x is in (A n B) n C.
By membership table, An (BnC) = (A n B) n C.
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safe side bank pays an interest rate of 8% per year on certificate accounts. how much money must be put into an account to earn $60 in one year?
Find the surface area of the pyramid. Round to the nearest tenth if necessary.
The surface area of the pyramid is 126. 22 in²
How to determine the valueThe formula for calculating the surface area of a triangular pyramid is expressed as;
SA = BA + 1/2(P + s)
Such that the parameters are;
SA is the surface area of the pyramid.BA is the base area of the pyramid.P is the perimeter of the pyramid.s is the slant heightFrom the information
Perimeter = 3(15.75) = 47. 25 in
Base area = 1/2 × 12.25 × 15.75 = 96. 47 in²
Substitute the values
Surface area = 96. 47 + 1/2 (47. 25 + 12.25)
add the values
Surface area = 96. 47 + 1/2 (59.5)
divide the values
Surface area = 126. 22 in²
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If u had 693 cats and 593 died
Answer:
you would have 100 cats left
Sarah is 13 years older than Mike. The sum of their ages is 37. How old is Sarah and how old is Mike? Enter your answer as on ordered pair (x,y).
Answer:
(24,13)
Step-by-step explanation:
24 is Sarah's age.
13 is Mike's age.
System:
\(\left \{24+13=37\)
I hope this helped!
Graph a line with a slope of 3/4 that contains the point (2,-3).
Answer:
Start at the y-intercept (0, -4.5) and then use rise over run (Up 3 and right 4)
Step-by-step explanation:
y - y1 = m(x - x1)
y + 3 = 3/4(x - 2)
y + 3 = 3/4x - 3/2
y = 3/4x - 9/2
I'm not sure what the answer is could anyone help?
a)From this 230 is divisible by 10.Then 995 and 526 are not divisible by 10.b)From this 230 and 995 are divisible by 5 and 526 is not divisible by 5.c) From this 230,995,526 are divisible by 2.
Divisibility by 10: A number is divisible by 10 if its last digit is 0. Therefore, 230 is divisible by 10 since its last digit is 0. 995 and 526 are not divisible by 10 since their last digits are not 0. The mathematical formula for divisibility by 10 is: (10 | N) = 0,Where N is the number that is being tested for divisibility. Calculation: For example, let's take the number 230. (10 | 230) = 0230/10 = 23 Therefore, 230 is divisible by 10. Divisibility by 5: A number is divisible by 5 if its last digit is 0 or 5. Therefore, 230 and 995 are divisible by 5 since their last digits are 0 and 5 respectively. 526 is not divisible by 5 since its last digit is not 0 or 5. The mathematical formula for divisibility by 5 is: (5 | N) = 0Where N is the number that is being tested for divisibility. Calculation: For example, let's take the number 995. (5 | 995) = 0995/5 = 199 .Therefore, 995 is divisible by 5. Divisibility by 2: A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8. Therefore, 230, 995, and 526 are all divisible by 2 since their last digits are 0, 5 and 6 respectively. The mathematical formula for divisibility by 2 is: (2 | N) = 0Where N is the number that is being tested for divisibility. Calculation: For example, let's take the number 526. (2 | 526) = 0.526/2 = 263 .Therefore, 526 is divisible by 2.
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Find the Surface area of the trapezoid
please help
show work
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
PLZ HELP! Also, give an explanation. :)
Answer: First option (your selected answer)
Step-by-step explanation:
(rotating an object 360° will bring it to its original position)
(rotating an object 180° will turn it upside-down)
(rotating an object 90° will make it sideways)
(to calculate the scale factor, pick a point on both triangles that are of the same corner)
ex: A: (-12,12) and A': (4,-4)
(ask yourself what you need to multiply the x and y coordinates of ΔABC by to get the resulting x and y coordinates of the ΔA'B'C')
\(-12*-\frac{1}{3}=4\\12*-\frac{1}{3}=-4\)
(you multiply -1/3 to get the x and y value of the second triangle)
(though the provided options do not display the negative scale factor, the scale factor should be negative)
ΔABC - ΔA'B'C', because ΔA'B'C' is obtained by dilating ΔABC by a scale factor of 1/3 and then rotating it about the origin by 180°
Find the volume of a pyramid inscribed in a cube with base area 100cm²
Answer: 600 \(cm^{3}\)
Step-by-step explanation:
The formula for the volume of a pyramid is, V=\(\frac{1}{3}\) BhSince the base of the pyramid is a square, the base area is \(10^{2} or 100 cm^{2}\).Soooo, substitute 100 for B and 18 for h in the formula.\(V=\frac{1}{3} (100)(18)\) = 6004. Therefore, the volume of the square pyramid is 600 \(cm^{3}\)
If Lupe walk 0 miles, he will earn $50 for his library fundraiser just by signing up to help.
But if Lupe walks 1 mile, he will earn $60 for his library fundraiser by signing up & walking, $10 for walking the one mile & $50 just for signing up to help.
How much did Lupe make per 1 mile?
Answer:
10
Step-by-step explanation:
60-50 I hope this helps have a nice day:)
∠A and ∠B are complementary. m∠A=29°. find m∠B.
Answer:
55 degrees
Step-by-step explanation:
Add the expressions up and set up an equation.
( 2 x − 29 ) + ( x + 23 ) = 90 Simplify and solve for x.
3 x − 6 = 90 3 x = 96 x = 32 Find angle B.
x + 23 = 32 + 23 = 55
Hope this helps, have a nice day/night! :D
Answer:
m∠B = 61°
Step-by-step explanation:
Complementary means two angles that add up to the sum of 90°.
Since we are given m∠A = 29°, subtract 29° from 90°.
90 - 29 = 61
m∠B = 61°
marie is building a fence around a yard in the shape of a square the area of the yard is 196 square feet how many feet of fencing does marie need for her yard? a.14 b.26 c.56 d.784 please help!!!
Answer:
I think it is 14 Feet
Step-by-step explanation:
Because if we multiply 14 by 14 we will get 196 I also did this test and that is what I put. I hope this helps
Is it easier for you to visualize the reaction by using pictures words or symbols?.
Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.
What is photosynthesis?
Photosynthesis is the process in which green plants prepare their own food in the presence of sunlight and light energy is converted into chemical energy by the process of cellular respiration.
The process of photosynthesis takes place in green plants only due to presence of chlorophyll and materials such as sunlight, water, carbon dioxide is required for the process of photosynthesis.
The equation of photosynthesis is represented below:
6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂.
The process of food manufacturing in plant is done through photosynthesis and the plants are known as autotrophs as they are the producers.
In the process of photosynthesis the reactant have 6 carbon dioxide molecules and six water molecules, and light energy converted into chemical energy due to presence of chlorophyll.
Therefore, Chemical reactions such as photosynthesis explains the manner in which green plants manufacture their own food using the energy derived from sunlight.
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