Answer:
huh???
Step-by-step explanation:
How many gallons Of 40 % Sulfuric acid solution should be mixed with 20 % Sulfuric acid solution to obtain 50 gallons of 25%
Sulfuric acid solution ?
One of the vertices of an equilateral triangle is on the vertex of a square and two other vertices are on the not adjacent sides of the same square. Find the side of the triangle if the side of the square is 10 ft.
Answer:
10.35 ftStep-by-step explanation:
Refer to attachment
Let the side of the triangle be a
The line segment x as per Pythagorean is: √(a² - 10²)
Therefore the vertices of the triangle are equidistant from the vertex of the square, so the distance x is same for both vertices
From the triangles we have side of the triangle:
a = √(100 + x²) anda = √(10 - x)² + (10 - x)²Comparing the two we have:
100 + x² = 2(10 - x)²100 + x² = 200 - 40x + 2x²x² - 40x + 100 = 0x² - 2*20x + 20² = 300(x - 20)² = 300x - 20 = ±10√3x = 20 ± 10√3x = 20 ± 17.32x = 37.32 - this is excluded as it can't be greater than side of the squarex = 2.68 ftSo the value of a is:
a = √(100 + x²)a = √100 + 2.68² = √107.1824 = 10.35 ftAnswer:
10√6 - 10√2
Step-by-step explanation:
The shorter leg of the small triangle created by the square and the equilatoral triangle = x
Other leg = 10
One of the triangles is a 45-45-90 triangle, so the hypotenuse, which also happens to be a side of the equilatoral triangle can be denoted as √2(10-x).
Using pythagoearn theorem, we know that relative to the other 2 of the 15-75-90 triangles, their hypotenueses which also happen to be sides of the equilatoral triangle are √(100+x^2)
So using transitivity, we can create this equation:
√(100+x^2)=√2(10-x)
Solving this using quadratic equations, we get that x= 20+10√3, x=20-10√3
The first equation can't be true since x has to be <10, so that means
x=20-10√3
We has substitute this into another equation to get a side length of the equilatoral triangle.
The answer is 10√6 - 10√2
A tree in Milan's backyard has been growing for 245 years. The tree is 14 meters tall.
What is the unit rate in meters per year?
Write your answer as a fraction or a mixed number in simplest form.
A turtle weights 153.7g what would be its weight in milligrams?
Answer:
153700
Step-by-step explanation:
Subtracting -9 from any number is the same as
Answer:
0
Step-by-step explanation:
Which number
is between 2.23 and 2.24 on a number line?
Answer:
There are infinity many numbers between 2.23 an 2.24, but if you want the exact middle, it's 2.235
Hope this helped :)
6 points Emily’s family needs to rent a moving truck to move their belongings to a different house. The rental cost for Trucks-A-Lot is $42 per day plus $0.72 per mile. The rental cost for Move-It-Truckers is $70 per day plus $0.12 per mile. Let m represent Emily’s mileage. Write an equation to represent the cost of renting each truck, and determine what will be the number if miles for which the truck cost the same amount.
If h(x) = -2x - 10, find h(-4).
Answer:
8 - 10 or -2
Step-by-step explanation:
h(-4) = -2(-4) - 10 = 8 - 10. If you want the answer to the problem, 8 - 10 = -2.
Help !! Plz don’t understand
Answer:
see the attachment
Step-by-step explanation:
We hope this assignment came with an explanation. Otherwise, it's a meaningless image of numbers and circles.
__
We suspect the top circle is supposed to contain the product of the left and right circles, and the bottom circle is supposed to contain their sum.
When you're given only the product and sum, it can work reasonably well to look at the factorization of the product, and the sums of the factor pairs. It usually doesn't take long to find the sum of interest, if the numbers you're looking for are integers. (For the last problem, we had to look at several factor pairs before we found the right one.)
Which factors affect the gravitational force between two objects?
EEEE
distance and velocity
mass and distance
mass and weight
acceleration and weight
Answer:
Newton's law also states that the strength of gravity between any two objects depends on two factors: the masses of the objects and the distance between them. Objects with greater mass have a stronger force of gravity between them.
Step-by-step explanation:
Find the Slope And Y Intercept
PLEASE HELP
Answer:
The y-intercept is -2
the slope is 2.5/1 or 2.5
Explantation:
The slope formula is m=y2-y1/x2-x1
we can use the points (1,0.5) and (0,-2) (i got these points from the graph)
m=-2-0.5/0-1
m=2.5 or 2.5/1
Which of the followings are true or false. Justify your answers
a. The solution set to a system of three equations in three unknowns cannot be a plane.
b. A system of linear equations cannot have only two solutions.
c. The solution set to a consistent rank 2 linear system in four unknowns would be a line in four-dimensional space.
d. A system of four equations in four unknowns always has a solution.
e. A system of four equations in four unknowns can have at most one solution
Answer:
a. True
b. True
c. False
d. False
e. False
Step-by-step explanation:
a
[tex]x-y-z=1\\x+2y-2z=2\\3x+3y-3=3\\\\\begin{pmatrix} 1 & 1 & -1|&1\\ 2&2&-2|&2\\3&3&-3|&3\end{pmatrix}\\\\\\R_2 \rightarrow R_2-R_1\\R_3 \rightarrow R_3-R_1\\\\\begin{pmatrix} 1 & 1 & -1|&1\\ 0&0&~~0|&0\\0&0&~~0|&0\end{pmatrix}\\\\x+y-z=1[/tex]
thus there is a plane
b. If a system of solution has more than one solution than it can have infinite amount of solutions so there can be any amount of solutions except 2.
c. The solution set of a consistent rank 2 linear system with four unknowns will be a plane in the four dimensional space.
d. Following is an example which proves it wrong i-e no solution
[tex]\\\\\\\\x_1=1\\x_2+x_3=2\\x_2+x_3+x_4=0\\[/tex]
e.as shown from following example it has infinite solutions
[tex]\\\\\\\\x_1+x_2=1\\2x_1+2x_2=2\\x_3=1\\x_4=1\\[/tex]
so a system can have more than one solution
please help to find log 11 base 2. PLEASE HURRY UP INEED TO SUBMIT MY HOMEWORK TOMORROW.
HELP ME PLEASE
The value for log₂11 is 3.459.
To find the logarithm of 11 base 2, we need to determine the power to which we must raise 2 to obtain the value 11. In other words, we need to solve the equation 2^x = 11 for x.
Finding the exact value of log₂11 can be challenging since 11 is not a power of 2. Therefore, we can approximate the answer using numerical methods.
One way to approach this is by using the bisection method. We start by considering a lower bound and an upper bound for the value of x. Since 2^3 = 8 and 2^4 = 16, we can choose the interval [3, 4] as a starting point.
Next, we evaluate the midpoint of the interval, x = (3 + 4) / 2 = 3.5, and calculate 2^3.5 ≈ 11.314. Since this is larger than 11, we update our upper bound to 3.5.
We repeat the process by evaluating the midpoint of the new interval [3, 3.5], which gives us x = (3 + 3.5) / 2 = 3.25. Calculating 2^3.25 ≈ 10.63, we see that it is smaller than 11. Thus, we update our lower bound to 3.25.
We continue this iterative process, halving the interval each time, until we reach a satisfactory level of precision. After several iterations, we find that the value of x is approximately 3.459.
Therefore, an approximation for log₂11 is 3.459.
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Factor the expression using the GCF.
7 + 14 =
Answer:
1+2
Step-by-step explanation:
Parallel Lines and Angle Relationships
#1 What is the value of y. Type your answer below. *
#2 If the m<4 is 110 degrees, what is m<1 ? (Give number value only.) *
#3 If e || f and a || b, what is the value of y. *
A) 87
B) 88
C) 91
D) 92
Answer:
1. y = 80°
2. m<1 = 70°
3. y = 92°
Step-by-step explanation:
1. Since lines c and b are parallel lines cut across by transversal a, therefore:
y = 80° (alternate exterior angles are congruent)
2. m<1 is the supplement of m<4, because the angle that forms a linear pair with <1, corresponds with <4.
Therefore: m<1 = 180° - 110° = 70°
3. First, find the value of x.
(x + 1)° + (x - 3)° = 180° (supplementary)
x + 1 + x - 3 = 180°
2x - 2 = 180°
2x = 180 + 2 (addition property of equality)
2x = 182
x = 182/2 (division property of equality)
x = 91
(x + 1)° = y° (alternate interior angles are congruent)
Substitute x = 91
91 + 1 = y
92° = y
is 5.32147 rational or irrational
Answer:
5.32147 is a rational number
Step-by-step explanation:
5.32147 is a rational number because it can be turned into a fraction.
Numbers that Make Sense A rational number is any number that can be expressed as a ratio (or percentage) of two integers.
Rational number:It can be represented as a ratio of 2 integers, with the denominator not being 0, whereas it cannot be expressed in the infraction. The number of Irrational have non-terminating decimals, whereas rational numbers have termination decimals.
[tex]\to 5.32147 \\\\\to \frac{532147 }{100000}[/tex]
Therefore, the given number is a "rational number".
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A survey of nonprofit organizations showed that online fundraising has increased in the past year. You want to estimate the population mean one-time gift donation. Based on a random sample of 55 nonprofits, the mean of one-time gift donation is $125. The value $125 is:________.
a. an interval estimate
b. a statistic
c. a parameter
d. a confidence interval
e. a point estimate
Answer:
e. a point estimate
Step-by-step explanation:
When an estimate for the unknown population parameter is expressed by a single value it is called a point estimate.
Example : If we wish to find the height of a very large group of students on the basis of a sample and we find it to be 64 inches. 64 inches is the point estimate.
Similarly the value given is the point estimate.
Point estimate of the population parameter provides as an estimate a single value calculated from the sample that is likely to be close in value to the unknown parameter. It is to be noted that a point estimate will not in general be equal to the population parameter as the random sample used is one of the many possible samples which could be chosen from the population.
One semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.
Required:
a. How many failed for exactly two of the three reasons?
b. How many failed because of poor attendance and not studying but not because of not turning in assignments?
c. How many failed because of exactly one of the three reasons?
d. How many failed because of poor attendance and not turning in assignments but not because of not studying?
Answer:
(a) 16 students failed for exactly two of the three reasons.
(b) 7 students failed because of poor attendance and not studying but not because of not turning in assignments.
(c) 14 students failed because of exactly one of the three reasons.
(d) 3 students failed because of poor attendance and not turning in assignments but not because of not studying.
Step-by-step explanation:
We are given that one semester in a chemistry class, 14 students failed due to poor attendance, 23 failed due to not studying, 15 failed because they did not turn in assignments, 9 failed because of poor attendance and not studying, 8 failed because of not studying and not turning in assignments, 5 failed because of poor attendance and not turning in assignments, and 2 failed because of all three of these reasons.
As shown in the diagram attached below, a Venn diagram represents the situation given in the question;
In the diagram below, 2 in represents purple color represents the number of students failed because of all three of these reasons.
7 represents the number of students who failed because of poor attendance and not studying but not due to not turning in assignments.
6 represents the number of students who failed because of not studying and not turning in assignments but not due to poor attendance.
3 represents the number of students who failed because of poor attendance and not turning in assignments but not due to not studying.
2 in red color represents the number of students who failed only due to poor attendance.
8 in red color represents the number of students who failed only due to not studying.
4 in red color represents the number of students who failed only due to not turning in assignments.
(a) The number of students who failed because of exactly two of the three reasons = 7 + 6 + 3 = 16 students.
(b) The number of students who failed because of poor attendance and not studying but not because of not turning in assignments = 9 - 2 = 7 students.
(c) The number of students who failed because of exactly one of the three reasons = 2 + 8 + 4 = 14 students.
(d) The number of students who failed because of poor attendance and not turning in assignments but not because of not studying = 5 - 2 = 3 students.
Roulette is a very popular game in many American casinos. In roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, bearing the numbers 00, 0, 1, 2, ..., 35, 36. The number of the arc on which the ball stops is the outcome of one play of the game. The numbers are also colored in the following manner:
Red: 1,3,5,7,9,12,14,16,18,19,21.23,25,27,30,32.34,36
Black: 2.4,6,8,10,11,13,15,17,20,22,24.26,28,29,31,33,35 Greerz: 00,O
Players may place bets on the table in a variety of ways, including bets on odd, even, red, black, high, low, etc. Define the following events:
A: (Outcome is an odd number (00 and 0 are considered neither odd nor even)]
B: (Outcome is a black number]
C: {Outcome is a low number (1-18))
Calculate the probabilities of the following events:
a. AUB
b. A ∩ C
c. BU C
d. Bc
e. A ∩ B ∩ C
Answer:
a. P(AUB) = 0.74
b. P(A∩C) = 0.24
c. P(BUC) = 0.71
d. P(Bc) = 0.55
e. P(A∩B∩C) = 0.11
Step-by-step explanation:
n(U) = Total number of elements in the set = number of elements in the universal set = 38
A: (Outcome is an odd number (00 and 0 are considered neither odd nor even)]
An odd number referred to any integer, that is not a fraction, which is not possible to be divided exactly by 2. Therefore, we have:
A: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35
B: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35
C: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
a. Calculate the probability of AUB
AUB picks not more than one each of the elements in both A and B without repetition. Therefore, we have:
AUB = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35
n(AUB) = number of elements in AUB = 28
P(AUB) = probability of AUB = n(AUB) / n(U) = 28 / 38 = 0.736842105263158 = 0.74
b. Calculate the probability of A ∩ C
A∩C picks only the elements that are common to both A and C. Therefore, we have:
A∩C: 1, 3, 5, 7, 9, 11, 13, 15, 17
n(A∩C) = number of elements in A∩C = 9
P(A∩C) = probability of A∩C = n(A∩C) / n(U) = 9 / 38 = 0.236842105263158 = 0.24
c. Calculate the probability of BUC
BUC picks not more than one each of the elements in both B and C without repetition. Therefore, we have:
BUC: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35
n(BUC) = number of elements in BUC = 27
P(BUC) = probability of A∩C = n(BUC) / n(U) = 27 / 38 = 0.710526315789474 = 0.71
d. Calculate the probability of Bc
Bc indicates B component it represents all the elements in the universal set excluding the elements in B. Therefore, we have:
Bc: 00, 0, 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36
n(Bc) = number of elements in Bc = 20
P(Bc) = probability of Bc = n(Bc) / n(U) = 20 / 38 = 0.526315789473684 = 0.55
e. Calculate the probability of A∩B∩C
A∩B∩C picks only the elements that are common to A, B and C. Therefore, we have:
A∩B∩C: 11, 13, 15, 17
n(Bc) = number of elements in A∩B∩C = 4
P(A∩B∩C) = probability of A∩B∩C = n(A∩B∩C) / n(U) = 4 / 38 = 0.105263157894737 = 0.11
Note: All the answers are rounded to 2 decimal places.
The sum of three consecutive multiples of 7 is 168 find the numbers
Answer:
the 3 numbers are 49 56 and 63
n − 9 ≥ −3
what is the solution inequailty
Answer:
n[tex]\geq[/tex]6
Step-by-step explanation:
Answer:
n ≥ 6
Step-by-step explanation:
[tex]n-9\geq -3\\\\\mathrm{Add\:}9\mathrm{\:to\:both\:sides}\\\\n-9+9\ge \:-3+9\\\\Simplify\\\\n\ge \:6[/tex]
HELP PLS I NEED THIS DONE ASAP
Answer:
a = 4, b = 0
Also, a = 0 and b = 0 :)
What is the value of the expression below when y=8 and z=8?
10y-3z
Answer:
We have to find the value of 10y - 4zSolution :Given Values
y = 8z = 8Substituting these values in 10y - 3z
we get,
= 10 × 8 - 3 × 8
= 80 - 24
= 56
Hencevalue of 10y - 3z is 56Growth models question
The recursive formula of the linear growth model is Pₙ = Pₙ ₋ ₁ + 5
The explicit formula of the model is P(n) = 7 + 5n
37 cars are sold in the 6th week
The recursive formula of the linear growth modelFrom the question, we have the following parameters that can be used in our computation:
P₀ = 7
P₁ = 12
So, the common difference is
d = 12 - 7
Evaluate
d = 5
The recursive formula of the linear growth model is
Pₙ = Pₙ ₋ ₁ + d
So, we have
Pₙ = Pₙ ₋ ₁ + 5
The explicit formula of the linear growth modelHere, we have
P₀ = 7
d = 5
The explicit formula of the linear growth model is
P(n) = P₀ + nd
So, we have
P(n) = 7 + 5n
Cars sold in the 6th weekThis means that
n = 6
So, we have
P(6) = 7 + 5 * 6
Evaluate
P(6) = 37
Hence, 37 cars are sold in the 6th week
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Use the given conditions to find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.
sin(u) = -3/5, 3π/2 < u < 2π
sin(2u) =
cos(2u) =
tan(2u)
Answer:
[tex]\sin(2u)=-\dfrac{24}{25}[/tex]
[tex]\cos(2u)=\dfrac{7}{25}[/tex]
[tex]\tan(2u)=-\dfrac{24}{7}[/tex]
Step-by-step explanation:
Given sin(u) = -3/5, use the trigonometric identity sin²θ + cos²θ = 1 to find cos(u):
[tex]\begin{aligned}\sin^2(u)+\cos^2(u)&=1\\\\\left(-\dfrac{3}{5}\right)^2+\cos^2(u)&=1\\\\\dfrac{9}{25}+\cos^2(u)&=1\\\\\cos^2(u)&=1-\dfrac{9}{25}\\\\\cos^2(u)&=\dfrac{16}{25}\\\\\cos(u)&=\dfrac{4}{5}\end{aligned}[/tex]
As u is in the interval 3π/2 < u < 2π, the angle is in quadrant IV of the unit circle. In quadrant IV, cos is positive and sin is negative. Therefore:
[tex]\sin(u)=-\dfrac{3}{5} \qquad \cos(u)=\dfrac{4}{5}[/tex]
Calculate tan(u) by using the identity tanθ = sinθ/cosθ:
[tex]\tan(u)=\dfrac{-\frac{3}{5}}{\frac{4}{5}}=-\dfrac{3}{4}[/tex]
[tex]\boxed{\begin{minipage}{5 cm}\underline{Double Angle Identities}\\\\$\sin (2\theta)=2\sin \theta \cos \theta $\\\\$\cos (2\theta)=\cos^2\theta-\sin^2\theta$\\\\$\tan (2\theta)=\dfrac{2\tan\theta}{1 -\tan^2\theta}$\\\end{minipage}}[/tex]
Use the double angle identities to find sin(2u), cos(2u) and tan(2u).
[tex]\hrulefill[/tex]
[tex]\begin{aligned}\sin (2u)&=2\sin u \cos u\\\\&=2\left(-\dfrac{3}{5}\right) \left(\dfrac{4}{5}\right)\\\\&=-\dfrac{24}{25}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
[tex]\begin{aligned}\cos (2u)&=\cos^2u - \sin^2u\\\\&=\left(\dfrac{4}{5}\right)^2-\left(-\dfrac{3}{5}\right)^2\\\\&=\dfrac{16}{25}-\dfrac{9}{25}\\\\&=\dfrac{7}{25}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
[tex]\begin{aligned}\tan (2u)&=\dfrac{2\tan(u)}{1 -\tan^2(u)}\\\\&=\dfrac{2\left(-\frac{3}{4}\right)}{1 -\left(-\frac{3}{4}\right)^2}\\\\&=\dfrac{-\frac{3}{2}}{1 -\frac{9}{16}}\\\\&=\dfrac{-\frac{3}{2}}{\frac{7}{16}}\\\\&=-\dfrac{3}{2} \cdot \dfrac{16}{7}\\\\&=-\dfrac{48}{14}\\\\&=-\dfrac{48\div2}{14\div2}\\\\&=-\dfrac{24}{7}\end{aligned}[/tex]
g=15yx for x
how do you solve it
Answer:
divide by 15 y to get x=g/15y
Step-by-step explanation:
Hope this helps
2 tens 3 tenths 1 thousandth _____ 20.31
Answer:
20.31
Step-by-step explanation:
2 tens = 20
3 tenths = 0.3
1 thousandths = 0.01
20.31
To make subtracting integers easier you can change all subtraction problems to
Answer:
ssssss
Step-by-step explanation:
Answer:addidion
Step-by-step explanation:
A candy bowl has 50 pieces of candy. Gumballs make up 20% of the
candy bowl. How many pieces of candy are gumballs?
Answer:
10 gumballs
Step-by-step explanation:
Since gumballs are 20 percent of 50 pieces(or 1/5), we divide 50 by 1/5.
We then get ten as our answer.
Andrew is choosing between four loans. Loan P has a nominal rate of 10.393%, compounded daily. Loan Q has a nominal rate of 10.516%, compounded weekly. Loan R has a nominal rate of 10.676%, compounded monthly. Loan S has a nominal rate of 10.755%, compounded annually. Which loan will give Andrew the best effective interest rate? a. loan P b. loan Q c. loan R d. loan SAndrew is choosing between four loans. Loan P has a nominal rate of 10.393%, compounded daily. Loan Q has a nominal rate of 10.516%, compounded weekly. Loan R has a nominal rate of 10.676%, compounded monthly. Loan S has a nominal rate of 10.755%, compounded annually. Which loan will give Andrew the best effective interest rate? a. loan P b. loan Q c. loan R d. loan S
Answer:
D as in Drink
Loan S as a Snake
Step-by-step explanation:
The loan that offers the lowest effective interest rate is loan P.
What is the effective interest rate?Effective interest rate is the actual interest rate that is paid on a loan. It takes into effect the compounding.
What loan offers he lowest effect interest rate?Effective annual rate = (1 + APR / m ) ^m - 1
M = number of compounding
Loan P = (1 + 0.10393/365)^365 - 1 = 10.95%
Loan Q = (1 + 0.10516/52)^52 - 1 = 11.08%
Loan R = (1 + 0.10676 / 12)^12 - 1 = 11.2%
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