Answer: 9:50 AM/PM
Step-by-step explanation: Since the shorthand (hour) is on the 9, the hour is 9:00. The long hand (minutes) is on the 10, so it is 50. So, therefore we have 9:50. We don't know if it's am or pm, so we don't know if it's in the morning or the afternoon.
Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?
The Correct answer is A. (-4,1) ordered pair generated by this model should be discarded because the values are unreasonable.
In algebra, a quadratic equation (from Latin quadratus 'rectangular') is any equation that can be rearranged in well-known form as ax²+bx+c=0 Where x represents an unknown value, and a, b, and c constitute recognized numbers.
One supposes usually that a ≠ zero; the one's equations with a = zero are taken into consideration degenerate because the equation then will become linear or even simpler. The numbers a, b, and c are the coefficients of the equation and can be prominent with the aid of calling them, respectively, the quadratic coefficient, the linear coefficient, and the consistent or loose time period.
The values of x that satisfy the equation are referred to as answers to the equation, and roots or zeros of the expression on its left-hand aspect. A quadratic equation has at most two answers. If there is handiest one solution, one says that it's miles a double root. If all the coefficients are real numbers, there are both actual solutions, a single actual double root, or two complicated answers which can be complicated conjugates of each other.
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Complete Question:
Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. which ordered pair generated by this model should be discarded because the values are unreasonable?
a linear ___ is a mathematical statement that two linear expressions, or a linear expression and a constant, are not equal.
A linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.
What is a linear equation?The mathematical assertion that two linear expressions, or a linear expression and a constant, are not equal is made via a linear equation.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A mathematical equation must take the form y=mx+b in order to be classified as a linear function (in which m is the slope and b is the y-intercept).
Therefore, a linear equation is used to prove the mathematical result that two linear expressions, or a linear expression and a constant, are not equivalent.
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Form a polynomial whose zeros and degree are given.
Zeros: - 3, multiplicity 1; - 1, multiplicity 2; degree 3
The polynomial of third degree whose zeros and degree are given, for zero of (-2), multiplicity 1 and for zero of (3), multiplicity 2 is [tex]f(x) = x^3 - 10x^2 - 15x + 18[/tex]
What is Polynomial?A polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
From the question statement, a third degree polynomial has a zero of (-2), multiplicity 1 and another zero of (3), multiplicity 2.
We need to determine the polynomial.
Since, (-2) is a zero of the polynomial, then (x+ 2) will be a factor of the polynomial. for zero of (-2), multiplicity is 1, means that the factor of (x + 2) is only multiplied once.
Similarly, (3) is another zero of the polynomial, then (x - 3) will be a factor of the polynomial.
For zero of (3), multiplicity is 2, this means that the factor of (x - 3) will be multiplied twice
Hence, our required polynomial is [tex]f(x) = x^3 - 10x^2 - 15x + 18[/tex]
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the class average is 85% and the standard deviation is 3%. a student from the class earned a 89%. what proportion of the class scored higher than the student assuming the grades are distributed normally? please round your answers to the nearest thousandth. (you'll need an r window and xpnorm to answer this.)
The proportion of the class that scored higher than the student will be 0.0912.
What is the z-score?The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.
The z-score is given as
z = (x - μ) / σ
Where μ is the mean, σ is the standard deviation, and x is the sample.
The class normal is 85% and the standard deviation is 3%. Then the student from the class who earned 89% higher will be given as,
z = (0.89 - 0.85) / 0.03
z = 0.04 / 0.03
z = 1.3333
Then the probability is given as,
P(x > 89%) = P(z > 1.3333)
P(x > 89%) = 0.091211
The proportion of the class that scored higher than the student will be 0.0912.
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The half-life of a certain radioactive substance is 13 days. There are 2.5 grand of the substance in totally. Type an expression for the amount of substance as a function of t. When will there be less than 1 g remaining? Please show work
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &\\ P=\textit{initial amount}\dotfill &2.5\\ t=\textit{elapsed time}\\ h=\textit{half-life}\dotfill &13 \end{cases} \\\\\\ ~\hfill {\Large \begin{array}{llll} A=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}} \end{array}} ~\hfill[/tex]
well, let's instead find when will there be 1 gram first off, then after that it's all downhill, so A = 1
[tex]\stackrel{A}{1}=2.5\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \cfrac{1}{2.5}=\left( \frac{1}{2} \right)^{\frac{t}{13}}\implies \log\left( \cfrac{1}{2.5} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{t}{13}} \right][/tex]
[tex]\log\left( \cfrac{1}{2.5} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]\implies \cfrac{\log\left( \frac{1}{2.5} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13}} \right]}=t\stackrel{\textit{after about 17 days and 5 hours}}{\implies 17.19\approx t ~\hfill }[/tex]
The angle measures of an isosceles triangle are (4x + 5)°, (4x + 5)°, 10°.
What is the measure (in degrees) of an exterior angle supplementary to one
of the base angles?
The measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.
What is an isosceles triangle?
An isosceles triangle, therefore, has both two equal sides and two equal angles. The name derives from the Greek iso (same) and skelos (leg)
In an isosceles triangle, the two base angles are equal. Therefore, the measure of each base angle is (4x + 5)°.
An exterior angle of a triangle is supplementary to one of the base angles if it forms a straight line with the base angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two base angles.
Therefore, the measure of an exterior angle supplementary to one of the base angles of this isosceles triangle is 2 * (4x + 5)° = 8x + 10°.
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if your sample gave a negative result for the disease-causing agent, does this mean that you do not have the disease? what reasons could there be for a negative result when you actually do have the disease?
A negative result does not mean that you do not have the disease. It could be a false negative.
The reasons that could be there for a negative result when there is actually the presence of the disease
The ELISA may not be sensitive enough to detect very low concentration of the disease agent, as might occur when one is tested soon after infection before a proper immune response occurs.
As HIV buds from the surface of the host cell, it incorporates some of the host cell Human leukocyte antigen into its envelope. False negatives usually occurs during the window between infection and an antibody response to the virus which is known as seroconversion.
Therefore, if the sample gave a negative result for the disease-causing agent, it does not mean that you do not have the disease
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find an equation of the tangent plane to the given parametric surface at the specified point. x = u v, y = 8u2, z = u − v; (2, 8, 0)
The equation for the normal line B gives us :
L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R
Find the solution ?
Full question is:
Find equations of the tangent plane and the normal line to the given surface at the specified point. x + y + z = 7e(xyz) at a specified point (0, 0, 7)
If we have a level surface, then it will give us
f(x,y,z) = x+y+z = 7e(xyz). where f is the function of the x, y, and z coordinates.
Now let us calculate the ∇ gradient of f at point (0,0,7):
∇ = (fx,fy,fz) = (1−7yz,1−7xz,1−7xy)
= (1, 1, 1)
We get the equation for the tangent plane A:
A: 1(x−0) + 1(y−0) + 1(z−7)=0
This can also be written as:
x+y+z = 7 ------------------------------------------------------------------(a)
The equation for the normal line B gives us :
L: (x,y,z) = (0,0,7) + t(1, 1, 1), t ∈ R --------------------------------(b)
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a standard card deck consists of 52 cards, made up of 13 cards of each of 4 different suits. how many unique 5 card hands exist that are all the same suit? hint: does order matter?
By the information provided in the question, we got to know that - there are 2598960 ways.
What are combinations?Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.
[tex]^nC_{r} = \frac{n!}{r!(n - r)!}[/tex]
You are choosing a subset of size 5 from a set of size 52.
[tex]Note that the order you are dealt these 5 cards is irrelevant.[/tex] Thus, order doesn’t matter.
Thus, this is a combination problem. The formula for this is:
[tex]Comb(52,5) = \frac{52!}{5! 13!} = 2598960.[/tex]
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Im so confused..How do I solve this?
We can shown that the triangles are congruent by a translation of 2 units left and then a reflection over the y-axis.
What are congruent triangles?Congruent triangles are triangles that have the same side lengths.
Transformations that keep the congruence of a triangle are given as follows:
Translation: the polygon is moved up/down or left/right.Rotation: over the x-axis or over the y-axis.One vertex of the original triangle is given as follows:
A(8,8).
The equivalent vertex on the reflected and translated triangle is given as follows:
A'(6,-8).
Considering the reflection over the y-axis that we can see from the image, the complete rule is given as follows:
(x,y) -> (x - 2, - y).
Meaning that the translation was two units left.
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You roll a 6- sided die what is p (greater than 3 or factor of 14)
Answer:
7
Step-by-step explanation:
Which equation has no solution?
O 4(x+3) + 2x= 6(x+2)
O 5+2(3+2x) = x+3 (x+1)
O 5(x+3) + x = 4 (x+3) + 3
O 4 + 6(2+x) = 2(3x+8)
We know that the equation (B) 5+2(3+2x) = x+3 (x+1) has no solution.
What are equations?The definition of equations in algebra is a mathematical statement that shows the equality of two mathematical equations.
For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
Solve equations to find the equation which has no solution as follows:
(A) 4(x+3) + 2x= 6(x+2)
4(x + 3) + 2x = 6(x + 2)
4x + 12 + 2x = 6x + 12
6x = 6x
L. H. S = R. H. S
(B) 5+2(3+2x) = x+3 (x+1)
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3x + 3
11 + 4x = 4x + 3
L. H. S ≠ R. H. S
(We got our answer and so we don't need to solve further options)
Therefore, we know that the equation (B) 5+2(3+2x) = x+3 (x+1) has no solution.
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Correct question:
Which equation has no solution?
a 4(x+3) + 2x= 6(x+2)
b 5+2(3+2x) = x+3 (x+1)
c 5(x+3) + x = 4 (x+3) + 3
d 4 + 6(2+x) = 2(3x+8)
A taxi charges $3 plus a fee of $1.25 for each mile traveled. the total cost of a ride, without a tip is $18. How many miles is the trip? two-step equations
Answer: 12 miles
Step-by-step explanation:
Let y represent the cost and x represent the number of miles!
y = 1.25x + 3
Now put the $18 in for y
18= 1.25x + 3
15 = 1.25x
x = 12 miles
Answer:
Step-by-step explanation:
We can model the cost of a taxi trip with y = 1.25x + 3, where y is the total cost and x is the miles traveled. $1.25 is charged per mile, and the initial $3 is added to find the total cost. We know that the total cost is $18, so we can put 18 in for y and solve for x:
18 = 1.25x + 3
15 = 1.25x (subtracted 3 from both sides)
12 = x (divided each side by 1.25)
So, the trip was 12 miles
Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. No less than 4 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
The required graph of the inequality has been shown and the solution is; 8 Nickels and 12 dimes.
How to solve a system of inequalities?
Inequality can be defined as the relation of the equation possessing the symbol of ( ≤, ≥, <, >).
Let the number of nickels be x and let the number of dimes be y,
We are told that Addison has x dimes and y nickels, having a minimum of 20 coins worth at most $1.60 combined. Thus, we can generate the equations as;
x + y = 20
x = 20 - y - - - - (1)
0.05x + 0.10y ≤ 1.60 - - - -(2)
We are also told that no less than 4 of the coins are dimes. Thus;
x ≥ 4
From the graph, one solution is given as 8 Nickels and 12 dimes.
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which measure of central tendency can be computed only from interval or ratio data? mode median mean all of these must be computed from interval or ratio data. none of these can be computed from interval or ratio data.
The mean can only be used with interval/ratio level data.
what is ratio data ?
Ratio data is a form of quantitative (numeric) data. It measures variables on a continuous scale, with an equal distance between adjacent values. While it shares these features with interval data (another type of quantitative data), a distinguishing property of ratio data is that it has a 'true zero.
What are mean , median and mode?
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Hence, the mean can only be used with interval/ratio level data.
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Numerical Integration Estimate the surface area of the oil spill using the Trapezoidal Rule and Simpson's Rule. Using a Tangent Line In Exercises 61-64, set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point. f(x) = x^3, (1, 1) y = x^3 - 2x. (-1, 1) f(x) = 1/x^2 + 1, (1, 1/2) y = 2/1 + 4x^2, (1/2, 1)
The area is 0.25
What is a tangent line?
The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together. A straight line has a slope of f'(c), where f' is the derivative of f, and is said to be tangent to a curve at a point x = c if it passes through the point (c, f(c)) on the curve. Space curves and curves in n-dimensional Euclidean space have a similar definition.
[tex]$$\begin{aligned}& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3-2 x\right] \\& f^{\prime}(x)=\frac{\mathrm{d}}{\mathrm{d} x}\left[x^3\right]-\frac{\mathrm{d}}{\mathrm{d} x}[2 x] \quad \text { Sum } / \text { Rest rule } \\& f^{\prime}(x)=3 x^{3-1}-2 \quad \text { Power rule } \\& f^{\prime}(x)=3 x^2-2 \\&\end{aligned}$$[/tex]
Now finding tangent for a=-1,
[tex]\begin{aligned}& y=f^{\prime}(a)(x-a)+f(a) \\& y=f^{\prime}(-1)(x+1)+f(-1) \\& y=\left(3(-1)^2-2\right)(x+1)+(-1)^3-2(-1) \\& \mathbf{y}=\mathbf{x}+\mathbf{2}\end{aligned}$$[/tex]
For the first area,
[tex]$$\begin{aligned}& A_1: \int_{-2}^{-\sqrt{2}} x+2 d x=\frac{1}{2} x^2+\left.2 x\right|_{-2} ^{-\sqrt{2}} \\& A_1=\frac{1}{2}(-\sqrt{2})^2+2(-\sqrt{2})-\left(\frac{1}{2}(-2)^2+2(-2)\right) \\& A_1=\mathbf{3}-\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{1}} \approx \mathbf{0 . 1 7 1 5 7 2 8 7 6} \ldots\end{aligned}$$[/tex]
For the second area,
[tex]$$\begin{aligned}& A_2: \int_{-\sqrt{2}}^{-1} x+2-\left(x^3-2 x\right) d x=-\frac{1}{4} x^4+\frac{3}{2} x^2+\left.2 x\right|_{-\sqrt{2}} ^{-1} \\& A_2=-\frac{1}{4}(-1)^4+\frac{3}{2}(-1)^2+2(-1)-\left(-\frac{1}{4}(-\sqrt{2})^4+\frac{3}{2}(-\sqrt{2})^2+2(-\sqrt{2})\right) \\& A_2=-\frac{\mathbf{1 1}}{\mathbf{4}}+\mathbf{2} \sqrt{\mathbf{2}} \text { squared units } \\& \mathbf{A}_{\mathbf{2}} \approx \mathbf{0 . 0 7 8 4 2 7 1 2 4} \ldots .\end{aligned}$$[/tex]
Hence, required area is
[tex]$$\begin{aligned}& A=A_1+A_2 \\& A=3-2 \sqrt{2}-\frac{11}{4}+2 \sqrt{2} \\& \mathbf{A}=\frac{\mathbf{1}}{\mathbf{4}}=\mathbf{0 . 2 5}\end{aligned}$$[/tex]
The area is 0.25
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There were 900 freshwater fish at an aquarium 212 fish are in the large tank there are 16 fish in each smaller tank How many smaller tanks are there
Answer: 43 small tanks
Step-by-step explanation:
First, take 900 - 212 = 688 fish in small tanks
Then take 688 divided by 16 fish in each tank = 43
So there are 43 smaller tanks
5.76 is 4.8% of what number?
Answer:
120
Step-by-step explanation:
Let the unknown number be x.
Therefore, if 5.76 is 4.8% of x:
[tex]\boxed{\begin{aligned}4.8\%\; \textsf{of} \; x&=5.76\\\\\implies \dfrac{4.8}{100}x&=5.76\\\\4.8x&=576\\\\x&=\dfrac{576}{4.8}\\\\x&=120 \end{aligned}}[/tex]
So the unknown number is 120.
the count in a bacteria culture was 400 after 10 minutes and 2000 after 30 minutes. assuming the count grows exponentially, what was the initial size of the culture?
The bacteria culture has an initial size of 79.7409
Given,
The count in a bacteria culture;
After 10 minutes is 400
After 30 minutes is 2000
Assume that the count grows exponentially;
We have to find the initial size of the culture;
Here,
The growth of population can be calculated using;
P = P₀ (1 + r)^t
Here,
Count of bacteria, P = 400 and 2000
Time period, t = 15 and 30
Initial size = P₀
So,
400 = P₀ × (1 + r)¹⁰
2000 = P₀ × (1 + r)³⁰
Take P₀ common.
Then,
400/(1 + r)¹⁰ = 2000/(1 + r)³⁰
(1 + r)³⁰/ (1 + r)¹⁰ = 2000/400
(1 + r)¹⁰ = 5
1 + r = 1.175
r = 0.175
Now,
The value of P₀ should be determined from the above equation;
That is,
400 = P₀ × (1 + 0.175)¹⁰
P₀ = 400/ (1 + 0.175)¹⁰
P₀ = 79.7409
Therefore,
The initial size of the bacterial culture is 79.7409
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what is the quotient of 3 1/5 divided by 1/3?
Answer:
peanut butter jelly
Step-by-step explanation:
I love that!
The value of the expression 3 ¹/₅ ÷ 1/3 will be 9.6 or 48/5.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
3 ¹/₅ and 1/3
Convert the mixed fraction number into a fraction number. Then we have
3 ¹/₅ = 16 / 5
Then the division of the numbers 16/5 and 1/3 will be given by putting a division sign between them. Then we have
⇒ 16/5 ÷ 1/3
⇒ (16/5) / (1/3)
⇒ (16/5) x (3)
⇒ 48/5
⇒ 9.6
The value of the expression 3 ¹/₅ ÷ 1/3 will be 9.6 or 48/5.
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A person saves 12.5% of his income how much does he spend in a month if his monthly income is Rs 10,000. Give full explanation 
Answer:
8750 Rs
Step-by-step explanation:
Saves
12.5 : 100 = x : 10 000
x = 10 000 * 12.5 / 100
x = 100 * 12.5
x = 1250 Rs
Total he spends
10 000 - 1250 = 8750 Rs
A regular polygon is shown, with one of its angle measures labeled a.
9 sided regular polygon with one angle labeled a
If m∠a = (5z + 65)°, find the value of z.
z = 15
z = 20
z = 23
z = 41
The measure of z in the polygon is (a) z = 15
How to determine the measure of z?From the question, we have the following parameters that can be used in our computation:
Shape = 9-sided polygon
Parameter to calculate = the measure of z
The sum of the interior angles is calculated using the following angle formula
The sum of the interior angles = ( n − 2 ) × 180 ∘ where n is the number of sides
In this case
n = 9
Substitute the known values in the above equation, so, we have the following representation
The sum of the interior angles = (9 − 2) × 180∘
Evaluate
The sum of the interior angles = 1260∘
So, the internal angle is
Angle = 1260/9
Evaluate
Angle = 140
This means that
5z + 65 = 140
So, we have
5z = 75
Divide by 5
z = 15
Hence, the angle is (a) z = 15
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Geometry- Can someone break this down for me in a simple way?
Answer:
z = 22
Step-by-step explanation:
Because we are given that angle measures TUW and VUW are the same, we can assume that both triangles are the same since they also have 90 degree angles and both their third angles are equal to 54. (I found that out by taking 180 degrees which is the total angle measure of all triangles, and subtracted it by 90 and 36).
Since they are the same, that means that side TW is the same length as side VW. With this information we can set up an expression:
2z = z + 22
Now, all we have to do is solve for z
2z = z + 22
-z - z
z = 22
Which numbers below are even? Check all that apply.
A. 5464
B. 1126
C. 9092
D. 6669
E. 4950
F. 6921
Answer: A, B, C, E
Step-by-step explanation:
a) what are the key features of a graph’s exponential functions?
B: explain how you find each key feature and what happens to the graphs if you were to add and subtract a constant term
C: how do increasing linear functions and exponential growth functions compare? How does this increase compare or differ?
Answer:
Check below/above
Step-by-step explanation:
A) The graph passes through the point (0,1).
The domain is all real numbers.
The range is y>0.
B) it would be a linear equation that shifts the graph vertically.
C) the slope of an exponential function continues to increase, while the slope of a linear function stays the same.
can someone help me with making the x the subject of the formula
100 point up for grabs pls helpppp
y =xa+ b
y =xa− b
y =x + 2 divided by two
Answer:
[tex]\textsf{1)} \quad x=\dfrac{y-b}{a}[/tex]
[tex]\textsf{2)} \quad x=\dfrac{y+b}{a}[/tex]
[tex]\textsf{3)} \quad x=2y-2[/tex]
Step-by-step explanation:
Question 1[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad &y & =xa+b\\\\&\textsf{Subtract $b$ from both sides}: \quad & y-b&=xa+b-b \\\\&\textsf{Simplify}: \quad &y-b&=xa \\\\&\textsf{Divide both sides by $a$}: \quad &\dfrac{y-b}{a} &=\dfrac{xa}{a} \\\\&\textsf{Simplify}: \quad &\dfrac{y-b}{a} &=x\\\\&\textsf{Switch sides}: \quad & x&=\dfrac{y-b}{a}\end{aligned}}[/tex]
Question 2[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad &y & =xa-b\\\\&\textsf{Add $b$ to both sides}: \quad & y+b&=xa-b+b \\\\&\textsf{Simplify}: \quad &y+b&=xa \\\\&\textsf{Divide both sides by $a$}: \quad &\dfrac{y+b}{a} &=\dfrac{xa}{a} \\\\&\textsf{Simplify}: \quad &\dfrac{y+b}{a} &=x\\\\&\textsf{Switch sides}: \quad & x&=\dfrac{y+b}{a}\end{aligned}}[/tex]
Question 3[tex]\boxed{\begin{aligned}&\textsf{Given}: \quad & y&=\dfrac{x+2}{2} \\\\&\textsf{Multiply both sides by $2$}: \quad & 2 \cdot y&=2 \cdot \dfrac{x+2}{2} \\\\&\textsf{Simplify}: \quad & 2y&=x+2 \\\\&\textsf{Subtract $2$ from both sides}: \quad & 2y-2&=x+2-2 \\\\&\textsf{Simplify}: \quad & 2y-2&=x \\\\&\textsf{Switch sides}: \quad &x&=2y-2\end{aligned}}[/tex]
A. f(x)=17.78(4.86)x
i.The value of the function when x=0 is?
ii. Find the ratio of output values that correspond to increases of 1 in the input value in order to determine the 1-unit growth factor.?
iii. Determine the 1-unit percent change.? %
B. h(x)=94.71(0.57)x
i. The value of the function when x=0 is?
ii. Find the ratio of output values that correspond to increases of 1 in the input value in order to determine the 1-unit growth factor.?
iii. Determine the 1-unit percent change.? %
-57 decrease
In this equation.
The value of the function at x=0 is 17.78(4.86)^0 = 17.78(1) = 17.78.
ii. The ratio of output values corresponding to an increment of 1 in input values is (4.86)^1 = 4.86.
iii. A percent change of 1 unit is (4.86 - 1) × 100% = 286% increase.
For the function h(x) = 94.71(0.57)^x:
Thus, the value of the function at x=0 is 94.71(0.57)^0 = 94.71(1) = 94.71.
ii. The ratio of the output value corresponding to an increment of 1 in the input value is (0.57)^2 = 0.57.
iii. Percentage change of 1 unit is (0.57 - 1) × 100% = -57 reduction
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3) Why does the following equation have no solutions? (Explain your answer with words and simplifying the equation)
The equation is false (we can remove the dependence with the variable x) that is why the equation has no solutions.
Why the equation has no solutions?Here we have the following linear equation:
5 - 4x - 7 - 10x = -8x - 4 - 6x - 10
We want to see why we don't have any solutions, to check that, we need to simplify both sides of the equation. Let's start by grouping like terms:
5 - 4x - 7 - 10x = -8x - 4 - 6x - 10
(5 - 7) + (-4x - 10x) = (-4 - 10) + (-8x - 6x)
-2 - 14x = -14 - 14x
Notice that now we can add 14x in both sides of the equation, then we will get:
-2 -14x + 14x = -14 - 14x + 14x
-2 = -14
So we have a false equation, this happens because the equation does not truly depend of the value of x.
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Studious athletes A university is concerned about the academic standing of its intercollegiate athletes. A study committee chooses an SRS of 50 of the 316 athletes to interview in detail. Suppose that $40 \%$ of the athletes have been told by coaches to neglect their studies on at least one occasion. What is the probability that at least 15 in the sample are among this group?
The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.
Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.
To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:
$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$
We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:
$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$
Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.
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A store sells grape jelly in 15-ounce jars for $13.59. Find the price per ounce
Answer:
91 cents per ounce
Step-by-step explanation:
Divide 13.59 by 15
Answer: $0.91
Step-by-step explanation:
Take $13.59 divided by 15 = $0.91 per ounce
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