Answer:
The numbers are 10 and 10Step-by-step explanation:
As described in the hint:
the numbers are x and 20 - x, their product is maximum possible value.The product is:
x(20 - x) = - x² + 20xThis is a quadratic expression ax² + bx + c with the leading coefficient of a = - 1, b = 20 and c = 0.
It has a maximum and no minimum value since a < 0.
The x-coordinate of the maximum is the vertex which is x = - b/2a.
The x- coordinate of the vertex is:
x = - 20/-2 = 10The maximum value itself is:
- 10² + 20*10 = - 100 + 200 =100Answer:
10 and 10.
[tex]f(x)=-x^2+20x[/tex]
Maximum value of the function is 100.
Step-by-step explanation:
Two numbers whose sum is a positive integer, and whose product is the maximum possible value have to be two positive integers.
Pairs of positive integers whose sum is 20:
1 and 192 and 183 and 174 and 165 and 156 and 147 and 138 and 129 and 1110 and 10The pair of numbers whose product is the maximum possible value is the pair of numbers that are closest to each other.
Therefore the pair of numbers is 10 and 10:
[tex]\implies x = 10[/tex]
[tex]\implies 20 - x = 10[/tex]
Form a quadratic function by multiplying:
[tex]\implies f(x)=x(20-x)[/tex]
[tex]\implies f(x)=20x-x^2[/tex]
[tex]\implies f(x)=-x^2+20x[/tex]
The maximum value of the function is the y-value of its vertex.
[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
To convert the function to vertex form, complete the square.
Factor out negative 1:
[tex]\implies f(x)=-(x^2-20x)[/tex]
Add and subtract the square of half the coefficient of the term in x:
[tex]\implies f(x)=-\left(x^2-20x+\left(\dfrac{-20}{2}\right)^2-\left(\dfrac{-20}{2}\right)^2\right)[/tex]
[tex]\implies f(x)=-(x^2-20x+100-100)[/tex]
[tex]\implies f(x)=-(x^2-20x+100)+100[/tex]
Factor the perfect square trinomial:
[tex]\implies f(x)=-(x-10)^2+100[/tex]
Therefore, the vertex of the function is (10, 100), and so the maximum value of the function is 100.
4.2 = 16.7 - 5y solve for y
Answer:
y = 2.5
Step-by-step explanation:
To double check this, you can do 5 times (2.5), then do 16.7 minus that answer so you do, 16.7- 12.5 which does indeed equal 4.2
Answer:
y = 2.5
Step-by-step explanation:
[tex]4.2 =16.7-5y[/tex]
Subtract 16.7 from both sides of the equation you get:
[tex]-12.5=-5y[/tex]
Divide by -5:
[tex]2.5=y[/tex]
Hope this answers your question :)
How do I solve this? I’ve been doing it regularly but I don’t know what to do now
On solving the 3 variable equation you will get the answer x=6, y=1, and z=2. It is solved by elimination method.
What is elimination method?
The elimination method involves removing a variable from a system of linear equations by employing addition or subtraction along with multiplication or division of the variable coefficients.
Now, consider the first two equations.
-3x + 3y +2z = -11
3x + 5y - 5z = 13
Multiply the upper eqation with 5 and lower eqation with 2 to make coefficient of z equal.
-15x + 15y + 10z = -55
6x + 10y - 10z = 26
Add these two equations to eliminate z.
-9x + 25y = -29 ... (1)
Now, consider second and third eqation from the the eqation given in the question.
3x + 5y - 5z = 13
5x - 6y - z = 22
Multiply the upper equation with 5 to make coefficient of z equal in both the equations.
3x + 5y - 5z = 13
25x - 30y - 5z = 110
Now, subtract the lower equation from the upper equation.
3x + 5y - 5z = 13
-25x + 30y + 5z = -110
To get the following equation:
-22x + 35y = -97 ... (2)
Now, consider equation (1) and (2).
-9x + 25y = -29
-22x + 35y = -97
Multiply the upper equation with 35 and lower equation with 25.
-315x + 875y = -1015
-550x + 875y = -2425
Now, subtract these two equations to get the following equation:
235x = 1410
x = 6
Substitute the value of x in equation (1).
-9x + 25y = -29
-9 (6) + 25y = -29
25y = 25
y = 1
Now, substitute the value of x and y in following eqation:
-3x + 3y + 2z = -11
-3(6) + 3(1) + 2z = -11
-15 + 2z = -11
2z = 4
z =2
Hence, on solving the 3 variables equation, you will get the answer x=6, y=1, and z=2.
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5. A sprinter runs at 12m/s. Convert this to km/h.
a) 2 km/h b) 12 km/h C) 3.6 km/h d) 43.2 km/h
Answer:
43.2km/h
Step-by-step explanation:
1km = 1000m
1h = 3600s
1km/h to m/s
= 1 × 1000/3600
= 1000/3600
1m/s to km/h
= 1 ÷ 1000/3600
= 1 × 3600/1000
Hence, 12m/s = 12 × 3600/1000
= 43.2km/h
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume the variable is positive.) ln x^2-1/x^7 , x>1
By using property of logarithms, We get the answer
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x
Given,
In the question:
The equation is :
In [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1
To solve by using by using property of logarithms to expand the expression as a sum, difference, and / or constant multiple of logarithms.
Now, According to the question:
We know that:
The property of logarithms is:
[tex]log_{a}{\frac{m}{n} } = log_{a}m - log_{a}n[/tex]
The given equation is :
In [tex]\frac{x^{2} -1}{x^7}[/tex] , x > 1
In [tex]\frac{x^{2} -1}{x^7}[/tex] = In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex]
Again, Using the another property of logarithms.
[tex]log_am^x = nlog_am[/tex] {x∈ R}
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [tex](x^2 -1)[/tex] - 7 In x
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In [ (x + 1)(x - 1)] - 7In x
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x
{Log (mn) = [tex]log_{a}m - log_{a}n[/tex]}
Hence, By using property of logarithms, We get the answer
In [tex](x^2 -1)[/tex] - In [tex]x^7[/tex] = In (x + 1) + In (x -1) - 7 In x
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4x + 9 > 1. Pls help
The length of a rectangular window is 5 feet more than its width. The area of the
window is 36 square feet. What are the dimensions of the window? Could a moving
company use that window to bring a standard upright piano into an apartment?
The dimensions of the window: Length = 9ft , width = 4ft
What are dimensions?
In mathematics, a dimension is the length or width of an area, region, or space in one direction.
The homes we live in and the items we use on a daily basis all have three dimensions: height, length, and width.
Here, we have
l = w + 5
Area = length × width
The linear equation of the given dimension is:
36 = (w + 5)w
w² + 5w - 36 = 0
(w + 9)(w - 4) = 0
w + 9 = 0
w = -9
We only measure positive numbers so, we disregard this value.
we take,
w - 4 = 0
w = 4
l = 4 + 5
l = 9
The length of the window is 9 ft and the width of the window is 4 ft.
Hence, the dimensions of the window: Length = 9ft , width = 4ft
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One of the legs of a right triangle measures 11 cm and the other leg measures 14 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
∴ The measure of the hypotenuse is 20cm (to the nearest tenth).
Step-by-step explanation:
Let the length of the hypotenuse be x cm.
x² = 11² + 14²
∴ x = 20cm (to the nearest tenth)
Rewrite in simplest terms: (-10x+2)+(-9x+8)
Answer: -19x + 10
Step-by-step explanation:
1. Remove parenthesis
-10x + 2 - 9x + 8
2. Collect like terms
(-10x - 9x) + (2 + 8)
3. Simplify
-19x + 10
Which of the following is the necessary condition for creating confidence intervals for the population mean? A. Known population parameter B. Normality of the population C. Known standard deviation of the estimator D. Normality of the estimator (e.g., sample mean)
Answer:
D. Normality of the estimator (e.g., sample mean)
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The question was incomplete. Check below the complete question.
Which of the following is the necessary condition for creating confidence intervals for the population mean? A. Known population parameter B. Normality of the population C. Known standard deviation of the estimator D. Normality of the estimator (e.g., sample mean)
Somebody please help.
Select the correct answer.
What is the exact value of cos 105°?
Check the picture below.
[tex]\textit{Sum and Difference Identities} \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ cos(105^o)\implies cos(60^o+45^o)\implies cos(60^o)\cdot cos(45^o)-sin(60^o)\cdot sin(45^o) \\\\\\ \cfrac{1}{2}\cdot \cfrac{\sqrt{2}}{2}~~ - ~~\cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{2}}{2}\implies \cfrac{\sqrt{2}}{4}~~ - ~~\cfrac{\sqrt{6}}{4}\implies {\Large \begin{array}{llll} \cfrac{\sqrt{2}-\sqrt{6}}{4} \end{array}}[/tex]
A rectangular prism has dimensions of 2cm x 3cm x 2cm the prism is 94g
Answer:
32 cm²
Step-by-step explanation:
Error Analysis On a math test a student, Jake, has to identify all the coefficients and constants of the expression 9 + 6b + y.
Jake says that 6 is a coefficient and 9 is a constant. Identify all the coefficients and constants of the expression. What error might Jake have made?
The coefficients of the expression are 6, 1.
The constant of the expression is 9.
The error Jake might have made is that: D. Jake did not include the coefficient 1.
What is a coefficient?In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.
Based on the algebraic expression provided, we can reasonably infer and logically deduce that there are two (2) coefficients and these include 6 as the coefficient of b and 1 as the coefficient of y.
This ultimately implies that, the error Jake made was not including the coefficient 1 for y.
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Complete Question:
On a math test a student, Jake, has to identify all the coefficients and constants of the expression 9 + 6b + y. Jake says that 6 is a coefficient and 9 is a constant. Identify all the coefficients and constants of the expression. What error might Jake have made?
The coefficient(s) of the expression is/are __
Use a comma to separate answers as needed.)
The constant(s) of the expression is/are __
(Use a comma to separate answers as needed.)
What error might Jake have made?
A. Jake said 9 is a coefficient. It is actually a constant.
OB. Jake said 6 is a constant. It is actually a coefficient.
OC. Jake did not include the constant 1.
OD. Jake did not include the coefficient 1.
solve for y
-8x+2y= -24
Answer:
y = -12 + 4x
Step-by-step explanation:
1. Add 8x to both sides of the equation.
2y = -24 + 8x
2. Divide each term in 2y = -24 + 8x by 2, then simplify.
• Simplify left side: cancel the common factor of 2
y = -24/2 + 8x/2
• Simplify right side: 2y/2 = -24/2 + 8x
y = -12 + 4x
On Saturday mornings, Eddie volunteers at the hospital where his mother works. One
Saturday, he answers phone calls at the information desk while the receptionist is away. The
he spends 40 minutes delivering flowers to patients' rooms. In all, Eddie volunteers at the
hospital for 90 minutes that day.
Which equation can you use to find the amount of time t that Eddie answers phone calls?
According to the concept of difference, the amount of time spend on answering the phone call is 50 minutes.
Difference:
Difference means the result of one of the important mathematical operations, which is obtained by subtracting two numbers and it tells us by how much a number differs from the other.
Given,
On Saturday mornings, Eddie volunteers at the hospital where his mother works. One Saturday, he answers phone calls at the information desk while the receptionist is away. The he spends 40 minutes delivering flowers to patients' rooms. In all, Eddie volunteers at the hospital for 90 minutes that day.
Here we need to find the amount of time spend on answering the phone calls.
While we looking into the given question, we have identified the following things,
Total amount of time spend by Eddie = 90 minutes
Time spend in delivering flowers = 40 minutes
So, the time spend by answering the phone calls is calculated as the difference between the total time and the flower delivering time
=> 90 - 40
=> 50
Therefore, he spent 50 minutes on answering the phone calls.
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Questions 1-4: The number of classes (X) a student takes in a given semester follows the following probability distribution:
X 0 1 2 3 4 5
P(X) 0.4 0.25 0.15 0.08 0.02 ???
1. What is the probability they take 5 classes?
2. What is the probability they take at least one class?
3. What is the probability a student will take 2 or 3 classes in a semester?
4. What is the expected number of classes a student will take in a given semester? (show your work on this one, and a screenshot of how you worked it out on the calculator or excel).
The probability to take 5 classes is 0.1, while the probability to take at least one class is 0.6, the probability to take 2 or 3 classes is 0.23 and the expectation of the distribution is 1.37.
1.
We know that in a probability distribution, the sum of all the probabilities is always equal to 1.
Let the probability of X = 5 be a
Hence,
0.4 + 0.25 + 0.15 + 0.08 + 0.02 + a = 1
or, 0.9 + a = 1
or, a = 1 - 0.9
or, a = 0.1
Hence the probability to take 5 classes is 0.1.
2.
We need to find P(X ≥ 1)
= 1 - P(X = 0)
we already know from the table that P(X = 0) is 0.4
Hence, P(X ≥ 1)
= 1 - 0.4
= 0.6
Hence, the probability to take at least one class is 0.6
3.
The probability to take 2 or 3 classes in a semester = P( X = 2) + P(X = 3)
= 0.15 + 0.08
= 0.23
4.
We know that the expectation of any distribution
= ∑xp(x)
where,
x is the random variable
p(x) is the probability of the random variable
Therefore,
E(X) = 0 X 0.4 + 1 X 0.25 + 2 X 0.15 + 3 X 0.08 + 4 X 0.02 + 5 X 0.1
= 0 + 0.25 + 0.30+ 0.24 + 0.08 + 0.50
= 1.37
Therefore the expectation of the given distribution is 1.37
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HELP HELP HELP HELPP
ONLY ANSWER IF YOU KNOW
Answer:
Step-by-step explanation:
1(x1)+ (-4)x2+ (-10)x3 = -40 Eq 1
0 + (1)x2 + 3(x3) = 14 Eq 2
0 + (-2)x2 + (-5)x3 = -23 Eq 3
from the 2nd equations we get
x2 + 3*x3 = 14
x2 = 14 - 3*x3
plug this into equation 3
(-2)*(14-3*x3) + (-5)x3 = -23
now solve for x3 :)
-28+6*x3-5*x3 = -23
-28 +x3 = -23
x3 = 5
nice !
now find x2
x2 = 14-3*(5)
x2 = -1
now find x1
x1 + (-4)*(-1) + (-10)*5 = -40
x1 +4 -50=-40
x1 = 6
X = [ 6 ; (-1) ; 5 ]
Find the length of each line segment
RS With R ( 6,5) and S (6,-4)
The Length of the line segment RS is 9 units
Line segment:In geometry, the line that is bounded by two distinct points is known as a Line segment. In simple words, we can say that a line segment is part of a straight line that connects two distinct points.
To find the length of the line segment we can use the distance formula
d = √ [ (x₂ - x₁)² + (y₂ - y₁)²]Where (x₁, y₁) and (x₂, y₂) are endpoints of Line segments
Here we have
R ( 6,5) and S (6,-4)
And we need to find the length of the line segment RS
Length of Line segment RS = distance between two points
= √ [ (6 - 6)² + (-4 - 5)²]
= √ [ (-9)²]
= 9 units
The Length of the line segment RS is 9 units
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[tex]2x^{2} +7x-4=0[/tex]
What is the factored form of n2 + n
The factored form of n2 + n is: n(n+1).
How to find the factored form?Given data:
n²+n
Now let find the factored form of n²+n
n²+n
Rewrite in factored form
n(n+1)
Hence,
n²+n = n(n+1)
Therefore n(n+1) is the factored form.
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a study of elephants is conducted to determine the average weight of a certain subspecies of elephants. the standard deviation for the population is 1500 pounds. at a 99% level, how many elephants need to be weighed so the average weight will be accurate to within 200 pounds?
The birth weight of elephants at the 99% confidence level is 3820 pounds
What is the standard deviation?
Standard deviation is defined as the amount of variation or the deviation of the numbers from each other.
The average birth weight of elephants is 200 pounds = 200
The deviation of 60 pounds. = 1500
The birth weight of elephants is at the 85th percentile. z = 99%= 1.645
Now from the formula of z-score:-
[tex]z=\sqrt{\frac{x-\mu}{\sigma} }[/tex]
[tex]1.64 =\sqrt{\frac{x-200}{1500} }\\[/tex]
[tex]1.645^{2} =\frac{x-200}{1500}[/tex]
2.68 = (x-200)/1500
2.68×1500=x-200
4020-200=x
3820=x
Hence the birth weight of elephants at the 99% level percentile is 3820 pounds
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Sadie and Cora each want to run for president of their school's student body council. In order to do so, they must collect a certain number of signatures and get a nomination. So far, Sadie has 10 signatures, and Cora has 20. Sadie is collecting signatures at an average rate of 3 per day, whereas Cora is averaging 2 signatures every day. Assuming that their rate of collection stays the same, eventually the two will have collected the same number of signatures. How many signatures will they both have?
The number of signatures that Sadie and Cora have is 40 signatures.
How many signature they have?Sadie has 10 and she is collecting signatures at an average rate of 3 per day. This will be:
10 + 3d
Cora has 20 and is averaging 2 signatures every day. This will be:
= 20 + 2d
The equation will be:
10 + 3d = 20 + 2d
Collect like terms
3d - 2d = 20 - 10
d = 10
Therefore, the number of signature will be:
= 10 + 3d
= 10 + 3(10)
= 10 + 30
= 40
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What is the y-intercept of each equation for 5x-2y=20
Step-by-step explanation:
The y intercept is the y value when x=0,
So plug in x=0,
[tex]5(0) - 2y = 20[/tex]
[tex] - 2y = 20[/tex]
[tex]y = - 10[/tex]
Write a formula for the sequence:
2.3,\ 2.8,\ 3.3,\ 3.8,\ ...2.3, 2.8, 3.3, 3.8, ...
A formula for the sequence 2.3, 2.8, 3.3, 3.8, ... is a_n = 1.8 + 0.5 n.
First, let us understand the arithmetic progression:
Arithmetic Progression (AP) is a number sequence in which the difference between any two consecutive numbers is a constant value.
We can find the common difference (d) by subtracting any two consecutive terms of arithmetic progression.
The nth term of an arithmetic progression is given by:
a_n = a + (n - 1)d
where
a = first term of an arithmetic progression
n = nth term of an arithmetic progression
d = common difference
We are given the following sequence;
2.3, 2.8, 3.3, 3.8, ...
We need to write a formula for the given sequence.
Let us find the common difference;
d = 2.8 - 2.3 = 0.5
a = 2.3
substitute the values in the above formula;
a_n = 2.3 + (n - 1) * 0.5
a_n = 2.3 + 0.5 n - 0.5
a_n = 1.8 + 0.5 n
So, the formula for the given sequence is a_n = 1.8 + 0.5 n.
Thus, a formula for the sequence 2.3, 2.8, 3.3, 3.8, ... is a_n = 1.8 + 0.5 n.
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a) Express the null and alternative hypotheses in symbolic form for this claim. Assume d = SUV-Car. Enter != for
≠
≠
.
H
0
:
μ
¯
d
H
0
:
μ
d
¯
H
a
:
μ
¯
d
H
a
:
μ
d
¯
b) What is the significance level?
α
=
α
=
c) What is the test statistic? Round to 3 decimal places.
=
a) The hypothesis are given as follows:
Null: [tex]H_0: \mu_d \geq 0[/tex]Alternative: [tex]H_1: \mu_d < 0[/tex]b) The significance level is of α = 0.1.
c) The test statistic is of: t = -2.69.
d) The p-value is of: 0.018
e) The decision is to reject the null hypothesis.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that SUVs sustain less damage, that is, the mean is equal or greater than zero, hence:
[tex]H_0: \mu_d \geq 0[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the SUVs sustain less damage, that is, the mean if less than zero, hence:
[tex]H_1: \mu_d < 0[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The sample of the differences is given as follows:
447, -893, -2373, 271, -1680, -1916, -1676.
Using a calculator from the above sample, the values of these parameters are given as follows:
[tex]\overline{x} = -1117, \mu = 0, s = 1100, n = 7[/tex]
Hence the test statistic is of:
t = (-1117 - 0)/(1100/sqrt(7))
t = -2.69.
What are the p-value and the test?Using a t-distribution calculator, considering a left-tailed test, as we are testing if the mean is less than a value, with 7 - 1 = 6 df and t = -2.69, the p-value is of 0.018.
Since this p-value is less than the significance level of 0.1, the decision is to reject the null hypothesis.
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A jeweler is dividing 3/8 a pound of rubies among 4 lots. What part of a pound will each lot weigh?
A 1/16
B 3/32
C 1/8
D 1/4
Answer:
B 3/32
Step-by-step explanation:
3/8 divided by 4
do the keep change flip method and solve
3/8 x 1/4
12.0.5f-2.3g
f=12,g=2
Answer:14.1099
Step-by-step explanation:
What is the equation of the line that passes through the point (-4, 5) and has an
undefined slope?
keeping in mind that a line with an undefined slope is a vertical line, Check the picture below.
Find the value of tan W rounded to the nearest hundredth, if necessary.
The value of tan W is 5/12
From the question, we have
tan W = 15/36
= 5/12 =0.41
Divide:
Divide, in its simplest form, means to divide into two or more equivalent portions, spaces, groups, or divisions. Divide, in plain English, means to provide the entire thing to a group in equal portions or to divide it into equal pieces. Let's say a square is divided into two triangles with equal areas by a diagonal. A division operation may or may not provide an integer as the outcome. The outcome may occasionally take the form of decimal numbers.
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ASAP PLEASE!
A particular dishwasher uses 4 gallons of water per load. Their advertising claims that hand washing the dishes uses 6 times as much water. According to this estimate, how many gallons of water would it save to wash 215 loads using the dishwasher instead of by hand?
Answer: 4,300 gallons of water
215 x 4 = 860 gallons of water using the dishwasher
215 x 6 x 4 = 5,160 gallons of water by hand
5,160 - 860 = 4,300 gallons of water saved by using the dishwasher.
- Your welcome, keep it up champ.
I Given:
2x-9
5
= 1
Prove: x = 7
It is proven that the value of x in the given expression 2x-9 -5 = 1 is 7.
Given: 2x-9 -5 = 1
We need to prove that x = 7
2x - 9 - 5 = 1
2x - 13 = 1
2x = 14
x = 7
Therefore, it is proven that the value of x in the given expression 2x-9 -5 = 1 is 7.
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