Therefore , the solution of equation comes out to be the depth of the river is 5+(6.5/3)*x.
What algebraic fundamentals are there?Algebraic fundamentals include: Algebraic expression addition and subtraction, algebraic expression division and multiplication, figuring out equations, literal formulas and equations, Applying verbal issues
Here,
Given : Let x = amount of rainfall (inches)
Let D = depth of river (feet)
Depth of river increases due to rainfall. Relationship of the depth of increase (in feet) to the amount of rainfall (inches) is:
6.5 feet / 3 inches rainfall
Depth will increase by (6.5/3)*x
Depth of river will be the initial depth plus the amount of increase due to rainfall. So:
D = 5 + (6.5/3)*x
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A college currently has 600 students enrolled
full time. Of these students, 400 are science
majors while 200 are liberal arts majors. If
350 of the students are male, and 250 of the
males are science majors, how many female
students are liberal arts majors?
(A) 200
(B) 150
(C) 100
(D) 50
Answer:
C) 100
Step-by-step explanation:
250+600-350-400
850-350-400
500-400=100
What is the value of z in the equation 4(2z + 3) = 12?
−13
12
0
12
Answer:
0
Step-by-step explanation:
8z +12 = 12
8z = 0
z =0
Answer:
The answer is 0
Step-by-step explanation:
4(2z+3)=12?=
We use the distributive property to distribute the 4 into the 2.
8z=3=12?=
8 + 3 is 12 so the z has no part to play in this.
z=0
You could also have divided from both sides of the equation, but doing it this way is easier for me.
Find the area of a triangle with base of 6m and height of 15m
Answer:
45 meters
Step-by-step explanation:
[tex]Area=\frac{1}{2}bh\\ A=\frac{1}{2}(6)(15)\\ A=3(15)\\A=45[/tex]
⊱________________________________________________________⊰
Answer:
A=45 m²
Step-by-step explanation:
The formula for the area of a triangle is, [tex]\bigstar\underline{\boxed{\sf{A=\frac{bh}{2}}}}[/tex].
where :
[tex]\triangleright\sf{A=Area,b=base,h=height}\triangleleft[/tex]
Substitute the values,
[tex]\large\begin{gathered}\sf{A=\frac{6*15}{2} \\ \sf{A=\frac{90}{2}\\\bigstar\underline{\boxed{\sf{A=45 \ m^2}}}} \end{gathered}[/tex]
Done !! Hope this made sense to you :)
[tex]\small\boldsymbol{Calligraphy}[/tex]
⊱______________________________________________________⊰
Type the correct answer in each box. Use numerals instead of words.
Consider function g.
6,
0,
-4,
-8<-2
-2 ≤ x < 4
4 x < 10
What are the values of the function when = -2and when = 4?
g(x)
=
g (-2) =
g (4) =
Reset
Next
When x = -2, we use the second part of the function, so g(-2)=0.
Similarly, g(4) = -4.
how much must be deposited today to have $45,000 in 5 years with a quarterly compounding and an APR of 7.3%
Answer:
$31,341.81
Step-by-step explanation:
The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years. We want to solve this for P:
A
------------------- = P
(1 + r/n)^(nt)
Substituting the given numerical values;
$45,000
--------------------------- = P
(1+0.073/4)^(4*5)
Using a calculator, we evaluate this expression, obtaining: $31,341.81
How large an equilateral triangle can you fit inside a 2-by-2 square?
Answer:
An equilateral triangle with a length of 2
Step-by-step explanation:
A 2-by-2 square implies that the square has a length and width of 2. Since equilateral triangles have the same length for all sides, it tells you that if one side is a certain length, all the other sides must have the same length. The largest length we can fit into this square would be 2 because any larger, the sides of the triangles would not fit into the square. Under the assumption that the length needs to be a whole number, the answer would be 2.
Emma throws an object upwards from a hill
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A non linear function is a function whose graph is not linear or can be represented by a straight line.
The function y = -16x² + 48x + 64 is a non linear function with a parabolic shape graph.
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a store marks up the wholesale price of a skateboard by 112%. The retail price is $35. What is the wholesale price of the skateboard?
The speed of the boat in still water is mph.
The speed of a river current is 3 mph. If a boat travels 30 miles downstream in the same time that it takes to travel 20 miles upstream, find the speed of the boat in still water.
Answer: the speed of the stream is 9mph
Simplify the following fractions.
Answer:
The solution for the above fraction is
[tex] \frac{146}{167} [/tex]
Step-by-step explanation:
Greetings!
look at the attachment above for the explanation.
(02.03 MC)
Choose the equation that represents the graph.
graph of a line passing through points negative 2 comma 0 and 0 comma negative 4
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
y = - 2x - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, - 4) ← 2 points on the line
m = [tex]\frac{-4-0}{0-(-2)}[/tex] = [tex]\frac{-4}{0+2}[/tex] = [tex]\frac{-4}{2}[/tex] = - 2
the line crosses the y- axis at (0, - 4 ) ⇒ c = - 4
y = - 2x - 4 ← equation of line
Sketch the function of f(x)=x^(3)-5x^(2)
The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
How to estimate the function of [tex]$f(x)=x^{3}-5x^{2}[/tex]?Put x = 0.
Replace the variable x with 0 in the expression.
[tex]f(0)=(0)^3-5(0)^2[/tex]
Raising 0 to any positive power yields 0.
f(0) = 0 − 5⋅0
f(0) = 0
y = 0
Put x = 1.
Replace the variable x with 1 in the expression.
[tex]f(1)=(1)^3-5(1)^2[/tex]
f(1) = 1− 5⋅1
f(1) = −4
y = −4
Put x = 2.
Replace the variable x with 2 in the expression.
[tex]f(2)=(2)^3-5(2)^2[/tex]
[tex]f(2)=8-5(2)^2[/tex]
f(2) = 8 − 5⋅4
f(2) = −12
y = −12
Put x = 3.
Replace the variable x with 3 in the expression.
[tex]f(3)=(3)^3-5(3)^2[/tex]
f(3) = 27 − 45
f(3) = −18
y = −18
Put x = 4.
Replace the variable x with 4 in the expression.
[tex]f(4)=(4)^3-5(4)^2[/tex]
[tex]f(4)=64-5(4)^2[/tex]
f(4) = 64 − 5 ⋅16
f(4) = 64 − 80
f(4) = −16
y = −16
The cubic function can be graphed using the function behavior and the points.
x 0 1 2 3 4
y 0 −4 −12 −18 −16
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Find two sets of parametric equations for the rectangular equation. y=(x-6)^2-7x.
If x=t+6 then y=
If x=7t then y=
Show all work !
The two sets of parametric equations for the rectangular equation are;
If x=t+6 then y= t²-7t-42.If x=7t then y= 49t² - 133t +36.What are the parametric equations from the rectangular equation?It follows from the task content that the parametric equations can be determined as follows;
By substituting the x= t+6 into the rectangular equation; we have;
y = (t+6-6)²-7(t+6)
y = t²-7t-42.
By substituting the x= 7t into the rectangular equation; we have;
y = (7t-6)² -7(7t)
y = 49t² - 84t +36 - 49t
y = 49t² - 133t +36.
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Which of the following terms completes the sentence below?
A sign chart helps you record data about a function's values around its
and
asymptotes.
The terms that completes the sentence are zeros; vertical. Option A
Function of a sign chart
The functions of a sign chart include;
It helps in the record of information about the functions values around its zeros and vertical asymptotesA sign chart indicates the sign of the result any mathematical operation between unknowns.From the mentioned functions, we can se that the terms that completes the sentence are zeros and vertical asymptotes.
Thus, the terms that completes the sentence are zeros; vertical. Option A
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A group of people were asked if they had run a red light in the last year. 150 responded yes and 185 responded no. Find the probability that if a person is chosen at random, they have run a red light in the past year
The probability that a person chosen at random have run a red light in the past year is 0.45.
Given that 150 people have responded yes and 185 have responded no in a group of people when they asked whether they have run a red light.
Probability lies between 0 and 1. The value of probability can be find by :
Probability= Number items/total items.
Number of people who said that they have run red light=150
Number of people who said that they have not run red light=185
Total people=150+185
=335 people
Probability that a person chosen at random have run red light in the past year=
=Number of people who said that they have run red lights / total people
=150/335
=0.447
After rounding off it will be 0.45.
Hence the probability that a person chosen at random have run a red light in the past year is 0.45.
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HELP PLSSSSSSSSSSSS!!!!!
Answer:
6 x 2 x 2 x 1
Step-by-step explanation:
6 x 2 = 12
12 x 2 = 24
24 x 1 = 24
Find the solution to m^2+9m=0
Work Shown:
m^2+9m=0
m(m+9)=0
m = 0 or m+9 = 0
m = 0 or m = -9
For more information, check out the topics about factoring and the zero product property.
If f(x) = 4x, which statements are true of g(x)? Select two options.
The two statements that are true for g(x ) are:
g(x) = [tex]4^{x}[/tex] - 1
g(x) is translated both vertically and horizontally.
What is a function?A function is a relation showing the relationship between two or more variables.
A function produces a unique output when a unique input is given to it. The input is called the domain and the output is called the Range.
Analysis:
If we use the values of x as 0,1,2,3
for x = 0
g(0) = [tex]4^{0}[/tex] -1 = 1 -1 = 0
for x = 1
g(1) = [tex]4^{1}[/tex] -1 = 4 - 1 = 3
for x = 2
g(2) = [tex]4^{2}[/tex] - 1 = 16 - 1 = 15
for x = 3
g(3) = [tex]4^{3}[/tex] - 1 = 64 - 1 = 63
Therefore g(x) = [tex]4^{x}[/tex] - 1
Also since the values of g(x) changes along the y - axis and x-axis also changes, therefore, g(x) is translated along both axes.
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Can anyone help with this?
The logarithmic function expresses the output variable, y, as a function of the logarithm of the input variable, x, as a function of a base b. The true statements are therefore;
I, II, and III onlyWhich statements are true based on the definition of a logarithm?The given logarithmic equation is presented as follows;
[tex]y = log_{b}(x) [/tex]
Therefore, we have;
[tex]x = {b}^{y} [/tex]
Where b = 1, we have that x will always be 1, therefore;
b ≠ 1Option III is true[tex]b = \sqrt[y]{x} [/tex]
Therefore;
x > 0Option I is trueWhich gives;
b > 0Option II is trueThe statements that are true is therefore;
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a circular garden has a diiameter of 6 yards what is the area of the garden use 3.14 for Tt
Given the diameter of the circular garden, the area of the garden is 28.36 yd².
What is the area of the garden?The area of a circle is expressed as; A = πr²
Given that;
Diameter d = 6ydRadius r = d/2 = 6yd/2 = 3ydArea A = ?A = πr²
A = 3.14 × (3yd)²
A = 3.14 × 9yd²
A = 28.36 yd²
Given the diameter of the circular garden, the area of the garden is 28.36 yd².
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022 A. Find the unit vector in the direction of F 2+3j+4k B. Find the distance between F1 = 3i+2j+ 5k and F2 = 3i +4j +5k C Find the component of each directed line segment whose initial point contains p, and the terminal point P₂ i.) P, (3,2,2), P₂(3,-2,-3) ii.) P₂(2,-3,-6), P3(-3,3,2)
By definition of vectors exist as quantities that contain magnitude (positive or negative) and direction.
A) The unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]
B) The distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.
C) i.) Required vector = −4j − 5k
ii.) Required vector = 5i − 6j − 8k
How to estimate unit vector?To estimate the unit vector in the direction of V = 2i+3j+4k
|V| [tex]$= \sqrt{2^2+3^2+4^2}[/tex]
[tex]$= \sqrt{29}[/tex]
A) Unit vector
[tex]$F= \frac{V}{ |V|}[/tex]
[tex]$F= \frac{2i+3j +4k}{2}[/tex]
[tex]$F = \frac{2i}{2} + \frac{3j}{2} +\frac{4k}{2}[/tex]
[tex]$F= i + \frac{3j}{2} +2k.[/tex]
Therefore, unit vector in the direction of [tex]$F = i + \frac{3j}{2} +2k.[/tex]
B) To estimate the distance between [tex]F_{1}[/tex] = 3i+2j+ 5k and [tex]F_{2}[/tex] = 3i +4j +5k
[tex]$d = \sqrt{(3-3)^{2}+(4-2)^{2}+(5-5)^{2}}[/tex]
= 2
Therefore, the distance between [tex]F_{1}[/tex] and [tex]F_{2}[/tex] exists 2.
C) i.) P, (3,2,2), P₂(3,-2,-3)
Required vector =|[tex]P_{1}[/tex]P₂|=(3−3)i + ((−2)-2)j + ((-3)-2)k
= −4j − 5k
ii.) P₂ (2,-3,-6), [tex]P_{3}[/tex] (-3,3,2)
Required vector =|P₂[tex]P_{3}[/tex]|=(-3-2)i + (3-(-3))j + (2-(-6))k
= 5i − 6j − 8k
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Solve for x if sqrt (3x-8) + 1 = sqrt (x+5)
The solution of x in the given expression [tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex] is 4. However, if it is [tex]\mathbf{\sqrt{(3x-8)+1} = \sqrt{(x+5)}}[/tex], it is 6.
What is the solution to algebraic expression?The solution to the given algebra expression involving surds can be seen in the steps below.
Given that:
[tex]\mathbf{\sqrt{(3x-8)}+1 = \sqrt{(x+5)}}[/tex]
Remove the square roots, we have:
12x - 32 = 4x² - 48x + 144
Solving the quadratic equation at the RHS and equating it to LHS, we have:
x = 11, x = 4
Verifying the solutions by replacing the value of x with the given equation:
x = 11 Falsex = 4 TrueTherefore, we can conclude that the value of x = 4
NOTE:
Given that:
[tex]\mathbf{\sqrt{(3x-8+1)} = \sqrt{(x+5)}}[/tex]
Square both sides
3x - 7 = x +5
Solve for x
3x - x = 5 + 7
2x = 12
x = 6
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Company A manufactures and sells gidgets. The owners have determined that the company has the monthly revenue and cost functions shown, such that x represents the number of gidgets sold.
R(x) = 16x
C(x) = 12x + 1,424
At what number of gidgets sold will the company break-even (the point where revenue equals cost)?
Considering the given equations for revenue and cost, the company will break-even when 356 widgets are sold.
What is the break-even point?The break-even point is the value of x for which:
R(x) = C(x).
In this problem, the functions are:
R(x) = 16x.C(x) = 12x + 1424.Hence:
R(x) = C(x)
16x = 12x + 1424
4x = 1424
x = 1424/4
x = 356
The company will break-even when 356 widgets are sold.
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The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 4.5 minutes and a standard deviation of 1 minute. Find the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot.
Using the normal distribution, it is found that the cut-off time which 75.8% of the college students exceed when trying to find a parking spot in the library parking lot is of 3.7 minutes.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 4.5, \sigma = 1[/tex]
The cut-off time is the 100 - 75.8 = 24.2th percentile, which is X when Z = -0.7, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.7 = \frac{X - 4.5}{1}[/tex]
X - 4.5 = -0.7
X = 3.7.
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The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
x –3 –2 0 1 2
h(x) 0 –23 –12 0 0
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
h(x) = x3 + 6x2 + 11x – 6
h(x) = x3 – 7x + 6
h(x) = x3 – 7x – 6
h(x) = x4 + 2x3 – 7x2 – 8x + 12
The equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
How to find the equation of a Polynomial?
From the given table, we see that the x-intercepts are;
(-3, 0), (1, 0) and (2, 0)
Now, we are told the the x-intercepts have a multiplicity of one which means they occur as roots only once. Thus, we can say that the roots in factor form are;
(x + 3), (x - 1), (x - 2)
Then, the polynomial will be;
h(x) = (x + 3) * (x - 1) * (x - 2)
h(x) = (x + 3)(x² - 3x + 2)
h(x) = x³ + 3x² - 3x² - 9x + 2x + 6
h(x) = x³ - 7x + 6
Thus, the equation of the polynomial function from the given table is; Option B: h(x) = x³ - 7x + 6
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help!
Nora and Annie are raising money to purchase books for their school's library. The number of books they will be able to purchase for the library depends on the amount of money they raise.
b = the number of books Nora and Annie will be able to purchase
m = the amount of money Nora and Annie raise
Which of the variables is independent and which is dependent?
Answer: B is dependent and M is independent
Step-by-step explanation:
This is because the question says that they are raising money to buy books. In order to buy the books, they must raise money. So they raise money than buy the books which makes buying the books dependent on how much they raise.
Easy points because I got points to blow,
Answer:
Did you know that the first person convicted of speeding was going eight mph.
Step-by-step explanation:
What is the total repayment made, including principal and interest, on a loan of $1,100 at 3.5% interest compounded annually over four years?
The total repayment made, including principal and interest is $1262.27
Compound interestThe formula for calculating the compound interest is calculated as shown below;
A = P(1+r)^t
where
P is the principal = $1100
rate = 3.5% = 0.035
time "t" =4 years
Substitute
A. = 1100(1+0.035)^4
A = 1100(1.035)^4
A = 1100(1.14752)
A = 1262.27
Hence the total repayment made, including principal and interest is $1262.27
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copy the problems onto your paper, mark the given and prove the statements asked. if PO is congruent to PR and UO is congruent to UR prove angle O is congruent to angle R
The two-column proof that proves that ∠O ≅ ∠R using the SSS and CPCTC theorems is shown in the image attached below.
What is the Side-side-side Congruence Theorem (SSS)?The side-side-side congruence theorem (SSS) states that when three sides of a triangle are congruent to the corresponding three sides of another triangle, then both triangles are considered congruent to each other.
What is the CPCTC Theorem?The CPCTC theorem states that when two triangles are proven to be congruent by any triangle congruent theorem, then all the corresponding parts of the congruent triangle are congruent. This implies that the corresponding sides and angles of both triangle are equal or congruent.
We are asked to prove that ∠O ≅ ∠R.
With the given image, we would draw segment UP. Thus, based on the reflexive property, UP ≅ UP (one pair of congruent sides).
We are given two pairs of corresponding sides already, which are: UO ≅ UR and PO ≅ PR.
This means that triangles OUP and RUP have three pairs of corresponding congruent sides. Therefore, ΔOUP ≅ ΔRUP.
Applying the CPCTC theorem, ∠O ≅ ∠R.
The two-column proof is attached in the image below.
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Please Help! Multiple Choice!
Using the z-distribution, the p-value would be given as follows:
b) 0.0086.
What are the hypothesis tested?At the null hypothesis we test if the means are equal, hence:
[tex]H_0: \mu_D - \mu_C = 0[/tex]
At the alternative hypothesis, it is tested if they are different, hence:
[tex]H_1: \mu_D - \mu_C \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:
[tex]\mu_D = 12, s_D = \frac{5.2}{\sqrt{73}} = 0.6086[/tex][tex]\mu_C = 14, s_C = \frac{4.1}{\sqrt{81}} = 0.4556[/tex]Hence, for the distribution of differences, they are given by:
[tex]\overline{x} = 12 - 14 = -2[/tex].[tex]s = \sqrt{0.6086^2 + 0.4556^2} = 0.76[/tex]What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{x} - \mu}{s}[/tex]
[tex]z = \frac{-2 - 0}{0.76}[/tex]
z = -2.63.
Using a z-distribution calculator, for a two-tailed test, with z = -2.63, the p-value is of 0.0086.
Hence option B is correct.
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