Answer: Length = 13 ft. , Width = 9 ft.
Step-by-step explanation:
Rectangle area = Length x width
Area = 117 ft.
Length = x + 4
Width = x
To solve
(x)(x + 4) = 117
x^2 + 4x = 117
x^2 + 4x - 117 = 0
(x - 9)(x + 13)
x = 9, -13
x = 9 (measurement cannot be negative)
Length
x + 4
9 + 4 = 13
Write this expression in simplified terms.
3×√3×6×√6
Answer:
54√2
Step-by-step explanation:
PWhat are the x- and y-intercepts of the line y = 4x + 12?
A. x-intercept = 3; y-intercept = -12
B. x-intercept = -3; y-intercept = 12
C. x-intercept = -12; y-intercept = 3
D. x-intercept = 12; y-intercept = -3
PLEASE HELP
Answer:
B
Step-by-step explanation:
when x is 0 y=4(0)+12 y=12
y is 0 y=4(-3) +12 = 12=12
Evaluate the expression.
Answer:
18
Step-by-step explanation:
Using order of operations:
[tex] \frac{15 - 9}{3} (19 - 10)[/tex]
[tex] \frac{6}{3} (9)[/tex]
[tex]2(9) = 18[/tex]
the line y=-3x+4 is reflected on the y-axis what is the equation of the reflected line
Answer:
x=0
Step-by-step explanation:
when the reflection falls on the y-axis the answer is x=0
A decision at the margin Crystal is a hard-working college senior. One Thursday, she decides to work nonstop until she has answered 100 practice problems for her math course. She starts work at 8:00 AM and uses a table to keep track of her progress throughout the day. She notices that as she gets tired, it takes her longer to solve each problem. Time Total Problems Answered 8:00 AM 0 9:00 AM 40 10:00 AM 70 11:00 AM 90 Noon 100 Use the table to answer the following questions. The marginal, or additional, gain from Crystal’s first hour of work, from 8:00 AM to 9:00 AM, is problems. The marginal gain from Crystal’s third hour of work, from 10:00 AM to 11:00 AM, is problems. Later, the teaching assistant in Crystal’s math course gives her some advice. “Based on past experience,” the teaching assistant says, “working on 35 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.” For simplicity, assume students always cover the same number of pages during each hour they spend reading. Given this information, in order to use her 4 hours of study time to get the best exam score possible, how many hours should she have spent working on problems, and how many should she have spent reading? 0 hours working on problems, 4 hours reading 1 hour working on problems, 3 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours reading
She should spend 1 hour working on problems , 3 hour reading , Option B is the right answer.
What is Margin gain ?The gain of the desired effect with respect to the previous gain is called margin gain
The marginal gain from 8:00 am to 9:00 am is
(40-0) = 40 problems
The marginal gain from 9:00 am to 10:00 am is
= 70-40 = 30 problems
The marginal gain from 10:00 am to 11:00 am is
(90-70) = 20 problems
As if she does more than one hour of problem solving her productivity decreases to 30 which is less than 1 hour of reading textbook
Therefore she should not spend more than 1 hour on problem solving.
Therefore Option B is the right answer.
1 hour working on problems , 3 hour reading
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NEED HELP ASAP WILL MARK BRAINLIEST!
Answer:
[tex]\boxed {1)log_{b}(75) = 4.317}[/tex]
[tex]\boxed {2)ln(20) = 2.9957}[/tex]
Step-by-step explanation:
[tex]\textsf {Question l :}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(3) = 1.099}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5) = 1.609}[/tex]
[tex]\textsf {Identities applied :}[/tex]
[tex]\boxed {log(ab) = loga + logb}[/tex]
[tex]\boxed {log(a)^{x} = xloga}[/tex]
[tex]\textsf {We can rewrite the problem as :}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(75)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(25 \times 3)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5^{2} \times 3)}[/tex]
[tex]\longrightarrow \mathsf {log_{b}(5)^{2} + log_{b}(3)}[/tex]
[tex]\longrightarrow \mathsf {2log_{b}(5) + log_{b}(3)}[/tex]
[tex]\textsf {Now, substitute the values :}[/tex]
[tex]\longrightarrow \mathsf {2(1.609) + (1.099)}[/tex]
[tex]\longrightarrow \mathsf {3.218 + 1.099}[/tex]
[tex]\longrightarrow \mathsf {4.317}[/tex]
[tex]\boxed {log_{b}(75) = 4.317}[/tex]
[tex]\textsf {Question ll :}[/tex]
[tex]\longrightarrow \mathsf {ln(4) = 1.3863}[/tex]
[tex]\longrightarrow \mathsf {ln(5) = 1.6094}[/tex]
[tex]\textsf {Rewriting the problem :}[/tex]
[tex]\longrightarrow \mathsf {ln(20)}[/tex]
[tex]\longrightarrow \mathsf {ln(4 \times 5)}[/tex]
[tex]\longrightarrow \mathsf {ln(4) + ln(5)}[/tex]
[tex]\longrightarrow \mathsf {1.3863 + 1.6094}[/tex]
[tex]\longrightarrow \mathsf {2.9957}[/tex]
[tex]\boxed {ln(20) = 2.9957}[/tex]
Answer:
[tex]\sf \log_b(75)=4.317[/tex]
[tex]\sf \ln (20)=2.9957[/tex]
Step-by-step explanation:
Question 1
Given:
[tex]\sf \log_b(3)=1.099[/tex]
[tex]\sf \log_b(5)=1.609[/tex]
To evaluate [tex]\sf \log_b(75)[/tex], replace 75 with (5 × 5 × 3):
[tex]\implies \sf \log_b(5 \cdot 5 \cdot 3)[/tex]
[tex]\textsf{Apply the Product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies \sf \log_b5+\log_b5+\log_b3[/tex]
Substitute the given values to solve:
[tex]\implies \sf 1.609 + 1.609 + 1.099=4.317[/tex]
Question 2
Given:
[tex]\sf \ln(4)=1.3863[/tex]
[tex]\sf \ln(5)=1.6094[/tex]
To evaluate ln(20) replace 20 with (4 × 5):
[tex]\implies \sf \ln (4 \cdot 5)[/tex]
[tex]\textsf{Apply the Product log law}: \quad \ln xy=\ln x + \ln y[/tex]
[tex]\implies \sf \ln (4)+\ln (5)[/tex]
Substitute the given values to solve:
[tex]\implies \sf 1.3863+1.6094=2.9957[/tex]
Some identical cylinders each have a radius of
5 cm and a length of 4 cm.
Rufus has enough paint to cover 2500 cm².
How many of these cylinders can Rufus paint
completely?
Answer:
8 cylinders
Step-by-step explanation:
The surface area of a cylinder is given by the formula ...
A = 2πr(r +l) . . . . . for radius r and length l
__
The cylinders Rufus has each have an area of ...
A = 2π(5 cm)(5 cm +4 cm) = 90π cm² ≈ 282.74 cm²
That means 2500 cm² of paint will cover ...
2500 cm²/(282.74 cm²/cylinder) ≈ 8.84 cylinders
Rufus has enough paint to cover 8 cylinders completely.
Calculate the a) future value of the annuity due, and b) total interest earned. (From Example 2)
2. Jay Smith deposited $5,000 into an annuity due at the beginning of each quarter for 3 years at 6%
compounded quarterly.
Answer:
value: $66,184.15interest: $6,184.15Step-by-step explanation:
The future value can be computed using the formula for an annuity due. It can also be found using any of a variety of calculators, apps, or spreadsheets.
__
formulaThe formula for the value of an annuity due with payment P, interest rate r, compounded n times per year for t years is ...
FV = P(1 +r/n)((1 +r/n)^(nt) -1)/(r/n)
FV = 5000(1 +0.06/4)((1 +0.06/4)^(4·3) -1)/(0.06/4) ≈ 66,184.148
FV ≈ 66,184.15
calculatorThe attached calculator screenshot shows the same result. The calculator needs to have the begin/end flag set to "begin" for the annuity due calculation.
__
a)The future value of the annuity due is $66,184.15.
b)The total interest earned is the difference between the total of deposits and the future value:
$66,184.15 -(12)(5000) = 6,184.15
A total of $6,184.15 in interest was earned by the annuity.
A local dry cleaner interviewed 17 candidates for the positions of the cashier, washer, salesperson, and delivery driver. How many ways can they fill the 4 positions?
HELP PLSPLSPLS
Using the permutation formula, it is found that there are 57,120 ways to fill the 4 positions.
There are different roles, hence the order is important, which means that the permutation formula is used.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 4 roles are chosen from a set of 17, hence the number of ways is given by:
[tex]P_{17,4} = \frac{17!}{13!} = 57120[/tex].
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.1 years, and standard deviation of 0.6 years.
If you randomly purchase one item, what is the probability it will last longer than 2 years?
The probability will last longer than 2 years will be 3.3%.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
First let us calculate the z score using the formula:
[tex]z = \dfrac{(x- \mu)} { s}[/tex]
where x = 2, u is the mean = 3.1 years, and s is the standard deviation
[tex]z =\dfrac{ (2 - 3.1) }{ 0.6}[/tex]
z = -1.83
From the standard probability tables, the p-value at z = -1.83 is:
P = 0.033 = 3.3%
Therefore the probability that will last longer than 2 years will be 3.3%.
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The figure shows a parallelogram PQRS of area 35cm². If T is a point on QR such that QT = 4 cm, TR = 3 cm, find the area of triangle PQT.
Answer:
area of a parallelogram equals to 1/2 x base x perpendicular height and area of a triangle equals to 1/2 base times height so you ought to search for the base in order to get the area of the triangle needed that's how I got the answer bye.
1) point)
Problem 2. Fill out the blank to make the given table a discrete probability distribution.
1) point)
2
3
4
P(x)
0.03
0.14
0.65
0.08
Explanation:
Add up the given decimal values
0.03+0.14+0.65+0.08 = 0.90
Recall that all of the P(X) values must add to 1 to represent 100% of all possible outcomes. So far we added to 0.90, so we're missing 1 - 0.90 = 0.10
As a check,
0.03+0.14+0.65+0.08 + 0.10 = 1
Which of the following displays is a relative frequency bar graph?
A bar graph titled eye color has color on the x-axis. Blue, 8; brown, 10; green, 6; hazel, 5; gray, 1.
A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.
A bar graph titled Caffeinated Drinks has drink on the x-axis. Coffee, 9; tea, 8; soda, 8; energy, 3.
A bar graph titled social media preferences has platform on the x-axis . Upstart, 4; Aster, 18; Babble, 15; Techy, 12.
Mark this and return
The answer choice which represents a relative frequency bar graph is; A bar graph titled social media preferences has platform on the x-axis. Upstart, 0.10; Aster, 0.25; Babble, 0.30; Techy, 0.35.
What is Relative frequency?The statistical definition of relative frequency is simply the ratio of the frequency of an event in a statistical experiment with respect to the total frequency. Hence, since the frequencies in the social media bar chart as decimals (fractions of a whole), it follows that it is a relative frequency representation.
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Answer Its B
Step-by-step explanation:Edge 2022 I guess
Geometry question! Please help thanks!
The measure of the angles are Z = 90, X = 90, V = 90, Y = ∠20, W = ∠8 and W = ∠20
How to solve the angles?The sum of angles on a straight line is 180 degrees.
This means that:
Z + 90 = 180
X + 90 = 180
V + 90 = 180
Solve for the variables
Z = 90;
X = 90
V = 90
Also, alternate angles are equal.
This means that:
Y = ∠20
W = ∠8
This is so because the above angles are alternate angles.
Lastly, corresponding angles are equal.
So, we have:
W = ∠20
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Consider the equation below. "-2(5x+8)=14+6x" The equation was solved using the following steps.
The equation -2(5x+8) = 14+6x solved using step by step representation is x = -15/8.
Solving steps for the EquationThe equation to be considered as given in the task content is; -2(5x+8)=14+6x.
It follows from the task content that the steps for solving the equation are as follows;
-2(5x+8) = 14+6x
Step 1: opening parenthesis-10x - 16 = 14 + 6x
Step 2: collect like terms-10x - 6x = 14 + 16
Step 3: evaluate-16x = 30
Step 4: Divisionx = 30/-16
x = -15/8
Hence, the value of x upon solving the equation is; -15/8.
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what are the solutions in the following equations?
Answer: (0, -6) and (1, -5)
Step-by-step explanation:
If [tex]x-y=6[/tex], then [tex]y=x-6[/tex]. Substituting this into the second equation,
[tex]x-6=x^{2}-6\\\\x^{2}-x=0\\\\x(x-1)=0\\\\x=0, 1[/tex]
If x=0, y=-6.
If x=1, y=-5.
So, the solutions are (0, -6) and (1, -5)
find x and y please please help
L1 and L2 are parallel
so the interior alternate angles are equal
4y - 40 = 3y ( interior alternate angles)
4y - 40 = x + 15 ( vertically opposite angles).
solving the first equation, we get
4y - 3y = 40
y = 40°
putting values of y= 40° in eq. 2, we get
4y - 40= x + 15
4(40) - 40 = x + 15
160 -40 = x + 15
120 - 15 = x
105° = x
X = 105° , Y = 40°Gabrielle's age is three times Mikhail's age. The sum of their ages is 36. What is Mikhail's age?
Answer:
Gabrielle is 27
Mikhail is 9
Step-by-step explanation:
g = 3m
g + m = 36
since g = 3m we can substitute it in the equation
g + m = 36 as
3m + m = 36
4m = 36
m = 9
3m = 27 which is g
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2 Math questions! Offering the brainliest to who answers
Answer:
first one L second one D
Step-by-step explanation:
Look at the tree shown in the diagram. What is the bight of the tree rounded to the nearest tenth foot?
Answer:
Correct answer is B, 69.3 feet
Step-by-step explanation:
Since we have a 30°-60°-90° right triangle, the length of the longer leg is √3 times the length of the shorter leg, so the length of the shorter leg is 1/√3, or √3/3 times the length of the longer leg.
[tex]120( \frac{ \sqrt{3} }{3}) = 40 \sqrt{3} = 69.3[/tex]
Figure ABCD is transformed to obtain figure A′B′C′D′:
DIAGRAM INCLUDED! 100 Points!
Part A: Write the sequence of transformations that changes figure ABCD to figure A′B′C′D′. Explain your answer and write the coordinates of the figure obtained after each transformation. (6 points)
Part B: Are the two figures congruent? Explain your answer. (4 points)
Answer:
Part A
Reflect over the y-axis: (x, y) → (-x, y)Part B
Two figures are congruent if they have the same shape and size. (They are allowed to be rotated, reflected and translated, but not resized).
Therefore, ABCD and A'B'C'D' are congruent. They are the same shape and size as they have only be reflected and translated.
F
10
A. 18
B. 28
C. 38
D. 48
G
8
H
If ZG ZH, find the perimeter of AFGH.
Answer:
The answer is 28
Step-by-step explanation:
ms..s.s..snskkzkzklzlzls
what is the value of the rational expression below when is equal to 5?
Answer:
[tex]\boxed {C. -2}[/tex]
Step-by-step explanation:
[tex]\textsf {Substitute x = 5 in the expression :}[/tex]
[tex]\longrightarrow \mathsf{\frac{15 - x}{x - 10}}[/tex]
[tex]\longrightarrow \mathsf{\frac{15 - 5}{5 - 10}}[/tex]
[tex]\longrightarrow \mathsf{\frac{10}{-5}}[/tex]
[tex]\longrightarrow \mathsf{-2}[/tex]
Which ordered pair is on the graph of the equation 4x + 3y = 13?
(1, 6)
(0, –3)
(1, –3)
(4, –1)
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, 1) and (0, 3). Everything to the left of the line is shaded.
Which linear inequality is represented by the graph?
y <2/3x + 3
y > 3/2x + 3
y > 2/3x + 3
y < 3/2x + 3
Answer:
The correct linear inequality is y<2/3x+3
Step-by-step explanation:
Linear inequalities are defined as expressions in which two linear expressions are compared using the inequality symbols
In the graph, the grey region corresponds to the region non-allowed by inequality. We see that for x=0, y is allowed to be only less than 3: this means that the correct inequality must be in the form y<mx+3, so only the 1st option or the 4th option.
In order to choose the correct option, we should find the value of m, the slope of the line in the graph. This slope can be found by calculating the variation of y divided by the variation of x:
m=dy/dx
Choosing for example the points x=0 (which corresponds to y=3) and x=3 , we find
So, the equation of the line is y=2/3x+3
and so the correct inequality is
y<2/3x+3
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how much would $500 invested at 3% interest compounded continuously be worth after 6 years? Round your answer to the nearest cent. Use 2.718 for e. A(t)=Pe^(rt)
You are given the equation
A(t) = P*e^(rt)
Where P = Principal
r = interest rate
t = time
e is a mathematical constant equivalent to approx 2.71828
You're told the initial Principal is $500, the interest rate is 3%, over 6 years. So you have everything that you need to solve the problem, just plug in the values and solve for A(6)
A(t) = P*e^(rt)
A(6) = 500 * e^(0.03 * 6)
A(6) = 500 * e^(0.18)
A(6) = 500 * 2.71828^(0.18)
A(6) = 500 * 1.19721
A(6) = 598.60861
So $500 invested 6 years ago at 3% would be worth $598.61 today.
find in factord form -9n+n^2=0
Answer:
n(-9+ n) =0
Step-by-step explanation:
-9n+n^2=0 Kind of use 'reverse distributive' property
n (-9 + n) = 0
If xy=3 yz=6 zx=2 find x+y+z
Rewrite, using the distributive
property (Algebra 1)
Answer:
[tex]24m + 32[/tex]
Step-by-step explanation:
[tex]8(3m + 4) = 24m + 32[/tex]
Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.
2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank.
Which statement is true about angles 3 and 5?
They are acute.
They are congruent.
They are complementary.
They are supplementary.Two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.
2 parallel horizontal lines are intersected by a third line. On the first horizontal line where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. On the second horizontal line, where the third line intersects, 4 angles are created. Labeled clockwise, from uppercase left, the angles are 5, 6, blank, blank.
Which statement is true about angles 3 and 5?
They are acute.
They are congruent.
They are complementary.
They are supplementary.
Answer:
4. They are supplementary
Answer:
4 they are supplemental
