The value of x from the equation 3x + 4 = 31 and x + 4 = 13 is 9.
How to solve equation?3x + 4 = 31
x + 4 = 13
From equation (2)
x + 4 = 13
subtract 4 from both sides
x = 13 - 4
x = 9
Substitute x = 9 into (1)
3x + 4 = 31
3(9) + 4 = 31
27 + 4 = 31
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A study of a local high school tried to determine the mean amount of money that each
student had saved. The study surveyed a random sample of 69 students in the high
school and found a mean savings of 5000 dollars with a standard deviation of 1400
dollars. At the 95% confidence level, find the margin of error for the mean, rounding
to the nearest whole number. (Do not write ).
Using the t-distribution, it is found that the margin of error for the 95% confidence interval is of $336.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The margin of error is given by:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 69 - 1 = 68 df, is t = 1.9955.
The standard deviation and sample size are given, respectively, by:
s = 1400, n = 69.
Hence, the margin of error in dollars is given by:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
[tex]M = 1.9955\frac{1400}{\sqrt{69}}[/tex]
M = 336.
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The athlete jogged a distance of 4850 yards in 20 minutes. What is the time needed to cover 9215 yards at the same rate?
Equation:
Answer
Answer:
38 minutes
Step-by-step explanation:
Yards covered in a minute = 4850/20 = 242.5
Time needed to cover 9215 yards = 9215/242.5 = 38 min
A football stadium holds 17,700 seats. The lower level has 300 seats less than 4 times the number of seats in the upper level. The middle level has 500 more seats than twice the number of seats in the upper level. Let x represent the seats in the upper level. Which equation can be used to find the number of seats in the upper level?
7 x + 200 = 17,700
6 x + 200 = 17,700
7 x minus 200 = 17,700
6 x minus 200 = 17,700
Answer:
6x + 200 = 17,000
Step-by-step explanation:
Lower level = 4x - 300
Mid level = 2x + 500
Combine the two equations to find the number of seats in the upper level
(2x + 500) × (4x - 300) = 17,000
Combine like terms
4x × 2x + 500 - 300 = 17,000
6x + 200 = 17,000
HELP ILL GIVE MONEY
Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 27 liters per minute. There are 700 liters in the pond to start.
Let W represent the total amount of water in the pond (in liters), and let I represent the total number of minutes that water has been added. Write an equation
relating W to T. Then use this equation to find the total amount of water after 17 minutes.
Equation:__
Total amount of water after 17 minutes: __liters
Answer: Equation: 27t +700 = w
Total amount of water after 17 minutes: 1159 L
Step-by-step explanation:
Equation: 27t +700 = w
let t = minutes
let w = total amount of water in pond (liters)
Total amount of water after 17 minutes: 1159 L
t = 17
therefore
27(17) +700 = 1159
Answer:
425 l
Step-by-step explanation:
Maya invested $2,100 in an account paying an interest rate of 7\tfrac{3}{8}7 8 3 % compounded continuously. Jack invested $2,100 in an account paying an interest rate of 7\tfrac{5}{8}7 8 5 % compounded monthly. After 12 years, how much more money would Jack have in his account than Maya, to the nearest dollar?
This are interest added on a sum of money invested. Jack will have $168.95 more than Maya in his account
Compound interestThis are interest added on a sum of money invested. The formula for calculating compound amount is given as;
A = P(1 +r/n)^nt
Given the following parameter
P =$2100
rate r = 7 5/8% = 0.07625
time t = 12 years
n =12 (monthly)
Substitute
A = 1200(1+0.07625/12)^12(12)
A = 1200 (2.4895)
A = $2987.46
For Maya
A = 1200(1+0.07375)^12
A = 2818.50
Take the difference
Difference =$2987.46 - $ 2818.5
Difference = $168.95
Hence Jack will have $168.95 more than Maya in his account
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Area of a Square
Side Length (cm)
1
2
Area (cm²)
1
4
3
9
4
16
5
25
Describe how the area of a square is related to the length of the side.
a.
As the length of the side increases, the area decreases.
b.
As the length of the side increases, the area increases and then decreases.
As the length of the side increases, the area increases.
CA
d.
As the length of the side increases, the area decreases and then increases.
The description of the area of a square is (c) as the length of the side increases, the area increases.
How to describe the area of a square?The table of values is given as:
Side Length (cm) Area (cm²)
1 1
2 4
3 9
4 16
5 25
In the above table, we can see that:
As length increases, the area also increases
Hence, the description of the area is (c) as the length of the side increases, the area increases.
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what is linear relationship
Step-by-step explanation:
a linear relationship is simply a straight line relationship.
any equation that can be pot in the form of y = mx + b is a linear relationship.
linear = straight
hope this helps
Are these numbers rational or irrational? -7 √10 (square root of 10) √16 (square root of 16) 52% 1.235 > > > > 1. Rational 2. Irrational please answer quickly
Answer:
hope you can understand
please help me Fast!!!!! slove the question in picture
Step-by-step explanation:
A)
Class Width=8
Median= 28.1
Modal Class= 20.5-28.5
B)
Mean=31.34
Which graph represents 2x + 3y < 6?
A
I believe that I am correct
Fabian took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.80 plus $4 per mile. The total fare was $44.80, not including the tip. How many miles was the taxi ride?
Answer:
10 miles
Step-by-step explanation:
total amount=$44.80
pick up fee=$4.80+$4 per mile
to get the miles of the taxi ride it will be=total amount-pick up fee÷$4
$44.80-$4.80÷$4
$40÷$4
=10 miles
THANK YOU
multiply: (a+b),(a+b) and (a+b)
Answer:
Here,
[tex](a + b) [(a + b)(a + b)][/tex]
[tex](a + b)( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex]a( {a}^{2} + 2ab + {b}^{2} ) + b( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex] {a}^{3} + {2a}^{2} b + {ab}^{2} + {a}^{2} b + {2ab}^{2} + {b}^{3} [/tex]
[tex] {a}^{3} + 3 {a}^{2} b + {3ab}^{2} + {b}^{3} [/tex]
Thus,[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]
Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.
a fridge costs €336 after a price increase of 40%. what was the original price
the original cost is "x", which is the 100% of the original price, and we also know that €336 is its price increased by 40%, namely 100% + 40% = 140%, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 336& 140 \end{array} \implies \cfrac{x}{336}~~=~~\cfrac{100}{140} \\\\\\ \cfrac{x}{336}=\cfrac{5}{7}\implies 7x=1680\implies x=\cfrac{1680}{7}\implies x=240[/tex]
The area of the base of a cylinder is 36 square inches and its height is 10 inches. A cone has the same area
for its base and the same height. What is the volume of the cone?
The volume of the cone is
in³.
I need help:((
find the area and the circumference of a circle with the diameter 6 yards
Answer:
area = 28.27
circumference = 18.85
Step-by-step explanation:
Using the formulas for area,
A = πr^2
d = 2r
Solving for area,
A = 1/4 πd^2 = 1/4 × π × 6^2 ≈ 28.27yd²
Using the formulas for circumference,
C = 2 πr
d = 2r
Solving for circumference,
C = πd = π × 6 ≈ 18.85yd
URGRENNTTT PLSS HELPP 50 POINTSS!!!!! Students were asked to simplify the expression cotangent theta plus tangent theta over cotangent theta. Two students' work is given.
Student A
Step 1: cotangent theta over cotangent theta plus tangent theta over cotangent theta
Step 2: 1 plus tangent theta over the quantity 1 over tangent theta end quantity
Step 3: 1 + tan2 θ
Step 4: sec2 θ Student B
Step 1: the quantity 1 over tangent theta end quantity plus tangent theta over the quantity cotangent theta
Step 2: the quantity 1 plus tangent squared theta end quantity over tangent theta all over cotangent theta
Step 3: secant squared theta over tangent squared theta
Step 4: csc2 θ
Part A: Which student simplified the expression incorrectly? Explain the errors that were made or the formulas that were misused. (5 points)
The student that simplified the expression incorrectly is student 2
How to determine the incorrect result?The steps are given as:
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)}[/tex]
Student 1:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]1 + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 3: 1 + tan²(Ф)Step 4: sec²(Ф)Student 2:
Step 1: [tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)}[/tex]Step 2: [tex]\frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]Step 3: sec²(Ф)/tan²(Ф)Step 4: csc²(Ф)As a general trigonometry rule;
[tex]\frac{\cot(\theta) + \tan(\theta)}{\cot(\theta)} = \sec^2(\theta)[/tex]
This means that student 1 is correct, while student 2 is not
The first error in student 2's workings is in step 2, where we have:
[tex]\frac{\cot(\theta)}{\cot(\theta)} + \frac{\tan(\theta)}{\cot(\theta)} = \frac{1 + \tan^2(\theta)}{\cot(\theta)/\tan(\theta)}[/tex]
The above expression is not justified and cannot be proved by any trigonometry rule
Since the step 2 is incorrect, the other steps cannot be used.
Hence, the student that simplified the expression incorrectly is student 2
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Question 14 of 14
Rachel buys
1
gallon of milk. Her sister Abby uses
1
1
2
quarts of the milk in a recipe. Then her mother uses
3
cups of the milk in a different recipe.
Select all of the true statements below.
A.
Rachel's mother uses more milk than her sister Abby uses.
B.
There are
56
fluid ounces of milk left.
C.
There are
9
cups of milk left.
D.
There is more than
1
4
gallon of milk left.
E.
There is more than
1
2
gallon of milk left.
The true statements are:
There are 56 fluid ounces of milk left.
There is more than 1 / 4 gallon of milk left.
What are the true statements?
The first step is to convert gallons to cups.
1 cup = 16 gallons
Then, convert quarts to cups
1 quart = 4 cups
1 1/2 x 4
3/2 x 4 = 6 cups
Total cups left = 16 - 6 - 3 = 7 cups
1 cup = 8 ounces
Total milk left in ounces: 8 x 7 = 56 ounces
1 cup = 1/16 gallons
Total milk left in gallons: 1 / 16 x 7 = 7/16 gallons
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Lydia is making tickets for her class
concert. Each ticket measures 4cm by
3cm. What is the maximum number of
the tickets that can be cut off a sheet of
bristol board measuring 48cm by 36cm
Can someone solve this eq (integration)
I did it but the answer I got is different to what my textbook says
Answer:
I hope you can help
The price of a new shirt was slashed from N1 500 to N1 250. Find the percentage decrease in the price of the shirt.
Answer:
The percent decrease is 16.67%.
Step-by-step explanation:
percent change = (new price - old price)/(old price) × 100%
percent change = (N1250 - N1500)/(N1500) × 100%
percent change = -250/1500 × 100%
percent change = -16.67%
A negative percent change is a percent decrease.
The percent decrease is 16.67%.
The function fis defined as follows.
f(x)=2x²+3
If the graph of fis translated vertically downward by 6 units, it becomes the graph of a function g.
Find the expression for g(x).
The expression of the translated function g(x) is gotten as; g(x) = 2x² - 3
How to Interpret Graph Translations?
We are given the function;
f(x) = 2x² + 3
Now, when we translate a function f(x) downwards, the new function becomes;
g(x) = f(x) - a
where a is the amount of units by which the graph was translated.
Thus for translation of 6 units vertically downwards;
g(x) = 2x² + 3 - 6
g(x) = 2x² - 3
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Factor higher degree polynomials
(x^2 - 4) (x^2 + 6x + 9)
[tex]~~~(x^2 -4)(x^2 +6x +9)\\\\=(x^2 -2^2)(x^2 +2 \cdot 3x +3^2)\\\\=(x+2)(x-2)(x+3)^2[/tex]
Marc Gasol scored 18 points on Monday, 29 points on Wednesday, and 8 points on Saturday. What
was his average number of points per game for those three nights?
Answer: 18.33 ppg
Step-by-step explanation:
He played three games
18+29+8=55
55/3=18.33
The current salaries in Sasha's department are $42,000, $32,000, $33,000, $38,000, and $50,000. Sasha wants to adjust the lowest salary up to $40,000. If Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary, Find the total cost for the increment?
The total cost for the increment if Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary is $13000.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The lowest salary is $32000, hence to increase to $40000, we need an additional $8000.
Also, giving every employee a $1,000 raise accounts for $5000 since there are 5 staff.
The total cost of increment = 8000 + 5000 = 13000
The total cost for the increment if Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary is $13000.
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if for 5 pounds of beans it cost 4 dollars than how much money is needed for 50 pounds of beans
Answer:
40 dollars
Step-by-step explanation:
We can use a ratio to solve the problem
5 pounds 50 pounds
---------------- = -----------------
4 dollars x dollars
Using cross products
5 * x = 4 * 50
5x = 200
Divide by 5
5x/5 = 200/5
x = 40
40 dollars
Step-by-step explanation:
[tex]\sf 5 \: pounds \longrightarrow 4 \: dollars[/tex]
[tex]\sf 1\: pounds \longrightarrow \dfrac{4}{5} \: dollars[/tex]
[tex]\sf 50\: pounds \longrightarrow \dfrac{4}{5}×50 \: dollars[/tex]
[tex]\sf \longmapsto 40 \: dollars[/tex]
The definition of a circle uses the undefined term _______.
O arc
O line
O plane
O ray
Answer:
The correct answer is:
Plane.
Step-by-step explanation: There are three terms generally considered to be undefined in geometry: point, line and plane.
A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is
The correct answer is;
⇒ Plane.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Since, We know that;
There are three terms generally considered to be undefined in geometry: point, line and plane.
Hence, A circle is the set of all points in a plane the same distance from a given point called the center.
And, The only of our options that is used in this definition is plane.
Thus, The correct answer is;
⇒ Plane.
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Bob wants to take his wife, Mary, to Europe in three years to commemorate their 40th wedding anniversary. He recently received a $25,000 inheritance from an uncle, which he plans to put towards the trip. Bill calculates that the trip will cost $30,000 and that he can earn 6% yearly compound interest on his investment. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, FVAD of $1, F (From the tables provided, select the appropriate factor(s).)
To calculate the future value, fill out the table below. Will he be able to pay for the trip with the money he has saved up? (Round up your totals to the nearest whole dollar amount.)
Answer:
10%
Explanation:
Use future value formula
Future Value = Present Value ((1+r)^n)
26,600 = 20,000 ((1+r)^3
26,600/20,000 = (1+r)^3
1.33 = (1+r)^3
1.33^1/3 = 1+r
1.0997 = 1+r
1.0997 - 1 = r
r = 0.997 = 9.97% = 10% (rounded of to the nearest whole percentage)
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Every day carla spends 2/3 of a hour cleaning her room. How long will she spend cleaning her room in 4 days
Answer:
see photo
Step-by-step explanation:
see photo for answer
sometimes when there is a fraction in the question it's a good idea to keep things as fractions and not decimals
Kenzie makes quilts from blue and purple pieces of fabric. The diagram shows the ratio of blue pieces to
purple pieces.
Blue pieces
Purple pieces
The table shows the number of purple pieces and the number of total pieces that Kenzie will make on two
of her quilts.
Based on the ratio, complete the missing values in the table.
Quilt Purple pieces Total pieces
A
56
B
20
The purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The question is incomplete.
The complete question is in the picture, please refer to the picture.
Total number of pieces = 3+5 = 8
So, the purple pieces = 5(5/8) = 35
Total pieces = 20/(5/8) = 4×8 = 32
Thus, the purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.
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3. Which test do you stretch your muscles by reaching for your toes?
Answer:
I think it's sit and reach sorry if I'm wrong