Answer:
Step-by-step explanation:
Let
n--------> the number
we know that
1) the sentence" Three less than the product of seven and a number" represent the expression------>
2) the sentence" is four more than the number"
represent the expression ------->
3) the complete sentence" Three less than the product of seven and a number is four more than the number" represent the expression
represent the expression ------->
therefore
the answer is
(7n-3) =(n+4)
It's Pre-calculus subject
1) The growth rate is 40%
2) The number of bacteria initially present is 990
3) The number after four hours is 4904
4) The function in terms of time is written as F(t) = 120e^-1.6t
What is the number of bacteria?We know that the number of the bacteria can be obtained on the basis of the function that we have. We know that the process of exponential increase of decrease would have to be modelled by the use of an exponential equation. In this case, we have the equation; n(t) = 990e^0.4t
We know that in this case, the time of the multiplication of the bacterial is t, the percent growth rate of the bacteria is 40% and the initial number of the bacteria is 990.
After 4 hours we have;
n(4) = 990e^0.4(4)
n(4) = 4904
b) Given that the initial temperature if the system is 120°F and the rate of the cooling is 1.6, the formula is written as;
F(t) = 120e^-1.6t
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Cameron invests money in a bank account
which gathers compound interest each year.
After 4 years there is $736.80 in the account.
After 7 years there is $788.82 in the account.
Work out the annual interest rate of the bank
account.
Give your answer as a percentage to 1 d.p.
first off, let's check the equation for each year.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$736.80\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ 736.80=P\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4}\implies 736.80=P\left(1+\frac{r}{100} \right)^4 \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$788.82\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases} \\\\\\ 788.82=P\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 7}\implies 788.82=P\left(1+\frac{r}{100} \right)^7 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{736.80=P\left(1+\frac{r}{100} \right)^4}\implies \cfrac{736.80}{\left(1+\frac{r}{100} \right)^4}=P \\\\\\ \stackrel{\textit{using the 2nd equation}}{788.82=P\left(1+\frac{r}{100} \right)^7}\implies \stackrel{\textit{substituting on the 2nd equation}}{788.82=\cfrac{736.80}{\left(1+\frac{r}{100} \right)^4}\left(1+\frac{r}{100} \right)^7}[/tex]
[tex]788.82=736.80\cfrac{ ~~ \left(1+\frac{r}{100} \right)^7 ~~ }{\left(1+\frac{r}{100} \right)^4}\implies 788.82=736.80\left(1+\frac{r}{100} \right)^3 \\\\\\ \cfrac{788.82}{736.80}=\left(1+\frac{r}{100} \right)^3\implies \sqrt[3]{\cfrac{788.82}{736.80}}=1+\cfrac{r}{100}\implies \sqrt[3]{\cfrac{788.82}{736.80}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[3]{\cfrac{788.82}{736.80}}=100+r\implies 100\sqrt[3]{\cfrac{788.82}{736.80}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{2.3}\approx r \end{array}}[/tex]
What is slope-intercept form?
O not this one
O a² +6² = = C
O Ax+By = C
O y = mx + b
Answer:
O y = mx + b
Step-by-step explanation:
y = y coordinate
m = slope
x = x coordinate
b = y intercept
Find an equation for the graph sketched below:
8
6
-5
f
on
N
-5-4-3-2-1
5 6
1 2 3 4 5
Answer:
[tex]f(x)=3^{x+1}-3[/tex]
Step-by-step explanation:
The curve of the graph shows it is Exponential: [tex]f(x)=b^{x-h}+k[/tex]
To find b, h, and k, we need to "un-transform" the graph from [tex]f(x)=b^{x}[/tex]
1. h = horizontal shift/translation; k = vertical translation:
(0,1) ⇒ (-1,-2), so h = -1 and k = -3 and [tex]f(x)=b^{x+1}-3[/tex]
2. Given the points (-1,-2), (0,0), and (1,6), use one of them to find b:
[tex]f(x)=b^{x+1}-3\\0=b^{0+1}-3\\0=b^{1}-3\\3=b^1\\3=b[/tex]
3. Place b, h, and k in their correct places in the function.
The chalk circle around a pitcher's mound has a diameter of 18 ft.
What is the area of the pitcher's circle?
Answer:
Exact area = 81π ft²
Approximate area = 254 ft²
Step-by-step explanation:
A = πr²
A = π × (9 ft)²
A = 81π ft²
A = 81(3.14) ft²
A = 254 ft²
[tex] \Large{\boxed{\sf A = 81 \pi \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]
[tex] \\ [/tex]
Explanation:The area of a circle is given by the following formula:
[tex] \Large{\sf A = \pi \times r^2 } [/tex]
Where:
A is the area of the circle.r is its radius.[tex] \\ [/tex]
We know that the diameter of a circle is twice its radius. Therefore, we can find the value of the circle's radius by dividing its diameter by 2.
[tex] \sf Diameter =2 \times radius \Longleftrightarrow radius = \dfrac{Diameter}{2} \\ \\ \\ \star \: \sf r = \dfrac{18 \ ft}{2} = \boxed{\sf 9 \ ft} [/tex]
[tex] \\ [/tex]
Now, substitute the value of the radius into the formula:
[tex] \sf A = \pi \times (9 \ ft)^2 = \boxed{\boxed{\sf 81 \pi \ \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]
[tex] \\ [/tex]
[tex] \hrulefill [/tex]
[tex] \\ [/tex]
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Directions: Choose the best answer to the question and fill in the corresponding oval on the Multiple Choice section of the Scantron sheet provided.
1. The population of Rochester has been increasing by 5% each year for the past 7 years. What is the growth factor?
A. 7
B. 1.05
C. 50
D. 5
2. Which of the following is not a point on the graph of the function y=4 x+1.
A. (0,4)
B. (-1,1)
C. (1,16)
D. (-2,0)
Answer:
1= 50
2=1,16
Step-by-step explanation:
because it not have graph
(Please Help!) For each quantity decide whether circumference or area would be needed to calculate it.
A: The distance around a ferris wheel
B:The amount of paint needed to paint a bullseye
C: The amount of whipped cream needed to go around the edge of a pie
D The amount of material needed to make a drum head (the part of the drum you hit).
The quantities we need circumference for are: A and C.
The quantities we need area for are: B and D.
What is the Circumference and Area of a Circular Shape?The circumference of a circular shape is described as the distance around the circular shape. It is calculated using the formula, 2πr.
On the other hand, the area of a circular shape is the amount of space a circular shape has. It is calculated as πr².
Therefore:
For quantity A, to know the distance around a Ferris wheel, we would need to calculate is the circumference, so also for quantity C.
For quantity B, to know the amount of paint needed, we would calculate the area, so also is it for quantity D.
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Yesterday, Jack drove 39 1/2 miles. He used 1 1/4
gallons of gasoline. What is the unit rate for miles per gallon?
Answer:
31 [tex]\frac{3}{5}[/tex] miles per gallon.
Step-by-step explanation:
[tex]\frac{39\frac{1}{2} }{1\frac{1}{4} }[/tex]
39 [tex]\frac{1}{2}[/tex] ÷ 1 [tex]\frac{1}{4}[/tex]
[tex]\frac{79}{2}[/tex] ÷ [tex]\frac{5}{4}[/tex]
[tex]\frac{79}{2}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{158}{5}[/tex] = 31 [tex]\frac{3}{5}[/tex] miles per gallon or 31.6 miles per gallon
Kyle needs 164 beads for a project. The beads are sold in packs of 2, 5, or 10. What is the least number of packs Kyle needs to buy. Explain
Answer: 17 packs
Step-by-step explanation: 16 packs of 10 equals 160 beads, and one pack of 5 will give you 164 beads with 1 left over.
Solve the following
(d). m(x)=xcos(-x)
By solving the following trigonometric function of m(x)= x cos(-x) we get m(x) = cos(x).
What is trigonometry ?
Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles. The ratios used to study this relationship are called trigonometric ratios, namely, sine, cosine, tangent, cotangent, secant, cosecant.Given that;
m(x) = x cos(-x)
m(x) = x cos (x) [ we know that cos(-x) = cos(x) ]
m(x)/x = x cos(x)/x [divide both sides by x]
m = cos(x)
Therefore, m(x)=x cos(-x) ⇒cos(x)
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Is 181 prime or composite? Justify your answer. A. 181 is prime because it has a factor of 9. B. 181 is prime because its only factors are 1 and itself. C. 181 is composite because it has a factor of 9. D. 181 is composite because it has a factor of 3.
HELPPPP ME
Answer:
B
Step-by-step explanation:
Assuming these 4 are the only possibilities:
A: This cannot be correct because if 181 were divisible by 9, it would not be prime, as the problem suggests.
C: This cannot be correct because 181/9 is 21.11, which is not a whole number
D: This cannot be correct because 181/3 is 60.333, which is not a whole number
Thus, the answer is B.
FUN FACT:
When seeing whether a number is divisible by 3, add up its digits, and if they are divisible by 3, so is the number. Example: 36 is divisible by 3 because 3 + 6 = 9, and 9 is divisible by 3. 181 is not, however, because 1+8+1=10, and 10 is not divisible by 3.
Same with 9! 459 is divisible by 9 because 4+5+9 = 18, which is divisible by 9. 181 is not, however, because 1+8+1 = 10, which is not divisible by 9.
I hope this helps!
Answer:
B. 181 is prime because its only factors are 1 and itself.
Step-by-step explanation:
Prime number
A whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc.
Composite number
A number that is divisible by a number other than 1 and itself (so it has more than 2 factors).
An example of a composite number is 6 as its factors are 1, 2, 3 and 6.
The factors of 181 are 1 and 181.
Therefore, it is prime because its only factors are 1 and itself.
Find the value of each variable.
Simplify. your answers as much as possible.
The value of each variable iS
x = 6
y = 4
What is angle bisector theorem?
The angle bisector theorem in geometry is concerned with the proportions of the two segments that a line that bisects the opposite angle divides a triangle's side into. It compares their proportional lengths to the proportional lengths of the triangle's other two sides.
Apply the angle bisector theorem to solve for x and y respectively.
✔️4/(9 - x) = 8/x
Cross multiply
4*x = 8(9 - x)
4x = 72 - 8x
Add 8x to both sides
4x + 8x = 72
12x = 72
12x/12 = 72/12
x = 6
✔️y/2 = 6/3
Cross multiply
3*y = 6*2
3y = 12
3y/3 = 12/3
y = 4
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Equals how many CC? Please I need help
1. 177.441177
2. 354.882354
3. 118.294118
4. 473.176472
5. 236.588236
perpendicular bisector of AB.
Which diagram shows a valid approach to this construction?
The diagram that shows a valid approach to the given construction is option a for the perpendicular bisector.
What is meant by perpendicular bisector?A perpendicular bisector is a section of a line that divides a straight segment into two congruent or equal segments. At exactly its midpoint, they split the line section. With the line segment it divides, a perpendicular bisector produces a 90° angle. A line segment that bisects another line segment at an angle of 90 degrees is referred to as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal pieces by intersecting it at a 90° angle. The term "perpendicular bisector" refers to a precise drawing in which a line is accurately divided in half by another line that is perpendicular to the first line. To divide into two equal portions, or bisect, is a verb.
Therefore, The diagram that shows a valid approach to the f=given construction is option a.
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Rectangle P Q R S has P Q=3 and Q R=4. Points T and V are on side P S such that P T=U S=1
Determine the measure of angle T Q U in degrees and rounded to 1 decimal place
The measure of angle TQU is 41.1°
What is angle of measure?
The measure of the angle is formed by the two lines or arms having a same vertex.
Solution:
We know that,
PQ² + PT² = QT² -------- By Pythagoras theorem
∴QT = √10
∵ PT + TU + US = 4
∴ TU = 4 - PT - US
TU = 4 - 1 - 1
∴TU = 2
Now, using Pythagoras theorem in triangle PQU
PQ² + PU² = QU²
∴ QU =√ 3² + 3² (∵PU = PT + TU = 1 + 2)
∴ QU = 3
Now using Heron's formula in triangle TQU
Semi-perimeter = (2 + √10 + 3)/2
= 4.08
Area of the triangle = [tex]\sqrt{S(S-TQ)((S-TU)(S-QU)}[/tex]
= [tex]\sqrt{4.08(0.92)(2.08)(1.08)}[/tex]
= 2.903 unit²
Now, we know that
Area of a scalene triangle = ab/2 × sin c
∴ 2.903 = (√10×3/)2 × sin T
∴ sin T = 2.903×2/3√10
sin T = 0.61
∴ ∠T = [tex]sin^{-1}[/tex](0.61)
∴∠T = 93.9°
Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)
∠U + ∠T + ∠Q = 180°
∴ ∠Q = 180 - 93.9 - 45
∴∠Q = 41.1°
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The measure of angle TQU is 41.1°
What is angle of measure?
The measure of the angle is formed by the two lines or arms having a same vertex.
We know that,
PQ² + PT² = QT² -------- By Pythagoras theorem
∴QT = √10
∵ PT + TU + US = 4
∴ TU = 4 - PT - US
TU = 4 - 1 - 1
∴TU = 2
Now, using Pythagoras theorem in triangle PQU
PQ² + PU² = QU²
∴ QU =√ 3² + 3² (∵PU = PT + TU = 1 + 2)
∴ QU = 3
Now using Heron's formula in triangle TQU
Semi-perimeter = (2 + √10 + 3)/2
= 4.08
Area of the triangle = 2.903 unit²
Now, we know that
Area of a scalene triangle = ab/2 × sin c
∴ 2.903 = (√10×3/)2 × sin T
∴ sin T = 2.903×2/3√10
sin T = 0.61
∴ ∠T = (0.61)
∴∠T = 93.9°
Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)
∠U + ∠T + ∠Q = 180°
∴ ∠Q = 180 - 93.9 - 45
∴∠Q = 41.1°
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The production costs, P, for a band to have a concert can be modeled by the equation P=850 + 5x. where X is the number of concert tickets sold. The band earns $50 for each ticket sold. The band's goal is for the amount earned on ticket sales minus production costs to equal $5,000 per concert. How many tickets does the band have to sell for each concert to meet the goal?
The band have to sell 76 tickets for each concert to meet the goal
How many tickets does the band have to sell for each concert to meet the goal? From the question, we have the following parameters that can be used in our computation:
P = 850 + 5x
Also, we have
Bonus = $50
This means that
Cost = 850 + 5x + 50x
So, we have
Cost= 850 + 55x
When they earn $5000, we have
850 + 55x = 5000
Evaluate the like terms
55x = 4150
Divide
x = 76
Hence, the number of tickets is 76
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A person jogs 4 miles in 1/5 hour what’s the persons speed in miles per hour
Answer:
Below
Step-by-step explanation:
WOW! THIS is not 'jogging' :
4 miles / 1/5 hr = 20 m/hr
Positive or negative domains
Answer:
I believe it is positive although I am not 100% sure.
Step-by-step explanation:
The arrows tend to go upwards even though it does have a curve at the bottom. It is still going upwards.
(7) The sum of five consecutive even integers is at least 400 . What is the minimum value of the first even integer? Choose from the following solutions:
A 80
B 70
C 76
D 82
Answer:
C 76
Step-by-step explanation:
let x = 1st number
let x+ 2 = 2nd number
let x + 4 = 3rd number
let x + 6 = 4th number
Let x + 8 = 5th number
x + x + 2 + x+ 4 + x + 6 + x + 8 = 400 Combine like terms
5x + 20 = 400 Subtract 20 from each side
5x = 380 Divide both sides by 5
x = 76
Check:
76 + 78 + 80 + 82 + 84 = 400
If there are 20 voters and 5 candidates , how many total points would there be in a Borda count
Answer:
25
Step-by-step explanation:
Solve each equation.
|x+5|=-3
Answer:
No solution
Step-by-step explanation:
The absolute value function outputs non-negative values.
Answer: No solutions
This is because absolute value is never negative. It represents distance, and negative distance does not make sense.
The smallest possible output of |x+5| is zero.
In what quadrant does the terminal side of -400 degrees lie?
Answer:
1st
Step-by-step explanation:
-400 degrees can also be seen as positive 40 degrees
A base of a right solid, which is 3 centimeters high, is shown in the picture below. Find
the volume of the right solid. All dimensions are in centimeters.
4
5
Answer:
5 i think
Step-by-step explanation:
if p(e)=0.47 find the odds in favor of e
0.53.The elements left over after the given set's components have been eliminated from the universal set are the complement of the set.
How do you determine the likelihood of a compliment?A pair of occurrences that are incompatible with one another are complementary to one another. For instance, the complement of a coin flip is tails when heads is the desired result. The Complement Rule asserts that the total of the probability of an event and its complement must equal 1, or for the event A, P(A) + P(A') = 1.The elements left over after the given set's components have been eliminated from the universal set are the complement of the set. A set's complement is denoted by the letters Ac or just A'. A' = - A is the formula for a complement in this instance.Explanation:
P(event E)=0.47
Consequently, P(not E)=1P(E) [P(E)+P(not E)=1] =10.47 =0.53
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What is the sign of {-z}/{-y} when z>0 and y>0 ?
Choose 1 answer:
A Positive
(B) Negative
Zero
(A) Positive
When z and y are both positive, the expression{ [tex]\frac{-z}{-y}[/tex] }is equal to [tex]\frac{-z}{-y}[/tex]. Since both z and y are positive, -z is negative and -y is negative, so the expression [tex]\frac{-z}{-y}[/tex] is equal to the positive number [tex]\frac{z}{\\y}[/tex].
Therefore, the sign of {-z}/{-y} when z>0 and y>0 is positive.
So the correct answer is:
(A) Positive
What is sign?
In mathematics, a sign is a symbol that is used to represent the relative size or value of a number or expression. The most common signs used in mathematics are the plus (+) and minus (-) signs, which are used to represent positive and negative numbers, respectively.
For example, the number 5 is a positive number, and it is represented using the plus sign. On the other hand, the number -5 is a negative number, and it is represented using the minus sign.
In addition to the plus and minus signs, there are also other signs used in mathematics, such as the equal sign (=), which is used to indicate that two quantities are equal, and the inequality signs (>, <, ≥, ≤), which are used to indicate that one quantity is greater than or less than another.
Overall, signs play a vital role in mathematics as they help to indicate the size and value of numbers and expressions, and they are essential for performing various mathematical operations and solving mathematical problems.
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please help i need to turn in tomorrow
Answer:
(I will only answer one and I think my explanation can help you understand so you do it yourself) For number 8: the slope-intercept form is: y=-1/3x-11
Step-by-step explanation:
x+3y=-33
3y=-x-33(take away x from both sides of the = sign)
y=-1/3x-11(divide 3 on both sides of the = sign)
Fill the missing fraction.
Z - 1 1/2 = 1 1/2
Answer:
Z=3
Step-by-step explanation:
1 1/2+1 1/2= 2+1=3
Use synthetic division to find the quotient and remainder when -x^4+2 x^3+12 x^2-16 is divided by x+2 by completing the parts below.
Using synthetic division we get, the remainder is 24
and the quotient is [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex]
What is synthetic division?
Particularly when we need to divide the polynomial by a linear factor, the Synthetic division provides a faster method of doing so. Instead of dividing factors, it is typically employed to determine the polynomial's zeroes or roots.
Here, in the question we have [tex]\frac{-x^{4} +2x^{3}+12x^{2} -16 }{x+2}[/tex]
First we find x from the divisor,
x+2=0
x=-2
Next, we arrange it in the division form with only the coefficients of the dividend terms.
[tex]-2 | -1 \space\ \space\ 2 \space\ \space\ 12 \space\ \space\ 0 \space\ \space\ -16\\[/tex]
[tex]2 \space\ -2 \space\ -20 \space\ 40[/tex]
----------------------------------
[tex]-1 \space\ \space\ 0 \space\ \space\ 10 \space\ \space\ -20 \space\ \space\ 24[/tex]
Therefore, we get the remainder as 24
And the quotient as [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex].
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A scuba diver is at an elevation of −18 ft. She then descends 30 ft deeper. What is the scuba diver’s new elevation?
Answer: -48
Step-by-step explanation:
-18-30 = -48
Please help, math modeling with distribution and statistics
The probability of having fewer than three television sets in the apartment is 0.7
How to find the probability of having fewer than three television setsProbability is solved by finding the ratio of required outcome to the total sample
In the given problem the total sample space is the sum of the frequencies which
sum of the frequencies
= 1 + 6 + 14 + 7 + 2
= 30
The required outcome is the number of people that have less than three tv sets in their apartment, In this case 3 is not inclusive from 2 to o is added
= 1 + 6 + 14
= 21
The probability P(X < 3) = 0.7
= 21 / 30
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