In a recent student government election, the number of vote of the winner is 51
How to determine the ratioAn ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
In a proportion, two ratios are specified to be equal to one another in an equation.
The number of votes of the winner is calculated by writing the ratio
= number of the students who voted / total number of students
let x be the number of students that voted the winner
85 / 100 = x / 60
100x = 60 * 85
x = 5100 / 100
x = 51
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The side length of a square is 5x - 7. Find x if the perimeter is 125.
The numerical value of x in the expression 5x - 7 is 7.65.
What is the numerical value of x?A square is simply a 2-dimentional plane figure with four equal sides and four right (90°) angles.
The perimeter of the square is the sum of the length of all four sides of the square.
P = 4l
Given the data in the question
Side length of square l = 5x - 7Perimeter P = 125Value of x = ?To find the value of x, plug the given values into the above equation and simplify.
P = 4l
125 = 4( 5x - 7 )
125 = 20x - 28
125 + 28 = 20x
153 = 20x
20x = 153
x = 153/20
x = 7.65
Therefore, the value of x is 7.65.
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In a lab experiment, 40 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 23 hours. How long would it be, to the nearest tenth of an hour, until there are 82 bacteria present?
The time needed until there are 82 bacteria is given as follows:
23.8 hours.
How to use the exponential function to find the time?An exponential function is defined as follows:
[tex]y = a(b)^{\frac{x}{n}}[/tex]
In which:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.The parameters for this problem are given as follows:
a = 40, b = 2, n = 23.
Hence the function is:
[tex]y = 40(2)^{\frac{x}{23}}[/tex]
There will be 82 bacteria at a time x when y = 82, hence:
[tex]82 = 40(2)^{\frac{x}{23}}[/tex]
[tex](2)^{\frac{x}{23}} = 2.05[/tex]
Applying the logarithm of base 2 to each side, we have that:
x/23 = log2(2.05)
x = 23 x log2(2.05)
x = 23.8 hours.
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Lilyana runs a cake decorating business, for which 10% of her orders come over the telephone. Let C be the
number of cake orders Lilyana receives in a month until she first gets an order over the telephone. Assume the
method of placing each cake order is independent.
Find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
You may round your answer to the nearest hundredth.
PC <5) =
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If Lilyana runs a cake decorating business for which 10% of her orders come over telephone , then probability that it takes fewer than 5 orders for Lilyana to get her first telephone is 0.3439 .
The geometric distribution is used to calculate the required probability ,
In this case, the success is a telephone order, and
the failure is an order placed in some other way.
Let probability of success is ⇒ p , and
let the number of orders needed to get the first telephone order be = x . Then, X follows a geometric distribution with parameter p, so we have:
Probability of P(X = k) is = (1-p)^(k-1) × p ;
where k is the number of orders needed.
the probability of success (p) is = 10% = 0.1
we have to find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
that means : P(X<5) = P(X=1) + P(X=2) + P(X=3) + P(X=4)
Substituting the values of p = 0.1 ,
we get ;
= (1-0.1)⁰ × 0.1 + (1-0.1)¹ × 0.1 + (1-0.1)² × 0.1 + (1-0.1)³ × 0.1
Simplifying further ,
we get ;
= 0.1 + 0.09 + 0.081 + 0.0729
Adding all the terms ,
we have ;
= 0.3439
Therefore , the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month is 0.3439.
The given question is incomplete , the complete question is
Lilyana runs a cake decorating business, for which 10% of her orders come over the telephone. Let C be the number of cake orders Lilyana receives in a month until she first gets an order over the telephone. Assume the method of placing each cake order is independent.
Find the probability that it takes fewer than 5 orders for Lilyana to get her first telephone order of the month.
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an automobile manufacturer claims that their car has a 55.7 miles/gallon (mpg) rating. an independent testing firm has been contracted to test the mpg for this car. after testing 91 cars they found a mean mpg of 55.2 with a variance of 3.24 mpg. is there sufficient evidence at the 0.05 level that the cars underperform the manufacturer's mpg rating? state the null and alternative hypotheses for the above scenario.
For the given case the Null hypothesis is The mean mpg of the 91 cars tested is equal to the manufacturer's mpg rating of 55.7 and the Alternative hypothesis is The mean mpg of the 91 cars tested is less than the manufacturer's mpg rating of 55.7.
In order to determine whether the cars underperform the manufacturer's mpg rating, the independent testing firm would need to perform a hypothesis test. To do this, they would need to compare their sample mean of 55.2 mpg with the manufacturer's mpg rating of 55.7. They would also need to know the standard deviation of the sample, which is 3.24.
The independent testing firm would then calculate the z-score by subtracting the manufacturer's rating from the sample mean, and dividing it by the standard deviation. If the z-score is greater than the critical value for a 0.05 level of significance, then there is sufficient evidence to reject the null hypothesis.
In this case, the z-score is -1.51. Since the critical value for a 0.05 level of significance is 1.96, the z-score is less than the critical value. Therefore, there is not sufficient evidence to reject the null hypothesis, and we cannot conclude that the cars underperform the manufacturer's mpg rating.
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King Neptune, a 34-foot tall statue that
welcomes visitors to Virginia Beach, casts a
3 13
5 -foot shadow. If Jane is 5’9" tall and is
standing nearby, find the length of her
shadow
The length of Jane's shadow is approximately 2.85 feet
To find the length of Jane's shadow, we can use the principle of similar triangles.
The ratio of the shadow length to the object height is the same for both King Neptune and Jane, then we can set up a proportion:
(shadow length of King Neptune) / (height of King Neptune) = (shadow length of Jane) / (height of Jane)
Given that King Neptune's shadow is 3 13 5 feet and the statue is 34 feet tall.
By substituting these values into the proportion:
(3 13 5 feet) / (34 feet) = (shadow length of Jane) / (5' 9")
To find the shadow length of Jane, we can cross-multiply and solve for the shadow length:
(3 13 5 feet) * (5' 9") = (shadow length of Jane) * (34 feet)
Converting Jane's height into feet: 5'9" = 5*12 +9 = 69 inches = 5.75 ft
(3 13 5 feet) * (5.75 ft) = (shadow length of Jane) * (34 feet)
shadow length of Jane = (313.5*5.75) / 34 = 2.85 ft
So, The length of Jane's shadow is approximately 2.85 feet.
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If the two triangles in the map below are similar, what is the distance from Arrow Road to the end of the forest (x)?
We can write the measurements as -
a = 7.8
b = 9.24
(B) = 50°
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is that two triangles in the map below are similar.
We can write -
{ 1 } -
sin (A) = a/c
a = c sin(A)
a = 12 sin(40°)
a = 12 x 0.65
a = 7.8
{ 2 } -
cos (A) = b/c
b = c cos(A)
b = c cos(40°)
b = 12 x 0.77
b = 9.24
{ 3 } -
tan (B) = b/a
tan (B) = 9.24/7.8
tan (B) = 1.19
(B) = 50°
Therefore, we can write the measurements as -
a = 7.8
b = 9.24
(B) = 50°
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The table shown below shows some values for functions f(x) and g(x). What is/are the solution(s) to f(x)=g(x)? Explain your answer(s). (4 points)
x –3 –2 –1 0 1 2
f(x) 0.4 4.5 7 11.3 15 16.2
g(x) 4 8 10 11.3 15 17
The solutions to the system of equations f(x) = g(x) are given as follows:
x = 0 and x = 1.
The reason for these solutions is that f(x) and g(x) have the same numeric value at x = 0 and at x = 1.
How to interpret the solution of a system of equations?A system of equations is composed by multiple equations.
The solution to the system of equations is the point of intersection of all these equations, which happen when all these equations have the same numeric value.
The x-values for which the numeric values of f(x) and g(x) are the same are given as follows:
x = 0 and x = 1.
Which are the solutions to the system of equations.
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The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries negative 2, 0, 2, 4. The second column is labeled cost (c) with entries negative 7, 0, 7, 14.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 0.5, 1, 1.5. The second column is labeled cost (c) with entries 0, 1.75, 3.5, 5.25.
A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 3, 6, 9. The second column is labeled cost (c) with entries 0, 10.5, 21, 31.5.
The table which matches the equation and includes only viable solutions is the third table.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side
Given that equation is,
c = 3.5b
Here b is the number of loaves of bread and c is the total cost of the bread.
All the table values matches the equation when we substitute the value of b and c in the equation.
But number of loaves of bread cannot be fractions or negative numbers.
So the most viable solution is the third table consisting of values of b as 0, 3, 6, 9 and corresponding value of c as 0, 10.5, 21, 31.5.
Hence the 2-column table with the first column labeled loaves (b) with entries 0, 3, 6, 9 and the second column labeled cost (c) with entries 0, 10.5, 21, 31.5 is the correct one.
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Answer:
The third one
Step-by-step explanation:
Caroline has a discount card that gives her 4% off the purchase of each pizza. If p is the cost of a regular pizza, how much does Caroline pay for her pizza?
A towns population is expected to grow between 5% and 8% per year for the next 10yr. if the current population is 50,000, write an inequality for the expected population, p, next year.
Answer: An inequality for the expected population, p, next year can be written using the information provided. Since the population is expected to grow between 5% and 8% per year, we can represent that as a range of growth rates: 0.05 <= growth rate <= 0.08
To find the expected population next year, we can use the formula:
p = population * (1 + growth rate)
where "population" is the current population of 50,000 and "growth rate" is the percentage increase. Since the growth rate is expected to be between 0.05 and 0.08, we can write the inequality as:
50,000 * (1 + 0.05) <= p <= 50,000 * (1 + 0.08)
This inequality represents the expected range of population next year, with the lower bound being the population if it grows by 5% and the upper bound being the population if it grows by 8%.
Simplifying the inequality:
52,500 <= p <= 54,000
So the expected population next year, p, is between 52,500 and 54,000.
Step-by-step explanation:
I need help on part b
Answer:
a) The pattern 6 has 26 sticks,b) The pattern number n has 4n + 2 sticks.--------------------------
If we put the number of sticks in a sequence we get:
6, 10, 14, ...As we see the difference of the terms is common and is 4, and the first term is 6. It is therefore an arithmetic progression with:
a = 6 and d = 4Use the nth term equation:
a(n) = a + (n - 1)dPart a)Substitute n = 6 to find the number of sticks of the 6th term:
a(6) = 6 + (6 - 1)*4 = 6 + 5*4 = 6 + 20 = 26Part b)Find the nth term:
a(n) = 6 + (n - 1)*4 = 6 + 4n - 4 = 4n + 2For the shape below, if side BD = 29 and side AC = 3x - 4, find x.
Answer:
x = 11
Step-by-step explanation:
We know that the answer we will get will be the same as BD because BD and AC are congrudent, meaning that they are exactly equal shape and size. To find 'x' our equation would be: 29 = 3x - 4. To figure this out we just add 29 and 4 which gives us 33 and then divide that by 3 which gives us 11 (our answer)
I don’t understand how to do this.
Answer:
6000
Step-by-step explanation:
Interest of 3% a year of principal of 200,000 = 6000
monthly payment of 843 also includes a portion of amortization of the principal itself, which you can ignore cause the question only asked for the interest portion.
this is an unclear question cause it didn't say PER YEAR interest paid. you only need to remember interest% * principal = ANNUAL interest payment $. Then you can divide that over 12 months, which is 500$ per month.
Which ordered pair is a solution of the equation? 6 x + 3 y = 15 6x+3y=15
Choose 1 answer:
(Choice A)
A
Only
(
3
,
−
2
)
(3,−2)left parenthesis, 3, comma, minus, 2, right parenthesis
(Choice B)
B
Only
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis
(Choice C)
C
Both
(
3
,
−
2
)
(3,−2)left parenthesis, 3, comma, minus, 2, right parenthesis and
(
2
,
2
)
(2,2)left parenthesis, 2, comma, 2, right parenthesis
(Choice D)
D
Neither
Neither of the ordered pairs is a solution of the equation 6x + 3y = 15.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Given linear equation is 6x + 3y = 15
Substitute each of the point given in the options.
A : (3, -2)
6x + 3y = (6 × 3) + (3 × -2) = 18 - 6 = 12 ≠ 15
B : (2, 2)
6x + 3y = (6 × 2) + (3 × 2) = 12 + 6 = 18 ≠ 15
Neither (3, -2) nor (2, 2) are the solutions of the equation.
Hence neither is the solution of the given linear equation.
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To describe a sequence of transformation that maps triangle ABC onto triangle a”b”c” a student starts with a reflection over x-axis
We can write the coordinates after reflection as -
A (x₁, y₁) → A" (x₁, - y₁)
B (x₂, y₂) → B" (x₂, - y₂)
C (x₃, y₃) → C" (x₃, - y₃)
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each other.Given is that to describe a sequence of transformation that maps triangle ΔABC onto triangle ΔA”B”C” a student starts with a reflection over x - axis.
Assume the coordinates of a triangle are -
A (x₁, y₁)
B (x₂, y₂)
C (x₃, y₃)
When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is taken to be the additive inverse.The reflection of point (x, y) across the x-axis is (x, -y).
So after the reflection over the {x} axis, we can write the coordinates as -
A" (x₁, - y₁)
B" (x₂, - y₂)
C" (x₃, - y₃)
Therefore, we can write the coordinates after reflection as -
A (x₁, y₁) → A" (x₁, - y₁)
B (x₂, y₂) → B" (x₂, - y₂)
C (x₃, y₃) → C" (x₃, - y₃)
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Explain your work please.
I need help in this problem
Answer:
b
Step-by-step explanation:
the sum of the 3 angles in the triangle = 180°
sum the 3 angles and equate to 180
2x + 1 + 5x + 5 + 90 = 180
7x + 96 = 180 ( subtract 96 from both sides )
7x = 84 ( divide both sides by 7 )
x = 12
0.18 rounded to the nearest tenth
Answer:
0.2
Step-by-step explanation:
8 is bigger than 5 so we will make 8 zero and will will add 1 to the next number
Answer:
0.2
Step-by-step explanation:
Hope this helps
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Gabriela has an average daily balance of $232. 94 on her credit card. Her card charges 9. 25% annual interest. What will her monthly finance charge be?
Her monthly finance charge will be: $1.80
Now, According to the question:
Gabriela has an average daily balance of $232. 94 on her credit card.
and, Her card charges 9. 25% annual interest.
Based on the given condition:
$232.94 × 9.25%
232.94 × 9.25/100
Calculate the product or quotient:
232.94 × 9.25/100 = 21.54694
21.54694 rounds up to 21.55
Her monthly finance charge will be:
21.55/12 = 1.7958333333
1.7958333333 round up 1.80
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01. De 200 melones, 80 resultaron en mal estado.
¿Qué porcentaje de los 200 están buenos para la venta?
200 melons are good in 60% of the cases.
Qué es bueno para la buena venta?Create a favourable first impression. Offers customers problems-solutions and a positive experience. Make good use of the newest technologies. clear language for business transactions. Maintain open communication.
The Most Important Characteristic for Sales. No matter what kind of sale it is, or what industry it is in, the most crucial factor that influences someone's decision to buy is always the price. And making oneself increasingly valuable is the key to selling and selling oneself.
200 equates to 100%.
Are good = 200 - 80 = 120
200me = 100%
120me = 100%/200me x = 120000%/200me x = 60%
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parallelogram has sides of lengths 35 inches and 75 inches. One angle has measure of140°. Find the length of each diagonal.
The length of diagonal of a parallelogram is 2546 inches.
What is a parallelogram?A quadrilateral with equal pairs of opposing sides and angles is referred to as a parallelogram. It has a pair of opposing sides that are parallel to one another. The inner angles are supplementary in nature, meaning that the sum of them equals 180 degrees. A parallelogram's diagonals are bisected by one another, or divided into two equal portions. A parallelogram's internal angles add up to 360 degrees.
The diagonals of parallelogram are given by:
x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)
Given the two sides are 35 and 75 inches.
We also know that the adjacent angles of parallelogram are supplementary:
∠A + ∠B = 180
140 + ∠B = 180
∠B = 40
Substitute the value of sides and angle in the equation:
x = √(a^2 + b^2 – 2ab cos A) = √(a^2 + b^2 + 2ab cos B)
x = √((35)^2 + (72)^2 + 2(35)(72) cos 140)
x = 1225 + 5184 + (5040)(-0.766)
x = 1225 + 5184 - 3860
x = 2546 inches
Hence, the length of diagonal is 2546 inches.
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How do you find the value of x and y?
Check the picture below.
[tex]5x+70=24x-25\implies 70=19x-25\implies 95=19x \\\\\\ \cfrac{95}{19}=x\implies \boxed{5=x} \\\\[-0.35em] ~\dotfill\\\\ 4y+2=x+y\implies 4y+2=5+y\implies 3y+2=5 \\\\\\ 3y=3\implies y=\cfrac{3}{3}\implies \boxed{y=1} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{5(5)+70}{\measuredangle R=95^o}\hspace{5em}\stackrel{24(5)-25}{\measuredangle C=95^o}\hspace{5em}\stackrel{4(1)+2}{QR=6}\hspace{5em}\stackrel{5+1}{BC=6}[/tex]
Decide whether triangles ABC and DEC are similar. Explain or show your reasoning.
Answer:
AAA similarity
Step-by-step explanation:
Similar triangles:In ΔECD,
∠E + ∠D + ∠ECD = 180° {Angle sum property}
∠E + 36 + 123 = 180°
∠E + 159 = 180
∠E = 180 - 159
∠E = 21°
In ΔACB,
∠A + ∠B + ∠ACB = 180° {Angle sum property}
∠ACB + 36 + 21 = 180°
∠ACB + 57 = 180
∠ACB = 180 - 57
∠ACB= 123°
In ΔECD & ΔBCA,
∠A ≅ ∠D
∠B ≅ ∠A
∠BCA ≅ ∠ECA
ΔECD ~ ΔBCA by Angle Angle Angle similarity.
mary divides a circle into sectors. the central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. what is the degree measure of the smallest possible sector angle?
The measure of the smallest possible sector angle possible is 8°.
Let [tex]$a_1$[/tex] be the first term of the arithmetic progression and [tex]$a_{12}$[/tex] be the last term of the arithmetic progression.
From the formula of the sum of an arithmetic progression, we have -
[tex]$12*\frac{a_1+a_{12}}{2}=360$[/tex]
simplifying we get,
[tex]$a_1 + a_{12} = 60$[/tex]
[tex]$a_{12}$[/tex] is the largest term of the progression and it can also be expressed as-
[tex]a_{12} = $a_1+11d$[/tex]
where d is a common difference.
Since each angle measure must be an integer, d should also be an integer.
[tex]$a_{12}-a_1=a_1+11d-a_1=11d$[/tex]
Since d is an integer, the difference between the first and last terms, 11d, must be divisible by 11.
Since the total difference should be less than 60, let's start checking multiples of 11 less than 60 for the total difference between [tex]$a_1$[/tex] and [tex]$a_{12}$[/tex].
Let us take the largest multiple because the maximum difference will give us the minimum value of the first term.
If the difference is 55, [tex]$a_1=\frac{60-55}{2}=2.5$[/tex], is not an integer.
If the difference is 44, [tex]$a_1=\frac{60-44}{2}= 8[/tex] . It satisfies the given conditions.
Hence, the measure of the smallest possible sector angle possible = 8°.
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Find the balance in the account after the given period. $2,600 deposit earning 4.2% compounded monthly, after 3 years. The balance after 3 years will be $ (Round to the nearest cent as needed.)
To find the balance of the account after 3 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the final amount, P is the initial principal, r is the interest rate, n is the number of times the interest is compounded per year, and t is the number of years.
In this case, the initial principal is $2,600, the interest rate is 4.2% (expressed as a decimal), the number of times the interest is compounded per year is 12 (monthly), and the number of years is 3.
So, we can plug these values into the formula:
A = 2600(1 + 0.042/12)^(12*3)
A = 2600(1.0035)^36
A = 2600 * 3.876
A = 10,049.6
The balance of the account after 3 years is $10,049.6.
4 painters that have completed 12 rooms in 8 hours. assuming they are working at the same efficiency, how many hours does it take 7 painters to paint 21 rooms?
Answer: We can use the concept of rates to solve this problem.
A rate is a ratio of the amount of work done to the amount of time it takes to do the work. We can find the rate of work for the 4 painters by dividing the number of rooms they painted by the number of hours it took them:
Rate = Rooms painted / Hours
Rate = 12 rooms / 8 hours = 1.5 rooms per hour
Now we can use this rate to find out how long it will take 7 painters to paint 21 rooms. To do this, we'll use the formula:
Time = Rooms / Rate
Time = 21 rooms / 1.5 rooms per hour = 14 hours
So it would take 7 painters working at the same efficiency as the 4 painters 14 hours to paint 21 rooms.
Step-by-step explanation:
help pls and thanks
An equation of a circle which represents the picture include the following: A. (x)² + (y)² = 25.
What is the equation of a circle?In Mathematics, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.From the information provided above, we have the following points on this circle:
P(–5, 0)Q(0, 5)R(5, 0)S(0, –5).Radius of the circle (r) = 5 units.Center of the circle (h, k) = (0, 0)Substituting the given points into the equation of a circle, we have the following;
(x - 0)² + (y - 0)² = 5²
(x)² + (y)² = 25.
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Evaluate each expression. Show your thinking 7+2^3
[tex]7+2^3[/tex]
[tex]7+(2^3)[/tex]
[tex]7+8[/tex]
[tex]=\fbox{15}[/tex]
If I Got 7 "(tokens or whatever you prefer) a minute for 9 hours/ 540 minutes, how many tokens would I have
Answer:
If you get 7 tokens a minute and you work for 9 hours, or 540 minutes, then you would have:
7 tokens/minute * 540 minutes = 3780 tokens
You would have 3780 tokens in total.
Answer:
3,780
Step-by-step explanation:
7* 540= 3780
because you get 7 every minute and there are 540 minutes
three quantities, the results of measurements, are to be added. they are 2.0800, 2.677, and 1.67. what is their sum to the correct number of significant figures?
Sum to the correct number of significant figures is 6.43
Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.
Significant figures are used to establish the number which is presented in the form of digits. These digits carry a meaningful representation of numbers. The term significant digits are also used often instead of figures. We can identify the number of significant digits by counting all the values starting from the 1st non-zero digit located on the left. For example, 12.45 has four significant digits.
Since the least precise measurement 1.67 is correct to only two decimal place.
2.0800
+ 2.677
+ 1.67
6.427
Therefore, the final result should be rounded off to 6.43 where Significant Figures: 3, Decimals: 2.
The arithmetic addition of given numbers to the correct number of significant figures is 6.43.
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