In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
students on bike = 576
% students on bike = 75%
total students = ?
Step 02:
total students
[tex]\text{ \% students on bike = }\frac{students\text{ on bike }}{\text{total students }}\cdot100[/tex][tex]\begin{gathered} 75\text{ = }\frac{576}{\text{total students }}\cdot100 \\ \text{total students = }\frac{576}{75}\cdot100 \end{gathered}[/tex]total students = 768
The answer is:
The number of total students is 768.
follow the order of operations and evaluate the exponential expression (5+1)^2-(9-5)^2x3
Question 7(Multiple Choice Worth 3 points)(05.04 LC)triangle PQR with side p across from angle P, side q across from angle Q, and side r across from angle RIf ∠R measures 18°, q equals 9.5, and p equals 6.0, then which length can be found using the Law of Cosines? p q RQ PQ
Answer
PQ
Explanation
It must be PQ because we have the measure of the other two sides and the angle opposite it.
simplify the following expression using the distributive property and combining like terms:3(y-4) -5(y+8)
3(y-4) - 5(y+8)
3y - 12 - 5y - 40
-2y - 52
The expression secθ - ((tan^2)(θ)/(sec)(θ)) simplifies to what expression?−tan θ−cot θcos θsec θ
Given the expression
[tex]sec(\theta)-\frac{tan^2(\theta)}{sec(\theta)}[/tex]express in sen and cos terms
[tex]\frac{1}{cos(\theta)}-\frac{\frac{sin^2(\theta)}{cos^2(\theta)}}{\frac{1}{cos(\theta)}}[/tex][tex]\frac{1}{cos(\theta)}-\frac{sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{1-sin^2(\theta)}{cos^(\theta)}[/tex][tex]\frac{cos^2(\theta)}{cos^(\theta)}[/tex][tex]cos^(\theta[/tex]then the correct answer is option C
Cos (angle)
A car is traveling at a speed of 70 kilometers per hour. What is the car's speed in miles per hour? How many miles will the car travel in 5 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
What is the car's speed in miles per hour?
Let's make a conversion:
[tex]\frac{70\operatorname{km}}{h}\times\frac{1mi}{1.6\operatorname{km}}=\frac{43.75mi}{h}[/tex]How many miles will the car travel in 5 hours?
1h---------------------->43.75mi
5h---------------------> x mi
[tex]\begin{gathered} \frac{1}{5}=\frac{43.75}{x} \\ x=5\times43.75 \\ x=218.75mi \end{gathered}[/tex]the points E,F,G and H all lie on the same line segment, in that order, such that ratio of EG:FG:GH is equal to 4:1:5. If EH=10, find EG
You have that the ratio of EG:FG:GH = 4:1:5.
Moreover, segment EH = 10.
In order to find EG you consider the following ratios:
EG/FG = 4/1
FG/GH = 1/5
Furthermore, EH = EG + FG + GH
You deposit $6000 in an account earning 6% interest compounded continuously. How much will you have in the account in 10 years?
Solution
Step 1:
Write the compounded interest continuously formula.
[tex]\text{A = Pe}^{rt}[/tex]Step 2:
Given data
P = $6000
r = 6% = 0.06
t = 10 years
Step 3:
Substitute in the formula
[tex]\begin{gathered} A\text{ = Pe}^{rt} \\ A\text{ = 6000 }\times\text{ 2.7183}^{10\times0.06} \\ A\text{ = 6000 }\times\text{ 2.7183}^{0.6} \\ A\text{ = 6000 }\times\text{ 1.822126} \\ A\text{ = \$10932.76} \end{gathered}[/tex]Final answer
A = $10933 ( nearest whole number)
find the minimum value of the function f(x)=2x2-22x+68 to the nearest hundredth
Minimum value of the function
[tex]f(x)=2x^2-22x+68[/tex]To calculate the minimum value we will use the derivative.
[tex]\begin{gathered} f^{\prime}(x)=4x-22 \\ 4x-22=0 \\ 4x=22 \\ x=\frac{22}{4} \\ x=5.5 \end{gathered}[/tex]The answer would be 5.5
The formula, = / + , converts temperatures between Celsius and Fahrenheit degrees. What is the temperature in degrees Celsius that is equivalent to 14 degrees FahrenheitA) -10B) -9 C) -8D) -7
Hello there. To answer this question, we need to plug in the value given by the question and solve for C, the temperature in Celsius.
We want to find the equivalent temperature in Celsius to 14 degrees Fahrenheit.
Knowing that F = 9/5C + 32, making F = 14 lead us to:
14 = 9/5C + 32
Subtract 32 on both sides of the equation
9/5C = -18
Multiply both sides of the equation by a factor of 5/9, in order to get:
C = 5/9 (-18) = -10.
This is the equivalent temperature we were looking for.
helpppppppppppppppppppppppppppppp
skill issue hahahahahhaahahhahaha
Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
The total salary earned by the Justin including the commission is $3959.25.
What exactly is the commission?A commission is extra money earned based on job performance.Members believe to be paid a specified amount of money depending on achievement marketed, sessions closed, recruits placed, and so on—when they agree to a commission-based position as well as commission framework (more by signing the agreement).For the given question;
The base salary of Justin is $1500.
The commission earned by Justin is 3%.
The jewelry of worth $82,975 last month.
Let x be the total commission earned.
Then,
3% of 82,975 = x
x = 3× 82,975 / 100
x = $2489.25
Total salary = base salary + commission
Total salary = $1500 + $2489.25
Total salary = $3959.25
Thus, the total salary earned by the Justin including the commission is $3959.25.
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Factor the given polynomial by finding the greatest common monomial Factor 6x^3y+9xy^3
Answer:
(3xy)(2x² + 3y²)
Step-by-step explanation:
Hello!
The greatest common factor for the coefficients is 3, as both terms have a coefficient with the greatest factor of 3.
The greatest common factor for the x-terms is x, as both terms has x to a minimum of the first power.
The greatest common factor for the y terms is y as both terms has y to a minimum of the first power.
Factor out 3xy:6x³y + 9xy³3xy(2x²) + 3xy(3y²)(3xy)(2x² + 3y²)The factored form is (3xy)(2x² + 3y²).
In the following diagram, we know that line AB is congruent to line BC and angle 1 is congruent to angle 2. Which of the three theorems (ASA, SAS, or SSS) would be used to justify that triangle ABC congruent triangle CDA?
The theorem that justifies why triangle ABC is congruent to triangle CDA is the: SAS.
What is the SAS Theorem?The SAS theorem states that if we can show that two triangles have a pair of corresponding congruent included angles, and two pairs of corresponding sides that are also congruent to each other, then we can prove that both triangles are congruent to each other.
The triangles, ABC and CDA have:
Two pair of corresponding sides that are congruent to each other, which are AB ≅ BC, and AC ≅ CA.
A pair of corresponding included angles, which is angle 1 ≅ angle 2.
Based on the above known information, we can conclude that triangle ABC is congruent to triangle CDA by SAS theorem.
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Solve the following system of equations by graphing. Graph the system below and enter the solution set as an ordered pair in the form (x,y).if there are no solutions enter none and inter all if there are infinite solutions X + 2y = 3 2x + 4y =12
System of equations:
[tex]x+2y=3[/tex][tex]2x+4y=12[/tex]To solve the system by graphing, we have to remember that the point in which both graphs meet is the solution of the system.
• Graph of both equations:
As we can see, there is no point in which both meet. Then, this system has no solution.
Answer: none
1 x(x-2) how I do this
x(x-2)
Apply the distributive property:
x(x)+x(-2)
x^2-2x
Identify the domain and range of the relation. Is the relation a function? Why or why not?
{(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
Domain: {-3, 0, 1, 2}
Range: {1, 2, 4, 5}
The relation is not a function because one of its x-values has two corresponding y-values.
What is the Domain and Range of a Relation?All the set of values of x in a relation are referred to as the range of a relation, while all the set of values of y in a relation are called the domain of the relation.
How to Determine if a Relation is a Function?If each of the x-values in a relation all have only one possible corresponding y-value, then the relation is a function.
Given the relation, {(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}:
The domain is: {-3, 0, 1, 2}
The range is: {1, 2, 4, 5}
The relation has two y-values, 4 and 1, that corresponds to the x-value, 2. Therefore, it is not a function.
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The given relation is not a function because its x-values have two corresponding y-values. Domain: {-3, 0, 1, 2} and Range: {1, 2, 4, 5}
What is the Domain and Range of a Relation?The domain of a function is the set of all the possible input values that are valid for the given function.
The range of a function is the set of all the possible output values that are valid for the given function.
Given the relation as {(-3, 1), (0, 2), (1, 5), (2, 4), (2, 1)}
Therefore,
The domain will be: {-3, 0, 1, 2}
The range will be: {1, 2, 4, 5}
The relation has two y-values, 4 and 1, which corresponds to the x-value, 2.
The given relation is not a function because its x-values have two corresponding y-values. Domain: {-3, 0, 1, 2} and Range: {1, 2, 4, 5}
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Writing a equation of a circle centers at the origin
ANSWER
[tex]x^2+y^2=100[/tex]EXPLANATION
The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = the center of the circle
r = radius of the circle (i.e. distance from any point on its circumference to the center of the circle)
The center of the circle is the origin, that is:
[tex](h,k)=(0,0)[/tex]To find the radius, apply the formula for distance between two points:
[tex]r=\sqrt[]{(x_1-h)^2+(y_1-k)^2_{}}[/tex]where (x1, y1) is the point the circle passes through
Hence, the radius is:
[tex]\begin{gathered} r=\sqrt[]{(0-0)^2+(-10-0)^2}=\sqrt[]{0+(-10)^2} \\ r=\sqrt[]{100} \\ r=10 \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(10)^2 \\ \Rightarrow x^2+y^2=100 \end{gathered}[/tex]3a^2 -3a - 36. solving quadratic by factoring. factor each expression. be sure to check for greatest common factor first.
we have the expression
[tex]3a^2-3a-36[/tex]step 1
Factor 3
[tex]3(a^2-a-12)[/tex]step 2
equate to zero
[tex]3(a^2-a-12)=0[/tex]step 3
Solve
[tex](a^2-a-12)=0[/tex][tex]\begin{gathered} a^2-a=12 \\ (a^2-a+\frac{1}{4}-\frac{1}{4})=12 \\ (a^2-a+\frac{1}{4})=12+\frac{1}{4} \\ (a^2-a+\frac{1}{4})=\frac{49}{4} \end{gathered}[/tex]Rewrite as perfect squares
[tex](a-\frac{1}{2})^2=\frac{49}{4}[/tex]take the square root on both sides
[tex]\begin{gathered} a-\frac{1}{2}=\pm\frac{7}{2} \\ a=\frac{1}{2}\pm\frac{7}{2} \end{gathered}[/tex]the values of a are
a=4 and a=-3
therefore
[tex]3(a^2-a-12)=3(a-4)(a+3)[/tex]Find the derivativef(x) = 1 / (x - 2)
ANSWER
[tex]\frac{df}{dx}=-\frac{1}{(x-2)^2}[/tex]EXPLANATION
We want to find the derivative of the given function:
[tex]f(x)=\frac{1}{x-2}[/tex]First, we have to rewrite the function as follows:
[tex]f(x)=(x-2)^{-1}[/tex]Next, make the following substitution:
[tex]a=x-2[/tex]The function now becomes:
[tex]f(x)=a^{-1}[/tex]Apply the chain rule of differentiation:
[tex]\frac{df}{dx}=\frac{df}{da}\cdot\frac{da}{dx}[/tex]Therefore, we have that:
[tex]\frac{df}{da}=-1\cdot a^{-1-1}=-a^{-2}[/tex]and:
[tex]\frac{da}{dx}=1[/tex]Therefore, the differentiation of the function is:
[tex]\begin{gathered} \frac{df}{dx}=-a^{-2}\cdot1 \\ \Rightarrow\frac{df}{dx}=-(x-2)^{-2}\cdot1 \\ \frac{df}{dx}=-\frac{1}{(x-2)^2} \end{gathered}[/tex]What is the solution to the equation below? Round your answer to two decimal places.ex = 5.9A.x = 124.50B.x = 1.77C.x = 365.04D.x = 0.77
We have the next given equation:
[tex]e^x=5.9[/tex]Now, we can solve for x using the exponent's properties:
Add both sides ln:
[tex]\ln e^x=\ln5.9[/tex]With the ln we can take down the exponent and simplify ln*e = 1.
Hence,
[tex]\begin{gathered} x=\ln(5.9) \\ x=1.77 \end{gathered}[/tex]Hence, the correct answer is option B.
Consider the complex number 2 = V17 (cos(104°) + i sin(104°)).Plot z in the complex plane below.If necessary, round the point's coordinates to the nearest integer.Im5+4+3+2+1 +ReA+-5+-4-3-2-112345-1+-2-3 +-4+-5 +
Recall that to plot a point in the complex plane we have to know its real part and its imaginary part.
The real part of the given number is
[tex]\sqrt[]{17}\cos 104^{\circ},[/tex]and its imaginary part is
[tex]\sqrt[]{17}\sin 104^{\circ}.[/tex]Simplifying the above expressions, and rounding to the nearest integer we get that:
[tex]\begin{gathered} \operatorname{Re}(z)=-1, \\ \operatorname{Im}(z)=4. \end{gathered}[/tex]Therefore, the point has coordinates (-1,4).
Answer:
Ariana is going to invest $62,000 and leave it in an account for 20 years. Assuming
the interest is compounded continuously, what interest rate, to the nearest tenth of a
percent, would be required in order for Ariana to end up with $233,000?
The rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.
What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/f))ⁿ ;
where A = amount that the depositor will receive
P = initial amount that the depositor has invested
R = rate of interest offered to the depositor
f = frequency of compounding offered per year
n = number of years.
Given, Amount that Ariana wants to end up receiving = A = $233,00
Principal amount that Ariana can invest = P = $62,000
Frequency of compounding offered per year = f = 1
Number of years = 20
Let the rate of interest offered to the depositor be = R
Following the formula established in the literature, we have:
233000 = 62000(1 + R)²⁰ ⇒ 3.76 = (1 + R)²⁰ ⇒ 1.07 = 1 + R ⇒ R = 0.07%
Thus, the rate of interest that Ariana should get in order to end up with a final amount of $233,000 is 0.07%.
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Hi, I always have a hard time with these, the whole question is in the picture.
we have that
x1 ----> number of cars with a 7,000 gal capacity
x2 ---> number of cats with a 14,000 gal capacity
x3 ---> number of cars with a 28,000 gal capacity
so
7000x1+14000x2+28000x3=462000
using a 3x3 system of equations solver
the solution is
x1=-2s-4t+66
x2=s
x3=t
The answer is option B
35×0.37 ..find out the solution and the reasoning behind the solution
Given:
Given that 35×0.37.
Required:
To find the solution and reasoning behind the solution.
Explanation:
Let us manipulate the multiplication.
[tex]35\times0.37=12.95[/tex]As there are two digits after decimal point in 0.37, we put decimal point after two digits from right to left in the product (solution) obtained after multiplication.
Final Answer:
The solution is 12.95.
Which statement describes how the reasonable domain
compares to the mathematical domain?
A statement which best describes how the reasonable domain compares to the mathematical domain is that: C. the mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of any graph comprises all the input numerical values or numbers which are primarily shown on the x-axis.
Next, we would evaluate the function which represents the perimeter of this rectangle by substituting the value of 2 as follows:
f(w) = 6w – 8
f(2) = 6(2) – 8
f(2) = 12 – 8
f(2) = 4.
For the length of this rectangle, we have:
Length = 2w - 4
Length = 2(2) - 4
Length = 4 - 4
Length = 0
Therefore, the width of this rectangle must be real numbers that are greater than 2.
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Complete Question:
A rectangle has a length that is equal to 4 less than twice the width. The function for the perimeter depending on the width can be expressed with the function f(w) = 6w – 8, where w is the width of the rectangle in centimeters.
Which statement describes how the reasonable domain compares to the mathematical domain?
Both the mathematical and reasonable domains include only positive real numbers.
Both the mathematical and reasonable domains include only positive whole numbers.
The mathematical domain includes all real numbers, while the reasonable domain includes only real numbers greater than 2.
The mathematical domain includes all real numbers, while the reasonable domain includes only whole numbers greater than 2.
Find the 52nd term.16, 36, 56, 76,…
Answer:
[tex]\text{ a}_{52}\text{ = 1,036}[/tex]Explanation:
Here, we want to find the 52nd term of the sequence
What we have to do here is to check if the sequence is geometric or arithmetic
We can see that:
[tex]\text{ 36-16 = 56-36=76-56 = 20}[/tex]Since the difference between the terms is constant, we can say that the terms have a common difference and that makes the sequence arithmetic
The nth term of an arithmetic sequence can be written as:
[tex]\text{ a}_n\text{ = a +(n-1)d}[/tex]where a is the first term which is given as 16 and d is the common difference which is 20 from the calculation above. n is the term number
We proceed to substitute these values into the formula above
Mathematically, we have this as:
[tex]\begin{gathered} a_{52}\text{ = 16 +(52-1)20} \\ a_{52}\text{ = 16 + (51}\times20) \\ a_{52}\text{ = 16 + 1020 = 1,036} \end{gathered}[/tex]A small radio transmitter broadcasts in a 60 mile radius. If you drive along a straight line from a city 75 miles north of the transmitter to a second city 76 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?
Answer:
Explanation:
We start by having a diagrammatic representation as follows:
In a poll, students were asked to choose which of six colors was their favorite. The circle graph shows how the students answered. If 11,000 students participated in the poll, how many chose green?Orange 13%Pink 7%Blue 10%Red 24%Purple 10%Green 36%
Total of 11,000 students
Green 36%
how many chose green?
Chose green = 11000 * 36/100 = 3960
36% of 11,000 is 3960
Answer:
3,960 students chose green
Evaluate 1312e 4 Sov? 3x²x3 dx (Type an exact answer.)
We have to solve the integral:
[tex]\int ^4_03x^2e^{x3}dx[/tex]We will apply a variable substitution in order to simplify the solution. We have a hint when we see that the derivative of x^3 is 3x^2, that is part of the factors.
[tex]\begin{gathered} u=x^3\Rightarrow du=(3x^2)dx \\ x=0\Rightarrow u=0^3=0 \\ x=4\Rightarrow u=4^3=64 \end{gathered}[/tex]Then, we can write:
[tex]\int ^4_03x^2e^{x3}dx=\int ^4_0e^{x3}(3x^2)dx=\int ^{64}_0e^udu[/tex]Then, we have a simpler integral to solve:
[tex]\int ^{64}_0e^udu=e^u+C=e^{64}-e^0=e^{64}-1[/tex]The exact solution is e^64-1.
There are 17 girls at a party with 30 guests. What fraction
of the party guests are girls?
Answer:
17/30
Step-by-step explanation:
There are 17 girls at a party with 30 guests. What fraction of the party guests are girls?
17/30
