Answer:
The number of pennies,nickels and dimes are (p,n,d)=(3,4,6).
Further explanation:
Given:
A box holding pennies, nickels and dimes contains thirteen coins in a box.
Total value is 83 cents.
Calculation:
Consider p,n and d be the number of pennies, nickel and dimes.
Now, total is 13 coins so [tex]p+n+d=13[/tex]
As we know that these following are US coin.
Penny=1 cent
Nickel=5 cents
Dime=10 cents
Step 1:
The value is already given as 83 cents that is 80+3 cents.
80 cents can be possible in many combinations as follows:
(N,D)=(0,8),(2,7),(4,6),(6,5),(8,4),(10,3),(12,2),(14,1),(16,0)
It is given that the total number of cents is 13 so we choose (4,6) as (n,d) .
So the value of nickel n=4
Dimes d=6
Step 2:
The value of p is calculated as follows:
Substitute 4 for n, 6 for d in equation [tex]p+n+d=13[/tex] as follows:
[tex]p+4+6=13[/tex]
[tex]p+10=13[/tex]
[tex]p=13-10[/tex]
p=3
Thus, the number of pennies,nickels and dimes are (p,n,d)=(3,4,6).
The problem can be represented by two equations based on the total coins and their total value. The number of pennies, nickels, and dimes cannot be precisely determined without extra constraints or assumptions.
Explanation:This problem is about the trio of pennies, nickels, and dimes, and their corresponding values; 1 cent, 5 cents, and 10 cents, respectively. Let's denote the number of pennies as P, nickels as N, and dimes as D.
From the problem, we know two key pieces of information:
There are 13 coins in total. Therefore: P + N + D = 13 The total value of all the coins is 83 cents. So: P(1 cent) + N(5 cents) + D(10 cents) = 83 cents
Mind this information, we'll try to solve it using the system of linear equations method. However, it's impossible to precisely calculate the number of each coin type without additional constraints or assumptions. This math problem is a common example of how real-life situations can pose complex mathematical challenges, requiring more information or advanced techniques of problem solving.
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. An individual wishes to invest $5000 over the next year in two types of investment: Investment A yields 5%, and investment B yields 8%. Market research recommends an allocation of at least 25% in A and at most 50% in B. Moreover, investment in A should be at least half the investment in B. How should the fund be allocated to the two investments?
This is a mathematical problem where the student needs to allocate $5000 between two investments, Investment A and B, fitting certain conditions. By developing a series of equations based on the conditions given, it is possible to determine the appropriate allocations.
Explanation:The subject of this question pertains to the allocation of funds in two investments, a process which involves applying principles of mathematics and financial planning. The person wants to invest $5000, with a certain percentage in Investment A (yielding 5%) and the rest in Investment B (yielding 8%), as per the stipulated conditions. To adhere to these requirements, let's denominate the investment in A as 'x' and that in B as 'y'. The restrictions provided, i.e., x needs to be at least 25% of $5000 (i.e., $1250) and y should not be more than 50% of $5000 (i.e., $2500), and x should be half the investment in y, lead us to the equation x = y/2. If you solve this system of equations, the allocations into A and B can be found. For instance, one feasible solution might be $2000 in A and $3000 in B. This ensures that A is at least 25%, B is at most 50%, and A is half of B, which abides by all the stipulations provided.
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The individual should allocate $1250 to Investment A and $3750 to Investment B.
Let's denote the amount invested in Investment A as[tex]\( x[/tex] and the amount invested in Investment B as[tex]\( y \)[/tex] . The individual has a total of $5000 to invest, so we have our first equation:\[ x + y = 5000 \]The individual wants to invest at least 25% of the total amount in Investment A, which gives us the second equation[tex]:\[ x \geq 0.25 \times 5000 \][ x \geq 1250 \][/tex]. The individual also wants to invest at most 50% of the total amount in Investment B, which gives us the third equation:[tex]\[ y \leq 0.50 \times 5000 \][ y \leq 2500 \[/tex]]. Additionally, the investment in A should be at least half the investment in B, leading to the fourth equation:[tex]\[ x \geq \frac{1}{2} y \][/tex] Now, let's solve these equations. From the first equation, we can express[tex]\( y \) in terms of \( x \):[ y = 5000 - x ]Substituting \( y \) into the inequality from the third equation, we get:[ 5000 - x \leq 2500 \][ x \geq 5000 - 2500 \][ x \geq 2500 \]This satisfies the condition from the second equation \( x \geq 1250 \).Now, we substitute \( y \) into the fourth equation:\[ x \geq \frac{1}{2} (5000 - x) \] 2x \geq 5000 - x \] 3x \geq 5000 \][ x \geq \frac{5000}{3} \][ x \geq 1666.\overline{6} Since \( x \)[/tex] must be a whole number of dollars, the smallest whole number that satisfies[tex]\( x \geq 1666.\overline{6} \) is \( x = 1667 \)[/tex] . However, we must also ensure that \( y \) is within the allowed range. Let's calculate [tex]\( y \) using \( x = 1667 \):\[ y = 5000 - x \]\[ y = 5000 - 1667 \]\[ y = 3333 \][/tex]
This allocation does not satisfy the condition that[tex]\( y \)[/tex] must be at most $2500. Therefore, we need to find the maximum value of \[tex]( x[/tex] that satisfies both [tex]\( x \geq 1666.\overline{6} \) and \( y \leq 2500 \).Since \( x \) must be at least half of \( y \), and \( y \) must be at most $2500, we can set \( x \) to half of $2500, which is $1250:\[ x = \frac{1}{2} \times 2500 x = 1250 \]Now, let's check if \( y \) is within the allowed range:[ y = 5000 - x \][ y = 5000 - 1250 \][ y = 3750 \][/tex]This allocation satisfies all the conditions:-[tex]\( x = 1250 \)[/tex] is more than 25% of the total investment.- [tex]\( y = 3750 \[/tex] ) is less than 50% of the total investment.- [tex]\( x \)[/tex] is half o[tex]f \( y \).[/tex] Therefore, the individual should allocate $1250 to Investment A and $3750 to Investment B.
What equation is equivalent to the equation 6x+9=12
Answer:
½ = x
Step-by-step explanation:
There is no illustration, but I can show you how to solve for x:
6x + 9 = 12
- 9 - 9
____________
6x = 3
__ __
6 6
x = ½
I am joyous to assist you anytime.
Answer:
[tex]x=\frac{1}{2}[/tex]
Step-by-step explanation:
We are given that an equation
[tex]6x+9=12[/tex]
We have to find the equation which is equivalent to given equation.
[tex]6x+9=12[/tex]
[tex]6x=12-9[/tex]
Subtraction property of equality
[tex]6x=3[/tex]
[tex]x=\frac{3}{6}[/tex]
Division property of equality
[tex]x=\frac{1}{2}[/tex]
Answer:[tex]x=\frac{1}{2}[/tex]
Let S = {1, 3, 5, 7}. Define the set J = {2j^2 − 11 | j ∈ S}. List the elements of J.
Answer: Elements of J = {-9,7,39,87}
Step-by-step explanation:
Since we have given that
S={1,3,5,7}
Define of set J is given by
[tex]J=\{2j^2-11:j\epsilon S\}[/tex]
Put j = 1
[tex]2j^2-11\\\\=2-11\\\\=-9[/tex]
Put j = 3
[tex]2(3)^2-11\\\\=2\times 9-11\\\\=18-11\\\\=7[/tex]
Put j = 5
[tex]2(5)^2-11\\\\=2\times 25-11\\\\=50-11\\\\=39[/tex]
Put j = 7
[tex]2(7)^2-11\\\\=2\times 49-11\\\\=98-11\\\\=87[/tex]
Hence, elements of J = {-9,7,39,87}
Thirty-three college freshmen were randomly selected for an on-campus survey at their university. The participants' mean GPA was 2.5, and the standard deviation was 0.5. What is the margin of error, assuming a 95% confidence level? (Assume a normal distribution.)
Answer: [tex]\pm0.1706[/tex]
Step-by-step explanation:
Given : Sample size : n= 33
Critical value for significance level of [tex]\alpha:0.05[/tex] : [tex]z_{\alpha/2}= 1.96[/tex]
Sample mean : [tex]\overline{x}=2.5[/tex]
Standard deviation : [tex]\sigma= 0.5[/tex]
We assume that this is a normal distribution.
Margin of error : [tex]E=\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
i.e. [tex]E=\pm (1.96)\dfrac{0.5}{\sqrt{33}}=\pm0.170596102837\approx\pm0.1706[/tex]
Hence, the margin of error is [tex]\pm0.1706[/tex]
john also bought a new ball. the new ball cost $300 which is three times the price of his old ball less $60. how much did he pay for his old ball?
Answer:
The cost of old ball is $120.
Step-by-step explanation:
Consider the provided information.
The cost of new ball is $300.
Which is three times the price of his old ball less $60.
Let the price of old ball is x.
Thus the above information can be written as:
[tex]3x-60=300[/tex]
[tex]3x=360[/tex]
[tex]x=120[/tex]
Hence, the cost of old ball is $120.
Trucks that travel on highways have to stop at various locations to be weighed and inspected for safe brakes and light systems. Of these trucks, 76% are on interstate commerce while 24% are intrastate. Of the intrastate trucks, 3.4% are flagged for safety defects compared to 0.7% of those that are on interstate business. Complete parts a through c below. a. Calculate the probability that a randomly chosen truck is an interstate truck and is not flagged for a safety violation. The probability is nothing. (Round to three decimal places as needed.)
Answer:
The reuired probability is 0.756
Step-by-step explanation:
Let the number of trucks be 'N'
1) Trucks on interstate highway N'= 76% of N =0.76N
2) Truck on intra-state highway N''= 24% of N = 0.24N
i) Number of trucks flagged on intrastate highway = 3.4% of N'' = [tex]\frac{3.4}{100}\times 0.24N=0.00816N[/tex]
ii) Number of trucks flagged on interstate highway = 0.7% of N' = [tex]\frac{0.7}{100}\times 0.76N=0.00532N[/tex]
Part a)
The probability that the truck is an interstate truck and is not flagged for safety is [tex]P(E)=P_{1}\times (1-P_{2})[/tex]
where
[tex]P_{1}[/tex] is the probability that the truck chosen is on interstate
[tex]P_{2}[/tex] is the probability that the truck chosen on interstate is flagged
[tex]\therefore P(E)=0.76\times (1-0.00532)=0.756[/tex]
A client who weights 176 pounds is receiving an IV infusion with esmolol hydrochloride (Brevibloc) at 48 ml/hour. The IV solution is labeled with the concentration of Brevibloc 10 mg/ml. How many mcg/kg/minute is the client receiving? (Enter numeric value only. Round to nearest whole number.) Submit
Answer:
[tex]0.1\frac{mg}{kg*min}=100 \frac{\mu g}{kg*min}[/tex]
Step-by-step explanation:
First write the weight of the client in kg, considering that 1 pound is 0.45 kg:
[tex]w=176lb* \frac{0.45kg}{1lb}=79.83kg[/tex]
Then, transform the infusion flow to ml/min, considering that 1 hour is 60 minutes:
[tex]48ml/h*\frac{1h}{60min}=0.8ml/min[/tex]
Now it is possible to calculate the to total mass flow injected to the client per minute:
[tex]0.8\frac{ml}{min}*10\frac{mg}{ml} =8mg/min[/tex]
To find the mass flow of Brevibloc injected by unit of weight of the pacient, just divide the total mass flow by the weight of the client:
[tex]8\frac{mg}{min}*\frac{1}{79.83kg}=0.1\frac{mg}{kg*min}[/tex]
In the question is not clear, but if you need the answer in micrograms/kg/minute just multiply by 1000:
[tex]0.1\frac{mg}{kg*min}*\frac{1000\mu g}{1mg}=100 \frac{\mu g}{kg*min}[/tex]
what is the product of :8.5x(-0.8)x(-12)
Answer:
The product of [tex]8.5 \times (-0.8) \times (-12)[/tex] is 81.6
Step-by-step explanation:
Given : [tex]8.5 \times (-0.8) \times (-12)[/tex]
To Find : Find the product
Solution:
[tex]8.5 \times (-0.8) \times (-12)[/tex]
[tex](-) \times (-) =+[/tex]
So, [tex]8.5 \times 9.6[/tex]
[tex]81.6[/tex]
Hence the product of [tex]8.5 \times (-0.8) \times (-12)[/tex] is 81.6
Step-by-step explanation:
The product of 8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12) is 81.6
Step-by-step explanation:
Given : 8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12)
To Find : Find the product
Solution:
8.5 \times (-0.8) \times (-12)8.5×(−0.8)×(−12)
(-) \times (-) =+(−)×(−)=+
So, 8.5 \times 9.68.5×9.6
81.681.6
(A) Which is the equation of Line b? 1. y=−14x+54 2. y=4x+3 3. y=x+5441 4. y=4x−3
(B) Which is the equation of Line d? 1. y=3x+3 2. y=−13x−3 3. y=13x+3 4. y=−3x−3
Check the picture below.
all we need to get the equation of the line is two points on it, in this case those would be (-3,2) and (1,1),
[tex]\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}}\implies \cfrac{-1}{1+3}\implies -\cfrac{1}{4}[/tex]
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{-\cfrac{1}{4}}[x-\stackrel{x_1}{(-3)}]\implies y-2=-\cfrac{1}{4}(x+3) \\\\\\ y-2=-\cfrac{1}{4}x-\cfrac{3}{4}\implies y=-\cfrac{1}{4}x-\cfrac{3}{4}+2\implies y=-\cfrac{1}{4}x+\cfrac{5}{4}[/tex]
The equation of line is 4y + x = 4.
What is the slope of the line?The slope of the line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
We have been given that Line b passes through the points (-3,2) and (1,1),
Let
x₁ = -3, y₁ = 2
x₂ = 1, y₂ = 1
∵ (y - y₁) = {(y₂ - y₁)/(x₂ -x₁ )}(x -x₁ )
Substitute values in the formula
(y - 2) = {(1 - 2)/(1 - (-3))}(x -(-3))
(y - 2) = {(-1)/(1+3)}(x+4)
(y - 2) = -1/4(x+4)
4y - 8 = -x - 4
4y + x = 4
Hence, the equation of line is 4y + x = 4.
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Help! BRANLIEST and 300 points!!!
PB is a line segment on a number line. It has endpoints at -2 and 12. What is the coordinate of its midpoint?
Find all solutions of the given system of equations and check your answer graphically. HINT [First eliminate all fractions and decimals; see Example 3.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).)
x/5 − y/4 = 1
x/6 + y = −4
(x, y) =
Answer:
(x,y)=(0,-4)
Step-by-step explanation:
Given : [tex]\frac{x}{5}- \frac{y}{4} = 1\\\\\frac{x}{6}+ y = -4[/tex]
To Find : (x,y)
Solution :
Equation 1 ) [tex]\frac{x}{5}- \frac{y}{4} = 1[/tex]
[tex]\frac{4x-5y}{20}= 1[/tex]
[tex]4x-5y= 20[/tex] ---A
Equation 2) [tex]\frac{x}{6}+ y = -4[/tex]
[tex]\frac{x+6y}{6} = -4[/tex]
[tex]x+6y = -24[/tex] ---B
Solve A and B by substitution
Substitute the value of x from B in A
[tex]4(-24-6y)-5y= 20[/tex]
[tex]-96-24y-5y= 20[/tex]
[tex]-96-29y= 20[/tex]
[tex]-96-20= 29y[/tex]
[tex]-116= 29y[/tex]
[tex]\frac{-116}{29}= y[/tex]
[tex]-4= y[/tex]
Substitute the value of y in B to get value of x
[tex]x+6(-4) = -24[/tex]
[tex]x-24= -24[/tex]
[tex]x=0[/tex]
So,(x,y)=(0,-4)
Check graphically
Plot the lines A and B on graph
[tex]x+6y = -24[/tex] -- Black line
[tex]4x-5y= 20[/tex] -- Purple line
Intersection point gives the solution
So, by graph intersection point is (0,-4)
Hence verified
So, (x,y)=(0,-4)
The solutions to the system of equations are (x, y) = (-16, -4). The equations are multiplied by factors to eliminate fractions and then solved using the method of substitution. The solution is checked graphically by plotting the lines and finding the intersection point.
Explanation:The subject of this question is a system of equations. We're asked to find all solutions to a given system of equations, and then to check our answer graphically. The equations given are x/5 - y/4 = 1 and x/6 + y = -4.
The first step is to eliminate fractions by multiplying each equation by a factor that will eliminate the fraction. For the first equation, this factor is 20, and for the second equation, it's 6, hence: 4x - 5y = 20 and x + 6y = -24.
Next, we can solve the system of equations using a method of our choice, for example, substitution or addition/subtraction. In this case, let's use substitution. We rearrange the first equation for x: x = (5y + 20) / 4. Substituting this into the second equation gives ((5y + 20) / 4) + 6y = -24. Solving for y, we find y = -4.
Then we substitute y = -4 into the first equation and find x. Hence, we get the solutions (x, y) = (-16, -4). In order to graphically check our solution, plot the system of lines representing the equations and find the point where they intersect. This intersection point corresponds to the solution of the system and should match our algebraic solution.
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For each of the following statements, write negation, contrapositive, converse and inverse. . If P is a square, then P is a rectangle .If n is prime, then n is odd or n is 2 .If 2 is a factor of n and 3 is a factor of n, then 6 is a factor of n
Answer:
i think it is E the last one
Step-by-step explanation:
Using Equation 3, what is the force of gravity between you and Earth, assuming all of the Earth's mass is at its center and you are standing at sea level? The mass of the Earth is approximately 5.900 x 1024 kg. At sea level, the distance to the center of the Earth is approximately 3,959 miles. Be mindful of your units, and show your work. Report your answer with four significant figures.
Answer:
679.1N
Step-by-step explanation:
Assuming equation 3 is Newton's universal law of gravity:
[tex]F_g = G\frac{m_1m_2}{d^2}[/tex]
Where G is the universal gravity constant:
[tex]G=6.673 x10^{-11}\frac{Nm^2}{kg^2}[/tex]
You need to express the radius of earth in m:
[tex]3959mi*\frac{1609m}{1mi}=6.370*10^6m[/tex]
If you weight 70Kg, just replace the values in the equation:
[tex]F_g = 6.673 *10^{-11}*\frac{70*5.900*10^{24}}{(6.370*10^6)^2}= 6.673 *10^{-11}*\frac{4.13*10^{26}}{4.058*10^{13}}=\\6.673*10^{-11}*1.018*10^{13}= 679.1N[/tex]
Find the dual of each of these compound propositions. b) (p /\ q/\ r) v s
Answer:
[tex](p\lor q \lor r)\land s[/tex]
Step-by-step explanation:
The dual of a compound preposition is obtained by replacing
[tex]\land \;with\;\lor[/tex]
[tex]\lor \;with\;\land[/tex]
and replacing T(true) with F(false) and F with T.
So, the dual of the compound proposition
[tex](p\land q \land r)\lor s[/tex]
is
[tex](p\lor q \lor r)\land s[/tex]
Answer: (p ∨q∨r)∧s
Step-by-step explanation:
Our proposition is:
(p /\ q/\ r) v s
This means
(P and Q and R ) or S
The proposition is true if P, Q and R are true, or if S is true.
Then the dual of this is
(P or Q or R) and S
The dual of a porposition can be obtained by changing the ∧ for ∨, the ∨ for ∧, the Trues for Falses and the Falses for Trues.
Then, the dual can be writted as:
(p ∨q∨r)∧s
The proposition is true if S is true, and P or Q or R are true.
A rose garden can be planted for $4000. The marginal cost of growing a rose is estimated to $0.30,
and the total revenue from selling 500 roses is estimated to $875. Write down the equations for
the Cost (5pts), Revenue (5pts) and Profit (5pts) functions and graph them all in the same
coordinate axes (30 pts). What is the break-even quantity? (5pt
Answer:
[tex]C(x)=4000+0.3x[/tex]
[tex]R(x)=1.75x[/tex]
[tex]Profit= 1.45x-4000[/tex]
Step-by-step explanation:
We are given that A rose garden can be planted for $4000.
The marginal cost of growing a rose is estimated to $0.30,
Let x be the number of roses
So, Marginal cost of growing x roses = [tex]0.3x[/tex]
Total cost = [tex]4000+0.3x[/tex]
So, Cost function : [tex]C(x)=4000+0.3x[/tex] ---A
Now we are given that the total revenue from selling 500 roses is estimated to $875
So, Marginal revenue = [tex]\frac{\text{Total revenue}}{\text{No. of roses}}[/tex]
Marginal revenue = [tex]\frac{875}{500}[/tex]
Marginal revenue = [tex]1.75[/tex]
Marginal revenue for x roses = [tex]1.75x[/tex]
So, Revenue function = [tex]R(x)=1.75x[/tex] ----B
Profit = Revenue - Cost
[tex]Profit= 1.75x-4000-0.3x[/tex]
[tex]Profit= 1.45x-4000[/tex] ---C
Now Plot A , B and C on Graph
[tex]C(x)=4000+0.3x[/tex] -- Green
[tex]R(x)=1.75x[/tex] -- Purple
[tex]Profit= 1.45x-4000[/tex] --- Black
Refer the attached graph
Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
x + y = 7
−x − y = −7
(x, y)
=
Solve the system by the elimination method. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
leftbrace2.gif
x + y = 12
2x + 3y = 31
Solve the system by the elimination method. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT. If the system is dependent, enter DEPENDENT.)
leftbrace2.gif
3x + y = 15
x + 2y = 10
Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.
A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?
x = $4,000 investors
y = $8,000 investors
Answer:
Part 1) The system has infinite solutions. Is a DEPENDENT system
Part 2) The solution of the system is the point (5,7)
Part 3) The solution of the system is the point (4,3)
Part 4) The number of investor that contributed with $4,000 was 33 and the number of investor that contributed with $8,000 was 27
Step-by-step explanation:
Part 1) we have
[tex]x+y=7[/tex] ------> equation A
[tex]-x-y=-7[/tex] ------> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
using a graphing tool
The system has infinity solutions (both lines are identical)
see the attached figure
Is a DEPENDENT system
Part 2) we have
[tex]x+y=12[/tex] ------> equation A
[tex]2x+3y=31[/tex] ------> equation B
Solve the system by the elimination method
Multiply equation A by -2 both sides
[tex]-2(x+y)=12(-2)[/tex]
[tex]-2x-2y=-24[/tex] ------> equation C
Adds equation B and C and solve for y
[tex]2x+3y=31\\-2x-2y=-24\\---------\\3y-2y=31-24\\y=7[/tex]
Find the value of x
substitute the value of y in the equation A (or B or C) and solve for x
[tex]x+(7)=12[/tex]
[tex]x=5[/tex]
The solution is the point (5,7)
Part 3) we have
[tex]3x+y=15[/tex] ------> equation A
[tex]x+2y=10[/tex] ------> equation B
Solve the system by the elimination method
Multiply equation A by -2 both sides
[tex]-2(3x+y)=15(-2)[/tex]
[tex]-6x-2y=-30[/tex] -----> equation C
Adds equation B and equation C
[tex]x+2y=10\\-6x-2y=-30\\---------\\x-6x=10-30\\-5x=-20\\x=4[/tex]
Find the value of y
substitute the value of x in the equation A (or B or C) and solve for y
[tex]3(4)+y=15[/tex]
[tex]12+y=15[/tex]
[tex]y=3[/tex]
therefore
The solution is the point (4,3)
Part 4) Formulate the situation as a system of two linear equations in two variables
Let
x ----> the number of investor that contributed with $4,000
y ----> the number of investor that contributed with $8,000
we have that
The system of equations is
[tex]x+y=60[/tex] ------> equation A
[tex]4,000x+8,000y=348,000[/tex] -----> equation B
Solve the system by elimination method
Multiply by -4,000 both sides equation A
[tex]-4,000(x+y)=60(-4,000)[/tex]
[tex]-4,000x-4,000y=-240,000[/tex] -----> equation C
Adds equation B and equation C and solve for y
[tex]4,000x+8,000y=348,000\\-4,000x-4,000y=-240,000\\-----------\\8,000y-4,000y=348,000-240,000\\4,000y=108,000\\y=27[/tex]
Find the value of x
Substitute the value of x in the equation A ( or equation B or equation C) and solve for x
[tex]x+27=60[/tex]
[tex]x=33[/tex]
so
The solution of the system is the point (33,27)
therefore
The number of investor that contributed with $4,000 was 33 and the number of investor that contributed with $8,000 was 27
A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is crawling on an adjacent wall at a point having coordinates (2.1, 1.9), where the units are meters, what is the distance of the fly from the corner of the room?
Answer: 2.83 units
Step-by-step explanation:
The distance between the two points (a,b) and (c,d) on the coordinate system is given by :-
[tex]D=\sqrt{(d-b)^2+(c-a)^2}[/tex]
Given : A certain corner of a room is selected as the origin (0,0) of a rectangular coordinate system.
If a fly is crawling on an adjacent wall at a point having coordinates (2.1, 1.9), then the distance of the fly from the corner (0,0) of the room will be :-
[tex]D=\sqrt{(2.1-0)^2+(1.9-0)^2}\\\\\Rightarrow\ D=\sqrt{4.41+3.61}\\\\\Rightarrow\ D=\sqrt{8.02}\\\\\Rightarrow\ D=2.8319604517\approx2.83\text{ units}[/tex]
Hence, the distance of the fly from the corner of the room = 2.83 units.
Final answer:
The distance of the fly from the corner of the room, given its coordinates on an adjacent wall are (2.1, 1.9), is approximately 2.83 meters. This distance is calculated using the Pythagorean theorem.
Explanation:
To find the distance of the fly from the corner of the room, given it is crawling on an adjacent wall at coordinates (2.1, 1.9) meters in a rectangular coordinate system, we use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this scenario, the two sides of the right-angled triangle are represented by the x-coordinate (2.1 meters) and the y-coordinate (1.9 meters) of the fly’s position.
To calculate the distance (d), we use the formula:
Plug the coordinates into the Pythagorean theorem equation: d^2 = 2.1^2 + 1.9^2.
Calculate the squares: 4.41 (2.1^2) + 3.61 (1.9^2).
Sum the results: 4.41 + 3.61 = 8.02.
Take the square root of the sum to find the distance: √8.02 ≈ 2.83 meters.
Therefore, the distance of the fly from the corner of the room is approximately 2.83 meters.
PLEASE HELP ASAP
if p=(8,12) is on the graph of f(x). which point is on the graph of g(x)=3f(x-2)+4?
Answer:
The point (10,40) is on the graph of g
Step-by-step explanation:
If the point (8,12) is on the graph of f(x) means that
f(8)=12
So, if you choose x=10, then x-2 = 8 and
g(10) = 3f(10-2)+4 = 3f(8)+4
But f(8) = 12, so
3f(8)+4 = 36+4 = 40
Hence g(10) = 40
Which means that the point (10,40) is on the graph of g
Find each of the following for f(x) = 3x^2 - 5x + 7.
(A) f(x + h)
(B) f(x + h) - f(x)
(C) [f(x + h) - f(x)]/h
Answer: The evaluations are done below.
Step-by-step explanation: We are given the following function :
[tex]f(x)=3x^2-5x+7.[/tex]
We are to find the value of the following expressions :
[tex](A)~f(x+h)\\\\(B)~f(x+h)-f(x)\\\\(C)~\dfrac{f(x+h)-f(x)}{h}[/tex]
To find the above expressions, we must use the given value of f(x) as follows :
[tex](A)~\textup{We have}\\\\f(x+h)\\\\=3(x+h)^2-5(x+h)+7\\\\=3(x^2+2xh+h^2)-5x-5h+7\\\\=3x^2+6xh+3h^2-5x-5h+7.[/tex]
[tex](B)~\textup{We have}\\\\f(x+h)-f(x)\\\\=(3x^2+6xh+3h^2-5x-5h+7)-(3x^2-5x+7)\\\\=6xh+3h^2-5h.[/tex]
[tex](C)~\textup{We have}\\\\\dfrac{f(x+h)-f(x)}{h}\\\\\\=\dfrac{6xh+3h^2-5h}{h}\\\\\\=\dfrac{h(6x+3h-5)}{h}\\\\=6x+3h-5.[/tex]
Thus, all the expressions are evaluated.
A salesperson had the following sales: $15.50, $18.98, s16.8, $14, $18.50, and $22. What was the average sale?
Final answer:
To find the average sale, add up all the sales ($105.78) and divide by the total number of sales (6), resulting in an average sale of $17.63.
Explanation:
To calculate the average sale made by the salesperson, we first need to add up all the sales and then divide by the total number of sales.
The sales were: $15.50, $18.98, $16.80, $14.00, $18.50, and $22.00.
First, let's find the total:
$15.50 + $18.98 + $16.80 + $14.00 + $18.50 + $22.00 = $105.78
Next, we divide this total by the number of sales to find the average. There were 6 sales in total.
Average Sale = Total Sales / Number of Sales
Average Sale = $105.78 / 6 = $17.63
Therefore, the average sale made by the salesperson was $17.63.
Order: Verapamil
HCl 0.075 mg/kg IV push over 2 min.
The label on the vial reads 5 mg/2 mL, and the patient weighs 80 kg. How many mL/min. will you administer?
A.
3 mL/min.
B.
1.2 mL/min.
C.
2.4 mL/min.
D.
0.6 mL/min.
If the weight of patient is 80 kg and the label reads 5 mg/2 mL, the administered dose will be 1.2 mL/min. Hence the correct option is B.
The order is Verapamil HCl 0.075 mg/kg IV push over 2 min.
Calculate the total amount of Verapamil needed:
0.075 mg/kg * 80 kg = 6 mg.
Find out how many mL contain 6 mg:
5 mg in 2 mL, so 6 mg will be in (6 mg * 2 mL) / 5mg = 2.4 mL.
Finally, calculate how many mL per minute:
Since the medication is to be given over 2 minutes, the rate will be 2.4 mL / 2 min = 1.2 mL/min.
The United States is about the only country that still uses the units feet, miles, and gallons. However, you might see some car specifications that give fuel efficiency as 7.6 km per kilogram of fuel. Given that a mile is 1.609 km, a gallon is 3.785 liters, and a liter of gasoline has a mass of 0.729 kg, what is the car’s fuel efficiency in miles per gallon?
To convert the car's fuel efficiency, it's necessary to convert kilometers to miles, and kilograms to gallons. Using the provided information, the car's fuel efficiency equates to approximately 24.4 miles per gallon.
Explanation:To convert the car's fuel efficiency from kilometers per kilogram to miles per gallon, we will use the given conversions:
1 mile = 1.609 kilometers1 gallon = 3.785 liters1 liter of gasoline = 0.729 kilogramsWe start with the given efficiency of 7.6 km/kg and convert km to miles:
7.6 km/kg * (1 mile / 1.609 km) = 4.721 miles/kg
Now we convert kg to gallons using the density of gasoline:
4.721 miles/kg * (1 kg / 0.729 liters) * (3.785 liters / 1 gallon) = 24.4 miles/gallon.
Therefore, the car's fuel efficiency is approximately 24.4 miles per gallon.
Assume that a password must be at least 8 characters long and include at least 1 digit and at least 1 special character. If people form their password by taking an English word of exactly 6 letters (assume that this password is not case-sensitive) and then adding (in either order) a digit and a special character (e.g flames#1), how many passwords would be possible? (10 points)
Answer:
10,932,240
Step-by-step explanation:
According to the Naspa World list American english have 16,564 6-letters words. Now about the special characters we have the next list !"#$%&'()*+,-./:;<=>?@[\]^_`{|}~ and considering the space as a special character we have a total of 33 special characters. For numbers we have a total of 10 digits.
Then to know how many possibles exists we have to find how many possibles are for the last two characters then.
[tex]33\cdot10=330[/tex]
That is the amount os possibles if always the special character go before de number, but as the number could be before the special character we have to multiply this quantity by 2.
Then we have 16,564 words for the first 6 characters and 660 options for the last two. To know the total amount of possibilities we just need to multiply this numbers, then:
[tex]16,564\cdot660=10,932,240[/tex]
Final answer:
To find the number of possible passwords, calculate the number of 6-letter words possible with 26 letters, then multiply by the number of digits (10), the number of special characters (32), and account for the two possible orders of digit and special character, leading to the formula 26⁶ * 10 * 32 * 2.
Explanation:
The question involves calculating the number of possible passwords that can be formed by using an English word of exactly 6 letters, followed by a digit and a special character in any order. To calculate this, we consider that there are 26 letters in the English alphabet, 10 possible digits (0-9), and assuming a common set of 32 possible special characters (for example, punctuation marks, symbols, etc.).
First, calculate the number of 6-letter English words that can be formed. Since the question mentions the word is not case-sensitive, each position in the word can be filled by any of the 26 letters. Therefore, the number of 6-letter words is 26⁶.
Then, for each of these words, a digit (10 choices) and a special character (32 choices) can be added in either order. Since the order matters, there are 2 different ways of arranging these two additional characters (digit-special character or special character-digit).
Therefore, the total number of possible passwords is calculated as 26⁶ * 10 * 32 * 2.
This approach highlights the significant number of combinations possible even with seemingly simple password creation rules, underlining the importance of complex passwords for enhancing security.
1) Meredith f ound some lace at a price of 4.0 5/meter in Ireland that she like too much for it. The same lace in the Canada would sell for $5.99/yd. W (S1 0.498 E) (1 yard 3 ft)
Answer: Ireland is €4.05/m
Canada is €3.26/m
Step-by-step explanation:
€4.05/m
$5.99/yd
To compare the prices, we need to transform one of them into the other. Let's transform the Canada price into Ireland price.
As $1 = €0.498
$5.99 * 0.498 = €2.983
€2.983/yd
1yd = 3ft
1ft = 0.3048m
3ft = 0.3048*3 = 0.9144 m
€2.983/yd = €2.983/3ft = €2.983/0.9144 m = €3.26/m
Ireland is €4.05/m
Canada is €3.26/m
the difference between roots of the quadratic equation x^2+x+c=0 is 6. find c.
Answer:
[tex]\displaystyle c = -\frac{35}{4} = -8.75[/tex].
Step-by-step explanation:
Let the smaller root to this equation be [tex]m[/tex]. The larger one will equal [tex]m + 6[/tex].
By the factor theorem, this equation is equivalent to
[tex]a(x - m)(x - (m+6))= 0[/tex], where [tex]a \ne 0[/tex].
Expand this expression:
[tex]a\cdot x^{2} - a(2m + 6)\cdot x + a(m^{2} + 6m) =0[/tex].
This equation and the one in the question shall differ only by the multiple of a non-zero constant. It will be helpful if that constant is equal to [tex]1[/tex]. That way, all constants in the two equations will be equal; [tex](m^{2} + 6m)[/tex] will be equal to [tex]c[/tex].
Compare this equation and the one in the question:
The coefficient of [tex]x^{2}[/tex] in the question is [tex]1[/tex] (which is omitted.) The coefficient of [tex]x^{2}[/tex] in this equation is [tex]a[/tex]. If all corresponding coefficients in the two equations are equal to each other, these two coefficients shall also be equal to each other. Therefore [tex]a = 1[/tex].
This equation will become:
[tex]x^{2} - (2m + 6)\cdot x + (m^{2} + 6m) =0[/tex].
Similarly, for the coefficient of [tex]x[/tex],
[tex]\displaystyle -(2m +6) = 1[/tex].
[tex]\displaystyle m = -\frac{7}{2}[/tex].
This equation will become:
[tex]x^{2} + x + \underbrace{\left(-\frac{35}{4}\right)}_{c} =0[/tex].
[tex]c[/tex] is the value of the constant term of this quadratic equation.
Answer: C= 35/4
Step-by-step explanation: As per Vieta's Theorem, when a polynomial is [tex]ax^2+bx+c =0[/tex] then two roots of the equation p & q are
p.q =c/a p+q= -b/aGiven [tex]x^2+x+c =0\\[/tex], a & b are 1 here, and p-q= 6
Therefore, p+q= -b/a= -1/1 = -1..............(Equation 1)
Also given p-q= 6............... (Equation 2)
Solving equation 1 & 2
2q = -7
q = -7/2 (value of one root q)
Putting the value of q in equation 2 we can get
p + 7/2 = 6
p = 6- 7/2
p = 5/2 ( Value of 2nd root p)
Again, as per the formula p.q = c/a, here p.q= c as a= 1
p.q = (-7/2 ) (5/2) = -35/4
So, The value of c is -35/4.
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On Monday the temperature was 6 Celsius overnight it fell to –2Celsius.
By how many degrees did the temperature fall?
pleased
Answer:
8 degrees
Step-by-step explanation:
6° - (-2°) = 8°
How do you find the rational zeros of "p(x)"
Answer:
Use the Rational Root Theorem.
Step-by-step explanation:
Any rational roots will be factors of the ratio of the constant (=p(0)) to the leading coefficient of the polynomial p(x). In the general case, that ratio is a rational number and the roots have numerator that is a factor of its numerator, and a denominator that is a factor of its denominator.
__
To see how this works, consider the polynomial with rational roots b/a and d/c. Factors of it will be ...
p(x) = (ax -b)(cx -d)( other factors if p(x) is of higher degree )
The leading coefficient here is ac; the constant term is bd. The rational root theorem says any rational roots are factors of (bd)/(ac), which b/a and d/c are.
A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?
x = $3,000 investors
y =
$6,000 investors
Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.
A jar contains 70 nickels and dimes worth $5.70. How many of each kind of coin are in the jar?
Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- and y-variables. Solve the system by the elimination method. Be sure to state your final answer in terms of the original question.
The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?
x= soda
y= hotdogs
Answer:
1) There were 34 $3,000 investors and 26 $6,000 investors.
2) There are 26 nickels and 44 dimes in the jar.
3) 1600 sodas and 1400 hot dogs were sold.
Step-by-step explanation:
1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $3,000 or $6,000. If the partnership raised $258,000, then how many investors contributed $3,000 and how many contributed $6,000?
x is the number of investors that contributed 3,000.
y is the number of investors that contributed 6,000.
Building the system:
There are 60 investors. So:
[tex]x + y = 60[/tex]
In all, the partnership raised $258,000. So:
[tex]3000x + 6000y = 258000[/tex]
Simplifying by 3000, we have:
[tex]x + 2y = 86[/tex]
Solving the system:
The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:
[tex]1)x + y = 60[/tex]
[tex]2)x + 2y = 86[/tex]
I am going to multiply 1) by -1, then add 1) and 2), so x is canceled.
[tex]1) - x - y = -60[/tex]
[tex]2) x + 2y = 86[/tex]
[tex]-x + x -y + 2y = -60 +86[/tex]
[tex]y = 26[/tex]
Now we get back to equation 1), and find x
[tex]x + y = 60[/tex]
[tex]x = 60-y = 60-26 = 34[/tex]
There were 34 $3,000 investors and 26 $6,000 investors.
2) A jar contains 70 nickels and dimes worth $5.70. How many of each kind of coin are in the jar?
I am going to say that x is the number of nickels and y is the number of dimes.
Each nickel is worth 5 cents and each dime is worth 10 cents.
Building the system:
There are 70 coins. So:
[tex]x + y = 70[/tex]
They are worth $5.70. So:
[tex]0.05x + 0.10y = 5.70[/tex]
Solving the system:
[tex]1) x+y = 70[/tex]
[tex]2) 0.05x + 0.10y = 5.70[/tex]
I am going to divide 1) by -10, so we can add and cancel y:
[tex]1) -0.1x -0.1y = -7[/tex]
[tex]2) 0.05x + 0.1y = 5.70[/tex]
[tex] -0.1x + 0.05x -0.1y + 0.1y = -1.3[/tex]
[tex]-0.05x = -1.3[/tex] *(-100)
[tex]5x = 130[/tex]
[tex]x = \frac{130}{5}[/tex]
[tex]x = 26[/tex]
Now:
[tex]x+y = 70[/tex]
[tex]y = 70 - x = 70 - 26 = 44[/tex]
There are 26 nickels and 44 dimes in the jar.
3) The concession stand at an ice hockey rink had receipts of $7400 from selling a total of 3000 sodas and hot dogs. If each soda sold for $2 and each hot dog sold for $3, how many of each were sold?
x is the nuber of sodas and y is the number of hot dogs.
Building the system:
3000 items were sold. So:
[tex]x + y = 3000[/tex]
$7,4000 was the total price of these items. So:
[tex]2x + 3y = 7400[/tex]
Solving the system:
[tex]1)x + y = 3000[/tex]
[tex]2)2x + 3y = 7400[/tex]
I am going to multiply 1) by -2, so we can cancel x
[tex]1) -2x -2y = -6000[/tex]
[tex]2) 2x + 3y = 7400[/tex]
[tex]-2x + 2x -2y + 3y = -6000 + 7400[/tex]
[tex]y = 1400[/tex]
Now, going back to 1)
[tex]x + y = 3000[/tex]
[tex]x = 3000-y = 3000-1400 = 1600[/tex]
1600 sodas and 1400 hot dogs were sold.
A solution consisting of 208 mg of dopamine in 32 mL of solution is administered at a rate of 12 mlht. Complete parts (a) and (b) below! a What is the flow rate in mg of dopamine per hour? mg/hr (Type an integer or decimal rounded to the nearest thousandth as needed) Enter your answer in the answer box and then click Check Answer
Answer:
78 mg/hr
Step-by-step explanation:
Data provided in the question;
Amount of dopamine contained in solution = 208 mg
Volume of solution = 32 mL
Dosage = 12 mL/h
Concentration of dopamine in solution = [tex]\frac{\textup{Amount of dopamine}}{\textup{Volume of solution}}[/tex]
or
Concentration of dopamine in solution = [tex]\frac{\textup{208 mg}}{\textup{32 mL}}[/tex]
or
Concentration of dopamine in solution = 6.5 mg/mL
Now,
The flow rate = Concentration × Dose
or
The flow rate = ( 6.5 mg/mL ) × ( 12 mL/hr )
or
The flow rate = 78 mg/hr
Answer:
Rate of flow of dopamine = 78 mght
Step-by-step explanation:
Given,
total amount of solution = 32 ml
total amount of dopamine in 32 ml solution = 208 mg
[tex]=>\textrm{total amount of dopamine in 1 ml solution }= \dfrac{208}{32}[/tex]
[tex]=\ \dfrac{13}{2}\ mg[/tex]
[tex]=>\ \textrm{ amount of dopamine in 12 ml solution }=\ \dfrac{208}{32}\times 12[/tex]
[tex]=\ \dfrac{13}{2}\times 12\ mg[/tex]
= 78 mg
Since, the rate of flow of solution = 12 mlht
That means 12 ml of solution is flowing in 1 unit time and 12 ml of solution contains 78 mg of dopamine, so the rate of flow of dopamine will be 78 mght.
multiply(5+2i)(4-3i) enter your answer in standard form
Answer:
26-7i
Step-by-step explanation:
1. expand it you will get : 20-15i+8i+6 ( notice that i^2= -1 )
2. simplify it: 26-7i
Using complex numbers, it is found that the result of the multiplication is: 26 - 7i
A complex number has the format: [tex]z = a + bi[/tex]The important relation is: [tex]i^2 = -1[/tex].In this problem, the multiplication is: [tex](5 + 2i)(4 - 3i)[/tex].
Applying the distributive property:
[tex](5 + 2i)(4 - 3i) = 20 - 15i + 8i -6i^2 = 20 - 7i + 6 = 26 - 7i[/tex]
The result is: 26 - 7i
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