A health insurance company advertises on television, on radio, and in the local newspaper. The marketing department has an advertising budget of $46,400 per month. A television ad costs $1000, a radio ad costs $200, and a newspaper ad costs $600. The department wants to run 64 ads per month, and have as many television ads as radio and newspaper ads combined. How many of each type of ad can the department run each month?
Answers
The number of each type of ad that the department can run each month are:
TV Ads = 32
Radio Ads = 12
News Ads = 20
How to solve Simultaneous equation word problems?x = number of tv ads
y = number of radio ads
z = number of news ads
Two formulas are indicated.
x + y + z = 64
1000x + 200y + 600z = 46400
they want as many tv ads as radio and news ads combined.
equation for that is x = y + z
since x = y + z, replace x with y + z in both equations to get;
y + z + y + z = 64
1000 * (y + z) + 200 * y + 600 * z = 46400
combine like terms and simplify to get:
2y + 2z = 64
1000y + 1000z + 200y + 600z = 46400
combine like terms again to get:
2y + 2z = 64
1200y + 1600z = 46400
Solving simultaneously gives:
y = 12
z = 20
Thus:
x = 12 + 20
x = 32
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Related Questions
Cuanto mide el largo de un rectángulo cuyo perímetro es 16cm y su área 12 cm al cuadrado ?
Answers
Hay dos rectángulos posibles que satisfacen las condiciones dadas: uno de 2 cm de largo y 6 cm de ancho, y otro de 6 cm de largo y 2 cm de ancho.
Y (4)
+4y ′′
+4y=0 A general solution with x as the independent variable is y(x)=
Answers
Answer:
Step-by-step explanation:
We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.
For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,
y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0
(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.
Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get
yp″=a1+2a2x....yp‴=2a2+3a3x+....
Substituting the general solution into the non-homogeneous equation, we get
a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)
So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:
a(n+1)=Y(n-2)/n^2
From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.
solve the given triangle by finding the missing angle and other side lengths
Answers
Answer:
angle B=122degree
Step-by-step explanation:
straight line AC =180degree, then 180-(21+37)=122 degree
a=b*sinA/sinB=84.5
c=b*sinC/sinB=141.9
Could someone help me on this one please!:)
Answers
Answer:
3 more customers
Step-by-step explanation:
You take the total times the theoretical probability.
150 times 0.12 equals 18.
18 should have won, but only 15 won.
18 - 15 = 3.
So you would expect 3 more to have won.
18-15=3 so we would’ve expected 3 more customers to win :)
Sound waves travel through the air at approximately 343 meters per second. A tuba player plays a constant note that has a wavelength of 4.61 meters.
Determine the period of the sound wave created by the tuba in seconds.
Answers
The period of the sound wave created by the tuba is approximately 0.0134 seconds.
The speed of sound in air is given as 343 meters per second. The formula relating the speed of sound, wavelength, and period of a wave is:
v = λ × f
Where:
v = speed of sound (343 m/s)
λ = wavelength (4.61 m)
f = frequency (unknown)
To find the period, we need to determine the frequency of the sound wave. The period (T) is the reciprocal of the frequency (f), so we can rewrite the formula as:
v = λ / T
Rearranging the equation to solve for the period (T), we get:
T = λ / v
Substituting the given values, we have:
T = 4.61 m / 343 m/s
Calculating the value, we find:
T ≈ 0.0134 seconds
Therefore, the period of the sound wave created by the tuba is approximately 0.0134 seconds.
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consider the mathematical sentence: 2=3 Does this sentence have an infinite number of solutions or no solutions? Determine the number of solution and explain your reasoning.
Answers
The mathematical sentence being considered is 2 = 3
We know that 2 cannot be equal to 3.
Therefore, there are no solutions
It can only have infinite number of solutions if 3 = 3
Thus, no solutions is the answer
Use the alternative curvature formula k= |a*v|/|v|^3 to find the curvature of the following parameterized curve. r(t) = (6+5t^2,t,0) K=
Answers
The curvature of the parameterized curve r(t) =\((6+5t^2\), t, 0) is k = 100 / (\(100t^2\) +\(1)^(3/2)\).
To use the alternative curvature formula, we first need to find the acceleration vector and the speed of the parameterized curve:
r(t) = (\(6+5t^2\), t, 0)
Velocity vector:
r'(t) = (10t, 1, 0)
Speed:
|v| = √(\(10^2t^2\) + \(1^2\)) = √(\(100t^2\)+ 1)
Acceleration vector:
r''(t) = (10, 0, 0)
Now, we can use the formula k= \(|a*v|/|v|^3\) to find the curvature:
k =\(|a*v|/|v|^3\)
k = |(10, 0, 0) x (10t, 1, 0)| / (\(100t^2\) + \(1)^(3/2)\)
k = |(0, 0, -100)| / \((100t^2 + 1)^(3/2)\)
k = 100 /\((100t^2 + 1)^(3/2)\)
A parametrized curve is a way to represent a curve in a coordinate system using a parameter, typically denoted by t. The parameter t represents the position of a point on the curve as it varies over some interval.
The curve is defined by a vector-valued function r(t) = (x(t), y(t), z(t)) where x(t), y(t), and z(t) are the component functions of the curve. As t varies, the function r(t) traces out the curve in three-dimensional space.
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Suppose that a particle moving along the x-axis encounters a resisting force that results in an acceleration of a =-=-0.10 V v. Given that x = 0 cm and v = 36 cm/s at time t = 0, find the velocity v and position x as a function of t for t 2 0. v= 2 cm/s Edit C x= 2 cm
Answers
The velocity of the particle v as a function of time t is given by v(t) = 36 - 0.10 * t^2 cm/s and the position x as a function of time t is given by x(t) = 36 * t - 0.05 * t^3 cm.
The problem states that at time t = 0, the particle has an initial velocity of v = 36 cm/s and is located at x = 0 cm. The particle is accelerating with a=-0.10 V v. This means that the velocity of the particle is changing by -0.10 V v each second. This can be expressed in terms of the time t as v(t) = 36 - 0.10 * t^2 cm/s. The position of the particle at any time t can be expressed as x(t) = x0 + v0 * t + 1/2 * a * t^2, where x0 is the initial position and v0 is the initial velocity. In this case, x0 = 0 and v0 = 36, so the position of the particle at any time t can be expressed as x(t) = 36 * t - 0.05 * t^3 cm. This means that the particle will move away from the origin (x=0) and its velocity will decrease each second.
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Need help will give brainliest and 5 stars! :)
Answers
The logarithmic function can be written exponentially as follows.\(t = 8^y.\)
What is logarithmic function?Exponents and logarithms are inverse operations of one another. We can rewrite an equation in logarithmic form as log_a(b) = x if it has the form axe = b. A number's logarithm is the exponent that must be raised in order to obtain that number. For instance, since 102 = 100, log_10(100) = 2. Similar to this, we can express an equation in exponential form, such as axe = b, if it is in logarithmic form, such as log_a(b) = x. The inverse function of the logarithmic function is the exponential function. As a result, when we apply a logarithm to an exponential expression, the original exponent is returned, and the opposite is true.
The given logarithmic expression is \(log_{8}(t) = y.\)
We know that if we have an equation in the form \(a^x = b\), we can rewrite it in logarithmic form as \(log_a(b) = x\) and vice versa.
Thus, \(log_{8}(t) = y\)
\(t = 8^y\)
Hence, the logarithmic function can be written exponentially as follows.\(t = 8^y.\)
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If f (1) = 1 and f(n) = f(n - 1)? + 3 then find the value of f(4).
Answers
Explanation
\(f\mleft(n\mright)=f\mleft(n-1\mright)^2+3\)
In a recursive formula, each term is defined as a function of its preceding term(s). A recursive formula designates the starting term, a1, and the nth term of the sequence, an
so, we can find the first 4 terms
Step 1
\(\begin{gathered} f\mleft(n\mright)=f\mleft(n-1\mright)^2+3 \\ f(1)=1 \\ f(2)=f(2-1)^2+3 \\ f(2)=f(1)^2+3 \\ f(2)=(1)^2+3 \\ f(2)=4 \\ f(3)=f(3-1)^2+3 \\ f(3)=f(2)^2+3 \\ f(3)=(4)^2+3 \\ f(3)=19 \\ f(4)=f(4-1)^2+3 \\ f(4)=f(3)^2+3 \\ f(4)=(19)^2+3 \\ f(4)=364 \end{gathered}\)
hence, the answer is
\(f(4)=364\)I hope this helps you
Dr. Mann mixed 9.357 g of chemical A, 12.082 g of chemical B, and 7.502 g of chemical C to make 5 doses of medicine. What is the total amount of medicine mixed by Dr. Mann?
Answers
Answer:
Step-by-step explanation:
9.357
12.082
+7.052
28.491 g
what is the answer? i need it graphed out for me
Answers
The graph of the piece-wise function in this problem is given by the image shown at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, based on which interval the input value of the function belongs to.
In this problem, the function has three definitions, given as follows:
Zero -> to the left of -1, with -1 inclusive.y = -x - 1, to the right of -1 and to the left of 2, inclusive at 2.y = -1, to the right of 2.Hence the graph is defined as follows:
Horizontal line at y = 0 to the left of -1, with a closed circle at point (-1,0).Decaying line between points (-1,0) and (2,-3), with a closed circle at (2,3).Constant line at y = -2 from x = 2 and until infinity.More can be learned about piece-wise functions at https//brainly.com/question/19358926
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Submit your answers to the following questions. Be sure to explain your reasoning for each; it is helpful to draw this out to get started to see any quantitative patterns that develop.
If you write the counting numbers in rows of 7 numbers each, like shown below (but you keep going), where all the number line up in seven vertical columns as you go. (Note in the example below, the number 13 is in the 2nd row and the 6th column.)
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
In which column would the number 100 land?
In which row?
Now write the counting numbers in rows of 6 numbers each. What’s the location of 100 in this array?
Write arrays with other length rows. Find a way to predict in which row and column 100 will land for any array of numbers.
Answers
The number 100 would land in column 2
The number 100 would land in row 14The location of 100 in rows of 6 numbers is row 16 and column 3The location of 100 in rows of n numbers is row q and column rIn which column would the number 100 land?Given that we have the array of numbers
The length of each row in the array is 7
Dividing 100 by 7, we have
100/7 = 14 Remainder 2
This means that
Column = 2
In which row would the number 100 land?In (a), we have
100/7 = 14 Remainder 2
This means that
Row = 14
The location of 100 in rows of 6 numbersHere, we have
The length of each row in the array is 6
Dividing 100 by 6, we have
100/6 = 16 Remainder 3
So, the location of 100 in rows of 6 numbers is row 16 and column 3
Predicting the row and column 100 will landLet the length of each row in the array be n
Dividing 100 by n, we have
100/n = q Remainder r
This means that the location of 100 in rows of n numbers is row q and column r
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Simplify 2f+ 6f help me pls
Answers
Answer:
\({ \tt{ = 2f + 6f}}\)
- Factorise out f as the common factor;
\({ \tt{ = f(2 + 6)}} \\ = 8f\)
What is the solution to this inequality? 1/3x − 7>−4
Answers
Add 7 to both sides.
1/3x > −4 + 7Add −4 and 7 to get 3.
1/3x > 3Multiply both sides by 3, the reciprocal of 1/3 . Since 1/3 is >0, the direction of inequality remains the same.
x > 3 × 3Multiply 3 and 3 to get 9.
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12
Select the correct answer.
The scatter plot represents the purchase prices and selling prices of X-ray machines made by five different manufacturers. Which of the following
points show errors of prediction or residuals?
OA.
OB.
O C.
O D.
Points (14, 25) and (15, 25)
Points (15, 25) and (18, 26)
Points (14, 25) and (16, 25)
Points (12, 24) and (18, 26)
Estimated Selling Price (in $1,000)
26.5
26-
25.5
25
24.5
24
23.5
10
11
12 13 14 15 16 17 18 19 20
Purchase Price (in $1,000)
Answers
The points on the scatter plot show the different predictions. The straight line drawn is called the line of regression.
Errors in prediction for each point can be determined by drawing a vertical line from the point to the line of regression. As seen in the image, all of the prediction points are found on the line except for points (14,25) and (16,25). Therefore, these points contain errors in prediction.
The graph that represent this data using the points is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The x and y values
Where
x = stars
y = price
To determine the graph that represent the data, we enter the x and y values in a graphing tool to create the graph
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A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
Answers
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
\(\pi = 0.5\)
Then the sample size for M = 0.04 is obtained as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)
\(0.04\sqrt{n} = 2.575 \times 0.5\)
\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)
\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)
n = 1037.
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2. Gerald was given the following problem to solve for the length of the “?”. He has made a mistake in his work. Identify and describe how he made his mistake. Then, solve the problem correctly.
Answers
Answer:
x = 18.7
Step-by-step explanation:
Gerald's answer is almost correct.
He just needs to switch the 14 and the x.
it should be
24/x = 18/14
solve for x by cross multiplication
18x = (24)(14)
18x = 336
x = 18.7
Please please look at the picture and answer the question thank you so much
Answers
Answer:
t = I/(Pr)
Step-by-step explanation:
We divide P*r on both sides to isolate t and we get t=I/(P*r)
what is the solution to this equation? −5(p−30)=−10 pls help asap
Answers
Answer:
p = 32
Step-by-step explanation:
-5(p -30) = -10
-5p + 150 = -10
-150 -150
_______________
-5p=-160
p = 32
what is the reciprocal for 4/9
Answers
Answer: 9/4
Step-by-step explanation:
Reciprocal means flip the fraction
The reciprocal of 4/9 is 9/4
Answer: the rciprocal is 9/4
Step-by-step explanation:
The sixth-graders at Tisha's school got to choose between a field trip to a museum and a field trip to a factory. 39 sixth-graders picked the museum. If there are 52 sixth-graders in all at Tisha's school, what percentage of the sixth-graders picked the museum
Answers
The sixth-graders at Tisha's faculty were given to choose among a field journey to a museum and a area journey to a manufacturing unit.
To calculate the percentage of 6th-graders the one picked the museum as their area journey desire, we need to divide the range of students who chose the museum with the aid of the entire number of sixth-graders, in addition to then multiply by means of 100.
Number of students who chose the museum = 39
Total number of sixth-graders = 52
Percentage of sixth-graders who picked the museum = (Number of students who chose the museum / Total number of sixth-graders) * 100
Percentage = (39 / 52) * 100
Percentage ≈ 0.75 * 100
Percentage ≈ 75
Therefore, approximately 75% of the sixth-graders picked the museum as their field trip choice.
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Find an equation of the line passing through the points.
(1, 0.6), (−9, −3.4)
Answers
First of all we need to find the slope using this formula :
Slope = [ y(A) - y(B) ] ÷ [ x(A) - x(B) ]
Suppose that :
A = ( 1 , 0.6 )
&
B = ( - 9 , - 3.4)
Thus :
Slope = [ 0.6 - ( - 3.4) ] ÷ [ 1 - ( -9 ) ]
Slope = [ 0.6 + 3.4 ] ÷ [ 1 + 9 ]
Slope = 4 ÷ 10
Slope = 4/10 = 2/5
________________________________
Now it's time to find the equation , to do that we just have to use the point-slope form formula of the linear equation which is like this :
y - y( A or B ) = Slope × ( x - x( A or B) )
We're almost done; just need to put the coordinates of point A or point B and the Slope to find the equation :
I'm gonna use A for it but you can do that with B , They will give same equation.
y - 0.6 = 2/5 × ( x - 1 )
y - 0.6 = 2/5 x - 2/5
y - 6/10 = 2/5 x - 2/5
y - 3/5 = 2/5 x - 2/5
Add both sides 3/5
y - 3/5 + 3/5 = 2/5 x - 2/5 + 3/5
y = 2/5 x + 1/5And we're done ...
he roots of the function f(x) = x2 – 2x – 3 are shown. What is the missing number?
x = –1 and x =
Answers
. The sum of a number and 43 is 107. Find the number.
Answers
Answer:
64
Step-by-step explanation:
The sum means addition
To put this into algebra :
x + 43 = 107
Subtract 43 from both sides:
x = 107 - 43
x = 64
Hope this helped and brainliest please.
Answer:
The missing number is 64.
{43 + 64 = 107}
Step-by-step explanation:
Given that,
→ Sum of a number and 43 is 107.
Let's form the equation,
→ 43 + x = 107
Now find the required value of x,
→ 43 + x = 107
→ x = 107 - 43
→ [ x = 64 ]
Hence, the number is 64.
Which inequality is graphed below
Answers
Answer:
wheres it at?
Step-by-step explanation:
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What is 21 rounded to the nearest ten?
Answers
Answer:
20
Step-by-step explanation:
the two closest are 20 and 30
21 is the next digit after 20 and the closest to it.
21 is 9 away from 30 and is farther.
Complete the square to re-write the quadratic function in vertex form:
y= x2 - 5x +9
Answer: y =
Submit Answer
Answers
If 6(2x+1) is equal to -36-2x, what is the value of 3x
Answers
12x + 6 = -36 - 2x
12x + 2x = -36-6
14x = -42
X = -3
Answer:
The value of 3x is -9
Step-by-step explanation:
Given Equation
\(6(2x + 1) = - 36 - 2x\)
Step 1
Distribute 6 in the expression.\(12x + 6 = - 36 - 2x\)
Step 2
Combine like terms and solve the equation for x-term\(12x + 2x = - 36 - 6 \\ 14x= - 42 \\ x = \frac{ - 42}{14} \longrightarrow \frac{ - 3}{1} \\ x = - 3\)
But we want to know what is the value of 3x.
Step 3
Substitute the value of -3 in 3x.\(3x = 3( - 3) \\ 3x = - 9\)
Hence, the value of 3x is -9
Hope this helps! If you have any questions that are related to the answer, feel free to use "Comment" feature!
A cylinder has a diameter of 5 centimeters and a height of 50 millimeters. Which of the following steps should be done
first in order to find the surface area of the cylinder?
O multiply the circumference of the circle by the height of the cylinder
o calculate the circumference of the circle
convert the diameter and the height to the same unit
o determine the radius and multiply by 2
NEXT QUESTION
ASK FOR HELP
TURN ITIN
Answers
Answer:
convert the diameter and the height to the same unit
Step-by-step explanation:
Answer: convert the diameter and the height to the same unit
Step-by-step explanation:
The surface area of a cylinder can be found with A = 2πrh + 2πr². To use this formula, all units of measurement must be the same.
This can be converting 5 centimeters to millimeters or converting 50 millimeters to 5 centimeters.