If the original price of the radio is 2,400 Naira and it is reduced by one third, then the discounted price is 1,600 Naira.
A store usually provides discount of some items to attract more customers and make greater sales.
Suppose the original price is p, the discount rate is d%, and the discounted price is q, then the discounted price can be calculated as:
q = (1 - d%) x p
Parameters given in the problem:
p = 2,400 Naira
d = 1/3
Hence,
q = (1 - 1/3) x 2400
q = 2/3 x 2400 = 1600
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g(x) = x ³ +5x
h(x) = x +5
find g(x) + h(x)
Answer:
[tex]g(x) + h(x) = x^3 + 6x + 5[/tex]
Step-by-step explanation:
We are told that:
[tex]g(x) = x^3 + 5x[/tex]
[tex]h(x) = x + 5[/tex],
and we are asked to find an expression for [tex]g(x) + h(x)[/tex].
In order to find the expression for [tex]g(x) + h(x)[/tex], we have to simply add the expressions of [tex]g(x)[/tex] and [tex]h(x)[/tex] together:
[tex]g(x) + h(x)[/tex]
= [tex]x^3 + 5x + x + 5[/tex]
= [tex]x^3 + 6x + 5[/tex]
a hospital director is told that 31% of the emergency room visitors are uninsured. the director wants to test the claim that the percentage of uninsured patients is below the expected percentage. a sample of 380 patients found that 95 were uninsured. find the value of the test statistic. round your answer to two decimal places.
The test statistic is -2.60 as a sample of 380 patients found that 95 were uninsured.
What is test statistic?A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. For instance, the Z-statistic, which has the typical normal distribution under the null hypothesis, is the test statistic for a Z-test. Here,
n=380
x=95
p=95/380
p=0.25
test=(0.25-0.31)/√(0.28(1-0.28)/380)
test=-2.60
The test statistic is -2.60 because 95 out of 380 patients in the sample did not have insurance.
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9) Willie took a trip to Oman. Upon leaving he decided to convert all of his Rials back into dollars. How many dollars did he receive if he exchanged 12 Rials at the rate of 1 Rial to $3?
10) A rectangle is 2 in wide and 1 in tall. If it is enlarged to a width of 14 in then how tall will it be?
number 9 is 36 12x3 is 36
The number of avocados used by a restaurant in a day varies directly with the number of orders of guacamole that day. It takes 6.5 avocados to make 4 orders of guacamole. How many avocados would it take to make 14 orders of guacamole?
Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.
What is the proportion?Proportion refers to the quantity of a value or variable contained in another value.
Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.
Proportions are depicted using fractions, decimals, or percentages.
The number of avocados required for 4 orders of guacamole = 6.5
The total number of orders of guacamole required = 14
The number of avocados to make 1 order = 6.5/4
The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)
Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.
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we get statistics of 2017-2018 average starting teacher salaries by state measured by nea. given that the salary of arkansas is 33323, the sample size is 3,600 and the standard deviation is 399.876. a. what is the margin of error for a 80% confidence interval in arkansas? symbolic expression b. if we want to get a 80% confidence interval with a small margin of error, say only 7%. how many people do you need to sample?
a) The margin of error for an 80% confidence interval in Arkansas is 0.1041
b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359
The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.
n = 3600
standard deviation = 399.876
Confidence Interval = 80%
a) α = 0.20
The margin of error = Zα/2 (σ / √n)
Zα/2 = 1.4395 --- (From the tabular value)
The margin of Error = 1.4395 + 399.876 / √3600
Therefore, the Margin of Error = 8.1041
b) Margin of Error = 0.07 = 7%
α = 0.20
Critical Value = 1.2816
Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²
n = [(1.2816 * 399.876) / 0.07]²
n = 53599358.98
Therefore, Sample size, n = 53599359
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If 8^y =16^y+2what is the value of y?
O-8.
O-4.
O-2.
O-1.
Answer:
-8
Step-by-step explanation:
Graph each side of the equation. The solution is the x-value of the point of intersection.
Can someone help me with this please! I really need it done PLS
increase the amount of the ingredients by 5 and by 20
Answer:
it's 50 g
Step-by-step explanation:
it's like a multiplying assberry kehe
A group of friends wanted to compare their average running speeds. They recorded the distance and amount of time each person ran one Saturday morning.
Select all the runners whose speeds are in a proportional relationship with each other.
Name Time (seconds) Distance (miles)
Liam 306.6 0.5
Taylor 756.36 1.2
Sarah 504.35 0.7
Ashley 459.9 0.75
Connor 600.5 1
Nathan 942.75 1.5
Juan 827.82 1.35
Katie 429.48 0.6
The runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.
We need to select all the runners whose speeds are in a proportional relationship with each other.
We find the speed using formula, speed = distance / time
Name Time (seconds) Distance (miles) Speed(mps)
Liam 306.6 0.5 0.5/306.6 = 0.0016
Taylor 756.36 1.2 1.2/756.36 = 0.0016
Sarah 504.35 0.7 0.7/504.35 = 0.0014
Ashley 459.9 0.75 0.75/459.9 = 0.0016
Connor 600.5 1 1/600.5 = 0.0017
Nathan 942.75 1.5 1.5/942.75 = 0.0016
Juan 827.82 1.35 1.35/827.82 = 0.0016
Katie 429.48 0.6 0.6/429.48 = 0.0014
Therefore, the runners whose speeds are in a proportional relationship with each other:
the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed of Sarah and Katie are equal.
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find two positive numbers whose product is 25 and whose sum is a minimum. (enter your answers as a comma-separated list.)
The required positive number whose product is 25 and whose sum is minimum is 5, 5
Sum of Two numbers
Sum of two numbers means adding two same or different number together
Let two positive numbers xy = 25
Divide both side by x
y = [tex]\frac{25}{x}[/tex] ----------Equation (1)
Sum of two positive numbers s = x + y -------Equation (2)
Substitute equation (1) into equation (2)
S = x + [tex]\frac{25}{x}[/tex]
differentiate with respect to x
[tex]\frac{ds}{dx} = \frac{d}{dx} (x + \frac{25}{x} ) = 1 - \frac{25}{x^{2} }[/tex]
[tex]\frac{ds}{dx} = 1-\frac{25}{x^{2} }[/tex] ---------- Equation (3)
[tex]\frac{ds}{dx} = 0[/tex]
[tex]1[/tex][tex]- \frac{25}{x^{2} }[/tex] = 0 ⇒ [tex]x^{2}[/tex] = 25
x = 5
Differentiate equation (3) again
[tex]\frac{d^{2}s }{dx^{2} } = 0 + \frac{50}{x^{2} }[/tex]
hence, at point x = 5, [tex]\frac{d^{2} s}{dx^{2} } = \frac{50}{5^{2} }[/tex] [tex]= \frac{50}{25} = 2[/tex]
Value of s minimum at point x = 5.
substitute the value of x into equation (1)
[tex]y = \frac{25}{x} = \frac{25}{5} = 5[/tex]
Therefore the required positive numbers are 5, 5.
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find the intervals of increase and decrease of 3/512(x-4)^2(x-8)(x-10)(x^2+16)
The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval (4, −∞).
What is an increasing and decreasing functions?
For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
We have,
[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]
[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
x = 4, 4i, −4i, 10, 8
∴ f′(x) = 0
x = 4,
Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)
In interval (−∞, 4), f′(x) < 0
Hence, the given function (f) is strictly decreasing in interval (−∞, 4)
In interval (4, −∞), f′(x) > 0
Hence, the given function (f) is strictly increasing in interval (4, −∞)
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what is the perimeter of rectangle ABDC, if AB=8 and AC=24 A. 32 B. 40 C. 64 D. 128
The perimeter of rectangle ABDC is 61.24 units.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The rectangle ABDC is given in the question which has:
AB = 8 and AC = 24
Here AC is the diagonal of the rectangle which is the hypotenuse in a right triangle.
As per Pythagoras's theorem,
AC² = AB² + BC²
24² = 8² + BC²
576 = 64 + BC²
BC² = 512
BC = 22.62
The perimeter of rectangle ABDC = 2(AB + BC)
The perimeter of rectangle ABDC = 2(8 + 22.62)
The perimeter of rectangle ABDC = 2(30.62)
The perimeter of rectangle ABDC = 61.24 units
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PLEASE HELP! WILL GIVE BRAINLIEST!
1. The linear function .f(2) = 79.4, therefore, test average for maths class after 2 test is: 79.4
2. Using the function table, the test average for science class is after the second test is: 84.
3. f(4) = 79.8
4. g(4) = 80
5. Science class was higher.
What is a Linear Function?The equation of a linear function is given as .f(x) = mx + b, given that m represents the slope/unit rate, and b is the y-intercept or starting value.
The linear function for average test score in maths class is given as, .f(x) = 0.2x + 79
Write the linear function for science class;
Slope (m) = change in y/change in x = (84 - 82)/(2 - 3) = 2/-1
Slope (m) = -2
Substitute m = -2 and (x, y) = (3, 82) into y = mx + b:
82 = -2(3) + b
82 = -6 + b
82 + 6 = b
88 = b
b = 88
Substitute m = -2 and b = 88 into g(x) = mx + b:
g(x) = -2x + 88
Part 1:
Substitute x = 2 into .f(x) = 0.2x + 79
.f(2) = 0.2(2) + 79
.f(2) = 79.4
Test average for maths class after 2 test is: 79.4
Part 2:
Using the function table, when x = 2, the test average for science class is: 84.
Part 3:
Substitute x = 4 into .f(x) = 0.2x + 79
.f(4) = 0.2(4)+ 79
.f(4) = 79.8
Part 4:
Substitute x = 4 into g(x) = -2x + 88
g(4) = -2(4) + 88
g(x) = 80
Part 5:
Science class had a higher test 4 average of 80.
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solve for x 4{x+1 1/3]=9 2/3
The solution for the expression is X =87/ 48 or 1.812
To solve for x in the equation we follow the step below:
Step 1: Open the bracket by multiply 4
= 4x +4x/3 = 9 2/3
= 4x + 4x /3 = 29/3
Step 2: Evaluate for X
= [tex]\frac{12x + 4x}{3}[/tex] = [tex]\frac{29}{3}[/tex]
= [tex]\frac{16x}{3}[/tex] =[tex]\frac{29}{3}[/tex]
Step 3: Cross multiply
: 3 (16x) = 3(29)
48x = 87
Step 3: Divide both sides by 48
=[tex]\frac{48x}{48}[/tex] =[tex]\frac{87}{48}[/tex]
x = [tex]\frac{87}{48}[/tex] = 1.812
Therefore, the solution for the expression is X =87/ 48 or 1.812
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Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours during the week and 14 hours on the weekend, she earns $250.90. If she works 15 hours during the week and 8 hours on the weekend, she earns $204.70. How much more does Charlotte earn per hour on the weekends than she earns during the week? Round to the nearest cent.
$0.40
$1.90
$2.30
$8.10
The amount that Charlotte earn per hour on the weekends than she earns during the week is: C. $2.30.
How to find the earning per hour?Number of dollars earn per hour during the week = x
Number of dollars earn per hour on the weekend =y
Formulate an equation
13x + 14y = 250.90 Equation 1
15x + 8y = 204.70 Equation 2
Solving for x and y by multiply equation 1 by -8 and equation 2 by 14 -104x - 112y = -2007.20
210x +112y = 2865.80
106x = 858.60
Divide both sides by 106x
x = 858.60/106
x = $8.10
Substitute x into eq 1 so as to solve for y
13(8.10) + 14y = 250.90
105.30 + 14y = 250.90
Subtract 105.30 from both sides
14y = 145.60
Divide both side by 14y
y = 145.60 /14
y = 10.40
Hence,
Additional earning per hour = y-x
Additional earning per hour = $10.40 - $8.10
Additional earning per hour=$2.30 per hours
Therefore the correct option is C.
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which one would be the correct answer?
3x²-2x+5 is the other factor of the above polynomial (6x³-x²+8x+5) other than (2x+1).
Describe a polynomial.In mathematics, a polynomial is an equation made up of coefficients and indeterminates, also referred to as variables. Only addition, subtraction, multiplication, and powers of positive-integer variables may be utilized to solve it. An example of a polynomial with one uncertain x is x² + 4x + 7.
Polynomials are commonly used in calculations in both mathematics and science. For instance, in the fundamental sciences of chemistry, physics, economics, and social science, they are used to define polynomial functions. They are also used in numerical analysis and calculus to approximate other functions. Simple word problems to complex scientific conundrums are all represented by polynomial equations. Polynomials are used in advanced mathematics.
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Ms. Lewinsky’s math class has k students. If p students earned a C or better on the last test, what fraction of the class did NOT eat a C or better on the last test?
Answer:
its "a" your welocome
Step-by-step explanation:
i did the test
i need help asap i need an awncer
3x=y-4z=-22
2x+3y+4z=32
x-y+2z=16
Answer:
3x + y - 4z = -222x + 3y + 4z = 32x - y + 2z = 16 Write and number each equation. Eq 1 3x+y-4z = 16. Eq 2 -222x+3y+4z = 16. Eq 3 32x-y+2z = 16
Step-by-step explanation:
Hope it helps you buddy(:
Answer: 16
You already got the answer- But whatever.
The values of [x], [y] and [z] are 2, 0 and 7.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written to express proportional relationship as -
y = kx {k is constant}
We have the following system of equation -
3x+y-4z=-22
2x+3y+4z=32
x-y+2z=16
We can write -
x - y + 2z = 16
x = 16 + y - 2z
So, we can write 3x + y - 4z = -22 as -
3(16 + y - 2z) + y - 4z = -22 ...eq[1]
and we can write 2x + 3y + 4z = 32 as -
2(16 + y - 2z) + 3y + 4z = 32 ...eq[2]
Plot eq[1] and eq[2], and find [y] and [z]. Refer to graph.
We get y = 0 and z = 7
So -
x = 16 + 0 - 14
x = 2
Therefore, the values of [x], [y] and [z] are 2, 0 and 7.
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EASY POINTS WILL GIVE BRAINLIST TO BEST ASWER!!
write the slope intercept form of the equation of the line through the given point with the given slope
through (-1, -4) slope = 5
Answer:
y=5x+1
Step-by-step explanation:
we already know the slope so we can put it in the slope intercept form
y=5x
And now we can put the coordinate points in there to find the y intercept
-4=5(-1)
-4=-5
We need to add 1 to make this equation true so the y intercept is 1
The equation will be
y=5x+1
Hopes this helps please mark brainliest
Answer:
y=5x+1
Steps are in the picture
A steel ball is melted down to make eight smaller identical balls. If the radius of the
original steel ball was 20 cm, calculate to the nearest millimetre the radius of each of the smaller balls.
The radius of each of the smaller balls is R = 2r.
Define volume of circle.You can use a tape measure, for instance, to directly measure the distance around the sphere's widest point. The radius of this circle, which serves as the sphere's circumference, is one. A circle's circumference is computed as 2 x x radius. Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We can use the following formula to get the volume of a sphere whose radius is "r": A sphere's volume is equal to 4/3r³.
Given,
A steel ball is melted down to make eight smaller identical balls. If the radius of the original steel ball was 20 cm:
Let the spherical ball's radius be R.
And with r being the radius of 8 similar balls,
According to the inquiry,
Volume of 8 similar balls = the volume of a larger sphere
3/4πR³ = 8 × 3/4πr³
R³ = 8r³
R = 2r
The radius of each of the smaller balls is R = 2r.
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Arun runs a farm stand that sells raspberries and grapes. Each pound of raspberries
sells for $1.50 and each pound of grapes sells for $2.75. Arun made $130.25 from
selling a total of 66 pounds of raspberries and grapes, Determine the number of
pounds of raspberries sold and the number of pounds of grapes sold.
Answer:
41 pounds of raspberries and 25 pounds of grapes
Step-by-step explanation:
x = pounds of raspberries
y = pounds of grapes
1.50x + 2.75y = 130.25
x + y = 66 --> y = -x + 66
Substitute and solve for x:
1.50x +2.75(-x +66) = 130.25
1.50x - 2.75x + 181.5 = 130.25
150x - 275x + 18150 = 13025
-125x +18150 = 13025
-125x = -5125
x = 41
Substitute x to find y:
41 + y = 66
y = 25
Answer:
There were 41 pounds of raspberries sold and 25 pounds of grapes sold.
Step-by-step explanation:
First, complete the story below so that it can be represented by the equation 5000-50x=4800-30x
Pool A started with 5000 liters of water, and 50 liters per minute are being (Drained out or Pumped back in)
Pool B started with 4800 liters of water, and 30 liters per minute are being (Drained out or Pumped back in)
The amount of water after x minutes is more in which pool? Pool A or Pool B?
Amount of water after x minutes is more in pool B.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
Pool A started with 5000 liters of water, and 50 liters per minute are being.
Pool B started with 4800 liters of water, and 30 liters per minute are being.
5000-50x=4800-30x
Add 30x on both sides
5000-50x+30x=4800-30x+30x
5000-20x=4800
5000-4800=20x
200=20x
Divide both sides by 20
20=x
Now substitute x in pool A equation
5000-50x
5000-50(20)=5000-1000
Pool A =4000
Now substitute x in pool B equation
4800-30x
4800-30(20)
4800-600
Pool B =4200
4200>4000
Pool B> Pool A
Hence amount of water after x minutes is more in pool B.
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How do you find if the vertical or horizontal asymptote is going to be approaching negative infinity or positive infinity. Provide examples.
Answer:
to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.
Step-by-step explanation:
Naomi is cutting patches in the shape of right triangles to make a quilt. Each triangle has a diagonal side of 14.5 inches and a short side of 5.5 inches. What is the length of the third side of each triangular patch?
WILL GIVE BRAINLIST TO BEST ANSWER! EASY POINTS
write the point slope form of the equation of the line through the given points.
through (-5, -1) and (-4, -5)
Answer:
y+1=-4(x+5)
Step-by-step explanation:
it changed to point slope form so now it’s different
the equation is y-y1=m(X-x1)
y-(-1)=m(x-(-5)
y+1=m(x+5)
Now to find slope y2-y1/x2-x1
-5+1/-4+5
-4/1
-4 is the slope so we just fill it in
y+1=-4(x+5)
Hopes this helps please mark brainliest
I am stuck on this. Can someone help me with my math homework
Answer: -5,5 = B
Step-by-step explanation:
Answer both of um I'll mark you brainliest
Answer:
1) 71.83
2) 43
3) 41
4) 755.66
5) 458
6) 1757.12
7) 123 meters
Help! Consider the following three systems of linear equations.
Answer:
b & d
Step-by-step explanation:
correct answer gets brainliest!
Answer:
x = 14
Step-by-step explanation:
the inscribed angle JKL is half the measure of its intercepted arc, that is
83 = [tex]\frac{1}{2}[/tex] arc JL = [tex]\frac{1}{2}[/tex](9x + 40) ← multiply both sides by 2 to clear the fraction
166 = 9x + 40 ( subtract 40 from both sides )
126 = 9x ( divide both sides by 9 )
14 = x
coppinger corp. is considering the use of a computer to assign probability distributions to the input variables used in the analysis. the computer would then randomly select input variables from their distributions and calculate npvs based on those selections. what kind of analysis is this? sensitivity analysis simulation analysis scenario analysis
Coppinger Corp is using Scenario Analysis.
Given, that Coppinger Corp is considering the use of a computer to assign probability distributions to the input variables used in the analysis.
The computer would then randomly select input variables from their distributions and calculate npvs based on those selections
Now, A scenario analysis consists of multiple inputs. For eg. a Company may consider how an increase in available fuel can impact their number of goods sold etc.
Here, also Coppinger Corp is assigning multiple values to the computer and getting outputs.
So, this can be the Scenario Analysis.
Hence, Coppinger Corp is using Scenario Analysis.
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pls help me with algebra