11*21+11*19+17*18/3=746/3=248.3
For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values
Highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18
what is greatest integer divisor ?
The greatest common divisor (GCD) of two nonzero integers a and b is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer. The GCD of a and b is generally denoted gcd(a, b).
For each value of 1 ≤ n ≤ 100, the highest common factor of 8n + 3 and 5n + 4 is written down. What is the sum of these values
Let gcd(8n + 3, 5n + 4) = d
⟹d|8n+3∧d|5n+4
⟹d|8(5n+4)−5(8n+3)
⟹d|17
Therefore highest common factor of 8n + 3 and 5n + 4 is either 1 or 17 for all n and its sum is 18
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A whole salmon, weighing 7 # 6 oz, costs $2.74/#. The fillets are removed, boned, and trimmed. The head, bones, and all trim is thrown into the trash. What is the total value of the remaining fillets, which now weigh only 4 # 15 oz? What is their price per pound? What is the salmon’s yield percentage? If the next salmon weighs 6 # 14 oz, how much boneless salmon fillet would you expect to yield from it after fabrication?
Using proportions, it is found that:
The total value of the remaining fillets is of $13.53.The price per pound is of $2.54.The salmon’s yield percentage is of 66.95%.You would expect to yield 4.6 pounds of boneless salmon fillet from the next salmon weighing 6 # 14 oz.What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
Before beginning the problem, we have that the symbol # represents a pound, which has 16 ounces.
The remaining fillets weight 4 # 15 oz = 4 pounds + 15/16 of a pound. Hence, considering the cost of $2.74 per pound:
4 x 2.74 + 15/16 x 2.74 = $13.53.
The total value of the remaining fillets is of $13.53.
The price per pound is still the same, of $2.54.
The yield is of 4 pounds + 15/16 of a pound = 4.9375 pounds out of 7 + 6/16 = 7.375 pounds, hence the percentage is:
4.9375/7.375 x 100% = 66.95%.
The salmon’s yield percentage is of 66.95%.
Hence, for 6 + 14/16 = 6.875 pounds, the yield would be of:
0.6695 x 6.875 = 4.6 pounds.
You would expect to yield 4.6 pounds of boneless salmon fillet from the next salmon weighing 6 # 14 oz.
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The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 106. If state A has more counties
than state B, how many counties does each state have?
Answer: State A has 54 counties and B has 52 counties
Step-by-step explanation: Since the number of counties are even integers, I did a guess and check. Divided 106 by two to get 53. Then realized that if you take away 1 from on of the 53's and add it to the other, they become consecutive even integers 52 and 54
The angles in a triangle are in the ratio 1 : 2 : 3.
a) Show that the triangle is a right-angled triangle.
b) The hypotenuse of the triangle is 19 cm long.
Calculate the length of the shortest side in the triangle.
Answer:
a) the largest angle is 90°, making it a right triangle
b) the shortest side is 9.5 cm long
Step-by-step explanation:
You want the largest angle and the shortest side in a triangle whose angles are in the ratio 1 : 2 : 3.
AnglesLet x represent the smallest angle. Then the other two angles are 2x and 3x. Their sum is ...
x +2x +3x = 180°
x = 30° . . . . . divide by 6
3x = 90° . . . . find the largest angle
The largest angle is 90°, a right angle. So, the triangle is a right-angled triangle.
SidesA triangle with angles of 30°, 60°, and 90° is a "special" right triangle. Its sides are in the ratio 1 : √3 : 2. That is, the shortest side is 1/2 the length of the longest side.
shortest side = 1/2(19 cm) = 9.5 cm
The length of the shortest side in the triangle is 9.5 cm.
__
Additional comment
In case you're not familiar with the side length ratios of the 30-60-90 special triangle, you can figure the side length from the Law of Sines. That tells you ...
a/sin(A) = b/sin(B) = c/sin(C)
where A, B, C are the angles; and a, b, c are their opposite sides.
The shortest side is opposite the smallest angle, so we have ...
a/sin(30°) = (19 cm)/sin(90°)
a = sin(30°)×(19 cm) = 1/2(19 cm) = 9.5 cm
The length of the shortest side is 9.5 cm.
Solve 19×50 numerically
The solution of expression 19×50 is found as 950.
What is defined as the distributive property?This property states that multiplying the product of two or more addends by a number produces the same outcome as multiplying each addend separately by the number and afterwards adding the products together.
The distributive property holds true for division the same way that it holds true for multiplication. However, with division, the concept of "breaking apart" or "distributing" can only be applied by dividing the numerator into lesser numbers that are exactly divisible even by divisor.In other words, the distributive property requires a phrase of the form:
A (B + C) can be simplified as A (B + C) = AB + AC.
This same applies foe the subtraction;
Thus, for the given numerical;
= 19×50
Using distributive property.
= (20 - 1)×50
Open the braces;
= 20×50 - 1×50
= 1000 - 50
= 950
Therefore, the solution of the numerical 19×50 is 950.
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4xº
(3x + 8)°
B
Find m
If angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.
Given that angle BAD=4x° and angle DAC=(3x+8)°.
We are required to find the equation showing the angle BAC.
Angle is basically the figure formed by two rays which is called the sides of the angle and sharing a common endpoint called the vertex of the angle.
∠BAD=4x° and ∠DAC=(3x+8)°
To find the equation showing angle BAC we have to just add the two expressions given in the equation.
∠BAC=∠BAD+∠DAC
∠BAC=4x+3x+8
∠BAC=(7x+8)°
Hence if angle BAD=4x° and angle DAC=(3x+8)° then the equation showing angle BAC is equal to (7x+8)°.
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There are 40 students in a class. 24 of those students are men. What percent of the class are women?
Answer: 40%
Step-by-step explanation:
c=class. m=men. w=women.
c=m+w
40=24+w
40-24=24-24+w
w=16
16/40=
4/10=
4*100%/10=
400%/10=40%
Melinda is at tennis practice. She hits 32 tennis balls a minute. She hit 45 tennis balls before practice. If Melinda hit a total of 1,645 tennis balls, how long was she at practice?
A. 45 minutes
B. 50 minutes
C. 60 minutes
D. 52 minutes
What value(s) of δ are an appropriate choice when proving the following limit?
limx→−2(x2+8x+17)=5
Enter your answer in terms of ε. You should assume that 0<δ<4.
Hercules and Gretta are hiking on the same trail. Hercules's elevation
5
is-26 feet whereas Gretta's elevation is -4-feet. How much
8
greater is Gretta's elevation than Hercules's?
Answer:
-22
Step-by-step explanation:
put the subtraction sign to the side
26 (Gretta's elevation)
- 4 (Hercules' elevation)
22
then re-add the subtraction sign (-22) then you have an answer
Is the function of f(x) discontinuous or continuous ?
f(x) = 1/x at x = 3
Answer: Continuous at x = 3
The function is only discontinuous at x = 0 since it causes a division by zero error. Everywhere else the function is a continuous curve.
Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD).
The perimeter of a rectangular traffic sign is 134 inches.
Also, its length is 9 inches longer than its width.
Find the dimensions of this sign.
The dimensions of the rectangular traffic sign whose perimeter is 134 inches according to the task content are; 38in by 29in.
What are the dimensions of the rectangular traffic sign?It then follows that from the task content that the dimensions of the rectangular traffic sign are to be determined.
Since the perimeter of a rectangle is given by;
P = 2(l+b)
where the length, l = b +9.
So therefore; 134 = 2(b+9 +b)
134 = 4b + 18
4b = 134 - 18
4b = 116
b = 29
In conclusion, the length, l of the traffic sign is; 29 +9
l = 38.
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In a study of bird migration, a researcher
recorded on a certain day a total of 262
birds, consisting of 65 geese, 84 ducks,
and 113 robins in the skies. Show
a possible equation for calculating the
probability that a random bird chosen
from among these is NOT a duck.
The probability that a random bird chosen from among these is NOT a duck is 0.67
Given the total number of birds = 262
No of geese = 65
No of ducks = 84
No of robins = 113
We need to find the probability that a random bird chosen from among these is not a duck is
P ( not a duck ) = (total number of birds - no of ducks) / total number of birds
= 262 - 84 / 262
= 178 / 262
= 0.67
The probability that a random bird chosen from among these is NOT a duck is 0.67.
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A point is randomly selected on the surface of a lake that has a maximum depth of 140 feet. Let y be the depth of the lake at the randomly chosen point.
(a)
What are possible values of y?
all real numbers from 0 to 140
all positive integers from 0 to 140
all real numbers from 1 to 140
all positive integers from 1 to 140
(b)
Is y discrete or continuous?
discrete
continuous
Rita’s recipe for berry pies requires blueberries, raspberries, and strawberries. The ratio of cups of blueberries to cups of raspberries is 1 : 3. The ratio of cups of raspberries to cups of strawberries is 4 : 3. A batch of eight berry pies has a total of 25 cups of berries. How many cups of strawberries are in each pie?
Using proportions, it is found that there are 1.125 cups of strawberries in each pie.
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
For this problem, from the ratios, we have that:
The ratio of cups of blueberries to cups of raspberries is 1 : 3, hence, for each 4 cups, 1 is blueberry and 3 is raspberry.The ratio of cups of raspberries to cups of strawberries is 4 : 3, hence, for each 7 cups, 4 are raspberries and 3 are strawberries.The least common multiple of 3 and 4 is 12, hence, multiplying 4 by 3, the ratio is:
Raspberries : Strawberries : Blueberries = 12 : 9 : 4
Meaning that our of 12 + 9 + 4 = 25 cups, we have that:
12 cups are of raspberries.9 cups are of strawberries.4 cups is of blueberries.There amounts are for 8 pies, hence, for a single pie:
9/8 = 1.125 cups.
There are 1.125 cups of strawberries in each pie.
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Let [tex] \rm|M|[/tex] denote the determinant of a square matrix M. Let [tex] \rm g : \bigg[0, \dfrac{\pi}{2} \bigg] \to \mathbb{R}[/tex] be the function defined by [tex] \rm g( \theta) = \sqrt{f( \theta) - 1} + \sqrt{f \bigg( \dfrac{\pi}{2} - \theta\bigg) - 1} [/tex] where
[tex] \rm f( \theta) = \dfrac{1}{2} \left| \begin{matrix} 1& \sin( \theta) &1 \\ - \sin( \theta) &1& \sin( \theta) \\ - 1& - \sin( \theta)&1 \end{matrix} \right | + \left| \begin{matrix} \sin(\pi) & \cos( \theta + \frac{\pi}{4} ) & \tan( \theta - \frac{\pi}{4} ) \\ \sin( \theta - \frac{\pi}{4} ) & - \cos( \frac{\pi}2 ) & \log_{e} ( \frac{4}\pi ) \\ \cot( \theta + \frac{\pi}{4} ) & \log_{e} ( \frac{\pi}4 )& \tan(\pi) \end{matrix} \right | [/tex]
Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g([tex]\theta [/tex]) , and p(2)=2-[tex]\sqrt{2}[/tex]. Then which of the following is True?
[tex] \rm(1) \: p \bigg( \frac{3 + \sqrt{2} }{4} \bigg) < 0 \\ \rm(2) \: p \bigg( \frac{1 + 3 \sqrt{2} }{4} \bigg) > 0 \\ \rm(3) \: p \bigg( \frac{5\sqrt{2} - 1 }{4} \bigg) > 0 \\ \rm(4) \: p \bigg( \frac{5 - \sqrt{2} }{4} \bigg) < 0[/tex]
The second matrix in the definition of [tex]f[/tex] is singular, since
[tex]\sin(\pi) = -\cos\left(\dfrac\pi2\right) = \tan(\pi) = 0[/tex]
[tex]\cos\left(\theta+\dfrac\pi4\right) = \sin\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \sin\left(\dfrac\pi4-\theta\right)=-\sin\left(\theta-\dfrac\pi4\right)[/tex]
[tex]\cot\left(\theta+\dfrac\pi4\right) = \tan\left(\dfrac\pi2 - \left(\theta+\dfrac\pi4\right)\right) = \tan\left(\dfrac\pi4 - \theta\right) = -\tan\left(\theta-\dfrac\pi4\right)[/tex]
[tex]\ln\left(\dfrac4\pi\right) = -\ln\left(\dfrac\pi4\right)[/tex]
In other words, it's antisymmetric; [tex]A^\top=-A[/tex]. It's easy to show that [tex]\det(A)=0[/tex] if [tex]A[/tex] is 3x3 and antisymmetric.
The other determinant reduces to
[tex]\begin{vmatrix}1 & \sin(\theta) & 1 \\ - \sin(\theta) & 1 & \sin(\theta) \\ -1 & -\sin(\theta) & 1 \end{vmatrix} = 2 + 2\sin^2(\theta)[/tex]
Hence
[tex]f(\theta) = 1 + \sin^2(\theta) \implies f\left(\dfrac\pi2\right) = 1 + \cos^2(\theta)[/tex]
With [tex]g[/tex] defined on [tex]\left[0,\frac\pi2\right][/tex], both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are non-negative. So
[tex]g(\theta) = \sqrt{f(\theta)-1} + \sqrt{f\left(\dfrac\pi2-\theta\right)-1} \\\\ ~~~~ = \sqrt{\sin^2(\theta)} + \sqrt{\cos^2(\theta)} \\\\ ~~~~ = |\sin(\theta)| + |\cos(\theta)| \\\\ ~~~~ = \sin(\theta) + \cos(\theta) \\\\ ~~~~ = \sqrt2\,\sin\left(\theta + \dfrac\pi4\right)[/tex]
which is maximized at [tex]t=\frac\pi4[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac\pi2\right)=\sqrt2[/tex], and minimized at [tex]t=0[/tex] and [tex]t=\frac\pi2[/tex] with a value of [tex]\sqrt2\,\sin\left(\frac{3\pi}4\right)=1[/tex].
Edit: The rest of my answer wouldn't fit. Continued in attachment.
what’s the distance between Y(3,0) and Z(-1,-2)
Exact Distance = [tex]2\sqrt{5}[/tex] units
Approximate Distance = 4.4721 units
=================================================
Let's use the distance formula
[tex](x_1,y_1) = (3,0) \text{ and } (x_2, y_2) = (-1,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-(-1))^2 + (0-(-2))^2}\\\\d = \sqrt{(3+1)^2 + (0+2)^2}\\\\d = \sqrt{(4)^2 + (2)^2}\\\\d = \sqrt{16 + 4}\\\\d = \sqrt{20}\\\\d = \sqrt{4*5}\\\\d = \sqrt{4}*\sqrt{5}\\\\d = 2\sqrt{5}\\\\d \approx 4.4721\\\\[/tex]
The exact distance is [tex]2\sqrt{5}[/tex] units.
That approximates to about 4.4721 units.
logs (20x + 5y) using the properties of logarithms to expand
The logarithmic expansion of logs(20x + 5y) by using the properties of logarithmic is log(5)+log(4x+y).
The basic logarithmic function is of the form f(x) = logₐx(r)n = logₐx, where a > 0. It is the inverse of the exponential function aⁿ = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic functions is very useful in various mathematical computations.
Given that, log(20x+5y) and we have to expand it by using the properties of logarithms. So, let's proceed to solve the question.
log(20x+5y)
we can write 20 in terms of powers like 20 = (2²)x5
log((2².5)x+5y)
log(5(2².5x/5+5y/5))
log(5(2²x+y))
log(5(4x+y))
∵ log(ab) = log(a)+log(b)
⇒log(5(4x+y)) = log(5)+log(4x+y)
Hence, on expanding log(20x+5y) by using the properties of logarithms we get log(5)+log(4x+y) as our required answer.
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The sum of the first 10 positive odd integers.
Answer:
1,3,5,7,9,11,13,15,17,19
add them all together
= 100
Step-by-step explanation:
hope this works :)
(3 + 16.4a) − (9 + 5.7a)
22.1a + (−12)
1.07a + (−12)
22.1a + (−6)
10.7a + (−6)
Answer:
10.7a + (−6)
Step-by-step explanation:
Solve |3x - 4| = 6
{-2/3, 10/3}
{-10/3, 10/3}
{-2/3, 2/3}
Answer:
{-2/3, 10/3}
Step-by-step explanation:
Let's solve your equation step-by-step.
|3x−4|=6
Solve Absolute Value.
|3x−4|=6
We know either3x−4=6or3x−4=−6
3x−4=6(Possibility 1)
3x−4+4=6+4(Add 4 to both sides)
3x=10
3x/3 = 10/3
(Divide both sides by 3)
x=10/3
3x−4=−6(Possibility 2)
3x−4+4=−6+4(Add 4 to both sides)
3x=−2
3x/3 = −2/3
(Divide both sides by 3)
x= −2/3
=
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O QUADRATIC, RATIONAL, AND RADICAL EQUATIONS
Solving a word problem using a quadratic equation with irration...
College Al...
initial
height
ground
A ball is thrown from an initial height of 3 feet with an initial upward velocity of 36 ft/s. The ball's height h (in feet) after t seconds is given by the following.
h=3+361-16r²
Find all values off for which the ball's height is 19 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
[=
alynn senn
seconds
DOD
X
0/5
Ś
A
The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.
What is a quadratic equation?
In algebra, a quadratic equation is any equation that can be rearranged in standard form as
ax² + b*x + c = 0
The figures a, b, and c are the portions of the equation and may be distinguished by calling them, independently, the quadratic measure, the direct measure, and the constant or free term.
The values of x that satisfy the equation are called results of the equation, and the roots or bottoms of the expression on its left-hand side.
A quadratic equation has at most two solutions.
Given,
Initial height h(0) = 3 ft
Initial upward velocity v(0) = 36 ft/sec
Given ball height after 't' seconds is h(t) = 3 + 36t - 16r²
for h= 19 ft
19 = 3 + 36 t - 16 r²
16 r² - 36 t + 16 = 0
4 r² - 9 t + 4 = 0
Quadratic equation for ax² + b*x + c = 0 is x = -b ±√b² - 4ac / 2a
By using the above formula we get
t = 9 ± √9² - 4*4*4 / 2*4
t = 9 ± √81 - 64 / 8
t = 9 ± √17 / 8
t = 9 + √17 / 8 t = 9 - √17 / 8
t = 9 + 0.5 t = 9 - 0.5
t = 9.5 t = 8.5
The values for which the ball's height is 19 feet are 9.5 sec and 8.5-sec using quadratic equations.
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It takes eva 6 minutes to fill an online order at her clothing boutique. If she has the help of briana, her store manager, it takes four minutes to fill an order. How long does it take Briana to fill an order alone? Use the equation 1/6 + 1/x = 1/4
Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.
Eva takes to fill an online order at her clothing boutique. = 6 minutes
If Eva and Briana fill an order together = 4 minutes
Briana will take minutes to fill an order alone at her clothing boutique = X minutes.
then the equation will be :
1/6 + 1/x = 1/4
1/x = 1/4 - 1/6
now solve equation by taking LCM
1/x = (6-4)/4x6
1/x = 2/24
1/x = 1/12
x = 12
so the value of x is 12
Briana will take minutes to fill an order alone at her clothing boutique is 12 minutes.
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Melanie receives a 9% commission on every house she sells. If she received a commission of $20,340, what was the value of the house she sold?
A brokerage company evaluated the three services its call centers provide for reliability. The results showed the following:
Service Reliability Percentage
Checking customer account status .85
Confirming orders .72
Stock quotes .96
Compute the over-all reliability of the call center (round to 2 decimals) _____________
Show computation:
If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.
Over-all reliability of the call centerUsing this formula to calculate the over-all reliability of the call center
Over-all reliability of the call center=Checking customer account status × Confirming orders× Stock quotes
Where:
Checking customer account status =.85
Confirming orders= .72
Stock quotes= .96
Let plug in the formula
Over-all reliability of the call center=.85×.72×.96
Over-all reliability of the call center=0.58752
Therefore If a brokerage company evaluated the three services its call centers provide for reliability. The over-all reliability of the call center is: 0.58752.
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to
80°
80
Find x.
100
Translate the sentence into an equation or formula.
The surface area SA of a rectangular prism is 2 times the sum of the width (w) times height (h), and length (
l
) times width, and length times height.
A translation of the equation for the surface area of this rectangular prism is given by: SA = 2(WH + LW + LH).
What is an equation?An equation can be defined as a mathematical expression which shows that two (2) or more thing are equal.
How to translate the sentence into an equation or formula?Mathematically, the surface area of a rectangular prism can be calculated by using this equation or formula:
SA = 2(WH + LW + LH)
Where:
SA represents the surface area of a rectangular prism.L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.In this context, we can reasonably and logically deduce that a translation of the equation for the surface area of this rectangular prism is given by:
SA = 2(WH + LW + LH).
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If x is an integer, which of the following is the solution set for 3|x|=15?
{0,5}
{−5,5}
{−5,0,5}
{0,45}
Write the ratio as a ratio of whole numbers in lowest terms
$0.60 to $0.80
Use the graph to determine which statement describes f(x).
-5
y = f(x)
5.
-5.
5
Option a is correct. f(x) has an inverse function because its graph passes the horizontal line test.
An inverse function is a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
From the graph we can see that the horizontal lines intersect less than 2 points, this shows that the f(x) has an inverse.
From the graph, it gets to know.
Hence from the given graph we get to know that f(x) is the inverse function.
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