Answer: Obtuse Angle
Step-by-step explanation: A 90 degree angle is a right angle anything larger then a right angle is a obtuse angle.
Answer:
It would be called an obtuse angle
Step-by-step explanation: so you see if it was exactly 90 degrees it would be called a right angle. Anything above 90 (b91 92 93 etc...) degrees would be an obtuse angle and anything below 90 ( 89 88 87 etc..) would be an acute angle except an 180 degree angle would be a straight angle. Hope that helps!
have a wonderful Sunday!
how do i do this? i have test on it tomorrow
The measure of the angle ∠ADC is 36°.
Given that a circle T, the inscribed angle ∠ABC = 72°, we need to find the measure of the angle ∠ADC,
So, according to the inscribed angle theorem,
2 ∠ABC = arc AC
arc AC = 144°
Now, since the whole circumference is 360°,
So,
arc ADC = 360° - arc AC
arc ADC = 216°
So,
∠ADC = 1/2 [arc ADC - arc AC]
∠ADC = 1/2 [216° - 144°]
∠ADC = 36°
Hence the measure of the angle ∠ADC is 36°.
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Find the LCM of A= 3^2 x 5^4 x 7 and B= 3^4 x 5^3 x 7 x11
The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.
Given are two numbers which are showed in the prime factorized form.
A = 3² × 5⁴ × 7
B = 3⁴ × 5³ × 7 × 11
Prime factorization is the factorization of a number in terms of prime numbers.
In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.
A = 3² × 5³ × 5 × 7
B = 3² × 3² × 5³ × 7 × 11
Bring down the primes in each column.
LCM = 3² × 3² × 5³ × 5 × 7 × 11
= 3898125
Hence the LCM is 3898125.
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Jim is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random.
This game is this: Jim rolls the number cube once. He wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. He loses $6.50 if a 5or 6 is rolled.
(a) Find the expected value of playing the game.
(b) What can Jim expect in the long run, after playing the game many times?
Jim can expect to gain money.
Jim can expect to lose money.
Jim can expect to break even (neither gain nor lose money).
part a.
the expected value of playing the game is found as -$0.50.
part b.)
Jim can expect to lose money in the long run if he plays the game many times because the expected value is negative.
How do we calculate?The expected outcomes and their corresponding values are:
If we roll a 1 = Jim wins $1.
If we roll a 2 =Jim wins $2.
If we roll a 3 = Jim wins $3.
If we roll a 4 = Jim wins $4.
If we roll a 5 or 6 = Jim loses $6.50.
We then calculate the value:
Expected value = (Probability of rolling a 1) × (Value of rolling a 1) + (Probability of rolling a 2) × (Value of rolling a 2) + (Probability of rolling a 3) × (Value of rolling a 3) + (Probability of rolling a 4) × (Value of rolling a 4) + (Probability of rolling a 5 or 6) × (Value of rolling a 5 or 6)
Expected value = (1/6) × $1 + (1/6) × $2 + (1/6) × $3 + (1/6) × $4 + (2/6) × (-$6.50)
EV = $1/6 + $2/6 + $3/6 + $4/6 - $13/6
EV = ($1 + $2 + $3 + $4 - $13)/6
EV = -$3/6
Expected value = -$0.50
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Essay Question.
You are purchasing a new car. In order to determine which car will provide maximum savings, you’ve researched miles per gallon (mpg) ratings of cars. If gas is $3.45 per gallon and you drive an average of 18,000 miles per year, the following rational equation is given:
a. You will find the gallons of gas consumed by the old car in one year when you divide [tex]\frac{18,000}{old\;miles\;per\;gallon}[/tex].
b. The amount of dollars you would save in the first year by switching to the 27 mpg car is $1,150.
c. The amount of dollars you would save after 5 years is $5,750.
d. Yes, the additional savings in gas be worth the extra $3000 over a 5 year loan.
e. The gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car is 23.4 mpg.
How to evaluate the rational equation?Based on the information provided about the car that would provide maximum savings, the following rational equation models the situation:
[tex]g(x)=3.45(\frac{18,000}{old\;miles\;per\;gallon})-3.45(\frac{18,000}{new\;miles\;per\;gallon})[/tex]
Note: "g(x) is used for calculating the amount of dollar savings for one year for driving a car that gets higher miles per gallon rate."
Part a.
Based on the rational equation, we can logically deduce that the expression [tex]\frac{18,000}{old\;miles\;per\;gallon}[/tex] would help to determine the gallons of gas consumed by the old car in one year.
Part b.
The amount of dollars you would save in the first year by switching to the 27 mpg car can be calculated as follows:
[tex]g(x)=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{27})[/tex]
g(x) = 3,450 - 2,300
g(x) = $1,150.
Part c.
The amount of dollars you would save after five years can be calculated as follows:
f(5) = 5g(x)
f(5) = 5 × $1,150
f(5) = $5,750
Part d.
[tex]g(x)=3.45(\frac{18,000}{27})-3.45(\frac{18,000}{33})[/tex]
g(x) = 2,300 - 1,881.82
g(x) = $418.18.
f(5) = 5g(x)
f(5) = 5 × $418.18
f(5) = $2,090.9
Next, we would subtract the cost in 5 years as follows;
Difference = $5,750 - $2,090.9
Difference = $3,659.1.
Therefore, $3,659.1 is greater than $3,000, so an additional savings is worth it.
Part e.
Lastly, we would determine the gas mileage your new car would have to be if you saved $800 per year over your 18 mpg current car;
[tex]800=3.45(\frac{18,000}{18})-3.45(\frac{18,000}{y})[/tex]
800 = 3,450 - 62,100/y
62,100/y = 3,450 - 800
62,100/y = 2,650
y = 62,100/2,650
y = 23.4 mpg.
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Use the information above to answer the questions that follow.
2.2.1
2.2.2
2.2.3
2.2.4
sanitation in Johannesburg if a property is 175 m².
Write down, to the nearest ten cents and excluding VAT, the cost for
Calculate the cost for 4,1 ke sanitation in Cape Town before the increase.
Mr Jones lives in Johannesburg and Ms Brown lives in Cape Town. They
both own a property with an area of 550 m² and each was billed for 22 kl
sanitation.
Use the table above to determine the difference in the cost of sanitation
for the two properties.
Explain how the tariff system used in Johannesburg is beneficial to
home owners in terms of water usage.
(2)
(8)
(2)
[34]
mor
MO
ud.
0
0
Mr. Jones in Johannesburg is billed R9,767.12 and Ms. Brown in Cape Town is billed R680.24 for their respective properties.
From the provided information for Cape Town's sanitation tariffs:
0-4.2 kl: R16.03 per kl
Since 4.1 ke is equivalent to 4100 liters, which is less than 4.2 kl, we can use the tariff rate for the 0-4.2 kl range.
Cost for 4.1 ke of sanitation
= 4.1 ke x R16.03 per kl
= 4100 liters x R16.03 per kl
= R65.83
For Mr. Jones and Ms. Brown, who own properties with an area of 550 m² each and were billed for 22 kl of sanitation.
we need to determine the applicable tariff rate based on the property size and calculate the cost.
In Johannesburg, based on the provided information, the tariff rate for properties larger than 300 m² to 1,000 m² is R443.96.
Cost of sanitation for Mr. Jones in Johannesburg:
= 22 kl x R443.96 per kl
= R9,767.12
Cost of sanitation for Ms. Brown in Cape Town:
= 22 kl x R30.92 per kl = R680.24
Therefore, Mr. Jones in Johannesburg is billed R9,767.12 and Ms. Brown in Cape Town is billed R680.24 for their respective properties.
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If the reliability is
r = 0.25,
the equation becomes
R(n) =
0.25n
0.75 + 0.25n
.
What percent improvement is there in the reliability when the test length is doubled?
The percentage improvement in reliability when test length is doubled is 15%
R(n) = 0.25n / (0.75 + 0.25n)
For a test length of 1substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(1) = 0.25(1) / (0.75 + 0.25(1))
R(1) = 0.25 / 1
R(1) = 0.25
For a test length of 2when test length is doubled , n = 2
substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(2) = 0.25(2) / (0.75 + 0.25(2))
R(2) = 0.5 / 1.25
R(2) = 0.4
Percentage improvement can be calculated thus ;
R(2)-R(1)/R(1) × 100%
(0.4-0.25)/0.25 × 100%
0.15 × 100%
=15%
Therefore, percentage improvement in reliability is 15%
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What the meaning of statement this?
Yes, the product of X and Y, that is X × Y is a set.
Given that, the product X×Y is a set because X×Y⊂PP(X∪Y).
A set is defined as a collection of elements or members, and X × Y meets this criteria as it is a collection of ordered pairs of elements from X and Y.
We can also prove this using set theory. The expression X × Y⊂PP(X∪Y) means that the set X × Y is a subset of the power set of the union of X and Y.
The power set of a set A is a set of all subsets of A, which means that PP(X∪Y) includes all of the possible combinations of the elements from X and Y.
So, the fact that X × Y⊂PP(X∪Y) proves that it is a subset of a set and thus is a set itself.
Yes, the product of X and Y, that is X × Y is a set.
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How to solve triangle inequalities?
Answer: The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
find inverse of function y=x2 x>=0
Answer:
The inverse function is:
f(x)=√x−2
Step-by-step explanation:
To find the inverse function of y=f(x) you have to transform the formula to calculate x in terms of y.
y=x2+2
x2=y−2
x=√y−2
Now we can change the letters to follow the convention that x is the independent variable and y is the function's value:
y=√x−2
You have to calculate the domain of the result function.
Here you have the expression under square root sign, so the domain is the set where x−2≥0
x−2≥0⇒x≥2
. Suppose a government agency has a monopoly in the provision of internet connections.
The marginal cost of providing internet connections is 1
2
, whereas the inverse demand
function is given by: p = 1
The government agency as a monopolist will produce and sell internet connections up to the point where the marginal cost is 1/2. The price will be set at 1, given the perfectly elastic demand function.
In the scenario where a government agency has a monopoly in the provision of internet connections and the inverse demand function is given by p = 1, we can analyze the market equilibrium and the implications for pricing and quantity.
The inverse demand function, p = 1, implies that the market demand for internet connections is perfectly elastic, meaning consumers are willing to purchase any quantity of internet connections at a price of 1. As a monopolist, the government agency has control over the supply of internet connections and can set the price to maximize its profits.
To determine the optimal pricing and quantity, the monopolist needs to consider the marginal cost of providing internet connections. In this case, the marginal cost is given as 1/2. The monopolist will aim to maximize its profits by equating marginal cost with marginal revenue.
Since the inverse demand function is p = 1, the revenue received by the monopolist for each unit sold is also 1. Therefore, the marginal revenue is also 1. The monopolist will produce up to the point where marginal cost equals marginal revenue, which in this case is 1/2.
As a result, the monopolist will produce and sell internet connections up to the quantity where the marginal cost is 1/2. The monopolist will set the price at 1 since consumers are willing to pay that price.
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According to the rational zero theorem, which is not possible zero of the function
(x)=2x^4-5x^3+10x^2-9
A. -9
B. -1/2
C. 1/3
D. 3
Answer:
C. 1/3
Step-by-step explanation:
You want to identify the rational number listed that cannot be a root of the given polynomial.
Rational root theoremPossible rational roots will be off the form ...
± (divisor of the constant) / (divisor of the leading coefficient)
ApplicationWhen the divisors are listed, this is ...
±{1, 3, 9}/{1, 2}
This shows you that 3 cannot be the denominator of any possible rational root.
1/3 is not a possible zero of the function
__
Additional comment
The list of possible roots is ±{1/2, 1, 3/2, 3, 9/2, 9}.
As it happens, neither of the two real roots is rational.
<95141404393>
x+y<3
write in slope form
the answer to this question is
m=1
Answer: y<-x+3
Step-by-step explanation:
Slope-Intercept Form formula is y=mx+b.
1. Rearrange the variables (subtract x). x+y<3 --> y<-x+3.
2. y<-x+3 is the final answer!
Very Simple!
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please help! maths hyperbolic functions
Answer:
See attachments.
Step-by-step explanation:
The quickest way to sketch the given functions, given that the coordinate plane is restricted to -5 ≤ x ≤ 5, is to substitute the values of x into the functions to find the points for the given interval. Plot these points on the given coordinate plane, and draw a continuous curve through the points.
Part (a)Given function:
[tex]y=\dfrac{5}{x}-2, \quad x > 0[/tex]
Substitute the values of x = 1, x = 2, x = 3, x = 4 and x = 5 into the function:
[tex]\begin{aligned}x=1 \implies y&=\dfrac{5}{1}-2\\&=5-2\\&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=2 \implies y&=\dfrac{5}{2}-2\\&=2.5-2\\&=0.5\end{aligned}[/tex]
[tex]\begin{aligned}x=3 \implies y&=\dfrac{5}{3}-2\\&=-0.333...\end{aligned}[/tex]
[tex]\begin{aligned}x=4 \implies y&=\dfrac{5}{4}-2\\&=1.25-2\\&=-0.75\end{aligned}[/tex]
[tex]\begin{aligned}x=5 \implies y&=\dfrac{5}{5}-2\\&=1-2\\&=-1\end{aligned}[/tex]
Plot the points (1, 3), (2, 0.5), (3, -0.333...), (4, -0.75) and (5, -1) on the given coordinate plane and draw a continuous curve through them.
End behaviour:
As x approaches 0 from the positive side, x tends to ∞.As x approaches ∞, y approaches -2.[tex]\hrulefill[/tex]
Part (b)Given function:
[tex]y=\dfrac{-2}{x+1}+3, \quad x < -1[/tex]
Substitute the values of x = -2, x = -3, x = -4 and x = -5 into the function:
[tex]\begin{aligned}x=-2 \implies y&=\dfrac{-2}{-2+1}+3\\&=2+3\\&=5\end{aligned}[/tex]
[tex]\begin{aligned}x=-3 \implies y&=\dfrac{-2}{-3+1}+3\\&=1+3\\&=4\end{aligned}[/tex]
[tex]\begin{aligned}x=-4 \implies y&=\dfrac{-2}{-4+1}+3\\&=0.666...+3\\&=3.666...\end{aligned}[/tex]
[tex]\begin{aligned}x=-5 \implies y&=\dfrac{-2}{-5+1}+3\\&=0.5+3\\&=3.5\end{aligned}[/tex]
Plot the points (-2, 5), (-3, 4), (-4, 3.666...) and (-5, 3.5) on the given coordinate plane and draw a continuous curve through them.
End behaviour:
As x approaches -1 from the negative side, x tends to ∞.As x approaches -∞, y approaches 3.A student is given the triangle attached. The student claims that sin(20°)=x/5in. Explain why this reasoning is incorrect.
The reasoning of the student is wrong because the claim doesn't abide by the sine rule and formula.
What is a sine rule and formula?The sine rule states that in a triangle, side “a” divided by the sine of angle A is equal to the side “b” divided by the sine of angle B is equal to the side “c” divided by the sine of angle C.
That is;
a/sinA= b/sinB = c/sinC
Therefore, the proper equation to find X = 5/sin98° = X/sin20°
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Question
Given the frequency table below, what is the relative frequency of the data value 8?
Value
4
5
6
7
8
Frequency
2
7
9
6
6
Answer:
2
3
5
5
7
13
14
17
21
31
52
Step-by-step explanation:
but I think the town & is the best. I am not coming out of my reward.. this will be the last one day.. this will not go on. I am not coming to the office until tomorrow as I'm working for, and if I don't get any of that, I'll break it up with a choice. I am a bit worried, so I was 165 2762
help me please
it’s past due
The measure of the ∠d is 65 degrees.
The measure of the ∠c is 89 degrees.
The measure of the arc a is 131 degrees.
The measure of arc b is 47 degrees.
How to determine the valuesThe value of each variable. For the circle, the dot represents the center.
1. The measure of ∠d is;
∠d+ 115°= 180°
∠d= 180°-115°= 65°
The measure of the ∠d is 65 degrees.
2. The measure of ∠c is,
∠c+ 91°= 180°
∠c =180°-91° =89°
The measure of the ∠c is 89 degrees.
3. The measure of arc a is,
The inscribed angle measures half that of the arc comprising;
arc a = 230 - 90
arc a = 131 degrees
4. The measure of arc b is,
The inscribed angle measures half that of the arc comprising;
arc b = 178 - 131
arc b = 47 degrees
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Please help me please only answer if correct
The value of x in the triangle is 9, the volume of the cylinder is 1272.3 yd³ and the volume of the sphere is 268.1 mi³.
What is the numerical value of x in the triangle?To solve for the value of x in the triangle, we use ratio:
[tex]\frac{20}{20 + 16}=\frac{45}{45 + 3x + 9}[/tex]
Simplify and solve for x:
20/36 = 45/(3x + 54 )
Cross mulltiply:
20( 3x + 54 ) = 36 × 45
60x + 1080 = 1620
60x = 1620 - 1080
60x = 540
x = 540/60
x = 9
Therefore, the value of x is 9.
Option A) 9 is the correct answer.
Question 2)
Height of ctlinder h = 5 yd
Diameter = 18 yd
Radius = diameter/2 = 18/2 = 9 yd
Volume of cylinder = π × (radius)² × height
Volume = π × 9² × 5
Volume = 1272.3 yd³
Therefore, the volume of the cylinder is 1272.3 yd³.
Option B) 1272.3 yd³ is the correct ansswer.
Question 3)
Radius of the sphere r = 4 mi
Volume = ?
Volume = 4/3 × π × ( radius )³
Volume = 4/3 × π × ( 4 )³
Volume = 268.1 mi³
Therefore, the volume of the sphere is 268.1 mi³.
Option B) 268.1 mi³ is the correct answer.
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Determine the equations of the following lines:
1. Parallel to x -3y = 9 and passing through the point (2;6)
2. Perpendicular to y + 1/4x -5 = 0 and passing though that point (-3;5)
Answer:
1) x - 3y = -16
2) 4x - y = -17
Step-by-step explanation:
Question 1To determine the equation of a line that is parallel to x - 3y = 9 and passes through the point (2, 6), we first need to find the slope of x - 3y = 9.
To do this, rearrange the equation so that it is in slope-intercept form.
Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.
[tex]\begin{aligned}x-3y&=9\\x-3y+3y-9&=9+3y-9\\x-9&=3y\\3y&=x-9\\y&=\dfrac{1}{3}x-3\end{aligned}[/tex]
Therefore, the slope of the given line is 1/3.
Parallel lines have the same slope.
Therefore, to find the equation of the parallel line that passes through point (2, 6), substitute m = 1/3 and the point (2, 6) into the point-slope formula:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\\implies y-6&=\dfrac{1}{3}(x-2)\end{aligned}[/tex]
Rearrange to standard form Ax + By = C (where A is positive):
[tex]\begin{aligned}y-6&=\dfrac{1}{3}(x-2)\\3y-18&=x-2\\-18&=x-3y-2\\x-3y&=-16\end{aligned}[/tex]
Therefore, the equation of the line in standard form that is parallel to x - 3y = 9 and passes through the point (2, 6) is:
[tex]\boxed{x-3y=-16}[/tex]
[tex]\hrulefill[/tex]
Question 2To determine the equation of a line that is perpendicular to y + 1/4x - 5 = 0 and passes through the point (-3, 5), we first need to find the slope of y + 1/4x - 5 = 0.
To do this, rearrange the equation so that it is in slope-intercept form.
Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.
[tex]\begin{aligned}y + \dfrac{1}{4}x - 5 &= 0\\y&=-\dfrac{1}{4}x+5 \end{aligned}[/tex]
Therefore, the slope of the given line is -1/4.
The slopes of perpendicular lines are negative reciprocals.
Therefore, the slope of the perpendicular line is 4.
Therefore, to find the equation of the perpendicular line that passes through point (-3, 5), substitute m = 4 and the point (-3, 5) into the point-slope formula:
[tex]\begin{aligned}y-y_1&=m(x-x_1)\\\\\implies y-5&=4(x-(-3))\end{aligned}[/tex]
Rearrange to standard form Ax + By = C (where A is positive):
[tex]\begin{aligned}y-5&=4(x-(-3))\\y-5&=4(x+3)\\y-5&=4x+12\\-5-12&=4x-y\\4x-y&=-17\end{aligned}[/tex]
Therefore, the equation of the line in standard form that is perpendicular to y + 1/4x - 5 = 0 and passes though point (-3, 5) is:
[tex]\boxed{4x-y=-17}[/tex]
if the percentage difference was 34.846% and the number of voters were 3066649 in 2016, calculate the number of registered voters (A) in 2011
Answer:
Step-by-step explanation:
convert an effective rate of 14,5% per annum, to a nominal rate per annum compounded half yearly
The nominal rate per annum compounded half-yearly, equivalent to an effective rate of 14.5% per annum, is approximately 14.900625%.
To convert an effective rate to a nominal rate compounded half-yearly, we can use the formula:
Nominal rate [tex]= (1 + r/m)^m - 1[/tex]
Where:
r = effective rate
m = number of compounding periods per year
In this case, the effective rate is 14.5% per annum, and we want to convert it to a nominal rate compounded half-yearly.
Since compounding is done semi-annually, m would be 2.
Plugging in the values:
Nominal rate [tex]= (1 + 0.145/2)^2 - 1[/tex]
Simplifying the expression inside the parentheses:
Nominal rate [tex]= (1 + 0.0725)^2 - 1[/tex]
Calculating the exponent:
Nominal rate [tex]= (1.0725)^2-1[/tex]
Performing the calculations:
Nominal rate = 1.14900625 - 1
Nominal rate = 0.14900625
Converting the nominal rate to a percentage:
Nominal rate = 14.900625%
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50 students are asked whether they like English, History or Geography.3 students like none of them,25 like English,25 like History and 11 like Geography,2 like English and history only,2 like Geography and history only.No student like English and geography. (A) represent the information in a venn diagram (B) use the ven diagram to calculate how many students like all three
Answer:
history Is a good subject
Two snails have shells that are similar in shape. The younger snail has a shell with a height of 3.9 centimeters and a volume of 3 cubic centimeters. The older snail has a shell with a volume of 10 cubic centimeters. Estimate the height of the older snail’s shell. Round your answer to the nearest tenth.
can someone pls answer this asap and show ur work
The estimated height of the older snail's shell is approximately 13 centimeters.
To estimate the height of the older snail's shell, we can use the concept of proportional relationships between the heights and volumes of the snail shells.
Let's denote the height of the older snail's shell as "h" (in centimeters). We can set up a proportion based on the relationship between the heights and volumes of the snail shells:
(height of younger snail) / (volume of younger snail) = (height of older snail) / (volume of older snail)
Substituting the given values:
3.9 / 3 = h / 10
To solve for "h," we can cross-multiply and then divide:
3 * h = 3.9 * 10
3h = 39
h = 39 / 3
h ≈ 13
The estimated height of the older snail's shell is approximately 13 centimeters.
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A store owner wishes to make a new tea with a unique flavor by mixing black tea and oolong tea. If he has 35 pounds of oolong tea that sells for $2.40 per pound, how much black tea worth $1.80 per pound must he mix with it so that he can sell the final mixture for $2.10 per pound?
Answer:
Step-by-step explanation:
To solve this problem, we can use the following formula:
(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture
Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.
We know that:
The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.
The store owner wants to sell the final mixture for $2.10 per pound.
The black tea is worth $1.80 per pound.
Using the formula above, we can write:
(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10
Simplifying this equation, we get:
84 + 1.8x = 73.5 + 2.1x
0.3x = 10.5
x = 35
Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.
I hope this helps! Let me know if you have any other questions.
Answer:
Step-by-step explanation:
Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.
The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:
Cost of oolong tea = 35 pounds × $2.40/pound = $84
The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:
Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x
Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:
$73.5 + $2.10x = $84
Now, let's solve for x to find the amount of black tea needed:
$2.10x = $84 - $73.5
$2.10x = $10.5
x = $10.5 / $2.10
x ≈ 5
Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.
There is a math oriented pizza restaurant that advertises their slices based on arc measurement and pie radius . Recently they had a lunch special for a Personal Pie with a radius of 4 inches . What would the area of a 135 slice of pizza be? Round your answer to the nearest hundredth.
The area of a 135 slice of pizza be,
⇒ 6,782.41 inches²
We have to given that;
Recently they had a lunch special for a Personal Pie with a radius of 4 inches .
Since, WE know that;
Area of circle is,
A = πr²
Where, r is radius of circle
Here, Radius of circle = 4 inches
Hence, Area of pizza is,
⇒ A = 3.14 x 4²
⇒ A = 50.24 inches²
Hence, the area of a 135 slice of pizza be,
⇒ 50.24 × 135
⇒ 6,782.41 inches²
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1. At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tor bought two pairs of gloves and two hats for
930.00. Find the prices of the hats and gloves.
(k pL.)
Let x-
Let v=
(pt.)
2. Aaliyah invested $10,000 in two mutual funds.
One of the funds rose 6% in one year, and the other rose 906 in one year. Aaliyah's investment rose a total of S684 in one vear. Find the amount she invested in each fund.
1. The price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.
2. Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.
1. Let's assume the price of a pair of gloves is represented by 'x' and the price of a hat is represented by 'y'.
From the given information, we can establish the following equations based on Cody and Tor's purchases:
Equation 1: 2x + 4y = 43.00 (Cody's purchase)
Equation 2: 2x + 2y = 30.00 (Tor's purchase)
To solve this system of equations, we can use a method like substitution or elimination.
Using the substitution method, we can rearrange Equation 2 to express x in terms of y:
2x = 30.00 - 2y
x = 15.00 - y
Now, we substitute this value of x into Equation 1:
2(15.00 - y) + 4y = 43.00
30.00 - 2y + 4y = 43.00
2y = 43.00 - 30.00
2y = 13.00
y = 6.50
Substituting this value of y back into Equation 2 to find x:
2x + 2(6.50) = 30.00
2x + 13.00 = 30.00
2x = 30.00 - 13.00
2x = 17.00
x = 8.50
Therefore, the price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.
2. Let's assume Aaliyah invested an amount represented by 'x' in the mutual fund that rose 6% and an amount represented by 'y' in the mutual fund that rose 9%.
From the given information, we can establish the following equations based on the rise in investment:
Equation 1: 0.06x + 0.09y = 684 (rise in investment)
Equation 2: x + y = 10,000 (total investment)
To solve this system of equations, we can use a method like substitution or elimination.
Using the substitution method, we can rearrange Equation 2 to express x in terms of y:
x = 10,000 - y
Now, we substitute this value of x into Equation 1:
0.06(10,000 - y) + 0.09y = 684
600 - 0.06y + 0.09y = 684
0.03y = 84
y = 2800
Substituting this value of y back into Equation 2 to find x:
x + 2800 = 10,000
x = 10,000 - 2800
x = 7200
Therefore, Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.
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HELP PLEASE 30 POINTS
Four transformations of the function f(x)=4x
are given below.
For each transformation, drag the expression that shows the result of that transformation into the box under it.
The expression that shows the result of that transformation are:
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
The given function is f(x) =4ˣ.
We have to find the transformations applied to the function f(x).
Graph transformation involves modifying an existing graph or graphed equation to create a different version of the original graph.
f(x) =4ˣ
We have to find 3f(x), f(3x), f(x+3) and f(x)+3.
3f(x) = 3.4ˣ
f(3x)=4³ˣ
f(x+3)=4ˣ⁺³
f(x)+3=4ˣ+3.
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if instead the triangle on the left had the same area as the circle on the right
If the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.
If the triangle on the left had the same area as the circle on the right, it would mean that the triangle would have to be larger than its current size. This is because the area of a circle is determined by the formula A=πr^2, where r is the radius of the circle.
Therefore, if the area of the circle is equal to the area of the triangle, the radius of the circle would have to be equal to the height of the triangle, and the base of the triangle would need to be wider.
This would result in a larger triangle with a greater surface area than the current triangle. The larger triangle would also have a longer perimeter, which would make it more difficult to enclose and would require more material to construct.
Additionally, the larger triangle would have a higher center of gravity, which could make it more difficult to balance and more prone to tipping over.
Overall, if the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.
It is important to consider both the area and the shape of an object when determining its practicality and effectiveness in a given situation.
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The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x =
The value of x from the given similar triangles is 10 units.
The given triangles are similar.
Here, 3x/(4x+2) = 20/28
3x/(4x+2) = 5/7
7×3x = 5(4x+2)
21x=20x+10
21x-20x=10
x=10 units
Therefore, the value of x from the given similar triangles is 10 units.
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Match the prompts together.
When matched, the prompts on asymptotes would be:
Vertical asymptote at x=0: The cost of producing pills can never reach 0.Decreasing on (0,∞): As the number of pills produced gets smaller, the average cost of production greatly increases.Horizontal asymptote at y=0: The cost of producing pills cannot be negative.Positive on (0,∞): As more pills are produced, the average cost per pill decreases.How to match the asymptote statements ?The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.
This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.
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Prompt:
A researcher wants to answer 2 research questions related to Americans level of trust
The researcher is using the General Social Survey which has the following questions:
Generally speaking, would you say that people can be trusted or that you can't be too careful in dealing with people? The response options for this variable are (Always trusted, Usually trusted, Usual not trusted, Always not trusted)
This trust variable is coded in the dataset with the name “cantrust”
In addition, in its demographic questions the GSS asks respondents to state their highest education degree achieved. The response options for this variable are: high school or less- college or higher. This educational attainment variable is coded “college” in the dataset.
Research question #1: What percentage of Americans believe strangers can always be trusted?
Create a frequency distribution table for the variable “cantrust”. Make sure you filter out all nonvalid responses (i.e. responses coded “IAP” or “NA” or are “Blank”).
Create and show a (relative) frequency distribution table
Create and show a pie chart with the distribution of responses
State what percentage of respondents say strangers can be “always trusted”?
Calculate and interpret the 95% confidence margin of error for the proportion of Americans that answer strangers can “always be trusted”
Calculate and interpret the 95% confidence interval and make a statement of what proportion of Americans say strangers can “always be trusted”
Explain why we go through the trouble of calculating margin of errors and confidence intervals.
The solution to all parts is shown below.
First, let's filter out all non-valid responses, such as "IAP" (Inapplicable), "NA" (Not Applicable), or "Blank."
Frequency distribution table for the variable "can trust":
| Response | Frequency |
| Always trusted | x |
| Usually trusted | y |
| Usually not trusted | z |
| Always not trusted | w |
Relative frequency distribution table for the variable "cantrust":
| Response | Relative Frequency |
| Always trusted | x/n |
| Usually trusted | y/n |
| Usually not trusted | z/n |
| Always not trusted | w/n |
Pie chart with the distribution of responses:
To find the percentage of respondents who say strangers can be "always trusted," we calculate the relative frequency or proportion for the "Always trusted" category.
Percentage of respondents who say strangers can be "always trusted"
= (x/n) x 100%
Now, let's calculate the 95% confidence margin of error for the proportion of Americans who answer strangers can "always be trusted":
Margin of error = (z-score) (standard error)
The z-score depends on the desired confidence level. For a 95% confidence level, the z-score is approximately 1.96.
The standard error can be calculated as:
Standard error = √[(p (1 - p)) / n]
Once we have the margin of error, we can calculate the 95% confidence interval as follows:
Confidence interval = p ± margin of error
The confidence interval provides a range within which the true proportion of Americans who say strangers can be "always trusted" is likely to fall.
By interpreting margin of errors and confidence intervals is essential because survey data is collected from a sample rather than the entire population.
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