( 1 ) If p varies directly as q, for p = 4.5 when q = 12, then the relationship between p and q is p = kq represented as 4.5 = (8/3)12
( 2 ) If p and q is 16 then the direct variation is 1
What is direct variation?Any time one quantity directly affects the other, such as when one quantity rises relative to the other and vice versa, there is a direct variation between the two variables. It is the relationship between two variables where one of the variables is a fixed multiple of the other. Since the two variables are directly correlated, they are also known as directly proportional.
There are two kinds of proportionalities: direct variation and inverse variation. When two quantities are multiplicatively connected by a constant, the relationship is said to be proportional. In a direct variation, the ratio of the two quantities stays the same, whereas in an inverse variation, the product of the two quantities stays the same.
If p varies directly as q
for p = 4.5
when q = 12
Then p = kq
4.5 = 12k
k = 12/4.5
k = 8/3
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Given ΔABC with m∠B = 62°, a = 14, and c = 16, what is the measure of A? Use the law of cosinus.
Given data,
[tex]\begin{gathered} \angle B=62 \\ a=14\text{ } \\ c=16 \end{gathered}[/tex]Use the law of cosines.
[tex]\begin{gathered} b^2=a^2+c^2-2acCos(B) \\ b^2=14^2+16^2-(2\times14\times16\times Cos(62)) \\ b^2=196+256-210.32 \\ b^2=241.68 \end{gathered}[/tex]Thus, the value of b is
[tex]b=15.54[/tex]The cosines formula for angle A isThus, angle A will be
[tex]a^2=b^2+c^2-2bcCos(A)[/tex][tex]\begin{gathered} A=cos^{-1}\lbrack\frac{b^2+c^2-a^2}{2bc}\rbrack \\ A=\cos ^{-1}\lbrack\frac{15.54^2+16^2-14^2}{2\times15.54\times16}\rbrack \\ A=52.67 \end{gathered}[/tex]Therefore, angle A is 52.67 degrees.
The length of a rectangular picture frame is 28 inches and its perimeter is 84 inches. What is the width of the picture frame? *
The perimeter of a rectangle can be calculated using the following formula:
[tex]P=2w+2l[/tex]Where
"w" represents the width of the rectangle
"l" represents the length of the rectangle
If you know the perimeter and length of a rectangle, you can use the formula to determine the width. The first step is to write the formula for the width:
-Pass 2l to the left side of the expression by applying the opposite operation to both sides of it:
[tex]P-2l=2w[/tex]-Divide both sides by 2
[tex]\begin{gathered} \frac{P-2l}{2}=\frac{2w}{2} \\ \frac{P-2l}{2}=w \end{gathered}[/tex]Now that we have determined a formula for w, replace the value of the length and perimeter and calculate the width:
P=84in
l=28in
[tex]\begin{gathered} w=\frac{84-2\cdot28}{2} \\ w=\frac{84-56}{2} \\ w=\frac{28}{2} \\ w=14 \end{gathered}[/tex]The width of the rectangular frame is 14 inches long
For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).If it does, find the constant of variation and write it in simplest form.3r - 81 = -7O Direct variation ( K =__)O Not direct variation10y = -5xO Direct variation ( K =__)O Not direct variation-Picture included-
Given:
The equations are given as,
[tex]\begin{gathered} 3x-8y=-7 \\ 10y\text{ = -5x} \end{gathered}[/tex]Required:
Direct and inverse variation verification.
Explanation:
(a) The equations are given as follows:
[tex]3x-8y\text{ = -7}[/tex]On simplifying further,
[tex]3x\text{ = 8y - 7}[/tex]The given equation is not a direct variation.
(b) The equation is given as,
[tex]\begin{gathered} 10y\text{ = -5x} \\ -5x\text{ = 10y} \\ x\text{ = -2y } \end{gathered}[/tex]The given equation represents inverse variation.
Answer:
Thus the required result is,
a) Not a direct variation
b) A direct variation( k = -2)
Sidney has $85,450 in a savings account. The interest rate is 12% per year and is not
compounded. How much will she have in total in 1 year?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years.
The amount that Sidney will have in her account in 1 year is $ 95,704.
Given that:-
Principal amount = $85,450
Interest Rate = 12 % per annum
i = prt
Where,
i represents interest,
p represents the principal,
r represents the interest rate, and
t represents the time (in years)
Hence, putting the values in the formula of simple interest, we get,
i = 85450*(12/100)*1 = $ 10,254
Hence, the amount that Sidney will have in her account in 1 year is
85450 + 10254 = $ 95,704
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Which expression is equivalent to 2 log4 x + 3 log4 y – 5 log4 z?
log base 4 of the quantity x squared y cubed all divided by z to the fifth end log
log base 4 of the quantity x squared z to the fifth all divided by y cubed end log
log base 4 of the quantity x times y to the fifth all divided by z to the fifth end log
log base 4 of the quantity xy divided by z end log
The expression equivalent to [tex]2 log_4 x + 3 log_4 y - 5 log_4 z[/tex] is the first option that is [tex]log_4(\frac{x^2y^3}{z^5} )[/tex].
Logarithms
A logarithm of a number with a base is equal to another number. A logarithm is just the opposite function of exponentiation.
For example, if [tex]10^2 = 100[/tex] then [tex]log_{10} 100 = 2[/tex].
In a log function of the form [tex]log_ab=x[/tex] ,
a is the base of the log
b is the argument of the log and,
x is the real number
It is the most convenient way to express large numbers.
The properties of logarithms are,
1) [tex]xlog_ab =log_ab^x[/tex]
2) [tex]log_ab-log_ac=log_a(\frac{b}{c} )[/tex]
Hence,
According to 1) , we can write,
[tex]2 log_4 x =log_4x^2\\3 log_4 y = log_4y^3\\ 5 log_4 z = log_4z^5[/tex]
According to 1) and 2), we can write,
[tex]2 log_4 x + 3 log_4 y - 5 log_4 z= log_4(\frac{x^2y^3}{z^5} )[/tex]
Hence, the answer is the first option.
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Please help me I’m miserable because I was sick.It’s 2:00AM and this is due at 8 somebody please help me and x does not equal 12 and D isn’t 95?
Here are some tips that may help you feel better:
1. Rest: Get plenty of sleep and rest as much as possible to allow your body to recover.
2. Hydration: Drink lots of fluids to stay hydrated and help flush out any toxins in your body.
3. Nutrition: Eat healthy foods that are easy to digest, such as soups, broths, and fruits.
4. Medication: Take any prescribed medication as directed and follow the instructions on the label.
5. Warmth: Use warm blankets and a hot water bottle to soothe aches and pains.
6. Avoiding stress: Stay away from stress as much as possible since it can interfere with your immune system's functioning.
7. Humidifier: Use a humidifier to help ease congestion and dryness in the air.It's also essential to see a doctor if your symptoms persist or worsen. Don't hesitate to seek medical attention if necessary.
Furthermore, the information given in the question, "x does not equal 12 and D isn't 95," seems unrelated to the context of the problem. It's unclear what information the question is asking for, so please provide more details if you have any.
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A) There are two parallel lines and a line that goes through them in this diagram. The line that goes through them causes perpendicular lines to form.
What are perpendicular lines?
Perpendicular lines are lines that intersect and create 90° angles. The two angles in this diagram are 90° due to this intersection.
B) There are two types of angles: supplementary and complementary: complementary angles are angles whose measurements add up to 90°. Supplementary angles are angles whose measurements add up to 180°. As you can see in this problem, the two angles (7x+11 and -1+8x) are 90°. When added they would equal 180°. These angles are supplementary.
C) Now that you know what supplementary angles are, you can use its characteristics to solve for x:
Since the two angles added up equal 180, write an equation that represents this: (7x+11) + (-1+8x) = 180Now, combine like terms: 10 +15x= 180Subtract both sides by 10: 15x= 170Divide both sides by 15 and you have your answer: x= 11.33D) Now, solve for the two equations by plugging in x [you final answers should be 90]:
(7x+11) = 7(11.33) +11 = 90.31 ≈ 90(-1+8x) = -1 + 8(11.33) = 89.65 ≈ 90
255 divided by 13 and reaminre
A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 2 of the next 5 vehicles are from out of state? (Round to 4 decimal places )
Using combinations, we concluded that the probability that fewer than 2 of the next 5 vehicles are from out of state is 0.907.
A checkpoint sees 75% of its traffic coming from within the state.
Therefore, there is a 0.75 percent chance that the car comes from the state.
1-0.75=0.25 represents the likelihood that the car is from outside the state.
Let x now act as the random variable. Consequently, n=9 and X=4
It is necessary to determine the likelihood that less than 2 of the following 5 automobiles are from another state.
We are to calculate the probability of x<2
p=0.25
q=0.75.
Using the formula,
P(x≤2) = ∑ ⁿCₓ pˣ q⁽ⁿ⁻ˣ⁾
P(x≤2) = ∑ ⁵C₂ p² q³ + ⁵C₁ p¹ q⁴ + ⁵C₀ p⁰ q⁵
P(x≤2) = ∑ [tex]\frac{5!}{2! 3!}[/tex] (0.25)² (0.75)³ + [tex]\frac{5!}{1! 4!}[/tex] (0.25)¹ (0.75)⁴ + [tex]\frac{5!}{0! 5!}[/tex] (0.75)⁵
P(x≤2) = 10 × 0.065 × 0.421875 + 5 × 0.25 × 0.3164 + 0.2373
P(x≤2) = 0.2742 + 0.3955 + 0.2373
P(x≤2) = 0.907
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the 4 winning numbers in a swimming club lottery were called out as follows the 1st number is the square root of 576 the 2nd number is a multiple of 8 between 30 and 39 the 3rd number is the cube of 3 the 4th number is the largest prime number less than 40 what we’re the 4 winning numbers?
The four winning numbers are 24, 32, 27 and 37 respectively
How to determine the numbersIt is important to note the following;
A prime number is a number than is divisible by 1 and itselfA square root is defined as the factor of a number which when multiplied by itself would give back the original numberThe cube of a number is that number to the exponent or power of 3A multiple is defined as the product of an integer, element or quantityFrom the information given;
a. First number = square root of 576
This is represented as
First number = √576
First number = 24
b. Second number = multiple of 8 between 30 and 39
Second number = 32
c. Third number = cube of 3
This is represented as;
Third number = 3³
Third number = 37
d. largest prime number less than 40
Fourth number = 37
Hence, the numbers are 24, 32, 27 and 37
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For the function f(x)=x2−8x+11, find x when f(x)=−4.(Use a comma to separate multiple solutions.)
Given function:
[tex]f(x)=x^2-8x+11[/tex]Finding x when f(x) = -4
[tex]x^2-8x+11=-4[/tex][tex]\begin{gathered} x^2-8x+15=0 \\ x^2-5x-3x+15=0 \end{gathered}[/tex][tex]\begin{gathered} x(x-5)-3(x-5)=0 \\ (x-3)(x-5)=0 \\ x=3,5 \end{gathered}[/tex]Thus, the value of x is 3 and 5.
Several members of a running club would like to survey the rest of the members to determine which 5K races the club should enter. They decide to use a random number table to sample 10 of the 78 members. The members are assigned the numbers 01–78. Refer to the given line from a random number table. Which numbers represent the first 5 members selected?
24000 75983 62200 91518 11198 88936
(A)24, 07, 59, 62, 20
(B)24, 00, 07, 59, 83
(C)24, 75, 36, 22, 51
(D)24, 75, 98, 36, 22
The numbers that represent the first 5 members selected is A. 24, 07, 59, 62, 20.
How to illustrate the information?From the information, the members of a running club would like to survey the rest of the members to determine which 5K races the club should enter.
In this case, they decide to use a random number table to sample 10 of the 78 members. The numbers illustrated are 24000 75983 62200 91518 11198 88936.
Therefore, the appropriate numbers chosen will be (24) 000 (7) (59) 83 (62)(20)0.
The correct option is A.
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Find the missing side length.Assume that all intersecting sides meet at right angles.Be sure to include the correct unit in your answer.4 yd8 yd14 yd12 yd?16 yd
For the given figure, all the intersecting sides meet at right angles
The lengths of the vertical sides are 14, 8, and ?
Let the missing side = x
So,
[tex]14=8+x[/tex]so,
[tex]x=14-8=6[/tex]so, the answer will be the length of the missing side = 6 yd
What’s the correct answer answer asap for brainlist
The option that is unique to only skeletal muscle is Option(B.) They can fatigue with too much movement or exercise.
Why do skeletal muscles get fatigued after heavy exercise?When muscles become fatigued, they provide less force over time.The skeletal muscles that move the bones in the body can become exhausted from overuse.Oxygen levels in the muscles are depleted by overexertion, such as intense exercise.In order to produce energy, the muscles briefly switch to anaerobic metabolism. Lactic acid and energy are produced in order to accomplish this. Muscle weariness results from lactic acid buildup in the muscles.Intracellular acidosis, which is mostly caused by lactic acid buildup, has been identified as the most important contributing factor to skeletal muscle weariness.To learn more about skeletal muscles visit:
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The angle of elevation of the top of a building from a point 80m away on level ground
is 25 0 . Calculate the height of the building to the nearest metre.
The height of the building to the nearest meter is 38 m.
In the question ,
it is given that
distance between the point and building is 80m
and the angle of elevation from the point to the top of the building is 25°
the figure formed from the data is shown below ,
where AB (h)is the height of the building .
So , From triangle ABC
tan25° = AB/BC
tan25° = h/80
simplifying further
we get ,
h = 80*tan25°
h = 80*(0.466)
h = 37.28
h ≈ 38
Therefore , The height of the building to the nearest meter is 38 m.
The given question is incomplete , the complete question is
The angle of elevation of the top of a building from a point 80m away on level ground is 25° . Calculate the height of the building to the nearest meter.
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profit is defined as earnings less expenses (earnings - expenses). At the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the festival's organizers for a vendor permit. Use the expression m=2p - 0.75p - 50 to answer the following questions.
The amount that will be made by the local festival given the expression m=2p - 0.75p - 50 is 225.
How to calculate the profit?From the information, at the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each.
The expression given was illustrated as:
m=2p - 0.75p - 50
Therefore since we are given the value of p as 220. This will be:
m=2p - 0.75p - 50
m = 2(220) - 0.75(220) - 50
m = 440 - 165 - 50
m = 440 - 215
m = 225
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At the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the festival's organizers for a vendor permit. Use the expression m=2p - 0.75p - 50 to answer the following questions.
Find the profit when the number of the ice cream pops represented by p is 220.
…Ajavsbyhsbwdujdnwiowbeuhsbwb
Answer:
alphabet
Step-by-step explanation:
Do exactly what it says and make sure u make the table of values
olution
2a.
The graph of as described is given below (showing at least five points)
The (clear) graph that has the dashed line of asymptotes
The table will be
Bb.
o write the equation
We start from
[tex]f(x)=2^x[/tex]Translate the graph up by 3 units
[tex]f(x)=2^x+3[/tex]Translate the graph 4 units to the left
[tex]f(x)=2^{x+4}+3[/tex]2c.
o get the equation of asymptotes
[tex]\begin{gathered} \lim _{x\to-\infty}f(x)=\lim _{x\to-\infty}(2^{x+4}+3)=0+3=3 \\ \text{The equation of asymptotes} \\ y=3 \end{gathered}[/tex]Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. 3, 4+i
(Please answer soon as possible thank you)
By algebra properties, the standard form with rational coefficients is the polynomial x³ - 11 · x² + 7 · x + 51, whose lead coefficient is 1 and comprise the roots 3 and 4 + i.
How to determine a polynomial of least degree
A polynomials of least degrees includes all the roots and the given lead coefficient, which can used in the following formula:
p = a · Π (x - rₐ)
Where:
a - Lead coefficientrₐ - a-th root of the polynomial.If we know polynomial has rational coefficients, then the complex root 4 + i has a "twin" equal to 4 - i in accordance with the quadratic formula, otherwise the polynomial will have at least an irrational coefficient. Then, the least degree polynomial is introduced below:
p = 1 · (x - 3) · (x - 4 - i) · (x - 4 + i)
Then, we expand the expression by algebra properties:
p = (x - 3) · [x² - 8 · x - (16 - i²)]
p = (x - 3) · (x² - 8 · x - 17)
p = x³ - 8 · x² - 17 · x - 3 · x² + 24 · x + 51
p = x³ - 11 · x² + 7 · x + 51
The standard form is the polynomial p = x³ - 11 · x² + 7 · x + 51.
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If 3^5 = x, which of the following expressions is equal to 3^11?
A) 243x
B) 3x^2
C) 9x^4
D) x^4
Answer:
b
Step-by-step explanation:
because it is tht simpl
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Which numbers are solutions of 4p+6<3p? Choose exactly two answers that are correct
Answer: -12 and -9
Step-by-step explanation:
4p + 6 <3p
4p - 3p < -6
p < -6
So, -12 < -6 is CORRECT
-9 < -6 is CORRECT
-6 is not less than -6 SO THIS IS INCORRECT
6 is not less than -6 so this is INCORRECT
lessons cost $3 for members and $5 for non-members if twice as many members as non-members takes lessons and the total fees collected are $132 how many non-members take lessons?
The number of non-members is 12 and the number of members is 24.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the number of members, and the number of non-members.
3x + 5y = 132
x = 2y
After solving the above two linear equations:
6y + 5y = 132
11y = 132
y = 132/11
y = 12 non-members
x = 24 members
Thus, the number of non-members is 12 and the number of members is 24.
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Help,,,,,,,,,,,,,,,,,,,,,
Need help answering these columns, if more info is needed then i will edit the post to fit it so there's enough information
Applying the definition of the midpoint of a line and other properties, the proof that shows that AC ≅ CD is shown in the image attached below.
What is the Midpoint of a Line?A line is divided into two equal parts by its midpoint. Thus, the midpoint of that line is that point where the line segment is bisected into two parts that are equal.
Given the image showing two lines that intersect each other at point C, the proof below shows that AC is congruent to CD:
1. C is the midpoint of line AE
C is the midpoint of line BD
AE is congruent to BD
(Reason: Given)
2. AC = CE; BC = CD
(Reason: Definition of midpoints)
3. AE = BD
(Reason: Definition of congruent segments)
4. AE = AC + CE;
BD = BC + CD
(Reason: Segment addition property)
5. AC + CE = BC + CD
(Reason: substitution property)
6. AC + AC = BC + BC
(Reason: substitution property)
7. 2AC = 2BC
(Reason: Simplify)
8. AC = CD
(Reason: division property)
9. AC ≅ CD
(Reason: definition of congruent segments).
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The graph of the derivative of a function, f, is shown. Use the graph to determine the interval on which f is increasing.
A. (-∞, 2)
B. (2, ∞)
C. (-∞, ∞)
D. (-1, ∞)
E. (-∞, 1)
Answer:
B) [tex](2,\infty)[/tex]
Step-by-step explanation:
Since we are given the graph of [tex]f'(x)[/tex], this gives us the value of the derivative, or the rate of change, of [tex]f(x)[/tex] given an x-value. For [tex]f(x)[/tex] to be increasing, then [tex]f'(x) > 0[/tex], which is a positive rate of change. As you may have noticed, when [tex]x > 2[/tex], the value of [tex]f'(x)[/tex] is positive. This means that f increases on the interval [tex](2,\infty)[/tex], or answer B.
How do you do multiplication? Give complete reasons and complete answers please.
Answer:
Step-by-step explanation:
Multiply like this
2 x 2
How to do this
Just double 2
Answer:
multiplication is like doing repeated addition so let’s try doing 5x5
In repeated addition form it would be 5+5+5+5+5 which equals 25
I don’t know how to really explain it but I hope this helps!
Step-by-step explanation:
Plot function h on the graph.
H(x) = {-4, x<-3
x>-3
x+5,
Given the function is plotted on the graph and attached below.
You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.
To: Determine whether a graph reflects a function using the vertical line test. Check the graph to check if any vertical lines that were generated would repeatedly cross the curve. If such a line exists, the graph does not depict a function.
Hence the required graph is created .
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in a residential neighborhood, the distribution of house valies is Unimodal and skewed to the right, with a median of $200,000 and an IQR of $100,000. for which of the following sample sizes is the sample median most likely to be above $250,000?A. n=10B. n=50C. n=100D. n=1000E. impossible to determine without more information
The smaller the sample size the greater the variability and higher the chance of getting an overestimate
From the given data
Median = $200,000
IQR = $100,000
The sample size for the median above to $250,000 is n =10
Because n=10 shows a sample with the fewest values, it is most likely that the sample median will be farther from the true median.
Answer : A) n = 10
the digram shows a triangle
Answer:
30 cm²Step-by-step explanation:
Area of triangle = 1/2 (base × height)
1/2(12*5)=
1/2*60=
30 cm²
Out of 250 racers who started the marathon, 217 completed the race, 24 gave up, and 9 were disqualified. What percentage did not complete the marathon? Round your answer to the nearest tenth of a percent.
Answer:
209 out of 230 completed that is 209/230 x 100% = 90.869 % the rest did NOT complete 100% - 90.8% = 9.13 %
TRUE OR FALSE?
For two setsA and B, (A U B)' = A' n B'.
The statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.
Let us check it with the help of an example.
Let A = {1,2,3,4,5,6} ,
B = {5,6,7,8,9,10} and ,
A universal set S = {1,2,3,4,....,15}
Now, we can write,
A ∪ B = {1,2,3,4,5,6,7,8,9,10}
LHS = (A ∪ B)' = {11,12,13,14,15}
A' = {7,8,9,10,11,12,13,14,15}
B' = {1,2,3,4,5,11,12,13,14,15}
RHS = A' ∩ B' = {7,8,9,10,11,12,13,14,15} ∩ {1,2,3,4,5,11,12,13,14,15} = {11,12,13,14,15}
As we can observe from above,
LHS = RHS
Hence, the statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.
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