Answer:
[tex]y=-2.5x+8[/tex]
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. So, first, transform the given equation into the slope-intercept form, [tex]y=mx+b[/tex].
[tex]5x+2y=6[/tex]
[tex]2y=-5x+6[/tex]
[tex]y=-\frac{5}{2} x+3[/tex]
Then, determine the equation of a line that has a slope of [tex]-\frac{5}{2}[/tex] and passes through (1, 5.5). Substitute all the known values and solve for b.
[tex]y=mx+b[/tex]
[tex]5.5 = -\frac{5}{2} *1+b[/tex]
[tex]5.5=-2.5+b[/tex]
[tex]b=8[/tex]
Therefore, the answer is [tex]y=-2.5x+8[/tex].
Question Find the area of a trapezoid whose height is 6 ft and whose bases are 9.7 ft and 6.3 ft.
Answer:
48 Square feet
Step-by-step explanation:
A=((a+b)/2)*h,
((6.3+9.7)/2)*6=48ft^2
"The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200, with 200 being the highest level of motivation. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 30 students who are at least 29 years of age, and their mean was 135.2"
Calculate the observed test statistic (Zobt or Tobt) for hypothesis test. Round up to the second decimal place.
Using the z-distribution, the observed test statistic is given as follows:
z = 3.69.
What are the hypothesis tested?At the null hypothesis, it is tested if older students have the same mean as the general population, that is:
[tex]H_0: \mu = 115[/tex]
At the alternative hypothesis, it is tested if they have a greater mean, that is:
[tex]H_0: \mu > 115[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are:
[tex]\overline{x} = 135.2, \mu = 115, \sigma = 30, n = 30[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{135.2 - 115}{\frac{30}{\sqrt{30}}}[/tex]
z = 3.69.
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What is the equation of the line in slope-intercept form?
[tex]y=\frac{3}{5}x+3[/tex]
Step-by-step explanation:Slope-intercept form is the most common form of a linear function.
Formula
The formula for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept. In this question, we must find both m and b by looking at a graph.
Slope
The slope is the change in y over the change in x. So, one way to find the slope is to identify 2 points on the graph and count the difference between them.
For example, the points (-5,0) and (0,3). First, the y-value increases by 3. Then, the x-value increases by 5. This gives us the final slope, [tex]\displaystyle\frac{3}{5}[/tex].Another way to find the slope is to use the formula [tex]\displaystyle\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]. You can plug in the values from both points and solve to get the same answer.
Y-Intercept
The y-intercept is easy to find from a graph. The y-intercept is wherever the line intersects with the y-axis (the vertical axis). In this case, the line intersects at y-value 3. So, 3 is the b-value in the equation.
Final Equation
Using the information above, we can say that the equation of the line in slop-intercept form is [tex]y=\frac{3}{5}x+3[/tex].
if f(x) = 3(x+5)+4/x, what is f(a+2)?
Answer:
A
Step-by-step explanation:
Substitute a + 2 for x:
f(a + 2) = 3 [ (a + 2) + 5 ] + 4 / (a + 2)
= 3 [ a + 7 ] + 4 / (a + 2)
Answer:
A.
Step-by-step explanation:
32. What is the perimeter of a regular octagon with a side length of 7 units?
11 units
35 units
49 units
56 units
Answer:
56
Step-by-step explanation:
solution
Here
P=8a=8·7=56
Answer:
56 units
Step-by-step explanation:
the perimeter of a rectangular octagon with sides of length a
is equal to: 8 × a
Then
the perimeter of a regular octagon with a side length of 7 units
is equal to: 8 × 7 = 56 units
3. The time for a swing to move forward and backward can be determined by the formula
T = 2√√√15₁
T represents the time, in seconds, taken by the swing to move through one
complete cycle (forward and back) and L represents the length of the rope supporting the swing.
9.8
Determine the length of the rope supporting a swing that takes 3.4 seconds to move through one
complete cycle. Show all steps and round the answer to the nearest tenth of a metre.
Step-by-step explanation:
T = 2×pi × sqrt(L/9.8)
now we know the time the swing should take for a complete back and forth cycle : 3 4 seconds.
the only unknown variable is now L (the length of the rope) :
3.4 = 2×pi × sqrt(L/9.8)
3.4/(2pi) = sqrt(L/9.8)
(3.4/(2pi))² = L/9.8
3.4²/(4pi²) = L/9.8
11.56/(4pi²) = L/9.8
2.89/pi² = L/9.8
9.8 × 2.89/pi² = L = 2.869618563... m ≈ 2.9 m
Find the missing length indicated. i need help with steps
The measure of the missing length from the given diagram is 25
Triangular altitude theoremAccording to the theorem, the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.
According to the given diagram, the expression below will be used to determine the value of x
x/60 = 60/144
Cross multiply yo have:
144x = 60 * 60
Simplify the result to have
144x = 3600
Divide both sides by 144
144x/144 = 3600/144
x = 3600/144
x = 25
Hence the measure of the missing length from the given diagram is 25
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question 3 of 8. Step 1 of 1
1/8
Correct
-
1
Incorrect
Adairy needs 385 gallons of milk containing 6 % butterfat. How many gallons each of milk containing 7 % butterfat and milk containing 2 % butterfat must be used to
obtain the desired 385 gallons?
308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.
CombinationSince a dairy needs 385 gallons of milk containing 6% butterfat, to determine how many gallons each of milk containing 7% butterfat and milk containing 2% butterfat must be used to obtain the desired 385 gallons, the following calculation must be performed:
385 x 0.06 = 23.1300 x 0.07 + 85 x 0.02 = 22.7310 x 0.07 + 75 x 0.02 = 23.2308 x 0.07 + 77 x 0.02 = 23.1Therefore, 308 gallons of 7% and 77 gallons of 2% are needed to obtain the desired 385 gallons.
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A shopkeeper sold 20 mobile sets of same brand for Rs 3,00.0000 at the same rate in a week What is the selling price of each mobile set
Answer:
15
Step-by-step explanation:
cost of 20 mobile set=300
cost of 1 mobile set
=cost of mobile set/number of mobile set
=300/20
=15
The cost of each mobile set is ₹1,50,000.
What is the unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.
Given that, a shopkeeper sold 20 mobile sets of same brand for ₹3,000,000.
The selling price of each mobile set = Total cost of mobile sets/Number of mobile sets
= 3,000,000/20
= ₹1,50,000
Therefore, the cost of each mobile set is ₹1,50,000.
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16
A Ferris wheel with a radius of 25 m makes 2 rotations every minute.
a. State the period of the Ferris wheel.
b. Complete a tables of values showing the height above the ground for 2 rotations of
Ferris wheel by assigning the correct variables
c. Graph 2 rotations of the Ferris wheel. (Hint: Time Vs Height above the platform)
d. State the amplitude of the Ferris wheel.
The period of this Ferris wheel can be calculated as 30 seconds. The amplitude is 25
How to solve for the period.a. We have 60 seconds in a minute
In a minute it makes 2 rotations. The period = 60 secs / 2 rotations
= 30 seconds
b. We have h = 25 - 25cos [tex]\frac{25}{30} t[/tex]
25 - 25cos[tex]\frac{25}{15} t[/tex]
We would have the table in the attachment
d. Amplitude
= max - min / 2
= 50 - 0 / 2
= 25
AC and BD intersect at point E which is inside the circle. Find the measure of Arc AB if Arc CD = 60 degrees and Angle CED = 35 degrees.
Th measure of arc AB will be 60 degrees
Circle theoremThe figure shown shows a circle with lines AC and BD intersecting the circle at the point E
From the figure given the measure of the arc AB is congruent to the arc CD.Given that the measure of arc CD is 60 degrees, hence the measure of arc AB will also be 60 degrees
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Match each expression to the scenario it represents.
Expressions
Scenario
the price of a game that’s been discounted
18% off its list price (x)
arrowRight
the price of a toy that sells for 18% more
than the amount (x) needed to build the toy
arrowRight
the volume of water remaining in a tank after
of its original volume (x) is drained out
arrowRight
the total amount of flour in a bakery after receiving new stock equal to of its current stock (x)
arrowRight
The expression matched with each scenario is;
Scenario 1: 0.82x
Scenario 2: 1.18x
Scenario 3: 7/10x
Scenario 4: 13/10x
AlgebraThe price of a game that’s been discounted
18% off its list price (x)
Total price = x
Discount = 18%x = 0.18x
New price = x - 0.18x
= 0.82x
The price of a toy that sells for 18% more
than the amount (x) needed to build the toy
Original price = x
Percentage increase = 18%x = 0.18x
New price = x + 0.18x
= 1.18x
The volume of water remaining in a tank after 3/10 of its original volume (x) is drained out
Original volume = x
Volume drained = 3/10x
New volume = x - 3/10x
= 7/10x
The total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)
Original stock = x
New stock = 3/10x
Total stock = x + 3/10x
= 13/10x
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A train is traveling at a speed of 60 miles per hour. What happens to the number of miles when the number of hours
changes?
O When the number of hours increases, the number of miles decreases.
O When the number of hours increases, the number of miles increases.
O When the number of hours decreases, the number of miles increases.
O When the number of hours decreases, the number of miles stays the same.
Intro
Done
When the number of hours decreases, the number of miles increases.
What is the relationship between number of hours and number of miles travelled?
Average speed is the total distance travelled per time.
Average speed = total distance / total time
There is an inverse relationship between the distance travelled and the time travelled. If time increases, the distance travelled decreases.
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Find the sum of the first 20 arithmetic progression 2, 7, 12, 17, 22
Answer: 5
Step-by-step explanation: 2 + 5 = 7, 7 + 5 = 12, 12 + 5 = 17, 17 + 5 = 22
Select all of the following true statements if R = real numbers, N = natural numbers, and S = {10, 11, 12,...}.
A. -15∈N
B. N⊂R
C. S⊂N
D. ∅⊂N
E. N∈S
F. {10.11.12,...}⊆S
The true statements are:
B. N⊂R
C. S⊂N
D. ∅⊂N
F. {10.11.12,...}⊆S
Subsets and SetsNote that:
All real numbers are numbers that can be found on the real number lineNatural numbers are positive whole numbersAll natural numbers are subsets of real numbersThe null set (∅) is a subset of every setA set is a proper subset of itselfFollowing the points highlighted above, the true statements in the given options re:
B. N⊂R
C. S⊂N
D. ∅⊂N
F. {10.11.12,...}⊆S
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HELP PLEASE
2. You are making necklaces for your friends. You have 72 blue beads and 42 red beads. Each friend will receive an identical necklace, and all beads must be used.
(A) What is the greatest number of friends who can receive a necklace? Explain your reasoning.
(B) How many of each color bead will each friend receive on the necklace? Explain your reasoning.
A. The greatest number of friends who can receive a necklace made from a combination of 72 blue and 42 red beads is 6.
B. Each friend will receive a necklace with 12 blue beads and 7 red beads.
How is this determined?The solution to this problem can be determined by considering the highest common factors of 72 and 42.
The common factors of 72 and 42 are 2 and 3.
The factors of 72 are 2, 3, and 12.
The factors of 42 are 2, 3, and 7.
2 x 3 = 6
When 6 divides 72 = 12
When 6 divides 42 = 7
Data and Calculations:Number of blue beads = 72
Number of red beads = 42
The highest number that can divide 72 and 42 without a remainder is 6.
Thus, each friend's necklace will contain 19 beads (12 blue beads and 7 red beads).
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If John has pairs of red, orange, yellow, blue, green, white and black socks, how many orders can he wear them in over 7 days? Repetition is allowed because John is alright with wearing dirty socks.
The order in which he can wear the socks with repetition in 7 days is 823, 543 orders
How to determine the order
The formula for calculating permutation with repetition is given as;
Permutation = [tex]n^r[/tex]
Where n = 7
r = 7
Substitute into the formula
Permutation = [tex]7^7[/tex]
Permutation = [tex]823, 543[/tex] ways
Thus, the order in which he can wear the socks with repetition in 7 days is 823, 543 orders
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In a recent year, the scores for the reading portion of a test were normally distributed, with a mean of 22.4 and a standard deviation of 5.1. Complete parts (a) through (d) below.
(a) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is less than 19.
The probability of a student scoring less than 19 is.
(Round to four decimal places as needed.)
(b) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is between 17.7 and 27.1.
The probability of a student scoring between 17.7 and 27.1 is.
(Round to four decimal places as needed.)
(c) Find the probability that a randomly selected high school student who took the reading portion of the test has a score that is more than 33.1.
The probability of a student scoring more than 33.1 is
3.1
is.
(Round to four decimal places as needed.)
(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
OA. None of the events are unusual because all the probabilities are greater than 0.05.
B. The event in part (c) is unusual because its probability is less than 0.05.
C. The events in parts (a) and (b) are unusual because its probabilities are less than 0.05.
D. The event in part (a) is unusual because its probability is less than 0.05.
Help me solve this
Using the normal distribution, we have that:
a) The probability of a student scoring less than 19 is 0.2709 = 27.09%.
b) The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
c) The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
d) The correct option is: B. The event in part (c) is unusual because its probability is less than 0.05.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 22.4, \sigma = 5.1[/tex]
Item a:
The probability is the p-value of Z when X = 19, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{19 - 22.4}{5.1}[/tex]
Z = -0.67.
Z = -0.67 has a p-value of 0.2709.
The probability of a student scoring less than 19 is 0.2709 = 27.09%.
Item b:
The probability is the p-value of Z when X = 27.1 subtracted by the p-value of Z when X = 17.7, hence:
X = 27.1:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{27.1 - 22.4}{5.1}[/tex]
Z = 0.92.
Z = 0.92 has a p-value of 0.8212.
X = 17.7:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.7 - 22.4}{5.1}[/tex]
Z = -0.92.
Z = -0.92 has a p-value of 0.1788.
0.8212 - 0.1788 = 0.6424.
The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.
Item c:
The probability is one subtracted by the p-value of Z when X = 33.1, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{33.1 - 22.4}{5.1}[/tex]
Z = 2.1.
Z = 2.1 has a p-value of 0.9821.
1 - 0.9821 = 0.0179.
The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.
Item d:
Probabilities less than 0.05 are unusual, hence the correct option is:
B. The event in part (c) is unusual because its probability is less than 0.05.
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Gcf of 12h3,36h3,12h6
The greatest common factor from the given information is 12h³.
What is the greatest common factor?The greatest common factor (GCF) of a given set of whole numbers is the largest value that can be divided by the set of numbers.
From the information given, we are to find the GCF of:
12h³ = (1 , 2, 3, 4, 6 , 12 )h³
36h³ = (1, 2, 3, 4, 6, 9, 12, 18, 36)h³
12h⁶ = (1, 2, 3, 4, 6, 12)h³ * h³
Therefore, we can conclude that the greatest common factor is 12h³.
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Write the following in simplified radical form.
3/40
Answer:
3.42
Step-by-step explanation:
1. Which one of the following statements expresses a true proportion? A. 3:49:12 OB. 2:1 1:2 OC. 54:9 = 6:3 OD. 7:98:9
Answer:
3:4 9:12
Step-by-step explanation:
Rewrite the ratios as fractions. 3:4 becomes 3/4, and 9:12 becomes 9/12, which simplifies to 3:4. Therefore A is a true proportion.
5·(3+6)x^{2} -6x^{2}
[tex]5·(3+6)x^{2} -6x^{2}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5(3+6)x^{2} -6x^{2} \end{gathered}$}[/tex]
Add 3 and 6 to get 9.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5\times9x^{2} -6x^{2} \end{gathered}$}[/tex]Multiply 5 and 9 to get 45.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 45x^{2} -6x^{2} \end{gathered}$}[/tex]Combine 45x² and −6x² to get 39x².
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \red{39x^{2} } \end{gathered}$} }[/tex]Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{What does \boxed{median} mean in math?}}[/tex]
[tex]\boxed{\text{Median}}\rightarrow\textsf{ is the number in the middle.}[/tex]
[tex]\huge\textbf{How do you find the \boxed{median}?}[/tex]
[tex]\text{You can found it by putting the numbers from \bf least to greatest.}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\text{Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95,}\\\text{72, 75}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\text{91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75}[/tex]
[tex]\huge\textbf{Rearrange the problems to:}[/tex]
[tex]\text{69,71,71,71,72,74,75,82,87, 89,89,91,95,95}[/tex]
[tex]\huge\textbf{The expression:}[/tex]
[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]
[tex]\mathsf{\dfrac{157}{2} = median}[/tex]
[tex]\mathsf{257\div2 = median}[/tex]
[tex]\mathsf{78.5 = median}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{78.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]La nota de Karina en su curso de nivelación matemática es 7 veces la cantidad de factores primos que tiene el siguiente polinomio:
P (a; b; c) =a(a +b-c) +b(a+ b-c) +c(a +b- c)
Hallar la nota que obtuvo.
Karina obtuvo una nota final de 84 de 100 puntos en su curso de nivelación matemática.
¿Qué nota obtuvo Karina obtuvo en su curso de nivelación matemática?
Antes de comenzar la resolución de este problema, asumimos que la base de calificación del curso de nivelación matemática es 100 y que la nota mínima para pasar es 70. Por otra parte, sabemos que la nota obtenida por Karina es divisible por 7 y que es el producto de aquel número primo y un polinomio formado por una relación de tres números primos, la cual es simplificada a continuación:
p (a, b, c) = a · (a + b - c) + b· (a + b - c) + c · (a + b - c)
p (a, b, c) = a² + a · b - a · c + a · b + b² - b · c + a · c - b · c - c²
p (a, b, c) = a² + 2 · a · b + b² - c²
p (a, b, c) = (a + b)² - c²
p (a, b, c) = (a + b + c) · (a + b - c)
Si asumimos que Karina obtuvo 84, entonces se tiene que 84 = 7 × 12 y 12 = 2 × 6. Tanto el dos como el seis son múltiplos de dos, entonces asumimos a = b = c y encontramos que:
n (2, 2, 2) = 7 · (2 + 2 + 2) · (2 + 2 - 2)
n (2, 2, 2) = 7 · 6 · 2
n (2, 2, 2) = 84
En síntesis, Karina obtuvo una nota final de 84 de 100 puntos en su curso de nivelación matemática.
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Factor the expression.
3r2 – 75
Answer:
3(r + 5)(r - 5)
Step-by-step explanation:
Both 3 and 75 are divisible by 3, so we take out a 3.
3(r^2 - 25)
Next, we can factor r^2 - 25. It's a difference of squares.
3(r + 5)(r - 5)
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How do the y-values in the table grow? The y-values increase by a factor of 49 for each x increase of 1. The y-values increase by 49 for each x increase of 1. The y-values increase by a factor of 7 for each x increase of 1. The y-values increase by 7 for each x increase of 1.
From the table, we can deduce that The y-values increase by a factor of 7 for each x increase of 1 and is denoted as option C.
What is a Factor?
This is defined as a number which divides another without leaving a remainder afterwards.
From the table, we can deduce that the y-values are divisible by 7 thereby making it a factor of it and confirming that it increase by a factor of 7 for each x increase of 1.
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Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 130 to 190 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.65 cm, y= 81.36 kg, r= 0.309, P-value= 0,002, and y= 106+1.15x. Find the best predicted value of y (weight) given an adult male who is 156 cm tall. Use a 0.10 significance level.
The best predicted weight of a person that is 156 cm is 285.4kg
We have the regression equation asy= 106+1.15
When the adult male is 156 cm tall the weight of this person would be calculated as:
y= 106+1.15*156
y = 106 + 179.4
y = 285.4
Hence we can arrive at the conclusion that the best predicted weight of a person that is 156 cm is 285.4kg
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Measure the length of this segment in inches.
Answer:
3 [tex]\frac{3}{4}[/tex] inches
Answer: I'm pretty sure it's 3 5/8, it's the S that's blocking the view but it gotta be 3 5/8.
Step-by-step explanation: PLS MAKE ME BRAINLIST
A vacant lot is being converted into a community garden. The garden and the walkway around its perimeter have an area of 572 ft. Find the width of the walkway, (x in the diagram below), if the garden is 14 ft. wide by 18 ft. long. Factoring or the quadratic equation formula can be used. a) 5) Solve for the specified variable A = 1/(a+b)h for a 6) Solve for x 14 feet x+10_I 33 Jeet b) A=1/(a+b)h for a
Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Volume: Answer, yd3
Answer:
The volume is
[tex]339.4 {yd}^{3} [/tex]
Step-by-step explanation:
The solution is in the image