K:
1/2 and 3/4 are NOT equivalent.
If you divide 1 by 2, the result is 0.5
If you divide 3 by 4, the result is 0.75
Therefore, they are NOT equivalent
1/2 and 2/4 are equivalent:
If you divide 1 by 2, the result is 0.5
If you divide 2 by 4, the result is also 0.5
Now, you can answer the question.
A floor has 15 1/2 tiles in an area of 2 2/5 sqft how many tiles are in a square foot
Since in 2 2/5 sqft are 15 1/2 tiles, then in 1 square foot, there are:
[tex]\frac{15\frac{1}{2}}{2\frac{2}{5}}[/tex]tiles.
To compute the above division we transform the mixed fractions into improper fractions:
[tex]\begin{gathered} 15\text{ }\frac{1}{2}=\frac{31}{2}, \\ 2\frac{2}{5}=\frac{12}{5}. \end{gathered}[/tex]Therefore:
[tex]\frac{15\frac{1}{2}}{2\frac{2}{5}}=\frac{\frac{31}{2}}{\frac{12}{5}}=\frac{31\times5}{12\times2}=\frac{155}{24}\text{.}[/tex]Answer: 6 11/24 tiles.
3.13 geom Which triangle congruence postulate or theorem proves that these triangles are congruent?
The AAS triangle congruence postulate proves that these triangles are congruent .
In the question,
two triangles are given that are triangle KLM and triangle XYZ .
Consider the triangle KLM and triangle XYZ .
we can see that
(i) angle L = angle Y = angle 1 .....given in the figure
(ii) angle m = angle Z = angle 2 .... given in the figure
(iii) side KM = side XZ ....given in the figure
From the above three statements we conclude that
ΔKLM ≅ ΔXYZ
both the triangles KLM and XYZ are congruent by AAS Congruence Postulate .
Therefore , The AAS triangle congruence postulate proves that these triangles are congruent .
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Express 72 1/2% asa fraction in its lowest term
The percentage of the number is 29/40 when The number is 72 1/2.
Given that,
The number is 72 1/2
We have to find the percentage of the number.
The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. Percentages are fractions when the denominator is 100. To put it another way, it's the relationship between a part and a whole in which the value of the whole is always assumed to be 100.
We have number,
72 1/2
145/2
145/2× 1/100
145/200
29/40
Therefore, The percentage of the number is 29/40 when The number is 72 1/2.
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use the unit circle to find sec(7/6)
Step 1
Draw the unit circle required
Step 2
Find the value sec(7π/6) in cosine
[tex]\begin{gathered} \sec (\frac{7\pi}{6})=\frac{1}{cos(\frac{7\pi}{6})} \\ \sec (x)=\frac{1}{cos(x)} \end{gathered}[/tex]Step 3
Find cos(7π/6)
The trigonometric unit circle and a trigonometric table gives;
[tex]\begin{gathered} \cos (\frac{7\pi}{6})=\cos (\frac{\pi}{6}+\pi) \\ \cos (\frac{7\pi}{6})=\text{cos}(\frac{\pi}{6})\cos (\pi)-\sin (\frac{\pi}{6})sin\pi=-\cos (\frac{\pi}{6}) \\ \cos (\frac{7\pi}{6})=\frac{\sqrt[]{3}}{2}(-1)-(\frac{1}{2})(0)=-\frac{\sqrt[]{3}}{2} \\ \cos (\frac{7\pi}{6})=-\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Step 4
Find sec(7π/6)
[tex]\begin{gathered} \sec (x)=\frac{1}{cos(x)} \\ \text{sec}(\frac{7\pi}{6})=\frac{1}{\cos (\frac{7\pi}{6})} \\ \text{sec}(\frac{7\pi}{6})=\frac{1}{-\frac{\sqrt[]{3}}{2}} \\ \text{sec}(\frac{7\pi}{6})=-\frac{2}{\sqrt[]{3}} \end{gathered}[/tex]Step 5
Rationalize the denominator
[tex]\begin{gathered} \sec (\frac{7\pi}{6})=-\frac{2}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{\sqrt[]{9}} \\ \sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{3} \end{gathered}[/tex]Hence,
[tex]\sec (\frac{7\pi}{6})=-\frac{2\sqrt[]{3}}{3}[/tex]Which inequality in factored form represents the region less than the quadratic function with zeros-40 and -50 and
includes the point (-55, -75) on the boundary line?
O y<-(x-40)(x-50)
O ys-(x+40)(x+50)
Oys-(x-40)(x - 50)
O y<-(x +40)(x+50)
Please help
The inequality that reflects the given region, according to the Factor Theorem, is:
y< -(x+40)(x+50)
What is the Factor Theorem?When completely factoring polynomials, the factor theorem is employed in mathematics. It is a theorem that relates the factors and zeros of a polynomial. If f(x) is a polynomial of degree n 1 and 'a' is any real number, then (x-a) is a factor of f(x) if f(a)=0.
According to the Factor Theorem, a polynomial function with roots x₁, x₂, ....xₙ is given by
f(x)=a(x-x₁)(x-x₂)...(x-xₙ)
In which a is the leading coefficient.
The roots are given as follows:
x₁=-40, x₂=-50
Hence:
y = a(x + 40)(x +50)
It includes the point (-55,-75), hence:
-75 = a(-55 + 40)(-55 +50)
a = 75/(15 x 5)
a = 1
The equation that is less than the region is:
y< -(x+40)(x+50)
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Answer:
d
Step-by-step explanation:
Answer to the nearest tenth:
12 is 90% of what number?
Answer:
13.33 is the answer im pretty sure
Step-by-step explanation:
Answer:
13.3
Step-by-step explanation:
1. If it's possible - try cutting the number down to 10%-:
We can do that by dividing 12 by 9, which would give us 10% of that
number.
2. We get 1.33, which is 10% of the number. To get 100 percent, we just need to multiply by 10
3: 1.33*10 is 13.3, so the answer has to be 13.3
There is a rope running from the top of a flagpole to a hook in the ground. The flagpole is 21 feet high, and the hook is 20 feet from its base. How long is the rope?
please help help me write a story to describe the graph
I'll start first by finding the slope of the line at t = 2 mins up to t = 6 mins, t = 6 mins up to t = 8 mins, and t = 14 mins up to t = 20 mins.
For the first interval (2 mins to 6 mins), we have the coordinates (2, 7) and (6, 5). The slope of the line is
[tex]m=\frac{5-7}{6-2}=-\frac{2}{4}=-\frac{1}{2}[/tex]For the second interval (6 mins up to 8 mins), we have the coordinates (6, 5) and (8,0). The slope of the line is
[tex]m=\frac{0-5}{8-6}=-\frac{5}{2}[/tex]For the last interval (14 mins up to 20 mins), we have the coordinates (14,0) and (20,9). The slope of the line is
[tex]m=\frac{9-0}{20-14}=\frac{9}{6}[/tex]The x-axis of the given graph pertains to time while its y-axis pertains to distance from home. Let's try to make a story about a person from work going home and will prepare something before going outside again.
For the first 2 mins, the person walks out of his office and will go to his car. Since he is still in the office, the distance from home does not change for the first two minutes.
For the next 4 mins (2 mins to 6 mins interval), he starts driving going home at a rate of 1/2 miles per minute. Because of traffic, he is driving slower than his usual driving speed. Upon passing away from the traffic, the person now travels at a rate of 5/2 miles per minute for 2 mins (6 to 8 mins interval). At the 8th minute mark, he is already home. He prepared something at home during the 8 min to 14 min interval time. After the preparation, he went again outside for some business trip, traveling at the speed of 9/6 miles per minute.
1. Mr. and Mrs. Ryan Miller bought a
refrigerator for $1,416. They agreed to
make 12 equal monthly payments. How
much more than $50 will each payment
be?
2. The $1,416 paid by the Millers (problem 1
to buy the refrigerator included an interest
charge of $188. What was the cash cost of
the refrigerator?
The monthly payment more than $50 is $68 and the original price of the refrigerator is $1228
Mr. and Mrs. Ryan Miller bought a refrigerator for $1,416.
They agreed to make 12 equal monthly payments
Monthly payment = 1416 / 12
The monthly payment is $118
more than $50 will each payment be = 118 - 50 = 68
The $1,416 paid by the Miller to buy the refrigerator included an interest charge of $188
The original price is 1416 - 188 = 1228
Therefore, the monthly payment more than $50 is $68 and the original price of the refrigerator is $1228
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2) A taxi service charges a fee of $2.50 and then an additional $2.70 per mile. Determine the relationship.
Data:
• Fixed fee: $2.50
,• Additional: $2.70 per mile
Procedure:
The relationship the problem is describing is a linear one with the form:
[tex]y=mx+b[/tex]In this case, we have a fixed fee that is represented by b in the linear equation, and an additional fee represented by m, which depends on the miles (x) travels.
Thus, the equation would be:
[tex]y=2.7x+2.5[/tex]Based on this equation, you can replace any value of miles (x) given to calculate the total price (y).
pls help me answer these questions
Answer:
Length: 10 m
Width: 6 m
Step-by-step explanation:
The layout of the floor is l x w, which is 100 cm by 60 cm. Now, the confusing part: 1 meter (m) = 10 centimeters (cm)
To set this problem up, you'd first have to go through the logic. For every 10 centimeters of the floor layout, it is equal to 1 meter of the actualy floor plan. So you would have to scale 100 cm and 60 cm by [tex]\frac{1}{10}[/tex] (or divide by 10).
We will ignore the units, for now
Length: 100 * [tex]\frac{1}{10}[/tex] = 10 or (100/10 = 10)
Width: 60 * [tex]\frac{1}{10}[/tex] = 6 or (60/10 = 6)
Now that we've finalized the numerical value, lets move on to the units. Since the question wants us to respond in meters, the length of 10 and the width 6 6 would be in meters.
So the answer would be:
Length: 10 m
Width: 6 m
Hope this helped!
If u = 1 + 3i and v = -2 − i, what is u + v?
Answer:
2i - 1
Step-by-step explanation:
The expression is,
→ u + v
Simplifying the expression,
→ u + v
→ (1 + 3i) + (-2 - i)
→ (3i - i) + (1 - 2)
→ 2i - 1
Hence, the answer is 2i - 1.
Step-by-step explanation:
you need to replace definition of both u and v into the equation
u + v = (1+3i) + (-2-i)
= 1 + 3i -2 - i
= 3i - i + 1 - 2
= 2i - 1
Sam bought a jacket for $34, which is one-third of the original price. How much did thejacket cost originally?
Let the original cost of the jacket be x.
Now, saying that one-third of the original cost of the jacket is $34, is mathematically equivalent to:
[tex]\frac{1}{3}\times x=34[/tex]Now we have to solve the resulting equation in order to obtain the value of x
This is done as follows:
[tex]\frac{1}{3}\times x=34[/tex][tex]\Rightarrow\frac{x}{3}=34[/tex][tex]\Rightarrow x=3\times34[/tex][tex]x=102[/tex]Therefore, the original cost of the jacket is $102
which of the following is the largest? half of 78a third of 114one-fifth of 190
Let's get the following value for the given statements and check which are the largest.
a) Half of 78.
We compute for the half of 78, which we divide 78 by 2. We have
[tex]\frac{78}{2}=39[/tex]b) A third of 114
A third of a number means we divide the number by 3. Dividing 114 by 3, we get
[tex]\frac{114}{3}=38[/tex]c) One-fifth of 190
One-fifth of a number means we divide the number by 3. Dividing 190 by 5, we get
[tex]\frac{190}{5}=38[/tex]As we can see on the results above, the largest is half of 78.
estimate 15.870 + 6.77 by first rounding each number to the nearest tenth
Given:
15.870 + 6.77
We are required to round each number to the nearest tenth before performing the addition.
The tenth digit is the number first number after the decimal point.
First step:
Round to the nearest tenth
15.870 ==> 15.9
6.77 ==> 6.8
Second step:
Add both numbers after rounding to the nearest tenth
15.9 + 6.8 = 22.7
ANSWER:
22.7
Solve the quadratic equation x² + 2√2x-6=0 for x
Step-by-step explanation:
D = b²-4ac
D = (2√2)²-4×1×(-6)
D = 8+24 = 32 = 4√2
X1 =
[tex] \\ \frac{ - 2 \sqrt{2} + 4 \sqrt{2} }{ 2 } = \frac{2 \sqrt{2} }{2} = \sqrt{2} [/tex]
X2 =
[tex] \frac{ - 2 \sqrt{2 } - 4 \sqrt{2} }{2} = - 3 \sqrt{2} [/tex]
You want to order posers to advertise your band. A company charges $109.95 for the first 100 posters and $65 for each additional 100 posters.
Write an equation that represents the cost (in dollars) of the posters of the number (in hundreds) of posters ordered (in slope- intercept form).
The equation that represents the total cost as a function of the number (in hundreds) of posters ordered, x is f(y) = 109.95 + 65x
let
y = total cost
x = numbers in hundreds
cost of first hundred = $109.95
Cost of additional hundred = $65
f(y) = 109.95 + 65x
The total cost of 1000 posters
1000 - first hundred = 900
additional hundreds = 900/100= 9
So,
f(y) = 109.95 + 65x
= 109.95 + 65(9)
= 109.95 + 585
= 694.95
f(y) = $694.95
Therefore, the total cost of 1000 posters is f(y) = $694.95
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During a snowstorm, Amelia tracked the amount of snow on the ground.When the storm began, there was 1 inch of snow on the ground. For the first 2hours of the storm, snow fell at a constant rate of 3 inches per hour. Thestorm then stopped for 3 hours and then started again at a constant rate of 1inch every 2 hours for the next 6 hours. Make a graph showing the inches ofsnow on the ground over time using the data that Amelia collected.
First, let's write on a table the information about the snow on the ground for the 11 hours it snowed:
period of time in hours amount of snow in inches
0 1
from 0 to 2 1 + t * 3 (initial amount plus 3 in/h * number of hours)
from 2 to 5 1 + 2*3 = 7 (the same amount as when it stopped raining)
from 5 to 11 7 + (t-5)/2 (amount at t = 5 plus 1 in/2h * number of
hours since hour 5)
Now, using this information on a graph, we obtain:
please help NEED FAST
a) The quadratic equation behind the parabola is y = (4 / 5) · x² - (8 / 5) · x - 1.
b) There are two x-intercepts: x₁ = - 0.5, x₂ = 2.5.
How to derive a quadratic equation and find its x-intercepts
Mathematically speaking, parabolas are represented by quadratic equations, whose standard form is introduced below:
y = a · x² + b · x + c
Where a, b, c are real coefficients.
The values of the three coefficients are found from the knowledge of three distinct points on Cartesian plane. First, choose the three points:
(x₁, y₁) = (- 0.5, 0), (x₂, y₂) = (2.5, 0), (x₃, y₃) = (0, - 1)
Second, construct the system of linear equations with all the given points and the standard form of the quadratic equation:
0.25 · a - 0.5 · b + c = 0
6.25 · a + 2.5 · b + c = 0
c = - 1
Third, solve the system by numerical methods:
(a, b, c) = (4 / 5, - 8 / 5, - 1)
Fourth, write the quadratic equation:
y = (4 / 5) · x² - (8 / 5) · x - 1
The x-intercepts of the quadratic equation are the points of the curve that pass through the x-axis. Then, the x-intercepts are x₁ = - 0.5 and x₂ = 2.5.
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Inscribed angles, I’m being asked for a, and b but I don’t understand this question
Given the figure of a circle.
There are 3 arcs with the following measures: a, 100, and 136
the sum of the measures of the arcs = 360
So, we can write the following equation:
[tex]a+100+136=360[/tex]Solve the equation to find (a):
[tex]\begin{gathered} a+236=360 \\ a=360-236=124 \end{gathered}[/tex]The angle (b) is the Inscribed angle opposite the arc (a)
[tex]b=\frac{1}{2}a=\frac{1}{2}*124=62[/tex]So, the answer will be:
[tex]\begin{gathered} a=124 \\ b=62 \end{gathered}[/tex]I am going to send the pictures Please solve question b(b) Canada like many countries use the metric system if the Canada news says it’s-2 degrees Celsius what is that in Fahrenheit ( Celsius is typically rounded to the tenth place
Given equation:
[tex]\text{ Wind Chill = }35.74\text{ }+\text{ }0.6215T\text{ }-\text{ 35}.75(V^{0.16})\text{ }+\text{ }0.4275T(V^{0.16})[/tex]Where T = temperature in Fahrenheit and
V = wind speed in miles per hour
Conversion formulas:
[tex]\begin{gathered} A_s\text{ = }M_s\text{ }\times\text{ }0.62 \\ F\text{ = 1.8C + 32} \end{gathered}[/tex]Question (b)
We are required to convert -2 degree Celsius to Fahrenheit
Using the conversion formula:
[tex]\begin{gathered} F\text{ = }1.8\text{ }\times-2\text{ + 32} \\ =\text{ 28.4} \end{gathered}[/tex]Answer: 28.4 F
You have 16 yellow beads, 20 red beads, and 24 orange beads to make identical bracelets. What is the greatest number of bracelets that you can make using all of the beads?
As per the concept of GCF, the greatest number of bracelets that you can make using all of the beads is 4.
GCF:
GCF means the largest positive integer not a decimal that divides evenly into all of the numbers in the set. also know as Highest common factor.
Given,
You have 16 yellow beads, 20 red beads, and 24 orange beads to make identical bracelets.
Here we need to find the greatest number of bracelets that you can make using all of the beads.
In order to find it, we have to find the prime factorization of each beads,
So, the prime factorizations of 16, 20 and 24 is,
Factors for 16 is 1, 2, 4, 8, and 16
Factors for 20 is 1, 2, 4, 5, 10, and 20
Factors for 24 is 1, 2, 3, 4, 6, 8, 12, and 24
While we looking into the factors, we have identified that the greatest common factor is 4.
Therefore, there are 4 bracelets that you can make using all of the beads.
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Which relation is a function?
I’m confused on this. can anyone help me out?
Answer:
The one the u have marked is a function.
Step-by-step explanation:
If you draw a vertical line through each one, each line only goes through one point
Find the arc-length of the sector of a circle with the given radius r and central angle 0. Give the answer in the given unit of measure, rounded to the nearest hundredth.r = 25 m; θ = 12π/7
Given a radius and a central angle in radian, the formula in solving arc length is:
[tex]AB=\theta\times r[/tex]Since the angle and radius are given already in the problem, let's plug it in to the formula above.
[tex]AB=\frac{12\pi}{7}(25m)[/tex]Then, solve.
[tex]AB=\frac{300\pi m}{7}=\frac{942.47779m}{7}\approx134.64m[/tex]Therefore, the length of an arc having a central angle of 12π/7 is approximately 134.64 meters.
I need help with this practice problem It’s asks to Drag the angle measure to each box to match the quadrant location of the terminal ray of the angle op
Note that the range in quadrants are :
[tex]\begin{gathered} Q1\colon\text{From}\quad 0\pi-0.5\pi \\ Q2\colon\text{From}\quad 0.5\pi-1.0\pi \\ Q3\colon\text{From}\quad 1.0\pi-1.5\pi \\ Q4\colon\text{From}\quad 1.5\pi-2\pi \end{gathered}[/tex]From the problem,
[tex]\begin{gathered} \frac{3\pi}{4}=0.75\pi\Rightarrow Q2 \\ \frac{57\pi}{8}=7.125\pi \\ \text{Note that 1 whole circle is}\quad 2\pi \\ \text{Subtracting three}\quad 2\pi \\ 7.125\pi-3(2\pi)=1.125\pi \\ \text{and}\quad 1.125\pi\quad \text{ is at Q3} \\ \\ \frac{13\pi}{6}=2.167\pi \\ Subtract\quad 2\pi \\ 2.167\pi-2\pi=0.167\pi\Rightarrow Q1 \end{gathered}[/tex]The first three answers are :
Q2, Q3 and Q1
For the second set, we have negative angles.
The range of negative angles will be the reversal of the positive angles.
This will be :
[tex]\begin{gathered} Q1\colon\text{From}\quad -1.5\pi\quad to\quad -2\pi \\ Q2\colon\text{From}\quad -1.0\pi\quad to\quad -1.5\pi \\ Q3\colon\text{From}\quad -0.5\pi\quad to\quad -1.0\pi \\ Q4\colon\text{From}\quad -0\pi\quad to\quad -0.5\pi \end{gathered}[/tex]The following angles are :
[tex]\begin{gathered} -\frac{35\pi}{4}=-8.75\pi \\ \text{Add four}\quad 2\pi \\ -8.75+4(2\pi)=-0.75\pi \\ -0.75\pi\Rightarrow Q3 \\ \\ -\frac{5\pi}{6}=-0.83\pi\Rightarrow Q3 \\ \\ -\frac{5\pi}{11}=-0.45\pi\Rightarrow Q4 \end{gathered}[/tex]The last three answers are :
Q3, Q3 and Q4
To summarized :
[tex]\begin{gathered} Q1\colon\frac{13\pi}{6} \\ Q2\colon\frac{3\pi}{4} \\ Q3\colon\frac{57\pi}{8},\quad -\frac{35\pi}{4},\quad -\frac{5\pi}{6} \\ Q4\colon-\frac{5\pi}{11} \end{gathered}[/tex]Given the lengths of the sides of a triangle, determine if it is an acute, anobtuse, or a right triangle.
Use the Pythagorean theorem to determine if the triangle is acute, obtuse or right triangle.
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where} \\ c\text{ is the longest side of the triangle} \\ a\text{ and }b\text{ are the other 2 sides} \end{gathered}[/tex][tex]\begin{gathered} a^2+b^2=c^2 \\ (18)^2+(29)^2\questeq(46)^2 \\ 324+841\questeq2116 \\ 1165\questeq2116 \\ 1165<2116 \end{gathered}[/tex][tex]\begin{gathered} \text{IF} \\ a^2+b^2c^2 \\ \text{THEN, the triangle is an acute triangle} \\ \\ \text{IF} \\ a^2+b^2=c^2 \\ \text{THEN, the triangle is a right triangle} \end{gathered}[/tex]Since the sum of the square of the side of the two angles is less than the square of the longest side, then given the length of a triangle 18-29-46, the triangle is an obtuse triangle.
if i did
what would i get?
?
be more specific :)
a store has 24 saltwater fish. the store has 4 tanks for the fish. each tank has an equal number of fish. how many fish are in each tank
Answer:
Step-by-step explanation:
Answer: 6
there are 24 fish and 4 tanks so divide 24 by 4 and you'll have 6
Answer:
the number of fish in each tank is 6
Step-by-step explanation:
becuause 24 divided be 4 is 6
Identify the sampling technique used (or to be used) in the following scenarios. Possible answers could be simple random, systematic random or stratified random sampling.
a)
This sampling technique is simple random sampling, since the students are selected at random by drawing their names from a piece of paper.
b)
Since there is a condition to select a resident (being the sixth resident of the list), this technique is classified as systematic random sampling.
c)
The 20 students were selected by using a table of random numbers without any criteria. Therefores, this is a simple random sampling technique.
d)
Since, among the 100 selected random people, there was a pre determined subgroup of 5 barangays, this is a stratified random sampling technique.
e)
Since everyone in the sample was selected at random by dwaring lots, this is a simple random sampling technique.
A circular dartboard has diameter 40cm. Its bull’s eye has diameter of 8 cm. if an amateur throws a dart and it hits the board, what is the probability that the dart hits the bull’s eye.
Answer:
a value of is required in the following exercises, use
A circular dartboard has diameter 40 Its bull's eye has diameter 8
a. If an amateur throws a dart and it hits the board. What is the probability that the dart hits the bull's eye?
b. After many throws, 75 darts have hit the target. Estimate the number hitting the bull's eye.
Step-by-step explanation:
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