Answer:
x = 30°
Step-by-step explanation:
If l and m are parallel lines, then corresponding angles should be congruent.
3x - 20 = 2x + 10
Add 20 to both sides,
3x = 2x + 10 + 20
3x = 2x + 30
Subtract 2x from both sides,
3x - 2x = 30
x = 30
NO LINKS!! Please help me
Answer:
[tex]\textsf{b)} \quad -\dfrac{\sqrt{7}}{4}[/tex]
Step-by-step explanation:
Trigonometric ratios
[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.H is the hypotenuse (the side opposite the right angle).[tex]\textsf{If}\; \cos(\theta)=-\dfrac{3}{4} \implies \sf A=3 \; \textsf{and} \; H=4.[/tex]
Use Pythagoras Theorem to calculate the length of the opposite side:
[tex]\sf \implies O^2+A^2=H^2[/tex]
[tex]\implies \sf O=\sqrt{H^2-A^2}[/tex]
[tex]\implies \textsf{O}=\sqrt{4^2-3^2}[/tex]
[tex]\implies \textsf{O}=\sqrt{7}[/tex]
Therefore, substituting the values of O and H into the sine ratio:
[tex]\implies \sin\theta=\dfrac{\sqrt{7}}{4}[/tex]
As the terminal side of the angle is in Quadrant III, and sine is negative in Quadrants III and IV, the exact value of sin(θ) is:
[tex]\implies \implies \sin\theta=-\dfrac{\sqrt{7}}{4}[/tex]
Cristian made an ankle bracelet using 6 red beads, 10 green beads, 4 purple beads, and 5 yellow beads. He wants to make a necklace that has the same ratio of color beads as the ankle bracelet. If the necklace has 15 yellow beads, how many purple beads will it have?
Answer:
Step-by-step explanation:
20
PLS HELP ASAP
(50 POINTS)
What is the
value of the function when x = -2?
Enter the answer in the box.
Answer: 334.600
Step-by-step explanation:
I should be that, you have to look at the line
Answer:
The right answer would be 1
Step-by-step explanation:
Note: Please make sure to properly format your answers. All dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). All percentage values in the answers need to include a percentage sign (%). For all items without specific rounding instructions, round your answers to two decimal places, show both decimal places (5.06).
A recent survey by the American Automobile Association showed that a family of two adults and two children on vacation in the United States will pay an average of $247 per day for food and lodging with a standard deviation of $60 per day. If the data are normally distributed, find the percentage of these families who spent:
a. Less than $167 per day. _____
b. Less than $367 per day. _____
c. More than $247 per day. _____
d. More than $350 per day. _____
e. Less than $67 per day. ______
f. Between $200 and $300 per day. _____
g. Between $360 and $400 per day. _____
h. More than the median. ____
i. Less than the mean. _____
Using the normal distribution, the percentages are given as follows:
a) 9.18%.
b) 97.72%.
c) 50%.
d) 4.27%.
e) 0.13%.
f) 59.29%.
g) 2.46%.
h) 50%.
i) 50%.
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.For this problem, the mean and the standard deviation are given as follows:
[tex]\mu = 247, \sigma = 60[/tex]
For item a, the proportion is the p-value of Z when Z = 167, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (167 - 247)/60
Z = -1.33.
Z = -1.33 has a p-value of 0.0918.
Hence the percentage is of 9.18%.
For item b, the proportion is the p-value of Z when Z = 367, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (367 - 247)/60
Z = 2.
Z = 2 has a p-value of 0.9772.
Hence the percentage is of 97.72%.
For item c, the proportion is one subtracted by the p-value of Z when X = 247, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (247 - 247)/60
Z = 0
Z = 0 has a p-value of 0.5.
Hence the percentage is of 50%.
For item d, the proportion is one subtracted by the p-value of Z when X = 350, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (350 - 247)/60
Z = 1.72
Z = 1.72 has a p-value of 0.9573.
1 - 0.9573 = 0.0427.
Hence the percentage is of 4.27%.
For item e, the proportion is the p-value of Z when Z = 67, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (67 - 247)/60
Z = -3.
Z = -3 has a p-value of 0.0013.
Hence the percentage is of 0.13%.
For item f, the proportion is the p-value of Z when X = 300 subtracted by the p-value of Z when X = 200, hence:
X = 300:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (300 - 247)/60
Z = 0.88.
Z = 0.88 has a p-value of 0.8106.
X = 200:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (200 - 247)/60
Z = -0.78.
Z = -0.78 has a p-value of 0.2177.
0.8106 - 0.2177 = 0.5929.
Hence the percentage is 59.29%.
For item g, the proportion is the p-value of Z when X = 400 subtracted by the p-value of Z when X = 360, hence:
X = 400:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (400 - 247)/60
Z = 2.55.
Z = 2.55 has a p-value of 0.9946.
X = 360:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (360 - 247)/60
Z = 1.88.
Z = 1.88 has a p-value of 0.97.
0.9946 - 0.97 = 0.0246
Hence the percentage is 2.46%.
For items h and i, the distribution is symmetric, hence median = mean and the percentages are of 50%.
More can be learned about the normal distribution at https://brainly.com/question/24808124
#SPJ1
If mpoq =19 mqor=31 and ros = 15 what is mpos
The m∠POS would be - 65° by the angle addition postulate and substitution postulate.
Given, m∠POQ = 19° , m∠QOR = 31° and m∠ROS = 15°
Angle Addition Postulate is the measure of the larger angle is the sum of the measures of the two smaller angles.
Substitution postulate states that a quantity may be substituted for its equality in any expression.
Then substitute the angle measurements into the resulting equation to find, m∠POS:
m∠POQ + m∠QOR = m∠POR (by angle addition)
m∠POR + m∠ROS = m∠POS (by substitution)
m∠POS = m∠POQ + m∠QOR + m∠ROS
= 19° + 31° + 15°
= 65°
Thus, the m∠POS would be - 65° by the angle addition postulate and substitution postulate.
Learn more about Angle addition postulate here:
brainly.com/question/14957499
#SPJ9
1.8x7+3 (1 point)
o 67
o 80
o 59
o 18
A package of 88 batteries costs $ 4 . 724.72 .
What is the cost per battery?
We get that the cost of the battery is $ 8.24 per battery.
We are given that the cost of 88 batteries = $ 724.72
We need to find the cost of one battery.
We will do this by diving the cost of 88 batteries by 88.
Using division, we get that:
cost of one battery = $ 724.72 ÷ 88
Simplifying the expression, we get that:
cost of one battery = $ 8.24 per battery.
Therefore, we get that the cost of the battery is $ 8.24 per battery.
Learn more about division here:
https://brainly.com/question/25289437
#SPJ9
Can Any one help me on this and explain it?
Answer: to be honest looks kinda hard
Step-by-step explanation:
I think both are 4
12 pages in 2 days = pages per day Submit
Answer:
6
Step-by-step explanation:
Answer:
6 pages per day
Step-by-step explanation:
12. Damian can make 3 free-throw shots in
10 seconds and 18 free-throw shots in
1 minute. What is the constant of
proportionality?
The constant of proportionality is 0.3.
How to calculate the constant?From the information, Damian can make 3 free-throw shots in 10 seconds and 18 free-throw shots in 1 minute.
Therefore, we can choose any of the figures to solve the question since it is constant.
The constant of proportionality will be:
= Number of throes / Time taken
= 3/10
= 0.3
The constant of proportionality is 0.3.
Learn more about constant on:
brainly.com/question/28413384
#SPJ1
The camera Melissa wanted for her birthday is on sale at 44% off the usual price. The amount of the discount is $96.80. What was the original price of the camera?
The original price of the camera is $220.00 based on the fact that discount of 44% is $96.80
What portion of the original price is the discount?
The discount of $96.80 in dollar terms, represents 44% of the original of the camera, in other words, we can determine the 1% of the original price of the camera by dividing the discount of $96.80 by 44
1% of the original price of the camera=$96.80/44
1% of the original price of the camera=$2.20
100% of the original price=1% of the original price of the camera*100
100% of the original price=$2.20*100
100% of the original price=$220.00
Find out more about discount on price on:brainly.com/question/4490594
#SPJ1
I am a two digit multiple of eleven. I am not odd. My digits, when multiplied, make a cube and a square out of me. What number am I? (30 pts) Explain and prove your answer. (70 pts)
The digit that when multiplied, make a cube and a square out of the number is 88.
How to calculate the value?It should be noted that this has to do with mental reasoning.
It should be noted that 8 × 8 = 64. This is the square of 8.
Also, it should be noted that 4 × 4 × 4 = 64. This gives the cube value.
Therefore, the number is 88.
Learn more about numbers on:
brainly.com/question/24644930
#SPJ1
former minnesota vikings quarterback brett favre throws a football at a speed of 35 meters per second . if the weight if the football is 0.4 kg, what would the kinetic energy of brett favre's pass be?
The kinetic energy of brett favre's will be 245 J.
To accelerate Associate in Nursing object, we've to use force. to use force, we want to try to to work. once work is completed on Associate in Nursing object, energy is transferred, and also the object moves with a replacement constant speed. we have a tendency to decision the energy that's transferred K.E., and it depends on the mass and speed achieved.Kinetic energy of Associate in Nursing object is that the live of the work Associate in Nursing object will treat virtue of its motion.Kinetic energy may be a scalar amount, and it's entirely represented by magnitude alone and is given by K.E = 1 /2 mv² .....(1) where "m" is that the body’s mass, and "v" is that the body’s speed.It is given that speed is 35 meters per second and mass of football is 0.4 kg .
Using equation (1) , we get
K.E = 1 /2 (0.4)(35)²
= 490 / 2
= 245 J
Learn more about kinetic energy here :
https://brainly.com/question/25959744
#SPJ1
Mum bought some steaks . She put 2/5 of them in the refrigerator and the rest in the freezer . She put 12 in the freezer . How many streaks did she buy
Answer: 20 steaks
Step-by-step explanation: 12x0.6= 20
what is 99 divided by 3
Answer: 33
Step-by-step explanation:
3*33=99
Answer: 33
Step-by-step explanation:
9/3 = 3
90/3 = 30
99/3 = 33
Find the perimeter of the triangle whose vertices are (−3,−1), (1,−1), and (1,2). Write the exact answer
According to the solving the perimeter of the tringle = 12 cm.
What is the formula for triangle perimeter?Add the lengths of the triangle's sides to find its perimeter. For instance, if a triangle comprises sides a, b, as well as c, the perimeter of the that triangle is P = a + b + c.
What exactly is a 2D shape?2D objects have two dimensions, for example, width and height. A rectangle or even a circle are two-dimensional shapes. Because they have without depth, 2D forms are absolutely flat and can not be physically handled.
According to the given data:Points of the tringles:
A (−3,−1),
B (1,−1),
C (1,2)
we know that the:
Perimeter of the triangle = sum of all the side of the triangle
= AB + BC + CA
So
Length of the AB :
A (−3,−1),
B (1,−1),
AB =√((x2 – x1)² + (y2 – y1)²).
AB = √((1 – (-3))² + (-1 – (-1))²).
AB = √((4) + (0))
= √(16)
= 4
Length of the BC :
B (1,−1),
C (1,2)
BC =√((x2 – x1)² + (y2 – y1)²).
BC =√((1 – 1)² + (2 – (-1))²).
BC =√(0)² + (3)²).
BC = √(9)
= 3
Length of the CA:
A (−3,−1),
C (1,2)
CA =√((x2 – x1)² + (y2 – y1)²).
CA =√((1 – (-3))² + (2 – (-1))²).
CA =√((4))² + (3)²).
CA =√(16 + 9)
CA =√(25)
= 5
The perimeter of the triangle asked = AB + BC + CA
= 4 + 3 + 5
= 12 cm
According to the solving the perimeter of the tringle = 12 cm.
To know more about triangle perimeter visit:
https://brainly.com/question/23935199
#SPJ9
What is the remainder of (2x^(3)+2x^(2)-9x+9) -:- (x+3)?
The remainder of (2x^(3)+2x^(2)-9x+9) -:- (x+3) is 54
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the remainder?The quotient expression is given as
(2x^(3) + 2x^(2) - 9x + 9) -:- (x+3)
Set the divisor of the expression to 0
So, we have
x + 3 = 0
Evaluate the value of x
So, we have
x = -3
Substitute 3 for x in 2x^(3) + 2x^(2) - 9x + 9
So, we have
2(3)^(3) + 2(3)^(2) - 9(3) + 9
Evaluate the expression
So, we have
54
Hence, the remainder of (2x^(3)+2x^(2)-9x+9) -:- (x+3) is 54
Read more about remainder theorem at
https://brainly.com/question/2552383
#SPJ1
please help!
maths geometry
Step-by-step explanation:
trapezium means especially
AD || BC
AC = BC tells us that ABC is an isoceles triangle (both legs are identically long, which makes also their angles with their baseline AB equal).
therefore, A1 = B = 80°.
and because the sum of all angles in a triangle is always 180°, we get
180 = 80 + 80 + C1
C1 = 20°
(e)(1)
because of the law of a line intersecting parallel lines with the same angles, and AC is intersecting the parallel lines AD and BC, we know that
C1 = A2 = 20°
(e)(2)
because also the sum of all angles around a single point on one side of a line is 180°, we know D1 + D2 = 180°.
we also know that D2 is an angle in an equilateral triangle (that means all 3 sides are equally long, and therefore all 3 angles are equal too = 180/3 = 60°) and therefore
D2 = 60°.
therefore, D1 = 180 - 60 = 120°.
so, for the triangle ACD we have
180 = A2 + D1 + C2 = 20 + 120 + C2
C2 = 40° = 2×20 = 2×C1
(f)(1)
a kite is a quadrilateral, and as such the sum of all angles is 360°.
again remember the symmetry of a kite, so the angles at H and at F must be equal.
H = F = x
so, we have
360 = 110 + 50 + H + F = 110 + 50 + 2x
200 = 2x
x = 100°
(f)(2)
after drawing EG we see that this line splits the kite into 2 equal (ahem, congruent) triangles due to the symmetry of a kite exactly along that line.
and that splits both angles E and G in half for each of the triangles.
again, the sum of all angles in a triangle is 180°, so
180 = 110/2 + 50/2 + x = 55 + 25 + x = 80 + x
x = 100°
on a map, two cities are 5 1/2 inches apart. the map uses a scale of 2 inches =75 miles
what is the actual distance between the two cities?
Answer:
187.5 miles
Step-by-step explanation:
We can use the rationing method to solve for this problem.
2 inches on map = 75 miles actual distance
1 inch on map = (75 ÷ 2) = 37.5 miles actual distance
5.5 inches on map = (37.5 × 5) = 187.5 miles actual distance
What is the value of the quantity negative one sixth cubed all raised to the power of negative 3? 10,077,696 1 −1 −10,077,696
Answer:-20 238
Step-by-step explanation:
Answer: The answer is not that
Step-by-step explanation:
The answer would be 1.
Question 5(Multiple Choice Worth 2 points)
(Multi-Step Percent Problems MC)
Oliver borrowed $2,500 to purchase a riding lawn mower for his lawn care business. The bank offered him an interest rate of 20% for 3 months Calculate the simple
interest using /-prt.
O $60
O$125
O$1,250
O$1,500
The 20% rate the bank borrowed Oliver the loan for 3 months gives an interest of $125.
How can the simple interest be calculated?The amount Oliver borrowed = $2,500
The interest rate applied to the loan = 20%
Required: To calculate the simple interest using the formula, I = P•R•T
Where;
I = The simple interest
P = The principal borrowed = $2,500
T = The time or loan duration = 3 months = 1/4 year
R = The rate at which the loan is applied = 20% = 0.2
Therefore;
I = $2,500 × 0.2/year × 3/12 year = $125
The correct option for the interest paid on the loan is therefore;
$125Learn more about simple interest calculations here:
https://brainly.com/question/20690803
#SPJ1
Answer:
125
Step-by-step explanation:
SOMEONE PLEASE HELPPPO
By evaluating the functions we get:
f(3)= -15f(-2) = -1g(4) = 23g(-5) = 77g(a) = 3*a^2 - 3*a - 13How to evaluate a function?Here we have the two functions:
f(x) = -2x - 5
g(x)= 3x^2 - 3x - 13
And we want to evaluate them in some values of x, first let's do the ones for f(x).
We just replace the variable x by the numbers.
f(3)= -2*3 - 5 = -10 - 5 = -15
f(-2) = -2*(-2) - 5 = 4 - 5 = -1
The ones for the function g(x) are:
g(4) = 3*4^2 -3*4 -13 = 23
g(-5) = 3*(-5)^2 - 3*(-5) - 13 = 77
g(a) = 3*a^2 - 3*a - 13
If you want to learn more about evaluating functions:
https://brainly.com/question/1719822
#SPJ1
Please help! How are you supposed to fill in something that isnt there? If you took the derviative of x wouldn't it be one?
Answer:
f'(5) = 1
Step-by-step explanation:
You are right. The derivative of f(x) = f'(x) = 1 a constant
If you plot y = f'(x) = 1 it will be a vertical line passing through x = 1 (See graph)
This means f'(x) is constant and equal to 1 for all values of y
So whether it is f'(5) or f'(100) the value = 1
f'(5) = 1
Does 8 over 10 plus 7 over 100 represents 0.87
Answer: Yes because it equals 87/100 which in decimal form is 0.87.
Step-by-step explanation:
In 1990, the cost of tuition at a large Midwestern university was $94 per credit hour. In 2004, tuition had risen to $290 per credit hour.
Determine a linear function
C
(
x
)
to represent the cost of tuition as a function of
x
, the number of years since 1990.
The linear function c(x) to represent the cost of tuition as a function of "the number of years since 1990" denoted by "x" is [tex][c(x) = 14x+94][/tex].
As per the question statement, the cost of tuition at a large Midwestern university was $94 per credit hour in 1994 while it had risen to $290 per credit hour in 2004.
We are required to determine a linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x".
To solve this question, we need to know the equation of a line passing through two points (x₁, y₁) and (x₂, y₂) which goes as
[tex](y-y_{1} )=(\frac{y_{2} -y_{1} }{x_{2} -x_{1}})(x-x_{1})[/tex].
Here, if we consider (x = 0) at 1990, c(x) = 94.
And since the standard form of conversion of functions into coordinate points goes as [y = f(x)], i.e., the ordinate is a function of the abscissa, therefore in this case, [y = c(x) = 94].
Thus, we can consider (x₁, y₁) as (0, 94).
Similarly, at 2004, [x = (2004-1990) = 14], and c(x) = 290, i.e.,
We can consider as (x₂, y₂) as (14, 290).
Using the values of (x₁, y₁) and (x₂, y₂), in the above mentioned standard equation of line passing through two points, we get,
[tex](y-94)=\frac{290-94}{14-0} (x-0)\\or, (y-94)=\frac{196}{14}x\\or,(y-94)=14x\\or,y=14x+94[/tex].
Hence, the linear function c(x) that represents the cost of tuition as a function of "the number of years since 1990", denoted by "x" is [tex][c(x) = 14x+94][/tex].
Linear Function: In Mathematics, a function is an operator which when provided with a input, gives a certain output, and when a function can be depicted in form of a linear equation, it is known as a linear function.To learn more about Linear Functions, click on the link below.
https://brainly.com/question/21107621
#SPJ9
What percent of a circle is 2/3 of a circle?
Answer: 66.66%
Step-by-step explanation:
1=100%
2/3=
1*2/3=
100%*2/3=
200%/3=66.66%
What’s the coefficient in this expression, 12x+z^4.
12
x
z
4
Answer:
12 is the coefficient.
Step-by-step explanation:
Please help me on this one’
Larry weighs 120 pounds and rides his bike at an average speed of 12 miles per hour. Jason weighs 90 pounds and rides his bike at an average speed of 9 miles per hour. Larry and Jason start at the same place and ride their bikes in opposite directions. How far apart, in miles, will Larry and Jason be after riding their bikes for 10 minutes? And Identify the information that is NOT needed to determine how far apart Larry and Jason will be after riding their bikes for 10 minutes.
After riding their bikes, Larry and Jason will be 3.5 miles apart after 10 minutes of their start.
We have Larry and Jason riding their bikes at the speed of 12 miles/hr and 9 miles/hr respectively in opposite directions.
We have to determine how far apart, in miles, will Larry and Jason be after riding their bikes for 10 minutes.
How will you calculate the distance traversed by a body ?The distance travelled can be calculated using the formula -
distance = speed x time
According to the question -
Average speed of Larry = 12 miles/hr
The distance covered by Larry in 10 minutes = d [1] = 12 x 10/60 =
2 miles.
Average speed of Jason = 9 miles/hr
The distance covered by Jason in 10 minutes = d [2] = 9 x 10/60 =
1.5 miles.
Distance between Jason and Larry after 10 minutes -
d[1] + d[2] = 2 + 1.5 = 3.5 miles.
Hence, Larry and Jason will be 3.5 miles apart after 10 min of riding in the opposite directions.
To solve more questions on Kinematics, visit the link below-
https://brainly.com/question/12389739
#SPJ1
Which function has an inverse that is a function?