Answer:
Step-by-step explanation:
2x+3x+4x=180 degrees
9x=180 fdegrees
x=180/9
x=20
2x=40
3x=60
4x=80
Answer:
18
Step-by-step explanation:
The measures of the angles of a triangle are in the ratio 2:3:4 means we have one interior angle measuring 2x, another measuring 3x, and the last one measuring 4x. We know the sum of the measures of the interior angles of a triangle is 180 degrees.
We need to solve the following equation to find first x, and then find the measurement of each interior angle of the triangle.
2x+3x+4x=180
(2+3+4)x=180
(9)x=180
x=180/9
x=20
So one interior angle measures 2x=2(20)=40.
Another measures 3x=3(20)=60.
The last measuring 4x=4(20)=80.
The exterior angles of this triangle therefore measure the following:
180-40=140
180-60=120
180-80=100
So the un-simplified ratio of the measures of the exterior angles is as follows:
140:120:100.
Let's simplify that.
It is easy to see each number is divisible by 10.
Let's reduce it by dividing each by 10:
14:12:10
Let's simplify more (as we want the most simplified ratio).
Each number is divisible by 2 since they are all even.
Let's reduce again but not by dividing by 2:
7:6:5
So the simplified ratio of the measures of the exterior angles of the triangle is a:b:c=7:6:5 and so a+b+c=7+6+5=18.
Answer is 18.
Jeremy's coach makes him run clockwise around a circular track with radius of 50 meters. Jeremy manages to maintain a constant speed around the track. He takes 48 seconds to finish one lap of the track. From his starting point, it takes him 12 seconds to reach the northernmost point of the track. Answer the following questions below assuming that the center of the track at the origin and the northernmost point is on the y-axis.
a. Give Jeremy's coordinates at his starting point.
b. Give Jeremy's coordinates when he has been running for 4 seconds.
c. Give Jeremy's coordinates when he has been running for 32 seconds.
Answer:
Coordinates of the starting point ( -50 ; 0 )
Coordinates 4 seconds later Q ( - 25*√3 ; 25 )
Coordinates 32 seconds later R ( 25 ; - 25*√3 )
Step-by-step explanation:
a) If Jeremy takes 48 seconds fr a lap then
The length of the lap ( length of the circle ) is:
L = 2*π*r ⇒ L = 100*π
If the time for one lap was 48 seconds at a constant speed, the speed was
v = 100*π / 48 [m/s]
v = 6,54 m/s
12 seconds is 1/4 0f 48 in that time he (she) reach the northernmost point, then he(she) necessarily started on the negative side of the x-axis the coordinates at this point are
( -50 ; 0 )
b) 4 seconds later, at v = 6,54 m/s by rule of three
In 12 seconds 90⁰
In 4 seconds (the third part ) x ??
x = 30⁰
sin 30⁰ = 1/2
cos 30⁰ = (√3)/2
And coordinates for the point are
sin 30⁰ = 1/2 = y/50 ⇒ y = 25
cos 30⁰ = (√3)/2 = x / 50 ⇒ x = 25*√3
coordinates of the point 4 seconds later
Q ( - 25*√3 ; 25 ) she (he) is in the negative part of x-axis
c) 32 seconds later
32 is 12 + 12 + 8
Then she (he) is 8 seconds below the positive side of x-axis
8 is 2/3 of 12 ( negative 60⁰ )
sin 60⁰ = (√3)/2 = y/50 y = 25*√3 negative
cos 60⁰ = 1/2 * 50 = X/50 x = 25
Coordinates of the point R
R ( 25 ; - 25*√3 )
Monica Ramirez works at the hospital as a nursing assistant. She works 15 hours per week and earns $8.50 per hour. What is Monica’s straight-time pay for each week? *
1 point
$120.00
$127.00
$127.50
$120.50
Answer:
Answer:
C. She makes $127.50 a week
Step-by-step explanation:
Since we are looking for how much she makes every week, we need to multiply her number of hours by the pay. She makes 8.50 per hour and works 15 hours.
8.5x15=127.5
She makes $127.50 a week
Step-by-step explanation:
The solution is Option C.
The total amount of straight time pay of Monica for the week is $ 127.50
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the total number of hours worked in the week by Monica be = T
The value of T = 15 hours
Let the earnings per hour of Monica be = $ 8.50
Now , the equation will be
Total straight line pay for Monica = number of hours worked in the week by Monica x earnings per hour of Monica
Substituting the values in the equation , we get
Total straight line pay for Monica A = 15 x 8.50
Total straight line pay for Monica A = $ 127.50
Therefore , the value of A is $ 127.50
Hence , The total amount of earnings of Monica for the week is $ 127.50
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In which of these situations would it be more appropriate to use a probability model rather than a regression/data-mining approach?
a. Predicting when the customer will make her next purchase.
b. Predicting which customer is most likely to churn in the next year.
c. Predicting the brand that the customer will buy during her next category purchase.
d. Predicting whether the customer will buy the brand at least once in the next year.
e. Predicting whether the customer will churn in the next year
Answer:
The correct options are b, c and d.
Step-by-step explanation:
The regression or data mining approach is used to predict the future value of the variable under study.
Whereas the probability model is used to predict the chances or likelihood of an event taking place.
Predicting which customer is most likely to churn in the next year.To predict which customer is most likely to churn in the next year, we need to compute the probability for customers who are likely to churn in the next year.
Thus, a probability model would be used.
Predicting the brand that the customer will buy during her next category purchase.Each brand has a specific probability of being purchased by a customer.
Thus, a probability model would be used.
Predicting whether the customer will buy the brand at least once in the next year.In this case also we need to compute the probability of a customer buying the brand at least once in the next year.
The correct options are b, c and d.
If the length of the legs of a right triangle are 18 and 34, what is the length of the hypotenuse? Round your
answer to the nearest tenth, if necessary.
Answer:
The answer is 38.5Step-by-step explanation:
Since we have been given the legs of the right angled triangle we can use Pythagoras theorem to find the hypotenuse
That's
[tex] {h}^{2} = {b}^{2} + {c}^{2} [/tex]
where
h is the hypotenuse
The legs of the triangle are 18 and 34 so the hypotenuse is
[tex] {h}^{2} = {18}^{2} + {34}^{2} [/tex]
[tex]h = \sqrt{324 + 1156} \\ h = \sqrt{1480} \\ h = 2 \sqrt{370} [/tex]
h = 38.47076
We have the final answer as
h = 38.5 to the nearest tenthHope this helps you
Answer:
38.5
Step-by-step explanation:
Hello!
To find the length of a missing side of a right triangle we use the equation
[tex]a^{2} +b^{2} =c^{2}[/tex]
a is a leg
b is the other leg
c is the hypotenuse
Put in what we know
[tex]18^{2} +34^{2}= c^{2}[/tex]
Simplify
[tex]324+1156 = c^{2}[/tex]
Simplify
[tex]1480 = c^{2}[/tex]
Take the square root of both sides
38.470 = c
Round to the nearest tenth
38.5 = c
Hope this helps!
On his fishing trip Justin rides on hist 12 km south. The fish aren’t biting so he changes location and goes 4 km west. What is Justin's displacement?
Answer:
Displacement= 12.65 km S 18.44°W
Step-by-step explanation:
Justin rides on hist 12 km south.
He changes location and goes 4 km west.
The displacement from his current location = X
X²= 12²+4²
X²= 144+16
X²= 160
X= √160
X= 4√10
X= 12.649 km
X= 12.65 km
His total distance covered=12+4
His total distance covered= 16 km
Tan ^-1 12/4= angle
71.56° = angle
90-71.56= 18.44°
Displacement= 12.65 km S 18.44°W
4. A recent poll of 1079 adults finds that 55% of Americans support a more stringent immigration law. Construct a 99% confidence interval of the proportion of the population that will support such a law.
Answer:
0.5306[tex]<\mu<[/tex]0.5694
Step-by-step explanation:
USing the formuls for calculating the confidence interval for the population proportion;
CI = p±Z*√[p(1-p)/n]
p is the percentage proportion of the population 55%
Z is the z-score at 99% confidence interval = 2.576
n is the sample size = 1079
CI = 0.55 ± 2.576*[0.55(1-0.55)/√1079]
CI = 0.55 ± 2.576*[0.55(0.45)/√1079]
CI = 0.55 ± 2.576*[0.2475/√1079]
CI = 0.55 ± 2.576*[0.2475/32.85]
CI = 0.55 ± 2.576*[0.00753]
CI = 0.55 ±0.0194
CI =(0.55-0.0194, 0.55+0.0194)
CI = (0.5306, 0.5694)
Hence, a 99% confidence interval of the proportion of the population that will support such a law is 0.5306[tex]<\mu<[/tex]0.5694
(10+i)^2 = (in form a+bi)
Answer:
99+20i
Step-by-step explanation:
(10+i)^2
➡
(10 + i) × (10 + i) = 100 + 10i + 10i + i^2 add like terms
100 + 20i + i^2 since i^2 = -1 we can write the expression like this
99 + 20i
True or false: the coordinate grid below shows the triangle transformed following the rule : (x,y)-> (x-4,y+3)
Answer: True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Step 1: Find the Coordinates of the Original Triangle
(2, -2)
(6, -3)
(5, 2)
Step 2: Apply the Transformation to the Coordinates
(2-(4),-2+(3)) -> (-2, 5)
(6-(4),-3+(3)) -> (2, 0)
(5-(4),2+(3)) -> (1, 5)
Step 3: Compare the points on the red triangle with the points you got
(-2, 5) = (-2, 5)
(2, 0) = (2, 0)
(1, 5) = (1, 5)
Because the coordinates are the same we can conclude that the triangle was transformed with the rule: (x,y)-> (x-4,y+3)
1440 men had sufficent food for 32 days in a camp
Answer:
the boy is gay
Step-by-step explanation:
kkkjssjska
Write an algebraic expression for the word expression.
the sum of 9 and a number x
The expression is ___
Answer: 9 + x
The word "sum" indicated that we are adding the two numbers, so we put the number and the variable in an expression that adds them together. There is no indication that there is anything else we need to add to this expression, so this is all you need. (The "x" is a variable, which can represent any number.)
The algebraic expression for the word expression is the sum of 9 and a number x will be 9 + x.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
In other meaning, expression is very useful to determine the end or root value of constraint.
As per the given phrase,
The sum of 9 and the number x.
The sum is an addition and represents by the symbol "+".
Therefore, 9 + x
Hence "The algebraic expression for the word expression is the sum of 9 and a number x will be 9 + x".
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Find the distance that 5,2 is from the origin
Answer:
Step-by-step explanation:feel pleasure to help u.
Find the value of (-3)4 +(-2)4 +(-1)4
the value of (-3)4+(-2)4×(-1)4 is -24
Answer:
98
Step-by-step explanation:
-3⁴ = -3*-3*-3*-3 = +81 = 81
-2⁴ = -2*-2*-2*-2 = +16 = 16
-1⁴ = -1*-1*-1*-1 = +1 = 1
Then:
(-3)⁴ + (-2)⁴ + (-1)⁴ = 81 + 16 + 1
= 98
Find the equation of the line that contains the point (7.9) and is perpendicular to the line 5x + 3y = 4. Write the equation in the form
y = mx + band identify m and b
Answer:
[tex]y = \frac{3}{5} x + \frac{24}{5} [/tex]
m= 3/5
b= 24/5
What is the area of this triangle?
Answer:
21 units²
Step-by-step explanation:
A=1/2bh
b=6
h=7
1/2(6)(7)=
1/2(42)=
21 units²
Over 4 days the temperature was 4, 6, -12, and -5 degrees. What was the average temperature?
Answer:
-1.75
Step-by-step explanation:
add -12 and -5, you get -17, and 4 and 6, get 10, add -17 and 10 to get -7, and divide by 4 and get -1.75
free cus i have 300,000 - 100 = ?
Answer:
Step-by-step explanation:
300,000-100
300,00 + -100
=299900
Answer:
299900
Step-by-step explanation:
A function is defined as (f of x) = -3^4√x-9. Evaluate (f of x) at x=81 A. -36 B. -18 C. -27 D. -12
Answer:
F(x) = -3^(27)
According to the way the question was arranged, the answer above is the answer.
But the options given none of them matches my answer.
Step-by-step explanation:
A function is defined as (f of x)
= -3^4√x-9.
F(x)= -3^(4√x-9) at x= 81
√x= √81
√x= 9
F(x)= -3^(4(9)-9)
F(x) = -3^(36-9)
F(x) = -3^(27)
pls helpppp c=30m+50 and c=20m+100. solve for c and show your work.
Answer:c=200
Step-by-step explanation:
30(5) + 50 = 200
20(5) + 100 = 200
-------------------------------|
100 30m
- 50 - 20m
——— ———
50 10m 50/10 = 5 [m=5]
30 POINTS! 3 questions! EASY 1. Jason is 22, which is 6 years older than twice his sister Taylor’s age.How old is Taylor? Enter your answer in the box.
2. Each month, Sal must pay for car insurance and fuel to drive a vehicle. Sal's parents agree to pay p percent of his car expenses. The cost of car insurance is the same every month, but the cost of fuel depends on d, the number of miles Sal drives. The expression (1−p)(0.10d+60) represents how much Sal must pay toward his monthly car expenses. Which part of the expression represents the percentage of the monthly expenses that Sal must pay?
A. 0.10d + 60
B. 1−p
C. 60
D. 0.10d
3. Which equation represents this sentence? Twenty-eight is the product of four and a number.
A. 28=4n
B. 28=4+n
C. 28=4n
D. 28=4n
Answer:
question 1: she is 8 years old Question 2: C-60
Step-by-step explanation:
the first three terms of an arithmetic progression is (x + 1), (4 x - 2) and 6 x - 3 if the last term is 18 find the value of x
Answer:
2
Step-by-step explanation:
Since it is AP, the common difference is same for any term:
(4x - 2) - (x + 1) = (6x - 3) - (4x - 2)3x - 3 = 2x -13x - 2x = 3 - 1x= 2The first 3 terms are:
3, 6, 9Since the last term is 18, it means this AP has 6 terms:
{3, 6, 9, 12, 15, 18}Answer: as we need to find the value of x only, it is = 2
What value does the 1 represents in the number 4,105.8
Answer:
the 1 represents the value of 100 of one-hundreth place
Step-by-step explanation:
Two rectangles have equal areas. If the base and altitude of one are 12mm and 8mm, and the base of the other is 16mm, what is the altitude of the second rectangle?
Answer:
6mm
Explanation:
since the area of both rectangle is equal, therefore :
Arectangle 1= Arectangle 2
base 1*altitude 1 =base 2*altitude 2
12mm*8mm = 16mm* altitude 2
96mm²= 16mm* altitude 2
96mm²/16mm = altitude 2
6mm = altitude 2
a company needs to refill printing paper. each one of printing paper costs $30 and a delivery fee of $10. write an equation to find the total cost of purchasing x number of boxes of printing paper.
Answer:
Cost in $= x(y(30))+10
Step-by-step explanation:
a company needs to refill printing paper. each one of printing paper costs $30 and a delivery fee of $10.
Let y be the number of paper in a box
Let x be the number of box to be purchased.
So it means for each x box, there are y paper costing $30 and a delivery fee for the box is $10
Cost in $= x(y(30))+10
A statistics practitioner would like to estimate a population mean to within 50 units with 99% confidence given that the population standard deviation is 250. What sample size should be used? b. Re-do part (a) changing the standard deviation to 50. c. Re-do part (a) using a 95% confidence leve
Answer:
(a) 167
(b) 7
(c) 97
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean μ is:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error is:
[tex]MOE=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
Then the formula to estimate the sample size is:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
(a)
For 99% confidence interval the critical value of z is:
z = 2.58.
The standard deviation is, 250.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{2.58\times 250}{50}]^{2}\\\\=(12.9)^{2}\\\\=166.41\\\\\approx 167[/tex]
The sample size that should be used is 167.
(b)
Now the standard deviation is, 50.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{2.58\times 50}{50}]^{2}\\\\=(2.58)^{2}\\\\=6.6564\\\\\approx 7[/tex]
The sample size that should be used is 7.
(c)
Now a 95% confidence level is used.
For 95% confidence interval the critical value of z is:
z = 1.96.
Compute the sample size as follows:
[tex]n=[\frac{z_{\alpha/2}\cdot \sigma }{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\times 250}{50}]^{2}\\\\=(9.8)^{2}\\\\=96.04\\\\\approx 97[/tex]
The sample size that should be used is 97.
A party planner is going to use an arch of balloons for a parade of recent graduates. The estimated curve the
balloons will create is modeled by the function given in the table, where x represents the distance in feet along
the ground from the start and f(x) represents the height in feet above the ground.
The planner needs a clearance of 9 feet under the arch. Has the planner met the minimum height?
No, because the width of the arch is 8 feet
Yes, because the width of the arch is 9.6 feet
No, because the maximum height of the arch is 8 feet
Yes, because the maximum height of the arch is 9.6
feet
Answer:
Option (4)
Step-by-step explanation:
Party planner has used an arc of balloons for the parade.
This arc starts from x = 0 along the ground and f(x) defines the height of the arch.
From the table attached, it is clear that at x = 4 maximum height of the arch is 9.6 feet.
Therefore, clearance space below the arc is 9.6 feet which is greater than 9 feet, minimum height required for the clearance of the parade.
Option (4) will be the answer.
Answer:
D. yes, because the maximum height of the arch is 9.6 feet
Step-by-step explanation:
EDGE 2020 :)
you invested $27000 in two account paying 2% and 8% annual interest respectively of the total interest earned for the year was $2100 how much was invested at each rate? the amount invested at 2% is
Answer:2100
Step-by-step explanation:
Which tables display linear functions?Check all that apply
Please help me!!!!!
Answer:
The first one and the last one. A and D.
Step-by-step explanation:
A linear equation is and equation where the line is going up on a graph. In order for that to happen, y must always be bigger than x. The first and last chart all the way to the right is the only one that has that trait. :)
Please help me with this is important and I’ll give you a brainless if the answer is right
Answer:
She subtracted 5 and got 6 instead of subtracting -5 which is 16
Step-by-step explanation:
11 - (-5)
Subtracting a negative is like adding
11 +5
16
She subtracted 5 and got 6 instead of subtracting -5 which is 16
A 1,000 ohm resistor has a tolerance of 20%. This means that the resistor actual value can be +-20%. What's the acceptable range of values for this resistor
Answer:
[800, 1200]
Step-by-step explanation:
We need to calculate the acceptable range of values for this resistor. The center point would be the nominal resistance: 1000 ohms.
20% above that would be 1.20(1000 ohms) = 1200 ohms, and 20% below would be (0.80)(1000 ohms) = 800 ohms.
Thus, the acceptable resistance range in ohms is [800, 1200]
Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25.
Answer:
asymptotes: x = -5, x = 5zero: x = 0Step-by-step explanation:
The function of interest is ...
[tex]f(x)=\dfrac{5x}{x^2-25}=\dfrac{5x}{(x-5)(x+5)}[/tex]
The asymptotes are found where the denominator is zero. It will be zero when either factor is zero, so at x = 5 and x = -5
__
The zeros are found where the numerator is zero. It will be zero for x = 0.
The asymptotes are x=-5, x=5; the zero is x=0.
Answer:
The asymptotes are x=-5, x=5; the zero is x=0.
Step-by-step explanation: