Answer:
P [ X < 67 ] = 0,66,81 or 66,81 %
Step-by-step explanation:
We assume Normal Distribution N ( μ ; σ ) N ( 76 ; 6 )
z score for 67 is :
z(s) = ( X - μ ) /σ
z(s) = ( 67 - 76 ) / 6
z(s) = - 9 / 6
z(s) = - 1,5
with 1,5 we fnd n z-table area undr the curve α = 0,6681
Then P [ X < 67 ] = 0,66,81 or 66,81 %
Points A( − 1, 7), B(2, 19), and C(3, y) are on the same line. Find y.
Answer: y=23
Step-by-step explanation:
If Points and A,B and C lines on the same line then they will have the same slopes so since we have the coordinates of A and B we will use the to write an equation in slope intercept form.
To write it in slope intercept form we will need to find the slope and the y intercept.
To find the slope you will find the change in the y coordinates and divide it by the change in the x coordinates.
Using the coordinates (-1,7) and (2,19) the y coordinates are 7 and 19 and the x coordinates are -1 and 2.
Slope : [tex]\frac{7-19}{-1-2} \frac{-12}{-3} = 4[/tex] In this case the slope is 4 so we will use that to find the y intercept by using point A coordinate.
The slope intercept formula says that y=mx +b where me is the slope and b is the y intercept.
7=4(-1) + b
7 = -4 + b
+4 +4
b= 11 The y intercept is 11.
Now we can write the whole equation as y=4x + 11 .
To answer the question now, where we need to find y , we will plot the x coordinate which is 3 into the equation and solve for y.
y = 4(3) + 11
y = 12 + 11
y = 23
Please answer this correctly without making mistakes
Answer:
2 13/15 miles
Step-by-step explanation:
Hey there!
Well first we need to find the distance between Lancaster and Hillsdale and Lancaster to Silvergrove.
9 + 7 13/15
= 16 13/15
LS is just 14 miles.
Now we can do,
16 13/15 - 14
= 2 13/15 miles
Hope this helps :)
Twelve dieters lost an average of 13.7 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the same diet, but without the herbal formula, and lost an average of 10.7 pounds during the same time. The standard deviation of the "fat-blocker" sample was 2.6 and the standard deviation of the control group was 2.4. Find the 95% confidence interval for the differences of the means.
Answer:
The 95% confidence interval is [tex]0.88 < \mu_1 - \mu_2 < 5.12[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean for fat-blocking [tex]\= x_1 = 13.7[/tex]
The sample size for fat-blocking [tex]n = 12[/tex]
The standard deviation for fat-blocking is [tex]\sigma_1 = 2.6[/tex]
The sample mean for control group is [tex]\= x _2 = 10.7[/tex]
The sample size for control group is [tex]n_2 = 12[/tex]
The standard deviation for control group is [tex]\sigma _2 = 2.4[/tex]
Given that the confidence level is 95% then the level of significance can me mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha =0.05[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
substituting values
[tex]df = 12 +12 - 2[/tex]
[tex]df = 22[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of 22 form the students t-distribution , the value is
[tex]t_{\frac{\alpha }{2}, df } = 2.074[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2}, df } * \sqrt{ \frac{\sigma^2_1 }{n_1 } + \frac{\sigma^2_2 }{n_2 } }[/tex]
substituting values
[tex]E = 2.07 4 * \sqrt{ \frac{ 2.6^2 }{12 } + \frac{2.4^2 }{12 } }[/tex]
[tex]E = 2.12[/tex]
the 95% confidence interval for the differences of the means is mathematically represented as
[tex]\= x_1 - \= x_2 - E < \mu_1 - \mu_2 < \= x_1 - \= x_2 + E[/tex]
substituting values
[tex]13.7 - 10.7 - 2.12 < \mu_1 - \mu_2 < 13.7 - 10.7 + 2.12[/tex]
[tex]0.88 < \mu_1 - \mu_2 < 5.12[/tex]
A TV Dinner Company Sells Three Types Of Dinners: A Chicken Dinner For $10, A Beef Dinner For $11, Or A Fish Dinner For $12. At One Particular Grocery Store, They Sold 200 Dinners For A Grand Total Of $2138. Required:a. If they sold three times as many chicken dinners as they did fish, then how many of each kind of dinner did they sell?b. Find the equation of the quadratic function that passes through the points (−1, 9), (2, 6), and (3, 17). Write your answer in the form y = ax2+bx+c.
Answer:
a) The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.
b) [tex]y=3x^{2}-4x+2[/tex]
Step-by-step explanation:
a)
In order to solve part a of the problem, we must start by setting our variables up:
C=# of Chicken dinners
B=# of Beef dinners
F=# of Fish dinners
Next we can use these variables to build our equations. We start by taking the fact that they sold a total of 200 dinners. The sum of all the variables should add up to that so we get:
C+B+F=200
Then the problem tells us the price of each dinner and the total amount of money they made from selling the dinners that day:
"A TV Dinner Company Sells Three Types Of Dinners: A Chicken Dinner For $10, A Beef Dinner For $11, Or A Fish Dinner For $12. For A Grand Total Of $2138"
So we can use this information to build our second equation:
10C+11B+12F=2138
We have two equations now but three variables, so we need an additional equation so we can finish solving this. The problem tells us that:
"they sold three times as many chicken dinners as they did fish"
which translates to:
C=3F
so now we have enough information to finish solving the problem. We can start by substituting the last equation into the previous two equations so we get:
C+B+F=200
3F+B+F=200
4F+B=200
and
10C+11B+12F=2138
10(3F)+11B+12F=2138
30F+11B+12F=2138
42F+11B=2138
So now we can take the two bolded equations and solve them simultaneously. We can solve them by using any method we wish. Let's solve it by substitution.
We start by solving the first equation for B so we get:
B=200-4F
and now we substitute it into the second equation:
42F+11(200-4F)=2138
and now we solve for F
42F+11(200-4F)=2138
42F+2200-44F=2138
-2F=2138-2200
[tex]F=\frac{-62}{-2}[/tex]
F=31
So now that we know the value of F, we can find the values of the rest of the variables so we can take the previous equations to figure this out:
B=200-4F
B=200-4(31)
B=200-124
B=76
and finally:
C=3F
C=3(31)
C=93
So
The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.
b) For the second part of the problem we need to build a system of equations to find the equation we are looking for. We were given three points:
(-1,9), (2,6) and (3,17)
so we need to substitute each of the points on the given quadratic equation so we get:
[tex]9=a(-1)^{2}+b(-1)+c[/tex]
eq.1: [tex]9=a-b+c[/tex]
[tex]6=a(2)^{2}+b(2)+c[/tex]
eq. 2: [tex]6=4a+2b+c[/tex]
[tex]17=a(3)^{2}+b(3)+c[/tex]
eq. 3: [tex]17=9a+3b+c[/tex]
So now that we have our three equations we can solve them simultaneously to get the values of a, b and c by using the method you feel more comfortable with. Let's solve it by elimination:
So let's take the first equations and let's subtract them:
[tex]9=a-b+c[/tex]
[tex]-6=-4a-2b-c[/tex]
-------------------------------
3=-3a-3b
And now we repeat the process with the first and third equations:
[tex]9=a-b+c[/tex]
[tex]-17=-9a-3b-c[/tex]
-------------------------------
-8=-8a-4b
So now we have two new equations we can solve simultaneously, but they can be simplified by dividing the first one into -3 and the second one into -4 so they become:
a+b=-1
2a+b=2
We can now solve them by substitution. Let's solve the first one for a and then let's substitute it into the second equation:
a=-1-b
let's substitute
2(-1-b)+b=2
and solve for b
-2-2b+b=2
-b=4
b=-4
Now we can find a:
a=-1-b
a=-1+4
a=3
and now we can find c:
c=9-a+b
c=9-3-4
c=2
So we can use these answers to build our equation:
[tex]y=ax^{2}+bx+c[/tex]
[tex]y=3x^{2}-4x+2[/tex]
Find the common ratio for the following sequence. Type a numerical answer in the space provided. If necessary, use the
/ key to represent a fraction bar. Do not type spaces in your answer.
2,-2, 2, -2, ...
Answer:
-1
Step-by-step explanation:
the common ratio in this geometric series is -1
Jaime went to the mall with $42. If he bought a T-shirt and had $18 left, how much did the T-shirt cost Jaime in dollars?
Answer:
$24
Step-by-step explanation:
You simply do $42-$18
=24
Answer:
$24
Step-by-step explanation:
At the start, Jaime had $42. In order to find out how much the T-shirt he purchased costs, we must subtract 18 from 42.
42 - 18 = 24
Jaime spent $24 on the T-shirt.
10) How many possible outfit combinations come from six shirts, three
slacks, and five ties? *
A 15
B 18
C 30
D 90
Answer:
The answer is D)90
Hope I helped
what number has 7 ten thousands, 1 thousand, 1 hundred, and no ones?
Answer:
[tex]71,100[/tex]
Step-by-step explanation:
If you are trying to find a number that is written in word form, we can just use place values to find what goes where.
A number is broken down into this:
Ten thousands, thousands, hundreds, tens, ones.
If they have 7 ten thousands, the first digit will be a 7.
If they have 1 thousand, the second digit will be a 1.
If they have 1 hundred, the third digit will be a 1.
Since nothing is stated about tens, we assume it's value is 0.
And since there are no ones, it's value is 0.
So:
71,100.
Hope this helped!
The value (in dollars) of an airplane depends on the flight hours as given by the formula V= 1,800,000 - 250x . After one year, the value of the plane is between $1,200,000 and $1,300,000. Which range for the flight hours does this correspond to?
a. 1800 <= x <= 2100
b. 2200<= x <= 2500
c. 1500<= x <= 1800
d. 2000<= x <= 2400
Answer:
D
Step-by-step explanation:
To determine the range we must solve this inequality;
● 1200000<1800000-250x<1300000
Substract 1800000 from both sides.
● 1200000-1800000<1800000-250x<1300000-1800000
● -600000< -250x < -500000
Divide both sides by 250
● -600000/250 < -250x/250 < -500000/250
● -2400 < -x < -2000
Multiply both sides by -1 and switch the signs
● 2000 < x < 2400
The correct option is D. 2000<= x <= 2400
Given, the value of an airplane depends on the flight hours,
[tex]V= 1800000-250x[/tex], here x is the flight hours.
We have to calculate the range of x After one year.
Since, [tex]V= 1800000-250x[/tex]
[tex]250x=1800000-V\\\\x=\dfrac{1800000-V}{250}[/tex]
Since the value of the plane is between $1,200,000 and $1,300,000. So,
[tex]x=\dfrac{1800000-1200000}{250}[/tex]
[tex]x=\dfrac{600000}{250}[/tex]
[tex]x=2400\\[/tex]
When V is 1300000 then x will be,
[tex]x=\dfrac{1800000-1300000}{250} \\[/tex]
[tex]x=\dfrac{500000}{250}[/tex]
[tex]x=2000[/tex]
Hence the range of x will be from 2000 to 2400.
The correct option is D. 2000<= x <= 2400.
For more details on range follow the link:
https://brainly.com/question/10185991
4(c+3) =4+c+c+c+c+17
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?
Answer:
Suppose that the height (in centimeters) of a candle is a linear function of
the amount of time (in hours) it has been burning.
After 11 hours of burning, a candle has a height of 23.4 centimeters.
After 30 hours of burning, its height is 12 centimeters.
What is the height of the candle after 13 hours?
:
Assign the given values as follows:
x1 = 11; y1 = 23.4
x2 = 30; y2 = 12
:
Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29
m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19
:
Find the equation using the point/slope formula: y - y1 = m(x - x1)
y - 23.4 = -11.4%2F19(x - 11)
y - 23.4 = -11.4%2F19x + 125.4%2F19
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 23.4
y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19
y = -11.4%2F19x + 570%2F19
y = -11.4%2F19x + 30, is the equation
:
What is the height of the candle after 13 hours?
x = 13
y = -11.4%2F19(13) + 30
y = -148.2%2F19 + 30
y = -7.8 + 30
y = 22.2 cm after 13 hrs
Solve this and get 12 points
Answer:
9
Step-by-step explanation:
First, find x. Since x is the average of the three number, add the three up and then divided by three. Thus:
[tex]x=\frac{13+-16+6}{3}=3/3=1[/tex]
y is the cube root of 8. Thus:
[tex]y=\sqrt[3]{8}=2[/tex]
So:
[tex]x^2+y^3\\=(1)^2+(2)^3\\=1+8=9[/tex]
Answer:
ljih
Step-by-step explanation:
Which values of x are point(s) of discontinuity for this function? Function x = –4 x = –2 x = 0 x = 2 x = 4
Answer:
x=0 and x=2
Step-by-step explanation:
We need to check at each point where the function changes definition
At x= -2
On the left side -4 on the right side = -( -2)^2 = -4 continuous
At x=0
The point is not defined since neither side has an equals sign
discontinuous
x =2
on the left side 2^2 =4 on the right side 2
It is discontinuous
Answer:
x = 0
x = 2
Step-by-step explanation:
Edge 2020
~theLocoCoco
Write in words how we would say the following
3 square
Answer:
Three to the second power
Step-by-step explanation:
Hey there!
3 square
Can be written as the following,
Three to the second power
Hope this helps :)
In the figure below, circle O has a central ángel of 120 degrees. what is the area shaded of the circle in terms of ,r, the radius? Leave your answer in terms of pi.
Answer:
the area of a section of a circle is [tex]\frac{1}{360}[/tex]* Θ * (area of the circle)
the theta/360 tells us the amount of circle currently in question
so , the answer will be 1/3 pi r^2 [A]
70 points! Please answer fast!
Answer:
slope = 2
Step-by-step explanation:
will make it so simple and short
slope = rise / run
slope = 6 / 3
slope = 2
Answer:
B
Step-by-step explanation:
The formula for slope is (y2-y1)/(x2-x1)
In this case it is (1+5)/(3-0)
6/3
2
1. Quadratics: The path of the longest shot put by the Women’s track team at Sun Devil U is modeledby h(x) = -0.015x2 + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) isthe height of the shot put above the ground. (Both x and h(x) are measured in feet.)a. [3 pts] Determine h(24). Round your answer to 2 decimal places.
Answer:
23.08 feetStep-by-step explanation:
If the path of the longest shot put by the Women’s track team at Sun Devil U is modeled by h(x) = -0.015x² + 1.08x + 5.8 where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground, to determine h(24), we will have to substitute x = 24 into the modeled equation as shown;
[tex]h(x) = -0.015x^2 + 1.08x + 5.8\\\\if \ x = 24;\\\\h(24) = -0.015(24)^2 + 1.08(24) + 5.8\\\\h(24) = -0.015(576)+25.92+5.8\\\\h(24) = -8.64+31.72\\\\h(24) = 23.08\\[/tex]
Hence the value of the height at the horizontal distance of 24 feet is 23.08 feet to 2 decimal place.
If 2( a^2 +b^2 ) = ( a+b)^2 , then
a. a+b =0
b. a =b
c. 2a =b
d. ab =0
Answer:
the answer is a=b
Step-by-step explanation:
There are 30 colored marbles inside a bag. Six marbles are yellow, 9 are red, 7 are white, and 8 are blue. One is drawn at random. Which color is most likely to be chosen? A. white B. red C. blue D. yellow Include ALL work please!
Answer:
red
Step-by-step explanation:
Since the bag contains more red marbles than any other color, you are most likely to pick a red marble
algebra pyramid please answer !! be the first to be marked as a brainliest .
Answer:
The first pyramid:
63x
39x 24x
23x 16x 8x
The second pyramid:
162x
82x 80x
4x 78x 2x
The third pyramid:
12a+2b
9a+b 3a+b
9a b 3a
The fourth pyramid:
-19a
-5a -14a
3a -8a -6a
Step-by-step explanation:
All that an alegbra pyramid is is adding the two terms below it.
So you can see how I added the terms that lied below each number, such as in number 1: I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.
Hope this helped!
Which of the following is the correct equation for the distance formula for the points (x1, y1) and (x2,y2)?
A. D=sqrt (x2-x1)^2+(y2-y1)^2
B. D=sqrt (x2-y2)^2+(y1-x1)^2
C. D=sqrt -(y2-y1)^2+(x2-x1)^2
D. D=sqrt (x1-x2)^2+(y2-y1)^2
Answer:
A. D=sqrt( (x2-x1)^2+(y2-y1)^2 )
Step-by-step explanation:
The distance between two points is the root of the sum of the squares of the differences in their corresponding coordinates. The equation of choice A is the usual formulation.
__
Comment on answer choices
Because the square of a number is the same as the square of its opposite, the formula in choice D is also correct.
You are studying for your final exam of the semester up to this point you received 3 exam scores of 61% 62% and 86% to receive a grade of c and the class you must have an average exam score between 70% and 79% for all four exams including the final find the widest range of scores that you can get on the final exam in order to receive a grade of C for the class 63 to 100% 71 to 100% 68 to 97
There will be a total of 4 test scores including the final exam. To get a 70, the 4 tests need to equal 4 x 70 = 280 points , to be 79, they have to equal 4 x 79 = 316 points.
The 3 already done = 61 + 62 + 86 = 209 points.
The final exam needs to be between :
280 -209 = 71
316 -209 = 107. The answer would be between 71 and 100%
An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm, how many of these components should she consider to be 90% sure of knowing the mean will be within ± 0.1 ±0.1 mm?
Answer:
She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
Step-by-step explanation:
We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.
And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.
As we know that the margin of error is given by the following formula;
The margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm
n = sample size of components
[tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%
[tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%
Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.
So, the margin of error = [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.1 mm = [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]
[tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]
[tex]\sqrt{n}[/tex] = 59.22
n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.
Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.
The set of natural numbers is: infinite finite
Answer:
A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number.
Step-by-step explanation:
Answer:
Finite
Step-by-step explanation:
please give me brainliest
ax+r=7 , solve for x
Answer:
3
Step-by-step explanation:
a is 4 and 3 is x so 4+3=7
Answer: a=2 {x=3} r=1. 2(3)+ 1= 7
Step-by-step explanation:
16% of 242 = ?
Please help me solve this
Answer:
16% of 242 = 38.72
Step-by-step explanation:
16% = 16/100 = 0.16
242 * 0.16 = 38.72
Answer:
38.72
Step-by-step explanation:
242 * .16 = 38.72
Solve and graph the inequality. 45x + 5 < −3
Answer:
x < -8/45
Step-by-step explanation:
Step 1: Write out inequality
45x + 5 < -3
Step 2: Subtract both sides by 5
45x + 5 - 5 < -3 - 5
45x < -8
Step 3: Divide both sides by 45
45x/45 < -8/45
x < -8/45
Step 4: Graph
Question: Complete the point-slope equation of the line through (1,3)and (5,1). Use exact numbers. Equation: y-3=(Answer ?)
Answer:
y - 3 = -1/2(x - 1)
Step-by-step explanation:
Hey there!
Well point slope form is,
[tex]y - y_{1} = m(x - x_{1})[/tex]
We can use the point (1,3)
y - 3 = m(x - 1)
Now we need to find slope with the following formula,
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex], we’ll use the points (1,3) and (5,1).
[tex]\frac{1-3}{5-1}[/tex]
-2/4
Slope or m = -1/2
y - 3 = -1/2(x - 1)
Hope this helps :)
Examine the two triangles. Are the triangles congruent? Justify your conclusions. If they are congruent, complete the following statement: "Yes, triangle __ congruent to triangle __ giving a detailed explanation of your reasoning. If they are not congruent, explain why you think so. Be specific in your answer and make sure to show your work.
Answer: The triangles are not congruent
==========================================
Explanation:
For triangle DEF, the missing angle D is
D+E+F = 180
D+80+60 = 180
D+140 = 180
D = 180-140
D = 40
While the missing angle K in triangle JKL is
J+K+L = 180
80+K+50 = 180
K+130 = 180
K = 180-130
K = 50
---------------------
The three angles for triangle DEF are
D = 40E = 80F = 60The three angles for triangle JKL are
J = 80K = 50L = 50We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.
The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.
Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.
The simplified form of the expression (5.23x + 3.76) − (3.67x − 6.39) is?
Answer:
1.56x+10.15
Step-by-step explanation:
Answer:
1.56x + 10.15
Step-by-step explanation:
(5.23x + 3.76) – (3.67x – 6.39)
(a + b) – (c – d) = a + b – c + d
Remove the parentheses and change the signs as needed:
5.23x + 3.76 – 3.67x + 6.39.
Group the like terms and simplify:
5.23x – 3.67x + 3.76 + 6.39
1.56x +10.15.
The simplified form of (5.23x + 3.76) – (3.67x – 6.39) is 1.56x + 10.15.
