Answer:
Step-by-step explanation:
y = mx + b is the slope-intercept form of a line where m is the number value of the slope and b is the number value of the y-intercept. Our slope is given as 7, therefore, m = 7 in our equation. Our y-intercept is given as -10; thus, b = -10. Filling that in gives us y = 7x - 10
what is the solution for 3(x+3)=12
Answer: 3×4=12
Step-by-step explanation:
Brackets: X=1 , so 1+3=4 and 3+4=12
The playground director has a total of
24 basketballs and footballs. He has
6 more footballs than basketballs, How
many of each does he have?
Answer:
9 basketballs
15 footballs
Step-by-step explanation:
The number of basketballs will be y.
The number of basketballs will be y + 6.
y + y + 6 = 24
2y + 6 = 24
2y + 6 - 6 = 24 - 6
2y = 18
2y ÷ 2 = 18 ÷ 2
y = 9
y + 6
9 + 6 = 15
HELP ME WITH THIS GEOMETRY QUESTION!!! 18 POINTS!
Answer:
72
72
96
120
Step-by-step explanation:
The arcs are in the ratio:
3 : 3 : 4 : 5
Add all numbers in the ratio:
3 + 3 + 4 + 5 = 15
In the ratio, the sum of all numbers is 15.
In the real circle, the sum of the measures of all the arcs is 360.
360/15 = 24
Multiply all numbers in the ratio by 24.
72 : 72 : 96 : 120
Answer:
72
72
96
120
in the right triangle AB, mc=90, a=4, and sinA=1/2. what is the length of the hypotenuse?
Given:
In a right angle triangle ABC, [tex]m\angle C=90^\circ , a=4[/tex] and [tex]\sin A=\dfrac{1}{2}[/tex].
To find:
The length of the hypotenuse.
Solution:
It is given that [tex]m\angle C[/tex], so opposite side of this angle is the hypotenuse, i.e., c.
In a right angle triangle,
[tex]\sin \theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]
In the given triangle,
[tex]\sin A=\dfrac{a}{c}[/tex]
Substituting the given values, we get
[tex]\dfrac{1}{2}=\dfrac{4}{c}[/tex]
By cross multiplication, we get
[tex]1\times c=4\times 2[/tex]
[tex]c=8[/tex]
Therefore, the length of the hypotenuse is 8 units.
I need help with this math problem please
Answer:
option D
Step-by-step explanation:
[tex]9x^2 + 6x - 17 = 0 , \ where \ a = 9 \ , \ b = 6 \ , c = - 17[/tex]
[tex]x = \frac{ - b \ \pm \sqrt{b^2 - 4ac}}{2a} \\\\x = \frac{-6 \pm \sqrt{36 - (4 \times 9 \times -17)}}{2 \times 9}\\\\x = \frac{-6 \pm \sqrt{ 36 + 612}}{18}\\\\x = \frac{-6 \pm \sqrt{ 648}}{18}\\\\x = \frac{-6 \pm \sqrt{ 2^3 \times 3^4}}{18}\\\\x = \frac{-6 \pm \sqrt{2 \times 2^2 \times 3^ 4 }}{18}\\\\x = \frac{-6 \pm ( 2 \times 9 )\sqrt{ 2}}{18}\\\\x = \frac{-6 \pm 18\sqrt{2}}{18}\\\\x = \frac{-1 \pm 3 \sqrt{ 2}}{3}[/tex]
Solve the inequality: w - (14) < 8
[tex]w - (14) < 8 \\ = w < 8 + 14 \\ \\ w = < 22[/tex]
Step by Step Explanation:
Move the constant to the right - hand side and change its signThen add the numbers ☆彡Hanna#CarryOnLearning
A calculator was used to perform a linear regression on the values in the
table. The results are shown to the right of the table.
х
y
1
9
N
6
LinReg
y = ax+b
0=-3.6
b=12.8
r2=.9969230769
r=-.9984603532
3
2
4
-2
5
-5
What is the line of best fit?
A. y = -3.6x + 12.8
O B. -0.998 = -3.6x + 12.8
O c. y = 12.8x - 3.6
D. y = -0.998x + 12.8
Answer:
Step-by-step explanation:
A y = -3.6x + 12.8
The line of best fit is,
⇒ y = - 3.6x + 12.8
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, Given that;
⇒ y = ax + b.
And, the best fitting line has values of a = - 3.6 and b = 12.8.
Hence, All you need do is put that into the general equation and try different values for it.
So you have y = - 3.6 x + 12.8
Now Let's run a couple of numbers.
The table shows 1 and 9 for the first entry. This means when x = 1, y should come pretty close to nine.
y = - 3.6(1) + 12.8
y = 9.2
Which is not a bad result for x = 1
You might want to check to see if anything else comes closer in your choices. If it does, then you have to try other points.
C
-0.998 = -3.6(1) + 12.8
This answer cannot work. We've already shown that x =1 will leave us close to 9 not -998
So, C is incorrect.
B
y = 12.8x - 3.6
Let x = 1
y = 12.8(1) - 3.6
y = 9.2 is right by coincidence. We must try another value. The hardest one is going to be 5 and - 5
y= 12.8*5 - 3.6
y = 64 - 3.6 which is no where's near - 5.
So B is wrong.
A
y = -0.998(1) + 12.8 Does this give 9 or anywhere near it? 11.802 You might argue that that is not a bad result. So let's try another pair.
x = 3. y should come to somewhere near 2.
y = -0.998 * 3 + 12.8 which comes to roughly nine. You can check this out.
It is not close enough to 2 to be acceptable.
Thus, The correct option is,
⇒ y = - 3.6x + 12.8
Learn more about the mathematical expression visit:
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Find the first three terms of the Maclaurin series for f(x) =
[tex]{e}^{ \frac{x}{2} } [/tex]
Step-by-step explanation:
Starting out with the Taylor series,
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(a)}{n!}(x-a)^n[/tex]
where [tex]f^{(n)}[/tex] is the nth derivative of f(x) and if we set a = 0, we get the special case of the Taylor series called the Maclaurin series:
[tex]\displaystyle f(x) = \sum_{n=0}^{\infty} \dfrac{f^{(n)}(0)}{n!}x^n[/tex]
Expanding this series up to the 1st 3 terms at a = 0,
[tex]f(x) = f(0) + \dfrac{f'(0)}{1!}x + \dfrac{f''(0)}{2!}x^2[/tex]
Let's find the derivatives of [tex]e^{\frac{x}{2}}[/tex]:
[tex]f'(x) = \frac{d}{dx} (e^{\frac{x}{2}}) = \frac{1}{2}e^{\frac{x}{2}} \Rightarrow f'(0) = \frac{1}{2}[/tex]
[tex]f''(x) = \frac{1}{4}e^{\frac{x}{2}} \Rightarrow f''(0) = \frac{1}{4}[/tex]
We can now write the Maclaurin series for [tex]e^{\frac{x}{2}}[/tex]as
[tex]e^{\frac{x}{2}} = 1 + \frac{1}{2} x + \frac{1}{8} x^2[/tex]
An installation technician for a specialized communication system is dispatched to a city only when 3 or more orders have been placed. Suppose the orders follow a Poisson distribution with a mean of 0.25 per week for a city with a population of 100,000 and suppose your city contains 800,000.
a. What is the probability that a technician is required after a one-week period?
b. If you are the first one in the city to place an order, what is the probability that you have to wait more than two weeks from the time you place your order until a technician is dispatched?
Answer:
0.3233
0.09
Step-by-step explanation:
Given that :
Mean, λ = 0.25 for a 100,000 per week
For a population of 800,000 :
λ = 800,000 / 100,000 * 0.25 = 8 * 0.25 = 2 orders per week
Probability that technician is required after one week ;
After one week, order is beyond 2 ; hence, order, x ≥ 3
P(x ≥ 3) = 1 - [p(x=0) + p(x= 1) + p(x =2)]
P(x ≥ 3) = 1 - e^-λ(1 + 2¹/1! + 2²/2!)
P(x ≥ 3) = 1 - e^-2(1+2+2) = 1 - e^-2*5 = 1 - e^-10
P(x ≥ 3) = 1 - e^-2 * 10
P(x ≥ 3) = 1 - 0.6766764
P(x ≥ 3) = 0.3233
B.)
Mean, λ for more than 2 weeks = 2 * 2 = 4
P(x < 2) = p(x = 0) + p(x = 1)
P(x < 2) = e^-4(0 + 4^1/1!)
P(x < 2) = e^-4(0 + 4) = e^-4(5)
P(x < 2) = e^-4(5) = 0.0183156 * 5 = 0.0915
P(x < 2) = 0.09
don’t understand this help please
Step-by-step explanation:
Since he sold $70,834 worth of cars, he earned an extra 5% commission on the sale. That means he got
0.05×($70,834) = $3,541.70
Therefore, his salary for the month m is
m = $2250 + 0.05s = $2,250 + $3,541.70 = $5,791.70
Carson is going to see a movie and is taking his 2 kids. Each movie ticket costs
$14 and there are an assortment of snacks available to purchase for $3.50
each. How much total money would Carson have to pay for his family if he
were to buy 2 snacks for everybody to share? How much would Carson have
to pay if he bought x Snacks for everybody to share?
Total cost with 2 snacks:
Total cost with x sn
acks:
49 dollars
Step-by-step explanation:
14 times 3 is 42 and 3.50 times 2 is 7, so 42 plus 7 is 49.
Total cost with 2 snacks = $35
Total cost with x snacks = 28+3.50x
Given :
Carson is going to see a movie and is taking his 2 kids. Movie ticket costs $14 and snacks cost $3.50.
Explanation :
Carson buys 2 snacks . we need to find the total cost that Carson have to pay where he buy 2 snacks.
Total cost = cost of ticket (2 kids) + cost of 2 snacks
[tex]Total \; cost = 14(2) + 2(3.50)=35[/tex]
Total cost with 2 snacks = $35
Total cost with x snacks = cost of ticket (2 kids) + cost of x snacks
[tex]Total \; cost = 14(2) + 3.50(x)\\Total \; cost = 28+3.50x[/tex]
Total cost with x snacks = 28+3.50x
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Suppose that y varies inversely with x. Write a function that models the inverse function x=7 when y=3
9514 1404 393
Answer:
y = 21/x
Step-by-step explanation:
The inverse variation relation means ...
y = k/x
For the given values, we can determine the constant k:
3 = k/7
3×7 = k = 21
Then the function is ...
y = 21/x
The Utica Boilermaker is a 15-kilometer road race. Sara is signed up
to nin this race and has done the following training runs:
I.
10 miles
II.
44,880 feet
III. 15,560 yards
Which run(s) are at least 15 kilometers?
Answer:
10 miles
Step-by-step explanation:
10 miles= 16093.44km
44880ft=13.679424km
15560yards= 14.228064
a bag contains 5white and 3red identical balls.if the balls are drawn at random after the other without replacement. what is the probability that the first red ball is picked at fifth draw
Answer:
2/7
Step-by-step explanation:
Use the digits 0 - 9 to fill in the blank.
[tex]243 \frac{1}{5} = blank[/tex]
Answer:
use 0-9 to fill in blanks
Step-by-step explanation:
Mathematics
Evaluate the equations or inequalities. Write the Letter of your answer to the corresponding boxes at the bottom of the page to discover the answer to the title questions.
How does an ESP Expert send his mail?
☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐
7 11 1 8 2 9 11 3 1 8 9 4 6 9 4 9 1 2 10 5
help po.
Step-by-step explanation:
ejdjbd x bxbx k wbu y DJ UK j HK JM dz
nb
[tex]\huge{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=}}[/tex]
[tex]HOLA!![/tex]
Answer:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=e^{\frac{1}{3} } }}[/tex]
Explanation:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{3n}{3^n \: n!}=}}[/tex]
For this we have to take into account:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{x^{n} }{n!} =e^{x} }}[/tex]
Using the properties of factorials and exponents we have:
[tex]n!=(n-1)n![/tex] Also. [tex]\frac{n^{x} }{ n^{y} }=n^{x-y}[/tex]
We replace:
[tex]{\boxed{ \sum_{n=1}^{\infty}\ \frac{1}{3^{n-1}.(n-1)! } }}[/tex]
Shape it:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} }}[/tex]
Finally:
[tex]{\boxed{ \sum_{n=1}^{\infty}\frac{(\frac{1}{3} )^{n-1} }{(n-1)!} =e^{\frac{1}{3} } }}[/tex]
A ream of a certain brand of paper weighs about 4.533 pounds. A ream contains 500 sheets of paper. How much does a sheet of paper weigh?
Step-by-step explanation:
As a ream or
500
sheets of paper weigh
4.818
pounds
One sheet of paper weighs
4.818
500
=
0.009636
pounds.
It is apparent that pound is too big a unit for a sheet of paper.
As each pound has
16
ounces, one can say
one sheet of paper weighs
0.009636
×
16
=
0.154176
ounces.
If ounce is too big, as we have
1
pound equal to
28.34952
grams
one sheet of paper weighs
0.154176
×
28.34952
≈
4.371
grams
please mark as brainliest
three-fifths of a number increased by ten
Answer: [tex]\frac{3}{5} x+10[/tex]
Step-by-step explanation:
three-fifths of a number means multiply three-fifths by a variable [tex]\frac{3}{5} x[/tex]
increased by 10 means addition +10
together it is [tex]\frac{3}{5}x +10[/tex]
Refer to the Lincolnville School District bus data. Information provided by manufacturers of school buses suggests the mean maintenance cost per year is $4,400 per bus with a standard deviation of $1,000. Compute the mean maintenance cost for the Lincolnville buses. Does the Lincolnville data seem to be in line with that reported by the manufacturer? Specifically, what is the probability of Lincolnville’s mean annual maintenance cost, or greater, given the manufacturer’s data?
Answer:
Step-by-step explanation:
Add all of the Maintenance costs up, divide by 80. (the number of costs).
Excel formula =SUM(F2:F81) 364151.00/80 = 4551.8875 Rounded to 4552 is your answer.
What equation can you write to solve for x?
Answer:
(3x) ° + (x+ 10)° = 90°
Step-by-step explanation:
(3x) ° + (x+ 10)° = 90°
3x + x + 10 = 90
4x = 90 - 10
4x = 80
x = 20
(3x) ° = 3 x 20 = 60°
(x + 10)° = 20 + 10 = 30°
Answer: you can either do 3x°(x+10)° or (x+10)°+3x°
the choice is yours. Hope this helps
I need help I’ll give u brainlest
Answer:
216 yd³
Step-by-step explanation:
Volume of a rectangular prism
= product of the three orthogonal sides
= 6yd * 6yd * 6yd
= 216 yd³
Answer:
216
Step-by-step explanation:
:)
Identify the type of observational study (cross-sectional, retrospective, or prospective) described below. A research company uses a device to record the viewing habits of about 7500 households, and the data collected today will be used to determine the proportion of households tuned to a particular sports program. Which type of observational study is described in the problem statement?
Answer:
Cross sectional study
Step-by-step explanation:
Cross sectional study, also known as traverse or prevalence study caloukdnbe defined as a form of observational study which involves analysing a certain sample of data which is selected based on a variable of interest. This data is collected at a given point in time across the sample population. In the scenario described above, the record of viewing habit of 7500 household smoke obtained today(point in time) will be used to determine the proportion tuned to a particular sport programme. (data collected is based on the variable to be analyzed).
The rectangle was rotated 360° around its center, point
C. Vertex D traces the path of a circle and lands back
Which best explains why the rotation represents an
isometric transformation?
upon itself.
y
O The angle at point D remained a right angle.
O The rectangle did not change shape or size.
O Point C remained the center of the rectangle.
5
D
4
Point C did not remain the center of the rectangle.
3
2+
1
с
+
1
43 -2 -11
2
3
4.
-2+
-3+
Answer:
O The rectangle did not change shape or size.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Isometric transformation is a transformation that preserves the shape and size of the figure. Types of isometric transformations are reflection, translation and rotation.
The rectangle represents an isometric transformation because the rectangle did not change shape or size.
given f(x) = 5x + 7,g(x) = 3x-1 find f(g(x))
Answer:
f(g(x)) = 15x + 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
FunctionsFunction NotationComposite FunctionsStep-by-step explanation:
Step 1: Define
Identify
f(x) = 5x + 7
g(x) = 3x - 1
Step 2: Find
Substitute in functions: f(g(x)) = 5(3x - 1) + 7[Distributive Property] Distribute 5: f(g(x)) = 15x - 5 + 7[Addition] Combine like terms: f(g(x)) = 15x + 2A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment
Answer:
(S, FS, FFS, FFF)
Step-by-step explanation:
According to the Question,
Given, A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful.however, he cannot try more than 3 times or the phone will lock him out.Let, S denote a successful attempt and F denote a failed attempt.So, the sample space for this random experiment is
{S, FS, FFS, FFF}
The person stops trying when he successfully enters the code or when he has failed at all 3 attempts .
A study is conducted to see how effective aspirin is in reducing temperature in children. A sample of 6 children suffering from influenza had their temperatures taken immediately before and 1 hour after administration of aspirin. The results are given below. We would like to conduct a paired differences t-test for this situation. The data follows:
Patient Temperature Before Temperature After Difference
1 103.7 102.6 1.1
2 103.7 102.7 1
3 100.7 98.8 1.9
4 102.7 103.5 -0.8
5 102.7 101.3 1.4
6 100.7 99.4 1.3
Mean 102.4 101.4 1
Std. Dev. 1.4 1.9 0.9
Required:
Calculate the appropriate test statistic of a matched pairs t-test for this data to see if taking aspirin will reduce a child's fever.
Answer:
Then t(s) is in the rejection region for H₀ we reject H₀ and conclude that the aspirin will reduce a child´s fever
Step-by-step explanation:
Tem.Before Tem.After diff.
103.7 102.6 1.1
103.7 102.7 1
100.7 98.8 1.9
102.7 103.5 -0.8
100.7 99.4 1.3
102.4 101.41 (Mean)
1.4 1.9 0.9 Std. Dev.
n = 6
df = 6 - 1 = 5
CI we propose to be 95 %
Then α = 5 % α = 0.05
The test is a one-tail test ( we want to know if taking aspirin will reduce a child´s fever
Hypothesis test
Null Hypothesis H₀ μd = 0
Alternative Hypothesis Hₐ μd > 0
(NOTE:) μd (average) = Temp Before - Temp. after
Therefore if μd > 0 means that there is a statistical difference between values before ( bigger ) and after or that the aspirin will reduce a child´s fever
To find t(c) from t-student table df = 5 and α = 0.05
t(c) = 2.015
To compute t(s)
t(s) = μd/ sd/√n t(s) = 0.98/ 0.9/√6
t(s) = 2.66
Comparing t(s) and t(c)
t(s) > t(c)
Then t(s) is in the rejection region for H₀ we reject H₀ and conclude that the aspirin will reduce a child´s fever
?? I got 5 minutes left, please help.
Answer:
Here we know that:
[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } }[/tex]
Where V is the speed, C = 3*10^8 m/s
We want to solve:
[tex]m(v) = \frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]
We can just isolate V from the above equation, so we will get:
[tex]\frac{M_0}{\sqrt{1 - \frac{V}{C} } } = 2*M_0[/tex]
[tex]\frac{1}{\sqrt{1 - \frac{V}{C} } } = 2[/tex]
[tex]1 = 2\sqrt{1 - \frac{V}{C} }[/tex]
[tex](1/2)^2 = 1 - \frac{V}{C}[/tex]
[tex]V = (1 - (1/4))*C = (3/4)*C = (3/4)*3*10^8 m/s = (9/4)*10^8 m/s[/tex]
That is the velocity such that the effective mass is twice the rest mass.
Your answer in part (b) read "one and one- fourth" is called a mixed number since it has a whole number part and a fraction part. What does the word "and" indicate in the name of this fraction?
9514 1404 393
Answer:
the end of the whole number and the beginning of the fraction
Step-by-step explanation:
The word "and" means the whole part and the fractional part should be considered together as having a value equal to their sum. It signifies the separation between the whole-number part and the fractional part.
__
It has the same meaning as when used in a decimal mixed number:
1.2 = "one and two tenths"
Find the P-value for the hypothesis test with a standardized test statistic z. Decide whether toreject the null hypothesis for the level of significance α.a. Left-tailed test, z = -1.32, α = 0.10b. Right-tailed test, z = 2.46, α = 0.01c. Two-tailed test, z = -1.68, α = 0.05
Answer:
1.) We don't reject the null
2.) We reject the Null
3.) We do not reject the null
Step-by-step explanation:
Obtaining p values using test statistic:
Given that ; we have a standardized test statistic and α - values ;
Let's define the decision region :
If Pvalue < α ; Reject H0 ; otherwise, fail to reject H0
A.)
Left tail , Z = - 1.32 ; α = 0.10
We can use the Pvalue calculator from Z score :
Pvalue = 0.934
Pvalue > α ; Hence, we fail to reject the null, H0
B.)
Right-tailed test, z = 2.46, α = 0.01
Pvalue from Zscore calculator ;
Pvalue = 0.0069
Pvalue < α ; Hence, we reject the null, H0
C.)
Two-tailed test, z = -1.68, α = 0.05
Pvalue from Zscore calculator ;
Pvalue = 0.093
Pvalue > α ; Hence, we fail to reject the null, H0
