Copy the diagram and oaloulate the sizes of
a bº and cº. What is the sum of the angles of
the triangle?
Answer:
sum of the angles of the triangle are 180°
Step-by-step explanation:
To find the sum of the interior angles, we use the formula( s-2*180), where s is the number of sides of the shape. If it is a pentagon, 5-2*180= 3*180= 540,
which shows that the sum of the interior angles of a pentagon is 540.
since, it is a triangle in the figure with 3 sides, 3-2*180=1*180=180.
The interior angles are unknown= a, b and c. we know that a+b+c=180 degrees and the exterior angles are mentioned. And we know that, opposite angles are equal. So, a is 40 degrees considering that 40 degrees is the opposite angle of a, b is 95 degrees whereas c is 45 degrees.
now, lets check if the angles indeed have a sum of 180 degrees,
40+95+45= 135+45 which gives 180 degrees.
Answer:
180°
Step-by-step explanation:
→ Angles in a triangles always add up to 180, we can prove this by calculating a, b and c so,
a = 40° (vertical angles are equal)
b = 95° (vertical angles are equal)
c = 45° (vertical angles are equal)
40 + 45 + 95 = 85 + 95 = 180°
A random sample of n = 8 E-glass fiber test specimens of a certain type yielded a sample mean interfacial shear yield stress of 32.9 and a sample standard deviation of 4.9. Assuming that interfacial shear yield stress is normally distributed, compute a 95% CI for true average stress. (Give answer accurate to 2 decimal places.)
Answer:
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=32.9[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=4.9 represent the sample standard deviation
n=8 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
the degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this cae would be [tex]t_{\alpha/2}=2.365[/tex]
Now we have everything in order to replace into formula (1):
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
PLEASE HELP!!! You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
Answer:
1140 ways.
Step-by-step explanation:
The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).
The 17 identical candies, can be distributed among the 4 children in :
=(17 + 4 - 1)C(4–1) = 20C3 ways.
= 20!/((20–3)!*3!) ways.
= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways
= 20*19*3 ways.
=1140 ways.
A random sample of 13 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 950 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student’s t.
1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 20. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
Answer:
1. The 99% confidence interval is from 941.527 to 958.473
2. The 99% confidence interval is from 933.054 to 966.946
3. The 99% confidence interval is from 916.108 to 983.892
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size,
s is the sample standard deviation,
[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level
The t-score corresponding to 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 13 - 1 = 12
From the t-table at α = 0.005 and DoF = 12
t-score = 3.055
1. 99% Confidence Interval when s = 10
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]
The 99% confidence interval is from 941.527 to 958.473
2. 99% Confidence Interval when s = 20
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]
The 99% confidence interval is from 933.054 to 966.946
3. 99% Confidence Interval when s = 40
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]
The 99% confidence interval is from 916.108 to 983.892
As the sample standard deviation increases, the range of confidence interval also increases.
algebra ...........................
Answer:
see explanation
Step-by-step explanation:
Given that y is inversely proportional to x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion
(a)
To find k use the condition when y = 7 , x = 9, that is
7 = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )
63 = k
y = [tex]\frac{63}{x}[/tex] ← equation of proportion
(b)
When x = 21, then
y = [tex]\frac{63}{21}[/tex] = 3
Please answer question now
Answer:
∠CED
or
∠DEC
its the same thing
Step-by-step explanation:
E is the angle
Two identical decks of 52 cards are mixed together, yielding a stack of 104 cards. How many different ways are there to order this stack of 104 cards?
Answer:
here the order will be 104! =[tex]1.029e^{166}[/tex]
Step-by-step explanation:
since the cards are to arranged in no particular order that is why we used combination to find the result.
Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.
Calculate
(14x5x4) / (28 x 2)
Answer:
5
Step-by-step explanation:
(14 × 5 × 4) ÷ (28 × 2)
Solve brackets.
280 ÷ 56
Divide.
= 5
i will give brainliest and 50 points pls help ASP
Answer:
Step-by-step explanation:
A trapezoid and two rectangulars are in the opening form of the geometric shapes and you should calculate their surface areas seperately which is:
12 cm and 30 cm first rectangular and its surface area is 12 x 30 = 360 cm^2second rectangular has 30 cm and 26 cm and 30 x 26 = 780 cm^2A trapezoid surface area is = [(24+29) /2] * 25 = 662.5 cm^2total surface area = 360 + 780 + 662.5 = 1802.5Answer:
Total surface area = 3744 cm^2
Step-by-step explanation:
All linear measurements are in cm
Surface area of BOTH bases
Ab = 2* (12+29)*24/2
= 984
Circumference of base
Cb = (25+12+26+29)
= 92
Height of prism
H = 30 (given)
Surface area of sides of prism
As= Cb*H
= 2760
Total Surface area of Prism
A = Ab + As
= 984 + 2760
= 3744 cm^2
Julie has three boxes of pens. The diagram shows expressions for the number of pens in each box. Look at these equations.
Equals B +12
B equals C +4
Write an equation to show the relationship between a + c
Answer:
a=c+16here,
a=b+12
b=a-12----> equation (i)
b= c+4
putting the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
hope this helps...
Good luck on your assignment...
The value of a + c is 16.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
a=b+12
So, b=a-12 ---- equation (i)
and, b= c+4
Substitute the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
Hence, the value of a+ c is 16.
Learn more about Algebra here:
https://brainly.com/question/24875240
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Please answer this correctly
Answer:
1/9
Step-by-step explanation:
first, u need 9 ---> 1/3
then u need 8 ---> 1/3 also
Multiply them and get...1/9
Choose the correct number to finish the sentence. For the function f(x)=√x+4, the average rate of change to the nearest hundredth over the interval 2 ≤ x ≤ 6 is? A. 0.2 B. 0.17 C. 0.16 D. 0.18
Answer:
See below under "explanation".
General Formulas and Concepts:
Algebra I
Functions
Function NotationAverage Rate of Change Formula:
[tex]\displaystyle \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}[/tex]
Step-by-step explanation:
*Note:
The function is unclear, so I will provide 2 possible answers.
Step 1: Define
Identify given.
[tex]\displaystyle \begin{aligned}1. \ f(x) & = \sqrt{x} + 4 \\2. \ f(x) & = \sqrt{x + 4} \\\end{aligned}[/tex]
[tex]\displaystyle \text{Interval: } 2 \leq x \leq 6[/tex]
Step 2: Find Average Rate of Change
For the 1st function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\big( \sqrt{b} + 4 \big) - \big( \sqrt{a} + 4 \big)}{b - a} \\& = \frac{\big( \sqrt{6} + 4 \big) - \big( \sqrt{2} + 4 \big)}{6 - 2} \\& = \frac{\sqrt{6} - \sqrt{2}}{4} \\& = 0.258819 \\& \approx \boxed{0.26} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 1st defined function, will be approximately 0.26.
For the 2nd function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\sqrt{b + 4} - \sqrt{a + 4} }{b - a} \\& = \frac{\sqrt{6 + 4} - \sqrt{2 + 4}}{6 - 2} \\& = \frac{\sqrt{10} - \sqrt{6}}{4} \\& = 0.178197 \\& \approx \boxed{0.18} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 2nd defined function, will be approximately 0.18.
---
Learn more about functions: https://brainly.com/question/16217435
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---
Topic: Algebra I
Joan is selling handmade bead necklaces
at a local art fair. She paid $180 to
reserve her booth. The cost of supplies
for each necklace averages $2. So, her
cost, y, for x necklaces is represented by
y = $180 + 2x. If she sells her necklaces
for $12, her revenue, y, is represented
by y = 12x.
The solution of this system is the break-
even point, the point beyond which she
starts making a profit.
HELP PLS QUICK
Answer:. x = 18
Step-by-step explanation:
Solve by substitution. Given: y= 12x. Rewrite the original equation y= 180 + 2x to 12x = 180 +2x. Subtract 2x from both sides. 10x = 180. Then divide both sides by 10.
x=18
So once she has sold 18 necklaces, she has covered her costs (180 + 36) and she begins to make a profit.
What is the measure of angle S?
480
56°
930
101°
Answer:
m∠s = 93°
Step-by-step explanation:
We know that any quadrilateral's sum of angles adds up to 360°. In that case,
360 - (56 + 132 + 79) = m∠s
m∠s = 93°
Answer:
S° = 93 °
Step-by-step explanation:
[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]
what 4.2 times 0.7 /a is 294 /b is 2.94 /c 29.4
Answer:
29.4
Step-by-step explanation:
Answer:
2.94
Step-by-step explanation:
4.2 × 0.7 = 2.94
simply expression 1+5v+v
Answer:
1 + 6v
Step-by-step explanation:
1+5v+v
Combine like terms
1 + 6v
Answer:
6v + 1
Step-by-step explanation:
1 + 5v + v
Apply rule : a = 1a
1 + 5v + 1v
Combine like terms.
5v + 1v + 1
(5 + 1)v + 1
(6)v + 1
6v + 1
Justin solved 15 problems of the recent math quiz. His classmate Jordan solved 3 more problems than Justin. Another classmate of Justin, Jeremy also solved some problems and they all together solved 37 problems. Who solved the most number of problems?
Answer:
Jordan
Step-by-step explanation:
Problems solved by Jordan = 15 + 3 = 18
Total problems solved = 37
Problems solved by Justin + problems solved by Jordan + problems solved by Jeremy = 37
15 + 18 + problems solved by Jeremy = 37
33 + problems solved by Jeremy = 37
Problems solved by Jeremy = 37 - 33
Problems solved by Jeremy = 4
So, Jordan solved most number of problems
Answer:
Jordan solved the most number of problems.
Step-by-step explanation:
Justin solved 15 problems
Jordan solved 15+3 = 18 problems
Jeremy solved 37 - (15+18) = 37 - 33 = 4 problems
Q‒1. [5×4 marks] a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? (150) b) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? c) How many odd numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? d) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? e) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once?
Answer:
a) 294
b) 180
c) 75
d) 174
e) 105
Step-by-step explanation:
I assume that for each problem, the first digit can't be 0.
a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.
6×7×7 = 294
b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.
6×6×5 = 180
c) Again, each digit can only be used once, but this time, the last digit must be odd.
If only the last digit is odd, there are 3×3×3 = 27 possible numbers.
If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.
If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.
If all three digits are odd, there are 3×2×1 = 6 possible numbers.
The total is 27 + 24 + 18 + 6 = 75.
d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.
If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.
If the first digit is greater than 3, there are 3×7×7 = 147 numbers.
The total is 6 + 21 + 147 = 174.
e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.
If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.
The total is 15 + 90 = 105.
It is known that 10% of the calculators shipped from a particular factory are defective. What is the probability that exactly three of five chosen calculators are defective
Answer:0.0081 or 0.81%
Step-by-step explanation:
The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, where
C5 3= 5!/3/2=4*5/2=10
p is the probability that one randomly selected calculator is defective= 10%=0.1
q is the probability that one randomly selected calculator is non-defective.
q=1-p=1-0.1=0.9
So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081
Which number is equivalent to [tex]\frac{3^4}{3^2}[/tex]?
A. 2
B. 9
C. 81
D. 729
Answer:
B. 9
Step-by-step explanation:
When there are exponents with the same base in a fraction, they can be simplified by subtracting.
We can take out 2 on both the top and bottom, leaving us with 3^2 over 1
3x3 is 9 and 9/1 is still 9
Answer:
9
Step-by-step explanation:
Since the bases are the same, we can subtract the exponents to accomplish the division
a^b / a^c = a^ (b-c)
3^4 / 3^2
3^ (4-2)
3^2
9
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: a) 8.779 years
b) 8.664 years
Step-by-step explanation:
a)
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
A: accumulated amount (balance)P: principal amount (original/initial investment)r: interest rate (convert to a decimal)n: number of times compounded per yeart: number of yearsGiven: A = 1800, P = 900, r = 8% = 0.08, n = 3, t = unknown
[tex]1800=900\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\2=\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=ln \bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=3t\ ln\bigg(1+\dfrac{0.08}{3}\bigg)\\\\\\\dfrac{ln\ 2}{3\ ln\bigg(1+\dfrac{0.08}{3}\bigg)}=t\\\\\\\large\boxed{8.779=t}[/tex]
b)
[tex]A=Pe^{rt}[/tex]
[tex]1800=900e^{0.08t}\\\\\\2=e^{0.08t}\\\\\\ln\ 2=0.08t\\\\\\\dfrac{ln\ 2}{0.08}=t\\\\\\\large\boxed{8.664=t}[/tex]
What is jc ? (Picture included)
Answer:
jc is 40 i think
Step-by-step explanation:
Answer:
40(Maybe)
Step-by-step explanation:
I'm not 100% sure that 40 is correct but I'm pretty sure it is.
How many different simple random samples of size 5 cab be obtained from a population whose size is 46
Answer:
1370754
Step-by-step explanation:
From what I can see, you are probably studying combinations and permutations at the moment. Since this is a question about how many groups of five can be produced from a sample size of 46, the groups are random and not in order, which may rule for us to use the combination formula.
Once you compute this, this answer is basically saying that 1370754 groups of 5 can be created from a sample size of 46
Please help I don’t understand And I need an explanation
Hey there! :)
Answer:
56 m².
Step-by-step explanation:
To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:
Solve for the rectangle: (A = l × w)
A = 8 × 5
A = 40 m²
Solve for the triangle: (A = 1/2 (bh))
A = 1/2(4 · 8)
A = 1/2(32)
A = 16 m².
Add up the two areas:
40 + 16 = 56 m².
Answer:
Area of triangle+ the area of rectangle
Step-by-step explanation:
Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²
Area of rectangle is length × breadth= 5×8: 40 m²
Area of the shape is 40m²+16m²= 56m²
Diane's bank is offering 5% interest, compounded monthly. If Diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? Round to the nearest tenth of a year.
Answer:
The time period is 13 years.
Step-by-step explanation:
Interest rate (r )= 5% or 5%/12 = 0.42% per months
The investment amount (Present value) = $10500
Final expected amount (future value) = $20000
Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.
Use the below formula to find the time period.
Future value = present value (1 + r )^n
20000 = 10500(1+0.0042)^n
1.9047619 = (1+0.0042)^n
1.9047619 = 1.0042^n
n = 153.74 months.
Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)
If I ride a bicycle at a rate of 5m/s,how long will it take me to ride a distance of 12km at the same rate?
Step-by-step explanation:
given,velocity = 5 m/s
and distance=12×1000=12000m
now,time =?
we have , v=s/t
or, t= s/v
so,t=12000/5
2400sec.....ans
=
Tammy and Lawrence like to bike competitively. Tammy biked seven less than three times the number of miles that Lawrence biked. If c represents the number of miles Lawrence biked, write an expression for the number of miles Tammy biked.
Answer:
3c - 7
Step-by-step explanation:
c - the number of miles Lawrence biked
Tammy biked seven less than three times the number of miles that Lawrence biked.
So, 3 x c (the # of miles Lawrence biked) - 7 (she biked seven less)
The answer is 3c - 7.
helpppppppppppppppppppppppp pleaseeeeeeeeeee
Answer:
6 stickers
Step-by-step explanation:
84/14 =6
Answer:
6 stickers each
Step-by-step explanation:
have a great day
Fathi has \$1.10$1.10dollar sign, 1, point, 10 in his printing account. Each sheet of paper he uses reduces his printing account balance by \$0.25$0.25dollar sign, 0, point, 25. Fathi wants to print out a PDF document that is 474747 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet. After Fathi prints, what will be the balance in his printing account?
Answer:
$-4.90.
Step-by-step explanation:
Fathi has $1.10. Each sheet costs him $0.25. He wants to print 47 pages.
If he prints double sided, then he will use 47 / 2 = 23.5 sheets of paper. But he can't print a half-sheet, so he will use 24 sheets of paper.
Each sheet costs $0.25. 0.25 * 24 = 6. The printing will cost him $6.
Since he only has $1.10, his remaining balance will be 1.1 - 6 = -4.9. The balance on his printing account will be $-4.90.
Hope this helps!
Answer:
-1.90
Step-by-step explanation:
Khan Academy
I got it right for sure
A 6-digit number has at least one even digit in its record. How many such numbers are there? (0 is an even digit)
Answer:
884,375
Step-by-step explanation:
The first digit can't be 0, so there are 9×10⁵ = 900,000 possible six-digit numbers.
Of those, the number of six-digit numbers that have only odd digits is 5⁶ = 15,625.
Numbers with at least one even digit are all numbers that don't have only odd digits. So the number of six-digit numbers with at least one even digit is:
900,000 − 15,625 = 884,375