Answer:
5 triangles from the vertex
Answer:
5 triangles from the vertex
Step-by-step explanation:
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
using the horizontal line test, which of the following can be confused about the inverse of the graph?
Answer:
I think D
Step-by-step explanation:
Verticle or horizontal line test, it would be a function either way
Fill in the blanks.
(x+_)^2=x^2+14x+_
Step-by-step explanation:
(ax + b)² = a²x² + 2abx + b²
In this case, a = 1, so:
14 = 2b
b = 7
(x + 7)² = x² + 14x + 49
A researcher compares the effectiveness of two different instructional methods for teaching anatomy. A sample of 146 students using Method 1 produces a testing average of 51.6. A sample of 180 students using Method 2 produces a testing average of 62.7. Assume the standard deviation is known to be 9.42 for Method 1 and 14.5 for Method 2. Determine the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2. Step 1 of 2: Find the critical value that should be used in constructing the confidence interval.
Answer:
The confidence interval is [tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 146[/tex]
The second sample size is [tex]n_2 = 180[/tex]
The first sample mean is [tex]\= x_1 = 51.6[/tex]
The second sample mean is [tex]\= x_2 = 62.7[/tex]
The first standard deviation is [tex]\sigma _1 = 9.42[/tex]
The second standard deviation is [tex]\sigma _2 = 14.5[/tex]
Given that the confidence level is 98% then the significance level is mathematically evaluated as
[tex]\alpha = (100 -98 )\%[/tex]
[tex]\alpha = 2 \%[/tex]
[tex]\alpha = 0.02[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the z-table , the value is [tex]Z_{\frac{\alpha }{2} } = 2.33[/tex]
The reason we are obtaining critical value of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\sigma_1^2}{n_1^2} + \frac{\sigma_2^2}{n_2^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
substituting values
[tex]E = 2.33 * \sqrt{ \frac{9.42^2}{146^2} + \frac{14.5^2}{180^2} }[/tex]
[tex]E = 0.2405[/tex]
The 98% confidence interval is mathematically represented as
[tex](\= x _ 1 - \= x_2 ) - E < \mu_1 -\mu_2 < (\= x _ 1 - \= x_2 ) + E[/tex]
substituting values
[tex](51.6 - 62.7) - 0.2405 < \mu_1 -\mu_2 < (51.6 - 62.7) + 0.2405[/tex]
[tex]-11.34 < \mu_1 -\mu_2 < -10.86[/tex]
(08.05 LC)The histogram shows the number of prizes won by different numbers of students at a quiz competition. Which of the following statements is correct regarding the number of students and the number of prizes won? A histogram titled Prizes Won is shown. The horizontal axis is labeled Number of Prizes with bins 0 to 5, 6 to 11, 12 to 17, and 18 to 23. The vertical axis labeled Students with values from 0 to 10 at intervals of 1. The first bin goes to 2, the second goes to 7, the third goes to 4, and the last goes to 10. A) A total of 10 students won all the prizes. B) Four students won 12, 13, 14, 15, 16, or 17 prizes. C) A total of 10 prizes were won by all the students. D) Four prizes were won by 12, 13, 14, 15, 16, or 17 students.
Answer: B.
Four students won 12, 13, 14, 15, 16, or 17 prizes
Answer:
Four students won 12, 13, 14, 15, 16, or 17 prizes!
Step-by-step explanation:
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
Learn more about cost at https://brainly.com/question/1153322
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Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 216x + 3, [−4, 5]
Answer:
absolute minimum = -749 and
absolute maximum = 467
Step-by-step explanation:
To get the absolute maximum and minimum of the function, the following steps must be followed.
First, we need to find the values of the function at the given interval [-4, 5].
Given the function f(x) = 6x³ − 9x² − 216x + 3
at x = -4;
f(-4) = 6(-4)³ − 9(-4)² − 216(-4) + 3
f(-4) = 6(-64) - 9(16)+864+3
f(-4) = -256- 144+864+3
f(-4) = 467
at x = 5;
f(5) = 6(5)³ − 9(5)² − 216(5) + 3
f(5) = 6(125) - 9(25)-1080+3
f(5) = 750- 225-1080+3
f(5) = -552
Then we will get the values of the function at the crirical points.
The critical points are the value of x when df/dx = 0
df/dx = 18x²-18x-216 = 0
18x²-18x-216 = 0
Dividing through by 18 will give;
x²-x-12 = 0
On factorizing the resulting quadratic equation;
(x²-4x)+(3x-12) = 0
x(x-4)+3(x-4) = 0
(x+3)(x-4) = 0
x+3 = 0 and x-4 = 0
x = -3 and x = 4 (critical points)
at x = -3;
f(-3) = 6(-3)³ − 9(-3)² − 216(-3) + 3
f(-3) = 6(-27) - 9(9)+648+3
f(-3) = -162-81+648+3
f(-3) = 408
at x = 4
f(4) = 6(4)³ − 9(4)² − 216(4) + 3
f(4) = 6(64) - 9(16)-864+3
f(4) = 256- 144-864+3
f(4) = -749
Based on the values gotten, it can be seen that the absolute minimum and maximum are -749 and 467 respectively
write the statement for 6x-3=9
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
The statement for [tex]6x - 3 = 9[/tex] is :
[tex]\boxed{Six (x) .minus. Three .equals. Nine.}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hope this helped you.
Could you maybe give brainliest..?
❀*May*❀
A random sample of 51 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.03 years, with sample standard deviation s = 0.82 years. However, it is thought that the overall population mean age of coyotes is μ = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use α = 0.01.
Answer:
Yes the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 51[/tex]
The sample mean is [tex]\= x = 2.03[/tex]
The sample standard deviation is [tex]\sigma = 0.82[/tex]
The population mean is [tex]\mu = 1.75[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is
[tex]H_o : \mu = 0.82[/tex]
The alternative hypothesis is
[tex]H_a : \mu >1.75[/tex]
The critical value of the the level significance [tex]\alpha[/tex] obtained from the critical value table for z-value is [tex]z_\alpha = 2.33[/tex]
Now the test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 2.03 - 1.75 }{\frac{0.82}{\sqrt{51} } }[/tex]
[tex]t = 2.44[/tex]
From that calculated and obtained value we see that the critical value of the level of significance is less than the test statistics so we reject the null hypothesis
Hence there sufficient evidence to proof that the sample data indicates that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years
Find a formula for an for the arithmetic sequence.
Answer:
a(n)= a(n+1)+4
Step-by-step explanation:
The first terms of this sequence are: 4,0, -4, -8, -12
Let 4 be a0 and 0 a1.
● a1-a0 = 0-4
●a1-a0 = -4
●a1 = -4+a0
So this relation links the first term with the second one.
replace 1 in a1 with n.
0 in a0 will be n-1
● an = -4+a(n-1)
Add one in n
● a(n+1) = a(n)-4
● a(n) = a(n+1)+4
If the wavelength of the violet color is 400 nm, what is the value of its frequency?
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------------- The frequency is ~7.5*1014 Hz
Since visible light has a wavelength spectrum of ~400 nm to ~700 nm, Violet light has a wavelength of ~400 nm and a frequency of ~7.5*1014 Hz.
Step-by-step explanation:
Speed = wavelength × frequency
3×10⁸ m/s = (400×10⁻⁹ m) f
f = 7.5×10¹⁴
Find the distance between the points (–9, 0) and (2, 5). Find the distance between the points (–9, 0) and (2, 5).
Answer:
sqrt( 146)
Step-by-step explanation:
To find the distance, we use the following formula
d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)
sqrt( ( -9-2) ^2 + ( 0-5) ^2)
sqrt( ( -11) ^2 + ( -5) ^2)
sqrt( 121+25)
sqrt( 146)
what is the slop of y= -5+4x
Hey there! :)
Answer:
m = 4.
Step-by-step explanation:
We are given the formula y = -5 + 4x. Rearrange the equation to be in proper slope-intercept form (y = mx + b)
Where 'm' is the slope and 'b' is the y-intercept. Therefore:
y = -5 + 4x becomes y = 4x - 5
The 'm' value is equivalent to 4, so the slope of the equation is 4.
Answer:
4
Step-by-step explanation:
because of y= mx + b where m is the slope
m= 4 in the equation
Solve for x: 125^(3x+7)=25^(5x−11)
Answer:
x = 43
Step-by-step explanation:
125^(3x+7)=25^(5x−11)
Rewriting the bases as powers of 5
125 = 5^3 and 25 = 5^2
5^3 ^ (3x+7) = 5^2^(5x-11)
We know a^b^c = a^ (b*c)
5^(3 * (3x+7)) = 5^(2*(5x-11))
Distribute
5^(9x+21) = 5^(10x-22)
The bases are the same so the exponents are the same
9x+21 = 10x-22
Subtract 9x from each side
9x+21 -9x = 10x-9x-22
21 = x-22
Add 22 to each side
21+22 = x-22+22
43 = x
What is 36/100 added with 4/10
Answer:
0.76 or 19/25
Step-by-step explanation:
Convert 4/10 so that it has a common denominator with 36/100.
4/10 x 10/10 = 40/100
Now that the denominator is the same, just add the top values.
40/100 + 36/100 = 76/100
We can also simplify the answer to be 19/25 by dividing the top and bottom by 4.
Answer:
19/25Step-by-step explanation:
[tex]\frac{36}{100}+\frac{4}{10}\\Let\: first\: deal\: with\: ;\frac{36}{100}\\\mathrm{Cancel\:the\:common\:factor:}\:4\\=\frac{9}{25}\\\\=\frac{9}{25}+\frac{4}{10}\\Now \:lets \:deal \:with ; \frac{4}{10}\\\mathrm{Cancel\:the\:common\:factor:}\:2\\=\frac{2}{5}\\=\frac{9}{25}+\frac{2}{5}\\\mathrm{Prime\:factorization\:of\:}25:\quad 5\times\:5\\\mathrm{Prime\:factorization\:of\:}5:\quad 5\\\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}25\mathrm{\:or\:}5\\[/tex]
[tex]\lim_{n \to \infty} a_n =5\cdot \:5\\\\\mathrm{Multiply\:the\:numbers:}\:5\cdot \:5=25\\=25\\\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}\\\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:25\\\mathrm{For}\:\frac{2}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}5\\\frac{2}{5}=\frac{2\times \:5}{5\times \:5}=\frac{10}{25}\\=\frac{9}{25}+\frac{10}{25}\\[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{9+10}{25}\\\\=\frac{19}{25}[/tex]
Pleased help with this
Answer:
A
Step-by-step explanation:
There are 42 students in an elementary statistics class. On the basis of years of experience, the instructor knows that the time needed to grade a randomly chosen first examination paper is a random variable with an expected value of 5 min and a standard deviation of 6 min. (Give answers accurate to 3 decimal places.)
(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?
1
(b) If the sports report begins at 11:10, what is the probability that he misses part of the report if he waits until grading is done before turning on the TV?
2
Answer:
A) 0.99413
B) 0.00022
Step-by-step explanation:
A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:
Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes
Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:
μ = n*μ_s ample = 42 × 5 = 210 minutes
While the standard deviation for the population would be:
σ = √nσ_sample = √(42 × 6) = 15.8745 minutes
To find the z-score, we will use the formula;
z = (x - μ)/σ
Thus;
z = (250 - 210)/15.8745
z = 2.52
From the z-distribution table attached, we have;
P(Z < 2.52) ≈ 0.99413
B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.
Thus, total time is now 250 + 10 = 260 minutes
Similar to the z-formula in A above, we have;
z = (260 - 210)/15.8745
z = 3.15
P(Z > 3.15) = 0.00022
Given: (in picture as I cannot type it like that.) Name the postulate or theorem you can use to prove: (also in the picture) A. HL Theorem B. AAS Theorem C. SAS Postulate D. ASA Postulate
Answer:
You need to use the AAS (angle angle side) congruency theorem
Step-by-step explanation:
youre welcome!!!
Answer:
The Angle-Angle-Side Postulate (AAS)
Step-by-step explanation:
It is given that angle 1 and 2 are equivalent so that is angle #1
It is given that angle 3 and 4 are also equivalent so that is angle #2
And finally, it is given that side TS and side TR are equivalent giving you that last side you need to prove the type of Postulate it is
If this helped, please consider giving me brainliest, it will help me a lot
Have a good day! :)
from the top of a building 10m high the angle of depression of a stone lying on the horizontal ground is 60° . calculate the distance of the stone from the foot of the building
Answer:
14.29cm
Step-by-step explanation:
Height of the building=10cm
Angle of depression=60°
We are therefore asked to find the distance from the stone to the
the foot of the building;Therefore we use Tan ratio which is opp/adj;
Let the distance from the stone to the foot of the building be x;
10/x=Tan60°
10/x=1.7/1
We then cross multiply to get 1.7x=10
x=10/1.7
=10*10/1.7*10
=100/17
=14.29cm.
-5/2x-3 is less than or equal to 2 what is the solution.
Answer: 1/4≤x
Step-by-step explanation:
-5/(2x-3)≤2
Multiply by (2x-3)
-5≤4x-6
Add 6
1≤4x
1/4≤x
Hope it helps <3
Answer:
[tex]x \geq 1/4[/tex]
Step-by-step explanation:
=> [tex]\frac{-5}{2x-3} \leq 2[/tex]
Multiplying both sides by (2x-3)
=> [tex]-5 \leq 2(2x-3)[/tex]
=> [tex]-5 \leq 4x-6[/tex]
Adding 6 to both sides
=> [tex]-5+6 \leq 4x[/tex]
=> [tex]4x\geq 1[/tex]
Dividing both sides by 4
=> [tex]x \geq 1/4[/tex]
How do I tell if scatterplot is linear?
Find the volume o the sphere.
Answer:
The volume of sphere is 267.95 units³.
Step-by-step explanation:
Given that the formula of volume of sphere is V = 4/3×π×r³ where r represents radius. Then, you have to substitute the values into the formula :
[tex]v = \frac{4}{3} \times \pi \times {r}^{3} [/tex]
[tex]let \: r = 4[/tex]
[tex]v = \frac{4}{3} \times \pi \times {4}^{3} [/tex]
[tex]v = \frac{4}{3} \times \pi \times 64[/tex]
[tex]v = \frac{256}{3} \times 3.14[/tex]
[tex]v = 267.95 \: {units}^{ 3} [/tex]
What is the slope of the line described by the equation y-1=3x
Answer:
Hey there!
The line can be expressed into y intercept form, y=3x+1.
Thus, in y=mx+b form, m is the slope, and we see that 3 is the slope of the line.
Let me know if this helps :)
Write these numbers in standard form 906000000
Answer:
9.06×10 to the power of 8(8 is superscript above 10)
Answer:
9.06 x 10^8
Step-by-step explanation:
906000000 = 9.06 x 10^8
8 decimal places in
What single transformation maps Triangle ABC onto A’B’C’
Answer:
Your answer is B
Step-by-step explanation:
rotating about/around the origin taking a shape and rotating it with the same values but around the point (0,0). so rotating your shape ABC around (0,0) with the same value would give you the shape A'B'C'
Lily is 14 years older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined age?
Answer:
30 years
Step-by-step explanation:
let the age of Ezekiel be x years
Given
Lily is 14 years older than her little brother Ezekiel
Age of Lily = x + 14 years
Next condition
after 8 years\
age of Ezekiel = x+8
age of Lily = x + 8 +14 = x + 22 years
Given
. In 8 years, Lily will be twice as old as Ezekiel will be then.
Thus,
x + 22 = 2(x+8)
=> x + 22 = 2x + 16
=> 22-16 = 2x -x
=> x = 6
Thus, age of Ezekiel = 8 years
age of lily = 8+14 = 22 years
sum of their age = 22 + 8 = 30 years answer.
A central angle is best described as which of the following?
A.
It has a measure greater than 180 degrees.
B.
It is an angle that has its vertex on the circle.
C.
It is an angle that has its vertex at the center of a circle.
D.
It is part of the circumference of a circle.
Answer:
C. It is an angle that has its vertex at the center of a circle.
Step-by-step explanation:
That's the definition.
A. is wrong. An angle with a measure greater than 180° is an obtuse angle,
B. is wrong. An angle that has its vertex on the circle is an inscribed angle.
D. is wrong. Part of the circumference of a circle is an arc.
Subtract the rational expressions: (x/x+2)-(2/x)
The time it takes to travel from home to the office is normally distributed with μ = 25 minutes and σ = 5 minutes. What is the probability the trip takes more than 40 minutes?
Answer:
The probability is [tex]P(X > x) = 0.0013499[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 25[/tex]
The standard deviation is [tex]\sigma = 5 \ minutes[/tex]
The random number [tex]x = 40[/tex]
Given that the time taken is normally distributed the probability is mathematically represented as
[tex]P(X > x) = P[\frac{X -\mu}{\sigma } > \frac{x -\mu}{\sigma } ][/tex]
Generally the z-score for the normally distributed data set is mathematically represented as
[tex]z = \frac{X - \mu}{\sigma }[/tex]
So
[tex]P(X > x) = P[Z > \frac{40 -25}{5 } ][/tex]
[tex]P(X > x) = 0.0013499[/tex]
This value is obtained from the z-table
Which point is a solution to the system of inequalities graphed here? y -5 x + 4 A. (1,6) B. (-6,0) C. (0,5) D. (5,0)
Answer:
D
Step-by-step explanation:
this is the only one inside the overlapping inequalitlies