Answers
Answer:
[tex]m = 10[/tex]
Step-by-step explanation:
Looking at the angles, we can see that this is a 30-60-90 triangle.
The side that is with the 30° angle and the 90° angle is represented by [tex]x\sqrt{3}[/tex].
So let's find x.
[tex]x\sqrt{3} = 5\sqrt{3}[/tex]
Divide both sides by [tex]\sqrt{3}[/tex]:
[tex]x = 5[/tex].
Now the hypotenuse is always [tex]2x[/tex] (the leg with the 90° and 60° is just x.) So,
[tex]2x = 2\cdot5 = 10[/tex].
Hope this helped!
Related Questions
Based on the dot plots shown in the images, which of the following is a true statement? A. Set B has the greater mode. B. Set A has more items than set B. C. Set A is more symmetric than set B. D. Set B has the greater range.
Answers
nolan completely fills a glass with water and then pours the water into a bowl. he does this until the bowl is completely filled with water. The full glass holds 1 1/3 cups of water the full bowl holds 4 2/3 cups of water How many full glasses of water does the bowl hold
Answers
Answer:
[tex]\bold{3\dfrac{1}{2 }}[/tex] full glasses of water the bowl holds.
Step-by-step explanation:
Full glass of water holds [tex]1\frac{1}{3}[/tex] cups of water.
Full bowl of water holds [tex]4\frac{2}{3}[/tex] cups of water.
To find:
How many full glasses of water does the bowl hold ?
Solution:
Let us convert the unit of cups of water to glass of water.
Given that
[tex]1\frac{1}{3}[/tex] or [tex]\frac{4}{3}[/tex] cups of water is equivalent to 1 full glass of water
Now, let us use unitary method to find the answer.
[tex]\frac{4}{3}[/tex] cups of water is equivalent to 1 full glass of water
1 cups of water is equivalent to [tex]\frac{3}{4}[/tex] full glass of water
[tex]4\frac{2}{3}[/tex] or [tex]\frac{14}{4}[/tex] cups of water is equivalent to [tex]\frac{3}{4}\times \frac{14}3 = \frac{14}{4}[/tex] full glass of water
[tex]\dfrac{14}{4} = \dfrac{7}{2} = \bold{3\dfrac{1}{2}}[/tex] full glass of water is the quantity the bowl holds.
please help
-3(-4x+4)=15+3x
Answers
Answer:
x=3
Step-by-step explanation:
● -3 (-4x+4) = 15 + 3x
Multiply -3 by (-4x+4) first
● (-3) × (-4x) + (-3)×(4) = 15 + 3x
● 12 x - 12 = 15 +3x
Add 12 to both sides
● 12x - 12 + 12 = 15 + 3x +12
● 12 x = 27 + 3x
Substract 3x from both sides
● 12x -3x = 27 + 3x - 3x
● 9x = 27
Dividr both sides by 9
● 9x/9 = 27/9
● x = 3
If one card is randomly selected from a well-shuffled standard deck of 52 cards, what is the probability that the card selected is not a spade
Answers
Answer:
Step-by-step explanation:
Given
Total Number of Cards = 52
Required
Probability of not picking a spade
Let P(S) represents the probability of picking a spade;
[tex]P(S) = \frac{n(S)}{Total}[/tex]
Where n(S) is the number of spades
[tex]n(S) = 13[/tex]
Substitute [tex]n(S) = 13[/tex] and 52 for Total
[tex]P(S) = \frac{13}{52}[/tex]
[tex]P(S) = \frac{1}{4}[/tex]
Let P(S') represents the probability of not picking a spade
In probability;
[tex]P(S) + P(S') = 1[/tex]
Substitute [tex]P(S) = \frac{1}{4}[/tex]
[tex]\frac{1}{4} + P(S') = 1[/tex]
[tex]P(S') = 1 - \frac{1}{4}[/tex]
[tex]P(S') = \frac{4-1}{4}[/tex]
[tex]P(S') = \frac{3}{4}[/tex]
[tex]P(S') = 0.75[/tex]
Hence, the probability of not selecting a spade is 3/4 or 0.75
Find the smallest positive integer that satisfies both of the following equations: = 3 (mod4) and = 5 (mod6)
Answers
Answer:
x=3mod4
Means that when x is divided by 4 it gives an unknown integer and a remainder of 3.
x/4 = Z + 3/4
Z= (x-3)/4
Where Z is the integer
x=5 mod6
x/6 = Y + 5/6
Y = (x-5)/6
Where Y is the integer
Z-Y must be an integer on equal to zero
(x-3)/4 - (x-5)/6
3(x-3)/12 - 2(x-5)/12
(3x-9-2x+10)/12
(x+1)/12
If it is equal to 0
x=-1. But x should be positive
If it is equal to 1
x=11
Hence the smallest possible number is 11
There are 937 entries for a talent show.
What is the value of the 3?
Answers
Answer:
the value of the 3 is 30
Step-by-step explanation:
the second digit to the left of a decimal is always tens column
49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Group of answer choices
Answers
Answer:
Stratified Random sampling.
Step-by-step explanation:
As per the scenario, It is stratified random sampling as it divides students into strata which represent Sophomores, Juniors, and Seniors.
Simple random samples of the given sizes of the proportional to the size of the stratum which is to be taken from every stratum that is to be about 10 percent of students from every class that is selected here.
Hence, according to the given situation, the correct answer is a random stratified sampling.
5/7 minus 2/9 please
Answers
Answer:
[tex]\large \boxed{31/63}[/tex]
Step-by-step explanation:
5/7 - 2/9
Make denominators equal by LCM.
(5 × 9)/(7 × 9) - (2 × 7)/(9 × 7)
45/63 - 14/63
Subtract fractions since denominators are equal.
(45 - 14)/63
31/63
Answer:
[tex]\frac{31}{63}[/tex]
Step-by-step explanation:
Find the LCM of 7 and 9: 63Find how much we increased each number to get to 63: we increased 7 by 9, and we increased 9 by 7Multiply the numerators by the corresponding increase numbers: 5 × 9 = 45, and 2 × 7 = 14Put the new numerators over the new denominators, so it looks like this: [tex]\frac{45}{63}[/tex] and [tex]\frac{14}{63}[/tex] Finally, subtract one from the other and here's what you get: [tex]\frac{31}{63}[/tex]Therefore, the answer is [tex]\frac{31}{63}[/tex].
Karmen returned a bicycle to Earl's Bike Shop. The sales receipt showed a total paid price of $211.86, including the 7% sales tax. What was the cost of the bicycle without the sales tax? Any help would be very appreciated! Thank you very much!
Answers
Answer:
$198
Step-by-step explanation:
198x.07=13.86
198+13.86=211.86
Find the SURFACE AREA of the composite figure below
ASAP
Answers
Answer:
248.26 cm²
Step-by-step explanation:
Surface area of the composite figure = (surface area of cuboid + surface area of hemisphere) - 2(base area of hemisphere)
Surface area of cuboid = [tex] 2(lw + lh + hw) [/tex]
Where,
l = 10 cm
w = 5 cm
h = 4 cm
Plug in the values into the formula:
[tex] SA = 2(10*5 + 10*4 + 4*5) [/tex]
[tex] SA = 2(50 + 40 + 20) [/tex]
[tex] SA = 2(110) = 220 cm^2 [/tex]
Surface area of hemisphere = 3πr²
Where,
π = 3.14
r = 3 cm
SA of hemisphere = 3*3.14*3² = 3*3.14*9 = 84.78 cm²
Base area of hemisphere = πr²
BA = 3.14*3² = 3.14*9 = 28.26 cm²
Surface area of the composite shape = (220 + 84.78) - 2(28.26)
= 304.78 - 56.52
SA = 248.26 cm²
A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed. What is the probability that the average thickness of the 100 sheets is less than 3.74 mm
Answers
Answer:
0.0090483
Approximately = 0.00905
Step-by-step explanation:
z = (x - μ)/σ, where
x is the raw score = 3.74
μ is the sample mean = population mean = 4 mm
σ is the sample standard deviation
This is calculated as:
= Population standard deviation/√n
Where n = number of samples = 100
σ = 1.1/√100
σ = 1.1/10 = 0.11
z = (3.74 - 4) / 0.11
z = -2.36364
Using the z score table to determine the probability,
The probability that the average thickness of the 100 sheets is less than 3.74 mm
P(x<3.74) = 0.0090483
Approximately = 0.00905
Using the normal distribution and the central limit theorem, it is found that there is a 0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means for size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean thickness of 4 mm, thus [tex]\mu = 4[/tex].Standard deviation of 1.1 mm, thus [tex]\sigma = 1.1[/tex].Sample of 100, thus [tex]n = 100, s = \frac{1.1}{\sqrt{100}} = 0.11[/tex].The probability is the p-value of Z when X = 3.74, then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3.74 - 4}{0.11}[/tex]
[tex]Z = -2.36[/tex]
[tex]Z = -2.36[/tex] has a p-value of 0.0091.
0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.
A similar problem is given at https://brainly.com/question/14228383
Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?
Answers
If you are wondering what happened to the 1, for any constant C, d/dx(C)=0.
Here is some information about the goals scored in some hockey games. Each game has four quarters. Please give the answer asap with full explanation and working out.
Answers
Answer:
8 home games and 10 away games
Step-by-step explanation:
Total home goals
= 8+5+9+8
= 30
Number of home games
= 30/3.75
= 8
Total away game goals
= 7+8+4+5
= 24
Number of away games
= 24/2.4
= 10
Answer:
i think it is 8 home and 10 away matches
Step-by-step explanation:
pls answer my question please
Answers
Bold = changed words
1. We play tennis every Sunday.
2. I own two dogs and a cat. I love animals.
3. My suitcase weighs four kilos (kilograms).
4. When Mary came in, I talked to my mother on the phone. OR: I talked to Mother on the phone when Mary came in.
5. We passed the hotel two minutes ago. OR: We passed by the hotel two minutes ago.
A tennis team played a total of 25 games and won 20 of them. What percent of the games did the team win?
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
80%
▹ Step-by-Step Explanation
20/25 = 0.8 → 80%
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Therefore the team won 80% of the games.
[tex]\sqrt{x+1+5=x}[/tex] Please help [tex]\sqrt{5x-x=0}[/tex] I actually can't do this, also thirty points
Answers
Answer:
It is undefined.
Step-by-step explanation:
Let's take a look at the first equation- if we simplify and move the terms, it becomes sqrt of 6 = 0, which results in an undefined value of x. The second equation works with x=0 but not the first so the value of x is undefined.
29. Identify the end behavior of the function f(x) = 3x^4 + x^3 − 7x^2 + 12.
options:
A. As x → –∞, y → +∞, and as x → +∞, y → –∞
B. As x → –∞, y → –∞, and as x → +∞, y → –∞
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
D. As x → –∞, y → –∞, and as x → +∞, y → +∞
Answers
Answer:
C. As x → –∞, y → +∞, and as x → +∞, y → +∞
Step-by-step explanation:
The leading coefficient of this even-degree function is positive, so y goes to +∞ when the magnitude of x gets large.
_____
When the function is even degree, its value for large magnitude x heads toward the infinity with the same sign as the leading coefficient.
When the function is odd degree, its value for large magnitude x will head toward the infinity with the sign that matches the product of the sign of x and the sign of the leading coefficient.
a) which function has the graph with the greatest slope?
b) which functions have graphs with y intercepts greater than 3?
c)which function has the graph with a y intercept closest to 0
Answers
Answer:
a). Function (4)
b). Function (2)
c). Function (3)
Step-by-step explanation:
Characteristics of the functions given,
Function (1),
Form the given graph,
Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]-\frac{4}{1}[/tex]
= -4
Y- intercept of the given function = 2
Function (2),
From he given table,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{5-3}{0+1}[/tex]
= 2
y-intercept = 5 [Value of y for x = 0]
Function (3),
y = -x - 1
By comparing this equation with y = mx + b
Where 'm' = slope
and b = y-intercept
Slope = (-1)
y-intercept = (-1)
Function (4),
Slope = 5
y-intercept = (-4)
(a). Greatest slope of the function → Function (4)
(b). y-intercept greater than 3 → Function (2)
(c). Function with y-intercept closest to 0 → Function (3)
Find the sum of the first 6 terms of 3 - 6 + 12 + …
Answers
Answer:
[tex] S_6 = -63 [/tex]
Step-by-step explanation:
The sequence above is a geometric sequence.
The common ratio (r) = [tex] \frac{-6}{3} = \frac{12}{-6} = -2 [/tex]
The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be: [tex] S_n = \frac{a_1(1 - r^n)}{1 - r} [/tex]
a1 = 3
r = -2
n = 6
Plug in the values into the formula
[tex] S_6 = \frac{3(1 - (-2^6)}{1 - (-2)} [/tex]
[tex] S_6 = \frac{3(1 - (64)}{1 + 2} [/tex]
[tex] S_6 = \frac{3(-63)}{3} [/tex]
[tex] S_6 = -63 [/tex]
line and passes through C -2,0 in the 1, -3) Quetion of the line in standard form
Answers
Answer:
[tex]\huge\boxed{x+y=-2}[/tex]
Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have two points (-2, 0) and (1, -3).
Substitute:
[tex]x_1=-2;\ y_1=0;\ x_2=1;\ y_2=-3[/tex]
[tex]m=\dfrac{-3-0}{1-(-2)}=\dfrac{-3}{1+2}=\dfrac{-3}{3}=-1\\\\y-0=-1(x-(-2))\\\\y=-(x+2)[/tex]
[tex]y=-x-2[/tex] add x to both sides
[tex]x+y=-2[/tex]
4/17 + 3/10 + 9/20 + 3/11 + 7/15
Answers
Answer:
[tex]\frac{19351}{11220}[/tex]
Step-by-step explanation:
[tex]\frac{2640+3366+5049+3060+5236}{11220} = \frac{19251}{11220}[/tex]
pt 2 4-7 please helppp
Answers
Answer:
f = 16
Step-by-step explanation:
8
8 x 2 = _f_ x
8
f = 16
Hi there! Hopefully this helps!
-----------------------------------------------------------------------------------------------------
Answer: f = 16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]2 = \frac{f}{8}[/tex]
Multiply both sides by 8.
[tex]2 \times 8 = f[/tex]
Multiply 2 and 8 to get 16.
[tex]16 = f[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]f = 16[/tex]
Find the perimeter of a rectangle that is 7 centimeters long and 7 centimeters wide
Answers
Answer:
28cm
Step-by-step explanation:
2L+2W=
14+14=28
(It’s a square)
Use the quadratic function to predict f(x) if x equals 2. f(x) = −3x2 + 180x − 285
Answers
Answer:
if x = 2
f(x) = -3x^2 + 180x -285
f(x) = -3*2*2 + 180*2 -285
f(x) = -12 + 360 -285
f (x) = 63
Step-by-step explanation:
In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle. A straight line is shown and is marked with three angles. The first angle measures 50 degrees. The second angle measures 60 degrees. The third angle is labeled x. The line between the 40 degree angle and angle x extends below the straight line. The angle formed is labeled angle y. Write and solve an equation to determine the measure of angle y.
Answers
Step-by-step explanation:
sorry but u should provide with a diagram for better understanding of ur question
Find the derivative of the function f(x) = (x3 - 2x + 1)(x – 3) using the product rule.
then by distributing and make sure they are the same answer
Answers
Answer:
Step-by-step explanation:
Hello, first, let's use the product rule.
Derivative of uv is u'v + u v', so it gives:
[tex]f(x)=(x^3-2x+1)(x-3)=u(x) \cdot v(x)\\\\f'(x)=u'(x)v(x)+u(x)v'(x)\\\\ \text{ **** } u(x)=x^3-2x+1 \ \ \ so \ \ \ u'(x)=3x^2-2\\\\\text{ **** } v(x)=x-3 \ \ \ so \ \ \ v'(x)=1\\\\f'(x)=(3x^2-2)(x-3)+(x^3-2x+1)(1)\\\\f'(x)=3x^3-9x^2-2x+6 + x^3-2x+1\\\\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Now, we distribute the expression of f(x) and find the derivative afterwards.
[tex]f(x)=(x^3-2x+1)(x-3)\\\\=x^4-2x^2+x-3x^3+6x-4\\\\=x^4-3x^3-2x^2+7x-4 \ \ \ so\\ \\\boxed{f'(x)=4x^3-9x^2-4x+7}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which of the following is the graph of the quadratic parent function
Answers
This is the graph of y = x^2. It is a parabola that opens upward and has its vertex at the origin. Applying various transformations to the parent function will allow us to produce any parabolic graph we want. In effect, the parent function is like the most basic building block.
A random sample of 1003 adult Americans was asked, "Do you think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without. Construct and interpret a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without out.
Answers
Answer:
The 95% confidence interval is [tex]0.503 < p < 0.535[/tex]
The interpretation is that there is 95% confidence that the true population proportion lie within the confidence interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 1003
The number that indicated television are a luxury is k = 521
Generally the sample mean is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
[tex]\r p = \frac{521}{1003}[/tex]
[tex]\r p = 0.519[/tex]
Given the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{ \frac{ 0.519 (1- 0.519 )}{1003} }[/tex]
=> [tex]E = 0.016[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.519 - 0.016 < p < 0.519 + 0.016[/tex]
=> [tex]0.503 < p < 0.535[/tex]
In a study of 24 criminals convicted of antitrust offenses, the average age was 60 years, with a standard deviation of 7.4 years. Construct a 95% confidence interval on the true mean age. (Give your answers correct to one decimal place.)___ to____ years
Answers
Answer: 56.9 years to 63.1 years.
Step-by-step explanation:
Confidence interval for population mean (when population standard deviation is unknown):
[tex]\overline{x}\pm t_{\alpha/2}{\dfrac{s}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex]= sample mean, n= sample size, s= sample standard deviation, [tex]t_{\alpha/2}[/tex]= Two tailed t-value for [tex]\alpha[/tex].
Given: n= 24
degree of freedom = n- 1= 23
[tex]\overline{x}[/tex]= 60 years
s= 7.4 years
[tex]\alpha=0.05[/tex]
Two tailed t-critical value for significance level of [tex]\alpha=0.05[/tex] and degree of freedom 23:
[tex]t_{\alpha/2}=2.0687[/tex]
A 95% confidence interval on the true mean age:
[tex]60\pm (2.0686){\dfrac{7.4}{\sqrt{24}}}\\\\\approx60\pm3.1\\\\=(60-3.1,\ 60+3.1)\\\\=(56.9,\ 63.1)[/tex]
Hence, a 95% confidence interval on the true mean age. : 56.9 years to 63.1 years.
a is inversely proportional to (b - 4).
If a = 8 and b = 22, express a in terms of b.
Answers
Answer:
Step-by-step explanation:
a is expressed in terms of b as a = 144/(b - 4).
If A is inversely proportional to (b - 4), we can express this relationship using the formula:
A = k/(b - 4),
where k is the constant of proportionality.
To determine the value of k, we can use the given information when a = 8 and b = 22:
8 = k/(22 - 4).
Simplifying the equation:
8 = k/18.
To isolate k, we multiply both sides of the equation by 18:
8 * 18 = k.
k = 144.
Now that we know the value of k, we can rewrite the equation in terms of b:
A = 144/(b - 4).
Therefore, a is expressed in terms of b as a = 144/(b - 4).
Learn more about proportional here
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