Answer:
Step-by-step explanation:
V = L * W * H
L = 4
W = 3
H = 2
V = 4 * 3 * 2
V = 24
Density = mass / Volume
density = 11.34
volume = 24
mass = ?
11.34 = mass / 24 Multiply both sides by 24
11.34 * 24 = 24 * mass /24
mass = 272.16 grams
Consider the following data. 15,−4,−10,8,14,−10,−2,−11
Step 1 of 3: Determine the mean of the given data
Step 2 of 3: Determine the median of the given data.
Step 3 of 3: Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.
Answer:
(a) The mean is 0
(b) The median is -30
(c) The mode is unimodal
Step-by-step explanation:
Given
[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]
Solving (a): The mean.
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]
[tex]\bar x =\frac{0}{8}[/tex]
[tex]\bar x =0[/tex]
Solving (b): The median
First, arrange the data
[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]
There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.
[tex]Median = \frac{-4-2}{2}[/tex]
[tex]Median = \frac{-6}{2}[/tex]
[tex]Median = -3[/tex]
Solving (c): The mode
The item that has occurs most is -10.
Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).
All of the benches in a park are red or blue. The ratio of red benches to blue benches in the park is 3 : 4. Based on this information, which of the following statements is true?
A. For every 4 benches in the park, 3 are red.
B. For every 7 benches in the park, 4 are red.
C. For every 3 red benches in the park, there are 4 blue benches.
D. For every 3 red benches in the park, there are 7 blue benches.
(I'll give brainly, likes, follow, etc for anybody who answers this question with some explanation.)
Answer:
The answer is C
Step-by-step explanation:
3 : 4
^ ^
II II
red blue
The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwise state that there is no solution.
[1 -5 -4
0 0 7]
A. X1 = - 4 + 5x2 X2 is free
B. (-4,7)
C. X1 = - 4 +5x2
X2=7
X3 is free
D. There is no solution.
Answer:
Option D (There is no solution) is the correct answer.
Step-by-step explanation:
According to the question, the matrix is:
⇒ [tex]\left[\begin{array}{ccc}1&-5&-4\\0&0&7\end{array}\right][/tex]
The linear equation will be:
⇒ [tex]x-5y=-4[/tex]
and
⇒ [tex]0.x+0.y=7[/tex]
i.e,
[tex]0=7[/tex] (Not possible)
Thus the above given matrix has no solution. So the above is the correct option.
NEED HELP ASAP!!
use the vertical line test to determine if the relation whose graph is provided is a function
(graph and answers pictured)
Answer:
Yes, this graph represents a function
Step-by-step explanation:
The function passes the vertical line test, which tests for if any input has more than one unique output by moving a vertical line from left to right. If the vertical line doesn't pass 2 or more points at a time, then the function is indeed a function.
Answer:
The graph does represent a function
Step-by-step explanation:
The function is at about 30y = x^3
Carrie works due south of her apartment. Her friend Sarah works due east of the
apartment. They leave for work at the same time. By the time Carrie is 5 miles from
their apartment the distance between them is 1 mile more than Sarah's distance
from the apartment. How far from the apartment is Sarah?
Answer:
3 miles
Step-by-step explanation:
5-1+2=3
From the calculation done using the pythagoras theorem, the distance from Sarah's apartment is 12m
What is the pythagoras theoremThis theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Using the pythagoras theorem
BC² = AB² + AC²
The sides of the triangle are x, x - 1 and 5
x² = (x-1)² + 5²
x² = (x-1)(x-1) +25
x² = x²-x-x -1 + 25
collect like terms
2x = 24
divide through the equation by 2
x = 24/2
= 12m
Read more on distance here: https://brainly.com/question/2854969
PLEASE HELP
Libby flips a quarter 2 times in a row.
What is the probability of the quarter landing on heads at least 1 time?
A. 1/4
B. 1/3
C. 3/4
D. 1/2
find the value of x, do not round until the final answer.
thank you!
Answer:
[tex]x\approx 5.48[/tex]
Step-by-step explanation:
Draw a line from the center of the circle O to the end of either side of the line marked as 4. This line represents two things:
A radius of the circleThe hypotenuse of a right triangle with legs 5.1 and 2In this case, both are important. Since [tex]x[/tex] is also a radius of the circle, the line must be equal to [tex]x[/tex], since all radii of a circle are equal. To find the length of this line, use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
Since we're solving for the hypotenuse and the two legs are 5.1 and 2, we have:
[tex]5.1^2+2^2=c^2,\\26.01+4=c^2,\\c^2=30.01,\\c=5.47813836992\approx \boxed{5.48}[/tex] (round as necessary).
prove that tan theta * sin theta = (1 - cos^2 theta)/(sqrt(1 - sin^2 theta))
Answer:
This identity holds as long as [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].
For the proof, make use of the fact that:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] (definition of tangents,) and
[tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] (Pythagorean identity,) which is equivalent to [tex]1 - \cos^{2}(\theta) = \sin^{2}(\theta)[/tex].
Step-by-step explanation:
Assume that [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex]. This requirement ensures that the [tex]\tan(\theta)[/tex] on the left-hand side takes a finite value. Doing so also ensures that the denominator [tex]\sqrt{1 - \sin^2(\theta)}[/tex] on the right-hand side is non-zero.
Make use of the fact that [tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] to rewrite the left-hand side:
[tex]\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}[/tex].
Apply the Pythagorean identity [tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex] and [tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] to rewrite this fraction:
[tex]\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}[/tex].
Hence, [tex]\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}[/tex].
Do anyone know this youll get 20 points
Answer:
A. Acute
B. 80 degrees
Step-by-step explanation:
What is the distance between A(-8, 4) and B(4, -1)?
Answer:
The distance between A(-8, 4) and B(4, -1) is 13 units.
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula given by:
[tex]\displaystyle d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
We have the two points A(-8, 4) and B(4, -1). Let A(-8, 4) be (x₁, y₁) and let B(4, -1) be (x₂, y₂). Substitute:
[tex]d=\sqrt{(4-(-8))^2+(-1-4)^2}[/tex]
Evaluate:
[tex]d=\sqrt{(12)^2+(-5)^2}[/tex]
So:
[tex]d=\sqrt{144+25}=\sqrt{169}=13\text{ units}[/tex]
The distance between A(-8, 4) and B(4, -1) is 13 units.
___________________________________
Problem:What is the distance between A(-8,4) and B(4,-1)Given:[tex]\quad\quad\quad\quad\tt{A.) x\tiny{1}\small{=-8}, y\tiny{1}\small{=4}}[/tex]
[tex]\quad\quad\quad\quad\tt{B.) x\tiny{2}\small{=4}, y\tiny{2}\small{=-1}}[/tex]
Formula for distance (d):[tex]\quad\quad\quad\quad\tt{d = \sqrt{(x \tiny{2} \small{ - x \tiny{1} \small {)}^{2} + (y \tiny{2} \small{ - y \tiny{1} \small{)}^{2} } }}} [/tex]
Solution:[tex]\quad\quad\quad\quad\tt{d = \sqrt{(4 - \small{ (- 8}{))}^{2} + ( \small{- 1)}\small{ - {4)}}^{2} }}[/tex]
[tex]\quad\quad\quad\quad\tt{d = \sqrt{ ( {12)}^{2} + {( -5)}^{2} }}[/tex]
[tex]\quad\quad\quad\quad\tt{d = \sqrt{ {144} + {25}}}[/tex]
[tex]\quad\quad\quad\quad\tt{d = \sqrt{ 169}}[/tex]
[tex]\quad\quad\quad\quad\tt{d = 13}[/tex]
So the final answer is:[tex]\quad\quad\quad\quad\boxed{\boxed{\tt{\color{magenta}d = 13}}}[/tex]
___________________________________
#CarryOnLearning
✍︎ C.Rose❀
The cost to make a path connecting all four landmarks is based on the proposal shown. The cost of path A is $29. The cost of path B is $59 The cost of path C is $32 The cost of path D is $38 Find the cost of the minimum spanning tree to connect all four landmarks?
Answer:
158
Step-by-step explanation:
The cost of the minimum spanning tree to connect all four landmarks will be $158.
What is Algebra?Algebra is the study of graphic formulas, while logic is the interpretation among those signs.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The cost to make a path connecting all four landmarks is based on the proposal shown.
The cost of path A is $29.
The cost of path B is $59.
The cost of path C is $32.
The cost of path D is $38.
Then the cost of the minimum spanning tree to connect all four landmarks will be
Total cost = cost of path A + cost of path B + cost of path C + cost of path D
Total cost = $29 + $59 + $32 + $38
Simplify the expression, then we have
Total cost = $29 + $59 + $32 + $38
Total cost = $158
More about the Algebra link is given below.
https://brainly.com/question/953809
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a tv cost £800 plus VAT at 20% what is the total cost of the tv?
Answer:
Given:
Cost = £ 800
Tax = 20%
To find:
The total cost
Solution:
Total cost = Cost + Tax
Tax = 20 % of cost
20 / 100 * 800
Tax = £ 160
Hence,
Total cost = £ 800 + £ 160
Total cost = £ 960
one lap around a field is 4/5 of a mile .Adrian ran these laps . how far did he run?
What is the measure of each angle of a regular 24-gon? If necessary, round to the
nearest tenth.
Answer:
165°
Step-by-step explanation:
Find the interior angle measure by using the formula, ((n - 2) x 180°) / n
Plug in 24 as n:
((n - 2) x 180°) / n
((24 - 2) x 180°) / 24
(22 x 180°) / 24
3960 / 24
= 165
So, the measure of each angle is 165°
Answer:
163.6
Step-by-step explanation:
180•(22-2)=180•20 =3600
3600/22= 163.636363…
Juan borrowed $1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%. What is the amount of interest he paid at the end of the loan
Answer:
The amount of interest he paid at the end of the loan is $ 311.85.
Step-by-step explanation:
Given that Juan borrowed $ 1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%, to determine what is the amount of interest he paid at the end of the loan, the following calculation must be performed:
(1500 x 0.0297) x 7 = X
44.55 x 7 = X
311.85 = X
Therefore, the amount of interest he paid at the end of the loan is $ 311.85.
A school class of 120 students is driven in 3 buses to a symphonic performance. There are 36 students in one of the buses, 40 in another, and 44 in the third bus. When the buses arrive, one of the 120 students is randomly chosen. Let X denote the number of students on the bus of that randomly chosen student, find E(X).
Answer:
40.2667
Step-by-step explanation:
P(X=36)= 36/120
P(X=40)= 40/120
P(X=44)=44/120
E(X) = 36(36/120)+40(40/120)+44(44/120)=1208/30=40.2667
hope this helps
If a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
A school class of 120 students is driven in 3 buses to a symphonic performance.
There are 36 students on one of the buses, 40 on another, and 44 on the third bus.
From the data given:
Let X be the total number of passengers on the bus carrying that randomly selected student,
Total number of students = 120
Let:
Probability:
P(X = 36) = 36/120
Probability:
P(X = 40)= 40/120
Probability:
P(X = 44)=44/120
E(X) = 36(36/120) + 40(40/120) + 44(44/120)
E(X) = 1208/30
E(X) = 40.26
Therefore, if a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.
Learn more about the probability here:
brainly.com/question/11234923
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Construct the sampling distribution of the sample means.?
Answer:
The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).
Step-by-step explanation:
Standard form for -3x^+ x=13
Answer:
to put the equation into standard for we must multiply the terms on the right side of the equation. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
Step-by-step explanation:
y
=
(
x
−
13
)
(
x
−
12
)
becomes:
y
=
(
x
×
x
)
−
(
x
×
12
)
−
(
13
×
x
)
+
(
13
×
12
)
y
=
x
2
−
12
x
−
13
x
+
156
We can now combine like terms:
y
=
x
2
+
(
−
12
−
13
)
x
+
156
y
=
x
2
+
(
−
25
)
x
+
156
y
=
x
2
−
25
x
+
156
Evaluate f(x) =
f(x) = x for x = 4.
3
Answer:
x=3
Step-by-step explanation:
There are 28 chocolate-covered peanuts in 1 ounce (oz). Jay bought a 62 oz. jar of chocolate-covered peanuts.
Problem:
audio
How many chocolate-covered peanuts were there in the jar that Jay bought?
Enter your answer in the box.
Answer:
1,736 chocolate cover peanuts
Step-by-step explanation:
do 28×62 hope this helps
Answer:
1736 chocolate-covered peanuts
Step-by-step explanation:
[tex]\frac{1}{62} :\frac{28}{y}[/tex]
1 · y = 62 · 28
y = 1736
In the radius of a circle with an area of 10 inches squared is reduced by half what is the area of the new circle
Answer:
Hence when the radius is halved the area is divided by 4
2.5 inches^2
Step-by-step explanation:
Given data
Area= 10inches^2
We know that the expression for the area of a circle is given as
Area= πr^2
10= 3.142*r^2
10/3.142= r^2
r^2= 3.18
Square both sides
r= √3.18
r= 1.78 inches
Now let us half the radius and find the area of the new circle
r/2= 1.78/2
r= 0.89
Area of the new circle is
Area= 3.142*0.89^2
Area= 3.142*0.7921
Area= 2.5 inches^2
HELP I WILL GIVE BRAINLYEST PLSSS HELP
Answer:
The answer is 0.5
Answer:
rhe answer is r= .50
Step-by-step explanation:
125-75=50
A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a standard deviation of penalties per game. What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be penalties per game or less
Answer:
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
We have that:
The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].
Sample of n games:
This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
Shawn thinks that helium prices next year might increase by 10%. He plans to buy 7 small balloons and x large balloons. He creates the following equation to find the total price for next year’s helium:P
Answer:
P = 7.7 C + 1.1 XC
Step-by-step explanation:
From the question, it is noted that the price of helium required to fill each of the balloons would increase by 10%. Let the current price of helium be C, so that;
10% of C = 0.1 C
The price of helium next year = C + 0.1 C
= 1.1 C
Cost of 7 small balloons = 1.1 C * 7
= 7.7 C
Cost of X large balloons = 1.1 C * X
= 1.1 XC
The total price, P for helium next year = 7.7 C + 1.1 XC
Thus, the equation to find the total price of helium that would fill the balloons next year is;
P = 7.7 C + 1.1 XC
Wally bought a television for $987.00. The finance charge was $205 and she paid for it over 24 months. (Finance Ch arg e: #Months)(12) Amount Financed Use the formula Approximate APR to calculate her approximate APR. Round the answer to the nearest tenth.
Answer:
10.4%Step-by-step explanation:
Principal is $987.Finance charge is $205Time is 2 yearsAPR = ((Finance charge/Principal)/Time)*100% (simplified for this case)APR = ((205/987)/2)*100% = 10.4%PLEASE HELP!!!
WILL MARK BRAINLIEST!!!!
If the measure of 0 is 90, then angle B=____
Multiple choice!
Thank you!!!
Answer:
angle B is 45 degree.
Step-by-step explanation:
since both radius are equal in a circle the triangle formed is ann isosceles triangle.
base angle of an isosceles triangle are equal
angle B be x
angle A = angle B (being base angles of a triangle)
then angle A is also x
angle A + angle B + angle C =180 degree (sum of interior angles of a triangle)
x + x + 90=180
2x =180-90
x=90/2
x=45 degree
What is the equation of the line that passes through the point (1,7)and has a slope of -1
?
Answer:
y = -x + 8
Step-by-step explanation:
First, plug in the slope.
y = mx + b
y = -1x + b
y = -x + b
Then, plug in the point.
7 = -(1) + b
7 = -1 + b
8 = b
Which expression gives the measure of XYZ?
V
110°
w
D
42
O A. 110° - 42°
O B. 2(110° + 42°)
O c. 2(110° - 42°)
OD. 110° +420
Answer:
1/2( 110+42)
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
<<XYZ = 1/2( 42+110)
Find the length of AB and round answer to the nearest hundredth
Answer:
AB ≈ 11.17 m
Step-by-step explanation:
The arc AB is calculated as
AB = circumference of circle × fraction of circle
= 2πr × [tex]\frac{80}{360}[/tex]
= 2π × 8 × [tex]\frac{8}{36}[/tex]
= 16π × [tex]\frac{2}{9}[/tex]
= [tex]\frac{32\pi }{9}[/tex] ≈ 11.17 m ( to the nearest hundredth )
Helppppppppp
What is the solution to the equation below ?
Answer: x=3
Step-by-step explanation:
First we're going to get rid of the fraction by multiplying both sides by the square root of x-2
Now square both sides
[tex](\sqrt{3x })^2=3^2(\sqrt{x-2 })^2\\3x=9(x-2)[/tex]
Next use the distributive property
[tex]3x=(9)(x)-(9)(2)\\3x=9x-18[/tex]
Now subtract 9x from both sides
[tex]3x-9x=9x-18-9x\\-6x=-18[/tex]
Finally divide -6 on both sides
[tex]\frac{-6x}{-6} =\frac{-18}{-6} \\x=3[/tex]
