Answer:
Exact Form:
[tex]\frac{28}{3}[/tex]
Decimal Form:
9.3¯ (where the three is repeating)
Mixed Number Form:
[tex]9\frac{1}{3}[/tex]
In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014, let the random variable C represent the number of households in the sample that had a computer. What are the mean and standard deviation of C ?
Answer:
The mean of C is 170 households
The standard deviation of C, is approximately 5 households
Step-by-step explanation:
The given parameters are;
The percentage of households in the United States that had a computer in 2014 = 85%
The size of the randomly selected sample in 2014, n = 200
The random variable representing the number of households that had a computer = C
Therefore, we have;
The probability of a household having a computer P = 85/100 = 0.85
Let
Therefore;
The mean (expected) number in the sample, μₓ, = E(x) = n × P is given as follows;
μₓ = 200 × 0.85 = 170
The mean of C = μₓ = 170
The variance, σ² = n × P × (1 - P) = 200 × 0.85 × (1 - 0.85) = 25.5
Therefore;
The standard deviation, σ = √(σ²) = √(25.5) ≈ 5.05
The standard deviation of C, σ ≈ 5 households (we round (down) to the nearest whole number)
The mean and the standard deviation of C are 170 and 5.05 respectively
The given parameters are:
[tex]\mathbf{n = 200}[/tex] -- the sample size
[tex]\mathbf{p = 85\%}[/tex] -- the proportion of household that had a computer
(a) The mean
This is calculated as:
[tex]\mathbf{\bar x = np}[/tex]
So, we have:
[tex]\mathbf{\bar x = 200 \times 85\%}[/tex]
[tex]\mathbf{\bar x = 170}[/tex]
(b) The standard deviation
This is calculated as:
[tex]\mathbf{\sigma = \sqrt{np(1 - p)}}[/tex]
So, we have:
[tex]\mathbf{\sigma = \sqrt{170 \times (1 - 85\%)}}[/tex]
[tex]\mathbf{\sigma = \sqrt{170 \times 15\%}}[/tex]
[tex]\mathbf{\sigma = \sqrt{25.5}}[/tex]
Take square roots
[tex]\mathbf{\sigma = 5.05}[/tex]
Hence, the mean and the standard deviation of C are 170 and 5.05 respectively
Read more about mean and standard deviation at:
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25 pts! Dont copy someone elses work plz
Explain why the equation (x-4)^2-28=8 has two solutions. Then solve the equation to find the solutions. Show your work
Answer:
x = −2 or x = 10
Step-by-step explanation:
for the explanation see the image
Can somebody plz answer all of them correct! (Only if u done this before)
thanks! WILL MARK BRAINLIEST
(Don’t judge me..I didn’t study so I need to do corrections)
Answer:
23) 53/100
24)2/5
25)3/5
26)11/50
27)17/50
28)19/1000
29)4/5
30)1/250
31)9/25
32)1 3/10
33)11 1/2
34) 7 3/40
Step-by-step explanation: Hope this helps!
if g(x)=x²-2 and p(x)=2x+3, find (g·p)(x)
If the pattern continues, how many tiles would be in the 62nd stage?
A. 127
B. 129
C. 131
D. 307
Justin and his children went into a grocery store and he bought $18 worth of bananas and mangos. Each banana costs $0.60 and each mango costs $1.50. He bought 2 more bananas than mangos. Graphically solve a system of equations to determine the number of bananas, x, and the number of mangos, y, that Justin bought.
Write an answer in y=mx+b form, please.
Two equations.
Answer:
x=10 and y= 8.
Step-by-step explanation:
Given that the cost of 1 banana = $0.60
Cost of 1 mango = $1.50.
Total cost= $ 18
Here, x be the number of bananas and y be the numbers of mangos,
As the number of bananas is 2 more than the number of mangos,
So, x=y+2
[tex]\Rightarrow y=x-2 \cdots(i)[/tex]
Cost of x bananas [tex]=\$ 0.60 \times x[/tex]
Cost of y mangos [tex]=\$ 1.50 \times y[/tex]
Total cost = 0.6x+1.5y
[tex]\Rightarrow 18 = 0.6x+1.5y\\\\\Rightarrow 1.5y=18-0.6x\\\\\Rightarrow y= 12 - 0.4 x \cdots(ii).[/tex]
Solving both the equations (i) as well as (ii), graphically as shown in the figure by plotting both the graphs.
Both the graphs intersect at the point (10,8) as shown in the graph.
So, the solution of both the equations is, (x,y)=(10,8). i.e
The number of bananas = x= 10 and
the number of mangos = y = 8.
Solve the triangle, find m∠A and m∠C. Round angles to the nearest degree.
m∠A= __∘
m∠C= __∘
Answer:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of the triangle is called the hypotenuse and the other two sides are called the legs.
Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides.
The cosine ratio is defined as:
[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]
Note the angle A of the figure has 17 as the adjacent leg and 38 as the hypotenuse, so we can directly apply the formula:
[tex]\displaystyle \cos A=\frac{17}{38}[/tex]
[tex]\cos A=0.4474[/tex]
Using a scientific calculator, we get the inverse cosine:
[tex]A=\arccos(0.4474)[/tex]
[tex]A\approx 63^\circ[/tex]
Since A+B+C=180°, we can solve for C:
C = 180° - A - B
C = 180° - 63° - 90°
C = 26°
Thus:
[tex]m\angle A=63^\circ\\m\angle C=26^\circ[/tex]
In the given right triangle ABC, m∠A ≈ 26.44° and m∠C ≈ 63.56°.
To solve the right triangle ABC, we can use trigonometric ratios. In a right triangle, the three main trigonometric ratios are:
1. Sine (sin): [tex]\(\sin(\theta) = \frac{{\text{opposite side}}}{{\text{hypotenuse}}}\)[/tex]
2. Cosine (cos): [tex]\(\cos(\theta) = \frac{{\text{adjacent side}}}{{\text{hypotenuse}}}\)[/tex]
3. Tangent (tan): [tex]\(\tan(\theta) = \frac{{\text{opposite side}}}{{\text{adjacent side}}}\)[/tex]
Given:
AC = 38
AB = 17
To find the angles m∠A and m∠C, we can use the sine and cosine ratios, respectively.
1. For m∠A:
[tex]\(\sin(m\angle A) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle A= \sin^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
2. For m∠C:
[tex]\(\cos(m\angle C) = \frac{{AB}}{{AC}} = \frac{{17}}{{38}}\)\\\\\(m\angle C = \cos^{-1}\left(\frac{{17}}{{38}}\right)\)[/tex]
Let's calculate the angles:
[tex]1. \(m\angle A \approx \sin^{-1}\left(\frac{{17}}{{38}}\right) \approx 26.44^\circ\)\\\\2. \(m\angle C \approx \cos^{-1}\left(\frac{{17}}{{38}}\right) \approx 63.56^\circ\)[/tex]
Therefore, m∠A ≈ 26.44° and m∠C ≈ 63.56° (rounded to the nearest degree).
To know more about right triangle, refer here:
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Which shows the equation below written in the form ax2 + bx + c = 0?
x + 9 = 4(x-1)^2
LOOK AT THE PICTURE REALLY EASY
Answer:
D
Step-by-step explanation:
We have the equation:
[tex]x+9=4(x-1)^2[/tex]
To convert this to standard form, we can simply expand.
First, expand the right-hand side:
[tex]x+9=4(x^2-2x+1)[/tex]
Distribute the right:
[tex]x+9=4x^2-8x+4[/tex]
Subtract 9 from both sides:
[tex]x=4x^2-8x-5[/tex]
Finally, subtract an x from both sides:
[tex]0=4x^2-9x-5[/tex]
Flip:
[tex]4x^2-9x-5=0[/tex]
Hence, our answer is D.
please answer quick and no the answer isn’t 15
Answer:
107
Step-by-step explanation:
The two angles would make a linear pair, which means they're supplementary to each other. Supplementary angles add up to 180.
This allows us to do 180 - 73 = 107
x would be 107.
What is the x intercept of 4y+9x=18
Answer:
Step-by-step explanation:
step 1. 4y+9x=18
step 2. 4y=-9x+18
step 3. idk
Answer:
(2,0)
plug 0 for y and solve
A cab company charges $3.10 flat rate in addition to $0.85 per mile. Rex has no more than $15 to spend on a ride. Write an inequality that represents Rex's situation. How many miles can Rex travel without exceeding his limit? Round off your answer to nearest tenth.
Answer:
Step-by-step explanation:
Let the total number of miles Rex can travel be x;
If a cab company charges $0.85 per mile, then x miles will cost $0.85x
If the flat rate rate charge is $3.10, the total price for x miles will be;
0.85x + 3.10
Since Rex has no more than $15 to spend on a ride, the inequality to represent the equation will be;
0.85x + 3.10 ≤ 15 (less than or equal to means that the total value cannot exceed $15)
Next is to solve for x
Given
0.85x + 3.10 ≤ 15
subtract 3.10 from both sides
0.85x + 3.10-3.10 ≤ 15-3.10
0.85x ≤ 15-3.10
0.85x ≤ 11.90
x ≤ 11.90/0.85
x ≤ 14
This means that Rex can travel 14 miles without exceeding his limit
Answer:
[tex]3.10 + 0.85m \leq 15[/tex]
[tex]m \leq 14.0[/tex]
Step-by-step explanation:
Given
[tex]Flat\ Rate = \$3.10[/tex]
[tex]Addition = \$0.85[/tex] (per mile)
[tex]Maximum\ Amount = \$15[/tex]
Required
Determine the inequality that represents the scenario and solve
Let the number of miles be represented by m.
The company's charges can be calculated using:
[tex]Flat\ Rate + Additional\ Charges * m[/tex]
Substitute values
[tex]\$3.10 + \$0.85 * m[/tex]
Rex can't exceed $15 implies that the company's charges can't exceed Rex's budget.
This is expressed as:
[tex]\$3.10 + \$0.85 * m \leq \$15[/tex]
[tex]\$3.10 + \$0.85m \leq \$15[/tex]
[tex]3.10 + 0.85m \leq 15[/tex] ---- The inequality
Solving for m: Collect Like Terms
[tex]0.85m \leq 15 - 3.10[/tex]
[tex]0.85m \leq 11.9[/tex]
Divide through by 0.85
[tex]m \leq 11.9/0.85[/tex]
[tex]m \leq 14.0[/tex] ---- The solution
Choose the correct answer choice.
Answer:
The T shirt choice
Step-by-step explanation:
Both values increase at the same rate therefore is proportional.
In 1927, Charles Lindburgh had his first solo flight across the Antlantic Ocean. He flew 3,610 miles in 33.5 hours. If he flew about the same number of miles each hour, how many miles did he fly each hour?
Answer:
107.76
Step-by-step explanation:
We are told in the above question that:
He flew 3,610 miles in 33.5 hours. If he flew about the same number of miles each hour, how many miles did he fly each hour?
We solve the above question by:
33.5 hours = 3610 miles
1 hour = x miles
Cross Multiply
33.5 hours × x miles = 3610 miles × 1 hour
x miles = 3610 miles × 1 hour/33.5 hours
x miles = 107.76119403 miles
Approximately = 107.76 miles per hour
Therefore, he flew 107.76 miles each hour
how do i simplify 4^(n-2)+4^(n-1)+...+4^0
add them all up or Mutiply and Divide all together I think
QUICK!!!!!
Analyze the conditional statement below and complete the instructions that follow.
If m is the midpoint of AB, then M divides AB into two congruent segments.
Identify the inverse of the converse of the conditional statement.
O If M is not the midpoint of AB, then M does not divide AB into two congruent segments.
If M is the midpoint of AB, then M divides AB into two congruent segments.
If M divides AB into two congruent segments, then M is the midpoint of AB.
Olf M does not divide AB into two congruent segments, then M is not the midpoint of AB.
Answer:
D. If M does not divide AB into two congruent segments, then M is not the midpoint of AB.
Step-by-step explanation:
A conditional statement is one that include 'if'. Thus it is also referred to as an 'if' statement.
Given a conditional statement:
If M is the midpoint of AB, then M divides AB into two congruent segments.
The converse of the given statement is done by interchanging the two parts of it. So that we have:
If M divides AB into two congruent segments, then M is the midpoint of AB.
Then, the inverse can be obtained by getting the negative of both parts of the converse. Therefore, the inverse is:
If M does not divide AB into two congruent segments, then M is not the midpoint of AB.
The correct option is D.
Find tan-1 1.4281 to the nearest degree.
a. 10°
b. 55°
C. 5°
d. 35°
Answer:
[tex]\:x=55^{\circ \:\:}[/tex]
Therefore, option 'b' is correct.
Step-by-step explanation:
Let x be the angle
tan x = 1.4281determining the [tex]\tan ^{-1}\left(1.4281\:\right)[/tex]
[tex]\:\tan \:x\:=1.4281\:[/tex]
[tex]x=\tan ^{-1}\left(1.4281\:\right)[/tex]
[tex]\:x=55^{\circ \:\:}[/tex]
Therefore, option 'b' is correct.
A restaurant freezes a cherry and lime juice mixture to create slushes. Cherry juice costs $5 per quart, and lime juice costs $3 per quart. Each day, the restaurant spends a total of $36 on 8 quarts of juice. The restaurant manager organizes the information in the table below.
Answer:
Answer is at the bottom!
Step-by-step explanation:
Cherry juice=5+5+5+5+5+5=30
Lime juice =3+3=6
6 cherry slushes and 2 lime slushes were sold.
Hope this helps!!
Answer:
6 cherry slushes and 2 lime
Step-by-step explanation:
7th grade math
please help, I will give brainliest
-19 = -2/3 x
find the value of x
Answer:
-19=-2/3x
3*-19=-2x
-57=-2x
-57/-2=x
57/2=x
x=28.5
Step-by-step explanation:
Answer:
x = [tex]\frac{57}{2}[/tex]
Step-by-step explanation:
Given
- 19 = - [tex]\frac{2}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )
- 57 = - 2x ( divide both sides by - 2 )
[tex]\frac{-57}{-2}[/tex] = x , that is
x = [tex]\frac{57}{2}[/tex]
Can someone help me cuz i need help
Answer:
f
klllllllllk
Step-by-step explanation:
An isosceles triangle has base angles that each measure 42 degrees.Which equation can be used to find z, the measure of the third angle of this isosceles triangle in degrees
Answer:
z+42+42=180
Step-by-step explanation:
Since it is an isosceles triangle, the two base angles are the same and remember all the angles add to 180. So use this equation:
z+42+42=180
If you need to find z, it is 96.
Check: 96+42+42=180
The figures below are similar. Find the length of the missing side.
90
10
7
Х
36
4
14
126
X=
Answer:
63
Step-by-step explanation:
multiply the side by 9
Solve - 2x - 7 > 5x + 14.
O A. x < -3
B. X > -3
C
C. x < -5
D. I > -5
please help
Answer:
hope this is not to hard to understand
Answer: Thanks for the points
Step-by-step explanation:
What is the image point of (-3,3) after the transformation R180° 0 T-3, -4?
Answer:
Image point → (6, 1)
Step-by-step explanation:
Given point → (-3, 3)
Transformation to be done → [tex]R_{180}0T_{-3,-4}[/tex]
Transformations to be done,
Step - (1). Translation of the given by 3 units left and 4 units down.
Step - (2). Followed by the rotation counterclockwise 180° about the origin.
Rule for step (1),
(x, y) → (x - 3, y - 4)
By this rule,
(-3, 3) → [(-3 - 3), (3 - 4)]
→ (-6, -1)
Rule for step -2,
(x, y) → (-x, -y)
(-6, -1) → (6, 1)
Therefore, following these two steps coordinates of the image point → (6, 1)
1092 is divisible into.?
Answer:
1092 is divisible into 1, 7, or 1092.
Step-by-step explanation:
Step-by-step explanation:
1092 / 1 = 1092
1092 / 2 = 546
1092 / 3 = 364
1092 / 4 = 273
1092 / 6 = 182
1092 / 7 = 156
1092 / 12 = 91
1092 / 13 = 84
1092 / 14 = 78
1092 / 21 = 52
1092 / 26 = 42
1092 / 28 = 39
1092 / 39 = 28
1092 / 42 = 26
1092 / 52 = 21
1092 / 78 = 14
1092 / 84 = 13
1092 / 91 = 12
1092 / 156 = 7
1092 / 182 = 6
1092 / 273 = 4
1092 / 364 = 3
1092 / 546 = 2
1092 / 1092 = 1
What is the Value of the angle AEX
Answer:
52
Step-by-step explanation:
I take it that x is somewhere near the end of the diagonal line, so you want to know the value of 3x + 1???
We know that (3x + 1) + (2x + 4) = 90 degrees. That's because AEF = 90 degrees.
So begin by removing the brackets.
3x + 1 + 2x + 4 = 90 Combine the like terms.
5x + 5 =90 Subtract 5 from both sides.
5x + 5 - 5 = 90 - 5 Combine
5x = 85 Divide by 5
x = 17
3x + 1 = 3*17 + 1 = 51 + 1 = 52
Given the following equations:
Equation 1
5x+2y=7
Equation 2
x+y=5
Find the value of 4x + y
Answer:
2Step-by-step explanation:
GivenEquations
5x+2y=7 x+y=5 To find The value of 4x + ySolutionSubtract the second equation from the first one side-by-side:
5x + 2y - (x+ y) = 7 - 55x - x + 2y - y = 24x + y = 2The answer is 2
What is the binary number for 23
Answer:
10111
Step-by-step explanation:
Answer:
♡ hi again, queen! ♡
- It's 10111.
have a great day!
✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧
Step-by-step explanation:
Find the slope of the line passing through each of the following pairs of points.
(5, 0), (−3, 0)
Answer:
0
Step-by-step explanation:
m= y2-y1/x2-x1
=0-0/-3-5
=0/-8
=0
Answer:
Slope = 0
Step-by-step explanation:
find the mausure of 1
Answer:
88
Step-by-step explanation:
Every triangle has a measure of 180, so if we know two of the angles we can find the last one easily. To find angle 1, we first must find angle 2. 2 must be equal to 42 because it is vertical to the other angle that is equal to 42 degrees. Then to find angle 1 do the operation 180-(50+42). This equals 88, which is the measure of angle 1.
A retail grocer bought a case of 12 packages of coffee for $52.32.
How much did the retailer pay for each package of coffee?
The retailer sold each package for $12.59.
What is the difference between the retailer’s cost and the selling price for each package of coffee?
Answer:
4.36
8.23
Step-by-step explanation:
Answer:
4.36
Step-by-step explanation: