Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 16[/tex]
The sample size is n = 64
The standard error of mean is mathematically evaluated as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x } = \frac{16 }{\sqrt{64} }[/tex]
[tex]\sigma _{\= x } = 2[/tex]
Generally the probability that the sample mean will be within 2 of the population mean is mathematically represented as
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < \frac{ \= x - \mu }{\sigma_{\= x }} < \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]
Generally [tex]\frac{ \= x - \mu }{\sigma_{\= x }} = Z (The \ standardized \ value \ of \ \= x )[/tex]
So
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( \mu - 2 ) - \mu }{\sigma_{\= x }} < Z< \frac{( \mu +2 ) - \mu }{\sigma_{\= x }} )[/tex]
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{( -2 }{\sigma_{\= x }} < Z< \frac{ 2 }{\sigma_{\= x }} )[/tex]
substituting values
[tex]P( \mu - 2 < \= x < \mu + 2) = P(\frac{-2 }{2} < Z< \frac{ 2 }{2} )[/tex]
[tex]P( \mu - 2 < \= x < \mu + 2) = P(-1< Z< 1 )[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = P(Z < 1) - P(Z < -1)[/tex]
From the normal distribution table [tex]P(Z < 1 ) = 0.84134[/tex]
[tex]P(Z < - 1) = 0.15866[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = 0.84134 - 0.15866[/tex]
=> [tex]P( \mu - 2 < \= x < \mu + 2) = 0.6826[/tex]
If is an angle bisector of ∠QOR and ∠QOP = 71°, then find the angle measure of ∠QOR. Question 8 options: A) 71° B) 142° C) 35.5° D) 35°
Answer: B. 142°.
Step-by-step explanation:
Given: OP is an angle bisector of ∠QOR and ∠QOP = 71°.
We know that an angle bisector divides an angle into two equal parts.
So, if OP is an angle bisector of ∠QOR and ∠QOP = 71°.
Then, the angle measure of ∠QOR = Twice of ∠QOP
⇒ Angle measure of ∠QOR = 2 (71°)
⇒ Angle measure of ∠QOR = 142°
Hence, correct option is B. 142°.
5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution
Answer:
C. Infinitely many solutions
Step-by-step explanation:
First, simplify the second equation by dividing it by 2
2y = 6x + 2
y = 3x + 1
Now, we can see that both equations are the same, both y = 3x + 1.
Since they are the same line, this means that there are infinitely many solutions.
So, the correct answer is C.
2/4= 4-2 true or false
Answer:
= Answer is falseStep-by-step explanation:
False is the ansThe admission to a local carnival ride is $8.25 per person and $1.50 for each ride.
Answer:
You would multiply 8.25 by 3 which equals 24.75. Then multiply 1.50 by 8 which is 12.00.
Step-by-step explanation:
Answer:
Step-by-step explanation:
5. Determine the number of square units in the area of the trapezoid whose bases are 3-X units and 10+X units and whose height is 6 units.
Answer:
39 units
Step-by-step explanation:
The formula for area of trapezoid is 1/2h(a+b) where a and b are the base/parallel sides.
We have,
a=3-x
b=10+x
h=6
Now,
Area=1/2h(a+b)
=1/2*6(3-x+10+x)=3(13)=39 units
In a regression analysis involving 30 observations, the following estimated regression equation was obtained. If required enter negative values as negative numbers.
In a regression analysis involving 30 observations
Interpret b1, b2, b3, and b4 in this estimated regression equation (to 1 decimal). Assume that for each coefficient statement, the remaining three variables are held constant. Enter negative values as negative numbers.
b1 = estimated change in y per 1 unit change in x1
b2 = estimated change in y per 1 unit change in x2
b3 = estimated change in y per 1 unit change in x3
b4 = estimated change in y per 1 unit change in x4
Predict y when x1 = 10, x2 = 5, x3 = 1, and x4 = 2 (to 1 decimal).
In this, question the equation is missing that's why in the solution we define the equation and its complete solution:
Let the given equation:
[tex]\bold{\hat{h}=17.6+3.8x_1-2.3x_2+7.6x_3+2.7x_4}[/tex]
[tex]\bold{b1 = 3.8}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_1}[/tex]
[tex]\bold{b2 = -2.3 }[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_2}[/tex]
[tex]\bold{b3 = 7.6 }[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_3}[/tex]
[tex]\bold{b4 = 2.7}[/tex] units expect changes in the y for each 1 unit change in [tex]\bold{x_4}[/tex]
Calculating the estimated value of the y when:
[tex]\to \bold{x_1 = 10}\\\\ \to \bold{x_2 = 5}\\\\\to \bold{x_3 = 1}\\\\\to \bold{x_4 = 2}\\\\[/tex]
Put the value into the above-given equation:
[tex]\to \bold{17.6 + 3.8(10) - 2.3(5) + 7.6(1) + 2.7(2)} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{17.6 + 38 - 11.5 + 7.6 + 5.4} \\\\\to \bold{68.6-11.5}\\\\\to \bold{57.1}[/tex]
So, the final answer is "57.1".
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find the number of permutations that can be formed from all letters in the word connecticut
3. Solve for x2=81 C. 10
Answer:
9
Step-by-step explanation:
9 x 9 = 81
Answer:
x = ±9
Step-by-step explanation:
x^2 = 81
Take the square root of each side
sqrt(x^2 ) = ±sqrt(81)
x = ±9
1/5 divided (-5/7) Can someone please help with this equation and show work
Answer:
-7/25
Step-by-step explanation:
1/5 ÷ -5/7
Copy dot flip
1/5 * -7/5
-7/25
If x - A = B, what is X?
9514 1404 393
Answer:
(a)
Step-by-step explanation:
Add A to both sides of the equation:
X -A +A = B +A
X = B + A
The sum of the two matrices is the matrix that is the sum of corresponding terms.
x11 = B11 +A11 = -9+2 = 7
x12= B12 +A12 = 5-7 = -2
These calculations are sufficient to match the answer with choice (a).
Joy is preparing 20 liters of a 25% saline solution. She has only a 40% solution and a 10% solution in her lab. How many liters of the 40% solution and how many liters of the 10% solution should she mix to make the 25% solution?
Answer:
10 Liters of 40% solution
Step-by-step explanation:
Answer:
10 liters of the 40% solution, and 10 liters of the 10% solution
Step-by-step explanation:
Let us say that x = the liters of the 40% solution, and y = liters of the 10% solution in her lab. We know that Joy is preparing a solution containing a total 20 liters, so x + y = 20. We can respectively create the following system of equations,
x + y = 20,
0.40x + 0.10y = 0.25 ( 20 )
And now we have to solve this system of equations for x and y, the liters of the 40% solution and the liters of the 10% solution,
[tex]\begin{bmatrix}x+y=20\\ 0.4x+0.1y=0.25\left(20\right)\end{bmatrix}[/tex] ( Substitute x as 20 - y )
[tex]0.4\left(20-y\right)+0.1y=0.25\cdot \:20\end{bmatrix}[/tex] ( Isolate y )
[tex]8-0.3y=5[/tex] ⇒ [tex]80-3y=50[/tex] ⇒ [tex]-3y=-30[/tex] ⇒ y = 10
[tex]x=20-10 = 10[/tex] ⇒ x = 10
Therefore, there are 10 liters of both the 40% and 10% solution.
Which of the following graphs is the same as y = log12X?
Answer:
Step-by-step explanation:
Matrices and determinants What is 4c?
Answer:
Answer is D.
Step-by-step explanation:
do 4 times every value in the ( )
Answer:
[tex]\boxed{\sf D}[/tex]
Step-by-step explanation:
A boat can travel 21 miles on 7 gallons of gasoline. How far can it travel on 17 gallons?
Answer:
51 miles
Step-by-step explanation:
Boat with 7 gallons of gas = 21 miles
Boat with 1 gallon of gas = 21/7 = 3 miles
Boat with 17 gallons of gas = 17 x 3 = 51 miles
Answer:
51 miles
Step-by-step explanation:
1 gallon = 3 miles
17 gallons = ? miles
17 * 3 = 51 miles
1.
a. AABC has a right angle at B, BC = 4, and has an area of 10 square units. What is the
length of AB?
Answer:
5 unitsStep-by-step explanation:
A right angled triangle is a triangle that has one of this angles to be 90°. According to the ΔABC, the angle at B is 90°.
Area of a triangle = 1/2 * base * height
According to the diagram shown, the base is BC and the height is AB which is the required side.
Area of the triangle = 1/2 * BC * AB
Given area of the triangle = 10 square units
BC = 4 units
AB is the required length.
Substituting this values into the formula above;
10 = 1/2 * 4 * AB
10 = 2AB
Dividing both sides by 2
2AB/2 = 10/2
AB = 5 units
Hence the length of AB is 5 units.
In a certain year Congress debated a bill. A poll of 1000 Americans indicated 401 opposed 293 favored 306 not sure. What is the probability that random person was in favor
Please answer this correctly without making mistakes
Answer:
The answer is 68 6/11
Step-by-step explanation:
If you enter the number into a calculator it shows you the exact decimal, therefore you can identify the answer.
Answer:
It is 68 6/11
Step-by-step explanation:
First I made all of the improper fractions into whole numbers and fractions and just saw which one was in the middle .
Nine million, twenty-seven thousand, four hundred and forty-eight
9,027,448
9027448
9027448
9027448
If you move from zero to 15 on the number line, you are representing all of the following exce
the opposite of -15
the opposite of 15
the absolute value of 15
the distance between zero and 15
Answer: the opposite of 15
Step-by-step explanation:
Every number 'a' on number line is exactly opposite of '-a'.
So, 15 is the opposite of '-15'
Also absolute value for any number gives its positive value, soabsolute value of 15 = 15
Moving 0 to 15 gives the distance between zero and 15.
So all statements are true except "the opposite of 15".
Hence, the required statement is "the opposite of 15".
Suppose that $2000 is invested at a rate of 2.6% , compounded semiannually. Assuming that no withdrawals are made, find the total amount after 10 years.
Answer:
$2,589.52
Step-by-step explanation:
[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]
We start with the compound interest formula above, where
A = future value
P = principal amount invested
r = annual rate of interest written as a decimal
n = number of times interest is compound per year
t = number of years
For this problem, we have
P = 2000
r = 0.026
n = 2
t = 10,
and we find A.
[tex] A = $2000(1 + \dfrac{0.026}{2})^{2 \times 10} [/tex]
[tex] A = $2589.52 [/tex]
Compound interest formula:
Total = principal x ( 1 + interest rate/compound) ^ (compounds x years)
Total = 2000 x 1+ 0.026/2^20
Total = $2,589.52
Transform the polar equation to a Cartesian (rectangular) equation: r= 4sinθ
options include:
x^2+y^2 = 4y
x^2+y^2 = -4
x^2+y^2 = 4
x^2+y^2 = -4y
Answer:
x^2 +y^2 = 4y
Step-by-step explanation:
Using the usual translation relations, we have ...
r^2 = x^2+y^2
x = r·cos(θ)
y = r·sin(θ)
Substituting for sin(θ) the equation becomes ...
r = 4sin(θ)
r = 4(y/r)
r^2 = 4y
Then, substituting for r^2 we get ...
x^2 +y^2 = 4y . . . . . matches the first choice
Ms. Lowder has 2 children, one in first grade and one in fifth grade. Both children need paper for school. Paper costs $2.29 per pack. If the first grader needs 2 packs of paper and the fifth grader needs 6 packs of paper, how much money will Ms. Lowder spend on paper?
the answer is she spend $18.32
What expression is equivalent to 18 1/5 ( -22 2/5 ) - (-40 1/5 )
(18 1/5 * (-22 2/5)) - (-40 1/5) = -367.48
Of 80 t shirts 10% are white, 30% are blue and the rest are red how many are red ?
10 % + 30 % = 40 %
100% - 40% = 60%
60% are red
Multiply total shirts by 60%
80 x 0.60 = 48
48 shirts are red
Answer:
48 shirts are red
Step-by-step explanation:
The percents have to add to 100
100 -10 -30 = 60
60% are red
80*60%
80*.6
48
2. Mandla spent one quarter of his pocket money on sweets. a. What fraction does he have left? b. If he had R40 pocket money, how much did he spend?
Answer:
a. 3/4 of pocket money left
b. R10
Step-by-step explanation:
a. 4/4 - 1/4 = 3/4
b. 40/4 = 10 = 1/4 of pocket money
(a). The fraction of pocket money left is 3/4
(b). If he had R40 pocket money, he spend R10.
What is the Ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
The operator that perform arithmetic operation are called arithmetic operators .
Operators which let do basic mathematical calculation
+ Addition operation : Adds values on either side of the operator.
For example 4 + 2 = 6
- Subtraction operation : Subtracts right hand operand from left hand operand.
for example 4 -2 = 2
* Multiplication operation : Multiplies values on either side of the operator
For example 4*2 = 8
Mandla spent one-quarter of his pocket money on sweets
Let x be the total amount of pocket money Mandla had originally
Solution of (a).
⇒ x - (1/4)x
⇒ (3/4)x
The fraction of pocket money left = 3/4
Solution of (b).
1/4 of pocket money
⇒ (1/4)x
⇒ (1/4)40
⇒ 10
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The time required for workers to produce each unit of a product decreases as the workers become more familiar with the production procedure. It is determined that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit. Find the time required for a new worker to produce units 10 through 19.
Answer: 2.79 hours.
Step-by-step explanation:
Given that the function for the learning process is T(x) = 2 + 0.3 1 x , where T(x) is the time, in hours, required to produce the xth unit
To calculate the time for the new worker to produce 10 units, substitute 10 for x in the equation above.
T(x) = 2 + 0.31 (10)
T(x) = 2 + 3.1
T(x) = 5.1 hours
To calculate the time for the new worker to produce 19 units, substitute 19 for x in the equation above.
T(x) = 2 + 0.31(19)
T(x) = 2 + 5.89
T(x) = 7.89 hours
The time required for a new worker to produce units 10 through 19 will be
7.89 - 5.1 = 2.79 hours
if x and y are linear pair of angel then x +y=
Answer: x + y = 180²
Step-by-step explanation:
A linear pair is a pair of adjacent, supplementary angles.
Adjacent means next to each other.
Supplementary means that the measures of the two angles add up to equal 180 degrees.
Therefore, by definition, if x and y are linear pairs of angles, then x + y = 180.
Solve for x if 2(1+3x)=14
Answer:
x=2
Step-by-step explanation:
2(1+3x)=14
Divide each side by 2
2/2(1+3x)=14/2
1+3x = 7
Subtract 1 from each side
3x =7-1
3x = 6
Divide by 3
3x/3 = 6/3
x =2
In the figure alongside, show that angle(a+b+c+d) = 4 right angles
Answer:
Proved
Step-by-step explanation:
a=180-x
c=a= 180-x
d=180-a = 180-(180-x) =x
b=d=x
adding every angle;
a+b+c+d= 180-x + x + 180-x + x
a+b+c+d = 180+180 = 360
a+b+c+d = 4 *90
The sum of the interior of the quadilateral is equal to 4 right angles.
The point where two lines meet is known as an angle
The given figure is a quadrilateral.
For the quadrilateral
The sum of opposite angles is 180degreesThe sum of all the interior angles is 360degreesAccording to the theorem;
a + c = 180 ...... 1
b + d = 180 ...... 2
Add both equations
a + b + c + d = 180 + 180
a + b + c + d = 360
Note that 1 right angle = 90degrees
4 right angles = 4(90) = 360 degrees
Therefore a + b + c + d = 4 right angles (Proved)
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{4.OA.A.3} There are 1,492 chairs in the auditorium. Ms. Jones wants to put them into 10 rows. If she splits the chairs evenly into 10 rows, how many chairs will Ms. Jones have left over?
Answer:
2 chairs will be left over.
Step-by-step explanation:
Given that
There are a total of 1492 chairs.
which are to divided in 10 rows evenly.
To find:
Number of chairs left ?
Solution:
Let the number of chairs in each row = [tex]x[/tex]
There are 10 rows so number of chairs in rows = 10[tex]x[/tex]
Let the number of chairs left = [tex]y[/tex]
Total number of chairs =10[tex]x[/tex] + [tex]y[/tex] = 1492
The above equation is like:
Divisor [tex]\times[/tex] Quotient + Remainder = Dividend
So, we have to find the remainder in this question where we are given Divisor and Dividend.
10 [tex]\times[/tex] 149 + 2 = 1492
So, dividing 1492 with 10, we get remainder as 2.
Hence, 2 chairs will be left.