Answer:
50
Step-by-step explanation:
Direct labour rate variance is $3,000
Direct labour efficiency variance is $5,000
Actual direct labour costs is $100,000
Therefore the standard direct labour production during the month of January can be calculated as follows
= 100,000/5,000-3,000
= 100,000/2,000
= 50
Luiza wants to go on a popular talent TV show. In order to be accepted, her audition must get at least 60%
positive votes from the people in the crowd. She was afraid she will not get enough votes, so she made a
video of her act and showed it to 60 random people from the crowd before the show. 50% of the people
said they would vote for her.
Let's test the hypothesis that the actual percentage of positive votes among the crowd is 60% versus the
alternative that the actual percentage is lower than that.
The table below sums up the results of 1000 simulations, each simulating a sample of 60 votes, assuming
there are 60% positive votes.
According to the simulations, what is the probability of getting a sample with 50% positive votes or less?
Let's agree that if the observed outcome has a probability less than 1% under the tested hypothesis, we
will reject the hypothesis.
What should we conclude regarding the hypothesis?
Choose 1 answer:
We cannot reject the hypothesis.
We should reject the hypothesis.
We cannot reject the null hypothesis as the p value is less than 0.01.
How to illustrate the hypothesis?From the information given, Luiza wants to go on a popular talent TV show and in order to be accepted, her audition must get at least 60% positive votes from the people in the crowd.
The observed outcome also has a probability less than 1% under the tested hypothesis. Based on the information, the test statistic will be - 1.58.
After this, this will be checked under the standard normal distribution table where the p value will be 0.0571.
Based on this information, we cannot reject the null hypothesis as the p value is less than 0.01.
In conclusion, the correct option is that we cannot reject the hypothesis.
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Determine whether the following sequence is geometric. If so, find the common ratio.
1,5,25,125,….
Answer:
Yes,
Common ratio = 5.
Step-by-step explanation:
If its geometric it will have a common ratio.
5/1 = 5
25/5 = 5
125/25 = 5
So its geometric with commo ratio 5.
The line l cuts the y-axis at (0, 5). l also passes through the point (2, 1). find the equation of the line which is parallel to l and which passes through the point (3, 0).
Answer: [tex]y=-2x+6[/tex]
Step-by-step explanation:
The slope of line l is
[tex]\frac{5-1}{0-2}=-2[/tex]
Since parallel lines have the same slope, the slope of the line we need to find is -2.
Substituting into point-slope form,
[tex]y=-2(x-3)\\\\y=-2x+6[/tex]
You have a standard deck of 52 playing cards. you draw 2 cards without replacement. which action, performed before the draws, increases the probability of drawing 2 face cards in a row?
a. removing all of the black cards
b. removing all non-face cards
c. removing all kings
d. removing all of the red cards
Answer:
Bet $100 and remove all non-face cards.
Step-by-step explanation:
Each option may be answered on the basis of the ratio of face cards to non-face cards, which we'll say is R.
a. removing all of the black cards No. The vale of R does not change. R is the same for both black and red cards, so removing one color does not change R.
b. removing all non-face cards Yes. The only cards left are face cards. The odds of drawing 2 face cards in a row from this modified deck is 100%
c. removing all kings No. Face cards are being removed and will thus lower the probability of picking one.
d. removing all of the red cards No. Same reasoning as in (a.).
please help asap..... Write the equation of the circle in general form. Show all your work.
will mark brainiest if correct.
Answer:
(x + 3)^2 + (y - 2)^2 = 25 .
Step-by-step explanation:
The center is at (-3, 2) and the radius is 5.
General form is
(x - h)^2 + (y - k)^2 = r^2
So here we have:
(x - (-3)^2 + (y - 2)^2 = 5^2
(x + 3)^2 + (y - 2)^2 = 25
Consider the given set of numbers 70, 81, 91, 83, 88, and 55. A new number equal to a 12% increase in the median of this set is added to the list. What percentage larger is the mean of the new list in comparison with the original
New mean is 2.53% larger than the original mean.
What is mean?
Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.
We can find the percentage larger is the mean of the new list in comparison with the original as shown below:
Given, set of number 55, 70, 81, 83, 88, 91
Median= (81+83)/2
= 164/2
= 82
Mean = (55+70+81+83+88+91)/6
= 468/6
= 78
New value which is added = 82*1.12
= 91.84
New Mean = (55+70+81+83+88+91+91.84)/7
= 559.84/7
= 79.97
Increase in mean = 79.97-78
=1.97
increase percentage (1.97/78) *100
= 2.53%
Hence, new mean is 2.53% larger than the original mean.
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A farmer claims that the average mass of an apple grown in his orchard is 100g. To test this claim, he measures the mass of 150 apples that are grown in his orchard and determines the average mass per apple to be 98g. The results are calculated to be statistically significant at the 0.01 level. What is the correct interpretation of this calculation
The data is significant at a significance level of 0.01 indicating that the average mass of apples in a farmer's orchard differs from 100g to a level of 0.01. Option C is correct.
Given as the farmer states that the average mass of an apple grown in his orchard is 100g, he measures the mass of 150 apples grown in his orchard and finds that the average mass per apple is 98g and the results are calculated as statistically significant at the 0.01 level.
The null hypothesis is:
H₀ = 100
Because of the farmer's claim.
The alternative hypothesis is:
H₁ ≠ 100
The alternative hypothesis tests the farmer's claim at a level of significance. Results are calculated as statistically significant at the 0.01 level.
This means that at the 0.01 level, the null hypothesis is rejected, i.e. H the average mass of the farmer's orchard differs from 100. Since it is significant at the 0.01 level, it will be significant at the 0.05, 0.1 and increasing levels.
Thus, at the significance level of 0.01, the average mass of apples grown in the farmer's orchard differs by 100 g. The correct answer is therefore given by option C.
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Ahmad has containers of two different sizes. The total capacity of 16 containers of one size is x gallons, and the total capacity of 8 containers of the other size is also x gallons, and . In terms of x, what is the capacity, in gallons, of each of the larger containers?
Answer:
x/8 gallons.
Step-by-step explanation:
The 8 containers have the larger capacity as the 2 totals are x and the other containers are 16 in total.
Capacity of each of the large containers = x/8 gallons.
Please answer quick and now
Answer:
[tex]140in {}^{3} [/tex]
Step-by-step explanation:
Substituting values of B and h into the Formular.
[tex]v = \frac{bh}{3} \\ v = \frac{15 \times 28}{3} = 140in {}^{3} [/tex]
Determine the measure of the indicated angle in the following triangle:
Answer:
Θ ≈ 58°
Step-by-step explanation:
using the Cosine Rule in the triangle
cosΘ = [tex]\frac{80^2+60^2-70^2}{2(80)(60)}[/tex] = [tex]\frac{64000+3600-4900}{9600}[/tex] = [tex]\frac{5100}{9600}[/tex] = [tex]\frac{51}{96}[/tex] , then
Θ = [tex]cos^{-1}[/tex] ( [tex]\frac{51}{96}[/tex] ) ≈ 58° ( to the nearest degree )
A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 29 ft long and 20 ft wide.
Find the area of the garden. Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
15.7 square feet
Step-by-step explanation:
To find the area of the garden we find the area of the rectangle and the area of the semicircle.
The area of the rectangle:
A=bh
A=(29)(20)
A=580ft^2
As shown in the picture, the width of the rectangle is 20 ft wide, which means that the diameter of the semicircle is also 20ft wide. The diameter is two times the radius, which means the radius of the semicircle is 10ft.
The area of a circle is represented by the equation: [tex]A=\pi r^{2}[/tex]
A semicircle is half of a circle, therefore the equation to find the area of a semicircle is: [tex]A=\frac{1}{2}\pi r^{2}[/tex]
Plugging our radius of 10ft in we get:
[tex]A=\frac{1}{2}\pi (10)\\ A=5\pi[/tex]
We use 3.14 for our value of [tex]\pi[/tex] to get:
[tex]A=5(3.14)\\A=15.7ft^{2}[/tex]
Therefore, the area of the rose garden is 15.7 square feet.
Can someone help me out? Pls it’s urgent!!! ASAP! (Geometry)
“Complete the proof”
1) [tex]\overline{WX} \cong \overline{UY}[/tex], [tex]\angle YXZ \cong \angle XYZ[/tex] (given)
2) [tex]\overline{XY} \perp \overline{XY}[/tex] (reflexive property)
3) [tex]\triangle WXY \cong \triangle UYX[/tex] (SAS)
4) [tex]\overline{WY} \perp\overline{ UX}[/tex] (CPCTC)
The manager of a food store noted that for every 20 persons who visit the store, they sell 6 burgers at $2.35 each, 8 aerated drinks at $1.60 each, and 4 pack of fries at $ 2.00 each. To the nearest cent, what is the average (arithmetic mean) amount of sales per person who comes in?
jeri is three years younger than laura, whose age is x. How old is jeri?
Answer:
x-3
Step-by-step explanation:
Laura's age goes first. You don't know what it is, so you have to leave it as x. You know Jeri is 3 years younger, so you subtract from x.
Phone chargers in a store are priced $19, $18, $15, $17, $19, $12, $19, and $15.
What display would best show the measures of variation?
(ignore my answer. i didn't mean to click)
The display that would best show the measures of variation of the given prices is; B: Box and Whisker Plot
What is the importance of Box and Whisker Plot?We are given the prices of Phone chargers in a store as;
$19, $18, $15, $17, $19, $12, $19, and $15.
Now, since we want to determine the display that would best show the measures of variation, the best display would be a box and whisker plot. This is because Box and Whisker plots are a great chart to use when showing the distribution of data points across a selected measure. These box and whisker plots display ranges within variables measured.
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What is the PERT weighted average based on an optimistic estimate of six days, a most likely estimate of eight days, and a pessimistic time of sixteen days
the PERT weighted average is 9 days
What is PERT weighted average?
PERT can be defined as an estimating technique that uses a weighted average of three numbers to get a final estimate.
The formula for finding the PERT weighted average is given as;
PERT weighted average = (Optimistic + (4 X Most Likely) + Pessimistic)/6
We have;
Optimistic = 6 daysMost likely = 8 daysPessimistic = 16 daysSubstitute the values into the formula
PERT weighted average = [tex]\frac{6 + 4(8) + 16 }{6}[/tex]
PERT weighted average = [tex]\frac{54}{6}[/tex]
PERT weighted average = 9 days
Thus, the PERT weighted average is 9 days
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CAN ANYONE HELP ME WITH QUESTION 6
Suppose there is a triangle with sides a, b, and c and angles A, B, and C. Using the known given information below and the law of cosines, what is the measure of angle C? Round your answer to the nearest whole number, if necessary.
A=29
C=24
B=101
The measure of angle C is obtained as 35 degrees
What is the angle C?Give that;
b^2 = a^2 + c^2 - 2ac Cos B
a = 29
c = 24
B = 101 degrees
b^2 = (29)^2 + (24)^2 - [2 * 29 * 24 cos 101]
b^2 = 841 + 576 + 266
b = 41 cm
Now;
b/sinB = c/sinC
bsinC = csinB
sinC = csinB/b
sinC = 24 * sin 101/41
C = sin-1(24 * sin 101/41)
C = 35 degrees
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Please help me ASAP!! I really appreciate it
Answer:
a = -1
Step-by-step explanation:
1. Subtract [tex]\frac{2}{3}[/tex] from both sides.
[tex]6a=-\frac{16}{3} - \frac{2}{3}[/tex]
2. Solve the side after the equal sign.
[tex]6a=-6[/tex]
3. Divide 6 from both sides.
[tex]a=-1[/tex]
4. Hope this helped!
[tex]:)[/tex]
Graph the following exponential functions and determine the y-intercept, domain, range, and
asymptote of each function.
f(x)=5(2)^x
The graph of the exponential function f(x) = 5(2)ˣ is as shown in the attached file.
How to draw the graph of an exponential Function?We want to draw the graph of the exponential function;
f(x) = 5(2)ˣ
At input of x = 0, we have;
f(x) = 5(2)⁰ = 5
At input of x = 1, we have;
f(x) = 5(2)¹ = 10
At x = -1, we have;
f(x) = 5(2)⁻¹ = 2.5
At x = -2, we have;
f(x) = 5(2)⁻² = 1.25
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Directions: The soccer team at your school wants to spray paint a design on the middle of the
playing field. The design will include this soccer ball. You have been asked to enlarge the drawing of
this ball to use for the painting on the field. Using the Text Editor and information you learned in this
Unit, write a brief essay in which you explain how to accurately enlarge or reduce the size of objects
such as the soccer ball. Include the steps that should be taken in order to complete a project like this,
and use concepts discussed in this Unit to support your plan. For example, you may want to include
scale factor, proportions, dilations, and similarity.
The steps that can be used to increase the ball is:
Scale factor = [tex]\frac{Scale diagram}{Original}[/tex]
What is Scale Factor?This refers to the measure for similar figures that is used to show the scale through which a figure is bigger or smaller than another.
Hence, we can see that from the given image, one can increase the size of the ball by making use of the scale factor which measures the scale diagram and then divides it from the original and this would retain the dimension but would make it larger.
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The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Select two options.
Based on the given inequality; x < 9 or x ≥ 14, the possible values of x are $8 and $14
Inequalityx < 9 or x ≥ 14
This means x less than 9 or greater or equal to 14From the options
All values less than 9 are
$8
All values greater than or equal to 14 are
$14
Therefore, based on the options given, the possible values of x are $8 and $14
Complete question:
The inequality x < 9 or x ≥ 14 can be used to represent the hourly wage, x, of each employee at a store. Which are possible values for x? Check all that apply. $8 $9 $11 $13 $14 $15
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TIME REMAINING
01:38:18
The function rule T–4, 6(x, y) could be used to describe which translation?
a parallelogram on a coordinate plane that is translated 4 units down and 6 units to the right
a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up
a rhombus on a coordinate plane that is translated 4 units down and 6 units to the left
a rectangle on a coordinate plane that is translated 4 units to the right and 6 units up
The translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up
How to determine the translation?The translation rule is given as:
T–4, 6(x, y)
This can be rewritten as
T(x- 4, y + 6)
The above represents a translation 4 units left and 6 units up
Hence, the translation that represents T–4, 6(x, y) is (b) a trapezoid on a coordinate plane that is translated 4 units to the left and 6 units up
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please im in a rush i need help
Answer:
28.5 ft²
Step-by-step explanation:
shaded area = area of triangle minus area of rectangle
shaded area = (1/2)bh - LW
base of triangle = 5 ft + 4 ft = 9 ft
height of triangle = 3 ft + 6 ft = 9 ft
shaded area = (1/2)(9 ft)(9 ft) - (4 ft)(3 ft)
shaded area = 40.5 ft² - 12 ft²
shaded area = 28.5 ft²
what is the measure of the largest side of an isosceles acute, if one side is 36
The measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.
What is an isosceles triangle?A triangle with two sides and angles of equal length and degrees is an isosceles triangle.
Acute Triangle:-
A triangle whose all angels are greater than and less than 90° i.e., all angels are acute is called an acute triangle.
Therefore, all the three angles are less than 90 degrees and two angles are equal.
If one angle is 36 degrees, the other two angles will be 72 degrees each.
If the two angles are 36 degrees each, the last angle will be 108 degrees. 108 degrees is greater than 90 degrees..
Therefore, the angles will be 36°, 36° and 72°.
Hence, the measure of the largest side of an isosceles acute triangle with one side of 36 degrees is 72 degrees.
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hi please help 10 Points
Percentage for lakeside is 38%
Percentage for Jungle is 26%
Percentage for Desert is 18%
Percentage for Coast is 12%
Percentage for Prairie is 6%
How to determine the percentageTo determine the percentage, divide the given value by the total number and multiply by 100
Total = 24000
Percentage for lakeside = [tex]\frac{9120}{24000}[/tex] × 100
% of lakeside = [tex]0. 38[/tex] × 100 = 38%
Percentage for Jungle = [tex]\frac{6240}{24000}[/tex] × 100
% of Jungle = [tex]0. 26[/tex] × 100 = 26%
Percentage for Desert = [tex]\frac{4320}{24000}[/tex] × 100
% of Desert = [tex]0. 18[/tex] × 100 = 18%
Percentage for Coast = [tex]\frac{2880}{24000}[/tex] × 100
% of coast = [tex]0. 12[/tex] × 100 = 12%
Percentage for Prairie = [tex]\frac{1440}{24000}[/tex] × 100
% of Prairie = [tex]0. 06[/tex] × 100 = 6%
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What is the denominator of the simplified expression? (startfraction 2 n over 6 n + 4 endfraction) (startfraction 3 n + 2 over 3 n minus 2 endfraction) 2 n 3n+2 3n-2
n/3n - 2.
The denominator of the given simplified expression is
The given expression is ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )
To find the denominator of the simplified expression :
First, simplify the given expression as below ;
( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 )
( 2n/2₍₃ₙ ₊ ₂₎ ( 3n + 2/ 3n - 2 ) ( here by taking the common term 2 outside the factor )
= (n/1) ( 1/ 3n - 2 ) ( here by simplifying the factors )
= n/3n - 2.
Therefore, ( 2n/6n + 4 ) ( 3n + 2/ 3n - 2 ) = n/3n - 2
Therefore the result of the given simplified expression is = n/3n - 2.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
See
The point D is
3 units left from origin
x coordinate=-31 units up from origin
y coordinate=1The point is
(-3,1)Direct variation
Multiply k=2
k(-3,1)2(-3,1)(-6,2)Option A
I really need help with this question
Answer:
39
Step-by-step explanation:
I assume the father's age is a 2-digit number. He is not 9 years old or younger, and he is not 100 years old or older.
The sum of the digits of a two-digit number goes up by 1 from one number to the next unless the number ends in 9.
For example, from 17 to 18, the sum of the digits goes from 8 to 9.
If the number ends in 9, for example, 29, the digits add to 11. Then the next number is 30, and now the sum of the digits is 3, which is less than 11.
The father's age now is a number whose sum of digits is not only greater than the sum of the digits next year, but it is 3 times greater.
Let's look at 2-digit number and the next number and the sum of their digits.
19, 20; sums: 10, 2; 10/2 = 5, not 3
29, 30; sums: 11, 3; 11/3 ≠ 3
39, 40; sums: 12, 4; 12/4 = 3
Answer: The father is 39 years old.
Answer: 39 years
Step-by-step explanation:
The father says that adding both of the digits in his age will be 3 times greater than adding both digits one year later. Before we even start answering the problem, this tells us that the father's age has 2 digits in it.
Let's represent the 10's digit with x, and the 1's digit with y. If the father's age was 45, for example, x would be 4 and y would be 5.
Let's first make an equation to represent this situation:
The sum of the digits of the father's age would be represented by x + y, as x and y are the 10's digit and 1's digit respectively.
The father's age next year would be one greater than the current year, which makes y become y + 1. Then, the sum of the digits would be x + y + 1.
Now, we must make the first equation 3 times larger than the second and solve for the sum.
[tex]x + y = 3(x+y+1)\\ x+y=3(x+y)+3\\ 1(x+y)-3(x+y)=3\\ -2(x+y)=3\\ x+y=\frac{3}{-2}=-\frac{3}{2}[/tex]
However, we can neither have a fraction or a negative as a sum of two digits in an age, as digits are always positive integers from 0 to 9.
This flaw came from the assumption that after 1 year, the sum of the digits will be x + y + 1. This isn't always true, as any number with its 1's digit of 9 turns into 0 the next year, and not 10. Instead, the x value increases by 1.
For example, someone the age 69 becomes 70 the next year, x increases by 1 and y becomes 0.
Let's make a new equation to try and see this.
We know that his current age has to have y = 9 for his new age to be y = 0. Therefore, the current sum of digits is x + 9.
The next year, we know that the 10's place will increase by 1 and the 1's place becomes 0. Therefore the sum of digits is x + 1 + 0, or x + 1.
Since the current sum of digits is 3 times greater than the sum next year, let's multiply the second equation by 3 to get equality. We just need to calculate the 10's digit, as the 1's digit is already 9.
[tex]x+9 = 3(x+1)\\ x+9=3x+3\\ 9=2x+3\\ 6=2x\\ x=3[/tex]
Since the 10's digit (or x) is 3 and the 1's digit (or y) is 9, the father's age is 39, and he will turn 40 next year.
The product of the proper positive integer factors of $n$ can be written as $n^{(ax b)/c}$, where $x$ is the number of positive divisors $n$ has, $c$ is a positive integer, and the greatest common factor of the three integers $a$, $b$, and $c$ is $1$. What is $a b c$
The value of a + b + c based on the product formula is 8.
How to calculate the value?From the information given, the product of the proper divisor is illustrated.
Based on the information, the addition of the symbols will be:
= a + b + c
= 3 + 3 + 2
= 8
In conclusion, the correct option is 8.
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