The decision rule is as follows: If Z < -1.96, reject the null hypothesis. If not, fail to reject the null hypothesis.
The decision rule in statistics is a statement that instructs on the null hypothesis’s rejection or acceptance. It is a predetermined criterion used to test a hypothesis. When the calculated test statistic falls outside the critical region, the null hypothesis is rejected. A chocolate chip producer wants to know if the 404.0 gramme setting on their bag-filling machine is correct.
It is suspected that the machine is underfilling the bags. The chocolate chip manufacturer uses a 41 bag sample with an average weight of 396.0 grams to determine whether the machine works correctly at 404.0 gram setting.
With a significance level of 0.05, the decision rule is as follows:
If Z < -1.96, reject the null hypothesis. If not, fail to reject the null hypothesis.
Z can be calculated as follows:
z = (x - μ) / (σ / √n)
where:
x = sample mean = 396.0
μ = population mean = 404.0
σ = standard deviation = 25.0
n = sample size = 41
Substitute the values in the equation:
z = (396.0 - 404.0) / (25.0 / √41)z = -2.67Z < -1.96
Thus, reject the null hypothesis that the machine is filling bags correctly at 404.0 gram setting.
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Please help, will give brainliest for correct answer.
80 points.
Answer:
Step-by-step explanation: DEFINITIONS vvvvv
Transformations
Refers to the movement of objects in the coordinate plane. There are 4 types: Translation, Reflection, Rotation, and Dilation
Reflection
transformation that flips a figure across a line to form its mirror image on the opposite side of the line
Translation
Transformation that slides a figure.
Rotation
A transformation in which a figure is turned around a point
Dilation
A transformation that changes the size of an object, but not the shape.
Congruence
correspondence of parts.
center of dilation
in a dilation, the fixed point about which the figure is enlarged or reduced
similar
Figures that have the same shape but not necessarily the same size
scale factor
The ratio of any two corresponding lengths in two similar geometric figures.
enlargement
a dilation with a scale factor greater than 1. Image will be greater than the pre-image
reduction
a dilation with a scale factor less than 1. Image will be smaller than the pre-image.
remote interior angles
the angles of a triangle that are not adjacent to a given exterior angle
Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Transversal
a line that intersects two or more lines at different points
SAS Theorem (Side-Angle-Side)
If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
Angle-Angle-Side (AAS) Theorem
If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.
Side-side-side (SSS) Theorem
If the sides of two triangles are in proportion, then the triangles are similar.
Angle-Side-Angle (ASA) Theorem
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
Angle-Angle-Angle (AAA)
does NOT prove triangles congruent because the sides could be different lengths.
Parallel lines
lines in the same plane that never intersect
7(g−10h+4) please helpppppppppppp
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{7(g - 10h + 4)}[/tex]
[tex]\large\text{\underline{Distribute} \boxed{\text{7}} \underline{within the parentheses}:}[/tex]
[tex]\mathsf{= 7(g - 10h + 4)}[/tex]
[tex]\mathsf{= 7(g) + 7(-10h) + 7(4)}[/tex]
[tex]\mathsf{= 7g - 70h + 28}[/tex]
[tex]\large\text{We \boxed{\text{cannot}} do anything further because we do NOT have any \underline{like}}\\\large\text{\underline{terms}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{\mathsf{7g - 70h + 28}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
profit = total income - total expenditure Calculate this company's a) total income. b) total expenditure. c) profit. Description Sales - Monday Wages - extra staff Stall hire fee Sales - Tuesday Supplies - stationery Sales - Wednesday Materials Online bulk order Money in £25.00 £20.00 £35.00 £100.00 Money out £110.00 £20.00 £6.00 £10.00
The company's total income, expenditure and profit is given respectively as follows:
a.) £180
b.) £146
C.) £34
How to calculate the profit of the company? seeTo calculate the profit of the company the formula such as given below is used.
Profit = total income - total expenditure
The total income = 25+20+35+100 = £180
The total expenditure = 110+20+6+10 = £146
Profit = 180-146 = £34
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To fill a pool, Barb uses two hoses. The first hose is rated to fill the pool in
10 hours. The second hose is rated to fill it in 5 hours. If Barb adds a third
hose that uses the slower rate, how long will it take to fill the pool.
It will take [1] hours to fill the pool.
Using division operation, the length it will take the three hoses to fill the pool is 8.33 hours.
What is the division operation?The division operation is one of the four basic mathematical operations, including addition, subtraction, and multiplication.
The division operation involves the dividend, the divisor, and the result called the product.
In this situation, it will take Hose A 10 hours to fill the pool and Hose B 5 hours. If the two hoses are in use, it will 7.5hours (10 + 5)/2.
When the third hose is added, it will take 8.33 hours (10 + 5 + 10)/3.
The first hose's filling rate for the pool = 10 hours
The second hose's filling rate for the pool = 5 hours
The third hose's filling rate for the pool = 10 hours (the slower rate)
The total number of hours used by the three hoses = 25 hours (10 + 5 + 10)
The number of hoses used = 3
The length of time it will take the 3 hoses to fill the pool = 8.33 hours (25/3)
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jenelle draws one from a standard deck of 52 cards. determine the probability of drawing either a two or a king? write your answer as a reduced fraction. answer
Answer:
2/13
Step-by-step explanation:
A standard deck of cards has four suits
Therefore there are four twos, one from each suit
There are also 4 kings, one from each suit
P(two) = 4 twos/52 cards = 4/ 52 = 1/13
PKing) = 4 kings/52 cards = 1/13
P(two or king) = P(two) + P(king)
= 1/13 + 1/3
= 2/13
the likelihood that the decision made based on the sample differs from the decision that would have been made if the entire population had been examined is
The likelihood that the decision made based on the sample differs from the decision that would have been made if the entire population had been examined is called sampling risk.
What is Sampling error?Sampling error refers to the disparity between a sample's characteristics and those of the population from which it was drawn. It arises from using a sample rather than the whole population to estimate statistics such as mean, variance, and proportions.
Since a sample only represents a portion of the population, it cannot be expected to have the same characteristics as the whole population. The study of sampling error is an essential part of statistical analysis, as it is a source of uncertainty in making inferences about the population from a sample.
To reduce the sampling error in your survey, you can utilize a larger sample size. It is also beneficial to ensure that the sample is chosen randomly and without bias.
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Brooke played her flute for 3/4 hour each day for 5 days and for 1/2 hour each day for 2 days how many hours did she play it in all
⇒To be able to answer this question to find how many hours Brooke played his flute for 5 days we ought to first convert the 5 days to hours.
⇒There are 24 hours in a day this means that in 5 days we have =24×5
=120 hours.
⇒We have 120 hours in 5 days , it is said that Brooke played her flute [tex]\frac{3}{4}[/tex],
Meaning she played the flute [tex]\frac{3}{4}[/tex] hours of 120 hours which is equal
[tex]\frac{3}{4} *\frac{120}{1}\\=90[/tex]
For 5 days Brooke played her flute 90 hours
⇒The next step is to convert the 2 days to hours which is equivalent to 24×2
=48 hours are in 2 days, it is said Brooke played the flute [tex]\frac{1}{2}[/tex] hours of 2 days. This simply is equivalent to
[tex]\frac{1}{2} *\frac{48}{1} \\=24[/tex]
⇒For 2 days Brooke played the flute 24 hours,
The total number of hours she played it all is =Number of hours she played it in 5 days+ Number of hours she played it in 2 days.
=90+24
=114
⇒In total of these 7 days she played the flute for 114 hours
The price of a new car is $28,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent. )
(a) What monthly payment will she be required to make if the car is financed over a period of 36 months? Over a period of 60 months?
36 months=$
60 months=$
(b) What will the interest charges be if she elects the 36-month plan? The 60-month plan?
36-month plan =$
60-month plan=$
(a) The monthly payment for a 36-month plan is $704.41, and for a 60-month plan is $488.08.
(b) The interest charges for the 36-month plan are $1,459.07, and for the 60-month plan are $3,369.10.
For a)
To calculate the monthly payment for a car loan, we need to use the formula for monthly payments:
M = [tex]P[r(1+r)^n / ((1+r)^n - 1)][/tex]
where M is the monthly payment, P is the principal (the loan amount), r is the monthly interest rate (the annual interest rate divided by 12), and n is the number of months over which the loan is to be repaid.
For the 36-month plan, the principal is 75% of $28,000, or $21,000. The monthly interest rate is 6% / 12, or 0.005. The number of months is 36. Plugging in these values, we get:
M = $[tex]21,000[0.005(1+0.005)^{36} / ((1+0.005)^{36} - 1)][/tex] = $704.41
For the 60-month plan, the principal, monthly interest rate, and a number of months are the same, but we change the number of months to 60:
M = $21,000[0.005[tex](1+0.005)^{60[/tex] / ([tex](1+0.005)^{60[/tex] - 1)] = $488.08
Therefore, the monthly payment for a 36-month plan is $704.41, and for a 60-month program is $488.08.
For b)
To calculate the total interest charges for the loan, we need to subtract the principal (the amount of the loan) from the total amount paid and round to the nearest cent:
For the 36-month plan, the total amount paid is $25,459.07 (36 x $704.41), so the interest charges are:
$25,459.07 - $21,000 = $4,459.07, rounded to $1,459.07
For the 60-month plan, the total amount paid is $29,284.80 (60 x $488.08), so the interest charges are:
$29,284.80 - $21,000 = $8,284.80, rounded to $3,369.10
Therefore, the interest charges for the 36-month plan are $1,459.07, and the 60-month plan are $3,369.10.
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I need the answer to this please hurry
Answer: 240 is your answer for 100% of the e-book
Step-by-step explanation: so if we look at the given facts, 180 is 75% of the e-book, now take this and divide 180 by 3, and you get 25% of the e-book (60 is 25%) so if we factor that back into the 180 75%, we now get 240 at 100% of the e-book read
In a population of tomato plants, mean fruit weight is 60 g and (hp) is 0.12. Predict the mean weight of the progeny if tomato plants whose fruit averaged 80 g were selected from the original population and interbred. Express your answer using three significant figures.
Hence, the predicted mean weight of progeny is 77.6 g (rounded off to three significant figures).
As given that the mean fruit weight of a population of tomato plants is 60 g and the heritability coefficient (h_p) is 0.12, it is required to predict the mean weight of the progeny if tomato plants whose fruit averaged 80 g were selected from the original population and interbred .
The formula for the predicted mean weight of progeny (MP) is given as: MP = mean weight of selected individuals + (h_p) × (mean weight of original population - mean weight of selected individuals)
Using the above formula, we have ,mean weight of selected individuals = 80 g mean weight of original population = 60 gh_p = 0.12Substituting the given values in the above formula, we get :[tex]MP = 80 + 0.12 × (60 - 80)MP = 80 + 0.12 × (-20)MP = 80 - 2.4MP = 77.6 g[/tex]
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HELP I’m struggling and it’s due today :,)) please help.
Will give brainliest :,,))))
Answer:
Step-by-step explanation:
4. a
x cannot be 0 because 2/0 cannot be calculated - we say that it is undefined.
b. x cannot be 1 as that would mke the denominator x - 1 = 0 which is undefined.
5 a. (9x - 5)(9x + 5)
b. (2x + 1)(x - 3).
6.
C. (x + 7)/3
7.
a. (-5, ∝)
b. (-∝, 2]
c.(-3, 7].
8.
y = kx
24 = 16k
k = 1.5
So, y = 1.5x
When x = 50
y = 1.5*50 = 75.
Solve these questions
Answer: 36
Step-by-step explanation: Since the sum of the angles in a triangle is 180 degrees, we can set up an equation:
x + 2x + 2x = 180
Simplifying the equation, we get:
5x = 180
Dividing both sides by 5, we get:
x = 36
Therefore, the value of x is 36 degrees.
Answer:
look at the photo.........................
Solve the equation where θ lies in the interval [0, 2pi). List the answers from least to greatest.
secθ=undefined
The solutions to the equation secθ = undefined from the least to greatest is π/2 and 3π/2.
What is the solution of the equation?The equation secθ = undefined means that the secant of θ is undefined. Recall that the secant function is defined as 1/cosine(θ).
Therefore, secant is undefined when the cosine of θ is equal to zero, since division by zero is undefined.
In the interval [0, 2π), the cosine function equals zero at θ = π/2 and θ = 3π/2.
Therefore, the solutions to the equation secθ = undefined in the interval [0, 2π) are θ = π/2 and θ = 3π/2.
Listing the solutions from least to greatest, we have:
θ = π/2 ≈ 1.571
θ = 3π/2 ≈ 4.712
Note that these values are given in radians.
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What is the percent of decrease from 98. 7 to 0?
0 is a 100% decrease of 98.7. Hope this helped!
Prove that the conditional "All dodecagons must have eleven sides" is false by a counterexample.
All dodecagons must have eleven sides is false and and can be proven through a counter example.
What are dodecagons?
A dodecagons is a polygon which has 12 sides, 12 vertices. In this word do means "Two" and deca means "Ten".
Similar to other polygons, a dodecagon is also a two-dimensional plane figure. A regular dodecagon polygon has 12 equal sides and has 12 equal measures of angles. Irregular dodecagons have unequal sides and angles. Also, a dodecagon can be a convex polygon or concave polygon.
What is a Polygon?
In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges.
So a dodecagon must have twelve sides even though it may be regular or irregular.
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A box contains 4 rows of eggs with 12 eggs in each row .if these eggs are arranged in 6 rows ,how many eggs will be in each row?
Answer:
8
Step-by-step explanation:
The box contains a total of 4 x 12 = 48 eggs.
If we arrange these eggs in 6 rows, we need to divide the total number of eggs by 6:
48 ÷ 6 = 8
Therefore, there will be 8 eggs in each row.
Which of the following is NOT a geometric sequence?
a. 20,−40,80,−160,320,...
b. 5,2.5,1.25,0.625,0.3125,...
c. 1,2,4,8,16,...
d. 100,50,10,5,1,...
Answer:
The sequence 100, 50, 10, 5, 1, ... is NOT a geometric sequence because there is no single constant ratio that multiplies each term to get the next one.
which three of the following theorems verify that triangle WXY=triangle PME?
The theοrem that verifies that WXY=PME is AA, which stands fοr "Angle-Angle" similarity theοrem.
What theοrem verifies that WXY=PME?Accοrding tο the AA similarity theοrem, if twο angles οf οne triangle are cοngruent tο twο angles οf anοther triangle, the triangles are similar.
In this case, we have twο cοrrespοnding angles in triangle WXY and triangle PME that are cοngruent: angle WXY is cοngruent tο angle PME because they are vertical angles, and angle XYW is cοngruent tο angle MEP because they are alternate interiοr angles fοrmed by parallel lines.
Therefοre, by the AA similarity theοrem, we can cοnclude that triangle WXY and triangle PME are similar.
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8x + 4 + 8x - 1 simplify the variable expression
I do not understand this
Pls help!
Answer:
16x + 3
Step-by-step explanation:
Simplify by combining like terms. Add the terms with x, then add the integers.
8x + 8x + 4 - 1 = 16x + 3
Please help and hurry
Answer: 90
Step-by-step explanation: I've done this before
math help needed detailed explanation
The percentage of 8th graders who send more than 50 texts is 56.15%
How to find the percentage?Here we want to find the percentage of eight grades who send more than 50 texts, and to get that we need to use the values in the table.
The formula for that percentage is:
P = 100%*(number that send more than 50 texts)/(total number)
On the table we can see that the total number of 8th gradesr is 130, and the number that send more than 50 messages is 73, then the percentage is:
P = 100%*(73/130)
P = 56.15%
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What are the integer solutions to the inequality below?
−
2
<
x
<
2
Answer:
the integer solutions to the inequality -2 < x < 2 are x = -1, 0, and 1.
Step-by-step explanation:
The inequality is written as:
-2 < x < 2
This inequality can be read as "x is greater than -2 and less than 2". In other words, x is between -2 and 2, but not including -2 or 2.
The integer solutions that satisfy this inequality are -1, 0, and 1.
Therefore, the integer solutions to the inequality -2 < x < 2 are x = -1, 0, and 1.
alexis puts dimes and quarters aside for the parking meter. she has a total of 20 coins and they are worth $3.80. how many quarters does alexis have?
Alexis has 12 quarters and 8 dimes.
Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.
We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:
10d + 25q = 380
To make things easier, let's divide both sides of the equation by 5:
2d + 5q = 76
Now we can use the first equation to solve for d in terms of q:
d + q = 20
d = 20 - q
Substituting this into the second equation gives:
2(20 - q) + 5q = 76
Expanding the parentheses and simplifying, we get:
40 - 2q + 5q = 76
3q = 36
q = 12
Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:
d + q = 20
d + 12 = 20
d = 8
The total value of 12 quarters and 8 dimes is:
12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80
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PLEASE HELP ASAP!!!!!!
Answer:
The greatest common factor (GCF) of -16x^2 - 6x^4 is 2x^2.
To find the GCF, we can factor out the common factors of the two terms. In this case, both terms have a factor of 2 and a factor of x^2.
-16x^2 - 6x^4 = 2x^2(-8 - 3x^2)
So the GCF is 2x^2.
Using _____, a supplier can use radio frequency identification (RFID) tags on each crate, case, or shipping unit to create a digital shipping list.
Using RFID (radio frequency identification) technology, a supplier can use RFID tags on each crate, case, or shipping unit to create a digital shipping list.
Radio frequency identification (RFID) technology is a wireless communication technology that enables the automatic identification and tracking of objects. RFID tags contain a microchip and an antenna, and are typically attached to or embedded within objects such as crates, cases, or shipping units.
These tags can store information such as a unique identification number or product details, which can be read wirelessly by RFID readers or scanners.
When used in shipping and logistics, suppliers can attach RFID tags to each crate, case, or shipping unit to create a digital shipping list. As the products move through the supply chain, the RFID tags can be read at various checkpoints, providing real-time information on the location and status of the products.
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What is i 48 equal to? Show steps how you get your answer please.
Answer: Bro Didnt give any context dont report if wrong
Step-by-step explanation:
i is the imaginary unit, which is defined as the square root of -1.
To find the value of i^48, we can use the fact that i^2 = -1, and simplify the expression as follows:
i^48 = (i^2)^24
Since i^2 = -1, we can substitute -1 in the above expression:
(i^2)^24 = (-1)^24
Any non-zero number raised to an even power is positive, so (-1)^24 = 1. Therefore:
i^48 = 1
Hence, i^48 is equal to 1.
Which equations can be used to solve for y, the length of the room? Select three options.
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
Please help!!!
Question below!!
1. Dilation is the process of enlarging or shrinking a figure or shape by a scale factor.
2. Reflection is the process of flipping a figure or shape over an axis. In this example, A'B'C' is reflected over the x-axis.
3. A pair of triangles that are congruent are triangles with the same size and shape.
4. A pair of triangles that are similar are triangles with the same shape but different sizes.
What is dilation?Dilation is a mathematical operation used to expand or contract a shape. It involves multiplying every point in the shape by a given scale factor. The scale factor determines how much the shape is changed. The result is a line segment twice the length of the original.
1. In this example, triangle ABC is dilated by a factor of 2 about the point (-1,4). This means that all points on the triangle ABC will be multiplied by the scale factor 2. So the coordinates of point A will become (N-1,6) x 2 = (-2,12), point B will become (-4,5) x 2 = (-8,10) and point C will become (-4,0) x 2 = (-8,0). The new triangle created by the dilation is A'B'C'.
2. This means that the x-coordinates of the points remain the same, but the y-coordinates are multiplied by -1. So the coordinates of point A' will become (-2,12) x -1 = (-2,-12), point B' will become (-8,10) x -1 = (-8,-10) and point C' will become (-8,0) x -1 = (-8,0). The new triangle created by the reflection is ABC'.
3. A pair of triangles that are congruent are triangles with the same size and shape. In other words, the sides and angles of the two triangles are all equal.
4. A pair of triangles that are similar are triangles with the same shape but different sizes. In other words, the angles of the two triangles are equal, but the sides are not necessarily the same length.
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a coffee distributor needs to mix a(n) kenya coffee blend that normally sells for $8.20 per pound with a breakfast coffee blend that normally sells for $14.00 per pound to create 10 pounds of a coffee that can sell for $9.36 per pound. how many pounds of each kind of coffee should they mix?
The coffee distributor should mix 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend to make 10 pounds of a coffee blend that can sell for $9.36 per pound.
We can use the idea of weighted averages to overcome this issue. Assume that 10 pounds of the desired blend require x pounds of Kenya coffee blend and y pounds of morning coffee blend.
The price of the Kenya coffee mix per pound is $8.20, while the price of the morning coffee blend per pound is $14.00. The required combination costs $9.36 per pound. On the basis of the weighted average, we can construct the following equation:
8.20x + 14.00y = 9.36(10) (10)
When we simplify this equation, we obtain:
8.20x + 14.00y = 93.60
Given that we are producing 10 pounds of the ideal blend, we also know that x + y = 10. To get the values of x and y, we can use substitution or elimination to solve this system of equations.
Use substitute now. We can find x from the second equation by solving in terms of y:
x = 10 - y
Substitute this into first equation, we get:
8.20(10 - y) + 14.00y = 93.60
82 - 8.20y + 14.00y = 93.60
5.80y = 11.60
y = 2
We obtain x = 8 by substituting y = 2 into x = 10 - y. Hence, to manufacture 10 pounds of a coffee mix that can be sold for $9.36 per pound, we'll need 8 pounds of Kenya coffee blend and 2 pounds of breakfast coffee blend.
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How do I solve this?
I would suggest finding k first.
If [tex]k^2-3k+5=0\\[/tex],
[tex]k=\frac{-(-3)\pm\sqrt{(-3)^2-4(1)(5)}}{2(1)}[/tex] by the quadratic formula.
[tex]k=\emptyset[/tex] by the discriminant being negative.
So the expression in terms of k that you need to find cannot be determined.