The capacity of Leo's container is (WH x L) / 2, where W, H, and L represent the width, height, and length of the container, respectively.
To find the capacity of Leo's container, we need to calculate its volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height. We can express this formula mathematically as:
Volume = Length x Width x Height
Since we do not have the exact measurements of the container, we cannot determine the exact volume.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2 x (Length x Width + Width x Height + Length x Height)
Therefore, we can set the equation for surface area equal to the equation for the total surface area of the container:
Surface Area = 2 x (Length x Width + Width x Height + Length x Height) = Total Surface Area of Container
Then we have:
Total Surface Area of Container = 2LW + 2WH + 2HL Surface Area of Material = 6LW
Since the material covers all six sides, we can set the surface area of the material equal to the total surface area of the container:
6LW = 2LW + 2WH + 2HL
Simplifying this equation, we get:
4LW = 2WH + 2HL
Dividing by 2, we get:
2LW = WH + HL
Multiplying by the height, we get:
2LWH = WH² + HL²
Now, we can rearrange this equation to get the volume of the container:
Volume = Length x Width x Height = (WH x L) / 2
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Complete Question:
Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has material covering all six sides.
What is the capacity of the container?
the following question has two parts first answer part A then answer part B
Isabella's mother has a garden with an area of 10 2/3 square feet she plants peas in 1/4 of the garden. calculate the area that was used for planting peas.
part B Isabella's mother sells the peas and gets 3 for each square foot so multiply your answer from part A by 3 to calculate how much money Isabella's mother made.
Answer: Part A:
If Isabella's mother has a garden with an area of 10 2/3 square feet, and she plants peas in 1/4 of the garden, we can calculate the area used for planting peas by multiplying the garden area by 1/4:
Area used for planting peas = (10 2/3 square feet) x (1/4) = (32/3) x (1/4) = 8/3 square feet
Therefore, the area used for planting peas is 8/3 square feet.
Part B:
If Isabella's mother sells the peas and gets 3 dollars for each square foot, we can calculate how much money she made by multiplying the area used for planting peas by 3:
Money made = (8/3 square feet) x (3 dollars/square foot) = 8 dollars
Therefore, Isabella's mother made 8 dollars by selling the peas she planted in her garden.
ax+b=dx-1 x=... if a≠d
According the given question the value οf x is (b+1)/(d-a).
What is simplificatiοn?Tο simplify simply means tο make anything easier. In mathematics, simplifying an equatiοn, fractiοn, οr prοblem means taking it and making it simpler.
Calculatiοns and prοblem-sοlving techniques simplify the issue. Simplifying shοuld have twο essential characteristics: it shοuld be algοrithmic, and it shοuld result in the same simplified fοrm when twο expressiοns fοr the same thing are simplified. These characteristics οf a simplificatiοn apprοach prοvide an algοrithm fοr determining whether twο expressiοns are equivalent.
Here, we have
Given: ax+b=dx-1, if a≠d
We have tο find the value οf x.
We apply simplificatiοn here and we get
ax+b = dx-1
b + 1 = dx - ax
b +1 = x(d-a)
x = (b+1)/(d-a)
Hence, the value οf x is (b+1)/(d-a).
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Animal shelters in a county need at least 15% of their animals to be adopted weekly to have room for the new animals that are brought into the various shelters. The county manager takes a random sample of shelters each week to estimate the overall proportion of animals that are adopted. If he concludes that the proportion has dropped below 15%, he will not accept any new animals into the shelters that week. He tests the hypotheses: H0: The adoption rate is 15%, and Ha: The adoption rate is less than 15%. What is a Type I error, and what is its consequence in this context?
The manager believes the adoption rate is still 15%, when it actually has dropped below 15%. The manager will accept more animals into the shelters and will run out of room.
The manager believes the adoption rate has dropped below 15%, when it actually has not. The manager will accept more animals into the shelters and will run out of room.
The manager believes the adoption rate has dropped below 15%, when it actually has not. The manager will not accept more animals into the shelters, when there actually is room to care for those animals.
The manager believes the adoption rate is still 15%, when it actually has dropped below 15%. The manager will not accept some animals into the shelters, thinking there will not be enough room, when they could have taken care of those animals.
answer c
Answer:
the amount will give 69 percentage of nothing thanks
A villager has a garden, as shown in the diagram (not to scale). In the middle of the garden is a pond that is approximately circular with a diameter of 40 m. The villager wishes to fertilise the garden. The recommended rate of application of the fertiliser is 25 g/m². How much fertiliser will be needed? (Round your answer appropriately, stating the units used.)
The amount of fertilizer needed for the garden is 508600 grams.
How to find the how much fertilizer needed to apply in the garden?In the middle of the garden is a pond that is approximately circular with a diameter of 40 m. Therefore, the fertilizer will not be applied in the pond area.
The villagers will only apply the fertilizer in the garden area. The recommended rate of application of the fertiliser is 25 g/m².
Therefore, let's find the fertilizer required for the garden.
area of the garden to be fertilized = area of trapezium - area of a circle
area of the garden to be fertilized = 1 / 2 (a + b)h - πr²
area of the garden to be fertilized = 1 / 2 (124 + 196)135 - 3.14(20)²
area of the garden to be fertilized = 1 / 2 (320)(135) - 1256
area of the garden to be fertilized = 43200 / 2 - 1256
area of the garden to be fertilized = 21600 - 1256
area of the garden to be fertilized = 20344 m²
Therefore,
1 m² = 25 grams
20344 m² = ?
Hence,
amount of fertiliser needed = 20344 × 25 = 508600 grams
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Create two sets of data with the following characteristics: -Each data set has 7 values, - The median of set 1 is greater than the median of set 2, - The IQRs of the data sets are the same. PLEASE HELP TY
The two sets of data are
Set 1: 5, 6, 7, 8, 9, 10, 20
Set 2: 1, 2, 3, 4, 5, 15, 16
Median of data:The median is a measure of central tendency in a data set that represents the middle value of the data when arranged in order.
To find the median of a data set, we need to arrange the values in ascending or descending order and then find the middle value.
IQR of Data:The IQR (Interquartile Range) is a measure of variability in a data set that represents the difference between the 75th percentile (third quartile) and the 25th percentile (first quartile).
To calculate the IQR of a data set, we need to find the values of the first quartile (Q1), and third quartile (Q3), and then subtract Q1 from Q3.
Here we have
Each data set has 7 values, -
The median of set 1 is greater than the median of set 2, -
The IQRs of the data sets are the same.
To create the sets assume a positive value as the median of the data and make sure that the value is in the middle of the data.
Similarly, take another positive value that is greater than the previous value and make sure that the value is also in the middle.
Now arrange the remaining values such that both sets of data have the same IQRs.
Here are two sets of data that meet the given characteristics:
Set 1: 5, 6, 7, 8, 9, 10, 20
Median: 8
IQR: 4 (Q3 = 9, Q1 = 5)
Set 2: 1, 2, 3, 4, 5, 15, 16
Median: 4
IQR: 4 (Q3 = 5, Q1 = 1)
Therefore,
The two sets of data are
Set 1: 5, 6, 7, 8, 9, 10, 20
Set 2: 1, 2, 3, 4, 5, 15, 16
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The fire department is having a BBQ fundraiser. The hot dogs costs $1.50 each and cans of soda cost 50.75 each. The department uses the algebraic expression 1.50x+0.75y to calcul customers' total expenses, a. What does the x variable represent? b. What does the y variable represent?
According to the algebraic expression 1.50x + 0.75y:
a) The x variable represents the number of hot dogs sold.b) The y variable represents the number of cans of soda sold. What is an algebraic expression?An algebraic expression is a combination of variables, values, numbers, and constants.
An algebraic expression is short of an equation, which consists of two or more algebraic expressions that are equated to each other.
The cost of hot dogs per unit = $1.50
The cost of cans of soda per unit = $0.75
Let the number of hot dogs bought = x
Let the number of cans of soda bought = y
Algebraic Expression:1.50x + 0.75y = Customer's total expenses
Thus, the variables x and y in the algebraic expression represent the number of units of each type of item sold during the BBQ fundraiser.
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Find the greatest common factor for the list of monomials. 63x^(2)y^(3)z,9x^(2)y^(3),90xy^(2)
Answer: is there a Pic it would help
Step-by-step explanation:
SOMEBODY PLEASE HELP ME
slant height is 18ft base length is 40ft
Answer:
1440 ft²
Step-by-step explanation:
The roof is made up of 4 congruent triangles.
We first solve for the area of one of the triangles using the formula:
A = (1/2) · b · h
↓ plugging in given values
A = (1/2) · 40 ft · 18 ft
A = 20 ft · 18 ft
A = 360 ft²
Now, we can solve for the surface area of the entire roof by multiplying the area of one of the triangles by 4 (because there are 4 congruent triangles).
SA = 360 ft² · 4 = 1440 ft²
—
Note that we can solve for the area of the triangles using the formula {A = (1/2) · b · h} because the slant height of a pyramid is perpendicular to the side of the pyramid's base that it connects to, thereby making it the height of the triangle that is the pyramid's side.
—
Determine the equation of the circle with center (7, -7) containing the point (11, -3).
We can say that after answering the offered question As a result, the equation for the circle with centre (7, -7) and point (11, -3) i[tex](x - 7)2 + (y + 7)2 = 32.[/tex]
What is equation?An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.
Determine the radius:
The radius of the circle is the distance between the circle's centre (7, -7) and any point on it (11, -3).
We may calculate the distance using the distance formula:
[tex]r = \sqrt((11 - 7)^2 + (-3 - (-7))\\v^2)\\r = \sqrt(4^2 + 4^2)\\r = \sqrt(32) (32)[/tex]
In the standard form equation of a circle, substitute the centre and radius:
A circle with centre (h, k) and radius r has the following standard form equation:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
With h = 7, k = -7, and r = sqrt(32), we get:
[tex](x - 7)^2 + (y + 7)^2 = 32[/tex]
As a result, the equation for the circle with centre (7, -7) and point (11, -3) is[tex](x - 7)2 + (y + 7)2 = 32.[/tex]
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A chef made 85 different meals. 34 people chose the same meal. What percent of his customers chose the same meal?
Answer: To find the percentage of customers who chose the same meal, we need to divide the number of people who chose the same meal by the total number of customers, and then multiply by 100 to convert to a percentage:
percentage = (34 / 85) x 100
percentage = 40
Therefore, 40% of the customers chose the same meal.
Step-by-step explanation:
Answer:
Its 40%
Step-by-step explanation: you divide 85 by 34 to get your answer
Need the answers for A and B
The sοlutiοn οf the given prοblem οf interest cοmes οut tο be Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.
What dοes interest actually mean?Tο calculate the simple interest rate, divide the amοunt by the cοst οf financing, the amοunt οf time left, and οther variables. The simple return strategy in marketing is principal student lοans hrs. This methοd is the mοst basic methοd fοr figuring οut invοlvement. The mοst typical methοd fοr calculating incοme is as a share οf the principal amοunt. Tο put this intο perspective, if he wants tο bοrrοw $100 frοm a single οf these friends .
Here,
a. The fοllοwing methοd can be used tο determine the mοnthly payment fοr a lοan:
=> The mοnthly payοut = (P*r) / (1 - (1+r)(-n)).
We must first determine the entire lοan amοunt, including interest, that Reh must pay back. After 4.5 years οf interest accrual, the lοan sum is:
=> [tex]9900 \times (1 + 0.0429/12)^{(12 \times 4.5)[/tex] = 12,723.97
The οverall debt balance is $12,723.97.
The numbers can then be entered intο the fοrmula as fοllοws:
=> (12723.97*(0.0429/12)) / (1 - (1+(0.0429/12))(-12*10))
is the fοrmula fοr the mοnthly payοut.
Payment due each mοnth: $131.19 (rοunded tο the nearest dοllar)
Reh's mοnthly payment is therefοre $131, rοunded tο the clοsest dοllar.
b. The fοllοwing fοrmula can be used tο determine the tοtal interest charged οver the lοan's term:
=> tοtal interest = (mοnthly payment X n) - P .
There have been a tοtal οf:
=> 120 is equal tο ten years times οne year.
The entire interest paid is thus:
=> ($3,943.80) (tοtal mοnthly installments * n) - P
=> (131.19 * 120) - 9900 (rοunded tο the nearest dοllar)
Sο, rοunded tο the clοsest dοllar, Reh will pay abοut $3,944 in interest fοr the duratiοn οf his lοan.
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An amusement park has 8 water slides and 26 other attractions.
What is the probability that a randomly selected attraction at this amusement park will be
a water slide?
Write your answer as a fraction or whole number.
P(water slide)
Answer:
The answer is 4/17
Step-by-step explanation:
A scale model of a building has a scale of 3 : 74
The height of the real building is 21 m.
Find the height of the scale model.
Give your answer in cm to 2 dp. need this ASAP
Answer:
0.85 m
Step-by-step explanation:
Model dimension : Real dimension
3 : 74
x : 21
[tex] \frac{21}{74} = \frac{x}{3} \\ x = 3 \times \frac{21}{74} \\ = \frac{63}{74} \\ = 0.851...[/tex]
Answer:
85.54 cm
Step-by-step explanation:
To find the height of the scale model, we need to use the scale ratio given: 3 : 74. This means that every 3 units on the model represent 74 units on the real building.
First, we need to determine the ratio of the heights. Let x be the height of the scale model. Then:
3 / 74 = x / 21
Solving for x, we get:
x = 21 * 3 / 74
x = 0.8554 m
To convert this to centimeters, we multiply by 100:
x = 85.54 cm
Therefore, the height of the scale model is 85.54 cm to 2 decimal places.
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How much larger is a circular pan with a 16 inches diameter than a squarebpan with sides measuring 16 inches
I WILL BRAINLIEST THE BEST ANSWER
The circular pan with a 16 inch diameter is 55.94 square inches (256-201.06) larger than the square pan with sides measuring 16 inches.
The area of a circle is given by the formula A=πr2, where r is the radius of the circle. The radius of a circle with a 16 inch diameter is 8 inches. Therefore, the area of this circle is A=π*82=201.06 square inches.
The area of a 16 inch square is given by the formula A=s2, where s is the length of the side of the square. The area of this square is A=162=256 square inches.
Therefore, the circular pan with a 16 inch diameter is 55.94 square inches (256-201.06) larger than the square pan with sides measuring 16 inches.
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Round to the nearest tenth.
Answer:
x=16.3
Step-by-step explanation:
sine: opposite side ÷ hypotenuse
sine(x)= 7 ÷ 25 = 0.28
sine^-1(0.28) = 16.3
x = 16.3
Answer:
16.3 rounded to the nearest tenth
Step-by-step explanation:
The formula for the sine rule is Sin A / a= Sin B / b = Sin C / c which is as, Sin V / v = Sin X / x = Sin S / s
Sin 90 / 25 = Sin X / 7, that is,
1 / 25 = Sin X / 7 (cross multiply)
Make Sin X the subject of the formula;
Sin X = 7 / 25
X = Sin^-1(7 / 25)
X = 16.26 = 16.3 rounded to the nearest tenth
19.
A quadrilateral
B trapezoid
rectangle
parallelogram
The shape shοwn is a a parallelοgram as twο sides are parallel and οppοsite angles are same. Thus, οptiοn D is cοrrect.
What is parallelοgram?A parallelοgram is a quadrilateral in which the οppοsite sides are parallel and equal. Parallelοgrams are classified intο three main types: square, rectangle, and rhοmbus, and each οf them has its οwn unique prοperties.
A parallelοgram is a special kind οf quadrilateral that is fοrmed by parallel lines. The angle between the adjacent sides οf a parallelοgram may vary but the οppοsite sides need tο be parallel fοr it tο be a parallelοgram. A quadrilateral will be a parallelοgram if its οppοsite sides are parallel and cοngruent. Hence, a parallelοgram is defined as a quadrilateral in which bοth pairs οf οppοsite sides are parallel and equal.
Given that:
One οf the twο οppοsite sides are equal
The οther twο sides are parallel
These are the traits οf a parallelοgram.
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Complete question:
What type of shape is show below:
curved surface area of a cone =
slant
surface area of a sphere
Trl, where r is the radius and 1 is the
height.
472, where r is the radius.
A sphere and a cone are shown below.
The surface area of the sphere is the same as the curved surface area of
the cone.
Work out the slant height of the cone.
If your answer is a decimal, give it to 1 d.p.
16 m
10 m
Answer:
735.1 square meters
Step-by-step explanation:
total surface area (TSA) of a cone can be calculated by using this mathematical expression:
Total surface area (TSA) of a cone = πr(l + r)
Total surface area (TSA) of a cone = πr(l + r)
Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)
Total surface area (TSA) of a cone = 3.142 × 6 × (39)
Total surface area (TSA) of a cone = 735.1 square meters.
The diameter of a circle is 25 m. Find its area to the nearest whole number.
Answer: 490.87 is the answer, rounded to a whole number is 491.
Step-by-step explanation: A≈490.87m²
Solving for A
A=1
4πd2=1
4·π·252≈490.87385m²
Not sure that's really an explanation but... Hope that makes since :)
PLEAASE HELP ME NEED IT RN
The Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.
How to solveThe distance between the Sun and the Earth is approximately 9.29 x 10^7 miles, and the distance between the Moon and the Earth is approximately 2.389 x 10^5 miles.
To find how much farther the Sun is from the Earth than the Moon, we can subtract the distance between the Moon and the Earth from the distance between the Sun and the Earth:
9.29 x 10^7 miles - 2.389 x 10^5 miles = 9.2661 x 10^7 miles
Therefore, the Sun is approximately 9.2661 x 10^7 miles farther than the Moon from Earth.
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Given the function y = x2+ 5x − 6 , list the zeros of the function
Answer:
Step-by-step explanation:
First we sould factor out the function:
y=x^2+5x-6
y=(x+6)(x-1)
Note: if you multiply out the factored equation, you will get your original equation.
Now, find what we need to plug in to make it equal 0.
If we plug in -6, then the (x+6) part equals 0. Since we are multiplying by 0, the whole thing equals 0.
If we plug in 1, then the (x-1) part equals 0. Since we are alo multiplying by 0 here, the function comes out to 0.
This means that at x=-6 and x=1 the function comes out to 0.
Pls help me ill give 20 points
Answer:
62.85 units
Step-by-step explanation:
s= rΘ
s= 4*5π/3= 20π/3
the perimeter= 20π/3*3
= 20π
= 20*22/7
= 440/7=62.85
Rewrite 10 + 12 using the GCF and factoring
Answer:
a)
=2×5+2×6
=10+12
=22
Ans. GCF (10, 12) = 2
A teacher has a large container of blue, red, and green beads. She reports to the students that the proportion of blue beads in the container is 0.30. The students feel the proportion of blue beads is lower than 0.30. A student randomly selects 60 beads and finds that 12 of the beads are blue. The P-value for the test of the hypotheses, H 0: p = 0.30 and H alpha: p less-than 0.30, is 0.045. What is the correct conclusion given Alpha = 0.05?
Because the P-value is less than Alpha = 0.05, the student should reject H0.
Because the P-value is less than Alpha = 0.05, the student should fail to reject H0.
Because the P-value is greater than Alpha = 0.05, the student should reject H0.
Because the P-value is greater than Alpha = 0.05, the student should fail to reject H0.
answer is a
Answer:
Red I think maybe we should try hi friends I am new to this app
On an average, five flood events in every 2 years are recorded at a location due to heavy rainfall. Number of occurrences of flood events in a year is found to follow a distribution, λx e−λ x! where λ is the expected number of flood events in a year. What is the probability of occurring not more than two flood events in a particular year at that location?
The probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.
The given distribution is λxe-λx! where λ is the expected number of flood events in a year. In order to calculate the probability of not more than two flood events in a particular year at that location.
The expected number of flood events in a year is given by: λ = (5 flood events) / (2 years) = 2.5 flood events per year
The given distribution is:λxe-λx! = 2.5xe-2.5x!
We need to find the probability of occurring not more than two flood events in a particular year at that location.
Therefore, the required probability is:P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)Here, P(x) represents the probability of x flood events.
The probability of x flood events can be calculated using the Poisson distribution formula:
P(x) = λxe-λx!Substitute λ = 2.5 and x = 0 in the above formula to get:P(0) = (2.5)0e-2.5 / 0! = e-2.5 ≈ 0.082Substitute λ = 2.5 and x = 1 in the above formula to get:P(1) = (2.5)1e-2.5 / 1! = 2.5e-2.5 ≈ 0.206Substitute λ = 2.5 and x = 2 in the above formula to get:P(2) = (2.5)2e-2.5 / 2! = 3.125e-2.5 ≈ 0.258Step 5
Now, add the above probabilities to find the required probability:P(x ≤ 2) = P(0) + P(1) + P(2)≈ 0.082 + 0.206 + 0.258 = 0.546Therefore, the probability of occurring not more than two flood events in a particular year at that location is approximately 0.546.
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Patricia opens a savings account with $1100 that earns 9% interest per year not compounded how much money will Patricia earn in 3 years.
Step-by-step explanation:
Her interest earned will be p r t
p = principal = amount of deposit = 1100 dollars
r = decimal interest rate = .09
t = time in years = 3
$ 1100 * .09 * 3 = $ 297 .
solve every single thing on tha page please
Answer:
Answer = 21 Sacks
Step-by-step explanation:
First, we need to calculate how much flour the baker will use in 20 days:
Amount of flour used per day for 64 loaves = 64 loaves/day x 400 g/loaf = 25,600 g/day
Amount of flour used in 20 days = 25,600 g/day x 20 days = 512,000 g
Next, we need to convert the amount of flour used into kilograms:
512,000 g ÷ 1000 g/kg = 512 kg
Finally, we need to calculate the minimum number of 25 kg sacks the baker should order:
Number of 25 kg sacks = 512 kg ÷ 25 kg/sack ≈ 20.48
Since the baker cannot order a fraction of a sack, he will need to order at least 21 sacks to last him for 20 days.
1/3(9k+12)=15
help with the explanation
Answer:
k=11/3
Step-by-step explanation:
Use distributive property.
3k+4=15
Subtract 4 from both sides.
3k=11
Divide 3 from both sides.
k=11/3
Answer: k=11/3 or 3.66
Step-by-step explanation:
3k+4=15 --Distribute 1/3 to 9k and 12.
3k=11 --Subtract 4 from both sides.
k=11/3 or 3.66
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a hospital director is told that 32% 32 % of the treated patients are uninsured. the director wants to test the claim that the percentage of uninsured patients is under the expected percentage. a sample of 160 160 patients found that 40 40 were uninsured. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is -1.75.
To test the claim that the percentage of uninsured patients is under the expected percentage of 32%, we can use a one-sample z-test. The null hypothesis is that the true percentage of uninsured patients is equal to 32%, while the alternative hypothesis is that the true percentage is less than 32%.
Using the sample data, we can calculate the sample proportion of uninsured patients as 40/160 = 0.25. We can then calculate the standard error of the sample proportion as sqrt[(0.32 x 0.68)/160] = 0.0385.
The test statistic can be calculated as (0.25 - 0.32)/0.0385 = -1.75.
To find the p-value associated with this test statistic, we can use a standard normal distribution table or a calculator to find the probability of a z-score less than -1.75. The p-value is approximately 0.04.
Since the p-value is less than the typical significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the percentage of uninsured patients is under the expected percentage of 32%.
Therefore, the correct answer is -1.75, which is the calculated value of the test statistic.
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PLEASE HELP ME! IT WAS DUE!
Answer:
one apple: 75 cents
one orange: 60 cents
Step-by-step explanation:
let x be price of one apple
let y be price of one orange
3x + 4y = 4.65
5x + 8y = 8.55
we can do elimination, substitution, or graphing.
this is elimination: (we're eliminating the x in this case to find y, and then use y to find x)
ORIGINAL EQUATIONS: (we're multiplying by 5 so we can eliminate x)
3x + 4y = 4.65
5x + 8y = 8.55
5(3x + 4y = 4.65) = 15x + 20y = 23.25
3(5x + 8y) = 8.55 = 15x + 24y = 25.65
(distribute, and then subtract to get one equation and eliminate x)
15x + 20y = 23.25
- 15x + 24y = 25.65
------------------------------
0 - 4y = - 2.4
so we got that, now we make it this: -4y = -2.4
divide both sides by -4.
-4y = -2.4
----- -----
-4 -4
y (orange variable) = 0.60
therefore, one orange cost 60 cents.
plug y (the 60 cents) back into one of the original equations (either works) and solve for x.
3x + 4y = 4.65
5x + 8y = 8.55
let's use this equation: 5x + 8y = 8.55
5x + 8(0.6) = 8.55
5x + 4.8 = 8.55
-4.8 -4.8
5x = 3.75
---- ------
5 5
x = 0.75
therefore, one apple cost 75 cents.
(also, there was an easier number to multiple the equations by)
3x + 4y = 4.65
5x + 8y = 8.55
We could have multiplied (3x + 4y = 4.65) with 2, distributing and bringing it to 6x + 8y = 9.30
Then subtract 6x + 8y = 9.30 from 5x + 8y = 8.55, and you would have solved and gotten x just fine, then plugged x back in to find y)
sorry this answer is so long...good luck :))
A circular drum has a radius of 4.2m and a height of 3.5m. How many full
bags of wheat can be emptied if the space required for one wheat bag is
5.39m³.
he volume of the drum can be calculated as follows:
Volume of drum = πr²h
= π(4.2m)²(3.5m)
≈ 246.33 m³
To find out how many full bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the volume of one wheat bag:
Number of full bags of wheat = Volume of drum ÷ Volume of one bag
= 246.33 m³ ÷ 5.39 m³
≈ 45.72
Therefore, the circular drum can hold approximately 45 full bags of wheat.
Answer: 45 Full of bags.
Step-by-step explanation:
The volume of the drum can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
V = π(4.2m)^2(3.5m)
V ≈ 246.73 m³
To find out how many bags of wheat can be emptied into the drum, we need to divide the volume of the drum by the space required for one bag:
246.73 m³ ÷ 5.39 m³/bag ≈ 45.81 bags
Since we can't have a fraction of a bag, we need to round down to the nearest whole number:
Number of bags = 45
Therefore, 45 full bags of wheat can be emptied into the drum.