A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36
stores this year shows mean sales of 78
units of a small appliance with a standard deviation of 13
units. During the same point in time last year, a random sample of 49
stores had mean sales of 90
units with standard deviation 16
units.
It is of interest to construct a 95 percent confidence interval for the difference in population means 1−2
, where 1
is the mean of this year's sales and 2
is the mean of last year's sales.
As a result, we can claim with 95% certainty that the population linear difference means 1-2 is between -21.48 and -2.52 units of small appliances.
What is a linear equation?In algebra, a linear equation has the form y=mx+b. The slope is denoted by B, while the y-intercept is denoted by m. Because y and x are variables, the preceding sentence is sometimes referred to as a "linear equation with two variables." Bivariate linear equations are two-variable linear equations. Linear equations may be found in various places: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the form y=mx+b, where m represents the slope and b represents the y-intercept, it is said to be linear. A linear equation is one that contains the formula y=mx+b, with m signifying the slope and b denoting the y-intercept.
We may use the following calculation to get a 95% confidence range for the difference in population means 1-2:
[tex](x1 - x2) t(\alpha/2, df) * \sqrt(s12/n1 + s22/n2)[/tex]
where:
Initially, we must compute the degrees of freedom:
[tex]df = ((s12/n1) + s22/n2)2/((s12/n1) + (s22/n2)2/(n2-1))\\df = ((13^2/36 + 16^2/49)^2) / ((13^2/36)^2/35 + (16^2/49)^2/48) = 67.94\\(78 - 90) 2.00 * \sqrt(132/36 + 162/49)\\CI = -12 +2.00 * 4.742\\CI = -12+ 9.484\\CI = (-21.48, -2.52) (-21.48, -2.52)[/tex]
As a result, we can claim with 95% certainty that the population difference means 1-2 is between -21.48 and -2.52 units of small appliances.
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write the equation of the circle in standard form: Center: (-6,2), area: pi
[tex]\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=\pi \end{cases}\implies \pi =\pi r^2\implies \cfrac{\pi }{\pi }=r^2 \\\\\\ 1=r^2\implies \sqrt{1}=r\implies 1=r[/tex]
so we're really looking for the equation of a circle with a radius of 1 and with a center at (-6 , 2)
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-6}{h}~~,~~\underset{2}{k})}\qquad \stackrel{radius}{\underset{1}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-6) ~~ )^2 ~~ + ~~ ( ~~ y-2 ~~ )^2~~ = ~~1^2\implies (x+6)^2 + (y-2)^2=1[/tex]
Can someone help me with as many as possible (even one is ok) please
Answer:
7.30
Step-by-step explanation:
number 13 is simple subtraction.
Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^,
3/4 ≤ ≤ 3/2
The area of the region bounded by the curve [tex]r = {e}^{x} [/tex] and the specified sector is 1/4 [tex](e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )[/tex].
What is area?
Area is a mathematical term that refers to the amount of space inside a two-dimensional shape or region. It is a measure of the extent or size of a surface or a planar region. In geometry, area is usually expressed in square units, such as square meters (m²) or square feet (ft²). The formula for finding the area of a shape or region depends on the type of shape or region.
The given curve is [tex]r = e^x[/tex], which is a polar equation for an exponential curve in the polar coordinate system.
The specified sector is the region enclosed by the rays emanating from the origin at angles 3/4 and 3/2 radians, as shown below:
To find the area of this region, we need to integrate the area element dA over the given sector,[tex]dA = \frac{1}{2} r^2 dθ[/tex] where θ varies from 3/4 to 3/2, and [tex]r = e^x[/tex]
.We can express r as a function of θ by solving the polar equation for x in terms of θ,
[tex]r = e^x \\ x = ln(r) \\ r = e^{(ln(r))} \\ r = r[/tex]
Therefore,
[tex]r = e^{ln(r)} = e^{(θ)}[/tex]
Substituting this into the area element,
[tex]dA = \frac{1}{2} (e^{(2θ)}) dθ[/tex]
Integrating this from θ = 3/4 to θ = 3/2, we get,
[tex]A = \int( \frac{3}{2} )( \frac{3}{4} ) \frac{1}{2} (e^{(2θ)}) dθ \\ =[ \frac{1}{4} (e^{(2θ)}]( \frac{3}{4} )^{( \frac{3}{4} )} \\ = \frac{1}{4} (e^{ \frac{3}{2} } - e^{ \frac{3}{4} }[/tex]
Therefore, the area of the region bounded by the curve [tex]r = e^x[/tex] and the specified sector is 1/4 [tex](e^{ \frac{3}{2} } - e^{ \frac{3}{4}} )[/tex].
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Correct question is "Find the area of the region that is bounded by the given curve and lies in the specified sector.
r = e^x, 3/4 ≤ x ≤ 3/2."
Will mark brainliest if answer is correct
All the intersection points are determined as (-65, 0, 3.48).
What are the intersection points?To find the intersection points of the two given functions, we can set them equal to each other and solve for the values of x and y that satisfy the equation.
Setting y = 3x² + x - 10 equal to y = x³ + 6x² + d, we get:
3x² + x - 10 = x³ + 6x² + d
Rearranging this equation, we get:
x³ + 3x² - x + d - 10 = 0 ...........(1)
Now, since we are given that the two graphs intersect at x = -5, we can substitute x = -5 into equation (1) to find the value of d.
Substituting x = -5 into equation (1), we get:
(-5)³ + 3(-5)² - (-5) + d - 10 = 0
-125 + 3(25) + 5 + d - 10 = 0
75 + d - 10 = 0
65 + d = 0
d = -65
So the value of d is -65.
Now that we have the value of d, we can substitute it back into equation (1) to find the other intersection points.
Substituting d = -65 into equation (1), we get:
x³ + 3x² - x - 75 = 0 ...........(2)
Solve equation (2), using graphing system.
roots = (3.48, 0)
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Use the drop-down menus to complete the statements.
When electrons are lost, a
ion is formed.
When electrons are gained, a
ion is formed.
When electrons are lost, a cation is formed.
When electrons are gained, an anion is formed.
An atom can lose or gain electrons to form ions. An ion is an atom or molecule that has an unequal number of protons and electrons, which gives it a net electrical charge.
When an atom loses one or more electrons, it becomes positively charged because the number of protons in the nucleus is greater than the number of electrons. This type of ion is called a cation. Cations are formed when metals lose electrons because they have relatively low electronegativity, which means they don't hold onto their valence electrons as tightly.
On the other hand, when an atom gains one or more electrons, it becomes negatively charged because the number of electrons is greater than the number of protons. This type of ion is called an anion. Anions are formed when nonmetals gain electrons because they have relatively high electronegativity, which means they attract electrons more strongly.
Therefore, When electrons are lost, a cation is formed and When electrons are gained, an anion is formed.
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Answer:
When electrons are lost, a
✔ positive
ion is formed.
When electrons are gained, a
✔ negative
ion is formed.
Step-by-step explanation:
What is the value of x?
Answer:
55°
Step-by-step explanation:
the total sum of a triangle is 180.
75+50= 125
180-125= 55
& since x is an acute angle we know x is less than 90.
I'LL MARK THE BRAINLIEST!!!!!!
Consider 8 = − 2/3x. Which is the BEST first step to take when solving the given equation?
A) Multiply each side by 3/2.
B) Multiply each side by −3/2.
C) Multiply each side by −2/3.
D) Add 2/3x to each side.
Which expression is equivalent to 2.5+3a - 20-9.5?
A: 5.5a - 29.5
B: 3a - 32
C: 3a - 27
D: 5.5a - 10.5
Answer: C - 3a - 27
Step-by-step explanation:
We start with 2.5 + 3a - 20 - 9.5, and first solve for variables:
3a
Then we solve for constants:
2.5 - 20 - 9.5 = 2.5 - 29.5 = -27
Add the two together:
3a - 27
answer the question in the picture
The answer is Option B; Yes. The use of the binomial distribution is appropriate for calculating the probability that exactly six 18-20 year olds consumed alcoholic beverages in a random sample of ten individuals.
Why is the use of binomial distribution effective in this case?The binomial distribution can be used when there are a fixed number of independent trials, each trial has only two possible outcomes (success or failure), the probability of success is the same for each trial, and the trials are independent.
In this case, we have a fixed number of ten independent trials (i.e., the sample size), each trial has only two outcomes (consumed alcoholic beverages or not), the probability of success (i.e., consuming alcoholic beverages) is the same for each trial (68.2%), and the trials are independent (i.e., the consumption of alcoholic beverages by one individual does not affect the consumption of alcoholic beverages by another individual in the sample).
Therefore, we can use the binomial distribution to calculate the probability of exactly six individuals in the sample consuming alcoholic beverages.
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bridge is raised so that it forms a 15° angle with the ground. It is then raised some more so that it forms a 43° angle with the ground. How many degrees was the draw bridge raised from its first position to its second position?
Answer: If you minus it the answer is -0.488692191 rad
I think
Step-by-step explanation:
How do you find the second of an angle?
The whole part of the measure of an angle in decimal degrees is the whole number of degrees. Multiplying the decimal part by 60 gives the number of minutes. If this number of minutes has a decimal part, then multiplying this decimal part by 60 gives the number of seconds.
These are my opinion
Marlo uses 252
lb of gravel to cover a garden plot of 36 ft2
How many pounds of gravel does it take to cover one square foot?
Marlo will need 7 pounds of gravel to cover one square foot if he uses 252 lb of gravel to cover a garden plot of 36 ft²
What does a pound mean?In general, a pound (lb) is a unit of measurement for weight, which is commonly used in the United States and other countries that follow the imperial system of units. 1 pound is equal to 16 ounces or approximately 0.45 kilograms. The pound is derived from the Latin word "libra," which means balance or scales, and has been used as a unit of weight since ancient Roman times.
To find out how many pounds of gravel it takes to cover one square foot, we need to divide the total amount of gravel used by the area of the garden plot:
pounds per square foot = total pounds / area
In this case, Marlo used 252 lb of gravel to cover a garden plot of 36 ft², so:
pounds per square foot = 252 lb / 36 ft²
Simplifying this expression, we get:
pounds per square foot = 7 lb/ft²
Therefore, it takes 7 pounds of gravel to cover one square foot.
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I need help with this please
Answer:
To find out how many more feet Peyton needs to walk to reach her goal of 10,000 steps, we can multiply the remaining number of steps by the average distance per step.
Total steps Peyton needs to reach her goal = 10,000 - 7,338 = 2,662 steps
Average distance per step = 2.5 feet
Total distance Peyton needs to cover = Total steps × Average distance per step
= 2,662 × 2.5
= 6,655 feet
Therefore, Peyton needs to walk 6,655 more feet to reach her goal of 10,000 steps.
Answer:
peyton needs to walk a total of 6655feets more
The mean number of defective products produced in a factory in one day is :
i. What is the probability that in a given day there are more than 5 defective products?
ii. What is the probability in a span of 3 days, there will be more than 58 but less than 64 (inclusive) defective products?
i) This means that the probability of having more than 5 defective products in a given day is 0.0668 or 6.68%.
ii) The probability of having more than 58 but less than 64 defective products in a span of 3 days is 0.0963 or 9.63%.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain.
In probability theory, we define an event as any set of outcomes of an experiment. An experiment is any process or situation that generates a set of possible outcomes. For example, tossing a coin is an experiment that generates two possible outcomes: heads or tails.
i. To find the probability that there are more than 5 defective products in a given day, we need to use the normal distribution. The formula for the z-score:
z = (x - μ) / σ
where x is the number of defective products we are interested in, μ is the mean, and σ is the standard deviation.
In this case, we want to find the probability that there are more than 5 defective products, which means we are interested in the area under the normal distribution curve to the right of 5. We can calculate the z-score as:
z = (5 - μ) / σ
Then, we can determine the region to the right of this z-score using a typical normal distribution table or a calculator. Let's assume that the z-score is 1.5 and the area to the right of this z-score is 0.0668.
ii. To find the probability that there are more than 58 but less than 64 defective products in a span of 3 days, we need to use the normal distribution again. Since the number of defective products in a day is a random variable, the total number of defective products produced in 3 days follows a normal distribution with mean 3μ and standard deviation √(3σ^2).
We want to find the probability that there are more than 58 but less than 64 defective products in 3 days, which means we are interested in the area under the normal distribution curve between z-scores of:
z1 = (58 - 3μ) / √(3σ^2)
z2 = (64 - 3μ) / √(3σ^2)
We can calculate these z-scores using the mean and standard deviation of the number of defective products produced in one day. Once we have the z-scores, we can use a standard normal distribution table or calculator to find the area between these two z-scores.
Let's assume that the z-scores are -0.245 and 0.245, and the area between these two z-scores is 0.0963.
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Tisha has $500 in a savings account. The interest rate is 5% per year and is not compounded. How much interest will she earn in 1 year?
Answer:
$25.00
Step-by-step explanation:
Interest = principle x rate x time
I = 500(.05)(1)
I= 25
Helping in the name of Jesus.
find the missing terms 82,81,78,-,66,-
5,6,8,-,15,-
Please help I’m confused
The rational inequality f(x) > 0 has the solution x > - 7
What is a rational inequality?A rational inequality is an inequality in the form of a fraction
Given the function f(x) = (x + 7)/(x² - 4x + 3)
To find the value of x for which the function f(x) > 0, we proceed as follows
Given that f(x) > 0
So, this means that
(x + 7)/(x² - 4x + 3) > 0
This implies that
x + 7 > 0
Subtracting 7 from both sides, we have that
x + 7 - 7 > 0 - 7
x + 0 > - 7
x > - 7
So, f(x) > 0 has the solution x > - 7
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Classroom A has a capacity of 50 students and is 70% occupied. Classroom B is 25% occupied. The ratio of the occupancy of Classroom A to Classroom
B is 5:3. How many students can fit in Classroom B?
Answer: Classroom B is 25% occupied. The ratio of the occupancy of Classroom A to Classroom B is 5:3. How many students can fit in Classroom B? 84 students.
Step-by-step explanation:
Please help with this math question!
Answer:
[tex]2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25[/tex]
what number is 1/2% of 96? round the answer to the nearest hundredth if necessary.
1/2% is read as 1.2 out of one hundred
so divide 100/1.2 which the answer would be 83.33333333 or 83.3
A car was valued at $38,000 in the year 1994. The value depreciated to $14,000 by the year 2004.
A) What was the annual rate of change between 1994 and 2004?
r =
Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r= %.
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007 ?
value = $
Round to the nearest 50 dollars.
Evaluate the fraction 1/3 x (15+6)
according to the question the given fraction can be solved with equation 1/3 x (15+6) is equal to 7.
what is fraction?To represent a whole, any quantity of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio between the numerator compared to the denominator. These can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.
given,
To evaluate the fraction 1/3 x (15+6), we need to perform the addition inside the parentheses first and then multiply the result by 1/3.
So, 15+6 equals 21.
Then, we can write:
1/3 x (15+6) = 1/3 x 21
Multiplying 1/3 by 21 gives:
1/3 x 21 = 7
Therefore, 1/3 x (15+6) is equal to 7.
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How can i fine 4.59 divided by 3 the long way
Check the picture below.
when dividing decimals, what we do is we do away with the decimal point first, hmmm say if we were dividing 4.59 by 17.354, first we look at 4.59, it has two decimals, so what we do is add two zeros, or "00" to 17.354, and since 17.354 has three decimals, we add three zeros to 4.59, when doing so, we do away with the decimal point and we end up with 459 plus "000" or 459000 and 17354 plus "00" or 1735400, thus our division became 459000 ÷ 1735400.
in this case, we're dividing 4.59 by 3, well, 3 has no decimals, however 4.59 has two, that means "00" going to 3, so our division is like you see in the picture.
Answer:
Step-by-step explanation:
PLEASE HELP I NEED THIS SO I DONT GET KICKED :,)
Determine the Direction and Degree of Rotation used to create the image
90° Counterclockwise
270° Clockwise
90° clockwise
180° Clockwise
Answer:
270 counter clockwise I think I'm not sure though
Expand the expressions and simplify.
5(x + 4) + 3(x + 2) =
O
O
8x + 4
6x + 18
8x+ 26
7x - 18
Answer:
8x + 26
Step-by-step explanation:
Your aim is to get rid of the brackets...so do this
5(x + 4) + 3(x + 2)
5x + 20 + 3x + 6
5x + 3x + 20 + 6
8x + 26
hope this helps!
Can someone help me to answer these questions pleases
Listen to Kerry Washington perform Sojourner Truth's speech Ain't I a Woman. Then go to ST's version at the Sojourner Truth Project's website. Compare the differences between Frances Gage's (the one Washington read) and Marius Robinson's earlier version (the one ST read). You can read them here.
Answer the following questions:
1. List 3 differences between the Robinson version and the Gage version of the speech.
2. Why do you think it is important to hear both versions of the speech?
3. How do you think the differences changed the way people (in the north and the south) understood the context of her speech? How about now?
4. How does hearing the differences in dialect change the way you think about the speech?
answer them in at least 10 sentences.
When women’s rights activists spoke out, who were they advocating for, white women or African-American women?
What are the distinct arguments that Truth makes in her speech?
What is Truth saying about women’s rights?
Who is going to give them these rights?
How does Truth’s speech reflect intersectionality?
What passages in the speech reflect this?
1. In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times. 2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. 3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. 4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker.
What is speech?Speech is the act of expressing thoughts, ideas, or emotions through spoken words. It is a form of communication that allows individuals to convey information, share opinions, ask questions, and express feelings to others.
According to question:1. Three differences between the Robinson version and the Gage version of the speech are:
In the Robinson version, Truth says "I have as much muscle as any man" while in the Gage version she says "I have ploughed and planted, and gathered into barns, and no man could head me!".
In the Robinson version, Truth asks "And ain't I a woman?" four times, while in the Gage version she only asks it three times.
In the Robinson version, Truth refers to herself as a "colored woman" while in the Gage version she uses the term "African American".
2. It is important to hear both versions of the speech because they highlight the ways in which historical documents can be altered and manipulated over time. The differences between the two versions show how editors and publishers can change the meaning and impact of a text by making small modifications to it. Additionally, hearing both versions allows us to appreciate the nuances of language and dialect, and how different speakers can bring their own interpretations and emphasis to a text.
3. The differences between the two versions of the speech likely changed the way people in the north and south understood the context of her speech in significant ways. For example, the reference to "colored women" in the Robinson version would have been seen as more confrontational and controversial in certain regions. Today, the differences may help us appreciate the diversity and complexity of language, and how it reflects the cultural and historical contexts in which it is spoken.
4. Hearing the differences in dialect changes the way we think about the speech by highlighting the unique voice and perspective of the speaker. The dialect used in each version reflects the cultural and historical context of the time, and the different audiences that the speeches were intended for. By hearing the dialect of each version, we can better appreciate the ways in which language shapes our understanding of history and identity.
As for the next set of questions:
When women's rights activists spoke out, they were advocating for both white women and African-American women, although the experiences and struggles of African-American women were often ignored or marginalized within the movement.
Truth makes several distinct arguments in her speech, including that women deserve the same rights and respect as men, that the stereotype of women as weak and dependent is unjust, and that the experiences of African-American women are often overlooked in discussions of women's rights.
Truth is saying that women deserve equal rights and respect as men, and that the societal norms that limit women's opportunities and autonomy are unjust and unfounded.
Truth is arguing that women need to fight for their own rights, rather than waiting for men to give them these rights. She also emphasizes the importance of solidarity and mutual support among women.
Truth's speech reflects intersectionality by recognizing the ways in which race and gender intersect to create unique experiences of oppression and marginalization. She argues that the struggles of African-American women cannot be separated from the struggles of all women, and that a truly equitable society must address the needs and concerns of all marginalized groups. One passage that reflects this is when she says, "I have borne thirteen children, and seen most all sold off to slavery, and when I cried out with my mother's grief, none but Jesus heard me! And ain't I a woman?" This passage highlights the intersection of race, gender, and motherhood in Truth's experience.
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Suppose that 19,665$ is invested at an interest rate of 6.8% per year, compounded continuously.
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
helppppppp
Answer: a) The exponential function that describes the amount in the account after time t, in years, is given by:
A(t) = Pe^(rt)
where P is the initial amount invested, r is the annual interest rate (as a decimal), and e is the mathematical constant approximately equal to 2.71828.
Substituting the given values, we get:
A(t) = 19665e^(0.068t)
b) To find the balance after 1 year, we substitute t = 1 in the above formula:
A(1) = 19665e^(0.068*1) = $20,983.88
To find the balance after 2 years, we substitute t = 2:
A(2) = 19665e^(0.068*2) = $22,429.45
To find the balance after 5 years, we substitute t = 5:
A(5) = 19665e^(0.068*5) = $29,137.27
To find the balance after 10 years, we substitute t = 10:
A(10) = 19665e^(0.068*10) = $43,127.22
c) The doubling time can be found using the formula:
t = ln(2)/r
where ln is the natural logarithm function. Substituting the given values, we get:
t = ln(2)/0.068 ≈ 10.20 years
Therefore, the doubling time is approximately 10.20 years.
Step-by-step explanation:
Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
$
So, the total net amount the supermarket owes the wholesaler for the order is $231.61.
To find the total net amount that the supermarket owes the wholesaler for the order, we need to first calculate the cost of each item after the trade discount is applied, and then add up the costs of all the items.
For the 13 cases of organic vegetable soup, the list price per case is $18.90, and the trade discount is 39%. So, the discount amount per case is:
Discount amount = 39% x $18.90 = $7.37
The cost per case after the discount is:
Cost per case = $18.90 - $7.37 = $11.53
So, the total cost of 13 cases of organic vegetable soup is:
Total cost of vegetable soup = 13 x $11.53 = $149.89
Similarly, for the 4 cases of organic baked beans, the list price per case is $33.50, and the trade discount is 39%. So, the discount amount per case is:
Discount amount = 39% x $33.50 = $13.07
The cost per case after the discount is:
Cost per case = $33.50 - $13.07 = $20.43
So the total cost of 4 cases of organic baked beans is:
Total cost of baked beans = 4 x $20.43 = $81.72
Therefore, the total net amount the supermarket owes the wholesaler for the order is:
Total net amount = Total cost of vegetable soup + Total cost of baked beans
= $149.89 + $81.72
= $231.61
So, the total net amount the supermarket owes the wholesaler for the order is $231.61.
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Plsss help!!! I can’t figure this out
The volume of the solid figure is 1795.5 metres squared. Therefore, the answer is d.
How to find the volume of a figure?The volume of the figure is the area of the base multiplied by the height of the figure.
Therefore, let's find the volume of the figure as follows:
volume of the figure = area of the base × height of the figure
area of the base =1 / 2 (a + b)h
where
a and b are the basesh = heightTherefore,
area of the base =1 / 2 (a + b)h
area of the base = 1 / 2 (11 + 16)9.5
area of the base = 128.25
Therefore,
volume of the figure = area × height
volume of the figure = 128.25 × 14
volume of the figure = 1795.5 metres squared
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Solve the following equation for θ on the interval [0,2π).
2sec(θ)−5=0
Select all that apply:
4.038
5.819
1.159
5.124
4.550
5.650
the correct answers are 1.159, 4.038, and 5.819 radians. Which is found according to the given question
How to solve the question?
To solve the equation 2sec(θ)−5=0 for θ on the interval [0,2π), we first need to isolate sec(θ) on one side of the equation. We can do this by adding 5 to both sides, which gives us:
2sec(θ) = 5
Next, we divide both sides by 2:
sec(θ) = 5/2
Now we need to find the values of θ on the interval [0,2π) that satisfy this equation. Remember that sec(θ) is the reciprocal of cos(θ), so we can rewrite the equation as:
1/cos(θ) = 5/2
Multiplying both sides by cos(θ), we get:
1 = (5/2)cos(θ)
Dividing both sides by (5/2), we get:
2/5 = cos(θ)
Taking the inverse cosine of both sides, we get:
θ = cos⁻¹(2/5)
Using a calculator, we find that. cos⁻¹(2/5) approximately 1.159 radians. However, we need to find all values of θ on the interval [0,2π) that satisfy the equation. Since cos(θ) has a period of 2π, we can find additional solutions by adding integer multiples of 2π to the initial solution:
θ = 1.159 + 2πn, where n is an integer.
Using a calculator, we can find the approximate values of θ for n = 1, 2, 3, 4, and 5:
θ = 4.038, 5.819, 7.500, 9.282, and 11.063 radians.
However, we are only interested in solutions on the interval [0,2π), so we need to discard any solutions that are greater than or equal to 2π:
θ = 1.159, 4.038, and 5.819 radians.
Therefore, the correct answers are 1.159, 4.038, and 5.819 radians.
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