The price per cup of salad dressing in a 2-pint bottle that costs $13.76 is $0.86.
To calculate the price per cup of salad dressing, we need to know that there are 2 cups in a pint. Therefore, there are 4 cups in a 2-pint bottle of salad dressing.
To find the price per cup, we divide the total cost of the bottle by the number of cups in the bottle.
$13.76 ÷ 4 cups = $3.44 per cup
Therefore, the price per cup of salad dressing is $0.86, which is obtained by dividing $3.44 by 4.
It is important to know the price per unit, whether it is per ounce, per pound, per liter, or per cup, to be able to compare the cost of different products accurately.
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Sylvia conducts an experiment using two long pieces of a cord and a spherical ball that has been cut in half. The radius of the spherical ball is 8 centimeters. She wraps the first cord around the hemisphere of the ball until it is completely covered, as shown in Figure 1. She cuts the cord and removes it from the ball. She then wraps the second cord around the bottom circle of the ball until it is completely covered, as shown in Figure 2. She again cuts the cord and removes it from the circular base.
Which of the following correctly compares the lengths of the cords and best justifies the reason for this relationship?
A - The length of the first cord must be approximately equal to the length of the second cord because the surface area of the hemisphere is the same as the area of its circular base.
B - The length of the first cord must be approximately 2 times the length of the second cord because the surface area of the hemisphere is 2 times the area of its circular base.
C - The length of the first cord must be approximately 4 times the length of the second cord because the surface area of the hemisphere is 4 times the area of its circular base.
D - The length of the first cord must be approximately 8 times the length of the second cord because the surface area of the hemisphere is 8 times the area of its circular base.
The option that correctly compares the lengths of the cords and best justifies the reason for the relationship is B - The length of the first cord must be approximately 2 times the length of the second cord because the surface area of the hemisphere is 2 times the area of its circular base.
How to compare the lengths of the cords?We can compare the lengths of the cords by these steps:
First, find the length of cord needed to wrap around the hemisphere of the ball (cord 1), using the formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Since our focus is on a hemisphere, we find half the circumference, πr only.
So, the length of cord 1 is πr = π(8) = 8π cm.
Next, we find the length of cord needed to wrap around the circular base of the ball (cord 2), using the formula for the circumference of a circle, also.
So, the length of cord 2 is 2πr = 2π(8) = 16π cm.
Then, we compare the lengths of the cords:
Length of cord 1 = 8π cm
Length of cord 2 = 16π cm
Finally, we simplify:
Length of cord 1 = π(8) = 8π cm
Length of cord 2 = 2π(8) = 16π cm
So, the length of the first cord must be approximately 2 times the length of the second cord because the surface area of a hemisphere is 2 times the area of its circular base is correct.
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Chelsea bought a bond with a face value of $5,000. The bond has a term of 4 years. Chelsea bought the bond at a 3 percent discount from the face value. The bond pays 3 percent annual interest, and Chelsea will receive eight semiannual payments. When the bond is redeemed at maturity, the total return (profit) will be decimal place.)
Chelsea's total return (profit) when the bond is redeemed at maturity is $50.
Chelsea paid for the bond with the 3% discount:
Discount = 3% of $5,000
= $150
Price paid for the bond = $5,000 - $150
= $4,850
Next, let's calculate how much Chelsea will receive in each semiannual payment:
Semiannual interest rate = 3% / 2
= 1.5%
Semiannual payment = Face value x Semiannual interest rate = $5,000 x 1.5% = $75
Since there are eight semiannual payments, Chelsea will receive a total of:
Total semiannual payments = Semiannual payment x Number of semiannual payments = $75 x 8 = $600
Finally, let's calculate the total return (profit) when the bond is redeemed at maturity:
Total interest earned = Annual interest rate x Term x Face value = 3% x 4 x $5,000 = $600
Face value at maturity = $5,000
Total return = Price paid + Total interest earned + Total semiannual payments - Face value at maturity
Total return = $4,850 + $600 + $600 - $5,000 = $50
Therefore, Chelsea's total return (profit) when the bond is redeemed at maturity is $50.
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A store sells two different fruit baskets with mangos and kiwis. The first basket has 2 mangos and 3 kiwis for $9.00. The second basket has 5 mangos and 2 kiwis for $14.25. Find the cost of each type of fruit.
a. Explain how you would write a system of equations to represent the information given.
b. Write the system of equations as a matrix.
c. Find the identity and inverse matrices for the coefficient matrix.
d. Use the inverse to solve the system.
e. Interpret your answer in this situation.
The cost of kiwis is $1.5 The cost of mangoes is $2.25. Cost, in popular usage, is the financial worth of the goods and services that producers and consumers purchase.
Cost, in popular usage, is the financial worth of the goods and services that producers and consumers purchase. The cost price, in accordance with fundamental economic discernment, is an estimation for the substitute opportunities forgone in choosing one good or pursuit over another.
2m + 3k = 9
5m + 2k = 14.25
m = mangoes
k = kiwis
10m + 15k = 45 equation 3
10m +4k = 28.5 equation 4
11k = 16.5
k = 1.5
2m + 3(1.5) = 9
m = 2.25
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The price of a CD radio cassette has been reduced from $16,999 to $13,999 . Calculate the rate of discount
The rate of discount for the CD radio cassette is 17.65%.
To calculate the rate of discount, we need to find the difference between the original price and the discounted price, and then divide that difference by the original price.
Original price: $16,999
Discounted price: $13,999
So, the Discount amount
= Original price - Discounted price
= $16,999 - $13,999
= $3,000
Rate of discount = (Discount amount / Original price) * 100%
= ($3,000 / $16,999) x 100%
≈ 17.65%
Therefore, the rate of discount for the CD radio cassette is 17.65%.
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DUE TOMORROW!!! PLS HELP!! 1 POINT!!!
What is the measure of the unknown angle? (1 point)
image of a one hundred ninety eight degree angle and an unknown angle
a
152°
b
157°
c
162°
d
169°
Answer:
162 Degrees
Step-by-step explanation:
Think of this as a circle.
If you subtract 360 from 198, you get 162.
Which would be your missing angle.
In a class of 36 students, 19 read Biology, 16 read Chemistry and 5 were not allowed to read both subjects. Illustrate the information on a venn diagram. Find how many students read: 1. 11. both Biology and Chemistry; only Chemistry.
Step-by-step explanation:
let u represent the universal set
B represent biology
C represent chemistry
n(u)=36
n(b)=19
n(c)=16
n(bun)=5
n(bnn)=x
19-x+x+16-x+5=36
19+16-x+5=36
19+16+5-x=36
40-x=36
40-36=x
x=4
:.4 students read both biology and chemistry
number of students who read only chemistry is
16-x
but x=4
16-4
=12
:.12 students read only chemistry
Find the volume of the pyramid. Round your answer to the nearest tenth, if necessary.
6inch(height) and 4inch(base)
The volume of the pyramid is 8 [tex]in^{2}[/tex]
What is Pyramid?Pyramid is a polygonal base and flat triangular faces, which join at a common point called the apex. A pyramid is formed by connecting the bases to an apex.
How to determine this
Volume of pyramid = 1/3 * Base area * Height
Base area = 4 inches square
Height = 4 inches
Volume of pyramid = 1/3 * 4 * 6
Volume of pyramid = 1/3 *24
Volume of pyramid = 24/3
Volume of pyramid = 8 [tex]in^{3}[/tex]
Therefore, the volume of the pyramid is 8 [tex]in^{3}[/tex]
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What is the equation of the line that passes through (0,2) and (-3,14) in slope intercept form?
Answer:
y = -4x + 2Step-by-step explanation:
Plug in the values of m and b that we found: y = -4x + 2 So, the equation of the line that passes through (0, 2) and (-3, 14) in slope-intercept form is y = -4x + 2.
Have a Nice Best Day : ) Please Give Me Brainliest
hi please help I don't want to pick the wrong question
Answer:
B
Step-by-step explanation:
[tex]\frac{4x^{2} }{12x^{2}-4}\\ = \frac{x^2}{3x^2-1}[/tex]
4 common leke cancel kar diya bas . nothing else
sabrina wants to test which brand of popcorn pops the most kernels. she picked a store brand, orville redenbacher, and popsecret. all three bags started with the same number of kernels. she popped each for 3 minutes in the same microwave, and then counted the number of kernels left over. what is her independent variable?
The independent variable in Sabrina's experiment is the brand of popcorn.
An independent variable is a variable that is manipulated by the experimenter and is expected to cause a change in the dependent variable. In this case, Sabrina wants to see which brand of popcorn pops the most kernels, so she is manipulating the brand of popcorn by testing three different brands: store brand, Orville Redenbacher, and PopSecret. The dependent variable in this experiment is the number of kernels left over after popping for 3 minutes in the same microwave. This variable is expected to change based on the brand of popcorn being tested. By manipulating the independent variable and measuring the resulting changes in the dependent variable, Sabrina can determine which brand of popcorn pops the most kernels.
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linear algebreacompute anx from this formula for x for arbitrary n>0. what is a good approximation to anx for n large?
To compute anx from the given formula for x for any arbitrary n>0, we need to first determine the values of a1, a2, a3,...an. Once we have these values, we can substitute them into the formula and solve for x. However, since we don't have any information about the values of a1, a2, a3,...an, we cannot provide an exact solution for x.
Regarding the second part of your question, i.e., finding a good approximation for anx when n is large, we can make use of the concept of content loaded linear algebra. Specifically, we can use the principle of least squares to find the best fit line for a set of data points. In this case, the data points would correspond to the values of anx for different values of n.
Once we have the best fit line, we can use it to make predictions about the value of anx for large values of n. However, it's important to note that this will only be an approximation and not an exact solution.
In summary, to compute anx from the given formula, we need to determine the values of a1, a2, a3,...an. To find a good approximation for anx for large values of n, we can use the principle of least squares to find the best fit line for a set of data points.
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A survey was dispersed throughout the county in order to gather information about the amount of money spent on groceries.
Is this survey numerical or categorical?
Select a Value
Is this survey univariate or bivariate?
Select a Value
R
The survey is numerical because it involves gathering information about the amount of money spent on groceries.
The given survey about the amount of money spent on groceries can be classified as follows:
Because data on how much was spent on food is being gathered, the survey is numerical. Numerical data deals with quantitative measurements or values.
The survey can be considered univariate since it focuses on a single variable, which is the amount of money spent on groceries.
Thus, univariate data analysis involves examining and summarizing data related to a single variable.
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Consider the initial value problem y'=ty(4-y)/(1+t), y(0)=ysubnot. (a) Determine how the solution behaves as t goes to infinity. (b) If y subnot equals 2, find the time T at which the solution first reaches the value 3.99. (c) Find the range of initial values for which the solution lies in the interval 3.99
Thus, the range of initial values for which the solution lies in the interval [3.99, 4] is ysubnot in (0, 4).
(a) As t goes to infinity, the denominator of the right-hand side approaches infinity while the numerator approaches 4ty. Thus, the solution approaches the equilibrium solution y=4.
(b) Using separation of variables and partial fractions, we can obtain the solution: y = 4 / (1 + 3e^(2t^2/2 + C)). Setting y = 3.99 and solving for t, we obtain t = sqrt[ln(3.99/0.01) / 2].
(c) We can rearrange the differential equation to obtain y'/(y(4-y)) = t/(1+t) and then integrate both sides. This gives ln|y/(4-y)| = C + ln(1+t) - t, where C is the constant of integration. To find the range of initial values for which the solution lies in the interval [3.99, 4], we need to solve the inequality 3.99 <= y <= 4 for y in terms of t. This gives the condition -∞ < t <= ln(999/1).
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pLSSS HELP
Which of the following is not a step when drawing an angle? (1 point)
a
Draw a ray
b
Connect the arrows with a straight line
c
Line up the baseline on the protractor with the ray
d
Draw arrows on both ends to make them rays
Drawing a straight line and adding arrowheads is an easy way to create rays that are useful in geometry and other mathematical applications.
To connect the arrows with a straight line, you simply need to draw a line segment that passes through both arrowheads. This will create a line that extends infinitely in both directions.
To turn the arrows into rays, you can add an arrowhead on one end of the line segment to indicate the direction of the ray. This will create two rays that originate from the same point and extend infinitely in opposite directions.
It is important to note that a ray is named based on the direction in which it travels, so you may need to specify which direction each ray is pointing.
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A number, n, rounded to one. is 2.7. place Complete the inequality to show the lower and bounds upper of Is n decimal □
The number n must be greater than or equal to 2.65 and less than 2.75 in order to round to 2.7 when rounded to one decimal place
If a number n rounded to one decimal place is 2.7, then we know that n lies between two numbers:
The lower bound is the number that is 0.05 less than 2.7, which is 2.65 (since the digit in the second decimal place is 5 or greater, we round up the last digit in the first decimal place).
The upper bound is the number that is 0.05 greater than 2.7, which is 2.75 (since the digit in the second decimal place is 5 or greater, we round up the last digit in the first decimal place).
Therefore, we can write the inequality as:
2.65 ≤ n < 2.75
This means that n must be greater than or equal to 2.65 and less than 2.75 in order to round to 2.7 when rounded to one decimal place.
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What is an inequality in algebra
Answer:
inequalitys are mathematical expressions involving the symbols >, <, ≥ and ≤
Step-by-step explanation:
It's usually used to solve for an unknown value, and graphs
A six-foot man casts a 15 foot shadow. At the same time a streetlight casts an 80-foot shadow.
The same six-foot tall man wants to indirectly measure the streetlight in screen 3. But it is a cloudy day and there are no shadows. So holding his phone by his eye, he uses the "level" feature on the Measure app to sight the top of the streetlight. Standing 20 feet away he finds an angle of elevation of 52.5 degrees.
Write and solve an equation to determine the height of the streetlight.
The height of the streetlight is 30 feet.
Let's call the height of the streetlight "h".
When the person is 16 feet from the streetlight, the length of their shadow will be 16 feet * (6 feet / h) = 96 feet / h.
When the person is 5 feet from the tip of the streetlight's shadow, the length of the streetlight's shadow will be h * (16 feet / 5 feet) = 3.2 * h.
Since the length of the person's shadow starts to appear beyond the streetlight's shadow when they are 5 feet from the tip of the streetlight's shadow, we know that 96 / h > 3.2 * h.
Solving for h, we get:
96 / h > 3.2 * h
96 > 3.2h
30 > h
So, the height of the streetlight is less than 30 feet.
To determine the exact height of the streetlight, we can use the equation:
96 / h = 3.2 * h
96 = 3.2h
30 = h
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complete question:
a six foot person walks from the base of a streetlight directly toward the tip of the shadow cast by the streetlight. when a person is 16 feet from the streetlight and 5 feet from the tip of the streetlight's shadow, the person's shadow starts to appear beyond the streetlight's shadow. what is the height of the streetlight?
A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose 3 tiles from the bag without looking. What is the probability that you choose the tiles with the letters A, B, and C? Enter your final answer as a fraction in simplest form.
There is a probability of ___ that the 3 tiles will be A, B, and C.
There is a probability of 1/17,576 that the 3 tiles will be A, B, and C
Given data ,
A bag contains 26 tiles, each with a different letter of the alphabet written on it
Now , you choose 3 tiles from the bag without looking
Let the probability be represented as P ( A )
where the probability of choosing a letter = 1/26
So , probability that you choose the tiles with the letters A, B, and C is
P ( A ) = 1/26 x 1/26 x 1/26
P ( A ) = 1/17,576
Hence , the probability is 1/17,576
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based on findings from a recent study on women's health, researchers created a 90 percent confidence interval of (0.42, 0.48) to estimate the percent of all women who do not find time to focus on their own health. based on the confidence interval, which of the following claims is not supported?
It provides a range of values within which the true percentage is likely to fall with a 90% level of confidence based on the Sample data.
Based on the confidence interval of (0.42, 0.48), the claim that is not supported is that less than 42% of all women do not find time to focus on their own health. This is because the lower bound of the interval is 0.42, indicating that at worst, 42% of all women do not find time to focus on their own health. Therefore, any claim that suggests a lower percentage is not supported by the confidence interval.
On the other hand, the confidence interval does support claims that suggest the percentage of women who do not find time to focus on their own health is at least 42% and no more than 48%. For example, a claim that states "between 42% and 48% of all women do not find time to focus on their own health" is supported by the confidence interval.
It is important to note that the confidence interval does not tell us anything about the actual percentage of women who do not find time to focus on their own health. Rather, it provides a range of values within which the true percentage is likely to fall with a 90% level of confidence based on the sample data.
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the association between the amount of money a person spends on bills per month and the amount of money the person has available to spend on entertainment is
The association between the amount of money a person spends on bills per month and the amount of money the person has available to spend on entertainment can vary greatly depending on individual circumstances.
For some people, their bills may take up a significant portion of their income, leaving them with very little discretionary spending. Others may have lower bills and more income, allowing them to spend more on entertainment.
It's important to note that there may also be other factors at play, such as a person's financial priorities and habits. For example, someone may choose to spend more on bills in order to pay off debt or save for the future, even if it means having less money for entertainment. On the other hand, someone else may prioritize entertainment spending and cut back on bills in order to afford it.
Overall, while there may be some correlation between bill spending and available entertainment funds, the relationship is complex and highly individualized. It's important for each person to assess their own financial situation and priorities in order to determine the best way to allocate their funds.
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The regular cost of a music system is $80 999 . During a sale it was sold for $69,999 . Calculate the rate of discount
Answer:
24.5%
Step-by-step explanation:
During a weekend, the manager of a mall gave away gift cards to every 80th person who visited the mall.
• On Saturday, 1,310 people visited the mall.
• On Sunday, 1,714 people visited the mall.
How many people received a gift card?
answer fast and explain pls
Answer:
37 people received a gift card over the weekend.
Step-by-step explanation:
To solve this problem, we need to find the total number of visitors who received a gift card on Saturday and Sunday separately and then add them.
For Saturday, we need to divide the total number of visitors by 80 to find how many received a gift card:
1,310 ÷ 80 = 16.375
We can't have a fraction of a person receiving a gift card, so we round down to 16. This means 16 people received a gift card on Saturday.
For Sunday, we do the same calculation:
1,714 ÷ 80 = 21.425
Again, we round down to 21. This means 21 people received a gift card on Sunday.
To find the total number of people who received a gift card, we add the number of people who received a gift card on Saturday and Sunday:
16 + 21 = 37
Therefore, a total of 37 people received a gift card over the weekend.
Answer: 404 gift cards to every person or either 202
Step-by-step explanation: because subtracting all the number you will get 404 then you have divided by 2 to get 202
Check the image..........................................................................
The combined cost of the notebooks and the pens will be; $5.5
We have been Given that Kendall bought 6 notebooks and 3 pens for a total of $27. The cost of one notebook is $1.50 more than the cost of one pen.
The two equations can be written;
6N + 3 P = 27
n = 1.5 +P
Solve the above equations by substitution method;
6(1.5 + P) + 3P = 27
9 +6p +3p = 27
9p = 18
p (pen): $2
N (notebook): $3.5
The combined cost will be;
Cost = 2 + 3.5
Cost = $5.5
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gland, a small landlocked nation, has a population of rats that is growing at a rate proportional to its size. in 2019, there were 9,325 rats in gland, and in 2022, there were 12,140. how big will the population of glandian rats be in 2031?
The predicted population of Glandian rats in 2031 will be approximately 33,290.
In the case of Gland, the population of rats is growing at a rate proportional to its size. This means that the growth can be modeled using an exponential function. Given the data from 2019 (9,325 rats) and 2022 (12,140 rats), we can find the growth rate (r) and use it to predict the population in 2031.
Let's denote the initial population as P0, the population after t years as Pt, the growth rate as r, and the time elapsed in years as t.
1. Calculate the annual growth rate:
Pt = P0 * (1 + r)^t
12,140 = 9,325 * (1 + r)^(2022-2019)
12,140 = 9,325 * (1 + r)^3
2. Solve for r:
(1 + r)^3 = 12,140 / 9,325
(1 + r)^3 ≈ 1.301
1 + r ≈ 1.091
r ≈ 0.091 or 9.1%
3. Predict the population in 2031:
P2031 = P0 * (1 + r)^(2031-2019)
P2031 = 9,325 * (1.091)^(2031-2019)
P2031 = 9,325 * (1.091)^12
P2031 ≈ 33,290 rats
So, the predicted population of Glandian rats in 2031 will be approximately 33,290.
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Will give brainliest and 50 points!!!!!!
Answer:
I'm not the best at explaining but here it is...
Step-by-step explanation:
on each side of a line, there are 2 angles. These angles match the ones on the other side of the line. So with that and what we know. We can figure it out.
m<1 is 40. M<4 is opposite of this angle witch makes it the same size. That makes m<4 alo 40.
m<3 is 140. M<2 is opposite of this angle making it the same. This makes m<2 also 140.
now we move down to the bottom 4 angles. These are the same as the top 4 making the values the same.
for a more simple view of the answers...
m<1 is 40
m<2 is 140
m<3 is 140
m<4 is 40
m<5 is 40
m<6 is 140
m<7 is 140
m<8 is 40
PLSPLSPLS WILL GIVE BRAINLY PLEASE
determine the vertical asymptotes and holes for the graph of the equation below.
x+1 / x^2-6x-7
Thee vertical asymptotes and holes for the graph of the equation are: B. Vertical asymptote, x = 7, Hole, x = -1.
What is a vertical asymptote?In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).
By critically observing the rational function shown above, we can logically deduce that its vertical asymptotes can be determined by factorizing the denominator as follows;
x² - 6x - 7 = 0
x² - 7x + x - 7 = 0
x(x - 7) + 1(x - 7) = 0
(x - 7)(x + 1) = 0
x = 7 or x = -1
Vertical asymptote, x = 7
Hole, x = -1.
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suppose that you want to construct a 95% confidence interval for estimating a population mean. how does the margin of error with a sample size of 100 compare with the margin of error with a sample size of 2500 if both samples have the same standard deviation
The margin of error is directly proportional to the sample size. As the sample size increases, the margin of error decreases.
What is sample?
In statistics, a sample refers to a subset of individuals or observations taken from a larger population. It is a representative portion of the population that is selected to gather information and make inferences about the entire population.
Given that the standard deviation is the same for both samples, with a sample size of 100 and a sample size of 2500, the margin of error will be smaller for the sample size of 2500 compared to the sample size of 100.
This means that with a larger sample size of 2500, we can expect a more precise estimation of the population mean, resulting in a narrower confidence interval. Conversely, with a smaller sample size of 100, the margin of error will be larger, resulting in a wider confidence interval and a less precise estimation of the population mean.
Therefore, the margin of error is directly proportional to the sample size. As the sample size increases, the margin of error decreases.
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in a certain town, 65% of households own a cell phone, 23% own a ipad, and 12% own both a cell phone and ipad. the probability that a randomly selected household owns neither a cell phone or ipad is
To find the probability that a randomly selected household owns neither a cell phone nor an iPad, we need to subtract the probability of owning at least one device from 1.
First, we can find the percentage of households that own at least one device: 65% own a cell phone , 23% own an iPad , 12% own both
To find the percentage that own at least one device, we add the percentages of cell phone and iPad owners and then subtract the percentage that own both: 65% + 23% - 12% = 76%
Therefore, 76% of households own at least one device.
To find the percentage of households that own neither device, we subtract 76% from 100%: 100% - 76% = 24%
So the probability that a randomly selected household owns neither a cell phone nor iPad is 24%.
In summary, the three paragraph answer is: The probability that a randomly selected household owns neither a cell phone nor iPad in a certain town is 24%. Therefore, the probability that a randomly selected household owns neither a cell phone nor an iPad is 100% - 76%, which equals 24%.
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Question
2 of 25
A teacher asked her students how many pets they own. Here are the results:
0,0,1,1,1,1,2,2,2,3,4,4,8
On a piece of paper, draw a dot plot to represent the data. Then determine
which answer choice matches the dot plot you drew.
Answer:
It's C
Step-by-step explanation:
You have two times 0 the the 2 points on 0 shows this,.....
Write the quadratic function g (x) = x² - 2x - 5 in vertex form.
Answer:
(x -1)2 = y - 4
Step-by-step explanation:
