We can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
What is differential?A differential equatiοn is an equatiοn that includes an unknοwn functiοn and its derivative. A differential equatiοn describes a relatiοnship between a functiοn and changes in the functiοn.
The given equatiοn relating weight (W) and height (h) fοr children between 5 and 13 years οld is:
ln(W) = ln(2.4) + 1.84h
We want tο estimate the change in weight when a child grοws frοm a height οf 1 m tο 1.1 m.
First, we need tο calculate the weight at h = 1 m and h = 1.1 m.
At h = 1 m, we have:
ln(W1) = ln(2.4) + 1.84(1)
ln(W1) = ln(2.4) + 1.84
ln(W1) ≈ 2.684
Sο the weight at h = 1 m is apprοximately W1 ≈ e².684 ≈ 14.66 kg.
Similarly, at h = 1.1 m, we have:
ln(W2) = ln(2.4) + 1.84(1.1)
ln(W2) = ln(2.4) + 2.024
ln(W2) ≈ 2.807
Sο the weight at h = 1.1 m is apprοximately W2 ≈ e².807 ≈ 16.59 kg.
Tο estimate the change in weight when the height increases frοm 1 m tο 1.1 m, we can use the differential οf the equatiοn:
dln(W) = 1.84dh
Using differentials, we can apprοximate the change in weight as:
dW ≈ W2 - W1
dW ≈ e².807 - e².684
dW ≈ 1.93 kg
Therefοre, we can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
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A committee of 8 people is to be chosen from 7 men and 5 women. What is the number of committee if a) the committee contains at least 3 men and at least 3 women, b) the oldest man or the oldest woman, but not both, must be included in the committee?
Answer:196 possible committees
Step-by-step explanation:
Part (a): Three cases:
Case 1: 3 men and 5 women: (7 C 3) * (5 C 5) = 35 * 1 = 35; or
Case 2: 4 men and 4 women: (7 C 4) * (5 C 4) = 35 * 5 = 175; or
Case 3: 5 men and 3 women: (7 C 5) * (5 C 3) = 21 * 10 = 210
35 + 175 + 210 = 420 possible committees
Part (b): Six cases:
Cases 1–3: Oldest man included (but not oldest woman):
Case 1: 3 men and 5 women: Not possible**; therefore, 0; or
Case 2: 4 men and 4 women: 1 * (6 C 3) * (4 C 4) = 20 * 1 = 20; or
Case 3: 5 men and 3 women: 1 * (6 C 4) * (4 C 3) = 15 * 4 = 60; or
Cases 4–6: Oldest woman included (but not oldest man):
Case 4: 3 men and 5 women: (6 C 3) * (5 C 5) = 20 * 1 = 20; or
Case 5: 4 men and 4 women: (6 C 4) * 1 * (4 C 3) = 15 * 4 = 60; or
Case 6: 5 men and 3 women: (6 C 5) * 1 * (4 C 2) = 6 * 6 = 36
0 + 20 + 60 + 20 + 60 + 36 = 196 possible committees
Can you solve this question?
m=?
b=?
The equation of the tangent line is y = -x/3 + 1/3 where
m = -1/3 and b = 1/3What is the equation of a tangent line to a curve?The equation of a tangent line to a curve is the equation of the line that touches the curve at that point and tangent to it.
To find the equation of the tangent line to the curve y = 1/(3sinx + 3cosx) at (0, 1/3), we know that the value of the tangent at that point is the derivative of the curve at that point.
so, differentiating y wiith respect to x, we have
y = 1/(3sinx + 3cosx)
= (3sinx + 3cosx)⁻¹
Let u = 3sinx + 3cosx
y = u⁻¹
dy/dx = du⁻¹/du du/dx
= -u⁻² du/dx
Now du/dx = d(3sinx + 3cosx)/dx
= d3sinx/dx + d3cosx/dx
= 3cosx - 3sinx
So, dy/dx = -u⁻² du/dx
= -(3sinx + 3cosx)⁻²(3cosx - 3sinx)
= -(3cosx - 3sinx)/3sinx + 3cosx)²
Now, at (0, 1/3)
dy/dx = -(3cosx - 3sinx)/3sinx + 3cosx)²
= -(3cos0 - 3sin0)/3sin0 + 3cos0)²
= -[3(1) - 3(0)]/[3(0) + 3(1))²
= -[3 - 0]/[0 + 3)²
= -3/3²
= -1/3
Now, the equation of a line in slope form passing through the point (x', y') is
(y - y')/(x - x') = m where m = slope
For the tangent line
m = dy/dx = -1/3, x = 0 and y = 1/3So, substituting the values of the variables into the equation we have
(y - y')/(x - x') = m
(y - 1/3)/(x - 0) = -1/3
(y - 1/3)/x = -1/3
y - 1/3 = -x/3
y = -x/3 + 1/3
Comparing this with the equation of a line in slope-intercept form y = mx + b where m = slope and b = y-intercept
m = -1/3 and b = 1/3So, the equation of the tangent line is y = -x/3 + 1/3 where
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Dosage Calculation question
To determine the number of milliliters (mLs) of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection, we can use the following formula:
How to calculate the adecuated dose of Erythromycin?To calculate the adecuated dose of Erythromycin we have to follow the following procedure:
Quantity (mLs) = (Dose x Volume) / ConcentrationWhere:
Dose = 0.4g (the ordered dose)Volume = 1 (since the dose is in grams)Concentration = 500mg/10mL (the concentration of Erythromycin sup)First, we need to convert the ordered dose from grams to milligrams (mg), as the concentration of Erythromycin sup is given in milligrams. 0.4g is equal to 400mg.
Next, we can substitute the values into the formula:
Quantity (mLs) = (400mg x 1) / (500mg/10mL)Quantity (mLs) = (400 x 1) / 50Quantity (mLs) = 8 mLsTherefore, the number of mLs of Erythromycin sup 500mg/10mL needed to administer Erythromycin 0.4g bid for infection is 8 mLs. It is important to note that the medication should be administered as prescribed by a healthcare provider, and the patient should complete the entire course of treatment, even if symptoms improve.
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The daily high temperatures, in degrees Fahrenheit, of Des Moines for one week were: Day Temperature (in Fahrenheit) Monday 64.5 Tuesday 64 Wednesday 66.5 Thursday 64 Friday 62.5 Saturday 61 Sunday 63 Using the data above, what is the standard error of the sample mean? Answer choices are rounded to the hundredths place.
Answer:0.65
Step-by-step explanation:
The standard error of the sample mean is approximately 0.682, rounded to the hundredths place.
To calculate the standard error of the sample mean, we need to find the sample mean and the standard deviation of the data. Then we can divide the standard deviation by the square root of the sample size.
First, let's calculate the sample mean:
Mean = (64.5 + 64 + 66.5 + 64 + 62.5 + 61 + 63) / 7 = 64.14
Next, let's calculate the standard deviation. We will use the sample formula for standard deviation (Bessel's correction):
Calculate the squared differences from the mean for each temperature:
(64.5 - 64.14)² = 0.1904
(64 - 64.14)² = 0.0204
(66.5 - 64.14)² = 5.5376
(64 - 64.14)² = 0.0204
(62.5 - 64.14)² = 2.6836
(61 - 64.14)² = 9.8324
(63 - 64.14)² = 1.2696
Calculate the sum of the squared differences:
Sum = 0.1904 + 0.0204 + 5.5376 + 0.0204 + 2.6836 + 9.8324 + 1.2696 = 19.5544
Calculate the variance:
Variance = Sum / (n - 1) = 19.5544 / (7 - 1) = 3.25907
Calculate the standard deviation:
Standard Deviation = sqrt(Variance) = sqrt(3.25907) = 1.80597
Finally, let's calculate the standard error of the sample mean:
Standard Error = Standard Deviation / sqrt(n) = 1.80597 / sqrt(7) ≈ 0.682
Therefore, the standard error of the sample mean is approximately 0.682, rounded to the hundredths place.
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Eric is planning an event at a hotel. Let g stand for the number of Eric’s guests. The two expressions represent the difference the cost of the rooms. Expression 1: (326 + 37g) - (287+ 23g). Expression 2: 38+ 14g. What can you tell about expression 2 and expression 1?
Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.
Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for Eric's guests. The first part of the expression (326 + 37g) represents the cost of the hotel room for all g guests, while the second part of the expression (287 + 23g) represents the cost of food and beverage for all g guests. To calculate the total cost of the hotel room and food and beverage, we can use the following formula: (326 + 37g) - (287 + 23g) = 39 + 14g.Expression 2, on the other hand, represents the difference in cost between the hotel room and the cost of food and beverage for a single guest. The first part of the expression (38 + 14g) represents the cost of the hotel room for one guest, while the second part of the expression (287 + 23g) represents the cost of food and beverage for one guest. To calculate the total cost of the hotel room and food and beverage for one guest, we can use the following formula: 38 + 14g.In conclusion, Expression 1 represents the difference in cost between the hotel room and the cost of food and beverage for all g guests, while Expression 2 represents the difference in cost between the hotel room and the cost of food and beverage for a single guest.
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Tanya buys 12 water bottles.
Of those bottles, 5 hold 300 milliliters each and 7 hold 1.5 liters each.
How much water, in liters, does Tanya buy?
Answer:
12 L 500 mL
Step-by-step explanation:
Question content area top Part 1 Find the surface area of the prism. Question content area bottom Part 1 The surface area is enter your response here .ar prism. The base of the prism is an isosceles triangle. 41 40 cm The surface area is cm2
The surface area of the given triangular prism having an isosceles triangle base with sides 40,41 and 43 cm, is 2274 cm².
What is area?Area is a measure of the size of a two-dimensional shape or surface, such as a rectangle, triangle, circle, or any other shape that has length and width. It is usually expressed in square units, such as square meters, square centimeters, square feet, or square inches.
To find the surface area of a triangular prism, we need to find the area of each face of the prism and add them up.
The triangular base of the prism is an isosceles triangle with sides of 40 cm, 41 cm, and 43 cm.We may use Heron's formula to determine the area of this triangle:
s = (40 + 41 + 43) / 2 = 62
A = √(s(s-40)(s-41)(s-43)) = √(622221*19) = 798
Therefore, the area of the triangular base is 798 cm².
The height of the prism is given as 18 cm, which is also the length of the rectangular side of the prism.
The two other faces of the prism are rectangles with lengths equal to the base of the triangle (41 cm), and widths equal to the height of the prism (18 cm). The area of each rectangle is:
A = lw = 4118 = 738
Therefore, the area of both rectangles is 2*738 = 1476 cm².
The total surface area of the prism is the sum of the area of the base and the area of both rectangular sides:
Total surface area = Area of base + 2*(Area of rectangle)
Total surface area = 798 + 2*738
Total surface area = 2274 cm².
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In a bag there are 80 beads. There are 35 yellow beads and 17 red beads. The rest of the beads are white. Work out what fraction of the beads are white. Give your answer in the simplest form.
Answer: 7/20
Step-by-step explanation:
35+17=52
80-52=28
28/80=7/20
Answer:
28
Step-by-step explanation:
35+17=52
80-52=28
so your answer is 28
Solve the following system of equations by linear combination:
3x – y = 7
x + y = 5
Answer:
x=3, y=2
Step-by-step explanation:
First Add both equations
3x-y=7 ---1
x+y=5 ---2
----------
so we get, 4x=12
so x=3
Now plug x back into equation 2 so we get y=2
Step-by-step explanation:
that means we optionally multiply one or both equations with some factors, so that one variable term has the same coefficient in both equations but with different signs.
and then we add both equations giving us one equation in the other variable, which we can solve.
and then we use that with any of the original equations to solve for the first variable.
in this case we don't need the multiplication step, as the terms in y have already the same coefficient (1) with different signs.
so, we add both equations
3x - y = 7
+ x + y = 5
------------------
4x 0 = 12
4x = 12
x = 12/4 = 3
x + y = 5
3 + y = 5
y = 5 - 3 = 2
According to komonews.com, the chances it will rain on any day in the 1st week of January in Seattle is about 0.614.
a) What is the probability that it will rain on January 1st?
b) What is the probability that it will rain for the first time in the New Year on January 3rd?
c) What is the probability that the people of Seattle get to wait at least 3 days until it rains for the first time in the New Year?
d) How many days, on average, do they wait for the first day of rain in the New Year?
e) If X = the number of days until it rains for the first time, is X binomial or geometric or neither? Explain.
(a) The probability of rain on January 1st is 0.614. (b) The probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083. (c) the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053. (d) They wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days. (e) The distribution of X is a geometric distribution.
a) The probability that it will rain on January 1st can be estimated using the information provided by komonews.com, which states that the chances of rain on any day in the first week of January in Seattle is about 0.614. Assuming that the probability of rain is constant across all days of the week, the probability of rain on January 1st is also 0.614.
b) The probability that it will rain for the first time in the New Year on January 3rd can be calculated by considering the probability of no rain for the first two days, followed by rain on the third day. The probability of no rain for the first two days is [tex](1-0.614)^2[/tex] = 0.136, and the probability of rain on the third day is 0.614. Therefore, the probability of rain for the first time in the New Year on January 3rd is 0.136*0.614 = 0.083.
c) The probability that the people of Seattle get to wait at least 3 days until it rains for the first time in the New Year can be calculated by considering the probability of no rain for the first three days. The probability of no rain for the first three days is [tex](1-0.614)^3[/tex] = 0.053. Therefore, the probability that people of Seattle get to wait at least 3 days until it rains for the first time in the New Year is 0.053.
d) The expected value or average of the number of days people in Seattle wait for the first day of rain in the New Year can be calculated by using the formula E(X) = 1/p, where p is the probability of rain on any given day. Therefore, the expected value or average number of days people in Seattle wait for the first day of rain in the New Year is 1/0.614 ≈ 1.63 days.
e) The number of days until it rains for the first time in the New Year, X, is a geometric random variable since it represents the number of trials until the first success (rain). The probability of success (rain) remains constant over time, and the trials (days) are independent of each other. Therefore, the distribution of X is a geometric distribution.
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lucy has 18 puzzles each with 250 pieces how many pieces are there in all (also its for 50 pts)
Answer:
4500
Step-by-step explanation:
250 x 18 = 4500
Stanley is throwing a party to watch the Super Bowl and is buying snacks for his
guests. He plans to buy pizzas (x) for $5 each and sub sandwiches (y) for $6.50
each. He plans to spend $130 on food. This situation can be represented by the
standard form equation: 5x + 6.50y = 130
Algebraically find the x-intercept and describe the meaning of the x-intercept in
the problem situation.
O The x-intercept is 26. It means that there were 26 sub sandwiches and 0 pizzas purchased.
O The pizza cost $26.
O The x-intercept is 5. It means that there were 5 pizzas and 0 sub sandwiches purchased.
O The x-intercept is 5. It means that there were 5 sub sandwiches and 0 pizzas purchased.
O The x-intercept is 6.50. It means that there were 6.50 sub sandwiches and 0 pizzas purchased.
O The x-intercept is 26. It means that there were 26 pizzas and 0 sub sandwiches purchased.
O The x-intercept is 6.50. It means that there were 6.50 pizzas and 0 sub sandwiches purchased
O The x-intercept is 20. It means that there were 20 pizzas and 0 sub sandwiches purchased.
O The x-intercept is 20. It means that there were 20 sub sandwiches and 0 pizzas purchased.
The x-intercept is 26. This means that if Stanley were to buy only pizzas (and no sub sandwiches), he would need to buy 26 pizzas to spend exactly $130 on food.
What do you mean by Algebraic expression ?
An algebraic expression is a mathematical phrase that contains one or more variables, numbers, and operations such as addition, subtraction, multiplication, division, and exponentiation.
The given equation is 5x + 6.50y = 130. To find the x-intercept, we set y = 0 and solve for x.
5x + 6.50(0) = 130
5x = 130
x = 26
Therefore, the x-intercept is 26. This means that if Stanley were to buy only pizzas (and no sub sandwiches), he would need to buy 26 pizzas to spend exactly $130 on food.
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Part C
Now you will attempt to copy your original triangle using only two of its sides and the included angle:
Using point E as the center, draw a circle with a radius equal to the length of
, which you calculated in part B.
Using point E as the vertex and
as one side of the angle, create an angle that is equal to the measure of
. Draw ray
.
Locate the intersection of the ray and the circle, and label the point F.
Complete
by drawing a polygon through points D, E, and F.
Take a screenshot of your results, save it, and insert the image below.
We want to copy the original triangle using only two of its sides and the included angle. To do this, we'll create a new triangle with the same side lengths and angle measures as the original triangle.
To copy a triangle using two of its sides and the included angle, follow these steps:
Using point E as the center, draw a circle with a radius equal to the length of side DE.Using point E as the vertex and side DE as one side of the angle, create an angle that is equal to the measure of angle D.Draw ray EF that extends from point E through the angle you created in step 2.Locate the intersection of ray EF and the circle you drew in step 1, and label the point of intersection F.Complete the triangle DEF by drawing a line segment that connects points D, E, and F.Learn more about vertex :
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If you roll a six sided die 300 times how many times would you expect to get a five
Answer:
50, because yes
2. In March, Sunshine Kindergarten was given a sum of $2000. It spent 10% of the sum given on books, 70% on food and the rest on cleaning services. In April the sum given was reduced. The kindergarten spent the same amount of money on books and reduced its spending of food by $240. It spent the remaining 20% of the sum given in April on cleaning services. By what percentage was the sum given to the kindergarten reduced?
The sum given to the kindergarten was reduced by 15%.
How to solve this problemLet's first find out how much money the kindergarten spent in March:
Books: 10% of $2000 = 0.1 x $2000 = $200Food: 70% of $2000 = 0.7 x $2000 = $1400Cleaning services: $2000 - $200 - $1400 = $400So, in April, the kindergarten spent the same amount on books, which was $200. It also reduced its spending on food by $240, which means it spent:
Food: $1400 - $240 = $1160
The remaining 20% of the sum given in April was spent on cleaning services, which means:
Cleaning services: 20% of sum given in April = 0.2 x $x (where x is the sum given in April)
We can set up an equation based on the above information:
$200 + $1160 + 0.2x = x
Simplifying and solving for "x":
$1360 + 0.2x = x
0.8x = $1360
x = $1700
Therefore, the sum given to the kindergarten in April was $1700, which means it was reduced by:
($2000 - $1700) / $2000 x 100% = 15%
So, the sum given to the kindergarten was reduced by 15%.
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a group of teachers and students go on a school trip. for every teachers on the trip, there are four male students and five female students
if there are 30 female students on the trip, how many male students are there ?
The number of male students that went on the school trip given that there are 30 female students is 24
Calculating how many male students are there?Given that we have the following statement:
Every teacher is assigned 4 male students and 5 female students
The above statement means that we have the following ratio
Ratio = Male : Female
So, we have the following equation
Male : Female = 4 : 5
When the number of female students is 30, we have the following
Male : 30 = 4 : 5
Express as fraction
Male/30 = 4/5
So, we have
Male = 4/5 * 30
Evaluate
Male = 24
Hence, the number of male students is 24
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cart a with mass m travels in the x direction with a speed of 4 m/s. it collides with car t b, which has mass 3m and is initially at rest. after the collision, cart a moves in the -x direction and cart b moves in the x direction. assume that the collision was perfectly elastic
After the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s.
In a perfectly elastic collision, the total momentum of the system is conserved, as well as the total kinetic energy. This means that the sum of the momenta of the carts before the collision is equal to the sum of the momenta after the collision. In this case, since cart b is initially at rest, its initial momentum is zero.
We can use conservation of momentum to determine the final velocities of the carts. Let the velocity of cart b after the collision be v, then the velocity of cart a after the collision is -4 m/s. The momentum of cart a before the collision is m(4 m/s) = 4m, and the momentum of cart b after the collision is 3mv.
Using conservation of momentum, we have:
m(4 m/s) + 0 = m(-4 m/s) + 3mv
Simplifying this equation, we get:
8m = 3mv + 4m
Dividing both sides by 3m, we get:
v = (8/3) - (4/3)v
Solving for v, we get:
v = 2 m/s
So after the collision, cart a moves in the negative x direction with a speed of 4 m/s, and cart b moves in the positive x direction with a speed of 2 m/s. We can verify that this satisfies conservation of momentum:
m(4 m/s) + 0 = m(-4 m/s) + 3m(2 m/s)
4m = 4m
This result shows that in a perfectly elastic collision, even though the carts exchange momentum, the total momentum of the system is conserved.
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Solve the equation for solutions in interval [0 , 2pi)
Sin(x/2)= square root 2 - sin (x/2)
Answer: We can simplify the given equation as follows:
sin(x/2) = sqrt(2) - sin(x/2)
2sin(x/2) = sqrt(2)
sin(x/2) = sqrt(2)/2
x/2 = pi/4 or x/2 = 3pi/4 (using the standard angles for sin)
x = pi/2 or x = 3pi/2
However, we need to check if these solutions satisfy the original equation since we simplified it along the way.
For x = pi/2, we have:
sin(pi/4) = sqrt(2) - sin(pi/4)
sqrt(2)/2 = sqrt(2) - sqrt(2)/2
sqrt(2)/2 = sqrt(2)/2
This is true, so x = pi/2 is a solution.
For x = 3pi/2, we have:
sin(3pi/4) = sqrt(2) - sin(3pi/4)
-sqrt(2)/2 = sqrt(2) - (-sqrt(2)/2)
-sqrt(2)/2 = sqrt(2)/2
This is not true, so x = 3pi/2 is not a solution.
Therefore, the only solution in the interval [0, 2pi) is x = pi/2.
Step-by-step explanation:
Help me out please and thank you
As a result, whereas the latter two expressions are not polynomials, the first two and last one are polynomial.
Define coefficientA coefficient in mathematics is a multiplicative factor in a polynomial term, a series term, or any expression . For instance, the first two terms of the polynomial with the variables x and y have coefficients of 7 and -3, respectively. The constant coefficient is the third term of 1.5.
Define polynomial?An expression made up of variables and coefficients and utilizing solely the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables is referred to as a polynomial.
Let's examine each phrase separately:
Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "3X² -5x⁴+2x-12" is a polynomial.
Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x⁵-5x⁴+4x³-3x²+2x-1" is a polynomial.
- Since it contains negative exponents of variables, which are not permitted in polynomials, "x⁻⁵-5x⁻⁴+4x⁻³+2x⁻¹ - 1" is not a polynomial.
- Because it contains division, which is not permitted in polynomials, "4/x⁴+3/x³-2/x²-1" is not a polynomial.
-Because it only uses addition, subtraction, multiplication, and non-negative integer exponents of variables, "x³-7x²+9x-5x⁴-20" is a polynomial.
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The equation 24b = t is used to find b, the cost of 1 bottle of water when sold in a 24‐pack case with a case price of t dollars. What is the cost of 1 bottle of water when the case price is $7.50?
The cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents.
The given equation is 24b = t, where b is the cost of one bottle of water and t is the price of a case of 24 bottles.
We are given that the price of the case is $7.50. Substituting this value in the equation, we get:
24b = 7.50
To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides by 24:
b = 7.50/24
Simplifying this expression, we get:
b = 0.3125
Therefore, the cost of 1 bottle of water when sold in a 24-pack case with a case price of $7.50 is $0.3125 or 31.25 cents. In other words, if you were to buy a case of 24 bottles of water for $7.50, each bottle of water would cost you about 31.25 cents.
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what is the volume of this sphere
use = 3.14 and round your answer to the nearest hundredth 7ft
Volume of sphere with radius r = 7 m is [tex]v_1=1,436.026 \ \text{m}^3[/tex].
Step-by-step explanation:
We know that volume of sphere [tex]=\dfrac{4}{3}\pi r^3[/tex] given that [tex]\pi =3.14,\ r=7 \ \text{ft}[/tex].
volume of sphere [tex]=\dfrac{4}{3}\pi r^3=v_1[/tex]
[tex]\implies v_1=\dfrac{4}{3}\pi r^3[/tex]
[tex]\implies v_1=\dfrac{4}{3}\pi(7)^3[/tex]
[tex]\implies v_1=\dfrac{4}{3}\pi (343)[/tex]
[tex]\implies v_1=\dfrac{4}{3}(3.14)(343)[/tex]
[tex]\implies v_1=1,436.026 \ \text{m}^3[/tex]
∴ Volume of sphere with radius r = 7 m is [tex]v_1=1,436.026 \ \text{m}^3[/tex].
Patients in a room who undergo heart surgery, infection after surgery is 9%. The length of hospital stay for patients who develop an infection following heart surgery can be modeled by a normal distribution with a mean of 6 days and a standard deviation of 2 days.
What is the probability that an infected patient’s length of stay will be greater
than 7 days?
What is the 70th percentile in stay length for a patient given that they have a
post-operative infection?
What is the probability that the average stay length of the next 2 infected patients
is less than than 5.5 days?
What is the probability that a patient is infected and then stays for 3 to 4 days?
1. The probability that an infected patient’s length of stay will be greater than 7 days is 0.3085.
2. The 70th percentile in stay length for a patient given that they have a
post-operative infection is 7.04.
3. The probability that the average stay length of the next 2 infected patients is less than 5.5 days is 0.3632.
4. The probability that a patient is infected and then stays for 3 to 4 days is 0.1587.
How to find the probability?1. Probability of an infected patient staying more than 7 days:
We can standardize the normal distribution using the formula: Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.
So, Z = (7 - 6) / 2 = 0.5.
Using a standard normal distribution table or calculator, we can find the probability that a patient will stay longer than 7 days as:
P(Z > 0.5) = 0.3085.
2. The 70th percentile in stay length for an infected patient:
We can use the inverse standard normal distribution function to find the Z-score corresponding to the 70th percentile.
Using a standard normal distribution table or calculator, we find that the Z-score corresponding to the 70th percentile is approximately 0.52.
So, Z = 0.52 = (X - 6) / 2.
Solving for X, we get:
X = 6 + 0.52 * 2 = 7.04.
3. Probability that the average stay length of the next 2 infected patients is less than 5.5 days:
The average length of stay of 2 infected patients can be modeled by a normal distribution with a mean of 6 days (the mean of a single infected patient's length of stay) and a standard deviation of σ/√2, where σ is the standard deviation of the length of stay of a single infected patient.
So, the standard deviation of the average length of stay of 2 infected patients is:
σ/√2 = 2/√2 = 1.414 days.
Using the standardized normal distribution formula, we get:
Z = (5.5 - 6) / 1.414 = -0.3536.
Using a standard normal distribution table or calculator, we can find the probability that the average stay length of the next 2 infected patients will be less than 5.5 days as:
P(Z < -0.3536) = 0.3632.
4. Probability that a patient is infected and then stays for 3 to 4 days:
We can standardize the normal distribution as before using the formula:
Z = (X - μ) / σ, where X is the length of stay, μ is the mean length of stay, and σ is the standard deviation of the length of stay.
For X = 3 days, Z = (3 - 6) / 2 = -1.5.
For X = 4 days, Z = (4 - 6) / 2 = -1.
Using a standard normal distribution table or calculator, we can find the probability that a patient is infected and then stays for 3 to 4 days as:
P(-1.5 < Z < -1) = P(Z < -1) - P(Z < -1.5) = 0.1587
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The area of the parallelogram
Answer:
28
Step-by-step explanation:
a = b * h
a = 4 * 7 = 28
Amy and laura recorded the average gad mileage of their vehicles each week for four weeks. What can be concluded about the relationships shown in the graph and table?
It would be important to have more information about the driving conditions, types of vehicles, and other factors that could influence gas mileage in order to draw more conclusive insights from this data.
Based on the graph provided, it appears that both Amy and Laura's average gas mileage fluctuated over the course of the four weeks. Amy's average gas mileage started at around 30 miles per gallon (mpg), decreased in week 2, and then increased again in weeks 3 and 4. Laura's average gas mileage started at around 25 mpg, increased in week 2, decreased in week 3, and then increased again in week 4.
However, one could make some tentative observations. For example, Amy's average gas mileage appears to be consistently higher than Laura's over the four-week period, and both of their average gas mileage values appear to be somewhat volatile, with significant changes occurring from week to week.
Overall, it would be important to have more information about the driving conditions, types of vehicles, and other factors that could influence gas mileage in order to draw more conclusive insights from this data.
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3 1/5 divided by 1 7/9 in simplest form
Answer:
To divide two mixed numbers, we first need to convert them into improper fractions.
Converting 3 1/5 to an improper fraction:
3 1/5 = (3 × 5 + 1) / 5 = 16/5
Converting 1 7/9 to an improper fraction:
1 7/9 = (1 × 9 + 7) / 9 = 16/9
Now we can rewrite the division problem as a multiplication problem by taking the reciprocal of the second fraction:
16/5 ÷ 16/9 = 16/5 × 9/16
We can simplify the expression by canceling out the common factor of 16 in the numerator and denominator:
(16 ÷ 16) / (5 ÷ 1) × (9 ÷ 16) / (1 ÷ 1) = 1 / 1 × 9 / 16 = 9/16
Therefore, 3 1/5 ÷ 1 7/9 = 9/16 in simplest form.
Step-by-step explanation:
Solution of expression 3 1/5 divided by 1 7/9 are, 9/5
We have,
To find 3 1/5 divided by 1 7/9 in simplest form.
Now, We can divide,
3 1/5 divided by 1 7/9
3 1/5 ÷ 1 7/9
16/5 ÷ 16/9
16 / 5 × 9/16
9 / 5
Therefore, Solution of expression are, 9/5
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1. The distance around Heather's bedroom is 44 feet.
The width of the room is 10 feet, what is the length of the room?
What is the probability that the code number for a new customer will begin with the number 7?
Answer:
Cannot be determined
Step-by-step explanation:
Without any additional information, we cannot accurately determine the probability that the code number for a new customer will begin with the number 7.
To calculate the probability, we would need to know the total number of possible code numbers that can be assigned to new customers and how many of those code numbers start with the number 7. If we have that information, we can calculate the probability as follows:
Probability = Number of code numbers starting with 7 / Total number of possible code numbers
For example, if there are 1000 possible code numbers and 50 of them start with the number 7, the probability of a new customer's code number starting with 7 would be:
Probability = 50 / 1000
Probability = 0.05 or 5%
5x + 1 over 4 y2 What is the value of the expression above when x = 3 and y = 2?
The value of the expression [tex]5x + 1 / 4 y^2\\[/tex] when x = 3 and y = 2 is 16.
What is an example of a word expression?When someone is experiencing "joy," for instance, the user wants them to feel shocked or very happy. The user will be positively impression if you convey surprise or extreme joy. When someone is experiencing "fright," they want them to feel extremely saddened or disgusted.
What are the names of expressive words?A phraseme is a multi-word , multi-morphemic statement whose components contain at least a single word that is selectionally limited. It is also known as a set phrase, persist longer, idiom phrase, multiword expression, or idiom.
To evaluate the expression [tex]5x + 1 / 4 y^2[/tex] when x = 3 and y = 2, we substitute x = 3 and y = 2 into the expression and simplify as follows:
[tex]5x + 1/4 y^2 = 5(3) + 1/4 (2)^2[/tex](substitute x = 3 and y = 2)
= 15 + 1/4(4)
= 15 + 1
= 16
Therefore, the value of the expression [tex]5x + 1 / 4 y^2[/tex]when x = 3 and y = 2 is 16.
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question
What is the value of the expression[tex]5x + 1 /4 y^2[/tex] when x = 3 and y = 2?
The height of an athlete was measured to be 165.5 cm. If the absolute error was 0.1, find the lower and the upper limits which the measurement lie.)
Answer:
The lower limit and upper limits of the athlete's height can be calculated by subtracting and adding the absolute error, respectively.
Lower Limit = 165.5 cm - 0.1 cm = 165.4 cm
Upper Limit = 165.5 cm + 0.1 cm = 165.6 cm
Therefore, the athlete's height lies between 165.4 cm and 165.6 cm, inclusive.
+
MONDAY
Use numbers 0-9 so that each problem
has the same sum.
1 7 1
+
17 1
Answer: See below
Step-by-step explanation:
To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:
Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.
Then, the addition problem becomes:
A B C
D E F
We know that the sum of each column must be the same, so:
C + F = 10 + B
B + E = 10 + A
We can rewrite these equations as:
C - B + F = 10
B - A + E = 10
Since we are given that the sum of the two numbers is the same, we know that:
C + F + D + E = 1112
We can substitute C and F in terms of A and B using the equations above:
C = 10 + B - F
F = 10 + C - B
Substituting these expressions into the equation for the sum, we get:
10 + B - F + C + D + E = 1112
Simplifying this equation, we get:
B - F + C + D + E = 1102
Now we can substitute in the expressions for C and F in terms of A and B:
B - (10 + B - F) + (10 + C - B) + D + E = 1102
Simplifying and canceling out terms, we get:
F - C - D - E = -92
We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.
Trying different values for A and D, we find that A = 2 and D = 3 works:
A B C
D E F
2 7 9
1 7 3
The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:
2 7 9
1 7 3
4 5 2