Tape diagrams are rectangular models used for multiplication and division model.
The equation is 8n = 32, and the value of n is 4.
The given parameters are:
\(Students = 32\)
\(Groups = 8\)
So, the equation is
\(Students = Groups \times n\)
Where n is the number of student in each group.
So, we have:
\(32 = 8\times n\)
\(32 = 8n\)
Divide both sides by 8
\(4 = n\)
Rewrite as:
\(n = 4\)
See attachment for the tape diagram
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A.N.'s burns are being treated by the open method with topical application of silver sulfadiazine (Silvadene). In caring for A.N., which interventions will you perform?
a. Shave all hair within the wound beds
b. Maintain the room temperature at 85 degree F (29.4 degree C)
c. Use clean technique when changing A.N.'s dressings
d. Monitor the CBC and WBC with differential frequently
e. Do not allow her to bathe for the initial 72 hours after injury
f. Apply a 1/16-inch film of medication, covering entire burn
In caring for A.N., we will perform a number of interventions. The first is to shave all hair within the wound beds, to minimize the risk of infection and reduce the amount of bacteria around the wound.
We will also maintain the room temperature at 85 degrees Fahrenheit (29.4 degrees Celsius) to ensure a warm and comfortable environment for A.N. when she is receiving treatment. We will also use clean technique when changing A.N.'s dressings to reduce the risk of infection. Additionally, we will monitor the CBC and WBC with differential frequently to ensure A.N. is receiving adequate treatment.
Furthermore, we will not allow her to bathe for the initial 72 hours after injury to reduce the chances of infection. Lastly, we will apply a 1/16-inch film of medication, covering the entire burn, to help aid in the healing process and reduce the risk of infection.
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We make 72 cookies and 18 cookies are eaten. What fraction represents the portion of the whole batch that remains?
Answer:
1/4
Step-by-step explanation:
Create a chart 18 over 72 and x over 100
Now we multiply 18 by 100 to get 1800
We take that 1800 and divide it by 72 to get 25/100
We can simplify this to 1/4
A public opinion poll in Ohio wants to determine whether registered voters support a recent school bond. They select a simple random sample of 50
registered voters from each county in the state and ask whether they approve or disapprove of the measure.
What is the population
What is the sample
Answer:
i hope this is what you are looking for
The population is all registered voters in Ohio, and the sample is the 50 registered voters from each county in Ohio that were randomly selected
Explanation:In this case, the population refers to all registered voters in Ohio, as they are the total group being studied. The sample is the subset of the population that is being evaluated to represent the entire population. In this question, the sample is the 50 registered voters from each county in Ohio that were randomly selected for the public opinion poll.
This scenario is an example of statistical sampling, a technique used in statistics to analyze a subset of a population and extrapolate insights or findings to the entire population.
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A line passes through the given points. Write an equation for the line in point-slope form. Then rewrite the equation in slope-intercept form. (1 , 1/2), (3, 2)
A) y + 1/2 = 3/4 ( x + 1 ) ; y = 3/4x + 1/4
B) y − 1/2 = 3 ( x − 1 ) ; y = 3x − 1/4
C) y − 1/2 = 3/4 ( x − 1 ) ; y = 3/4x − 1/4
Answer: C
Step-by-step explanation:
Find Slope first
\(m=\frac{y2-y1}{x2-x1}\)
\(m=\frac{2-.5}{3-1}\)
\(m=1.5/2\\m=3/4\)
Slope is 3/4
Chose a point to put in point slope form
(1,1/2)
y − y1 = m(x − x1)
\(y-\frac{1}{2} =\frac{3}{4} (x-1)\)
\(y-\frac{1}{2} = \frac{3}{4}x-\frac{3}{4}\)
add 1/2 to both side
Find The Area Of This Shape.
Answer:
34.65 mi²
Step-by-step explanation:
Area of parallelogramam = b · h
b = 6.3 mi
h = 5.5 mi
Let's solve
6.3 · 5.5 = 34.65 mi²
So, the area of the shape is 34.65 mi²
Inverses, contrapositives and converses. Below are examples of mathematical statements you’ll encounter in this class. Assume x, y, a, b, c are integers.
If the difference x − y is even then x and y are also even.
If a divides b or a divides c then a divides bc. (Note: a divides b means that the fraction b/a is an integer. For example, 3 divides 6 but 3 does not divide 7.)
If x2 ≥ 100 and x ≥ 0, then x ≥ 10.
(i) (9 pts.) State the inverse, contrapositive and converse of each statement above. When possible, avoid using the word "not." Instead, replace "not even" with "odd", etc.
Recall that for P → Q,
contrapositive: ¬Q →¬P
converse: Q → P
inverse: ¬(P → Q) = ¬(¬P ∨ Q) = P ∧ ¬Q
(ii) (3 pts.) Then indicate their truth values. Thus, for each statement you must determine whether the statement itself, its inverse, contrapositive and converse are true or false. That’s four true/false answers for each statement.
1. Statement: True
Inverse: True
Contrapositive: True
Converse: True
2. Statement: True
Inverse: True
Contrapositive: True
Converse: True
3. Statement: True
Inverse: True
Contrapositive: True
Converse: True
(i)
Statement: If the difference x - y is even, then x and y are also even.
Inverse: If x and y are not even, then the difference x - y is not even.
Contrapositive: If x and y are not even, then the difference x - y is not even.
Converse: If x and y are even, then the difference x - y is even.
Statement: If a divides b or a divides c, then a divides bc.
Inverse: If a does not divide b and a does not divide c, then a does not divide bc.
Contrapositive: If a does not divide b and a does not divide c, then a does not divide bc.
Converse: If a divides bc, then a divides b or a divides c.
Statement: If x^2 ≥ 100 and x ≥ 0, then x ≥ 10.
Inverse: If x^2 < 100 or x < 0, then x < 10.
Contrapositive: If x^2 < 100 or x < 0, then x < 10.
Converse: If x ≥ 10, then x^2 ≥ 100.
(ii)
For each statement, we need to evaluate the truth values of the statement, inverse, contrapositive, and converse.
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
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PLEASEEEE HELPPPPPPPP ASAPPPPPP
Answer:
y=2.75x+3
Step-by-step explanation:
$2.75 per sandwich (coefficient)
Solid $3 fee (y-intercept)
y=mx+b ---> y=2.75x+3
write the smallest 4 digit number and express it in terms of its prime number
Answer:
The smallest 4-digit whole number is 1000, and its prime factors are 2 and 5
Step-by-step explanation:
Lily is 22 years old. Monica is 3 years older than Lily and 2 years younger than Christine. How old is Christine
Answer:
she would be 20 years old if lily is 22
a 3x3x3 cube is made of 27 small cubes of which one is blue and 26 are white. the surface of the cube is formed by 3x3 squares. the small cubes are arranged in such a way that the surface is as much white as possible. what fraction of the surface of the cube is white
The fraction of the surface of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-\(\frac{13}{27}\)= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer
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The fraction of the surface area of the cube which is white is 14/27
Given 27 cubes of 1 centimetre are conjoined to form a large cube of 3x3x3
To maximise the value of the surface area, in this case, taken as white, other than the cube in the centre, the rest of the cubes must have their white surface area exposed.
• Total Number of cubes where white surface area is exposed is = 27 – 1 = 26
Although, on each surface of the 3x3x3 cube, there are 9 smaller cube surfaces, and there will be a total of 6 surfaces for the bigger cube.
• Total number of cube surfaces exposed in blue = 9 * 6 = 54
• Therefore, the greatest fraction in blue= 26/54 = 13/27
Therefore the fraction of the surface of the cube is white is = 1-(13/27)
= 14/27
The fraction of the surface of the cube which is white is 14/27 is the answer.
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Your children are 3 and 5 years old now, and you want an inexpensive policy that covers your family at least until the youngest is 22. based on the given information, what is the best policy to buy? a. whole life policy b. 10-year term policy c. 15-year term policy d. 20-year term policy please select the best answer from the choices provided a b c d
Subtraction is a mathematical operation. The best policy to buy is a 20-year term policy.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Since we want the policy to last till the younger child is 22 years. And the present age of the younger child is 3 years. Therefore, the period for which the policy must work is 19 years (22-3).
Therefore, the best policy to buy is a 20-year term policy.
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v²=u²+2as. If u = 12, a = -3 and s=18, Find v
Answer:
v=6
Step-by-step explanation:
v²=u²+2as
v²=12²+2(-3)(18)
v²=144-108
v²=30
v=6
Value of the expression 6x-2y 5y when x=10 and y=3.
Answer:
-150
Step-by-step explanation:
Multiply & Divide left to right
\(60-2*35*3\)
Once again Multiply & Divide
\(60-210\)
Add & Subtract
Final Answer: \(-150\)
The area of a square room is 125 square feet. To the nearest foot, what is the length of one side of the room?
Answer:
Side = \(5\sqrt5\ \text{feet}\)
Step-by-step explanation:
Given that,
Area of a square room is 125 square feet
We need to find the length of one side of the room.
The area of a square shaped room is given by :
\(A=x^2\)
Where, x is side of the square room
\(x=\sqrt{A} \\\\x=\sqrt{125}\\\\x=\sqrt{5\times 5\times 5}\\\\x=5\sqrt5\ \text{feet}\)
So, the side of the room is \(5\sqrt5\ \text{feet}\).
3.95/12 full explanation please. I keep getting .32 , even though its .33
Answer: 0.33
Step-by-step explanation:
3.95/12=0.3291666666...
You then use the 9 to round UP to 0.33
As a sample size is increased, which of the following statements best describes the change in the standard error of the sample mean and the size of the confidence interval for the true mean?
A) The standard error decreases and the confidence interval narrows.
B The confidence interval widens while the standard error decreases.
C) The standard error increases while the confidence interval narrows.
The correct answer is: A) The standard error decreases and the confidence interval narrows.
As the sample size increases, the standard error of the sample mean decreases. The standard error measures the variability or spread of the sample means around the true population mean. With a larger sample size, there is more information available, which leads to a more precise estimate of the true population mean. Consequently, the standard error decreases.
Moreover, with a larger sample size, the confidence interval for the true mean becomes narrower. The confidence interval represents the range within which we are confident that the true population mean lies. A larger sample size provides more reliable and precise estimates, reducing the uncertainty associated with the estimate of the population mean. Consequently, the confidence interval becomes narrower.
Therefore, statement A is the most accurate description of the change in the standard error of the sample mean and the size of the confidence interval for the true mean as the sample size increases.
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Find and classify the critical points of f(x,y)=8r³+ y² + 6xy
The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point
To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.
Taking the partial derivative with respect to x, we have:
∂f/∂x = 24x^2 + 6y = 0.
Taking the partial derivative with respect to y, we have:
∂f/∂y = 2y + 6x = 0.
Solving these two equations simultaneously, we get:
24x^2 + 6y = 0,
2y + 6x = 0.
From the second equation, we can solve for y in terms of x:
Y = -3x.
Substituting this into the first equation:
24x^2 + 6(-3x) = 0,
24x^2 – 18x = 0,
6x(4x – 3) = 0.
Therefore, we have two possibilities for x:
1. x = 0,
2. 4x – 3 = 0, which gives x = ¾.
Substituting these values back into y = -3x, we get the corresponding y-values:
1. x = 0 ⇒ y = 0,
2. x = ¾ ⇒ y = -9/4.
Hence, the critical points of the function are (0, 0) and (3/4, -9/4).
To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.
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What is the distance on the unit circle between successive fourth roots of root3/2 - 1/2i
The distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.
To find the distance between successive fourth roots of a complex number on the unit circle, we can use the concept of the angle between the roots. Let's proceed step by step:
The given complex number is √3/2 - 1/2i. This complex number lies on the unit circle because its magnitude is equal to 1.
1. Convert the given complex number to trigonometric form:
√3/2 - 1/2i = cos(θ) + i*sin(θ)
By comparing the real and imaginary parts, we can determine the angle θ:
cos(θ) = √3/2
sin(θ) = -1/2
Using the unit circle, we can find that θ = 5π/6 (or 150 degrees). This angle represents the position of the given complex number on the unit circle.
2. Find the angle between successive fourth roots:
Since we are interested in the fourth roots, we divide the angle θ by 4:
θ/4 = (5π/6) / 4 = 5π/24
This angle represents the angular distance between two successive fourth roots on the unit circle.
3. Calculate the distance between the two points:
To find the distance, we multiply the angular distance by the radius of the unit circle (which is 1):
Distance = (5π/24) * 1 = 5π/24
Therefore, the distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.
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What is SSS SAS ASA AAS?.
Answer:
SSS: Side-Side-Side
SAS: Side-Angle-Side
ASA: Angle-Side-Angle
AAS: Angle-Angle-Side
Step-by-step explanation:
They are the conditions used to determine whether two triangles are congruent or not.
Assume that a sample is used to estimate a population mean p. Find the margin of error M.E. that corresponds to a sample of size 8 with a mean of 23.6 and a standard deviation of 21.9 at a confidence level of 98%. Report ME accurate to one decimal place because the sample statistics are presented with this accuracy. M.E. = Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. > Next Question
The margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694
We would utilize the t distribution in the estimation of the margin of error because the population standard deviation is unknown (and the sample size is less than 30).
Error margin = t-critical * standard deviation/square root sample size
It is given in the above question that,
Standard deviation is given as = 8.6
And, the Sample size which is given is = 22
Also, the confidence level which given is = 95%
Then the alpha will be = 100% - 95%
= 5% = 0.05
Now, the critical value, t would be = alpha / 2
= 0.05 /2 = 0.025
Also, the sample we'll consider will be = given sample size - 1 = 22 -1 = 21
To find the margin error, we'll put all the values in the formula
Error margin = t-critical * standard deviation/square root sample size
= 0.215 / 4.58
= 0.04694
Hence, the margin error M.E. that corresponds to a sample of size 22 with a mean of 69.3 and a standard deviation of 8.6 at a confidence level of 95% is 0.04694
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solveeee for x !!!!!!!
How can you identify a linear function?
Answer:
Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept.
Step-by-step explanation:
please help asap!!! will give brainliest
The values of function g(x) are as follows:
-20-5-12What is a function?An expression, rule, or law in mathematics that specifies the relationship between an independent variable and a dependent variable (the dependent variable).
Given, a relation between two functions in terms of variables
For x = -2 and f(x) = 1the value of g(x) = x* f(x) = -2 *1 = -2
For x = -0 and f(x) = -2the value of g(x) = x* f(x) = 0 *-2 = 0
For x = 1 and f(x) = -5the value of g(x) = x* f(x) = 1 *-5 = -5
For x = 3 and f(x) = -4the value of g(x) = x* f(x) = 3 *-4 = -12
Therefore, The values of the given function are -2, 0, -5, and -12.
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Complete question:
g(x) = x f(x)
5 plus 6 times 8 plus 9 times 10 plus 8 plus 4 plus 2 plus 9 plus 8 plus 7 plus 5 plus 7 plus 6 times 7 times 9 times 8 times 5 times 4 times 3 times 2 times 1 times 6 times 8 times 9 times 12 times 17 times 19 times 20 times 12 times 11 times 13 times 14 times 15 times 16
i dont know
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A Right triangle has one acute angle of 43. what is the measure of the other acute angle
90 + 43 + x = 180
By Euclidean geometry, the measure of the missing angle, the other acute angle, of the right triangle is equal to 47°.
How to find the measure of the measing angle of the right triangleRight triangles are triangles of which one of its angles is a right angle and the other two angles are acute angles. According to the statement, the measure of an acute angle of the right triangle is equal to 43°.
By Euclidean geometry, the sum of the internal angles in any triangle equals a measure of 180°. Then, the measure of the missing angle is:
90° + α + β = 180°
If we know that α = 43°, then the value of β is:
α + β = 90°
43° + β = 90°
β = 47°
The measure of the missing angle is equal to 47°.
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A truck arrives on the job site to deliver a specified mix with a W/C ratio of 0.45. The mix was batched as follows: Cement: 22 lbs., Sand:41 lbs., Gravel: 57 lbs., Water: 8 lbs. How many gallons of water can be added to the mix and still remain in spec
Therefore, You can add approximately 0.228 gallons of water to the mix and still remain within the specified W/C ratio of 0.45.
The total weight of the mix is 22 + 41 + 57 + 8 = 128 lbs. To calculate the current W/C ratio, we need to convert the weight of water to gallons. One gallon of water weighs approximately 8.34 lbs. Therefore, the current weight of water is 8/8.34 = 0.96 gallons. The current W/C ratio is 0.96/128 = 0.0075. To remain within spec with a W/C ratio of 0.45, we can use the formula: (water weight + x)/(total weight) = 0.45, where x is the additional weight of water needed. Solving for x, we get x = (0.45 x 128) - 8 = 50.4 lbs. Converting to gallons, this is 50.4/8.34 = 6.05 gallons. Therefore, 6.05 gallons of water can be added to the mix and still remain within spec.
To determine how many gallons of water can be added to the mix and still remain within the specified W/C ratio of 0.45, follow these steps:
1. Calculate the required amount of water for the specified W/C ratio: Cement weight x W/C ratio = 22 lbs. x 0.45 = 9.9 lbs. of water.
2. Subtract the initial water content from the required amount: 9.9 lbs. - 8 lbs. = 1.9 lbs. of additional water needed.
3. Convert the additional water weight to gallons: 1.9 lbs. / 8.34 lbs./gallon (water density) ≈ 0.228 gallons.
Therefore, You can add approximately 0.228 gallons of water to the mix and still remain within the specified W/C ratio of 0.45.
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find the measurement for angle A
Answer: that is a 45 degree angle
Step-by-step explanation: 90 / 2 is 45
Answer:
∠ A = 44°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 angles and equate to 180, that is
x + 59 + x + 51 + 84 = 180, simplify
2x + 194 = 180 ( subtract 194 from both sides )
2x = - 14 ( divide both sides by 2 )
x = - 7
Thus
∠ A = x + 51 = - 7 + 51 = 44°
If a 18 ft tall tree casts a 9 ft long shadow
then how tall is an adult giraffe standing near it that casts a 7
ft shadow?
Answer:
\( \boxed{ \tt{the \: adult \: giraffe \: is \to \: 14 \: ft}}\)
The height of the giraffe standing near it which casts a shadow of 7 feet is 14 feet.
What is Scale Factor?Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.
Given that,
Actual height of the tree = 18 feet
Height of the shadow = 9 feet
Actual height = 2 × Shadow height
So, here the scale factor is 2.
Given Shadow height of the giraffe = 7 feet
Actual height of the giraffe = 2 × height of shadow of the giraffe
= 2 × 7 feet
= 14 feet
Hence the height of the giraffe is 14 feet.
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Cole found BC in ΔABC . His work is shown below. Identify the first step in which his work shows an error. A Step 1: 92 + 152 = c2 B Step 2: 81 + 225 = c2 C Step 3: 306 = c2 D Step 4: 306−−−√ =c E Step 5: c≈17, so BCis about 17 in.
Answer: A
Step-by-step explanation:
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