The two-way table is of the class survey is:
Vanilla Ice Cream | Strawberry Ice Cream | Total
Chocolate Cake | 12 | 3 | 15
Yellow Cake | 11 | 4 | 15
Total | 23 | 7 | 30
A two-way table summarizing the data from Mrs. Robinson's class survey on cake and ice cream preferences can be constructed as follows.
1: Create a table with rows for Chocolate Cake and Yellow Cake, and columns for Vanilla Ice Cream, Strawberry Ice Cream, and Total.
2: Fill in the given information:
15 students chose Chocolate Cake and 15 students chose Yellow Cake, so put 15 in the Total column for both rows.12 students who chose Chocolate Cake also chose Vanilla Ice Cream, so put 12 in the intersection of Chocolate Cake and Vanilla Ice Cream.There were 7 students in all that chose Strawberry Ice Cream, so put 7 in the Total row of the Strawberry Ice Cream column.3: Complete the table using the given information:
Since 12 students who chose Chocolate Cake also chose Vanilla Ice Cream, 3 students chose Chocolate Cake and Strawberry Ice Cream (15 total - 12).There are 7 students in total who chose Strawberry Ice Cream, so 4 students chose Yellow Cake and Strawberry Ice Cream (7 total - 3).The remaining 11 students chose Yellow Cake and Vanilla Ice Cream (15 total - 4).So, the completed two-way table is:
Vanilla Ice Cream | Strawberry Ice Cream | Total
Chocolate Cake | 12 | 3 | 15
Yellow Cake | 11 | 4 | 15
Total | 23 | 7 | 30
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Use the data in MEAP00 to answer this question.
Estimate the model
by OLS, and report the results in the usual form. Is each explanatory variable statistically significant at the 5% level?
Obtain the fitted values from the regression in part (i). What is the range of fitted values? How does it compare with the range of the actual data on math4?
Obtain the residuals from the regression in part (i). What is the building code of the school that has the largest (positive) residual? Provide an interpretation of this residual.
Add quadratics of all explanatory variables to the equation, and test them for joint significance. Would you leave them in the model?
Returning to the model in part (i), divide the dependent variable and each explanatory variable by its sample standard deviation, and rerun the regression. (Include an intercept unless you also first subtract the mean from each variable.) In terms of standard deviation units, which explanatory variable has the largest effect on the math pass rate?
The range of the actual data on math4 is the difference between the maximum and minimum values of this variable in the dataset. The building code of the school with the largest positive residual is the one that has the highest difference between the actual and predicted values of math4.Whether or not to leave them in the model would depend on the specific research question and the improvement in model fit. The explanatory variable with the largest effect on the math pass rate will have the highest absolute value of the standardized coefficient.
MEAP00 is a dataset that contains information on the performance of students on the Michigan Educational Assessment Program (MEAP) test. To answer the questions posed, we first need to estimate a regression model using Ordinary Least Squares (OLS) and report the results in the usual form. The dependent variable in this model is math4, which is the percentage of students who passed the math portion of the MEAP test, and the explanatory variables are the building code (BC), the variable MEAP00, and a variable named variable.
After running the regression, we need to check whether each explanatory variable is statistically significant at the 5% level. We can do this by looking at the p-values of the coefficients. If the p-value is less than 0.05, then we can reject the null hypothesis that the coefficient is zero and conclude that the variable is statistically significant.
We also need to obtain the fitted values from the regression and compare them to the range of the actual data on math4. The range of the fitted values will depend on the specific values of the explanatory variables in the dataset. The range of the actual data on math4 is the difference between the maximum and minimum values of this variable in the dataset.
Next, we need to obtain the residuals from the regression and identify the building code of the school that has the largest positive residual. The residual is the difference between the actual value of the dependent variable and the value predicted by the regression model. A positive residual means that the actual value of math4 is higher than the predicted value. The building code of the school with the largest positive residual is the one that has the highest difference between the actual and predicted values of math4. An interpretation of this residual could be that the school has a program or teaching method that is particularly effective in helping students pass the math portion of the MEAP test.
We are also asked to add quadratics of all explanatory variables to the equation and test them for joint significance. Quadratics are added to capture non-linear relationships between the explanatory variables and the dependent variable. To test the joint significance of the quadratic terms, we can use an F-test. If the F-statistic is greater than the critical value, then we can reject the null hypothesis that all quadratic terms are zero and conclude that they are jointly significant. Whether or not to leave them in the model would depend on the specific research question and the improvement in model fit.
Finally, we are asked to rerun the regression after dividing the dependent variable and each explanatory variable by its sample standard deviation. This standardizes the variables and allows us to compare the size of their effects in standard deviation units. The explanatory variable with the largest effect on the math pass rate will have the highest absolute value of the standardized coefficient.
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round to nearest ten 8,990.97
Answer:
8990
Step-by-step explanation:
The 9 underlined is in the tens place.
8990.97 ⇒ 8990
Since you can't round up, you replace everything after the underlined 9 with 0's.
8990.00 = 8990
what do you like the most about yourself even though you guys are amazing and probably have so much too like
Answer:
i don't know I just like my personality
Anna made a scale drawing, in inches, of a building using a scale of 1:600. Her scale drawing was 6 inches long. Greg made a scale drawing of the same building using a scale of 1:300. How long, in inches, was Greg's scale drawing? A 2 B 3 C 12 D 50
you'll get 30 points.
Answer:
C.12
Step-by-step explanation:
Answer:
i dont exactly know but the answer is C ?
Step-by-step explanation:
The students at a high school collected $3,800 to buy stuffed animals to give to a children’s hospital. The students bought both stuffed bears and stuffed dogs. Each bear cost $7, and each dog cost $8. The students bought a total of 500 stuffed animals and spent all the money. How many stuffed dogs did the students buy? A. 200 B. 205 C. 295 D. 300
Answer:
D. 300
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Variables
Stuffed bears = b
Stuffed dogs = d
Step 2: Define Systems
$7b + $8d = $3800
b + d = 500
Step 3: Rewrite Systems
b + d = 500
[Equality Property] Multiply everything by -7: -7b - 7d = -3500Step 4: Redefine Systems
7b + 8d = 3800
-7b - 7d = -3500
Step 5: Solve for d
Elimination
Combine 2 equations: d = 300Step 6: Define Answer
d = 300 means that the students bought 300 stuffed dogs.
Answer:
D
Step-by-step explanation:
Remark
Let the stuffed bear = x
Let the stuffed dog = y
Equations
x + y = 500 (1)
7x + 8y = 3800 (2)
Solution
There are two ways you could do this. You can use substitution or you could use multiplying equation 1 by either 7 or 8 to get rid of the x or y.
Multiply (1) by 7
7x + 7y = 3500 (3) Write equation (2) below (3) and subtract
7x + 8y = 3800 Subtract
-y = - 300 Multiply by - 1
y = 300
Use the result for y to get x using equation 1
x + y = 500
x + 300 = 500 Subtract 300
x = 500 - 300
x = 200
Stuffed bears = 200
Stuffed dogs = 300
the difference of three times a number, and five
Answer:
\(un \: known \: = x \\ three \: times \: a \: number = 3x \\ so \: we \: can \: written \: as = 3 x - 5\)
Find the 4th term in the sequencewith the following definition:aj = 0an = 2(an-1-3)
Answer:
-60
Explanation:
To find the 4th term we need to also find the 2nd and 3rd terms as follows:
\(\begin{gathered} a_n=2(a_{n-1}-3) \\ a_2=2(a_{2-1}-3) \\ a_2=2(a_1-3) \\ a_2=2(0-3) \\ a_2=2(-3) \\ a_2=-6 \end{gathered}\)\(\begin{gathered} a_3=2(a_{_2}-3) \\ a_3=2(-6-3) \\ a_3=3(-9) \\ a_3=-27 \end{gathered}\)Finally, we can calculate the value of the 4th term as:
\(\begin{gathered} a_4=2(a_3-3) \\ a_4=2(-27-3) \\ a_4=2(-30) \\ a_4=-60 \end{gathered}\)So, the answer is -60
Consider a population regression model. For simplicity, ignore the subscript i that we normally attach with the variables. If k=2, then the model can be written as:
A. Y= β0 + β1X1 + β2X2 + e
B. Y = β0 + β1X1 + β2X2 +
C. Y = β0 + β1X1 + β2X2 = β0 + β1X1 + β2X2
D. Y = β0 + β1X1 + β2X2 + e
Among the given options (A, B, C, D), the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.
In a population regression model, we are interested in modeling the relationship between a dependent variable (Y) and one or more independent variables (X1, X2, etc.). The model equation consists of the regression coefficients (β0, β1, β2, etc.) that represent the effect of each independent variable on the dependent variable, and the error term (e) that captures the unexplained variation in the data.
Among the given options, only option D includes all the necessary components of a population regression model with two independent variables (k = 2). It includes the dependent variable Y, the regression coefficients β0, β1, and β2 for the independent variables X1 and X2, respectively, and the error term e.
Options A, B, and C are incorrect because they either omit the error term or have an incomplete equation. The error term is crucial in accounting for the unobserved factors and random variation in the relationship between the variables.
Therefore, the correct population regression model when k = 2 is option D: Y = β0 + β1X1 + β2X2 + e.
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Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Order the polynomial -x 4 y 2 + 7x 3 y 3 - 3xy 5 + 2x 2 y 4 in descending powers of x.
Answer:
See under for the sequence
Step-by-step explanation:
The term with -X⁴ comes first because 4 is the highest power of x.
Then comes 7x³y³ because 3 is the second highest power
Then 2x²y⁴ because 2 comes next
Then -3xy⁵ because x is raised to 1 power which is the lowest
In the data set below, what is the mean absolute deviation?
8 4 2 3 6
If the answer is a decimal, round it to the nearest tenth.
mean absolute deviation (MAD):
The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).
We have,
In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.
To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:
mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6
Next, we calculate the deviation of each data point from the mean:
|4 - 6.6| = 2.6
|5 - 6.6| = 1.6
|7 - 6.6| = 0.4
|9 - 6.6| = 2.4
|8 - 6.6| = 1.4
Then we find the average of these deviations, which gives us the mean absolute deviation:
MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6
Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).
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The average age of undergraduate students at grand canyon university is 44. if the standard deviation is 4, what percentage of undergraduate students are between 36 and 52 years old?
75% is percentage of undergraduate students are between 36 and 52 years old.
What is percentage and example?
A percentage is a ratio or fraction where the full value is always 100. For example, if Sam received 30% marks in his math test, it signifies that he scored 30 marks out of 100. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.The percentage is used to determine “how much” or “how many.” A percentage number aids in calculating the exact amount or figure that is being discussed. Fractions are compared.This would be true if k=3, but k=2
because (36-44)/4 = -2 and (52-44)/4 = 2
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14. Find b: (a+b)m/c -K= p/r
15. Find x: r=m(1/x+c + 3/y)
16. Find t: a/c+x= M(1/R+1/T)
17. Find y: a/k+c= M(x/y+d)
The value of b in the equation (a+b)m/c - K = p/r can be found by evaluating (p/r * c - am + Kc) divided by m.
Starting with the equation:
(a+b)m/c - K = p/r
First, multiply both sides of the equation by c to eliminate the denominator:
(a+b)m - Kc = p/r * c
Next, distribute the m to the terms inside the parentheses:
am + bm - Kc = p/r * c
Rearrange the equation to isolate the term containing b:
bm = p/r * c - am + Kc
Finally, divide both sides of the equation by m to solve for b:
b = (p/r * c - am + Kc) / m
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how do i solve this?
Answer:
y = 6
Step-by-step explanation:
You solve by using the pythagorean theorem, which is:
\(a^{2} +b^{2} =c^{2}\)
Where a and b are legs of the triangle, and c is the hypotenuse, or y in this case. So let's rearrange this equation for c:
\(c=\sqrt{a^{2} +b^{2} }\)
Now, we can substitute in the known values and solve:
\(c=\sqrt{3.6^{2} +4.8^{2} } = \sqrt{36} = 6\)
Therefore, the value of y is 6
Hope this helps!
What is the value of k if one of the zeros of the quadratic polynomial K 2 x2 2x 5?
If one of the zeros in the quadratic polynomial is 4, then the value of k is 3.
What is polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. A polynomial is a mathematical expression that only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are also known as indeterminates in mathematics.
Here,
4 is a root/zero of polynomial
P(x) = (k-2) x² - 2 x - (k+5)
P(4) = 0
(k - 2) 4² - 2 * 4 - (k+5) = 0
15 k - 45 = 0
k = 3
The value of k if 4 is one of the zeros of the quadratic polynomial is 3.
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Complete question:
If one of the zeros of a quadratic polynomial(k-2)x^2-2x-(k+5) is 4 , find value of k.
Geometry Translation Please help me. This is worth alot of point.
Value Grocery Mart and Market City are both having a sale on the same popular crackers. McKayla is trying to determine which sale is the better deal: Using the given table and equation, determine which store has the better deal on crackers? Explain your reasoning. (Remember to round your answers to the nearest penny.) Value Grocery Mart: 12 6 3 20 15 Number of Boxes of Crackers 10 5 Cost (in dollars) Market City: c = 1.75b, where c represents the cost in dollars, and b represents the number of boxes of crackers
The same well-liked crackers are discounted at Value Grocery Mart and Market City are 5.25, 10.5, 15.75, and 21.
As the cost per pack is C=1.75b. C is the Cost in dollars.
3×1.75=5.25
6×1.75=10.5
9×1.75=15.75
12×1.75=21
What are chart and tabular forms?An example of a chart is one that uses symbols to depict the data, such as bars in a bar chart, columns in a line chart, or slices in a pie chart. A chart can convey various information by representing tabular numerical data, functions, or certain types of quality structures.
Users can change numerous rows and columns in a table at once using a tabular form and a single page.
A chart displays data that can be shown as a table, graph, or diagram. There are different ways to convey vast amounts of information in it.
Here, the table is.
Number of Boxes of Crackers ║ Grocery Mart ║ Market City:
3 ║ 5 ║ 5.25
6 ║ 10 ║ 10.5
9 ║ 15 ║ 15.75
12 ║ 20 ║ 21
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a sample of 25 days of operation shows a sample mean of 290 rooms occupied per day and a sample standard deviation of 20 rooms.
The sample mean and sample standard deviation provide valuable information about a set of data, but they should be used with caution when making inferences about the population. It is important to use statistical methods to determine the reliability of these estimates and to account for sources of variability in the data.
Firstly, the sample mean is a measure of central tendency that represents the average value of a set of data. In this case, the sample mean of 290 rooms occupied per day is the sum of the number of rooms occupied each day over the 25-day period divided by the total number of days. It is important to note that the sample mean is only representative of the specific sample of 25 days and may not accurately reflect the population mean.
Secondly, the sample standard deviation is a measure of dispersion that indicates how spread out the data is from the mean. A smaller standard deviation means that the data points are closer to the mean, while a larger standard deviation means that the data points are more spread out. In this case, the sample standard deviation of 20 rooms indicates that there is some variability in the number of rooms occupied each day.
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Which of the following are important properties of the arithmetic mean? Check all that apply. Multiple select question. The mean is always less than the median. All of the values in the data are used in calculating the mean. Σ(X-X)=0 i.e. the sum of the deviations is zero. There is only one mean for a set of data. The mean can be calculated for nominal data.
Answer:
All of the values in the data are used in calculating the mean.
The sum of the deviations is zero.
There is only one mean for a set of data.
Step-by-step explanation:
Required
True statement about arithmetic mean
(a) False
The mean can be equal to, greater than or less than the median
(b) True
The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.
(c) True
All mean literally represent the distance of each value from the average; so, when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e.\(\sum(x - \bar x) = 0\)
(d) True
The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.
(e) False
Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.
5.explain why reaction rates decline with time and use this information to correctly process the data (by choosing the proper data points to do linear regression
Reaction rates decline with time because the reactants are consumed over time, reducing the number of reactant particles available for reaction.
What are reactants?The components that are involved in a chemical reaction are known as reactants. They are the beginning ingredients that are changed into new compounds, known as products, through a chemical process. The left side of a chemical equation is often used to represent reactants, whereas the right side is used to indicate products. The quantity and kind of reactants and products affect the kind of chemical reaction that takes place. Pure substances, such as elements or compounds, or combinations of substances, can function as reactants with time. In a chemical reaction, reactants are changed into products by chemical bonds being broken and formed, releasing or absorbing energy in the process.
How to solve?
As the number of reactant particles decreases, the rate of reaction also decreases. This phenomenon can be observed in many chemical reactions, including reactions that involve the decay of radioactive elements.To correctly process data on the decline of reaction rates with time, it is important to choose the appropriate data points for linear regression. This typically involves selecting data points at regular intervals, such as every minute or every hour, to accurately represent the decline in reaction rates over time. By choosing the right data points and performing linear regression, it is possible to accurately model the decline in reaction rates and make predictions about future reactions.
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Please help asap. fill fill
Answer:
24
Step-by-step explanation:
(2+2)x(7+4-5)
4x(11-5)
4x6
24
Answer:
24
Step-by-step explanation:
To solve this problem, we simply plug in the given values of x and y and then simplify using the order of operations.
(y + 2) * (x + 4 - 5)
==> plug in x = 7 and y = 2
(2 + 2) * (7 + 4 - 5)
==> simplify operations in parenthesis
4 * 6
==> multiply 4 and 6
= 24
Which point is the image of Q ?
A
B
C
D
Suppose A ∈ Rm×n has linearly independent columns, and C ∈ Rl×n has linearly independent
rows. Let d ∈Rl and b ∈Rm. Show how to solve the linearly constrained least squares problem:
Find x∗∈{x ∈Rn : Cx = d} which minimizes ∥b −Ax∥2.
It is enough to reduce this problem to the usual unconstrained least squares problem.
Additional Conditions: m >= n >= l
The linearly constrained least squares problem, we can reduce it to the unconstrained least squares problem by using the method of Lagrange multipliers.
To solve the linearly constrained least squares problem, we can introduce a Lagrange multiplier λ and define the Lagrangian function L(x, λ) = ∥b - Ax∥² + λᵀ(Cx - d). The goal is to minimize this function with respect to x and λ. Taking the partial derivatives of L with respect to x and λ and setting them to zero, we obtain two equations: AᵀAx + CᵀCλ = Aᵀb and Cx = d. Multiplying the first equation by its transpose, we get AᵀAxxᵀ + CᵀCλxᵀ = Aᵀbxᵀ. Since the columns of A are linearly independent, AᵀAx is invertible, and we can solve for x in terms of λ as x = (AᵀA)⁻¹(Aᵀb - CᵀCλ). Substituting this expression for x into Cx = d, we can solve for λ. Finally, substituting the value of λ back into x, we obtain the solution to the linearly constrained least squares problem.
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Amy has scored 77, 87, and 74 on her previous three tests. What score does she need on her next test so that her average (mean) is 76?
After scoring 77, 87, and 74 on her previous three tests, Amy needs to score 66 on her next test in order to have an average of 76.
To find the score that Amy needs on her next test to have an average of 76, we need to use the formula for the mean of a set of numbers:
Mean = (Sum of all numbers) / (Total number of numbers)
We know that Amy's current scores are 77, 87, and 74, and we want her average to be 76. Let's call the score she needs on her next test "x".
So, we can plug these values into the formula:
76 = (77 + 87 + 74 + x) / 4
Now, we just need to solve for x:
76 * 4 = 77 + 87 + 74 + x
304 = 238 + x
x = 304 - 238
x = 66
So, Amy needs to score a 66 on her next test in order to have an average of 76.
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In the figure below, m L 1 = (x + 48)° and m 2 = 2x°.
Find the angle measures.
Answer:
∠ 1 = 62° , ∠ 2 = 28°
Step-by-step explanation:
angles 1 and 2 form a right angle = 90° , that is
∠ 1 + ∠ 2 = 90 ( substitute values )
x + 48 + 2x = 90
3x + 48 = 90 ( subtract 48 from both sides )
3x = 42 ( divide both sides by 3 )
x = 14
Then
∠ 1 = x + 48 = 14 + 48 = 62°
∠ 2 = 2x = 2 × 14 = 28°
Which steps should be used to graph the equation below?
y – 4 = y minus 4 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2)
a 1. Plot the point (2, 4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
b 1. Plot the point (2, 4).
2. From that point, count left 1 unit and down 3 units and plot a second point.
3. Draw a line through the two points.
c 1. Plot the point (–2,4).
2. From that point, count left 3 units and down 1 unit and plot a second point.
3. Draw a line through the two points.
d 1. Plot the point (–2,4).
2. From that point, count left 1 unit and down 3 units and plot a second point.
3. Draw a line through the two points.
The steps to grapj the given equation y – 4 = y minus 4 equals StartFraction one-third EndFraction left-parenthesis x plus 2 right-parenthesis.(x + 2) is C.
1. Plot the point (–2,4).2. From that point, count left 3 units and down 1 unit and plot a second point.3. Draw a line through the two points.Calculations and ParametersGiven
y - 4 = (1/3) (x+ 2)
The steps should be used to graph the equation is given below:
y - 4 = (1/3) (x+ 2)
y - 4 = 0 => y = 4
x + 2 = 0 => x = -2
Plot point ( - 2 , 4)
count left 3 units and down 1 unit and plot a second point.
as for every 3 units change in x, there is one unit change in y
x going left & y going down is the same direction
Draw a line through the two points.
Therefore, the correct answer is option C.
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a licensed nurse practitioner is instructed to give a patient 1500 milllgrams of an antiobiotic over a period of 36 hours. if the antibiotic is to be give every 2 hours starting immediately, how antibiotivc should be given in each dose? to answer this question , solve the equation 18x=1500.
The antibiotic should be given in each dose as 83.33 milligrams (rounded to two decimal places).
The formula 18x = 1500, where x is the quantity of the antibiotic administered in each dose, can be used to calculate how much antibiotic should be administered in each dose. Dividing both the sides of the equation by 18, we have,
x = 1500 / 18
x ≈ 83.33
There is no further work to be done in the calculations stage since this value has already been rounded to two decimal places. Therefore, the antibiotic dosage should be 83.33 mg in magnitude, rounded to two decimal places.
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A.8 B.9 C.11 D.14 math.........again
Answer:
i pretty sure 9
Step-by-step explanation:
Answer:
The value of x is 11.
Step-by-step explanation:
Given :
Here we have given that the angles of a triangle are :
\(\pink\star\) 62⁰\(\pink\star\) 69⁰\(\pink\star\) 4x + 5\(\begin{gathered}\end{gathered}\)
To Find :
\(\pink\star\) We need to find the value of x.\(\begin{gathered}\end{gathered}\)
As we know that :
\(\pink\star\) The sum of the angles of a triangle is always 180 degrees.\(\begin{gathered}\end{gathered}\)
Solution :
Now, according to the question :
\(\begin{gathered}\quad\longrightarrow{\sf{Sum \: of \: all \: angles = {180}^{0}}} \\\\\quad\longrightarrow{\sf{{62} + {69} + 4x + 5 = {180}}}\\\\\quad\longrightarrow{\sf{{131} + 4x + 5 = {180}}}\\\\\quad\longrightarrow{\sf{4x + 5 = {180} - {131}}}\\\\\quad\longrightarrow{\sf{4x + 5 = 49}}\\\\\quad\longrightarrow{\sf{4x = 49 - 5}}\\\\\quad\longrightarrow{\sf{4x = 44}}\\\\\quad\longrightarrow{\sf{x = \frac{44}{4}}}\\\\\quad\longrightarrow{\sf{x = 11}} \\ \\ \quad{\star{\underline{\boxed{\sf{\purple{x = 11}}}}}}\end{gathered}\)
Hence, the value of x is 11.
\(\rule{300}{2.5}\)
Pablo drove 715 miles in 11 hours.
At the same rate, how many miles would he drive in 9 hours?
Answer:
585 miles
Step-by-step explanation:
divide 715 by 11 so that you can see the mph (miles per hour). Then multiply that number by 9 for the amount of miles he would travel in nine hours
715/11=65
65x9=585
plot the graph of y=cos x
Step-by-step explanation:
\(\displaystyle \boxed {y = sin\:(x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-\frac{\pi}{2}} \hookrightarrow \frac{-\frac{\pi}{2}}{1} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1\)
OR
\(\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{2\pi} \hookrightarrow \frac{2}{1}\pi \\ Amplitude \hookrightarrow 1\)
You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of \(\displaystyle y = sin\:x,\)in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted \(\displaystyle \frac{\pi}{2}\:unit\)to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD \(\displaystyle \frac{\pi}{2}\:unit,\)which means the C-term will be negative, and by perfourming your calculations, you will arrive at \(\displaystyle \boxed{-\frac{\pi}{2}} = \frac{-\frac{\pi}{2}}{1}.\)So, the sine graph of the cosine graph, accourding to the horisontal shift, is \(\displaystyle y = sin\:(x + \frac{\pi}{2}).\)Now, with all that being said, in this case, sinse you ONLY have a wourd problem to wourk with, you MUST use the above formula for calculating the period. Onse you do that, the rest should be easy. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \(\displaystyle y = 0,\)in which each crest is extended one unit beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.
I am delighted to assist you at any time.
Answer:
Step-by-step explanation:
Cosine is a trigonometric function defined as the ratio of length of adjacent side and the hypothesis in a right-angle triangle.
It is a periodic function with a period of 2pi.
Graph of its plot is attached.
Graph the ordered pair ( -2, 5) and its reflection over the y-axis. Name the coordinates for the reflection
Answer:
The ordered pair (-2,5) reflected over the y-axis is (2,5)
Step-by-step explanation: