Answer: 3.5
Step-by-step explanation:
A = 2, B = 7, C = 6
(7a + b)/c
=(7(2)+7)/(6)
=(14+7)/6
=21/6
=3.5
One leg of a right triangle is 2cm longer than the other leg. The hypotenuse is 10cm long. Determine the length of the shorter leg.
Answer:
shorter leg = 6 cm
Step-by-step explanation:
let n be the shorter leg then n + 2 is the longer leg.
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
n² + (n + 2)² = 10² , that is
n² + n² + 4n + 4 = 100
2n² + 4n + 4 = 100 ( subtract 100 from both sides )
2n² + 4n - 96 = 0 ( divide through by 2 )
n² + 2n - 48 = 0 ← in standard form
(n + 8)(n - 6) = 0 ← in factored form
equate each factor to zero and solve for n
n + 8 = 0 ⇒ n = - 8
n - 6 = 0 ⇒ n = 6
However , n > 0 then n = 6
the shorter leg is 6 cm long
The marginal cost of a product is modeled by dc dx = 14 3 14x 5 where x is the number of units. when x = 17, c = 120. (a) find the cost function. (round your constant term to two decimal places.)
The cost function is mathematically given as
\(C=\frac{3(14 x+5)^{\frac{2}{3}}}{2}+61.589\)
What is the cost function?Generally, the equation for the expression is mathematically given as
\(&\frac{d C}{d x}=\frac{14}{\sqrt[3]{14 x+5}} \\\)
\(&d C=14(14 x+5)^{-\frac{1}{3}} d x \\\\&\int d C=\int 14(14 x+5)^{-\frac{1}{3}} d x \\\\&C=\frac{14(14 x+5)^{\frac{2}{3}}}{\frac{2}{3}(14)}+C_{1} \\\\&C=\frac{3(14 x+5)^{\frac{2}{3}}}{2}+C_{1} \\\\\)
x=17, C=120
\(&120=\frac{3(14(17)+5)^{\frac{2}{3}}}{2}+C_{1} \\&120=\frac{3(247)^{\frac{2}{3}}}{2}+C_{1} \\\)
\(120=58.411+C_{1} \\C_{1}=120-58.411\)
\(C_{1}=61.589\)
In conclusion, put \(C_{1}=61.589\) in equation 1
\(C=\frac{3(14 x+5)^{\frac{2}{3}}}{2}+61.589\)
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a circle has a circumference of 615.44615.44615, point, 44 units. what is the radius of the circle? use 3.14 for \piπpi and enter your answer as a decimal. units
Answer:
98 units.
Step-by-step explanation:
Circumference = 2 * pi * radius
615.44 = 2 * 3.14 * r
r = 615.44 / (2 * 3.14)
=2 * 3.14
= 98 units.
Someone Smart Help With Math!
Answer:
-48. You multiply the figures
Answer:
B. -48
Explanation:
Simply -16 multiplied by 3. When one negative number is multiplied, the product is a negative. When two negative numbers are multiplied together, the product is positive.
In ΔEFG, g = 34 inches, e = 72 inches and ∠F=21°. Find the area of ΔEFG, to the nearest square inch.
The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.
To find the area of triangle EFG, we can use the formula:
\(Area = (1/2) \times base \times height\)
In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.
First, let's find the length of FG. We can use the law of cosines:
FG² = EF² + EG² - 2 * EF * EG * cos(∠F)
EF = 72 inches
EG = 34 inches
∠F = 21°
Plugging these values into the equation:
FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)
Solving for FG, we get:
FG ≈ 83.02 inches
Next, we need to find the height. We can use the formula:
height = \(EF \times sin( \angle F)\)
Plugging in the values:
height = 72 * sin(21°)
height ≈ 25.52 inches
Now we can calculate the area:
\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)
Area ≈ 1060.78 square inches
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Find the value of x in the triangle shown below.
Answer:
√80
Step-by-step explanation:
Pythagorean Theorem: a^2+b^2=c^2
a = 4, b = 8
4^2+8^2 = 16+64 = 80
c^2 = 80
c^2 = √80 ≈ 8.94
a random telephone survey of 1,051 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. the survey results showed that 664 of those surveyed planned to file their taxes electronically. (round your answers to the nearest whole number.)
The percentage of adults who planned to file their taxes electronically is approximately 63%.
A random telephone survey of 1,051 adults (aged 18 and older) was conducted by an online tax preparation and e-filing service. The survey results showed that 664 of those surveyed planned to file their taxes electronically.
Total number of adults surveyed = 1,051
Number of adults who planned to file their taxes electronically = 664
Percentage of adults who planned to file their taxes electronically is;
= (Number of adults who planned to file their taxes electronically / Total number of adults surveyed) x 100%
=(664/1051) x 100%
= 63.16 %
Therefore, the percentage of adults who planned to file their taxes electronically is approximately 63%.
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Find the difference of (-x^2 + 9xy) - (x^2 + 6xy - 8y^2)
Difference of (-x² + 9xy) and (x² + 6xy - 8y²) is - 2x² + 3xy + 8y².
What is subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Given expression,
(-x² + 9xy) - (x² + 6xy - 8y²)
Distributing negative sign
-x² + 9xy - x² - 6xy + 8y²
Adding like terms
- 2x² + 3xy + 8y²
Hence, - 2x² + 3xy + 8y² is the difference of (-x² + 9xy) and (x² + 6xy - 8y²).
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If tan A = 4/3 and tan Band tan B= 12/5calculate and simplify the following:tan (A - B) =
There are some relations between the trigonometric functions. Tan(A-B) is only one of them and it is expressed by the following:
\(\begin{gathered} \tan (A-B)=\frac{(\tan A-\tan B)}{(1+(\tan A)\cdot(\tan B))} \\ \tan (A-B)=\frac{(\frac{4}{3}-\frac{12}{5})}{(1+(\frac{4}{3})\cdot(\frac{12}{5}))} \end{gathered}\)So, to get the answer we just solve the arithmetic operations as following:
\(\begin{gathered} \tan (A-B)=\frac{(\frac{20-36}{15})}{(1+(\frac{48}{15}))} \\ \tan (A-B)=\frac{(\frac{-16}{15})}{(\frac{5}{5}+(\frac{16}{5}))} \\ \tan (A-B)=\frac{\frac{-16}{15}}{\frac{21}{5}} \\ \tan (A-B)=\frac{-16\cdot5}{15\cdot21} \\ \tan (A-B)=\frac{-80}{315} \\ \tan (A-B)=-\frac{16}{63} \end{gathered}\)find slope of the line using (5,-5),(7,3) A. m=1/4 B. m=0 C. m= undefined D. m=4
show that each wff is a tautology by using equivalences to show that each wff is equivalent to true.A → Ꞁ (Ꞁ A v ¬ B) v Ꞁ B
The given WFF is equivalent to "true" using logical equivalences. Therefore, it is a tautology.
To show that a well-formed formula (WFF) is a tautology, we need to demonstrate that it is logically equivalent to the statement "true" regardless of the truth values assigned to its variables. Let's analyze the given WFF step by step and apply logical equivalences to show that it is equivalent to "true."
The given WFF is:
A → (¬A v ¬B) v B
We'll use logical equivalences to transform this expression:
Implication Elimination (→):
A → (¬A v ¬B) v B
≡ ¬A v (¬A v ¬B) v B
Associativity (v):
¬A v (¬A v ¬B) v B
≡ (¬A v ¬A) v (¬B v B)
Negation Law (¬P v P ≡ true):
(¬A v ¬A) v (¬B v B)
≡ true v (¬B v B)
Identity Law (true v P ≡ true):
true v (¬B v B)
≡ true
Hence, we have shown that the given WFF is equivalent to "true" using logical equivalences. Therefore, it is a tautology.
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68 is the product of Victor's savings and 4.
Just tell me the equation and ill answer it
use the fundamental theorem to evaluate the definite integral exactly. ∫10(y2 y6)dy
Using the fundamental theorem of calculus, we can evaluate the definite integral ∫[1 to 0] (y^2 + y^6) dy exactly.
To evaluate the definite integral ∫[1 to 0] (y^2 + y^6) dy, we can apply the fundamental theorem of calculus. The fundamental theorem states that if F(x) is an antiderivative of a function f(x) on an interval [a, b], then the definite integral of f(x) from a to b is equal to F(b) - F(a).
Let's find the antiderivative of the integrand (y^2 + y^6). The antiderivative of y^2 with respect to y is (1/3)y^3, and the antiderivative of y^6 is (1/7)y^7. Thus, the antiderivative of the integrand is (1/3)y^3 + (1/7)y^7.
Applying the fundamental theorem of calculus, the definite integral becomes [(1/3)(0^3) + (1/7)(0^7)] - [(1/3)(1^3) + (1/7)(1^7)]. Simplifying, we get (0 + 0) - (1/3 + 1/7) = -10/21.
Therefore, the exact value of the definite integral ∫[1 to 0] (y^2 + y^6) dy is -10/21.
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FILL THE BLANK.
For a 2x2 contingency table, testing for independence with the chi-square test is the same as conducting a ____________ test comparing two proportions.
The chi-square test for independence in a 2x2 contingency table is equivalent to comparing two proportions to determine if they are significantly different.
For a 2x2 contingency table, testing for independence with the chi-square test is the same as conducting a test comparing two proportions, specifically the two proportions of one variable (column) against the proportions of another variable (row).
1. Start with a 2x2 contingency table, which is a table that displays the counts or frequencies of two categorical variables. The table has two rows and two columns.
2. Calculate the marginal totals, which are the row and column totals. These represent the totals for each category of the variables.
3. Compute the expected frequencies under the assumption of independence. To do this, multiply the row total for each cell by the column total for the same cell, and divide by the total sample size.
4. Use the chi-square test statistic formula to calculate the chi-square value. This formula involves subtracting the expected frequency from the observed frequency for each cell, squaring the difference, dividing by the expected frequency, and summing up these values for all cells.
5. Determine the degrees of freedom for the chi-square test. In this case, it is (number of rows - 1) multiplied by (number of columns - 1), which is (2-1) x (2-1) = 1.
6. Compare the calculated chi-square value to the critical chi-square value from the chi-square distribution table at the desired significance level (e.g., 0.05).
7. If the calculated chi-square value is greater than the critical chi-square value, then the proportions of the two variables are significantly different, indicating dependence. If the calculated chi-square value is not greater, then the proportions are not significantly different, suggesting independence.
In summary, testing for independence with the chi-square test for a 2x2 contingency table is equivalent to conducting a test comparing two proportions, where the proportions represent the distribution of one variable against another.
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A man wants to measure the height of a nearby building. He places a 5 ft pole in the shadow of the building so that the shadow of the pole is exactly covered by
the shadow of the building. The total length of the building's shadow is 167 ft, and the pole casts a shadow that is 4.5 ft long, How tall is the building? Round
your answer to the nearest foot. (The figure is not drawn to scale.)
Building
Х
$
Pole
Shadow of pold
Shadow of building
The height of the building to the nearest foot is 186 feet.
The situation form two similar right triangle.
Properties of right triangle:One of its angle is 90 degrees.The angles and sides can be found using trigonometric ratios.Similar triangles:Similar triangle are not necessarily the same size. There corresponding angles are the same. The corresponding sides are a ratio. Therefore, we will establish a ratio of the triangles.
x = height of the building
Using similar triangle ratio:
5 / x = 4.5 / 1675 / x = 4.5 / 167
cross multiply
167 × 5 = 4.5x
4.5x = 835
x = 835 / 4.5
x = 185.555555556
x = 186 ft.
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Write the equation for each translation of the graph of y = 1 2 x − 2 + 3. one unit up
The equation for translation of the graph given is y = |x/2-2| + 4
Given is a function y = |x/2-2| + 3, it is translated one unit up, we need to find the translated function.
We know that, f(x) + k moves f(x) by k units up.
So, y = |x/2-2| + 3 → y = |x/2-2| + 3 + 1
y = |x/2-2| + 4
Hence, the equation for translation of the graph given is y = |x/2-2| + 4
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True/False. the amount of rainfall in your state last month is an example of discrete data.
Answer: False
Step-by-step explanation:
Discrete means secret and that data is not discrete as it can be acess by anyone.
True. The amount of rainfall in your state last month is an example of discrete data.
Explanation:The answer to the question is True. The amount of rainfall in a state last month is an example of discrete data.
Discrete data is a type of data that can only take on specific values. In this case, the amount of rainfall can be measured in specific units, such as inches or millimeters, and cannot have values between those units.
Other examples of discrete data include the number of students in a classroom, the number of cars passing through a toll booth, or the number of coins in a piggy bank.
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help me pleasee, my brain won't work
The given fractions have equal value, so Liam is correct.
How to find the equivalent fractions?Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.
Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.
Thus, we can say that:
The fraction -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.
The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient
The fractions have equal value, so Liam is correct
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madelyn is creating a media center. there are 7 televisions and 7 sets of speakers to choose from. for the dvd player, madelyn has 2 options. how many different entertainment centers can madelyn make?
The total number of different entertainment centers Madelyn can make is 7 × 7 × 2 = 98. Answer: 98.
Madelyn is creating a media center.
There are 7 televisions and 7 sets of speakers to choose from. For the DVD player, Madelyn has 2 options.
We are supposed to determine how many different entertainment centers Madelyn can make.
Therefore, we need to use the multiplication principle of counting.
According to the multiplication principle of counting, if an event can occur in m ways and a second event can occur in n ways, then the two events can occur in m x n ways.
Let's use the multiplication principle of counting to solve this problem.
The number of ways Madelyn can choose a TV is 7.
The number of ways Madelyn can choose a set of speakers is 7.
The number of ways Madelyn can choose a DVD player is 2.
Therefore, the total number of different entertainment centers Madelyn can make is 7 × 7 × 2 = 98. Answer: 98.
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Which property is used in the following expression ? 5(2 + 7) = 10 + 35
Answer:
That equation is using associative property : )
Step-by-step explanation:
In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=". The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any equality is an equation.
The purpose of the critical value is to ........ divide the region into rejection and non-rejection regions divide the region into rejection and non-rejection regions determine which tailed test to use determine which tailed test to use make the problem harder to work make the problem harder to work determine the level of significance
The critical value determines the boundary for rejecting or not rejecting the null hypothesis in a hypothesis test.
The purpose of the critical value is to divide the region into rejection and non-rejection regions. It helps determine the boundaries for rejecting or not rejecting the null hypothesis in a hypothesis test.
The critical value is based on the chosen level of significance and the distribution of the test statistic, such as the t-distribution or the standard normal distribution.
By comparing the test statistic to the critical value, we can make decisions regarding the acceptance or rejection of the null hypothesis.
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Find the length of the third side. If necessary, round to the nearest tenth. 5 and 9
Answer:
is it a right triangle?
Step-by-step explanation:
Answer:
1. Is it a right triangle?
2. Are you looking for the hypotenuse?
Step-by-step explanation:
What is stapel scale (Type of interval scale)
The Stapel scale is a type of interval scale used in survey research to measure attitudes and opinions. It is a unipolar scale with a range of numerical values, typically from -5 to +5 or -10 to +10, with a neutral point of zero in the center.
The Stapel scale is a type of interval scale that is commonly used in market research. It is a unipolar rating scale that measures attitudes and opinions towards a particular object or concept.
The scale consists of a single horizontal line, with a numerical scale ranging from -5 to +5, and a single adjective or phrase representing the concept being measured placed at one end of the line.
Respondents are asked to rate the concept by placing a mark on the line, with higher values indicating more positive attitudes or opinions and lower values indicating more negative attitudes or opinions.
The Stapel scale is often used in situations where a traditional bipolar scale (such as the Likert scale) may not be appropriate.By using the Stapel scale, researchers can gather precise and nuanced data about people's attitudes and opinions, making it a valuable tool in survey research.
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What is the measure of the central angle that defines the shaded area below if the shaded area takes up 70% of the circle?
Polynomials Find the sum, difference, or product. 19. (5x
3
+4x
2
−3x)−(x
2
+7x+2) 23. 2(2−5t)+t
2
(t−1)−(t
4
−1)
Answer:
Step-by-step explanation:
-----------------------------------------
according to statistics reported on cnbc, a surprising number of motor vehicles are not covered by insurance. sample results, consistent with the cnbc report, showed 46 out of 200 vehicles were not covered by insurance. Develop a 95% confidence interval for the population proportion
The 95% confidence interval for the given population proportion is between 0.1716 to 0.2884.
How to find the confidence interval for a population proportion?The confidence interval for a population proportion is calculated by the formula,
\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)
Where \(\bar{p}\) is the sample proportion and α is the level of significance.
Calculation:It is given that,
The statistics reported on CNBC projects, a surprising number of motor vehicles are not covered by insurance. The sample results are
The sample size n = 200;
The number of successes = 46
So, the sample proportion \(\bar{p}\) = 46/200 = 0.23
For a 95% confidence interval, the level of significance is
α = 1 - 95/100 = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
Then, the z-score for the value 0.025 is
\(z_{\alpha/2}\) = 1.96 (from the table)
Thus, the confidence interval is
\(C.I = \bar{p}\pm z_{\alpha/2}\sqrt{\frac{\bar{p}(1-\bar{p})}{n} }\)
⇒ C.I = 0.23 ± (1.96) × \(\sqrt{\frac{0.23(1-0.23)}{200} }\)
⇒ C.I = 0.23 ± 1.96 × 0.0298
⇒ C.I = 0.23 ± 0.0584
So, the upper limit is 0.23 + 0.0584 = 0.2884 and the lower limit is 0.23 - 0.0584 = 0.1716.
Therefore, the 95% confidence interval for the given population proportion lies between 0.1716 to 0.2884.
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A study examines scores on an employment test and job performance sik months later. This study is most likely attempting to establish a. criterion validity b. face validity c. reliability d. construct validity 11. In the study by Korn, Davis, and Davis, it was determined that department chairs rated B. F. Skinner higher on their "all time" list than historians did. The study featured a(n)scale of measurement. a. nominal b. ordinal c. interval d. ratio
The study is most likely attempting to establish is Criterion validity and the study featured a(n) scale of measurement is Ordinal scale.
10). The study is most likely attempting to establish is: By criterion validity.
Criterion validity measures how well one measure predicts the outcome for another measure.
Here, we are judging how well the scores on the employment test predict the performance of the person.
Nominal Scale: This scale is used to assign labels to variables that have no numerical values.
For eg : Gender (male and female) , colour (brown blue black white)
Ordinal scale: It matters how the values are arranged, but it makes no difference how much they differ.
For eg: 1: Food applications rated from 1 to 5, 5 being the best. If a app is rated as 2 and other is rated as 4 does not mean the later is twice as good as the first.
Interval scale: An interval scale is a numerical scale where the order and size of the difference between the numbers are known. Absolute zero does not indicate absence in an interval scale, it only means there is no value.
For eg: Temperature in degree Celsius. If T1=5o Celsius and T2=15o Celsius this means is a temperature difference of 10o , but with T3=0o does not mean there is no temperature.
Ratio scale: The ratio scale is another numerical scale where the order and size of the difference between the values are known, and where absolute zero denotes the absence of values.
For eg: Salary of people
11). The study featured a(n)scale of measurement is: By ordinal scale
We will rank the chairs on a scale where order counts and the size of the difference is not particularly significant.
Hence, for 10th the option A is correct and for 11th the option B is correct.
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If f(x) is given as an equation and g(x) is given as a table, how i can tell they are inverses
Answer: f(x) and g(x) both represent y of the equations
Step-by-step explanation: f(x) and g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.
tony spent $60 on video games , each video game cost $6 . how many video games did tony buy
Answer:
10
Step-by-step explanation:
8.Points W
and V
create WV¯¯¯¯¯¯¯¯¯.
Point W
is located at (−6,−6)
and point V
is located at (−6,−2).
Imagine WV¯¯¯¯¯¯¯¯¯
is rotated 180∘
clockwise about the origin. Answer the following questions about W′V′¯¯¯¯¯¯¯¯¯¯¯¯.
A: What are the coordinates of point W′?
B: What are the coordinates of point V′?
Answer:
A: What are the coordinates of point W'?
The coordinates of point W' are (6, 6).
B: What are the coordinates of point V'?
The coordinates of point V' are (6, 2).
maybe i think so