Yes, because it is expected that as safety rating increases then the price should also increase is the sign of the coefficient for the variable safety rating make sense (option a).
The sign of the coefficient for the variable "safety rating" is positive (1625.20), indicating that as the safety rating increases, the price of the used car also increases. This result aligns with our expectations, as a higher safety rating is generally associated with more advanced safety features and technologies, which can increase the desirability and value of the car.
Customers are often willing to pay a premium for vehicles with better safety ratings, considering the added protection and peace of mind. Therefore, the answer is (a) Yes, because it is expected that as safety rating increases, the price should also increase. This positive relationship suggests that safety rating is a significant factor in determining the price of a used car in this regression analysis.
To know more about coefficient:
https://brainly.com/question/13431100
#SPJ4
The complete question is:
Consider the following computer output from a multiple regression analysis relating the price of a used car to the variables: age of car, mileage, and safety rating.
Coefficients Standard Error t Stat P-value
Intercept 45205.41 5456.70 8.28 0.0000
Age (Year) −23013.84 2757.66 −8.345 0.0000
Mileage −1421.51 110.72 −12.839 0.0000
Safety Rating 1625.20 176.77 9.194 0.0000
Does the sign of the coefficient for the variable safety rating make sense?
(a) Yes, because it is expected that as safety rating increases then the price should also increase.
(b) Yes, because it is expected that as safety rating increases then the price should decrease.
(c) No, because it is expected that as safety rating increases then the price should decrease.
(d) No, because it is expected that as safety rating increases then the price should also increase.
In how many ways can the letters in the word payment be arranged using 5 letters?
To determine the number of ways the letters in the word "payment" can be arranged using 5 letters, we can utilize the concept of permutations.
A permutation is an arrangement of objects where the order matters. In this case, we want to arrange the letters of the word "payment" using only 5 out of the 7 letters available. To calculate the number of arrangements, we use the formula for permutations: nPr = n! / (n - r)!, where n is the total number of objects (letters) and r is the number of objects to be selected (5 in this case).
In the word "payment," there are 7 letters. Therefore, we have 7 options to choose from for the first position, 6 options for the second position, 5 options for the third position, 4 options for the fourth position, and 3 options for the fifth position. Hence, the number of arrangements is:
7P5 = 7! / (7 - 5)! = 7! / 2! = 7 * 6 * 5 * 4 * 3 = 2,520. Therefore, there are 2,520 different ways to arrange the letters of the word "payment" using only 5 letters.
Learn more about payment here: brainly.com/question/32320091
#SPJ11
The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer. 115 182 255 419 442 461 517 739 743 789 807 865 925 984 1026 1063 1064 1165 1191 1222 1222 1252 1277 1290 1358 1369 1409 1455 1479 1519 1578 1578 1599 1604 1605 1696 1736 1799 1815 1853 1899 1926 1966
(a) Can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution?
(b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean=1191.6, s=506.6.]
(a) Yes, a confidence interval for the true average lifetime can be calculated without assuming anything about the nature of the lifetime distribution.
(b) Using the given data, we can calculate a confidence interval with a 99% confidence level for the true average lifetime, with a mean of 1191.6 and a standard deviation of 506.6.
(a) It is possible to calculate a confidence interval for the true average lifetime without assuming any specific distribution. This can be done using methods such as the t-distribution or bootstrap resampling. These techniques do not require assumptions about the underlying distribution and provide a reliable estimate of the confidence interval.
(b) To calculate a confidence interval with a 99% confidence level for the true average lifetime, we can use the sample mean (1191.6) and the sample standard deviation (506.6). The formula for calculating the confidence interval is:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
The critical value depends on the desired confidence level and the sample size. For a 99% confidence level, the critical value can be obtained from the t-distribution table or statistical software.
The standard error is calculated as the sample standard deviation divided by the square root of the sample size.
Once we have the critical value and the standard error, we can calculate the confidence interval by adding and subtracting the product of the critical value and the standard error from the sample mean.
Interpreting the confidence interval means that we are 99% confident that the true average lifetime falls within the calculated range. In this case, the confidence interval provides a range of values within which we can expect the true average lifetime of individuals suffering from blood cancer to lie with 99% confidence.
Learn more about standard deviation here:
brainly.com/question/12402189
#SPJ11
Mark wants to paint a mural. he has 1 1 8 gallons of yellow paint, 1 1 9 gallons of green paint, and 7 8 gallon of blue paint. mark plans to use 3 4 gallon of each paint color. how many gallons of paint will he have left after painting the mural? enter your answer as a simplified fraction.
Mark will have [tex]\( \frac{3}{8}\)[/tex] gallons of yellow paint, [tex]\( \frac{1}{4}\)[/tex] gallons of green paint, and [tex]\( \frac{1}{8}\)[/tex] gallons of blue paint left after painting the mural.
To calculate the amount of paint Mark will have left after painting the mural, we need to subtract the total amount of paint used from the initial amount of paint he has.
The initial amounts of paint are:
Yellow paint: [tex]\(1 \frac{1}{8}\) gallons[/tex]
Green paint: [tex]\(1 \frac{1}{9}\) gallons[/tex]
Blue paint: [tex]\( \frac{7}{8}\) gallons[/tex]
The amount of paint used for each color is:
Yellow paint: [tex]\( \frac{3}{4}\) gallons[/tex]
Green paint: [tex]\( \frac{3}{4}\) gallons[/tex]
Blue paint: [tex]\( \frac{3}{4}\) gallons[/tex]
To find the remaining amount of paint, we subtract the amount used from the initial amount for each color:
Remaining yellow paint = Initial yellow paint - Yellow paint used
Remaining green paint = Initial green paint - Green paint used
Remaining blue paint = Initial blue paint - Blue paint used
Calculating the remaining amounts for each color:
Remaining yellow paint = [tex]\(1 \frac{1}{8} - \frac{3}{4}\) gallons[/tex]
Remaining green paint = [tex]\(1 \frac{1}{9} - \frac{3}{4}\) gallons[/tex]
Remaining blue paint = [tex]\( \frac{7}{8} - \frac{3}{4}\) gallons[/tex]
To simplify the fractions, we need to find a common denominator. The common denominator for 8 and 4 is 8. Converting the fractions to have a common denominator:
Remaining yellow paint = [tex]\( \frac{8}{8} \cdot \frac{9}{8} - \frac{3}{4} \cdot \frac{2}{2}\) gallons[/tex]
Remaining green paint = [tex]\( \frac{8}{8} \cdot \frac{9}{9} - \frac{3}{4} \cdot \frac{2}{2}\) gallons[/tex]
Remaining blue paint = [tex]\( \frac{7}{8} - \frac{3}{4}\) gallons[/tex]
Simplifying the fractions:
Remaining yellow paint = [tex]\( \frac{72}{64} - \frac{6}{8}\) gallons[/tex]
Remaining green paint = [tex]\( \frac{72}{72} - \frac{6}{8}\) gallons[/tex]
Remaining blue paint = [tex]\( \frac{7}{8} - \frac{3}{4}\) gallons[/tex]
Combining the fractions:
Remaining yellow paint = [tex]\( \frac{72 - 48}{64}\) gallons[/tex]
Remaining green paint = [tex]\( \frac{72 - 54}{72}\) gallons[/tex]
Remaining blue paint = [tex]\( \frac{7 - 6}{8}\) gallons[/tex]
Calculating the values:
Remaining yellow paint = [tex]\( \frac{24}{64}\) gallons[/tex]
Remaining green paint = [tex]\( \frac{18}{72}\) gallons[/tex]
Remaining blue paint = [tex]\( \frac{1}{8}\) gallons[/tex]
Simplifying the fractions:
Remaining yellow paint = [tex]\( \frac{3}{8}\) gallons[/tex]
Remaining green paint = [tex]\( \frac{1}{4}\) gallons[/tex]
Remaining blue paint = [tex]\( \frac{1}{8}\) gallons[/tex]
Therefore, Mark will have [tex]\( \frac{3}{8}\)[/tex] gallons of yellow paint, [tex]\( \frac{1}{4}\)[/tex] gallons of green paint, and [tex]\( \frac{1}{8}\)[/tex] gallons of blue paint left after painting the mural.
To know more about gallons visit -
brainly.com/question/14514086
#SPJ11
Solve by substitution.
x-4 y=22
2 x+5 y=-21
To solve the given system of equations using the method of substitution, we will start by isolating one variable in one of the equations and substituting it into the other equation.
Let's solve the first equation, x - 4y = 22, for x:
x = 22 + 4y
Now, substitute this expression for x in the second equation, 2x + 5y = -21:
2(22 + 4y) + 5y = -21
Distribute the 2:
44 + 8y + 5y = -21
Combine like terms:
13y + 44 = -21
Subtract 44 from both sides:
13y = -21 - 44
13y = -65
Divide both sides by 13:
y = -65/13
y = -5
Now, substitute the value of y back into the first equation to solve for x:
x - 4(-5) = 22
x + 20 = 22
Subtract 20 from both sides:
x = 22 - 20
x = 2
Therefore, the solution to the system of equations is x = 2 and y = -5.
To know more about variable visit:
https://brainly.com/question/15078630
#SPJ11
Write the inequality that represents the sentence.
Six less than a number is greater than 54 .
The inequality that represents the sentence "Six less than a number is greater than 54" is x - 6 > 54.
An inequality is a mathematical statement that compares the relative size or value between two expressions or quantities. It expresses a relationship of inequality, indicating that one quantity is greater than, less than, greater than or equal to, or less than or equal to another quantity.
To represent the given sentence as an inequality, we need to translate the words into mathematical symbols.
Let's assume the unknown number as 'x'. "Six less than a number" can be written as x - 6.
The phrase "is greater than" indicates that the expression on the left side is larger than the value on the right side.
The value on the right side of the inequality is 54.
Combining the expressions, we get x - 6 > 54, which represents the inequality.
learn more about inequality here
https://brainly.com/question/30231190
#SPJ11
two airports are located at the points a and c, shown in the figure below. each of the airports locates an airplane at point b and measures the angles of elevation to the airplane. given the elevation angles in the figure and that the two airports at a and c are 743 meters apart, what is the distance, in meters, from the airport at point c to the airplane
To find the distance from the airport at point C to the airplane, we can use the concept of trigonometry. Let's label the angles of elevation from airports A and C to the airplane as angle A and angle C, respectively.
Since we know the distance between the two airports (743 meters) and the angles of elevation, we can use the tangent function to calculate the distances from each airport to the airplane.
Let's say the distance from airport A to the airplane is x meters. Using trigonometry, we have:
tan(angle A) = x / 743
Similarly, let's say the distance from airport C to the airplane is y meters:
tan(angle C) = y / 743
Now, we can rearrange the equations to solve for x and y:
x = 743 * tan(angle A)
y = 743 * tan(angle C)
So, the distance from the airport at point C to the airplane is y meters, which is equal to 743 multiplied by the tangent of angle C.
To know more about concept of trigonometry visit:
https://brainly.com/question/11016599
#SPJ11
The state fair has set up the location of the midway, livestock competition, and food vendors. The fair planners decide that they want to locate the portable restrooms the same distance from each location. Copy the positions of points M, L , and F . Then find the location for the restrooms and label it R .
The location for the portable restrooms should be equidistant from points M, L, and F. Label the location as point R.
To find the location for the restrooms, we need to determine the midpoint of points M, L, and F. The midpoint is the point that is equidistant from all three points. Use the midpoint formula to calculate the coordinates of point R. To find the location for the portable restrooms, we need to locate the midpoint of points M, L, and F. The midpoint is the point that is equidistant from all three points. To calculate the midpoint, we use the midpoint formula, which is (x1 + x2) / 2 for the x-coordinate and (y1 + y2) / 2 for the y-coordinate.
Let's assume that the coordinates of point M are (xM, yM), the coordinates of point L are (xL, yL), and the coordinates of point F are (xF, yF). We can use these coordinates to find the midpoint.
The x-coordinate of the midpoint is calculated as (xM + xL + xF) / 3, and the y-coordinate is calculated as (yM + yL + yF) / 3. Therefore, the coordinates of point R, the location for the portable restrooms, are ((xM + xL + xF) / 3, (yM + yL + yF) / 3). Label this location as point R on the map. This will ensure that the portable restrooms are located the same distance from each of the three locations: the midway, livestock competition, and food vendors.
To know more about state fair, visit:
https://brainly.com/question/30618796
#SPJ11
The concentration of carbon monoxide (CO) in a gas sample is measured by a spectrophotometer and found to be 85 ppm. Through long experience with this instrument, it is believed that its measurements are unbiased and normally distributed, with an uncertainty (standard deviation) of 8 ppm. Find a 95% confidence interval for the concentration of CO in this sample. What is the upper limit of the confidence interval
Since we don't know the sample size, we can't calculate the exact value of the upper limit.
To find the 95% confidence interval for the concentration of CO in this sample,
Use the formula
CI = X ± (Zα/2)(σ/√n)
where,
X is the sample mean (85 ppm)
Zα/2 is the critical value from the standard normal distribution,
which can be found using a table or calculator (for a 95% confidence interval, Zα/2 = 1.96)
σ is the standard deviation of the population (8 ppm)
n is the sample size (which we don't know, but assume to be large enough for the central limit theorem to apply)
Put in these values, we get,
⇒ CI = 85 ± (1.96)(8/√n)
To find the upper limit of the confidence interval,
we just need to add the second term to the sample mean,
Upper Limit = 85 + (1.96)(8/√n)
Since we don't know the sample size,
we can't calculate the exact value of the upper limit.
Therefore, we can say that with 95% confidence, the true concentration of CO in the sample lies somewhere between the lower and upper limits of the confidence interval.
To learn more about statistics visit:
https://brainly.com/question/30765535
#SPJ4
A carpenter is working with a beam that is 10 feet long and in the shape of a rectangular prism. he cuts the beam in half. what happens to the surface area and the volume of the beam?
- The surface area of each cut beam will be half of the surface area of the original beam.
- The volume of each cut beam will be half of the volume of the original beam.
When the carpenter cuts the beam in half, the resulting shape will be two shorter beams of equal length.
Let's analyze the changes in surface area and volume after cutting the beam:
1. Surface Area:
The surface area of a rectangular prism is given by the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height of the prism, respectively.
Before cutting the beam, the length of the beam is 10 feet. So, the surface area of the original beam is 2(10w + 10h + wh).
After cutting the beam in half, each resulting beam will have a length of 5 feet. Therefore, the surface area of each cut beam is 2(5w + 5h + wh).
Comparing the surface area before and after cutting the beam, we can observe the following:
- The length (l) of the beam has reduced by half.
- The width (w) and height (h) remain the same.
As a result, the surface area of each cut beam will be half of the surface area of the original beam. Therefore, the total surface area of both cut beams will also be half of the surface area of the original beam.
2. Volume:
The volume of a rectangular prism is given by the formula: V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.
Before cutting the beam, the length of the beam is 10 feet. So, the volume of the original beam is 10wh.
After cutting the beam in half, each resulting beam will have a length of 5 feet. Therefore, the volume of each cut beam is 5wh.
Comparing the volume before and after cutting the beam, we can observe the following:
- The length (l) of the beam has reduced by half.
- The width (w) and height (h) remain the same.
As a result, the volume of each cut beam will be half of the volume of the original beam. Therefore, the total volume of both cut beams will also be half of the volume of the original beam.
Learn more about surface area on:
https://brainly.com/question/20771646
#SPJ11
one us dollar is worth 0.72 euro how many euro is 125.29 dollars worth?
125.29 dollars is worth approximately 90.17 euros.
To find out how many euros 125.29 dollars is worth, we can use the conversion rate between the US dollar and the euro. Given that one US dollar is worth 0.72 euro, we can set up a proportion to solve for the unknown value:
1 dollar / 0.72 euro = 125.29 dollars / x euro
To solve for x, we cross-multiply and divide:
1 * x = 0.72 * 125.29
x = (0.72 * 125.29) / 1
x ≈ 90.17
It's important to note that exchange rates can fluctuate, so the conversion rate mentioned here might not reflect the current rate. It's always recommended to check for the most up-to-date exchange rate when conducting currency conversions.
for more such questions on proportion
https://brainly.com/question/19994681
#SPJ8
Which expression is NOT equivalent to (25 x⁴y)¹/³ ?
a. x ³√25xy
b. 5 x ³√xy
c. ³√25x⁴y
d. ⁶√625 x⁸y²
The expression that is not equivalent to (25 x⁴y)¹/³ is 5 x³√xy. The correct answer is option (b).
To determine which expression is not equivalent to (25 x⁴y)¹/³, we need to simplify each option and compare them.
Option a, x³√25xy, simplifies to x√25xy, which can be rewritten as x√(5x)√y. This is equivalent to (25 x⁴y)¹/³.
Option b, 5 x³√xy, simplifies to 5 x√xy, which cannot be rearranged to match the given expression of (25 x⁴y)¹/³. Therefore, option b is not equivalent.
Option c, ³√25x⁴y, represents the cube root of 25x⁴y, which is equivalent to (25 x⁴y)¹/³.
Option d, ⁶√625 x⁸y², simplifies to ⁶√625 x²y, which cannot be rearranged to match the given expression. Hence, option (b) is the correct answer.
To know more about expression refer here
brainly.com/question/15994491
#SPJ11
Consider quadrilateral A B C D on sphere P. Note that it has four sides with DC- ⟂ CB-, AB- ⟂ CB-, and DC- ≅ AB-
a. Is CD-⟂ DA-? Explain your reasoning.
Yes, CD- is perpendicular to DA-.
This can be reasoned as follows:
In quadrilateral ABCD on sphere P, we are given that DC- ⟂ CB- and AB- ⟂ CB-. From these perpendicularities, we can conclude that angle DCB is a right angle and angle ABC is also a right angle. Since opposite angles in a quadrilateral on a sphere are congruent, angle ADC is also a right angle.
Now, let's consider sides DC- and DA-. We are given that DC- ≅ AB-. Since congruent sides in a quadrilateral on a sphere are opposite sides, we can conclude that side DA- is congruent to side DC-.
In a right-angled triangle, if one side is perpendicular to another, then the triangle is a right-angled triangle. Therefore, since angle ADC is a right angle and side DA- is congruent to side DC-, we can deduce that CD- is perpendicular to DA-.
Know more about quadrilateral here:
https://brainly.com/question/29934291
#SPJ11
Use a half-angle identity to find the exact value of each expression. sin 7.5°
Using the half-angle identity, we found that the exact value of sin 7.5° is 0.13052619222.
This was determined by applying the half-angle formula for sine, sin (θ/2) = ±√[(1 - cos θ) / 2].
To find the exact value of sin 7.5° using a half-angle identity, we can use the half-angle formula for sine:
sin (θ/2) = ±√[(1 - cos θ) / 2]
In this case, θ = 15° (since 7.5° is half of 15°). So, let's substitute θ = 15° into the formula:
sin (15°/2) = ±√[(1 - cos 15°) / 2]
Now, we need to find the exact value of cos 15°. We can use a calculator to find an approximate value, which is approximately 0.96592582628.
Substituting this value into the formula:
sin (15°/2) = ±√[(1 - 0.96592582628) / 2]
= ±√[0.03407417372 / 2]
= ±√0.01703708686
= ±0.13052619222
Since 7.5° is in the first quadrant, the value of sin 7.5° is positive.
sin 7.5° = 0.13052619222
To know more about the half-angle identity visit:
https://brainly.com/question/14308845
#SPJ11
Consider a single spin of the spinner. a spinner contains 4 equal sections: 1, 2, 4 and 3. sections 1 and 4 are shaded. the spinner is pointed at number 2. which events are mutually exclusive? select two options.
The two mutually exclusive events where we have a spinner with 4 sections: 1, 2, 4, and 3, where sections 1 and 4 are shaded and the spinner is pointed at number 2 are: Selecting a shaded section (1 or 4)
and Selecting an unshaded section (2 or 3)
The term "mutually exclusive" refers to events that cannot occur at the same time.
To determine which events are mutually exclusive, we need to consider the possibilities:
1. Selecting a shaded section (1 or 4): This event is mutually exclusive with selecting an unshaded section (2 or 3). The two options cannot happen simultaneously.
2. Selecting an unshaded section (2 or 3): This event is mutually exclusive with selecting a shaded section (1 or 4). Again, these two options cannot occur at the same time.
Learn more about Mutually exclusive events here: https://brainly.com/question/12961938
#SPJ11
2. researchers collected data on 77 brands of cereal at a local supermarket.25 for each brand, the sugar content (grams per serving) and the shelf in the store on which the cereal was located (1
Researchers collected data on 77 brands of cereal at a local supermarket. For each brand, they recorded the sugar content (in grams per serving) and the shelf on which the cereal was located. The purpose of this data collection was to understand the relationship between sugar content and cereal shelf placement.
To analyze this data, the researchers likely used statistical methods such as correlation analysis. This analysis would help determine if there is a relationship between the sugar content of cereals and their shelf placement.
In a correlation analysis, a correlation coefficient is calculated. This coefficient measures the strength and direction of the relationship between two variables - in this case, sugar content and shelf placement. The correlation coefficient can range from -1 to 1. A value of -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.
The researchers might have found that there was a positive correlation between sugar content and shelf placement. This would mean that cereals with higher sugar content tended to be placed on higher shelves, while cereals with lower sugar content were placed on lower shelves. However, without the actual data and analysis results, it is not possible to say for certain.
In conclusion, researchers collected data on 77 brands of cereal to investigate the relationship between sugar content and shelf placement. Statistical analysis, such as correlation analysis, would be used to determine if there is a relationship between these two variables.
Learn more about supermarket here :-
https://brainly.com/question/32798381
#SPJ11
Find all real square roots of each number. 361/25
To find real square roots of 361/25, simplify the fraction, find the square root of the numerator and denominator separately, and simplify. (19/5) is the only real square root of 361/25.
To find all the real square roots of the number 361/25, we can first simplify the fraction. 361/25 is equal to (19^2)/(5^2).
Now, let's find the square root of the numerator and the denominator separately.
The square root of 19^2 is 19, and the square root of 5^2 is 5.
Therefore, the simplified square root of 361/25 is (19/5).
Since the question asks for all the real square roots, we can say that (19/5) is the only real square root of 361/25.
To know more about real square roots Visit:
https://brainly.com/question/12881942
#SPJ11
A sphere has a volume of `668\ cm^{3}`. what is the radius of the sphere to the nearest thousandth
We find that the radius of the sphere to the nearest thousandth is approximately 4.727 cm.
To find the radius of the sphere, we can use the formula for the volume of a sphere, which is given by:
[tex]V = (4/3) * π * r^3[/tex]
Here, V represents the volume of the sphere and r represents the radius.
Given that the volume of the sphere is 668 cm^3, we can substitute this value into the formula:
[tex]668 = (4/3) * π * r^3[/tex]
To solve for the radius, we can isolate r by dividing both sides of the equation by (4/3) * π:
[tex]r^3[/tex] = (668 / (4/3) * π)
Simplifying the right side of the equation:
[tex]r^3[/tex] = 501 / π
Now, to solve for r, we can take the cube root of both sides:
[tex]r = (501 / π)^(1/3)[/tex]
Calculating the value, we find that the radius of the sphere to the nearest thousandth is approximately 4.727 cm.
To know more about radius visit:
https://brainly.com/question/13449316
#SPJ11
In hopes of encouraging healthier snacks at school, jordan brought in a tray of carrot sticks and apple slices to share. he brought 84 snacks in all. 21 of the snacks were carrot sticks. what percentage of the snacks were carrot sticks?
25% of the snacks were carrot sticks.
To find the percentage of snacks that were carrot sticks, we need to divide the number of carrot sticks by the total number of snacks and then multiply by 100.
The number of carrot sticks is given as 21, and the total number of snacks is given as 84.
Percentage of carrot sticks = (Number of carrot sticks / Total number of snacks) * 100
Percentage of carrot sticks = (21 / 84) * 100
Simplifying the expression:
Percentage of carrot sticks = 0.25 * 100
Percentage of carrot sticks = 25%
To know more about number visit:
brainly.com/question/3589540
#SPJ11
a. Sketch a triangle. Specify three of its measures so that you can use the Law of Cosines to find the remaining measures.
In triangle ABC the measure of side c is 7 cm, measure of angle A is 98° and measure of angle B is 22°.
In the given triangle ABC, AB=c, AC=b=5 cm, BC=a=8 cm and ∠C=60°.
To find AB or c:
Use cosine formula, that is
The formula for the cosine rule is c=√(a²+b²-2ab cosC)
Substitute a, b and ∠C values in cosine law, we get
c=√(8²+5²-2×8×5 cos60°)
c=√(8²+5²-2×8×5× 1/2)
c=√(64+25-40)
c=√49
c=7 cm
To find angle A:
Substitute a, b and c values in cosine law, we get
a=√(b²+c²-2bc cosA)
8=√(5²+7²-2×5×7 cosA)
8²=25+49-70 cosA
64=74-70 cosA
64-74=-70cosA
-10=-70cosA
cosA=10/70
cosA=0.1429
∠A=98°
To find angle B:
By using angle sum property in triangle ABC, we get
∠A+∠B+∠C=180°
98°+∠B+60°=180°
∠B=180°-158°
∠B=22°
Therefore, in triangle ABC the measure of side c is 7 cm, measure of angle A is 98° and measure of angle B is 22°.
Learn more about the cosine rule here:
brainly.com/question/26952873.
#SPJ4
Find the sum of the first 47 terms of the following series, to the nearest integer. 13, 18,23,... 13,18,23,...
The sum of the first 47 terms of the series is 6144.
To find the sum of the first 47 terms of the series, we need to identify the pattern and use the formula for the sum of an arithmetic series.
The given series starts with 13 and increases by 5 each time. So, the common difference is 5.
The formula for the sum of an arithmetic series is:
Sum = (n/2) * (2a + (n-1)d)
where:
- n is the number of terms
- a is the first term
- d is the common difference
In this case, n = 47, a = 13, and d = 5.
Using the formula, we can calculate the sum as follows:
[tex]Sum = (47/2) * (2 * 13 + (47-1) * 5) \\ = (47/2) * (26 + 46 * 5) \\ = (47/2) * (26 + 230) \\ = (47/2) * 256 \\ = 24 * 256 \\ = 6144[/tex]
Therefore, the sum of the first 47 terms of the series is 6144.
To know more about increases visit:
https://brainly.com/question/33491846
#SPJ11
Find the measures of the angles of each triangle.
The ratio of the measures of the three angles is 6: 9: 10 .
The measures of the angles in the triangle are:
Angle 1: 43.2 degrees
Angle 2: 64.8 degrees
Angle 3: 72 degrees
To find the measures of the angles in the triangle, let's assume the three angles have the following ratios:
Angle 1: 6x
Angle 2: 9x
Angle 3: 10x
The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:
6x + 9x + 10x = 18
Combining like terms:
25x = 180
Now, solve for x:
x = 180 / 25
x = 7.2
Now that we have the value of x, we can find the measures of the angles:
Angle 1 = 6x = 6 * 7.2 = 43.2 degrees
Angle 2 = 9x = 9 * 7.2 = 64.8 degrees
Angle 3 = 10x = 10 * 7.2 = 72 degrees
Know more about measures of the angles, here:
https://brainly.com/question/14050276
#SPJ11
A student identification card consists of 4 digits selected from 10 possible digits from 0 to 9 . Digits cannot be repeated.
A. How many possible identification numbers are there?
The total number of possible identification numbers can be calculated using the concept of permutations. Since there are 10 possible digits and each digit can only be used once, we need to calculate the number of permutations of 4 digits taken from a set of 10 digits.
The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items and r is the number of items being chosen. To calculate the number of possible identification numbers, we need to consider the combination of 4 digits selected from a set of 10 possible digits without repetition.
In this case, we can use the concept of combinations. The formula for calculating combinations is:
C(n, k) = n! / (k! * (n - k)!)
Where:
- n is the total number of items to choose from (in this case, 10 digits from 0 to 9).
- k is the number of items to choose (in this case, 4 digits).
Plugging in the values, we have:
C(10, 4) = 10! / (4! * (10 - 4)!)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 210
Therefore, there are 210 possible identification numbers that can be formed using 4 digits selected from 10 possible digits without repetition.
To know more about digits, visit:
https://brainly.com/question/13371877
#SPJ11
Quadrilateral DEFG is a rectangle.
If m ∠ EDF=5 x-3 and m ∠ D F G=3 x+7 , find m ∠ E D F .
The measure of angle EDF in the rectangle DEFG is 22.
In a rectangle, opposite angles are congruent, meaning they have the same measure. Since DEFG is a rectangle, angles DFG and EDF are congruent. Therefore, we can set up an equation based on the given angle measures: m∠EDF = m∠DFG.
m∠EDF = 5x - 3
m∠DFG = 3x + 7
Setting the two angles equal to each other, we have:
5x - 3 = 3x + 7
Simplifying the equation by subtracting 3x from both sides, we get:
2x - 3 = 7
Adding 3 to both sides, we have:
2x = 10
Finally, dividing both sides by 2, we find:
x = 5
To find m∠EDF, we substitute the value of x back into the expression for m∠EDF:
m∠EDF = 5x - 3
m∠EDF = 5(5) - 3
m∠EDF = 25 - 3
m∠EDF = 22
learn more about congruent
https://brainly.com/question/30612076
#SPJ11
Y is directly proportional to x. when x has a certain value, y equals to 4. find the value of y when x is halfed
When x is halfed, the value of y becomes 2.
According to the given information, y is directly proportional to x. This means that as x increases or decreases, y will also increase or decrease by the same factor.
We are told that when x has a certain value, y equals 4. This means that when x = 1, y = 4.
To find the value of y when x is halfed, we can use the concept of direct proportionality. If x is halfed, it becomes x/2. Since y is directly proportional to x, we can also halve y to find its new value.
So, when x is halved, y will also be halved. Therefore, when x = 1/2, y = 4/2 = 2.
In summary, when x is halfed, the value of y becomes 2.
Know more about directly proportional here,
https://brainly.com/question/32890782
#SPJ11
b. In a triangle, sine and cosine are ratios between side lengths. What ratios produce the values in (a)?
The sine and cosine ratios can be used to calculate the values in (a) by comparing the side lengths of the triangle.
b. In a triangle, sine and cosine are ratios between side lengths. What ratios produce the values in (a)?
The ratios that produce the values in (a) are sine and cosine.
Sine is defined as the ratio of the length of the side opposite the angle to the hypotenuse.
Cosine is defined as the ratio of the length of the adjacent side to the hypotenuse.
Therefore, the sine and cosine ratios can be used to calculate the values in (a) by comparing the side lengths of the triangle.
To know more about rations refer here:
https://brainly.com/question/23130410
#SPJ11
A trader sold an article for #82,000 and made a loss of 5%.how much must he sell it to make a profit of 12%,.?
The trader must sell the article for approximately #96,673.68 to make a profit of 12%.To find the selling price needed to make a profit of 12%, we need to first calculate the cost price of the article.
Given that the trader sold the article for #82,000 and incurred a loss of 5%, we can use the following formula:
Selling Price = Cost Price - Loss
Since the loss is given as a percentage, we can rewrite it as:
Loss = (Loss % / 100) * Cost Price
Substituting the given values:
#82,000 = Cost Price - (5/100) * Cost Price
Simplifying:
#82,000 = Cost Price - 0.05 * Cost Price
#82,000 = Cost Price * (1 - 0.05)
#82,000 = Cost Price * 0.95
Now, let's solve for the Cost Price:
Cost Price = #82,000 / 0.95
Cost Price ≈ #86,315.79
To find the selling price needed to make a profit of 12%, we can use the following formula:
Selling Price = Cost Price + Profit
Since the profit is given as a percentage, we can rewrite it as:
Profit = (Profit % / 100) * Cost Price
Substituting the given values:
Profit = (12/100) * #86,315.79
Profit ≈ #10,357.89
Now, let's find the selling price:
Selling Price = Cost Price + Profit
Selling Price = #86,315.79 + #10,357.89
Selling Price ≈ #96,673.68
Therefore, the trader must sell the article for approximately #96,673.68 to make a profit of 12%.
To know more about Profit visit-
brainly.com/question/32864864
#SPJ11
a glass sculpture in the shape of a right square prism is shwon. the base of the sculpture's outer shape is a square s
The surface area of the glass sculpture in the shape of a right square prism can be represented by the equation 10s^2, where s represents the side length of the base square.
A glass sculpture in the shape of a right square prism is shown. The base of the sculpture's outer shape is a square. To find the surface area of the sculpture, we need to calculate the area of each face and then add them together.
To calculate the surface area, we can use the formula: Surface Area = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.
Since the base of the sculpture is a square, we know that the length (l) and width (w) are equal. Let's call this side length s.
To find the surface area, we can substitute the values into the formula:
Surface Area = 2s^2 + 2s*h + 2s*h.
Since the sculpture is a right square prism, we can assume that the height (h) is also equal to the side length (s).
Substituting the values:
Surface Area = 2s^2 + 2s*s + 2s*s.
Simplifying the equation:
Surface Area = 2s^2 + 4s^2 + 4s^2.
Combining like terms:
Surface Area = 10s^2.
So, the surface area of the glass sculpture in the shape of a right square prism can be represented by the equation 10s^2, where s represents the side length of the base square.
Learn more about surface area
brainly.com/question/29298005
#SPJ11
There are 5 identical coins, each with one side labeled heads and the other side labeled tails. You throw the coins on the floor and consider two possible outcomes: 1.) 4 coins show heads and 1 shows tails.
The probability of getting 4 coins showing heads and 1 showing tails is approximately 15.625%.
When throwing the 5 identical coins, there are a total of 32 possible outcomes. This is because each coin has 2 possible outcomes (heads or tails), and since there are 5 coins, we multiply 2 by itself 5 times [tex](2^5 = 32).[/tex]
To determine the probability of getting 4 coins showing heads and 1 showing tails, we need to calculate the number of favorable outcomes. In this case, we have 5 different ways to choose which coin shows tails (since there are 5 coins), and for each of those choices, there is only 1 possible outcome where that specific coin shows tails and the other 4 coins show heads.
So, the probability of getting 4 coins showing heads and 1 showing tails is 5/32.
To calculate the probability as a decimal or percentage, we simply divide 5 by 32:
5/32 ≈ 0.15625 ≈ 15.625%
Therefore, the probability of getting 4 coins showing heads and 1 showing tails is approximately 0.15625 or 15.625%.
To know more about probability visit :
brainly.com/question/14210034
#SPJ11
Let t1 and t2 be linear transformations given by t1 x1 x2 = 2x1 x2 x1 x2 t2 x1 x2 = 3x1 2x2 x1 x2 .
The linear transformations t1 and t2 are given by t1(x1, x2) = 2x1x2 and t2(x1, x2) = 3x1 + 2x2.
The linear transformations t1 and t2 are defined as functions that take in a pair of coordinates (x1, x2) and produce a new pair of coordinates. For t1, the new pair of coordinates is obtained by multiplying the first coordinate, x1, with the second coordinate, x2, and then multiplying the result by 2. So, t1(x1, x2) = 2x1x2.
Similarly, for t2, the new pair of coordinates is obtained by multiplying the first coordinate, x1, by 3 and adding it to the product of the second coordinate, x2, and 2. Hence, t2(x1, x2) = 3x1 + 2x2.
Know more about linear transformations here:
https://brainly.com/question/13595405
#SPJ11
If each color is divided equally among four daughters, how much more pink sand will be available for each girl than purple sand?
If each color is divided equally among four daughters, there will be an equal amount of pink and purple sand available for each girl.
When the colors are divided equally among four daughters, it means that the total amount of pink sand is divided into four equal portions and distributed among the daughters, and the same applies to the purple sand. Since the distribution is equal, each daughter will receive the same amount of pink sand and the same amount of purple sand. Therefore, there won't be any difference in the amount of pink and purple sand for each girl.
To know more about equally,
https://brainly.com/question/28960700
#SPJ11
