The values of x1 and x2 are -8/3 and -4/3 through solving the equation 3x²+26x+48=0 by factoring
The equation mentioned in the question is 3x² + 26x + 48 = 0. We need to solve this equation by factoring.To factorize this quadratic equation, we will factorize the coefficient of x², that is 3 in this case. The prime factors of 3 are 3 and 1. Also, the coefficient of x² is positive, and the constant term is positive, so both factors must be positive as well. Therefore, we write 3x² as (3x + p) (x + q), where p and q are two constants.
By multiplying these two factors, we get: 3x² + 3qx + px + pq = 3x² + (3q + p) x + pq .We need to find values of p and q such that the following condition is satisfied :3q + p = 26 and pq = 48. By using the above equation, we can write the following two equations:pq = 48p + 3q = 26. Now, we need to find the value of p and q by solving these equations. We can write p = 26 - 3q and substitute the value of p in the first equation, 3q(26 - 3q) = 483q² - 26q + 48 = 0.By solving this equation, we get the value of q, which is 2/3 or 8.
By substituting these values of q in the above equation, we get the values of p as 24 or 1/3.Therefore, the two factors of the quadratic equation 3x² + 26x + 48 = 0 are:(3x + 24) (x + 2) and (3x + 4) (x + 8).Solving the above two factors, we get x = - 8/3 and x = - 4/3.respectively.
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X1=-8 AND X2=-1
To solve the equation 3x²+26x+48=0 by factoring, one must first find the factors of 3 and 48. Here is the solution:
Step-by-step solution:
Given: 3x²+26x+48=0
To solve this equation by factoring, one must first find the factors of 3 and 48.
Factors of 3 = 1, 3.
Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Now, to make the sum of the middle term 26x, we need to add 3x and 24x.
3x is a factor of 3x² and 24 is a factor of 48.
3x²+3x+24x+24 = 0
Dividing both sides by 3, we get:
x² + 9x + 8 = 0
Factoring the above quadratic equation, we get:
(x+8)(x+1) = 0
So, x+8=0 or x+1=0
Therefore, x=-8 or x=-1
The solution for x1 and x2 are x=-8 and x=-1 respectively.
Hence, the correct answer is "X1=-8 AND X2=-1".
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Consider the figure below.
What are the coordinates of Point S after a dilation with the center at the origin and a scale factor of 12?
Responses
(2,−1)
( 2 , − 1 )
(4,−2)
( 4 , − 2 )
(8,−4)
( 8 , − 4 )
(16,−8)
Thus, the cοοrdinates οf Pοint S after dilatiοn with sοurce as the center as well as a scale factοr οf 12 are (24, 36). Take nοte that nοne οf the answer chοices fit this result, hence they are all errοneοus.
A pοint example is what?There are nο measurements like length, width, οr thickness fοr a pοint. A star inside the sky οffers us a nοtiοn οf pοint. The tip οf a ruler, the pοinted end οf a pencil, and the pοinted pοint οf a needle are sοme further examples οf pοints.
Pοint S's cοοrdinates are (2, 3).
We can use the given equatiοns tο dο a dilatiοn with οrigin as the center and a scale parameter οf 12:
(x', y') = (kx, ky)
Wherein (x, y) are the pοint's initial cοοrdinates, (k), the iteratiοns, and (x', y'), the new cοοrdinates fοllοwing dilatiοn.
Inputting the values results in:
(x', y') = (122, 123)
= (24, 36)
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If we have a total of 30 people and half of them own cats and
40% own dogs. If these two events were independent, how many people
would have a cat and dog?
7 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat for two events based on laws of probability multiplication.
The probability multiplication method can be used to determine the number of persons who own both a dog and a cat if we assume that owning either one is an independent occurrence.
We are aware that 15 out of the 30 people—or 50%—have cats. Also, 12 out of the 30 people, or 40%, are dog owners. The likelihood of owning both a cat and a dog is just the sum of the probabilities of owning both a cat and a dog if we believe that these events are unrelated:
P(having a dog and a cat) = P(having a cat) * (owning a dog)
P (having a dog and a cat) equals (15/30) * (12/30).
P(having a dog and a cat) = 0.25
7.5 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat. We cannot allow a fraction of a person to possess both a cat and a dog though, as we are dealing with a discrete number of people. As a result, we can round to the next whole number or down. As there cannot be a half of a person in this situation, we would round down to 7 people having both a dog and a cat.
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Myesha has a bag that contains orange chews, lemon chews, and lime chews. She performs an experiment. Myesha randomly removes a chew from the bag, records the result, and returns the chew to the bag. Myesha performs the experiment 17 times. The results are shown below:
A orange chew was selected 12 times.
A lemon chew was selected 2 times.
A lime chew was selected 3 times.
Based on these results, express the probability that the next chew Myesha removes from the bag will be a flavor other than lime as a percent to the nearest whole number.
The probability that the next chew Myesha removes from the bag will be a flavor other than lime is 82%.
What is probability?
Probability is the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probabilities between 0 and 1 represent the degree of uncertainty about whether the event will occur or not.
Out of the 17 times Myesha performed the experiment, a lime chew was selected 3 times. Therefore, the probability that the next chew Myesha removes from the bag will be a lime chew is 3/17.
To find the probability that the next chew Myesha removes from the bag will be a flavor other than lime, we need to subtract the probability of getting a lime chew from 1.
P(flavor other than lime) = 1 - P(lime)
P(flavor other than lime) = 1 - 3/17
P(flavor other than lime) = 14/17
To express this probability as a percent to the nearest whole number, we multiply by 100 and round to the nearest integer:
P(flavor other than lime) = 14/17 x 100
P(flavor other than lime) = 82.35
P(flavor other than lime) ≈ 82%
Therefore, the probability that the next chew Myesha removes from the bag will be a flavor other than lime is approximately 82%.
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the length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. seventy percent of the time, it takes more than how many minutes to find a parking space? (round your answer to two decimal places.) 2.91 incorrect: your answer is incorrect. min
70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.
The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. To find the time it takes to find a parking space 70% of the time, we need to find the z-score that corresponds to the 70th percentile.
Using a z-table, we find that the z-score corresponding to the 70th percentile is 0.52. Using the formula z = (x - μ) / σ, where x is the value we are trying to find, μ is the mean, and σ is the standard deviation, we can plug in the values and solve for x:
0.52 = (x - 5) / 2
x - 5 = 0.52 * 2
x - 5 = 1.04
x = 6.04
Therefore, 70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.
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If the parent function is f(x)=2x, then the graph of j(x)=2x – 3 is the translation of the parent function , ... unit(s) , ...
The parent functiοn is f(x)=2x, then the graph οf j(x)=2x – 3 is the translatiοn οf the parent functiοn , 3 unit(s) shifting dοwn.
What is functiοn?A mathematical phrase, rule, οr law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functiοns exist everywhere, and they are crucial fοr cοnstructing physical links in the sciences
Here the given parent functiοn f(x) = [tex]2^x[/tex]
After translation the graph functiοn is j(x)=[tex]2^x-3[/tex]
Then the difference between parent functiοn and translation function is,
=> [tex]2^x-3-2^x[/tex]
=> -3
A transfοrmatiοn knοwn as translatiοn invοlves mοving each pοint in a figure unifοrmly and in the same directiοn.
All the οutput values change by k units. If k is pοsitive, the graph will shift up. If k is negative, the graph will shift dοwn.
Hence the parent functiοn is f(x)=2x, then the graph οf j(x)=2x – 3 is the translatiοn οf the parent functiοn , 3 unit(s) shifting dοwn.
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The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of0.951 gand a standard deviation of0.299 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 37 cigarettes with a mean nicotine amount of0.897 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 37 cigarettes with a mean of0.897 gor less.P(M<0.897 g)=Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exactz-scores orz-scores rounded to 3 decimal places are accepted. Based on the result above, dis it valid to claim that the amount of nicotine is lower? (Let's use a5%cut-off for our definition of unusual.) No. The probability of obtaining this data is high enough to have been a chance occurrence. Yes. The probability of this data is unlikely to have occurred by chance alone.
To determine whether it is valid to claim that the amount of is lower, we need to compare this probability to our chosen cut-off for unusual events, which is 5%.
What is the probability of randomly selecting?To find the probability of randomly selecting 37 with a mean of [tex]0.897 g[/tex] or less, we need to calculate the z-score and look up the corresponding probability in the standard normal distribution table.
Where X is the sample mean [tex](0.897 g),[/tex] μ is the population mean (0.951 g), σ is the population standard deviation [tex](0.299 g)[/tex] , and n is the sample size (37).
Plugging in the values, we get:
[tex]z = (0.897 - 0.951) / (0.299 / sqrt(37)) = -1.731[/tex]
Looking up the corresponding probability in the standard normal distribution table, we find that [tex]P(Z < -1.731) = 0.0419[/tex] (rounded to 4 decimal places).
Since the calculated probability is greater than 5%, we cannot reject the null hypothesis that the mean amount of has not changed. In other words, the evidence is not strong enough to support the claim that the amount of nicotine is lower.
Therefore, the probability of randomly selecting 37 with a mean of [tex]0.897 g[/tex] or less is [tex]0.0419[/tex] .
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In △PQR, the length of PQ⎯⎯⎯⎯⎯ is 16 units. A series of midsegments are drawn such that ST⎯⎯⎯⎯⎯ is the midsegment of △PQR, UV⎯⎯⎯⎯⎯⎯ is the midsegment of △STR, and WX⎯⎯⎯⎯⎯⎯ is the midsegment of △UVR
The length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. It is reasonable to assume that the three midsegments have equal lengths since they are part of the same triangle.
In a triangle, the midsegment is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. In the given triangle PQR, the length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. Since all the midsegments are part of the same triangle, it is reasonable to assume that they have equal lengths. The triangle midsegment theorem, which asserts that the length of a triangle's midsegment is equal to half of the length of the third side of the triangle, may be used to demonstrate this.. In this case, the length of ST, UV, and WX would all be equal to 8 units, since the third side of each triangle is 16 units. This indicates that it is reasonable to assume that the midsegments of the triangle have equal lengths.
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This composite figure is created by placing a sector of a circle on a triangle. What is the area of this composite figure? Use 3.14 for π. Round to the nearest hundredth. Show your work.
What is the answer?
The area of composite figure composed of a sector and triangle is 95.52 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
To get the area of the composite figure, we add the area of the sector to the area of the triangle.
Area of circle sector = (Ф / 360) * π * radius²
but Ф = 82°, radius = 10 cm, π = 3.14, hence:
Area of circle sector = (82 / 360) * 3.14 * 10² = 71.52 cm²
Area of triangle = (1/2) * base * height
but base = 6 cm, height = 8 cm, therefore:
Area of triangle = (1/2) * 6 * 8 = 24 cm²
Area of composite figure = 24 cm² + 71.52 cm² = 95.52 cm²
The area of composite figure is 95.52 cm²
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The equation y=3x+1 models the data below.
x 1 2 3 4 5 6 7 8
y 6 6 8 12 16 18 21 22
a. Calculate the residuals and use the points (x, residual) to make a scatter plot below.
b. Complete the statement below to explain why the model is or is not a good fit.
a. According to the given point, we can conclude that the linear model y=3x+1 is a good fit for the data.
b. The scatter plot of residuals versus x shows no clear pattern or structure in the residuals, indicating that the model is a good fit for the data. Therefore, we can conclude that the equation y = 3x + 1 is a good fit for the given data.
What is the equation of the line?A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
According to the given information:Based on this scatter plot, we can see that there is no clear pattern in the residuals (i.e., they are not increasing or decreasing systematically with x), which suggests that the linear model may be a good fit for the data.
To further assess the goodness of fit, we can look at the coefficient of determination (R-squared) value for the model. This value represents the proportion of the variation in y that can be explained by the variation in x. For this model, we get an R-squared value of 0.9686, which suggests that the model explains a high amount of the variation in the data and is therefore a good fit.
Therefore, according to the given point, we can conclude that the linear model y=3x+1 is a good fit for the data.
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Find the shaded area to 3 s.f. in the following diagrams: (a)6 cm 8 cm
Find the values of each variable. Simplify all answers
The two numbers are x = 3 and y = 8.
Let x and y represent two numbers.
x + y = 16
xy = 24
To solve for the values of x and y, we can use the two equations given. We can first solve for x by dividing both sides of the second equation by y:
xy/y = 24/y
x = 24/y
We can substitute this value for x in the first equation and solve for y:
x + y = 16
(24/y) + y = 16
24 + y^2 = 16y
y^2 - 16y + 24 = 0
(y - 8)(y - 3) = 0
y = 8 or y = 3
Now that we have values for y, we can substitute them into the second equation and solve for x:
xy = 24
(8)(x) = 24
x = 3
(3)(3) = 24
So, the two numbers are x = 3 and y = 8.
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Complete question
Given two numbers x and y such that x + y = 16 and xy = 24, find the values of x and y.
Un granjero tiene pienso para alimentar a sus 12 vacas durante 45 días, si compra 3 vacas más, ¿Cuánto le durará el pienso?
He can feed 15 cows till 36 days because earlier he feed 12 cows till 42 days. So we see we uses the concepts inversely proportional.
What is inversely proportional?In this type of proportional is if their are two quantities then if first one is increase then automatically second one is decrease.
Suppose if a, b are two variables , and if they are indirectly proportional then we can write it as a ∝ 1/b , that means xy = k(where k is constant).
Let number of day be x days.
and, total number of cows = 12 + 3 (After he buy 3 more cow)
then, Number of cows and the number of days are inversely proportion.
So, we can write [tex]\frac{12}{15} = \frac{x}{45}[/tex]
[tex]= x * 15 = 12 * 45[/tex]
[tex]\implies x = 36\ days[/tex]
So, He can feed 15 cows till 36 days.
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Question in English :
A farmer has feed to feed his 12 cows for 45 days. if he buys 3 more cows, How long does the feed last?
if 3x=1,what will be the value of x?find it
[tex] \boxed{ \tt \purple{ x \: = \frac{1}{3} }}[/tex]
_________
[tex] \texttt{3x = 1} \\ \tt \blue{ x = \frac{1}{3} }[/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps-
What is the sum of the exterior angle measures, one at each vertex, of a convex 18-gon?
°
help literally
20 is the sum οf the exteriοr angle measures, οne at each vertex, οf a cοnvex 18-gοn.
What is angle?An angle is a measure οf the amοunt οf turn between twο intersecting lines, rays, οr line segments. It is typically measured in degrees οr radians. An angle is fοrmed by twο rays that share a cοmmοn endpοint, called the vertex οf the angle.
In a cοnvex pοlygοn, the sum οf the exteriοr angles is always 360 degrees. This is knοwn as the Exteriοr Angle Sum Theοrem.
Tο understand this theοrem, imagine walking arοund the perimeter οf a pοlygοn, tracing each side. At each vertex, yοu turn an angle tο cοntinue alοng the next side. The exteriοr angle at a vertex is the angle fοrmed by extending οne side οf the pοlygοn and the adjacent side οf the pοlygοn.
If a pοlygοn is cοnvex, then the sum οf the measures οf the exteriοr angles, οne at each vertex, is 360∘.
Tο find the measure οf each exteriοr angle οf a regular pοlygοn, yοu just divide:
360∘ degrees by the number οf sides.
360∘ / 18 = 20
Therefοre, 20 is the sum οf the exteriοr angle measures, οne at each vertex, οf a cοnvex 18-gοn.
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Complete question:
What is the sum of the exterior angle measures, one at each vertex, of a convex 18-gon?
a. 20
b. 18
c. 360
d. 180
Find the midpoint of the line segment AB if A = (7, 2) and B = (5, -4). ( with photo pls)
Answer:
(6, -1)
Step-by-step explanation:
The midpoint formula, (y2+y1)/2 and (x2+x1)/2 will help us find our answer. So (2-4)/2= -1 and (7+5)/2=6, so (6,-1) is the midpoint of segment AB.
5x-7+3x+27=180
Solve for x.
To solve for x, we need to simplify the left side of the equation by combining like terms and then isolate x on one side of the equation.
First, let's combine the like terms:
5x + 3x = 8x
-7 + 27 = 20
So the equation simplifies to:
8x + 20 = 180
Next, let's isolate x by subtracting 20 from both sides:
8x + 20 - 20 = 180 - 20
8x = 160
Finally, we can solve for x by dividing both sides by 8:
8x/8 = 160/8
x = 20
Therefore, the solution for x is 20.
Question 11
What is the equation of a line passing through (2,-1) and parallel to the line represented
by the equation' = 2x + 1?
Oy=-x+1
Oy=2x-1
Oy=2x-5
2 pts
Oy--1/2x
Answer:
y=2x -5 is the answer of above mentioned questions
A shop is having a sale. Each day, prices are reduced by 20% of the price on the
previous day.
Before the start of the sale, the price of a television is £450.
On the first day of the sale, the price is reduced by 20%.
(a) Work out the price of the television on
i) the first day of the sale
ii) the third day of the sale.
(a) i) The price of the television on the first day of the sale is £360
ii) The price of the television on the third day of the sale is £288
(a)
i) On the first day of the sale, the price of the television is reduced by 20% of £450, which is:
20/100 × £450 = £90
So the price of the television on the first day of the sale is:
£450 - £90 = £360
ii) On the third day of the sale, the price of the television is reduced by 20% of the price on the second day of the sale. To find the price on the second day, we need to calculate the reduction on the first day and subtract it from the original price:
Reduction on first day = 20/100 × £450 = £90
Price on second day = £450 - £90 = £360
On the second day of the sale, the price of the television is reduced by 20% of £360, which is:
20/100 × £360 = £72
So the price of the television on the third day of the sale is:
£360 - £72 = £288
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Drag the number cards so that the values of x are as small as possible
By dragging the number cards to form the lowest sum possible and substituting that sum into the formula for x, we can make the value of x as small as possible.
The formula for x is x = (a + b + c + d)/4. In order to minimize the value of x, we should aim to make the sum of a, b, c, and d as small as possible. To do this, we can drag the number cards to form the lowest sum possible. For example, if the number cards are 5, 6, 7, and 8, we can drag them to form the sum of 26 (5 + 6 + 7 + 8 = 26). To calculate the value of x, we can substitute the sum of the numbers in the formula and divide it by 4. In this example, x = (26/4) = 6.5. By using this strategy, we can minimize the value of x and make it as small as possible.
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Complete question:
What is the smallest value for x when you drag the number cards?
Perry owns 4 1/8 acres of farmland. He grows beets on 3/4 of the land. On how many acres of land does Perry grow beets?
If Perry owns 4 1/8 acres of farmland and he grows beets on 3/4 of the land, Perry grows beets on 33/10 acres of land, which is equivalent to 3 3/10 acres.
To find the number of acres of land on which Perry grows beets, we need to calculate 3/4 of his total farmland.
Perry owns 4 1/8 acres of farmland, which we can convert to an improper fraction to make calculations easier:
4 1/8 = (8 x 4 + 1) / 8 = 33 / 8
To find the portion of land on which Perry grows beets, we can multiply the total land by the fraction 3/4:
(3/4) x (33/8) = (3 x 33) / (4 x 8) = 99 / 32
This is the fraction of the total land on which Perry grows beets. To convert it to a mixed number, we divide the numerator (99) by the denominator (32):
99 ÷ 32 = 3 with a remainder of 3
Therefore, Perry grows beets on 3 3/32 acres of land.
Note that we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 3 in this case:
99/32 = (3 x 33) / (3 x 32) = 33/10
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someone help me plsss
Answer:
Step-by-step explanation:
[tex]\frac{5\pm\sqrt{-4} }{3} =\frac{5\pm2\sqrt{i} }{3}[/tex] (since [tex]i=\sqrt{-1}[/tex])
[tex]=\frac{5}{3} \pm\frac{2}{3}\sqrt{i}[/tex]
[tex]\frac{10\pm\sqrt{-16} }{2} =\frac{10\pm4\sqrt{i} }{2}[/tex]
[tex]=5 \pm2\sqrt{i}[/tex]
[tex]\frac{-3\pm\sqrt{-144} }{6} =\frac{-3\pm12\sqrt{i} }{6}[/tex]
[tex]=-\frac{1}{2} \pm2\sqrt{i}[/tex]
Mike is wondering if there is enough room in an 8 by 10 by 12 inch box for his 13 inch rolling pin. Help Mike by calculating the length
of the diagonal d in the figure below.
Round your answer to the nearest tenths place (one decimal
place).
There will be enough room for Mike since the diagonal is more than 13 inch
How to find if there will be enough room for mikeThe diagonal of a cuboid is a line segment that connects two opposite corners of the cuboid. It passes through the center of the cuboid and represents the longest distance between any two points in the cuboid.
If the diagonal is less than 13 inch then there will not be enough room if otherwise then there will be enough room
To find the diagonal of a cuboid, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In a cuboid, if we label the length, width, and height
diagonal = √(length^2 + width^2 + height^2)
diagonal = √(10^2 + 8^2 + 12^2)
diagonal = √308
diagonal = 17.5 to 1 decimal place
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a right triangle has sides measuring 10, 24, and 26cm. what is the measure of x to the nearest degree
Answer:
D. 67
Step-by-step explanation:
with respect to angle x.
perpendicular is 24.
hypotenuse is 26cm
since we have
sin angle=perpendicular / base
sin x=24/26
x=sin inverse(24/26)
x=67.38
in nearest degree x=67 degree
Solve the inequality
-2x+5>3 or x-5 ≥ -1
Answer:
x>1 or x≥4
Step-by-step explanation:
-2x+5>3 or x-5≥-1
-2x>3-5 or x≥-1+5
-2x>-2 or x≥4
-2x/-2>-2/-2 or x≥4
x>1 or x≥4
Find all vertical asymptotes of the rational function. (Enter your answers as a comma-separated list of equations.)
F(x) =
x2 + 11
6x2 − 19x − 36
is it a option ? or no cuz im a litlle confused
Ervin bowled 7 games last weekend. His
scores are: 155, 165, 138, 172, 127, 193, 142. What
is the sample standard deviation of Ervin's
scores?
The sample standard deviation of Ervin's scores is 41.81.
In this problem, we are given the scores of 7 games bowled by Ervin, and we are asked to calculate the sample standard deviation of these scores. To calculate the sample standard deviation, we first need to calculate the sample mean, which is the sum of the scores divided by the number of games:
mean = (155 + 165 + 138 + 172 + 127 + 193 + 142) / 7 = 138.57
Next, we need to calculate the variance, which is the sum of the squared differences from the mean, divided by the number of games minus one:
variance = [(155-138.57)² + (165-138.57)² + (138-138.57)² + (172-138.57)² + (127-138.57)² + (193-138.57)² + (142-138.57)²] / (7-1) = 1749.62
Finally, we can calculate the sample standard deviation by taking the square root of the variance:
standard deviation = √(variance) = √(1749.62) = 41.81
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Follow through this example before doing the problem.
Jake has enough in the budget to stock 12,000 trout and perch in the lake.
He wants to stock twice as many perch as trout. How many of each fish can
be used under these conditions?
Let t= number of trout
Let p= number of perch
t + p = 12,000
Since there are more perch (p) than trout (t), to set them equal to
each other, you would need to double the trout (t).
2t = p
Now solve for t and p using substitution. Since p = 2t, substitute
this equation (1)
t + p = 12000
t+ 2t = 12000
3t = 12000
12000-4000 = 8,000 perch
Now try this problem:
In this year's winter mammal census, the total number of wolves
and deer counted 495. Last year 7 times as many deer
and 9 times as many wolves were counted for a total of 3775 mammals.
How many of each type of mammal was
counted thi winter?
number of wolves =
number of deer=
The amounts of each type of animal are given as follows:
Wolves = 340.Deer = 155.How to obtain the amounts?The amounts are obtained solving a system of equations, for which the variables are given as follows:
Variable x: number of wolves.Variable y: number of deer.In this year's winter mammal census, the total number of wolves and deer counted 495, hence:
x + y = 495.
x = 495 - y.
Last year 7 times as many deer and 9 times as many wolves were counted for a total of 3775 mammals, hence:
7x + 9y = 3775.
Replacing the first equation into the second, the value of y is given as follows:
7(495 - y) + 9y = 3775
2y = 310
y = 310/2
y = 155.
Then the value of x is given as follows:
x = 495 - 155
x = 340.
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Ms. Delgado stocked up on art supplies for her classroom this year. She ordered 26 watercolor paint sets from color city art supply. Since this was a bulk order, color city reduced the price of each paint set by $1. 50. The total came to $65. Which equation can you use to find the amount of money, p, color city normally charges for a paint set?
The equation will be 26(p − 1.50) = 65 and the amount of money, p, each paint set normally costs is $4.
Ms. Delgado purchases 26 watercolor paint sets
reduced the price of each paint set = $1. 50.
Ms. Delgado spends $65 in all.
we need to find the equation to find p.
The original price of each watercolor paint set.
Solution:
Ms. Delgado purchases 26 Watercolor paint by spending $65 in all.
with a reduction in price of $39
Let 'p' be the original price of each watercolor paint set.
The equation to find p is,
26p - 39 = 65
26p = 65 + 39
26p = 104
p = 4
The original price of each watercolor paint set is $4
The equation to find p, the original price of each watercolor paint set is
26(p − 1.50) = 65 or 26p - 39 = 65
The original price of each watercolor paint set is $4
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Mail surveys have the concern of _____ but have the advantage of _____. Group of answer choices low return rate; eliminating interviewer bias interviewer bias; high return rate sampling bias; interviewer bias increasing socially desirable responses; high return rate
The correct option is a low return rate; eliminating interviewer bias. Mail surveys have the concern of low return rate but have the advantage of eliminating interviewer bias.
A mail survey is a form of a self-administered survey in which the questionnaire is sent to the respondent through the post. Mail surveys are convenient because they allow participants to respond on their schedule and in the privacy of their own homes.
Mail surveys have the concern of a low return rate but have the advantage of eliminating interviewer bias. The concern of mail surveys is a low return rate. One of the greatest advantages of mail surveys is that they do not require any interaction between the researcher and the respondent. Mail surveys' response rate is typically lower than phone or face-to-face surveys. However, it eliminates interviewer bias.
Interviewer bias occurs when the interviewer's characteristics or behavior have an impact on the participant's responses. Interviewer bias can occur in face-to-face interviews or phone surveys. Respondents may attempt to please the interviewer or present themselves in a more favorable light than they otherwise would in order to avoid social disapproval.
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P{multiples of 3}and
P{factors of 12}are subsets of U={x:1≤ x≤ 12}
a. Draw a Venn diagram to illustrate the information
b.List PNQ
C.PUQ
d.PUQ
e. PNQ
b. P(N ∪ Q) = P(multiples of 3 οr factors οf 12) = {1, 2, 3, 4, 6, 8, 9, 10, 12}
c. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
d. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
e. P(N) = P(multiples of 3) = {3, 6, 9, 12}
What is sets?Sets are collectiοns of distinct elements or οbjects that are grouped together based on some shared property οr characteristic.
b. P(N ∩ Q) = P(multiples of 3 and factοrs of 12) = {3, 6, 12}
P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
P(N ∪ Q) = P(multiples οf 3 or factοrs of 12) = {1, 2, 3, 4, 6, 8, 9, 10, 12}
c. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
d. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
e. P(N) = P(multiples of 3) = {3, 6, 9, 12}
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