Answer: D
Step-by-step explanation:
Answer: Choice D
[tex]x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]
==================================================
Explanation:
Compare the given equation x² + 3x + 7 = 0 to ax² + bx + c = 0 to find that,
a = 1b = 3c = 7Those values are plugged into the quadratic formula to get the following:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-3\pm\sqrt{(3)^2-4(1)(7)}}{2(1)}\\\\x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]
which points us to choice D being the final answer.
--------------
Side note:
The discriminant [tex]d = b^2 - 4ac = (3)^2-4(1)(7) = -19[/tex] is negative, so there are no real solutions. Instead, the two solutions are non-real complex numbers.
The average time it takes college freshmen to complete the mason basic reasoning test is 24.6 minutes. the standard deviation is 5.8 minutes. find the probability that the average completion time for a sample of 28 students will be more than 24 minutes. give your answer as a percent rounded to two decimal places (to the nearest hundredth).
The probability that the average completion time for a sample of 28 students will be more than 24 minutes is 0.46
The mean of freshman mason basic completion time is 24.6 minutes
The standard deviation is 5.8 minutes
The probability of completion for a sample of 28 students will be more than 24 minutes and can be found using the normal distribution,
P(x > 24)
We need to find the standard form of this random sample using the formula,
Z = X - μ / σ
where Z is the standard form
X is the random sample
μ is the mean
σ is the standard deviation
Let us substitute the known values in the above equation, we get
Z = 24 - 24.6/5.8
= -0.6 / 5.8
= -0.103
So the standard form is
P(x > 24) = P(z > -0.103)
By using the z-table, we could find the value of z,
P(z > -0.103) = 0.46
Therefore, the probability is 0.46
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Find the value of (2.4) · (1.3). Show your reasoning.
The evaluation of the expression (2.4) · (1.3) gives 3.12
How to evaluate the expression?From the question, we have the following expression that can be used in our computation:
(2.4) · (1.3)
Express as products
This gives
(2.4) * (1.3)
Remove the brackets
So, we have the following representation
2.4 * 1.3
Evaluate the product
3.12
Hence, the solution is 3.12
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If f(x) = x, when g(x) = f(x) - 10 is graphed on the same coordinate grid, which statement describes the relationship of the graphs of f and g?
The graph g(x) is graph of f(x) translated down 10 units.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is plotted as a series of markers, or dots, and is then connected to one another by a straight line.
Usually, data that changes over time is represented by a line graph.
Given:
f(x) = x, when g(x) = f(x) - 10
As, from the graph we can see that both function f(x) and g(x) shows a parallel relation.
Also, the function f(x) is subtracted from 10 then the function is translated down by 10 units.
Hence, g(x) is graph of f(x) translated down 10 units.
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Neel buys 8 dog treats for 4.40. what cost per dog treats
The cost per dog treat is 0.55 dollars
How to determine this,
The cost of 8 dog treats is 4.40 dollars
And the number of 1 dog treat is x dollar
x dollar=4.40 dollars×1 dog treat/8 dog treats
x=0.55 dollar per one dog treat
To complete the table,
For 18 dog treats
when 1 dog treat is 0.55 dollar
18 dog treats is x dollar
x=18 dog treats×0.55 dollar/1 dog treat
x=9.9dollars
For 25 dog treats,
when 1 dog treat is 0.55 dollar
for 25 dog treats is x dollar
x=25 dog treats×0.55 dollar/1 dog treat
x=13.75 dollars
For 6.05 dollars,
when 1 dog treat is 0.55 dollar
x dog treat is 6.05 dollars
x=6.05 dollars×1 dog treat/0.55 dollar
x=11 dog treat
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Answer:
Step-by-step explanation: 0.55
A ditch used to drain storm water has the shape of a trapezoid with the wider base being 24 feet and the height being 6 feet. The shorter base has an unknown length of x-feet. Set up and solve an equation to find the value of x if the drainage ditch as an area of 96 square feet.
The value of the shorter base which is x is 8 feet.
What is a trapezium?A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper.
It has four sides and four vertices.
The trapezium is made of a rectangle and triangles.
Area of a trapezium = 1/2 (a + b ) h
where a = small base, b = big base and h = height.
from the above, b = 24 feet, h = 6 feet, a = x and area = 96 square feet
substituting the above into the equation
1/2 ( 24 + x) x 6 = 96
6(24 + x) = 96 x 2
6(24 + x ) = 192
multiplying the terms by 6
144 + 6x = 192
6x = 192 - 144
6x = 48
x = 48/6
x = 8 feet
In conclusion, the value of x is 8 feet
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Complete the square to re-write the quadratic function in vertex form:
y = 7x²56x + 117
The answer to the given quadratic equation is y = ( x + 4 )²
How do we solve a question by completing the square method?A(x + m)2 + n is the formula for completing the square, where m is any real number and n is a constant factor.
The following straightforward formula can be used to finish the square instead of the intricate step-by-step procedure. Find the following in order to complete the square in the phrase ax2 + bx + c:
N = c - (b2/4a) and m = b/2a
Enter these numbers where they belong: ax2 + bx + c = a(x + m)2 + n. These equations are geometrically derived.
Given : A quadratic equation y = 7x² + 56x + 117
this can also written as y = x² + 8 x + 17
y = x² + 4² - 4² + 17
y = ( x + 4 )²
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the team is going to a race and can only enter 5 participants. what is the probability of randomly selecting a race squad of 5 participants with exactly 3 women? round your answer to three decimal places. enter your solution into variable
The probability that the squad will have exactly three women members is 0.389
Total number of people in CU Boulder triathlon = 21
Number of Men = 9
Number of Women = 12
We are told that a 5-member squad is selected and now we want to find the probability that the squad will have exactly 3 women members.
Thus;
P(exactly 3 womens) = (12C3 * 9C2)/(21C5)
P(exactly 3 womens) =7920/1716
P(exactly 3 womens) = 0.389
Hence, the probability that the squad will have exactly three women members is 0.389
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Let d represent:
I do not drink bottled water.
Lett represent:
I eat pizza.
What is the symbolic representation of the following statement?
I do not eat pizza or I do not drink bottled water
I eat pizza or drink bottled water, for example, is a symbolic representation of the following statement.
What is meant by symbolic representation?Traditionally, symbolic representation is defined as the representation of a principal, such as a nation, through a symbol, such as a flag, that evokes specific meanings and emotions about the nation. The use of physical or psychological processes to represent an object (either another object or an idea) in a symbolic form is referred to as symbolic representation (Carlson, Sroufe, & Egeland, 2004). A written character or mark that is used to represent something; a letter, figure, or sign that is traditionally used to represent some object, process, etc. (Oxford English Dictionary). Figures denoting the planets, signs of the zodiac, and so on are examples of something visible that represents something else that is invisible by association or convention. Synonyms include symbol, symbolization, and symbolization.To learn more about symbolic representation, refer to:
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about 2% of the population has a particular genetic mutation. 300 people are randomly selected. find the standard deviation for the number of people with the genetic mutation in such groups of 300.
0.0147 is the standard deviation for the number of people .
How to interpret a standard deviation?
The term "standard deviation" (or "") refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high. The standard deviation calculates how much the data vary from the mean value. It is helpful for contrasting data sets that might have the same mean but a different range.standard deviation = sqrt(p*(1-p)/n)
= sqrt(0.07 * 0.93/300)
= 0.0147
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what is the 5th letter of the alphabet
The 5th letter of the alphabet is E.
What is an alphabet?An alphabet is a standardized collection of basic written symbols or graphemes that represent the phonemes of different spoken languages.
The letter a begins the English alphabet and ends with the letter z. The alphabet is always written in the same order: a-b-c-d-e-f-g-h-i-j-k-l-m-n-o-p-q-r-s-t-u-v-w-x-y-z. A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z. This is known as "alphabetical order."
The set of 26 symbols represents sounds used in speech and writing. Each character in a syllabary, for example, represents a syllable, whereas characters in logographic systems represent words, morphemes, or other semantic units. In this case, E is the 5th letter.
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Write the equation of the line that passes through the points (−3,−5) and (−2,−4). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The pair of points (−6, y) and (4, 8) lie on a line with a slope of 5/2. Set up and solve for the missing y-value using the slope formula. Show all work to receive credit.
Given the slope of the line and the pair of points, the missing y - value can be found to be - 17
How to find the missing y - value?The slope formula is:
y = Slope(x) + y - intercept
Using the point (4, 8), the y - intercept can be found by the formula:
8 = 5/2 (4) + y - intercept
y - intercept = 8 - 10
y - intercept = -2
The missing y value is therefore:
y = Slope(x) + y - intercept
= -6 (5/2) - 2
= -15 - 2
= - 17
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my computer crashes on average once every 4 months. what is the probability that it will not crash in a period of 4 months.
The probability that a computer will not crash in a period of 4 months is 0.632.There is a 75% chance that the computer will not crash in a period of 4 months.
To solve this problem stepwise, first calculate the probability that the computer will crash in a given month. This can be done by using the Poisson distribution. The probability that the computer will crash in a given month is 0.0333.
Next, calculate the probability that the computer will not crash in a given month. This is simply 1 - 0.0333, or 0.9667.
Now, to calculate the probability that the computer will not crash in a period of 4 months, simply take the probability of not crashing in a given month and raise it to the 4th power. This gives us a probability of 0.632.
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you have $4000 with which to build a rectangular enclosure with fencing. the fencing material costs $30 per meter. you also want to have two partitions across the width of the enclosure, so that there will be three separated spaces in the enclosure. the material for the partitions costs $25 per meter. what is the maximum area you can achieve for the enclosure? (round your answer to the nearest whole number.) incorrect: your answer is incorrect. m2
The enclosure can be as large as 606 m2 in total.
Given that,
Let x be length of y be width of enclosure
fencing material cost $ 30 / m
Partition material cost $25/m
Total cost = (x+x+y+y)x 30+(y + y) x 25
c= 60(x+y) + 50y = 60 x + 110 y
4000 = 60 x + 110y
y = ( 400 - 6x / 11)
Now,Area of enclosure = x*y
A = x*(400 - 6x / 11)
A'(x)= 400-12x/11
for maximum area A'(x) = 0
400 - 12x/11 = 0,12x = 400,x = 100/3
A " ( x) = - 12/11 < 0 i.e., maximum
y = 400 - 6( 400/12 ) = 200/11 m
Maximum area = xy = 100/3 * 200/11 = 20000/33
=606.0606
A max = 606m²
Hence, the maximum area you can achieve for the enclosure is 606m²
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PLEASE HELP!
4. The last couple of years in the winter season, Mrs. Blair has had to take many days off for one of her kids being sick. She has determined that each kid has a 63% chance of getting sick at some point in the winter months. She has 4 kids.
a) What is the probability that all her kids get sick this winter?
b) What is the probability that at least one kid will get sick this winter?
5. Challenge Problem: If A U B = S (Sample Space), P (A and B) = .25, P (A) = .35, then P(B) = ???
Step-by-step explanation:
4a)
that means all 4 events happen in combination as one event.
so, we have to multiply the probabilities of all 4 events.
that means
0.63⁴ = 0.15752961... ≈ 0.16
so, there is a 16% chance that all 4 children get sick.
in other words, the probabilty for that is about 0.16.
b)
the probabilty of at least 1 kids getting sick is the opposite of the probability of no kids is getting sick.
the probability of getting sick is 0.63, so the probability of not getting sick is 1 - 0.63 = 0.37.
the probability of no kids getting sick is similar to a)
0.37⁴ = 0.01874161 ≈ 0.02
the probabilty of at least one kid getting sick is the opposite of that :
1 - 0.01874161... = 0.98125839 ≈ 0.98
5)
A u B is the sample space. so, any possible event is either part of A or B or both.
that means
P(A') = 0.35 = 1 - P(A)
P(A) = 1 - 0.35 = 0.65
P(A and B') = P(of every A that is not B) = 0.25.
because P(A) = 0.65
that means that
P(A and B) = P(every A that is also B) =
= 0.65 - 0.25 = 0.4
P(B) = P(A') + P(A and B) = 0.35 + 0.4 = 0.75
FYI
we could have gotten this directly from
P(A and B') = P(of every A that is not B = everything that is only A) = 0.25.
because
P(A and B')' = P(of everything that is not "only A" = everything that is B) = P(B) = 1 - 0.25 = 0.75
The price for a taxi cab in a small city is $4.00 per mile, x, while traveling, and $0.50 every minute, y, while waiting. If you have $40 to spend on a cab ride, the inequality 4,00x+0.50y<=40 represents your situation. Graph this inequality in the first quadrant only.
Use the graphing tool to graph the inequality
The graph of the linear inequality 4x + 0.5y ≤ 40 is given by the image at the end of the answer.
How to graph the linear inequality?The first step in graphing the linear inequality is identifying the domain of the situation.
Only numbers in the first quadrant are plotted, hence the first two constrains for the domain are given as follows:
x > 0.y > 0.The inequality is a linear inequality, hence the next step is identify the intercepts and then trace a line connecting them.
The x-intercept is the value of when y = 0, hence:
4x = 40
x = 40/4
x = 10.
Hence it is represented by point (10,0).
The y-intercept is the value of y when x = 0, hence:
0.5y = 40
2 x 0.5y = 2 x 40
y = 80.
Hence it is represented by point (0,80).
The values less than the inequality are plotted, hence the graph is composed by the points on the first quadrant and below the line 4x + 0.5y = 40, as shown by the image at the end of the answer.
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Given the relation {(3,4),(-2,1),(0,6),
(5,-3)), what is the domain of the
relation? Pls help I’m stressing out about it and ik i SHOULDN’T but I can’t help it tbh
Answer:
I think that the answer is going to be 34-21+6=19
Choose the correct word(s) to complete the snetence below. A group of related facts that use the same numbers is called a(n)
Answer: The answer is Fact Family
Step-by-step explanation:
in this exercise you are asked to approximate the growth of the world population using the logistic differential equation:
From the logistic population differential equation for approximate the growth of the world population , which is given here as [tex]P = L/1+ e^{-k(x-x_{0} )[/tex]
The general form of the logistic population equation is given as [tex]dP/dt = kP(1- P/L)[/tex]. While k is the relative growth rate, L is the carrying capacity.An ordinary differential equation with a logistic function as the solution is known as a logistic differential equation. Standard exponential functions do not account for the limitations that prevent infinite growth, but logistic functions correct this oversight. This is how bounded growth is represented by logistic functions. These contexts include machine learning, chess ratings, medical therapy (e.g., modelling tumour growth), economics, and even language adoption research.
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Hello I’m doing my math homework I just need the answers for 23 and that’s just it . ABCDEF all right thank you please get me ASAP,
Answer:
A. -9, -6, 8, 13
B. -4/5, -1/2, -.2, .25
C. -8/3, -2 1/2, 9/2, 4.75
D. -8, -3, -1, 4
E. -1/2, -1/4, .5, 3/4
F. -3/2, -5/4, -4/5, 1.5
Step-by-step explanation:
The easiest thing to do is to put them all in the same format. Fractions are just division problems, so just divide. 4/5 is 4 divided by 5, which is .8.
Remember, the farther a negative number is from 0 on the number line, the smaller it is. So, -8 is smaller than -5. -5 is smaller than -2, etc.
IM BEGGING FOR HELP !!! find the volume of each shape and then compare do not reduce your fractions.
Answer:
64/125 > 150/512
Step-by-step explanation:
4/5 *4/5 *4/5 = 64/125 (also equals 0.512)
5/8 * 6/8 * 5/8 = 150/512 (also equals 0.293)
Therefore: 0.512 > 0.293
Can anyone state the vertex of the graph?
There is no vertex in the graph and the transformations from are
Vertical shift down 2Horizontal shift left 4How to determine the vertex of the graph?By definition, a graph that has a vertex would have an obvious maximum or minimum point on it
In this case, there is no point that can be regarded as the minimum or the maximum in this graph
This means that the graph has no maximum or minimum; in other words, there is no vertex
The transformation from the parent functionThe parent function of the above graph is a cubic function
A cubic function passes through the origin
However in this graph, we can see that the graph is 4 units to the left of the origin and 2 units below the origin
This means that the transformation is (x - 4, y - 2)
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34°
56°
124°
146°
Some help would be nice
Answer:
146 degrees
Step-by-step explanation:
Sum of all triangle angles equal 180 degrees
We know 2
56 and 90 so we add them
90+56=146
Now we subtract to 180 to find the third angle of the triangle
180-146=34
To find x we gotta subtract 34 from 180 since it’s on a flat plane
180-34=146
angle x=146 degrees
hopes this helps please mark brainliest
Ramundo is shopping for a new pair of rollerblades. Roller World sells a pair of rollerblades for $94 regular price. Currently, the rollerblades are on sale for 15% off. Outdoor Adventures sells the same pair of rollerblades for $81.50 with no discount. The sales tax rate in Ramundo's city is 6%.
Part A
To get the better deal, Ramundo should buy the rollerblades from , 1 of 2.
Select Choice
.
Part B
In doing so, he will save , 2 of 2.
Select Choice
(after tax) over the other store.
Ramundo will get a better deal at Roller worlds.
This is a question of percentages.
Given that:-
Regular price of rollerblades at roller world = $ 94
Discount at rollerworld = 15 %
Price of rollerblades at Outdoor adventures = $ 81.50
Sales tax = 6 %
Price of rollerblades at roller world after discount = 94 - (15/100)*94 = 94 - 14.1 = $79.9
Price of rollerblades at roller world after sales tax = 79.9 + (6/100)*79.9 = 79.9 + 4.794 = $ 84.694
Price of rollerblades at outdoor adventures = $81.50
Price of rollerblades at roller world after sales tax = 81.50 + (6/100)*81.50 = 81.50 + 4.89 = $ 87.39
As,
$ 84.694 < $ 87.39
Ramundo will get a better deal at Roller worlds.
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Tyshawn has $600 to spend at a bicycle store for some new gear and biking outfits.
Assume all prices listed include tax.
• He buys a new bicycle for $237.49.
He buys 3 bicycle reflectors for $14.57 each and a pair of bike gloves for $34.52.
He plans to spend some or all of the money he has left to buy new biking outfits
for $71.07 each.
●
●
Use the drop-down menu below to write an inequality representing o, the number of
outfits he can buy while staying within his budget.
Answer: The answer would be 4 biking outfits o=4
Step-by-step explanation:
First add all the money he spent excluding the outfits. The answer would be 315.72. Then subtract 600 and 315.72 = 284.28. Last multiply 71.07 by 4 which gets you 284.28. The EXACT amount he has left. Answer is he can be 4 new biking outfits within his budget. Hope I could help!
If Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
The time taken to label 750 books if Clare labels books at 15 books per minute is 50 minutes.
How to calculate the time used?In this situation, Clare volunteers at a library during the summer and has to label 750 books and she labels books at 15 books per minute and she takes no breaks.
Let the time taken to label the 750 books be represented by x.
This will be illustrated as:
1/x = 15/750
Cross multiply
(15 × x) = (750 × 1)
15x = 750
Divide
x = 750 / 15
x = 50
The time is 50 minutes.
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Complete question
Clare volunteers at a library during the summer and has to label 750 books. Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.
11. Write an equation in vertex form for the parabola below.
Answer:
Step-by-step explanation:
1. The vertex is where the parabola is changing from increasing to decreasing
2. From the picture, we can see that the vertex is at (1,2)
3. The formula for vertex form is f(x)=a(x-h)^2+k
4. Vertex is (1,2) or (h,k)
5. You can see that the parabola opens upside down like a "n" so it has been reflected in the x axis
6. So, your equaltion is f(x)=-(x-1)^2+2
7. In this cause you can see that a=-1, but if not given you would choose a random point on the parabola and plug it in :). Example:(0,1): 1 = a(0-1)^2+2
a=-1.
8. Your answer: f(x)=-(x-1)^2+2
The perimeter of a rectangle is 84 feet. The ratio of the width to the length is
2:5. Find the length and the width.
The width of the rectangle is 12 feet and the length is 30 feet.
What is perimeter?The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.
Given that, The perimeter of a rectangle is 84 feet. The ratio of the width to the length is 2:5.
Let the width be 2x and length be 5x,
Perimeter = 2(l+w)
2(2x+5x) = 84
2x+5x = 84/2
2x+5x = 42
7x = 42
x = 42/7
x = 6
Therefore, width = 6x2 = 12
Length = 5x6 = 30
Hence, The width of the rectangle is 12 feet and the length is 30 feet.
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if 15% of adults in a certain country work from home, what is the probability that fewer than 60 out of a random sample of 500 adults will work from home?
The probability that fewer than 60 adults will work from home will be 2%.
we have to use the Normal probability distribution to find the probability
In a normal distribution with mean μ, SD σ, z-score Z of a measure X is given by
Z = (X-μ)/ σ
here,
15% adults work from home , So p= 0.15
n = 500
∴ μ = np = 500(0.15) = 75
σ = [tex]\sqrt{np(1-p)}[/tex]
σ = 7.98
Now we have selected adults(60) less than n (500)
So using the continuity correction , the probability is P(X< 60 - 0.5)
= P( X< 59.5)
which is the p-value of Z when X = 59.5
∴ Z = (X-μ)/ σ
Z = (59.5 - 75)/7.98
Z = - 1.98
so the p-value is 0.02
0.02 = 2% probability that fewer than 60 adults will work from home.
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A chocolatier makes chocolate bon-bons in the shape of a sphere with a radius of 1.7 cm. The chocolate used in the bon-bons has a density of 1.32 g/cm^3 3 . If the chocolate used costs $0.03 per gram, how much would the chocolate for 190 bon-bons cost, to the nearest cent?
The cost of 190 bon-bons is $154.8
According to the question ,
The shape of chocolate bon-bons is Sphere
Radius of sphere = 1.7cm
Density = 1.32g/cm³
[tex]Volume \ of\ sphere = \frac{4}{3}\pi r^{3}\\[/tex]
[tex]Volume of chocolate bon-bons = \frac{4}{3}\pi (1.7)^{3}[/tex]
[tex]= \frac{4}{3}\pi (4.913)\\= 20.5795cm^{3}[/tex]
Weight of bon-bons = volume × density
weight = 20.5795 × 1.32
= 27.1649g
Given , the cost of chocolate = $0.03
then cost of bon-bons = 0.03 × 27.1649
= $0.81494
We have to find cost of 190 bon-bons.
Cost of 190 bon-bons = 190 × 0.81494
= $ 154.8
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