Answer:
Step-by-step explanation:
The formula is
[tex]y=45(4)^x[/tex]
which models the exponential function
[tex]y=a(b)^x[/tex] where a is the initial amount of whatever it is you have (in our case it's bacteria), b is the growth rate (ours is 4 which means that every day the number from the day before increases by a factor of 4), and x is the number of days. We plug into the formula the values we have, starting with x = 1:
[tex]y=45(4)^1[/tex]
Always raise what's inside the parenthesis first, then multiply in the 45. 4 to the first is 4, and 4 multiplied by 45 is 180. After the first day, there are 180 bacteria present in the culture.
Next, x = 2:
[tex]y=45(4)^2[/tex] which simplifies to
y = 45(16) so
y = 720.
Next, x = 3:
[tex]y=45(4)^3[/tex] which simplifies to
y = 45(64) so
y = 2880
Twelve less than the product of three and a number is less than 21
Answer:
11
Step-by-step explanation:
3 times 11 gives you 33 which would be the product
3 x 11 = 33
subtract the 12(twelve) from the 33(product)
33 - 12 = 21
If an image of a triangle is congruent to the pre image what is the scale factor of the dilation
Answer:
1
Step-by-step explanation:
Because the pre image and dilated image are congruent, the scale factor is 1.
Line segment AB is drawn in the coordinate plane. Carlos graphed the set of points that are the same distance from both point A and point B. What did Carlos graph?
Answer:
Carlos graphed the perpendicular bisector of the segment that joins the two points. (a line)
Step-by-step explanation:
Carlos graphed the set of points that are equidistant from both point A and point B.
Carlos graphed the perpendicular bisector of the segment that joins the two points. (a line)
find the length here
Answer:
The correct answer is
D) 66.35
The sine of the angle = the length of the opposite side. the length of the hypotenuse.
The cosine of the angle = the length of the adjacent side. the length of the hypotenuse.
The tangent of the angle = the length of the opposite side. the length of the adjacent side.
So in shorthand notation:
sin = o/h cos = a/h tan = o/a
Often remembered by: soh cah toa
Answer:
C
Step-by-step explanation:
BC is the opposite of angle 54, adi is AC=39
tan54=opp/adj.
BC=AC(tan54)
BC=39(1.376)=53.6789 close to 53.68
School administrators asked a group of students and teachers which of two
school logo ideas, logo A or logo B, they prefer. This table shows the results.
Logo A
Logo B
Total
Students
67
33
100
Teachers
11
14
25
Total
78
47
125
Are being a student and preferring logo A independent events? Why or why
not?
O A. No, they are not independent, because Astudent) = 0.8 and
A student|logo A) = 0 62.
B. No, they are not independent because P(student) = 0.8 and
A student logo A) 0.86.
C. Yes, they are independent because P(student) = 0.8 and
A student logo A) 0.86
D. Yes, they are independent, because student) = 0.8 and
A student logo A) = 0.62
Answer:
The events are not independent
[tex]P(S) = 0.8[/tex]
[tex]P(Logo\ A) = 0.62[/tex]
Step-by-step explanation:
Given
--------------Logo A --- Logo B ---Total
Students ----- 67----------33--------100
Teachers ----- 11 ----- ----- 14 ----- 25
Total ----- ------78-----------47--------125
Required
Determine if being a student and preferring logo A are independent events
Let P(S) represent probability of being a student
Let P(Logo A) represent probability of preferring logo A
Let P(S n Logo A) represent probability of being a student and preferring logo A
To determine if they are independent, we have to calculate
P(S), P(Logo A) and P(S n Logo A)
P(S) = Total Students / Total Population
[tex]P(S) = 100/125 = 0.8[/tex]
P(Logo A) = Total that prefers Logo A / Total Population
[tex]P(Logo\ A) = 78/125 =0.624[/tex]
P(S n Logo A) = Number of students that prefer logo A / Total Population
[tex]P(S\ n\ Logo\ A) = 67/125 = 0.536[/tex]
If the events are independent, then the following condition must be satisfied
[tex]P(S\ n\ Logo\ A) = P(S) * P(Logo\ A)[/tex]
Substitute the values of P(S), P(Logo A) and P(S n Logo A)
[tex]0.536 = 0.8 * 0.536[/tex]
[tex]0.536 \neq 0.4288[/tex]
Since they are not equal, then the events are not independent
[tex]P(S) = 0.8[/tex]
[tex]P(Logo\ A) = 0.62[/tex]
Answer: b
Step-by-step explanation: just took the quiz
3x + 43 = 4x + 2(4 + 2)
Answer:
x = 31
Step-by-step explanation:
[tex]3x+43=4x+2(4+2)\\\\\rightarrow 2*4=8\\\rightarrow 2*2=4\\\\3x+43=4x+8+4\\\\3x+43=4x+12\\\\3x+43-43=4x+12-43\\\\3x=4x-31\\\\3x-4x=4x-31-4x\\\\-x=-31\\\\\frac{-x}{-1}=\frac{-31}{-1}\\\\\boxed{x=31}[/tex]
Answer:
x=31
Step-by-step explanation:
first we simlify to get the simplist equation. 3x + 43 = 4x + 12. then 4x - 3x equalls and 43 - 12 equals 31.
Please explain how you got your answer also. A class has 21 girls and 12 boys. What is the probability that a boy's name is drawn at random?
12 over 21
21 over 12
12 over 33
21 over 33
The following table shows the possible meal combinations when choosing an entrée and a side dish at Marty's Diner. Side Dish Entrée burger with salad burger with fries burger with fruit tacos with salad tacos with fries tacos with fruit pizza with salad pizza with fries pizza with fruit What is the probability of selecting a combination that includes a burger or a salad? Enter your answer as a reduced fraction, like this: 3/14
Answer:
5/9
Step-by-step explanation:
There are 9 total combinations and 3 of them include a burger, 2 of them that have salad but not a burger. If you add them together it equals 5/9
The probability of selecting a combination that includes a burger or a salad is 5/9
Since the total of 6 outcomes include fries or fruit as the side dish.
There is a total of 9 possible meal combinations. A person must choose an Entree and a side dish.
The Entrees consist of burgers, tacos, and pizzas.
The side dishes consist of salad, fries, and fruit.
To find the number of combinations consisting of fries or fruit, we calculate the individual combinations.
With fries as side dish, which can choose a burger, a pizza or a taco as your Entree.
There are 3 combinations each, there are a total of 6 combinations with fruit or fries as the side dish.
There are 9 total combinations and 3 include a burger, rest 2 that have salad but not a burger.
then probability = 5/9
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ2
PLEASE HELP!!! And please SHOW YOUR WORK! *grade 9 work*
Answer:
4028.5
Step-by-step explanation:
V=4000+4.75 (6)
V= 4000+28.5
V=4028.5
Please Vote Brainliest!
Answer: Hope this helps <3
Step-by-step explanation:
[tex]V=4000+4.75n\\\\Substitute\\V = 4000 + 4.75(6)\\\\Multiply\\\\V = 4000+28.5\\\\Add\\\\V = 4028.5[/tex]
Determine the domain and range of the given function.
The domain is
4
The range is
2
х
-2
2.
4
-4
Answer: domain is all real numbers and range is all real numbers greater than or equal to -2
Step-by-step explanation:
find the value of a and b for which the system of equations has infinitely many solutions : 2x + 3y = 7 ; (a-b)x + (a+b)y = 3a + b - 2
Answer:
a= 5 and b=1
Step-by-step explanation:
To solve, we will follow the steps below:
2x + 3y = 7
(a-b)x + (a+b)y = 3a + b - 2
We should note that since it has infinitely many solutions then,
[tex]\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } = \frac{c_{1} }{c_{2} }[/tex]
Hence
2/a-b = 3/a+b = 7/3a +b-2
2/a-b = 3/a+b
cross-multiply
3(a-b) = 2( a+b)
open the bracket
3a - 3b = 2a + 2b
collect like term
3a - 2a = 2b + 3b
a = 5b -------------------------------------------(1)
Similarly
3/a+b = 7/3a +b-2
cross-multiply
7(a+b) = 3(3a+b -2)
7a + 7b = 9a + 3b -6
take all the variables to the left-hand side of the equation
7a - 9a+ 7b-3b = -6
-2a + 4b = -6 ---------------------------------(2)
but a = 5b
substitute a= 5b in equation (2) and solve for b
-2(5) + 4b = -6
-10 + 4b = -6
add 10 to both-side of the equation
-10 + 10+ 4b = -6+10
4b = 4
divide both-side of the equation by 4
b = 1
substitute b= 1 in equation (1)
a = 5b
a =5(1)
a=5
Therefore, a= 5 and b=1
If n is the term, what is the first integer value of n where the sequence 2n² is greater than 50?
Answer:
The 6th term is first integer value of n greater then 50 in the 2n^2 sequence.
Step-by-step explanation:
2n^2 sequence:
2,8,18,32,50,72
A new pair of sunglasses is regularly priced at $130.00. What
will the price be after at 35% discount? *
Answer:
$ 84.50
Step-by-step explanation:
Regular price = $130
Discount = 35% of 130
= [tex]\frac{35}{100}*130[/tex]
= 0.35 * 130
= $ 45.50
Price of the sunglasses after discount = Regular price - discount
= 130 - 45.50
= $ 84.50
Find the number if: 5/9 of it is 90 PLEASE EXPLAIN
Answer:
The number is 162Step-by-step explanation:
Let the number be x
5/9 of the number is 90
Which is
5/9 of x = 90
5/9 × x = 90
5/9x = 90
Multiply through by 9
That's
5x = 810
Divide both sides by 5
5x/5 = 810/5
x = 162
Therefore the number is 162
Hope this helps you
graph the parobola. y=4x^2-7
Answer:
Step-by-step explanation:
y=4x^2-7
vertex(0,-7)
Identify the transformation on the figure shown.
A) rotation about the x-axis
B) rotation about the y-axis
C) reflection over the x-axis
D) reflection over the y-axis
Thank you
Answer:
It is a reflection over the y-axis (D)
Step-by-step explanation:
Each corresponding point is equidistant from the y-axis and follows the rule (x,y) turns to (-x,y). For example the point (1,1) is mapped to (-1,1) and both points are 1 unit away from the y-axis so we know that one is the reflection of the other.
Answer:
reflection over y axis
Step-by-step explanation:
did it on usatestprep and made a 100
21 POINTS!!!!!!!!!!!!!!!!! HEEEELPPPPPPP
Find the area of a trapezoid with bases of 5 feet and a 7 feet, and a height of 3 feet a. 18 b. 36 c. 72 d. 40
Answer:
The answer is option A. 18Step-by-step explanation:
Area of a trapezoid = 1/2(a + b) × h
where
h is the height
a and b are the other sides
From the question
h = 3 feet
a = 5 feet
b = 7 feet
Area = 1/2(5+7) × 3
= 1/2 ( 12) × 3
= 6 × 3
The answer is
= 18
Hope this helps you.
12/31/2019: At the end of the first year of operations, Yolandi Company had $900,000 in sales and accounts receivable of $350,000. XYZ's management has estimated that $9,000 in accounts receivable would be uncollectible.
Answer:
The journal entry to record bad debt expense should be:
December 31, 2019, bad debt expense
Dr Bad debt expense 9,000
Cr Allowance for doubtful accounts 9,000
Net account receivables = $350,000 - $9,000 = $341,000
The allowance for doubtful accounts is a contra asset account that decreases the balance of accounts receivable (balance sheet). Bad debt expense is included in the income expenses and decreases total sales.
Please help meeeee thanks
Answer:
A)21
B) 70
C)89
Step-by-step explanation:
Answer:
b=70°a=21°c= 89°Step-by-step explanation:
b=180° - 110° =70°
a = 21°
C= 180° - b - a= 180 - 70 - 21= 89°
[tex]good \: luck[/tex]
Given: Q = 7m + 3n, R = 11 - 2m, S = n + 5, and T = -m - 3n + 8.
Simplify Q + S - T.
-8m - 7n - 3
8m + 7n - 3
-8m + 7n - 3
8m - 7n - 3
Answer:
The second: 8m + 7n - 3Step-by-step explanation:
Q = 7m + 3n,
R = 11 - 2m,
S = n + 5,
T = -m - 3n + 8.
Q + S - T = 7m + 3n + (n + 5) - (-m - 3n + 8)
Q + S - T = 7m + 3n + n + 5 + m + 3n - 8
Q + S - T = 8m + 7n - 3
The sum of 54 anid six times a number is 216. Find the number.
Answer:
x = 27
Step-by-step explanation:
Step 1: Write out equation
54 + 6x = 216
Step 2: Solve for x
6x = 162
x = 27
Answer:
x=27
Step-by-step explanation:
54+6x=216
Collect like terms:
6x=216-54
6x=162
Divide both sides by the coefficient of x
6x\6=162\6
x=27
If x = 6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
Answer:
The discriminant equals to 0
Step-by-step explanation:
We have to remember our discriminant rules;
d > 0, we have 2 real roots
d = 0, we have 1 real root
d < 0, we have 2 complex roots
Graph this following function
Answer:
Please find attached the graph of the following function;
[tex]\left\{\begin{matrix}x - 1 & if & -2 \leq x < 0\\ 1 & if & x = 0 \\ 3 & if & 0 < x \leq 2\end{matrix}\right.[/tex]
Step-by-step explanation:
We note that the function is linear from x = 2 to just before x = 0
The linear relationship of the function f(x) with x changes just before x = 0
At x = 0, the value of f(x) is indicated as 1
From just after x = 0, the function is a straight horizontal line y = 3
The function also changes value immediately after x = 0 to the line y = 3
The areas where the function is defined are shown in continuous lines
Jessica saved a total of $58.50 to spend on school supplies. She wants to buy one backpack for $36.25 and she wants to spend the rest on folders with paper. Each folder filled with paper costs $3.89. Select the inequality that shows how many folders filled with paper (x) Jessica can buy. A. $36.25+$3.89x≥$58.50 B. $36.25+$3.89x≤$58.50 C. $36.25x+$3.89≥$58.50 D. $36.25x+$3.89x≤$58.50
Answer:
B. $36.25+$3.89x≤$58.50
Step-by-step explanation:
It has to be less than or equal to $58.50
Answer:
$36.25+$3.89x≤$58.50
Step-by-step explanation:
Let x be the number of folders with paper Jessica buys. If Jessica buys x folders for $3.89 each, then she pays $3.89x for all x folders.
She wants to buy one backpack for $36.25, so her total buying costs
$36.25 + $3.89x
Jessica saved a total of $58.50 to spend on school supplies, then her total buying cannot exceed this sum, so the answer would be $58.50.
Please answer it in two minutes
Answer:
p = 3
Step-by-step explanation:
We have a right triangle with both legs equal, whose hypotenuse is 3 times the root of 2.
We know both legs are equal because we have identical opposite angles in this right rectangle.
If we apply the Pythagorean theorem, we obtain:
[tex]p^2+p^2=(3\sqrt{2})^2=9\cdot 2=18\\\\2p^2=18\\\\p^2=18/2=9\\\\p=\sqrt{9}\\\\p=3[/tex]
Angle ABC is bisected by line segment AD. If angle ABC measures 108° and one of the smaller angles created by line AD measures (5x+4), what is the value of x?
Answer:
x = 10
Step-by-step explanation:
One of the smaller angles that is created by the angle bisector measures 5x+4.
An angle bisector cuts an angle into two equal parts. So, 5x+4 = 1/2 (108) or
2(5x+4)=108 (divide both sides by 1/2)
10x+8=108 (distribute)
10x=100 (subtract 8 from both sides)
x=10 (divide by 10)
x=10
What is the area of the rhombus shown below? AC=17 BD=15 AB=11.2 Answers: A. 255 square units B. 190.4 square units C. 16 square units D. 127.5 square units
Answer:
D. 127.5 square units
Step-by-step explanation:
AC=17
BD=15
AB=11.5
Diagonal (1&2) are given, base of the rhombus is also given.
Height is not given
Area of a rhombus given the diagonals
=1/2×d1×d2
Where,
d1=AC=17
d2=BD=15
Area of a rhombus=1/2×d1×d2
=1/2×17*15
=1/2×255
=127.5
D. 127.5 square units
Answer:
D for sure
Step-by-step explanation:
Dependent variable C depends on both independent variable A and independent variable B. Which statement is correct?
A: the relationship between independent variable A and Dependent variable C and the relationship between independent variable A and Dependent variable C can both be analysed using the same scatterplot.
B: the relationship between independent variable A and Dependent variable C and the relationship between independent variable A and Dependent variable C can both be analysed, but they must analyzed using separate scatterplotd.
C: Only the relationship between independent variable A and dependent variable C can be analyzed a scatterplotd.
D: Only the relationship between independent variable B
and dependent variable C can be analyzed a scatterplotd.
Answer:
B
the relationship between independent variable A and Dependent variable C and the relationship between independent variable A and Dependent variable C can both be analysed, but they must analyzed using separate scatterplotd
Answer:
its B
Step-by-step explanation:
use the elimination method to solve the system of equations. choose the correct ordered pair x+y=3 y=8
Answer:
(-5, 8)
Step-by-step explanation:
Step 1: Multiply 2nd equation by -1
x + y = 3
-y = -8
Step 2: Elimination
x = -5
Step 3: Find y
y = 8