Answer:
C. 32,768
Step-by-step explanation:
Step 1
Convert the number of hours to minutes
2.5 hours to minutes = 2 hrs 30 minutes to minutes is calculated as
1 hour = 60 minutes
2 hours 30 minutes =
Cross multiply
(60 minutes × 2 hours) + 30 minutes = 150 minutes.
Step 2
We are told in the question that the bacteria population doubles every 10 minute interval
Find the number of intervals in 150 minutes
= 150 minutes / 10 minutes interval
= 15 intervals
Step 3
The number of bacteria present after 2.5 hours is calculated using the formula of
= Amount of bacterium × 2ⁿ
Where n = number of intervals = 15
Amount of bacterium = single bacterium = 1
Number of bacteria = 1 × 2¹⁵
= 32,768
Therefore, when you start with a single bacterium in a petri dish, the number of bacteria that will there be in 2.5 hours is 32,768
what is the recursive formula for this geometric sequence? 2,-10,50,-250,...
Answer:
an = an-1 * (-5)
a1= 2
Step-by-step explanation:
The recursive formula is
an = an-1 * r
a1= initial term
where a1 is the initial term and r is the common ratio
a1 =2 or the starting term
r = second term / first term = -10/2 = -5
an = an-1 * (-5)
a1= 2
Answer:
The correct answer is D
Step-by-step explanation:
2 and -5
Solve the system of equations and choose the correct ordered pair. 3x-5y+2=21 and 2y=7x+4
Answer:
(-2 ; -5)
Step-by-step explanation:
2*y = 7*x + 47*x - 2*y = -4
(7/2)*x - (2/2)*y = -4/2
(7/2)*x - y = -2
(7/2)*x + 2 = y
3*x - 5*y + 2 = 213*x - 5*y = 21 - 2
3*x - 5*y = 19
3*x - 5*[(7/2)*x + 2] = 19
3*x - 35/2*x - 10 = 19
- 29/2*x = 29
- 1/2*x = 1
x = -2
⇒ y = -5
Answer : (-2 ; -5)
A father requires his son to do chores for 4 to 6 hours a week. If the son wants to do
chores daily, how many hours per day is this (in interval notation)?
Answer: 5 hours and 15 mins
Step-by-step explanation: 45 mins x 7 = 5 hours and 15 mins. I checked so it should be correct. [tex]45x2= 1[/tex]hour and 30 mins.So I multiplied 1 hr 30 x 3 which gave me 4 hr 30 then added 45 mins, then I got 5 hr 15 min.
So in conclusion the answer is 5 hours and 15 mins.
Thank You
a squared paper shows the nets of cuboid A and cuboid B. do the two cuboids have the same surface area? plzzzzzzzzz answer
Answer:
No it doesn't have the same surfaces
The cuboid A and B have different surface areas.
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
Formula for the surface area of cuboidSA=2lw + 2lh + 2hw
Where,
SA is the surface area of a cuboid
l is the length of the cuboid
h is the height of the cuboid
w is the width of the cuboid
Let the area of each cube is one unit.
So, for the cuboid A
Length = 3 unit
Width = 2 unit
Height = 3 unit
Therefore, the surface area of cuboid A = ( 3 × 2 + 3 × 2 + 2 × 2 ) 2
⇒ Surface area of cuboid A = 32 square unit
For cuboid B
Length = 4 unit
Width = 1 unit
Height = 3 unit
Therefore,
The surface area of cuboid B = (4 × 1 + 4 × 3 + 3 × 1)2
⇒ Surface area of cuboid B = 38 square unit
Hence, the cuboid A and B have different surface areas.
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Which Anna quality graft is the solution to X/ < -3
Answer:
Well the following inequality [tex]x<-3[/tex] as a graph is in the image below.
Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times? P (k successes) = Subscript n Baseline C Subscript k Baseline p Superscript k Baseline (1 minus p) Superscript n minus k. Subscript n Baseline C Subscript k Baseline = StartFraction n factorial Over (n minus k) factorial times k factorial EndFraction Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) squared (one-sixth) Superscript 5 Subscript 7 Baseline C Subscript 5 Baseline (one-sixth) Superscript 5 Baseline (five-sixths) squared Subscript 7 Baseline C Subscript 2 Baseline (one-sixth) squared (five-eighths) Superscript 5 Subscript 7 Baseline C Subscript 2 Baseline (two-sixths) squared (four-sixths) Superscript 5
Answer:
Rolling a 4 on the first try has a probability of (1/6). Meaning, it is one event out of the six possible events of the die. Rolling a 4 a second time also has a probability of (1/6), because nothing has changed on the die.
Answer:
Subscript 7 Baseline C Subscript 2 Baseline (one-sixth) squared (five-eighths) Superscript 5
Step-by-step explanation:
The answer above is correct.
What is the approximate value of x in the diagram below? use one of the trigonometric ratios in the table.
Answer:
x = 31.64
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 36 = 23/x
x tan 36 =23
x = 23/tan 36
x=31.63686382
Rounding to 2 decimal places
x = 31.64
Answer:
D. 31.64
Step-by-step explanation:
A quadrilateral has angle measures of 120 degrees ,37 degrees and 48 degrees what is the measure of the forth angle
Answer:
Let the fourth angle be x
Angles in a quadrilateral add up to 360°
To find the fourth angle add all the known angles and subtract them from 360°
That's
x + 120+37+48=360
x + 205 = 360
x = 360-205
x = 155°
Therefore the fourth angle is 155°
Hope this helps
Which of the following best describes the slope of the line below?
O A. Undefined
O B. Negative
O c. Positive
O D. Zero
Answer:
zero or undefined
Answer:
it's d zero.
Step-by-step explanation:
just took the test
Jeremy and Arnold are working on a project for math class in which they are to identify the quadratic equation that represents a rain gauge that sits off the ground. Graph each of the equations and then determine which one could represent the position of the rain catcher that sits above the ground. The x-axis represents the ground. 1. y = x2 + 11x + 24 2. y = –x2 – 6x – 8 Direction of Parabola: ______ Direction of Parabola: ______ Location of vertex with respect Location of vertex with respect to the x axis: _____________ to the x axis: _____________ Determine if the graph depicts Determine if the graph depicts the rain gauge. ___________ the rain gauge. ___________ Why or why not? ___________ Why or why not? ___________ _________________________ _________________________ _________________________ _________________________ 3. y = x2 – 2x + 3 4. y = x2 + 4x + 4 Direction of Parabola: ______ Direction of Parabola: ______ Location of vertex with respect Location of vertex with respect to the x axis: _____________ to the x axis: _____________ Determine if the graph depicts Determine if the graph depicts the rain gauge. ___________ the rain gauge. ___________ Why or why not? ___________ Why or why not? ___________ _________________________ _________________________ _________________________ _________________________ 5. y = 3x2 + 21x + 30 Direction of Parabola: ______ Location of vertex with respect to the x axis: _____________ Determine if the graph depicts the rain gauge. ___________ Why or why not? ___________ _________________________ _________________________
Answer: see below
Step-by-step explanation:
Given ax² + bx + c = 0
If a > 0 (positive), then parabola opens UP
If a < 0 (negative), then parabola opens (DOWN)
Axis of Symmetry: [tex]x=\dfrac{-b}{2a}[/tex]
Max/Min: Plug axis of symmetry into the given equation and solve for y.
1) y = x² + 11x + 24
a=1 b=11
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(11)}{2(1)}=\dfrac{-11}{2}=-3.5\\\\\\\text{Minimum:}\quad y=(-3.5)^2+11(-3.5)+24 = -6.25[/tex]
2) y = -x² - 6x - 8
a=-1 b=-6
a< 0 so parabola opens DOWN
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-6)}{2(-1)}=\dfrac{6}{-2}=-3\\\\\\\text{Maximum:}\quad y=(-3)^2-6(-3)-8 = 1[/tex]
3) y = x² - 2x + 3
a=1 b=-2
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(-2)}{2(1)}=\dfrac{2}{2}=1\\\\\\\text{Minimum:}\quad y=(1)^2-2(1)+3 = 2[/tex]
4) y = x² + 4x + 4
a=1 b=4
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(4)}{2(1)}=\dfrac{-4}{2}=-2\\\\\\\text{Minimum:}\quad y=(-2)^2+4(-2)+4 = 0[/tex]
5) y = 3x² + 21x + 30
a=3 b=21
a> 0 so parabola opens UP
[tex]\text{Axis of symmetry:}\quad x=\dfrac{-(21)}{2(3)}=\dfrac{-21}{6}=-3.5\\\\\\\text{Minimum:}\quad y=3(-3.5)^2+21(-3.5)+30 = -6.75[/tex]
Find the vertex of the function given below.
y= x2 - 6x +1
Answer:
V( 3, -8 )
Step-by-step explanation:
Parable equation is of the form:
( x - h )² = 4p*(y - k)
In that expression, vertex has coordinates V ( h, k )
Then all we have to do is transform the given equation
y = x² - 6x + 1 or x² - 6x = y - 1 (1)
We can get a perfect square trinomial in the first member of the equation according to:
x² - 6x = ( x - 3 )² - 9
(x - 3 )² = x² - 6x + 9
By substitution en equation (1)
( x - 3 )² - 9 = y - 1
( x - 3 )² = y -1 + 9
( x - 3 )² = y + 8
( x - 3 )² = (y + 8 )
Then vertex coordinates are
V( 3 , -8)
Algebraically find the point where the cable and the strut intersect. Interpret your answer. (10 points)
Answer:
√2x+8=x-8
2x+8=x^2-16x+64
-x^2+18x-56=0
x^2-18x+56=0
x(x-4)-14(x-4)=0
(X-4)(x-14)=0
x=4(extraneous) ,x=14
—> x=14
Step-by-step explanation:
Answer: (14,6)
Step-by-step explanation:
Right on edg 2022.
Please answer this question now
Answer:
C = (2,2)
Step-by-step explanation:
B = (10 ; 2)
M = (6 ; 2)
C = (x ; y )
|___________|___________|
B (10;2) M (6;2) C ( x; y)
So:
dBM = dMC
√[(2-2)^2 + (6-10)^2] = √[(y-2)^2 + (x - 6)^2]
(2-2)^2 - (6-10)^2 = (y-2)^2 + (x - 6)^2
0 + (-4)^2 = (y-2)^2 + (x - 6)^2
16 = (y-2)^2 + (x - 6)^2
16 - (x - 6)^2 = (y-2)^2
Also:
2*dBM = dBC
2*√[(2-2)^2 + (6-10)^2] = √[(y-2)^2 + (x - 10)^2]
4*[(0)^2 + (-4)^2] = (y-2)^2 + (x - 10)^2
4*(16) = (y-2)^2 + (x - 10)^2
64 = (y-2)^2 + (x - 10)^2
64 = 16 - (x - 6)^2 + (x - 10)^2
48 = (x - 10)^2 - (x - 6)^2
48 = x^2 - 20*x + 100 - x^2 + 12*x - 36
48 = - 20*x + 100 + 12*x - 36
8*x = 16
x = 2
Thus:
16 - (x - 6)^2 = (y-2)^2
16 - (2 - 6)^2 = (y-2)^2
16 - (-4)^2 = (y-2)^2
16 - 16 = (y-2)^2
0 = (y-2)^2
0 = y - 2
2 = y
⇒ C = (2,2)
Please help with this
Find the area of this circle. Area = _______ in2. Use 3.14 for pi and round to the nearest tenth. A. 35.8 B. 28.3 C. 254.3 D. 1017.4
Answer:
A ≈ 254.5 in²
Option C
Step-by-step explanation:
Area of a Circle Formula: A = πr²
d = 2r
Since we are given diameter d, we simply divide by 2 to get radius r:
r = 18/2 = 9
Then we simply plug it into the formula:
A = π(9)²
A = 81π
A = 254.469
A circle with a radius of 9 inches has an area of 254.3 square inches. The of aarea circle is calculated using the formula πr², where π is a mathematical constant approximately equal to 3.14 and r is the radius of the circle.
Hence, the correct option is C.
The area of a circle is calculated using the formula A = πr², where A is the area and r is the radius of the circle. In this case, the radius is 9 inches, so the area is given by:
In this case, the radius is 9 inches, so the area of circle is given by,
Area = pi × [tex]9^{2}[/tex]
Area = 3.14 × 81
Area= 254.3
The value of pi is approximately 3.14, so the area of the circle is approximately 254.3. However, the question asks for the area rounded to the nearest tenth, so the answer is 254.3.
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PLEASE HELP!!!!
Find the product. Write your answer in
exponential form.
2^6•2^-5
Answer:
2^1
According to the product of powers with the same base, a^m * a^n = a^m+n.
Basically, when you're multiplying exponents with the same base, you can add the powers together to get the answer.
2^6 * 2^-5
The bases are the same, so we can apply this rule.
6 + -5 = 1
This gives you the answer of 2^1.
This year at the state fair they held two hot dog eating contests. The first contest had 19 contestants and the winner would be the person that ate the most regular-sized hot dogs in 15 minutes. The second contest had 23 contestants and the winner would be the person that ate the most jumbo-sized hot dogs in 15 minutes. The data from both contests are shown in the box-and-whisker plots above. Using the box-and-whisker plots, the results for the____-sized hot dog contest has greater variability. The difference in the medians of the two contests is approximately _____times the interquartile range.
Answer:
*regular-sized hot dog contest has greater variability
*The difference in the medians of the two contests is approximately 2 times the interquartile range.
Step-by-step explanation:
Variability of the data from both contests can be compared using the range or interquartile range of each set of data from both contests.
The greater the value of the range or interquartile range, the greater the variability.
Range for regular-sized hot dog contest = 32 - 17 = 15
Range for Jumbo-sized hot dog contest = 22 - 8 = 14
Interquartile range for regular-sized hot dog contest = 27 - 22 = 5
Interquartile range for jumbo-sized hot dog contest = 16 - 11 = 5
Median for regular-sized hot dog contest = 23
Median for jumbo-sized hot dog contest = 14
The difference in the median of both contests = 23 - 14 = 9, which is approximately 2 times the interquartile range (5)
Thus, results for the regular-sized hot dog contest has greater variability, be side its range is 5, which is greater than that for jumbo-sized contest.
The difference in the medians of the two contests is approximately 2 times the interquartile range.
The interquartile range of both contests is 5. The median difference between both contests is 9, it is approximately 2 times 5. (i.e. 9/5 = 1.8 ≈ 2).
Expand to write an equivalent expression: -1/4(-8x+12y)
Answer:
8x -12
Step-by-step explanation:
Use the distributive property. 16 outside wishes to go inside and multiply each term; you get 16x/2 which is 8x minus ¾ of 16 which is 12.
Answer:
2x-3y
Step-by-step explanation:
To expand this expression, use the distributive property.
[tex]-\frac{1}{4}(-8x+12y)[/tex]
To distribute, multiply each term inside the parentheses by the number outside the parentheses.
[tex](-\frac{1}{4}*-8x)+(-\frac{1}{4} *12y)[/tex]
Multiply -1/4 and -8x first.
[tex]((-\frac{1}{4}*-8)x)+(-\frac{1}{4} *12y)[/tex]
[tex]2x+(-\frac{1}{4} *12y)[/tex]
Next, multiply -1/4 and 12y.
[tex]2x+ ((-\frac{1}{4} *12)y)[/tex]
[tex]2x+ -3y[/tex]
A +- becomes a -
[tex]2x-3y[/tex]
PLs help me pls ssssssssssssssssss
Answer:
The answer is p/6-4/5.
hope it helps
Answer:
no
Step-by-step explanation:
Help please. (Given: y ∥ x Prove: m∠5 + m∠2 + m∠6 = 180)
Answer:
Step-by-step explanation:
Concepts used :
sum of angles at a point on straight line is 180
if a transversal intersects two parallel lines then alternate angles are equal.
____________________________________________
∠∠∠∠∠
m∠1 + m∠2 + m∠3 = 180 ____________(A)
reason :sum of angles at a point on straight line is 180
these angles lie on LAM at point A
m∠1 = m∠5
Reason: alternate angles y ∥ x and AC is transversal
m∠3 = m∠6
Reason: alternate angles y ∥ x and AB is transversal
Substituting m∠1 with m∠5 and m∠3 with m∠6
in equation A---m∠1 + m∠2 + m∠3 = 180
m∠5 + m∠2 + m∠6 = 180
Hence proved.
Answer:
The answers are below. Hope this helped. I sacrificed my answers ˙-˙ :)
Step-by-step explanation:
<1 congruent to <5 Given
<3 congruent to <6 Alternate Interior Angles theorem
m<1 = m<5 Alternate Interior Angles theorem
m<3 = m<6 Definition of congruent angles
m<1+m<2+m<3=m< LAM Definition of congruent angles
m<1+m<2+m<3=180 Angle additon postulate
m<5+m<2+m<6=180 Definition of straight angle
Isabel purchased bananas and apples at a grocery store. She spent a total of $9.90 on 3 pounds of apples and 2 pounds of bananas. If the apple cost 3 times as much per pound as bananas, what is the cost per pound of apples??
A) $0.90
B) $1.80
C) $2.70
D) $3.60
Answer:
C. $2.70
If one pound of apples cost 3 times the amount of a pound of bananas, then a pound of apples costs; $2.70.
The cost per pound of apples will be $2.70, which is the correct answer would be option (C).
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let the cost per pound of apples be x, and the cost per pound of banana be y
She spent a total of $9.90 on 3 pounds of apples and 2 pounds of bananas.
So, 3x + 2y = 9.90 ....(i)
And the apple cost 3 times as much per pound as bananas.
So, x = 3y
y = x/3 ....(ii)
Substitute the value of y = x/3 in the equation (i), and solve
3x + 2(x/3) = 9.90
3x + 2x/3 = 9.90
11x/3 = 9.90
11x = 2.97
x = 2.97/11
x = 2.70
Thus, the cost per pound of apples will be $2.70.
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solve the math problem please
Answer:
B, x≥2
Step-by-step explanation:
54 - 10x ≤ 20 + 7x - subtract 20
34 - 10x ≤ 7x - add 10x to 7x
34 ≤ 17x - divide 34 by 7
2 ≤ x - flip the equation - x ≥ 2
Hope this is helpful!
Answer:
Choice B
Step-by-step explanation:
TRUST ME. IF YOU WANT EXPLANATION:
54 - 10x < = 20 + 7x
54 - 20 < = 7x + 10x
34 < = 17x
34/17 < = x
2 < = x.....or x > = 2....its B trust me
9 cans of paint are needed to
paint 4 rooms. Exactly how
many cans of paint are needed to
paint 10 rooms? How many cans
of paint should be purchased?
Exact:
Purchased:
Answer:
Step-by-step explanation:
Write and solve an equation of ratios:
9 4
----- = -----
x 10
Then 4x = 90, and x = 22.5
It will take exactly 22.5 cans of paint to cover 10 rooms. The painter must buy 23 cans.
Can someone help me out please :)
Students in a class sit two major exams.
75% of students pass the maths exam.
80% of those who pass
the maths exam
also pass the science exam. 40% of those
who fail the maths exam pass the science
exam. Find the probability that a student
chosen at random:
(b) fails both exams.
%
Answer:
15%
Step-by-step explanation:
25% fail math
60% of the 25% above fail science
thus,
[tex] \frac{25}{100} \times 60\%[/tex]
=15% of total student
PLEASE HELP
Prison M and pyramid N and have the same base area and the same height. Cylinder P and prism Q have the same height in the same base perimeter. Come Z has the same base area of cylinder y, but its height is three times the height of the cylinder y. The figures? And? Have the same volume
9514 1404 393
Answer:
Cone Z, cylinder Y
Step-by-step explanation:
Pointy objects such as pyramids and cones have 1/3 the volume of a prism (or cylinder) with the same base area. So, for a cone and cylinder of the same base area to have the same volume, the cone must be 3 times as high.
The figures described as having that relationship are ...
cone Z, cylinder Y
_____
Additional comment
The perimeter of a prism is not sufficient to define its base area, unless the shape of the base is well-enough defined. However, the perimeter of the base is useful for determining the lateral surface area. Unfortunately, that is not of any interest in this problem.
The quotient is ??
The remainder is ??
Answer:
The quotient is 10x + 16
The remainder is 28x² + 10x + 22
Step-by-step explanation:
x³ - 3x² + x - 2) 10x⁴ - 14x³ - 10x² + 6x - 10 (10x + 16
10x⁴ - 30x³+ 10x² - 20x
16x³ - 20x² + 26x - 10
16x³ - 48x² + 16x - 32
28x² + 10x + 22
Therefore, the quotient is 10x + 16
The remainder is 28x² + 10x + 22
Graph the line that passes through the points (4, 3) and (1,6) and determine the equation of the line.
Answer:
y = -x + 7
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope Formula: [tex]m = \frac{y2-y1}{x2-x1}[/tex]
Step 1: Find slope
m = (6 - 3)/(1 - 4)
m = -1
Step 2: Find b
y = -x + b
6 = -1 + b
b = 7
Step 3: Rewrite linear equation
y = -x + 7
Answer:
y = -x + 7
Step-by-step explanation:
(x1, y1) = (4 , 3)
(x2, y2) = (1 , 6)
[tex]slope=\frac{y_{2}-y{1}}{x_{2}-x_{1}}\\\\=\frac{6-3}{1-4}\\\\=\frac{3}{-3}\\\\=-1\\\\y-y_{1}=m(x-x_{1})\\\\[/tex]
m = - 1; (4,3)
y - 3 = (-1)(x -4)
y - 3 = -x + 4
y = -x + 4 + 3
y = -x + 7
how can you tell that 4:1 and 12:3 are equivalent ratios?
Answer:
They are equivalent.
Step-by-step explanation:
You can tell because 4:1 can go into 12:3.
If you multiply 4 by 3 you will get 12.
If you multiply 1 by 3 you would get 3.
12:3=4:1
Hope this helps!
Step-by-step explanation: Two ratios are equal if the fractions that represent the are equal.
So we first write the ratios 4 : 1 and 12 : 3 as the fractions 4/1 and 12/3.
Now, to determine whether the two fractions are equal,
we write each fraction in lowest terms.
Notice that 4/1 or 4 is already in lowest terms.
So let's move on.
12/3 can be simplified to 4.
So we have 4 = 4 which is true.
So that's how we know the ratios 4 : 1 and 12 : 3 are equal.
Help please, I'm not timed
Answer:
B 30% you can divide 160 the total by 10then multiply and you can check B and C
What shape will you get if you take a cross section of a square pyramid parallel to its base? ANSWERS: A rectangle A triangle A square A parallelogram
Answer:
A square
Step-by-step explanation:
Since the base is a square, any plane of the pyramid parallel to the base is shaped like a square (except the very top one which is a point).
Square shape will you get if you take a cross section of a square pyramid parallel to its base
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
'A square pyramid is a three-dimensional geometric shape having a square base and four triangular faces/sides that meet at a single point (called vertex) is called a square pyramid.'
According to the given problem,
If a square pyramid is cut along the plane, then the cross-section of the solid is square. Because it is a square pyramid.
Hence, we concluded that square could be formed by slicing the square pyramid by a plane.
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