The insect population after 4 weeks will be 160 to the nearest whole number.
The student is asking about the function f(x) = 10(2)ˣ, which models an insect population after x weeks.
To find the population after 4 weeks, we need to substitute x with 4 in the function:
f(4) = 10(2)⁴
Now we calculate the value:
f(4) = 10(16) = 160
So, to the nearest whole number, the insect population after 4 weeks will be 160.
There are three boys and three girls at a party. In how many ways can they be seated if they can sit down four at a time?
Answer:
6 Ways. (I could be wrong. If I am, I will come back and edit)
Step-by-step explanation:
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BBGB
BGBB
BGBG
BGGG
BGGB
The number of the ways of sitting of the three girls and three boys will be 4.
What are permutation and combination?Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.
Given that there are three boys and three girls at the party. The number of the ways will be calculated as,
N = ⁴C₃
N = (4!) / (3)!(4-1)!
N = 4
Therefore, the number of the ways of sitting of the three girls and three boys will be 4.
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-5 < x - 4 greater than it equal 1
We have expression [tex]-5 < x - 4 \geq 1[/tex] that renders the system of inequalities,
[tex]
\begin{cases}
-5 < x - 4 \\
x - 4 \geq 1
\end{cases}
[/tex]
Which can be simplified to,
[tex]
\begin{cases}
x > -1 \\
x \geq 5
\end{cases}
[/tex]
So what we get is something greater than -1 and at the same time greater or equal to 5, so the solution is,
[tex]x\in(\infty,-1)\cap(\infty, 5]=\boxed{(\infty,5]}[/tex].
Hope this helps.
A dog shelter had 20 puppies last month. This month, 31 puppies are at the shelter!
What is the percent of increase?
Answer:11
Step-by-step explanation:
Because I said so
HELP ASAP MARKJNG AS BRAINLIST
Answer:
114°
Step-by-step explanation:
By property of intersecting chords inside a circle.
[tex] \because \angle \: 1 = \frac{1}{2} (x + y) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} (96 + 132) \\ \\ \therefore \: \angle \: 1 = \frac{1}{2} \times 228\\ \\ \huge \red { \boxed{\therefore \: \angle \: 1 = 114 \degree}}[/tex]
If you could only plot 5 points to graph y=sinx, which points would you choose? How would you connect these points? Please explain
If you could only plot 5 points to graph y = cosx, which points would you choose? How would you connect these points? Please explain this too!
Answer:
For both graph I would choose the following points: 0°, 90°, 180°, 270° and 360°. I would connect the points (in both cases) with an smooth arc.
Step-by-step explanation:
x sin(x) cos(x)
0° 0 1
90° 1 0
180° 0 -1
270° -1 0
360° 0 1
A circle has a sector with area 1/2 pi and central angle of 1/9 pi radians. What is the area of the circle
Answer:
[tex]9\pi[/tex] sq. units.
Step-by-step explanation:
It is given that a circle has a sector with area [tex]\frac{1}{2}\pi[/tex] and central angle of [tex]\frac{1}{9}\pi[/tex] radians.
We know that, the area of sector is
[tex]A=\dfrac{1}{2}r^2\theta[/tex]
where, r is radius and [tex]\theta[/tex] is central angle in radian.
Substitute the values of A and [tex]\theta[/tex].
[tex]\dfrac{1}{2}\pi=\dfrac{1}{2}r^2(\dfrac{1}{9}\pi)[/tex]
[tex]1=r^2(\dfrac{1}{9})[/tex]
[tex]9=r^2[/tex]
[tex]3=r[/tex]
The radius of the circle is 3 units.
So, the area of circle is
[tex]A=\pi r^2[/tex]
[tex]A=\pi (3)^2[/tex]
[tex]A=9\pi[/tex]
Therefore, the area of circle is [tex]9\pi[/tex] sq. units.
a) Work out the value of (square root of 5)^2 x (square root of 3)^2?
Answer:
15
Step-by-step explanation:
Square root of 5=√5
Square of the square root=(√5)^2
=5
Square root of 3=√3
Square of the square root=(√3)^2
=3
So (square root of 5)^2×(square root of 3)^2
5×3
15
Therefore the final answer is 15
12(x - 4) + 4(x + 7)
Answer:
16x -20
Step-by-step explanation:
12(x - 4) + 4(x + 7)
12x - 48 + 4x +28
16x - 20
Answer:
16x - 20
Step-by-step explanation:
Given
12(x - 4) + 4(x + 7) ← distribute both parenthesis
= 12x - 48 + 4x + 28 ← collect like terms
= 16x - 20
Simplify to create an equivalent
1+ 46p - 9)
Choose 1 answer:
Answer:
[tex]8 + 46p[/tex]
Step-by-step explanation:
Step 1: Combine like terms
[tex]1 + 46p - 9[/tex]
[tex](1 - 9) + 46p[/tex]
[tex]8 + 46p[/tex]
Answer: [tex]8 + 46p[/tex]
You can also pull out a two from both
[tex]8 + 46p[/tex]
[tex]2(4 + 23p)[/tex]
PLEASE HELP ME I DONT UNDERSTAND
Answer:
Picture #1: x=16 ; y=10
Picture #2: x=21 ; y=15
Picture #3: x=18
Step-by-step explanation:
Picture #1:
(8x-14)* and (5x+34)* are Alternate Exterior Angle so they are congruent. And (8x-14)* and (5y+16)* are supplementary so they equal 180*.
Picture #2:
(6x+7)* and (3x-16)* are supplementary so they equal 180*. And (6x+7)* and (11y-32)* are Vertical Angles so they are congruent.
Picture #3:
(7x-6)* and (4x-7)* are supplementary so they equal 180*.
_____the number or variable that is raised to a power in an exponential expression
Answer:
Base
Step-by-step explanation:
To give an example, in the expression [tex]10^6[/tex], 10 is our base and 6 is our exponent or power.
Started at 15 degrees and dropped 4 degrees and dropped 4 degrees each minute
Answer:
15-4 11 -4x
Step-by-step explanation:
Rhonda grows and sells pumpkins. The function C = 3n + 25 represents her cost, in dollars, for producing n pumpkins. Her revenue, or the amount she receives for selling n pumpkins, can be represented by the function R = 5n. Which function represents Rhonda’s profit, P, for selling n pumpkins?
Answer:
2n + 25
Step-by-step explanation:
Cost of pumpkin (C) = 3n + 25
Revenue (R) I.e selling price = 5n
Her profit (P) = Selling price (R) - cost price (c)
P = R - C
P = 5n - (3n + 25)
P = 2n - 25
The expression for her profit (p) = 2n - 25
Answer:
P = 2n – 25
Step-by-step explanation:
:)
Solve the systems of equations by substitution
3/8x + 1/3y = 17/24
X + 7y = 8
Answer:
If your solving for y...
The answer would be: y = -9/8x + 17/8 I believe.
For the second one... it would be : y = -1/7x + 8/7
Step-by-step explanation:
what is the answer to this problem
Answer:
-5 > -7
-2 < 2
-10 < -3
-9 < 2
5 > -9
Step-by-step explanation:
please give me brainliest
I need help with this please I’ll mark as brilliant
What is the volume of a sphere with a radius of 1 foot? (Use 3.14 for π.) 37.68 ft 3 12.56 ft 3 4.19 ft 3 50.24 ft 3
What two numbers added equal 40 but when subtracted equal 10?
PLZ!!!!!!!!!!!!!!!!!!!! HELPPPPPPPPPPPPPPPPPPPP
Answer:
25 and 15
You can easily make a system of equations:
x + y = 40
x - y = 10
Solving for x on equation 2 gets x = 10 + y.
Plugging in this into the first equation, you get 10 + y + y = 40
Thus, 10 + 2y = 40
y = 15.
Plugging this back into either equation gets x = 25.
Point B has coordinates (4,2). The x-coordinate of point A is negative 1. The distance between point A and point B is 13 units. What are the possible coordinates of point A?
The possible coordinates of point A are
Answer:
5.8 and 7.4
Step-by-step explanation:
A school bus has 23
seats that will fit 3
students each and
one seat that will fit 2
students. How many
students will fit on
the bus?
Answer:
101
Step-by-step explanation:
Answer:
The correct answer is 71.
6 times a number is 16 less than the square of that number. Find the positive
solution
Answer:
8
Step-by-step explanation:
I need help with is math
Answer: 9
Step-by-step explanation:
A right pyramid with a square base has a base length
of x inches, and the height is two inches longer than
the length of the base. Which expression represents
the volume in terms of x?
x
(x
+ 2)
cubic inches
X(X
+ 2)
03
cubic inches
cubic inches
x+2
cubic inches
Answer:
x = 20
Step-by-step explanation:
-10x=-200
x = -200/ -10
x = 20
Answer:
A. x^2 (x+2) / 3
Step-by-step explanation:
If the gradient of a line C is 2/3 what is the gradient of the line which is perpendicular to C
Final answer:
The gradient of the line perpendicular to a line with a gradient of 2/3 is -3/2 since perpendicular slopes are negative reciprocals of each other.
Explanation:
If the gradient of a line C is 2/3, we need to find the gradient of the line which is perpendicular to C. In mathematics, particularly in coordinate geometry, the slopes (or gradients) of two perpendicular lines are negative reciprocals of each other. This means that if the slope of the first line is m, the slope of the line perpendicular to it will be -1/m.
Therefore, the gradient of the line perpendicular to line C, which has a gradient of 2/3, will be the negative reciprocal of 2/3.
perpendicular = -1 / (2/3) = -3/2
So, the gradient of the line perpendicular to C is -3/2.
Which of the following explains why Cosine 60 degrees = sine 30 degrees using the unit circle? E2020?
Answer:
A
Step-by-step explanation:
he side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the y (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.
Explanation of Cosine 60 = Sine 30
Cosine :
The trigonometric function that is equal to the ratio of the side adjacent to an acute angle (in a right-angled triangle) to the hypotenuse.
Sine :
The trigonometric function that is equal to the ratio of the side opposite a given angle (in a right-angled triangle) to the hypotenuse.
So, these are the reasons :
⇒ The side opposite a 30 degree angle is the same as a side adjacent to 60 degree angle in a right triangle.
⇒ On a unit circle, the y (sin) distance of a 30 degree angle is the same as the x (cos) distance of a 60 degree angle.
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Janet has $120. If she saves $20 per week, in how many days will she have $500? *
Answer:
19 weeks
Step-by-step explanation:
Make an equation
120+20x=500
Subtract 120 on both sides
20x=380
Divide by 20 on both sides
x=19
Hope this helps!
Write the equation of a line with slope of -1/4 and contains the point (4,-3)
Answer:
y = -1/4x -2
Step-by-step explanation:
We can use the slope intercept form of a line
y = mx+b where m is the slope and b is the y intercept
y = -1/4x +b
Substitute the point into the equation
-3 = -1/4(4) +b
-3 = -1 +b
Add 1 to each side
-3 +1 = -1 +1 b
-2 =b
y = -1/4x -2
Help 10 points!!!!!!!
Answer:
B.
Step-by-step explanation:
Hope this helps!
Answer:
i think A
Step-by-step explanation:
Which of the following fractions is the largest: 13/16, 3/4, 7/10, or 5/8?
From the given set of fractions, 13/16 is the largest fraction.
The given set of fractions are 13/16, 3/4, 7/10, and 5/8.
We need to check which of the given fractions is the largest.
How to order the fractions?To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator by the denominator and then multiplying the top and bottom of the fraction by your answer.
Now, the LCM of denominators of the fractions is as follows:
16, 4, 10 an 8 LCM= 2×2×2×2×5=80
Make the denominators equal to LCM.
That is, 65/80, 60/80, 56/80, and 50/80
Here, 65/80 is the largest, since the numerator is the greatest number.
Therefore, from the given set of fractions 13/16 is the largest fraction.
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jada earns $7 per hour mowing her neighbors' lawns. andre gets paid $5 per hour for the first hour of babysitting and $8 per hour for any additional hours he babysits. what is the number of hours they both can work so that they get paid the same amount?
jada 2 andre 3 hours