(a) The probability that both missiles will hit the target is 1/10.
(b) The probability that at least one missile will hit the target is 11/20.
To find the probability that both missiles will hit, we multiply the individual probabilities of each missile hitting
P(both missiles hit) = P(first missile hits) × P(second missile hits)
P(both missiles hit) = (1/4) × (2/5)
P(both missiles hit) = 2/20
P(both missiles hit) = 1/10
So the probability that both missiles will hit the target is 1/10.
(b) To find the probability that at least one missile will hit, we need to find the probability that both missiles miss and then subtract that from 1 (since the probability of either missile hitting is the complement of both missiles missing)
P(at least one missile hits) = 1 - P(both missiles miss)
P(at least one missile hits) = 1 - P(first missile misses) × P(second missile misses)
P(at least one missile hits) = 1 - (3/4) × (3/5)
P(at least one missile hits) = 1 - 9/20
P(at least one missile hits) = 11/20
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The temperature at the point (x,y) on a metal plate is
T=x/x2+y2
Find the direction of greatest increase in heat from the point (2, 5).
The direction of the greatest increase in heat from the point (2, 5) is in the direction of the vector (-21, -20).
To find the direction of the greatest increase in heat from point (2, 5), we need to find the gradient vector of the temperature function T(x,y) at that point, and then determine the direction in which the gradient vector points.
The gradient vector of T(x,y) is given by:
∇T(x,y) = (∂T/∂x)i + (∂T/∂y)j
where i and j are the unit vectors in the x and y directions, respectively.
Taking the partial derivatives of T(x,y) with respect to x and y, we get:
∂T/∂x = (x² - y²)/(x² + y²)²
∂T/∂y = -2xy/(x² + y²)²
Substituting x = 2 and y = 5, we get:
∂T/∂x = (4 - 25)/(29)² = -21/1681
∂T/∂y = -20/1681
Therefore, the gradient vector of T(x,y) at the point (2, 5) is:
∇T(2,5) = (-21/1681)i - (20/1681)j
The direction of the greatest increase in heat from points (2, 5) is in the direction of the gradient vector. We can normalize the gradient vector to get the unit vector in this direction:
u = (∇T(2,5))/|∇T(2,5)|
where |∇T(2,5)| is the magnitude of the gradient vector, given by:
|∇T(2,5)| = √((-21/1681)² + (-20/1681)²) = sqrt(841)/1681 = 1/41
Thus, the unit vector in the direction of greatest increase in heat from the point (2, 5) is:
u = (-21/1681i - 20/1681j)/(1/41) = -21i - 20j
Therefore, the direction of the greatest increase in heat from points (2, 5) is in the direction of the vector (-21, -20).
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Please help this is due today
Using multiplication we know that after 141 min there will be 400,000 bacteria present.
What is multiplication?One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.
A product is the output of a multiplication operation.
When you take a single number and multiply it by several, you are multiplying.
A 5 multiplied by 4 results in 20 (5 + 5 + 5 + 5).
We multiplied the number five by four times.
Multiplication is commonly referred to as "times" because of this.
So, in the given situation:
At the initial stage, the number of bacteria is: 50,000
Then, after 47 min: 50,000 * 2 = 100,000
Then, after 47 min which is after 94 min: 100,000 * 2 = 200,000
Then, after 47 min which is after 141 min: 200,000 * 2 = 400,000
Therefore, using multiplication we know that after 141 min there will be 400,000 bacteria present.
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The length of a rectangle is three feet less than two times the width. The perimeter is 27 feet. Find the dimensions.
Answer:
l = 2w - 3
2(2w - 3) + 2w = 27
4w - 6 + 2w = 27
6w - 6 = 27
6w = 33, so w = 5.5 feet and l = 8 feet
Answer:
Width: 5.5 feet
Length: 8 feet
Step-by-step explanation:
Let's begin by assigning variables to stand in for the rectangle's width and length.
Let x represent the rectangle's width.
The length is three feet shorter than double the width, according to the problem. As a result, the length may be written as:
2x - 3
The lengths of all the sides make up a rectangle's perimeter, which in this instance is:
2w + 2l
By substituting the width and length measurements we discovered:
2x + 2(2x - 3)
Simplifying:
2x + 4x - 6 = 27
6x = 33
x = 5.5
The rectangle is 5.5 feet wide as a result.
We may change x into the expression we discovered earlier to figure out the length:
2(5.5) - 3 = 8
The rectangle is 8 feet long as a result.
As a result, the rectangle's measurements are:
Width: 5.5 feet
Length: 8 feet
a random sample of 20 gas stations was selected to estimate the gas prices in the us and had an average of $3.40 and a standard deviation of$0.22. test at a 10% alpha level if the true average price is under $3.50. what type of error could have occurred? and what are the chances of that happening?
If a random sample of 20 gas stations was selected to estimate the gas prices. The type of error that could have occurred is a type I error, which is the rejection of a true null hypothesis. The probability of making a type I error is equal to the level of significance (α), which is 10% in this case. So, there is a 10% chance of making a type I error in this test.
What type of error could have occurred?To test if the true average gas price is under $3.50, we can use a one-tailed t-test with a null hypothesis of:
H0: μ >= $3.50
And an alternative hypothesis of:
Ha: μ < $3.50
where μ is the true population mean gas price.
Using a t-test with a sample size of 20, we can calculate the t-value as:
t = (x -bar - μ) / (s / sqrt(n))
where x-bar is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Plugging in the given values, we get:
t = (3.40 - 3.50) / (0.22 / sqrt(20))
t = -2.03
Looking up the t-distribution table with degrees of freedom (df) = 19 and a 10% alpha level (α = 0.10), we find the critical t-value as -1.325.
Since our calculated t-value (-2.03) is less than the critical t-value (-1.325), we reject the null hypothesis in favor of the alternative hypothesis. Therefore, we can conclude that there is sufficient evidence to suggest that the true average gas price is under $3.50.
The type of error that could have occurred is a Type I error, which is rejecting a true null hypothesis. In this case, it means that we conclude that the true average gas price is under $3.50 when it's actually not. The probability of making a Type I error is equal to the alpha level, which is 10% in this case. So there's a 10% chance that we falsely reject the null hypothesis.
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PROBLEM SOLVING A wire is bent to form four semicircles. How long is the wire to the nearest hundredth? Justify your answer.
According to the nearest hundredth, the length of the wire in the photograph is 200 cm.
What in mathematics is a semicircle?
By dividing a circle into two halves along a diameter line, a semicircle is created, which is a half-circle.
The wire will be cut into four semicircles, each of which will have a circumference equal to its length.
Therefore, if one semicircle has a diameter of 32 cm, its radius is 32/2 cm, or 16 cm.
Right now, a circle's circumference equals 2*(pi)*(radius).
Since this is a semicircle, its circumference is equal to (pi)*(radius), or one-half of a circle.
The circumference of four semicircles is then equal to four * pi * radius.
Pi has a value of 22/7.
Thus, the length of the wire is 4*(22/7)*16 cm, which, when rounded to the nearest hundredth, is 200 cm.
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Hence, 201 [tex]cm^{2}[/tex] long is the wire to the nearest hundredth.
What is the semicircle?In mathematics, a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180°. It has only one line of symmetry.
What is the circumference?In geometry, the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure .
In other words ,The meaning of circumference is the distance around a circle or any curved geometrical shape. It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface.
According to figure
diameter of all semi circle (d) = 32 cm.
so radius of all semi circle r = [tex]\frac{32}{2}[/tex] = 16 cm.
length of wire = circumference of semicircle =
⇒ total length length of wire = 4 * circumference of semicircle
{∵ no. of semicircle=4
∴ total length length of wire = 4 * [tex]\pi*r[/tex]
∴ total length length of wire = 4 *3.14*16 {we know that , [tex]\pi=3.14[/tex]
∴ total length length of wire =200.96[tex]cm^{2}[/tex] ≅ 201[tex]cm^{2}[/tex]
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Object 1: Cereal Box
3D shape: Rectangular Prism
Dimensions:
length = 12 inches
width = 8 inches
height = 1.75 inches
Object 1 3D shape: Rectangular Prism (cereal box)
SA Formula:
Surface Area:
Answer:
The surface area (SA) formula for a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height.
For the cereal box object given, we have:
l = 12 inches
w = 8 inches
h = 1.75 inches
So, substituting these values into the formula, we get:
SA = 2(12)(8) + 2(12)(1.75) + 2(8)(1.75)
SA = 192 + 42 + 28
SA = 262 square inches
Therefore, the surface area of the rectangular prism cereal box is 262 square inches.
Step-by-step explanation:
The SURFACE AREA OF THE RECTANGULAR PRISM is 262 in²
SURFACE AREA (S.A) OF RECTANGULAR PRISM= 2lw+2lh+2wh
LENGTH=12 inches
WIDTH= 8 inches
HEIGHT=1.75 inches
Applying the formula
We get
S.A=2*(12*8)+2*(12*1.75)+2*9(8*1.75)
S.A = 192+42+28 sq inches
S.A= 262 sq inches
Clive wants to estimate the number of fish in apond.
Clive catches 50 fish from the pond. He marks each fish with a dye.
He then puts the fish back in the pond.
The next day, Clive catches 40 fish from the pond. 8 of these fish have been marked with the dye.
Work out an estimate for the number of fish in the pond.
Answer: 50
Step-by-step explanation
One method to estimate the number of fish in the pond is to use the mark-and-recapture method. This method assumes that the proportion of marked fish in the second sample is the same as the proportion of marked fish in the entire population. Using this assumption, we can estimate the total number of fish in the pond as follows:
Let N be the total number of fish in the pond.
Let M be the number of fish caught in the first sample (50 fish).
Let R be the number of marked fish caught in the second sample (8 fish).
Let r be the unknown total number of marked fish in the pond.
According to the mark-and-recapture method, we have the following proportion:
M/N = R/r
We can rearrange this equation to solve for N:
N = M * r / R
Substituting the values given in the problem, we have:
N = 50 * r / 8
Simplifying, we get:
N = 6.25 * r
This means that the estimated total number of fish in the pond is 6.25 times the number of marked fish in the second sample. Since we know that 8 fish were marked in the second sample, the estimate for the total number of fish in the pond is:
N = 6.25 * 8 = 50
Therefore, the estimated number of fish in the pond is 50
Identify the side lengths of the following triangle.
The side lengths of the triangle are CA = 42.0 and BC = 36.4
Identifying the side lengths of the triangle.From the question, we have the following parameters that can be used in our computation:
The triangle
Using the tangent rratio, we have
tan(60) = BC/21
So, we have
BC = 21 * tan(60)
Evaluate
BC = 36.4
Next, we have
CA = √[36.4^2 + 21^2] -- pythagoras theorem
Evaluate
CA = 42.0
Hence, the side lengths are CA = 42.0 and BC = 36.4
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Last week, Austin's Diner sold 2 milkshakes with whipped cream on top and 23 milkshakes without whipped cream. What percentage of the milkshakes had whipped cream?
Answer:
8%
Step-by-step explanation:
You want to know what percentage of milkshakes had whipped cream if 2 had whipped cream and 23 didn't.
PercentageThe fraction of the total number that had whipped cream is ...
2/(2+23) = 2/25
The percentage is found by multiplying the fraction by 100%:
2/25 × 100% = 8%
8% of the milkshakes had whipped cream.
Find the value of X. If a segment looks like a tangent, it is a tangent
Using the laws of outside angle, we can find the value of the angle x° to be = 77°.
Define outside angle theorem?The measure of an exterior angle is equal to the sum of the measures of the two distant interior angles of the triangle, according to the external angle theorem. According to the exterior angle inequality theorem, any triangle's outside angle has a measure bigger than either of its opposing interior angles.
Here in the question,
The measure of the 2 arcs is given as 85° and 172°.
The measure of the 3rd arc that is subtended by the tangents is:
360° - 85° - 172°
= 103°
As per the outside angle theorem,
x° = 180° - 103°
= 77°
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how is this answer wrong?
Answer:
its taking the immage on the right and moving it ounter clockwise 90°
$1,328 + $30x > $1,538 solve for x
Answer:
Greater than 7.
Step-by-step explanation:
To solve for x in the inequality, we need to isolate x on one side of the equation. First, we need to subtract
$ [tex]\large \boxed{\mathrm{1328}}[/tex]
from each side, giving $30x > $210. Then, we divide both sides by 30 to find that x > 7. Therefore, to make the inequality true, x needs to be greater than 7.
pls explain how to do this math and answer it pls
Answer: A.
Step-by-step explanation: It is parallel because of the angles that are the same and if u fill all the angles up angles 2 and 6 will be congruent there fore its parallel
Answer:
A. Yes, because angles 2 and 6 are congruent.
Step-by-step explanation:
The lines arent touching, parallel. Angles 2 and 6 share the same angle, congruent.
what is the area under the sine curve from 0 to pi?
Work Shown:
[tex]\displaystyle \int \sin(x) dx = -\cos(x)+C\\\\\displaystyle \int f(x)dx = g(x)+C\\\\\displaystyle \int_{a}^{b} f(x)dx = g(b)-g(a)\\\\\displaystyle \int_{0}^{\pi} f(x)dx = g(\pi)-g(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)-(-\cos(0))\\\\[/tex]
[tex]\displaystyle \int_{0}^{\pi} \sin(x) dx = -\cos(\pi)+\cos(0)\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = -(-1)+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 1+1\\\\\displaystyle \int_{0}^{\pi} \sin(x) dx = 2\\\\[/tex]
The area is 2 square units. You can use WolframAlpha or GeoGebra to confirm.
HELP!!!! I WILL GIVE YOU BRAINIEST
Answer:
Distant with current is 30, distance against current is 24.
Rate with current is 6, rate against current is 4.
Time with current is 8 hours, time against current is 14
Step-by-step explanation:
2nd question answer: 24 - 6x = 8.
15x1/5=
im doing my homework its kinda confusing lol!
Answer:
3
Step-by-step explanation:
(15×1)÷5=
Solve for a and b: 2a - 3b=5 -3a+b=3
Answer:
a = -2 b = -3
Step-by-step explanation:
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PLEASE HELP SOSOSOSOSOS
Consider this system of equations
{10x + 13y + 15z = 4
{ 12x - 2y + 5z = - 8
{ 2x + 2y - 6z = 4
The system can be represented by the following matrix equation where A is a 3 x 3 matrix and ⇾b is a 3D vector
[ x
A [ y = ⇾b
[ z
Find A and ⇾b
The given system of equations can be represented in matrix form as:
| 10 13 15 | | x | | 4 |
| 12 -2 5 | x | y | = |-8 |
| 2 2 -6 | | z | | 4 |
Therefore, the matrix A is:
| 10 13 15 |
| 12 -2 5 |
| 2 2 -6 |
And the vector ⇾b is:
| 4 |
|-8 |
| 4 |
what is the equation in point slope form equation for line (-3,5) and (1,-1)
Considering the expression of a line, the equation of the line that passes through the pair of points (-3,5) and (1,-1) is y=-1.5x +0.5.
Definition of linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope of the line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope and the value of one of the points, the value of the ordinate to the origin can be obtained.
Equation in this caseIn this case, being (x₁, y₁)= (-3, 5) and (x₂, y₂)= (1, -1), the slope m can be calculated as:
m= ( -1 -5)÷ (1 - (-3))
m= ( -1 -5)÷ (1 + 3)
m= (-6)÷ 4
m= -1.5
Considering point 2 and the slope m, you obtain:
-1= -1.5×1 + b
-1= -1.5 +b
-1 + 1.5= b
0.5= b
Finally, the equation of the line is y=-1.5x +0.5.
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What is ¨the area of a parking lot¨ unit of measurement
A - Square meters
B - Yards
C - Cubic inches
D - Cubic feet
E - Square centimeters
The probability that A occurs is 2/3. The probability that B occurs is 3/7. The probability that A and B occur is 1/7. Are the events A and B independent or dependent?
P(A and B) is not equal to P(A) * P(B), we can conclude that events A and B are dependent.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
According to the given information:We can determine if events A and B are independent or dependent by comparing the probability of both events occurring together with the product of their individual probabilities.
P(A and B) = 1/7
P(A) = 2/3
P(B) = 3/7
If A and B are independent events, then P(A and B) = P(A) * P(B). However, in this case, P(A and B) is not equal to P(A) * P(B):
P(A) * P(B) = (2/3) * (3/7) = 2/7
Since P(A and B) is not equal to P(A) * P(B), we can conclude that events A and B are dependent.
Events A and B are dependent since the probability of their intersection is not equal to the product of their individual probabilities. Specifically, P(A and B) = 1/7 while P(A)*P(B) = 2/7.
Therefore, P(A and B) is not equal to P(A) * P(B), we can conclude that events A and B are dependent.
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The variable in the equation 11 = –2z + 8 is z. Remembering the formula ax + b = c, what are the values of the constants in the equation?
A) a= -8, b = 8, c= 11
B) a= -2, b= 8, c= 11
C) a= -11, b= 8, c= 11
D) a= 8, b= -8, c= 11
Answer: The given equation is 11 = -2z + 8, which can be rearranged into the form of ax + b = c by moving the terms containing z to one side:
-2z + 8 = 11
-2z = 11 - 8
-2z = 3
z = -3/2
Comparing this with the standard form ax + b = c, we see that:
a = -2
b = 8
c = 11
Therefore, the correct answer is option B: a = -2, b = 8, c = 11.
Step-by-step explanation:
At the store, Jami buys a soda for $1.89, a candy bar for $1.78 and a sandwich for $4.98. How much money does she spend at the store?
1. (07.01 MC) Masha solved an equation, as shown below: Step 1: 8x = 64 Step 2: x= 64 – 8 Step 3: x = 76 Part A: Is Masha's solution correct or incorrect? If the solution is incorrect, explain why it is incorrect and show the correct steps to solve the equation. (6 points) Part B: How many solutions does this equation have? (4 points)
(1) The right solution of given equation is 8.(2)The equation 8x = 64 has only one solution
What is an Equation means ?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Part A: Masha's solution is incorrect.
In Step 2, Instead of dividing 64/8 she did mistake she subtract 64 by 8
So, the correct step to solving this equation is
8x = 64
x = 64/8
x=8
Hence the right solution of given equation is 8
Part B: The equation 8x = 64 has only one solution, which is x = 8. This is because there is only one value of x that satisfies the equation.
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(1) The right solution of given equation is 8.
(2)The equation 8x = 64 has only one solution
What is an Equation means ?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Part A: Masha's solution is incorrect.
In Step 2, Instead of dividing 64/8 she did mistake she subtract 64 by 8
So, the correct step to solving this equation is
8x = 64
x = 64/8
x=8
Hence the right solution of given equation is 8
Part B: The equation 8x = 64 has only one solution, which is x = 8. This is because there is only one value of x that satisfies the equation.
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Can someone show me step by step of how to do this please and correctly
What is the area of the circle? Approximate using pi equals 22 over 7 and round to the nearest square yard.
a circle with radius labeled 18 yards
57 square yards
113 square yards
1,018 square yards
2,037 square yards
Points earned on this question: 0
A culture of bacteria in a petri dish has an initial population of 1500 cells and grows at a rate (in cells/day) of N′(t)=200(t+2)−12 Assume t is measured in days.
a) What is the population after 14 days? After 34 days?
b) Find the population N(t) at any time t≥0
The population N(t) at any time t≥0 is given by the function N(t) = 100t^2 + 800t + 1332.
a) To find the population after 14 days, we need to integrate the given rate function from 0 to 14:
N(14) - N(0) = ∫(0 to 14) N'(t) dt
N(14) - 1500 = ∫(0 to 14) [200(t+2) - 12] dt
N(14) - 1500 = [100[tex]t^2[/tex] + 800t - 168] evaluated from t=0 to t=14
N(14) = 1500 + [100(14[tex])^2[/tex] + 800(14) - 168] - [100(0[tex])^2[/tex] + 800(0) - 168]
N(14) = 1500 + 17,512
N(14) = 19,012
So the population after 14 days is 19,012 cells.
To find the population after 34 days, we can use the same method:
N(34) - N(0) = ∫(0 to 34) N'(t) dt
N(34) - 1500 = ∫(0 to 34) [200(t+2) - 12] dt
N(34) - 1500 = [100[tex]t^2[/tex] + 800t - 168] evaluated from t=0 to t=34
N(34) = 1500 + [100(34[tex])^2[/tex]+ 800(34) - 168] - [100(0[tex])^2[/tex] + 800(0) - 168]
N(34) = 1500 + 116,768
N(34) = 118,268
So the population after 34 days is 118,268 cells.
b) To find the population N(t) at any time t≥0, we can integrate the given rate function from 0 to t:
N(t) - N(0) = ∫(0 to t) N'(x) dx
N(t) - 1500 = ∫(0 to t) [200(x+2) - 12] dx
N(t) = 1500 + ∫(0 to t) [200(x+2) - 12] dx
N(t) = 1500 + [100[tex]x^2[/tex] + 800x - 168] evaluated from x=0 to x=t
N(t) = 1500 + 100[tex]t^2[/tex] + 800t - 168
N(t) = 100t^2 + 800t + 1332
So the population N(t) at any time t≥0 is given by the function N(t) = 100[tex]t^2[/tex]+ 800t + 1332.
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a) The population after 14 days is 22,788 cells, and the population after 34 days is 126,056 cells.
b) The population at any time t≥0 is given by the equation N(t) = [tex]100t^2[/tex] + 388t + 1500, where t is measured in days and N(t) is the number of cells in the culture at time t.
a) To find the population after 14 days, we can use the given rate equation to calculate the growth rate at t=14 as follows:
N'(14) = 200(14+2) - 12 = 2808 cells/day
Then we can use the following formula to calculate the population after 14 days:
N(14) = N(0) + ∫N'(t) dt, from t=0 to t=14
N(14) = 1500 + ∫(200(t+2) - 12) dt, from t=0 to t=14
N(14) = 1500 + [tex][100t^2 + 400t - 12t][/tex]from t=0 to t=14
N(14) = 1500 + [tex][100(14)^2 + 400(14) - 12(14)] - [100(0)^2 + 400(0) - 12(0)][/tex]
N(14) = 1500 + 21288
N(14) = 22788 cells
Similarly, to find the population after 34 days, we can use the given rate equation to calculate the growth rate at t=34 as follows:
N'(34) = 200(34+2) - 12 = 6772 cells/day
Then we can use the same formula as above to calculate the population after 34 days:
N(34) = N(0) + ∫N'(t) dt, from t=0 to t=34
N(34) = 1500 + ∫(200(t+2) - 12) dt, from t=0 to t=34
N(34) = [tex]1500 + [100t^2 + 400t - 12t] from t=0 to t=34[/tex]
N(34) =[tex]1500 + [100(34)^2 + 400(34) - 12(34)] - [100(0)^2 + 400(0) - 12(0)][/tex]
N(34) = 1500 + 124556
N(34) = 126056 cells
b) To find the population N(t) at any time t≥0, we can use the same formula as above:
N(t) = N(0) + ∫N'(t) dt, from t=0 to t=t
N(t) = 1500 + ∫(200(t+2) - 12) dt, from t=0 to t=t
N(t) = [tex]1500 + [100t^2 + 400t - 12t][/tex] from t=0 to t=t
N(t) = [tex]1500 + 100t^2 + 388t[/tex]
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A basketball player was successful on 18 out of his 24 last free throws attempts. If he attempts 20 free- throws in the next game, about how many will he make if the ratio is the same as the first game?
He needs to make 15 throws if the ratio is the same as the first game
From the question, we have the following parameters that can be used in our computation:
Player was successful on 18 out of his 24 last free throws attempts
Using the above as a guide, we have the following:
Proportion = 18/24
For the number of games, we have
Throws made = Proportion * Number of throws
Substitute the known values in the above equation, so, we have the following representation
Throws made = 18/24 * 20
Evaluate
Throws made = 15
Hence, the number of throws made is 15
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Choose ALL answers that describe the quadrilateral below.
All answers that describe the quadrilateral are parallelogram and rhombus.
How is the diagram a rhombus and parallelogram?In the diagram provided as seen from online sources, the lines, BO=OD and this equals x. Next, SO=OC which equals s. Since the diagonals bisect each other, we can refer to this as a parallelogram.
Next, angle ABO equals angle ADO and since the opposite sides are parallel and equal, we can also refer to the quadrilateral as a rhombus.
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Wanda's first book was such a hit that she decided to do a follow-up. This one's called 101 Ways to Reinvent Leftovers.
Two publishers have offered to buy the book. The first has offered to pay her $70,000 up front and a $2 royalty for every book it sells. The second has offered to pay $40,000 up front and a $3.50 royalty for every book it sells. Over what range of sales will Wanda make more from the second deal than she will from the first deal?
So Wanda will make more money from the second deal than the first deal if she sells more than 20,000 books.
What is inequality?In mathematics, an inequality is a statement that two values or expressions are not equal. It describes a relationship that is either greater than, less than, or not equal to another value or expression. Inequalities are often represented using symbols such as > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).
Here,
To determine the range of sales for which Wanda would make more from the second deal than the first deal, we need to set up an inequality that compares the total earnings for each deal. Let's let x be the number of books sold.
For the first deal, Wanda will earn:
Total earnings = $70,000 + $2x
For the second deal, Wanda will earn:
Total earnings = $40,000 + $3.50x
We want to find the range of x values for which the second deal earns more than the first deal. Mathematically, we can express this as:
$40,000 + $3.50x > $70,000 + $2x
Subtracting $2x from both sides gives:
$40,000 + $1.50x > $70,000
Subtracting $40,000 from both sides gives:
$1.50x > $30,000
Dividing both sides by $1.50 gives:
x > 20,000
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If the luminosity of a lightbulb is 100 W and the brightness is measured to be 0.01 what is the distance to the lightbulb?